LMFDB - Embedded newform 74.6.a.c.1.2

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			1.2
Root			$9.57214$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} +1.11745 q^{3} +16.0000 q^{4} -14.0000 q^{5} -4.46979 q^{6} +32.2315 q^{7} -64.0000 q^{8} -241.751 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +1.11745 q^{3} +16.0000 q^{4} -14.0000 q^{5} -4.46979 q^{6} +32.2315 q^{7} -64.0000 q^{8} -241.751 q^{9} +56.0000 q^{10} +573.043 q^{11} +17.8792 q^{12} -93.2552 q^{13} -128.926 q^{14} -15.6443 q^{15} +256.000 q^{16} -2039.45 q^{17} +967.005 q^{18} -1543.45 q^{19} -224.000 q^{20} +36.0170 q^{21} -2292.17 q^{22} +853.172 q^{23} -71.5166 q^{24} -2929.00 q^{25} +373.021 q^{26} -541.684 q^{27} +515.704 q^{28} -6975.72 q^{29} +62.5770 q^{30} -9290.16 q^{31} -1024.00 q^{32} +640.345 q^{33} +8157.81 q^{34} -451.241 q^{35} -3868.02 q^{36} -1369.00 q^{37} +6173.80 q^{38} -104.208 q^{39} +896.000 q^{40} +16791.4 q^{41} -144.068 q^{42} +11000.4 q^{43} +9168.69 q^{44} +3384.52 q^{45} -3412.69 q^{46} -13591.4 q^{47} +286.066 q^{48} -15768.1 q^{49} +11716.0 q^{50} -2278.98 q^{51} -1492.08 q^{52} +34584.3 q^{53} +2166.74 q^{54} -8022.60 q^{55} -2062.82 q^{56} -1724.72 q^{57} +27902.9 q^{58} +31665.7 q^{59} -250.308 q^{60} -20985.7 q^{61} +37160.6 q^{62} -7792.01 q^{63} +4096.00 q^{64} +1305.57 q^{65} -2561.38 q^{66} +15296.7 q^{67} -32631.3 q^{68} +953.375 q^{69} +1804.97 q^{70} -45832.4 q^{71} +15472.1 q^{72} -43416.0 q^{73} +5476.00 q^{74} -3273.00 q^{75} -24695.2 q^{76} +18470.0 q^{77} +416.831 q^{78} +69831.2 q^{79} -3584.00 q^{80} +58140.3 q^{81} -67165.4 q^{82} -104801. q^{83} +576.272 q^{84} +28552.4 q^{85} -44001.6 q^{86} -7795.00 q^{87} -36674.8 q^{88} -41850.2 q^{89} -13538.1 q^{90} -3005.76 q^{91} +13650.8 q^{92} -10381.3 q^{93} +54365.5 q^{94} +21608.3 q^{95} -1144.27 q^{96} -128871. q^{97} +63072.5 q^{98} -138534. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.11745	0.0716843	0.0358421	−	0.999357i	$-0.488589\pi$
$3$	1.11745	0.0716843	0.0358421	+	0.999357i	$0.488589\pi$
$4$	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	$0.539964\pi$
$6$	−4.46979	−0.0506884
$7$	32.2315	0.248620	0.124310	−	0.992243i	$-0.460328\pi$
$7$	32.2315	0.248620	0.124310	+	0.992243i	$0.460328\pi$
$8$	−64.0000	−0.353553
$9$	−241.751	−0.994861
$10$	56.0000	0.177088
$11$	573.043	1.42793	0.713963	−	0.700184i	$-0.246899\pi$
$11$	573.043	1.42793	0.713963	+	0.700184i	$0.246899\pi$
$12$	17.8792	0.0358421
$13$	−93.2552	−0.153043	−0.0765217	−	0.997068i	$-0.524381\pi$
$13$	−93.2552	−0.153043	−0.0765217	+	0.997068i	$0.524381\pi$
$14$	−128.926	−0.175801
$15$	−15.6443	−0.0179526
$16$	256.000	0.250000
$17$	−2039.45	−1.71156	−0.855779	−	0.517342i	$-0.826922\pi$
$17$	−2039.45	−1.71156	−0.855779	+	0.517342i	$0.826922\pi$
$18$	967.005	0.703473
$19$	−1543.45	−0.980863	−0.490432	−	0.871480i	$-0.663161\pi$
$19$	−1543.45	−0.980863	−0.490432	+	0.871480i	$0.663161\pi$
$20$	−224.000	−0.125220
$21$	36.0170	0.0178221
$22$	−2292.17	−1.00970
$23$	853.172	0.336292	0.168146	−	0.985762i	$-0.446222\pi$
$23$	853.172	0.336292	0.168146	+	0.985762i	$0.446222\pi$
$24$	−71.5166	−0.0253442
$25$	−2929.00	−0.937280
$26$	373.021	0.108218
$27$	−541.684	−0.143000
$28$	515.704	0.124310
$29$	−6975.72	−1.54026	−0.770130	−	0.637887i	$-0.779809\pi$
$29$	−6975.72	−1.54026	−0.770130	+	0.637887i	$0.779809\pi$
$30$	62.5770	0.0126944
$31$	−9290.16	−1.73628	−0.868138	−	0.496323i	$-0.834683\pi$
$31$	−9290.16	−1.73628	−0.868138	+	0.496323i	$0.834683\pi$
$32$	−1024.00	−0.176777
$33$	640.345	0.102360
$34$	8157.81	1.21025
$35$	−451.241	−0.0622642
$36$	−3868.02	−0.497431
$37$	−1369.00	−0.164399
$37$	−1369.00	−0.164399
$38$	6173.80	0.693575
$39$	−104.208	−0.0109708
$40$	896.000	0.0885438
$41$	16791.4	1.56001	0.780003	−	0.625776i	$-0.215218\pi$
$41$	16791.4	1.56001	0.780003	+	0.625776i	$0.215218\pi$
$42$	−144.068	−0.0126021
$43$	11000.4	0.907272	0.453636	−	0.891187i	$-0.350127\pi$
$43$	11000.4	0.907272	0.453636	+	0.891187i	$0.350127\pi$
$44$	9168.69	0.713963
$45$	3384.52	0.249153
$46$	−3412.69	−0.237795
$47$	−13591.4	−0.897467	−0.448733	−	0.893666i	$-0.648125\pi$
$47$	−13591.4	−0.897467	−0.448733	+	0.893666i	$0.648125\pi$
$48$	286.066	0.0179211
$49$	−15768.1	−0.938188
$50$	11716.0	0.662757
$51$	−2278.98	−0.122692
$52$	−1492.08	−0.0765217
$53$	34584.3	1.69118	0.845590	−	0.533833i	$-0.179249\pi$
$53$	34584.3	1.69118	0.845590	+	0.533833i	$0.179249\pi$
$54$	2166.74	0.101116
$55$	−8022.60	−0.357609
$56$	−2062.82	−0.0879004
$57$	−1724.72	−0.0703125
$58$	27902.9	1.08913
$59$	31665.7	1.18429	0.592146	−	0.805831i	$-0.298281\pi$
$59$	31665.7	1.18429	0.592146	+	0.805831i	$0.298281\pi$
$60$	−250.308	−0.00897629
$61$	−20985.7	−0.722103	−0.361052	−	0.932546i	$-0.617582\pi$
$61$	−20985.7	−0.722103	−0.361052	+	0.932546i	$0.617582\pi$
$62$	37160.6	1.22773
$63$	−7792.01	−0.247342
$64$	4096.00	0.125000
$65$	1305.57	0.0383281
$66$	−2561.38	−0.0723793
$67$	15296.7	0.416305	0.208152	−	0.978096i	$-0.433255\pi$
$67$	15296.7	0.416305	0.208152	+	0.978096i	$0.433255\pi$
$68$	−32631.3	−0.855779
$69$	953.375	0.0241069
$70$	1804.97	0.0440275
$71$	−45832.4	−1.07901	−0.539506	−	0.841982i	$-0.681389\pi$
$71$	−45832.4	−1.07901	−0.539506	+	0.841982i	$0.681389\pi$
$72$	15472.1	0.351737
$73$	−43416.0	−0.953547	−0.476774	−	0.879026i	$-0.658194\pi$
$73$	−43416.0	−0.953547	−0.476774	+	0.879026i	$0.658194\pi$
$74$	5476.00	0.116248
$75$	−3273.00	−0.0671882
$76$	−24695.2	−0.490432
$77$	18470.0	0.355010
$78$	416.831	0.00775753
$79$	69831.2	1.25887	0.629436	−	0.777052i	$-0.283286\pi$
$79$	69831.2	1.25887	0.629436	+	0.777052i	$0.283286\pi$
$80$	−3584.00	−0.0626099
$81$	58140.3	0.984611
$82$	−67165.4	−1.10309
$83$	−104801.	−1.66982	−0.834911	−	0.550386i	$-0.814481\pi$
$83$	−104801.	−1.66982	−0.834911	+	0.550386i	$0.814481\pi$
$84$	576.272	0.00891106
$85$	28552.4	0.428642
$86$	−44001.6	−0.641538
$87$	−7795.00	−0.110412
$88$	−36674.8	−0.504848
$89$	−41850.2	−0.560045	−0.280022	−	0.959993i	$-0.590342\pi$
$89$	−41850.2	−0.560045	−0.280022	+	0.959993i	$0.590342\pi$
$90$	−13538.1	−0.176178
$91$	−3005.76	−0.0380496
$92$	13650.8	0.168146
$93$	−10381.3	−0.124464
$94$	54365.5	0.634605
$95$	21608.3	0.245647
$96$	−1144.27	−0.0126721
$97$	−128871.	−1.39067	−0.695336	−	0.718684i	$-0.744745\pi$
$97$	−128871.	−1.39067	−0.695336	+	0.718684i	$0.744745\pi$
$98$	63072.5	0.663399
$99$	−138534.	−1.42059
$100$	−46864.0	−0.468640
$101$	171281.	1.67072	0.835362	−	0.549701i	$-0.185258\pi$
$101$	171281.	1.67072	0.835362	+	0.549701i	$0.185258\pi$
$102$	9115.93	0.0867562
$103$	38817.2	0.360521	0.180261	−	0.983619i	$-0.442306\pi$
$103$	38817.2	0.360521	0.180261	+	0.983619i	$0.442306\pi$
$104$	5968.33	0.0541090
$105$	−504.238	−0.00446337
$106$	−138337.	−1.19584
$107$	110996.	0.937236	0.468618	−	0.883401i	$-0.344752\pi$
$107$	110996.	0.937236	0.468618	+	0.883401i	$0.344752\pi$
$108$	−8666.94	−0.0715001
$109$	−42300.7	−0.341021	−0.170510	−	0.985356i	$-0.554542\pi$
$109$	−42300.7	−0.341021	−0.170510	+	0.985356i	$0.554542\pi$
$110$	32090.4	0.252868
$111$	−1529.79	−0.0117848
$112$	8251.27	0.0621549
$113$	169786.	1.25085	0.625426	−	0.780283i	$-0.284925\pi$
$113$	169786.	1.25085	0.625426	+	0.780283i	$0.284925\pi$
$114$	6898.89	0.0497184
$115$	−11944.4	−0.0842209
$116$	−111611.	−0.770130
$117$	22544.6	0.152257
$118$	−126663.	−0.837421
$119$	−65734.7	−0.425527
$120$	1001.23	0.00634720
$121$	167327.	1.03897
$122$	83942.9	0.510604
$123$	18763.4	0.111828
$124$	−148642.	−0.868138
$125$	84756.0	0.485172
$126$	31168.0	0.174897
$127$	−192976.	−1.06168	−0.530842	−	0.847471i	$-0.678124\pi$
$127$	−192976.	−1.06168	−0.530842	+	0.847471i	$0.678124\pi$
$128$	−16384.0	−0.0883883
$129$	12292.4	0.0650371
$130$	−5222.29	−0.0271021
$131$	−20701.4	−0.105396	−0.0526978	−	0.998611i	$-0.516782\pi$
$131$	−20701.4	−0.105396	−0.0526978	+	0.998611i	$0.516782\pi$
$132$	10245.5	0.0511799
$133$	−49747.7	−0.243862
$134$	−61186.9	−0.294372
$135$	7583.58	0.0358129
$136$	130525.	0.605127
$137$	240791.	1.09607	0.548037	−	0.836454i	$-0.315375\pi$
$137$	240791.	1.09607	0.548037	+	0.836454i	$0.315375\pi$
$138$	−3813.50	−0.0170461
$139$	−116355.	−0.510797	−0.255398	−	0.966836i	$-0.582207\pi$
$139$	−116355.	−0.510797	−0.255398	+	0.966836i	$0.582207\pi$
$140$	−7219.86	−0.0311321
$141$	−15187.6	−0.0643343
$142$	183329.	0.762977
$143$	−53439.2	−0.218535
$144$	−61888.3	−0.248715
$145$	97660.0	0.385742
$146$	173664.	0.674260
$147$	−17620.1	−0.0672533
$148$	−21904.0	−0.0821995
$149$	−228459.	−0.843028	−0.421514	−	0.906822i	$-0.638501\pi$
$149$	−228459.	−0.843028	−0.421514	+	0.906822i	$0.638501\pi$
$150$	13092.0	0.0475093
$151$	14858.6	0.0530317	0.0265159	−	0.999648i	$-0.491559\pi$
$151$	14858.6	0.0530317	0.0265159	+	0.999648i	$0.491559\pi$
$152$	98780.8	0.346787
$153$	493041.	1.70276
$154$	−73880.2	−0.251030
$155$	130062.	0.434832
$156$	−1667.32	−0.00548540
$157$	195245.	0.632164	0.316082	−	0.948732i	$-0.397633\pi$
$157$	195245.	0.632164	0.316082	+	0.948732i	$0.397633\pi$
$158$	−279325.	−0.890158
$159$	38646.2	0.121231
$160$	14336.0	0.0442719
$161$	27499.0	0.0836089
$162$	−232561.	−0.696225
$163$	−163569.	−0.482206	−0.241103	−	0.970500i	$-0.577509\pi$
$163$	−163569.	−0.482206	−0.241103	+	0.970500i	$0.577509\pi$
$164$	268662.	0.780003
$165$	−8964.83	−0.0256349
$166$	419204.	1.18074
$167$	472206.	1.31021	0.655104	−	0.755539i	$-0.272625\pi$
$167$	472206.	1.31021	0.655104	+	0.755539i	$0.272625\pi$
$168$	−2305.09	−0.00630107
$169$	−362596.	−0.976578
$170$	−114209.	−0.303096
$171$	373131.	0.975823
$172$	176006.	0.453636
$173$	5989.90	0.0152161	0.00760806	−	0.999971i	$-0.497578\pi$
$173$	5989.90	0.0152161	0.00760806	+	0.999971i	$0.497578\pi$
$174$	31180.0	0.0780733
$175$	−94406.1	−0.233026
$176$	146699.	0.356981
$177$	35384.7	0.0848951
$178$	167401.	0.396011
$179$	−195634.	−0.456366	−0.228183	−	0.973618i	$-0.573278\pi$
$179$	−195634.	−0.456366	−0.228183	+	0.973618i	$0.573278\pi$
$180$	54152.3	0.124576
$181$	−609170.	−1.38211	−0.691054	−	0.722804i	$-0.742853\pi$
$181$	−609170.	−1.38211	−0.691054	+	0.722804i	$0.742853\pi$
$182$	12023.0	0.0269051
$183$	−23450.4	−0.0517635
$184$	−54603.0	−0.118897
$185$	19166.0	0.0411720
$186$	41525.0	0.0880091
$187$	−1.16869e6	−2.44398
$188$	−217462.	−0.448733
$189$	−17459.3	−0.0355527
$190$	−86433.2	−0.173699
$191$	−866515.	−1.71867	−0.859336	−	0.511412i	$-0.829123\pi$
$191$	−866515.	−1.71867	−0.859336	+	0.511412i	$0.829123\pi$
$192$	4577.06	0.00896053
$193$	666485.	1.28794	0.643972	−	0.765049i	$-0.277285\pi$
$193$	666485.	1.28794	0.643972	+	0.765049i	$0.277285\pi$
$194$	515483.	0.983354
$195$	1458.91	0.00274752
$196$	−252290.	−0.469094
$197$	865523.	1.58896	0.794480	−	0.607290i	$-0.207743\pi$
$197$	865523.	1.58896	0.794480	+	0.607290i	$0.207743\pi$
$198$	554136.	1.00451
$199$	−171040.	−0.306171	−0.153085	−	0.988213i	$-0.548921\pi$
$199$	−171040.	−0.306171	−0.153085	+	0.988213i	$0.548921\pi$
$200$	187456.	0.331379
$201$	17093.3	0.0298425
$202$	−685122.	−1.18138
$203$	−224838.	−0.382939
$204$	−36463.7	−0.0613459
$205$	−235079.	−0.390687
$206$	−155269.	−0.254927
$207$	−206255.	−0.334564
$208$	−23873.3	−0.0382609
$209$	−884463.	−1.40060
$210$	2016.95	0.00315608
$211$	−805656.	−1.24579	−0.622893	−	0.782307i	$-0.714043\pi$
$211$	−805656.	−1.24579	−0.622893	+	0.782307i	$0.714043\pi$
$212$	553349.	0.845590
$213$	−51215.2	−0.0773482
$214$	−443985.	−0.662726
$215$	−154006.	−0.227217
$216$	34667.8	0.0505582
$217$	−299436.	−0.431673
$218$	169203.	0.241138
$219$	−48515.0	−0.0683543
$220$	−128362.	−0.178805
$221$	190190.	0.261943
$222$	6119.14	0.00833313
$223$	517259.	0.696539	0.348270	−	0.937394i	$-0.386769\pi$
$223$	517259.	0.696539	0.348270	+	0.937394i	$0.386769\pi$
$224$	−33005.1	−0.0439502
$225$	708090.	0.932464
$226$	−679144.	−0.884486
$227$	−848677.	−1.09315	−0.546573	−	0.837412i	$-0.684068\pi$
$227$	−848677.	−1.09315	−0.546573	+	0.837412i	$0.684068\pi$
$228$	−27595.6	−0.0351562
$229$	451795.	0.569314	0.284657	−	0.958629i	$-0.408120\pi$
$229$	451795.	0.569314	0.284657	+	0.958629i	$0.408120\pi$
$230$	47777.6	0.0595532
$231$	20639.3	0.0254487
$232$	446446.	0.544564
$233$	−14249.2	−0.0171950	−0.00859749	−	0.999963i	$-0.502737\pi$
$233$	−14249.2	−0.0171950	−0.00859749	+	0.999963i	$0.502737\pi$
$234$	−90178.3	−0.107662
$235$	190279.	0.224761
$236$	506651.	0.592146
$237$	78032.7	0.0902414
$238$	262939.	0.300893
$239$	−1.15414e6	−1.30696	−0.653480	−	0.756944i	$-0.726692\pi$
$239$	−1.15414e6	−1.30696	−0.653480	+	0.756944i	$0.726692\pi$
$240$	−4004.93	−0.00448815
$241$	−1.08127e6	−1.19920	−0.599600	−	0.800300i	$-0.704674\pi$
$241$	−1.08127e6	−1.19920	−0.599600	+	0.800300i	$0.704674\pi$
$242$	−669309.	−0.734663
$243$	196598.	0.213581
$244$	−335772.	−0.361052
$245$	220754.	0.234959
$246$	−75053.8	−0.0790742
$247$	143935.	0.150115
$248$	594570.	0.613866
$249$	−117110.	−0.119700
$250$	−339024.	−0.343068
$251$	863094.	0.864717	0.432358	−	0.901702i	$-0.357682\pi$
$251$	863094.	0.864717	0.432358	+	0.901702i	$0.357682\pi$
$252$	−124672.	−0.123671
$253$	488904.	0.480200
$254$	771906.	0.750723
$255$	31905.7	0.0307269
$256$	65536.0	0.0625000
$257$	331821.	0.313380	0.156690	−	0.987648i	$-0.449918\pi$
$257$	331821.	0.313380	0.156690	+	0.987648i	$0.449918\pi$
$258$	−49169.5	−0.0459882
$259$	−44124.9	−0.0408728
$260$	20889.2	0.0191641
$261$	1.68639e6	1.53234
$262$	82805.7	0.0745259
$263$	1.89854e6	1.69251	0.846255	−	0.532778i	$-0.178852\pi$
$263$	1.89854e6	1.69251	0.846255	+	0.532778i	$0.178852\pi$
$264$	−40982.1	−0.0361897
$265$	−484181.	−0.423538
$266$	198991.	0.172436
$267$	−46765.4	−0.0401464
$268$	244748.	0.208152
$269$	442377.	0.372745	0.186372	−	0.982479i	$-0.440327\pi$
$269$	442377.	0.372745	0.186372	+	0.982479i	$0.440327\pi$
$270$	−30334.3	−0.0253236
$271$	1.32807e6	1.09849	0.549247	−	0.835660i	$-0.314915\pi$
$271$	1.32807e6	1.09849	0.549247	+	0.835660i	$0.314915\pi$
$272$	−522100.	−0.427889
$273$	−3358.77	−0.00272756
$274$	−963166.	−0.775041
$275$	−1.67844e6	−1.33837
$276$	15254.0	0.0120534
$277$	558271.	0.437165	0.218583	−	0.975818i	$-0.429857\pi$
$277$	558271.	0.437165	0.218583	+	0.975818i	$0.429857\pi$
$278$	465420.	0.361188
$279$	2.24591e6	1.72735
$280$	28879.4	0.0220137
$281$	−176383.	−0.133258	−0.0666288	−	0.997778i	$-0.521224\pi$
$281$	−176383.	−0.133258	−0.0666288	+	0.997778i	$0.521224\pi$
$282$	60750.5	0.0454912
$283$	892042.	0.662094	0.331047	−	0.943614i	$-0.392598\pi$
$283$	892042.	0.662094	0.331047	+	0.943614i	$0.392598\pi$
$284$	−733318.	−0.539506
$285$	24146.1	0.0176090
$286$	213757.	0.154527
$287$	541211.	0.387848
$288$	247553.	0.175868
$289$	2.73951e6	1.92943
$290$	−390640.	−0.272761
$291$	−144006.	−0.0996894
$292$	−694655.	−0.476774
$293$	−1.07341e6	−0.730462	−0.365231	−	0.930917i	$-0.619010\pi$
$293$	−1.07341e6	−0.730462	−0.365231	+	0.930917i	$0.619010\pi$
$294$	70480.2	0.0475553
$295$	−443320.	−0.296594
$296$	87616.0	0.0581238
$297$	−310408.	−0.204194
$298$	913835.	0.596111
$299$	−79562.7	−0.0514673
$300$	−52368.0	−0.0335941
$301$	354560.	0.225566
$302$	−59434.5	−0.0374991
$303$	191397.	0.119765
$304$	−395123.	−0.245216
$305$	293800.	0.180843
$306$	−1.97216e6	−1.20404
$307$	−923646.	−0.559319	−0.279660	−	0.960099i	$-0.590222\pi$
$307$	−923646.	−0.559319	−0.279660	+	0.960099i	$0.590222\pi$
$308$	295521.	0.177505
$309$	43376.2	0.0258437
$310$	−520249.	−0.307473
$311$	−1.24855e6	−0.731988	−0.365994	−	0.930617i	$-0.619271\pi$
$311$	−1.24855e6	−0.731988	−0.365994	+	0.930617i	$0.619271\pi$
$312$	6669.30	0.00387877
$313$	235981.	0.136150	0.0680748	−	0.997680i	$-0.478314\pi$
$313$	235981.	0.136150	0.0680748	+	0.997680i	$0.478314\pi$
$314$	−780978.	−0.447007
$315$	109088.	0.0619443
$316$	1.11730e6	0.629436
$317$	336846.	0.188271	0.0941355	−	0.995559i	$-0.469991\pi$
$317$	336846.	0.188271	0.0941355	+	0.995559i	$0.469991\pi$
$318$	−154585.	−0.0857232
$319$	−3.99739e6	−2.19938
$320$	−57344.0	−0.0313050
$321$	124032.	0.0671851
$322$	−109996.	−0.0591204
$323$	3.14779e6	1.67880
$324$	930244.	0.492305
$325$	273145.	0.143445
$326$	654276.	0.340971
$327$	−47268.8	−0.0244458
$328$	−1.07465e6	−0.551545
$329$	−438070.	−0.223128
$330$	35859.3	0.0181266
$331$	1.20964e6	0.606859	0.303429	−	0.952854i	$-0.401868\pi$
$331$	1.20964e6	0.606859	0.303429	+	0.952854i	$0.401868\pi$
$332$	−1.67682e6	−0.834911
$333$	330958.	0.163554
$334$	−1.88882e6	−0.926457
$335$	−214154.	−0.104259
$336$	9220.36	0.00445553
$337$	−1.98197e6	−0.950653	−0.475326	−	0.879810i	$-0.657670\pi$
$337$	−1.98197e6	−0.950653	−0.475326	+	0.879810i	$0.657670\pi$
$338$	1.45039e6	0.690545
$339$	189727.	0.0896664
$340$	456838.	0.214321
$341$	−5.32366e6	−2.47927
$342$	−1.49252e6	−0.690011
$343$	−1.04995e6	−0.481872
$344$	−704026.	−0.320769
$345$	−13347.2	−0.00603732
$346$	−23959.6	−0.0107594
$347$	−1.86501e6	−0.831493	−0.415746	−	0.909481i	$-0.636480\pi$
$347$	−1.86501e6	−0.831493	−0.415746	+	0.909481i	$0.636480\pi$
$348$	−124720.	−0.0552062
$349$	1.78309e6	0.783628	0.391814	−	0.920044i	$-0.371848\pi$
$349$	1.78309e6	0.783628	0.391814	+	0.920044i	$0.371848\pi$
$350$	377624.	0.164775
$351$	50514.9	0.0218852
$352$	−586796.	−0.252424
$353$	−1.88132e6	−0.803572	−0.401786	−	0.915734i	$-0.631610\pi$
$353$	−1.88132e6	−0.803572	−0.401786	+	0.915734i	$0.631610\pi$
$354$	−141539.	−0.0600299
$355$	641653.	0.270227
$356$	−669603.	−0.280022
$357$	−73455.0	−0.0305036
$358$	782538.	0.322699
$359$	−319594.	−0.130877	−0.0654384	−	0.997857i	$-0.520845\pi$
$359$	−319594.	−0.130877	−0.0654384	+	0.997857i	$0.520845\pi$
$360$	−216609.	−0.0880888
$361$	−93862.6	−0.0379075
$362$	2.43668e6	0.977297
$363$	186979.	0.0744779
$364$	−48092.1	−0.0190248
$365$	607823.	0.238806
$366$	93801.8	0.0366023
$367$	4.38040e6	1.69765	0.848827	−	0.528671i	$-0.177310\pi$
$367$	4.38040e6	1.69765	0.848827	+	0.528671i	$0.177310\pi$
$368$	218412.	0.0840731
$369$	−4.05933e6	−1.55199
$370$	−76664.0	−0.0291130
$371$	1.11471e6	0.420461
$372$	−166100.	−0.0622318
$373$	−1.53536e6	−0.571398	−0.285699	−	0.958319i	$-0.592226\pi$
$373$	−1.53536e6	−0.571398	−0.285699	+	0.958319i	$0.592226\pi$
$374$	4.67478e6	1.72815
$375$	94710.4	0.0347792
$376$	869847.	0.317302
$377$	650522.	0.235727
$378$	69837.2	0.0251395
$379$	881949.	0.315388	0.157694	−	0.987488i	$-0.449594\pi$
$379$	881949.	0.315388	0.157694	+	0.987488i	$0.449594\pi$
$380$	345733.	0.122823
$381$	−215641.	−0.0761060
$382$	3.46606e6	1.21528
$383$	3.40690e6	1.18676	0.593379	−	0.804923i	$-0.297794\pi$
$383$	3.40690e6	1.18676	0.593379	+	0.804923i	$0.297794\pi$
$384$	−18308.3	−0.00633605
$385$	−258581.	−0.0889087
$386$	−2.66594e6	−0.910715
$387$	−2.65936e6	−0.902609
$388$	−2.06193e6	−0.695336
$389$	−2.57316e6	−0.862168	−0.431084	−	0.902312i	$-0.641869\pi$
$389$	−2.57316e6	−0.862168	−0.431084	+	0.902312i	$0.641869\pi$
$390$	−5835.64	−0.00194279
$391$	−1.74000e6	−0.575584
$392$	1.00916e6	0.331700
$393$	−23132.8	−0.00755520
$394$	−3.46209e6	−1.12356
$395$	−977637.	−0.315272
$396$	−2.21654e6	−0.710294
$397$	490985.	0.156348	0.0781739	−	0.996940i	$-0.475091\pi$
$397$	490985.	0.156348	0.0781739	+	0.996940i	$0.475091\pi$
$398$	684158.	0.216496
$399$	−55590.5	−0.0174811
$400$	−749824.	−0.234320
$401$	1.29013e6	0.400655	0.200328	−	0.979729i	$-0.435799\pi$
$401$	1.29013e6	0.400655	0.200328	+	0.979729i	$0.435799\pi$
$402$	−68373.1	−0.0211018
$403$	866355.	0.265726
$404$	2.74049e6	0.835362
$405$	−813964.	−0.246585
$406$	899352.	0.270779
$407$	−784496.	−0.234749
$408$	145855.	0.0433781
$409$	3.42970e6	1.01379	0.506896	−	0.862007i	$-0.330793\pi$
$409$	3.42970e6	1.01379	0.506896	+	0.862007i	$0.330793\pi$
$410$	940316.	0.276257
$411$	269072.	0.0785712
$412$	621075.	0.180261
$413$	1.02063e6	0.294439
$414$	825022.	0.236573
$415$	1.46721e6	0.418189
$416$	95493.3	0.0270545
$417$	−130021.	−0.0366161
$418$	3.53785e6	0.990373
$419$	−5.45105e6	−1.51686	−0.758430	−	0.651755i	$-0.774033\pi$
$419$	−5.45105e6	−1.51686	−0.758430	+	0.651755i	$0.774033\pi$
$420$	−8067.81	−0.00223168
$421$	−2.89424e6	−0.795847	−0.397924	−	0.917419i	$-0.630269\pi$
$421$	−2.89424e6	−0.795847	−0.397924	+	0.917419i	$0.630269\pi$
$422$	3.22263e6	0.880904
$423$	3.28573e6	0.892855
$424$	−2.21340e6	−0.597922
$425$	5.97356e6	1.60421
$426$	204861.	0.0546934
$427$	−676402.	−0.179529
$428$	1.77594e6	0.468618
$429$	−59715.5	−0.0156655
$430$	616022.	0.160667
$431$	−4.09214e6	−1.06110	−0.530552	−	0.847653i	$-0.678015\pi$
$431$	−4.09214e6	−1.06110	−0.530552	+	0.847653i	$0.678015\pi$
$432$	−138671.	−0.0357500
$433$	−7.04228e6	−1.80507	−0.902534	−	0.430618i	$-0.858296\pi$
$433$	−7.04228e6	−1.80507	−0.902534	+	0.430618i	$0.858296\pi$
$434$	1.19774e6	0.305239
$435$	109130.	0.0276516
$436$	−676811.	−0.170510
$437$	−1.31683e6	−0.329857
$438$	194060.	0.0483338
$439$	1.97627e6	0.489424	0.244712	−	0.969596i	$-0.421307\pi$
$439$	1.97627e6	0.489424	0.244712	+	0.969596i	$0.421307\pi$
$440$	513447.	0.126434
$441$	3.81197e6	0.933367
$442$	−760759.	−0.185221
$443$	2.34952e6	0.568813	0.284406	−	0.958704i	$-0.408204\pi$
$443$	2.34952e6	0.568813	0.284406	+	0.958704i	$0.408204\pi$
$444$	−24476.6	−0.00589241
$445$	585903.	0.140257
$446$	−2.06903e6	−0.492528
$447$	−255291.	−0.0604319
$448$	132020.	0.0310775
$449$	−1.75785e6	−0.411496	−0.205748	−	0.978605i	$-0.565963\pi$
$449$	−1.75785e6	−0.411496	−0.205748	+	0.978605i	$0.565963\pi$
$450$	−2.83236e6	−0.659351
$451$	9.62217e6	2.22757
$452$	2.71658e6	0.625426
$453$	16603.7	0.00380154
$454$	3.39471e6	0.772970
$455$	42080.6	0.00952913
$456$	110382.	0.0248592
$457$	−4.66058e6	−1.04388	−0.521939	−	0.852983i	$-0.674791\pi$
$457$	−4.66058e6	−1.04388	−0.521939	+	0.852983i	$0.674791\pi$
$458$	−1.80718e6	−0.402566
$459$	1.10474e6	0.244753
$460$	−191111.	−0.0421105
$461$	−7.28158e6	−1.59578	−0.797891	−	0.602802i	$-0.794051\pi$
$461$	−7.28158e6	−1.59578	−0.797891	+	0.602802i	$0.794051\pi$
$462$	−82557.2	−0.0179949
$463$	6.55367e6	1.42080	0.710399	−	0.703800i	$-0.248515\pi$
$463$	6.55367e6	1.42080	0.710399	+	0.703800i	$0.248515\pi$
$464$	−1.78578e6	−0.385065
$465$	145338.	0.0311706
$466$	56996.9	0.0121587
$467$	−6.71018e6	−1.42378	−0.711888	−	0.702293i	$-0.752160\pi$
$467$	−6.71018e6	−1.42378	−0.711888	+	0.702293i	$0.752160\pi$
$468$	360713.	0.0761285
$469$	493037.	0.103502
$470$	−761116.	−0.158930
$471$	218175.	0.0453162
$472$	−2.02660e6	−0.418711
$473$	6.30370e6	1.29552
$474$	−312131.	−0.0638103
$475$	4.52076e6	0.919343
$476$	−1.05176e6	−0.212764
$477$	−8.36081e6	−1.68249
$478$	4.61655e6	0.924161
$479$	5.77964e6	1.15097	0.575483	−	0.817814i	$-0.304814\pi$
$479$	5.77964e6	1.15097	0.575483	+	0.817814i	$0.304814\pi$
$480$	16019.7	0.00317360
$481$	127666.	0.0251602
$482$	4.32508e6	0.847962
$483$	30728.7	0.00599345
$484$	2.67724e6	0.519485
$485$	1.80419e6	0.348280
$486$	−786392.	−0.151025
$487$	−1.74432e6	−0.333276	−0.166638	−	0.986018i	$-0.553291\pi$
$487$	−1.74432e6	−0.333276	−0.166638	+	0.986018i	$0.553291\pi$
$488$	1.34309e6	0.255302
$489$	−182780.	−0.0345666
$490$	−883015.	−0.166141
$491$	−8.13304e6	−1.52247	−0.761236	−	0.648475i	$-0.775407\pi$
$491$	−8.13304e6	−1.52247	−0.761236	+	0.648475i	$0.775407\pi$
$492$	300215.	0.0559139
$493$	1.42267e7	2.63624
$494$	−575739.	−0.106147
$495$	1.93947e6	0.355771
$496$	−2.37828e6	−0.434069
$497$	−1.47725e6	−0.268264
$498$	468438.	0.0846406
$499$	−1.01214e6	−0.181966	−0.0909831	−	0.995852i	$-0.529001\pi$
$499$	−1.01214e6	−0.181966	−0.0909831	+	0.995852i	$0.529001\pi$
$500$	1.35610e6	0.242586
$501$	527665.	0.0939213
$502$	−3.45238e6	−0.611447
$503$	2.83749e6	0.500052	0.250026	−	0.968239i	$-0.419561\pi$
$503$	2.83749e6	0.500052	0.250026	+	0.968239i	$0.419561\pi$
$504$	498689.	0.0874487
$505$	−2.39793e6	−0.418415
$506$	−1.95562e6	−0.339553
$507$	−405182.	−0.0700053
$508$	−3.08762e6	−0.530842
$509$	−8.45313e6	−1.44618	−0.723091	−	0.690753i	$-0.757279\pi$
$509$	−8.45313e6	−1.44618	−0.723091	+	0.690753i	$0.757279\pi$
$510$	−127623.	−0.0217272
$511$	−1.39936e6	−0.237071
$512$	−262144.	−0.0441942
$513$	836062.	0.140264
$514$	−1.32729e6	−0.221593
$515$	−543441.	−0.0902889
$516$	196678.	0.0325186
$517$	−7.78844e6	−1.28152
$518$	176500.	0.0289015
$519$	6693.39	0.00109076
$520$	−83556.7	−0.0135510
$521$	−273078.	−0.0440749	−0.0220375	−	0.999757i	$-0.507015\pi$
$521$	−273078.	−0.0440749	−0.0220375	+	0.999757i	$0.507015\pi$
$522$	−6.74555e6	−1.08353
$523$	480959.	0.0768871	0.0384436	−	0.999261i	$-0.487760\pi$
$523$	480959.	0.0768871	0.0384436	+	0.999261i	$0.487760\pi$
$524$	−331223.	−0.0526978
$525$	−105494.	−0.0167043
$526$	−7.59418e6	−1.19679
$527$	1.89468e7	2.97174
$528$	163928.	0.0255899
$529$	−5.70844e6	−0.886907
$530$	1.93672e6	0.299487
$531$	−7.65522e6	−1.17821
$532$	−795964.	−0.121931
$533$	−1.56588e6	−0.238749
$534$	187062.	0.0283878
$535$	−1.55395e6	−0.234721
$536$	−978990.	−0.147186
$537$	−218611.	−0.0327142
$538$	−1.76951e6	−0.263570
$539$	−9.03582e6	−1.33966
$540$	121337.	0.0179065
$541$	1.00092e7	1.47030	0.735150	−	0.677904i	$-0.237111\pi$
$541$	1.00092e7	1.47030	0.735150	+	0.677904i	$0.237111\pi$
$542$	−5.31228e6	−0.776753
$543$	−680715.	−0.0990753
$544$	2.08840e6	0.302564
$545$	592209.	0.0854051
$546$	13435.1	0.00192868
$547$	7.36238e6	1.05208	0.526042	−	0.850459i	$-0.323676\pi$
$547$	7.36238e6	1.05208	0.526042	+	0.850459i	$0.323676\pi$
$548$	3.85266e6	0.548037
$549$	5.07333e6	0.718393
$550$	6.71377e6	0.946368
$551$	1.07667e7	1.51078
$552$	−61016.0	−0.00852307
$553$	2.25077e6	0.312981
$554$	−2.23308e6	−0.309123
$555$	21417.0	0.00295139
$556$	−1.86168e6	−0.255398
$557$	2.98427e6	0.407567	0.203784	−	0.979016i	$-0.434676\pi$
$557$	2.98427e6	0.407567	0.203784	+	0.979016i	$0.434676\pi$
$558$	−8.98363e6	−1.22142
$559$	−1.02584e6	−0.138852
$560$	−115518.	−0.0155661
$561$	−1.30595e6	−0.175195
$562$	705534.	0.0942274
$563$	−1.43621e7	−1.90962	−0.954812	−	0.297210i	$-0.903944\pi$
$563$	−1.43621e7	−1.90962	−0.954812	+	0.297210i	$0.903944\pi$
$564$	−243002.	−0.0321671
$565$	−2.37700e6	−0.313263
$566$	−3.56817e6	−0.468171
$567$	1.87395e6	0.244794
$568$	2.93327e6	0.381488
$569$	−1.43394e7	−1.85674	−0.928371	−	0.371656i	$-0.878790\pi$
$569$	−1.43394e7	−1.85674	−0.928371	+	0.371656i	$0.878790\pi$
$570$	−96584.5	−0.0124515
$571$	−1.52553e7	−1.95807	−0.979037	−	0.203681i	$-0.934710\pi$
$571$	−1.52553e7	−1.95807	−0.979037	+	0.203681i	$0.934710\pi$
$572$	−855028.	−0.109267
$573$	−968285.	−0.123202
$574$	−2.16484e6	−0.274250
$575$	−2.49894e6	−0.315200
$576$	−990213.	−0.124358
$577$	−2.26600e6	−0.283348	−0.141674	−	0.989913i	$-0.545248\pi$
$577$	−2.26600e6	−0.283348	−0.141674	+	0.989913i	$0.545248\pi$
$578$	−1.09581e7	−1.36431
$579$	744762.	0.0923254
$580$	1.56256e6	0.192871
$581$	−3.37789e6	−0.415151
$582$	576025.	0.0704910
$583$	1.98183e7	2.41488
$584$	2.77862e6	0.337130
$585$	−315624.	−0.0381312
$586$	4.29365e6	0.516514
$587$	317358.	0.0380149	0.0190075	−	0.999819i	$-0.493949\pi$
$587$	317358.	0.0380149	0.0190075	+	0.999819i	$0.493949\pi$
$588$	−281921.	−0.0336267
$589$	1.43389e7	1.70305
$590$	1.77328e6	0.209723
$591$	967176.	0.113903
$592$	−350464.	−0.0410997
$593$	8.92618e6	1.04239	0.521194	−	0.853438i	$-0.325487\pi$
$593$	8.92618e6	1.04239	0.521194	+	0.853438i	$0.325487\pi$
$594$	1.24163e6	0.144387
$595$	920286.	0.106569
$596$	−3.65534e6	−0.421514
$597$	−191128.	−0.0219476
$598$	318251.	0.0363929
$599$	−5.28318e6	−0.601629	−0.300814	−	0.953683i	$-0.597258\pi$
$599$	−5.28318e6	−0.601629	−0.300814	+	0.953683i	$0.597258\pi$
$600$	209472.	0.0237546
$601$	−6.71348e6	−0.758161	−0.379081	−	0.925364i	$-0.623760\pi$
$601$	−6.71348e6	−0.758161	−0.379081	+	0.925364i	$0.623760\pi$
$602$	−1.41824e6	−0.159499
$603$	−3.69800e6	−0.414165
$604$	237738.	0.0265159
$605$	−2.34258e6	−0.260199
$606$	−765588.	−0.0846863
$607$	1.11112e6	0.122402	0.0612010	−	0.998125i	$-0.480507\pi$
$607$	1.11112e6	0.122402	0.0612010	+	0.998125i	$0.480507\pi$
$608$	1.58049e6	0.173394
$609$	−251245.	−0.0274507
$610$	−1.17520e6	−0.127876
$611$	1.26747e6	0.137351
$612$	7.88865e6	0.851381
$613$	1.28371e6	0.137980	0.0689898	−	0.997617i	$-0.478022\pi$
$613$	1.28371e6	0.137980	0.0689898	+	0.997617i	$0.478022\pi$
$614$	3.69459e6	0.395498
$615$	−262688.	−0.0280061
$616$	−1.18208e6	−0.125515
$617$	−8.97647e6	−0.949277	−0.474638	−	0.880181i	$-0.657421\pi$
$617$	−8.97647e6	−0.949277	−0.474638	+	0.880181i	$0.657421\pi$
$618$	−173505.	−0.0182743
$619$	5.79152e6	0.607528	0.303764	−	0.952747i	$-0.401757\pi$
$619$	5.79152e6	0.607528	0.303764	+	0.952747i	$0.401757\pi$
$620$	2.08099e6	0.217416
$621$	−462150.	−0.0480899
$622$	4.99419e6	0.517594
$623$	−1.34890e6	−0.139238
$624$	−26677.2	−0.00274270
$625$	7.96654e6	0.815774
$626$	−943924.	−0.0962723
$627$	−988341.	−0.100401
$628$	3.12391e6	0.316082
$629$	2.79201e6	0.281378
$630$	−436353.	−0.0438012
$631$	6.51079e6	0.650969	0.325485	−	0.945547i	$-0.394473\pi$
$631$	6.51079e6	0.650969	0.325485	+	0.945547i	$0.394473\pi$
$632$	−4.46920e6	−0.445079
$633$	−900279.	−0.0893033
$634$	−1.34739e6	−0.133128
$635$	2.70167e6	0.265888
$636$	618339.	0.0606155
$637$	1.47046e6	0.143584
$638$	1.59895e7	1.55519
$639$	1.10800e7	1.07347
$640$	229376.	0.0221359
$641$	1.55201e7	1.49193	0.745966	−	0.665984i	$-0.231988\pi$
$641$	1.55201e7	1.49193	0.745966	+	0.665984i	$0.231988\pi$
$642$	−496130.	−0.0475070
$643$	1.43129e6	0.136521	0.0682606	−	0.997668i	$-0.478255\pi$
$643$	1.43129e6	0.136521	0.0682606	+	0.997668i	$0.478255\pi$
$644$	439984.	0.0418045
$645$	−172093.	−0.0162879
$646$	−1.25912e7	−1.18709
$647$	−1.21014e7	−1.13652	−0.568259	−	0.822850i	$-0.692383\pi$
$647$	−1.21014e7	−1.13652	−0.568259	+	0.822850i	$0.692383\pi$
$648$	−3.72098e6	−0.348112
$649$	1.81458e7	1.69108
$650$	−1.09258e6	−0.101431
$651$	−334604.	−0.0309441
$652$	−2.61711e6	−0.241103
$653$	−1.68824e7	−1.54935	−0.774677	−	0.632357i	$-0.782088\pi$
$653$	−1.68824e7	−1.54935	−0.774677	+	0.632357i	$0.782088\pi$
$654$	189075.	0.0172858
$655$	289820.	0.0263952
$656$	4.29859e6	0.390001
$657$	1.04959e7	0.948647
$658$	1.75228e6	0.157775
$659$	1.99965e7	1.79366	0.896831	−	0.442374i	$-0.145863\pi$
$659$	1.99965e7	1.79366	0.896831	+	0.442374i	$0.145863\pi$
$660$	−143437.	−0.0128175
$661$	3.85059e6	0.342786	0.171393	−	0.985203i	$-0.445173\pi$
$661$	3.85059e6	0.342786	0.171393	+	0.985203i	$0.445173\pi$
$662$	−4.83858e6	−0.429114
$663$	212527.	0.0187772
$664$	6.70726e6	0.590371
$665$	696468.	0.0610727
$666$	−1.32383e6	−0.115650
$667$	−5.95149e6	−0.517977
$668$	7.55529e6	0.655104
$669$	578009.	0.0499309
$670$	856616.	0.0737224
$671$	−1.20257e7	−1.03111
$672$	−36881.4	−0.00315054
$673$	8.67399e6	0.738213	0.369106	−	0.929387i	$-0.379664\pi$
$673$	8.67399e6	0.738213	0.369106	+	0.929387i	$0.379664\pi$
$674$	7.92787e6	0.672213
$675$	1.58659e6	0.134031
$676$	−5.80154e6	−0.488289
$677$	1.65825e7	1.39052	0.695261	−	0.718758i	$-0.255289\pi$
$677$	1.65825e7	1.39052	0.695261	+	0.718758i	$0.255289\pi$
$678$	−758908.	−0.0634037
$679$	−4.15370e6	−0.345749
$680$	−1.82735e6	−0.151548
$681$	−948352.	−0.0783613
$682$	2.12946e7	1.75311
$683$	−1.41433e7	−1.16011	−0.580055	−	0.814578i	$-0.696969\pi$
$683$	−1.41433e7	−1.16011	−0.580055	+	0.814578i	$0.696969\pi$
$684$	5.97010e6	0.487911
$685$	−3.37108e6	−0.274500
$686$	4.19978e6	0.340735
$687$	504857.	0.0408109
$688$	2.81610e6	0.226818
$689$	−3.22517e6	−0.258824
$690$	53389.0	0.00426903
$691$	−1.65966e7	−1.32228	−0.661139	−	0.750263i	$-0.729927\pi$
$691$	−1.65966e7	−1.32228	−0.661139	+	0.750263i	$0.729927\pi$
$692$	95838.3	0.00760806
$693$	−4.46516e6	−0.353186
$694$	7.46006e6	0.587954
$695$	1.62897e6	0.127924
$696$	498880.	0.0390367
$697$	−3.42452e7	−2.67004
$698$	−7.13236e6	−0.554109
$699$	−15922.8	−0.00123261
$700$	−1.51050e6	−0.116513
$701$	1.53917e6	0.118302	0.0591508	−	0.998249i	$-0.481161\pi$
$701$	1.53917e6	0.118302	0.0591508	+	0.998249i	$0.481161\pi$
$702$	−202059.	−0.0154752
$703$	2.11298e6	0.161253
$704$	2.34718e6	0.178491
$705$	212627.	0.0161118
$706$	7.52526e6	0.568211
$707$	5.52063e6	0.415375
$708$	566156.	0.0424476
$709$	−1.16109e6	−0.0867462	−0.0433731	−	0.999059i	$-0.513810\pi$
$709$	−1.16109e6	−0.0867462	−0.0433731	+	0.999059i	$0.513810\pi$
$710$	−2.56661e6	−0.191080
$711$	−1.68818e7	−1.25240
$712$	2.67841e6	0.198006
$713$	−7.92610e6	−0.583896
$714$	293820.	0.0215693
$715$	748149.	0.0547297
$716$	−3.13015e6	−0.228183
$717$	−1.28969e6	−0.0936885
$718$	1.27838e6	0.0925438
$719$	−6.72124e6	−0.484872	−0.242436	−	0.970167i	$-0.577946\pi$
$719$	−6.72124e6	−0.484872	−0.242436	+	0.970167i	$0.577946\pi$
$720$	866437.	0.0622882
$721$	1.25114e6	0.0896328
$722$	375450.	0.0268046
$723$	−1.20826e6	−0.0859637
$724$	−9.74671e6	−0.691054
$725$	2.04319e7	1.44365
$726$	−747918.	−0.0526638
$727$	−2.43741e7	−1.71038	−0.855191	−	0.518313i	$-0.826560\pi$
$727$	−2.43741e7	−1.71038	−0.855191	+	0.518313i	$0.826560\pi$
$728$	192368.	0.0134526
$729$	−1.39084e7	−0.969300
$730$	−2.43129e6	−0.168861
$731$	−2.24348e7	−1.55285
$732$	−375207.	−0.0258817
$733$	7.54540e6	0.518707	0.259354	−	0.965782i	$-0.416491\pi$
$733$	7.54540e6	0.518707	0.259354	+	0.965782i	$0.416491\pi$
$734$	−1.75216e7	−1.20042
$735$	246681.	0.0168429
$736$	−873648.	−0.0594487
$737$	8.76568e6	0.594452
$738$	1.62373e7	1.09742
$739$	−2.49386e7	−1.67981	−0.839907	−	0.542730i	$-0.817391\pi$
$739$	−2.49386e7	−1.67981	−0.839907	+	0.542730i	$0.817391\pi$
$740$	306656.	0.0205860
$741$	160839.	0.0107609
$742$	−4.45882e6	−0.297311
$743$	7.12958e6	0.473796	0.236898	−	0.971534i	$-0.423869\pi$
$743$	7.12958e6	0.473796	0.236898	+	0.971534i	$0.423869\pi$
$744$	664401.	0.0440046
$745$	3.19842e6	0.211128
$746$	6.14145e6	0.404039
$747$	2.53358e7	1.66124
$748$	−1.86991e7	−1.22199
$749$	3.57758e6	0.233015
$750$	−378841.	−0.0245926
$751$	−9.44883e6	−0.611334	−0.305667	−	0.952139i	$-0.598879\pi$
$751$	−9.44883e6	−0.611334	−0.305667	+	0.952139i	$0.598879\pi$
$752$	−3.47939e6	−0.224367
$753$	964462.	0.0619866
$754$	−2.60209e6	−0.166684
$755$	−208021.	−0.0132813
$756$	−279349.	−0.0177763
$757$	−1.07500e7	−0.681821	−0.340911	−	0.940096i	$-0.610735\pi$
$757$	−1.07500e7	−0.681821	−0.340911	+	0.940096i	$0.610735\pi$
$758$	−3.52779e6	−0.223013
$759$	546325.	0.0344228
$760$	−1.38293e6	−0.0868493
$761$	3.94653e6	0.247033	0.123516	−	0.992343i	$-0.460583\pi$
$761$	3.94653e6	0.247033	0.123516	+	0.992343i	$0.460583\pi$
$762$	862564.	0.0538151
$763$	−1.36341e6	−0.0847845
$764$	−1.38642e7	−0.859336
$765$	−6.90257e6	−0.426439
$766$	−1.36276e7	−0.839165
$767$	−2.95299e6	−0.181248
$768$	73233.0	0.00448027
$769$	755505.	0.0460704	0.0230352	−	0.999735i	$-0.492667\pi$
$769$	755505.	0.0460704	0.0230352	+	0.999735i	$0.492667\pi$
$770$	1.03432e6	0.0628679
$771$	370793.	0.0224644
$772$	1.06638e7	0.643972
$773$	1.06768e6	0.0642679	0.0321340	−	0.999484i	$-0.489770\pi$
$773$	1.06768e6	0.0642679	0.0321340	+	0.999484i	$0.489770\pi$
$774$	1.06374e7	0.638241
$775$	2.72109e7	1.62738
$776$	8.24773e6	0.491677
$777$	−49307.3	−0.00292994
$778$	1.02926e7	0.609645
$779$	−2.59166e7	−1.53015
$780$	23342.5	0.00137376
$781$	−2.62639e7	−1.54075
$782$	6.96002e6	0.406999
$783$	3.77863e6	0.220257
$784$	−4.03664e6	−0.234547
$785$	−2.73342e6	−0.158319
$786$	92531.0	0.00534233
$787$	−1.14213e7	−0.657325	−0.328662	−	0.944447i	$-0.606598\pi$
$787$	−1.14213e7	−0.657325	−0.328662	+	0.944447i	$0.606598\pi$
$788$	1.38484e7	0.794480
$789$	2.12152e6	0.121326
$790$	3.91055e6	0.222931
$791$	5.47246e6	0.310987
$792$	8.86617e6	0.502254
$793$	1.95703e6	0.110513
$794$	−1.96394e6	−0.110555
$795$	−541046.	−0.0303610
$796$	−2.73663e6	−0.153085
$797$	−9.61914e6	−0.536402	−0.268201	−	0.963363i	$-0.586429\pi$
$797$	−9.61914e6	−0.536402	−0.268201	+	0.963363i	$0.586429\pi$
$798$	222362.	0.0123610
$799$	2.77190e7	1.53607
$800$	2.99930e6	0.165689
$801$	1.01173e7	0.557167
$802$	−5.16050e6	−0.283306
$803$	−2.48792e7	−1.36159
$804$	273492.	0.0149213
$805$	−384986.	−0.0209390
$806$	−3.46542e6	−0.187896
$807$	494333.	0.0267199
$808$	−1.09620e7	−0.590690
$809$	2.71417e7	1.45803	0.729014	−	0.684498i	$-0.239979\pi$
$809$	2.71417e7	1.45803	0.729014	+	0.684498i	$0.239979\pi$
$810$	3.25585e6	0.174362
$811$	−6.58940e6	−0.351798	−0.175899	−	0.984408i	$-0.556283\pi$
$811$	−6.58940e6	−0.351798	−0.175899	+	0.984408i	$0.556283\pi$
$812$	−3.59741e6	−0.191469
$813$	1.48405e6	0.0787448
$814$	3.13798e6	0.165993
$815$	2.28997e6	0.120763
$816$	−583419.	−0.0306729
$817$	−1.69786e7	−0.889909
$818$	−1.37188e7	−0.716859
$819$	726646.	0.0378541
$820$	−3.76126e6	−0.195344
$821$	1.99871e7	1.03488	0.517442	−	0.855718i	$-0.326884\pi$
$821$	1.99871e7	1.03488	0.517442	+	0.855718i	$0.326884\pi$
$822$	−1.07629e6	−0.0555582
$823$	2.46714e7	1.26968	0.634840	−	0.772644i	$-0.281066\pi$
$823$	2.46714e7	1.26968	0.634840	+	0.772644i	$0.281066\pi$
$824$	−2.48430e6	−0.127464
$825$	−1.87557e6	−0.0959398
$826$	−4.08253e6	−0.208199
$827$	−1.76672e7	−0.898266	−0.449133	−	0.893465i	$-0.648267\pi$
$827$	−1.76672e7	−0.898266	−0.449133	+	0.893465i	$0.648267\pi$
$828$	−3.30009e6	−0.167282
$829$	1.35698e7	0.685783	0.342891	−	0.939375i	$-0.388594\pi$
$829$	1.35698e7	0.685783	0.342891	+	0.939375i	$0.388594\pi$
$830$	−5.86885e6	−0.295705
$831$	623839.	0.0313379
$832$	−381973.	−0.0191304
$833$	3.21584e7	1.60576
$834$	520082.	0.0258915
$835$	−6.61088e6	−0.328128
$836$	−1.41514e7	−0.700300
$837$	5.03233e6	0.248288
$838$	2.18042e7	1.07258
$839$	−1.64726e7	−0.807898	−0.403949	−	0.914782i	$-0.632363\pi$
$839$	−1.64726e7	−0.807898	−0.403949	+	0.914782i	$0.632363\pi$
$840$	32271.3	0.00157804
$841$	2.81495e7	1.37240
$842$	1.15770e7	0.562749
$843$	−197099.	−0.00955247
$844$	−1.28905e7	−0.622893
$845$	5.07635e6	0.244574
$846$	−1.31429e7	−0.631344
$847$	5.39321e6	0.258309
$848$	8.85359e6	0.422795
$849$	996810.	0.0474617
$850$	−2.38942e7	−1.13435
$851$	−1.16799e6	−0.0552861
$852$	−819444.	−0.0386741
$853$	6.37437e6	0.299961	0.149980	−	0.988689i	$-0.452079\pi$
$853$	6.37437e6	0.299961	0.149980	+	0.988689i	$0.452079\pi$
$854$	2.70561e6	0.126946
$855$	−5.22383e6	−0.244385
$856$	−7.10376e6	−0.331363
$857$	−871536.	−0.0405353	−0.0202676	−	0.999795i	$-0.506452\pi$
$857$	−871536.	−0.0405353	−0.0202676	+	0.999795i	$0.506452\pi$
$858$	238862.	0.0110772
$859$	−3.58110e7	−1.65590	−0.827950	−	0.560803i	$-0.810493\pi$
$859$	−3.58110e7	−1.65590	−0.827950	+	0.560803i	$0.810493\pi$
$860$	−2.46409e6	−0.113608
$861$	604774.	0.0278026
$862$	1.63686e7	0.750314
$863$	3.36316e7	1.53716	0.768582	−	0.639751i	$-0.220963\pi$
$863$	3.36316e7	1.53716	0.768582	+	0.639751i	$0.220963\pi$
$864$	554684.	0.0252791
$865$	−83858.5	−0.00381072
$866$	2.81691e7	1.27638
$867$	3.06126e6	0.138310
$868$	−4.79097e6	−0.215836
$869$	4.00163e7	1.79758
$870$	−436520.	−0.0195527
$871$	−1.42650e6	−0.0637127
$872$	2.70724e6	0.120569
$873$	3.11547e7	1.38353
$874$	5.26731e6	0.233244
$875$	2.73181e6	0.120623
$876$	−776241.	−0.0341772
$877$	8.39900e6	0.368747	0.184373	−	0.982856i	$-0.440974\pi$
$877$	8.39900e6	0.368747	0.184373	+	0.982856i	$0.440974\pi$
$878$	−7.90508e6	−0.346075
$879$	−1.19948e6	−0.0523626
$880$	−2.05379e6	−0.0894023
$881$	3.36198e7	1.45934	0.729668	−	0.683801i	$-0.239675\pi$
$881$	3.36198e7	1.45934	0.729668	+	0.683801i	$0.239675\pi$
$882$	−1.52479e7	−0.659990
$883$	−3.95894e7	−1.70875	−0.854373	−	0.519661i	$-0.826058\pi$
$883$	−3.95894e7	−1.70875	−0.854373	+	0.519661i	$0.826058\pi$
$884$	3.04304e6	0.130971
$885$	−495386.	−0.0212611
$886$	−9.39807e6	−0.402211
$887$	1.07166e7	0.457351	0.228676	−	0.973503i	$-0.426560\pi$
$887$	1.07166e7	0.457351	0.228676	+	0.973503i	$0.426560\pi$
$888$	97906.3	0.00416656
$889$	−6.21992e6	−0.263955
$890$	−2.34361e6	−0.0991769
$891$	3.33169e7	1.40595
$892$	8.27614e6	0.348270
$893$	2.09776e7	0.880292
$894$	1.02116e6	0.0427318
$895$	2.73888e6	0.114292
$896$	−528081.	−0.0219751
$897$	−88907.2	−0.00368940
$898$	7.03139e6	0.290972
$899$	6.48055e7	2.67432
$900$	1.13294e7	0.466232
$901$	−7.05331e7	−2.89455
$902$	−3.84887e7	−1.57513
$903$	396202.	0.0161695
$904$	−1.08663e7	−0.442243
$905$	8.52837e6	0.346134
$906$	−66414.9	−0.00268810
$907$	−1.76828e7	−0.713729	−0.356864	−	0.934156i	$-0.616154\pi$
$907$	−1.76828e7	−0.713729	−0.356864	+	0.934156i	$0.616154\pi$
$908$	−1.35788e7	−0.546573
$909$	−4.14073e7	−1.66214
$910$	−168322.	−0.00673812
$911$	1.29131e7	0.515506	0.257753	−	0.966211i	$-0.417018\pi$
$911$	1.29131e7	0.515506	0.257753	+	0.966211i	$0.417018\pi$
$912$	−441529.	−0.0175781
$913$	−6.00554e7	−2.38438
$914$	1.86423e7	0.738133
$915$	328306.	0.0129636
$916$	7.22871e6	0.284657
$917$	−667239.	−0.0262034
$918$	−4.41896e6	−0.173067
$919$	2.87397e7	1.12252	0.561259	−	0.827640i	$-0.310317\pi$
$919$	2.87397e7	1.12252	0.561259	+	0.827640i	$0.310317\pi$
$920$	764442.	0.0297766
$921$	−1.03213e6	−0.0400944
$922$	2.91263e7	1.12839
$923$	4.27411e6	0.165136
$924$	330229.	0.0127243
$925$	4.00980e6	0.154088
$926$	−2.62147e7	−1.00466
$927$	−9.38411e6	−0.358669
$928$	7.14313e6	0.272282
$929$	−4.78157e7	−1.81774	−0.908870	−	0.417081i	$-0.863053\pi$
$929$	−4.78157e7	−1.81774	−0.908870	+	0.417081i	$0.863053\pi$
$930$	−581350.	−0.0220410
$931$	2.43373e7	0.920234
$932$	−227988.	−0.00859749
$933$	−1.39519e6	−0.0524720
$934$	2.68407e7	1.00676
$935$	1.63617e7	0.612069
$936$	−1.44285e6	−0.0538310
$937$	−2.14618e7	−0.798578	−0.399289	−	0.916825i	$-0.630743\pi$
$937$	−2.14618e7	−0.798578	−0.399289	+	0.916825i	$0.630743\pi$
$938$	−1.97215e6	−0.0731867
$939$	263696.	0.00975978
$940$	3.04447e6	0.112381
$941$	−6.15694e6	−0.226668	−0.113334	−	0.993557i	$-0.536153\pi$
$941$	−6.15694e6	−0.226668	−0.113334	+	0.993557i	$0.536153\pi$
$942$	−872702.	−0.0320434
$943$	1.43259e7	0.524618
$944$	8.10642e6	0.296073
$945$	244430.	0.00890380
$946$	−2.52148e7	−0.916068
$947$	−2.64772e6	−0.0959395	−0.0479697	−	0.998849i	$-0.515275\pi$
$947$	−2.64772e6	−0.0959395	−0.0479697	+	0.998849i	$0.515275\pi$
$948$	1.24852e6	0.0451207
$949$	4.04876e6	0.145934
$950$	−1.80831e7	−0.650074
$951$	376408.	0.0134961
$952$	4.20702e6	0.150447
$953$	2.90206e7	1.03508	0.517540	−	0.855659i	$-0.326848\pi$
$953$	2.90206e7	1.03508	0.517540	+	0.855659i	$0.326848\pi$
$954$	3.34432e7	1.18970
$955$	1.21312e7	0.430423
$956$	−1.84662e7	−0.653480
$957$	−4.46687e6	−0.157661
$958$	−2.31186e7	−0.813856
$959$	7.76107e6	0.272505
$960$	−64078.9	−0.00224407
$961$	5.76778e7	2.01465
$962$	−510666.	−0.0177909
$963$	−2.68335e7	−0.932420
$964$	−1.73003e7	−0.599600
$965$	−9.33079e6	−0.322552
$966$	−122915.	−0.00423801
$967$	−5.64337e7	−1.94076	−0.970382	−	0.241576i	$-0.922336\pi$
$967$	−5.64337e7	−1.94076	−0.970382	+	0.241576i	$0.922336\pi$
$968$	−1.07089e7	−0.367332
$969$	3.51749e6	0.120344
$970$	−7.21676e6	−0.246271
$971$	2.27921e7	0.775777	0.387888	−	0.921706i	$-0.373205\pi$
$971$	2.27921e7	0.775777	0.387888	+	0.921706i	$0.373205\pi$
$972$	3.14557e6	0.106791
$973$	−3.75030e6	−0.126994
$974$	6.97729e6	0.235662
$975$	305225.	0.0102827
$976$	−5.37235e6	−0.180526
$977$	−2.54962e6	−0.0854554	−0.0427277	−	0.999087i	$-0.513605\pi$
$977$	−2.54962e6	−0.0854554	−0.0427277	+	0.999087i	$0.513605\pi$
$978$	731119.	0.0244422
$979$	−2.39820e7	−0.799702
$980$	3.53206e6	0.117480
$981$	1.02262e7	0.339268
$982$	3.25322e7	1.07655
$983$	−1.31829e7	−0.435138	−0.217569	−	0.976045i	$-0.569813\pi$
$983$	−1.31829e7	−0.435138	−0.217569	+	0.976045i	$0.569813\pi$
$984$	−1.20086e6	−0.0395371
$985$	−1.21173e7	−0.397939
$986$	−5.69066e7	−1.86411
$987$	−489521.	−0.0159948
$988$	2.30296e6	0.0750573
$989$	9.38523e6	0.305109
$990$	−7.75790e6	−0.251568
$991$	1.59650e7	0.516398	0.258199	−	0.966092i	$-0.416871\pi$
$991$	1.59650e7	0.516398	0.258199	+	0.966092i	$0.416871\pi$
$992$	9.51312e6	0.306933
$993$	1.35171e6	0.0435022
$994$	5.90899e6	0.189691
$995$	2.39455e6	0.0766773
$996$	−1.87375e6	−0.0598500
$997$	4.15647e7	1.32430	0.662151	−	0.749370i	$-0.269644\pi$
$997$	4.15647e7	1.32430	0.662151	+	0.749370i	$0.269644\pi$
$998$	4.04857e6	0.128670
$999$	741565.	0.0235091

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.a.c.1.2	✓	3
3.2	odd	2		666.6.a.i.1.2		3
4.3	odd	2		592.6.a.c.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.a.c.1.2	✓	3	1.1	even	1	trivial
592.6.a.c.1.2		3	4.3	odd	2
666.6.a.i.1.2		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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +1.11745 q^{3} +16.0000 q^{4} -14.0000 q^{5} -4.46979 q^{6} +32.2315 q^{7} -64.0000 q^{8} -241.751 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +1.11745 q^{3} +16.0000 q^{4} -14.0000 q^{5} -4.46979 q^{6} +32.2315 q^{7} -64.0000 q^{8} -241.751 q^{9} +56.0000 q^{10} +573.043 q^{11} +17.8792 q^{12} -93.2552 q^{13} -128.926 q^{14} -15.6443 q^{15} +256.000 q^{16} -2039.45 q^{17} +967.005 q^{18} -1543.45 q^{19} -224.000 q^{20} +36.0170 q^{21} -2292.17 q^{22} +853.172 q^{23} -71.5166 q^{24} -2929.00 q^{25} +373.021 q^{26} -541.684 q^{27} +515.704 q^{28} -6975.72 q^{29} +62.5770 q^{30} -9290.16 q^{31} -1024.00 q^{32} +640.345 q^{33} +8157.81 q^{34} -451.241 q^{35} -3868.02 q^{36} -1369.00 q^{37} +6173.80 q^{38} -104.208 q^{39} +896.000 q^{40} +16791.4 q^{41} -144.068 q^{42} +11000.4 q^{43} +9168.69 q^{44} +3384.52 q^{45} -3412.69 q^{46} -13591.4 q^{47} +286.066 q^{48} -15768.1 q^{49} +11716.0 q^{50} -2278.98 q^{51} -1492.08 q^{52} +34584.3 q^{53} +2166.74 q^{54} -8022.60 q^{55} -2062.82 q^{56} -1724.72 q^{57} +27902.9 q^{58} +31665.7 q^{59} -250.308 q^{60} -20985.7 q^{61} +37160.6 q^{62} -7792.01 q^{63} +4096.00 q^{64} +1305.57 q^{65} -2561.38 q^{66} +15296.7 q^{67} -32631.3 q^{68} +953.375 q^{69} +1804.97 q^{70} -45832.4 q^{71} +15472.1 q^{72} -43416.0 q^{73} +5476.00 q^{74} -3273.00 q^{75} -24695.2 q^{76} +18470.0 q^{77} +416.831 q^{78} +69831.2 q^{79} -3584.00 q^{80} +58140.3 q^{81} -67165.4 q^{82} -104801. q^{83} +576.272 q^{84} +28552.4 q^{85} -44001.6 q^{86} -7795.00 q^{87} -36674.8 q^{88} -41850.2 q^{89} -13538.1 q^{90} -3005.76 q^{91} +13650.8 q^{92} -10381.3 q^{93} +54365.5 q^{94} +21608.3 q^{95} -1144.27 q^{96} -128871. q^{97} +63072.5 q^{98} -138534. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 12 q^{2} - 8 q^{3} + 48 q^{4} - 42 q^{5} + 32 q^{6} + 84 q^{7} - 192 q^{8} + 193 q^{9}+O(q^{10}) \) 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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