LMFDB - Embedded newform 983.6.a.b.1.10

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			1.10
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)

$f(q)$	$=$	$q-10.6888 q^{2} -2.78158 q^{3} +82.2511 q^{4} +63.0885 q^{5} +29.7318 q^{6} -133.230 q^{7} -537.126 q^{8} -235.263 q^{9} +O(q^{10})$	\(q-10.6888 q^{2} -2.78158 q^{3} +82.2511 q^{4} +63.0885 q^{5} +29.7318 q^{6} -133.230 q^{7} -537.126 q^{8} -235.263 q^{9} -674.342 q^{10} -520.644 q^{11} -228.788 q^{12} +832.917 q^{13} +1424.07 q^{14} -175.485 q^{15} +3109.21 q^{16} -500.818 q^{17} +2514.68 q^{18} +8.57451 q^{19} +5189.10 q^{20} +370.589 q^{21} +5565.08 q^{22} -3525.32 q^{23} +1494.06 q^{24} +855.153 q^{25} -8902.91 q^{26} +1330.33 q^{27} -10958.3 q^{28} -8302.63 q^{29} +1875.74 q^{30} +5714.23 q^{31} -16045.8 q^{32} +1448.21 q^{33} +5353.16 q^{34} -8405.26 q^{35} -19350.6 q^{36} -4908.31 q^{37} -91.6515 q^{38} -2316.82 q^{39} -33886.5 q^{40} -9348.85 q^{41} -3961.16 q^{42} -641.942 q^{43} -42823.6 q^{44} -14842.4 q^{45} +37681.5 q^{46} -9958.04 q^{47} -8648.52 q^{48} +943.151 q^{49} -9140.59 q^{50} +1393.07 q^{51} +68508.4 q^{52} +9246.87 q^{53} -14219.6 q^{54} -32846.6 q^{55} +71561.1 q^{56} -23.8507 q^{57} +88745.4 q^{58} -11118.1 q^{59} -14433.9 q^{60} +13407.2 q^{61} -61078.4 q^{62} +31344.0 q^{63} +72016.4 q^{64} +52547.4 q^{65} -15479.7 q^{66} -30227.2 q^{67} -41192.9 q^{68} +9805.94 q^{69} +89842.4 q^{70} -15354.0 q^{71} +126366. q^{72} -3752.01 q^{73} +52464.1 q^{74} -2378.68 q^{75} +705.263 q^{76} +69365.2 q^{77} +24764.1 q^{78} +32589.2 q^{79} +196156. q^{80} +53468.5 q^{81} +99928.3 q^{82} -64470.6 q^{83} +30481.4 q^{84} -31595.8 q^{85} +6861.61 q^{86} +23094.4 q^{87} +279651. q^{88} +105721. q^{89} +158648. q^{90} -110969. q^{91} -289961. q^{92} -15894.6 q^{93} +106440. q^{94} +540.952 q^{95} +44632.8 q^{96} -119437. q^{97} -10081.2 q^{98} +122488. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−10.6888	−1.88954	−0.944768	−	0.327739i	$-0.893713\pi$
$2$	−10.6888	−1.88954	−0.944768	+	0.327739i	$0.893713\pi$
$3$	−2.78158	−0.178438	−0.0892192	−	0.996012i	$-0.528437\pi$
$3$	−2.78158	−0.178438	−0.0892192	+	0.996012i	$0.528437\pi$
$4$	82.2511	2.57035
$5$	63.0885	1.12856	0.564280	−	0.825583i	$-0.309154\pi$
$5$	63.0885	1.12856	0.564280	+	0.825583i	$0.309154\pi$
$6$	29.7318	0.337166
$7$	−133.230	−1.02768	−0.513838	−	0.857887i	$-0.671777\pi$
$7$	−133.230	−1.02768	−0.513838	+	0.857887i	$0.671777\pi$
$8$	−537.126	−2.96723
$9$	−235.263	−0.968160
$10$	−674.342	−2.13246
$11$	−520.644	−1.29736	−0.648678	−	0.761063i	$-0.724678\pi$
$11$	−520.644	−1.29736	−0.648678	+	0.761063i	$0.724678\pi$
$12$	−228.788	−0.458649
$13$	832.917	1.36692	0.683460	−	0.729988i	$-0.260474\pi$
$13$	832.917	1.36692	0.683460	+	0.729988i	$0.260474\pi$
$14$	1424.07	1.94183
$15$	−175.485	−0.201378
$16$	3109.21	3.03634
$17$	−500.818	−0.420298	−0.210149	−	0.977669i	$-0.567395\pi$
$17$	−500.818	−0.420298	−0.210149	+	0.977669i	$0.567395\pi$
$18$	2514.68	1.82937
$19$	8.57451	0.00544911	0.00272455	−	0.999996i	$-0.499133\pi$
$19$	8.57451	0.00544911	0.00272455	+	0.999996i	$0.499133\pi$
$20$	5189.10	2.90079
$21$	370.589	0.183377
$22$	5565.08	2.45140
$23$	−3525.32	−1.38956	−0.694782	−	0.719221i	$-0.744499\pi$
$23$	−3525.32	−1.38956	−0.694782	+	0.719221i	$0.744499\pi$
$24$	1494.06	0.529468
$25$	855.153	0.273649
$26$	−8902.91	−2.58285
$27$	1330.33	0.351195
$28$	−10958.3	−2.64148
$29$	−8302.63	−1.83325	−0.916623	−	0.399753i	$-0.869096\pi$
$29$	−8302.63	−1.83325	−0.916623	+	0.399753i	$0.869096\pi$
$30$	1875.74	0.380512
$31$	5714.23	1.06796	0.533978	−	0.845498i	$-0.320697\pi$
$31$	5714.23	1.06796	0.533978	+	0.845498i	$0.320697\pi$
$32$	−16045.8	−2.77005
$33$	1448.21	0.231498
$34$	5353.16	0.794169
$35$	−8405.26	−1.15979
$36$	−19350.6	−2.48851
$37$	−4908.31	−0.589424	−0.294712	−	0.955586i	$-0.595224\pi$
$37$	−4908.31	−0.589424	−0.294712	+	0.955586i	$0.595224\pi$
$38$	−91.6515	−0.0102963
$39$	−2316.82	−0.243911
$40$	−33886.5	−3.34870
$41$	−9348.85	−0.868558	−0.434279	−	0.900778i	$-0.642997\pi$
$41$	−9348.85	−0.868558	−0.434279	+	0.900778i	$0.642997\pi$
$42$	−3961.16	−0.346497
$43$	−641.942	−0.0529449	−0.0264725	−	0.999650i	$-0.508427\pi$
$43$	−641.942	−0.0529449	−0.0264725	+	0.999650i	$0.508427\pi$
$44$	−42823.6	−3.33466
$45$	−14842.4	−1.09263
$46$	37681.5	2.62563
$47$	−9958.04	−0.657550	−0.328775	−	0.944408i	$-0.606636\pi$
$47$	−9958.04	−0.657550	−0.328775	+	0.944408i	$0.606636\pi$
$48$	−8648.52	−0.541800
$49$	943.151	0.0561166
$50$	−9140.59	−0.517070
$51$	1393.07	0.0749974
$52$	68508.4	3.51346
$53$	9246.87	0.452173	0.226087	−	0.974107i	$-0.427407\pi$
$53$	9246.87	0.452173	0.226087	+	0.974107i	$0.427407\pi$
$54$	−14219.6	−0.663596
$55$	−32846.6	−1.46414
$56$	71561.1	3.04935
$57$	−23.8507	−0.000972329 0
$58$	88745.4	3.46399
$59$	−11118.1	−0.415817	−0.207908	−	0.978148i	$-0.566666\pi$
$59$	−11118.1	−0.415817	−0.207908	+	0.978148i	$0.566666\pi$
$60$	−14433.9	−0.517613
$61$	13407.2	0.461334	0.230667	−	0.973033i	$-0.425909\pi$
$61$	13407.2	0.461334	0.230667	+	0.973033i	$0.425909\pi$
$62$	−61078.4	−2.01794
$63$	31344.0	0.994954
$64$	72016.4	2.19777
$65$	52547.4	1.54265
$66$	−15479.7	−0.437424
$67$	−30227.2	−0.822643	−0.411322	−	0.911490i	$-0.634933\pi$
$67$	−30227.2	−0.822643	−0.411322	+	0.911490i	$0.634933\pi$
$68$	−41192.9	−1.08031
$69$	9805.94	0.247951
$70$	89842.4	2.19147
$71$	−15354.0	−0.361474	−0.180737	−	0.983531i	$-0.557848\pi$
$71$	−15354.0	−0.361474	−0.180737	+	0.983531i	$0.557848\pi$
$72$	126366.	2.87275
$73$	−3752.01	−0.0824057	−0.0412028	−	0.999151i	$-0.513119\pi$
$73$	−3752.01	−0.0824057	−0.0412028	+	0.999151i	$0.513119\pi$
$74$	52464.1	1.11374
$75$	−2378.68	−0.0488295
$76$	705.263	0.0140061
$77$	69365.2	1.33326
$78$	24764.1	0.460879
$79$	32589.2	0.587497	0.293748	−	0.955883i	$-0.405097\pi$
$79$	32589.2	0.587497	0.293748	+	0.955883i	$0.405097\pi$
$80$	196156.	3.42670
$81$	53468.5	0.905493
$82$	99928.3	1.64117
$83$	−64470.6	−1.02723	−0.513613	−	0.858022i	$-0.671693\pi$
$83$	−64470.6	−1.02723	−0.513613	+	0.858022i	$0.671693\pi$
$84$	30481.4	0.471342
$85$	−31595.8	−0.474332
$86$	6861.61	0.100041
$87$	23094.4	0.327121
$88$	279651.	3.84955
$89$	105721.	1.41478	0.707389	−	0.706825i	$-0.249873\pi$
$89$	105721.	1.41478	0.707389	+	0.706825i	$0.249873\pi$
$90$	158648.	2.06456
$91$	−110969.	−1.40475
$92$	−289961.	−3.57166
$93$	−15894.6	−0.190564
$94$	106440.	1.24247
$95$	540.952	0.00614965
$96$	44632.8	0.494283
$97$	−119437.	−1.28887	−0.644435	−	0.764659i	$-0.722907\pi$
$97$	−119437.	−1.28887	−0.644435	+	0.764659i	$0.722907\pi$
$98$	−10081.2	−0.106034
$99$	122488.	1.25605
$100$	70337.3	0.703373
$101$	−89083.9	−0.868952	−0.434476	−	0.900683i	$-0.643066\pi$
$101$	−89083.9	−0.868952	−0.434476	+	0.900683i	$0.643066\pi$
$102$	−14890.2	−0.141710
$103$	33541.0	0.311518	0.155759	−	0.987795i	$-0.450218\pi$
$103$	33541.0	0.311518	0.155759	+	0.987795i	$0.450218\pi$
$104$	−447381.	−4.05597
$105$	23379.9	0.206952
$106$	−98838.2	−0.854398
$107$	−92674.1	−0.782527	−0.391263	−	0.920279i	$-0.627962\pi$
$107$	−92674.1	−0.782527	−0.391263	+	0.920279i	$0.627962\pi$
$108$	109421.	0.902694
$109$	−24350.5	−0.196309	−0.0981547	−	0.995171i	$-0.531294\pi$
$109$	−24350.5	−0.196309	−0.0981547	+	0.995171i	$0.531294\pi$
$110$	351092.	2.76656
$111$	13652.8	0.105176
$112$	−414240.	−3.12037
$113$	−30708.5	−0.226236	−0.113118	−	0.993582i	$-0.536084\pi$
$113$	−30708.5	−0.226236	−0.113118	+	0.993582i	$0.536084\pi$
$114$	254.936	0.00183725
$115$	−222407.	−1.56821
$116$	−682901.	−4.71208
$117$	−195954.	−1.32340
$118$	118840.	0.785701
$119$	66723.8	0.431930
$120$	94257.8	0.597536
$121$	110019.	0.683132
$122$	−143308.	−0.871707
$123$	26004.6	0.154984
$124$	470002.	2.74502
$125$	−143201.	−0.819731
$126$	−335031.	−1.88000
$127$	12535.9	0.0689680	0.0344840	−	0.999405i	$-0.489021\pi$
$127$	12535.9	0.0689680	0.0344840	+	0.999405i	$0.489021\pi$
$128$	−256305.	−1.38271
$129$	1785.61	0.00944741
$130$	−561671.	−2.91490
$131$	337550.	1.71854	0.859270	−	0.511522i	$-0.170918\pi$
$131$	337550.	1.71854	0.859270	+	0.511522i	$0.170918\pi$
$132$	119117.	0.595031
$133$	−1142.38	−0.00559991
$134$	323094.	1.55441
$135$	83928.2	0.396345
$136$	269003.	1.24712
$137$	343365.	1.56299	0.781493	−	0.623914i	$-0.214459\pi$
$137$	343365.	1.56299	0.781493	+	0.623914i	$0.214459\pi$
$138$	−104814.	−0.468513
$139$	−51559.9	−0.226347	−0.113174	−	0.993575i	$-0.536102\pi$
$139$	−51559.9	−0.226347	−0.113174	+	0.993575i	$0.536102\pi$
$140$	−691342.	−2.98107
$141$	27699.1	0.117332
$142$	164117.	0.683018
$143$	−433653.	−1.77338
$144$	−731483.	−2.93966
$145$	−523800.	−2.06893
$146$	40104.6	0.155709
$147$	−2623.45	−0.0100133
$148$	−403714.	−1.51502
$149$	−282619.	−1.04288	−0.521441	−	0.853287i	$-0.674605\pi$
$149$	−282619.	−1.04288	−0.521441	+	0.853287i	$0.674605\pi$
$150$	25425.3	0.0922651
$151$	526846.	1.88036	0.940180	−	0.340677i	$-0.110656\pi$
$151$	526846.	1.88036	0.940180	+	0.340677i	$0.110656\pi$
$152$	−4605.59	−0.0161688
$153$	117824.	0.406916
$154$	−741433.	−2.51924
$155$	360502.	1.20525
$156$	−190561.	−0.626936
$157$	−65109.3	−0.210811	−0.105406	−	0.994429i	$-0.533614\pi$
$157$	−65109.3	−0.210811	−0.105406	+	0.994429i	$0.533614\pi$
$158$	−348340.	−1.11010
$159$	−25720.9	−0.0806851
$160$	−1.01231e6	−3.12617
$161$	469677.	1.42802
$162$	−571515.	−1.71096
$163$	−586809.	−1.72993	−0.864963	−	0.501835i	$-0.832658\pi$
$163$	−586809.	−1.72993	−0.864963	+	0.501835i	$0.832658\pi$
$164$	−768954.	−2.23250
$165$	91365.5	0.261260
$166$	689115.	1.94098
$167$	300626.	0.834132	0.417066	−	0.908876i	$-0.363058\pi$
$167$	300626.	0.834132	0.417066	+	0.908876i	$0.363058\pi$
$168$	−199053.	−0.544121
$169$	322458.	0.868472
$170$	337723.	0.896268
$171$	−2017.26	−0.00527560
$172$	−52800.4	−0.136087
$173$	234963.	0.596876	0.298438	−	0.954429i	$-0.403534\pi$
$173$	234963.	0.596876	0.298438	+	0.954429i	$0.403534\pi$
$174$	−246852.	−0.618108
$175$	−113932.	−0.281222
$176$	−1.61879e6	−3.93922
$177$	30926.0	0.0741977
$178$	−1.13004e6	−2.67327
$179$	−344901.	−0.804567	−0.402283	−	0.915515i	$-0.631783\pi$
$179$	−344901.	−0.804567	−0.402283	+	0.915515i	$0.631783\pi$
$180$	−1.22080e6	−2.80843
$181$	−434527.	−0.985871	−0.492936	−	0.870066i	$-0.664076\pi$
$181$	−434527.	−0.985871	−0.492936	+	0.870066i	$0.664076\pi$
$182$	1.18613e6	2.65433
$183$	−37293.3	−0.0823196
$184$	1.89354e6	4.12316
$185$	−309658.	−0.665200
$186$	169894.	0.360078
$187$	260748.	0.545277
$188$	−819060.	−1.69013
$189$	−177239.	−0.360915
$190$	−5782.15	−0.0116200
$191$	−120924.	−0.239844	−0.119922	−	0.992783i	$-0.538265\pi$
$191$	−120924.	−0.239844	−0.119922	+	0.992783i	$0.538265\pi$
$192$	−200319.	−0.392166
$193$	160024.	0.309238	0.154619	−	0.987974i	$-0.450585\pi$
$193$	160024.	0.309238	0.154619	+	0.987974i	$0.450585\pi$
$194$	1.27664e6	2.43537
$195$	−146165.	−0.275268
$196$	77575.3	0.144239
$197$	190409.	0.349561	0.174781	−	0.984607i	$-0.444078\pi$
$197$	190409.	0.349561	0.174781	+	0.984607i	$0.444078\pi$
$198$	−1.30926e6	−2.37335
$199$	172270.	0.308374	0.154187	−	0.988042i	$-0.450724\pi$
$199$	172270.	0.308374	0.154187	+	0.988042i	$0.450724\pi$
$200$	−459325.	−0.811980
$201$	84079.4	0.146791
$202$	952203.	1.64192
$203$	1.10616e6	1.88398
$204$	114581.	0.192769
$205$	−589805.	−0.980220
$206$	−358514.	−0.588625
$207$	829376.	1.34532
$208$	2.58972e6	4.15044
$209$	−4464.27	−0.00706943
$210$	−249904.	−0.391043
$211$	222533.	0.344103	0.172051	−	0.985088i	$-0.444960\pi$
$211$	222533.	0.344103	0.172051	+	0.985088i	$0.444960\pi$
$212$	760566.	1.16224
$213$	42708.5	0.0645008
$214$	990578.	1.47861
$215$	−40499.1	−0.0597516
$216$	−714553.	−1.04208
$217$	−761305.	−1.09751
$218$	260278.	0.370934
$219$	10436.5	0.0147043
$220$	−2.70167e6	−3.76336
$221$	−417140.	−0.574515
$222$	−145933.	−0.198734
$223$	835391.	1.12494	0.562468	−	0.826819i	$-0.309852\pi$
$223$	835391.	1.12494	0.562468	+	0.826819i	$0.309852\pi$
$224$	2.13778e6	2.84671
$225$	−201186.	−0.264936
$226$	328238.	0.427481
$227$	−744213.	−0.958589	−0.479295	−	0.877654i	$-0.659107\pi$
$227$	−744213.	−0.958589	−0.479295	+	0.877654i	$0.659107\pi$
$228$	−1961.74	−0.00249923
$229$	−985759.	−1.24217	−0.621087	−	0.783742i	$-0.713309\pi$
$229$	−985759.	−1.24217	−0.621087	+	0.783742i	$0.713309\pi$
$230$	2.37727e6	2.96318
$231$	−192945.	−0.237905
$232$	4.45956e6	5.43966
$233$	783725.	0.945745	0.472873	−	0.881131i	$-0.343217\pi$
$233$	783725.	0.945745	0.472873	+	0.881131i	$0.343217\pi$
$234$	2.09452e6	2.50061
$235$	−628237.	−0.742086
$236$	−914480.	−1.06879
$237$	−90649.3	−0.104832
$238$	−713200.	−0.816148
$239$	−1.41630e6	−1.60384	−0.801920	−	0.597432i	$-0.796188\pi$
$239$	−1.41630e6	−1.60384	−0.801920	+	0.597432i	$0.796188\pi$
$240$	−545622.	−0.611454
$241$	−368356.	−0.408531	−0.204265	−	0.978916i	$-0.565481\pi$
$241$	−368356.	−0.408531	−0.204265	+	0.978916i	$0.565481\pi$
$242$	−1.17598e6	−1.29080
$243$	−471996.	−0.512770
$244$	1.10276e6	1.18579
$245$	59501.9	0.0633309
$246$	−277958.	−0.292848
$247$	7141.85	0.00744849
$248$	−3.06926e6	−3.16887
$249$	179330.	0.183297
$250$	1.53065e6	1.54891
$251$	−1.75204e6	−1.75533	−0.877665	−	0.479274i	$-0.840900\pi$
$251$	−1.75204e6	−1.75533	−0.877665	+	0.479274i	$0.840900\pi$
$252$	2.57808e6	2.55738
$253$	1.83543e6	1.80276
$254$	−133995.	−0.130318
$255$	87886.3	0.0846391
$256$	435072.	0.414917
$257$	820435.	0.774839	0.387420	−	0.921904i	$-0.373366\pi$
$257$	820435.	0.774839	0.387420	+	0.921904i	$0.373366\pi$
$258$	−19086.1	−0.0178512
$259$	653933.	0.605736
$260$	4.32209e6	3.96515
$261$	1.95330e6	1.77488
$262$	−3.60802e6	−3.24725
$263$	55700.8	0.0496561	0.0248280	−	0.999692i	$-0.492096\pi$
$263$	55700.8	0.0496561	0.0248280	+	0.999692i	$0.492096\pi$
$264$	−777873.	−0.686908
$265$	583371.	0.510305
$266$	12210.7	0.0105812
$267$	−294073.	−0.252451
$268$	−2.48622e6	−2.11448
$269$	131661.	0.110937	0.0554686	−	0.998460i	$-0.482335\pi$
$269$	131661.	0.110937	0.0554686	+	0.998460i	$0.482335\pi$
$270$	−897094.	−0.748908
$271$	−1.41306e6	−1.16880	−0.584398	−	0.811467i	$-0.698669\pi$
$271$	−1.41306e6	−1.16880	−0.584398	+	0.811467i	$0.698669\pi$
$272$	−1.55715e6	−1.27617
$273$	308670.	0.250661
$274$	−3.67017e6	−2.95332
$275$	−445230.	−0.355020
$276$	806550.	0.637322
$277$	1.29199e6	1.01172	0.505859	−	0.862616i	$-0.331175\pi$
$277$	1.29199e6	1.01172	0.505859	+	0.862616i	$0.331175\pi$
$278$	551115.	0.427691
$279$	−1.34435e6	−1.03395
$280$	4.51468e6	3.44138
$281$	1.84446e6	1.39349	0.696745	−	0.717319i	$-0.254631\pi$
$281$	1.84446e6	1.39349	0.696745	+	0.717319i	$0.254631\pi$
$282$	−296071.	−0.221704
$283$	−2.59108e6	−1.92316	−0.961580	−	0.274526i	$-0.911479\pi$
$283$	−2.59108e6	−1.92316	−0.961580	+	0.274526i	$0.911479\pi$
$284$	−1.26289e6	−0.929113
$285$	−1504.70	−0.00109733
$286$	4.63525e6	3.35087
$287$	1.24554e6	0.892595
$288$	3.77499e6	2.68185
$289$	−1.16904e6	−0.823349
$290$	5.59881e6	3.90932
$291$	332223.	0.229984
$292$	−308607.	−0.211811
$293$	−191783.	−0.130509	−0.0652547	−	0.997869i	$-0.520786\pi$
$293$	−191783.	−0.130509	−0.0652547	+	0.997869i	$0.520786\pi$
$294$	28041.6	0.0189206
$295$	−701426.	−0.469275
$296$	2.63638e6	1.74896
$297$	−692626.	−0.455625
$298$	3.02087e6	1.97056
$299$	−2.93630e6	−1.89942
$300$	−195649.	−0.125509
$301$	85525.7	0.0544102
$302$	−5.63137e6	−3.55301
$303$	247794.	0.155054
$304$	26660.0	0.0165453
$305$	845843.	0.520643
$306$	−1.25940e6	−0.768883
$307$	1.78768e6	1.08254	0.541269	−	0.840849i	$-0.317944\pi$
$307$	1.78768e6	1.08254	0.541269	+	0.840849i	$0.317944\pi$
$308$	5.70537e6	3.42694
$309$	−93297.0	−0.0555868
$310$	−3.85334e6	−2.27737
$311$	−2.95486e6	−1.73235	−0.866176	−	0.499738i	$-0.833429\pi$
$311$	−2.95486e6	−1.73235	−0.866176	+	0.499738i	$0.833429\pi$
$312$	1.24443e6	0.723740
$313$	1.76332e6	1.01735	0.508675	−	0.860959i	$-0.330136\pi$
$313$	1.76332e6	1.01735	0.508675	+	0.860959i	$0.330136\pi$
$314$	695942.	0.398335
$315$	1.97744e6	1.12287
$316$	2.68049e6	1.51007
$317$	1.20364e6	0.672742	0.336371	−	0.941730i	$-0.390800\pi$
$317$	1.20364e6	0.672742	0.336371	+	0.941730i	$0.390800\pi$
$318$	274926.	0.152457
$319$	4.32272e6	2.37837
$320$	4.54340e6	2.48031
$321$	257780.	0.139633
$322$	−5.02030e6	−2.69830
$323$	−4294.27	−0.00229025
$324$	4.39784e6	2.32743
$325$	712272.	0.374057
$326$	6.27230e6	3.26876
$327$	67732.8	0.0350291
$328$	5.02151e6	2.57721
$329$	1.32671e6	0.675748
$330$	−976590.	−0.493660
$331$	162714.	0.0816308	0.0408154	−	0.999167i	$-0.487004\pi$
$331$	162714.	0.0816308	0.0408154	+	0.999167i	$0.487004\pi$
$332$	−5.30278e6	−2.64033
$333$	1.15474e6	0.570656
$334$	−3.21334e6	−1.57612
$335$	−1.90699e6	−0.928403
$336$	1.15224e6	0.556794
$337$	1.97106e6	0.945423	0.472711	−	0.881217i	$-0.343275\pi$
$337$	1.97106e6	0.945423	0.472711	+	0.881217i	$0.343275\pi$
$338$	−3.44669e6	−1.64101
$339$	85418.0	0.0403692
$340$	−2.59879e6	−1.21920
$341$	−2.97508e6	−1.38552
$342$	21562.2	0.00996845
$343$	2.11354e6	0.970006
$344$	344804.	0.157100
$345$	618642.	0.279828
$346$	−2.51148e6	−1.12782
$347$	−56959.5	−0.0253946	−0.0126973	−	0.999919i	$-0.504042\pi$
$347$	−56959.5	−0.0253946	−0.0126973	+	0.999919i	$0.504042\pi$
$348$	1.89954e6	0.840816
$349$	−1.49028e6	−0.654946	−0.327473	−	0.944861i	$-0.606197\pi$
$349$	−1.49028e6	−0.654946	−0.327473	+	0.944861i	$0.606197\pi$
$350$	1.21780e6	0.531380
$351$	1.10805e6	0.480056
$352$	8.35417e6	3.59374
$353$	3.37120e6	1.43995	0.719976	−	0.693999i	$-0.244153\pi$
$353$	3.37120e6	1.43995	0.719976	+	0.693999i	$0.244153\pi$
$354$	−330563.	−0.140199
$355$	−968663.	−0.407945
$356$	8.69571e6	3.63647
$357$	−185598.	−0.0770729
$358$	3.68659e6	1.52026
$359$	−2.76635e6	−1.13285	−0.566424	−	0.824114i	$-0.691673\pi$
$359$	−2.76635e6	−1.13285	−0.566424	+	0.824114i	$0.691673\pi$
$360$	7.97222e6	3.24208
$361$	−2.47603e6	−0.999970
$362$	4.64459e6	1.86284
$363$	−306027.	−0.121897
$364$	−9.12735e6	−3.61070
$365$	−236709.	−0.0929998
$366$	398622.	0.155546
$367$	−2.33187e6	−0.903730	−0.451865	−	0.892086i	$-0.649241\pi$
$367$	−2.33187e6	−0.903730	−0.451865	+	0.892086i	$0.649241\pi$
$368$	−1.09610e7	−4.21919
$369$	2.19944e6	0.840903
$370$	3.30988e6	1.25692
$371$	−1.23196e6	−0.464687
$372$	−1.30735e6	−0.489817
$373$	1.83727e6	0.683755	0.341878	−	0.939745i	$-0.388937\pi$
$373$	1.83727e6	0.683755	0.341878	+	0.939745i	$0.388937\pi$
$374$	−2.78709e6	−1.03032
$375$	398325.	0.146271
$376$	5.34872e6	1.95110
$377$	−6.91540e6	−2.50590
$378$	1.89448e6	0.681961
$379$	−1.42216e6	−0.508571	−0.254285	−	0.967129i	$-0.581840\pi$
$379$	−1.42216e6	−0.508571	−0.254285	+	0.967129i	$0.581840\pi$
$380$	44494.0	0.0158067
$381$	−34869.7	−0.0123065
$382$	1.29254e6	0.453195
$383$	2.89859e6	1.00969	0.504847	−	0.863209i	$-0.331549\pi$
$383$	2.89859e6	1.00969	0.504847	+	0.863209i	$0.331549\pi$
$384$	712931.	0.246729
$385$	4.37615e6	1.50467
$386$	−1.71047e6	−0.584317
$387$	151025.	0.0512592
$388$	−9.82382e6	−3.31284
$389$	1.62026e6	0.542888	0.271444	−	0.962454i	$-0.412499\pi$
$389$	1.62026e6	0.542888	0.271444	+	0.962454i	$0.412499\pi$
$390$	1.56233e6	0.520130
$391$	1.76554e6	0.584031
$392$	−506591.	−0.166511
$393$	−938922.	−0.306654
$394$	−2.03526e6	−0.660508
$395$	2.05600e6	0.663025
$396$	1.00748e7	3.22848
$397$	4.48411e6	1.42791	0.713954	−	0.700193i	$-0.246903\pi$
$397$	4.48411e6	1.42791	0.713954	+	0.700193i	$0.246903\pi$
$398$	−1.84137e6	−0.582684
$399$	3177.62	0.000999239 0
$400$	2.65885e6	0.830892
$401$	−2.50157e6	−0.776875	−0.388437	−	0.921475i	$-0.626985\pi$
$401$	−2.50157e6	−0.776875	−0.388437	+	0.921475i	$0.626985\pi$
$402$	−898711.	−0.277367
$403$	4.75948e6	1.45981
$404$	−7.32725e6	−2.23351
$405$	3.37324e6	1.02190
$406$	−1.18235e7	−3.55985
$407$	2.55548e6	0.764692
$408$	−748252.	−0.222534
$409$	2.95577e6	0.873700	0.436850	−	0.899534i	$-0.356094\pi$
$409$	2.95577e6	0.873700	0.436850	+	0.899534i	$0.356094\pi$
$410$	6.30432e6	1.85216
$411$	−955097.	−0.278897
$412$	2.75879e6	0.800710
$413$	1.48127e6	0.427325
$414$	−8.86506e6	−2.54203
$415$	−4.06735e6	−1.15929
$416$	−1.33648e7	−3.78644
$417$	143418.	0.0403890
$418$	47717.8	0.0133579
$419$	3.64461e6	1.01418	0.507091	−	0.861892i	$-0.330721\pi$
$419$	3.64461e6	1.01418	0.507091	+	0.861892i	$0.330721\pi$
$420$	1.92302e6	0.531938
$421$	6.12503e6	1.68424	0.842118	−	0.539294i	$-0.181309\pi$
$421$	6.12503e6	1.68424	0.842118	+	0.539294i	$0.181309\pi$
$422$	−2.37862e6	−0.650195
$423$	2.34276e6	0.636614
$424$	−4.96673e6	−1.34170
$425$	−428276.	−0.115014
$426$	−456504.	−0.121877
$427$	−1.78624e6	−0.474101
$428$	−7.62255e6	−2.01137
$429$	1.20624e6	0.316439
$430$	432888.	0.112903
$431$	−2.92606e6	−0.758734	−0.379367	−	0.925246i	$-0.623858\pi$
$431$	−2.92606e6	−0.758734	−0.379367	+	0.925246i	$0.623858\pi$
$432$	4.13627e6	1.06635
$433$	3.12734e6	0.801595	0.400798	−	0.916167i	$-0.368733\pi$
$433$	3.12734e6	0.801595	0.400798	+	0.916167i	$0.368733\pi$
$434$	8.13746e6	2.07379
$435$	1.45699e6	0.369176
$436$	−2.00285e6	−0.504584
$437$	−30227.8	−0.00757188
$438$	−111554.	−0.0277844
$439$	800045.	0.198131	0.0990657	−	0.995081i	$-0.468415\pi$
$439$	800045.	0.198131	0.0990657	+	0.995081i	$0.468415\pi$
$440$	1.76428e7	4.34446
$441$	−221888.	−0.0543298
$442$	4.45874e6	1.08557
$443$	−4.25485e6	−1.03009	−0.515045	−	0.857163i	$-0.672225\pi$
$443$	−4.25485e6	−1.03009	−0.515045	+	0.857163i	$0.672225\pi$
$444$	1.12296e6	0.270338
$445$	6.66980e6	1.59666
$446$	−8.92935e6	−2.12561
$447$	786126.	0.186090
$448$	−9.59473e6	−2.25859
$449$	6.96171e6	1.62967	0.814836	−	0.579691i	$-0.196827\pi$
$449$	6.96171e6	1.62967	0.814836	+	0.579691i	$0.196827\pi$
$450$	2.15044e6	0.500606
$451$	4.86742e6	1.12683
$452$	−2.52581e6	−0.581505
$453$	−1.46546e6	−0.335528
$454$	7.95477e6	1.81129
$455$	−7.00088e6	−1.58535
$456$	12810.8	0.00288513
$457$	6.57413e6	1.47248	0.736238	−	0.676723i	$-0.236601\pi$
$457$	6.57413e6	1.47248	0.736238	+	0.676723i	$0.236601\pi$
$458$	1.05366e7	2.34713
$459$	−666251.	−0.147607
$460$	−1.82932e7	−4.03084
$461$	−2.58519e6	−0.566552	−0.283276	−	0.959038i	$-0.591421\pi$
$461$	−2.58519e6	−0.566552	−0.283276	+	0.959038i	$0.591421\pi$
$462$	2.06236e6	0.449530
$463$	−5.21430e6	−1.13043	−0.565215	−	0.824944i	$-0.691207\pi$
$463$	−5.21430e6	−1.13043	−0.565215	+	0.824944i	$0.691207\pi$
$464$	−2.58147e7	−5.56636
$465$	−1.00276e6	−0.215063
$466$	−8.37711e6	−1.78702
$467$	−1.37919e6	−0.292639	−0.146320	−	0.989237i	$-0.546743\pi$
$467$	−1.37919e6	−0.292639	−0.146320	+	0.989237i	$0.546743\pi$
$468$	−1.61175e7	−3.40159
$469$	4.02717e6	0.845410
$470$	6.71512e6	1.40220
$471$	181107.	0.0376168
$472$	5.97184e6	1.23382
$473$	334223.	0.0686884
$474$	968935.	0.198084
$475$	7332.52	0.00149114
$476$	5.48811e6	1.11021
$477$	−2.17544e6	−0.437776
$478$	1.51386e7	3.03051
$479$	3.05011e6	0.607402	0.303701	−	0.952767i	$-0.401778\pi$
$479$	3.05011e6	0.607402	0.303701	+	0.952767i	$0.401778\pi$
$480$	2.81581e6	0.557828
$481$	−4.08821e6	−0.805695
$482$	3.93729e6	0.771934
$483$	−1.30644e6	−0.254814
$484$	9.04920e6	1.75589
$485$	−7.53508e6	−1.45457
$486$	5.04508e6	0.968897
$487$	9.68362e6	1.85019	0.925093	−	0.379742i	$-0.123987\pi$
$487$	9.68362e6	1.85019	0.925093	+	0.379742i	$0.123987\pi$
$488$	−7.20138e6	−1.36888
$489$	1.63226e6	0.308685
$490$	−636006.	−0.119666
$491$	3.97088e6	0.743332	0.371666	−	0.928367i	$-0.378787\pi$
$491$	3.97088e6	0.743332	0.371666	+	0.928367i	$0.378787\pi$
$492$	2.13891e6	0.398363
$493$	4.15811e6	0.770510
$494$	−76338.1	−0.0140742
$495$	7.72759e6	1.41753
$496$	1.77668e7	3.24268
$497$	2.04561e6	0.371478
$498$	−1.91683e6	−0.346346
$499$	−7.37520e6	−1.32594	−0.662968	−	0.748648i	$-0.730703\pi$
$499$	−7.37520e6	−1.32594	−0.662968	+	0.748648i	$0.730703\pi$
$500$	−1.17785e7	−2.10699
$501$	−836213.	−0.148841
$502$	1.87272e7	3.31676
$503$	−6.21390e6	−1.09508	−0.547538	−	0.836781i	$-0.684435\pi$
$503$	−6.21390e6	−1.09508	−0.547538	+	0.836781i	$0.684435\pi$
$504$	−1.68357e7	−2.95226
$505$	−5.62016e6	−0.980665
$506$	−1.96187e7	−3.40638
$507$	−896941.	−0.154969
$508$	1.03110e6	0.177272
$509$	−5.81655e6	−0.995110	−0.497555	−	0.867432i	$-0.665769\pi$
$509$	−5.81655e6	−0.995110	−0.497555	+	0.867432i	$0.665769\pi$
$510$	−939402.	−0.159929
$511$	499880.	0.0846863
$512$	3.55134e6	0.598711
$513$	11406.9	0.00191370
$514$	−8.76950e6	−1.46409
$515$	2.11605e6	0.351567
$516$	146869.	0.0242831
$517$	5.18459e6	0.853077
$518$	−6.98978e6	−1.14456
$519$	−653568.	−0.106506
$520$	−2.82246e7	−4.57741
$521$	6.00281e6	0.968858	0.484429	−	0.874830i	$-0.339027\pi$
$521$	6.00281e6	0.968858	0.484429	+	0.874830i	$0.339027\pi$
$522$	−2.08785e7	−3.35369
$523$	−1.01106e6	−0.161630	−0.0808152	−	0.996729i	$-0.525752\pi$
$523$	−1.01106e6	−0.161630	−0.0808152	+	0.996729i	$0.525752\pi$
$524$	2.77639e7	4.41725
$525$	316910.	0.0501809
$526$	−595377.	−0.0938269
$527$	−2.86179e6	−0.448860
$528$	4.50280e6	0.702907
$529$	5.99151e6	0.930887
$530$	−6.23555e6	−0.964240
$531$	2.61568e6	0.402577
$532$	−93962.0	−0.0143937
$533$	−7.78682e6	−1.18725
$534$	3.14329e6	0.477015
$535$	−5.84667e6	−0.883129
$536$	1.62358e7	2.44097
$537$	959370.	0.143566
$538$	−1.40730e6	−0.209620
$539$	−491046.	−0.0728031
$540$	6.90319e6	1.01874
$541$	−8.98643e6	−1.32006	−0.660031	−	0.751239i	$-0.729457\pi$
$541$	−8.98643e6	−1.32006	−0.660031	+	0.751239i	$0.729457\pi$
$542$	1.51040e7	2.20848
$543$	1.20867e6	0.175917
$544$	8.03605e6	1.16425
$545$	−1.53623e6	−0.221547
$546$	−3.29932e6	−0.473634
$547$	1.07603e7	1.53764	0.768822	−	0.639463i	$-0.220843\pi$
$547$	1.07603e7	1.53764	0.768822	+	0.639463i	$0.220843\pi$
$548$	2.82422e7	4.01742
$549$	−3.15423e6	−0.446645
$550$	4.75899e6	0.670824
$551$	−71191.0	−0.00998955
$552$	−5.26703e6	−0.735729
$553$	−4.34184e6	−0.603756
$554$	−1.38099e7	−1.91168
$555$	861337.	0.118697
$556$	−4.24086e6	−0.581791
$557$	−8.60549e6	−1.17527	−0.587635	−	0.809126i	$-0.699941\pi$
$557$	−8.60549e6	−1.17527	−0.587635	+	0.809126i	$0.699941\pi$
$558$	1.43695e7	1.95369
$559$	−534684.	−0.0723715
$560$	−2.61337e7	−3.52153
$561$	−725291.	−0.0972983
$562$	−1.97152e7	−2.63305
$563$	1.09958e7	1.46203	0.731013	−	0.682364i	$-0.239048\pi$
$563$	1.09958e7	1.46203	0.731013	+	0.682364i	$0.239048\pi$
$564$	2.27828e6	0.301585
$565$	−1.93735e6	−0.255321
$566$	2.76957e7	3.63388
$567$	−7.12359e6	−0.930553
$568$	8.24705e6	1.07258
$569$	4.91737e6	0.636726	0.318363	−	0.947969i	$-0.396867\pi$
$569$	4.91737e6	0.636726	0.318363	+	0.947969i	$0.396867\pi$
$570$	16083.5	0.00207345
$571$	7.59615e6	0.974997	0.487498	−	0.873124i	$-0.337909\pi$
$571$	7.59615e6	0.974997	0.487498	+	0.873124i	$0.337909\pi$
$572$	−3.56685e7	−4.55821
$573$	336360.	0.0427974
$574$	−1.33134e7	−1.68659
$575$	−3.01469e6	−0.380253
$576$	−1.69428e7	−2.12779
$577$	3.81032e6	0.476456	0.238228	−	0.971209i	$-0.423434\pi$
$577$	3.81032e6	0.476456	0.238228	+	0.971209i	$0.423434\pi$
$578$	1.24957e7	1.55575
$579$	−445120.	−0.0551799
$580$	−4.30832e7	−5.31787
$581$	8.58940e6	1.05566
$582$	−3.55107e6	−0.434563
$583$	−4.81433e6	−0.586630
$584$	2.01530e6	0.244517
$585$	−1.23625e7	−1.49353
$586$	2.04994e6	0.246602
$587$	−1.42353e7	−1.70518	−0.852592	−	0.522577i	$-0.824971\pi$
$587$	−1.42353e7	−1.70518	−0.852592	+	0.522577i	$0.824971\pi$
$588$	−215782.	−0.0257378
$589$	48996.7	0.00581940
$590$	7.49743e6	0.886711
$591$	−529639.	−0.0623751
$592$	−1.52610e7	−1.78969
$593$	1.38681e7	1.61949	0.809746	−	0.586781i	$-0.199605\pi$
$593$	1.38681e7	1.61949	0.809746	+	0.586781i	$0.199605\pi$
$594$	7.40336e6	0.860920
$595$	4.20950e6	0.487460
$596$	−2.32457e7	−2.68057
$597$	−479184.	−0.0550258
$598$	3.13856e7	3.58903
$599$	−1.08054e7	−1.23048	−0.615239	−	0.788340i	$-0.710941\pi$
$599$	−1.08054e7	−1.23048	−0.615239	+	0.788340i	$0.710941\pi$
$600$	1.27765e6	0.144888
$601$	2.73587e6	0.308965	0.154482	−	0.987996i	$-0.450629\pi$
$601$	2.73587e6	0.308965	0.154482	+	0.987996i	$0.450629\pi$
$602$	−914170.	−0.102810
$603$	7.11134e6	0.796450
$604$	4.33337e7	4.83318
$605$	6.94094e6	0.770956
$606$	−2.64863e6	−0.292981
$607$	4.22364e6	0.465281	0.232640	−	0.972563i	$-0.425264\pi$
$607$	4.22364e6	0.465281	0.232640	+	0.972563i	$0.425264\pi$
$608$	−137585.	−0.0150943
$609$	−3.07686e6	−0.336175
$610$	−9.04107e6	−0.983774
$611$	−8.29422e6	−0.898819
$612$	9.69115e6	1.04592
$613$	9.65627e6	1.03791	0.518953	−	0.854803i	$-0.326322\pi$
$613$	9.65627e6	1.03791	0.518953	+	0.854803i	$0.326322\pi$
$614$	−1.91082e7	−2.04550
$615$	1.64059e6	0.174909
$616$	−3.72579e7	−3.95609
$617$	9.56585e6	1.01160	0.505802	−	0.862649i	$-0.331197\pi$
$617$	9.56585e6	1.01160	0.505802	+	0.862649i	$0.331197\pi$
$618$	997236.	0.105033
$619$	−1.62036e7	−1.69975	−0.849876	−	0.526982i	$-0.823323\pi$
$619$	−1.62036e7	−1.69975	−0.849876	+	0.526982i	$0.823323\pi$
$620$	2.96517e7	3.09792
$621$	−4.68982e6	−0.488008
$622$	3.15840e7	3.27334
$623$	−1.40852e7	−1.45393
$624$	−7.20350e6	−0.740597
$625$	−1.17067e7	−1.19877
$626$	−1.88478e7	−1.92232
$627$	12417.7	0.00126146
$628$	−5.35531e6	−0.541858
$629$	2.45817e6	0.247734
$630$	−2.11366e7	−2.12170
$631$	884545.	0.0884395	0.0442198	−	0.999022i	$-0.485920\pi$
$631$	884545.	0.0884395	0.0442198	+	0.999022i	$0.485920\pi$
$632$	−1.75045e7	−1.74324
$633$	−618993.	−0.0614011
$634$	−1.28655e7	−1.27117
$635$	790874.	0.0778346
$636$	−2.11557e6	−0.207389
$637$	785566.	0.0767069
$638$	−4.62048e7	−4.49402
$639$	3.61223e6	0.349964
$640$	−1.61699e7	−1.56047
$641$	1.79122e7	1.72188	0.860940	−	0.508707i	$-0.169876\pi$
$641$	1.79122e7	1.72188	0.860940	+	0.508707i	$0.169876\pi$
$642$	−2.75537e6	−0.263841
$643$	2.13129e6	0.203290	0.101645	−	0.994821i	$-0.467589\pi$
$643$	2.13129e6	0.203290	0.101645	+	0.994821i	$0.467589\pi$
$644$	3.86314e7	3.67051
$645$	112651.	0.0106620
$646$	45900.7	0.00432751
$647$	3.38697e6	0.318090	0.159045	−	0.987271i	$-0.449158\pi$
$647$	3.38697e6	0.318090	0.159045	+	0.987271i	$0.449158\pi$
$648$	−2.87193e7	−2.68681
$649$	5.78859e6	0.539462
$650$	−7.61335e6	−0.706793
$651$	2.11763e6	0.195838
$652$	−4.82657e7	−4.44651
$653$	1.19374e7	1.09554	0.547768	−	0.836630i	$-0.315478\pi$
$653$	1.19374e7	1.09554	0.547768	+	0.836630i	$0.315478\pi$
$654$	−723984.	−0.0661888
$655$	2.12955e7	1.93948
$656$	−2.90676e7	−2.63724
$657$	882709.	0.0797819
$658$	−1.41809e7	−1.27685
$659$	−1.41820e7	−1.27211	−0.636056	−	0.771643i	$-0.719435\pi$
$659$	−1.41820e7	−1.27211	−0.636056	+	0.771643i	$0.719435\pi$
$660$	7.51491e6	0.671528
$661$	−387826.	−0.0345250	−0.0172625	−	0.999851i	$-0.505495\pi$
$661$	−387826.	−0.0345250	−0.0172625	+	0.999851i	$0.505495\pi$
$662$	−1.73922e6	−0.154244
$663$	1.16031e6	0.102515
$664$	3.46288e7	3.04802
$665$	−72070.9	−0.00631984
$666$	−1.23429e7	−1.07828
$667$	2.92694e7	2.54741
$668$	2.47268e7	2.14401
$669$	−2.32370e6	−0.200732
$670$	2.03835e7	1.75425
$671$	−6.98040e6	−0.598514
$672$	−5.94641e6	−0.507962
$673$	5.05171e6	0.429933	0.214967	−	0.976621i	$-0.431036\pi$
$673$	5.05171e6	0.429933	0.214967	+	0.976621i	$0.431036\pi$
$674$	−2.10684e7	−1.78641
$675$	1.13763e6	0.0961042
$676$	2.65225e7	2.23228
$677$	5.80065e6	0.486413	0.243207	−	0.969975i	$-0.421801\pi$
$677$	5.80065e6	0.486413	0.243207	+	0.969975i	$0.421801\pi$
$678$	−913018.	−0.0762791
$679$	1.59125e7	1.32454
$680$	1.69710e7	1.40745
$681$	2.07009e6	0.171049
$682$	3.18001e7	2.61799
$683$	−1.33376e7	−1.09402	−0.547010	−	0.837126i	$-0.684234\pi$
$683$	−1.33376e7	−1.09402	−0.547010	+	0.837126i	$0.684234\pi$
$684$	−165922.	−0.0135601
$685$	2.16624e7	1.76392
$686$	−2.25912e7	−1.83286
$687$	2.74197e6	0.221651
$688$	−1.99593e6	−0.160759
$689$	7.70187e6	0.618085
$690$	−6.61256e6	−0.528746
$691$	9.63622e6	0.767735	0.383868	−	0.923388i	$-0.374592\pi$
$691$	9.63622e6	0.767735	0.383868	+	0.923388i	$0.374592\pi$
$692$	1.93260e7	1.53418
$693$	−1.63191e7	−1.29081
$694$	608830.	0.0479841
$695$	−3.25284e6	−0.255447
$696$	−1.24046e7	−0.970645
$697$	4.68208e6	0.365053
$698$	1.59294e7	1.23754
$699$	−2.17999e6	−0.168757
$700$	−9.37102e6	−0.722839
$701$	1.05949e7	0.814334	0.407167	−	0.913354i	$-0.366517\pi$
$701$	1.05949e7	0.814334	0.407167	+	0.913354i	$0.366517\pi$
$702$	−1.18438e7	−0.907083
$703$	−42086.3	−0.00321183
$704$	−3.74949e7	−2.85129
$705$	1.74749e6	0.132417
$706$	−3.60342e7	−2.72084
$707$	1.18686e7	0.893000
$708$	2.54370e6	0.190714
$709$	9.09644e6	0.679604	0.339802	−	0.940497i	$-0.389640\pi$
$709$	9.09644e6	0.679604	0.339802	+	0.940497i	$0.389640\pi$
$710$	1.03539e7	0.770827
$711$	−7.66702e6	−0.568790
$712$	−5.67858e7	−4.19797
$713$	−2.01445e7	−1.48399
$714$	1.98382e6	0.145632
$715$	−2.73585e7	−2.00137
$716$	−2.83685e7	−2.06802
$717$	3.93955e6	0.286187
$718$	2.95691e7	2.14056
$719$	1.92469e7	1.38848	0.694239	−	0.719745i	$-0.255741\pi$
$719$	1.92469e7	1.38848	0.694239	+	0.719745i	$0.255741\pi$
$720$	−4.61481e7	−3.31759
$721$	−4.46866e6	−0.320139
$722$	2.64658e7	1.88948
$723$	1.02461e6	0.0728976
$724$	−3.57403e7	−2.53403
$725$	−7.10002e6	−0.501666
$726$	3.27107e6	0.230329
$727$	1.72224e7	1.20853	0.604265	−	0.796784i	$-0.293467\pi$
$727$	1.72224e7	1.20853	0.604265	+	0.796784i	$0.293467\pi$
$728$	5.96045e7	4.16822
$729$	−1.16799e7	−0.813995
$730$	2.53014e6	0.175727
$731$	321496.	0.0222527
$732$	−3.06742e6	−0.211590
$733$	−1.60526e7	−1.10353	−0.551766	−	0.833999i	$-0.686046\pi$
$733$	−1.60526e7	−1.10353	−0.551766	+	0.833999i	$0.686046\pi$
$734$	2.49250e7	1.70763
$735$	−165509.	−0.0113007
$736$	5.65666e7	3.84916
$737$	1.57376e7	1.06726
$738$	−2.35094e7	−1.58892
$739$	−1.09686e7	−0.738822	−0.369411	−	0.929266i	$-0.620441\pi$
$739$	−1.09686e7	−0.738822	−0.369411	+	0.929266i	$0.620441\pi$
$740$	−2.54697e7	−1.70980
$741$	−19865.6	−0.00132910
$742$	1.31682e7	0.878044
$743$	−8.95403e6	−0.595041	−0.297520	−	0.954715i	$-0.596160\pi$
$743$	−8.95403e6	−0.595041	−0.297520	+	0.954715i	$0.596160\pi$
$744$	8.53739e6	0.565448
$745$	−1.78300e7	−1.17696
$746$	−1.96383e7	−1.29198
$747$	1.51675e7	0.994520
$748$	2.14468e7	1.40155
$749$	1.23469e7	0.804183
$750$	−4.25763e6	−0.276385
$751$	6.61240e6	0.427818	0.213909	−	0.976854i	$-0.431380\pi$
$751$	6.61240e6	0.427818	0.213909	+	0.976854i	$0.431380\pi$
$752$	−3.09617e7	−1.99655
$753$	4.87343e6	0.313218
$754$	7.39176e7	4.73499
$755$	3.32379e7	2.12210
$756$	−1.45781e7	−0.927676
$757$	−9.39866e6	−0.596109	−0.298055	−	0.954549i	$-0.596338\pi$
$757$	−9.39866e6	−0.596109	−0.298055	+	0.954549i	$0.596338\pi$
$758$	1.52013e7	0.960963
$759$	−5.10540e6	−0.321681
$760$	−290560.	−0.0182474
$761$	−1.33343e7	−0.834655	−0.417328	−	0.908756i	$-0.637033\pi$
$761$	−1.33343e7	−0.834655	−0.417328	+	0.908756i	$0.637033\pi$
$762$	372717.	0.0232537
$763$	3.24421e6	0.201742
$764$	−9.94615e6	−0.616483
$765$	7.43333e6	0.459229
$766$	−3.09826e7	−1.90785
$767$	−9.26049e6	−0.568389
$768$	−1.21019e6	−0.0740371
$769$	1.58062e7	0.963857	0.481928	−	0.876211i	$-0.339937\pi$
$769$	1.58062e7	0.963857	0.481928	+	0.876211i	$0.339937\pi$
$770$	−4.67759e7	−2.84312
$771$	−2.28211e6	−0.138261
$772$	1.31622e7	0.794849
$773$	−4.11164e6	−0.247495	−0.123747	−	0.992314i	$-0.539491\pi$
$773$	−4.11164e6	−0.247495	−0.123747	+	0.992314i	$0.539491\pi$
$774$	−1.61428e6	−0.0968561
$775$	4.88654e6	0.292245
$776$	6.41526e7	3.82437
$777$	−1.81896e6	−0.108087
$778$	−1.73187e7	−1.02581
$779$	−80161.8	−0.00473286
$780$	−1.20222e7	−0.707536
$781$	7.99399e6	0.468960
$782$	−1.88716e7	−1.10355
$783$	−1.10452e7	−0.643827
$784$	2.93246e6	0.170389
$785$	−4.10764e6	−0.237913
$786$	1.00360e7	0.579433
$787$	−1.98159e7	−1.14045	−0.570225	−	0.821488i	$-0.693144\pi$
$787$	−1.98159e7	−1.14045	−0.570225	+	0.821488i	$0.693144\pi$
$788$	1.56614e7	0.898494
$789$	−154936.	−0.00886054
$790$	−2.19762e7	−1.25281
$791$	4.09128e6	0.232497
$792$	−6.57916e7	−3.72698
$793$	1.11671e7	0.630606
$794$	−4.79299e7	−2.69808
$795$	−1.62269e6	−0.0910580
$796$	1.41694e7	0.792629
$797$	−7.53629e6	−0.420254	−0.210127	−	0.977674i	$-0.567388\pi$
$797$	−7.53629e6	−0.420254	−0.210127	+	0.977674i	$0.567388\pi$
$798$	−33965.0	−0.00188810
$799$	4.98717e6	0.276367
$800$	−1.37217e7	−0.758021
$801$	−2.48723e7	−1.36973
$802$	2.67388e7	1.46793
$803$	1.95346e6	0.106910
$804$	6.91563e6	0.377304
$805$	2.96312e7	1.61161
$806$	−5.08732e7	−2.75837
$807$	−366226.	−0.0197954
$808$	4.78493e7	2.57838
$809$	1.51793e7	0.815418	0.407709	−	0.913112i	$-0.366328\pi$
$809$	1.51793e7	0.815418	0.407709	+	0.913112i	$0.366328\pi$
$810$	−3.60560e7	−1.93092
$811$	1.50064e7	0.801171	0.400585	−	0.916259i	$-0.368807\pi$
$811$	1.50064e7	0.801171	0.400585	+	0.916259i	$0.368807\pi$
$812$	9.09827e7	4.84249
$813$	3.93055e6	0.208558
$814$	−2.73151e7	−1.44491
$815$	−3.70209e7	−1.95233
$816$	4.33134e6	0.227718
$817$	−5504.34	−0.000288503 0
$818$	−3.15937e7	−1.65089
$819$	2.61069e7	1.36002
$820$	−4.85121e7	−2.51951
$821$	6.25774e6	0.324011	0.162005	−	0.986790i	$-0.448204\pi$
$821$	6.25774e6	0.324011	0.162005	+	0.986790i	$0.448204\pi$
$822$	1.02089e7	0.526985
$823$	2.14156e7	1.10212	0.551062	−	0.834464i	$-0.314223\pi$
$823$	2.14156e7	1.10212	0.551062	+	0.834464i	$0.314223\pi$
$824$	−1.80158e7	−0.924346
$825$	1.23844e6	0.0633492
$826$	−1.58330e7	−0.807446
$827$	−1.16008e7	−0.589825	−0.294913	−	0.955524i	$-0.595291\pi$
$827$	−1.16008e7	−0.589825	−0.294913	+	0.955524i	$0.595291\pi$
$828$	6.82171e7	3.45794
$829$	−3.64974e7	−1.84449	−0.922243	−	0.386610i	$-0.873646\pi$
$829$	−3.64974e7	−1.84449	−0.922243	+	0.386610i	$0.873646\pi$
$830$	4.34752e7	2.19052
$831$	−3.59377e6	−0.180529
$832$	5.99837e7	3.00417
$833$	−472347.	−0.0235857
$834$	−1.53297e6	−0.0763166
$835$	1.89660e7	0.941368
$836$	−367191.	−0.0181709
$837$	7.60178e6	0.375061
$838$	−3.89566e7	−1.91633
$839$	−1.18111e7	−0.579275	−0.289637	−	0.957136i	$-0.593535\pi$
$839$	−1.18111e7	−0.579275	−0.289637	+	0.957136i	$0.593535\pi$
$840$	−1.25579e7	−0.614073
$841$	4.84225e7	2.36079
$842$	−6.54694e7	−3.18242
$843$	−5.13052e6	−0.248652
$844$	1.83036e7	0.884464
$845$	2.03433e7	0.980123
$846$	−2.50413e7	−1.20291
$847$	−1.46578e7	−0.702038
$848$	2.87505e7	1.37295
$849$	7.20730e6	0.343165
$850$	4.57777e6	0.217324
$851$	1.73033e7	0.819042
$852$	3.51282e6	0.165789
$853$	8.29850e6	0.390505	0.195253	−	0.980753i	$-0.437447\pi$
$853$	8.29850e6	0.390505	0.195253	+	0.980753i	$0.437447\pi$
$854$	1.90929e7	0.895831
$855$	−127266.	−0.00595384
$856$	4.97777e7	2.32194
$857$	1.43830e7	0.668958	0.334479	−	0.942403i	$-0.391440\pi$
$857$	1.43830e7	0.668958	0.334479	+	0.942403i	$0.391440\pi$
$858$	−1.28933e7	−0.597924
$859$	−1.31324e7	−0.607242	−0.303621	−	0.952793i	$-0.598196\pi$
$859$	−1.31324e7	−0.607242	−0.303621	+	0.952793i	$0.598196\pi$
$860$	−3.33110e6	−0.153582
$861$	−3.46458e6	−0.159273
$862$	3.12762e7	1.43366
$863$	2.99071e7	1.36693	0.683467	−	0.729981i	$-0.260471\pi$
$863$	2.99071e7	1.36693	0.683467	+	0.729981i	$0.260471\pi$
$864$	−2.13462e7	−0.972828
$865$	1.48235e7	0.673611
$866$	−3.34276e7	−1.51464
$867$	3.25177e6	0.146917
$868$	−6.26182e7	−2.82099
$869$	−1.69673e7	−0.762192
$870$	−1.55735e7	−0.697572
$871$	−2.51768e7	−1.12449
$872$	1.30793e7	0.582495
$873$	2.80990e7	1.24783
$874$	323100.	0.0143073
$875$	1.90786e7	0.842417
$876$	858416.	0.0377953
$877$	−990766.	−0.0434983	−0.0217491	−	0.999763i	$-0.506924\pi$
$877$	−990766.	−0.0434983	−0.0217491	+	0.999763i	$0.506924\pi$
$878$	−8.55155e6	−0.374376
$879$	533460.	0.0232879
$880$	−1.02127e8	−4.44564
$881$	−3.78403e7	−1.64253	−0.821267	−	0.570544i	$-0.806732\pi$
$881$	−3.78403e7	−1.64253	−0.821267	+	0.570544i	$0.806732\pi$
$882$	2.37173e6	0.102658
$883$	−2.46261e7	−1.06290	−0.531451	−	0.847089i	$-0.678353\pi$
$883$	−2.46261e7	−1.06290	−0.531451	+	0.847089i	$0.678353\pi$
$884$	−3.43102e7	−1.47670
$885$	1.95107e6	0.0837366
$886$	4.54794e7	1.94639
$887$	2.83320e7	1.20912	0.604558	−	0.796561i	$-0.293350\pi$
$887$	2.83320e7	1.20912	0.604558	+	0.796561i	$0.293350\pi$
$888$	−7.33330e6	−0.312081
$889$	−1.67016e6	−0.0708768
$890$	−7.12924e7	−3.01695
$891$	−2.78380e7	−1.17475
$892$	6.87118e7	2.89148
$893$	−85385.3	−0.00358306
$894$	−8.40277e6	−0.351624
$895$	−2.17593e7	−0.908002
$896$	3.41474e7	1.42098
$897$	8.16754e6	0.338930
$898$	−7.44126e7	−3.07933
$899$	−4.74431e7	−1.95783
$900$	−1.65478e7	−0.680978
$901$	−4.63100e6	−0.190048
$902$	−5.20271e7	−2.12918
$903$	−237896.	−0.00970887
$904$	1.64943e7	0.671295
$905$	−2.74136e7	−1.11262
$906$	1.56641e7	0.633993
$907$	−2.07036e7	−0.835656	−0.417828	−	0.908526i	$-0.637208\pi$
$907$	−2.07036e7	−0.835656	−0.417828	+	0.908526i	$0.637208\pi$
$908$	−6.12124e7	−2.46391
$909$	2.09581e7	0.841284
$910$	7.48312e7	2.99557
$911$	2.80302e7	1.11900	0.559501	−	0.828830i	$-0.310993\pi$
$911$	2.80302e7	1.11900	0.559501	+	0.828830i	$0.310993\pi$
$912$	−74156.8	−0.00295232
$913$	3.35662e7	1.33268
$914$	−7.02698e7	−2.78230
$915$	−2.35278e6	−0.0929027
$916$	−8.10798e7	−3.19282
$917$	−4.49717e7	−1.76610
$918$	7.12145e6	0.278908
$919$	1.97260e7	0.770460	0.385230	−	0.922821i	$-0.374122\pi$
$919$	1.97260e7	0.770460	0.385230	+	0.922821i	$0.374122\pi$
$920$	1.19460e8	4.65323
$921$	−4.97257e6	−0.193166
$922$	2.76326e7	1.07052
$923$	−1.27886e7	−0.494106
$924$	−1.58699e7	−0.611498
$925$	−4.19736e6	−0.161295
$926$	5.57348e7	2.13599
$927$	−7.89096e6	−0.301599
$928$	1.33223e8	5.07818
$929$	−4.52573e7	−1.72048	−0.860239	−	0.509891i	$-0.829686\pi$
$929$	−4.52573e7	−1.72048	−0.860239	+	0.509891i	$0.829686\pi$
$930$	1.07184e7	0.406370
$931$	8087.06	0.000305785 0
$932$	6.44623e7	2.43089
$933$	8.21918e6	0.309118
$934$	1.47420e7	0.552953
$935$	1.64502e7	0.615378
$936$	1.05252e8	3.92683
$937$	1.00217e7	0.372902	0.186451	−	0.982464i	$-0.440301\pi$
$937$	1.00217e7	0.372902	0.186451	+	0.982464i	$0.440301\pi$
$938$	−4.30457e7	−1.59743
$939$	−4.90481e6	−0.181534
$940$	−5.16732e7	−1.90742
$941$	3.77126e7	1.38839	0.694196	−	0.719786i	$-0.255760\pi$
$941$	3.77126e7	1.38839	0.694196	+	0.719786i	$0.255760\pi$
$942$	−1.93582e6	−0.0710783
$943$	3.29577e7	1.20692
$944$	−3.45687e7	−1.26256
$945$	−1.11817e7	−0.407314
$946$	−3.57246e6	−0.129789
$947$	−4.97813e7	−1.80381	−0.901907	−	0.431931i	$-0.857832\pi$
$947$	−4.97813e7	−1.80381	−0.901907	+	0.431931i	$0.857832\pi$
$948$	−7.45601e6	−0.269455
$949$	−3.12511e6	−0.112642
$950$	−78376.1	−0.00281757
$951$	−3.34802e6	−0.120043
$952$	−3.58391e7	−1.28164
$953$	3.81283e7	1.35992	0.679962	−	0.733247i	$-0.261996\pi$
$953$	3.81283e7	1.35992	0.679962	+	0.733247i	$0.261996\pi$
$954$	2.32530e7	0.827194
$955$	−7.62891e6	−0.270679
$956$	−1.16492e8	−4.12243
$957$	−1.20240e7	−0.424393
$958$	−3.26021e7	−1.14771
$959$	−4.57464e7	−1.60624
$960$	−1.26378e7	−0.442583
$961$	4.02324e6	0.140530
$962$	4.36982e7	1.52239
$963$	2.18028e7	0.757611
$964$	−3.02977e7	−1.05007
$965$	1.00957e7	0.348994
$966$	1.39643e7	0.481480
$967$	2.51514e7	0.864959	0.432480	−	0.901644i	$-0.357639\pi$
$967$	2.51514e7	0.864959	0.432480	+	0.901644i	$0.357639\pi$
$968$	−5.90942e7	−2.02701
$969$	11944.8	0.000408669 0
$970$	8.05413e7	2.74846
$971$	−3.80896e6	−0.129646	−0.0648228	−	0.997897i	$-0.520648\pi$
$971$	−3.80896e6	−0.129646	−0.0648228	+	0.997897i	$0.520648\pi$
$972$	−3.88222e7	−1.31800
$973$	6.86931e6	0.232611
$974$	−1.03507e8	−3.49599
$975$	−1.98124e6	−0.0667460
$976$	4.16860e7	1.40077
$977$	9.91083e6	0.332180	0.166090	−	0.986111i	$-0.446886\pi$
$977$	9.91083e6	0.332180	0.166090	+	0.986111i	$0.446886\pi$
$978$	−1.74469e7	−0.583272
$979$	−5.50432e7	−1.83547
$980$	4.89410e6	0.162783
$981$	5.72876e6	0.190059
$982$	−4.24440e7	−1.40455
$983$	966289.	0.0318950
$983$	966289.	0.0318950
$984$	−1.39677e7	−0.459873
$985$	1.20126e7	0.394501
$986$	−4.44453e7	−1.45591
$987$	−3.69034e6	−0.120579
$988$	587426.	0.0191452
$989$	2.26305e6	0.0735704
$990$	−8.25989e7	−2.67847
$991$	−2.63772e6	−0.0853187	−0.0426594	−	0.999090i	$-0.513583\pi$
$991$	−2.63772e6	−0.0853187	−0.0426594	+	0.999090i	$0.513583\pi$
$992$	−9.16896e7	−2.95829
$993$	−452601.	−0.0145661
$994$	−2.18652e7	−0.701921
$995$	1.08683e7	0.348019
$996$	1.47501e7	0.471136
$997$	1.80622e7	0.575484	0.287742	−	0.957708i	$-0.407095\pi$
$997$	1.80622e7	0.575484	0.287742	+	0.957708i	$0.407095\pi$
$998$	7.88323e7	2.50540
$999$	−6.52965e6	−0.207003

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.6.a.b.1.10	✓	218

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.6.a.b.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-10.6888 q^{2} -2.78158 q^{3} +82.2511 q^{4} +63.0885 q^{5} +29.7318 q^{6} -133.230 q^{7} -537.126 q^{8} -235.263 q^{9} +O(q^{10})\)	\(q-10.6888 q^{2} -2.78158 q^{3} +82.2511 q^{4} +63.0885 q^{5} +29.7318 q^{6} -133.230 q^{7} -537.126 q^{8} -235.263 q^{9} -674.342 q^{10} -520.644 q^{11} -228.788 q^{12} +832.917 q^{13} +1424.07 q^{14} -175.485 q^{15} +3109.21 q^{16} -500.818 q^{17} +2514.68 q^{18} +8.57451 q^{19} +5189.10 q^{20} +370.589 q^{21} +5565.08 q^{22} -3525.32 q^{23} +1494.06 q^{24} +855.153 q^{25} -8902.91 q^{26} +1330.33 q^{27} -10958.3 q^{28} -8302.63 q^{29} +1875.74 q^{30} +5714.23 q^{31} -16045.8 q^{32} +1448.21 q^{33} +5353.16 q^{34} -8405.26 q^{35} -19350.6 q^{36} -4908.31 q^{37} -91.6515 q^{38} -2316.82 q^{39} -33886.5 q^{40} -9348.85 q^{41} -3961.16 q^{42} -641.942 q^{43} -42823.6 q^{44} -14842.4 q^{45} +37681.5 q^{46} -9958.04 q^{47} -8648.52 q^{48} +943.151 q^{49} -9140.59 q^{50} +1393.07 q^{51} +68508.4 q^{52} +9246.87 q^{53} -14219.6 q^{54} -32846.6 q^{55} +71561.1 q^{56} -23.8507 q^{57} +88745.4 q^{58} -11118.1 q^{59} -14433.9 q^{60} +13407.2 q^{61} -61078.4 q^{62} +31344.0 q^{63} +72016.4 q^{64} +52547.4 q^{65} -15479.7 q^{66} -30227.2 q^{67} -41192.9 q^{68} +9805.94 q^{69} +89842.4 q^{70} -15354.0 q^{71} +126366. q^{72} -3752.01 q^{73} +52464.1 q^{74} -2378.68 q^{75} +705.263 q^{76} +69365.2 q^{77} +24764.1 q^{78} +32589.2 q^{79} +196156. q^{80} +53468.5 q^{81} +99928.3 q^{82} -64470.6 q^{83} +30481.4 q^{84} -31595.8 q^{85} +6861.61 q^{86} +23094.4 q^{87} +279651. q^{88} +105721. q^{89} +158648. q^{90} -110969. q^{91} -289961. q^{92} -15894.6 q^{93} +106440. q^{94} +540.952 q^{95} +44632.8 q^{96} -119437. q^{97} -10081.2 q^{98} +122488. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9}+O(q^{10}) \) 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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