LMFDB - Embedded newform 51.6.e.a.4.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [51,6,Mod(4,51)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(51, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("51.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	51.e (of order $4$, degree $2$, 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:	$8.17957481046$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			4.4
Character	$\chi$	$=$	51.4
Dual form			51.6.e.a.13.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.59084i q^{2} +(-6.36396 + 6.36396i) q^{3} -11.4392 q^{4} +(50.2012 - 50.2012i) q^{5} +(41.9439 + 41.9439i) q^{6} +(116.537 + 116.537i) q^{7} -135.513i q^{8} -81.0000i q^{9} +O(q^{10})$	\(q-6.59084i q^{2} +(-6.36396 + 6.36396i) q^{3} -11.4392 q^{4} +(50.2012 - 50.2012i) q^{5} +(41.9439 + 41.9439i) q^{6} +(116.537 + 116.537i) q^{7} -135.513i q^{8} -81.0000i q^{9} +(-330.868 - 330.868i) q^{10} +(-467.651 - 467.651i) q^{11} +(72.7986 - 72.7986i) q^{12} +691.750 q^{13} +(768.077 - 768.077i) q^{14} +638.958i q^{15} -1259.20 q^{16} +(-1105.89 - 443.705i) q^{17} -533.858 q^{18} -1483.03i q^{19} +(-574.262 + 574.262i) q^{20} -1483.27 q^{21} +(-3082.21 + 3082.21i) q^{22} +(2075.45 + 2075.45i) q^{23} +(862.399 + 862.399i) q^{24} -1915.33i q^{25} -4559.21i q^{26} +(515.481 + 515.481i) q^{27} +(-1333.09 - 1333.09i) q^{28} +(5350.53 - 5350.53i) q^{29} +4211.27 q^{30} +(-2868.49 + 2868.49i) q^{31} +3962.77i q^{32} +5952.22 q^{33} +(-2924.39 + 7288.72i) q^{34} +11700.6 q^{35} +926.575i q^{36} +(5423.85 - 5423.85i) q^{37} -9774.42 q^{38} +(-4402.27 + 4402.27i) q^{39} +(-6802.92 - 6802.92i) q^{40} +(10271.5 + 10271.5i) q^{41} +9776.03i q^{42} +12906.7i q^{43} +(5349.55 + 5349.55i) q^{44} +(-4066.30 - 4066.30i) q^{45} +(13679.0 - 13679.0i) q^{46} -20819.5 q^{47} +(8013.49 - 8013.49i) q^{48} +10354.8i q^{49} -12623.6 q^{50} +(9861.54 - 4214.09i) q^{51} -7913.06 q^{52} +19900.0i q^{53} +(3397.45 - 3397.45i) q^{54} -46953.3 q^{55} +(15792.3 - 15792.3i) q^{56} +(9437.95 + 9437.95i) q^{57} +(-35264.5 - 35264.5i) q^{58} +33149.6i q^{59} -7309.16i q^{60} +(-6244.99 - 6244.99i) q^{61} +(18905.8 + 18905.8i) q^{62} +(9439.50 - 9439.50i) q^{63} -14176.4 q^{64} +(34726.7 - 34726.7i) q^{65} -39230.2i q^{66} +57875.2 q^{67} +(12650.4 + 5075.63i) q^{68} -26416.2 q^{69} -77116.9i q^{70} +(-27004.2 + 27004.2i) q^{71} -10976.6 q^{72} +(-644.023 + 644.023i) q^{73} +(-35747.7 - 35747.7i) q^{74} +(12189.1 + 12189.1i) q^{75} +16964.7i q^{76} -108997. i q^{77} +(29014.7 + 29014.7i) q^{78} +(20307.8 + 20307.8i) q^{79} +(-63213.4 + 63213.4i) q^{80} -6561.00 q^{81} +(67697.8 - 67697.8i) q^{82} +35358.1i q^{83} +16967.5 q^{84} +(-77791.4 + 33242.3i) q^{85} +85066.2 q^{86} +68101.2i q^{87} +(-63372.8 + 63372.8i) q^{88} -20097.8 q^{89} +(-26800.3 + 26800.3i) q^{90} +(80614.5 + 80614.5i) q^{91} +(-23741.5 - 23741.5i) q^{92} -36510.0i q^{93} +137218. i q^{94} +(-74450.0 - 74450.0i) q^{95} +(-25218.9 - 25218.9i) q^{96} +(-27423.3 + 27423.3i) q^{97} +68246.6 q^{98} +(-37879.7 + 37879.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 576 q^{4} + 76 q^{5} - 180 q^{6} + 236 q^{7}+O(q^{10}) $ 32 * q - 576 * q^4 + 76 * q^5 - 180 * q^6 + 236 * q^7	\( 32 q - 576 q^{4} + 76 q^{5} - 180 q^{6} + 236 q^{7} + 724 q^{10} - 672 q^{11} - 2684 q^{13} + 2832 q^{14} + 8824 q^{16} - 4868 q^{17} + 1296 q^{18} + 4464 q^{20} - 3528 q^{21} - 1628 q^{22} + 5584 q^{23} + 10872 q^{24} - 36792 q^{28} + 4820 q^{29} - 1728 q^{30} + 13880 q^{31} + 7236 q^{33} + 5068 q^{34} - 12152 q^{35} - 33328 q^{37} - 29256 q^{38} - 11160 q^{39} - 43288 q^{40} - 50932 q^{41} + 116000 q^{44} - 6156 q^{45} + 47596 q^{46} - 16552 q^{47} + 27360 q^{48} + 139080 q^{50} + 12924 q^{51} + 186888 q^{52} - 14580 q^{54} - 129428 q^{55} - 117024 q^{56} + 19440 q^{57} - 212912 q^{58} + 118952 q^{61} - 219736 q^{62} + 19116 q^{63} - 143848 q^{64} + 220976 q^{65} + 98632 q^{67} + 367680 q^{68} + 156060 q^{69} - 205512 q^{71} - 62208 q^{72} - 40924 q^{73} - 178760 q^{74} - 58896 q^{75} + 87012 q^{78} - 309916 q^{79} - 664992 q^{80} - 209952 q^{81} + 350116 q^{82} + 6264 q^{84} + 335336 q^{85} + 1139576 q^{86} - 307696 q^{88} - 62680 q^{89} + 58644 q^{90} + 174460 q^{91} - 94256 q^{92} + 367240 q^{95} - 508824 q^{96} - 299020 q^{97} - 1191536 q^{98} - 54432 q^{99}+O(q^{100}) \) 32 * q - 576 * q^4 + 76 * q^5 - 180 * q^6 + 236 * q^7 + 724 * q^10 - 672 * q^11 - 2684 * q^13 + 2832 * q^14 + 8824 * q^16 - 4868 * q^17 + 1296 * q^18 + 4464 * q^20 - 3528 * q^21 - 1628 * q^22 + 5584 * q^23 + 10872 * q^24 - 36792 * q^28 + 4820 * q^29 - 1728 * q^30 + 13880 * q^31 + 7236 * q^33 + 5068 * q^34 - 12152 * q^35 - 33328 * q^37 - 29256 * q^38 - 11160 * q^39 - 43288 * q^40 - 50932 * q^41 + 116000 * q^44 - 6156 * q^45 + 47596 * q^46 - 16552 * q^47 + 27360 * q^48 + 139080 * q^50 + 12924 * q^51 + 186888 * q^52 - 14580 * q^54 - 129428 * q^55 - 117024 * q^56 + 19440 * q^57 - 212912 * q^58 + 118952 * q^61 - 219736 * q^62 + 19116 * q^63 - 143848 * q^64 + 220976 * q^65 + 98632 * q^67 + 367680 * q^68 + 156060 * q^69 - 205512 * q^71 - 62208 * q^72 - 40924 * q^73 - 178760 * q^74 - 58896 * q^75 + 87012 * q^78 - 309916 * q^79 - 664992 * q^80 - 209952 * q^81 + 350116 * q^82 + 6264 * q^84 + 335336 * q^85 + 1139576 * q^86 - 307696 * q^88 - 62680 * q^89 + 58644 * q^90 + 174460 * q^91 - 94256 * q^92 + 367240 * q^95 - 508824 * q^96 - 299020 * q^97 - 1191536 * q^98 - 54432 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	6.59084i		−	1.16511i	−0.812792	−	0.582554i	$-0.802054\pi$
$2$		−	6.59084i		−	1.16511i	0.812792	−	0.582554i	$-0.197946\pi$
$3$	−6.36396	+	6.36396i	−0.408248	+	0.408248i
$3$	−6.36396	+	6.36396i	−0.408248	+	0.408248i
$4$	−11.4392			−0.357475
$5$	50.2012	−	50.2012i	0.898027	−	0.898027i	−0.0972344	−	0.995262i	$-0.531000\pi$
$5$	50.2012	−	50.2012i	0.898027	−	0.898027i	0.995262	+	0.0972344i	$0.0309996\pi$
$6$	41.9439	+	41.9439i	0.475653	+	0.475653i
$7$	116.537	+	116.537i	0.898916	+	0.898916i	0.995340	−	0.0964247i	$-0.0307407\pi$
$7$	116.537	+	116.537i	0.898916	+	0.898916i	−0.0964247	+	0.995340i	$0.530741\pi$
$8$		−	135.513i		−	0.748611i
$9$		−	81.0000i		−	0.333333i
$10$	−330.868	−	330.868i	−1.04630	−	1.04630i
$11$	−467.651	−	467.651i	−1.16531	−	1.16531i	−0.983297	−	0.182009i	$-0.941740\pi$
$11$	−467.651	−	467.651i	−1.16531	−	1.16531i	−0.182009	−	0.983297i	$-0.558260\pi$
$12$	72.7986	−	72.7986i	0.145939	−	0.145939i
$13$	691.750			1.13525			0.567624	−	0.823288i	$-0.307863\pi$
$13$	691.750			1.13525			0.567624	+	0.823288i	$0.307863\pi$
$14$	768.077	−	768.077i	1.04733	−	1.04733i
$15$			638.958i			0.733236i
$16$	−1259.20			−1.22969
$17$	−1105.89	−	443.705i	−0.928085	−	0.372368i
$17$	−1105.89	−	443.705i	−0.928085	−	0.372368i
$18$	−533.858			−0.388369
$19$		−	1483.03i		−	0.942467i	−0.882008	−	0.471234i	$-0.843809\pi$
$19$		−	1483.03i		−	0.942467i	0.882008	−	0.471234i	$-0.156191\pi$
$20$	−574.262	+	574.262i	−0.321022	+	0.321022i
$21$	−1483.27			−0.733961
$22$	−3082.21	+	3082.21i	−1.35771	+	1.35771i
$23$	2075.45	+	2075.45i	0.818076	+	0.818076i	0.985829	−	0.167753i	$-0.0536511\pi$
$23$	2075.45	+	2075.45i	0.818076	+	0.818076i	−0.167753	+	0.985829i	$0.553651\pi$
$24$	862.399	+	862.399i	0.305619	+	0.305619i
$25$		−	1915.33i		−	0.612905i
$26$		−	4559.21i		−	1.32269i
$27$	515.481	+	515.481i	0.136083	+	0.136083i
$28$	−1333.09	−	1333.09i	−0.321340	−	0.321340i
$29$	5350.53	−	5350.53i	1.18141	−	1.18141i	0.202036	−	0.979378i	$-0.435244\pi$
$29$	5350.53	−	5350.53i	1.18141	−	1.18141i	0.979378	−	0.202036i	$-0.0647557\pi$
$30$	4211.27			0.854299
$31$	−2868.49	+	2868.49i	−0.536105	+	0.536105i	−0.922383	−	0.386278i	$-0.873761\pi$
$31$	−2868.49	+	2868.49i	−0.536105	+	0.536105i	0.386278	+	0.922383i	$0.373761\pi$
$32$			3962.77i			0.684106i
$33$	5952.22			0.951469
$34$	−2924.39	+	7288.72i	−0.433849	+	1.08132i
$35$	11700.6			1.61450
$36$			926.575i			0.119158i
$37$	5423.85	−	5423.85i	0.651333	−	0.651333i	−0.301981	−	0.953314i	$-0.597648\pi$
$37$	5423.85	−	5423.85i	0.651333	−	0.651333i	0.953314	+	0.301981i	$0.0976479\pi$
$38$	−9774.42			−1.09808
$39$	−4402.27	+	4402.27i	−0.463463	+	0.463463i
$40$	−6802.92	−	6802.92i	−0.672273	−	0.672273i
$41$	10271.5	+	10271.5i	0.954276	+	0.954276i	0.998999	−	0.0447235i	$-0.0142407\pi$
$41$	10271.5	+	10271.5i	0.954276	+	0.954276i	−0.0447235	+	0.998999i	$0.514241\pi$
$42$			9776.03i			0.855144i
$43$			12906.7i			1.06450i	0.846588	+	0.532249i	$0.178653\pi$
$43$			12906.7i			1.06450i	−0.846588	+	0.532249i	$0.821347\pi$
$44$	5349.55	+	5349.55i	0.416568	+	0.416568i
$45$	−4066.30	−	4066.30i	−0.299342	−	0.299342i
$46$	13679.0	−	13679.0i	0.953146	−	0.953146i
$47$	−20819.5			−1.37476			−0.687378	−	0.726300i	$-0.741238\pi$
$47$	−20819.5			−1.37476			−0.687378	+	0.726300i	$0.741238\pi$
$48$	8013.49	−	8013.49i	0.502017	−	0.502017i
$49$			10354.8i			0.616098i
$50$	−12623.6			−0.714101
$51$	9861.54	−	4214.09i	0.530908	−	0.226871i
$52$	−7913.06			−0.405823
$53$			19900.0i			0.973112i	0.873649	+	0.486556i	$0.161747\pi$
$53$			19900.0i			0.973112i	−0.873649	+	0.486556i	$0.838253\pi$
$54$	3397.45	−	3397.45i	0.158551	−	0.158551i
$55$	−46953.3			−2.09295
$56$	15792.3	−	15792.3i	0.672938	−	0.672938i
$57$	9437.95	+	9437.95i	0.384761	+	0.384761i
$58$	−35264.5	−	35264.5i	−1.37647	−	1.37647i
$59$			33149.6i			1.23979i	0.784685	+	0.619895i	$0.212825\pi$
$59$			33149.6i			1.23979i	−0.784685	+	0.619895i	$0.787175\pi$
$60$		−	7309.16i		−	0.262114i
$61$	−6244.99	−	6244.99i	−0.214886	−	0.214886i	0.591454	−	0.806339i	$-0.298554\pi$
$61$	−6244.99	−	6244.99i	−0.214886	−	0.214886i	−0.806339	+	0.591454i	$0.798554\pi$
$62$	18905.8	+	18905.8i	0.624620	+	0.624620i
$63$	9439.50	−	9439.50i	0.299639	−	0.299639i
$64$	−14176.4			−0.432630
$65$	34726.7	−	34726.7i	1.01948	−	1.01948i
$66$		−	39230.2i		−	1.10856i
$67$	57875.2			1.57509			0.787546	−	0.616256i	$-0.211352\pi$
$67$	57875.2			1.57509			0.787546	+	0.616256i	$0.211352\pi$
$68$	12650.4	+	5075.63i	0.331767	+	0.133112i
$69$	−26416.2			−0.667956
$70$		−	77116.9i		−	1.88107i
$71$	−27004.2	+	27004.2i	−0.635749	+	0.635749i	−0.949504	−	0.313755i	$-0.898413\pi$
$71$	−27004.2	+	27004.2i	−0.635749	+	0.635749i	0.313755	+	0.949504i	$0.398413\pi$
$72$	−10976.6			−0.249537
$73$	−644.023	+	644.023i	−0.0141447	+	0.0141447i	−0.714144	−	0.699999i	$-0.753184\pi$
$73$	−644.023	+	644.023i	−0.0141447	+	0.0141447i	0.699999	+	0.714144i	$0.253184\pi$
$74$	−35747.7	−	35747.7i	−0.758873	−	0.758873i
$75$	12189.1	+	12189.1i	0.250218	+	0.250218i
$76$			16964.7i			0.336908i
$77$		−	108997.i		−	2.09502i
$78$	29014.7	+	29014.7i	0.539984	+	0.539984i
$79$	20307.8	+	20307.8i	0.366096	+	0.366096i	0.866051	−	0.499956i	$-0.166650\pi$
$79$	20307.8	+	20307.8i	0.366096	+	0.366096i	−0.499956	+	0.866051i	$0.666650\pi$
$80$	−63213.4	+	63213.4i	−1.10429	+	1.10429i
$81$	−6561.00			−0.111111
$82$	67697.8	−	67697.8i	1.11183	−	1.11183i
$83$			35358.1i			0.563370i	0.959507	+	0.281685i	$0.0908933\pi$
$83$			35358.1i			0.563370i	−0.959507	+	0.281685i	$0.909107\pi$
$84$	16967.5			0.262373
$85$	−77791.4	+	33242.3i	−1.16784	+	0.499049i
$86$	85066.2			1.24025
$87$			68101.2i			0.964620i
$88$	−63372.8	+	63372.8i	−0.872361	+	0.872361i
$89$	−20097.8			−0.268951			−0.134476	−	0.990917i	$-0.542935\pi$
$89$	−20097.8			−0.268951			−0.134476	+	0.990917i	$0.542935\pi$
$90$	−26800.3	+	26800.3i	−0.348766	+	0.348766i
$91$	80614.5	+	80614.5i	1.02049	+	1.02049i
$92$	−23741.5	−	23741.5i	−0.292442	−	0.292442i
$93$		−	36510.0i		−	0.437728i
$94$			137218.i			1.60174i
$95$	−74450.0	−	74450.0i	−0.846361	−	0.846361i
$96$	−25218.9	−	25218.9i	−0.279285	−	0.279285i
$97$	−27423.3	+	27423.3i	−0.295931	+	0.295931i	−0.839418	−	0.543487i	$-0.817104\pi$
$97$	−27423.3	+	27423.3i	−0.295931	+	0.295931i	0.543487	+	0.839418i	$0.317104\pi$
$98$	68246.6			0.717821
$99$	−37879.7	+	37879.7i	−0.388435	+	0.388435i
$100$			21909.8i			0.219098i
$101$	20763.8			0.202537			0.101268	−	0.994859i	$-0.467710\pi$
$101$	20763.8			0.202537			0.101268	+	0.994859i	$0.467710\pi$
$102$	−27774.4	−	64995.8i	−0.264329	−	0.618565i
$103$	87970.7			0.817043			0.408521	−	0.912749i	$-0.366045\pi$
$103$	87970.7			0.817043			0.408521	+	0.912749i	$0.366045\pi$
$104$		−	93741.1i		−	0.849859i
$105$	−74462.2	+	74462.2i	−0.659117	+	0.659117i
$106$	131158.			1.13378
$107$	100649.	−	100649.i	0.849862	−	0.849862i	−0.140254	−	0.990116i	$-0.544792\pi$
$107$	100649.	−	100649.i	0.849862	−	0.849862i	0.990116	+	0.140254i	$0.0447918\pi$
$108$	−5896.69	−	5896.69i	−0.0486462	−	0.0486462i
$109$	−8311.99	−	8311.99i	−0.0670098	−	0.0670098i	0.672808	−	0.739817i	$-0.265088\pi$
$109$	−8311.99	−	8311.99i	−0.0670098	−	0.0670098i	−0.739817	+	0.672808i	$0.765088\pi$
$110$			309462.i			2.43851i
$111$			69034.3i			0.531811i
$112$	−146743.	−	146743.i	−1.10538	−	1.10538i
$113$	−37857.4	−	37857.4i	−0.278904	−	0.278904i	0.553768	−	0.832671i	$-0.313190\pi$
$113$	−37857.4	−	37857.4i	−0.278904	−	0.278904i	−0.832671	+	0.553768i	$0.813190\pi$
$114$	62204.0	−	62204.0i	0.448287	−	0.448287i
$115$	208381.			1.46931
$116$	−61205.8	+	61205.8i	−0.422326	+	0.422326i
$117$		−	56031.7i		−	0.378416i
$118$	218484.			1.44449
$119$	−77168.5	−	180585.i	−0.499543	−	1.16900i
$120$	86587.1			0.548908
$121$			276344.i			1.71588i
$122$	−41159.7	+	41159.7i	−0.250365	+	0.250365i
$123$	−130735.			−0.779163
$124$	32813.3	−	32813.3i	0.191644	−	0.191644i
$125$	60727.0	+	60727.0i	0.347621	+	0.347621i
$126$	−62214.3	−	62214.3i	−0.349111	−	0.349111i
$127$			6416.02i			0.0352985i	0.999844	+	0.0176493i	$0.00561822\pi$
$127$			6416.02i			0.0352985i	−0.999844	+	0.0176493i	$0.994382\pi$
$128$			220243.i			1.18817i
$129$	−82137.9	−	82137.9i	−0.434579	−	0.434579i
$130$	−228878.	−	228878.i	−1.18781	−	1.18781i
$131$	−32059.7	+	32059.7i	−0.163223	+	0.163223i	−0.783993	−	0.620770i	$-0.786820\pi$
$131$	−32059.7	+	32059.7i	−0.163223	+	0.163223i	0.620770	+	0.783993i	$0.286820\pi$
$132$	−68088.7			−0.340126
$133$	172828.	−	172828.i	0.847198	−	0.847198i
$134$		−	381446.i		−	1.83515i
$135$	51755.6			0.244412
$136$	−60127.9	+	149862.i	−0.278759	+	0.694774i
$137$	199509.			0.908158			0.454079	−	0.890962i	$-0.349968\pi$
$137$	199509.			0.908158			0.454079	+	0.890962i	$0.349968\pi$
$138$			174105.i			0.778241i
$139$	79694.6	−	79694.6i	0.349858	−	0.349858i	−0.510198	−	0.860057i	$-0.670428\pi$
$139$	79694.6	−	79694.6i	0.349858	−	0.349858i	0.860057	+	0.510198i	$0.170428\pi$
$140$	−133846.			−0.577144
$141$	132494.	−	132494.i	0.561242	−	0.561242i
$142$	177980.	+	177980.i	0.740716	+	0.740716i
$143$	−323497.	−	323497.i	−1.32291	−	1.32291i
$144$			101995.i			0.409896i
$145$		−	537207.i		−	2.12188i
$146$	4244.66	+	4244.66i	0.0164801	+	0.0164801i
$147$	−65897.3	−	65897.3i	−0.251521	−	0.251521i
$148$	−62044.4	+	62044.4i	−0.232835	+	0.232835i
$149$	−176656.			−0.651873			−0.325937	−	0.945392i	$-0.605680\pi$
$149$	−176656.			−0.651873			−0.325937	+	0.945392i	$0.605680\pi$
$150$	80336.3	−	80336.3i	0.291530	−	0.291530i
$151$			205320.i			0.732804i	0.930457	+	0.366402i	$0.119411\pi$
$151$			205320.i			0.732804i	−0.930457	+	0.366402i	$0.880589\pi$
$152$	−200970.			−0.705541
$153$	−35940.1	+	89576.7i	−0.124123	+	0.309362i
$154$	−718384.			−2.44093
$155$			288004.i			0.962874i
$156$	50358.4	−	50358.4i	0.165676	−	0.165676i
$157$	−131550.			−0.425934			−0.212967	−	0.977059i	$-0.568313\pi$
$157$	−131550.			−0.425934			−0.212967	+	0.977059i	$0.568313\pi$
$158$	133845.	−	133845.i	0.426541	−	0.426541i
$159$	−126643.	−	126643.i	−0.397271	−	0.397271i
$160$	198936.	+	198936.i	0.614346	+	0.614346i
$161$			483735.i			1.47076i
$162$			43242.5i			0.129456i
$163$	−230501.	−	230501.i	−0.679521	−	0.679521i	0.280371	−	0.959892i	$-0.409543\pi$
$163$	−230501.	−	230501.i	−0.679521	−	0.679521i	−0.959892	+	0.280371i	$0.909543\pi$
$164$	−117498.	−	117498.i	−0.341130	−	0.341130i
$165$	298809.	−	298809.i	0.854445	−	0.854445i
$166$	233040.			0.656386
$167$	−4537.81	+	4537.81i	−0.0125909	+	0.0125909i	−0.713374	−	0.700783i	$-0.752834\pi$
$167$	−4537.81	+	4537.81i	−0.0125909	+	0.0125909i	0.700783	+	0.713374i	$0.252834\pi$
$168$			201003.i			0.549451i
$169$	107225.			0.288788
$170$	219094.	+	512711.i	0.581446	+	1.36066i
$171$	−120125.			−0.314156
$172$		−	147643.i		−	0.380531i
$173$	−232221.	+	232221.i	−0.589910	+	0.589910i	−0.937607	−	0.347697i	$-0.886964\pi$
$173$	−232221.	+	232221.i	−0.589910	+	0.589910i	0.347697	+	0.937607i	$0.386964\pi$
$174$	448844.			1.12389
$175$	223207.	−	223207.i	0.550950	−	0.550950i
$176$	588866.	+	588866.i	1.43296	+	1.43296i
$177$	−210963.	−	210963.i	−0.506142	−	0.506142i
$178$			132462.i			0.313357i
$179$			147798.i			0.344776i	0.985029	+	0.172388i	$0.0551482\pi$
$179$			147798.i			0.344776i	−0.985029	+	0.172388i	$0.944852\pi$
$180$	46515.2	+	46515.2i	0.107007	+	0.107007i
$181$	−148119.	−	148119.i	−0.336058	−	0.336058i	0.518823	−	0.854882i	$-0.326370\pi$
$181$	−148119.	−	148119.i	−0.336058	−	0.336058i	−0.854882	+	0.518823i	$0.826370\pi$
$182$	531317.	−	531317.i	1.18898	−	1.18898i
$183$	79485.7			0.175453
$184$	281251.	−	281251.i	0.612420	−	0.612420i
$185$		−	544568.i		−	1.16983i
$186$	−240631.			−0.510000
$187$	309669.	+	724668.i	0.647581	+	1.51543i
$188$	238158.			0.491441
$189$			120145.i			0.244654i
$190$	−490688.	+	490688.i	−0.986101	+	0.986101i
$191$	372000.			0.737835			0.368918	−	0.929462i	$-0.379728\pi$
$191$	372000.			0.737835			0.368918	+	0.929462i	$0.379728\pi$
$192$	90218.1	−	90218.1i	0.176620	−	0.176620i
$193$	−434425.	−	434425.i	−0.839501	−	0.839501i	0.149292	−	0.988793i	$-0.452300\pi$
$193$	−434425.	−	434425.i	−0.839501	−	0.839501i	−0.988793	+	0.149292i	$0.952300\pi$
$194$	180743.	+	180743.i	0.344792	+	0.344792i
$195$			441999.i			0.832405i
$196$		−	118450.i		−	0.220240i
$197$	−570131.	−	570131.i	−1.04667	−	1.04667i	−0.998856	−	0.0478115i	$-0.984775\pi$
$197$	−570131.	−	570131.i	−1.04667	−	1.04667i	−0.0478115	−	0.998856i	$-0.515225\pi$
$198$	249659.	+	249659.i	0.452569	+	0.452569i
$199$	−524488.	+	524488.i	−0.938865	+	0.938865i	−0.998236	−	0.0593713i	$-0.981090\pi$
$199$	−524488.	+	524488.i	−0.938865	+	0.938865i	0.0593713	+	0.998236i	$0.481090\pi$
$200$	−259552.			−0.458828
$201$	−368316.	+	368316.i	−0.643028	+	0.643028i
$202$		−	136851.i		−	0.235977i
$203$	1.24707e6			2.12398
$204$	−112808.	+	48205.8i	−0.189786	+	0.0811005i
$205$	1.03128e6			1.71393
$206$		−	579801.i		−	0.951943i
$207$	168112.	−	168112.i	0.272692	−	0.272692i
$208$	−871051.			−1.39600
$209$	−693541.	+	693541.i	−1.09826	+	1.09826i
$210$	490769.	+	490769.i	0.767942	+	0.767942i
$211$	314376.	+	314376.i	0.486120	+	0.486120i	0.907079	−	0.420959i	$-0.138307\pi$
$211$	314376.	+	314376.i	0.486120	+	0.486120i	−0.420959	+	0.907079i	$0.638307\pi$
$212$		−	227640.i		−	0.347863i
$213$		−	343707.i		−	0.519087i
$214$	−663359.	−	663359.i	−0.990180	−	0.990180i
$215$	647933.	+	647933.i	0.955948	+	0.955948i
$216$	69854.4	−	69854.4i	0.101873	−	0.101873i
$217$	−668572.			−0.963826
$218$	−54783.0	+	54783.0i	−0.0780737	+	0.0780737i
$219$		−	8197.08i		−	0.0115491i
$220$	537108.			0.748178
$221$	−764996.	−	306933.i	−1.05361	−	0.422730i
$222$	454994.			0.619617
$223$		−	55842.5i		−	0.0751974i	−0.999293	−	0.0375987i	$-0.988029\pi$
$223$		−	55842.5i		−	0.0751974i	0.999293	−	0.0375987i	$-0.0119709\pi$
$224$	−461809.	+	461809.i	−0.614954	+	0.614954i
$225$	−155142.			−0.204302
$226$	−249512.	+	249512.i	−0.324953	+	0.324953i
$227$	−776577.	−	776577.i	−1.00028	−	1.00028i	−1.00000		0.000276220i	$-0.999912\pi$
$227$	−776577.	−	776577.i	−1.00028	−	1.00028i	−0.000276220	−	1.00000i	$-0.500088\pi$
$228$	−107963.	−	107963.i	−0.137542	−	0.137542i
$229$			808069.i			1.01826i	0.860689	+	0.509131i	$0.170033\pi$
$229$			808069.i			1.01826i	−0.860689	+	0.509131i	$0.829967\pi$
$230$		−	1.37340e6i		−	1.71190i
$231$	693655.	+	693655.i	0.855290	+	0.855290i
$232$	−725067.	−	725067.i	−0.884419	−	0.884419i
$233$	592086.	−	592086.i	0.714488	−	0.714488i	−0.252983	−	0.967471i	$-0.581412\pi$
$233$	592086.	−	592086.i	0.714488	−	0.714488i	0.967471	+	0.252983i	$0.0814117\pi$
$234$	−369296.			−0.440895
$235$	−1.04516e6	+	1.04516e6i	−1.23457	+	1.23457i
$236$		−	379205.i		−	0.443194i
$237$	−258476.			−0.298916
$238$	−1.19021e6	+	508605.i	−1.36201	+	0.582021i
$239$	−799962.			−0.905889			−0.452944	−	0.891539i	$-0.649626\pi$
$239$	−799962.			−0.905889			−0.452944	+	0.891539i	$0.649626\pi$
$240$		−	804575.i		−	0.901651i
$241$	468322.	−	468322.i	0.519400	−	0.519400i	−0.397989	−	0.917390i	$-0.630292\pi$
$241$	468322.	−	468322.i	0.519400	−	0.519400i	0.917390	+	0.397989i	$0.130292\pi$
$242$	1.82134e6			1.99918
$243$	41753.9	−	41753.9i	0.0453609	−	0.0453609i
$244$	71437.7	+	71437.7i	0.0768162	+	0.0768162i
$245$	519822.	+	519822.i	0.553273	+	0.553273i
$246$			861652.i			0.907808i
$247$		−	1.02589e6i		−	1.06993i
$248$	388718.	+	388718.i	0.401334	+	0.401334i
$249$	−225018.	−	225018.i	−0.229995	−	0.229995i
$250$	400242.	−	400242.i	0.405016	−	0.405016i
$251$	−846085.			−0.847676			−0.423838	−	0.905738i	$-0.639317\pi$
$251$	−846085.			−0.847676			−0.423838	+	0.905738i	$0.639317\pi$
$252$	−107980.	+	107980.i	−0.107113	+	0.107113i
$253$		−	1.94118e6i		−	1.90662i
$254$	42287.0			0.0411266
$255$	283509.	−	706614.i	0.273034	−	0.680506i
$256$	997942.			0.951711
$257$		−	486286.i		−	0.459261i	−0.973278	−	0.229630i	$-0.926248\pi$
$257$		−	486286.i		−	0.459261i	0.973278	−	0.229630i	$-0.0737517\pi$
$258$	−541358.	+	541358.i	−0.506332	+	0.506332i
$259$	1.26416e6			1.17099
$260$	−397246.	+	397246.i	−0.364440	+	0.364440i
$261$	−433393.	−	433393.i	−0.393805	−	0.393805i
$262$	211301.	+	211301.i	0.190172	+	0.190172i
$263$			1.49143e6i			1.32957i	0.747033	+	0.664787i	$0.231478\pi$
$263$			1.49143e6i			1.32957i	−0.747033	+	0.664787i	$0.768522\pi$
$264$		−	806604.i		−	0.712279i
$265$	999003.	+	999003.i	0.873881	+	0.873881i
$266$	−1.13908e6	−	1.13908e6i	−0.987077	−	0.987077i
$267$	127902.	−	127902.i	0.109799	−	0.109799i
$268$	−662046.			−0.563056
$269$	295388.	−	295388.i	0.248893	−	0.248893i	−0.571623	−	0.820516i	$-0.693686\pi$
$269$	295388.	−	295388.i	0.248893	−	0.248893i	0.820516	+	0.571623i	$0.193686\pi$
$270$		−	341113.i		−	0.284766i
$271$	1.97791e6			1.63600			0.818002	−	0.575216i	$-0.195082\pi$
$271$	1.97791e6			1.63600			0.818002	+	0.575216i	$0.195082\pi$
$272$	1.39253e6	+	558713.i	1.14125	+	0.457896i
$273$	−1.02605e6			−0.833228
$274$		−	1.31493e6i		−	1.05810i
$275$	−895706.	+	895706.i	−0.714223	+	0.714223i
$276$	302180.			0.238778
$277$	1.22255e6	−	1.22255e6i	0.957342	−	0.957342i	−0.0417848	−	0.999127i	$-0.513304\pi$
$277$	1.22255e6	−	1.22255e6i	0.957342	−	0.957342i	0.999127	+	0.0417848i	$0.0133044\pi$
$278$	−525255.	−	525255.i	−0.407622	−	0.407622i
$279$	232348.	+	232348.i	0.178702	+	0.178702i
$280$		−	1.58558e6i		−	1.20863i
$281$			1.38727e6i			1.04808i	0.851693	+	0.524041i	$0.175576\pi$
$281$			1.38727e6i			1.04808i	−0.851693	+	0.524041i	$0.824424\pi$
$282$	−873250.	−	873250.i	−0.653907	−	0.653907i
$283$	−310459.	−	310459.i	−0.230430	−	0.230430i	0.582442	−	0.812872i	$-0.302097\pi$
$283$	−310459.	−	310459.i	−0.230430	−	0.230430i	−0.812872	+	0.582442i	$0.802097\pi$
$284$	308906.	−	308906.i	0.227264	−	0.227264i
$285$	947594.			0.691051
$286$	−2.13212e6	+	2.13212e6i	−1.54133	+	1.54133i
$287$			2.39402e6i			1.71563i
$288$	320984.			0.228035
$289$	1.02611e6	+	981375.i	0.722684	+	0.691179i
$290$	−3.54065e6			−2.47222
$291$		−	349042.i		−	0.241627i
$292$	7367.11	−	7367.11i	0.00505638	−	0.00505638i
$293$	512256.			0.348592			0.174296	−	0.984693i	$-0.444235\pi$
$293$	512256.			0.348592			0.174296	+	0.984693i	$0.444235\pi$
$294$	−434319.	+	434319.i	−0.293049	+	0.293049i
$295$	1.66415e6	+	1.66415e6i	1.11336	+	1.11336i
$296$	−735002.	−	735002.i	−0.487595	−	0.487595i
$297$		−	482130.i		−	0.317156i
$298$			1.16431e6i			0.759502i
$299$	1.43570e6	+	1.43570e6i	0.928719	+	0.928719i
$300$	−139433.	−	139433.i	−0.0894465	−	0.0894465i
$301$	−1.50411e6	+	1.50411e6i	−0.956894	+	0.956894i
$302$	1.35323e6			0.853795
$303$	−132140.	+	132140.i	−0.0826853	+	0.0826853i
$304$			1.86743e6i			1.15894i
$305$	−627013.			−0.385946
$306$	590386.	+	236876.i	0.360440	+	0.144616i
$307$	−279126.			−0.169026			−0.0845131	−	0.996422i	$-0.526933\pi$
$307$	−279126.			−0.169026			−0.0845131	+	0.996422i	$0.526933\pi$
$308$			1.24684e6i			0.748918i
$309$	−559842.	+	559842.i	−0.333556	+	0.333556i
$310$	1.89819e6			1.12185
$311$	2.16907e6	−	2.16907e6i	1.27166	−	1.27166i	0.326448	−	0.945215i	$-0.394148\pi$
$311$	2.16907e6	−	2.16907e6i	1.27166	−	1.27166i	0.945215	−	0.326448i	$-0.105852\pi$
$312$	596565.	+	596565.i	0.346953	+	0.346953i
$313$	1.50721e6	+	1.50721e6i	0.869585	+	0.869585i	0.992426	−	0.122841i	$-0.0392005\pi$
$313$	1.50721e6	+	1.50721e6i	0.869585	+	0.869585i	−0.122841	+	0.992426i	$0.539201\pi$
$314$			867026.i			0.496259i
$315$		−	947749.i		−	0.538167i
$316$	−232305.	−	232305.i	−0.130870	−	0.130870i
$317$	−2.21848e6	−	2.21848e6i	−1.23996	−	1.23996i	−0.960017	−	0.279941i	$-0.909685\pi$
$317$	−2.21848e6	−	2.21848e6i	−1.23996	−	1.23996i	−0.279941	−	0.960017i	$-0.590315\pi$
$318$	−834682.	+	834682.i	−0.462864	+	0.462864i
$319$	−5.00436e6			−2.75342
$320$	−711673.	+	711673.i	−0.388513	+	0.388513i
$321$			1.28105e6i			0.693909i
$322$	3.18822e6			1.71360
$323$	−658029.	+	1.64006e6i	−0.350945	+	0.874690i
$324$	75052.6			0.0397194
$325$		−	1.32493e6i		−	0.695800i
$326$	−1.51919e6	+	1.51919e6i	−0.791715	+	0.791715i
$327$	105794.			0.0547133
$328$	1.39192e6	−	1.39192e6i	0.714381	−	0.714381i
$329$	−2.42624e6	−	2.42624e6i	−1.23579	−	1.23579i
$330$	−1.96940e6	−	1.96940e6i	−0.995520	−	0.995520i
$331$		−	2.12840e6i		−	1.06778i	−0.845553	−	0.533892i	$-0.820729\pi$
$331$		−	2.12840e6i		−	1.06778i	0.845553	−	0.533892i	$-0.179271\pi$
$332$		−	404468.i		−	0.201391i
$333$	−439332.	−	439332.i	−0.217111	−	0.217111i
$334$	29908.0	+	29908.0i	0.0146697	+	0.0146697i
$335$	2.90541e6	−	2.90541e6i	1.41447	−	1.41447i
$336$	1.86774e6			0.902543
$337$	530770.	−	530770.i	0.254584	−	0.254584i	−0.568263	−	0.822847i	$-0.692384\pi$
$337$	530770.	−	530770.i	0.254584	−	0.254584i	0.822847	+	0.568263i	$0.192384\pi$
$338$		−	706702.i		−	0.336469i
$339$	481846.			0.227724
$340$	889871.	−	380265.i	0.417474	−	0.178397i
$341$	2.68291e6			1.24945
$342$			791728.i			0.366025i
$343$	751925.	−	751925.i	0.345095	−	0.345095i
$344$	1.74903e6			0.796894
$345$	−1.32613e6	+	1.32613e6i	−0.599843	+	0.599843i
$346$	1.53053e6	+	1.53053e6i	0.687309	+	0.687309i
$347$	700750.	+	700750.i	0.312420	+	0.312420i	0.845847	−	0.533426i	$-0.179096\pi$
$347$	700750.	+	700750.i	0.312420	+	0.312420i	−0.533426	+	0.845847i	$0.679096\pi$
$348$		−	779023.i		−	0.344828i
$349$		−	123632.i		−	0.0543336i	−0.999631	−	0.0271668i	$-0.991351\pi$
$349$		−	123632.i		−	0.0543336i	0.999631	−	0.0271668i	$-0.00864853\pi$
$350$	−1.47112e6	−	1.47112e6i	−0.641916	−	0.641916i
$351$	356584.	+	356584.i	0.154488	+	0.154488i
$352$	1.85319e6	−	1.85319e6i	0.797193	−	0.797193i
$353$	−593695.			−0.253587			−0.126793	−	0.991929i	$-0.540469\pi$
$353$	−593695.			−0.253587			−0.126793	+	0.991929i	$0.540469\pi$
$354$	−1.39042e6	+	1.39042e6i	−0.589710	+	0.589710i
$355$			2.71129e6i			1.14184i
$356$	229903.			0.0961434
$357$	1.64033e6	+	658137.i	0.681179	+	0.273304i
$358$	974115.			0.401701
$359$		−	1.15838e6i		−	0.474369i	−0.971465	−	0.237184i	$-0.923775\pi$
$359$		−	1.15838e6i		−	0.474369i	0.971465	−	0.237184i	$-0.0762246\pi$
$360$	−551037.	+	551037.i	−0.224091	+	0.224091i
$361$	276719.			0.111756
$362$	−976230.	+	976230.i	−0.391544	+	0.391544i
$363$	−1.75864e6	−	1.75864e6i	−0.700504	−	0.700504i
$364$	−922165.	−	922165.i	−0.364800	−	0.364800i
$365$			64661.5i			0.0254047i
$366$		−	523878.i		−	0.204422i
$367$	−124628.	−	124628.i	−0.0483005	−	0.0483005i	0.682544	−	0.730844i	$-0.260874\pi$
$367$	−124628.	−	124628.i	−0.0483005	−	0.0483005i	−0.730844	+	0.682544i	$0.760874\pi$
$368$	−2.61341e6	−	2.61341e6i	−1.00598	−	1.00598i
$369$	831991.	−	831991.i	0.318092	−	0.318092i
$370$	−3.58916e6			−1.36298
$371$	−2.31908e6	+	2.31908e6i	−0.874745	+	0.874745i
$372$			417645.i			0.156477i
$373$	−5.21591e6			−1.94115			−0.970573	−	0.240807i	$-0.922588\pi$
$373$	−5.21591e6			−1.94115			−0.970573	+	0.240807i	$0.922588\pi$
$374$	4.77617e6	−	2.04098e6i	1.76563	−	0.754501i
$375$	−772928.			−0.283832
$376$			2.82131e6i			1.02916i
$377$	3.70123e6	−	3.70123e6i	1.34120	−	1.34120i
$378$	791858.			0.285048
$379$	−1.92704e6	+	1.92704e6i	−0.689118	+	0.689118i	−0.962037	−	0.272919i	$-0.912011\pi$
$379$	−1.92704e6	+	1.92704e6i	−0.689118	+	0.689118i	0.272919	+	0.962037i	$0.412011\pi$
$380$	851648.	+	851648.i	0.302553	+	0.302553i
$381$	−40831.3	−	40831.3i	−0.0144106	−	0.0144106i
$382$		−	2.45179e6i		−	0.859657i
$383$		−	1.60287e6i		−	0.558343i	−0.960241	−	0.279172i	$-0.909940\pi$
$383$		−	1.60287e6i		−	0.558343i	0.960241	−	0.279172i	$-0.0900598\pi$
$384$	−1.40162e6	−	1.40162e6i	−0.485067	−	0.485067i
$385$	−5.47180e6	−	5.47180e6i	−1.88139	−	1.88139i
$386$	−2.86322e6	+	2.86322e6i	−0.978109	+	0.978109i
$387$	1.04544e6			0.354833
$388$	313701.	−	313701.i	0.105788	−	0.105788i
$389$			972040.i			0.325694i	0.986651	+	0.162847i	$0.0520677\pi$
$389$			972040.i			0.325694i	−0.986651	+	0.162847i	$0.947932\pi$
$390$	2.91314e6			0.969841
$391$	−1.37432e6	−	3.21611e6i	−0.454619	−	1.06387i
$392$	1.40321e6			0.461218
$393$		−	408054.i		−	0.133271i
$394$	−3.75764e6	+	3.75764e6i	−1.21948	+	1.21948i
$395$	2.03895e6			0.657527
$396$	433314.	−	433314.i	0.138856	−	0.138856i
$397$	4.32581e6	+	4.32581e6i	1.37750	+	1.37750i	0.848824	+	0.528676i	$0.177311\pi$
$397$	4.32581e6	+	4.32581e6i	1.37750	+	1.37750i	0.528676	+	0.848824i	$0.322689\pi$
$398$	3.45682e6	+	3.45682e6i	1.09388	+	1.09388i
$399$			2.19974e6i			0.691734i
$400$			2.41178e6i			0.753682i
$401$	−2.83619e6	−	2.83619e6i	−0.880793	−	0.880793i	0.112822	−	0.993615i	$-0.464011\pi$
$401$	−2.83619e6	−	2.83619e6i	−0.880793	−	0.880793i	−0.993615	+	0.112822i	$0.964011\pi$
$402$	2.42751e6	+	2.42751e6i	0.749197	+	0.749197i
$403$	−1.98428e6	+	1.98428e6i	−0.608612	+	0.608612i
$404$	−237521.			−0.0724018
$405$	−329370.	+	329370.i	−0.0997808	+	0.0997808i
$406$		−	8.21925e6i		−	2.47467i
$407$	−5.07293e6			−1.51800
$408$	−571064.	−	1.33637e6i	−0.169838	−	0.397443i
$409$	2.64123e6			0.780724			0.390362	−	0.920662i	$-0.372350\pi$
$409$	2.64123e6			0.780724			0.390362	+	0.920662i	$0.372350\pi$
$410$		−	6.79703e6i		−	1.99691i
$411$	−1.26967e6	+	1.26967e6i	−0.370754	+	0.370754i
$412$	−1.00631e6			−0.292072
$413$	−3.86315e6	+	3.86315e6i	−1.11447	+	1.11447i
$414$	−1.10800e6	−	1.10800e6i	−0.317715	−	0.317715i
$415$	1.77502e6	+	1.77502e6i	0.505921	+	0.505921i
$416$			2.74124e6i			0.776630i
$417$			1.01435e6i			0.285658i
$418$	4.57102e6	+	4.57102e6i	1.27959	+	1.27959i
$419$	1.00001e6	+	1.00001e6i	0.278271	+	0.278271i	0.832418	−	0.554148i	$-0.186956\pi$
$419$	1.00001e6	+	1.00001e6i	0.278271	+	0.278271i	−0.554148	+	0.832418i	$0.686956\pi$
$420$	851788.	−	851788.i	0.235618	−	0.235618i
$421$	−3.39345e6			−0.933116			−0.466558	−	0.884491i	$-0.654506\pi$
$421$	−3.39345e6			−0.933116			−0.466558	+	0.884491i	$0.654506\pi$
$422$	2.07200e6	−	2.07200e6i	0.566382	−	0.566382i
$423$			1.68638e6i			0.458252i
$424$	2.69671e6			0.728482
$425$	−849842.	+	2.11814e6i	−0.228226	+	0.568828i
$426$	−2.26532e6			−0.604792
$427$		−	1.45555e6i		−	0.386328i
$428$	−1.15134e6	+	1.15134e6i	−0.303804	+	0.303804i
$429$	4.11745e6			1.08015
$430$	4.27043e6	−	4.27043e6i	1.11378	−	1.11378i
$431$	−294536.	−	294536.i	−0.0763739	−	0.0763739i	0.667888	−	0.744262i	$-0.267199\pi$
$431$	−294536.	−	294536.i	−0.0763739	−	0.0763739i	−0.744262	+	0.667888i	$0.767199\pi$
$432$	−649093.	−	649093.i	−0.167339	−	0.167339i
$433$			716201.i			0.183576i	0.995779	+	0.0917878i	$0.0292581\pi$
$433$			716201.i			0.183576i	−0.995779	+	0.0917878i	$0.970742\pi$
$434$			4.40645e6i			1.12296i
$435$	3.41876e6	+	3.41876e6i	0.866255	+	0.866255i
$436$	95082.5	+	95082.5i	0.0239543	+	0.0239543i
$437$	3.07796e6	−	3.07796e6i	0.771010	−	0.771010i
$438$	−54025.7			−0.0134560
$439$	−651546.	+	651546.i	−0.161356	+	0.161356i	−0.783167	−	0.621811i	$-0.786397\pi$
$439$	−651546.	+	651546.i	−0.161356	+	0.161356i	0.621811	+	0.783167i	$0.286397\pi$
$440$			6.36278e6i			1.56681i
$441$	838736.			0.205366
$442$	−2.02295e6	+	5.04197e6i	−0.492526	+	1.22756i
$443$	5.69532e6			1.37882			0.689412	−	0.724369i	$-0.257869\pi$
$443$	5.69532e6			1.37882			0.689412	+	0.724369i	$0.257869\pi$
$444$		−	789697.i		−	0.190109i
$445$	−1.00894e6	+	1.00894e6i	−0.241526	+	0.241526i
$446$	−368049.			−0.0876130
$447$	1.12423e6	−	1.12423e6i	0.266126	−	0.266126i
$448$	−1.65208e6	−	1.65208e6i	−0.388897	−	0.388897i
$449$	−3.05843e6	−	3.05843e6i	−0.715951	−	0.715951i	0.251822	−	0.967773i	$-0.418970\pi$
$449$	−3.05843e6	−	3.05843e6i	−0.715951	−	0.715951i	−0.967773	+	0.251822i	$0.918970\pi$
$450$			1.02251e6i			0.238034i
$451$		−	9.60695e6i		−	2.22405i
$452$	433058.	+	433058.i	0.0997011	+	0.0997011i
$453$	−1.30665e6	−	1.30665e6i	−0.299166	−	0.299166i
$454$	−5.11830e6	+	5.11830e6i	−1.16543	+	1.16543i
$455$	8.09389e6			1.83286
$456$	1.27896e6	−	1.27896e6i	0.288036	−	0.288036i
$457$		−	6.72517e6i		−	1.50630i	−0.657847	−	0.753152i	$-0.728533\pi$
$457$		−	6.72517e6i		−	1.50630i	0.657847	−	0.753152i	$-0.271467\pi$
$458$	5.32585e6			1.18638
$459$	−341341.	−	798784.i	−0.0756235	−	0.176969i
$460$	−2.38371e6			−0.525241
$461$		−	1.61028e6i		−	0.352897i	−0.984310	−	0.176448i	$-0.943539\pi$
$461$		−	1.61028e6i		−	0.352897i	0.984310	−	0.176448i	$-0.0564609\pi$
$462$	4.57177e6	−	4.57177e6i	0.996504	−	0.996504i
$463$	−6.18966e6			−1.34188			−0.670941	−	0.741511i	$-0.734110\pi$
$463$	−6.18966e6			−1.34188			−0.670941	+	0.741511i	$0.734110\pi$
$464$	−6.73739e6	+	6.73739e6i	−1.45277	+	1.45277i
$465$	−1.83285e6	−	1.83285e6i	−0.393092	−	0.393092i
$466$	−3.90234e6	−	3.90234e6i	−0.832455	−	0.832455i
$467$			8.42877e6i			1.78843i	0.447638	+	0.894215i	$0.352265\pi$
$467$			8.42877e6i			1.78843i	−0.447638	+	0.894215i	$0.647735\pi$
$468$			640958.i			0.135274i
$469$	6.74461e6	+	6.74461e6i	1.41587	+	1.41587i
$470$	6.88852e6	+	6.88852e6i	1.43840	+	1.43840i
$471$	837180.	−	837180.i	0.173887	−	0.173887i
$472$	4.49220e6			0.928120
$473$	6.03584e6	−	6.03584e6i	1.24047	−	1.24047i
$474$			1.70357e6i			0.348269i
$475$	−2.84049e6			−0.577643
$476$	882746.	+	2.06574e6i	0.178574	+	0.417887i
$477$	1.61190e6			0.324371
$478$			5.27243e6i			1.05546i
$479$	−1.92260e6	+	1.92260e6i	−0.382870	+	0.382870i	−0.872135	−	0.489265i	$-0.837265\pi$
$479$	−1.92260e6	+	1.92260e6i	−0.382870	+	0.382870i	0.489265	+	0.872135i	$0.337265\pi$
$480$	−2.53204e6			−0.501611
$481$	3.75195e6	−	3.75195e6i	0.739424	−	0.739424i
$482$	−3.08664e6	−	3.08664e6i	−0.605157	−	0.605157i
$483$	−3.07847e6	−	3.07847e6i	−0.600436	−	0.600436i
$484$		−	3.16115e6i		−	0.613383i
$485$			2.75337e6i			0.531509i
$486$	−275194.	−	275194.i	−0.0528503	−	0.0528503i
$487$	4.05514e6	+	4.05514e6i	0.774788	+	0.774788i	0.978939	−	0.204151i	$-0.0654434\pi$
$487$	4.05514e6	+	4.05514e6i	0.774788	+	0.774788i	−0.204151	+	0.978939i	$0.565443\pi$
$488$	−846277.	+	846277.i	−0.160866	+	0.160866i
$489$	2.93379e6			0.554827
$490$	3.42606e6	−	3.42606e6i	0.644622	−	0.644622i
$491$		−	3.24772e6i		−	0.607960i	−0.952678	−	0.303980i	$-0.901684\pi$
$491$		−	3.24772e6i		−	0.607960i	0.952678	−	0.303980i	$-0.0983156\pi$
$492$	1.49550e6			0.278531
$493$	−8.29114e6	+	3.54302e6i	−1.53637	+	0.656532i
$494$	−6.76145e6			−1.24659
$495$			3.80322e6i			0.697651i
$496$	3.61201e6	−	3.61201e6i	0.659241	−	0.659241i
$497$	−6.29398e6			−1.14297
$498$	−1.48305e6	+	1.48305e6i	−0.267969	+	0.267969i
$499$	−7.30623e6	−	7.30623e6i	−1.31354	−	1.31354i	−0.918790	−	0.394746i	$-0.870833\pi$
$499$	−7.30623e6	−	7.30623e6i	−1.31354	−	1.31354i	−0.394746	−	0.918790i	$-0.629167\pi$
$500$	−694668.	−	694668.i	−0.124266	−	0.124266i
$501$		−	57756.9i		−	0.0102804i
$502$			5.57641e6i			0.987633i
$503$	−5.67491e6	−	5.67491e6i	−1.00009	−	1.00009i	−1.00000		8.96820e-5i	$-0.999971\pi$
$503$	−5.67491e6	−	5.67491e6i	−1.00009	−	1.00009i	−8.96820e−5	−	1.00000i	$-0.500029\pi$
$504$	−1.27918e6	−	1.27918e6i	−0.224313	−	0.224313i
$505$	1.04237e6	−	1.04237e6i	0.181884	−	0.181884i
$506$	−1.27940e7			−2.22141
$507$	−682375.	+	682375.i	−0.117897	+	0.117897i
$508$		−	73394.1i		−	0.0126183i
$509$	−5.07877e6			−0.868888			−0.434444	−	0.900699i	$-0.643055\pi$
$509$	−5.07877e6			−0.868888			−0.434444	+	0.900699i	$0.643055\pi$
$510$	−4.65718e6	−	1.86856e6i	−0.792862	−	0.318114i
$511$	−150105.			−0.0254298
$512$			470500.i			0.0793204i
$513$	764474.	−	764474.i	0.128254	−	0.128254i
$514$	−3.20504e6			−0.535088
$515$	4.41624e6	−	4.41624e6i	0.733727	−	0.733727i
$516$	939591.	+	939591.i	0.155351	+	0.155351i
$517$	9.73626e6	+	9.73626e6i	1.60201	+	1.60201i
$518$		−	8.33187e6i		−	1.36433i
$519$		−	2.95569e6i		−	0.481660i
$520$	−4.70592e6	−	4.70592e6i	−0.763196	−	0.763196i
$521$	5.40920e6	+	5.40920e6i	0.873050	+	0.873050i	0.992804	−	0.119754i	$-0.0382106\pi$
$521$	5.40920e6	+	5.40920e6i	0.873050	+	0.873050i	−0.119754	+	0.992804i	$0.538211\pi$
$522$	−2.85643e6	+	2.85643e6i	−0.458825	+	0.458825i
$523$	−2.03504e6			−0.325326			−0.162663	−	0.986682i	$-0.552008\pi$
$523$	−2.03504e6			−0.325326			−0.162663	+	0.986682i	$0.552008\pi$
$524$	366738.	−	366738.i	0.0583482	−	0.0583482i
$525$			2.84096e6i			0.449849i
$526$	9.82975e6			1.54910
$527$	4.44499e6	−	1.89946e6i	0.697179	−	0.297923i
$528$	−7.49504e6			−1.17001
$529$			2.17868e6i			0.338497i
$530$	6.58427e6	−	6.58427e6i	1.01817	−	1.01817i
$531$	2.68512e6			0.413263
$532$	−1.97701e6	+	1.97701e6i	−0.302852	+	0.302852i
$533$	7.10530e6	+	7.10530e6i	1.08334	+	1.08334i
$534$	−842980.	−	842980.i	−0.127928	−	0.127928i
$535$		−	1.01054e7i		−	1.52640i
$536$		−	7.84285e6i		−	1.17913i
$537$	−940582.	−	940582.i	−0.140754	−	0.140754i
$538$	−1.94686e6	−	1.94686e6i	−0.289987	−	0.289987i
$539$	4.84241e6	−	4.84241e6i	0.717943	−	0.717943i
$540$	−592042.			−0.0873712
$541$	440994.	−	440994.i	0.0647797	−	0.0647797i	−0.673975	−	0.738754i	$-0.735414\pi$
$541$	440994.	−	440994.i	0.0647797	−	0.0647797i	0.738754	+	0.673975i	$0.235414\pi$
$542$		−	1.30361e7i		−	1.90612i
$543$	1.88525e6			0.274390
$544$	1.75830e6	−	4.38236e6i	0.254739	−	0.634909i
$545$	−834544.			−0.120353
$546$			6.76257e6i			0.970800i
$547$	−3.13093e6	+	3.13093e6i	−0.447409	+	0.447409i	−0.894492	−	0.447083i	$-0.852463\pi$
$547$	−3.13093e6	+	3.13093e6i	−0.447409	+	0.447409i	0.447083	+	0.894492i	$0.352463\pi$
$548$	−2.28222e6			−0.324644
$549$	−505844.	+	505844.i	−0.0716285	+	0.0716285i
$550$	5.90345e6	+	5.90345e6i	0.832146	+	0.832146i
$551$	−7.93501e6	−	7.93501e6i	−1.11344	−	1.11344i
$552$			3.57974e6i			0.500039i
$553$			4.73321e6i			0.658178i
$554$	−8.05763e6	−	8.05763e6i	−1.11541	−	1.11541i
$555$	3.46561e6	+	3.46561e6i	0.477581	+	0.477581i
$556$	−911643.	+	911643.i	−0.125066	+	0.125066i
$557$	2.08074e6			0.284171			0.142085	−	0.989854i	$-0.454619\pi$
$557$	2.08074e6			0.284171			0.142085	+	0.989854i	$0.454619\pi$
$558$	1.53137e6	−	1.53137e6i	0.208207	−	0.208207i
$559$			8.92822e6i			1.20847i
$560$	−1.47334e7			−1.98533
$561$	−6.58248e6	−	2.64103e6i	−0.883044	−	0.354297i
$562$	9.14327e6			1.22113
$563$			1.30774e7i			1.73881i	0.494102	+	0.869404i	$0.335497\pi$
$563$			1.30774e7i			1.73881i	−0.494102	+	0.869404i	$0.664503\pi$
$564$	−1.51563e6	+	1.51563e6i	−0.200630	+	0.200630i
$565$	−3.80097e6			−0.500926
$566$	−2.04619e6	+	2.04619e6i	−0.268475	+	0.268475i
$567$	−764600.	−	764600.i	−0.0998795	−	0.0998795i
$568$	3.65942e6	+	3.65942e6i	0.475928	+	0.475928i
$569$			1.08273e7i			1.40197i	0.713176	+	0.700985i	$0.247256\pi$
$569$			1.08273e7i			1.40197i	−0.713176	+	0.700985i	$0.752744\pi$
$570$		−	6.24544e6i		−	0.805148i
$571$	2.13950e6	+	2.13950e6i	0.274614	+	0.274614i	0.830954	−	0.556340i	$-0.187795\pi$
$571$	2.13950e6	+	2.13950e6i	0.274614	+	0.274614i	−0.556340	+	0.830954i	$0.687795\pi$
$572$	3.70055e6	+	3.70055e6i	0.472908	+	0.472908i
$573$	−2.36739e6	+	2.36739e6i	−0.301220	+	0.301220i
$574$	1.57786e7			1.99889
$575$	3.97518e6	−	3.97518e6i	0.501403	−	0.501403i
$576$			1.14829e6i			0.144210i
$577$	1.17526e6			0.146959			0.0734793	−	0.997297i	$-0.476590\pi$
$577$	1.17526e6			0.146959			0.0734793	+	0.997297i	$0.476590\pi$
$578$	6.46809e6	−	6.76292e6i	0.805297	−	0.842004i
$579$	5.52932e6			0.685450
$580$			6.14521e6i			0.758520i
$581$	−4.12053e6	+	4.12053e6i	−0.506422	+	0.506422i
$582$	−2.30048e6			−0.281521
$583$	9.30624e6	−	9.30624e6i	1.13397	−	1.13397i
$584$	87273.5	+	87273.5i	0.0105889	+	0.0105889i
$585$	−2.81286e6	−	2.81286e6i	−0.339828	−	0.339828i
$586$		−	3.37620e6i		−	0.406147i
$587$			3.51748e6i			0.421344i	0.977557	+	0.210672i	$0.0675652\pi$
$587$			3.51748e6i			0.421344i	−0.977557	+	0.210672i	$0.932435\pi$
$588$	753812.	+	753812.i	0.0899125	+	0.0899125i
$589$	4.25407e6	+	4.25407e6i	0.505261	+	0.505261i
$590$	1.09682e7	−	1.09682e7i	1.29719	−	1.29719i
$591$	7.25658e6			0.854601
$592$	−6.82970e6	+	6.82970e6i	−0.800935	+	0.800935i
$593$			1.88306e6i			0.219902i	0.993937	+	0.109951i	$0.0350693\pi$
$593$			1.88306e6i			0.219902i	−0.993937	+	0.109951i	$0.964931\pi$
$594$	−3.17764e6			−0.369521
$595$	−1.29395e7	−	5.19162e6i	−1.49839	−	0.601189i
$596$	2.02080e6			0.233028
$597$		−	6.67564e6i		−	0.766580i
$598$	9.46244e6	−	9.46244e6i	1.08206	−	1.08206i
$599$	−1.22157e7			−1.39108			−0.695538	−	0.718489i	$-0.744834\pi$
$599$	−1.22157e7			−1.39108			−0.695538	+	0.718489i	$0.744834\pi$
$600$	1.65178e6	−	1.65178e6i	0.187316	−	0.187316i
$601$	8.91840e6	+	8.91840e6i	1.00717	+	1.00717i	0.999974	+	0.00719171i	$0.00228921\pi$
$601$	8.91840e6	+	8.91840e6i	1.00717	+	1.00717i	0.00719171	+	0.999974i	$0.497711\pi$
$602$	9.91336e6	+	9.91336e6i	1.11488	+	1.11488i
$603$		−	4.68789e6i		−	0.525030i
$604$		−	2.34869e6i		−	0.261959i
$605$	1.38728e7	+	1.38728e7i	1.54090	+	1.54090i
$606$	870915.	+	870915.i	0.0963372	+	0.0963372i
$607$	−5.91075e6	+	5.91075e6i	−0.651134	+	0.651134i	−0.953266	−	0.302132i	$-0.902302\pi$
$607$	−5.91075e6	+	5.91075e6i	−0.651134	+	0.651134i	0.302132	+	0.953266i	$0.402302\pi$
$608$	5.87690e6			0.644747
$609$	−7.93631e6	+	7.93631e6i	−0.867112	+	0.867112i
$610$			4.13254e6i			0.449669i
$611$	−1.44019e7			−1.56069
$612$	411126.	−	1.02469e6i	0.0443707	−	0.110589i
$613$	−4.46064e6			−0.479453			−0.239727	−	0.970840i	$-0.577058\pi$
$613$	−4.46064e6			−0.479453			−0.239727	+	0.970840i	$0.577058\pi$
$614$			1.83967e6i			0.196934i
$615$	−6.56305e6	+	6.56305e6i	−0.699710	+	0.699710i
$616$	−1.47706e7			−1.56836
$617$	1.77551e6	−	1.77551e6i	0.187763	−	0.187763i	−0.606965	−	0.794728i	$-0.707613\pi$
$617$	1.77551e6	−	1.77551e6i	0.187763	−	0.187763i	0.794728	+	0.606965i	$0.207613\pi$
$618$	3.68983e6	+	3.68983e6i	0.388629	+	0.388629i
$619$	−1.00231e7	−	1.00231e7i	−1.05142	−	1.05142i	−0.998604	−	0.0528187i	$-0.983179\pi$
$619$	−1.00231e7	−	1.00231e7i	−1.05142	−	1.05142i	−0.0528187	−	0.998604i	$-0.516821\pi$
$620$		−	3.29453e6i		−	0.344203i
$621$			2.13971e6i			0.222652i
$622$	−1.42960e7	−	1.42960e7i	−1.48162	−	1.48162i
$623$	−2.34214e6	−	2.34214e6i	−0.241765	−	0.241765i
$624$	5.54333e6	−	5.54333e6i	0.569914	−	0.569914i
$625$	1.20825e7			1.23725
$626$	9.93377e6	−	9.93377e6i	1.01316	−	1.01316i
$627$		−	8.82733e6i		−	0.896728i
$628$	1.50483e6			0.152261
$629$	−8.40474e6	+	3.59156e6i	−0.847028	+	0.361957i
$630$	−6.24647e6			−0.627022
$631$			5.20140e6i			0.520052i	0.965602	+	0.260026i	$0.0837311\pi$
$631$			5.20140e6i			0.520052i	−0.965602	+	0.260026i	$0.916269\pi$
$632$	2.75197e6	−	2.75197e6i	0.274063	−	0.274063i
$633$	−4.00136e6			−0.396915
$634$	−1.46216e7	+	1.46216e7i	−1.44468	+	1.44468i
$635$	322092.	+	322092.i	0.0316990	+	0.0316990i
$636$	1.44869e6	+	1.44869e6i	0.142015	+	0.142015i
$637$			7.16291e6i			0.699424i
$638$			3.29830e7i			3.20803i
$639$	2.18734e6	+	2.18734e6i	0.211916	+	0.211916i
$640$	1.10565e7	+	1.10565e7i	1.06701	+	1.06701i
$641$	−1.06971e7	+	1.06971e7i	−1.02830	+	1.02830i	−0.0287168	+	0.999588i	$0.509142\pi$
$641$	−1.06971e7	+	1.06971e7i	−1.02830	+	1.02830i	−0.999588	+	0.0287168i	$0.990858\pi$
$642$	8.44318e6			0.808479
$643$	9.73009e6	−	9.73009e6i	0.928089	−	0.928089i	−0.0694936	−	0.997582i	$-0.522138\pi$
$643$	9.73009e6	−	9.73009e6i	0.928089	−	0.928089i	0.997582	+	0.0694936i	$0.0221384\pi$
$644$		−	5.53354e6i		−	0.525761i
$645$	−8.24685e6			−0.780528
$646$	1.08094e7	+	4.33696e6i	1.01911	+	0.408888i
$647$	−5.27093e6			−0.495024			−0.247512	−	0.968885i	$-0.579613\pi$
$647$	−5.27093e6			−0.495024			−0.247512	+	0.968885i	$0.579613\pi$
$648$			889101.i			0.0831790i
$649$	1.55024e7	−	1.55024e7i	1.44473	−	1.44473i
$650$	−8.73240e6			−0.810681
$651$	4.25476e6	−	4.25476e6i	0.393480	−	0.393480i
$652$	2.63674e6	+	2.63674e6i	0.242912	+	0.242912i
$653$	1.29325e7	+	1.29325e7i	1.18686	+	1.18686i	0.977930	+	0.208931i	$0.0669985\pi$
$653$	1.29325e7	+	1.29325e7i	1.18686	+	1.18686i	0.208931	+	0.977930i	$0.433002\pi$
$654$		−	697274.i		−	0.0637469i
$655$			3.21888e6i			0.293158i
$656$	−1.29339e7	−	1.29339e7i	−1.17346	−	1.17346i
$657$	52165.9	+	52165.9i	0.00471491	+	0.00471491i
$658$	−1.59910e7	+	1.59910e7i	−1.43983	+	1.43983i
$659$	1.65422e6			0.148382			0.0741910	−	0.997244i	$-0.476363\pi$
$659$	1.65422e6			0.148382			0.0741910	+	0.997244i	$0.476363\pi$
$660$	−3.41814e6	+	3.41814e6i	−0.305442	+	0.305442i
$661$			4.09363e6i			0.364422i	0.983259	+	0.182211i	$0.0583255\pi$
$661$			4.09363e6i			0.364422i	−0.983259	+	0.182211i	$0.941675\pi$
$662$	−1.40279e7			−1.24408
$663$	6.82172e6	−	2.91509e6i	0.602712	−	0.257554i
$664$	4.79148e6			0.421745
$665$		−	1.73524e7i		−	1.52161i
$666$	−2.89556e6	+	2.89556e6i	−0.252958	+	0.252958i
$667$	2.22096e7			1.93297
$668$	51908.9	−	51908.9i	0.00450091	−	0.00450091i
$669$	355380.	+	355380.i	0.0306992	+	0.0306992i
$670$	−1.91491e7	−	1.91491e7i	−1.64801	−	1.64801i
$671$			5.84095e6i			0.500815i
$672$		−	5.87787e6i		−	0.502108i
$673$	−6.38472e6	−	6.38472e6i	−0.543381	−	0.543381i	0.381137	−	0.924518i	$-0.375532\pi$
$673$	−6.38472e6	−	6.38472e6i	−0.543381	−	0.543381i	−0.924518	+	0.381137i	$0.875532\pi$
$674$	−3.49822e6	−	3.49822e6i	−0.296618	−	0.296618i
$675$	987316.	−	987316.i	0.0834059	−	0.0834059i
$676$	−1.22657e6			−0.103234
$677$	2.30681e6	−	2.30681e6i	0.193437	−	0.193437i	−0.603742	−	0.797180i	$-0.706324\pi$
$677$	2.30681e6	−	2.30681e6i	0.193437	−	0.193437i	0.797180	+	0.603742i	$0.206324\pi$
$678$		−	3.17577e6i		−	0.265323i
$679$	−6.39167e6			−0.532034
$680$	4.50476e6	+	1.05417e7i	0.373593	+	0.874259i
$681$	9.88421e6			0.816722
$682$		−	1.76826e7i		−	1.45575i
$683$	9.60064e6	−	9.60064e6i	0.787496	−	0.787496i	−0.193587	−	0.981083i	$-0.562012\pi$
$683$	9.60064e6	−	9.60064e6i	0.787496	−	0.787496i	0.981083	+	0.193587i	$0.0620122\pi$
$684$	1.37414e6			0.112303
$685$	1.00156e7	−	1.00156e7i	0.815550	−	0.815550i
$686$	−4.95582e6	−	4.95582e6i	−0.402073	−	0.402073i
$687$	−5.14252e6	−	5.14252e6i	−0.415704	−	0.415704i
$688$		−	1.62521e7i		−	1.30900i
$689$			1.37658e7i			1.10472i
$690$	8.74030e6	+	8.74030e6i	0.698881	+	0.698881i
$691$	257584.	+	257584.i	0.0205222	+	0.0205222i	0.717293	−	0.696771i	$-0.245381\pi$
$691$	257584.	+	257584.i	0.0205222	+	0.0205222i	−0.696771	+	0.717293i	$0.745381\pi$
$692$	2.65642e6	−	2.65642e6i	0.210878	−	0.210878i
$693$	−8.82878e6			−0.698341
$694$	4.61853e6	−	4.61853e6i	0.364003	−	0.364003i
$695$		−	8.00154e6i		−	0.628364i
$696$	9.22859e6			0.722125
$697$	−6.80158e6	−	1.59166e7i	−0.530307	−	1.24099i
$698$	−814841.			−0.0633045
$699$			7.53602e6i			0.583377i
$700$	−2.55331e6	+	2.55331e6i	−0.196951	+	0.196951i
$701$	3.83646e6			0.294874			0.147437	−	0.989071i	$-0.452898\pi$
$701$	3.83646e6			0.294874			0.147437	+	0.989071i	$0.452898\pi$
$702$	2.35019e6	−	2.35019e6i	0.179995	−	0.179995i
$703$	−8.04373e6	−	8.04373e6i	−0.613860	−	0.613860i
$704$	6.62961e6	+	6.62961e6i	0.504146	+	0.504146i
$705$		−	1.33028e7i		−	1.00802i
$706$			3.91295e6i			0.295456i
$707$	2.41975e6	+	2.41975e6i	0.182063	+	0.182063i
$708$	2.41324e6	+	2.41324e6i	0.180933	+	0.180933i
$709$	425008.	−	425008.i	0.0317528	−	0.0317528i	−0.691052	−	0.722805i	$-0.742853\pi$
$709$	425008.	−	425008.i	0.0317528	−	0.0317528i	0.722805	+	0.691052i	$0.242853\pi$
$710$	1.78697e7			1.33037
$711$	1.64493e6	−	1.64493e6i	0.122032	−	0.122032i
$712$			2.72351e6i			0.201340i
$713$	−1.19069e7			−0.877149
$714$	4.33768e6	−	1.08112e7i	0.318428	−	0.793646i
$715$	−3.24799e7			−2.37602
$716$		−	1.69069e6i		−	0.123249i
$717$	5.09093e6	−	5.09093e6i	0.369827	−	0.369827i
$718$	−7.63472e6			−0.552691
$719$	1.16154e7	−	1.16154e7i	0.837941	−	0.837941i	−0.150647	−	0.988588i	$-0.548136\pi$
$719$	1.16154e7	−	1.16154e7i	0.837941	−	0.837941i	0.988588	+	0.150647i	$0.0481356\pi$
$720$	5.12028e6	+	5.12028e6i	0.368097	+	0.368097i
$721$	1.02518e7	+	1.02518e7i	0.734452	+	0.734452i
$722$		−	1.82381e6i		−	0.130208i
$723$			5.96077e6i			0.424089i
$724$	1.69436e6	+	1.69436e6i	0.120132	+	0.120132i
$725$	−1.02480e7	−	1.02480e7i	−0.724095	−	0.724095i
$726$	−1.15909e7	+	1.15909e7i	−0.816162	+	0.816162i
$727$	−2.46746e7			−1.73146			−0.865732	−	0.500507i	$-0.833147\pi$
$727$	−2.46746e7			−1.73146			−0.865732	+	0.500507i	$0.833147\pi$
$728$	1.09243e7	−	1.09243e7i	0.763951	−	0.763951i
$729$			531441.i			0.0370370i
$730$	426174.			0.0295992
$731$	5.72678e6	−	1.42734e7i	0.396385	−	0.987945i
$732$	−909253.			−0.0627202
$733$			1.98692e7i			1.36591i	0.730462	+	0.682953i	$0.239305\pi$
$733$			1.98692e7i			1.36591i	−0.730462	+	0.682953i	$0.760695\pi$
$734$	−821406.	+	821406.i	−0.0562753	+	0.0562753i
$735$	−6.61625e6			−0.451745
$736$	−8.22454e6	+	8.22454e6i	−0.559651	+	0.559651i
$737$	−2.70654e7	−	2.70654e7i	−1.83546	−	1.83546i
$738$	−5.48352e6	−	5.48352e6i	−0.370611	−	0.370611i
$739$			1.53847e7i			1.03628i	0.855294	+	0.518142i	$0.173376\pi$
$739$			1.53847e7i			1.03628i	−0.855294	+	0.518142i	$0.826624\pi$
$740$			6.22942e6i			0.418185i
$741$	6.52870e6	+	6.52870e6i	0.436799	+	0.436799i
$742$	1.52847e7	+	1.52847e7i	1.01917	+	1.01917i
$743$	686550.	−	686550.i	0.0456247	−	0.0456247i	−0.683926	−	0.729551i	$-0.739729\pi$
$743$	686550.	−	686550.i	0.0456247	−	0.0456247i	0.729551	+	0.683926i	$0.239729\pi$
$744$	−4.94758e6			−0.327688
$745$	−8.86836e6	+	8.86836e6i	−0.585400	+	0.585400i
$746$			3.43773e7i			2.26164i
$747$	2.86401e6			0.187790
$748$	−3.54237e6	−	8.28961e6i	−0.231494	−	0.541727i
$749$	2.34586e7			1.52791
$750$			5.09425e6i			0.330694i
$751$	7.55138e6	−	7.55138e6i	0.488570	−	0.488570i	−0.419285	−	0.907855i	$-0.637719\pi$
$751$	7.55138e6	−	7.55138e6i	0.488570	−	0.488570i	0.907855	+	0.419285i	$0.137719\pi$
$752$	2.62159e7			1.69052
$753$	5.38445e6	−	5.38445e6i	0.346062	−	0.346062i
$754$	−2.43942e7	−	2.43942e7i	−1.56264	−	1.56264i
$755$	1.03073e7	+	1.03073e7i	0.658078	+	0.658078i
$756$		−	1.37436e6i		−	0.0874576i
$757$		−	1.95676e7i		−	1.24107i	−0.784177	−	0.620537i	$-0.786915\pi$
$757$		−	1.95676e7i		−	1.24107i	0.784177	−	0.620537i	$-0.213085\pi$
$758$	1.27008e7	+	1.27008e7i	0.802896	+	0.802896i
$759$	1.23536e7	+	1.23536e7i	0.778374	+	0.778374i
$760$	−1.00889e7	+	1.00889e7i	−0.633595	+	0.633595i
$761$	−2.10792e7			−1.31945			−0.659725	−	0.751507i	$-0.729327\pi$
$761$	−2.10792e7			−1.31945			−0.659725	+	0.751507i	$0.729327\pi$
$762$	−269113.	+	269113.i	−0.0167898	+	0.0167898i
$763$		−	1.93731e6i		−	0.120472i
$764$	−4.25538e6			−0.263758
$765$	2.69262e6	+	6.30110e6i	0.166350	+	0.389281i
$766$	−1.05643e7			−0.650530
$767$			2.29312e7i			1.40747i
$768$	−6.35086e6	+	6.35086e6i	−0.388534	+	0.388534i
$769$	−5.58168e6			−0.340368			−0.170184	−	0.985412i	$-0.554436\pi$
$769$	−5.58168e6			−0.340368			−0.170184	+	0.985412i	$0.554436\pi$
$770$	−3.60638e7	+	3.60638e7i	−2.19202	+	2.19202i
$771$	3.09471e6	+	3.09471e6i	0.187492	+	0.187492i
$772$	4.96947e6	+	4.96947e6i	0.300100	+	0.300100i
$773$		−	2.19311e7i		−	1.32012i	−0.751214	−	0.660059i	$-0.770531\pi$
$773$		−	2.19311e7i		−	1.32012i	0.751214	−	0.660059i	$-0.229469\pi$
$774$		−	6.89036e6i		−	0.413418i
$775$	5.49411e6	+	5.49411e6i	0.328582	+	0.328582i
$776$	3.71622e6	+	3.71622e6i	0.221537	+	0.221537i
$777$	−8.04505e6	+	8.04505e6i	−0.478053	+	0.478053i
$778$	6.40656e6			0.379469
$779$	1.52329e7	−	1.52329e7i	0.899374	−	0.899374i
$780$		−	5.05611e6i		−	0.297564i
$781$	2.52571e7			1.48168
$782$	−2.11968e7	+	9.05796e6i	−1.23952	+	0.529680i
$783$	5.51619e6			0.321540
$784$		−	1.30387e7i		−	0.757608i
$785$	−6.60398e6	+	6.60398e6i	−0.382500	+	0.382500i
$786$	−2.68942e6			−0.155275
$787$	−1.88933e7	+	1.88933e7i	−1.08735	+	1.08735i	−0.0915508	+	0.995800i	$0.529182\pi$
$787$	−1.88933e7	+	1.88933e7i	−1.08735	+	1.08735i	−0.995800	+	0.0915508i	$0.970818\pi$
$788$	6.52184e6	+	6.52184e6i	0.374157	+	0.374157i
$789$	−9.49138e6	−	9.49138e6i	−0.542796	−	0.542796i
$790$		−	1.34384e7i		−	0.766090i
$791$		−	8.82357e6i		−	0.501422i
$792$	5.13319e6	+	5.13319e6i	0.290787	+	0.290787i
$793$	−4.31997e6	−	4.31997e6i	−0.243948	−	0.243948i
$794$	2.85108e7	−	2.85108e7i	1.60493	−	1.60493i
$795$	−1.27152e7			−0.713521
$796$	5.99972e6	−	5.99972e6i	0.335621	−	0.335621i
$797$		−	2.48255e7i		−	1.38437i	−0.721720	−	0.692185i	$-0.756648\pi$
$797$		−	2.48255e7i		−	1.38437i	0.721720	−	0.692185i	$-0.243352\pi$
$798$	1.44981e7			0.805945
$799$	2.30240e7	+	9.23773e6i	1.27589	+	0.511915i
$800$	7.59000e6			0.419292
$801$			1.62792e6i			0.0896505i
$802$	−1.86929e7	+	1.86929e7i	−1.02622	+	1.02622i
$803$	602356.			0.0329659
$804$	4.21324e6	−	4.21324e6i	0.229866	−	0.229866i
$805$	2.42841e7	+	2.42841e7i	1.32078	+	1.32078i
$806$	1.30781e7	+	1.30781e7i	0.709098	+	0.709098i
$807$			3.75968e6i			0.203220i
$808$		−	2.81377e6i		−	0.151621i
$809$	1.90044e7	+	1.90044e7i	1.02090	+	1.02090i	0.999777	+	0.0211240i	$0.00672449\pi$
$809$	1.90044e7	+	1.90044e7i	1.02090	+	1.02090i	0.0211240	+	0.999777i	$0.493276\pi$
$810$	2.17083e6	+	2.17083e6i	0.116255	+	0.116255i
$811$	1.43669e7	−	1.43669e7i	0.767026	−	0.767026i	−0.210556	−	0.977582i	$-0.567527\pi$
$811$	1.43669e7	−	1.43669e7i	0.767026	−	0.767026i	0.977582	+	0.210556i	$0.0675274\pi$
$812$	−1.42655e7			−0.759270
$813$	−1.25874e7	+	1.25874e7i	−0.667895	+	0.667895i
$814$			3.34349e7i			1.76864i
$815$	−2.31428e7			−1.22046
$816$	−1.24176e7	+	5.30638e6i	−0.652850	+	0.278980i
$817$	1.91411e7			1.00325
$818$		−	1.74079e7i		−	0.909627i
$819$	6.52977e6	−	6.52977e6i	0.340164	−	0.340164i
$820$	−1.17971e7			−0.612687
$821$	−6.47314e6	+	6.47314e6i	−0.335164	+	0.335164i	−0.854544	−	0.519380i	$-0.826163\pi$
$821$	−6.47314e6	+	6.47314e6i	−0.335164	+	0.335164i	0.519380	+	0.854544i	$0.326163\pi$
$822$	8.36818e6	+	8.36818e6i	0.431968	+	0.431968i
$823$	−2.09522e7	−	2.09522e7i	−1.07828	−	1.07828i	−0.996664	−	0.0816111i	$-0.973993\pi$
$823$	−2.09522e7	−	2.09522e7i	−1.07828	−	1.07828i	−0.0816111	−	0.996664i	$-0.526007\pi$
$824$		−	1.19212e7i		−	0.611647i
$825$		−	1.14005e7i		−	0.583160i
$826$	2.54614e7	+	2.54614e7i	1.29847	+	1.29847i
$827$	−5.59273e6	−	5.59273e6i	−0.284355	−	0.284355i	0.550488	−	0.834843i	$-0.314442\pi$
$827$	−5.59273e6	−	5.59273e6i	−0.284355	−	0.284355i	−0.834843	+	0.550488i	$0.814442\pi$
$828$	−1.92306e6	+	1.92306e6i	−0.0974805	+	0.0974805i
$829$	2.39231e7			1.20901			0.604506	−	0.796601i	$-0.293371\pi$
$829$	2.39231e7			1.20901			0.604506	+	0.796601i	$0.293371\pi$
$830$	1.16989e7	−	1.16989e7i	0.589453	−	0.589453i
$831$			1.55605e7i			0.781666i
$832$	−9.80653e6			−0.491142
$833$	4.59446e6	−	1.14512e7i	0.229415	−	0.571792i
$834$	6.68540e6			0.332822
$835$			455607.i			0.0226139i
$836$	7.93355e6	−	7.93355e6i	0.392601	−	0.392601i
$837$	−2.95731e6			−0.145909
$838$	6.59088e6	−	6.59088e6i	0.324215	−	0.324215i
$839$	−6.75264e6	−	6.75264e6i	−0.331184	−	0.331184i	0.521852	−	0.853036i	$-0.325241\pi$
$839$	−6.75264e6	−	6.75264e6i	−0.331184	−	0.331184i	−0.853036	+	0.521852i	$0.825241\pi$
$840$	1.00906e7	+	1.00906e7i	0.493422	+	0.493422i
$841$		−	3.67453e7i		−	1.79148i
$842$			2.23657e7i			1.08718i
$843$	−8.82853e6	−	8.82853e6i	−0.427877	−	0.427877i
$844$	−3.59621e6	−	3.59621e6i	−0.173776	−	0.173776i
$845$	5.38282e6	−	5.38282e6i	0.259339	−	0.259339i
$846$	1.11147e7			0.533913
$847$	−3.22043e7	+	3.22043e7i	−1.54243	+	1.54243i
$848$		−	2.50580e7i		−	1.19662i
$849$	3.95150e6			0.188145
$850$	1.39603e7	+	5.60118e6i	0.662746	+	0.265908i
$851$	2.25139e7			1.06568
$852$			3.93174e6i			0.185561i
$853$	−1.12476e7	+	1.12476e7i	−0.529283	+	0.529283i	−0.920359	−	0.391075i	$-0.872103\pi$
$853$	−1.12476e7	+	1.12476e7i	−0.529283	+	0.529283i	0.391075	+	0.920359i	$0.372103\pi$
$854$	−9.59327e6			−0.450113
$855$	−6.03045e6	+	6.03045e6i	−0.282120	+	0.282120i
$856$	−1.36392e7	−	1.36392e7i	−0.636216	−	0.636216i
$857$	−848267.	−	848267.i	−0.0394530	−	0.0394530i	0.687105	−	0.726558i	$-0.258881\pi$
$857$	−848267.	−	848267.i	−0.0394530	−	0.0394530i	−0.726558	+	0.687105i	$0.758881\pi$
$858$		−	2.71375e7i		−	1.25849i
$859$		−	1.12704e7i		−	0.521144i	−0.965454	−	0.260572i	$-0.916089\pi$
$859$		−	1.12704e7i		−	0.521144i	0.965454	−	0.260572i	$-0.0839111\pi$
$860$	−7.41184e6	−	7.41184e6i	−0.341727	−	0.341727i
$861$	−1.52354e7	−	1.52354e7i	−0.700402	−	0.700402i
$862$	−1.94124e6	+	1.94124e6i	−0.0889838	+	0.0889838i
$863$	−2.04907e7			−0.936547			−0.468274	−	0.883584i	$-0.655124\pi$
$863$	−2.04907e7			−0.936547			−0.468274	+	0.883584i	$0.655124\pi$
$864$	−2.04273e6	+	2.04273e6i	−0.0930951	+	0.0930951i
$865$			2.33156e7i			1.05951i
$866$	4.72037e6			0.213885
$867$	−1.27755e7	+	284681.i	−0.577207	+	0.0128621i
$868$	7.64792e6			0.344544
$869$		−	1.89939e7i		−	0.853227i
$870$	2.25325e7	−	2.25325e7i	1.00928	−	1.00928i
$871$	4.00352e7			1.78812
$872$	−1.12638e6	+	1.12638e6i	−0.0501643	+	0.0501643i
$873$	2.22129e6	+	2.22129e6i	0.0986438	+	0.0986438i
$874$	−2.02864e7	−	2.02864e7i	−0.898309	−	0.898309i
$875$			1.41539e7i			0.624964i
$876$			93768.0i			0.00412852i
$877$	1.81186e7	+	1.81186e7i	0.795473	+	0.795473i	0.982378	−	0.186905i	$-0.0598458\pi$
$877$	1.81186e7	+	1.81186e7i	0.795473	+	0.795473i	−0.186905	+	0.982378i	$0.559846\pi$
$878$	4.29424e6	+	4.29424e6i	0.187997	+	0.187997i
$879$	−3.25998e6	+	3.25998e6i	−0.142312	+	0.142312i
$880$	5.91236e7			2.57368
$881$	−1.99087e7	+	1.99087e7i	−0.864179	+	0.864179i	−0.991820	−	0.127642i	$-0.959259\pi$
$881$	−1.99087e7	+	1.99087e7i	−0.864179	+	0.864179i	0.127642	+	0.991820i	$0.459259\pi$
$882$		−	5.52798e6i		−	0.239274i
$883$	−3.16029e7			−1.36403			−0.682017	−	0.731336i	$-0.738897\pi$
$883$	−3.16029e7			−1.36403			−0.682017	+	0.731336i	$0.738897\pi$
$884$	8.75094e6	+	3.51107e6i	0.376638	+	0.151115i
$885$	−2.11812e7			−0.909059
$886$		−	3.75370e7i		−	1.60648i
$887$	−357604.	+	357604.i	−0.0152613	+	0.0152613i	−0.714696	−	0.699435i	$-0.753435\pi$
$887$	−357604.	+	357604.i	−0.0152613	+	0.0152613i	0.699435	+	0.714696i	$0.253435\pi$
$888$	9.35504e6			0.398119
$889$	−747704.	+	747704.i	−0.0317304	+	0.0317304i
$890$	6.64973e6	+	6.64973e6i	0.281403	+	0.281403i
$891$	3.06826e6	+	3.06826e6i	0.129478	+	0.129478i
$892$			638793.i			0.0268812i
$893$			3.08760e7i			1.29566i
$894$	−7.40964e6	−	7.40964e6i	−0.310065	−	0.310065i
$895$	7.41966e6	+	7.41966e6i	0.309618	+	0.309618i
$896$	−2.56665e7	+	2.56665e7i	−1.06806	+	1.06806i
$897$	−1.82734e7			−0.758296
$898$	−2.01577e7	+	2.01577e7i	−0.834160	+	0.834160i
$899$			3.06960e7i			1.26672i
$900$	1.77470e6			0.0730328
$901$	8.82973e6	−	2.20071e7i	0.362356	−	0.903131i
$902$	−6.33179e7			−2.59125
$903$		−	1.91442e7i		−	0.781300i
$904$	−5.13017e6	+	5.13017e6i	−0.208790	+	0.208790i
$905$	−1.48715e7			−0.603579
$906$	−8.61189e6	+	8.61189e6i	−0.348560	+	0.348560i
$907$	−2.16729e7	−	2.16729e7i	−0.874778	−	0.874778i	0.118210	−	0.992989i	$-0.462284\pi$
$907$	−2.16729e7	−	2.16729e7i	−0.874778	−	0.874778i	−0.992989	+	0.118210i	$0.962284\pi$
$908$	8.88342e6	+	8.88342e6i	0.357574	+	0.357574i
$909$		−	1.68187e6i		−	0.0675123i
$910$		−	5.33456e7i		−	2.13548i
$911$	−1.83069e7	−	1.83069e7i	−0.730835	−	0.730835i	0.239950	−	0.970785i	$-0.422869\pi$
$911$	−1.83069e7	−	1.83069e7i	−0.730835	−	0.730835i	−0.970785	+	0.239950i	$0.922869\pi$
$912$	−1.18843e7	−	1.18843e7i	−0.473135	−	0.473135i
$913$	1.65352e7	−	1.65352e7i	0.656498	−	0.656498i
$914$	−4.43245e7			−1.75501
$915$	3.99028e6	−	3.99028e6i	0.157562	−	0.157562i
$916$		−	9.24366e6i		−	0.364003i
$917$	−7.47229e6			−0.293448
$918$	−5.26466e6	+	2.24973e6i	−0.206188	+	0.0881095i
$919$	−7.05793e6			−0.275669			−0.137835	−	0.990455i	$-0.544014\pi$
$919$	−7.05793e6			−0.275669			−0.137835	+	0.990455i	$0.544014\pi$
$920$		−	2.82383e7i		−	1.09994i
$921$	1.77635e6	−	1.77635e6i	0.0690047	−	0.0690047i
$922$	−1.06131e7			−0.411163
$923$	−1.86802e7	+	1.86802e7i	−0.721733	+	0.721733i
$924$	−7.93485e6	−	7.93485e6i	−0.305745	−	0.305745i
$925$	−1.03885e7	−	1.03885e7i	−0.399206	−	0.399206i
$926$			4.07951e7i			1.56344i
$927$		−	7.12562e6i		−	0.272348i
$928$	2.12029e7	+	2.12029e7i	0.808212	+	0.808212i
$929$	−1.40147e7	−	1.40147e7i	−0.532776	−	0.532776i	0.388622	−	0.921397i	$-0.372951\pi$
$929$	−1.40147e7	−	1.40147e7i	−0.532776	−	0.532776i	−0.921397	+	0.388622i	$0.872951\pi$
$930$	−1.20800e7	+	1.20800e7i	−0.457994	+	0.457994i
$931$	1.53564e7			0.580652
$932$	−6.77298e6	+	6.77298e6i	−0.255411	+	0.255411i
$933$			2.76077e7i			1.03831i
$934$	5.55527e7			2.08371
$935$	5.19250e7	+	2.08334e7i	1.94244	+	0.779349i
$936$	−7.59303e6			−0.283286
$937$			3.95512e7i			1.47167i	0.677160	+	0.735836i	$0.263210\pi$
$937$			3.95512e7i			1.47167i	−0.677160	+	0.735836i	$0.736790\pi$
$938$	4.44526e7	−	4.44526e7i	1.64964	−	1.64964i
$939$	−1.91836e7			−0.710013
$940$	1.19558e7	−	1.19558e7i	0.441327	−	0.441327i
$941$	2.35330e7	+	2.35330e7i	0.866371	+	0.866371i	0.992069	−	0.125697i	$-0.0401168\pi$
$941$	2.35330e7	+	2.35330e7i	0.866371	+	0.866371i	−0.125697	+	0.992069i	$0.540117\pi$
$942$	−5.51772e6	−	5.51772e6i	−0.202597	−	0.202597i
$943$			4.26360e7i			1.56134i
$944$		−	4.17419e7i		−	1.52455i
$945$	6.03144e6	+	6.03144e6i	0.219706	+	0.219706i
$946$	−3.97813e7	−	3.97813e7i	−1.44528	−	1.44528i
$947$	1.87799e7	−	1.87799e7i	0.680486	−	0.680486i	−0.279624	−	0.960110i	$-0.590210\pi$
$947$	1.87799e7	−	1.87799e7i	0.680486	−	0.680486i	0.960110	+	0.279624i	$0.0902097\pi$
$948$	2.95675e6			0.106855
$949$	−445503.	+	445503.i	−0.0160578	+	0.0160578i
$950$			1.87212e7i			0.673016i
$951$	2.82366e7			1.01242
$952$	−2.44716e7	+	1.04573e7i	−0.875124	+	0.373963i
$953$	9.45763e6			0.337326			0.168663	−	0.985674i	$-0.446055\pi$
$953$	9.45763e6			0.337326			0.168663	+	0.985674i	$0.446055\pi$
$954$		−	1.06238e7i		−	0.377927i
$955$	1.86749e7	−	1.86749e7i	0.662596	−	0.662596i
$956$	9.15093e6			0.323832
$957$	3.18476e7	−	3.18476e7i	1.12408	−	1.12408i
$958$	1.26716e7	+	1.26716e7i	0.446084	+	0.446084i
$959$	2.32502e7	+	2.32502e7i	0.816357	+	0.816357i
$960$		−	9.05812e6i		−	0.317220i
$961$			1.21726e7i			0.425183i
$962$	−2.47285e7	−	2.47285e7i	−0.861509	−	0.861509i
$963$	−8.15254e6	−	8.15254e6i	−0.283287	−	0.283287i
$964$	−5.35723e6	+	5.35723e6i	−0.185673	+	0.185673i
$965$	−4.36173e7			−1.50779
$966$	−2.02897e7	+	2.02897e7i	−0.699573	+	0.699573i
$967$		−	3.85246e7i		−	1.32486i	−0.749122	−	0.662432i	$-0.769524\pi$
$967$		−	3.85246e7i		−	1.32486i	0.749122	−	0.662432i	$-0.230476\pi$
$968$	3.74482e7			1.28452
$969$	−6.24962e6	−	1.46250e7i	−0.213818	−	0.500363i
$970$	1.81470e7			0.619265
$971$		−	1.38466e7i		−	0.471299i	−0.971838	−	0.235649i	$-0.924278\pi$
$971$		−	1.38466e7i		−	0.471299i	0.971838	−	0.235649i	$-0.0757217\pi$
$972$	−477632.	+	477632.i	−0.0162154	+	0.0162154i
$973$	1.85748e7			0.628986
$974$	2.67268e7	−	2.67268e7i	0.902711	−	0.902711i
$975$	8.43180e6	+	8.43180e6i	0.284059	+	0.284059i
$976$	7.86369e6	+	7.86369e6i	0.264242	+	0.264242i
$977$		−	5.49648e7i		−	1.84225i	−0.389270	−	0.921123i	$-0.627273\pi$
$977$		−	5.49648e7i		−	1.84225i	0.389270	−	0.921123i	$-0.372727\pi$
$978$		−	1.93362e7i		−	0.646433i
$979$	9.39876e6	+	9.39876e6i	0.313411	+	0.313411i
$980$	−5.94635e6	−	5.94635e6i	−0.197781	−	0.197781i
$981$	−673271.	+	673271.i	−0.0223366	+	0.0223366i
$982$	−2.14052e7			−0.708338
$983$	152256.	−	152256.i	0.00502564	−	0.00502564i	−0.704589	−	0.709615i	$-0.748869\pi$
$983$	152256.	−	152256.i	0.00502564	−	0.00502564i	0.709615	+	0.704589i	$0.248869\pi$
$984$			1.77163e7i			0.583290i
$985$	−5.72425e7			−1.87987
$986$	2.33515e7	+	5.46456e7i	0.764930	+	1.79004i
$987$	3.08810e7			1.00902
$988$			1.17353e7i			0.382474i
$989$	−2.67873e7	+	2.67873e7i	−0.870840	+	0.870840i
$990$	2.50664e7			0.812838
$991$	−1.41715e7	+	1.41715e7i	−0.458386	+	0.458386i	−0.898125	−	0.439739i	$-0.855071\pi$
$991$	−1.41715e7	+	1.41715e7i	−0.458386	+	0.458386i	0.439739	+	0.898125i	$0.355071\pi$
$992$	−1.13672e7	−	1.13672e7i	−0.366753	−	0.366753i
$993$	1.35451e7	+	1.35451e7i	0.435921	+	0.435921i
$994$			4.14826e7i			1.33168i
$995$			5.26599e7i			1.68625i
$996$	2.57402e6	+	2.57402e6i	0.0822174	+	0.0822174i
$997$	3.76576e7	+	3.76576e7i	1.19982	+	1.19982i	0.974221	+	0.225596i	$0.0724328\pi$
$997$	3.76576e7	+	3.76576e7i	1.19982	+	1.19982i	0.225596	+	0.974221i	$0.427567\pi$
$998$	−4.81542e7	+	4.81542e7i	−1.53041	+	1.53041i
$999$	5.59178e6			0.177270

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.6.e.a.4.4	✓	32
3.2	odd	2		153.6.f.c.55.13		32
17.8	even	8		867.6.a.o.1.4		16
17.9	even	8		867.6.a.n.1.4		16
17.13	even	4	inner	51.6.e.a.13.13	yes	32
51.47	odd	4		153.6.f.c.64.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.6.e.a.4.4	✓	32	1.1	even	1	trivial
51.6.e.a.13.13	yes	32	17.13	even	4	inner
153.6.f.c.55.13		32	3.2	odd	2
153.6.f.c.64.4		32	51.47	odd	4
867.6.a.n.1.4		16	17.9	even	8
867.6.a.o.1.4		16	17.8	even	8

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:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	51.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-6.59084i q^{2} +(-6.36396 + 6.36396i) q^{3} -11.4392 q^{4} +(50.2012 - 50.2012i) q^{5} +(41.9439 + 41.9439i) q^{6} +(116.537 + 116.537i) q^{7} -135.513i q^{8} -81.0000i q^{9} +O(q^{10})\)	\(q-6.59084i q^{2} +(-6.36396 + 6.36396i) q^{3} -11.4392 q^{4} +(50.2012 - 50.2012i) q^{5} +(41.9439 + 41.9439i) q^{6} +(116.537 + 116.537i) q^{7} -135.513i q^{8} -81.0000i q^{9} +(-330.868 - 330.868i) q^{10} +(-467.651 - 467.651i) q^{11} +(72.7986 - 72.7986i) q^{12} +691.750 q^{13} +(768.077 - 768.077i) q^{14} +638.958i q^{15} -1259.20 q^{16} +(-1105.89 - 443.705i) q^{17} -533.858 q^{18} -1483.03i q^{19} +(-574.262 + 574.262i) q^{20} -1483.27 q^{21} +(-3082.21 + 3082.21i) q^{22} +(2075.45 + 2075.45i) q^{23} +(862.399 + 862.399i) q^{24} -1915.33i q^{25} -4559.21i q^{26} +(515.481 + 515.481i) q^{27} +(-1333.09 - 1333.09i) q^{28} +(5350.53 - 5350.53i) q^{29} +4211.27 q^{30} +(-2868.49 + 2868.49i) q^{31} +3962.77i q^{32} +5952.22 q^{33} +(-2924.39 + 7288.72i) q^{34} +11700.6 q^{35} +926.575i q^{36} +(5423.85 - 5423.85i) q^{37} -9774.42 q^{38} +(-4402.27 + 4402.27i) q^{39} +(-6802.92 - 6802.92i) q^{40} +(10271.5 + 10271.5i) q^{41} +9776.03i q^{42} +12906.7i q^{43} +(5349.55 + 5349.55i) q^{44} +(-4066.30 - 4066.30i) q^{45} +(13679.0 - 13679.0i) q^{46} -20819.5 q^{47} +(8013.49 - 8013.49i) q^{48} +10354.8i q^{49} -12623.6 q^{50} +(9861.54 - 4214.09i) q^{51} -7913.06 q^{52} +19900.0i q^{53} +(3397.45 - 3397.45i) q^{54} -46953.3 q^{55} +(15792.3 - 15792.3i) q^{56} +(9437.95 + 9437.95i) q^{57} +(-35264.5 - 35264.5i) q^{58} +33149.6i q^{59} -7309.16i q^{60} +(-6244.99 - 6244.99i) q^{61} +(18905.8 + 18905.8i) q^{62} +(9439.50 - 9439.50i) q^{63} -14176.4 q^{64} +(34726.7 - 34726.7i) q^{65} -39230.2i q^{66} +57875.2 q^{67} +(12650.4 + 5075.63i) q^{68} -26416.2 q^{69} -77116.9i q^{70} +(-27004.2 + 27004.2i) q^{71} -10976.6 q^{72} +(-644.023 + 644.023i) q^{73} +(-35747.7 - 35747.7i) q^{74} +(12189.1 + 12189.1i) q^{75} +16964.7i q^{76} -108997. i q^{77} +(29014.7 + 29014.7i) q^{78} +(20307.8 + 20307.8i) q^{79} +(-63213.4 + 63213.4i) q^{80} -6561.00 q^{81} +(67697.8 - 67697.8i) q^{82} +35358.1i q^{83} +16967.5 q^{84} +(-77791.4 + 33242.3i) q^{85} +85066.2 q^{86} +68101.2i q^{87} +(-63372.8 + 63372.8i) q^{88} -20097.8 q^{89} +(-26800.3 + 26800.3i) q^{90} +(80614.5 + 80614.5i) q^{91} +(-23741.5 - 23741.5i) q^{92} -36510.0i q^{93} +137218. i q^{94} +(-74450.0 - 74450.0i) q^{95} +(-25218.9 - 25218.9i) q^{96} +(-27423.3 + 27423.3i) q^{97} +68246.6 q^{98} +(-37879.7 + 37879.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 576 q^{4} + 76 q^{5} - 180 q^{6} + 236 q^{7}+O(q^{10}) \) 32 * q - 576 * q^4 + 76 * q^5 - 180 * q^6 + 236 * q^7	\( 32 q - 576 q^{4} + 76 q^{5} - 180 q^{6} + 236 q^{7} + 724 q^{10} - 672 q^{11} - 2684 q^{13} + 2832 q^{14} + 8824 q^{16} - 4868 q^{17} + 1296 q^{18} + 4464 q^{20} - 3528 q^{21} - 1628 q^{22} + 5584 q^{23} + 10872 q^{24} - 36792 q^{28} + 4820 q^{29} - 1728 q^{30} + 13880 q^{31} + 7236 q^{33} + 5068 q^{34} - 12152 q^{35} - 33328 q^{37} - 29256 q^{38} - 11160 q^{39} - 43288 q^{40} - 50932 q^{41} + 116000 q^{44} - 6156 q^{45} + 47596 q^{46} - 16552 q^{47} + 27360 q^{48} + 139080 q^{50} + 12924 q^{51} + 186888 q^{52} - 14580 q^{54} - 129428 q^{55} - 117024 q^{56} + 19440 q^{57} - 212912 q^{58} + 118952 q^{61} - 219736 q^{62} + 19116 q^{63} - 143848 q^{64} + 220976 q^{65} + 98632 q^{67} + 367680 q^{68} + 156060 q^{69} - 205512 q^{71} - 62208 q^{72} - 40924 q^{73} - 178760 q^{74} - 58896 q^{75} + 87012 q^{78} - 309916 q^{79} - 664992 q^{80} - 209952 q^{81} + 350116 q^{82} + 6264 q^{84} + 335336 q^{85} + 1139576 q^{86} - 307696 q^{88} - 62680 q^{89} + 58644 q^{90} + 174460 q^{91} - 94256 q^{92} + 367240 q^{95} - 508824 q^{96} - 299020 q^{97} - 1191536 q^{98} - 54432 q^{99}+O(q^{100}) \) 32 * q - 576 * q^4 + 76 * q^5 - 180 * q^6 + 236 * q^7 + 724 * q^10 - 672 * q^11 - 2684 * q^13 + 2832 * q^14 + 8824 * q^16 - 4868 * q^17 + 1296 * q^18 + 4464 * q^20 - 3528 * q^21 - 1628 * q^22 + 5584 * q^23 + 10872 * q^24 - 36792 * q^28 + 4820 * q^29 - 1728 * q^30 + 13880 * q^31 + 7236 * q^33 + 5068 * q^34 - 12152 * q^35 - 33328 * q^37 - 29256 * q^38 - 11160 * q^39 - 43288 * q^40 - 50932 * q^41 + 116000 * q^44 - 6156 * q^45 + 47596 * q^46 - 16552 * q^47 + 27360 * q^48 + 139080 * q^50 + 12924 * q^51 + 186888 * q^52 - 14580 * q^54 - 129428 * q^55 - 117024 * q^56 + 19440 * q^57 - 212912 * q^58 + 118952 * q^61 - 219736 * q^62 + 19116 * q^63 - 143848 * q^64 + 220976 * q^65 + 98632 * q^67 + 367680 * q^68 + 156060 * q^69 - 205512 * q^71 - 62208 * q^72 - 40924 * q^73 - 178760 * q^74 - 58896 * q^75 + 87012 * q^78 - 309916 * q^79 - 664992 * q^80 - 209952 * q^81 + 350116 * q^82 + 6264 * q^84 + 335336 * q^85 + 1139576 * q^86 - 307696 * q^88 - 62680 * q^89 + 58644 * q^90 + 174460 * q^91 - 94256 * q^92 + 367240 * q^95 - 508824 * q^96 - 299020 * q^97 - 1191536 * q^98 - 54432 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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