LMFDB - Embedded newform 354.6.a.e.1.4

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:	$0$
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} - 1060x^{3} + 10546x^{2} + 78584x - 857860 $ x^5 - x^4 - 1060x^3 + 10546x^2 + 78584*x - 857860
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$23.7650$ 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)

$f(q)$	$=$	$q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +71.6358 q^{5} -36.0000 q^{6} +12.9515 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +71.6358 q^{5} -36.0000 q^{6} +12.9515 q^{7} +64.0000 q^{8} +81.0000 q^{9} +286.543 q^{10} +255.933 q^{11} -144.000 q^{12} +531.009 q^{13} +51.8058 q^{14} -644.722 q^{15} +256.000 q^{16} -65.1064 q^{17} +324.000 q^{18} -198.566 q^{19} +1146.17 q^{20} -116.563 q^{21} +1023.73 q^{22} +2205.75 q^{23} -576.000 q^{24} +2006.69 q^{25} +2124.04 q^{26} -729.000 q^{27} +207.223 q^{28} -4247.44 q^{29} -2578.89 q^{30} -6562.02 q^{31} +1024.00 q^{32} -2303.40 q^{33} -260.425 q^{34} +927.789 q^{35} +1296.00 q^{36} +11894.2 q^{37} -794.265 q^{38} -4779.08 q^{39} +4584.69 q^{40} +17835.5 q^{41} -466.253 q^{42} +10195.2 q^{43} +4094.93 q^{44} +5802.50 q^{45} +8822.99 q^{46} -7823.36 q^{47} -2304.00 q^{48} -16639.3 q^{49} +8026.77 q^{50} +585.957 q^{51} +8496.15 q^{52} -24850.5 q^{53} -2916.00 q^{54} +18334.0 q^{55} +828.893 q^{56} +1787.10 q^{57} -16989.8 q^{58} -3481.00 q^{59} -10315.6 q^{60} +14896.3 q^{61} -26248.1 q^{62} +1049.07 q^{63} +4096.00 q^{64} +38039.3 q^{65} -9213.58 q^{66} +55384.3 q^{67} -1041.70 q^{68} -19851.7 q^{69} +3711.15 q^{70} -14432.9 q^{71} +5184.00 q^{72} +43227.3 q^{73} +47576.8 q^{74} -18060.2 q^{75} -3177.06 q^{76} +3314.70 q^{77} -19116.3 q^{78} -13960.8 q^{79} +18338.8 q^{80} +6561.00 q^{81} +71342.0 q^{82} -35241.5 q^{83} -1865.01 q^{84} -4663.95 q^{85} +40780.7 q^{86} +38226.9 q^{87} +16379.7 q^{88} +79275.4 q^{89} +23210.0 q^{90} +6877.34 q^{91} +35292.0 q^{92} +59058.2 q^{93} -31293.5 q^{94} -14224.5 q^{95} -9216.00 q^{96} +121587. q^{97} -66557.0 q^{98} +20730.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 20 q^{2} - 45 q^{3} + 80 q^{4} + 166 q^{5} - 180 q^{6} - 198 q^{7} + 320 q^{8} + 405 q^{9}+O(q^{10}) $ 5 * q + 20 * q^2 - 45 * q^3 + 80 * q^4 + 166 * q^5 - 180 * q^6 - 198 * q^7 + 320 * q^8 + 405 * q^9	\( 5 q + 20 q^{2} - 45 q^{3} + 80 q^{4} + 166 q^{5} - 180 q^{6} - 198 q^{7} + 320 q^{8} + 405 q^{9} + 664 q^{10} - 516 q^{11} - 720 q^{12} + 1018 q^{13} - 792 q^{14} - 1494 q^{15} + 1280 q^{16} + 3004 q^{17} + 1620 q^{18} - 114 q^{19} + 2656 q^{20} + 1782 q^{21} - 2064 q^{22} - 1302 q^{23} - 2880 q^{24} + 8967 q^{25} + 4072 q^{26} - 3645 q^{27} - 3168 q^{28} + 16372 q^{29} - 5976 q^{30} - 4784 q^{31} + 5120 q^{32} + 4644 q^{33} + 12016 q^{34} - 9702 q^{35} + 6480 q^{36} + 5016 q^{37} - 456 q^{38} - 9162 q^{39} + 10624 q^{40} + 5440 q^{41} + 7128 q^{42} + 5494 q^{43} - 8256 q^{44} + 13446 q^{45} - 5208 q^{46} + 19470 q^{47} - 11520 q^{48} + 80323 q^{49} + 35868 q^{50} - 27036 q^{51} + 16288 q^{52} + 63310 q^{53} - 14580 q^{54} + 62324 q^{55} - 12672 q^{56} + 1026 q^{57} + 65488 q^{58} - 17405 q^{59} - 23904 q^{60} + 71776 q^{61} - 19136 q^{62} - 16038 q^{63} + 20480 q^{64} - 39492 q^{65} + 18576 q^{66} + 79962 q^{67} + 48064 q^{68} + 11718 q^{69} - 38808 q^{70} + 9928 q^{71} + 25920 q^{72} + 92772 q^{73} + 20064 q^{74} - 80703 q^{75} - 1824 q^{76} + 42750 q^{77} - 36648 q^{78} - 18444 q^{79} + 42496 q^{80} + 32805 q^{81} + 21760 q^{82} + 106030 q^{83} + 28512 q^{84} + 283366 q^{85} + 21976 q^{86} - 147348 q^{87} - 33024 q^{88} + 315950 q^{89} + 53784 q^{90} + 354078 q^{91} - 20832 q^{92} + 43056 q^{93} + 77880 q^{94} + 371662 q^{95} - 46080 q^{96} + 268078 q^{97} + 321292 q^{98} - 41796 q^{99}+O(q^{100}) \) 5 * q + 20 * q^2 - 45 * q^3 + 80 * q^4 + 166 * q^5 - 180 * q^6 - 198 * q^7 + 320 * q^8 + 405 * q^9 + 664 * q^10 - 516 * q^11 - 720 * q^12 + 1018 * q^13 - 792 * q^14 - 1494 * q^15 + 1280 * q^16 + 3004 * q^17 + 1620 * q^18 - 114 * q^19 + 2656 * q^20 + 1782 * q^21 - 2064 * q^22 - 1302 * q^23 - 2880 * q^24 + 8967 * q^25 + 4072 * q^26 - 3645 * q^27 - 3168 * q^28 + 16372 * q^29 - 5976 * q^30 - 4784 * q^31 + 5120 * q^32 + 4644 * q^33 + 12016 * q^34 - 9702 * q^35 + 6480 * q^36 + 5016 * q^37 - 456 * q^38 - 9162 * q^39 + 10624 * q^40 + 5440 * q^41 + 7128 * q^42 + 5494 * q^43 - 8256 * q^44 + 13446 * q^45 - 5208 * q^46 + 19470 * q^47 - 11520 * q^48 + 80323 * q^49 + 35868 * q^50 - 27036 * q^51 + 16288 * q^52 + 63310 * q^53 - 14580 * q^54 + 62324 * q^55 - 12672 * q^56 + 1026 * q^57 + 65488 * q^58 - 17405 * q^59 - 23904 * q^60 + 71776 * q^61 - 19136 * q^62 - 16038 * q^63 + 20480 * q^64 - 39492 * q^65 + 18576 * q^66 + 79962 * q^67 + 48064 * q^68 + 11718 * q^69 - 38808 * q^70 + 9928 * q^71 + 25920 * q^72 + 92772 * q^73 + 20064 * q^74 - 80703 * q^75 - 1824 * q^76 + 42750 * q^77 - 36648 * q^78 - 18444 * q^79 + 42496 * q^80 + 32805 * q^81 + 21760 * q^82 + 106030 * q^83 + 28512 * q^84 + 283366 * q^85 + 21976 * q^86 - 147348 * q^87 - 33024 * q^88 + 315950 * q^89 + 53784 * q^90 + 354078 * q^91 - 20832 * q^92 + 43056 * q^93 + 77880 * q^94 + 371662 * q^95 - 46080 * q^96 + 268078 * q^97 + 321292 * q^98 - 41796 * 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
$5$	71.6358	1.28146	0.640730	−	0.767766i	$-0.278632\pi$
$5$	71.6358	1.28146	0.640730	+	0.767766i	$0.278632\pi$
$6$	−36.0000	−0.408248
$7$	12.9515	0.0999019	0.0499509	−	0.998752i	$-0.484094\pi$
$7$	12.9515	0.0999019	0.0499509	+	0.998752i	$0.484094\pi$
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	286.543	0.906130
$11$	255.933	0.637741	0.318870	−	0.947798i	$-0.396696\pi$
$11$	255.933	0.637741	0.318870	+	0.947798i	$0.396696\pi$
$12$	−144.000	−0.288675
$13$	531.009	0.871452	0.435726	−	0.900079i	$-0.356492\pi$
$13$	531.009	0.871452	0.435726	+	0.900079i	$0.356492\pi$
$14$	51.8058	0.0706413
$15$	−644.722	−0.739852
$16$	256.000	0.250000
$17$	−65.1064	−0.0546388	−0.0273194	−	0.999627i	$-0.508697\pi$
$17$	−65.1064	−0.0546388	−0.0273194	+	0.999627i	$0.508697\pi$
$18$	324.000	0.235702
$19$	−198.566	−0.126189	−0.0630945	−	0.998008i	$-0.520097\pi$
$19$	−198.566	−0.126189	−0.0630945	+	0.998008i	$0.520097\pi$
$20$	1146.17	0.640730
$21$	−116.563	−0.0576784
$22$	1023.73	0.450951
$23$	2205.75	0.869433	0.434717	−	0.900567i	$-0.356849\pi$
$23$	2205.75	0.869433	0.434717	+	0.900567i	$0.356849\pi$
$24$	−576.000	−0.204124
$25$	2006.69	0.642142
$26$	2124.04	0.616210
$27$	−729.000	−0.192450
$28$	207.223	0.0499509
$29$	−4247.44	−0.937847	−0.468924	−	0.883239i	$-0.655358\pi$
$29$	−4247.44	−0.937847	−0.468924	+	0.883239i	$0.655358\pi$
$30$	−2578.89	−0.523154
$31$	−6562.02	−1.22640	−0.613202	−	0.789926i	$-0.710119\pi$
$31$	−6562.02	−1.22640	−0.613202	+	0.789926i	$0.710119\pi$
$32$	1024.00	0.176777
$33$	−2303.40	−0.368200
$34$	−260.425	−0.0386355
$35$	927.789	0.128020
$36$	1296.00	0.166667
$37$	11894.2	1.42834	0.714168	−	0.699974i	$-0.246805\pi$
$37$	11894.2	1.42834	0.714168	+	0.699974i	$0.246805\pi$
$38$	−794.265	−0.0892291
$39$	−4779.08	−0.503133
$40$	4584.69	0.453065
$41$	17835.5	1.65701	0.828506	−	0.559981i	$-0.189191\pi$
$41$	17835.5	1.65701	0.828506	+	0.559981i	$0.189191\pi$
$42$	−466.253	−0.0407848
$43$	10195.2	0.840860	0.420430	−	0.907325i	$-0.361879\pi$
$43$	10195.2	0.840860	0.420430	+	0.907325i	$0.361879\pi$
$44$	4094.93	0.318870
$45$	5802.50	0.427154
$46$	8822.99	0.614782
$47$	−7823.36	−0.516593	−0.258297	−	0.966066i	$-0.583161\pi$
$47$	−7823.36	−0.516593	−0.258297	+	0.966066i	$0.583161\pi$
$48$	−2304.00	−0.144338
$49$	−16639.3	−0.990020
$50$	8026.77	0.454063
$51$	585.957	0.0315457
$52$	8496.15	0.435726
$53$	−24850.5	−1.21519	−0.607597	−	0.794246i	$-0.707866\pi$
$53$	−24850.5	−1.21519	−0.607597	+	0.794246i	$0.707866\pi$
$54$	−2916.00	−0.136083
$55$	18334.0	0.817240
$56$	828.893	0.0353206
$57$	1787.10	0.0728553
$58$	−16989.8	−0.663158
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	−10315.6	−0.369926
$61$	14896.3	0.512570	0.256285	−	0.966601i	$-0.417502\pi$
$61$	14896.3	0.512570	0.256285	+	0.966601i	$0.417502\pi$
$62$	−26248.1	−0.867198
$63$	1049.07	0.0333006
$64$	4096.00	0.125000
$65$	38039.3	1.11673
$66$	−9213.58	−0.260357
$67$	55384.3	1.50730	0.753650	−	0.657276i	$-0.228292\pi$
$67$	55384.3	1.50730	0.753650	+	0.657276i	$0.228292\pi$
$68$	−1041.70	−0.0273194
$69$	−19851.7	−0.501968
$70$	3711.15	0.0905240
$71$	−14432.9	−0.339788	−0.169894	−	0.985462i	$-0.554342\pi$
$71$	−14432.9	−0.339788	−0.169894	+	0.985462i	$0.554342\pi$
$72$	5184.00	0.117851
$73$	43227.3	0.949403	0.474701	−	0.880147i	$-0.342556\pi$
$73$	43227.3	0.949403	0.474701	+	0.880147i	$0.342556\pi$
$74$	47576.8	1.00999
$75$	−18060.2	−0.370741
$76$	−3177.06	−0.0630945
$77$	3314.70	0.0637115
$78$	−19116.3	−0.355769
$79$	−13960.8	−0.251676	−0.125838	−	0.992051i	$-0.540162\pi$
$79$	−13960.8	−0.251676	−0.125838	+	0.992051i	$0.540162\pi$
$80$	18338.8	0.320365
$81$	6561.00	0.111111
$82$	71342.0	1.17168
$83$	−35241.5	−0.561511	−0.280756	−	0.959779i	$-0.590585\pi$
$83$	−35241.5	−0.561511	−0.280756	+	0.959779i	$0.590585\pi$
$84$	−1865.01	−0.0288392
$85$	−4663.95	−0.0700175
$86$	40780.7	0.594578
$87$	38226.9	0.541466
$88$	16379.7	0.225475
$89$	79275.4	1.06087	0.530437	−	0.847725i	$-0.322028\pi$
$89$	79275.4	1.06087	0.530437	+	0.847725i	$0.322028\pi$
$90$	23210.0	0.302043
$91$	6877.34	0.0870597
$92$	35292.0	0.434717
$93$	59058.2	0.708064
$94$	−31293.5	−0.365287
$95$	−14224.5	−0.161706
$96$	−9216.00	−0.102062
$97$	121587.	1.31207	0.656035	−	0.754730i	$-0.272232\pi$
$97$	121587.	1.31207	0.656035	+	0.754730i	$0.272232\pi$
$98$	−66557.0	−0.700050
$99$	20730.6	0.212580
$100$	32107.1	0.321071
$101$	157001.	1.53143	0.765716	−	0.643179i	$-0.222385\pi$
$101$	157001.	1.53143	0.765716	+	0.643179i	$0.222385\pi$
$102$	2343.83	0.0223062
$103$	131677.	1.22297	0.611485	−	0.791256i	$-0.290573\pi$
$103$	131677.	1.22297	0.611485	+	0.791256i	$0.290573\pi$
$104$	33984.6	0.308105
$105$	−8350.10	−0.0739126
$106$	−99402.0	−0.859271
$107$	−11534.5	−0.0973958	−0.0486979	−	0.998814i	$-0.515507\pi$
$107$	−11534.5	−0.0973958	−0.0486979	+	0.998814i	$0.515507\pi$
$108$	−11664.0	−0.0962250
$109$	7920.62	0.0638547	0.0319273	−	0.999490i	$-0.489835\pi$
$109$	7920.62	0.0638547	0.0319273	+	0.999490i	$0.489835\pi$
$110$	73335.9	0.577876
$111$	−107048.	−0.824651
$112$	3315.57	0.0249755
$113$	220388.	1.62365	0.811824	−	0.583902i	$-0.198475\pi$
$113$	220388.	1.62365	0.811824	+	0.583902i	$0.198475\pi$
$114$	7148.39	0.0515164
$115$	158011.	1.11414
$116$	−67959.0	−0.468924
$117$	43011.7	0.290484
$118$	−13924.0	−0.0920575
$119$	−843.222	−0.00545852
$120$	−41262.2	−0.261577
$121$	−95549.4	−0.593286
$122$	59585.1	0.362441
$123$	−160519.	−0.956676
$124$	−104992.	−0.613202
$125$	−80110.9	−0.458582
$126$	4196.27	0.0235471
$127$	54900.5	0.302042	0.151021	−	0.988531i	$-0.451744\pi$
$127$	54900.5	0.302042	0.151021	+	0.988531i	$0.451744\pi$
$128$	16384.0	0.0883883
$129$	−91756.6	−0.485471
$130$	152157.	0.789649
$131$	−133501.	−0.679681	−0.339840	−	0.940483i	$-0.610373\pi$
$131$	−133501.	−0.679681	−0.339840	+	0.940483i	$0.610373\pi$
$132$	−36854.3	−0.184100
$133$	−2571.72	−0.0126065
$134$	221537.	1.06582
$135$	−52222.5	−0.246617
$136$	−4166.81	−0.0193177
$137$	−54416.9	−0.247704	−0.123852	−	0.992301i	$-0.539525\pi$
$137$	−54416.9	−0.247704	−0.123852	+	0.992301i	$0.539525\pi$
$138$	−79406.9	−0.354945
$139$	−15230.3	−0.0668607	−0.0334304	−	0.999441i	$-0.510643\pi$
$139$	−15230.3	−0.0668607	−0.0334304	+	0.999441i	$0.510643\pi$
$140$	14844.6	0.0640102
$141$	70410.3	0.298255
$142$	−57731.6	−0.240266
$143$	135903.	0.555761
$144$	20736.0	0.0833333
$145$	−304269.	−1.20181
$146$	172909.	0.671329
$147$	149753.	0.571588
$148$	190307.	0.714168
$149$	−280470.	−1.03495	−0.517476	−	0.855698i	$-0.673128\pi$
$149$	−280470.	−1.03495	−0.517476	+	0.855698i	$0.673128\pi$
$150$	−72240.9	−0.262153
$151$	−182988.	−0.653099	−0.326550	−	0.945180i	$-0.605886\pi$
$151$	−182988.	−0.653099	−0.326550	+	0.945180i	$0.605886\pi$
$152$	−12708.2	−0.0446145
$153$	−5273.62	−0.0182129
$154$	13258.8	0.0450508
$155$	−470076.	−1.57159
$156$	−76465.3	−0.251567
$157$	−107840.	−0.349164	−0.174582	−	0.984643i	$-0.555857\pi$
$157$	−107840.	−0.349164	−0.174582	+	0.984643i	$0.555857\pi$
$158$	−55843.2	−0.177962
$159$	223654.	0.701592
$160$	73355.1	0.226532
$161$	28567.7	0.0868580
$162$	26244.0	0.0785674
$163$	−273992.	−0.807736	−0.403868	−	0.914817i	$-0.632334\pi$
$163$	−273992.	−0.807736	−0.403868	+	0.914817i	$0.632334\pi$
$164$	285368.	0.828506
$165$	−165006.	−0.471834
$166$	−140966.	−0.397048
$167$	−536328.	−1.48812	−0.744062	−	0.668110i	$-0.767103\pi$
$167$	−536328.	−1.48812	−0.744062	+	0.668110i	$0.767103\pi$
$168$	−7460.04	−0.0203924
$169$	−89322.3	−0.240571
$170$	−18655.8	−0.0495098
$171$	−16083.9	−0.0420630
$172$	163123.	0.420430
$173$	−215553.	−0.547568	−0.273784	−	0.961791i	$-0.588275\pi$
$173$	−215553.	−0.547568	−0.273784	+	0.961791i	$0.588275\pi$
$174$	152908.	0.382874
$175$	25989.6	0.0641511
$176$	65518.8	0.159435
$177$	31329.0	0.0751646
$178$	317102.	0.750151
$179$	404066.	0.942583	0.471292	−	0.881977i	$-0.343788\pi$
$179$	404066.	0.942583	0.471292	+	0.881977i	$0.343788\pi$
$180$	92840.0	0.213577
$181$	−60363.2	−0.136954	−0.0684771	−	0.997653i	$-0.521814\pi$
$181$	−60363.2	−0.136954	−0.0684771	+	0.997653i	$0.521814\pi$
$182$	27509.4	0.0615605
$183$	−134066.	−0.295932
$184$	141168.	0.307391
$185$	852050.	1.83036
$186$	236233.	0.500677
$187$	−16662.9	−0.0348454
$188$	−125174.	−0.258297
$189$	−9441.61	−0.0192261
$190$	−56897.8	−0.114344
$191$	−600194.	−1.19044	−0.595221	−	0.803562i	$-0.702935\pi$
$191$	−600194.	−1.19044	−0.595221	+	0.803562i	$0.702935\pi$
$192$	−36864.0	−0.0721688
$193$	−103301.	−0.199623	−0.0998117	−	0.995006i	$-0.531824\pi$
$193$	−103301.	−0.199623	−0.0998117	+	0.995006i	$0.531824\pi$
$194$	486347.	0.927774
$195$	−342354.	−0.644745
$196$	−266228.	−0.495010
$197$	257159.	0.472102	0.236051	−	0.971741i	$-0.424147\pi$
$197$	257159.	0.472102	0.236051	+	0.971741i	$0.424147\pi$
$198$	82922.2	0.150317
$199$	−1.04444e6	−1.86961	−0.934803	−	0.355166i	$-0.884424\pi$
$199$	−1.04444e6	−1.86961	−0.934803	+	0.355166i	$0.884424\pi$
$200$	128428.	0.227031
$201$	−498459.	−0.870240
$202$	628002.	1.08289
$203$	−55010.5	−0.0936927
$204$	9375.32	0.0157729
$205$	1.27766e6	2.12339
$206$	526707.	0.864770
$207$	178666.	0.289811
$208$	135938.	0.217863
$209$	−50819.6	−0.0804759
$210$	−33400.4	−0.0522641
$211$	−27187.9	−0.0420407	−0.0210204	−	0.999779i	$-0.506691\pi$
$211$	−27187.9	−0.0420407	−0.0210204	+	0.999779i	$0.506691\pi$
$212$	−397608.	−0.607597
$213$	129896.	0.196176
$214$	−46138.1	−0.0688693
$215$	730340.	1.07753
$216$	−46656.0	−0.0680414
$217$	−84987.8	−0.122520
$218$	31682.5	0.0451521
$219$	−389045.	−0.548138
$220$	293343.	0.408620
$221$	−34572.1	−0.0476151
$222$	−428191.	−0.583116
$223$	−1.19954e6	−1.61530	−0.807650	−	0.589663i	$-0.799261\pi$
$223$	−1.19954e6	−1.61530	−0.807650	+	0.589663i	$0.799261\pi$
$224$	13262.3	0.0176603
$225$	162542.	0.214047
$226$	881552.	1.14809
$227$	−124076.	−0.159817	−0.0799087	−	0.996802i	$-0.525463\pi$
$227$	−124076.	−0.159817	−0.0799087	+	0.996802i	$0.525463\pi$
$228$	28593.5	0.0364276
$229$	655911.	0.826525	0.413263	−	0.910612i	$-0.364389\pi$
$229$	655911.	0.826525	0.413263	+	0.910612i	$0.364389\pi$
$230$	632042.	0.787819
$231$	−29832.3	−0.0367839
$232$	−271836.	−0.331579
$233$	−458419.	−0.553188	−0.276594	−	0.960987i	$-0.589206\pi$
$233$	−458419.	−0.553188	−0.276594	+	0.960987i	$0.589206\pi$
$234$	172047.	0.205403
$235$	−560433.	−0.661994
$236$	−55696.0	−0.0650945
$237$	125647.	0.145305
$238$	−3372.89	−0.00385975
$239$	1.04070e6	1.17851	0.589253	−	0.807948i	$-0.299422\pi$
$239$	1.04070e6	1.17851	0.589253	+	0.807948i	$0.299422\pi$
$240$	−165049.	−0.184963
$241$	694797.	0.770575	0.385288	−	0.922797i	$-0.374102\pi$
$241$	694797.	0.770575	0.385288	+	0.922797i	$0.374102\pi$
$242$	−382198.	−0.419517
$243$	−59049.0	−0.0641500
$244$	238340.	0.256285
$245$	−1.19197e6	−1.26867
$246$	−642078.	−0.676472
$247$	−105441.	−0.109968
$248$	−419969.	−0.433599
$249$	317173.	0.324189
$250$	−320444.	−0.324266
$251$	−1.46211e6	−1.46486	−0.732431	−	0.680841i	$-0.761614\pi$
$251$	−1.46211e6	−1.46486	−0.732431	+	0.680841i	$0.761614\pi$
$252$	16785.1	0.0166503
$253$	564523.	0.554473
$254$	219602.	0.213576
$255$	41975.5	0.0404246
$256$	65536.0	0.0625000
$257$	1.38834e6	1.31119	0.655593	−	0.755114i	$-0.272419\pi$
$257$	1.38834e6	1.31119	0.655593	+	0.755114i	$0.272419\pi$
$258$	−367027.	−0.343280
$259$	154047.	0.142694
$260$	608628.	0.558366
$261$	−344042.	−0.312616
$262$	−534002.	−0.480607
$263$	−390691.	−0.348293	−0.174146	−	0.984720i	$-0.555717\pi$
$263$	−390691.	−0.348293	−0.174146	+	0.984720i	$0.555717\pi$
$264$	−147417.	−0.130178
$265$	−1.78019e6	−1.55722
$266$	−10286.9	−0.00891415
$267$	−713479.	−0.612495
$268$	886148.	0.753650
$269$	−594886.	−0.501249	−0.250624	−	0.968084i	$-0.580636\pi$
$269$	−594886.	−0.501249	−0.250624	+	0.968084i	$0.580636\pi$
$270$	−208890.	−0.174385
$271$	1.08469e6	0.897190	0.448595	−	0.893735i	$-0.351925\pi$
$271$	1.08469e6	0.897190	0.448595	+	0.893735i	$0.351925\pi$
$272$	−16667.2	−0.0136597
$273$	−61896.1	−0.0502639
$274$	−217668.	−0.175153
$275$	513579.	0.409520
$276$	−317628.	−0.250984
$277$	−1.28215e6	−1.00402	−0.502008	−	0.864863i	$-0.667405\pi$
$277$	−1.28215e6	−1.00402	−0.502008	+	0.864863i	$0.667405\pi$
$278$	−60921.2	−0.0472777
$279$	−531524.	−0.408801
$280$	59378.5	0.0452620
$281$	1.52115e6	1.14923	0.574614	−	0.818425i	$-0.305152\pi$
$281$	1.52115e6	1.14923	0.574614	+	0.818425i	$0.305152\pi$
$282$	281641.	0.210898
$283$	−1.65401e6	−1.22764	−0.613822	−	0.789444i	$-0.710369\pi$
$283$	−1.65401e6	−1.22764	−0.613822	+	0.789444i	$0.710369\pi$
$284$	−230926.	−0.169894
$285$	128020.	0.0933611
$286$	543611.	0.392982
$287$	230996.	0.165539
$288$	82944.0	0.0589256
$289$	−1.41562e6	−0.997015
$290$	−1.21707e6	−0.849811
$291$	−1.09428e6	−0.757524
$292$	691636.	0.474701
$293$	−727566.	−0.495112	−0.247556	−	0.968874i	$-0.579627\pi$
$293$	−727566.	−0.495112	−0.247556	+	0.968874i	$0.579627\pi$
$294$	599013.	0.404174
$295$	−249364.	−0.166832
$296$	761228.	0.504993
$297$	−186575.	−0.122733
$298$	−1.12188e6	−0.731822
$299$	1.17127e6	0.757670
$300$	−288964.	−0.185370
$301$	132042.	0.0840035
$302$	−731950.	−0.461811
$303$	−1.41300e6	−0.884173
$304$	−50833.0	−0.0315473
$305$	1.06711e6	0.656838
$306$	−21094.5	−0.0128785
$307$	−1.66256e6	−1.00677	−0.503386	−	0.864062i	$-0.667913\pi$
$307$	−1.66256e6	−1.00677	−0.503386	+	0.864062i	$0.667913\pi$
$308$	53035.3	0.0318558
$309$	−1.18509e6	−0.706082
$310$	−1.88030e6	−1.11128
$311$	−1.44458e6	−0.846916	−0.423458	−	0.905916i	$-0.639184\pi$
$311$	−1.44458e6	−0.846916	−0.423458	+	0.905916i	$0.639184\pi$
$312$	−305861.	−0.177884
$313$	690977.	0.398660	0.199330	−	0.979932i	$-0.436123\pi$
$313$	690977.	0.398660	0.199330	+	0.979932i	$0.436123\pi$
$314$	−431359.	−0.246897
$315$	75150.9	0.0426734
$316$	−223373.	−0.125838
$317$	865408.	0.483697	0.241848	−	0.970314i	$-0.422246\pi$
$317$	865408.	0.483697	0.241848	+	0.970314i	$0.422246\pi$
$318$	894618.	0.496101
$319$	−1.08706e6	−0.598103
$320$	293420.	0.160183
$321$	103811.	0.0562315
$322$	114271.	0.0614179
$323$	12927.9	0.00689481
$324$	104976.	0.0555556
$325$	1.06557e6	0.559596
$326$	−1.09597e6	−0.571155
$327$	−71285.5	−0.0368665
$328$	1.14147e6	0.585842
$329$	−101324.	−0.0516087
$330$	−660023.	−0.333637
$331$	122779.	0.0615962	0.0307981	−	0.999526i	$-0.490195\pi$
$331$	122779.	0.0615962	0.0307981	+	0.999526i	$0.490195\pi$
$332$	−563863.	−0.280756
$333$	963430.	0.476112
$334$	−2.14531e6	−1.05226
$335$	3.96750e6	1.93154
$336$	−29840.2	−0.0144196
$337$	−964440.	−0.462595	−0.231297	−	0.972883i	$-0.574297\pi$
$337$	−964440.	−0.462595	−0.231297	+	0.972883i	$0.574297\pi$
$338$	−357289.	−0.170109
$339$	−1.98349e6	−0.937414
$340$	−74623.2	−0.0350087
$341$	−1.67944e6	−0.782128
$342$	−64335.5	−0.0297430
$343$	−433178.	−0.198807
$344$	652492.	0.297289
$345$	−1.42210e6	−0.643252
$346$	−862211.	−0.387189
$347$	−757629.	−0.337779	−0.168890	−	0.985635i	$-0.554018\pi$
$347$	−757629.	−0.337779	−0.168890	+	0.985635i	$0.554018\pi$
$348$	611631.	0.270733
$349$	−588141.	−0.258475	−0.129237	−	0.991614i	$-0.541253\pi$
$349$	−588141.	−0.258475	−0.129237	+	0.991614i	$0.541253\pi$
$350$	103958.	0.0453617
$351$	−387106.	−0.167711
$352$	262075.	0.112738
$353$	3.64739e6	1.55792	0.778962	−	0.627072i	$-0.215747\pi$
$353$	3.64739e6	1.55792	0.778962	+	0.627072i	$0.215747\pi$
$354$	125316.	0.0531494
$355$	−1.03391e6	−0.435425
$356$	1.26841e6	0.530437
$357$	7589.00	0.00315148
$358$	1.61626e6	0.666507
$359$	2.86472e6	1.17313	0.586565	−	0.809902i	$-0.300480\pi$
$359$	2.86472e6	1.17313	0.586565	+	0.809902i	$0.300480\pi$
$360$	371360.	0.151022
$361$	−2.43667e6	−0.984076
$362$	−241453.	−0.0968413
$363$	859944.	0.342534
$364$	110037.	0.0435299
$365$	3.09662e6	1.21662
$366$	−536266.	−0.209256
$367$	−160595.	−0.0622398	−0.0311199	−	0.999516i	$-0.509907\pi$
$367$	−160595.	−0.0622398	−0.0311199	+	0.999516i	$0.509907\pi$
$368$	564671.	0.217358
$369$	1.44467e6	0.552337
$370$	3.40820e6	1.29426
$371$	−321850.	−0.121400
$372$	944931.	0.354032
$373$	−2.12030e6	−0.789089	−0.394544	−	0.918877i	$-0.629098\pi$
$373$	−2.12030e6	−0.789089	−0.394544	+	0.918877i	$0.629098\pi$
$374$	−66651.4	−0.0246394
$375$	720998.	0.264762
$376$	−500695.	−0.182643
$377$	−2.25543e6	−0.817289
$378$	−37766.5	−0.0135949
$379$	−1.24328e6	−0.444600	−0.222300	−	0.974978i	$-0.571356\pi$
$379$	−1.24328e6	−0.444600	−0.222300	+	0.974978i	$0.571356\pi$
$380$	−227591.	−0.0808531
$381$	−494105.	−0.174384
$382$	−2.40077e6	−0.841769
$383$	2.55843e6	0.891201	0.445601	−	0.895232i	$-0.352990\pi$
$383$	2.55843e6	0.891201	0.445601	+	0.895232i	$0.352990\pi$
$384$	−147456.	−0.0510310
$385$	237452.	0.0816438
$386$	−413204.	−0.141155
$387$	825810.	0.280287
$388$	1.94539e6	0.656035
$389$	−105134.	−0.0352265	−0.0176132	−	0.999845i	$-0.505607\pi$
$389$	−105134.	−0.0352265	−0.0176132	+	0.999845i	$0.505607\pi$
$390$	−1.36941e6	−0.455904
$391$	−143608.	−0.0475048
$392$	−1.06491e6	−0.350025
$393$	1.20151e6	0.392414
$394$	1.02864e6	0.333827
$395$	−1.00009e6	−0.322513
$396$	331689.	0.106290
$397$	−5.41574e6	−1.72457	−0.862286	−	0.506422i	$-0.830968\pi$
$397$	−5.41574e6	−1.72457	−0.862286	+	0.506422i	$0.830968\pi$
$398$	−4.17775e6	−1.32201
$399$	23145.5	0.00727838
$400$	513713.	0.160535
$401$	4.61716e6	1.43388	0.716942	−	0.697133i	$-0.245541\pi$
$401$	4.61716e6	1.43388	0.716942	+	0.697133i	$0.245541\pi$
$402$	−1.99383e6	−0.615352
$403$	−3.48449e6	−1.06875
$404$	2.51201e6	0.765716
$405$	470003.	0.142385
$406$	−220042.	−0.0662507
$407$	3.04411e6	0.910909
$408$	37501.3	0.0111531
$409$	−3.09176e6	−0.913896	−0.456948	−	0.889493i	$-0.651057\pi$
$409$	−3.09176e6	−0.913896	−0.456948	+	0.889493i	$0.651057\pi$
$410$	5.11064e6	1.50147
$411$	489752.	0.143012
$412$	2.10683e6	0.611485
$413$	−45084.0	−0.0130061
$414$	714662.	0.204927
$415$	−2.52455e6	−0.719555
$416$	543753.	0.154052
$417$	137073.	0.0386021
$418$	−203279.	−0.0569051
$419$	1.30713e6	0.363734	0.181867	−	0.983323i	$-0.441786\pi$
$419$	1.30713e6	0.363734	0.181867	+	0.983323i	$0.441786\pi$
$420$	−133602.	−0.0369563
$421$	−4.88694e6	−1.34379	−0.671896	−	0.740646i	$-0.734520\pi$
$421$	−4.88694e6	−1.34379	−0.671896	+	0.740646i	$0.734520\pi$
$422$	−108752.	−0.0297273
$423$	−633693.	−0.172198
$424$	−1.59043e6	−0.429636
$425$	−130648.	−0.0350858
$426$	519584.	0.138718
$427$	192928.	0.0512067
$428$	−184552.	−0.0486979
$429$	−1.22312e6	−0.320869
$430$	2.92136e6	0.761928
$431$	4.15438e6	1.07724	0.538620	−	0.842549i	$-0.318946\pi$
$431$	4.15438e6	1.07724	0.538620	+	0.842549i	$0.318946\pi$
$432$	−186624.	−0.0481125
$433$	1.48900e6	0.381659	0.190830	−	0.981623i	$-0.438882\pi$
$433$	1.48900e6	0.381659	0.190830	+	0.981623i	$0.438882\pi$
$434$	−339951.	−0.0866347
$435$	2.73842e6	0.693868
$436$	126730.	0.0319273
$437$	−437987.	−0.109713
$438$	−1.55618e6	−0.387592
$439$	−972866.	−0.240930	−0.120465	−	0.992718i	$-0.538439\pi$
$439$	−972866.	−0.240930	−0.120465	+	0.992718i	$0.538439\pi$
$440$	1.17337e6	0.288938
$441$	−1.34778e6	−0.330007
$442$	−138288.	−0.0336690
$443$	2.26223e6	0.547680	0.273840	−	0.961775i	$-0.411706\pi$
$443$	2.26223e6	0.547680	0.273840	+	0.961775i	$0.411706\pi$
$444$	−1.71276e6	−0.412325
$445$	5.67896e6	1.35947
$446$	−4.79817e6	−1.14219
$447$	2.52423e6	0.597530
$448$	53049.2	0.0124877
$449$	40767.3	0.00954323	0.00477162	−	0.999989i	$-0.498481\pi$
$449$	40767.3	0.00954323	0.00477162	+	0.999989i	$0.498481\pi$
$450$	650168.	0.151354
$451$	4.56469e6	1.05674
$452$	3.52621e6	0.811824
$453$	1.64689e6	0.377067
$454$	−496305.	−0.113008
$455$	492664.	0.111564
$456$	114374.	0.0257582
$457$	3.97172e6	0.889587	0.444793	−	0.895633i	$-0.353277\pi$
$457$	3.97172e6	0.889587	0.444793	+	0.895633i	$0.353277\pi$
$458$	2.62364e6	0.584442
$459$	47462.5	0.0105152
$460$	2.52817e6	0.557072
$461$	2.77796e6	0.608799	0.304399	−	0.952545i	$-0.401544\pi$
$461$	2.77796e6	0.608799	0.304399	+	0.952545i	$0.401544\pi$
$462$	−119329.	−0.0260101
$463$	66484.4	0.0144134	0.00720671	−	0.999974i	$-0.497706\pi$
$463$	66484.4	0.0144134	0.00720671	+	0.999974i	$0.497706\pi$
$464$	−1.08734e6	−0.234462
$465$	4.23068e6	0.907357
$466$	−1.83368e6	−0.391163
$467$	−1.44244e6	−0.306059	−0.153030	−	0.988222i	$-0.548903\pi$
$467$	−1.44244e6	−0.306059	−0.153030	+	0.988222i	$0.548903\pi$
$468$	688188.	0.145242
$469$	717307.	0.150582
$470$	−2.24173e6	−0.468101
$471$	970558.	0.201590
$472$	−222784.	−0.0460287
$473$	2.60928e6	0.536251
$474$	502589.	0.102746
$475$	−398461.	−0.0810312
$476$	−13491.6	−0.00272926
$477$	−2.01289e6	−0.405064
$478$	4.16281e6	0.833330
$479$	1.05946e6	0.210982	0.105491	−	0.994420i	$-0.466359\pi$
$479$	1.05946e6	0.210982	0.105491	+	0.994420i	$0.466359\pi$
$480$	−660196.	−0.130789
$481$	6.31592e6	1.24473
$482$	2.77919e6	0.544879
$483$	−257109.	−0.0501475
$484$	−1.52879e6	−0.296643
$485$	8.70998e6	1.68137
$486$	−236196.	−0.0453609
$487$	−3.81150e6	−0.728238	−0.364119	−	0.931352i	$-0.618630\pi$
$487$	−3.81150e6	−0.728238	−0.364119	+	0.931352i	$0.618630\pi$
$488$	953361.	0.181221
$489$	2.46593e6	0.466346
$490$	−4.76787e6	−0.897086
$491$	7.41772e6	1.38857	0.694283	−	0.719702i	$-0.255722\pi$
$491$	7.41772e6	1.38857	0.694283	+	0.719702i	$0.255722\pi$
$492$	−2.56831e6	−0.478338
$493$	276535.	0.0512428
$494$	−421762.	−0.0777589
$495$	1.48505e6	0.272413
$496$	−1.67988e6	−0.306601
$497$	−186927.	−0.0339454
$498$	1.26869e6	0.229236
$499$	3.67729e6	0.661115	0.330557	−	0.943786i	$-0.392763\pi$
$499$	3.67729e6	0.661115	0.330557	+	0.943786i	$0.392763\pi$
$500$	−1.28177e6	−0.229291
$501$	4.82695e6	0.859169
$502$	−5.84845e6	−1.03581
$503$	−1.99454e6	−0.351499	−0.175749	−	0.984435i	$-0.556235\pi$
$503$	−1.99454e6	−0.351499	−0.175749	+	0.984435i	$0.556235\pi$
$504$	67140.4	0.0117735
$505$	1.12469e7	1.96247
$506$	2.25809e6	0.392072
$507$	803901.	0.138894
$508$	878408.	0.151021
$509$	1.83731e6	0.314331	0.157166	−	0.987572i	$-0.449764\pi$
$509$	1.83731e6	0.314331	0.157166	+	0.987572i	$0.449764\pi$
$510$	167902.	0.0285845
$511$	559856.	0.0948471
$512$	262144.	0.0441942
$513$	144755.	0.0242851
$514$	5.55338e6	0.927149
$515$	9.43277e6	1.56719
$516$	−1.46811e6	−0.242735
$517$	−2.00226e6	−0.329453
$518$	616189.	0.100900
$519$	1.93997e6	0.316139
$520$	2.43451e6	0.394824
$521$	−1.04609e7	−1.68840	−0.844199	−	0.536030i	$-0.819923\pi$
$521$	−1.04609e7	−1.68840	−0.844199	+	0.536030i	$0.819923\pi$
$522$	−1.37617e6	−0.221053
$523$	−1.16300e7	−1.85920	−0.929601	−	0.368568i	$-0.879848\pi$
$523$	−1.16300e7	−1.85920	−0.929601	+	0.368568i	$0.879848\pi$
$524$	−2.13601e6	−0.339840
$525$	−233906.	−0.0370377
$526$	−1.56276e6	−0.246280
$527$	427229.	0.0670092
$528$	−589669.	−0.0920500
$529$	−1.57102e6	−0.244086
$530$	−7.12074e6	−1.10112
$531$	−281961.	−0.0433963
$532$	−41147.6	−0.00630326
$533$	9.47081e6	1.44401
$534$	−2.85391e6	−0.433100
$535$	−826286.	−0.124809
$536$	3.54459e6	0.532911
$537$	−3.63659e6	−0.544201
$538$	−2.37954e6	−0.354436
$539$	−4.25853e6	−0.631376
$540$	−835560.	−0.123309
$541$	5.24778e6	0.770873	0.385436	−	0.922734i	$-0.374051\pi$
$541$	5.24778e6	0.770873	0.385436	+	0.922734i	$0.374051\pi$
$542$	4.33878e6	0.634409
$543$	543269.	0.0790706
$544$	−66668.9	−0.00965887
$545$	567400.	0.0818273
$546$	−247584.	−0.0355420
$547$	−1.89296e6	−0.270503	−0.135252	−	0.990811i	$-0.543184\pi$
$547$	−1.89296e6	−0.270503	−0.135252	+	0.990811i	$0.543184\pi$
$548$	−870670.	−0.123852
$549$	1.20660e6	0.170857
$550$	2.05431e6	0.289574
$551$	843398.	0.118346
$552$	−1.27051e6	−0.177472
$553$	−180813.	−0.0251429
$554$	−5.12862e6	−0.709947
$555$	−7.66845e6	−1.05676
$556$	−243685.	−0.0334304
$557$	−1.15175e7	−1.57297	−0.786484	−	0.617611i	$-0.788101\pi$
$557$	−1.15175e7	−1.57297	−0.786484	+	0.617611i	$0.788101\pi$
$558$	−2.12610e6	−0.289066
$559$	5.41373e6	0.732770
$560$	237514.	0.0320051
$561$	149966.	0.0201180
$562$	6.08460e6	0.812627
$563$	359994.	0.0478657	0.0239328	−	0.999714i	$-0.492381\pi$
$563$	359994.	0.0478657	0.0239328	+	0.999714i	$0.492381\pi$
$564$	1.12656e6	0.149128
$565$	1.57877e7	2.08064
$566$	−6.61605e6	−0.868075
$567$	84974.5	0.0111002
$568$	−923705.	−0.120133
$569$	−1.18983e7	−1.54065	−0.770327	−	0.637650i	$-0.779907\pi$
$569$	−1.18983e7	−1.54065	−0.770327	+	0.637650i	$0.779907\pi$
$570$	512081.	0.0660163
$571$	−4.70889e6	−0.604405	−0.302202	−	0.953244i	$-0.597722\pi$
$571$	−4.70889e6	−0.604405	−0.302202	+	0.953244i	$0.597722\pi$
$572$	2.17444e6	0.277880
$573$	5.40174e6	0.687302
$574$	923983.	0.117053
$575$	4.42626e6	0.558299
$576$	331776.	0.0416667
$577$	450723.	0.0563599	0.0281799	−	0.999603i	$-0.491029\pi$
$577$	450723.	0.0563599	0.0281799	+	0.999603i	$0.491029\pi$
$578$	−5.66247e6	−0.704996
$579$	929710.	0.115253
$580$	−4.86830e6	−0.600907
$581$	−456428.	−0.0560960
$582$	−4.37713e6	−0.535651
$583$	−6.36006e6	−0.774978
$584$	2.76654e6	0.335665
$585$	3.08118e6	0.372244
$586$	−2.91027e6	−0.350097
$587$	476192.	0.0570409	0.0285205	−	0.999593i	$-0.490920\pi$
$587$	476192.	0.0570409	0.0285205	+	0.999593i	$0.490920\pi$
$588$	2.39605e6	0.285794
$589$	1.30300e6	0.154759
$590$	−997457.	−0.117968
$591$	−2.31443e6	−0.272568
$592$	3.04491e6	0.357084
$593$	−4.67169e6	−0.545554	−0.272777	−	0.962077i	$-0.587942\pi$
$593$	−4.67169e6	−0.545554	−0.272777	+	0.962077i	$0.587942\pi$
$594$	−746300.	−0.0867856
$595$	−60404.9	−0.00699488
$596$	−4.48752e6	−0.517476
$597$	9.39995e6	1.07942
$598$	4.68509e6	0.535753
$599$	−2.44188e6	−0.278072	−0.139036	−	0.990287i	$-0.544400\pi$
$599$	−2.44188e6	−0.278072	−0.139036	+	0.990287i	$0.544400\pi$
$600$	−1.15585e6	−0.131077
$601$	5.04261e6	0.569468	0.284734	−	0.958607i	$-0.408095\pi$
$601$	5.04261e6	0.569468	0.284734	+	0.958607i	$0.408095\pi$
$602$	528170.	0.0593995
$603$	4.48613e6	0.502433
$604$	−2.92780e6	−0.326550
$605$	−6.84476e6	−0.760273
$606$	−5.65202e6	−0.625205
$607$	1.79310e7	1.97530	0.987649	−	0.156682i	$-0.0500797\pi$
$607$	1.79310e7	1.97530	0.987649	+	0.156682i	$0.0500797\pi$
$608$	−203332.	−0.0223073
$609$	495095.	0.0540935
$610$	4.26843e6	0.464454
$611$	−4.15428e6	−0.450187
$612$	−84377.8	−0.00910647
$613$	5.59834e6	0.601739	0.300870	−	0.953665i	$-0.402723\pi$
$613$	5.59834e6	0.601739	0.300870	+	0.953665i	$0.402723\pi$
$614$	−6.65024e6	−0.711896
$615$	−1.14989e7	−1.22594
$616$	212141.	0.0225254
$617$	−1.42287e7	−1.50471	−0.752354	−	0.658759i	$-0.771082\pi$
$617$	−1.42287e7	−1.50471	−0.752354	+	0.658759i	$0.771082\pi$
$618$	−4.74036e6	−0.499275
$619$	−3.32232e6	−0.348510	−0.174255	−	0.984701i	$-0.555752\pi$
$619$	−3.32232e6	−0.348510	−0.174255	+	0.984701i	$0.555752\pi$
$620$	−7.52121e6	−0.785794
$621$	−1.60799e6	−0.167323
$622$	−5.77832e6	−0.598860
$623$	1.02673e6	0.105983
$624$	−1.22344e6	−0.125783
$625$	−1.20097e7	−1.22980
$626$	2.76391e6	0.281895
$627$	457377.	0.0464628
$628$	−1.72544e6	−0.174582
$629$	−774387.	−0.0780426
$630$	300604.	0.0301747
$631$	−1.56756e7	−1.56730	−0.783648	−	0.621205i	$-0.786643\pi$
$631$	−1.56756e7	−1.56730	−0.783648	+	0.621205i	$0.786643\pi$
$632$	−893491.	−0.0889810
$633$	244692.	0.0242722
$634$	3.46163e6	0.342025
$635$	3.93284e6	0.387055
$636$	3.57847e6	0.350796
$637$	−8.83560e6	−0.862755
$638$	−4.34824e6	−0.422923
$639$	−1.16906e6	−0.113263
$640$	1.17368e6	0.113266
$641$	−1.70720e6	−0.164111	−0.0820556	−	0.996628i	$-0.526148\pi$
$641$	−1.70720e6	−0.164111	−0.0820556	+	0.996628i	$0.526148\pi$
$642$	415243.	0.0397617
$643$	5.09026e6	0.485526	0.242763	−	0.970086i	$-0.421946\pi$
$643$	5.09026e6	0.485526	0.242763	+	0.970086i	$0.421946\pi$
$644$	457082.	0.0434290
$645$	−6.57306e6	−0.622112
$646$	51711.7	0.00487537
$647$	−1.20242e7	−1.12927	−0.564633	−	0.825342i	$-0.690982\pi$
$647$	−1.20242e7	−1.12927	−0.564633	+	0.825342i	$0.690982\pi$
$648$	419904.	0.0392837
$649$	−890902.	−0.0830268
$650$	4.26229e6	0.395694
$651$	764890.	0.0707370
$652$	−4.38388e6	−0.403868
$653$	2.07996e7	1.90885	0.954426	−	0.298447i	$-0.0964686\pi$
$653$	2.07996e7	1.90885	0.954426	+	0.298447i	$0.0964686\pi$
$654$	−285142.	−0.0260686
$655$	−9.56343e6	−0.870984
$656$	4.56589e6	0.414253
$657$	3.50141e6	0.316468
$658$	−405296.	−0.0364928
$659$	−1.36674e7	−1.22595	−0.612973	−	0.790104i	$-0.710026\pi$
$659$	−1.36674e7	−1.22595	−0.612973	+	0.790104i	$0.710026\pi$
$660$	−2.64009e6	−0.235917
$661$	1.13900e7	1.01396	0.506979	−	0.861958i	$-0.330762\pi$
$661$	1.13900e7	1.01396	0.506979	+	0.861958i	$0.330762\pi$
$662$	491115.	0.0435551
$663$	311149.	0.0274906
$664$	−2.25545e6	−0.198524
$665$	−184228.	−0.0161548
$666$	3.85372e6	0.336662
$667$	−9.36878e6	−0.815395
$668$	−8.58125e6	−0.744062
$669$	1.07959e7	0.932594
$670$	1.58700e7	1.36581
$671$	3.81244e6	0.326887
$672$	−119361.	−0.0101962
$673$	7.15107e6	0.608602	0.304301	−	0.952576i	$-0.401577\pi$
$673$	7.15107e6	0.608602	0.304301	+	0.952576i	$0.401577\pi$
$674$	−3.85776e6	−0.327104
$675$	−1.46288e6	−0.123580
$676$	−1.42916e6	−0.120286
$677$	−1.07668e7	−0.902849	−0.451425	−	0.892309i	$-0.649084\pi$
$677$	−1.07668e7	−0.902849	−0.451425	+	0.892309i	$0.649084\pi$
$678$	−7.93397e6	−0.662852
$679$	1.57473e6	0.131078
$680$	−298493.	−0.0247549
$681$	1.11669e6	0.0922706
$682$	−6.71775e6	−0.553048
$683$	−1.80242e7	−1.47844	−0.739220	−	0.673464i	$-0.764806\pi$
$683$	−1.80242e7	−1.47844	−0.739220	+	0.673464i	$0.764806\pi$
$684$	−257342.	−0.0210315
$685$	−3.89820e6	−0.317422
$686$	−1.73271e6	−0.140578
$687$	−5.90320e6	−0.477195
$688$	2.60997e6	0.210215
$689$	−1.31958e7	−1.05898
$690$	−5.68838e6	−0.454848
$691$	1.08955e7	0.868063	0.434032	−	0.900898i	$-0.357091\pi$
$691$	1.08955e7	0.868063	0.434032	+	0.900898i	$0.357091\pi$
$692$	−3.44884e6	−0.273784
$693$	268491.	0.0212372
$694$	−3.03052e6	−0.238846
$695$	−1.09103e6	−0.0856794
$696$	2.44652e6	0.191437
$697$	−1.16120e6	−0.0905371
$698$	−2.35256e6	−0.182769
$699$	4.12577e6	0.319383
$700$	415834.	0.0320756
$701$	1.46982e7	1.12972	0.564858	−	0.825188i	$-0.308931\pi$
$701$	1.46982e7	1.12972	0.564858	+	0.825188i	$0.308931\pi$
$702$	−1.54842e6	−0.118590
$703$	−2.36179e6	−0.180240
$704$	1.04830e6	0.0797176
$705$	5.04390e6	0.382203
$706$	1.45896e7	1.10162
$707$	2.03339e6	0.152993
$708$	501264.	0.0375823
$709$	−718405.	−0.0536728	−0.0268364	−	0.999640i	$-0.508543\pi$
$709$	−718405.	−0.0536728	−0.0268364	+	0.999640i	$0.508543\pi$
$710$	−4.13565e6	−0.307892
$711$	−1.13082e6	−0.0838921
$712$	5.07363e6	0.375075
$713$	−1.44742e7	−1.06628
$714$	30356.0	0.00222843
$715$	9.73550e6	0.712186
$716$	6.46506e6	0.471292
$717$	−9.36633e6	−0.680411
$718$	1.14589e7	0.829528
$719$	4.55303e6	0.328457	0.164229	−	0.986422i	$-0.447487\pi$
$719$	4.55303e6	0.328457	0.164229	+	0.986422i	$0.447487\pi$
$720$	1.48544e6	0.106788
$721$	1.70540e6	0.122177
$722$	−9.74668e6	−0.695847
$723$	−6.25317e6	−0.444892
$724$	−965811.	−0.0684771
$725$	−8.52330e6	−0.602231
$726$	3.43978e6	0.242208
$727$	2.33656e7	1.63961	0.819805	−	0.572643i	$-0.194082\pi$
$727$	2.33656e7	1.63961	0.819805	+	0.572643i	$0.194082\pi$
$728$	440150.	0.0307803
$729$	531441.	0.0370370
$730$	1.23865e7	0.860282
$731$	−663771.	−0.0459436
$732$	−2.14506e6	−0.147966
$733$	2.24762e7	1.54513	0.772563	−	0.634938i	$-0.218974\pi$
$733$	2.24762e7	1.54513	0.772563	+	0.634938i	$0.218974\pi$
$734$	−642382.	−0.0440102
$735$	1.07277e7	0.732468
$736$	2.25869e6	0.153696
$737$	1.41747e7	0.961267
$738$	5.77870e6	0.390561
$739$	−6.32970e6	−0.426356	−0.213178	−	0.977013i	$-0.568381\pi$
$739$	−6.32970e6	−0.426356	−0.213178	+	0.977013i	$0.568381\pi$
$740$	1.36328e7	0.915179
$741$	948965.	0.0634899
$742$	−1.28740e6	−0.0858428
$743$	−1.51747e6	−0.100843	−0.0504217	−	0.998728i	$-0.516057\pi$
$743$	−1.51747e6	−0.100843	−0.0504217	+	0.998728i	$0.516057\pi$
$744$	3.77972e6	0.250339
$745$	−2.00917e7	−1.32625
$746$	−8.48121e6	−0.557970
$747$	−2.85456e6	−0.187170
$748$	−266606.	−0.0174227
$749$	−149389.	−0.00973003
$750$	2.88399e6	0.187215
$751$	−2.03603e7	−1.31730	−0.658650	−	0.752449i	$-0.728872\pi$
$751$	−2.03603e7	−1.31730	−0.658650	+	0.752449i	$0.728872\pi$
$752$	−2.00278e6	−0.129148
$753$	1.31590e7	0.845739
$754$	−9.02171e6	−0.577910
$755$	−1.31085e7	−0.836921
$756$	−151066.	−0.00961306
$757$	−2.67860e7	−1.69890	−0.849449	−	0.527670i	$-0.823066\pi$
$757$	−2.67860e7	−1.69890	−0.849449	+	0.527670i	$0.823066\pi$
$758$	−4.97310e6	−0.314380
$759$	−5.08071e6	−0.320125
$760$	−910366.	−0.0571718
$761$	1.57945e7	0.988654	0.494327	−	0.869276i	$-0.335414\pi$
$761$	1.57945e7	0.988654	0.494327	+	0.869276i	$0.335414\pi$
$762$	−1.97642e6	−0.123308
$763$	102584.	0.00637920
$764$	−9.60310e6	−0.595221
$765$	−377780.	−0.0233392
$766$	1.02337e7	0.630175
$767$	−1.84844e6	−0.113453
$768$	−589824.	−0.0360844
$769$	−2.44447e7	−1.49062	−0.745312	−	0.666715i	$-0.767700\pi$
$769$	−2.44447e7	−1.49062	−0.745312	+	0.666715i	$0.767700\pi$
$770$	949806.	0.0577309
$771$	−1.24951e7	−0.757014
$772$	−1.65282e6	−0.0998117
$773$	1.32843e7	0.799633	0.399817	−	0.916595i	$-0.369074\pi$
$773$	1.32843e7	0.799633	0.399817	+	0.916595i	$0.369074\pi$
$774$	3.30324e6	0.198193
$775$	−1.31680e7	−0.787525
$776$	7.78156e6	0.463887
$777$	−1.38642e6	−0.0823841
$778$	−420536.	−0.0249089
$779$	−3.54153e6	−0.209097
$780$	−5.47766e6	−0.322373
$781$	−3.69385e6	−0.216697
$782$	−574433.	−0.0335910
$783$	3.09638e6	0.180489
$784$	−4.25965e6	−0.247505
$785$	−7.72520e6	−0.447441
$786$	4.80602e6	0.277479
$787$	−3.14224e7	−1.80843	−0.904216	−	0.427076i	$-0.859544\pi$
$787$	−3.14224e7	−1.80843	−0.904216	+	0.427076i	$0.859544\pi$
$788$	4.11454e6	0.236051
$789$	3.51622e6	0.201087
$790$	−4.00037e6	−0.228051
$791$	2.85435e6	0.162206
$792$	1.32676e6	0.0751585
$793$	7.91005e6	0.446680
$794$	−2.16630e7	−1.21946
$795$	1.60217e7	0.899063
$796$	−1.67110e7	−0.934803
$797$	2.11193e6	0.117770	0.0588848	−	0.998265i	$-0.481246\pi$
$797$	2.11193e6	0.117770	0.0588848	+	0.998265i	$0.481246\pi$
$798$	92582.0	0.00514659
$799$	509351.	0.0282260
$800$	2.05485e6	0.113516
$801$	6.42131e6	0.353624
$802$	1.84686e7	1.01391
$803$	1.10633e7	0.605473
$804$	−7.97534e6	−0.435120
$805$	2.04647e6	0.111305
$806$	−1.39380e7	−0.755722
$807$	5.35398e6	0.289396
$808$	1.00480e7	0.541443
$809$	3.50541e7	1.88307	0.941537	−	0.336909i	$-0.109381\pi$
$809$	3.50541e7	1.88307	0.941537	+	0.336909i	$0.109381\pi$
$810$	1.88001e6	0.100681
$811$	−1.01948e7	−0.544283	−0.272141	−	0.962257i	$-0.587732\pi$
$811$	−1.01948e7	−0.544283	−0.272141	+	0.962257i	$0.587732\pi$
$812$	−880168.	−0.0468463
$813$	−9.76225e6	−0.517993
$814$	1.21765e7	0.644110
$815$	−1.96277e7	−1.03508
$816$	150005.	0.00788643
$817$	−2.02442e6	−0.106107
$818$	−1.23670e7	−0.646222
$819$	557065.	0.0290199
$820$	2.04426e7	1.06170
$821$	1.22885e7	0.636269	0.318135	−	0.948046i	$-0.396944\pi$
$821$	1.22885e7	0.636269	0.318135	+	0.948046i	$0.396944\pi$
$822$	1.95901e6	0.101125
$823$	7.80440e6	0.401643	0.200821	−	0.979628i	$-0.435639\pi$
$823$	7.80440e6	0.401643	0.200821	+	0.979628i	$0.435639\pi$
$824$	8.42731e6	0.432385
$825$	−4.62221e6	−0.236436
$826$	−180336.	−0.00919671
$827$	−2.93191e7	−1.49069	−0.745345	−	0.666679i	$-0.767715\pi$
$827$	−2.93191e7	−1.49069	−0.745345	+	0.666679i	$0.767715\pi$
$828$	2.85865e6	0.144906
$829$	1.17427e7	0.593446	0.296723	−	0.954964i	$-0.404106\pi$
$829$	1.17427e7	0.593446	0.296723	+	0.954964i	$0.404106\pi$
$830$	−1.00982e7	−0.508802
$831$	1.15394e7	0.579669
$832$	2.17501e6	0.108932
$833$	1.08332e6	0.0540935
$834$	548290.	0.0272958
$835$	−3.84203e7	−1.90697
$836$	−813114.	−0.0402379
$837$	4.78371e6	0.236021
$838$	5.22852e6	0.257199
$839$	−9.16431e6	−0.449464	−0.224732	−	0.974421i	$-0.572151\pi$
$839$	−9.16431e6	−0.449464	−0.224732	+	0.974421i	$0.572151\pi$
$840$	−534406.	−0.0261320
$841$	−2.47042e6	−0.120443
$842$	−1.95478e7	−0.950204
$843$	−1.36903e7	−0.663507
$844$	−435007.	−0.0210204
$845$	−6.39868e6	−0.308282
$846$	−2.53477e6	−0.121762
$847$	−1.23750e6	−0.0592704
$848$	−6.36173e6	−0.303798
$849$	1.48861e7	0.708781
$850$	−522594.	−0.0248094
$851$	2.62356e7	1.24184
$852$	2.07834e6	0.0980882
$853$	−9.42456e6	−0.443495	−0.221747	−	0.975104i	$-0.571176\pi$
$853$	−9.42456e6	−0.443495	−0.221747	+	0.975104i	$0.571176\pi$
$854$	771714.	0.0362086
$855$	−1.15218e6	−0.0539021
$856$	−738210.	−0.0344346
$857$	2.90064e7	1.34909	0.674545	−	0.738234i	$-0.264340\pi$
$857$	2.90064e7	1.34909	0.674545	+	0.738234i	$0.264340\pi$
$858$	−4.89250e6	−0.226888
$859$	−2.53080e7	−1.17024	−0.585119	−	0.810947i	$-0.698952\pi$
$859$	−2.53080e7	−1.17024	−0.585119	+	0.810947i	$0.698952\pi$
$860$	1.16854e7	0.538765
$861$	−2.07896e6	−0.0955737
$862$	1.66175e7	0.761724
$863$	−3.87638e7	−1.77174	−0.885869	−	0.463935i	$-0.846437\pi$
$863$	−3.87638e7	−1.77174	−0.885869	+	0.463935i	$0.846437\pi$
$864$	−746496.	−0.0340207
$865$	−1.54413e7	−0.701687
$866$	5.95601e6	0.269874
$867$	1.27406e7	0.575627
$868$	−1.35980e6	−0.0612600
$869$	−3.57303e6	−0.160504
$870$	1.09537e7	0.490639
$871$	2.94096e7	1.31354
$872$	506919.	0.0225760
$873$	9.84853e6	0.437357
$874$	−1.75195e6	−0.0775788
$875$	−1.03755e6	−0.0458132
$876$	−6.22473e6	−0.274069
$877$	1.21218e7	0.532194	0.266097	−	0.963946i	$-0.414266\pi$
$877$	1.21218e7	0.532194	0.266097	+	0.963946i	$0.414266\pi$
$878$	−3.89146e6	−0.170364
$879$	6.54810e6	0.285853
$880$	4.69349e6	0.204310
$881$	−3.28253e7	−1.42485	−0.712424	−	0.701749i	$-0.752403\pi$
$881$	−3.28253e7	−1.42485	−0.712424	+	0.701749i	$0.752403\pi$
$882$	−5.39112e6	−0.233350
$883$	5.17653e6	0.223428	0.111714	−	0.993740i	$-0.464366\pi$
$883$	5.17653e6	0.223428	0.111714	+	0.993740i	$0.464366\pi$
$884$	−553153.	−0.0238075
$885$	2.24428e6	0.0963205
$886$	9.04892e6	0.387269
$887$	1.85818e7	0.793009	0.396505	−	0.918033i	$-0.370223\pi$
$887$	1.85818e7	0.793009	0.396505	+	0.918033i	$0.370223\pi$
$888$	−6.85105e6	−0.291558
$889$	711042.	0.0301745
$890$	2.27158e7	0.961288
$891$	1.67918e6	0.0708601
$892$	−1.91927e7	−0.807650
$893$	1.55346e6	0.0651884
$894$	1.00969e7	0.422518
$895$	2.89456e7	1.20788
$896$	212197.	0.00883016
$897$	−1.05414e7	−0.437441
$898$	163069.	0.00674809
$899$	2.78718e7	1.15018
$900$	2.60067e6	0.107024
$901$	1.61793e6	0.0663967
$902$	1.82588e7	0.747231
$903$	−1.18838e6	−0.0484995
$904$	1.41048e7	0.574047
$905$	−4.32417e6	−0.175502
$906$	6.58755e6	0.266627
$907$	−4.66344e6	−0.188230	−0.0941149	−	0.995561i	$-0.530002\pi$
$907$	−4.66344e6	−0.188230	−0.0941149	+	0.995561i	$0.530002\pi$
$908$	−1.98522e6	−0.0799087
$909$	1.27170e7	0.510477
$910$	1.97066e6	0.0788874
$911$	−3.07444e7	−1.22735	−0.613677	−	0.789557i	$-0.710310\pi$
$911$	−3.07444e7	−1.22735	−0.613677	+	0.789557i	$0.710310\pi$
$912$	457497.	0.0182138
$913$	−9.01944e6	−0.358099
$914$	1.58869e7	0.629033
$915$	−9.60396e6	−0.379225
$916$	1.04946e7	0.413263
$917$	−1.72903e6	−0.0679014
$918$	189850.	0.00743540
$919$	9.50961e6	0.371427	0.185714	−	0.982604i	$-0.440540\pi$
$919$	9.50961e6	0.371427	0.185714	+	0.982604i	$0.440540\pi$
$920$	1.01127e7	0.393910
$921$	1.49630e7	0.581260
$922$	1.11118e7	0.430486
$923$	−7.66400e6	−0.296109
$924$	−477317.	−0.0183919
$925$	2.38680e7	0.917194
$926$	265938.	0.0101918
$927$	1.06658e7	0.407657
$928$	−4.34938e6	−0.165789
$929$	−1.72822e7	−0.656991	−0.328495	−	0.944506i	$-0.606541\pi$
$929$	−1.72822e7	−0.656991	−0.328495	+	0.944506i	$0.606541\pi$
$930$	1.69227e7	0.641598
$931$	3.30400e6	0.124930
$932$	−7.33470e6	−0.276594
$933$	1.30012e7	0.488967
$934$	−5.76976e6	−0.216417
$935$	−1.19366e6	−0.0446530
$936$	2.75275e6	0.102702
$937$	3.68759e7	1.37213	0.686063	−	0.727542i	$-0.259338\pi$
$937$	3.68759e7	1.37213	0.686063	+	0.727542i	$0.259338\pi$
$938$	2.86923e6	0.106478
$939$	−6.21879e6	−0.230166
$940$	−8.96693e6	−0.330997
$941$	1.56643e7	0.576683	0.288342	−	0.957528i	$-0.406896\pi$
$941$	1.56643e7	0.576683	0.288342	+	0.957528i	$0.406896\pi$
$942$	3.88223e6	0.142546
$943$	3.93406e7	1.44066
$944$	−891136.	−0.0325472
$945$	−676358.	−0.0246375
$946$	1.04371e7	0.379187
$947$	−3.97773e7	−1.44132	−0.720660	−	0.693289i	$-0.756161\pi$
$947$	−3.97773e7	−1.44132	−0.720660	+	0.693289i	$0.756161\pi$
$948$	2.01035e6	0.0726527
$949$	2.29541e7	0.827359
$950$	−1.59385e6	−0.0572977
$951$	−7.78868e6	−0.279262
$952$	−53966.2	−0.00192988
$953$	−1.26781e7	−0.452193	−0.226096	−	0.974105i	$-0.572596\pi$
$953$	−1.26781e7	−0.452193	−0.226096	+	0.974105i	$0.572596\pi$
$954$	−8.05156e6	−0.286424
$955$	−4.29954e7	−1.52550
$956$	1.66513e7	0.589253
$957$	9.78353e6	0.345315
$958$	4.23783e6	0.149186
$959$	−704778.	−0.0247461
$960$	−2.64078e6	−0.0924815
$961$	1.44310e7	0.504066
$962$	2.52637e7	0.880155
$963$	−934297.	−0.0324653
$964$	1.11167e7	0.385288
$965$	−7.40006e6	−0.255810
$966$	−1.02844e6	−0.0354596
$967$	2.56050e6	0.0880559	0.0440280	−	0.999030i	$-0.485981\pi$
$967$	2.56050e6	0.0880559	0.0440280	+	0.999030i	$0.485981\pi$
$968$	−6.11516e6	−0.209758
$969$	−116351.	−0.00398072
$970$	3.48399e7	1.18891
$971$	2.96573e7	1.00945	0.504723	−	0.863281i	$-0.331595\pi$
$971$	2.96573e7	1.00945	0.504723	+	0.863281i	$0.331595\pi$
$972$	−944784.	−0.0320750
$973$	−197254.	−0.00667951
$974$	−1.52460e7	−0.514942
$975$	−9.59015e6	−0.323083
$976$	3.81344e6	0.128142
$977$	−1.08136e6	−0.0362437	−0.0181218	−	0.999836i	$-0.505769\pi$
$977$	−1.08136e6	−0.0362437	−0.0181218	+	0.999836i	$0.505769\pi$
$978$	9.86372e6	0.329757
$979$	2.02892e7	0.676562
$980$	−1.90715e7	−0.634336
$981$	641570.	0.0212849
$982$	2.96709e7	0.981865
$983$	−2.75305e7	−0.908721	−0.454360	−	0.890818i	$-0.650132\pi$
$983$	−2.75305e7	−0.908721	−0.454360	+	0.890818i	$0.650132\pi$
$984$	−1.02732e7	−0.338236
$985$	1.84218e7	0.604980
$986$	1.10614e6	0.0362342
$987$	911916.	0.0297963
$988$	−1.68705e6	−0.0549838
$989$	2.24880e7	0.731072
$990$	5.94020e6	0.192625
$991$	2.76586e7	0.894634	0.447317	−	0.894375i	$-0.352380\pi$
$991$	2.76586e7	0.894634	0.447317	+	0.894375i	$0.352380\pi$
$992$	−6.71951e6	−0.216800
$993$	−1.10501e6	−0.0355626
$994$	−747708.	−0.0240030
$995$	−7.48192e7	−2.39583
$996$	5.07477e6	0.162094
$997$	−2.68504e6	−0.0855486	−0.0427743	−	0.999085i	$-0.513620\pi$
$997$	−2.68504e6	−0.0855486	−0.0427743	+	0.999085i	$0.513620\pi$
$998$	1.47092e7	0.467479
$999$	−8.67087e6	−0.274884

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.a.e.1.4	✓	5
3.2	odd	2		1062.6.a.c.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.a.e.1.4	✓	5	1.1	even	1	trivial
1062.6.a.c.1.2		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)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +71.6358 q^{5} -36.0000 q^{6} +12.9515 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +71.6358 q^{5} -36.0000 q^{6} +12.9515 q^{7} +64.0000 q^{8} +81.0000 q^{9} +286.543 q^{10} +255.933 q^{11} -144.000 q^{12} +531.009 q^{13} +51.8058 q^{14} -644.722 q^{15} +256.000 q^{16} -65.1064 q^{17} +324.000 q^{18} -198.566 q^{19} +1146.17 q^{20} -116.563 q^{21} +1023.73 q^{22} +2205.75 q^{23} -576.000 q^{24} +2006.69 q^{25} +2124.04 q^{26} -729.000 q^{27} +207.223 q^{28} -4247.44 q^{29} -2578.89 q^{30} -6562.02 q^{31} +1024.00 q^{32} -2303.40 q^{33} -260.425 q^{34} +927.789 q^{35} +1296.00 q^{36} +11894.2 q^{37} -794.265 q^{38} -4779.08 q^{39} +4584.69 q^{40} +17835.5 q^{41} -466.253 q^{42} +10195.2 q^{43} +4094.93 q^{44} +5802.50 q^{45} +8822.99 q^{46} -7823.36 q^{47} -2304.00 q^{48} -16639.3 q^{49} +8026.77 q^{50} +585.957 q^{51} +8496.15 q^{52} -24850.5 q^{53} -2916.00 q^{54} +18334.0 q^{55} +828.893 q^{56} +1787.10 q^{57} -16989.8 q^{58} -3481.00 q^{59} -10315.6 q^{60} +14896.3 q^{61} -26248.1 q^{62} +1049.07 q^{63} +4096.00 q^{64} +38039.3 q^{65} -9213.58 q^{66} +55384.3 q^{67} -1041.70 q^{68} -19851.7 q^{69} +3711.15 q^{70} -14432.9 q^{71} +5184.00 q^{72} +43227.3 q^{73} +47576.8 q^{74} -18060.2 q^{75} -3177.06 q^{76} +3314.70 q^{77} -19116.3 q^{78} -13960.8 q^{79} +18338.8 q^{80} +6561.00 q^{81} +71342.0 q^{82} -35241.5 q^{83} -1865.01 q^{84} -4663.95 q^{85} +40780.7 q^{86} +38226.9 q^{87} +16379.7 q^{88} +79275.4 q^{89} +23210.0 q^{90} +6877.34 q^{91} +35292.0 q^{92} +59058.2 q^{93} -31293.5 q^{94} -14224.5 q^{95} -9216.00 q^{96} +121587. q^{97} -66557.0 q^{98} +20730.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 20 q^{2} - 45 q^{3} + 80 q^{4} + 166 q^{5} - 180 q^{6} - 198 q^{7} + 320 q^{8} + 405 q^{9}+O(q^{10}) \) 5 * q + 20 * q^2 - 45 * q^3 + 80 * q^4 + 166 * q^5 - 180 * q^6 - 198 * q^7 + 320 * q^8 + 405 * q^9	\( 5 q + 20 q^{2} - 45 q^{3} + 80 q^{4} + 166 q^{5} - 180 q^{6} - 198 q^{7} + 320 q^{8} + 405 q^{9} + 664 q^{10} - 516 q^{11} - 720 q^{12} + 1018 q^{13} - 792 q^{14} - 1494 q^{15} + 1280 q^{16} + 3004 q^{17} + 1620 q^{18} - 114 q^{19} + 2656 q^{20} + 1782 q^{21} - 2064 q^{22} - 1302 q^{23} - 2880 q^{24} + 8967 q^{25} + 4072 q^{26} - 3645 q^{27} - 3168 q^{28} + 16372 q^{29} - 5976 q^{30} - 4784 q^{31} + 5120 q^{32} + 4644 q^{33} + 12016 q^{34} - 9702 q^{35} + 6480 q^{36} + 5016 q^{37} - 456 q^{38} - 9162 q^{39} + 10624 q^{40} + 5440 q^{41} + 7128 q^{42} + 5494 q^{43} - 8256 q^{44} + 13446 q^{45} - 5208 q^{46} + 19470 q^{47} - 11520 q^{48} + 80323 q^{49} + 35868 q^{50} - 27036 q^{51} + 16288 q^{52} + 63310 q^{53} - 14580 q^{54} + 62324 q^{55} - 12672 q^{56} + 1026 q^{57} + 65488 q^{58} - 17405 q^{59} - 23904 q^{60} + 71776 q^{61} - 19136 q^{62} - 16038 q^{63} + 20480 q^{64} - 39492 q^{65} + 18576 q^{66} + 79962 q^{67} + 48064 q^{68} + 11718 q^{69} - 38808 q^{70} + 9928 q^{71} + 25920 q^{72} + 92772 q^{73} + 20064 q^{74} - 80703 q^{75} - 1824 q^{76} + 42750 q^{77} - 36648 q^{78} - 18444 q^{79} + 42496 q^{80} + 32805 q^{81} + 21760 q^{82} + 106030 q^{83} + 28512 q^{84} + 283366 q^{85} + 21976 q^{86} - 147348 q^{87} - 33024 q^{88} + 315950 q^{89} + 53784 q^{90} + 354078 q^{91} - 20832 q^{92} + 43056 q^{93} + 77880 q^{94} + 371662 q^{95} - 46080 q^{96} + 268078 q^{97} + 321292 q^{98} - 41796 q^{99}+O(q^{100}) \) 5 * q + 20 * q^2 - 45 * q^3 + 80 * q^4 + 166 * q^5 - 180 * q^6 - 198 * q^7 + 320 * q^8 + 405 * q^9 + 664 * q^10 - 516 * q^11 - 720 * q^12 + 1018 * q^13 - 792 * q^14 - 1494 * q^15 + 1280 * q^16 + 3004 * q^17 + 1620 * q^18 - 114 * q^19 + 2656 * q^20 + 1782 * q^21 - 2064 * q^22 - 1302 * q^23 - 2880 * q^24 + 8967 * q^25 + 4072 * q^26 - 3645 * q^27 - 3168 * q^28 + 16372 * q^29 - 5976 * q^30 - 4784 * q^31 + 5120 * q^32 + 4644 * q^33 + 12016 * q^34 - 9702 * q^35 + 6480 * q^36 + 5016 * q^37 - 456 * q^38 - 9162 * q^39 + 10624 * q^40 + 5440 * q^41 + 7128 * q^42 + 5494 * q^43 - 8256 * q^44 + 13446 * q^45 - 5208 * q^46 + 19470 * q^47 - 11520 * q^48 + 80323 * q^49 + 35868 * q^50 - 27036 * q^51 + 16288 * q^52 + 63310 * q^53 - 14580 * q^54 + 62324 * q^55 - 12672 * q^56 + 1026 * q^57 + 65488 * q^58 - 17405 * q^59 - 23904 * q^60 + 71776 * q^61 - 19136 * q^62 - 16038 * q^63 + 20480 * q^64 - 39492 * q^65 + 18576 * q^66 + 79962 * q^67 + 48064 * q^68 + 11718 * q^69 - 38808 * q^70 + 9928 * q^71 + 25920 * q^72 + 92772 * q^73 + 20064 * q^74 - 80703 * q^75 - 1824 * q^76 + 42750 * q^77 - 36648 * q^78 - 18444 * q^79 + 42496 * q^80 + 32805 * q^81 + 21760 * q^82 + 106030 * q^83 + 28512 * q^84 + 283366 * q^85 + 21976 * q^86 - 147348 * q^87 - 33024 * q^88 + 315950 * q^89 + 53784 * q^90 + 354078 * q^91 - 20832 * q^92 + 43056 * q^93 + 77880 * q^94 + 371662 * q^95 - 46080 * q^96 + 268078 * q^97 + 321292 * q^98 - 41796 * q^99

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