LMFDB - Embedded newform 21.7.h.a.11.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,7,Mod(2,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("21.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	21.h (of order $6$, 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:	$4.83113575602$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.10
Character	$\chi$	$=$	21.11
Dual form			21.7.h.a.2.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.69684 - 3.28907i) q^{2} +(-24.6534 + 11.0094i) q^{3} +(-10.3640 + 17.9510i) q^{4} +(-57.4599 + 33.1745i) q^{5} +(-104.236 + 143.806i) q^{6} +(-329.948 + 93.7191i) q^{7} +557.353i q^{8} +(486.585 - 542.841i) q^{9} +O(q^{10})$	\(q+(5.69684 - 3.28907i) q^{2} +(-24.6534 + 11.0094i) q^{3} +(-10.3640 + 17.9510i) q^{4} +(-57.4599 + 33.1745i) q^{5} +(-104.236 + 143.806i) q^{6} +(-329.948 + 93.7191i) q^{7} +557.353i q^{8} +(486.585 - 542.841i) q^{9} +(-218.227 + 377.979i) q^{10} +(603.143 + 348.225i) q^{11} +(57.8782 - 556.654i) q^{12} -824.771 q^{13} +(-1571.41 + 1619.13i) q^{14} +(1051.35 - 1450.47i) q^{15} +(1169.88 + 2026.29i) q^{16} +(-4784.05 - 2762.07i) q^{17} +(986.554 - 4692.89i) q^{18} +(2527.23 + 4377.29i) q^{19} -1375.28i q^{20} +(7102.56 - 5943.04i) q^{21} +4581.35 q^{22} +(17221.4 - 9942.79i) q^{23} +(-6136.14 - 13740.7i) q^{24} +(-5611.41 + 9719.25i) q^{25} +(-4698.59 + 2712.73i) q^{26} +(-6019.63 + 18739.9i) q^{27} +(1737.23 - 6894.19i) q^{28} +23408.7i q^{29} +(1218.70 - 11721.0i) q^{30} +(-23180.0 + 40149.0i) q^{31} +(-17562.4 - 10139.7i) q^{32} +(-18703.3 - 1944.68i) q^{33} -36338.6 q^{34} +(15849.7 - 16330.9i) q^{35} +(4701.55 + 14360.7i) q^{36} +(24177.8 + 41877.2i) q^{37} +(28794.4 + 16624.5i) q^{38} +(20333.4 - 9080.25i) q^{39} +(-18489.9 - 32025.4i) q^{40} -15904.7i q^{41} +(20915.1 - 57217.4i) q^{42} +21757.0 q^{43} +(-12501.9 + 7217.99i) q^{44} +(-9950.65 + 47333.8i) q^{45} +(65405.1 - 113285. i) q^{46} +(-33042.5 + 19077.1i) q^{47} +(-51149.9 - 37075.4i) q^{48} +(100082. - 61844.9i) q^{49} +73825.4i q^{50} +(148352. + 15424.9i) q^{51} +(8547.91 - 14805.4i) q^{52} +(-193312. - 111609. i) q^{53} +(27344.1 + 126557. i) q^{54} -46208.7 q^{55} +(-52234.6 - 183898. i) q^{56} +(-110496. - 80091.9i) q^{57} +(76992.9 + 133356. i) q^{58} +(271755. + 156898. i) q^{59} +(15141.0 + 33905.4i) q^{60} +(-126472. - 219056. i) q^{61} +304963. i q^{62} +(-109673. + 224712. i) q^{63} -283145. q^{64} +(47391.2 - 27361.3i) q^{65} +(-112946. + 50438.0i) q^{66} +(82947.6 - 143669. i) q^{67} +(99163.6 - 57252.1i) q^{68} +(-315103. + 434722. i) q^{69} +(36579.5 - 145166. i) q^{70} -298965. i q^{71} +(302554. + 271200. i) q^{72} +(-2216.28 + 3838.71i) q^{73} +(275474. + 159045. i) q^{74} +(31337.2 - 301391. i) q^{75} -104769. q^{76} +(-231641. - 58370.1i) q^{77} +(85970.8 - 118607. i) q^{78} +(310276. + 537413. i) q^{79} +(-134442. - 77620.3i) q^{80} +(-57911.3 - 528276. i) q^{81} +(-52311.7 - 90606.6i) q^{82} -414931. i q^{83} +(33072.3 + 189091. i) q^{84} +366521. q^{85} +(123946. - 71560.3i) q^{86} +(-257716. - 577104. i) q^{87} +(-194084. + 336164. i) q^{88} +(-649685. + 375096. i) q^{89} +(98996.9 + 302381. i) q^{90} +(272131. - 77296.8i) q^{91} +412188. i q^{92} +(129450. - 1.24501e6i) q^{93} +(-125492. + 217359. i) q^{94} +(-290428. - 167679. i) q^{95} +(544605. + 56625.4i) q^{96} +212245. q^{97} +(366742. - 681499. i) q^{98} +(482511. - 157970. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9}+O(q^{10}) $ 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9	$ 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9} - 930 q^{10} - 404 q^{12} + 3632 q^{13} + 5450 q^{15} - 13706 q^{16} + 1612 q^{18} + 6830 q^{19} - 11333 q^{21} - 27348 q^{22} - 54498 q^{24} - 7640 q^{25} + 13268 q^{27} + 88522 q^{28} + 32380 q^{30} + 69410 q^{31} - 85459 q^{33} - 31344 q^{34} + 399028 q^{36} - 71830 q^{37} + 104570 q^{39} + 230250 q^{40} - 467782 q^{42} - 498904 q^{43} - 85375 q^{45} - 342660 q^{46} - 324728 q^{48} + 395668 q^{49} + 42177 q^{51} + 218000 q^{52} - 402122 q^{54} + 231660 q^{55} + 786782 q^{57} + 459522 q^{58} + 1021150 q^{60} + 153158 q^{61} + 179011 q^{63} - 1399412 q^{64} + 80896 q^{66} - 977098 q^{67} - 1520742 q^{69} - 139650 q^{70} - 1001352 q^{72} - 488350 q^{73} + 1434610 q^{75} + 6196280 q^{76} + 245176 q^{78} + 380762 q^{79} + 893531 q^{81} - 3665004 q^{82} + 1231496 q^{84} - 912540 q^{85} + 1452416 q^{87} - 1522482 q^{88} - 11713820 q^{90} - 1529416 q^{91} - 1690071 q^{93} - 3034044 q^{94} + 7549346 q^{96} + 7212176 q^{97} + 435866 q^{99}+O(q^{100}) $ 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9 - 930 * q^10 - 404 * q^12 + 3632 * q^13 + 5450 * q^15 - 13706 * q^16 + 1612 * q^18 + 6830 * q^19 - 11333 * q^21 - 27348 * q^22 - 54498 * q^24 - 7640 * q^25 + 13268 * q^27 + 88522 * q^28 + 32380 * q^30 + 69410 * q^31 - 85459 * q^33 - 31344 * q^34 + 399028 * q^36 - 71830 * q^37 + 104570 * q^39 + 230250 * q^40 - 467782 * q^42 - 498904 * q^43 - 85375 * q^45 - 342660 * q^46 - 324728 * q^48 + 395668 * q^49 + 42177 * q^51 + 218000 * q^52 - 402122 * q^54 + 231660 * q^55 + 786782 * q^57 + 459522 * q^58 + 1021150 * q^60 + 153158 * q^61 + 179011 * q^63 - 1399412 * q^64 + 80896 * q^66 - 977098 * q^67 - 1520742 * q^69 - 139650 * q^70 - 1001352 * q^72 - 488350 * q^73 + 1434610 * q^75 + 6196280 * q^76 + 245176 * q^78 + 380762 * q^79 + 893531 * q^81 - 3665004 * q^82 + 1231496 * q^84 - 912540 * q^85 + 1452416 * q^87 - 1522482 * q^88 - 11713820 * q^90 - 1529416 * q^91 - 1690071 * q^93 - 3034044 * q^94 + 7549346 * q^96 + 7212176 * q^97 + 435866 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	5.69684	−	3.28907i	0.712105	−	0.411134i	−0.0997347	−	0.995014i	$-0.531799\pi$
$2$	5.69684	−	3.28907i	0.712105	−	0.411134i	0.811840	+	0.583880i	$0.198466\pi$
$3$	−24.6534	+	11.0094i	−0.913091	+	0.407757i
$3$	−24.6534	+	11.0094i	−0.913091	+	0.407757i
$4$	−10.3640	+	17.9510i	−0.161937	+	0.280484i
$5$	−57.4599	+	33.1745i	−0.459679	+	0.265396i	−0.711909	−	0.702271i	$-0.752169\pi$
$5$	−57.4599	+	33.1745i	−0.459679	+	0.265396i	0.252230	+	0.967667i	$0.418836\pi$
$6$	−104.236	+	143.806i	−0.482574	+	0.665769i
$7$	−329.948	+	93.7191i	−0.961948	+	0.273234i
$7$	−329.948	+	93.7191i	−0.961948	+	0.273234i
$8$			557.353i			1.08858i
$9$	486.585	−	542.841i	0.667469	−	0.744638i
$10$	−218.227	+	377.979i	−0.218227	+	0.377979i
$11$	603.143	+	348.225i	0.453150	+	0.261626i	0.709160	−	0.705048i	$-0.249075\pi$
$11$	603.143	+	348.225i	0.453150	+	0.261626i	−0.256010	+	0.966674i	$0.582408\pi$
$12$	57.8782	−	556.654i	0.0334944	−	0.322138i
$13$	−824.771			−0.375408			−0.187704	−	0.982226i	$-0.560105\pi$
$13$	−824.771			−0.375408			−0.187704	+	0.982226i	$0.560105\pi$
$14$	−1571.41	+	1619.13i	−0.572672	+	0.590061i
$15$	1051.35	−	1450.47i	0.311512	−	0.429768i
$16$	1169.88	+	2026.29i	0.285615	+	0.494700i
$17$	−4784.05	−	2762.07i	−0.973752	−	0.562196i	−0.0733743	−	0.997304i	$-0.523377\pi$
$17$	−4784.05	−	2762.07i	−0.973752	−	0.562196i	−0.900378	+	0.435108i	$0.856710\pi$
$18$	986.554	−	4692.89i	0.169162	−	0.804680i
$19$	2527.23	+	4377.29i	0.368454	+	0.638182i	0.989324	−	0.145732i	$-0.0465538\pi$
$19$	2527.23	+	4377.29i	0.368454	+	0.638182i	−0.620870	+	0.783914i	$0.713220\pi$
$20$		−	1375.28i		−	0.171910i
$21$	7102.56	−	5943.04i	0.766933	−	0.641728i
$22$	4581.35			0.430254
$23$	17221.4	−	9942.79i	1.41542	−	0.817193i	0.419528	−	0.907742i	$-0.362196\pi$
$23$	17221.4	−	9942.79i	1.41542	−	0.817193i	0.995892	+	0.0905491i	$0.0288622\pi$
$24$	−6136.14	−	13740.7i	−0.443876	−	0.993972i
$25$	−5611.41	+	9719.25i	−0.359130	+	0.622032i
$26$	−4698.59	+	2712.73i	−0.267330	+	0.154343i
$27$	−6019.63	+	18739.9i	−0.305829	+	0.952087i
$28$	1737.23	−	6894.19i	0.0791377	−	0.314057i
$29$			23408.7i			0.959805i	0.877322	+	0.479902i	$0.159328\pi$
$29$			23408.7i			0.959805i	−0.877322	+	0.479902i	$0.840672\pi$
$30$	1218.70	−	11721.0i	0.0451370	−	0.434113i
$31$	−23180.0	+	40149.0i	−0.778088	+	1.34769i	0.154954	+	0.987922i	$0.450477\pi$
$31$	−23180.0	+	40149.0i	−0.778088	+	1.34769i	−0.933042	+	0.359767i	$0.882856\pi$
$32$	−17562.4	−	10139.7i	−0.535962	−	0.309438i
$33$	−18703.3	−	1944.68i	−0.520447	−	0.0541136i
$34$	−36338.6			−0.924552
$35$	15849.7	−	16330.9i	0.369672	−	0.380897i
$36$	4701.55	+	14360.7i	0.100771	+	0.307799i
$37$	24177.8	+	41877.2i	0.477323	+	0.826747i	0.999662	−	0.0259906i	$-0.00827401\pi$
$37$	24177.8	+	41877.2i	0.477323	+	0.826747i	−0.522340	+	0.852738i	$0.674941\pi$
$38$	28794.4	+	16624.5i	0.524757	+	0.302968i
$39$	20333.4	−	9080.25i	0.342781	−	0.153075i
$40$	−18489.9	−	32025.4i	−0.288905	−	0.500397i
$41$		−	15904.7i		−	0.230767i	−0.993321	−	0.115384i	$-0.963190\pi$
$41$		−	15904.7i		−	0.230767i	0.993321	−	0.115384i	$-0.0368097\pi$
$42$	20915.1	−	57217.4i	0.282301	−	0.772290i
$43$	21757.0			0.273649			0.136824	−	0.990595i	$-0.456310\pi$
$43$	21757.0			0.273649			0.136824	+	0.990595i	$0.456310\pi$
$44$	−12501.9	+	7217.99i	−0.146764	+	0.0847341i
$45$	−9950.65	+	47333.8i	−0.109198	+	0.519438i
$46$	65405.1	−	113285.i	0.671952	−	1.16386i
$47$	−33042.5	+	19077.1i	−0.318258	+	0.183747i	−0.650616	−	0.759407i	$-0.725489\pi$
$47$	−33042.5	+	19077.1i	−0.318258	+	0.183747i	0.332358	+	0.943153i	$0.392156\pi$
$48$	−51149.9	−	37075.4i	−0.462510	−	0.335245i
$49$	100082.	−	61844.9i	0.850687	−	0.525673i
$50$			73825.4i			0.590603i
$51$	148352.	+	15424.9i	1.11836	+	0.116282i
$52$	8547.91	−	14805.4i	0.0607925	−	0.105296i
$53$	−193312.	−	111609.i	−1.29847	−	0.749670i	−0.318328	−	0.947981i	$-0.603121\pi$
$53$	−193312.	−	111609.i	−1.29847	−	0.749670i	−0.980139	+	0.198310i	$0.936455\pi$
$54$	27344.1	+	126557.i	0.173653	+	0.803723i
$55$	−46208.7			−0.277738
$56$	−52234.6	−	183898.i	−0.297437	−	1.04716i
$57$	−110496.	−	80091.9i	−0.596655	−	0.432478i
$58$	76992.9	+	133356.i	0.394609	+	0.683482i
$59$	271755.	+	156898.i	1.32319	+	0.763944i	0.984236	−	0.176860i	$-0.0565938\pi$
$59$	271755.	+	156898.i	1.32319	+	0.763944i	0.338953	+	0.940803i	$0.389927\pi$
$60$	15141.0	+	33905.4i	0.0700974	+	0.156969i
$61$	−126472.	−	219056.i	−0.557192	−	0.965085i	−0.997729	−	0.0673504i	$-0.978545\pi$
$61$	−126472.	−	219056.i	−0.557192	−	0.965085i	0.440538	−	0.897734i	$-0.354788\pi$
$62$			304963.i			1.27959i
$63$	−109673.	+	224712.i	−0.438610	+	0.898677i
$64$	−283145.			−1.08011
$65$	47391.2	−	27361.3i	0.172567	−	0.0996316i
$66$	−112946.	+	50438.0i	−0.392861	+	0.175439i
$67$	82947.6	−	143669.i	0.275791	−	0.477683i	−0.694544	−	0.719451i	$-0.744394\pi$
$67$	82947.6	−	143669.i	0.275791	−	0.477683i	0.970334	+	0.241767i	$0.0777270\pi$
$68$	99163.6	−	57252.1i	0.315374	−	0.182081i
$69$	−315103.	+	434722.i	−0.959191	+	1.32332i
$70$	36579.5	−	145166.i	0.106646	−	0.423223i
$71$		−	298965.i		−	0.835307i	−0.908606	−	0.417653i	$-0.862853\pi$
$71$		−	298965.i		−	0.835307i	0.908606	−	0.417653i	$-0.137147\pi$
$72$	302554.	+	271200.i	0.810598	+	0.726594i
$73$	−2216.28	+	3838.71i	−0.00569714	+	0.00986773i	−0.868860	−	0.495058i	$-0.835147\pi$
$73$	−2216.28	+	3838.71i	−0.00569714	+	0.00986773i	0.863163	+	0.504926i	$0.168480\pi$
$74$	275474.	+	159045.i	0.679808	+	0.392487i
$75$	31337.2	−	301391.i	0.0742808	−	0.714409i
$76$	−104769.			−0.238666
$77$	−231641.	−	58370.1i	−0.507392	−	0.127855i
$78$	85970.8	−	118607.i	0.181162	−	0.249935i
$79$	310276.	+	537413.i	0.629313	+	1.09000i	0.987690	+	0.156425i	$0.0499969\pi$
$79$	310276.	+	537413.i	0.629313	+	1.09000i	−0.358377	+	0.933577i	$0.616670\pi$
$80$	−134442.	−	77620.3i	−0.262583	−	0.151602i
$81$	−57911.3	−	528276.i	−0.108970	−	0.994045i
$82$	−52311.7	−	90606.6i	−0.0948762	−	0.164330i
$83$		−	414931.i		−	0.725674i	−0.931853	−	0.362837i	$-0.881808\pi$
$83$		−	414931.i		−	0.725674i	0.931853	−	0.362837i	$-0.118192\pi$
$84$	33072.3	+	189091.i	0.0557991	+	0.319032i
$85$	366521.			0.596818
$86$	123946.	−	71560.3i	0.194867	−	0.112506i
$87$	−257716.	−	577104.i	−0.391367	−	0.876389i
$88$	−194084.	+	336164.i	−0.284801	+	0.493290i
$89$	−649685.	+	375096.i	−0.921580	+	0.532074i	−0.884139	−	0.467224i	$-0.845254\pi$
$89$	−649685.	+	375096.i	−0.921580	+	0.532074i	−0.0374412	+	0.999299i	$0.511921\pi$
$90$	98996.9	+	302381.i	0.135798	+	0.414789i
$91$	272131.	−	77296.8i	0.361123	−	0.102574i
$92$			412188.i			0.529336i
$93$	129450.	−	1.24501e6i	0.160936	−	1.54783i
$94$	−125492.	+	217359.i	−0.151089	+	0.261694i
$95$	−290428.	−	167679.i	−0.338741	−	0.195572i
$96$	544605.	+	56625.4i	0.615557	+	0.0640026i
$97$	212245.			0.232553			0.116276	−	0.993217i	$-0.462904\pi$
$97$	212245.			0.232553			0.116276	+	0.993217i	$0.462904\pi$
$98$	366742.	−	681499.i	0.389657	−	0.724081i
$99$	482511.	−	157970.i	0.497281	−	0.162805i
$100$	−116313.	−	201460.i	−0.116313	−	0.201460i
$101$	1.27401e6	+	735552.i	1.23654	+	0.713920i	0.968386	−	0.249455i	$-0.0802516\pi$
$101$	1.27401e6	+	735552.i	1.23654	+	0.713920i	0.268159	+	0.963375i	$0.413585\pi$
$102$	895872.	−	400067.i	0.844200	−	0.376992i
$103$	372502.	+	645192.i	0.340892	+	0.590442i	0.984599	−	0.174830i	$-0.0559377\pi$
$103$	372502.	+	645192.i	0.340892	+	0.590442i	−0.643707	+	0.765272i	$0.722604\pi$
$104$		−	459688.i		−	0.408661i
$105$	−210955.	+	577110.i	−0.182231	+	0.498529i
$106$	−1.46836e6			−1.23286
$107$	−1.33788e6	+	772428.i	−1.09211	+	0.630531i	−0.934138	−	0.356912i	$-0.883830\pi$
$107$	−1.33788e6	+	772428.i	−1.09211	+	0.630531i	−0.157974	+	0.987443i	$0.550496\pi$
$108$	−274012.	−	302278.i	−0.217520	−	0.239958i
$109$	−958591.	+	1.66033e6i	−0.740208	+	1.28208i	0.212192	+	0.977228i	$0.431940\pi$
$109$	−958591.	+	1.66033e6i	−0.740208	+	1.28208i	−0.952400	+	0.304850i	$0.901394\pi$
$110$	−263244.	+	151984.i	−0.197779	+	0.114188i
$111$	−1.05711e6	−	766234.i	−0.772950	−	0.560263i
$112$	−575902.	−	558931.i	−0.409916	−	0.397836i
$113$			1.61984e6i			1.12263i	0.827601	+	0.561317i	$0.189705\pi$
$113$			1.61984e6i			1.12263i	−0.827601	+	0.561317i	$0.810295\pi$
$114$	−892908.	−	92840.3i	−0.602688	−	0.0626646i
$115$	−659694.	+	1.14262e6i	−0.433759	+	0.751293i
$116$	−420208.	−	242607.i	−0.269209	−	0.155428i
$117$	−401321.	+	447719.i	−0.250573	+	0.279543i
$118$	2.06420e6			1.25633
$119$	1.83735e6	+	462983.i	1.09031	+	0.274742i
$120$	808421.	+	585974.i	0.467836	+	0.339105i
$121$	−643260.	−	1.11416e6i	−0.363103	−	0.628913i
$122$	−1.44098e6	−	831951.i	−0.793559	−	0.458161i
$123$	175102.	+	392106.i	0.0940968	+	0.210711i
$124$	−480475.	−	832207.i	−0.252003	−	0.436482i
$125$		−	1.78132e6i		−	0.912038i
$126$	114302.	+	1.64087e6i	0.0571403	+	0.820281i
$127$	2.34506e6			1.14484			0.572418	−	0.819962i	$-0.306005\pi$
$127$	2.34506e6			1.14484			0.572418	+	0.819962i	$0.306005\pi$
$128$	−489039.	+	282347.i	−0.233192	+	0.134634i
$129$	−536385.	+	239532.i	−0.249866	+	0.111582i
$130$	179987.	−	311746.i	0.0819239	−	0.141896i
$131$	3.22497e6	−	1.86194e6i	1.43454	−	0.828229i	0.437073	−	0.899426i	$-0.356015\pi$
$131$	3.22497e6	−	1.86194e6i	1.43454	−	0.828229i	0.997462	+	0.0711964i	$0.0226817\pi$
$132$	228750.	−	315588.i	0.0994578	−	0.137214i
$133$	−1.24409e6	−	1.20743e6i	−0.528806	−	0.513223i
$134$		−	1.09128e6i		−	0.453548i
$135$	−275800.	−	1.27649e6i	−0.112097	−	0.518820i
$136$	1.53945e6	−	2.66640e6i	0.611996	−	1.06001i
$137$	−66461.5	−	38371.6i	−0.0258469	−	0.0149227i	0.487021	−	0.873390i	$-0.338084\pi$
$137$	−66461.5	−	38371.6i	−0.0258469	−	0.0149227i	−0.512868	+	0.858468i	$0.671417\pi$
$138$	−365259.	+	3.51294e6i	−0.138983	+	1.33670i
$139$	4.61947e6			1.72008			0.860038	−	0.510230i	$-0.170440\pi$
$139$	4.61947e6			1.72008			0.860038	+	0.510230i	$0.170440\pi$
$140$	128890.	+	453771.i	0.0469715	+	0.165368i
$141$	604584.	−	834096.i	0.215675	−	0.297549i
$142$	−983319.	−	1.70316e6i	−0.343423	−	0.594826i
$143$	−497455.	−	287205.i	−0.170116	−	0.0982165i
$144$	1.66920e6	+	350904.i	0.559012	+	0.117517i
$145$	−776570.	−	1.34506e6i	−0.254728	−	0.441202i
$146$			29158.1i			0.00936915i
$147$	−1.78650e6	+	2.62654e6i	−0.562408	+	0.826860i
$148$	−1.00231e6			−0.309185
$149$	−1.08263e6	+	625060.i	−0.327283	+	0.188957i	−0.654634	−	0.755946i	$-0.727177\pi$
$149$	−1.08263e6	+	625060.i	−0.327283	+	0.188957i	0.327351	+	0.944903i	$0.393844\pi$
$150$	−812775.	−	1.82005e6i	−0.240822	−	0.539274i
$151$	−2.72866e6	+	4.72617e6i	−0.792534	+	1.37271i	0.131859	+	0.991268i	$0.457905\pi$
$151$	−2.72866e6	+	4.72617e6i	−0.792534	+	1.37271i	−0.924393	+	0.381441i	$0.875428\pi$
$152$	−2.43970e6	+	1.40856e6i	−0.694712	+	0.401092i
$153$	−3.82721e6	+	1.25299e6i	−1.06858	+	0.349844i
$154$	−1.51161e6	+	429360.i	−0.413882	+	0.117560i
$155$		−	3.07594e6i		−	0.826005i
$156$	−47736.3	+	459112.i	−0.0125740	+	0.120933i
$157$	1.44836e6	−	2.50863e6i	0.374263	−	0.648243i	−0.615953	−	0.787783i	$-0.711229\pi$
$157$	1.44836e6	−	2.50863e6i	0.374263	−	0.648243i	0.990216	+	0.139540i	$0.0445623\pi$
$158$	3.53519e6	+	2.04104e6i	0.896274	+	0.517464i
$159$	5.99455e6	+	623285.i	1.49130	+	0.155058i
$160$	1.34551e6			0.328494
$161$	−4.75034e6	+	4.89458e6i	−1.13828	+	1.17284i
$162$	−2.06745e6	−	2.81903e6i	−0.486284	−	0.663063i
$163$	244572.	+	423611.i	0.0564734	+	0.0978149i	0.892880	−	0.450295i	$-0.148681\pi$
$163$	244572.	+	423611.i	0.0564734	+	0.0978149i	−0.836407	+	0.548109i	$0.815348\pi$
$164$	285504.	+	164836.i	0.0647264	+	0.0373698i
$165$	1.13920e6	−	508731.i	0.253600	−	0.113250i
$166$	−1.36474e6	−	2.36380e6i	−0.298349	−	0.516756i
$167$			2.69550e6i			0.578749i	0.957216	+	0.289375i	$0.0934473\pi$
$167$			2.69550e6i			0.578749i	−0.957216	+	0.289375i	$0.906553\pi$
$168$	3.31237e6	+	3.95864e6i	0.698572	+	0.834868i
$169$	−4.14656e6			−0.859069
$170$	2.08801e6	−	1.20551e6i	0.424997	−	0.245372i
$171$	3.60588e6	+	758039.i	0.721146	+	0.151601i
$172$	−225489.	+	390559.i	−0.0443139	+	0.0767540i
$173$	546938.	−	315775.i	0.105633	−	0.0609873i	−0.446253	−	0.894907i	$-0.647242\pi$
$173$	546938.	−	315775.i	0.105633	−	0.0609873i	0.551886	+	0.833920i	$0.313908\pi$
$174$	−3.36631e6	−	2.44003e6i	−0.639008	−	0.463177i
$175$	940595.	−	3.73274e6i	0.175505	−	0.696488i
$176$			1.62953e6i			0.298898i
$177$	−8.42706e6	−	876205.i	−1.51969	−	0.158011i
$178$	−2.46744e6	+	4.27373e6i	−0.437508	+	0.757786i
$179$	1.23874e6	+	715187.i	0.215984	+	0.124698i	0.604089	−	0.796917i	$-0.293537\pi$
$179$	1.23874e6	+	715187.i	0.215984	+	0.124698i	−0.388105	+	0.921615i	$0.626870\pi$
$180$	−746558.	−	669190.i	−0.128011	−	0.114745i
$181$	3.92186e6			0.661388			0.330694	−	0.943738i	$-0.392717\pi$
$181$	3.92186e6			0.661388			0.330694	+	0.943738i	$0.392717\pi$
$182$	1.29606e6	−	1.33541e6i	0.214986	−	0.221513i
$183$	5.52965e6	+	4.00810e6i	0.902286	+	0.654011i
$184$	5.54165e6	+	9.59841e6i	0.889580	+	1.54080i
$185$	−2.77851e6	−	1.60417e6i	−0.438830	−	0.253359i
$186$	−3.35747e6	−	7.51840e6i	−0.521763	−	1.16839i
$187$	−1.92364e6	−	3.33185e6i	−0.294171	−	0.509519i
$188$		−	790860.i		−	0.119022i
$189$	229876.	−	6.74735e6i	0.0340492	−	0.999420i
$190$	−2.20603e6			−0.321626
$191$	410709.	−	237123.i	0.0589432	−	0.0340309i	−0.470239	−	0.882539i	$-0.655832\pi$
$191$	410709.	−	237123.i	0.0589432	−	0.0340309i	0.529182	+	0.848508i	$0.322499\pi$
$192$	6.98050e6	−	3.11726e6i	0.986240	−	0.440423i
$193$	109690.	−	189988.i	0.0152579	−	0.0264274i	−0.858296	−	0.513156i	$-0.828476\pi$
$193$	109690.	−	189988.i	0.0152579	−	0.0264274i	0.873554	+	0.486728i	$0.161810\pi$
$194$	1.20912e6	−	698088.i	0.165602	−	0.0956104i
$195$	−867124.	+	1.19630e6i	−0.116944	+	0.161338i
$196$	72921.1	+	2.43753e6i	0.00968468	+	0.323730i
$197$		−	7.90337e6i		−	1.03374i	−0.856062	−	0.516872i	$-0.827096\pi$
$197$		−	7.90337e6i		−	1.03374i	0.856062	−	0.516872i	$-0.172904\pi$
$198$	2.22921e6	−	2.48694e6i	0.287181	−	0.320383i
$199$	−4.44349e6	+	7.69635e6i	−0.563852	+	0.976620i	0.433304	+	0.901248i	$0.357348\pi$
$199$	−4.44349e6	+	7.69635e6i	−0.563852	+	0.976620i	−0.997155	+	0.0753721i	$0.975986\pi$
$200$	−5.41705e6	−	3.12754e6i	−0.677132	−	0.390942i
$201$	−463225.	+	4.45515e6i	−0.0570433	+	0.548624i
$202$	9.67714e6			1.17407
$203$	−2.19384e6	−	7.72365e6i	−0.262251	−	0.923282i
$204$	−1.81441e6	+	2.50320e6i	−0.213720	+	0.294852i
$205$	527630.	+	913882.i	0.0612446	+	0.106079i
$206$	4.24417e6	+	2.45037e6i	0.485502	+	0.280304i
$207$	2.98233e6	−	1.41865e7i	0.336236	−	1.59943i
$208$	−964883.	−	1.67123e6i	−0.107222	−	0.185714i
$209$			3.52017e6i			0.385589i
$210$	696379.	+	3.98155e6i	0.0751948	+	0.429927i
$211$	3.95802e6			0.421337			0.210669	−	0.977558i	$-0.432436\pi$
$211$	3.95802e6			0.421337			0.210669	+	0.977558i	$0.432436\pi$
$212$	4.00696e6	−	2.31342e6i	0.420540	−	0.242799i
$213$	3.29144e6	+	7.37053e6i	0.340602	+	0.762711i
$214$	−5.08114e6	+	8.80080e6i	−0.518466	+	0.898009i
$215$	−1.25015e6	+	721776.i	−0.125791	+	0.0726252i
$216$	−1.04448e7	−	3.35506e6i	−1.03642	−	0.332919i
$217$	3.88548e6	−	1.54195e7i	0.380246	−	1.50901i
$218$			1.26115e7i			1.21730i
$219$	12376.9	−	119038.i	0.00117837	−	0.0113332i
$220$	478906.	−	829490.i	0.0449762	−	0.0779010i
$221$	3.94574e6	+	2.27807e6i	0.365554	+	0.211053i
$222$	−8.54239e6	−	888197.i	−0.780766	−	0.0811802i
$223$	−2.07065e7			−1.86720			−0.933601	−	0.358313i	$-0.883352\pi$
$223$	−2.07065e7			−1.86720			−0.933601	+	0.358313i	$0.883352\pi$
$224$	6.74496e6	+	1.69963e6i	0.600116	+	0.151220i
$225$	2.54558e6	+	7.77534e6i	0.223480	+	0.682609i
$226$	5.32779e6	+	9.22800e6i	0.461553	+	0.799433i
$227$	−4.71060e6	−	2.71967e6i	−0.402716	−	0.232508i	0.284939	−	0.958546i	$-0.408027\pi$
$227$	−4.71060e6	−	2.71967e6i	−0.402716	−	0.232508i	−0.687655	+	0.726038i	$0.741360\pi$
$228$	2.58291e6	−	1.15344e6i	0.217924	−	0.0973177i
$229$	636788.	+	1.10295e6i	0.0530259	+	0.0918436i	0.891320	−	0.453375i	$-0.149780\pi$
$229$	636788.	+	1.10295e6i	0.0530259	+	0.0918436i	−0.838294	+	0.545218i	$0.816447\pi$
$230$			8.67912e6i			0.713333i
$231$	6.35337e6	−	1.11121e6i	0.515429	−	0.0901492i
$232$	−1.30469e7			−1.04482
$233$	1.16591e7	−	6.73138e6i	0.921716	−	0.532153i	0.0375341	−	0.999295i	$-0.488050\pi$
$233$	1.16591e7	−	6.73138e6i	0.921716	−	0.532153i	0.884182	+	0.467142i	$0.154716\pi$
$234$	−813681.	+	3.87056e6i	−0.0635048	+	0.302083i
$235$	1.26575e6	−	2.19234e6i	0.0975311	−	0.168929i
$236$	−5.63294e6	+	3.25218e6i	−0.428547	+	0.247422i
$237$	−1.35660e7	−	9.83313e6i	−1.01908	−	0.738664i
$238$	1.19899e7	−	3.40562e6i	0.889371	−	0.252619i
$239$		−	1.37101e6i		−	0.100426i	−0.998739	−	0.0502132i	$-0.984010\pi$
$239$		−	1.37101e6i		−	0.100426i	0.998739	−	0.0502132i	$-0.0159901\pi$
$240$	4.16902e6	+	433475.i	0.301579	+	0.0313567i
$241$	−6.49292e6	+	1.12461e7i	−0.463862	+	0.803432i	−0.999149	−	0.0412376i	$-0.986870\pi$
$241$	−6.49292e6	+	1.12461e7i	−0.463862	+	0.803432i	0.535287	+	0.844670i	$0.320203\pi$
$242$	−7.32910e6	−	4.23146e6i	−0.517136	−	0.298568i
$243$	7.24373e6	+	1.23863e7i	0.504828	+	0.863220i
$244$	5.24301e6			0.360921
$245$	−3.69905e6	+	6.87378e6i	−0.251531	+	0.467409i
$246$	2.28719e6	+	1.65784e6i	0.153637	+	0.111362i
$247$	−2.08438e6	−	3.61026e6i	−0.138321	−	0.239578i
$248$	−2.23772e7	−	1.29195e7i	−1.46707	−	0.847011i
$249$	4.56815e6	+	1.02295e7i	0.295898	+	0.662606i
$250$	−5.85891e6	−	1.01479e7i	−0.374970	−	0.649467i
$251$			1.87672e7i			1.18680i	0.804907	+	0.593401i	$0.202215\pi$
$251$			1.87672e7i			1.18680i	−0.804907	+	0.593401i	$0.797785\pi$
$252$	−2.89714e6	−	4.29765e6i	−0.181037	−	0.268552i
$253$	1.38493e7			0.855197
$254$	1.33595e7	−	7.71309e6i	0.815244	−	0.470681i
$255$	−9.03600e6	+	4.03519e6i	−0.544949	+	0.243356i
$256$	7.20332e6	−	1.24765e7i	0.429351	−	0.743658i
$257$	−7.23297e6	+	4.17596e6i	−0.426105	+	0.246012i	−0.697686	−	0.716404i	$-0.745787\pi$
$257$	−7.23297e6	+	4.17596e6i	−0.426105	+	0.246012i	0.271581	+	0.962416i	$0.412454\pi$
$258$	−2.26786e6	+	3.12878e6i	−0.132056	+	0.182187i
$259$	−1.19021e7	−	1.15514e7i	−0.685054	−	0.664867i
$260$			1.13429e6i			0.0645363i
$261$	1.27072e7	+	1.13903e7i	0.714707	+	0.640640i
$262$	1.22481e7	−	2.12143e7i	0.681027	−	1.17957i
$263$	−5.57378e6	−	3.21803e6i	−0.306396	−	0.176898i	0.338917	−	0.940816i	$-0.389940\pi$
$263$	−5.57378e6	−	3.21803e6i	−0.306396	−	0.176898i	−0.645313	+	0.763919i	$0.723273\pi$
$264$	1.08387e6	−	1.04243e7i	0.0589070	−	0.566548i
$265$	1.48102e7			0.795837
$266$	−1.10587e7	−	2.78663e6i	−0.587570	−	0.148059i
$267$	1.18874e7	−	1.64001e7i	0.624529	−	0.861613i
$268$	1.71934e6	+	2.97798e6i	0.0893216	+	0.154710i
$269$	2.66372e7	+	1.53790e7i	1.36846	+	0.790080i	0.990731	−	0.135836i	$-0.0433720\pi$
$269$	2.66372e7	+	1.53790e7i	1.36846	+	0.790080i	0.377728	+	0.925917i	$0.376705\pi$
$270$	−5.76966e6	−	6.36484e6i	−0.293129	−	0.323368i
$271$	−2.63106e6	−	4.55713e6i	−0.132197	−	0.228973i	0.792326	−	0.610098i	$-0.208870\pi$
$271$	−2.63106e6	−	4.55713e6i	−0.132197	−	0.228973i	−0.924523	+	0.381125i	$0.875537\pi$
$272$		−	1.29252e7i		−	0.642287i
$273$	−5.85799e6	+	4.90164e6i	−0.287912	+	0.240909i
$274$	−504828.			−0.0245410
$275$	−6.76896e6	+	3.90806e6i	−0.325480	+	0.187916i
$276$	−4.53795e6	−	1.01618e7i	−0.215840	−	0.483332i
$277$	−369234.	+	639531.i	−0.0173725	+	0.0300900i	−0.874581	−	0.484880i	$-0.838863\pi$
$277$	−369234.	+	639531.i	−0.0173725	+	0.0300900i	0.857208	+	0.514970i	$0.172197\pi$
$278$	2.63164e7	−	1.51938e7i	1.22488	−	0.707182i
$279$	1.05155e7	+	3.21189e7i	0.484190	+	1.47893i
$280$	9.10210e6	+	8.83387e6i	0.414636	+	0.402418i
$281$		−	2.15513e7i		−	0.971300i	−0.874153	−	0.485650i	$-0.838583\pi$
$281$		−	2.15513e7i		−	0.971300i	0.874153	−	0.485650i	$-0.161417\pi$
$282$	700817.	−	6.74024e6i	0.0312505	−	0.300558i
$283$	2.00616e6	−	3.47477e6i	0.0885128	−	0.153309i	−0.818370	−	0.574692i	$-0.805122\pi$
$283$	2.00616e6	−	3.47477e6i	0.0885128	−	0.153309i	0.906883	+	0.421383i	$0.138455\pi$
$284$	5.36671e6	+	3.09847e6i	0.234290	+	0.135267i
$285$	9.00611e6	+	936412.i	0.389048	+	0.0404513i
$286$	−3.77856e6			−0.161521
$287$	1.49057e6	+	5.24772e6i	0.0630533	+	0.221986i
$288$	−1.40498e7	+	4.59978e6i	−0.588157	+	0.192557i
$289$	3.18928e6	+	5.52399e6i	0.132129	+	0.228854i
$290$	−8.84800e6	−	5.10839e6i	−0.362786	−	0.209455i
$291$	−5.23256e6	+	2.33669e6i	−0.212342	+	0.0948249i
$292$	−45939.0	−	79568.8i	−0.00184516	−	0.00319591i
$293$		−	3.06845e7i		−	1.21988i	−0.792448	−	0.609940i	$-0.791194\pi$
$293$		−	3.06845e7i		−	1.21988i	0.792448	−	0.609940i	$-0.208806\pi$
$294$	−1.53853e6	+	2.08389e7i	−0.0605430	+	0.820037i
$295$	−2.08200e7			−0.810990
$296$	−2.33404e7	+	1.34756e7i	−0.899980	+	0.519604i
$297$	−1.01564e7	+	9.20667e6i	−0.387677	+	0.351425i
$298$	−4.11173e6	+	7.12173e6i	−0.155373	+	0.269114i
$299$	−1.42037e7	+	8.20052e6i	−0.531360	+	0.306781i
$300$	5.08548e6	+	3.68615e6i	0.188351	+	0.136524i
$301$	−7.17867e6	+	2.03905e6i	−0.263236	+	0.0747700i
$302$			3.58990e7i			1.30335i
$303$	−3.95068e7	−	4.10773e6i	−1.42018	−	0.147664i
$304$	−5.91311e6	+	1.02418e7i	−0.210472	+	0.364549i
$305$	1.45341e7	+	8.39128e6i	0.512259	+	0.295753i
$306$	−1.76818e7	+	1.97261e7i	−0.617110	+	0.688457i
$307$	−7.56198e6			−0.261349			−0.130674	−	0.991425i	$-0.541714\pi$
$307$	−7.56198e6			−0.261349			−0.130674	+	0.991425i	$0.541714\pi$
$308$	3.44852e6	−	3.55323e6i	0.118027	−	0.121611i
$309$	−1.62866e7	−	1.18052e7i	−0.552022	−	0.400126i
$310$	−1.01170e7	−	1.75231e7i	−0.339599	−	0.588203i
$311$	4.11760e7	+	2.37730e7i	1.36887	+	0.790319i	0.990784	−	0.135450i	$-0.0432479\pi$
$311$	4.11760e7	+	2.37730e7i	1.36887	+	0.790319i	0.378089	+	0.925769i	$0.376581\pi$
$312$	5.06091e6	+	1.13329e7i	0.166634	+	0.373145i
$313$	1.45386e7	+	2.51816e7i	0.474121	+	0.821201i	0.999561	−	0.0296294i	$-0.00943270\pi$
$313$	1.45386e7	+	2.51816e7i	0.474121	+	0.821201i	−0.525440	+	0.850831i	$0.676099\pi$
$314$		−	1.90550e7i		−	0.615490i
$315$	−1.15288e6	−	1.65502e7i	−0.0368852	−	0.529508i
$316$	−1.28628e7			−0.407637
$317$	−2.54469e7	+	1.46918e7i	−0.798834	+	0.461207i	−0.843063	−	0.537814i	$-0.819250\pi$
$317$	−2.54469e7	+	1.46918e7i	−0.798834	+	0.461207i	0.0442294	+	0.999021i	$0.485917\pi$
$318$	3.62001e7	−	1.61658e7i	1.12571	−	0.502707i
$319$	−8.15148e6	+	1.41188e7i	−0.251110	+	0.434936i
$320$	1.62695e7	−	9.39318e6i	0.496505	−	0.286657i
$321$	2.44795e7	−	3.37723e7i	0.740094	−	1.02105i
$322$	−1.09633e7	+	4.35079e7i	−0.328379	+	1.30317i
$323$		−	2.79215e7i		−	0.828575i
$324$	1.00833e7	+	4.43549e6i	0.296460	+	0.130409i
$325$	4.62813e6	−	8.01615e6i	0.134820	−	0.233515i
$326$	2.78658e6	+	1.60883e6i	0.0804301	+	0.0464363i
$327$	5.35330e6	−	5.14864e7i	0.153101	−	1.47248i
$328$	8.86453e6			0.251208
$329$	9.11443e6	−	9.39117e6i	0.255942	−	0.263713i
$330$	4.81661e6	−	6.64509e6i	0.134029	−	0.184909i
$331$	−1.71441e7	−	2.96945e7i	−0.472749	−	0.818826i	0.526764	−	0.850011i	$-0.323405\pi$
$331$	−1.71441e7	−	2.96945e7i	−0.472749	−	0.818826i	−0.999514	+	0.0311858i	$0.990072\pi$
$332$	7.44840e6	+	4.30034e6i	0.203540	+	0.117514i
$333$	3.44972e7	+	7.25211e6i	0.934225	+	0.196396i
$334$	8.86571e6	+	1.53559e7i	0.237944	+	0.412130i
$335$			1.10070e7i			0.292775i
$336$	2.03515e7	+	7.43922e6i	0.536511	+	0.196115i
$337$	5.34960e7			1.39776			0.698878	−	0.715241i	$-0.253683\pi$
$337$	5.34960e7			1.39776			0.698878	+	0.715241i	$0.253683\pi$
$338$	−2.36223e7	+	1.36384e7i	−0.611748	+	0.353193i
$339$	−1.78336e7	−	3.99348e7i	−0.457761	−	1.02507i
$340$	−3.79862e6	+	6.57940e6i	−0.0966471	+	0.167398i
$341$	−2.79617e7	+	1.61437e7i	−0.705182	+	0.407137i
$342$	2.30354e7	−	7.54158e6i	0.575860	−	0.188532i
$343$	−2.72260e7	+	2.97852e7i	−0.674685	+	0.738106i
$344$			1.21263e7i			0.297889i
$345$	3.68409e6	−	3.54324e7i	0.0897167	−	0.862867i
$346$	2.07721e6	−	3.59784e6i	0.0501479	−	0.0868587i
$347$	−3.17861e7	−	1.83517e7i	−0.760762	−	0.439226i	0.0688072	−	0.997630i	$-0.478081\pi$
$347$	−3.17861e7	−	1.83517e7i	−0.760762	−	0.439226i	−0.829569	+	0.558404i	$0.811414\pi$
$348$	1.30305e7	+	1.35485e6i	0.309189	+	0.0321480i
$349$	3.14402e7			0.739620			0.369810	−	0.929107i	$-0.379423\pi$
$349$	3.14402e7			0.739620			0.369810	+	0.929107i	$0.379423\pi$
$350$	−6.91885e6	−	2.43585e7i	−0.161373	−	0.568129i
$351$	4.96481e6	−	1.54561e7i	0.114810	−	0.357421i
$352$	−7.06176e6	−	1.22313e7i	−0.161914	−	0.280443i
$353$	−2.35735e7	−	1.36102e7i	−0.535920	−	0.309414i	0.207503	−	0.978234i	$-0.433466\pi$
$353$	−2.35735e7	−	1.36102e7i	−0.535920	−	0.309414i	−0.743424	+	0.668820i	$0.766799\pi$
$354$	−5.08896e7	+	2.27256e7i	−1.14715	+	0.512278i
$355$	9.91802e6	+	1.71785e7i	0.221687	+	0.383973i
$356$		−	1.55500e7i		−	0.344651i
$357$	−5.03941e7	+	8.81399e6i	−1.10758	+	0.193717i
$358$	9.40921e6			0.205071
$359$	−3.24692e7	+	1.87461e7i	−0.701760	+	0.405162i	−0.808003	−	0.589179i	$-0.799451\pi$
$359$	−3.24692e7	+	1.87461e7i	−0.701760	+	0.405162i	0.106242	+	0.994340i	$0.466118\pi$
$360$	−2.63816e7	−	5.54602e6i	−0.565450	−	0.118871i
$361$	1.07492e7	−	1.86181e7i	0.228483	−	0.395744i
$362$	2.23422e7	−	1.28993e7i	0.470978	−	0.271919i
$363$	2.81248e7	+	2.03859e7i	0.587990	+	0.426197i
$364$	−1.43282e6	+	5.68612e6i	−0.0297089	+	0.117899i
$365$		−	294096.i		−	0.00604798i
$366$	4.46845e7	+	4.64608e6i	0.911409	+	0.0947639i
$367$	1.03822e6	−	1.79824e6i	0.0210034	−	0.0363789i	−0.855333	−	0.518079i	$-0.826647\pi$
$367$	1.03822e6	−	1.79824e6i	0.0210034	−	0.0363789i	0.876336	+	0.481700i	$0.159981\pi$
$368$	4.02940e7	+	2.32638e7i	0.808531	+	0.466806i
$369$	−8.63372e6	−	7.73898e6i	−0.171838	−	0.154030i
$370$	−2.11050e7			−0.416658
$371$	7.42428e7	+	1.87080e7i	1.45389	+	0.366359i
$372$	2.10075e7	+	1.52270e7i	0.408080	+	0.295792i
$373$	−5.00434e6	−	8.66777e6i	−0.0964318	−	0.167025i	0.813773	−	0.581182i	$-0.197410\pi$
$373$	−5.00434e6	−	8.66777e6i	−0.0964318	−	0.167025i	−0.910205	+	0.414157i	$0.864076\pi$
$374$	−2.19174e7	−	1.26540e7i	−0.418961	−	0.241887i
$375$	1.96114e7	+	4.39158e7i	0.371890	+	0.832773i
$376$	−1.06327e7	−	1.84164e7i	−0.200023	−	0.346450i
$377$		−	1.93068e7i		−	0.360318i
$378$	−2.08830e7	−	3.91947e7i	−0.386649	−	0.725691i
$379$	3.16574e7			0.581511			0.290755	−	0.956797i	$-0.406093\pi$
$379$	3.16574e7			0.581511			0.290755	+	0.956797i	$0.406093\pi$
$380$	6.01999e6	−	3.47564e6i	0.109710	−	0.0633409i
$381$	−5.78139e7	+	2.58178e7i	−1.04534	+	0.466815i
$382$	1.55983e6	−	2.70170e6i	0.0279825	−	0.0484672i
$383$	−7.81038e6	+	4.50932e6i	−0.139020	+	0.0802629i	−0.567897	−	0.823100i	$-0.692243\pi$
$383$	−7.81038e6	+	4.50932e6i	−0.139020	+	0.0802629i	0.428877	+	0.903363i	$0.358909\pi$
$384$	8.94802e6	−	1.23449e7i	0.158028	−	0.218018i
$385$	1.52465e7	−	4.33064e6i	0.267170	−	0.0758874i
$386$		−	1.44311e6i		−	0.0250922i
$387$	1.05866e7	−	1.18106e7i	0.182652	−	0.203769i
$388$	−2.19970e6	+	3.80999e6i	−0.0376589	+	0.0652272i
$389$	−6.99549e6	−	4.03885e6i	−0.118842	−	0.0686134i	0.439401	−	0.898291i	$-0.355191\pi$
$389$	−6.99549e6	−	4.03885e6i	−0.118842	−	0.0686134i	−0.558243	+	0.829678i	$0.688524\pi$
$390$	−1.00515e6	+	9.66717e6i	−0.0169448	+	0.162969i
$391$	−1.09851e8			−1.83769
$392$	3.44694e7	+	5.57813e7i	0.572237	+	0.926041i
$393$	−5.90077e7	+	8.14082e7i	−0.972145	+	1.34119i
$394$	−2.59948e7	−	4.50242e7i	−0.425008	−	0.736135i
$395$	−3.56568e7	−	2.05865e7i	−0.578564	−	0.334034i
$396$	−2.16503e6	+	1.02987e7i	−0.0348641	+	0.165843i
$397$	2.40751e7	+	4.16992e7i	0.384765	+	0.666433i	0.991737	−	0.128291i	$-0.0409490\pi$
$397$	2.40751e7	+	4.16992e7i	0.384765	+	0.666433i	−0.606971	+	0.794724i	$0.707616\pi$
$398$			5.84599e7i			0.927275i
$399$	4.39642e7	+	1.60705e7i	0.692118	+	0.252995i
$400$	−2.62587e7			−0.410292
$401$	8.72146e7	−	5.03534e7i	1.35256	−	0.780900i	0.363951	−	0.931418i	$-0.381428\pi$
$401$	8.72146e7	−	5.03534e7i	1.35256	−	0.780900i	0.988607	+	0.150518i	$0.0480943\pi$
$402$	1.20144e7	+	2.69039e7i	0.184937	+	0.414130i
$403$	1.91182e7	−	3.31137e7i	0.292100	−	0.505932i
$404$	−2.64077e7	+	1.52465e7i	−0.400485	+	0.231220i
$405$	2.08529e7	+	2.84335e7i	0.313907	+	0.428021i
$406$	−3.79016e7	−	3.67847e7i	−0.566343	−	0.549654i
$407$			3.36773e7i			0.499521i
$408$	−8.59713e6	+	8.26845e7i	−0.126582	+	1.21743i
$409$	2.83875e7	−	4.91687e7i	0.414914	−	0.718652i	−0.580506	−	0.814256i	$-0.697145\pi$
$409$	2.83875e7	−	4.91687e7i	0.414914	−	0.718652i	0.995419	+	0.0956046i	$0.0304784\pi$
$410$	6.01165e6	+	3.47083e6i	0.0872252	+	0.0503595i
$411$	2.06095e6	+	214288.i	0.0296854	+	0.00308655i
$412$	−1.54424e7			−0.220812
$413$	−1.04369e8	−	2.62995e7i	−1.48157	−	0.373334i
$414$	−2.96706e7	−	9.06274e7i	−0.418143	−	1.27720i
$415$	1.37651e7	+	2.38419e7i	0.192591	+	0.333577i
$416$	1.44849e7	+	8.36289e6i	0.201204	+	0.116165i
$417$	−1.13886e8	+	5.08577e7i	−1.57059	+	0.701373i
$418$	1.15781e7	+	2.00539e7i	0.158529	+	0.274580i
$419$		−	4.76327e7i		−	0.647535i	−0.946137	−	0.323767i	$-0.895050\pi$
$419$		−	4.76327e7i		−	0.647535i	0.946137	−	0.323767i	$-0.104950\pi$
$420$	−8.17334e6	−	9.76801e6i	−0.110319	−	0.131843i
$421$	4.52744e7			0.606745			0.303373	−	0.952872i	$-0.401887\pi$
$421$	4.52744e7			0.606745			0.303373	+	0.952872i	$0.401887\pi$
$422$	2.25482e7	−	1.30182e7i	0.300037	−	0.173226i
$423$	−5.72216e6	+	2.72195e7i	−0.0756030	+	0.359632i
$424$	6.22054e7	−	1.07743e8i	0.816076	−	1.41349i
$425$	5.36905e7	−	3.09982e7i	0.699408	−	0.403803i
$426$	4.29930e7	+	3.11630e7i	0.556121	+	0.403097i
$427$	6.22589e7	+	6.04242e7i	0.799683	+	0.776117i
$428$		−	3.20217e7i		−	0.408426i
$429$	1.54259e7	+	1.60391e6i	0.195380	+	0.0203147i
$430$	−4.74795e6	+	8.22369e6i	−0.0597174	+	0.103434i
$431$	−3.09039e7	−	1.78424e7i	−0.385995	−	0.222855i	0.294428	−	0.955674i	$-0.404871\pi$
$431$	−3.09039e7	−	1.78424e7i	−0.385995	−	0.222855i	−0.680424	+	0.732819i	$0.738204\pi$
$432$	−4.50148e7	+	9.72594e6i	−0.558347	+	0.120637i
$433$	−4.90389e7			−0.604056			−0.302028	−	0.953299i	$-0.597664\pi$
$433$	−4.90389e7			−0.604056			−0.302028	+	0.953299i	$0.597664\pi$
$434$	−2.85809e7	−	1.00622e8i	−0.349628	−	1.23090i
$435$	3.39535e7	+	2.46107e7i	0.412493	+	0.298990i
$436$	−1.98697e7	−	3.44153e7i	−0.239735	−	0.415233i
$437$	8.70449e7	+	5.02554e7i	1.04304	+	0.602197i
$438$	−321014.	−	718847.i	−0.00382033	−	0.00855488i
$439$	−1.80621e6	−	3.12844e6i	−0.0213488	−	0.0369772i	0.855154	−	0.518375i	$-0.173463\pi$
$439$	−1.80621e6	−	3.12844e6i	−0.0213488	−	0.0369772i	−0.876502	+	0.481397i	$0.840129\pi$
$440$		−	2.57546e7i		−	0.302340i
$441$	1.51267e7	−	8.44216e7i	0.176371	−	0.984324i
$442$	2.99710e7			0.347084
$443$	6.88023e6	−	3.97230e6i	0.0791392	−	0.0456911i	−0.459908	−	0.887966i	$-0.652118\pi$
$443$	6.88023e6	−	3.97230e6i	0.0791392	−	0.0456911i	0.539047	+	0.842275i	$0.318784\pi$
$444$	2.47105e7	−	1.10349e7i	0.282314	−	0.126072i
$445$	2.48872e7	−	4.31059e7i	0.282421	−	0.489167i
$446$	−1.17962e8	+	6.81051e7i	−1.32965	+	0.767671i
$447$	1.98091e7	−	2.73291e7i	0.221790	−	0.305986i
$448$	9.34231e7	−	2.65361e7i	1.03901	−	0.295123i
$449$			8.36672e7i			0.924306i	0.886800	+	0.462153i	$0.152923\pi$
$449$			8.36672e7i			0.924306i	−0.886800	+	0.462153i	$0.847077\pi$
$450$	4.00754e7	+	3.59223e7i	0.439785	+	0.394209i
$451$	5.53841e6	−	9.59280e6i	0.0603747	−	0.104572i
$452$	−2.90777e7	−	1.67880e7i	−0.314880	−	0.181796i
$453$	1.52383e7	−	1.46557e8i	0.163924	−	1.57657i
$454$	−3.57807e7			−0.382368
$455$	−1.30724e7	+	1.34693e7i	−0.138778	+	0.142991i
$456$	4.46395e7	−	6.15855e7i	0.470787	−	0.649507i
$457$	6.93037e7	+	1.20038e8i	0.726119	+	1.25768i	0.958512	+	0.285053i	$0.0920113\pi$
$457$	6.93037e7	+	1.20038e8i	0.726119	+	1.25768i	−0.232392	+	0.972622i	$0.574655\pi$
$458$	7.25536e6	+	4.18888e6i	0.0755201	+	0.0436016i
$459$	8.05591e7	−	7.30260e7i	0.833061	−	0.755161i
$460$	−1.36741e7	−	2.36843e7i	−0.140484	−	0.243325i
$461$			6.46347e7i			0.659725i	0.944029	+	0.329862i	$0.107002\pi$
$461$			6.46347e7i			0.659725i	−0.944029	+	0.329862i	$0.892998\pi$
$462$	3.25393e7	−	2.72271e7i	0.329976	−	0.276106i
$463$	−1.21889e8			−1.22807			−0.614035	−	0.789279i	$-0.710455\pi$
$463$	−1.21889e8			−1.22807			−0.614035	+	0.789279i	$0.710455\pi$
$464$	−4.74328e7	+	2.73853e7i	−0.474816	+	0.274135i
$465$	3.38643e7	+	7.58325e7i	0.336809	+	0.754218i
$466$	4.42800e7	−	7.66953e7i	0.437573	−	0.757898i
$467$	4.43386e7	−	2.55989e7i	0.435343	−	0.251345i	−0.266277	−	0.963896i	$-0.585794\pi$
$467$	4.43386e7	−	2.55989e7i	0.435343	−	0.251345i	0.701620	+	0.712551i	$0.252460\pi$
$468$	−3.87770e6	−	1.18442e7i	−0.0378300	−	0.115550i
$469$	−1.39038e7	+	5.51773e7i	−0.134777	+	0.534862i
$470$		−	1.66525e7i		−	0.160393i
$471$	−8.08844e6	+	7.77920e7i	−0.0774109	+	0.744513i
$472$	−8.74476e7	+	1.51464e8i	−0.831614	+	1.44040i
$473$	1.31226e7	+	7.57632e6i	0.124004	+	0.0715937i
$474$	−1.09625e8	−	1.13983e7i	−1.02938	−	0.107030i
$475$	−5.67253e7			−0.529292
$476$	−2.73532e7	+	2.81837e7i	−0.253622	+	0.261323i
$477$	−1.54648e8	+	5.06305e7i	−1.42492	+	0.466506i
$478$	−4.50936e6	−	7.81045e6i	−0.0412887	−	0.0715142i
$479$	−1.69759e7	−	9.80106e6i	−0.154464	−	0.0891798i	0.420776	−	0.907165i	$-0.361758\pi$
$479$	−1.69759e7	−	9.80106e6i	−0.154464	−	0.0891798i	−0.575240	+	0.817985i	$0.695091\pi$
$480$	−3.31715e7	+	1.48133e7i	−0.299945	+	0.133946i
$481$	−1.99412e7	−	3.45391e7i	−0.179191	−	0.310367i
$482$			8.54227e7i			0.762838i
$483$	6.32258e7	−	1.72967e8i	0.561117	−	1.53505i
$484$	2.66669e7			0.235200
$485$	−1.21955e7	+	7.04110e6i	−0.106900	+	0.0617185i
$486$	8.20057e7	+	4.67374e7i	0.714390	+	0.407151i
$487$	−9.65961e7	+	1.67309e8i	−0.836320	+	1.44855i	0.0566307	+	0.998395i	$0.481964\pi$
$487$	−9.65961e7	+	1.67309e8i	−0.836320	+	1.44855i	−0.892951	+	0.450154i	$0.851369\pi$
$488$	1.22091e8	−	7.04895e7i	1.05057	−	0.606548i
$489$	−1.06933e7	−	7.75088e6i	−0.0914500	−	0.0662864i
$490$	1.53544e6	+	5.13253e7i	0.0130511	+	0.436258i
$491$		−	1.00270e8i		−	0.847085i	−0.905876	−	0.423543i	$-0.860786\pi$
$491$		−	1.00270e8i		−	0.847085i	0.905876	−	0.423543i	$-0.139214\pi$
$492$	−8.85342e6	−	920536.i	−0.0743388	−	0.00772939i
$493$	6.46564e7	−	1.11988e8i	0.539598	−	0.934612i
$494$	−2.37488e7	−	1.37114e7i	−0.196998	−	0.113737i
$495$	−2.24844e7	+	2.50840e7i	−0.185382	+	0.206814i
$496$	−1.08471e8			−0.888936
$497$	2.80188e7	+	9.86431e7i	0.228234	+	0.803521i
$498$	5.96696e7	+	4.32507e7i	0.483131	+	0.350191i
$499$	4.87188e7	+	8.43834e7i	0.392098	+	0.679134i	0.992726	−	0.120395i	$-0.0384161\pi$
$499$	4.87188e7	+	8.43834e7i	0.392098	+	0.679134i	−0.600628	+	0.799529i	$0.705083\pi$
$500$	3.19765e7	+	1.84616e7i	0.255812	+	0.147693i
$501$	−2.96759e7	−	6.64534e7i	−0.235989	−	0.528450i
$502$	6.17267e7	+	1.06914e8i	0.487935	+	0.845128i
$503$			1.14370e8i			0.898685i	0.893360	+	0.449342i	$0.148342\pi$
$503$			1.14370e8i			0.898685i	−0.893360	+	0.449342i	$0.851658\pi$
$504$	−1.25244e8	−	6.11267e7i	−0.978282	−	0.477463i
$505$	−9.76062e7			−0.757885
$506$	7.88973e7	−	4.55514e7i	0.608991	−	0.351601i
$507$	1.02227e8	−	4.56513e7i	0.784408	−	0.350291i
$508$	−2.43042e7	+	4.20961e7i	−0.185392	+	0.321108i
$509$	−7.07146e7	+	4.08271e7i	−0.536236	+	0.309596i	−0.743552	−	0.668678i	$-0.766860\pi$
$509$	−7.07146e7	+	4.08271e7i	−0.536236	+	0.309596i	0.207316	+	0.978274i	$0.433527\pi$
$510$	−3.82047e7	+	5.27079e7i	−0.288009	+	0.397343i
$511$	371497.	−	1.47428e6i	0.00278415	−	0.0110489i
$512$		−	1.30909e8i		−	0.975351i
$513$	−9.72430e7	+	2.10104e7i	−0.720288	+	0.155626i
$514$	−2.74701e7	+	4.75795e7i	−0.202288	+	0.350373i
$515$	−4.28078e7	−	2.47151e7i	−0.313401	−	0.180942i
$516$	1.25926e6	−	1.21111e7i	0.00916568	−	0.0881526i
$517$	−2.65725e7			−0.192292
$518$	−1.05798e8	−	2.66595e7i	−0.761180	−	0.191806i
$519$	−1.00074e7	+	1.38064e7i	−0.0715846	+	0.0987595i
$520$	1.52499e7	+	2.64136e7i	0.108457	+	0.187853i
$521$	−1.11407e8	−	6.43207e7i	−0.787768	−	0.454818i	0.0514085	−	0.998678i	$-0.483629\pi$
$521$	−1.11407e8	−	6.43207e7i	−0.787768	−	0.454818i	−0.839176	+	0.543860i	$0.816962\pi$
$522$	1.09854e8	+	2.30939e7i	0.772335	+	0.162363i
$523$	−1.29930e7	−	2.25046e7i	−0.0908250	−	0.157314i	0.817033	−	0.576590i	$-0.195617\pi$
$523$	−1.29930e7	−	2.25046e7i	−0.0908250	−	0.157314i	−0.907859	+	0.419277i	$0.862284\pi$
$524$			7.71883e7i			0.536485i
$525$	1.79065e7	+	1.02380e8i	0.123746	+	0.707520i
$526$	−4.23373e7			−0.290915
$527$	2.21789e8	−	1.28050e8i	1.51533	−	0.874876i
$528$	−1.79401e7	−	4.01734e7i	−0.121878	−	0.272921i
$529$	1.23700e8	−	2.14255e8i	0.835610	−	1.44732i
$530$	8.43716e7	−	4.87120e7i	0.566720	−	0.327196i
$531$	2.17403e8	−	7.11757e7i	1.45205	−	0.475388i
$532$	3.45682e7	−	9.81882e6i	0.229584	−	0.0652116i
$533$			1.31177e7i			0.0866317i
$534$	1.37795e7	−	1.32527e8i	0.0904921	−	0.870324i
$535$	5.12498e7	−	8.87672e7i	0.334681	−	0.579684i
$536$	8.00746e7	+	4.62311e7i	0.519997	+	0.300220i
$537$	−3.84130e7	−	3.99400e6i	−0.248059	−	0.0257920i
$538$	2.02331e8			1.29932
$539$	8.18999e7	−	2.45011e6i	0.523019	−	0.0156466i
$540$	2.57726e7	+	8.27867e6i	0.163673	+	0.0525750i
$541$	−1.12905e7	−	1.95558e7i	−0.0713055	−	0.123505i	0.828168	−	0.560480i	$-0.189383\pi$
$541$	−1.12905e7	−	1.95558e7i	−0.0713055	−	0.123505i	−0.899474	+	0.436975i	$0.856050\pi$
$542$	−2.99775e7	−	1.73075e7i	−0.188277	−	0.108702i
$543$	−9.66874e7	+	4.31775e7i	−0.603907	+	0.269685i
$544$	5.60129e7	+	9.70171e7i	0.347929	+	0.602631i
$545$		−	1.27203e8i		−	0.785793i
$546$	−1.72502e7	+	4.71912e7i	−0.105978	+	0.289924i
$547$	2.44583e8			1.49439			0.747197	−	0.664603i	$-0.231399\pi$
$547$	2.44583e8			1.49439			0.747197	+	0.664603i	$0.231399\pi$
$548$	1.37761e6	−	795365.i	0.00837115	−	0.00483309i
$549$	−1.80452e8	−	3.79351e7i	−1.09055	−	0.229258i
$550$	−2.57078e7	+	4.45272e7i	−0.154517	+	0.267632i
$551$	−1.02467e8	+	5.91591e7i	−0.612530	+	0.353644i
$552$	−2.42294e8	−	1.75624e8i	−1.44054	−	1.04416i
$553$	−1.52741e8	−	1.48240e8i	−0.903191	−	0.876575i
$554$			4.85775e6i			0.0285697i
$555$	8.61608e7	+	8.95859e6i	0.504000	+	0.0524035i
$556$	−4.78761e7	+	8.29239e7i	−0.278545	+	0.482453i
$557$	−4.19332e6	−	2.42102e6i	−0.0242657	−	0.0140098i	0.487818	−	0.872945i	$-0.337793\pi$
$557$	−4.19332e6	−	2.42102e6i	−0.0242657	−	0.0140098i	−0.512084	+	0.858936i	$0.671126\pi$
$558$	1.65546e8	+	1.48391e8i	0.952834	+	0.854090i
$559$	−1.79445e7			−0.102730
$560$	5.16335e7	+	1.30109e7i	0.294014	+	0.0740870i
$561$	8.41061e7	+	6.09633e7i	0.476364	+	0.345287i
$562$	−7.08837e7	−	1.22774e8i	−0.399335	−	0.691668i
$563$	−2.58387e8	−	1.49180e8i	−1.44792	−	0.835958i	−0.449564	−	0.893248i	$-0.648421\pi$
$563$	−2.58387e8	−	1.49180e8i	−1.44792	−	0.835958i	−0.998358	+	0.0572897i	$0.981754\pi$
$564$	8.70692e6	+	1.94974e7i	0.0485319	+	0.108678i
$565$	−5.37375e7	−	9.30760e7i	−0.297942	−	0.516051i
$566$		−	2.63936e7i		−	0.145563i
$567$	6.86173e7	+	1.68876e8i	0.376430	+	0.926445i
$568$	1.66629e8			0.909298
$569$	−1.64780e8	+	9.51358e7i	−0.894475	+	0.516425i	−0.875403	−	0.483393i	$-0.839404\pi$
$569$	−1.64780e8	+	9.51358e7i	−0.894475	+	0.516425i	−0.0190711	+	0.999818i	$0.506071\pi$
$570$	5.43863e7	−	2.42872e7i	0.293674	−	0.131145i
$571$	−6.56426e7	+	1.13696e8i	−0.352596	+	0.610714i	−0.986703	−	0.162531i	$-0.948034\pi$
$571$	−6.56426e7	+	1.13696e8i	−0.352596	+	0.610714i	0.634108	+	0.773245i	$0.281368\pi$
$572$	1.03112e7	−	5.95319e6i	0.0550963	−	0.0318098i
$573$	−7.51480e6	+	1.03676e7i	−0.0399442	+	0.0551078i
$574$	2.57517e7	+	2.49928e7i	0.136167	+	0.132154i
$575$			2.23172e8i			1.17392i
$576$	−1.37774e8	+	1.53703e8i	−0.720941	+	0.804292i
$577$	1.39506e7	−	2.41632e7i	0.0726216	−	0.125784i	−0.827428	−	0.561572i	$-0.810197\pi$
$577$	1.39506e7	−	2.41632e7i	0.0726216	−	0.125784i	0.900050	+	0.435788i	$0.143530\pi$
$578$	3.63376e7	+	2.09795e7i	0.188180	+	0.108646i
$579$	−612569.	+	5.89149e6i	−0.00315587	+	0.0303522i
$580$	3.21935e7			0.165000
$581$	3.88870e7	+	1.36906e8i	0.198278	+	0.698060i
$582$	−2.21235e7	+	3.05220e7i	−0.112224	+	0.154826i
$583$	−7.77298e7	−	1.34632e8i	−0.392267	−	0.679427i
$584$	−2.13952e6	−	1.23525e6i	−0.0107418	−	0.00620179i
$585$	8.20700e6	−	3.90395e7i	0.0409937	−	0.195001i
$586$	−1.00924e8	−	1.74805e8i	−0.501534	−	0.868682i
$587$		−	4.50405e7i		−	0.222684i	−0.993782	−	0.111342i	$-0.964485\pi$
$587$		−	4.50405e7i		−	0.222684i	0.993782	−	0.111342i	$-0.0355149\pi$
$588$	−2.86336e7	−	5.92908e7i	−0.140846	−	0.291646i
$589$	−2.34325e8			−1.14676
$590$	−1.18608e8	+	6.84786e7i	−0.577510	+	0.333426i
$591$	8.70115e7	+	1.94845e8i	0.421516	+	0.943903i
$592$	−5.65703e7	+	9.79827e7i	−0.272661	+	0.472263i
$593$	4.76852e6	−	2.75311e6i	0.0228675	−	0.0132026i	−0.488523	−	0.872551i	$-0.662464\pi$
$593$	4.76852e6	−	2.75311e6i	0.0228675	−	0.0132026i	0.511390	+	0.859349i	$0.329131\pi$
$594$	−2.75780e7	+	8.58541e7i	−0.131584	+	0.409639i
$595$	−1.20933e8	+	3.43500e7i	−0.574108	+	0.163071i
$596$		−	2.59124e7i		−	0.122397i
$597$	2.48149e7	−	2.38662e8i	0.116624	−	1.12166i
$598$	−5.39442e7	+	9.34342e7i	−0.252256	+	0.436920i
$599$	3.14579e8	+	1.81622e8i	1.46369	+	0.845062i	0.999179	−	0.0405046i	$-0.0128966\pi$
$599$	3.14579e8	+	1.81622e8i	1.46369	+	0.845062i	0.464512	+	0.885567i	$0.346230\pi$
$600$	1.67981e8	+	1.74659e7i	0.777692	+	0.0808606i
$601$	2.03084e8			0.935517			0.467759	−	0.883856i	$-0.345062\pi$
$601$	2.03084e8			0.935517			0.467759	+	0.883856i	$0.345062\pi$
$602$	−3.41892e7	+	3.52273e7i	−0.156711	+	0.161469i
$603$	−3.76286e7	−	1.14935e8i	−0.171619	−	0.524203i
$604$	−5.65595e7	−	9.79639e7i	−0.256682	−	0.444586i
$605$	7.39232e7	+	4.26796e7i	0.333822	+	0.192732i
$606$	−2.38575e8	+	1.06540e8i	−1.07203	+	0.478734i
$607$	−5.60658e7	−	9.71089e7i	−0.250687	−	0.434203i	0.713028	−	0.701136i	$-0.247323\pi$
$607$	−5.60658e7	−	9.71089e7i	−0.250687	−	0.434203i	−0.963715	+	0.266933i	$0.913990\pi$
$608$		−	1.02501e8i		−	0.456055i
$609$	1.39119e8	+	1.66262e8i	0.615933	+	0.736105i
$610$	1.10398e8			0.486376
$611$	2.72525e7	−	1.57342e7i	0.119477	−	0.0689798i
$612$	1.71727e7	−	8.16880e7i	0.0749177	−	0.356373i
$613$	−3.83093e7	+	6.63536e7i	−0.166311	+	0.288060i	−0.937120	−	0.349007i	$-0.886519\pi$
$613$	−3.83093e7	+	6.63536e7i	−0.166311	+	0.288060i	0.770809	+	0.637067i	$0.219852\pi$
$614$	−4.30794e7	+	2.48719e7i	−0.186108	+	0.107449i
$615$	−2.30692e7	−	1.67214e7i	−0.0991762	−	0.0718866i
$616$	3.25327e7	−	1.29106e8i	0.139181	−	0.552337i
$617$			1.59298e7i			0.0678196i	0.999425	+	0.0339098i	$0.0107959\pi$
$617$			1.59298e7i			0.0678196i	−0.999425	+	0.0339098i	$0.989204\pi$
$618$	−1.31610e8	−	1.36842e7i	−0.557603	−	0.0579769i
$619$	1.30151e8	−	2.25428e8i	0.548751	−	0.950465i	−0.449609	−	0.893225i	$-0.648437\pi$
$619$	1.30151e8	−	2.25428e8i	0.548751	−	0.950465i	0.998360	−	0.0572397i	$-0.0182299\pi$
$620$	5.52160e7	+	3.18790e7i	0.231681	+	0.133761i
$621$	8.26606e7	+	3.82580e8i	0.345163	+	1.59752i
$622$	3.12764e8			1.29971
$623$	1.79209e8	−	1.84650e8i	0.741131	−	0.763634i
$624$	4.21869e7	+	3.05787e7i	0.173630	+	0.125853i
$625$	−2.85838e7	−	4.95086e7i	−0.117079	−	0.202787i
$626$	1.65648e8	+	9.56369e7i	0.675248	+	0.389855i
$627$	−3.87551e7	−	8.67844e7i	−0.157227	−	0.352078i
$628$	3.00215e7	+	5.19988e7i	0.121214	+	0.209949i
$629$		−	2.67123e8i		−	1.07340i
$630$	−6.10028e7	−	9.04922e7i	−0.243965	−	0.361901i
$631$	−8.31931e7			−0.331130			−0.165565	−	0.986199i	$-0.552945\pi$
$631$	−8.31931e7			−0.331130			−0.165565	+	0.986199i	$0.552945\pi$
$632$	−2.99529e8	+	1.72933e8i	−1.18655	+	0.685058i
$633$	−9.75787e7	+	4.35755e7i	−0.384719	+	0.171803i
$634$	−9.66445e7	+	1.67393e8i	−0.379236	+	0.656856i
$635$	−1.34747e8	+	7.77962e7i	−0.526257	+	0.303835i
$636$	−7.33160e7	+	1.01148e8i	−0.284989	+	0.393176i
$637$	−8.25451e7	+	5.10078e7i	−0.319354	+	0.197342i
$638$			1.07243e8i			0.412960i
$639$	−1.62291e8	−	1.45472e8i	−0.622001	−	0.557541i
$640$	1.87334e7	−	3.24472e7i	0.0714623	−	0.123776i
$641$	−4.13537e8	−	2.38755e8i	−1.57015	−	0.906524i	−0.996150	−	0.0876653i	$-0.972059\pi$
$641$	−4.13537e8	−	2.38755e8i	−1.57015	−	0.906524i	−0.573995	−	0.818859i	$-0.694607\pi$
$642$	2.83759e7	−	2.72911e8i	0.107237	−	1.03137i
$643$	1.79150e8			0.673880			0.336940	−	0.941526i	$-0.390608\pi$
$643$	1.79150e8			0.673880			0.336940	+	0.941526i	$0.390608\pi$
$644$	−3.86299e7	−	1.36001e8i	−0.144632	−	0.509194i
$645$	2.28742e7	−	3.15578e7i	0.0852447	−	0.117605i
$646$	−9.18360e7	−	1.59065e8i	−0.340655	−	0.590032i
$647$	1.90784e8	+	1.10149e8i	0.704415	+	0.406694i	0.808990	−	0.587823i	$-0.200015\pi$
$647$	1.90784e8	+	1.10149e8i	0.704415	+	0.406694i	−0.104575	+	0.994517i	$0.533348\pi$
$648$	2.94436e8	−	3.22770e7i	1.08210	−	0.118623i
$649$	1.09272e8	+	1.89264e8i	0.399736	+	0.692362i
$650$		−	6.08890e7i		−	0.221717i
$651$	7.39694e7	+	4.22920e8i	0.268108	+	1.53291i
$652$	−1.01390e7			−0.0365806
$653$	−1.16639e8	+	6.73418e7i	−0.418895	+	0.241849i	−0.694605	−	0.719392i	$-0.744421\pi$
$653$	−1.16639e8	+	6.73418e7i	−0.418895	+	0.241849i	0.275709	+	0.961241i	$0.411087\pi$
$654$	−1.38846e8	−	3.10917e8i	−0.496362	−	1.11151i
$655$	−1.23537e8	+	2.13973e8i	−0.439617	+	0.761439i
$656$	3.22276e7	−	1.86066e7i	0.114161	−	0.0659106i
$657$	1.00540e6	+	3.07095e6i	0.00354522	+	0.0108287i
$658$	2.10352e7	−	8.34781e7i	0.0738362	−	0.293018i
$659$		−	3.76030e8i		−	1.31391i	−0.753928	−	0.656957i	$-0.771843\pi$
$659$		−	3.76030e8i		−	1.31391i	0.753928	−	0.656957i	$-0.228157\pi$
$660$	−2.67448e6	+	2.57223e7i	−0.00930266	+	0.0894700i
$661$	2.90919e7	−	5.03887e7i	0.100732	−	0.174473i	−0.811254	−	0.584693i	$-0.801215\pi$
$661$	2.90919e7	−	5.03887e7i	0.100732	−	0.174473i	0.911987	+	0.410220i	$0.134548\pi$
$662$	−1.95335e8	−	1.12776e8i	−0.673294	−	0.388727i
$663$	−1.22356e8	−	1.27220e7i	−0.419842	−	0.0436532i
$664$	2.31263e8			0.789954
$665$	1.11541e8	+	2.81066e7i	0.379288	+	0.0955749i
$666$	2.20378e8	−	7.21498e7i	0.746011	−	0.244237i
$667$	2.32748e8	+	4.03131e8i	0.784346	+	1.35853i
$668$	−4.83868e7	−	2.79361e7i	−0.162330	−	0.0937210i
$669$	5.10486e8	−	2.27966e8i	1.70493	−	0.761364i
$670$	3.62027e7	+	6.27050e7i	0.120370	+	0.208486i
$671$		−	1.76163e8i		−	0.583104i
$672$	−1.84998e8	+	3.23565e7i	−0.609621	+	0.106624i
$673$	−1.71549e8			−0.562786			−0.281393	−	0.959593i	$-0.590796\pi$
$673$	−1.71549e8			−0.562786			−0.281393	+	0.959593i	$0.590796\pi$
$674$	3.04758e8	−	1.75952e8i	0.995350	−	0.574665i
$675$	−1.48359e8	−	1.63664e8i	−0.482396	−	0.532158i
$676$	4.29749e7	−	7.44347e7i	0.139115	−	0.240955i
$677$	4.36085e8	−	2.51774e8i	1.40542	−	0.811417i	0.410475	−	0.911872i	$-0.365363\pi$
$677$	4.36085e8	−	2.51774e8i	1.40542	−	0.811417i	0.994942	+	0.100455i	$0.0320297\pi$
$678$	−2.32943e8	−	1.68846e8i	−0.747414	−	0.541754i
$679$	−7.00297e7	+	1.98914e7i	−0.223704	+	0.0635412i
$680$			2.04282e8i			0.649684i
$681$	1.46074e8	+	1.51881e7i	0.462523	+	0.0480909i
$682$	−1.06196e8	+	1.83936e8i	−0.334776	+	0.579849i
$683$	4.47198e8	+	2.58190e8i	1.40358	+	0.810359i	0.994758	−	0.102255i	$-0.0326056\pi$
$683$	4.47198e8	+	2.58190e8i	1.40358	+	0.810359i	0.408824	+	0.912613i	$0.365939\pi$
$684$	−5.09788e7	+	5.68727e7i	−0.159302	+	0.177720i
$685$	5.09183e6			0.0158417
$686$	−5.71362e7	+	2.59230e8i	−0.176986	+	0.802995i
$687$	−2.78419e7	−	2.01808e7i	−0.0858673	−	0.0622399i
$688$	2.54531e7	+	4.40860e7i	0.0781583	+	0.135374i
$689$	1.59438e8	+	9.20516e7i	0.487455	+	0.281432i
$690$	−9.55522e7	−	2.13970e8i	−0.290866	−	0.651338i
$691$	−2.03098e8	−	3.51777e8i	−0.615563	−	1.06619i	−0.990285	−	0.139049i	$-0.955595\pi$
$691$	−2.03098e8	−	3.51777e8i	−0.615563	−	1.06619i	0.374722	−	0.927137i	$-0.377738\pi$
$692$			1.30907e7i			0.0395045i
$693$	−1.44399e8	+	9.73423e7i	−0.433874	+	0.292484i
$694$	−2.41441e8			−0.722324
$695$	−2.65434e8	+	1.53248e8i	−0.790683	+	0.456501i
$696$	3.21651e8	−	1.43639e8i	0.954019	−	0.426034i
$697$	−4.39299e7	+	7.60888e7i	−0.129736	+	0.224710i
$698$	1.79110e8	−	1.03409e8i	0.526688	−	0.304083i
$699$	−2.13328e8	+	2.94312e8i	−0.624622	+	0.861740i
$700$	5.72580e7	+	5.55707e7i	0.166933	+	0.162014i
$701$		−	1.61640e8i		−	0.469239i	−0.972087	−	0.234619i	$-0.924616\pi$
$701$		−	1.61640e8i		−	0.469239i	0.972087	−	0.234619i	$-0.0753843\pi$
$702$	−2.25526e7	−	1.04381e8i	−0.0651907	−	0.301724i
$703$	−1.22206e8	+	2.11667e8i	−0.351743	+	0.609237i
$704$	−1.70777e8	−	9.85981e7i	−0.489453	−	0.282586i
$705$	−7.06863e6	+	6.79838e7i	−0.0201729	+	0.194016i
$706$	−1.79060e8			−0.508842
$707$	−4.89294e8	−	1.23295e8i	−1.38456	−	0.348888i
$708$	1.03067e8	−	1.42193e8i	0.290415	−	0.400662i
$709$	2.99324e8	+	5.18444e8i	0.839851	+	1.45466i	0.890019	+	0.455923i	$0.150691\pi$
$709$	2.99324e8	+	5.18444e8i	0.839851	+	1.45466i	−0.0501682	+	0.998741i	$0.515976\pi$
$710$	1.13003e8	+	6.52422e7i	0.315729	+	0.182286i
$711$	4.42705e8	+	9.30669e7i	1.23170	+	0.258932i
$712$	−2.09061e8	−	3.62104e8i	−0.579206	−	1.00321i
$713$			9.21896e8i			2.54339i
$714$	−2.58097e8	+	2.15962e8i	−0.709069	+	0.593311i
$715$	3.81116e7			0.104265
$716$	−2.56766e7	+	1.48244e7i	−0.0699517	+	0.0403866i
$717$	1.50941e7	+	3.38002e7i	0.0409495	+	0.0916984i
$718$	−1.23315e8	+	2.13588e8i	−0.333152	+	0.577035i
$719$	−5.37512e8	+	3.10332e8i	−1.44611	+	0.834912i	−0.998247	−	0.0591908i	$-0.981148\pi$
$719$	−5.37512e8	+	3.10332e8i	−1.44611	+	0.834912i	−0.447863	+	0.894102i	$0.647815\pi$
$720$	−1.07553e8	+	3.52119e7i	−0.288155	+	0.0943392i
$721$	−1.83373e8	−	1.77969e8i	−0.489248	−	0.474831i
$722$		−	1.41419e8i		−	0.375748i
$723$	3.62600e7	−	3.48738e8i	0.0959430	−	0.922749i
$724$	−4.06461e7	+	7.04011e7i	−0.107103	+	0.185509i
$725$	−2.27515e8	−	1.31356e8i	−0.597029	−	0.344695i
$726$	2.27273e8	+	2.36308e7i	0.593935	+	0.0617545i
$727$	−1.61816e8			−0.421132			−0.210566	−	0.977580i	$-0.567531\pi$
$727$	−1.61816e8			−0.421132			−0.210566	+	0.977580i	$0.567531\pi$
$728$	4.30816e7	+	1.51673e8i	0.111660	+	0.393111i
$729$	−3.14949e8	−	2.25615e8i	−0.812938	−	0.582351i
$730$	−967303.	−	1.67542e6i	−0.00248653	−	0.00430680i
$731$	−1.04086e8	−	6.00943e7i	−0.266466	−	0.153844i
$732$	−1.29258e8	+	5.77226e7i	−0.329553	+	0.147168i
$733$	2.88495e8	+	4.99689e8i	0.732532	+	1.26878i	0.955798	+	0.294026i	$0.0949951\pi$
$733$	2.88495e8	+	4.99689e8i	0.732532	+	1.26878i	−0.223265	+	0.974758i	$0.571672\pi$
$734$		−	1.36591e7i		−	0.0345409i
$735$	1.55180e7	−	2.10187e8i	0.0390818	−	0.529351i
$736$	−4.03266e8			−1.01148
$737$	1.00059e8	−	5.77688e7i	0.249949	−	0.144308i
$738$	−7.46390e7	−	1.56908e7i	−0.185694	−	0.0390371i
$739$	−5.88627e7	+	1.01953e8i	−0.145850	+	0.252620i	−0.929690	−	0.368343i	$-0.879925\pi$
$739$	−5.88627e7	+	1.01953e8i	−0.145850	+	0.252620i	0.783840	+	0.620963i	$0.213258\pi$
$740$	5.75928e7	−	3.32512e7i	0.142126	−	0.0820565i
$741$	9.11341e7	+	6.60574e7i	0.223989	+	0.162356i
$742$	4.84481e8	−	1.37613e8i	1.18595	−	0.336859i
$743$			4.99500e8i			1.21778i	0.793255	+	0.608890i	$0.208385\pi$
$743$			4.99500e8i			1.21778i	−0.793255	+	0.608890i	$0.791615\pi$
$744$	6.93910e8	+	7.21494e7i	1.68494	+	0.175192i
$745$	4.14720e7	−	7.18317e7i	0.100297	−	0.173719i
$746$	−5.70179e7	−	3.29193e7i	−0.137339	−	0.0792929i
$747$	−2.25241e8	−	2.01899e8i	−0.540364	−	0.484365i
$748$	7.97464e7			0.190549
$749$	3.69041e8	−	3.80246e8i	0.878272	−	0.904940i
$750$	2.56165e8	+	1.85678e8i	0.607206	+	0.440126i
$751$	1.86246e7	+	3.22587e7i	0.0439711	+	0.0761601i	0.887173	−	0.461436i	$-0.152666\pi$
$751$	1.86246e7	+	3.22587e7i	0.0439711	+	0.0761601i	−0.843202	+	0.537596i	$0.819332\pi$
$752$	−7.73116e7	−	4.46359e7i	−0.181799	−	0.104962i
$753$	−2.06616e8	−	4.62676e8i	−0.483927	−	1.08366i
$754$	−6.35014e7	−	1.09988e8i	−0.148139	−	0.256584i
$755$		−	3.62087e8i		−	0.841341i
$756$	1.18739e8	+	7.40560e7i	0.274807	+	0.171394i
$757$	3.37798e8			0.778699			0.389350	−	0.921090i	$-0.372700\pi$
$757$	3.37798e8			0.778699			0.389350	+	0.921090i	$0.372700\pi$
$758$	1.80347e8	−	1.04124e8i	0.414097	−	0.239079i
$759$	−3.41433e8	+	1.52473e8i	−0.780873	+	0.348712i
$760$	9.34564e7	−	1.61871e8i	0.212896	−	0.368747i
$761$	3.20644e8	−	1.85124e8i	0.727561	−	0.420058i	−0.0899682	−	0.995945i	$-0.528677\pi$
$761$	3.20644e8	−	1.85124e8i	0.727561	−	0.420058i	0.817529	+	0.575887i	$0.195343\pi$
$762$	−2.44440e8	+	3.37234e8i	−0.552468	+	0.762196i
$763$	1.60681e8	−	6.37661e8i	0.361735	−	1.43554i
$764$			9.83015e6i			0.0220435i
$765$	1.78343e8	−	1.98962e8i	0.398357	−	0.444413i
$766$	−2.96630e7	+	5.13778e7i	−0.0659977	+	0.114311i
$767$	−2.24136e8	−	1.29405e8i	−0.496735	−	0.286790i
$768$	−4.02273e7	+	3.86894e8i	−0.0888050	+	0.854098i
$769$	2.18577e8			0.480646			0.240323	−	0.970693i	$-0.422747\pi$
$769$	2.18577e8			0.480646			0.240323	+	0.970693i	$0.422747\pi$
$770$	7.26129e7	−	7.48177e7i	0.159053	−	0.163882i
$771$	1.32343e8	−	1.82583e8i	0.288760	−	0.398379i
$772$	2.27365e6	+	3.93807e6i	0.00494164	+	0.00855918i
$773$	9.67046e7	+	5.58324e7i	0.209367	+	0.120878i	0.601017	−	0.799236i	$-0.294762\pi$
$773$	9.67046e7	+	5.58324e7i	0.209367	+	0.120878i	−0.391650	+	0.920114i	$0.628096\pi$
$774$	2.14644e7	−	1.02103e8i	0.0462910	−	0.220200i
$775$	−2.60145e8	−	4.50585e8i	−0.558870	−	0.967991i
$776$			1.18295e8i			0.253152i
$777$	4.20602e8	+	1.53746e8i	0.896621	+	0.327748i
$778$	−5.31363e7			−0.112837
$779$	6.96194e7	−	4.01948e7i	0.147271	−	0.0850271i
$780$	−1.24879e7	−	2.79641e7i	−0.0263151	−	0.0589275i
$781$	1.04107e8	−	1.80319e8i	0.218538	−	0.378519i
$782$	−6.25802e8	+	3.61307e8i	−1.30863	+	0.755538i
$783$	−4.38677e8	−	1.40911e8i	−0.913817	−	0.293536i
$784$	2.42400e8	+	1.30445e8i	0.503020	+	0.270695i
$785$			1.92194e8i			0.397311i
$786$	−6.84001e7	+	6.57850e8i	−0.140860	+	1.35475i
$787$	3.55944e8	−	6.16513e8i	0.730226	−	1.26479i	−0.226560	−	0.973997i	$-0.572748\pi$
$787$	3.55944e8	−	6.16513e8i	0.730226	−	1.26479i	0.956786	−	0.290792i	$-0.0939186\pi$
$788$	1.41873e8	+	8.19104e7i	0.289948	+	0.167402i
$789$	1.72842e8	+	1.79712e7i	0.351898	+	0.0365887i
$790$	−2.70842e8			−0.549331
$791$	−1.51810e8	−	5.34465e8i	−0.306741	−	1.07991i
$792$	8.80449e7	+	2.68929e8i	0.177227	+	0.541330i
$793$	1.04310e8	+	1.80671e8i	0.209174	+	0.362300i
$794$	2.74304e8	+	1.58369e8i	0.547987	+	0.316380i
$795$	−3.65123e8	+	1.63052e8i	−0.726672	+	0.324508i
$796$	−9.21046e7	−	1.59530e8i	−0.182617	−	0.316302i
$797$		−	4.14474e8i		−	0.818695i	−0.912379	−	0.409348i	$-0.865756\pi$
$797$		−	4.14474e8i		−	0.818695i	0.912379	−	0.409348i	$-0.134244\pi$
$798$	3.03314e8	−	5.30501e7i	0.596876	−	0.104394i
$799$	2.10769e8			0.413206
$800$	1.97100e8	−	1.13795e8i	0.384960	−	0.222257i
$801$	−1.12510e8	+	5.35192e8i	−0.218923	+	1.04139i
$802$	3.31232e8	−	5.73710e8i	0.642109	−	1.11217i
$803$	−2.67347e6	+	1.54353e6i	−0.00516332	+	0.00298104i
$804$	−7.51734e7	−	5.44885e7i	−0.144643	−	0.104842i
$805$	1.10579e8	−	4.38832e8i	0.211975	−	0.841222i
$806$		−	2.51525e8i		−	0.480370i
$807$	−8.26013e8	−	8.58849e7i	−1.57169	−	0.163417i
$808$	−4.09962e8	+	7.10075e8i	−0.777159	+	1.34608i
$809$	−1.03739e8	−	5.98936e7i	−0.195927	−	0.113119i	0.398827	−	0.917026i	$-0.369417\pi$
$809$	−1.03739e8	−	5.98936e7i	−0.195927	−	0.113119i	−0.594754	+	0.803907i	$0.702751\pi$
$810$	2.12315e8	+	9.33946e7i	0.399509	+	0.175738i
$811$	−1.83712e8			−0.344410			−0.172205	−	0.985061i	$-0.555089\pi$
$811$	−1.83712e8			−0.344410			−0.172205	+	0.985061i	$0.555089\pi$
$812$	1.61384e8	+	4.06663e7i	0.301434	+	0.0759567i
$813$	1.15036e8	+	8.33825e7i	0.214073	+	0.155168i
$814$	1.10767e8	+	1.91854e8i	0.205370	+	0.355711i
$815$	−2.81062e7	−	1.62271e7i	−0.0519193	−	0.0299756i
$816$	1.42299e8	+	3.18650e8i	0.261897	+	0.586467i
$817$	5.49849e7	+	9.52366e7i	0.100827	+	0.174638i
$818$		−	3.73475e8i		−	0.682341i
$819$	9.04552e7	−	1.85336e8i	0.164658	−	0.337370i
$820$	−2.18734e7			−0.0396711
$821$	2.73208e8	−	1.57737e8i	0.493701	−	0.285038i	−0.232408	−	0.972618i	$-0.574660\pi$
$821$	2.73208e8	−	1.57737e8i	0.493701	−	0.285038i	0.726108	+	0.687580i	$0.241327\pi$
$822$	1.24457e7	−	5.55787e6i	0.0224081	−	0.0100067i
$823$	−1.92392e7	+	3.33232e7i	−0.0345133	+	0.0597788i	−0.882766	−	0.469813i	$-0.844321\pi$
$823$	−1.92392e7	+	3.33232e7i	−0.0345133	+	0.0597788i	0.848253	+	0.529592i	$0.177655\pi$
$824$	−3.59600e8	+	2.07615e8i	−0.642743	+	0.371088i
$825$	1.23853e8	−	1.70870e8i	0.220569	−	0.304301i
$826$	−6.81078e8	+	1.93455e8i	−1.20853	+	0.343272i
$827$			6.64958e8i			1.17565i	0.808988	+	0.587825i	$0.200016\pi$
$827$			6.64958e8i			1.17565i	−0.808988	+	0.587825i	$0.799984\pi$
$828$	2.23752e8	+	2.00564e8i	0.394164	+	0.353316i
$829$	−3.05620e8	+	5.29350e8i	−0.536437	+	0.929136i	0.462656	+	0.886538i	$0.346897\pi$
$829$	−3.05620e8	+	5.29350e8i	−0.536437	+	0.929136i	−0.999092	+	0.0425975i	$0.986437\pi$
$830$	1.56835e8	+	9.05489e7i	0.274290	+	0.158361i
$831$	2.06200e6	−	1.98317e7i	0.00359324	−	0.0345587i
$832$	2.33530e8			0.405482
$833$	−6.49619e8	+	1.94340e7i	−1.12389	+	0.0336222i
$834$	−4.81515e8	+	6.64308e8i	−0.830064	+	1.14517i
$835$	−8.94219e7	−	1.54883e8i	−0.153598	−	0.266039i
$836$	−6.31905e7	−	3.64830e7i	−0.108152	−	0.0624413i
$837$	−6.12854e8	−	6.76074e8i	−1.04515	−	1.15297i
$838$	−1.56667e8	−	2.71356e8i	−0.266224	−	0.461113i
$839$			7.78319e8i			1.31787i	0.752201	+	0.658934i	$0.228992\pi$
$839$			7.78319e8i			1.31787i	−0.752201	+	0.658934i	$0.771008\pi$
$840$	−3.21654e8	−	1.17577e8i	−0.542689	−	0.198373i
$841$	4.68573e7			0.0787752
$842$	2.57921e8	−	1.48911e8i	0.432067	−	0.249454i
$843$	2.37267e8	+	5.31313e8i	0.396054	+	0.886885i
$844$	−4.10208e7	+	7.10501e7i	−0.0682302	+	0.118178i
$845$	2.38261e8	−	1.37560e8i	0.394896	−	0.227993i
$846$	5.69286e7	+	1.73886e8i	0.0940198	+	0.287179i
$847$	3.16660e8	+	3.07329e8i	0.521127	+	0.505770i
$848$		−	5.22275e8i		−	0.856469i
$849$	−1.12035e7	+	1.07752e8i	−0.0183076	+	0.176076i
$850$	2.03911e8	−	3.53184e8i	0.332035	−	0.575101i
$851$	8.32753e8	+	4.80790e8i	1.35122	+	0.780129i
$852$	−1.66420e8	−	1.73036e7i	−0.269084	−	0.0279781i
$853$	−7.77463e8			−1.25266			−0.626329	−	0.779559i	$-0.715443\pi$
$853$	−7.77463e8			−1.25266			−0.626329	+	0.779559i	$0.715443\pi$
$854$	5.53419e8	+	1.39453e8i	0.888547	+	0.223900i
$855$	−2.32341e8	+	7.60664e7i	−0.371730	+	0.121701i
$856$	−4.30515e8	−	7.45674e8i	−0.686384	−	1.18885i
$857$	−1.34313e8	−	7.75458e7i	−0.213391	−	0.123201i	0.389495	−	0.921028i	$-0.372649\pi$
$857$	−1.34313e8	−	7.75458e7i	−0.213391	−	0.123201i	−0.602886	+	0.797827i	$0.705983\pi$
$858$	9.31545e7	−	4.15998e7i	0.147483	−	0.0658612i
$859$	1.49561e8	+	2.59048e8i	0.235961	+	0.408696i	0.959551	−	0.281533i	$-0.0908430\pi$
$859$	1.49561e8	+	2.59048e8i	0.235961	+	0.408696i	−0.723591	+	0.690229i	$0.757510\pi$
$860$		−	2.99219e7i		−	0.0470429i
$861$	−9.45222e7	−	1.12964e8i	−0.148090	−	0.176983i
$862$	−2.34740e8			−0.366493
$863$	−1.56018e8	+	9.00769e7i	−0.242740	+	0.140146i	−0.616436	−	0.787405i	$-0.711424\pi$
$863$	−1.56018e8	+	9.00769e7i	−0.242740	+	0.140146i	0.373695	+	0.927552i	$0.378091\pi$
$864$	2.95735e8	−	2.68081e8i	0.458524	−	0.415647i
$865$	−2.09513e7	+	3.62888e7i	−0.0323715	+	0.0560691i
$866$	−2.79367e8	+	1.61293e8i	−0.430151	+	0.248348i
$867$	−1.39443e8	−	1.01073e8i	−0.213963	−	0.155088i
$868$	2.36525e8	+	2.29555e8i	0.361675	+	0.351017i
$869$			4.32183e8i			0.658579i
$870$	2.74374e8	+	2.85281e7i	0.416663	+	0.0433227i
$871$	−6.84128e7	+	1.18494e8i	−0.103534	+	0.179326i
$872$	−9.25389e8	−	5.34274e8i	−1.39565	−	0.805776i
$873$	1.03275e8	−	1.15215e8i	0.155222	−	0.173167i
$874$	6.61175e8			0.990335
$875$	1.66944e8	+	5.87744e8i	0.249199	+	0.877333i
$876$	2.00856e6	+	1.45588e6i	0.00298795	+	0.00216578i
$877$	−1.11962e8	−	1.93924e8i	−0.165986	−	0.287496i	0.771019	−	0.636812i	$-0.219747\pi$
$877$	−1.11962e8	−	1.93924e8i	−0.165986	−	0.287496i	−0.937005	+	0.349316i	$0.886414\pi$
$878$	−2.05793e7	−	1.18815e7i	−0.0304052	−	0.0175545i
$879$	3.37819e8	+	7.56480e8i	0.497414	+	1.11386i
$880$	−5.40586e7	−	9.36323e7i	−0.0793263	−	0.137397i
$881$			2.77136e8i			0.405289i	0.979252	+	0.202645i	$0.0649537\pi$
$881$			2.77136e8i			0.405289i	−0.979252	+	0.202645i	$0.935046\pi$
$882$	−1.91495e8	−	5.30690e8i	−0.279094	−	0.773455i
$883$	1.26602e9			1.83890			0.919452	−	0.393203i	$-0.128633\pi$
$883$	1.26602e9			1.83890			0.919452	+	0.393203i	$0.128633\pi$
$884$	−8.17872e7	+	4.72199e7i	−0.118394	+	0.0683546i
$885$	5.13285e8	−	2.29217e8i	0.740507	−	0.330686i
$886$	2.61304e7	−	4.52592e7i	0.0375703	−	0.0650737i
$887$	5.24508e8	−	3.02825e8i	0.751591	−	0.433931i	−0.0746774	−	0.997208i	$-0.523793\pi$
$887$	5.24508e8	−	3.02825e8i	0.751591	−	0.433931i	0.826269	+	0.563276i	$0.190459\pi$
$888$	4.27063e8	−	5.89184e8i	0.609892	−	0.841418i
$889$	−7.73749e8	+	2.19777e8i	−1.10127	+	0.312808i
$890$		−	3.27424e8i		−	0.464451i
$891$	1.49030e8	−	3.38792e8i	0.210688	−	0.478961i
$892$	2.14602e8	−	3.71701e8i	0.302370	−	0.523720i
$893$	−1.67012e8	−	9.64245e7i	−0.234527	−	0.135404i
$894$	2.29622e7	−	2.20843e8i	0.0321367	−	0.309080i
$895$	−9.49038e7			−0.132378
$896$	1.34896e8	−	1.38992e8i	0.187532	−	0.193226i
$897$	2.59888e8	−	3.58546e8i	0.360088	−	0.496784i
$898$	2.75187e8	+	4.76639e8i	0.380014	+	0.658204i
$899$	−9.39834e8	−	5.42614e8i	−1.29352	−	0.746813i
$900$	−1.65957e8	−	3.48880e7i	−0.227650	−	0.0478573i
$901$	6.16542e8	+	1.06788e9i	0.842924	+	1.45999i
$902$		−	7.28649e7i		−	0.0992885i
$903$	1.54530e8	−	1.29303e8i	0.209870	−	0.175608i
$904$	−9.02825e8			−1.22208
$905$	−2.25350e8	+	1.30106e8i	−0.304026	+	0.175530i
$906$	−3.95228e8	−	8.85034e8i	−0.531450	−	1.19008i
$907$	−3.94123e8	+	6.82642e8i	−0.528214	+	0.914894i	0.471245	+	0.882003i	$0.343805\pi$
$907$	−3.94123e8	+	6.82642e8i	−0.528214	+	0.914894i	−0.999459	+	0.0328915i	$0.989528\pi$
$908$	9.76412e7	−	5.63732e7i	0.130429	−	0.0753034i
$909$	1.01920e9	−	3.33678e8i	1.35697	−	0.444259i
$910$	−3.01697e7	+	1.19728e8i	−0.0400357	+	0.158881i
$911$		−	1.49408e9i		−	1.97615i	−0.153976	−	0.988075i	$-0.549208\pi$
$911$		−	1.49408e9i		−	1.97615i	0.153976	−	0.988075i	$-0.450792\pi$
$912$	3.30221e7	−	3.17596e8i	0.0435331	−	0.418688i
$913$	1.44489e8	−	2.50263e8i	0.189855	−	0.328839i
$914$	7.89625e8	+	4.55890e8i	1.03415	+	0.597065i
$915$	−4.50699e8	−	4.68616e7i	−0.588334	−	0.0611721i
$916$	−2.63986e7			−0.0343475
$917$	−8.89573e8	+	9.16583e8i	−1.15365	+	1.18868i
$918$	2.18745e8	−	6.80983e8i	0.282755	−	0.880254i
$919$	2.98707e8	+	5.17375e8i	0.384856	+	0.666590i	0.991749	−	0.128193i	$-0.0409178\pi$
$919$	2.98707e8	+	5.17375e8i	0.384856	+	0.666590i	−0.606893	+	0.794783i	$0.707584\pi$
$920$	−6.36844e8	−	3.67682e8i	−0.817843	−	0.472182i
$921$	1.86429e8	−	8.32531e7i	0.238635	−	0.106567i
$922$	2.12588e8	+	3.68214e8i	0.271235	+	0.469794i
$923$			2.46578e8i			0.313580i
$924$	−4.58989e7	+	1.25566e8i	−0.0581817	+	0.159168i
$925$	−5.42687e8			−0.685684
$926$	−6.94385e8	+	4.00903e8i	−0.874515	+	0.504902i
$927$	5.31490e8	+	1.11731e8i	0.667200	+	0.140261i
$928$	2.37356e8	−	4.11112e8i	0.297000	−	0.514419i
$929$	1.07426e9	−	6.20222e8i	1.33986	−	0.773571i	0.353078	−	0.935594i	$-0.385135\pi$
$929$	1.07426e9	−	6.20222e8i	1.33986	−	0.773571i	0.986787	+	0.162023i	$0.0518018\pi$
$930$	4.42339e8	+	3.20624e8i	0.549928	+	0.398609i
$931$	5.23644e8	+	2.81794e8i	0.648914	+	0.349206i
$932$			2.79056e8i			0.344702i
$933$	−1.27686e9	−	1.32762e8i	−1.57216	−	0.163466i
$934$	1.68393e8	−	2.91666e8i	0.206673	−	0.357968i
$935$	2.21064e8	+	1.27632e8i	0.270448	+	0.156143i
$936$	−2.49538e8	−	2.23677e8i	−0.304305	−	0.272769i
$937$	−1.45542e8			−0.176917			−0.0884585	−	0.996080i	$-0.528194\pi$
$937$	−1.45542e8			−0.176917			−0.0884585	+	0.996080i	$0.528194\pi$
$938$	1.02274e8	+	3.60067e8i	0.123925	+	0.436289i
$939$	−6.35661e8	−	4.60751e8i	−0.767765	−	0.556505i
$940$	2.62364e7	+	4.54427e7i	0.0315878	+	0.0547117i
$941$	2.91954e8	+	1.68560e8i	0.350386	+	0.202295i	0.664855	−	0.746972i	$-0.268493\pi$
$941$	2.91954e8	+	1.68560e8i	0.350386	+	0.202295i	−0.314470	+	0.949268i	$0.601827\pi$
$942$	2.09785e8	+	4.69772e8i	0.250970	+	0.561998i
$943$	−1.58137e8	−	2.73901e8i	−0.188581	−	0.326632i
$944$			7.34208e8i			0.872776i
$945$	2.10631e8	+	3.95328e8i	0.249590	+	0.468449i
$946$	9.96763e7			0.117738
$947$	3.13694e7	−	1.81111e7i	0.0369365	−	0.0213253i	−0.481418	−	0.876491i	$-0.659878\pi$
$947$	3.13694e7	−	1.81111e7i	0.0369365	−	0.0213253i	0.518355	+	0.855166i	$0.326545\pi$
$948$	3.17112e8	−	1.41612e8i	0.372209	−	0.166217i
$949$	1.82792e6	−	3.16606e6i	0.00213875	−	0.00370442i
$950$	−3.23155e8	+	1.86574e8i	−0.376912	+	0.217610i
$951$	4.65605e8	−	6.42358e8i	0.541347	−	0.746854i
$952$	−2.58045e8	+	1.02405e9i	−0.299078	+	1.18689i
$953$		−	1.20343e9i		−	1.39041i	−0.718811	−	0.695205i	$-0.755313\pi$
$953$		−	1.20343e9i		−	1.39041i	0.718811	−	0.695205i	$-0.244687\pi$
$954$	−7.14480e8	+	7.97084e8i	−0.822896	+	0.918034i
$955$	−1.57329e7	+	2.72501e7i	−0.0180633	+	0.0312866i
$956$	2.46110e7	+	1.42092e7i	0.0281680	+	0.0162628i
$957$	4.55224e7	−	4.37820e8i	0.0519385	−	0.499527i
$958$	−1.28946e8			−0.146660
$959$	2.55250e7	+	6.43191e6i	0.0289408	+	0.00729263i
$960$	−2.97685e8	+	4.10692e8i	−0.336468	+	0.464197i
$961$	−6.30875e8	−	1.09271e9i	−0.710842	−	1.23121i
$962$	−2.27203e8	−	1.31176e8i	−0.255205	−	0.147343i
$963$	−2.31689e8	+	1.10211e9i	−0.259434	+	1.23409i
$964$	−1.34585e8	−	2.33108e8i	−0.150233	−	0.260211i
$965$			1.45556e7i			0.0161975i
$966$	−2.08713e8	−	1.19332e9i	−0.231536	−	1.32381i
$967$	1.16933e9			1.29317			0.646586	−	0.762841i	$-0.276196\pi$
$967$	1.16933e9			1.29317			0.646586	+	0.762841i	$0.276196\pi$
$968$	6.20980e8	−	3.58523e8i	0.684623	−	0.395267i
$969$	3.07400e8	+	6.88362e8i	0.337857	+	0.756564i
$970$	−4.63174e7	+	8.02241e7i	−0.0507492	+	0.0879001i
$971$	2.74967e8	−	1.58752e8i	0.300347	−	0.173405i	−0.342252	−	0.939608i	$-0.611190\pi$
$971$	2.74967e8	−	1.58752e8i	0.300347	−	0.173405i	0.642599	+	0.766203i	$0.277856\pi$
$972$	−2.97419e8	+	1.66088e6i	−0.323870	+	0.00180858i
$973$	−1.52419e9	+	4.32933e8i	−1.65462	+	0.469983i
$974$			1.27085e9i			1.37536i
$975$	−2.58460e7	+	2.48579e8i	−0.0278856	+	0.268195i
$976$	2.95914e8	−	5.12538e8i	0.318285	−	0.551286i
$977$	1.04559e8	+	6.03673e7i	0.112119	+	0.0647319i	0.555011	−	0.831843i	$-0.312714\pi$
$977$	1.04559e8	+	6.03673e7i	0.112119	+	0.0647319i	−0.442892	+	0.896575i	$0.646047\pi$
$978$	−8.64111e7	−	8.98461e6i	−0.0923747	−	0.00960467i
$979$	−5.22471e8			−0.556819
$980$	−8.50540e7	−	1.37641e8i	−0.0903683	−	0.146241i
$981$	4.34858e8	+	1.32825e9i	0.460618	+	1.40693i
$982$	−3.29796e8	−	5.71223e8i	−0.348266	−	0.603214i
$983$	1.02296e9	+	5.90608e8i	1.07696	+	0.621783i	0.930074	−	0.367371i	$-0.119742\pi$
$983$	1.02296e9	+	5.90608e8i	1.07696	+	0.621783i	0.146884	+	0.989154i	$0.453075\pi$
$984$	−2.18541e8	+	9.75934e7i	−0.229376	+	0.102432i
$985$	2.62190e8	+	4.54126e8i	0.274351	+	0.475191i
$986$		−	8.50639e8i		−	0.887390i
$987$	−1.21311e8	+	3.31869e8i	−0.126167	+	0.345156i
$988$	8.64101e7			0.0895970
$989$	3.74686e8	−	2.16325e8i	0.387328	−	0.223624i
$990$	−4.55874e7	+	2.16852e8i	−0.0469828	+	0.223490i
$991$	−5.41017e7	+	9.37069e7i	−0.0555892	+	0.0962833i	−0.892481	−	0.451085i	$-0.851037\pi$
$991$	−5.41017e7	+	9.37069e7i	−0.0555892	+	0.0962833i	0.836892	+	0.547368i	$0.184370\pi$
$992$	8.14193e8	−	4.70075e8i	0.834051	−	0.481540i
$993$	7.49580e8	+	5.43324e8i	0.765544	+	0.554895i
$994$	4.84063e8	+	4.69798e8i	0.492882	+	0.478357i
$995$		−	5.89642e8i		−	0.598576i
$996$	−2.30973e8	−	2.40155e7i	−0.233767	−	0.0243060i
$997$	−1.44590e8	+	2.50437e8i	−0.145899	+	0.252705i	−0.929708	−	0.368297i	$-0.879941\pi$
$997$	−1.44590e8	+	2.50437e8i	−0.145899	+	0.252705i	0.783809	+	0.621002i	$0.213274\pi$
$998$	5.55086e8	+	3.20479e8i	0.558430	+	0.322410i
$999$	−9.30317e8	+	2.01005e8i	−0.933114	+	0.201609i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.7.h.a.11.10	yes	28
3.2	odd	2	inner	21.7.h.a.11.5	yes	28
7.2	even	3	inner	21.7.h.a.2.5	✓	28
7.3	odd	6		147.7.b.d.50.10		14
7.4	even	3		147.7.b.e.50.10		14
21.2	odd	6	inner	21.7.h.a.2.10	yes	28
21.11	odd	6		147.7.b.e.50.5		14
21.17	even	6		147.7.b.d.50.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.h.a.2.5	✓	28	7.2	even	3	inner
21.7.h.a.2.10	yes	28	21.2	odd	6	inner
21.7.h.a.11.5	yes	28	3.2	odd	2	inner
21.7.h.a.11.10	yes	28	1.1	even	1	trivial
147.7.b.d.50.5		14	21.17	even	6
147.7.b.d.50.10		14	7.3	odd	6
147.7.b.e.50.5		14	21.11	odd	6
147.7.b.e.50.10		14	7.4	even	3

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	21.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.69684 - 3.28907i) q^{2} +(-24.6534 + 11.0094i) q^{3} +(-10.3640 + 17.9510i) q^{4} +(-57.4599 + 33.1745i) q^{5} +(-104.236 + 143.806i) q^{6} +(-329.948 + 93.7191i) q^{7} +557.353i q^{8} +(486.585 - 542.841i) q^{9} +O(q^{10})\)	\(q+(5.69684 - 3.28907i) q^{2} +(-24.6534 + 11.0094i) q^{3} +(-10.3640 + 17.9510i) q^{4} +(-57.4599 + 33.1745i) q^{5} +(-104.236 + 143.806i) q^{6} +(-329.948 + 93.7191i) q^{7} +557.353i q^{8} +(486.585 - 542.841i) q^{9} +(-218.227 + 377.979i) q^{10} +(603.143 + 348.225i) q^{11} +(57.8782 - 556.654i) q^{12} -824.771 q^{13} +(-1571.41 + 1619.13i) q^{14} +(1051.35 - 1450.47i) q^{15} +(1169.88 + 2026.29i) q^{16} +(-4784.05 - 2762.07i) q^{17} +(986.554 - 4692.89i) q^{18} +(2527.23 + 4377.29i) q^{19} -1375.28i q^{20} +(7102.56 - 5943.04i) q^{21} +4581.35 q^{22} +(17221.4 - 9942.79i) q^{23} +(-6136.14 - 13740.7i) q^{24} +(-5611.41 + 9719.25i) q^{25} +(-4698.59 + 2712.73i) q^{26} +(-6019.63 + 18739.9i) q^{27} +(1737.23 - 6894.19i) q^{28} +23408.7i q^{29} +(1218.70 - 11721.0i) q^{30} +(-23180.0 + 40149.0i) q^{31} +(-17562.4 - 10139.7i) q^{32} +(-18703.3 - 1944.68i) q^{33} -36338.6 q^{34} +(15849.7 - 16330.9i) q^{35} +(4701.55 + 14360.7i) q^{36} +(24177.8 + 41877.2i) q^{37} +(28794.4 + 16624.5i) q^{38} +(20333.4 - 9080.25i) q^{39} +(-18489.9 - 32025.4i) q^{40} -15904.7i q^{41} +(20915.1 - 57217.4i) q^{42} +21757.0 q^{43} +(-12501.9 + 7217.99i) q^{44} +(-9950.65 + 47333.8i) q^{45} +(65405.1 - 113285. i) q^{46} +(-33042.5 + 19077.1i) q^{47} +(-51149.9 - 37075.4i) q^{48} +(100082. - 61844.9i) q^{49} +73825.4i q^{50} +(148352. + 15424.9i) q^{51} +(8547.91 - 14805.4i) q^{52} +(-193312. - 111609. i) q^{53} +(27344.1 + 126557. i) q^{54} -46208.7 q^{55} +(-52234.6 - 183898. i) q^{56} +(-110496. - 80091.9i) q^{57} +(76992.9 + 133356. i) q^{58} +(271755. + 156898. i) q^{59} +(15141.0 + 33905.4i) q^{60} +(-126472. - 219056. i) q^{61} +304963. i q^{62} +(-109673. + 224712. i) q^{63} -283145. q^{64} +(47391.2 - 27361.3i) q^{65} +(-112946. + 50438.0i) q^{66} +(82947.6 - 143669. i) q^{67} +(99163.6 - 57252.1i) q^{68} +(-315103. + 434722. i) q^{69} +(36579.5 - 145166. i) q^{70} -298965. i q^{71} +(302554. + 271200. i) q^{72} +(-2216.28 + 3838.71i) q^{73} +(275474. + 159045. i) q^{74} +(31337.2 - 301391. i) q^{75} -104769. q^{76} +(-231641. - 58370.1i) q^{77} +(85970.8 - 118607. i) q^{78} +(310276. + 537413. i) q^{79} +(-134442. - 77620.3i) q^{80} +(-57911.3 - 528276. i) q^{81} +(-52311.7 - 90606.6i) q^{82} -414931. i q^{83} +(33072.3 + 189091. i) q^{84} +366521. q^{85} +(123946. - 71560.3i) q^{86} +(-257716. - 577104. i) q^{87} +(-194084. + 336164. i) q^{88} +(-649685. + 375096. i) q^{89} +(98996.9 + 302381. i) q^{90} +(272131. - 77296.8i) q^{91} +412188. i q^{92} +(129450. - 1.24501e6i) q^{93} +(-125492. + 217359. i) q^{94} +(-290428. - 167679. i) q^{95} +(544605. + 56625.4i) q^{96} +212245. q^{97} +(366742. - 681499. i) q^{98} +(482511. - 157970. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9}+O(q^{10}) \) 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9	\( 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9} - 930 q^{10} - 404 q^{12} + 3632 q^{13} + 5450 q^{15} - 13706 q^{16} + 1612 q^{18} + 6830 q^{19} - 11333 q^{21} - 27348 q^{22} - 54498 q^{24} - 7640 q^{25} + 13268 q^{27} + 88522 q^{28} + 32380 q^{30} + 69410 q^{31} - 85459 q^{33} - 31344 q^{34} + 399028 q^{36} - 71830 q^{37} + 104570 q^{39} + 230250 q^{40} - 467782 q^{42} - 498904 q^{43} - 85375 q^{45} - 342660 q^{46} - 324728 q^{48} + 395668 q^{49} + 42177 q^{51} + 218000 q^{52} - 402122 q^{54} + 231660 q^{55} + 786782 q^{57} + 459522 q^{58} + 1021150 q^{60} + 153158 q^{61} + 179011 q^{63} - 1399412 q^{64} + 80896 q^{66} - 977098 q^{67} - 1520742 q^{69} - 139650 q^{70} - 1001352 q^{72} - 488350 q^{73} + 1434610 q^{75} + 6196280 q^{76} + 245176 q^{78} + 380762 q^{79} + 893531 q^{81} - 3665004 q^{82} + 1231496 q^{84} - 912540 q^{85} + 1452416 q^{87} - 1522482 q^{88} - 11713820 q^{90} - 1529416 q^{91} - 1690071 q^{93} - 3034044 q^{94} + 7549346 q^{96} + 7212176 q^{97} + 435866 q^{99}+O(q^{100}) \) 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9 - 930 * q^10 - 404 * q^12 + 3632 * q^13 + 5450 * q^15 - 13706 * q^16 + 1612 * q^18 + 6830 * q^19 - 11333 * q^21 - 27348 * q^22 - 54498 * q^24 - 7640 * q^25 + 13268 * q^27 + 88522 * q^28 + 32380 * q^30 + 69410 * q^31 - 85459 * q^33 - 31344 * q^34 + 399028 * q^36 - 71830 * q^37 + 104570 * q^39 + 230250 * q^40 - 467782 * q^42 - 498904 * q^43 - 85375 * q^45 - 342660 * q^46 - 324728 * q^48 + 395668 * q^49 + 42177 * q^51 + 218000 * q^52 - 402122 * q^54 + 231660 * q^55 + 786782 * q^57 + 459522 * q^58 + 1021150 * q^60 + 153158 * q^61 + 179011 * q^63 - 1399412 * q^64 + 80896 * q^66 - 977098 * q^67 - 1520742 * q^69 - 139650 * q^70 - 1001352 * q^72 - 488350 * q^73 + 1434610 * q^75 + 6196280 * q^76 + 245176 * q^78 + 380762 * q^79 + 893531 * q^81 - 3665004 * q^82 + 1231496 * q^84 - 912540 * q^85 + 1452416 * q^87 - 1522482 * q^88 - 11713820 * q^90 - 1529416 * q^91 - 1690071 * q^93 - 3034044 * q^94 + 7549346 * q^96 + 7212176 * q^97 + 435866 * q^99

Introduction

L-functions

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