LMFDB - Embedded newform 8.6.b.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,6,Mod(5,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	8.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:	$1.28307055850$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.218489.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 8x + 64 $ x^4 - x^3 - 2x^2 - 8x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.1
Root			$2.38600 - 1.51888i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.6.b.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.77200 - 3.03776i) q^{2} -23.6095i q^{3} +(13.5440 + 28.9924i) q^{4} +1.38521i q^{5} +(-71.7200 + 112.665i) q^{6} +160.704 q^{7} +(23.4400 - 179.495i) q^{8} -314.408 q^{9} +O(q^{10})$	\(q+(-4.77200 - 3.03776i) q^{2} -23.6095i q^{3} +(13.5440 + 28.9924i) q^{4} +1.38521i q^{5} +(-71.7200 + 112.665i) q^{6} +160.704 q^{7} +(23.4400 - 179.495i) q^{8} -314.408 q^{9} +(4.20793 - 6.61022i) q^{10} -129.129i q^{11} +(684.496 - 319.767i) q^{12} +759.659i q^{13} +(-766.880 - 488.181i) q^{14} +32.7041 q^{15} +(-657.120 + 785.347i) q^{16} +323.408 q^{17} +(1500.36 + 955.097i) q^{18} +198.511i q^{19} +(-40.1605 + 18.7613i) q^{20} -3794.14i q^{21} +(-392.264 + 616.204i) q^{22} -1193.15 q^{23} +(-4237.79 - 553.407i) q^{24} +3123.08 q^{25} +(2307.66 - 3625.10i) q^{26} +1685.91i q^{27} +(2176.58 + 4659.20i) q^{28} +5987.24i q^{29} +(-156.064 - 99.3472i) q^{30} -4872.45 q^{31} +(5521.47 - 1751.50i) q^{32} -3048.67 q^{33} +(-1543.30 - 982.437i) q^{34} +222.609i q^{35} +(-4258.34 - 9115.45i) q^{36} -3698.56i q^{37} +(603.031 - 947.297i) q^{38} +17935.2 q^{39} +(248.638 + 32.4693i) q^{40} -10437.9 q^{41} +(-11525.7 + 18105.6i) q^{42} -9873.11i q^{43} +(3743.76 - 1748.93i) q^{44} -435.521i q^{45} +(5693.73 + 3624.51i) q^{46} -6297.98 q^{47} +(18541.6 + 15514.3i) q^{48} +9018.79 q^{49} +(-14903.3 - 9487.18i) q^{50} -7635.50i q^{51} +(-22024.4 + 10288.8i) q^{52} +21728.1i q^{53} +(5121.39 - 8045.16i) q^{54} +178.871 q^{55} +(3766.91 - 28845.6i) q^{56} +4686.75 q^{57} +(18187.8 - 28571.1i) q^{58} +33513.4i q^{59} +(442.944 + 948.170i) q^{60} -48506.8i q^{61} +(23251.3 + 14801.3i) q^{62} -50526.7 q^{63} +(-31669.1 - 8414.75i) q^{64} -1052.29 q^{65} +(14548.3 + 9261.14i) q^{66} +33182.4i q^{67} +(4380.24 + 9376.38i) q^{68} +28169.7i q^{69} +(676.232 - 1062.29i) q^{70} +59464.1 q^{71} +(-7369.74 + 56434.8i) q^{72} +51278.6 q^{73} +(-11235.4 + 17649.5i) q^{74} -73734.4i q^{75} +(-5755.33 + 2688.64i) q^{76} -20751.6i q^{77} +(-85586.7 - 54482.8i) q^{78} -73724.5 q^{79} +(-1087.87 - 910.248i) q^{80} -36597.7 q^{81} +(49809.6 + 31707.8i) q^{82} -61628.0i q^{83} +(110001. - 51387.9i) q^{84} +447.988i q^{85} +(-29992.1 + 47114.5i) q^{86} +141356. q^{87} +(-23178.1 - 3026.79i) q^{88} -106735. q^{89} +(-1323.01 + 2078.31i) q^{90} +122080. i q^{91} +(-16160.1 - 34592.4i) q^{92} +115036. i q^{93} +(30054.0 + 19131.8i) q^{94} -274.980 q^{95} +(-41352.1 - 130359. i) q^{96} +12562.9 q^{97} +(-43037.7 - 27397.0i) q^{98} +40599.2i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 20 q^{4} - 116 q^{6} + 96 q^{7} - 248 q^{8} - 164 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 20 * q^4 - 116 * q^6 + 96 * q^7 - 248 * q^8 - 164 * q^9	\( 4 q - 2 q^{2} + 20 q^{4} - 116 q^{6} + 96 q^{7} - 248 q^{8} - 164 q^{9} + 632 q^{10} + 1576 q^{12} - 2384 q^{14} - 416 q^{15} - 3312 q^{16} + 200 q^{17} + 4754 q^{18} + 4624 q^{20} - 5636 q^{22} + 2336 q^{23} - 7792 q^{24} + 1556 q^{25} + 5608 q^{26} + 5152 q^{28} - 2128 q^{30} - 12928 q^{31} + 5408 q^{32} - 2352 q^{33} - 4772 q^{34} - 10164 q^{36} + 15980 q^{38} + 35104 q^{39} + 16032 q^{40} - 4568 q^{41} - 26144 q^{42} - 29112 q^{44} + 29200 q^{46} - 54720 q^{47} + 35616 q^{48} + 9828 q^{49} - 47498 q^{50} - 36560 q^{52} + 23288 q^{54} + 85472 q^{55} + 40768 q^{56} - 2032 q^{57} + 3784 q^{58} + 2592 q^{60} + 34496 q^{62} - 153440 q^{63} - 41920 q^{64} - 19520 q^{65} + 43224 q^{66} + 10344 q^{68} - 68928 q^{70} + 206688 q^{71} - 83272 q^{72} + 39976 q^{73} + 17464 q^{74} + 99944 q^{76} - 174064 q^{78} - 247872 q^{79} - 35520 q^{80} + 29684 q^{81} + 161132 q^{82} + 196672 q^{84} - 18500 q^{86} + 307872 q^{87} - 167216 q^{88} - 84632 q^{89} + 142280 q^{90} - 49056 q^{92} - 98784 q^{94} - 259744 q^{95} - 115648 q^{96} - 99576 q^{97} - 117042 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 20 * q^4 - 116 * q^6 + 96 * q^7 - 248 * q^8 - 164 * q^9 + 632 * q^10 + 1576 * q^12 - 2384 * q^14 - 416 * q^15 - 3312 * q^16 + 200 * q^17 + 4754 * q^18 + 4624 * q^20 - 5636 * q^22 + 2336 * q^23 - 7792 * q^24 + 1556 * q^25 + 5608 * q^26 + 5152 * q^28 - 2128 * q^30 - 12928 * q^31 + 5408 * q^32 - 2352 * q^33 - 4772 * q^34 - 10164 * q^36 + 15980 * q^38 + 35104 * q^39 + 16032 * q^40 - 4568 * q^41 - 26144 * q^42 - 29112 * q^44 + 29200 * q^46 - 54720 * q^47 + 35616 * q^48 + 9828 * q^49 - 47498 * q^50 - 36560 * q^52 + 23288 * q^54 + 85472 * q^55 + 40768 * q^56 - 2032 * q^57 + 3784 * q^58 + 2592 * q^60 + 34496 * q^62 - 153440 * q^63 - 41920 * q^64 - 19520 * q^65 + 43224 * q^66 + 10344 * q^68 - 68928 * q^70 + 206688 * q^71 - 83272 * q^72 + 39976 * q^73 + 17464 * q^74 + 99944 * q^76 - 174064 * q^78 - 247872 * q^79 - 35520 * q^80 + 29684 * q^81 + 161132 * q^82 + 196672 * q^84 - 18500 * q^86 + 307872 * q^87 - 167216 * q^88 - 84632 * q^89 + 142280 * q^90 - 49056 * q^92 - 98784 * q^94 - 259744 * q^95 - 115648 * q^96 - 99576 * q^97 - 117042 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$1$

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 $

$2$	−4.77200	−	3.03776i	−0.843579	−	0.537006i
$2$	−4.77200	−	3.03776i	−0.843579	−	0.537006i
$3$		−	23.6095i		−	1.51455i	−0.653096	−	0.757275i	$-0.726530\pi$
$3$		−	23.6095i		−	1.51455i	0.653096	−	0.757275i	$-0.273470\pi$
$4$	13.5440	+	28.9924i	0.423250	+	0.906013i
$5$			1.38521i			0.0247794i	0.999923	+	0.0123897i	$0.00394386\pi$
$5$			1.38521i			0.0247794i	−0.999923	+	0.0123897i	$0.996056\pi$
$6$	−71.7200	+	112.665i	−0.813322	+	1.27764i
$7$	160.704			1.23960			0.619800	−	0.784760i	$-0.287214\pi$
$7$	160.704			1.23960			0.619800	+	0.784760i	$0.287214\pi$
$8$	23.4400	−	179.495i	0.129489	−	0.991581i
$9$	−314.408			−1.29386
$10$	4.20793	−	6.61022i	0.0133067	−	0.0209033i
$11$		−	129.129i		−	0.321768i	−0.986973	−	0.160884i	$-0.948566\pi$
$11$		−	129.129i		−	0.321768i	0.986973	−	0.160884i	$-0.0514345\pi$
$12$	684.496	−	319.767i	1.37220	−	0.641033i
$13$			759.659i			1.24670i	0.781945	+	0.623348i	$0.214228\pi$
$13$			759.659i			1.24670i	−0.781945	+	0.623348i	$0.785772\pi$
$14$	−766.880	−	488.181i	−1.04570	−	0.665672i
$15$	32.7041			0.0375296
$16$	−657.120	+	785.347i	−0.641719	+	0.766940i
$17$	323.408			0.271412			0.135706	−	0.990749i	$-0.456670\pi$
$17$	323.408			0.271412			0.135706	+	0.990749i	$0.456670\pi$
$18$	1500.36	+	955.097i	1.09147	+	0.694810i
$19$			198.511i			0.126154i	0.998009	+	0.0630771i	$0.0200914\pi$
$19$			198.511i			0.126154i	−0.998009	+	0.0630771i	$0.979909\pi$
$20$	−40.1605	+	18.7613i	−0.0224504	+	0.0104879i
$21$		−	3794.14i		−	1.87744i
$22$	−392.264	+	616.204i	−0.172791	+	0.271436i
$23$	−1193.15			−0.470302			−0.235151	−	0.971959i	$-0.575558\pi$
$23$	−1193.15			−0.470302			−0.235151	+	0.971959i	$0.575558\pi$
$24$	−4237.79	−	553.407i	−1.50180	−	0.196118i
$25$	3123.08			0.999386
$26$	2307.66	−	3625.10i	0.669483	−	1.05169i
$27$			1685.91i			0.445066i
$28$	2176.58	+	4659.20i	0.524661	+	1.12309i
$29$			5987.24i			1.32200i	0.750386	+	0.661000i	$0.229868\pi$
$29$			5987.24i			1.32200i	−0.750386	+	0.661000i	$0.770132\pi$
$30$	−156.064	−	99.3472i	−0.0316591	−	0.0201536i
$31$	−4872.45			−0.910632			−0.455316	−	0.890330i	$-0.650474\pi$
$31$	−4872.45			−0.910632			−0.455316	+	0.890330i	$0.650474\pi$
$32$	5521.47	−	1751.50i	0.953191	−	0.302368i
$33$	−3048.67			−0.487333
$34$	−1543.30	−	982.437i	−0.228957	−	0.145750i
$35$			222.609i			0.0307165i
$36$	−4258.34	−	9115.45i	−0.547627	−	1.17225i
$37$		−	3698.56i		−	0.444149i	−0.975030	−	0.222074i	$-0.928717\pi$
$37$		−	3698.56i		−	0.444149i	0.975030	−	0.222074i	$-0.0712828\pi$
$38$	603.031	−	947.297i	0.0677455	−	0.106421i
$39$	17935.2			1.88818
$40$	248.638	+	32.4693i	0.0245707	+	0.00320866i
$41$	−10437.9			−0.969734			−0.484867	−	0.874588i	$-0.661132\pi$
$41$	−10437.9			−0.969734			−0.484867	+	0.874588i	$0.661132\pi$
$42$	−11525.7	+	18105.6i	−1.00819	+	1.58377i
$43$		−	9873.11i		−	0.814297i	−0.913362	−	0.407148i	$-0.866523\pi$
$43$		−	9873.11i		−	0.814297i	0.913362	−	0.407148i	$-0.133477\pi$
$44$	3743.76	−	1748.93i	0.291526	−	0.136188i
$45$		−	435.521i		−	0.0320610i
$46$	5693.73	+	3624.51i	0.396736	+	0.252555i
$47$	−6297.98			−0.415869			−0.207935	−	0.978143i	$-0.566674\pi$
$47$	−6297.98			−0.415869			−0.207935	+	0.978143i	$0.566674\pi$
$48$	18541.6	+	15514.3i	1.16157	+	0.971915i
$49$	9018.79			0.536609
$50$	−14903.3	−	9487.18i	−0.843061	−	0.536676i
$51$		−	7635.50i		−	0.411067i
$52$	−22024.4	+	10288.8i	−1.12952	+	0.527664i
$53$			21728.1i			1.06251i	0.847212	+	0.531255i	$0.178279\pi$
$53$			21728.1i			1.06251i	−0.847212	+	0.531255i	$0.821721\pi$
$54$	5121.39	−	8045.16i	0.239003	−	0.375449i
$55$	178.871			0.00797320
$56$	3766.91	−	28845.6i	0.160515	−	1.22916i
$57$	4686.75			0.191067
$58$	18187.8	−	28571.1i	0.709921	−	1.11521i
$59$			33513.4i			1.25340i	0.779261	+	0.626699i	$0.215594\pi$
$59$			33513.4i			1.25340i	−0.779261	+	0.626699i	$0.784406\pi$
$60$	442.944	+	948.170i	0.0158844	+	0.0340023i
$61$		−	48506.8i		−	1.66908i	−0.550944	−	0.834542i	$-0.685732\pi$
$61$		−	48506.8i		−	1.66908i	0.550944	−	0.834542i	$-0.314268\pi$
$62$	23251.3	+	14801.3i	0.768190	+	0.489015i
$63$	−50526.7			−1.60387
$64$	−31669.1	−	8414.75i	−0.966465	−	0.256798i
$65$	−1052.29			−0.0308923
$66$	14548.3	+	9261.14i	0.411104	+	0.261701i
$67$			33182.4i			0.903068i	0.892254	+	0.451534i	$0.149123\pi$
$67$			33182.4i			0.903068i	−0.892254	+	0.451534i	$0.850877\pi$
$68$	4380.24	+	9376.38i	0.114875	+	0.245903i
$69$			28169.7i			0.712295i
$70$	676.232	−	1062.29i	0.0164949	−	0.0259118i
$71$	59464.1			1.39994			0.699970	−	0.714173i	$-0.253197\pi$
$71$	59464.1			1.39994			0.699970	+	0.714173i	$0.253197\pi$
$72$	−7369.74	+	56434.8i	−0.167541	+	1.28297i
$73$	51278.6			1.12624			0.563118	−	0.826377i	$-0.309602\pi$
$73$	51278.6			1.12624			0.563118	+	0.826377i	$0.309602\pi$
$74$	−11235.4	+	17649.5i	−0.238510	+	0.374675i
$75$		−	73734.4i		−	1.51362i
$76$	−5755.33	+	2688.64i	−0.114297	+	0.0533948i
$77$		−	20751.6i		−	0.398863i
$78$	−85586.7	−	54482.8i	−1.59283	−	1.01396i
$79$	−73724.5			−1.32906			−0.664530	−	0.747262i	$-0.731368\pi$
$79$	−73724.5			−1.32906			−0.664530	+	0.747262i	$0.731368\pi$
$80$	−1087.87	−	910.248i	−0.0190043	−	0.0159014i
$81$	−36597.7			−0.619785
$82$	49809.6	+	31707.8i	0.818047	+	0.520752i
$83$		−	61628.0i		−	0.981935i	−0.871178	−	0.490967i	$-0.836643\pi$
$83$		−	61628.0i		−	0.981935i	0.871178	−	0.490967i	$-0.163357\pi$
$84$	110001.	−	51387.9i	1.70098	−	0.794625i
$85$			447.988i			0.00672541i
$86$	−29992.1	+	47114.5i	−0.437282	+	0.686923i
$87$	141356.			2.00223
$88$	−23178.1	−	3026.79i	−0.319059	−	0.0416654i
$89$	−106735.			−1.42834			−0.714169	−	0.699974i	$-0.753195\pi$
$89$	−106735.			−1.42834			−0.714169	+	0.699974i	$0.753195\pi$
$90$	−1323.01	+	2078.31i	−0.0172170	+	0.0270460i
$91$			122080.i			1.54540i
$92$	−16160.1	−	34592.4i	−0.199055	−	0.426099i
$93$			115036.i			1.37920i
$94$	30054.0	+	19131.8i	0.350818	+	0.223324i
$95$	−274.980			−0.00312602
$96$	−41352.1	−	130359.i	−0.457951	−	1.44366i
$97$	12562.9			0.135569			0.0677846	−	0.997700i	$-0.478407\pi$
$97$	12562.9			0.135569			0.0677846	+	0.997700i	$0.478407\pi$
$98$	−43037.7	−	27397.0i	−0.452672	−	0.288162i
$99$			40599.2i			0.416323i
$100$	42299.0	+	90545.7i	0.422990	+	0.905457i
$101$		−	64962.8i		−	0.633667i	−0.948481	−	0.316834i	$-0.897380\pi$
$101$		−	64962.8i		−	0.633667i	0.948481	−	0.316834i	$-0.102620\pi$
$102$	−23194.8	+	36436.6i	−0.220745	+	0.346767i
$103$	−69035.9			−0.641183			−0.320591	−	0.947218i	$-0.603882\pi$
$103$	−69035.9			−0.641183			−0.320591	+	0.947218i	$0.603882\pi$
$104$	136355.	+	17806.4i	1.23620	+	0.161434i
$105$	5255.68			0.0465217
$106$	66004.9	−	103687.i	0.570574	−	0.896311i
$107$		−	187322.i		−	1.58172i	−0.612000	−	0.790858i	$-0.709635\pi$
$107$		−	187322.i		−	1.58172i	0.612000	−	0.790858i	$-0.290365\pi$
$108$	−48878.6	+	22834.0i	−0.403236	+	0.188374i
$109$			49350.5i			0.397855i	0.980014	+	0.198928i	$0.0637459\pi$
$109$			49350.5i			0.397855i	−0.980014	+	0.198928i	$0.936254\pi$
$110$	−853.571	−	543.367i	−0.00672602	−	0.00428165i
$111$	−87321.2			−0.672686
$112$	−105602.	+	126208.i	−0.795475	+	0.950699i
$113$	171100.			1.26053			0.630266	−	0.776379i	$-0.282946\pi$
$113$	171100.			1.26053			0.630266	+	0.776379i	$0.282946\pi$
$114$	−22365.2	−	14237.2i	−0.161180	−	0.102604i
$115$		−	1652.76i		−	0.0116538i
$116$	−173584.	+	81091.2i	−1.19775	+	0.559537i
$117$		−	238843.i		−	1.61305i
$118$	101806.	−	159926.i	0.673082	−	1.05734i
$119$	51973.0			0.336442
$120$	766.584	−	5870.23i	0.00485967	−	0.0372136i
$121$	144377.			0.896466
$122$	−147352.	+	231475.i	−0.896307	+	1.40800i
$123$			246433.i			1.46871i
$124$	−65992.5	−	141264.i	−0.385425	−	0.825045i
$125$			8654.89i			0.0495435i
$126$	241113.	+	153488.i	1.35299	+	0.861287i
$127$	−90479.7			−0.497785			−0.248892	−	0.968531i	$-0.580067\pi$
$127$	−90479.7			−0.497785			−0.248892	+	0.968531i	$0.580067\pi$
$128$	125563.	+	136358.i	0.677388	+	0.735626i
$129$	−233099.			−1.23329
$130$	5021.51	+	3196.60i	0.0260601	+	0.0165893i
$131$			94491.0i			0.481074i	0.970640	+	0.240537i	$0.0773236\pi$
$131$			94491.0i			0.481074i	−0.970640	+	0.240537i	$0.922676\pi$
$132$	−41291.2	−	88388.4i	−0.206264	−	0.441530i
$133$			31901.6i			0.156381i
$134$	100800.	−	158346.i	0.484953	−	0.761809i
$135$	−2335.34			−0.0110285
$136$	7580.70	−	58050.2i	0.0351449	−	0.269127i
$137$	−5516.81			−0.0251123			−0.0125561	−	0.999921i	$-0.503997\pi$
$137$	−5516.81			−0.0251123			−0.0125561	+	0.999921i	$0.503997\pi$
$138$	85572.9	−	134426.i	0.382506	−	0.600877i
$139$		−	164489.i		−	0.722104i	−0.932546	−	0.361052i	$-0.882418\pi$
$139$		−	164489.i		−	0.722104i	0.932546	−	0.361052i	$-0.117582\pi$
$140$	−6453.96	+	3015.01i	−0.0278295	+	0.0130008i
$141$			148692.i			0.629854i
$142$	−283763.	−	180638.i	−1.18096	−	0.751775i
$143$	98094.2			0.401147
$144$	206604.	−	246919.i	0.830294	−	0.992314i
$145$	−8293.57			−0.0327583
$146$	−244702.	−	155772.i	−0.950068	−	0.604795i
$147$		−	212929.i		−	0.812722i
$148$	107230.	−	50093.3i	0.402405	−	0.187986i
$149$			423122.i			1.56135i	0.624939	+	0.780674i	$0.285124\pi$
$149$			423122.i			1.56135i	−0.624939	+	0.780674i	$0.714876\pi$
$150$	−223987.	+	351861.i	−0.812822	+	1.27686i
$151$	−39975.1			−0.142675			−0.0713373	−	0.997452i	$-0.522727\pi$
$151$	−39975.1			−0.142675			−0.0713373	+	0.997452i	$0.522727\pi$
$152$	35631.9	+	4653.12i	0.125092	+	0.0163356i
$153$	−101682.			−0.351169
$154$	−63038.3	+	99026.6i	−0.214192	+	0.336473i
$155$		−	6749.36i		−	0.0225649i
$156$	242914.	+	519984.i	0.799174	+	1.71072i
$157$		−	367453.i		−	1.18974i	−0.803822	−	0.594870i	$-0.797203\pi$
$157$		−	367453.i		−	1.18974i	0.803822	−	0.594870i	$-0.202797\pi$
$158$	351814.	+	223958.i	1.12117	+	0.713712i
$159$	512991.			1.60922
$160$	2426.19	+	7648.39i	0.00749248	+	0.0236195i
$161$	−191744.			−0.582986
$162$	174644.	+	111175.i	0.522838	+	0.332828i
$163$		−	16030.9i		−	0.0472596i	−0.999721	−	0.0236298i	$-0.992478\pi$
$163$		−	16030.9i		−	0.0472596i	0.999721	−	0.0236298i	$-0.00752230\pi$
$164$	−141371.	−	302619.i	−0.410440	−	0.878591i
$165$		−	4223.05i		−	0.0120758i
$166$	−187211.	+	294089.i	−0.527304	+	0.828339i
$167$	−248107.			−0.688412			−0.344206	−	0.938894i	$-0.611852\pi$
$167$	−248107.			−0.688412			−0.344206	+	0.938894i	$0.611852\pi$
$168$	−681031.	−	88934.8i	−1.86163	−	0.243108i
$169$	−205789.			−0.554251
$170$	1360.88	−	2137.80i	0.00361158	−	0.00567341i
$171$		−	62413.6i		−	0.163226i
$172$	286245.	−	133721.i	0.737763	−	0.344651i
$173$		−	574094.i		−	1.45837i	−0.684317	−	0.729185i	$-0.739899\pi$
$173$		−	574094.i		−	1.45837i	0.684317	−	0.729185i	$-0.260101\pi$
$174$	−674549.	−	429405.i	−1.68904	−	1.07521i
$175$	501892.			1.23884
$176$	101411.	+	84853.3i	0.246777	+	0.206484i
$177$	791235.			1.89833
$178$	509338.	+	324235.i	1.20491	+	0.767025i
$179$			305296.i			0.712177i	0.934452	+	0.356088i	$0.115890\pi$
$179$			305296.i			0.712177i	−0.934452	+	0.356088i	$0.884110\pi$
$180$	12626.8	−	5898.69i	0.0290477	−	0.0135698i
$181$			421682.i			0.956728i	0.878162	+	0.478364i	$0.158770\pi$
$181$			421682.i			0.956728i	−0.878162	+	0.478364i	$0.841230\pi$
$182$	370851.	−	582568.i	0.829891	−	1.30367i
$183$	−1.14522e6			−2.52791
$184$	−27967.5	+	214165.i	−0.0608989	+	0.466342i
$185$	5123.28			0.0110057
$186$	349452.	−	548952.i	0.740637	−	1.16346i
$187$		−	41761.4i		−	0.0873315i
$188$	−85299.9	−	182594.i	−0.176017	−	0.376783i
$189$			270932.i			0.551705i
$190$	1312.20	+	835.323i	0.00263704	+	0.00167869i
$191$	−424231.			−0.841431			−0.420716	−	0.907193i	$-0.638221\pi$
$191$	−424231.			−0.841431			−0.420716	+	0.907193i	$0.638221\pi$
$192$	−198668.	+	747692.i	−0.388933	+	1.46376i
$193$	−373902.			−0.722545			−0.361272	−	0.932460i	$-0.617658\pi$
$193$	−373902.			−0.722545			−0.361272	+	0.932460i	$0.617658\pi$
$194$	−59950.2	−	38163.1i	−0.114363	−	0.0728014i
$195$			24843.9i			0.0467880i
$196$	122151.	+	261477.i	0.227120	+	0.486175i
$197$			112848.i			0.207171i	0.994621	+	0.103586i	$0.0330316\pi$
$197$			112848.i			0.207171i	−0.994621	+	0.103586i	$0.966968\pi$
$198$	123331.	−	193740.i	0.223568	−	0.351201i
$199$	262938.			0.470675			0.235338	−	0.971914i	$-0.424380\pi$
$199$	262938.			0.470675			0.235338	+	0.971914i	$0.424380\pi$
$200$	73205.1	−	560578.i	0.129410	−	0.990972i
$201$	783419.			1.36774
$202$	−197342.	+	310003.i	−0.340283	+	0.534548i
$203$			962173.i			1.63875i
$204$	221372.	−	103415.i	0.372432	−	0.173984i
$205$		−	14458.6i		−	0.0240294i
$206$	329439.	+	209715.i	0.540888	+	0.344319i
$207$	375137.			0.608505
$208$	−596596.	−	499187.i	−0.956141	−	0.800028i
$209$	25633.6			0.0405923
$210$	−25080.1	−	15965.5i	−0.0392447	−	0.0249824i
$211$		−	272968.i		−	0.422090i	−0.977476	−	0.211045i	$-0.932313\pi$
$211$		−	272968.i		−	0.422090i	0.977476	−	0.211045i	$-0.0676866\pi$
$212$	−629951.	+	294286.i	−0.962648	+	0.449707i
$213$		−	1.40392e6i		−	2.12028i
$214$	−569039.	+	893899.i	−0.849390	+	1.33430i
$215$	13676.3			0.0201777
$216$	302613.	+	39517.8i	0.441319	+	0.0576313i
$217$	−783022.			−1.12882
$218$	149915.	−	235501.i	0.213650	−	0.335622i
$219$		−	1.21066e6i		−	1.70574i
$220$	2422.63	+	5185.89i	0.00337466	+	0.00722382i
$221$			245680.i			0.338368i
$222$	416697.	+	265261.i	0.567463	+	0.361236i
$223$	1.00553e6			1.35405			0.677023	−	0.735962i	$-0.263270\pi$
$223$	1.00553e6			1.35405			0.677023	+	0.735962i	$0.263270\pi$
$224$	887323.	−	281473.i	1.18158	−	0.374815i
$225$	−981922.			−1.29307
$226$	−816490.	−	519761.i	−1.06336	−	0.676913i
$227$		−	554991.i		−	0.714861i	−0.933940	−	0.357430i	$-0.883653\pi$
$227$		−	554991.i		−	0.714861i	0.933940	−	0.357430i	$-0.116347\pi$
$228$	63477.4	+	135880.i	0.0808690	+	0.173109i
$229$			476013.i			0.599832i	0.953966	+	0.299916i	$0.0969587\pi$
$229$			476013.i			0.599832i	−0.953966	+	0.299916i	$0.903041\pi$
$230$	−5020.71	+	7887.00i	−0.00625814	+	0.00983087i
$231$	−489934.			−0.604098
$232$	1.07468e6	+	140341.i	1.31087	+	0.171185i
$233$	914141.			1.10312			0.551561	−	0.834135i	$-0.314032\pi$
$233$	914141.			1.10312			0.551561	+	0.834135i	$0.314032\pi$
$234$	−725548.	+	1.13976e6i	−0.866217	+	1.36074i
$235$		−	8724.01i		−	0.0103050i
$236$	−971635.	+	453906.i	−1.13559	+	0.530501i
$237$			1.74060e6i			2.01293i
$238$	−248015.	−	157882.i	−0.283815	−	0.180671i
$239$	375827.			0.425592			0.212796	−	0.977097i	$-0.431743\pi$
$239$	375827.			0.425592			0.212796	+	0.977097i	$0.431743\pi$
$240$	−21490.5	+	25684.0i	−0.0240834	+	0.0287829i
$241$	612110.			0.678870			0.339435	−	0.940629i	$-0.389764\pi$
$241$	612110.			0.678870			0.339435	+	0.940629i	$0.389764\pi$
$242$	−688966.	−	438582.i	−0.756239	−	0.481407i
$243$			1.27373e6i			1.38376i
$244$	1.40633e6	−	656977.i	1.51221	−	0.706440i
$245$			12492.9i			0.0132968i
$246$	748605.	−	1.17598e6i	0.788705	−	1.23897i
$247$	−150801.			−0.157276
$248$	−114210.	+	874582.i	−0.117917	+	0.902966i
$249$	−1.45501e6			−1.48719
$250$	26291.5	−	41301.2i	0.0266051	−	0.0417938i
$251$		−	462623.i		−	0.463493i	−0.972776	−	0.231746i	$-0.925556\pi$
$251$		−	462623.i		−	0.463493i	0.972776	−	0.231746i	$-0.0744440\pi$
$252$	−684333.	−	1.46489e6i	−0.678838	−	1.45313i
$253$			154071.i			0.151328i
$254$	431769.	+	274856.i	0.419921	+	0.267313i
$255$	10576.8			0.0101860
$256$	−184963.	−	1.03213e6i	−0.176394	−	0.984320i
$257$	−583345.			−0.550925			−0.275463	−	0.961312i	$-0.588831\pi$
$257$	−583345.			−0.550925			−0.275463	+	0.961312i	$0.588831\pi$
$258$	1.11235e6	+	708099.i	1.04038	+	0.662285i
$259$		−	594374.i		−	0.550567i
$260$	−14252.2	−	30508.3i	−0.0130752	−	0.0279888i
$261$		−	1.88244e6i		−	1.71048i
$262$	287041.	−	450911.i	0.258339	−	0.405824i
$263$	−411975.			−0.367267			−0.183633	−	0.982995i	$-0.558786\pi$
$263$	−411975.			−0.367267			−0.183633	+	0.982995i	$0.558786\pi$
$264$	−71461.0	+	547223.i	−0.0631044	+	0.483230i
$265$	−30098.0			−0.0263283
$266$	96909.5	−	152234.i	0.0839773	−	0.131919i
$267$			2.51995e6i			2.16329i
$268$	−962037.	+	449422.i	−0.818191	+	0.382224i
$269$		−	1.14460e6i		−	0.964436i	−0.876051	−	0.482218i	$-0.839831\pi$
$269$		−	1.14460e6i		−	0.964436i	0.876051	−	0.482218i	$-0.160169\pi$
$270$	11144.2	+	7094.19i	0.00930337	+	0.00592234i
$271$	−1.21607e6			−1.00586			−0.502928	−	0.864329i	$-0.667744\pi$
$271$	−1.21607e6			−1.00586			−0.502928	+	0.864329i	$0.667744\pi$
$272$	−212518.	+	253987.i	−0.174170	+	0.208157i
$273$	2.88225e6			2.34059
$274$	26326.2	+	16758.7i	0.0211842	+	0.0134854i
$275$		−	403281.i		−	0.321570i
$276$	−816708.	+	381531.i	−0.645349	+	0.301479i
$277$			806054.i			0.631196i	0.948893	+	0.315598i	$0.102205\pi$
$277$			806054.i			0.631196i	−0.948893	+	0.315598i	$0.897795\pi$
$278$	−499679.	+	784942.i	−0.387774	+	0.609152i
$279$	1.53194e6			1.17823
$280$	39957.2	+	5217.95i	0.0304579	+	0.00397745i
$281$	1.19824e6			0.905272			0.452636	−	0.891695i	$-0.350484\pi$
$281$	1.19824e6			0.905272			0.452636	+	0.891695i	$0.350484\pi$
$282$	451691.	−	709559.i	0.338235	−	0.531332i
$283$		−	1.46287e6i		−	1.08578i	−0.839805	−	0.542888i	$-0.817331\pi$
$283$		−	1.46287e6i		−	1.08578i	0.839805	−	0.542888i	$-0.182669\pi$
$284$	805382.	+	1.72401e6i	0.592524	+	1.26836i
$285$			6492.13i			0.00473451i
$286$	−468105.	−	297987.i	−0.338399	−	0.215418i
$287$	−1.67741e6			−1.20208
$288$	−1.73600e6	+	550686.i	−1.23330	+	0.391222i
$289$	−1.31526e6			−0.926336
$290$	39576.9	+	25193.9i	0.0276342	+	0.0175914i
$291$		−	296604.i		−	0.205326i
$292$	694518.	+	1.48669e6i	0.476679	+	1.02038i
$293$			750723.i			0.510870i	0.966826	+	0.255435i	$0.0822187\pi$
$293$			750723.i			0.510870i	−0.966826	+	0.255435i	$0.917781\pi$
$294$	−646828.	+	1.01610e6i	−0.436436	+	0.685595i
$295$	−46423.1			−0.0310584
$296$	−663874.	−	86694.4i	−0.440410	−	0.0575125i
$297$	217700.			0.143208
$298$	1.28534e6	−	2.01914e6i	0.838452	−	1.31712i
$299$		−	906390.i		−	0.586323i
$300$	2.13774e6	−	998658.i	1.37136	−	0.640640i
$301$		−	1.58665e6i		−	1.00940i
$302$	190761.	+	121435.i	0.120357	+	0.0766170i
$303$	−1.53374e6			−0.959721
$304$	−155900.	−	130446.i	−0.0967527	−	0.0809555i
$305$	67192.0			0.0413588
$306$	485227.	+	308886.i	0.296239	+	0.188580i
$307$			2.06754e6i			1.25201i	0.779819	+	0.626005i	$0.215311\pi$
$307$			2.06754e6i			1.25201i	−0.779819	+	0.626005i	$0.784689\pi$
$308$	601638.	−	281059.i	0.361375	−	0.168819i
$309$			1.62990e6i			0.971103i
$310$	−20502.9	+	32207.9i	−0.0121175	+	0.0190353i
$311$	3.06896e6			1.79924			0.899621	−	0.436671i	$-0.143843\pi$
$311$	3.06896e6			1.79924			0.899621	+	0.436671i	$0.143843\pi$
$312$	420401.	−	3.21928e6i	0.244499	−	1.87229i
$313$	−115148.			−0.0664345			−0.0332173	−	0.999448i	$-0.510575\pi$
$313$	−115148.			−0.0664345			−0.0332173	+	0.999448i	$0.510575\pi$
$314$	−1.11623e6	+	1.75348e6i	−0.638897	+	1.00364i
$315$		−	69989.9i		−	0.0397429i
$316$	−998526.	−	2.13745e6i	−0.562525	−	1.20414i
$317$		−	1.29930e6i		−	0.726210i	−0.931748	−	0.363105i	$-0.881717\pi$
$317$		−	1.29930e6i		−	0.726210i	0.931748	−	0.363105i	$-0.118283\pi$
$318$	−2.44799e6	−	1.55834e6i	−1.35751	−	0.864162i
$319$	773127.			0.425377
$320$	11656.2	−	43868.3i	0.00636329	−	0.0239484i
$321$	−4.42257e6			−2.39559
$322$	915005.	+	582474.i	0.491795	+	0.313067i
$323$			64200.2i			0.0342397i
$324$	−495679.	−	1.06106e6i	−0.262324	−	0.561534i
$325$			2.37248e6i			1.24593i
$326$	−48698.2	+	76499.7i	−0.0253787	+	0.0398672i
$327$	1.16514e6			0.602571
$328$	−244664.	+	1.87355e6i	−0.125570	+	0.961569i
$329$	−1.01211e6			−0.515512
$330$	−12828.6	+	20152.4i	−0.00648477	+	0.0101869i
$331$			2.02113e6i			1.01397i	0.861955	+	0.506985i	$0.169240\pi$
$331$			2.02113e6i			1.01397i	−0.861955	+	0.506985i	$0.830760\pi$
$332$	1.78674e6	−	834689.i	0.889646	−	0.415604i
$333$			1.16286e6i			0.574667i
$334$	1.18397e6	+	753691.i	0.580730	+	0.369681i
$335$	−45964.5			−0.0223775
$336$	2.97972e6	+	2.49321e6i	1.43988	+	1.20479i
$337$	2.88553e6			1.38405			0.692023	−	0.721875i	$-0.256719\pi$
$337$	2.88553e6			1.38405			0.692023	+	0.721875i	$0.256719\pi$
$338$	982027.	+	625139.i	0.467554	+	0.297636i
$339$		−	4.03958e6i		−	1.90914i
$340$	−12988.2	+	6067.55i	−0.00609331	+	0.00284653i
$341$			629175.i			0.293012i
$342$	−189598.	+	297838.i	−0.0876532	+	0.137694i
$343$	−1.25160e6			−0.574419
$344$	−1.77218e6	−	231426.i	−0.807441	−	0.105443i
$345$	−39020.9			−0.0176502
$346$	−1.74396e6	+	2.73958e6i	−0.783153	+	1.23025i
$347$		−	1.01894e6i		−	0.454281i	−0.973862	−	0.227141i	$-0.927062\pi$
$347$		−	1.01894e6i		−	0.454281i	0.973862	−	0.227141i	$-0.0729377\pi$
$348$	1.91452e6	+	4.09824e6i	0.847446	+	1.81405i
$349$		−	1.53786e6i		−	0.675854i	−0.941172	−	0.337927i	$-0.890274\pi$
$349$		−	1.53786e6i		−	0.675854i	0.941172	−	0.337927i	$-0.109726\pi$
$350$	−2.39503e6	−	1.52463e6i	−1.04506	−	0.665264i
$351$	−1.28072e6			−0.554862
$352$	−226170.	−	712983.i	−0.0972922	−	0.306706i
$353$	−490388.			−0.209461			−0.104731	−	0.994501i	$-0.533398\pi$
$353$	−490388.			−0.209461			−0.104731	+	0.994501i	$0.533398\pi$
$354$	−3.77578e6	−	2.40358e6i	−1.60139	−	1.01942i
$355$			82370.2i			0.0346896i
$356$	−1.44562e6	−	3.09450e6i	−0.604544	−	1.29409i
$357$		−	1.22706e6i		−	0.509558i
$358$	927415.	−	1.45687e6i	0.382443	−	0.600777i
$359$	3.19930e6			1.31014			0.655072	−	0.755567i	$-0.272638\pi$
$359$	3.19930e6			1.31014			0.655072	+	0.755567i	$0.272638\pi$
$360$	−78173.9	−	10208.6i	−0.0317911	−	0.00415156i
$361$	2.43669e6			0.984085
$362$	1.28097e6	−	2.01227e6i	0.513768	−	0.807075i
$363$		−	3.40866e6i		−	1.35774i
$364$	−3.53940e6	+	1.65346e6i	−1.40016	+	0.654093i
$365$			71031.6i			0.0279074i
$366$	5.46500e6	+	3.47891e6i	2.13249	+	1.35750i
$367$	−2.06745e6			−0.801252			−0.400626	−	0.916242i	$-0.631207\pi$
$367$	−2.06745e6			−0.801252			−0.400626	+	0.916242i	$0.631207\pi$
$368$	784044.	−	937039.i	0.301801	−	0.360693i
$369$	3.28175e6			1.25470
$370$	−24448.3	−	15563.3i	−0.00928419	−	0.00591013i
$371$			3.49180e6i			1.31709i
$372$	−3.33517e6	+	1.55805e6i	−1.24957	+	0.583746i
$373$		−	4.93913e6i		−	1.83814i	−0.394095	−	0.919070i	$-0.628942\pi$
$373$		−	4.93913e6i		−	1.83814i	0.394095	−	0.919070i	$-0.371058\pi$
$374$	−126861.	+	199286.i	−0.0468975	+	0.0736710i
$375$	204338.			0.0750361
$376$	−147625.	+	1.13046e6i	−0.0538505	+	0.412368i
$377$	−4.54826e6			−1.64813
$378$	823028.	−	1.29289e6i	0.296268	−	0.465406i
$379$			5.21670e6i			1.86551i	0.360510	+	0.932755i	$0.382603\pi$
$379$			5.21670e6i			1.86551i	−0.360510	+	0.932755i	$0.617397\pi$
$380$	−3724.33	−	7972.32i	−0.00132309	−	0.00283221i
$381$			2.13618e6i			0.753920i
$382$	2.02443e6	+	1.28871e6i	0.709814	+	0.451853i
$383$	−4.22327e6			−1.47113			−0.735566	−	0.677453i	$-0.763084\pi$
$383$	−4.22327e6			−1.47113			−0.735566	+	0.677453i	$0.763084\pi$
$384$	3.21935e6	−	2.96448e6i	1.11414	−	1.02594i
$385$	28745.2			0.00988358
$386$	1.78426e6	+	1.13583e6i	0.609523	+	0.388010i
$387$			3.10418e6i			1.05359i
$388$	170152.	+	364229.i	0.0573797	+	0.122827i
$389$			615402.i			0.206198i	0.994671	+	0.103099i	$0.0328759\pi$
$389$			615402.i			0.206198i	−0.994671	+	0.103099i	$0.967124\pi$
$390$	75470.0	−	118555.i	0.0251254	−	0.0394693i
$391$	−385875.			−0.127645
$392$	211401.	−	1.61883e6i	0.0694851	−	0.532092i
$393$	2.23088e6			0.728611
$394$	342807.	−	538513.i	0.111252	−	0.174765i
$395$		−	102124.i		−	0.0329332i
$396$	−1.17707e6	+	549876.i	−0.377194	+	0.176209i
$397$			1.60554e6i			0.511263i	0.966774	+	0.255632i	$0.0822835\pi$
$397$			1.60554e6i			0.511263i	−0.966774	+	0.255632i	$0.917717\pi$
$398$	−1.25474e6	−	798744.i	−0.397051	−	0.252755i
$399$	753180.			0.236846
$400$	−2.05224e6	+	2.45270e6i	−0.641325	+	0.766469i
$401$	1.47973e6			0.459539			0.229769	−	0.973245i	$-0.426203\pi$
$401$	1.47973e6			0.459539			0.229769	+	0.973245i	$0.426203\pi$
$402$	−3.73848e6	−	2.37984e6i	−1.15380	−	0.734485i
$403$		−	3.70140e6i		−	1.13528i
$404$	1.88343e6	−	879856.i	0.574111	−	0.268200i
$405$		−	50695.4i		−	0.0153579i
$406$	2.92285e6	−	4.59149e6i	0.880019	−	1.38242i
$407$	−477592.			−0.142913
$408$	−1.37054e6	−	178976.i	−0.407606	−	0.0532287i
$409$	1.15560e6			0.341584			0.170792	−	0.985307i	$-0.445367\pi$
$409$	1.15560e6			0.341584			0.170792	+	0.985307i	$0.445367\pi$
$410$	−43921.9	+	68996.6i	−0.0129039	+	0.0202707i
$411$			130249.i			0.0380338i
$412$	−935022.	−	2.00152e6i	−0.271381	−	0.580920i
$413$			5.38575e6i			1.55371i
$414$	−1.79015e6	−	1.13958e6i	−0.513322	−	0.326770i
$415$	85367.6			0.0243317
$416$	1.33054e6	+	4.19444e6i	0.376961	+	1.18834i
$417$	−3.88350e6			−1.09366
$418$	−122324.	−	77868.8i	−0.0342428	−	0.0217983i
$419$		−	1.84397e6i		−	0.513121i	−0.966528	−	0.256560i	$-0.917411\pi$
$419$		−	1.84397e6i		−	0.513121i	0.966528	−	0.256560i	$-0.0825893\pi$
$420$	71182.9	+	152375.i	0.0196903	+	0.0421492i
$421$		−	4.13061e6i		−	1.13582i	−0.823091	−	0.567909i	$-0.807752\pi$
$421$		−	4.13061e6i		−	1.13582i	0.823091	−	0.567909i	$-0.192248\pi$
$422$	−829211.	+	1.30260e6i	−0.226665	+	0.356066i
$423$	1.98014e6			0.538077
$424$	3.90010e6	+	509309.i	1.05356	+	0.137583i
$425$	1.01003e6			0.271245
$426$	−4.26477e6	+	6.69950e6i	−1.13860	+	1.78862i
$427$		−	7.79524e6i		−	2.06900i
$428$	5.43091e6	−	2.53708e6i	1.43305	−	0.669461i
$429$		−	2.31595e6i		−	0.607556i
$430$	−65263.4	−	41545.4i	−0.0170215	−	0.0108356i
$431$	3.44366e6			0.892950			0.446475	−	0.894796i	$-0.352679\pi$
$431$	3.44366e6			0.892950			0.446475	+	0.894796i	$0.352679\pi$
$432$	−1.32402e6	−	1.10784e6i	−0.341339	−	0.285607i
$433$	−2.41696e6			−0.619511			−0.309755	−	0.950816i	$-0.600247\pi$
$433$	−2.41696e6			−0.619511			−0.309755	+	0.950816i	$0.600247\pi$
$434$	3.73658e6	+	2.37864e6i	0.952249	+	0.606183i
$435$			195807.i			0.0496141i
$436$	−1.43079e6	+	668403.i	−0.360462	+	0.168392i
$437$		−	236854.i		−	0.0593305i
$438$	−3.67770e6	+	5.77728e6i	−0.915992	+	1.43893i
$439$	−3.22639e6			−0.799015			−0.399507	−	0.916730i	$-0.630819\pi$
$439$	−3.22639e6			−0.799015			−0.399507	+	0.916730i	$0.630819\pi$
$440$	4192.74	−	32106.5i	0.00103244	−	0.00790607i
$441$	−2.83558e6			−0.694298
$442$	746317.	−	1.17239e6i	0.181705	−	0.285440i
$443$			6.44624e6i			1.56062i	0.625393	+	0.780310i	$0.284939\pi$
$443$			6.44624e6i			1.56062i	−0.625393	+	0.780310i	$0.715061\pi$
$444$	−1.18268e6	−	2.53165e6i	−0.284714	−	0.609462i
$445$		−	147850.i		−	0.0353933i
$446$	−4.79840e6	−	3.05457e6i	−1.14224	−	0.727130i
$447$	9.98969e6			2.36474
$448$	−5.08936e6	−	1.35229e6i	−1.19803	−	0.318327i
$449$	−1.82600e6			−0.427450			−0.213725	−	0.976894i	$-0.568560\pi$
$449$	−1.82600e6			−0.427450			−0.213725	+	0.976894i	$0.568560\pi$
$450$	4.68573e6	+	2.98285e6i	1.09080	+	0.694384i
$451$			1.34783e6i			0.312029i
$452$	2.31738e6	+	4.96060e6i	0.533520	+	1.14206i
$453$			943791.i			0.216088i
$454$	−1.68593e6	+	2.64842e6i	−0.383884	+	0.603041i
$455$	−169107.			−0.0382941
$456$	109858.	−	841250.i	0.0247411	−	0.189458i
$457$	2.26865e6			0.508132			0.254066	−	0.967187i	$-0.418232\pi$
$457$	2.26865e6			0.508132			0.254066	+	0.967187i	$0.418232\pi$
$458$	1.44601e6	−	2.27153e6i	0.322113	−	0.506006i
$459$			545237.i			0.120796i
$460$	47917.6	−	22385.1i	0.0105585	−	0.00493246i
$461$			2.82378e6i			0.618840i	0.950925	+	0.309420i	$0.100135\pi$
$461$			2.82378e6i			0.618840i	−0.950925	+	0.309420i	$0.899865\pi$
$462$	2.33797e6	+	1.48830e6i	0.509605	+	0.324404i
$463$	3.05836e6			0.663035			0.331517	−	0.943449i	$-0.392439\pi$
$463$	3.05836e6			0.663035			0.331517	+	0.943449i	$0.392439\pi$
$464$	−4.70206e6	−	3.93433e6i	−1.01389	−	0.848352i
$465$	−159349.			−0.0341756
$466$	−4.36228e6	−	2.77694e6i	−0.930570	−	0.592383i
$467$		−	5.19478e6i		−	1.10224i	−0.834427	−	0.551119i	$-0.814201\pi$
$467$		−	5.19478e6i		−	1.10224i	0.834427	−	0.551119i	$-0.185799\pi$
$468$	6.92464e6	−	3.23489e6i	1.46144	−	0.682724i
$469$			5.33254e6i			1.11944i
$470$	−26501.5	+	41631.0i	−0.00553383	+	0.00869305i
$471$	−8.67537e6			−1.80192
$472$	6.01550e6	+	785556.i	1.24285	+	0.162301i
$473$	−1.27491e6			−0.262014
$474$	5.28753e6	−	8.30614e6i	1.08095	−	1.69806i
$475$			619967.i			0.126077i
$476$	703922.	+	1.50682e6i	0.142399	+	0.304821i
$477$		−	6.83151e6i		−	1.37474i
$478$	−1.79345e6	−	1.14167e6i	−0.359020	−	0.228545i
$479$	−8.27094e6			−1.64708			−0.823542	−	0.567255i	$-0.808006\pi$
$479$	−8.27094e6			−1.64708			−0.823542	+	0.567255i	$0.808006\pi$
$480$	180575.	−	57281.2i	0.0357729	−	0.0113477i
$481$	2.80965e6			0.553719
$482$	−2.92099e6	−	1.85944e6i	−0.572680	−	0.364557i
$483$			4.52699e6i			0.882961i
$484$	1.95544e6	+	4.18583e6i	0.379429	+	0.812209i
$485$			17402.2i			0.00335932i
$486$	3.86929e6	−	6.07824e6i	0.743088	−	1.16731i
$487$	−4.95663e6			−0.947031			−0.473515	−	0.880786i	$-0.657015\pi$
$487$	−4.95663e6			−0.947031			−0.473515	+	0.880786i	$0.657015\pi$
$488$	−8.70675e6	−	1.13700e6i	−1.65503	−	0.216128i
$489$	−378482.			−0.0715770
$490$	37950.5	−	59616.2i	0.00714047	−	0.0112169i
$491$		−	6.01801e6i		−	1.12655i	−0.826271	−	0.563273i	$-0.809542\pi$
$491$		−	6.01801e6i		−	1.12655i	0.826271	−	0.563273i	$-0.190458\pi$
$492$	−7.14469e6	+	3.33769e6i	−1.33067	+	0.621632i
$493$			1.93632e6i			0.358806i
$494$	719623.	+	458098.i	0.132675	+	0.0844580i
$495$	−56238.4			−0.0103162
$496$	3.20178e6	−	3.82656e6i	0.584370	−	0.698400i
$497$	9.55613e6			1.73537
$498$	6.94329e6	+	4.41996e6i	1.25456	+	0.798629i
$499$			7.87834e6i			1.41639i	0.706016	+	0.708196i	$0.250491\pi$
$499$			7.87834e6i			1.41639i	−0.706016	+	0.708196i	$0.749509\pi$
$500$	−250926.	+	117222.i	−0.0448870	+	0.0209693i
$501$			5.85769e6i			1.04263i
$502$	−1.40534e6	+	2.20764e6i	−0.248898	+	0.390993i
$503$	9.09472e6			1.60276			0.801382	−	0.598153i	$-0.204099\pi$
$503$	9.09472e6			1.60276			0.801382	+	0.598153i	$0.204099\pi$
$504$	−1.18435e6	+	9.06930e6i	−0.207684	+	1.59037i
$505$	89987.0			0.0157019
$506$	468030.	−	735226.i	0.0812639	−	0.127657i
$507$			4.85858e6i			0.839440i
$508$	−1.22546e6	−	2.62322e6i	−0.210687	−	0.450999i
$509$		−	1.07691e7i		−	1.84241i	−0.389076	−	0.921206i	$-0.627206\pi$
$509$		−	1.07691e7i		−	1.84241i	0.389076	−	0.921206i	$-0.372794\pi$
$510$	−50472.3	−	32129.7i	−0.00859266	−	0.00546992i
$511$	8.24068e6			1.39608
$512$	−2.25273e6	+	5.48722e6i	−0.379783	+	0.925076i
$513$	−334672.			−0.0561470
$514$	2.78372e6	+	1.77206e6i	0.464749	+	0.295850i
$515$		−	95629.1i		−	0.0158881i
$516$	−3.15709e6	−	6.75810e6i	−0.521991	−	1.11738i
$517$			813253.i			0.133813i
$518$	−1.80557e6	+	2.83635e6i	−0.295658	+	0.464447i
$519$	−1.35541e7			−2.20877
$520$	−24665.6	+	188880.i	−0.00400022	+	0.0306322i
$521$	−1.88429e6			−0.304126			−0.152063	−	0.988371i	$-0.548592\pi$
$521$	−1.88429e6			−0.304126			−0.152063	+	0.988371i	$0.548592\pi$
$522$	−5.71839e6	+	8.98299e6i	−0.918539	+	1.44293i
$523$			2.14270e6i			0.342537i	0.985224	+	0.171269i	$0.0547866\pi$
$523$			2.14270e6i			0.342537i	−0.985224	+	0.171269i	$0.945213\pi$
$524$	−2.73952e6	+	1.27979e6i	−0.435859	+	0.203615i
$525$		−	1.18494e7i		−	1.87628i
$526$	1.96595e6	+	1.25148e6i	0.309818	+	0.197224i
$527$	−1.57579e6			−0.247156
$528$	2.00334e6	−	2.39427e6i	0.312731	−	0.373755i
$529$	−5.01273e6			−0.778816
$530$	143628.	+	91430.6i	0.0222100	+	0.0141384i
$531$		−	1.05369e7i		−	1.62172i
$532$	−924904.	+	432075.i	−0.141683	+	0.0661882i
$533$		−	7.92923e6i		−	1.20896i
$534$	7.65502e6	−	1.20252e7i	1.16170	−	1.82490i
$535$	259479.			0.0391939
$536$	5.95608e6	+	777796.i	0.895465	+	0.116938i
$537$	7.20787e6			1.07863
$538$	−3.47703e6	+	5.46204e6i	−0.517908	+	0.813578i
$539$		−	1.16459e6i		−	0.172664i
$540$	−31629.8	−	67707.0i	−0.00466780	−	0.00999193i
$541$			9.23309e6i			1.35629i	0.734926	+	0.678147i	$0.237217\pi$
$541$			9.23309e6i			1.35629i	−0.734926	+	0.678147i	$0.762783\pi$
$542$	5.80309e6	+	3.69413e6i	0.848518	+	0.540150i
$543$	9.95569e6			1.44901
$544$	1.78569e6	−	566450.i	0.258707	−	0.0820662i
$545$	−68360.7			−0.00985859
$546$	−1.37541e7	−	8.75560e6i	−1.97447	−	1.25691i
$547$		−	6.30413e6i		−	0.900858i	−0.892812	−	0.450429i	$-0.851271\pi$
$547$		−	6.30413e6i		−	0.900858i	0.892812	−	0.450429i	$-0.148729\pi$
$548$	−74719.7	−	159946.i	−0.0106288	−	0.0227521i
$549$			1.52509e7i			2.15956i
$550$	−1.22507e6	+	1.92446e6i	−0.172685	+	0.271270i
$551$	−1.18853e6			−0.166776
$552$	5.05633e6	+	660300.i	0.706298	+	0.0922345i
$553$	−1.18478e7			−1.64750
$554$	2.44860e6	−	3.84649e6i	0.338956	−	0.532464i
$555$		−	120958.i		−	0.0166687i
$556$	4.76893e6	−	2.22784e6i	0.654236	−	0.305631i
$557$			6.50282e6i			0.888104i	0.896001	+	0.444052i	$0.146460\pi$
$557$			6.50282e6i			0.888104i	−0.896001	+	0.444052i	$0.853540\pi$
$558$	−7.31041e6	−	4.65366e6i	−0.993931	−	0.632717i
$559$	7.50020e6			1.01518
$560$	−174825.	−	146281.i	−0.0235577	−	0.0197114i
$561$	−985966.			−0.132268
$562$	−5.71802e6	−	3.63998e6i	−0.763668	−	0.486136i
$563$			6.06434e6i			0.806329i	0.915127	+	0.403165i	$0.132090\pi$
$563$			6.06434e6i			0.806329i	−0.915127	+	0.403165i	$0.867910\pi$
$564$	−4.31094e6	+	2.01389e6i	−0.570656	+	0.266586i
$565$			237009.i			0.0312352i
$566$	−4.44385e6	+	6.98082e6i	−0.583067	+	0.915937i
$567$	−5.88140e6			−0.768286
$568$	1.39384e6	−	1.06735e7i	0.181277	−	1.38815i
$569$	8.67931e6			1.12384			0.561920	−	0.827191i	$-0.310063\pi$
$569$	8.67931e6			1.12384			0.561920	+	0.827191i	$0.310063\pi$
$570$	19721.5	−	30980.5i	0.00254246	−	0.00399393i
$571$		−	5.13091e6i		−	0.658573i	−0.944230	−	0.329287i	$-0.893192\pi$
$571$		−	5.13091e6i		−	0.658573i	0.944230	−	0.329287i	$-0.106808\pi$
$572$	1.32859e6	+	2.84399e6i	0.169785	+	0.363444i
$573$			1.00159e7i			1.27439i
$574$	8.00460e6	+	5.09557e6i	1.01405	+	0.645525i
$575$	−3.72631e6			−0.470013
$576$	9.95703e6	+	2.64567e6i	1.25047	+	0.332261i
$577$	−1.05397e7			−1.31792			−0.658962	−	0.752176i	$-0.729004\pi$
$577$	−1.05397e7			−1.31792			−0.658962	+	0.752176i	$0.729004\pi$
$578$	6.27644e6	+	3.99546e6i	0.781437	+	0.497447i
$579$			8.82764e6i			1.09433i
$580$	−112328.	−	240451.i	−0.0138650	−	0.0296794i
$581$		−	9.90387e6i		−	1.21721i
$582$	−901012.	+	1.41539e6i	−0.110261	+	0.173209i
$583$	2.80574e6			0.341881
$584$	1.20197e6	−	9.20427e6i	0.145835	−	1.11675i
$585$	330847.			0.0399704
$586$	2.28052e6	−	3.58245e6i	0.274340	−	0.430959i
$587$			5.07345e6i			0.607727i	0.952716	+	0.303863i	$0.0982767\pi$
$587$			5.07345e6i			0.607727i	−0.952716	+	0.303863i	$0.901723\pi$
$588$	6.17333e6	−	2.88391e6i	0.736336	−	0.343985i
$589$		−	967237.i		−	0.114880i
$590$	221531.	+	141022.i	0.0262002	+	0.0166785i
$591$	2.66429e6			0.313771
$592$	2.90465e6	+	2.43040e6i	0.340636	+	0.285019i
$593$	−1.41356e7			−1.65073			−0.825366	−	0.564599i	$-0.809031\pi$
$593$	−1.41356e7			−1.65073			−0.825366	+	0.564599i	$0.809031\pi$
$594$	−1.03886e6	−	661321.i	−0.120807	−	0.0769035i
$595$			71993.4i			0.00833682i
$596$	−1.22673e7	+	5.73076e6i	−1.41460	+	0.660841i
$597$		−	6.20784e6i		−	0.712861i
$598$	−2.75340e6	+	4.32529e6i	−0.314859	+	0.494610i
$599$	7.17896e6			0.817512			0.408756	−	0.912644i	$-0.365963\pi$
$599$	7.17896e6			0.817512			0.408756	+	0.912644i	$0.365963\pi$
$600$	−1.32350e7	−	1.72834e6i	−1.50088	−	0.195997i
$601$	−3.61001e6			−0.407683			−0.203841	−	0.979004i	$-0.565343\pi$
$601$	−3.61001e6			−0.407683			−0.203841	+	0.979004i	$0.565343\pi$
$602$	−4.81986e6	+	7.57149e6i	−0.542055	+	0.851511i
$603$		−	1.04328e7i		−	1.16844i
$604$	−541422.	−	1.15897e6i	−0.0603870	−	0.129265i
$605$			199992.i			0.0222138i
$606$	7.31900e6	+	4.65913e6i	0.809600	+	0.515375i
$607$	4.03263e6			0.444239			0.222119	−	0.975020i	$-0.428703\pi$
$607$	4.03263e6			0.444239			0.222119	+	0.975020i	$0.428703\pi$
$608$	347693.	+	1.09608e6i	0.0381450	+	0.120249i
$609$	2.27164e7			2.48197
$610$	−320641.	−	204113.i	−0.0348894	−	0.0222099i
$611$		−	4.78432e6i		−	0.518462i
$612$	−1.37718e6	−	2.94801e6i	−0.148632	−	0.318164i
$613$		−	1.31815e7i		−	1.41682i	−0.705801	−	0.708410i	$-0.749413\pi$
$613$		−	1.31815e7i		−	1.41682i	0.705801	−	0.708410i	$-0.250587\pi$
$614$	6.28069e6	−	9.86630e6i	0.672336	−	1.05617i
$615$	−341361.			−0.0363937
$616$	−3.72481e6	−	486418.i	−0.395505	−	0.0516485i
$617$	7.04507e6			0.745027			0.372514	−	0.928027i	$-0.378496\pi$
$617$	7.04507e6			0.745027			0.372514	+	0.928027i	$0.378496\pi$
$618$	4.95126e6	−	7.77790e6i	0.521488	−	0.819202i
$619$			6.48539e6i			0.680314i	0.940369	+	0.340157i	$0.110480\pi$
$619$			6.48539e6i			0.680314i	−0.940369	+	0.340157i	$0.889520\pi$
$620$	195680.	−	91413.3i	0.0204441	−	0.00955059i
$621$		−	2.01155e6i		−	0.209315i
$622$	−1.46451e7	−	9.32276e6i	−1.51780	−	0.966203i
$623$	−1.71527e7			−1.77057
$624$	−1.17856e7	+	1.40853e7i	−1.21168	+	1.44812i
$625$	9.74764e6			0.998158
$626$	549484.	+	349791.i	0.0560428	+	0.0356757i
$627$		−	605196.i		−	0.0614791i
$628$	1.06533e7	−	4.97678e6i	1.07792	−	0.503558i
$629$		−	1.19614e6i		−	0.120547i
$630$	−212613.	+	333992.i	−0.0213421	+	0.0335262i
$631$	−4.09103e6			−0.409034			−0.204517	−	0.978863i	$-0.565562\pi$
$631$	−4.09103e6			−0.409034			−0.204517	+	0.978863i	$0.565562\pi$
$632$	−1.72811e6	+	1.32332e7i	−0.172099	+	1.31787i
$633$	−6.44463e6			−0.639276
$634$	−3.94698e6	+	6.20028e6i	−0.389979	+	0.612616i
$635$		−	125333.i		−	0.0123348i
$636$	6.94795e6	+	1.48728e7i	0.681104	+	1.45798i
$637$			6.85121e6i			0.668989i
$638$	−3.68936e6	−	2.34857e6i	−0.358839	−	0.228430i
$639$	−1.86960e7			−1.81133
$640$	−188885.	+	173931.i	−0.0182283	+	0.0167852i
$641$	8.17877e6			0.786218			0.393109	−	0.919492i	$-0.371400\pi$
$641$	8.17877e6			0.786218			0.393109	+	0.919492i	$0.371400\pi$
$642$	2.11045e7	+	1.34347e7i	2.02087	+	1.28644i
$643$		−	1.41619e7i		−	1.35081i	−0.737448	−	0.675404i	$-0.763969\pi$
$643$		−	1.41619e7i		−	1.35081i	0.737448	−	0.675404i	$-0.236031\pi$
$644$	−2.59699e6	−	5.55914e6i	−0.246749	−	0.528193i
$645$		−	322891.i		−	0.0305602i
$646$	195025.	−	306364.i	0.0183869	−	0.0288839i
$647$	1.23662e7			1.16138			0.580690	−	0.814124i	$-0.302783\pi$
$647$	1.23662e7			1.16138			0.580690	+	0.814124i	$0.302783\pi$
$648$	−857852.	+	6.56912e6i	−0.0802555	+	0.614567i
$649$	4.32756e6			0.403303
$650$	7.20702e6	−	1.13215e7i	0.669072	−	1.05104i
$651$			1.84868e7i			1.70965i
$652$	464776.	−	217123.i	0.0428178	−	0.0200026i
$653$			1.99967e7i			1.83517i	0.397543	+	0.917584i	$0.369863\pi$
$653$			1.99967e7i			1.83517i	−0.397543	+	0.917584i	$0.630137\pi$
$654$	−5.56005e6	−	3.53942e6i	−0.508316	−	0.323584i
$655$	−130890.			−0.0119207
$656$	6.85894e6	−	8.19735e6i	0.622296	−	0.743728i
$657$	−1.61224e7			−1.45719
$658$	4.82980e6	+	3.07455e6i	0.434875	+	0.276833i
$659$			1.68566e7i			1.51202i	0.654562	+	0.756009i	$0.272853\pi$
$659$			1.68566e7i			1.51202i	−0.654562	+	0.756009i	$0.727147\pi$
$660$	122436.	−	57197.0i	0.0109408	−	0.00511109i
$661$		−	1.65602e6i		−	0.147422i	−0.997280	−	0.0737111i	$-0.976516\pi$
$661$		−	1.65602e6i		−	0.147422i	0.997280	−	0.0737111i	$-0.0234843\pi$
$662$	6.13972e6	−	9.64485e6i	0.544507	−	0.855363i
$663$	5.80038e6			0.512475
$664$	−1.10619e7	−	1.44456e6i	−0.973668	−	0.127150i
$665$	−44190.3			−0.00387501
$666$	3.53249e6	−	5.54916e6i	0.308599	−	0.484777i
$667$		−	7.14369e6i		−	0.621739i
$668$	−3.36037e6	−	7.19323e6i	−0.291370	−	0.623710i
$669$		−	2.37401e7i		−	2.05077i
$670$	219343.	+	139629.i	0.0188771	+	0.0120168i
$671$	−6.26364e6			−0.537057
$672$	−6.64545e6	−	2.09493e7i	−0.567676	−	1.78956i
$673$	1.37081e7			1.16665			0.583324	−	0.812240i	$-0.301752\pi$
$673$	1.37081e7			1.16665			0.583324	+	0.812240i	$0.301752\pi$
$674$	−1.37698e7	−	8.76555e6i	−1.16755	−	0.743241i
$675$			5.26523e6i			0.444793i
$676$	−2.78721e6	−	5.96633e6i	−0.234587	−	0.502158i
$677$			2.21494e6i			0.185734i	0.995679	+	0.0928669i	$0.0296031\pi$
$677$			2.21494e6i			0.185734i	−0.995679	+	0.0928669i	$0.970397\pi$
$678$	−1.22713e7	+	1.92769e7i	−1.02522	+	1.61051i
$679$	2.01891e6			0.168052
$680$	80411.7	+	10500.8i	0.00666879	+	0.000870867i
$681$	−1.31031e7			−1.08269
$682$	1.91128e6	−	3.00242e6i	0.157349	−	0.247179i
$683$		−	532823.i		−	0.0437050i	−0.999761	−	0.0218525i	$-0.993044\pi$
$683$		−	532823.i		−	0.0437050i	0.999761	−	0.0218525i	$-0.00695643\pi$
$684$	1.80952e6	−	845330.i	0.147885	−	0.0690854i
$685$		−	7641.93i		−	0.000622267i
$686$	5.97262e6	+	3.80205e6i	0.484568	+	0.308466i
$687$	1.12384e7			0.908476
$688$	7.75381e6	+	6.48781e6i	0.624517	+	0.522549i
$689$	−1.65060e7			−1.32463
$690$	186208.	+	118536.i	0.0148893	+	0.00947826i
$691$			5.63330e6i			0.448816i	0.974495	+	0.224408i	$0.0720448\pi$
$691$			5.63330e6i			0.448816i	−0.974495	+	0.224408i	$0.927955\pi$
$692$	1.66444e7	−	7.77553e6i	1.32130	−	0.617255i
$693$			6.52446e6i			0.516074i
$694$	−3.09530e6	+	4.86238e6i	−0.243952	+	0.383222i
$695$	227852.			0.0178933
$696$	3.31338e6	−	2.53727e7i	0.259268	−	1.98538i
$697$	−3.37569e6			−0.263197
$698$	−4.67165e6	+	7.33866e6i	−0.362937	+	0.570136i
$699$		−	2.15824e7i		−	1.67073i
$700$	6.79762e6	+	1.45511e7i	0.524339	+	1.12240i
$701$			5.94926e6i			0.457265i	0.973513	+	0.228633i	$0.0734254\pi$
$701$			5.94926e6i			0.457265i	−0.973513	+	0.228633i	$0.926575\pi$
$702$	6.11158e6	+	3.89051e6i	0.468070	+	0.297964i
$703$	734207.			0.0560312
$704$	−1.08659e6	+	4.08941e6i	−0.0826293	+	0.310977i
$705$	−205970.			−0.0156074
$706$	2.34013e6	+	1.48968e6i	0.176697	+	0.112482i
$707$		−	1.04398e7i		−	0.785494i
$708$	1.07165e7	+	2.29398e7i	0.803470	+	1.71991i
$709$			8.89034e6i			0.664206i	0.943243	+	0.332103i	$0.107758\pi$
$709$			8.89034e6i			0.664206i	−0.943243	+	0.332103i	$0.892242\pi$
$710$	250221.	−	393071.i	0.0186285	−	0.0292634i
$711$	2.31796e7			1.71962
$712$	−2.50187e6	+	1.91584e7i	−0.184954	+	1.41631i
$713$	5.81358e6			0.428272
$714$	−3.72750e6	+	5.85551e6i	−0.273636	+	0.429853i
$715$			135881.i			0.00994015i
$716$	−8.85125e6	+	4.13492e6i	−0.645241	+	0.301429i
$717$		−	8.87308e6i		−	0.644579i
$718$	−1.52671e7	−	9.71871e6i	−1.10521	−	0.703554i
$719$	−1.23030e7			−0.887539			−0.443769	−	0.896141i	$-0.646359\pi$
$719$	−1.23030e7			−0.887539			−0.443769	+	0.896141i	$0.646359\pi$
$720$	342035.	+	286189.i	0.0245889	+	0.0205742i
$721$	−1.10943e7			−0.794811
$722$	−1.16279e7	−	7.40209e6i	−0.830153	−	0.528459i
$723$		−	1.44516e7i		−	1.02818i
$724$	−1.22256e7	+	5.71126e6i	−0.866807	+	0.404935i
$725$			1.86986e7i			1.32119i
$726$	−1.03547e7	+	1.62661e7i	−0.729115	+	1.14536i
$727$	−4.81217e6			−0.337679			−0.168840	−	0.985644i	$-0.554002\pi$
$727$	−4.81217e6			−0.337679			−0.168840	+	0.985644i	$0.554002\pi$
$728$	2.19128e7	+	2.86157e6i	1.53239	+	0.200113i
$729$	2.11789e7			1.47599
$730$	215777.	−	338963.i	0.0149864	−	0.0235421i
$731$		−	3.19304e6i		−	0.221010i
$732$	−1.55109e7	−	3.32027e7i	−1.06994	−	2.29032i
$733$		−	2.11550e6i		−	0.145430i	−0.997353	−	0.0727148i	$-0.976834\pi$
$733$		−	2.11550e6i		−	0.145430i	0.997353	−	0.0727148i	$-0.0231663\pi$
$734$	9.86585e6	+	6.28041e6i	0.675919	+	0.430277i
$735$	294951.			0.0201387
$736$	−6.58796e6	+	2.08981e6i	−0.448287	+	0.142204i
$737$	4.28481e6			0.290578
$738$	−1.56605e7	−	9.96918e6i	−1.05844	−	0.673781i
$739$		−	3.53365e6i		−	0.238019i	−0.992893	−	0.119010i	$-0.962028\pi$
$739$		−	3.53365e6i		−	0.238019i	0.992893	−	0.119010i	$-0.0379719\pi$
$740$	69389.7	+	148536.i	0.00465817	+	0.00997133i
$741$			3.56034e6i			0.238202i
$742$	1.06073e7	−	1.66629e7i	0.707283	−	1.11107i
$743$	2.10515e7			1.39898			0.699489	−	0.714643i	$-0.253411\pi$
$743$	2.10515e7			1.39898			0.699489	+	0.714643i	$0.253411\pi$
$744$	2.06484e7	+	2.69645e6i	1.36759	+	0.178591i
$745$	−586112.			−0.0386892
$746$	−1.50039e7	+	2.35695e7i	−0.987091	+	1.55062i
$747$			1.93763e7i			1.27049i
$748$	1.21076e6	−	565617.i	0.0791235	−	0.0369631i
$749$		−	3.01033e7i		−	1.96070i
$750$	−975100.	−	620729.i	−0.0632988	−	0.0402948i
$751$	−9.76794e6			−0.631980			−0.315990	−	0.948763i	$-0.602337\pi$
$751$	−9.76794e6			−0.631980			−0.315990	+	0.948763i	$0.602337\pi$
$752$	4.13853e6	−	4.94610e6i	0.266871	−	0.318947i
$753$	−1.09223e7			−0.701983
$754$	2.17043e7	+	1.38165e7i	1.39033	+	0.885056i
$755$		−	55373.8i		−	0.00353538i
$756$	−7.85499e6	+	3.66951e6i	−0.499851	+	0.233509i
$757$		−	3.90009e6i		−	0.247363i	−0.992322	−	0.123682i	$-0.960530\pi$
$757$		−	3.90009e6i		−	0.247363i	0.992322	−	0.123682i	$-0.0394701\pi$
$758$	1.58471e7	−	2.48941e7i	1.00179	−	1.57370i
$759$	3.63753e6			0.229194
$760$	−6445.53	+	49357.6i	−0.000404785	+	0.00309970i
$761$	−1.28261e7			−0.802845			−0.401422	−	0.915893i	$-0.631484\pi$
$761$	−1.28261e7			−0.802845			−0.401422	+	0.915893i	$0.631484\pi$
$762$	6.48920e6	−	1.01938e7i	0.404859	−	0.635991i
$763$			7.93082e6i			0.493181i
$764$	−5.74578e6	−	1.22995e7i	−0.356136	−	0.762348i
$765$		−	140851.i		−	0.00870174i
$766$	2.01534e7	+	1.28293e7i	1.24102	+	0.790006i
$767$	−2.54588e7			−1.56261
$768$	−2.43682e7	+	4.36688e6i	−1.49080	+	0.267158i
$769$	1.15731e7			0.705724			0.352862	−	0.935675i	$-0.385208\pi$
$769$	1.15731e7			0.705724			0.352862	+	0.935675i	$0.385208\pi$
$770$	−137172.	−	87321.2i	−0.00833758	−	0.00530754i
$771$			1.37725e7i			0.834404i
$772$	−5.06413e6	−	1.08403e7i	−0.305817	−	0.654635i
$773$			3.69152e6i			0.222206i	0.993809	+	0.111103i	$0.0354384\pi$
$773$			3.69152e6i			0.222206i	−0.993809	+	0.111103i	$0.964562\pi$
$774$	9.42977e6	−	1.48132e7i	0.565782	−	0.888783i
$775$	−1.52171e7			−0.910073
$776$	294475.	−	2.25498e6i	0.0175547	−	0.134428i
$777$	−1.40329e7			−0.833861
$778$	1.86944e6	−	2.93670e6i	0.110730	−	0.173944i
$779$		−	2.07204e6i		−	0.122336i
$780$	−720286.	+	336486.i	−0.0423905	+	0.0198030i
$781$		−	7.67855e6i		−	0.450455i
$782$	1.84140e6	+	1.17220e6i	0.107679	+	0.0685463i
$783$	−1.00939e7			−0.588378
$784$	−5.92643e6	+	7.08288e6i	−0.344352	+	0.411547i
$785$	508998.			0.0294810
$786$	−1.06458e7	−	6.77689e6i	−0.614640	−	0.391268i
$787$			3.15075e7i			1.81333i	0.421851	+	0.906665i	$0.361381\pi$
$787$			3.15075e7i			1.81333i	−0.421851	+	0.906665i	$0.638619\pi$
$788$	−3.27175e6	+	1.52842e6i	−0.187700	+	0.0876853i
$789$			9.72652e6i			0.556244i
$790$	−310228.	+	487335.i	−0.0176853	+	0.0277818i
$791$	2.74965e7			1.56256
$792$	7.28737e6	+	951648.i	0.412818	+	0.0539093i
$793$	3.68487e7			2.08084
$794$	4.87725e6	−	7.66164e6i	0.274551	−	0.431291i
$795$			710599.i			0.0398755i
$796$	3.56124e6	+	7.62322e6i	0.199213	+	0.426438i
$797$			1.13115e7i			0.630775i	0.948963	+	0.315387i	$0.102134\pi$
$797$			1.13115e7i			0.630775i	−0.948963	+	0.315387i	$0.897866\pi$
$798$	−3.59418e6	−	2.28798e6i	−0.199799	−	0.127188i
$799$	−2.03682e6			−0.112872
$800$	1.72440e7	−	5.47008e6i	0.952606	−	0.302182i
$801$	3.35583e7			1.84807
$802$	−7.06128e6	−	4.49507e6i	−0.387657	−	0.246775i
$803$		−	6.62156e6i		−	0.362386i
$804$	1.06106e7	+	2.27132e7i	0.578897	+	1.23919i
$805$		−	265606.i		−	0.0144460i
$806$	−1.12440e7	+	1.76631e7i	−0.609652	+	0.957699i
$807$	−2.70235e7			−1.46069
$808$	−1.16605e7	−	1.52273e6i	−0.628332	−	0.0820530i
$809$	−1.87371e7			−1.00654			−0.503271	−	0.864128i	$-0.667870\pi$
$809$	−1.87371e7			−1.00654			−0.503271	+	0.864128i	$0.667870\pi$
$810$	−154001.	+	241919.i	−0.00824727	+	0.0129556i
$811$		−	1.04019e6i		−	0.0555341i	−0.999614	−	0.0277671i	$-0.991160\pi$
$811$		−	1.04019e6i		−	0.0555341i	0.999614	−	0.0277671i	$-0.00883967\pi$
$812$	−2.78957e7	+	1.30317e7i	−1.48473	+	0.693602i
$813$			2.87108e7i			1.52342i
$814$	2.27907e6	+	1.45081e6i	0.120558	+	0.0767450i
$815$	22206.2			0.00117106
$816$	5.99652e6	+	5.01744e6i	0.315263	+	0.263789i
$817$	1.95992e6			0.102727
$818$	−5.51451e6	−	3.51043e6i	−0.288153	−	0.183433i
$819$		−	3.83831e7i		−	1.99954i
$820$	419191.	−	195828.i	0.0217709	−	0.0101704i
$821$		−	2.89521e7i		−	1.49907i	−0.661965	−	0.749535i	$-0.730277\pi$
$821$		−	2.89521e7i		−	1.49907i	0.661965	−	0.749535i	$-0.269723\pi$
$822$	395666.	−	621549.i	0.0204244	−	0.0320845i
$823$	−1.73232e7			−0.891517			−0.445758	−	0.895153i	$-0.647066\pi$
$823$	−1.73232e7			−0.891517			−0.445758	+	0.895153i	$0.647066\pi$
$824$	−1.61820e6	+	1.23916e7i	−0.0830262	+	0.635785i
$825$	−9.52125e6			−0.487034
$826$	1.63606e7	−	2.57008e7i	0.834352	−	1.31068i
$827$		−	7.19436e6i		−	0.365787i	−0.983133	−	0.182893i	$-0.941454\pi$
$827$		−	7.19436e6i		−	0.365787i	0.983133	−	0.182893i	$-0.0585463\pi$
$828$	5.08086e6	+	1.08761e7i	0.257550	+	0.551313i
$829$		−	2.28187e7i		−	1.15320i	−0.817026	−	0.576600i	$-0.804379\pi$
$829$		−	2.28187e7i		−	1.15320i	0.817026	−	0.576600i	$-0.195621\pi$
$830$	−407374.	−	259326.i	−0.0205257	−	0.0130663i
$831$	1.90305e7			0.955978
$832$	6.39235e6	−	2.40578e7i	0.320149	−	1.20489i
$833$	2.91675e6			0.145642
$834$	1.85321e7	+	1.17972e7i	0.922591	+	0.587303i
$835$		−	343680.i		−	0.0170584i
$836$	347182.	+	743180.i	0.0171807	+	0.0367772i
$837$		−	8.21451e6i		−	0.405292i
$838$	−5.60155e6	+	8.79945e6i	−0.275549	+	0.432858i
$839$	1.81694e7			0.891121			0.445560	−	0.895252i	$-0.353004\pi$
$839$	1.81694e7			0.891121			0.445560	+	0.895252i	$0.353004\pi$
$840$	123193.	−	943369.i	0.00602405	−	0.0461300i
$841$	−1.53359e7			−0.747684
$842$	−1.25478e7	+	1.97113e7i	−0.609941	+	0.958152i
$843$		−	2.82899e7i		−	1.37108i
$844$	7.91399e6	−	3.69707e6i	0.382419	−	0.178650i
$845$		−	285061.i		−	0.0137340i
$846$	−9.44921e6	−	6.01518e6i	−0.453910	−	0.288950i
$847$	2.32019e7			1.11126
$848$	−1.70641e7	−	1.42780e7i	−0.814882	−	0.681832i
$849$	−3.45376e7			−1.64446
$850$	−4.81986e6	−	3.06823e6i	−0.228817	−	0.145660i
$851$			4.41295e6i			0.208884i
$852$	4.07030e7	−	1.90147e7i	1.92100	−	0.897408i
$853$		−	2.58313e7i		−	1.21555i	−0.794108	−	0.607776i	$-0.792062\pi$
$853$		−	2.58313e7i		−	1.21555i	0.794108	−	0.607776i	$-0.207938\pi$
$854$	−2.36801e7	+	3.71989e7i	−1.11106	+	1.74536i
$855$	86455.8			0.00404463
$856$	−3.36234e7	−	4.39083e6i	−1.56840	−	0.204815i
$857$	1.83988e7			0.855731			0.427866	−	0.903842i	$-0.359266\pi$
$857$	1.83988e7			0.855731			0.427866	+	0.903842i	$0.359266\pi$
$858$	−7.03531e6	+	1.10517e7i	−0.326261	+	0.512522i
$859$			2.69993e7i			1.24845i	0.781246	+	0.624224i	$0.214585\pi$
$859$			2.69993e7i			1.24845i	−0.781246	+	0.624224i	$0.785415\pi$
$860$	185232.	+	396509.i	0.00854023	+	0.0182813i
$861$			3.96028e7i			1.82061i
$862$	−1.64332e7	−	1.04610e7i	−0.753274	−	0.479519i
$863$	3.05160e7			1.39477			0.697383	−	0.716699i	$-0.254348\pi$
$863$	3.05160e7			1.39477			0.697383	+	0.716699i	$0.254348\pi$
$864$	2.95287e6	+	9.30870e6i	0.134574	+	0.424233i
$865$	795240.			0.0361375
$866$	1.15337e7	+	7.34214e6i	0.522606	+	0.332681i
$867$			3.10527e7i			1.40298i
$868$	−1.06053e7	−	2.27017e7i	−0.477773	−	1.02273i
$869$			9.51999e6i			0.427648i
$870$	594815.	−	934391.i	0.0266430	−	0.0418534i
$871$	−2.52073e7			−1.12585
$872$	8.85818e6	+	1.15678e6i	0.394506	+	0.0515179i
$873$	−3.94988e6			−0.175408
$874$	−719508.	+	1.13027e6i	−0.0318608	+	0.0500499i
$875$			1.39088e6i			0.0614141i
$876$	3.51000e7	−	1.63972e7i	1.54542	−	0.721954i
$877$			2.80238e7i			1.23035i	0.788391	+	0.615174i	$0.210914\pi$
$877$			2.80238e7i			1.23035i	−0.788391	+	0.615174i	$0.789086\pi$
$878$	1.53963e7	+	9.80099e6i	0.674032	+	0.429075i
$879$	1.77242e7			0.773738
$880$	−117540.	+	140476.i	−0.00511655	+	0.00611496i
$881$	−8.04971e6			−0.349414			−0.174707	−	0.984620i	$-0.555898\pi$
$881$	−8.04971e6			−0.349414			−0.174707	+	0.984620i	$0.555898\pi$
$882$	1.35314e7	+	8.61382e6i	0.585695	+	0.372842i
$883$		−	8.61922e6i		−	0.372020i	−0.982548	−	0.186010i	$-0.940444\pi$
$883$		−	8.61922e6i		−	0.372020i	0.982548	−	0.186010i	$-0.0595556\pi$
$884$	−7.12286e6	+	3.32749e6i	−0.306566	+	0.143214i
$885$			1.09603e6i			0.0470395i
$886$	1.95821e7	−	3.07615e7i	0.838061	−	1.31651i
$887$	6.77038e6			0.288937			0.144469	−	0.989509i	$-0.453853\pi$
$887$	6.77038e6			0.288937			0.144469	+	0.989509i	$0.453853\pi$
$888$	−2.04681e6	+	1.56737e7i	−0.0871055	+	0.667022i
$889$	−1.45404e7			−0.617054
$890$	−449133.	+	705540.i	−0.0190064	+	0.0298570i
$891$			4.72583e6i			0.199427i
$892$	1.36189e7	+	2.91528e7i	0.573100	+	1.22678i
$893$		−	1.25022e6i		−	0.0524636i
$894$	−4.76708e7	−	3.03463e7i	−1.99484	−	1.26988i
$895$	−422898.			−0.0176473
$896$	2.01785e7	+	2.19134e7i	0.839690	+	0.911883i
$897$	−2.13994e7			−0.888015
$898$	8.71369e6	+	5.54696e6i	0.360588	+	0.229543i
$899$		−	2.91725e7i		−	1.20386i
$900$	−1.32992e7	−	2.84683e7i	−0.547290	−	1.17153i
$901$			7.02706e6i			0.288378i
$902$	4.09440e6	−	6.43187e6i	0.167561	−	0.263221i
$903$	−3.74600e7			−1.52879
$904$	4.01059e6	−	3.07117e7i	0.163225	−	1.24992i
$905$	−584117.			−0.0237071
$906$	2.86701e6	−	4.50377e6i	0.116040	−	0.182287i
$907$		−	3.35760e7i		−	1.35522i	−0.735421	−	0.677611i	$-0.763015\pi$
$907$		−	3.35760e7i		−	1.35522i	0.735421	−	0.677611i	$-0.236985\pi$
$908$	1.60905e7	−	7.51680e6i	0.647673	−	0.302565i
$909$			2.04248e7i			0.819877i
$910$	806977.	+	513706.i	0.0323041	+	0.0205642i
$911$	−3.92094e7			−1.56529			−0.782645	−	0.622469i	$-0.786130\pi$
$911$	−3.92094e7			−1.56529			−0.782645	+	0.622469i	$0.786130\pi$
$912$	−3.07976e6	+	3.68073e6i	−0.122611	+	0.146537i
$913$	−7.95797e6			−0.315955
$914$	−1.08260e7	−	6.89161e6i	−0.428649	−	0.272869i
$915$		−	1.58637e6i		−	0.0626400i
$916$	−1.38008e7	+	6.44712e6i	−0.543456	+	0.253879i
$917$			1.51851e7i			0.596340i
$918$	1.65630e6	−	2.60187e6i	0.0648683	−	0.101901i
$919$	1.65806e7			0.647609			0.323804	−	0.946124i	$-0.395038\pi$
$919$	1.65806e7			0.647609			0.323804	+	0.946124i	$0.395038\pi$
$920$	−296664.	−	38740.9i	−0.0115557	−	0.00150904i
$921$	4.88136e7			1.89623
$922$	8.57797e6	−	1.34751e7i	0.332321	−	0.522040i
$923$			4.51725e7i			1.74530i
$924$	−6.63567e6	−	1.42044e7i	−0.255685	−	0.547321i
$925$		−	1.15509e7i		−	0.443876i
$926$	−1.45945e7	−	9.29057e6i	−0.559322	−	0.356053i
$927$	2.17054e7			0.829601
$928$	1.04867e7	+	3.30584e7i	0.399730	+	1.26012i
$929$	3.97202e7			1.50998			0.754992	−	0.655734i	$-0.227641\pi$
$929$	3.97202e7			1.50998			0.754992	+	0.655734i	$0.227641\pi$
$930$	760413.	+	484064.i	0.0288298	+	0.0183525i
$931$			1.79033e6i			0.0676955i
$932$	1.23811e7	+	2.65032e7i	0.466897	+	0.999443i
$933$		−	7.24565e7i		−	2.72504i
$934$	−1.57805e7	+	2.47895e7i	−0.591907	+	0.929824i
$935$	57848.2			0.00216402
$936$	−4.28712e7	−	5.59849e6i	−1.59947	−	0.208873i
$937$	2.47490e7			0.920891			0.460446	−	0.887688i	$-0.347690\pi$
$937$	2.47490e7			0.920891			0.460446	+	0.887688i	$0.347690\pi$
$938$	1.61990e7	−	2.54469e7i	0.601148	−	0.944339i
$939$			2.71858e6i			0.100618i
$940$	252930.	−	118158.i	0.00933643	−	0.00436158i
$941$		−	3.63378e7i		−	1.33778i	−0.743361	−	0.668890i	$-0.766770\pi$
$941$		−	3.63378e7i		−	1.33778i	0.743361	−	0.668890i	$-0.233230\pi$
$942$	4.13989e7	+	2.63537e7i	1.52006	+	0.967641i
$943$	1.24540e7			0.456067
$944$	−2.63197e7	−	2.20223e7i	−0.961281	−	0.804329i
$945$	−375298.			−0.0136709
$946$	6.08385e6	+	3.87286e6i	0.221030	+	0.140703i
$947$		−	5.78262e6i		−	0.209532i	−0.994497	−	0.104766i	$-0.966591\pi$
$947$		−	5.78262e6i		−	0.209532i	0.994497	−	0.104766i	$-0.0334093\pi$
$948$	−5.04642e7	+	2.35747e7i	−1.82374	+	0.851971i
$949$			3.89543e7i			1.40407i
$950$	1.88331e6	−	2.95849e6i	0.0677039	−	0.106356i
$951$	−3.06759e7			−1.09988
$952$	1.21825e6	−	9.32891e6i	0.0435656	−	0.333610i
$953$	−4.95180e7			−1.76616			−0.883081	−	0.469220i	$-0.844535\pi$
$953$	−4.95180e7			−1.76616			−0.883081	+	0.469220i	$0.844535\pi$
$954$	−2.07525e7	+	3.26000e7i	−0.738243	+	1.15970i
$955$		−	587648.i		−	0.0208501i
$956$	5.09020e6	+	1.08961e7i	0.180132	+	0.385591i
$957$		−	1.82531e7i		−	0.644254i
$958$	3.94689e7	+	2.51251e7i	1.38945	+	0.884494i
$959$	−886573.			−0.0311292
$960$	−1.03571e6	−	275197.i	−0.0362710	−	0.00963751i
$961$	−4.88839e6			−0.170749
$962$	−1.34076e7	−	8.53504e6i	−0.467105	−	0.297350i
$963$			5.88954e7i			2.04652i
$964$	8.29042e6	+	1.77465e7i	0.287332	+	0.615065i
$965$		−	517932.i		−	0.0179042i
$966$	1.37519e7	−	2.16028e7i	0.474155	−	0.744847i
$967$	−1.73855e7			−0.597891			−0.298945	−	0.954270i	$-0.596635\pi$
$967$	−1.73855e7			−0.597891			−0.298945	+	0.954270i	$0.596635\pi$
$968$	3.38419e6	−	2.59149e7i	0.116083	−	0.888918i
$969$	1.51573e6			0.0518577
$970$	52863.9	−	83043.6i	0.00180397	−	0.00283385i
$971$		−	5.82121e7i		−	1.98137i	−0.136186	−	0.990683i	$-0.543484\pi$
$971$		−	5.82121e7i		−	1.98137i	0.136186	−	0.990683i	$-0.456516\pi$
$972$	−3.69285e7	+	1.72514e7i	−1.25371	+	0.585677i
$973$		−	2.64341e7i		−	0.895121i
$974$	2.36530e7	+	1.50571e7i	0.798895	+	0.508561i
$975$	5.60130e7			1.88702
$976$	3.80947e7	+	3.18748e7i	1.28009	+	1.07108i
$977$	2.03137e7			0.680853			0.340426	−	0.940271i	$-0.389429\pi$
$977$	2.03137e7			0.680853			0.340426	+	0.940271i	$0.389429\pi$
$978$	1.80612e6	+	1.14974e6i	0.0603809	+	0.0384373i
$979$			1.37826e7i			0.459593i
$980$	−362200.	+	169204.i	−0.0120471	+	0.00562789i
$981$		−	1.55162e7i		−	0.514769i
$982$	−1.82813e7	+	2.87180e7i	−0.604962	+	0.950331i
$983$	−5.54003e7			−1.82864			−0.914321	−	0.404991i	$-0.867275\pi$
$983$	−5.54003e7			−1.82864			−0.914321	+	0.404991i	$0.867275\pi$
$984$	4.42336e7	+	5.77640e6i	1.45634	+	0.190182i
$985$	−156319.			−0.00513357
$986$	5.88208e6	−	9.24013e6i	0.192681	−	0.302681i
$987$			2.38954e7i			0.780768i
$988$	−2.04245e6	−	4.37209e6i	−0.0665670	−	0.142494i
$989$			1.17801e7i			0.382965i
$990$	268370.	+	170839.i	0.00870253	+	0.00553986i
$991$	−9.26753e6			−0.299764			−0.149882	−	0.988704i	$-0.547889\pi$
$991$	−9.26753e6			−0.299764			−0.149882	+	0.988704i	$0.547889\pi$
$992$	−2.69031e7	+	8.53410e6i	−0.868007	+	0.275346i
$993$	4.77179e7			1.53571
$994$	−4.56019e7	−	2.90292e7i	−1.46392	−	0.931901i
$995$			364224.i			0.0116630i
$996$	−1.97066e7	−	4.21841e7i	−0.629453	−	1.34741i
$997$			5.53912e7i			1.76483i	0.470471	+	0.882415i	$0.344084\pi$
$997$			5.53912e7i			1.76483i	−0.470471	+	0.882415i	$0.655916\pi$
$998$	2.39325e7	−	3.75955e7i	0.760611	−	1.19484i
$999$	6.23544e6			0.197676

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.6.b.a.5.1	✓	4
3.2	odd	2		72.6.d.b.37.4		4
4.3	odd	2		32.6.b.a.17.4		4
5.2	odd	4		200.6.f.a.149.5		8
5.3	odd	4		200.6.f.a.149.4		8
5.4	even	2		200.6.d.a.101.4		4
8.3	odd	2		32.6.b.a.17.1		4
8.5	even	2	inner	8.6.b.a.5.2	yes	4
12.11	even	2		288.6.d.b.145.2		4
16.3	odd	4		256.6.a.n.1.1		4
16.5	even	4		256.6.a.k.1.1		4
16.11	odd	4		256.6.a.n.1.4		4
16.13	even	4		256.6.a.k.1.4		4
20.3	even	4		800.6.f.a.49.2		8
20.7	even	4		800.6.f.a.49.7		8
20.19	odd	2		800.6.d.a.401.1		4
24.5	odd	2		72.6.d.b.37.3		4
24.11	even	2		288.6.d.b.145.3		4
40.3	even	4		800.6.f.a.49.8		8
40.13	odd	4		200.6.f.a.149.6		8
40.19	odd	2		800.6.d.a.401.4		4
40.27	even	4		800.6.f.a.49.1		8
40.29	even	2		200.6.d.a.101.3		4
40.37	odd	4		200.6.f.a.149.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.6.b.a.5.1	✓	4	1.1	even	1	trivial
8.6.b.a.5.2	yes	4	8.5	even	2	inner
32.6.b.a.17.1		4	8.3	odd	2
32.6.b.a.17.4		4	4.3	odd	2
72.6.d.b.37.3		4	24.5	odd	2
72.6.d.b.37.4		4	3.2	odd	2
200.6.d.a.101.3		4	40.29	even	2
200.6.d.a.101.4		4	5.4	even	2
200.6.f.a.149.3		8	40.37	odd	4
200.6.f.a.149.4		8	5.3	odd	4
200.6.f.a.149.5		8	5.2	odd	4
200.6.f.a.149.6		8	40.13	odd	4
256.6.a.k.1.1		4	16.5	even	4
256.6.a.k.1.4		4	16.13	even	4
256.6.a.n.1.1		4	16.3	odd	4
256.6.a.n.1.4		4	16.11	odd	4
288.6.d.b.145.2		4	12.11	even	2
288.6.d.b.145.3		4	24.11	even	2
800.6.d.a.401.1		4	20.19	odd	2
800.6.d.a.401.4		4	40.19	odd	2
800.6.f.a.49.1		8	40.27	even	4
800.6.f.a.49.2		8	20.3	even	4
800.6.f.a.49.7		8	20.7	even	4
800.6.f.a.49.8		8	40.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.77200 - 3.03776i) q^{2} -23.6095i q^{3} +(13.5440 + 28.9924i) q^{4} +1.38521i q^{5} +(-71.7200 + 112.665i) q^{6} +160.704 q^{7} +(23.4400 - 179.495i) q^{8} -314.408 q^{9} +O(q^{10})\)	\(q+(-4.77200 - 3.03776i) q^{2} -23.6095i q^{3} +(13.5440 + 28.9924i) q^{4} +1.38521i q^{5} +(-71.7200 + 112.665i) q^{6} +160.704 q^{7} +(23.4400 - 179.495i) q^{8} -314.408 q^{9} +(4.20793 - 6.61022i) q^{10} -129.129i q^{11} +(684.496 - 319.767i) q^{12} +759.659i q^{13} +(-766.880 - 488.181i) q^{14} +32.7041 q^{15} +(-657.120 + 785.347i) q^{16} +323.408 q^{17} +(1500.36 + 955.097i) q^{18} +198.511i q^{19} +(-40.1605 + 18.7613i) q^{20} -3794.14i q^{21} +(-392.264 + 616.204i) q^{22} -1193.15 q^{23} +(-4237.79 - 553.407i) q^{24} +3123.08 q^{25} +(2307.66 - 3625.10i) q^{26} +1685.91i q^{27} +(2176.58 + 4659.20i) q^{28} +5987.24i q^{29} +(-156.064 - 99.3472i) q^{30} -4872.45 q^{31} +(5521.47 - 1751.50i) q^{32} -3048.67 q^{33} +(-1543.30 - 982.437i) q^{34} +222.609i q^{35} +(-4258.34 - 9115.45i) q^{36} -3698.56i q^{37} +(603.031 - 947.297i) q^{38} +17935.2 q^{39} +(248.638 + 32.4693i) q^{40} -10437.9 q^{41} +(-11525.7 + 18105.6i) q^{42} -9873.11i q^{43} +(3743.76 - 1748.93i) q^{44} -435.521i q^{45} +(5693.73 + 3624.51i) q^{46} -6297.98 q^{47} +(18541.6 + 15514.3i) q^{48} +9018.79 q^{49} +(-14903.3 - 9487.18i) q^{50} -7635.50i q^{51} +(-22024.4 + 10288.8i) q^{52} +21728.1i q^{53} +(5121.39 - 8045.16i) q^{54} +178.871 q^{55} +(3766.91 - 28845.6i) q^{56} +4686.75 q^{57} +(18187.8 - 28571.1i) q^{58} +33513.4i q^{59} +(442.944 + 948.170i) q^{60} -48506.8i q^{61} +(23251.3 + 14801.3i) q^{62} -50526.7 q^{63} +(-31669.1 - 8414.75i) q^{64} -1052.29 q^{65} +(14548.3 + 9261.14i) q^{66} +33182.4i q^{67} +(4380.24 + 9376.38i) q^{68} +28169.7i q^{69} +(676.232 - 1062.29i) q^{70} +59464.1 q^{71} +(-7369.74 + 56434.8i) q^{72} +51278.6 q^{73} +(-11235.4 + 17649.5i) q^{74} -73734.4i q^{75} +(-5755.33 + 2688.64i) q^{76} -20751.6i q^{77} +(-85586.7 - 54482.8i) q^{78} -73724.5 q^{79} +(-1087.87 - 910.248i) q^{80} -36597.7 q^{81} +(49809.6 + 31707.8i) q^{82} -61628.0i q^{83} +(110001. - 51387.9i) q^{84} +447.988i q^{85} +(-29992.1 + 47114.5i) q^{86} +141356. q^{87} +(-23178.1 - 3026.79i) q^{88} -106735. q^{89} +(-1323.01 + 2078.31i) q^{90} +122080. i q^{91} +(-16160.1 - 34592.4i) q^{92} +115036. i q^{93} +(30054.0 + 19131.8i) q^{94} -274.980 q^{95} +(-41352.1 - 130359. i) q^{96} +12562.9 q^{97} +(-43037.7 - 27397.0i) q^{98} +40599.2i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 20 q^{4} - 116 q^{6} + 96 q^{7} - 248 q^{8} - 164 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 20 * q^4 - 116 * q^6 + 96 * q^7 - 248 * q^8 - 164 * q^9	\( 4 q - 2 q^{2} + 20 q^{4} - 116 q^{6} + 96 q^{7} - 248 q^{8} - 164 q^{9} + 632 q^{10} + 1576 q^{12} - 2384 q^{14} - 416 q^{15} - 3312 q^{16} + 200 q^{17} + 4754 q^{18} + 4624 q^{20} - 5636 q^{22} + 2336 q^{23} - 7792 q^{24} + 1556 q^{25} + 5608 q^{26} + 5152 q^{28} - 2128 q^{30} - 12928 q^{31} + 5408 q^{32} - 2352 q^{33} - 4772 q^{34} - 10164 q^{36} + 15980 q^{38} + 35104 q^{39} + 16032 q^{40} - 4568 q^{41} - 26144 q^{42} - 29112 q^{44} + 29200 q^{46} - 54720 q^{47} + 35616 q^{48} + 9828 q^{49} - 47498 q^{50} - 36560 q^{52} + 23288 q^{54} + 85472 q^{55} + 40768 q^{56} - 2032 q^{57} + 3784 q^{58} + 2592 q^{60} + 34496 q^{62} - 153440 q^{63} - 41920 q^{64} - 19520 q^{65} + 43224 q^{66} + 10344 q^{68} - 68928 q^{70} + 206688 q^{71} - 83272 q^{72} + 39976 q^{73} + 17464 q^{74} + 99944 q^{76} - 174064 q^{78} - 247872 q^{79} - 35520 q^{80} + 29684 q^{81} + 161132 q^{82} + 196672 q^{84} - 18500 q^{86} + 307872 q^{87} - 167216 q^{88} - 84632 q^{89} + 142280 q^{90} - 49056 q^{92} - 98784 q^{94} - 259744 q^{95} - 115648 q^{96} - 99576 q^{97} - 117042 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 20 * q^4 - 116 * q^6 + 96 * q^7 - 248 * q^8 - 164 * q^9 + 632 * q^10 + 1576 * q^12 - 2384 * q^14 - 416 * q^15 - 3312 * q^16 + 200 * q^17 + 4754 * q^18 + 4624 * q^20 - 5636 * q^22 + 2336 * q^23 - 7792 * q^24 + 1556 * q^25 + 5608 * q^26 + 5152 * q^28 - 2128 * q^30 - 12928 * q^31 + 5408 * q^32 - 2352 * q^33 - 4772 * q^34 - 10164 * q^36 + 15980 * q^38 + 35104 * q^39 + 16032 * q^40 - 4568 * q^41 - 26144 * q^42 - 29112 * q^44 + 29200 * q^46 - 54720 * q^47 + 35616 * q^48 + 9828 * q^49 - 47498 * q^50 - 36560 * q^52 + 23288 * q^54 + 85472 * q^55 + 40768 * q^56 - 2032 * q^57 + 3784 * q^58 + 2592 * q^60 + 34496 * q^62 - 153440 * q^63 - 41920 * q^64 - 19520 * q^65 + 43224 * q^66 + 10344 * q^68 - 68928 * q^70 + 206688 * q^71 - 83272 * q^72 + 39976 * q^73 + 17464 * q^74 + 99944 * q^76 - 174064 * q^78 - 247872 * q^79 - 35520 * q^80 + 29684 * q^81 + 161132 * q^82 + 196672 * q^84 - 18500 * q^86 + 307872 * q^87 - 167216 * q^88 - 84632 * q^89 + 142280 * q^90 - 49056 * q^92 - 98784 * q^94 - 259744 * q^95 - 115648 * q^96 - 99576 * q^97 - 117042 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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