LMFDB - Embedded newform 1045.6.a.d.1.4

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:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-9.62194 q^{2} +30.2604 q^{3} +60.5817 q^{4} -25.0000 q^{5} -291.163 q^{6} +83.2794 q^{7} -275.011 q^{8} +672.690 q^{9} +O(q^{10})$	\(q-9.62194 q^{2} +30.2604 q^{3} +60.5817 q^{4} -25.0000 q^{5} -291.163 q^{6} +83.2794 q^{7} -275.011 q^{8} +672.690 q^{9} +240.548 q^{10} +121.000 q^{11} +1833.22 q^{12} +902.851 q^{13} -801.309 q^{14} -756.509 q^{15} +707.524 q^{16} -238.770 q^{17} -6472.58 q^{18} -361.000 q^{19} -1514.54 q^{20} +2520.07 q^{21} -1164.25 q^{22} +1359.14 q^{23} -8321.93 q^{24} +625.000 q^{25} -8687.18 q^{26} +13002.6 q^{27} +5045.20 q^{28} +1651.04 q^{29} +7279.08 q^{30} -3365.27 q^{31} +1992.60 q^{32} +3661.50 q^{33} +2297.43 q^{34} -2081.98 q^{35} +40752.7 q^{36} +5442.85 q^{37} +3473.52 q^{38} +27320.6 q^{39} +6875.27 q^{40} +17049.3 q^{41} -24247.9 q^{42} -7227.08 q^{43} +7330.38 q^{44} -16817.3 q^{45} -13077.5 q^{46} +9311.47 q^{47} +21409.9 q^{48} -9871.54 q^{49} -6013.71 q^{50} -7225.26 q^{51} +54696.2 q^{52} +16022.4 q^{53} -125110. q^{54} -3025.00 q^{55} -22902.7 q^{56} -10924.0 q^{57} -15886.2 q^{58} -43658.2 q^{59} -45830.6 q^{60} -10302.0 q^{61} +32380.5 q^{62} +56021.2 q^{63} -41813.4 q^{64} -22571.3 q^{65} -35230.8 q^{66} -44951.7 q^{67} -14465.1 q^{68} +41127.9 q^{69} +20032.7 q^{70} +37941.3 q^{71} -184997. q^{72} +63180.7 q^{73} -52370.8 q^{74} +18912.7 q^{75} -21870.0 q^{76} +10076.8 q^{77} -262877. q^{78} +7999.70 q^{79} -17688.1 q^{80} +229999. q^{81} -164047. q^{82} +81861.0 q^{83} +152670. q^{84} +5969.24 q^{85} +69538.5 q^{86} +49961.2 q^{87} -33276.3 q^{88} +23633.6 q^{89} +161815. q^{90} +75188.9 q^{91} +82338.7 q^{92} -101834. q^{93} -89594.4 q^{94} +9025.00 q^{95} +60296.7 q^{96} -57941.3 q^{97} +94983.3 q^{98} +81395.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9}+O(q^{10}) $ 37 * q + 4 * q^2 + 27 * q^3 + 616 * q^4 - 925 * q^5 + 141 * q^6 - 79 * q^7 + 72 * q^8 + 3140 * q^9	\( 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9} - 100 q^{10} + 4477 q^{11} + 872 q^{12} + 719 q^{13} - 625 q^{14} - 675 q^{15} + 6940 q^{16} + 119 q^{17} - 4237 q^{18} - 13357 q^{19} - 15400 q^{20} + 2905 q^{21} + 484 q^{22} - 1252 q^{23} + 5884 q^{24} + 23125 q^{25} + 13201 q^{26} + 9918 q^{27} + 15461 q^{28} + 13221 q^{29} - 3525 q^{30} + 6419 q^{31} + 13173 q^{32} + 3267 q^{33} + 35415 q^{34} + 1975 q^{35} + 80543 q^{36} + 9037 q^{37} - 1444 q^{38} - 6184 q^{39} - 1800 q^{40} + 52577 q^{41} - 28578 q^{42} + 963 q^{43} + 74536 q^{44} - 78500 q^{45} - 10531 q^{46} + 49346 q^{47} + 80107 q^{48} + 70288 q^{49} + 2500 q^{50} + 140786 q^{51} + 165062 q^{52} - 34457 q^{53} + 34216 q^{54} - 111925 q^{55} - 64095 q^{56} - 9747 q^{57} - 126140 q^{58} + 56521 q^{59} - 21800 q^{60} + 6613 q^{61} + 494 q^{62} - 125618 q^{63} - 140426 q^{64} - 17975 q^{65} + 17061 q^{66} - 43534 q^{67} - 138520 q^{68} + 34618 q^{69} + 15625 q^{70} + 95986 q^{71} - 42192 q^{72} + 109218 q^{73} - 182005 q^{74} + 16875 q^{75} - 222376 q^{76} - 9559 q^{77} - 369624 q^{78} + 64943 q^{79} - 173500 q^{80} + 388941 q^{81} - 126926 q^{82} + 109741 q^{83} - 112886 q^{84} - 2975 q^{85} + 43866 q^{86} + 142492 q^{87} + 8712 q^{88} - 119092 q^{89} + 105925 q^{90} + 349320 q^{91} + 433396 q^{92} - 108630 q^{93} + 196160 q^{94} + 333925 q^{95} + 376630 q^{96} + 68774 q^{97} + 310926 q^{98} + 379940 q^{99}+O(q^{100}) \) 37 * q + 4 * q^2 + 27 * q^3 + 616 * q^4 - 925 * q^5 + 141 * q^6 - 79 * q^7 + 72 * q^8 + 3140 * q^9 - 100 * q^10 + 4477 * q^11 + 872 * q^12 + 719 * q^13 - 625 * q^14 - 675 * q^15 + 6940 * q^16 + 119 * q^17 - 4237 * q^18 - 13357 * q^19 - 15400 * q^20 + 2905 * q^21 + 484 * q^22 - 1252 * q^23 + 5884 * q^24 + 23125 * q^25 + 13201 * q^26 + 9918 * q^27 + 15461 * q^28 + 13221 * q^29 - 3525 * q^30 + 6419 * q^31 + 13173 * q^32 + 3267 * q^33 + 35415 * q^34 + 1975 * q^35 + 80543 * q^36 + 9037 * q^37 - 1444 * q^38 - 6184 * q^39 - 1800 * q^40 + 52577 * q^41 - 28578 * q^42 + 963 * q^43 + 74536 * q^44 - 78500 * q^45 - 10531 * q^46 + 49346 * q^47 + 80107 * q^48 + 70288 * q^49 + 2500 * q^50 + 140786 * q^51 + 165062 * q^52 - 34457 * q^53 + 34216 * q^54 - 111925 * q^55 - 64095 * q^56 - 9747 * q^57 - 126140 * q^58 + 56521 * q^59 - 21800 * q^60 + 6613 * q^61 + 494 * q^62 - 125618 * q^63 - 140426 * q^64 - 17975 * q^65 + 17061 * q^66 - 43534 * q^67 - 138520 * q^68 + 34618 * q^69 + 15625 * q^70 + 95986 * q^71 - 42192 * q^72 + 109218 * q^73 - 182005 * q^74 + 16875 * q^75 - 222376 * q^76 - 9559 * q^77 - 369624 * q^78 + 64943 * q^79 - 173500 * q^80 + 388941 * q^81 - 126926 * q^82 + 109741 * q^83 - 112886 * q^84 - 2975 * q^85 + 43866 * q^86 + 142492 * q^87 + 8712 * q^88 - 119092 * q^89 + 105925 * q^90 + 349320 * q^91 + 433396 * q^92 - 108630 * q^93 + 196160 * q^94 + 333925 * q^95 + 376630 * q^96 + 68774 * q^97 + 310926 * q^98 + 379940 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−9.62194	−1.70093	−0.850467	−	0.526028i	$-0.823681\pi$
$2$	−9.62194	−1.70093	−0.850467	+	0.526028i	$0.823681\pi$
$3$	30.2604	1.94120	0.970602	−	0.240691i	$-0.0773740\pi$
$3$	30.2604	1.94120	0.970602	+	0.240691i	$0.0773740\pi$
$4$	60.5817	1.89318
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−291.163	−3.30186
$7$	83.2794	0.642381	0.321190	−	0.947015i	$-0.395917\pi$
$7$	83.2794	0.642381	0.321190	+	0.947015i	$0.395917\pi$
$8$	−275.011	−1.51923
$9$	672.690	2.76827
$10$	240.548	0.760681
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	1833.22	3.67504
$13$	902.851	1.48169	0.740846	−	0.671675i	$-0.234425\pi$
$13$	902.851	1.48169	0.740846	+	0.671675i	$0.234425\pi$
$14$	−801.309	−1.09265
$15$	−756.509	−0.868133
$16$	707.524	0.690942
$17$	−238.770	−0.200381	−0.100191	−	0.994968i	$-0.531945\pi$
$17$	−238.770	−0.200381	−0.100191	+	0.994968i	$0.531945\pi$
$18$	−6472.58	−4.70865
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−1514.54	−0.846654
$21$	2520.07	1.24699
$22$	−1164.25	−0.512851
$23$	1359.14	0.535727	0.267863	−	0.963457i	$-0.413682\pi$
$23$	1359.14	0.535727	0.267863	+	0.963457i	$0.413682\pi$
$24$	−8321.93	−2.94914
$25$	625.000	0.200000
$26$	−8687.18	−2.52026
$27$	13002.6	3.43258
$28$	5045.20	1.21614
$29$	1651.04	0.364555	0.182278	−	0.983247i	$-0.441653\pi$
$29$	1651.04	0.364555	0.182278	+	0.983247i	$0.441653\pi$
$30$	7279.08	1.47664
$31$	−3365.27	−0.628950	−0.314475	−	0.949266i	$-0.601829\pi$
$31$	−3365.27	−0.628950	−0.314475	+	0.949266i	$0.601829\pi$
$32$	1992.60	0.343989
$33$	3661.50	0.585295
$34$	2297.43	0.340835
$35$	−2081.98	−0.287281
$36$	40752.7	5.24083
$37$	5442.85	0.653615	0.326808	−	0.945091i	$-0.394027\pi$
$37$	5442.85	0.653615	0.326808	+	0.945091i	$0.394027\pi$
$38$	3473.52	0.390221
$39$	27320.6	2.87627
$40$	6875.27	0.679422
$41$	17049.3	1.58397	0.791984	−	0.610542i	$-0.209048\pi$
$41$	17049.3	1.58397	0.791984	+	0.610542i	$0.209048\pi$
$42$	−24247.9	−2.12105
$43$	−7227.08	−0.596062	−0.298031	−	0.954556i	$-0.596330\pi$
$43$	−7227.08	−0.596062	−0.298031	+	0.954556i	$0.596330\pi$
$44$	7330.38	0.570814
$45$	−16817.3	−1.23801
$46$	−13077.5	−0.911236
$47$	9311.47	0.614856	0.307428	−	0.951571i	$-0.400532\pi$
$47$	9311.47	0.614856	0.307428	+	0.951571i	$0.400532\pi$
$48$	21409.9	1.34126
$49$	−9871.54	−0.587347
$50$	−6013.71	−0.340187
$51$	−7225.26	−0.388980
$52$	54696.2	2.80510
$53$	16022.4	0.783498	0.391749	−	0.920072i	$-0.371870\pi$
$53$	16022.4	0.783498	0.391749	+	0.920072i	$0.371870\pi$
$54$	−125110.	−5.83858
$55$	−3025.00	−0.134840
$56$	−22902.7	−0.975927
$57$	−10924.0	−0.445343
$58$	−15886.2	−0.620084
$59$	−43658.2	−1.63281	−0.816405	−	0.577480i	$-0.804036\pi$
$59$	−43658.2	−1.63281	−0.816405	+	0.577480i	$0.804036\pi$
$60$	−45830.6	−1.64353
$61$	−10302.0	−0.354484	−0.177242	−	0.984167i	$-0.556718\pi$
$61$	−10302.0	−0.354484	−0.177242	+	0.984167i	$0.556718\pi$
$62$	32380.5	1.06980
$63$	56021.2	1.77828
$64$	−41813.4	−1.27604
$65$	−22571.3	−0.662633
$66$	−35230.8	−0.995548
$67$	−44951.7	−1.22337	−0.611687	−	0.791100i	$-0.709509\pi$
$67$	−44951.7	−1.22337	−0.611687	+	0.791100i	$0.709509\pi$
$68$	−14465.1	−0.379357
$69$	41127.9	1.03995
$70$	20032.7	0.488647
$71$	37941.3	0.893237	0.446619	−	0.894724i	$-0.352628\pi$
$71$	37941.3	0.893237	0.446619	+	0.894724i	$0.352628\pi$
$72$	−184997.	−4.20565
$73$	63180.7	1.38764	0.693821	−	0.720148i	$-0.255926\pi$
$73$	63180.7	1.38764	0.693821	+	0.720148i	$0.255926\pi$
$74$	−52370.8	−1.11176
$75$	18912.7	0.388241
$76$	−21870.0	−0.434325
$77$	10076.8	0.193685
$78$	−262877.	−4.89234
$79$	7999.70	0.144214	0.0721068	−	0.997397i	$-0.477028\pi$
$79$	7999.70	0.144214	0.0721068	+	0.997397i	$0.477028\pi$
$80$	−17688.1	−0.308998
$81$	229999.	3.89506
$82$	−164047.	−2.69423
$83$	81861.0	1.30431	0.652157	−	0.758084i	$-0.273864\pi$
$83$	81861.0	1.30431	0.652157	+	0.758084i	$0.273864\pi$
$84$	152670.	2.36078
$85$	5969.24	0.0896131
$86$	69538.5	1.01386
$87$	49961.2	0.707676
$88$	−33276.3	−0.458067
$89$	23633.6	0.316267	0.158134	−	0.987418i	$-0.449452\pi$
$89$	23633.6	0.316267	0.158134	+	0.987418i	$0.449452\pi$
$90$	161815.	2.10577
$91$	75188.9	0.951810
$92$	82338.7	1.01423
$93$	−101834.	−1.22092
$94$	−89594.4	−1.04583
$95$	9025.00	0.102598
$96$	60296.7	0.667752
$97$	−57941.3	−0.625257	−0.312629	−	0.949875i	$-0.601210\pi$
$97$	−57941.3	−0.625257	−0.312629	+	0.949875i	$0.601210\pi$
$98$	94983.3	0.999039
$99$	81395.5	0.834665
$100$	37863.5	0.378635
$101$	83286.7	0.812404	0.406202	−	0.913783i	$-0.366853\pi$
$101$	83286.7	0.812404	0.406202	+	0.913783i	$0.366853\pi$
$102$	69520.9	0.661630
$103$	−55130.0	−0.512030	−0.256015	−	0.966673i	$-0.582410\pi$
$103$	−55130.0	−0.512030	−0.256015	+	0.966673i	$0.582410\pi$
$104$	−248294.	−2.25104
$105$	−63001.6	−0.557672
$106$	−154166.	−1.33268
$107$	−159934.	−1.35046	−0.675229	−	0.737608i	$-0.735955\pi$
$107$	−159934.	−1.35046	−0.675229	+	0.737608i	$0.735955\pi$
$108$	787718.	6.49847
$109$	−217783.	−1.75573	−0.877866	−	0.478907i	$-0.841033\pi$
$109$	−217783.	−1.75573	−0.877866	+	0.478907i	$0.841033\pi$
$110$	29106.4	0.229354
$111$	164703.	1.26880
$112$	58922.2	0.443848
$113$	14129.1	0.104092	0.0520461	−	0.998645i	$-0.483426\pi$
$113$	14129.1	0.104092	0.0520461	+	0.998645i	$0.483426\pi$
$114$	105110.	0.757499
$115$	−33978.4	−0.239584
$116$	100023.	0.690167
$117$	607339.	4.10173
$118$	420076.	2.77730
$119$	−19884.6	−0.128721
$120$	208048.	1.31890
$121$	14641.0	0.0909091
$122$	99125.1	0.602954
$123$	515917.	3.07480
$124$	−203874.	−1.19071
$125$	−15625.0	−0.0894427
$126$	−539033.	−3.02474
$127$	242748.	1.33551	0.667755	−	0.744381i	$-0.267255\pi$
$127$	242748.	1.33551	0.667755	+	0.744381i	$0.267255\pi$
$128$	338563.	1.82648
$129$	−218694.	−1.15708
$130$	217179.	1.12709
$131$	174870.	0.890299	0.445150	−	0.895456i	$-0.353150\pi$
$131$	174870.	0.890299	0.445150	+	0.895456i	$0.353150\pi$
$132$	221820.	1.10807
$133$	−30063.9	−0.147372
$134$	432522.	2.08088
$135$	−325064.	−1.53509
$136$	65664.2	0.304426
$137$	222428.	1.01248	0.506241	−	0.862392i	$-0.331035\pi$
$137$	222428.	1.01248	0.506241	+	0.862392i	$0.331035\pi$
$138$	−395730.	−1.76889
$139$	−397453.	−1.74481	−0.872405	−	0.488783i	$-0.837441\pi$
$139$	−397453.	−1.74481	−0.872405	+	0.488783i	$0.837441\pi$
$140$	−126130.	−0.543874
$141$	281769.	1.19356
$142$	−365069.	−1.51934
$143$	109245.	0.446747
$144$	475944.	1.91271
$145$	−41276.1	−0.163034
$146$	−607921.	−2.36029
$147$	−298717.	−1.14016
$148$	329737.	1.23741
$149$	−105932.	−0.390894	−0.195447	−	0.980714i	$-0.562616\pi$
$149$	−105932.	−0.390894	−0.195447	+	0.980714i	$0.562616\pi$
$150$	−181977.	−0.660372
$151$	450330.	1.60727	0.803634	−	0.595124i	$-0.202897\pi$
$151$	450330.	1.60727	0.803634	+	0.595124i	$0.202897\pi$
$152$	99278.9	0.348536
$153$	−160618.	−0.554709
$154$	−96958.4	−0.329446
$155$	84131.9	0.281275
$156$	1.65513e6	5.44528
$157$	−31840.6	−0.103094	−0.0515469	−	0.998671i	$-0.516415\pi$
$157$	−31840.6	−0.103094	−0.0515469	+	0.998671i	$0.516415\pi$
$158$	−76972.6	−0.245298
$159$	484843.	1.52093
$160$	−49814.9	−0.153836
$161$	113188.	0.344140
$162$	−2.21304e6	−6.62523
$163$	−340469.	−1.00371	−0.501855	−	0.864952i	$-0.667349\pi$
$163$	−340469.	−1.00371	−0.501855	+	0.864952i	$0.667349\pi$
$164$	1.03287e6	2.99873
$165$	−91537.6	−0.261752
$166$	−787662.	−2.21855
$167$	−310396.	−0.861241	−0.430620	−	0.902533i	$-0.641705\pi$
$167$	−310396.	−0.861241	−0.430620	+	0.902533i	$0.641705\pi$
$168$	−693045.	−1.89447
$169$	443848.	1.19541
$170$	−57435.6	−0.152426
$171$	−242841.	−0.635085
$172$	−437828.	−1.12845
$173$	610538.	1.55095	0.775474	−	0.631380i	$-0.217511\pi$
$173$	610538.	1.55095	0.775474	+	0.631380i	$0.217511\pi$
$174$	−480723.	−1.20371
$175$	52049.6	0.128476
$176$	85610.4	0.208327
$177$	−1.32111e6	−3.16962
$178$	−227401.	−0.537950
$179$	−270182.	−0.630267	−0.315133	−	0.949047i	$-0.602049\pi$
$179$	−270182.	−0.630267	−0.315133	+	0.949047i	$0.602049\pi$
$180$	−1.01882e6	−2.34377
$181$	−520599.	−1.18116	−0.590578	−	0.806981i	$-0.701100\pi$
$181$	−520599.	−1.18116	−0.590578	+	0.806981i	$0.701100\pi$
$182$	−723463.	−1.61897
$183$	−311742.	−0.688125
$184$	−373777.	−0.813894
$185$	−136071.	−0.292306
$186$	979845.	2.07671
$187$	−28891.1	−0.0604172
$188$	564104.	1.16403
$189$	1.08285e6	2.20502
$190$	−86838.0	−0.174512
$191$	−352737.	−0.699629	−0.349814	−	0.936819i	$-0.613755\pi$
$191$	−352737.	−0.699629	−0.349814	+	0.936819i	$0.613755\pi$
$192$	−1.26529e6	−2.47706
$193$	427477.	0.826076	0.413038	−	0.910714i	$-0.364468\pi$
$193$	427477.	0.826076	0.413038	+	0.910714i	$0.364468\pi$
$194$	557507.	1.06352
$195$	−683015.	−1.28631
$196$	−598034.	−1.11195
$197$	−31990.0	−0.0587285	−0.0293643	−	0.999569i	$-0.509348\pi$
$197$	−31990.0	−0.0587285	−0.0293643	+	0.999569i	$0.509348\pi$
$198$	−783182.	−1.41971
$199$	−894860.	−1.60185	−0.800926	−	0.598763i	$-0.795659\pi$
$199$	−894860.	−1.60185	−0.800926	+	0.598763i	$0.795659\pi$
$200$	−171882.	−0.303847
$201$	−1.36025e6	−2.37482
$202$	−801379.	−1.38185
$203$	137498.	0.234183
$204$	−437718.	−0.736409
$205$	−426232.	−0.708372
$206$	530457.	0.870929
$207$	914277.	1.48304
$208$	638789.	1.02376
$209$	−43681.0	−0.0691714
$210$	606198.	0.948563
$211$	−408988.	−0.632418	−0.316209	−	0.948690i	$-0.602410\pi$
$211$	−408988.	−0.632418	−0.316209	+	0.948690i	$0.602410\pi$
$212$	970663.	1.48330
$213$	1.14812e6	1.73396
$214$	1.53887e6	2.29704
$215$	180677.	0.266567
$216$	−3.57585e6	−5.21489
$217$	−280258.	−0.404026
$218$	2.09550e6	2.98638
$219$	1.91187e6	2.69369
$220$	−183260.	−0.255276
$221$	−215573.	−0.296903
$222$	−1.58476e6	−2.15815
$223$	−888037.	−1.19583	−0.597914	−	0.801560i	$-0.704004\pi$
$223$	−888037.	−1.19583	−0.597914	+	0.801560i	$0.704004\pi$
$224$	165942.	0.220972
$225$	420431.	0.553654
$226$	−135949.	−0.177054
$227$	115489.	0.148756	0.0743780	−	0.997230i	$-0.476303\pi$
$227$	115489.	0.148756	0.0743780	+	0.997230i	$0.476303\pi$
$228$	−661794.	−0.843112
$229$	633026.	0.797687	0.398844	−	0.917019i	$-0.369412\pi$
$229$	633026.	0.797687	0.398844	+	0.917019i	$0.369412\pi$
$230$	326938.	0.407517
$231$	304928.	0.375982
$232$	−454055.	−0.553845
$233$	−93730.7	−0.113108	−0.0565538	−	0.998400i	$-0.518011\pi$
$233$	−93730.7	−0.113108	−0.0565538	+	0.998400i	$0.518011\pi$
$234$	−5.84378e6	−6.97676
$235$	−232787.	−0.274972
$236$	−2.64489e6	−3.09120
$237$	242074.	0.279948
$238$	191328.	0.218946
$239$	196338.	0.222336	0.111168	−	0.993802i	$-0.464541\pi$
$239$	196338.	0.222336	0.111168	+	0.993802i	$0.464541\pi$
$240$	−535249.	−0.599829
$241$	−601173.	−0.666740	−0.333370	−	0.942796i	$-0.608186\pi$
$241$	−601173.	−0.666740	−0.333370	+	0.942796i	$0.608186\pi$
$242$	−140875.	−0.154630
$243$	3.80023e6	4.12852
$244$	−624111.	−0.671101
$245$	246789.	0.262670
$246$	−4.96413e6	−5.23004
$247$	−325929.	−0.339923
$248$	925487.	0.955523
$249$	2.47715e6	2.53194
$250$	150343.	0.152136
$251$	1.24739e6	1.24973	0.624866	−	0.780732i	$-0.285154\pi$
$251$	1.24739e6	1.24973	0.624866	+	0.780732i	$0.285154\pi$
$252$	3.39386e6	3.36661
$253$	164455.	0.161528
$254$	−2.33571e6	−2.27161
$255$	180631.	0.173957
$256$	−1.91960e6	−1.83067
$257$	−1.08988e6	−1.02931	−0.514655	−	0.857397i	$-0.672080\pi$
$257$	−1.08988e6	−1.02931	−0.514655	+	0.857397i	$0.672080\pi$
$258$	2.10426e6	1.96811
$259$	453277.	0.419870
$260$	−1.36741e6	−1.25448
$261$	1.11064e6	1.00919
$262$	−1.68258e6	−1.51434
$263$	−27912.7	−0.0248836	−0.0124418	−	0.999923i	$-0.503960\pi$
$263$	−27912.7	−0.0248836	−0.0124418	+	0.999923i	$0.503960\pi$
$264$	−1.00695e6	−0.889200
$265$	−400560.	−0.350391
$266$	289273.	0.250670
$267$	715160.	0.613939
$268$	−2.72325e6	−2.31606
$269$	133011.	0.112074	0.0560372	−	0.998429i	$-0.482153\pi$
$269$	133011.	0.112074	0.0560372	+	0.998429i	$0.482153\pi$
$270$	3.12775e6	2.61109
$271$	1.81068e6	1.49768	0.748840	−	0.662750i	$-0.230611\pi$
$271$	1.81068e6	1.49768	0.748840	+	0.662750i	$0.230611\pi$
$272$	−168935.	−0.138452
$273$	2.27524e6	1.84766
$274$	−2.14018e6	−1.72216
$275$	75625.0	0.0603023
$276$	2.49160e6	1.96882
$277$	−19923.4	−0.0156014	−0.00780069	−	0.999970i	$-0.502483\pi$
$277$	−19923.4	−0.0156014	−0.00780069	+	0.999970i	$0.502483\pi$
$278$	3.82426e6	2.96781
$279$	−2.26379e6	−1.74111
$280$	572569.	0.436448
$281$	−1.33600e6	−1.00935	−0.504674	−	0.863310i	$-0.668387\pi$
$281$	−1.33600e6	−1.00935	−0.504674	+	0.863310i	$0.668387\pi$
$282$	−2.71116e6	−2.03017
$283$	2.67306e6	1.98401	0.992003	−	0.126214i	$-0.0402825\pi$
$283$	2.67306e6	1.98401	0.992003	+	0.126214i	$0.0402825\pi$
$284$	2.29855e6	1.69106
$285$	273100.	0.199163
$286$	−1.05115e6	−0.759887
$287$	1.41985e6	1.01751
$288$	1.34040e6	0.952254
$289$	−1.36285e6	−0.959847
$290$	397156.	0.277310
$291$	−1.75332e6	−1.21375
$292$	3.82759e6	2.62705
$293$	−1.11064e6	−0.755796	−0.377898	−	0.925847i	$-0.623353\pi$
$293$	−1.11064e6	−0.755796	−0.377898	+	0.925847i	$0.623353\pi$
$294$	2.87423e6	1.93934
$295$	1.09145e6	0.730215
$296$	−1.49684e6	−0.992995
$297$	1.57331e6	1.03496
$298$	1.01927e6	0.664886
$299$	1.22710e6	0.793782
$300$	1.14576e6	0.735008
$301$	−601867.	−0.382899
$302$	−4.33304e6	−2.73386
$303$	2.52029e6	1.57704
$304$	−255416.	−0.158513
$305$	257550.	0.158530
$306$	1.54546e6	0.943524
$307$	2.77236e6	1.67882	0.839410	−	0.543498i	$-0.182900\pi$
$307$	2.77236e6	1.67882	0.839410	+	0.543498i	$0.182900\pi$
$308$	610470.	0.366680
$309$	−1.66825e6	−0.993954
$310$	−809512.	−0.478430
$311$	−2.26090e6	−1.32550	−0.662751	−	0.748840i	$-0.730611\pi$
$311$	−2.26090e6	−1.32550	−0.662751	+	0.748840i	$0.730611\pi$
$312$	−7.51347e6	−4.36972
$313$	−103700.	−0.0598300	−0.0299150	−	0.999552i	$-0.509524\pi$
$313$	−103700.	−0.0598300	−0.0299150	+	0.999552i	$0.509524\pi$
$314$	306369.	0.175356
$315$	−1.40053e6	−0.795273
$316$	484635.	0.273022
$317$	200586.	0.112112	0.0560560	−	0.998428i	$-0.482147\pi$
$317$	200586.	0.112112	0.0560560	+	0.998428i	$0.482147\pi$
$318$	−4.66513e6	−2.58700
$319$	199776.	0.109918
$320$	1.04534e6	0.570664
$321$	−4.83966e6	−2.62152
$322$	−1.08909e6	−0.585360
$323$	86195.8	0.0459706
$324$	1.39337e7	7.37403
$325$	564282.	0.296338
$326$	3.27597e6	1.70724
$327$	−6.59020e6	−3.40823
$328$	−4.68874e6	−2.40642
$329$	775454.	0.394972
$330$	880769.	0.445223
$331$	2.08232e6	1.04467	0.522334	−	0.852741i	$-0.325061\pi$
$331$	2.08232e6	1.04467	0.522334	+	0.852741i	$0.325061\pi$
$332$	4.95928e6	2.46930
$333$	3.66135e6	1.80938
$334$	2.98661e6	1.46491
$335$	1.12379e6	0.547109
$336$	1.78301e6	0.861598
$337$	−3.17787e6	−1.52427	−0.762134	−	0.647419i	$-0.775848\pi$
$337$	−3.17787e6	−1.52427	−0.762134	+	0.647419i	$0.775848\pi$
$338$	−4.27067e6	−2.03331
$339$	427551.	0.202064
$340$	361626.	0.169653
$341$	−407198.	−0.189636
$342$	2.33660e6	1.08024
$343$	−2.22177e6	−1.01968
$344$	1.98753e6	0.905559
$345$	−1.02820e6	−0.465082
$346$	−5.87455e6	−2.63806
$347$	1.71434e6	0.764319	0.382159	−	0.924096i	$-0.375181\pi$
$347$	1.71434e6	0.764319	0.382159	+	0.924096i	$0.375181\pi$
$348$	3.02673e6	1.33976
$349$	−2.03921e6	−0.896185	−0.448092	−	0.893987i	$-0.647896\pi$
$349$	−2.03921e6	−0.896185	−0.448092	+	0.893987i	$0.647896\pi$
$350$	−500818.	−0.218529
$351$	1.17394e7	5.08602
$352$	241104.	0.103717
$353$	−2.52464e6	−1.07836	−0.539178	−	0.842192i	$-0.681265\pi$
$353$	−2.52464e6	−1.07836	−0.539178	+	0.842192i	$0.681265\pi$
$354$	1.27117e7	5.39131
$355$	−948533.	−0.399468
$356$	1.43176e6	0.598750
$357$	−601715.	−0.249874
$358$	2.59968e6	1.07204
$359$	298575.	0.122269	0.0611347	−	0.998130i	$-0.480528\pi$
$359$	298575.	0.122269	0.0611347	+	0.998130i	$0.480528\pi$
$360$	4.62493e6	1.88083
$361$	130321.	0.0526316
$362$	5.00917e6	2.00907
$363$	443042.	0.176473
$364$	4.55507e6	1.80195
$365$	−1.57952e6	−0.620572
$366$	2.99956e6	1.17046
$367$	3.92397e6	1.52076	0.760379	−	0.649480i	$-0.225013\pi$
$367$	3.92397e6	1.52076	0.760379	+	0.649480i	$0.225013\pi$
$368$	961621.	0.370156
$369$	1.14689e7	4.38485
$370$	1.30927e6	0.497192
$371$	1.33434e6	0.503304
$372$	−6.16930e6	−2.31142
$373$	1.42624e6	0.530786	0.265393	−	0.964140i	$-0.414498\pi$
$373$	1.42624e6	0.530786	0.265393	+	0.964140i	$0.414498\pi$
$374$	277988.	0.102766
$375$	−472818.	−0.173627
$376$	−2.56076e6	−0.934111
$377$	1.49065e6	0.540158
$378$	−1.04191e7	−3.75059
$379$	4.60057e6	1.64518	0.822591	−	0.568633i	$-0.192528\pi$
$379$	4.60057e6	1.64518	0.822591	+	0.568633i	$0.192528\pi$
$380$	546749.	0.194236
$381$	7.34566e6	2.59250
$382$	3.39401e6	1.19002
$383$	1.88052e6	0.655060	0.327530	−	0.944841i	$-0.393784\pi$
$383$	1.88052e6	0.655060	0.327530	+	0.944841i	$0.393784\pi$
$384$	1.02450e7	3.54557
$385$	−251920.	−0.0866186
$386$	−4.11316e6	−1.40510
$387$	−4.86158e6	−1.65006
$388$	−3.51018e6	−1.18372
$389$	−4.09377e6	−1.37167	−0.685835	−	0.727757i	$-0.740563\pi$
$389$	−4.09377e6	−1.37167	−0.685835	+	0.727757i	$0.740563\pi$
$390$	6.57193e6	2.18792
$391$	−324520.	−0.107349
$392$	2.71478e6	0.892318
$393$	5.29162e6	1.72825
$394$	307806.	0.0998933
$395$	−199993.	−0.0644943
$396$	4.93107e6	1.58017
$397$	−1.73250e6	−0.551694	−0.275847	−	0.961202i	$-0.588958\pi$
$397$	−1.73250e6	−0.551694	−0.275847	+	0.961202i	$0.588958\pi$
$398$	8.61029e6	2.72465
$399$	−909744.	−0.286080
$400$	442203.	0.138188
$401$	4.60663e6	1.43061	0.715307	−	0.698811i	$-0.246287\pi$
$401$	4.60663e6	1.43061	0.715307	+	0.698811i	$0.246287\pi$
$402$	1.30883e7	4.03941
$403$	−3.03834e6	−0.931910
$404$	5.04564e6	1.53802
$405$	−5.74998e6	−1.74192
$406$	−1.32300e6	−0.398330
$407$	658585.	0.197072
$408$	1.98702e6	0.590953
$409$	−4.95850e6	−1.46569	−0.732845	−	0.680395i	$-0.761808\pi$
$409$	−4.95850e6	−1.46569	−0.732845	+	0.680395i	$0.761808\pi$
$410$	4.10118e6	1.20489
$411$	6.73074e6	1.96543
$412$	−3.33987e6	−0.969363
$413$	−3.63583e6	−1.04889
$414$	−8.79711e6	−2.52255
$415$	−2.04653e6	−0.583307
$416$	1.79902e6	0.509685
$417$	−1.20271e7	−3.38703
$418$	420296.	0.117656
$419$	3.33283e6	0.927423	0.463711	−	0.885986i	$-0.346517\pi$
$419$	3.33283e6	0.927423	0.463711	+	0.885986i	$0.346517\pi$
$420$	−3.81674e6	−1.05577
$421$	−1.32054e6	−0.363116	−0.181558	−	0.983380i	$-0.558114\pi$
$421$	−1.32054e6	−0.363116	−0.181558	+	0.983380i	$0.558114\pi$
$422$	3.93525e6	1.07570
$423$	6.26373e6	1.70209
$424$	−4.40633e6	−1.19032
$425$	−149231.	−0.0400762
$426$	−1.10471e7	−2.94934
$427$	−857943.	−0.227714
$428$	−9.68907e6	−2.55666
$429$	3.30579e6	0.867227
$430$	−1.73846e6	−0.453413
$431$	2.91066e6	0.754742	0.377371	−	0.926062i	$-0.376828\pi$
$431$	2.91066e6	0.754742	0.377371	+	0.926062i	$0.376828\pi$
$432$	9.19964e6	2.37171
$433$	2.26184e6	0.579753	0.289876	−	0.957064i	$-0.406386\pi$
$433$	2.26184e6	0.579753	0.289876	+	0.957064i	$0.406386\pi$
$434$	2.69663e6	0.687221
$435$	−1.24903e6	−0.316482
$436$	−1.31937e7	−3.32391
$437$	−490648.	−0.122904
$438$	−1.83959e7	−4.58180
$439$	−600097.	−0.148614	−0.0743071	−	0.997235i	$-0.523675\pi$
$439$	−600097.	−0.148614	−0.0743071	+	0.997235i	$0.523675\pi$
$440$	831908.	0.204854
$441$	−6.64049e6	−1.62594
$442$	2.07423e6	0.505012
$443$	−6.40330e6	−1.55023	−0.775113	−	0.631823i	$-0.782307\pi$
$443$	−6.40330e6	−1.55023	−0.775113	+	0.631823i	$0.782307\pi$
$444$	9.97796e6	2.40206
$445$	−590839.	−0.141439
$446$	8.54464e6	2.03403
$447$	−3.20553e6	−0.758806
$448$	−3.48220e6	−0.819706
$449$	−7.40357e6	−1.73311	−0.866554	−	0.499083i	$-0.833670\pi$
$449$	−7.40357e6	−1.73311	−0.866554	+	0.499083i	$0.833670\pi$
$450$	−4.04536e6	−0.941730
$451$	2.06296e6	0.477584
$452$	855963.	0.197065
$453$	1.36271e7	3.12003
$454$	−1.11122e6	−0.253024
$455$	−1.87972e6	−0.425662
$456$	3.00422e6	0.676580
$457$	−715767.	−0.160318	−0.0801588	−	0.996782i	$-0.525543\pi$
$457$	−715767.	−0.160318	−0.0801588	+	0.996782i	$0.525543\pi$
$458$	−6.09093e6	−1.35681
$459$	−3.10462e6	−0.687823
$460$	−2.05847e6	−0.453575
$461$	6.75561e6	1.48051	0.740256	−	0.672325i	$-0.234704\pi$
$461$	6.75561e6	1.48051	0.740256	+	0.672325i	$0.234704\pi$
$462$	−2.93400e6	−0.639521
$463$	−173646.	−0.0376455	−0.0188228	−	0.999823i	$-0.505992\pi$
$463$	−173646.	−0.0376455	−0.0188228	+	0.999823i	$0.505992\pi$
$464$	1.16815e6	0.251886
$465$	2.54586e6	0.546012
$466$	901871.	0.192389
$467$	4.35205e6	0.923425	0.461712	−	0.887030i	$-0.347235\pi$
$467$	4.35205e6	0.923425	0.461712	+	0.887030i	$0.347235\pi$
$468$	3.67936e7	7.76529
$469$	−3.74355e6	−0.785871
$470$	2.23986e6	0.467709
$471$	−963510.	−0.200126
$472$	1.20065e7	2.48062
$473$	−874477.	−0.179720
$474$	−2.32922e6	−0.476173
$475$	−225625.	−0.0458831
$476$	−1.20464e6	−0.243691
$477$	1.07781e7	2.16893
$478$	−1.88915e6	−0.378179
$479$	2.20031e6	0.438172	0.219086	−	0.975706i	$-0.429692\pi$
$479$	2.20031e6	0.438172	0.219086	+	0.975706i	$0.429692\pi$
$480$	−1.50742e6	−0.298628
$481$	4.91408e6	0.968456
$482$	5.78444e6	1.13408
$483$	3.42511e6	0.668047
$484$	886976.	0.172107
$485$	1.44853e6	0.279624
$486$	−3.65656e7	−7.02234
$487$	2.27275e6	0.434239	0.217120	−	0.976145i	$-0.430334\pi$
$487$	2.27275e6	0.434239	0.217120	+	0.976145i	$0.430334\pi$
$488$	2.83316e6	0.538544
$489$	−1.03027e7	−1.94840
$490$	−2.37458e6	−0.446784
$491$	3.63465e6	0.680391	0.340196	−	0.940355i	$-0.389507\pi$
$491$	3.63465e6	0.680391	0.340196	+	0.940355i	$0.389507\pi$
$492$	3.12551e7	5.82115
$493$	−394219.	−0.0730499
$494$	3.13607e6	0.578187
$495$	−2.03489e6	−0.373274
$496$	−2.38101e6	−0.434568
$497$	3.15973e6	0.573798
$498$	−2.38349e7	−4.30666
$499$	6.27043e6	1.12732	0.563659	−	0.826008i	$-0.309393\pi$
$499$	6.27043e6	1.12732	0.563659	+	0.826008i	$0.309393\pi$
$500$	−946588.	−0.169331
$501$	−9.39269e6	−1.67184
$502$	−1.20023e7	−2.12571
$503$	−1.11199e7	−1.95965	−0.979827	−	0.199846i	$-0.935956\pi$
$503$	−1.11199e7	−1.95965	−0.979827	+	0.199846i	$0.935956\pi$
$504$	−1.54064e7	−2.70163
$505$	−2.08217e6	−0.363318
$506$	−1.58238e6	−0.274748
$507$	1.34310e7	2.32054
$508$	1.47061e7	2.52836
$509$	−1.12202e6	−0.191959	−0.0959793	−	0.995383i	$-0.530598\pi$
$509$	−1.12202e6	−0.191959	−0.0959793	+	0.995383i	$0.530598\pi$
$510$	−1.73802e6	−0.295890
$511$	5.26165e6	0.891394
$512$	7.63627e6	1.28738
$513$	−4.69393e6	−0.787487
$514$	1.04868e7	1.75079
$515$	1.37825e6	0.228987
$516$	−1.32489e7	−2.19055
$517$	1.12669e6	0.185386
$518$	−4.36141e6	−0.714171
$519$	1.84751e7	3.01071
$520$	6.20735e6	1.00669
$521$	−1.22520e6	−0.197748	−0.0988741	−	0.995100i	$-0.531524\pi$
$521$	−1.22520e6	−0.197748	−0.0988741	+	0.995100i	$0.531524\pi$
$522$	−1.06865e7	−1.71656
$523$	8.52103e6	1.36219	0.681096	−	0.732195i	$-0.261504\pi$
$523$	8.52103e6	1.36219	0.681096	+	0.732195i	$0.261504\pi$
$524$	1.05939e7	1.68549
$525$	1.57504e6	0.249398
$526$	268574.	0.0423253
$527$	803525.	0.126030
$528$	2.59060e6	0.404405
$529$	−4.58909e6	−0.712997
$530$	3.85416e6	0.595992
$531$	−2.93684e7	−4.52006
$532$	−1.82132e6	−0.279002
$533$	1.53930e7	2.34695
$534$	−6.88123e6	−1.04427
$535$	3.99835e6	0.603943
$536$	1.23622e7	1.85859
$537$	−8.17582e6	−1.22348
$538$	−1.27982e6	−0.190631
$539$	−1.19446e6	−0.177092
$540$	−1.96929e7	−2.90621
$541$	1.32374e7	1.94451	0.972253	−	0.233930i	$-0.0751587\pi$
$541$	1.32374e7	1.94451	0.972253	+	0.233930i	$0.0751587\pi$
$542$	−1.74223e7	−2.54746
$543$	−1.57535e7	−2.29286
$544$	−475771.	−0.0689288
$545$	5.44458e6	0.785187
$546$	−2.18923e7	−3.14274
$547$	−8.93374e6	−1.27663	−0.638315	−	0.769775i	$-0.720368\pi$
$547$	−8.93374e6	−1.27663	−0.638315	+	0.769775i	$0.720368\pi$
$548$	1.34750e7	1.91681
$549$	−6.93004e6	−0.981308
$550$	−727659.	−0.102570
$551$	−596026.	−0.0836347
$552$	−1.13106e7	−1.57993
$553$	666210.	0.0926400
$554$	191701.	0.0265369
$555$	−4.11757e6	−0.567425
$556$	−2.40783e7	−3.30324
$557$	4.35992e6	0.595444	0.297722	−	0.954653i	$-0.403773\pi$
$557$	4.35992e6	0.595444	0.297722	+	0.954653i	$0.403773\pi$
$558$	2.17820e7	2.96151
$559$	−6.52498e6	−0.883181
$560$	−1.47305e6	−0.198495
$561$	−874256.	−0.117282
$562$	1.28549e7	1.71684
$563$	7.79872e6	1.03694	0.518468	−	0.855097i	$-0.326502\pi$
$563$	7.79872e6	1.03694	0.518468	+	0.855097i	$0.326502\pi$
$564$	1.70700e7	2.25962
$565$	−353227.	−0.0465514
$566$	−2.57200e7	−3.37466
$567$	1.91542e7	2.50211
$568$	−1.04343e7	−1.35704
$569$	6.30429e6	0.816311	0.408155	−	0.912912i	$-0.366172\pi$
$569$	6.30429e6	0.816311	0.408155	+	0.912912i	$0.366172\pi$
$570$	−2.62775e6	−0.338764
$571$	−1.93891e6	−0.248867	−0.124434	−	0.992228i	$-0.539711\pi$
$571$	−1.93891e6	−0.248867	−0.124434	+	0.992228i	$0.539711\pi$
$572$	6.61824e6	0.845771
$573$	−1.06740e7	−1.35812
$574$	−1.36617e7	−1.73072
$575$	849460.	0.107145
$576$	−2.81275e7	−3.53244
$577$	1.76842e6	0.221130	0.110565	−	0.993869i	$-0.464734\pi$
$577$	1.76842e6	0.221130	0.110565	+	0.993869i	$0.464734\pi$
$578$	1.31132e7	1.63264
$579$	1.29356e7	1.60358
$580$	−2.50057e6	−0.308652
$581$	6.81734e6	0.837866
$582$	1.68704e7	2.06451
$583$	1.93871e6	0.236233
$584$	−1.73754e7	−2.10815
$585$	−1.51835e7	−1.83435
$586$	1.06865e7	1.28556
$587$	7.66283e6	0.917897	0.458949	−	0.888463i	$-0.348226\pi$
$587$	7.66283e6	0.917897	0.458949	+	0.888463i	$0.348226\pi$
$588$	−1.80967e7	−2.15852
$589$	1.21486e6	0.144291
$590$	−1.05019e7	−1.24205
$591$	−968030.	−0.114004
$592$	3.85095e6	0.451610
$593$	−7.43254e6	−0.867962	−0.433981	−	0.900922i	$-0.642892\pi$
$593$	−7.43254e6	−0.867962	−0.433981	+	0.900922i	$0.642892\pi$
$594$	−1.51383e7	−1.76040
$595$	497115.	0.0575657
$596$	−6.41751e6	−0.740032
$597$	−2.70788e7	−3.10952
$598$	−1.18071e7	−1.35017
$599$	1.51333e7	1.72333	0.861663	−	0.507481i	$-0.169423\pi$
$599$	1.51333e7	1.72333	0.861663	+	0.507481i	$0.169423\pi$
$600$	−5.20121e6	−0.589829
$601$	1.08045e7	1.22016	0.610080	−	0.792340i	$-0.291137\pi$
$601$	1.08045e7	1.22016	0.610080	+	0.792340i	$0.291137\pi$
$602$	5.79112e6	0.651286
$603$	−3.02385e7	−3.38663
$604$	2.72817e7	3.04284
$605$	−366025.	−0.0406558
$606$	−2.42500e7	−2.68244
$607$	−6.90150e6	−0.760277	−0.380138	−	0.924930i	$-0.624124\pi$
$607$	−6.90150e6	−0.760277	−0.380138	+	0.924930i	$0.624124\pi$
$608$	−719327.	−0.0789164
$609$	4.16073e6	0.454597
$610$	−2.47813e6	−0.269649
$611$	8.40687e6	0.911027
$612$	−9.73050e6	−1.05016
$613$	−1.38636e7	−1.49013	−0.745066	−	0.666991i	$-0.767582\pi$
$613$	−1.38636e7	−1.49013	−0.745066	+	0.666991i	$0.767582\pi$
$614$	−2.66755e7	−2.85556
$615$	−1.28979e7	−1.37509
$616$	−2.77123e6	−0.294253
$617$	−2.49051e6	−0.263376	−0.131688	−	0.991291i	$-0.542040\pi$
$617$	−2.49051e6	−0.263376	−0.131688	+	0.991291i	$0.542040\pi$
$618$	1.60518e7	1.69065
$619$	−1.75527e6	−0.184127	−0.0920633	−	0.995753i	$-0.529346\pi$
$619$	−1.75527e6	−0.184127	−0.0920633	+	0.995753i	$0.529346\pi$
$620$	5.09685e6	0.532504
$621$	1.76723e7	1.83892
$622$	2.17542e7	2.25459
$623$	1.96819e6	0.203164
$624$	1.93300e7	1.98733
$625$	390625.	0.0400000
$626$	997798.	0.101767
$627$	−1.32180e6	−0.134276
$628$	−1.92896e6	−0.195175
$629$	−1.29959e6	−0.130972
$630$	1.34758e7	1.35271
$631$	1.94825e7	1.94792	0.973959	−	0.226724i	$-0.0728014\pi$
$631$	1.94825e7	1.94792	0.973959	+	0.226724i	$0.0728014\pi$
$632$	−2.20001e6	−0.219094
$633$	−1.23761e7	−1.22765
$634$	−1.93002e6	−0.190695
$635$	−6.06871e6	−0.597258
$636$	2.93726e7	2.87939
$637$	−8.91253e6	−0.870267
$638$	−1.92223e6	−0.186962
$639$	2.55228e7	2.47272
$640$	−8.46407e6	−0.816826
$641$	−5.43407e6	−0.522372	−0.261186	−	0.965288i	$-0.584114\pi$
$641$	−5.43407e6	−0.522372	−0.261186	+	0.965288i	$0.584114\pi$
$642$	4.65669e7	4.45902
$643$	7.33261e6	0.699409	0.349704	−	0.936860i	$-0.386282\pi$
$643$	7.33261e6	0.699409	0.349704	+	0.936860i	$0.386282\pi$
$644$	6.85712e6	0.651519
$645$	5.46735e6	0.517461
$646$	−829371.	−0.0781929
$647$	49065.0	0.00460798	0.00230399	−	0.999997i	$-0.499267\pi$
$647$	49065.0	0.00460798	0.00230399	+	0.999997i	$0.499267\pi$
$648$	−6.32523e7	−5.91751
$649$	−5.28264e6	−0.492311
$650$	−5.42949e6	−0.504052
$651$	−8.48071e6	−0.784296
$652$	−2.06261e7	−1.90020
$653$	8.26043e6	0.758088	0.379044	−	0.925379i	$-0.376253\pi$
$653$	8.26043e6	0.758088	0.379044	+	0.925379i	$0.376253\pi$
$654$	6.34105e7	5.79718
$655$	−4.37174e6	−0.398154
$656$	1.20628e7	1.09443
$657$	4.25010e7	3.84137
$658$	−7.46137e6	−0.671821
$659$	1.58627e7	1.42287	0.711433	−	0.702754i	$-0.248047\pi$
$659$	1.58627e7	1.42287	0.711433	+	0.702754i	$0.248047\pi$
$660$	−5.54550e6	−0.495543
$661$	1.00428e7	0.894026	0.447013	−	0.894528i	$-0.352488\pi$
$661$	1.00428e7	0.894026	0.447013	+	0.894528i	$0.352488\pi$
$662$	−2.00360e7	−1.77691
$663$	−6.52333e6	−0.576349
$664$	−2.25127e7	−1.98156
$665$	751597.	0.0659069
$666$	−3.52293e7	−3.07764
$667$	2.24399e6	0.195302
$668$	−1.88043e7	−1.63048
$669$	−2.68723e7	−2.32135
$670$	−1.08131e7	−0.930596
$671$	−1.24654e6	−0.106881
$672$	5.02147e6	0.428951
$673$	8.86701e6	0.754639	0.377320	−	0.926083i	$-0.376846\pi$
$673$	8.86701e6	0.754639	0.377320	+	0.926083i	$0.376846\pi$
$674$	3.05773e7	2.59268
$675$	8.12661e6	0.686515
$676$	2.68890e7	2.26312
$677$	7.56193e6	0.634105	0.317052	−	0.948408i	$-0.397307\pi$
$677$	7.56193e6	0.634105	0.317052	+	0.948408i	$0.397307\pi$
$678$	−4.11387e6	−0.343698
$679$	−4.82531e6	−0.401653
$680$	−1.64161e6	−0.136143
$681$	3.49473e6	0.288766
$682$	3.91804e6	0.322558
$683$	−1.22277e7	−1.00298	−0.501490	−	0.865163i	$-0.667215\pi$
$683$	−1.22277e7	−1.00298	−0.501490	+	0.865163i	$0.667215\pi$
$684$	−1.47117e7	−1.20233
$685$	−5.56069e6	−0.452796
$686$	2.13778e7	1.73441
$687$	1.91556e7	1.54847
$688$	−5.11333e6	−0.411844
$689$	1.44658e7	1.16090
$690$	9.89326e6	0.791073
$691$	1.43128e7	1.14032	0.570162	−	0.821532i	$-0.306880\pi$
$691$	1.43128e7	1.14032	0.570162	+	0.821532i	$0.306880\pi$
$692$	3.69874e7	2.93622
$693$	6.77857e6	0.536173
$694$	−1.64953e7	−1.30006
$695$	9.93631e6	0.780303
$696$	−1.37399e7	−1.07513
$697$	−4.07085e6	−0.317397
$698$	1.96211e7	1.52435
$699$	−2.83632e6	−0.219565
$700$	3.15325e6	0.243228
$701$	479201.	0.0368318	0.0184159	−	0.999830i	$-0.494138\pi$
$701$	479201.	0.0368318	0.0184159	+	0.999830i	$0.494138\pi$
$702$	−1.12956e8	−8.65098
$703$	−1.96487e6	−0.149950
$704$	−5.05942e6	−0.384742
$705$	−7.04421e6	−0.533777
$706$	2.42919e7	1.83421
$707$	6.93606e6	0.521873
$708$	−8.00352e7	−6.00065
$709$	7.13363e6	0.532960	0.266480	−	0.963840i	$-0.414139\pi$
$709$	7.13363e6	0.532960	0.266480	+	0.963840i	$0.414139\pi$
$710$	9.12673e6	0.679468
$711$	5.38132e6	0.399222
$712$	−6.49949e6	−0.480484
$713$	−4.57386e6	−0.336945
$714$	5.78966e6	0.425018
$715$	−2.73113e6	−0.199791
$716$	−1.63681e7	−1.19321
$717$	5.94126e6	0.431599
$718$	−2.87287e6	−0.207972
$719$	−2.31329e6	−0.166881	−0.0834406	−	0.996513i	$-0.526591\pi$
$719$	−2.31329e6	−0.166881	−0.0834406	+	0.996513i	$0.526591\pi$
$720$	−1.18986e7	−0.855392
$721$	−4.59119e6	−0.328918
$722$	−1.25394e6	−0.0895228
$723$	−1.81917e7	−1.29428
$724$	−3.15388e7	−2.23614
$725$	1.03190e6	0.0729110
$726$	−4.26292e6	−0.300169
$727$	−1.62649e7	−1.14134	−0.570669	−	0.821180i	$-0.693316\pi$
$727$	−1.62649e7	−1.14134	−0.570669	+	0.821180i	$0.693316\pi$
$728$	−2.06778e7	−1.44602
$729$	5.91067e7	4.11925
$730$	1.51980e7	1.05555
$731$	1.72561e6	0.119440
$732$	−1.88858e7	−1.30274
$733$	2.22711e6	0.153103	0.0765513	−	0.997066i	$-0.475609\pi$
$733$	2.22711e6	0.153103	0.0765513	+	0.997066i	$0.475609\pi$
$734$	−3.77562e7	−2.58671
$735$	7.46791e6	0.509895
$736$	2.70821e6	0.184284
$737$	−5.43915e6	−0.368861
$738$	−1.10353e8	−7.45835
$739$	5.39595e6	0.363460	0.181730	−	0.983348i	$-0.441830\pi$
$739$	5.39595e6	0.363460	0.181730	+	0.983348i	$0.441830\pi$
$740$	−8.24342e6	−0.553386
$741$	−9.86274e6	−0.659861
$742$	−1.28389e7	−0.856086
$743$	2.14587e6	0.142604	0.0713020	−	0.997455i	$-0.477285\pi$
$743$	2.14587e6	0.142604	0.0713020	+	0.997455i	$0.477285\pi$
$744$	2.80056e7	1.85487
$745$	2.64829e6	0.174813
$746$	−1.37232e7	−0.902832
$747$	5.50671e7	3.61069
$748$	−1.75027e6	−0.114380
$749$	−1.33192e7	−0.867509
$750$	4.54943e6	0.295327
$751$	9.37185e6	0.606353	0.303177	−	0.952934i	$-0.401953\pi$
$751$	9.37185e6	0.606353	0.303177	+	0.952934i	$0.401953\pi$
$752$	6.58809e6	0.424830
$753$	3.77464e7	2.42598
$754$	−1.43429e7	−0.918774
$755$	−1.12582e7	−0.718792
$756$	6.56007e7	4.17449
$757$	−4.20633e6	−0.266787	−0.133393	−	0.991063i	$-0.542587\pi$
$757$	−4.20633e6	−0.266787	−0.133393	+	0.991063i	$0.542587\pi$
$758$	−4.42664e7	−2.79835
$759$	4.97648e6	0.313558
$760$	−2.48197e6	−0.155870
$761$	3.16783e7	1.98290	0.991450	−	0.130488i	$-0.0416545\pi$
$761$	3.16783e7	1.98290	0.991450	+	0.130488i	$0.0416545\pi$
$762$	−7.06794e7	−4.40967
$763$	−1.81369e7	−1.12785
$764$	−2.13694e7	−1.32452
$765$	4.01545e6	0.248073
$766$	−1.80943e7	−1.11421
$767$	−3.94169e7	−2.41932
$768$	−5.80878e7	−3.55371
$769$	2.94446e7	1.79552	0.897758	−	0.440488i	$-0.145195\pi$
$769$	2.94446e7	1.79552	0.897758	+	0.440488i	$0.145195\pi$
$770$	2.42396e6	0.147333
$771$	−3.29802e7	−1.99810
$772$	2.58973e7	1.56391
$773$	−9.22477e6	−0.555273	−0.277637	−	0.960686i	$-0.589551\pi$
$773$	−9.22477e6	−0.555273	−0.277637	+	0.960686i	$0.589551\pi$
$774$	4.67779e7	2.80665
$775$	−2.10330e6	−0.125790
$776$	1.59345e7	0.949912
$777$	1.37163e7	0.815053
$778$	3.93900e7	2.33312
$779$	−6.15479e6	−0.363387
$780$	−4.13782e7	−2.43520
$781$	4.59090e6	0.269321
$782$	3.12251e6	0.182594
$783$	2.14678e7	1.25136
$784$	−6.98435e6	−0.405823
$785$	796016.	0.0461050
$786$	−5.09156e7	−2.93964
$787$	−1.20919e7	−0.695920	−0.347960	−	0.937509i	$-0.613125\pi$
$787$	−1.20919e7	−0.695920	−0.347960	+	0.937509i	$0.613125\pi$
$788$	−1.93801e6	−0.111183
$789$	−844649.	−0.0483041
$790$	1.92432e6	0.109701
$791$	1.17666e6	0.0668668
$792$	−2.23846e7	−1.26805
$793$	−9.30116e6	−0.525236
$794$	1.66700e7	0.938394
$795$	−1.21211e7	−0.680180
$796$	−5.42121e7	−3.03259
$797$	−2.22938e7	−1.24319	−0.621596	−	0.783338i	$-0.713515\pi$
$797$	−2.22938e7	−1.24319	−0.621596	+	0.783338i	$0.713515\pi$
$798$	8.75350e6	0.486602
$799$	−2.22330e6	−0.123206
$800$	1.24537e6	0.0687977
$801$	1.58981e7	0.875514
$802$	−4.43247e7	−2.43338
$803$	7.64486e6	0.418390
$804$	−8.24065e7	−4.49595
$805$	−2.82970e6	−0.153904
$806$	2.92347e7	1.58512
$807$	4.02496e6	0.217559
$808$	−2.29047e7	−1.23423
$809$	5.41299e6	0.290781	0.145391	−	0.989374i	$-0.453556\pi$
$809$	5.41299e6	0.290781	0.145391	+	0.989374i	$0.453556\pi$
$810$	5.53259e7	2.96289
$811$	1.68730e7	0.900827	0.450414	−	0.892820i	$-0.351277\pi$
$811$	1.68730e7	0.900827	0.450414	+	0.892820i	$0.351277\pi$
$812$	8.32985e6	0.443350
$813$	5.47920e7	2.90730
$814$	−6.33686e6	−0.335207
$815$	8.51171e6	0.448872
$816$	−5.11204e6	−0.268763
$817$	2.60898e6	0.136746
$818$	4.77104e7	2.49304
$819$	5.05788e7	2.63487
$820$	−2.58218e7	−1.34107
$821$	−7.60574e6	−0.393807	−0.196904	−	0.980423i	$-0.563089\pi$
$821$	−7.60574e6	−0.393807	−0.196904	+	0.980423i	$0.563089\pi$
$822$	−6.47628e7	−3.34307
$823$	−1.15033e7	−0.592004	−0.296002	−	0.955187i	$-0.595654\pi$
$823$	−1.15033e7	−0.592004	−0.296002	+	0.955187i	$0.595654\pi$
$824$	1.51614e7	0.777893
$825$	2.28844e6	0.117059
$826$	3.49837e7	1.78409
$827$	6.70471e6	0.340891	0.170446	−	0.985367i	$-0.445479\pi$
$827$	6.70471e6	0.340891	0.170446	+	0.985367i	$0.445479\pi$
$828$	5.53884e7	2.80765
$829$	−2.05713e7	−1.03962	−0.519811	−	0.854281i	$-0.673998\pi$
$829$	−2.05713e7	−1.03962	−0.519811	+	0.854281i	$0.673998\pi$
$830$	1.96915e7	0.992166
$831$	−602888.	−0.0302855
$832$	−3.77513e7	−1.89070
$833$	2.35702e6	0.117693
$834$	1.15724e8	5.76112
$835$	7.75989e6	0.385159
$836$	−2.64627e6	−0.130954
$837$	−4.37573e7	−2.15892
$838$	−3.20683e7	−1.57749
$839$	2.14361e7	1.05133	0.525667	−	0.850690i	$-0.323816\pi$
$839$	2.14361e7	1.05133	0.525667	+	0.850690i	$0.323816\pi$
$840$	1.73261e7	0.847234
$841$	−1.77852e7	−0.867100
$842$	1.27061e7	0.617637
$843$	−4.04279e7	−1.95935
$844$	−2.47772e7	−1.19728
$845$	−1.10962e7	−0.534604
$846$	−6.02692e7	−2.89514
$847$	1.21929e6	0.0583982
$848$	1.13362e7	0.541351
$849$	8.08879e7	3.85136
$850$	1.43589e6	0.0681670
$851$	7.39757e6	0.350159
$852$	6.95549e7	3.28268
$853$	7.69594e6	0.362150	0.181075	−	0.983469i	$-0.442042\pi$
$853$	7.69594e6	0.362150	0.181075	+	0.983469i	$0.442042\pi$
$854$	8.25508e6	0.387326
$855$	6.07103e6	0.284019
$856$	4.39836e7	2.05166
$857$	−3.11955e6	−0.145091	−0.0725455	−	0.997365i	$-0.523112\pi$
$857$	−3.11955e6	−0.145091	−0.0725455	+	0.997365i	$0.523112\pi$
$858$	−3.18081e7	−1.47510
$859$	−3.48395e7	−1.61097	−0.805487	−	0.592614i	$-0.798096\pi$
$859$	−3.48395e7	−1.61097	−0.805487	+	0.592614i	$0.798096\pi$
$860$	1.09457e7	0.504659
$861$	4.29653e7	1.97519
$862$	−2.80062e7	−1.28377
$863$	−7.88699e6	−0.360483	−0.180241	−	0.983622i	$-0.557688\pi$
$863$	−7.88699e6	−0.360483	−0.180241	+	0.983622i	$0.557688\pi$
$864$	2.59089e7	1.18077
$865$	−1.52634e7	−0.693605
$866$	−2.17633e7	−0.986122
$867$	−4.12402e7	−1.86326
$868$	−1.69785e7	−0.764892
$869$	967964.	0.0434820
$870$	1.20181e7	0.538315
$871$	−4.05847e7	−1.81266
$872$	5.98927e7	2.66737
$873$	−3.89765e7	−1.73088
$874$	4.72098e6	0.209052
$875$	−1.30124e6	−0.0574563
$876$	1.15824e8	5.09964
$877$	−3.83765e7	−1.68487	−0.842435	−	0.538798i	$-0.818879\pi$
$877$	−3.83765e7	−1.68487	−0.842435	+	0.538798i	$0.818879\pi$
$878$	5.77410e6	0.252783
$879$	−3.36084e7	−1.46715
$880$	−2.14026e6	−0.0931665
$881$	−1.53622e7	−0.666826	−0.333413	−	0.942781i	$-0.608200\pi$
$881$	−1.53622e7	−0.666826	−0.333413	+	0.942781i	$0.608200\pi$
$882$	6.38943e7	2.76561
$883$	−4.06962e7	−1.75651	−0.878257	−	0.478189i	$-0.841294\pi$
$883$	−4.06962e7	−1.75651	−0.878257	+	0.478189i	$0.841294\pi$
$884$	−1.30598e7	−0.562090
$885$	3.30278e7	1.41750
$886$	6.16122e7	2.63683
$887$	−2.43220e7	−1.03798	−0.518992	−	0.854779i	$-0.673692\pi$
$887$	−2.43220e7	−1.03798	−0.518992	+	0.854779i	$0.673692\pi$
$888$	−4.52950e7	−1.92761
$889$	2.02159e7	0.857906
$890$	5.68502e6	0.240578
$891$	2.78299e7	1.17440
$892$	−5.37988e7	−2.26391
$893$	−3.36144e6	−0.141058
$894$	3.08434e7	1.29068
$895$	6.75456e6	0.281864
$896$	2.81953e7	1.17329
$897$	3.71324e7	1.54089
$898$	7.12367e7	2.94790
$899$	−5.55621e6	−0.229287
$900$	2.54704e7	1.04817
$901$	−3.82566e6	−0.156998
$902$	−1.98497e7	−0.812339
$903$	−1.82127e7	−0.743285
$904$	−3.88565e6	−0.158140
$905$	1.30150e7	0.528229
$906$	−1.31120e8	−5.30697
$907$	7.72688e6	0.311879	0.155939	−	0.987767i	$-0.450160\pi$
$907$	7.72688e6	0.311879	0.155939	+	0.987767i	$0.450160\pi$
$908$	6.99650e6	0.281622
$909$	5.60261e7	2.24896
$910$	1.80866e7	0.724024
$911$	2.58177e7	1.03067	0.515337	−	0.856987i	$-0.327667\pi$
$911$	2.58177e7	1.03067	0.515337	+	0.856987i	$0.327667\pi$
$912$	−7.72899e6	−0.307706
$913$	9.90519e6	0.393265
$914$	6.88707e6	0.272690
$915$	7.79355e6	0.307739
$916$	3.83497e7	1.51016
$917$	1.45630e7	0.571911
$918$	2.98725e7	1.16994
$919$	−4.19768e7	−1.63953	−0.819767	−	0.572697i	$-0.805897\pi$
$919$	−4.19768e7	−1.63953	−0.819767	+	0.572697i	$0.805897\pi$
$920$	9.34443e6	0.363985
$921$	8.38928e7	3.25893
$922$	−6.50020e7	−2.51825
$923$	3.42554e7	1.32350
$924$	1.84730e7	0.711801
$925$	3.40178e6	0.130723
$926$	1.67082e6	0.0640326
$927$	−3.70854e7	−1.41744
$928$	3.28986e6	0.125403
$929$	−2.88475e7	−1.09665	−0.548326	−	0.836264i	$-0.684735\pi$
$929$	−2.88475e7	−1.09665	−0.548326	+	0.836264i	$0.684735\pi$
$930$	−2.44961e7	−0.928731
$931$	3.56363e6	0.134747
$932$	−5.67836e6	−0.214133
$933$	−6.84157e7	−2.57307
$934$	−4.18751e7	−1.57068
$935$	722278.	0.0270194
$936$	−1.67025e8	−6.23148
$937$	1.87280e7	0.696855	0.348427	−	0.937336i	$-0.386716\pi$
$937$	1.87280e7	0.696855	0.348427	+	0.937336i	$0.386716\pi$
$938$	3.60202e7	1.33672
$939$	−3.13801e6	−0.116142
$940$	−1.41026e7	−0.520571
$941$	−2.97868e7	−1.09660	−0.548302	−	0.836280i	$-0.684726\pi$
$941$	−2.97868e7	−1.09660	−0.548302	+	0.836280i	$0.684726\pi$
$942$	9.27083e6	0.340401
$943$	2.31723e7	0.848574
$944$	−3.08892e7	−1.12818
$945$	−2.70712e7	−0.986115
$946$	8.41416e6	0.305691
$947$	4.27401e7	1.54868	0.774339	−	0.632771i	$-0.218083\pi$
$947$	4.27401e7	1.54868	0.774339	+	0.632771i	$0.218083\pi$
$948$	1.46652e7	0.529991
$949$	5.70428e7	2.05606
$950$	2.17095e6	0.0780442
$951$	6.06980e6	0.217632
$952$	5.46848e6	0.195557
$953$	−1.28385e7	−0.457914	−0.228957	−	0.973437i	$-0.573531\pi$
$953$	−1.28385e7	−0.457914	−0.228957	+	0.973437i	$0.573531\pi$
$954$	−1.03706e8	−3.68921
$955$	8.81843e6	0.312884
$956$	1.18945e7	0.420921
$957$	6.04530e6	0.213372
$958$	−2.11712e7	−0.745302
$959$	1.85236e7	0.650399
$960$	3.16322e7	1.10778
$961$	−1.73041e7	−0.604422
$962$	−4.72830e7	−1.64728
$963$	−1.07586e8	−3.73844
$964$	−3.64200e7	−1.26226
$965$	−1.06869e7	−0.369432
$966$	−3.29562e7	−1.13630
$967$	−3.11472e7	−1.07116	−0.535578	−	0.844486i	$-0.679906\pi$
$967$	−3.11472e7	−1.07116	−0.535578	+	0.844486i	$0.679906\pi$
$968$	−4.02643e6	−0.138112
$969$	2.60832e6	0.0892382
$970$	−1.39377e7	−0.475621
$971$	−2.55114e7	−0.868332	−0.434166	−	0.900833i	$-0.642957\pi$
$971$	−2.55114e7	−0.868332	−0.434166	+	0.900833i	$0.642957\pi$
$972$	2.30224e8	7.81602
$973$	−3.30996e7	−1.12083
$974$	−2.18683e7	−0.738613
$975$	1.70754e7	0.575253
$976$	−7.28891e6	−0.244928
$977$	4.49635e7	1.50704	0.753518	−	0.657427i	$-0.228355\pi$
$977$	4.49635e7	1.50704	0.753518	+	0.657427i	$0.228355\pi$
$978$	9.91320e7	3.31411
$979$	2.85966e6	0.0953582
$980$	1.49509e7	0.497280
$981$	−1.46501e8	−4.86034
$982$	−3.49723e7	−1.15730
$983$	−3.96418e7	−1.30849	−0.654244	−	0.756284i	$-0.727013\pi$
$983$	−3.96418e7	−1.30849	−0.654244	+	0.756284i	$0.727013\pi$
$984$	−1.41883e8	−4.67135
$985$	799751.	0.0262642
$986$	3.79315e6	0.124253
$987$	2.34655e7	0.766721
$988$	−1.97453e7	−0.643535
$989$	−9.82258e6	−0.319326
$990$	1.95796e7	0.634914
$991$	3.34609e7	1.08231	0.541157	−	0.840922i	$-0.317986\pi$
$991$	3.34609e7	1.08231	0.541157	+	0.840922i	$0.317986\pi$
$992$	−6.70563e6	−0.216352
$993$	6.30119e7	2.02791
$994$	−3.04027e7	−0.975993
$995$	2.23715e7	0.716370
$996$	1.50070e8	4.79341
$997$	−1.96029e7	−0.624571	−0.312285	−	0.949988i	$-0.601095\pi$
$997$	−1.96029e7	−0.624571	−0.312285	+	0.949988i	$0.601095\pi$
$998$	−6.03337e7	−1.91749
$999$	7.07711e7	2.24358

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.d.1.4	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.d.1.4	✓	37	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)

\(f(q)\)	\(=\)	\(q-9.62194 q^{2} +30.2604 q^{3} +60.5817 q^{4} -25.0000 q^{5} -291.163 q^{6} +83.2794 q^{7} -275.011 q^{8} +672.690 q^{9} +O(q^{10})\)	\(q-9.62194 q^{2} +30.2604 q^{3} +60.5817 q^{4} -25.0000 q^{5} -291.163 q^{6} +83.2794 q^{7} -275.011 q^{8} +672.690 q^{9} +240.548 q^{10} +121.000 q^{11} +1833.22 q^{12} +902.851 q^{13} -801.309 q^{14} -756.509 q^{15} +707.524 q^{16} -238.770 q^{17} -6472.58 q^{18} -361.000 q^{19} -1514.54 q^{20} +2520.07 q^{21} -1164.25 q^{22} +1359.14 q^{23} -8321.93 q^{24} +625.000 q^{25} -8687.18 q^{26} +13002.6 q^{27} +5045.20 q^{28} +1651.04 q^{29} +7279.08 q^{30} -3365.27 q^{31} +1992.60 q^{32} +3661.50 q^{33} +2297.43 q^{34} -2081.98 q^{35} +40752.7 q^{36} +5442.85 q^{37} +3473.52 q^{38} +27320.6 q^{39} +6875.27 q^{40} +17049.3 q^{41} -24247.9 q^{42} -7227.08 q^{43} +7330.38 q^{44} -16817.3 q^{45} -13077.5 q^{46} +9311.47 q^{47} +21409.9 q^{48} -9871.54 q^{49} -6013.71 q^{50} -7225.26 q^{51} +54696.2 q^{52} +16022.4 q^{53} -125110. q^{54} -3025.00 q^{55} -22902.7 q^{56} -10924.0 q^{57} -15886.2 q^{58} -43658.2 q^{59} -45830.6 q^{60} -10302.0 q^{61} +32380.5 q^{62} +56021.2 q^{63} -41813.4 q^{64} -22571.3 q^{65} -35230.8 q^{66} -44951.7 q^{67} -14465.1 q^{68} +41127.9 q^{69} +20032.7 q^{70} +37941.3 q^{71} -184997. q^{72} +63180.7 q^{73} -52370.8 q^{74} +18912.7 q^{75} -21870.0 q^{76} +10076.8 q^{77} -262877. q^{78} +7999.70 q^{79} -17688.1 q^{80} +229999. q^{81} -164047. q^{82} +81861.0 q^{83} +152670. q^{84} +5969.24 q^{85} +69538.5 q^{86} +49961.2 q^{87} -33276.3 q^{88} +23633.6 q^{89} +161815. q^{90} +75188.9 q^{91} +82338.7 q^{92} -101834. q^{93} -89594.4 q^{94} +9025.00 q^{95} +60296.7 q^{96} -57941.3 q^{97} +94983.3 q^{98} +81395.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9}+O(q^{10}) \) 37 * q + 4 * q^2 + 27 * q^3 + 616 * q^4 - 925 * q^5 + 141 * q^6 - 79 * q^7 + 72 * q^8 + 3140 * q^9	\( 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9} - 100 q^{10} + 4477 q^{11} + 872 q^{12} + 719 q^{13} - 625 q^{14} - 675 q^{15} + 6940 q^{16} + 119 q^{17} - 4237 q^{18} - 13357 q^{19} - 15400 q^{20} + 2905 q^{21} + 484 q^{22} - 1252 q^{23} + 5884 q^{24} + 23125 q^{25} + 13201 q^{26} + 9918 q^{27} + 15461 q^{28} + 13221 q^{29} - 3525 q^{30} + 6419 q^{31} + 13173 q^{32} + 3267 q^{33} + 35415 q^{34} + 1975 q^{35} + 80543 q^{36} + 9037 q^{37} - 1444 q^{38} - 6184 q^{39} - 1800 q^{40} + 52577 q^{41} - 28578 q^{42} + 963 q^{43} + 74536 q^{44} - 78500 q^{45} - 10531 q^{46} + 49346 q^{47} + 80107 q^{48} + 70288 q^{49} + 2500 q^{50} + 140786 q^{51} + 165062 q^{52} - 34457 q^{53} + 34216 q^{54} - 111925 q^{55} - 64095 q^{56} - 9747 q^{57} - 126140 q^{58} + 56521 q^{59} - 21800 q^{60} + 6613 q^{61} + 494 q^{62} - 125618 q^{63} - 140426 q^{64} - 17975 q^{65} + 17061 q^{66} - 43534 q^{67} - 138520 q^{68} + 34618 q^{69} + 15625 q^{70} + 95986 q^{71} - 42192 q^{72} + 109218 q^{73} - 182005 q^{74} + 16875 q^{75} - 222376 q^{76} - 9559 q^{77} - 369624 q^{78} + 64943 q^{79} - 173500 q^{80} + 388941 q^{81} - 126926 q^{82} + 109741 q^{83} - 112886 q^{84} - 2975 q^{85} + 43866 q^{86} + 142492 q^{87} + 8712 q^{88} - 119092 q^{89} + 105925 q^{90} + 349320 q^{91} + 433396 q^{92} - 108630 q^{93} + 196160 q^{94} + 333925 q^{95} + 376630 q^{96} + 68774 q^{97} + 310926 q^{98} + 379940 q^{99}+O(q^{100}) \) 37 * q + 4 * q^2 + 27 * q^3 + 616 * q^4 - 925 * q^5 + 141 * q^6 - 79 * q^7 + 72 * q^8 + 3140 * q^9 - 100 * q^10 + 4477 * q^11 + 872 * q^12 + 719 * q^13 - 625 * q^14 - 675 * q^15 + 6940 * q^16 + 119 * q^17 - 4237 * q^18 - 13357 * q^19 - 15400 * q^20 + 2905 * q^21 + 484 * q^22 - 1252 * q^23 + 5884 * q^24 + 23125 * q^25 + 13201 * q^26 + 9918 * q^27 + 15461 * q^28 + 13221 * q^29 - 3525 * q^30 + 6419 * q^31 + 13173 * q^32 + 3267 * q^33 + 35415 * q^34 + 1975 * q^35 + 80543 * q^36 + 9037 * q^37 - 1444 * q^38 - 6184 * q^39 - 1800 * q^40 + 52577 * q^41 - 28578 * q^42 + 963 * q^43 + 74536 * q^44 - 78500 * q^45 - 10531 * q^46 + 49346 * q^47 + 80107 * q^48 + 70288 * q^49 + 2500 * q^50 + 140786 * q^51 + 165062 * q^52 - 34457 * q^53 + 34216 * q^54 - 111925 * q^55 - 64095 * q^56 - 9747 * q^57 - 126140 * q^58 + 56521 * q^59 - 21800 * q^60 + 6613 * q^61 + 494 * q^62 - 125618 * q^63 - 140426 * q^64 - 17975 * q^65 + 17061 * q^66 - 43534 * q^67 - 138520 * q^68 + 34618 * q^69 + 15625 * q^70 + 95986 * q^71 - 42192 * q^72 + 109218 * q^73 - 182005 * q^74 + 16875 * q^75 - 222376 * q^76 - 9559 * q^77 - 369624 * q^78 + 64943 * q^79 - 173500 * q^80 + 388941 * q^81 - 126926 * q^82 + 109741 * q^83 - 112886 * q^84 - 2975 * q^85 + 43866 * q^86 + 142492 * q^87 + 8712 * q^88 - 119092 * q^89 + 105925 * q^90 + 349320 * q^91 + 433396 * q^92 - 108630 * q^93 + 196160 * q^94 + 333925 * q^95 + 376630 * q^96 + 68774 * q^97 + 310926 * q^98 + 379940 * q^99

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