LMFDB - Embedded newform 1045.6.a.h.1.26

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			1.26
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.23724 q^{2} +30.2941 q^{3} -14.0458 q^{4} +25.0000 q^{5} +128.363 q^{6} -150.534 q^{7} -195.107 q^{8} +674.732 q^{9} +O(q^{10})$	\(q+4.23724 q^{2} +30.2941 q^{3} -14.0458 q^{4} +25.0000 q^{5} +128.363 q^{6} -150.534 q^{7} -195.107 q^{8} +674.732 q^{9} +105.931 q^{10} +121.000 q^{11} -425.505 q^{12} +588.197 q^{13} -637.848 q^{14} +757.352 q^{15} -377.249 q^{16} +1111.39 q^{17} +2859.00 q^{18} +361.000 q^{19} -351.145 q^{20} -4560.29 q^{21} +512.706 q^{22} -3979.65 q^{23} -5910.59 q^{24} +625.000 q^{25} +2492.33 q^{26} +13078.9 q^{27} +2114.37 q^{28} -2158.32 q^{29} +3209.08 q^{30} +7387.66 q^{31} +4644.93 q^{32} +3665.59 q^{33} +4709.24 q^{34} -3763.35 q^{35} -9477.16 q^{36} -203.200 q^{37} +1529.64 q^{38} +17818.9 q^{39} -4877.68 q^{40} +1104.72 q^{41} -19323.0 q^{42} +10167.8 q^{43} -1699.54 q^{44} +16868.3 q^{45} -16862.7 q^{46} +14934.1 q^{47} -11428.4 q^{48} +5853.48 q^{49} +2648.27 q^{50} +33668.7 q^{51} -8261.70 q^{52} -37495.1 q^{53} +55418.6 q^{54} +3025.00 q^{55} +29370.2 q^{56} +10936.2 q^{57} -9145.31 q^{58} +49179.7 q^{59} -10637.6 q^{60} +15368.7 q^{61} +31303.3 q^{62} -101570. q^{63} +31753.7 q^{64} +14704.9 q^{65} +15532.0 q^{66} -51352.9 q^{67} -15610.4 q^{68} -120560. q^{69} -15946.2 q^{70} -36314.1 q^{71} -131645. q^{72} +36194.7 q^{73} -861.006 q^{74} +18933.8 q^{75} -5070.54 q^{76} -18214.6 q^{77} +75502.9 q^{78} +64524.0 q^{79} -9431.23 q^{80} +232255. q^{81} +4680.96 q^{82} +44414.8 q^{83} +64053.0 q^{84} +27784.9 q^{85} +43083.6 q^{86} -65384.3 q^{87} -23608.0 q^{88} +76753.4 q^{89} +71475.0 q^{90} -88543.6 q^{91} +55897.5 q^{92} +223803. q^{93} +63279.1 q^{94} +9025.00 q^{95} +140714. q^{96} +61168.3 q^{97} +24802.6 q^{98} +81642.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.23724	0.749045	0.374522	−	0.927218i	$-0.377807\pi$
$2$	4.23724	0.749045	0.374522	+	0.927218i	$0.377807\pi$
$3$	30.2941	1.94337	0.971684	−	0.236286i	$-0.0759302\pi$
$3$	30.2941	1.94337	0.971684	+	0.236286i	$0.0759302\pi$
$4$	−14.0458	−0.438932
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	128.363	1.45567
$7$	−150.534	−1.16115	−0.580576	−	0.814206i	$-0.697173\pi$
$7$	−150.534	−1.16115	−0.580576	+	0.814206i	$0.697173\pi$
$8$	−195.107	−1.07782
$9$	674.732	2.77668
$10$	105.931	0.334983
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−425.505	−0.853005
$13$	588.197	0.965305	0.482652	−	0.875812i	$-0.339673\pi$
$13$	588.197	0.965305	0.482652	+	0.875812i	$0.339673\pi$
$14$	−637.848	−0.869756
$15$	757.352	0.869100
$16$	−377.249	−0.368407
$17$	1111.39	0.932708	0.466354	−	0.884598i	$-0.345567\pi$
$17$	1111.39	0.932708	0.466354	+	0.884598i	$0.345567\pi$
$18$	2859.00	2.07986
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−351.145	−0.196296
$21$	−4560.29	−2.25655
$22$	512.706	0.225846
$23$	−3979.65	−1.56865	−0.784324	−	0.620351i	$-0.786990\pi$
$23$	−3979.65	−1.56865	−0.784324	+	0.620351i	$0.786990\pi$
$24$	−5910.59	−2.09461
$25$	625.000	0.200000
$26$	2492.33	0.723057
$27$	13078.9	3.45273
$28$	2114.37	0.509667
$29$	−2158.32	−0.476563	−0.238282	−	0.971196i	$-0.576584\pi$
$29$	−2158.32	−0.476563	−0.238282	+	0.971196i	$0.576584\pi$
$30$	3209.08	0.650995
$31$	7387.66	1.38071	0.690356	−	0.723470i	$-0.257454\pi$
$31$	7387.66	1.38071	0.690356	+	0.723470i	$0.257454\pi$
$32$	4644.93	0.801871
$33$	3665.59	0.585947
$34$	4709.24	0.698640
$35$	−3763.35	−0.519283
$36$	−9477.16	−1.21877
$37$	−203.200	−0.0244016	−0.0122008	−	0.999926i	$-0.503884\pi$
$37$	−203.200	−0.0244016	−0.0122008	+	0.999926i	$0.503884\pi$
$38$	1529.64	0.171843
$39$	17818.9	1.87594
$40$	−4877.68	−0.482018
$41$	1104.72	0.102634	0.0513172	−	0.998682i	$-0.483658\pi$
$41$	1104.72	0.102634	0.0513172	+	0.998682i	$0.483658\pi$
$42$	−19323.0	−1.69025
$43$	10167.8	0.838606	0.419303	−	0.907846i	$-0.362275\pi$
$43$	10167.8	0.838606	0.419303	+	0.907846i	$0.362275\pi$
$44$	−1699.54	−0.132343
$45$	16868.3	1.24177
$46$	−16862.7	−1.17499
$47$	14934.1	0.986127	0.493064	−	0.869993i	$-0.335877\pi$
$47$	14934.1	0.986127	0.493064	+	0.869993i	$0.335877\pi$
$48$	−11428.4	−0.715951
$49$	5853.48	0.348276
$50$	2648.27	0.149809
$51$	33668.7	1.81259
$52$	−8261.70	−0.423703
$53$	−37495.1	−1.83352	−0.916758	−	0.399443i	$-0.869204\pi$
$53$	−37495.1	−1.83352	−0.916758	+	0.399443i	$0.869204\pi$
$54$	55418.6	2.58625
$55$	3025.00	0.134840
$56$	29370.2	1.25152
$57$	10936.2	0.445839
$58$	−9145.31	−0.356967
$59$	49179.7	1.83931	0.919657	−	0.392722i	$-0.128467\pi$
$59$	49179.7	1.83931	0.919657	+	0.392722i	$0.128467\pi$
$60$	−10637.6	−0.381476
$61$	15368.7	0.528827	0.264413	−	0.964409i	$-0.414822\pi$
$61$	15368.7	0.528827	0.264413	+	0.964409i	$0.414822\pi$
$62$	31303.3	1.03421
$63$	−101570.	−3.22415
$64$	31753.7	0.969045
$65$	14704.9	0.431697
$66$	15532.0	0.438901
$67$	−51352.9	−1.39758	−0.698792	−	0.715325i	$-0.746279\pi$
$67$	−51352.9	−1.39758	−0.698792	+	0.715325i	$0.746279\pi$
$68$	−15610.4	−0.409395
$69$	−120560.	−3.04846
$70$	−15946.2	−0.388967
$71$	−36314.1	−0.854928	−0.427464	−	0.904032i	$-0.640593\pi$
$71$	−36314.1	−0.854928	−0.427464	+	0.904032i	$0.640593\pi$
$72$	−131645.	−2.99277
$73$	36194.7	0.794946	0.397473	−	0.917614i	$-0.369887\pi$
$73$	36194.7	0.794946	0.397473	+	0.917614i	$0.369887\pi$
$74$	−861.006	−0.0182779
$75$	18933.8	0.388673
$76$	−5070.54	−0.100698
$77$	−18214.6	−0.350101
$78$	75502.9	1.40516
$79$	64524.0	1.16320	0.581599	−	0.813476i	$-0.302427\pi$
$79$	64524.0	1.16320	0.581599	+	0.813476i	$0.302427\pi$
$80$	−9431.23	−0.164757
$81$	232255.	3.93325
$82$	4680.96	0.0768777
$83$	44414.8	0.707673	0.353837	−	0.935307i	$-0.384877\pi$
$83$	44414.8	0.707673	0.353837	+	0.935307i	$0.384877\pi$
$84$	64053.0	0.990470
$85$	27784.9	0.417120
$86$	43083.6	0.628153
$87$	−65384.3	−0.926137
$88$	−23608.0	−0.324976
$89$	76753.4	1.02712	0.513562	−	0.858053i	$-0.328326\pi$
$89$	76753.4	1.02712	0.513562	+	0.858053i	$0.328326\pi$
$90$	71475.0	0.930139
$91$	−88543.6	−1.12087
$92$	55897.5	0.688530
$93$	223803.	2.68323
$94$	63279.1	0.738654
$95$	9025.00	0.102598
$96$	140714.	1.55833
$97$	61168.3	0.660081	0.330040	−	0.943967i	$-0.392938\pi$
$97$	61168.3	0.660081	0.330040	+	0.943967i	$0.392938\pi$
$98$	24802.6	0.260874
$99$	81642.6	0.837199
$100$	−8778.63	−0.0877863
$101$	37533.1	0.366110	0.183055	−	0.983103i	$-0.441401\pi$
$101$	37533.1	0.366110	0.183055	+	0.983103i	$0.441401\pi$
$102$	142662.	1.35771
$103$	76699.2	0.712357	0.356179	−	0.934418i	$-0.384079\pi$
$103$	76699.2	0.712357	0.356179	+	0.934418i	$0.384079\pi$
$104$	−114761.	−1.04043
$105$	−114007.	−1.00916
$106$	−158876.	−1.37339
$107$	41864.7	0.353499	0.176750	−	0.984256i	$-0.443442\pi$
$107$	41864.7	0.353499	0.176750	+	0.984256i	$0.443442\pi$
$108$	−183704.	−1.51551
$109$	−230423.	−1.85763	−0.928815	−	0.370545i	$-0.879171\pi$
$109$	−230423.	−1.85763	−0.928815	+	0.370545i	$0.879171\pi$
$110$	12817.6	0.101001
$111$	−6155.75	−0.0474213
$112$	56788.8	0.427777
$113$	85066.0	0.626701	0.313350	−	0.949638i	$-0.398549\pi$
$113$	85066.0	0.626701	0.313350	+	0.949638i	$0.398549\pi$
$114$	46339.2	0.333953
$115$	−99491.3	−0.701521
$116$	30315.3	0.209179
$117$	396875.	2.68034
$118$	208386.	1.37773
$119$	−167303.	−1.08302
$120$	−147765.	−0.936738
$121$	14641.0	0.0909091
$122$	65121.0	0.396115
$123$	33466.5	0.199456
$124$	−103766.	−0.606038
$125$	15625.0	0.0894427
$126$	−430377.	−2.41503
$127$	−47249.6	−0.259950	−0.129975	−	0.991517i	$-0.541490\pi$
$127$	−47249.6	−0.259950	−0.129975	+	0.991517i	$0.541490\pi$
$128$	−14090.0	−0.0760127
$129$	308026.	1.62972
$130$	62308.3	0.323361
$131$	340870.	1.73544	0.867721	−	0.497051i	$-0.165584\pi$
$131$	340870.	1.73544	0.867721	+	0.497051i	$0.165584\pi$
$132$	−51486.1	−0.257191
$133$	−54342.8	−0.266387
$134$	−217594.	−1.04685
$135$	326973.	1.54411
$136$	−216841.	−1.00530
$137$	299267.	1.36225	0.681126	−	0.732166i	$-0.261490\pi$
$137$	299267.	1.36225	0.681126	+	0.732166i	$0.261490\pi$
$138$	−510841.	−2.28343
$139$	265897.	1.16728	0.583641	−	0.812012i	$-0.301628\pi$
$139$	265897.	1.16728	0.583641	+	0.812012i	$0.301628\pi$
$140$	52859.3	0.227930
$141$	452414.	1.91641
$142$	−153871.	−0.640379
$143$	71171.8	0.291050
$144$	−254542.	−1.02295
$145$	−53958.0	−0.213126
$146$	153366.	0.595451
$147$	177326.	0.676828
$148$	2854.11	0.0107107
$149$	−247437.	−0.913061	−0.456530	−	0.889708i	$-0.650908\pi$
$149$	−247437.	−0.913061	−0.456530	+	0.889708i	$0.650908\pi$
$150$	80227.1	0.291134
$151$	44760.3	0.159754	0.0798768	−	0.996805i	$-0.474547\pi$
$151$	44760.3	0.159754	0.0798768	+	0.996805i	$0.474547\pi$
$152$	−70433.7	−0.247270
$153$	749893.	2.58983
$154$	−77179.6	−0.262241
$155$	184692.	0.617473
$156$	−250281.	−0.823410
$157$	−169357.	−0.548344	−0.274172	−	0.961681i	$-0.588404\pi$
$157$	−169357.	−0.548344	−0.274172	+	0.961681i	$0.588404\pi$
$158$	273404.	0.871287
$159$	−1.13588e6	−3.56320
$160$	116123.	0.358608
$161$	599073.	1.82144
$162$	984118.	2.94618
$163$	−161699.	−0.476694	−0.238347	−	0.971180i	$-0.576606\pi$
$163$	−161699.	−0.476694	−0.238347	+	0.971180i	$0.576606\pi$
$164$	−15516.7	−0.0450495
$165$	91639.6	0.262044
$166$	188196.	0.530079
$167$	−61426.4	−0.170437	−0.0852184	−	0.996362i	$-0.527159\pi$
$167$	−61426.4	−0.170437	−0.0852184	+	0.996362i	$0.527159\pi$
$168$	889745.	2.43216
$169$	−25317.4	−0.0681870
$170$	117731.	0.312441
$171$	243578.	0.637013
$172$	−142816.	−0.368091
$173$	631415.	1.60398	0.801991	−	0.597336i	$-0.203774\pi$
$173$	631415.	1.60398	0.801991	+	0.597336i	$0.203774\pi$
$174$	−277049.	−0.693719
$175$	−94083.7	−0.232231
$176$	−45647.2	−0.111079
$177$	1.48985e6	3.57446
$178$	325223.	0.769362
$179$	−496197.	−1.15750	−0.578750	−	0.815505i	$-0.696459\pi$
$179$	−496197.	−1.15750	−0.578750	+	0.815505i	$0.696459\pi$
$180$	−236929.	−0.545051
$181$	525950.	1.19329	0.596647	−	0.802504i	$-0.296499\pi$
$181$	525950.	1.19329	0.596647	+	0.802504i	$0.296499\pi$
$182$	−375180.	−0.839579
$183$	465582.	1.02770
$184$	776459.	1.69073
$185$	−5080.00	−0.0109127
$186$	948305.	2.00986
$187$	134479.	0.281222
$188$	−209761.	−0.432843
$189$	−1.96882e6	−4.00915
$190$	38241.1	0.0768504
$191$	−373073.	−0.739963	−0.369982	−	0.929039i	$-0.620636\pi$
$191$	−373073.	−0.739963	−0.369982	+	0.929039i	$0.620636\pi$
$192$	961948.	1.88321
$193$	419834.	0.811305	0.405653	−	0.914027i	$-0.367044\pi$
$193$	419834.	0.811305	0.405653	+	0.914027i	$0.367044\pi$
$194$	259185.	0.494430
$195$	445472.	0.838946
$196$	−82216.8	−0.152869
$197$	−18299.7	−0.0335952	−0.0167976	−	0.999859i	$-0.505347\pi$
$197$	−18299.7	−0.0335952	−0.0167976	+	0.999859i	$0.505347\pi$
$198$	345939.	0.627100
$199$	−311052.	−0.556801	−0.278401	−	0.960465i	$-0.589804\pi$
$199$	−311052.	−0.556801	−0.278401	+	0.960465i	$0.589804\pi$
$200$	−121942.	−0.215565
$201$	−1.55569e6	−2.71602
$202$	159037.	0.274233
$203$	324900.	0.553363
$204$	−472904.	−0.795605
$205$	27618.0	0.0458995
$206$	324993.	0.533588
$207$	−2.68520e6	−4.35563
$208$	−221897.	−0.355625
$209$	43681.0	0.0691714
$210$	−483076.	−0.755905
$211$	−273598.	−0.423065	−0.211532	−	0.977371i	$-0.567845\pi$
$211$	−273598.	−0.423065	−0.211532	+	0.977371i	$0.567845\pi$
$212$	526649.	0.804788
$213$	−1.10010e6	−1.66144
$214$	177391.	0.264787
$215$	254196.	0.375036
$216$	−2.55179e6	−3.72144
$217$	−1.11209e6	−1.60322
$218$	−976356.	−1.39145
$219$	1.09649e6	1.54487
$220$	−42488.6	−0.0591855
$221$	653719.	0.900347
$222$	−26083.4	−0.0355207
$223$	−72710.5	−0.0979119	−0.0489559	−	0.998801i	$-0.515589\pi$
$223$	−72710.5	−0.0979119	−0.0489559	+	0.998801i	$0.515589\pi$
$224$	−699220.	−0.931095
$225$	421708.	0.555335
$226$	360445.	0.469427
$227$	−1.36055e6	−1.75246	−0.876232	−	0.481889i	$-0.839951\pi$
$227$	−1.36055e6	−1.75246	−0.876232	+	0.481889i	$0.839951\pi$
$228$	−153607.	−0.195693
$229$	−39730.4	−0.0500650	−0.0250325	−	0.999687i	$-0.507969\pi$
$229$	−39730.4	−0.0500650	−0.0250325	+	0.999687i	$0.507969\pi$
$230$	−421569.	−0.525471
$231$	−551795.	−0.680374
$232$	421103.	0.513652
$233$	1.15333e6	1.39176	0.695878	−	0.718160i	$-0.255015\pi$
$233$	1.15333e6	1.39176	0.695878	+	0.718160i	$0.255015\pi$
$234$	1.68166e6	2.00769
$235$	373351.	0.441010
$236$	−690769.	−0.807333
$237$	1.95470e6	2.26052
$238$	−708901.	−0.811228
$239$	−308324.	−0.349150	−0.174575	−	0.984644i	$-0.555855\pi$
$239$	−308324.	−0.349150	−0.174575	+	0.984644i	$0.555855\pi$
$240$	−285711.	−0.320183
$241$	−1.34710e6	−1.49402	−0.747010	−	0.664813i	$-0.768511\pi$
$241$	−1.34710e6	−1.49402	−0.747010	+	0.664813i	$0.768511\pi$
$242$	62037.4	0.0680950
$243$	3.85776e6	4.19102
$244$	−215866.	−0.232119
$245$	146337.	0.155754
$246$	141806.	0.149402
$247$	212339.	0.221456
$248$	−1.44139e6	−1.48816
$249$	1.34551e6	1.37527
$250$	66206.8	0.0669966
$251$	−789378.	−0.790862	−0.395431	−	0.918496i	$-0.629405\pi$
$251$	−789378.	−0.790862	−0.395431	+	0.918496i	$0.629405\pi$
$252$	1.42663e6	1.41518
$253$	−481538.	−0.472965
$254$	−200208.	−0.194714
$255$	841717.	0.810617
$256$	−1.07582e6	−1.02598
$257$	−858421.	−0.810713	−0.405357	−	0.914159i	$-0.632853\pi$
$257$	−858421.	−0.810713	−0.405357	+	0.914159i	$0.632853\pi$
$258$	1.30518e6	1.22073
$259$	30588.5	0.0283340
$260$	−206543.	−0.189486
$261$	−1.45629e6	−1.32326
$262$	1.44435e6	1.29992
$263$	−229614.	−0.204696	−0.102348	−	0.994749i	$-0.532635\pi$
$263$	−229614.	−0.204696	−0.102348	+	0.994749i	$0.532635\pi$
$264$	−715182.	−0.631548
$265$	−937377.	−0.819973
$266$	−230263.	−0.199536
$267$	2.32518e6	1.99608
$268$	721293.	0.613444
$269$	−1.15944e6	−0.976938	−0.488469	−	0.872581i	$-0.662444\pi$
$269$	−1.15944e6	−0.976938	−0.488469	+	0.872581i	$0.662444\pi$
$270$	1.38546e6	1.15661
$271$	−1.66731e6	−1.37910	−0.689548	−	0.724240i	$-0.742191\pi$
$271$	−1.66731e6	−1.37910	−0.689548	+	0.724240i	$0.742191\pi$
$272$	−419273.	−0.343617
$273$	−2.68235e6	−2.17825
$274$	1.26807e6	1.02039
$275$	75625.0	0.0603023
$276$	1.69336e6	1.33807
$277$	−512844.	−0.401593	−0.200796	−	0.979633i	$-0.564353\pi$
$277$	−512844.	−0.401593	−0.200796	+	0.979633i	$0.564353\pi$
$278$	1.12667e6	0.874346
$279$	4.98469e6	3.83379
$280$	734256.	0.559696
$281$	−776877.	−0.586930	−0.293465	−	0.955970i	$-0.594808\pi$
$281$	−776877.	−0.586930	−0.293465	+	0.955970i	$0.594808\pi$
$282$	1.91698e6	1.43548
$283$	929041.	0.689555	0.344777	−	0.938684i	$-0.387954\pi$
$283$	929041.	0.689555	0.344777	+	0.938684i	$0.387954\pi$
$284$	510061.	0.375255
$285$	273404.	0.199385
$286$	301572.	0.218010
$287$	−166298.	−0.119174
$288$	3.13409e6	2.22654
$289$	−184660.	−0.130056
$290$	−228633.	−0.159641
$291$	1.85304e6	1.28278
$292$	−508384.	−0.348927
$293$	1.89236e6	1.28776	0.643879	−	0.765128i	$-0.277324\pi$
$293$	1.89236e6	1.28776	0.643879	+	0.765128i	$0.277324\pi$
$294$	751372.	0.506975
$295$	1.22949e6	0.822566
$296$	39645.7	0.0263007
$297$	1.58255e6	1.04104
$298$	−1.04845e6	−0.683924
$299$	−2.34082e6	−1.51422
$300$	−265941.	−0.170601
$301$	−1.53061e6	−0.973749
$302$	189660.	0.119663
$303$	1.13703e6	0.711486
$304$	−136187.	−0.0845185
$305$	384218.	0.236498
$306$	3.17748e6	1.93990
$307$	−1.59561e6	−0.966230	−0.483115	−	0.875557i	$-0.660495\pi$
$307$	−1.59561e6	−0.966230	−0.483115	+	0.875557i	$0.660495\pi$
$308$	255839.	0.153670
$309$	2.32353e6	1.38437
$310$	782582.	0.462515
$311$	1.34922e6	0.791012	0.395506	−	0.918463i	$-0.370569\pi$
$311$	1.34922e6	0.791012	0.395506	+	0.918463i	$0.370569\pi$
$312$	−3.47659e6	−2.02194
$313$	−234279.	−0.135167	−0.0675837	−	0.997714i	$-0.521529\pi$
$313$	−234279.	−0.135167	−0.0675837	+	0.997714i	$0.521529\pi$
$314$	−717604.	−0.410734
$315$	−2.53925e6	−1.44188
$316$	−906292.	−0.510564
$317$	−1.31562e6	−0.735332	−0.367666	−	0.929958i	$-0.619843\pi$
$317$	−1.31562e6	−0.735332	−0.367666	+	0.929958i	$0.619843\pi$
$318$	−4.81299e6	−2.66899
$319$	−261157.	−0.143689
$320$	793841.	0.433370
$321$	1.26825e6	0.686979
$322$	2.53842e6	1.36434
$323$	401213.	0.213978
$324$	−3.26221e6	−1.72643
$325$	367623.	0.193061
$326$	−685159.	−0.357065
$327$	−6.98045e6	−3.61006
$328$	−215539.	−0.110622
$329$	−2.24808e6	−1.14504
$330$	388299.	0.196282
$331$	−476921.	−0.239263	−0.119632	−	0.992818i	$-0.538171\pi$
$331$	−476921.	−0.239263	−0.119632	+	0.992818i	$0.538171\pi$
$332$	−623842.	−0.310620
$333$	−137105.	−0.0677554
$334$	−260278.	−0.127665
$335$	−1.28382e6	−0.625019
$336$	1.72037e6	0.831328
$337$	−873815.	−0.419126	−0.209563	−	0.977795i	$-0.567204\pi$
$337$	−873815.	−0.419126	−0.209563	+	0.977795i	$0.567204\pi$
$338$	−107276.	−0.0510751
$339$	2.57700e6	1.21791
$340$	−390261.	−0.183087
$341$	893907.	0.416300
$342$	1.03210e6	0.477151
$343$	1.64888e6	0.756751
$344$	−1.98382e6	−0.903870
$345$	−3.01400e6	−1.36331
$346$	2.67546e6	1.20145
$347$	−3.36573e6	−1.50057	−0.750284	−	0.661116i	$-0.770083\pi$
$347$	−3.36573e6	−1.50057	−0.750284	+	0.661116i	$0.770083\pi$
$348$	918376.	0.406511
$349$	−3.26633e6	−1.43548	−0.717739	−	0.696312i	$-0.754823\pi$
$349$	−3.26633e6	−1.43548	−0.717739	+	0.696312i	$0.754823\pi$
$350$	−398655.	−0.173951
$351$	7.69299e6	3.33294
$352$	562037.	0.241773
$353$	1.07868e6	0.460739	0.230369	−	0.973103i	$-0.426007\pi$
$353$	1.07868e6	0.460739	0.230369	+	0.973103i	$0.426007\pi$
$354$	6.31287e6	2.67743
$355$	−907852.	−0.382335
$356$	−1.07806e6	−0.450837
$357$	−5.06828e6	−2.10470
$358$	−2.10250e6	−0.867020
$359$	1.91309e6	0.783428	0.391714	−	0.920087i	$-0.371882\pi$
$359$	1.91309e6	0.783428	0.391714	+	0.920087i	$0.371882\pi$
$360$	−3.29113e6	−1.33841
$361$	130321.	0.0526316
$362$	2.22857e6	0.893831
$363$	443536.	0.176670
$364$	1.24367e6	0.491984
$365$	904868.	0.355511
$366$	1.97278e6	0.769797
$367$	−4.20377e6	−1.62920	−0.814599	−	0.580025i	$-0.803043\pi$
$367$	−4.20377e6	−1.62920	−0.814599	+	0.580025i	$0.803043\pi$
$368$	1.50132e6	0.577902
$369$	745390.	0.284982
$370$	−21525.2	−0.00817414
$371$	5.64429e6	2.12899
$372$	−3.14349e6	−1.17775
$373$	−2.59648e6	−0.966303	−0.483152	−	0.875537i	$-0.660508\pi$
$373$	−2.59648e6	−0.966303	−0.483152	+	0.875537i	$0.660508\pi$
$374$	569818.	0.210648
$375$	473345.	0.173820
$376$	−2.91374e6	−1.06287
$377$	−1.26952e6	−0.460029
$378$	−8.34238e6	−3.00303
$379$	−3.60874e6	−1.29050	−0.645250	−	0.763972i	$-0.723247\pi$
$379$	−3.60874e6	−1.29050	−0.645250	+	0.763972i	$0.723247\pi$
$380$	−126763.	−0.0450334
$381$	−1.43139e6	−0.505178
$382$	−1.58080e6	−0.554266
$383$	−1.77825e6	−0.619435	−0.309717	−	0.950829i	$-0.600234\pi$
$383$	−1.77825e6	−0.619435	−0.309717	+	0.950829i	$0.600234\pi$
$384$	−426844.	−0.147721
$385$	−455365.	−0.156570
$386$	1.77894e6	0.607704
$387$	6.86057e6	2.32854
$388$	−859158.	−0.289730
$389$	−3.91248e6	−1.31093	−0.655463	−	0.755228i	$-0.727526\pi$
$389$	−3.91248e6	−1.31093	−0.655463	+	0.755228i	$0.727526\pi$
$390$	1.88757e6	0.628409
$391$	−4.42296e6	−1.46309
$392$	−1.14205e6	−0.375381
$393$	1.03263e7	3.37260
$394$	−77540.0	−0.0251643
$395$	1.61310e6	0.520198
$396$	−1.14674e6	−0.367473
$397$	3.20932e6	1.02197	0.510983	−	0.859591i	$-0.329281\pi$
$397$	3.20932e6	1.02197	0.510983	+	0.859591i	$0.329281\pi$
$398$	−1.31800e6	−0.417069
$399$	−1.64626e6	−0.517687
$400$	−235781.	−0.0736815
$401$	2.00750e6	0.623440	0.311720	−	0.950174i	$-0.399095\pi$
$401$	2.00750e6	0.623440	0.311720	+	0.950174i	$0.399095\pi$
$402$	−6.59183e6	−2.03442
$403$	4.34540e6	1.33281
$404$	−527183.	−0.160697
$405$	5.80637e6	1.75900
$406$	1.37668e6	0.414494
$407$	−24587.2	−0.00735737
$408$	−6.56900e6	−1.95366
$409$	3.21385e6	0.949986	0.474993	−	0.879990i	$-0.342451\pi$
$409$	3.21385e6	0.949986	0.474993	+	0.879990i	$0.342451\pi$
$410$	117024.	0.0343808
$411$	9.06603e6	2.64736
$412$	−1.07730e6	−0.312676
$413$	−7.40322e6	−2.13573
$414$	−1.13778e7	−3.26256
$415$	1.11037e6	0.316481
$416$	2.73213e6	0.774050
$417$	8.05509e6	2.26846
$418$	185087.	0.0518125
$419$	6.59965e6	1.83648	0.918239	−	0.396026i	$-0.129611\pi$
$419$	6.59965e6	1.83648	0.918239	+	0.396026i	$0.129611\pi$
$420$	1.60132e6	0.442951
$421$	−316763.	−0.0871021	−0.0435511	−	0.999051i	$-0.513867\pi$
$421$	−316763.	−0.0871021	−0.0435511	+	0.999051i	$0.513867\pi$
$422$	−1.15930e6	−0.316894
$423$	1.00765e7	2.73816
$424$	7.31556e6	1.97621
$425$	694621.	0.186542
$426$	−4.66140e6	−1.24449
$427$	−2.31352e6	−0.614049
$428$	−588024.	−0.155162
$429$	2.15609e6	0.565618
$430$	1.07709e6	0.280919
$431$	−1.42492e6	−0.369485	−0.184743	−	0.982787i	$-0.559145\pi$
$431$	−1.42492e6	−0.369485	−0.184743	+	0.982787i	$0.559145\pi$
$432$	−4.93402e6	−1.27201
$433$	−2.23597e6	−0.573120	−0.286560	−	0.958062i	$-0.592512\pi$
$433$	−2.23597e6	−0.573120	−0.286560	+	0.958062i	$0.592512\pi$
$434$	−4.71221e6	−1.20088
$435$	−1.63461e6	−0.414181
$436$	3.23647e6	0.815372
$437$	−1.43665e6	−0.359873
$438$	4.64607e6	1.15718
$439$	923807.	0.228781	0.114390	−	0.993436i	$-0.463509\pi$
$439$	923807.	0.228781	0.114390	+	0.993436i	$0.463509\pi$
$440$	−590199.	−0.145334
$441$	3.94953e6	0.967050
$442$	2.76996e6	0.674401
$443$	−5.67670e6	−1.37432	−0.687158	−	0.726508i	$-0.741142\pi$
$443$	−5.67670e6	−1.37432	−0.687158	+	0.726508i	$0.741142\pi$
$444$	86462.6	0.0208147
$445$	1.91884e6	0.459344
$446$	−308092.	−0.0733404
$447$	−7.49589e6	−1.77441
$448$	−4.78000e6	−1.12521
$449$	−6.15891e6	−1.44174	−0.720872	−	0.693068i	$-0.756259\pi$
$449$	−6.15891e6	−1.44174	−0.720872	+	0.693068i	$0.756259\pi$
$450$	1.78688e6	0.415971
$451$	133671.	0.0309454
$452$	−1.19482e6	−0.275079
$453$	1.35597e6	0.310460
$454$	−5.76497e6	−1.31267
$455$	−2.21359e6	−0.501267
$456$	−2.13372e6	−0.480536
$457$	4.20604e6	0.942069	0.471034	−	0.882115i	$-0.343881\pi$
$457$	4.20604e6	0.942069	0.471034	+	0.882115i	$0.343881\pi$
$458$	−168347.	−0.0375010
$459$	1.45359e7	3.22039
$460$	1.39744e6	0.307920
$461$	2.64804e6	0.580325	0.290163	−	0.956977i	$-0.406291\pi$
$461$	2.64804e6	0.580325	0.290163	+	0.956977i	$0.406291\pi$
$462$	−2.33809e6	−0.509631
$463$	6.89012e6	1.49374	0.746869	−	0.664971i	$-0.231556\pi$
$463$	6.89012e6	1.49374	0.746869	+	0.664971i	$0.231556\pi$
$464$	814224.	0.175569
$465$	5.59506e6	1.19998
$466$	4.88693e6	1.04249
$467$	1310.40	0.000278043 0	0.000139022	−	1.00000i	$-0.499956\pi$
$467$	1310.40	0.000278043 0	0.000139022		1.00000i	$0.499956\pi$
$468$	−5.57444e6	−1.17649
$469$	7.73036e6	1.62281
$470$	1.58198e6	0.330336
$471$	−5.13051e6	−1.06563
$472$	−9.59531e6	−1.98246
$473$	1.23031e6	0.252849
$474$	8.28251e6	1.69323
$475$	225625.	0.0458831
$476$	2.34990e6	0.475370
$477$	−2.52991e7	−5.09108
$478$	−1.30644e6	−0.261529
$479$	−819814.	−0.163259	−0.0816293	−	0.996663i	$-0.526012\pi$
$479$	−819814.	−0.163259	−0.0816293	+	0.996663i	$0.526012\pi$
$480$	3.51785e6	0.696906
$481$	−119522.	−0.0235550
$482$	−5.70797e6	−1.11909
$483$	1.81484e7	3.53973
$484$	−205645.	−0.0399029
$485$	1.52921e6	0.295197
$486$	1.63463e7	3.13926
$487$	−2.21552e6	−0.423306	−0.211653	−	0.977345i	$-0.567885\pi$
$487$	−2.21552e6	−0.423306	−0.211653	+	0.977345i	$0.567885\pi$
$488$	−2.99855e6	−0.569982
$489$	−4.89854e6	−0.926391
$490$	620064.	0.116667
$491$	1.79410e6	0.335847	0.167924	−	0.985800i	$-0.446294\pi$
$491$	1.79410e6	0.335847	0.167924	+	0.985800i	$0.446294\pi$
$492$	−470064.	−0.0875476
$493$	−2.39874e6	−0.444494
$494$	899731.	0.165881
$495$	2.04107e6	0.374407
$496$	−2.78699e6	−0.508664
$497$	5.46650e6	0.992702
$498$	5.70123e6	1.03014
$499$	−1.51130e6	−0.271706	−0.135853	−	0.990729i	$-0.543377\pi$
$499$	−1.51130e6	−0.271706	−0.135853	+	0.990729i	$0.543377\pi$
$500$	−219466.	−0.0392592
$501$	−1.86086e6	−0.331221
$502$	−3.34478e6	−0.592391
$503$	4.44043e6	0.782538	0.391269	−	0.920276i	$-0.372036\pi$
$503$	4.44043e6	0.782538	0.391269	+	0.920276i	$0.372036\pi$
$504$	1.98170e7	3.47506
$505$	938328.	0.163729
$506$	−2.04039e6	−0.354272
$507$	−766967.	−0.132512
$508$	663660.	0.114100
$509$	−3.49788e6	−0.598425	−0.299213	−	0.954186i	$-0.596724\pi$
$509$	−3.49788e6	−0.598425	−0.299213	+	0.954186i	$0.596724\pi$
$510$	3.56656e6	0.607188
$511$	−5.44853e6	−0.923054
$512$	−4.10762e6	−0.692494
$513$	4.72150e6	0.792111
$514$	−3.63733e6	−0.607261
$515$	1.91748e6	0.318576
$516$	−4.32647e6	−0.715335
$517$	1.80702e6	0.297329
$518$	129611.	0.0212235
$519$	1.91281e7	3.11713
$520$	−2.86903e6	−0.465294
$521$	−3.92971e6	−0.634259	−0.317129	−	0.948382i	$-0.602719\pi$
$521$	−3.92971e6	−0.634259	−0.317129	+	0.948382i	$0.602719\pi$
$522$	−6.17064e6	−0.991183
$523$	1.78307e6	0.285045	0.142523	−	0.989792i	$-0.454479\pi$
$523$	1.78307e6	0.285045	0.142523	+	0.989792i	$0.454479\pi$
$524$	−4.78779e6	−0.761741
$525$	−2.85018e6	−0.451309
$526$	−972928.	−0.153326
$527$	8.21060e6	1.28780
$528$	−1.38284e6	−0.215867
$529$	9.40130e6	1.46066
$530$	−3.97189e6	−0.614197
$531$	3.31831e7	5.10718
$532$	763288.	0.116926
$533$	649793.	0.0990734
$534$	9.85232e6	1.49515
$535$	1.04662e6	0.158090
$536$	1.00193e7	1.50635
$537$	−1.50318e7	−2.24945
$538$	−4.91282e6	−0.731771
$539$	708271.	0.105009
$540$	−4.59261e6	−0.677758
$541$	6.99189e6	1.02707	0.513537	−	0.858068i	$-0.328335\pi$
$541$	6.99189e6	1.02707	0.513537	+	0.858068i	$0.328335\pi$
$542$	−7.06481e6	−1.03300
$543$	1.59332e7	2.31901
$544$	5.16235e6	0.747911
$545$	−5.76057e6	−0.830757
$546$	−1.13658e7	−1.63161
$547$	2.39193e6	0.341807	0.170903	−	0.985288i	$-0.445331\pi$
$547$	2.39193e6	0.341807	0.170903	+	0.985288i	$0.445331\pi$
$548$	−4.20345e6	−0.597936
$549$	1.03698e7	1.46838
$550$	320441.	0.0451691
$551$	−779153.	−0.109331
$552$	2.35221e7	3.28571
$553$	−9.71305e6	−1.35065
$554$	−2.17304e6	−0.300811
$555$	−153894.	−0.0212075
$556$	−3.73473e6	−0.512357
$557$	1.15066e7	1.57148	0.785742	−	0.618554i	$-0.212281\pi$
$557$	1.15066e7	1.57148	0.785742	+	0.618554i	$0.212281\pi$
$558$	2.11213e7	2.87168
$559$	5.98070e6	0.809510
$560$	1.41972e6	0.191308
$561$	4.07391e6	0.546518
$562$	−3.29181e6	−0.439637
$563$	−9.07824e6	−1.20707	−0.603533	−	0.797338i	$-0.706241\pi$
$563$	−9.07824e6	−1.20707	−0.603533	+	0.797338i	$0.706241\pi$
$564$	−6.35452e6	−0.841172
$565$	2.12665e6	0.280269
$566$	3.93657e6	0.516508
$567$	−3.49622e7	−4.56711
$568$	7.08514e6	0.921462
$569$	−1.25723e7	−1.62793	−0.813965	−	0.580914i	$-0.802695\pi$
$569$	−1.25723e7	−1.62793	−0.813965	+	0.580914i	$0.802695\pi$
$570$	1.15848e6	0.149349
$571$	1.21360e7	1.55770	0.778851	−	0.627209i	$-0.215803\pi$
$571$	1.21360e7	1.55770	0.778851	+	0.627209i	$0.215803\pi$
$572$	−999666.	−0.127751
$573$	−1.13019e7	−1.43802
$574$	−704644.	−0.0892668
$575$	−2.48728e6	−0.313730
$576$	2.14252e7	2.69072
$577$	−1.50912e7	−1.88706	−0.943529	−	0.331290i	$-0.892516\pi$
$577$	−1.50912e7	−1.88706	−0.943529	+	0.331290i	$0.892516\pi$
$578$	−782449.	−0.0974174
$579$	1.27185e7	1.57666
$580$	757884.	0.0935476
$581$	−6.68594e6	−0.821717
$582$	7.85176e6	0.960859
$583$	−4.53691e6	−0.552826
$584$	−7.06184e6	−0.856813
$585$	9.92189e6	1.19868
$586$	8.01837e6	0.964588
$587$	6.67664e6	0.799766	0.399883	−	0.916566i	$-0.369051\pi$
$587$	6.67664e6	0.799766	0.399883	+	0.916566i	$0.369051\pi$
$588$	−2.49068e6	−0.297081
$589$	2.66695e6	0.316757
$590$	5.20965e6	0.616139
$591$	−554372.	−0.0652879
$592$	76657.0	0.00898974
$593$	3.62301e6	0.423090	0.211545	−	0.977368i	$-0.432151\pi$
$593$	3.62301e6	0.423090	0.211545	+	0.977368i	$0.432151\pi$
$594$	6.70565e6	0.779785
$595$	−4.18256e6	−0.484340
$596$	3.47546e6	0.400771
$597$	−9.42304e6	−1.08207
$598$	−9.91861e6	−1.13422
$599$	1.61683e7	1.84119	0.920595	−	0.390519i	$-0.127704\pi$
$599$	1.61683e7	1.84119	0.920595	+	0.390519i	$0.127704\pi$
$600$	−3.69412e6	−0.418922
$601$	2.94016e6	0.332036	0.166018	−	0.986123i	$-0.446909\pi$
$601$	2.94016e6	0.332036	0.166018	+	0.986123i	$0.446909\pi$
$602$	−6.48554e6	−0.729382
$603$	−3.46495e7	−3.88064
$604$	−628695.	−0.0701209
$605$	366025.	0.0406558
$606$	4.81787e6	0.532935
$607$	1.64254e7	1.80944	0.904721	−	0.426004i	$-0.140079\pi$
$607$	1.64254e7	1.80944	0.904721	+	0.426004i	$0.140079\pi$
$608$	1.67682e6	0.183962
$609$	9.84256e6	1.07539
$610$	1.62802e6	0.177148
$611$	8.78416e6	0.951913
$612$	−1.05329e7	−1.13676
$613$	1.71560e7	1.84402	0.922009	−	0.387167i	$-0.126546\pi$
$613$	1.71560e7	1.84402	0.922009	+	0.387167i	$0.126546\pi$
$614$	−6.76098e6	−0.723750
$615$	836663.	0.0891995
$616$	3.55380e6	0.377347
$617$	−18914.3	−0.00200022	−0.00100011	−	0.999999i	$-0.500318\pi$
$617$	−18914.3	−0.00200022	−0.00100011	+	0.999999i	$0.500318\pi$
$618$	9.84537e6	1.03696
$619$	−8.73426e6	−0.916219	−0.458110	−	0.888896i	$-0.651473\pi$
$619$	−8.73426e6	−0.916219	−0.458110	+	0.888896i	$0.651473\pi$
$620$	−2.59414e6	−0.271028
$621$	−5.20496e7	−5.41613
$622$	5.71698e6	0.592503
$623$	−1.15540e7	−1.19265
$624$	−6.72216e6	−0.691111
$625$	390625.	0.0400000
$626$	−992695.	−0.101246
$627$	1.32328e6	0.134426
$628$	2.37875e6	0.240686
$629$	−225835.	−0.0227596
$630$	−1.07594e7	−1.08003
$631$	−1.53402e7	−1.53376	−0.766882	−	0.641789i	$-0.778193\pi$
$631$	−1.53402e7	−1.53376	−0.766882	+	0.641789i	$0.778193\pi$
$632$	−1.25891e7	−1.25372
$633$	−8.28840e6	−0.822170
$634$	−5.57461e6	−0.550797
$635$	−1.18124e6	−0.116253
$636$	1.59544e7	1.56400
$637$	3.44300e6	0.336193
$638$	−1.10658e6	−0.107630
$639$	−2.45023e7	−2.37386
$640$	−352250.	−0.0339939
$641$	−1.54605e7	−1.48620	−0.743100	−	0.669181i	$-0.766645\pi$
$641$	−1.54605e7	−1.48620	−0.743100	+	0.669181i	$0.766645\pi$
$642$	5.37389e6	0.514578
$643$	−1.17170e7	−1.11761	−0.558805	−	0.829299i	$-0.688740\pi$
$643$	−1.17170e7	−1.11761	−0.558805	+	0.829299i	$0.688740\pi$
$644$	−8.41447e6	−0.799488
$645$	7.70064e6	0.728832
$646$	1.70004e6	0.160279
$647$	6.07933e6	0.570946	0.285473	−	0.958387i	$-0.407849\pi$
$647$	6.07933e6	0.570946	0.285473	+	0.958387i	$0.407849\pi$
$648$	−4.53145e7	−4.23936
$649$	5.95074e6	0.554574
$650$	1.55771e6	0.144611
$651$	−3.36899e7	−3.11564
$652$	2.27120e6	0.209236
$653$	1.10280e7	1.01208	0.506038	−	0.862511i	$-0.331110\pi$
$653$	1.10280e7	1.01208	0.506038	+	0.862511i	$0.331110\pi$
$654$	−2.95778e7	−2.70409
$655$	8.52174e6	0.776113
$656$	−416755.	−0.0378113
$657$	2.44217e7	2.20731
$658$	−9.52566e6	−0.857690
$659$	−1.42165e7	−1.27520	−0.637602	−	0.770366i	$-0.720073\pi$
$659$	−1.42165e7	−1.27520	−0.637602	+	0.770366i	$0.720073\pi$
$660$	−1.28715e6	−0.115019
$661$	−7.14648e6	−0.636193	−0.318096	−	0.948058i	$-0.603044\pi$
$661$	−7.14648e6	−0.636193	−0.318096	+	0.948058i	$0.603044\pi$
$662$	−2.02083e6	−0.179219
$663$	1.98038e7	1.74971
$664$	−8.66564e6	−0.762747
$665$	−1.35857e6	−0.119132
$666$	−580949.	−0.0507519
$667$	8.58936e6	0.747560
$668$	862783.	0.0748101
$669$	−2.20270e6	−0.190279
$670$	−5.43986e6	−0.468167
$671$	1.85962e6	0.159447
$672$	−2.11822e7	−1.80946
$673$	−1.01936e7	−0.867545	−0.433772	−	0.901023i	$-0.642818\pi$
$673$	−1.01936e7	−0.867545	−0.433772	+	0.901023i	$0.642818\pi$
$674$	−3.70256e6	−0.313944
$675$	8.17434e6	0.690547
$676$	355603.	0.0299294
$677$	7.78579e6	0.652876	0.326438	−	0.945219i	$-0.394151\pi$
$677$	7.78579e6	0.652876	0.326438	+	0.945219i	$0.394151\pi$
$678$	1.09194e7	0.912269
$679$	−9.20791e6	−0.766455
$680$	−5.42102e6	−0.449582
$681$	−4.12166e7	−3.40568
$682$	3.78770e6	0.311827
$683$	−1.29372e7	−1.06118	−0.530589	−	0.847629i	$-0.678029\pi$
$683$	−1.29372e7	−1.06118	−0.530589	+	0.847629i	$0.678029\pi$
$684$	−3.42126e6	−0.279605
$685$	7.48168e6	0.609218
$686$	6.98669e6	0.566841
$687$	−1.20360e6	−0.0972948
$688$	−3.83581e6	−0.308949
$689$	−2.20545e7	−1.76990
$690$	−1.27710e7	−1.02118
$691$	2.43896e7	1.94316	0.971581	−	0.236706i	$-0.0760677\pi$
$691$	2.43896e7	1.94316	0.971581	+	0.236706i	$0.0760677\pi$
$692$	−8.86874e6	−0.704039
$693$	−1.22900e7	−0.972116
$694$	−1.42614e7	−1.12399
$695$	6.64741e6	0.522024
$696$	1.27569e7	0.998214
$697$	1.22778e6	0.0957279
$698$	−1.38402e7	−1.07524
$699$	3.49390e7	2.70469
$700$	1.32148e6	0.101933
$701$	−1.09165e7	−0.839053	−0.419526	−	0.907743i	$-0.637804\pi$
$701$	−1.09165e7	−0.839053	−0.419526	+	0.907743i	$0.637804\pi$
$702$	3.25970e7	2.49652
$703$	−73355.1	−0.00559812
$704$	3.84219e6	0.292178
$705$	1.13103e7	0.857044
$706$	4.57061e6	0.345114
$707$	−5.65001e6	−0.425109
$708$	−2.09262e7	−1.56894
$709$	−2.01691e7	−1.50686	−0.753428	−	0.657530i	$-0.771601\pi$
$709$	−2.01691e7	−1.50686	−0.753428	+	0.657530i	$0.771601\pi$
$710$	−3.84679e6	−0.286386
$711$	4.35364e7	3.22982
$712$	−1.49751e7	−1.10706
$713$	−2.94003e7	−2.16585
$714$	−2.14755e7	−1.57651
$715$	1.77930e6	0.130162
$716$	6.96948e6	0.508064
$717$	−9.34039e6	−0.678527
$718$	8.10621e6	0.586823
$719$	−2.06915e7	−1.49269	−0.746345	−	0.665559i	$-0.768193\pi$
$719$	−2.06915e7	−1.49269	−0.746345	+	0.665559i	$0.768193\pi$
$720$	−6.36355e6	−0.457476
$721$	−1.15458e7	−0.827156
$722$	552201.	0.0394234
$723$	−4.08091e7	−2.90343
$724$	−7.38739e6	−0.523775
$725$	−1.34895e6	−0.0953127
$726$	1.87937e6	0.132334
$727$	−729926.	−0.0512204	−0.0256102	−	0.999672i	$-0.508153\pi$
$727$	−729926.	−0.0512204	−0.0256102	+	0.999672i	$0.508153\pi$
$728$	1.72755e7	1.20810
$729$	6.04296e7	4.21144
$730$	3.83414e6	0.266294
$731$	1.13005e7	0.782174
$732$	−6.53947e6	−0.451092
$733$	2.53067e7	1.73970	0.869852	−	0.493313i	$-0.164214\pi$
$733$	2.53067e7	1.73970	0.869852	+	0.493313i	$0.164214\pi$
$734$	−1.78124e7	−1.22034
$735$	4.43314e6	0.302687
$736$	−1.84852e7	−1.25785
$737$	−6.21370e6	−0.421387
$738$	3.15840e6	0.213465
$739$	−8.07415e6	−0.543858	−0.271929	−	0.962317i	$-0.587662\pi$
$739$	−8.07415e6	−0.543858	−0.271929	+	0.962317i	$0.587662\pi$
$740$	71352.7	0.00478995
$741$	6.43262e6	0.430370
$742$	2.39162e7	1.59471
$743$	1.32693e7	0.881815	0.440908	−	0.897553i	$-0.354657\pi$
$743$	1.32693e7	0.881815	0.440908	+	0.897553i	$0.354657\pi$
$744$	−4.36655e7	−2.89205
$745$	−6.18594e6	−0.408333
$746$	−1.10019e7	−0.723805
$747$	2.99681e7	1.96498
$748$	−1.88886e6	−0.123437
$749$	−6.30206e6	−0.410467
$750$	2.00568e6	0.130199
$751$	9.42113e6	0.609541	0.304771	−	0.952426i	$-0.401420\pi$
$751$	9.42113e6	0.609541	0.304771	+	0.952426i	$0.401420\pi$
$752$	−5.63386e6	−0.363297
$753$	−2.39135e7	−1.53693
$754$	−5.37924e6	−0.344582
$755$	1.11901e6	0.0714440
$756$	2.76537e7	1.75974
$757$	−3.08754e7	−1.95827	−0.979136	−	0.203208i	$-0.934863\pi$
$757$	−3.08754e7	−1.95827	−0.979136	+	0.203208i	$0.934863\pi$
$758$	−1.52911e7	−0.966642
$759$	−1.45878e7	−0.919145
$760$	−1.76084e6	−0.110582
$761$	−1.16459e7	−0.728973	−0.364487	−	0.931209i	$-0.618756\pi$
$761$	−1.16459e7	−0.728973	−0.364487	+	0.931209i	$0.618756\pi$
$762$	−6.06512e6	−0.378401
$763$	3.46864e7	2.15699
$764$	5.24011e6	0.324793
$765$	1.87473e7	1.15821
$766$	−7.53486e6	−0.463985
$767$	2.89274e7	1.77550
$768$	−3.25910e7	−1.99386
$769$	2.50019e6	0.152460	0.0762302	−	0.997090i	$-0.475712\pi$
$769$	2.50019e6	0.152460	0.0762302	+	0.997090i	$0.475712\pi$
$770$	−1.92949e6	−0.117278
$771$	−2.60051e7	−1.57551
$772$	−5.89691e6	−0.356108
$773$	2.13576e7	1.28559	0.642796	−	0.766038i	$-0.277774\pi$
$773$	2.13576e7	1.28559	0.642796	+	0.766038i	$0.277774\pi$
$774$	2.90699e7	1.74418
$775$	4.61729e6	0.276142
$776$	−1.19344e7	−0.711451
$777$	926650.	0.0550634
$778$	−1.65781e7	−0.981942
$779$	398804.	0.0235459
$780$	−6.25702e6	−0.368240
$781$	−4.39400e6	−0.257770
$782$	−1.87411e7	−1.09592
$783$	−2.82285e7	−1.64545
$784$	−2.20822e6	−0.128307
$785$	−4.23392e6	−0.245227
$786$	4.37552e7	2.52623
$787$	2.24620e7	1.29274	0.646371	−	0.763023i	$-0.276286\pi$
$787$	2.24620e7	1.29274	0.646371	+	0.763023i	$0.276286\pi$
$788$	257034.	0.0147460
$789$	−6.95594e6	−0.397799
$790$	6.83509e6	0.389652
$791$	−1.28053e7	−0.727695
$792$	−1.59290e7	−0.902354
$793$	9.03984e6	0.510479
$794$	1.35987e7	0.765499
$795$	−2.83970e7	−1.59351
$796$	4.36898e6	0.244398
$797$	−3.13685e7	−1.74923	−0.874617	−	0.484814i	$-0.838887\pi$
$797$	−3.13685e7	−1.74923	−0.874617	+	0.484814i	$0.838887\pi$
$798$	−6.97562e6	−0.387771
$799$	1.65976e7	0.919769
$800$	2.90308e6	0.160374
$801$	5.17880e7	2.85199
$802$	8.50625e6	0.466984
$803$	4.37956e6	0.239685
$804$	2.18509e7	1.19215
$805$	1.49768e7	0.814573
$806$	1.84125e7	0.998332
$807$	−3.51241e7	−1.89855
$808$	−7.32298e6	−0.394602
$809$	1.14708e7	0.616201	0.308101	−	0.951354i	$-0.400307\pi$
$809$	1.14708e7	0.616201	0.308101	+	0.951354i	$0.400307\pi$
$810$	2.46030e7	1.31757
$811$	−3.51749e6	−0.187794	−0.0938968	−	0.995582i	$-0.529932\pi$
$811$	−3.51749e6	−0.187794	−0.0938968	+	0.995582i	$0.529932\pi$
$812$	−4.56349e6	−0.242888
$813$	−5.05098e7	−2.68009
$814$	−104182.	−0.00551100
$815$	−4.04249e6	−0.213184
$816$	−1.27015e7	−0.667773
$817$	3.67059e6	0.192389
$818$	1.36178e7	0.711582
$819$	−5.97432e7	−3.11228
$820$	−387917.	−0.0201467
$821$	−3.54513e7	−1.83559	−0.917793	−	0.397060i	$-0.870030\pi$
$821$	−3.54513e7	−1.83559	−0.917793	+	0.397060i	$0.870030\pi$
$822$	3.84149e7	1.98299
$823$	5.01167e6	0.257918	0.128959	−	0.991650i	$-0.458836\pi$
$823$	5.01167e6	0.257918	0.128959	+	0.991650i	$0.458836\pi$
$824$	−1.49646e7	−0.767796
$825$	2.29099e6	0.117189
$826$	−3.13692e7	−1.59975
$827$	6.52507e6	0.331758	0.165879	−	0.986146i	$-0.446954\pi$
$827$	6.52507e6	0.331758	0.165879	+	0.986146i	$0.446954\pi$
$828$	3.77158e7	1.91182
$829$	1.15714e7	0.584788	0.292394	−	0.956298i	$-0.405548\pi$
$829$	1.15714e7	0.584788	0.292394	+	0.956298i	$0.405548\pi$
$830$	4.70490e6	0.237058
$831$	−1.55362e7	−0.780442
$832$	1.86774e7	0.935423
$833$	6.50552e6	0.324840
$834$	3.41314e7	1.69918
$835$	−1.53566e6	−0.0762217
$836$	−613535.	−0.0303615
$837$	9.66228e7	4.76723
$838$	2.79643e7	1.37560
$839$	−1.25237e7	−0.614224	−0.307112	−	0.951673i	$-0.599363\pi$
$839$	−1.25237e7	−0.614224	−0.307112	+	0.951673i	$0.599363\pi$
$840$	2.22436e7	1.08770
$841$	−1.58528e7	−0.772887
$842$	−1.34220e6	−0.0652434
$843$	−2.35348e7	−1.14062
$844$	3.84291e6	0.185696
$845$	−632934.	−0.0304942
$846$	4.26965e7	2.05100
$847$	−2.20397e6	−0.105559
$848$	1.41450e7	0.675481
$849$	2.81445e7	1.34006
$850$	2.94328e6	0.139728
$851$	808665.	0.0382776
$852$	1.54518e7	0.729258
$853$	1.57438e7	0.740860	0.370430	−	0.928860i	$-0.379210\pi$
$853$	1.57438e7	0.740860	0.370430	+	0.928860i	$0.379210\pi$
$854$	−9.80292e6	−0.459950
$855$	6.08946e6	0.284881
$856$	−8.16810e6	−0.381010
$857$	−1.02727e7	−0.477784	−0.238892	−	0.971046i	$-0.576784\pi$
$857$	−1.02727e7	−0.477784	−0.238892	+	0.971046i	$0.576784\pi$
$858$	9.13585e6	0.423673
$859$	1.31596e7	0.608498	0.304249	−	0.952593i	$-0.401595\pi$
$859$	1.31596e7	0.608498	0.304249	+	0.952593i	$0.401595\pi$
$860$	−3.57039e6	−0.164615
$861$	−5.03785e6	−0.231599
$862$	−6.03772e6	−0.276761
$863$	−2.32373e7	−1.06208	−0.531042	−	0.847346i	$-0.678199\pi$
$863$	−2.32373e7	−1.06208	−0.531042	+	0.847346i	$0.678199\pi$
$864$	6.07508e7	2.76865
$865$	1.57854e7	0.717323
$866$	−9.47432e6	−0.429293
$867$	−5.59412e6	−0.252746
$868$	1.56203e7	0.703703
$869$	7.80740e6	0.350717
$870$	−6.92622e6	−0.310240
$871$	−3.02056e7	−1.34909
$872$	4.49571e7	2.00220
$873$	4.12722e7	1.83283
$874$	−6.08745e6	−0.269561
$875$	−2.35209e6	−0.103857
$876$	−1.54010e7	−0.678094
$877$	−3.95297e7	−1.73550	−0.867749	−	0.497003i	$-0.834434\pi$
$877$	−3.95297e7	−1.73550	−0.867749	+	0.497003i	$0.834434\pi$
$878$	3.91439e6	0.171367
$879$	5.73272e7	2.50259
$880$	−1.14118e6	−0.0496760
$881$	2.60409e7	1.13036	0.565180	−	0.824968i	$-0.308807\pi$
$881$	2.60409e7	1.13036	0.565180	+	0.824968i	$0.308807\pi$
$882$	1.67351e7	0.724364
$883$	−2.29303e7	−0.989712	−0.494856	−	0.868975i	$-0.664779\pi$
$883$	−2.29303e7	−0.989712	−0.494856	+	0.868975i	$0.664779\pi$
$884$	−9.18201e6	−0.395191
$885$	3.72464e7	1.59855
$886$	−2.40535e7	−1.02942
$887$	2.89588e7	1.23587	0.617933	−	0.786231i	$-0.287970\pi$
$887$	2.89588e7	1.23587	0.617933	+	0.786231i	$0.287970\pi$
$888$	1.20103e6	0.0511119
$889$	7.11268e6	0.301841
$890$	8.13056e6	0.344069
$891$	2.81028e7	1.18592
$892$	1.02128e6	0.0429766
$893$	5.39119e6	0.226233
$894$	−3.17619e7	−1.32911
$895$	−1.24049e7	−0.517650
$896$	2.12102e6	0.0882624
$897$	−7.09130e7	−2.94269
$898$	−2.60968e7	−1.07993
$899$	−1.59449e7	−0.657996
$900$	−5.92323e6	−0.243754
$901$	−4.16718e7	−1.71014
$902$	566397.	0.0231795
$903$	−4.63683e7	−1.89235
$904$	−1.65970e7	−0.675473
$905$	1.31487e7	0.533658
$906$	5.74558e6	0.232548
$907$	−2.44075e7	−0.985158	−0.492579	−	0.870268i	$-0.663946\pi$
$907$	−2.44075e7	−0.985158	−0.492579	+	0.870268i	$0.663946\pi$
$908$	1.91100e7	0.769212
$909$	2.53248e7	1.01657
$910$	−9.37951e6	−0.375471
$911$	−1.45898e7	−0.582442	−0.291221	−	0.956656i	$-0.594061\pi$
$911$	−1.45898e7	−0.582442	−0.291221	+	0.956656i	$0.594061\pi$
$912$	−4.12566e6	−0.164250
$913$	5.37419e6	0.213371
$914$	1.78220e7	0.705652
$915$	1.16395e7	0.459603
$916$	558046.	0.0219751
$917$	−5.13125e7	−2.01511
$918$	6.15919e7	2.41222
$919$	−2.39040e7	−0.933646	−0.466823	−	0.884351i	$-0.654602\pi$
$919$	−2.39040e7	−0.933646	−0.466823	+	0.884351i	$0.654602\pi$
$920$	1.94115e7	0.756117
$921$	−4.83375e7	−1.87774
$922$	1.12204e7	0.434690
$923$	−2.13598e7	−0.825265
$924$	7.75041e6	0.298638
$925$	−127000.	−0.00488033
$926$	2.91951e7	1.11888
$927$	5.17514e7	1.97799
$928$	−1.00252e7	−0.382142
$929$	−288588.	−0.0109708	−0.00548541	−	0.999985i	$-0.501746\pi$
$929$	−288588.	−0.0109708	−0.00548541	+	0.999985i	$0.501746\pi$
$930$	2.37076e7	0.898836
$931$	2.11311e6	0.0799000
$932$	−1.61994e7	−0.610886
$933$	4.08735e7	1.53723
$934$	5552.49	0.000208267 0
$935$	3.36197e6	0.125766
$936$	−7.74332e7	−2.88893
$937$	−7.56089e6	−0.281335	−0.140668	−	0.990057i	$-0.544925\pi$
$937$	−7.56089e6	−0.281335	−0.140668	+	0.990057i	$0.544925\pi$
$938$	3.27554e7	1.21556
$939$	−7.09726e6	−0.262680
$940$	−5.24402e6	−0.193573
$941$	2.64396e7	0.973378	0.486689	−	0.873575i	$-0.338205\pi$
$941$	2.64396e7	0.973378	0.486689	+	0.873575i	$0.338205\pi$
$942$	−2.17392e7	−0.798208
$943$	−4.39640e6	−0.160997
$944$	−1.85530e7	−0.677617
$945$	−4.92206e7	−1.79295
$946$	5.21311e6	0.189395
$947$	2.92341e7	1.05929	0.529645	−	0.848219i	$-0.322325\pi$
$947$	2.92341e7	1.05929	0.529645	+	0.848219i	$0.322325\pi$
$948$	−2.74553e7	−0.992214
$949$	2.12896e7	0.767366
$950$	956027.	0.0343685
$951$	−3.98556e7	−1.42902
$952$	3.26419e7	1.16730
$953$	−3.75610e7	−1.33969	−0.669845	−	0.742501i	$-0.733640\pi$
$953$	−3.75610e7	−1.33969	−0.669845	+	0.742501i	$0.733640\pi$
$954$	−1.07199e8	−3.81345
$955$	−9.32682e6	−0.330922
$956$	4.33066e6	0.153253
$957$	−7.91150e6	−0.279241
$958$	−3.47375e6	−0.122288
$959$	−4.50499e7	−1.58178
$960$	2.40487e7	0.842197
$961$	2.59484e7	0.906363
$962$	−506441.	−0.0176438
$963$	2.82475e7	0.981553
$964$	1.89211e7	0.655772
$965$	1.04958e7	0.362827
$966$	7.68990e7	2.65142
$967$	−1.43690e7	−0.494152	−0.247076	−	0.968996i	$-0.579470\pi$
$967$	−1.43690e7	−0.494152	−0.247076	+	0.968996i	$0.579470\pi$
$968$	−2.85656e6	−0.0979840
$969$	1.21544e7	0.415838
$970$	6.47962e6	0.221116
$971$	2.35975e7	0.803189	0.401594	−	0.915818i	$-0.368456\pi$
$971$	2.35975e7	0.803189	0.401594	+	0.915818i	$0.368456\pi$
$972$	−5.41854e7	−1.83957
$973$	−4.00265e7	−1.35539
$974$	−9.38771e6	−0.317075
$975$	1.11368e7	0.375188
$976$	−5.79784e6	−0.194824
$977$	−1.97244e7	−0.661101	−0.330550	−	0.943788i	$-0.607234\pi$
$977$	−1.97244e7	−0.661101	−0.330550	+	0.943788i	$0.607234\pi$
$978$	−2.07563e7	−0.693909
$979$	9.28716e6	0.309689
$980$	−2.05542e6	−0.0683653
$981$	−1.55474e8	−5.15803
$982$	7.60201e6	0.251565
$983$	2.47247e7	0.816108	0.408054	−	0.912958i	$-0.366207\pi$
$983$	2.47247e7	0.816108	0.408054	+	0.912958i	$0.366207\pi$
$984$	−6.52955e6	−0.214979
$985$	−457492.	−0.0150242
$986$	−1.01640e7	−0.332946
$987$	−6.81036e7	−2.22524
$988$	−2.98247e6	−0.0972041
$989$	−4.04645e7	−1.31548
$990$	8.64848e6	0.280448
$991$	1.01465e7	0.328196	0.164098	−	0.986444i	$-0.447529\pi$
$991$	1.01465e7	0.328196	0.164098	+	0.986444i	$0.447529\pi$
$992$	3.43152e7	1.10715
$993$	−1.44479e7	−0.464976
$994$	2.31629e7	0.743578
$995$	−7.77630e6	−0.249009
$996$	−1.88987e7	−0.603649
$997$	3.01361e6	0.0960172	0.0480086	−	0.998847i	$-0.484713\pi$
$997$	3.01361e6	0.0960172	0.0480086	+	0.998847i	$0.484713\pi$
$998$	−6.40373e6	−0.203520
$999$	−2.65764e6	−0.0842524

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.h.1.26	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.h.1.26	✓	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)

\(f(q)\)	\(=\)	\(q+4.23724 q^{2} +30.2941 q^{3} -14.0458 q^{4} +25.0000 q^{5} +128.363 q^{6} -150.534 q^{7} -195.107 q^{8} +674.732 q^{9} +O(q^{10})\)	\(q+4.23724 q^{2} +30.2941 q^{3} -14.0458 q^{4} +25.0000 q^{5} +128.363 q^{6} -150.534 q^{7} -195.107 q^{8} +674.732 q^{9} +105.931 q^{10} +121.000 q^{11} -425.505 q^{12} +588.197 q^{13} -637.848 q^{14} +757.352 q^{15} -377.249 q^{16} +1111.39 q^{17} +2859.00 q^{18} +361.000 q^{19} -351.145 q^{20} -4560.29 q^{21} +512.706 q^{22} -3979.65 q^{23} -5910.59 q^{24} +625.000 q^{25} +2492.33 q^{26} +13078.9 q^{27} +2114.37 q^{28} -2158.32 q^{29} +3209.08 q^{30} +7387.66 q^{31} +4644.93 q^{32} +3665.59 q^{33} +4709.24 q^{34} -3763.35 q^{35} -9477.16 q^{36} -203.200 q^{37} +1529.64 q^{38} +17818.9 q^{39} -4877.68 q^{40} +1104.72 q^{41} -19323.0 q^{42} +10167.8 q^{43} -1699.54 q^{44} +16868.3 q^{45} -16862.7 q^{46} +14934.1 q^{47} -11428.4 q^{48} +5853.48 q^{49} +2648.27 q^{50} +33668.7 q^{51} -8261.70 q^{52} -37495.1 q^{53} +55418.6 q^{54} +3025.00 q^{55} +29370.2 q^{56} +10936.2 q^{57} -9145.31 q^{58} +49179.7 q^{59} -10637.6 q^{60} +15368.7 q^{61} +31303.3 q^{62} -101570. q^{63} +31753.7 q^{64} +14704.9 q^{65} +15532.0 q^{66} -51352.9 q^{67} -15610.4 q^{68} -120560. q^{69} -15946.2 q^{70} -36314.1 q^{71} -131645. q^{72} +36194.7 q^{73} -861.006 q^{74} +18933.8 q^{75} -5070.54 q^{76} -18214.6 q^{77} +75502.9 q^{78} +64524.0 q^{79} -9431.23 q^{80} +232255. q^{81} +4680.96 q^{82} +44414.8 q^{83} +64053.0 q^{84} +27784.9 q^{85} +43083.6 q^{86} -65384.3 q^{87} -23608.0 q^{88} +76753.4 q^{89} +71475.0 q^{90} -88543.6 q^{91} +55897.5 q^{92} +223803. q^{93} +63279.1 q^{94} +9025.00 q^{95} +140714. q^{96} +61168.3 q^{97} +24802.6 q^{98} +81642.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9}+O(q^{10}) \) 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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