LMFDB - Embedded newform 1045.6.a.g.1.12

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:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-4.54694 q^{2} -4.48487 q^{3} -11.3254 q^{4} -25.0000 q^{5} +20.3924 q^{6} +16.9538 q^{7} +196.998 q^{8} -222.886 q^{9} +O(q^{10})$	\(q-4.54694 q^{2} -4.48487 q^{3} -11.3254 q^{4} -25.0000 q^{5} +20.3924 q^{6} +16.9538 q^{7} +196.998 q^{8} -222.886 q^{9} +113.673 q^{10} -121.000 q^{11} +50.7928 q^{12} +146.556 q^{13} -77.0880 q^{14} +112.122 q^{15} -533.324 q^{16} -1037.23 q^{17} +1013.45 q^{18} +361.000 q^{19} +283.134 q^{20} -76.0358 q^{21} +550.179 q^{22} +754.013 q^{23} -883.510 q^{24} +625.000 q^{25} -666.382 q^{26} +2089.44 q^{27} -192.008 q^{28} +865.884 q^{29} -509.811 q^{30} -6161.09 q^{31} -3878.93 q^{32} +542.670 q^{33} +4716.24 q^{34} -423.846 q^{35} +2524.26 q^{36} +5622.35 q^{37} -1641.44 q^{38} -657.286 q^{39} -4924.94 q^{40} -11997.3 q^{41} +345.730 q^{42} +3711.42 q^{43} +1370.37 q^{44} +5572.15 q^{45} -3428.45 q^{46} +2618.87 q^{47} +2391.89 q^{48} -16519.6 q^{49} -2841.84 q^{50} +4651.86 q^{51} -1659.80 q^{52} +30893.0 q^{53} -9500.55 q^{54} +3025.00 q^{55} +3339.87 q^{56} -1619.04 q^{57} -3937.12 q^{58} +1175.88 q^{59} -1269.82 q^{60} -25693.7 q^{61} +28014.1 q^{62} -3778.77 q^{63} +34703.7 q^{64} -3663.91 q^{65} -2467.49 q^{66} -28561.3 q^{67} +11747.0 q^{68} -3381.65 q^{69} +1927.20 q^{70} -49698.7 q^{71} -43908.0 q^{72} -16918.6 q^{73} -25564.5 q^{74} -2803.05 q^{75} -4088.46 q^{76} -2051.41 q^{77} +2988.64 q^{78} +35033.4 q^{79} +13333.1 q^{80} +44790.4 q^{81} +54551.1 q^{82} -108619. q^{83} +861.133 q^{84} +25930.8 q^{85} -16875.6 q^{86} -3883.38 q^{87} -23836.7 q^{88} -56519.5 q^{89} -25336.2 q^{90} +2484.69 q^{91} -8539.47 q^{92} +27631.7 q^{93} -11907.8 q^{94} -9025.00 q^{95} +17396.5 q^{96} -90692.6 q^{97} +75113.4 q^{98} +26969.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9}+O(q^{10}) $ 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9} - 300 q^{10} - 4719 q^{11} + 872 q^{12} - 717 q^{13} + 2647 q^{14} - 675 q^{15} + 15078 q^{16} + 2155 q^{17} + 3293 q^{18} + 14079 q^{19} - 16750 q^{20} + 6891 q^{21} - 1452 q^{22} + 1296 q^{23} - 3138 q^{24} + 24375 q^{25} + 2585 q^{26} + 3846 q^{27} - 20901 q^{28} - 7635 q^{29} - 1725 q^{30} + 9595 q^{31} - 43 q^{32} - 3267 q^{33} - 28383 q^{34} + 6275 q^{35} + 80573 q^{36} - 28965 q^{37} + 4332 q^{38} + 21358 q^{39} - 6750 q^{40} + 19627 q^{41} + 12478 q^{42} + 3711 q^{43} - 81070 q^{44} - 91650 q^{45} + 37459 q^{46} + 38450 q^{47} - 12259 q^{48} + 78758 q^{49} + 7500 q^{50} - 68114 q^{51} - 50322 q^{52} + 20631 q^{53} - 124732 q^{54} + 117975 q^{55} + 94893 q^{56} + 9747 q^{57} - 148140 q^{58} + 170405 q^{59} - 21800 q^{60} - 22345 q^{61} + 246390 q^{62} - 151688 q^{63} + 340312 q^{64} + 17925 q^{65} - 8349 q^{66} - 16408 q^{67} - 32276 q^{68} + 93536 q^{69} - 66175 q^{70} + 119338 q^{71} + 135668 q^{72} - 141606 q^{73} + 71843 q^{74} + 16875 q^{75} + 241870 q^{76} + 30371 q^{77} + 708290 q^{78} + 14727 q^{79} - 376950 q^{80} + 441659 q^{81} - 219870 q^{82} + 384909 q^{83} + 877024 q^{84} - 53875 q^{85} + 250290 q^{86} - 77038 q^{87} - 32670 q^{88} + 443394 q^{89} - 82325 q^{90} - 207088 q^{91} - 237112 q^{92} + 396718 q^{93} + 409516 q^{94} - 351975 q^{95} + 100332 q^{96} - 152942 q^{97} + 895680 q^{98} - 443586 q^{99}+O(q^{100}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9 - 300 * q^10 - 4719 * q^11 + 872 * q^12 - 717 * q^13 + 2647 * q^14 - 675 * q^15 + 15078 * q^16 + 2155 * q^17 + 3293 * q^18 + 14079 * q^19 - 16750 * q^20 + 6891 * q^21 - 1452 * q^22 + 1296 * q^23 - 3138 * q^24 + 24375 * q^25 + 2585 * q^26 + 3846 * q^27 - 20901 * q^28 - 7635 * q^29 - 1725 * q^30 + 9595 * q^31 - 43 * q^32 - 3267 * q^33 - 28383 * q^34 + 6275 * q^35 + 80573 * q^36 - 28965 * q^37 + 4332 * q^38 + 21358 * q^39 - 6750 * q^40 + 19627 * q^41 + 12478 * q^42 + 3711 * q^43 - 81070 * q^44 - 91650 * q^45 + 37459 * q^46 + 38450 * q^47 - 12259 * q^48 + 78758 * q^49 + 7500 * q^50 - 68114 * q^51 - 50322 * q^52 + 20631 * q^53 - 124732 * q^54 + 117975 * q^55 + 94893 * q^56 + 9747 * q^57 - 148140 * q^58 + 170405 * q^59 - 21800 * q^60 - 22345 * q^61 + 246390 * q^62 - 151688 * q^63 + 340312 * q^64 + 17925 * q^65 - 8349 * q^66 - 16408 * q^67 - 32276 * q^68 + 93536 * q^69 - 66175 * q^70 + 119338 * q^71 + 135668 * q^72 - 141606 * q^73 + 71843 * q^74 + 16875 * q^75 + 241870 * q^76 + 30371 * q^77 + 708290 * q^78 + 14727 * q^79 - 376950 * q^80 + 441659 * q^81 - 219870 * q^82 + 384909 * q^83 + 877024 * q^84 - 53875 * q^85 + 250290 * q^86 - 77038 * q^87 - 32670 * q^88 + 443394 * q^89 - 82325 * q^90 - 207088 * q^91 - 237112 * q^92 + 396718 * q^93 + 409516 * q^94 - 351975 * q^95 + 100332 * q^96 - 152942 * q^97 + 895680 * q^98 - 443586 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−4.54694	−0.803792	−0.401896	−	0.915685i	$-0.631649\pi$
$2$	−4.54694	−0.803792	−0.401896	+	0.915685i	$0.631649\pi$
$3$	−4.48487	−0.287705	−0.143852	−	0.989599i	$-0.545949\pi$
$3$	−4.48487	−0.287705	−0.143852	+	0.989599i	$0.545949\pi$
$4$	−11.3254	−0.353918
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	20.3924	0.231255
$7$	16.9538	0.130774	0.0653872	−	0.997860i	$-0.479172\pi$
$7$	16.9538	0.130774	0.0653872	+	0.997860i	$0.479172\pi$
$8$	196.998	1.08827
$9$	−222.886	−0.917226
$10$	113.673	0.359467
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	50.7928	0.101824
$13$	146.556	0.240517	0.120259	−	0.992743i	$-0.461628\pi$
$13$	146.556	0.240517	0.120259	+	0.992743i	$0.461628\pi$
$14$	−77.0880	−0.105116
$15$	112.122	0.128665
$16$	−533.324	−0.520825
$17$	−1037.23	−0.870471	−0.435235	−	0.900317i	$-0.643335\pi$
$17$	−1037.23	−0.870471	−0.435235	+	0.900317i	$0.643335\pi$
$18$	1013.45	0.737259
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	283.134	0.158277
$21$	−76.0358	−0.0376244
$22$	550.179	0.242353
$23$	754.013	0.297207	0.148604	−	0.988897i	$-0.452522\pi$
$23$	754.013	0.297207	0.148604	+	0.988897i	$0.452522\pi$
$24$	−883.510	−0.313100
$25$	625.000	0.200000
$26$	−666.382	−0.193326
$27$	2089.44	0.551595
$28$	−192.008	−0.0462834
$29$	865.884	0.191190	0.0955949	−	0.995420i	$-0.469525\pi$
$29$	865.884	0.191190	0.0955949	+	0.995420i	$0.469525\pi$
$30$	−509.811	−0.103420
$31$	−6161.09	−1.15147	−0.575736	−	0.817636i	$-0.695284\pi$
$31$	−6161.09	−1.15147	−0.575736	+	0.817636i	$0.695284\pi$
$32$	−3878.93	−0.669634
$33$	542.670	0.0867463
$34$	4716.24	0.699678
$35$	−423.846	−0.0584841
$36$	2524.26	0.324622
$37$	5622.35	0.675171	0.337585	−	0.941295i	$-0.390390\pi$
$37$	5622.35	0.675171	0.337585	+	0.941295i	$0.390390\pi$
$38$	−1641.44	−0.184403
$39$	−657.286	−0.0691979
$40$	−4924.94	−0.486689
$41$	−11997.3	−1.11462	−0.557308	−	0.830306i	$-0.688166\pi$
$41$	−11997.3	−1.11462	−0.557308	+	0.830306i	$0.688166\pi$
$42$	345.730	0.0302422
$43$	3711.42	0.306104	0.153052	−	0.988218i	$-0.451090\pi$
$43$	3711.42	0.306104	0.153052	+	0.988218i	$0.451090\pi$
$44$	1370.37	0.106710
$45$	5572.15	0.410196
$46$	−3428.45	−0.238893
$47$	2618.87	0.172929	0.0864646	−	0.996255i	$-0.472443\pi$
$47$	2618.87	0.172929	0.0864646	+	0.996255i	$0.472443\pi$
$48$	2391.89	0.149844
$49$	−16519.6	−0.982898
$50$	−2841.84	−0.160758
$51$	4651.86	0.250439
$52$	−1659.80	−0.0851232
$53$	30893.0	1.51067	0.755336	−	0.655337i	$-0.227473\pi$
$53$	30893.0	1.51067	0.755336	+	0.655337i	$0.227473\pi$
$54$	−9500.55	−0.443368
$55$	3025.00	0.134840
$56$	3339.87	0.142318
$57$	−1619.04	−0.0660040
$58$	−3937.12	−0.153677
$59$	1175.88	0.0439777	0.0219889	−	0.999758i	$-0.493000\pi$
$59$	1175.88	0.0439777	0.0219889	+	0.999758i	$0.493000\pi$
$60$	−1269.82	−0.0455370
$61$	−25693.7	−0.884100	−0.442050	−	0.896990i	$-0.645749\pi$
$61$	−25693.7	−0.884100	−0.442050	+	0.896990i	$0.645749\pi$
$62$	28014.1	0.925545
$63$	−3778.77	−0.119950
$64$	34703.7	1.05907
$65$	−3663.91	−0.107562
$66$	−2467.49	−0.0697260
$67$	−28561.3	−0.777304	−0.388652	−	0.921385i	$-0.627059\pi$
$67$	−28561.3	−0.777304	−0.388652	+	0.921385i	$0.627059\pi$
$68$	11747.0	0.308075
$69$	−3381.65	−0.0855079
$70$	1927.20	0.0470091
$71$	−49698.7	−1.17004	−0.585018	−	0.811020i	$-0.698913\pi$
$71$	−49698.7	−1.17004	−0.585018	+	0.811020i	$0.698913\pi$
$72$	−43908.0	−0.998188
$73$	−16918.6	−0.371584	−0.185792	−	0.982589i	$-0.559485\pi$
$73$	−16918.6	−0.371584	−0.185792	+	0.982589i	$0.559485\pi$
$74$	−25564.5	−0.542697
$75$	−2803.05	−0.0575410
$76$	−4088.46	−0.0811943
$77$	−2051.41	−0.0394300
$78$	2988.64	0.0556208
$79$	35033.4	0.631560	0.315780	−	0.948832i	$-0.397734\pi$
$79$	35033.4	0.631560	0.315780	+	0.948832i	$0.397734\pi$
$80$	13333.1	0.232920
$81$	44790.4	0.758529
$82$	54551.1	0.895919
$83$	−108619.	−1.73065	−0.865324	−	0.501213i	$-0.832887\pi$
$83$	−108619.	−1.73065	−0.865324	+	0.501213i	$0.832887\pi$
$84$	861.133	0.0133160
$85$	25930.8	0.389286
$86$	−16875.6	−0.246044
$87$	−3883.38	−0.0550062
$88$	−23836.7	−0.328125
$89$	−56519.5	−0.756351	−0.378176	−	0.925734i	$-0.623448\pi$
$89$	−56519.5	−0.756351	−0.378176	+	0.925734i	$0.623448\pi$
$90$	−25336.2	−0.329712
$91$	2484.69	0.0314535
$92$	−8539.47	−0.105187
$93$	27631.7	0.331284
$94$	−11907.8	−0.138999
$95$	−9025.00	−0.102598
$96$	17396.5	0.192657
$97$	−90692.6	−0.978684	−0.489342	−	0.872092i	$-0.662763\pi$
$97$	−90692.6	−0.978684	−0.489342	+	0.872092i	$0.662763\pi$
$98$	75113.4	0.790046
$99$	26969.2	0.276554
$100$	−7078.35	−0.0707835
$101$	−156407.	−1.52564	−0.762821	−	0.646609i	$-0.776186\pi$
$101$	−156407.	−1.52564	−0.762821	+	0.646609i	$0.776186\pi$
$102$	−21151.7	−0.201301
$103$	−82335.2	−0.764703	−0.382351	−	0.924017i	$-0.624886\pi$
$103$	−82335.2	−0.764703	−0.382351	+	0.924017i	$0.624886\pi$
$104$	28871.2	0.261747
$105$	1900.90	0.0168262
$106$	−140469.	−1.21427
$107$	176399.	1.48949	0.744743	−	0.667352i	$-0.232572\pi$
$107$	176399.	1.48949	0.744743	+	0.667352i	$0.232572\pi$
$108$	−23663.7	−0.195219
$109$	−111408.	−0.898152	−0.449076	−	0.893493i	$-0.648247\pi$
$109$	−111408.	−0.898152	−0.449076	+	0.893493i	$0.648247\pi$
$110$	−13754.5	−0.108383
$111$	−25215.5	−0.194250
$112$	−9041.90	−0.0681106
$113$	−56968.3	−0.419699	−0.209849	−	0.977734i	$-0.567297\pi$
$113$	−56968.3	−0.419699	−0.209849	+	0.977734i	$0.567297\pi$
$114$	7361.67	0.0530535
$115$	−18850.3	−0.132915
$116$	−9806.45	−0.0676655
$117$	−32665.3	−0.220608
$118$	−5346.65	−0.0353490
$119$	−17585.1	−0.113835
$120$	22087.7	0.140023
$121$	14641.0	0.0909091
$122$	116828.	0.710633
$123$	53806.5	0.320680
$124$	69776.6	0.407526
$125$	−15625.0	−0.0894427
$126$	17181.8	0.0964147
$127$	106005.	0.583198	0.291599	−	0.956541i	$-0.405813\pi$
$127$	106005.	0.583198	0.291599	+	0.956541i	$0.405813\pi$
$128$	−33669.4	−0.181640
$129$	−16645.2	−0.0880675
$130$	16659.5	0.0864579
$131$	−97366.4	−0.495713	−0.247857	−	0.968797i	$-0.579726\pi$
$131$	−97366.4	−0.495713	−0.247857	+	0.968797i	$0.579726\pi$
$132$	−6145.93	−0.0307010
$133$	6120.34	0.0300017
$134$	129866.	0.624791
$135$	−52236.0	−0.246681
$136$	−204333.	−0.947306
$137$	145595.	0.662743	0.331371	−	0.943500i	$-0.392489\pi$
$137$	145595.	0.662743	0.331371	+	0.943500i	$0.392489\pi$
$138$	15376.2	0.0687306
$139$	−174521.	−0.766145	−0.383073	−	0.923718i	$-0.625134\pi$
$139$	−174521.	−0.766145	−0.383073	+	0.923718i	$0.625134\pi$
$140$	4800.21	0.0206986
$141$	−11745.3	−0.0497526
$142$	225977.	0.940467
$143$	−17733.3	−0.0725186
$144$	118871.	0.477714
$145$	−21647.1	−0.0855027
$146$	76927.8	0.298676
$147$	74088.2	0.282784
$148$	−63675.2	−0.238955
$149$	−193651.	−0.714587	−0.357293	−	0.933992i	$-0.616300\pi$
$149$	−193651.	−0.714587	−0.357293	+	0.933992i	$0.616300\pi$
$150$	12745.3	0.0462510
$151$	−304481.	−1.08672	−0.543360	−	0.839500i	$-0.682848\pi$
$151$	−304481.	−1.08672	−0.543360	+	0.839500i	$0.682848\pi$
$152$	71116.2	0.249666
$153$	231185.	0.798419
$154$	9327.65	0.0316935
$155$	154027.	0.514954
$156$	7444.00	0.0244904
$157$	38911.2	0.125987	0.0629935	−	0.998014i	$-0.479935\pi$
$157$	38911.2	0.125987	0.0629935	+	0.998014i	$0.479935\pi$
$158$	−159295.	−0.507644
$159$	−138551.	−0.434628
$160$	96973.3	0.299469
$161$	12783.4	0.0388671
$162$	−203659.	−0.609700
$163$	−659392.	−1.94390	−0.971952	−	0.235178i	$-0.924433\pi$
$163$	−659392.	−1.94390	−0.971952	+	0.235178i	$0.924433\pi$
$164$	135874.	0.394482
$165$	−13566.7	−0.0387941
$166$	493882.	1.39108
$167$	409190.	1.13536	0.567680	−	0.823249i	$-0.307841\pi$
$167$	409190.	1.13536	0.567680	+	0.823249i	$0.307841\pi$
$168$	−14978.9	−0.0409455
$169$	−349814.	−0.942152
$170$	−117906.	−0.312906
$171$	−80461.8	−0.210426
$172$	−42033.2	−0.108336
$173$	438666.	1.11434	0.557172	−	0.830397i	$-0.311887\pi$
$173$	438666.	1.11434	0.557172	+	0.830397i	$0.311887\pi$
$174$	17657.5	0.0442136
$175$	10596.1	0.0261549
$176$	64532.3	0.157035
$177$	−5273.67	−0.0126526
$178$	256991.	0.607949
$179$	−201504.	−0.470057	−0.235029	−	0.971988i	$-0.575518\pi$
$179$	−201504.	−0.470057	−0.235029	+	0.971988i	$0.575518\pi$
$180$	−63106.6	−0.145176
$181$	187688.	0.425833	0.212917	−	0.977070i	$-0.431704\pi$
$181$	187688.	0.425833	0.212917	+	0.977070i	$0.431704\pi$
$182$	−11297.7	−0.0252821
$183$	115233.	0.254360
$184$	148539.	0.323441
$185$	−140559.	−0.301946
$186$	−125640.	−0.266284
$187$	125505.	0.262457
$188$	−29659.6	−0.0612027
$189$	35424.0	0.0721346
$190$	41036.1	0.0824674
$191$	−347845.	−0.689926	−0.344963	−	0.938616i	$-0.612109\pi$
$191$	−347845.	−0.689926	−0.344963	+	0.938616i	$0.612109\pi$
$192$	−155641.	−0.304700
$193$	11927.6	0.0230494	0.0115247	−	0.999934i	$-0.496331\pi$
$193$	11927.6	0.0230494	0.0115247	+	0.999934i	$0.496331\pi$
$194$	412373.	0.786659
$195$	16432.2	0.0309462
$196$	187090.	0.347865
$197$	−436688.	−0.801688	−0.400844	−	0.916146i	$-0.631283\pi$
$197$	−436688.	−0.801688	−0.400844	+	0.916146i	$0.631283\pi$
$198$	−122627.	−0.222292
$199$	633345.	1.13372	0.566862	−	0.823813i	$-0.308157\pi$
$199$	633345.	1.13372	0.566862	+	0.823813i	$0.308157\pi$
$200$	123124.	0.217654
$201$	128094.	0.223634
$202$	711173.	1.22630
$203$	14680.1	0.0250028
$204$	−52684.0	−0.0886347
$205$	299933.	0.498471
$206$	374373.	0.614662
$207$	−168059.	−0.272606
$208$	−78162.0	−0.125267
$209$	−43681.0	−0.0691714
$210$	−8643.25	−0.0135247
$211$	−278689.	−0.430936	−0.215468	−	0.976511i	$-0.569128\pi$
$211$	−278689.	−0.430936	−0.215468	+	0.976511i	$0.569128\pi$
$212$	−349874.	−0.534654
$213$	222893.	0.336625
$214$	−802074.	−1.19724
$215$	−92785.4	−0.136894
$216$	411615.	0.600284
$217$	−104454.	−0.150583
$218$	506565.	0.721928
$219$	75877.7	0.106907
$220$	−34259.2	−0.0477222
$221$	−152013.	−0.209363
$222$	114653.	0.156137
$223$	577340.	0.777444	0.388722	−	0.921355i	$-0.372917\pi$
$223$	577340.	0.777444	0.388722	+	0.921355i	$0.372917\pi$
$224$	−65762.8	−0.0875710
$225$	−139304.	−0.183445
$226$	259031.	0.337351
$227$	1.33127e6	1.71475	0.857376	−	0.514691i	$-0.172093\pi$
$227$	1.33127e6	1.71475	0.857376	+	0.514691i	$0.172093\pi$
$228$	18336.2	0.0233600
$229$	985540.	1.24190	0.620949	−	0.783851i	$-0.286748\pi$
$229$	985540.	1.24190	0.620949	+	0.783851i	$0.286748\pi$
$230$	85711.3	0.106836
$231$	9200.34	0.0113442
$232$	170577.	0.208066
$233$	595932.	0.719129	0.359564	−	0.933120i	$-0.382925\pi$
$233$	595932.	0.719129	0.359564	+	0.933120i	$0.382925\pi$
$234$	148527.	0.177323
$235$	−65471.6	−0.0773363
$236$	−13317.3	−0.0155645
$237$	−157121.	−0.181703
$238$	79958.3	0.0915000
$239$	−920498.	−1.04239	−0.521193	−	0.853439i	$-0.674513\pi$
$239$	−920498.	−1.04239	−0.521193	+	0.853439i	$0.674513\pi$
$240$	−59797.3	−0.0670122
$241$	1.52608e6	1.69252	0.846261	−	0.532769i	$-0.178848\pi$
$241$	1.52608e6	1.69252	0.846261	+	0.532769i	$0.178848\pi$
$242$	−66571.7	−0.0730720
$243$	−708613.	−0.769828
$244$	290990.	0.312899
$245$	412989.	0.439565
$246$	−244655.	−0.257760
$247$	52906.8	0.0551784
$248$	−1.21372e6	−1.25311
$249$	487140.	0.497916
$250$	71045.9	0.0718934
$251$	−1.63317e6	−1.63624	−0.818122	−	0.575045i	$-0.804984\pi$
$251$	−1.63317e6	−1.63624	−0.818122	+	0.575045i	$0.804984\pi$
$252$	42796.0	0.0424523
$253$	−91235.6	−0.0896113
$254$	−481997.	−0.468770
$255$	−116297.	−0.112000
$256$	−957424.	−0.913071
$257$	690063.	0.651712	0.325856	−	0.945419i	$-0.394348\pi$
$257$	690063.	0.651712	0.325856	+	0.945419i	$0.394348\pi$
$258$	75684.9	0.0707880
$259$	95320.5	0.0882951
$260$	41495.1	0.0380683
$261$	−192993.	−0.175364
$262$	442719.	0.398451
$263$	867982.	0.773786	0.386893	−	0.922125i	$-0.373548\pi$
$263$	867982.	0.773786	0.386893	+	0.922125i	$0.373548\pi$
$264$	106905.	0.0944033
$265$	−772325.	−0.675593
$266$	−27828.8	−0.0241152
$267$	253483.	0.217606
$268$	323467.	0.275102
$269$	−1.17893e6	−0.993363	−0.496681	−	0.867933i	$-0.665448\pi$
$269$	−1.17893e6	−0.993363	−0.496681	+	0.867933i	$0.665448\pi$
$270$	237514.	0.198280
$271$	641347.	0.530481	0.265241	−	0.964182i	$-0.414549\pi$
$271$	641347.	0.530481	0.265241	+	0.964182i	$0.414549\pi$
$272$	553182.	0.453363
$273$	−11143.5	−0.00904932
$274$	−662011.	−0.532708
$275$	−75625.0	−0.0603023
$276$	38298.5	0.0302628
$277$	820365.	0.642403	0.321202	−	0.947011i	$-0.395913\pi$
$277$	820365.	0.642403	0.321202	+	0.947011i	$0.395913\pi$
$278$	793537.	0.615822
$279$	1.37322e6	1.05616
$280$	−83496.7	−0.0636464
$281$	1.79601e6	1.35689	0.678443	−	0.734653i	$-0.262655\pi$
$281$	1.79601e6	1.35689	0.678443	+	0.734653i	$0.262655\pi$
$282$	53405.1	0.0399908
$283$	−1.26997e6	−0.942598	−0.471299	−	0.881973i	$-0.656215\pi$
$283$	−1.26997e6	−0.942598	−0.471299	+	0.881973i	$0.656215\pi$
$284$	562856.	0.414097
$285$	40476.0	0.0295179
$286$	80632.2	0.0582899
$287$	−203401.	−0.145763
$288$	864560.	0.614206
$289$	−344003.	−0.242280
$290$	98428.0	0.0687264
$291$	406745.	0.281572
$292$	191609.	0.131510
$293$	−2.87261e6	−1.95482	−0.977411	−	0.211349i	$-0.932214\pi$
$293$	−2.87261e6	−1.95482	−0.977411	+	0.211349i	$0.932214\pi$
$294$	−336874.	−0.227300
$295$	−29397.0	−0.0196674
$296$	1.10759e6	0.734768
$297$	−252822.	−0.166312
$298$	880521.	0.574379
$299$	110505.	0.0714834
$300$	31745.5	0.0203648
$301$	62922.8	0.0400306
$302$	1.38446e6	0.873498
$303$	701466.	0.438935
$304$	−192530.	−0.119485
$305$	642342.	0.395382
$306$	−1.05118e6	−0.641763
$307$	2.43062e6	1.47188	0.735939	−	0.677048i	$-0.236741\pi$
$307$	2.43062e6	1.47188	0.735939	+	0.677048i	$0.236741\pi$
$308$	23233.0	0.0139550
$309$	369263.	0.220009
$310$	−700352.	−0.413916
$311$	611775.	0.358667	0.179333	−	0.983788i	$-0.442606\pi$
$311$	611775.	0.358667	0.179333	+	0.983788i	$0.442606\pi$
$312$	−129484.	−0.0753059
$313$	−2.07014e6	−1.19437	−0.597185	−	0.802104i	$-0.703714\pi$
$313$	−2.07014e6	−1.19437	−0.597185	+	0.802104i	$0.703714\pi$
$314$	−176927.	−0.101267
$315$	94469.3	0.0536432
$316$	−396766.	−0.223520
$317$	−664791.	−0.371567	−0.185783	−	0.982591i	$-0.559482\pi$
$317$	−664791.	−0.371567	−0.185783	+	0.982591i	$0.559482\pi$
$318$	629984.	0.349351
$319$	−104772.	−0.0576459
$320$	−867591.	−0.473631
$321$	−791127.	−0.428532
$322$	−58125.4	−0.0312411
$323$	−374441.	−0.199700
$324$	−507268.	−0.268457
$325$	91597.6	0.0481034
$326$	2.99822e6	1.56250
$327$	499651.	0.258403
$328$	−2.36345e6	−1.21300
$329$	44399.8	0.0226147
$330$	61687.1	0.0311824
$331$	793031.	0.397851	0.198925	−	0.980015i	$-0.436255\pi$
$331$	793031.	0.397851	0.198925	+	0.980015i	$0.436255\pi$
$332$	1.23014e6	0.612507
$333$	−1.25314e6	−0.619284
$334$	−1.86056e6	−0.912595
$335$	714032.	0.347621
$336$	40551.8	0.0195957
$337$	−1.60528e6	−0.769973	−0.384986	−	0.922922i	$-0.625794\pi$
$337$	−1.60528e6	−0.769973	−0.384986	+	0.922922i	$0.625794\pi$
$338$	1.59058e6	0.757294
$339$	255496.	0.120749
$340$	−293676.	−0.137775
$341$	745492.	0.347182
$342$	365855.	0.169139
$343$	−565013.	−0.259312
$344$	731141.	0.333123
$345$	84541.3	0.0382403
$346$	−1.99459e6	−0.895701
$347$	−673223.	−0.300148	−0.150074	−	0.988675i	$-0.547951\pi$
$347$	−673223.	−0.300148	−0.150074	+	0.988675i	$0.547951\pi$
$348$	43980.7	0.0194677
$349$	4.18154e6	1.83769	0.918845	−	0.394618i	$-0.129123\pi$
$349$	4.18154e6	1.83769	0.918845	+	0.394618i	$0.129123\pi$
$350$	−48180.0	−0.0210231
$351$	306220.	0.132668
$352$	469351.	0.201902
$353$	3.59926e6	1.53736	0.768681	−	0.639632i	$-0.220913\pi$
$353$	3.59926e6	1.53736	0.768681	+	0.639632i	$0.220913\pi$
$354$	23979.1	0.0101701
$355$	1.24247e6	0.523256
$356$	640104.	0.267686
$357$	78866.9	0.0327510
$358$	916225.	0.377828
$359$	1.48415e6	0.607774	0.303887	−	0.952708i	$-0.401715\pi$
$359$	1.48415e6	0.607774	0.303887	+	0.952708i	$0.401715\pi$
$360$	1.09770e6	0.446403
$361$	130321.	0.0526316
$362$	−853404.	−0.342281
$363$	−65663.0	−0.0261550
$364$	−28140.0	−0.0111319
$365$	422965.	0.166177
$366$	−523957.	−0.204453
$367$	−1.96859e6	−0.762939	−0.381470	−	0.924381i	$-0.624582\pi$
$367$	−1.96859e6	−0.762939	−0.381470	+	0.924381i	$0.624582\pi$
$368$	−402134.	−0.154793
$369$	2.67404e6	1.02235
$370$	639112.	0.242702
$371$	523755.	0.197557
$372$	−312939.	−0.117247
$373$	2.27472e6	0.846556	0.423278	−	0.906000i	$-0.360879\pi$
$373$	2.27472e6	0.846556	0.423278	+	0.906000i	$0.360879\pi$
$374$	−570665.	−0.210961
$375$	70076.2	0.0257331
$376$	515910.	0.188194
$377$	126901.	0.0459844
$378$	−161071.	−0.0579812
$379$	−747223.	−0.267210	−0.133605	−	0.991035i	$-0.542655\pi$
$379$	−747223.	−0.267210	−0.133605	+	0.991035i	$0.542655\pi$
$380$	102211.	0.0363112
$381$	−475418.	−0.167789
$382$	1.58163e6	0.554558
$383$	3.94248e6	1.37332	0.686662	−	0.726977i	$-0.259075\pi$
$383$	3.94248e6	1.37332	0.686662	+	0.726977i	$0.259075\pi$
$384$	151003.	0.0522586
$385$	51285.4	0.0176336
$386$	−54234.1	−0.0185270
$387$	−827223.	−0.280766
$388$	1.02713e6	0.346373
$389$	5.55116e6	1.85998	0.929992	−	0.367579i	$-0.119813\pi$
$389$	5.55116e6	1.85998	0.929992	+	0.367579i	$0.119813\pi$
$390$	−74716.0	−0.0248744
$391$	−782088.	−0.258710
$392$	−3.25432e6	−1.06966
$393$	436676.	0.142619
$394$	1.98559e6	0.644391
$395$	−875836.	−0.282442
$396$	−305436.	−0.0978773
$397$	5.49440e6	1.74962	0.874810	−	0.484466i	$-0.160986\pi$
$397$	5.49440e6	1.74962	0.874810	+	0.484466i	$0.160986\pi$
$398$	−2.87978e6	−0.911279
$399$	−27448.9	−0.00863164
$400$	−333328.	−0.104165
$401$	5.63983e6	1.75148	0.875739	−	0.482784i	$-0.160375\pi$
$401$	5.63983e6	1.75148	0.875739	+	0.482784i	$0.160375\pi$
$402$	−582434.	−0.179755
$403$	−902946.	−0.276949
$404$	1.77137e6	0.539952
$405$	−1.11976e6	−0.339225
$406$	−66749.3	−0.0200970
$407$	−680305.	−0.203572
$408$	916406.	0.272545
$409$	3.83703e6	1.13419	0.567097	−	0.823651i	$-0.308067\pi$
$409$	3.83703e6	1.13419	0.567097	+	0.823651i	$0.308067\pi$
$410$	−1.36378e6	−0.400667
$411$	−652975.	−0.190674
$412$	932476.	0.270642
$413$	19935.7	0.00575116
$414$	764153.	0.219119
$415$	2.71546e6	0.773969
$416$	−568482.	−0.161058
$417$	782705.	0.220424
$418$	198615.	0.0555995
$419$	−2.65500e6	−0.738804	−0.369402	−	0.929270i	$-0.620438\pi$
$419$	−2.65500e6	−0.738804	−0.369402	+	0.929270i	$0.620438\pi$
$420$	−21528.3	−0.00595507
$421$	3.22844e6	0.887743	0.443871	−	0.896091i	$-0.353605\pi$
$421$	3.22844e6	0.887743	0.443871	+	0.896091i	$0.353605\pi$
$422$	1.26718e6	0.346383
$423$	−583708.	−0.158615
$424$	6.08585e6	1.64402
$425$	−648271.	−0.174094
$426$	−1.01348e6	−0.270577
$427$	−435606.	−0.115618
$428$	−1.99778e6	−0.527155
$429$	79531.6	0.0208640
$430$	421890.	0.110034
$431$	6.30187e6	1.63409	0.817046	−	0.576573i	$-0.195610\pi$
$431$	6.30187e6	1.63409	0.817046	+	0.576573i	$0.195610\pi$
$432$	−1.11435e6	−0.287284
$433$	4.01093e6	1.02808	0.514038	−	0.857767i	$-0.328149\pi$
$433$	4.01093e6	1.02808	0.514038	+	0.857767i	$0.328149\pi$
$434$	474947.	0.121038
$435$	97084.5	0.0245995
$436$	1.26174e6	0.317872
$437$	272199.	0.0681840
$438$	−345011.	−0.0859306
$439$	3.87345e6	0.959261	0.479630	−	0.877471i	$-0.340771\pi$
$439$	3.87345e6	0.959261	0.479630	+	0.877471i	$0.340771\pi$
$440$	595918.	0.146742
$441$	3.68198e6	0.901540
$442$	691194.	0.168284
$443$	−6.04282e6	−1.46295	−0.731477	−	0.681867i	$-0.761168\pi$
$443$	−6.04282e6	−1.46295	−0.731477	+	0.681867i	$0.761168\pi$
$444$	285575.	0.0687485
$445$	1.41299e6	0.338251
$446$	−2.62513e6	−0.624904
$447$	868502.	0.205590
$448$	588360.	0.138499
$449$	−6.54493e6	−1.53211	−0.766054	−	0.642777i	$-0.777782\pi$
$449$	−6.54493e6	−1.53211	−0.766054	+	0.642777i	$0.777782\pi$
$450$	633405.	0.147452
$451$	1.45168e6	0.336069
$452$	645187.	0.148539
$453$	1.36556e6	0.312655
$454$	−6.05320e6	−1.37830
$455$	−62117.3	−0.0140664
$456$	−318947.	−0.0718301
$457$	−2.74966e6	−0.615868	−0.307934	−	0.951408i	$-0.599638\pi$
$457$	−2.74966e6	−0.615868	−0.307934	+	0.951408i	$0.599638\pi$
$458$	−4.48119e6	−0.998228
$459$	−2.16724e6	−0.480148
$460$	213487.	0.0470410
$461$	440009.	0.0964294	0.0482147	−	0.998837i	$-0.484647\pi$
$461$	440009.	0.0964294	0.0482147	+	0.998837i	$0.484647\pi$
$462$	−41833.3	−0.00911838
$463$	−5.67529e6	−1.23037	−0.615184	−	0.788383i	$-0.710918\pi$
$463$	−5.67529e6	−1.23037	−0.615184	+	0.788383i	$0.710918\pi$
$464$	−461797.	−0.0995764
$465$	−690793.	−0.148155
$466$	−2.70966e6	−0.578030
$467$	−6.27727e6	−1.33192	−0.665961	−	0.745987i	$-0.731978\pi$
$467$	−6.27727e6	−1.33192	−0.665961	+	0.745987i	$0.731978\pi$
$468$	369947.	0.0780772
$469$	−484223.	−0.101651
$470$	297695.	0.0621624
$471$	−174512.	−0.0362471
$472$	231646.	0.0478596
$473$	−449081.	−0.0922938
$474$	714417.	0.146051
$475$	225625.	0.0458831
$476$	199158.	0.0402883
$477$	−6.88561e6	−1.38563
$478$	4.18545e6	0.837861
$479$	6.67361e6	1.32899	0.664495	−	0.747293i	$-0.268647\pi$
$479$	6.67361e6	1.32899	0.664495	+	0.747293i	$0.268647\pi$
$480$	−434913.	−0.0861588
$481$	823991.	0.162390
$482$	−6.93898e6	−1.36044
$483$	−57332.0	−0.0111823
$484$	−165815.	−0.0321743
$485$	2.26731e6	0.437681
$486$	3.22202e6	0.618782
$487$	3.38011e6	0.645815	0.322907	−	0.946431i	$-0.395340\pi$
$487$	3.38011e6	0.645815	0.322907	+	0.946431i	$0.395340\pi$
$488$	−5.06159e6	−0.962139
$489$	2.95729e6	0.559271
$490$	−1.87784e6	−0.353319
$491$	−4.50856e6	−0.843983	−0.421991	−	0.906600i	$-0.638669\pi$
$491$	−4.50856e6	−0.843983	−0.421991	+	0.906600i	$0.638669\pi$
$492$	−609378.	−0.113494
$493$	−898124.	−0.166425
$494$	−240564.	−0.0443520
$495$	−674230.	−0.123679
$496$	3.28586e6	0.599715
$497$	−842584.	−0.153011
$498$	−2.21500e6	−0.400221
$499$	−1.61545e6	−0.290431	−0.145216	−	0.989400i	$-0.546388\pi$
$499$	−1.61545e6	−0.290431	−0.145216	+	0.989400i	$0.546388\pi$
$500$	176959.	0.0316554
$501$	−1.83517e6	−0.326649
$502$	7.42593e6	1.31520
$503$	8.92052e6	1.57206	0.786032	−	0.618186i	$-0.212132\pi$
$503$	8.92052e6	1.57206	0.786032	+	0.618186i	$0.212132\pi$
$504$	−744409.	−0.130538
$505$	3.91018e6	0.682288
$506$	414842.	0.0720289
$507$	1.56887e6	0.271062
$508$	−1.20054e6	−0.206404
$509$	7.61811e6	1.30333	0.651663	−	0.758509i	$-0.274072\pi$
$509$	7.61811e6	1.30333	0.651663	+	0.758509i	$0.274072\pi$
$510$	528793.	0.0900244
$511$	−286835.	−0.0485937
$512$	5.43077e6	0.915559
$513$	754288.	0.126545
$514$	−3.13767e6	−0.523841
$515$	2.05838e6	0.341985
$516$	188513.	0.0311686
$517$	−316883.	−0.0521401
$518$	−433416.	−0.0709710
$519$	−1.96736e6	−0.320602
$520$	−721781.	−0.117057
$521$	6.44138e6	1.03964	0.519822	−	0.854275i	$-0.325998\pi$
$521$	6.44138e6	1.03964	0.519822	+	0.854275i	$0.325998\pi$
$522$	877529.	0.140957
$523$	955476.	0.152745	0.0763723	−	0.997079i	$-0.475666\pi$
$523$	955476.	0.152745	0.0763723	+	0.997079i	$0.475666\pi$
$524$	1.10271e6	0.175442
$525$	−47522.4	−0.00752489
$526$	−3.94666e6	−0.621964
$527$	6.39049e6	1.00232
$528$	−289419.	−0.0451796
$529$	−5.86781e6	−0.911668
$530$	3.51171e6	0.543037
$531$	−262087.	−0.0403375
$532$	−69315.0	−0.0106181
$533$	−1.75828e6	−0.268084
$534$	−1.15257e6	−0.174910
$535$	−4.40997e6	−0.666118
$536$	−5.62651e6	−0.845915
$537$	903719.	0.135238
$538$	5.36053e6	0.798458
$539$	1.99887e6	0.296355
$540$	591592.	0.0873047
$541$	−7.65022e6	−1.12378	−0.561889	−	0.827212i	$-0.689925\pi$
$541$	−7.65022e6	−1.12378	−0.561889	+	0.827212i	$0.689925\pi$
$542$	−2.91616e6	−0.426397
$543$	−841756.	−0.122514
$544$	4.02336e6	0.582897
$545$	2.78520e6	0.401666
$546$	50668.9	0.00727377
$547$	361602.	0.0516729	0.0258364	−	0.999666i	$-0.491775\pi$
$547$	361602.	0.0516729	0.0258364	+	0.999666i	$0.491775\pi$
$548$	−1.64892e6	−0.234556
$549$	5.72676e6	0.810920
$550$	343862.	0.0484705
$551$	312584.	0.0438620
$552$	−666178.	−0.0930556
$553$	593951.	0.0825920
$554$	−3.73015e6	−0.516359
$555$	630389.	0.0868712
$556$	1.97652e6	0.271152
$557$	−5.32229e6	−0.726876	−0.363438	−	0.931618i	$-0.618397\pi$
$557$	−5.32229e6	−0.726876	−0.363438	+	0.931618i	$0.618397\pi$
$558$	−6.24395e6	−0.848934
$559$	543931.	0.0736232
$560$	226047.	0.0304600
$561$	−562875.	−0.0755101
$562$	−8.16635e6	−1.09065
$563$	205094.	0.0272698	0.0136349	−	0.999907i	$-0.495660\pi$
$563$	205094.	0.0272698	0.0136349	+	0.999907i	$0.495660\pi$
$564$	133020.	0.0176083
$565$	1.42421e6	0.187695
$566$	5.77447e6	0.757654
$567$	759369.	0.0991963
$568$	−9.79054e6	−1.27331
$569$	−3.30344e6	−0.427746	−0.213873	−	0.976861i	$-0.568608\pi$
$569$	−3.30344e6	−0.427746	−0.213873	+	0.976861i	$0.568608\pi$
$570$	−184042.	−0.0237263
$571$	−1.31488e6	−0.168770	−0.0843851	−	0.996433i	$-0.526893\pi$
$571$	−1.31488e6	−0.168770	−0.0843851	+	0.996433i	$0.526893\pi$
$572$	200836.	0.0256656
$573$	1.56004e6	0.198495
$574$	924851.	0.117163
$575$	471258.	0.0594414
$576$	−7.73495e6	−0.971408
$577$	−8.34525e6	−1.04352	−0.521759	−	0.853093i	$-0.674724\pi$
$577$	−8.34525e6	−1.04352	−0.521759	+	0.853093i	$0.674724\pi$
$578$	1.56416e6	0.194743
$579$	−53493.8	−0.00663143
$580$	245161.	0.0302609
$581$	−1.84150e6	−0.226325
$582$	−1.84944e6	−0.226325
$583$	−3.73805e6	−0.455485
$584$	−3.33292e6	−0.404383
$585$	816633.	0.0986591
$586$	1.30616e7	1.57127
$587$	−8.78582e6	−1.05241	−0.526207	−	0.850356i	$-0.676386\pi$
$587$	−8.78582e6	−1.05241	−0.526207	+	0.850356i	$0.676386\pi$
$588$	−839076.	−0.100082
$589$	−2.22415e6	−0.264166
$590$	133666.	0.0158085
$591$	1.95849e6	0.230650
$592$	−2.99854e6	−0.351646
$593$	−3.10224e6	−0.362275	−0.181138	−	0.983458i	$-0.557978\pi$
$593$	−3.10224e6	−0.362275	−0.181138	+	0.983458i	$0.557978\pi$
$594$	1.14957e6	0.133680
$595$	439627.	0.0509087
$596$	2.19317e6	0.252905
$597$	−2.84047e6	−0.326178
$598$	−502461.	−0.0574578
$599$	−5.84801e6	−0.665950	−0.332975	−	0.942936i	$-0.608052\pi$
$599$	−5.84801e6	−0.665950	−0.332975	+	0.942936i	$0.608052\pi$
$600$	−552194.	−0.0626200
$601$	7.48011e6	0.844737	0.422369	−	0.906424i	$-0.361199\pi$
$601$	7.48011e6	0.844737	0.422369	+	0.906424i	$0.361199\pi$
$602$	−286106.	−0.0321763
$603$	6.36591e6	0.712963
$604$	3.44836e6	0.384609
$605$	−366025.	−0.0406558
$606$	−3.18952e6	−0.352812
$607$	8.39867e6	0.925207	0.462604	−	0.886565i	$-0.346915\pi$
$607$	8.39867e6	0.925207	0.462604	+	0.886565i	$0.346915\pi$
$608$	−1.40030e6	−0.153625
$609$	−65838.2	−0.00719341
$610$	−2.92069e6	−0.317805
$611$	383811.	0.0415924
$612$	−2.61825e6	−0.282574
$613$	−1.69109e7	−1.81767	−0.908835	−	0.417156i	$-0.863027\pi$
$613$	−1.69109e7	−1.81767	−0.908835	+	0.417156i	$0.863027\pi$
$614$	−1.10519e7	−1.18308
$615$	−1.34516e6	−0.143413
$616$	−404124.	−0.0429104
$617$	6.93600e6	0.733493	0.366747	−	0.930321i	$-0.380472\pi$
$617$	6.93600e6	0.733493	0.366747	+	0.930321i	$0.380472\pi$
$618$	−1.67902e6	−0.176841
$619$	−7.64396e6	−0.801848	−0.400924	−	0.916111i	$-0.631311\pi$
$619$	−7.64396e6	−0.801848	−0.400924	+	0.916111i	$0.631311\pi$
$620$	−1.74442e6	−0.182251
$621$	1.57546e6	0.163938
$622$	−2.78170e6	−0.288294
$623$	−958223.	−0.0989114
$624$	350547.	0.0360400
$625$	390625.	0.0400000
$626$	9.41279e6	0.960025
$627$	195904.	0.0199010
$628$	−440684.	−0.0445890
$629$	−5.83169e6	−0.587717
$630$	−429546.	−0.0431180
$631$	−3.62217e6	−0.362156	−0.181078	−	0.983469i	$-0.557959\pi$
$631$	−3.62217e6	−0.362156	−0.181078	+	0.983469i	$0.557959\pi$
$632$	6.90151e6	0.687308
$633$	1.24988e6	0.123982
$634$	3.02276e6	0.298663
$635$	−2.65012e6	−0.260814
$636$	1.56914e6	0.153822
$637$	−2.42105e6	−0.236404
$638$	476392.	0.0463354
$639$	1.10771e7	1.07319
$640$	841736.	0.0812318
$641$	−3.19827e6	−0.307446	−0.153723	−	0.988114i	$-0.549126\pi$
$641$	−3.19827e6	−0.307446	−0.153723	+	0.988114i	$0.549126\pi$
$642$	3.59720e6	0.344451
$643$	1.09049e7	1.04014	0.520071	−	0.854123i	$-0.325905\pi$
$643$	1.09049e7	1.04014	0.520071	+	0.854123i	$0.325905\pi$
$644$	−144777.	−0.0137558
$645$	416131.	0.0393850
$646$	1.70256e6	0.160517
$647$	−7.38169e6	−0.693258	−0.346629	−	0.938002i	$-0.612674\pi$
$647$	−7.38169e6	−0.693258	−0.346629	+	0.938002i	$0.612674\pi$
$648$	8.82361e6	0.825484
$649$	−142281.	−0.0132598
$650$	−416489.	−0.0386652
$651$	468464.	0.0433235
$652$	7.46786e6	0.687982
$653$	8.55757e6	0.785358	0.392679	−	0.919676i	$-0.371548\pi$
$653$	8.55757e6	0.785358	0.392679	+	0.919676i	$0.371548\pi$
$654$	−2.27188e6	−0.207702
$655$	2.43416e6	0.221690
$656$	6.39847e6	0.580519
$657$	3.77092e6	0.340826
$658$	−201883.	−0.0181776
$659$	−8.88900e6	−0.797332	−0.398666	−	0.917096i	$-0.630527\pi$
$659$	−8.88900e6	−0.797332	−0.398666	+	0.917096i	$0.630527\pi$
$660$	153648.	0.0137299
$661$	−1.93060e7	−1.71865	−0.859326	−	0.511429i	$-0.829116\pi$
$661$	−1.93060e7	−1.71865	−0.859326	+	0.511429i	$0.829116\pi$
$662$	−3.60586e6	−0.319789
$663$	681759.	0.0602348
$664$	−2.13976e7	−1.88341
$665$	−153008.	−0.0134172
$666$	5.69796e6	0.497776
$667$	652888.	0.0568230
$668$	−4.63423e6	−0.401824
$669$	−2.58930e6	−0.223674
$670$	−3.24666e6	−0.279415
$671$	3.10893e6	0.266566
$672$	294938.	0.0251946
$673$	−1.83227e7	−1.55938	−0.779689	−	0.626167i	$-0.784623\pi$
$673$	−1.83227e7	−1.55938	−0.779689	+	0.626167i	$0.784623\pi$
$674$	7.29909e6	0.618898
$675$	1.30590e6	0.110319
$676$	3.96177e6	0.333444
$677$	−3.64313e6	−0.305494	−0.152747	−	0.988265i	$-0.548812\pi$
$677$	−3.64313e6	−0.305494	−0.152747	+	0.988265i	$0.548812\pi$
$678$	−1.16172e6	−0.0970574
$679$	−1.53759e6	−0.127987
$680$	5.10832e6	0.423648
$681$	−5.97057e6	−0.493342
$682$	−3.38971e6	−0.279062
$683$	−1.36744e7	−1.12165	−0.560825	−	0.827935i	$-0.689516\pi$
$683$	−1.36744e7	−1.12165	−0.560825	+	0.827935i	$0.689516\pi$
$684$	911259.	0.0744735
$685$	−3.63988e6	−0.296388
$686$	2.56908e6	0.208433
$687$	−4.42002e6	−0.357300
$688$	−1.97939e6	−0.159426
$689$	4.52756e6	0.363343
$690$	−384404.	−0.0307373
$691$	965043.	0.0768868	0.0384434	−	0.999261i	$-0.487760\pi$
$691$	965043.	0.0768868	0.0384434	+	0.999261i	$0.487760\pi$
$692$	−4.96805e6	−0.394386
$693$	457231.	0.0361662
$694$	3.06110e6	0.241257
$695$	4.36303e6	0.342630
$696$	−765017.	−0.0598616
$697$	1.24440e7	0.970240
$698$	−1.90132e7	−1.47712
$699$	−2.67268e6	−0.206897
$700$	−120005.	−0.00925668
$701$	1.48448e7	1.14098	0.570491	−	0.821304i	$-0.306753\pi$
$701$	1.48448e7	1.14098	0.570491	+	0.821304i	$0.306753\pi$
$702$	−1.39236e6	−0.106638
$703$	2.02967e6	0.154895
$704$	−4.19914e6	−0.319322
$705$	293632.	0.0222500
$706$	−1.63656e7	−1.23572
$707$	−2.65170e6	−0.199515
$708$	59726.3	0.00447798
$709$	−3.40526e6	−0.254410	−0.127205	−	0.991876i	$-0.540601\pi$
$709$	−3.40526e6	−0.254410	−0.127205	+	0.991876i	$0.540601\pi$
$710$	−5.64942e6	−0.420589
$711$	−7.80846e6	−0.579284
$712$	−1.11342e7	−0.823114
$713$	−4.64554e6	−0.342226
$714$	−358603.	−0.0263250
$715$	443333.	0.0324313
$716$	2.28210e6	0.166362
$717$	4.12832e6	0.299899
$718$	−6.74835e6	−0.488524
$719$	2.40584e7	1.73558	0.867791	−	0.496928i	$-0.165539\pi$
$719$	2.40584e7	1.73558	0.867791	+	0.496928i	$0.165539\pi$
$720$	−2.97176e6	−0.213640
$721$	−1.39590e6	−0.100004
$722$	−592561.	−0.0423049
$723$	−6.84427e6	−0.486947
$724$	−2.12563e6	−0.150710
$725$	541178.	0.0382380
$726$	298566.	0.0210232
$727$	−1.65079e7	−1.15839	−0.579197	−	0.815188i	$-0.696634\pi$
$727$	−1.65079e7	−1.15839	−0.579197	+	0.815188i	$0.696634\pi$
$728$	489478.	0.0342298
$729$	−7.70603e6	−0.537046
$730$	−1.92319e6	−0.133572
$731$	−3.84961e6	−0.266454
$732$	−1.30505e6	−0.0900225
$733$	−1.50097e7	−1.03184	−0.515920	−	0.856637i	$-0.672550\pi$
$733$	−1.50097e7	−1.03184	−0.515920	+	0.856637i	$0.672550\pi$
$734$	8.95105e6	0.613245
$735$	−1.85220e6	−0.126465
$736$	−2.92477e6	−0.199020
$737$	3.45592e6	0.234366
$738$	−1.21587e7	−0.821760
$739$	2.42784e7	1.63534	0.817670	−	0.575687i	$-0.195265\pi$
$739$	2.42784e7	1.63534	0.817670	+	0.575687i	$0.195265\pi$
$740$	1.59188e6	0.106864
$741$	−237280.	−0.0158751
$742$	−2.38148e6	−0.158795
$743$	−2.59662e7	−1.72559	−0.862793	−	0.505558i	$-0.831287\pi$
$743$	−2.59662e7	−1.72559	−0.862793	+	0.505558i	$0.831287\pi$
$744$	5.44339e6	0.360526
$745$	4.84128e6	0.319573
$746$	−1.03430e7	−0.680455
$747$	2.42095e7	1.58740
$748$	−1.42139e6	−0.0928881
$749$	2.99064e6	0.194787
$750$	−318632.	−0.0206841
$751$	−9.72943e6	−0.629488	−0.314744	−	0.949177i	$-0.601919\pi$
$751$	−9.72943e6	−0.629488	−0.314744	+	0.949177i	$0.601919\pi$
$752$	−1.39670e6	−0.0900658
$753$	7.32458e6	0.470755
$754$	−577010.	−0.0369619
$755$	7.61202e6	0.485996
$756$	−401190.	−0.0255297
$757$	2.07682e7	1.31722	0.658612	−	0.752483i	$-0.271144\pi$
$757$	2.07682e7	1.31722	0.658612	+	0.752483i	$0.271144\pi$
$758$	3.39757e6	0.214781
$759$	409180.	0.0257816
$760$	−1.77790e6	−0.111654
$761$	−2.62827e7	−1.64516	−0.822580	−	0.568649i	$-0.807466\pi$
$761$	−2.62827e7	−1.64516	−0.822580	+	0.568649i	$0.807466\pi$
$762$	2.16169e6	0.134867
$763$	−1.88879e6	−0.117455
$764$	3.93948e6	0.244177
$765$	−5.77962e6	−0.357064
$766$	−1.79262e7	−1.10387
$767$	172332.	0.0105774
$768$	4.29393e6	0.262695
$769$	2.01149e7	1.22660	0.613298	−	0.789852i	$-0.289843\pi$
$769$	2.01149e7	1.22660	0.613298	+	0.789852i	$0.289843\pi$
$770$	−233191.	−0.0141738
$771$	−3.09484e6	−0.187501
$772$	−135085.	−0.00815760
$773$	1.76143e7	1.06027	0.530136	−	0.847913i	$-0.322141\pi$
$773$	1.76143e7	1.06027	0.530136	+	0.847913i	$0.322141\pi$
$774$	3.76133e6	0.225678
$775$	−3.85068e6	−0.230294
$776$	−1.78662e7	−1.06507
$777$	−427500.	−0.0254029
$778$	−2.52408e7	−1.49504
$779$	−4.33104e6	−0.255710
$780$	−186100.	−0.0109524
$781$	6.01355e6	0.352779
$782$	3.55610e6	0.207949
$783$	1.80921e6	0.105459
$784$	8.81029e6	0.511918
$785$	−972780.	−0.0563431
$786$	−1.98554e6	−0.114636
$787$	1.93756e7	1.11511	0.557556	−	0.830139i	$-0.311739\pi$
$787$	1.93756e7	1.11511	0.557556	+	0.830139i	$0.311739\pi$
$788$	4.94565e6	0.283732
$789$	−3.89279e6	−0.222622
$790$	3.98237e6	0.227025
$791$	−965832.	−0.0548859
$792$	5.31287e6	0.300965
$793$	−3.76557e6	−0.212641
$794$	−2.49827e7	−1.40633
$795$	3.46378e6	0.194371
$796$	−7.17286e6	−0.401245
$797$	−5.08250e6	−0.283421	−0.141710	−	0.989908i	$-0.545260\pi$
$797$	−5.08250e6	−0.283421	−0.141710	+	0.989908i	$0.545260\pi$
$798$	124809.	0.00693805
$799$	−2.71638e6	−0.150530
$800$	−2.42433e6	−0.133927
$801$	1.25974e7	0.693745
$802$	−2.56439e7	−1.40783
$803$	2.04715e6	0.112037
$804$	−1.45071e6	−0.0791480
$805$	−319585.	−0.0173819
$806$	4.10564e6	0.222609
$807$	5.28736e6	0.285795
$808$	−3.08118e7	−1.66031
$809$	2.93729e7	1.57789	0.788944	−	0.614465i	$-0.210628\pi$
$809$	2.93729e7	1.57789	0.788944	+	0.614465i	$0.210628\pi$
$810$	5.09148e6	0.272666
$811$	3.88535e6	0.207433	0.103717	−	0.994607i	$-0.466926\pi$
$811$	3.88535e6	0.207433	0.103717	+	0.994607i	$0.466926\pi$
$812$	−166257.	−0.00884891
$813$	−2.87636e6	−0.152622
$814$	3.09330e6	0.163629
$815$	1.64848e7	0.869341
$816$	−2.48095e6	−0.130435
$817$	1.33982e6	0.0702250
$818$	−1.74467e7	−0.911656
$819$	−553802.	−0.0288500
$820$	−3.39685e6	−0.176418
$821$	6.21232e6	0.321659	0.160830	−	0.986982i	$-0.448583\pi$
$821$	6.21232e6	0.321659	0.160830	+	0.986982i	$0.448583\pi$
$822$	2.96904e6	0.153263
$823$	−3.04205e7	−1.56555	−0.782775	−	0.622305i	$-0.786196\pi$
$823$	−3.04205e7	−1.56555	−0.782775	+	0.622305i	$0.786196\pi$
$824$	−1.62198e7	−0.832202
$825$	339169.	0.0173493
$826$	−90646.2	−0.00462274
$827$	−1.45079e7	−0.737632	−0.368816	−	0.929502i	$-0.620237\pi$
$827$	−1.45079e7	−0.737632	−0.368816	+	0.929502i	$0.620237\pi$
$828$	1.90333e6	0.0964801
$829$	1.82100e6	0.0920289	0.0460144	−	0.998941i	$-0.485348\pi$
$829$	1.82100e6	0.0920289	0.0460144	+	0.998941i	$0.485348\pi$
$830$	−1.23470e7	−0.622111
$831$	−3.67923e6	−0.184822
$832$	5.08604e6	0.254725
$833$	1.71347e7	0.855584
$834$	−3.55891e6	−0.177175
$835$	−1.02298e7	−0.507749
$836$	494703.	0.0244810
$837$	−1.28732e7	−0.635146
$838$	1.20721e7	0.593845
$839$	1.83032e7	0.897679	0.448840	−	0.893612i	$-0.351837\pi$
$839$	1.83032e7	0.897679	0.448840	+	0.893612i	$0.351837\pi$
$840$	374472.	0.0183114
$841$	−1.97614e7	−0.963446
$842$	−1.46795e7	−0.713561
$843$	−8.05488e6	−0.390382
$844$	3.15625e6	0.152516
$845$	8.74536e6	0.421343
$846$	2.65408e6	0.127494
$847$	248221.	0.0118886
$848$	−1.64760e7	−0.786796
$849$	5.69565e6	0.271190
$850$	2.94765e6	0.139936
$851$	4.23933e6	0.200666
$852$	−2.52434e6	−0.119138
$853$	−2.24955e7	−1.05858	−0.529289	−	0.848442i	$-0.677541\pi$
$853$	−2.24955e7	−1.05858	−0.529289	+	0.848442i	$0.677541\pi$
$854$	1.98067e6	0.0929327
$855$	2.01155e6	0.0941054
$856$	3.47502e7	1.62096
$857$	3.26063e7	1.51652	0.758262	−	0.651950i	$-0.226049\pi$
$857$	3.26063e7	1.51652	0.758262	+	0.651950i	$0.226049\pi$
$858$	−361625.	−0.0167703
$859$	−4.12506e7	−1.90743	−0.953713	−	0.300717i	$-0.902774\pi$
$859$	−4.12506e7	−1.90743	−0.953713	+	0.300717i	$0.902774\pi$
$860$	1.05083e6	0.0484491
$861$	912227.	0.0419368
$862$	−2.86542e7	−1.31347
$863$	4.16941e7	1.90567	0.952834	−	0.303492i	$-0.0981526\pi$
$863$	4.16941e7	1.90567	0.952834	+	0.303492i	$0.0981526\pi$
$864$	−8.10480e6	−0.369367
$865$	−1.09667e7	−0.498349
$866$	−1.82374e7	−0.826360
$867$	1.54281e6	0.0697052
$868$	1.18298e6	0.0532940
$869$	−4.23905e6	−0.190423
$870$	−441437.	−0.0197729
$871$	−4.18583e6	−0.186955
$872$	−2.19471e7	−0.977431
$873$	2.02141e7	0.897674
$874$	−1.23767e6	−0.0548058
$875$	−264904.	−0.0116968
$876$	−859343.	−0.0378361
$877$	−2.69926e7	−1.18507	−0.592536	−	0.805544i	$-0.701873\pi$
$877$	−2.69926e7	−1.18507	−0.592536	+	0.805544i	$0.701873\pi$
$878$	−1.76123e7	−0.771047
$879$	1.28833e7	0.562411
$880$	−1.61331e6	−0.0702280
$881$	8.02450e6	0.348320	0.174160	−	0.984717i	$-0.444279\pi$
$881$	8.02450e6	0.348320	0.174160	+	0.984717i	$0.444279\pi$
$882$	−1.67417e7	−0.724651
$883$	−678082.	−0.0292671	−0.0146336	−	0.999893i	$-0.504658\pi$
$883$	−678082.	−0.0292671	−0.0146336	+	0.999893i	$0.504658\pi$
$884$	1.72160e6	0.0740973
$885$	131842.	0.00565842
$886$	2.74763e7	1.17591
$887$	−4.86004e6	−0.207411	−0.103705	−	0.994608i	$-0.533070\pi$
$887$	−4.86004e6	−0.207411	−0.103705	+	0.994608i	$0.533070\pi$
$888$	−4.96740e6	−0.211396
$889$	1.79719e6	0.0762674
$890$	−6.42477e6	−0.271883
$891$	−5.41964e6	−0.228705
$892$	−6.53858e6	−0.275151
$893$	945410.	0.0396727
$894$	−3.94902e6	−0.165252
$895$	5.03760e6	0.210216
$896$	−570826.	−0.0237538
$897$	−495602.	−0.0205661
$898$	2.97594e7	1.23150
$899$	−5.33479e6	−0.220150
$900$	1.57766e6	0.0649245
$901$	−3.20433e7	−1.31500
$902$	−6.60068e6	−0.270130
$903$	−282201.	−0.0115170
$904$	−1.12226e7	−0.456745
$905$	−4.69219e6	−0.190438
$906$	−6.20911e6	−0.251309
$907$	3.14824e7	1.27072	0.635360	−	0.772216i	$-0.280852\pi$
$907$	3.14824e7	1.27072	0.635360	+	0.772216i	$0.280852\pi$
$908$	−1.50771e7	−0.606881
$909$	3.48609e7	1.39936
$910$	282443.	0.0113065
$911$	−1.32509e7	−0.528992	−0.264496	−	0.964387i	$-0.585206\pi$
$911$	−1.32509e7	−0.528992	−0.264496	+	0.964387i	$0.585206\pi$
$912$	863473.	0.0343765
$913$	1.31428e7	0.521810
$914$	1.25025e7	0.495030
$915$	−2.88082e6	−0.113753
$916$	−1.11616e7	−0.439529
$917$	−1.65073e6	−0.0648267
$918$	9.85429e6	0.385939
$919$	1.72896e7	0.675298	0.337649	−	0.941272i	$-0.390368\pi$
$919$	1.72896e7	0.675298	0.337649	+	0.941272i	$0.390368\pi$
$920$	−3.71347e6	−0.144647
$921$	−1.09010e7	−0.423466
$922$	−2.00069e6	−0.0775092
$923$	−7.28366e6	−0.281414
$924$	−104197.	−0.00401491
$925$	3.51397e6	0.135034
$926$	2.58052e7	0.988961
$927$	1.83514e7	0.701405
$928$	−3.35871e6	−0.128027
$929$	−2.20989e7	−0.840100	−0.420050	−	0.907501i	$-0.637988\pi$
$929$	−2.20989e7	−0.840100	−0.420050	+	0.907501i	$0.637988\pi$
$930$	3.14099e6	0.119086
$931$	−5.96356e6	−0.225492
$932$	−6.74914e6	−0.254512
$933$	−2.74373e6	−0.103190
$934$	2.85424e7	1.07059
$935$	−3.13763e6	−0.117374
$936$	−6.43499e6	−0.240081
$937$	3.84660e7	1.43129	0.715646	−	0.698463i	$-0.246132\pi$
$937$	3.84660e7	1.43129	0.715646	+	0.698463i	$0.246132\pi$
$938$	2.20173e6	0.0817067
$939$	9.28431e6	0.343626
$940$	741490.	0.0273707
$941$	−4.41128e7	−1.62402	−0.812009	−	0.583646i	$-0.801626\pi$
$941$	−4.41128e7	−1.62402	−0.812009	+	0.583646i	$0.801626\pi$
$942$	793495.	0.0291351
$943$	−9.04614e6	−0.331272
$944$	−627125.	−0.0229047
$945$	−885601.	−0.0322596
$946$	2.04195e6	0.0741850
$947$	−7.77713e6	−0.281802	−0.140901	−	0.990024i	$-0.545000\pi$
$947$	−7.77713e6	−0.281802	−0.140901	+	0.990024i	$0.545000\pi$
$948$	1.77945e6	0.0643079
$949$	−2.47952e6	−0.0893723
$950$	−1.02590e6	−0.0368805
$951$	2.98150e6	0.106902
$952$	−3.46422e6	−0.123883
$953$	−4.53442e7	−1.61730	−0.808648	−	0.588292i	$-0.799800\pi$
$953$	−4.53442e7	−1.61730	−0.808648	+	0.588292i	$0.799800\pi$
$954$	3.13085e7	1.11376
$955$	8.69613e6	0.308544
$956$	1.04250e7	0.368918
$957$	469889.	0.0165850
$958$	−3.03445e7	−1.06823
$959$	2.46839e6	0.0866698
$960$	3.89104e6	0.136266
$961$	9.32991e6	0.325888
$962$	−3.74663e6	−0.130528
$963$	−3.93168e7	−1.36619
$964$	−1.72834e7	−0.599013
$965$	−298190.	−0.0103080
$966$	260685.	0.00898821
$967$	−1.90184e6	−0.0654045	−0.0327023	−	0.999465i	$-0.510411\pi$
$967$	−1.90184e6	−0.0654045	−0.0327023	+	0.999465i	$0.510411\pi$
$968$	2.88424e6	0.0989335
$969$	1.67932e6	0.0574546
$970$	−1.03093e7	−0.351804
$971$	2.67690e7	0.911136	0.455568	−	0.890201i	$-0.349436\pi$
$971$	2.67690e7	0.911136	0.455568	+	0.890201i	$0.349436\pi$
$972$	8.02530e6	0.272456
$973$	−2.95880e6	−0.100192
$974$	−1.53691e7	−0.519101
$975$	−410804.	−0.0138396
$976$	1.37031e7	0.460461
$977$	5.49808e7	1.84278	0.921392	−	0.388634i	$-0.127053\pi$
$977$	5.49808e7	1.84278	0.921392	+	0.388634i	$0.127053\pi$
$978$	−1.34466e7	−0.449538
$979$	6.83886e6	0.228048
$980$	−4.67725e6	−0.155570
$981$	2.48313e7	0.823809
$982$	2.05001e7	0.678387
$983$	−2.36634e6	−0.0781077	−0.0390538	−	0.999237i	$-0.512434\pi$
$983$	−2.36634e6	−0.0781077	−0.0390538	+	0.999237i	$0.512434\pi$
$984$	1.05998e7	0.348986
$985$	1.09172e7	0.358526
$986$	4.08371e6	0.133771
$987$	−199128.	−0.00650637
$988$	−599189.	−0.0195286
$989$	2.79846e6	0.0909762
$990$	3.06568e6	0.0994120
$991$	4.86002e6	0.157200	0.0786002	−	0.996906i	$-0.474955\pi$
$991$	4.86002e6	0.157200	0.0786002	+	0.996906i	$0.474955\pi$
$992$	2.38985e7	0.771065
$993$	−3.55664e6	−0.114464
$994$	3.83118e6	0.122989
$995$	−1.58336e7	−0.507017
$996$	−5.51704e6	−0.176221
$997$	2.15299e7	0.685969	0.342985	−	0.939341i	$-0.388562\pi$
$997$	2.15299e7	0.685969	0.342985	+	0.939341i	$0.388562\pi$
$998$	7.34537e6	0.233446
$999$	1.17476e7	0.372421

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.g.1.12	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.g.1.12	✓	39	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)

\(f(q)\)	\(=\)	\(q-4.54694 q^{2} -4.48487 q^{3} -11.3254 q^{4} -25.0000 q^{5} +20.3924 q^{6} +16.9538 q^{7} +196.998 q^{8} -222.886 q^{9} +O(q^{10})\)	\(q-4.54694 q^{2} -4.48487 q^{3} -11.3254 q^{4} -25.0000 q^{5} +20.3924 q^{6} +16.9538 q^{7} +196.998 q^{8} -222.886 q^{9} +113.673 q^{10} -121.000 q^{11} +50.7928 q^{12} +146.556 q^{13} -77.0880 q^{14} +112.122 q^{15} -533.324 q^{16} -1037.23 q^{17} +1013.45 q^{18} +361.000 q^{19} +283.134 q^{20} -76.0358 q^{21} +550.179 q^{22} +754.013 q^{23} -883.510 q^{24} +625.000 q^{25} -666.382 q^{26} +2089.44 q^{27} -192.008 q^{28} +865.884 q^{29} -509.811 q^{30} -6161.09 q^{31} -3878.93 q^{32} +542.670 q^{33} +4716.24 q^{34} -423.846 q^{35} +2524.26 q^{36} +5622.35 q^{37} -1641.44 q^{38} -657.286 q^{39} -4924.94 q^{40} -11997.3 q^{41} +345.730 q^{42} +3711.42 q^{43} +1370.37 q^{44} +5572.15 q^{45} -3428.45 q^{46} +2618.87 q^{47} +2391.89 q^{48} -16519.6 q^{49} -2841.84 q^{50} +4651.86 q^{51} -1659.80 q^{52} +30893.0 q^{53} -9500.55 q^{54} +3025.00 q^{55} +3339.87 q^{56} -1619.04 q^{57} -3937.12 q^{58} +1175.88 q^{59} -1269.82 q^{60} -25693.7 q^{61} +28014.1 q^{62} -3778.77 q^{63} +34703.7 q^{64} -3663.91 q^{65} -2467.49 q^{66} -28561.3 q^{67} +11747.0 q^{68} -3381.65 q^{69} +1927.20 q^{70} -49698.7 q^{71} -43908.0 q^{72} -16918.6 q^{73} -25564.5 q^{74} -2803.05 q^{75} -4088.46 q^{76} -2051.41 q^{77} +2988.64 q^{78} +35033.4 q^{79} +13333.1 q^{80} +44790.4 q^{81} +54551.1 q^{82} -108619. q^{83} +861.133 q^{84} +25930.8 q^{85} -16875.6 q^{86} -3883.38 q^{87} -23836.7 q^{88} -56519.5 q^{89} -25336.2 q^{90} +2484.69 q^{91} -8539.47 q^{92} +27631.7 q^{93} -11907.8 q^{94} -9025.00 q^{95} +17396.5 q^{96} -90692.6 q^{97} +75113.4 q^{98} +26969.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9}+O(q^{10}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9} - 300 q^{10} - 4719 q^{11} + 872 q^{12} - 717 q^{13} + 2647 q^{14} - 675 q^{15} + 15078 q^{16} + 2155 q^{17} + 3293 q^{18} + 14079 q^{19} - 16750 q^{20} + 6891 q^{21} - 1452 q^{22} + 1296 q^{23} - 3138 q^{24} + 24375 q^{25} + 2585 q^{26} + 3846 q^{27} - 20901 q^{28} - 7635 q^{29} - 1725 q^{30} + 9595 q^{31} - 43 q^{32} - 3267 q^{33} - 28383 q^{34} + 6275 q^{35} + 80573 q^{36} - 28965 q^{37} + 4332 q^{38} + 21358 q^{39} - 6750 q^{40} + 19627 q^{41} + 12478 q^{42} + 3711 q^{43} - 81070 q^{44} - 91650 q^{45} + 37459 q^{46} + 38450 q^{47} - 12259 q^{48} + 78758 q^{49} + 7500 q^{50} - 68114 q^{51} - 50322 q^{52} + 20631 q^{53} - 124732 q^{54} + 117975 q^{55} + 94893 q^{56} + 9747 q^{57} - 148140 q^{58} + 170405 q^{59} - 21800 q^{60} - 22345 q^{61} + 246390 q^{62} - 151688 q^{63} + 340312 q^{64} + 17925 q^{65} - 8349 q^{66} - 16408 q^{67} - 32276 q^{68} + 93536 q^{69} - 66175 q^{70} + 119338 q^{71} + 135668 q^{72} - 141606 q^{73} + 71843 q^{74} + 16875 q^{75} + 241870 q^{76} + 30371 q^{77} + 708290 q^{78} + 14727 q^{79} - 376950 q^{80} + 441659 q^{81} - 219870 q^{82} + 384909 q^{83} + 877024 q^{84} - 53875 q^{85} + 250290 q^{86} - 77038 q^{87} - 32670 q^{88} + 443394 q^{89} - 82325 q^{90} - 207088 q^{91} - 237112 q^{92} + 396718 q^{93} + 409516 q^{94} - 351975 q^{95} + 100332 q^{96} - 152942 q^{97} + 895680 q^{98} - 443586 q^{99}+O(q^{100}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9 - 300 * q^10 - 4719 * q^11 + 872 * q^12 - 717 * q^13 + 2647 * q^14 - 675 * q^15 + 15078 * q^16 + 2155 * q^17 + 3293 * q^18 + 14079 * q^19 - 16750 * q^20 + 6891 * q^21 - 1452 * q^22 + 1296 * q^23 - 3138 * q^24 + 24375 * q^25 + 2585 * q^26 + 3846 * q^27 - 20901 * q^28 - 7635 * q^29 - 1725 * q^30 + 9595 * q^31 - 43 * q^32 - 3267 * q^33 - 28383 * q^34 + 6275 * q^35 + 80573 * q^36 - 28965 * q^37 + 4332 * q^38 + 21358 * q^39 - 6750 * q^40 + 19627 * q^41 + 12478 * q^42 + 3711 * q^43 - 81070 * q^44 - 91650 * q^45 + 37459 * q^46 + 38450 * q^47 - 12259 * q^48 + 78758 * q^49 + 7500 * q^50 - 68114 * q^51 - 50322 * q^52 + 20631 * q^53 - 124732 * q^54 + 117975 * q^55 + 94893 * q^56 + 9747 * q^57 - 148140 * q^58 + 170405 * q^59 - 21800 * q^60 - 22345 * q^61 + 246390 * q^62 - 151688 * q^63 + 340312 * q^64 + 17925 * q^65 - 8349 * q^66 - 16408 * q^67 - 32276 * q^68 + 93536 * q^69 - 66175 * q^70 + 119338 * q^71 + 135668 * q^72 - 141606 * q^73 + 71843 * q^74 + 16875 * q^75 + 241870 * q^76 + 30371 * q^77 + 708290 * q^78 + 14727 * q^79 - 376950 * q^80 + 441659 * q^81 - 219870 * q^82 + 384909 * q^83 + 877024 * q^84 - 53875 * q^85 + 250290 * q^86 - 77038 * q^87 - 32670 * q^88 + 443394 * q^89 - 82325 * q^90 - 207088 * q^91 - 237112 * q^92 + 396718 * q^93 + 409516 * q^94 - 351975 * q^95 + 100332 * q^96 - 152942 * q^97 + 895680 * q^98 - 443586 * q^99

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