LMFDB - Embedded newform 294.8.e.v.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,8,Mod(67,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("294.67");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	294.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$91.8411974923$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.2
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	294.67
Dual form			294.8.e.v.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.00000 + 6.92820i) q^{2} +(-13.5000 + 23.3827i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-110.251 - 190.961i) q^{5} -216.000 q^{6} -512.000 q^{8} +(-364.500 - 631.333i) q^{9} +(882.010 - 1527.69i) q^{10} +(-1902.72 + 3295.60i) q^{11} +(-864.000 - 1496.49i) q^{12} -14144.9 q^{13} +5953.57 q^{15} +(-2048.00 - 3547.24i) q^{16} +(-18453.5 + 31962.4i) q^{17} +(2916.00 - 5050.66i) q^{18} +(27799.3 + 48149.8i) q^{19} +14112.2 q^{20} -30443.5 q^{22} +(3199.24 + 5541.24i) q^{23} +(6912.00 - 11971.9i) q^{24} +(14751.8 - 25550.9i) q^{25} +(-56579.6 - 97998.7i) q^{26} +19683.0 q^{27} -76212.3 q^{29} +(23814.3 + 41247.5i) q^{30} +(56994.7 - 98717.7i) q^{31} +(16384.0 - 28377.9i) q^{32} +(-51373.4 - 88981.3i) q^{33} -295256. q^{34} +46656.0 q^{36} +(111964. + 193928. i) q^{37} +(-222394. + 385198. i) q^{38} +(190956. - 330746. i) q^{39} +(56448.6 + 97771.9i) q^{40} -557937. q^{41} +11062.0 q^{43} +(-121774. - 210919. i) q^{44} +(-80373.2 + 139210. i) q^{45} +(-25593.9 + 44329.9i) q^{46} +(-123498. - 213904. i) q^{47} +110592. q^{48} +236029. q^{50} +(-498244. - 862984. i) q^{51} +(452637. - 783990. i) q^{52} +(599552. - 1.03845e6i) q^{53} +(78732.0 + 136368. i) q^{54} +839108. q^{55} -1.50116e6 q^{57} +(-304849. - 528014. i) q^{58} +(838966. - 1.45313e6i) q^{59} +(-190514. + 329980. i) q^{60} +(-1.20784e6 - 2.09204e6i) q^{61} +911915. q^{62} +262144. q^{64} +(1.55949e6 + 2.70112e6i) q^{65} +(410987. - 711851. i) q^{66} +(1.53718e6 - 2.66248e6i) q^{67} +(-1.18102e6 - 2.04559e6i) q^{68} -172759. q^{69} +2.91784e6 q^{71} +(186624. + 323242. i) q^{72} +(-1.60749e6 + 2.78425e6i) q^{73} +(-895713. + 1.55142e6i) q^{74} +(398299. + 689874. i) q^{75} -3.55831e6 q^{76} +3.05530e6 q^{78} +(-2.67331e6 - 4.63032e6i) q^{79} +(-451589. + 782175. i) q^{80} +(-265720. + 460241. i) q^{81} +(-2.23175e6 - 3.86550e6i) q^{82} +4.28665e6 q^{83} +8.13808e6 q^{85} +(44248.1 + 76639.9i) q^{86} +(1.02887e6 - 1.78205e6i) q^{87} +(974192. - 1.68735e6i) q^{88} +(-1.47625e6 - 2.55694e6i) q^{89} -1.28597e6 q^{90} -409502. q^{92} +(1.53886e6 + 2.66538e6i) q^{93} +(987981. - 1.71123e6i) q^{94} +(6.12981e6 - 1.06171e7i) q^{95} +(442368. + 766204. i) q^{96} -1.15030e7 q^{97} +2.77416e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 16 q^{2} - 54 q^{3} - 128 q^{4} - 540 q^{5} - 864 q^{6} - 2048 q^{8} - 1458 q^{9} + 4320 q^{10} - 1196 q^{11} - 3456 q^{12} - 24624 q^{13} + 29160 q^{15} - 8192 q^{16} - 29484 q^{17} + 11664 q^{18}+ \cdots + 1743768 q^{99}+O(q^{100}) $ 4 * q + 16 * q^2 - 54 * q^3 - 128 * q^4 - 540 * q^5 - 864 * q^6 - 2048 * q^8 - 1458 * q^9 + 4320 * q^10 - 1196 * q^11 - 3456 * q^12 - 24624 * q^13 + 29160 * q^15 - 8192 * q^16 - 29484 * q^17 + 11664 * q^18 + 47088 * q^19 + 69120 * q^20 - 19136 * q^22 + 94052 * q^23 + 27648 * q^24 + 5550 * q^25 - 98496 * q^26 + 78732 * q^27 - 341200 * q^29 + 116640 * q^30 + 258984 * q^31 + 65536 * q^32 - 32292 * q^33 - 471744 * q^34 + 186624 * q^36 + 648856 * q^37 - 376704 * q^38 + 332424 * q^39 + 276480 * q^40 - 1211112 * q^41 - 1396960 * q^43 - 76544 * q^44 - 393660 * q^45 - 752416 * q^46 - 816912 * q^47 + 442368 * q^48 + 88800 * q^50 - 796068 * q^51 + 787968 * q^52 + 1923508 * q^53 + 314928 * q^54 + 10800 * q^55 - 2542752 * q^57 - 1364800 * q^58 + 81864 * q^59 - 933120 * q^60 - 1616544 * q^61 + 4143744 * q^62 + 1048576 * q^64 + 2533380 * q^65 + 258336 * q^66 + 5424 * q^67 - 1886976 * q^68 - 5078808 * q^69 - 4985928 * q^71 + 746496 * q^72 - 4710744 * q^73 - 5190848 * q^74 + 149850 * q^75 - 6027264 * q^76 + 5318784 * q^78 - 3416656 * q^79 - 2211840 * q^80 - 1062882 * q^81 - 4844448 * q^82 + 17842896 * q^83 + 11532920 * q^85 - 5587840 * q^86 + 4606200 * q^87 + 612352 * q^88 - 12374532 * q^89 - 6298560 * q^90 - 12038656 * q^92 + 6992568 * q^93 + 6535296 * q^94 + 9540520 * q^95 + 1769472 * q^96 - 22593168 * q^97 + 1743768 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	4.00000	+	6.92820i	0.353553	+	0.612372i
$2$	4.00000	+	6.92820i	0.353553	+	0.612372i
$3$	−13.5000	+	23.3827i	−0.288675	+	0.500000i
$3$	−13.5000	+	23.3827i	−0.288675	+	0.500000i
$4$	−32.0000	+	55.4256i	−0.250000	+	0.433013i
$5$	−110.251	−	190.961i	−0.394447	−	0.683202i	0.598584	−	0.801060i	$-0.295730\pi$
$5$	−110.251	−	190.961i	−0.394447	−	0.683202i	−0.993030	+	0.117858i	$0.962397\pi$
$6$	−216.000			−0.408248
$7$		0			0
$7$		0			0
$8$	−512.000			−0.353553
$9$	−364.500	−	631.333i	−0.166667	−	0.288675i
$10$	882.010	−	1527.69i	0.278916	−	0.483097i
$11$	−1902.72	+	3295.60i	−0.431023	+	0.746553i	−0.996962	−	0.0778940i	$-0.975180\pi$
$11$	−1902.72	+	3295.60i	−0.431023	+	0.746553i	0.565939	+	0.824447i	$0.308514\pi$
$12$	−864.000	−	1496.49i	−0.144338	−	0.250000i
$13$	−14144.9			−1.78566			−0.892828	−	0.450397i	$-0.851282\pi$
$13$	−14144.9			−1.78566			−0.892828	+	0.450397i	$0.851282\pi$
$14$		0			0
$15$	5953.57			0.455468
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	−18453.5	+	31962.4i	−0.910976	+	1.57786i	−0.0982889	+	0.995158i	$0.531337\pi$
$17$	−18453.5	+	31962.4i	−0.910976	+	1.57786i	−0.812688	+	0.582700i	$0.801996\pi$
$18$	2916.00	−	5050.66i	0.117851	−	0.204124i
$19$	27799.3	+	48149.8i	0.929814	+	1.61048i	0.783631	+	0.621227i	$0.213366\pi$
$19$	27799.3	+	48149.8i	0.929814	+	1.61048i	0.146183	+	0.989258i	$0.453301\pi$
$20$	14112.2			0.394447
$21$		0			0
$22$	−30443.5			−0.609558
$23$	3199.24	+	5541.24i	0.0548276	+	0.0949641i	0.892137	−	0.451766i	$-0.149206\pi$
$23$	3199.24	+	5541.24i	0.0548276	+	0.0949641i	−0.837309	+	0.546730i	$0.815872\pi$
$24$	6912.00	−	11971.9i	0.102062	−	0.176777i
$25$	14751.8	−	25550.9i	0.188823	−	0.327052i
$26$	−56579.6	−	97998.7i	−0.631325	−	1.09349i
$27$	19683.0			0.192450
$28$		0			0
$29$	−76212.3			−0.580272			−0.290136	−	0.956985i	$-0.593701\pi$
$29$	−76212.3			−0.580272			−0.290136	+	0.956985i	$0.593701\pi$
$30$	23814.3	+	41247.5i	0.161032	+	0.278916i
$31$	56994.7	−	98717.7i	0.343612	−	0.595154i	−0.641488	−	0.767133i	$-0.721683\pi$
$31$	56994.7	−	98717.7i	0.343612	−	0.595154i	0.985101	+	0.171979i	$0.0550161\pi$
$32$	16384.0	−	28377.9i	0.0883883	−	0.153093i
$33$	−51373.4	−	88981.3i	−0.248851	−	0.431023i
$34$	−295256.			−1.28832
$35$		0			0
$36$	46656.0			0.166667
$37$	111964.	+	193928.i	0.363390	+	0.629410i	0.988516	−	0.151114i	$-0.0482859\pi$
$37$	111964.	+	193928.i	0.363390	+	0.629410i	−0.625126	+	0.780524i	$0.714953\pi$
$38$	−222394.	+	385198.i	−0.657478	+	1.13878i
$39$	190956.	−	330746.i	0.515475	−	0.892828i
$40$	56448.6	+	97771.9i	0.139458	+	0.241548i
$41$	−557937.			−1.26428			−0.632138	−	0.774856i	$-0.717823\pi$
$41$	−557937.			−1.26428			−0.632138	+	0.774856i	$0.717823\pi$
$42$		0			0
$43$	11062.0			0.0212175			0.0106088	−	0.999944i	$-0.496623\pi$
$43$	11062.0			0.0212175			0.0106088	+	0.999944i	$0.496623\pi$
$44$	−121774.	−	210919.i	−0.215511	−	0.373277i
$45$	−80373.2	+	139210.i	−0.131482	+	0.227734i
$46$	−25593.9	+	44329.9i	−0.0387689	+	0.0671498i
$47$	−123498.	−	213904.i	−0.173507	−	0.300522i	0.766137	−	0.642678i	$-0.222176\pi$
$47$	−123498.	−	213904.i	−0.173507	−	0.300522i	−0.939643	+	0.342155i	$0.888843\pi$
$48$	110592.			0.144338
$49$		0			0
$50$	236029.			0.267036
$51$	−498244.	−	862984.i	−0.525953	−	0.910976i
$52$	452637.	−	783990.i	0.446414	−	0.773212i
$53$	599552.	−	1.03845e6i	0.553174	−	0.958125i	−0.444870	−	0.895595i	$-0.646750\pi$
$53$	599552.	−	1.03845e6i	0.553174	−	0.958125i	0.998043	−	0.0625293i	$-0.0199167\pi$
$54$	78732.0	+	136368.i	0.0680414	+	0.117851i
$55$	839108.			0.680062
$56$		0			0
$57$	−1.50116e6			−1.07366
$58$	−304849.	−	528014.i	−0.205157	−	0.355343i
$59$	838966.	−	1.45313e6i	0.531817	−	0.921134i	−0.467493	−	0.883997i	$-0.654843\pi$
$59$	838966.	−	1.45313e6i	0.531817	−	0.921134i	0.999310	−	0.0371376i	$-0.0118240\pi$
$60$	−190514.	+	329980.i	−0.113867	+	0.197223i
$61$	−1.20784e6	−	2.09204e6i	−0.681327	−	1.18009i	−0.974576	−	0.224057i	$-0.928070\pi$
$61$	−1.20784e6	−	2.09204e6i	−0.681327	−	1.18009i	0.293249	−	0.956036i	$-0.405263\pi$
$62$	911915.			0.485941
$63$		0			0
$64$	262144.			0.125000
$65$	1.55949e6	+	2.70112e6i	0.704347	+	1.21996i
$66$	410987.	−	711851.i	0.175964	−	0.304779i
$67$	1.53718e6	−	2.66248e6i	0.624401	−	1.08150i	−0.364255	−	0.931299i	$-0.618676\pi$
$67$	1.53718e6	−	2.66248e6i	0.624401	−	1.08150i	0.988656	−	0.150196i	$-0.0479904\pi$
$68$	−1.18102e6	−	2.04559e6i	−0.455488	−	0.788929i
$69$	−172759.			−0.0633094
$70$		0			0
$71$	2.91784e6			0.967514			0.483757	−	0.875202i	$-0.339272\pi$
$71$	2.91784e6			0.967514			0.483757	+	0.875202i	$0.339272\pi$
$72$	186624.	+	323242.i	0.0589256	+	0.102062i
$73$	−1.60749e6	+	2.78425e6i	−0.483635	+	0.837680i	−0.999823	−	0.0187949i	$-0.994017\pi$
$73$	−1.60749e6	+	2.78425e6i	−0.483635	+	0.837680i	0.516189	+	0.856475i	$0.327350\pi$
$74$	−895713.	+	1.55142e6i	−0.256956	+	0.445060i
$75$	398299.	+	689874.i	0.109017	+	0.188823i
$76$	−3.55831e6			−0.929814
$77$		0			0
$78$	3.05530e6			0.728991
$79$	−2.67331e6	−	4.63032e6i	−0.610036	−	1.05661i	−0.991234	−	0.132120i	$-0.957822\pi$
$79$	−2.67331e6	−	4.63032e6i	−0.610036	−	1.05661i	0.381198	−	0.924493i	$-0.375512\pi$
$80$	−451589.	+	782175.i	−0.0986117	+	0.170801i
$81$	−265720.	+	460241.i	−0.0555556	+	0.0962250i
$82$	−2.23175e6	−	3.86550e6i	−0.446989	−	0.774208i
$83$	4.28665e6			0.822896			0.411448	−	0.911433i	$-0.365023\pi$
$83$	4.28665e6			0.822896			0.411448	+	0.911433i	$0.365023\pi$
$84$		0			0
$85$	8.13808e6			1.43733
$86$	44248.1	+	76639.9i	0.00750153	+	0.0129930i
$87$	1.02887e6	−	1.78205e6i	0.167510	−	0.290136i
$88$	974192.	−	1.68735e6i	0.152390	−	0.263946i
$89$	−1.47625e6	−	2.55694e6i	−0.221970	−	0.384463i	0.733436	−	0.679758i	$-0.237915\pi$
$89$	−1.47625e6	−	2.55694e6i	−0.221970	−	0.384463i	−0.955406	+	0.295295i	$0.904582\pi$
$90$	−1.28597e6			−0.185944
$91$		0			0
$92$	−409502.			−0.0548276
$93$	1.53886e6	+	2.66538e6i	0.198385	+	0.343612i
$94$	987981.	−	1.71123e6i	0.122688	−	0.212501i
$95$	6.12981e6	−	1.06171e7i	0.733524	−	1.27050i
$96$	442368.	+	766204.i	0.0510310	+	0.0883883i
$97$	−1.15030e7			−1.27971			−0.639853	−	0.768497i	$-0.721005\pi$
$97$	−1.15030e7			−1.27971			−0.639853	+	0.768497i	$0.721005\pi$
$98$		0			0
$99$	2.77416e6			0.287348
$100$	944116.	+	1.63526e6i	0.0944116	+	0.163526i
$101$	99546.8	−	172420.i	0.00961397	−	0.0166519i	−0.861178	−	0.508303i	$-0.830273\pi$
$101$	99546.8	−	172420.i	0.00961397	−	0.0166519i	0.870792	+	0.491651i	$0.163606\pi$
$102$	3.98595e6	−	6.90387e6i	0.371905	−	0.644158i
$103$	6.79419e6	+	1.17679e7i	0.612643	+	1.06113i	0.990793	+	0.135385i	$0.0432271\pi$
$103$	6.79419e6	+	1.17679e7i	0.612643	+	1.06113i	−0.378150	+	0.925744i	$0.623440\pi$
$104$	7.24218e6			0.631325
$105$		0			0
$106$	9.59283e6			0.782306
$107$	7.50474e6	+	1.29986e7i	0.592233	+	1.02578i	0.993931	+	0.110005i	$0.0350868\pi$
$107$	7.50474e6	+	1.29986e7i	0.592233	+	1.02578i	−0.401698	+	0.915772i	$0.631580\pi$
$108$	−629856.	+	1.09094e6i	−0.0481125	+	0.0833333i
$109$	224692.	−	389179.i	0.0166187	−	0.0287843i	−0.857596	−	0.514323i	$-0.828043\pi$
$109$	224692.	−	389179.i	0.0166187	−	0.0287843i	0.874215	+	0.485539i	$0.161377\pi$
$110$	3.35643e6	+	5.81351e6i	0.240438	+	0.416451i
$111$	−6.04606e6			−0.419607
$112$		0			0
$113$	1.83610e7			1.19707			0.598537	−	0.801095i	$-0.295749\pi$
$113$	1.83610e7			1.19707			0.598537	+	0.801095i	$0.295749\pi$
$114$	−6.00464e6	−	1.04004e7i	−0.379595	−	0.657478i
$115$	705440.	−	1.22186e6i	0.0432531	−	0.0749166i
$116$	2.43879e6	−	4.22411e6i	0.145068	−	0.251265i
$117$	5.15581e6	+	8.93013e6i	0.297609	+	0.515475i
$118$	1.34235e7			0.752103
$119$		0			0
$120$	−3.04823e6			−0.161032
$121$	2.50291e6	+	4.33517e6i	0.128439	+	0.222463i
$122$	9.66273e6	−	1.67363e7i	0.481771	−	0.834451i
$123$	7.53216e6	−	1.30461e7i	0.364965	−	0.632138i
$124$	3.64766e6	+	6.31793e6i	0.171806	+	0.297577i
$125$	−2.37324e7			−1.08682
$126$		0			0
$127$	1.71281e7			0.741986			0.370993	−	0.928636i	$-0.379017\pi$
$127$	1.71281e7			0.741986			0.370993	+	0.928636i	$0.379017\pi$
$128$	1.04858e6	+	1.81619e6i	0.0441942	+	0.0765466i
$129$	−149337.	+	258660.i	−0.00612497	+	0.0106088i
$130$	−1.24759e7	+	2.16090e7i	−0.498048	+	0.862645i
$131$	−3.73459e6	−	6.46851e6i	−0.145142	−	0.251394i	0.784284	−	0.620402i	$-0.213031\pi$
$131$	−3.73459e6	−	6.46851e6i	−0.145142	−	0.251394i	−0.929426	+	0.369009i	$0.879697\pi$
$132$	6.57579e6			0.248851
$133$		0			0
$134$	2.45949e7			0.883037
$135$	−2.17008e6	−	3.75868e6i	−0.0759113	−	0.131482i
$136$	9.44818e6	−	1.63647e7i	0.322079	−	0.557857i
$137$	973816.	−	1.68670e6i	0.0323560	−	0.0560422i	−0.849394	−	0.527759i	$-0.823032\pi$
$137$	973816.	−	1.68670e6i	0.0323560	−	0.0560422i	0.881750	+	0.471717i	$0.156366\pi$
$138$	−691035.	−	1.19691e6i	−0.0223833	−	0.0387689i
$139$	−4.71929e7			−1.49048			−0.745238	−	0.666798i	$-0.767664\pi$
$139$	−4.71929e7			−1.49048			−0.745238	+	0.666798i	$0.767664\pi$
$140$		0			0
$141$	6.66887e6			0.200348
$142$	1.16714e7	+	2.02154e7i	0.342068	+	0.592479i
$143$	2.69137e7	−	4.66160e7i	0.769658	−	1.33309i
$144$	−1.49299e6	+	2.58594e6i	−0.0416667	+	0.0721688i
$145$	8.40250e6	+	1.45536e7i	0.228887	+	0.396443i
$146$	−2.57198e7			−0.683963
$147$		0			0
$148$	−1.43314e7			−0.363390
$149$	−893303.	−	1.54725e6i	−0.0221231	−	0.0383184i	0.854752	−	0.519037i	$-0.173709\pi$
$149$	−893303.	−	1.54725e6i	−0.0221231	−	0.0383184i	−0.876875	+	0.480718i	$0.840376\pi$
$150$	−3.18639e6	+	5.51899e6i	−0.0770868	+	0.133518i
$151$	1.75733e7	−	3.04378e7i	0.415369	−	0.719440i	−0.580098	−	0.814546i	$-0.696986\pi$
$151$	1.75733e7	−	3.04378e7i	0.415369	−	0.719440i	0.995467	+	0.0951068i	$0.0303193\pi$
$152$	−1.42332e7	−	2.46527e7i	−0.328739	−	0.569392i
$153$	2.69052e7			0.607318
$154$		0			0
$155$	−2.51349e7			−0.542147
$156$	1.22212e7	+	2.11677e7i	0.257737	+	0.446414i
$157$	4.42756e7	−	7.66876e7i	0.913094	−	1.58153i	0.103426	−	0.994637i	$-0.467020\pi$
$157$	4.42756e7	−	7.66876e7i	0.913094	−	1.58153i	0.809668	−	0.586888i	$-0.199647\pi$
$158$	2.13865e7	−	3.70425e7i	0.431360	−	0.747138i
$159$	1.61879e7	+	2.80383e7i	0.319375	+	0.553174i
$160$	−7.22543e6			−0.139458
$161$		0			0
$162$	−4.25153e6			−0.0785674
$163$	−1.54636e7	−	2.67837e7i	−0.279675	−	0.484411i	0.691629	−	0.722253i	$-0.256893\pi$
$163$	−1.54636e7	−	2.67837e7i	−0.279675	−	0.484411i	−0.971304	+	0.237842i	$0.923560\pi$
$164$	1.78540e7	−	3.09240e7i	0.316069	−	0.547448i
$165$	−1.13280e7	+	1.96206e7i	−0.196317	+	0.340031i
$166$	1.71466e7	+	2.96988e7i	0.290938	+	0.503919i
$167$	−7.46317e7			−1.23998			−0.619991	−	0.784609i	$-0.712864\pi$
$167$	−7.46317e7			−1.23998			−0.619991	+	0.784609i	$0.712864\pi$
$168$		0			0
$169$	1.37329e8			2.18857
$170$	3.25523e7	+	5.63823e7i	0.508172	+	0.880180i
$171$	2.02657e7	−	3.51012e7i	0.309938	−	0.536828i
$172$	−353985.	+	613119.i	−0.00530438	+	0.00918746i
$173$	4.01678e7	+	6.95727e7i	0.589817	+	1.02159i	0.994256	+	0.107028i	$0.0341334\pi$
$173$	4.01678e7	+	6.95727e7i	0.589817	+	1.02159i	−0.404439	+	0.914565i	$0.632533\pi$
$174$	1.64618e7			0.236895
$175$		0			0
$176$	1.55871e7			0.215511
$177$	2.26521e7	+	3.92346e7i	0.307045	+	0.531817i
$178$	1.18100e7	−	2.04555e7i	0.156957	−	0.271857i
$179$	−4.49879e7	+	7.79213e7i	−0.586286	+	1.01548i	0.408427	+	0.912791i	$0.366077\pi$
$179$	−4.49879e7	+	7.79213e7i	−0.586286	+	1.01548i	−0.994714	+	0.102687i	$0.967256\pi$
$180$	−5.14388e6	−	8.90947e6i	−0.0657412	−	0.113867i
$181$	−9.33169e6			−0.116973			−0.0584865	−	0.998288i	$-0.518627\pi$
$181$	−9.33169e6			−0.116973			−0.0584865	+	0.998288i	$0.518627\pi$
$182$		0			0
$183$	6.52234e7			0.786728
$184$	−1.63801e6	−	2.83711e6i	−0.0193845	−	0.0335749i
$185$	2.46884e7	−	4.27615e7i	0.286676	−	0.496538i
$186$	−1.23109e7	+	2.13230e7i	−0.140279	+	0.242970i
$187$	−7.02236e7	−	1.21631e8i	−0.785303	−	1.36018i
$188$	1.58077e7			0.173507
$189$		0			0
$190$	9.80770e7			1.03736
$191$	5.62008e7	+	9.73426e7i	0.583614	+	1.01085i	0.995047	+	0.0994084i	$0.0316950\pi$
$191$	5.62008e7	+	9.73426e7i	0.583614	+	1.01085i	−0.411433	+	0.911440i	$0.634972\pi$
$192$	−3.53894e6	+	6.12963e6i	−0.0360844	+	0.0625000i
$193$	2.47686e7	−	4.29004e7i	0.247999	−	0.429547i	−0.714971	−	0.699154i	$-0.753560\pi$
$193$	2.47686e7	−	4.29004e7i	0.247999	−	0.429547i	0.962971	+	0.269606i	$0.0868936\pi$
$194$	−4.60120e7	−	7.96951e7i	−0.452444	−	0.783657i
$195$	−8.42126e7			−0.813309
$196$		0			0
$197$	−1.92824e8			−1.79693			−0.898463	−	0.439050i	$-0.855315\pi$
$197$	−1.92824e8			−1.79693			−0.898463	+	0.439050i	$0.855315\pi$
$198$	1.10967e7	+	1.92200e7i	0.101593	+	0.175964i
$199$	2.09621e7	−	3.63075e7i	0.188560	−	0.326596i	−0.756210	−	0.654329i	$-0.772951\pi$
$199$	2.09621e7	−	3.63075e7i	0.188560	−	0.326596i	0.944770	+	0.327733i	$0.106285\pi$
$200$	−7.55293e6	+	1.30821e7i	−0.0667591	+	0.115630i
$201$	4.15040e7	+	7.18870e7i	0.360498	+	0.624401i
$202$	1.59275e6			0.0135962
$203$		0			0
$204$	6.37752e7			0.525953
$205$	6.15133e7	+	1.06544e8i	0.498690	+	0.863756i
$206$	−5.43535e7	+	9.41431e7i	−0.433204	+	0.750332i
$207$	2.33224e6	−	4.03956e6i	0.0182759	−	0.0316547i
$208$	2.89687e7	+	5.01753e7i	0.223207	+	0.386606i
$209$	−2.11577e8			−1.60308
$210$		0			0
$211$	−8.18818e7			−0.600066			−0.300033	−	0.953929i	$-0.596998\pi$
$211$	−8.18818e7			−0.600066			−0.300033	+	0.953929i	$0.596998\pi$
$212$	3.83713e7	+	6.64611e7i	0.276587	+	0.479062i
$213$	−3.93908e7	+	6.82269e7i	−0.279297	+	0.483757i
$214$	−6.00379e7	+	1.03989e8i	−0.418772	+	0.725334i
$215$	−1.21960e6	−	2.11241e6i	−0.00836919	−	0.0144959i
$216$	−1.00777e7			−0.0680414
$217$		0			0
$218$	3.59508e6			0.0235023
$219$	−4.34022e7	−	7.51747e7i	−0.279227	−	0.483635i
$220$	−2.68515e7	+	4.65081e7i	−0.170016	+	0.294476i
$221$	2.61023e8	−	4.52104e8i	1.62669	−	2.81751i
$222$	−2.41843e7	−	4.18884e7i	−0.148353	−	0.256956i
$223$	2.88078e8			1.73958			0.869788	−	0.493426i	$-0.164256\pi$
$223$	2.88078e8			1.73958			0.869788	+	0.493426i	$0.164256\pi$
$224$		0			0
$225$	−2.15082e7			−0.125882
$226$	7.34439e7	+	1.27209e8i	0.423230	+	0.733056i
$227$	1.36256e8	−	2.36003e8i	0.773154	−	1.33914i	−0.162673	−	0.986680i	$-0.552012\pi$
$227$	1.36256e8	−	2.36003e8i	0.773154	−	1.33914i	0.935826	−	0.352461i	$-0.114655\pi$
$228$	4.80372e7	−	8.32028e7i	0.268414	−	0.464907i
$229$	1.27290e8	+	2.20474e8i	0.700441	+	1.21320i	0.968312	+	0.249745i	$0.0803467\pi$
$229$	1.27290e8	+	2.20474e8i	0.700441	+	1.21320i	−0.267871	+	0.963455i	$0.586320\pi$
$230$	1.12870e7			0.0611692
$231$		0			0
$232$	3.90207e7			0.205157
$233$	−1.36471e8	−	2.36374e8i	−0.706795	−	1.22421i	−0.966040	−	0.258394i	$-0.916807\pi$
$233$	−1.36471e8	−	2.36374e8i	−0.706795	−	1.22421i	0.259244	−	0.965812i	$-0.416526\pi$
$234$	−4.12465e7	+	7.14410e7i	−0.210442	+	0.364496i
$235$	−2.72315e7	+	4.71664e7i	−0.136878	+	0.237080i
$236$	5.36938e7	+	9.30004e7i	0.265909	+	0.460567i
$237$	1.44359e8			0.704409
$238$		0			0
$239$	2.70843e8			1.28329			0.641645	−	0.767001i	$-0.278252\pi$
$239$	2.70843e8			1.28329			0.641645	+	0.767001i	$0.278252\pi$
$240$	−1.21929e7	−	2.11187e7i	−0.0569335	−	0.0986117i
$241$	3.96331e7	−	6.86465e7i	0.182389	−	0.315907i	−0.760305	−	0.649567i	$-0.774950\pi$
$241$	3.96331e7	−	6.86465e7i	0.182389	−	0.315907i	0.942694	+	0.333660i	$0.108284\pi$
$242$	−2.00233e7	+	3.46814e7i	−0.0908201	+	0.157305i
$243$	−7.17445e6	−	1.24265e7i	−0.0320750	−	0.0555556i
$244$	1.54604e8			0.681327
$245$		0			0
$246$	1.20514e8			0.516139
$247$	−3.93218e8	−	6.81073e8i	−1.66033	−	2.87577i
$248$	−2.91813e7	+	5.05435e7i	−0.121485	+	0.210419i
$249$	−5.78698e7	+	1.00233e8i	−0.237550	+	0.411448i
$250$	−9.49295e7	−	1.64423e8i	−0.384248	−	0.665537i
$251$	−1.87379e8			−0.747934			−0.373967	−	0.927442i	$-0.622003\pi$
$251$	−1.87379e8			−0.747934			−0.373967	+	0.927442i	$0.622003\pi$
$252$		0			0
$253$	−2.43490e7			−0.0945277
$254$	6.85124e7	+	1.18667e8i	0.262332	+	0.454372i
$255$	−1.09864e8	+	1.90290e8i	−0.414921	+	0.718664i
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	−1.92556e8	−	3.33517e8i	−0.707607	−	1.22561i	−0.965743	−	0.259502i	$-0.916442\pi$
$257$	−1.92556e8	−	3.33517e8i	−0.707607	−	1.22561i	0.258136	−	0.966109i	$-0.416892\pi$
$258$	−2.38940e6			−0.00866202
$259$		0			0
$260$	−1.99615e8			−0.704347
$261$	2.77794e7	+	4.81153e7i	0.0967121	+	0.167510i
$262$	2.98768e7	−	5.17481e7i	0.102631	−	0.177762i
$263$	−1.07700e8	+	1.86542e8i	−0.365065	+	0.632312i	−0.988787	−	0.149335i	$-0.952287\pi$
$263$	−1.07700e8	+	1.86542e8i	−0.365065	+	0.632312i	0.623721	+	0.781647i	$0.285620\pi$
$264$	2.63032e7	+	4.55584e7i	0.0879821	+	0.152390i
$265$	−2.64406e8			−0.872790
$266$		0			0
$267$	7.97174e7			0.256309
$268$	9.83797e7	+	1.70399e8i	0.312201	+	0.540748i
$269$	−3.00751e8	+	5.20917e8i	−0.942051	+	1.63168i	−0.180501	+	0.983575i	$0.557772\pi$
$269$	−3.00751e8	+	5.20917e8i	−0.942051	+	1.63168i	−0.761550	+	0.648106i	$0.775561\pi$
$270$	1.73606e7	−	3.00694e7i	0.0536774	−	0.0929720i
$271$	6.27156e7	+	1.08627e8i	0.191418	+	0.331546i	0.945720	−	0.324981i	$-0.105358\pi$
$271$	6.27156e7	+	1.08627e8i	0.191418	+	0.331546i	−0.754302	+	0.656527i	$0.772025\pi$
$272$	1.51171e8			0.455488
$273$		0			0
$274$	1.55811e7			0.0457583
$275$	5.61371e7	+	9.72323e7i	0.162774	+	0.281933i
$276$	5.52828e6	−	9.57526e6i	0.0158274	−	0.0274138i
$277$	3.09398e7	−	5.35894e7i	0.0874659	−	0.151495i	−0.818973	−	0.573831i	$-0.805456\pi$
$277$	3.09398e7	−	5.35894e7i	0.0874659	−	0.151495i	0.906439	+	0.422336i	$0.138790\pi$
$278$	−1.88772e8	−	3.26962e8i	−0.526963	−	0.912727i
$279$	−8.30983e7			−0.229075
$280$		0			0
$281$	−2.52689e8			−0.679384			−0.339692	−	0.940537i	$-0.610323\pi$
$281$	−2.52689e8			−0.679384			−0.339692	+	0.940537i	$0.610323\pi$
$282$	2.66755e7	+	4.62033e7i	0.0708338	+	0.122688i
$283$	4.31746e7	−	7.47806e7i	0.113234	−	0.196127i	−0.803839	−	0.594847i	$-0.797212\pi$
$283$	4.31746e7	−	7.47806e7i	0.113234	−	0.196127i	0.917072	+	0.398721i	$0.130546\pi$
$284$	−9.33709e7	+	1.61723e8i	−0.241878	+	0.418946i
$285$	1.65505e8	+	2.86663e8i	0.423500	+	0.733524i
$286$	4.30620e8			1.08846
$287$		0			0
$288$	−2.38879e7			−0.0589256
$289$	−4.75893e8	−	8.24271e8i	−1.15976	−	2.00876i
$290$	−6.72200e7	+	1.16428e8i	−0.161847	+	0.280328i
$291$	1.55291e8	−	2.68971e8i	0.369419	−	0.639853i
$292$	−1.02879e8	−	1.78192e8i	−0.241817	−	0.418840i
$293$	3.33476e7			0.0774512			0.0387256	−	0.999250i	$-0.487670\pi$
$293$	3.33476e7			0.0774512			0.0387256	+	0.999250i	$0.487670\pi$
$294$		0			0
$295$	−3.69988e8			−0.839095
$296$	−5.73257e7	−	9.92909e7i	−0.128478	−	0.222530i
$297$	−3.74512e7	+	6.48674e7i	−0.0829503	+	0.143674i
$298$	7.14642e6	−	1.23780e7i	0.0156434	−	0.0270952i
$299$	−4.52529e7	−	7.83802e7i	−0.0979032	−	0.169573i
$300$	−5.09823e7			−0.109017
$301$		0			0
$302$	2.81173e8			0.587420
$303$	2.68776e6	+	4.65534e6i	0.00555063	+	0.00961397i
$304$	1.13866e8	−	1.97221e8i	0.232453	−	0.402621i
$305$	−2.66332e8	+	4.61301e8i	−0.537494	+	0.930968i
$306$	1.07621e8	+	1.86405e8i	0.214719	+	0.371905i
$307$	4.79908e8			0.946617			0.473308	−	0.880897i	$-0.343060\pi$
$307$	4.79908e8			0.946617			0.473308	+	0.880897i	$0.343060\pi$
$308$		0			0
$309$	−3.66886e8			−0.707419
$310$	−1.00540e8	−	1.74140e8i	−0.191678	−	0.331996i
$311$	−1.60818e8	+	2.78544e8i	−0.303160	+	0.525089i	−0.976850	−	0.213925i	$-0.931375\pi$
$311$	−1.60818e8	+	2.78544e8i	−0.303160	+	0.525089i	0.673690	+	0.739014i	$0.264708\pi$
$312$	−9.77695e7	+	1.69342e8i	−0.182248	+	0.315662i
$313$	−1.47955e8	−	2.56265e8i	−0.272724	−	0.472372i	0.696834	−	0.717232i	$-0.254591\pi$
$313$	−1.47955e8	−	2.56265e8i	−0.272724	−	0.472372i	−0.969558	+	0.244860i	$0.921258\pi$
$314$	7.08409e8			1.29131
$315$		0			0
$316$	3.42184e8			0.610036
$317$	3.74994e7	+	6.49509e7i	0.0661176	+	0.114519i	0.897189	−	0.441646i	$-0.145605\pi$
$317$	3.74994e7	+	6.49509e7i	0.0661176	+	0.114519i	−0.831072	+	0.556165i	$0.812272\pi$
$318$	−1.29503e8	+	2.24306e8i	−0.225832	+	0.391153i
$319$	1.45010e8	−	2.51165e8i	0.250111	−	0.433204i
$320$	−2.89017e7	−	5.00592e7i	−0.0493059	−	0.0854003i
$321$	−4.05256e8			−0.683852
$322$		0			0
$323$	−2.05197e9			−3.38815
$324$	−1.70061e7	−	2.94555e7i	−0.0277778	−	0.0481125i
$325$	−2.08663e8	+	3.61415e8i	−0.337174	+	0.584002i
$326$	1.23709e8	−	2.14270e8i	0.197760	−	0.342531i
$327$	6.06670e6	+	1.05078e7i	0.00959478	+	0.0166187i
$328$	2.85664e8			0.446989
$329$		0			0
$330$	−1.81247e8			−0.277634
$331$	9.36163e7	+	1.62148e8i	0.141891	+	0.245762i	0.928209	−	0.372060i	$-0.121349\pi$
$331$	9.36163e7	+	1.62148e8i	0.141891	+	0.245762i	−0.786318	+	0.617822i	$0.788015\pi$
$332$	−1.37173e8	+	2.37590e8i	−0.205724	+	0.356324i
$333$	8.16219e7	−	1.41373e8i	0.121130	−	0.209803i
$334$	−2.98527e8	−	5.17063e8i	−0.438400	−	0.759331i
$335$	−6.77906e8			−0.985173
$336$		0			0
$337$	1.59335e8			0.226782			0.113391	−	0.993550i	$-0.463829\pi$
$337$	1.59335e8			0.226782			0.113391	+	0.993550i	$0.463829\pi$
$338$	5.49318e8	+	9.51446e8i	0.773776	+	1.34022i
$339$	−2.47873e8	+	4.29329e8i	−0.345566	+	0.598537i
$340$	−2.60419e8	+	4.51058e8i	−0.359332	+	0.622381i
$341$	2.16890e8	+	3.75664e8i	0.296209	+	0.513049i
$342$	3.24251e8			0.438318
$343$		0			0
$344$	−5.66375e6			−0.00750153
$345$	1.90469e7	+	3.29902e7i	0.0249722	+	0.0432531i
$346$	−3.21343e8	+	5.56582e8i	−0.417063	+	0.722375i
$347$	−2.78351e7	+	4.82118e7i	−0.0357635	+	0.0619441i	−0.883353	−	0.468708i	$-0.844720\pi$
$347$	−2.78351e7	+	4.82118e7i	−0.0357635	+	0.0619441i	0.847590	+	0.530652i	$0.178053\pi$
$348$	6.58474e7	+	1.14051e8i	0.0837551	+	0.145068i
$349$	−1.84067e8			−0.231786			−0.115893	−	0.993262i	$-0.536973\pi$
$349$	−1.84067e8			−0.231786			−0.115893	+	0.993262i	$0.536973\pi$
$350$		0			0
$351$	−2.78414e8			−0.343650
$352$	6.23483e7	+	1.07990e8i	0.0761948	+	0.131973i
$353$	−4.96968e8	+	8.60774e8i	−0.601336	+	1.04154i	0.391283	+	0.920270i	$0.372031\pi$
$353$	−4.96968e8	+	8.60774e8i	−0.601336	+	1.04154i	−0.992619	+	0.121274i	$0.961302\pi$
$354$	−1.81217e8	+	3.13877e8i	−0.217113	+	0.376052i
$355$	−3.21695e8	−	5.57193e8i	−0.381633	−	0.661007i
$356$	1.88960e8			0.221970
$357$		0			0
$358$	−7.19806e8			−0.829134
$359$	5.74095e7	+	9.94361e7i	0.0654867	+	0.113426i	0.896910	−	0.442214i	$-0.145807\pi$
$359$	5.74095e7	+	9.94361e7i	0.0654867	+	0.113426i	−0.831423	+	0.555640i	$0.812473\pi$
$360$	4.11511e7	−	7.12757e7i	0.0464860	−	0.0805161i
$361$	−1.09866e9	+	1.90294e9i	−1.22911	+	2.12888i
$362$	−3.73268e7	−	6.46519e7i	−0.0413562	−	0.0716310i
$363$	−1.35157e8			−0.148309
$364$		0			0
$365$	7.08910e8			0.763073
$366$	2.60894e8	+	4.51881e8i	0.278150	+	0.481771i
$367$	7.27488e8	−	1.26005e9i	0.768236	−	1.33062i	−0.170282	−	0.985395i	$-0.554468\pi$
$367$	7.27488e8	−	1.26005e9i	0.768236	−	1.33062i	0.938518	−	0.345229i	$-0.112199\pi$
$368$	1.31041e7	−	2.26969e7i	0.0137069	−	0.0237410i
$369$	2.03368e8	+	3.52244e8i	0.210713	+	0.364965i
$370$	3.95014e8			0.405421
$371$		0			0
$372$	−1.96974e8			−0.198385
$373$	−5.45409e8	−	9.44677e8i	−0.544179	−	0.942545i	−0.998658	−	0.0517880i	$-0.983508\pi$
$373$	−5.45409e8	−	9.44677e8i	−0.544179	−	0.942545i	0.454479	−	0.890757i	$-0.349825\pi$
$374$	5.61788e8	−	9.73046e8i	0.555293	−	0.961796i
$375$	3.20387e8	−	5.54927e8i	0.313737	−	0.543408i
$376$	6.32308e7	+	1.09519e8i	0.0613439	+	0.106251i
$377$	1.07801e9			1.03617
$378$		0			0
$379$	−1.61693e9			−1.52564			−0.762821	−	0.646609i	$-0.776186\pi$
$379$	−1.61693e9			−1.52564			−0.762821	+	0.646609i	$0.776186\pi$
$380$	3.92308e8	+	6.79497e8i	0.366762	+	0.635251i
$381$	−2.31229e8	+	4.00501e8i	−0.214193	+	0.370993i
$382$	−4.49606e8	+	7.78740e8i	−0.412677	+	0.714778i
$383$	4.91728e8	+	8.51698e8i	0.447228	+	0.774622i	0.998204	−	0.0598991i	$-0.0190779\pi$
$383$	4.91728e8	+	8.51698e8i	0.447228	+	0.774622i	−0.550976	+	0.834521i	$0.685745\pi$
$384$	−5.66231e7			−0.0510310
$385$		0			0
$386$	3.96297e8			0.350724
$387$	−4.03211e6	−	6.98381e6i	−0.00353625	−	0.00612497i
$388$	3.68096e8	−	6.37561e8i	0.319926	−	0.554129i
$389$	8.81559e8	−	1.52690e9i	0.759325	−	1.31519i	−0.183870	−	0.982950i	$-0.558863\pi$
$389$	8.81559e8	−	1.52690e9i	0.759325	−	1.31519i	0.943195	−	0.332239i	$-0.107804\pi$
$390$	−3.36850e8	−	5.83442e8i	−0.287548	−	0.498048i
$391$	−2.36148e8			−0.199786
$392$		0			0
$393$	2.01668e8			0.167596
$394$	−7.71297e8	−	1.33593e9i	−0.635309	−	1.10039i
$395$	−5.89473e8	+	1.02100e9i	−0.481253	+	0.833555i
$396$	−8.87732e7	+	1.53760e8i	−0.0718371	+	0.124426i
$397$	8.20301e8	+	1.42080e9i	0.657970	+	1.13964i	0.981140	+	0.193297i	$0.0619182\pi$
$397$	8.20301e8	+	1.42080e9i	0.657970	+	1.13964i	−0.323170	+	0.946341i	$0.604749\pi$
$398$	3.35394e8			0.266664
$399$		0			0
$400$	−1.20847e8			−0.0944116
$401$	2.17035e8	+	3.75916e8i	0.168084	+	0.291129i	0.937746	−	0.347322i	$-0.112909\pi$
$401$	2.17035e8	+	3.75916e8i	0.168084	+	0.291129i	−0.769662	+	0.638451i	$0.779575\pi$
$402$	−3.32032e8	+	5.75096e8i	−0.254911	+	0.441518i
$403$	−8.06184e8	+	1.39635e9i	−0.613573	+	1.06274i
$404$	6.37100e6	+	1.10349e7i	0.00480698	+	0.00832594i
$405$	1.17184e8			0.0876549
$406$		0			0
$407$	−8.52145e8			−0.626517
$408$	2.55101e8	+	4.41848e8i	0.185952	+	0.322079i
$409$	1.09965e9	−	1.90464e9i	0.794733	−	1.37652i	−0.128276	−	0.991738i	$-0.540944\pi$
$409$	1.09965e9	−	1.90464e9i	0.794733	−	1.37652i	0.923009	−	0.384779i	$-0.125722\pi$
$410$	−4.92106e8	+	8.52353e8i	−0.352627	+	0.610768i
$411$	2.62930e7	+	4.55409e7i	0.0186807	+	0.0323560i
$412$	−8.69657e8			−0.612643
$413$		0			0
$414$	3.73159e7			0.0258460
$415$	−4.72609e8	−	8.18582e8i	−0.324589	−	0.562204i
$416$	−2.31750e8	+	4.01403e8i	−0.157831	+	0.273372i
$417$	6.37104e8	−	1.10350e9i	0.430263	−	0.745238i
$418$	−8.46307e8	−	1.46585e9i	−0.566775	−	0.981684i
$419$	−1.43802e9			−0.955027			−0.477513	−	0.878624i	$-0.658462\pi$
$419$	−1.43802e9			−0.955027			−0.477513	+	0.878624i	$0.658462\pi$
$420$		0			0
$421$	−1.37853e9			−0.900388			−0.450194	−	0.892931i	$-0.648645\pi$
$421$	−1.37853e9			−0.900388			−0.450194	+	0.892931i	$0.648645\pi$
$422$	−3.27527e8	−	5.67294e8i	−0.212155	−	0.367464i
$423$	−9.00298e7	+	1.55936e8i	−0.0578355	+	0.100174i
$424$	−3.06971e8	+	5.31689e8i	−0.195576	+	0.338748i
$425$	5.44445e8	+	9.43006e8i	0.344027	+	0.595872i
$426$	−6.30253e8			−0.394986
$427$		0			0
$428$	−9.60607e8			−0.592233
$429$	7.26671e8	+	1.25863e9i	0.444362	+	0.769658i
$430$	9.75681e6	−	1.68993e7i	0.00591791	−	0.0102501i
$431$	−9.69657e7	+	1.67950e8i	−0.0583375	+	0.101044i	−0.893719	−	0.448627i	$-0.851913\pi$
$431$	−9.69657e7	+	1.67950e8i	−0.0583375	+	0.101044i	0.835382	+	0.549670i	$0.185247\pi$
$432$	−4.03108e7	−	6.98203e7i	−0.0240563	−	0.0416667i
$433$	4.64589e8			0.275018			0.137509	−	0.990501i	$-0.456090\pi$
$433$	4.64589e8			0.275018			0.137509	+	0.990501i	$0.456090\pi$
$434$		0			0
$435$	−4.53735e8			−0.264296
$436$	1.43803e7	+	2.49074e7i	0.00830933	+	0.0143922i
$437$	−1.77873e8	+	3.08085e8i	−0.101959	+	0.176598i
$438$	3.47217e8	−	6.01398e8i	0.197443	−	0.341981i
$439$	−1.12723e9	−	1.95242e9i	−0.635897	−	1.10141i	−0.986324	−	0.164817i	$-0.947297\pi$
$439$	−1.12723e9	−	1.95242e9i	−0.635897	−	1.10141i	0.350427	−	0.936590i	$-0.386037\pi$
$440$	−4.29623e8			−0.240438
$441$		0			0
$442$	4.17636e9			2.30049
$443$	−1.80132e9	−	3.11998e9i	−0.984414	−	1.70506i	−0.644512	−	0.764594i	$-0.722939\pi$
$443$	−1.80132e9	−	3.11998e9i	−0.984414	−	1.70506i	−0.339902	−	0.940461i	$-0.610394\pi$
$444$	1.93474e8	−	3.35107e8i	0.104902	−	0.181695i
$445$	−3.25517e8	+	5.63811e8i	−0.175111	+	0.303301i
$446$	1.15231e9	+	1.99586e9i	0.615033	+	1.06527i
$447$	4.82384e7			0.0255456
$448$		0			0
$449$	1.86794e9			0.973867			0.486934	−	0.873439i	$-0.338115\pi$
$449$	1.86794e9			0.973867			0.486934	+	0.873439i	$0.338115\pi$
$450$	−8.60326e7	−	1.49013e8i	−0.0445061	−	0.0770868i
$451$	1.06160e9	−	1.83874e9i	0.544932	−	0.943849i
$452$	−5.87551e8	+	1.01767e9i	−0.299269	+	0.518349i
$453$	4.74479e8	+	8.21821e8i	0.239813	+	0.415369i
$454$	2.18010e9			1.09340
$455$		0			0
$456$	7.68595e8			0.379595
$457$	−1.07584e9	−	1.86340e9i	−0.527278	−	0.913273i	−0.999495	−	0.0317900i	$-0.989879\pi$
$457$	−1.07584e9	−	1.86340e9i	−0.527278	−	0.913273i	0.472216	−	0.881483i	$-0.343454\pi$
$458$	−1.01832e9	+	1.76379e9i	−0.495287	+	0.857862i
$459$	−3.63220e8	+	6.29115e8i	−0.175318	+	0.303659i
$460$	4.51481e7	+	7.81989e7i	0.0216266	+	0.0374583i
$461$	−1.44475e9			−0.686812			−0.343406	−	0.939187i	$-0.611581\pi$
$461$	−1.44475e9			−0.686812			−0.343406	+	0.939187i	$0.611581\pi$
$462$		0			0
$463$	3.91947e9			1.83525			0.917623	−	0.397452i	$-0.130106\pi$
$463$	3.91947e9			1.83525			0.917623	+	0.397452i	$0.130106\pi$
$464$	1.56083e8	+	2.70343e8i	0.0725340	+	0.125633i
$465$	3.39322e8	−	5.87723e8i	0.156504	−	0.271073i
$466$	1.09177e9	−	1.89099e9i	0.499780	−	0.865644i
$467$	1.04920e9	+	1.81727e9i	0.476705	+	0.825678i	0.999644	−	0.0266928i	$-0.00849760\pi$
$467$	1.04920e9	+	1.81727e9i	0.476705	+	0.825678i	−0.522938	+	0.852370i	$0.675164\pi$
$468$	−6.59944e8			−0.297609
$469$		0			0
$470$	−4.35705e8			−0.193575
$471$	1.19544e9	+	2.07056e9i	0.527175	+	0.913094i
$472$	−4.29551e8	+	7.44004e8i	−0.188026	+	0.325670i
$473$	−2.10479e7	+	3.64560e7i	−0.00914523	+	0.0158400i
$474$	5.77436e8	+	1.00015e9i	0.249046	+	0.431360i
$475$	1.64036e9			0.702282
$476$		0			0
$477$	−8.74147e8			−0.368782
$478$	1.08337e9	+	1.87646e9i	0.453712	+	0.785852i
$479$	−5.49879e8	+	9.52418e8i	−0.228609	+	0.395962i	−0.957396	−	0.288778i	$-0.906751\pi$
$479$	−5.49879e8	+	9.52418e8i	−0.228609	+	0.395962i	0.728787	+	0.684740i	$0.240084\pi$
$480$	9.75433e7	−	1.68950e8i	0.0402581	−	0.0697290i
$481$	−1.58372e9	−	2.74309e9i	−0.648890	−	1.12391i
$482$	6.34129e8			0.257937
$483$		0			0
$484$	−3.20373e8			−0.128439
$485$	1.26822e9	+	2.19662e9i	0.504776	+	0.874298i
$486$	5.73956e7	−	9.94121e7i	0.0226805	−	0.0392837i
$487$	1.23669e9	−	2.14202e9i	0.485189	−	0.840372i	−0.514666	−	0.857391i	$-0.672084\pi$
$487$	1.23669e9	−	2.14202e9i	0.485189	−	0.840372i	0.999855	+	0.0170185i	$0.00541741\pi$
$488$	6.18415e8	+	1.07113e9i	0.240885	+	0.417226i
$489$	8.35034e8			0.322941
$490$		0			0
$491$	4.19153e9			1.59804			0.799020	−	0.601305i	$-0.205352\pi$
$491$	4.19153e9			1.59804			0.799020	+	0.601305i	$0.205352\pi$
$492$	4.82058e8	+	8.34949e8i	0.182483	+	0.316069i
$493$	1.40638e9	−	2.43592e9i	0.528614	−	0.915587i
$494$	3.14574e9	−	5.44859e9i	1.17403	−	2.03348i
$495$	−3.05855e8	−	5.29756e8i	−0.113344	−	0.196317i
$496$	−4.66901e8			−0.171806
$497$		0			0
$498$	−9.25917e8			−0.335946
$499$	9.99120e8	+	1.73053e9i	0.359970	+	0.623486i	0.987955	−	0.154739i	$-0.0494537\pi$
$499$	9.99120e8	+	1.73053e9i	0.359970	+	0.623486i	−0.627986	+	0.778225i	$0.716120\pi$
$500$	7.59436e8	−	1.31538e9i	0.271704	−	0.470605i
$501$	1.00753e9	−	1.74509e9i	0.357952	−	0.619991i
$502$	−7.49517e8	−	1.29820e9i	−0.264435	−	0.458014i
$503$	−2.68826e9			−0.941855			−0.470927	−	0.882172i	$-0.656081\pi$
$503$	−2.68826e9			−0.941855			−0.470927	+	0.882172i	$0.656081\pi$
$504$		0			0
$505$	−4.39007e7			−0.0151688
$506$	−9.73959e7	−	1.68695e8i	−0.0334206	−	0.0578861i
$507$	−1.85395e9	+	3.21113e9i	−0.631785	+	1.09428i
$508$	−5.48099e8	+	9.49335e8i	−0.185497	+	0.321290i
$509$	9.35055e8	+	1.61956e9i	0.314286	+	0.544359i	0.979285	−	0.202485i	$-0.0649017\pi$
$509$	9.35055e8	+	1.61956e9i	0.314286	+	0.544359i	−0.665000	+	0.746844i	$0.731568\pi$
$510$	−1.75783e9			−0.586786
$511$		0			0
$512$	−1.34218e8			−0.0441942
$513$	5.47173e8	+	9.47732e8i	0.178943	+	0.309938i
$514$	1.54045e9	−	2.66814e9i	0.500354	−	0.866638i
$515$	1.49814e9	−	2.59485e9i	0.483310	−	0.837118i
$516$	−9.55758e6	−	1.65542e7i	−0.00306249	−	0.00530438i
$517$	9.39925e8			0.299141
$518$		0			0
$519$	−2.16906e9			−0.681062
$520$	−7.98460e8	−	1.38297e9i	−0.249024	−	0.431322i
$521$	1.85730e9	−	3.21693e9i	0.575372	−	0.996574i	−0.420629	−	0.907233i	$-0.638191\pi$
$521$	1.85730e9	−	3.21693e9i	0.575372	−	0.996574i	0.996001	−	0.0893412i	$-0.0284762\pi$
$522$	−2.22235e8	+	3.84922e8i	−0.0683858	+	0.118448i
$523$	−3.65332e8	−	6.32774e8i	−0.111669	−	0.193416i	0.804774	−	0.593581i	$-0.202286\pi$
$523$	−3.65332e8	−	6.32774e8i	−0.111669	−	0.193416i	−0.916443	+	0.400165i	$0.868953\pi$
$524$	4.78028e8			0.145142
$525$		0			0
$526$	−1.72320e9			−0.516280
$527$	2.10350e9	+	3.64337e9i	0.626045	+	1.08434i
$528$	−2.10425e8	+	3.64467e8i	−0.0622128	+	0.107756i
$529$	1.68194e9	−	2.91321e9i	0.493988	−	0.855612i
$530$	−1.05762e9	−	1.83186e9i	−0.308578	−	0.534473i
$531$	−1.22321e9			−0.354545
$532$		0			0
$533$	7.89197e9			2.25756
$534$	3.18870e8	+	5.52299e8i	0.0906189	+	0.156957i
$535$	1.65481e9	−	2.86622e9i	0.467209	−	0.809230i
$536$	−7.87038e8	+	1.36319e9i	−0.220759	+	0.382366i
$537$	−1.21467e9	−	2.10387e9i	−0.338493	−	0.586286i
$538$	−4.81202e9			−1.33226
$539$		0			0
$540$	2.77770e8			0.0759113
$541$	−3.24574e9	−	5.62179e9i	−0.881300	−	1.52646i	−0.849897	−	0.526949i	$-0.823336\pi$
$541$	−3.24574e9	−	5.62179e9i	−0.881300	−	1.52646i	−0.0314033	−	0.999507i	$-0.509998\pi$
$542$	−5.01725e8	+	8.69013e8i	−0.135353	+	0.234438i
$543$	1.25978e8	−	2.18200e8i	0.0337672	−	0.0584865i
$544$	6.04684e8	+	1.04734e9i	0.161039	+	0.278928i
$545$	−9.90905e7			−0.0262207
$546$		0			0
$547$	2.88823e9			0.754530			0.377265	−	0.926105i	$-0.376865\pi$
$547$	2.88823e9			0.754530			0.377265	+	0.926105i	$0.376865\pi$
$548$	6.23242e7	+	1.07949e8i	0.0161780	+	0.0280211i
$549$	−8.80516e8	+	1.52510e9i	−0.227109	+	0.393364i
$550$	−4.49097e8	+	7.77859e8i	−0.115099	+	0.199357i
$551$	−2.11865e9	−	3.66960e9i	−0.539545	−	0.934520i
$552$	8.84525e7			0.0223833
$553$		0			0
$554$	4.95037e8			0.123695
$555$	6.66586e8	+	1.15456e9i	0.165513	+	0.286676i
$556$	1.51017e9	−	2.61570e9i	0.372619	−	0.645395i
$557$	−1.94149e9	+	3.36276e9i	−0.476039	+	0.824524i	−0.999623	−	0.0274500i	$-0.991261\pi$
$557$	−1.94149e9	+	3.36276e9i	−0.476039	+	0.824524i	0.523584	+	0.851974i	$0.324595\pi$
$558$	−3.32393e8	−	5.75722e8i	−0.0809902	−	0.140279i
$559$	−1.56471e8			−0.0378872
$560$		0			0
$561$	3.79207e9			0.906790
$562$	−1.01076e9	−	1.75068e9i	−0.240198	−	0.416036i
$563$	−3.46353e9	+	5.99901e9i	−0.817974	+	1.41677i	0.0891992	+	0.996014i	$0.471569\pi$
$563$	−3.46353e9	+	5.99901e9i	−0.817974	+	1.41677i	−0.907173	+	0.420758i	$0.861764\pi$
$564$	−2.13404e8	+	3.69626e8i	−0.0500871	+	0.0867533i
$565$	−2.02432e9	−	3.50623e9i	−0.472182	−	0.817844i
$566$	6.90794e8			0.160137
$567$		0			0
$568$	−1.49393e9			−0.342068
$569$	9.80026e7	+	1.69745e8i	0.0223020	+	0.0386283i	0.876961	−	0.480562i	$-0.159567\pi$
$569$	9.80026e7	+	1.69745e8i	0.0223020	+	0.0386283i	−0.854659	+	0.519190i	$0.826234\pi$
$570$	−1.32404e9	+	2.29330e9i	−0.299460	+	0.518680i
$571$	−2.36103e9	+	4.08942e9i	−0.530731	+	0.919254i	0.468626	+	0.883397i	$0.344749\pi$
$571$	−2.36103e9	+	4.08942e9i	−0.530731	+	0.919254i	−0.999357	+	0.0358567i	$0.988584\pi$
$572$	1.72248e9	+	2.98342e9i	0.384829	+	0.666544i
$573$	−3.03484e9			−0.673899
$574$		0			0
$575$	1.88778e8			0.0414109
$576$	−9.55515e7	−	1.65500e8i	−0.0208333	−	0.0360844i
$577$	4.17825e9	−	7.23694e9i	0.905480	−	1.56834i	0.0852087	−	0.996363i	$-0.472844\pi$
$577$	4.17825e9	−	7.23694e9i	0.905480	−	1.56834i	0.820271	−	0.571975i	$-0.193822\pi$
$578$	3.80714e9	−	6.59416e9i	0.820072	−	1.42041i
$579$	6.68751e8	+	1.15831e9i	0.143182	+	0.247999i
$580$	−1.07552e9			−0.228887
$581$		0			0
$582$	2.48465e9			0.522438
$583$	2.28156e9	+	3.95177e9i	0.476861	+	0.825947i
$584$	8.23034e8	−	1.42554e9i	0.170991	−	0.296165i
$585$	1.13687e9	−	1.96912e9i	0.234782	−	0.406655i
$586$	1.33390e8	+	2.31039e8i	0.0273831	+	0.0474290i
$587$	2.01155e9			0.410485			0.205243	−	0.978711i	$-0.434202\pi$
$587$	2.01155e9			0.410485			0.205243	+	0.978711i	$0.434202\pi$
$588$		0			0
$589$	6.33765e9			1.27798
$590$	−1.47995e9	−	2.56335e9i	−0.296665	−	0.513838i
$591$	2.60313e9	−	4.50875e9i	0.518728	−	0.898463i
$592$	4.58605e8	−	7.94328e8i	0.0908475	−	0.157352i
$593$	−6.52838e7	−	1.13075e8i	−0.0128562	−	0.0222677i	0.859526	−	0.511093i	$-0.170759\pi$
$593$	−6.52838e7	−	1.13075e8i	−0.0128562	−	0.0222677i	−0.872382	+	0.488825i	$0.837426\pi$
$594$	−5.99219e8			−0.117310
$595$		0			0
$596$	1.14343e8			0.0221231
$597$	5.65978e8	+	9.80302e8i	0.108865	+	0.188560i
$598$	3.62023e8	−	6.27042e8i	0.0692280	−	0.119906i
$599$	8.31755e8	−	1.44064e9i	0.158125	−	0.273881i	−0.776067	−	0.630650i	$-0.782788\pi$
$599$	8.31755e8	−	1.44064e9i	0.158125	−	0.273881i	0.934193	+	0.356769i	$0.116122\pi$
$600$	−2.03929e8	−	3.53216e8i	−0.0385434	−	0.0667591i
$601$	5.05389e9			0.949653			0.474826	−	0.880080i	$-0.342511\pi$
$601$	5.05389e9			0.949653			0.474826	+	0.880080i	$0.342511\pi$
$602$		0			0
$603$	−2.24121e9			−0.416268
$604$	1.12469e9	+	1.94802e9i	0.207684	+	0.359720i
$605$	5.51899e8	−	9.55916e8i	0.101325	−	0.175500i
$606$	−2.15021e7	+	3.72428e7i	−0.00392489	+	0.00679810i
$607$	−1.75321e9	−	3.03665e9i	−0.318181	−	0.551106i	0.661928	−	0.749568i	$-0.269739\pi$
$607$	−1.75321e9	−	3.03665e9i	−0.318181	−	0.551106i	−0.980109	+	0.198462i	$0.936405\pi$
$608$	1.82185e9			0.328739
$609$		0			0
$610$	−4.26131e9			−0.760132
$611$	1.74686e9	+	3.02565e9i	0.309823	+	0.536630i
$612$	−8.60966e8	+	1.49124e9i	−0.151829	+	0.262976i
$613$	−4.40788e8	+	7.63467e8i	−0.0772890	+	0.133868i	−0.902079	−	0.431570i	$-0.857960\pi$
$613$	−4.40788e8	+	7.63467e8i	−0.0772890	+	0.133868i	0.824790	+	0.565439i	$0.191293\pi$
$614$	1.91963e9	+	3.32490e9i	0.334679	+	0.579682i
$615$	−3.32172e9			−0.575838
$616$		0			0
$617$	−6.58346e9			−1.12838			−0.564191	−	0.825644i	$-0.690812\pi$
$617$	−6.58346e9			−1.12838			−0.564191	+	0.825644i	$0.690812\pi$
$618$	−1.46755e9	−	2.54186e9i	−0.250111	−	0.433204i
$619$	1.88463e9	−	3.26428e9i	0.319381	−	0.553185i	−0.660978	−	0.750406i	$-0.729858\pi$
$619$	1.88463e9	−	3.26428e9i	0.319381	−	0.553185i	0.980359	+	0.197221i	$0.0631916\pi$
$620$	8.04318e8	−	1.39312e9i	0.135537	−	0.234757i
$621$	6.29706e7	+	1.09068e8i	0.0105516	+	0.0182759i
$622$	−2.57308e9			−0.428733
$623$		0			0
$624$	−1.56431e9			−0.257737
$625$	1.46404e9	+	2.53579e9i	0.239868	+	0.415464i
$626$	1.18364e9	−	2.05012e9i	0.192845	−	0.334017i
$627$	2.85629e9	−	4.94723e9i	0.462770	−	0.801542i
$628$	2.83364e9	+	4.90800e9i	0.456547	+	0.790763i
$629$	−8.26452e9			−1.32416
$630$		0			0
$631$	−7.72520e9			−1.22407			−0.612036	−	0.790830i	$-0.709649\pi$
$631$	−7.72520e9			−1.22407			−0.612036	+	0.790830i	$0.709649\pi$
$632$	1.36874e9	+	2.37072e9i	0.215680	+	0.373569i
$633$	1.10540e9	−	1.91462e9i	0.173224	−	0.300033i
$634$	−2.99995e8	+	5.19607e8i	−0.0467522	+	0.0809772i
$635$	−1.88839e9	−	3.27079e9i	−0.292674	−	0.506927i
$636$	−2.07205e9			−0.319375
$637$		0			0
$638$	2.32017e9			0.353710
$639$	−1.06355e9	−	1.84213e9i	−0.161252	−	0.279297i
$640$	2.31214e8	−	4.00474e8i	0.0348645	−	0.0603871i
$641$	−6.11783e9	+	1.05964e10i	−0.917476	+	1.58911i	−0.114240	+	0.993453i	$0.536443\pi$
$641$	−6.11783e9	+	1.05964e10i	−0.917476	+	1.58911i	−0.803236	+	0.595661i	$0.796890\pi$
$642$	−1.62102e9	−	2.80770e9i	−0.241778	−	0.418772i
$643$	8.16042e9			1.21053			0.605263	−	0.796026i	$-0.293068\pi$
$643$	8.16042e9			1.21053			0.605263	+	0.796026i	$0.293068\pi$
$644$		0			0
$645$	6.58585e7			0.00966391
$646$	−8.20790e9	−	1.42165e10i	−1.19789	−	2.07481i
$647$	−1.20190e9	+	2.08176e9i	−0.174463	+	0.302179i	−0.939975	−	0.341242i	$-0.889152\pi$
$647$	−1.20190e9	+	2.08176e9i	−0.174463	+	0.302179i	0.765512	+	0.643422i	$0.222486\pi$
$648$	1.36049e8	−	2.35644e8i	0.0196419	−	0.0340207i
$649$	3.19263e9	+	5.52980e9i	0.458451	+	0.794060i
$650$	−3.33861e9			−0.476835
$651$		0			0
$652$	1.97934e9			0.279675
$653$	1.40617e9	+	2.43555e9i	0.197624	+	0.342295i	0.947758	−	0.318991i	$-0.103344\pi$
$653$	1.40617e9	+	2.43555e9i	0.197624	+	0.342295i	−0.750133	+	0.661287i	$0.770011\pi$
$654$	−4.85336e7	+	8.40626e7i	−0.00678454	+	0.0117512i
$655$	−8.23488e8	+	1.42632e9i	−0.114502	+	0.198323i
$656$	1.14266e9	+	1.97914e9i	0.158035	+	0.273724i
$657$	2.34372e9			0.322423
$658$		0			0
$659$	1.76359e9			0.240049			0.120024	−	0.992771i	$-0.461703\pi$
$659$	1.76359e9			0.240049			0.120024	+	0.992771i	$0.461703\pi$
$660$	−7.24990e8	−	1.25572e9i	−0.0981585	−	0.170016i
$661$	−1.74428e9	+	3.02118e9i	−0.234915	+	0.406884i	−0.959248	−	0.282566i	$-0.908814\pi$
$661$	−1.74428e9	+	3.02118e9i	−0.234915	+	0.406884i	0.724333	+	0.689450i	$0.242148\pi$
$662$	−7.48931e8	+	1.29719e9i	−0.100332	+	0.173780i
$663$	7.04761e9	+	1.22068e10i	0.939171	+	1.62669i
$664$	−2.19477e9			−0.290938
$665$		0			0
$666$	1.30595e9			0.171304
$667$	−2.43821e8	−	4.22310e8i	−0.0318149	−	0.0551051i
$668$	2.38821e9	−	4.13651e9i	0.309996	−	0.536928i
$669$	−3.88905e9	+	6.73604e9i	−0.502172	+	0.869788i
$670$	−2.71162e9	−	4.69667e9i	−0.348311	−	0.603293i
$671$	9.19273e9			1.17467
$672$		0			0
$673$	6.31949e9			0.799152			0.399576	−	0.916700i	$-0.369157\pi$
$673$	6.31949e9			0.799152			0.399576	+	0.916700i	$0.369157\pi$
$674$	6.37342e8	+	1.10391e9i	0.0801794	+	0.138875i
$675$	2.90360e8	−	5.02918e8i	0.0363391	−	0.0629411i
$676$	−4.39454e9	+	7.61157e9i	−0.547142	+	0.947678i
$677$	3.32439e9	+	5.75801e9i	0.411767	+	0.713201i	0.995083	−	0.0990440i	$-0.0315785\pi$
$677$	3.32439e9	+	5.75801e9i	0.411767	+	0.713201i	−0.583316	+	0.812245i	$0.698245\pi$
$678$	−3.96597e9			−0.488704
$679$		0			0
$680$	−4.16670e9			−0.508172
$681$	3.67892e9	+	6.37207e9i	0.446380	+	0.773154i
$682$	−1.73512e9	+	3.00531e9i	−0.209452	+	0.362781i
$683$	−1.62500e9	+	2.81458e9i	−0.195156	+	0.338019i	−0.946951	−	0.321377i	$-0.895854\pi$
$683$	−1.62500e9	+	2.81458e9i	−0.195156	+	0.338019i	0.751796	+	0.659396i	$0.229188\pi$
$684$	1.29700e9	+	2.24648e9i	0.154969	+	0.268414i
$685$	−4.29458e8			−0.0510509
$686$		0			0
$687$	−6.87368e9			−0.808800
$688$	−2.26550e7	−	3.92396e7i	−0.00265219	−	0.00459373i
$689$	−8.48060e9	+	1.46888e10i	−0.987778	+	1.71088i
$690$	−1.52375e8	+	2.63921e8i	−0.0176580	+	0.0305846i
$691$	1.82009e9	+	3.15249e9i	0.209856	+	0.363481i	0.951669	−	0.307126i	$-0.0993673\pi$
$691$	1.82009e9	+	3.15249e9i	0.209856	+	0.363481i	−0.741813	+	0.670606i	$0.766034\pi$
$692$	−5.14148e9			−0.589817
$693$		0			0
$694$	−4.45362e8			−0.0505772
$695$	5.20308e9	+	9.01200e9i	0.587914	+	1.01830i
$696$	−5.26779e8	+	9.12408e8i	−0.0592238	+	0.102579i
$697$	1.02959e10	−	1.78330e10i	1.15173	−	1.99485i
$698$	−7.36269e8	−	1.27526e9i	−0.0819488	−	0.141940i
$699$	7.36942e9			0.816137
$700$		0			0
$701$	1.06079e10			1.16310			0.581548	−	0.813512i	$-0.302447\pi$
$701$	1.06079e10			1.16310			0.581548	+	0.813512i	$0.302447\pi$
$702$	−1.11366e9	−	1.92891e9i	−0.121499	−	0.210442i
$703$	−6.22505e9	+	1.07821e10i	−0.675770	+	1.17047i
$704$	−4.98786e8	+	8.63923e8i	−0.0538778	+	0.0933191i
$705$	−7.35251e8	−	1.27349e9i	−0.0790267	−	0.136878i
$706$	−7.95149e9			−0.850417
$707$		0			0
$708$	−2.89947e9			−0.307045
$709$	2.62241e8	+	4.54214e8i	0.0276336	+	0.0478629i	0.879512	−	0.475878i	$-0.157869\pi$
$709$	2.62241e8	+	4.54214e8i	0.0276336	+	0.0478629i	−0.851878	+	0.523740i	$0.824536\pi$
$710$	2.57356e9	−	4.45754e9i	0.269855	−	0.467403i
$711$	−1.94885e9	+	3.37550e9i	−0.203345	+	0.352204i
$712$	7.55839e8	+	1.30915e9i	0.0784783	+	0.135928i
$713$	7.29358e8			0.0753577
$714$		0			0
$715$	−1.18691e10			−1.21436
$716$	−2.87922e9	−	4.98696e9i	−0.293143	−	0.507739i
$717$	−3.65638e9	+	6.33304e9i	−0.370454	+	0.641645i
$718$	−4.59276e8	+	7.95489e8i	−0.0463061	+	0.0802045i
$719$	−2.21700e9	−	3.83995e9i	−0.222441	−	0.385278i	0.733108	−	0.680112i	$-0.238069\pi$
$719$	−2.21700e9	−	3.83995e9i	−0.222441	−	0.385278i	−0.955549	+	0.294834i	$0.904736\pi$
$720$	6.58417e8			0.0657412
$721$		0			0
$722$	−1.75786e10			−1.73822
$723$	1.07009e9	+	1.85346e9i	0.105302	+	0.182389i
$724$	2.98614e8	−	5.17215e8i	0.0292432	−	0.0506508i
$725$	−1.12427e9	+	1.94729e9i	−0.109569	+	0.189779i
$726$	−5.40629e8	−	9.36397e8i	−0.0524350	−	0.0908201i
$727$	1.87597e10			1.81074			0.905368	−	0.424628i	$-0.139595\pi$
$727$	1.87597e10			1.81074			0.905368	+	0.424628i	$0.139595\pi$
$728$		0			0
$729$	3.87420e8			0.0370370
$730$	2.83564e9	+	4.91147e9i	0.269787	+	0.467285i
$731$	−2.04133e8	+	3.53568e8i	−0.0193287	+	0.0334782i
$732$	−2.08715e9	+	3.61505e9i	−0.196682	+	0.340663i
$733$	−1.57148e9	−	2.72188e9i	−0.147382	−	0.255273i	0.782877	−	0.622176i	$-0.213751\pi$
$733$	−1.57148e9	−	2.72188e9i	−0.147382	−	0.255273i	−0.930259	+	0.366903i	$0.880418\pi$
$734$	1.16398e10			1.08645
$735$		0			0
$736$	2.09665e8			0.0193845
$737$	5.84965e9	+	1.01319e10i	0.538262	+	0.932298i
$738$	−1.62695e9	+	2.81795e9i	−0.148996	+	0.258069i
$739$	−1.06383e10	+	1.84260e10i	−0.969652	+	1.67949i	−0.273091	+	0.961988i	$0.588046\pi$
$739$	−1.06383e10	+	1.84260e10i	−0.969652	+	1.67949i	−0.696561	+	0.717498i	$0.745287\pi$
$740$	1.58006e9	+	2.73674e9i	0.143338	+	0.248269i
$741$	2.12338e10			1.91718
$742$		0			0
$743$	−4.69792e9			−0.420189			−0.210095	−	0.977681i	$-0.567377\pi$
$743$	−4.69792e9			−0.420189			−0.210095	+	0.977681i	$0.567377\pi$
$744$	−7.87895e8	−	1.36467e9i	−0.0701395	−	0.121485i
$745$	−1.96976e8	+	3.41172e8i	−0.0174528	+	0.0302292i
$746$	4.36327e9	−	7.55741e9i	0.384792	−	0.666480i
$747$	−1.56248e9	−	2.70630e9i	−0.137149	−	0.237550i
$748$	8.98862e9			0.785303
$749$		0			0
$750$	5.12620e9			0.443691
$751$	−9.00494e9	−	1.55970e10i	−0.775785	−	1.34370i	−0.934352	−	0.356350i	$-0.884021\pi$
$751$	−9.00494e9	−	1.55970e10i	−0.775785	−	1.34370i	0.158568	−	0.987348i	$-0.449312\pi$
$752$	−5.05846e8	+	8.76151e8i	−0.0433767	+	0.0751306i
$753$	2.52962e9	−	4.38143e9i	0.215910	−	0.373967i
$754$	4.31206e9	+	7.46870e9i	0.366340	+	0.634520i
$755$	−7.74991e9			−0.655363
$756$		0			0
$757$	−8.12535e9			−0.680780			−0.340390	−	0.940284i	$-0.610559\pi$
$757$	−8.12535e9			−0.680780			−0.340390	+	0.940284i	$0.610559\pi$
$758$	−6.46770e9	−	1.12024e10i	−0.539396	−	0.934262i
$759$	3.28711e8	−	5.69345e8i	0.0272878	−	0.0472638i
$760$	−3.13846e9	+	5.43598e9i	−0.259340	+	0.449190i
$761$	−7.87964e9	−	1.36479e10i	−0.648127	−	1.12259i	−0.983570	−	0.180529i	$-0.942219\pi$
$761$	−7.87964e9	−	1.36479e10i	−0.648127	−	1.12259i	0.335442	−	0.942061i	$-0.391114\pi$
$762$	−3.69967e9			−0.302915
$763$		0			0
$764$	−7.19370e9			−0.583614
$765$	−2.96633e9	−	5.13783e9i	−0.239555	−	0.414921i
$766$	−3.93382e9	+	6.81358e9i	−0.316238	+	0.547740i
$767$	−1.18671e10	+	2.05544e10i	−0.949643	+	1.64483i
$768$	−2.26492e8	−	3.92296e8i	−0.0180422	−	0.0312500i
$769$	−1.41256e10			−1.12012			−0.560058	−	0.828453i	$-0.689221\pi$
$769$	−1.41256e10			−1.12012			−0.560058	+	0.828453i	$0.689221\pi$
$770$		0			0
$771$	1.03980e10			0.817074
$772$	1.58519e9	+	2.74563e9i	0.124000	+	0.214774i
$773$	7.72780e9	−	1.33849e10i	0.601766	−	1.04229i	−0.390788	−	0.920481i	$-0.627797\pi$
$773$	7.72780e9	−	1.33849e10i	0.601766	−	1.04229i	0.992554	−	0.121808i	$-0.0388694\pi$
$774$	3.22568e7	−	5.58705e7i	0.00250051	−	0.00433101i
$775$	−1.68155e9	−	2.91253e9i	−0.129764	−	0.224758i
$776$	5.88954e9			0.452444
$777$		0			0
$778$	1.41049e10			1.07385
$779$	−1.55103e10	−	2.68646e10i	−1.17554	−	2.03610i
$780$	2.69480e9	−	4.66754e9i	0.203327	−	0.352173i
$781$	−5.55183e9	+	9.61605e9i	−0.417020	+	0.722300i
$782$	−9.44593e8	−	1.63608e9i	−0.0706352	−	0.122344i
$783$	−1.50009e9			−0.111673
$784$		0			0
$785$	−1.95258e10			−1.44067
$786$	8.06672e8	+	1.39720e9i	0.0592541	+	0.102631i
$787$	−1.24275e10	+	2.15250e10i	−0.908807	+	1.57410i	−0.0930843	+	0.995658i	$0.529673\pi$
$787$	−1.24275e10	+	2.15250e10i	−0.908807	+	1.57410i	−0.815723	+	0.578442i	$0.803661\pi$
$788$	6.17038e9	−	1.06874e10i	0.449231	−	0.778092i
$789$	−2.90790e9	−	5.03663e9i	−0.210771	−	0.365065i
$790$	−9.43156e9			−0.680595
$791$		0			0
$792$	−1.42037e9			−0.101593
$793$	1.70848e10	+	2.95917e10i	1.21662	+	2.10724i
$794$	−6.56241e9	+	1.13664e10i	−0.465255	+	0.805846i
$795$	3.56947e9	−	6.18251e9i	0.251953	−	0.436395i
$796$	1.34158e9	+	2.32368e9i	0.0942801	+	0.163298i
$797$	−4.81698e9			−0.337032			−0.168516	−	0.985699i	$-0.553897\pi$
$797$	−4.81698e9			−0.337032			−0.168516	+	0.985699i	$0.553897\pi$
$798$		0			0
$799$	9.11585e9			0.632242
$800$	−4.83388e8	−	8.37252e8i	−0.0333796	−	0.0578151i
$801$	−1.07619e9	+	1.86401e9i	−0.0739900	+	0.128154i
$802$	−1.73628e9	+	3.00733e9i	−0.118853	+	0.205859i
$803$	−6.11719e9	−	1.05953e10i	−0.416915	−	0.722118i
$804$	−5.31251e9			−0.360498
$805$		0			0
$806$	−1.28989e10			−0.867724
$807$	−8.12029e9	−	1.40647e10i	−0.543894	−	0.942051i
$808$	−5.09680e7	+	8.82791e7i	−0.00339905	+	0.00588733i
$809$	5.00614e9	−	8.67090e9i	0.332417	−	0.575764i	−0.650568	−	0.759448i	$-0.725469\pi$
$809$	5.00614e9	−	8.67090e9i	0.332417	−	0.575764i	0.982985	+	0.183684i	$0.0588025\pi$
$810$	4.68736e8	+	8.11875e8i	0.0309907	+	0.0536774i
$811$	−5.30389e9			−0.349158			−0.174579	−	0.984643i	$-0.555856\pi$
$811$	−5.30389e9			−0.349158			−0.174579	+	0.984643i	$0.555856\pi$
$812$		0			0
$813$	−3.38664e9			−0.221031
$814$	−3.40858e9	−	5.90383e9i	−0.221507	−	0.383662i
$815$	−3.40976e9	+	5.90588e9i	−0.220634	+	0.382149i
$816$	−2.04081e9	+	3.53478e9i	−0.131488	+	0.227744i
$817$	3.07516e8	+	5.32634e8i	0.0197283	+	0.0341705i
$818$	1.75943e10			1.12392
$819$		0			0
$820$	−7.87370e9			−0.498690
$821$	−2.16185e8	−	3.74443e8i	−0.0136340	−	0.0236148i	0.859128	−	0.511761i	$-0.171007\pi$
$821$	−2.16185e8	−	3.74443e8i	−0.0136340	−	0.0236148i	−0.872762	+	0.488146i	$0.837673\pi$
$822$	−2.10344e8	+	3.64327e8i	−0.0132093	+	0.0228791i
$823$	2.33980e9	−	4.05265e9i	0.146312	−	0.253420i	−0.783550	−	0.621329i	$-0.786593\pi$
$823$	2.33980e9	−	4.05265e9i	0.146312	−	0.253420i	0.929862	+	0.367909i	$0.119926\pi$
$824$	−3.47863e9	−	6.02516e9i	−0.216602	−	0.375166i
$825$	−3.03140e9			−0.187955
$826$		0			0
$827$	−2.16354e10			−1.33013			−0.665067	−	0.746784i	$-0.731597\pi$
$827$	−2.16354e10			−1.33013			−0.665067	+	0.746784i	$0.731597\pi$
$828$	1.49264e8	+	2.58532e8i	0.00913793	+	0.0158274i
$829$	7.34829e9	−	1.27276e10i	0.447966	−	0.775900i	−0.550287	−	0.834975i	$-0.685482\pi$
$829$	7.34829e9	−	1.27276e10i	0.447966	−	0.775900i	0.998254	+	0.0590752i	$0.0188152\pi$
$830$	3.78087e9	−	6.54866e9i	0.229519	−	0.397538i
$831$	8.35376e8	+	1.44691e9i	0.0504985	+	0.0874659i
$832$	−3.70800e9			−0.223207
$833$		0			0
$834$	1.01937e10			0.608484
$835$	8.22824e9	+	1.42517e10i	0.489107	+	0.847159i
$836$	6.77046e9	−	1.17268e10i	0.400771	−	0.694155i
$837$	1.12183e9	−	1.94306e9i	0.0661282	−	0.114537i
$838$	−5.75208e9	−	9.96289e9i	−0.337653	−	0.584832i
$839$	−2.93033e9			−0.171297			−0.0856485	−	0.996325i	$-0.527296\pi$
$839$	−2.93033e9			−0.171297			−0.0856485	+	0.996325i	$0.527296\pi$
$840$		0			0
$841$	−1.14416e10			−0.663284
$842$	−5.51413e9	−	9.55075e9i	−0.318335	−	0.551372i
$843$	3.41131e9	−	5.90856e9i	0.196121	−	0.339692i
$844$	2.62022e9	−	4.53835e9i	0.150016	−	0.259836i
$845$	−1.51407e10	−	2.62245e10i	−0.863274	−	1.49523i
$846$	−1.44048e9			−0.0817918
$847$		0			0
$848$	−4.91153e9			−0.276587
$849$	1.16571e9	+	2.01908e9i	0.0653755	+	0.113234i
$850$	−4.35556e9	+	7.54405e9i	−0.243264	+	0.421345i
$851$	−7.16400e8	+	1.24084e9i	−0.0398476	+	0.0690180i
$852$	−2.52101e9	−	4.36652e9i	−0.139649	−	0.241878i
$853$	2.34416e10			1.29320			0.646600	−	0.762829i	$-0.276190\pi$
$853$	2.34416e10			1.29320			0.646600	+	0.762829i	$0.276190\pi$
$854$		0			0
$855$	−8.93727e9			−0.489016
$856$	−3.84243e9	−	6.65528e9i	−0.209386	−	0.362667i
$857$	2.10011e9	−	3.63751e9i	0.113975	−	0.197411i	−0.803394	−	0.595447i	$-0.796975\pi$
$857$	2.10011e9	−	3.63751e9i	0.113975	−	0.197411i	0.917370	+	0.398036i	$0.130308\pi$
$858$	−5.81337e9	+	1.00690e10i	−0.314212	+	0.544231i
$859$	−9.88718e8	−	1.71251e9i	−0.0532226	−	0.0921843i	0.838187	−	0.545383i	$-0.183616\pi$
$859$	−9.88718e8	−	1.71251e9i	−0.0532226	−	0.0921843i	−0.891409	+	0.453199i	$0.850283\pi$
$860$	1.56109e8			0.00836919
$861$		0			0
$862$	−1.55145e9			−0.0825017
$863$	−1.03263e10	−	1.78857e10i	−0.546900	−	0.947258i	−0.998485	−	0.0550302i	$-0.982474\pi$
$863$	−1.03263e10	−	1.78857e10i	−0.546900	−	0.947258i	0.451585	−	0.892228i	$-0.350859\pi$
$864$	3.22486e8	−	5.58563e8i	0.0170103	−	0.0294628i
$865$	8.85711e9	−	1.53410e10i	0.465303	−	0.805928i
$866$	1.85835e9	+	3.21876e9i	0.0972335	+	0.168413i
$867$	2.56982e10			1.33917
$868$		0			0
$869$	2.03463e10			1.05176
$870$	−1.81494e9	−	3.14357e9i	−0.0934426	−	0.161847i
$871$	−2.17433e10	+	3.76605e10i	−1.11497	+	1.93118i
$872$	−1.15043e8	+	1.99260e8i	−0.00587558	+	0.0101768i
$873$	4.19284e9	+	7.26222e9i	0.213284	+	0.369419i
$874$	−2.84597e9			−0.144192
$875$		0			0
$876$	5.55548e9			0.279227
$877$	−1.45284e10	−	2.51640e10i	−0.727312	−	1.25974i	−0.958015	−	0.286717i	$-0.907436\pi$
$877$	−1.45284e10	−	2.51640e10i	−0.727312	−	1.25974i	0.230703	−	0.973024i	$-0.425897\pi$
$878$	9.01785e9	−	1.56194e10i	0.449647	−	0.778812i
$879$	−4.50193e8	+	7.79757e8i	−0.0223582	+	0.0387256i
$880$	−1.71849e9	−	2.97652e9i	−0.0850078	−	0.147238i
$881$	−2.13607e10			−1.05245			−0.526223	−	0.850347i	$-0.676392\pi$
$881$	−2.13607e10			−1.05245			−0.526223	+	0.850347i	$0.676392\pi$
$882$		0			0
$883$	−3.01885e9			−0.147564			−0.0737818	−	0.997274i	$-0.523507\pi$
$883$	−3.01885e9			−0.147564			−0.0737818	+	0.997274i	$0.523507\pi$
$884$	1.67054e10	+	2.89347e10i	0.813346	+	1.40876i
$885$	4.99484e9	−	8.65132e9i	0.242226	−	0.419547i
$886$	1.44106e10	−	2.49598e10i	0.696086	−	1.20566i
$887$	1.07132e10	+	1.85558e10i	0.515449	+	0.892784i	0.999839	+	0.0179321i	$0.00570828\pi$
$887$	1.07132e10	+	1.85558e10i	0.515449	+	0.892784i	−0.484390	+	0.874852i	$0.660958\pi$
$888$	3.09559e9			0.148353
$889$		0			0
$890$	−5.20826e9			−0.247644
$891$	−1.01118e9	−	1.75142e9i	−0.0478914	−	0.0829503i
$892$	−9.21850e9	+	1.59669e10i	−0.434894	+	0.753258i
$893$	6.86629e9	−	1.18928e10i	0.322658	−	0.558860i
$894$	1.92953e8	+	3.34205e8i	0.00903174	+	0.0156434i
$895$	1.98399e10			0.925035
$896$		0			0
$897$	2.44365e9			0.113049
$898$	7.47174e9	+	1.29414e10i	0.344314	+	0.596369i
$899$	−4.34369e9	+	7.52350e9i	−0.199389	+	0.345351i
$900$	6.88261e8	−	1.19210e9i	0.0314705	−	0.0545086i
$901$	2.21277e10	+	3.83262e10i	1.00786	+	1.74566i
$902$	1.69856e10			0.770650
$903$		0			0
$904$	−9.40082e9			−0.423230
$905$	1.02883e9	+	1.78199e9i	0.0461396	+	0.0799162i
$906$	−3.79583e9	+	6.57457e9i	−0.169574	+	0.293710i
$907$	8.22034e7	−	1.42380e8i	0.00365817	−	0.00633614i	−0.864191	−	0.503165i	$-0.832169\pi$
$907$	8.22034e7	−	1.42380e8i	0.00365817	−	0.00633614i	0.867849	+	0.496829i	$0.165502\pi$
$908$	8.72040e9	+	1.51042e10i	0.386577	+	0.669571i
$909$	−1.45139e8			−0.00640931
$910$		0			0
$911$	1.81509e10			0.795395			0.397697	−	0.917517i	$-0.369809\pi$
$911$	1.81509e10			0.795395			0.397697	+	0.917517i	$0.369809\pi$
$912$	3.07438e9	+	5.32498e9i	0.134207	+	0.232453i
$913$	−8.15629e9	+	1.41271e10i	−0.354687	+	0.614335i
$914$	8.60670e9	−	1.49072e10i	0.372842	−	0.645781i
$915$	−7.19097e9	−	1.24551e10i	−0.310323	−	0.537494i
$916$	−1.62932e10			−0.700441
$917$		0			0
$918$	−5.81152e9			−0.247936
$919$	2.73816e9	+	4.74263e9i	0.116373	+	0.201565i	0.918328	−	0.395820i	$-0.129540\pi$
$919$	2.73816e9	+	4.74263e9i	0.116373	+	0.201565i	−0.801954	+	0.597385i	$0.796206\pi$
$920$	−3.61185e8	+	6.25591e8i	−0.0152923	+	0.0264870i
$921$	−6.47876e9	+	1.12215e10i	−0.273265	+	0.473308i
$922$	−5.77898e9	−	1.00095e10i	−0.242825	−	0.420585i
$923$	−4.12725e10			−1.72765
$924$		0			0
$925$	6.60670e9			0.274466
$926$	1.56779e10	+	2.71549e10i	0.648857	+	1.12385i
$927$	4.95297e9	−	8.57879e9i	0.204214	−	0.353710i
$928$	−1.24866e9	+	2.16275e9i	−0.0512893	+	0.0888357i
$929$	−1.57892e10	−	2.73478e10i	−0.646110	−	1.11909i	−0.984044	−	0.177925i	$-0.943062\pi$
$929$	−1.57892e10	−	2.73478e10i	−0.646110	−	1.11909i	0.337935	−	0.941170i	$-0.390272\pi$
$930$	5.42915e9			0.221331
$931$		0			0
$932$	1.74682e10			0.706795
$933$	−4.34207e9	−	7.52069e9i	−0.175030	−	0.303160i
$934$	−8.39361e9	+	1.45382e10i	−0.337081	+	0.583842i
$935$	−1.54845e10	+	2.68199e10i	−0.619521	+	1.07304i
$936$	−2.63978e9	−	4.57223e9i	−0.105221	−	0.182248i
$937$	−4.72463e10			−1.87620			−0.938100	−	0.346366i	$-0.887416\pi$
$937$	−4.72463e10			−1.87620			−0.938100	+	0.346366i	$0.887416\pi$
$938$		0			0
$939$	7.98955e9			0.314915
$940$	−1.74282e9	−	3.01865e9i	−0.0684392	−	0.118540i
$941$	2.08047e9	−	3.60348e9i	0.0813949	−	0.140980i	−0.822454	−	0.568831i	$-0.807396\pi$
$941$	2.08047e9	−	3.60348e9i	0.0813949	−	0.140980i	0.903849	+	0.427851i	$0.140729\pi$
$942$	−9.56352e9	+	1.65645e10i	−0.372769	+	0.645655i
$943$	−1.78497e9	−	3.09167e9i	−0.0693172	−	0.120061i
$944$	−6.87281e9			−0.265909
$945$		0			0
$946$	−3.36766e8			−0.0129333
$947$	−1.45868e10	−	2.52651e10i	−0.558130	−	0.966709i	−0.997653	−	0.0684774i	$-0.978186\pi$
$947$	−1.45868e10	−	2.52651e10i	−0.558130	−	0.966709i	0.439523	−	0.898231i	$-0.355147\pi$
$948$	−4.61949e9	+	8.00119e9i	−0.176102	+	0.305018i
$949$	2.27377e10	−	3.93829e10i	0.863606	−	1.49581i
$950$	6.56144e9	+	1.13647e10i	0.248294	+	0.430058i
$951$	−2.02497e9			−0.0763460
$952$		0			0
$953$	1.91663e10			0.717320			0.358660	−	0.933468i	$-0.383234\pi$
$953$	1.91663e10			0.717320			0.358660	+	0.933468i	$0.383234\pi$
$954$	−3.49659e9	−	6.05627e9i	−0.130384	−	0.225832i
$955$	1.23924e10	−	2.14643e10i	0.460409	−	0.797452i
$956$	−8.66698e9	+	1.50116e10i	−0.320823	+	0.555681i
$957$	3.91528e9	+	6.78147e9i	0.144401	+	0.250111i
$958$	−8.79806e9			−0.323301
$959$		0			0
$960$	1.56069e9			0.0569335
$961$	7.25952e9	+	1.25739e10i	0.263861	+	0.457021i
$962$	1.26698e10	−	2.19447e10i	0.458834	−	0.794724i
$963$	5.47096e9	−	9.47597e9i	0.197411	−	0.341926i
$964$	2.53652e9	+	4.39338e9i	0.0911944	+	0.157953i
$965$	−1.09231e10			−0.391290
$966$		0			0
$967$	−1.26859e10			−0.451157			−0.225579	−	0.974225i	$-0.572427\pi$
$967$	−1.26859e10			−0.451157			−0.225579	+	0.974225i	$0.572427\pi$
$968$	−1.28149e9	−	2.21961e9i	−0.0454100	−	0.0786525i
$969$	2.77017e10	−	4.79807e10i	0.978076	−	1.69408i
$970$	−1.01458e10	+	1.75730e10i	−0.356931	+	0.618222i
$971$	−1.55549e10	−	2.69420e10i	−0.545257	−	0.944413i	−0.998591	−	0.0530720i	$-0.983099\pi$
$971$	−1.55549e10	−	2.69420e10i	−0.545257	−	0.944413i	0.453334	−	0.891341i	$-0.350235\pi$
$972$	9.18330e8			0.0320750
$973$		0			0
$974$	1.97871e10			0.686161
$975$	−5.63390e9	−	9.75820e9i	−0.194667	−	0.337174i
$976$	−4.94732e9	+	8.56901e9i	−0.170332	+	0.295023i
$977$	−1.52997e10	+	2.64998e10i	−0.524870	+	0.909101i	0.474711	+	0.880142i	$0.342553\pi$
$977$	−1.52997e10	+	2.64998e10i	−0.524870	+	0.909101i	−0.999581	+	0.0289591i	$0.990781\pi$
$978$	3.34014e9	+	5.78529e9i	0.114177	+	0.197760i
$979$	1.12355e10			0.382697
$980$		0			0
$981$	−3.27602e8			−0.0110791
$982$	1.67661e10	+	2.90398e10i	0.564992	+	0.978595i
$983$	7.81777e9	−	1.35408e10i	0.262510	−	0.454680i	−0.704398	−	0.709805i	$-0.748783\pi$
$983$	7.81777e9	−	1.35408e10i	0.262510	−	0.454680i	0.966908	+	0.255125i	$0.0821165\pi$
$984$	−3.85646e9	+	6.67959e9i	−0.129035	+	0.223495i
$985$	2.12591e10	+	3.68219e10i	0.708792	+	1.22766i
$986$	2.25021e10			0.747574
$987$		0			0
$988$	5.03319e10			1.66033
$989$	3.53900e7	+	6.12973e7i	0.00116331	+	0.00201490i
$990$	2.44684e9	−	4.23805e9i	0.0801461	−	0.138817i
$991$	2.06482e10	−	3.57637e10i	0.673944	−	1.16730i	−0.302833	−	0.953044i	$-0.597932\pi$
$991$	2.06482e10	−	3.57637e10i	0.673944	−	1.16730i	0.976776	−	0.214261i	$-0.0687343\pi$
$992$	−1.86760e9	−	3.23478e9i	−0.0607426	−	0.105209i
$993$	−5.05528e9			−0.163841
$994$		0			0
$995$	−9.24441e9			−0.297508
$996$	−3.70367e9	−	6.41494e9i	−0.118775	−	0.205724i
$997$	2.08264e10	−	3.60723e10i	0.665550	−	1.15277i	−0.313586	−	0.949560i	$-0.601531\pi$
$997$	2.08264e10	−	3.60723e10i	0.665550	−	1.15277i	0.979136	−	0.203206i	$-0.0651361\pi$
$998$	−7.99296e9	+	1.38442e10i	−0.254537	+	0.440871i
$999$	2.20379e9	+	3.81708e9i	0.0699344	+	0.121130i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.8.e.v.67.2		4
7.2	even	3	inner	294.8.e.v.79.2		4
7.3	odd	6		294.8.a.n.1.2	✓	2
7.4	even	3		294.8.a.q.1.1	yes	2
7.5	odd	6		294.8.e.y.79.1		4
7.6	odd	2		294.8.e.y.67.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.8.a.n.1.2	✓	2	7.3	odd	6
294.8.a.q.1.1	yes	2	7.4	even	3
294.8.e.v.67.2		4	1.1	even	1	trivial
294.8.e.v.79.2		4	7.2	even	3	inner
294.8.e.y.67.1		4	7.6	odd	2
294.8.e.y.79.1		4	7.5	odd	6

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	294.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.00000 + 6.92820i) q^{2} +(-13.5000 + 23.3827i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-110.251 - 190.961i) q^{5} -216.000 q^{6} -512.000 q^{8} +(-364.500 - 631.333i) q^{9} +(882.010 - 1527.69i) q^{10} +(-1902.72 + 3295.60i) q^{11} +(-864.000 - 1496.49i) q^{12} -14144.9 q^{13} +5953.57 q^{15} +(-2048.00 - 3547.24i) q^{16} +(-18453.5 + 31962.4i) q^{17} +(2916.00 - 5050.66i) q^{18} +(27799.3 + 48149.8i) q^{19} +14112.2 q^{20} -30443.5 q^{22} +(3199.24 + 5541.24i) q^{23} +(6912.00 - 11971.9i) q^{24} +(14751.8 - 25550.9i) q^{25} +(-56579.6 - 97998.7i) q^{26} +19683.0 q^{27} -76212.3 q^{29} +(23814.3 + 41247.5i) q^{30} +(56994.7 - 98717.7i) q^{31} +(16384.0 - 28377.9i) q^{32} +(-51373.4 - 88981.3i) q^{33} -295256. q^{34} +46656.0 q^{36} +(111964. + 193928. i) q^{37} +(-222394. + 385198. i) q^{38} +(190956. - 330746. i) q^{39} +(56448.6 + 97771.9i) q^{40} -557937. q^{41} +11062.0 q^{43} +(-121774. - 210919. i) q^{44} +(-80373.2 + 139210. i) q^{45} +(-25593.9 + 44329.9i) q^{46} +(-123498. - 213904. i) q^{47} +110592. q^{48} +236029. q^{50} +(-498244. - 862984. i) q^{51} +(452637. - 783990. i) q^{52} +(599552. - 1.03845e6i) q^{53} +(78732.0 + 136368. i) q^{54} +839108. q^{55} -1.50116e6 q^{57} +(-304849. - 528014. i) q^{58} +(838966. - 1.45313e6i) q^{59} +(-190514. + 329980. i) q^{60} +(-1.20784e6 - 2.09204e6i) q^{61} +911915. q^{62} +262144. q^{64} +(1.55949e6 + 2.70112e6i) q^{65} +(410987. - 711851. i) q^{66} +(1.53718e6 - 2.66248e6i) q^{67} +(-1.18102e6 - 2.04559e6i) q^{68} -172759. q^{69} +2.91784e6 q^{71} +(186624. + 323242. i) q^{72} +(-1.60749e6 + 2.78425e6i) q^{73} +(-895713. + 1.55142e6i) q^{74} +(398299. + 689874. i) q^{75} -3.55831e6 q^{76} +3.05530e6 q^{78} +(-2.67331e6 - 4.63032e6i) q^{79} +(-451589. + 782175. i) q^{80} +(-265720. + 460241. i) q^{81} +(-2.23175e6 - 3.86550e6i) q^{82} +4.28665e6 q^{83} +8.13808e6 q^{85} +(44248.1 + 76639.9i) q^{86} +(1.02887e6 - 1.78205e6i) q^{87} +(974192. - 1.68735e6i) q^{88} +(-1.47625e6 - 2.55694e6i) q^{89} -1.28597e6 q^{90} -409502. q^{92} +(1.53886e6 + 2.66538e6i) q^{93} +(987981. - 1.71123e6i) q^{94} +(6.12981e6 - 1.06171e7i) q^{95} +(442368. + 766204. i) q^{96} -1.15030e7 q^{97} +2.77416e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 16 q^{2} - 54 q^{3} - 128 q^{4} - 540 q^{5} - 864 q^{6} - 2048 q^{8} - 1458 q^{9} + 4320 q^{10} - 1196 q^{11} - 3456 q^{12} - 24624 q^{13} + 29160 q^{15} - 8192 q^{16} - 29484 q^{17} + 11664 q^{18}+ \cdots + 1743768 q^{99}+O(q^{100}) \) 4 * q + 16 * q^2 - 54 * q^3 - 128 * q^4 - 540 * q^5 - 864 * q^6 - 2048 * q^8 - 1458 * q^9 + 4320 * q^10 - 1196 * q^11 - 3456 * q^12 - 24624 * q^13 + 29160 * q^15 - 8192 * q^16 - 29484 * q^17 + 11664 * q^18 + 47088 * q^19 + 69120 * q^20 - 19136 * q^22 + 94052 * q^23 + 27648 * q^24 + 5550 * q^25 - 98496 * q^26 + 78732 * q^27 - 341200 * q^29 + 116640 * q^30 + 258984 * q^31 + 65536 * q^32 - 32292 * q^33 - 471744 * q^34 + 186624 * q^36 + 648856 * q^37 - 376704 * q^38 + 332424 * q^39 + 276480 * q^40 - 1211112 * q^41 - 1396960 * q^43 - 76544 * q^44 - 393660 * q^45 - 752416 * q^46 - 816912 * q^47 + 442368 * q^48 + 88800 * q^50 - 796068 * q^51 + 787968 * q^52 + 1923508 * q^53 + 314928 * q^54 + 10800 * q^55 - 2542752 * q^57 - 1364800 * q^58 + 81864 * q^59 - 933120 * q^60 - 1616544 * q^61 + 4143744 * q^62 + 1048576 * q^64 + 2533380 * q^65 + 258336 * q^66 + 5424 * q^67 - 1886976 * q^68 - 5078808 * q^69 - 4985928 * q^71 + 746496 * q^72 - 4710744 * q^73 - 5190848 * q^74 + 149850 * q^75 - 6027264 * q^76 + 5318784 * q^78 - 3416656 * q^79 - 2211840 * q^80 - 1062882 * q^81 - 4844448 * q^82 + 17842896 * q^83 + 11532920 * q^85 - 5587840 * q^86 + 4606200 * q^87 + 612352 * q^88 - 12374532 * q^89 - 6298560 * q^90 - 12038656 * q^92 + 6992568 * q^93 + 6535296 * q^94 + 9540520 * q^95 + 1769472 * q^96 - 22593168 * q^97 + 1743768 * q^99

Introduction

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