LMFDB - Embedded newform 1045.6.a.d.1.18

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			1.18
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)

$f(q)$	$=$	$q+0.242878 q^{2} -26.7520 q^{3} -31.9410 q^{4} -25.0000 q^{5} -6.49745 q^{6} -185.794 q^{7} -15.5298 q^{8} +472.668 q^{9} +O(q^{10})$	\(q+0.242878 q^{2} -26.7520 q^{3} -31.9410 q^{4} -25.0000 q^{5} -6.49745 q^{6} -185.794 q^{7} -15.5298 q^{8} +472.668 q^{9} -6.07194 q^{10} +121.000 q^{11} +854.485 q^{12} +17.1526 q^{13} -45.1252 q^{14} +668.799 q^{15} +1018.34 q^{16} +388.724 q^{17} +114.800 q^{18} -361.000 q^{19} +798.525 q^{20} +4970.36 q^{21} +29.3882 q^{22} -531.446 q^{23} +415.454 q^{24} +625.000 q^{25} +4.16599 q^{26} -6144.08 q^{27} +5934.45 q^{28} +1033.96 q^{29} +162.436 q^{30} +2546.25 q^{31} +744.287 q^{32} -3236.99 q^{33} +94.4123 q^{34} +4644.85 q^{35} -15097.5 q^{36} -13198.5 q^{37} -87.6788 q^{38} -458.867 q^{39} +388.246 q^{40} -8037.68 q^{41} +1207.19 q^{42} +3057.86 q^{43} -3864.86 q^{44} -11816.7 q^{45} -129.076 q^{46} -4762.35 q^{47} -27242.6 q^{48} +17712.5 q^{49} +151.798 q^{50} -10399.1 q^{51} -547.872 q^{52} -4727.80 q^{53} -1492.26 q^{54} -3025.00 q^{55} +2885.35 q^{56} +9657.46 q^{57} +251.125 q^{58} +14499.9 q^{59} -21362.1 q^{60} -39222.6 q^{61} +618.427 q^{62} -87819.0 q^{63} -32406.1 q^{64} -428.816 q^{65} -786.192 q^{66} +19056.9 q^{67} -12416.2 q^{68} +14217.2 q^{69} +1128.13 q^{70} -10089.2 q^{71} -7340.46 q^{72} -53195.8 q^{73} -3205.63 q^{74} -16720.0 q^{75} +11530.7 q^{76} -22481.1 q^{77} -111.448 q^{78} -20642.1 q^{79} -25458.5 q^{80} +49507.9 q^{81} -1952.17 q^{82} -90758.2 q^{83} -158758. q^{84} -9718.10 q^{85} +742.687 q^{86} -27660.4 q^{87} -1879.11 q^{88} +57831.9 q^{89} -2870.01 q^{90} -3186.86 q^{91} +16974.9 q^{92} -68117.2 q^{93} -1156.67 q^{94} +9025.00 q^{95} -19911.1 q^{96} -14786.1 q^{97} +4301.96 q^{98} +57192.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.242878	0.0429351	0.0214675	−	0.999770i	$-0.493166\pi$
$2$	0.242878	0.0429351	0.0214675	+	0.999770i	$0.493166\pi$
$3$	−26.7520	−1.71614	−0.858070	−	0.513533i	$-0.828337\pi$
$3$	−26.7520	−1.71614	−0.858070	+	0.513533i	$0.828337\pi$
$4$	−31.9410	−0.998157
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−6.49745	−0.0736826
$7$	−185.794	−1.43313	−0.716567	−	0.697518i	$-0.754288\pi$
$7$	−185.794	−1.43313	−0.716567	+	0.697518i	$0.754288\pi$
$8$	−15.5298	−0.0857910
$9$	472.668	1.94514
$10$	−6.07194	−0.0192012
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	854.485	1.71298
$13$	17.1526	0.0281496	0.0140748	−	0.999901i	$-0.495520\pi$
$13$	17.1526	0.0281496	0.0140748	+	0.999901i	$0.495520\pi$
$14$	−45.1252	−0.0615318
$15$	668.799	0.767481
$16$	1018.34	0.994473
$17$	388.724	0.326226	0.163113	−	0.986607i	$-0.447846\pi$
$17$	388.724	0.326226	0.163113	+	0.986607i	$0.447846\pi$
$18$	114.800	0.0835146
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	798.525	0.446389
$21$	4970.36	2.45946
$22$	29.3882	0.0129454
$23$	−531.446	−0.209479	−0.104739	−	0.994500i	$-0.533401\pi$
$23$	−531.446	−0.209479	−0.104739	+	0.994500i	$0.533401\pi$
$24$	415.454	0.147229
$25$	625.000	0.200000
$26$	4.16599	0.00120861
$27$	−6144.08	−1.62199
$28$	5934.45	1.43049
$29$	1033.96	0.228301	0.114151	−	0.993463i	$-0.463585\pi$
$29$	1033.96	0.228301	0.114151	+	0.993463i	$0.463585\pi$
$30$	162.436	0.0329519
$31$	2546.25	0.475879	0.237940	−	0.971280i	$-0.423528\pi$
$31$	2546.25	0.475879	0.237940	+	0.971280i	$0.423528\pi$
$32$	744.287	0.128489
$33$	−3236.99	−0.517436
$34$	94.4123	0.0140066
$35$	4644.85	0.640917
$36$	−15097.5	−1.94155
$37$	−13198.5	−1.58497	−0.792486	−	0.609891i	$-0.791213\pi$
$37$	−13198.5	−1.58497	−0.792486	+	0.609891i	$0.791213\pi$
$38$	−87.6788	−0.00984998
$39$	−458.867	−0.0483086
$40$	388.246	0.0383669
$41$	−8037.68	−0.746743	−0.373372	−	0.927682i	$-0.621798\pi$
$41$	−8037.68	−0.746743	−0.373372	+	0.927682i	$0.621798\pi$
$42$	1207.19	0.105597
$43$	3057.86	0.252201	0.126101	−	0.992017i	$-0.459754\pi$
$43$	3057.86	0.252201	0.126101	+	0.992017i	$0.459754\pi$
$44$	−3864.86	−0.300956
$45$	−11816.7	−0.869892
$46$	−129.076	−0.00899398
$47$	−4762.35	−0.314468	−0.157234	−	0.987561i	$-0.550258\pi$
$47$	−4762.35	−0.314468	−0.157234	+	0.987561i	$0.550258\pi$
$48$	−27242.6	−1.70666
$49$	17712.5	1.05388
$50$	151.798	0.00858702
$51$	−10399.1	−0.559850
$52$	−547.872	−0.0280977
$53$	−4727.80	−0.231190	−0.115595	−	0.993296i	$-0.536877\pi$
$53$	−4727.80	−0.231190	−0.115595	+	0.993296i	$0.536877\pi$
$54$	−1492.26	−0.0696402
$55$	−3025.00	−0.134840
$56$	2885.35	0.122950
$57$	9657.46	0.393710
$58$	251.125	0.00980212
$59$	14499.9	0.542293	0.271147	−	0.962538i	$-0.412597\pi$
$59$	14499.9	0.542293	0.271147	+	0.962538i	$0.412597\pi$
$60$	−21362.1	−0.766066
$61$	−39222.6	−1.34962	−0.674810	−	0.737992i	$-0.735774\pi$
$61$	−39222.6	−1.34962	−0.674810	+	0.737992i	$0.735774\pi$
$62$	618.427	0.0204319
$63$	−87819.0	−2.78764
$64$	−32406.1	−0.988956
$65$	−428.816	−0.0125889
$66$	−786.192	−0.0222161
$67$	19056.9	0.518640	0.259320	−	0.965791i	$-0.416502\pi$
$67$	19056.9	0.518640	0.259320	+	0.965791i	$0.416502\pi$
$68$	−12416.2	−0.325625
$69$	14217.2	0.359495
$70$	1128.13	0.0275178
$71$	−10089.2	−0.237525	−0.118763	−	0.992923i	$-0.537893\pi$
$71$	−10089.2	−0.237525	−0.118763	+	0.992923i	$0.537893\pi$
$72$	−7340.46	−0.166875
$73$	−53195.8	−1.16834	−0.584171	−	0.811630i	$-0.698580\pi$
$73$	−53195.8	−1.16834	−0.584171	+	0.811630i	$0.698580\pi$
$74$	−3205.63	−0.0680509
$75$	−16720.0	−0.343228
$76$	11530.7	0.228993
$77$	−22481.1	−0.432106
$78$	−111.448	−0.00207414
$79$	−20642.1	−0.372123	−0.186062	−	0.982538i	$-0.559572\pi$
$79$	−20642.1	−0.372123	−0.186062	+	0.982538i	$0.559572\pi$
$80$	−25458.5	−0.444742
$81$	49507.9	0.838421
$82$	−1952.17	−0.0320615
$83$	−90758.2	−1.44607	−0.723037	−	0.690809i	$-0.757255\pi$
$83$	−90758.2	−1.44607	−0.723037	+	0.690809i	$0.757255\pi$
$84$	−158758.	−2.45493
$85$	−9718.10	−0.145893
$86$	742.687	0.0108283
$87$	−27660.4	−0.391797
$88$	−1879.11	−0.0258670
$89$	57831.9	0.773913	0.386956	−	0.922098i	$-0.373526\pi$
$89$	57831.9	0.773913	0.386956	+	0.922098i	$0.373526\pi$
$90$	−2870.01	−0.0373489
$91$	−3186.86	−0.0403422
$92$	16974.9	0.209092
$93$	−68117.2	−0.816676
$94$	−1156.67	−0.0135017
$95$	9025.00	0.102598
$96$	−19911.1	−0.220505
$97$	−14786.1	−0.159560	−0.0797800	−	0.996812i	$-0.525422\pi$
$97$	−14786.1	−0.159560	−0.0797800	+	0.996812i	$0.525422\pi$
$98$	4301.96	0.0452482
$99$	57192.9	0.586481
$100$	−19963.1	−0.199631
$101$	110097.	1.07392	0.536959	−	0.843609i	$-0.319573\pi$
$101$	110097.	1.07392	0.536959	+	0.843609i	$0.319573\pi$
$102$	−2525.72	−0.0240372
$103$	37337.9	0.346782	0.173391	−	0.984853i	$-0.444528\pi$
$103$	37337.9	0.346782	0.173391	+	0.984853i	$0.444528\pi$
$104$	−266.377	−0.00241498
$105$	−124259.	−1.09990
$106$	−1148.28	−0.00992616
$107$	−10803.2	−0.0912205	−0.0456102	−	0.998959i	$-0.514523\pi$
$107$	−10803.2	−0.0912205	−0.0456102	+	0.998959i	$0.514523\pi$
$108$	196248.	1.61900
$109$	−154074.	−1.24212	−0.621060	−	0.783763i	$-0.713297\pi$
$109$	−154074.	−1.24212	−0.621060	+	0.783763i	$0.713297\pi$
$110$	−734.704	−0.00578937
$111$	353087.	2.72003
$112$	−189202.	−1.42521
$113$	−267317.	−1.96939	−0.984693	−	0.174297i	$-0.944235\pi$
$113$	−267317.	−1.96939	−0.984693	+	0.174297i	$0.944235\pi$
$114$	2345.58	0.0169040
$115$	13286.2	0.0936817
$116$	−33025.7	−0.227880
$117$	8107.50	0.0547548
$118$	3521.69	0.0232834
$119$	−72222.6	−0.467526
$120$	−10386.3	−0.0658430
$121$	14641.0	0.0909091
$122$	−9526.28	−0.0579460
$123$	215024.	1.28152
$124$	−81329.8	−0.475002
$125$	−15625.0	−0.0894427
$126$	−21329.3	−0.119688
$127$	−43470.6	−0.239159	−0.119579	−	0.992825i	$-0.538155\pi$
$127$	−43470.6	−0.239159	−0.119579	+	0.992825i	$0.538155\pi$
$128$	−31687.9	−0.170950
$129$	−81803.9	−0.432813
$130$	−104.150	−0.000540505 0
$131$	−35669.3	−0.181600	−0.0908000	−	0.995869i	$-0.528942\pi$
$131$	−35669.3	−0.181600	−0.0908000	+	0.995869i	$0.528942\pi$
$132$	103393.	0.516482
$133$	67071.7	0.328784
$134$	4628.50	0.0222678
$135$	153602.	0.725375
$136$	−6036.82	−0.0279873
$137$	156610.	0.712884	0.356442	−	0.934317i	$-0.383990\pi$
$137$	156610.	0.712884	0.356442	+	0.934317i	$0.383990\pi$
$138$	3453.05	0.0154349
$139$	−34766.7	−0.152625	−0.0763126	−	0.997084i	$-0.524315\pi$
$139$	−34766.7	−0.152625	−0.0763126	+	0.997084i	$0.524315\pi$
$140$	−148361.	−0.639736
$141$	127402.	0.539672
$142$	−2450.43	−0.0101982
$143$	2075.47	0.00848742
$144$	481337.	1.93439
$145$	−25848.9	−0.102099
$146$	−12920.1	−0.0501629
$147$	−473844.	−1.80860
$148$	421574.	1.58205
$149$	189401.	0.698901	0.349450	−	0.936955i	$-0.386368\pi$
$149$	189401.	0.698901	0.349450	+	0.936955i	$0.386368\pi$
$150$	−4060.91	−0.0147365
$151$	236993.	0.845849	0.422924	−	0.906165i	$-0.361004\pi$
$151$	236993.	0.845849	0.422924	+	0.906165i	$0.361004\pi$
$152$	5606.27	0.0196818
$153$	183737.	0.634555
$154$	−5460.15	−0.0185525
$155$	−63656.3	−0.212820
$156$	14656.7	0.0482196
$157$	84001.8	0.271982	0.135991	−	0.990710i	$-0.456578\pi$
$157$	84001.8	0.271982	0.135991	+	0.990710i	$0.456578\pi$
$158$	−5013.51	−0.0159771
$159$	126478.	0.396755
$160$	−18607.2	−0.0574619
$161$	98739.6	0.300211
$162$	12024.4	0.0359977
$163$	−41861.4	−0.123409	−0.0617043	−	0.998094i	$-0.519654\pi$
$163$	−41861.4	−0.123409	−0.0617043	+	0.998094i	$0.519654\pi$
$164$	256732.	0.745367
$165$	80924.7	0.231404
$166$	−22043.1	−0.0620873
$167$	−224751.	−0.623607	−0.311804	−	0.950147i	$-0.600933\pi$
$167$	−224751.	−0.623607	−0.311804	+	0.950147i	$0.600933\pi$
$168$	−77188.9	−0.211000
$169$	−370999.	−0.999208
$170$	−2360.31	−0.00626392
$171$	−170633.	−0.446245
$172$	−97671.3	−0.251736
$173$	−160273.	−0.407142	−0.203571	−	0.979060i	$-0.565255\pi$
$173$	−160273.	−0.407142	−0.203571	+	0.979060i	$0.565255\pi$
$174$	−6718.09	−0.0168218
$175$	−116121.	−0.286627
$176$	123219.	0.299845
$177$	−387900.	−0.930651
$178$	14046.1	0.0332280
$179$	−285039.	−0.664923	−0.332462	−	0.943117i	$-0.607879\pi$
$179$	−285039.	−0.664923	−0.332462	+	0.943117i	$0.607879\pi$
$180$	377438.	0.868288
$181$	−56488.5	−0.128163	−0.0640817	−	0.997945i	$-0.520412\pi$
$181$	−56488.5	−0.128163	−0.0640817	+	0.997945i	$0.520412\pi$
$182$	−774.016	−0.00173209
$183$	1.04928e6	2.31614
$184$	8253.27	0.0179714
$185$	329963.	0.708821
$186$	−16544.1	−0.0350640
$187$	47035.6	0.0983609
$188$	152114.	0.313889
$189$	1.14153e6	2.32453
$190$	2191.97	0.00440505
$191$	−648981.	−1.28721	−0.643603	−	0.765359i	$-0.722561\pi$
$191$	−648981.	−1.28721	−0.643603	+	0.765359i	$0.722561\pi$
$192$	866928.	1.69719
$193$	−102530.	−0.198132	−0.0990662	−	0.995081i	$-0.531586\pi$
$193$	−102530.	−0.198132	−0.0990662	+	0.995081i	$0.531586\pi$
$194$	−3591.21	−0.00685072
$195$	11471.7	0.0216043
$196$	−565755.	−1.05193
$197$	−825860.	−1.51615	−0.758073	−	0.652170i	$-0.773859\pi$
$197$	−825860.	−1.51615	−0.758073	+	0.652170i	$0.773859\pi$
$198$	13890.9	0.0251806
$199$	−549583.	−0.983787	−0.491893	−	0.870655i	$-0.663695\pi$
$199$	−549583.	−0.983787	−0.491893	+	0.870655i	$0.663695\pi$
$200$	−9706.15	−0.0171582
$201$	−509810.	−0.890058
$202$	26740.0	0.0461087
$203$	−192103.	−0.327186
$204$	332159.	0.558818
$205$	200942.	0.333954
$206$	9068.53	0.0148891
$207$	−251198.	−0.407465
$208$	17467.2	0.0279940
$209$	−43681.0	−0.0691714
$210$	−30179.7	−0.0472245
$211$	1.17529e6	1.81735	0.908675	−	0.417503i	$-0.137095\pi$
$211$	1.17529e6	1.81735	0.908675	+	0.417503i	$0.137095\pi$
$212$	151011.	0.230764
$213$	269905.	0.407626
$214$	−2623.85	−0.00391656
$215$	−76446.6	−0.112788
$216$	95416.5	0.139152
$217$	−473079.	−0.681999
$218$	−37421.1	−0.0533305
$219$	1.42309e6	2.00504
$220$	96621.6	0.134591
$221$	6667.63	0.00918314
$222$	85756.9	0.116785
$223$	−329045.	−0.443092	−0.221546	−	0.975150i	$-0.571110\pi$
$223$	−329045.	−0.443092	−0.221546	+	0.975150i	$0.571110\pi$
$224$	−138284.	−0.184142
$225$	295418.	0.389027
$226$	−64925.4	−0.0845558
$227$	−571504.	−0.736130	−0.368065	−	0.929800i	$-0.619980\pi$
$227$	−571504.	−0.736130	−0.368065	+	0.929800i	$0.619980\pi$
$228$	−308469.	−0.392984
$229$	−484412.	−0.610417	−0.305208	−	0.952286i	$-0.598726\pi$
$229$	−484412.	−0.610417	−0.305208	+	0.952286i	$0.598726\pi$
$230$	3226.91	0.00402223
$231$	601414.	0.741555
$232$	−16057.2	−0.0195862
$233$	589624.	0.711517	0.355758	−	0.934578i	$-0.384223\pi$
$233$	589624.	0.711517	0.355758	+	0.934578i	$0.384223\pi$
$234$	1969.13	0.00235090
$235$	119059.	0.140635
$236$	−463141.	−0.541294
$237$	552218.	0.638615
$238$	−17541.3	−0.0200733
$239$	87291.9	0.0988506	0.0494253	−	0.998778i	$-0.484261\pi$
$239$	87291.9	0.0988506	0.0494253	+	0.998778i	$0.484261\pi$
$240$	681066.	0.763239
$241$	−425805.	−0.472246	−0.236123	−	0.971723i	$-0.575877\pi$
$241$	−425805.	−0.472246	−0.236123	+	0.971723i	$0.575877\pi$
$242$	3555.97	0.00390319
$243$	168577.	0.183140
$244$	1.25281e6	1.34713
$245$	−442812.	−0.471307
$246$	52224.5	0.0550220
$247$	−6192.10	−0.00645796
$248$	−39542.9	−0.0408262
$249$	2.42796e6	2.48167
$250$	−3794.96	−0.00384023
$251$	1.01713e6	1.01905	0.509523	−	0.860457i	$-0.329822\pi$
$251$	1.01713e6	1.01905	0.509523	+	0.860457i	$0.329822\pi$
$252$	2.80503e6	2.78250
$253$	−64305.0	−0.0631602
$254$	−10558.0	−0.0102683
$255$	259978.	0.250373
$256$	1.02930e6	0.981617
$257$	−901042.	−0.850966	−0.425483	−	0.904967i	$-0.639896\pi$
$257$	−901042.	−0.850966	−0.425483	+	0.904967i	$0.639896\pi$
$258$	−19868.3	−0.0185828
$259$	2.45221e6	2.27148
$260$	13696.8	0.0125657
$261$	488719.	0.444077
$262$	−8663.27	−0.00779702
$263$	770621.	0.686991	0.343496	−	0.939154i	$-0.388389\pi$
$263$	770621.	0.686991	0.343496	+	0.939154i	$0.388389\pi$
$264$	50269.9	0.0443913
$265$	118195.	0.103391
$266$	16290.2	0.0141164
$267$	−1.54712e6	−1.32814
$268$	−608697.	−0.517684
$269$	−606563.	−0.511087	−0.255544	−	0.966797i	$-0.582254\pi$
$269$	−606563.	−0.511087	−0.255544	+	0.966797i	$0.582254\pi$
$270$	37306.5	0.0311440
$271$	698640.	0.577870	0.288935	−	0.957349i	$-0.406699\pi$
$271$	698640.	0.577870	0.288935	+	0.957349i	$0.406699\pi$
$272$	395853.	0.324423
$273$	85254.7	0.0692328
$274$	38037.1	0.0306077
$275$	75625.0	0.0603023
$276$	−454113.	−0.358832
$277$	−2.02530e6	−1.58595	−0.792975	−	0.609255i	$-0.791469\pi$
$277$	−2.02530e6	−1.58595	−0.792975	+	0.609255i	$0.791469\pi$
$278$	−8444.04	−0.00655297
$279$	1.20353e6	0.925651
$280$	−72133.8	−0.0549850
$281$	426598.	0.322294	0.161147	−	0.986930i	$-0.448481\pi$
$281$	426598.	0.322294	0.161147	+	0.986930i	$0.448481\pi$
$282$	30943.2	0.0231709
$283$	1.80012e6	1.33609	0.668043	−	0.744122i	$-0.267132\pi$
$283$	1.80012e6	1.33609	0.668043	+	0.744122i	$0.267132\pi$
$284$	322258.	0.237087
$285$	−241437.	−0.176072
$286$	504.084	0.000364408 0
$287$	1.49336e6	1.07018
$288$	351801.	0.249928
$289$	−1.26875e6	−0.893576
$290$	−6278.13	−0.00438364
$291$	395557.	0.273827
$292$	1.69913e6	1.16619
$293$	−2.78493e6	−1.89516	−0.947579	−	0.319522i	$-0.896478\pi$
$293$	−2.78493e6	−1.89516	−0.947579	+	0.319522i	$0.896478\pi$
$294$	−115086.	−0.0776523
$295$	−362497.	−0.242521
$296$	204971.	0.135976
$297$	−743434.	−0.489048
$298$	46001.1	0.0300074
$299$	−9115.70	−0.00589674
$300$	534053.	0.342595
$301$	−568133.	−0.361438
$302$	57560.2	0.0363166
$303$	−2.94530e6	−1.84299
$304$	−367621.	−0.228148
$305$	980564.	0.603568
$306$	44625.7	0.0272447
$307$	2.08598e6	1.26318	0.631588	−	0.775304i	$-0.282404\pi$
$307$	2.08598e6	1.26318	0.631588	+	0.775304i	$0.282404\pi$
$308$	718069.	0.431310
$309$	−998862.	−0.595126
$310$	−15460.7	−0.00913743
$311$	1.58569e6	0.929644	0.464822	−	0.885404i	$-0.346118\pi$
$311$	1.58569e6	0.929644	0.464822	+	0.885404i	$0.346118\pi$
$312$	7126.12	0.00414445
$313$	−833825.	−0.481077	−0.240538	−	0.970640i	$-0.577324\pi$
$313$	−833825.	−0.481077	−0.240538	+	0.970640i	$0.577324\pi$
$314$	20402.2	0.0116776
$315$	2.19548e6	1.24667
$316$	659330.	0.371437
$317$	−512971.	−0.286711	−0.143356	−	0.989671i	$-0.545789\pi$
$317$	−512971.	−0.286711	−0.143356	+	0.989671i	$0.545789\pi$
$318$	30718.6	0.0170347
$319$	125109.	0.0688353
$320$	810153.	0.442275
$321$	289006.	0.156547
$322$	23981.6	0.0128896
$323$	−140329.	−0.0748414
$324$	−1.58133e6	−0.836875
$325$	10720.4	0.00562992
$326$	−10167.2	−0.00529856
$327$	4.12179e6	2.13165
$328$	124824.	0.0640639
$329$	884818.	0.450676
$330$	19654.8	0.00993536
$331$	3.59867e6	1.80539	0.902697	−	0.430277i	$-0.141584\pi$
$331$	3.59867e6	1.80539	0.902697	+	0.430277i	$0.141584\pi$
$332$	2.89891e6	1.44341
$333$	−6.23853e6	−3.08299
$334$	−54587.0	−0.0267746
$335$	−476423.	−0.231943
$336$	5.06152e6	2.44587
$337$	187462.	0.0899164	0.0449582	−	0.998989i	$-0.485685\pi$
$337$	187462.	0.0899164	0.0449582	+	0.998989i	$0.485685\pi$
$338$	−90107.3	−0.0429011
$339$	7.15127e6	3.37974
$340$	310406.	0.145624
$341$	308096.	0.143483
$342$	−41443.0	−0.0191596
$343$	−168233.	−0.0772106
$344$	−47488.1	−0.0216366
$345$	−355431.	−0.160771
$346$	−38926.8	−0.0174807
$347$	−3.92955e6	−1.75194	−0.875970	−	0.482366i	$-0.839778\pi$
$347$	−3.92955e6	−1.75194	−0.875970	+	0.482366i	$0.839778\pi$
$348$	883502.	0.391074
$349$	1.96728e6	0.864576	0.432288	−	0.901736i	$-0.357706\pi$
$349$	1.96728e6	0.864576	0.432288	+	0.901736i	$0.357706\pi$
$350$	−28203.3	−0.0123064
$351$	−105387.	−0.0456583
$352$	90058.7	0.0387408
$353$	836024.	0.357093	0.178547	−	0.983931i	$-0.442860\pi$
$353$	836024.	0.357093	0.178547	+	0.983931i	$0.442860\pi$
$354$	−94212.3	−0.0399576
$355$	252229.	0.106224
$356$	−1.84721e6	−0.772486
$357$	1.93210e6	0.802341
$358$	−69229.5	−0.0285485
$359$	−3.55938e6	−1.45760	−0.728799	−	0.684727i	$-0.759921\pi$
$359$	−3.55938e6	−1.45760	−0.728799	+	0.684727i	$0.759921\pi$
$360$	183511.	0.0746289
$361$	130321.	0.0526316
$362$	−13719.8	−0.00550270
$363$	−391676.	−0.156013
$364$	101791.	0.0402678
$365$	1.32990e6	0.522499
$366$	254847.	0.0994435
$367$	−2.86951e6	−1.11210	−0.556048	−	0.831150i	$-0.687683\pi$
$367$	−2.86951e6	−1.11210	−0.556048	+	0.831150i	$0.687683\pi$
$368$	−541193.	−0.208321
$369$	−3.79916e6	−1.45252
$370$	80140.7	0.0304333
$371$	878397.	0.331327
$372$	2.17573e6	0.815170
$373$	1.13374e6	0.421929	0.210965	−	0.977494i	$-0.432340\pi$
$373$	1.13374e6	0.421929	0.210965	+	0.977494i	$0.432340\pi$
$374$	11423.9	0.00422313
$375$	418000.	0.153496
$376$	73958.6	0.0269786
$377$	17735.1	0.00642658
$378$	277253.	0.0998037
$379$	−4.60412e6	−1.64645	−0.823226	−	0.567714i	$-0.807828\pi$
$379$	−4.60412e6	−1.64645	−0.823226	+	0.567714i	$0.807828\pi$
$380$	−288268.	−0.102409
$381$	1.16292e6	0.410430
$382$	−157623.	−0.0552663
$383$	−233621.	−0.0813796	−0.0406898	−	0.999172i	$-0.512956\pi$
$383$	−233621.	−0.0813796	−0.0406898	+	0.999172i	$0.512956\pi$
$384$	847714.	0.293374
$385$	562027.	0.193244
$386$	−24902.1	−0.00850683
$387$	1.44536e6	0.490566
$388$	472283.	0.159266
$389$	−4.48738e6	−1.50355	−0.751777	−	0.659418i	$-0.770803\pi$
$389$	−4.48738e6	−1.50355	−0.751777	+	0.659418i	$0.770803\pi$
$390$	2786.21	0.000927582 0
$391$	−206586.	−0.0683374
$392$	−275072.	−0.0904130
$393$	954224.	0.311651
$394$	−200583.	−0.0650958
$395$	516053.	0.166418
$396$	−1.82680e6	−0.585400
$397$	−3.52134e6	−1.12132	−0.560662	−	0.828045i	$-0.689453\pi$
$397$	−3.52134e6	−1.12132	−0.560662	+	0.828045i	$0.689453\pi$
$398$	−133481.	−0.0422390
$399$	−1.79430e6	−0.564239
$400$	636463.	0.198895
$401$	−2.63222e6	−0.817449	−0.408724	−	0.912658i	$-0.634026\pi$
$401$	−2.63222e6	−0.817449	−0.408724	+	0.912658i	$0.634026\pi$
$402$	−123821.	−0.0382147
$403$	43674.9	0.0133958
$404$	−3.51660e6	−1.07194
$405$	−1.23770e6	−0.374953
$406$	−46657.6	−0.0140478
$407$	−1.59702e6	−0.477887
$408$	161497.	0.0480301
$409$	−2.73023e6	−0.807033	−0.403517	−	0.914972i	$-0.632212\pi$
$409$	−2.73023e6	−0.807033	−0.403517	+	0.914972i	$0.632212\pi$
$410$	48804.3	0.0143383
$411$	−4.18964e6	−1.22341
$412$	−1.19261e6	−0.346143
$413$	−2.69399e6	−0.777180
$414$	−61010.3	−0.0174945
$415$	2.26896e6	0.646704
$416$	12766.5	0.00361691
$417$	930077.	0.261926
$418$	−10609.1	−0.00296988
$419$	−1.91204e6	−0.532062	−0.266031	−	0.963964i	$-0.585712\pi$
$419$	−1.91204e6	−0.532062	−0.266031	+	0.963964i	$0.585712\pi$
$420$	3.96896e6	1.09788
$421$	5.26671e6	1.44822	0.724109	−	0.689686i	$-0.242251\pi$
$421$	5.26671e6	1.44822	0.724109	+	0.689686i	$0.242251\pi$
$422$	285451.	0.0780281
$423$	−2.25101e6	−0.611684
$424$	73421.9	0.0198340
$425$	242952.	0.0652453
$426$	65553.9	0.0175015
$427$	7.28732e6	1.93419
$428$	345065.	0.0910523
$429$	−55522.9	−0.0145656
$430$	−18567.2	−0.00484255
$431$	−4.28772e6	−1.11182	−0.555908	−	0.831244i	$-0.687629\pi$
$431$	−4.28772e6	−1.11182	−0.555908	+	0.831244i	$0.687629\pi$
$432$	−6.25677e6	−1.61302
$433$	−22726.1	−0.00582513	−0.00291257	−	0.999996i	$-0.500927\pi$
$433$	−22726.1	−0.00582513	−0.00291257	+	0.999996i	$0.500927\pi$
$434$	−114900.	−0.0292817
$435$	691510.	0.175217
$436$	4.92128e6	1.23983
$437$	191852.	0.0480577
$438$	345637.	0.0860866
$439$	−4.28858e6	−1.06207	−0.531034	−	0.847351i	$-0.678196\pi$
$439$	−4.28858e6	−1.06207	−0.531034	+	0.847351i	$0.678196\pi$
$440$	46977.7	0.0115681
$441$	8.37213e6	2.04993
$442$	1619.42	0.000394279 0
$443$	−6.96744e6	−1.68680	−0.843400	−	0.537285i	$-0.819450\pi$
$443$	−6.96744e6	−1.68680	−0.843400	+	0.537285i	$0.819450\pi$
$444$	−1.12780e7	−2.71502
$445$	−1.44580e6	−0.346104
$446$	−79917.7	−0.0190242
$447$	−5.06684e6	−1.19941
$448$	6.02087e6	1.41731
$449$	−1.62772e6	−0.381035	−0.190517	−	0.981684i	$-0.561017\pi$
$449$	−1.62772e6	−0.381035	−0.190517	+	0.981684i	$0.561017\pi$
$450$	71750.3	0.0167029
$451$	−972560.	−0.225152
$452$	8.53838e6	1.96576
$453$	−6.34002e6	−1.45159
$454$	−138805.	−0.0316058
$455$	79671.4	0.0180416
$456$	−149979.	−0.0337767
$457$	1.21461e6	0.272049	0.136025	−	0.990705i	$-0.456567\pi$
$457$	1.21461e6	0.272049	0.136025	+	0.990705i	$0.456567\pi$
$458$	−117653.	−0.0262083
$459$	−2.38835e6	−0.529135
$460$	−424373.	−0.0935090
$461$	619154.	0.135689	0.0678447	−	0.997696i	$-0.478388\pi$
$461$	619154.	0.135689	0.0678447	+	0.997696i	$0.478388\pi$
$462$	146070.	0.0318387
$463$	4.19652e6	0.909782	0.454891	−	0.890547i	$-0.349678\pi$
$463$	4.19652e6	0.909782	0.454891	+	0.890547i	$0.349678\pi$
$464$	1.05292e6	0.227039
$465$	1.70293e6	0.365229
$466$	143206.	0.0305490
$467$	4.77918e6	1.01406	0.507028	−	0.861930i	$-0.330744\pi$
$467$	4.77918e6	1.01406	0.507028	+	0.861930i	$0.330744\pi$
$468$	−258962.	−0.0546539
$469$	−3.54067e6	−0.743281
$470$	28916.7	0.00603816
$471$	−2.24722e6	−0.466759
$472$	−225181.	−0.0465239
$473$	370002.	0.0760415
$474$	134121.	0.0274190
$475$	−225625.	−0.0458831
$476$	2.30686e6	0.466664
$477$	−2.23468e6	−0.449696
$478$	21201.2	0.00424416
$479$	6.75097e6	1.34440	0.672198	−	0.740372i	$-0.265350\pi$
$479$	6.75097e6	1.34440	0.672198	+	0.740372i	$0.265350\pi$
$480$	497778.	0.0986127
$481$	−226389.	−0.0446163
$482$	−103418.	−0.0202759
$483$	−2.64148e6	−0.515204
$484$	−467648.	−0.0907415
$485$	369652.	0.0713574
$486$	40943.6	0.00786313
$487$	1.36827e6	0.261426	0.130713	−	0.991420i	$-0.458273\pi$
$487$	1.36827e6	0.261426	0.130713	+	0.991420i	$0.458273\pi$
$488$	609120.	0.115785
$489$	1.11988e6	0.211786
$490$	−107549.	−0.0202356
$491$	−1.73604e6	−0.324979	−0.162490	−	0.986710i	$-0.551952\pi$
$491$	−1.73604e6	−0.324979	−0.162490	+	0.986710i	$0.551952\pi$
$492$	−6.86808e6	−1.27915
$493$	401924.	0.0744778
$494$	−1503.92	−0.000277273 0
$495$	−1.42982e6	−0.262282
$496$	2.59295e6	0.473249
$497$	1.87451e6	0.340406
$498$	589697.	0.106551
$499$	−4.32115e6	−0.776870	−0.388435	−	0.921476i	$-0.626984\pi$
$499$	−4.32115e6	−0.776870	−0.388435	+	0.921476i	$0.626984\pi$
$500$	499078.	0.0892778
$501$	6.01254e6	1.07020
$502$	247039.	0.0437528
$503$	6.30623e6	1.11135	0.555674	−	0.831401i	$-0.312460\pi$
$503$	6.30623e6	1.11135	0.555674	+	0.831401i	$0.312460\pi$
$504$	1.36381e6	0.239155
$505$	−2.75242e6	−0.480270
$506$	−15618.2	−0.00271179
$507$	9.92495e6	1.71478
$508$	1.38849e6	0.238718
$509$	−5.11463e6	−0.875023	−0.437511	−	0.899213i	$-0.644140\pi$
$509$	−5.11463e6	−0.875023	−0.437511	+	0.899213i	$0.644140\pi$
$510$	63142.9	0.0107498
$511$	9.88347e6	1.67439
$512$	1.26401e6	0.213096
$513$	2.21801e6	0.372109
$514$	−218843.	−0.0365363
$515$	−933447.	−0.155086
$516$	2.61290e6	0.432015
$517$	−576245.	−0.0948158
$518$	595587.	0.0975261
$519$	4.28763e6	0.698713
$520$	6659.43	0.00108001
$521$	−8.38462e6	−1.35328	−0.676642	−	0.736312i	$-0.736566\pi$
$521$	−8.38462e6	−1.35328	−0.676642	+	0.736312i	$0.736566\pi$
$522$	118699.	0.0190665
$523$	−6.06895e6	−0.970196	−0.485098	−	0.874460i	$-0.661216\pi$
$523$	−6.06895e6	−0.970196	−0.485098	+	0.874460i	$0.661216\pi$
$524$	1.13931e6	0.181265
$525$	3.10648e6	0.491892
$526$	187166.	0.0294960
$527$	989789.	0.155244
$528$	−3.29636e6	−0.514576
$529$	−6.15391e6	−0.956119
$530$	28706.9	0.00443912
$531$	6.85363e6	1.05483
$532$	−2.14234e6	−0.328178
$533$	−137867.	−0.0210205
$534$	−375760.	−0.0570239
$535$	270080.	0.0407950
$536$	−295951.	−0.0444946
$537$	7.62535e6	1.14110
$538$	−147321.	−0.0219436
$539$	2.14321e6	0.317755
$540$	−4.90620e6	−0.724038
$541$	9.22749e6	1.35547	0.677735	−	0.735306i	$-0.262961\pi$
$541$	9.22749e6	1.35547	0.677735	+	0.735306i	$0.262961\pi$
$542$	169684.	0.0248109
$543$	1.51118e6	0.219946
$544$	289322.	0.0419164
$545$	3.85185e6	0.555493
$546$	20706.5	0.00297252
$547$	−8.35179e6	−1.19347	−0.596735	−	0.802439i	$-0.703536\pi$
$547$	−8.35179e6	−1.19347	−0.596735	+	0.802439i	$0.703536\pi$
$548$	−5.00229e6	−0.711570
$549$	−1.85393e7	−2.62519
$550$	18367.6	0.00258908
$551$	−373259.	−0.0523758
$552$	−220791.	−0.0308414
$553$	3.83519e6	0.533303
$554$	−491899.	−0.0680929
$555$	−8.82717e6	−1.21644
$556$	1.11048e6	0.152344
$557$	−1.56839e6	−0.214198	−0.107099	−	0.994248i	$-0.534156\pi$
$557$	−1.56839e6	−0.214198	−0.107099	+	0.994248i	$0.534156\pi$
$558$	292311.	0.0397429
$559$	52450.4	0.00709936
$560$	4.73004e6	0.637375
$561$	−1.25830e6	−0.168801
$562$	103611.	0.0138377
$563$	6.75157e6	0.897705	0.448853	−	0.893606i	$-0.351833\pi$
$563$	6.75157e6	0.897705	0.448853	+	0.893606i	$0.351833\pi$
$564$	−4.06936e6	−0.538677
$565$	6.68293e6	0.880736
$566$	437208.	0.0573650
$567$	−9.19828e6	−1.20157
$568$	156683.	0.0203775
$569$	−7.04345e6	−0.912021	−0.456011	−	0.889974i	$-0.650722\pi$
$569$	−7.04345e6	−0.912021	−0.456011	+	0.889974i	$0.650722\pi$
$570$	−58639.5	−0.00755968
$571$	9.96168e6	1.27862	0.639311	−	0.768948i	$-0.279220\pi$
$571$	9.96168e6	1.27862	0.639311	+	0.768948i	$0.279220\pi$
$572$	−66292.5	−0.00847178
$573$	1.73615e7	2.20903
$574$	362702.	0.0459484
$575$	−332154.	−0.0418957
$576$	−1.53173e7	−1.92366
$577$	−3.86936e6	−0.483838	−0.241919	−	0.970296i	$-0.577777\pi$
$577$	−3.86936e6	−0.483838	−0.241919	+	0.970296i	$0.577777\pi$
$578$	−308151.	−0.0383658
$579$	2.74287e6	0.340023
$580$	825641.	0.101911
$581$	1.68624e7	2.07242
$582$	96071.9	0.0117568
$583$	−572063.	−0.0697064
$584$	826122.	0.100233
$585$	−202688.	−0.0244871
$586$	−676397.	−0.0813687
$587$	−3.12161e6	−0.373924	−0.186962	−	0.982367i	$-0.559864\pi$
$587$	−3.12161e6	−0.373924	−0.186962	+	0.982367i	$0.559864\pi$
$588$	1.51351e7	1.80526
$589$	−919197.	−0.109174
$590$	−88042.4	−0.0104127
$591$	2.20934e7	2.60192
$592$	−1.34406e7	−1.57621
$593$	−777793.	−0.0908295	−0.0454148	−	0.998968i	$-0.514461\pi$
$593$	−777793.	−0.0908295	−0.0454148	+	0.998968i	$0.514461\pi$
$594$	−180563.	−0.0209973
$595$	1.80557e6	0.209084
$596$	−6.04964e6	−0.697612
$597$	1.47024e7	1.68832
$598$	−2214.00	−0.000253177 0
$599$	−4.18004e6	−0.476007	−0.238003	−	0.971264i	$-0.576493\pi$
$599$	−4.18004e6	−0.476007	−0.238003	+	0.971264i	$0.576493\pi$
$600$	259659.	0.0294459
$601$	−7.41714e6	−0.837626	−0.418813	−	0.908073i	$-0.637554\pi$
$601$	−7.41714e6	−0.837626	−0.418813	+	0.908073i	$0.637554\pi$
$602$	−137987.	−0.0155184
$603$	9.00760e6	1.00883
$604$	−7.56979e6	−0.844289
$605$	−366025.	−0.0406558
$606$	−715348.	−0.0791290
$607$	6.51771e6	0.717998	0.358999	−	0.933338i	$-0.383118\pi$
$607$	6.51771e6	0.717998	0.358999	+	0.933338i	$0.383118\pi$
$608$	−268687.	−0.0294774
$609$	5.13914e6	0.561497
$610$	238157.	0.0259142
$611$	−81686.9	−0.00885216
$612$	−5.86876e6	−0.633385
$613$	−4.25847e6	−0.457723	−0.228861	−	0.973459i	$-0.573500\pi$
$613$	−4.25847e6	−0.457723	−0.228861	+	0.973459i	$0.573500\pi$
$614$	506637.	0.0542345
$615$	−5.37560e6	−0.573111
$616$	349128.	0.0370708
$617$	8.29757e6	0.877482	0.438741	−	0.898614i	$-0.355425\pi$
$617$	8.29757e6	0.877482	0.438741	+	0.898614i	$0.355425\pi$
$618$	−242601.	−0.0255518
$619$	256026.	0.0268570	0.0134285	−	0.999910i	$-0.495725\pi$
$619$	256026.	0.0268570	0.0134285	+	0.999910i	$0.495725\pi$
$620$	2.03325e6	0.212427
$621$	3.26525e6	0.339772
$622$	385128.	0.0399143
$623$	−1.07448e7	−1.10912
$624$	−467282.	−0.0480417
$625$	390625.	0.0400000
$626$	−202517.	−0.0206551
$627$	1.16855e6	0.118708
$628$	−2.68310e6	−0.271480
$629$	−5.13059e6	−0.517059
$630$	533232.	0.0535260
$631$	2.86013e6	0.285964	0.142982	−	0.989725i	$-0.454331\pi$
$631$	2.86013e6	0.285964	0.142982	+	0.989725i	$0.454331\pi$
$632$	320569.	0.0319248
$633$	−3.14413e7	−3.11883
$634$	−124589.	−0.0123100
$635$	1.08676e6	0.106955
$636$	−4.03983e6	−0.396023
$637$	303816.	0.0296662
$638$	30386.1	0.00295545
$639$	−4.76883e6	−0.462019
$640$	792197.	0.0764510
$641$	1.34807e7	1.29589	0.647944	−	0.761688i	$-0.275629\pi$
$641$	1.34807e7	1.29589	0.647944	+	0.761688i	$0.275629\pi$
$642$	70193.2	0.00672136
$643$	7.82701e6	0.746566	0.373283	−	0.927717i	$-0.378232\pi$
$643$	7.82701e6	0.746566	0.373283	+	0.927717i	$0.378232\pi$
$644$	−3.15384e6	−0.299658
$645$	2.04510e6	0.193560
$646$	−34082.8	−0.00321332
$647$	−4.32933e6	−0.406593	−0.203297	−	0.979117i	$-0.565166\pi$
$647$	−4.32933e6	−0.406593	−0.203297	+	0.979117i	$0.565166\pi$
$648$	−768849.	−0.0719290
$649$	1.75449e6	0.163508
$650$	2603.74	0.000241721 0
$651$	1.26558e7	1.17041
$652$	1.33710e6	0.123181
$653$	−807156.	−0.0740755	−0.0370378	−	0.999314i	$-0.511792\pi$
$653$	−807156.	−0.0740755	−0.0370378	+	0.999314i	$0.511792\pi$
$654$	1.00109e6	0.0915226
$655$	891732.	0.0812140
$656$	−8.18510e6	−0.742616
$657$	−2.51440e7	−2.27259
$658$	214902.	0.0193498
$659$	−5.22078e6	−0.468298	−0.234149	−	0.972201i	$-0.575230\pi$
$659$	−5.22078e6	−0.468298	−0.234149	+	0.972201i	$0.575230\pi$
$660$	−2.58482e6	−0.230978
$661$	860599.	0.0766120	0.0383060	−	0.999266i	$-0.487804\pi$
$661$	860599.	0.0766120	0.0383060	+	0.999266i	$0.487804\pi$
$662$	874036.	0.0775147
$663$	−178372.	−0.0157596
$664$	1.40946e6	0.124060
$665$	−1.67679e6	−0.147037
$666$	−1.51520e6	−0.132368
$667$	−549493.	−0.0478242
$668$	7.17878e6	0.622457
$669$	8.80261e6	0.760407
$670$	−115712.	−0.00995848
$671$	−4.74593e6	−0.406926
$672$	3.69937e6	0.316013
$673$	1.14263e7	0.972454	0.486227	−	0.873833i	$-0.338373\pi$
$673$	1.14263e7	0.972454	0.486227	+	0.873833i	$0.338373\pi$
$674$	45530.3	0.00386057
$675$	−3.84005e6	−0.324397
$676$	1.18501e7	0.997366
$677$	−5.12342e6	−0.429623	−0.214812	−	0.976655i	$-0.568914\pi$
$677$	−5.12342e6	−0.429623	−0.214812	+	0.976655i	$0.568914\pi$
$678$	1.73688e6	0.145110
$679$	2.74717e6	0.228671
$680$	150920.	0.0125163
$681$	1.52889e7	1.26330
$682$	74829.7	0.00616046
$683$	−1.97048e7	−1.61630	−0.808148	−	0.588979i	$-0.799530\pi$
$683$	−1.97048e7	−1.61630	−0.808148	+	0.588979i	$0.799530\pi$
$684$	5.45020e6	0.445422
$685$	−3.91526e6	−0.318811
$686$	−40860.1	−0.00331504
$687$	1.29590e7	1.04756
$688$	3.11395e6	0.250807
$689$	−81094.1	−0.00650791
$690$	−86326.2	−0.00690271
$691$	1.67342e7	1.33324	0.666622	−	0.745396i	$-0.267739\pi$
$691$	1.67342e7	1.33324	0.666622	+	0.745396i	$0.267739\pi$
$692$	5.11929e6	0.406392
$693$	−1.06261e7	−0.840506
$694$	−954399.	−0.0752197
$695$	869167.	0.0682561
$696$	429562.	0.0336126
$697$	−3.12444e6	−0.243607
$698$	477809.	0.0371207
$699$	−1.57736e7	−1.22106
$700$	3.70903e6	0.286099
$701$	1.37815e7	1.05926	0.529629	−	0.848229i	$-0.322331\pi$
$701$	1.37815e7	1.05926	0.529629	+	0.848229i	$0.322331\pi$
$702$	−25596.2	−0.00196034
$703$	4.76467e6	0.363617
$704$	−3.92114e6	−0.298182
$705$	−3.18506e6	−0.241349
$706$	203051.	0.0153318
$707$	−2.04553e7	−1.53907
$708$	1.23899e7	0.928936
$709$	1.16607e7	0.871185	0.435592	−	0.900144i	$-0.356539\pi$
$709$	1.16607e7	0.871185	0.435592	+	0.900144i	$0.356539\pi$
$710$	61260.8	0.00456076
$711$	−9.75688e6	−0.723830
$712$	−898119.	−0.0663948
$713$	−1.35320e6	−0.0996866
$714$	469263.	0.0344486
$715$	−51886.7	−0.00379569
$716$	9.10443e6	0.663698
$717$	−2.33523e6	−0.169641
$718$	−864493.	−0.0625821
$719$	−3.78334e6	−0.272931	−0.136466	−	0.990645i	$-0.543574\pi$
$719$	−3.78334e6	−0.272931	−0.136466	+	0.990645i	$0.543574\pi$
$720$	−1.20334e7	−0.865084
$721$	−6.93716e6	−0.496985
$722$	31652.0	0.00225974
$723$	1.13911e7	0.810440
$724$	1.80430e6	0.127927
$725$	646224.	0.0456602
$726$	−95129.2	−0.00669842
$727$	−8.47831e6	−0.594940	−0.297470	−	0.954731i	$-0.596143\pi$
$727$	−8.47831e6	−0.594940	−0.297470	+	0.954731i	$0.596143\pi$
$728$	49491.4	0.00346100
$729$	−1.65402e7	−1.15271
$730$	323002.	0.0224335
$731$	1.18867e6	0.0822747
$732$	−3.35151e7	−2.31187
$733$	8.40453e6	0.577768	0.288884	−	0.957364i	$-0.406716\pi$
$733$	8.40453e6	0.577768	0.288884	+	0.957364i	$0.406716\pi$
$734$	−696939.	−0.0477480
$735$	1.18461e7	0.808829
$736$	−395548.	−0.0269157
$737$	2.30589e6	0.156376
$738$	−922730.	−0.0623640
$739$	−9.91391e6	−0.667780	−0.333890	−	0.942612i	$-0.608361\pi$
$739$	−9.91391e6	−0.667780	−0.333890	+	0.942612i	$0.608361\pi$
$740$	−1.05394e7	−0.707514
$741$	165651.	0.0110828
$742$	213343.	0.0142255
$743$	−2.68981e7	−1.78751	−0.893757	−	0.448552i	$-0.851940\pi$
$743$	−2.68981e7	−1.78751	−0.893757	+	0.448552i	$0.851940\pi$
$744$	1.05785e6	0.0700635
$745$	−4.73501e6	−0.312558
$746$	275359.	0.0181156
$747$	−4.28985e7	−2.81281
$748$	−1.50236e6	−0.0981796
$749$	2.00717e6	0.130731
$750$	101523.	0.00659037
$751$	−1.57134e7	−1.01665	−0.508324	−	0.861166i	$-0.669735\pi$
$751$	−1.57134e7	−1.01665	−0.508324	+	0.861166i	$0.669735\pi$
$752$	−4.84970e6	−0.312730
$753$	−2.72103e7	−1.74882
$754$	4307.45	0.000275926 0
$755$	−5.92482e6	−0.378275
$756$	−3.64618e7	−2.32024
$757$	1.61425e7	1.02384	0.511920	−	0.859033i	$-0.328935\pi$
$757$	1.61425e7	1.02384	0.511920	+	0.859033i	$0.328935\pi$
$758$	−1.11824e6	−0.0706905
$759$	1.72029e6	0.108392
$760$	−140157.	−0.00880197
$761$	−1.52953e7	−0.957409	−0.478704	−	0.877976i	$-0.658893\pi$
$761$	−1.52953e7	−0.957409	−0.478704	+	0.877976i	$0.658893\pi$
$762$	282448.	0.0176218
$763$	2.86261e7	1.78012
$764$	2.07291e7	1.28483
$765$	−4.59344e6	−0.283782
$766$	−56741.3	−0.00349404
$767$	248711.	0.0152653
$768$	−2.75358e7	−1.68459
$769$	8.83749e6	0.538906	0.269453	−	0.963014i	$-0.413157\pi$
$769$	8.83749e6	0.538906	0.269453	+	0.963014i	$0.413157\pi$
$770$	136504.	0.00829694
$771$	2.41046e7	1.46038
$772$	3.27490e6	0.197767
$773$	−2.70908e7	−1.63070	−0.815349	−	0.578969i	$-0.803455\pi$
$773$	−2.70908e7	−1.63070	−0.815349	+	0.578969i	$0.803455\pi$
$774$	351044.	0.0210625
$775$	1.59141e6	0.0951759
$776$	229625.	0.0136888
$777$	−6.56015e7	−3.89817
$778$	−1.08988e6	−0.0645552
$779$	2.90160e6	0.171315
$780$	−366417.	−0.0215645
$781$	−1.22079e6	−0.0716165
$782$	−50175.1	−0.00293407
$783$	−6.35272e6	−0.370301
$784$	1.80373e7	1.04805
$785$	−2.10005e6	−0.121634
$786$	231759.	0.0133808
$787$	−6.25423e6	−0.359946	−0.179973	−	0.983672i	$-0.557601\pi$
$787$	−6.25423e6	−0.359946	−0.179973	+	0.983672i	$0.557601\pi$
$788$	2.63788e7	1.51335
$789$	−2.06156e7	−1.17897
$790$	125338.	0.00714519
$791$	4.96660e7	2.82240
$792$	−888196.	−0.0503148
$793$	−672770.	−0.0379912
$794$	−855254.	−0.0481442
$795$	−3.16195e6	−0.177434
$796$	1.75542e7	0.981973
$797$	−9.86334e6	−0.550019	−0.275010	−	0.961441i	$-0.588681\pi$
$797$	−9.86334e6	−0.550019	−0.275010	+	0.961441i	$0.588681\pi$
$798$	−435795.	−0.0242256
$799$	−1.85124e6	−0.102588
$800$	465179.	0.0256978
$801$	2.73353e7	1.50537
$802$	−639306.	−0.0350972
$803$	−6.43669e6	−0.352269
$804$	1.62839e7	0.888418
$805$	−2.46849e6	−0.134258
$806$	10607.6	0.000575150 0
$807$	1.62268e7	0.877098
$808$	−1.70978e6	−0.0921325
$809$	2.01499e7	1.08243	0.541217	−	0.840883i	$-0.317964\pi$
$809$	2.01499e7	1.08243	0.541217	+	0.840883i	$0.317964\pi$
$810$	−300609.	−0.0160986
$811$	1.24569e7	0.665055	0.332527	−	0.943094i	$-0.392099\pi$
$811$	1.24569e7	0.665055	0.332527	+	0.943094i	$0.392099\pi$
$812$	6.13598e6	0.326583
$813$	−1.86900e7	−0.991706
$814$	−387881.	−0.0205181
$815$	1.04654e6	0.0551900
$816$	−1.05899e7	−0.556756
$817$	−1.10389e6	−0.0578589
$818$	−663112.	−0.0346500
$819$	−1.50633e6	−0.0784710
$820$	−6.41829e6	−0.333338
$821$	−1.46949e7	−0.760866	−0.380433	−	0.924808i	$-0.624225\pi$
$821$	−1.46949e7	−0.760866	−0.380433	+	0.924808i	$0.624225\pi$
$822$	−1.01757e6	−0.0525272
$823$	−2.93901e7	−1.51252	−0.756262	−	0.654269i	$-0.772976\pi$
$823$	−2.93901e7	−1.51252	−0.756262	+	0.654269i	$0.772976\pi$
$824$	−579851.	−0.0297508
$825$	−2.02312e6	−0.103487
$826$	−654310.	−0.0333683
$827$	1.67116e7	0.849677	0.424838	−	0.905269i	$-0.360331\pi$
$827$	1.67116e7	0.849677	0.424838	+	0.905269i	$0.360331\pi$
$828$	8.02351e6	0.406713
$829$	2.93304e7	1.48229	0.741143	−	0.671347i	$-0.234284\pi$
$829$	2.93304e7	1.48229	0.741143	+	0.671347i	$0.234284\pi$
$830$	551078.	0.0277663
$831$	5.41807e7	2.72171
$832$	−555850.	−0.0278387
$833$	6.88527e6	0.343802
$834$	225895.	0.0112458
$835$	5.61878e6	0.278886
$836$	1.39522e6	0.0690439
$837$	−1.56444e7	−0.771870
$838$	−464392.	−0.0228441
$839$	3.23605e7	1.58712	0.793561	−	0.608491i	$-0.208225\pi$
$839$	3.23605e7	1.58712	0.793561	+	0.608491i	$0.208225\pi$
$840$	1.92972e6	0.0943619
$841$	−1.94421e7	−0.947879
$842$	1.27916e6	0.0621793
$843$	−1.14123e7	−0.553102
$844$	−3.75399e7	−1.81400
$845$	9.27497e6	0.446859
$846$	−546721.	−0.0262627
$847$	−2.72021e6	−0.130285
$848$	−4.81451e6	−0.229912
$849$	−4.81567e7	−2.29291
$850$	59007.7	0.00280131
$851$	7.01431e6	0.332018
$852$	−8.62105e6	−0.406875
$853$	−2.52790e7	−1.18956	−0.594781	−	0.803888i	$-0.702761\pi$
$853$	−2.52790e7	−1.18956	−0.594781	+	0.803888i	$0.702761\pi$
$854$	1.76993e6	0.0830444
$855$	4.26583e6	0.199567
$856$	167772.	0.00782590
$857$	1.86108e6	0.0865592	0.0432796	−	0.999063i	$-0.486219\pi$
$857$	1.86108e6	0.0865592	0.0432796	+	0.999063i	$0.486219\pi$
$858$	−13485.3	−0.000625376 0
$859$	5.65854e6	0.261651	0.130825	−	0.991405i	$-0.458237\pi$
$859$	5.65854e6	0.261651	0.130825	+	0.991405i	$0.458237\pi$
$860$	2.44178e6	0.112580
$861$	−3.99502e7	−1.83659
$862$	−1.04139e6	−0.0477359
$863$	2.81125e7	1.28491	0.642455	−	0.766324i	$-0.277916\pi$
$863$	2.81125e7	1.28491	0.642455	+	0.766324i	$0.277916\pi$
$864$	−4.57296e6	−0.208407
$865$	4.00684e6	0.182080
$866$	−5519.67	−0.000250103 0
$867$	3.39416e7	1.53350
$868$	1.51106e7	0.680742
$869$	−2.49770e6	−0.112199
$870$	167952.	0.00752294
$871$	326876.	0.0145995
$872$	2.39274e6	0.106563
$873$	−6.98891e6	−0.310366
$874$	46596.6	0.00206336
$875$	2.90303e6	0.128183
$876$	−4.54550e7	−2.00134
$877$	1.14060e7	0.500766	0.250383	−	0.968147i	$-0.419444\pi$
$877$	1.14060e7	0.500766	0.250383	+	0.968147i	$0.419444\pi$
$878$	−1.04160e6	−0.0456000
$879$	7.45024e7	3.25236
$880$	−3.08048e6	−0.134095
$881$	2.34989e7	1.02002	0.510010	−	0.860169i	$-0.329642\pi$
$881$	2.34989e7	1.02002	0.510010	+	0.860169i	$0.329642\pi$
$882$	2.03340e6	0.0880140
$883$	−1.70472e7	−0.735787	−0.367893	−	0.929868i	$-0.619921\pi$
$883$	−1.70472e7	−0.735787	−0.367893	+	0.929868i	$0.619921\pi$
$884$	−212971.	−0.00916621
$885$	9.69751e6	0.416200
$886$	−1.69223e6	−0.0724229
$887$	2.35864e7	1.00659	0.503294	−	0.864115i	$-0.332121\pi$
$887$	2.35864e7	1.00659	0.503294	+	0.864115i	$0.332121\pi$
$888$	−5.48338e6	−0.233354
$889$	8.07658e6	0.342747
$890$	−351151.	−0.0148600
$891$	5.99046e6	0.252793
$892$	1.05100e7	0.442275
$893$	1.71921e6	0.0721440
$894$	−1.23062e6	−0.0514968
$895$	7.12597e6	0.297363
$896$	5.88743e6	0.244994
$897$	243863.	0.0101196
$898$	−395337.	−0.0163598
$899$	2.63272e6	0.108644
$900$	−9.43594e6	−0.388310
$901$	−1.83781e6	−0.0754203
$902$	−236213.	−0.00966690
$903$	1.51987e7	0.620279
$904$	4.15139e6	0.168956
$905$	1.41221e6	0.0573164
$906$	−1.53985e6	−0.0623244
$907$	−1.06289e7	−0.429011	−0.214505	−	0.976723i	$-0.568814\pi$
$907$	−1.06289e7	−0.429011	−0.214505	+	0.976723i	$0.568814\pi$
$908$	1.82544e7	0.734773
$909$	5.20392e7	2.08892
$910$	19350.4	0.000774616 0
$911$	2.31975e6	0.0926073	0.0463036	−	0.998927i	$-0.485256\pi$
$911$	2.31975e6	0.0926073	0.0463036	+	0.998927i	$0.485256\pi$
$912$	9.83459e6	0.391534
$913$	−1.09817e7	−0.436008
$914$	295002.	0.0116805
$915$	−2.62320e7	−1.03581
$916$	1.54726e7	0.609292
$917$	6.62714e6	0.260257
$918$	−580077.	−0.0227185
$919$	3.59790e7	1.40527	0.702637	−	0.711549i	$-0.252006\pi$
$919$	3.59790e7	1.40527	0.702637	+	0.711549i	$0.252006\pi$
$920$	−206332.	−0.00803705
$921$	−5.58040e7	−2.16779
$922$	150378.	0.00582584
$923$	−173056.	−0.00668624
$924$	−1.92098e7	−0.740188
$925$	−8.24908e6	−0.316994
$926$	1.01924e6	0.0390615
$927$	1.76484e7	0.674538
$928$	769561.	0.0293341
$929$	2.97980e7	1.13279	0.566393	−	0.824135i	$-0.308338\pi$
$929$	2.97980e7	1.13279	0.566393	+	0.824135i	$0.308338\pi$
$930$	413604.	0.0156811
$931$	−6.39421e6	−0.241776
$932$	−1.88332e7	−0.710205
$933$	−4.24203e7	−1.59540
$934$	1.16076e6	0.0435385
$935$	−1.17589e6	−0.0439883
$936$	−125908.	−0.00469747
$937$	−4.80069e7	−1.78630	−0.893151	−	0.449757i	$-0.851511\pi$
$937$	−4.80069e7	−1.78630	−0.893151	+	0.449757i	$0.851511\pi$
$938$	−859948.	−0.0319128
$939$	2.23065e7	0.825595
$940$	−3.80286e6	−0.140375
$941$	−4.55712e7	−1.67771	−0.838855	−	0.544355i	$-0.816774\pi$
$941$	−4.55712e7	−1.67771	−0.838855	+	0.544355i	$0.816774\pi$
$942$	−545798.	−0.0200403
$943$	4.27160e6	0.156427
$944$	1.47658e7	0.539296
$945$	−2.85384e7	−1.03956
$946$	89865.1	0.00326485
$947$	−571054.	−0.0206920	−0.0103460	−	0.999946i	$-0.503293\pi$
$947$	−571054.	−0.0206920	−0.0103460	+	0.999946i	$0.503293\pi$
$948$	−1.76384e7	−0.637438
$949$	−912448.	−0.0328884
$950$	−54799.2	−0.00197000
$951$	1.37230e7	0.492037
$952$	1.12161e6	0.0401096
$953$	1.17982e7	0.420809	0.210405	−	0.977614i	$-0.432522\pi$
$953$	1.17982e7	0.420809	0.210405	+	0.977614i	$0.432522\pi$
$954$	−542753.	−0.0193077
$955$	1.62245e7	0.575656
$956$	−2.78819e6	−0.0986684
$957$	−3.34691e6	−0.118131
$958$	1.63966e6	0.0577217
$959$	−2.90973e7	−1.02166
$960$	−2.16732e7	−0.759005
$961$	−2.21458e7	−0.773539
$962$	−54984.9	−0.00191560
$963$	−5.10632e6	−0.177436
$964$	1.36006e7	0.471375
$965$	2.56324e6	0.0886075
$966$	−641556.	−0.0221203
$967$	−1.99830e7	−0.687218	−0.343609	−	0.939113i	$-0.611650\pi$
$967$	−1.99830e7	−0.687218	−0.343609	+	0.939113i	$0.611650\pi$
$968$	−227372.	−0.00779918
$969$	3.75409e6	0.128438
$970$	89780.2	0.00306374
$971$	2.67110e7	0.909163	0.454581	−	0.890705i	$-0.349789\pi$
$971$	2.67110e7	0.909163	0.454581	+	0.890705i	$0.349789\pi$
$972$	−5.38453e6	−0.182802
$973$	6.45945e6	0.218732
$974$	332321.	0.0112243
$975$	−286792.	−0.00966173
$976$	−3.99419e7	−1.34216
$977$	3.99957e7	1.34053	0.670265	−	0.742122i	$-0.266180\pi$
$977$	3.99957e7	1.34053	0.670265	+	0.742122i	$0.266180\pi$
$978$	271993.	0.00909307
$979$	6.99765e6	0.233344
$980$	1.41439e7	0.470439
$981$	−7.28259e7	−2.41609
$982$	−421645.	−0.0139530
$983$	2.01130e6	0.0663886	0.0331943	−	0.999449i	$-0.489432\pi$
$983$	2.01130e6	0.0663886	0.0331943	+	0.999449i	$0.489432\pi$
$984$	−3.33929e6	−0.109943
$985$	2.06465e7	0.678041
$986$	97618.3	0.00319771
$987$	−2.36706e7	−0.773422
$988$	197782.	0.00644606
$989$	−1.62509e6	−0.0528308
$990$	−347271.	−0.0112611
$991$	−4.25344e7	−1.37580	−0.687902	−	0.725803i	$-0.741468\pi$
$991$	−4.25344e7	−1.37580	−0.687902	+	0.725803i	$0.741468\pi$
$992$	1.89514e6	0.0611452
$993$	−9.62715e7	−3.09831
$994$	455276.	0.0146153
$995$	1.37396e7	0.439963
$996$	−7.75516e7	−2.47709
$997$	1.39182e7	0.443451	0.221726	−	0.975109i	$-0.428831\pi$
$997$	1.39182e7	0.443451	0.221726	+	0.975109i	$0.428831\pi$
$998$	−1.04951e6	−0.0333550
$999$	8.10928e7	2.57080

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.d.1.18	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.d.1.18	✓	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)

\(f(q)\)	\(=\)	\(q+0.242878 q^{2} -26.7520 q^{3} -31.9410 q^{4} -25.0000 q^{5} -6.49745 q^{6} -185.794 q^{7} -15.5298 q^{8} +472.668 q^{9} +O(q^{10})\)	\(q+0.242878 q^{2} -26.7520 q^{3} -31.9410 q^{4} -25.0000 q^{5} -6.49745 q^{6} -185.794 q^{7} -15.5298 q^{8} +472.668 q^{9} -6.07194 q^{10} +121.000 q^{11} +854.485 q^{12} +17.1526 q^{13} -45.1252 q^{14} +668.799 q^{15} +1018.34 q^{16} +388.724 q^{17} +114.800 q^{18} -361.000 q^{19} +798.525 q^{20} +4970.36 q^{21} +29.3882 q^{22} -531.446 q^{23} +415.454 q^{24} +625.000 q^{25} +4.16599 q^{26} -6144.08 q^{27} +5934.45 q^{28} +1033.96 q^{29} +162.436 q^{30} +2546.25 q^{31} +744.287 q^{32} -3236.99 q^{33} +94.4123 q^{34} +4644.85 q^{35} -15097.5 q^{36} -13198.5 q^{37} -87.6788 q^{38} -458.867 q^{39} +388.246 q^{40} -8037.68 q^{41} +1207.19 q^{42} +3057.86 q^{43} -3864.86 q^{44} -11816.7 q^{45} -129.076 q^{46} -4762.35 q^{47} -27242.6 q^{48} +17712.5 q^{49} +151.798 q^{50} -10399.1 q^{51} -547.872 q^{52} -4727.80 q^{53} -1492.26 q^{54} -3025.00 q^{55} +2885.35 q^{56} +9657.46 q^{57} +251.125 q^{58} +14499.9 q^{59} -21362.1 q^{60} -39222.6 q^{61} +618.427 q^{62} -87819.0 q^{63} -32406.1 q^{64} -428.816 q^{65} -786.192 q^{66} +19056.9 q^{67} -12416.2 q^{68} +14217.2 q^{69} +1128.13 q^{70} -10089.2 q^{71} -7340.46 q^{72} -53195.8 q^{73} -3205.63 q^{74} -16720.0 q^{75} +11530.7 q^{76} -22481.1 q^{77} -111.448 q^{78} -20642.1 q^{79} -25458.5 q^{80} +49507.9 q^{81} -1952.17 q^{82} -90758.2 q^{83} -158758. q^{84} -9718.10 q^{85} +742.687 q^{86} -27660.4 q^{87} -1879.11 q^{88} +57831.9 q^{89} -2870.01 q^{90} -3186.86 q^{91} +16974.9 q^{92} -68117.2 q^{93} -1156.67 q^{94} +9025.00 q^{95} -19911.1 q^{96} -14786.1 q^{97} +4301.96 q^{98} +57192.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9}+O(q^{10}) \) 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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