LMFDB - Embedded newform 354.6.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,6,Mod(1,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, 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("354.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	354.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:	$56.7758722138$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 290x^{3} - 616x^{2} + 4720x + 11900 $ x^5 - x^4 - 290x^3 - 616x^2 + 4720*x + 11900
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$18.0461$ of defining polynomial
Character	$\chi$	$=$	354.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +67.3400 q^{5} -36.0000 q^{6} -165.056 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +67.3400 q^{5} -36.0000 q^{6} -165.056 q^{7} -64.0000 q^{8} +81.0000 q^{9} -269.360 q^{10} -178.147 q^{11} +144.000 q^{12} +328.809 q^{13} +660.224 q^{14} +606.060 q^{15} +256.000 q^{16} +347.621 q^{17} -324.000 q^{18} +116.594 q^{19} +1077.44 q^{20} -1485.51 q^{21} +712.587 q^{22} -4824.60 q^{23} -576.000 q^{24} +1409.68 q^{25} -1315.24 q^{26} +729.000 q^{27} -2640.90 q^{28} -3874.97 q^{29} -2424.24 q^{30} -491.704 q^{31} -1024.00 q^{32} -1603.32 q^{33} -1390.48 q^{34} -11114.9 q^{35} +1296.00 q^{36} -6942.62 q^{37} -466.375 q^{38} +2959.28 q^{39} -4309.76 q^{40} +3081.91 q^{41} +5942.02 q^{42} +7910.52 q^{43} -2850.35 q^{44} +5454.54 q^{45} +19298.4 q^{46} -13918.4 q^{47} +2304.00 q^{48} +10436.5 q^{49} -5638.72 q^{50} +3128.59 q^{51} +5260.94 q^{52} +27715.7 q^{53} -2916.00 q^{54} -11996.4 q^{55} +10563.6 q^{56} +1049.34 q^{57} +15499.9 q^{58} +3481.00 q^{59} +9696.96 q^{60} -42878.5 q^{61} +1966.82 q^{62} -13369.5 q^{63} +4096.00 q^{64} +22142.0 q^{65} +6413.28 q^{66} +15155.4 q^{67} +5561.94 q^{68} -43421.4 q^{69} +44459.5 q^{70} -44824.7 q^{71} -5184.00 q^{72} +17504.8 q^{73} +27770.5 q^{74} +12687.1 q^{75} +1865.50 q^{76} +29404.2 q^{77} -11837.1 q^{78} -31341.8 q^{79} +17239.0 q^{80} +6561.00 q^{81} -12327.6 q^{82} -77439.9 q^{83} -23768.1 q^{84} +23408.8 q^{85} -31642.1 q^{86} -34874.8 q^{87} +11401.4 q^{88} +37077.3 q^{89} -21818.2 q^{90} -54271.9 q^{91} -77193.6 q^{92} -4425.34 q^{93} +55673.5 q^{94} +7851.43 q^{95} -9216.00 q^{96} -40538.7 q^{97} -41746.1 q^{98} -14429.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 20 q^{2} + 45 q^{3} + 80 q^{4} - 10 q^{5} - 180 q^{6} - 162 q^{7} - 320 q^{8} + 405 q^{9}+O(q^{10}) $ 5 * q - 20 * q^2 + 45 * q^3 + 80 * q^4 - 10 * q^5 - 180 * q^6 - 162 * q^7 - 320 * q^8 + 405 * q^9	\( 5 q - 20 q^{2} + 45 q^{3} + 80 q^{4} - 10 q^{5} - 180 q^{6} - 162 q^{7} - 320 q^{8} + 405 q^{9} + 40 q^{10} - 228 q^{11} + 720 q^{12} - 386 q^{13} + 648 q^{14} - 90 q^{15} + 1280 q^{16} + 1304 q^{17} - 1620 q^{18} + 342 q^{19} - 160 q^{20} - 1458 q^{21} + 912 q^{22} - 78 q^{23} - 2880 q^{24} - 3585 q^{25} + 1544 q^{26} + 3645 q^{27} - 2592 q^{28} - 4576 q^{29} + 360 q^{30} - 14456 q^{31} - 5120 q^{32} - 2052 q^{33} - 5216 q^{34} - 5622 q^{35} + 6480 q^{36} - 21684 q^{37} - 1368 q^{38} - 3474 q^{39} + 640 q^{40} - 15484 q^{41} + 5832 q^{42} - 22094 q^{43} - 3648 q^{44} - 810 q^{45} + 312 q^{46} - 4890 q^{47} + 11520 q^{48} + 3955 q^{49} + 14340 q^{50} + 11736 q^{51} - 6176 q^{52} + 12686 q^{53} - 14580 q^{54} - 40468 q^{55} + 10368 q^{56} + 3078 q^{57} + 18304 q^{58} + 17405 q^{59} - 1440 q^{60} - 17792 q^{61} + 57824 q^{62} - 13122 q^{63} + 20480 q^{64} + 67704 q^{65} + 8208 q^{66} - 33042 q^{67} + 20864 q^{68} - 702 q^{69} + 22488 q^{70} + 16172 q^{71} - 25920 q^{72} - 40092 q^{73} + 86736 q^{74} - 32265 q^{75} + 5472 q^{76} + 33330 q^{77} + 13896 q^{78} - 51216 q^{79} - 2560 q^{80} + 32805 q^{81} + 61936 q^{82} + 7526 q^{83} - 23328 q^{84} - 92546 q^{85} + 88376 q^{86} - 41184 q^{87} + 14592 q^{88} + 4210 q^{89} + 3240 q^{90} - 263742 q^{91} - 1248 q^{92} - 130104 q^{93} + 19560 q^{94} - 220798 q^{95} - 46080 q^{96} - 279974 q^{97} - 15820 q^{98} - 18468 q^{99}+O(q^{100}) \) 5 * q - 20 * q^2 + 45 * q^3 + 80 * q^4 - 10 * q^5 - 180 * q^6 - 162 * q^7 - 320 * q^8 + 405 * q^9 + 40 * q^10 - 228 * q^11 + 720 * q^12 - 386 * q^13 + 648 * q^14 - 90 * q^15 + 1280 * q^16 + 1304 * q^17 - 1620 * q^18 + 342 * q^19 - 160 * q^20 - 1458 * q^21 + 912 * q^22 - 78 * q^23 - 2880 * q^24 - 3585 * q^25 + 1544 * q^26 + 3645 * q^27 - 2592 * q^28 - 4576 * q^29 + 360 * q^30 - 14456 * q^31 - 5120 * q^32 - 2052 * q^33 - 5216 * q^34 - 5622 * q^35 + 6480 * q^36 - 21684 * q^37 - 1368 * q^38 - 3474 * q^39 + 640 * q^40 - 15484 * q^41 + 5832 * q^42 - 22094 * q^43 - 3648 * q^44 - 810 * q^45 + 312 * q^46 - 4890 * q^47 + 11520 * q^48 + 3955 * q^49 + 14340 * q^50 + 11736 * q^51 - 6176 * q^52 + 12686 * q^53 - 14580 * q^54 - 40468 * q^55 + 10368 * q^56 + 3078 * q^57 + 18304 * q^58 + 17405 * q^59 - 1440 * q^60 - 17792 * q^61 + 57824 * q^62 - 13122 * q^63 + 20480 * q^64 + 67704 * q^65 + 8208 * q^66 - 33042 * q^67 + 20864 * q^68 - 702 * q^69 + 22488 * q^70 + 16172 * q^71 - 25920 * q^72 - 40092 * q^73 + 86736 * q^74 - 32265 * q^75 + 5472 * q^76 + 33330 * q^77 + 13896 * q^78 - 51216 * q^79 - 2560 * q^80 + 32805 * q^81 + 61936 * q^82 + 7526 * q^83 - 23328 * q^84 - 92546 * q^85 + 88376 * q^86 - 41184 * q^87 + 14592 * q^88 + 4210 * q^89 + 3240 * q^90 - 263742 * q^91 - 1248 * q^92 - 130104 * q^93 + 19560 * q^94 - 220798 * q^95 - 46080 * q^96 - 279974 * q^97 - 15820 * q^98 - 18468 * 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 $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	16.0000	0.500000
$5$	67.3400	1.20462	0.602308	−	0.798264i	$-0.294248\pi$
$5$	67.3400	1.20462	0.602308	+	0.798264i	$0.294248\pi$
$6$	−36.0000	−0.408248
$7$	−165.056	−1.27317	−0.636585	−	0.771206i	$-0.719654\pi$
$7$	−165.056	−1.27317	−0.636585	+	0.771206i	$0.719654\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−269.360	−0.851791
$11$	−178.147	−0.443911	−0.221956	−	0.975057i	$-0.571244\pi$
$11$	−178.147	−0.443911	−0.221956	+	0.975057i	$0.571244\pi$
$12$	144.000	0.288675
$13$	328.809	0.539617	0.269808	−	0.962914i	$-0.413040\pi$
$13$	328.809	0.539617	0.269808	+	0.962914i	$0.413040\pi$
$14$	660.224	0.900267
$15$	606.060	0.695485
$16$	256.000	0.250000
$17$	347.621	0.291732	0.145866	−	0.989304i	$-0.453403\pi$
$17$	347.621	0.291732	0.145866	+	0.989304i	$0.453403\pi$
$18$	−324.000	−0.235702
$19$	116.594	0.0740954	0.0370477	−	0.999313i	$-0.488205\pi$
$19$	116.594	0.0740954	0.0370477	+	0.999313i	$0.488205\pi$
$20$	1077.44	0.602308
$21$	−1485.51	−0.735065
$22$	712.587	0.313893
$23$	−4824.60	−1.90170	−0.950850	−	0.309653i	$-0.899787\pi$
$23$	−4824.60	−1.90170	−0.950850	+	0.309653i	$0.899787\pi$
$24$	−576.000	−0.204124
$25$	1409.68	0.451097
$26$	−1315.24	−0.381567
$27$	729.000	0.192450
$28$	−2640.90	−0.636585
$29$	−3874.97	−0.855606	−0.427803	−	0.903872i	$-0.640712\pi$
$29$	−3874.97	−0.855606	−0.427803	+	0.903872i	$0.640712\pi$
$30$	−2424.24	−0.491782
$31$	−491.704	−0.0918966	−0.0459483	−	0.998944i	$-0.514631\pi$
$31$	−491.704	−0.0918966	−0.0459483	+	0.998944i	$0.514631\pi$
$32$	−1024.00	−0.176777
$33$	−1603.32	−0.256292
$34$	−1390.48	−0.206285
$35$	−11114.9	−1.53368
$36$	1296.00	0.166667
$37$	−6942.62	−0.833718	−0.416859	−	0.908971i	$-0.636869\pi$
$37$	−6942.62	−0.833718	−0.416859	+	0.908971i	$0.636869\pi$
$38$	−466.375	−0.0523934
$39$	2959.28	0.311548
$40$	−4309.76	−0.425896
$41$	3081.91	0.286325	0.143163	−	0.989699i	$-0.454273\pi$
$41$	3081.91	0.286325	0.143163	+	0.989699i	$0.454273\pi$
$42$	5942.02	0.519770
$43$	7910.52	0.652430	0.326215	−	0.945296i	$-0.394227\pi$
$43$	7910.52	0.652430	0.326215	+	0.945296i	$0.394227\pi$
$44$	−2850.35	−0.221956
$45$	5454.54	0.401538
$46$	19298.4	1.34470
$47$	−13918.4	−0.919061	−0.459530	−	0.888162i	$-0.651982\pi$
$47$	−13918.4	−0.919061	−0.459530	+	0.888162i	$0.651982\pi$
$48$	2304.00	0.144338
$49$	10436.5	0.620963
$50$	−5638.72	−0.318974
$51$	3128.59	0.168431
$52$	5260.94	0.269808
$53$	27715.7	1.35530	0.677652	−	0.735382i	$-0.262997\pi$
$53$	27715.7	1.35530	0.677652	+	0.735382i	$0.262997\pi$
$54$	−2916.00	−0.136083
$55$	−11996.4	−0.534742
$56$	10563.6	0.450134
$57$	1049.34	0.0427790
$58$	15499.9	0.605005
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	9696.96	0.347742
$61$	−42878.5	−1.47542	−0.737709	−	0.675119i	$-0.764092\pi$
$61$	−42878.5	−1.47542	−0.737709	+	0.675119i	$0.764092\pi$
$62$	1966.82	0.0649807
$63$	−13369.5	−0.424390
$64$	4096.00	0.125000
$65$	22142.0	0.650030
$66$	6413.28	0.181226
$67$	15155.4	0.412459	0.206230	−	0.978504i	$-0.433881\pi$
$67$	15155.4	0.412459	0.206230	+	0.978504i	$0.433881\pi$
$68$	5561.94	0.145866
$69$	−43421.4	−1.09795
$70$	44459.5	1.08448
$71$	−44824.7	−1.05529	−0.527645	−	0.849465i	$-0.676925\pi$
$71$	−44824.7	−1.05529	−0.527645	+	0.849465i	$0.676925\pi$
$72$	−5184.00	−0.117851
$73$	17504.8	0.384459	0.192229	−	0.981350i	$-0.438428\pi$
$73$	17504.8	0.384459	0.192229	+	0.981350i	$0.438428\pi$
$74$	27770.5	0.589528
$75$	12687.1	0.260441
$76$	1865.50	0.0370477
$77$	29404.2	0.565174
$78$	−11837.1	−0.220298
$79$	−31341.8	−0.565009	−0.282505	−	0.959266i	$-0.591165\pi$
$79$	−31341.8	−0.565009	−0.282505	+	0.959266i	$0.591165\pi$
$80$	17239.0	0.301154
$81$	6561.00	0.111111
$82$	−12327.6	−0.202463
$83$	−77439.9	−1.23387	−0.616935	−	0.787014i	$-0.711626\pi$
$83$	−77439.9	−1.23387	−0.616935	+	0.787014i	$0.711626\pi$
$84$	−23768.1	−0.367533
$85$	23408.8	0.351424
$86$	−31642.1	−0.461337
$87$	−34874.8	−0.493984
$88$	11401.4	0.156946
$89$	37077.3	0.496172	0.248086	−	0.968738i	$-0.420198\pi$
$89$	37077.3	0.496172	0.248086	+	0.968738i	$0.420198\pi$
$90$	−21818.2	−0.283930
$91$	−54271.9	−0.687024
$92$	−77193.6	−0.950850
$93$	−4425.34	−0.0530565
$94$	55673.5	0.649874
$95$	7851.43	0.0892564
$96$	−9216.00	−0.102062
$97$	−40538.7	−0.437462	−0.218731	−	0.975785i	$-0.570192\pi$
$97$	−40538.7	−0.437462	−0.218731	+	0.975785i	$0.570192\pi$
$98$	−41746.1	−0.439087
$99$	−14429.9	−0.147970
$100$	22554.9	0.225549
$101$	31256.8	0.304888	0.152444	−	0.988312i	$-0.451286\pi$
$101$	31256.8	0.304888	0.152444	+	0.988312i	$0.451286\pi$
$102$	−12514.4	−0.119099
$103$	−179267.	−1.66497	−0.832484	−	0.554048i	$-0.813082\pi$
$103$	−179267.	−1.66497	−0.832484	+	0.554048i	$0.813082\pi$
$104$	−21043.8	−0.190783
$105$	−100034.	−0.885471
$106$	−110863.	−0.958345
$107$	174778.	1.47580	0.737901	−	0.674909i	$-0.235817\pi$
$107$	174778.	1.47580	0.737901	+	0.674909i	$0.235817\pi$
$108$	11664.0	0.0962250
$109$	−80360.9	−0.647856	−0.323928	−	0.946082i	$-0.605004\pi$
$109$	−80360.9	−0.647856	−0.323928	+	0.946082i	$0.605004\pi$
$110$	47985.6	0.378120
$111$	−62483.6	−0.481347
$112$	−42254.4	−0.318293
$113$	−39497.5	−0.290987	−0.145494	−	0.989359i	$-0.546477\pi$
$113$	−39497.5	−0.290987	−0.145494	+	0.989359i	$0.546477\pi$
$114$	−4197.37	−0.0302493
$115$	−324889.	−2.29082
$116$	−61999.6	−0.427803
$117$	26633.5	0.179872
$118$	−13924.0	−0.0920575
$119$	−57377.0	−0.371424
$120$	−38787.9	−0.245891
$121$	−129315.	−0.802943
$122$	171514.	1.04328
$123$	27737.2	0.165310
$124$	−7867.27	−0.0459483
$125$	−115510.	−0.661216
$126$	53478.2	0.300089
$127$	−136023.	−0.748348	−0.374174	−	0.927359i	$-0.622074\pi$
$127$	−136023.	−0.748348	−0.374174	+	0.927359i	$0.622074\pi$
$128$	−16384.0	−0.0883883
$129$	71194.6	0.376680
$130$	−88568.0	−0.459641
$131$	−152260.	−0.775189	−0.387594	−	0.921830i	$-0.626694\pi$
$131$	−152260.	−0.775189	−0.387594	+	0.921830i	$0.626694\pi$
$132$	−25653.1	−0.128146
$133$	−19244.5	−0.0943361
$134$	−60621.7	−0.291653
$135$	49090.9	0.231828
$136$	−22247.7	−0.103143
$137$	283228.	1.28924	0.644621	−	0.764502i	$-0.277015\pi$
$137$	283228.	1.28924	0.644621	+	0.764502i	$0.277015\pi$
$138$	173686.	0.776366
$139$	−17536.1	−0.0769833	−0.0384917	−	0.999259i	$-0.512255\pi$
$139$	−17536.1	−0.0769833	−0.0384917	+	0.999259i	$0.512255\pi$
$140$	−177838.	−0.766840
$141$	−125265.	−0.530620
$142$	179299.	0.746203
$143$	−58576.2	−0.239542
$144$	20736.0	0.0833333
$145$	−260941.	−1.03068
$146$	−70019.2	−0.271853
$147$	93928.7	0.358513
$148$	−111082.	−0.416859
$149$	395878.	1.46082	0.730408	−	0.683011i	$-0.239330\pi$
$149$	395878.	1.46082	0.730408	+	0.683011i	$0.239330\pi$
$150$	−50748.5	−0.184160
$151$	−270442.	−0.965234	−0.482617	−	0.875832i	$-0.660314\pi$
$151$	−270442.	−0.965234	−0.482617	+	0.875832i	$0.660314\pi$
$152$	−7462.00	−0.0261967
$153$	28157.3	0.0972439
$154$	−117617.	−0.399639
$155$	−33111.4	−0.110700
$156$	47348.5	0.155774
$157$	369496.	1.19636	0.598178	−	0.801363i	$-0.295891\pi$
$157$	369496.	1.19636	0.598178	+	0.801363i	$0.295891\pi$
$158$	125367.	0.399522
$159$	249442.	0.782486
$160$	−68956.2	−0.212948
$161$	796330.	2.42119
$162$	−26244.0	−0.0785674
$163$	−513123.	−1.51270	−0.756349	−	0.654168i	$-0.773019\pi$
$163$	−513123.	−1.51270	−0.756349	+	0.654168i	$0.773019\pi$
$164$	49310.5	0.143163
$165$	−107968.	−0.308733
$166$	309760.	0.872478
$167$	−245485.	−0.681136	−0.340568	−	0.940220i	$-0.610619\pi$
$167$	−245485.	−0.681136	−0.340568	+	0.940220i	$0.610619\pi$
$168$	95072.3	0.259885
$169$	−263178.	−0.708814
$170$	−93635.2	−0.248495
$171$	9444.09	0.0246985
$172$	126568.	0.326215
$173$	−356695.	−0.906113	−0.453056	−	0.891482i	$-0.649666\pi$
$173$	−356695.	−0.906113	−0.453056	+	0.891482i	$0.649666\pi$
$174$	139499.	0.349300
$175$	−232676.	−0.574324
$176$	−45605.6	−0.110978
$177$	31329.0	0.0751646
$178$	−148309.	−0.350847
$179$	−361622.	−0.843572	−0.421786	−	0.906695i	$-0.638597\pi$
$179$	−361622.	−0.843572	−0.421786	+	0.906695i	$0.638597\pi$
$180$	87272.7	0.200769
$181$	−167386.	−0.379773	−0.189886	−	0.981806i	$-0.560812\pi$
$181$	−167386.	−0.379773	−0.189886	+	0.981806i	$0.560812\pi$
$182$	217088.	0.485799
$183$	−385907.	−0.851833
$184$	308775.	0.672352
$185$	−467516.	−1.00431
$186$	17701.3	0.0375166
$187$	−61927.5	−0.129503
$188$	−222694.	−0.459530
$189$	−120326.	−0.245022
$190$	−31405.7	−0.0631138
$191$	−101681.	−0.201677	−0.100839	−	0.994903i	$-0.532153\pi$
$191$	−101681.	−0.201677	−0.100839	+	0.994903i	$0.532153\pi$
$192$	36864.0	0.0721688
$193$	−466069.	−0.900651	−0.450326	−	0.892864i	$-0.648692\pi$
$193$	−466069.	−0.900651	−0.450326	+	0.892864i	$0.648692\pi$
$194$	162155.	0.309332
$195$	199278.	0.375295
$196$	166984.	0.310481
$197$	−537460.	−0.986690	−0.493345	−	0.869834i	$-0.664226\pi$
$197$	−537460.	−0.986690	−0.493345	+	0.869834i	$0.664226\pi$
$198$	57719.5	0.104631
$199$	−378114.	−0.676846	−0.338423	−	0.940994i	$-0.609893\pi$
$199$	−378114.	−0.676846	−0.338423	+	0.940994i	$0.609893\pi$
$200$	−90219.5	−0.159487
$201$	136399.	0.238133
$202$	−125027.	−0.215588
$203$	639588.	1.08933
$204$	50057.4	0.0842157
$205$	207536.	0.344912
$206$	717066.	1.17731
$207$	−390793.	−0.633900
$208$	84175.1	0.134904
$209$	−20770.8	−0.0328918
$210$	400136.	0.626122
$211$	374476.	0.579053	0.289527	−	0.957170i	$-0.406502\pi$
$211$	374476.	0.579053	0.289527	+	0.957170i	$0.406502\pi$
$212$	443452.	0.677652
$213$	−403423.	−0.609272
$214$	−699113.	−1.04355
$215$	532694.	0.785926
$216$	−46656.0	−0.0680414
$217$	81158.8	0.117000
$218$	321443.	0.458103
$219$	157543.	0.221967
$220$	−191942.	−0.267371
$221$	114301.	0.157423
$222$	249934.	0.340364
$223$	1.17465e6	1.58178	0.790889	−	0.611960i	$-0.209619\pi$
$223$	1.17465e6	1.58178	0.790889	+	0.611960i	$0.209619\pi$
$224$	169017.	0.225067
$225$	114184.	0.150366
$226$	157990.	0.205759
$227$	889107.	1.14522	0.572611	−	0.819828i	$-0.305931\pi$
$227$	889107.	1.14522	0.572611	+	0.819828i	$0.305931\pi$
$228$	16789.5	0.0213895
$229$	52995.5	0.0667806	0.0333903	−	0.999442i	$-0.489370\pi$
$229$	52995.5	0.0667806	0.0333903	+	0.999442i	$0.489370\pi$
$230$	1.29956e6	1.61985
$231$	264638.	0.326304
$232$	247998.	0.302502
$233$	−8377.47	−0.0101093	−0.00505467	−	0.999987i	$-0.501609\pi$
$233$	−8377.47	−0.0101093	−0.00505467	+	0.999987i	$0.501609\pi$
$234$	−106534.	−0.127189
$235$	−937264.	−1.10711
$236$	55696.0	0.0650945
$237$	−282076.	−0.326208
$238$	229508.	0.262637
$239$	−526944.	−0.596719	−0.298360	−	0.954454i	$-0.596439\pi$
$239$	−526944.	−0.596719	−0.298360	+	0.954454i	$0.596439\pi$
$240$	155151.	0.173871
$241$	1.06339e6	1.17937	0.589684	−	0.807634i	$-0.299252\pi$
$241$	1.06339e6	1.17937	0.589684	+	0.807634i	$0.299252\pi$
$242$	517259.	0.567766
$243$	59049.0	0.0641500
$244$	−686056.	−0.737709
$245$	702796.	0.748021
$246$	−110949.	−0.116892
$247$	38337.1	0.0399831
$248$	31469.1	0.0324904
$249$	−696959.	−0.712375
$250$	462039.	0.467551
$251$	−287356.	−0.287896	−0.143948	−	0.989585i	$-0.545980\pi$
$251$	−287356.	−0.287896	−0.143948	+	0.989585i	$0.545980\pi$
$252$	−213913.	−0.212195
$253$	859487.	0.844186
$254$	544093.	0.529162
$255$	210679.	0.202895
$256$	65536.0	0.0625000
$257$	979321.	0.924894	0.462447	−	0.886647i	$-0.346971\pi$
$257$	979321.	0.924894	0.462447	+	0.886647i	$0.346971\pi$
$258$	−284779.	−0.266353
$259$	1.14592e6	1.06146
$260$	354272.	0.325015
$261$	−313873.	−0.285202
$262$	609040.	0.548141
$263$	1.79778e6	1.60268	0.801341	−	0.598207i	$-0.204120\pi$
$263$	1.79778e6	1.60268	0.801341	+	0.598207i	$0.204120\pi$
$264$	102612.	0.0906130
$265$	1.86638e6	1.63262
$266$	76978.0	0.0667057
$267$	333695.	0.286465
$268$	242487.	0.206230
$269$	−1.11363e6	−0.938342	−0.469171	−	0.883107i	$-0.655447\pi$
$269$	−1.11363e6	−0.938342	−0.469171	+	0.883107i	$0.655447\pi$
$270$	−196364.	−0.163927
$271$	785670.	0.649855	0.324928	−	0.945739i	$-0.394660\pi$
$271$	785670.	0.649855	0.324928	+	0.945739i	$0.394660\pi$
$272$	88991.0	0.0729329
$273$	−488447.	−0.396653
$274$	−1.13291e6	−0.911632
$275$	−251130.	−0.200247
$276$	−694743.	−0.548973
$277$	−517730.	−0.405419	−0.202710	−	0.979239i	$-0.564975\pi$
$277$	−517730.	−0.405419	−0.202710	+	0.979239i	$0.564975\pi$
$278$	70144.5	0.0544354
$279$	−39828.0	−0.0306322
$280$	711353.	0.542238
$281$	1.36219e6	1.02913	0.514565	−	0.857451i	$-0.327953\pi$
$281$	1.36219e6	1.02913	0.514565	+	0.857451i	$0.327953\pi$
$282$	501062.	0.375205
$283$	1.71452e6	1.27256	0.636279	−	0.771459i	$-0.280473\pi$
$283$	1.71452e6	1.27256	0.636279	+	0.771459i	$0.280473\pi$
$284$	−717196.	−0.527645
$285$	70662.8	0.0515322
$286$	234305.	0.169382
$287$	−508688.	−0.364541
$288$	−82944.0	−0.0589256
$289$	−1.29902e6	−0.914893
$290$	1.04376e6	0.728798
$291$	−364848.	−0.252569
$292$	280077.	0.192229
$293$	973139.	0.662225	0.331113	−	0.943591i	$-0.392576\pi$
$293$	973139.	0.662225	0.331113	+	0.943591i	$0.392576\pi$
$294$	−375715.	−0.253507
$295$	234411.	0.156828
$296$	444328.	0.294764
$297$	−129869.	−0.0854307
$298$	−1.58351e6	−1.03295
$299$	−1.58637e6	−1.02619
$300$	202994.	0.130221
$301$	−1.30568e6	−0.830654
$302$	1.08177e6	0.682523
$303$	281311.	0.176027
$304$	29848.0	0.0185238
$305$	−2.88744e6	−1.77731
$306$	−112629.	−0.0687618
$307$	−1.94189e6	−1.17592	−0.587962	−	0.808888i	$-0.700070\pi$
$307$	−1.94189e6	−1.17592	−0.587962	+	0.808888i	$0.700070\pi$
$308$	470467.	0.282587
$309$	−1.61340e6	−0.961270
$310$	132445.	0.0782768
$311$	2.17712e6	1.27639	0.638193	−	0.769876i	$-0.279682\pi$
$311$	2.17712e6	1.27639	0.638193	+	0.769876i	$0.279682\pi$
$312$	−189394.	−0.110149
$313$	−317409.	−0.183130	−0.0915649	−	0.995799i	$-0.529187\pi$
$313$	−317409.	−0.183130	−0.0915649	+	0.995799i	$0.529187\pi$
$314$	−1.47798e6	−0.845952
$315$	−900306.	−0.511227
$316$	−501468.	−0.282505
$317$	1.29412e6	0.723311	0.361656	−	0.932312i	$-0.382212\pi$
$317$	1.29412e6	0.723311	0.361656	+	0.932312i	$0.382212\pi$
$318$	−997767.	−0.553301
$319$	690314.	0.379813
$320$	275825.	0.150577
$321$	1.57300e6	0.852054
$322$	−3.18532e6	−1.71204
$323$	40530.4	0.0216160
$324$	104976.	0.0555556
$325$	463515.	0.243420
$326$	2.05249e6	1.06964
$327$	−723248.	−0.374040
$328$	−197242.	−0.101231
$329$	2.29731e6	1.17012
$330$	431870.	0.218308
$331$	−1.71839e6	−0.862089	−0.431044	−	0.902331i	$-0.641855\pi$
$331$	−1.71839e6	−0.862089	−0.431044	+	0.902331i	$0.641855\pi$
$332$	−1.23904e6	−0.616935
$333$	−562352.	−0.277906
$334$	981941.	0.481636
$335$	1.02057e6	0.496855
$336$	−380289.	−0.183766
$337$	−79378.5	−0.0380740	−0.0190370	−	0.999819i	$-0.506060\pi$
$337$	−79378.5	−0.0380740	−0.0190370	+	0.999819i	$0.506060\pi$
$338$	1.05271e6	0.501207
$339$	−355478.	−0.168002
$340$	374541.	0.175712
$341$	87595.5	0.0407939
$342$	−37776.4	−0.0174645
$343$	1.05149e6	0.482579
$344$	−506273.	−0.230669
$345$	−2.92400e6	−1.32260
$346$	1.42678e6	0.640718
$347$	4.25195e6	1.89568	0.947838	−	0.318753i	$-0.103264\pi$
$347$	4.25195e6	1.89568	0.947838	+	0.318753i	$0.103264\pi$
$348$	−557996.	−0.246992
$349$	577731.	0.253900	0.126950	−	0.991909i	$-0.459481\pi$
$349$	577731.	0.253900	0.126950	+	0.991909i	$0.459481\pi$
$350$	930705.	0.406108
$351$	239702.	0.103849
$352$	182422.	0.0784731
$353$	−4.21055e6	−1.79846	−0.899232	−	0.437472i	$-0.855874\pi$
$353$	−4.21055e6	−1.79846	−0.899232	+	0.437472i	$0.855874\pi$
$354$	−125316.	−0.0531494
$355$	−3.01850e6	−1.27122
$356$	593236.	0.248086
$357$	−516393.	−0.214442
$358$	1.44649e6	0.596496
$359$	−1.67481e6	−0.685850	−0.342925	−	0.939363i	$-0.611418\pi$
$359$	−1.67481e6	−0.685850	−0.342925	+	0.939363i	$0.611418\pi$
$360$	−349091.	−0.141965
$361$	−2.46250e6	−0.994510
$362$	669546.	0.268540
$363$	−1.16383e6	−0.463579
$364$	−868351.	−0.343512
$365$	1.17877e6	0.463125
$366$	1.54363e6	0.602337
$367$	132312.	0.0512785	0.0256392	−	0.999671i	$-0.491838\pi$
$367$	132312.	0.0512785	0.0256392	+	0.999671i	$0.491838\pi$
$368$	−1.23510e6	−0.475425
$369$	249634.	0.0954418
$370$	1.87007e6	0.710154
$371$	−4.57465e6	−1.72553
$372$	−70805.4	−0.0265283
$373$	1.35953e6	0.505960	0.252980	−	0.967471i	$-0.418589\pi$
$373$	1.35953e6	0.505960	0.252980	+	0.967471i	$0.418589\pi$
$374$	247710.	0.0915724
$375$	−1.03959e6	−0.381753
$376$	890776.	0.324937
$377$	−1.27413e6	−0.461699
$378$	481304.	0.173257
$379$	−1.89078e6	−0.676151	−0.338075	−	0.941119i	$-0.609776\pi$
$379$	−1.89078e6	−0.676151	−0.338075	+	0.941119i	$0.609776\pi$
$380$	125623.	0.0446282
$381$	−1.22421e6	−0.432059
$382$	406725.	0.142607
$383$	1.53188e6	0.533616	0.266808	−	0.963750i	$-0.414031\pi$
$383$	1.53188e6	0.533616	0.266808	+	0.963750i	$0.414031\pi$
$384$	−147456.	−0.0510310
$385$	1.98008e6	0.680818
$386$	1.86427e6	0.636856
$387$	640752.	0.217477
$388$	−648619.	−0.218731
$389$	657631.	0.220347	0.110174	−	0.993912i	$-0.464859\pi$
$389$	657631.	0.220347	0.110174	+	0.993912i	$0.464859\pi$
$390$	−797112.	−0.265374
$391$	−1.67713e6	−0.554786
$392$	−667937.	−0.219544
$393$	−1.37034e6	−0.447556
$394$	2.14984e6	0.697695
$395$	−2.11055e6	−0.680619
$396$	−230878.	−0.0739852
$397$	−2.16505e6	−0.689431	−0.344715	−	0.938707i	$-0.612025\pi$
$397$	−2.16505e6	−0.689431	−0.344715	+	0.938707i	$0.612025\pi$
$398$	1.51245e6	0.478602
$399$	−173201.	−0.0544650
$400$	360878.	0.112774
$401$	2.68912e6	0.835122	0.417561	−	0.908649i	$-0.362885\pi$
$401$	2.68912e6	0.835122	0.417561	+	0.908649i	$0.362885\pi$
$402$	−545595.	−0.168386
$403$	−161677.	−0.0495890
$404$	500108.	0.152444
$405$	441818.	0.133846
$406$	−2.55835e6	−0.770274
$407$	1.23680e6	0.370097
$408$	−200230.	−0.0595495
$409$	−2.76973e6	−0.818707	−0.409353	−	0.912376i	$-0.634246\pi$
$409$	−2.76973e6	−0.818707	−0.409353	+	0.912376i	$0.634246\pi$
$410$	−830143.	−0.243890
$411$	2.54905e6	0.744344
$412$	−2.86826e6	−0.832484
$413$	−574560.	−0.165753
$414$	1.56317e6	0.448235
$415$	−5.21480e6	−1.48634
$416$	−336700.	−0.0953917
$417$	−157825.	−0.0444464
$418$	83083.2	0.0232580
$419$	1.71408e6	0.476975	0.238487	−	0.971146i	$-0.423348\pi$
$419$	1.71408e6	0.476975	0.238487	+	0.971146i	$0.423348\pi$
$420$	−1.60054e6	−0.442735
$421$	−332952.	−0.0915538	−0.0457769	−	0.998952i	$-0.514576\pi$
$421$	−332952.	−0.0915538	−0.0457769	+	0.998952i	$0.514576\pi$
$422$	−1.49791e6	−0.409452
$423$	−1.12739e6	−0.306354
$424$	−1.77381e6	−0.479173
$425$	490034.	0.131599
$426$	1.61369e6	0.430820
$427$	7.07736e6	1.87846
$428$	2.79645e6	0.737901
$429$	−527186.	−0.138300
$430$	−2.13078e6	−0.555734
$431$	4.18104e6	1.08416	0.542078	−	0.840328i	$-0.317638\pi$
$431$	4.18104e6	1.08416	0.542078	+	0.840328i	$0.317638\pi$
$432$	186624.	0.0481125
$433$	1.47553e6	0.378207	0.189104	−	0.981957i	$-0.439442\pi$
$433$	1.47553e6	0.378207	0.189104	+	0.981957i	$0.439442\pi$
$434$	−324635.	−0.0827315
$435$	−2.34847e6	−0.595061
$436$	−1.28577e6	−0.323928
$437$	−562518.	−0.140907
$438$	−630172.	−0.156955
$439$	2.64417e6	0.654830	0.327415	−	0.944881i	$-0.393823\pi$
$439$	2.64417e6	0.654830	0.327415	+	0.944881i	$0.393823\pi$
$440$	767770.	0.189060
$441$	845358.	0.206988
$442$	−457204.	−0.111315
$443$	−2.41560e6	−0.584811	−0.292406	−	0.956294i	$-0.594456\pi$
$443$	−2.41560e6	−0.584811	−0.292406	+	0.956294i	$0.594456\pi$
$444$	−999737.	−0.240674
$445$	2.49678e6	0.597697
$446$	−4.69859e6	−1.11849
$447$	3.56290e6	0.843402
$448$	−676070.	−0.159146
$449$	−2.57582e6	−0.602975	−0.301488	−	0.953470i	$-0.597483\pi$
$449$	−2.57582e6	−0.602975	−0.301488	+	0.953470i	$0.597483\pi$
$450$	−456736.	−0.106325
$451$	−549031.	−0.127103
$452$	−631961.	−0.145494
$453$	−2.43398e6	−0.557278
$454$	−3.55643e6	−0.809794
$455$	−3.65467e6	−0.827599
$456$	−67158.0	−0.0151247
$457$	5.82365e6	1.30438	0.652191	−	0.758054i	$-0.273850\pi$
$457$	5.82365e6	1.30438	0.652191	+	0.758054i	$0.273850\pi$
$458$	−211982.	−0.0472210
$459$	253416.	0.0561438
$460$	−5.19822e6	−1.14541
$461$	4.40020e6	0.964317	0.482158	−	0.876084i	$-0.339853\pi$
$461$	4.40020e6	0.964317	0.482158	+	0.876084i	$0.339853\pi$
$462$	−1.05855e6	−0.230732
$463$	2.12349e6	0.460361	0.230180	−	0.973148i	$-0.426068\pi$
$463$	2.12349e6	0.460361	0.230180	+	0.973148i	$0.426068\pi$
$464$	−991993.	−0.213901
$465$	−298002.	−0.0639127
$466$	33509.9	0.00714838
$467$	1.07512e6	0.228120	0.114060	−	0.993474i	$-0.463614\pi$
$467$	1.07512e6	0.228120	0.114060	+	0.993474i	$0.463614\pi$
$468$	426137.	0.0899361
$469$	−2.50149e6	−0.525131
$470$	3.74906e6	0.782848
$471$	3.32547e6	0.690717
$472$	−222784.	−0.0460287
$473$	−1.40923e6	−0.289621
$474$	1.12830e6	0.230664
$475$	164360.	0.0334242
$476$	−918031.	−0.185712
$477$	2.24498e6	0.451768
$478$	2.10778e6	0.421944
$479$	−625789.	−0.124620	−0.0623102	−	0.998057i	$-0.519847\pi$
$479$	−625789.	−0.124620	−0.0623102	+	0.998057i	$0.519847\pi$
$480$	−620606.	−0.122946
$481$	−2.28280e6	−0.449888
$482$	−4.25355e6	−0.833939
$483$	7.16697e6	1.39787
$484$	−2.06904e6	−0.401471
$485$	−2.72987e6	−0.526973
$486$	−236196.	−0.0453609
$487$	−1.87676e6	−0.358581	−0.179290	−	0.983796i	$-0.557380\pi$
$487$	−1.87676e6	−0.358581	−0.179290	+	0.983796i	$0.557380\pi$
$488$	2.74423e6	0.521639
$489$	−4.61810e6	−0.873357
$490$	−2.81118e6	−0.528931
$491$	5.43966e6	1.01828	0.509141	−	0.860683i	$-0.329963\pi$
$491$	5.43966e6	1.01828	0.509141	+	0.860683i	$0.329963\pi$
$492$	443795.	0.0826550
$493$	−1.34702e6	−0.249607
$494$	−153348.	−0.0282723
$495$	−971709.	−0.178247
$496$	−125876.	−0.0229742
$497$	7.39860e6	1.34356
$498$	2.78784e6	0.503725
$499$	3.38611e6	0.608766	0.304383	−	0.952550i	$-0.401550\pi$
$499$	3.38611e6	0.608766	0.304383	+	0.952550i	$0.401550\pi$
$500$	−1.84816e6	−0.330608
$501$	−2.20937e6	−0.393254
$502$	1.14942e6	0.203573
$503$	884304.	0.155841	0.0779205	−	0.996960i	$-0.475172\pi$
$503$	884304.	0.155841	0.0779205	+	0.996960i	$0.475172\pi$
$504$	855651.	0.150045
$505$	2.10483e6	0.367273
$506$	−3.43795e6	−0.596929
$507$	−2.36860e6	−0.409234
$508$	−2.17637e6	−0.374174
$509$	−477580.	−0.0817055	−0.0408527	−	0.999165i	$-0.513007\pi$
$509$	−477580.	−0.0817055	−0.0408527	+	0.999165i	$0.513007\pi$
$510$	−842717.	−0.143468
$511$	−2.88927e6	−0.489482
$512$	−262144.	−0.0441942
$513$	84996.8	0.0142597
$514$	−3.91728e6	−0.653999
$515$	−1.20718e7	−2.00565
$516$	1.13911e6	0.188340
$517$	2.47951e6	0.407981
$518$	−4.58369e6	−0.750569
$519$	−3.21026e6	−0.523144
$520$	−1.41709e6	−0.229820
$521$	8.41620e6	1.35838	0.679191	−	0.733962i	$-0.262331\pi$
$521$	8.41620e6	1.35838	0.679191	+	0.733962i	$0.262331\pi$
$522$	1.25549e6	0.201668
$523$	3.77399e6	0.603318	0.301659	−	0.953416i	$-0.402460\pi$
$523$	3.77399e6	0.603318	0.301659	+	0.953416i	$0.402460\pi$
$524$	−2.43616e6	−0.387594
$525$	−2.09409e6	−0.331586
$526$	−7.19113e6	−1.13327
$527$	−170927.	−0.0268092
$528$	−410450.	−0.0640731
$529$	1.68404e7	2.61646
$530$	−7.46552e6	−1.15444
$531$	281961.	0.0433963
$532$	−307912.	−0.0471680
$533$	1.01336e6	0.154506
$534$	−1.33478e6	−0.202562
$535$	1.17696e7	1.77777
$536$	−969947.	−0.145826
$537$	−3.25460e6	−0.487037
$538$	4.45453e6	0.663508
$539$	−1.85923e6	−0.275652
$540$	785454.	0.115914
$541$	−2.84719e6	−0.418237	−0.209119	−	0.977890i	$-0.567059\pi$
$541$	−2.84719e6	−0.418237	−0.209119	+	0.977890i	$0.567059\pi$
$542$	−3.14268e6	−0.459517
$543$	−1.50648e6	−0.219262
$544$	−355964.	−0.0515714
$545$	−5.41150e6	−0.780417
$546$	1.95379e6	0.280476
$547$	−8.35725e6	−1.19425	−0.597125	−	0.802148i	$-0.703690\pi$
$547$	−8.35725e6	−1.19425	−0.597125	+	0.802148i	$0.703690\pi$
$548$	4.53165e6	0.644621
$549$	−3.47316e6	−0.491806
$550$	1.00452e6	0.141596
$551$	−451798.	−0.0633964
$552$	2.77897e6	0.388183
$553$	5.17315e6	0.719353
$554$	2.07092e6	0.286675
$555$	−4.20765e6	−0.579838
$556$	−280578.	−0.0384917
$557$	1.09568e6	0.149640	0.0748199	−	0.997197i	$-0.476162\pi$
$557$	1.09568e6	0.149640	0.0748199	+	0.997197i	$0.476162\pi$
$558$	159312.	0.0216602
$559$	2.60105e6	0.352062
$560$	−2.84541e6	−0.383420
$561$	−557348.	−0.0747686
$562$	−5.44874e6	−0.727705
$563$	−8.40580e6	−1.11766	−0.558828	−	0.829284i	$-0.688749\pi$
$563$	−8.40580e6	−1.11766	−0.558828	+	0.829284i	$0.688749\pi$
$564$	−2.00425e6	−0.265310
$565$	−2.65977e6	−0.350528
$566$	−6.85809e6	−0.899834
$567$	−1.08293e6	−0.141463
$568$	2.86878e6	0.373101
$569$	7.87143e6	1.01923	0.509616	−	0.860402i	$-0.329787\pi$
$569$	7.87143e6	1.01923	0.509616	+	0.860402i	$0.329787\pi$
$570$	−282651.	−0.0364388
$571$	−5.94366e6	−0.762894	−0.381447	−	0.924391i	$-0.624574\pi$
$571$	−5.94366e6	−0.762894	−0.381447	+	0.924391i	$0.624574\pi$
$572$	−937220.	−0.119771
$573$	−915130.	−0.116438
$574$	2.03475e6	0.257769
$575$	−6.80114e6	−0.857852
$576$	331776.	0.0416667
$577$	1.12627e7	1.40832	0.704162	−	0.710039i	$-0.251323\pi$
$577$	1.12627e7	1.40832	0.704162	+	0.710039i	$0.251323\pi$
$578$	5.19607e6	0.646927
$579$	−4.19462e6	−0.519991
$580$	−4.17505e6	−0.515338
$581$	1.27819e7	1.57093
$582$	1.45939e6	0.178593
$583$	−4.93747e6	−0.601635
$584$	−1.12031e6	−0.135927
$585$	1.79350e6	0.216677
$586$	−3.89255e6	−0.468264
$587$	9.55699e6	1.14479	0.572395	−	0.819978i	$-0.306014\pi$
$587$	9.55699e6	1.14479	0.572395	+	0.819978i	$0.306014\pi$
$588$	1.50286e6	0.179257
$589$	−57329.6	−0.00680912
$590$	−937643.	−0.110894
$591$	−4.83714e6	−0.569666
$592$	−1.77731e6	−0.208429
$593$	7.97236e6	0.931001	0.465501	−	0.885048i	$-0.345874\pi$
$593$	7.97236e6	0.931001	0.465501	+	0.885048i	$0.345874\pi$
$594$	519476.	0.0604087
$595$	−3.86377e6	−0.447423
$596$	6.33404e6	0.730408
$597$	−3.40302e6	−0.390777
$598$	6.34549e6	0.725625
$599$	−1.30618e7	−1.48743	−0.743716	−	0.668496i	$-0.766938\pi$
$599$	−1.30618e7	−1.48743	−0.743716	+	0.668496i	$0.766938\pi$
$600$	−811975.	−0.0920799
$601$	1.64622e7	1.85910	0.929548	−	0.368701i	$-0.120197\pi$
$601$	1.64622e7	1.85910	0.929548	+	0.368701i	$0.120197\pi$
$602$	5.22272e6	0.587361
$603$	1.22759e6	0.137486
$604$	−4.32708e6	−0.482617
$605$	−8.70806e6	−0.967237
$606$	−1.12524e6	−0.124470
$607$	2.54979e6	0.280888	0.140444	−	0.990089i	$-0.455147\pi$
$607$	2.54979e6	0.280888	0.140444	+	0.990089i	$0.455147\pi$
$608$	−119392.	−0.0130983
$609$	5.75629e6	0.628926
$610$	1.15498e7	1.25675
$611$	−4.57649e6	−0.495940
$612$	450517.	0.0486220
$613$	−1.06857e7	−1.14856	−0.574280	−	0.818659i	$-0.694718\pi$
$613$	−1.06857e7	−1.14856	−0.574280	+	0.818659i	$0.694718\pi$
$614$	7.76757e6	0.831504
$615$	1.86782e6	0.199135
$616$	−1.88187e6	−0.199819
$617$	1.33601e7	1.41285	0.706424	−	0.707789i	$-0.250307\pi$
$617$	1.33601e7	1.41285	0.706424	+	0.707789i	$0.250307\pi$
$618$	6.45360e6	0.679721
$619$	455702.	0.0478029	0.0239015	−	0.999714i	$-0.492391\pi$
$619$	455702.	0.0478029	0.0239015	+	0.999714i	$0.492391\pi$
$620$	−529782.	−0.0553500
$621$	−3.51713e6	−0.365982
$622$	−8.70850e6	−0.902542
$623$	−6.11983e6	−0.631712
$624$	757576.	0.0778870
$625$	−1.21837e7	−1.24761
$626$	1.26964e6	0.129492
$627$	−186937.	−0.0189901
$628$	5.91194e6	0.598178
$629$	−2.41340e6	−0.243222
$630$	3.60122e6	0.361492
$631$	1.62206e7	1.62178	0.810892	−	0.585196i	$-0.198983\pi$
$631$	1.62206e7	1.62178	0.810892	+	0.585196i	$0.198983\pi$
$632$	2.00587e6	0.199761
$633$	3.37029e6	0.334316
$634$	−5.17647e6	−0.511458
$635$	−9.15980e6	−0.901471
$636$	3.99107e6	0.391243
$637$	3.43162e6	0.335082
$638$	−2.76125e6	−0.268568
$639$	−3.63080e6	−0.351763
$640$	−1.10330e6	−0.106474
$641$	1.06511e6	0.102388	0.0511940	−	0.998689i	$-0.483697\pi$
$641$	1.06511e6	0.102388	0.0511940	+	0.998689i	$0.483697\pi$
$642$	−6.29202e6	−0.602493
$643$	−7.52255e6	−0.717526	−0.358763	−	0.933429i	$-0.616801\pi$
$643$	−7.52255e6	−0.717526	−0.358763	+	0.933429i	$0.616801\pi$
$644$	1.27413e7	1.21059
$645$	4.79425e6	0.453755
$646$	−162122.	−0.0152848
$647$	8.64481e6	0.811886	0.405943	−	0.913898i	$-0.366943\pi$
$647$	8.64481e6	0.811886	0.405943	+	0.913898i	$0.366943\pi$
$648$	−419904.	−0.0392837
$649$	−620129.	−0.0577923
$650$	−1.85406e6	−0.172124
$651$	730429.	0.0675500
$652$	−8.20996e6	−0.756349
$653$	1.30804e7	1.20043	0.600215	−	0.799839i	$-0.295082\pi$
$653$	1.30804e7	1.20043	0.600215	+	0.799839i	$0.295082\pi$
$654$	2.89299e6	0.264486
$655$	−1.02532e7	−0.933804
$656$	788968.	0.0715813
$657$	1.41789e6	0.128153
$658$	−9.18926e6	−0.827400
$659$	−1.61565e7	−1.44922	−0.724609	−	0.689160i	$-0.757980\pi$
$659$	−1.61565e7	−1.44922	−0.724609	+	0.689160i	$0.757980\pi$
$660$	−1.72748e6	−0.154367
$661$	−4.83189e6	−0.430144	−0.215072	−	0.976598i	$-0.568999\pi$
$661$	−4.83189e6	−0.430144	−0.215072	+	0.976598i	$0.568999\pi$
$662$	6.87357e6	0.609589
$663$	1.02871e6	0.0908884
$664$	4.95615e6	0.436239
$665$	−1.29593e6	−0.113639
$666$	2.24941e6	0.196509
$667$	1.86952e7	1.62710
$668$	−3.92776e6	−0.340568
$669$	1.05718e7	0.913240
$670$	−4.08227e6	−0.351329
$671$	7.63867e6	0.654955
$672$	1.52116e6	0.129942
$673$	176472.	0.0150189	0.00750945	−	0.999972i	$-0.497610\pi$
$673$	176472.	0.0150189	0.00750945	+	0.999972i	$0.497610\pi$
$674$	317514.	0.0269224
$675$	1.02766e6	0.0868137
$676$	−4.21084e6	−0.354407
$677$	−1.50335e7	−1.26063	−0.630315	−	0.776340i	$-0.717074\pi$
$677$	−1.50335e7	−1.26063	−0.630315	+	0.776340i	$0.717074\pi$
$678$	1.42191e6	0.118795
$679$	6.69115e6	0.556963
$680$	−1.49816e6	−0.124247
$681$	8.00196e6	0.661194
$682$	−350382.	−0.0288457
$683$	−6.00912e6	−0.492900	−0.246450	−	0.969155i	$-0.579264\pi$
$683$	−6.00912e6	−0.492900	−0.246450	+	0.969155i	$0.579264\pi$
$684$	151105.	0.0123492
$685$	1.90726e7	1.55304
$686$	−4.20595e6	−0.341235
$687$	476959.	0.0385558
$688$	2.02509e6	0.163107
$689$	9.11319e6	0.731345
$690$	1.16960e7	0.935222
$691$	−4.97683e6	−0.396513	−0.198257	−	0.980150i	$-0.563528\pi$
$691$	−4.97683e6	−0.396513	−0.198257	+	0.980150i	$0.563528\pi$
$692$	−5.70713e6	−0.453056
$693$	2.38174e6	0.188391
$694$	−1.70078e7	−1.34044
$695$	−1.18088e6	−0.0927353
$696$	2.23198e6	0.174650
$697$	1.07134e6	0.0835302
$698$	−2.31092e6	−0.179534
$699$	−75397.2	−0.00583663
$700$	−3.72282e6	−0.287162
$701$	−383215.	−0.0294542	−0.0147271	−	0.999892i	$-0.504688\pi$
$701$	−383215.	−0.0294542	−0.0147271	+	0.999892i	$0.504688\pi$
$702$	−958807.	−0.0734325
$703$	−809466.	−0.0617747
$704$	−729689.	−0.0554889
$705$	−8.43538e6	−0.639193
$706$	1.68422e7	1.27171
$707$	−5.15912e6	−0.388175
$708$	501264.	0.0375823
$709$	−2.29343e7	−1.71344	−0.856720	−	0.515781i	$-0.827502\pi$
$709$	−2.29343e7	−1.71344	−0.856720	+	0.515781i	$0.827502\pi$
$710$	1.20740e7	0.898887
$711$	−2.53868e6	−0.188336
$712$	−2.37294e6	−0.175423
$713$	2.37228e6	0.174760
$714$	2.06557e6	0.151633
$715$	−3.94453e6	−0.288556
$716$	−5.78595e6	−0.421786
$717$	−4.74250e6	−0.344516
$718$	6.69923e6	0.484969
$719$	−2.03997e7	−1.47164	−0.735819	−	0.677179i	$-0.763202\pi$
$719$	−2.03997e7	−1.47164	−0.735819	+	0.677179i	$0.763202\pi$
$720$	1.39636e6	0.100385
$721$	2.95890e7	2.11979
$722$	9.85002e6	0.703225
$723$	9.57050e6	0.680909
$724$	−2.67818e6	−0.189886
$725$	−5.46247e6	−0.385961
$726$	4.65533e6	0.327800
$727$	416368.	0.0292174	0.0146087	−	0.999893i	$-0.495350\pi$
$727$	416368.	0.0292174	0.0146087	+	0.999893i	$0.495350\pi$
$728$	3.47340e6	0.242900
$729$	531441.	0.0370370
$730$	−4.71509e6	−0.327479
$731$	2.74986e6	0.190334
$732$	−6.17451e6	−0.425917
$733$	8.61805e6	0.592447	0.296223	−	0.955119i	$-0.404273\pi$
$733$	8.61805e6	0.592447	0.296223	+	0.955119i	$0.404273\pi$
$734$	−529249.	−0.0362593
$735$	6.32516e6	0.431870
$736$	4.94039e6	0.336176
$737$	−2.69989e6	−0.183095
$738$	−998538.	−0.0674875
$739$	2.08062e6	0.140146	0.0700732	−	0.997542i	$-0.477677\pi$
$739$	2.08062e6	0.140146	0.0700732	+	0.997542i	$0.477677\pi$
$740$	−7.48026e6	−0.502155
$741$	345034.	0.0230843
$742$	1.82986e7	1.22014
$743$	2.39836e7	1.59383	0.796915	−	0.604092i	$-0.206464\pi$
$743$	2.39836e7	1.59383	0.796915	+	0.604092i	$0.206464\pi$
$744$	283222.	0.0187583
$745$	2.66584e7	1.75972
$746$	−5.43812e6	−0.357768
$747$	−6.27263e6	−0.411290
$748$	−990840.	−0.0647515
$749$	−2.88482e7	−1.87895
$750$	4.15835e6	0.269940
$751$	−1.78108e7	−1.15235	−0.576175	−	0.817326i	$-0.695455\pi$
$751$	−1.78108e7	−1.15235	−0.576175	+	0.817326i	$0.695455\pi$
$752$	−3.56311e6	−0.229765
$753$	−2.58621e6	−0.166217
$754$	5.09650e6	0.326471
$755$	−1.82116e7	−1.16274
$756$	−1.92521e6	−0.122511
$757$	−1.17306e7	−0.744011	−0.372005	−	0.928231i	$-0.621330\pi$
$757$	−1.17306e7	−0.744011	−0.372005	+	0.928231i	$0.621330\pi$
$758$	7.56313e6	0.478111
$759$	7.73538e6	0.487391
$760$	−502491.	−0.0315569
$761$	1.89667e7	1.18722	0.593609	−	0.804753i	$-0.297702\pi$
$761$	1.89667e7	1.18722	0.593609	+	0.804753i	$0.297702\pi$
$762$	4.89683e6	0.305512
$763$	1.32641e7	0.824831
$764$	−1.62690e6	−0.100839
$765$	1.89611e6	0.117141
$766$	−6.12753e6	−0.377323
$767$	1.14458e6	0.0702521
$768$	589824.	0.0360844
$769$	9.39663e6	0.573002	0.286501	−	0.958080i	$-0.407508\pi$
$769$	9.39663e6	0.573002	0.286501	+	0.958080i	$0.407508\pi$
$770$	−7.92032e6	−0.481411
$771$	8.81389e6	0.533988
$772$	−7.45710e6	−0.450326
$773$	−1.10060e7	−0.662495	−0.331247	−	0.943544i	$-0.607469\pi$
$773$	−1.10060e7	−0.662495	−0.331247	+	0.943544i	$0.607469\pi$
$774$	−2.56301e6	−0.153779
$775$	−693145.	−0.0414543
$776$	2.59447e6	0.154666
$777$	1.03133e7	0.612837
$778$	−2.63052e6	−0.155809
$779$	359331.	0.0212154
$780$	3.18845e6	0.187648
$781$	7.98538e6	0.468455
$782$	6.70853e6	0.392293
$783$	−2.82486e6	−0.164661
$784$	2.67175e6	0.155241
$785$	2.48819e7	1.44115
$786$	5.48136e6	0.316470
$787$	−1.29645e7	−0.746139	−0.373070	−	0.927803i	$-0.621695\pi$
$787$	−1.29645e7	−0.746139	−0.373070	+	0.927803i	$0.621695\pi$
$788$	−8.59936e6	−0.493345
$789$	1.61800e7	0.925309
$790$	8.44222e6	0.481270
$791$	6.51931e6	0.370476
$792$	923512.	0.0523154
$793$	−1.40988e7	−0.796160
$794$	8.66018e6	0.487501
$795$	1.67974e7	0.942594
$796$	−6.04982e6	−0.338423
$797$	5.33311e6	0.297396	0.148698	−	0.988883i	$-0.452492\pi$
$797$	5.33311e6	0.297396	0.148698	+	0.988883i	$0.452492\pi$
$798$	692802.	0.0385125
$799$	−4.83832e6	−0.268119
$800$	−1.44351e6	−0.0797435
$801$	3.00326e6	0.165391
$802$	−1.07565e7	−0.590521
$803$	−3.11842e6	−0.170666
$804$	2.18238e6	0.119067
$805$	5.36249e7	2.91660
$806$	646707.	0.0350647
$807$	−1.00227e7	−0.541752
$808$	−2.00043e6	−0.107794
$809$	−1.25824e7	−0.675913	−0.337956	−	0.941162i	$-0.609736\pi$
$809$	−1.25824e7	−0.675913	−0.337956	+	0.941162i	$0.609736\pi$
$810$	−1.76727e6	−0.0946435
$811$	−1.54902e7	−0.826999	−0.413499	−	0.910504i	$-0.635694\pi$
$811$	−1.54902e7	−0.826999	−0.413499	+	0.910504i	$0.635694\pi$
$812$	1.02334e7	0.544666
$813$	7.07103e6	0.375194
$814$	−4.94722e6	−0.261698
$815$	−3.45537e7	−1.82222
$816$	800919.	0.0421078
$817$	922317.	0.0483420
$818$	1.10789e7	0.578913
$819$	−4.39603e6	−0.229008
$820$	3.32057e6	0.172456
$821$	8.84507e6	0.457977	0.228988	−	0.973429i	$-0.426458\pi$
$821$	8.84507e6	0.457977	0.228988	+	0.973429i	$0.426458\pi$
$822$	−1.01962e7	−0.526331
$823$	1.56270e6	0.0804224	0.0402112	−	0.999191i	$-0.487197\pi$
$823$	1.56270e6	0.0804224	0.0402112	+	0.999191i	$0.487197\pi$
$824$	1.14731e7	0.588655
$825$	−2.26017e6	−0.115613
$826$	2.29824e6	0.117205
$827$	−3.69979e7	−1.88111	−0.940553	−	0.339648i	$-0.889692\pi$
$827$	−3.69979e7	−1.88111	−0.940553	+	0.339648i	$0.889692\pi$
$828$	−6.25268e6	−0.316950
$829$	−3.24368e6	−0.163927	−0.0819637	−	0.996635i	$-0.526119\pi$
$829$	−3.24368e6	−0.163927	−0.0819637	+	0.996635i	$0.526119\pi$
$830$	2.08592e7	1.05100
$831$	−4.65957e6	−0.234069
$832$	1.34680e6	0.0674521
$833$	3.62795e6	0.181155
$834$	631301.	0.0314283
$835$	−1.65310e7	−0.820507
$836$	−332333.	−0.0164459
$837$	−358452.	−0.0176855
$838$	−6.85631e6	−0.337272
$839$	2.82905e7	1.38751	0.693754	−	0.720212i	$-0.255956\pi$
$839$	2.82905e7	1.38751	0.693754	+	0.720212i	$0.255956\pi$
$840$	6.40217e6	0.313061
$841$	−5.49574e6	−0.267939
$842$	1.33181e6	0.0647383
$843$	1.22597e7	0.594169
$844$	5.99162e6	0.289527
$845$	−1.77224e7	−0.853848
$846$	4.50956e6	0.216625
$847$	2.13442e7	1.02228
$848$	7.09523e6	0.338826
$849$	1.54307e7	0.734711
$850$	−1.96014e6	−0.0930548
$851$	3.34954e7	1.58548
$852$	−6.45476e6	−0.304636
$853$	−7.44085e6	−0.350147	−0.175073	−	0.984555i	$-0.556016\pi$
$853$	−7.44085e6	−0.350147	−0.175073	+	0.984555i	$0.556016\pi$
$854$	−2.83094e7	−1.32827
$855$	635965.	0.0297521
$856$	−1.11858e7	−0.521775
$857$	1.80080e7	0.837555	0.418778	−	0.908089i	$-0.362459\pi$
$857$	1.80080e7	0.837555	0.418778	+	0.908089i	$0.362459\pi$
$858$	2.10874e6	0.0977926
$859$	−1.60124e7	−0.740410	−0.370205	−	0.928950i	$-0.620713\pi$
$859$	−1.60124e7	−0.740410	−0.370205	+	0.928950i	$0.620713\pi$
$860$	8.52311e6	0.392963
$861$	−4.57819e6	−0.210468
$862$	−1.67242e7	−0.766614
$863$	−2.92123e7	−1.33518	−0.667588	−	0.744531i	$-0.732673\pi$
$863$	−2.92123e7	−1.33518	−0.667588	+	0.744531i	$0.732673\pi$
$864$	−746496.	−0.0340207
$865$	−2.40199e7	−1.09152
$866$	−5.90214e6	−0.267433
$867$	−1.16912e7	−0.528213
$868$	1.29854e6	0.0585000
$869$	5.58343e6	0.250814
$870$	9.39387e6	0.420771
$871$	4.98324e6	0.222570
$872$	5.14310e6	0.229052
$873$	−3.28363e6	−0.145821
$874$	2.25007e6	0.0996364
$875$	1.90656e7	0.841841
$876$	2.52069e6	0.110984
$877$	2.43345e7	1.06837	0.534187	−	0.845366i	$-0.320618\pi$
$877$	2.43345e7	1.06837	0.534187	+	0.845366i	$0.320618\pi$
$878$	−1.05767e7	−0.463035
$879$	8.75825e6	0.382336
$880$	−3.07108e6	−0.133686
$881$	−1.81786e7	−0.789079	−0.394539	−	0.918879i	$-0.629096\pi$
$881$	−1.81786e7	−0.789079	−0.394539	+	0.918879i	$0.629096\pi$
$882$	−3.38143e6	−0.146362
$883$	1.04512e7	0.451090	0.225545	−	0.974233i	$-0.427584\pi$
$883$	1.04512e7	0.451090	0.225545	+	0.974233i	$0.427584\pi$
$884$	1.82881e6	0.0787116
$885$	2.10970e6	0.0905444
$886$	9.66240e6	0.413524
$887$	−1.94454e7	−0.829864	−0.414932	−	0.909852i	$-0.636195\pi$
$887$	−1.94454e7	−0.829864	−0.414932	+	0.909852i	$0.636195\pi$
$888$	3.99895e6	0.170182
$889$	2.24515e7	0.952775
$890$	−9.98714e6	−0.422635
$891$	−1.16882e6	−0.0493235
$892$	1.87944e7	0.790889
$893$	−1.62280e6	−0.0680982
$894$	−1.42516e7	−0.596375
$895$	−2.43516e7	−1.01618
$896$	2.70428e6	0.112533
$897$	−1.42774e7	−0.592470
$898$	1.03033e7	0.426368
$899$	1.90534e6	0.0786273
$900$	1.82694e6	0.0751829
$901$	9.63457e6	0.395385
$902$	2.19613e6	0.0898754
$903$	−1.17511e7	−0.479578
$904$	2.52784e6	0.102880
$905$	−1.12718e7	−0.457480
$906$	9.73593e6	0.394055
$907$	−2.49460e7	−1.00689	−0.503447	−	0.864026i	$-0.667935\pi$
$907$	−2.49460e7	−1.00689	−0.503447	+	0.864026i	$0.667935\pi$
$908$	1.42257e7	0.572611
$909$	2.53180e6	0.101629
$910$	1.46187e7	0.585201
$911$	−2.75421e7	−1.09951	−0.549757	−	0.835325i	$-0.685280\pi$
$911$	−2.75421e7	−1.09951	−0.549757	+	0.835325i	$0.685280\pi$
$912$	268632.	0.0106947
$913$	1.37957e7	0.547729
$914$	−2.32946e7	−0.922338
$915$	−2.59870e7	−1.02613
$916$	847928.	0.0333903
$917$	2.51314e7	0.986948
$918$	−1.01366e6	−0.0396997
$919$	3.12679e7	1.22126	0.610632	−	0.791914i	$-0.290915\pi$
$919$	3.12679e7	1.22126	0.610632	+	0.791914i	$0.290915\pi$
$920$	2.07929e7	0.809926
$921$	−1.74770e7	−0.678920
$922$	−1.76008e7	−0.681875
$923$	−1.47388e7	−0.569452
$924$	4.23420e6	0.163152
$925$	−9.78687e6	−0.376088
$926$	−8.49397e6	−0.325524
$927$	−1.45206e7	−0.554990
$928$	3.96797e6	0.151251
$929$	−4.54575e7	−1.72809	−0.864045	−	0.503414i	$-0.832077\pi$
$929$	−4.54575e7	−1.72809	−0.864045	+	0.503414i	$0.832077\pi$
$930$	1.19201e6	0.0451931
$931$	1.21683e6	0.0460105
$932$	−134039.	−0.00505467
$933$	1.95941e7	0.736922
$934$	−4.30047e6	−0.161305
$935$	−4.17020e6	−0.156001
$936$	−1.70455e6	−0.0635944
$937$	−2.41680e7	−0.899273	−0.449636	−	0.893212i	$-0.648446\pi$
$937$	−2.41680e7	−0.899273	−0.449636	+	0.893212i	$0.648446\pi$
$938$	1.00060e7	0.371324
$939$	−2.85668e6	−0.105730
$940$	−1.49962e7	−0.553557
$941$	5.04937e7	1.85893	0.929466	−	0.368909i	$-0.120269\pi$
$941$	5.04937e7	1.85893	0.929466	+	0.368909i	$0.120269\pi$
$942$	−1.33019e7	−0.488411
$943$	−1.48690e7	−0.544505
$944$	891136.	0.0325472
$945$	−8.10275e6	−0.295157
$946$	5.63693e6	0.204793
$947$	6.36565e6	0.230658	0.115329	−	0.993327i	$-0.463208\pi$
$947$	6.36565e6	0.230658	0.115329	+	0.993327i	$0.463208\pi$
$948$	−4.51321e6	−0.163104
$949$	5.75573e6	0.207460
$950$	−657439.	−0.0236345
$951$	1.16471e7	0.417604
$952$	3.67213e6	0.131318
$953$	−2.26896e7	−0.809273	−0.404636	−	0.914478i	$-0.632602\pi$
$953$	−2.26896e7	−0.809273	−0.404636	+	0.914478i	$0.632602\pi$
$954$	−8.97990e6	−0.319448
$955$	−6.84721e6	−0.242944
$956$	−8.43111e6	−0.298360
$957$	6.21282e6	0.219285
$958$	2.50316e6	0.0881199
$959$	−4.67485e7	−1.64143
$960$	2.48242e6	0.0869356
$961$	−2.83874e7	−0.991555
$962$	9.13119e6	0.318119
$963$	1.41570e7	0.491934
$964$	1.70142e7	0.589684
$965$	−3.13851e7	−1.08494
$966$	−2.86679e7	−0.988446
$967$	−1.62930e7	−0.560317	−0.280158	−	0.959954i	$-0.590387\pi$
$967$	−1.62930e7	−0.560317	−0.280158	+	0.959954i	$0.590387\pi$
$968$	8.27614e6	0.283883
$969$	364774.	0.0124800
$970$	1.09195e7	0.372626
$971$	−4.82356e7	−1.64180	−0.820899	−	0.571073i	$-0.806527\pi$
$971$	−4.82356e7	−1.64180	−0.820899	+	0.571073i	$0.806527\pi$
$972$	944784.	0.0320750
$973$	2.89445e6	0.0980129
$974$	7.50705e6	0.253555
$975$	4.17164e6	0.140538
$976$	−1.09769e7	−0.368855
$977$	−4.01169e7	−1.34459	−0.672297	−	0.740281i	$-0.734692\pi$
$977$	−4.01169e7	−1.34459	−0.672297	+	0.740281i	$0.734692\pi$
$978$	1.84724e7	0.617556
$979$	−6.60519e6	−0.220256
$980$	1.12447e7	0.374011
$981$	−6.50923e6	−0.215952
$982$	−2.17586e7	−0.720034
$983$	1.61555e7	0.533257	0.266628	−	0.963799i	$-0.414090\pi$
$983$	1.61555e7	0.533257	0.266628	+	0.963799i	$0.414090\pi$
$984$	−1.77518e6	−0.0584459
$985$	−3.61926e7	−1.18858
$986$	5.38809e6	0.176499
$987$	2.06758e7	0.675569
$988$	613393.	0.0199916
$989$	−3.81651e7	−1.24073
$990$	3.88683e6	0.126040
$991$	2.87496e7	0.929925	0.464962	−	0.885330i	$-0.346068\pi$
$991$	2.87496e7	0.929925	0.464962	+	0.885330i	$0.346068\pi$
$992$	503505.	0.0162452
$993$	−1.54655e7	−0.497727
$994$	−2.95944e7	−0.950043
$995$	−2.54622e7	−0.815338
$996$	−1.11513e7	−0.356188
$997$	2.06561e7	0.658129	0.329065	−	0.944307i	$-0.393267\pi$
$997$	2.06561e7	0.658129	0.329065	+	0.944307i	$0.393267\pi$
$998$	−1.35445e7	−0.430462
$999$	−5.06117e6	−0.160449

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.a.c.1.5	✓	5
3.2	odd	2		1062.6.a.f.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.a.c.1.5	✓	5	1.1	even	1	trivial
1062.6.a.f.1.1		5	3.2	odd	2

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	354.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +67.3400 q^{5} -36.0000 q^{6} -165.056 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +67.3400 q^{5} -36.0000 q^{6} -165.056 q^{7} -64.0000 q^{8} +81.0000 q^{9} -269.360 q^{10} -178.147 q^{11} +144.000 q^{12} +328.809 q^{13} +660.224 q^{14} +606.060 q^{15} +256.000 q^{16} +347.621 q^{17} -324.000 q^{18} +116.594 q^{19} +1077.44 q^{20} -1485.51 q^{21} +712.587 q^{22} -4824.60 q^{23} -576.000 q^{24} +1409.68 q^{25} -1315.24 q^{26} +729.000 q^{27} -2640.90 q^{28} -3874.97 q^{29} -2424.24 q^{30} -491.704 q^{31} -1024.00 q^{32} -1603.32 q^{33} -1390.48 q^{34} -11114.9 q^{35} +1296.00 q^{36} -6942.62 q^{37} -466.375 q^{38} +2959.28 q^{39} -4309.76 q^{40} +3081.91 q^{41} +5942.02 q^{42} +7910.52 q^{43} -2850.35 q^{44} +5454.54 q^{45} +19298.4 q^{46} -13918.4 q^{47} +2304.00 q^{48} +10436.5 q^{49} -5638.72 q^{50} +3128.59 q^{51} +5260.94 q^{52} +27715.7 q^{53} -2916.00 q^{54} -11996.4 q^{55} +10563.6 q^{56} +1049.34 q^{57} +15499.9 q^{58} +3481.00 q^{59} +9696.96 q^{60} -42878.5 q^{61} +1966.82 q^{62} -13369.5 q^{63} +4096.00 q^{64} +22142.0 q^{65} +6413.28 q^{66} +15155.4 q^{67} +5561.94 q^{68} -43421.4 q^{69} +44459.5 q^{70} -44824.7 q^{71} -5184.00 q^{72} +17504.8 q^{73} +27770.5 q^{74} +12687.1 q^{75} +1865.50 q^{76} +29404.2 q^{77} -11837.1 q^{78} -31341.8 q^{79} +17239.0 q^{80} +6561.00 q^{81} -12327.6 q^{82} -77439.9 q^{83} -23768.1 q^{84} +23408.8 q^{85} -31642.1 q^{86} -34874.8 q^{87} +11401.4 q^{88} +37077.3 q^{89} -21818.2 q^{90} -54271.9 q^{91} -77193.6 q^{92} -4425.34 q^{93} +55673.5 q^{94} +7851.43 q^{95} -9216.00 q^{96} -40538.7 q^{97} -41746.1 q^{98} -14429.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 20 q^{2} + 45 q^{3} + 80 q^{4} - 10 q^{5} - 180 q^{6} - 162 q^{7} - 320 q^{8} + 405 q^{9}+O(q^{10}) \) 5 * q - 20 * q^2 + 45 * q^3 + 80 * q^4 - 10 * q^5 - 180 * q^6 - 162 * q^7 - 320 * q^8 + 405 * q^9	\( 5 q - 20 q^{2} + 45 q^{3} + 80 q^{4} - 10 q^{5} - 180 q^{6} - 162 q^{7} - 320 q^{8} + 405 q^{9} + 40 q^{10} - 228 q^{11} + 720 q^{12} - 386 q^{13} + 648 q^{14} - 90 q^{15} + 1280 q^{16} + 1304 q^{17} - 1620 q^{18} + 342 q^{19} - 160 q^{20} - 1458 q^{21} + 912 q^{22} - 78 q^{23} - 2880 q^{24} - 3585 q^{25} + 1544 q^{26} + 3645 q^{27} - 2592 q^{28} - 4576 q^{29} + 360 q^{30} - 14456 q^{31} - 5120 q^{32} - 2052 q^{33} - 5216 q^{34} - 5622 q^{35} + 6480 q^{36} - 21684 q^{37} - 1368 q^{38} - 3474 q^{39} + 640 q^{40} - 15484 q^{41} + 5832 q^{42} - 22094 q^{43} - 3648 q^{44} - 810 q^{45} + 312 q^{46} - 4890 q^{47} + 11520 q^{48} + 3955 q^{49} + 14340 q^{50} + 11736 q^{51} - 6176 q^{52} + 12686 q^{53} - 14580 q^{54} - 40468 q^{55} + 10368 q^{56} + 3078 q^{57} + 18304 q^{58} + 17405 q^{59} - 1440 q^{60} - 17792 q^{61} + 57824 q^{62} - 13122 q^{63} + 20480 q^{64} + 67704 q^{65} + 8208 q^{66} - 33042 q^{67} + 20864 q^{68} - 702 q^{69} + 22488 q^{70} + 16172 q^{71} - 25920 q^{72} - 40092 q^{73} + 86736 q^{74} - 32265 q^{75} + 5472 q^{76} + 33330 q^{77} + 13896 q^{78} - 51216 q^{79} - 2560 q^{80} + 32805 q^{81} + 61936 q^{82} + 7526 q^{83} - 23328 q^{84} - 92546 q^{85} + 88376 q^{86} - 41184 q^{87} + 14592 q^{88} + 4210 q^{89} + 3240 q^{90} - 263742 q^{91} - 1248 q^{92} - 130104 q^{93} + 19560 q^{94} - 220798 q^{95} - 46080 q^{96} - 279974 q^{97} - 15820 q^{98} - 18468 q^{99}+O(q^{100}) \) 5 * q - 20 * q^2 + 45 * q^3 + 80 * q^4 - 10 * q^5 - 180 * q^6 - 162 * q^7 - 320 * q^8 + 405 * q^9 + 40 * q^10 - 228 * q^11 + 720 * q^12 - 386 * q^13 + 648 * q^14 - 90 * q^15 + 1280 * q^16 + 1304 * q^17 - 1620 * q^18 + 342 * q^19 - 160 * q^20 - 1458 * q^21 + 912 * q^22 - 78 * q^23 - 2880 * q^24 - 3585 * q^25 + 1544 * q^26 + 3645 * q^27 - 2592 * q^28 - 4576 * q^29 + 360 * q^30 - 14456 * q^31 - 5120 * q^32 - 2052 * q^33 - 5216 * q^34 - 5622 * q^35 + 6480 * q^36 - 21684 * q^37 - 1368 * q^38 - 3474 * q^39 + 640 * q^40 - 15484 * q^41 + 5832 * q^42 - 22094 * q^43 - 3648 * q^44 - 810 * q^45 + 312 * q^46 - 4890 * q^47 + 11520 * q^48 + 3955 * q^49 + 14340 * q^50 + 11736 * q^51 - 6176 * q^52 + 12686 * q^53 - 14580 * q^54 - 40468 * q^55 + 10368 * q^56 + 3078 * q^57 + 18304 * q^58 + 17405 * q^59 - 1440 * q^60 - 17792 * q^61 + 57824 * q^62 - 13122 * q^63 + 20480 * q^64 + 67704 * q^65 + 8208 * q^66 - 33042 * q^67 + 20864 * q^68 - 702 * q^69 + 22488 * q^70 + 16172 * q^71 - 25920 * q^72 - 40092 * q^73 + 86736 * q^74 - 32265 * q^75 + 5472 * q^76 + 33330 * q^77 + 13896 * q^78 - 51216 * q^79 - 2560 * q^80 + 32805 * q^81 + 61936 * q^82 + 7526 * q^83 - 23328 * q^84 - 92546 * q^85 + 88376 * q^86 - 41184 * q^87 + 14592 * q^88 + 4210 * q^89 + 3240 * q^90 - 263742 * q^91 - 1248 * q^92 - 130104 * q^93 + 19560 * q^94 - 220798 * q^95 - 46080 * q^96 - 279974 * q^97 - 15820 * q^98 - 18468 * q^99

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