LMFDB - Embedded newform 1045.6.a.h.1.7

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:	$40$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-7.39269 q^{2} -19.3511 q^{3} +22.6518 q^{4} +25.0000 q^{5} +143.057 q^{6} -146.772 q^{7} +69.1080 q^{8} +131.466 q^{9} +O(q^{10})$	\(q-7.39269 q^{2} -19.3511 q^{3} +22.6518 q^{4} +25.0000 q^{5} +143.057 q^{6} -146.772 q^{7} +69.1080 q^{8} +131.466 q^{9} -184.817 q^{10} +121.000 q^{11} -438.339 q^{12} -290.683 q^{13} +1085.04 q^{14} -483.778 q^{15} -1235.75 q^{16} +629.266 q^{17} -971.886 q^{18} +361.000 q^{19} +566.296 q^{20} +2840.20 q^{21} -894.515 q^{22} -2112.75 q^{23} -1337.32 q^{24} +625.000 q^{25} +2148.93 q^{26} +2158.31 q^{27} -3324.65 q^{28} +2754.69 q^{29} +3576.42 q^{30} -8008.70 q^{31} +6924.08 q^{32} -2341.49 q^{33} -4651.97 q^{34} -3669.30 q^{35} +2977.95 q^{36} +6739.80 q^{37} -2668.76 q^{38} +5625.04 q^{39} +1727.70 q^{40} -16645.2 q^{41} -20996.7 q^{42} +13627.2 q^{43} +2740.87 q^{44} +3286.65 q^{45} +15618.9 q^{46} +19919.5 q^{47} +23913.2 q^{48} +4734.97 q^{49} -4620.43 q^{50} -12177.0 q^{51} -6584.51 q^{52} +7651.14 q^{53} -15955.7 q^{54} +3025.00 q^{55} -10143.1 q^{56} -6985.75 q^{57} -20364.6 q^{58} +14099.1 q^{59} -10958.5 q^{60} +29553.0 q^{61} +59205.8 q^{62} -19295.5 q^{63} -11643.5 q^{64} -7267.07 q^{65} +17309.9 q^{66} +13489.6 q^{67} +14254.0 q^{68} +40884.1 q^{69} +27126.0 q^{70} -17584.2 q^{71} +9085.34 q^{72} -25822.4 q^{73} -49825.2 q^{74} -12094.5 q^{75} +8177.32 q^{76} -17759.4 q^{77} -41584.2 q^{78} +21373.1 q^{79} -30893.8 q^{80} -73711.9 q^{81} +123053. q^{82} -32928.2 q^{83} +64335.8 q^{84} +15731.7 q^{85} -100742. q^{86} -53306.4 q^{87} +8362.07 q^{88} -65793.3 q^{89} -24297.2 q^{90} +42664.1 q^{91} -47857.7 q^{92} +154977. q^{93} -147259. q^{94} +9025.00 q^{95} -133989. q^{96} +45671.0 q^{97} -35004.1 q^{98} +15907.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9}+O(q^{10}) $ 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + 600 q^{10} + 4840 q^{11} + 2312 q^{12} + 2661 q^{13} + 395 q^{14} + 1575 q^{15} + 15974 q^{16} + 8249 q^{17} + 7225 q^{18} + 14440 q^{19} + 17250 q^{20} + 6845 q^{21} + 2904 q^{22} + 13948 q^{23} + 9740 q^{24} + 25000 q^{25} + 11581 q^{26} + 27864 q^{27} + 37879 q^{28} + 12965 q^{29} + 9125 q^{30} + 4411 q^{31} + 30751 q^{32} + 7623 q^{33} - 17739 q^{34} + 20975 q^{35} + 71345 q^{36} + 5729 q^{37} + 8664 q^{38} - 23560 q^{39} + 21150 q^{40} + 34059 q^{41} + 48528 q^{42} + 68593 q^{43} + 83490 q^{44} + 88875 q^{45} + 43829 q^{46} + 91592 q^{47} + 26539 q^{48} + 152447 q^{49} + 15000 q^{50} - 23170 q^{51} + 46798 q^{52} + 24361 q^{53} + 136436 q^{54} + 121000 q^{55} - 35393 q^{56} + 22743 q^{57} + 77722 q^{58} + 212881 q^{59} + 57800 q^{60} + 137627 q^{61} + 82606 q^{62} + 243832 q^{63} + 259580 q^{64} + 66525 q^{65} + 44165 q^{66} + 78752 q^{67} + 565000 q^{68} + 46134 q^{69} + 9875 q^{70} + 28888 q^{71} - 65574 q^{72} + 291074 q^{73} + 151963 q^{74} + 39375 q^{75} + 249090 q^{76} + 101519 q^{77} - 136222 q^{78} + 87079 q^{79} + 399350 q^{80} + 471360 q^{81} - 74882 q^{82} + 346989 q^{83} - 159196 q^{84} + 206225 q^{85} - 207742 q^{86} + 294612 q^{87} + 102366 q^{88} + 126718 q^{89} + 180625 q^{90} - 239900 q^{91} + 274196 q^{92} + 321654 q^{93} - 418108 q^{94} + 361000 q^{95} + 342154 q^{96} + 137404 q^{97} - 89356 q^{98} + 430155 q^{99}+O(q^{100}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9 + 600 * q^10 + 4840 * q^11 + 2312 * q^12 + 2661 * q^13 + 395 * q^14 + 1575 * q^15 + 15974 * q^16 + 8249 * q^17 + 7225 * q^18 + 14440 * q^19 + 17250 * q^20 + 6845 * q^21 + 2904 * q^22 + 13948 * q^23 + 9740 * q^24 + 25000 * q^25 + 11581 * q^26 + 27864 * q^27 + 37879 * q^28 + 12965 * q^29 + 9125 * q^30 + 4411 * q^31 + 30751 * q^32 + 7623 * q^33 - 17739 * q^34 + 20975 * q^35 + 71345 * q^36 + 5729 * q^37 + 8664 * q^38 - 23560 * q^39 + 21150 * q^40 + 34059 * q^41 + 48528 * q^42 + 68593 * q^43 + 83490 * q^44 + 88875 * q^45 + 43829 * q^46 + 91592 * q^47 + 26539 * q^48 + 152447 * q^49 + 15000 * q^50 - 23170 * q^51 + 46798 * q^52 + 24361 * q^53 + 136436 * q^54 + 121000 * q^55 - 35393 * q^56 + 22743 * q^57 + 77722 * q^58 + 212881 * q^59 + 57800 * q^60 + 137627 * q^61 + 82606 * q^62 + 243832 * q^63 + 259580 * q^64 + 66525 * q^65 + 44165 * q^66 + 78752 * q^67 + 565000 * q^68 + 46134 * q^69 + 9875 * q^70 + 28888 * q^71 - 65574 * q^72 + 291074 * q^73 + 151963 * q^74 + 39375 * q^75 + 249090 * q^76 + 101519 * q^77 - 136222 * q^78 + 87079 * q^79 + 399350 * q^80 + 471360 * q^81 - 74882 * q^82 + 346989 * q^83 - 159196 * q^84 + 206225 * q^85 - 207742 * q^86 + 294612 * q^87 + 102366 * q^88 + 126718 * q^89 + 180625 * q^90 - 239900 * q^91 + 274196 * q^92 + 321654 * q^93 - 418108 * q^94 + 361000 * q^95 + 342154 * q^96 + 137404 * q^97 - 89356 * q^98 + 430155 * 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 $

$2$	−7.39269	−1.30686	−0.653428	−	0.756989i	$-0.726670\pi$
$2$	−7.39269	−1.30686	−0.653428	+	0.756989i	$0.726670\pi$
$3$	−19.3511	−1.24137	−0.620687	−	0.784058i	$-0.713146\pi$
$3$	−19.3511	−1.24137	−0.620687	+	0.784058i	$0.713146\pi$
$4$	22.6518	0.707870
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	143.057	1.62230
$7$	−146.772	−1.13213	−0.566067	−	0.824359i	$-0.691536\pi$
$7$	−146.772	−1.13213	−0.566067	+	0.824359i	$0.691536\pi$
$8$	69.1080	0.381771
$9$	131.466	0.541012
$10$	−184.817	−0.584443
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−438.339	−0.878732
$13$	−290.683	−0.477047	−0.238524	−	0.971137i	$-0.576663\pi$
$13$	−290.683	−0.477047	−0.238524	+	0.971137i	$0.576663\pi$
$14$	1085.04	1.47953
$15$	−483.778	−0.555160
$16$	−1235.75	−1.20679
$17$	629.266	0.528095	0.264048	−	0.964510i	$-0.414942\pi$
$17$	629.266	0.528095	0.264048	+	0.964510i	$0.414942\pi$
$18$	−971.886	−0.707024
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	566.296	0.316569
$21$	2840.20	1.40540
$22$	−894.515	−0.394032
$23$	−2112.75	−0.832776	−0.416388	−	0.909187i	$-0.636704\pi$
$23$	−2112.75	−0.832776	−0.416388	+	0.909187i	$0.636704\pi$
$24$	−1337.32	−0.473921
$25$	625.000	0.200000
$26$	2148.93	0.623431
$27$	2158.31	0.569776
$28$	−3324.65	−0.801404
$29$	2754.69	0.608244	0.304122	−	0.952633i	$-0.401637\pi$
$29$	2754.69	0.608244	0.304122	+	0.952633i	$0.401637\pi$
$30$	3576.42	0.725513
$31$	−8008.70	−1.49678	−0.748389	−	0.663260i	$-0.769173\pi$
$31$	−8008.70	−1.49678	−0.748389	+	0.663260i	$0.769173\pi$
$32$	6924.08	1.19533
$33$	−2341.49	−0.374289
$34$	−4651.97	−0.690144
$35$	−3669.30	−0.506305
$36$	2977.95	0.382966
$37$	6739.80	0.809361	0.404681	−	0.914458i	$-0.367383\pi$
$37$	6739.80	0.809361	0.404681	+	0.914458i	$0.367383\pi$
$38$	−2668.76	−0.299813
$39$	5625.04	0.592194
$40$	1727.70	0.170733
$41$	−16645.2	−1.54643	−0.773214	−	0.634145i	$-0.781352\pi$
$41$	−16645.2	−1.54643	−0.773214	+	0.634145i	$0.781352\pi$
$42$	−20996.7	−1.83666
$43$	13627.2	1.12392	0.561960	−	0.827165i	$-0.310048\pi$
$43$	13627.2	1.12392	0.561960	+	0.827165i	$0.310048\pi$
$44$	2740.87	0.213431
$45$	3286.65	0.241948
$46$	15618.9	1.08832
$47$	19919.5	1.31533	0.657663	−	0.753312i	$-0.271545\pi$
$47$	19919.5	1.31533	0.657663	+	0.753312i	$0.271545\pi$
$48$	23913.2	1.49808
$49$	4734.97	0.281726
$50$	−4620.43	−0.261371
$51$	−12177.0	−0.655564
$52$	−6584.51	−0.337687
$53$	7651.14	0.374142	0.187071	−	0.982346i	$-0.440101\pi$
$53$	7651.14	0.374142	0.187071	+	0.982346i	$0.440101\pi$
$54$	−15955.7	−0.744615
$55$	3025.00	0.134840
$56$	−10143.1	−0.432216
$57$	−6985.75	−0.284791
$58$	−20364.6	−0.794887
$59$	14099.1	0.527305	0.263653	−	0.964618i	$-0.415073\pi$
$59$	14099.1	0.527305	0.263653	+	0.964618i	$0.415073\pi$
$60$	−10958.5	−0.392981
$61$	29553.0	1.01690	0.508449	−	0.861092i	$-0.330219\pi$
$61$	29553.0	1.01690	0.508449	+	0.861092i	$0.330219\pi$
$62$	59205.8	1.95607
$63$	−19295.5	−0.612498
$64$	−11643.5	−0.355331
$65$	−7267.07	−0.213342
$66$	17309.9	0.489141
$67$	13489.6	0.367124	0.183562	−	0.983008i	$-0.441237\pi$
$67$	13489.6	0.367124	0.183562	+	0.983008i	$0.441237\pi$
$68$	14254.0	0.373823
$69$	40884.1	1.03379
$70$	27126.0	0.661668
$71$	−17584.2	−0.413977	−0.206989	−	0.978343i	$-0.566366\pi$
$71$	−17584.2	−0.413977	−0.206989	+	0.978343i	$0.566366\pi$
$72$	9085.34	0.206543
$73$	−25822.4	−0.567138	−0.283569	−	0.958952i	$-0.591519\pi$
$73$	−25822.4	−0.567138	−0.283569	+	0.958952i	$0.591519\pi$
$74$	−49825.2	−1.05772
$75$	−12094.5	−0.248275
$76$	8177.32	0.162397
$77$	−17759.4	−0.341351
$78$	−41584.2	−0.773912
$79$	21373.1	0.385300	0.192650	−	0.981268i	$-0.438292\pi$
$79$	21373.1	0.385300	0.192650	+	0.981268i	$0.438292\pi$
$80$	−30893.8	−0.539693
$81$	−73711.9	−1.24832
$82$	123053.	2.02096
$83$	−32928.2	−0.524653	−0.262327	−	0.964979i	$-0.584490\pi$
$83$	−32928.2	−0.524653	−0.262327	+	0.964979i	$0.584490\pi$
$84$	64335.8	0.994842
$85$	15731.7	0.236171
$86$	−100742.	−1.46880
$87$	−53306.4	−0.755059
$88$	8362.07	0.115108
$89$	−65793.3	−0.880454	−0.440227	−	0.897887i	$-0.645102\pi$
$89$	−65793.3	−0.880454	−0.440227	+	0.897887i	$0.645102\pi$
$90$	−24297.2	−0.316191
$91$	42664.1	0.540081
$92$	−47857.7	−0.589498
$93$	154977.	1.85806
$94$	−147259.	−1.71894
$95$	9025.00	0.102598
$96$	−133989.	−1.48385
$97$	45671.0	0.492845	0.246423	−	0.969162i	$-0.420745\pi$
$97$	45671.0	0.492845	0.246423	+	0.969162i	$0.420745\pi$
$98$	−35004.1	−0.368175
$99$	15907.4	0.163121
$100$	14157.4	0.141574
$101$	−164941.	−1.60889	−0.804443	−	0.594030i	$-0.797536\pi$
$101$	−164941.	−1.60889	−0.804443	+	0.594030i	$0.797536\pi$
$102$	90020.8	0.856727
$103$	87907.3	0.816454	0.408227	−	0.912880i	$-0.366147\pi$
$103$	87907.3	0.816454	0.408227	+	0.912880i	$0.366147\pi$
$104$	−20088.5	−0.182123
$105$	71005.0	0.628515
$106$	−56562.5	−0.488950
$107$	2831.49	0.0239086	0.0119543	−	0.999929i	$-0.496195\pi$
$107$	2831.49	0.0239086	0.0119543	+	0.999929i	$0.496195\pi$
$108$	48889.7	0.403328
$109$	−131698.	−1.06172	−0.530862	−	0.847458i	$-0.678132\pi$
$109$	−131698.	−1.06172	−0.530862	+	0.847458i	$0.678132\pi$
$110$	−22362.9	−0.176216
$111$	−130423.	−1.00472
$112$	181374.	1.36625
$113$	−42959.1	−0.316489	−0.158245	−	0.987400i	$-0.550583\pi$
$113$	−42959.1	−0.316489	−0.158245	+	0.987400i	$0.550583\pi$
$114$	51643.5	0.372181
$115$	−52818.7	−0.372429
$116$	62398.8	0.430558
$117$	−38214.9	−0.258088
$118$	−104230.	−0.689111
$119$	−92358.5	−0.597874
$120$	−33432.9	−0.211944
$121$	14641.0	0.0909091
$122$	−218476.	−1.32894
$123$	322104.	1.91970
$124$	−181412.	−1.05953
$125$	15625.0	0.0894427
$126$	142646.	0.800446
$127$	−227861.	−1.25361	−0.626803	−	0.779177i	$-0.715637\pi$
$127$	−227861.	−1.25361	−0.626803	+	0.779177i	$0.715637\pi$
$128$	−135494.	−0.730962
$129$	−263701.	−1.39521
$130$	53723.2	0.278807
$131$	8268.41	0.0420963	0.0210482	−	0.999778i	$-0.493300\pi$
$131$	8268.41	0.0420963	0.0210482	+	0.999778i	$0.493300\pi$
$132$	−53039.0	−0.264948
$133$	−52984.6	−0.259729
$134$	−99724.5	−0.479778
$135$	53957.8	0.254812
$136$	43487.3	0.201611
$137$	−33715.1	−0.153470	−0.0767349	−	0.997052i	$-0.524450\pi$
$137$	−33715.1	−0.153470	−0.0767349	+	0.997052i	$0.524450\pi$
$138$	−302243.	−1.35101
$139$	−239796.	−1.05270	−0.526350	−	0.850268i	$-0.676440\pi$
$139$	−239796.	−1.05270	−0.526350	+	0.850268i	$0.676440\pi$
$140$	−83116.3	−0.358399
$141$	−385465.	−1.63281
$142$	129994.	0.541008
$143$	−35172.6	−0.143835
$144$	−162459.	−0.652888
$145$	68867.3	0.272015
$146$	190897.	0.741167
$147$	−91626.9	−0.349728
$148$	152669.	0.572923
$149$	−454045.	−1.67546	−0.837728	−	0.546088i	$-0.816116\pi$
$149$	−454045.	−1.67546	−0.837728	+	0.546088i	$0.816116\pi$
$150$	89410.5	0.324459
$151$	382487.	1.36513	0.682565	−	0.730825i	$-0.260864\pi$
$151$	382487.	1.36513	0.682565	+	0.730825i	$0.260864\pi$
$152$	24948.0	0.0875843
$153$	82727.0	0.285706
$154$	131290.	0.446096
$155$	−200217.	−0.669380
$156$	127418.	0.419197
$157$	−248952.	−0.806058	−0.403029	−	0.915187i	$-0.632043\pi$
$157$	−248952.	−0.806058	−0.403029	+	0.915187i	$0.632043\pi$
$158$	−158004.	−0.503531
$159$	−148058.	−0.464451
$160$	173102.	0.534567
$161$	310092.	0.942814
$162$	544929.	1.63137
$163$	−346459.	−1.02137	−0.510684	−	0.859768i	$-0.670608\pi$
$163$	−346459.	−1.02137	−0.510684	+	0.859768i	$0.670608\pi$
$164$	−377045.	−1.09467
$165$	−58537.1	−0.167387
$166$	243428.	0.685646
$167$	−298716.	−0.828835	−0.414417	−	0.910087i	$-0.636015\pi$
$167$	−298716.	−0.828835	−0.414417	+	0.910087i	$0.636015\pi$
$168$	196280.	0.536542
$169$	−286796.	−0.772426
$170$	−116299.	−0.308642
$171$	47459.2	0.124117
$172$	308681.	0.795589
$173$	291249.	0.739860	0.369930	−	0.929060i	$-0.379382\pi$
$173$	291249.	0.739860	0.369930	+	0.929060i	$0.379382\pi$
$174$	394077.	0.986753
$175$	−91732.4	−0.226427
$176$	−149526.	−0.363861
$177$	−272834.	−0.654583
$178$	486389.	1.15063
$179$	−364669.	−0.850680	−0.425340	−	0.905034i	$-0.639846\pi$
$179$	−364669.	−0.850680	−0.425340	+	0.905034i	$0.639846\pi$
$180$	74448.6	0.171268
$181$	−237066.	−0.537864	−0.268932	−	0.963159i	$-0.586671\pi$
$181$	−237066.	−0.537864	−0.268932	+	0.963159i	$0.586671\pi$
$182$	−315402.	−0.705807
$183$	−571884.	−1.26235
$184$	−146008.	−0.317930
$185$	168495.	0.361957
$186$	−1.14570e6	−2.42822
$187$	76141.2	0.159227
$188$	451213.	0.931081
$189$	−316779.	−0.645063
$190$	−66719.0	−0.134081
$191$	243534.	0.483032	0.241516	−	0.970397i	$-0.422355\pi$
$191$	243534.	0.483032	0.241516	+	0.970397i	$0.422355\pi$
$192$	225315.	0.441099
$193$	−111541.	−0.215547	−0.107773	−	0.994176i	$-0.534372\pi$
$193$	−111541.	−0.215547	−0.107773	+	0.994176i	$0.534372\pi$
$194$	−337631.	−0.644078
$195$	140626.	0.264837
$196$	107256.	0.199425
$197$	−809702.	−1.48648	−0.743241	−	0.669024i	$-0.766712\pi$
$197$	−809702.	−1.48648	−0.743241	+	0.669024i	$0.766712\pi$
$198$	−117598.	−0.213176
$199$	433450.	0.775902	0.387951	−	0.921680i	$-0.373183\pi$
$199$	433450.	0.775902	0.387951	+	0.921680i	$0.373183\pi$
$200$	43192.5	0.0763542
$201$	−261039.	−0.455738
$202$	1.21936e6	2.10258
$203$	−404311.	−0.688613
$204$	−275832.	−0.464054
$205$	−416131.	−0.691584
$206$	−649871.	−1.06699
$207$	−277754.	−0.450542
$208$	359212.	0.575696
$209$	43681.0	0.0691714
$210$	−524918.	−0.821378
$211$	573956.	0.887509	0.443754	−	0.896148i	$-0.353646\pi$
$211$	573956.	0.887509	0.443754	+	0.896148i	$0.353646\pi$
$212$	173313.	0.264844
$213$	340274.	0.513901
$214$	−20932.3	−0.0312451
$215$	340680.	0.502632
$216$	149156.	0.217524
$217$	1.17545e6	1.69455
$218$	973599.	1.38752
$219$	499692.	0.704031
$220$	68521.8	0.0954492
$221$	−182917.	−0.251926
$222$	964174.	1.31302
$223$	841529.	1.13320	0.566601	−	0.823993i	$-0.308258\pi$
$223$	841529.	1.13320	0.566601	+	0.823993i	$0.308258\pi$
$224$	−1.01626e6	−1.35327
$225$	82166.2	0.108202
$226$	317583.	0.413605
$227$	−637312.	−0.820894	−0.410447	−	0.911884i	$-0.634627\pi$
$227$	−637312.	−0.820894	−0.410447	+	0.911884i	$0.634627\pi$
$228$	−158240.	−0.201595
$229$	18135.0	0.0228522	0.0114261	−	0.999935i	$-0.496363\pi$
$229$	18135.0	0.0228522	0.0114261	+	0.999935i	$0.496363\pi$
$230$	390472.	0.486711
$231$	343664.	0.423745
$232$	190371.	0.232210
$233$	124792.	0.150590	0.0752949	−	0.997161i	$-0.476010\pi$
$233$	124792.	0.150590	0.0752949	+	0.997161i	$0.476010\pi$
$234$	282511.	0.337284
$235$	497987.	0.588232
$236$	319371.	0.373264
$237$	−413593.	−0.478302
$238$	682778.	0.781335
$239$	1.56271e6	1.76963	0.884815	−	0.465942i	$-0.154284\pi$
$239$	1.56271e6	1.76963	0.884815	+	0.465942i	$0.154284\pi$
$240$	597830.	0.669961
$241$	−997492.	−1.10628	−0.553142	−	0.833087i	$-0.686571\pi$
$241$	−997492.	−1.10628	−0.553142	+	0.833087i	$0.686571\pi$
$242$	−108236.	−0.118805
$243$	901939.	0.979854
$244$	669430.	0.719832
$245$	118374.	0.125992
$246$	−2.38121e6	−2.50877
$247$	−104937.	−0.109442
$248$	−553465.	−0.571427
$249$	637197.	0.651291
$250$	−115511.	−0.116889
$251$	−1.50770e6	−1.51054	−0.755269	−	0.655415i	$-0.772494\pi$
$251$	−1.50770e6	−1.51054	−0.755269	+	0.655415i	$0.772494\pi$
$252$	−437078.	−0.433569
$253$	−255643.	−0.251092
$254$	1.68451e6	1.63828
$255$	−304425.	−0.293177
$256$	1.37426e6	1.31059
$257$	−1.67098e6	−1.57811	−0.789057	−	0.614320i	$-0.789430\pi$
$257$	−1.67098e6	−1.57811	−0.789057	+	0.614320i	$0.789430\pi$
$258$	1.94946e6	1.82333
$259$	−989212.	−0.916305
$260$	−164613.	−0.151018
$261$	362148.	0.329067
$262$	−61125.8	−0.0550138
$263$	1.55468e6	1.38596	0.692981	−	0.720956i	$-0.256297\pi$
$263$	1.55468e6	1.38596	0.692981	+	0.720956i	$0.256297\pi$
$264$	−161815.	−0.142893
$265$	191279.	0.167321
$266$	391699.	0.339428
$267$	1.27317e6	1.09297
$268$	305565.	0.259876
$269$	14513.9	0.0122293	0.00611467	−	0.999981i	$-0.498054\pi$
$269$	14513.9	0.0122293	0.00611467	+	0.999981i	$0.498054\pi$
$270$	−398893.	−0.333002
$271$	1.14149e6	0.944171	0.472085	−	0.881553i	$-0.343501\pi$
$271$	1.14149e6	0.944171	0.472085	+	0.881553i	$0.343501\pi$
$272$	−777617.	−0.637300
$273$	−825598.	−0.670443
$274$	249245.	0.200563
$275$	75625.0	0.0603023
$276$	926100.	0.731788
$277$	319339.	0.250065	0.125033	−	0.992153i	$-0.460096\pi$
$277$	319339.	0.250065	0.125033	+	0.992153i	$0.460096\pi$
$278$	1.77274e6	1.37573
$279$	−1.05287e6	−0.809775
$280$	−253578.	−0.193293
$281$	1.00269e6	0.757533	0.378766	−	0.925492i	$-0.376348\pi$
$281$	1.00269e6	0.757533	0.378766	+	0.925492i	$0.376348\pi$
$282$	2.84962e6	2.13385
$283$	−106053.	−0.0787146	−0.0393573	−	0.999225i	$-0.512531\pi$
$283$	−106053.	−0.0787146	−0.0393573	+	0.999225i	$0.512531\pi$
$284$	−398314.	−0.293042
$285$	−174644.	−0.127362
$286$	260020.	0.187972
$287$	2.44305e6	1.75076
$288$	910280.	0.646687
$289$	−1.02388e6	−0.721116
$290$	−509114.	−0.355484
$291$	−883784.	−0.611806
$292$	−584924.	−0.401460
$293$	1.39442e6	0.948909	0.474454	−	0.880280i	$-0.342645\pi$
$293$	1.39442e6	0.948909	0.474454	+	0.880280i	$0.342645\pi$
$294$	677369.	0.457043
$295$	352478.	0.235818
$296$	465774.	0.308991
$297$	261156.	0.171794
$298$	3.35661e6	2.18958
$299$	614140.	0.397273
$300$	−273962.	−0.175746
$301$	−2.00009e6	−1.27243
$302$	−2.82761e6	−1.78403
$303$	3.19179e6	1.99723
$304$	−446107.	−0.276857
$305$	738825.	0.454770
$306$	−611575.	−0.373376
$307$	−671438.	−0.406593	−0.203297	−	0.979117i	$-0.565166\pi$
$307$	−671438.	−0.406593	−0.203297	+	0.979117i	$0.565166\pi$
$308$	−402283.	−0.241632
$309$	−1.70111e6	−1.01353
$310$	1.48015e6	0.874782
$311$	3.00896e6	1.76407	0.882034	−	0.471187i	$-0.156174\pi$
$311$	3.00896e6	1.76407	0.882034	+	0.471187i	$0.156174\pi$
$312$	388735.	0.226083
$313$	711477.	0.410488	0.205244	−	0.978711i	$-0.434201\pi$
$313$	711477.	0.410488	0.205244	+	0.978711i	$0.434201\pi$
$314$	1.84042e6	1.05340
$315$	−482387.	−0.273917
$316$	484139.	0.272742
$317$	2.04508e6	1.14304	0.571520	−	0.820588i	$-0.306354\pi$
$317$	2.04508e6	1.14304	0.571520	+	0.820588i	$0.306354\pi$
$318$	1.09455e6	0.606970
$319$	333318.	0.183392
$320$	−291087.	−0.158909
$321$	−54792.4	−0.0296796
$322$	−2.29241e6	−1.23212
$323$	227165.	0.121153
$324$	−1.66971e6	−0.883647
$325$	−181677.	−0.0954094
$326$	2.56126e6	1.33478
$327$	2.54850e6	1.31800
$328$	−1.15032e6	−0.590382
$329$	−2.92362e6	−1.48913
$330$	432747.	0.218751
$331$	−2.46567e6	−1.23699	−0.618493	−	0.785790i	$-0.712256\pi$
$331$	−2.46567e6	−1.23699	−0.618493	+	0.785790i	$0.712256\pi$
$332$	−745884.	−0.371386
$333$	886053.	0.437874
$334$	2.20832e6	1.08317
$335$	337240.	0.164183
$336$	−3.50978e6	−1.69603
$337$	1.72494e6	0.827368	0.413684	−	0.910421i	$-0.364242\pi$
$337$	1.72494e6	0.827368	0.413684	+	0.910421i	$0.364242\pi$
$338$	2.12020e6	1.00945
$339$	831306.	0.392882
$340$	356351.	0.167179
$341$	−969052.	−0.451296
$342$	−350851.	−0.162202
$343$	1.77183e6	0.813182
$344$	941747.	0.429080
$345$	1.02210e6	0.462324
$346$	−2.15312e6	−0.966890
$347$	−2.63722e6	−1.17577	−0.587886	−	0.808944i	$-0.700040\pi$
$347$	−2.63722e6	−1.17577	−0.587886	+	0.808944i	$0.700040\pi$
$348$	−1.20749e6	−0.534484
$349$	1.08701e6	0.477716	0.238858	−	0.971054i	$-0.423227\pi$
$349$	1.08701e6	0.477716	0.238858	+	0.971054i	$0.423227\pi$
$350$	678149.	0.295907
$351$	−627384.	−0.271810
$352$	837814.	0.360405
$353$	−1.06521e6	−0.454988	−0.227494	−	0.973780i	$-0.573053\pi$
$353$	−1.06521e6	−0.454988	−0.227494	+	0.973780i	$0.573053\pi$
$354$	2.01697e6	0.855445
$355$	−439605.	−0.185136
$356$	−1.49034e6	−0.623247
$357$	1.78724e6	0.742186
$358$	2.69589e6	1.11172
$359$	−1.24317e6	−0.509089	−0.254544	−	0.967061i	$-0.581925\pi$
$359$	−1.24317e6	−0.509089	−0.254544	+	0.967061i	$0.581925\pi$
$360$	227134.	0.0923687
$361$	130321.	0.0526316
$362$	1.75255e6	0.702910
$363$	−283320.	−0.112852
$364$	966420.	0.382307
$365$	−645559.	−0.253632
$366$	4.22776e6	1.64971
$367$	5.05589e6	1.95944	0.979722	−	0.200363i	$-0.0642122\pi$
$367$	5.05589e6	1.95944	0.979722	+	0.200363i	$0.0642122\pi$
$368$	2.61084e6	1.00499
$369$	−2.18828e6	−0.836636
$370$	−1.24563e6	−0.473026
$371$	−1.12297e6	−0.423579
$372$	3.51052e6	1.31527
$373$	−998244.	−0.371505	−0.185752	−	0.982597i	$-0.559472\pi$
$373$	−998244.	−0.371505	−0.185752	+	0.982597i	$0.559472\pi$
$374$	−562888.	−0.208086
$375$	−302361.	−0.111032
$376$	1.37660e6	0.502154
$377$	−800742.	−0.290161
$378$	2.34185e6	0.843004
$379$	−2.18871e6	−0.782691	−0.391345	−	0.920244i	$-0.627990\pi$
$379$	−2.18871e6	−0.782691	−0.391345	+	0.920244i	$0.627990\pi$
$380$	204433.	0.0726260
$381$	4.40937e6	1.55620
$382$	−1.80037e6	−0.631253
$383$	−2.37391e6	−0.826926	−0.413463	−	0.910521i	$-0.635681\pi$
$383$	−2.37391e6	−0.826926	−0.413463	+	0.910521i	$0.635681\pi$
$384$	2.62196e6	0.907398
$385$	−443985.	−0.152657
$386$	824587.	0.281688
$387$	1.79151e6	0.608054
$388$	1.03453e6	0.348871
$389$	−297093.	−0.0995449	−0.0497725	−	0.998761i	$-0.515850\pi$
$389$	−297093.	−0.0995449	−0.0497725	+	0.998761i	$0.515850\pi$
$390$	−1.03960e6	−0.346104
$391$	−1.32948e6	−0.439785
$392$	327224.	0.107555
$393$	−160003.	−0.0522573
$394$	5.98588e6	1.94262
$395$	534327.	0.172311
$396$	360331.	0.115469
$397$	764974.	0.243596	0.121798	−	0.992555i	$-0.461134\pi$
$397$	764974.	0.243596	0.121798	+	0.992555i	$0.461134\pi$
$398$	−3.20436e6	−1.01399
$399$	1.02531e6	0.322421
$400$	−772346.	−0.241358
$401$	−349381.	−0.108502	−0.0542511	−	0.998527i	$-0.517277\pi$
$401$	−349381.	−0.108502	−0.0542511	+	0.998527i	$0.517277\pi$
$402$	1.92978e6	0.595584
$403$	2.32799e6	0.714034
$404$	−3.73622e6	−1.13888
$405$	−1.84280e6	−0.558265
$406$	2.98895e6	0.899918
$407$	815515.	0.244032
$408$	−841528.	−0.250275
$409$	3.79084e6	1.12054	0.560270	−	0.828310i	$-0.310697\pi$
$409$	3.79084e6	1.12054	0.560270	+	0.828310i	$0.310697\pi$
$410$	3.07632e6	0.903800
$411$	652425.	0.190514
$412$	1.99126e6	0.577944
$413$	−2.06935e6	−0.596980
$414$	2.05335e6	0.588793
$415$	−823204.	−0.234632
$416$	−2.01271e6	−0.570228
$417$	4.64032e6	1.30680
$418$	−322920.	−0.0903971
$419$	411814.	0.114595	0.0572976	−	0.998357i	$-0.481752\pi$
$419$	411814.	0.114595	0.0572976	+	0.998357i	$0.481752\pi$
$420$	1.60839e6	0.444907
$421$	−5.65192e6	−1.55414	−0.777071	−	0.629413i	$-0.783296\pi$
$421$	−5.65192e6	−1.55414	−0.777071	+	0.629413i	$0.783296\pi$
$422$	−4.24308e6	−1.15985
$423$	2.61873e6	0.711607
$424$	528755.	0.142837
$425$	393291.	0.105619
$426$	−2.51554e6	−0.671594
$427$	−4.33755e6	−1.15126
$428$	64138.4	0.0169242
$429$	680630.	0.178553
$430$	−2.51854e6	−0.656867
$431$	−5.59468e6	−1.45072	−0.725358	−	0.688372i	$-0.758326\pi$
$431$	−5.59468e6	−1.45072	−0.725358	+	0.688372i	$0.758326\pi$
$432$	−2.66714e6	−0.687600
$433$	563067.	0.144325	0.0721624	−	0.997393i	$-0.477010\pi$
$433$	563067.	0.144325	0.0721624	+	0.997393i	$0.477010\pi$
$434$	−8.68974e6	−2.21454
$435$	−1.33266e6	−0.337673
$436$	−2.98319e6	−0.751563
$437$	−762703.	−0.191052
$438$	−3.69406e6	−0.920066
$439$	−3.85036e6	−0.953543	−0.476771	−	0.879027i	$-0.658193\pi$
$439$	−3.85036e6	−0.953543	−0.476771	+	0.879027i	$0.658193\pi$
$440$	209052.	0.0514780
$441$	622487.	0.152417
$442$	1.35225e6	0.329231
$443$	−2.65243e6	−0.642146	−0.321073	−	0.947054i	$-0.604044\pi$
$443$	−2.65243e6	−0.642146	−0.321073	+	0.947054i	$0.604044\pi$
$444$	−2.95431e6	−0.711212
$445$	−1.64483e6	−0.393751
$446$	−6.22116e6	−1.48093
$447$	8.78627e6	2.07987
$448$	1.70894e6	0.402282
$449$	1.11700e6	0.261479	0.130740	−	0.991417i	$-0.458265\pi$
$449$	1.11700e6	0.261479	0.130740	+	0.991417i	$0.458265\pi$
$450$	−607429.	−0.141405
$451$	−2.01407e6	−0.466266
$452$	−973102.	−0.224033
$453$	−7.40155e6	−1.69464
$454$	4.71145e6	1.07279
$455$	1.06660e6	0.241531
$456$	−482771.	−0.108725
$457$	−147285.	−0.0329889	−0.0164944	−	0.999864i	$-0.505251\pi$
$457$	−147285.	−0.0329889	−0.0164944	+	0.999864i	$0.505251\pi$
$458$	−134066.	−0.0298645
$459$	1.35815e6	0.300896
$460$	−1.19644e6	−0.263631
$461$	4.07718e6	0.893527	0.446763	−	0.894652i	$-0.352577\pi$
$461$	4.07718e6	0.893527	0.446763	+	0.894652i	$0.352577\pi$
$462$	−2.54060e6	−0.553773
$463$	1.75470e6	0.380409	0.190204	−	0.981744i	$-0.439085\pi$
$463$	1.75470e6	0.380409	0.190204	+	0.981744i	$0.439085\pi$
$464$	−3.40412e6	−0.734023
$465$	3.87443e6	0.830951
$466$	−922546.	−0.196799
$467$	7.54932e6	1.60183	0.800914	−	0.598779i	$-0.204347\pi$
$467$	7.54932e6	1.60183	0.800914	+	0.598779i	$0.204347\pi$
$468$	−865638.	−0.182693
$469$	−1.97990e6	−0.415633
$470$	−3.68147e6	−0.768734
$471$	4.81750e6	1.00062
$472$	974362.	0.201310
$473$	1.64889e6	0.338874
$474$	3.05756e6	0.625071
$475$	225625.	0.0458831
$476$	−2.09209e6	−0.423217
$477$	1.00586e6	0.202415
$478$	−1.15526e7	−2.31265
$479$	−1.70742e6	−0.340018	−0.170009	−	0.985442i	$-0.554380\pi$
$479$	−1.70742e6	−0.340018	−0.170009	+	0.985442i	$0.554380\pi$
$480$	−3.34972e6	−0.663598
$481$	−1.95914e6	−0.386103
$482$	7.37415e6	1.44575
$483$	−6.00063e6	−1.17039
$484$	331646.	0.0643518
$485$	1.14177e6	0.220407
$486$	−6.66776e6	−1.28053
$487$	710728.	0.135794	0.0678970	−	0.997692i	$-0.478371\pi$
$487$	710728.	0.135794	0.0678970	+	0.997692i	$0.478371\pi$
$488$	2.04235e6	0.388222
$489$	6.70437e6	1.26790
$490$	−875104.	−0.164653
$491$	6.22231e6	1.16479	0.582395	−	0.812906i	$-0.302116\pi$
$491$	6.22231e6	1.16479	0.582395	+	0.812906i	$0.302116\pi$
$492$	7.29624e6	1.35890
$493$	1.73343e6	0.321211
$494$	775763.	0.143025
$495$	397684.	0.0729500
$496$	9.89677e6	1.80630
$497$	2.58086e6	0.468677
$498$	−4.71060e6	−0.851144
$499$	−1.34037e6	−0.240976	−0.120488	−	0.992715i	$-0.538446\pi$
$499$	−1.34037e6	−0.240976	−0.120488	+	0.992715i	$0.538446\pi$
$500$	353935.	0.0633138
$501$	5.78050e6	1.02889
$502$	1.11460e7	1.97405
$503$	3.20947e6	0.565605	0.282803	−	0.959178i	$-0.408736\pi$
$503$	3.20947e6	0.565605	0.282803	+	0.959178i	$0.408736\pi$
$504$	−1.33347e6	−0.233834
$505$	−4.12352e6	−0.719515
$506$	1.88989e6	0.328140
$507$	5.54983e6	0.958870
$508$	−5.16148e6	−0.887391
$509$	3.89575e6	0.666495	0.333247	−	0.942839i	$-0.391856\pi$
$509$	3.89575e6	0.666495	0.333247	+	0.942839i	$0.391856\pi$
$510$	2.25052e6	0.383140
$511$	3.78999e6	0.642076
$512$	−5.82364e6	−0.981793
$513$	779150.	0.130716
$514$	1.23530e7	2.06237
$515$	2.19768e6	0.365130
$516$	−5.97332e6	−0.987624
$517$	2.41026e6	0.396586
$518$	7.31294e6	1.19748
$519$	−5.63600e6	−0.918444
$520$	−502213.	−0.0814478
$521$	−2.61329e6	−0.421788	−0.210894	−	0.977509i	$-0.567637\pi$
$521$	−2.61329e6	−0.421788	−0.210894	+	0.977509i	$0.567637\pi$
$522$	−2.67725e6	−0.430043
$523$	−2.90631e6	−0.464609	−0.232304	−	0.972643i	$-0.574627\pi$
$523$	−2.90631e6	−0.464609	−0.232304	+	0.972643i	$0.574627\pi$
$524$	187295.	0.0297987
$525$	1.77512e6	0.281080
$526$	−1.14933e7	−1.81125
$527$	−5.03960e6	−0.790441
$528$	2.89350e6	0.451688
$529$	−1.97263e6	−0.306484
$530$	−1.41406e6	−0.218665
$531$	1.85355e6	0.285278
$532$	−1.20020e6	−0.183855
$533$	4.83848e6	0.737719
$534$	−9.41218e6	−1.42836
$535$	70787.1	0.0106923
$536$	932240.	0.140157
$537$	7.05676e6	1.05601
$538$	−107297.	−0.0159820
$539$	572931.	0.0849436
$540$	1.22224e6	0.180374
$541$	6.98556e6	1.02614	0.513071	−	0.858346i	$-0.328508\pi$
$541$	6.98556e6	1.02614	0.513071	+	0.858346i	$0.328508\pi$
$542$	−8.43871e6	−1.23389
$543$	4.58749e6	0.667691
$544$	4.35709e6	0.631247
$545$	−3.29244e6	−0.474817
$546$	6.10339e6	0.876172
$547$	−1.20223e7	−1.71798	−0.858991	−	0.511991i	$-0.828908\pi$
$547$	−1.20223e7	−1.71798	−0.858991	+	0.511991i	$0.828908\pi$
$548$	−763709.	−0.108637
$549$	3.88521e6	0.550154
$550$	−559072.	−0.0788063
$551$	994443.	0.139541
$552$	2.82542e6	0.394670
$553$	−3.13696e6	−0.436211
$554$	−2.36078e6	−0.326799
$555$	−3.26057e6	−0.449325
$556$	−5.43182e6	−0.745175
$557$	9.42098e6	1.28664	0.643321	−	0.765596i	$-0.277556\pi$
$557$	9.42098e6	1.28664	0.643321	+	0.765596i	$0.277556\pi$
$558$	7.78354e6	1.05826
$559$	−3.96119e6	−0.536162
$560$	4.53434e6	0.611004
$561$	−1.47342e6	−0.197660
$562$	−7.41259e6	−0.989986
$563$	8.70608e6	1.15758	0.578791	−	0.815476i	$-0.303525\pi$
$563$	8.70608e6	1.15758	0.578791	+	0.815476i	$0.303525\pi$
$564$	−8.73148e6	−1.15582
$565$	−1.07398e6	−0.141538
$566$	784014.	0.102869
$567$	1.08188e7	1.41326
$568$	−1.21521e6	−0.158045
$569$	−9.75811e6	−1.26353	−0.631765	−	0.775160i	$-0.717669\pi$
$569$	−9.75811e6	−1.26353	−0.631765	+	0.775160i	$0.717669\pi$
$570$	1.29109e6	0.166444
$571$	−302924.	−0.0388815	−0.0194408	−	0.999811i	$-0.506189\pi$
$571$	−302924.	−0.0388815	−0.0194408	+	0.999811i	$0.506189\pi$
$572$	−796725.	−0.101817
$573$	−4.71265e6	−0.599624
$574$	−1.80607e7	−2.28799
$575$	−1.32047e6	−0.166555
$576$	−1.53072e6	−0.192238
$577$	7.83821e6	0.980116	0.490058	−	0.871690i	$-0.336976\pi$
$577$	7.83821e6	0.980116	0.490058	+	0.871690i	$0.336976\pi$
$578$	7.56923e6	0.942394
$579$	2.15844e6	0.267574
$580$	1.55997e6	0.192551
$581$	4.83293e6	0.593977
$582$	6.53354e6	0.799542
$583$	925788.	0.112808
$584$	−1.78453e6	−0.216517
$585$	−955372.	−0.115420
$586$	−1.03085e7	−1.24009
$587$	8.67070e6	1.03863	0.519313	−	0.854584i	$-0.326188\pi$
$587$	8.67070e6	1.03863	0.519313	+	0.854584i	$0.326188\pi$
$588$	−2.07552e6	−0.247562
$589$	−2.89114e6	−0.343385
$590$	−2.60576e6	−0.308180
$591$	1.56686e7	1.84528
$592$	−8.32872e6	−0.976729
$593$	1.62125e7	1.89328	0.946639	−	0.322295i	$-0.104454\pi$
$593$	1.62125e7	1.89328	0.946639	+	0.322295i	$0.104454\pi$
$594$	−1.93064e6	−0.224510
$595$	−2.30896e6	−0.267377
$596$	−1.02849e7	−1.18600
$597$	−8.38775e6	−0.963185
$598$	−4.54015e6	−0.519179
$599$	−7.19688e6	−0.819553	−0.409777	−	0.912186i	$-0.634393\pi$
$599$	−7.19688e6	−0.819553	−0.409777	+	0.912186i	$0.634393\pi$
$600$	−835823.	−0.0947843
$601$	8.00885e6	0.904448	0.452224	−	0.891904i	$-0.350631\pi$
$601$	8.00885e6	0.904448	0.452224	+	0.891904i	$0.350631\pi$
$602$	1.47860e7	1.66288
$603$	1.77342e6	0.198618
$604$	8.66403e6	0.966335
$605$	366025.	0.0406558
$606$	−2.35959e7	−2.61009
$607$	−1.11815e7	−1.23177	−0.615885	−	0.787836i	$-0.711201\pi$
$607$	−1.11815e7	−1.23177	−0.615885	+	0.787836i	$0.711201\pi$
$608$	2.49959e6	0.274227
$609$	7.82387e6	0.854827
$610$	−5.46191e6	−0.594319
$611$	−5.79026e6	−0.627473
$612$	1.87392e6	0.202243
$613$	−95683.3	−0.0102845	−0.00514227	−	0.999987i	$-0.501637\pi$
$613$	−95683.3	−0.0102845	−0.00514227	+	0.999987i	$0.501637\pi$
$614$	4.96374e6	0.531359
$615$	8.05259e6	0.858515
$616$	−1.22732e6	−0.130318
$617$	6.37710e6	0.674389	0.337195	−	0.941435i	$-0.390522\pi$
$617$	6.37710e6	0.674389	0.337195	+	0.941435i	$0.390522\pi$
$618$	1.25757e7	1.32453
$619$	−8.34353e6	−0.875232	−0.437616	−	0.899162i	$-0.644177\pi$
$619$	−8.34353e6	−0.875232	−0.437616	+	0.899162i	$0.644177\pi$
$620$	−4.53529e6	−0.473834
$621$	−4.55997e6	−0.474496
$622$	−2.22443e7	−2.30538
$623$	9.65660e6	0.996791
$624$	−6.95116e6	−0.714654
$625$	390625.	0.0400000
$626$	−5.25973e6	−0.536448
$627$	−845276.	−0.0858677
$628$	−5.63922e6	−0.570585
$629$	4.24113e6	0.427420
$630$	3.56614e6	0.357970
$631$	−3.39585e6	−0.339527	−0.169764	−	0.985485i	$-0.554300\pi$
$631$	−3.39585e6	−0.339527	−0.169764	+	0.985485i	$0.554300\pi$
$632$	1.47705e6	0.147096
$633$	−1.11067e7	−1.10173
$634$	−1.51186e7	−1.49379
$635$	−5.69653e6	−0.560630
$636$	−3.35379e6	−0.328771
$637$	−1.37637e6	−0.134397
$638$	−2.46411e6	−0.239667
$639$	−2.31172e6	−0.223967
$640$	−3.38735e6	−0.326896
$641$	−1.60191e7	−1.53991	−0.769953	−	0.638101i	$-0.779720\pi$
$641$	−1.60191e7	−1.53991	−0.769953	+	0.638101i	$0.779720\pi$
$642$	405063.	0.0387869
$643$	6.29683e6	0.600612	0.300306	−	0.953843i	$-0.402911\pi$
$643$	6.29683e6	0.600612	0.300306	+	0.953843i	$0.402911\pi$
$644$	7.02416e6	0.667390
$645$	−6.59253e6	−0.623955
$646$	−1.67936e6	−0.158330
$647$	366875.	0.0344554	0.0172277	−	0.999852i	$-0.494516\pi$
$647$	366875.	0.0344554	0.0172277	+	0.999852i	$0.494516\pi$
$648$	−5.09408e6	−0.476572
$649$	1.70599e6	0.158988
$650$	1.34308e6	0.124686
$651$	−2.27463e7	−2.10358
$652$	−7.84793e6	−0.722997
$653$	−1.80708e7	−1.65842	−0.829208	−	0.558941i	$-0.811208\pi$
$653$	−1.80708e7	−1.65842	−0.829208	+	0.558941i	$0.811208\pi$
$654$	−1.88402e7	−1.72243
$655$	206710.	0.0188260
$656$	2.05694e7	1.86621
$657$	−3.39476e6	−0.306828
$658$	2.16134e7	1.94607
$659$	1.84594e7	1.65578	0.827891	−	0.560889i	$-0.189540\pi$
$659$	1.84594e7	1.65578	0.827891	+	0.560889i	$0.189540\pi$
$660$	−1.32597e6	−0.118488
$661$	1.15118e7	1.02480	0.512401	−	0.858746i	$-0.328756\pi$
$661$	1.15118e7	1.02480	0.512401	+	0.858746i	$0.328756\pi$
$662$	1.82279e7	1.61656
$663$	3.53965e6	0.312735
$664$	−2.27560e6	−0.200298
$665$	−1.32462e6	−0.116154
$666$	−6.55032e6	−0.572238
$667$	−5.81997e6	−0.506531
$668$	−6.76648e6	−0.586707
$669$	−1.62845e7	−1.40673
$670$	−2.49311e6	−0.214563
$671$	3.57592e6	0.306606
$672$	1.96658e7	1.67992
$673$	−8.94979e6	−0.761685	−0.380842	−	0.924640i	$-0.624366\pi$
$673$	−8.94979e6	−0.761685	−0.380842	+	0.924640i	$0.624366\pi$
$674$	−1.27519e7	−1.08125
$675$	1.34894e6	0.113955
$676$	−6.49647e6	−0.546777
$677$	−1.68147e7	−1.40999	−0.704996	−	0.709212i	$-0.749051\pi$
$677$	−1.68147e7	−1.40999	−0.704996	+	0.709212i	$0.749051\pi$
$678$	−6.14559e6	−0.513439
$679$	−6.70321e6	−0.557967
$680$	1.08718e6	0.0901634
$681$	1.23327e7	1.01904
$682$	7.16390e6	0.589778
$683$	2.58389e6	0.211944	0.105972	−	0.994369i	$-0.466205\pi$
$683$	2.58389e6	0.211944	0.105972	+	0.994369i	$0.466205\pi$
$684$	1.07504e6	0.0878585
$685$	−842877.	−0.0686338
$686$	−1.30986e7	−1.06271
$687$	−350932.	−0.0283682
$688$	−1.68398e7	−1.35633
$689$	−2.22406e6	−0.178483
$690$	−7.55608e6	−0.604190
$691$	−3.81079e6	−0.303613	−0.151806	−	0.988410i	$-0.548509\pi$
$691$	−3.81079e6	−0.303613	−0.151806	+	0.988410i	$0.548509\pi$
$692$	6.59733e6	0.523725
$693$	−2.33475e6	−0.184675
$694$	1.94962e7	1.53656
$695$	−5.99490e6	−0.470782
$696$	−3.68389e6	−0.288260
$697$	−1.04743e7	−0.816661
$698$	−8.03593e6	−0.624306
$699$	−2.41486e6	−0.186939
$700$	−2.07791e6	−0.160281
$701$	−1.47857e7	−1.13644	−0.568220	−	0.822877i	$-0.692368\pi$
$701$	−1.47857e7	−1.13644	−0.568220	+	0.822877i	$0.692368\pi$
$702$	4.63805e6	0.355216
$703$	2.43307e6	0.185680
$704$	−1.40886e6	−0.107136
$705$	−9.63661e6	−0.730216
$706$	7.87479e6	0.594603
$707$	2.42087e7	1.82147
$708$	−6.18019e6	−0.463360
$709$	1.60514e7	1.19922	0.599610	−	0.800293i	$-0.295323\pi$
$709$	1.60514e7	1.19922	0.599610	+	0.800293i	$0.295323\pi$
$710$	3.24986e6	0.241946
$711$	2.80983e6	0.208452
$712$	−4.54684e6	−0.336132
$713$	1.69204e7	1.24648
$714$	−1.32125e7	−0.969929
$715$	−879316.	−0.0643250
$716$	−8.26043e6	−0.602171
$717$	−3.02401e7	−2.19678
$718$	9.19035e6	0.665305
$719$	1.48803e7	1.07347	0.536735	−	0.843751i	$-0.319657\pi$
$719$	1.48803e7	1.07347	0.536735	+	0.843751i	$0.319657\pi$
$720$	−4.06148e6	−0.291980
$721$	−1.29023e7	−0.924335
$722$	−963423.	−0.0687818
$723$	1.93026e7	1.37331
$724$	−5.36998e6	−0.380738
$725$	1.72168e6	0.121649
$726$	2.09449e6	0.147482
$727$	−1.13433e7	−0.795980	−0.397990	−	0.917390i	$-0.630292\pi$
$727$	−1.13433e7	−0.795980	−0.397990	+	0.917390i	$0.630292\pi$
$728$	2.94843e6	0.206187
$729$	458467.	0.0319514
$730$	4.77242e6	0.331460
$731$	8.57513e6	0.593536
$732$	−1.29542e7	−0.893581
$733$	8.52183e6	0.585831	0.292916	−	0.956138i	$-0.405374\pi$
$733$	8.52183e6	0.585831	0.292916	+	0.956138i	$0.405374\pi$
$734$	−3.73766e7	−2.56071
$735$	−2.29067e6	−0.156403
$736$	−1.46288e7	−0.995441
$737$	1.63224e6	0.110692
$738$	1.61773e7	1.09336
$739$	2.37127e7	1.59724	0.798621	−	0.601834i	$-0.205563\pi$
$739$	2.37127e7	1.59724	0.798621	+	0.601834i	$0.205563\pi$
$740$	3.81672e6	0.256219
$741$	2.03064e6	0.135859
$742$	8.30178e6	0.553556
$743$	−5.70098e6	−0.378859	−0.189429	−	0.981894i	$-0.560664\pi$
$743$	−5.70098e6	−0.378859	−0.189429	+	0.981894i	$0.560664\pi$
$744$	1.07102e7	0.709355
$745$	−1.13511e7	−0.749286
$746$	7.37970e6	0.485503
$747$	−4.32893e6	−0.283844
$748$	1.72474e6	0.112712
$749$	−415582.	−0.0270678
$750$	2.23526e6	0.145103
$751$	9.70865e6	0.628144	0.314072	−	0.949399i	$-0.398307\pi$
$751$	9.70865e6	0.628144	0.314072	+	0.949399i	$0.398307\pi$
$752$	−2.46156e7	−1.58732
$753$	2.91757e7	1.87514
$754$	5.91963e6	0.379198
$755$	9.56217e6	0.610505
$756$	−7.17563e6	−0.456621
$757$	1.23613e7	0.784014	0.392007	−	0.919962i	$-0.371781\pi$
$757$	1.23613e7	0.784014	0.392007	+	0.919962i	$0.371781\pi$
$758$	1.61805e7	1.02286
$759$	4.94697e6	0.311699
$760$	623699.	0.0391689
$761$	5.49551e6	0.343991	0.171995	−	0.985098i	$-0.444979\pi$
$761$	5.49551e6	0.343991	0.171995	+	0.985098i	$0.444979\pi$
$762$	−3.25971e7	−2.03372
$763$	1.93295e7	1.20201
$764$	5.51649e6	0.341924
$765$	2.06818e6	0.127771
$766$	1.75495e7	1.08067
$767$	−4.09837e6	−0.251549
$768$	−2.65934e7	−1.62694
$769$	−1.61749e7	−0.986340	−0.493170	−	0.869933i	$-0.664162\pi$
$769$	−1.61749e7	−0.986340	−0.493170	+	0.869933i	$0.664162\pi$
$770$	3.28224e6	0.199500
$771$	3.23353e7	1.95903
$772$	−2.52661e6	−0.152579
$773$	−4.01033e6	−0.241397	−0.120698	−	0.992689i	$-0.538513\pi$
$773$	−4.01033e6	−0.241397	−0.120698	+	0.992689i	$0.538513\pi$
$774$	−1.32441e7	−0.794638
$775$	−5.00544e6	−0.299356
$776$	3.15623e6	0.188154
$777$	1.91424e7	1.13748
$778$	2.19632e6	0.130091
$779$	−6.00892e6	−0.354775
$780$	3.18544e6	0.187470
$781$	−2.12769e6	−0.124819
$782$	9.82844e6	0.574735
$783$	5.94548e6	0.346563
$784$	−5.85125e6	−0.339984
$785$	−6.22380e6	−0.360480
$786$	1.18285e6	0.0682927
$787$	−1.65055e7	−0.949928	−0.474964	−	0.880005i	$-0.657539\pi$
$787$	−1.65055e7	−0.949928	−0.474964	+	0.880005i	$0.657539\pi$
$788$	−1.83413e7	−1.05224
$789$	−3.00848e7	−1.72050
$790$	−3.95011e6	−0.225186
$791$	6.30518e6	0.358308
$792$	1.09933e6	0.0622750
$793$	−8.59056e6	−0.485108
$794$	−5.65522e6	−0.318345
$795$	−3.70145e6	−0.207709
$796$	9.81845e6	0.549238
$797$	−2.30531e7	−1.28554	−0.642768	−	0.766061i	$-0.722214\pi$
$797$	−2.30531e7	−1.28554	−0.642768	+	0.766061i	$0.722214\pi$
$798$	−7.57981e6	−0.421358
$799$	1.25347e7	0.694617
$800$	4.32755e6	0.239066
$801$	−8.64957e6	−0.476336
$802$	2.58287e6	0.141797
$803$	−3.12451e6	−0.170999
$804$	−5.91302e6	−0.322604
$805$	7.75230e6	0.421639
$806$	−1.72101e7	−0.933139
$807$	−280860.	−0.0151812
$808$	−1.13987e7	−0.614226
$809$	1.65307e7	0.888015	0.444008	−	0.896023i	$-0.353556\pi$
$809$	1.65307e7	0.888015	0.444008	+	0.896023i	$0.353556\pi$
$810$	1.36232e7	0.729571
$811$	−2.70828e7	−1.44591	−0.722956	−	0.690894i	$-0.757217\pi$
$811$	−2.70828e7	−1.44591	−0.722956	+	0.690894i	$0.757217\pi$
$812$	−9.15839e6	−0.487449
$813$	−2.20892e7	−1.17207
$814$	−6.02885e6	−0.318914
$815$	−8.66147e6	−0.456770
$816$	1.50478e7	0.791128
$817$	4.91941e6	0.257845
$818$	−2.80245e7	−1.46438
$819$	5.60887e6	0.292190
$820$	−9.42613e6	−0.489552
$821$	2.62757e7	1.36049	0.680247	−	0.732983i	$-0.261872\pi$
$821$	2.62757e7	1.36049	0.680247	+	0.732983i	$0.261872\pi$
$822$	−4.82317e6	−0.248974
$823$	1.65264e7	0.850509	0.425255	−	0.905074i	$-0.360185\pi$
$823$	1.65264e7	0.850509	0.425255	+	0.905074i	$0.360185\pi$
$824$	6.07510e6	0.311699
$825$	−1.46343e6	−0.0748577
$826$	1.52981e7	0.780166
$827$	1.10371e7	0.561168	0.280584	−	0.959830i	$-0.409472\pi$
$827$	1.10371e7	0.561168	0.280584	+	0.959830i	$0.409472\pi$
$828$	−6.29165e6	−0.318925
$829$	−2.38371e7	−1.20467	−0.602334	−	0.798244i	$-0.705762\pi$
$829$	−2.38371e7	−1.20467	−0.602334	+	0.798244i	$0.705762\pi$
$830$	6.08569e6	0.306630
$831$	−6.17957e6	−0.310424
$832$	3.38456e6	0.169510
$833$	2.97956e6	0.148778
$834$	−3.43044e7	−1.70779
$835$	−7.46791e6	−0.370666
$836$	989455.	0.0489644
$837$	−1.72853e7	−0.852829
$838$	−3.04442e6	−0.149759
$839$	8.55014e6	0.419342	0.209671	−	0.977772i	$-0.432761\pi$
$839$	8.55014e6	0.419342	0.209671	+	0.977772i	$0.432761\pi$
$840$	4.90701e6	0.239949
$841$	−1.29228e7	−0.630039
$842$	4.17829e7	2.03104
$843$	−1.94032e7	−0.940382
$844$	1.30012e7	0.628241
$845$	−7.16991e6	−0.345439
$846$	−1.93595e7	−0.929968
$847$	−2.14889e6	−0.102921
$848$	−9.45492e6	−0.451511
$849$	2.05224e6	0.0977143
$850$	−2.90748e6	−0.138029
$851$	−1.42395e7	−0.674017
$852$	7.70783e6	0.363775
$853$	−1.05018e7	−0.494185	−0.247092	−	0.968992i	$-0.579475\pi$
$853$	−1.05018e7	−0.494185	−0.247092	+	0.968992i	$0.579475\pi$
$854$	3.20662e7	1.50453
$855$	1.18648e6	0.0555066
$856$	195678.	0.00912763
$857$	−2.88217e7	−1.34050	−0.670252	−	0.742134i	$-0.733814\pi$
$857$	−2.88217e7	−1.34050	−0.670252	+	0.742134i	$0.733814\pi$
$858$	−5.03169e6	−0.233343
$859$	2.47036e7	1.14229	0.571145	−	0.820849i	$-0.306499\pi$
$859$	2.47036e7	1.14229	0.571145	+	0.820849i	$0.306499\pi$
$860$	7.71702e6	0.355798
$861$	−4.72757e7	−2.17335
$862$	4.13597e7	1.89587
$863$	1.01327e7	0.463125	0.231563	−	0.972820i	$-0.425616\pi$
$863$	1.01327e7	0.463125	0.231563	+	0.972820i	$0.425616\pi$
$864$	1.49443e7	0.681070
$865$	7.28123e6	0.330876
$866$	−4.16258e6	−0.188611
$867$	1.98132e7	0.895175
$868$	2.66261e7	1.19952
$869$	2.58614e6	0.116172
$870$	9.85193e6	0.441289
$871$	−3.92120e6	−0.175135
$872$	−9.10135e6	−0.405336
$873$	6.00417e6	0.266635
$874$	5.63842e6	0.249677
$875$	−2.29331e6	−0.101261
$876$	1.13189e7	0.498363
$877$	−3.95944e6	−0.173834	−0.0869170	−	0.996216i	$-0.527701\pi$
$877$	−3.95944e6	−0.173834	−0.0869170	+	0.996216i	$0.527701\pi$
$878$	2.84645e7	1.24614
$879$	−2.69836e7	−1.17795
$880$	−3.73815e6	−0.162724
$881$	2.12036e7	0.920386	0.460193	−	0.887819i	$-0.347780\pi$
$881$	2.12036e7	0.920386	0.460193	+	0.887819i	$0.347780\pi$
$882$	−4.60185e6	−0.199187
$883$	3.30777e7	1.42769	0.713844	−	0.700305i	$-0.246953\pi$
$883$	3.30777e7	1.42769	0.713844	+	0.700305i	$0.246953\pi$
$884$	−4.14341e6	−0.178331
$885$	−6.82084e6	−0.292739
$886$	1.96086e7	0.839192
$887$	2.75313e7	1.17494	0.587472	−	0.809244i	$-0.300123\pi$
$887$	2.75313e7	1.17494	0.587472	+	0.809244i	$0.300123\pi$
$888$	−9.01324e6	−0.383574
$889$	3.34436e7	1.41925
$890$	1.21597e7	0.514575
$891$	−8.91914e6	−0.376382
$892$	1.90622e7	0.802159
$893$	7.19094e6	0.301757
$894$	−6.49542e7	−2.71809
$895$	−9.11673e6	−0.380436
$896$	1.98867e7	0.827547
$897$	−1.18843e7	−0.493165
$898$	−8.25764e6	−0.341716
$899$	−2.20615e7	−0.910407
$900$	1.86122e6	0.0765932
$901$	4.81461e6	0.197583
$902$	1.48894e7	0.609342
$903$	3.87039e7	1.57956
$904$	−2.96881e6	−0.120826
$905$	−5.92664e6	−0.240540
$906$	5.47173e7	2.21465
$907$	−1.11608e6	−0.0450483	−0.0225241	−	0.999746i	$-0.507170\pi$
$907$	−1.11608e6	−0.0450483	−0.0225241	+	0.999746i	$0.507170\pi$
$908$	−1.44363e7	−0.581087
$909$	−2.16841e7	−0.870426
$910$	−7.88505e6	−0.315647
$911$	−9.15815e6	−0.365605	−0.182802	−	0.983150i	$-0.558517\pi$
$911$	−9.15815e6	−0.365605	−0.182802	+	0.983150i	$0.558517\pi$
$912$	8.63267e6	0.343683
$913$	−3.98431e6	−0.158189
$914$	1.08883e6	0.0431117
$915$	−1.42971e7	−0.564541
$916$	410791.	0.0161764
$917$	−1.21357e6	−0.0476586
$918$	−1.00404e7	−0.393228
$919$	−1.06789e7	−0.417099	−0.208549	−	0.978012i	$-0.566874\pi$
$919$	−1.06789e7	−0.417099	−0.208549	+	0.978012i	$0.566874\pi$
$920$	−3.65020e6	−0.142183
$921$	1.29931e7	0.504735
$922$	−3.01413e7	−1.16771
$923$	5.11142e6	0.197487
$924$	7.78463e6	0.299956
$925$	4.21237e6	0.161872
$926$	−1.29720e7	−0.497139
$927$	1.15568e7	0.441712
$928$	1.90737e7	0.727051
$929$	1.15207e7	0.437963	0.218982	−	0.975729i	$-0.429726\pi$
$929$	1.15207e7	0.437963	0.218982	+	0.975729i	$0.429726\pi$
$930$	−2.86425e7	−1.08593
$931$	1.70932e6	0.0646324
$932$	2.82676e6	0.106598
$933$	−5.82267e7	−2.18987
$934$	−5.58098e7	−2.09336
$935$	1.90353e6	0.0712083
$936$	−2.64095e6	−0.0985306
$937$	−2.44097e7	−0.908266	−0.454133	−	0.890934i	$-0.650051\pi$
$937$	−2.44097e7	−0.908266	−0.454133	+	0.890934i	$0.650051\pi$
$938$	1.46368e7	0.543172
$939$	−1.37679e7	−0.509569
$940$	1.12803e7	0.416392
$941$	2.23972e7	0.824553	0.412277	−	0.911059i	$-0.364734\pi$
$941$	2.23972e7	0.824553	0.412277	+	0.911059i	$0.364734\pi$
$942$	−3.56143e7	−1.30767
$943$	3.51672e7	1.28783
$944$	−1.74230e7	−0.636346
$945$	−7.91948e6	−0.288481
$946$	−1.21897e7	−0.442860
$947$	−3.61678e7	−1.31053	−0.655265	−	0.755399i	$-0.727443\pi$
$947$	−3.61678e7	−1.31053	−0.655265	+	0.755399i	$0.727443\pi$
$948$	−9.36864e6	−0.338576
$949$	7.50612e6	0.270552
$950$	−1.66798e6	−0.0599626
$951$	−3.95745e7	−1.41894
$952$	−6.38271e6	−0.228251
$953$	8.72664e6	0.311254	0.155627	−	0.987816i	$-0.450260\pi$
$953$	8.72664e6	0.311254	0.155627	+	0.987816i	$0.450260\pi$
$954$	−7.43604e6	−0.264528
$955$	6.08835e6	0.216019
$956$	3.53982e7	1.25267
$957$	−6.45007e6	−0.227659
$958$	1.26224e7	0.444355
$959$	4.94843e6	0.173748
$960$	5.63286e6	0.197265
$961$	3.55101e7	1.24035
$962$	1.44833e7	0.504581
$963$	372244.	0.0129349
$964$	−2.25950e7	−0.783106
$965$	−2.78852e6	−0.0963953
$966$	4.43608e7	1.52952
$967$	3.25632e7	1.11985	0.559927	−	0.828542i	$-0.310829\pi$
$967$	3.25632e7	1.11985	0.559927	+	0.828542i	$0.310829\pi$
$968$	1.01181e6	0.0347065
$969$	−4.39590e6	−0.150397
$970$	−8.44078e6	−0.288040
$971$	−3.58431e7	−1.21999	−0.609997	−	0.792403i	$-0.708830\pi$
$971$	−3.58431e7	−1.21999	−0.609997	+	0.792403i	$0.708830\pi$
$972$	2.04306e7	0.693610
$973$	3.51953e7	1.19180
$974$	−5.25419e6	−0.177463
$975$	3.51565e6	0.118439
$976$	−3.65202e7	−1.22718
$977$	−6.28527e6	−0.210663	−0.105331	−	0.994437i	$-0.533590\pi$
$977$	−6.28527e6	−0.210663	−0.105331	+	0.994437i	$0.533590\pi$
$978$	−4.95633e7	−1.65696
$979$	−7.96099e6	−0.265467
$980$	2.68139e6	0.0891858
$981$	−1.73137e7	−0.574405
$982$	−4.59996e7	−1.52221
$983$	2.75803e7	0.910363	0.455181	−	0.890399i	$-0.349574\pi$
$983$	2.75803e7	0.910363	0.455181	+	0.890399i	$0.349574\pi$
$984$	2.22599e7	0.732886
$985$	−2.02426e7	−0.664775
$986$	−1.28147e7	−0.419776
$987$	5.65753e7	1.84856
$988$	−2.37701e6	−0.0774708
$989$	−2.87908e7	−0.935973
$990$	−2.93996e6	−0.0953351
$991$	−2.14001e7	−0.692202	−0.346101	−	0.938197i	$-0.612494\pi$
$991$	−2.14001e7	−0.692202	−0.346101	+	0.938197i	$0.612494\pi$
$992$	−5.54529e7	−1.78914
$993$	4.77134e7	1.53556
$994$	−1.90795e7	−0.612493
$995$	1.08363e7	0.346994
$996$	1.44337e7	0.461030
$997$	8.41165e6	0.268005	0.134003	−	0.990981i	$-0.457217\pi$
$997$	8.41165e6	0.268005	0.134003	+	0.990981i	$0.457217\pi$
$998$	9.90896e6	0.314921
$999$	1.45466e7	0.461155

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.h.1.7	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.h.1.7	✓	40	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)

\(f(q)\)	\(=\)	\(q-7.39269 q^{2} -19.3511 q^{3} +22.6518 q^{4} +25.0000 q^{5} +143.057 q^{6} -146.772 q^{7} +69.1080 q^{8} +131.466 q^{9} +O(q^{10})\)	\(q-7.39269 q^{2} -19.3511 q^{3} +22.6518 q^{4} +25.0000 q^{5} +143.057 q^{6} -146.772 q^{7} +69.1080 q^{8} +131.466 q^{9} -184.817 q^{10} +121.000 q^{11} -438.339 q^{12} -290.683 q^{13} +1085.04 q^{14} -483.778 q^{15} -1235.75 q^{16} +629.266 q^{17} -971.886 q^{18} +361.000 q^{19} +566.296 q^{20} +2840.20 q^{21} -894.515 q^{22} -2112.75 q^{23} -1337.32 q^{24} +625.000 q^{25} +2148.93 q^{26} +2158.31 q^{27} -3324.65 q^{28} +2754.69 q^{29} +3576.42 q^{30} -8008.70 q^{31} +6924.08 q^{32} -2341.49 q^{33} -4651.97 q^{34} -3669.30 q^{35} +2977.95 q^{36} +6739.80 q^{37} -2668.76 q^{38} +5625.04 q^{39} +1727.70 q^{40} -16645.2 q^{41} -20996.7 q^{42} +13627.2 q^{43} +2740.87 q^{44} +3286.65 q^{45} +15618.9 q^{46} +19919.5 q^{47} +23913.2 q^{48} +4734.97 q^{49} -4620.43 q^{50} -12177.0 q^{51} -6584.51 q^{52} +7651.14 q^{53} -15955.7 q^{54} +3025.00 q^{55} -10143.1 q^{56} -6985.75 q^{57} -20364.6 q^{58} +14099.1 q^{59} -10958.5 q^{60} +29553.0 q^{61} +59205.8 q^{62} -19295.5 q^{63} -11643.5 q^{64} -7267.07 q^{65} +17309.9 q^{66} +13489.6 q^{67} +14254.0 q^{68} +40884.1 q^{69} +27126.0 q^{70} -17584.2 q^{71} +9085.34 q^{72} -25822.4 q^{73} -49825.2 q^{74} -12094.5 q^{75} +8177.32 q^{76} -17759.4 q^{77} -41584.2 q^{78} +21373.1 q^{79} -30893.8 q^{80} -73711.9 q^{81} +123053. q^{82} -32928.2 q^{83} +64335.8 q^{84} +15731.7 q^{85} -100742. q^{86} -53306.4 q^{87} +8362.07 q^{88} -65793.3 q^{89} -24297.2 q^{90} +42664.1 q^{91} -47857.7 q^{92} +154977. q^{93} -147259. q^{94} +9025.00 q^{95} -133989. q^{96} +45671.0 q^{97} -35004.1 q^{98} +15907.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9}+O(q^{10}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + 600 q^{10} + 4840 q^{11} + 2312 q^{12} + 2661 q^{13} + 395 q^{14} + 1575 q^{15} + 15974 q^{16} + 8249 q^{17} + 7225 q^{18} + 14440 q^{19} + 17250 q^{20} + 6845 q^{21} + 2904 q^{22} + 13948 q^{23} + 9740 q^{24} + 25000 q^{25} + 11581 q^{26} + 27864 q^{27} + 37879 q^{28} + 12965 q^{29} + 9125 q^{30} + 4411 q^{31} + 30751 q^{32} + 7623 q^{33} - 17739 q^{34} + 20975 q^{35} + 71345 q^{36} + 5729 q^{37} + 8664 q^{38} - 23560 q^{39} + 21150 q^{40} + 34059 q^{41} + 48528 q^{42} + 68593 q^{43} + 83490 q^{44} + 88875 q^{45} + 43829 q^{46} + 91592 q^{47} + 26539 q^{48} + 152447 q^{49} + 15000 q^{50} - 23170 q^{51} + 46798 q^{52} + 24361 q^{53} + 136436 q^{54} + 121000 q^{55} - 35393 q^{56} + 22743 q^{57} + 77722 q^{58} + 212881 q^{59} + 57800 q^{60} + 137627 q^{61} + 82606 q^{62} + 243832 q^{63} + 259580 q^{64} + 66525 q^{65} + 44165 q^{66} + 78752 q^{67} + 565000 q^{68} + 46134 q^{69} + 9875 q^{70} + 28888 q^{71} - 65574 q^{72} + 291074 q^{73} + 151963 q^{74} + 39375 q^{75} + 249090 q^{76} + 101519 q^{77} - 136222 q^{78} + 87079 q^{79} + 399350 q^{80} + 471360 q^{81} - 74882 q^{82} + 346989 q^{83} - 159196 q^{84} + 206225 q^{85} - 207742 q^{86} + 294612 q^{87} + 102366 q^{88} + 126718 q^{89} + 180625 q^{90} - 239900 q^{91} + 274196 q^{92} + 321654 q^{93} - 418108 q^{94} + 361000 q^{95} + 342154 q^{96} + 137404 q^{97} - 89356 q^{98} + 430155 q^{99}+O(q^{100}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9 + 600 * q^10 + 4840 * q^11 + 2312 * q^12 + 2661 * q^13 + 395 * q^14 + 1575 * q^15 + 15974 * q^16 + 8249 * q^17 + 7225 * q^18 + 14440 * q^19 + 17250 * q^20 + 6845 * q^21 + 2904 * q^22 + 13948 * q^23 + 9740 * q^24 + 25000 * q^25 + 11581 * q^26 + 27864 * q^27 + 37879 * q^28 + 12965 * q^29 + 9125 * q^30 + 4411 * q^31 + 30751 * q^32 + 7623 * q^33 - 17739 * q^34 + 20975 * q^35 + 71345 * q^36 + 5729 * q^37 + 8664 * q^38 - 23560 * q^39 + 21150 * q^40 + 34059 * q^41 + 48528 * q^42 + 68593 * q^43 + 83490 * q^44 + 88875 * q^45 + 43829 * q^46 + 91592 * q^47 + 26539 * q^48 + 152447 * q^49 + 15000 * q^50 - 23170 * q^51 + 46798 * q^52 + 24361 * q^53 + 136436 * q^54 + 121000 * q^55 - 35393 * q^56 + 22743 * q^57 + 77722 * q^58 + 212881 * q^59 + 57800 * q^60 + 137627 * q^61 + 82606 * q^62 + 243832 * q^63 + 259580 * q^64 + 66525 * q^65 + 44165 * q^66 + 78752 * q^67 + 565000 * q^68 + 46134 * q^69 + 9875 * q^70 + 28888 * q^71 - 65574 * q^72 + 291074 * q^73 + 151963 * q^74 + 39375 * q^75 + 249090 * q^76 + 101519 * q^77 - 136222 * q^78 + 87079 * q^79 + 399350 * q^80 + 471360 * q^81 - 74882 * q^82 + 346989 * q^83 - 159196 * q^84 + 206225 * q^85 - 207742 * q^86 + 294612 * q^87 + 102366 * q^88 + 126718 * q^89 + 180625 * q^90 - 239900 * q^91 + 274196 * q^92 + 321654 * q^93 - 418108 * q^94 + 361000 * q^95 + 342154 * q^96 + 137404 * q^97 - 89356 * q^98 + 430155 * q^99

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