LMFDB - Embedded newform 74.6.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,6,Mod(1,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("74.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	74.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:	$11.8684026662$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.324233.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 77x - 140 $ x^3 - 77*x - 140
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-7.66368$ of defining polynomial
Character	$\chi$	$=$	74.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} -25.5252 q^{3} +16.0000 q^{4} -14.0000 q^{5} +102.101 q^{6} +203.072 q^{7} -64.0000 q^{8} +408.537 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -25.5252 q^{3} +16.0000 q^{4} -14.0000 q^{5} +102.101 q^{6} +203.072 q^{7} -64.0000 q^{8} +408.537 q^{9} +56.0000 q^{10} +60.7624 q^{11} -408.403 q^{12} -726.368 q^{13} -812.289 q^{14} +357.353 q^{15} +256.000 q^{16} +1661.51 q^{17} -1634.15 q^{18} -2104.58 q^{19} -224.000 q^{20} -5183.46 q^{21} -243.050 q^{22} -518.899 q^{23} +1633.61 q^{24} -2929.00 q^{25} +2905.47 q^{26} -4225.35 q^{27} +3249.16 q^{28} +4431.24 q^{29} -1429.41 q^{30} -6047.99 q^{31} -1024.00 q^{32} -1550.97 q^{33} -6646.05 q^{34} -2843.01 q^{35} +6536.58 q^{36} -1369.00 q^{37} +8418.33 q^{38} +18540.7 q^{39} +896.000 q^{40} -6612.77 q^{41} +20733.8 q^{42} -16157.7 q^{43} +972.199 q^{44} -5719.51 q^{45} +2075.60 q^{46} +6756.57 q^{47} -6534.45 q^{48} +24431.3 q^{49} +11716.0 q^{50} -42410.5 q^{51} -11621.9 q^{52} +5131.03 q^{53} +16901.4 q^{54} -850.674 q^{55} -12996.6 q^{56} +53719.9 q^{57} -17725.0 q^{58} -46340.3 q^{59} +5717.65 q^{60} -15827.9 q^{61} +24192.0 q^{62} +82962.4 q^{63} +4096.00 q^{64} +10169.1 q^{65} +6203.90 q^{66} -752.265 q^{67} +26584.2 q^{68} +13245.0 q^{69} +11372.0 q^{70} -14300.9 q^{71} -26146.3 q^{72} +56682.1 q^{73} +5476.00 q^{74} +74763.4 q^{75} -33673.3 q^{76} +12339.2 q^{77} -74162.8 q^{78} -103255. q^{79} -3584.00 q^{80} +8578.71 q^{81} +26451.1 q^{82} -123238. q^{83} -82935.4 q^{84} -23261.2 q^{85} +64630.6 q^{86} -113108. q^{87} -3888.80 q^{88} -22172.6 q^{89} +22878.0 q^{90} -147505. q^{91} -8302.38 q^{92} +154376. q^{93} -27026.3 q^{94} +29464.2 q^{95} +26137.8 q^{96} +54327.5 q^{97} -97725.3 q^{98} +24823.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 12 q^{2} - 8 q^{3} + 48 q^{4} - 42 q^{5} + 32 q^{6} + 84 q^{7} - 192 q^{8} + 193 q^{9}+O(q^{10}) $ 3 * q - 12 * q^2 - 8 * q^3 + 48 * q^4 - 42 * q^5 + 32 * q^6 + 84 * q^7 - 192 * q^8 + 193 * q^9	\( 3 q - 12 q^{2} - 8 q^{3} + 48 q^{4} - 42 q^{5} + 32 q^{6} + 84 q^{7} - 192 q^{8} + 193 q^{9} + 168 q^{10} + 304 q^{11} - 128 q^{12} - 806 q^{13} - 336 q^{14} + 112 q^{15} + 768 q^{16} + 246 q^{17} - 772 q^{18} - 4442 q^{19} - 672 q^{20} - 7630 q^{21} - 1216 q^{22} - 2898 q^{23} + 512 q^{24} - 8787 q^{25} + 3224 q^{26} - 8324 q^{27} + 1344 q^{28} - 1790 q^{29} - 448 q^{30} - 14606 q^{31} - 3072 q^{32} - 6322 q^{33} - 984 q^{34} - 1176 q^{35} + 3088 q^{36} - 4107 q^{37} + 17768 q^{38} + 18660 q^{39} + 2688 q^{40} + 8044 q^{41} + 30520 q^{42} - 8150 q^{43} + 4864 q^{44} - 2702 q^{45} + 11592 q^{46} + 19788 q^{47} - 2048 q^{48} + 14749 q^{49} + 35148 q^{50} - 34452 q^{51} - 12896 q^{52} + 38328 q^{53} + 33296 q^{54} - 4256 q^{55} - 5376 q^{56} + 38968 q^{57} + 7160 q^{58} - 17062 q^{59} + 1792 q^{60} - 32890 q^{61} + 58424 q^{62} + 71204 q^{63} + 12288 q^{64} + 11284 q^{65} + 25288 q^{66} + 5540 q^{67} + 3936 q^{68} - 38836 q^{69} + 4704 q^{70} - 14892 q^{71} - 12352 q^{72} - 2492 q^{73} + 16428 q^{74} + 23432 q^{75} - 71072 q^{76} + 80710 q^{77} - 74640 q^{78} - 129958 q^{79} - 10752 q^{80} + 1987 q^{81} - 32176 q^{82} - 139996 q^{83} - 122080 q^{84} - 3444 q^{85} + 32600 q^{86} - 108524 q^{87} - 19456 q^{88} - 58606 q^{89} + 10808 q^{90} - 152572 q^{91} - 46368 q^{92} + 156008 q^{93} - 79152 q^{94} + 62188 q^{95} + 8192 q^{96} + 29814 q^{97} - 58996 q^{98} - 122356 q^{99}+O(q^{100}) \) 3 * q - 12 * q^2 - 8 * q^3 + 48 * q^4 - 42 * q^5 + 32 * q^6 + 84 * q^7 - 192 * q^8 + 193 * q^9 + 168 * q^10 + 304 * q^11 - 128 * q^12 - 806 * q^13 - 336 * q^14 + 112 * q^15 + 768 * q^16 + 246 * q^17 - 772 * q^18 - 4442 * q^19 - 672 * q^20 - 7630 * q^21 - 1216 * q^22 - 2898 * q^23 + 512 * q^24 - 8787 * q^25 + 3224 * q^26 - 8324 * q^27 + 1344 * q^28 - 1790 * q^29 - 448 * q^30 - 14606 * q^31 - 3072 * q^32 - 6322 * q^33 - 984 * q^34 - 1176 * q^35 + 3088 * q^36 - 4107 * q^37 + 17768 * q^38 + 18660 * q^39 + 2688 * q^40 + 8044 * q^41 + 30520 * q^42 - 8150 * q^43 + 4864 * q^44 - 2702 * q^45 + 11592 * q^46 + 19788 * q^47 - 2048 * q^48 + 14749 * q^49 + 35148 * q^50 - 34452 * q^51 - 12896 * q^52 + 38328 * q^53 + 33296 * q^54 - 4256 * q^55 - 5376 * q^56 + 38968 * q^57 + 7160 * q^58 - 17062 * q^59 + 1792 * q^60 - 32890 * q^61 + 58424 * q^62 + 71204 * q^63 + 12288 * q^64 + 11284 * q^65 + 25288 * q^66 + 5540 * q^67 + 3936 * q^68 - 38836 * q^69 + 4704 * q^70 - 14892 * q^71 - 12352 * q^72 - 2492 * q^73 + 16428 * q^74 + 23432 * q^75 - 71072 * q^76 + 80710 * q^77 - 74640 * q^78 - 129958 * q^79 - 10752 * q^80 + 1987 * q^81 - 32176 * q^82 - 139996 * q^83 - 122080 * q^84 - 3444 * q^85 + 32600 * q^86 - 108524 * q^87 - 19456 * q^88 - 58606 * q^89 + 10808 * q^90 - 152572 * q^91 - 46368 * q^92 + 156008 * q^93 - 79152 * q^94 + 62188 * q^95 + 8192 * q^96 + 29814 * q^97 - 58996 * q^98 - 122356 * 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 $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	−25.5252	−1.63744	−0.818722	−	0.574191i	$-0.805317\pi$
$3$	−25.5252	−1.63744	−0.818722	+	0.574191i	$0.805317\pi$
$4$	16.0000	0.500000
$5$	−14.0000	−0.250440	−0.125220	−	0.992129i	$-0.539964\pi$
$5$	−14.0000	−0.250440	−0.125220	+	0.992129i	$0.539964\pi$
$6$	102.101	1.15785
$7$	203.072	1.56641	0.783205	−	0.621764i	$-0.213584\pi$
$7$	203.072	1.56641	0.783205	+	0.621764i	$0.213584\pi$
$8$	−64.0000	−0.353553
$9$	408.537	1.68122
$10$	56.0000	0.177088
$11$	60.7624	0.151410	0.0757048	−	0.997130i	$-0.475879\pi$
$11$	60.7624	0.151410	0.0757048	+	0.997130i	$0.475879\pi$
$12$	−408.403	−0.818722
$13$	−726.368	−1.19206	−0.596030	−	0.802962i	$-0.703256\pi$
$13$	−726.368	−1.19206	−0.596030	+	0.802962i	$0.703256\pi$
$14$	−812.289	−1.10762
$15$	357.353	0.410081
$16$	256.000	0.250000
$17$	1661.51	1.39438	0.697191	−	0.716886i	$-0.254433\pi$
$17$	1661.51	1.39438	0.697191	+	0.716886i	$0.254433\pi$
$18$	−1634.15	−1.18880
$19$	−2104.58	−1.33746	−0.668732	−	0.743503i	$-0.733163\pi$
$19$	−2104.58	−1.33746	−0.668732	+	0.743503i	$0.733163\pi$
$20$	−224.000	−0.125220
$21$	−5183.46	−2.56491
$22$	−243.050	−0.107063
$23$	−518.899	−0.204533	−0.102266	−	0.994757i	$-0.532609\pi$
$23$	−518.899	−0.204533	−0.102266	+	0.994757i	$0.532609\pi$
$24$	1633.61	0.578924
$25$	−2929.00	−0.937280
$26$	2905.47	0.842914
$27$	−4225.35	−1.11546
$28$	3249.16	0.783205
$29$	4431.24	0.978431	0.489215	−	0.872163i	$-0.337283\pi$
$29$	4431.24	0.978431	0.489215	+	0.872163i	$0.337283\pi$
$30$	−1429.41	−0.289971
$31$	−6047.99	−1.13033	−0.565167	−	0.824976i	$-0.691188\pi$
$31$	−6047.99	−1.13033	−0.565167	+	0.824976i	$0.691188\pi$
$32$	−1024.00	−0.176777
$33$	−1550.97	−0.247925
$34$	−6646.05	−0.985976
$35$	−2843.01	−0.392291
$36$	6536.58	0.840610
$37$	−1369.00	−0.164399
$37$	−1369.00	−0.164399
$38$	8418.33	0.945730
$39$	18540.7	1.95193
$40$	896.000	0.0885438
$41$	−6612.77	−0.614361	−0.307180	−	0.951651i	$-0.599386\pi$
$41$	−6612.77	−0.614361	−0.307180	+	0.951651i	$0.599386\pi$
$42$	20733.8	1.81366
$43$	−16157.7	−1.33262	−0.666312	−	0.745673i	$-0.732128\pi$
$43$	−16157.7	−1.33262	−0.666312	+	0.745673i	$0.732128\pi$
$44$	972.199	0.0757048
$45$	−5719.51	−0.421044
$46$	2075.60	0.144627
$47$	6756.57	0.446151	0.223075	−	0.974801i	$-0.428390\pi$
$47$	6756.57	0.446151	0.223075	+	0.974801i	$0.428390\pi$
$48$	−6534.45	−0.409361
$49$	24431.3	1.45364
$50$	11716.0	0.662757
$51$	−42410.5	−2.28322
$52$	−11621.9	−0.596030
$53$	5131.03	0.250908	0.125454	−	0.992099i	$-0.459961\pi$
$53$	5131.03	0.250908	0.125454	+	0.992099i	$0.459961\pi$
$54$	16901.4	0.788749
$55$	−850.674	−0.0379190
$56$	−12996.6	−0.553809
$57$	53719.9	2.19002
$58$	−17725.0	−0.691855
$59$	−46340.3	−1.73312	−0.866561	−	0.499072i	$-0.833674\pi$
$59$	−46340.3	−1.73312	−0.866561	+	0.499072i	$0.833674\pi$
$60$	5717.65	0.205040
$61$	−15827.9	−0.544628	−0.272314	−	0.962208i	$-0.587789\pi$
$61$	−15827.9	−0.544628	−0.272314	+	0.962208i	$0.587789\pi$
$62$	24192.0	0.799267
$63$	82962.4	2.63348
$64$	4096.00	0.125000
$65$	10169.1	0.298539
$66$	6203.90	0.175309
$67$	−752.265	−0.0204731	−0.0102366	−	0.999948i	$-0.503258\pi$
$67$	−752.265	−0.0204731	−0.0102366	+	0.999948i	$0.503258\pi$
$68$	26584.2	0.697191
$69$	13245.0	0.334911
$70$	11372.0	0.277392
$71$	−14300.9	−0.336680	−0.168340	−	0.985729i	$-0.553841\pi$
$71$	−14300.9	−0.336680	−0.168340	+	0.985729i	$0.553841\pi$
$72$	−26146.3	−0.594401
$73$	56682.1	1.24491	0.622456	−	0.782655i	$-0.286135\pi$
$73$	56682.1	1.24491	0.622456	+	0.782655i	$0.286135\pi$
$74$	5476.00	0.116248
$75$	74763.4	1.53474
$76$	−33673.3	−0.668732
$77$	12339.2	0.237170
$78$	−74162.8	−1.38022
$79$	−103255.	−1.86141	−0.930707	−	0.365766i	$-0.880807\pi$
$79$	−103255.	−1.86141	−0.930707	+	0.365766i	$0.880807\pi$
$80$	−3584.00	−0.0626099
$81$	8578.71	0.145281
$82$	26451.1	0.434419
$83$	−123238.	−1.96359	−0.981793	−	0.189953i	$-0.939166\pi$
$83$	−123238.	−1.96359	−0.981793	+	0.189953i	$0.939166\pi$
$84$	−82935.4	−1.28245
$85$	−23261.2	−0.349208
$86$	64630.6	0.942307
$87$	−113108.	−1.60212
$88$	−3888.80	−0.0535314
$89$	−22172.6	−0.296716	−0.148358	−	0.988934i	$-0.547399\pi$
$89$	−22172.6	−0.296716	−0.148358	+	0.988934i	$0.547399\pi$
$90$	22878.0	0.297723
$91$	−147505.	−1.86725
$92$	−8302.38	−0.102266
$93$	154376.	1.85086
$94$	−27026.3	−0.315476
$95$	29464.2	0.334954
$96$	26137.8	0.289462
$97$	54327.5	0.586261	0.293130	−	0.956072i	$-0.405303\pi$
$97$	54327.5	0.586261	0.293130	+	0.956072i	$0.405303\pi$
$98$	−97725.3	−1.02788
$99$	24823.7	0.254553
$100$	−46864.0	−0.468640
$101$	−162484.	−1.58492	−0.792462	−	0.609922i	$-0.791201\pi$
$101$	−162484.	−1.58492	−0.792462	+	0.609922i	$0.791201\pi$
$102$	169642.	1.61448
$103$	−177220.	−1.64596	−0.822980	−	0.568070i	$-0.807690\pi$
$103$	−177220.	−1.64596	−0.822980	+	0.568070i	$0.807690\pi$
$104$	46487.5	0.421457
$105$	72568.5	0.642354
$106$	−20524.1	−0.177419
$107$	193114.	1.63063	0.815315	−	0.579018i	$-0.196564\pi$
$107$	193114.	1.63063	0.815315	+	0.579018i	$0.196564\pi$
$108$	−67605.7	−0.557730
$109$	83541.6	0.673498	0.336749	−	0.941594i	$-0.390673\pi$
$109$	83541.6	0.673498	0.336749	+	0.941594i	$0.390673\pi$
$110$	3402.70	0.0268128
$111$	34944.0	0.269194
$112$	51986.5	0.391602
$113$	41276.4	0.304092	0.152046	−	0.988373i	$-0.451414\pi$
$113$	41276.4	0.304092	0.152046	+	0.988373i	$0.451414\pi$
$114$	−214880.	−1.54858
$115$	7264.59	0.0512231
$116$	70899.8	0.489215
$117$	−296748.	−2.00412
$118$	185361.	1.22550
$119$	337407.	2.18417
$120$	−22870.6	−0.144985
$121$	−157359.	−0.977075
$122$	63311.8	0.385110
$123$	168792.	1.00598
$124$	−96767.9	−0.565167
$125$	84756.0	0.485172
$126$	−331850.	−1.86215
$127$	201378.	1.10791	0.553953	−	0.832548i	$-0.313119\pi$
$127$	201378.	1.10791	0.553953	+	0.832548i	$0.313119\pi$
$128$	−16384.0	−0.0883883
$129$	412428.	2.18209
$130$	−40676.6	−0.211099
$131$	247225.	1.25867	0.629337	−	0.777132i	$-0.283326\pi$
$131$	247225.	1.25867	0.629337	+	0.777132i	$0.283326\pi$
$132$	−24815.6	−0.123962
$133$	−427382.	−2.09502
$134$	3009.06	0.0144767
$135$	59155.0	0.279355
$136$	−106337.	−0.492988
$137$	−64445.4	−0.293353	−0.146677	−	0.989185i	$-0.546858\pi$
$137$	−64445.4	−0.293353	−0.146677	+	0.989185i	$0.546858\pi$
$138$	−52980.0	−0.236818
$139$	5583.10	0.0245097	0.0122549	−	0.999925i	$-0.496099\pi$
$139$	5583.10	0.0245097	0.0122549	+	0.999925i	$0.496099\pi$
$140$	−45488.2	−0.196146
$141$	−172463.	−0.730547
$142$	57203.6	0.238069
$143$	−44135.9	−0.180489
$144$	104585.	0.420305
$145$	−62037.3	−0.245038
$146$	−226728.	−0.880285
$147$	−623615.	−2.38025
$148$	−21904.0	−0.0821995
$149$	390651.	1.44153	0.720764	−	0.693180i	$-0.243791\pi$
$149$	390651.	1.44153	0.720764	+	0.693180i	$0.243791\pi$
$150$	−299053.	−1.08523
$151$	−62658.6	−0.223634	−0.111817	−	0.993729i	$-0.535667\pi$
$151$	−62658.6	−0.223634	−0.111817	+	0.993729i	$0.535667\pi$
$152$	134693.	0.472865
$153$	678789.	2.34426
$154$	−49356.7	−0.167704
$155$	84671.9	0.283081
$156$	296651.	0.975965
$157$	49651.0	0.160760	0.0803801	−	0.996764i	$-0.474387\pi$
$157$	49651.0	0.160760	0.0803801	+	0.996764i	$0.474387\pi$
$158$	413020.	1.31622
$159$	−130971.	−0.410848
$160$	14336.0	0.0442719
$161$	−105374.	−0.320382
$162$	−34314.9	−0.102729
$163$	479004.	1.41211	0.706057	−	0.708155i	$-0.250472\pi$
$163$	479004.	1.41211	0.706057	+	0.708155i	$0.250472\pi$
$164$	−105804.	−0.307180
$165$	21713.6	0.0620902
$166$	492953.	1.38847
$167$	143567.	0.398348	0.199174	−	0.979964i	$-0.436174\pi$
$167$	143567.	0.398348	0.199174	+	0.979964i	$0.436174\pi$
$168$	331742.	0.906832
$169$	156317.	0.421007
$170$	93044.8	0.246928
$171$	−859799.	−2.24857
$172$	−258523.	−0.666312
$173$	−289074.	−0.734333	−0.367167	−	0.930155i	$-0.619672\pi$
$173$	−289074.	−0.734333	−0.367167	+	0.930155i	$0.619672\pi$
$174$	452433.	1.13287
$175$	−594798.	−1.46816
$176$	15555.2	0.0378524
$177$	1.18285e6	2.83789
$178$	88690.3	0.209810
$179$	−580785.	−1.35482	−0.677412	−	0.735604i	$-0.736898\pi$
$179$	−580785.	−1.35482	−0.677412	+	0.735604i	$0.736898\pi$
$180$	−91512.2	−0.210522
$181$	6278.48	0.0142448	0.00712242	−	0.999975i	$-0.497733\pi$
$181$	6278.48	0.0142448	0.00712242	+	0.999975i	$0.497733\pi$
$182$	590020.	1.32035
$183$	404012.	0.891798
$184$	33209.5	0.0723133
$185$	19166.0	0.0411720
$186$	−617505.	−1.30875
$187$	100958.	0.211123
$188$	108105.	0.223075
$189$	−858052.	−1.74727
$190$	−117857.	−0.236848
$191$	−307177.	−0.609264	−0.304632	−	0.952470i	$-0.598533\pi$
$191$	−307177.	−0.609264	−0.304632	+	0.952470i	$0.598533\pi$
$192$	−104551.	−0.204680
$193$	−60119.5	−0.116178	−0.0580888	−	0.998311i	$-0.518501\pi$
$193$	−60119.5	−0.116178	−0.0580888	+	0.998311i	$0.518501\pi$
$194$	−217310.	−0.414549
$195$	−259570.	−0.488841
$196$	390901.	0.726820
$197$	−241668.	−0.443664	−0.221832	−	0.975085i	$-0.571204\pi$
$197$	−241668.	−0.443664	−0.221832	+	0.975085i	$0.571204\pi$
$198$	−99294.7	−0.179996
$199$	−775719.	−1.38858	−0.694292	−	0.719694i	$-0.744282\pi$
$199$	−775719.	−1.38858	−0.694292	+	0.719694i	$0.744282\pi$
$200$	187456.	0.331379
$201$	19201.7	0.0335236
$202$	649938.	1.12071
$203$	899861.	1.53262
$204$	−678568.	−1.14161
$205$	92578.7	0.153860
$206$	708880.	1.16387
$207$	−211989.	−0.343865
$208$	−185950.	−0.298015
$209$	−127880.	−0.202505
$210$	−290274.	−0.454213
$211$	−227217.	−0.351345	−0.175673	−	0.984449i	$-0.556210\pi$
$211$	−227217.	−0.351345	−0.175673	+	0.984449i	$0.556210\pi$
$212$	82096.5	0.125454
$213$	365033.	0.551294
$214$	−772458.	−1.15303
$215$	226207.	0.333742
$216$	270423.	0.394374
$217$	−1.22818e6	−1.77057
$218$	−334166.	−0.476235
$219$	−1.44682e6	−2.03847
$220$	−13610.8	−0.0189595
$221$	−1.20687e6	−1.66219
$222$	−139776.	−0.190349
$223$	−1.15653e6	−1.55738	−0.778692	−	0.627407i	$-0.784116\pi$
$223$	−1.15653e6	−1.55738	−0.778692	+	0.627407i	$0.784116\pi$
$224$	−207946.	−0.276905
$225$	−1.19660e6	−1.57577
$226$	−165106.	−0.215026
$227$	37701.8	0.0485621	0.0242810	−	0.999705i	$-0.492270\pi$
$227$	37701.8	0.0485621	0.0242810	+	0.999705i	$0.492270\pi$
$228$	859519.	1.09501
$229$	701765.	0.884307	0.442153	−	0.896940i	$-0.354215\pi$
$229$	701765.	0.884307	0.442153	+	0.896940i	$0.354215\pi$
$230$	−29058.3	−0.0362202
$231$	−314960.	−0.388352
$232$	−283599.	−0.345928
$233$	946536.	1.14221	0.571107	−	0.820876i	$-0.306514\pi$
$233$	946536.	1.14221	0.571107	+	0.820876i	$0.306514\pi$
$234$	1.18699e6	1.41712
$235$	−94592.0	−0.111734
$236$	−741445.	−0.866561
$237$	2.63560e6	3.04796
$238$	−1.34963e6	−1.54444
$239$	−708838.	−0.802698	−0.401349	−	0.915925i	$-0.631458\pi$
$239$	−708838.	−0.802698	−0.401349	+	0.915925i	$0.631458\pi$
$240$	91482.4	0.102520
$241$	−190560.	−0.211343	−0.105672	−	0.994401i	$-0.533699\pi$
$241$	−190560.	−0.211343	−0.105672	+	0.994401i	$0.533699\pi$
$242$	629436.	0.690896
$243$	807788.	0.877570
$244$	−253247.	−0.272314
$245$	−342038.	−0.364049
$246$	−675169.	−0.711336
$247$	1.52870e6	1.59434
$248$	387072.	0.399634
$249$	3.14568e6	3.21526
$250$	−339024.	−0.343068
$251$	1.79115e6	1.79452	0.897258	−	0.441507i	$-0.145556\pi$
$251$	1.79115e6	1.79452	0.897258	+	0.441507i	$0.145556\pi$
$252$	1.32740e6	1.31674
$253$	−31529.6	−0.0309683
$254$	−805512.	−0.783408
$255$	593747.	0.571809
$256$	65536.0	0.0625000
$257$	−106877.	−0.100937	−0.0504684	−	0.998726i	$-0.516071\pi$
$257$	−106877.	−0.100937	−0.0504684	+	0.998726i	$0.516071\pi$
$258$	−1.64971e6	−1.54297
$259$	−278006.	−0.257516
$260$	162706.	0.149270
$261$	1.81032e6	1.64496
$262$	−988899.	−0.890017
$263$	−937957.	−0.836168	−0.418084	−	0.908408i	$-0.637298\pi$
$263$	−937957.	−0.836168	−0.418084	+	0.908408i	$0.637298\pi$
$264$	99262.4	0.0876546
$265$	−71834.4	−0.0628374
$266$	1.70953e6	1.48140
$267$	565960.	0.485856
$268$	−12036.2	−0.0102366
$269$	−2.26921e6	−1.91203	−0.956013	−	0.293325i	$-0.905238\pi$
$269$	−2.26921e6	−1.91203	−0.956013	+	0.293325i	$0.905238\pi$
$270$	−236620.	−0.197534
$271$	1.40004e6	1.15803	0.579013	−	0.815318i	$-0.303438\pi$
$271$	1.40004e6	1.15803	0.579013	+	0.815318i	$0.303438\pi$
$272$	425347.	0.348595
$273$	3.76510e6	3.05752
$274$	257782.	0.207432
$275$	−177973.	−0.141913
$276$	211920.	0.167456
$277$	232528.	0.182086	0.0910428	−	0.995847i	$-0.470980\pi$
$277$	232528.	0.182086	0.0910428	+	0.995847i	$0.470980\pi$
$278$	−22332.4	−0.0173310
$279$	−2.47083e6	−1.90034
$280$	181953.	0.138696
$281$	−1.42943e6	−1.07994	−0.539968	−	0.841686i	$-0.681564\pi$
$281$	−1.42943e6	−1.07994	−0.539968	+	0.841686i	$0.681564\pi$
$282$	689852.	0.516575
$283$	−1.22644e6	−0.910288	−0.455144	−	0.890418i	$-0.650412\pi$
$283$	−1.22644e6	−0.910288	−0.455144	+	0.890418i	$0.650412\pi$
$284$	−228814.	−0.168340
$285$	−752079.	−0.548468
$286$	176543.	0.127625
$287$	−1.34287e6	−0.962341
$288$	−418341.	−0.297201
$289$	1.34077e6	0.944299
$290$	248149.	0.173268
$291$	−1.38672e6	−0.959968
$292$	906913.	0.622456
$293$	−533674.	−0.363168	−0.181584	−	0.983375i	$-0.558122\pi$
$293$	−533674.	−0.363168	−0.181584	+	0.983375i	$0.558122\pi$
$294$	2.49446e6	1.68309
$295$	648765.	0.434042
$296$	87616.0	0.0581238
$297$	−256743.	−0.168891
$298$	−1.56260e6	−1.01931
$299$	376911.	0.243815
$300$	1.19621e6	0.767371
$301$	−3.28117e6	−2.08743
$302$	250634.	0.158133
$303$	4.14745e6	2.59522
$304$	−538773.	−0.334366
$305$	221591.	0.136396
$306$	−2.71516e6	−1.65764
$307$	−3.16257e6	−1.91511	−0.957556	−	0.288247i	$-0.906928\pi$
$307$	−3.16257e6	−1.91511	−0.957556	+	0.288247i	$0.906928\pi$
$308$	197427.	0.118585
$309$	4.52358e6	2.69517
$310$	−338688.	−0.200168
$311$	1.99037e6	1.16690	0.583448	−	0.812151i	$-0.301703\pi$
$311$	1.99037e6	1.16690	0.583448	+	0.812151i	$0.301703\pi$
$312$	−1.18660e6	−0.690112
$313$	925777.	0.534128	0.267064	−	0.963679i	$-0.413946\pi$
$313$	925777.	0.534128	0.267064	+	0.963679i	$0.413946\pi$
$314$	−198604.	−0.113675
$315$	−1.16147e6	−0.659528
$316$	−1.65208e6	−0.930707
$317$	2.81841e6	1.57528	0.787638	−	0.616138i	$-0.211304\pi$
$317$	2.81841e6	1.57528	0.787638	+	0.616138i	$0.211304\pi$
$318$	523883.	0.290513
$319$	269253.	0.148144
$320$	−57344.0	−0.0313050
$321$	−4.92929e6	−2.67006
$322$	421496.	0.226545
$323$	−3.49679e6	−1.86494
$324$	137259.	0.0726406
$325$	2.12753e6	1.11729
$326$	−1.91601e6	−0.998515
$327$	−2.13242e6	−1.10282
$328$	423217.	0.217209
$329$	1.37207e6	0.698855
$330$	−86854.6	−0.0439044
$331$	3.36125e6	1.68629	0.843143	−	0.537690i	$-0.180703\pi$
$331$	3.36125e6	1.68629	0.843143	+	0.537690i	$0.180703\pi$
$332$	−1.97181e6	−0.981793
$333$	−559286.	−0.276391
$334$	−574266.	−0.281674
$335$	10531.7	0.00512728
$336$	−1.32697e6	−0.641227
$337$	−337462.	−0.161864	−0.0809320	−	0.996720i	$-0.525790\pi$
$337$	−337462.	−0.161864	−0.0809320	+	0.996720i	$0.525790\pi$
$338$	−625268.	−0.297697
$339$	−1.05359e6	−0.497934
$340$	−372179.	−0.174604
$341$	−367491.	−0.171144
$342$	3.43920e6	1.58998
$343$	1.54829e6	0.710585
$344$	1.03409e6	0.471153
$345$	−185430.	−0.0838750
$346$	1.15629e6	0.519252
$347$	−2.35355e6	−1.04930	−0.524650	−	0.851318i	$-0.675804\pi$
$347$	−2.35355e6	−1.04930	−0.524650	+	0.851318i	$0.675804\pi$
$348$	−1.80973e6	−0.801062
$349$	−3.03701e6	−1.33470	−0.667348	−	0.744746i	$-0.732570\pi$
$349$	−3.03701e6	−1.33470	−0.667348	+	0.744746i	$0.732570\pi$
$350$	2.37919e6	1.03815
$351$	3.06916e6	1.32969
$352$	−62220.7	−0.0267657
$353$	4.07565e6	1.74085	0.870423	−	0.492304i	$-0.163845\pi$
$353$	4.07565e6	1.74085	0.870423	+	0.492304i	$0.163845\pi$
$354$	−4.73139e6	−2.00669
$355$	200212.	0.0843180
$356$	−354761.	−0.148358
$357$	−8.61239e6	−3.57646
$358$	2.32314e6	0.958005
$359$	958355.	0.392455	0.196228	−	0.980558i	$-0.437131\pi$
$359$	958355.	0.392455	0.196228	+	0.980558i	$0.437131\pi$
$360$	366049.	0.148862
$361$	1.95317e6	0.788811
$362$	−25113.9	−0.0100726
$363$	4.01662e6	1.59991
$364$	−2.36008e6	−0.933627
$365$	−793549.	−0.311775
$366$	−1.61605e6	−0.630596
$367$	2.82146e6	1.09347	0.546737	−	0.837304i	$-0.315870\pi$
$367$	2.82146e6	1.09347	0.546737	+	0.837304i	$0.315870\pi$
$368$	−132838.	−0.0511332
$369$	−2.70156e6	−1.03288
$370$	−76664.0	−0.0291130
$371$	1.04197e6	0.393025
$372$	2.47002e6	0.925430
$373$	4.28017e6	1.59290	0.796451	−	0.604703i	$-0.206708\pi$
$373$	4.28017e6	1.59290	0.796451	+	0.604703i	$0.206708\pi$
$374$	−403831.	−0.149286
$375$	−2.16341e6	−0.794441
$376$	−432421.	−0.157738
$377$	−3.21871e6	−1.16635
$378$	3.43221e6	1.23550
$379$	2.87336e6	1.02752	0.513762	−	0.857933i	$-0.328251\pi$
$379$	2.87336e6	1.02752	0.513762	+	0.857933i	$0.328251\pi$
$380$	471427.	0.167477
$381$	−5.14022e6	−1.81413
$382$	1.22871e6	0.430815
$383$	−2.12253e6	−0.739361	−0.369680	−	0.929159i	$-0.620533\pi$
$383$	−2.12253e6	−0.739361	−0.369680	+	0.929159i	$0.620533\pi$
$384$	418205.	0.144731
$385$	−172748.	−0.0593966
$386$	240478.	0.0821499
$387$	−6.60100e6	−2.24043
$388$	869241.	0.293130
$389$	−1.96464e6	−0.658278	−0.329139	−	0.944281i	$-0.606759\pi$
$389$	−1.96464e6	−0.658278	−0.329139	+	0.944281i	$0.606759\pi$
$390$	1.03828e6	0.345663
$391$	−862158.	−0.285197
$392$	−1.56360e6	−0.513939
$393$	−6.31046e6	−2.06101
$394$	966673.	0.313718
$395$	1.44557e6	0.466172
$396$	397179.	0.127276
$397$	−2.94926e6	−0.939155	−0.469578	−	0.882891i	$-0.655594\pi$
$397$	−2.94926e6	−0.939155	−0.469578	+	0.882891i	$0.655594\pi$
$398$	3.10288e6	0.981876
$399$	1.09090e7	3.43047
$400$	−749824.	−0.234320
$401$	4.12365e6	1.28062	0.640311	−	0.768116i	$-0.278806\pi$
$401$	4.12365e6	1.28062	0.640311	+	0.768116i	$0.278806\pi$
$402$	−76806.9	−0.0237047
$403$	4.39307e6	1.34743
$404$	−2.59975e6	−0.792462
$405$	−120102.	−0.0363842
$406$	−3.59945e6	−1.08373
$407$	−83183.8	−0.0248916
$408$	2.71427e6	0.807240
$409$	−5.72638e6	−1.69267	−0.846335	−	0.532652i	$-0.821196\pi$
$409$	−5.72638e6	−1.69267	−0.846335	+	0.532652i	$0.821196\pi$
$410$	−370315.	−0.108796
$411$	1.64498e6	0.480349
$412$	−2.83552e6	−0.822980
$413$	−9.41043e6	−2.71478
$414$	847957.	0.243149
$415$	1.72533e6	0.491760
$416$	743800.	0.210728
$417$	−142510.	−0.0401333
$418$	511519.	0.143193
$419$	6.17571e6	1.71851	0.859255	−	0.511547i	$-0.170927\pi$
$419$	6.17571e6	1.71851	0.859255	+	0.511547i	$0.170927\pi$
$420$	1.16110e6	0.321177
$421$	−3040.98	−0.000836196 0	−0.000418098	−	1.00000i	$-0.500133\pi$
$421$	−3040.98	−0.000836196 0	−0.000418098		1.00000i	$0.500133\pi$
$422$	908867.	0.248439
$423$	2.76031e6	0.750078
$424$	−328386.	−0.0887095
$425$	−4.86657e6	−1.30693
$426$	−1.46013e6	−0.389824
$427$	−3.21422e6	−0.853111
$428$	3.08983e6	0.815315
$429$	1.12658e6	0.295541
$430$	−904829.	−0.235991
$431$	2.19720e6	0.569741	0.284870	−	0.958566i	$-0.408049\pi$
$431$	2.19720e6	0.569741	0.284870	+	0.958566i	$0.408049\pi$
$432$	−1.08169e6	−0.278865
$433$	3.94357e6	1.01081	0.505406	−	0.862882i	$-0.331343\pi$
$433$	3.94357e6	1.01081	0.505406	+	0.862882i	$0.331343\pi$
$434$	4.91272e6	1.25198
$435$	1.58352e6	0.401236
$436$	1.33667e6	0.336749
$437$	1.09207e6	0.273555
$438$	5.78729e6	1.44142
$439$	−3.53108e6	−0.874474	−0.437237	−	0.899346i	$-0.644043\pi$
$439$	−3.53108e6	−0.874474	−0.437237	+	0.899346i	$0.644043\pi$
$440$	54443.2	0.0134064
$441$	9.98108e6	2.44389
$442$	4.82748e6	1.17534
$443$	1.82682e6	0.442270	0.221135	−	0.975243i	$-0.429024\pi$
$443$	1.82682e6	0.442270	0.221135	+	0.975243i	$0.429024\pi$
$444$	559104.	0.134597
$445$	310416.	0.0743095
$446$	4.62613e6	1.10124
$447$	−9.97145e6	−2.36042
$448$	831784.	0.195801
$449$	5.36528e6	1.25596	0.627981	−	0.778228i	$-0.283881\pi$
$449$	5.36528e6	1.25596	0.627981	+	0.778228i	$0.283881\pi$
$450$	4.78641e6	1.11424
$451$	−401808.	−0.0930202
$452$	660422.	0.152046
$453$	1.59937e6	0.366188
$454$	−150807.	−0.0343386
$455$	2.06507e6	0.467634
$456$	−3.43808e6	−0.774290
$457$	−2.69973e6	−0.604685	−0.302342	−	0.953199i	$-0.597769\pi$
$457$	−2.69973e6	−0.604685	−0.302342	+	0.953199i	$0.597769\pi$
$458$	−2.80706e6	−0.625299
$459$	−7.02048e6	−1.55538
$460$	116233.	0.0256116
$461$	−229486.	−0.0502926	−0.0251463	−	0.999684i	$-0.508005\pi$
$461$	−229486.	−0.0502926	−0.0251463	+	0.999684i	$0.508005\pi$
$462$	1.25984e6	0.274606
$463$	60211.6	0.0130535	0.00652676	−	0.999979i	$-0.497922\pi$
$463$	60211.6	0.0130535	0.00652676	+	0.999979i	$0.497922\pi$
$464$	1.13440e6	0.244608
$465$	−2.16127e6	−0.463528
$466$	−3.78614e6	−0.807667
$467$	−2.44458e6	−0.518696	−0.259348	−	0.965784i	$-0.583508\pi$
$467$	−2.44458e6	−0.518696	−0.259348	+	0.965784i	$0.583508\pi$
$468$	−4.74796e6	−1.00206
$469$	−152764.	−0.0320693
$470$	378368.	0.0790078
$471$	−1.26735e6	−0.263236
$472$	2.96578e6	0.612751
$473$	−981779.	−0.201772
$474$	−1.05424e7	−2.15523
$475$	6.16433e6	1.25358
$476$	5.39851e6	1.09209
$477$	2.09621e6	0.421832
$478$	2.83535e6	0.567593
$479$	−1.03492e6	−0.206095	−0.103047	−	0.994676i	$-0.532859\pi$
$479$	−1.03492e6	−0.206095	−0.103047	+	0.994676i	$0.532859\pi$
$480$	−365929.	−0.0724927
$481$	994397.	0.195973
$482$	762239.	0.149442
$483$	2.68969e6	0.524608
$484$	−2.51774e6	−0.488538
$485$	−760586.	−0.146823
$486$	−3.23115e6	−0.620535
$487$	4.28974e6	0.819613	0.409807	−	0.912172i	$-0.365596\pi$
$487$	4.28974e6	0.819613	0.409807	+	0.912172i	$0.365596\pi$
$488$	1.01299e6	0.192555
$489$	−1.22267e7	−2.31226
$490$	1.36815e6	0.257421
$491$	−5.73079e6	−1.07278	−0.536390	−	0.843970i	$-0.680212\pi$
$491$	−5.73079e6	−1.07278	−0.536390	+	0.843970i	$0.680212\pi$
$492$	2.70068e6	0.502991
$493$	7.36256e6	1.36431
$494$	−6.11481e6	−1.12737
$495$	−347532.	−0.0637501
$496$	−1.54829e6	−0.282584
$497$	−2.90411e6	−0.527379
$498$	−1.25827e7	−2.27353
$499$	−4.72353e6	−0.849211	−0.424605	−	0.905378i	$-0.639587\pi$
$499$	−4.72353e6	−0.849211	−0.424605	+	0.905378i	$0.639587\pi$
$500$	1.35610e6	0.242586
$501$	−3.66457e6	−0.652272
$502$	−7.16459e6	−1.26891
$503$	6.01108e6	1.05933	0.529666	−	0.848206i	$-0.322317\pi$
$503$	6.01108e6	1.05933	0.529666	+	0.848206i	$0.322317\pi$
$504$	−5.30959e6	−0.931076
$505$	2.27478e6	0.396928
$506$	126118.	0.0218979
$507$	−3.99002e6	−0.689375
$508$	3.22205e6	0.553953
$509$	−32586.1	−0.00557490	−0.00278745	−	0.999996i	$-0.500887\pi$
$509$	−32586.1	−0.00557490	−0.00278745	+	0.999996i	$0.500887\pi$
$510$	−2.37499e6	−0.404330
$511$	1.15105e7	1.95004
$512$	−262144.	−0.0441942
$513$	8.89261e6	1.49189
$514$	427506.	0.0713731
$515$	2.48108e6	0.412214
$516$	6.59884e6	1.09105
$517$	410546.	0.0675516
$518$	1.11202e6	0.182091
$519$	7.37866e6	1.20243
$520$	−650825.	−0.105549
$521$	−268257.	−0.0432969	−0.0216485	−	0.999766i	$-0.506891\pi$
$521$	−268257.	−0.0432969	−0.0216485	+	0.999766i	$0.506891\pi$
$522$	−7.24129e6	−1.16316
$523$	9.51541e6	1.52115	0.760577	−	0.649247i	$-0.224916\pi$
$523$	9.51541e6	1.52115	0.760577	+	0.649247i	$0.224916\pi$
$524$	3.95559e6	0.629337
$525$	1.51824e7	2.40404
$526$	3.75183e6	0.591260
$527$	−1.00488e7	−1.57612
$528$	−397049.	−0.0619812
$529$	−6.16709e6	−0.958166
$530$	287338.	0.0444327
$531$	−1.89317e7	−2.91376
$532$	−6.83812e6	−1.04751
$533$	4.80330e6	0.732355
$534$	−2.26384e6	−0.343552
$535$	−2.70360e6	−0.408374
$536$	48145.0	0.00723834
$537$	1.48247e7	2.21845
$538$	9.07683e6	1.35201
$539$	1.48451e6	0.220095
$540$	946480.	0.139678
$541$	9.58852e6	1.40850	0.704252	−	0.709950i	$-0.251282\pi$
$541$	9.58852e6	1.40850	0.704252	+	0.709950i	$0.251282\pi$
$542$	−5.60018e6	−0.818849
$543$	−160259.	−0.0233251
$544$	−1.70139e6	−0.246494
$545$	−1.16958e6	−0.168671
$546$	−1.50604e7	−2.16200
$547$	−4.65044e6	−0.664547	−0.332273	−	0.943183i	$-0.607816\pi$
$547$	−4.65044e6	−0.664547	−0.332273	+	0.943183i	$0.607816\pi$
$548$	−1.03113e6	−0.146677
$549$	−6.46629e6	−0.915640
$550$	711893.	0.100348
$551$	−9.32591e6	−1.30862
$552$	−847680.	−0.118409
$553$	−2.09682e7	−2.91574
$554$	−930112.	−0.128754
$555$	−489216.	−0.0674168
$556$	89329.5	0.0122549
$557$	2.08063e6	0.284155	0.142078	−	0.989856i	$-0.454622\pi$
$557$	2.08063e6	0.284155	0.142078	+	0.989856i	$0.454622\pi$
$558$	9.88331e6	1.34374
$559$	1.17364e7	1.58857
$560$	−727811.	−0.0980728
$561$	−2.57696e6	−0.345702
$562$	5.71773e6	0.763630
$563$	−1.47877e7	−1.96620	−0.983101	−	0.183063i	$-0.941399\pi$
$563$	−1.47877e7	−1.96620	−0.983101	+	0.183063i	$0.941399\pi$
$564$	−2.75941e6	−0.365273
$565$	−577870.	−0.0761568
$566$	4.90574e6	0.643671
$567$	1.74210e6	0.227570
$568$	915257.	0.119034
$569$	−9.23276e6	−1.19550	−0.597752	−	0.801681i	$-0.703939\pi$
$569$	−9.23276e6	−1.19550	−0.597752	+	0.801681i	$0.703939\pi$
$570$	3.00832e6	0.387826
$571$	1.21663e7	1.56160	0.780798	−	0.624783i	$-0.214813\pi$
$571$	1.21663e7	1.56160	0.780798	+	0.624783i	$0.214813\pi$
$572$	−706174.	−0.0902447
$573$	7.84076e6	0.997635
$574$	5.37148e6	0.680478
$575$	1.51986e6	0.191705
$576$	1.67337e6	0.210153
$577$	−5.73049e6	−0.716559	−0.358280	−	0.933614i	$-0.616637\pi$
$577$	−5.73049e6	−0.716559	−0.358280	+	0.933614i	$0.616637\pi$
$578$	−5.36308e6	−0.667720
$579$	1.53456e6	0.190234
$580$	−992597.	−0.122519
$581$	−2.50262e7	−3.07578
$582$	5.54689e6	0.678800
$583$	311774.	0.0379899
$584$	−3.62765e6	−0.440143
$585$	4.15447e6	0.501910
$586$	2.13470e6	0.256798
$587$	−733228.	−0.0878302	−0.0439151	−	0.999035i	$-0.513983\pi$
$587$	−733228.	−0.0878302	−0.0439151	+	0.999035i	$0.513983\pi$
$588$	−9.97783e6	−1.19013
$589$	1.27285e7	1.51178
$590$	−2.59506e6	−0.306914
$591$	6.16863e6	0.726474
$592$	−350464.	−0.0410997
$593$	−54312.8	−0.00634257	−0.00317129	−	0.999995i	$-0.501009\pi$
$593$	−54312.8	−0.00634257	−0.00317129	+	0.999995i	$0.501009\pi$
$594$	1.02697e6	0.119424
$595$	−4.72370e6	−0.547003
$596$	6.25042e6	0.720764
$597$	1.98004e7	2.27373
$598$	−1.50765e6	−0.172404
$599$	5.98863e6	0.681963	0.340981	−	0.940070i	$-0.389241\pi$
$599$	5.98863e6	0.681963	0.340981	+	0.940070i	$0.389241\pi$
$600$	−4.78485e6	−0.542614
$601$	6.90499e6	0.779789	0.389894	−	0.920860i	$-0.372511\pi$
$601$	6.90499e6	0.779789	0.389894	+	0.920860i	$0.372511\pi$
$602$	1.31247e7	1.47604
$603$	−307328.	−0.0344198
$604$	−1.00254e6	−0.111817
$605$	2.20302e6	0.244698
$606$	−1.65898e7	−1.83510
$607$	−1.07186e7	−1.18078	−0.590389	−	0.807119i	$-0.701026\pi$
$607$	−1.07186e7	−1.18078	−0.590389	+	0.807119i	$0.701026\pi$
$608$	2.15509e6	0.236433
$609$	−2.29692e7	−2.50958
$610$	−886365.	−0.0964468
$611$	−4.90776e6	−0.531839
$612$	1.08606e7	1.17213
$613$	−4.16502e6	−0.447678	−0.223839	−	0.974626i	$-0.571859\pi$
$613$	−4.16502e6	−0.447678	−0.223839	+	0.974626i	$0.571859\pi$
$614$	1.26503e7	1.35419
$615$	−2.36309e6	−0.251938
$616$	−789706.	−0.0838521
$617$	−7.60294e6	−0.804024	−0.402012	−	0.915634i	$-0.631689\pi$
$617$	−7.60294e6	−0.804024	−0.402012	+	0.915634i	$0.631689\pi$
$618$	−1.80943e7	−1.90577
$619$	4.37874e6	0.459328	0.229664	−	0.973270i	$-0.426237\pi$
$619$	4.37874e6	0.459328	0.229664	+	0.973270i	$0.426237\pi$
$620$	1.35475e6	0.141540
$621$	2.19253e6	0.228148
$622$	−7.96147e6	−0.825120
$623$	−4.50264e6	−0.464779
$624$	4.74642e6	0.487983
$625$	7.96654e6	0.815774
$626$	−3.70311e6	−0.377686
$627$	3.26416e6	0.331590
$628$	794415.	0.0803801
$629$	−2.27461e6	−0.229235
$630$	4.64589e6	0.466356
$631$	1.12884e7	1.12865	0.564326	−	0.825552i	$-0.309136\pi$
$631$	1.12884e7	1.12865	0.564326	+	0.825552i	$0.309136\pi$
$632$	6.60831e6	0.658109
$633$	5.79975e6	0.575308
$634$	−1.12737e7	−1.11389
$635$	−2.81929e6	−0.277464
$636$	−2.09553e6	−0.205424
$637$	−1.77461e7	−1.73283
$638$	−1.07701e6	−0.104754
$639$	−5.84244e6	−0.566033
$640$	229376.	0.0221359
$641$	2.76057e6	0.265371	0.132685	−	0.991158i	$-0.457640\pi$
$641$	2.76057e6	0.265371	0.132685	+	0.991158i	$0.457640\pi$
$642$	1.97172e7	1.88802
$643$	−1.31527e7	−1.25454	−0.627272	−	0.778800i	$-0.715829\pi$
$643$	−1.31527e7	−1.25454	−0.627272	+	0.778800i	$0.715829\pi$
$644$	−1.68598e6	−0.160191
$645$	−5.77399e6	−0.546483
$646$	1.39872e7	1.31871
$647$	1.61388e7	1.51569	0.757843	−	0.652437i	$-0.226253\pi$
$647$	1.61388e7	1.51569	0.757843	+	0.652437i	$0.226253\pi$
$648$	−549038.	−0.0513647
$649$	−2.81575e6	−0.262411
$650$	−8.51012e6	−0.790046
$651$	3.13495e7	2.89920
$652$	7.66406e6	0.706057
$653$	5.25554e6	0.482319	0.241159	−	0.970486i	$-0.422472\pi$
$653$	5.25554e6	0.482319	0.241159	+	0.970486i	$0.422472\pi$
$654$	8.52967e6	0.779808
$655$	−3.46115e6	−0.315222
$656$	−1.69287e6	−0.153590
$657$	2.31567e7	2.09297
$658$	−5.48829e6	−0.494165
$659$	−1.46606e6	−0.131504	−0.0657519	−	0.997836i	$-0.520945\pi$
$659$	−1.46606e6	−0.131504	−0.0657519	+	0.997836i	$0.520945\pi$
$660$	347418.	0.0310451
$661$	1.17116e7	1.04259	0.521295	−	0.853376i	$-0.325449\pi$
$661$	1.17116e7	1.04259	0.521295	+	0.853376i	$0.325449\pi$
$662$	−1.34450e7	−1.19238
$663$	3.08056e7	2.72174
$664$	7.88724e6	0.694233
$665$	5.98335e6	0.524675
$666$	2.23715e6	0.195438
$667$	−2.29937e6	−0.200121
$668$	2.29707e6	0.199174
$669$	2.95207e7	2.55013
$670$	−42126.8	−0.00362553
$671$	−961745.	−0.0824619
$672$	5.30786e6	0.453416
$673$	−4.31708e6	−0.367411	−0.183706	−	0.982981i	$-0.558809\pi$
$673$	−4.31708e6	−0.367411	−0.183706	+	0.982981i	$0.558809\pi$
$674$	1.34985e6	0.114455
$675$	1.23761e7	1.04550
$676$	2.50107e6	0.210503
$677$	1.55704e7	1.30565	0.652826	−	0.757508i	$-0.273583\pi$
$677$	1.55704e7	1.30565	0.652826	+	0.757508i	$0.273583\pi$
$678$	4.21436e6	0.352093
$679$	1.10324e7	0.918324
$680$	1.48872e6	0.123464
$681$	−962347.	−0.0795177
$682$	1.46996e6	0.121017
$683$	−1.03333e7	−0.847592	−0.423796	−	0.905758i	$-0.639303\pi$
$683$	−1.03333e7	−0.847592	−0.423796	+	0.905758i	$0.639303\pi$
$684$	−1.37568e7	−1.12429
$685$	902236.	0.0734673
$686$	−6.19315e6	−0.502459
$687$	−1.79127e7	−1.44800
$688$	−4.13636e6	−0.333156
$689$	−3.72702e6	−0.299098
$690$	741720.	0.0593086
$691$	−2.15832e7	−1.71958	−0.859788	−	0.510650i	$-0.829405\pi$
$691$	−2.15832e7	−1.71958	−0.859788	+	0.510650i	$0.829405\pi$
$692$	−4.62518e6	−0.367167
$693$	5.04100e6	0.398734
$694$	9.41419e6	0.741967
$695$	−78163.4	−0.00613820
$696$	7.23893e6	0.566437
$697$	−1.09872e7	−0.856653
$698$	1.21480e7	0.943772
$699$	−2.41605e7	−1.87031
$700$	−9.51678e6	−0.734082
$701$	−7.29001e6	−0.560316	−0.280158	−	0.959954i	$-0.590387\pi$
$701$	−7.29001e6	−0.560316	−0.280158	+	0.959954i	$0.590387\pi$
$702$	−1.22766e7	−0.940236
$703$	2.88117e6	0.219878
$704$	248883.	0.0189262
$705$	2.41448e6	0.182958
$706$	−1.63026e7	−1.23096
$707$	−3.29961e7	−2.48264
$708$	1.89255e7	1.41894
$709$	1.19097e7	0.889785	0.444892	−	0.895584i	$-0.353242\pi$
$709$	1.19097e7	0.889785	0.444892	+	0.895584i	$0.353242\pi$
$710$	−800850.	−0.0596218
$711$	−4.21834e7	−3.12945
$712$	1.41905e6	0.104905
$713$	3.13830e6	0.231191
$714$	3.44496e7	2.52894
$715$	617902.	0.0452017
$716$	−9.29256e6	−0.677412
$717$	1.80932e7	1.31437
$718$	−3.83342e6	−0.277508
$719$	1.59354e7	1.14959	0.574794	−	0.818298i	$-0.305082\pi$
$719$	1.59354e7	1.14959	0.574794	+	0.818298i	$0.305082\pi$
$720$	−1.46419e6	−0.105261
$721$	−3.59884e7	−2.57825
$722$	−7.81269e6	−0.557773
$723$	4.86408e6	0.346063
$724$	100456.	0.00712242
$725$	−1.29791e7	−0.917064
$726$	−1.60665e7	−1.13130
$727$	−736589.	−0.0516880	−0.0258440	−	0.999666i	$-0.508227\pi$
$727$	−736589.	−0.0516880	−0.0258440	+	0.999666i	$0.508227\pi$
$728$	9.44032e6	0.660174
$729$	−2.27036e7	−1.58225
$730$	3.17420e6	0.220458
$731$	−2.68462e7	−1.85818
$732$	6.46419e6	0.445899
$733$	1.55661e7	1.07009	0.535043	−	0.844825i	$-0.320295\pi$
$733$	1.55661e7	1.07009	0.535043	+	0.844825i	$0.320295\pi$
$734$	−1.12858e7	−0.773204
$735$	8.73060e6	0.596109
$736$	531353.	0.0361567
$737$	−45709.5	−0.00309983
$738$	1.08062e7	0.730354
$739$	2.04390e7	1.37673	0.688365	−	0.725365i	$-0.258329\pi$
$739$	2.04390e7	1.37673	0.688365	+	0.725365i	$0.258329\pi$
$740$	306656.	0.0205860
$741$	−3.90204e7	−2.61064
$742$	−4.16788e6	−0.277911
$743$	5.69626e6	0.378545	0.189273	−	0.981925i	$-0.439387\pi$
$743$	5.69626e6	0.378545	0.189273	+	0.981925i	$0.439387\pi$
$744$	−9.88009e6	−0.654377
$745$	−5.46911e6	−0.361016
$746$	−1.71207e7	−1.12635
$747$	−5.03473e7	−3.30122
$748$	1.61532e6	0.105561
$749$	3.92162e7	2.55423
$750$	8.65366e6	0.561755
$751$	−1.98477e7	−1.28414	−0.642068	−	0.766647i	$-0.721924\pi$
$751$	−1.98477e7	−1.28414	−0.642068	+	0.766647i	$0.721924\pi$
$752$	1.72968e6	0.111538
$753$	−4.57194e7	−2.93842
$754$	1.28748e7	0.824733
$755$	877220.	0.0560069
$756$	−1.37288e7	−0.873633
$757$	−2.70853e7	−1.71788	−0.858942	−	0.512074i	$-0.828878\pi$
$757$	−2.70853e7	−1.71788	−0.858942	+	0.512074i	$0.828878\pi$
$758$	−1.14934e7	−0.726569
$759$	804799.	0.0507088
$760$	−1.88571e6	−0.118424
$761$	2.06463e7	1.29235	0.646176	−	0.763188i	$-0.276367\pi$
$761$	2.06463e7	1.29235	0.646176	+	0.763188i	$0.276367\pi$
$762$	2.05609e7	1.28279
$763$	1.69650e7	1.05497
$764$	−4.91483e6	−0.304632
$765$	−9.50304e6	−0.587096
$766$	8.49011e6	0.522807
$767$	3.36601e7	2.06598
$768$	−1.67282e6	−0.102340
$769$	−1.74458e7	−1.06384	−0.531919	−	0.846795i	$-0.678529\pi$
$769$	−1.74458e7	−1.06384	−0.531919	+	0.846795i	$0.678529\pi$
$770$	690993.	0.0419998
$771$	2.72805e6	0.165278
$772$	−961912.	−0.0580888
$773$	1.67941e7	1.01090	0.505450	−	0.862856i	$-0.331327\pi$
$773$	1.67941e7	1.01090	0.505450	+	0.862856i	$0.331327\pi$
$774$	2.64040e7	1.58423
$775$	1.77146e7	1.05944
$776$	−3.47696e6	−0.207274
$777$	7.09616e6	0.421668
$778$	7.85857e6	0.465473
$779$	1.39171e7	0.821686
$780$	−4.15311e6	−0.244420
$781$	−868957.	−0.0509766
$782$	3.44863e6	0.201665
$783$	−1.87236e7	−1.09140
$784$	6.25442e6	0.363410
$785$	−695114.	−0.0402607
$786$	2.52418e7	1.45735
$787$	−2.05824e7	−1.18456	−0.592282	−	0.805730i	$-0.701773\pi$
$787$	−2.05824e7	−1.18456	−0.592282	+	0.805730i	$0.701773\pi$
$788$	−3.86669e6	−0.221832
$789$	2.39416e7	1.36918
$790$	−5.78228e6	−0.329633
$791$	8.38209e6	0.476333
$792$	−1.58872e6	−0.0899981
$793$	1.14969e7	0.649229
$794$	1.17971e7	0.664083
$795$	1.83359e6	0.102893
$796$	−1.24115e7	−0.694292
$797$	−1.36759e7	−0.762622	−0.381311	−	0.924447i	$-0.624527\pi$
$797$	−1.36759e7	−0.762622	−0.381311	+	0.924447i	$0.624527\pi$
$798$	−4.36361e7	−2.42571
$799$	1.12261e7	0.622104
$800$	2.99930e6	0.165689
$801$	−9.05831e6	−0.498845
$802$	−1.64946e7	−0.905536
$803$	3.44414e6	0.188492
$804$	307228.	0.0167618
$805$	1.47524e6	0.0802364
$806$	−1.75723e7	−0.952775
$807$	5.79220e7	3.13083
$808$	1.03990e7	0.560355
$809$	6.36320e6	0.341826	0.170913	−	0.985286i	$-0.445328\pi$
$809$	6.36320e6	0.341826	0.170913	+	0.985286i	$0.445328\pi$
$810$	480408.	0.0257275
$811$	8.47861e6	0.452660	0.226330	−	0.974051i	$-0.427327\pi$
$811$	8.47861e6	0.452660	0.226330	+	0.974051i	$0.427327\pi$
$812$	1.43978e7	0.766312
$813$	−3.57364e7	−1.89620
$814$	332735.	0.0176010
$815$	−6.70605e6	−0.353649
$816$	−1.08571e7	−0.570805
$817$	3.40052e7	1.78234
$818$	2.29055e7	1.19690
$819$	−6.02612e7	−3.13927
$820$	1.48126e6	0.0769302
$821$	1.94787e6	0.100856	0.0504280	−	0.998728i	$-0.483941\pi$
$821$	1.94787e6	0.100856	0.0504280	+	0.998728i	$0.483941\pi$
$822$	−6.57994e6	−0.339658
$823$	1.19823e7	0.616651	0.308326	−	0.951281i	$-0.400231\pi$
$823$	1.19823e7	0.616651	0.308326	+	0.951281i	$0.400231\pi$
$824$	1.13421e7	0.581935
$825$	4.54280e6	0.232375
$826$	3.76417e7	1.91964
$827$	7.49515e6	0.381080	0.190540	−	0.981679i	$-0.438976\pi$
$827$	7.49515e6	0.381080	0.190540	+	0.981679i	$0.438976\pi$
$828$	−3.39183e6	−0.171932
$829$	−3.71290e7	−1.87641	−0.938203	−	0.346085i	$-0.887511\pi$
$829$	−3.71290e7	−1.87641	−0.938203	+	0.346085i	$0.887511\pi$
$830$	−6.90134e6	−0.347727
$831$	−5.93532e6	−0.298155
$832$	−2.97520e6	−0.149007
$833$	4.05930e7	2.02693
$834$	570039.	0.0283785
$835$	−2.00993e6	−0.0997620
$836$	−2.04607e6	−0.101252
$837$	2.55549e7	1.26084
$838$	−2.47029e7	−1.21517
$839$	−1.36908e7	−0.671464	−0.335732	−	0.941958i	$-0.608984\pi$
$839$	−1.36908e7	−0.671464	−0.335732	+	0.941958i	$0.608984\pi$
$840$	−4.64438e6	−0.227107
$841$	−875274.	−0.0426731
$842$	12163.9	0.000591280 0
$843$	3.64866e7	1.76833
$844$	−3.63547e6	−0.175673
$845$	−2.18844e6	−0.105437
$846$	−1.10412e7	−0.530385
$847$	−3.19552e7	−1.53050
$848$	1.31354e6	0.0627271
$849$	3.13050e7	1.49054
$850$	1.94663e7	0.924136
$851$	710373.	0.0336250
$852$	5.84053e6	0.275647
$853$	−1.05322e7	−0.495619	−0.247810	−	0.968809i	$-0.579711\pi$
$853$	−1.05322e7	−0.495619	−0.247810	+	0.968809i	$0.579711\pi$
$854$	1.28569e7	0.603240
$855$	1.20372e7	0.563131
$856$	−1.23593e7	−0.576515
$857$	2.48579e7	1.15614	0.578072	−	0.815985i	$-0.303805\pi$
$857$	2.48579e7	1.15614	0.578072	+	0.815985i	$0.303805\pi$
$858$	−4.50631e6	−0.208979
$859$	6.89754e6	0.318942	0.159471	−	0.987203i	$-0.449021\pi$
$859$	6.89754e6	0.318942	0.159471	+	0.987203i	$0.449021\pi$
$860$	3.61932e6	0.166871
$861$	3.42770e7	1.57578
$862$	−8.78882e6	−0.402868
$863$	−2.49635e7	−1.14098	−0.570491	−	0.821304i	$-0.693247\pi$
$863$	−2.49635e7	−1.14098	−0.570491	+	0.821304i	$0.693247\pi$
$864$	4.32676e6	0.197187
$865$	4.04703e6	0.183906
$866$	−1.57743e7	−0.714752
$867$	−3.42234e7	−1.54624
$868$	−1.96509e7	−0.885284
$869$	−6.27402e6	−0.281836
$870$	−6.33407e6	−0.283716
$871$	546421.	0.0244052
$872$	−5.34666e6	−0.238118
$873$	2.21948e7	0.985633
$874$	−4.36826e6	−0.193433
$875$	1.72116e7	0.759978
$876$	−2.31491e7	−1.01924
$877$	2.57466e7	1.13037	0.565184	−	0.824965i	$-0.308805\pi$
$877$	2.57466e7	1.13037	0.565184	+	0.824965i	$0.308805\pi$
$878$	1.41243e7	0.618346
$879$	1.36221e7	0.594666
$880$	−217773.	−0.00947974
$881$	−1.37226e7	−0.595657	−0.297829	−	0.954619i	$-0.596262\pi$
$881$	−1.37226e7	−0.595657	−0.297829	+	0.954619i	$0.596262\pi$
$882$	−3.99243e7	−1.72809
$883$	−341833.	−0.0147541	−0.00737705	−	0.999973i	$-0.502348\pi$
$883$	−341833.	−0.0147541	−0.00737705	+	0.999973i	$0.502348\pi$
$884$	−1.93099e7	−0.831093
$885$	−1.65599e7	−0.710720
$886$	−7.30730e6	−0.312732
$887$	3.21677e7	1.37281	0.686405	−	0.727219i	$-0.259188\pi$
$887$	3.21677e7	1.37281	0.686405	+	0.727219i	$0.259188\pi$
$888$	−2.23642e6	−0.0951745
$889$	4.08943e7	1.73543
$890$	−1.24166e6	−0.0525447
$891$	521264.	0.0219970
$892$	−1.85045e7	−0.778692
$893$	−1.42198e7	−0.596711
$894$	3.98858e7	1.66907
$895$	8.13099e6	0.339301
$896$	−3.32713e6	−0.138452
$897$	−9.62074e6	−0.399234
$898$	−2.14611e7	−0.888100
$899$	−2.68001e7	−1.10595
$900$	−1.91457e7	−0.787887
$901$	8.52528e6	0.349862
$902$	1.60723e6	0.0657752
$903$	8.37526e7	3.41805
$904$	−2.64169e6	−0.107513
$905$	−87898.7	−0.00356747
$906$	−6.39750e6	−0.258934
$907$	−2.48227e7	−1.00191	−0.500957	−	0.865472i	$-0.667018\pi$
$907$	−2.48227e7	−1.00191	−0.500957	+	0.865472i	$0.667018\pi$
$908$	603229.	0.0242810
$909$	−6.63808e7	−2.66460
$910$	−8.26028e6	−0.330667
$911$	2.49017e7	0.994108	0.497054	−	0.867720i	$-0.334415\pi$
$911$	2.49017e7	0.994108	0.497054	+	0.867720i	$0.334415\pi$
$912$	1.37523e7	0.547505
$913$	−7.48825e6	−0.297306
$914$	1.07989e7	0.427577
$915$	−5.65616e6	−0.223341
$916$	1.12282e7	0.442153
$917$	5.02045e7	1.97160
$918$	2.80819e7	1.09982
$919$	6.65508e6	0.259935	0.129968	−	0.991518i	$-0.458513\pi$
$919$	6.65508e6	0.259935	0.129968	+	0.991518i	$0.458513\pi$
$920$	−464933.	−0.0181101
$921$	8.07253e7	3.13589
$922$	917945.	0.0355623
$923$	1.03877e7	0.401343
$924$	−5.03936e6	−0.194176
$925$	4.00980e6	0.154088
$926$	−240847.	−0.00923024
$927$	−7.24008e7	−2.76722
$928$	−4.53759e6	−0.172964
$929$	−1.28619e7	−0.488952	−0.244476	−	0.969655i	$-0.578616\pi$
$929$	−1.28619e7	−0.488952	−0.244476	+	0.969655i	$0.578616\pi$
$930$	8.64507e6	0.327764
$931$	−5.14177e7	−1.94419
$932$	1.51446e7	0.571107
$933$	−5.08045e7	−1.91073
$934$	9.77833e6	0.366773
$935$	−1.41341e6	−0.0528735
$936$	1.89919e7	0.708562
$937$	2.61509e6	0.0973054	0.0486527	−	0.998816i	$-0.484507\pi$
$937$	2.61509e6	0.0973054	0.0486527	+	0.998816i	$0.484507\pi$
$938$	611056.	0.0226764
$939$	−2.36307e7	−0.874605
$940$	−1.51347e6	−0.0558669
$941$	2.79369e7	1.02850	0.514250	−	0.857640i	$-0.328070\pi$
$941$	2.79369e7	1.02850	0.514250	+	0.857640i	$0.328070\pi$
$942$	5.06941e6	0.186136
$943$	3.43136e6	0.125657
$944$	−1.18631e7	−0.433280
$945$	1.20127e7	0.437585
$946$	3.92712e6	0.142674
$947$	3.52173e7	1.27609	0.638045	−	0.769999i	$-0.279743\pi$
$947$	3.52173e7	1.27609	0.638045	+	0.769999i	$0.279743\pi$
$948$	4.21697e7	1.52398
$949$	−4.11720e7	−1.48401
$950$	−2.46573e7	−0.886414
$951$	−7.19406e7	−2.57943
$952$	−2.15941e7	−0.772222
$953$	−4.79928e6	−0.171176	−0.0855882	−	0.996331i	$-0.527277\pi$
$953$	−4.79928e6	−0.171176	−0.0855882	+	0.996331i	$0.527277\pi$
$954$	−8.38486e6	−0.298280
$955$	4.30048e6	0.152584
$956$	−1.13414e7	−0.401349
$957$	−6.87274e6	−0.242577
$958$	4.13967e6	0.145731
$959$	−1.30871e7	−0.459511
$960$	1.46372e6	0.0512601
$961$	7.94908e6	0.277657
$962$	−3.97759e6	−0.138574
$963$	7.88943e7	2.74145
$964$	−3.04896e6	−0.105672
$965$	841673.	0.0290955
$966$	−1.07588e7	−0.370954
$967$	−3.91925e7	−1.34783	−0.673917	−	0.738807i	$-0.735390\pi$
$967$	−3.91925e7	−1.34783	−0.673917	+	0.738807i	$0.735390\pi$
$968$	1.00710e7	0.345448
$969$	8.92564e7	3.05373
$970$	3.04234e6	0.103819
$971$	4.24033e7	1.44328	0.721642	−	0.692266i	$-0.243387\pi$
$971$	4.24033e7	1.44328	0.721642	+	0.692266i	$0.243387\pi$
$972$	1.29246e7	0.438785
$973$	1.13377e6	0.0383922
$974$	−1.71590e7	−0.579554
$975$	−5.43057e7	−1.82951
$976$	−4.05195e6	−0.136157
$977$	2.01492e7	0.675339	0.337669	−	0.941265i	$-0.390361\pi$
$977$	2.01492e7	0.675339	0.337669	+	0.941265i	$0.390361\pi$
$978$	4.89067e7	1.63501
$979$	−1.34726e6	−0.0449257
$980$	−5.47261e6	−0.182024
$981$	3.41298e7	1.13230
$982$	2.29232e7	0.758570
$983$	1.88867e6	0.0623407	0.0311704	−	0.999514i	$-0.490077\pi$
$983$	1.88867e6	0.0623407	0.0311704	+	0.999514i	$0.490077\pi$
$984$	−1.08027e7	−0.355668
$985$	3.38336e6	0.111111
$986$	−2.94502e7	−0.964710
$987$	−3.50224e7	−1.14434
$988$	2.44592e7	0.797169
$989$	8.38419e6	0.272565
$990$	1.39013e6	0.0450782
$991$	−2.46586e7	−0.797597	−0.398799	−	0.917039i	$-0.630573\pi$
$991$	−2.46586e7	−0.797597	−0.398799	+	0.917039i	$0.630573\pi$
$992$	6.19315e6	0.199817
$993$	−8.57967e7	−2.76120
$994$	1.16165e7	0.372913
$995$	1.08601e7	0.347756
$996$	5.03309e7	1.60763
$997$	−4.57335e6	−0.145713	−0.0728563	−	0.997342i	$-0.523211\pi$
$997$	−4.57335e6	−0.145713	−0.0728563	+	0.997342i	$0.523211\pi$
$998$	1.88941e7	0.600483
$999$	5.78451e6	0.183380

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.a.c.1.1	✓	3
3.2	odd	2		666.6.a.i.1.3		3
4.3	odd	2		592.6.a.c.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.a.c.1.1	✓	3	1.1	even	1	trivial
592.6.a.c.1.3		3	4.3	odd	2
666.6.a.i.1.3		3	3.2	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	74.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -25.5252 q^{3} +16.0000 q^{4} -14.0000 q^{5} +102.101 q^{6} +203.072 q^{7} -64.0000 q^{8} +408.537 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -25.5252 q^{3} +16.0000 q^{4} -14.0000 q^{5} +102.101 q^{6} +203.072 q^{7} -64.0000 q^{8} +408.537 q^{9} +56.0000 q^{10} +60.7624 q^{11} -408.403 q^{12} -726.368 q^{13} -812.289 q^{14} +357.353 q^{15} +256.000 q^{16} +1661.51 q^{17} -1634.15 q^{18} -2104.58 q^{19} -224.000 q^{20} -5183.46 q^{21} -243.050 q^{22} -518.899 q^{23} +1633.61 q^{24} -2929.00 q^{25} +2905.47 q^{26} -4225.35 q^{27} +3249.16 q^{28} +4431.24 q^{29} -1429.41 q^{30} -6047.99 q^{31} -1024.00 q^{32} -1550.97 q^{33} -6646.05 q^{34} -2843.01 q^{35} +6536.58 q^{36} -1369.00 q^{37} +8418.33 q^{38} +18540.7 q^{39} +896.000 q^{40} -6612.77 q^{41} +20733.8 q^{42} -16157.7 q^{43} +972.199 q^{44} -5719.51 q^{45} +2075.60 q^{46} +6756.57 q^{47} -6534.45 q^{48} +24431.3 q^{49} +11716.0 q^{50} -42410.5 q^{51} -11621.9 q^{52} +5131.03 q^{53} +16901.4 q^{54} -850.674 q^{55} -12996.6 q^{56} +53719.9 q^{57} -17725.0 q^{58} -46340.3 q^{59} +5717.65 q^{60} -15827.9 q^{61} +24192.0 q^{62} +82962.4 q^{63} +4096.00 q^{64} +10169.1 q^{65} +6203.90 q^{66} -752.265 q^{67} +26584.2 q^{68} +13245.0 q^{69} +11372.0 q^{70} -14300.9 q^{71} -26146.3 q^{72} +56682.1 q^{73} +5476.00 q^{74} +74763.4 q^{75} -33673.3 q^{76} +12339.2 q^{77} -74162.8 q^{78} -103255. q^{79} -3584.00 q^{80} +8578.71 q^{81} +26451.1 q^{82} -123238. q^{83} -82935.4 q^{84} -23261.2 q^{85} +64630.6 q^{86} -113108. q^{87} -3888.80 q^{88} -22172.6 q^{89} +22878.0 q^{90} -147505. q^{91} -8302.38 q^{92} +154376. q^{93} -27026.3 q^{94} +29464.2 q^{95} +26137.8 q^{96} +54327.5 q^{97} -97725.3 q^{98} +24823.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 12 q^{2} - 8 q^{3} + 48 q^{4} - 42 q^{5} + 32 q^{6} + 84 q^{7} - 192 q^{8} + 193 q^{9}+O(q^{10}) \) 3 * q - 12 * q^2 - 8 * q^3 + 48 * q^4 - 42 * q^5 + 32 * q^6 + 84 * q^7 - 192 * q^8 + 193 * q^9	\( 3 q - 12 q^{2} - 8 q^{3} + 48 q^{4} - 42 q^{5} + 32 q^{6} + 84 q^{7} - 192 q^{8} + 193 q^{9} + 168 q^{10} + 304 q^{11} - 128 q^{12} - 806 q^{13} - 336 q^{14} + 112 q^{15} + 768 q^{16} + 246 q^{17} - 772 q^{18} - 4442 q^{19} - 672 q^{20} - 7630 q^{21} - 1216 q^{22} - 2898 q^{23} + 512 q^{24} - 8787 q^{25} + 3224 q^{26} - 8324 q^{27} + 1344 q^{28} - 1790 q^{29} - 448 q^{30} - 14606 q^{31} - 3072 q^{32} - 6322 q^{33} - 984 q^{34} - 1176 q^{35} + 3088 q^{36} - 4107 q^{37} + 17768 q^{38} + 18660 q^{39} + 2688 q^{40} + 8044 q^{41} + 30520 q^{42} - 8150 q^{43} + 4864 q^{44} - 2702 q^{45} + 11592 q^{46} + 19788 q^{47} - 2048 q^{48} + 14749 q^{49} + 35148 q^{50} - 34452 q^{51} - 12896 q^{52} + 38328 q^{53} + 33296 q^{54} - 4256 q^{55} - 5376 q^{56} + 38968 q^{57} + 7160 q^{58} - 17062 q^{59} + 1792 q^{60} - 32890 q^{61} + 58424 q^{62} + 71204 q^{63} + 12288 q^{64} + 11284 q^{65} + 25288 q^{66} + 5540 q^{67} + 3936 q^{68} - 38836 q^{69} + 4704 q^{70} - 14892 q^{71} - 12352 q^{72} - 2492 q^{73} + 16428 q^{74} + 23432 q^{75} - 71072 q^{76} + 80710 q^{77} - 74640 q^{78} - 129958 q^{79} - 10752 q^{80} + 1987 q^{81} - 32176 q^{82} - 139996 q^{83} - 122080 q^{84} - 3444 q^{85} + 32600 q^{86} - 108524 q^{87} - 19456 q^{88} - 58606 q^{89} + 10808 q^{90} - 152572 q^{91} - 46368 q^{92} + 156008 q^{93} - 79152 q^{94} + 62188 q^{95} + 8192 q^{96} + 29814 q^{97} - 58996 q^{98} - 122356 q^{99}+O(q^{100}) \) 3 * q - 12 * q^2 - 8 * q^3 + 48 * q^4 - 42 * q^5 + 32 * q^6 + 84 * q^7 - 192 * q^8 + 193 * q^9 + 168 * q^10 + 304 * q^11 - 128 * q^12 - 806 * q^13 - 336 * q^14 + 112 * q^15 + 768 * q^16 + 246 * q^17 - 772 * q^18 - 4442 * q^19 - 672 * q^20 - 7630 * q^21 - 1216 * q^22 - 2898 * q^23 + 512 * q^24 - 8787 * q^25 + 3224 * q^26 - 8324 * q^27 + 1344 * q^28 - 1790 * q^29 - 448 * q^30 - 14606 * q^31 - 3072 * q^32 - 6322 * q^33 - 984 * q^34 - 1176 * q^35 + 3088 * q^36 - 4107 * q^37 + 17768 * q^38 + 18660 * q^39 + 2688 * q^40 + 8044 * q^41 + 30520 * q^42 - 8150 * q^43 + 4864 * q^44 - 2702 * q^45 + 11592 * q^46 + 19788 * q^47 - 2048 * q^48 + 14749 * q^49 + 35148 * q^50 - 34452 * q^51 - 12896 * q^52 + 38328 * q^53 + 33296 * q^54 - 4256 * q^55 - 5376 * q^56 + 38968 * q^57 + 7160 * q^58 - 17062 * q^59 + 1792 * q^60 - 32890 * q^61 + 58424 * q^62 + 71204 * q^63 + 12288 * q^64 + 11284 * q^65 + 25288 * q^66 + 5540 * q^67 + 3936 * q^68 - 38836 * q^69 + 4704 * q^70 - 14892 * q^71 - 12352 * q^72 - 2492 * q^73 + 16428 * q^74 + 23432 * q^75 - 71072 * q^76 + 80710 * q^77 - 74640 * q^78 - 129958 * q^79 - 10752 * q^80 + 1987 * q^81 - 32176 * q^82 - 139996 * q^83 - 122080 * q^84 - 3444 * q^85 + 32600 * q^86 - 108524 * q^87 - 19456 * q^88 - 58606 * q^89 + 10808 * q^90 - 152572 * q^91 - 46368 * q^92 + 156008 * q^93 - 79152 * q^94 + 62188 * q^95 + 8192 * q^96 + 29814 * q^97 - 58996 * q^98 - 122356 * q^99

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