LMFDB - Embedded newform 1045.6.a.f.1.2

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:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-10.4263 q^{2} +23.9600 q^{3} +76.7073 q^{4} +25.0000 q^{5} -249.814 q^{6} -14.0559 q^{7} -466.130 q^{8} +331.082 q^{9} +O(q^{10})$	\(q-10.4263 q^{2} +23.9600 q^{3} +76.7073 q^{4} +25.0000 q^{5} -249.814 q^{6} -14.0559 q^{7} -466.130 q^{8} +331.082 q^{9} -260.657 q^{10} -121.000 q^{11} +1837.91 q^{12} -307.277 q^{13} +146.550 q^{14} +599.000 q^{15} +2405.37 q^{16} -2109.57 q^{17} -3451.95 q^{18} -361.000 q^{19} +1917.68 q^{20} -336.779 q^{21} +1261.58 q^{22} +4276.67 q^{23} -11168.5 q^{24} +625.000 q^{25} +3203.76 q^{26} +2110.45 q^{27} -1078.19 q^{28} +1583.95 q^{29} -6245.34 q^{30} +3487.51 q^{31} -10162.9 q^{32} -2899.16 q^{33} +21995.0 q^{34} -351.397 q^{35} +25396.4 q^{36} -8380.67 q^{37} +3763.89 q^{38} -7362.37 q^{39} -11653.3 q^{40} -10518.6 q^{41} +3511.35 q^{42} +9545.56 q^{43} -9281.58 q^{44} +8277.05 q^{45} -44589.7 q^{46} +12749.5 q^{47} +57632.7 q^{48} -16609.4 q^{49} -6516.42 q^{50} -50545.3 q^{51} -23570.4 q^{52} +19509.5 q^{53} -22004.1 q^{54} -3025.00 q^{55} +6551.87 q^{56} -8649.56 q^{57} -16514.7 q^{58} -25162.7 q^{59} +45947.7 q^{60} -19835.0 q^{61} -36361.8 q^{62} -4653.65 q^{63} +28989.4 q^{64} -7681.93 q^{65} +30227.5 q^{66} +25864.4 q^{67} -161819. q^{68} +102469. q^{69} +3663.76 q^{70} +19670.3 q^{71} -154327. q^{72} -2621.66 q^{73} +87379.2 q^{74} +14975.0 q^{75} -27691.3 q^{76} +1700.76 q^{77} +76762.1 q^{78} +107218. q^{79} +60134.3 q^{80} -29886.6 q^{81} +109670. q^{82} +85993.7 q^{83} -25833.4 q^{84} -52739.3 q^{85} -99524.6 q^{86} +37951.3 q^{87} +56401.8 q^{88} +67405.2 q^{89} -86298.8 q^{90} +4319.05 q^{91} +328051. q^{92} +83560.8 q^{93} -132930. q^{94} -9025.00 q^{95} -243503. q^{96} +113261. q^{97} +173175. q^{98} -40060.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9}+O(q^{10}) $ 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9} + 200 q^{10} - 4598 q^{11} + 2312 q^{12} + 41 q^{13} + 23 q^{14} + 1575 q^{15} + 7196 q^{16} - 2431 q^{17} - 1689 q^{18} - 13718 q^{19} + 15400 q^{20} - 1577 q^{21} - 968 q^{22} + 9284 q^{23} + 7598 q^{24} + 23750 q^{25} + 13129 q^{26} + 9228 q^{27} - 1079 q^{28} - 559 q^{29} + 3725 q^{30} + 11147 q^{31} + 11051 q^{32} - 7623 q^{33} + 40895 q^{34} + 6875 q^{35} + 55887 q^{36} + 41579 q^{37} - 2888 q^{38} + 24982 q^{39} + 6600 q^{40} + 18597 q^{41} + 61360 q^{42} + 25353 q^{43} - 74536 q^{44} + 75725 q^{45} + 1611 q^{46} + 63516 q^{47} + 187737 q^{48} + 141609 q^{49} + 5000 q^{50} + 107546 q^{51} + 60018 q^{52} + 123045 q^{53} + 256696 q^{54} - 114950 q^{55} + 157335 q^{56} - 22743 q^{57} + 218938 q^{58} + 132925 q^{59} + 57800 q^{60} - 59107 q^{61} + 166982 q^{62} + 130582 q^{63} + 313126 q^{64} + 1025 q^{65} - 18029 q^{66} + 162534 q^{67} + 182980 q^{68} + 178552 q^{69} + 575 q^{70} + 157840 q^{71} + 98630 q^{72} - 63010 q^{73} + 122683 q^{74} + 39375 q^{75} - 222376 q^{76} - 33275 q^{77} + 277272 q^{78} - 16385 q^{79} + 179900 q^{80} + 290354 q^{81} + 362302 q^{82} + 138461 q^{83} + 446870 q^{84} - 60775 q^{85} + 643902 q^{86} + 291602 q^{87} - 31944 q^{88} + 224792 q^{89} - 42225 q^{90} + 498548 q^{91} + 581088 q^{92} + 134210 q^{93} + 35864 q^{94} - 342950 q^{95} + 377376 q^{96} + 292216 q^{97} - 58230 q^{98} - 366509 q^{99}+O(q^{100}) \) 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9 + 200 * q^10 - 4598 * q^11 + 2312 * q^12 + 41 * q^13 + 23 * q^14 + 1575 * q^15 + 7196 * q^16 - 2431 * q^17 - 1689 * q^18 - 13718 * q^19 + 15400 * q^20 - 1577 * q^21 - 968 * q^22 + 9284 * q^23 + 7598 * q^24 + 23750 * q^25 + 13129 * q^26 + 9228 * q^27 - 1079 * q^28 - 559 * q^29 + 3725 * q^30 + 11147 * q^31 + 11051 * q^32 - 7623 * q^33 + 40895 * q^34 + 6875 * q^35 + 55887 * q^36 + 41579 * q^37 - 2888 * q^38 + 24982 * q^39 + 6600 * q^40 + 18597 * q^41 + 61360 * q^42 + 25353 * q^43 - 74536 * q^44 + 75725 * q^45 + 1611 * q^46 + 63516 * q^47 + 187737 * q^48 + 141609 * q^49 + 5000 * q^50 + 107546 * q^51 + 60018 * q^52 + 123045 * q^53 + 256696 * q^54 - 114950 * q^55 + 157335 * q^56 - 22743 * q^57 + 218938 * q^58 + 132925 * q^59 + 57800 * q^60 - 59107 * q^61 + 166982 * q^62 + 130582 * q^63 + 313126 * q^64 + 1025 * q^65 - 18029 * q^66 + 162534 * q^67 + 182980 * q^68 + 178552 * q^69 + 575 * q^70 + 157840 * q^71 + 98630 * q^72 - 63010 * q^73 + 122683 * q^74 + 39375 * q^75 - 222376 * q^76 - 33275 * q^77 + 277272 * q^78 - 16385 * q^79 + 179900 * q^80 + 290354 * q^81 + 362302 * q^82 + 138461 * q^83 + 446870 * q^84 - 60775 * q^85 + 643902 * q^86 + 291602 * q^87 - 31944 * q^88 + 224792 * q^89 - 42225 * q^90 + 498548 * q^91 + 581088 * q^92 + 134210 * q^93 + 35864 * q^94 - 342950 * q^95 + 377376 * q^96 + 292216 * q^97 - 58230 * q^98 - 366509 * 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 $

$2$	−10.4263	−1.84312	−0.921561	−	0.388233i	$-0.873086\pi$
$2$	−10.4263	−1.84312	−0.921561	+	0.388233i	$0.873086\pi$
$3$	23.9600	1.53704	0.768518	−	0.639829i	$-0.220995\pi$
$3$	23.9600	1.53704	0.768518	+	0.639829i	$0.220995\pi$
$4$	76.7073	2.39710
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−249.814	−2.83295
$7$	−14.0559	−0.108421	−0.0542104	−	0.998530i	$-0.517264\pi$
$7$	−14.0559	−0.108421	−0.0542104	+	0.998530i	$0.517264\pi$
$8$	−466.130	−2.57503
$9$	331.082	1.36248
$10$	−260.657	−0.824270
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	1837.91	3.68443
$13$	−307.277	−0.504281	−0.252140	−	0.967691i	$-0.581134\pi$
$13$	−307.277	−0.504281	−0.252140	+	0.967691i	$0.581134\pi$
$14$	146.550	0.199833
$15$	599.000	0.687383
$16$	2405.37	2.34900
$17$	−2109.57	−1.77040	−0.885201	−	0.465209i	$-0.845979\pi$
$17$	−2109.57	−1.77040	−0.885201	+	0.465209i	$0.845979\pi$
$18$	−3451.95	−2.51121
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	1917.68	1.07202
$21$	−336.779	−0.166647
$22$	1261.58	0.555722
$23$	4276.67	1.68572	0.842861	−	0.538132i	$-0.180870\pi$
$23$	4276.67	1.68572	0.842861	+	0.538132i	$0.180870\pi$
$24$	−11168.5	−3.95791
$25$	625.000	0.200000
$26$	3203.76	0.929451
$27$	2110.45	0.557141
$28$	−1078.19	−0.259896
$29$	1583.95	0.349740	0.174870	−	0.984592i	$-0.444050\pi$
$29$	1583.95	0.349740	0.174870	+	0.984592i	$0.444050\pi$
$30$	−6245.34	−1.26693
$31$	3487.51	0.651796	0.325898	−	0.945405i	$-0.394333\pi$
$31$	3487.51	0.651796	0.325898	+	0.945405i	$0.394333\pi$
$32$	−10162.9	−1.75446
$33$	−2899.16	−0.463434
$34$	21995.0	3.26307
$35$	−351.397	−0.0484873
$36$	25396.4	3.26600
$37$	−8380.67	−1.00641	−0.503204	−	0.864167i	$-0.667846\pi$
$37$	−8380.67	−1.00641	−0.503204	+	0.864167i	$0.667846\pi$
$38$	3763.89	0.422841
$39$	−7362.37	−0.775097
$40$	−11653.3	−1.15159
$41$	−10518.6	−0.977236	−0.488618	−	0.872498i	$-0.662499\pi$
$41$	−10518.6	−0.977236	−0.488618	+	0.872498i	$0.662499\pi$
$42$	3511.35	0.307150
$43$	9545.56	0.787282	0.393641	−	0.919264i	$-0.371215\pi$
$43$	9545.56	0.787282	0.393641	+	0.919264i	$0.371215\pi$
$44$	−9281.58	−0.722753
$45$	8277.05	0.609319
$46$	−44589.7	−3.10699
$47$	12749.5	0.841876	0.420938	−	0.907089i	$-0.361701\pi$
$47$	12749.5	0.841876	0.420938	+	0.907089i	$0.361701\pi$
$48$	57632.7	3.61049
$49$	−16609.4	−0.988245
$50$	−6516.42	−0.368625
$51$	−50545.3	−2.72117
$52$	−23570.4	−1.20881
$53$	19509.5	0.954016	0.477008	−	0.878899i	$-0.341721\pi$
$53$	19509.5	0.954016	0.477008	+	0.878899i	$0.341721\pi$
$54$	−22004.1	−1.02688
$55$	−3025.00	−0.134840
$56$	6551.87	0.279187
$57$	−8649.56	−0.352620
$58$	−16514.7	−0.644614
$59$	−25162.7	−0.941083	−0.470541	−	0.882378i	$-0.655941\pi$
$59$	−25162.7	−0.941083	−0.470541	+	0.882378i	$0.655941\pi$
$60$	45947.7	1.64773
$61$	−19835.0	−0.682508	−0.341254	−	0.939971i	$-0.610852\pi$
$61$	−19835.0	−0.682508	−0.341254	+	0.939971i	$0.610852\pi$
$62$	−36361.8	−1.20134
$63$	−4653.65	−0.147721
$64$	28989.4	0.884685
$65$	−7681.93	−0.225521
$66$	30227.5	0.854165
$67$	25864.4	0.703908	0.351954	−	0.936017i	$-0.385517\pi$
$67$	25864.4	0.703908	0.351954	+	0.936017i	$0.385517\pi$
$68$	−161819.	−4.24383
$69$	102469.	2.59101
$70$	3663.76	0.0893680
$71$	19670.3	0.463090	0.231545	−	0.972824i	$-0.425622\pi$
$71$	19670.3	0.463090	0.231545	+	0.972824i	$0.425622\pi$
$72$	−154327.	−3.50842
$73$	−2621.66	−0.0575798	−0.0287899	−	0.999585i	$-0.509165\pi$
$73$	−2621.66	−0.0575798	−0.0287899	+	0.999585i	$0.509165\pi$
$74$	87379.2	1.85494
$75$	14975.0	0.307407
$76$	−27691.3	−0.549933
$77$	1700.76	0.0326901
$78$	76762.1	1.42860
$79$	107218.	1.93286	0.966430	−	0.256932i	$-0.0827115\pi$
$79$	107218.	1.93286	0.966430	+	0.256932i	$0.0827115\pi$
$80$	60134.3	1.05050
$81$	−29886.6	−0.506132
$82$	109670.	1.80117
$83$	85993.7	1.37016	0.685080	−	0.728468i	$-0.259767\pi$
$83$	85993.7	1.37016	0.685080	+	0.728468i	$0.259767\pi$
$84$	−25833.4	−0.399469
$85$	−52739.3	−0.791748
$86$	−99524.6	−1.45106
$87$	37951.3	0.537563
$88$	56401.8	0.776401
$89$	67405.2	0.902025	0.451013	−	0.892518i	$-0.351063\pi$
$89$	67405.2	0.902025	0.451013	+	0.892518i	$0.351063\pi$
$90$	−86298.8	−1.12305
$91$	4319.05	0.0546745
$92$	328051.	4.04085
$93$	83560.8	1.00183
$94$	−132930.	−1.55168
$95$	−9025.00	−0.102598
$96$	−243503.	−2.69666
$97$	113261.	1.22223	0.611113	−	0.791544i	$-0.290722\pi$
$97$	113261.	1.22223	0.611113	+	0.791544i	$0.290722\pi$
$98$	173175.	1.82146
$99$	−40060.9	−0.410802
$100$	47942.0	0.479420
$101$	106498.	1.03881	0.519407	−	0.854527i	$-0.326153\pi$
$101$	106498.	1.03881	0.519407	+	0.854527i	$0.326153\pi$
$102$	527000.	5.01545
$103$	−19530.9	−0.181396	−0.0906982	−	0.995878i	$-0.528910\pi$
$103$	−19530.9	−0.181396	−0.0906982	+	0.995878i	$0.528910\pi$
$104$	143231.	1.29854
$105$	−8419.47	−0.0745266
$106$	−203411.	−1.75837
$107$	−86472.2	−0.730158	−0.365079	−	0.930977i	$-0.618958\pi$
$107$	−86472.2	−0.730158	−0.365079	+	0.930977i	$0.618958\pi$
$108$	161887.	1.33552
$109$	214686.	1.73076	0.865380	−	0.501116i	$-0.167077\pi$
$109$	214686.	1.73076	0.865380	+	0.501116i	$0.167077\pi$
$110$	31539.5	0.248527
$111$	−200801.	−1.54689
$112$	−33809.6	−0.254680
$113$	−45683.9	−0.336563	−0.168282	−	0.985739i	$-0.553822\pi$
$113$	−45683.9	−0.336563	−0.168282	+	0.985739i	$0.553822\pi$
$114$	90182.8	0.649922
$115$	106917.	0.753877
$116$	121500.	0.838362
$117$	−101734.	−0.687071
$118$	262354.	1.73453
$119$	29651.9	0.191948
$120$	−279212.	−1.77003
$121$	14641.0	0.0909091
$122$	206805.	1.25795
$123$	−252026.	−1.50205
$124$	267518.	1.56242
$125$	15625.0	0.0894427
$126$	48520.2	0.272268
$127$	66922.9	0.368184	0.184092	−	0.982909i	$-0.441065\pi$
$127$	66922.9	0.368184	0.184092	+	0.982909i	$0.441065\pi$
$128$	22961.8	0.123874
$129$	228712.	1.21008
$130$	80094.0	0.415663
$131$	216733.	1.10343	0.551717	−	0.834031i	$-0.313973\pi$
$131$	216733.	1.10343	0.551717	+	0.834031i	$0.313973\pi$
$132$	−222387.	−1.11090
$133$	5074.17	0.0248734
$134$	−269670.	−1.29739
$135$	52761.2	0.249161
$136$	983335.	4.55884
$137$	327153.	1.48919	0.744593	−	0.667519i	$-0.232644\pi$
$137$	327153.	1.48919	0.744593	+	0.667519i	$0.232644\pi$
$138$	−1.06837e6	−4.77556
$139$	−269796.	−1.18440	−0.592201	−	0.805790i	$-0.701741\pi$
$139$	−269796.	−1.18440	−0.592201	+	0.805790i	$0.701741\pi$
$140$	−26954.7	−0.116229
$141$	305478.	1.29399
$142$	−205088.	−0.853533
$143$	37180.6	0.152046
$144$	796376.	3.20045
$145$	39598.6	0.156408
$146$	27334.2	0.106127
$147$	−397962.	−1.51897
$148$	−642858.	−2.41246
$149$	339352.	1.25223	0.626115	−	0.779731i	$-0.284644\pi$
$149$	339352.	1.25223	0.626115	+	0.779731i	$0.284644\pi$
$150$	−156134.	−0.566589
$151$	−29206.6	−0.104241	−0.0521205	−	0.998641i	$-0.516598\pi$
$151$	−29206.6	−0.104241	−0.0521205	+	0.998641i	$0.516598\pi$
$152$	168273.	0.590753
$153$	−698441.	−2.41213
$154$	−17732.6	−0.0602519
$155$	87187.8	0.291492
$156$	−564747.	−1.85799
$157$	242419.	0.784905	0.392452	−	0.919772i	$-0.371627\pi$
$157$	242419.	0.784905	0.392452	+	0.919772i	$0.371627\pi$
$158$	−1.11789e6	−3.56250
$159$	467447.	1.46636
$160$	−254073.	−0.784617
$161$	−60112.3	−0.182767
$162$	311606.	0.932864
$163$	−604706.	−1.78269	−0.891344	−	0.453327i	$-0.850237\pi$
$163$	−604706.	−1.78269	−0.891344	+	0.453327i	$0.850237\pi$
$164$	−806855.	−2.34253
$165$	−72479.0	−0.207254
$166$	−896594.	−2.52537
$167$	255321.	0.708428	0.354214	−	0.935164i	$-0.384749\pi$
$167$	255321.	0.708428	0.354214	+	0.935164i	$0.384749\pi$
$168$	156983.	0.429120
$169$	−276874.	−0.745701
$170$	549874.	1.45929
$171$	−119521.	−0.312574
$172$	732214.	1.88719
$173$	−5361.15	−0.0136189	−0.00680946	−	0.999977i	$-0.502168\pi$
$173$	−5361.15	−0.0136189	−0.00680946	+	0.999977i	$0.502168\pi$
$174$	−395691.	−0.990794
$175$	−8784.92	−0.0216842
$176$	−291050.	−0.708249
$177$	−602899.	−1.44648
$178$	−702786.	−1.66254
$179$	102611.	0.239365	0.119682	−	0.992812i	$-0.461812\pi$
$179$	102611.	0.239365	0.119682	+	0.992812i	$0.461812\pi$
$180$	634910.	1.46060
$181$	−413315.	−0.937745	−0.468872	−	0.883266i	$-0.655340\pi$
$181$	−413315.	−0.937745	−0.468872	+	0.883266i	$0.655340\pi$
$182$	−45031.6	−0.100772
$183$	−475247.	−1.04904
$184$	−1.99348e6	−4.34078
$185$	−209517.	−0.450080
$186$	−871228.	−1.84650
$187$	255258.	0.533796
$188$	977979.	2.01806
$189$	−29664.2	−0.0604057
$190$	94097.2	0.189100
$191$	−97868.9	−0.194116	−0.0970580	−	0.995279i	$-0.530943\pi$
$191$	−97868.9	−0.194116	−0.0970580	+	0.995279i	$0.530943\pi$
$192$	694586.	1.35979
$193$	31358.3	0.0605982	0.0302991	−	0.999541i	$-0.490354\pi$
$193$	31358.3	0.0605982	0.0302991	+	0.999541i	$0.490354\pi$
$194$	−1.18089e6	−2.25271
$195$	−184059.	−0.346634
$196$	−1.27406e6	−2.36892
$197$	871635.	1.60018	0.800091	−	0.599879i	$-0.204785\pi$
$197$	871635.	1.60018	0.800091	+	0.599879i	$0.204785\pi$
$198$	417686.	0.757159
$199$	527284.	0.943869	0.471935	−	0.881634i	$-0.343556\pi$
$199$	527284.	0.943869	0.471935	+	0.881634i	$0.343556\pi$
$200$	−291331.	−0.515006
$201$	619712.	1.08193
$202$	−1.11038e6	−1.91466
$203$	−22263.7	−0.0379191
$204$	−3.87719e6	−6.52292
$205$	−262966.	−0.437033
$206$	203634.	0.334336
$207$	1.41593e6	2.29676
$208$	−739116.	−1.18455
$209$	43681.0	0.0691714
$210$	87783.7	0.137362
$211$	−452211.	−0.699254	−0.349627	−	0.936889i	$-0.613692\pi$
$211$	−452211.	−0.699254	−0.349627	+	0.936889i	$0.613692\pi$
$212$	1.49652e6	2.28687
$213$	471301.	0.711786
$214$	901583.	1.34577
$215$	238639.	0.352083
$216$	−983744.	−1.43466
$217$	−49020.0	−0.0706682
$218$	−2.23837e6	−3.19000
$219$	−62815.1	−0.0885021
$220$	−232039.	−0.323225
$221$	648223.	0.892779
$222$	2.09361e6	2.85110
$223$	1.01422e6	1.36575	0.682876	−	0.730534i	$-0.260729\pi$
$223$	1.01422e6	1.36575	0.682876	+	0.730534i	$0.260729\pi$
$224$	142849.	0.190220
$225$	206926.	0.272496
$226$	476313.	0.620328
$227$	425468.	0.548027	0.274014	−	0.961726i	$-0.411649\pi$
$227$	425468.	0.548027	0.274014	+	0.961726i	$0.411649\pi$
$228$	−663484.	−0.845266
$229$	348334.	0.438942	0.219471	−	0.975619i	$-0.429567\pi$
$229$	348334.	0.438942	0.219471	+	0.975619i	$0.429567\pi$
$230$	−1.11474e6	−1.38949
$231$	40750.2	0.0502459
$232$	−738325.	−0.900591
$233$	1.11874e6	1.35002	0.675008	−	0.737811i	$-0.264140\pi$
$233$	1.11874e6	1.35002	0.675008	+	0.737811i	$0.264140\pi$
$234$	1.06071e6	1.26636
$235$	318737.	0.376499
$236$	−1.93016e6	−2.25587
$237$	2.56895e6	2.97087
$238$	−309158.	−0.353784
$239$	−1.55958e6	−1.76609	−0.883046	−	0.469286i	$-0.844511\pi$
$239$	−1.55958e6	−1.76609	−0.883046	+	0.469286i	$0.844511\pi$
$240$	1.44082e6	1.61466
$241$	500053.	0.554592	0.277296	−	0.960785i	$-0.410562\pi$
$241$	500053.	0.554592	0.277296	+	0.960785i	$0.410562\pi$
$242$	−152651.	−0.167557
$243$	−1.22892e6	−1.33508
$244$	−1.52149e6	−1.63604
$245$	−415236.	−0.441957
$246$	2.62770e6	2.76846
$247$	110927.	0.115690
$248$	−1.62564e6	−1.67839
$249$	2.06041e6	2.10599
$250$	−162911.	−0.164854
$251$	−1.03659e6	−1.03854	−0.519270	−	0.854610i	$-0.673796\pi$
$251$	−1.03659e6	−1.03854	−0.519270	+	0.854610i	$0.673796\pi$
$252$	−356969.	−0.354102
$253$	−517477.	−0.508264
$254$	−697757.	−0.678609
$255$	−1.26363e6	−1.21694
$256$	−1.16707e6	−1.11300
$257$	−96893.1	−0.0915082	−0.0457541	−	0.998953i	$-0.514569\pi$
$257$	−96893.1	−0.0915082	−0.0457541	+	0.998953i	$0.514569\pi$
$258$	−2.38461e6	−2.23033
$259$	117798.	0.109116
$260$	−589260.	−0.540597
$261$	524416.	0.476513
$262$	−2.25972e6	−2.03377
$263$	−2.04166e6	−1.82010	−0.910048	−	0.414504i	$-0.863955\pi$
$263$	−2.04166e6	−1.82010	−0.910048	+	0.414504i	$0.863955\pi$
$264$	1.35139e6	1.19336
$265$	487737.	0.426649
$266$	−52904.7	−0.0458448
$267$	1.61503e6	1.38644
$268$	1.98399e6	1.68734
$269$	1.16811e6	0.984247	0.492124	−	0.870525i	$-0.336221\pi$
$269$	1.16811e6	0.984247	0.492124	+	0.870525i	$0.336221\pi$
$270$	−550103.	−0.459234
$271$	5263.47	0.00435360	0.00217680	−	0.999998i	$-0.499307\pi$
$271$	5263.47	0.00435360	0.00217680	+	0.999998i	$0.499307\pi$
$272$	−5.07430e6	−4.15867
$273$	103485.	0.0840367
$274$	−3.41098e6	−2.74475
$275$	−75625.0	−0.0603023
$276$	7.86011e6	6.21092
$277$	578215.	0.452783	0.226392	−	0.974036i	$-0.427307\pi$
$277$	578215.	0.452783	0.226392	+	0.974036i	$0.427307\pi$
$278$	2.81297e6	2.18300
$279$	1.15465e6	0.888057
$280$	163797.	0.124856
$281$	593502.	0.448391	0.224195	−	0.974544i	$-0.428025\pi$
$281$	593502.	0.448391	0.224195	+	0.974544i	$0.428025\pi$
$282$	−3.18500e6	−2.38499
$283$	422190.	0.313358	0.156679	−	0.987650i	$-0.449921\pi$
$283$	422190.	0.313358	0.156679	+	0.987650i	$0.449921\pi$
$284$	1.50886e6	1.11008
$285$	−216239.	−0.157697
$286$	−387655.	−0.280240
$287$	147848.	0.105953
$288$	−3.36476e6	−2.39041
$289$	3.03043e6	2.13432
$290$	−412866.	−0.288280
$291$	2.71374e6	1.87860
$292$	−201101.	−0.138025
$293$	118629.	0.0807274	0.0403637	−	0.999185i	$-0.487148\pi$
$293$	118629.	0.0807274	0.0403637	+	0.999185i	$0.487148\pi$
$294$	4.14926e6	2.79964
$295$	−629068.	−0.420865
$296$	3.90648e6	2.59153
$297$	−255364.	−0.167984
$298$	−3.53817e6	−2.30801
$299$	−1.31412e6	−0.850076
$300$	1.14869e6	0.736886
$301$	−134171.	−0.0853577
$302$	304516.	0.192129
$303$	2.55169e6	1.59670
$304$	−868339.	−0.538897
$305$	−495875.	−0.305227
$306$	7.28214e6	4.44586
$307$	−2.53172e6	−1.53310	−0.766548	−	0.642187i	$-0.778027\pi$
$307$	−2.53172e6	−1.53310	−0.766548	+	0.642187i	$0.778027\pi$
$308$	130461.	0.0783615
$309$	−467960.	−0.278813
$310$	−909044.	−0.537255
$311$	−1.77305e6	−1.03949	−0.519745	−	0.854322i	$-0.673973\pi$
$311$	−1.77305e6	−1.03949	−0.519745	+	0.854322i	$0.673973\pi$
$312$	3.43182e6	1.99590
$313$	958071.	0.552760	0.276380	−	0.961048i	$-0.410865\pi$
$313$	958071.	0.552760	0.276380	+	0.961048i	$0.410865\pi$
$314$	−2.52752e6	−1.44668
$315$	−116341.	−0.0660628
$316$	8.22440e6	4.63326
$317$	1.56617e6	0.875370	0.437685	−	0.899128i	$-0.355798\pi$
$317$	1.56617e6	0.875370	0.437685	+	0.899128i	$0.355798\pi$
$318$	−4.87373e6	−2.70267
$319$	−191657.	−0.105451
$320$	724734.	0.395643
$321$	−2.07187e6	−1.12228
$322$	626747.	0.336863
$323$	761555.	0.406158
$324$	−2.29252e6	−1.21325
$325$	−192048.	−0.100856
$326$	6.30484e6	3.28571
$327$	5.14387e6	2.66024
$328$	4.90305e6	2.51641
$329$	−179205.	−0.0912769
$330$	755686.	0.381994
$331$	−894202.	−0.448607	−0.224303	−	0.974519i	$-0.572011\pi$
$331$	−894202.	−0.448607	−0.224303	+	0.974519i	$0.572011\pi$
$332$	6.59634e6	3.28441
$333$	−2.77469e6	−1.37121
$334$	−2.66205e6	−1.30572
$335$	646611.	0.314797
$336$	−810078.	−0.391452
$337$	−3.58062e6	−1.71745	−0.858723	−	0.512440i	$-0.828742\pi$
$337$	−3.58062e6	−1.71745	−0.858723	+	0.512440i	$0.828742\pi$
$338$	2.88676e6	1.37442
$339$	−1.09459e6	−0.517310
$340$	−4.04549e6	−1.89790
$341$	−421989.	−0.196524
$342$	1.24616e6	0.576112
$343$	469697.	0.215567
$344$	−4.44947e6	−2.02727
$345$	2.56172e6	1.15874
$346$	55896.8	0.0251013
$347$	851351.	0.379564	0.189782	−	0.981826i	$-0.439222\pi$
$347$	851351.	0.379564	0.189782	+	0.981826i	$0.439222\pi$
$348$	2.91114e6	1.28859
$349$	−2.70359e6	−1.18817	−0.594084	−	0.804403i	$-0.702485\pi$
$349$	−2.70359e6	−1.18817	−0.594084	+	0.804403i	$0.702485\pi$
$350$	91594.0	0.0399666
$351$	−648493.	−0.280955
$352$	1.22971e6	0.528989
$353$	−748472.	−0.319697	−0.159849	−	0.987142i	$-0.551101\pi$
$353$	−748472.	−0.319697	−0.159849	+	0.987142i	$0.551101\pi$
$354$	6.28600e6	2.66604
$355$	491758.	0.207100
$356$	5.17047e6	2.16225
$357$	710459.	0.295031
$358$	−1.06985e6	−0.441178
$359$	2.77643e6	1.13697	0.568487	−	0.822692i	$-0.307529\pi$
$359$	2.77643e6	1.13697	0.568487	+	0.822692i	$0.307529\pi$
$360$	−3.85819e6	−1.56901
$361$	130321.	0.0526316
$362$	4.30934e6	1.72838
$363$	350799.	0.139730
$364$	331303.	0.131060
$365$	−65541.6	−0.0257505
$366$	4.95506e6	1.93351
$367$	1.31468e6	0.509511	0.254756	−	0.967005i	$-0.418005\pi$
$367$	1.31468e6	0.509511	0.254756	+	0.967005i	$0.418005\pi$
$368$	1.02870e7	3.95975
$369$	−3.48253e6	−1.33146
$370$	2.18448e6	0.829552
$371$	−274223.	−0.103435
$372$	6.40972e6	2.40150
$373$	2.02442e6	0.753407	0.376703	−	0.926334i	$-0.377058\pi$
$373$	2.02442e6	0.753407	0.376703	+	0.926334i	$0.377058\pi$
$374$	−2.66139e6	−0.983852
$375$	374375.	0.137477
$376$	−5.94293e6	−2.16786
$377$	−486710.	−0.176367
$378$	309287.	0.111335
$379$	−3.47696e6	−1.24337	−0.621686	−	0.783267i	$-0.713552\pi$
$379$	−3.47696e6	−1.24337	−0.621686	+	0.783267i	$0.713552\pi$
$380$	−692283.	−0.245937
$381$	1.60347e6	0.565912
$382$	1.02041e6	0.357780
$383$	345565.	0.120374	0.0601869	−	0.998187i	$-0.480830\pi$
$383$	345565.	0.120374	0.0601869	+	0.998187i	$0.480830\pi$
$384$	550164.	0.190399
$385$	42519.0	0.0146195
$386$	−326950.	−0.111690
$387$	3.16036e6	1.07265
$388$	8.68795e6	2.92980
$389$	4.93740e6	1.65434	0.827169	−	0.561953i	$-0.189950\pi$
$389$	4.93740e6	1.65434	0.827169	+	0.561953i	$0.189950\pi$
$390$	1.91905e6	0.638889
$391$	−9.02193e6	−2.98440
$392$	7.74216e6	2.54476
$393$	5.19292e6	1.69602
$394$	−9.08791e6	−2.94933
$395$	2.68045e6	0.864401
$396$	−3.07296e6	−0.984735
$397$	3.65145e6	1.16276	0.581378	−	0.813633i	$-0.302514\pi$
$397$	3.65145e6	1.16276	0.581378	+	0.813633i	$0.302514\pi$
$398$	−5.49761e6	−1.73967
$399$	121577.	0.0382314
$400$	1.50336e6	0.469799
$401$	384820.	0.119508	0.0597540	−	0.998213i	$-0.480968\pi$
$401$	384820.	0.119508	0.0597540	+	0.998213i	$0.480968\pi$
$402$	−6.46129e6	−1.99413
$403$	−1.07163e6	−0.328688
$404$	8.16917e6	2.49015
$405$	−747165.	−0.226349
$406$	232128.	0.0698895
$407$	1.01406e6	0.303444
$408$	2.35607e7	7.00710
$409$	4.35020e6	1.28588	0.642941	−	0.765915i	$-0.277714\pi$
$409$	4.35020e6	1.28588	0.642941	+	0.765915i	$0.277714\pi$
$410$	2.74175e6	0.805506
$411$	7.83858e6	2.28893
$412$	−1.49816e6	−0.434826
$413$	353684.	0.102033
$414$	−1.47629e7	−4.23321
$415$	2.14984e6	0.612754
$416$	3.12283e6	0.884739
$417$	−6.46432e6	−1.82047
$418$	−455430.	−0.127491
$419$	87516.0	0.0243530	0.0121765	−	0.999926i	$-0.496124\pi$
$419$	87516.0	0.0243530	0.0121765	+	0.999926i	$0.496124\pi$
$420$	−645835.	−0.178648
$421$	−3.17119e6	−0.872000	−0.436000	−	0.899947i	$-0.643605\pi$
$421$	−3.17119e6	−0.872000	−0.436000	+	0.899947i	$0.643605\pi$
$422$	4.71488e6	1.28881
$423$	4.22113e6	1.14704
$424$	−9.09395e6	−2.45662
$425$	−1.31848e6	−0.354080
$426$	−4.91392e6	−1.31191
$427$	278798.	0.0739981
$428$	−6.63304e6	−1.75026
$429$	890847.	0.233701
$430$	−2.48812e6	−0.648932
$431$	2.66777e6	0.691761	0.345880	−	0.938279i	$-0.387580\pi$
$431$	2.66777e6	0.691761	0.345880	+	0.938279i	$0.387580\pi$
$432$	5.07641e6	1.30872
$433$	−6.16043e6	−1.57903	−0.789517	−	0.613729i	$-0.789669\pi$
$433$	−6.16043e6	−1.57903	−0.789517	+	0.613729i	$0.789669\pi$
$434$	511096.	0.130250
$435$	948784.	0.240405
$436$	1.64679e7	4.14881
$437$	−1.54388e6	−0.386731
$438$	654928.	0.163120
$439$	4.03615e6	0.999553	0.499777	−	0.866154i	$-0.333415\pi$
$439$	4.03615e6	0.999553	0.499777	+	0.866154i	$0.333415\pi$
$440$	1.41004e6	0.347217
$441$	−5.49909e6	−1.34646
$442$	−6.75856e6	−1.64550
$443$	−1.57332e6	−0.380896	−0.190448	−	0.981697i	$-0.560994\pi$
$443$	−1.57332e6	−0.380896	−0.190448	+	0.981697i	$0.560994\pi$
$444$	−1.54029e7	−3.70804
$445$	1.68513e6	0.403398
$446$	−1.05746e7	−2.51725
$447$	8.13087e6	1.92472
$448$	−407471.	−0.0959183
$449$	5.13860e6	1.20290	0.601449	−	0.798911i	$-0.294590\pi$
$449$	5.13860e6	1.20290	0.601449	+	0.798911i	$0.294590\pi$
$450$	−2.15747e6	−0.502243
$451$	1.27275e6	0.294648
$452$	−3.50428e6	−0.806777
$453$	−699791.	−0.160222
$454$	−4.43605e6	−1.01008
$455$	107976.	0.0244512
$456$	4.03182e6	0.908008
$457$	−2.75361e6	−0.616753	−0.308377	−	0.951264i	$-0.599786\pi$
$457$	−2.75361e6	−0.616753	−0.308377	+	0.951264i	$0.599786\pi$
$458$	−3.63183e6	−0.809024
$459$	−4.45214e6	−0.986363
$460$	8.20128e6	1.80712
$461$	1.56850e6	0.343742	0.171871	−	0.985119i	$-0.445019\pi$
$461$	1.56850e6	0.343742	0.171871	+	0.985119i	$0.445019\pi$
$462$	−424873.	−0.0926093
$463$	7.11838e6	1.54322	0.771612	−	0.636094i	$-0.219451\pi$
$463$	7.11838e6	1.54322	0.771612	+	0.636094i	$0.219451\pi$
$464$	3.80998e6	0.821538
$465$	2.08902e6	0.448033
$466$	−1.16643e7	−2.48824
$467$	−4.35164e6	−0.923338	−0.461669	−	0.887052i	$-0.652749\pi$
$467$	−4.35164e6	−0.923338	−0.461669	+	0.887052i	$0.652749\pi$
$468$	−7.80374e6	−1.64698
$469$	−363547.	−0.0763183
$470$	−3.32324e6	−0.693933
$471$	5.80835e6	1.20643
$472$	1.17291e7	2.42332
$473$	−1.15501e6	−0.237374
$474$	−2.67845e7	−5.47568
$475$	−225625.	−0.0458831
$476$	2.27451e6	0.460120
$477$	6.45923e6	1.29983
$478$	1.62606e7	3.25513
$479$	−2.97775e6	−0.592993	−0.296497	−	0.955034i	$-0.595818\pi$
$479$	−2.97775e6	−0.592993	−0.296497	+	0.955034i	$0.595818\pi$
$480$	−6.08758e6	−1.20598
$481$	2.57519e6	0.507512
$482$	−5.21369e6	−1.02218
$483$	−1.44029e6	−0.280920
$484$	1.12307e6	0.217918
$485$	2.83153e6	0.546596
$486$	1.28131e7	2.46072
$487$	5.26511e6	1.00597	0.502985	−	0.864295i	$-0.332235\pi$
$487$	5.26511e6	1.00597	0.502985	+	0.864295i	$0.332235\pi$
$488$	9.24571e6	1.75748
$489$	−1.44888e7	−2.74006
$490$	4.32936e6	0.814580
$491$	1.48791e6	0.278531	0.139265	−	0.990255i	$-0.455526\pi$
$491$	1.48791e6	0.278531	0.139265	+	0.990255i	$0.455526\pi$
$492$	−1.93323e7	−3.60056
$493$	−3.34144e6	−0.619180
$494$	−1.15656e6	−0.213231
$495$	−1.00152e6	−0.183716
$496$	8.38877e6	1.53107
$497$	−276484.	−0.0502086
$498$	−2.14824e7	−3.88159
$499$	−5.66118e6	−1.01778	−0.508892	−	0.860830i	$-0.669945\pi$
$499$	−5.66118e6	−1.01778	−0.508892	+	0.860830i	$0.669945\pi$
$500$	1.19855e6	0.214403
$501$	6.11749e6	1.08888
$502$	1.08078e7	1.91416
$503$	1.07642e7	1.89698	0.948490	−	0.316806i	$-0.102610\pi$
$503$	1.07642e7	1.89698	0.948490	+	0.316806i	$0.102610\pi$
$504$	2.16921e6	0.380386
$505$	2.66245e6	0.464572
$506$	5.39535e6	0.936793
$507$	−6.63389e6	−1.14617
$508$	5.13347e6	0.882576
$509$	3.50938e6	0.600394	0.300197	−	0.953877i	$-0.402948\pi$
$509$	3.50938e6	0.600394	0.300197	+	0.953877i	$0.402948\pi$
$510$	1.31750e7	2.24298
$511$	36849.8	0.00624284
$512$	1.14334e7	1.92752
$513$	−761872.	−0.127817
$514$	1.01023e6	0.168661
$515$	−488272.	−0.0811230
$516$	1.75438e7	2.90068
$517$	−1.54269e6	−0.253835
$518$	−1.22819e6	−0.201114
$519$	−128453.	−0.0209328
$520$	3.58078e6	0.580724
$521$	−1.09556e7	−1.76824	−0.884120	−	0.467260i	$-0.845241\pi$
$521$	−1.09556e7	−1.76824	−0.884120	+	0.467260i	$0.845241\pi$
$522$	−5.46771e6	−0.878272
$523$	2.67919e6	0.428302	0.214151	−	0.976801i	$-0.431302\pi$
$523$	2.67919e6	0.428302	0.214151	+	0.976801i	$0.431302\pi$
$524$	1.66250e7	2.64505
$525$	−210487.	−0.0333293
$526$	2.12869e7	3.35466
$527$	−7.35715e6	−1.15394
$528$	−6.97356e6	−1.08860
$529$	1.18535e7	1.84166
$530$	−5.08528e6	−0.786366
$531$	−8.33093e6	−1.28220
$532$	389226.	0.0596242
$533$	3.23214e6	0.492801
$534$	−1.68388e7	−2.55539
$535$	−2.16180e6	−0.326537
$536$	−1.20562e7	−1.81259
$537$	2.45855e6	0.367912
$538$	−1.21791e7	−1.81409
$539$	2.00974e6	0.297967
$540$	4.04717e6	0.597264
$541$	−5.45451e6	−0.801240	−0.400620	−	0.916244i	$-0.631205\pi$
$541$	−5.45451e6	−0.801240	−0.400620	+	0.916244i	$0.631205\pi$
$542$	−54878.4	−0.00802422
$543$	−9.90303e6	−1.44135
$544$	2.14394e7	3.10610
$545$	5.36714e6	0.774019
$546$	−1.07896e6	−0.154890
$547$	6.51305e6	0.930714	0.465357	−	0.885123i	$-0.345926\pi$
$547$	6.51305e6	0.930714	0.465357	+	0.885123i	$0.345926\pi$
$548$	2.50950e7	3.56973
$549$	−6.56702e6	−0.929903
$550$	788487.	0.111144
$551$	−571804.	−0.0802358
$552$	−4.77639e7	−6.67194
$553$	−1.50704e6	−0.209562
$554$	−6.02863e6	−0.834535
$555$	−5.02002e6	−0.691788
$556$	−2.06953e7	−2.83913
$557$	−6.70737e6	−0.916040	−0.458020	−	0.888942i	$-0.651441\pi$
$557$	−6.70737e6	−0.916040	−0.458020	+	0.888942i	$0.651441\pi$
$558$	−1.20387e7	−1.63680
$559$	−2.93313e6	−0.397011
$560$	−845240.	−0.113896
$561$	6.11599e6	0.820464
$562$	−6.18802e6	−0.826439
$563$	4.08097e6	0.542615	0.271308	−	0.962493i	$-0.412544\pi$
$563$	4.08097e6	0.542615	0.271308	+	0.962493i	$0.412544\pi$
$564$	2.34324e7	3.10184
$565$	−1.14210e6	−0.150516
$566$	−4.40187e6	−0.577558
$567$	420082.	0.0548753
$568$	−9.16894e6	−1.19247
$569$	−6.53990e6	−0.846819	−0.423410	−	0.905938i	$-0.639167\pi$
$569$	−6.53990e6	−0.846819	−0.423410	+	0.905938i	$0.639167\pi$
$570$	2.25457e6	0.290654
$571$	−1.12862e7	−1.44864	−0.724318	−	0.689466i	$-0.757845\pi$
$571$	−1.12862e7	−1.44864	−0.724318	+	0.689466i	$0.757845\pi$
$572$	2.85202e6	0.364470
$573$	−2.34494e6	−0.298363
$574$	−1.54151e6	−0.195284
$575$	2.67292e6	0.337144
$576$	9.59786e6	1.20536
$577$	−1.08951e7	−1.36236	−0.681178	−	0.732118i	$-0.738532\pi$
$577$	−1.08951e7	−1.36236	−0.681178	+	0.732118i	$0.738532\pi$
$578$	−3.15961e7	−3.93382
$579$	751345.	0.0931415
$580$	3.03750e6	0.374927
$581$	−1.20872e6	−0.148554
$582$	−2.82942e7	−3.46250
$583$	−2.36064e6	−0.287647
$584$	1.22204e6	0.148270
$585$	−2.54335e6	−0.307267
$586$	−1.23686e6	−0.148790
$587$	8.72634e6	1.04529	0.522645	−	0.852550i	$-0.324945\pi$
$587$	8.72634e6	1.04529	0.522645	+	0.852550i	$0.324945\pi$
$588$	−3.05266e7	−3.64112
$589$	−1.25899e6	−0.149532
$590$	6.55884e6	0.775706
$591$	2.08844e7	2.45954
$592$	−2.01586e7	−2.36405
$593$	−8.61838e6	−1.00644	−0.503221	−	0.864158i	$-0.667852\pi$
$593$	−8.61838e6	−1.00644	−0.503221	+	0.864158i	$0.667852\pi$
$594$	2.66250e6	0.309616
$595$	741296.	0.0858419
$596$	2.60307e7	3.00172
$597$	1.26337e7	1.45076
$598$	1.37014e7	1.56680
$599$	−1.58853e7	−1.80895	−0.904477	−	0.426523i	$-0.859738\pi$
$599$	−1.58853e7	−1.80895	−0.904477	+	0.426523i	$0.859738\pi$
$600$	−6.98031e6	−0.791583
$601$	−8.94528e6	−1.01020	−0.505100	−	0.863061i	$-0.668545\pi$
$601$	−8.94528e6	−1.01020	−0.505100	+	0.863061i	$0.668545\pi$
$602$	1.39891e6	0.157325
$603$	8.56325e6	0.959059
$604$	−2.24036e6	−0.249876
$605$	366025.	0.0406558
$606$	−2.66047e7	−2.94291
$607$	5.48853e6	0.604622	0.302311	−	0.953209i	$-0.402242\pi$
$607$	5.48853e6	0.604622	0.302311	+	0.953209i	$0.402242\pi$
$608$	3.66881e6	0.402500
$609$	−533439.	−0.0582830
$610$	5.17014e6	0.562571
$611$	−3.91763e6	−0.424542
$612$	−5.35755e7	−5.78213
$613$	9.12134e6	0.980409	0.490205	−	0.871607i	$-0.336922\pi$
$613$	9.12134e6	0.980409	0.490205	+	0.871607i	$0.336922\pi$
$614$	2.63964e7	2.82569
$615$	−6.30066e6	−0.671735
$616$	−792776.	−0.0841780
$617$	1.56160e7	1.65142	0.825711	−	0.564093i	$-0.190774\pi$
$617$	1.56160e7	1.65142	0.825711	+	0.564093i	$0.190774\pi$
$618$	4.87908e6	0.513886
$619$	−46355.8	−0.00486270	−0.00243135	−	0.999997i	$-0.500774\pi$
$619$	−46355.8	−0.00486270	−0.00243135	+	0.999997i	$0.500774\pi$
$620$	6.68794e6	0.698736
$621$	9.02568e6	0.939184
$622$	1.84863e7	1.91591
$623$	−947439.	−0.0977983
$624$	−1.77092e7	−1.82070
$625$	390625.	0.0400000
$626$	−9.98912e6	−1.01881
$627$	1.04660e6	0.106319
$628$	1.85953e7	1.88150
$629$	1.76796e7	1.78175
$630$	1.21301e6	0.121762
$631$	−6.45690e6	−0.645581	−0.322790	−	0.946471i	$-0.604621\pi$
$631$	−6.45690e6	−0.645581	−0.322790	+	0.946471i	$0.604621\pi$
$632$	−4.99776e7	−4.97717
$633$	−1.08350e7	−1.07478
$634$	−1.63294e7	−1.61342
$635$	1.67307e6	0.164657
$636$	3.58566e7	3.51501
$637$	5.10370e6	0.498353
$638$	1.99827e6	0.194358
$639$	6.51249e6	0.630950
$640$	574044.	0.0553981
$641$	5.95660e6	0.572603	0.286301	−	0.958140i	$-0.407574\pi$
$641$	5.95660e6	0.572603	0.286301	+	0.958140i	$0.407574\pi$
$642$	2.16019e7	2.06850
$643$	−3.35378e6	−0.319895	−0.159947	−	0.987126i	$-0.551132\pi$
$643$	−3.35378e6	−0.319895	−0.159947	+	0.987126i	$0.551132\pi$
$644$	−4.61105e6	−0.438112
$645$	5.71779e6	0.541164
$646$	−7.94018e6	−0.748599
$647$	2.47133e6	0.232098	0.116049	−	0.993244i	$-0.462977\pi$
$647$	2.47133e6	0.232098	0.116049	+	0.993244i	$0.462977\pi$
$648$	1.39311e7	1.30331
$649$	3.04469e6	0.283747
$650$	2.00235e6	0.185890
$651$	−1.17452e6	−0.108620
$652$	−4.63854e7	−4.27329
$653$	−1.95295e6	−0.179229	−0.0896147	−	0.995977i	$-0.528564\pi$
$653$	−1.95295e6	−0.179229	−0.0896147	+	0.995977i	$0.528564\pi$
$654$	−5.36314e7	−4.90315
$655$	5.41832e6	0.493471
$656$	−2.53012e7	−2.29552
$657$	−867986.	−0.0784511
$658$	1.86844e6	0.168235
$659$	1.66635e7	1.49470	0.747349	−	0.664432i	$-0.231327\pi$
$659$	1.66635e7	1.49470	0.747349	+	0.664432i	$0.231327\pi$
$660$	−5.55967e6	−0.496809
$661$	1.49073e6	0.132707	0.0663535	−	0.997796i	$-0.478863\pi$
$661$	1.49073e6	0.132707	0.0663535	+	0.997796i	$0.478863\pi$
$662$	9.32320e6	0.826837
$663$	1.55314e7	1.37223
$664$	−4.00843e7	−3.52821
$665$	126854.	0.0111237
$666$	2.89297e7	2.52731
$667$	6.77400e6	0.589564
$668$	1.95850e7	1.69817
$669$	2.43008e7	2.09921
$670$	−6.74174e6	−0.580210
$671$	2.40004e6	0.205784
$672$	3.42265e6	0.292375
$673$	1.02316e7	0.870772	0.435386	−	0.900244i	$-0.356612\pi$
$673$	1.02316e7	0.870772	0.435386	+	0.900244i	$0.356612\pi$
$674$	3.73325e7	3.16546
$675$	1.31903e6	0.111428
$676$	−2.12382e7	−1.78752
$677$	2.24112e7	1.87929	0.939644	−	0.342155i	$-0.111157\pi$
$677$	2.24112e7	1.87929	0.939644	+	0.342155i	$0.111157\pi$
$678$	1.14125e7	0.953465
$679$	−1.59198e6	−0.132515
$680$	2.45834e7	2.03877
$681$	1.01942e7	0.842338
$682$	4.39977e6	0.362218
$683$	2.05024e7	1.68172	0.840859	−	0.541255i	$-0.182050\pi$
$683$	2.05024e7	1.68172	0.840859	+	0.541255i	$0.182050\pi$
$684$	−9.16810e6	−0.749271
$685$	8.17881e6	0.665984
$686$	−4.89719e6	−0.397317
$687$	8.34608e6	0.674669
$688$	2.29606e7	1.84932
$689$	−5.99482e6	−0.481092
$690$	−2.67092e7	−2.13569
$691$	3.24877e6	0.258835	0.129418	−	0.991590i	$-0.458689\pi$
$691$	3.24877e6	0.258835	0.129418	+	0.991590i	$0.458689\pi$
$692$	−411239.	−0.0326459
$693$	563091.	0.0445395
$694$	−8.87642e6	−0.699583
$695$	−6.74491e6	−0.529681
$696$	−1.76903e7	−1.38424
$697$	2.21898e7	1.73010
$698$	2.81884e7	2.18994
$699$	2.68050e7	2.07502
$700$	−673867.	−0.0519792
$701$	−1.70070e7	−1.30717	−0.653586	−	0.756852i	$-0.726736\pi$
$701$	−1.70070e7	−1.30717	−0.653586	+	0.756852i	$0.726736\pi$
$702$	6.76137e6	0.517835
$703$	3.02542e6	0.230886
$704$	−3.50771e6	−0.266743
$705$	7.63695e6	0.578692
$706$	7.80378e6	0.589241
$707$	−1.49692e6	−0.112629
$708$	−4.62468e7	−3.46735
$709$	−6.98459e6	−0.521826	−0.260913	−	0.965362i	$-0.584024\pi$
$709$	−6.98459e6	−0.521826	−0.260913	+	0.965362i	$0.584024\pi$
$710$	−5.12721e6	−0.381711
$711$	3.54980e7	2.63348
$712$	−3.14196e7	−2.32274
$713$	1.49149e7	1.09875
$714$	−7.40744e6	−0.543779
$715$	929514.	0.0679972
$716$	7.87099e6	0.573782
$717$	−3.73676e7	−2.71455
$718$	−2.89478e7	−2.09558
$719$	−1.06389e7	−0.767493	−0.383747	−	0.923438i	$-0.625366\pi$
$719$	−1.06389e7	−0.767493	−0.383747	+	0.923438i	$0.625366\pi$
$720$	1.99094e7	1.43129
$721$	274524.	0.0196672
$722$	−1.35876e6	−0.0970065
$723$	1.19813e7	0.852427
$724$	−3.17043e7	−2.24787
$725$	989966.	0.0699480
$726$	−3.65752e6	−0.257540
$727$	6.92620e6	0.486025	0.243013	−	0.970023i	$-0.421864\pi$
$727$	6.92620e6	0.486025	0.243013	+	0.970023i	$0.421864\pi$
$728$	−2.01324e6	−0.140789
$729$	−2.21825e7	−1.54594
$730$	683355.	0.0474612
$731$	−2.01370e7	−1.39380
$732$	−3.64549e7	−2.51466
$733$	−2.42428e7	−1.66657	−0.833284	−	0.552846i	$-0.813542\pi$
$733$	−2.42428e7	−1.66657	−0.833284	+	0.552846i	$0.813542\pi$
$734$	−1.37072e7	−0.939092
$735$	−9.94905e6	−0.679303
$736$	−4.34634e7	−2.95753
$737$	−3.12960e6	−0.212236
$738$	3.63098e7	2.45405
$739$	−2.60621e7	−1.75549	−0.877744	−	0.479130i	$-0.840952\pi$
$739$	−2.60621e7	−1.75549	−0.877744	+	0.479130i	$0.840952\pi$
$740$	−1.60715e7	−1.07889
$741$	2.65782e6	0.177819
$742$	2.85912e6	0.190644
$743$	−4.03062e6	−0.267855	−0.133928	−	0.990991i	$-0.542759\pi$
$743$	−4.03062e6	−0.267855	−0.133928	+	0.990991i	$0.542759\pi$
$744$	−3.89502e7	−2.57975
$745$	8.48379e6	0.560014
$746$	−2.11072e7	−1.38862
$747$	2.84710e7	1.86681
$748$	1.95801e7	1.27956
$749$	1.21544e6	0.0791643
$750$	−3.90334e6	−0.253386
$751$	8.33860e6	0.539503	0.269751	−	0.962930i	$-0.413059\pi$
$751$	8.33860e6	0.539503	0.269751	+	0.962930i	$0.413059\pi$
$752$	3.06673e7	1.97756
$753$	−2.48368e7	−1.59627
$754$	5.07458e6	0.325066
$755$	−730165.	−0.0466180
$756$	−2.27546e6	−0.144799
$757$	−2.34044e7	−1.48442	−0.742212	−	0.670166i	$-0.766223\pi$
$757$	−2.34044e7	−1.48442	−0.742212	+	0.670166i	$0.766223\pi$
$758$	3.62517e7	2.29169
$759$	−1.23987e7	−0.781220
$760$	4.20683e6	0.264193
$761$	685858.	0.0429312	0.0214656	−	0.999770i	$-0.493167\pi$
$761$	685858.	0.0429312	0.0214656	+	0.999770i	$0.493167\pi$
$762$	−1.67183e7	−1.04305
$763$	−3.01759e6	−0.187650
$764$	−7.50726e6	−0.465316
$765$	−1.74610e7	−1.07874
$766$	−3.60295e6	−0.221864
$767$	7.73194e6	0.474570
$768$	−2.79629e7	−1.71072
$769$	−2.76018e7	−1.68315	−0.841573	−	0.540143i	$-0.818370\pi$
$769$	−2.76018e7	−1.68315	−0.841573	+	0.540143i	$0.818370\pi$
$770$	−443315.	−0.0269455
$771$	−2.32156e6	−0.140651
$772$	2.40541e6	0.145260
$773$	2.00066e7	1.20427	0.602137	−	0.798393i	$-0.294316\pi$
$773$	2.00066e7	1.20427	0.602137	+	0.798393i	$0.294316\pi$
$774$	−3.29508e7	−1.97703
$775$	2.17970e6	0.130359
$776$	−5.27944e7	−3.14727
$777$	2.82243e6	0.167715
$778$	−5.14787e7	−3.04915
$779$	3.79722e6	0.224193
$780$	−1.41187e7	−0.830917
$781$	−2.38011e6	−0.139627
$782$	9.40651e7	5.50062
$783$	3.34283e6	0.194854
$784$	−3.99519e7	−2.32138
$785$	6.06047e6	0.351020
$786$	−5.41429e7	−3.12597
$787$	2.49245e7	1.43447	0.717233	−	0.696833i	$-0.245408\pi$
$787$	2.49245e7	1.43447	0.717233	+	0.696833i	$0.245408\pi$
$788$	6.68608e7	3.83580
$789$	−4.89182e7	−2.79755
$790$	−2.79471e7	−1.59320
$791$	642127.	0.0364905
$792$	1.86736e7	1.05783
$793$	6.09485e6	0.344176
$794$	−3.80710e7	−2.14310
$795$	1.16862e7	0.655774
$796$	4.04465e7	2.26255
$797$	1.02597e7	0.572120	0.286060	−	0.958212i	$-0.407654\pi$
$797$	1.02597e7	0.572120	0.286060	+	0.958212i	$0.407654\pi$
$798$	−1.26760e6	−0.0704651
$799$	−2.68960e7	−1.49046
$800$	−6.35182e6	−0.350892
$801$	2.23167e7	1.22899
$802$	−4.01224e6	−0.220268
$803$	317221.	0.0173610
$804$	4.75364e7	2.59350
$805$	−1.50281e6	−0.0817360
$806$	1.11732e7	0.605812
$807$	2.79880e7	1.51282
$808$	−4.96420e7	−2.67498
$809$	−6.40889e6	−0.344280	−0.172140	−	0.985073i	$-0.555068\pi$
$809$	−6.40889e6	−0.344280	−0.172140	+	0.985073i	$0.555068\pi$
$810$	7.79015e6	0.417189
$811$	2.61406e7	1.39561	0.697805	−	0.716288i	$-0.254160\pi$
$811$	2.61406e7	1.39561	0.697805	+	0.716288i	$0.254160\pi$
$812$	−1.70779e6	−0.0908959
$813$	126113.	0.00669164
$814$	−1.05729e7	−0.559284
$815$	−1.51177e7	−0.797242
$816$	−1.21580e8	−6.39202
$817$	−3.44595e6	−0.180615
$818$	−4.53564e7	−2.37004
$819$	1.42996e6	0.0744928
$820$	−2.01714e7	−1.04761
$821$	2.74201e7	1.41975	0.709874	−	0.704329i	$-0.248752\pi$
$821$	2.74201e7	1.41975	0.709874	+	0.704329i	$0.248752\pi$
$822$	−8.17272e7	−4.21878
$823$	3.52103e7	1.81205	0.906025	−	0.423225i	$-0.139102\pi$
$823$	3.52103e7	1.81205	0.906025	+	0.423225i	$0.139102\pi$
$824$	9.10394e6	0.467101
$825$	−1.81198e6	−0.0926867
$826$	−3.68761e6	−0.188059
$827$	−2.06868e7	−1.05179	−0.525896	−	0.850549i	$-0.676270\pi$
$827$	−2.06868e7	−1.05179	−0.525896	+	0.850549i	$0.676270\pi$
$828$	1.08612e8	5.50556
$829$	−1.18447e7	−0.598602	−0.299301	−	0.954159i	$-0.596753\pi$
$829$	−1.18447e7	−0.598602	−0.299301	+	0.954159i	$0.596753\pi$
$830$	−2.24149e7	−1.12938
$831$	1.38540e7	0.695943
$832$	−8.90778e6	−0.446130
$833$	3.50388e7	1.74959
$834$	6.73988e7	3.35534
$835$	6.38303e6	0.316818
$836$	3.35065e6	0.165811
$837$	7.36021e6	0.363142
$838$	−912466.	−0.0448856
$839$	9.21162e6	0.451784	0.225892	−	0.974152i	$-0.427470\pi$
$839$	9.21162e6	0.451784	0.225892	+	0.974152i	$0.427470\pi$
$840$	3.92457e6	0.191908
$841$	−1.80023e7	−0.877682
$842$	3.30637e7	1.60720
$843$	1.42203e7	0.689192
$844$	−3.46879e7	−1.67618
$845$	−6.92184e6	−0.333488
$846$	−4.40107e7	−2.11413
$847$	−205792.	−0.00985644
$848$	4.69275e7	2.24098
$849$	1.01157e7	0.481643
$850$	1.37469e7	0.652614
$851$	−3.58413e7	−1.69652
$852$	3.61522e7	1.70622
$853$	2.40976e7	1.13397	0.566984	−	0.823729i	$-0.308110\pi$
$853$	2.40976e7	1.13397	0.566984	+	0.823729i	$0.308110\pi$
$854$	−2.90683e6	−0.136388
$855$	−2.98802e6	−0.139787
$856$	4.03073e7	1.88018
$857$	−3.51219e7	−1.63353	−0.816763	−	0.576974i	$-0.804234\pi$
$857$	−3.51219e7	−1.63353	−0.816763	+	0.576974i	$0.804234\pi$
$858$	−9.28821e6	−0.430739
$859$	−1.09177e7	−0.504834	−0.252417	−	0.967619i	$-0.581226\pi$
$859$	−1.09177e7	−0.504834	−0.252417	+	0.967619i	$0.581226\pi$
$860$	1.83053e7	0.843979
$861$	3.54245e6	0.162853
$862$	−2.78150e7	−1.27500
$863$	−1.38845e6	−0.0634605	−0.0317303	−	0.999496i	$-0.510102\pi$
$863$	−1.38845e6	−0.0634605	−0.0317303	+	0.999496i	$0.510102\pi$
$864$	−2.14483e7	−0.977480
$865$	−134029.	−0.00609057
$866$	6.42304e7	2.91035
$867$	7.26092e7	3.28053
$868$	−3.76019e6	−0.169399
$869$	−1.29734e7	−0.582779
$870$	−9.89228e6	−0.443096
$871$	−7.94756e6	−0.354967
$872$	−1.00072e8	−4.45676
$873$	3.74987e7	1.66525
$874$	1.60969e7	0.712793
$875$	−219623.	−0.00969745
$876$	−4.81837e6	−0.212149
$877$	3.19928e6	0.140460	0.0702301	−	0.997531i	$-0.477627\pi$
$877$	3.19928e6	0.140460	0.0702301	+	0.997531i	$0.477627\pi$
$878$	−4.20820e7	−1.84230
$879$	2.84235e6	0.124081
$880$	−7.27625e6	−0.316739
$881$	3.26300e7	1.41637	0.708186	−	0.706026i	$-0.249514\pi$
$881$	3.26300e7	1.41637	0.708186	+	0.706026i	$0.249514\pi$
$882$	5.73350e7	2.48169
$883$	9.68841e6	0.418168	0.209084	−	0.977898i	$-0.432952\pi$
$883$	9.68841e6	0.418168	0.209084	+	0.977898i	$0.432952\pi$
$884$	4.97234e7	2.14008
$885$	−1.50725e7	−0.646884
$886$	1.64038e7	0.702038
$887$	−1.50380e7	−0.641773	−0.320886	−	0.947118i	$-0.603981\pi$
$887$	−1.50380e7	−0.641773	−0.320886	+	0.947118i	$0.603981\pi$
$888$	9.35994e7	3.98328
$889$	−940660.	−0.0399189
$890$	−1.75696e7	−0.743512
$891$	3.61628e6	0.152605
$892$	7.77984e7	3.27385
$893$	−4.60257e6	−0.193140
$894$	−8.47747e7	−3.54750
$895$	2.56527e6	0.107047
$896$	−322748.	−0.0134305
$897$	−3.14864e7	−1.30660
$898$	−5.35765e7	−2.21709
$899$	5.52403e6	0.227959
$900$	1.58728e7	0.653200
$901$	−4.11566e7	−1.68899
$902$	−1.32701e7	−0.543072
$903$	−3.21474e6	−0.131198
$904$	2.12946e7	0.866661
$905$	−1.03329e7	−0.419372
$906$	7.29621e6	0.295309
$907$	−1.81609e7	−0.733025	−0.366513	−	0.930413i	$-0.619448\pi$
$907$	−1.81609e7	−0.733025	−0.366513	+	0.930413i	$0.619448\pi$
$908$	3.26365e7	1.31368
$909$	3.52596e7	1.41536
$910$	−1.12579e6	−0.0450665
$911$	−2.43731e7	−0.973003	−0.486501	−	0.873680i	$-0.661727\pi$
$911$	−2.43731e7	−0.973003	−0.486501	+	0.873680i	$0.661727\pi$
$912$	−2.08054e7	−0.828303
$913$	−1.04052e7	−0.413119
$914$	2.87099e7	1.13675
$915$	−1.18812e7	−0.469145
$916$	2.67197e7	1.05219
$917$	−3.04637e6	−0.119635
$918$	4.64192e7	1.81799
$919$	−3.38897e7	−1.32367	−0.661834	−	0.749651i	$-0.730221\pi$
$919$	−3.38897e7	−1.32367	−0.661834	+	0.749651i	$0.730221\pi$
$920$	−4.98371e7	−1.94126
$921$	−6.06600e7	−2.35642
$922$	−1.63536e7	−0.633559
$923$	−6.04425e6	−0.233528
$924$	3.12584e6	0.120444
$925$	−5.23792e6	−0.201282
$926$	−7.42182e7	−2.84435
$927$	−6.46633e6	−0.247149
$928$	−1.60975e7	−0.613604
$929$	4.62191e7	1.75704	0.878522	−	0.477703i	$-0.158530\pi$
$929$	4.62191e7	1.75704	0.878522	+	0.477703i	$0.158530\pi$
$930$	−2.17807e7	−0.825781
$931$	5.99601e6	0.226719
$932$	8.58154e7	3.23612
$933$	−4.24823e7	−1.59773
$934$	4.53714e7	1.70183
$935$	6.38145e6	0.238721
$936$	4.74213e7	1.76923
$937$	−2.21448e6	−0.0823991	−0.0411995	−	0.999151i	$-0.513118\pi$
$937$	−2.21448e6	−0.0823991	−0.0411995	+	0.999151i	$0.513118\pi$
$938$	3.79044e6	0.140664
$939$	2.29554e7	0.849612
$940$	2.44495e7	0.902506
$941$	5.14983e7	1.89591	0.947957	−	0.318398i	$-0.103145\pi$
$941$	5.14983e7	1.89591	0.947957	+	0.318398i	$0.103145\pi$
$942$	−6.05595e7	−2.22359
$943$	−4.49847e7	−1.64735
$944$	−6.05257e7	−2.21060
$945$	−741604.	−0.0270142
$946$	1.20425e7	0.437510
$947$	4.82995e7	1.75012	0.875060	−	0.484015i	$-0.160822\pi$
$947$	4.82995e7	1.75012	0.875060	+	0.484015i	$0.160822\pi$
$948$	1.97057e8	7.12149
$949$	805578.	0.0290364
$950$	2.35243e6	0.0845683
$951$	3.75255e7	1.34548
$952$	−1.38216e7	−0.494273
$953$	2.22865e7	0.794895	0.397447	−	0.917625i	$-0.369896\pi$
$953$	2.22865e7	0.794895	0.397447	+	0.917625i	$0.369896\pi$
$954$	−6.73458e7	−2.39574
$955$	−2.44672e6	−0.0868113
$956$	−1.19631e8	−4.23350
$957$	−4.59211e6	−0.162081
$958$	3.10469e7	1.09296
$959$	−4.59841e6	−0.161459
$960$	1.73646e7	0.608118
$961$	−1.64664e7	−0.575162
$962$	−2.68496e7	−0.935408
$963$	−2.86294e7	−0.994824
$964$	3.83577e7	1.32941
$965$	783958.	0.0271003
$966$	1.50169e7	0.517770
$967$	2.63065e7	0.904686	0.452343	−	0.891844i	$-0.350588\pi$
$967$	2.63065e7	0.904686	0.452343	+	0.891844i	$0.350588\pi$
$968$	−6.82461e6	−0.234094
$969$	1.82469e7	0.624279
$970$	−2.95223e7	−1.00744
$971$	3.58157e6	0.121906	0.0609530	−	0.998141i	$-0.480586\pi$
$971$	3.58157e6	0.121906	0.0609530	+	0.998141i	$0.480586\pi$
$972$	−9.42672e7	−3.20033
$973$	3.79222e6	0.128414
$974$	−5.48955e7	−1.85413
$975$	−4.60148e6	−0.155019
$976$	−4.77106e7	−1.60321
$977$	−1.36559e7	−0.457705	−0.228852	−	0.973461i	$-0.573497\pi$
$977$	−1.36559e7	−0.457705	−0.228852	+	0.973461i	$0.573497\pi$
$978$	1.51064e8	5.05026
$979$	−8.15603e6	−0.271971
$980$	−3.18516e7	−1.05941
$981$	7.10786e7	2.35812
$982$	−1.55134e7	−0.513366
$983$	2.80941e7	0.927324	0.463662	−	0.886012i	$-0.346535\pi$
$983$	2.80941e7	0.927324	0.463662	+	0.886012i	$0.346535\pi$
$984$	1.17477e8	3.86782
$985$	2.17909e7	0.715623
$986$	3.48388e7	1.14122
$987$	−4.29376e6	−0.140296
$988$	8.50892e6	0.277320
$989$	4.08232e7	1.32714
$990$	1.04422e7	0.338612
$991$	9.94402e6	0.321646	0.160823	−	0.986983i	$-0.448585\pi$
$991$	9.94402e6	0.321646	0.160823	+	0.986983i	$0.448585\pi$
$992$	−3.54433e7	−1.14355
$993$	−2.14251e7	−0.689524
$994$	2.88270e6	0.0925407
$995$	1.31821e7	0.422111
$996$	1.58048e8	5.04826
$997$	8.15400e6	0.259796	0.129898	−	0.991527i	$-0.458535\pi$
$997$	8.15400e6	0.259796	0.129898	+	0.991527i	$0.458535\pi$
$998$	5.90251e7	1.87590
$999$	−1.76870e7	−0.560712

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.f.1.2	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.f.1.2	✓	38	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)

\(f(q)\)	\(=\)	\(q-10.4263 q^{2} +23.9600 q^{3} +76.7073 q^{4} +25.0000 q^{5} -249.814 q^{6} -14.0559 q^{7} -466.130 q^{8} +331.082 q^{9} +O(q^{10})\)	\(q-10.4263 q^{2} +23.9600 q^{3} +76.7073 q^{4} +25.0000 q^{5} -249.814 q^{6} -14.0559 q^{7} -466.130 q^{8} +331.082 q^{9} -260.657 q^{10} -121.000 q^{11} +1837.91 q^{12} -307.277 q^{13} +146.550 q^{14} +599.000 q^{15} +2405.37 q^{16} -2109.57 q^{17} -3451.95 q^{18} -361.000 q^{19} +1917.68 q^{20} -336.779 q^{21} +1261.58 q^{22} +4276.67 q^{23} -11168.5 q^{24} +625.000 q^{25} +3203.76 q^{26} +2110.45 q^{27} -1078.19 q^{28} +1583.95 q^{29} -6245.34 q^{30} +3487.51 q^{31} -10162.9 q^{32} -2899.16 q^{33} +21995.0 q^{34} -351.397 q^{35} +25396.4 q^{36} -8380.67 q^{37} +3763.89 q^{38} -7362.37 q^{39} -11653.3 q^{40} -10518.6 q^{41} +3511.35 q^{42} +9545.56 q^{43} -9281.58 q^{44} +8277.05 q^{45} -44589.7 q^{46} +12749.5 q^{47} +57632.7 q^{48} -16609.4 q^{49} -6516.42 q^{50} -50545.3 q^{51} -23570.4 q^{52} +19509.5 q^{53} -22004.1 q^{54} -3025.00 q^{55} +6551.87 q^{56} -8649.56 q^{57} -16514.7 q^{58} -25162.7 q^{59} +45947.7 q^{60} -19835.0 q^{61} -36361.8 q^{62} -4653.65 q^{63} +28989.4 q^{64} -7681.93 q^{65} +30227.5 q^{66} +25864.4 q^{67} -161819. q^{68} +102469. q^{69} +3663.76 q^{70} +19670.3 q^{71} -154327. q^{72} -2621.66 q^{73} +87379.2 q^{74} +14975.0 q^{75} -27691.3 q^{76} +1700.76 q^{77} +76762.1 q^{78} +107218. q^{79} +60134.3 q^{80} -29886.6 q^{81} +109670. q^{82} +85993.7 q^{83} -25833.4 q^{84} -52739.3 q^{85} -99524.6 q^{86} +37951.3 q^{87} +56401.8 q^{88} +67405.2 q^{89} -86298.8 q^{90} +4319.05 q^{91} +328051. q^{92} +83560.8 q^{93} -132930. q^{94} -9025.00 q^{95} -243503. q^{96} +113261. q^{97} +173175. q^{98} -40060.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9}+O(q^{10}) \) 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9} + 200 q^{10} - 4598 q^{11} + 2312 q^{12} + 41 q^{13} + 23 q^{14} + 1575 q^{15} + 7196 q^{16} - 2431 q^{17} - 1689 q^{18} - 13718 q^{19} + 15400 q^{20} - 1577 q^{21} - 968 q^{22} + 9284 q^{23} + 7598 q^{24} + 23750 q^{25} + 13129 q^{26} + 9228 q^{27} - 1079 q^{28} - 559 q^{29} + 3725 q^{30} + 11147 q^{31} + 11051 q^{32} - 7623 q^{33} + 40895 q^{34} + 6875 q^{35} + 55887 q^{36} + 41579 q^{37} - 2888 q^{38} + 24982 q^{39} + 6600 q^{40} + 18597 q^{41} + 61360 q^{42} + 25353 q^{43} - 74536 q^{44} + 75725 q^{45} + 1611 q^{46} + 63516 q^{47} + 187737 q^{48} + 141609 q^{49} + 5000 q^{50} + 107546 q^{51} + 60018 q^{52} + 123045 q^{53} + 256696 q^{54} - 114950 q^{55} + 157335 q^{56} - 22743 q^{57} + 218938 q^{58} + 132925 q^{59} + 57800 q^{60} - 59107 q^{61} + 166982 q^{62} + 130582 q^{63} + 313126 q^{64} + 1025 q^{65} - 18029 q^{66} + 162534 q^{67} + 182980 q^{68} + 178552 q^{69} + 575 q^{70} + 157840 q^{71} + 98630 q^{72} - 63010 q^{73} + 122683 q^{74} + 39375 q^{75} - 222376 q^{76} - 33275 q^{77} + 277272 q^{78} - 16385 q^{79} + 179900 q^{80} + 290354 q^{81} + 362302 q^{82} + 138461 q^{83} + 446870 q^{84} - 60775 q^{85} + 643902 q^{86} + 291602 q^{87} - 31944 q^{88} + 224792 q^{89} - 42225 q^{90} + 498548 q^{91} + 581088 q^{92} + 134210 q^{93} + 35864 q^{94} - 342950 q^{95} + 377376 q^{96} + 292216 q^{97} - 58230 q^{98} - 366509 q^{99}+O(q^{100}) \) 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9 + 200 * q^10 - 4598 * q^11 + 2312 * q^12 + 41 * q^13 + 23 * q^14 + 1575 * q^15 + 7196 * q^16 - 2431 * q^17 - 1689 * q^18 - 13718 * q^19 + 15400 * q^20 - 1577 * q^21 - 968 * q^22 + 9284 * q^23 + 7598 * q^24 + 23750 * q^25 + 13129 * q^26 + 9228 * q^27 - 1079 * q^28 - 559 * q^29 + 3725 * q^30 + 11147 * q^31 + 11051 * q^32 - 7623 * q^33 + 40895 * q^34 + 6875 * q^35 + 55887 * q^36 + 41579 * q^37 - 2888 * q^38 + 24982 * q^39 + 6600 * q^40 + 18597 * q^41 + 61360 * q^42 + 25353 * q^43 - 74536 * q^44 + 75725 * q^45 + 1611 * q^46 + 63516 * q^47 + 187737 * q^48 + 141609 * q^49 + 5000 * q^50 + 107546 * q^51 + 60018 * q^52 + 123045 * q^53 + 256696 * q^54 - 114950 * q^55 + 157335 * q^56 - 22743 * q^57 + 218938 * q^58 + 132925 * q^59 + 57800 * q^60 - 59107 * q^61 + 166982 * q^62 + 130582 * q^63 + 313126 * q^64 + 1025 * q^65 - 18029 * q^66 + 162534 * q^67 + 182980 * q^68 + 178552 * q^69 + 575 * q^70 + 157840 * q^71 + 98630 * q^72 - 63010 * q^73 + 122683 * q^74 + 39375 * q^75 - 222376 * q^76 - 33275 * q^77 + 277272 * q^78 - 16385 * q^79 + 179900 * q^80 + 290354 * q^81 + 362302 * q^82 + 138461 * q^83 + 446870 * q^84 - 60775 * q^85 + 643902 * q^86 + 291602 * q^87 - 31944 * q^88 + 224792 * q^89 - 42225 * q^90 + 498548 * q^91 + 581088 * q^92 + 134210 * q^93 + 35864 * q^94 - 342950 * q^95 + 377376 * q^96 + 292216 * q^97 - 58230 * q^98 - 366509 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more