LMFDB - Embedded newform 583.6.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [583,6,Mod(1,583)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(583, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("583.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 583 = 11 \cdot 53 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	583.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:	$93.5037669510$
Analytic rank:	$1$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	583.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.02958 q^{2} -0.934504 q^{3} +32.4742 q^{4} -106.766 q^{5} +7.50368 q^{6} -253.610 q^{7} -3.80766 q^{8} -242.127 q^{9} +O(q^{10})$	\(q-8.02958 q^{2} -0.934504 q^{3} +32.4742 q^{4} -106.766 q^{5} +7.50368 q^{6} -253.610 q^{7} -3.80766 q^{8} -242.127 q^{9} +857.288 q^{10} -121.000 q^{11} -30.3473 q^{12} -419.078 q^{13} +2036.38 q^{14} +99.7734 q^{15} -1008.60 q^{16} -132.602 q^{17} +1944.18 q^{18} -2852.47 q^{19} -3467.15 q^{20} +237.000 q^{21} +971.580 q^{22} +3445.60 q^{23} +3.55827 q^{24} +8274.01 q^{25} +3365.02 q^{26} +453.353 q^{27} -8235.78 q^{28} -3733.26 q^{29} -801.139 q^{30} +1280.96 q^{31} +8220.49 q^{32} +113.075 q^{33} +1064.74 q^{34} +27077.0 q^{35} -7862.87 q^{36} +2536.45 q^{37} +22904.1 q^{38} +391.630 q^{39} +406.529 q^{40} -6658.64 q^{41} -1903.01 q^{42} -8926.23 q^{43} -3929.38 q^{44} +25850.9 q^{45} -27666.7 q^{46} +13411.9 q^{47} +942.541 q^{48} +47511.0 q^{49} -66436.8 q^{50} +123.917 q^{51} -13609.2 q^{52} -2809.00 q^{53} -3640.23 q^{54} +12918.7 q^{55} +965.660 q^{56} +2665.64 q^{57} +29976.5 q^{58} -23935.2 q^{59} +3240.06 q^{60} -39307.5 q^{61} -10285.6 q^{62} +61405.7 q^{63} -33731.9 q^{64} +44743.3 q^{65} -907.945 q^{66} +4980.32 q^{67} -4306.14 q^{68} -3219.93 q^{69} -217417. q^{70} -75261.3 q^{71} +921.936 q^{72} -11149.8 q^{73} -20366.7 q^{74} -7732.10 q^{75} -92631.7 q^{76} +30686.8 q^{77} -3144.62 q^{78} +63955.9 q^{79} +107684. q^{80} +58413.1 q^{81} +53466.1 q^{82} +101531. q^{83} +7696.37 q^{84} +14157.4 q^{85} +71673.9 q^{86} +3488.75 q^{87} +460.727 q^{88} -8693.50 q^{89} -207572. q^{90} +106282. q^{91} +111893. q^{92} -1197.06 q^{93} -107692. q^{94} +304547. q^{95} -7682.08 q^{96} +113376. q^{97} -381494. q^{98} +29297.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 16 q^{2} + 906 q^{4} - 225 q^{5} - 197 q^{6} - 341 q^{7} - 1152 q^{8} + 4240 q^{9}+O(q^{10}) $ 54 * q - 16 * q^2 + 906 * q^4 - 225 * q^5 - 197 * q^6 - 341 * q^7 - 1152 * q^8 + 4240 * q^9	\( 54 q - 16 q^{2} + 906 q^{4} - 225 q^{5} - 197 q^{6} - 341 q^{7} - 1152 q^{8} + 4240 q^{9} - 233 q^{10} - 6534 q^{11} - 327 q^{12} - 1455 q^{13} + 2254 q^{14} - 694 q^{15} + 16610 q^{16} - 9275 q^{17} - 6797 q^{18} - 2515 q^{19} - 6840 q^{20} - 4744 q^{21} + 1936 q^{22} - 6307 q^{23} - 5681 q^{24} + 26923 q^{25} - 5196 q^{26} - 5190 q^{27} - 36405 q^{28} - 8356 q^{29} - 28719 q^{30} - 4357 q^{31} - 68580 q^{32} + 9406 q^{34} - 3747 q^{35} + 38059 q^{36} - 25798 q^{37} - 32169 q^{38} - 28347 q^{39} - 15014 q^{40} - 89685 q^{41} - 103207 q^{42} - 26640 q^{43} - 109626 q^{44} - 66786 q^{45} - 28271 q^{46} - 26237 q^{47} - 20371 q^{48} + 132327 q^{49} - 189646 q^{50} + 10856 q^{51} - 179789 q^{52} - 151686 q^{53} - 167182 q^{54} + 27225 q^{55} + 24845 q^{56} - 33857 q^{57} - 31384 q^{58} - 49035 q^{59} - 183481 q^{60} - 101718 q^{61} - 103315 q^{62} - 214794 q^{63} + 154912 q^{64} - 55703 q^{65} + 23837 q^{66} + 105905 q^{67} - 267681 q^{68} - 56033 q^{69} - 90034 q^{70} - 107016 q^{71} - 580829 q^{72} - 161641 q^{73} - 259552 q^{74} - 69519 q^{75} - 240846 q^{76} + 41261 q^{77} - 65716 q^{78} - 35649 q^{79} - 279887 q^{80} + 316682 q^{81} + 206196 q^{82} - 326347 q^{83} - 29955 q^{84} - 189486 q^{85} - 444656 q^{86} - 222331 q^{87} + 139392 q^{88} - 633400 q^{89} + 110940 q^{90} - 25954 q^{91} + 18304 q^{92} - 191747 q^{93} - 62405 q^{94} - 515756 q^{95} - 527591 q^{96} - 405641 q^{97} - 919621 q^{98} - 513040 q^{99}+O(q^{100}) \) 54 * q - 16 * q^2 + 906 * q^4 - 225 * q^5 - 197 * q^6 - 341 * q^7 - 1152 * q^8 + 4240 * q^9 - 233 * q^10 - 6534 * q^11 - 327 * q^12 - 1455 * q^13 + 2254 * q^14 - 694 * q^15 + 16610 * q^16 - 9275 * q^17 - 6797 * q^18 - 2515 * q^19 - 6840 * q^20 - 4744 * q^21 + 1936 * q^22 - 6307 * q^23 - 5681 * q^24 + 26923 * q^25 - 5196 * q^26 - 5190 * q^27 - 36405 * q^28 - 8356 * q^29 - 28719 * q^30 - 4357 * q^31 - 68580 * q^32 + 9406 * q^34 - 3747 * q^35 + 38059 * q^36 - 25798 * q^37 - 32169 * q^38 - 28347 * q^39 - 15014 * q^40 - 89685 * q^41 - 103207 * q^42 - 26640 * q^43 - 109626 * q^44 - 66786 * q^45 - 28271 * q^46 - 26237 * q^47 - 20371 * q^48 + 132327 * q^49 - 189646 * q^50 + 10856 * q^51 - 179789 * q^52 - 151686 * q^53 - 167182 * q^54 + 27225 * q^55 + 24845 * q^56 - 33857 * q^57 - 31384 * q^58 - 49035 * q^59 - 183481 * q^60 - 101718 * q^61 - 103315 * q^62 - 214794 * q^63 + 154912 * q^64 - 55703 * q^65 + 23837 * q^66 + 105905 * q^67 - 267681 * q^68 - 56033 * q^69 - 90034 * q^70 - 107016 * q^71 - 580829 * q^72 - 161641 * q^73 - 259552 * q^74 - 69519 * q^75 - 240846 * q^76 + 41261 * q^77 - 65716 * q^78 - 35649 * q^79 - 279887 * q^80 + 316682 * q^81 + 206196 * q^82 - 326347 * q^83 - 29955 * q^84 - 189486 * q^85 - 444656 * q^86 - 222331 * q^87 + 139392 * q^88 - 633400 * q^89 + 110940 * q^90 - 25954 * q^91 + 18304 * q^92 - 191747 * q^93 - 62405 * q^94 - 515756 * q^95 - 527591 * q^96 - 405641 * q^97 - 919621 * q^98 - 513040 * 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 $

$2$	−8.02958	−1.41944	−0.709722	−	0.704482i	$-0.751179\pi$
$2$	−8.02958	−1.41944	−0.709722	+	0.704482i	$0.751179\pi$
$3$	−0.934504	−0.0599485	−0.0299742	−	0.999551i	$-0.509543\pi$
$3$	−0.934504	−0.0599485	−0.0299742	+	0.999551i	$0.509543\pi$
$4$	32.4742	1.01482
$5$	−106.766	−1.90989	−0.954945	−	0.296781i	$-0.904087\pi$
$5$	−106.766	−1.90989	−0.954945	+	0.296781i	$0.904087\pi$
$6$	7.50368	0.0850934
$7$	−253.610	−1.95624	−0.978118	−	0.208052i	$-0.933288\pi$
$7$	−253.610	−1.95624	−0.978118	+	0.208052i	$0.933288\pi$
$8$	−3.80766	−0.0210345
$9$	−242.127	−0.996406
$10$	857.288	2.71098
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−30.3473	−0.0608368
$13$	−419.078	−0.687759	−0.343880	−	0.939014i	$-0.611741\pi$
$13$	−419.078	−0.687759	−0.343880	+	0.939014i	$0.611741\pi$
$14$	2036.38	2.77677
$15$	99.7734	0.114495
$16$	−1008.60	−0.984962
$17$	−132.602	−0.111283	−0.0556413	−	0.998451i	$-0.517720\pi$
$17$	−132.602	−0.111283	−0.0556413	+	0.998451i	$0.517720\pi$
$18$	1944.18	1.41434
$19$	−2852.47	−1.81275	−0.906373	−	0.422478i	$-0.861160\pi$
$19$	−2852.47	−1.81275	−0.906373	+	0.422478i	$0.861160\pi$
$20$	−3467.15	−1.93819
$21$	237.000	0.117273
$22$	971.580	0.427978
$23$	3445.60	1.35814	0.679071	−	0.734072i	$-0.262383\pi$
$23$	3445.60	1.35814	0.679071	+	0.734072i	$0.262383\pi$
$24$	3.55827	0.00126099
$25$	8274.01	2.64768
$26$	3365.02	0.976235
$27$	453.353	0.119681
$28$	−8235.78	−1.98522
$29$	−3733.26	−0.824315	−0.412158	−	0.911113i	$-0.635225\pi$
$29$	−3733.26	−0.824315	−0.412158	+	0.911113i	$0.635225\pi$
$30$	−801.139	−0.162519
$31$	1280.96	0.239404	0.119702	−	0.992810i	$-0.461806\pi$
$31$	1280.96	0.239404	0.119702	+	0.992810i	$0.461806\pi$
$32$	8220.49	1.41913
$33$	113.075	0.0180751
$34$	1064.74	0.157959
$35$	27077.0	3.73620
$36$	−7862.87	−1.01117
$37$	2536.45	0.304595	0.152297	−	0.988335i	$-0.451333\pi$
$37$	2536.45	0.304595	0.152297	+	0.988335i	$0.451333\pi$
$38$	22904.1	2.57309
$39$	391.630	0.0412301
$40$	406.529	0.0401737
$41$	−6658.64	−0.618623	−0.309311	−	0.950961i	$-0.600099\pi$
$41$	−6658.64	−0.618623	−0.309311	+	0.950961i	$0.600099\pi$
$42$	−1903.01	−0.166463
$43$	−8926.23	−0.736202	−0.368101	−	0.929786i	$-0.619992\pi$
$43$	−8926.23	−0.736202	−0.368101	+	0.929786i	$0.619992\pi$
$44$	−3929.38	−0.305979
$45$	25850.9	1.90303
$46$	−27666.7	−1.92781
$47$	13411.9	0.885617	0.442809	−	0.896616i	$-0.353982\pi$
$47$	13411.9	0.885617	0.442809	+	0.896616i	$0.353982\pi$
$48$	942.541	0.0590469
$49$	47511.0	2.82686
$50$	−66436.8	−3.75824
$51$	123.917	0.00667123
$52$	−13609.2	−0.697951
$53$	−2809.00	−0.137361
$53$	−2809.00	−0.137361
$54$	−3640.23	−0.169881
$55$	12918.7	0.575854
$56$	965.660	0.0411485
$57$	2665.64	0.108671
$58$	29976.5	1.17007
$59$	−23935.2	−0.895171	−0.447586	−	0.894241i	$-0.647716\pi$
$59$	−23935.2	−0.895171	−0.447586	+	0.894241i	$0.647716\pi$
$60$	3240.06	0.116192
$61$	−39307.5	−1.35254	−0.676270	−	0.736653i	$-0.736405\pi$
$61$	−39307.5	−1.35254	−0.676270	+	0.736653i	$0.736405\pi$
$62$	−10285.6	−0.339821
$63$	61405.7	1.94921
$64$	−33731.9	−1.02941
$65$	44743.3	1.31354
$66$	−907.945	−0.0256566
$67$	4980.32	0.135541	0.0677704	−	0.997701i	$-0.478411\pi$
$67$	4980.32	0.135541	0.0677704	+	0.997701i	$0.478411\pi$
$68$	−4306.14	−0.112932
$69$	−3219.93	−0.0814185
$70$	−217417.	−5.30332
$71$	−75261.3	−1.77184	−0.885922	−	0.463834i	$-0.846473\pi$
$71$	−75261.3	−1.77184	−0.885922	+	0.463834i	$0.846473\pi$
$72$	921.936	0.0209589
$73$	−11149.8	−0.244884	−0.122442	−	0.992476i	$-0.539073\pi$
$73$	−11149.8	−0.244884	−0.122442	+	0.992476i	$0.539073\pi$
$74$	−20366.7	−0.432355
$75$	−7732.10	−0.158725
$76$	−92631.7	−1.83961
$77$	30686.8	0.589827
$78$	−3144.62	−0.0585238
$79$	63955.9	1.15296	0.576478	−	0.817112i	$-0.304427\pi$
$79$	63955.9	1.15296	0.576478	+	0.817112i	$0.304427\pi$
$80$	107684.	1.88117
$81$	58413.1	0.989231
$82$	53466.1	0.878100
$83$	101531.	1.61772	0.808860	−	0.588001i	$-0.200085\pi$
$83$	101531.	1.61772	0.808860	+	0.588001i	$0.200085\pi$
$84$	7696.37	0.119011
$85$	14157.4	0.212538
$86$	71673.9	1.04500
$87$	3488.75	0.0494164
$88$	460.727	0.00634215
$89$	−8693.50	−0.116337	−0.0581687	−	0.998307i	$-0.518526\pi$
$89$	−8693.50	−0.116337	−0.0581687	+	0.998307i	$0.518526\pi$
$90$	−207572.	−2.70124
$91$	106282.	1.34542
$92$	111893.	1.37827
$93$	−1197.06	−0.0143519
$94$	−107692.	−1.25708
$95$	304547.	3.46215
$96$	−7682.08	−0.0850747
$97$	113376.	1.22347	0.611733	−	0.791064i	$-0.290473\pi$
$97$	113376.	1.22347	0.611733	+	0.791064i	$0.290473\pi$
$98$	−381494.	−4.01256
$99$	29297.3	0.300428
$100$	268692.	2.68692
$101$	134546.	1.31240	0.656202	−	0.754585i	$-0.272162\pi$
$101$	134546.	1.31240	0.656202	+	0.754585i	$0.272162\pi$
$102$	−995.002	−0.00946943
$103$	−136507.	−1.26783	−0.633916	−	0.773402i	$-0.718554\pi$
$103$	−136507.	−1.26783	−0.633916	+	0.773402i	$0.718554\pi$
$104$	1595.70	0.0144667
$105$	−25303.5	−0.223979
$106$	22555.1	0.194976
$107$	−41716.4	−0.352247	−0.176123	−	0.984368i	$-0.556356\pi$
$107$	−41716.4	−0.352247	−0.176123	+	0.984368i	$0.556356\pi$
$108$	14722.3	0.121455
$109$	100035.	0.806466	0.403233	−	0.915097i	$-0.367886\pi$
$109$	100035.	0.806466	0.403233	+	0.915097i	$0.367886\pi$
$110$	−103732.	−0.817392
$111$	−2370.32	−0.0182600
$112$	255791.	1.92682
$113$	−80941.1	−0.596311	−0.298156	−	0.954517i	$-0.596371\pi$
$113$	−80941.1	−0.596311	−0.298156	+	0.954517i	$0.596371\pi$
$114$	−21404.0	−0.154253
$115$	−367873.	−2.59390
$116$	−121235.	−0.836531
$117$	101470.	0.685287
$118$	192189.	1.27064
$119$	33629.2	0.217695
$120$	−379.903	−0.00240835
$121$	14641.0	0.0909091
$122$	315623.	1.91985
$123$	6222.53	0.0370855
$124$	41598.2	0.242952
$125$	−549740.	−3.14689
$126$	−493062.	−2.76679
$127$	−17325.7	−0.0953195	−0.0476598	−	0.998864i	$-0.515176\pi$
$127$	−17325.7	−0.0953195	−0.0476598	+	0.998864i	$0.515176\pi$
$128$	7797.23	0.0420645
$129$	8341.59	0.0441342
$130$	−359270.	−1.86450
$131$	193324.	0.984253	0.492127	−	0.870524i	$-0.336220\pi$
$131$	193324.	0.984253	0.492127	+	0.870524i	$0.336220\pi$
$132$	3672.02	0.0183430
$133$	723415.	3.54616
$134$	−39989.9	−0.192392
$135$	−48402.7	−0.228579
$136$	504.903	0.00234078
$137$	−386339.	−1.75860	−0.879300	−	0.476269i	$-0.841989\pi$
$137$	−386339.	−1.75860	−0.879300	+	0.476269i	$0.841989\pi$
$138$	25854.7	0.115569
$139$	126900.	0.557090	0.278545	−	0.960423i	$-0.410148\pi$
$139$	126900.	0.557090	0.278545	+	0.960423i	$0.410148\pi$
$140$	879303.	3.79156
$141$	−12533.5	−0.0530914
$142$	604317.	2.51503
$143$	50708.4	0.207367
$144$	244209.	0.981422
$145$	398586.	1.57435
$146$	89528.5	0.347599
$147$	−44399.2	−0.169466
$148$	82369.3	0.309108
$149$	−139121.	−0.513366	−0.256683	−	0.966496i	$-0.582630\pi$
$149$	−139121.	−0.513366	−0.256683	+	0.966496i	$0.582630\pi$
$150$	62085.5	0.225300
$151$	−209571.	−0.747978	−0.373989	−	0.927433i	$-0.622010\pi$
$151$	−209571.	−0.747978	−0.373989	+	0.927433i	$0.622010\pi$
$152$	10861.2	0.0381303
$153$	32106.5	0.110883
$154$	−246402.	−0.837226
$155$	−136763.	−0.457236
$156$	12717.9	0.0418411
$157$	353397.	1.14423	0.572116	−	0.820173i	$-0.306123\pi$
$157$	353397.	1.14423	0.572116	+	0.820173i	$0.306123\pi$
$158$	−513539.	−1.63656
$159$	2625.02	0.00823455
$160$	−877670.	−2.71039
$161$	−873838.	−2.65685
$162$	−469033.	−1.40416
$163$	399921.	1.17898	0.589488	−	0.807777i	$-0.299330\pi$
$163$	399921.	1.17898	0.589488	+	0.807777i	$0.299330\pi$
$164$	−216234.	−0.627790
$165$	−12072.6	−0.0345215
$166$	−815252.	−2.29626
$167$	−553054.	−1.53453	−0.767266	−	0.641329i	$-0.778384\pi$
$167$	−553054.	−1.53453	−0.767266	+	0.641329i	$0.778384\pi$
$168$	−902.413	−0.00246679
$169$	−195667.	−0.526987
$170$	−113678.	−0.301685
$171$	690659.	1.80623
$172$	−289872.	−0.747111
$173$	−205647.	−0.522405	−0.261203	−	0.965284i	$-0.584119\pi$
$173$	−205647.	−0.522405	−0.261203	+	0.965284i	$0.584119\pi$
$174$	−28013.2	−0.0701438
$175$	−2.09837e6	−5.17949
$176$	122041.	0.296977
$177$	22367.5	0.0536641
$178$	69805.2	0.165134
$179$	498142.	1.16204	0.581019	−	0.813890i	$-0.302654\pi$
$179$	498142.	1.16204	0.581019	+	0.813890i	$0.302654\pi$
$180$	839489.	1.93123
$181$	25720.7	0.0583562	0.0291781	−	0.999574i	$-0.490711\pi$
$181$	25720.7	0.0583562	0.0291781	+	0.999574i	$0.490711\pi$
$182$	−853403.	−1.90975
$183$	36733.0	0.0810827
$184$	−13119.7	−0.0285679
$185$	−270807.	−0.581743
$186$	9611.92	0.0203717
$187$	16044.8	0.0335530
$188$	435541.	0.898741
$189$	−114975.	−0.234125
$190$	−2.44539e6	−4.91432
$191$	615107.	1.22002	0.610010	−	0.792394i	$-0.291165\pi$
$191$	615107.	1.22002	0.610010	+	0.792394i	$0.291165\pi$
$192$	31522.6	0.0617118
$193$	−761926.	−1.47238	−0.736189	−	0.676776i	$-0.763377\pi$
$193$	−761926.	−1.47238	−0.736189	+	0.676776i	$0.763377\pi$
$194$	−910363.	−1.73664
$195$	−41812.8	−0.0787450
$196$	1.54288e6	2.86875
$197$	−473150.	−0.868628	−0.434314	−	0.900762i	$-0.643009\pi$
$197$	−473150.	−0.868628	−0.434314	+	0.900762i	$0.643009\pi$
$198$	−235245.	−0.426440
$199$	510220.	0.913324	0.456662	−	0.889640i	$-0.349045\pi$
$199$	510220.	0.913324	0.456662	+	0.889640i	$0.349045\pi$
$200$	−31504.6	−0.0556928
$201$	−4654.13	−0.00812546
$202$	−1.08035e6	−1.86288
$203$	946792.	1.61256
$204$	4024.11	0.00677009
$205$	710917.	1.18150
$206$	1.09609e6	1.79962
$207$	−834272.	−1.35326
$208$	422682.	0.677416
$209$	345149.	0.546563
$210$	203177.	0.317926
$211$	−492066.	−0.760882	−0.380441	−	0.924805i	$-0.624228\pi$
$211$	−492066.	−0.760882	−0.380441	+	0.924805i	$0.624228\pi$
$212$	−91220.0	−0.139396
$213$	70331.9	0.106219
$214$	334965.	0.499994
$215$	953019.	1.40606
$216$	−1726.21	−0.00251744
$217$	−324864.	−0.468331
$218$	−803240.	−1.14473
$219$	10419.6	0.0146804
$220$	419525.	0.584387
$221$	55570.5	0.0765357
$222$	19032.7	0.0259190
$223$	−255472.	−0.344019	−0.172009	−	0.985095i	$-0.555026\pi$
$223$	−255472.	−0.344019	−0.172009	+	0.985095i	$0.555026\pi$
$224$	−2.08480e6	−2.77616
$225$	−2.00336e6	−2.63817
$226$	649923.	0.846430
$227$	−349196.	−0.449785	−0.224892	−	0.974384i	$-0.572203\pi$
$227$	−349196.	−0.449785	−0.224892	+	0.974384i	$0.572203\pi$
$228$	86564.7	0.110282
$229$	1.39179e6	1.75383	0.876913	−	0.480649i	$-0.159599\pi$
$229$	1.39179e6	1.75383	0.876913	+	0.480649i	$0.159599\pi$
$230$	2.95387e6	3.68190
$231$	−28676.9	−0.0353592
$232$	14215.0	0.0173391
$233$	−705693.	−0.851581	−0.425791	−	0.904822i	$-0.640004\pi$
$233$	−705693.	−0.851581	−0.425791	+	0.904822i	$0.640004\pi$
$234$	−814761.	−0.972726
$235$	−1.43194e6	−1.69143
$236$	−777275.	−0.908437
$237$	−59767.1	−0.0691180
$238$	−270028.	−0.309006
$239$	−1.03286e6	−1.16962	−0.584811	−	0.811169i	$-0.698831\pi$
$239$	−1.03286e6	−1.16962	−0.584811	+	0.811169i	$0.698831\pi$
$240$	−100632.	−0.112773
$241$	−790214.	−0.876399	−0.438200	−	0.898878i	$-0.644384\pi$
$241$	−790214.	−0.876399	−0.438200	+	0.898878i	$0.644384\pi$
$242$	−117561.	−0.129040
$243$	−164752.	−0.178984
$244$	−1.27648e6	−1.37258
$245$	−5.07257e6	−5.39899
$246$	−49964.3	−0.0526407
$247$	1.19541e6	1.24673
$248$	−4877.46	−0.00503575
$249$	−94881.1	−0.0969799
$250$	4.41418e6	4.46684
$251$	−1.08577e6	−1.08781	−0.543907	−	0.839146i	$-0.683055\pi$
$251$	−1.08577e6	−1.08781	−0.543907	+	0.839146i	$0.683055\pi$
$252$	1.99410e6	1.97809
$253$	−416918.	−0.409495
$254$	139118.	0.135301
$255$	−13230.1	−0.0127413
$256$	1.01681e6	0.969707
$257$	16860.0	0.0159230	0.00796149	−	0.999968i	$-0.497466\pi$
$257$	16860.0	0.0159230	0.00796149	+	0.999968i	$0.497466\pi$
$258$	−66979.5	−0.0626459
$259$	−643269.	−0.595859
$260$	1.45300e6	1.33301
$261$	903922.	0.821353
$262$	−1.55231e6	−1.39709
$263$	−550681.	−0.490920	−0.245460	−	0.969407i	$-0.578939\pi$
$263$	−550681.	−0.490920	−0.245460	+	0.969407i	$0.578939\pi$
$264$	−430.551	−0.000380202 0
$265$	299906.	0.262344
$266$	−5.80872e6	−5.03357
$267$	8124.11	0.00697425
$268$	161732.	0.137549
$269$	495867.	0.417815	0.208908	−	0.977935i	$-0.433009\pi$
$269$	495867.	0.417815	0.208908	+	0.977935i	$0.433009\pi$
$270$	388654.	0.324454
$271$	1.12385e6	0.929579	0.464790	−	0.885421i	$-0.346130\pi$
$271$	1.12385e6	0.929579	0.464790	+	0.885421i	$0.346130\pi$
$272$	133742.	0.109609
$273$	−99321.2	−0.0806558
$274$	3.10214e6	2.49623
$275$	−1.00116e6	−0.798306
$276$	−104565.	−0.0826251
$277$	2.17908e6	1.70637	0.853185	−	0.521608i	$-0.174668\pi$
$277$	2.17908e6	1.70637	0.853185	+	0.521608i	$0.174668\pi$
$278$	−1.01896e6	−0.790757
$279$	−310155.	−0.238544
$280$	−103100.	−0.0785892
$281$	950312.	0.717960	0.358980	−	0.933345i	$-0.383125\pi$
$281$	950312.	0.717960	0.358980	+	0.933345i	$0.383125\pi$
$282$	100639.	0.0753602
$283$	−1.17330e6	−0.870851	−0.435426	−	0.900225i	$-0.643402\pi$
$283$	−1.17330e6	−0.870851	−0.435426	+	0.900225i	$0.643402\pi$
$284$	−2.44405e6	−1.79810
$285$	−284601.	−0.207550
$286$	−407167.	−0.294346
$287$	1.68870e6	1.21017
$288$	−1.99040e6	−1.41403
$289$	−1.40227e6	−0.987616
$290$	−3.20048e6	−2.23470
$291$	−105950.	−0.0733449
$292$	−362082.	−0.248513
$293$	1.25185e6	0.851891	0.425946	−	0.904749i	$-0.359941\pi$
$293$	1.25185e6	0.851891	0.425946	+	0.904749i	$0.359941\pi$
$294$	356507.	0.240547
$295$	2.55546e6	1.70968
$296$	−9657.94	−0.00640701
$297$	−54855.7	−0.0360853
$298$	1.11708e6	0.728694
$299$	−1.44397e6	−0.934075
$300$	−251094.	−0.161077
$301$	2.26378e6	1.44018
$302$	1.68277e6	1.06171
$303$	−125734.	−0.0786766
$304$	2.87700e6	1.78549
$305$	4.19671e6	2.58321
$306$	−257802.	−0.157392
$307$	1.06133e6	0.642693	0.321347	−	0.946962i	$-0.395865\pi$
$307$	1.06133e6	0.642693	0.321347	+	0.946962i	$0.395865\pi$
$308$	996529.	0.598568
$309$	127566.	0.0760046
$310$	1.09815e6	0.649020
$311$	−1.16176e6	−0.681107	−0.340554	−	0.940225i	$-0.610614\pi$
$311$	−1.16176e6	−0.681107	−0.340554	+	0.940225i	$0.610614\pi$
$312$	−1491.19	−0.000867256 0
$313$	−2.15999e6	−1.24621	−0.623105	−	0.782138i	$-0.714129\pi$
$313$	−2.15999e6	−1.24621	−0.623105	+	0.782138i	$0.714129\pi$
$314$	−2.83763e6	−1.62417
$315$	−6.55605e6	−3.72277
$316$	2.07692e6	1.17004
$317$	174528.	0.0975475	0.0487737	−	0.998810i	$-0.484469\pi$
$317$	174528.	0.0975475	0.0487737	+	0.998810i	$0.484469\pi$
$318$	−21077.8	−0.0116885
$319$	451725.	0.248540
$320$	3.60142e6	1.96607
$321$	38984.1	0.0211167
$322$	7.01656e6	3.77124
$323$	378243.	0.201727
$324$	1.89692e6	1.00389
$325$	−3.46745e6	−1.82097
$326$	−3.21120e6	−1.67349
$327$	−93483.2	−0.0483464
$328$	25353.8	0.0130124
$329$	−3.40139e6	−1.73248
$330$	96937.8	0.0490014
$331$	−747340.	−0.374928	−0.187464	−	0.982271i	$-0.560027\pi$
$331$	−747340.	−0.374928	−0.187464	+	0.982271i	$0.560027\pi$
$332$	3.29714e6	1.64169
$333$	−614143.	−0.303500
$334$	4.44079e6	2.17818
$335$	−531729.	−0.258868
$336$	−239038.	−0.115510
$337$	1.37900e6	0.661438	0.330719	−	0.943729i	$-0.392709\pi$
$337$	1.37900e6	0.661438	0.330719	+	0.943729i	$0.392709\pi$
$338$	1.57112e6	0.748029
$339$	75639.8	0.0357479
$340$	459750.	0.215687
$341$	−154996.	−0.0721831
$342$	−5.54570e6	−2.56384
$343$	−7.78684e6	−3.57376
$344$	33988.0	0.0154857
$345$	343779.	0.155501
$346$	1.65126e6	0.741525
$347$	−381220.	−0.169962	−0.0849810	−	0.996383i	$-0.527083\pi$
$347$	−381220.	−0.169962	−0.0849810	+	0.996383i	$0.527083\pi$
$348$	113294.	0.0501487
$349$	3.42528e6	1.50533	0.752665	−	0.658403i	$-0.228768\pi$
$349$	3.42528e6	1.50533	0.752665	+	0.658403i	$0.228768\pi$
$350$	1.68490e7	7.35199
$351$	−189990.	−0.0823120
$352$	−994679.	−0.427884
$353$	−222498.	−0.0950361	−0.0475181	−	0.998870i	$-0.515131\pi$
$353$	−222498.	−0.0950361	−0.0475181	+	0.998870i	$0.515131\pi$
$354$	−179602.	−0.0761732
$355$	8.03535e6	3.38403
$356$	−282314.	−0.118061
$357$	−31426.6	−0.0130505
$358$	−3.99987e6	−1.64945
$359$	−172868.	−0.0707912	−0.0353956	−	0.999373i	$-0.511269\pi$
$359$	−172868.	−0.0707912	−0.0353956	+	0.999373i	$0.511269\pi$
$360$	−98431.5	−0.0400293
$361$	5.66048e6	2.28605
$362$	−206527.	−0.0828333
$363$	−13682.1	−0.00544986
$364$	3.45143e6	1.36536
$365$	1.19042e6	0.467702
$366$	−294951.	−0.115092
$367$	482201.	0.186880	0.0934401	−	0.995625i	$-0.470214\pi$
$367$	482201.	0.186880	0.0934401	+	0.995625i	$0.470214\pi$
$368$	−3.47523e6	−1.33772
$369$	1.61223e6	0.616400
$370$	2.17447e6	0.825751
$371$	712390.	0.268710
$372$	−38873.7	−0.0145646
$373$	4.30374e6	1.60167	0.800837	−	0.598883i	$-0.204388\pi$
$373$	4.30374e6	1.60167	0.800837	+	0.598883i	$0.204388\pi$
$374$	−128833.	−0.0476266
$375$	513734.	0.188651
$376$	−51068.0	−0.0186285
$377$	1.56453e6	0.566930
$378$	923200.	0.332327
$379$	849707.	0.303858	0.151929	−	0.988391i	$-0.451451\pi$
$379$	849707.	0.303858	0.151929	+	0.988391i	$0.451451\pi$
$380$	9.88993e6	3.51345
$381$	16190.9	0.00571426
$382$	−4.93905e6	−1.73175
$383$	−1.37516e6	−0.479022	−0.239511	−	0.970894i	$-0.576987\pi$
$383$	−1.37516e6	−0.479022	−0.239511	+	0.970894i	$0.576987\pi$
$384$	−7286.54	−0.00252170
$385$	−3.27631e6	−1.12651
$386$	6.11794e6	2.08996
$387$	2.16128e6	0.733556
$388$	3.68180e6	1.24160
$389$	1.18163e6	0.395919	0.197960	−	0.980210i	$-0.436568\pi$
$389$	1.18163e6	0.395919	0.197960	+	0.980210i	$0.436568\pi$
$390$	335739.	0.111774
$391$	−456893.	−0.151138
$392$	−180906.	−0.0594616
$393$	−180662.	−0.0590045
$394$	3.79920e6	1.23297
$395$	−6.82833e6	−2.20202
$396$	951407.	0.304880
$397$	86490.5	0.0275418	0.0137709	−	0.999905i	$-0.495616\pi$
$397$	86490.5	0.0275418	0.0137709	+	0.999905i	$0.495616\pi$
$398$	−4.09686e6	−1.29641
$399$	−676034.	−0.212587
$400$	−8.34517e6	−2.60787
$401$	668738.	0.207680	0.103840	−	0.994594i	$-0.466887\pi$
$401$	668738.	0.207680	0.103840	+	0.994594i	$0.466887\pi$
$402$	37370.7	0.0115336
$403$	−536822.	−0.164652
$404$	4.36928e6	1.33185
$405$	−6.23654e6	−1.88932
$406$	−7.60235e6	−2.28893
$407$	−306911.	−0.0918388
$408$	−471.834	−0.000140326 0
$409$	−2.44044e6	−0.721373	−0.360687	−	0.932687i	$-0.617458\pi$
$409$	−2.44044e6	−0.721373	−0.360687	+	0.932687i	$0.617458\pi$
$410$	−5.70837e6	−1.67708
$411$	361035.	0.105425
$412$	−4.43296e6	−1.28662
$413$	6.07019e6	1.75117
$414$	6.69885e6	1.92088
$415$	−1.08401e7	−3.08967
$416$	−3.44502e6	−0.976020
$417$	−118589.	−0.0333967
$418$	−2.77140e6	−0.775816
$419$	421807.	0.117376	0.0586879	−	0.998276i	$-0.481308\pi$
$419$	421807.	0.117376	0.0586879	+	0.998276i	$0.481308\pi$
$420$	−821712.	−0.227298
$421$	4.37683e6	1.20352	0.601762	−	0.798676i	$-0.294466\pi$
$421$	4.37683e6	1.20352	0.601762	+	0.798676i	$0.294466\pi$
$422$	3.95109e6	1.08003
$423$	−3.24738e6	−0.882435
$424$	10695.7	0.00288932
$425$	−1.09715e6	−0.294641
$426$	−564736.	−0.150772
$427$	9.96876e6	2.64589
$428$	−1.35471e6	−0.357467
$429$	−47387.2	−0.0124313
$430$	−7.65234e6	−1.99583
$431$	4.45587e6	1.15542	0.577709	−	0.816243i	$-0.303947\pi$
$431$	4.45587e6	1.15542	0.577709	+	0.816243i	$0.303947\pi$
$432$	−457252.	−0.117882
$433$	−2.54283e6	−0.651774	−0.325887	−	0.945409i	$-0.605663\pi$
$433$	−2.54283e6	−0.651774	−0.325887	+	0.945409i	$0.605663\pi$
$434$	2.60853e6	0.664769
$435$	−372480.	−0.0943800
$436$	3.24856e6	0.818417
$437$	−9.82847e6	−2.46197
$438$	−83664.7	−0.0208381
$439$	7.91186e6	1.95937	0.979687	−	0.200533i	$-0.0642675\pi$
$439$	7.91186e6	1.95937	0.979687	+	0.200533i	$0.0642675\pi$
$440$	−49190.0	−0.0121128
$441$	−1.15037e7	−2.81670
$442$	−446208.	−0.108638
$443$	1.64743e6	0.398838	0.199419	−	0.979914i	$-0.436095\pi$
$443$	1.64743e6	0.398838	0.199419	+	0.979914i	$0.436095\pi$
$444$	−76974.4	−0.0185306
$445$	928171.	0.222192
$446$	2.05134e6	0.488315
$447$	130009.	0.0307755
$448$	8.55474e6	2.01378
$449$	6.01554e6	1.40818	0.704091	−	0.710110i	$-0.251355\pi$
$449$	6.01554e6	1.40818	0.704091	+	0.710110i	$0.251355\pi$
$450$	1.60861e7	3.74473
$451$	805696.	0.186522
$452$	−2.62850e6	−0.605148
$453$	195845.	0.0448401
$454$	2.80390e6	0.638444
$455$	−1.13474e7	−2.56960
$456$	−10149.9	−0.00228585
$457$	1.11543e6	0.249835	0.124918	−	0.992167i	$-0.460133\pi$
$457$	1.11543e6	0.249835	0.124918	+	0.992167i	$0.460133\pi$
$458$	−1.11755e7	−2.48946
$459$	−60115.5	−0.0133185
$460$	−1.19464e7	−2.63234
$461$	−3.39925e6	−0.744957	−0.372479	−	0.928041i	$-0.621492\pi$
$461$	−3.39925e6	−0.744957	−0.372479	+	0.928041i	$0.621492\pi$
$462$	230264.	0.0501904
$463$	−2.77692e6	−0.602021	−0.301010	−	0.953621i	$-0.597324\pi$
$463$	−2.77692e6	−0.602021	−0.301010	+	0.953621i	$0.597324\pi$
$464$	3.76537e6	0.811919
$465$	127806.	0.0274106
$466$	5.66642e6	1.20877
$467$	−7.58745e6	−1.60992	−0.804959	−	0.593331i	$-0.797813\pi$
$467$	−7.58745e6	−1.60992	−0.804959	+	0.593331i	$0.797813\pi$
$468$	3.29516e6	0.695443
$469$	−1.26306e6	−0.265150
$470$	1.14979e7	2.40089
$471$	−330251.	−0.0685949
$472$	91136.9	0.0188295
$473$	1.08007e6	0.221973
$474$	479905.	0.0981090
$475$	−2.36014e7	−4.79958
$476$	1.09208e6	0.220921
$477$	680134.	0.136867
$478$	8.29341e6	1.66021
$479$	−3.15756e6	−0.628800	−0.314400	−	0.949291i	$-0.601803\pi$
$479$	−3.15756e6	−0.628800	−0.314400	+	0.949291i	$0.601803\pi$
$480$	820186.	0.162483
$481$	−1.06297e6	−0.209488
$482$	6.34509e6	1.24400
$483$	816606.	0.159274
$484$	475455.	0.0922563
$485$	−1.21047e7	−2.33669
$486$	1.32289e6	0.254058
$487$	6.02704e6	1.15155	0.575773	−	0.817609i	$-0.304701\pi$
$487$	6.02704e6	1.15155	0.575773	+	0.817609i	$0.304701\pi$
$488$	149669.	0.0284501
$489$	−373727.	−0.0706778
$490$	4.07306e7	7.66356
$491$	9.71566e6	1.81873	0.909365	−	0.415998i	$-0.136568\pi$
$491$	9.71566e6	1.81873	0.909365	+	0.415998i	$0.136568\pi$
$492$	202072.	0.0376351
$493$	495038.	0.0917320
$494$	−9.59862e6	−1.76967
$495$	−3.12796e6	−0.573784
$496$	−1.29198e6	−0.235804
$497$	1.90870e7	3.46615
$498$	761856.	0.137657
$499$	3.78982e6	0.681346	0.340673	−	0.940182i	$-0.389345\pi$
$499$	3.78982e6	0.681346	0.340673	+	0.940182i	$0.389345\pi$
$500$	−1.78524e7	−3.19353
$501$	516831.	0.0919929
$502$	8.71830e6	1.54409
$503$	−144871.	−0.0255306	−0.0127653	−	0.999919i	$-0.504063\pi$
$503$	−144871.	−0.0255306	−0.0127653	+	0.999919i	$0.504063\pi$
$504$	−233812.	−0.0410006
$505$	−1.43650e7	−2.50655
$506$	3.34767e6	0.581255
$507$	182851.	0.0315921
$508$	−562639.	−0.0967320
$509$	9.43631e6	1.61439	0.807194	−	0.590286i	$-0.200985\pi$
$509$	9.43631e6	1.61439	0.807194	+	0.590286i	$0.200985\pi$
$510$	106233.	0.0180856
$511$	2.82771e6	0.479052
$512$	−8.41408e6	−1.41851
$513$	−1.29317e6	−0.216952
$514$	−135379.	−0.0226018
$515$	1.45743e7	2.42142
$516$	270887.	0.0447882
$517$	−1.62284e6	−0.267024
$518$	5.16519e6	0.845788
$519$	192178.	0.0313174
$520$	−170367.	−0.0276298
$521$	−5.54574e6	−0.895087	−0.447544	−	0.894262i	$-0.647701\pi$
$521$	−5.54574e6	−0.895087	−0.447544	+	0.894262i	$0.647701\pi$
$522$	−7.25812e6	−1.16586
$523$	−9.06277e6	−1.44879	−0.724397	−	0.689383i	$-0.757882\pi$
$523$	−9.06277e6	−1.44879	−0.724397	+	0.689383i	$0.757882\pi$
$524$	6.27803e6	0.998839
$525$	1.96094e6	0.310503
$526$	4.42174e6	0.696833
$527$	−169858.	−0.0266415
$528$	−114047.	−0.0178033
$529$	5.43582e6	0.844551
$530$	−2.40812e6	−0.372382
$531$	5.79534e6	0.891954
$532$	2.34923e7	3.59871
$533$	2.79049e6	0.425463
$534$	−65233.2	−0.00989955
$535$	4.45390e6	0.672753
$536$	−18963.3	−0.00285104
$537$	−465516.	−0.0696624
$538$	−3.98160e6	−0.593065
$539$	−5.74883e6	−0.852330
$540$	−1.57184e6	−0.231966
$541$	−3.57964e6	−0.525831	−0.262915	−	0.964819i	$-0.584684\pi$
$541$	−3.57964e6	−0.525831	−0.262915	+	0.964819i	$0.584684\pi$
$542$	−9.02408e6	−1.31949
$543$	−24036.1	−0.00349836
$544$	−1.09005e6	−0.157925
$545$	−1.06804e7	−1.54026
$546$	797508.	0.114486
$547$	9.89402e6	1.41385	0.706927	−	0.707286i	$-0.250081\pi$
$547$	9.89402e6	1.41385	0.706927	+	0.707286i	$0.250081\pi$
$548$	−1.25460e7	−1.78466
$549$	9.51739e6	1.34768
$550$	8.03886e6	1.13315
$551$	1.06490e7	1.49427
$552$	12260.4	0.00171260
$553$	−1.62199e7	−2.25546
$554$	−1.74971e7	−2.42210
$555$	253070.	0.0348746
$556$	4.12098e6	0.565345
$557$	2.37861e6	0.324851	0.162426	−	0.986721i	$-0.448068\pi$
$557$	2.37861e6	0.324851	0.162426	+	0.986721i	$0.448068\pi$
$558$	2.49041e6	0.338599
$559$	3.74078e6	0.506329
$560$	−2.73098e7	−3.68001
$561$	−14994.0	−0.00201145
$562$	−7.63061e6	−1.01910
$563$	−447386.	−0.0594855	−0.0297428	−	0.999558i	$-0.509469\pi$
$563$	−447386.	−0.0594855	−0.0297428	+	0.999558i	$0.509469\pi$
$564$	−407015.	−0.0538782
$565$	8.64177e6	1.13889
$566$	9.42113e6	1.23612
$567$	−1.48142e7	−1.93517
$568$	286569.	0.0372699
$569$	8.51037e6	1.10197	0.550983	−	0.834517i	$-0.314253\pi$
$569$	8.51037e6	1.10197	0.550983	+	0.834517i	$0.314253\pi$
$570$	2.28522e6	0.294606
$571$	−7.30109e6	−0.937125	−0.468563	−	0.883430i	$-0.655228\pi$
$571$	−7.30109e6	−0.937125	−0.468563	+	0.883430i	$0.655228\pi$
$572$	1.64672e6	0.210440
$573$	−574820.	−0.0731383
$574$	−1.35595e7	−1.71777
$575$	2.85089e7	3.59593
$576$	8.16739e6	1.02572
$577$	8.17034e6	1.02165	0.510823	−	0.859686i	$-0.329341\pi$
$577$	8.17034e6	1.02165	0.510823	+	0.859686i	$0.329341\pi$
$578$	1.12597e7	1.40187
$579$	712022.	0.0882668
$580$	1.29438e7	1.59768
$581$	−2.57493e7	−3.16464
$582$	850737.	0.104109
$583$	339889.	0.0414158
$584$	42454.7	0.00515103
$585$	−1.08336e7	−1.30882
$586$	−1.00519e7	−1.20921
$587$	1.34853e7	1.61534	0.807672	−	0.589631i	$-0.200727\pi$
$587$	1.34853e7	1.61534	0.807672	+	0.589631i	$0.200727\pi$
$588$	−1.44183e6	−0.171977
$589$	−3.65390e6	−0.433979
$590$	−2.05193e7	−2.42679
$591$	442161.	0.0520729
$592$	−2.55827e6	−0.300014
$593$	−1.05634e7	−1.23358	−0.616791	−	0.787127i	$-0.711568\pi$
$593$	−1.05634e7	−1.23358	−0.616791	+	0.787127i	$0.711568\pi$
$594$	440468.	0.0512211
$595$	−3.59046e6	−0.415774
$596$	−4.51785e6	−0.520974
$597$	−476803.	−0.0547524
$598$	1.15945e7	1.32587
$599$	7.00080e6	0.797224	0.398612	−	0.917120i	$-0.369492\pi$
$599$	7.00080e6	0.797224	0.398612	+	0.917120i	$0.369492\pi$
$600$	29441.2	0.00333870
$601$	−1.15553e7	−1.30495	−0.652476	−	0.757810i	$-0.726270\pi$
$601$	−1.15553e7	−1.30495	−0.652476	+	0.757810i	$0.726270\pi$
$602$	−1.81772e7	−2.04426
$603$	−1.20587e6	−0.135054
$604$	−6.80565e6	−0.759062
$605$	−1.56316e6	−0.173626
$606$	1.00959e6	0.111677
$607$	574325.	0.0632682	0.0316341	−	0.999500i	$-0.489929\pi$
$607$	574325.	0.0632682	0.0316341	+	0.999500i	$0.489929\pi$
$608$	−2.34487e7	−2.57252
$609$	−884781.	−0.0966702
$610$	−3.36978e7	−3.66671
$611$	−5.62064e6	−0.609091
$612$	1.04263e6	0.112526
$613$	6.84316e6	0.735538	0.367769	−	0.929917i	$-0.380122\pi$
$613$	6.84316e6	0.735538	0.367769	+	0.929917i	$0.380122\pi$
$614$	−8.52202e6	−0.912267
$615$	−664355.	−0.0708292
$616$	−116845.	−0.0124067
$617$	−1.21710e7	−1.28710	−0.643550	−	0.765404i	$-0.722539\pi$
$617$	−1.21710e7	−1.28710	−0.643550	+	0.765404i	$0.722539\pi$
$618$	−1.02430e6	−0.107884
$619$	4.56141e6	0.478490	0.239245	−	0.970959i	$-0.423100\pi$
$619$	4.56141e6	0.478490	0.239245	+	0.970959i	$0.423100\pi$
$620$	−4.44128e6	−0.464011
$621$	1.56207e6	0.162544
$622$	9.32845e6	0.966793
$623$	2.20476e6	0.227583
$624$	−394998.	−0.0406101
$625$	3.28373e7	3.36254
$626$	1.73438e7	1.76893
$627$	−322543.	−0.0327656
$628$	1.14763e7	1.16119
$629$	−336338.	−0.0338961
$630$	5.26424e7	5.28426
$631$	−2.60550e6	−0.260506	−0.130253	−	0.991481i	$-0.541579\pi$
$631$	−2.60550e6	−0.260506	−0.130253	+	0.991481i	$0.541579\pi$
$632$	−243522.	−0.0242519
$633$	459838.	0.0456137
$634$	−1.40138e6	−0.138463
$635$	1.84980e6	0.182050
$636$	85245.5	0.00835658
$637$	−1.99108e7	−1.94420
$638$	−3.62716e6	−0.352789
$639$	1.82228e7	1.76548
$640$	−832480.	−0.0803385
$641$	3.44890e6	0.331540	0.165770	−	0.986164i	$-0.446989\pi$
$641$	3.44890e6	0.331540	0.165770	+	0.986164i	$0.446989\pi$
$642$	−313026.	−0.0299739
$643$	8.36039e6	0.797442	0.398721	−	0.917072i	$-0.369454\pi$
$643$	8.36039e6	0.797442	0.398721	+	0.917072i	$0.369454\pi$
$644$	−2.83772e7	−2.69622
$645$	−890600.	−0.0842914
$646$	−3.03713e6	−0.286340
$647$	−1.17115e7	−1.09990	−0.549950	−	0.835198i	$-0.685353\pi$
$647$	−1.17115e7	−1.09990	−0.549950	+	0.835198i	$0.685353\pi$
$648$	−222417.	−0.0208080
$649$	2.89615e6	0.269904
$650$	2.78422e7	2.58476
$651$	303587.	0.0280757
$652$	1.29871e7	1.19645
$653$	8.14901e6	0.747863	0.373931	−	0.927456i	$-0.378010\pi$
$653$	8.14901e6	0.747863	0.373931	+	0.927456i	$0.378010\pi$
$654$	750631.	0.0686250
$655$	−2.06404e7	−1.87982
$656$	6.71591e6	0.609320
$657$	2.69967e6	0.244004
$658$	2.73118e7	2.45915
$659$	−694775.	−0.0623204	−0.0311602	−	0.999514i	$-0.509920\pi$
$659$	−694775.	−0.0623204	−0.0311602	+	0.999514i	$0.509920\pi$
$660$	−392047.	−0.0350331
$661$	−517794.	−0.0460950	−0.0230475	−	0.999734i	$-0.507337\pi$
$661$	−517794.	−0.0460950	−0.0230475	+	0.999734i	$0.507337\pi$
$662$	6.00083e6	0.532189
$663$	−51930.9	−0.00458820
$664$	−386595.	−0.0340280
$665$	−7.72362e7	−6.77278
$666$	4.93131e6	0.430801
$667$	−1.28633e7	−1.11954
$668$	−1.79600e7	−1.55727
$669$	238740.	0.0206234
$670$	4.26956e6	0.367448
$671$	4.75620e6	0.407806
$672$	1.94825e6	0.166426
$673$	1.93323e7	1.64530	0.822652	−	0.568545i	$-0.192494\pi$
$673$	1.93323e7	1.64530	0.822652	+	0.568545i	$0.192494\pi$
$674$	−1.10728e7	−0.938874
$675$	3.75105e6	0.316879
$676$	−6.35412e6	−0.534797
$677$	1.47788e6	0.123928	0.0619639	−	0.998078i	$-0.480264\pi$
$677$	1.47788e6	0.123928	0.0619639	+	0.998078i	$0.480264\pi$
$678$	−607356.	−0.0507422
$679$	−2.87533e7	−2.39339
$680$	−53906.5	−0.00447063
$681$	326325.	0.0269639
$682$	1.24456e6	0.102460
$683$	−7.39683e6	−0.606728	−0.303364	−	0.952875i	$-0.598110\pi$
$683$	−7.39683e6	−0.606728	−0.303364	+	0.952875i	$0.598110\pi$
$684$	2.24286e7	1.83300
$685$	4.12479e7	3.35873
$686$	6.25251e7	5.07276
$687$	−1.30064e6	−0.105139
$688$	9.00300e6	0.725130
$689$	1.17719e6	0.0944710
$690$	−2.76040e6	−0.220724
$691$	4.69205e6	0.373824	0.186912	−	0.982377i	$-0.440152\pi$
$691$	4.69205e6	0.373824	0.186912	+	0.982377i	$0.440152\pi$
$692$	−6.67823e6	−0.530147
$693$	−7.43009e6	−0.587708
$694$	3.06104e6	0.241251
$695$	−1.35486e7	−1.06398
$696$	−13284.0	−0.00103945
$697$	882949.	0.0688420
$698$	−2.75035e7	−2.13673
$699$	659473.	0.0510510
$700$	−6.81429e7	−5.25625
$701$	1.88997e7	1.45265	0.726324	−	0.687352i	$-0.241227\pi$
$701$	1.88997e7	1.45265	0.726324	+	0.687352i	$0.241227\pi$
$702$	1.52554e6	0.116837
$703$	−7.23515e6	−0.552153
$704$	4.08156e6	0.310380
$705$	1.33815e6	0.101399
$706$	1.78656e6	0.134898
$707$	−3.41222e7	−2.56737
$708$	726367.	0.0544594
$709$	9.54037e6	0.712770	0.356385	−	0.934339i	$-0.384009\pi$
$709$	9.54037e6	0.712770	0.356385	+	0.934339i	$0.384009\pi$
$710$	−6.45205e7	−4.80344
$711$	−1.54854e7	−1.14881
$712$	33101.9	0.00244710
$713$	4.41368e6	0.325145
$714$	252342.	0.0185244
$715$	−5.41394e6	−0.396049
$716$	1.61768e7	1.17926
$717$	965209.	0.0701171
$718$	1.38806e6	0.100484
$719$	−9.53236e6	−0.687667	−0.343834	−	0.939031i	$-0.611726\pi$
$719$	−9.53236e6	−0.687667	−0.343834	+	0.939031i	$0.611726\pi$
$720$	−2.60733e7	−1.87441
$721$	3.46195e7	2.48018
$722$	−4.54513e7	−3.24491
$723$	738458.	0.0525388
$724$	835260.	0.0592210
$725$	−3.08890e7	−2.18253
$726$	109861.	0.00773577
$727$	−5.42385e6	−0.380603	−0.190301	−	0.981726i	$-0.560947\pi$
$727$	−5.42385e6	−0.380603	−0.190301	+	0.981726i	$0.560947\pi$
$728$	−404687.	−0.0283003
$729$	−1.40404e7	−0.978502
$730$	−9.55861e6	−0.663877
$731$	1.18363e6	0.0819265
$732$	1.19287e6	0.0822843
$733$	−1.19190e7	−0.819368	−0.409684	−	0.912227i	$-0.634361\pi$
$733$	−1.19190e7	−0.819368	−0.409684	+	0.912227i	$0.634361\pi$
$734$	−3.87188e6	−0.265266
$735$	4.74033e6	0.323661
$736$	2.83245e7	1.92738
$737$	−602618.	−0.0408671
$738$	−1.29456e7	−0.874944
$739$	8.69866e6	0.585924	0.292962	−	0.956124i	$-0.405359\pi$
$739$	8.69866e6	0.585924	0.292962	+	0.956124i	$0.405359\pi$
$740$	−8.79425e6	−0.590363
$741$	−1.11711e6	−0.0747397
$742$	−5.72020e6	−0.381418
$743$	−2.34525e7	−1.55854	−0.779268	−	0.626691i	$-0.784409\pi$
$743$	−2.34525e7	−1.55854	−0.779268	+	0.626691i	$0.784409\pi$
$744$	4558.01	0.000301886 0
$745$	1.48534e7	0.980473
$746$	−3.45572e7	−2.27348
$747$	−2.45834e7	−1.61191
$748$	521043.	0.0340502
$749$	1.05797e7	0.689078
$750$	−4.12507e6	−0.267780
$751$	−1.94475e7	−1.25824	−0.629120	−	0.777308i	$-0.716585\pi$
$751$	−1.94475e7	−1.25824	−0.629120	+	0.777308i	$0.716585\pi$
$752$	−1.35273e7	−0.872299
$753$	1.01466e6	0.0652127
$754$	−1.25625e7	−0.804725
$755$	2.23751e7	1.42856
$756$	−3.73371e6	−0.237595
$757$	1.56133e7	0.990275	0.495137	−	0.868815i	$-0.335118\pi$
$757$	1.56133e7	0.990275	0.495137	+	0.868815i	$0.335118\pi$
$758$	−6.82279e6	−0.431310
$759$	389611.	0.0245486
$760$	−1.15961e6	−0.0728247
$761$	2.58210e7	1.61626	0.808130	−	0.589004i	$-0.200480\pi$
$761$	2.58210e7	1.61626	0.808130	+	0.589004i	$0.200480\pi$
$762$	−130007.	−0.00811106
$763$	−2.53699e7	−1.57764
$764$	1.99751e7	1.23810
$765$	−3.42788e6	−0.211774
$766$	1.10420e7	0.679945
$767$	1.00307e7	0.615662
$768$	−950214.	−0.0581324
$769$	−1.10884e7	−0.676167	−0.338084	−	0.941116i	$-0.609779\pi$
$769$	−1.10884e7	−0.676167	−0.338084	+	0.941116i	$0.609779\pi$
$770$	2.63074e7	1.59901
$771$	−15755.7	−0.000954558 0
$772$	−2.47429e7	−1.49420
$773$	1.59907e7	0.962538	0.481269	−	0.876573i	$-0.340176\pi$
$773$	1.59907e7	0.962538	0.481269	+	0.876573i	$0.340176\pi$
$774$	−1.73542e7	−1.04124
$775$	1.05987e7	0.633866
$776$	−431697.	−0.0257350
$777$	601138.	0.0357208
$778$	−9.48798e6	−0.561985
$779$	1.89936e7	1.12141
$780$	−1.35784e6	−0.0799119
$781$	9.10661e6	0.534231
$782$	3.66866e6	0.214531
$783$	−1.69248e6	−0.0986553
$784$	−4.79196e7	−2.78435
$785$	−3.77308e7	−2.18536
$786$	1.45064e6	0.0837535
$787$	−237970.	−0.0136957	−0.00684786	−	0.999977i	$-0.502180\pi$
$787$	−237970.	−0.0136957	−0.00684786	+	0.999977i	$0.502180\pi$
$788$	−1.53652e7	−0.881500
$789$	514614.	0.0294299
$790$	5.48286e7	3.12564
$791$	2.05275e7	1.16653
$792$	−111554.	−0.00631936
$793$	1.64729e7	0.930222
$794$	−694483.	−0.0390940
$795$	−280263.	−0.0157271
$796$	1.65690e7	0.926859
$797$	6.22172e6	0.346948	0.173474	−	0.984838i	$-0.444501\pi$
$797$	6.22172e6	0.346948	0.173474	+	0.984838i	$0.444501\pi$
$798$	5.42827e6	0.301755
$799$	−1.77845e6	−0.0985539
$800$	6.80164e7	3.75741
$801$	2.10493e6	0.115919
$802$	−5.36969e6	−0.294790
$803$	1.34913e6	0.0738354
$804$	−151139.	−0.00824587
$805$	9.32964e7	5.07429
$806$	4.31046e6	0.233715
$807$	−463389.	−0.0250474
$808$	−512305.	−0.0276058
$809$	6.41617e6	0.344671	0.172336	−	0.985038i	$-0.444869\pi$
$809$	6.41617e6	0.344671	0.172336	+	0.985038i	$0.444869\pi$
$810$	5.00769e7	2.68179
$811$	−1.74790e7	−0.933179	−0.466590	−	0.884474i	$-0.654518\pi$
$811$	−1.74790e7	−0.933179	−0.466590	+	0.884474i	$0.654518\pi$
$812$	3.07463e7	1.63645
$813$	−1.05025e6	−0.0557269
$814$	2.46436e6	0.130360
$815$	−4.26980e7	−2.25171
$816$	−124983.	−0.00657090
$817$	2.54618e7	1.33455
$818$	1.95957e7	1.02395
$819$	−2.57338e7	−1.34058
$820$	2.30865e7	1.19901
$821$	−2.38750e6	−0.123619	−0.0618095	−	0.998088i	$-0.519687\pi$
$821$	−2.38750e6	−0.123619	−0.0618095	+	0.998088i	$0.519687\pi$
$822$	−2.89896e6	−0.149645
$823$	−9.09768e6	−0.468200	−0.234100	−	0.972213i	$-0.575214\pi$
$823$	−9.09768e6	−0.468200	−0.234100	+	0.972213i	$0.575214\pi$
$824$	519772.	0.0266683
$825$	935584.	0.0478572
$826$	−4.87411e7	−2.48568
$827$	1.93449e7	0.983565	0.491782	−	0.870718i	$-0.336346\pi$
$827$	1.93449e7	0.983565	0.491782	+	0.870718i	$0.336346\pi$
$828$	−2.70923e7	−1.37332
$829$	2.03233e6	0.102709	0.0513545	−	0.998680i	$-0.483646\pi$
$829$	2.03233e6	0.102709	0.0513545	+	0.998680i	$0.483646\pi$
$830$	8.70413e7	4.38561
$831$	−2.03636e6	−0.102294
$832$	1.41363e7	0.707989
$833$	−6.30005e6	−0.314580
$834$	952218.	0.0474047
$835$	5.90474e7	2.93079
$836$	1.12084e7	0.554663
$837$	580727.	0.0286522
$838$	−3.38693e6	−0.166608
$839$	−1.83849e7	−0.901690	−0.450845	−	0.892602i	$-0.648877\pi$
$839$	−1.83849e7	−0.901690	−0.450845	+	0.892602i	$0.648877\pi$
$840$	96347.2	0.00471130
$841$	−6.57391e6	−0.320504
$842$	−3.51441e7	−1.70833
$843$	−888070.	−0.0430406
$844$	−1.59795e7	−0.772158
$845$	2.08906e7	1.00649
$846$	2.60751e7	1.25257
$847$	−3.71310e6	−0.177840
$848$	2.83316e6	0.135295
$849$	1.09646e6	0.0522062
$850$	8.80965e6	0.418227
$851$	8.73960e6	0.413683
$852$	2.28397e6	0.107793
$853$	1.77316e7	0.834400	0.417200	−	0.908815i	$-0.363012\pi$
$853$	1.77316e7	0.834400	0.417200	+	0.908815i	$0.363012\pi$
$854$	−8.00450e7	−3.75569
$855$	−7.37390e7	−3.44970
$856$	158842.	0.00740935
$857$	2.57555e7	1.19789	0.598947	−	0.800789i	$-0.295586\pi$
$857$	2.57555e7	1.19789	0.598947	+	0.800789i	$0.295586\pi$
$858$	380500.	0.0176456
$859$	3.05210e7	1.41129	0.705645	−	0.708566i	$-0.250658\pi$
$859$	3.05210e7	1.41129	0.705645	+	0.708566i	$0.250658\pi$
$860$	3.09485e7	1.42690
$861$	−1.57809e6	−0.0725480
$862$	−3.57788e7	−1.64005
$863$	3.80992e7	1.74136	0.870681	−	0.491848i	$-0.163678\pi$
$863$	3.80992e7	1.74136	0.870681	+	0.491848i	$0.163678\pi$
$864$	3.72678e6	0.169844
$865$	2.19562e7	0.997737
$866$	2.04178e7	0.925156
$867$	1.31043e6	0.0592061
$868$	−1.05497e7	−0.475271
$869$	−7.73867e6	−0.347630
$870$	2.99086e6	0.133967
$871$	−2.08714e6	−0.0932194
$872$	−380899.	−0.0169636
$873$	−2.74514e7	−1.21907
$874$	7.89185e7	3.49462
$875$	1.39420e8	6.15607
$876$	338367.	0.0148980
$877$	−4.21333e7	−1.84981	−0.924903	−	0.380203i	$-0.875854\pi$
$877$	−4.21333e7	−1.84981	−0.924903	+	0.380203i	$0.875854\pi$
$878$	−6.35289e7	−2.78122
$879$	−1.16986e6	−0.0510696
$880$	−1.30298e7	−0.567194
$881$	−1.32995e7	−0.577292	−0.288646	−	0.957436i	$-0.593205\pi$
$881$	−1.32995e7	−0.577292	−0.288646	+	0.957436i	$0.593205\pi$
$882$	9.23698e7	3.99814
$883$	4.34811e6	0.187672	0.0938358	−	0.995588i	$-0.470087\pi$
$883$	4.34811e6	0.187672	0.0938358	+	0.995588i	$0.470087\pi$
$884$	1.80461e6	0.0776698
$885$	−2.38809e6	−0.102493
$886$	−1.32281e7	−0.566128
$887$	1.71335e7	0.731202	0.365601	−	0.930772i	$-0.380863\pi$
$887$	1.71335e7	0.731202	0.365601	+	0.930772i	$0.380863\pi$
$888$	9025.38	0.000384090 0
$889$	4.39397e6	0.186467
$890$	−7.45283e6	−0.315389
$891$	−7.06799e6	−0.298265
$892$	−8.29626e6	−0.349117
$893$	−3.82571e7	−1.60540
$894$	−1.04392e6	−0.0436841
$895$	−5.31847e7	−2.21937
$896$	−1.97745e6	−0.0822880
$897$	1.34940e6	0.0559963
$898$	−4.83023e7	−1.99883
$899$	−4.78216e6	−0.197345
$900$	−6.50575e7	−2.67726
$901$	372479.	0.0152859
$902$	−6.46940e6	−0.264757
$903$	−2.11551e6	−0.0863368
$904$	308196.	0.0125431
$905$	−2.74610e6	−0.111454
$906$	−1.57255e6	−0.0636480
$907$	4.22612e7	1.70578	0.852892	−	0.522088i	$-0.174847\pi$
$907$	4.22612e7	1.70578	0.852892	+	0.522088i	$0.174847\pi$
$908$	−1.13399e7	−0.456450
$909$	−3.25772e7	−1.30769
$910$	9.11145e7	3.64741
$911$	181020.	0.00722655	0.00361328	−	0.999993i	$-0.498850\pi$
$911$	181020.	0.00722655	0.00361328	+	0.999993i	$0.498850\pi$
$912$	−2.68857e6	−0.107037
$913$	−1.22853e7	−0.487761
$914$	−8.95648e6	−0.354627
$915$	−3.92184e6	−0.154859
$916$	4.51974e7	1.77982
$917$	−4.90288e7	−1.92543
$918$	482702.	0.0189048
$919$	8.71012e6	0.340201	0.170100	−	0.985427i	$-0.445591\pi$
$919$	8.71012e6	0.340201	0.170100	+	0.985427i	$0.445591\pi$
$920$	1.40074e6	0.0545616
$921$	−991815.	−0.0385285
$922$	2.72946e7	1.05742
$923$	3.15403e7	1.21860
$924$	−931261.	−0.0358832
$925$	2.09866e7	0.806470
$926$	2.22975e7	0.854535
$927$	3.30520e7	1.26328
$928$	−3.06892e7	−1.16981
$929$	−1.12921e6	−0.0429275	−0.0214637	−	0.999770i	$-0.506833\pi$
$929$	−1.12921e6	−0.0429275	−0.0214637	+	0.999770i	$0.506833\pi$
$930$	−1.02623e6	−0.0389078
$931$	−1.35524e8	−5.12438
$932$	−2.29168e7	−0.864201
$933$	1.08567e6	0.0408313
$934$	6.09241e7	2.28519
$935$	−1.71305e6	−0.0640826
$936$	−386363.	−0.0144147
$937$	−1.01123e7	−0.376270	−0.188135	−	0.982143i	$-0.560244\pi$
$937$	−1.01123e7	−0.376270	−0.188135	+	0.982143i	$0.560244\pi$
$938$	1.01418e7	0.376365
$939$	2.01852e6	0.0747084
$940$	−4.65011e7	−1.71650
$941$	−4.90482e7	−1.80572	−0.902858	−	0.429940i	$-0.858535\pi$
$941$	−4.90482e7	−1.80572	−0.902858	+	0.429940i	$0.858535\pi$
$942$	2.65178e6	0.0973666
$943$	−2.29430e7	−0.840178
$944$	2.41410e7	0.881709
$945$	1.22754e7	0.447154
$946$	−8.67254e6	−0.315078
$947$	5.16516e7	1.87158	0.935791	−	0.352555i	$-0.114687\pi$
$947$	5.16516e7	1.87158	0.935791	+	0.352555i	$0.114687\pi$
$948$	−1.94089e6	−0.0701422
$949$	4.67265e6	0.168421
$950$	1.89509e8	6.81273
$951$	−163097.	−0.00584782
$952$	−128048.	−0.00457912
$953$	−6.23090e6	−0.222238	−0.111119	−	0.993807i	$-0.535443\pi$
$953$	−6.23090e6	−0.222238	−0.111119	+	0.993807i	$0.535443\pi$
$954$	−5.46119e6	−0.194275
$955$	−6.56726e7	−2.33011
$956$	−3.35412e7	−1.18695
$957$	−422139.	−0.0148996
$958$	2.53539e7	0.892545
$959$	9.79794e7	3.44023
$960$	−3.36554e6	−0.117863
$961$	−2.69883e7	−0.942686
$962$	8.53521e6	0.297356
$963$	1.01006e7	0.350981
$964$	−2.56616e7	−0.889386
$965$	8.13479e7	2.81208
$966$	−6.55700e6	−0.226080
$967$	3.39470e6	0.116744	0.0583721	−	0.998295i	$-0.481409\pi$
$967$	3.39470e6	0.116744	0.0583721	+	0.998295i	$0.481409\pi$
$968$	−55747.9	−0.00191223
$969$	−353470.	−0.0120932
$970$	9.71959e7	3.31679
$971$	−1.04629e7	−0.356125	−0.178062	−	0.984019i	$-0.556983\pi$
$971$	−1.04629e7	−0.356125	−0.178062	+	0.984019i	$0.556983\pi$
$972$	−5.35019e6	−0.181637
$973$	−3.21831e7	−1.08980
$974$	−4.83946e7	−1.63455
$975$	3.24035e6	0.109164
$976$	3.96455e7	1.33220
$977$	−1.21554e7	−0.407410	−0.203705	−	0.979032i	$-0.565298\pi$
$977$	−1.21554e7	−0.407410	−0.203705	+	0.979032i	$0.565298\pi$
$978$	3.00087e6	0.100323
$979$	1.05191e6	0.0350771
$980$	−1.64728e8	−5.47900
$981$	−2.42212e7	−0.803568
$982$	−7.80127e7	−2.58159
$983$	1.26967e7	0.419091	0.209545	−	0.977799i	$-0.432802\pi$
$983$	1.26967e7	0.419091	0.209545	+	0.977799i	$0.432802\pi$
$984$	−23693.3	−0.000780076 0
$985$	5.05164e7	1.65898
$986$	−3.97495e6	−0.130208
$987$	3.17862e6	0.103859
$988$	3.88199e7	1.26521
$989$	−3.07562e7	−0.999867
$990$	2.51162e7	0.814454
$991$	4.70380e6	0.152147	0.0760737	−	0.997102i	$-0.475762\pi$
$991$	4.70380e6	0.152147	0.0760737	+	0.997102i	$0.475762\pi$
$992$	1.05301e7	0.339746
$993$	698392.	0.0224764
$994$	−1.53261e8	−4.92000
$995$	−5.44742e7	−1.74435
$996$	−3.08119e6	−0.0984170
$997$	4.14545e7	1.32079	0.660395	−	0.750919i	$-0.270389\pi$
$997$	4.14545e7	1.32079	0.660395	+	0.750919i	$0.270389\pi$
$998$	−3.04307e7	−0.967132
$999$	1.14991e6	0.0364543

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	583.6.a.b.1.12	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
583.6.a.b.1.12	✓	54	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:	\( N \)	\(=\)	\( 583 = 11 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	583.a (trivial)

\(f(q)\)	\(=\)	\(q-8.02958 q^{2} -0.934504 q^{3} +32.4742 q^{4} -106.766 q^{5} +7.50368 q^{6} -253.610 q^{7} -3.80766 q^{8} -242.127 q^{9} +O(q^{10})\)	\(q-8.02958 q^{2} -0.934504 q^{3} +32.4742 q^{4} -106.766 q^{5} +7.50368 q^{6} -253.610 q^{7} -3.80766 q^{8} -242.127 q^{9} +857.288 q^{10} -121.000 q^{11} -30.3473 q^{12} -419.078 q^{13} +2036.38 q^{14} +99.7734 q^{15} -1008.60 q^{16} -132.602 q^{17} +1944.18 q^{18} -2852.47 q^{19} -3467.15 q^{20} +237.000 q^{21} +971.580 q^{22} +3445.60 q^{23} +3.55827 q^{24} +8274.01 q^{25} +3365.02 q^{26} +453.353 q^{27} -8235.78 q^{28} -3733.26 q^{29} -801.139 q^{30} +1280.96 q^{31} +8220.49 q^{32} +113.075 q^{33} +1064.74 q^{34} +27077.0 q^{35} -7862.87 q^{36} +2536.45 q^{37} +22904.1 q^{38} +391.630 q^{39} +406.529 q^{40} -6658.64 q^{41} -1903.01 q^{42} -8926.23 q^{43} -3929.38 q^{44} +25850.9 q^{45} -27666.7 q^{46} +13411.9 q^{47} +942.541 q^{48} +47511.0 q^{49} -66436.8 q^{50} +123.917 q^{51} -13609.2 q^{52} -2809.00 q^{53} -3640.23 q^{54} +12918.7 q^{55} +965.660 q^{56} +2665.64 q^{57} +29976.5 q^{58} -23935.2 q^{59} +3240.06 q^{60} -39307.5 q^{61} -10285.6 q^{62} +61405.7 q^{63} -33731.9 q^{64} +44743.3 q^{65} -907.945 q^{66} +4980.32 q^{67} -4306.14 q^{68} -3219.93 q^{69} -217417. q^{70} -75261.3 q^{71} +921.936 q^{72} -11149.8 q^{73} -20366.7 q^{74} -7732.10 q^{75} -92631.7 q^{76} +30686.8 q^{77} -3144.62 q^{78} +63955.9 q^{79} +107684. q^{80} +58413.1 q^{81} +53466.1 q^{82} +101531. q^{83} +7696.37 q^{84} +14157.4 q^{85} +71673.9 q^{86} +3488.75 q^{87} +460.727 q^{88} -8693.50 q^{89} -207572. q^{90} +106282. q^{91} +111893. q^{92} -1197.06 q^{93} -107692. q^{94} +304547. q^{95} -7682.08 q^{96} +113376. q^{97} -381494. q^{98} +29297.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 16 q^{2} + 906 q^{4} - 225 q^{5} - 197 q^{6} - 341 q^{7} - 1152 q^{8} + 4240 q^{9}+O(q^{10}) \) 54 * q - 16 * q^2 + 906 * q^4 - 225 * q^5 - 197 * q^6 - 341 * q^7 - 1152 * q^8 + 4240 * q^9	\( 54 q - 16 q^{2} + 906 q^{4} - 225 q^{5} - 197 q^{6} - 341 q^{7} - 1152 q^{8} + 4240 q^{9} - 233 q^{10} - 6534 q^{11} - 327 q^{12} - 1455 q^{13} + 2254 q^{14} - 694 q^{15} + 16610 q^{16} - 9275 q^{17} - 6797 q^{18} - 2515 q^{19} - 6840 q^{20} - 4744 q^{21} + 1936 q^{22} - 6307 q^{23} - 5681 q^{24} + 26923 q^{25} - 5196 q^{26} - 5190 q^{27} - 36405 q^{28} - 8356 q^{29} - 28719 q^{30} - 4357 q^{31} - 68580 q^{32} + 9406 q^{34} - 3747 q^{35} + 38059 q^{36} - 25798 q^{37} - 32169 q^{38} - 28347 q^{39} - 15014 q^{40} - 89685 q^{41} - 103207 q^{42} - 26640 q^{43} - 109626 q^{44} - 66786 q^{45} - 28271 q^{46} - 26237 q^{47} - 20371 q^{48} + 132327 q^{49} - 189646 q^{50} + 10856 q^{51} - 179789 q^{52} - 151686 q^{53} - 167182 q^{54} + 27225 q^{55} + 24845 q^{56} - 33857 q^{57} - 31384 q^{58} - 49035 q^{59} - 183481 q^{60} - 101718 q^{61} - 103315 q^{62} - 214794 q^{63} + 154912 q^{64} - 55703 q^{65} + 23837 q^{66} + 105905 q^{67} - 267681 q^{68} - 56033 q^{69} - 90034 q^{70} - 107016 q^{71} - 580829 q^{72} - 161641 q^{73} - 259552 q^{74} - 69519 q^{75} - 240846 q^{76} + 41261 q^{77} - 65716 q^{78} - 35649 q^{79} - 279887 q^{80} + 316682 q^{81} + 206196 q^{82} - 326347 q^{83} - 29955 q^{84} - 189486 q^{85} - 444656 q^{86} - 222331 q^{87} + 139392 q^{88} - 633400 q^{89} + 110940 q^{90} - 25954 q^{91} + 18304 q^{92} - 191747 q^{93} - 62405 q^{94} - 515756 q^{95} - 527591 q^{96} - 405641 q^{97} - 919621 q^{98} - 513040 q^{99}+O(q^{100}) \) 54 * q - 16 * q^2 + 906 * q^4 - 225 * q^5 - 197 * q^6 - 341 * q^7 - 1152 * q^8 + 4240 * q^9 - 233 * q^10 - 6534 * q^11 - 327 * q^12 - 1455 * q^13 + 2254 * q^14 - 694 * q^15 + 16610 * q^16 - 9275 * q^17 - 6797 * q^18 - 2515 * q^19 - 6840 * q^20 - 4744 * q^21 + 1936 * q^22 - 6307 * q^23 - 5681 * q^24 + 26923 * q^25 - 5196 * q^26 - 5190 * q^27 - 36405 * q^28 - 8356 * q^29 - 28719 * q^30 - 4357 * q^31 - 68580 * q^32 + 9406 * q^34 - 3747 * q^35 + 38059 * q^36 - 25798 * q^37 - 32169 * q^38 - 28347 * q^39 - 15014 * q^40 - 89685 * q^41 - 103207 * q^42 - 26640 * q^43 - 109626 * q^44 - 66786 * q^45 - 28271 * q^46 - 26237 * q^47 - 20371 * q^48 + 132327 * q^49 - 189646 * q^50 + 10856 * q^51 - 179789 * q^52 - 151686 * q^53 - 167182 * q^54 + 27225 * q^55 + 24845 * q^56 - 33857 * q^57 - 31384 * q^58 - 49035 * q^59 - 183481 * q^60 - 101718 * q^61 - 103315 * q^62 - 214794 * q^63 + 154912 * q^64 - 55703 * q^65 + 23837 * q^66 + 105905 * q^67 - 267681 * q^68 - 56033 * q^69 - 90034 * q^70 - 107016 * q^71 - 580829 * q^72 - 161641 * q^73 - 259552 * q^74 - 69519 * q^75 - 240846 * q^76 + 41261 * q^77 - 65716 * q^78 - 35649 * q^79 - 279887 * q^80 + 316682 * q^81 + 206196 * q^82 - 326347 * q^83 - 29955 * q^84 - 189486 * q^85 - 444656 * q^86 - 222331 * q^87 + 139392 * q^88 - 633400 * q^89 + 110940 * q^90 - 25954 * q^91 + 18304 * q^92 - 191747 * q^93 - 62405 * q^94 - 515756 * q^95 - 527591 * q^96 - 405641 * q^97 - 919621 * q^98 - 513040 * q^99

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