LMFDB - Embedded newform 471.6.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,6,Mod(1,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, 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("471.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	471.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:	$75.5407791319$
Analytic rank:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	471.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.55243 q^{2} -9.00000 q^{3} -11.2754 q^{4} +65.2180 q^{5} +40.9718 q^{6} +201.026 q^{7} +197.008 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.55243 q^{2} -9.00000 q^{3} -11.2754 q^{4} +65.2180 q^{5} +40.9718 q^{6} +201.026 q^{7} +197.008 q^{8} +81.0000 q^{9} -296.900 q^{10} -552.177 q^{11} +101.479 q^{12} +352.674 q^{13} -915.157 q^{14} -586.962 q^{15} -536.052 q^{16} +478.207 q^{17} -368.747 q^{18} -174.635 q^{19} -735.359 q^{20} -1809.23 q^{21} +2513.74 q^{22} -2902.56 q^{23} -1773.07 q^{24} +1128.39 q^{25} -1605.52 q^{26} -729.000 q^{27} -2266.65 q^{28} -5179.19 q^{29} +2672.10 q^{30} -3964.39 q^{31} -3863.92 q^{32} +4969.59 q^{33} -2177.00 q^{34} +13110.5 q^{35} -913.308 q^{36} -12237.3 q^{37} +795.013 q^{38} -3174.07 q^{39} +12848.5 q^{40} -3174.84 q^{41} +8236.41 q^{42} +15544.7 q^{43} +6226.01 q^{44} +5282.66 q^{45} +13213.7 q^{46} +5458.94 q^{47} +4824.47 q^{48} +23604.5 q^{49} -5136.90 q^{50} -4303.86 q^{51} -3976.54 q^{52} +18286.3 q^{53} +3318.72 q^{54} -36011.8 q^{55} +39603.8 q^{56} +1571.71 q^{57} +23577.9 q^{58} +18160.6 q^{59} +6618.23 q^{60} -27896.1 q^{61} +18047.6 q^{62} +16283.1 q^{63} +34743.9 q^{64} +23000.7 q^{65} -22623.7 q^{66} +7415.75 q^{67} -5391.98 q^{68} +26123.0 q^{69} -59684.7 q^{70} -38988.3 q^{71} +15957.7 q^{72} -20896.1 q^{73} +55709.3 q^{74} -10155.5 q^{75} +1969.08 q^{76} -111002. q^{77} +14449.7 q^{78} +12539.4 q^{79} -34960.3 q^{80} +6561.00 q^{81} +14453.2 q^{82} -43303.0 q^{83} +20399.9 q^{84} +31187.7 q^{85} -70766.2 q^{86} +46612.7 q^{87} -108783. q^{88} -30909.4 q^{89} -24048.9 q^{90} +70896.7 q^{91} +32727.5 q^{92} +35679.5 q^{93} -24851.4 q^{94} -11389.3 q^{95} +34775.3 q^{96} -156960. q^{97} -107458. q^{98} -44726.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 8 q^{2} - 270 q^{3} + 470 q^{4} - 136 q^{5} + 72 q^{6} + 68 q^{7} - 261 q^{8} + 2430 q^{9}+O(q^{10}) $ 30 * q - 8 * q^2 - 270 * q^3 + 470 * q^4 - 136 * q^5 + 72 * q^6 + 68 * q^7 - 261 * q^8 + 2430 * q^9	\( 30 q - 8 q^{2} - 270 q^{3} + 470 q^{4} - 136 q^{5} + 72 q^{6} + 68 q^{7} - 261 q^{8} + 2430 q^{9} - 383 q^{10} - 875 q^{11} - 4230 q^{12} + 101 q^{13} - 2279 q^{14} + 1224 q^{15} + 7454 q^{16} - 4042 q^{17} - 648 q^{18} + 846 q^{19} - 5089 q^{20} - 612 q^{21} - 700 q^{22} - 5902 q^{23} + 2349 q^{24} + 12880 q^{25} - 7567 q^{26} - 21870 q^{27} - 375 q^{28} - 10301 q^{29} + 3447 q^{30} - 4099 q^{31} - 1560 q^{32} + 7875 q^{33} - 3683 q^{34} - 20686 q^{35} + 38070 q^{36} + 8468 q^{37} - 11848 q^{38} - 909 q^{39} - 5132 q^{40} - 47958 q^{41} + 20511 q^{42} + 63916 q^{43} + 3101 q^{44} - 11016 q^{45} + 19654 q^{46} + 8589 q^{47} - 67086 q^{48} + 27834 q^{49} + 121727 q^{50} + 36378 q^{51} + 56510 q^{52} + 10134 q^{53} + 5832 q^{54} - 11473 q^{55} - 68192 q^{56} - 7614 q^{57} + 32006 q^{58} - 64236 q^{59} + 45801 q^{60} - 98194 q^{61} - 67276 q^{62} + 5508 q^{63} + 138849 q^{64} - 155917 q^{65} + 6300 q^{66} + 62323 q^{67} - 117531 q^{68} + 53118 q^{69} - 220939 q^{70} - 179713 q^{71} - 21141 q^{72} - 148343 q^{73} - 214732 q^{74} - 115920 q^{75} - 189758 q^{76} - 142357 q^{77} + 68103 q^{78} + 26916 q^{79} - 463727 q^{80} + 196830 q^{81} - 206514 q^{82} - 89285 q^{83} + 3375 q^{84} - 23932 q^{85} - 477235 q^{86} + 92709 q^{87} - 114708 q^{88} - 474411 q^{89} - 31023 q^{90} + 51305 q^{91} - 1030074 q^{92} + 36891 q^{93} - 485800 q^{94} - 169960 q^{95} + 14040 q^{96} - 169188 q^{97} - 629739 q^{98} - 70875 q^{99}+O(q^{100}) \) 30 * q - 8 * q^2 - 270 * q^3 + 470 * q^4 - 136 * q^5 + 72 * q^6 + 68 * q^7 - 261 * q^8 + 2430 * q^9 - 383 * q^10 - 875 * q^11 - 4230 * q^12 + 101 * q^13 - 2279 * q^14 + 1224 * q^15 + 7454 * q^16 - 4042 * q^17 - 648 * q^18 + 846 * q^19 - 5089 * q^20 - 612 * q^21 - 700 * q^22 - 5902 * q^23 + 2349 * q^24 + 12880 * q^25 - 7567 * q^26 - 21870 * q^27 - 375 * q^28 - 10301 * q^29 + 3447 * q^30 - 4099 * q^31 - 1560 * q^32 + 7875 * q^33 - 3683 * q^34 - 20686 * q^35 + 38070 * q^36 + 8468 * q^37 - 11848 * q^38 - 909 * q^39 - 5132 * q^40 - 47958 * q^41 + 20511 * q^42 + 63916 * q^43 + 3101 * q^44 - 11016 * q^45 + 19654 * q^46 + 8589 * q^47 - 67086 * q^48 + 27834 * q^49 + 121727 * q^50 + 36378 * q^51 + 56510 * q^52 + 10134 * q^53 + 5832 * q^54 - 11473 * q^55 - 68192 * q^56 - 7614 * q^57 + 32006 * q^58 - 64236 * q^59 + 45801 * q^60 - 98194 * q^61 - 67276 * q^62 + 5508 * q^63 + 138849 * q^64 - 155917 * q^65 + 6300 * q^66 + 62323 * q^67 - 117531 * q^68 + 53118 * q^69 - 220939 * q^70 - 179713 * q^71 - 21141 * q^72 - 148343 * q^73 - 214732 * q^74 - 115920 * q^75 - 189758 * q^76 - 142357 * q^77 + 68103 * q^78 + 26916 * q^79 - 463727 * q^80 + 196830 * q^81 - 206514 * q^82 - 89285 * q^83 + 3375 * q^84 - 23932 * q^85 - 477235 * q^86 + 92709 * q^87 - 114708 * q^88 - 474411 * q^89 - 31023 * q^90 + 51305 * q^91 - 1030074 * q^92 + 36891 * q^93 - 485800 * q^94 - 169960 * q^95 + 14040 * q^96 - 169188 * q^97 - 629739 * q^98 - 70875 * 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 $

$2$	−4.55243	−0.804763	−0.402382	−	0.915472i	$-0.631817\pi$
$2$	−4.55243	−0.804763	−0.402382	+	0.915472i	$0.631817\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−11.2754	−0.352356
$5$	65.2180	1.16666	0.583328	−	0.812237i	$-0.301750\pi$
$5$	65.2180	1.16666	0.583328	+	0.812237i	$0.301750\pi$
$6$	40.9718	0.464630
$7$	201.026	1.55063	0.775314	−	0.631577i	$-0.217592\pi$
$7$	201.026	1.55063	0.775314	+	0.631577i	$0.217592\pi$
$8$	197.008	1.08833
$9$	81.0000	0.333333
$10$	−296.900	−0.938881
$11$	−552.177	−1.37593	−0.687965	−	0.725744i	$-0.741496\pi$
$11$	−552.177	−1.37593	−0.687965	+	0.725744i	$0.741496\pi$
$12$	101.479	0.203433
$13$	352.674	0.578782	0.289391	−	0.957211i	$-0.406547\pi$
$13$	352.674	0.578782	0.289391	+	0.957211i	$0.406547\pi$
$14$	−915.157	−1.24789
$15$	−586.962	−0.673569
$16$	−536.052	−0.523489
$17$	478.207	0.401323	0.200661	−	0.979661i	$-0.435691\pi$
$17$	478.207	0.401323	0.200661	+	0.979661i	$0.435691\pi$
$18$	−368.747	−0.268254
$19$	−174.635	−0.110981	−0.0554903	−	0.998459i	$-0.517672\pi$
$19$	−174.635	−0.110981	−0.0554903	+	0.998459i	$0.517672\pi$
$20$	−735.359	−0.411078
$21$	−1809.23	−0.895255
$22$	2513.74	1.10730
$23$	−2902.56	−1.14409	−0.572046	−	0.820221i	$-0.693850\pi$
$23$	−2902.56	−1.14409	−0.572046	+	0.820221i	$0.693850\pi$
$24$	−1773.07	−0.628346
$25$	1128.39	0.361084
$26$	−1605.52	−0.465783
$27$	−729.000	−0.192450
$28$	−2266.65	−0.546373
$29$	−5179.19	−1.14358	−0.571790	−	0.820400i	$-0.693751\pi$
$29$	−5179.19	−1.14358	−0.571790	+	0.820400i	$0.693751\pi$
$30$	2672.10	0.542063
$31$	−3964.39	−0.740921	−0.370460	−	0.928848i	$-0.620800\pi$
$31$	−3964.39	−0.740921	−0.370460	+	0.928848i	$0.620800\pi$
$32$	−3863.92	−0.667042
$33$	4969.59	0.794393
$34$	−2177.00	−0.322970
$35$	13110.5	1.80905
$36$	−913.308	−0.117452
$37$	−12237.3	−1.46954	−0.734768	−	0.678319i	$-0.762709\pi$
$37$	−12237.3	−1.46954	−0.734768	+	0.678319i	$0.762709\pi$
$38$	795.013	0.0893131
$39$	−3174.07	−0.334160
$40$	12848.5	1.26970
$41$	−3174.84	−0.294959	−0.147480	−	0.989065i	$-0.547116\pi$
$41$	−3174.84	−0.294959	−0.147480	+	0.989065i	$0.547116\pi$
$42$	8236.41	0.720468
$43$	15544.7	1.28207	0.641035	−	0.767511i	$-0.278505\pi$
$43$	15544.7	1.28207	0.641035	+	0.767511i	$0.278505\pi$
$44$	6226.01	0.484818
$45$	5282.66	0.388885
$46$	13213.7	0.920723
$47$	5458.94	0.360466	0.180233	−	0.983624i	$-0.442315\pi$
$47$	5458.94	0.360466	0.180233	+	0.983624i	$0.442315\pi$
$48$	4824.47	0.302236
$49$	23604.5	1.40444
$50$	−5136.90	−0.290587
$51$	−4303.86	−0.231704
$52$	−3976.54	−0.203938
$53$	18286.3	0.894202	0.447101	−	0.894484i	$-0.352457\pi$
$53$	18286.3	0.894202	0.447101	+	0.894484i	$0.352457\pi$
$54$	3318.72	0.154877
$55$	−36011.8	−1.60524
$56$	39603.8	1.68759
$57$	1571.71	0.0640747
$58$	23577.9	0.920311
$59$	18160.6	0.679202	0.339601	−	0.940570i	$-0.389708\pi$
$59$	18160.6	0.679202	0.339601	+	0.940570i	$0.389708\pi$
$60$	6618.23	0.237336
$61$	−27896.1	−0.959885	−0.479943	−	0.877300i	$-0.659343\pi$
$61$	−27896.1	−0.959885	−0.479943	+	0.877300i	$0.659343\pi$
$62$	18047.6	0.596266
$63$	16283.1	0.516876
$64$	34743.9	1.06030
$65$	23000.7	0.675239
$66$	−22623.7	−0.639298
$67$	7415.75	0.201822	0.100911	−	0.994895i	$-0.467824\pi$
$67$	7415.75	0.201822	0.100911	+	0.994895i	$0.467824\pi$
$68$	−5391.98	−0.141409
$69$	26123.0	0.660542
$70$	−59684.7	−1.45585
$71$	−38988.3	−0.917885	−0.458943	−	0.888466i	$-0.651772\pi$
$71$	−38988.3	−0.917885	−0.458943	+	0.888466i	$0.651772\pi$
$72$	15957.7	0.362775
$73$	−20896.1	−0.458942	−0.229471	−	0.973315i	$-0.573700\pi$
$73$	−20896.1	−0.458942	−0.229471	+	0.973315i	$0.573700\pi$
$74$	55709.3	1.18263
$75$	−10155.5	−0.208472
$76$	1969.08	0.0391047
$77$	−111002.	−2.13355
$78$	14449.7	0.268920
$79$	12539.4	0.226053	0.113026	−	0.993592i	$-0.463946\pi$
$79$	12539.4	0.226053	0.113026	+	0.993592i	$0.463946\pi$
$80$	−34960.3	−0.610731
$81$	6561.00	0.111111
$82$	14453.2	0.237372
$83$	−43303.0	−0.689959	−0.344979	−	0.938610i	$-0.612114\pi$
$83$	−43303.0	−0.689959	−0.344979	+	0.938610i	$0.612114\pi$
$84$	20399.9	0.315449
$85$	31187.7	0.468205
$86$	−70766.2	−1.03176
$87$	46612.7	0.660246
$88$	−108783.	−1.49746
$89$	−30909.4	−0.413633	−0.206817	−	0.978380i	$-0.566310\pi$
$89$	−30909.4	−0.413633	−0.206817	+	0.978380i	$0.566310\pi$
$90$	−24048.9	−0.312960
$91$	70896.7	0.897476
$92$	32727.5	0.403128
$93$	35679.5	0.427771
$94$	−24851.4	−0.290089
$95$	−11389.3	−0.129476
$96$	34775.3	0.385117
$97$	−156960.	−1.69380	−0.846898	−	0.531756i	$-0.821532\pi$
$97$	−156960.	−1.69380	−0.846898	+	0.531756i	$0.821532\pi$
$98$	−107458.	−1.13024
$99$	−44726.3	−0.458643
$100$	−12723.0	−0.127230
$101$	49730.7	0.485089	0.242545	−	0.970140i	$-0.422018\pi$
$101$	49730.7	0.485089	0.242545	+	0.970140i	$0.422018\pi$
$102$	19593.0	0.186467
$103$	−113360.	−1.05285	−0.526425	−	0.850222i	$-0.676468\pi$
$103$	−113360.	−1.05285	−0.526425	+	0.850222i	$0.676468\pi$
$104$	69479.7	0.629904
$105$	−117995.	−1.04445
$106$	−83246.9	−0.719620
$107$	−183845.	−1.55236	−0.776178	−	0.630514i	$-0.782844\pi$
$107$	−183845.	−1.55236	−0.776178	+	0.630514i	$0.782844\pi$
$108$	8219.77	0.0678110
$109$	1688.55	0.0136128	0.00680640	−	0.999977i	$-0.497833\pi$
$109$	1688.55	0.0136128	0.00680640	+	0.999977i	$0.497833\pi$
$110$	163941.	1.29183
$111$	110135.	0.848437
$112$	−107760.	−0.811735
$113$	−5872.19	−0.0432618	−0.0216309	−	0.999766i	$-0.506886\pi$
$113$	−5872.19	−0.0432618	−0.0216309	+	0.999766i	$0.506886\pi$
$114$	−7155.11	−0.0515649
$115$	−189299.	−1.33476
$116$	58397.4	0.402948
$117$	28566.6	0.192927
$118$	−82674.6	−0.546597
$119$	96132.1	0.622302
$120$	−115636.	−0.733063
$121$	143848.	0.893182
$122$	126995.	0.772480
$123$	28573.6	0.170295
$124$	44700.1	0.261068
$125$	−130215.	−0.745395
$126$	−74127.7	−0.415962
$127$	296237.	1.62978	0.814892	−	0.579613i	$-0.196796\pi$
$127$	296237.	1.62978	0.814892	+	0.579613i	$0.196796\pi$
$128$	−34523.6	−0.186248
$129$	−139903.	−0.740204
$130$	−104709.	−0.543408
$131$	153859.	0.783330	0.391665	−	0.920108i	$-0.371899\pi$
$131$	153859.	0.783330	0.391665	+	0.920108i	$0.371899\pi$
$132$	−56034.1	−0.279910
$133$	−35106.2	−0.172089
$134$	−33759.7	−0.162419
$135$	−47543.9	−0.224523
$136$	94210.7	0.436770
$137$	−162073.	−0.737749	−0.368875	−	0.929479i	$-0.620257\pi$
$137$	−162073.	−0.737749	−0.368875	+	0.929479i	$0.620257\pi$
$138$	−118923.	−0.531580
$139$	−15420.2	−0.0676944	−0.0338472	−	0.999427i	$-0.510776\pi$
$139$	−15420.2	−0.0676944	−0.0338472	+	0.999427i	$0.510776\pi$
$140$	−147826.	−0.637429
$141$	−49130.5	−0.208115
$142$	177491.	0.738680
$143$	−194738.	−0.796364
$144$	−43420.2	−0.174496
$145$	−337776.	−1.33416
$146$	95128.0	0.369340
$147$	−212440.	−0.810856
$148$	137980.	0.517800
$149$	−391475.	−1.44457	−0.722284	−	0.691597i	$-0.756908\pi$
$149$	−391475.	−1.44457	−0.722284	+	0.691597i	$0.756908\pi$
$150$	46232.1	0.167770
$151$	408010.	1.45623	0.728113	−	0.685458i	$-0.240398\pi$
$151$	408010.	1.45623	0.728113	+	0.685458i	$0.240398\pi$
$152$	−34404.5	−0.120783
$153$	38734.8	0.133774
$154$	505328.	1.71701
$155$	−258549.	−0.864399
$156$	35788.9	0.117743
$157$	−24649.0	−0.0798087
$157$	−24649.0	−0.0798087
$158$	−57084.9	−0.181919
$159$	−164576.	−0.516268
$160$	−251997.	−0.778208
$161$	−583490.	−1.77406
$162$	−29868.5	−0.0894181
$163$	68049.7	0.200612	0.100306	−	0.994957i	$-0.468018\pi$
$163$	68049.7	0.200612	0.100306	+	0.994957i	$0.468018\pi$
$164$	35797.6	0.103931
$165$	324107.	0.926783
$166$	197134.	0.555253
$167$	−86204.3	−0.239187	−0.119594	−	0.992823i	$-0.538159\pi$
$167$	−86204.3	−0.239187	−0.119594	+	0.992823i	$0.538159\pi$
$168$	−356434.	−0.974330
$169$	−246914.	−0.665011
$170$	−141980.	−0.376794
$171$	−14145.4	−0.0369935
$172$	−175273.	−0.451746
$173$	113333.	0.287900	0.143950	−	0.989585i	$-0.454019\pi$
$173$	113333.	0.287900	0.143950	+	0.989585i	$0.454019\pi$
$174$	−212201.	−0.531342
$175$	226835.	0.559907
$176$	295995.	0.720283
$177$	−163445.	−0.392138
$178$	140713.	0.332877
$179$	−185506.	−0.432739	−0.216369	−	0.976312i	$-0.569422\pi$
$179$	−185506.	−0.432739	−0.216369	+	0.976312i	$0.569422\pi$
$180$	−59564.1	−0.137026
$181$	−224925.	−0.510318	−0.255159	−	0.966899i	$-0.582128\pi$
$181$	−224925.	−0.510318	−0.255159	+	0.966899i	$0.582128\pi$
$182$	−322752.	−0.722255
$183$	251065.	0.554190
$184$	−571827.	−1.24515
$185$	−798090.	−1.71444
$186$	−162428.	−0.344254
$187$	−264055.	−0.552192
$188$	−61551.8	−0.127012
$189$	−146548.	−0.298418
$190$	51849.1	0.104198
$191$	491714.	0.975280	0.487640	−	0.873045i	$-0.337858\pi$
$191$	491714.	0.975280	0.487640	+	0.873045i	$0.337858\pi$
$192$	−312695.	−0.612164
$193$	−77523.1	−0.149809	−0.0749044	−	0.997191i	$-0.523865\pi$
$193$	−77523.1	−0.149809	−0.0749044	+	0.997191i	$0.523865\pi$
$194$	714551.	1.36310
$195$	−207006.	−0.389850
$196$	−266150.	−0.494865
$197$	−241736.	−0.443789	−0.221894	−	0.975071i	$-0.571224\pi$
$197$	−241736.	−0.443789	−0.221894	+	0.975071i	$0.571224\pi$
$198$	203613.	0.369099
$199$	288503.	0.516437	0.258219	−	0.966087i	$-0.416865\pi$
$199$	288503.	0.516437	0.258219	+	0.966087i	$0.416865\pi$
$200$	222301.	0.392977
$201$	−66741.8	−0.116522
$202$	−226396.	−0.390382
$203$	−1.04115e6	−1.77327
$204$	48527.8	0.0816423
$205$	−207057.	−0.344116
$206$	516063.	0.847295
$207$	−235107.	−0.381364
$208$	−189052.	−0.302986
$209$	96429.3	0.152701
$210$	537162.	0.840538
$211$	1.17770e6	1.82107	0.910536	−	0.413429i	$-0.135669\pi$
$211$	1.17770e6	1.82107	0.910536	+	0.413429i	$0.135669\pi$
$212$	−206185.	−0.315078
$213$	350895.	0.529941
$214$	836939.	1.24928
$215$	1.01380e6	1.49573
$216$	−143619.	−0.209449
$217$	−796945.	−1.14889
$218$	−7687.00	−0.0109551
$219$	188065.	0.264971
$220$	406048.	0.565615
$221$	168651.	0.232278
$222$	−501383.	−0.682790
$223$	1.11204e6	1.49747	0.748734	−	0.662871i	$-0.230662\pi$
$223$	1.11204e6	1.49747	0.748734	+	0.662871i	$0.230662\pi$
$224$	−776749.	−1.03433
$225$	91399.4	0.120361
$226$	26732.7	0.0348155
$227$	−86712.1	−0.111690	−0.0558451	−	0.998439i	$-0.517785\pi$
$227$	−86712.1	−0.111690	−0.0558451	+	0.998439i	$0.517785\pi$
$228$	−17721.7	−0.0225771
$229$	754620.	0.950910	0.475455	−	0.879740i	$-0.342283\pi$
$229$	754620.	0.950910	0.475455	+	0.879740i	$0.342283\pi$
$230$	861770.	1.07417
$231$	999017.	1.23181
$232$	−1.02034e6	−1.24459
$233$	−1.12006e6	−1.35162	−0.675808	−	0.737078i	$-0.736205\pi$
$233$	−1.12006e6	−1.35162	−0.675808	+	0.737078i	$0.736205\pi$
$234$	−130047.	−0.155261
$235$	356021.	0.420539
$236$	−204768.	−0.239321
$237$	−112855.	−0.130512
$238$	−437634.	−0.500806
$239$	−858326.	−0.971981	−0.485990	−	0.873964i	$-0.661541\pi$
$239$	−858326.	−0.971981	−0.485990	+	0.873964i	$0.661541\pi$
$240$	314642.	0.352605
$241$	1.15476e6	1.28071	0.640355	−	0.768079i	$-0.278787\pi$
$241$	1.15476e6	1.28071	0.640355	+	0.768079i	$0.278787\pi$
$242$	−654857.	−0.718800
$243$	−59049.0	−0.0641500
$244$	314540.	0.338222
$245$	1.53944e6	1.63850
$246$	−130079.	−0.137047
$247$	−61589.2	−0.0642336
$248$	−781016.	−0.806364
$249$	389727.	0.398348
$250$	592795.	0.599866
$251$	−1.31282e6	−1.31529	−0.657645	−	0.753328i	$-0.728447\pi$
$251$	−1.31282e6	−1.31529	−0.657645	+	0.753328i	$0.728447\pi$
$252$	−183599.	−0.182124
$253$	1.60272e6	1.57419
$254$	−1.34860e6	−1.31159
$255$	−280689.	−0.270318
$256$	−954639.	−0.910414
$257$	158000.	0.149219	0.0746094	−	0.997213i	$-0.476229\pi$
$257$	158000.	0.149219	0.0746094	+	0.997213i	$0.476229\pi$
$258$	636896.	0.595689
$259$	−2.46001e6	−2.27870
$260$	−259342.	−0.237925
$261$	−419514.	−0.381193
$262$	−700432.	−0.630395
$263$	−720868.	−0.642638	−0.321319	−	0.946971i	$-0.604126\pi$
$263$	−720868.	−0.642638	−0.321319	+	0.946971i	$0.604126\pi$
$264$	979049.	0.864559
$265$	1.19259e6	1.04322
$266$	159818.	0.138491
$267$	278185.	0.238811
$268$	−83615.6	−0.0711132
$269$	1.49949e6	1.26346	0.631731	−	0.775188i	$-0.282345\pi$
$269$	1.49949e6	1.26346	0.631731	+	0.775188i	$0.282345\pi$
$270$	216440.	0.180688
$271$	−205651.	−0.170102	−0.0850508	−	0.996377i	$-0.527105\pi$
$271$	−205651.	−0.170102	−0.0850508	+	0.996377i	$0.527105\pi$
$272$	−256344.	−0.210088
$273$	−638070.	−0.518158
$274$	737825.	0.593713
$275$	−623069.	−0.496826
$276$	−294547.	−0.232746
$277$	−1.19222e6	−0.933589	−0.466795	−	0.884366i	$-0.654591\pi$
$277$	−1.19222e6	−0.933589	−0.466795	+	0.884366i	$0.654591\pi$
$278$	70199.3	0.0544780
$279$	−321115.	−0.246974
$280$	2.58288e6	1.96883
$281$	−1.91378e6	−1.44586	−0.722928	−	0.690923i	$-0.757204\pi$
$281$	−1.91378e6	−1.44586	−0.722928	+	0.690923i	$0.757204\pi$
$282$	223663.	0.167483
$283$	−1.40033e6	−1.03935	−0.519676	−	0.854363i	$-0.673947\pi$
$283$	−1.40033e6	−1.03935	−0.519676	+	0.854363i	$0.673947\pi$
$284$	439609.	0.323423
$285$	102504.	0.0747530
$286$	886532.	0.640884
$287$	−638226.	−0.457372
$288$	−312978.	−0.222347
$289$	−1.19117e6	−0.838940
$290$	1.53770e6	1.07369
$291$	1.41264e6	0.977913
$292$	235612.	0.161711
$293$	−2.05845e6	−1.40079	−0.700393	−	0.713757i	$-0.746992\pi$
$293$	−2.05845e6	−1.40079	−0.700393	+	0.713757i	$0.746992\pi$
$294$	967120.	0.652547
$295$	1.18439e6	0.792395
$296$	−2.41084e6	−1.59933
$297$	402537.	0.264798
$298$	1.78216e6	1.16253
$299$	−1.02366e6	−0.662180
$300$	114507.	0.0734564
$301$	3.12490e6	1.98801
$302$	−1.85744e6	−1.17192
$303$	−447577.	−0.280066
$304$	93613.4	0.0580971
$305$	−1.81933e6	−1.11985
$306$	−176337.	−0.107657
$307$	1.09839e6	0.665135	0.332568	−	0.943079i	$-0.392085\pi$
$307$	1.09839e6	0.665135	0.332568	+	0.943079i	$0.392085\pi$
$308$	1.25159e6	0.751771
$309$	1.02024e6	0.607863
$310$	1.17703e6	0.695636
$311$	494711.	0.290035	0.145018	−	0.989429i	$-0.453676\pi$
$311$	494711.	0.290035	0.145018	+	0.989429i	$0.453676\pi$
$312$	−625317.	−0.363675
$313$	−1.25365e6	−0.723293	−0.361647	−	0.932315i	$-0.617785\pi$
$313$	−1.25365e6	−0.723293	−0.361647	+	0.932315i	$0.617785\pi$
$314$	112213.	0.0642271
$315$	1.06195e6	0.603016
$316$	−141387.	−0.0796512
$317$	−1.89595e6	−1.05969	−0.529846	−	0.848094i	$-0.677750\pi$
$317$	−1.89595e6	−1.05969	−0.529846	+	0.848094i	$0.677750\pi$
$318$	749222.	0.415473
$319$	2.85983e6	1.57349
$320$	2.26593e6	1.23700
$321$	1.65460e6	0.896253
$322$	2.65629e6	1.42770
$323$	−83511.6	−0.0445390
$324$	−73977.9	−0.0391507
$325$	397953.	0.208989
$326$	−309791.	−0.161445
$327$	−15196.9	−0.00785936
$328$	−625469.	−0.321012
$329$	1.09739e6	0.558948
$330$	−1.47547e6	−0.745841
$331$	166451.	0.0835055	0.0417528	−	0.999128i	$-0.486706\pi$
$331$	166451.	0.0835055	0.0417528	+	0.999128i	$0.486706\pi$
$332$	488259.	0.243111
$333$	−991218.	−0.489845
$334$	392439.	0.192489
$335$	483640.	0.235456
$336$	969844.	0.468656
$337$	3.17345e6	1.52215	0.761074	−	0.648665i	$-0.224672\pi$
$337$	3.17345e6	1.52215	0.761074	+	0.648665i	$0.224672\pi$
$338$	1.12406e6	0.535176
$339$	52849.8	0.0249772
$340$	−351654.	−0.164975
$341$	2.18904e6	1.01945
$342$	64396.0	0.0297710
$343$	1.36647e6	0.627142
$344$	3.06244e6	1.39531
$345$	1.70369e6	0.770625
$346$	−515942.	−0.231692
$347$	2.06038e6	0.918595	0.459298	−	0.888282i	$-0.348101\pi$
$347$	2.06038e6	0.918595	0.459298	+	0.888282i	$0.348101\pi$
$348$	−525577.	−0.232642
$349$	3.89888e6	1.71347	0.856734	−	0.515758i	$-0.172490\pi$
$349$	3.89888e6	1.71347	0.856734	+	0.515758i	$0.172490\pi$
$350$	−1.03265e6	−0.450592
$351$	−257099.	−0.111387
$352$	2.13357e6	0.917803
$353$	−1.28037e6	−0.546888	−0.273444	−	0.961888i	$-0.588163\pi$
$353$	−1.28037e6	−0.546888	−0.273444	+	0.961888i	$0.588163\pi$
$354$	744071.	0.315578
$355$	−2.54274e6	−1.07086
$356$	348516.	0.145746
$357$	−865189.	−0.359286
$358$	844504.	0.348252
$359$	−1.58043e6	−0.647203	−0.323601	−	0.946193i	$-0.604894\pi$
$359$	−1.58043e6	−0.647203	−0.323601	+	0.946193i	$0.604894\pi$
$360$	1.04073e6	0.423234
$361$	−2.44560e6	−0.987683
$362$	1.02395e6	0.410685
$363$	−1.29463e6	−0.515679
$364$	−799389.	−0.316231
$365$	−1.36280e6	−0.535428
$366$	−1.14296e6	−0.445992
$367$	−2.59571e6	−1.00598	−0.502992	−	0.864291i	$-0.667767\pi$
$367$	−2.59571e6	−1.00598	−0.502992	+	0.864291i	$0.667767\pi$
$368$	1.55592e6	0.598919
$369$	−257162.	−0.0983198
$370$	3.63325e6	1.37972
$371$	3.67602e6	1.38657
$372$	−402301.	−0.150728
$373$	−380562.	−0.141629	−0.0708147	−	0.997489i	$-0.522560\pi$
$373$	−380562.	−0.141629	−0.0708147	+	0.997489i	$0.522560\pi$
$374$	1.20209e6	0.444384
$375$	1.17194e6	0.430354
$376$	1.07546e6	0.392304
$377$	−1.82657e6	−0.661884
$378$	667149.	0.240156
$379$	−1.53022e6	−0.547212	−0.273606	−	0.961842i	$-0.588216\pi$
$379$	−1.53022e6	−0.547212	−0.273606	+	0.961842i	$0.588216\pi$
$380$	128419.	0.0456217
$381$	−2.66613e6	−0.940956
$382$	−2.23849e6	−0.784869
$383$	−3.36511e6	−1.17220	−0.586100	−	0.810239i	$-0.699337\pi$
$383$	−3.36511e6	−1.17220	−0.586100	+	0.810239i	$0.699337\pi$
$384$	310712.	0.107530
$385$	−7.23932e6	−2.48912
$386$	352918.	0.120561
$387$	1.25912e6	0.427357
$388$	1.76979e6	0.596820
$389$	−2.27226e6	−0.761350	−0.380675	−	0.924709i	$-0.624308\pi$
$389$	−2.27226e6	−0.761350	−0.380675	+	0.924709i	$0.624308\pi$
$390$	942381.	0.313737
$391$	−1.38802e6	−0.459150
$392$	4.65028e6	1.52849
$393$	−1.38473e6	−0.452256
$394$	1.10049e6	0.357145
$395$	817797.	0.263726
$396$	504307.	0.161606
$397$	−1.13496e6	−0.361412	−0.180706	−	0.983537i	$-0.557838\pi$
$397$	−1.13496e6	−0.361412	−0.180706	+	0.983537i	$0.557838\pi$
$398$	−1.31339e6	−0.415610
$399$	315956.	0.0993559
$400$	−604875.	−0.189023
$401$	2.15275e6	0.668548	0.334274	−	0.942476i	$-0.391509\pi$
$401$	2.15275e6	0.668548	0.334274	+	0.942476i	$0.391509\pi$
$402$	303837.	0.0937725
$403$	−1.39814e6	−0.428832
$404$	−560734.	−0.170924
$405$	427895.	0.129628
$406$	4.73977e6	1.42706
$407$	6.75713e6	2.02198
$408$	−847896.	−0.252169
$409$	1.13178e6	0.334544	0.167272	−	0.985911i	$-0.446504\pi$
$409$	1.13178e6	0.334544	0.167272	+	0.985911i	$0.446504\pi$
$410$	942610.	0.276932
$411$	1.45866e6	0.425940
$412$	1.27818e6	0.370978
$413$	3.65075e6	1.05319
$414$	1.07031e6	0.306908
$415$	−2.82414e6	−0.804944
$416$	−1.36271e6	−0.386072
$417$	138782.	0.0390834
$418$	−438987.	−0.122888
$419$	1.63600e6	0.455249	0.227624	−	0.973749i	$-0.426904\pi$
$419$	1.63600e6	0.455249	0.227624	+	0.973749i	$0.426904\pi$
$420$	1.33044e6	0.368020
$421$	−4.68148e6	−1.28729	−0.643647	−	0.765323i	$-0.722579\pi$
$421$	−4.68148e6	−1.28729	−0.643647	+	0.765323i	$0.722579\pi$
$422$	−5.36138e6	−1.46553
$423$	442174.	0.120155
$424$	3.60254e6	0.973183
$425$	539603.	0.144911
$426$	−1.59742e6	−0.426477
$427$	−5.60785e6	−1.48842
$428$	2.07292e6	0.546983
$429$	1.75265e6	0.459781
$430$	−4.61523e6	−1.20371
$431$	−3.00979e6	−0.780446	−0.390223	−	0.920720i	$-0.627602\pi$
$431$	−3.00979e6	−0.780446	−0.390223	+	0.920720i	$0.627602\pi$
$432$	390782.	0.100745
$433$	2.25082e6	0.576928	0.288464	−	0.957491i	$-0.406855\pi$
$433$	2.25082e6	0.576928	0.288464	+	0.957491i	$0.406855\pi$
$434$	3.62804e6	0.924586
$435$	3.03999e6	0.770280
$436$	−19039.1	−0.00479656
$437$	506888.	0.126972
$438$	−856152.	−0.213239
$439$	−6.15138e6	−1.52339	−0.761695	−	0.647936i	$-0.775632\pi$
$439$	−6.15138e6	−1.52339	−0.761695	+	0.647936i	$0.775632\pi$
$440$	−7.09463e6	−1.74702
$441$	1.91196e6	0.468148
$442$	−767773.	−0.186929
$443$	2.67283e6	0.647086	0.323543	−	0.946214i	$-0.395126\pi$
$443$	2.67283e6	0.647086	0.323543	+	0.946214i	$0.395126\pi$
$444$	−1.24182e6	−0.298952
$445$	−2.01585e6	−0.482567
$446$	−5.06247e6	−1.20511
$447$	3.52327e6	0.834021
$448$	6.98443e6	1.64413
$449$	3.26726e6	0.764834	0.382417	−	0.923990i	$-0.375092\pi$
$449$	3.26726e6	0.764834	0.382417	+	0.923990i	$0.375092\pi$
$450$	−416089.	−0.0968623
$451$	1.75307e6	0.405843
$452$	66211.4	0.0152436
$453$	−3.67209e6	−0.840752
$454$	394750.	0.0898841
$455$	4.62374e6	1.04704
$456$	309640.	0.0697342
$457$	1.06210e6	0.237890	0.118945	−	0.992901i	$-0.462049\pi$
$457$	1.06210e6	0.237890	0.118945	+	0.992901i	$0.462049\pi$
$458$	−3.43535e6	−0.765257
$459$	−348613.	−0.0772346
$460$	2.13442e6	0.470312
$461$	8.34215e6	1.82821	0.914104	−	0.405480i	$-0.132896\pi$
$461$	8.34215e6	1.82821	0.914104	+	0.405480i	$0.132896\pi$
$462$	−4.54795e6	−0.991313
$463$	−6.50616e6	−1.41050	−0.705248	−	0.708960i	$-0.749164\pi$
$463$	−6.50616e6	−1.41050	−0.705248	+	0.708960i	$0.749164\pi$
$464$	2.77631e6	0.598651
$465$	2.32694e6	0.499061
$466$	5.09901e6	1.08773
$467$	−6.92804e6	−1.47000	−0.735002	−	0.678065i	$-0.762819\pi$
$467$	−6.92804e6	−1.47000	−0.735002	+	0.678065i	$0.762819\pi$
$468$	−322100.	−0.0679792
$469$	1.49076e6	0.312950
$470$	−1.62076e6	−0.338434
$471$	221841.	0.0460776
$472$	3.57778e6	0.739194
$473$	−8.58343e6	−1.76404
$474$	513764.	0.105031
$475$	−197056.	−0.0400733
$476$	−1.08393e6	−0.219272
$477$	1.48119e6	0.298067
$478$	3.90747e6	0.782214
$479$	2.87589e6	0.572708	0.286354	−	0.958124i	$-0.407557\pi$
$479$	2.87589e6	0.572708	0.286354	+	0.958124i	$0.407557\pi$
$480$	2.26798e6	0.449299
$481$	−4.31577e6	−0.850541
$482$	−5.25698e6	−1.03067
$483$	5.25141e6	1.02425
$484$	−1.62194e6	−0.314718
$485$	−1.02366e7	−1.97608
$486$	268816.	0.0516256
$487$	−4.37970e6	−0.836801	−0.418401	−	0.908263i	$-0.637409\pi$
$487$	−4.37970e6	−0.836801	−0.418401	+	0.908263i	$0.637409\pi$
$488$	−5.49576e6	−1.04467
$489$	−612447.	−0.115823
$490$	−7.00818e6	−1.31861
$491$	−3.47819e6	−0.651103	−0.325551	−	0.945524i	$-0.605550\pi$
$491$	−3.47819e6	−0.651103	−0.325551	+	0.945524i	$0.605550\pi$
$492$	−322178.	−0.0600045
$493$	−2.47672e6	−0.458945
$494$	280380.	0.0516928
$495$	−2.91696e6	−0.535078
$496$	2.12512e6	0.387864
$497$	−7.83767e6	−1.42330
$498$	−1.77421e6	−0.320576
$499$	4.37267e6	0.786132	0.393066	−	0.919510i	$-0.371414\pi$
$499$	4.37267e6	0.786132	0.393066	+	0.919510i	$0.371414\pi$
$500$	1.46823e6	0.262645
$501$	775839.	0.138095
$502$	5.97653e6	1.05850
$503$	1.80102e6	0.317395	0.158697	−	0.987327i	$-0.449271\pi$
$503$	1.80102e6	0.317395	0.158697	+	0.987327i	$0.449271\pi$
$504$	3.20791e6	0.562529
$505$	3.24334e6	0.565932
$506$	−7.29628e6	−1.26685
$507$	2.22223e6	0.383944
$508$	−3.34019e6	−0.574265
$509$	573848.	0.0981753	0.0490876	−	0.998794i	$-0.484369\pi$
$509$	573848.	0.0981753	0.0490876	+	0.998794i	$0.484369\pi$
$510$	1.27782e6	0.217542
$511$	−4.20066e6	−0.711649
$512$	5.45068e6	0.918915
$513$	127309.	0.0213582
$514$	−719283.	−0.120086
$515$	−7.39311e6	−1.22831
$516$	1.57746e6	0.260816
$517$	−3.01430e6	−0.495975
$518$	1.11990e7	1.83381
$519$	−1.02000e6	−0.166219
$520$	4.53133e6	0.734881
$521$	−5.40492e6	−0.872359	−0.436179	−	0.899860i	$-0.643669\pi$
$521$	−5.40492e6	−0.872359	−0.436179	+	0.899860i	$0.643669\pi$
$522$	1.90981e6	0.306770
$523$	−1.01661e6	−0.162517	−0.0812587	−	0.996693i	$-0.525894\pi$
$523$	−1.01661e6	−0.162517	−0.0812587	+	0.996693i	$0.525894\pi$
$524$	−1.73482e6	−0.276011
$525$	−2.04152e6	−0.323262
$526$	3.28170e6	0.517171
$527$	−1.89580e6	−0.297348
$528$	−2.66396e6	−0.415856
$529$	1.98849e6	0.308947
$530$	−5.42920e6	−0.839549
$531$	1.47100e6	0.226401
$532$	395836.	0.0606368
$533$	−1.11968e6	−0.170717
$534$	−1.26642e6	−0.192187
$535$	−1.19900e7	−1.81106
$536$	1.46096e6	0.219648
$537$	1.66956e6	0.249842
$538$	−6.82631e6	−1.01679
$539$	−1.30338e7	−1.93242
$540$	536077.	0.0791121
$541$	−1.91950e6	−0.281965	−0.140983	−	0.990012i	$-0.545026\pi$
$541$	−1.91950e6	−0.281965	−0.140983	+	0.990012i	$0.545026\pi$
$542$	936213.	0.136891
$543$	2.02432e6	0.294632
$544$	−1.84775e6	−0.267699
$545$	110124.	0.0158814
$546$	2.90477e6	0.416994
$547$	−1.95579e6	−0.279481	−0.139741	−	0.990188i	$-0.544627\pi$
$547$	−1.95579e6	−0.279481	−0.139741	+	0.990188i	$0.544627\pi$
$548$	1.82744e6	0.259951
$549$	−2.25959e6	−0.319962
$550$	2.83648e6	0.399827
$551$	904467.	0.126915
$552$	5.14644e6	0.718885
$553$	2.52075e6	0.350524
$554$	5.42748e6	0.751318
$555$	7.18281e6	0.989833
$556$	173869.	0.0238526
$557$	1.22254e7	1.66965	0.834824	−	0.550517i	$-0.185570\pi$
$557$	1.22254e7	1.66965	0.834824	+	0.550517i	$0.185570\pi$
$558$	1.46185e6	0.198755
$559$	5.48222e6	0.742040
$560$	−7.02792e6	−0.947015
$561$	2.37649e6	0.318808
$562$	8.71232e6	1.16357
$563$	1.33740e7	1.77824	0.889118	−	0.457678i	$-0.151319\pi$
$563$	1.33740e7	1.77824	0.889118	+	0.457678i	$0.151319\pi$
$564$	553966.	0.0733306
$565$	−382973.	−0.0504716
$566$	6.37488e6	0.836433
$567$	1.31893e6	0.172292
$568$	−7.68101e6	−0.998959
$569$	−1.15829e7	−1.49982	−0.749909	−	0.661541i	$-0.769903\pi$
$569$	−1.15829e7	−1.49982	−0.749909	+	0.661541i	$0.769903\pi$
$570$	−466642.	−0.0601585
$571$	−8.28632e6	−1.06358	−0.531791	−	0.846875i	$-0.678481\pi$
$571$	−8.28632e6	−1.06358	−0.531791	+	0.846875i	$0.678481\pi$
$572$	2.19575e6	0.280604
$573$	−4.42543e6	−0.563078
$574$	2.90548e6	0.368076
$575$	−3.27521e6	−0.413113
$576$	2.81426e6	0.353433
$577$	7.50846e6	0.938882	0.469441	−	0.882964i	$-0.344455\pi$
$577$	7.50846e6	0.938882	0.469441	+	0.882964i	$0.344455\pi$
$578$	5.42274e6	0.675148
$579$	697707.	0.0864922
$580$	3.80856e6	0.470101
$581$	−8.70504e6	−1.06987
$582$	−6.43096e6	−0.786989
$583$	−1.00972e7	−1.23036
$584$	−4.11670e6	−0.499479
$585$	1.86306e6	0.225080
$586$	9.37095e6	1.12730
$587$	−1.53404e7	−1.83756	−0.918782	−	0.394766i	$-0.870826\pi$
$587$	−1.53404e7	−1.83756	−0.918782	+	0.394766i	$0.870826\pi$
$588$	2.39535e6	0.285710
$589$	692320.	0.0822278
$590$	−5.39187e6	−0.637690
$591$	2.17563e6	0.256222
$592$	6.55981e6	0.769285
$593$	48952.9	0.00571665	0.00285833	−	0.999996i	$-0.499090\pi$
$593$	48952.9	0.00571665	0.00285833	+	0.999996i	$0.499090\pi$
$594$	−1.83252e6	−0.213099
$595$	6.26954e6	0.726012
$596$	4.41403e6	0.509003
$597$	−2.59653e6	−0.298165
$598$	4.66012e6	0.532898
$599$	−1.15935e7	−1.32023	−0.660114	−	0.751166i	$-0.729492\pi$
$599$	−1.15935e7	−1.32023	−0.660114	+	0.751166i	$0.729492\pi$
$600$	−2.00071e6	−0.226886
$601$	1.10970e7	1.25319	0.626596	−	0.779344i	$-0.284448\pi$
$601$	1.10970e7	1.25319	0.626596	+	0.779344i	$0.284448\pi$
$602$	−1.42259e7	−1.59988
$603$	600676.	0.0672739
$604$	−4.60048e6	−0.513110
$605$	9.38147e6	1.04204
$606$	2.03756e6	0.225387
$607$	−532250.	−0.0586332	−0.0293166	−	0.999570i	$-0.509333\pi$
$607$	−532250.	−0.0586332	−0.0293166	+	0.999570i	$0.509333\pi$
$608$	674775.	0.0740287
$609$	9.37037e6	1.02380
$610$	8.28236e6	0.901218
$611$	1.92523e6	0.208631
$612$	−436750.	−0.0471362
$613$	1.10826e7	1.19122	0.595609	−	0.803275i	$-0.296911\pi$
$613$	1.10826e7	1.19122	0.595609	+	0.803275i	$0.296911\pi$
$614$	−5.00033e6	−0.535276
$615$	1.86351e6	0.198675
$616$	−2.18683e7	−2.32200
$617$	−1.06810e7	−1.12954	−0.564769	−	0.825249i	$-0.691035\pi$
$617$	−1.06810e7	−1.12954	−0.564769	+	0.825249i	$0.691035\pi$
$618$	−4.64457e6	−0.489186
$619$	−1.69927e7	−1.78252	−0.891262	−	0.453490i	$-0.850179\pi$
$619$	−1.69927e7	−1.78252	−0.891262	+	0.453490i	$0.850179\pi$
$620$	2.91525e6	0.304577
$621$	2.11596e6	0.220181
$622$	−2.25214e6	−0.233410
$623$	−6.21360e6	−0.641391
$624$	1.70147e6	0.174929
$625$	−1.20186e7	−1.23070
$626$	5.70714e6	0.582080
$627$	−867863.	−0.0881622
$628$	277927.	0.0281211
$629$	−5.85195e6	−0.589758
$630$	−4.83446e6	−0.485285
$631$	1.46077e7	1.46053	0.730263	−	0.683166i	$-0.239397\pi$
$631$	1.46077e7	1.46053	0.730263	+	0.683166i	$0.239397\pi$
$632$	2.47037e6	0.246019
$633$	−1.05993e7	−1.05140
$634$	8.63119e6	0.852801
$635$	1.93200e7	1.90139
$636$	1.85567e6	0.181910
$637$	8.32469e6	0.812867
$638$	−1.30191e7	−1.26628
$639$	−3.15805e6	−0.305962
$640$	−2.25156e6	−0.217287
$641$	−9.83760e6	−0.945680	−0.472840	−	0.881148i	$-0.656771\pi$
$641$	−9.83760e6	−0.945680	−0.472840	+	0.881148i	$0.656771\pi$
$642$	−7.53245e6	−0.721271
$643$	1.63474e7	1.55927	0.779636	−	0.626233i	$-0.215404\pi$
$643$	1.63474e7	1.55927	0.779636	+	0.626233i	$0.215404\pi$
$644$	6.57908e6	0.625102
$645$	−9.12416e6	−0.863563
$646$	380181.	0.0358434
$647$	4.41852e6	0.414970	0.207485	−	0.978238i	$-0.433472\pi$
$647$	4.41852e6	0.414970	0.207485	+	0.978238i	$0.433472\pi$
$648$	1.29257e6	0.120925
$649$	−1.00278e7	−0.934534
$650$	−1.81165e6	−0.168187
$651$	7.17251e6	0.663313
$652$	−767287.	−0.0706869
$653$	−1.01730e7	−0.933609	−0.466804	−	0.884361i	$-0.654595\pi$
$653$	−1.01730e7	−0.933609	−0.466804	+	0.884361i	$0.654595\pi$
$654$	69183.0	0.00632492
$655$	1.00344e7	0.913876
$656$	1.70188e6	0.154408
$657$	−1.69258e6	−0.152981
$658$	−4.99579e6	−0.449821
$659$	4.24400e6	0.380682	0.190341	−	0.981718i	$-0.439041\pi$
$659$	4.24400e6	0.380682	0.190341	+	0.981718i	$0.439041\pi$
$660$	−3.65443e6	−0.326558
$661$	3.34464e6	0.297746	0.148873	−	0.988856i	$-0.452435\pi$
$661$	3.34464e6	0.297746	0.148873	+	0.988856i	$0.452435\pi$
$662$	−757754.	−0.0672022
$663$	−1.51786e6	−0.134106
$664$	−8.53105e6	−0.750900
$665$	−2.28955e6	−0.200769
$666$	4.51245e6	0.394209
$667$	1.50329e7	1.30836
$668$	971989.	0.0842791
$669$	−1.00083e7	−0.864564
$670$	−2.20174e6	−0.189487
$671$	1.54036e7	1.32073
$672$	6.99074e6	0.597173
$673$	4.70278e6	0.400236	0.200118	−	0.979772i	$-0.435867\pi$
$673$	4.70278e6	0.400236	0.200118	+	0.979772i	$0.435867\pi$
$674$	−1.44469e7	−1.22497
$675$	−822594.	−0.0694906
$676$	2.78405e6	0.234321
$677$	790149.	0.0662579	0.0331289	−	0.999451i	$-0.489453\pi$
$677$	790149.	0.0662579	0.0331289	+	0.999451i	$0.489453\pi$
$678$	−240595.	−0.0201007
$679$	−3.15532e7	−2.62645
$680$	6.14423e6	0.509560
$681$	780409.	0.0644843
$682$	−9.96545e6	−0.820420
$683$	7.43829e6	0.610128	0.305064	−	0.952332i	$-0.401322\pi$
$683$	7.43829e6	0.610128	0.305064	+	0.952332i	$0.401322\pi$
$684$	159495.	0.0130349
$685$	−1.05701e7	−0.860699
$686$	−6.22077e6	−0.504701
$687$	−6.79158e6	−0.549008
$688$	−8.33279e6	−0.671149
$689$	6.44909e6	0.517548
$690$	−7.75593e6	−0.620170
$691$	1.00061e7	0.797206	0.398603	−	0.917124i	$-0.369495\pi$
$691$	1.00061e7	0.797206	0.398603	+	0.917124i	$0.369495\pi$
$692$	−1.27788e6	−0.101444
$693$	−8.99115e6	−0.711185
$694$	−9.37974e6	−0.739252
$695$	−1.00567e6	−0.0789761
$696$	9.18308e6	0.718563
$697$	−1.51823e6	−0.118374
$698$	−1.77494e7	−1.37894
$699$	1.00806e7	0.780356
$700$	−2.55766e6	−0.197287
$701$	−2.40890e7	−1.85150	−0.925750	−	0.378136i	$-0.876565\pi$
$701$	−2.40890e7	−1.85150	−0.925750	+	0.378136i	$0.876565\pi$
$702$	1.17043e6	0.0896399
$703$	2.13705e6	0.163090
$704$	−1.91848e7	−1.45890
$705$	−3.20419e6	−0.242798
$706$	5.82879e6	0.440115
$707$	9.99718e6	0.752192
$708$	1.84291e6	0.138172
$709$	−1.24590e7	−0.930821	−0.465410	−	0.885095i	$-0.654093\pi$
$709$	−1.24590e7	−0.930821	−0.465410	+	0.885095i	$0.654093\pi$
$710$	1.15756e7	0.861785
$711$	1.01569e6	0.0753510
$712$	−6.08940e6	−0.450168
$713$	1.15069e7	0.847682
$714$	3.93871e6	0.289140
$715$	−1.27004e7	−0.929082
$716$	2.09166e6	0.152478
$717$	7.72494e6	0.561173
$718$	7.19481e6	0.520845
$719$	2.03223e7	1.46606	0.733029	−	0.680198i	$-0.238106\pi$
$719$	2.03223e7	1.46606	0.733029	+	0.680198i	$0.238106\pi$
$720$	−2.83178e6	−0.203577
$721$	−2.27883e7	−1.63258
$722$	1.11334e7	0.794851
$723$	−1.03929e7	−0.739418
$724$	2.53612e6	0.179814
$725$	−5.84413e6	−0.412928
$726$	5.89371e6	0.414999
$727$	−1.12261e7	−0.787758	−0.393879	−	0.919162i	$-0.628867\pi$
$727$	−1.12261e7	−0.787758	−0.393879	+	0.919162i	$0.628867\pi$
$728$	1.39672e7	0.976746
$729$	531441.	0.0370370
$730$	6.20406e6	0.430892
$731$	7.43360e6	0.514524
$732$	−2.83086e6	−0.195272
$733$	1.05457e7	0.724960	0.362480	−	0.931991i	$-0.381930\pi$
$733$	1.05457e7	0.724960	0.362480	+	0.931991i	$0.381930\pi$
$734$	1.18168e7	0.809578
$735$	−1.38549e7	−0.945990
$736$	1.12152e7	0.763158
$737$	−4.09480e6	−0.277693
$738$	1.17071e6	0.0791241
$739$	2.61857e7	1.76381	0.881907	−	0.471423i	$-0.156260\pi$
$739$	2.61857e7	1.76381	0.881907	+	0.471423i	$0.156260\pi$
$740$	8.99879e6	0.604094
$741$	554303.	0.0370853
$742$	−1.67348e7	−1.11586
$743$	2.58629e7	1.71872	0.859361	−	0.511369i	$-0.170861\pi$
$743$	2.58629e7	1.71872	0.859361	+	0.511369i	$0.170861\pi$
$744$	7.02915e6	0.465554
$745$	−2.55312e7	−1.68531
$746$	1.73248e6	0.113978
$747$	−3.50755e6	−0.229986
$748$	2.97732e6	0.194568
$749$	−3.69576e7	−2.40713
$750$	−5.33515e6	−0.346333
$751$	−6.80898e6	−0.440537	−0.220268	−	0.975439i	$-0.570693\pi$
$751$	−6.80898e6	−0.440537	−0.220268	+	0.975439i	$0.570693\pi$
$752$	−2.92628e6	−0.188700
$753$	1.18154e7	0.759384
$754$	8.31531e6	0.532660
$755$	2.66096e7	1.69891
$756$	1.65239e6	0.105150
$757$	1.56560e7	0.992979	0.496489	−	0.868043i	$-0.334622\pi$
$757$	1.56560e7	0.992979	0.496489	+	0.868043i	$0.334622\pi$
$758$	6.96621e6	0.440376
$759$	−1.44245e7	−0.908859
$760$	−2.24379e6	−0.140912
$761$	−2.19042e7	−1.37109	−0.685543	−	0.728032i	$-0.740435\pi$
$761$	−2.19042e7	−1.37109	−0.685543	+	0.728032i	$0.740435\pi$
$762$	1.21374e7	0.757246
$763$	339443.	0.0211084
$764$	−5.54428e6	−0.343646
$765$	2.52620e6	0.156068
$766$	1.53194e7	0.943344
$767$	6.40476e6	0.393110
$768$	8.59175e6	0.525628
$769$	1.93706e7	1.18121	0.590606	−	0.806960i	$-0.298889\pi$
$769$	1.93706e7	1.18121	0.590606	+	0.806960i	$0.298889\pi$
$770$	3.29565e7	2.00315
$771$	−1.42200e6	−0.0861516
$772$	874104.	0.0527861
$773$	9.41180e6	0.566532	0.283266	−	0.959041i	$-0.408582\pi$
$773$	9.41180e6	0.566532	0.283266	+	0.959041i	$0.408582\pi$
$774$	−5.73207e6	−0.343921
$775$	−4.47336e6	−0.267535
$776$	−3.09225e7	−1.84340
$777$	2.21401e7	1.31561
$778$	1.03443e7	0.612707
$779$	554438.	0.0327348
$780$	2.33408e6	0.137366
$781$	2.15284e7	1.26295
$782$	6.31887e6	0.369507
$783$	3.77563e6	0.220082
$784$	−1.26532e7	−0.735210
$785$	−1.60756e6	−0.0931092
$786$	6.30389e6	0.363959
$787$	2.08637e7	1.20075	0.600377	−	0.799717i	$-0.295017\pi$
$787$	2.08637e7	1.20075	0.600377	+	0.799717i	$0.295017\pi$
$788$	2.72567e6	0.156372
$789$	6.48781e6	0.371027
$790$	−3.72296e6	−0.212237
$791$	−1.18046e6	−0.0670829
$792$	−8.81144e6	−0.499154
$793$	−9.83824e6	−0.555565
$794$	5.16680e6	0.290851
$795$	−1.07333e7	−0.602306
$796$	−3.25299e6	−0.181970
$797$	−3.01113e7	−1.67913	−0.839564	−	0.543261i	$-0.817189\pi$
$797$	−3.01113e7	−1.67913	−0.839564	+	0.543261i	$0.817189\pi$
$798$	−1.43836e6	−0.0799580
$799$	2.61051e6	0.144663
$800$	−4.36000e6	−0.240858
$801$	−2.50366e6	−0.137878
$802$	−9.80024e6	−0.538023
$803$	1.15383e7	0.631473
$804$	752540.	0.0410572
$805$	−3.80540e7	−2.06972
$806$	6.36492e6	0.345108
$807$	−1.34954e7	−0.729460
$808$	9.79736e6	0.527935
$809$	2.16297e7	1.16193	0.580965	−	0.813929i	$-0.302675\pi$
$809$	2.16297e7	1.16193	0.580965	+	0.813929i	$0.302675\pi$
$810$	−1.94796e6	−0.104320
$811$	3.25765e7	1.73921	0.869605	−	0.493749i	$-0.164374\pi$
$811$	3.25765e7	1.73921	0.869605	+	0.493749i	$0.164374\pi$
$812$	1.17394e7	0.624822
$813$	1.85086e6	0.0982082
$814$	−3.07613e7	−1.62721
$815$	4.43806e6	0.234045
$816$	2.30710e6	0.121294
$817$	−2.71465e6	−0.142285
$818$	−5.15234e6	−0.269229
$819$	5.74263e6	0.299159
$820$	2.33465e6	0.121251
$821$	−1.41139e7	−0.730783	−0.365392	−	0.930854i	$-0.619065\pi$
$821$	−1.41139e7	−0.730783	−0.365392	+	0.930854i	$0.619065\pi$
$822$	−6.64042e6	−0.342781
$823$	5.73161e6	0.294969	0.147485	−	0.989064i	$-0.452882\pi$
$823$	5.73161e6	0.294969	0.147485	+	0.989064i	$0.452882\pi$
$824$	−2.23328e7	−1.14584
$825$	5.60762e6	0.286843
$826$	−1.66198e7	−0.847568
$827$	−2.38835e6	−0.121432	−0.0607160	−	0.998155i	$-0.519338\pi$
$827$	−2.38835e6	−0.121432	−0.0607160	+	0.998155i	$0.519338\pi$
$828$	2.65093e6	0.134376
$829$	−2.19546e7	−1.10953	−0.554766	−	0.832007i	$-0.687192\pi$
$829$	−2.19546e7	−1.10953	−0.554766	+	0.832007i	$0.687192\pi$
$830$	1.28567e7	0.647789
$831$	1.07299e7	0.539008
$832$	1.22533e7	0.613683
$833$	1.12878e7	0.563635
$834$	−631794.	−0.0314529
$835$	−5.62207e6	−0.279049
$836$	−1.08728e6	−0.0538053
$837$	2.89004e6	0.142590
$838$	−7.44778e6	−0.366368
$839$	2.15412e7	1.05649	0.528244	−	0.849092i	$-0.322851\pi$
$839$	2.15412e7	1.05649	0.528244	+	0.849092i	$0.322851\pi$
$840$	−2.32459e7	−1.13671
$841$	6.31283e6	0.307775
$842$	2.13121e7	1.03597
$843$	1.72240e7	0.834765
$844$	−1.32790e7	−0.641667
$845$	−1.61032e7	−0.775838
$846$	−2.01297e6	−0.0966965
$847$	2.89172e7	1.38499
$848$	−9.80240e6	−0.468104
$849$	1.26029e7	0.600070
$850$	−2.45650e6	−0.116619
$851$	3.55193e7	1.68128
$852$	−3.95648e6	−0.186728
$853$	−2.75012e7	−1.29413	−0.647066	−	0.762434i	$-0.724004\pi$
$853$	−2.75012e7	−1.29413	−0.647066	+	0.762434i	$0.724004\pi$
$854$	2.55293e7	1.19783
$855$	−922536.	−0.0431587
$856$	−3.62189e7	−1.68947
$857$	3.90764e7	1.81745	0.908725	−	0.417394i	$-0.137057\pi$
$857$	3.90764e7	1.81745	0.908725	+	0.417394i	$0.137057\pi$
$858$	−7.97879e6	−0.370015
$859$	−1.35351e7	−0.625863	−0.312931	−	0.949776i	$-0.601311\pi$
$859$	−1.35351e7	−0.625863	−0.312931	+	0.949776i	$0.601311\pi$
$860$	−1.14310e7	−0.527032
$861$	5.74403e6	0.264064
$862$	1.37018e7	0.628074
$863$	−3.54131e7	−1.61859	−0.809295	−	0.587403i	$-0.800151\pi$
$863$	−3.54131e7	−1.61859	−0.809295	+	0.587403i	$0.800151\pi$
$864$	2.81680e6	0.128372
$865$	7.39137e6	0.335880
$866$	−1.02467e7	−0.464291
$867$	1.07206e7	0.484362
$868$	8.98588e6	0.404819
$869$	−6.92398e6	−0.311033
$870$	−1.38393e7	−0.619893
$871$	2.61534e6	0.116811
$872$	332658.	0.0148152
$873$	−1.27138e7	−0.564599
$874$	−2.30757e6	−0.102182
$875$	−2.61766e7	−1.15583
$876$	−2.12051e6	−0.0933641
$877$	2.40062e7	1.05396	0.526980	−	0.849878i	$-0.323324\pi$
$877$	2.40062e7	1.05396	0.526980	+	0.849878i	$0.323324\pi$
$878$	2.80037e7	1.22597
$879$	1.85261e7	0.808744
$880$	1.93042e7	0.840322
$881$	2.65570e7	1.15276	0.576380	−	0.817182i	$-0.304465\pi$
$881$	2.65570e7	1.15276	0.576380	+	0.817182i	$0.304465\pi$
$882$	−8.70408e6	−0.376748
$883$	−7.83414e6	−0.338134	−0.169067	−	0.985605i	$-0.554076\pi$
$883$	−7.83414e6	−0.338134	−0.169067	+	0.985605i	$0.554076\pi$
$884$	−1.90161e6	−0.0818448
$885$	−1.06596e7	−0.457489
$886$	−1.21679e7	−0.520751
$887$	−7.04744e6	−0.300762	−0.150381	−	0.988628i	$-0.548050\pi$
$887$	−7.04744e6	−0.300762	−0.150381	+	0.988628i	$0.548050\pi$
$888$	2.16976e7	0.923376
$889$	5.95513e7	2.52719
$890$	9.17701e6	0.388352
$891$	−3.62283e6	−0.152881
$892$	−1.25387e7	−0.527642
$893$	−953322.	−0.0400047
$894$	−1.60394e7	−0.671190
$895$	−1.20983e7	−0.504857
$896$	−6.94014e6	−0.288801
$897$	9.21291e6	0.382310
$898$	−1.48739e7	−0.615510
$899$	2.05323e7	0.847302
$900$	−1.03057e6	−0.0424101
$901$	8.74462e6	0.358863
$902$	−7.98073e6	−0.326608
$903$	−2.81241e7	−1.14778
$904$	−1.15687e6	−0.0470829
$905$	−1.46692e7	−0.595366
$906$	1.67169e7	0.676606
$907$	2.06412e7	0.833137	0.416569	−	0.909104i	$-0.363233\pi$
$907$	2.06412e7	0.833137	0.416569	+	0.909104i	$0.363233\pi$
$908$	977714.	0.0393547
$909$	4.02819e6	0.161696
$910$	−2.10492e7	−0.842623
$911$	2.45737e7	0.981011	0.490505	−	0.871438i	$-0.336812\pi$
$911$	2.45737e7	0.981011	0.490505	+	0.871438i	$0.336812\pi$
$912$	−842521.	−0.0335424
$913$	2.39109e7	0.949334
$914$	−4.83515e6	−0.191445
$915$	1.63740e7	0.646549
$916$	−8.50864e6	−0.335059
$917$	3.09297e7	1.21465
$918$	1.58704e6	0.0621555
$919$	−2.98117e7	−1.16439	−0.582195	−	0.813049i	$-0.697806\pi$
$919$	−2.98117e7	−1.16439	−0.582195	+	0.813049i	$0.697806\pi$
$920$	−3.72934e7	−1.45266
$921$	−9.88549e6	−0.384016
$922$	−3.79770e7	−1.47127
$923$	−1.37502e7	−0.531256
$924$	−1.12643e7	−0.434035
$925$	−1.38084e7	−0.530626
$926$	2.96188e7	1.13512
$927$	−9.18215e6	−0.350950
$928$	2.00120e7	0.762816
$929$	−4.75576e7	−1.80793	−0.903963	−	0.427612i	$-0.859355\pi$
$929$	−4.75576e7	−1.80793	−0.903963	+	0.427612i	$0.859355\pi$
$930$	−1.05932e7	−0.401626
$931$	−4.12217e6	−0.155866
$932$	1.26292e7	0.476250
$933$	−4.45240e6	−0.167452
$934$	3.15394e7	1.18300
$935$	−1.72211e7	−0.644217
$936$	5.62785e6	0.209968
$937$	−1.24439e7	−0.463030	−0.231515	−	0.972831i	$-0.574368\pi$
$937$	−1.24439e7	−0.463030	−0.231515	+	0.972831i	$0.574368\pi$
$938$	−6.78657e6	−0.251851
$939$	1.12828e7	0.417593
$940$	−4.01428e6	−0.148180
$941$	−1.97146e7	−0.725796	−0.362898	−	0.931829i	$-0.618213\pi$
$941$	−1.97146e7	−0.725796	−0.362898	+	0.931829i	$0.618213\pi$
$942$	−1.00992e6	−0.0370815
$943$	9.21515e6	0.337461
$944$	−9.73501e6	−0.355555
$945$	−9.55757e6	−0.348151
$946$	3.90755e7	1.41963
$947$	−2.98959e7	−1.08327	−0.541634	−	0.840614i	$-0.682194\pi$
$947$	−2.98959e7	−1.08327	−0.541634	+	0.840614i	$0.682194\pi$
$948$	1.27248e6	0.0459866
$949$	−7.36952e6	−0.265628
$950$	897082.	0.0322495
$951$	1.70636e7	0.611813
$952$	1.89388e7	0.677268
$953$	−3.91400e7	−1.39601	−0.698005	−	0.716093i	$-0.745929\pi$
$953$	−3.91400e7	−1.39601	−0.698005	+	0.716093i	$0.745929\pi$
$954$	−6.74300e6	−0.239873
$955$	3.20686e7	1.13782
$956$	9.67798e6	0.342484
$957$	−2.57384e7	−0.908452
$958$	−1.30923e7	−0.460894
$959$	−3.25809e7	−1.14397
$960$	−2.03933e7	−0.714184
$961$	−1.29128e7	−0.451036
$962$	1.96472e7	0.684484
$963$	−1.48914e7	−0.517452
$964$	−1.30204e7	−0.451266
$965$	−5.05590e6	−0.174775
$966$	−2.39066e7	−0.824282
$967$	4.60480e7	1.58360	0.791798	−	0.610783i	$-0.209145\pi$
$967$	4.60480e7	1.58360	0.791798	+	0.610783i	$0.209145\pi$
$968$	2.83392e7	0.972074
$969$	751605.	0.0257146
$970$	4.66016e7	1.59027
$971$	616637.	0.0209885	0.0104943	−	0.999945i	$-0.496660\pi$
$971$	616637.	0.0209885	0.0104943	+	0.999945i	$0.496660\pi$
$972$	665801.	0.0226037
$973$	−3.09986e6	−0.104969
$974$	1.99383e7	0.673427
$975$	−3.58158e6	−0.120660
$976$	1.49538e7	0.502489
$977$	3.99987e7	1.34063	0.670315	−	0.742076i	$-0.266159\pi$
$977$	3.99987e7	1.34063	0.670315	+	0.742076i	$0.266159\pi$
$978$	2.78812e6	0.0932104
$979$	1.70674e7	0.569130
$980$	−1.73578e7	−0.577337
$981$	136773.	0.00453760
$982$	1.58342e7	0.523983
$983$	1.55441e7	0.513077	0.256538	−	0.966534i	$-0.417418\pi$
$983$	1.55441e7	0.513077	0.256538	+	0.966534i	$0.417418\pi$
$984$	5.62922e6	0.185336
$985$	−1.57656e7	−0.517748
$986$	1.12751e7	0.369342
$987$	−9.87651e6	−0.322709
$988$	694443.	0.0226331
$989$	−4.51194e7	−1.46681
$990$	1.32792e7	0.430611
$991$	−3.54519e7	−1.14671	−0.573357	−	0.819306i	$-0.694359\pi$
$991$	−3.54519e7	−1.14671	−0.573357	+	0.819306i	$0.694359\pi$
$992$	1.53181e7	0.494225
$993$	−1.49805e6	−0.0482119
$994$	3.56804e7	1.14542
$995$	1.88156e7	0.602504
$996$	−4.39433e6	−0.140360
$997$	4.43009e7	1.41148	0.705740	−	0.708471i	$-0.250615\pi$
$997$	4.43009e7	1.41148	0.705740	+	0.708471i	$0.250615\pi$
$998$	−1.99063e7	−0.632650
$999$	8.92097e6	0.282812

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.6.a.b.1.12	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.6.a.b.1.12	✓	30	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	471.a (trivial)

\(f(q)\)	\(=\)	\(q-4.55243 q^{2} -9.00000 q^{3} -11.2754 q^{4} +65.2180 q^{5} +40.9718 q^{6} +201.026 q^{7} +197.008 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.55243 q^{2} -9.00000 q^{3} -11.2754 q^{4} +65.2180 q^{5} +40.9718 q^{6} +201.026 q^{7} +197.008 q^{8} +81.0000 q^{9} -296.900 q^{10} -552.177 q^{11} +101.479 q^{12} +352.674 q^{13} -915.157 q^{14} -586.962 q^{15} -536.052 q^{16} +478.207 q^{17} -368.747 q^{18} -174.635 q^{19} -735.359 q^{20} -1809.23 q^{21} +2513.74 q^{22} -2902.56 q^{23} -1773.07 q^{24} +1128.39 q^{25} -1605.52 q^{26} -729.000 q^{27} -2266.65 q^{28} -5179.19 q^{29} +2672.10 q^{30} -3964.39 q^{31} -3863.92 q^{32} +4969.59 q^{33} -2177.00 q^{34} +13110.5 q^{35} -913.308 q^{36} -12237.3 q^{37} +795.013 q^{38} -3174.07 q^{39} +12848.5 q^{40} -3174.84 q^{41} +8236.41 q^{42} +15544.7 q^{43} +6226.01 q^{44} +5282.66 q^{45} +13213.7 q^{46} +5458.94 q^{47} +4824.47 q^{48} +23604.5 q^{49} -5136.90 q^{50} -4303.86 q^{51} -3976.54 q^{52} +18286.3 q^{53} +3318.72 q^{54} -36011.8 q^{55} +39603.8 q^{56} +1571.71 q^{57} +23577.9 q^{58} +18160.6 q^{59} +6618.23 q^{60} -27896.1 q^{61} +18047.6 q^{62} +16283.1 q^{63} +34743.9 q^{64} +23000.7 q^{65} -22623.7 q^{66} +7415.75 q^{67} -5391.98 q^{68} +26123.0 q^{69} -59684.7 q^{70} -38988.3 q^{71} +15957.7 q^{72} -20896.1 q^{73} +55709.3 q^{74} -10155.5 q^{75} +1969.08 q^{76} -111002. q^{77} +14449.7 q^{78} +12539.4 q^{79} -34960.3 q^{80} +6561.00 q^{81} +14453.2 q^{82} -43303.0 q^{83} +20399.9 q^{84} +31187.7 q^{85} -70766.2 q^{86} +46612.7 q^{87} -108783. q^{88} -30909.4 q^{89} -24048.9 q^{90} +70896.7 q^{91} +32727.5 q^{92} +35679.5 q^{93} -24851.4 q^{94} -11389.3 q^{95} +34775.3 q^{96} -156960. q^{97} -107458. q^{98} -44726.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 8 q^{2} - 270 q^{3} + 470 q^{4} - 136 q^{5} + 72 q^{6} + 68 q^{7} - 261 q^{8} + 2430 q^{9}+O(q^{10}) \) 30 * q - 8 * q^2 - 270 * q^3 + 470 * q^4 - 136 * q^5 + 72 * q^6 + 68 * q^7 - 261 * q^8 + 2430 * q^9	\( 30 q - 8 q^{2} - 270 q^{3} + 470 q^{4} - 136 q^{5} + 72 q^{6} + 68 q^{7} - 261 q^{8} + 2430 q^{9} - 383 q^{10} - 875 q^{11} - 4230 q^{12} + 101 q^{13} - 2279 q^{14} + 1224 q^{15} + 7454 q^{16} - 4042 q^{17} - 648 q^{18} + 846 q^{19} - 5089 q^{20} - 612 q^{21} - 700 q^{22} - 5902 q^{23} + 2349 q^{24} + 12880 q^{25} - 7567 q^{26} - 21870 q^{27} - 375 q^{28} - 10301 q^{29} + 3447 q^{30} - 4099 q^{31} - 1560 q^{32} + 7875 q^{33} - 3683 q^{34} - 20686 q^{35} + 38070 q^{36} + 8468 q^{37} - 11848 q^{38} - 909 q^{39} - 5132 q^{40} - 47958 q^{41} + 20511 q^{42} + 63916 q^{43} + 3101 q^{44} - 11016 q^{45} + 19654 q^{46} + 8589 q^{47} - 67086 q^{48} + 27834 q^{49} + 121727 q^{50} + 36378 q^{51} + 56510 q^{52} + 10134 q^{53} + 5832 q^{54} - 11473 q^{55} - 68192 q^{56} - 7614 q^{57} + 32006 q^{58} - 64236 q^{59} + 45801 q^{60} - 98194 q^{61} - 67276 q^{62} + 5508 q^{63} + 138849 q^{64} - 155917 q^{65} + 6300 q^{66} + 62323 q^{67} - 117531 q^{68} + 53118 q^{69} - 220939 q^{70} - 179713 q^{71} - 21141 q^{72} - 148343 q^{73} - 214732 q^{74} - 115920 q^{75} - 189758 q^{76} - 142357 q^{77} + 68103 q^{78} + 26916 q^{79} - 463727 q^{80} + 196830 q^{81} - 206514 q^{82} - 89285 q^{83} + 3375 q^{84} - 23932 q^{85} - 477235 q^{86} + 92709 q^{87} - 114708 q^{88} - 474411 q^{89} - 31023 q^{90} + 51305 q^{91} - 1030074 q^{92} + 36891 q^{93} - 485800 q^{94} - 169960 q^{95} + 14040 q^{96} - 169188 q^{97} - 629739 q^{98} - 70875 q^{99}+O(q^{100}) \) 30 * q - 8 * q^2 - 270 * q^3 + 470 * q^4 - 136 * q^5 + 72 * q^6 + 68 * q^7 - 261 * q^8 + 2430 * q^9 - 383 * q^10 - 875 * q^11 - 4230 * q^12 + 101 * q^13 - 2279 * q^14 + 1224 * q^15 + 7454 * q^16 - 4042 * q^17 - 648 * q^18 + 846 * q^19 - 5089 * q^20 - 612 * q^21 - 700 * q^22 - 5902 * q^23 + 2349 * q^24 + 12880 * q^25 - 7567 * q^26 - 21870 * q^27 - 375 * q^28 - 10301 * q^29 + 3447 * q^30 - 4099 * q^31 - 1560 * q^32 + 7875 * q^33 - 3683 * q^34 - 20686 * q^35 + 38070 * q^36 + 8468 * q^37 - 11848 * q^38 - 909 * q^39 - 5132 * q^40 - 47958 * q^41 + 20511 * q^42 + 63916 * q^43 + 3101 * q^44 - 11016 * q^45 + 19654 * q^46 + 8589 * q^47 - 67086 * q^48 + 27834 * q^49 + 121727 * q^50 + 36378 * q^51 + 56510 * q^52 + 10134 * q^53 + 5832 * q^54 - 11473 * q^55 - 68192 * q^56 - 7614 * q^57 + 32006 * q^58 - 64236 * q^59 + 45801 * q^60 - 98194 * q^61 - 67276 * q^62 + 5508 * q^63 + 138849 * q^64 - 155917 * q^65 + 6300 * q^66 + 62323 * q^67 - 117531 * q^68 + 53118 * q^69 - 220939 * q^70 - 179713 * q^71 - 21141 * q^72 - 148343 * q^73 - 214732 * q^74 - 115920 * q^75 - 189758 * q^76 - 142357 * q^77 + 68103 * q^78 + 26916 * q^79 - 463727 * q^80 + 196830 * q^81 - 206514 * q^82 - 89285 * q^83 + 3375 * q^84 - 23932 * q^85 - 477235 * q^86 + 92709 * q^87 - 114708 * q^88 - 474411 * q^89 - 31023 * q^90 + 51305 * q^91 - 1030074 * q^92 + 36891 * q^93 - 485800 * q^94 - 169960 * q^95 + 14040 * q^96 - 169188 * q^97 - 629739 * q^98 - 70875 * q^99

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