LMFDB - Embedded newform 1045.6.a.a.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,6,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1045.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:	$167.601091705$
Analytic rank:	$1$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.58946 q^{2} +14.9980 q^{3} +41.7788 q^{4} -25.0000 q^{5} -128.825 q^{6} -101.857 q^{7} -83.9948 q^{8} -18.0599 q^{9} +O(q^{10})$	\(q-8.58946 q^{2} +14.9980 q^{3} +41.7788 q^{4} -25.0000 q^{5} -128.825 q^{6} -101.857 q^{7} -83.9948 q^{8} -18.0599 q^{9} +214.737 q^{10} +121.000 q^{11} +626.599 q^{12} -1106.27 q^{13} +874.899 q^{14} -374.950 q^{15} -615.452 q^{16} +12.4757 q^{17} +155.125 q^{18} +361.000 q^{19} -1044.47 q^{20} -1527.66 q^{21} -1039.32 q^{22} +4629.12 q^{23} -1259.75 q^{24} +625.000 q^{25} +9502.24 q^{26} -3915.38 q^{27} -4255.48 q^{28} +2482.37 q^{29} +3220.62 q^{30} -2459.26 q^{31} +7974.24 q^{32} +1814.76 q^{33} -107.160 q^{34} +2546.43 q^{35} -754.520 q^{36} -5180.54 q^{37} -3100.80 q^{38} -16591.8 q^{39} +2099.87 q^{40} +16348.1 q^{41} +13121.7 q^{42} -603.684 q^{43} +5055.24 q^{44} +451.497 q^{45} -39761.7 q^{46} +26642.6 q^{47} -9230.55 q^{48} -6432.10 q^{49} -5368.41 q^{50} +187.111 q^{51} -46218.6 q^{52} +34909.5 q^{53} +33631.0 q^{54} -3025.00 q^{55} +8555.48 q^{56} +5414.28 q^{57} -21322.2 q^{58} +40640.4 q^{59} -15665.0 q^{60} +3809.65 q^{61} +21123.7 q^{62} +1839.53 q^{63} -48799.9 q^{64} +27656.7 q^{65} -15587.8 q^{66} +2357.71 q^{67} +521.220 q^{68} +69427.6 q^{69} -21872.5 q^{70} -17855.7 q^{71} +1516.94 q^{72} +36264.3 q^{73} +44498.0 q^{74} +9373.75 q^{75} +15082.2 q^{76} -12324.7 q^{77} +142515. q^{78} -41189.2 q^{79} +15386.3 q^{80} -54334.3 q^{81} -140421. q^{82} -105550. q^{83} -63823.7 q^{84} -311.893 q^{85} +5185.32 q^{86} +37230.5 q^{87} -10163.4 q^{88} -49517.6 q^{89} -3878.11 q^{90} +112681. q^{91} +193399. q^{92} -36884.0 q^{93} -228846. q^{94} -9025.00 q^{95} +119598. q^{96} +143098. q^{97} +55248.2 q^{98} -2185.24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9}+O(q^{10}) $ 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9	\( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9} + 100 q^{10} + 4235 q^{11} - 568 q^{12} - 717 q^{13} - 2585 q^{14} + 675 q^{15} + 3356 q^{16} - 3349 q^{17} - 5533 q^{18} + 12635 q^{19} - 13000 q^{20} + 289 q^{21} - 484 q^{22} - 820 q^{23} - 21748 q^{24} + 21875 q^{25} - 6267 q^{26} - 13650 q^{27} - 6487 q^{28} - 13357 q^{29} + 7275 q^{30} - 15341 q^{31} - 16405 q^{32} - 3267 q^{33} - 1255 q^{34} - 2925 q^{35} + 23487 q^{36} - 511 q^{37} - 1444 q^{38} - 33584 q^{39} + 12450 q^{40} - 36855 q^{41} + 16330 q^{42} + 10991 q^{43} + 62920 q^{44} - 51150 q^{45} - 20443 q^{46} - 33594 q^{47} + 36221 q^{48} + 23422 q^{49} - 2500 q^{50} - 53530 q^{51} + 89382 q^{52} + 13103 q^{53} + 65776 q^{54} - 105875 q^{55} + 130911 q^{56} - 9747 q^{57} + 127808 q^{58} - 161139 q^{59} + 14200 q^{60} - 91587 q^{61} + 131818 q^{62} + 16590 q^{63} - 23186 q^{64} + 17925 q^{65} - 35211 q^{66} + 39210 q^{67} + 26300 q^{68} - 23174 q^{69} + 64625 q^{70} - 167772 q^{71} + 135820 q^{72} - 5106 q^{73} - 256965 q^{74} - 16875 q^{75} + 187720 q^{76} + 14157 q^{77} + 492812 q^{78} - 156897 q^{79} - 83900 q^{80} + 31279 q^{81} + 46818 q^{82} - 185627 q^{83} + 165864 q^{84} + 83725 q^{85} - 159946 q^{86} - 112092 q^{87} - 60258 q^{88} - 144420 q^{89} + 138325 q^{90} - 442480 q^{91} - 205876 q^{92} + 125910 q^{93} - 110044 q^{94} - 315875 q^{95} - 554286 q^{96} + 41200 q^{97} + 41052 q^{98} + 247566 q^{99}+O(q^{100}) \) 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9 + 100 * q^10 + 4235 * q^11 - 568 * q^12 - 717 * q^13 - 2585 * q^14 + 675 * q^15 + 3356 * q^16 - 3349 * q^17 - 5533 * q^18 + 12635 * q^19 - 13000 * q^20 + 289 * q^21 - 484 * q^22 - 820 * q^23 - 21748 * q^24 + 21875 * q^25 - 6267 * q^26 - 13650 * q^27 - 6487 * q^28 - 13357 * q^29 + 7275 * q^30 - 15341 * q^31 - 16405 * q^32 - 3267 * q^33 - 1255 * q^34 - 2925 * q^35 + 23487 * q^36 - 511 * q^37 - 1444 * q^38 - 33584 * q^39 + 12450 * q^40 - 36855 * q^41 + 16330 * q^42 + 10991 * q^43 + 62920 * q^44 - 51150 * q^45 - 20443 * q^46 - 33594 * q^47 + 36221 * q^48 + 23422 * q^49 - 2500 * q^50 - 53530 * q^51 + 89382 * q^52 + 13103 * q^53 + 65776 * q^54 - 105875 * q^55 + 130911 * q^56 - 9747 * q^57 + 127808 * q^58 - 161139 * q^59 + 14200 * q^60 - 91587 * q^61 + 131818 * q^62 + 16590 * q^63 - 23186 * q^64 + 17925 * q^65 - 35211 * q^66 + 39210 * q^67 + 26300 * q^68 - 23174 * q^69 + 64625 * q^70 - 167772 * q^71 + 135820 * q^72 - 5106 * q^73 - 256965 * q^74 - 16875 * q^75 + 187720 * q^76 + 14157 * q^77 + 492812 * q^78 - 156897 * q^79 - 83900 * q^80 + 31279 * q^81 + 46818 * q^82 - 185627 * q^83 + 165864 * q^84 + 83725 * q^85 - 159946 * q^86 - 112092 * q^87 - 60258 * q^88 - 144420 * q^89 + 138325 * q^90 - 442480 * q^91 - 205876 * q^92 + 125910 * q^93 - 110044 * q^94 - 315875 * q^95 - 554286 * q^96 + 41200 * q^97 + 41052 * q^98 + 247566 * 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 $

$2$	−8.58946	−1.51842	−0.759208	−	0.650848i	$-0.774414\pi$
$2$	−8.58946	−1.51842	−0.759208	+	0.650848i	$0.774414\pi$
$3$	14.9980	0.962122	0.481061	−	0.876687i	$-0.340251\pi$
$3$	14.9980	0.962122	0.481061	+	0.876687i	$0.340251\pi$
$4$	41.7788	1.30559
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−128.825	−1.46090
$7$	−101.857	−0.785682	−0.392841	−	0.919606i	$-0.628508\pi$
$7$	−101.857	−0.785682	−0.392841	+	0.919606i	$0.628508\pi$
$8$	−83.9948	−0.464010
$9$	−18.0599	−0.0743205
$10$	214.737	0.679056
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	626.599	1.25614
$13$	−1106.27	−1.81552	−0.907761	−	0.419487i	$-0.862210\pi$
$13$	−1106.27	−1.81552	−0.907761	+	0.419487i	$0.862210\pi$
$14$	874.899	1.19299
$15$	−374.950	−0.430274
$16$	−615.452	−0.601028
$17$	12.4757	0.0104699	0.00523495	−	0.999986i	$-0.498334\pi$
$17$	12.4757	0.0104699	0.00523495	+	0.999986i	$0.498334\pi$
$18$	155.125	0.112849
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−1044.47	−0.583877
$21$	−1527.66	−0.755922
$22$	−1039.32	−0.457820
$23$	4629.12	1.82465	0.912324	−	0.409470i	$-0.134286\pi$
$23$	4629.12	1.82465	0.912324	+	0.409470i	$0.134286\pi$
$24$	−1259.75	−0.446435
$25$	625.000	0.200000
$26$	9502.24	2.75672
$27$	−3915.38	−1.03363
$28$	−4255.48	−1.02578
$29$	2482.37	0.548114	0.274057	−	0.961713i	$-0.411634\pi$
$29$	2482.37	0.548114	0.274057	+	0.961713i	$0.411634\pi$
$30$	3220.62	0.653335
$31$	−2459.26	−0.459621	−0.229811	−	0.973235i	$-0.573811\pi$
$31$	−2459.26	−0.459621	−0.229811	+	0.973235i	$0.573811\pi$
$32$	7974.24	1.37662
$33$	1814.76	0.290091
$34$	−107.160	−0.0158977
$35$	2546.43	0.351368
$36$	−754.520	−0.0970319
$37$	−5180.54	−0.622115	−0.311057	−	0.950391i	$-0.600683\pi$
$37$	−5180.54	−0.622115	−0.311057	+	0.950391i	$0.600683\pi$
$38$	−3100.80	−0.348349
$39$	−16591.8	−1.74676
$40$	2099.87	0.207512
$41$	16348.1	1.51882	0.759411	−	0.650611i	$-0.225487\pi$
$41$	16348.1	1.51882	0.759411	+	0.650611i	$0.225487\pi$
$42$	13121.7	1.14781
$43$	−603.684	−0.0497896	−0.0248948	−	0.999690i	$-0.507925\pi$
$43$	−603.684	−0.0497896	−0.0248948	+	0.999690i	$0.507925\pi$
$44$	5055.24	0.393650
$45$	451.497	0.0332371
$46$	−39761.7	−2.77057
$47$	26642.6	1.75927	0.879634	−	0.475651i	$-0.157788\pi$
$47$	26642.6	1.75927	0.879634	+	0.475651i	$0.157788\pi$
$48$	−9230.55	−0.578262
$49$	−6432.10	−0.382703
$50$	−5368.41	−0.303683
$51$	187.111	0.0100733
$52$	−46218.6	−2.37033
$53$	34909.5	1.70708	0.853539	−	0.521029i	$-0.174452\pi$
$53$	34909.5	1.70708	0.853539	+	0.521029i	$0.174452\pi$
$54$	33631.0	1.56948
$55$	−3025.00	−0.134840
$56$	8555.48	0.364565
$57$	5414.28	0.220726
$58$	−21322.2	−0.832265
$59$	40640.4	1.51995	0.759973	−	0.649955i	$-0.225212\pi$
$59$	40640.4	1.51995	0.759973	+	0.649955i	$0.225212\pi$
$60$	−15665.0	−0.561761
$61$	3809.65	0.131087	0.0655437	−	0.997850i	$-0.479122\pi$
$61$	3809.65	0.131087	0.0655437	+	0.997850i	$0.479122\pi$
$62$	21123.7	0.697896
$63$	1839.53	0.0583923
$64$	−48799.9	−1.48926
$65$	27656.7	0.811927
$66$	−15587.8	−0.440479
$67$	2357.71	0.0641657	0.0320829	−	0.999485i	$-0.489786\pi$
$67$	2357.71	0.0641657	0.0320829	+	0.999485i	$0.489786\pi$
$68$	521.220	0.0136694
$69$	69427.6	1.75553
$70$	−21872.5	−0.533523
$71$	−17855.7	−0.420370	−0.210185	−	0.977662i	$-0.567407\pi$
$71$	−17855.7	−0.420370	−0.210185	+	0.977662i	$0.567407\pi$
$72$	1516.94	0.0344855
$73$	36264.3	0.796474	0.398237	−	0.917283i	$-0.369622\pi$
$73$	36264.3	0.796474	0.398237	+	0.917283i	$0.369622\pi$
$74$	44498.0	0.944629
$75$	9373.75	0.192424
$76$	15082.2	0.299522
$77$	−12324.7	−0.236892
$78$	142515.	2.65230
$79$	−41189.2	−0.742533	−0.371267	−	0.928526i	$-0.621076\pi$
$79$	−41189.2	−0.742533	−0.371267	+	0.928526i	$0.621076\pi$
$80$	15386.3	0.268788
$81$	−54334.3	−0.920156
$82$	−140421.	−2.30621
$83$	−105550.	−1.68176	−0.840879	−	0.541223i	$-0.817962\pi$
$83$	−105550.	−1.68176	−0.840879	+	0.541223i	$0.817962\pi$
$84$	−63823.7	−0.986924
$85$	−311.893	−0.00468228
$86$	5185.32	0.0756013
$87$	37230.5	0.527353
$88$	−10163.4	−0.139904
$89$	−49517.6	−0.662651	−0.331325	−	0.943517i	$-0.607496\pi$
$89$	−49517.6	−0.662651	−0.331325	+	0.943517i	$0.607496\pi$
$90$	−3878.11	−0.0504678
$91$	112681.	1.42642
$92$	193399.	2.38224
$93$	−36884.0	−0.442212
$94$	−228846.	−2.67130
$95$	−9025.00	−0.102598
$96$	119598.	1.32448
$97$	143098.	1.54421	0.772103	−	0.635497i	$-0.219205\pi$
$97$	143098.	1.54421	0.772103	+	0.635497i	$0.219205\pi$
$98$	55248.2	0.581103
$99$	−2185.24	−0.0224085
$100$	26111.8	0.261118
$101$	−78985.3	−0.770447	−0.385224	−	0.922823i	$-0.625876\pi$
$101$	−78985.3	−0.770447	−0.385224	+	0.922823i	$0.625876\pi$
$102$	−1607.18	−0.0152955
$103$	−185482.	−1.72269	−0.861347	−	0.508017i	$-0.830379\pi$
$103$	−185482.	−1.72269	−0.861347	+	0.508017i	$0.830379\pi$
$104$	92920.7	0.842421
$105$	38191.4	0.338059
$106$	−299853.	−2.59206
$107$	−168418.	−1.42210	−0.711048	−	0.703143i	$-0.751779\pi$
$107$	−168418.	−1.42210	−0.711048	+	0.703143i	$0.751779\pi$
$108$	−163580.	−1.34949
$109$	−139629.	−1.12567	−0.562833	−	0.826571i	$-0.690289\pi$
$109$	−139629.	−1.12567	−0.562833	+	0.826571i	$0.690289\pi$
$110$	25983.1	0.204743
$111$	−77697.7	−0.598550
$112$	62688.3	0.472217
$113$	−52681.2	−0.388114	−0.194057	−	0.980990i	$-0.562165\pi$
$113$	−52681.2	−0.388114	−0.194057	+	0.980990i	$0.562165\pi$
$114$	−46505.7	−0.335154
$115$	−115728.	−0.816007
$116$	103710.	0.715611
$117$	19979.0	0.134931
$118$	−349079.	−2.30791
$119$	−1270.74	−0.00822602
$120$	31493.9	0.199652
$121$	14641.0	0.0909091
$122$	−32722.9	−0.199045
$123$	245189.	1.46129
$124$	−102745.	−0.600076
$125$	−15625.0	−0.0894427
$126$	−15800.6	−0.0886638
$127$	348938.	1.91973	0.959863	−	0.280470i	$-0.0904903\pi$
$127$	348938.	1.91973	0.959863	+	0.280470i	$0.0904903\pi$
$128$	163989.	0.884689
$129$	−9054.05	−0.0479037
$130$	−237556.	−1.23284
$131$	−187351.	−0.953843	−0.476922	−	0.878946i	$-0.658247\pi$
$131$	−187351.	−0.953843	−0.476922	+	0.878946i	$0.658247\pi$
$132$	75818.5	0.378739
$133$	−36770.5	−0.180248
$134$	−20251.4	−0.0974303
$135$	97884.4	0.462252
$136$	−1047.89	−0.00485814
$137$	−18620.1	−0.0847581	−0.0423790	−	0.999102i	$-0.513494\pi$
$137$	−18620.1	−0.0847581	−0.0423790	+	0.999102i	$0.513494\pi$
$138$	−596345.	−2.66563
$139$	60165.5	0.264125	0.132063	−	0.991241i	$-0.457840\pi$
$139$	60165.5	0.264125	0.132063	+	0.991241i	$0.457840\pi$
$140$	106387.	0.458742
$141$	399586.	1.69263
$142$	153371.	0.638296
$143$	−133858.	−0.547401
$144$	11115.0	0.0446686
$145$	−62059.1	−0.245124
$146$	−311490.	−1.20938
$147$	−96468.6	−0.368208
$148$	−216437.	−0.812225
$149$	−99091.0	−0.365652	−0.182826	−	0.983145i	$-0.558525\pi$
$149$	−99091.0	−0.365652	−0.182826	+	0.983145i	$0.558525\pi$
$150$	−80515.5	−0.292180
$151$	310003.	1.10643	0.553215	−	0.833038i	$-0.313401\pi$
$151$	310003.	1.10643	0.553215	+	0.833038i	$0.313401\pi$
$152$	−30322.1	−0.106451
$153$	−225.310	−0.000778128 0
$154$	105863.	0.359701
$155$	61481.5	0.205549
$156$	−693186.	−2.28054
$157$	248076.	0.803221	0.401611	−	0.915811i	$-0.368451\pi$
$157$	248076.	0.803221	0.401611	+	0.915811i	$0.368451\pi$
$158$	353793.	1.12747
$159$	523572.	1.64242
$160$	−199356.	−0.615643
$161$	−471510.	−1.43359
$162$	466702.	1.39718
$163$	−405601.	−1.19572	−0.597861	−	0.801600i	$-0.703982\pi$
$163$	−405601.	−1.19572	−0.597861	+	0.801600i	$0.703982\pi$
$164$	683003.	1.98296
$165$	−45369.0	−0.129733
$166$	906619.	2.55361
$167$	273156.	0.757912	0.378956	−	0.925415i	$-0.376283\pi$
$167$	273156.	0.757912	0.378956	+	0.925415i	$0.376283\pi$
$168$	128315.	0.350756
$169$	852535.	2.29612
$170$	2678.99	0.00710966
$171$	−6519.61	−0.0170503
$172$	−25221.2	−0.0650047
$173$	−337079.	−0.856281	−0.428140	−	0.903712i	$-0.640831\pi$
$173$	−337079.	−0.856281	−0.428140	+	0.903712i	$0.640831\pi$
$174$	−319790.	−0.800741
$175$	−63660.8	−0.157136
$176$	−74469.7	−0.181217
$177$	609525.	1.46237
$178$	425330.	1.00618
$179$	333057.	0.776938	0.388469	−	0.921462i	$-0.373004\pi$
$179$	333057.	0.776938	0.388469	+	0.921462i	$0.373004\pi$
$180$	18863.0	0.0433940
$181$	−422234.	−0.957982	−0.478991	−	0.877820i	$-0.658997\pi$
$181$	−422234.	−0.957982	−0.478991	+	0.877820i	$0.658997\pi$
$182$	−967872.	−2.16591
$183$	57137.2	0.126122
$184$	−388822.	−0.846655
$185$	129513.	0.278218
$186$	316813.	0.671462
$187$	1509.56	0.00315679
$188$	1.11310e6	2.29688
$189$	398810.	0.812103
$190$	77519.9	0.155786
$191$	481187.	0.954401	0.477200	−	0.878794i	$-0.341652\pi$
$191$	481187.	0.954401	0.477200	+	0.878794i	$0.341652\pi$
$192$	−731901.	−1.43285
$193$	−281783.	−0.544530	−0.272265	−	0.962222i	$-0.587773\pi$
$193$	−281783.	−0.544530	−0.272265	+	0.962222i	$0.587773\pi$
$194$	−1.22914e6	−2.34475
$195$	414795.	0.781173
$196$	−268725.	−0.499653
$197$	207492.	0.380923	0.190461	−	0.981695i	$-0.439002\pi$
$197$	207492.	0.380923	0.190461	+	0.981695i	$0.439002\pi$
$198$	18770.1	0.0340254
$199$	−158732.	−0.284140	−0.142070	−	0.989857i	$-0.545376\pi$
$199$	−158732.	−0.284140	−0.142070	+	0.989857i	$0.545376\pi$
$200$	−52496.8	−0.0928020
$201$	35360.9	0.0617353
$202$	678441.	1.16986
$203$	−252847.	−0.430643
$204$	7817.26	0.0131516
$205$	−408702.	−0.679238
$206$	1.59319e6	2.61577
$207$	−83601.3	−0.135609
$208$	680855.	1.09118
$209$	43681.0	0.0691714
$210$	−328043.	−0.513314
$211$	−426244.	−0.659101	−0.329550	−	0.944138i	$-0.606897\pi$
$211$	−426244.	−0.659101	−0.329550	+	0.944138i	$0.606897\pi$
$212$	1.45848e6	2.22874
$213$	−267800.	−0.404447
$214$	1.44662e6	2.15933
$215$	15092.1	0.0222666
$216$	328871.	0.479614
$217$	250493.	0.361116
$218$	1.19934e6	1.70923
$219$	543892.	0.766306
$220$	−126381.	−0.176045
$221$	−13801.5	−0.0190084
$222$	667381.	0.908849
$223$	−233193.	−0.314017	−0.157008	−	0.987597i	$-0.550185\pi$
$223$	−233193.	−0.314017	−0.157008	+	0.987597i	$0.550185\pi$
$224$	−812234.	−1.08159
$225$	−11287.4	−0.0148641
$226$	452503.	0.589319
$227$	1.39126e6	1.79202	0.896012	−	0.444030i	$-0.146452\pi$
$227$	1.39126e6	1.79202	0.896012	+	0.444030i	$0.146452\pi$
$228$	226202.	0.288177
$229$	−355639.	−0.448147	−0.224074	−	0.974572i	$-0.571936\pi$
$229$	−355639.	−0.448147	−0.224074	+	0.974572i	$0.571936\pi$
$230$	994041.	1.23904
$231$	−184846.	−0.227919
$232$	−208506.	−0.254330
$233$	−1.13227e6	−1.36635	−0.683174	−	0.730255i	$-0.739401\pi$
$233$	−1.13227e6	−1.36635	−0.683174	+	0.730255i	$0.739401\pi$
$234$	−171609.	−0.204881
$235$	−666065.	−0.786769
$236$	1.69791e6	1.98442
$237$	−617756.	−0.714408
$238$	10915.0	0.0124905
$239$	−484010.	−0.548100	−0.274050	−	0.961715i	$-0.588363\pi$
$239$	−484010.	−0.548100	−0.274050	+	0.961715i	$0.588363\pi$
$240$	230764.	0.258607
$241$	−958550.	−1.06310	−0.531548	−	0.847028i	$-0.678389\pi$
$241$	−958550.	−1.06310	−0.531548	+	0.847028i	$0.678389\pi$
$242$	−125758.	−0.138038
$243$	136531.	0.148325
$244$	159163.	0.171146
$245$	160802.	0.171150
$246$	−2.10604e6	−2.21885
$247$	−399363.	−0.416510
$248$	206565.	0.213269
$249$	−1.58304e6	−1.61806
$250$	134210.	0.135811
$251$	−135008.	−0.135262	−0.0676311	−	0.997710i	$-0.521544\pi$
$251$	−135008.	−0.135262	−0.0676311	+	0.997710i	$0.521544\pi$
$252$	76853.4	0.0762363
$253$	560124.	0.550152
$254$	−2.99719e6	−2.91494
$255$	−4677.77	−0.00450493
$256$	153017.	0.145929
$257$	770427.	0.727610	0.363805	−	0.931475i	$-0.381477\pi$
$257$	770427.	0.727610	0.363805	+	0.931475i	$0.381477\pi$
$258$	77769.4	0.0727377
$259$	527675.	0.488784
$260$	1.15546e6	1.06004
$261$	−44831.2	−0.0407361
$262$	1.60924e6	1.44833
$263$	−120791.	−0.107682	−0.0538412	−	0.998550i	$-0.517146\pi$
$263$	−120791.	−0.107682	−0.0538412	+	0.998550i	$0.517146\pi$
$264$	−152430.	−0.134605
$265$	−872736.	−0.763429
$266$	315839.	0.273691
$267$	−742665.	−0.637551
$268$	98502.3	0.0837740
$269$	1.46523e6	1.23460	0.617299	−	0.786729i	$-0.288227\pi$
$269$	1.46523e6	1.23460	0.617299	+	0.786729i	$0.288227\pi$
$270$	−840774.	−0.701892
$271$	−570509.	−0.471889	−0.235944	−	0.971767i	$-0.575818\pi$
$271$	−570509.	−0.471889	−0.235944	+	0.971767i	$0.575818\pi$
$272$	−7678.20	−0.00629270
$273$	1.69000e6	1.37239
$274$	159937.	0.128698
$275$	75625.0	0.0603023
$276$	2.90060e6	2.29200
$277$	−2.35380e6	−1.84319	−0.921597	−	0.388149i	$-0.873115\pi$
$277$	−2.35380e6	−1.84319	−0.921597	+	0.388149i	$0.873115\pi$
$278$	−516789.	−0.401052
$279$	44413.9	0.0341593
$280$	−213887.	−0.163038
$281$	−154261.	−0.116544	−0.0582722	−	0.998301i	$-0.518559\pi$
$281$	−154261.	−0.116544	−0.0582722	+	0.998301i	$0.518559\pi$
$282$	−3.43223e6	−2.57012
$283$	1.49727e6	1.11131	0.555654	−	0.831414i	$-0.312468\pi$
$283$	1.49727e6	1.11131	0.555654	+	0.831414i	$0.312468\pi$
$284$	−745991.	−0.548830
$285$	−135357.	−0.0987117
$286$	1.14977e6	0.831182
$287$	−1.66517e6	−1.19331
$288$	−144014.	−0.102311
$289$	−1.41970e6	−0.999890
$290$	533055.	0.372200
$291$	2.14619e6	1.48572
$292$	1.51508e6	1.03987
$293$	−485837.	−0.330614	−0.165307	−	0.986242i	$-0.552861\pi$
$293$	−485837.	−0.330614	−0.165307	+	0.986242i	$0.552861\pi$
$294$	828613.	0.559092
$295$	−1.01601e6	−0.679740
$296$	435138.	0.288667
$297$	−473761.	−0.311651
$298$	851138.	0.555213
$299$	−5.12105e6	−3.31269
$300$	391624.	0.251227
$301$	61489.6	0.0391188
$302$	−2.66276e6	−1.68002
$303$	−1.18462e6	−0.741265
$304$	−222178.	−0.137885
$305$	−95241.4	−0.0586241
$306$	1935.29	0.00118152
$307$	−1.02917e6	−0.623223	−0.311611	−	0.950210i	$-0.600869\pi$
$307$	−1.02917e6	−0.623223	−0.311611	+	0.950210i	$0.600869\pi$
$308$	−514913.	−0.309284
$309$	−2.78186e6	−1.65744
$310$	−528093.	−0.312109
$311$	1.95057e6	1.14357	0.571783	−	0.820405i	$-0.306252\pi$
$311$	1.95057e6	1.14357	0.571783	+	0.820405i	$0.306252\pi$
$312$	1.39363e6	0.810512
$313$	−689983.	−0.398086	−0.199043	−	0.979991i	$-0.563783\pi$
$313$	−689983.	−0.398086	−0.199043	+	0.979991i	$0.563783\pi$
$314$	−2.13084e6	−1.21962
$315$	−45988.2	−0.0261138
$316$	−1.72084e6	−0.969443
$317$	319576.	0.178618	0.0893091	−	0.996004i	$-0.471534\pi$
$317$	319576.	0.178618	0.0893091	+	0.996004i	$0.471534\pi$
$318$	−4.49720e6	−2.49387
$319$	300366.	0.165263
$320$	1.22000e6	0.666015
$321$	−2.52593e6	−1.36823
$322$	4.05001e6	2.17679
$323$	4503.73	0.00240196
$324$	−2.27002e6	−1.20134
$325$	−691417.	−0.363105
$326$	3.48389e6	1.81560
$327$	−2.09416e6	−1.08303
$328$	−1.37315e6	−0.704749
$329$	−2.71374e6	−1.38223
$330$	389695.	0.196988
$331$	794125.	0.398400	0.199200	−	0.979959i	$-0.436166\pi$
$331$	794125.	0.398400	0.199200	+	0.979959i	$0.436166\pi$
$332$	−4.40976e6	−2.19568
$333$	93559.8	0.0462358
$334$	−2.34626e6	−1.15083
$335$	−58942.7	−0.0286958
$336$	940199.	0.454330
$337$	−2.82020e6	−1.35271	−0.676356	−	0.736575i	$-0.736442\pi$
$337$	−2.82020e6	−1.35271	−0.676356	+	0.736575i	$0.736442\pi$
$338$	−7.32281e6	−3.48647
$339$	−790113.	−0.373413
$340$	−13030.5	−0.00611313
$341$	−297570.	−0.138581
$342$	56000.0	0.0258894
$343$	2.36707e6	1.08637
$344$	50706.3	0.0231029
$345$	−1.73569e6	−0.785099
$346$	2.89532e6	1.30019
$347$	1.33439e6	0.594920	0.297460	−	0.954734i	$-0.403861\pi$
$347$	1.33439e6	0.594920	0.297460	+	0.954734i	$0.403861\pi$
$348$	1.55545e6	0.688505
$349$	176853.	0.0777231	0.0388615	−	0.999245i	$-0.487627\pi$
$349$	176853.	0.0777231	0.0388615	+	0.999245i	$0.487627\pi$
$350$	546812.	0.238599
$351$	4.33145e6	1.87657
$352$	964883.	0.415067
$353$	565927.	0.241726	0.120863	−	0.992669i	$-0.461434\pi$
$353$	565927.	0.241726	0.120863	+	0.992669i	$0.461434\pi$
$354$	−5.23549e6	−2.22049
$355$	446393.	0.187995
$356$	−2.06879e6	−0.865149
$357$	−19058.6	−0.00791444
$358$	−2.86078e6	−1.17971
$359$	−712457.	−0.291758	−0.145879	−	0.989302i	$-0.546601\pi$
$359$	−712457.	−0.291758	−0.145879	+	0.989302i	$0.546601\pi$
$360$	−37923.4	−0.0154224
$361$	130321.	0.0526316
$362$	3.62677e6	1.45462
$363$	219586.	0.0874657
$364$	4.70770e6	1.86232
$365$	−906607.	−0.356194
$366$	−490778.	−0.191506
$367$	1.50310e6	0.582537	0.291269	−	0.956641i	$-0.405923\pi$
$367$	1.50310e6	0.582537	0.291269	+	0.956641i	$0.405923\pi$
$368$	−2.84900e6	−1.09666
$369$	−295244.	−0.112880
$370$	−1.11245e6	−0.422451
$371$	−3.55578e6	−1.34122
$372$	−1.54097e6	−0.577347
$373$	−1.43524e6	−0.534137	−0.267068	−	0.963678i	$-0.586055\pi$
$373$	−1.43524e6	−0.534137	−0.267068	+	0.963678i	$0.586055\pi$
$374$	−12966.3	−0.00479333
$375$	−234344.	−0.0860548
$376$	−2.23784e6	−0.816318
$377$	−2.74616e6	−0.995113
$378$	−3.42556e6	−1.23311
$379$	−1.07968e6	−0.386098	−0.193049	−	0.981189i	$-0.561838\pi$
$379$	−1.07968e6	−0.386098	−0.193049	+	0.981189i	$0.561838\pi$
$380$	−377054.	−0.133951
$381$	5.23338e6	1.84701
$382$	−4.13314e6	−1.44918
$383$	69759.0	0.0242998	0.0121499	−	0.999926i	$-0.496132\pi$
$383$	69759.0	0.0242998	0.0121499	+	0.999926i	$0.496132\pi$
$384$	2.45951e6	0.851179
$385$	308118.	0.105941
$386$	2.42036e6	0.826823
$387$	10902.5	0.00370039
$388$	5.97848e6	2.01610
$389$	4.41349e6	1.47880	0.739398	−	0.673268i	$-0.235110\pi$
$389$	4.41349e6	1.47880	0.739398	+	0.673268i	$0.235110\pi$
$390$	−3.56287e6	−1.18615
$391$	57751.5	0.0191039
$392$	540263.	0.177578
$393$	−2.80989e6	−0.917714
$394$	−1.78225e6	−0.578399
$395$	1.02973e6	0.332071
$396$	−91296.9	−0.0292562
$397$	2.01974e6	0.643160	0.321580	−	0.946882i	$-0.395786\pi$
$397$	2.01974e6	0.643160	0.321580	+	0.946882i	$0.395786\pi$
$398$	1.36342e6	0.431442
$399$	−551484.	−0.173421
$400$	−384658.	−0.120206
$401$	−2.55469e6	−0.793374	−0.396687	−	0.917954i	$-0.629840\pi$
$401$	−2.55469e6	−0.793374	−0.396687	+	0.917954i	$0.629840\pi$
$402$	−303731.	−0.0937399
$403$	2.72060e6	0.834453
$404$	−3.29991e6	−1.00589
$405$	1.35836e6	0.411506
$406$	2.17182e6	0.653896
$407$	−626845.	−0.187575
$408$	−15716.3	−0.00467413
$409$	−4.29813e6	−1.27049	−0.635245	−	0.772311i	$-0.719101\pi$
$409$	−4.29813e6	−1.27049	−0.635245	+	0.772311i	$0.719101\pi$
$410$	3.51053e6	1.03137
$411$	−279265.	−0.0815476
$412$	−7.74921e6	−2.24913
$413$	−4.13952e6	−1.19419
$414$	718090.	0.205910
$415$	2.63875e6	0.752105
$416$	−8.82164e6	−2.49929
$417$	902362.	0.254121
$418$	−375196.	−0.105031
$419$	−3.31460e6	−0.922351	−0.461176	−	0.887309i	$-0.652572\pi$
$419$	−3.31460e6	−0.922351	−0.461176	+	0.887309i	$0.652572\pi$
$420$	1.59559e6	0.441366
$421$	−6.61492e6	−1.81895	−0.909473	−	0.415764i	$-0.863514\pi$
$421$	−6.61492e6	−1.81895	−0.909473	+	0.415764i	$0.863514\pi$
$422$	3.66120e6	1.00079
$423$	−481162.	−0.130750
$424$	−2.93221e6	−0.792102
$425$	7797.31	0.00209398
$426$	2.30026e6	0.614119
$427$	−388041.	−0.102993
$428$	−7.03631e6	−1.85667
$429$	−2.00761e6	−0.526667
$430$	−129633.	−0.0338099
$431$	−602321.	−0.156183	−0.0780917	−	0.996946i	$-0.524883\pi$
$431$	−602321.	−0.156183	−0.0780917	+	0.996946i	$0.524883\pi$
$432$	2.40973e6	0.621239
$433$	−3.83159e6	−0.982107	−0.491054	−	0.871129i	$-0.663388\pi$
$433$	−3.83159e6	−0.982107	−0.491054	+	0.871129i	$0.663388\pi$
$434$	−2.15160e6	−0.548325
$435$	−930763.	−0.235839
$436$	−5.83354e6	−1.46966
$437$	1.67111e6	0.418603
$438$	−4.67173e6	−1.16357
$439$	−862738.	−0.213657	−0.106829	−	0.994277i	$-0.534070\pi$
$439$	−862738.	−0.213657	−0.106829	+	0.994277i	$0.534070\pi$
$440$	254084.	0.0625671
$441$	116163.	0.0284427
$442$	118547.	0.0288626
$443$	−5.67125e6	−1.37300	−0.686499	−	0.727131i	$-0.740853\pi$
$443$	−5.67125e6	−1.37300	−0.686499	+	0.727131i	$0.740853\pi$
$444$	−3.24612e6	−0.781460
$445$	1.23794e6	0.296346
$446$	2.00300e6	0.476808
$447$	−1.48617e6	−0.351802
$448$	4.97063e6	1.17008
$449$	1.70948e6	0.400174	0.200087	−	0.979778i	$-0.435878\pi$
$449$	1.70948e6	0.400174	0.200087	+	0.979778i	$0.435878\pi$
$450$	96952.8	0.0225699
$451$	1.97812e6	0.457942
$452$	−2.20096e6	−0.506717
$453$	4.64943e6	1.06452
$454$	−1.19502e7	−2.72104
$455$	−2.81703e6	−0.637916
$456$	−454771.	−0.102419
$457$	543304.	0.121689	0.0608446	−	0.998147i	$-0.480621\pi$
$457$	543304.	0.121689	0.0608446	+	0.998147i	$0.480621\pi$
$458$	3.05475e6	0.680474
$459$	−48847.1	−0.0108220
$460$	−4.83498e6	−1.06537
$461$	−8.83295e6	−1.93577	−0.967885	−	0.251394i	$-0.919111\pi$
$461$	−8.83295e6	−1.93577	−0.967885	+	0.251394i	$0.919111\pi$
$462$	1.58773e6	0.346076
$463$	−3.69969e6	−0.802070	−0.401035	−	0.916063i	$-0.631349\pi$
$463$	−3.69969e6	−0.802070	−0.401035	+	0.916063i	$0.631349\pi$
$464$	−1.52778e6	−0.329432
$465$	922099.	0.197763
$466$	9.72562e6	2.07469
$467$	5.36028e6	1.13735	0.568677	−	0.822561i	$-0.307456\pi$
$467$	5.36028e6	1.13735	0.568677	+	0.822561i	$0.307456\pi$
$468$	834701.	0.176164
$469$	−240150.	−0.0504139
$470$	5.72114e6	1.19464
$471$	3.72064e6	0.772797
$472$	−3.41358e6	−0.705270
$473$	−73045.8	−0.0150121
$474$	5.30619e6	1.08477
$475$	225625.	0.0458831
$476$	−53090.1	−0.0107398
$477$	−630460.	−0.126871
$478$	4.15739e6	0.832244
$479$	−6.09423e6	−1.21361	−0.606806	−	0.794850i	$-0.707549\pi$
$479$	−6.09423e6	−1.21361	−0.606806	+	0.794850i	$0.707549\pi$
$480$	−2.98994e6	−0.592324
$481$	5.73106e6	1.12946
$482$	8.23343e6	1.61422
$483$	−7.07170e6	−1.37929
$484$	611684.	0.118690
$485$	−3.57746e6	−0.690590
$486$	−1.17272e6	−0.225219
$487$	612452.	0.117017	0.0585086	−	0.998287i	$-0.481366\pi$
$487$	612452.	0.117017	0.0585086	+	0.998287i	$0.481366\pi$
$488$	−319991.	−0.0608259
$489$	−6.08321e6	−1.15043
$490$	−1.38121e6	−0.259877
$491$	4.24144e6	0.793981	0.396990	−	0.917823i	$-0.370055\pi$
$491$	4.24144e6	0.793981	0.396990	+	0.917823i	$0.370055\pi$
$492$	1.02437e7	1.90785
$493$	30969.3	0.00573870
$494$	3.43031e6	0.632435
$495$	54631.1	0.0100214
$496$	1.51356e6	0.276245
$497$	1.81873e6	0.330277
$498$	1.35975e7	2.45689
$499$	−6.31322e6	−1.13501	−0.567505	−	0.823370i	$-0.692091\pi$
$499$	−6.31322e6	−1.13501	−0.567505	+	0.823370i	$0.692091\pi$
$500$	−652794.	−0.116775
$501$	4.09679e6	0.729204
$502$	1.15965e6	0.205384
$503$	9.89756e6	1.74425	0.872124	−	0.489285i	$-0.162742\pi$
$503$	9.89756e6	1.74425	0.872124	+	0.489285i	$0.162742\pi$
$504$	−154511.	−0.0270946
$505$	1.97463e6	0.344555
$506$	−4.81116e6	−0.835360
$507$	1.27863e7	2.20915
$508$	1.45782e7	2.50637
$509$	−9.74841e6	−1.66778	−0.833891	−	0.551929i	$-0.813892\pi$
$509$	−9.74841e6	−1.66778	−0.833891	+	0.551929i	$0.813892\pi$
$510$	40179.5	0.00684036
$511$	−3.69378e6	−0.625776
$512$	−6.56200e6	−1.10627
$513$	−1.41345e6	−0.237130
$514$	−6.61755e6	−1.10481
$515$	4.63704e6	0.770412
$516$	−378268.	−0.0625425
$517$	3.22375e6	0.530439
$518$	−4.53245e6	−0.742178
$519$	−5.05551e6	−0.823847
$520$	−2.32302e6	−0.376742
$521$	4.90838e6	0.792217	0.396108	−	0.918204i	$-0.370360\pi$
$521$	4.90838e6	0.792217	0.396108	+	0.918204i	$0.370360\pi$
$522$	385076.	0.0618543
$523$	4.30288e6	0.687868	0.343934	−	0.938994i	$-0.388240\pi$
$523$	4.30288e6	0.687868	0.343934	+	0.938994i	$0.388240\pi$
$524$	−7.82729e6	−1.24533
$525$	−954785.	−0.151184
$526$	1.03753e6	0.163507
$527$	−30681.0	−0.00481219
$528$	−1.11690e6	−0.174353
$529$	1.49924e7	2.32934
$530$	7.49633e6	1.15920
$531$	−733960.	−0.112963
$532$	−1.53623e6	−0.235329
$533$	−1.80853e7	−2.75746
$534$	6.37910e6	0.968068
$535$	4.21045e6	0.635981
$536$	−198035.	−0.0297736
$537$	4.99519e6	0.747509
$538$	−1.25856e7	−1.87463
$539$	−778284.	−0.115389
$540$	4.08950e6	0.603511
$541$	−9.22099e6	−1.35452	−0.677258	−	0.735745i	$-0.736832\pi$
$541$	−9.22099e6	−1.35452	−0.677258	+	0.735745i	$0.736832\pi$
$542$	4.90037e6	0.716523
$543$	−6.33267e6	−0.921696
$544$	99484.2	0.0144131
$545$	3.49073e6	0.503413
$546$	−1.45162e7	−2.08387
$547$	−1.30097e6	−0.185909	−0.0929544	−	0.995670i	$-0.529631\pi$
$547$	−1.30097e6	−0.185909	−0.0929544	+	0.995670i	$0.529631\pi$
$548$	−777927.	−0.110659
$549$	−68801.9	−0.00974248
$550$	−649578.	−0.0915640
$551$	896134.	0.125746
$552$	−5.83156e6	−0.814586
$553$	4.19542e6	0.583395
$554$	2.02179e7	2.79873
$555$	1.94244e6	0.267680
$556$	2.51364e6	0.344839
$557$	−4.94824e6	−0.675792	−0.337896	−	0.941184i	$-0.609715\pi$
$557$	−4.94824e6	−0.675792	−0.337896	+	0.941184i	$0.609715\pi$
$558$	−381491.	−0.0518680
$559$	667836.	0.0903941
$560$	−1.56721e6	−0.211182
$561$	22640.4	0.00303722
$562$	1.32502e6	0.176963
$563$	2.22662e6	0.296057	0.148028	−	0.988983i	$-0.452707\pi$
$563$	2.22662e6	0.296057	0.148028	+	0.988983i	$0.452707\pi$
$564$	1.66942e7	2.20988
$565$	1.31703e6	0.173570
$566$	−1.28608e7	−1.68743
$567$	5.53434e6	0.722950
$568$	1.49979e6	0.195056
$569$	−1.28039e7	−1.65792	−0.828959	−	0.559310i	$-0.811066\pi$
$569$	−1.28039e7	−1.65792	−0.828959	+	0.559310i	$0.811066\pi$
$570$	1.16264e6	0.149885
$571$	−8.20632e6	−1.05332	−0.526658	−	0.850077i	$-0.676555\pi$
$571$	−8.20632e6	−1.05332	−0.526658	+	0.850077i	$0.676555\pi$
$572$	−5.59244e6	−0.714680
$573$	7.21685e6	0.918250
$574$	1.43029e7	1.81194
$575$	2.89320e6	0.364930
$576$	881320.	0.110682
$577$	−2.22032e6	−0.277636	−0.138818	−	0.990318i	$-0.544330\pi$
$577$	−2.22032e6	−0.277636	−0.138818	+	0.990318i	$0.544330\pi$
$578$	1.21945e7	1.51825
$579$	−4.22618e6	−0.523904
$580$	−2.59276e6	−0.320031
$581$	1.07511e7	1.32133
$582$	−1.84346e7	−2.25593
$583$	4.22404e6	0.514703
$584$	−3.04601e6	−0.369572
$585$	−499476.	−0.0603428
$586$	4.17307e6	0.502010
$587$	−4.37234e6	−0.523744	−0.261872	−	0.965103i	$-0.584340\pi$
$587$	−4.37234e6	−0.523744	−0.261872	+	0.965103i	$0.584340\pi$
$588$	−4.03035e6	−0.480727
$589$	−887792.	−0.105444
$590$	8.72698e6	1.03213
$591$	3.11197e6	0.366494
$592$	3.18837e6	0.373908
$593$	−1.04895e6	−0.122495	−0.0612474	−	0.998123i	$-0.519508\pi$
$593$	−1.04895e6	−0.122495	−0.0612474	+	0.998123i	$0.519508\pi$
$594$	4.06935e6	0.473215
$595$	31768.5	0.00367879
$596$	−4.13991e6	−0.477392
$597$	−2.38066e6	−0.273377
$598$	4.39870e7	5.03004
$599$	−1.29838e7	−1.47855	−0.739274	−	0.673405i	$-0.764831\pi$
$599$	−1.29838e7	−1.47855	−0.739274	+	0.673405i	$0.764831\pi$
$600$	−787347.	−0.0892869
$601$	5.73753e6	0.647946	0.323973	−	0.946066i	$-0.394981\pi$
$601$	5.73753e6	0.647946	0.323973	+	0.946066i	$0.394981\pi$
$602$	−528162.	−0.0593986
$603$	−42579.9	−0.00476883
$604$	1.29516e7	1.44454
$605$	−366025.	−0.0406558
$606$	1.01753e7	1.12555
$607$	−1.28614e7	−1.41683	−0.708413	−	0.705798i	$-0.750589\pi$
$607$	−1.28614e7	−1.41683	−0.708413	+	0.705798i	$0.750589\pi$
$608$	2.87870e6	0.315818
$609$	−3.79220e6	−0.414332
$610$	818072.	0.0890158
$611$	−2.94738e7	−3.19399
$612$	−9413.17	−0.00101591
$613$	8.16806e6	0.877946	0.438973	−	0.898500i	$-0.355342\pi$
$613$	8.16806e6	0.877946	0.438973	+	0.898500i	$0.355342\pi$
$614$	8.84005e6	0.946311
$615$	−6.12971e6	−0.653510
$616$	1.03521e6	0.109920
$617$	−1.44089e6	−0.152377	−0.0761885	−	0.997093i	$-0.524275\pi$
$617$	−1.44089e6	−0.152377	−0.0761885	+	0.997093i	$0.524275\pi$
$618$	2.38946e7	2.51669
$619$	−1.59472e7	−1.67286	−0.836428	−	0.548077i	$-0.815360\pi$
$619$	−1.59472e7	−1.67286	−0.836428	+	0.548077i	$0.815360\pi$
$620$	2.56862e6	0.268362
$621$	−1.81248e7	−1.88601
$622$	−1.67544e7	−1.73641
$623$	5.04373e6	0.520633
$624$	1.02115e7	1.04985
$625$	390625.	0.0400000
$626$	5.92658e6	0.604461
$627$	655128.	0.0665514
$628$	1.03643e7	1.04868
$629$	−64630.8	−0.00651348
$630$	395014.	0.0396516
$631$	4.42811e6	0.442737	0.221368	−	0.975190i	$-0.428948\pi$
$631$	4.42811e6	0.442737	0.221368	+	0.975190i	$0.428948\pi$
$632$	3.45968e6	0.344543
$633$	−6.39280e6	−0.634136
$634$	−2.74498e6	−0.271217
$635$	−8.72345e6	−0.858527
$636$	2.18742e7	2.14432
$637$	7.11562e6	0.694807
$638$	−2.57998e6	−0.250937
$639$	322472.	0.0312421
$640$	−4.09973e6	−0.395645
$641$	3.60536e6	0.346580	0.173290	−	0.984871i	$-0.444560\pi$
$641$	3.60536e6	0.346580	0.173290	+	0.984871i	$0.444560\pi$
$642$	2.16964e7	2.07754
$643$	−1.78546e6	−0.170303	−0.0851516	−	0.996368i	$-0.527137\pi$
$643$	−1.78546e6	−0.170303	−0.0851516	+	0.996368i	$0.527137\pi$
$644$	−1.96991e7	−1.87168
$645$	226351.	0.0214232
$646$	−38684.6	−0.00364718
$647$	2.00329e7	1.88141	0.940706	−	0.339224i	$-0.110164\pi$
$647$	2.00329e7	1.88141	0.940706	+	0.339224i	$0.110164\pi$
$648$	4.56380e6	0.426962
$649$	4.91749e6	0.458281
$650$	5.93890e6	0.551344
$651$	3.75690e6	0.347438
$652$	−1.69455e7	−1.56112
$653$	−544330.	−0.0499550	−0.0249775	−	0.999688i	$-0.507951\pi$
$653$	−544330.	−0.0499550	−0.0249775	+	0.999688i	$0.507951\pi$
$654$	1.79877e7	1.64449
$655$	4.68377e6	0.426572
$656$	−1.00615e7	−0.912854
$657$	−654928.	−0.0591943
$658$	2.33096e7	2.09879
$659$	−1.70456e7	−1.52897	−0.764487	−	0.644639i	$-0.777007\pi$
$659$	−1.70456e7	−1.52897	−0.764487	+	0.644639i	$0.777007\pi$
$660$	−1.89546e6	−0.169377
$661$	4.50019e6	0.400615	0.200308	−	0.979733i	$-0.435806\pi$
$661$	4.50019e6	0.400615	0.200308	+	0.979733i	$0.435806\pi$
$662$	−6.82110e6	−0.604936
$663$	−206994.	−0.0182884
$664$	8.86567e6	0.780353
$665$	919262.	0.0806093
$666$	−803628.	−0.0702053
$667$	1.14912e7	1.00011
$668$	1.14121e7	0.989521
$669$	−3.49742e6	−0.302122
$670$	506286.	0.0435722
$671$	460968.	0.0395243
$672$	−1.21819e7	−1.04062
$673$	1.48540e7	1.26417	0.632087	−	0.774898i	$-0.282199\pi$
$673$	1.48540e7	1.26417	0.632087	+	0.774898i	$0.282199\pi$
$674$	2.42240e7	2.05398
$675$	−2.44711e6	−0.206726
$676$	3.56179e7	2.99779
$677$	1.22587e6	0.102795	0.0513976	−	0.998678i	$-0.483632\pi$
$677$	1.22587e6	0.102795	0.0513976	+	0.998678i	$0.483632\pi$
$678$	6.78664e6	0.566997
$679$	−1.45756e7	−1.21326
$680$	26197.4	0.00217263
$681$	2.08661e7	1.72415
$682$	2.55597e6	0.210424
$683$	2.77574e6	0.227681	0.113841	−	0.993499i	$-0.463685\pi$
$683$	2.77574e6	0.227681	0.113841	+	0.993499i	$0.463685\pi$
$684$	−272382.	−0.0222607
$685$	465503.	0.0379050
$686$	−2.03319e7	−1.64956
$687$	−5.33387e6	−0.431172
$688$	371539.	0.0299249
$689$	−3.86192e7	−3.09924
$690$	1.49086e7	1.19211
$691$	8.14982e6	0.649311	0.324655	−	0.945832i	$-0.394752\pi$
$691$	8.14982e6	0.649311	0.324655	+	0.945832i	$0.394752\pi$
$692$	−1.40828e7	−1.11795
$693$	222583.	0.0176059
$694$	−1.14617e7	−0.903336
$695$	−1.50414e6	−0.118120
$696$	−3.12717e6	−0.244697
$697$	203954.	0.0159019
$698$	−1.51908e6	−0.118016
$699$	−1.69818e7	−1.31459
$700$	−2.65967e6	−0.205156
$701$	1.46479e7	1.12585	0.562924	−	0.826508i	$-0.309676\pi$
$701$	1.46479e7	1.12585	0.562924	+	0.826508i	$0.309676\pi$
$702$	−3.72049e7	−2.84942
$703$	−1.87017e6	−0.142723
$704$	−5.90479e6	−0.449027
$705$	−9.98965e6	−0.756968
$706$	−4.86101e6	−0.367041
$707$	8.04523e6	0.605327
$708$	2.54652e7	1.90926
$709$	−8.14216e6	−0.608309	−0.304154	−	0.952623i	$-0.598374\pi$
$709$	−8.14216e6	−0.608309	−0.304154	+	0.952623i	$0.598374\pi$
$710$	−3.83427e6	−0.285455
$711$	743872.	0.0551854
$712$	4.15922e6	0.307477
$713$	−1.13842e7	−0.838647
$714$	163703.	0.0120174
$715$	3.34646e6	0.244805
$716$	1.39147e7	1.01436
$717$	−7.25919e6	−0.527339
$718$	6.11962e6	0.443010
$719$	−1.03240e7	−0.744776	−0.372388	−	0.928077i	$-0.621461\pi$
$719$	−1.03240e7	−0.744776	−0.372388	+	0.928077i	$0.621461\pi$
$720$	−277875.	−0.0199764
$721$	1.88927e7	1.35349
$722$	−1.11939e6	−0.0799167
$723$	−1.43763e7	−1.02283
$724$	−1.76405e7	−1.25073
$725$	1.55148e6	0.109623
$726$	−1.88612e6	−0.132809
$727$	2.46477e7	1.72958	0.864790	−	0.502134i	$-0.167452\pi$
$727$	2.46477e7	1.72958	0.864790	+	0.502134i	$0.167452\pi$
$728$	−9.46465e6	−0.661875
$729$	1.52509e7	1.06286
$730$	7.78726e6	0.540851
$731$	−7531.38	−0.000521292 0
$732$	2.38713e6	0.164664
$733$	−5.10818e6	−0.351161	−0.175581	−	0.984465i	$-0.556180\pi$
$733$	−5.10818e6	−0.351161	−0.175581	+	0.984465i	$0.556180\pi$
$734$	−1.29108e7	−0.884534
$735$	2.41172e6	0.164667
$736$	3.69137e7	2.51185
$737$	285283.	0.0193467
$738$	2.53599e6	0.171398
$739$	4.76508e6	0.320966	0.160483	−	0.987039i	$-0.448695\pi$
$739$	4.76508e6	0.320966	0.160483	+	0.987039i	$0.448695\pi$
$740$	5.41092e6	0.363238
$741$	−5.98964e6	−0.400733
$742$	3.05422e7	2.03653
$743$	1.31081e7	0.871101	0.435550	−	0.900164i	$-0.356554\pi$
$743$	1.31081e7	0.871101	0.435550	+	0.900164i	$0.356554\pi$
$744$	3.09806e6	0.205191
$745$	2.47727e6	0.163525
$746$	1.23279e7	0.811042
$747$	1.90622e6	0.124989
$748$	63067.6	0.00412147
$749$	1.71546e7	1.11732
$750$	2.01289e6	0.130667
$751$	−1.62719e7	−1.05278	−0.526392	−	0.850242i	$-0.676455\pi$
$751$	−1.62719e7	−1.05278	−0.526392	+	0.850242i	$0.676455\pi$
$752$	−1.63972e7	−1.05737
$753$	−2.02486e6	−0.130139
$754$	2.35880e7	1.51100
$755$	−7.75008e6	−0.494811
$756$	1.66618e7	1.06027
$757$	1.69701e7	1.07633	0.538166	−	0.842839i	$-0.319118\pi$
$757$	1.69701e7	1.07633	0.538166	+	0.842839i	$0.319118\pi$
$758$	9.27387e6	0.586257
$759$	8.40074e6	0.529314
$760$	758053.	0.0476064
$761$	2.34271e7	1.46641	0.733206	−	0.680006i	$-0.238023\pi$
$761$	2.34271e7	1.46641	0.733206	+	0.680006i	$0.238023\pi$
$762$	−4.49519e7	−2.80453
$763$	1.42222e7	0.884416
$764$	2.01034e7	1.24605
$765$	5632.74	0.000347989 0
$766$	−599192.	−0.0368972
$767$	−4.49591e7	−2.75950
$768$	2.29495e6	0.140401
$769$	−1.67206e7	−1.01961	−0.509807	−	0.860289i	$-0.670283\pi$
$769$	−1.67206e7	−1.01961	−0.509807	+	0.860289i	$0.670283\pi$
$770$	−2.64657e6	−0.160863
$771$	1.15549e7	0.700050
$772$	−1.17726e7	−0.710932
$773$	1.87135e7	1.12644	0.563218	−	0.826308i	$-0.309563\pi$
$773$	1.87135e7	1.12644	0.563218	+	0.826308i	$0.309563\pi$
$774$	−93646.2	−0.00561873
$775$	−1.53704e6	−0.0919242
$776$	−1.20195e7	−0.716528
$777$	7.91407e6	0.470270
$778$	−3.79095e7	−2.24543
$779$	5.90166e6	0.348442
$780$	1.73297e7	1.01989
$781$	−2.16054e6	−0.126746
$782$	−496055.	−0.0290077
$783$	−9.71940e6	−0.566546
$784$	3.95865e6	0.230015
$785$	−6.20189e6	−0.359211
$786$	2.41354e7	1.39347
$787$	−1.03206e7	−0.593977	−0.296989	−	0.954881i	$-0.595982\pi$
$787$	−1.03206e7	−0.593977	−0.296989	+	0.954881i	$0.595982\pi$
$788$	8.66879e6	0.497328
$789$	−1.81162e6	−0.103604
$790$	−8.84483e6	−0.504222
$791$	5.36596e6	0.304934
$792$	183549.	0.0103978
$793$	−4.21450e6	−0.237992
$794$	−1.73485e7	−0.976585
$795$	−1.30893e7	−0.734512
$796$	−6.63164e6	−0.370969
$797$	−1.42305e7	−0.793552	−0.396776	−	0.917915i	$-0.629871\pi$
$797$	−1.42305e7	−0.793552	−0.396776	+	0.917915i	$0.629871\pi$
$798$	4.73695e6	0.263325
$799$	332385.	0.0184194
$800$	4.98390e6	0.275324
$801$	894282.	0.0492485
$802$	2.19434e7	1.20467
$803$	4.38798e6	0.240146
$804$	1.47734e6	0.0806009
$805$	1.17877e7	0.641122
$806$	−2.33685e7	−1.26705
$807$	2.19756e7	1.18783
$808$	6.63436e6	0.357496
$809$	1.15314e7	0.619456	0.309728	−	0.950825i	$-0.399762\pi$
$809$	1.15314e7	0.619456	0.309728	+	0.950825i	$0.399762\pi$
$810$	−1.16676e7	−0.624838
$811$	−2.90545e7	−1.55118	−0.775590	−	0.631237i	$-0.782547\pi$
$811$	−2.90545e7	−1.55118	−0.775590	+	0.631237i	$0.782547\pi$
$812$	−1.05637e7	−0.562243
$813$	−8.55650e6	−0.454015
$814$	5.38426e6	0.284816
$815$	1.01400e7	0.534743
$816$	−115158.	−0.00605435
$817$	−217930.	−0.0114225
$818$	3.69186e7	1.92913
$819$	−2.03501e6	−0.106013
$820$	−1.70751e7	−0.886805
$821$	−1.87323e7	−0.969913	−0.484957	−	0.874538i	$-0.661165\pi$
$821$	−1.87323e7	−0.969913	−0.484957	+	0.874538i	$0.661165\pi$
$822$	2.39873e6	0.123823
$823$	2.58256e7	1.32908	0.664538	−	0.747254i	$-0.268628\pi$
$823$	2.58256e7	1.32908	0.664538	+	0.747254i	$0.268628\pi$
$824$	1.55795e7	0.799348
$825$	1.13422e6	0.0580182
$826$	3.55562e7	1.81328
$827$	1.64877e7	0.838293	0.419146	−	0.907919i	$-0.362329\pi$
$827$	1.64877e7	0.838293	0.419146	+	0.907919i	$0.362329\pi$
$828$	−3.49277e6	−0.177049
$829$	−7.94642e6	−0.401592	−0.200796	−	0.979633i	$-0.564353\pi$
$829$	−7.94642e6	−0.401592	−0.200796	+	0.979633i	$0.564353\pi$
$830$	−2.26655e7	−1.14201
$831$	−3.53024e7	−1.77338
$832$	5.39858e7	2.70378
$833$	−80244.9	−0.00400687
$834$	−7.75080e6	−0.385861
$835$	−6.82889e6	−0.338949
$836$	1.82494e6	0.0903094
$837$	9.62893e6	0.475077
$838$	2.84706e7	1.40051
$839$	3.10279e7	1.52177	0.760883	−	0.648889i	$-0.224766\pi$
$839$	3.10279e7	1.52177	0.760883	+	0.648889i	$0.224766\pi$
$840$	−3.20788e6	−0.156863
$841$	−1.43490e7	−0.699571
$842$	5.68186e7	2.76192
$843$	−2.31361e6	−0.112130
$844$	−1.78080e7	−0.860514
$845$	−2.13134e7	−1.02686
$846$	4.13292e6	0.198532
$847$	−1.49129e6	−0.0714257
$848$	−2.14851e7	−1.02600
$849$	2.24561e7	1.06921
$850$	−66974.7	−0.00317953
$851$	−2.39813e7	−1.13514
$852$	−1.11884e7	−0.528041
$853$	8.72466e6	0.410560	0.205280	−	0.978703i	$-0.434190\pi$
$853$	8.72466e6	0.410560	0.205280	+	0.978703i	$0.434190\pi$
$854$	3.33306e6	0.156386
$855$	162990.	0.00762512
$856$	1.41462e7	0.659867
$857$	716160.	0.0333087	0.0166544	−	0.999861i	$-0.494699\pi$
$857$	716160.	0.0333087	0.0166544	+	0.999861i	$0.494699\pi$
$858$	1.72443e7	0.799699
$859$	3.41500e7	1.57909	0.789547	−	0.613691i	$-0.210316\pi$
$859$	3.41500e7	1.57909	0.789547	+	0.613691i	$0.210316\pi$
$860$	630530.	0.0290710
$861$	−2.49742e7	−1.14811
$862$	5.17361e6	0.237151
$863$	2.36845e7	1.08252	0.541262	−	0.840854i	$-0.317947\pi$
$863$	2.36845e7	1.08252	0.541262	+	0.840854i	$0.317947\pi$
$864$	−3.12221e7	−1.42291
$865$	8.42697e6	0.382940
$866$	3.29113e7	1.49125
$867$	−2.12927e7	−0.962017
$868$	1.04653e7	0.471469
$869$	−4.98390e6	−0.223882
$870$	7.99475e6	0.358102
$871$	−2.60826e6	−0.116494
$872$	1.17281e7	0.522321
$873$	−2.58434e6	−0.114766
$874$	−1.43540e7	−0.635613
$875$	1.59152e6	0.0702736
$876$	2.27231e7	1.00048
$877$	−2.14563e6	−0.0942010	−0.0471005	−	0.998890i	$-0.514998\pi$
$877$	−2.14563e6	−0.0942010	−0.0471005	+	0.998890i	$0.514998\pi$
$878$	7.41045e6	0.324421
$879$	−7.28658e6	−0.318091
$880$	1.86174e6	0.0810425
$881$	2.68107e7	1.16377	0.581886	−	0.813270i	$-0.302315\pi$
$881$	2.68107e7	1.16377	0.581886	+	0.813270i	$0.302315\pi$
$882$	−997776.	−0.0431879
$883$	−2.09859e7	−0.905788	−0.452894	−	0.891564i	$-0.649608\pi$
$883$	−2.09859e7	−0.905788	−0.452894	+	0.891564i	$0.649608\pi$
$884$	−576609.	−0.0248171
$885$	−1.52381e7	−0.653993
$886$	4.87130e7	2.08478
$887$	2.56050e7	1.09274	0.546368	−	0.837545i	$-0.316010\pi$
$887$	2.56050e7	1.09274	0.546368	+	0.837545i	$0.316010\pi$
$888$	6.52620e6	0.277733
$889$	−3.55419e7	−1.50829
$890$	−1.06332e7	−0.449977
$891$	−6.57445e6	−0.277437
$892$	−9.74251e6	−0.409976
$893$	9.61798e6	0.403604
$894$	1.27654e7	0.534183
$895$	−8.32643e6	−0.347457
$896$	−1.67035e7	−0.695085
$897$	−7.68055e7	−3.18721
$898$	−1.46835e7	−0.607630
$899$	−6.10478e6	−0.251925
$900$	−471575.	−0.0194064
$901$	435520.	0.0178729
$902$	−1.69910e7	−0.695347
$903$	922221.	0.0376371
$904$	4.42495e6	0.180089
$905$	1.05559e7	0.428422
$906$	−3.99361e7	−1.61639
$907$	1.84581e7	0.745021	0.372511	−	0.928028i	$-0.378497\pi$
$907$	1.84581e7	0.745021	0.372511	+	0.928028i	$0.378497\pi$
$908$	5.81252e7	2.33965
$909$	1.42647e6	0.0572600
$910$	2.41968e7	0.968622
$911$	2.63853e7	1.05333	0.526667	−	0.850072i	$-0.323441\pi$
$911$	2.63853e7	1.05333	0.526667	+	0.850072i	$0.323441\pi$
$912$	−3.33223e6	−0.132662
$913$	−1.27716e7	−0.507069
$914$	−4.66669e6	−0.184775
$915$	−1.42843e6	−0.0564035
$916$	−1.48582e7	−0.585096
$917$	1.90830e7	0.749418
$918$	419570.	0.0164323
$919$	−1.76623e7	−0.689855	−0.344927	−	0.938629i	$-0.612096\pi$
$919$	−1.76623e7	−0.689855	−0.344927	+	0.938629i	$0.612096\pi$
$920$	9.72056e6	0.378636
$921$	−1.54356e7	−0.599616
$922$	7.58703e7	2.93930
$923$	1.97532e7	0.763191
$924$	−7.72266e6	−0.297569
$925$	−3.23783e6	−0.124423
$926$	3.17783e7	1.21788
$927$	3.34978e6	0.128031
$928$	1.97950e7	0.754545
$929$	5.93955e6	0.225795	0.112897	−	0.993607i	$-0.463987\pi$
$929$	5.93955e6	0.225795	0.112897	+	0.993607i	$0.463987\pi$
$930$	−7.92034e6	−0.300287
$931$	−2.32199e6	−0.0877982
$932$	−4.73050e7	−1.78389
$933$	2.92547e7	1.10025
$934$	−4.60419e7	−1.72698
$935$	−37739.0	−0.00141176
$936$	−1.67814e6	−0.0626091
$937$	−4.23291e7	−1.57504	−0.787518	−	0.616292i	$-0.788634\pi$
$937$	−4.23291e7	−1.57504	−0.787518	+	0.616292i	$0.788634\pi$
$938$	2.06276e6	0.0765493
$939$	−1.03484e7	−0.383008
$940$	−2.78274e7	−1.02720
$941$	−1.47699e7	−0.543756	−0.271878	−	0.962332i	$-0.587645\pi$
$941$	−1.47699e7	−0.543756	−0.271878	+	0.962332i	$0.587645\pi$
$942$	−3.19583e7	−1.17343
$943$	7.56772e7	2.77132
$944$	−2.50122e7	−0.913529
$945$	−9.97024e6	−0.363184
$946$	627424.	0.0227947
$947$	−3.38749e7	−1.22745	−0.613723	−	0.789521i	$-0.710329\pi$
$947$	−3.38749e7	−1.22745	−0.613723	+	0.789521i	$0.710329\pi$
$948$	−2.58091e7	−0.932722
$949$	−4.01180e7	−1.44602
$950$	−1.93800e6	−0.0696697
$951$	4.79300e6	0.171853
$952$	106736.	0.00381696
$953$	−575145.	−0.0205138	−0.0102569	−	0.999947i	$-0.503265\pi$
$953$	−575145.	−0.0205138	−0.0102569	+	0.999947i	$0.503265\pi$
$954$	5.41531e6	0.192643
$955$	−1.20297e7	−0.426821
$956$	−2.02214e7	−0.715593
$957$	4.50489e6	0.159003
$958$	5.23461e7	1.84277
$959$	1.89659e6	0.0665929
$960$	1.82975e7	0.640788
$961$	−2.25812e7	−0.788748
$962$	−4.92267e7	−1.71500
$963$	3.04161e6	0.105691
$964$	−4.00471e7	−1.38796
$965$	7.04458e6	0.243521
$966$	6.07421e7	2.09434
$967$	3.28322e7	1.12910	0.564552	−	0.825398i	$-0.309049\pi$
$967$	3.28322e7	1.12910	0.564552	+	0.825398i	$0.309049\pi$
$968$	−1.22977e6	−0.0421827
$969$	67546.9	0.00231098
$970$	3.07284e7	1.04860
$971$	−3.30923e7	−1.12637	−0.563183	−	0.826332i	$-0.690423\pi$
$971$	−3.30923e7	−1.12637	−0.563183	+	0.826332i	$0.690423\pi$
$972$	5.70409e6	0.193651
$973$	−6.12829e6	−0.207519
$974$	−5.26063e6	−0.177681
$975$	−1.03699e7	−0.349351
$976$	−2.34466e6	−0.0787871
$977$	2.97407e7	0.996817	0.498408	−	0.866942i	$-0.333918\pi$
$977$	2.97407e7	0.996817	0.498408	+	0.866942i	$0.333918\pi$
$978$	5.22515e7	1.74683
$979$	−5.99163e6	−0.199797
$980$	6.71814e6	0.223452
$981$	2.52168e6	0.0836600
$982$	−3.64317e7	−1.20559
$983$	1.38106e6	0.0455857	0.0227929	−	0.999740i	$-0.492744\pi$
$983$	1.38106e6	0.0455857	0.0227929	+	0.999740i	$0.492744\pi$
$984$	−2.05946e7	−0.678055
$985$	−5.18731e6	−0.170354
$986$	−266009.	−0.00871374
$987$	−4.07007e7	−1.32987
$988$	−1.66849e7	−0.543790
$989$	−2.79453e6	−0.0908484
$990$	−469252.	−0.0152166
$991$	−4.21091e7	−1.36205	−0.681023	−	0.732262i	$-0.738464\pi$
$991$	−4.21091e7	−1.36205	−0.681023	+	0.732262i	$0.738464\pi$
$992$	−1.96107e7	−0.632724
$993$	1.19103e7	0.383309
$994$	−1.56219e7	−0.501498
$995$	3.96830e6	0.127071
$996$	−6.61376e7	−2.11252
$997$	−3.14275e7	−1.00132	−0.500658	−	0.865645i	$-0.666909\pi$
$997$	−3.14275e7	−1.00132	−0.500658	+	0.865645i	$0.666909\pi$
$998$	5.42271e7	1.72342
$999$	2.02837e7	0.643035

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.a.1.6	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.a.1.6	✓	35	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-8.58946 q^{2} +14.9980 q^{3} +41.7788 q^{4} -25.0000 q^{5} -128.825 q^{6} -101.857 q^{7} -83.9948 q^{8} -18.0599 q^{9} +O(q^{10})\)	\(q-8.58946 q^{2} +14.9980 q^{3} +41.7788 q^{4} -25.0000 q^{5} -128.825 q^{6} -101.857 q^{7} -83.9948 q^{8} -18.0599 q^{9} +214.737 q^{10} +121.000 q^{11} +626.599 q^{12} -1106.27 q^{13} +874.899 q^{14} -374.950 q^{15} -615.452 q^{16} +12.4757 q^{17} +155.125 q^{18} +361.000 q^{19} -1044.47 q^{20} -1527.66 q^{21} -1039.32 q^{22} +4629.12 q^{23} -1259.75 q^{24} +625.000 q^{25} +9502.24 q^{26} -3915.38 q^{27} -4255.48 q^{28} +2482.37 q^{29} +3220.62 q^{30} -2459.26 q^{31} +7974.24 q^{32} +1814.76 q^{33} -107.160 q^{34} +2546.43 q^{35} -754.520 q^{36} -5180.54 q^{37} -3100.80 q^{38} -16591.8 q^{39} +2099.87 q^{40} +16348.1 q^{41} +13121.7 q^{42} -603.684 q^{43} +5055.24 q^{44} +451.497 q^{45} -39761.7 q^{46} +26642.6 q^{47} -9230.55 q^{48} -6432.10 q^{49} -5368.41 q^{50} +187.111 q^{51} -46218.6 q^{52} +34909.5 q^{53} +33631.0 q^{54} -3025.00 q^{55} +8555.48 q^{56} +5414.28 q^{57} -21322.2 q^{58} +40640.4 q^{59} -15665.0 q^{60} +3809.65 q^{61} +21123.7 q^{62} +1839.53 q^{63} -48799.9 q^{64} +27656.7 q^{65} -15587.8 q^{66} +2357.71 q^{67} +521.220 q^{68} +69427.6 q^{69} -21872.5 q^{70} -17855.7 q^{71} +1516.94 q^{72} +36264.3 q^{73} +44498.0 q^{74} +9373.75 q^{75} +15082.2 q^{76} -12324.7 q^{77} +142515. q^{78} -41189.2 q^{79} +15386.3 q^{80} -54334.3 q^{81} -140421. q^{82} -105550. q^{83} -63823.7 q^{84} -311.893 q^{85} +5185.32 q^{86} +37230.5 q^{87} -10163.4 q^{88} -49517.6 q^{89} -3878.11 q^{90} +112681. q^{91} +193399. q^{92} -36884.0 q^{93} -228846. q^{94} -9025.00 q^{95} +119598. q^{96} +143098. q^{97} +55248.2 q^{98} -2185.24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9}+O(q^{10}) \) 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9	\( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9} + 100 q^{10} + 4235 q^{11} - 568 q^{12} - 717 q^{13} - 2585 q^{14} + 675 q^{15} + 3356 q^{16} - 3349 q^{17} - 5533 q^{18} + 12635 q^{19} - 13000 q^{20} + 289 q^{21} - 484 q^{22} - 820 q^{23} - 21748 q^{24} + 21875 q^{25} - 6267 q^{26} - 13650 q^{27} - 6487 q^{28} - 13357 q^{29} + 7275 q^{30} - 15341 q^{31} - 16405 q^{32} - 3267 q^{33} - 1255 q^{34} - 2925 q^{35} + 23487 q^{36} - 511 q^{37} - 1444 q^{38} - 33584 q^{39} + 12450 q^{40} - 36855 q^{41} + 16330 q^{42} + 10991 q^{43} + 62920 q^{44} - 51150 q^{45} - 20443 q^{46} - 33594 q^{47} + 36221 q^{48} + 23422 q^{49} - 2500 q^{50} - 53530 q^{51} + 89382 q^{52} + 13103 q^{53} + 65776 q^{54} - 105875 q^{55} + 130911 q^{56} - 9747 q^{57} + 127808 q^{58} - 161139 q^{59} + 14200 q^{60} - 91587 q^{61} + 131818 q^{62} + 16590 q^{63} - 23186 q^{64} + 17925 q^{65} - 35211 q^{66} + 39210 q^{67} + 26300 q^{68} - 23174 q^{69} + 64625 q^{70} - 167772 q^{71} + 135820 q^{72} - 5106 q^{73} - 256965 q^{74} - 16875 q^{75} + 187720 q^{76} + 14157 q^{77} + 492812 q^{78} - 156897 q^{79} - 83900 q^{80} + 31279 q^{81} + 46818 q^{82} - 185627 q^{83} + 165864 q^{84} + 83725 q^{85} - 159946 q^{86} - 112092 q^{87} - 60258 q^{88} - 144420 q^{89} + 138325 q^{90} - 442480 q^{91} - 205876 q^{92} + 125910 q^{93} - 110044 q^{94} - 315875 q^{95} - 554286 q^{96} + 41200 q^{97} + 41052 q^{98} + 247566 q^{99}+O(q^{100}) \) 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9 + 100 * q^10 + 4235 * q^11 - 568 * q^12 - 717 * q^13 - 2585 * q^14 + 675 * q^15 + 3356 * q^16 - 3349 * q^17 - 5533 * q^18 + 12635 * q^19 - 13000 * q^20 + 289 * q^21 - 484 * q^22 - 820 * q^23 - 21748 * q^24 + 21875 * q^25 - 6267 * q^26 - 13650 * q^27 - 6487 * q^28 - 13357 * q^29 + 7275 * q^30 - 15341 * q^31 - 16405 * q^32 - 3267 * q^33 - 1255 * q^34 - 2925 * q^35 + 23487 * q^36 - 511 * q^37 - 1444 * q^38 - 33584 * q^39 + 12450 * q^40 - 36855 * q^41 + 16330 * q^42 + 10991 * q^43 + 62920 * q^44 - 51150 * q^45 - 20443 * q^46 - 33594 * q^47 + 36221 * q^48 + 23422 * q^49 - 2500 * q^50 - 53530 * q^51 + 89382 * q^52 + 13103 * q^53 + 65776 * q^54 - 105875 * q^55 + 130911 * q^56 - 9747 * q^57 + 127808 * q^58 - 161139 * q^59 + 14200 * q^60 - 91587 * q^61 + 131818 * q^62 + 16590 * q^63 - 23186 * q^64 + 17925 * q^65 - 35211 * q^66 + 39210 * q^67 + 26300 * q^68 - 23174 * q^69 + 64625 * q^70 - 167772 * q^71 + 135820 * q^72 - 5106 * q^73 - 256965 * q^74 - 16875 * q^75 + 187720 * q^76 + 14157 * q^77 + 492812 * q^78 - 156897 * q^79 - 83900 * q^80 + 31279 * q^81 + 46818 * q^82 - 185627 * q^83 + 165864 * q^84 + 83725 * q^85 - 159946 * q^86 - 112092 * q^87 - 60258 * q^88 - 144420 * q^89 + 138325 * q^90 - 442480 * q^91 - 205876 * q^92 + 125910 * q^93 - 110044 * q^94 - 315875 * q^95 - 554286 * q^96 + 41200 * q^97 + 41052 * q^98 + 247566 * q^99

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