LMFDB - Embedded newform 983.6.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,6,Mod(1,983)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("983.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	983.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:	$157.657294876$
Analytic rank:	$0$
Dimension:	$218$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.8442 q^{2} -6.29114 q^{3} +85.5966 q^{4} +9.46707 q^{5} +68.2223 q^{6} -20.0151 q^{7} -581.212 q^{8} -203.422 q^{9} +O(q^{10})$	\(q-10.8442 q^{2} -6.29114 q^{3} +85.5966 q^{4} +9.46707 q^{5} +68.2223 q^{6} -20.0151 q^{7} -581.212 q^{8} -203.422 q^{9} -102.663 q^{10} +426.348 q^{11} -538.500 q^{12} -345.797 q^{13} +217.048 q^{14} -59.5586 q^{15} +3563.68 q^{16} -368.580 q^{17} +2205.94 q^{18} -1670.70 q^{19} +810.349 q^{20} +125.918 q^{21} -4623.40 q^{22} +1585.92 q^{23} +3656.48 q^{24} -3035.37 q^{25} +3749.89 q^{26} +2808.50 q^{27} -1713.22 q^{28} -1899.41 q^{29} +645.865 q^{30} -5820.35 q^{31} -20046.5 q^{32} -2682.21 q^{33} +3996.96 q^{34} -189.484 q^{35} -17412.2 q^{36} -3132.17 q^{37} +18117.4 q^{38} +2175.45 q^{39} -5502.37 q^{40} -7773.73 q^{41} -1365.48 q^{42} +10301.0 q^{43} +36493.9 q^{44} -1925.81 q^{45} -17198.1 q^{46} -21531.6 q^{47} -22419.6 q^{48} -16406.4 q^{49} +32916.2 q^{50} +2318.79 q^{51} -29599.0 q^{52} -26715.2 q^{53} -30455.9 q^{54} +4036.27 q^{55} +11633.0 q^{56} +10510.6 q^{57} +20597.6 q^{58} -11518.8 q^{59} -5098.01 q^{60} +15944.8 q^{61} +63117.0 q^{62} +4071.50 q^{63} +103350. q^{64} -3273.68 q^{65} +29086.5 q^{66} +47112.6 q^{67} -31549.2 q^{68} -9977.25 q^{69} +2054.81 q^{70} +80759.6 q^{71} +118231. q^{72} +43851.8 q^{73} +33965.9 q^{74} +19096.0 q^{75} -143006. q^{76} -8533.40 q^{77} -23591.0 q^{78} +20007.9 q^{79} +33737.6 q^{80} +31762.8 q^{81} +84299.8 q^{82} +73897.8 q^{83} +10778.1 q^{84} -3489.38 q^{85} -111706. q^{86} +11949.5 q^{87} -247799. q^{88} -94733.5 q^{89} +20883.8 q^{90} +6921.15 q^{91} +135750. q^{92} +36616.6 q^{93} +233493. q^{94} -15816.7 q^{95} +126115. q^{96} -177595. q^{97} +177914. q^{98} -86728.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9}+O(q^{10}) $ 218 * q + 35 * q^2 + 70 * q^3 + 3685 * q^4 + 253 * q^5 + 529 * q^6 + 1567 * q^7 + 1695 * q^8 + 19812 * q^9	\( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9} + 2133 q^{10} + 1752 q^{11} + 3512 q^{12} + 5990 q^{13} + 2319 q^{14} + 4639 q^{15} + 66105 q^{16} + 10656 q^{17} + 11911 q^{18} + 11511 q^{19} + 10012 q^{20} + 12225 q^{21} + 19401 q^{22} + 9767 q^{23} + 21725 q^{24} + 185207 q^{25} + 7708 q^{26} + 23764 q^{27} + 77808 q^{28} + 25772 q^{29} + 15736 q^{30} + 35900 q^{31} + 60155 q^{32} + 70026 q^{33} + 17236 q^{34} + 28782 q^{35} + 382874 q^{36} + 126082 q^{37} + 62164 q^{38} + 54264 q^{39} + 102846 q^{40} + 70480 q^{41} + 102244 q^{42} + 137413 q^{43} + 116278 q^{44} + 93481 q^{45} + 126122 q^{46} + 63218 q^{47} + 124701 q^{48} + 732031 q^{49} + 131089 q^{50} + 109902 q^{51} + 229519 q^{52} + 102608 q^{53} + 149130 q^{54} + 167596 q^{55} + 87868 q^{56} + 408318 q^{57} + 304579 q^{58} + 67460 q^{59} + 150523 q^{60} + 195132 q^{61} + 132294 q^{62} + 374425 q^{63} + 1296639 q^{64} + 347092 q^{65} + 147397 q^{66} + 381238 q^{67} + 296321 q^{68} + 139362 q^{69} + 325675 q^{70} + 147818 q^{71} + 646059 q^{72} + 961992 q^{73} + 167410 q^{74} + 167324 q^{75} + 504875 q^{76} + 284328 q^{77} + 284295 q^{78} + 285792 q^{79} + 444932 q^{80} + 1980282 q^{81} + 336676 q^{82} + 276734 q^{83} + 378474 q^{84} + 1021245 q^{85} + 156051 q^{86} + 500457 q^{87} + 1068101 q^{88} + 398983 q^{89} + 463961 q^{90} + 273517 q^{91} + 577884 q^{92} + 967833 q^{93} + 224775 q^{94} + 482817 q^{95} + 780445 q^{96} + 1636277 q^{97} + 495958 q^{98} + 627643 q^{99}+O(q^{100}) \) 218 * q + 35 * q^2 + 70 * q^3 + 3685 * q^4 + 253 * q^5 + 529 * q^6 + 1567 * q^7 + 1695 * q^8 + 19812 * q^9 + 2133 * q^10 + 1752 * q^11 + 3512 * q^12 + 5990 * q^13 + 2319 * q^14 + 4639 * q^15 + 66105 * q^16 + 10656 * q^17 + 11911 * q^18 + 11511 * q^19 + 10012 * q^20 + 12225 * q^21 + 19401 * q^22 + 9767 * q^23 + 21725 * q^24 + 185207 * q^25 + 7708 * q^26 + 23764 * q^27 + 77808 * q^28 + 25772 * q^29 + 15736 * q^30 + 35900 * q^31 + 60155 * q^32 + 70026 * q^33 + 17236 * q^34 + 28782 * q^35 + 382874 * q^36 + 126082 * q^37 + 62164 * q^38 + 54264 * q^39 + 102846 * q^40 + 70480 * q^41 + 102244 * q^42 + 137413 * q^43 + 116278 * q^44 + 93481 * q^45 + 126122 * q^46 + 63218 * q^47 + 124701 * q^48 + 732031 * q^49 + 131089 * q^50 + 109902 * q^51 + 229519 * q^52 + 102608 * q^53 + 149130 * q^54 + 167596 * q^55 + 87868 * q^56 + 408318 * q^57 + 304579 * q^58 + 67460 * q^59 + 150523 * q^60 + 195132 * q^61 + 132294 * q^62 + 374425 * q^63 + 1296639 * q^64 + 347092 * q^65 + 147397 * q^66 + 381238 * q^67 + 296321 * q^68 + 139362 * q^69 + 325675 * q^70 + 147818 * q^71 + 646059 * q^72 + 961992 * q^73 + 167410 * q^74 + 167324 * q^75 + 504875 * q^76 + 284328 * q^77 + 284295 * q^78 + 285792 * q^79 + 444932 * q^80 + 1980282 * q^81 + 336676 * q^82 + 276734 * q^83 + 378474 * q^84 + 1021245 * q^85 + 156051 * q^86 + 500457 * q^87 + 1068101 * q^88 + 398983 * q^89 + 463961 * q^90 + 273517 * q^91 + 577884 * q^92 + 967833 * q^93 + 224775 * q^94 + 482817 * q^95 + 780445 * q^96 + 1636277 * q^97 + 495958 * q^98 + 627643 * 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 $

$2$	−10.8442	−1.91700	−0.958500	−	0.285091i	$-0.907976\pi$
$2$	−10.8442	−1.91700	−0.958500	+	0.285091i	$0.907976\pi$
$3$	−6.29114	−0.403577	−0.201788	−	0.979429i	$-0.564675\pi$
$3$	−6.29114	−0.403577	−0.201788	+	0.979429i	$0.564675\pi$
$4$	85.5966	2.67489
$5$	9.46707	0.169352	0.0846761	−	0.996409i	$-0.473014\pi$
$5$	9.46707	0.169352	0.0846761	+	0.996409i	$0.473014\pi$
$6$	68.2223	0.773657
$7$	−20.0151	−0.154388	−0.0771938	−	0.997016i	$-0.524596\pi$
$7$	−20.0151	−0.154388	−0.0771938	+	0.997016i	$0.524596\pi$
$8$	−581.212	−3.21077
$9$	−203.422	−0.837126
$10$	−102.663	−0.324648
$11$	426.348	1.06239	0.531193	−	0.847251i	$-0.321744\pi$
$11$	426.348	1.06239	0.531193	+	0.847251i	$0.321744\pi$
$12$	−538.500	−1.07952
$13$	−345.797	−0.567495	−0.283748	−	0.958899i	$-0.591578\pi$
$13$	−345.797	−0.567495	−0.283748	+	0.958899i	$0.591578\pi$
$14$	217.048	0.295961
$15$	−59.5586	−0.0683465
$16$	3563.68	3.48016
$17$	−368.580	−0.309321	−0.154661	−	0.987968i	$-0.549428\pi$
$17$	−368.580	−0.309321	−0.154661	+	0.987968i	$0.549428\pi$
$18$	2205.94	1.60477
$19$	−1670.70	−1.06173	−0.530866	−	0.847456i	$-0.678133\pi$
$19$	−1670.70	−1.06173	−0.530866	+	0.847456i	$0.678133\pi$
$20$	810.349	0.452999
$21$	125.918	0.0623073
$22$	−4623.40	−2.03660
$23$	1585.92	0.625119	0.312559	−	0.949898i	$-0.398814\pi$
$23$	1585.92	0.625119	0.312559	+	0.949898i	$0.398814\pi$
$24$	3656.48	1.29579
$25$	−3035.37	−0.971320
$26$	3749.89	1.08789
$27$	2808.50	0.741421
$28$	−1713.22	−0.412971
$29$	−1899.41	−0.419396	−0.209698	−	0.977766i	$-0.567248\pi$
$29$	−1899.41	−0.419396	−0.209698	+	0.977766i	$0.567248\pi$
$30$	645.865	0.131020
$31$	−5820.35	−1.08779	−0.543894	−	0.839154i	$-0.683051\pi$
$31$	−5820.35	−1.08779	−0.543894	+	0.839154i	$0.683051\pi$
$32$	−20046.5	−3.46070
$33$	−2682.21	−0.428754
$34$	3996.96	0.592970
$35$	−189.484	−0.0261459
$36$	−17412.2	−2.23922
$37$	−3132.17	−0.376133	−0.188066	−	0.982156i	$-0.560222\pi$
$37$	−3132.17	−0.376133	−0.188066	+	0.982156i	$0.560222\pi$
$38$	18117.4	2.03534
$39$	2175.45	0.229028
$40$	−5502.37	−0.543751
$41$	−7773.73	−0.722220	−0.361110	−	0.932523i	$-0.617602\pi$
$41$	−7773.73	−0.722220	−0.361110	+	0.932523i	$0.617602\pi$
$42$	−1365.48	−0.119443
$43$	10301.0	0.849590	0.424795	−	0.905290i	$-0.360346\pi$
$43$	10301.0	0.849590	0.424795	+	0.905290i	$0.360346\pi$
$44$	36493.9	2.84177
$45$	−1925.81	−0.141769
$46$	−17198.1	−1.19835
$47$	−21531.6	−1.42178	−0.710888	−	0.703305i	$-0.751707\pi$
$47$	−21531.6	−1.42178	−0.710888	+	0.703305i	$0.751707\pi$
$48$	−22419.6	−1.40451
$49$	−16406.4	−0.976164
$50$	32916.2	1.86202
$51$	2318.79	0.124835
$52$	−29599.0	−1.51799
$53$	−26715.2	−1.30638	−0.653190	−	0.757194i	$-0.726570\pi$
$53$	−26715.2	−1.30638	−0.653190	+	0.757194i	$0.726570\pi$
$54$	−30455.9	−1.42130
$55$	4036.27	0.179917
$56$	11633.0	0.495704
$57$	10510.6	0.428490
$58$	20597.6	0.803983
$59$	−11518.8	−0.430800	−0.215400	−	0.976526i	$-0.569105\pi$
$59$	−11518.8	−0.430800	−0.215400	+	0.976526i	$0.569105\pi$
$60$	−5098.01	−0.182820
$61$	15944.8	0.548650	0.274325	−	0.961637i	$-0.411546\pi$
$61$	15944.8	0.548650	0.274325	+	0.961637i	$0.411546\pi$
$62$	63117.0	2.08529
$63$	4071.50	0.129242
$64$	103350.	3.15400
$65$	−3273.68	−0.0961065
$66$	29086.5	0.821923
$67$	47112.6	1.28218	0.641092	−	0.767464i	$-0.278482\pi$
$67$	47112.6	1.28218	0.641092	+	0.767464i	$0.278482\pi$
$68$	−31549.2	−0.827402
$69$	−9977.25	−0.252283
$70$	2054.81	0.0501217
$71$	80759.6	1.90129	0.950644	−	0.310283i	$-0.100424\pi$
$71$	80759.6	1.90129	0.950644	+	0.310283i	$0.100424\pi$
$72$	118231.	2.68782
$73$	43851.8	0.963120	0.481560	−	0.876413i	$-0.340070\pi$
$73$	43851.8	0.963120	0.481560	+	0.876413i	$0.340070\pi$
$74$	33965.9	0.721047
$75$	19096.0	0.392002
$76$	−143006.	−2.84002
$77$	−8533.40	−0.164019
$78$	−23591.0	−0.439047
$79$	20007.9	0.360689	0.180344	−	0.983604i	$-0.442279\pi$
$79$	20007.9	0.360689	0.180344	+	0.983604i	$0.442279\pi$
$80$	33737.6	0.589372
$81$	31762.8	0.537906
$82$	84299.8	1.38450
$83$	73897.8	1.17743	0.588717	−	0.808340i	$-0.299633\pi$
$83$	73897.8	1.17743	0.588717	+	0.808340i	$0.299633\pi$
$84$	10778.1	0.166665
$85$	−3489.38	−0.0523842
$86$	−111706.	−1.62867
$87$	11949.5	0.169258
$88$	−247799.	−3.41108
$89$	−94733.5	−1.26773	−0.633867	−	0.773442i	$-0.718533\pi$
$89$	−94733.5	−1.26773	−0.633867	+	0.773442i	$0.718533\pi$
$90$	20883.8	0.271771
$91$	6921.15	0.0876143
$92$	135750.	1.67213
$93$	36616.6	0.439006
$94$	233493.	2.72555
$95$	−15816.7	−0.179807
$96$	126115.	1.39666
$97$	−177595.	−1.91647	−0.958233	−	0.285988i	$-0.907678\pi$
$97$	−177595.	−1.91647	−0.958233	+	0.285988i	$0.907678\pi$
$98$	177914.	1.87131
$99$	−86728.4	−0.889352
$100$	−259818.	−2.59818
$101$	−63135.4	−0.615843	−0.307921	−	0.951412i	$-0.599633\pi$
$101$	−63135.4	−0.615843	−0.307921	+	0.951412i	$0.599633\pi$
$102$	−25145.4	−0.239309
$103$	142282.	1.32147	0.660734	−	0.750620i	$-0.270245\pi$
$103$	142282.	1.32147	0.660734	+	0.750620i	$0.270245\pi$
$104$	200981.	1.82210
$105$	1192.07	0.0105519
$106$	289705.	2.50433
$107$	−200337.	−1.69162	−0.845808	−	0.533488i	$-0.820881\pi$
$107$	−200337.	−1.69162	−0.845808	+	0.533488i	$0.820881\pi$
$108$	240398.	1.98322
$109$	−99505.3	−0.802195	−0.401098	−	0.916035i	$-0.631371\pi$
$109$	−99505.3	−0.802195	−0.401098	+	0.916035i	$0.631371\pi$
$110$	−43770.1	−0.344902
$111$	19704.9	0.151798
$112$	−71327.5	−0.537294
$113$	163213.	1.20243	0.601213	−	0.799089i	$-0.294684\pi$
$113$	163213.	1.20243	0.601213	+	0.799089i	$0.294684\pi$
$114$	−113979.	−0.821416
$115$	15014.0	0.105865
$116$	−162583.	−1.12184
$117$	70342.5	0.475065
$118$	124912.	0.825844
$119$	7377.18	0.0477554
$120$	34616.2	0.219445
$121$	20721.8	0.128666
$122$	−172909.	−1.05176
$123$	48905.6	0.291471
$124$	−498202.	−2.90972
$125$	−58320.7	−0.333847
$126$	−44152.2	−0.247757
$127$	−287300.	−1.58061	−0.790307	−	0.612711i	$-0.790079\pi$
$127$	−287300.	−1.58061	−0.790307	+	0.612711i	$0.790079\pi$
$128$	−479262.	−2.58552
$129$	−64805.2	−0.342875
$130$	35500.4	0.184236
$131$	282492.	1.43823	0.719114	−	0.694893i	$-0.244548\pi$
$131$	282492.	1.43823	0.719114	+	0.694893i	$0.244548\pi$
$132$	−229588.	−1.14687
$133$	33439.3	0.163918
$134$	−510899.	−2.45795
$135$	26588.3	0.125561
$136$	214223.	0.993160
$137$	−208274.	−0.948057	−0.474028	−	0.880510i	$-0.657201\pi$
$137$	−208274.	−0.948057	−0.474028	+	0.880510i	$0.657201\pi$
$138$	108195.	0.483627
$139$	−323119.	−1.41849	−0.709244	−	0.704963i	$-0.750963\pi$
$139$	−323119.	−1.41849	−0.709244	+	0.704963i	$0.750963\pi$
$140$	−16219.2	−0.0699374
$141$	135458.	0.573796
$142$	−875772.	−3.64477
$143$	−147430.	−0.602900
$144$	−724930.	−2.91333
$145$	−17981.9	−0.0710256
$146$	−475538.	−1.84630
$147$	103215.	0.393957
$148$	−268103.	−1.00612
$149$	−358232.	−1.32190	−0.660951	−	0.750429i	$-0.729847\pi$
$149$	−358232.	−1.32190	−0.660951	+	0.750429i	$0.729847\pi$
$150$	−207080.	−0.751468
$151$	91783.3	0.327583	0.163792	−	0.986495i	$-0.447628\pi$
$151$	91783.3	0.327583	0.163792	+	0.986495i	$0.447628\pi$
$152$	971032.	3.40898
$153$	74977.2	0.258941
$154$	92537.9	0.314425
$155$	−55101.6	−0.184219
$156$	186211.	0.612625
$157$	217101.	0.702930	0.351465	−	0.936201i	$-0.385684\pi$
$157$	217101.	0.702930	0.351465	+	0.936201i	$0.385684\pi$
$158$	−216969.	−0.691441
$159$	168069.	0.527224
$160$	−189782.	−0.586076
$161$	−31742.4	−0.0965106
$162$	−344442.	−1.03117
$163$	525207.	1.54832	0.774161	−	0.632989i	$-0.218172\pi$
$163$	525207.	1.54832	0.774161	+	0.632989i	$0.218172\pi$
$164$	−665404.	−1.93186
$165$	−25392.7	−0.0726105
$166$	−801362.	−2.25714
$167$	−161940.	−0.449328	−0.224664	−	0.974436i	$-0.572128\pi$
$167$	−161940.	−0.449328	−0.224664	+	0.974436i	$0.572128\pi$
$168$	−73184.8	−0.200054
$169$	−251718.	−0.677949
$170$	37839.5	0.100421
$171$	339857.	0.888804
$172$	881733.	2.27256
$173$	−297600.	−0.755992	−0.377996	−	0.925807i	$-0.623387\pi$
$173$	−297600.	−0.755992	−0.377996	+	0.925807i	$0.623387\pi$
$174$	−129582.	−0.324469
$175$	60753.3	0.149960
$176$	1.51937e6	3.69727
$177$	72466.0	0.173861
$178$	1.02731e6	2.43025
$179$	−518396.	−1.20929	−0.604643	−	0.796496i	$-0.706684\pi$
$179$	−518396.	−1.20929	−0.604643	+	0.796496i	$0.706684\pi$
$180$	−164842.	−0.379217
$181$	437061.	0.991621	0.495810	−	0.868431i	$-0.334871\pi$
$181$	437061.	0.991621	0.495810	+	0.868431i	$0.334871\pi$
$182$	−75054.3	−0.167957
$183$	−100311.	−0.221422
$184$	−921757.	−2.00711
$185$	−29652.5	−0.0636989
$186$	−397077.	−0.841575
$187$	−157144.	−0.328619
$188$	−1.84303e6	−3.80310
$189$	−56212.4	−0.114466
$190$	171519.	0.344690
$191$	−936961.	−1.85839	−0.929197	−	0.369584i	$-0.879500\pi$
$191$	−936961.	−1.85839	−0.929197	+	0.369584i	$0.879500\pi$
$192$	−650190.	−1.27288
$193$	548124.	1.05922	0.529610	−	0.848241i	$-0.322338\pi$
$193$	548124.	1.05922	0.529610	+	0.848241i	$0.322338\pi$
$194$	1.92587e6	3.67387
$195$	20595.2	0.0387863
$196$	−1.40433e6	−2.61114
$197$	−871325.	−1.59961	−0.799806	−	0.600258i	$-0.795064\pi$
$197$	−871325.	−1.59961	−0.799806	+	0.600258i	$0.795064\pi$
$198$	940500.	1.70489
$199$	507526.	0.908501	0.454251	−	0.890874i	$-0.349907\pi$
$199$	507526.	0.908501	0.454251	+	0.890874i	$0.349907\pi$
$200$	1.76420e6	3.11869
$201$	−296392.	−0.517459
$202$	684653.	1.18057
$203$	38016.9	0.0647496
$204$	198480.	0.333920
$205$	−73594.4	−0.122310
$206$	−1.54293e6	−2.53325
$207$	−322611.	−0.523303
$208$	−1.23231e6	−1.97497
$209$	−712301.	−1.12797
$210$	−12927.1	−0.0202279
$211$	−73648.8	−0.113883	−0.0569416	−	0.998378i	$-0.518135\pi$
$211$	−73648.8	−0.113883	−0.0569416	+	0.998378i	$0.518135\pi$
$212$	−2.28673e6	−3.49443
$213$	−508069.	−0.767316
$214$	2.17249e6	3.24283
$215$	97520.6	0.143880
$216$	−1.63233e6	−2.38053
$217$	116495.	0.167941
$218$	1.07906e6	1.53781
$219$	−275878.	−0.388693
$220$	345491.	0.481260
$221$	127454.	0.175538
$222$	−213684.	−0.290998
$223$	663339.	0.893251	0.446625	−	0.894721i	$-0.352626\pi$
$223$	663339.	0.893251	0.446625	+	0.894721i	$0.352626\pi$
$224$	401233.	0.534289
$225$	617461.	0.813117
$226$	−1.76991e6	−2.30505
$227$	1.02691e6	1.32272	0.661361	−	0.750068i	$-0.269979\pi$
$227$	1.02691e6	1.32272	0.661361	+	0.750068i	$0.269979\pi$
$228$	899673.	1.14617
$229$	592166.	0.746199	0.373099	−	0.927791i	$-0.378295\pi$
$229$	592166.	0.746199	0.373099	+	0.927791i	$0.378295\pi$
$230$	−162815.	−0.202944
$231$	53684.8	0.0661944
$232$	1.10396e6	1.34658
$233$	−100583.	−0.121376	−0.0606881	−	0.998157i	$-0.519329\pi$
$233$	−100583.	−0.121376	−0.0606881	+	0.998157i	$0.519329\pi$
$234$	−762808.	−0.910700
$235$	−203841.	−0.240781
$236$	−985966.	−1.15234
$237$	−125872.	−0.145566
$238$	−79999.5	−0.0915472
$239$	109691.	0.124216	0.0621080	−	0.998069i	$-0.480218\pi$
$239$	109691.	0.124216	0.0621080	+	0.998069i	$0.480218\pi$
$240$	−212248.	−0.237857
$241$	286748.	0.318022	0.159011	−	0.987277i	$-0.449169\pi$
$241$	286748.	0.318022	0.159011	+	0.987277i	$0.449169\pi$
$242$	−224711.	−0.246653
$243$	−882289.	−0.958507
$244$	1.36482e6	1.46758
$245$	−155321.	−0.165315
$246$	−530342.	−0.558751
$247$	577723.	0.602528
$248$	3.38285e6	3.49264
$249$	−464901.	−0.475184
$250$	632441.	0.639985
$251$	618205.	0.619367	0.309683	−	0.950840i	$-0.399777\pi$
$251$	618205.	0.619367	0.309683	+	0.950840i	$0.399777\pi$
$252$	348507.	0.345708
$253$	676155.	0.664118
$254$	3.11553e6	3.03004
$255$	21952.1	0.0211411
$256$	1.89001e6	1.80245
$257$	−297985.	−0.281424	−0.140712	−	0.990051i	$-0.544939\pi$
$257$	−297985.	−0.281424	−0.140712	+	0.990051i	$0.544939\pi$
$258$	702760.	0.657291
$259$	62690.7	0.0580703
$260$	−280216.	−0.257075
$261$	386382.	0.351087
$262$	−3.06340e6	−2.75708
$263$	2.05316e6	1.83035	0.915176	−	0.403055i	$-0.132052\pi$
$263$	2.05316e6	1.83035	0.915176	+	0.403055i	$0.132052\pi$
$264$	1.55893e6	1.37663
$265$	−252915.	−0.221238
$266$	−362622.	−0.314232
$267$	595981.	0.511628
$268$	4.03268e6	3.42970
$269$	−1.65687e6	−1.39607	−0.698034	−	0.716065i	$-0.745942\pi$
$269$	−1.65687e6	−1.39607	−0.698034	+	0.716065i	$0.745942\pi$
$270$	−288328.	−0.240701
$271$	−925376.	−0.765412	−0.382706	−	0.923870i	$-0.625008\pi$
$271$	−925376.	−0.765412	−0.382706	+	0.923870i	$0.625008\pi$
$272$	−1.31350e6	−1.07649
$273$	−43541.9	−0.0353591
$274$	2.25857e6	1.81743
$275$	−1.29413e6	−1.03192
$276$	−854019.	−0.674831
$277$	2.02578e6	1.58633	0.793165	−	0.609006i	$-0.208432\pi$
$277$	2.02578e6	1.58633	0.793165	+	0.609006i	$0.208432\pi$
$278$	3.50397e6	2.71924
$279$	1.18398e6	0.910616
$280$	110131.	0.0839484
$281$	−1.79001e6	−1.35235	−0.676177	−	0.736739i	$-0.736364\pi$
$281$	−1.79001e6	−1.35235	−0.676177	+	0.736739i	$0.736364\pi$
$282$	−1.46893e6	−1.09997
$283$	796060.	0.590853	0.295427	−	0.955365i	$-0.404538\pi$
$283$	796060.	0.590853	0.295427	+	0.955365i	$0.404538\pi$
$284$	6.91274e6	5.08574
$285$	99504.8	0.0725657
$286$	1.59876e6	1.15576
$287$	155592.	0.111502
$288$	4.07789e6	2.89704
$289$	−1.28401e6	−0.904320
$290$	194999.	0.136156
$291$	1.11727e6	0.773441
$292$	3.75357e6	2.57624
$293$	−1.76375e6	−1.20024	−0.600119	−	0.799911i	$-0.704880\pi$
$293$	−1.76375e6	−1.20024	−0.600119	+	0.799911i	$0.704880\pi$
$294$	−1.11928e6	−0.755216
$295$	−109049.	−0.0729568
$296$	1.82045e6	1.20768
$297$	1.19740e6	0.787676
$298$	3.88474e6	2.53409
$299$	−548407.	−0.354752
$300$	1.63455e6	1.04856
$301$	−206176.	−0.131166
$302$	−995317.	−0.627977
$303$	397194.	0.248540
$304$	−5.95385e6	−3.69500
$305$	150951.	0.0929150
$306$	−813068.	−0.496390
$307$	−1.09890e6	−0.665446	−0.332723	−	0.943025i	$-0.607967\pi$
$307$	−1.09890e6	−0.665446	−0.332723	+	0.943025i	$0.607967\pi$
$308$	−730430.	−0.438734
$309$	−895115.	−0.533313
$310$	597533.	0.353149
$311$	−2.87121e6	−1.68331	−0.841653	−	0.540018i	$-0.818417\pi$
$311$	−2.87121e6	−1.68331	−0.841653	+	0.540018i	$0.818417\pi$
$312$	−1.26440e6	−0.735356
$313$	−2.23921e6	−1.29192	−0.645959	−	0.763372i	$-0.723542\pi$
$313$	−2.23921e6	−1.29192	−0.645959	+	0.763372i	$0.723542\pi$
$314$	−2.35428e6	−1.34752
$315$	38545.2	0.0218874
$316$	1.71260e6	0.964804
$317$	1.13419e6	0.633925	0.316962	−	0.948438i	$-0.397337\pi$
$317$	1.13419e6	0.633925	0.316962	+	0.948438i	$0.397337\pi$
$318$	−1.82258e6	−1.01069
$319$	−809811.	−0.445561
$320$	978424.	0.534136
$321$	1.26035e6	0.682697
$322$	344221.	0.185011
$323$	615788.	0.328417
$324$	2.71879e6	1.43884
$325$	1.04962e6	0.551220
$326$	−5.69544e6	−2.96813
$327$	626002.	0.323747
$328$	4.51818e6	2.31888
$329$	430957.	0.219505
$330$	275364.	0.139194
$331$	2.94247e6	1.47619	0.738095	−	0.674696i	$-0.235725\pi$
$331$	2.94247e6	1.47619	0.738095	+	0.674696i	$0.235725\pi$
$332$	6.32540e6	3.14951
$333$	637151.	0.314871
$334$	1.75611e6	0.861362
$335$	446019.	0.217141
$336$	448731.	0.216839
$337$	1.94542e6	0.933122	0.466561	−	0.884489i	$-0.345493\pi$
$337$	1.94542e6	0.933122	0.466561	+	0.884489i	$0.345493\pi$
$338$	2.72968e6	1.29963
$339$	−1.02679e6	−0.485271
$340$	−298679.	−0.140122
$341$	−2.48149e6	−1.15565
$342$	−3.68548e6	−1.70384
$343$	664769.	0.305095
$344$	−5.98708e6	−2.72784
$345$	−94455.4	−0.0427247
$346$	3.22723e6	1.44924
$347$	−2.76176e6	−1.23130	−0.615648	−	0.788021i	$-0.711106\pi$
$347$	−2.76176e6	−1.23130	−0.615648	+	0.788021i	$0.711106\pi$
$348$	1.02283e6	0.452748
$349$	724667.	0.318475	0.159237	−	0.987240i	$-0.449096\pi$
$349$	724667.	0.318475	0.159237	+	0.987240i	$0.449096\pi$
$350$	−658821.	−0.287473
$351$	−971169.	−0.420753
$352$	−8.54679e6	−3.67660
$353$	−688974.	−0.294284	−0.147142	−	0.989115i	$-0.547007\pi$
$353$	−688974.	−0.294284	−0.147142	+	0.989115i	$0.547007\pi$
$354$	−785836.	−0.333291
$355$	764556.	0.321987
$356$	−8.10886e6	−3.39105
$357$	−46410.8	−0.0192730
$358$	5.62159e6	2.31820
$359$	−1.36503e6	−0.558994	−0.279497	−	0.960147i	$-0.590168\pi$
$359$	−1.36503e6	−0.558994	−0.279497	+	0.960147i	$0.590168\pi$
$360$	1.11930e6	0.455188
$361$	315148.	0.127276
$362$	−4.73957e6	−1.90094
$363$	−130364.	−0.0519266
$364$	592427.	0.234359
$365$	415148.	0.163106
$366$	1.08779e6	0.424467
$367$	−1.32454e6	−0.513335	−0.256668	−	0.966500i	$-0.582625\pi$
$367$	−1.32454e6	−0.513335	−0.256668	+	0.966500i	$0.582625\pi$
$368$	5.65172e6	2.17551
$369$	1.58134e6	0.604589
$370$	321557.	0.122111
$371$	534708.	0.201689
$372$	3.13425e6	1.17429
$373$	−3.80150e6	−1.41476	−0.707381	−	0.706832i	$-0.750123\pi$
$373$	−3.80150e6	−1.41476	−0.707381	+	0.706832i	$0.750123\pi$
$374$	1.70410e6	0.629963
$375$	366903.	0.134733
$376$	1.25144e7	4.56500
$377$	656810.	0.238005
$378$	609578.	0.219432
$379$	3.89675e6	1.39349	0.696747	−	0.717317i	$-0.254630\pi$
$379$	3.89675e6	1.39349	0.696747	+	0.717317i	$0.254630\pi$
$380$	−1.35385e6	−0.480963
$381$	1.80744e6	0.637899
$382$	1.01606e7	3.56254
$383$	1.20909e6	0.421175	0.210587	−	0.977575i	$-0.432462\pi$
$383$	1.20909e6	0.421175	0.210587	+	0.977575i	$0.432462\pi$
$384$	3.01511e6	1.04346
$385$	−80786.3	−0.0277770
$386$	−5.94397e6	−2.03052
$387$	−2.09545e6	−0.711214
$388$	−1.52015e7	−5.12634
$389$	2.72935e6	0.914502	0.457251	−	0.889338i	$-0.348834\pi$
$389$	2.72935e6	0.914502	0.457251	+	0.889338i	$0.348834\pi$
$390$	−223338.	−0.0743535
$391$	−584540.	−0.193363
$392$	9.53559e6	3.13424
$393$	−1.77719e6	−0.580435
$394$	9.44882e6	3.06646
$395$	189416.	0.0610834
$396$	−7.42366e6	−2.37892
$397$	6.04383e6	1.92458	0.962290	−	0.272024i	$-0.0876931\pi$
$397$	6.04383e6	1.92458	0.962290	+	0.272024i	$0.0876931\pi$
$398$	−5.50371e6	−1.74160
$399$	−210371.	−0.0661536
$400$	−1.08171e7	−3.38035
$401$	3.21977e6	0.999916	0.499958	−	0.866050i	$-0.333349\pi$
$401$	3.21977e6	0.999916	0.499958	+	0.866050i	$0.333349\pi$
$402$	3.21413e6	0.991970
$403$	2.01266e6	0.617315
$404$	−5.40418e6	−1.64731
$405$	300701.	0.0910955
$406$	−412263.	−0.124125
$407$	−1.33540e6	−0.399599
$408$	−1.34771e6	−0.400816
$409$	−4.23818e6	−1.25277	−0.626385	−	0.779514i	$-0.715466\pi$
$409$	−4.23818e6	−1.25277	−0.626385	+	0.779514i	$0.715466\pi$
$410$	798072.	0.234467
$411$	1.31028e6	0.382613
$412$	1.21788e7	3.53478
$413$	230549.	0.0665102
$414$	3.49846e6	1.00317
$415$	699596.	0.199401
$416$	6.93201e6	1.96393
$417$	2.03279e6	0.572468
$418$	7.72433e6	2.16232
$419$	230204.	0.0640587	0.0320293	−	0.999487i	$-0.489803\pi$
$419$	230204.	0.0640587	0.0320293	+	0.999487i	$0.489803\pi$
$420$	102037.	0.0282251
$421$	−7.26824e6	−1.99859	−0.999296	−	0.0375094i	$-0.988058\pi$
$421$	−7.26824e6	−1.99859	−0.999296	+	0.0375094i	$0.988058\pi$
$422$	798662.	0.218314
$423$	4.37999e6	1.19021
$424$	1.55272e7	4.19449
$425$	1.11878e6	0.300450
$426$	5.50960e6	1.47094
$427$	−319137.	−0.0847048
$428$	−1.71482e7	−4.52489
$429$	927501.	0.243316
$430$	−1.05753e6	−0.275818
$431$	746378.	0.193538	0.0967689	−	0.995307i	$-0.469149\pi$
$431$	746378.	0.193538	0.0967689	+	0.995307i	$0.469149\pi$
$432$	1.00086e7	2.58026
$433$	−3.63010e6	−0.930462	−0.465231	−	0.885189i	$-0.654029\pi$
$433$	−3.63010e6	−0.930462	−0.465231	+	0.885189i	$0.654029\pi$
$434$	−1.26329e6	−0.321943
$435$	113126.	0.0286643
$436$	−8.51731e6	−2.14579
$437$	−2.64961e6	−0.663709
$438$	2.99167e6	0.745124
$439$	3.39759e6	0.841413	0.420707	−	0.907197i	$-0.361782\pi$
$439$	3.39759e6	0.841413	0.420707	+	0.907197i	$0.361782\pi$
$440$	−2.34593e6	−0.577674
$441$	3.33742e6	0.817173
$442$	−1.38213e6	−0.336507
$443$	7.22817e6	1.74992	0.874961	−	0.484193i	$-0.160887\pi$
$443$	7.22817e6	1.74992	0.874961	+	0.484193i	$0.160887\pi$
$444$	1.68667e6	0.406044
$445$	−896848.	−0.214694
$446$	−7.19338e6	−1.71236
$447$	2.25369e6	0.533489
$448$	−2.06857e6	−0.486939
$449$	1.63522e6	0.382789	0.191395	−	0.981513i	$-0.438699\pi$
$449$	1.63522e6	0.382789	0.191395	+	0.981513i	$0.438699\pi$
$450$	−6.69587e6	−1.55875
$451$	−3.31432e6	−0.767277
$452$	1.39705e7	3.21636
$453$	−577422.	−0.132205
$454$	−1.11360e7	−2.53566
$455$	65523.0	0.0148377
$456$	−6.10889e6	−1.37578
$457$	8.20454e6	1.83765	0.918827	−	0.394660i	$-0.129138\pi$
$457$	8.20454e6	1.83765	0.918827	+	0.394660i	$0.129138\pi$
$458$	−6.42156e6	−1.43046
$459$	−1.03516e6	−0.229337
$460$	1.28515e6	0.283178
$461$	6.98236e6	1.53021	0.765103	−	0.643908i	$-0.222688\pi$
$461$	6.98236e6	1.53021	0.765103	+	0.643908i	$0.222688\pi$
$462$	−582168.	−0.126895
$463$	110113.	0.0238718	0.0119359	−	0.999929i	$-0.496201\pi$
$463$	110113.	0.0238718	0.0119359	+	0.999929i	$0.496201\pi$
$464$	−6.76890e6	−1.45956
$465$	346652.	0.0743466
$466$	1.09074e6	0.232678
$467$	6.41293e6	1.36071	0.680353	−	0.732885i	$-0.261827\pi$
$467$	6.41293e6	1.36071	0.680353	+	0.732885i	$0.261827\pi$
$468$	6.02108e6	1.27075
$469$	−942964.	−0.197953
$470$	2.21049e6	0.461577
$471$	−1.36581e6	−0.283686
$472$	6.69483e6	1.38320
$473$	4.39183e6	0.902594
$474$	1.36498e6	0.279049
$475$	5.07121e6	1.03128
$476$	631461.	0.127741
$477$	5.43446e6	1.09360
$478$	−1.18951e6	−0.238122
$479$	−546265.	−0.108784	−0.0543920	−	0.998520i	$-0.517322\pi$
$479$	−546265.	−0.108784	−0.0543920	+	0.998520i	$0.517322\pi$
$480$	1.19394e6	0.236527
$481$	1.08309e6	0.213454
$482$	−3.10955e6	−0.609649
$483$	199696.	0.0389494
$484$	1.77371e6	0.344168
$485$	−1.68130e6	−0.324558
$486$	9.56772e6	1.83746
$487$	−8.76809e6	−1.67526	−0.837631	−	0.546237i	$-0.816060\pi$
$487$	−8.76809e6	−1.67526	−0.837631	+	0.546237i	$0.816060\pi$
$488$	−9.26732e6	−1.76159
$489$	−3.30415e6	−0.624866
$490$	1.68433e6	0.316910
$491$	5.03324e6	0.942202	0.471101	−	0.882079i	$-0.343857\pi$
$491$	5.03324e6	0.942202	0.471101	+	0.882079i	$0.343857\pi$
$492$	4.18615e6	0.779654
$493$	700086.	0.129728
$494$	−6.26494e6	−1.15505
$495$	−821064.	−0.150614
$496$	−2.07419e7	−3.78568
$497$	−1.61641e6	−0.293536
$498$	5.04148e6	0.910929
$499$	8.37591e6	1.50585	0.752923	−	0.658108i	$-0.228643\pi$
$499$	8.37591e6	1.50585	0.752923	+	0.658108i	$0.228643\pi$
$500$	−4.99205e6	−0.893005
$501$	1.01879e6	0.181338
$502$	−6.70393e6	−1.18733
$503$	3.70089e6	0.652208	0.326104	−	0.945334i	$-0.394264\pi$
$503$	3.70089e6	0.652208	0.326104	+	0.945334i	$0.394264\pi$
$504$	−2.36641e6	−0.414966
$505$	−597708.	−0.104294
$506$	−7.33236e6	−1.27311
$507$	1.58359e6	0.273604
$508$	−2.45919e7	−4.22797
$509$	2.86019e6	0.489328	0.244664	−	0.969608i	$-0.421322\pi$
$509$	2.86019e6	0.489328	0.244664	+	0.969608i	$0.421322\pi$
$510$	−238053.	−0.0405274
$511$	−877699.	−0.148694
$512$	−5.15922e6	−0.869779
$513$	−4.69217e6	−0.787191
$514$	3.23140e6	0.539490
$515$	1.34699e6	0.223793
$516$	−5.54710e6	−0.917153
$517$	−9.17995e6	−1.51048
$518$	−679831.	−0.111321
$519$	1.87224e6	0.305101
$520$	1.90270e6	0.308576
$521$	−5.93078e6	−0.957233	−0.478616	−	0.878024i	$-0.658861\pi$
$521$	−5.93078e6	−0.957233	−0.478616	+	0.878024i	$0.658861\pi$
$522$	−4.19000e6	−0.673035
$523$	1.17887e7	1.88457	0.942284	−	0.334814i	$-0.108673\pi$
$523$	1.17887e7	1.88457	0.942284	+	0.334814i	$0.108673\pi$
$524$	2.41803e7	3.84710
$525$	−382207.	−0.0605203
$526$	−2.22649e7	−3.50878
$527$	2.14527e6	0.336476
$528$	−9.55856e6	−1.49213
$529$	−3.92119e6	−0.609227
$530$	2.74266e6	0.424114
$531$	2.34316e6	0.360634
$532$	2.86229e6	0.438464
$533$	2.68813e6	0.409857
$534$	−6.46293e6	−0.980791
$535$	−1.89660e6	−0.286479
$536$	−2.73824e7	−4.11680
$537$	3.26130e6	0.488040
$538$	1.79674e7	2.67626
$539$	−6.99484e6	−1.03706
$540$	2.27586e6	0.335863
$541$	−2.98550e6	−0.438554	−0.219277	−	0.975663i	$-0.570370\pi$
$541$	−2.98550e6	−0.438554	−0.219277	+	0.975663i	$0.570370\pi$
$542$	1.00350e7	1.46729
$543$	−2.74961e6	−0.400195
$544$	7.38875e6	1.07047
$545$	−942024.	−0.135853
$546$	472177.	0.0677834
$547$	6.87408e6	0.982304	0.491152	−	0.871074i	$-0.336576\pi$
$547$	6.87408e6	0.982304	0.491152	+	0.871074i	$0.336576\pi$
$548$	−1.78276e7	−2.53595
$549$	−3.24352e6	−0.459289
$550$	1.40338e7	1.97819
$551$	3.17335e6	0.445286
$552$	5.79890e6	0.810024
$553$	−400459.	−0.0556859
$554$	−2.19680e7	−3.04100
$555$	186548.	0.0257074
$556$	−2.76579e7	−3.79430
$557$	2.41950e6	0.330436	0.165218	−	0.986257i	$-0.447167\pi$
$557$	2.41950e6	0.330436	0.165218	+	0.986257i	$0.447167\pi$
$558$	−1.28394e7	−1.74565
$559$	−3.56206e6	−0.482139
$560$	−675262.	−0.0909918
$561$	988612.	0.132623
$562$	1.94112e7	2.59246
$563$	−946938.	−0.125907	−0.0629536	−	0.998016i	$-0.520052\pi$
$563$	−946938.	−0.125907	−0.0629536	+	0.998016i	$0.520052\pi$
$564$	1.15947e7	1.53484
$565$	1.54515e6	0.203633
$566$	−8.63263e6	−1.13267
$567$	−635736.	−0.0830460
$568$	−4.69384e7	−6.10460
$569$	3.60865e6	0.467266	0.233633	−	0.972325i	$-0.424939\pi$
$569$	3.60865e6	0.467266	0.233633	+	0.972325i	$0.424939\pi$
$570$	−1.07905e6	−0.139109
$571$	−31002.3	−0.00397927	−0.00198964	−	0.999998i	$-0.500633\pi$
$571$	−31002.3	−0.00397927	−0.00198964	+	0.999998i	$0.500633\pi$
$572$	−1.26195e7	−1.61269
$573$	5.89455e6	0.750004
$574$	−1.68727e6	−0.213749
$575$	−4.81387e6	−0.607190
$576$	−2.10237e7	−2.64029
$577$	−1.08997e7	−1.36293	−0.681466	−	0.731850i	$-0.738657\pi$
$577$	−1.08997e7	−1.36293	−0.681466	+	0.731850i	$0.738657\pi$
$578$	1.39240e7	1.73358
$579$	−3.44833e6	−0.427476
$580$	−1.53919e6	−0.189986
$581$	−1.47907e6	−0.181781
$582$	−1.21159e7	−1.48269
$583$	−1.13900e7	−1.38788
$584$	−2.54872e7	−3.09236
$585$	665937.	0.0804533
$586$	1.91264e7	2.30086
$587$	3.48044e6	0.416907	0.208453	−	0.978032i	$-0.433157\pi$
$587$	3.48044e6	0.416907	0.208453	+	0.978032i	$0.433157\pi$
$588$	8.83484e6	1.05379
$589$	9.72407e6	1.15494
$590$	1.18255e6	0.139858
$591$	5.48163e6	0.645566
$592$	−1.11621e7	−1.30900
$593$	−500870.	−0.0584909	−0.0292454	−	0.999572i	$-0.509310\pi$
$593$	−500870.	−0.0584909	−0.0292454	+	0.999572i	$0.509310\pi$
$594$	−1.29848e7	−1.50998
$595$	69840.2	0.00808748
$596$	−3.06635e7	−3.53595
$597$	−3.19291e6	−0.366650
$598$	5.94703e6	0.680060
$599$	−81219.1	−0.00924893	−0.00462446	−	0.999989i	$-0.501472\pi$
$599$	−81219.1	−0.00924893	−0.00462446	+	0.999989i	$0.501472\pi$
$600$	−1.10988e7	−1.25863
$601$	2.79622e6	0.315781	0.157890	−	0.987457i	$-0.449531\pi$
$601$	2.79622e6	0.315781	0.157890	+	0.987457i	$0.449531\pi$
$602$	2.23581e6	0.251446
$603$	−9.58373e6	−1.07335
$604$	7.85634e6	0.876250
$605$	196175.	0.0217899
$606$	−4.30725e6	−0.476451
$607$	1.25739e7	1.38516	0.692578	−	0.721343i	$-0.256475\pi$
$607$	1.25739e7	1.38516	0.692578	+	0.721343i	$0.256475\pi$
$608$	3.34917e7	3.67433
$609$	−239170.	−0.0261314
$610$	−1.63694e6	−0.178118
$611$	7.44555e6	0.806852
$612$	6.41779e6	0.692639
$613$	−1.24200e6	−0.133496	−0.0667482	−	0.997770i	$-0.521262\pi$
$613$	−1.24200e6	−0.133496	−0.0667482	+	0.997770i	$0.521262\pi$
$614$	1.19167e7	1.27566
$615$	462993.	0.0493613
$616$	4.95971e6	0.526629
$617$	−1.48940e6	−0.157507	−0.0787535	−	0.996894i	$-0.525094\pi$
$617$	−1.48940e6	−0.157507	−0.0787535	+	0.996894i	$0.525094\pi$
$618$	9.70680e6	1.02236
$619$	−6.12435e6	−0.642441	−0.321221	−	0.947004i	$-0.604093\pi$
$619$	−6.12435e6	−0.642441	−0.321221	+	0.947004i	$0.604093\pi$
$620$	−4.71651e6	−0.492767
$621$	4.45406e6	0.463476
$622$	3.11359e7	3.22690
$623$	1.89610e6	0.195723
$624$	7.75262e6	0.797053
$625$	8.93342e6	0.914782
$626$	2.42825e7	2.47661
$627$	4.48118e6	0.455223
$628$	1.85831e7	1.88026
$629$	1.15446e6	0.116346
$630$	−417992.	−0.0419582
$631$	−1.51491e6	−0.151465	−0.0757327	−	0.997128i	$-0.524130\pi$
$631$	−1.51491e6	−0.151465	−0.0757327	+	0.997128i	$0.524130\pi$
$632$	−1.16288e7	−1.15809
$633$	463335.	0.0459606
$634$	−1.22994e7	−1.21523
$635$	−2.71989e6	−0.267680
$636$	1.43862e7	1.41027
$637$	5.67328e6	0.553969
$638$	8.78175e6	0.854141
$639$	−1.64282e7	−1.59162
$640$	−4.53721e6	−0.437864
$641$	−1.15234e7	−1.10773	−0.553866	−	0.832606i	$-0.686848\pi$
$641$	−1.15234e7	−1.10773	−0.553866	+	0.832606i	$0.686848\pi$
$642$	−1.36675e7	−1.30873
$643$	5.48164e6	0.522857	0.261429	−	0.965223i	$-0.415806\pi$
$643$	5.48164e6	0.522857	0.261429	+	0.965223i	$0.415806\pi$
$644$	−2.71704e6	−0.258156
$645$	−613515.	−0.0580666
$646$	−6.67773e6	−0.629575
$647$	5.77200e6	0.542083	0.271041	−	0.962568i	$-0.412632\pi$
$647$	5.77200e6	0.542083	0.271041	+	0.962568i	$0.412632\pi$
$648$	−1.84609e7	−1.72709
$649$	−4.91100e6	−0.457676
$650$	−1.13823e7	−1.05669
$651$	−732885.	−0.0677771
$652$	4.49559e7	4.14160
$653$	5.88996e6	0.540542	0.270271	−	0.962784i	$-0.412887\pi$
$653$	5.88996e6	0.540542	0.270271	+	0.962784i	$0.412887\pi$
$654$	−6.78848e6	−0.620624
$655$	2.67437e6	0.243567
$656$	−2.77031e7	−2.51344
$657$	−8.92041e6	−0.806253
$658$	−4.67338e6	−0.420791
$659$	1.19312e7	1.07021	0.535105	−	0.844786i	$-0.320272\pi$
$659$	1.19312e7	1.07021	0.535105	+	0.844786i	$0.320272\pi$
$660$	−2.17353e6	−0.194225
$661$	2.80719e6	0.249901	0.124951	−	0.992163i	$-0.460123\pi$
$661$	2.80719e6	0.249901	0.124951	+	0.992163i	$0.460123\pi$
$662$	−3.19088e7	−2.82986
$663$	−801830.	−0.0708432
$664$	−4.29503e7	−3.78047
$665$	316572.	0.0277599
$666$	−6.90939e6	−0.603607
$667$	−3.01232e6	−0.262172
$668$	−1.38615e7	−1.20190
$669$	−4.17315e6	−0.360495
$670$	−4.83671e6	−0.416259
$671$	6.79805e6	0.582879
$672$	−2.52421e6	−0.215626
$673$	1.82144e7	1.55016	0.775080	−	0.631863i	$-0.217709\pi$
$673$	1.82144e7	1.55016	0.775080	+	0.631863i	$0.217709\pi$
$674$	−2.10965e7	−1.78880
$675$	−8.52485e6	−0.720157
$676$	−2.15462e7	−1.81344
$677$	1.33845e6	0.112235	0.0561177	−	0.998424i	$-0.482128\pi$
$677$	1.33845e6	0.112235	0.0561177	+	0.998424i	$0.482128\pi$
$678$	1.11348e7	0.930265
$679$	3.55458e6	0.295879
$680$	2.02807e6	0.168194
$681$	−6.46044e6	−0.533819
$682$	2.69098e7	2.21539
$683$	6.38403e6	0.523653	0.261826	−	0.965115i	$-0.415675\pi$
$683$	6.38403e6	0.523653	0.261826	+	0.965115i	$0.415675\pi$
$684$	2.90906e7	2.37746
$685$	−1.97175e6	−0.160555
$686$	−7.20889e6	−0.584868
$687$	−3.72540e6	−0.301148
$688$	3.67096e7	2.95671
$689$	9.23804e6	0.741365
$690$	1.02429e6	0.0819033
$691$	9.16905e6	0.730515	0.365258	−	0.930906i	$-0.380981\pi$
$691$	9.16905e6	0.730515	0.365258	+	0.930906i	$0.380981\pi$
$692$	−2.54735e7	−2.02220
$693$	1.73588e6	0.137305
$694$	2.99491e7	2.36040
$695$	−3.05899e6	−0.240224
$696$	−6.94517e6	−0.543450
$697$	2.86524e6	0.223398
$698$	−7.85843e6	−0.610516
$699$	632779.	0.0489846
$700$	5.20028e6	0.401126
$701$	−1.72942e7	−1.32925	−0.664624	−	0.747178i	$-0.731408\pi$
$701$	−1.72942e7	−1.32925	−0.664624	+	0.747178i	$0.731408\pi$
$702$	1.05316e7	0.806584
$703$	5.23293e6	0.399353
$704$	4.40632e7	3.35077
$705$	1.28239e6	0.0971735
$706$	7.47137e6	0.564142
$707$	1.26366e6	0.0950785
$708$	6.20284e6	0.465059
$709$	1.73539e7	1.29653	0.648264	−	0.761416i	$-0.275495\pi$
$709$	1.73539e7	1.29653	0.648264	+	0.761416i	$0.275495\pi$
$710$	−8.29100e6	−0.617250
$711$	−4.07003e6	−0.301942
$712$	5.50602e7	4.07041
$713$	−9.23062e6	−0.679997
$714$	503288.	0.0369463
$715$	−1.39573e6	−0.102102
$716$	−4.43729e7	−3.23471
$717$	−690083.	−0.0501307
$718$	1.48027e7	1.07159
$719$	−2.96207e6	−0.213684	−0.106842	−	0.994276i	$-0.534074\pi$
$719$	−2.96207e6	−0.213684	−0.106842	+	0.994276i	$0.534074\pi$
$720$	−6.86296e6	−0.493379
$721$	−2.84779e6	−0.204018
$722$	−3.41753e6	−0.243988
$723$	−1.80397e6	−0.128346
$724$	3.74109e7	2.65248
$725$	5.76543e6	0.407368
$726$	1.41369e6	0.0995433
$727$	1.25737e7	0.882320	0.441160	−	0.897428i	$-0.354567\pi$
$727$	1.25737e7	0.882320	0.441160	+	0.897428i	$0.354567\pi$
$728$	−4.02266e6	−0.281309
$729$	−2.16776e6	−0.151075
$730$	−4.50195e6	−0.312675
$731$	−3.79676e6	−0.262796
$732$	−8.58629e6	−0.592281
$733$	2.30416e7	1.58399	0.791997	−	0.610525i	$-0.209041\pi$
$733$	2.30416e7	1.58399	0.791997	+	0.610525i	$0.209041\pi$
$734$	1.43636e7	0.984064
$735$	977142.	0.0667175
$736$	−3.17922e7	−2.16335
$737$	2.00864e7	1.36218
$738$	−1.71484e7	−1.15900
$739$	−1.33952e7	−0.902272	−0.451136	−	0.892455i	$-0.648981\pi$
$739$	−1.33952e7	−0.902272	−0.451136	+	0.892455i	$0.648981\pi$
$740$	−2.53815e6	−0.170388
$741$	−3.63454e6	−0.243166
$742$	−5.79848e6	−0.386638
$743$	2.22038e7	1.47555	0.737777	−	0.675045i	$-0.235876\pi$
$743$	2.22038e7	1.47555	0.737777	+	0.675045i	$0.235876\pi$
$744$	−2.12820e7	−1.40955
$745$	−3.39141e6	−0.223867
$746$	4.12243e7	2.71210
$747$	−1.50324e7	−0.985660
$748$	−1.34510e7	−0.879021
$749$	4.00977e6	0.261165
$750$	−3.97877e6	−0.258283
$751$	2.08648e7	1.34994	0.674971	−	0.737844i	$-0.264156\pi$
$751$	2.08648e7	1.34994	0.674971	+	0.737844i	$0.264156\pi$
$752$	−7.67317e7	−4.94801
$753$	−3.88921e6	−0.249962
$754$	−7.12258e6	−0.456256
$755$	868919.	0.0554769
$756$	−4.81159e6	−0.306185
$757$	1.35666e7	0.860464	0.430232	−	0.902718i	$-0.358432\pi$
$757$	1.35666e7	0.860464	0.430232	+	0.902718i	$0.358432\pi$
$758$	−4.22572e7	−2.67133
$759$	−4.25378e6	−0.268022
$760$	9.19283e6	0.577318
$761$	8.18181e6	0.512139	0.256069	−	0.966658i	$-0.417572\pi$
$761$	8.18181e6	0.512139	0.256069	+	0.966658i	$0.417572\pi$
$762$	−1.96002e7	−1.22285
$763$	1.99161e6	0.123849
$764$	−8.02006e7	−4.97101
$765$	709815.	0.0438522
$766$	−1.31116e7	−0.807392
$767$	3.98315e6	0.244477
$768$	−1.18903e7	−0.727427
$769$	−3.19276e7	−1.94693	−0.973464	−	0.228840i	$-0.926507\pi$
$769$	−3.19276e7	−1.94693	−0.973464	+	0.228840i	$0.926507\pi$
$770$	876063.	0.0532486
$771$	1.87466e6	0.113576
$772$	4.69176e7	2.83330
$773$	−1.69224e7	−1.01862	−0.509311	−	0.860583i	$-0.670100\pi$
$773$	−1.69224e7	−1.01862	−0.509311	+	0.860583i	$0.670100\pi$
$774$	2.27235e7	1.36340
$775$	1.76669e7	1.05659
$776$	1.03220e8	6.15334
$777$	−394396.	−0.0234358
$778$	−2.95976e7	−1.75310
$779$	1.29876e7	0.766805
$780$	1.76288e6	0.103749
$781$	3.44317e7	2.01990
$782$	6.33887e6	0.370676
$783$	−5.33450e6	−0.310949
$784$	−5.84672e7	−3.39721
$785$	2.05531e6	0.119043
$786$	1.92722e7	1.11269
$787$	1.99929e7	1.15064	0.575318	−	0.817929i	$-0.304878\pi$
$787$	1.99929e7	1.15064	0.575318	+	0.817929i	$0.304878\pi$
$788$	−7.45825e7	−4.27879
$789$	−1.29167e7	−0.738687
$790$	−2.05406e6	−0.117097
$791$	−3.26672e6	−0.185640
$792$	5.04076e7	2.85550
$793$	−5.51367e6	−0.311356
$794$	−6.55405e7	−3.68942
$795$	1.59112e6	0.0892865
$796$	4.34425e7	2.43014
$797$	1.78884e6	0.0997529	0.0498764	−	0.998755i	$-0.484117\pi$
$797$	1.78884e6	0.0997529	0.0498764	+	0.998755i	$0.484117\pi$
$798$	2.28130e6	0.126817
$799$	7.93612e6	0.439786
$800$	6.08486e7	3.36144
$801$	1.92708e7	1.06125
$802$	−3.49158e7	−1.91684
$803$	1.86961e7	1.02321
$804$	−2.53701e7	−1.38415
$805$	−300508.	−0.0163443
$806$	−2.18256e7	−1.18339
$807$	1.04236e7	0.563420
$808$	3.66951e7	1.97733
$809$	2.99178e7	1.60716	0.803580	−	0.595197i	$-0.202926\pi$
$809$	2.99178e7	1.60716	0.803580	+	0.595197i	$0.202926\pi$
$810$	−3.26086e6	−0.174630
$811$	−3.66868e7	−1.95865	−0.979327	−	0.202281i	$-0.935165\pi$
$811$	−3.66868e7	−1.95865	−0.979327	+	0.202281i	$0.935165\pi$
$812$	3.25412e6	0.173198
$813$	5.82167e6	0.308902
$814$	1.44813e7	0.766031
$815$	4.97217e6	0.262212
$816$	8.26343e6	0.434445
$817$	−1.72100e7	−0.902038
$818$	4.59596e7	2.40156
$819$	−1.40791e6	−0.0733442
$820$	−6.29943e6	−0.327165
$821$	−1.79085e7	−0.927258	−0.463629	−	0.886029i	$-0.653453\pi$
$821$	−1.79085e7	−0.927258	−0.463629	+	0.886029i	$0.653453\pi$
$822$	−1.42090e7	−0.733470
$823$	1.56081e7	0.803249	0.401624	−	0.915805i	$-0.368446\pi$
$823$	1.56081e7	0.803249	0.401624	+	0.915805i	$0.368446\pi$
$824$	−8.26959e7	−4.24293
$825$	8.14153e6	0.416458
$826$	−2.50012e6	−0.127500
$827$	−2.85223e6	−0.145017	−0.0725087	−	0.997368i	$-0.523101\pi$
$827$	−2.85223e6	−0.145017	−0.0725087	+	0.997368i	$0.523101\pi$
$828$	−2.76144e7	−1.39978
$829$	1.60380e7	0.810521	0.405260	−	0.914201i	$-0.367181\pi$
$829$	1.60380e7	0.810521	0.405260	+	0.914201i	$0.367181\pi$
$830$	−7.58655e6	−0.382251
$831$	−1.27445e7	−0.640206
$832$	−3.57382e7	−1.78988
$833$	6.04708e6	0.301949
$834$	−2.20439e7	−1.09742
$835$	−1.53310e6	−0.0760946
$836$	−6.09705e7	−3.01720
$837$	−1.63464e7	−0.806509
$838$	−2.49638e6	−0.122801
$839$	1.34570e7	0.659999	0.329999	−	0.943981i	$-0.392951\pi$
$839$	1.34570e7	0.659999	0.329999	+	0.943981i	$0.392951\pi$
$840$	−692846.	−0.0338796
$841$	−1.69034e7	−0.824107
$842$	7.88183e7	3.83130
$843$	1.12612e7	0.545778
$844$	−6.30409e6	−0.304625
$845$	−2.38303e6	−0.114812
$846$	−4.74975e7	−2.28163
$847$	−414749.	−0.0198645
$848$	−9.52046e7	−4.54641
$849$	−5.00812e6	−0.238455
$850$	−1.21323e7	−0.575963
$851$	−4.96738e6	−0.235128
$852$	−4.34890e7	−2.05249
$853$	2.39928e6	0.112904	0.0564518	−	0.998405i	$-0.482021\pi$
$853$	2.39928e6	0.112904	0.0564518	+	0.998405i	$0.482021\pi$
$854$	3.46079e6	0.162379
$855$	3.21745e6	0.150521
$856$	1.16438e8	5.43139
$857$	−2.52993e7	−1.17668	−0.588338	−	0.808615i	$-0.700217\pi$
$857$	−2.52993e7	−1.17668	−0.588338	+	0.808615i	$0.700217\pi$
$858$	−1.00580e7	−0.466437
$859$	−2.20624e7	−1.02016	−0.510082	−	0.860126i	$-0.670385\pi$
$859$	−2.20624e7	−1.02016	−0.510082	+	0.860126i	$0.670385\pi$
$860$	8.34743e6	0.384863
$861$	−978850.	−0.0449996
$862$	−8.09387e6	−0.371012
$863$	−2.99085e7	−1.36700	−0.683498	−	0.729952i	$-0.739542\pi$
$863$	−2.99085e7	−1.36700	−0.683498	+	0.729952i	$0.739542\pi$
$864$	−5.63006e7	−2.56583
$865$	−2.81740e6	−0.128029
$866$	3.93655e7	1.78370
$867$	8.07785e6	0.364962
$868$	9.97155e6	0.449225
$869$	8.53031e6	0.383191
$870$	−1.22676e6	−0.0549494
$871$	−1.62914e7	−0.727633
$872$	5.78337e7	2.57567
$873$	3.61266e7	1.60432
$874$	2.87328e7	1.27233
$875$	1.16729e6	0.0515419
$876$	−2.36142e7	−1.03971
$877$	2.41666e7	1.06100	0.530501	−	0.847684i	$-0.322004\pi$
$877$	2.41666e7	1.06100	0.530501	+	0.847684i	$0.322004\pi$
$878$	−3.68441e7	−1.61299
$879$	1.10960e7	0.484388
$880$	1.43840e7	0.626141
$881$	2.52300e7	1.09516	0.547580	−	0.836754i	$-0.315549\pi$
$881$	2.52300e7	1.09516	0.547580	+	0.836754i	$0.315549\pi$
$882$	−3.61916e7	−1.56652
$883$	−2.11423e7	−0.912536	−0.456268	−	0.889842i	$-0.650814\pi$
$883$	−2.11423e7	−0.912536	−0.456268	+	0.889842i	$0.650814\pi$
$884$	1.09096e7	0.469547
$885$	686041.	0.0294437
$886$	−7.83836e7	−3.35460
$887$	−4.84808e6	−0.206900	−0.103450	−	0.994635i	$-0.532988\pi$
$887$	−4.84808e6	−0.206900	−0.103450	+	0.994635i	$0.532988\pi$
$888$	−1.14527e7	−0.487390
$889$	5.75033e6	0.244027
$890$	9.72560e6	0.411568
$891$	1.35420e7	0.571464
$892$	5.67795e7	2.38935
$893$	3.59729e7	1.50955
$894$	−2.44394e7	−1.02270
$895$	−4.90769e6	−0.204795
$896$	9.59249e6	0.399173
$897$	3.45010e6	0.143170
$898$	−1.77326e7	−0.733807
$899$	1.10552e7	0.456214
$900$	5.28525e7	2.17500
$901$	9.84672e6	0.404091
$902$	3.59411e7	1.47087
$903$	1.29708e6	0.0529356
$904$	−9.48613e7	−3.86072
$905$	4.13769e6	0.167933
$906$	6.26167e6	0.253437
$907$	2.43107e6	0.0981248	0.0490624	−	0.998796i	$-0.484377\pi$
$907$	2.43107e6	0.0981248	0.0490624	+	0.998796i	$0.484377\pi$
$908$	8.79001e7	3.53814
$909$	1.28431e7	0.515538
$910$	−710545.	−0.0284438
$911$	−1.35358e7	−0.540367	−0.270183	−	0.962809i	$-0.587084\pi$
$911$	−1.35358e7	−0.540367	−0.270183	+	0.962809i	$0.587084\pi$
$912$	3.74565e7	1.49121
$913$	3.15062e7	1.25089
$914$	−8.89717e7	−3.52279
$915$	−949653.	−0.0374983
$916$	5.06874e7	1.99600
$917$	−5.65410e6	−0.222045
$918$	1.12255e7	0.439640
$919$	3.87885e7	1.51500	0.757502	−	0.652833i	$-0.226420\pi$
$919$	3.87885e7	1.51500	0.757502	+	0.652833i	$0.226420\pi$
$920$	−8.72634e6	−0.339909
$921$	6.91333e6	0.268558
$922$	−7.57180e7	−2.93340
$923$	−2.79264e7	−1.07897
$924$	4.59523e6	0.177063
$925$	9.50732e6	0.365345
$926$	−1.19408e6	−0.0457622
$927$	−2.89432e7	−1.10623
$928$	3.80766e7	1.45140
$929$	1.14924e7	0.436891	0.218445	−	0.975849i	$-0.429901\pi$
$929$	1.14924e7	0.436891	0.218445	+	0.975849i	$0.429901\pi$
$930$	−3.75916e6	−0.142522
$931$	2.74102e7	1.03643
$932$	−8.60953e6	−0.324668
$933$	1.80631e7	0.679343
$934$	−6.95430e7	−2.60847
$935$	−1.48769e6	−0.0556523
$936$	−4.08839e7	−1.52533
$937$	−2.58073e7	−0.960271	−0.480135	−	0.877194i	$-0.659412\pi$
$937$	−2.58073e7	−0.960271	−0.480135	+	0.877194i	$0.659412\pi$
$938$	1.02257e7	0.379477
$939$	1.40872e7	0.521388
$940$	−1.74481e7	−0.644063
$941$	−5.08863e7	−1.87338	−0.936692	−	0.350153i	$-0.886130\pi$
$941$	−5.08863e7	−1.87338	−0.936692	+	0.350153i	$0.886130\pi$
$942$	1.48111e7	0.543827
$943$	−1.23285e7	−0.451473
$944$	−4.10492e7	−1.49925
$945$	−532167.	−0.0193851
$946$	−4.76258e7	−1.73027
$947$	−2.11506e6	−0.0766385	−0.0383193	−	0.999266i	$-0.512200\pi$
$947$	−2.11506e6	−0.0766385	−0.0383193	+	0.999266i	$0.512200\pi$
$948$	−1.07742e7	−0.389372
$949$	−1.51638e7	−0.546566
$950$	−5.49932e7	−1.97697
$951$	−7.13534e6	−0.255837
$952$	−4.28770e6	−0.153332
$953$	−4.43252e6	−0.158095	−0.0790476	−	0.996871i	$-0.525188\pi$
$953$	−4.43252e6	−0.158095	−0.0790476	+	0.996871i	$0.525188\pi$
$954$	−5.89323e7	−2.09644
$955$	−8.87027e6	−0.314723
$956$	9.38920e6	0.332264
$957$	5.09463e6	0.179818
$958$	5.92381e6	0.208539
$959$	4.16863e6	0.146368
$960$	−6.15540e6	−0.215565
$961$	5.24727e6	0.183284
$962$	−1.17453e7	−0.409191
$963$	4.07529e7	1.41610
$964$	2.45446e7	0.850675
$965$	5.18913e6	0.179381
$966$	−2.16554e6	−0.0746661
$967$	4.56153e6	0.156872	0.0784358	−	0.996919i	$-0.475007\pi$
$967$	4.56153e6	0.156872	0.0784358	+	0.996919i	$0.475007\pi$
$968$	−1.20437e7	−0.413117
$969$	−3.87401e6	−0.132541
$970$	1.82324e7	0.622177
$971$	1.43825e6	0.0489538	0.0244769	−	0.999700i	$-0.492208\pi$
$971$	1.43825e6	0.0489538	0.0244769	+	0.999700i	$0.492208\pi$
$972$	−7.55209e7	−2.56390
$973$	6.46726e6	0.218997
$974$	9.50829e7	3.21148
$975$	−6.60332e6	−0.222459
$976$	5.68223e7	1.90939
$977$	−7.59482e6	−0.254555	−0.127277	−	0.991867i	$-0.540624\pi$
$977$	−7.59482e6	−0.254555	−0.127277	+	0.991867i	$0.540624\pi$
$978$	3.58308e7	1.19787
$979$	−4.03894e7	−1.34682
$980$	−1.32949e7	−0.442201
$981$	2.02415e7	0.671538
$982$	−5.45815e7	−1.80620
$983$	966289.	0.0318950
$983$	966289.	0.0318950
$984$	−2.84245e7	−0.935847
$985$	−8.24890e6	−0.270898
$986$	−7.59187e6	−0.248689
$987$	−2.71121e6	−0.0885870
$988$	4.94511e7	1.61170
$989$	1.63366e7	0.531095
$990$	8.90378e6	0.288726
$991$	1.98452e7	0.641905	0.320953	−	0.947095i	$-0.395997\pi$
$991$	1.98452e7	0.641905	0.320953	+	0.947095i	$0.395997\pi$
$992$	1.16678e8	3.76451
$993$	−1.85115e7	−0.595756
$994$	1.75287e7	0.562708
$995$	4.80478e6	0.153857
$996$	−3.97939e7	−1.27107
$997$	−9.61879e6	−0.306466	−0.153233	−	0.988190i	$-0.548969\pi$
$997$	−9.61879e6	−0.306466	−0.153233	+	0.988190i	$0.548969\pi$
$998$	−9.08300e7	−2.88671
$999$	−8.79670e6	−0.278873

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.6.a.b.1.6	✓	218

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.6.a.b.1.6	✓	218	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:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q-10.8442 q^{2} -6.29114 q^{3} +85.5966 q^{4} +9.46707 q^{5} +68.2223 q^{6} -20.0151 q^{7} -581.212 q^{8} -203.422 q^{9} +O(q^{10})\)	\(q-10.8442 q^{2} -6.29114 q^{3} +85.5966 q^{4} +9.46707 q^{5} +68.2223 q^{6} -20.0151 q^{7} -581.212 q^{8} -203.422 q^{9} -102.663 q^{10} +426.348 q^{11} -538.500 q^{12} -345.797 q^{13} +217.048 q^{14} -59.5586 q^{15} +3563.68 q^{16} -368.580 q^{17} +2205.94 q^{18} -1670.70 q^{19} +810.349 q^{20} +125.918 q^{21} -4623.40 q^{22} +1585.92 q^{23} +3656.48 q^{24} -3035.37 q^{25} +3749.89 q^{26} +2808.50 q^{27} -1713.22 q^{28} -1899.41 q^{29} +645.865 q^{30} -5820.35 q^{31} -20046.5 q^{32} -2682.21 q^{33} +3996.96 q^{34} -189.484 q^{35} -17412.2 q^{36} -3132.17 q^{37} +18117.4 q^{38} +2175.45 q^{39} -5502.37 q^{40} -7773.73 q^{41} -1365.48 q^{42} +10301.0 q^{43} +36493.9 q^{44} -1925.81 q^{45} -17198.1 q^{46} -21531.6 q^{47} -22419.6 q^{48} -16406.4 q^{49} +32916.2 q^{50} +2318.79 q^{51} -29599.0 q^{52} -26715.2 q^{53} -30455.9 q^{54} +4036.27 q^{55} +11633.0 q^{56} +10510.6 q^{57} +20597.6 q^{58} -11518.8 q^{59} -5098.01 q^{60} +15944.8 q^{61} +63117.0 q^{62} +4071.50 q^{63} +103350. q^{64} -3273.68 q^{65} +29086.5 q^{66} +47112.6 q^{67} -31549.2 q^{68} -9977.25 q^{69} +2054.81 q^{70} +80759.6 q^{71} +118231. q^{72} +43851.8 q^{73} +33965.9 q^{74} +19096.0 q^{75} -143006. q^{76} -8533.40 q^{77} -23591.0 q^{78} +20007.9 q^{79} +33737.6 q^{80} +31762.8 q^{81} +84299.8 q^{82} +73897.8 q^{83} +10778.1 q^{84} -3489.38 q^{85} -111706. q^{86} +11949.5 q^{87} -247799. q^{88} -94733.5 q^{89} +20883.8 q^{90} +6921.15 q^{91} +135750. q^{92} +36616.6 q^{93} +233493. q^{94} -15816.7 q^{95} +126115. q^{96} -177595. q^{97} +177914. q^{98} -86728.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9}+O(q^{10}) \) 218 * q + 35 * q^2 + 70 * q^3 + 3685 * q^4 + 253 * q^5 + 529 * q^6 + 1567 * q^7 + 1695 * q^8 + 19812 * q^9	\( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9} + 2133 q^{10} + 1752 q^{11} + 3512 q^{12} + 5990 q^{13} + 2319 q^{14} + 4639 q^{15} + 66105 q^{16} + 10656 q^{17} + 11911 q^{18} + 11511 q^{19} + 10012 q^{20} + 12225 q^{21} + 19401 q^{22} + 9767 q^{23} + 21725 q^{24} + 185207 q^{25} + 7708 q^{26} + 23764 q^{27} + 77808 q^{28} + 25772 q^{29} + 15736 q^{30} + 35900 q^{31} + 60155 q^{32} + 70026 q^{33} + 17236 q^{34} + 28782 q^{35} + 382874 q^{36} + 126082 q^{37} + 62164 q^{38} + 54264 q^{39} + 102846 q^{40} + 70480 q^{41} + 102244 q^{42} + 137413 q^{43} + 116278 q^{44} + 93481 q^{45} + 126122 q^{46} + 63218 q^{47} + 124701 q^{48} + 732031 q^{49} + 131089 q^{50} + 109902 q^{51} + 229519 q^{52} + 102608 q^{53} + 149130 q^{54} + 167596 q^{55} + 87868 q^{56} + 408318 q^{57} + 304579 q^{58} + 67460 q^{59} + 150523 q^{60} + 195132 q^{61} + 132294 q^{62} + 374425 q^{63} + 1296639 q^{64} + 347092 q^{65} + 147397 q^{66} + 381238 q^{67} + 296321 q^{68} + 139362 q^{69} + 325675 q^{70} + 147818 q^{71} + 646059 q^{72} + 961992 q^{73} + 167410 q^{74} + 167324 q^{75} + 504875 q^{76} + 284328 q^{77} + 284295 q^{78} + 285792 q^{79} + 444932 q^{80} + 1980282 q^{81} + 336676 q^{82} + 276734 q^{83} + 378474 q^{84} + 1021245 q^{85} + 156051 q^{86} + 500457 q^{87} + 1068101 q^{88} + 398983 q^{89} + 463961 q^{90} + 273517 q^{91} + 577884 q^{92} + 967833 q^{93} + 224775 q^{94} + 482817 q^{95} + 780445 q^{96} + 1636277 q^{97} + 495958 q^{98} + 627643 q^{99}+O(q^{100}) \) 218 * q + 35 * q^2 + 70 * q^3 + 3685 * q^4 + 253 * q^5 + 529 * q^6 + 1567 * q^7 + 1695 * q^8 + 19812 * q^9 + 2133 * q^10 + 1752 * q^11 + 3512 * q^12 + 5990 * q^13 + 2319 * q^14 + 4639 * q^15 + 66105 * q^16 + 10656 * q^17 + 11911 * q^18 + 11511 * q^19 + 10012 * q^20 + 12225 * q^21 + 19401 * q^22 + 9767 * q^23 + 21725 * q^24 + 185207 * q^25 + 7708 * q^26 + 23764 * q^27 + 77808 * q^28 + 25772 * q^29 + 15736 * q^30 + 35900 * q^31 + 60155 * q^32 + 70026 * q^33 + 17236 * q^34 + 28782 * q^35 + 382874 * q^36 + 126082 * q^37 + 62164 * q^38 + 54264 * q^39 + 102846 * q^40 + 70480 * q^41 + 102244 * q^42 + 137413 * q^43 + 116278 * q^44 + 93481 * q^45 + 126122 * q^46 + 63218 * q^47 + 124701 * q^48 + 732031 * q^49 + 131089 * q^50 + 109902 * q^51 + 229519 * q^52 + 102608 * q^53 + 149130 * q^54 + 167596 * q^55 + 87868 * q^56 + 408318 * q^57 + 304579 * q^58 + 67460 * q^59 + 150523 * q^60 + 195132 * q^61 + 132294 * q^62 + 374425 * q^63 + 1296639 * q^64 + 347092 * q^65 + 147397 * q^66 + 381238 * q^67 + 296321 * q^68 + 139362 * q^69 + 325675 * q^70 + 147818 * q^71 + 646059 * q^72 + 961992 * q^73 + 167410 * q^74 + 167324 * q^75 + 504875 * q^76 + 284328 * q^77 + 284295 * q^78 + 285792 * q^79 + 444932 * q^80 + 1980282 * q^81 + 336676 * q^82 + 276734 * q^83 + 378474 * q^84 + 1021245 * q^85 + 156051 * q^86 + 500457 * q^87 + 1068101 * q^88 + 398983 * q^89 + 463961 * q^90 + 273517 * q^91 + 577884 * q^92 + 967833 * q^93 + 224775 * q^94 + 482817 * q^95 + 780445 * q^96 + 1636277 * q^97 + 495958 * q^98 + 627643 * q^99

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