LMFDB - Embedded newform 983.6.a.b.1.13

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			1.13
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)

$f(q)$	$=$	$q-10.1039 q^{2} +11.1728 q^{3} +70.0889 q^{4} +83.9898 q^{5} -112.889 q^{6} +92.1063 q^{7} -384.847 q^{8} -118.168 q^{9} +O(q^{10})$	\(q-10.1039 q^{2} +11.1728 q^{3} +70.0889 q^{4} +83.9898 q^{5} -112.889 q^{6} +92.1063 q^{7} -384.847 q^{8} -118.168 q^{9} -848.625 q^{10} +477.515 q^{11} +783.092 q^{12} +269.922 q^{13} -930.634 q^{14} +938.405 q^{15} +1645.61 q^{16} -580.521 q^{17} +1193.95 q^{18} +2268.66 q^{19} +5886.76 q^{20} +1029.09 q^{21} -4824.77 q^{22} -2670.32 q^{23} -4299.83 q^{24} +3929.29 q^{25} -2727.27 q^{26} -4035.27 q^{27} +6455.63 q^{28} +5373.39 q^{29} -9481.56 q^{30} -1889.71 q^{31} -4312.00 q^{32} +5335.20 q^{33} +5865.53 q^{34} +7735.99 q^{35} -8282.24 q^{36} +3338.12 q^{37} -22922.3 q^{38} +3015.80 q^{39} -32323.2 q^{40} -15411.9 q^{41} -10397.8 q^{42} -15134.9 q^{43} +33468.5 q^{44} -9924.87 q^{45} +26980.7 q^{46} -4547.83 q^{47} +18386.2 q^{48} -8323.43 q^{49} -39701.2 q^{50} -6486.07 q^{51} +18918.6 q^{52} +33881.1 q^{53} +40772.0 q^{54} +40106.4 q^{55} -35446.8 q^{56} +25347.4 q^{57} -54292.3 q^{58} -1532.55 q^{59} +65771.8 q^{60} +4352.91 q^{61} +19093.5 q^{62} -10884.0 q^{63} -9091.53 q^{64} +22670.7 q^{65} -53906.4 q^{66} +64667.0 q^{67} -40688.1 q^{68} -29835.1 q^{69} -78163.8 q^{70} +59387.8 q^{71} +45476.4 q^{72} +39174.7 q^{73} -33728.1 q^{74} +43901.4 q^{75} +159008. q^{76} +43982.2 q^{77} -30471.4 q^{78} +33132.8 q^{79} +138215. q^{80} -16370.7 q^{81} +155721. q^{82} +11074.2 q^{83} +72127.8 q^{84} -48757.8 q^{85} +152922. q^{86} +60036.1 q^{87} -183770. q^{88} +53964.6 q^{89} +100280. q^{90} +24861.6 q^{91} -187160. q^{92} -21113.5 q^{93} +45950.8 q^{94} +190544. q^{95} -48177.3 q^{96} +164307. q^{97} +84099.1 q^{98} -56426.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−10.1039	−1.78614	−0.893068	−	0.449923i	$-0.851452\pi$
$2$	−10.1039	−1.78614	−0.893068	+	0.449923i	$0.851452\pi$
$3$	11.1728	0.716738	0.358369	−	0.933580i	$-0.383333\pi$
$3$	11.1728	0.716738	0.358369	+	0.933580i	$0.383333\pi$
$4$	70.0889	2.19028
$5$	83.9898	1.50246	0.751228	−	0.660043i	$-0.229462\pi$
$5$	83.9898	1.50246	0.751228	+	0.660043i	$0.229462\pi$
$6$	−112.889	−1.28019
$7$	92.1063	0.710468	0.355234	−	0.934777i	$-0.384401\pi$
$7$	92.1063	0.710468	0.355234	+	0.934777i	$0.384401\pi$
$8$	−384.847	−2.12600
$9$	−118.168	−0.486286
$10$	−848.625	−2.68359
$11$	477.515	1.18989	0.594943	−	0.803768i	$-0.297175\pi$
$11$	477.515	1.18989	0.594943	+	0.803768i	$0.297175\pi$
$12$	783.092	1.56986
$13$	269.922	0.442976	0.221488	−	0.975163i	$-0.428909\pi$
$13$	269.922	0.442976	0.221488	+	0.975163i	$0.428909\pi$
$14$	−930.634	−1.26899
$15$	938.405	1.07687
$16$	1645.61	1.60704
$17$	−580.521	−0.487187	−0.243593	−	0.969877i	$-0.578326\pi$
$17$	−580.521	−0.487187	−0.243593	+	0.969877i	$0.578326\pi$
$18$	1193.95	0.868573
$19$	2268.66	1.44173	0.720867	−	0.693073i	$-0.243744\pi$
$19$	2268.66	1.44173	0.720867	+	0.693073i	$0.243744\pi$
$20$	5886.76	3.29080
$21$	1029.09	0.509219
$22$	−4824.77	−2.12530
$23$	−2670.32	−1.05255	−0.526276	−	0.850314i	$-0.676412\pi$
$23$	−2670.32	−1.05255	−0.526276	+	0.850314i	$0.676412\pi$
$24$	−4299.83	−1.52378
$25$	3929.29	1.25737
$26$	−2727.27	−0.791215
$27$	−4035.27	−1.06528
$28$	6455.63	1.55612
$29$	5373.39	1.18646	0.593231	−	0.805032i	$-0.297852\pi$
$29$	5373.39	1.18646	0.593231	+	0.805032i	$0.297852\pi$
$30$	−9481.56	−1.92343
$31$	−1889.71	−0.353176	−0.176588	−	0.984285i	$-0.556506\pi$
$31$	−1889.71	−0.353176	−0.176588	+	0.984285i	$0.556506\pi$
$32$	−4312.00	−0.744395
$33$	5335.20	0.852837
$34$	5865.53	0.870181
$35$	7735.99	1.06745
$36$	−8282.24	−1.06510
$37$	3338.12	0.400865	0.200432	−	0.979708i	$-0.435765\pi$
$37$	3338.12	0.400865	0.200432	+	0.979708i	$0.435765\pi$
$38$	−22922.3	−2.57513
$39$	3015.80	0.317498
$40$	−32323.2	−3.19422
$41$	−15411.9	−1.43185	−0.715924	−	0.698178i	$-0.753994\pi$
$41$	−15411.9	−1.43185	−0.715924	+	0.698178i	$0.753994\pi$
$42$	−10397.8	−0.909535
$43$	−15134.9	−1.24827	−0.624136	−	0.781316i	$-0.714549\pi$
$43$	−15134.9	−1.24827	−0.624136	+	0.781316i	$0.714549\pi$
$44$	33468.5	2.60618
$45$	−9924.87	−0.730624
$46$	26980.7	1.88000
$47$	−4547.83	−0.300303	−0.150151	−	0.988663i	$-0.547976\pi$
$47$	−4547.83	−0.300303	−0.150151	+	0.988663i	$0.547976\pi$
$48$	18386.2	1.15183
$49$	−8323.43	−0.495236
$50$	−39701.2	−2.24584
$51$	−6486.07	−0.349185
$52$	18918.6	0.970241
$53$	33881.1	1.65679	0.828395	−	0.560145i	$-0.189255\pi$
$53$	33881.1	1.65679	0.828395	+	0.560145i	$0.189255\pi$
$54$	40772.0	1.90273
$55$	40106.4	1.78775
$56$	−35446.8	−1.51045
$57$	25347.4	1.03335
$58$	−54292.3	−2.11918
$59$	−1532.55	−0.0573170	−0.0286585	−	0.999589i	$-0.509124\pi$
$59$	−1532.55	−0.0573170	−0.0286585	+	0.999589i	$0.509124\pi$
$60$	65771.8	2.35864
$61$	4352.91	0.149780	0.0748902	−	0.997192i	$-0.476139\pi$
$61$	4352.91	0.149780	0.0748902	+	0.997192i	$0.476139\pi$
$62$	19093.5	0.630820
$63$	−10884.0	−0.345491
$64$	−9091.53	−0.277451
$65$	22670.7	0.665552
$66$	−53906.4	−1.52328
$67$	64667.0	1.75993	0.879966	−	0.475037i	$-0.157565\pi$
$67$	64667.0	1.75993	0.879966	+	0.475037i	$0.157565\pi$
$68$	−40688.1	−1.06707
$69$	−29835.1	−0.754404
$70$	−78163.8	−1.90660
$71$	59387.8	1.39814	0.699071	−	0.715052i	$-0.253597\pi$
$71$	59387.8	1.39814	0.699071	+	0.715052i	$0.253597\pi$
$72$	45476.4	1.03384
$73$	39174.7	0.860397	0.430198	−	0.902734i	$-0.358444\pi$
$73$	39174.7	0.860397	0.430198	+	0.902734i	$0.358444\pi$
$74$	−33728.1	−0.715999
$75$	43901.4	0.901208
$76$	159008.	3.15780
$77$	43982.2	0.845376
$78$	−30471.4	−0.567094
$79$	33132.8	0.597297	0.298649	−	0.954363i	$-0.403464\pi$
$79$	33132.8	0.597297	0.298649	+	0.954363i	$0.403464\pi$
$80$	138215.	2.41451
$81$	−16370.7	−0.277239
$82$	155721.	2.55747
$83$	11074.2	0.176448	0.0882239	−	0.996101i	$-0.471881\pi$
$83$	11074.2	0.176448	0.0882239	+	0.996101i	$0.471881\pi$
$84$	72127.8	1.11533
$85$	−48757.8	−0.731976
$86$	152922.	2.22958
$87$	60036.1	0.850382
$88$	−183770.	−2.52970
$89$	53964.6	0.722161	0.361081	−	0.932535i	$-0.382408\pi$
$89$	53964.6	0.722161	0.361081	+	0.932535i	$0.382408\pi$
$90$	100280.	1.30499
$91$	24861.6	0.314720
$92$	−187160.	−2.30538
$93$	−21113.5	−0.253135
$94$	45950.8	0.536381
$95$	190544.	2.16614
$96$	−48177.3	−0.533536
$97$	164307.	1.77307	0.886535	−	0.462661i	$-0.153105\pi$
$97$	164307.	1.77307	0.886535	+	0.462661i	$0.153105\pi$
$98$	84099.1	0.884558
$99$	−56426.8	−0.578625
$100$	275400.	2.75400
$101$	−57449.6	−0.560381	−0.280191	−	0.959944i	$-0.590398\pi$
$101$	−57449.6	−0.560381	−0.280191	+	0.959944i	$0.590398\pi$
$102$	65534.6	0.623692
$103$	129196.	1.19993	0.599964	−	0.800027i	$-0.295182\pi$
$103$	129196.	1.19993	0.599964	+	0.800027i	$0.295182\pi$
$104$	−103879.	−0.941767
$105$	86433.1	0.765080
$106$	−342331.	−2.95925
$107$	−178656.	−1.50854	−0.754271	−	0.656563i	$-0.772010\pi$
$107$	−178656.	−1.50854	−0.754271	+	0.656563i	$0.772010\pi$
$108$	−282828.	−2.33326
$109$	−63428.6	−0.511351	−0.255675	−	0.966763i	$-0.582298\pi$
$109$	−63428.6	−0.511351	−0.255675	+	0.966763i	$0.582298\pi$
$110$	−405232.	−3.19317
$111$	37296.3	0.287315
$112$	151571.	1.14175
$113$	4074.31	0.0300164	0.0150082	−	0.999887i	$-0.495223\pi$
$113$	4074.31	0.0300164	0.0150082	+	0.999887i	$0.495223\pi$
$114$	−256107.	−1.84570
$115$	−224280.	−1.58141
$116$	376615.	2.59868
$117$	−31896.1	−0.215413
$118$	15484.7	0.102376
$119$	−53469.6	−0.346130
$120$	−361142.	−2.28942
$121$	66969.8	0.415830
$122$	−43981.4	−0.267528
$123$	−172195.	−1.02626
$124$	−132448.	−0.773554
$125$	67552.3	0.386692
$126$	109971.	0.617093
$127$	103121.	0.567335	0.283667	−	0.958923i	$-0.408449\pi$
$127$	103121.	0.567335	0.283667	+	0.958923i	$0.408449\pi$
$128$	229844.	1.23996
$129$	−169100.	−0.894684
$130$	−229063.	−1.18877
$131$	88847.4	0.452341	0.226171	−	0.974088i	$-0.427379\pi$
$131$	88847.4	0.452341	0.226171	+	0.974088i	$0.427379\pi$
$132$	373939.	1.86795
$133$	208958.	1.02431
$134$	−653389.	−3.14348
$135$	−338922.	−1.60053
$136$	223412.	1.03576
$137$	81182.5	0.369540	0.184770	−	0.982782i	$-0.440846\pi$
$137$	81182.5	0.369540	0.184770	+	0.982782i	$0.440846\pi$
$138$	301451.	1.34747
$139$	−140316.	−0.615985	−0.307992	−	0.951389i	$-0.599657\pi$
$139$	−140316.	−0.615985	−0.307992	+	0.951389i	$0.599657\pi$
$140$	542207.	2.33800
$141$	−50812.2	−0.215239
$142$	−600048.	−2.49727
$143$	128892.	0.527091
$144$	−194458.	−0.781482
$145$	451310.	1.78261
$146$	−395818.	−1.53678
$147$	−92996.3	−0.354954
$148$	233965.	0.878006
$149$	443513.	1.63659	0.818297	−	0.574796i	$-0.194919\pi$
$149$	443513.	1.63659	0.818297	+	0.574796i	$0.194919\pi$
$150$	−443575.	−1.60968
$151$	−12301.9	−0.0439066	−0.0219533	−	0.999759i	$-0.506989\pi$
$151$	−12301.9	−0.0439066	−0.0219533	+	0.999759i	$0.506989\pi$
$152$	−873086.	−3.06512
$153$	68598.7	0.236912
$154$	−444392.	−1.50996
$155$	−158717.	−0.530631
$156$	211374.	0.695409
$157$	289717.	0.938048	0.469024	−	0.883185i	$-0.344606\pi$
$157$	289717.	0.938048	0.469024	+	0.883185i	$0.344606\pi$
$158$	−334771.	−1.06685
$159$	378548.	1.18748
$160$	−362164.	−1.11842
$161$	−245953.	−0.747804
$162$	165408.	0.495187
$163$	−190033.	−0.560223	−0.280111	−	0.959967i	$-0.590371\pi$
$163$	−190033.	−0.560223	−0.280111	+	0.959967i	$0.590371\pi$
$164$	−1.08020e6	−3.13615
$165$	448103.	1.28135
$166$	−111892.	−0.315160
$167$	420659.	1.16718	0.583591	−	0.812048i	$-0.301647\pi$
$167$	420659.	1.16718	0.583591	+	0.812048i	$0.301647\pi$
$168$	−396042.	−1.08260
$169$	−298435.	−0.803772
$170$	492645.	1.30741
$171$	−268082.	−0.701096
$172$	−1.06079e6	−2.73406
$173$	438445.	1.11378	0.556891	−	0.830586i	$-0.311994\pi$
$173$	438445.	1.11378	0.556891	+	0.830586i	$0.311994\pi$
$174$	−606599.	−1.51890
$175$	361913.	0.893323
$176$	785804.	1.91220
$177$	−17122.9	−0.0410813
$178$	−545254.	−1.28988
$179$	−263956.	−0.615742	−0.307871	−	0.951428i	$-0.599617\pi$
$179$	−263956.	−0.615742	−0.307871	+	0.951428i	$0.599617\pi$
$180$	−695624.	−1.60027
$181$	−43575.4	−0.0988655	−0.0494327	−	0.998777i	$-0.515741\pi$
$181$	−43575.4	−0.0988655	−0.0494327	+	0.998777i	$0.515741\pi$
$182$	−251199.	−0.562133
$183$	48634.4	0.107353
$184$	1.02766e6	2.23772
$185$	280368.	0.602282
$186$	213328.	0.452133
$187$	−277207.	−0.579697
$188$	−318752.	−0.657747
$189$	−371674.	−0.756846
$190$	−1.92524e6	−3.86902
$191$	−723024.	−1.43407	−0.717033	−	0.697039i	$-0.754500\pi$
$191$	−723024.	−1.43407	−0.717033	+	0.697039i	$0.754500\pi$
$192$	−101578.	−0.198860
$193$	−96242.1	−0.185982	−0.0929912	−	0.995667i	$-0.529643\pi$
$193$	−96242.1	−0.185982	−0.0929912	+	0.995667i	$0.529643\pi$
$194$	−1.66014e6	−3.16694
$195$	253297.	0.477027
$196$	−583380.	−1.08470
$197$	−631560.	−1.15944	−0.579721	−	0.814815i	$-0.696839\pi$
$197$	−631560.	−1.15944	−0.579721	+	0.814815i	$0.696839\pi$
$198$	570131.	1.03350
$199$	1.02351e6	1.83214	0.916069	−	0.401021i	$-0.131345\pi$
$199$	1.02351e6	1.83214	0.916069	+	0.401021i	$0.131345\pi$
$200$	−1.51218e6	−2.67317
$201$	722514.	1.26141
$202$	580465.	1.00092
$203$	494923.	0.842943
$204$	−454601.	−0.764813
$205$	−1.29444e6	−2.15129
$206$	−1.30538e6	−2.14323
$207$	315545.	0.511842
$208$	444187.	0.711881
$209$	1.08332e6	1.71550
$210$	−873311.	−1.36654
$211$	−681640.	−1.05402	−0.527010	−	0.849859i	$-0.676687\pi$
$211$	−681640.	−1.05402	−0.527010	+	0.849859i	$0.676687\pi$
$212$	2.37469e6	3.62883
$213$	663530.	1.00210
$214$	1.80512e6	2.69446
$215$	−1.27118e6	−1.87547
$216$	1.55296e6	2.26478
$217$	−174054.	−0.250920
$218$	640877.	0.913342
$219$	437693.	0.616679
$220$	2.81102e6	3.91567
$221$	−156695.	−0.215812
$222$	−376838.	−0.513184
$223$	−39325.0	−0.0529549	−0.0264775	−	0.999649i	$-0.508429\pi$
$223$	−39325.0	−0.0529549	−0.0264775	+	0.999649i	$0.508429\pi$
$224$	−397162.	−0.528869
$225$	−464315.	−0.611443
$226$	−41166.5	−0.0536133
$227$	−417302.	−0.537509	−0.268754	−	0.963209i	$-0.586612\pi$
$227$	−417302.	−0.537509	−0.268754	+	0.963209i	$0.586612\pi$
$228$	1.77657e6	2.26332
$229$	−489324.	−0.616606	−0.308303	−	0.951288i	$-0.599761\pi$
$229$	−489324.	−0.616606	−0.308303	+	0.951288i	$0.599761\pi$
$230$	2.26610e6	2.82462
$231$	491406.	0.605913
$232$	−2.06793e6	−2.52242
$233$	−614394.	−0.741408	−0.370704	−	0.928751i	$-0.620883\pi$
$233$	−614394.	−0.741408	−0.370704	+	0.928751i	$0.620883\pi$
$234$	322275.	0.384757
$235$	−381971.	−0.451192
$236$	−107415.	−0.125540
$237$	370188.	0.428106
$238$	540252.	0.618236
$239$	390390.	0.442083	0.221041	−	0.975264i	$-0.429054\pi$
$239$	390390.	0.442083	0.221041	+	0.975264i	$0.429054\pi$
$240$	1.54425e6	1.73057
$241$	−137387.	−0.152371	−0.0761854	−	0.997094i	$-0.524274\pi$
$241$	−137387.	−0.152371	−0.0761854	+	0.997094i	$0.524274\pi$
$242$	−676656.	−0.742728
$243$	797663.	0.866570
$244$	305091.	0.328061
$245$	−699083.	−0.744070
$246$	1.73984e6	1.83304
$247$	612362.	0.638654
$248$	727249.	0.750852
$249$	123730.	0.126467
$250$	−682542.	−0.690684
$251$	−68722.7	−0.0688519	−0.0344260	−	0.999407i	$-0.510960\pi$
$251$	−68722.7	−0.0688519	−0.0344260	+	0.999407i	$0.510960\pi$
$252$	−762846.	−0.756721
$253$	−1.27512e6	−1.25242
$254$	−1.04193e6	−1.01334
$255$	−544764.	−0.524635
$256$	−2.03139e6	−1.93729
$257$	−1.41601e6	−1.33731	−0.668656	−	0.743572i	$-0.733130\pi$
$257$	−1.41601e6	−1.33731	−0.668656	+	0.743572i	$0.733130\pi$
$258$	1.70857e6	1.59803
$259$	307462.	0.284801
$260$	1.58897e6	1.45774
$261$	−634961.	−0.576960
$262$	−897705.	−0.807943
$263$	1.47941e6	1.31886	0.659431	−	0.751765i	$-0.270797\pi$
$263$	1.47941e6	1.31886	0.659431	+	0.751765i	$0.270797\pi$
$264$	−2.05324e6	−1.81313
$265$	2.84566e6	2.48925
$266$	−2.11129e6	−1.82955
$267$	602938.	0.517601
$268$	4.53244e6	3.85474
$269$	1.69003e6	1.42402	0.712008	−	0.702172i	$-0.247786\pi$
$269$	1.69003e6	1.42402	0.712008	+	0.702172i	$0.247786\pi$
$270$	3.42443e6	2.85877
$271$	2.03391e6	1.68232	0.841159	−	0.540788i	$-0.181874\pi$
$271$	2.03391e6	1.68232	0.841159	+	0.540788i	$0.181874\pi$
$272$	−955311.	−0.782929
$273$	277774.	0.225572
$274$	−820260.	−0.660048
$275$	1.87630e6	1.49613
$276$	−2.09111e6	−1.65236
$277$	124293.	0.0973298	0.0486649	−	0.998815i	$-0.484503\pi$
$277$	124293.	0.0973298	0.0486649	+	0.998815i	$0.484503\pi$
$278$	1.41774e6	1.10023
$279$	223303.	0.171745
$280$	−2.97717e6	−2.26939
$281$	2.03105e6	1.53446	0.767228	−	0.641375i	$-0.221636\pi$
$281$	2.03105e6	1.53446	0.767228	+	0.641375i	$0.221636\pi$
$282$	513401.	0.384445
$283$	−1.09604e6	−0.813505	−0.406753	−	0.913538i	$-0.633339\pi$
$283$	−1.09604e6	−0.813505	−0.406753	+	0.913538i	$0.633339\pi$
$284$	4.16242e6	3.06232
$285$	2.12892e6	1.55256
$286$	−1.30231e6	−0.941457
$287$	−1.41953e6	−1.01728
$288$	509538.	0.361989
$289$	−1.08285e6	−0.762649
$290$	−4.56000e6	−3.18397
$291$	1.83577e6	1.27083
$292$	2.74571e6	1.88451
$293$	−2.06158e6	−1.40291	−0.701456	−	0.712713i	$-0.747466\pi$
$293$	−2.06158e6	−1.40291	−0.701456	+	0.712713i	$0.747466\pi$
$294$	939626.	0.633996
$295$	−128718.	−0.0861163
$296$	−1.28467e6	−0.852238
$297$	−1.92690e6	−1.26756
$298$	−4.48121e6	−2.92318
$299$	−720779.	−0.466256
$300$	3.07700e6	1.97390
$301$	−1.39402e6	−0.886857
$302$	124297.	0.0784231
$303$	−641875.	−0.401647
$304$	3.73333e6	2.31693
$305$	365600.	0.225039
$306$	−693115.	−0.423157
$307$	470715.	0.285044	0.142522	−	0.989792i	$-0.454479\pi$
$307$	470715.	0.285044	0.142522	+	0.989792i	$0.454479\pi$
$308$	3.08266e6	1.85161
$309$	1.44348e6	0.860034
$310$	1.60366e6	0.947779
$311$	−704181.	−0.412841	−0.206421	−	0.978463i	$-0.566182\pi$
$311$	−704181.	−0.412841	−0.206421	+	0.978463i	$0.566182\pi$
$312$	−1.16062e6	−0.675000
$313$	1.16354e6	0.671304	0.335652	−	0.941986i	$-0.391043\pi$
$313$	1.16354e6	0.671304	0.335652	+	0.941986i	$0.391043\pi$
$314$	−2.92727e6	−1.67548
$315$	−914144.	−0.519084
$316$	2.32224e6	1.30825
$317$	975454.	0.545204	0.272602	−	0.962127i	$-0.412116\pi$
$317$	975454.	0.545204	0.272602	+	0.962127i	$0.412116\pi$
$318$	−3.82481e6	−2.12101
$319$	2.56588e6	1.41175
$320$	−763596.	−0.416858
$321$	−1.99609e6	−1.08123
$322$	2.48509e6	1.33568
$323$	−1.31700e6	−0.702394
$324$	−1.14741e6	−0.607231
$325$	1.06060e6	0.556987
$326$	1.92008e6	1.00063
$327$	−708678.	−0.366505
$328$	5.93123e6	3.04411
$329$	−418884.	−0.213355
$330$	−4.52759e6	−2.28866
$331$	−250856.	−0.125851	−0.0629253	−	0.998018i	$-0.520043\pi$
$331$	−250856.	−0.125851	−0.0629253	+	0.998018i	$0.520043\pi$
$332$	776177.	0.386470
$333$	−394458.	−0.194935
$334$	−4.25030e6	−2.08475
$335$	5.43137e6	2.64422
$336$	1.69348e6	0.818337
$337$	193327.	0.0927295	0.0463647	−	0.998925i	$-0.485236\pi$
$337$	193327.	0.0927295	0.0463647	+	0.998925i	$0.485236\pi$
$338$	3.01536e6	1.43565
$339$	45521.6	0.0215139
$340$	−3.41738e6	−1.60323
$341$	−902366.	−0.420239
$342$	2.70867e6	1.25225
$343$	−2.31467e6	−1.06232
$344$	5.82463e6	2.65382
$345$	−2.50584e6	−1.13346
$346$	−4.43001e6	−1.98936
$347$	4.07137e6	1.81517	0.907583	−	0.419872i	$-0.137925\pi$
$347$	4.07137e6	1.81517	0.907583	+	0.419872i	$0.137925\pi$
$348$	4.20786e6	1.86257
$349$	−2.64448e6	−1.16219	−0.581093	−	0.813837i	$-0.697375\pi$
$349$	−2.64448e6	−1.16219	−0.581093	+	0.813837i	$0.697375\pi$
$350$	−3.65673e6	−1.59560
$351$	−1.08921e6	−0.471893
$352$	−2.05904e6	−0.885746
$353$	−505685.	−0.215995	−0.107997	−	0.994151i	$-0.534444\pi$
$353$	−505685.	−0.215995	−0.107997	+	0.994151i	$0.534444\pi$
$354$	173008.	0.0733768
$355$	4.98797e6	2.10065
$356$	3.78232e6	1.58173
$357$	−597408.	−0.248085
$358$	2.66699e6	1.09980
$359$	−2.84043e6	−1.16318	−0.581591	−	0.813482i	$-0.697569\pi$
$359$	−2.84043e6	−1.16318	−0.581591	+	0.813482i	$0.697569\pi$
$360$	3.81956e6	1.55330
$361$	2.67071e6	1.07860
$362$	440282.	0.176587
$363$	748243.	0.298041
$364$	1.74252e6	0.689325
$365$	3.29028e6	1.29271
$366$	−491397.	−0.191748
$367$	4.12207e6	1.59753	0.798767	−	0.601641i	$-0.205486\pi$
$367$	4.12207e6	1.59753	0.798767	+	0.601641i	$0.205486\pi$
$368$	−4.39431e6	−1.69150
$369$	1.82119e6	0.696288
$370$	−2.83281e6	−1.07576
$371$	3.12066e6	1.17710
$372$	−1.47982e6	−0.554436
$373$	4.46906e6	1.66320	0.831600	−	0.555375i	$-0.187425\pi$
$373$	4.46906e6	1.66320	0.831600	+	0.555375i	$0.187425\pi$
$374$	2.80088e6	1.03542
$375$	754752.	0.277157
$376$	1.75022e6	0.638443
$377$	1.45040e6	0.525574
$378$	3.75536e6	1.35183
$379$	−1.56293e6	−0.558910	−0.279455	−	0.960159i	$-0.590154\pi$
$379$	−1.56293e6	−0.558910	−0.279455	+	0.960159i	$0.590154\pi$
$380$	1.33550e7	4.74445
$381$	1.15216e6	0.406630
$382$	7.30537e6	2.56144
$383$	−5.36347e6	−1.86831	−0.934156	−	0.356866i	$-0.883845\pi$
$383$	−5.36347e6	−1.86831	−0.934156	+	0.356866i	$0.883845\pi$
$384$	2.56801e6	0.888727
$385$	3.69406e6	1.27014
$386$	972421.	0.332190
$387$	1.78846e6	0.607017
$388$	1.15161e7	3.88352
$389$	−1.38150e6	−0.462890	−0.231445	−	0.972848i	$-0.574345\pi$
$389$	−1.38150e6	−0.462890	−0.231445	+	0.972848i	$0.574345\pi$
$390$	−2.55928e6	−0.852034
$391$	1.55018e6	0.512789
$392$	3.20324e6	1.05287
$393$	992678.	0.324210
$394$	6.38123e6	2.07092
$395$	2.78282e6	0.897413
$396$	−3.95489e6	−1.26735
$397$	−2.88886e6	−0.919920	−0.459960	−	0.887940i	$-0.652136\pi$
$397$	−2.88886e6	−0.919920	−0.459960	+	0.887940i	$0.652136\pi$
$398$	−1.03414e7	−3.27245
$399$	2.33465e6	0.734159
$400$	6.46608e6	2.02065
$401$	−4.47634e6	−1.39015	−0.695075	−	0.718937i	$-0.744629\pi$
$401$	−4.47634e6	−1.39015	−0.695075	+	0.718937i	$0.744629\pi$
$402$	−7.30022e6	−2.25305
$403$	−510075.	−0.156449
$404$	−4.02658e6	−1.22739
$405$	−1.37497e6	−0.416540
$406$	−5.00066e6	−1.50561
$407$	1.59400e6	0.476984
$408$	2.49614e6	0.742367
$409$	3.80021e6	1.12331	0.561654	−	0.827372i	$-0.310165\pi$
$409$	3.80021e6	1.12331	0.561654	+	0.827372i	$0.310165\pi$
$410$	1.30789e7	3.84249
$411$	907039.	0.264863
$412$	9.05519e6	2.62818
$413$	−141157.	−0.0407219
$414$	−3.18824e6	−0.914219
$415$	930118.	0.265105
$416$	−1.16390e6	−0.329749
$417$	−1.56773e6	−0.441500
$418$	−1.09458e7	−3.06411
$419$	−2.04594e6	−0.569321	−0.284660	−	0.958628i	$-0.591881\pi$
$419$	−2.04594e6	−0.569321	−0.284660	+	0.958628i	$0.591881\pi$
$420$	6.05800e6	1.67574
$421$	−5.73412e6	−1.57674	−0.788372	−	0.615199i	$-0.789076\pi$
$421$	−5.73412e6	−1.57674	−0.788372	+	0.615199i	$0.789076\pi$
$422$	6.88723e6	1.88262
$423$	537406.	0.146033
$424$	−1.30390e7	−3.52233
$425$	−2.28104e6	−0.612576
$426$	−6.70425e6	−1.78989
$427$	400931.	0.106414
$428$	−1.25218e7	−3.30413
$429$	1.44009e6	0.377787
$430$	1.28439e7	3.34985
$431$	−668121.	−0.173246	−0.0866228	−	0.996241i	$-0.527607\pi$
$431$	−668121.	−0.173246	−0.0866228	+	0.996241i	$0.527607\pi$
$432$	−6.64048e6	−1.71195
$433$	1.51092e6	0.387277	0.193638	−	0.981073i	$-0.437971\pi$
$433$	1.51092e6	0.387277	0.193638	+	0.981073i	$0.437971\pi$
$434$	1.75863e6	0.448177
$435$	5.04242e6	1.27766
$436$	−4.44564e6	−1.12000
$437$	−6.05805e6	−1.51750
$438$	−4.42241e6	−1.10147
$439$	1.07725e6	0.266781	0.133390	−	0.991064i	$-0.457414\pi$
$439$	1.07725e6	0.266781	0.133390	+	0.991064i	$0.457414\pi$
$440$	−1.54348e7	−3.80076
$441$	983559.	0.240826
$442$	1.58324e6	0.385470
$443$	−1.29313e6	−0.313063	−0.156531	−	0.987673i	$-0.550031\pi$
$443$	−1.29313e6	−0.313063	−0.156531	+	0.987673i	$0.550031\pi$
$444$	2.61406e6	0.629300
$445$	4.53248e6	1.08502
$446$	397336.	0.0945846
$447$	4.95530e6	1.17301
$448$	−837387.	−0.197120
$449$	−6.56603e6	−1.53705	−0.768524	−	0.639821i	$-0.779008\pi$
$449$	−6.56603e6	−1.53705	−0.768524	+	0.639821i	$0.779008\pi$
$450$	4.69139e6	1.09212
$451$	−7.35942e6	−1.70374
$452$	285564.	0.0657442
$453$	−137447.	−0.0314695
$454$	4.21638e6	0.960064
$455$	2.08812e6	0.472853
$456$	−9.75486e6	−2.19689
$457$	−6.53355e6	−1.46339	−0.731693	−	0.681634i	$-0.761270\pi$
$457$	−6.53355e6	−1.46339	−0.731693	+	0.681634i	$0.761270\pi$
$458$	4.94408e6	1.10134
$459$	2.34256e6	0.518989
$460$	−1.57195e7	−3.46374
$461$	−1.51097e6	−0.331133	−0.165566	−	0.986199i	$-0.552945\pi$
$461$	−1.51097e6	−0.331133	−0.165566	+	0.986199i	$0.552945\pi$
$462$	−4.96512e6	−1.08224
$463$	5.22309e6	1.13233	0.566167	−	0.824290i	$-0.308426\pi$
$463$	5.22309e6	1.13233	0.566167	+	0.824290i	$0.308426\pi$
$464$	8.84251e6	1.90669
$465$	−1.77332e6	−0.380324
$466$	6.20778e6	1.32425
$467$	−3.51880e6	−0.746625	−0.373313	−	0.927706i	$-0.621778\pi$
$467$	−3.51880e6	−0.746625	−0.373313	+	0.927706i	$0.621778\pi$
$468$	−2.23556e6	−0.471815
$469$	5.95624e6	1.25037
$470$	3.85940e6	0.805889
$471$	3.23696e6	0.672335
$472$	589796.	0.121856
$473$	−7.22716e6	−1.48530
$474$	−3.74034e6	−0.764655
$475$	8.91422e6	1.81280
$476$	−3.74763e6	−0.758122
$477$	−4.00364e6	−0.805674
$478$	−3.94446e6	−0.789619
$479$	−847395.	−0.168751	−0.0843756	−	0.996434i	$-0.526890\pi$
$479$	−847395.	−0.168751	−0.0843756	+	0.996434i	$0.526890\pi$
$480$	−4.04640e6	−0.801615
$481$	901034.	0.177574
$482$	1.38814e6	0.272155
$483$	−2.74800e6	−0.535980
$484$	4.69384e6	0.910783
$485$	1.38001e7	2.66396
$486$	−8.05951e6	−1.54781
$487$	−3.39374e6	−0.648419	−0.324209	−	0.945985i	$-0.605098\pi$
$487$	−3.39374e6	−0.648419	−0.324209	+	0.945985i	$0.605098\pi$
$488$	−1.67520e6	−0.318433
$489$	−2.12321e6	−0.401533
$490$	7.06347e6	1.32901
$491$	8.62314e6	1.61422	0.807108	−	0.590404i	$-0.201031\pi$
$491$	8.62314e6	1.61422	0.807108	+	0.590404i	$0.201031\pi$
$492$	−1.20690e7	−2.24780
$493$	−3.11937e6	−0.578028
$494$	−6.18725e6	−1.14072
$495$	−4.73928e6	−0.869359
$496$	−3.10973e6	−0.567569
$497$	5.46999e6	0.993334
$498$	−1.25016e6	−0.225887
$499$	9.06737e6	1.63016	0.815080	−	0.579349i	$-0.196693\pi$
$499$	9.06737e6	1.63016	0.815080	+	0.579349i	$0.196693\pi$
$500$	4.73467e6	0.846963
$501$	4.69995e6	0.836564
$502$	694368.	0.122979
$503$	−1.29692e6	−0.228557	−0.114278	−	0.993449i	$-0.536456\pi$
$503$	−1.29692e6	−0.228557	−0.114278	+	0.993449i	$0.536456\pi$
$504$	4.18866e6	0.734513
$505$	−4.82518e6	−0.841948
$506$	1.28837e7	2.23699
$507$	−3.33437e6	−0.576094
$508$	7.22766e6	1.24262
$509$	4.01808e6	0.687424	0.343712	−	0.939075i	$-0.388316\pi$
$509$	4.01808e6	0.687424	0.343712	+	0.939075i	$0.388316\pi$
$510$	5.50424e6	0.937070
$511$	3.60824e6	0.611284
$512$	1.31700e7	2.22029
$513$	−9.15465e6	−1.53585
$514$	1.43072e7	2.38862
$515$	1.08511e7	1.80284
$516$	−1.18520e7	−1.95961
$517$	−2.17166e6	−0.357326
$518$	−3.10657e6	−0.508694
$519$	4.89868e6	0.798290
$520$	−8.72476e6	−1.41496
$521$	−766140.	−0.123656	−0.0618278	−	0.998087i	$-0.519693\pi$
$521$	−766140.	−0.123656	−0.0618278	+	0.998087i	$0.519693\pi$
$522$	6.41558e6	1.03053
$523$	1.70949e6	0.273282	0.136641	−	0.990621i	$-0.456369\pi$
$523$	1.70949e6	0.273282	0.136641	+	0.990621i	$0.456369\pi$
$524$	6.22722e6	0.990754
$525$	4.04359e6	0.640279
$526$	−1.49478e7	−2.35567
$527$	1.09702e6	0.172063
$528$	8.77967e6	1.37054
$529$	694265.	0.107866
$530$	−2.87523e7	−4.44614
$531$	181097.	0.0278725
$532$	1.46456e7	2.24351
$533$	−4.16002e6	−0.634275
$534$	−6.09203e6	−0.924505
$535$	−1.50053e7	−2.26652
$536$	−2.48869e7	−3.74161
$537$	−2.94914e6	−0.441326
$538$	−1.70759e7	−2.54348
$539$	−3.97456e6	−0.589274
$540$	−2.37546e7	−3.50561
$541$	5.04291e6	0.740777	0.370389	−	0.928877i	$-0.379224\pi$
$541$	5.04291e6	0.740777	0.370389	+	0.928877i	$0.379224\pi$
$542$	−2.05504e7	−3.00485
$543$	−486861.	−0.0708607
$544$	2.50320e6	0.362659
$545$	−5.32736e6	−0.768282
$546$	−2.80660e6	−0.402902
$547$	5.51464e6	0.788041	0.394021	−	0.919102i	$-0.371084\pi$
$547$	5.51464e6	0.788041	0.394021	+	0.919102i	$0.371084\pi$
$548$	5.68999e6	0.809395
$549$	−514373.	−0.0728362
$550$	−1.89579e7	−2.67229
$551$	1.21904e7	1.71056
$552$	1.14819e7	1.60386
$553$	3.05174e6	0.424361
$554$	−1.25584e6	−0.173844
$555$	3.13251e6	0.431678
$556$	−9.83459e6	−1.34918
$557$	1.37797e7	1.88193	0.940964	−	0.338506i	$-0.109922\pi$
$557$	1.37797e7	1.88193	0.940964	+	0.338506i	$0.109922\pi$
$558$	−2.25623e6	−0.306759
$559$	−4.08525e6	−0.552955
$560$	1.27304e7	1.71543
$561$	−3.09720e6	−0.415491
$562$	−2.05215e7	−2.74075
$563$	−8.45879e6	−1.12470	−0.562351	−	0.826899i	$-0.690103\pi$
$563$	−8.45879e6	−1.12470	−0.562351	+	0.826899i	$0.690103\pi$
$564$	−3.56137e6	−0.471432
$565$	342201.	0.0450983
$566$	1.10743e7	1.45303
$567$	−1.50785e6	−0.196970
$568$	−2.28552e7	−2.97245
$569$	−1.31533e7	−1.70315	−0.851577	−	0.524229i	$-0.824354\pi$
$569$	−1.31533e7	−1.70315	−0.851577	+	0.524229i	$0.824354\pi$
$570$	−2.15104e7	−2.77308
$571$	2.46087e6	0.315863	0.157932	−	0.987450i	$-0.449517\pi$
$571$	2.46087e6	0.315863	0.157932	+	0.987450i	$0.449517\pi$
$572$	9.03390e6	1.15448
$573$	−8.07823e6	−1.02785
$574$	1.43428e7	1.81700
$575$	−1.04925e7	−1.32345
$576$	1.07432e6	0.134921
$577$	1.48373e7	1.85530	0.927652	−	0.373445i	$-0.121824\pi$
$577$	1.48373e7	1.85530	0.927652	+	0.373445i	$0.121824\pi$
$578$	1.09410e7	1.36219
$579$	−1.07530e6	−0.133301
$580$	3.16319e7	3.90440
$581$	1.02000e6	0.125360
$582$	−1.85485e7	−2.26987
$583$	1.61787e7	1.97139
$584$	−1.50763e7	−1.82920
$585$	−2.67895e6	−0.323649
$586$	2.08300e7	2.50579
$587$	−72382.7	−0.00867041	−0.00433520	−	0.999991i	$-0.501380\pi$
$587$	−72382.7	−0.00867041	−0.00433520	+	0.999991i	$0.501380\pi$
$588$	−6.51801e6	−0.777449
$589$	−4.28711e6	−0.509186
$590$	1.30056e6	0.153815
$591$	−7.05633e6	−0.831017
$592$	5.49325e6	0.644206
$593$	−6.08575e6	−0.710685	−0.355343	−	0.934736i	$-0.615636\pi$
$593$	−6.08575e6	−0.710685	−0.355343	+	0.934736i	$0.615636\pi$
$594$	1.94692e7	2.26403
$595$	−4.49090e6	−0.520046
$596$	3.10854e7	3.58460
$597$	1.14355e7	1.31316
$598$	7.28268e6	0.832796
$599$	−7.51115e6	−0.855342	−0.427671	−	0.903935i	$-0.640666\pi$
$599$	−7.51115e6	−0.855342	−0.427671	+	0.903935i	$0.640666\pi$
$600$	−1.68953e7	−1.91597
$601$	8.67236e6	0.979380	0.489690	−	0.871897i	$-0.337110\pi$
$601$	8.67236e6	0.979380	0.489690	+	0.871897i	$0.337110\pi$
$602$	1.40851e7	1.58405
$603$	−7.64154e6	−0.855831
$604$	−862226.	−0.0961676
$605$	5.62478e6	0.624766
$606$	6.48545e6	0.717395
$607$	1.30687e7	1.43966	0.719832	−	0.694148i	$-0.244219\pi$
$607$	1.30687e7	1.43966	0.719832	+	0.694148i	$0.244219\pi$
$608$	−9.78245e6	−1.07322
$609$	5.52970e6	0.604169
$610$	−3.69399e6	−0.401949
$611$	−1.22756e6	−0.133027
$612$	4.80801e6	0.518904
$613$	1.59208e6	0.171125	0.0855627	−	0.996333i	$-0.472731\pi$
$613$	1.59208e6	0.171125	0.0855627	+	0.996333i	$0.472731\pi$
$614$	−4.75606e6	−0.509127
$615$	−1.44626e7	−1.54191
$616$	−1.69264e7	−1.79727
$617$	−1.78890e7	−1.89179	−0.945894	−	0.324476i	$-0.894812\pi$
$617$	−1.78890e7	−1.89179	−0.945894	+	0.324476i	$0.894812\pi$
$618$	−1.45848e7	−1.53614
$619$	1.72254e7	1.80693	0.903467	−	0.428658i	$-0.141013\pi$
$619$	1.72254e7	1.80693	0.903467	+	0.428658i	$0.141013\pi$
$620$	−1.11243e7	−1.16223
$621$	1.07755e7	1.12126
$622$	7.11498e6	0.737390
$623$	4.97048e6	0.513072
$624$	4.96283e6	0.510233
$625$	−6.60533e6	−0.676386
$626$	−1.17563e7	−1.19904
$627$	1.21038e7	1.22956
$628$	2.03060e7	2.05459
$629$	−1.93785e6	−0.195296
$630$	9.23642e6	0.927155
$631$	1.33630e7	1.33607	0.668037	−	0.744128i	$-0.267135\pi$
$631$	1.33630e7	1.33607	0.668037	+	0.744128i	$0.267135\pi$
$632$	−1.27511e7	−1.26985
$633$	−7.61586e6	−0.755457
$634$	−9.85590e6	−0.973807
$635$	8.66114e6	0.852395
$636$	2.65320e7	2.60092
$637$	−2.24668e6	−0.219378
$638$	−2.59254e7	−2.52158
$639$	−7.01771e6	−0.679897
$640$	1.93045e7	1.86299
$641$	−1.64699e7	−1.58324	−0.791620	−	0.611014i	$-0.790762\pi$
$641$	−1.64699e7	−1.58324	−0.791620	+	0.611014i	$0.790762\pi$
$642$	2.01683e7	1.93122
$643$	−1.27938e7	−1.22032	−0.610158	−	0.792280i	$-0.708894\pi$
$643$	−1.27938e7	−1.22032	−0.610158	+	0.792280i	$0.708894\pi$
$644$	−1.72386e7	−1.63790
$645$	−1.42027e7	−1.34422
$646$	1.33069e7	1.25457
$647$	−6.56382e6	−0.616448	−0.308224	−	0.951314i	$-0.599735\pi$
$647$	−6.56382e6	−0.616448	−0.308224	+	0.951314i	$0.599735\pi$
$648$	6.30021e6	0.589410
$649$	−731814.	−0.0682008
$650$	−1.07162e7	−0.994853
$651$	−1.94468e6	−0.179844
$652$	−1.33192e7	−1.22704
$653$	3.04532e6	0.279479	0.139740	−	0.990188i	$-0.455373\pi$
$653$	3.04532e6	0.279479	0.139740	+	0.990188i	$0.455373\pi$
$654$	7.16042e6	0.654627
$655$	7.46228e6	0.679623
$656$	−2.53620e7	−2.30104
$657$	−4.62918e6	−0.418399
$658$	4.23236e6	0.381082
$659$	1.61883e6	0.145207	0.0726037	−	0.997361i	$-0.476869\pi$
$659$	1.61883e6	0.145207	0.0726037	+	0.997361i	$0.476869\pi$
$660$	3.14070e7	2.80651
$661$	1.64054e7	1.46044	0.730220	−	0.683212i	$-0.239418\pi$
$661$	1.64054e7	1.46044	0.730220	+	0.683212i	$0.239418\pi$
$662$	2.53463e6	0.224786
$663$	−1.75073e6	−0.154681
$664$	−4.26186e6	−0.375128
$665$	1.75503e7	1.53897
$666$	3.98556e6	0.348180
$667$	−1.43487e7	−1.24881
$668$	2.94835e7	2.55645
$669$	−439372.	−0.0379548
$670$	−5.48781e7	−4.72293
$671$	2.07858e6	0.178222
$672$	−4.43743e6	−0.379060
$673$	−2.02644e6	−0.172463	−0.0862315	−	0.996275i	$-0.527482\pi$
$673$	−2.02644e6	−0.172463	−0.0862315	+	0.996275i	$0.527482\pi$
$674$	−1.95336e6	−0.165627
$675$	−1.58557e7	−1.33945
$676$	−2.09170e7	−1.76048
$677$	7.18710e6	0.602673	0.301337	−	0.953518i	$-0.402567\pi$
$677$	7.18710e6	0.602673	0.301337	+	0.953518i	$0.402567\pi$
$678$	−459946.	−0.0384267
$679$	1.51337e7	1.25971
$680$	1.87643e7	1.55618
$681$	−4.66245e6	−0.385253
$682$	9.11742e6	0.750604
$683$	−3.41833e6	−0.280390	−0.140195	−	0.990124i	$-0.544773\pi$
$683$	−3.41833e6	−0.280390	−0.140195	+	0.990124i	$0.544773\pi$
$684$	−1.87896e7	−1.53559
$685$	6.81850e6	0.555217
$686$	2.33872e7	1.89744
$687$	−5.46714e6	−0.441945
$688$	−2.49062e7	−2.00602
$689$	9.14525e6	0.733918
$690$	2.53188e7	2.02451
$691$	−2.02356e7	−1.61221	−0.806103	−	0.591775i	$-0.798427\pi$
$691$	−2.02356e7	−1.61221	−0.806103	+	0.591775i	$0.798427\pi$
$692$	3.07301e7	2.43949
$693$	−5.19727e6	−0.411095
$694$	−4.11367e7	−3.24213
$695$	−1.17851e7	−0.925490
$696$	−2.31047e7	−1.80791
$697$	8.94693e6	0.697577
$698$	2.67195e7	2.07582
$699$	−6.86453e6	−0.531395
$700$	2.53661e7	1.95663
$701$	−7.88122e6	−0.605757	−0.302879	−	0.953029i	$-0.597948\pi$
$701$	−7.88122e6	−0.605757	−0.302879	+	0.953029i	$0.597948\pi$
$702$	1.10053e7	0.842865
$703$	7.57306e6	0.577940
$704$	−4.34134e6	−0.330136
$705$	−4.26771e6	−0.323386
$706$	5.10940e6	0.385796
$707$	−5.29147e6	−0.398133
$708$	−1.20013e6	−0.0899795
$709$	1.85798e6	0.138812	0.0694058	−	0.997589i	$-0.477890\pi$
$709$	1.85798e6	0.138812	0.0694058	+	0.997589i	$0.477890\pi$
$710$	−5.03980e7	−3.75204
$711$	−3.91522e6	−0.290458
$712$	−2.07681e7	−1.53531
$713$	5.04613e6	0.371736
$714$	6.03615e6	0.443113
$715$	1.08256e7	0.791932
$716$	−1.85004e7	−1.34865
$717$	4.36176e6	0.316858
$718$	2.86994e7	2.07760
$719$	−3.80664e6	−0.274612	−0.137306	−	0.990529i	$-0.543844\pi$
$719$	−3.80664e6	−0.274612	−0.137306	+	0.990529i	$0.543844\pi$
$720$	−1.63325e7	−1.17414
$721$	1.18997e7	0.852510
$722$	−2.69847e7	−1.92652
$723$	−1.53500e6	−0.109210
$724$	−3.05415e6	−0.216543
$725$	2.11136e7	1.49183
$726$	−7.56018e6	−0.532342
$727$	7.06549e6	0.495799	0.247900	−	0.968786i	$-0.420260\pi$
$727$	7.06549e6	0.495799	0.247900	+	0.968786i	$0.420260\pi$
$728$	−9.56789e6	−0.669095
$729$	1.28902e7	0.898343
$730$	−3.32447e7	−2.30895
$731$	8.78614e6	0.608141
$732$	3.40873e6	0.235134
$733$	8.05083e6	0.553453	0.276726	−	0.960949i	$-0.410750\pi$
$733$	8.05083e6	0.553453	0.276726	+	0.960949i	$0.410750\pi$
$734$	−4.16490e7	−2.85341
$735$	−7.81075e6	−0.533303
$736$	1.15144e7	0.783515
$737$	3.08795e7	2.09412
$738$	−1.84011e7	−1.24366
$739$	2.20197e7	1.48320	0.741600	−	0.670842i	$-0.234067\pi$
$739$	2.20197e7	1.48320	0.741600	+	0.670842i	$0.234067\pi$
$740$	1.96507e7	1.31916
$741$	6.84182e6	0.457748
$742$	−3.15309e7	−2.10245
$743$	−1.70610e7	−1.13379	−0.566895	−	0.823790i	$-0.691856\pi$
$743$	−1.70610e7	−1.13379	−0.566895	+	0.823790i	$0.691856\pi$
$744$	8.12544e6	0.538164
$745$	3.72506e7	2.45891
$746$	−4.51550e7	−2.97070
$747$	−1.30861e6	−0.0858042
$748$	−1.94292e7	−1.26970
$749$	−1.64553e7	−1.07177
$750$	−7.62594e6	−0.495040
$751$	4.57862e6	0.296234	0.148117	−	0.988970i	$-0.452679\pi$
$751$	4.57862e6	0.296234	0.148117	+	0.988970i	$0.452679\pi$
$752$	−7.48395e6	−0.482599
$753$	−767828.	−0.0493488
$754$	−1.46547e7	−0.938747
$755$	−1.03323e6	−0.0659677
$756$	−2.60502e7	−1.65770
$757$	−2.92356e6	−0.185427	−0.0927133	−	0.995693i	$-0.529554\pi$
$757$	−2.92356e6	−0.185427	−0.0927133	+	0.995693i	$0.529554\pi$
$758$	1.57917e7	0.998289
$759$	−1.42467e7	−0.897656
$760$	−7.33304e7	−4.60521
$761$	5.95068e6	0.372482	0.186241	−	0.982504i	$-0.440370\pi$
$761$	5.95068e6	0.372482	0.186241	+	0.982504i	$0.440370\pi$
$762$	−1.16413e7	−0.726297
$763$	−5.84218e6	−0.363298
$764$	−5.06760e7	−3.14101
$765$	5.76159e6	0.355950
$766$	5.41920e7	3.33706
$767$	−413669.	−0.0253901
$768$	−2.26964e7	−1.38853
$769$	2.39326e7	1.45940	0.729699	−	0.683768i	$-0.239660\pi$
$769$	2.39326e7	1.45940	0.729699	+	0.683768i	$0.239660\pi$
$770$	−3.73244e7	−2.26864
$771$	−1.58208e7	−0.958503
$772$	−6.74550e6	−0.407353
$773$	−2.65289e7	−1.59688	−0.798438	−	0.602077i	$-0.794340\pi$
$773$	−2.65289e7	−1.59688	−0.798438	+	0.602077i	$0.794340\pi$
$774$	−1.80704e7	−1.08422
$775$	−7.42523e6	−0.444074
$776$	−6.32329e7	−3.76954
$777$	3.43523e6	0.204128
$778$	1.39586e7	0.826784
$779$	−3.49644e7	−2.06434
$780$	1.77533e7	1.04482
$781$	2.83586e7	1.66363
$782$	−1.56628e7	−0.915911
$783$	−2.16831e7	−1.26391
$784$	−1.36971e7	−0.795864
$785$	2.43333e7	1.40938
$786$	−1.00299e7	−0.579084
$787$	1.06251e7	0.611501	0.305751	−	0.952112i	$-0.401093\pi$
$787$	1.06251e7	0.611501	0.305751	+	0.952112i	$0.401093\pi$
$788$	−4.42654e7	−2.53950
$789$	1.65292e7	0.945279
$790$	−2.81174e7	−1.60290
$791$	375270.	0.0213257
$792$	2.17157e7	1.23016
$793$	1.17495e6	0.0663492
$794$	2.91888e7	1.64310
$795$	3.17942e7	1.78414
$796$	7.17365e7	4.01289
$797$	−7.80356e6	−0.435158	−0.217579	−	0.976043i	$-0.569816\pi$
$797$	−7.80356e6	−0.435158	−0.217579	+	0.976043i	$0.569816\pi$
$798$	−2.35891e7	−1.31131
$799$	2.64011e6	0.146304
$800$	−1.69431e7	−0.935983
$801$	−6.37687e6	−0.351177
$802$	4.52285e7	2.48300
$803$	1.87065e7	1.02377
$804$	5.06402e7	2.76284
$805$	−2.06576e7	−1.12354
$806$	5.15375e6	0.279438
$807$	1.88825e7	1.02065
$808$	2.21093e7	1.19137
$809$	9.39426e6	0.504651	0.252326	−	0.967642i	$-0.418805\pi$
$809$	9.39426e6	0.504651	0.252326	+	0.967642i	$0.418805\pi$
$810$	1.38926e7	0.743996
$811$	761984.	0.0406812	0.0203406	−	0.999793i	$-0.493525\pi$
$811$	761984.	0.0406812	0.0203406	+	0.999793i	$0.493525\pi$
$812$	3.46887e7	1.84628
$813$	2.27245e7	1.20578
$814$	−1.61057e7	−0.851957
$815$	−1.59609e7	−0.841710
$816$	−1.06735e7	−0.561155
$817$	−3.43360e7	−1.79968
$818$	−3.83970e7	−2.00638
$819$	−2.93783e6	−0.153044
$820$	−9.07262e7	−4.71192
$821$	4.85128e6	0.251188	0.125594	−	0.992082i	$-0.459916\pi$
$821$	4.85128e6	0.251188	0.125594	+	0.992082i	$0.459916\pi$
$822$	−9.16464e6	−0.473081
$823$	3.79956e7	1.95539	0.977695	−	0.210028i	$-0.0673557\pi$
$823$	3.79956e7	1.95539	0.977695	+	0.210028i	$0.0673557\pi$
$824$	−4.97205e7	−2.55104
$825$	2.09636e7	1.07233
$826$	1.42624e6	0.0727348
$827$	−1.34489e7	−0.683789	−0.341895	−	0.939738i	$-0.611069\pi$
$827$	−1.34489e7	−0.683789	−0.341895	+	0.939738i	$0.611069\pi$
$828$	2.21162e7	1.12108
$829$	−218170.	−0.0110258	−0.00551288	−	0.999985i	$-0.501755\pi$
$829$	−218170.	−0.0110258	−0.00551288	+	0.999985i	$0.501755\pi$
$830$	−9.39783e6	−0.473513
$831$	1.38870e6	0.0697600
$832$	−2.45401e6	−0.122904
$833$	4.83192e6	0.241272
$834$	1.58402e7	0.788578
$835$	3.53311e7	1.75364
$836$	7.59287e7	3.75742
$837$	7.62549e6	0.376231
$838$	2.06719e7	1.01688
$839$	−3.43422e7	−1.68431	−0.842157	−	0.539232i	$-0.818715\pi$
$839$	−3.43422e7	−1.68431	−0.842157	+	0.539232i	$0.818715\pi$
$840$	−3.32635e7	−1.62656
$841$	8.36221e6	0.407691
$842$	5.79370e7	2.81628
$843$	2.26926e7	1.09980
$844$	−4.77754e7	−2.30860
$845$	−2.50655e7	−1.20763
$846$	−5.42990e6	−0.260835
$847$	6.16834e6	0.295434
$848$	5.57550e7	2.66253
$849$	−1.22459e7	−0.583070
$850$	2.30474e7	1.09414
$851$	−8.91385e6	−0.421931
$852$	4.65061e7	2.19488
$853$	7.09656e6	0.333945	0.166973	−	0.985962i	$-0.446601\pi$
$853$	7.09656e6	0.333945	0.166973	+	0.985962i	$0.446601\pi$
$854$	−4.05097e6	−0.190070
$855$	−2.25162e7	−1.05337
$856$	6.87551e7	3.20716
$857$	2.88278e7	1.34078	0.670392	−	0.742007i	$-0.266126\pi$
$857$	2.88278e7	1.34078	0.670392	+	0.742007i	$0.266126\pi$
$858$	−1.45505e7	−0.674778
$859$	497231.	0.0229919	0.0114960	−	0.999934i	$-0.496341\pi$
$859$	497231.	0.0229919	0.0114960	+	0.999934i	$0.496341\pi$
$860$	−8.90956e7	−4.10781
$861$	−1.58602e7	−0.729125
$862$	6.75063e6	0.309440
$863$	−7.69974e6	−0.351924	−0.175962	−	0.984397i	$-0.556304\pi$
$863$	−7.69974e6	−0.351924	−0.175962	+	0.984397i	$0.556304\pi$
$864$	1.74001e7	0.792988
$865$	3.68249e7	1.67341
$866$	−1.52662e7	−0.691728
$867$	−1.20985e7	−0.546620
$868$	−1.21993e7	−0.549585
$869$	1.58214e7	0.710716
$870$	−5.09481e7	−2.28208
$871$	1.74551e7	0.779608
$872$	2.44103e7	1.08713
$873$	−1.94157e7	−0.862220
$874$	6.12099e7	2.71046
$875$	6.22200e6	0.274732
$876$	3.06774e7	1.35070
$877$	9.02341e6	0.396161	0.198080	−	0.980186i	$-0.436529\pi$
$877$	9.02341e6	0.396161	0.198080	+	0.980186i	$0.436529\pi$
$878$	−1.08844e7	−0.476506
$879$	−2.30337e7	−1.00552
$880$	6.59996e7	2.87299
$881$	1.29739e7	0.563158	0.281579	−	0.959538i	$-0.409142\pi$
$881$	1.29739e7	0.563158	0.281579	+	0.959538i	$0.409142\pi$
$882$	−9.93779e6	−0.430148
$883$	−1.47949e7	−0.638574	−0.319287	−	0.947658i	$-0.603443\pi$
$883$	−1.47949e7	−0.638574	−0.319287	+	0.947658i	$0.603443\pi$
$884$	−1.09826e7	−0.472689
$885$	−1.43815e6	−0.0617228
$886$	1.30656e7	0.559173
$887$	−1.16353e6	−0.0496556	−0.0248278	−	0.999692i	$-0.507904\pi$
$887$	−1.16353e6	−0.0496556	−0.0248278	+	0.999692i	$0.507904\pi$
$888$	−1.43534e7	−0.610831
$889$	9.49813e6	0.403073
$890$	−4.57958e7	−1.93798
$891$	−7.81726e6	−0.329883
$892$	−2.75624e6	−0.115986
$893$	−1.03175e7	−0.432957
$894$	−5.00679e7	−2.09515
$895$	−2.21696e7	−0.925125
$896$	2.11701e7	0.880952
$897$	−8.05315e6	−0.334183
$898$	6.63426e7	2.74537
$899$	−1.01542e7	−0.419030
$900$	−3.25433e7	−1.33923
$901$	−1.96687e7	−0.807166
$902$	7.43589e7	3.04310
$903$	−1.55752e7	−0.635644
$904$	−1.56799e6	−0.0638147
$905$	−3.65989e6	−0.148541
$906$	1.38875e6	0.0562088
$907$	1.25758e7	0.507595	0.253798	−	0.967257i	$-0.418320\pi$
$907$	1.25758e7	0.507595	0.253798	+	0.967257i	$0.418320\pi$
$908$	−2.92482e7	−1.17729
$909$	6.78868e6	0.272506
$910$	−2.10981e7	−0.844580
$911$	1.12385e7	0.448655	0.224328	−	0.974514i	$-0.427981\pi$
$911$	1.12385e7	0.448655	0.224328	+	0.974514i	$0.427981\pi$
$912$	4.17119e7	1.66063
$913$	5.28809e6	0.209953
$914$	6.60144e7	2.61381
$915$	4.08479e6	0.161294
$916$	−3.42962e7	−1.35054
$917$	8.18340e6	0.321374
$918$	−2.36690e7	−0.926985
$919$	2.13836e7	0.835204	0.417602	−	0.908630i	$-0.362871\pi$
$919$	2.13836e7	0.835204	0.417602	+	0.908630i	$0.362871\pi$
$920$	8.63133e7	3.36208
$921$	5.25922e6	0.204302
$922$	1.52666e7	0.591448
$923$	1.60301e7	0.619344
$924$	3.44421e7	1.32712
$925$	1.31165e7	0.504037
$926$	−5.27736e7	−2.02250
$927$	−1.52667e7	−0.583508
$928$	−2.31701e7	−0.883196
$929$	321078.	0.0122059	0.00610297	−	0.999981i	$-0.498057\pi$
$929$	321078.	0.0122059	0.00610297	+	0.999981i	$0.498057\pi$
$930$	1.79174e7	0.679310
$931$	−1.88830e7	−0.713998
$932$	−4.30622e7	−1.62389
$933$	−7.86770e6	−0.295899
$934$	3.55536e7	1.33357
$935$	−2.32826e7	−0.870969
$936$	1.22751e7	0.457968
$937$	4.56579e7	1.69890	0.849448	−	0.527672i	$-0.176935\pi$
$937$	4.56579e7	1.69890	0.849448	+	0.527672i	$0.176935\pi$
$938$	−6.01813e7	−2.23334
$939$	1.30000e7	0.481149
$940$	−2.67720e7	−0.988236
$941$	−1.98991e6	−0.0732589	−0.0366294	−	0.999329i	$-0.511662\pi$
$941$	−1.98991e6	−0.0732589	−0.0366294	+	0.999329i	$0.511662\pi$
$942$	−3.27060e7	−1.20088
$943$	4.11547e7	1.50709
$944$	−2.52197e6	−0.0921108
$945$	−3.12168e7	−1.13713
$946$	7.30225e7	2.65295
$947$	−4.51668e6	−0.163661	−0.0818304	−	0.996646i	$-0.526077\pi$
$947$	−4.51668e6	−0.163661	−0.0818304	+	0.996646i	$0.526077\pi$
$948$	2.59461e7	0.937671
$949$	1.05741e7	0.381135
$950$	−9.00685e7	−3.23790
$951$	1.08986e7	0.390768
$952$	2.05776e7	0.735873
$953$	2.37134e7	0.845788	0.422894	−	0.906179i	$-0.361014\pi$
$953$	2.37134e7	0.845788	0.422894	+	0.906179i	$0.361014\pi$
$954$	4.04524e7	1.43904
$955$	−6.07267e7	−2.15462
$956$	2.73620e7	0.968284
$957$	2.86681e7	1.01186
$958$	8.56200e6	0.301412
$959$	7.47742e6	0.262546
$960$	−8.53154e6	−0.298778
$961$	−2.50581e7	−0.875267
$962$	−9.10396e6	−0.317170
$963$	2.11113e7	0.733583
$964$	−9.62928e6	−0.333735
$965$	−8.08336e6	−0.279430
$966$	2.77655e7	0.957333
$967$	−1.67228e7	−0.575099	−0.287549	−	0.957766i	$-0.592841\pi$
$967$	−1.67228e7	−0.575099	−0.287549	+	0.957766i	$0.592841\pi$
$968$	−2.57731e7	−0.884053
$969$	−1.47147e7	−0.503432
$970$	−1.39435e8	−4.75819
$971$	−2.46679e7	−0.839623	−0.419812	−	0.907611i	$-0.637904\pi$
$971$	−2.46679e7	−0.839623	−0.419812	+	0.907611i	$0.637904\pi$
$972$	5.59073e7	1.89803
$973$	−1.29240e7	−0.437637
$974$	3.42900e7	1.15816
$975$	1.18500e7	0.399214
$976$	7.16320e6	0.240703
$977$	3.41251e7	1.14377	0.571884	−	0.820335i	$-0.306213\pi$
$977$	3.41251e7	1.14377	0.571884	+	0.820335i	$0.306213\pi$
$978$	2.14527e7	0.717193
$979$	2.57689e7	0.859290
$980$	−4.89980e7	−1.62972
$981$	7.49521e6	0.248663
$982$	−8.71274e7	−2.88321
$983$	966289.	0.0318950
$983$	966289.	0.0318950
$984$	6.62687e7	2.18183
$985$	−5.30447e7	−1.74201
$986$	3.15178e7	1.03244
$987$	−4.68012e6	−0.152920
$988$	4.29198e7	1.39883
$989$	4.04151e7	1.31387
$990$	4.78852e7	1.55279
$991$	5.64753e6	0.182673	0.0913365	−	0.995820i	$-0.470886\pi$
$991$	5.64753e6	0.182673	0.0913365	+	0.995820i	$0.470886\pi$
$992$	8.14843e6	0.262903
$993$	−2.80278e6	−0.0902019
$994$	−5.52683e7	−1.77423
$995$	8.59642e7	2.75271
$996$	8.67211e6	0.276998
$997$	−3.16306e7	−1.00779	−0.503895	−	0.863765i	$-0.668100\pi$
$997$	−3.16306e7	−1.00779	−0.503895	+	0.863765i	$0.668100\pi$
$998$	−9.16159e7	−2.91169
$999$	−1.34702e7	−0.427033

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.6.a.b.1.13	✓	218

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.6.a.b.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-10.1039 q^{2} +11.1728 q^{3} +70.0889 q^{4} +83.9898 q^{5} -112.889 q^{6} +92.1063 q^{7} -384.847 q^{8} -118.168 q^{9} +O(q^{10})\)	\(q-10.1039 q^{2} +11.1728 q^{3} +70.0889 q^{4} +83.9898 q^{5} -112.889 q^{6} +92.1063 q^{7} -384.847 q^{8} -118.168 q^{9} -848.625 q^{10} +477.515 q^{11} +783.092 q^{12} +269.922 q^{13} -930.634 q^{14} +938.405 q^{15} +1645.61 q^{16} -580.521 q^{17} +1193.95 q^{18} +2268.66 q^{19} +5886.76 q^{20} +1029.09 q^{21} -4824.77 q^{22} -2670.32 q^{23} -4299.83 q^{24} +3929.29 q^{25} -2727.27 q^{26} -4035.27 q^{27} +6455.63 q^{28} +5373.39 q^{29} -9481.56 q^{30} -1889.71 q^{31} -4312.00 q^{32} +5335.20 q^{33} +5865.53 q^{34} +7735.99 q^{35} -8282.24 q^{36} +3338.12 q^{37} -22922.3 q^{38} +3015.80 q^{39} -32323.2 q^{40} -15411.9 q^{41} -10397.8 q^{42} -15134.9 q^{43} +33468.5 q^{44} -9924.87 q^{45} +26980.7 q^{46} -4547.83 q^{47} +18386.2 q^{48} -8323.43 q^{49} -39701.2 q^{50} -6486.07 q^{51} +18918.6 q^{52} +33881.1 q^{53} +40772.0 q^{54} +40106.4 q^{55} -35446.8 q^{56} +25347.4 q^{57} -54292.3 q^{58} -1532.55 q^{59} +65771.8 q^{60} +4352.91 q^{61} +19093.5 q^{62} -10884.0 q^{63} -9091.53 q^{64} +22670.7 q^{65} -53906.4 q^{66} +64667.0 q^{67} -40688.1 q^{68} -29835.1 q^{69} -78163.8 q^{70} +59387.8 q^{71} +45476.4 q^{72} +39174.7 q^{73} -33728.1 q^{74} +43901.4 q^{75} +159008. q^{76} +43982.2 q^{77} -30471.4 q^{78} +33132.8 q^{79} +138215. q^{80} -16370.7 q^{81} +155721. q^{82} +11074.2 q^{83} +72127.8 q^{84} -48757.8 q^{85} +152922. q^{86} +60036.1 q^{87} -183770. q^{88} +53964.6 q^{89} +100280. q^{90} +24861.6 q^{91} -187160. q^{92} -21113.5 q^{93} +45950.8 q^{94} +190544. q^{95} -48177.3 q^{96} +164307. q^{97} +84099.1 q^{98} -56426.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9}+O(q^{10}) \) 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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