LMFDB - Embedded newform 1045.6.a.d.1.9

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			1.9
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)

$f(q)$	$=$	$q-7.19884 q^{2} -12.8812 q^{3} +19.8234 q^{4} -25.0000 q^{5} +92.7298 q^{6} +73.5738 q^{7} +87.6577 q^{8} -77.0744 q^{9} +O(q^{10})$	\(q-7.19884 q^{2} -12.8812 q^{3} +19.8234 q^{4} -25.0000 q^{5} +92.7298 q^{6} +73.5738 q^{7} +87.6577 q^{8} -77.0744 q^{9} +179.971 q^{10} +121.000 q^{11} -255.349 q^{12} -848.280 q^{13} -529.647 q^{14} +322.030 q^{15} -1265.38 q^{16} +81.2632 q^{17} +554.847 q^{18} -361.000 q^{19} -495.584 q^{20} -947.720 q^{21} -871.060 q^{22} -4587.72 q^{23} -1129.14 q^{24} +625.000 q^{25} +6106.64 q^{26} +4122.95 q^{27} +1458.48 q^{28} -4427.11 q^{29} -2318.25 q^{30} -1001.00 q^{31} +6304.24 q^{32} -1558.63 q^{33} -585.001 q^{34} -1839.35 q^{35} -1527.87 q^{36} +2968.49 q^{37} +2598.78 q^{38} +10926.9 q^{39} -2191.44 q^{40} +8119.55 q^{41} +6822.49 q^{42} +6418.93 q^{43} +2398.63 q^{44} +1926.86 q^{45} +33026.3 q^{46} +2487.08 q^{47} +16299.7 q^{48} -11393.9 q^{49} -4499.28 q^{50} -1046.77 q^{51} -16815.8 q^{52} -31317.8 q^{53} -29680.4 q^{54} -3025.00 q^{55} +6449.31 q^{56} +4650.12 q^{57} +31870.1 q^{58} -6955.23 q^{59} +6383.72 q^{60} -22228.9 q^{61} +7206.02 q^{62} -5670.66 q^{63} -4891.03 q^{64} +21207.0 q^{65} +11220.3 q^{66} +1301.80 q^{67} +1610.91 q^{68} +59095.4 q^{69} +13241.2 q^{70} +61434.6 q^{71} -6756.16 q^{72} +48957.7 q^{73} -21369.7 q^{74} -8050.76 q^{75} -7156.23 q^{76} +8902.43 q^{77} -78660.9 q^{78} -90190.4 q^{79} +31634.5 q^{80} -34379.5 q^{81} -58451.4 q^{82} -56491.9 q^{83} -18787.0 q^{84} -2031.58 q^{85} -46208.9 q^{86} +57026.6 q^{87} +10606.6 q^{88} -67429.2 q^{89} -13871.2 q^{90} -62411.2 q^{91} -90944.0 q^{92} +12894.0 q^{93} -17904.1 q^{94} +9025.00 q^{95} -81206.3 q^{96} -127602. q^{97} +82022.9 q^{98} -9326.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−7.19884	−1.27259	−0.636294	−	0.771447i	$-0.719533\pi$
$2$	−7.19884	−1.27259	−0.636294	+	0.771447i	$0.719533\pi$
$3$	−12.8812	−0.826330	−0.413165	−	0.910656i	$-0.635577\pi$
$3$	−12.8812	−0.826330	−0.413165	+	0.910656i	$0.635577\pi$
$4$	19.8234	0.619480
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	92.7298	1.05158
$7$	73.5738	0.567516	0.283758	−	0.958896i	$-0.408419\pi$
$7$	73.5738	0.567516	0.283758	+	0.958896i	$0.408419\pi$
$8$	87.6577	0.484245
$9$	−77.0744	−0.317179
$10$	179.971	0.569119
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−255.349	−0.511895
$13$	−848.280	−1.39213	−0.696067	−	0.717977i	$-0.745068\pi$
$13$	−848.280	−1.39213	−0.696067	+	0.717977i	$0.745068\pi$
$14$	−529.647	−0.722214
$15$	322.030	0.369546
$16$	−1265.38	−1.23572
$17$	81.2632	0.0681980	0.0340990	−	0.999418i	$-0.489144\pi$
$17$	81.2632	0.0681980	0.0340990	+	0.999418i	$0.489144\pi$
$18$	554.847	0.403638
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−495.584	−0.277040
$21$	−947.720	−0.468956
$22$	−871.060	−0.383700
$23$	−4587.72	−1.80833	−0.904164	−	0.427186i	$-0.859505\pi$
$23$	−4587.72	−1.80833	−0.904164	+	0.427186i	$0.859505\pi$
$24$	−1129.14	−0.400146
$25$	625.000	0.200000
$26$	6106.64	1.77161
$27$	4122.95	1.08842
$28$	1458.48	0.351565
$29$	−4427.11	−0.977520	−0.488760	−	0.872418i	$-0.662551\pi$
$29$	−4427.11	−0.977520	−0.488760	+	0.872418i	$0.662551\pi$
$30$	−2318.25	−0.470280
$31$	−1001.00	−0.187080	−0.0935402	−	0.995616i	$-0.529818\pi$
$31$	−1001.00	−0.187080	−0.0935402	+	0.995616i	$0.529818\pi$
$32$	6304.24	1.08832
$33$	−1558.63	−0.249148
$34$	−585.001	−0.0867880
$35$	−1839.35	−0.253801
$36$	−1527.87	−0.196486
$37$	2968.49	0.356477	0.178238	−	0.983987i	$-0.442960\pi$
$37$	2968.49	0.356477	0.178238	+	0.983987i	$0.442960\pi$
$38$	2598.78	0.291952
$39$	10926.9	1.15036
$40$	−2191.44	−0.216561
$41$	8119.55	0.754349	0.377174	−	0.926142i	$-0.376896\pi$
$41$	8119.55	0.754349	0.377174	+	0.926142i	$0.376896\pi$
$42$	6822.49	0.596787
$43$	6418.93	0.529410	0.264705	−	0.964329i	$-0.414725\pi$
$43$	6418.93	0.529410	0.264705	+	0.964329i	$0.414725\pi$
$44$	2398.63	0.186780
$45$	1926.86	0.141847
$46$	33026.3	2.30126
$47$	2487.08	0.164227	0.0821136	−	0.996623i	$-0.473833\pi$
$47$	2487.08	0.164227	0.0821136	+	0.996623i	$0.473833\pi$
$48$	16299.7	1.02112
$49$	−11393.9	−0.677925
$50$	−4499.28	−0.254518
$51$	−1046.77	−0.0563541
$52$	−16815.8	−0.862399
$53$	−31317.8	−1.53144	−0.765722	−	0.643171i	$-0.777618\pi$
$53$	−31317.8	−1.53144	−0.765722	+	0.643171i	$0.777618\pi$
$54$	−29680.4	−1.38512
$55$	−3025.00	−0.134840
$56$	6449.31	0.274817
$57$	4650.12	0.189573
$58$	31870.1	1.24398
$59$	−6955.23	−0.260124	−0.130062	−	0.991506i	$-0.541518\pi$
$59$	−6955.23	−0.260124	−0.130062	+	0.991506i	$0.541518\pi$
$60$	6383.72	0.228926
$61$	−22228.9	−0.764882	−0.382441	−	0.923980i	$-0.624916\pi$
$61$	−22228.9	−0.764882	−0.382441	+	0.923980i	$0.624916\pi$
$62$	7206.02	0.238076
$63$	−5670.66	−0.180004
$64$	−4891.03	−0.149262
$65$	21207.0	0.622581
$66$	11220.3	0.317063
$67$	1301.80	0.0354289	0.0177145	−	0.999843i	$-0.494361\pi$
$67$	1301.80	0.0354289	0.0177145	+	0.999843i	$0.494361\pi$
$68$	1610.91	0.0422473
$69$	59095.4	1.49428
$70$	13241.2	0.322984
$71$	61434.6	1.44633	0.723165	−	0.690676i	$-0.242687\pi$
$71$	61434.6	1.44633	0.723165	+	0.690676i	$0.242687\pi$
$72$	−6756.16	−0.153592
$73$	48957.7	1.07526	0.537631	−	0.843180i	$-0.319319\pi$
$73$	48957.7	1.07526	0.537631	+	0.843180i	$0.319319\pi$
$74$	−21369.7	−0.453648
$75$	−8050.76	−0.165266
$76$	−7156.23	−0.142118
$77$	8902.43	0.171113
$78$	−78660.9	−1.46394
$79$	−90190.4	−1.62590	−0.812948	−	0.582337i	$-0.802139\pi$
$79$	−90190.4	−1.62590	−0.812948	+	0.582337i	$0.802139\pi$
$80$	31634.5	0.552633
$81$	−34379.5	−0.582219
$82$	−58451.4	−0.959975
$83$	−56491.9	−0.900101	−0.450051	−	0.893003i	$-0.648594\pi$
$83$	−56491.9	−0.900101	−0.450051	+	0.893003i	$0.648594\pi$
$84$	−18787.0	−0.290509
$85$	−2031.58	−0.0304991
$86$	−46208.9	−0.673720
$87$	57026.6	0.807754
$88$	10606.6	0.146005
$89$	−67429.2	−0.902346	−0.451173	−	0.892436i	$-0.648994\pi$
$89$	−67429.2	−0.902346	−0.451173	+	0.892436i	$0.648994\pi$
$90$	−13871.2	−0.180512
$91$	−62411.2	−0.790058
$92$	−90944.0	−1.12022
$93$	12894.0	0.154590
$94$	−17904.1	−0.208994
$95$	9025.00	0.102598
$96$	−81206.3	−0.899314
$97$	−127602.	−1.37698	−0.688491	−	0.725245i	$-0.741726\pi$
$97$	−127602.	−1.37698	−0.688491	+	0.725245i	$0.741726\pi$
$98$	82022.9	0.862720
$99$	−9326.00	−0.0956329
$100$	12389.6	0.123896
$101$	−23580.6	−0.230013	−0.115006	−	0.993365i	$-0.536689\pi$
$101$	−23580.6	−0.230013	−0.115006	+	0.993365i	$0.536689\pi$
$102$	7535.53	0.0717155
$103$	−180090.	−1.67262	−0.836309	−	0.548258i	$-0.815291\pi$
$103$	−180090.	−1.67262	−0.836309	+	0.548258i	$0.815291\pi$
$104$	−74358.3	−0.674134
$105$	23693.0	0.209723
$106$	225452.	1.94890
$107$	−21270.0	−0.179601	−0.0898003	−	0.995960i	$-0.528623\pi$
$107$	−21270.0	−0.179601	−0.0898003	+	0.995960i	$0.528623\pi$
$108$	81730.7	0.674257
$109$	75655.7	0.609923	0.304962	−	0.952365i	$-0.401356\pi$
$109$	75655.7	0.609923	0.304962	+	0.952365i	$0.401356\pi$
$110$	21776.5	0.171596
$111$	−38237.7	−0.294567
$112$	−93099.0	−0.701294
$113$	−93274.9	−0.687177	−0.343589	−	0.939120i	$-0.611643\pi$
$113$	−93274.9	−0.687177	−0.343589	+	0.939120i	$0.611643\pi$
$114$	−33475.5	−0.241248
$115$	114693.	0.808709
$116$	−87760.3	−0.605554
$117$	65380.7	0.441555
$118$	50069.6	0.331031
$119$	5978.85	0.0387035
$120$	28228.4	0.178951
$121$	14641.0	0.0909091
$122$	160023.	0.973379
$123$	−104590.	−0.623341
$124$	−19843.1	−0.115893
$125$	−15625.0	−0.0894427
$126$	40822.2	0.229071
$127$	−150844.	−0.829885	−0.414943	−	0.909848i	$-0.636198\pi$
$127$	−150844.	−0.829885	−0.414943	+	0.909848i	$0.636198\pi$
$128$	−166526.	−0.898374
$129$	−82683.7	−0.437467
$130$	−152666.	−0.792289
$131$	−263966.	−1.34391	−0.671953	−	0.740594i	$-0.734544\pi$
$131$	−263966.	−1.34391	−0.671953	+	0.740594i	$0.734544\pi$
$132$	−30897.2	−0.154342
$133$	−26560.2	−0.130197
$134$	−9371.47	−0.0450864
$135$	−103074.	−0.486758
$136$	7123.35	0.0330246
$137$	140917.	0.641447	0.320724	−	0.947173i	$-0.396074\pi$
$137$	140917.	0.641447	0.320724	+	0.947173i	$0.396074\pi$
$138$	−425418.	−1.90160
$139$	60173.4	0.264160	0.132080	−	0.991239i	$-0.457834\pi$
$139$	60173.4	0.264160	0.132080	+	0.991239i	$0.457834\pi$
$140$	−36462.0	−0.157225
$141$	−32036.6	−0.135706
$142$	−442258.	−1.84058
$143$	−102642.	−0.419744
$144$	97528.5	0.391945
$145$	110678.	0.437160
$146$	−352439.	−1.36836
$147$	146767.	0.560190
$148$	58845.4	0.220830
$149$	−219996.	−0.811799	−0.405900	−	0.913918i	$-0.633042\pi$
$149$	−219996.	−0.811799	−0.405900	+	0.913918i	$0.633042\pi$
$150$	57956.2	0.210316
$151$	146011.	0.521126	0.260563	−	0.965457i	$-0.416092\pi$
$151$	146011.	0.521126	0.260563	+	0.965457i	$0.416092\pi$
$152$	−31644.4	−0.111093
$153$	−6263.31	−0.0216310
$154$	−64087.2	−0.217756
$155$	25024.9	0.0836649
$156$	216607.	0.712626
$157$	311911.	1.00991	0.504954	−	0.863146i	$-0.331509\pi$
$157$	311911.	1.00991	0.504954	+	0.863146i	$0.331509\pi$
$158$	649267.	2.06909
$159$	403411.	1.26548
$160$	−157606.	−0.486713
$161$	−337536.	−1.02626
$162$	247492.	0.740925
$163$	−427712.	−1.26091	−0.630453	−	0.776228i	$-0.717131\pi$
$163$	−427712.	−1.26091	−0.630453	+	0.776228i	$0.717131\pi$
$164$	160957.	0.467304
$165$	38965.7	0.111422
$166$	406677.	1.14546
$167$	−511488.	−1.41920	−0.709602	−	0.704603i	$-0.751125\pi$
$167$	−511488.	−1.41920	−0.709602	+	0.704603i	$0.751125\pi$
$168$	−83075.0	−0.227089
$169$	348286.	0.938035
$170$	14625.0	0.0388128
$171$	27823.9	0.0727658
$172$	127245.	0.327959
$173$	−147493.	−0.374676	−0.187338	−	0.982295i	$-0.559986\pi$
$173$	−147493.	−0.374676	−0.187338	+	0.982295i	$0.559986\pi$
$174$	−410526.	−1.02794
$175$	45983.6	0.113503
$176$	−153111.	−0.372585
$177$	89591.7	0.214949
$178$	485413.	1.14832
$179$	39961.6	0.0932203	0.0466102	−	0.998913i	$-0.485158\pi$
$179$	39961.6	0.0932203	0.0466102	+	0.998913i	$0.485158\pi$
$180$	38196.8	0.0878711
$181$	682276.	1.54797	0.773987	−	0.633201i	$-0.218259\pi$
$181$	682276.	1.54797	0.773987	+	0.633201i	$0.218259\pi$
$182$	449289.	1.00542
$183$	286336.	0.632045
$184$	−402149.	−0.875674
$185$	−74212.2	−0.159421
$186$	−92822.2	−0.196730
$187$	9832.85	0.0205625
$188$	49302.3	0.101736
$189$	303341.	0.617698
$190$	−64969.6	−0.130565
$191$	60644.0	0.120283	0.0601415	−	0.998190i	$-0.480845\pi$
$191$	60644.0	0.120283	0.0601415	+	0.998190i	$0.480845\pi$
$192$	63002.4	0.123340
$193$	−586266.	−1.13293	−0.566463	−	0.824087i	$-0.691689\pi$
$193$	−586266.	−1.13293	−0.566463	+	0.824087i	$0.691689\pi$
$194$	918587.	1.75233
$195$	−273172.	−0.514457
$196$	−225865.	−0.419961
$197$	−832108.	−1.52762	−0.763808	−	0.645444i	$-0.776672\pi$
$197$	−832108.	−1.52762	−0.763808	+	0.645444i	$0.776672\pi$
$198$	67136.4	0.121701
$199$	−1.05479e6	−1.88813	−0.944066	−	0.329756i	$-0.893033\pi$
$199$	−1.05479e6	−1.88813	−0.944066	+	0.329756i	$0.893033\pi$
$200$	54786.1	0.0968490
$201$	−16768.8	−0.0292760
$202$	169753.	0.292711
$203$	−325720.	−0.554758
$204$	−20750.5	−0.0349102
$205$	−202989.	−0.337355
$206$	1.29644e6	2.12855
$207$	353596.	0.573563
$208$	1.07340e6	1.72029
$209$	−43681.0	−0.0691714
$210$	−170562.	−0.266891
$211$	−692382.	−1.07063	−0.535315	−	0.844652i	$-0.679807\pi$
$211$	−692382.	−1.07063	−0.535315	+	0.844652i	$0.679807\pi$
$212$	−620824.	−0.948700
$213$	−791352.	−1.19515
$214$	153119.	0.228558
$215$	−160473.	−0.236759
$216$	361408.	0.527064
$217$	−73647.1	−0.106171
$218$	−544634.	−0.776181
$219$	−630635.	−0.888521
$220$	−59965.7	−0.0835307
$221$	−68934.0	−0.0949408
$222$	275267.	0.374863
$223$	649969.	0.875246	0.437623	−	0.899158i	$-0.355820\pi$
$223$	649969.	0.875246	0.437623	+	0.899158i	$0.355820\pi$
$224$	463827.	0.617641
$225$	−48171.5	−0.0634357
$226$	671471.	0.874493
$227$	−40773.1	−0.0525181	−0.0262591	−	0.999655i	$-0.508359\pi$
$227$	−40773.1	−0.0525181	−0.0262591	+	0.999655i	$0.508359\pi$
$228$	92181.0	0.117437
$229$	−667928.	−0.841669	−0.420834	−	0.907138i	$-0.638263\pi$
$229$	−667928.	−0.841669	−0.420834	+	0.907138i	$0.638263\pi$
$230$	−825657.	−1.02915
$231$	−114674.	−0.141395
$232$	−388071.	−0.473359
$233$	−512169.	−0.618050	−0.309025	−	0.951054i	$-0.600003\pi$
$233$	−512169.	−0.618050	−0.309025	+	0.951054i	$0.600003\pi$
$234$	−470665.	−0.561917
$235$	−62177.0	−0.0734446
$236$	−137876.	−0.161142
$237$	1.16176e6	1.34353
$238$	−43040.8	−0.0492536
$239$	1.10902e6	1.25587	0.627936	−	0.778265i	$-0.283900\pi$
$239$	1.10902e6	1.25587	0.627936	+	0.778265i	$0.283900\pi$
$240$	−407491.	−0.456657
$241$	−71425.5	−0.0792156	−0.0396078	−	0.999215i	$-0.512611\pi$
$241$	−71425.5	−0.0792156	−0.0396078	+	0.999215i	$0.512611\pi$
$242$	−105398.	−0.115690
$243$	−559027.	−0.607319
$244$	−440652.	−0.473829
$245$	284847.	0.303177
$246$	752924.	0.793256
$247$	306229.	0.319377
$248$	−87745.1	−0.0905927
$249$	727685.	0.743781
$250$	112482.	0.113824
$251$	−813776.	−0.815305	−0.407653	−	0.913137i	$-0.633653\pi$
$251$	−813776.	−0.815305	−0.407653	+	0.913137i	$0.633653\pi$
$252$	−112412.	−0.111509
$253$	−555114.	−0.545231
$254$	1.08590e6	1.05610
$255$	26169.2	0.0252023
$256$	1.35531e6	1.29252
$257$	494618.	0.467129	0.233565	−	0.972341i	$-0.424961\pi$
$257$	494618.	0.467129	0.233565	+	0.972341i	$0.424961\pi$
$258$	595227.	0.556715
$259$	218403.	0.202306
$260$	420394.	0.385677
$261$	341217.	0.310048
$262$	1.90025e6	1.71024
$263$	141264.	0.125934	0.0629668	−	0.998016i	$-0.479944\pi$
$263$	141264.	0.125934	0.0629668	+	0.998016i	$0.479944\pi$
$264$	−136626.	−0.120649
$265$	782945.	0.684883
$266$	191202.	0.165687
$267$	868570.	0.745636
$268$	25806.1	0.0219475
$269$	389148.	0.327894	0.163947	−	0.986469i	$-0.447577\pi$
$269$	389148.	0.327894	0.163947	+	0.986469i	$0.447577\pi$
$270$	742011.	0.619443
$271$	−1.23768e6	−1.02373	−0.511865	−	0.859066i	$-0.671045\pi$
$271$	−1.23768e6	−1.02373	−0.511865	+	0.859066i	$0.671045\pi$
$272$	−102829.	−0.0842740
$273$	803932.	0.652849
$274$	−1.01444e6	−0.816298
$275$	75625.0	0.0603023
$276$	1.17147e6	0.925674
$277$	−1.66889e6	−1.30686	−0.653428	−	0.756989i	$-0.726670\pi$
$277$	−1.66889e6	−1.30686	−0.653428	+	0.756989i	$0.726670\pi$
$278$	−433179.	−0.336167
$279$	77151.2	0.0593379
$280$	−161233.	−0.122902
$281$	2.35503e6	1.77922	0.889612	−	0.456716i	$-0.150975\pi$
$281$	2.35503e6	1.77922	0.889612	+	0.456716i	$0.150975\pi$
$282$	230627.	0.172698
$283$	−585018.	−0.434213	−0.217107	−	0.976148i	$-0.569662\pi$
$283$	−585018.	−0.434213	−0.217107	+	0.976148i	$0.569662\pi$
$284$	1.21784e6	0.895972
$285$	−116253.	−0.0847797
$286$	738903.	0.534161
$287$	597386.	0.428105
$288$	−485896.	−0.345193
$289$	−1.41325e6	−0.995349
$290$	−796753.	−0.556325
$291$	1.64367e6	1.13784
$292$	970507.	0.666103
$293$	−685086.	−0.466204	−0.233102	−	0.972452i	$-0.574888\pi$
$293$	−685086.	−0.466204	−0.233102	+	0.972452i	$0.574888\pi$
$294$	−1.05655e6	−0.712891
$295$	173881.	0.116331
$296$	260211.	0.172622
$297$	498876.	0.328172
$298$	1.58371e6	1.03309
$299$	3.89167e6	2.51743
$300$	−159593.	−0.102379
$301$	472266.	0.300449
$302$	−1.05111e6	−0.663179
$303$	303747.	0.190066
$304$	456803.	0.283495
$305$	555724.	0.342065
$306$	45088.6	0.0275273
$307$	1.25651e6	0.760886	0.380443	−	0.924804i	$-0.375772\pi$
$307$	1.25651e6	0.760886	0.380443	+	0.924804i	$0.375772\pi$
$308$	176476.	0.106001
$309$	2.31978e6	1.38214
$310$	−180150.	−0.106471
$311$	302974.	0.177625	0.0888124	−	0.996048i	$-0.471693\pi$
$311$	302974.	0.177625	0.0888124	+	0.996048i	$0.471693\pi$
$312$	957825.	0.557057
$313$	2.21337e6	1.27701	0.638503	−	0.769620i	$-0.279554\pi$
$313$	2.21337e6	1.27701	0.638503	+	0.769620i	$0.279554\pi$
$314$	−2.24540e6	−1.28520
$315$	141766.	0.0805002
$316$	−1.78788e6	−1.00721
$317$	811929.	0.453806	0.226903	−	0.973917i	$-0.427140\pi$
$317$	811929.	0.453806	0.226903	+	0.973917i	$0.427140\pi$
$318$	−2.90409e6	−1.61043
$319$	−535681.	−0.294733
$320$	122276.	0.0667522
$321$	273983.	0.148409
$322$	2.42987e6	1.30600
$323$	−29336.0	−0.0156457
$324$	−681517.	−0.360673
$325$	−530175.	−0.278427
$326$	3.07903e6	1.60461
$327$	−974537.	−0.503998
$328$	711741.	0.365290
$329$	182984.	0.0932016
$330$	−280508.	−0.141795
$331$	3.18025e6	1.59548	0.797741	−	0.603001i	$-0.206028\pi$
$331$	3.18025e6	1.59548	0.797741	+	0.603001i	$0.206028\pi$
$332$	−1.11986e6	−0.557595
$333$	−228794.	−0.113067
$334$	3.68213e6	1.80606
$335$	−32545.1	−0.0158443
$336$	1.19923e6	0.579500
$337$	−3.13039e6	−1.50149	−0.750747	−	0.660590i	$-0.770306\pi$
$337$	−3.13039e6	−1.50149	−0.750747	+	0.660590i	$0.770306\pi$
$338$	−2.50726e6	−1.19373
$339$	1.20149e6	0.567835
$340$	−40272.8	−0.0188936
$341$	−121121.	−0.0564069
$342$	−200300.	−0.0926008
$343$	−2.07485e6	−0.952250
$344$	562669.	0.256364
$345$	−1.47738e6	−0.668260
$346$	1.06178e6	0.476809
$347$	−1.12618e6	−0.502091	−0.251046	−	0.967975i	$-0.580774\pi$
$347$	−1.12618e6	−0.502091	−0.251046	+	0.967975i	$0.580774\pi$
$348$	1.13046e6	0.500388
$349$	2.64382e6	1.16190	0.580950	−	0.813939i	$-0.302681\pi$
$349$	2.64382e6	1.16190	0.580950	+	0.813939i	$0.302681\pi$
$350$	−331029.	−0.144443
$351$	−3.49741e6	−1.51523
$352$	762813.	0.328142
$353$	−3.26444e6	−1.39435	−0.697175	−	0.716901i	$-0.745560\pi$
$353$	−3.26444e6	−1.39435	−0.697175	+	0.716901i	$0.745560\pi$
$354$	−644957.	−0.273541
$355$	−1.53587e6	−0.646818
$356$	−1.33667e6	−0.558986
$357$	−77014.8	−0.0319819
$358$	−287678.	−0.118631
$359$	2.28438e6	0.935473	0.467737	−	0.883868i	$-0.345070\pi$
$359$	2.28438e6	0.935473	0.467737	+	0.883868i	$0.345070\pi$
$360$	168904.	0.0686885
$361$	130321.	0.0526316
$362$	−4.91160e6	−1.96993
$363$	−188594.	−0.0751209
$364$	−1.23720e6	−0.489425
$365$	−1.22394e6	−0.480871
$366$	−2.06129e6	−0.804332
$367$	−2.63663e6	−1.02184	−0.510921	−	0.859628i	$-0.670696\pi$
$367$	−2.63663e6	−1.02184	−0.510921	+	0.859628i	$0.670696\pi$
$368$	5.80521e6	2.23459
$369$	−625809.	−0.239263
$370$	534242.	0.202877
$371$	−2.30417e6	−0.869120
$372$	255603.	0.0957655
$373$	3.34052e6	1.24320	0.621602	−	0.783333i	$-0.286482\pi$
$373$	3.34052e6	1.24320	0.621602	+	0.783333i	$0.286482\pi$
$374$	−70785.2	−0.0261676
$375$	201269.	0.0739092
$376$	218012.	0.0795262
$377$	3.75543e6	1.36084
$378$	−2.18370e6	−0.786076
$379$	820793.	0.293519	0.146759	−	0.989172i	$-0.453116\pi$
$379$	820793.	0.293519	0.146759	+	0.989172i	$0.453116\pi$
$380$	178906.	0.0635573
$381$	1.94305e6	0.685759
$382$	−436566.	−0.153071
$383$	4.23644e6	1.47572	0.737860	−	0.674953i	$-0.235836\pi$
$383$	4.23644e6	1.47572	0.737860	+	0.674953i	$0.235836\pi$
$384$	2.14506e6	0.742353
$385$	−222561.	−0.0765239
$386$	4.22044e6	1.44175
$387$	−494735.	−0.167917
$388$	−2.52950e6	−0.853013
$389$	5.13506e6	1.72057	0.860283	−	0.509816i	$-0.170287\pi$
$389$	5.13506e6	1.72057	0.860283	+	0.509816i	$0.170287\pi$
$390$	1.96652e6	0.654692
$391$	−372813.	−0.123324
$392$	−998762.	−0.328282
$393$	3.40020e6	1.11051
$394$	5.99021e6	1.94402
$395$	2.25476e6	0.727122
$396$	−184873.	−0.0592427
$397$	2.49295e6	0.793846	0.396923	−	0.917852i	$-0.370078\pi$
$397$	2.49295e6	0.793846	0.396923	+	0.917852i	$0.370078\pi$
$398$	7.59325e6	2.40281
$399$	342127.	0.107586
$400$	−790864.	−0.247145
$401$	1.72607e6	0.536040	0.268020	−	0.963413i	$-0.413631\pi$
$401$	1.72607e6	0.536040	0.268020	+	0.963413i	$0.413631\pi$
$402$	120716.	0.0372563
$403$	849125.	0.260441
$404$	−467447.	−0.142488
$405$	859487.	0.260376
$406$	2.34481e6	0.705979
$407$	359187.	0.107482
$408$	−91757.4	−0.0272892
$409$	1.03825e6	0.306898	0.153449	−	0.988157i	$-0.450962\pi$
$409$	1.03825e6	0.306898	0.153449	+	0.988157i	$0.450962\pi$
$410$	1.46128e6	0.429314
$411$	−1.81518e6	−0.530047
$412$	−3.56999e6	−1.03615
$413$	−511723.	−0.147625
$414$	−2.54548e6	−0.729909
$415$	1.41230e6	0.402537
$416$	−5.34776e6	−1.51509
$417$	−775106.	−0.218284
$418$	314453.	0.0880268
$419$	6.53457e6	1.81837	0.909185	−	0.416393i	$-0.136706\pi$
$419$	6.53457e6	1.81837	0.909185	+	0.416393i	$0.136706\pi$
$420$	469675.	0.129919
$421$	−1.69297e6	−0.465527	−0.232763	−	0.972533i	$-0.574777\pi$
$421$	−1.69297e6	−0.465527	−0.232763	+	0.972533i	$0.574777\pi$
$422$	4.98435e6	1.36247
$423$	−191690.	−0.0520894
$424$	−2.74524e6	−0.741594
$425$	50789.5	0.0136396
$426$	5.69682e6	1.52093
$427$	−1.63547e6	−0.434083
$428$	−421643.	−0.111259
$429$	1.32215e6	0.346847
$430$	1.15522e6	0.301297
$431$	−2.98121e6	−0.773036	−0.386518	−	0.922282i	$-0.626322\pi$
$431$	−2.98121e6	−0.773036	−0.386518	+	0.922282i	$0.626322\pi$
$432$	−5.21710e6	−1.34499
$433$	4.66152e6	1.19484	0.597418	−	0.801930i	$-0.296193\pi$
$433$	4.66152e6	1.19484	0.597418	+	0.801930i	$0.296193\pi$
$434$	530174.	0.135112
$435$	−1.42566e6	−0.361239
$436$	1.49975e6	0.377835
$437$	1.65617e6	0.414859
$438$	4.53984e6	1.13072
$439$	−5.74377e6	−1.42245	−0.711223	−	0.702966i	$-0.751859\pi$
$439$	−5.74377e6	−1.42245	−0.711223	+	0.702966i	$0.751859\pi$
$440$	−265165.	−0.0652956
$441$	878177.	0.215023
$442$	496245.	0.120820
$443$	−541221.	−0.131028	−0.0655142	−	0.997852i	$-0.520869\pi$
$443$	−541221.	−0.131028	−0.0655142	+	0.997852i	$0.520869\pi$
$444$	−758000.	−0.182479
$445$	1.68573e6	0.403542
$446$	−4.67902e6	−1.11383
$447$	2.83381e6	0.670814
$448$	−359852.	−0.0847089
$449$	−6.91800e6	−1.61944	−0.809720	−	0.586816i	$-0.800381\pi$
$449$	−6.91800e6	−1.61944	−0.809720	+	0.586816i	$0.800381\pi$
$450$	346779.	0.0807275
$451$	982465.	0.227445
$452$	−1.84902e6	−0.425693
$453$	−1.88080e6	−0.430622
$454$	293519.	0.0668340
$455$	1.56028e6	0.353325
$456$	407619.	0.0917998
$457$	−1.14365e6	−0.256155	−0.128078	−	0.991764i	$-0.540881\pi$
$457$	−1.14365e6	−0.256155	−0.128078	+	0.991764i	$0.540881\pi$
$458$	4.80831e6	1.07110
$459$	335044.	0.0742284
$460$	2.27360e6	0.500979
$461$	163716.	0.0358789	0.0179395	−	0.999839i	$-0.494289\pi$
$461$	163716.	0.0358789	0.0179395	+	0.999839i	$0.494289\pi$
$462$	825521.	0.179938
$463$	−4.91950e6	−1.06652	−0.533260	−	0.845952i	$-0.679033\pi$
$463$	−4.91950e6	−1.06652	−0.533260	+	0.845952i	$0.679033\pi$
$464$	5.60199e6	1.20795
$465$	−322351.	−0.0691348
$466$	3.68703e6	0.786523
$467$	−879315.	−0.186575	−0.0932873	−	0.995639i	$-0.529737\pi$
$467$	−879315.	−0.186575	−0.0932873	+	0.995639i	$0.529737\pi$
$468$	1.29606e6	0.273534
$469$	95778.6	0.0201065
$470$	447603.	0.0934648
$471$	−4.01779e6	−0.834517
$472$	−609679.	−0.125964
$473$	776691.	0.159623
$474$	−8.36334e6	−1.70976
$475$	−225625.	−0.0458831
$476$	118521.	0.0239760
$477$	2.41380e6	0.485741
$478$	−7.98367e6	−1.59821
$479$	6.61073e6	1.31647	0.658234	−	0.752813i	$-0.271304\pi$
$479$	6.61073e6	1.31647	0.658234	+	0.752813i	$0.271304\pi$
$480$	2.03016e6	0.402186
$481$	−2.51811e6	−0.496263
$482$	514181.	0.100809
$483$	4.34787e6	0.848026
$484$	290234.	0.0563164
$485$	3.19005e6	0.615805
$486$	4.02435e6	0.772867
$487$	−5.46303e6	−1.04379	−0.521893	−	0.853011i	$-0.674774\pi$
$487$	−5.46303e6	−1.04379	−0.521893	+	0.853011i	$0.674774\pi$
$488$	−1.94854e6	−0.370390
$489$	5.50945e6	1.04192
$490$	−2.05057e6	−0.385820
$491$	5.97016e6	1.11759	0.558795	−	0.829306i	$-0.311264\pi$
$491$	5.97016e6	1.11759	0.558795	+	0.829306i	$0.311264\pi$
$492$	−2.07332e6	−0.386147
$493$	−359762.	−0.0666649
$494$	−2.20450e6	−0.406436
$495$	233150.	0.0427683
$496$	1.26664e6	0.231180
$497$	4.51998e6	0.820815
$498$	−5.23849e6	−0.946526
$499$	−2.54686e6	−0.457882	−0.228941	−	0.973440i	$-0.573526\pi$
$499$	−2.54686e6	−0.457882	−0.228941	+	0.973440i	$0.573526\pi$
$500$	−309740.	−0.0554080
$501$	6.58859e6	1.17273
$502$	5.85824e6	1.03755
$503$	−8.22604e6	−1.44968	−0.724838	−	0.688919i	$-0.758086\pi$
$503$	−8.22604e6	−1.44968	−0.724838	+	0.688919i	$0.758086\pi$
$504$	−497077.	−0.0871660
$505$	589515.	0.102865
$506$	3.99618e6	0.693855
$507$	−4.48635e6	−0.775127
$508$	−2.99023e6	−0.514097
$509$	2.07444e6	0.354901	0.177450	−	0.984130i	$-0.443215\pi$
$509$	2.07444e6	0.354901	0.177450	+	0.984130i	$0.443215\pi$
$510$	−188388.	−0.0320722
$511$	3.60201e6	0.610228
$512$	−4.42782e6	−0.746474
$513$	−1.48838e6	−0.249702
$514$	−3.56068e6	−0.594463
$515$	4.50225e6	0.748018
$516$	−1.63907e6	−0.271002
$517$	300937.	0.0495164
$518$	−1.57225e6	−0.257452
$519$	1.89989e6	0.309606
$520$	1.85896e6	0.301482
$521$	9.52888e6	1.53797	0.768984	−	0.639268i	$-0.220762\pi$
$521$	9.52888e6	1.53797	0.768984	+	0.639268i	$0.220762\pi$
$522$	−2.45637e6	−0.394564
$523$	−1.12853e7	−1.80409	−0.902045	−	0.431642i	$-0.857934\pi$
$523$	−1.12853e7	−1.80409	−0.902045	+	0.431642i	$0.857934\pi$
$524$	−5.23269e6	−0.832523
$525$	−592325.	−0.0937911
$526$	−1.01694e6	−0.160262
$527$	−81344.2	−0.0127585
$528$	1.97226e6	0.307878
$529$	1.46108e7	2.27005
$530$	−5.63630e6	−0.871574
$531$	536070.	0.0825059
$532$	−526512.	−0.0806546
$533$	−6.88765e6	−1.05015
$534$	−6.25270e6	−0.948887
$535$	531750.	0.0803199
$536$	114113.	0.0171563
$537$	−514754.	−0.0770307
$538$	−2.80142e6	−0.417275
$539$	−1.37866e6	−0.204402
$540$	−2.04327e6	−0.301537
$541$	−6.16105e6	−0.905026	−0.452513	−	0.891758i	$-0.649472\pi$
$541$	−6.16105e6	−0.905026	−0.452513	+	0.891758i	$0.649472\pi$
$542$	8.90986e6	1.30279
$543$	−8.78854e6	−1.27914
$544$	512303.	0.0742215
$545$	−1.89139e6	−0.272766
$546$	−5.78738e6	−0.830808
$547$	−4.53590e6	−0.648180	−0.324090	−	0.946026i	$-0.605058\pi$
$547$	−4.53590e6	−0.648180	−0.324090	+	0.946026i	$0.605058\pi$
$548$	2.79344e6	0.397364
$549$	1.71328e6	0.242604
$550$	−544413.	−0.0767399
$551$	1.59819e6	0.224258
$552$	5.18016e6	0.723595
$553$	−6.63565e6	−0.922722
$554$	1.20141e7	1.66309
$555$	955943.	0.131735
$556$	1.19284e6	0.163642
$557$	−470108.	−0.0642036	−0.0321018	−	0.999485i	$-0.510220\pi$
$557$	−470108.	−0.0642036	−0.0321018	+	0.999485i	$0.510220\pi$
$558$	−555399.	−0.0755127
$559$	−5.44505e6	−0.737009
$560$	2.32747e6	0.313628
$561$	−126659.	−0.0169914
$562$	−1.69535e7	−2.26422
$563$	−3.53160e6	−0.469570	−0.234785	−	0.972047i	$-0.575439\pi$
$563$	−3.53160e6	−0.469570	−0.234785	+	0.972047i	$0.575439\pi$
$564$	−635073.	−0.0840671
$565$	2.33187e6	0.307315
$566$	4.21145e6	0.552574
$567$	−2.52943e6	−0.330419
$568$	5.38522e6	0.700378
$569$	7.27132e6	0.941526	0.470763	−	0.882260i	$-0.343979\pi$
$569$	7.27132e6	0.941526	0.470763	+	0.882260i	$0.343979\pi$
$570$	836887.	0.107890
$571$	7.58063e6	0.973004	0.486502	−	0.873679i	$-0.338273\pi$
$571$	7.58063e6	0.973004	0.486502	+	0.873679i	$0.338273\pi$
$572$	−2.03471e6	−0.260023
$573$	−781168.	−0.0993934
$574$	−4.30049e6	−0.544802
$575$	−2.86732e6	−0.361666
$576$	376973.	0.0473429
$577$	−9.26465e6	−1.15848	−0.579241	−	0.815156i	$-0.696651\pi$
$577$	−9.26465e6	−1.15848	−0.579241	+	0.815156i	$0.696651\pi$
$578$	1.01738e7	1.26667
$579$	7.55182e6	0.936171
$580$	2.19401e6	0.270812
$581$	−4.15633e6	−0.510822
$582$	−1.18325e7	−1.44800
$583$	−3.78945e6	−0.461748
$584$	4.29152e6	0.520690
$585$	−1.63452e6	−0.197469
$586$	4.93183e6	0.593286
$587$	−3.84773e6	−0.460902	−0.230451	−	0.973084i	$-0.574020\pi$
$587$	−3.84773e6	−0.460902	−0.230451	+	0.973084i	$0.574020\pi$
$588$	2.90942e6	0.347027
$589$	361360.	0.0429192
$590$	−1.25174e6	−0.148042
$591$	1.07186e7	1.26231
$592$	−3.75627e6	−0.440507
$593$	6.39847e6	0.747204	0.373602	−	0.927589i	$-0.378123\pi$
$593$	6.39847e6	0.747204	0.373602	+	0.927589i	$0.378123\pi$
$594$	−3.59133e6	−0.417628
$595$	−149471.	−0.0173087
$596$	−4.36106e6	−0.502893
$597$	1.35869e7	1.56022
$598$	−2.80155e7	−3.20366
$599$	7.34534e6	0.836459	0.418230	−	0.908341i	$-0.362651\pi$
$599$	7.34534e6	0.836459	0.418230	+	0.908341i	$0.362651\pi$
$600$	−705711.	−0.0800292
$601$	−1.71181e6	−0.193317	−0.0966585	−	0.995318i	$-0.530815\pi$
$601$	−1.71181e6	−0.193317	−0.0966585	+	0.995318i	$0.530815\pi$
$602$	−3.39977e6	−0.382347
$603$	−100336.	−0.0112373
$604$	2.89443e6	0.322827
$605$	−366025.	−0.0406558
$606$	−2.18663e6	−0.241876
$607$	−5.40451e6	−0.595367	−0.297684	−	0.954665i	$-0.596214\pi$
$607$	−5.40451e6	−0.595367	−0.297684	+	0.954665i	$0.596214\pi$
$608$	−2.27583e6	−0.249678
$609$	4.19566e6	0.458414
$610$	−4.00057e6	−0.435308
$611$	−2.10974e6	−0.228626
$612$	−124160.	−0.0133999
$613$	−1.67330e7	−1.79855	−0.899275	−	0.437384i	$-0.855905\pi$
$613$	−1.67330e7	−1.79855	−0.899275	+	0.437384i	$0.855905\pi$
$614$	−9.04541e6	−0.968294
$615$	2.61474e6	0.278767
$616$	780367.	0.0828604
$617$	−7.41278e6	−0.783914	−0.391957	−	0.919984i	$-0.628202\pi$
$617$	−7.41278e6	−0.783914	−0.391957	+	0.919984i	$0.628202\pi$
$618$	−1.66997e7	−1.75889
$619$	−4.08529e6	−0.428544	−0.214272	−	0.976774i	$-0.568738\pi$
$619$	−4.08529e6	−0.428544	−0.214272	+	0.976774i	$0.568738\pi$
$620$	496078.	0.0518287
$621$	−1.89149e7	−1.96823
$622$	−2.18106e6	−0.226043
$623$	−4.96103e6	−0.512096
$624$	−1.38267e7	−1.42153
$625$	390625.	0.0400000
$626$	−1.59337e7	−1.62510
$627$	562664.	0.0571584
$628$	6.18313e6	0.625618
$629$	241229.	0.0243110
$630$	−1.02055e6	−0.102444
$631$	−4.50064e6	−0.449987	−0.224994	−	0.974360i	$-0.572236\pi$
$631$	−4.50064e6	−0.449987	−0.224994	+	0.974360i	$0.572236\pi$
$632$	−7.90588e6	−0.787332
$633$	8.91872e6	0.884695
$634$	−5.84495e6	−0.577508
$635$	3.77109e6	0.371136
$636$	7.99696e6	0.783939
$637$	9.66521e6	0.943763
$638$	3.85628e6	0.375074
$639$	−4.73503e6	−0.458745
$640$	4.16315e6	0.401765
$641$	1.80205e7	1.73229	0.866146	−	0.499791i	$-0.166590\pi$
$641$	1.80205e7	1.73229	0.866146	+	0.499791i	$0.166590\pi$
$642$	−1.97236e6	−0.188864
$643$	3.20719e6	0.305912	0.152956	−	0.988233i	$-0.451121\pi$
$643$	3.20719e6	0.305912	0.152956	+	0.988233i	$0.451121\pi$
$644$	−6.69110e6	−0.635745
$645$	2.06709e6	0.195641
$646$	211186.	0.0199105
$647$	−1.76089e7	−1.65375	−0.826877	−	0.562383i	$-0.809885\pi$
$647$	−1.76089e7	−1.65375	−0.826877	+	0.562383i	$0.809885\pi$
$648$	−3.01362e6	−0.281937
$649$	−841582.	−0.0784305
$650$	3.81665e6	0.354322
$651$	948664.	0.0877324
$652$	−8.47869e6	−0.781106
$653$	−3.14686e6	−0.288799	−0.144399	−	0.989520i	$-0.546125\pi$
$653$	−3.14686e6	−0.288799	−0.144399	+	0.989520i	$0.546125\pi$
$654$	7.01554e6	0.641382
$655$	6.59914e6	0.601013
$656$	−1.02743e7	−0.932167
$657$	−3.77339e6	−0.341050
$658$	−1.31727e6	−0.118607
$659$	9.07536e6	0.814049	0.407024	−	0.913417i	$-0.366566\pi$
$659$	9.07536e6	0.814049	0.407024	+	0.913417i	$0.366566\pi$
$660$	772431.	0.0690239
$661$	−1.35682e7	−1.20787	−0.603933	−	0.797035i	$-0.706401\pi$
$661$	−1.35682e7	−1.20787	−0.603933	+	0.797035i	$0.706401\pi$
$662$	−2.28942e7	−2.03039
$663$	887953.	0.0784524
$664$	−4.95195e6	−0.435869
$665$	664004.	0.0582259
$666$	1.64706e6	0.143887
$667$	2.03103e7	1.76768
$668$	−1.01394e7	−0.879168
$669$	−8.37238e6	−0.723242
$670$	234287.	0.0201633
$671$	−2.68970e6	−0.230620
$672$	−5.97466e6	−0.510375
$673$	−7.18506e6	−0.611494	−0.305747	−	0.952113i	$-0.598906\pi$
$673$	−7.18506e6	−0.611494	−0.305747	+	0.952113i	$0.598906\pi$
$674$	2.25352e7	1.91078
$675$	2.57684e6	0.217685
$676$	6.90420e6	0.581094
$677$	−2.35641e7	−1.97597	−0.987984	−	0.154554i	$-0.950606\pi$
$677$	−2.35641e7	−1.97597	−0.987984	+	0.154554i	$0.950606\pi$
$678$	−8.64937e6	−0.722620
$679$	−9.38817e6	−0.781459
$680$	−178084.	−0.0147690
$681$	525207.	0.0433973
$682$	871928.	0.0717827
$683$	1.79704e7	1.47403	0.737013	−	0.675878i	$-0.236236\pi$
$683$	1.79704e7	1.47403	0.737013	+	0.675878i	$0.236236\pi$
$684$	551562.	0.0450769
$685$	−3.52292e6	−0.286864
$686$	1.49365e7	1.21182
$687$	8.60372e6	0.695496
$688$	−8.12240e6	−0.654204
$689$	2.65662e7	2.13198
$690$	1.06355e7	0.850420
$691$	−1.43450e7	−1.14289	−0.571446	−	0.820639i	$-0.693617\pi$
$691$	−1.43450e7	−1.14289	−0.571446	+	0.820639i	$0.693617\pi$
$692$	−2.92381e6	−0.232105
$693$	−686150.	−0.0542732
$694$	8.10717e6	0.638955
$695$	−1.50434e6	−0.118136
$696$	4.99882e6	0.391151
$697$	659821.	0.0514451
$698$	−1.90325e7	−1.47862
$699$	6.59736e6	0.510713
$700$	911551.	0.0703130
$701$	2.36304e7	1.81625	0.908126	−	0.418698i	$-0.137513\pi$
$701$	2.36304e7	1.81625	0.908126	+	0.418698i	$0.137513\pi$
$702$	2.51773e7	1.92827
$703$	−1.07162e6	−0.0817813
$704$	−591815.	−0.0450043
$705$	800915.	0.0606895
$706$	2.35002e7	1.77443
$707$	−1.73492e6	−0.130536
$708$	1.77601e6	0.133156
$709$	1.20566e7	0.900760	0.450380	−	0.892837i	$-0.351289\pi$
$709$	1.20566e7	0.900760	0.450380	+	0.892837i	$0.351289\pi$
$710$	1.10565e7	0.823133
$711$	6.95137e6	0.515699
$712$	−5.91069e6	−0.436957
$713$	4.59229e6	0.338303
$714$	554418.	0.0406997
$715$	2.56605e6	0.187715
$716$	792174.	0.0577481
$717$	−1.42855e7	−1.03776
$718$	−1.64449e7	−1.19047
$719$	−2.68638e7	−1.93796	−0.968980	−	0.247139i	$-0.920510\pi$
$719$	−2.68638e7	−1.93796	−0.968980	+	0.247139i	$0.920510\pi$
$720$	−2.43821e6	−0.175283
$721$	−1.32499e7	−0.949238
$722$	−938161.	−0.0669783
$723$	920047.	0.0654583
$724$	1.35250e7	0.958939
$725$	−2.76695e6	−0.195504
$726$	1.35766e6	0.0955980
$727$	2.43344e7	1.70759	0.853795	−	0.520609i	$-0.174295\pi$
$727$	2.43344e7	1.70759	0.853795	+	0.520609i	$0.174295\pi$
$728$	−5.47082e6	−0.382582
$729$	1.55552e7	1.08407
$730$	8.81098e6	0.611951
$731$	521623.	0.0361047
$732$	5.67614e6	0.391539
$733$	2.00533e7	1.37856	0.689281	−	0.724494i	$-0.257927\pi$
$733$	2.00533e7	1.37856	0.689281	+	0.724494i	$0.257927\pi$
$734$	1.89807e7	1.30038
$735$	−3.66918e6	−0.250525
$736$	−2.89221e7	−1.96804
$737$	157518.	0.0106822
$738$	4.50510e6	0.304484
$739$	5.08168e6	0.342292	0.171146	−	0.985246i	$-0.445253\pi$
$739$	5.08168e6	0.342292	0.171146	+	0.985246i	$0.445253\pi$
$740$	−1.47114e6	−0.0987583
$741$	−3.94460e6	−0.263911
$742$	1.65874e7	1.10603
$743$	2.73319e7	1.81634	0.908172	−	0.418598i	$-0.137478\pi$
$743$	2.73319e7	1.81634	0.908172	+	0.418598i	$0.137478\pi$
$744$	1.13026e6	0.0748595
$745$	5.49989e6	0.363048
$746$	−2.40479e7	−1.58209
$747$	4.35408e6	0.285493
$748$	194920.	0.0127380
$749$	−1.56492e6	−0.101926
$750$	−1.44890e6	−0.0940560
$751$	−1.00988e7	−0.653389	−0.326695	−	0.945130i	$-0.605935\pi$
$751$	−1.00988e7	−0.653389	−0.326695	+	0.945130i	$0.605935\pi$
$752$	−3.14711e6	−0.202940
$753$	1.04824e7	0.673711
$754$	−2.70348e7	−1.73179
$755$	−3.65027e6	−0.233055
$756$	6.01324e6	0.382652
$757$	7.47435e6	0.474060	0.237030	−	0.971502i	$-0.423826\pi$
$757$	7.47435e6	0.474060	0.237030	+	0.971502i	$0.423826\pi$
$758$	−5.90876e6	−0.373528
$759$	7.15054e6	0.450541
$760$	791111.	0.0496825
$761$	1.54984e6	0.0970118	0.0485059	−	0.998823i	$-0.484554\pi$
$761$	1.54984e6	0.0970118	0.0485059	+	0.998823i	$0.484554\pi$
$762$	−1.39877e7	−0.872689
$763$	5.56628e6	0.346141
$764$	1.20217e6	0.0745129
$765$	156583.	0.00967366
$766$	−3.04975e7	−1.87798
$767$	5.89998e6	0.362128
$768$	−1.74580e7	−1.06805
$769$	−8.05654e6	−0.491284	−0.245642	−	0.969361i	$-0.578999\pi$
$769$	−8.05654e6	−0.491284	−0.245642	+	0.969361i	$0.578999\pi$
$770$	1.60218e6	0.0973834
$771$	−6.37128e6	−0.386003
$772$	−1.16218e7	−0.701825
$773$	180271.	0.0108512	0.00542558	−	0.999985i	$-0.498273\pi$
$773$	180271.	0.0108512	0.00542558	+	0.999985i	$0.498273\pi$
$774$	3.56152e6	0.213690
$775$	−625623.	−0.0374161
$776$	−1.11853e7	−0.666796
$777$	−2.81330e6	−0.167172
$778$	−3.69665e7	−2.18957
$779$	−2.93116e6	−0.173059
$780$	−5.41519e6	−0.318696
$781$	7.43359e6	0.436085
$782$	2.68382e6	0.156941
$783$	−1.82527e7	−1.06396
$784$	1.44176e7	0.837729
$785$	−7.79778e6	−0.451645
$786$	−2.44775e7	−1.41322
$787$	1.47533e6	0.0849087	0.0424544	−	0.999098i	$-0.486482\pi$
$787$	1.47533e6	0.0849087	0.0424544	+	0.999098i	$0.486482\pi$
$788$	−1.64952e7	−0.946327
$789$	−1.81965e6	−0.104063
$790$	−1.62317e7	−0.925327
$791$	−6.86259e6	−0.389984
$792$	−817496.	−0.0463098
$793$	1.88564e7	1.06482
$794$	−1.79463e7	−1.01024
$795$	−1.00853e7	−0.565939
$796$	−2.09094e7	−1.16966
$797$	2.40059e7	1.33867	0.669334	−	0.742962i	$-0.266579\pi$
$797$	2.40059e7	1.33867	0.669334	+	0.742962i	$0.266579\pi$
$798$	−2.46292e6	−0.136912
$799$	202108.	0.0112000
$800$	3.94015e6	0.217665
$801$	5.19707e6	0.286205
$802$	−1.24257e7	−0.682158
$803$	5.92388e6	0.324203
$804$	−332414.	−0.0181359
$805$	8.43840e6	0.458955
$806$	−6.11272e6	−0.331434
$807$	−5.01270e6	−0.270949
$808$	−2.06702e6	−0.111382
$809$	1.34386e7	0.721908	0.360954	−	0.932584i	$-0.382451\pi$
$809$	1.34386e7	0.721908	0.360954	+	0.932584i	$0.382451\pi$
$810$	−6.18731e6	−0.331352
$811$	6.63743e6	0.354363	0.177181	−	0.984178i	$-0.443302\pi$
$811$	6.63743e6	0.354363	0.177181	+	0.984178i	$0.443302\pi$
$812$	−6.45686e6	−0.343662
$813$	1.59428e7	0.845938
$814$	−2.58573e6	−0.136780
$815$	1.06928e7	0.563894
$816$	1.32456e6	0.0696381
$817$	−2.31724e6	−0.121455
$818$	−7.47421e6	−0.390555
$819$	4.81031e6	0.250590
$820$	−4.02392e6	−0.208985
$821$	−8.62983e6	−0.446832	−0.223416	−	0.974723i	$-0.571721\pi$
$821$	−8.62983e6	−0.446832	−0.223416	+	0.974723i	$0.571721\pi$
$822$	1.30672e7	0.674532
$823$	1.34683e6	0.0693130	0.0346565	−	0.999399i	$-0.488966\pi$
$823$	1.34683e6	0.0693130	0.0346565	+	0.999399i	$0.488966\pi$
$824$	−1.57863e7	−0.809957
$825$	−974142.	−0.0498296
$826$	3.68381e6	0.187866
$827$	1.45914e7	0.741879	0.370940	−	0.928657i	$-0.379036\pi$
$827$	1.45914e7	0.741879	0.370940	+	0.928657i	$0.379036\pi$
$828$	7.00945e6	0.355311
$829$	2.12420e7	1.07352	0.536758	−	0.843736i	$-0.319649\pi$
$829$	2.12420e7	1.07352	0.536758	+	0.843736i	$0.319649\pi$
$830$	−1.01669e7	−0.512264
$831$	2.14973e7	1.07989
$832$	4.14897e6	0.207793
$833$	−925904.	−0.0462332
$834$	5.57987e6	0.277785
$835$	1.27872e7	0.634687
$836$	−865904.	−0.0428503
$837$	−4.12705e6	−0.203623
$838$	−4.70414e7	−2.31403
$839$	−1.76764e7	−0.866940	−0.433470	−	0.901168i	$-0.642711\pi$
$839$	−1.76764e7	−0.866940	−0.433470	+	0.901168i	$0.642711\pi$
$840$	2.07687e6	0.101557
$841$	−911814.	−0.0444546
$842$	1.21874e7	0.592424
$843$	−3.03357e7	−1.47023
$844$	−1.37253e7	−0.663235
$845$	−8.70715e6	−0.419502
$846$	1.37995e6	0.0662883
$847$	1.07719e6	0.0515924
$848$	3.96290e7	1.89244
$849$	7.53574e6	0.358803
$850$	−365626.	−0.0173576
$851$	−1.36186e7	−0.644626
$852$	−1.56873e7	−0.740369
$853$	−1.15412e7	−0.543099	−0.271549	−	0.962425i	$-0.587536\pi$
$853$	−1.15412e7	−0.543099	−0.271549	+	0.962425i	$0.587536\pi$
$854$	1.17735e7	0.552408
$855$	−695596.	−0.0325418
$856$	−1.86448e6	−0.0869707
$857$	−1.58275e7	−0.736140	−0.368070	−	0.929798i	$-0.619981\pi$
$857$	−1.58275e7	−0.736140	−0.368070	+	0.929798i	$0.619981\pi$
$858$	−9.51797e6	−0.441393
$859$	−2.48790e7	−1.15040	−0.575202	−	0.818011i	$-0.695077\pi$
$859$	−2.48790e7	−1.15040	−0.575202	+	0.818011i	$0.695077\pi$
$860$	−3.18112e6	−0.146668
$861$	−7.69506e6	−0.353756
$862$	2.14613e7	0.983757
$863$	−2.53476e7	−1.15854	−0.579269	−	0.815136i	$-0.696662\pi$
$863$	−2.53476e7	−1.15854	−0.579269	+	0.815136i	$0.696662\pi$
$864$	2.59920e7	1.18456
$865$	3.68733e6	0.167560
$866$	−3.35576e7	−1.52053
$867$	1.82044e7	0.822487
$868$	−1.45993e6	−0.0657709
$869$	−1.09130e7	−0.490226
$870$	1.02631e7	0.459708
$871$	−1.10429e6	−0.0493218
$872$	6.63180e6	0.295352
$873$	9.83484e6	0.436749
$874$	−1.19225e7	−0.527944
$875$	−1.14959e6	−0.0507602
$876$	−1.25013e7	−0.550421
$877$	6.73544e6	0.295711	0.147855	−	0.989009i	$-0.452763\pi$
$877$	6.73544e6	0.295711	0.147855	+	0.989009i	$0.452763\pi$
$878$	4.13485e7	1.81019
$879$	8.82474e6	0.385239
$880$	3.82778e6	0.166625
$881$	3.00776e7	1.30558	0.652790	−	0.757539i	$-0.273598\pi$
$881$	3.00776e7	1.30558	0.652790	+	0.757539i	$0.273598\pi$
$882$	−6.32186e6	−0.273636
$883$	−1.17894e7	−0.508851	−0.254426	−	0.967092i	$-0.581886\pi$
$883$	−1.17894e7	−0.508851	−0.254426	+	0.967092i	$0.581886\pi$
$884$	−1.36650e6	−0.0588139
$885$	−2.23979e6	−0.0961280
$886$	3.89617e6	0.166745
$887$	4.63875e7	1.97967	0.989834	−	0.142228i	$-0.0454268\pi$
$887$	4.63875e7	1.97967	0.989834	+	0.142228i	$0.0454268\pi$
$888$	−3.35183e6	−0.142643
$889$	−1.10982e7	−0.470973
$890$	−1.21353e7	−0.513542
$891$	−4.15991e6	−0.175546
$892$	1.28846e7	0.542198
$893$	−897836.	−0.0376763
$894$	−2.04002e7	−0.853670
$895$	−999041.	−0.0416894
$896$	−1.22520e7	−0.509842
$897$	−5.01294e7	−2.08023
$898$	4.98016e7	2.06088
$899$	4.43153e6	0.182875
$900$	−954921.	−0.0392972
$901$	−2.54498e6	−0.104442
$902$	−7.07262e6	−0.289443
$903$	−6.08335e6	−0.248270
$904$	−8.17626e6	−0.332762
$905$	−1.70569e7	−0.692275
$906$	1.35396e7	0.548005
$907$	3.45839e7	1.39591	0.697953	−	0.716144i	$-0.254095\pi$
$907$	3.45839e7	1.39591	0.697953	+	0.716144i	$0.254095\pi$
$908$	−808261.	−0.0325339
$909$	1.81746e6	0.0729551
$910$	−1.12322e7	−0.449637
$911$	2.15205e7	0.859124	0.429562	−	0.903037i	$-0.358668\pi$
$911$	2.15205e7	0.859124	0.429562	+	0.903037i	$0.358668\pi$
$912$	−5.88417e6	−0.234260
$913$	−6.83553e6	−0.271391
$914$	8.23296e6	0.325980
$915$	−7.15839e6	−0.282659
$916$	−1.32406e7	−0.521397
$917$	−1.94210e7	−0.762689
$918$	−2.41193e6	−0.0944622
$919$	1.70375e7	0.665453	0.332726	−	0.943023i	$-0.392031\pi$
$919$	1.70375e7	0.665453	0.332726	+	0.943023i	$0.392031\pi$
$920$	1.00537e7	0.391613
$921$	−1.61854e7	−0.628743
$922$	−1.17857e6	−0.0456591
$923$	−5.21137e7	−2.01348
$924$	−2.27323e6	−0.0875917
$925$	1.85531e6	0.0712953
$926$	3.54147e7	1.35724
$927$	1.38803e7	0.530519
$928$	−2.79096e7	−1.06386
$929$	2.01749e7	0.766960	0.383480	−	0.923549i	$-0.374725\pi$
$929$	2.01749e7	0.766960	0.383480	+	0.923549i	$0.374725\pi$
$930$	2.32056e6	0.0879801
$931$	4.11319e6	0.155527
$932$	−1.01529e7	−0.382870
$933$	−3.90267e6	−0.146777
$934$	6.33005e6	0.237433
$935$	−245821.	−0.00919582
$936$	5.73112e6	0.213821
$937$	5.05481e7	1.88086	0.940428	−	0.339993i	$-0.110425\pi$
$937$	5.05481e7	1.88086	0.940428	+	0.339993i	$0.110425\pi$
$938$	−689495.	−0.0255873
$939$	−2.85108e7	−1.05523
$940$	−1.23256e6	−0.0454975
$941$	−2.06492e7	−0.760203	−0.380102	−	0.924945i	$-0.624111\pi$
$941$	−2.06492e7	−0.760203	−0.380102	+	0.924945i	$0.624111\pi$
$942$	2.89235e7	1.06200
$943$	−3.72502e7	−1.36411
$944$	8.80102e6	0.321442
$945$	−7.58352e6	−0.276243
$946$	−5.59128e6	−0.203134
$947$	5.53654e6	0.200615	0.100307	−	0.994956i	$-0.468017\pi$
$947$	5.53654e6	0.200615	0.100307	+	0.994956i	$0.468017\pi$
$948$	2.30300e7	0.832288
$949$	−4.15299e7	−1.49691
$950$	1.62424e6	0.0583903
$951$	−1.04586e7	−0.374993
$952$	524092.	0.0187420
$953$	−9.30355e6	−0.331831	−0.165915	−	0.986140i	$-0.553058\pi$
$953$	−9.30355e6	−0.331831	−0.165915	+	0.986140i	$0.553058\pi$
$954$	−1.73766e7	−0.618149
$955$	−1.51610e6	−0.0537922
$956$	2.19845e7	0.777988
$957$	6.90022e6	0.243547
$958$	−4.75896e7	−1.67532
$959$	1.03678e7	0.364032
$960$	−1.57506e6	−0.0551594
$961$	−2.76272e7	−0.965001
$962$	1.81275e7	0.631538
$963$	1.63937e6	0.0569655
$964$	−1.41589e6	−0.0490725
$965$	1.46567e7	0.506660
$966$	−3.12997e7	−1.07919
$967$	1.17302e7	0.403402	0.201701	−	0.979447i	$-0.435353\pi$
$967$	1.17302e7	0.403402	0.201701	+	0.979447i	$0.435353\pi$
$968$	1.28340e6	0.0440223
$969$	377884.	0.0129285
$970$	−2.29647e7	−0.783666
$971$	−3.67726e7	−1.25163	−0.625815	−	0.779972i	$-0.715233\pi$
$971$	−3.67726e7	−1.25163	−0.625815	+	0.779972i	$0.715233\pi$
$972$	−1.10818e7	−0.376222
$973$	4.42719e6	0.149915
$974$	3.93275e7	1.32831
$975$	6.82930e6	0.230072
$976$	2.81281e7	0.945183
$977$	6.33361e6	0.212283	0.106141	−	0.994351i	$-0.466150\pi$
$977$	6.33361e6	0.212283	0.106141	+	0.994351i	$0.466150\pi$
$978$	−3.96617e7	−1.32594
$979$	−8.15894e6	−0.272068
$980$	5.64663e6	0.187812
$981$	−5.83112e6	−0.193455
$982$	−4.29782e7	−1.42223
$983$	1.97402e7	0.651580	0.325790	−	0.945442i	$-0.394370\pi$
$983$	1.97402e7	0.651580	0.325790	+	0.945442i	$0.394370\pi$
$984$	−9.16809e6	−0.301850
$985$	2.08027e7	0.683170
$986$	2.58987e6	0.0848370
$987$	−2.35706e6	−0.0770153
$988$	6.07049e6	0.197848
$989$	−2.94483e7	−0.957346
$990$	−1.67841e6	−0.0544265
$991$	67570.4	0.00218561	0.00109280	−	0.999999i	$-0.499652\pi$
$991$	67570.4	0.00218561	0.00109280	+	0.999999i	$0.499652\pi$
$992$	−6.31052e6	−0.203604
$993$	−4.09655e7	−1.31839
$994$	−3.25386e7	−1.04456
$995$	2.63697e7	0.844398
$996$	1.44252e7	0.460757
$997$	1.87868e6	0.0598570	0.0299285	−	0.999552i	$-0.490472\pi$
$997$	1.87868e6	0.0598570	0.0299285	+	0.999552i	$0.490472\pi$
$998$	1.83345e7	0.582696
$999$	1.22389e7	0.387998

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.d.1.9	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.d.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-7.19884 q^{2} -12.8812 q^{3} +19.8234 q^{4} -25.0000 q^{5} +92.7298 q^{6} +73.5738 q^{7} +87.6577 q^{8} -77.0744 q^{9} +O(q^{10})\)	\(q-7.19884 q^{2} -12.8812 q^{3} +19.8234 q^{4} -25.0000 q^{5} +92.7298 q^{6} +73.5738 q^{7} +87.6577 q^{8} -77.0744 q^{9} +179.971 q^{10} +121.000 q^{11} -255.349 q^{12} -848.280 q^{13} -529.647 q^{14} +322.030 q^{15} -1265.38 q^{16} +81.2632 q^{17} +554.847 q^{18} -361.000 q^{19} -495.584 q^{20} -947.720 q^{21} -871.060 q^{22} -4587.72 q^{23} -1129.14 q^{24} +625.000 q^{25} +6106.64 q^{26} +4122.95 q^{27} +1458.48 q^{28} -4427.11 q^{29} -2318.25 q^{30} -1001.00 q^{31} +6304.24 q^{32} -1558.63 q^{33} -585.001 q^{34} -1839.35 q^{35} -1527.87 q^{36} +2968.49 q^{37} +2598.78 q^{38} +10926.9 q^{39} -2191.44 q^{40} +8119.55 q^{41} +6822.49 q^{42} +6418.93 q^{43} +2398.63 q^{44} +1926.86 q^{45} +33026.3 q^{46} +2487.08 q^{47} +16299.7 q^{48} -11393.9 q^{49} -4499.28 q^{50} -1046.77 q^{51} -16815.8 q^{52} -31317.8 q^{53} -29680.4 q^{54} -3025.00 q^{55} +6449.31 q^{56} +4650.12 q^{57} +31870.1 q^{58} -6955.23 q^{59} +6383.72 q^{60} -22228.9 q^{61} +7206.02 q^{62} -5670.66 q^{63} -4891.03 q^{64} +21207.0 q^{65} +11220.3 q^{66} +1301.80 q^{67} +1610.91 q^{68} +59095.4 q^{69} +13241.2 q^{70} +61434.6 q^{71} -6756.16 q^{72} +48957.7 q^{73} -21369.7 q^{74} -8050.76 q^{75} -7156.23 q^{76} +8902.43 q^{77} -78660.9 q^{78} -90190.4 q^{79} +31634.5 q^{80} -34379.5 q^{81} -58451.4 q^{82} -56491.9 q^{83} -18787.0 q^{84} -2031.58 q^{85} -46208.9 q^{86} +57026.6 q^{87} +10606.6 q^{88} -67429.2 q^{89} -13871.2 q^{90} -62411.2 q^{91} -90944.0 q^{92} +12894.0 q^{93} -17904.1 q^{94} +9025.00 q^{95} -81206.3 q^{96} -127602. q^{97} +82022.9 q^{98} -9326.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 4 q^{2} + 27 q^{3} + 616 q^{4} - 925 q^{5} + 141 q^{6} - 79 q^{7} + 72 q^{8} + 3140 q^{9}+O(q^{10}) \) 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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