LMFDB - Embedded newform 983.6.a.a.1.9

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:	$1$
Dimension:	$191$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-10.4383 q^{2} -14.1728 q^{3} +76.9585 q^{4} +25.9677 q^{5} +147.941 q^{6} +174.030 q^{7} -469.291 q^{8} -42.1308 q^{9} +O(q^{10})$	\(q-10.4383 q^{2} -14.1728 q^{3} +76.9585 q^{4} +25.9677 q^{5} +147.941 q^{6} +174.030 q^{7} -469.291 q^{8} -42.1308 q^{9} -271.059 q^{10} +316.871 q^{11} -1090.72 q^{12} -834.400 q^{13} -1816.58 q^{14} -368.036 q^{15} +2435.94 q^{16} +6.13889 q^{17} +439.774 q^{18} +2487.26 q^{19} +1998.44 q^{20} -2466.50 q^{21} -3307.60 q^{22} +2548.80 q^{23} +6651.18 q^{24} -2450.68 q^{25} +8709.73 q^{26} +4041.11 q^{27} +13393.1 q^{28} -4343.66 q^{29} +3841.68 q^{30} +2040.61 q^{31} -10409.8 q^{32} -4490.96 q^{33} -64.0797 q^{34} +4519.17 q^{35} -3242.32 q^{36} +7638.63 q^{37} -25962.8 q^{38} +11825.8 q^{39} -12186.4 q^{40} +7842.15 q^{41} +25746.1 q^{42} -22392.5 q^{43} +24385.9 q^{44} -1094.04 q^{45} -26605.2 q^{46} -17589.4 q^{47} -34524.1 q^{48} +13479.6 q^{49} +25581.0 q^{50} -87.0055 q^{51} -64214.1 q^{52} +26870.3 q^{53} -42182.4 q^{54} +8228.42 q^{55} -81670.9 q^{56} -35251.5 q^{57} +45340.6 q^{58} -51065.1 q^{59} -28323.5 q^{60} -2014.80 q^{61} -21300.6 q^{62} -7332.03 q^{63} +30710.5 q^{64} -21667.5 q^{65} +46878.1 q^{66} -49098.9 q^{67} +472.440 q^{68} -36123.7 q^{69} -47172.5 q^{70} -26129.4 q^{71} +19771.6 q^{72} -49189.9 q^{73} -79734.4 q^{74} +34733.1 q^{75} +191416. q^{76} +55145.2 q^{77} -123442. q^{78} +49377.5 q^{79} +63255.7 q^{80} -47036.2 q^{81} -81858.9 q^{82} +52017.1 q^{83} -189818. q^{84} +159.413 q^{85} +233740. q^{86} +61562.0 q^{87} -148705. q^{88} +112929. q^{89} +11419.9 q^{90} -145211. q^{91} +196152. q^{92} -28921.3 q^{93} +183603. q^{94} +64588.4 q^{95} +147536. q^{96} +25371.1 q^{97} -140704. q^{98} -13350.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 191 q - 37 q^{2} - 74 q^{3} + 2821 q^{4} - 247 q^{5} - 335 q^{6} - 1569 q^{7} - 1761 q^{8} + 13251 q^{9}+O(q^{10}) $ 191 * q - 37 * q^2 - 74 * q^3 + 2821 * q^4 - 247 * q^5 - 335 * q^6 - 1569 * q^7 - 1761 * q^8 + 13251 * q^9	\( 191 q - 37 q^{2} - 74 q^{3} + 2821 q^{4} - 247 q^{5} - 335 q^{6} - 1569 q^{7} - 1761 q^{8} + 13251 q^{9} - 2867 q^{10} - 1878 q^{11} - 3400 q^{12} - 6854 q^{13} - 1601 q^{14} - 3461 q^{15} + 38457 q^{16} - 10730 q^{17} - 17249 q^{18} - 5817 q^{19} - 9988 q^{20} - 15999 q^{21} - 20287 q^{22} - 15625 q^{23} - 19747 q^{24} + 67082 q^{25} - 9868 q^{26} - 22892 q^{27} - 72720 q^{28} - 17960 q^{29} - 27464 q^{30} - 25604 q^{31} - 68869 q^{32} - 60654 q^{33} - 42876 q^{34} - 30018 q^{35} + 172922 q^{36} - 114862 q^{37} + 4404 q^{38} - 73500 q^{39} - 137154 q^{40} - 90896 q^{41} - 10652 q^{42} - 121447 q^{43} - 57962 q^{44} - 109019 q^{45} - 136262 q^{46} - 86994 q^{47} - 133347 q^{48} + 278242 q^{49} - 93911 q^{50} - 66966 q^{51} - 284241 q^{52} - 122112 q^{53} - 130806 q^{54} - 134904 q^{55} - 100292 q^{56} - 423426 q^{57} - 307669 q^{58} - 85704 q^{59} - 238277 q^{60} - 206736 q^{61} - 190602 q^{62} - 387623 q^{63} + 411903 q^{64} - 244408 q^{65} - 113963 q^{66} - 337002 q^{67} - 388031 q^{68} - 165342 q^{69} - 183925 q^{70} - 174806 q^{71} - 753621 q^{72} - 1009738 q^{73} - 204958 q^{74} - 282676 q^{75} - 326869 q^{76} - 332288 q^{77} - 591801 q^{78} - 488092 q^{79} - 259068 q^{80} + 385959 q^{81} - 523996 q^{82} - 315720 q^{83} - 750486 q^{84} - 1001755 q^{85} - 287709 q^{86} - 316995 q^{87} - 836923 q^{88} - 298065 q^{89} - 751039 q^{90} - 521459 q^{91} - 640932 q^{92} - 554391 q^{93} - 623481 q^{94} - 491883 q^{95} - 767843 q^{96} - 1468693 q^{97} - 714146 q^{98} - 842507 q^{99}+O(q^{100}) \) 191 * q - 37 * q^2 - 74 * q^3 + 2821 * q^4 - 247 * q^5 - 335 * q^6 - 1569 * q^7 - 1761 * q^8 + 13251 * q^9 - 2867 * q^10 - 1878 * q^11 - 3400 * q^12 - 6854 * q^13 - 1601 * q^14 - 3461 * q^15 + 38457 * q^16 - 10730 * q^17 - 17249 * q^18 - 5817 * q^19 - 9988 * q^20 - 15999 * q^21 - 20287 * q^22 - 15625 * q^23 - 19747 * q^24 + 67082 * q^25 - 9868 * q^26 - 22892 * q^27 - 72720 * q^28 - 17960 * q^29 - 27464 * q^30 - 25604 * q^31 - 68869 * q^32 - 60654 * q^33 - 42876 * q^34 - 30018 * q^35 + 172922 * q^36 - 114862 * q^37 + 4404 * q^38 - 73500 * q^39 - 137154 * q^40 - 90896 * q^41 - 10652 * q^42 - 121447 * q^43 - 57962 * q^44 - 109019 * q^45 - 136262 * q^46 - 86994 * q^47 - 133347 * q^48 + 278242 * q^49 - 93911 * q^50 - 66966 * q^51 - 284241 * q^52 - 122112 * q^53 - 130806 * q^54 - 134904 * q^55 - 100292 * q^56 - 423426 * q^57 - 307669 * q^58 - 85704 * q^59 - 238277 * q^60 - 206736 * q^61 - 190602 * q^62 - 387623 * q^63 + 411903 * q^64 - 244408 * q^65 - 113963 * q^66 - 337002 * q^67 - 388031 * q^68 - 165342 * q^69 - 183925 * q^70 - 174806 * q^71 - 753621 * q^72 - 1009738 * q^73 - 204958 * q^74 - 282676 * q^75 - 326869 * q^76 - 332288 * q^77 - 591801 * q^78 - 488092 * q^79 - 259068 * q^80 + 385959 * q^81 - 523996 * q^82 - 315720 * q^83 - 750486 * q^84 - 1001755 * q^85 - 287709 * q^86 - 316995 * q^87 - 836923 * q^88 - 298065 * q^89 - 751039 * q^90 - 521459 * q^91 - 640932 * q^92 - 554391 * q^93 - 623481 * q^94 - 491883 * q^95 - 767843 * q^96 - 1468693 * q^97 - 714146 * q^98 - 842507 * 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 $

$2$	−10.4383	−1.84525	−0.922626	−	0.385697i	$-0.873961\pi$
$2$	−10.4383	−1.84525	−0.922626	+	0.385697i	$0.873961\pi$
$3$	−14.1728	−0.909188	−0.454594	−	0.890699i	$-0.650216\pi$
$3$	−14.1728	−0.909188	−0.454594	+	0.890699i	$0.650216\pi$
$4$	76.9585	2.40495
$5$	25.9677	0.464525	0.232262	−	0.972653i	$-0.425387\pi$
$5$	25.9677	0.464525	0.232262	+	0.972653i	$0.425387\pi$
$6$	147.941	1.67768
$7$	174.030	1.34239	0.671197	−	0.741279i	$-0.265781\pi$
$7$	174.030	1.34239	0.671197	+	0.741279i	$0.265781\pi$
$8$	−469.291	−2.59249
$9$	−42.1308	−0.173378
$10$	−271.059	−0.857165
$11$	316.871	0.789589	0.394794	−	0.918769i	$-0.370816\pi$
$11$	316.871	0.789589	0.394794	+	0.918769i	$0.370816\pi$
$12$	−1090.72	−2.18655
$13$	−834.400	−1.36935	−0.684677	−	0.728847i	$-0.740057\pi$
$13$	−834.400	−1.36935	−0.684677	+	0.728847i	$0.740057\pi$
$14$	−1816.58	−2.47705
$15$	−368.036	−0.422340
$16$	2435.94	2.37884
$17$	6.13889	0.00515190	0.00257595	−	0.999997i	$-0.499180\pi$
$17$	6.13889	0.00515190	0.00257595	+	0.999997i	$0.499180\pi$
$18$	439.774	0.319925
$19$	2487.26	1.58065	0.790327	−	0.612686i	$-0.209911\pi$
$19$	2487.26	1.58065	0.790327	+	0.612686i	$0.209911\pi$
$20$	1998.44	1.11716
$21$	−2466.50	−1.22049
$22$	−3307.60	−1.45699
$23$	2548.80	1.00465	0.502327	−	0.864678i	$-0.332477\pi$
$23$	2548.80	1.00465	0.502327	+	0.864678i	$0.332477\pi$
$24$	6651.18	2.35706
$25$	−2450.68	−0.784217
$26$	8709.73	2.52680
$27$	4041.11	1.06682
$28$	13393.1	3.22839
$29$	−4343.66	−0.959094	−0.479547	−	0.877516i	$-0.659199\pi$
$29$	−4343.66	−0.959094	−0.479547	+	0.877516i	$0.659199\pi$
$30$	3841.68	0.779324
$31$	2040.61	0.381379	0.190690	−	0.981650i	$-0.438928\pi$
$31$	2040.61	0.381379	0.190690	+	0.981650i	$0.438928\pi$
$32$	−10409.8	−1.79708
$33$	−4490.96	−0.717885
$34$	−64.0797	−0.00950655
$35$	4519.17	0.623575
$36$	−3242.32	−0.416965
$37$	7638.63	0.917299	0.458650	−	0.888617i	$-0.348333\pi$
$37$	7638.63	0.917299	0.458650	+	0.888617i	$0.348333\pi$
$38$	−25962.8	−2.91670
$39$	11825.8	1.24500
$40$	−12186.4	−1.20428
$41$	7842.15	0.728577	0.364289	−	0.931286i	$-0.381312\pi$
$41$	7842.15	0.728577	0.364289	+	0.931286i	$0.381312\pi$
$42$	25746.1	2.25211
$43$	−22392.5	−1.84685	−0.923426	−	0.383776i	$-0.874623\pi$
$43$	−22392.5	−1.84685	−0.923426	+	0.383776i	$0.874623\pi$
$44$	24385.9	1.89892
$45$	−1094.04	−0.0805382
$46$	−26605.2	−1.85384
$47$	−17589.4	−1.16146	−0.580731	−	0.814095i	$-0.697233\pi$
$47$	−17589.4	−1.16146	−0.580731	+	0.814095i	$0.697233\pi$
$48$	−34524.1	−2.16282
$49$	13479.6	0.802021
$50$	25581.0	1.44708
$51$	−87.0055	−0.00468405
$52$	−64214.1	−3.29323
$53$	26870.3	1.31396	0.656980	−	0.753908i	$-0.271834\pi$
$53$	26870.3	1.31396	0.656980	+	0.753908i	$0.271834\pi$
$54$	−42182.4	−1.96855
$55$	8228.42	0.366783
$56$	−81670.9	−3.48014
$57$	−35251.5	−1.43711
$58$	45340.6	1.76977
$59$	−51065.1	−1.90983	−0.954913	−	0.296885i	$-0.904052\pi$
$59$	−51065.1	−1.90983	−0.954913	+	0.296885i	$0.904052\pi$
$60$	−28323.5	−1.01571
$61$	−2014.80	−0.0693279	−0.0346639	−	0.999399i	$-0.511036\pi$
$61$	−2014.80	−0.0693279	−0.0346639	+	0.999399i	$0.511036\pi$
$62$	−21300.6	−0.703740
$63$	−7332.03	−0.232741
$64$	30710.5	0.937211
$65$	−21667.5	−0.636099
$66$	46878.1	1.32468
$67$	−49098.9	−1.33624	−0.668121	−	0.744053i	$-0.732901\pi$
$67$	−49098.9	−1.33624	−0.668121	+	0.744053i	$0.732901\pi$
$68$	472.440	0.0123901
$69$	−36123.7	−0.913419
$70$	−47172.5	−1.15065
$71$	−26129.4	−0.615153	−0.307576	−	0.951523i	$-0.599518\pi$
$71$	−26129.4	−0.615153	−0.307576	+	0.951523i	$0.599518\pi$
$72$	19771.6	0.449480
$73$	−49189.9	−1.08036	−0.540180	−	0.841549i	$-0.681644\pi$
$73$	−49189.9	−1.08036	−0.540180	+	0.841549i	$0.681644\pi$
$74$	−79734.4	−1.69265
$75$	34733.1	0.713000
$76$	191416.	3.80140
$77$	55145.2	1.05994
$78$	−123442.	−2.29734
$79$	49377.5	0.890147	0.445073	−	0.895494i	$-0.353178\pi$
$79$	49377.5	0.890147	0.445073	+	0.895494i	$0.353178\pi$
$80$	63255.7	1.10503
$81$	−47036.2	−0.796563
$82$	−81858.9	−1.34441
$83$	52017.1	0.828802	0.414401	−	0.910094i	$-0.363991\pi$
$83$	52017.1	0.828802	0.414401	+	0.910094i	$0.363991\pi$
$84$	−189818.	−2.93522
$85$	159.413	0.00239319
$86$	233740.	3.40791
$87$	61562.0	0.871997
$88$	−148705.	−2.04700
$89$	112929.	1.51123	0.755615	−	0.655016i	$-0.227338\pi$
$89$	112929.	1.51123	0.755615	+	0.655016i	$0.227338\pi$
$90$	11419.9	0.148613
$91$	−145211.	−1.83821
$92$	196152.	2.41614
$93$	−28921.3	−0.346745
$94$	183603.	2.14319
$95$	64588.4	0.734252
$96$	147536.	1.63388
$97$	25371.1	0.273785	0.136892	−	0.990586i	$-0.456289\pi$
$97$	25371.1	0.273785	0.136892	+	0.990586i	$0.456289\pi$
$98$	−140704.	−1.47993
$99$	−13350.0	−0.136897
$100$	−188600.	−1.88600
$101$	−77488.1	−0.755843	−0.377922	−	0.925838i	$-0.623361\pi$
$101$	−77488.1	−0.755843	−0.377922	+	0.925838i	$0.623361\pi$
$102$	908.191	0.00864324
$103$	−128888.	−1.19707	−0.598536	−	0.801096i	$-0.704251\pi$
$103$	−128888.	−1.19707	−0.598536	+	0.801096i	$0.704251\pi$
$104$	391576.	3.55004
$105$	−64049.4	−0.566947
$106$	−280480.	−2.42459
$107$	−84526.9	−0.713732	−0.356866	−	0.934156i	$-0.616155\pi$
$107$	−84526.9	−0.713732	−0.356866	+	0.934156i	$0.616155\pi$
$108$	310998.	2.56565
$109$	−79614.1	−0.641835	−0.320918	−	0.947107i	$-0.603991\pi$
$109$	−79614.1	−0.641835	−0.320918	+	0.947107i	$0.603991\pi$
$110$	−85890.9	−0.676808
$111$	−108261.	−0.833997
$112$	423927.	3.19335
$113$	−45949.7	−0.338522	−0.169261	−	0.985571i	$-0.554138\pi$
$113$	−45949.7	−0.338522	−0.169261	+	0.985571i	$0.554138\pi$
$114$	367966.	2.65183
$115$	66186.5	0.466686
$116$	−334282.	−2.30658
$117$	35153.9	0.237415
$118$	533033.	3.52411
$119$	1068.35	0.00691588
$120$	172716.	1.09491
$121$	−60643.7	−0.376549
$122$	21031.2	0.127927
$123$	−111146.	−0.662414
$124$	157043.	0.917198
$125$	−144788.	−0.828813
$126$	76534.1	0.429466
$127$	56604.6	0.311417	0.155709	−	0.987803i	$-0.450234\pi$
$127$	56604.6	0.311417	0.155709	+	0.987803i	$0.450234\pi$
$128$	12546.4	0.0676855
$129$	317366.	1.67914
$130$	226172.	1.17376
$131$	116710.	0.594195	0.297097	−	0.954847i	$-0.403981\pi$
$131$	116710.	0.594195	0.297097	+	0.954847i	$0.403981\pi$
$132$	−345618.	−1.72648
$133$	432858.	2.12186
$134$	512510.	2.46570
$135$	104938.	0.495564
$136$	−2880.93	−0.0133563
$137$	−70345.7	−0.320211	−0.160105	−	0.987100i	$-0.551183\pi$
$137$	−70345.7	−0.320211	−0.160105	+	0.987100i	$0.551183\pi$
$138$	377071.	1.68549
$139$	−65918.5	−0.289381	−0.144691	−	0.989477i	$-0.546219\pi$
$139$	−65918.5	−0.289381	−0.144691	+	0.989477i	$0.546219\pi$
$140$	347788.	1.49967
$141$	249291.	1.05599
$142$	272747.	1.13511
$143$	−264397.	−1.08123
$144$	−102628.	−0.412438
$145$	−112795.	−0.445523
$146$	513459.	1.99354
$147$	−191044.	−0.729187
$148$	587857.	2.20606
$149$	−80512.0	−0.297095	−0.148547	−	0.988905i	$-0.547460\pi$
$149$	−80512.0	−0.297095	−0.148547	+	0.988905i	$0.547460\pi$
$150$	−362555.	−1.31567
$151$	305333.	1.08976	0.544880	−	0.838514i	$-0.316575\pi$
$151$	305333.	1.08976	0.544880	+	0.838514i	$0.316575\pi$
$152$	−1.16725e6	−4.09783
$153$	−258.636	−0.000893225 0
$154$	−575623.	−1.95585
$155$	52990.1	0.177160
$156$	910096.	2.99417
$157$	−440460.	−1.42612	−0.713062	−	0.701101i	$-0.752692\pi$
$157$	−440460.	−1.42612	−0.713062	+	0.701101i	$0.752692\pi$
$158$	−515418.	−1.64254
$159$	−380828.	−1.19464
$160$	−270318.	−0.834785
$161$	443569.	1.34864
$162$	490979.	1.46986
$163$	226032.	0.666347	0.333174	−	0.942865i	$-0.391880\pi$
$163$	226032.	0.666347	0.333174	+	0.942865i	$0.391880\pi$
$164$	603520.	1.75219
$165$	−116620.	−0.333475
$166$	−542971.	−1.52935
$167$	−416650.	−1.15606	−0.578029	−	0.816016i	$-0.696178\pi$
$167$	−416650.	−1.15606	−0.578029	+	0.816016i	$0.696178\pi$
$168$	1.15751e6	3.16410
$169$	324930.	0.875131
$170$	−1664.00	−0.00441603
$171$	−104790.	−0.274050
$172$	−1.72330e6	−4.44159
$173$	698107.	1.77340	0.886700	−	0.462346i	$-0.152992\pi$
$173$	698107.	1.77340	0.886700	+	0.462346i	$0.152992\pi$
$174$	−642604.	−1.60905
$175$	−426492.	−1.05273
$176$	771878.	1.87831
$177$	723737.	1.73639
$178$	−1.17879e6	−2.78860
$179$	305517.	0.712693	0.356347	−	0.934354i	$-0.384022\pi$
$179$	305517.	0.712693	0.356347	+	0.934354i	$0.384022\pi$
$180$	−84195.6	−0.193690
$181$	364344.	0.826637	0.413319	−	0.910586i	$-0.364370\pi$
$181$	364344.	0.826637	0.413319	+	0.910586i	$0.364370\pi$
$182$	1.51576e6	3.39196
$183$	28555.5	0.0630321
$184$	−1.19613e6	−2.60455
$185$	198358.	0.426108
$186$	301890.	0.639832
$187$	1945.24	0.00406788
$188$	−1.35365e6	−2.79326
$189$	703276.	1.43209
$190$	−674194.	−1.35488
$191$	649853.	1.28894	0.644469	−	0.764631i	$-0.277079\pi$
$191$	649853.	1.28894	0.644469	+	0.764631i	$0.277079\pi$
$192$	−435255.	−0.852101
$193$	−433892.	−0.838471	−0.419236	−	0.907877i	$-0.637702\pi$
$193$	−433892.	−0.838471	−0.419236	+	0.907877i	$0.637702\pi$
$194$	−264831.	−0.505202
$195$	307089.	0.578333
$196$	1.03737e6	1.92882
$197$	−118403.	−0.217368	−0.108684	−	0.994076i	$-0.534664\pi$
$197$	−118403.	−0.217368	−0.108684	+	0.994076i	$0.534664\pi$
$198$	139352.	0.252609
$199$	−401847.	−0.719330	−0.359665	−	0.933081i	$-0.617109\pi$
$199$	−401847.	−0.719330	−0.359665	+	0.933081i	$0.617109\pi$
$200$	1.15008e6	2.03308
$201$	695871.	1.21489
$202$	808846.	1.39472
$203$	−755929.	−1.28748
$204$	−6695.81	−0.0112649
$205$	203643.	0.338442
$206$	1.34538e6	2.20890
$207$	−107383.	−0.174184
$208$	−2.03254e6	−3.25748
$209$	788140.	1.24807
$210$	668568.	1.04616
$211$	391190.	0.604898	0.302449	−	0.953166i	$-0.402196\pi$
$211$	391190.	0.604898	0.302449	+	0.953166i	$0.402196\pi$
$212$	2.06789e6	3.16001
$213$	370327.	0.559289
$214$	882318.	1.31702
$215$	−581483.	−0.857908
$216$	−1.89646e6	−2.76572
$217$	355129.	0.511961
$218$	831037.	1.18435
$219$	697160.	0.982250
$220$	633247.	0.882097
$221$	−5122.29	−0.00705478
$222$	1.13006e6	1.53893
$223$	−1.37828e6	−1.85598	−0.927992	−	0.372601i	$-0.878466\pi$
$223$	−1.37828e6	−1.85598	−0.927992	+	0.372601i	$0.878466\pi$
$224$	−1.81162e6	−2.41238
$225$	103249.	0.135966
$226$	479638.	0.624658
$227$	452053.	0.582271	0.291135	−	0.956682i	$-0.405967\pi$
$227$	452053.	0.582271	0.291135	+	0.956682i	$0.405967\pi$
$228$	−2.71290e6	−3.45618
$229$	1.55425e6	1.95854	0.979271	−	0.202553i	$-0.0649240\pi$
$229$	1.55425e6	1.95854	0.979271	+	0.202553i	$0.0649240\pi$
$230$	−690876.	−0.861153
$231$	−781564.	−0.963684
$232$	2.03844e6	2.48644
$233$	−239636.	−0.289176	−0.144588	−	0.989492i	$-0.546186\pi$
$233$	−239636.	−0.289176	−0.144588	+	0.989492i	$0.546186\pi$
$234$	−366948.	−0.438091
$235$	−456755.	−0.539528
$236$	−3.92989e6	−4.59304
$237$	−699819.	−0.809310
$238$	−11151.8	−0.0127615
$239$	−1.05383e6	−1.19338	−0.596688	−	0.802473i	$-0.703517\pi$
$239$	−1.05383e6	−1.19338	−0.596688	+	0.802473i	$0.703517\pi$
$240$	−896513.	−1.00468
$241$	577145.	0.640092	0.320046	−	0.947402i	$-0.396302\pi$
$241$	577145.	0.640092	0.320046	+	0.947402i	$0.396302\pi$
$242$	633018.	0.694828
$243$	−315353.	−0.342596
$244$	−155056.	−0.166730
$245$	350033.	0.372558
$246$	1.16017e6	1.22232
$247$	−2.07537e6	−2.16447
$248$	−957642.	−0.988721
$249$	−737229.	−0.753536
$250$	1.51134e6	1.52937
$251$	499187.	0.500126	0.250063	−	0.968230i	$-0.419549\pi$
$251$	499187.	0.500126	0.250063	+	0.968230i	$0.419549\pi$
$252$	−564262.	−0.559731
$253$	807641.	0.793263
$254$	−590857.	−0.574643
$255$	−2259.33	−0.00217585
$256$	−1.11370e6	−1.06211
$257$	1.47398e6	1.39206	0.696031	−	0.718012i	$-0.254948\pi$
$257$	1.47398e6	1.39206	0.696031	+	0.718012i	$0.254948\pi$
$258$	−3.31276e6	−3.09843
$259$	1.32935e6	1.23138
$260$	−1.66749e6	−1.52979
$261$	183002.	0.166285
$262$	−1.21825e6	−1.09644
$263$	−82467.3	−0.0735178	−0.0367589	−	0.999324i	$-0.511703\pi$
$263$	−82467.3	−0.0735178	−0.0367589	+	0.999324i	$0.511703\pi$
$264$	2.10757e6	1.86111
$265$	697759.	0.610367
$266$	−4.51831e6	−3.91536
$267$	−1.60052e6	−1.37399
$268$	−3.77858e6	−3.21360
$269$	−1.85427e6	−1.56240	−0.781201	−	0.624280i	$-0.785393\pi$
$269$	−1.85427e6	−1.56240	−0.781201	+	0.624280i	$0.785393\pi$
$270$	−1.09538e6	−0.914441
$271$	−2.32764e6	−1.92527	−0.962637	−	0.270796i	$-0.912713\pi$
$271$	−2.32764e6	−1.92527	−0.962637	+	0.270796i	$0.912713\pi$
$272$	14953.9	0.0122556
$273$	2.05805e6	1.67128
$274$	734291.	0.590869
$275$	−776549.	−0.619209
$276$	−2.78003e6	−2.19673
$277$	−570572.	−0.446798	−0.223399	−	0.974727i	$-0.571715\pi$
$277$	−570572.	−0.446798	−0.223399	+	0.974727i	$0.571715\pi$
$278$	688078.	0.533981
$279$	−85972.7	−0.0661226
$280$	−2.12081e6	−1.61661
$281$	1.33583e6	1.00922	0.504610	−	0.863347i	$-0.331636\pi$
$281$	1.33583e6	1.00922	0.504610	+	0.863347i	$0.331636\pi$
$282$	−2.60218e6	−1.94856
$283$	−2.38619e6	−1.77108	−0.885540	−	0.464563i	$-0.846211\pi$
$283$	−2.38619e6	−1.77108	−0.885540	+	0.464563i	$0.846211\pi$
$284$	−2.01088e6	−1.47941
$285$	−915400.	−0.667573
$286$	2.75986e6	1.99514
$287$	1.36477e6	0.978037
$288$	438572.	0.311573
$289$	−1.41982e6	−0.999973
$290$	1.17739e6	0.822102
$291$	−359580.	−0.248922
$292$	−3.78558e6	−2.59821
$293$	2.54576e6	1.73240	0.866201	−	0.499696i	$-0.166555\pi$
$293$	2.54576e6	1.73240	0.866201	+	0.499696i	$0.166555\pi$
$294$	1.99417e6	1.34553
$295$	−1.32604e6	−0.887161
$296$	−3.58474e6	−2.37809
$297$	1.28051e6	0.842350
$298$	840410.	0.548215
$299$	−2.12672e6	−1.37573
$300$	2.67300e6	1.71473
$301$	−3.89698e6	−2.47920
$302$	−3.18716e6	−2.01088
$303$	1.09823e6	0.687204
$304$	6.05880e6	3.76013
$305$	−52319.8	−0.0322045
$306$	2699.73	0.00164822
$307$	1.86844e6	1.13144	0.565721	−	0.824597i	$-0.308598\pi$
$307$	1.86844e6	1.13144	0.565721	+	0.824597i	$0.308598\pi$
$308$	4.24389e6	2.54910
$309$	1.82671e6	1.08836
$310$	−553127.	−0.326905
$311$	1.96063e6	1.14946	0.574730	−	0.818343i	$-0.305107\pi$
$311$	1.96063e6	1.14946	0.574730	+	0.818343i	$0.305107\pi$
$312$	−5.54975e6	−3.22765
$313$	−2.34309e6	−1.35185	−0.675925	−	0.736971i	$-0.736256\pi$
$313$	−2.34309e6	−1.35185	−0.675925	+	0.736971i	$0.736256\pi$
$314$	4.59766e6	2.63156
$315$	−190396.	−0.108114
$316$	3.80002e6	2.14076
$317$	1.80958e6	1.01142	0.505708	−	0.862705i	$-0.331231\pi$
$317$	1.80958e6	1.01142	0.505708	+	0.862705i	$0.331231\pi$
$318$	3.97520e6	2.20440
$319$	−1.37638e6	−0.757290
$320$	797482.	0.435357
$321$	1.19799e6	0.648917
$322$	−4.63011e6	−2.48858
$323$	15269.0	0.00814337
$324$	−3.61984e6	−1.91570
$325$	2.04485e6	1.07387
$326$	−2.35939e6	−1.22958
$327$	1.12836e6	0.583549
$328$	−3.68025e6	−1.88883
$329$	−3.06108e6	−1.55914
$330$	1.21732e6	0.615345
$331$	2.83274e6	1.42114	0.710569	−	0.703628i	$-0.248438\pi$
$331$	2.83274e6	1.42114	0.710569	+	0.703628i	$0.248438\pi$
$332$	4.00315e6	1.99323
$333$	−321821.	−0.159039
$334$	4.34912e6	2.13322
$335$	−1.27499e6	−0.620717
$336$	−6.00825e6	−2.90335
$337$	−1.35485e6	−0.649854	−0.324927	−	0.945739i	$-0.605340\pi$
$337$	−1.35485e6	−0.649854	−0.324927	+	0.945739i	$0.605340\pi$
$338$	−3.39172e6	−1.61484
$339$	651237.	0.307780
$340$	12268.2	0.00575550
$341$	646612.	0.301133
$342$	1.09383e6	0.505691
$343$	−579076.	−0.265766
$344$	1.05086e7	4.78795
$345$	−938051.	−0.424305
$346$	−7.28706e6	−3.27237
$347$	−3.91847e6	−1.74700	−0.873499	−	0.486826i	$-0.838155\pi$
$347$	−3.91847e6	−1.74700	−0.873499	+	0.486826i	$0.838155\pi$
$348$	4.73772e6	2.09711
$349$	305289.	0.134167	0.0670837	−	0.997747i	$-0.478631\pi$
$349$	305289.	0.134167	0.0670837	+	0.997747i	$0.478631\pi$
$350$	4.45186e6	1.94255
$351$	−3.37190e6	−1.46086
$352$	−3.29856e6	−1.41895
$353$	2.38529e6	1.01884	0.509418	−	0.860519i	$-0.329861\pi$
$353$	2.38529e6	1.01884	0.509418	+	0.860519i	$0.329861\pi$
$354$	−7.55459e6	−3.20408
$355$	−678520.	−0.285753
$356$	8.69085e6	3.63444
$357$	−15141.6	−0.00628783
$358$	−3.18908e6	−1.31510
$359$	−1.32244e6	−0.541553	−0.270777	−	0.962642i	$-0.587280\pi$
$359$	−1.32244e6	−0.541553	−0.270777	+	0.962642i	$0.587280\pi$
$360$	513423.	0.208794
$361$	3.71035e6	1.49846
$362$	−3.80314e6	−1.52535
$363$	859493.	0.342354
$364$	−1.11752e7	−4.42081
$365$	−1.27735e6	−0.501854
$366$	−298071.	−0.116310
$367$	639030.	0.247660	0.123830	−	0.992303i	$-0.460482\pi$
$367$	639030.	0.247660	0.123830	+	0.992303i	$0.460482\pi$
$368$	6.20872e6	2.38991
$369$	−330396.	−0.126319
$370$	−2.07052e6	−0.786277
$371$	4.67624e6	1.76385
$372$	−2.22574e6	−0.833906
$373$	−718534.	−0.267408	−0.133704	−	0.991021i	$-0.542687\pi$
$373$	−718534.	−0.267408	−0.133704	+	0.991021i	$0.542687\pi$
$374$	−20305.0	−0.00750627
$375$	2.05205e6	0.753546
$376$	8.25453e6	3.01108
$377$	3.62435e6	1.31334
$378$	−7.34102e6	−2.64257
$379$	−896339.	−0.320534	−0.160267	−	0.987074i	$-0.551236\pi$
$379$	−896339.	−0.320534	−0.160267	+	0.987074i	$0.551236\pi$
$380$	4.97062e6	1.76584
$381$	−802248.	−0.283137
$382$	−6.78337e6	−2.37841
$383$	546474.	0.190359	0.0951794	−	0.995460i	$-0.469658\pi$
$383$	546474.	0.190359	0.0951794	+	0.995460i	$0.469658\pi$
$384$	−177819.	−0.0615388
$385$	1.43199e6	0.492368
$386$	4.52910e6	1.54719
$387$	943415.	0.320203
$388$	1.95252e6	0.658439
$389$	−1.43671e6	−0.481388	−0.240694	−	0.970601i	$-0.577375\pi$
$389$	−1.43671e6	−0.481388	−0.240694	+	0.970601i	$0.577375\pi$
$390$	−3.20549e6	−1.06717
$391$	15646.8	0.00517588
$392$	−6.32583e6	−2.07923
$393$	−1.65411e6	−0.540235
$394$	1.23592e6	0.401098
$395$	1.28222e6	0.413495
$396$	−1.02740e6	−0.329231
$397$	−5.91460e6	−1.88343	−0.941714	−	0.336415i	$-0.890786\pi$
$397$	−5.91460e6	−1.88343	−0.941714	+	0.336415i	$0.890786\pi$
$398$	4.19461e6	1.32735
$399$	−6.13483e6	−1.92917
$400$	−5.96970e6	−1.86553
$401$	172542.	0.0535838	0.0267919	−	0.999641i	$-0.491471\pi$
$401$	172542.	0.0535838	0.0267919	+	0.999641i	$0.491471\pi$
$402$	−7.26372e6	−2.24179
$403$	−1.70269e6	−0.522243
$404$	−5.96337e6	−1.81777
$405$	−1.22142e6	−0.370023
$406$	7.89063e6	2.37573
$407$	2.42046e6	0.724289
$408$	40830.9	0.0121433
$409$	−3.53155e6	−1.04389	−0.521947	−	0.852978i	$-0.674794\pi$
$409$	−3.53155e6	−1.04389	−0.521947	+	0.852978i	$0.674794\pi$
$410$	−2.12569e6	−0.624511
$411$	996998.	0.291132
$412$	−9.91905e6	−2.87890
$413$	−8.88687e6	−2.56374
$414$	1.12090e6	0.321414
$415$	1.35076e6	0.384999
$416$	8.68591e6	2.46083
$417$	934252.	0.263102
$418$	−8.22686e6	−2.30300
$419$	2.59979e6	0.723440	0.361720	−	0.932287i	$-0.382190\pi$
$419$	2.59979e6	0.723440	0.361720	+	0.932287i	$0.382190\pi$
$420$	−4.92915e6	−1.36348
$421$	1.71665e6	0.472038	0.236019	−	0.971748i	$-0.424157\pi$
$421$	1.71665e6	0.472038	0.236019	+	0.971748i	$0.424157\pi$
$422$	−4.08337e6	−1.11619
$423$	741053.	0.201372
$424$	−1.26100e7	−3.40643
$425$	−15044.4	−0.00404021
$426$	−3.86559e6	−1.03203
$427$	−350637.	−0.0930653
$428$	−6.50506e6	−1.71649
$429$	3.74726e6	0.983038
$430$	6.06970e6	1.58306
$431$	4.85358e6	1.25855	0.629273	−	0.777184i	$-0.283353\pi$
$431$	4.85358e6	1.25855	0.629273	+	0.777184i	$0.283353\pi$
$432$	9.84389e6	2.53780
$433$	2.59078e6	0.664065	0.332032	−	0.943268i	$-0.392266\pi$
$433$	2.59078e6	0.664065	0.332032	+	0.943268i	$0.392266\pi$
$434$	−3.70695e6	−0.944696
$435$	1.59863e6	0.405064
$436$	−6.12698e6	−1.54358
$437$	6.33952e6	1.58801
$438$	−7.27718e6	−1.81250
$439$	2.90401e6	0.719178	0.359589	−	0.933111i	$-0.382917\pi$
$439$	2.90401e6	0.719178	0.359589	+	0.933111i	$0.382917\pi$
$440$	−3.86152e6	−0.950883
$441$	−567904.	−0.139052
$442$	53468.1	0.0130178
$443$	3.33047e6	0.806299	0.403150	−	0.915134i	$-0.367915\pi$
$443$	3.33047e6	0.806299	0.403150	+	0.915134i	$0.367915\pi$
$444$	−8.33160e6	−2.00572
$445$	2.93251e6	0.702004
$446$	1.43869e7	3.42476
$447$	1.14108e6	0.270115
$448$	5.34456e6	1.25811
$449$	−5.04947e6	−1.18203	−0.591017	−	0.806659i	$-0.701273\pi$
$449$	−5.04947e6	−1.18203	−0.591017	+	0.806659i	$0.701273\pi$
$450$	−1.07775e6	−0.250891
$451$	2.48495e6	0.575277
$452$	−3.53622e6	−0.814129
$453$	−4.32743e6	−0.990797
$454$	−4.71868e6	−1.07444
$455$	−3.77079e6	−0.853895
$456$	1.65432e7	3.72570
$457$	1.55144e6	0.347491	0.173745	−	0.984791i	$-0.444413\pi$
$457$	1.55144e6	0.347491	0.173745	+	0.984791i	$0.444413\pi$
$458$	−1.62238e7	−3.61400
$459$	24807.9	0.00549616
$460$	5.09361e6	1.12236
$461$	−321095.	−0.0703690	−0.0351845	−	0.999381i	$-0.511202\pi$
$461$	−321095.	−0.0703690	−0.0351845	+	0.999381i	$0.511202\pi$
$462$	8.15821e6	1.77824
$463$	7.21597e6	1.56438	0.782190	−	0.623040i	$-0.214103\pi$
$463$	7.21597e6	1.56438	0.782190	+	0.623040i	$0.214103\pi$
$464$	−1.05809e7	−2.28154
$465$	−751020.	−0.161072
$466$	2.50140e6	0.533603
$467$	−8.39522e6	−1.78131	−0.890656	−	0.454678i	$-0.849754\pi$
$467$	−8.39522e6	−1.78131	−0.890656	+	0.454678i	$0.849754\pi$
$468$	2.70539e6	0.570973
$469$	−8.54471e6	−1.79376
$470$	4.76776e6	0.995565
$471$	6.24257e6	1.29661
$472$	2.39644e7	4.95121
$473$	−7.09555e6	−1.45825
$474$	7.30494e6	1.49338
$475$	−6.09547e6	−1.23958
$476$	82218.8	0.0166324
$477$	−1.13206e6	−0.227811
$478$	1.10003e7	2.20208
$479$	−373014.	−0.0742825	−0.0371413	−	0.999310i	$-0.511825\pi$
$479$	−373014.	−0.0742825	−0.0371413	+	0.999310i	$0.511825\pi$
$480$	3.83117e6	0.758977
$481$	−6.37367e6	−1.25611
$482$	−6.02442e6	−1.18113
$483$	−6.28663e6	−1.22617
$484$	−4.66704e6	−0.905584
$485$	658828.	0.127180
$486$	3.29176e6	0.632175
$487$	520952.	0.0995349	0.0497675	−	0.998761i	$-0.484152\pi$
$487$	520952.	0.0995349	0.0497675	+	0.998761i	$0.484152\pi$
$488$	945529.	0.179732
$489$	−3.20351e6	−0.605835
$490$	−3.65376e6	−0.687464
$491$	6.05563e6	1.13359	0.566795	−	0.823859i	$-0.308183\pi$
$491$	6.05563e6	1.13359	0.566795	+	0.823859i	$0.308183\pi$
$492$	−8.55359e6	−1.59307
$493$	−26665.3	−0.00494116
$494$	2.16633e7	3.99400
$495$	−346670.	−0.0635920
$496$	4.97081e6	0.907241
$497$	−4.54730e6	−0.825777
$498$	7.69543e6	1.39046
$499$	−9.59695e6	−1.72537	−0.862684	−	0.505743i	$-0.831218\pi$
$499$	−9.59695e6	−1.72537	−0.862684	+	0.505743i	$0.831218\pi$
$500$	−1.11426e7	−1.99325
$501$	5.90511e6	1.05107
$502$	−5.21068e6	−0.922858
$503$	−540497.	−0.0952519	−0.0476259	−	0.998865i	$-0.515166\pi$
$503$	−540497.	−0.0952519	−0.0476259	+	0.998865i	$0.515166\pi$
$504$	3.44086e6	0.603379
$505$	−2.01219e6	−0.351108
$506$	−8.43042e6	−1.46377
$507$	−4.60518e6	−0.795658
$508$	4.35620e6	0.748943
$509$	684501.	0.117106	0.0585531	−	0.998284i	$-0.481351\pi$
$509$	684501.	0.117106	0.0585531	+	0.998284i	$0.481351\pi$
$510$	23583.6	0.00401500
$511$	−8.56053e6	−1.45027
$512$	1.12237e7	1.89217
$513$	1.00513e7	1.68627
$514$	−1.53859e7	−2.56870
$515$	−3.34693e6	−0.556070
$516$	2.44240e7	4.03824
$517$	−5.57356e6	−0.917078
$518$	−1.38762e7	−2.27220
$519$	−9.89415e6	−1.61235
$520$	1.01683e7	1.64908
$521$	−6.62489e6	−1.06926	−0.534632	−	0.845085i	$-0.679550\pi$
$521$	−6.62489e6	−1.06926	−0.534632	+	0.845085i	$0.679550\pi$
$522$	−1.91023e6	−0.306839
$523$	4.64605e6	0.742727	0.371364	−	0.928488i	$-0.378890\pi$
$523$	4.64605e6	0.742727	0.371364	+	0.928488i	$0.378890\pi$
$524$	8.98180e6	1.42901
$525$	6.04460e6	0.957127
$526$	860820.	0.135659
$527$	12527.1	0.00196483
$528$	−1.09397e7	−1.70774
$529$	60042.4	0.00932865
$530$	−7.28343e6	−1.12628
$531$	2.15141e6	0.331121
$532$	3.33121e7	5.10297
$533$	−6.54349e6	−0.997680
$534$	1.67068e7	2.53536
$535$	−2.19497e6	−0.331546
$536$	2.30417e7	3.46419
$537$	−4.33004e6	−0.647972
$538$	1.93555e7	2.88302
$539$	4.27128e6	0.633266
$540$	8.07590e6	1.19181
$541$	969238.	0.142376	0.0711881	−	0.997463i	$-0.477321\pi$
$541$	969238.	0.142376	0.0711881	+	0.997463i	$0.477321\pi$
$542$	2.42966e7	3.55261
$543$	−5.16379e6	−0.751569
$544$	−63904.4	−0.00925835
$545$	−2.06740e6	−0.298148
$546$	−2.14826e7	−3.08393
$547$	−129320.	−0.0184798	−0.00923991	−	0.999957i	$-0.502941\pi$
$547$	−129320.	−0.0184798	−0.00923991	+	0.999957i	$0.502941\pi$
$548$	−5.41370e6	−0.770092
$549$	84885.2	0.0120199
$550$	8.10587e6	1.14260
$551$	−1.08038e7	−1.51600
$552$	1.69525e7	2.36803
$553$	8.59319e6	1.19493
$554$	5.95581e6	0.824454
$555$	−2.81129e6	−0.387412
$556$	−5.07299e6	−0.695948
$557$	−8.68585e6	−1.18624	−0.593122	−	0.805112i	$-0.702105\pi$
$557$	−8.68585e6	−1.18624	−0.593122	+	0.805112i	$0.702105\pi$
$558$	897410.	0.122013
$559$	1.86843e7	2.52899
$560$	1.10084e7	1.48339
$561$	−27569.5	−0.00369847
$562$	−1.39438e7	−1.86227
$563$	5.22750e6	0.695062	0.347531	−	0.937669i	$-0.387020\pi$
$563$	5.22750e6	0.695062	0.347531	+	0.937669i	$0.387020\pi$
$564$	1.91851e7	2.53960
$565$	−1.19321e6	−0.157252
$566$	2.49078e7	3.26809
$567$	−8.18573e6	−1.06930
$568$	1.22623e7	1.59478
$569$	−7.51471e6	−0.973042	−0.486521	−	0.873669i	$-0.661734\pi$
$569$	−7.51471e6	−0.973042	−0.486521	+	0.873669i	$0.661734\pi$
$570$	9.55524e6	1.23184
$571$	−7.26642e6	−0.932675	−0.466338	−	0.884607i	$-0.654427\pi$
$571$	−7.26642e6	−0.932675	−0.466338	+	0.884607i	$0.654427\pi$
$572$	−2.03476e7	−2.60030
$573$	−9.21026e6	−1.17189
$574$	−1.42459e7	−1.80472
$575$	−6.24629e6	−0.787866
$576$	−1.29386e6	−0.162491
$577$	1.20427e7	1.50585	0.752927	−	0.658104i	$-0.228641\pi$
$577$	1.20427e7	1.50585	0.752927	+	0.658104i	$0.228641\pi$
$578$	1.48205e7	1.84520
$579$	6.14948e6	0.762328
$580$	−8.68053e6	−1.07146
$581$	9.05255e6	1.11258
$582$	3.75341e6	0.459323
$583$	8.51441e6	1.03749
$584$	2.30844e7	2.80082
$585$	912866.	0.110285
$586$	−2.65735e7	−3.19672
$587$	2.62564e6	0.314514	0.157257	−	0.987558i	$-0.449735\pi$
$587$	2.62564e6	0.314514	0.157257	+	0.987558i	$0.449735\pi$
$588$	−1.47024e7	−1.75366
$589$	5.07553e6	0.602828
$590$	1.38417e7	1.63704
$591$	1.67810e6	0.197628
$592$	1.86072e7	2.18211
$593$	5.96621e6	0.696725	0.348363	−	0.937360i	$-0.386738\pi$
$593$	5.96621e6	0.696725	0.348363	+	0.937360i	$0.386738\pi$
$594$	−1.33664e7	−1.55435
$595$	27742.7	0.00321260
$596$	−6.19608e6	−0.714499
$597$	5.69531e6	0.654006
$598$	2.21994e7	2.53856
$599$	−8.50713e6	−0.968760	−0.484380	−	0.874858i	$-0.660955\pi$
$599$	−8.50713e6	−0.968760	−0.484380	+	0.874858i	$0.660955\pi$
$600$	−1.62999e7	−1.84845
$601$	−4.91240e6	−0.554764	−0.277382	−	0.960760i	$-0.589467\pi$
$601$	−4.91240e6	−0.554764	−0.277382	+	0.960760i	$0.589467\pi$
$602$	4.06779e7	4.57475
$603$	2.06858e6	0.231674
$604$	2.34980e7	2.62082
$605$	−1.57478e6	−0.174916
$606$	−1.14636e7	−1.26806
$607$	−8.50761e6	−0.937208	−0.468604	−	0.883408i	$-0.655243\pi$
$607$	−8.50761e6	−0.937208	−0.468604	+	0.883408i	$0.655243\pi$
$608$	−2.58918e7	−2.84055
$609$	1.07137e7	1.17056
$610$	546131.	0.0594254
$611$	1.46766e7	1.59045
$612$	−19904.2	−0.00214816
$613$	−7.25159e6	−0.779439	−0.389720	−	0.920934i	$-0.627428\pi$
$613$	−7.25159e6	−0.779439	−0.389720	+	0.920934i	$0.627428\pi$
$614$	−1.95033e7	−2.08779
$615$	−2.88619e6	−0.307707
$616$	−2.58791e7	−2.74788
$617$	4.55689e6	0.481899	0.240949	−	0.970538i	$-0.422541\pi$
$617$	4.55689e6	0.481899	0.240949	+	0.970538i	$0.422541\pi$
$618$	−1.90678e7	−2.00830
$619$	−2.55511e6	−0.268030	−0.134015	−	0.990979i	$-0.542787\pi$
$619$	−2.55511e6	−0.268030	−0.134015	+	0.990979i	$0.542787\pi$
$620$	4.07804e6	0.426061
$621$	1.03000e7	1.07179
$622$	−2.04657e7	−2.12104
$623$	1.96531e7	2.02867
$624$	2.88069e7	2.96166
$625$	3.89857e6	0.399213
$626$	2.44579e7	2.49450
$627$	−1.11702e7	−1.13473
$628$	−3.38971e7	−3.42976
$629$	46892.7	0.00472584
$630$	1.98741e6	0.199497
$631$	5.65433e6	0.565337	0.282669	−	0.959218i	$-0.408780\pi$
$631$	5.65433e6	0.565337	0.282669	+	0.959218i	$0.408780\pi$
$632$	−2.31724e7	−2.30770
$633$	−5.54427e6	−0.549965
$634$	−1.88890e7	−1.86632
$635$	1.46989e6	0.144661
$636$	−2.93079e7	−2.87304
$637$	−1.12473e7	−1.09825
$638$	1.43671e7	1.39739
$639$	1.10085e6	0.106654
$640$	325802.	0.0314416
$641$	−731737.	−0.0703412	−0.0351706	−	0.999381i	$-0.511197\pi$
$641$	−731737.	−0.0703412	−0.0351706	+	0.999381i	$0.511197\pi$
$642$	−1.25049e7	−1.19741
$643$	−1.17204e7	−1.11793	−0.558964	−	0.829192i	$-0.688801\pi$
$643$	−1.17204e7	−1.11793	−0.558964	+	0.829192i	$0.688801\pi$
$644$	3.41364e7	3.24342
$645$	8.24126e6	0.780000
$646$	−159383.	−0.0150266
$647$	−1.72195e7	−1.61718	−0.808592	−	0.588369i	$-0.799770\pi$
$647$	−1.72195e7	−1.61718	−0.808592	+	0.588369i	$0.799770\pi$
$648$	2.20737e7	2.06508
$649$	−1.61810e7	−1.50798
$650$	−2.13447e7	−1.98156
$651$	−5.03318e6	−0.465468
$652$	1.73951e7	1.60253
$653$	1.52076e7	1.39565	0.697827	−	0.716266i	$-0.254150\pi$
$653$	1.52076e7	1.39565	0.697827	+	0.716266i	$0.254150\pi$
$654$	−1.17782e7	−1.07679
$655$	3.03068e6	0.276018
$656$	1.91030e7	1.73317
$657$	2.07241e6	0.187310
$658$	3.19525e7	2.87701
$659$	1.21246e7	1.08756	0.543781	−	0.839227i	$-0.316992\pi$
$659$	1.21246e7	1.08756	0.543781	+	0.839227i	$0.316992\pi$
$660$	−8.97490e6	−0.801991
$661$	5.61465e6	0.499826	0.249913	−	0.968268i	$-0.419598\pi$
$661$	5.61465e6	0.499826	0.249913	+	0.968268i	$0.419598\pi$
$662$	−2.95690e7	−2.62236
$663$	72597.4	0.00641412
$664$	−2.44111e7	−2.14866
$665$	1.12403e7	0.985655
$666$	3.35927e6	0.293467
$667$	−1.10711e7	−0.963557
$668$	−3.20647e7	−2.78027
$669$	1.95341e7	1.68744
$670$	1.33087e7	1.14538
$671$	−638433.	−0.0547405
$672$	2.56757e7	2.19331
$673$	−1.24302e7	−1.05789	−0.528945	−	0.848656i	$-0.677412\pi$
$673$	−1.24302e7	−1.05789	−0.528945	+	0.848656i	$0.677412\pi$
$674$	1.41423e7	1.19914
$675$	−9.90346e6	−0.836619
$676$	2.50061e7	2.10465
$677$	−1.46959e7	−1.23233	−0.616163	−	0.787619i	$-0.711314\pi$
$677$	−1.46959e7	−1.23233	−0.616163	+	0.787619i	$0.711314\pi$
$678$	−6.79782e6	−0.567931
$679$	4.41533e6	0.367527
$680$	−74811.1	−0.00620431
$681$	−6.40688e6	−0.529394
$682$	−6.74954e6	−0.555665
$683$	−1.01998e7	−0.836640	−0.418320	−	0.908300i	$-0.637381\pi$
$683$	−1.01998e7	−0.836640	−0.418320	+	0.908300i	$0.637381\pi$
$684$	−8.06448e6	−0.659077
$685$	−1.82672e6	−0.148746
$686$	6.04458e6	0.490406
$687$	−2.20282e7	−1.78068
$688$	−5.45468e7	−4.39337
$689$	−2.24205e7	−1.79928
$690$	9.79167e6	0.782950
$691$	7.19307e6	0.573085	0.286542	−	0.958068i	$-0.407494\pi$
$691$	7.19307e6	0.573085	0.286542	+	0.958068i	$0.407494\pi$
$692$	5.37252e7	4.26494
$693$	−2.32331e6	−0.183770
$694$	4.09022e7	3.22365
$695$	−1.71175e6	−0.134425
$696$	−2.88905e7	−2.26064
$697$	48142.1	0.00375356
$698$	−3.18670e6	−0.247573
$699$	3.39632e6	0.262915
$700$	−3.28222e7	−2.53176
$701$	−9.31041e6	−0.715606	−0.357803	−	0.933797i	$-0.616474\pi$
$701$	−9.31041e6	−0.715606	−0.357803	+	0.933797i	$0.616474\pi$
$702$	3.51970e7	2.69565
$703$	1.89992e7	1.44993
$704$	9.73128e6	0.740011
$705$	6.47352e6	0.490532
$706$	−2.48984e7	−1.88001
$707$	−1.34853e7	−1.01464
$708$	5.56977e7	4.17594
$709$	8.26760e6	0.617681	0.308840	−	0.951114i	$-0.400059\pi$
$709$	8.26760e6	0.617681	0.308840	+	0.951114i	$0.400059\pi$
$710$	7.08260e6	0.527287
$711$	−2.08031e6	−0.154332
$712$	−5.29966e7	−3.91785
$713$	5.20112e6	0.383154
$714$	158053.	0.0116026
$715$	−6.86579e6	−0.502256
$716$	2.35121e7	1.71399
$717$	1.49358e7	1.08500
$718$	1.38041e7	0.999302
$719$	−4.68221e6	−0.337776	−0.168888	−	0.985635i	$-0.554018\pi$
$719$	−4.68221e6	−0.337776	−0.168888	+	0.985635i	$0.554018\pi$
$720$	−2.66501e6	−0.191588
$721$	−2.24305e7	−1.60694
$722$	−3.87298e7	−2.76504
$723$	−8.17978e6	−0.581964
$724$	2.80394e7	1.98802
$725$	1.06449e7	0.752138
$726$	−8.97166e6	−0.631729
$727$	−1.98545e7	−1.39323	−0.696615	−	0.717446i	$-0.745311\pi$
$727$	−1.98545e7	−1.39323	−0.696615	+	0.717446i	$0.745311\pi$
$728$	6.81461e7	4.76555
$729$	1.58993e7	1.10805
$730$	1.33334e7	0.926046
$731$	−137465.	−0.00951480
$732$	2.19759e6	0.151589
$733$	−1.60035e7	−1.10016	−0.550081	−	0.835112i	$-0.685403\pi$
$733$	−1.60035e7	−1.10016	−0.550081	+	0.835112i	$0.685403\pi$
$734$	−6.67039e6	−0.456995
$735$	−4.96096e6	−0.338725
$736$	−2.65324e7	−1.80544
$737$	−1.55580e7	−1.05508
$738$	3.44878e6	0.233090
$739$	−1.37241e7	−0.924430	−0.462215	−	0.886768i	$-0.652945\pi$
$739$	−1.37241e7	−0.924430	−0.462215	+	0.886768i	$0.652945\pi$
$740$	1.52653e7	1.02477
$741$	2.94138e7	1.96791
$742$	−4.88121e7	−3.25475
$743$	1.43676e6	0.0954798	0.0477399	−	0.998860i	$-0.484798\pi$
$743$	1.43676e6	0.0954798	0.0477399	+	0.998860i	$0.484798\pi$
$744$	1.35725e7	0.898933
$745$	−2.09071e6	−0.138008
$746$	7.50028e6	0.493436
$747$	−2.19152e6	−0.143696
$748$	149703.	0.00978307
$749$	−1.47102e7	−0.958109
$750$	−2.14200e7	−1.39048
$751$	2.32652e6	0.150525	0.0752623	−	0.997164i	$-0.476021\pi$
$751$	2.32652e6	0.150525	0.0752623	+	0.997164i	$0.476021\pi$
$752$	−4.28466e7	−2.76294
$753$	−7.07490e6	−0.454708
$754$	−3.78321e7	−2.42344
$755$	7.92880e6	0.506221
$756$	5.41230e7	3.44412
$757$	−2.35042e7	−1.49076	−0.745378	−	0.666642i	$-0.767731\pi$
$757$	−2.35042e7	−1.49076	−0.745378	+	0.666642i	$0.767731\pi$
$758$	9.35627e6	0.591466
$759$	−1.14466e7	−0.721225
$760$	−3.03107e7	−1.90354
$761$	1.50618e7	0.942792	0.471396	−	0.881922i	$-0.343750\pi$
$761$	1.50618e7	0.942792	0.471396	+	0.881922i	$0.343750\pi$
$762$	8.37412e6	0.522458
$763$	−1.38553e7	−0.861596
$764$	5.00117e7	3.09983
$765$	−6716.19	−0.000414925 0
$766$	−5.70427e6	−0.351260
$767$	4.26087e7	2.61523
$768$	1.57843e7	0.965655
$769$	−1.33838e6	−0.0816138	−0.0408069	−	0.999167i	$-0.512993\pi$
$769$	−1.33838e6	−0.0816138	−0.0408069	+	0.999167i	$0.512993\pi$
$770$	−1.49476e7	−0.908542
$771$	−2.08905e7	−1.26565
$772$	−3.33917e7	−2.01648
$773$	3.38279e6	0.203623	0.101811	−	0.994804i	$-0.467536\pi$
$773$	3.38279e6	0.203623	0.101811	+	0.994804i	$0.467536\pi$
$774$	−9.84766e6	−0.590855
$775$	−5.00089e6	−0.299084
$776$	−1.19064e7	−0.709784
$777$	−1.88407e7	−1.11955
$778$	1.49968e7	0.888282
$779$	1.95054e7	1.15163
$780$	2.36331e7	1.39086
$781$	−8.27964e6	−0.485718
$782$	−163326.	−0.00955079
$783$	−1.75532e7	−1.02318
$784$	3.28353e7	1.90788
$785$	−1.14377e7	−0.662470
$786$	1.72661e7	0.996869
$787$	−2.50830e7	−1.44359	−0.721793	−	0.692109i	$-0.756682\pi$
$787$	−2.50830e7	−1.44359	−0.721793	+	0.692109i	$0.756682\pi$
$788$	−9.11208e6	−0.522760
$789$	1.16880e6	0.0668415
$790$	−1.33842e7	−0.763002
$791$	−7.99664e6	−0.454429
$792$	6.26505e6	0.354904
$793$	1.68115e6	0.0949344
$794$	6.17385e7	3.47540
$795$	−9.88922e6	−0.554938
$796$	−3.09256e7	−1.72996
$797$	−2.32784e7	−1.29810	−0.649050	−	0.760746i	$-0.724833\pi$
$797$	−2.32784e7	−1.29810	−0.649050	+	0.760746i	$0.724833\pi$
$798$	6.40373e7	3.55980
$799$	−107979.	−0.00598374
$800$	2.55110e7	1.40930
$801$	−4.75779e6	−0.262014
$802$	−1.80105e6	−0.0988756
$803$	−1.55869e7	−0.853040
$804$	5.35532e7	2.92176
$805$	1.15185e7	0.626477
$806$	1.77732e7	0.963669
$807$	2.62803e7	1.42052
$808$	3.63645e7	1.95952
$809$	−2.97422e7	−1.59772	−0.798862	−	0.601514i	$-0.794564\pi$
$809$	−2.97422e7	−1.59772	−0.798862	+	0.601514i	$0.794564\pi$
$810$	1.27496e7	0.682785
$811$	567039.	0.0302734	0.0151367	−	0.999885i	$-0.495182\pi$
$811$	567039.	0.0302734	0.0151367	+	0.999885i	$0.495182\pi$
$812$	−5.81752e7	−3.09633
$813$	3.29892e7	1.75044
$814$	−2.52655e7	−1.33650
$815$	5.86953e6	0.309535
$816$	−211940.	−0.0111426
$817$	−5.56960e7	−2.91923
$818$	3.68634e7	1.92625
$819$	6.11785e6	0.318705
$820$	1.56720e7	0.813937
$821$	3.16675e7	1.63967	0.819833	−	0.572602i	$-0.194066\pi$
$821$	3.16675e7	1.63967	0.819833	+	0.572602i	$0.194066\pi$
$822$	−1.04070e7	−0.537211
$823$	2.66201e7	1.36997	0.684984	−	0.728558i	$-0.259809\pi$
$823$	2.66201e7	1.36997	0.684984	+	0.728558i	$0.259809\pi$
$824$	6.04861e7	3.10340
$825$	1.10059e7	0.562977
$826$	9.27640e7	4.73074
$827$	−2.83331e7	−1.44055	−0.720277	−	0.693686i	$-0.755985\pi$
$827$	−2.83331e7	−1.44055	−0.720277	+	0.693686i	$0.755985\pi$
$828$	−8.26403e6	−0.418905
$829$	−8.79920e6	−0.444689	−0.222345	−	0.974968i	$-0.571371\pi$
$829$	−8.79920e6	−0.444689	−0.222345	+	0.974968i	$0.571371\pi$
$830$	−1.40997e7	−0.710419
$831$	8.08662e6	0.406223
$832$	−2.56249e7	−1.28337
$833$	82749.5	0.00413193
$834$	−9.75202e6	−0.485489
$835$	−1.08194e7	−0.537017
$836$	6.06541e7	3.00154
$837$	8.24635e6	0.406863
$838$	−2.71374e7	−1.33493
$839$	3.62630e7	1.77852	0.889261	−	0.457400i	$-0.151219\pi$
$839$	3.62630e7	1.77852	0.889261	+	0.457400i	$0.151219\pi$
$840$	3.00578e7	1.46980
$841$	−1.64373e6	−0.0801382
$842$	−1.79190e7	−0.871029
$843$	−1.89325e7	−0.917571
$844$	3.01054e7	1.45475
$845$	8.43769e6	0.406520
$846$	−7.73535e6	−0.371581
$847$	−1.05538e7	−0.505478
$848$	6.54542e7	3.12571
$849$	3.38190e7	1.61024
$850$	157039.	0.00745520
$851$	1.94693e7	0.921568
$852$	2.84998e7	1.34506
$853$	−3.43083e7	−1.61446	−0.807228	−	0.590240i	$-0.799033\pi$
$853$	−3.43083e7	−1.61446	−0.807228	+	0.590240i	$0.799033\pi$
$854$	3.66006e6	0.171729
$855$	−2.72116e6	−0.127303
$856$	3.96677e7	1.85034
$857$	−3.17014e7	−1.47444	−0.737218	−	0.675655i	$-0.763861\pi$
$857$	−3.17014e7	−1.47444	−0.737218	+	0.675655i	$0.763861\pi$
$858$	−3.91151e7	−1.81395
$859$	1.25073e6	0.0578338	0.0289169	−	0.999582i	$-0.490794\pi$
$859$	1.25073e6	0.0578338	0.0289169	+	0.999582i	$0.490794\pi$
$860$	−4.47500e7	−2.06323
$861$	−1.93427e7	−0.889220
$862$	−5.06632e7	−2.32233
$863$	−3.05177e7	−1.39484	−0.697422	−	0.716661i	$-0.745670\pi$
$863$	−3.05177e7	−1.39484	−0.697422	+	0.716661i	$0.745670\pi$
$864$	−4.20670e7	−1.91716
$865$	1.81282e7	0.823788
$866$	−2.70434e7	−1.22537
$867$	2.01229e7	0.909164
$868$	2.73302e7	1.23124
$869$	1.56463e7	0.702850
$870$	−1.66870e7	−0.747445
$871$	4.09681e7	1.82979
$872$	3.73622e7	1.66395
$873$	−1.06890e6	−0.0474682
$874$	−6.61739e7	−2.93028
$875$	−2.51974e7	−1.11259
$876$	5.36524e7	2.36226
$877$	1.91977e6	0.0842850	0.0421425	−	0.999112i	$-0.486582\pi$
$877$	1.91977e6	0.0842850	0.0421425	+	0.999112i	$0.486582\pi$
$878$	−3.03130e7	−1.32706
$879$	−3.60807e7	−1.57508
$880$	2.00439e7	0.872521
$881$	−2.97239e7	−1.29023	−0.645113	−	0.764087i	$-0.723190\pi$
$881$	−2.97239e7	−1.29023	−0.645113	+	0.764087i	$0.723190\pi$
$882$	5.92796e6	0.256587
$883$	−2.37699e7	−1.02595	−0.512973	−	0.858405i	$-0.671456\pi$
$883$	−2.37699e7	−1.02595	−0.512973	+	0.858405i	$0.671456\pi$
$884$	−394204.	−0.0169664
$885$	1.87938e7	0.806596
$886$	−3.47645e7	−1.48782
$887$	−3.70538e7	−1.58134	−0.790668	−	0.612245i	$-0.790267\pi$
$887$	−3.70538e7	−1.58134	−0.790668	+	0.612245i	$0.790267\pi$
$888$	5.08059e7	2.16213
$889$	9.85092e6	0.418044
$890$	−3.06105e7	−1.29537
$891$	−1.49044e7	−0.628957
$892$	−1.06070e8	−4.46355
$893$	−4.37493e7	−1.83587
$894$	−1.19110e7	−0.498430
$895$	7.93357e6	0.331063
$896$	2.18346e6	0.0908606
$897$	3.01416e7	1.25079
$898$	5.27080e7	2.18115
$899$	−8.86375e6	−0.365778
$900$	7.94588e6	0.326991
$901$	164954.	0.00676939
$902$	−2.59387e7	−1.06153
$903$	5.52313e7	2.25406
$904$	2.15638e7	0.877614
$905$	9.46118e6	0.383993
$906$	4.51711e7	1.82827
$907$	1.16408e7	0.469857	0.234929	−	0.972013i	$-0.424514\pi$
$907$	1.16408e7	0.469857	0.234929	+	0.972013i	$0.424514\pi$
$908$	3.47893e7	1.40033
$909$	3.26463e6	0.131046
$910$	3.93607e7	1.57565
$911$	−1.33558e7	−0.533182	−0.266591	−	0.963810i	$-0.585897\pi$
$911$	−1.33558e7	−0.533182	−0.266591	+	0.963810i	$0.585897\pi$
$912$	−8.58704e7	−3.41866
$913$	1.64827e7	0.654413
$914$	−1.61944e7	−0.641208
$915$	741520.	0.0292799
$916$	1.19613e8	4.71020
$917$	2.03110e7	0.797643
$918$	−258953.	−0.0101418
$919$	2.18953e7	0.855190	0.427595	−	0.903970i	$-0.359361\pi$
$919$	2.18953e7	0.855190	0.427595	+	0.903970i	$0.359361\pi$
$920$	−3.10607e7	−1.20988
$921$	−2.64810e7	−1.02869
$922$	3.35169e6	0.129848
$923$	2.18023e7	0.842362
$924$	−6.01480e7	−2.31761
$925$	−1.87198e7	−0.719362
$926$	−7.53226e7	−2.88668
$927$	5.43016e6	0.207546
$928$	4.52166e7	1.72356
$929$	−1.56045e7	−0.593212	−0.296606	−	0.955000i	$-0.595855\pi$
$929$	−1.56045e7	−0.593212	−0.296606	+	0.955000i	$0.595855\pi$
$930$	7.83938e6	0.297218
$931$	3.35271e7	1.26772
$932$	−1.84420e7	−0.695455
$933$	−2.77877e7	−1.04508
$934$	8.76320e7	3.28697
$935$	50513.4	0.00188963
$936$	−1.64974e7	−0.615497
$937$	2.46774e7	0.918228	0.459114	−	0.888377i	$-0.348167\pi$
$937$	2.46774e7	0.918228	0.459114	+	0.888377i	$0.348167\pi$
$938$	8.91924e7	3.30994
$939$	3.32082e7	1.22909
$940$	−3.51512e7	−1.29754
$941$	1.58026e7	0.581773	0.290886	−	0.956758i	$-0.406050\pi$
$941$	1.58026e7	0.581773	0.290886	+	0.956758i	$0.406050\pi$
$942$	−6.51619e7	−2.39258
$943$	1.99881e7	0.731968
$944$	−1.24391e8	−4.54318
$945$	1.82625e7	0.665242
$946$	7.40656e7	2.69085
$947$	−5.69761e6	−0.206451	−0.103226	−	0.994658i	$-0.532916\pi$
$947$	−5.69761e6	−0.206451	−0.103226	+	0.994658i	$0.532916\pi$
$948$	−5.38570e7	−1.94635
$949$	4.10440e7	1.47940
$950$	6.36264e7	2.28733
$951$	−2.56469e7	−0.919567
$952$	−501369.	−0.0179294
$953$	4.07738e7	1.45428	0.727141	−	0.686488i	$-0.240848\pi$
$953$	4.07738e7	1.45428	0.727141	+	0.686488i	$0.240848\pi$
$954$	1.18168e7	0.420369
$955$	1.68752e7	0.598743
$956$	−8.11014e7	−2.87001
$957$	1.95072e7	0.688519
$958$	3.89364e6	0.137070
$959$	−1.22423e7	−0.429849
$960$	−1.13026e7	−0.395822
$961$	−2.44650e7	−0.854550
$962$	6.65304e7	2.31783
$963$	3.56118e6	0.123745
$964$	4.44162e7	1.53939
$965$	−1.12672e7	−0.389491
$966$	6.56218e7	2.26259
$967$	1.11238e7	0.382548	0.191274	−	0.981537i	$-0.438738\pi$
$967$	1.11238e7	0.382548	0.191274	+	0.981537i	$0.438738\pi$
$968$	2.84595e7	0.976201
$969$	−216405.	−0.00740385
$970$	−6.87706e6	−0.234679
$971$	−1.44146e7	−0.490631	−0.245316	−	0.969443i	$-0.578892\pi$
$971$	−1.44146e7	−0.490631	−0.245316	+	0.969443i	$0.578892\pi$
$972$	−2.42691e7	−0.823926
$973$	−1.14718e7	−0.388463
$974$	−5.43787e6	−0.183667
$975$	−2.89813e7	−0.976350
$976$	−4.90793e6	−0.164920
$977$	−505761.	−0.0169515	−0.00847577	−	0.999964i	$-0.502698\pi$
$977$	−505761.	−0.0169515	−0.00847577	+	0.999964i	$0.502698\pi$
$978$	3.34393e7	1.11792
$979$	3.57840e7	1.19325
$980$	2.69380e7	0.895985
$981$	3.35420e6	0.111280
$982$	−6.32106e7	−2.09176
$983$	−966289.	−0.0318950
$983$	−966289.	−0.0318950
$984$	5.21596e7	1.71730
$985$	−3.07464e6	−0.100973
$986$	278341.	0.00911768
$987$	4.33842e7	1.41755
$988$	−1.59717e8	−5.20546
$989$	−5.70741e7	−1.85545
$990$	3.61865e6	0.117343
$991$	−3.31402e7	−1.07194	−0.535970	−	0.844237i	$-0.680054\pi$
$991$	−3.31402e7	−1.07194	−0.535970	+	0.844237i	$0.680054\pi$
$992$	−2.12423e7	−0.685367
$993$	−4.01479e7	−1.29208
$994$	4.74662e7	1.52377
$995$	−1.04351e7	−0.334147
$996$	−5.67360e7	−1.81222
$997$	−3.31739e7	−1.05696	−0.528480	−	0.848946i	$-0.677238\pi$
$997$	−3.31739e7	−1.05696	−0.528480	+	0.848946i	$0.677238\pi$
$998$	1.00176e8	3.18374
$999$	3.08685e7	0.978594

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.6.a.a.1.9	✓	191

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.6.a.a.1.9	✓	191	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)

\(f(q)\)	\(=\)	\(q-10.4383 q^{2} -14.1728 q^{3} +76.9585 q^{4} +25.9677 q^{5} +147.941 q^{6} +174.030 q^{7} -469.291 q^{8} -42.1308 q^{9} +O(q^{10})\)	\(q-10.4383 q^{2} -14.1728 q^{3} +76.9585 q^{4} +25.9677 q^{5} +147.941 q^{6} +174.030 q^{7} -469.291 q^{8} -42.1308 q^{9} -271.059 q^{10} +316.871 q^{11} -1090.72 q^{12} -834.400 q^{13} -1816.58 q^{14} -368.036 q^{15} +2435.94 q^{16} +6.13889 q^{17} +439.774 q^{18} +2487.26 q^{19} +1998.44 q^{20} -2466.50 q^{21} -3307.60 q^{22} +2548.80 q^{23} +6651.18 q^{24} -2450.68 q^{25} +8709.73 q^{26} +4041.11 q^{27} +13393.1 q^{28} -4343.66 q^{29} +3841.68 q^{30} +2040.61 q^{31} -10409.8 q^{32} -4490.96 q^{33} -64.0797 q^{34} +4519.17 q^{35} -3242.32 q^{36} +7638.63 q^{37} -25962.8 q^{38} +11825.8 q^{39} -12186.4 q^{40} +7842.15 q^{41} +25746.1 q^{42} -22392.5 q^{43} +24385.9 q^{44} -1094.04 q^{45} -26605.2 q^{46} -17589.4 q^{47} -34524.1 q^{48} +13479.6 q^{49} +25581.0 q^{50} -87.0055 q^{51} -64214.1 q^{52} +26870.3 q^{53} -42182.4 q^{54} +8228.42 q^{55} -81670.9 q^{56} -35251.5 q^{57} +45340.6 q^{58} -51065.1 q^{59} -28323.5 q^{60} -2014.80 q^{61} -21300.6 q^{62} -7332.03 q^{63} +30710.5 q^{64} -21667.5 q^{65} +46878.1 q^{66} -49098.9 q^{67} +472.440 q^{68} -36123.7 q^{69} -47172.5 q^{70} -26129.4 q^{71} +19771.6 q^{72} -49189.9 q^{73} -79734.4 q^{74} +34733.1 q^{75} +191416. q^{76} +55145.2 q^{77} -123442. q^{78} +49377.5 q^{79} +63255.7 q^{80} -47036.2 q^{81} -81858.9 q^{82} +52017.1 q^{83} -189818. q^{84} +159.413 q^{85} +233740. q^{86} +61562.0 q^{87} -148705. q^{88} +112929. q^{89} +11419.9 q^{90} -145211. q^{91} +196152. q^{92} -28921.3 q^{93} +183603. q^{94} +64588.4 q^{95} +147536. q^{96} +25371.1 q^{97} -140704. q^{98} -13350.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 191 q - 37 q^{2} - 74 q^{3} + 2821 q^{4} - 247 q^{5} - 335 q^{6} - 1569 q^{7} - 1761 q^{8} + 13251 q^{9}+O(q^{10}) \) 191 * q - 37 * q^2 - 74 * q^3 + 2821 * q^4 - 247 * q^5 - 335 * q^6 - 1569 * q^7 - 1761 * q^8 + 13251 * q^9	\( 191 q - 37 q^{2} - 74 q^{3} + 2821 q^{4} - 247 q^{5} - 335 q^{6} - 1569 q^{7} - 1761 q^{8} + 13251 q^{9} - 2867 q^{10} - 1878 q^{11} - 3400 q^{12} - 6854 q^{13} - 1601 q^{14} - 3461 q^{15} + 38457 q^{16} - 10730 q^{17} - 17249 q^{18} - 5817 q^{19} - 9988 q^{20} - 15999 q^{21} - 20287 q^{22} - 15625 q^{23} - 19747 q^{24} + 67082 q^{25} - 9868 q^{26} - 22892 q^{27} - 72720 q^{28} - 17960 q^{29} - 27464 q^{30} - 25604 q^{31} - 68869 q^{32} - 60654 q^{33} - 42876 q^{34} - 30018 q^{35} + 172922 q^{36} - 114862 q^{37} + 4404 q^{38} - 73500 q^{39} - 137154 q^{40} - 90896 q^{41} - 10652 q^{42} - 121447 q^{43} - 57962 q^{44} - 109019 q^{45} - 136262 q^{46} - 86994 q^{47} - 133347 q^{48} + 278242 q^{49} - 93911 q^{50} - 66966 q^{51} - 284241 q^{52} - 122112 q^{53} - 130806 q^{54} - 134904 q^{55} - 100292 q^{56} - 423426 q^{57} - 307669 q^{58} - 85704 q^{59} - 238277 q^{60} - 206736 q^{61} - 190602 q^{62} - 387623 q^{63} + 411903 q^{64} - 244408 q^{65} - 113963 q^{66} - 337002 q^{67} - 388031 q^{68} - 165342 q^{69} - 183925 q^{70} - 174806 q^{71} - 753621 q^{72} - 1009738 q^{73} - 204958 q^{74} - 282676 q^{75} - 326869 q^{76} - 332288 q^{77} - 591801 q^{78} - 488092 q^{79} - 259068 q^{80} + 385959 q^{81} - 523996 q^{82} - 315720 q^{83} - 750486 q^{84} - 1001755 q^{85} - 287709 q^{86} - 316995 q^{87} - 836923 q^{88} - 298065 q^{89} - 751039 q^{90} - 521459 q^{91} - 640932 q^{92} - 554391 q^{93} - 623481 q^{94} - 491883 q^{95} - 767843 q^{96} - 1468693 q^{97} - 714146 q^{98} - 842507 q^{99}+O(q^{100}) \) 191 * q - 37 * q^2 - 74 * q^3 + 2821 * q^4 - 247 * q^5 - 335 * q^6 - 1569 * q^7 - 1761 * q^8 + 13251 * q^9 - 2867 * q^10 - 1878 * q^11 - 3400 * q^12 - 6854 * q^13 - 1601 * q^14 - 3461 * q^15 + 38457 * q^16 - 10730 * q^17 - 17249 * q^18 - 5817 * q^19 - 9988 * q^20 - 15999 * q^21 - 20287 * q^22 - 15625 * q^23 - 19747 * q^24 + 67082 * q^25 - 9868 * q^26 - 22892 * q^27 - 72720 * q^28 - 17960 * q^29 - 27464 * q^30 - 25604 * q^31 - 68869 * q^32 - 60654 * q^33 - 42876 * q^34 - 30018 * q^35 + 172922 * q^36 - 114862 * q^37 + 4404 * q^38 - 73500 * q^39 - 137154 * q^40 - 90896 * q^41 - 10652 * q^42 - 121447 * q^43 - 57962 * q^44 - 109019 * q^45 - 136262 * q^46 - 86994 * q^47 - 133347 * q^48 + 278242 * q^49 - 93911 * q^50 - 66966 * q^51 - 284241 * q^52 - 122112 * q^53 - 130806 * q^54 - 134904 * q^55 - 100292 * q^56 - 423426 * q^57 - 307669 * q^58 - 85704 * q^59 - 238277 * q^60 - 206736 * q^61 - 190602 * q^62 - 387623 * q^63 + 411903 * q^64 - 244408 * q^65 - 113963 * q^66 - 337002 * q^67 - 388031 * q^68 - 165342 * q^69 - 183925 * q^70 - 174806 * q^71 - 753621 * q^72 - 1009738 * q^73 - 204958 * q^74 - 282676 * q^75 - 326869 * q^76 - 332288 * q^77 - 591801 * q^78 - 488092 * q^79 - 259068 * q^80 + 385959 * q^81 - 523996 * q^82 - 315720 * q^83 - 750486 * q^84 - 1001755 * q^85 - 287709 * q^86 - 316995 * q^87 - 836923 * q^88 - 298065 * q^89 - 751039 * q^90 - 521459 * q^91 - 640932 * q^92 - 554391 * q^93 - 623481 * q^94 - 491883 * q^95 - 767843 * q^96 - 1468693 * q^97 - 714146 * q^98 - 842507 * q^99

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