LMFDB - Embedded newform 65.6.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,6,Mod(1,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("65.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	65.a (trivial)

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:	yes
Analytic conductor:	$10.4249482878$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 163x^{4} - 8x^{3} + 6120x^{2} + 6624x - 19440 $ x^6 - 163x^4 - 8x^3 + 6120x^2 + 6624x - 19440
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$9.61672$ of defining polynomial
Character	$\chi$	$=$	65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.61672 q^{2} +28.9791 q^{3} +60.4813 q^{4} -25.0000 q^{5} +278.684 q^{6} -189.995 q^{7} +273.896 q^{8} +596.790 q^{9} +O(q^{10})$	\(q+9.61672 q^{2} +28.9791 q^{3} +60.4813 q^{4} -25.0000 q^{5} +278.684 q^{6} -189.995 q^{7} +273.896 q^{8} +596.790 q^{9} -240.418 q^{10} -566.944 q^{11} +1752.69 q^{12} +169.000 q^{13} -1827.13 q^{14} -724.478 q^{15} +698.582 q^{16} -686.585 q^{17} +5739.16 q^{18} +125.865 q^{19} -1512.03 q^{20} -5505.88 q^{21} -5452.14 q^{22} +3481.79 q^{23} +7937.27 q^{24} +625.000 q^{25} +1625.23 q^{26} +10252.5 q^{27} -11491.1 q^{28} +1909.26 q^{29} -6967.10 q^{30} +6579.43 q^{31} -2046.61 q^{32} -16429.5 q^{33} -6602.70 q^{34} +4749.87 q^{35} +36094.6 q^{36} +6923.49 q^{37} +1210.41 q^{38} +4897.47 q^{39} -6847.40 q^{40} -1117.84 q^{41} -52948.5 q^{42} -3465.64 q^{43} -34289.5 q^{44} -14919.8 q^{45} +33483.4 q^{46} +7747.01 q^{47} +20244.3 q^{48} +19291.0 q^{49} +6010.45 q^{50} -19896.6 q^{51} +10221.3 q^{52} -15186.2 q^{53} +98595.7 q^{54} +14173.6 q^{55} -52038.8 q^{56} +3647.45 q^{57} +18360.8 q^{58} -48418.6 q^{59} -43817.4 q^{60} -14031.1 q^{61} +63272.5 q^{62} -113387. q^{63} -42036.3 q^{64} -4225.00 q^{65} -157998. q^{66} -33089.4 q^{67} -41525.5 q^{68} +100899. q^{69} +45678.2 q^{70} +21014.6 q^{71} +163459. q^{72} -83446.8 q^{73} +66581.3 q^{74} +18112.0 q^{75} +7612.47 q^{76} +107716. q^{77} +47097.6 q^{78} +74858.5 q^{79} -17464.6 q^{80} +152089. q^{81} -10750.0 q^{82} +51860.8 q^{83} -333003. q^{84} +17164.6 q^{85} -33328.1 q^{86} +55328.7 q^{87} -155284. q^{88} +122582. q^{89} -143479. q^{90} -32109.1 q^{91} +210583. q^{92} +190666. q^{93} +74500.8 q^{94} -3146.62 q^{95} -59309.0 q^{96} +19305.3 q^{97} +185516. q^{98} -338346. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 38 q^{3} + 134 q^{4} - 150 q^{5} + 318 q^{6} + 220 q^{7} + 24 q^{8} + 518 q^{9}+O(q^{10}) $ 6 * q + 38 * q^3 + 134 * q^4 - 150 * q^5 + 318 * q^6 + 220 * q^7 + 24 * q^8 + 518 * q^9	\( 6 q + 38 q^{3} + 134 q^{4} - 150 q^{5} + 318 q^{6} + 220 q^{7} + 24 q^{8} + 518 q^{9} - 170 q^{11} + 2238 q^{12} + 1014 q^{13} - 1440 q^{14} - 950 q^{15} + 3506 q^{16} + 728 q^{17} + 7788 q^{18} + 1218 q^{19} - 3350 q^{20} - 396 q^{21} + 5154 q^{22} + 8954 q^{23} + 12618 q^{24} + 3750 q^{25} + 13112 q^{27} + 13212 q^{28} + 8364 q^{29} - 7950 q^{30} + 2862 q^{31} - 29672 q^{32} - 3772 q^{33} - 21484 q^{34} - 5500 q^{35} - 2138 q^{36} + 13840 q^{37} - 27706 q^{38} + 6422 q^{39} - 600 q^{40} + 2248 q^{41} - 47028 q^{42} + 3822 q^{43} - 73482 q^{44} - 12950 q^{45} - 39886 q^{46} - 10860 q^{47} + 13962 q^{48} + 85902 q^{49} - 55028 q^{51} + 22646 q^{52} + 6584 q^{53} + 45504 q^{54} + 4250 q^{55} - 188800 q^{56} + 11692 q^{57} - 88500 q^{58} - 28874 q^{59} - 55950 q^{60} + 972 q^{61} + 123466 q^{62} - 125236 q^{63} + 14022 q^{64} - 25350 q^{65} - 158040 q^{66} + 60040 q^{67} + 3504 q^{68} + 153088 q^{69} + 36000 q^{70} - 74174 q^{71} + 298668 q^{72} + 48960 q^{73} + 226112 q^{74} + 23750 q^{75} - 93422 q^{76} + 231588 q^{77} + 53742 q^{78} + 214508 q^{79} - 87650 q^{80} + 116006 q^{81} + 58732 q^{82} + 123260 q^{83} - 235268 q^{84} - 18200 q^{85} - 304666 q^{86} + 228144 q^{87} + 127622 q^{88} + 94028 q^{89} - 194700 q^{90} + 37180 q^{91} + 430298 q^{92} + 192892 q^{93} - 125920 q^{94} - 30450 q^{95} - 385858 q^{96} + 246284 q^{97} - 4736 q^{98} - 32270 q^{99}+O(q^{100}) \) 6 * q + 38 * q^3 + 134 * q^4 - 150 * q^5 + 318 * q^6 + 220 * q^7 + 24 * q^8 + 518 * q^9 - 170 * q^11 + 2238 * q^12 + 1014 * q^13 - 1440 * q^14 - 950 * q^15 + 3506 * q^16 + 728 * q^17 + 7788 * q^18 + 1218 * q^19 - 3350 * q^20 - 396 * q^21 + 5154 * q^22 + 8954 * q^23 + 12618 * q^24 + 3750 * q^25 + 13112 * q^27 + 13212 * q^28 + 8364 * q^29 - 7950 * q^30 + 2862 * q^31 - 29672 * q^32 - 3772 * q^33 - 21484 * q^34 - 5500 * q^35 - 2138 * q^36 + 13840 * q^37 - 27706 * q^38 + 6422 * q^39 - 600 * q^40 + 2248 * q^41 - 47028 * q^42 + 3822 * q^43 - 73482 * q^44 - 12950 * q^45 - 39886 * q^46 - 10860 * q^47 + 13962 * q^48 + 85902 * q^49 - 55028 * q^51 + 22646 * q^52 + 6584 * q^53 + 45504 * q^54 + 4250 * q^55 - 188800 * q^56 + 11692 * q^57 - 88500 * q^58 - 28874 * q^59 - 55950 * q^60 + 972 * q^61 + 123466 * q^62 - 125236 * q^63 + 14022 * q^64 - 25350 * q^65 - 158040 * q^66 + 60040 * q^67 + 3504 * q^68 + 153088 * q^69 + 36000 * q^70 - 74174 * q^71 + 298668 * q^72 + 48960 * q^73 + 226112 * q^74 + 23750 * q^75 - 93422 * q^76 + 231588 * q^77 + 53742 * q^78 + 214508 * q^79 - 87650 * q^80 + 116006 * q^81 + 58732 * q^82 + 123260 * q^83 - 235268 * q^84 - 18200 * q^85 - 304666 * q^86 + 228144 * q^87 + 127622 * q^88 + 94028 * q^89 - 194700 * q^90 + 37180 * q^91 + 430298 * q^92 + 192892 * q^93 - 125920 * q^94 - 30450 * q^95 - 385858 * q^96 + 246284 * q^97 - 4736 * q^98 - 32270 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	9.61672	1.70001	0.850006	−	0.526773i	$-0.176598\pi$
$2$	9.61672	1.70001	0.850006	+	0.526773i	$0.176598\pi$
$3$	28.9791	1.85901	0.929506	−	0.368807i	$-0.120234\pi$
$3$	28.9791	1.85901	0.929506	+	0.368807i	$0.120234\pi$
$4$	60.4813	1.89004
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	278.684	3.16034
$7$	−189.995	−1.46554	−0.732768	−	0.680478i	$-0.761772\pi$
$7$	−189.995	−1.46554	−0.732768	+	0.680478i	$0.761772\pi$
$8$	273.896	1.51308
$9$	596.790	2.45593
$10$	−240.418	−0.760268
$11$	−566.944	−1.41273	−0.706363	−	0.707849i	$-0.749666\pi$
$11$	−566.944	−1.41273	−0.706363	+	0.707849i	$0.749666\pi$
$12$	1752.69	3.51361
$13$	169.000	0.277350
$13$	169.000	0.277350
$14$	−1827.13	−2.49143
$15$	−724.478	−0.831376
$16$	698.582	0.682209
$17$	−686.585	−0.576198	−0.288099	−	0.957601i	$-0.593023\pi$
$17$	−686.585	−0.576198	−0.288099	+	0.957601i	$0.593023\pi$
$18$	5739.16	4.17510
$19$	125.865	0.0799872	0.0399936	−	0.999200i	$-0.487266\pi$
$19$	125.865	0.0799872	0.0399936	+	0.999200i	$0.487266\pi$
$20$	−1512.03	−0.845251
$21$	−5505.88	−2.72445
$22$	−5452.14	−2.40165
$23$	3481.79	1.37241	0.686203	−	0.727410i	$-0.259276\pi$
$23$	3481.79	1.37241	0.686203	+	0.727410i	$0.259276\pi$
$24$	7937.27	2.81283
$25$	625.000	0.200000
$26$	1625.23	0.471498
$27$	10252.5	2.70659
$28$	−11491.1	−2.76992
$29$	1909.26	0.421570	0.210785	−	0.977532i	$-0.432398\pi$
$29$	1909.26	0.421570	0.210785	+	0.977532i	$0.432398\pi$
$30$	−6967.10	−1.41335
$31$	6579.43	1.22966	0.614828	−	0.788661i	$-0.289225\pi$
$31$	6579.43	1.22966	0.614828	+	0.788661i	$0.289225\pi$
$32$	−2046.61	−0.353314
$33$	−16429.5	−2.62628
$34$	−6602.70	−0.979544
$35$	4749.87	0.655408
$36$	36094.6	4.64180
$37$	6923.49	0.831421	0.415710	−	0.909497i	$-0.363533\pi$
$37$	6923.49	0.831421	0.415710	+	0.909497i	$0.363533\pi$
$38$	1210.41	0.135979
$39$	4897.47	0.515597
$40$	−6847.40	−0.676669
$41$	−1117.84	−0.103853	−0.0519266	−	0.998651i	$-0.516536\pi$
$41$	−1117.84	−0.103853	−0.0519266	+	0.998651i	$0.516536\pi$
$42$	−52948.5	−4.63160
$43$	−3465.64	−0.285833	−0.142916	−	0.989735i	$-0.545648\pi$
$43$	−3465.64	−0.285833	−0.142916	+	0.989735i	$0.545648\pi$
$44$	−34289.5	−2.67011
$45$	−14919.8	−1.09832
$46$	33483.4	2.33311
$47$	7747.01	0.511552	0.255776	−	0.966736i	$-0.417669\pi$
$47$	7747.01	0.511552	0.255776	+	0.966736i	$0.417669\pi$
$48$	20244.3	1.26824
$49$	19291.0	1.14780
$50$	6010.45	0.340002
$51$	−19896.6	−1.07116
$52$	10221.3	0.524203
$53$	−15186.2	−0.742609	−0.371305	−	0.928511i	$-0.621089\pi$
$53$	−15186.2	−0.742609	−0.371305	+	0.928511i	$0.621089\pi$
$54$	98595.7	4.60123
$55$	14173.6	0.631791
$56$	−52038.8	−2.21747
$57$	3647.45	0.148697
$58$	18360.8	0.716675
$59$	−48418.6	−1.81085	−0.905424	−	0.424508i	$-0.860447\pi$
$59$	−48418.6	−1.81085	−0.905424	+	0.424508i	$0.860447\pi$
$60$	−43817.4	−1.57133
$61$	−14031.1	−0.482801	−0.241400	−	0.970426i	$-0.577607\pi$
$61$	−14031.1	−0.482801	−0.241400	+	0.970426i	$0.577607\pi$
$62$	63272.5	2.09043
$63$	−113387.	−3.59925
$64$	−42036.3	−1.28285
$65$	−4225.00	−0.124035
$66$	−157998.	−4.46470
$67$	−33089.4	−0.900537	−0.450268	−	0.892893i	$-0.648672\pi$
$67$	−33089.4	−0.900537	−0.450268	+	0.892893i	$0.648672\pi$
$68$	−41525.5	−1.08904
$69$	100899.	2.55132
$70$	45678.2	1.11420
$71$	21014.6	0.494738	0.247369	−	0.968921i	$-0.420434\pi$
$71$	21014.6	0.494738	0.247369	+	0.968921i	$0.420434\pi$
$72$	163459.	3.71601
$73$	−83446.8	−1.83275	−0.916373	−	0.400325i	$-0.868897\pi$
$73$	−83446.8	−1.83275	−0.916373	+	0.400325i	$0.868897\pi$
$74$	66581.3	1.41342
$75$	18112.0	0.371802
$76$	7612.47	0.151179
$77$	107716.	2.07040
$78$	47097.6	0.876521
$79$	74858.5	1.34950	0.674751	−	0.738045i	$-0.264251\pi$
$79$	74858.5	1.34950	0.674751	+	0.738045i	$0.264251\pi$
$80$	−17464.6	−0.305093
$81$	152089.	2.57565
$82$	−10750.0	−0.176552
$83$	51860.8	0.826311	0.413156	−	0.910660i	$-0.364427\pi$
$83$	51860.8	0.826311	0.413156	+	0.910660i	$0.364427\pi$
$84$	−333003.	−5.14932
$85$	17164.6	0.257684
$86$	−33328.1	−0.485919
$87$	55328.7	0.783705
$88$	−155284.	−2.13756
$89$	122582.	1.64041	0.820205	−	0.572070i	$-0.193859\pi$
$89$	122582.	1.64041	0.820205	+	0.572070i	$0.193859\pi$
$90$	−143479.	−1.86716
$91$	−32109.1	−0.406467
$92$	210583.	2.59390
$93$	190666.	2.28595
$94$	74500.8	0.869644
$95$	−3146.62	−0.0357714
$96$	−59309.0	−0.656814
$97$	19305.3	0.208328	0.104164	−	0.994560i	$-0.466783\pi$
$97$	19305.3	0.208328	0.104164	+	0.994560i	$0.466783\pi$
$98$	185516.	1.95127
$99$	−338346.	−3.46955
$100$	37800.8	0.378008
$101$	−83222.2	−0.811775	−0.405888	−	0.913923i	$-0.633038\pi$
$101$	−83222.2	−0.811775	−0.405888	+	0.913923i	$0.633038\pi$
$102$	−191340.	−1.82098
$103$	109529.	1.01727	0.508634	−	0.860983i	$-0.330151\pi$
$103$	109529.	1.01727	0.508634	+	0.860983i	$0.330151\pi$
$104$	46288.5	0.419652
$105$	137647.	1.21841
$106$	−146042.	−1.26244
$107$	−65171.1	−0.550295	−0.275148	−	0.961402i	$-0.588727\pi$
$107$	−65171.1	−0.550295	−0.275148	+	0.961402i	$0.588727\pi$
$108$	620086.	5.11555
$109$	−180012.	−1.45123	−0.725615	−	0.688101i	$-0.758445\pi$
$109$	−180012.	−1.45123	−0.725615	+	0.688101i	$0.758445\pi$
$110$	136303.	1.07405
$111$	200637.	1.54562
$112$	−132727.	−0.999802
$113$	−63753.0	−0.469683	−0.234841	−	0.972034i	$-0.575457\pi$
$113$	−63753.0	−0.469683	−0.234841	+	0.972034i	$0.575457\pi$
$114$	35076.5	0.252787
$115$	−87044.7	−0.613759
$116$	115474.	0.796785
$117$	100858.	0.681151
$118$	−465628.	−3.07846
$119$	130448.	0.844440
$120$	−198432.	−1.25794
$121$	160374.	0.995797
$122$	−134933.	−0.820767
$123$	−32394.0	−0.193064
$124$	397932.	2.32410
$125$	−15625.0	−0.0894427
$126$	−1.09041e6	−6.11877
$127$	−18792.2	−0.103388	−0.0516939	−	0.998663i	$-0.516462\pi$
$127$	−18792.2	−0.103388	−0.0516939	+	0.998663i	$0.516462\pi$
$128$	−338760.	−1.82754
$129$	−100431.	−0.531367
$130$	−40630.6	−0.210860
$131$	−18190.6	−0.0926122	−0.0463061	−	0.998927i	$-0.514745\pi$
$131$	−18190.6	−0.0926122	−0.0463061	+	0.998927i	$0.514745\pi$
$132$	−993679.	−4.96377
$133$	−23913.7	−0.117224
$134$	−318211.	−1.53092
$135$	−256313.	−1.21042
$136$	−188053.	−0.871833
$137$	106188.	0.483363	0.241682	−	0.970356i	$-0.422301\pi$
$137$	106188.	0.483363	0.241682	+	0.970356i	$0.422301\pi$
$138$	970319.	4.33727
$139$	33944.0	0.149014	0.0745069	−	0.997221i	$-0.476262\pi$
$139$	33944.0	0.149014	0.0745069	+	0.997221i	$0.476262\pi$
$140$	287278.	1.23875
$141$	224502.	0.950981
$142$	202092.	0.841061
$143$	−95813.5	−0.391820
$144$	416907.	1.67546
$145$	−47731.5	−0.188532
$146$	−802484.	−3.11569
$147$	559037.	2.13377
$148$	418741.	1.57142
$149$	248671.	0.917612	0.458806	−	0.888536i	$-0.348277\pi$
$149$	248671.	0.917612	0.458806	+	0.888536i	$0.348277\pi$
$150$	174178.	0.632068
$151$	62344.4	0.222513	0.111256	−	0.993792i	$-0.464512\pi$
$151$	62344.4	0.222513	0.111256	+	0.993792i	$0.464512\pi$
$152$	34473.9	0.121027
$153$	−409747.	−1.41510
$154$	1.03588e6	3.51971
$155$	−164486.	−0.549919
$156$	296205.	0.974499
$157$	−275219.	−0.891106	−0.445553	−	0.895256i	$-0.646993\pi$
$157$	−275219.	−0.891106	−0.445553	+	0.895256i	$0.646993\pi$
$158$	719893.	2.29417
$159$	−440084.	−1.38052
$160$	51165.3	0.158007
$161$	−661521.	−2.01131
$162$	1.46260e6	4.37863
$163$	−53135.9	−0.156646	−0.0783229	−	0.996928i	$-0.524957\pi$
$163$	−53135.9	−0.156646	−0.0783229	+	0.996928i	$0.524957\pi$
$164$	−67608.4	−0.196287
$165$	410738.	1.17451
$166$	498730.	1.40474
$167$	412563.	1.14472	0.572360	−	0.820002i	$-0.306028\pi$
$167$	412563.	1.14472	0.572360	+	0.820002i	$0.306028\pi$
$168$	−1.50804e6	−4.12230
$169$	28561.0	0.0769231
$170$	165067.	0.438065
$171$	75114.9	0.196443
$172$	−209606.	−0.540235
$173$	−584248.	−1.48416	−0.742082	−	0.670309i	$-0.766162\pi$
$173$	−584248.	−1.48416	−0.742082	+	0.670309i	$0.766162\pi$
$174$	532081.	1.33231
$175$	−118747.	−0.293107
$176$	−396057.	−0.963775
$177$	−1.40313e6	−3.36639
$178$	1.17884e6	2.78872
$179$	−19918.7	−0.0464652	−0.0232326	−	0.999730i	$-0.507396\pi$
$179$	−19918.7	−0.0464652	−0.0232326	+	0.999730i	$0.507396\pi$
$180$	−902365.	−2.07588
$181$	585612.	1.32866	0.664329	−	0.747440i	$-0.268717\pi$
$181$	585612.	1.32866	0.664329	+	0.747440i	$0.268717\pi$
$182$	−308784.	−0.690998
$183$	−406610.	−0.897533
$184$	953648.	2.07656
$185$	−173087.	−0.371823
$186$	1.83358e6	3.88614
$187$	389255.	0.814011
$188$	468549.	0.966853
$189$	−1.94793e6	−3.96660
$190$	−30260.2	−0.0608117
$191$	−257249.	−0.510235	−0.255117	−	0.966910i	$-0.582114\pi$
$191$	−257249.	−0.510235	−0.255117	+	0.966910i	$0.582114\pi$
$192$	−1.21818e6	−2.38483
$193$	729315.	1.40936	0.704680	−	0.709525i	$-0.251091\pi$
$193$	729315.	1.40936	0.704680	+	0.709525i	$0.251091\pi$
$194$	185653.	0.354159
$195$	−122437.	−0.230582
$196$	1.16674e6	2.16938
$197$	614173.	1.12752	0.563761	−	0.825938i	$-0.309354\pi$
$197$	614173.	1.12752	0.563761	+	0.825938i	$0.309354\pi$
$198$	−3.25378e6	−5.89828
$199$	−2188.99	−0.00391842	−0.00195921	−	0.999998i	$-0.500624\pi$
$199$	−2188.99	−0.00391842	−0.00195921	+	0.999998i	$0.500624\pi$
$200$	171185.	0.302615
$201$	−958901.	−1.67411
$202$	−800325.	−1.38003
$203$	−362749.	−0.617827
$204$	−1.20337e6	−2.02453
$205$	27946.0	0.0464446
$206$	1.05331e6	1.72937
$207$	2.07790e6	3.37053
$208$	118060.	0.189211
$209$	−71358.3	−0.113000
$210$	1.32371e6	2.07131
$211$	95873.8	0.148250	0.0741248	−	0.997249i	$-0.476384\pi$
$211$	95873.8	0.148250	0.0741248	+	0.997249i	$0.476384\pi$
$212$	−918483.	−1.40356
$213$	608985.	0.919725
$214$	−626732.	−0.935508
$215$	86641.0	0.127828
$216$	2.80813e6	4.09527
$217$	−1.25006e6	−1.80211
$218$	−1.73113e6	−2.46711
$219$	−2.41822e6	−3.40710
$220$	857237.	1.19411
$221$	−116033.	−0.159809
$222$	1.92947e6	2.62757
$223$	822496.	1.10757	0.553786	−	0.832659i	$-0.313183\pi$
$223$	822496.	1.10757	0.553786	+	0.832659i	$0.313183\pi$
$224$	388845.	0.517794
$225$	372994.	0.491185
$226$	−613095.	−0.798466
$227$	−431133.	−0.555325	−0.277662	−	0.960679i	$-0.589560\pi$
$227$	−431133.	−0.555325	−0.277662	+	0.960679i	$0.589560\pi$
$228$	220603.	0.281044
$229$	962073.	1.21233	0.606163	−	0.795341i	$-0.292708\pi$
$229$	962073.	1.21233	0.606163	+	0.795341i	$0.292708\pi$
$230$	−837084.	−1.04340
$231$	3.12153e6	3.84890
$232$	522939.	0.637869
$233$	−517023.	−0.623907	−0.311953	−	0.950097i	$-0.600983\pi$
$233$	−517023.	−0.623907	−0.311953	+	0.950097i	$0.600983\pi$
$234$	969918.	1.15797
$235$	−193675.	−0.228773
$236$	−2.92842e6	−3.42257
$237$	2.16934e6	2.50874
$238$	1.25448e6	1.43556
$239$	−573574.	−0.649523	−0.324761	−	0.945796i	$-0.605284\pi$
$239$	−573574.	−0.649523	−0.324761	+	0.945796i	$0.605284\pi$
$240$	−506108.	−0.567172
$241$	−967200.	−1.07269	−0.536344	−	0.843999i	$-0.680195\pi$
$241$	−967200.	−1.07269	−0.536344	+	0.843999i	$0.680195\pi$
$242$	1.54227e6	1.69287
$243$	1.91606e6	2.08158
$244$	−848620.	−0.912513
$245$	−482275.	−0.513310
$246$	−311524.	−0.328212
$247$	21271.2	0.0221845
$248$	1.80208e6	1.86057
$249$	1.50288e6	1.53612
$250$	−150261.	−0.152054
$251$	−1.51519e6	−1.51804	−0.759018	−	0.651069i	$-0.774321\pi$
$251$	−1.51519e6	−1.51804	−0.759018	+	0.651069i	$0.774321\pi$
$252$	−6.85779e6	−6.80272
$253$	−1.97398e6	−1.93883
$254$	−180720.	−0.175760
$255$	497416.	0.479037
$256$	−1.91259e6	−1.82399
$257$	408239.	0.385551	0.192775	−	0.981243i	$-0.438251\pi$
$257$	408239.	0.385551	0.192775	+	0.981243i	$0.438251\pi$
$258$	−965819.	−0.903330
$259$	−1.31543e6	−1.21848
$260$	−255533.	−0.234431
$261$	1.13943e6	1.03535
$262$	−174934.	−0.157442
$263$	−1.24387e6	−1.10888	−0.554440	−	0.832224i	$-0.687068\pi$
$263$	−1.24387e6	−1.10888	−0.554440	+	0.832224i	$0.687068\pi$
$264$	−4.49999e6	−3.97376
$265$	379656.	0.332105
$266$	−229971.	−0.199282
$267$	3.55233e6	3.04954
$268$	−2.00129e6	−1.70205
$269$	−971010.	−0.818169	−0.409084	−	0.912497i	$-0.634152\pi$
$269$	−971010.	−0.818169	−0.409084	+	0.912497i	$0.634152\pi$
$270$	−2.46489e6	−2.05773
$271$	647163.	0.535292	0.267646	−	0.963517i	$-0.413754\pi$
$271$	647163.	0.535292	0.267646	+	0.963517i	$0.413754\pi$
$272$	−479636.	−0.393088
$273$	−930494.	−0.755626
$274$	1.02118e6	0.821724
$275$	−354340.	−0.282545
$276$	6.10251e6	4.82209
$277$	684624.	0.536109	0.268054	−	0.963404i	$-0.413619\pi$
$277$	684624.	0.536109	0.268054	+	0.963404i	$0.413619\pi$
$278$	326430.	0.253325
$279$	3.92654e6	3.01995
$280$	1.30097e6	0.991682
$281$	−2.08097e6	−1.57217	−0.786085	−	0.618118i	$-0.787895\pi$
$281$	−2.08097e6	−1.57217	−0.786085	+	0.618118i	$0.787895\pi$
$282$	2.15897e6	1.61668
$283$	2.09568e6	1.55546	0.777730	−	0.628598i	$-0.216371\pi$
$283$	2.09568e6	1.55546	0.777730	+	0.628598i	$0.216371\pi$
$284$	1.27099e6	0.935075
$285$	−91186.4	−0.0664994
$286$	−921411.	−0.666098
$287$	212384.	0.152201
$288$	−1.22140e6	−0.867712
$289$	−948458.	−0.667995
$290$	−459020.	−0.320507
$291$	559450.	0.387284
$292$	−5.04697e6	−3.46396
$293$	170648.	0.116127	0.0580633	−	0.998313i	$-0.481507\pi$
$293$	170648.	0.116127	0.0580633	+	0.998313i	$0.481507\pi$
$294$	5.37610e6	3.62743
$295$	1.21046e6	0.809836
$296$	1.89632e6	1.25800
$297$	−5.81261e6	−3.82367
$298$	2.39140e6	1.55995
$299$	588422.	0.380637
$300$	1.09543e6	0.702721
$301$	658453.	0.418898
$302$	599549.	0.378275
$303$	−2.41171e6	−1.50910
$304$	87926.9	0.0545680
$305$	350778.	0.215915
$306$	−3.94042e6	−2.40569
$307$	−42275.0	−0.0255998	−0.0127999	−	0.999918i	$-0.504074\pi$
$307$	−42275.0	−0.0255998	−0.0127999	+	0.999918i	$0.504074\pi$
$308$	6.51482e6	3.91314
$309$	3.17405e6	1.89111
$310$	−1.58181e6	−0.934869
$311$	−1.35058e6	−0.791808	−0.395904	−	0.918292i	$-0.629569\pi$
$311$	−1.35058e6	−0.791808	−0.395904	+	0.918292i	$0.629569\pi$
$312$	1.34140e6	0.780138
$313$	2.22900e6	1.28603	0.643013	−	0.765856i	$-0.277684\pi$
$313$	2.22900e6	1.28603	0.643013	+	0.765856i	$0.277684\pi$
$314$	−2.64670e6	−1.51489
$315$	2.83468e6	1.60963
$316$	4.52754e6	2.55061
$317$	−3.24898e6	−1.81593	−0.907964	−	0.419048i	$-0.862364\pi$
$317$	−3.24898e6	−1.81593	−0.907964	+	0.419048i	$0.862364\pi$
$318$	−4.23216e6	−2.34690
$319$	−1.08244e6	−0.595564
$320$	1.05091e6	0.573706
$321$	−1.88860e6	−1.02301
$322$	−6.36166e6	−3.41925
$323$	−86416.9	−0.0460885
$324$	9.19856e6	4.86808
$325$	105625.	0.0554700
$326$	−510993.	−0.266300
$327$	−5.21661e6	−2.69786
$328$	−306172.	−0.157138
$329$	−1.47189e6	−0.749698
$330$	3.94995e6	1.99667
$331$	1.81129e6	0.908694	0.454347	−	0.890825i	$-0.349873\pi$
$331$	1.81129e6	0.908694	0.454347	+	0.890825i	$0.349873\pi$
$332$	3.13660e6	1.56176
$333$	4.13187e6	2.04191
$334$	3.96750e6	1.94604
$335$	827234.	0.402732
$336$	−3.84631e6	−1.85864
$337$	−1.43117e6	−0.686461	−0.343231	−	0.939251i	$-0.611521\pi$
$337$	−1.43117e6	−0.686461	−0.343231	+	0.939251i	$0.611521\pi$
$338$	274663.	0.130770
$339$	−1.84751e6	−0.873146
$340$	1.03814e6	0.487032
$341$	−3.73016e6	−1.73717
$342$	722359.	0.333955
$343$	−471949.	−0.216601
$344$	−949225.	−0.432487
$345$	−2.52248e6	−1.14098
$346$	−5.61855e6	−2.52310
$347$	2.89201e6	1.28937	0.644683	−	0.764450i	$-0.276989\pi$
$347$	2.89201e6	1.28937	0.644683	+	0.764450i	$0.276989\pi$
$348$	3.34635e6	1.48123
$349$	−3.29833e6	−1.44954	−0.724771	−	0.688990i	$-0.758054\pi$
$349$	−3.29833e6	−1.44954	−0.724771	+	0.688990i	$0.758054\pi$
$350$	−1.14195e6	−0.498286
$351$	1.73268e6	0.750672
$352$	1.16031e6	0.499136
$353$	2.87329e6	1.22728	0.613639	−	0.789587i	$-0.289705\pi$
$353$	2.87329e6	1.22728	0.613639	+	0.789587i	$0.289705\pi$
$354$	−1.34935e7	−5.72290
$355$	−525365.	−0.221254
$356$	7.41393e6	3.10044
$357$	3.78026e6	1.56982
$358$	−191552.	−0.0789914
$359$	−655112.	−0.268274	−0.134137	−	0.990963i	$-0.542826\pi$
$359$	−655112.	−0.268274	−0.134137	+	0.990963i	$0.542826\pi$
$360$	−4.08646e6	−1.66185
$361$	−2.46026e6	−0.993602
$362$	5.63166e6	2.25873
$363$	4.64750e6	1.85120
$364$	−1.94200e6	−0.768238
$365$	2.08617e6	0.819629
$366$	−3.91025e6	−1.52582
$367$	3.46555e6	1.34310	0.671549	−	0.740960i	$-0.265629\pi$
$367$	3.46555e6	1.34310	0.671549	+	0.740960i	$0.265629\pi$
$368$	2.43231e6	0.936268
$369$	−667116.	−0.255056
$370$	−1.66453e6	−0.632103
$371$	2.88531e6	1.08832
$372$	1.15317e7	4.32053
$373$	3.97540e6	1.47948	0.739739	−	0.672894i	$-0.234949\pi$
$373$	3.97540e6	1.47948	0.739739	+	0.672894i	$0.234949\pi$
$374$	3.74336e6	1.38383
$375$	−452799.	−0.166275
$376$	2.12188e6	0.774017
$377$	322665.	0.116923
$378$	−1.87327e7	−6.74326
$379$	−187178.	−0.0669357	−0.0334679	−	0.999440i	$-0.510655\pi$
$379$	−187178.	−0.0669357	−0.0334679	+	0.999440i	$0.510655\pi$
$380$	−190312.	−0.0676093
$381$	−544583.	−0.192199
$382$	−2.47389e6	−0.867405
$383$	−2.85416e6	−0.994216	−0.497108	−	0.867689i	$-0.665605\pi$
$383$	−2.85416e6	−0.994216	−0.497108	+	0.867689i	$0.665605\pi$
$384$	−9.81696e6	−3.39742
$385$	−2.69291e6	−0.925912
$386$	7.01362e6	2.39593
$387$	−2.06826e6	−0.701985
$388$	1.16761e6	0.393747
$389$	−3.54177e6	−1.18671	−0.593357	−	0.804939i	$-0.702198\pi$
$389$	−3.54177e6	−1.18671	−0.593357	+	0.804939i	$0.702198\pi$
$390$	−1.17744e6	−0.391992
$391$	−2.39054e6	−0.790778
$392$	5.28373e6	1.73670
$393$	−527147.	−0.172167
$394$	5.90633e6	1.91680
$395$	−1.87146e6	−0.603516
$396$	−2.04636e7	−6.55759
$397$	−1.24829e6	−0.397501	−0.198751	−	0.980050i	$-0.563688\pi$
$397$	−1.24829e6	−0.397501	−0.198751	+	0.980050i	$0.563688\pi$
$398$	−21050.9	−0.00666136
$399$	−692997.	−0.217921
$400$	436614.	0.136442
$401$	−2.74122e6	−0.851299	−0.425650	−	0.904888i	$-0.639954\pi$
$401$	−2.74122e6	−0.851299	−0.425650	+	0.904888i	$0.639954\pi$
$402$	−9.22148e6	−2.84600
$403$	1.11192e6	0.341045
$404$	−5.03339e6	−1.53429
$405$	−3.80224e6	−1.15187
$406$	−3.48846e6	−1.05031
$407$	−3.92523e6	−1.17457
$408$	−5.44961e6	−1.62075
$409$	6.13745e6	1.81418	0.907089	−	0.420940i	$-0.138300\pi$
$409$	6.13745e6	1.81418	0.907089	+	0.420940i	$0.138300\pi$
$410$	268749.	0.0789563
$411$	3.07723e6	0.898579
$412$	6.62444e6	1.92267
$413$	9.19928e6	2.65386
$414$	1.99825e7	5.72994
$415$	−1.29652e6	−0.369538
$416$	−345877.	−0.0979916
$417$	983668.	0.277018
$418$	−686232.	−0.192101
$419$	1.95897e6	0.545120	0.272560	−	0.962139i	$-0.412130\pi$
$419$	1.95897e6	0.545120	0.272560	+	0.962139i	$0.412130\pi$
$420$	8.32507e6	2.30284
$421$	5.26629e6	1.44810	0.724051	−	0.689746i	$-0.242278\pi$
$421$	5.26629e6	1.44810	0.724051	+	0.689746i	$0.242278\pi$
$422$	921991.	0.252026
$423$	4.62334e6	1.25633
$424$	−4.15945e6	−1.12363
$425$	−429116.	−0.115240
$426$	5.85644e6	1.56354
$427$	2.66584e6	0.707562
$428$	−3.94163e6	−1.04008
$429$	−2.77659e6	−0.728398
$430$	833202.	0.217310
$431$	−3.23336e6	−0.838420	−0.419210	−	0.907889i	$-0.637693\pi$
$431$	−3.23336e6	−0.838420	−0.419210	+	0.907889i	$0.637693\pi$
$432$	7.16224e6	1.84646
$433$	−3.49771e6	−0.896529	−0.448265	−	0.893901i	$-0.647958\pi$
$433$	−3.49771e6	−0.896529	−0.448265	+	0.893901i	$0.647958\pi$
$434$	−1.20214e7	−3.06360
$435$	−1.38322e6	−0.350483
$436$	−1.08874e7	−2.74288
$437$	438235.	0.109775
$438$	−2.32553e7	−5.79211
$439$	−29404.2	−0.00728197	−0.00364098	−	0.999993i	$-0.501159\pi$
$439$	−29404.2	−0.00728197	−0.00364098	+	0.999993i	$0.501159\pi$
$440$	3.88209e6	0.955948
$441$	1.15127e7	2.81890
$442$	−1.11586e6	−0.271677
$443$	545860.	0.132151	0.0660757	−	0.997815i	$-0.478952\pi$
$443$	545860.	0.132151	0.0660757	+	0.997815i	$0.478952\pi$
$444$	1.21348e7	2.92128
$445$	−3.06455e6	−0.733614
$446$	7.90971e6	1.88288
$447$	7.20626e6	1.70585
$448$	7.98668e6	1.88006
$449$	−5.46505e6	−1.27932	−0.639658	−	0.768660i	$-0.720924\pi$
$449$	−5.46505e6	−1.27932	−0.639658	+	0.768660i	$0.720924\pi$
$450$	3.58698e6	0.835021
$451$	633752.	0.146716
$452$	−3.85586e6	−0.887719
$453$	1.80669e6	0.413654
$454$	−4.14609e6	−0.944059
$455$	802728.	0.181777
$456$	999024.	0.224990
$457$	−5.34706e6	−1.19764	−0.598818	−	0.800885i	$-0.704363\pi$
$457$	−5.34706e6	−1.19764	−0.598818	+	0.800885i	$0.704363\pi$
$458$	9.25198e6	2.06097
$459$	−7.03924e6	−1.55953
$460$	−5.26457e6	−1.16003
$461$	3.14978e6	0.690284	0.345142	−	0.938550i	$-0.387831\pi$
$461$	3.14978e6	0.690284	0.345142	+	0.938550i	$0.387831\pi$
$462$	3.00188e7	6.54318
$463$	−5.22334e6	−1.13239	−0.566194	−	0.824272i	$-0.691585\pi$
$463$	−5.22334e6	−1.13239	−0.566194	+	0.824272i	$0.691585\pi$
$464$	1.33378e6	0.287599
$465$	−4.76665e6	−1.02231
$466$	−4.97206e6	−1.06065
$467$	6.64502e6	1.40995	0.704976	−	0.709231i	$-0.250958\pi$
$467$	6.64502e6	1.40995	0.704976	+	0.709231i	$0.250958\pi$
$468$	6.09999e6	1.28740
$469$	6.28681e6	1.31977
$470$	−1.86252e6	−0.388917
$471$	−7.97561e6	−1.65658
$472$	−1.32617e7	−2.73995
$473$	1.96482e6	0.403804
$474$	2.08619e7	4.26489
$475$	78665.5	0.0159974
$476$	7.88963e6	1.59602
$477$	−9.06300e6	−1.82379
$478$	−5.51590e6	−1.10420
$479$	6.76505e6	1.34720	0.673600	−	0.739096i	$-0.264747\pi$
$479$	6.76505e6	1.34720	0.673600	+	0.739096i	$0.264747\pi$
$480$	1.48273e6	0.293736
$481$	1.17007e6	0.230595
$482$	−9.30129e6	−1.82358
$483$	−1.91703e7	−3.73905
$484$	9.69962e6	1.88209
$485$	−482632.	−0.0931669
$486$	1.84262e7	3.53871
$487$	1.34500e6	0.256980	0.128490	−	0.991711i	$-0.458987\pi$
$487$	1.34500e6	0.256980	0.128490	+	0.991711i	$0.458987\pi$
$488$	−3.84307e6	−0.730515
$489$	−1.53983e6	−0.291207
$490$	−4.63791e6	−0.872633
$491$	−7.33455e6	−1.37300	−0.686498	−	0.727131i	$-0.740853\pi$
$491$	−7.33455e6	−1.37300	−0.686498	+	0.727131i	$0.740853\pi$
$492$	−1.95923e6	−0.364899
$493$	−1.31087e6	−0.242908
$494$	204559.	0.0377138
$495$	8.45866e6	1.55163
$496$	4.59627e6	0.838883
$497$	−3.99267e6	−0.725057
$498$	1.44528e7	2.61143
$499$	4.61062e6	0.828912	0.414456	−	0.910069i	$-0.363972\pi$
$499$	4.61062e6	0.828912	0.414456	+	0.910069i	$0.363972\pi$
$500$	−945020.	−0.169050
$501$	1.19557e7	2.12805
$502$	−1.45711e7	−2.58068
$503$	7.67903e6	1.35328	0.676638	−	0.736316i	$-0.263436\pi$
$503$	7.67903e6	1.35328	0.676638	+	0.736316i	$0.263436\pi$
$504$	−3.10563e7	−5.44594
$505$	2.08056e6	0.363037
$506$	−1.89832e7	−3.29604
$507$	827673.	0.143001
$508$	−1.13658e6	−0.195407
$509$	3.69348e6	0.631890	0.315945	−	0.948778i	$-0.397678\pi$
$509$	3.69348e6	0.631890	0.315945	+	0.948778i	$0.397678\pi$
$510$	4.78351e6	0.814369
$511$	1.58545e7	2.68596
$512$	−7.55257e6	−1.27327
$513$	1.29043e6	0.216492
$514$	3.92592e6	0.655441
$515$	−2.73822e6	−0.454936
$516$	−6.07421e6	−1.00430
$517$	−4.39212e6	−0.722683
$518$	−1.26501e7	−2.07143
$519$	−1.69310e7	−2.75908
$520$	−1.15721e6	−0.187674
$521$	1.07885e7	1.74127	0.870636	−	0.491927i	$-0.163707\pi$
$521$	1.07885e7	1.74127	0.870636	+	0.491927i	$0.163707\pi$
$522$	1.09576e7	1.76010
$523$	7.52060e6	1.20226	0.601130	−	0.799151i	$-0.294717\pi$
$523$	7.52060e6	1.20226	0.601130	+	0.799151i	$0.294717\pi$
$524$	−1.10019e6	−0.175041
$525$	−3.44118e6	−0.544890
$526$	−1.19619e7	−1.88511
$527$	−4.51734e6	−0.708526
$528$	−1.14774e7	−1.79167
$529$	5.68650e6	0.883498
$530$	3.65104e6	0.564582
$531$	−2.88957e7	−4.44731
$532$	−1.44633e6	−0.221558
$533$	−188915.	−0.0288037
$534$	3.41617e7	5.18426
$535$	1.62928e6	0.246099
$536$	−9.06305e6	−1.36258
$537$	−577226.	−0.0863794
$538$	−9.33793e6	−1.39090
$539$	−1.09369e7	−1.62152
$540$	−1.55022e7	−2.28774
$541$	−5.06833e6	−0.744512	−0.372256	−	0.928130i	$-0.621416\pi$
$541$	−5.06833e6	−0.744512	−0.372256	+	0.928130i	$0.621416\pi$
$542$	6.22358e6	0.910002
$543$	1.69705e7	2.46999
$544$	1.40517e6	0.203579
$545$	4.50031e6	0.649010
$546$	−8.94830e6	−1.28457
$547$	6.41454e6	0.916636	0.458318	−	0.888788i	$-0.348452\pi$
$547$	6.41454e6	0.916636	0.458318	+	0.888788i	$0.348452\pi$
$548$	6.42238e6	0.913576
$549$	−8.37364e6	−1.18572
$550$	−3.40759e6	−0.480330
$551$	240309.	0.0337202
$552$	2.76359e7	3.86034
$553$	−1.42227e7	−1.97774
$554$	6.58384e6	0.911391
$555$	−5.01592e6	−0.691223
$556$	2.05298e6	0.281642
$557$	−4.77336e6	−0.651908	−0.325954	−	0.945386i	$-0.605685\pi$
$557$	−4.77336e6	−0.651908	−0.325954	+	0.945386i	$0.605685\pi$
$558$	3.77604e7	5.13394
$559$	−585693.	−0.0792758
$560$	3.31817e6	0.447125
$561$	1.12803e7	1.51326
$562$	−2.00121e7	−2.67271
$563$	−4.94279e6	−0.657205	−0.328603	−	0.944468i	$-0.606578\pi$
$563$	−4.94279e6	−0.657205	−0.328603	+	0.944468i	$0.606578\pi$
$564$	1.35781e7	1.79739
$565$	1.59383e6	0.210048
$566$	2.01536e7	2.64430
$567$	−2.88962e7	−3.77471
$568$	5.75582e6	0.748577
$569$	1.01177e7	1.31008	0.655042	−	0.755592i	$-0.272651\pi$
$569$	1.01177e7	1.31008	0.655042	+	0.755592i	$0.272651\pi$
$570$	−876914.	−0.113050
$571$	−4.01134e6	−0.514872	−0.257436	−	0.966295i	$-0.582878\pi$
$571$	−4.01134e6	−0.514872	−0.257436	+	0.966295i	$0.582878\pi$
$572$	−5.79492e6	−0.740555
$573$	−7.45485e6	−0.948533
$574$	2.04243e6	0.258743
$575$	2.17612e6	0.274481
$576$	−2.50869e7	−3.15058
$577$	715280.	0.0894410	0.0447205	−	0.999000i	$-0.485760\pi$
$577$	715280.	0.0894410	0.0447205	+	0.999000i	$0.485760\pi$
$578$	−9.12105e6	−1.13560
$579$	2.11349e7	2.62002
$580$	−2.88686e6	−0.356333
$581$	−9.85327e6	−1.21099
$582$	5.38008e6	0.658386
$583$	8.60974e6	1.04910
$584$	−2.28558e7	−2.77309
$585$	−2.52144e6	−0.304620
$586$	1.64107e6	0.197417
$587$	7.23624e6	0.866798	0.433399	−	0.901202i	$-0.357314\pi$
$587$	7.23624e6	0.866798	0.433399	+	0.901202i	$0.357314\pi$
$588$	3.38112e7	4.03290
$589$	828119.	0.0983568
$590$	1.16407e7	1.37673
$591$	1.77982e7	2.09608
$592$	4.83663e6	0.567203
$593$	−9.23201e6	−1.07810	−0.539050	−	0.842274i	$-0.681217\pi$
$593$	−9.23201e6	−1.07810	−0.539050	+	0.842274i	$0.681217\pi$
$594$	−5.58982e7	−6.50028
$595$	−3.26119e6	−0.377645
$596$	1.50399e7	1.73432
$597$	−63435.0	−0.00728439
$598$	5.65869e6	0.647087
$599$	−1.13007e7	−1.28688	−0.643441	−	0.765495i	$-0.722494\pi$
$599$	−1.13007e7	−1.28688	−0.643441	+	0.765495i	$0.722494\pi$
$600$	4.96080e6	0.562566
$601$	−1.57883e6	−0.178299	−0.0891494	−	0.996018i	$-0.528415\pi$
$601$	−1.57883e6	−0.178299	−0.0891494	+	0.996018i	$0.528415\pi$
$602$	6.33216e6	0.712132
$603$	−1.97474e7	−2.21165
$604$	3.77067e6	0.420558
$605$	−4.00935e6	−0.445334
$606$	−2.31927e7	−2.56549
$607$	1.76228e7	1.94135	0.970673	−	0.240405i	$-0.0772803\pi$
$607$	1.76228e7	1.94135	0.970673	+	0.240405i	$0.0772803\pi$
$608$	−257596.	−0.0282606
$609$	−1.05122e7	−1.14855
$610$	3.37334e6	0.367058
$611$	1.30925e6	0.141879
$612$	−2.47820e7	−2.67460
$613$	985236.	0.105898	0.0529492	−	0.998597i	$-0.483138\pi$
$613$	985236.	0.105898	0.0529492	+	0.998597i	$0.483138\pi$
$614$	−406546.	−0.0435200
$615$	809851.	0.0863410
$616$	2.95031e7	3.13268
$617$	1.09020e7	1.15290	0.576451	−	0.817132i	$-0.304437\pi$
$617$	1.09020e7	1.15290	0.576451	+	0.817132i	$0.304437\pi$
$618$	3.05239e7	3.21491
$619$	1.39085e7	1.45900	0.729499	−	0.683982i	$-0.239753\pi$
$619$	1.39085e7	1.45900	0.729499	+	0.683982i	$0.239753\pi$
$620$	−9.94830e6	−1.03937
$621$	3.56971e7	3.71453
$622$	−1.29882e7	−1.34608
$623$	−2.32900e7	−2.40408
$624$	3.42129e6	0.351745
$625$	390625.	0.0400000
$626$	2.14357e7	2.18626
$627$	−2.06790e6	−0.210068
$628$	−1.66456e7	−1.68422
$629$	−4.75357e6	−0.479063
$630$	2.72603e7	2.73640
$631$	−3.18595e6	−0.318541	−0.159271	−	0.987235i	$-0.550914\pi$
$631$	−3.18595e6	−0.318541	−0.159271	+	0.987235i	$0.550914\pi$
$632$	2.05035e7	2.04190
$633$	2.77834e6	0.275598
$634$	−3.12445e7	−3.08710
$635$	469806.	0.0462364
$636$	−2.66168e7	−2.60924
$637$	3.26018e6	0.318341
$638$	−1.04095e7	−1.01247
$639$	1.25413e7	1.21504
$640$	8.46899e6	0.817301
$641$	−9.63334e6	−0.926044	−0.463022	−	0.886347i	$-0.653235\pi$
$641$	−9.63334e6	−0.926044	−0.463022	+	0.886347i	$0.653235\pi$
$642$	−1.81622e7	−1.73912
$643$	1.78705e7	1.70455	0.852276	−	0.523093i	$-0.175222\pi$
$643$	1.78705e7	1.70455	0.852276	+	0.523093i	$0.175222\pi$
$644$	−4.00096e7	−3.80146
$645$	2.51078e6	0.237634
$646$	−831047.	−0.0783510
$647$	1.14547e6	0.107578	0.0537891	−	0.998552i	$-0.482870\pi$
$647$	1.14547e6	0.107578	0.0537891	+	0.998552i	$0.482870\pi$
$648$	4.16567e7	3.89716
$649$	2.74506e7	2.55823
$650$	1.01577e6	0.0942997
$651$	−3.62256e7	−3.35014
$652$	−3.21372e6	−0.296067
$653$	−1.04972e7	−0.963366	−0.481683	−	0.876345i	$-0.659974\pi$
$653$	−1.04972e7	−0.963366	−0.481683	+	0.876345i	$0.659974\pi$
$654$	−5.01666e7	−4.58639
$655$	454765.	0.0414175
$656$	−780903.	−0.0708496
$657$	−4.98002e7	−4.50109
$658$	−1.41548e7	−1.27449
$659$	−1.21009e7	−1.08543	−0.542717	−	0.839915i	$-0.682605\pi$
$659$	−1.21009e7	−1.08543	−0.542717	+	0.839915i	$0.682605\pi$
$660$	2.48420e7	2.21986
$661$	−6.81298e6	−0.606504	−0.303252	−	0.952910i	$-0.598072\pi$
$661$	−6.81298e6	−0.606504	−0.303252	+	0.952910i	$0.598072\pi$
$662$	1.74186e7	1.54479
$663$	−3.36253e6	−0.297086
$664$	1.42045e7	1.25027
$665$	597842.	0.0524242
$666$	3.97350e7	3.47127
$667$	6.64764e6	0.578566
$668$	2.49523e7	2.16357
$669$	2.38352e7	2.05899
$670$	7.95528e6	0.684649
$671$	7.95486e6	0.682066
$672$	1.12684e7	0.962585
$673$	−9.41818e6	−0.801548	−0.400774	−	0.916177i	$-0.631259\pi$
$673$	−9.41818e6	−0.801548	−0.400774	+	0.916177i	$0.631259\pi$
$674$	−1.37631e7	−1.16699
$675$	6.40783e6	0.541317
$676$	1.72741e6	0.145388
$677$	2.81424e6	0.235988	0.117994	−	0.993014i	$-0.462354\pi$
$677$	2.81424e6	0.235988	0.117994	+	0.993014i	$0.462354\pi$
$678$	−1.77670e7	−1.48436
$679$	−3.66790e6	−0.305312
$680$	4.70133e6	0.389895
$681$	−1.24939e7	−1.03236
$682$	−3.58719e7	−2.95321
$683$	1.31222e6	0.107635	0.0538176	−	0.998551i	$-0.482861\pi$
$683$	1.31222e6	0.107635	0.0538176	+	0.998551i	$0.482861\pi$
$684$	4.54304e6	0.371284
$685$	−2.65470e6	−0.216167
$686$	−4.53860e6	−0.368224
$687$	2.78800e7	2.25373
$688$	−2.42103e6	−0.194998
$689$	−2.56647e6	−0.205963
$690$	−2.42580e7	−1.93969
$691$	−8.31043e6	−0.662107	−0.331054	−	0.943612i	$-0.607404\pi$
$691$	−8.31043e6	−0.662107	−0.331054	+	0.943612i	$0.607404\pi$
$692$	−3.53361e7	−2.80513
$693$	6.42840e7	5.08476
$694$	2.78117e7	2.19194
$695$	−848600.	−0.0666410
$696$	1.51543e7	1.18581
$697$	767492.	0.0598401
$698$	−3.17191e7	−2.46424
$699$	−1.49829e7	−1.15985
$700$	−7.18195e6	−0.553984
$701$	−1.04904e7	−0.806298	−0.403149	−	0.915134i	$-0.632084\pi$
$701$	−1.04904e7	−0.806298	−0.403149	+	0.915134i	$0.632084\pi$
$702$	1.66627e7	1.27615
$703$	871424.	0.0665030
$704$	2.38322e7	1.81231
$705$	−5.61254e6	−0.425292
$706$	2.76316e7	2.08639
$707$	1.58118e7	1.18969
$708$	−8.48630e7	−6.36261
$709$	1.69019e7	1.26276	0.631380	−	0.775474i	$-0.282489\pi$
$709$	1.69019e7	1.26276	0.631380	+	0.775474i	$0.282489\pi$
$710$	−5.05229e6	−0.376134
$711$	4.46748e7	3.31428
$712$	3.35748e7	2.48207
$713$	2.29082e7	1.68759
$714$	3.63537e7	2.66872
$715$	2.39534e6	0.175227
$716$	−1.20471e6	−0.0878211
$717$	−1.66217e7	−1.20747
$718$	−6.30003e6	−0.456070
$719$	−4.94815e6	−0.356961	−0.178481	−	0.983943i	$-0.557118\pi$
$719$	−4.94815e6	−0.356961	−0.178481	+	0.983943i	$0.557118\pi$
$720$	−1.04227e7	−0.749286
$721$	−2.08099e7	−1.49084
$722$	−2.36596e7	−1.68913
$723$	−2.80286e7	−1.99414
$724$	3.54185e7	2.51122
$725$	1.19329e6	0.0843141
$726$	4.46937e7	3.14706
$727$	1.84144e7	1.29218	0.646089	−	0.763262i	$-0.276404\pi$
$727$	1.84144e7	1.29218	0.646089	+	0.763262i	$0.276404\pi$
$728$	−8.79456e6	−0.615015
$729$	1.85679e7	1.29403
$730$	2.00621e7	1.39338
$731$	2.37946e6	0.164696
$732$	−2.45923e7	−1.69637
$733$	−1.37224e7	−0.943344	−0.471672	−	0.881774i	$-0.656349\pi$
$733$	−1.37224e7	−0.943344	−0.471672	+	0.881774i	$0.656349\pi$
$734$	3.33273e7	2.28328
$735$	−1.39759e7	−0.954250
$736$	−7.12586e6	−0.484890
$737$	1.87598e7	1.27221
$738$	−6.41546e6	−0.433598
$739$	−3.74000e6	−0.251919	−0.125960	−	0.992035i	$-0.540201\pi$
$739$	−3.74000e6	−0.251919	−0.125960	+	0.992035i	$0.540201\pi$
$740$	−1.04685e7	−0.702759
$741$	616420.	0.0412412
$742$	2.77472e7	1.85016
$743$	8.50626e6	0.565284	0.282642	−	0.959226i	$-0.408789\pi$
$743$	8.50626e6	0.565284	0.282642	+	0.959226i	$0.408789\pi$
$744$	5.22227e7	3.45881
$745$	−6.21677e6	−0.410369
$746$	3.82303e7	2.51513
$747$	3.09500e7	2.02936
$748$	2.35426e7	1.53851
$749$	1.23822e7	0.806477
$750$	−4.35444e6	−0.282670
$751$	−1.43639e7	−0.929335	−0.464667	−	0.885485i	$-0.653826\pi$
$751$	−1.43639e7	−0.929335	−0.464667	+	0.885485i	$0.653826\pi$
$752$	5.41192e6	0.348985
$753$	−4.39088e7	−2.82205
$754$	3.10298e6	0.198770
$755$	−1.55861e6	−0.0995108
$756$	−1.17813e8	−7.49703
$757$	1.37525e7	0.872253	0.436126	−	0.899885i	$-0.356350\pi$
$757$	1.37525e7	0.872253	0.436126	+	0.899885i	$0.356350\pi$
$758$	−1.80004e6	−0.113791
$759$	−5.72041e7	−3.60432
$760$	−861848.	−0.0541248
$761$	−1.54163e7	−0.964978	−0.482489	−	0.875902i	$-0.660267\pi$
$761$	−1.54163e7	−0.964978	−0.482489	+	0.875902i	$0.660267\pi$
$762$	−5.23710e6	−0.326741
$763$	3.42014e7	2.12683
$764$	−1.55587e7	−0.964364
$765$	1.02437e7	0.632852
$766$	−2.74476e7	−1.69018
$767$	−8.18274e6	−0.502239
$768$	−5.54253e7	−3.39082
$769$	−2.69620e7	−1.64413	−0.822065	−	0.569393i	$-0.807178\pi$
$769$	−2.69620e7	−1.64413	−0.822065	+	0.569393i	$0.807178\pi$
$770$	−2.58969e7	−1.57406
$771$	1.18304e7	0.716743
$772$	4.41099e7	2.66375
$773$	−2.34249e7	−1.41003	−0.705017	−	0.709191i	$-0.749061\pi$
$773$	−2.34249e7	−1.41003	−0.705017	+	0.709191i	$0.749061\pi$
$774$	−1.98899e7	−1.19338
$775$	4.11214e6	0.245931
$776$	5.28764e6	0.315216
$777$	−3.81199e7	−2.26516
$778$	−3.40602e7	−2.01743
$779$	−140697.	−0.00830693
$780$	−7.40513e6	−0.435809
$781$	−1.19141e7	−0.698930
$782$	−2.29892e7	−1.34433
$783$	1.95748e7	1.14102
$784$	1.34764e7	0.783037
$785$	6.88047e6	0.398515
$786$	−5.06943e6	−0.292686
$787$	6.92601e6	0.398608	0.199304	−	0.979938i	$-0.436132\pi$
$787$	6.92601e6	0.398608	0.199304	+	0.979938i	$0.436132\pi$
$788$	3.71459e7	2.13106
$789$	−3.60462e7	−2.06142
$790$	−1.79973e7	−1.02598
$791$	1.21127e7	0.688337
$792$	−9.26718e7	−5.24970
$793$	−2.37126e6	−0.133905
$794$	−1.20044e7	−0.675757
$795$	1.10021e7	0.617387
$796$	−132393.	−0.00740597
$797$	−6.71294e6	−0.374341	−0.187170	−	0.982327i	$-0.559932\pi$
$797$	−6.71294e6	−0.374341	−0.187170	+	0.982327i	$0.559932\pi$
$798$	−6.66436e6	−0.370468
$799$	−5.31898e6	−0.294755
$800$	−1.27913e6	−0.0706627
$801$	7.31559e7	4.02873
$802$	−2.63615e7	−1.44722
$803$	4.73096e7	2.58917
$804$	−5.79955e7	−3.16413
$805$	1.65380e7	0.899485
$806$	1.06931e7	0.579781
$807$	−2.81390e7	−1.52099
$808$	−2.27943e7	−1.22828
$809$	1.59763e7	0.858235	0.429117	−	0.903249i	$-0.358825\pi$
$809$	1.59763e7	0.858235	0.429117	+	0.903249i	$0.358825\pi$
$810$	−3.65650e7	−1.95818
$811$	−2.53698e7	−1.35445	−0.677227	−	0.735774i	$-0.736819\pi$
$811$	−2.53698e7	−1.35445	−0.677227	+	0.735774i	$0.736819\pi$
$812$	−2.19395e7	−1.16772
$813$	1.87542e7	0.995114
$814$	−3.77478e7	−1.99678
$815$	1.32840e6	0.0700541
$816$	−1.38994e7	−0.730755
$817$	−436202.	−0.0228630
$818$	5.90221e7	3.08412
$819$	−1.91624e7	−0.998252
$820$	1.69021e6	0.0877821
$821$	1.23967e7	0.641874	0.320937	−	0.947101i	$-0.396002\pi$
$821$	1.23967e7	0.641874	0.320937	+	0.947101i	$0.396002\pi$
$822$	2.95929e7	1.52759
$823$	−1.23249e7	−0.634286	−0.317143	−	0.948378i	$-0.602723\pi$
$823$	−1.23249e7	−0.634286	−0.317143	+	0.948378i	$0.602723\pi$
$824$	2.99995e7	1.53920
$825$	−1.02685e7	−0.525255
$826$	8.84669e7	4.51160
$827$	−2.17696e6	−0.110684	−0.0553422	−	0.998467i	$-0.517625\pi$
$827$	−2.17696e6	−0.110684	−0.0553422	+	0.998467i	$0.517625\pi$
$828$	1.25674e8	6.37043
$829$	−948009.	−0.0479100	−0.0239550	−	0.999713i	$-0.507626\pi$
$829$	−948009.	−0.0479100	−0.0239550	+	0.999713i	$0.507626\pi$
$830$	−1.24683e7	−0.628218
$831$	1.98398e7	0.996633
$832$	−7.10414e6	−0.355798
$833$	−1.32449e7	−0.661358
$834$	9.45966e6	0.470934
$835$	−1.03141e7	−0.511934
$836$	−4.31584e6	−0.213575
$837$	6.74558e7	3.32817
$838$	1.88388e7	0.926711
$839$	2.05015e7	1.00550	0.502748	−	0.864433i	$-0.332322\pi$
$839$	2.05015e7	1.00550	0.502748	+	0.864433i	$0.332322\pi$
$840$	3.77010e7	1.84355
$841$	−1.68659e7	−0.822278
$842$	5.06444e7	2.46179
$843$	−6.03046e7	−2.92268
$844$	5.79856e6	0.280198
$845$	−714025.	−0.0344010
$846$	4.44614e7	2.13578
$847$	−3.04702e7	−1.45938
$848$	−1.06088e7	−0.506615
$849$	6.07310e7	2.89162
$850$	−4.12668e6	−0.195909
$851$	2.41061e7	1.14105
$852$	3.68322e7	1.73832
$853$	3.75405e7	1.76655	0.883277	−	0.468851i	$-0.155332\pi$
$853$	3.75405e7	1.76655	0.883277	+	0.468851i	$0.155332\pi$
$854$	2.56366e7	1.20286
$855$	−1.87787e6	−0.0878518
$856$	−1.78501e7	−0.832639
$857$	2.62833e7	1.22244	0.611221	−	0.791460i	$-0.290678\pi$
$857$	2.62833e7	1.22244	0.611221	+	0.791460i	$0.290678\pi$
$858$	−2.67017e7	−1.23828
$859$	−1.04479e7	−0.483110	−0.241555	−	0.970387i	$-0.577657\pi$
$859$	−1.04479e7	−0.483110	−0.241555	+	0.970387i	$0.577657\pi$
$860$	5.24016e6	0.241601
$861$	6.15470e6	0.282943
$862$	−3.10944e7	−1.42532
$863$	−8.76214e6	−0.400482	−0.200241	−	0.979747i	$-0.564173\pi$
$863$	−8.76214e6	−0.400482	−0.200241	+	0.979747i	$0.564173\pi$
$864$	−2.09829e7	−0.956274
$865$	1.46062e7	0.663739
$866$	−3.36365e7	−1.52411
$867$	−2.74855e7	−1.24181
$868$	−7.56050e7	−3.40605
$869$	−4.24406e7	−1.90648
$870$	−1.33020e7	−0.595826
$871$	−5.59210e6	−0.249764
$872$	−4.93047e7	−2.19582
$873$	1.15212e7	0.511637
$874$	4.21438e6	0.186619
$875$	2.96867e6	0.131082
$876$	−1.46257e8	−6.43955
$877$	−1.51823e7	−0.666558	−0.333279	−	0.942828i	$-0.608155\pi$
$877$	−1.51823e7	−0.666558	−0.333279	+	0.942828i	$0.608155\pi$
$878$	−282772.	−0.0123794
$879$	4.94523e6	0.215881
$880$	9.90142e6	0.431013
$881$	2.86755e7	1.24472	0.622359	−	0.782732i	$-0.286175\pi$
$881$	2.86755e7	1.24472	0.622359	+	0.782732i	$0.286175\pi$
$882$	1.10714e8	4.79217
$883$	−1.89214e6	−0.0816681	−0.0408340	−	0.999166i	$-0.513001\pi$
$883$	−1.89214e6	−0.0816681	−0.0408340	+	0.999166i	$0.513001\pi$
$884$	−7.01781e6	−0.302045
$885$	3.50782e7	1.50550
$886$	5.24938e6	0.224659
$887$	1.08388e7	0.462564	0.231282	−	0.972887i	$-0.425708\pi$
$887$	1.08388e7	0.462564	0.231282	+	0.972887i	$0.425708\pi$
$888$	5.49536e7	2.33864
$889$	3.57043e6	0.151519
$890$	−2.94710e7	−1.24715
$891$	−8.62262e7	−3.63869
$892$	4.97456e7	2.09335
$893$	975077.	0.0409176
$894$	6.93006e7	2.89997
$895$	497967.	0.0207799
$896$	6.43626e7	2.67833
$897$	1.70520e7	0.707609
$898$	−5.25558e7	−2.17485
$899$	1.25618e7	0.518387
$900$	2.25591e7	0.928360
$901$	1.04266e7	0.427890
$902$	6.09462e6	0.249419
$903$	1.90814e7	0.778737
$904$	−1.74617e7	−0.710666
$905$	−1.46403e7	−0.594194
$906$	1.73744e7	0.703217
$907$	−2.32175e7	−0.937123	−0.468561	−	0.883431i	$-0.655227\pi$
$907$	−2.32175e7	−0.937123	−0.468561	+	0.883431i	$0.655227\pi$
$908$	−2.60755e7	−1.04959
$909$	−4.96662e7	−1.99366
$910$	7.71961e6	0.309024
$911$	−2.42940e6	−0.0969849	−0.0484924	−	0.998824i	$-0.515442\pi$
$911$	−2.42940e6	−0.0969849	−0.0484924	+	0.998824i	$0.515442\pi$
$912$	2.54805e6	0.101443
$913$	−2.94021e7	−1.16735
$914$	−5.14212e7	−2.03599
$915$	1.01652e7	0.401389
$916$	5.81874e7	2.29134
$917$	3.45612e6	0.135727
$918$	−6.76943e7	−2.65122
$919$	−3.69038e7	−1.44139	−0.720697	−	0.693251i	$-0.756178\pi$
$919$	−3.69038e7	−1.44139	−0.720697	+	0.693251i	$0.756178\pi$
$920$	−2.38412e7	−0.928664
$921$	−1.22509e6	−0.0475904
$922$	3.02906e7	1.17349
$923$	3.55147e6	0.137216
$924$	1.88794e8	7.27458
$925$	4.32718e6	0.166284
$926$	−5.02314e7	−1.92507
$927$	6.53657e7	2.49833
$928$	−3.90751e6	−0.148947
$929$	2.16356e7	0.822489	0.411245	−	0.911525i	$-0.365094\pi$
$929$	2.16356e7	0.822489	0.411245	+	0.911525i	$0.365094\pi$
$930$	−4.58395e7	−1.73793
$931$	2.42806e6	0.0918090
$932$	−3.12702e7	−1.17921
$933$	−3.91387e7	−1.47198
$934$	6.39033e7	2.39693
$935$	−9.73138e6	−0.364037
$936$	2.76245e7	1.03063
$937$	−1.41082e7	−0.524956	−0.262478	−	0.964938i	$-0.584540\pi$
$937$	−1.41082e7	−0.524956	−0.262478	+	0.964938i	$0.584540\pi$
$938$	6.04584e7	2.24362
$939$	6.45945e7	2.39074
$940$	−1.17137e7	−0.432390
$941$	−4.39029e7	−1.61629	−0.808145	−	0.588983i	$-0.799528\pi$
$941$	−4.39029e7	−1.61629	−0.808145	+	0.588983i	$0.799528\pi$
$942$	−7.66992e7	−2.81620
$943$	−3.89208e6	−0.142529
$944$	−3.38244e7	−1.23538
$945$	4.86982e7	1.77392
$946$	1.88951e7	0.686471
$947$	4.04056e6	0.146409	0.0732044	−	0.997317i	$-0.476677\pi$
$947$	4.04056e6	0.146409	0.0732044	+	0.997317i	$0.476677\pi$
$948$	1.31204e8	4.74162
$949$	−1.41025e7	−0.508312
$950$	756504.	0.0271958
$951$	−9.41526e7	−3.37583
$952$	3.57291e7	1.27770
$953$	2.21804e7	0.791110	0.395555	−	0.918442i	$-0.370552\pi$
$953$	2.21804e7	0.791110	0.395555	+	0.918442i	$0.370552\pi$
$954$	−8.71563e7	−3.10047
$955$	6.43122e6	0.228184
$956$	−3.46905e7	−1.22762
$957$	−3.13683e7	−1.10716
$958$	6.50576e7	2.29026
$959$	−2.01752e7	−0.708387
$960$	3.04544e7	1.06653
$961$	1.46597e7	0.512055
$962$	1.12522e7	0.392013
$963$	−3.88935e7	−1.35148
$964$	−5.84975e7	−2.02742
$965$	−1.82329e7	−0.630285
$966$	−1.84356e8	−6.35643
$967$	2.23431e7	0.768383	0.384191	−	0.923253i	$-0.374480\pi$
$967$	2.23431e7	0.768383	0.384191	+	0.923253i	$0.374480\pi$
$968$	4.39258e7	1.50672
$969$	−2.50429e6	−0.0856791
$970$	−4.64134e6	−0.158385
$971$	−5.29498e7	−1.80226	−0.901128	−	0.433554i	$-0.857259\pi$
$971$	−5.29498e7	−1.80226	−0.901128	+	0.433554i	$0.857259\pi$
$972$	1.15885e8	3.93426
$973$	−6.44919e6	−0.218385
$974$	1.29345e7	0.436869
$975$	3.06092e6	0.103119
$976$	−9.80190e6	−0.329371
$977$	1.28543e7	0.430836	0.215418	−	0.976522i	$-0.430889\pi$
$977$	1.28543e7	0.430836	0.215418	+	0.976522i	$0.430889\pi$
$978$	−1.48081e7	−0.495054
$979$	−6.94972e7	−2.31745
$980$	−2.91686e7	−0.970176
$981$	−1.07430e8	−3.56412
$982$	−7.05343e7	−2.33411
$983$	−2.18478e7	−0.721149	−0.360574	−	0.932730i	$-0.617419\pi$
$983$	−2.18478e7	−0.721149	−0.360574	+	0.932730i	$0.617419\pi$
$984$	−8.87260e6	−0.292121
$985$	−1.53543e7	−0.504243
$986$	−1.26063e7	−0.412947
$987$	−4.26541e7	−1.39370
$988$	1.28651e6	0.0419295
$989$	−1.20666e7	−0.392279
$990$	8.13445e7	2.63779
$991$	1.64896e7	0.533368	0.266684	−	0.963784i	$-0.414072\pi$
$991$	1.64896e7	0.533368	0.266684	+	0.963784i	$0.414072\pi$
$992$	−1.34655e7	−0.434454
$993$	5.24896e7	1.68927
$994$	−3.83964e7	−1.23261
$995$	54724.7	0.00175237
$996$	9.08961e7	2.90333
$997$	5.04197e7	1.60643	0.803216	−	0.595688i	$-0.203121\pi$
$997$	5.04197e7	1.60643	0.803216	+	0.595688i	$0.203121\pi$
$998$	4.43391e7	1.40916
$999$	7.09833e7	2.25031

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.6.a.d.1.6	✓	6
3.2	odd	2		585.6.a.m.1.1		6
4.3	odd	2		1040.6.a.q.1.1		6
5.2	odd	4		325.6.b.g.274.11		12
5.3	odd	4		325.6.b.g.274.2		12
5.4	even	2		325.6.a.g.1.1		6
13.12	even	2		845.6.a.h.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.6.a.d.1.6	✓	6	1.1	even	1	trivial
325.6.a.g.1.1		6	5.4	even	2
325.6.b.g.274.2		12	5.3	odd	4
325.6.b.g.274.11		12	5.2	odd	4
585.6.a.m.1.1		6	3.2	odd	2
845.6.a.h.1.1		6	13.12	even	2
1040.6.a.q.1.1		6	4.3	odd	2

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	65.a (trivial)

\(f(q)\)	\(=\)	\(q+9.61672 q^{2} +28.9791 q^{3} +60.4813 q^{4} -25.0000 q^{5} +278.684 q^{6} -189.995 q^{7} +273.896 q^{8} +596.790 q^{9} +O(q^{10})\)	\(q+9.61672 q^{2} +28.9791 q^{3} +60.4813 q^{4} -25.0000 q^{5} +278.684 q^{6} -189.995 q^{7} +273.896 q^{8} +596.790 q^{9} -240.418 q^{10} -566.944 q^{11} +1752.69 q^{12} +169.000 q^{13} -1827.13 q^{14} -724.478 q^{15} +698.582 q^{16} -686.585 q^{17} +5739.16 q^{18} +125.865 q^{19} -1512.03 q^{20} -5505.88 q^{21} -5452.14 q^{22} +3481.79 q^{23} +7937.27 q^{24} +625.000 q^{25} +1625.23 q^{26} +10252.5 q^{27} -11491.1 q^{28} +1909.26 q^{29} -6967.10 q^{30} +6579.43 q^{31} -2046.61 q^{32} -16429.5 q^{33} -6602.70 q^{34} +4749.87 q^{35} +36094.6 q^{36} +6923.49 q^{37} +1210.41 q^{38} +4897.47 q^{39} -6847.40 q^{40} -1117.84 q^{41} -52948.5 q^{42} -3465.64 q^{43} -34289.5 q^{44} -14919.8 q^{45} +33483.4 q^{46} +7747.01 q^{47} +20244.3 q^{48} +19291.0 q^{49} +6010.45 q^{50} -19896.6 q^{51} +10221.3 q^{52} -15186.2 q^{53} +98595.7 q^{54} +14173.6 q^{55} -52038.8 q^{56} +3647.45 q^{57} +18360.8 q^{58} -48418.6 q^{59} -43817.4 q^{60} -14031.1 q^{61} +63272.5 q^{62} -113387. q^{63} -42036.3 q^{64} -4225.00 q^{65} -157998. q^{66} -33089.4 q^{67} -41525.5 q^{68} +100899. q^{69} +45678.2 q^{70} +21014.6 q^{71} +163459. q^{72} -83446.8 q^{73} +66581.3 q^{74} +18112.0 q^{75} +7612.47 q^{76} +107716. q^{77} +47097.6 q^{78} +74858.5 q^{79} -17464.6 q^{80} +152089. q^{81} -10750.0 q^{82} +51860.8 q^{83} -333003. q^{84} +17164.6 q^{85} -33328.1 q^{86} +55328.7 q^{87} -155284. q^{88} +122582. q^{89} -143479. q^{90} -32109.1 q^{91} +210583. q^{92} +190666. q^{93} +74500.8 q^{94} -3146.62 q^{95} -59309.0 q^{96} +19305.3 q^{97} +185516. q^{98} -338346. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 38 q^{3} + 134 q^{4} - 150 q^{5} + 318 q^{6} + 220 q^{7} + 24 q^{8} + 518 q^{9}+O(q^{10}) \) 6 * q + 38 * q^3 + 134 * q^4 - 150 * q^5 + 318 * q^6 + 220 * q^7 + 24 * q^8 + 518 * q^9	\( 6 q + 38 q^{3} + 134 q^{4} - 150 q^{5} + 318 q^{6} + 220 q^{7} + 24 q^{8} + 518 q^{9} - 170 q^{11} + 2238 q^{12} + 1014 q^{13} - 1440 q^{14} - 950 q^{15} + 3506 q^{16} + 728 q^{17} + 7788 q^{18} + 1218 q^{19} - 3350 q^{20} - 396 q^{21} + 5154 q^{22} + 8954 q^{23} + 12618 q^{24} + 3750 q^{25} + 13112 q^{27} + 13212 q^{28} + 8364 q^{29} - 7950 q^{30} + 2862 q^{31} - 29672 q^{32} - 3772 q^{33} - 21484 q^{34} - 5500 q^{35} - 2138 q^{36} + 13840 q^{37} - 27706 q^{38} + 6422 q^{39} - 600 q^{40} + 2248 q^{41} - 47028 q^{42} + 3822 q^{43} - 73482 q^{44} - 12950 q^{45} - 39886 q^{46} - 10860 q^{47} + 13962 q^{48} + 85902 q^{49} - 55028 q^{51} + 22646 q^{52} + 6584 q^{53} + 45504 q^{54} + 4250 q^{55} - 188800 q^{56} + 11692 q^{57} - 88500 q^{58} - 28874 q^{59} - 55950 q^{60} + 972 q^{61} + 123466 q^{62} - 125236 q^{63} + 14022 q^{64} - 25350 q^{65} - 158040 q^{66} + 60040 q^{67} + 3504 q^{68} + 153088 q^{69} + 36000 q^{70} - 74174 q^{71} + 298668 q^{72} + 48960 q^{73} + 226112 q^{74} + 23750 q^{75} - 93422 q^{76} + 231588 q^{77} + 53742 q^{78} + 214508 q^{79} - 87650 q^{80} + 116006 q^{81} + 58732 q^{82} + 123260 q^{83} - 235268 q^{84} - 18200 q^{85} - 304666 q^{86} + 228144 q^{87} + 127622 q^{88} + 94028 q^{89} - 194700 q^{90} + 37180 q^{91} + 430298 q^{92} + 192892 q^{93} - 125920 q^{94} - 30450 q^{95} - 385858 q^{96} + 246284 q^{97} - 4736 q^{98} - 32270 q^{99}+O(q^{100}) \) 6 * q + 38 * q^3 + 134 * q^4 - 150 * q^5 + 318 * q^6 + 220 * q^7 + 24 * q^8 + 518 * q^9 - 170 * q^11 + 2238 * q^12 + 1014 * q^13 - 1440 * q^14 - 950 * q^15 + 3506 * q^16 + 728 * q^17 + 7788 * q^18 + 1218 * q^19 - 3350 * q^20 - 396 * q^21 + 5154 * q^22 + 8954 * q^23 + 12618 * q^24 + 3750 * q^25 + 13112 * q^27 + 13212 * q^28 + 8364 * q^29 - 7950 * q^30 + 2862 * q^31 - 29672 * q^32 - 3772 * q^33 - 21484 * q^34 - 5500 * q^35 - 2138 * q^36 + 13840 * q^37 - 27706 * q^38 + 6422 * q^39 - 600 * q^40 + 2248 * q^41 - 47028 * q^42 + 3822 * q^43 - 73482 * q^44 - 12950 * q^45 - 39886 * q^46 - 10860 * q^47 + 13962 * q^48 + 85902 * q^49 - 55028 * q^51 + 22646 * q^52 + 6584 * q^53 + 45504 * q^54 + 4250 * q^55 - 188800 * q^56 + 11692 * q^57 - 88500 * q^58 - 28874 * q^59 - 55950 * q^60 + 972 * q^61 + 123466 * q^62 - 125236 * q^63 + 14022 * q^64 - 25350 * q^65 - 158040 * q^66 + 60040 * q^67 + 3504 * q^68 + 153088 * q^69 + 36000 * q^70 - 74174 * q^71 + 298668 * q^72 + 48960 * q^73 + 226112 * q^74 + 23750 * q^75 - 93422 * q^76 + 231588 * q^77 + 53742 * q^78 + 214508 * q^79 - 87650 * q^80 + 116006 * q^81 + 58732 * q^82 + 123260 * q^83 - 235268 * q^84 - 18200 * q^85 - 304666 * q^86 + 228144 * q^87 + 127622 * q^88 + 94028 * q^89 - 194700 * q^90 + 37180 * q^91 + 430298 * q^92 + 192892 * q^93 - 125920 * q^94 - 30450 * q^95 - 385858 * q^96 + 246284 * q^97 - 4736 * q^98 - 32270 * q^99

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