LMFDB - Embedded newform 354.6.a.b.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:	$1$
Dimension:	$4$
Coefficient field:	4.4.32832.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 9x^{2} + 10x + 1 $ x^4 - 2x^3 - 9x^2 + 10*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-2.68575$ 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)

$f(q)$	$=$	$q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +47.2837 q^{5} +36.0000 q^{6} -178.753 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +47.2837 q^{5} +36.0000 q^{6} -178.753 q^{7} +64.0000 q^{8} +81.0000 q^{9} +189.135 q^{10} -309.297 q^{11} +144.000 q^{12} -470.836 q^{13} -715.014 q^{14} +425.553 q^{15} +256.000 q^{16} -1314.87 q^{17} +324.000 q^{18} -1140.19 q^{19} +756.539 q^{20} -1608.78 q^{21} -1237.19 q^{22} -861.137 q^{23} +576.000 q^{24} -889.255 q^{25} -1883.35 q^{26} +729.000 q^{27} -2860.05 q^{28} +2217.03 q^{29} +1702.21 q^{30} -2546.32 q^{31} +1024.00 q^{32} -2783.68 q^{33} -5259.47 q^{34} -8452.11 q^{35} +1296.00 q^{36} -2377.43 q^{37} -4560.75 q^{38} -4237.53 q^{39} +3026.15 q^{40} -7668.97 q^{41} -6435.12 q^{42} +12680.5 q^{43} -4948.76 q^{44} +3829.98 q^{45} -3444.55 q^{46} -6094.92 q^{47} +2304.00 q^{48} +15145.8 q^{49} -3557.02 q^{50} -11833.8 q^{51} -7533.38 q^{52} -15991.3 q^{53} +2916.00 q^{54} -14624.7 q^{55} -11440.2 q^{56} -10261.7 q^{57} +8868.13 q^{58} -3481.00 q^{59} +6808.85 q^{60} +21694.2 q^{61} -10185.3 q^{62} -14479.0 q^{63} +4096.00 q^{64} -22262.9 q^{65} -11134.7 q^{66} +63881.1 q^{67} -21037.9 q^{68} -7750.23 q^{69} -33808.5 q^{70} +63960.2 q^{71} +5184.00 q^{72} +23997.2 q^{73} -9509.73 q^{74} -8003.30 q^{75} -18243.0 q^{76} +55288.0 q^{77} -16950.1 q^{78} -20779.9 q^{79} +12104.6 q^{80} +6561.00 q^{81} -30675.9 q^{82} -86016.3 q^{83} -25740.5 q^{84} -62171.7 q^{85} +50722.0 q^{86} +19953.3 q^{87} -19795.0 q^{88} -99720.0 q^{89} +15319.9 q^{90} +84163.6 q^{91} -13778.2 q^{92} -22916.9 q^{93} -24379.7 q^{94} -53912.3 q^{95} +9216.00 q^{96} -91614.2 q^{97} +60583.1 q^{98} -25053.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 16 q^{2} + 36 q^{3} + 64 q^{4} - 104 q^{5} + 144 q^{6} - 162 q^{7} + 256 q^{8} + 324 q^{9}+O(q^{10}) $ 4 * q + 16 * q^2 + 36 * q^3 + 64 * q^4 - 104 * q^5 + 144 * q^6 - 162 * q^7 + 256 * q^8 + 324 * q^9	\( 4 q + 16 q^{2} + 36 q^{3} + 64 q^{4} - 104 q^{5} + 144 q^{6} - 162 q^{7} + 256 q^{8} + 324 q^{9} - 416 q^{10} - 676 q^{11} + 576 q^{12} - 792 q^{13} - 648 q^{14} - 936 q^{15} + 1024 q^{16} - 2474 q^{17} + 1296 q^{18} - 4538 q^{19} - 1664 q^{20} - 1458 q^{21} - 2704 q^{22} - 1238 q^{23} + 2304 q^{24} - 832 q^{25} - 3168 q^{26} + 2916 q^{27} - 2592 q^{28} - 4958 q^{29} - 3744 q^{30} - 7138 q^{31} + 4096 q^{32} - 6084 q^{33} - 9896 q^{34} - 13554 q^{35} + 5184 q^{36} - 13570 q^{37} - 18152 q^{38} - 7128 q^{39} - 6656 q^{40} - 13826 q^{41} - 5832 q^{42} - 1236 q^{43} - 10816 q^{44} - 8424 q^{45} - 4952 q^{46} - 12410 q^{47} + 9216 q^{48} - 24622 q^{49} - 3328 q^{50} - 22266 q^{51} - 12672 q^{52} - 50904 q^{53} + 11664 q^{54} - 20872 q^{55} - 10368 q^{56} - 40842 q^{57} - 19832 q^{58} - 13924 q^{59} - 14976 q^{60} - 70622 q^{61} - 28552 q^{62} - 13122 q^{63} + 16384 q^{64} + 17460 q^{65} - 24336 q^{66} - 50012 q^{67} - 39584 q^{68} - 11142 q^{69} - 54216 q^{70} + 21192 q^{71} + 20736 q^{72} - 13358 q^{73} - 54280 q^{74} - 7488 q^{75} - 72608 q^{76} + 98658 q^{77} - 28512 q^{78} + 6464 q^{79} - 26624 q^{80} + 26244 q^{81} - 55304 q^{82} + 51506 q^{83} - 23328 q^{84} + 61786 q^{85} - 4944 q^{86} - 44622 q^{87} - 43264 q^{88} + 90738 q^{89} - 33696 q^{90} + 48870 q^{91} - 19808 q^{92} - 64242 q^{93} - 49640 q^{94} + 171394 q^{95} + 36864 q^{96} - 266068 q^{97} - 98488 q^{98} - 54756 q^{99}+O(q^{100}) \) 4 * q + 16 * q^2 + 36 * q^3 + 64 * q^4 - 104 * q^5 + 144 * q^6 - 162 * q^7 + 256 * q^8 + 324 * q^9 - 416 * q^10 - 676 * q^11 + 576 * q^12 - 792 * q^13 - 648 * q^14 - 936 * q^15 + 1024 * q^16 - 2474 * q^17 + 1296 * q^18 - 4538 * q^19 - 1664 * q^20 - 1458 * q^21 - 2704 * q^22 - 1238 * q^23 + 2304 * q^24 - 832 * q^25 - 3168 * q^26 + 2916 * q^27 - 2592 * q^28 - 4958 * q^29 - 3744 * q^30 - 7138 * q^31 + 4096 * q^32 - 6084 * q^33 - 9896 * q^34 - 13554 * q^35 + 5184 * q^36 - 13570 * q^37 - 18152 * q^38 - 7128 * q^39 - 6656 * q^40 - 13826 * q^41 - 5832 * q^42 - 1236 * q^43 - 10816 * q^44 - 8424 * q^45 - 4952 * q^46 - 12410 * q^47 + 9216 * q^48 - 24622 * q^49 - 3328 * q^50 - 22266 * q^51 - 12672 * q^52 - 50904 * q^53 + 11664 * q^54 - 20872 * q^55 - 10368 * q^56 - 40842 * q^57 - 19832 * q^58 - 13924 * q^59 - 14976 * q^60 - 70622 * q^61 - 28552 * q^62 - 13122 * q^63 + 16384 * q^64 + 17460 * q^65 - 24336 * q^66 - 50012 * q^67 - 39584 * q^68 - 11142 * q^69 - 54216 * q^70 + 21192 * q^71 + 20736 * q^72 - 13358 * q^73 - 54280 * q^74 - 7488 * q^75 - 72608 * q^76 + 98658 * q^77 - 28512 * q^78 + 6464 * q^79 - 26624 * q^80 + 26244 * q^81 - 55304 * q^82 + 51506 * q^83 - 23328 * q^84 + 61786 * q^85 - 4944 * q^86 - 44622 * q^87 - 43264 * q^88 + 90738 * q^89 - 33696 * q^90 + 48870 * q^91 - 19808 * q^92 - 64242 * q^93 - 49640 * q^94 + 171394 * q^95 + 36864 * q^96 - 266068 * q^97 - 98488 * q^98 - 54756 * 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
$5$	47.2837	0.845836	0.422918	−	0.906168i	$-0.361006\pi$
$5$	47.2837	0.845836	0.422918	+	0.906168i	$0.361006\pi$
$6$	36.0000	0.408248
$7$	−178.753	−1.37883	−0.689413	−	0.724369i	$-0.742131\pi$
$7$	−178.753	−1.37883	−0.689413	+	0.724369i	$0.742131\pi$
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	189.135	0.598096
$11$	−309.297	−0.770716	−0.385358	−	0.922767i	$-0.625922\pi$
$11$	−309.297	−0.770716	−0.385358	+	0.922767i	$0.625922\pi$
$12$	144.000	0.288675
$13$	−470.836	−0.772701	−0.386351	−	0.922352i	$-0.626264\pi$
$13$	−470.836	−0.772701	−0.386351	+	0.922352i	$0.626264\pi$
$14$	−715.014	−0.974977
$15$	425.553	0.488344
$16$	256.000	0.250000
$17$	−1314.87	−1.10347	−0.551734	−	0.834020i	$-0.686034\pi$
$17$	−1314.87	−1.10347	−0.551734	+	0.834020i	$0.686034\pi$
$18$	324.000	0.235702
$19$	−1140.19	−0.724590	−0.362295	−	0.932063i	$-0.618007\pi$
$19$	−1140.19	−0.724590	−0.362295	+	0.932063i	$0.618007\pi$
$20$	756.539	0.422918
$21$	−1608.78	−0.796065
$22$	−1237.19	−0.544979
$23$	−861.137	−0.339432	−0.169716	−	0.985493i	$-0.554285\pi$
$23$	−861.137	−0.339432	−0.169716	+	0.985493i	$0.554285\pi$
$24$	576.000	0.204124
$25$	−889.255	−0.284562
$26$	−1883.35	−0.546382
$27$	729.000	0.192450
$28$	−2860.05	−0.689413
$29$	2217.03	0.489527	0.244764	−	0.969583i	$-0.421290\pi$
$29$	2217.03	0.489527	0.244764	+	0.969583i	$0.421290\pi$
$30$	1702.21	0.345311
$31$	−2546.32	−0.475893	−0.237946	−	0.971278i	$-0.576474\pi$
$31$	−2546.32	−0.475893	−0.237946	+	0.971278i	$0.576474\pi$
$32$	1024.00	0.176777
$33$	−2783.68	−0.444973
$34$	−5259.47	−0.780269
$35$	−8452.11	−1.16626
$36$	1296.00	0.166667
$37$	−2377.43	−0.285498	−0.142749	−	0.989759i	$-0.545594\pi$
$37$	−2377.43	−0.285498	−0.142749	+	0.989759i	$0.545594\pi$
$38$	−4560.75	−0.512363
$39$	−4237.53	−0.446119
$40$	3026.15	0.299048
$41$	−7668.97	−0.712488	−0.356244	−	0.934393i	$-0.615943\pi$
$41$	−7668.97	−0.712488	−0.356244	+	0.934393i	$0.615943\pi$
$42$	−6435.12	−0.562903
$43$	12680.5	1.04584	0.522920	−	0.852382i	$-0.324843\pi$
$43$	12680.5	1.04584	0.522920	+	0.852382i	$0.324843\pi$
$44$	−4948.76	−0.385358
$45$	3829.98	0.281945
$46$	−3444.55	−0.240015
$47$	−6094.92	−0.402460	−0.201230	−	0.979544i	$-0.564494\pi$
$47$	−6094.92	−0.402460	−0.201230	+	0.979544i	$0.564494\pi$
$48$	2304.00	0.144338
$49$	15145.8	0.901159
$50$	−3557.02	−0.201215
$51$	−11833.8	−0.637087
$52$	−7533.38	−0.386351
$53$	−15991.3	−0.781977	−0.390988	−	0.920396i	$-0.627867\pi$
$53$	−15991.3	−0.781977	−0.390988	+	0.920396i	$0.627867\pi$
$54$	2916.00	0.136083
$55$	−14624.7	−0.651900
$56$	−11440.2	−0.487488
$57$	−10261.7	−0.418342
$58$	8868.13	0.346148
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	6808.85	0.244172
$61$	21694.2	0.746481	0.373240	−	0.927735i	$-0.378247\pi$
$61$	21694.2	0.746481	0.373240	+	0.927735i	$0.378247\pi$
$62$	−10185.3	−0.336507
$63$	−14479.0	−0.459608
$64$	4096.00	0.125000
$65$	−22262.9	−0.653578
$66$	−11134.7	−0.314644
$67$	63881.1	1.73854	0.869271	−	0.494335i	$-0.164588\pi$
$67$	63881.1	1.73854	0.869271	+	0.494335i	$0.164588\pi$
$68$	−21037.9	−0.551734
$69$	−7750.23	−0.195971
$70$	−33808.5	−0.824670
$71$	63960.2	1.50579	0.752894	−	0.658142i	$-0.228657\pi$
$71$	63960.2	1.50579	0.752894	+	0.658142i	$0.228657\pi$
$72$	5184.00	0.117851
$73$	23997.2	0.527051	0.263526	−	0.964652i	$-0.415115\pi$
$73$	23997.2	0.527051	0.263526	+	0.964652i	$0.415115\pi$
$74$	−9509.73	−0.201878
$75$	−8003.30	−0.164292
$76$	−18243.0	−0.362295
$77$	55288.0	1.06268
$78$	−16950.1	−0.315454
$79$	−20779.9	−0.374607	−0.187303	−	0.982302i	$-0.559975\pi$
$79$	−20779.9	−0.374607	−0.187303	+	0.982302i	$0.559975\pi$
$80$	12104.6	0.211459
$81$	6561.00	0.111111
$82$	−30675.9	−0.503805
$83$	−86016.3	−1.37052	−0.685261	−	0.728298i	$-0.740312\pi$
$83$	−86016.3	−1.37052	−0.685261	+	0.728298i	$0.740312\pi$
$84$	−25740.5	−0.398033
$85$	−62171.7	−0.933352
$86$	50722.0	0.739521
$87$	19953.3	0.282629
$88$	−19795.0	−0.272489
$89$	−99720.0	−1.33447	−0.667233	−	0.744849i	$-0.732521\pi$
$89$	−99720.0	−1.33447	−0.667233	+	0.744849i	$0.732521\pi$
$90$	15319.9	0.199365
$91$	84163.6	1.06542
$92$	−13778.2	−0.169716
$93$	−22916.9	−0.274757
$94$	−24379.7	−0.284582
$95$	−53912.3	−0.612884
$96$	9216.00	0.102062
$97$	−91614.2	−0.988630	−0.494315	−	0.869283i	$-0.664581\pi$
$97$	−91614.2	−0.988630	−0.494315	+	0.869283i	$0.664581\pi$
$98$	60583.1	0.637215
$99$	−25053.1	−0.256905
$100$	−14228.1	−0.142281
$101$	−118268.	−1.15362	−0.576811	−	0.816878i	$-0.695703\pi$
$101$	−118268.	−1.15362	−0.576811	+	0.816878i	$0.695703\pi$
$102$	−47335.2	−0.450489
$103$	−8572.22	−0.0796160	−0.0398080	−	0.999207i	$-0.512675\pi$
$103$	−8572.22	−0.0796160	−0.0398080	+	0.999207i	$0.512675\pi$
$104$	−30133.5	−0.273191
$105$	−76069.0	−0.673340
$106$	−63965.2	−0.552941
$107$	78912.4	0.666325	0.333162	−	0.942869i	$-0.391884\pi$
$107$	78912.4	0.666325	0.333162	+	0.942869i	$0.391884\pi$
$108$	11664.0	0.0962250
$109$	−64396.8	−0.519156	−0.259578	−	0.965722i	$-0.583584\pi$
$109$	−64396.8	−0.519156	−0.259578	+	0.965722i	$0.583584\pi$
$110$	−58498.9	−0.460963
$111$	−21396.9	−0.164833
$112$	−45760.9	−0.344706
$113$	65404.1	0.481847	0.240923	−	0.970544i	$-0.422550\pi$
$113$	65404.1	0.481847	0.240923	+	0.970544i	$0.422550\pi$
$114$	−41046.8	−0.295813
$115$	−40717.7	−0.287104
$116$	35472.5	0.244764
$117$	−38137.7	−0.257567
$118$	−13924.0	−0.0920575
$119$	235037.	1.52149
$120$	27235.4	0.172656
$121$	−65386.1	−0.405996
$122$	86776.7	0.527841
$123$	−69020.8	−0.411355
$124$	−40741.2	−0.237946
$125$	−189809.	−1.08653
$126$	−57916.1	−0.324992
$127$	−59431.9	−0.326972	−0.163486	−	0.986546i	$-0.552274\pi$
$127$	−59431.9	−0.326972	−0.163486	+	0.986546i	$0.552274\pi$
$128$	16384.0	0.0883883
$129$	114125.	0.603816
$130$	−89051.5	−0.462150
$131$	206647.	1.05208	0.526042	−	0.850459i	$-0.323675\pi$
$131$	206647.	1.05208	0.526042	+	0.850459i	$0.323675\pi$
$132$	−44538.8	−0.222487
$133$	203812.	0.999083
$134$	255524.	1.22934
$135$	34469.8	0.162781
$136$	−84151.5	−0.390135
$137$	−220990.	−1.00594	−0.502968	−	0.864305i	$-0.667759\pi$
$137$	−220990.	−1.00594	−0.502968	+	0.864305i	$0.667759\pi$
$138$	−31000.9	−0.138573
$139$	179452.	0.787792	0.393896	−	0.919155i	$-0.371127\pi$
$139$	179452.	0.787792	0.393896	+	0.919155i	$0.371127\pi$
$140$	−135234.	−0.583130
$141$	−54854.2	−0.232361
$142$	255841.	1.06475
$143$	145628.	0.595533
$144$	20736.0	0.0833333
$145$	104829.	0.414060
$146$	95988.7	0.372681
$147$	136312.	0.520284
$148$	−38038.9	−0.142749
$149$	3499.85	0.0129147	0.00645735	−	0.999979i	$-0.497945\pi$
$149$	3499.85	0.0129147	0.00645735	+	0.999979i	$0.497945\pi$
$150$	−32013.2	−0.116172
$151$	61391.4	0.219111	0.109556	−	0.993981i	$-0.465057\pi$
$151$	61391.4	0.219111	0.109556	+	0.993981i	$0.465057\pi$
$152$	−72972.0	−0.256181
$153$	−106504.	−0.367822
$154$	221152.	0.751430
$155$	−120399.	−0.402527
$156$	−67800.4	−0.223060
$157$	−533939.	−1.72879	−0.864396	−	0.502812i	$-0.832299\pi$
$157$	−533939.	−1.72879	−0.864396	+	0.502812i	$0.832299\pi$
$158$	−83119.6	−0.264887
$159$	−143922.	−0.451474
$160$	48418.5	0.149524
$161$	153931.	0.468017
$162$	26244.0	0.0785674
$163$	337125.	0.993853	0.496927	−	0.867793i	$-0.334462\pi$
$163$	337125.	0.993853	0.496927	+	0.867793i	$0.334462\pi$
$164$	−122704.	−0.356244
$165$	−131622.	−0.376374
$166$	−344065.	−0.969105
$167$	106850.	0.296470	0.148235	−	0.988952i	$-0.452641\pi$
$167$	106850.	0.296470	0.148235	+	0.988952i	$0.452641\pi$
$168$	−102962.	−0.281451
$169$	−149606.	−0.402933
$170$	−248687.	−0.659980
$171$	−92355.2	−0.241530
$172$	202888.	0.522920
$173$	313358.	0.796022	0.398011	−	0.917381i	$-0.369701\pi$
$173$	313358.	0.796022	0.398011	+	0.917381i	$0.369701\pi$
$174$	79813.1	0.199849
$175$	158957.	0.392361
$176$	−79180.1	−0.192679
$177$	−31329.0	−0.0751646
$178$	−398880.	−0.943610
$179$	−466713.	−1.08872	−0.544361	−	0.838851i	$-0.683228\pi$
$179$	−466713.	−1.08872	−0.544361	+	0.838851i	$0.683228\pi$
$180$	61279.6	0.140973
$181$	−239257.	−0.542835	−0.271417	−	0.962462i	$-0.587492\pi$
$181$	−239257.	−0.542835	−0.271417	+	0.962462i	$0.587492\pi$
$182$	336654.	0.753365
$183$	195248.	0.430981
$184$	−55112.8	−0.120007
$185$	−112414.	−0.241485
$186$	−91667.6	−0.194282
$187$	406685.	0.850460
$188$	−97518.7	−0.201230
$189$	−130311.	−0.265355
$190$	−215649.	−0.433375
$191$	−340820.	−0.675992	−0.337996	−	0.941148i	$-0.609749\pi$
$191$	−340820.	−0.675992	−0.337996	+	0.941148i	$0.609749\pi$
$192$	36864.0	0.0721688
$193$	587061.	1.13446	0.567231	−	0.823559i	$-0.308015\pi$
$193$	587061.	1.13446	0.567231	+	0.823559i	$0.308015\pi$
$194$	−366457.	−0.699067
$195$	−200366.	−0.377344
$196$	242332.	0.450579
$197$	352417.	0.646981	0.323490	−	0.946231i	$-0.395144\pi$
$197$	352417.	0.646981	0.323490	+	0.946231i	$0.395144\pi$
$198$	−100212.	−0.181660
$199$	−505246.	−0.904419	−0.452210	−	0.891912i	$-0.649364\pi$
$199$	−505246.	−0.904419	−0.452210	+	0.891912i	$0.649364\pi$
$200$	−56912.3	−0.100608
$201$	574930.	1.00375
$202$	−473072.	−0.815734
$203$	−396302.	−0.674972
$204$	−189341.	−0.318544
$205$	−362617.	−0.602648
$206$	−34288.9	−0.0562970
$207$	−69752.1	−0.113144
$208$	−120534.	−0.193175
$209$	352657.	0.558453
$210$	−304276.	−0.476124
$211$	791336.	1.22364	0.611822	−	0.790996i	$-0.290437\pi$
$211$	791336.	1.22364	0.611822	+	0.790996i	$0.290437\pi$
$212$	−255861.	−0.390988
$213$	575641.	0.869367
$214$	315650.	0.471163
$215$	599581.	0.884609
$216$	46656.0	0.0680414
$217$	455164.	0.656173
$218$	−257587.	−0.367099
$219$	215974.	0.304293
$220$	−233995.	−0.325950
$221$	619087.	0.852650
$222$	−85587.5	−0.116554
$223$	−374260.	−0.503977	−0.251989	−	0.967730i	$-0.581085\pi$
$223$	−374260.	−0.503977	−0.251989	+	0.967730i	$0.581085\pi$
$224$	−183043.	−0.243744
$225$	−72029.7	−0.0948539
$226$	261616.	0.340717
$227$	−129433.	−0.166717	−0.0833586	−	0.996520i	$-0.526565\pi$
$227$	−129433.	−0.166717	−0.0833586	+	0.996520i	$0.526565\pi$
$228$	−164187.	−0.209171
$229$	238151.	0.300098	0.150049	−	0.988679i	$-0.452057\pi$
$229$	238151.	0.300098	0.150049	+	0.988679i	$0.452057\pi$
$230$	−162871.	−0.203013
$231$	497592.	0.613540
$232$	141890.	0.173074
$233$	150307.	0.181380	0.0906898	−	0.995879i	$-0.471093\pi$
$233$	150307.	0.181380	0.0906898	+	0.995879i	$0.471093\pi$
$234$	−152551.	−0.182127
$235$	−288190.	−0.340415
$236$	−55696.0	−0.0650945
$237$	−187019.	−0.216279
$238$	940148.	1.07585
$239$	453898.	0.514000	0.257000	−	0.966411i	$-0.417266\pi$
$239$	453898.	0.514000	0.257000	+	0.966411i	$0.417266\pi$
$240$	108942.	0.122086
$241$	1.21312e6	1.34543	0.672716	−	0.739901i	$-0.265128\pi$
$241$	1.21312e6	1.34543	0.672716	+	0.739901i	$0.265128\pi$
$242$	−261544.	−0.287083
$243$	59049.0	0.0641500
$244$	347107.	0.373240
$245$	716148.	0.762232
$246$	−276083.	−0.290872
$247$	536842.	0.559892
$248$	−162965.	−0.168254
$249$	−774147.	−0.791271
$250$	−759235.	−0.768292
$251$	1.24289e6	1.24523	0.622615	−	0.782529i	$-0.286070\pi$
$251$	1.24289e6	1.24523	0.622615	+	0.782529i	$0.286070\pi$
$252$	−231664.	−0.229804
$253$	266348.	0.261606
$254$	−237728.	−0.231204
$255$	−559546.	−0.538871
$256$	65536.0	0.0625000
$257$	−423490.	−0.399954	−0.199977	−	0.979801i	$-0.564087\pi$
$257$	−423490.	−0.399954	−0.199977	+	0.979801i	$0.564087\pi$
$258$	456498.	0.426962
$259$	424974.	0.393652
$260$	−356206.	−0.326789
$261$	179580.	0.163176
$262$	826587.	0.743936
$263$	1.73628e6	1.54785	0.773927	−	0.633274i	$-0.218290\pi$
$263$	1.73628e6	1.54785	0.773927	+	0.633274i	$0.218290\pi$
$264$	−178155.	−0.157322
$265$	−756127.	−0.661424
$266$	815250.	0.706458
$267$	−897480.	−0.770454
$268$	1.02210e6	0.869271
$269$	−513518.	−0.432688	−0.216344	−	0.976317i	$-0.569413\pi$
$269$	−513518.	−0.432688	−0.216344	+	0.976317i	$0.569413\pi$
$270$	137879.	0.115104
$271$	−810772.	−0.670619	−0.335309	−	0.942108i	$-0.608841\pi$
$271$	−810772.	−0.670619	−0.335309	+	0.942108i	$0.608841\pi$
$272$	−336606.	−0.275867
$273$	757472.	0.615120
$274$	−883958.	−0.711304
$275$	275044.	0.219316
$276$	−124004.	−0.0979856
$277$	979506.	0.767022	0.383511	−	0.923536i	$-0.374715\pi$
$277$	979506.	0.767022	0.383511	+	0.923536i	$0.374715\pi$
$278$	717809.	0.557053
$279$	−206252.	−0.158631
$280$	−540935.	−0.412335
$281$	1.31389e6	0.992643	0.496321	−	0.868139i	$-0.334684\pi$
$281$	1.31389e6	0.992643	0.496321	+	0.868139i	$0.334684\pi$
$282$	−219417.	−0.164304
$283$	−2.12015e6	−1.57362	−0.786809	−	0.617196i	$-0.788269\pi$
$283$	−2.12015e6	−1.57362	−0.786809	+	0.617196i	$0.788269\pi$
$284$	1.02336e6	0.752894
$285$	−485210.	−0.353849
$286$	582514.	0.421106
$287$	1.37085e6	0.982396
$288$	82944.0	0.0589256
$289$	309018.	0.217640
$290$	419317.	0.292784
$291$	−824528.	−0.570786
$292$	383955.	0.263526
$293$	1.92182e6	1.30781	0.653905	−	0.756577i	$-0.273130\pi$
$293$	1.92182e6	1.30781	0.653905	+	0.756577i	$0.273130\pi$
$294$	545248.	0.367896
$295$	−164594.	−0.110118
$296$	−152156.	−0.100939
$297$	−225478.	−0.148324
$298$	13999.4	0.00913207
$299$	405455.	0.262279
$300$	−128053.	−0.0821459
$301$	−2.26668e6	−1.44203
$302$	245565.	0.154935
$303$	−1.06441e6	−0.666044
$304$	−291888.	−0.181148
$305$	1.02578e6	0.631400
$306$	−426017.	−0.260090
$307$	−2.34762e6	−1.42162	−0.710808	−	0.703386i	$-0.751671\pi$
$307$	−2.34762e6	−1.42162	−0.710808	+	0.703386i	$0.751671\pi$
$308$	884607.	0.531342
$309$	−77150.0	−0.0459663
$310$	−481598.	−0.284630
$311$	−1.13892e6	−0.667719	−0.333860	−	0.942623i	$-0.608351\pi$
$311$	−1.13892e6	−0.667719	−0.333860	+	0.942623i	$0.608351\pi$
$312$	−271202.	−0.157727
$313$	−336402.	−0.194088	−0.0970439	−	0.995280i	$-0.530939\pi$
$313$	−336402.	−0.194088	−0.0970439	+	0.995280i	$0.530939\pi$
$314$	−2.13576e6	−1.22244
$315$	−684621.	−0.388753
$316$	−332478.	−0.187303
$317$	2.51320e6	1.40468	0.702341	−	0.711840i	$-0.252138\pi$
$317$	2.51320e6	1.40468	0.702341	+	0.711840i	$0.252138\pi$
$318$	−575686.	−0.319241
$319$	−685722.	−0.377287
$320$	193674.	0.105729
$321$	710212.	0.384703
$322$	615725.	0.330938
$323$	1.49920e6	0.799561
$324$	104976.	0.0555556
$325$	418694.	0.219881
$326$	1.34850e6	0.702760
$327$	−579571.	−0.299735
$328$	−490814.	−0.251903
$329$	1.08949e6	0.554922
$330$	−526490.	−0.266137
$331$	−1.05887e6	−0.531217	−0.265609	−	0.964081i	$-0.585573\pi$
$331$	−1.05887e6	−0.531217	−0.265609	+	0.964081i	$0.585573\pi$
$332$	−1.37626e6	−0.685261
$333$	−192572.	−0.0951661
$334$	427398.	0.209636
$335$	3.02053e6	1.47052
$336$	−411848.	−0.199016
$337$	−1.41882e6	−0.680537	−0.340268	−	0.940328i	$-0.610518\pi$
$337$	−1.41882e6	−0.680537	−0.340268	+	0.940328i	$0.610518\pi$
$338$	−598425.	−0.284917
$339$	588637.	0.278194
$340$	−994748.	−0.466676
$341$	787571.	0.366779
$342$	−369421.	−0.170788
$343$	296950.	0.136285
$344$	811552.	0.369760
$345$	−366459.	−0.165759
$346$	1.25343e6	0.562872
$347$	2.99100e6	1.33350	0.666750	−	0.745282i	$-0.267685\pi$
$347$	2.99100e6	1.33350	0.666750	+	0.745282i	$0.267685\pi$
$348$	319253.	0.141314
$349$	3.46761e6	1.52394	0.761968	−	0.647614i	$-0.224233\pi$
$349$	3.46761e6	1.52394	0.761968	+	0.647614i	$0.224233\pi$
$350$	635829.	0.277441
$351$	−343240.	−0.148706
$352$	−316721.	−0.136245
$353$	1.07677e6	0.459925	0.229962	−	0.973200i	$-0.426140\pi$
$353$	1.07677e6	0.459925	0.229962	+	0.973200i	$0.426140\pi$
$354$	−125316.	−0.0531494
$355$	3.02427e6	1.27365
$356$	−1.59552e6	−0.667233
$357$	2.11533e6	0.878432
$358$	−1.86685e6	−0.769843
$359$	−450932.	−0.184661	−0.0923305	−	0.995728i	$-0.529432\pi$
$359$	−450932.	−0.184661	−0.0923305	+	0.995728i	$0.529432\pi$
$360$	245119.	0.0996827
$361$	−1.17607e6	−0.474969
$362$	−957027.	−0.383842
$363$	−588475.	−0.234402
$364$	1.34662e6	0.532710
$365$	1.13467e6	0.445799
$366$	780990.	0.304749
$367$	3.29225e6	1.27593	0.637967	−	0.770064i	$-0.279776\pi$
$367$	3.29225e6	1.27593	0.637967	+	0.770064i	$0.279776\pi$
$368$	−220451.	−0.0848580
$369$	−621187.	−0.237496
$370$	−449655.	−0.170756
$371$	2.85850e6	1.07821
$372$	−366671.	−0.137378
$373$	−2.09921e6	−0.781240	−0.390620	−	0.920552i	$-0.627739\pi$
$373$	−2.09921e6	−0.781240	−0.390620	+	0.920552i	$0.627739\pi$
$374$	1.62674e6	0.601366
$375$	−1.70828e6	−0.627307
$376$	−390075.	−0.142291
$377$	−1.04386e6	−0.378258
$378$	−521245.	−0.187634
$379$	−2.23546e6	−0.799408	−0.399704	−	0.916644i	$-0.630887\pi$
$379$	−2.23546e6	−0.799408	−0.399704	+	0.916644i	$0.630887\pi$
$380$	−862596.	−0.306442
$381$	−534887.	−0.188777
$382$	−1.36328e6	−0.477998
$383$	1.24217e6	0.432698	0.216349	−	0.976316i	$-0.430585\pi$
$383$	1.24217e6	0.432698	0.216349	+	0.976316i	$0.430585\pi$
$384$	147456.	0.0510310
$385$	2.61422e6	0.898856
$386$	2.34824e6	0.802186
$387$	1.02712e6	0.348613
$388$	−1.46583e6	−0.494315
$389$	−5.09474e6	−1.70706	−0.853529	−	0.521045i	$-0.825542\pi$
$389$	−5.09474e6	−1.70706	−0.853529	+	0.521045i	$0.825542\pi$
$390$	−801463.	−0.266822
$391$	1.13228e6	0.374552
$392$	969329.	0.318608
$393$	1.85982e6	0.607421
$394$	1.40967e6	0.457484
$395$	−982550.	−0.316856
$396$	−400849.	−0.128453
$397$	−2.32486e6	−0.740323	−0.370162	−	0.928967i	$-0.620698\pi$
$397$	−2.32486e6	−0.740323	−0.370162	+	0.928967i	$0.620698\pi$
$398$	−2.02098e6	−0.639521
$399$	1.83431e6	0.576821
$400$	−227649.	−0.0711404
$401$	−2.70622e6	−0.840433	−0.420216	−	0.907424i	$-0.638046\pi$
$401$	−2.70622e6	−0.840433	−0.420216	+	0.907424i	$0.638046\pi$
$402$	2.29972e6	0.709757
$403$	1.19890e6	0.367723
$404$	−1.89229e6	−0.576811
$405$	310228.	0.0939818
$406$	−1.58521e6	−0.477278
$407$	735334.	0.220038
$408$	−757363.	−0.225244
$409$	−4.80754e6	−1.42107	−0.710533	−	0.703663i	$-0.751546\pi$
$409$	−4.80754e6	−1.42107	−0.710533	+	0.703663i	$0.751546\pi$
$410$	−1.45047e6	−0.426136
$411$	−1.98891e6	−0.580777
$412$	−137155.	−0.0398080
$413$	622241.	0.179508
$414$	−279008.	−0.0800049
$415$	−4.06717e6	−1.15924
$416$	−482136.	−0.136596
$417$	1.61507e6	0.454832
$418$	1.41063e6	0.394886
$419$	−3.45983e6	−0.962763	−0.481381	−	0.876511i	$-0.659865\pi$
$419$	−3.45983e6	−0.962763	−0.481381	+	0.876511i	$0.659865\pi$
$420$	−1.21710e6	−0.336670
$421$	2.50428e6	0.688618	0.344309	−	0.938856i	$-0.388113\pi$
$421$	2.50428e6	0.688618	0.344309	+	0.938856i	$0.388113\pi$
$422$	3.16534e6	0.865246
$423$	−493688.	−0.134153
$424$	−1.02344e6	−0.276471
$425$	1.16925e6	0.314004
$426$	2.30257e6	0.614735
$427$	−3.87791e6	−1.02927
$428$	1.26260e6	0.333162
$429$	1.31066e6	0.343831
$430$	2.39832e6	0.625513
$431$	−6.16634e6	−1.59895	−0.799474	−	0.600700i	$-0.794888\pi$
$431$	−6.16634e6	−1.59895	−0.799474	+	0.600700i	$0.794888\pi$
$432$	186624.	0.0481125
$433$	−7.35155e6	−1.88434	−0.942170	−	0.335136i	$-0.891218\pi$
$433$	−7.35155e6	−1.88434	−0.942170	+	0.335136i	$0.891218\pi$
$434$	1.82066e6	0.463984
$435$	943464.	0.239057
$436$	−1.03035e6	−0.259578
$437$	981858.	0.245949
$438$	863898.	0.215168
$439$	−3.75478e6	−0.929873	−0.464936	−	0.885344i	$-0.653923\pi$
$439$	−3.75478e6	−0.929873	−0.464936	+	0.885344i	$0.653923\pi$
$440$	−935982.	−0.230481
$441$	1.22681e6	0.300386
$442$	2.47635e6	0.602915
$443$	4.72887e6	1.14485	0.572424	−	0.819958i	$-0.306003\pi$
$443$	4.72887e6	1.14485	0.572424	+	0.819958i	$0.306003\pi$
$444$	−342350.	−0.0824163
$445$	−4.71513e6	−1.12874
$446$	−1.49704e6	−0.356366
$447$	31498.7	0.00745630
$448$	−732174.	−0.172353
$449$	−1.95059e6	−0.456616	−0.228308	−	0.973589i	$-0.573319\pi$
$449$	−1.95059e6	−0.456616	−0.228308	+	0.973589i	$0.573319\pi$
$450$	−288119.	−0.0670718
$451$	2.37199e6	0.549126
$452$	1.04647e6	0.240923
$453$	552522.	0.126504
$454$	−517732.	−0.117887
$455$	3.97956e6	0.901170
$456$	−656748.	−0.147906
$457$	−2.06708e6	−0.462986	−0.231493	−	0.972837i	$-0.574361\pi$
$457$	−2.06708e6	−0.462986	−0.231493	+	0.972837i	$0.574361\pi$
$458$	952603.	0.212201
$459$	−958538.	−0.212362
$460$	−651484.	−0.143552
$461$	6.42586e6	1.40825	0.704124	−	0.710077i	$-0.251340\pi$
$461$	6.42586e6	1.40825	0.704124	+	0.710077i	$0.251340\pi$
$462$	1.99037e6	0.433839
$463$	1.30211e6	0.282290	0.141145	−	0.989989i	$-0.454922\pi$
$463$	1.30211e6	0.282290	0.141145	+	0.989989i	$0.454922\pi$
$464$	567560.	0.122382
$465$	−1.08360e6	−0.232399
$466$	601227.	0.128255
$467$	−416998.	−0.0884793	−0.0442396	−	0.999021i	$-0.514087\pi$
$467$	−416998.	−0.0884793	−0.0442396	+	0.999021i	$0.514087\pi$
$468$	−610204.	−0.128784
$469$	−1.14190e7	−2.39715
$470$	−1.15276e6	−0.240710
$471$	−4.80545e6	−0.998118
$472$	−222784.	−0.0460287
$473$	−3.92205e6	−0.806046
$474$	−748077.	−0.152933
$475$	1.01392e6	0.206191
$476$	3.76059e6	0.760744
$477$	−1.29529e6	−0.260659
$478$	1.81559e6	0.363453
$479$	−6.02639e6	−1.20010	−0.600051	−	0.799961i	$-0.704853\pi$
$479$	−6.02639e6	−1.20010	−0.600051	+	0.799961i	$0.704853\pi$
$480$	435766.	0.0863278
$481$	1.11938e6	0.220605
$482$	4.85249e6	0.951364
$483$	1.38538e6	0.270210
$484$	−1.04618e6	−0.202998
$485$	−4.33186e6	−0.836218
$486$	236196.	0.0453609
$487$	−1.61644e6	−0.308843	−0.154422	−	0.988005i	$-0.549351\pi$
$487$	−1.61644e6	−0.308843	−0.154422	+	0.988005i	$0.549351\pi$
$488$	1.38843e6	0.263921
$489$	3.03413e6	0.573801
$490$	2.86459e6	0.538980
$491$	−3.38551e6	−0.633754	−0.316877	−	0.948467i	$-0.602634\pi$
$491$	−3.38551e6	−0.633754	−0.316877	+	0.948467i	$0.602634\pi$
$492$	−1.10433e6	−0.205678
$493$	−2.91510e6	−0.540177
$494$	2.14737e6	0.395903
$495$	−1.18460e6	−0.217300
$496$	−651859.	−0.118973
$497$	−1.14331e7	−2.07622
$498$	−3.09659e6	−0.559513
$499$	−7.37864e6	−1.32655	−0.663277	−	0.748374i	$-0.730835\pi$
$499$	−7.37864e6	−1.32655	−0.663277	+	0.748374i	$0.730835\pi$
$500$	−3.03694e6	−0.543264
$501$	961646.	0.171167
$502$	4.97157e6	0.880510
$503$	844238.	0.148780	0.0743901	−	0.997229i	$-0.476299\pi$
$503$	844238.	0.148780	0.0743901	+	0.997229i	$0.476299\pi$
$504$	−926658.	−0.162496
$505$	−5.59214e6	−0.975775
$506$	1.06539e6	0.184983
$507$	−1.34646e6	−0.232633
$508$	−950910.	−0.163486
$509$	4.82514e6	0.825498	0.412749	−	0.910845i	$-0.364569\pi$
$509$	4.82514e6	0.825498	0.412749	+	0.910845i	$0.364569\pi$
$510$	−2.23818e6	−0.381039
$511$	−4.28957e6	−0.726711
$512$	262144.	0.0441942
$513$	−831197.	−0.139447
$514$	−1.69396e6	−0.282810
$515$	−405326.	−0.0673420
$516$	1.82599e6	0.301908
$517$	1.88514e6	0.310183
$518$	1.69990e6	0.278354
$519$	2.82022e6	0.459583
$520$	−1.42482e6	−0.231075
$521$	−2.16045e6	−0.348698	−0.174349	−	0.984684i	$-0.555782\pi$
$521$	−2.16045e6	−0.348698	−0.174349	+	0.984684i	$0.555782\pi$
$522$	718318.	0.115383
$523$	133818.	0.0213924	0.0106962	−	0.999943i	$-0.496595\pi$
$523$	133818.	0.0213924	0.0106962	+	0.999943i	$0.496595\pi$
$524$	3.30635e6	0.526042
$525$	1.43062e6	0.226530
$526$	6.94512e6	1.09450
$527$	3.34808e6	0.525132
$528$	−712621.	−0.111243
$529$	−5.69479e6	−0.884786
$530$	−3.02451e6	−0.467697
$531$	−281961.	−0.0433963
$532$	3.26100e6	0.499541
$533$	3.61083e6	0.550540
$534$	−3.58992e6	−0.544793
$535$	3.73127e6	0.563602
$536$	4.08839e6	0.614668
$537$	−4.20042e6	−0.628574
$538$	−2.05407e6	−0.305957
$539$	−4.68455e6	−0.694538
$540$	551517.	0.0813906
$541$	−2.52544e6	−0.370974	−0.185487	−	0.982647i	$-0.559386\pi$
$541$	−2.52544e6	−0.370974	−0.185487	+	0.982647i	$0.559386\pi$
$542$	−3.24309e6	−0.474199
$543$	−2.15331e6	−0.313406
$544$	−1.34642e6	−0.195067
$545$	−3.04492e6	−0.439121
$546$	3.02989e6	0.434956
$547$	5.91087e6	0.844662	0.422331	−	0.906442i	$-0.361212\pi$
$547$	5.91087e6	0.844662	0.422331	+	0.906442i	$0.361212\pi$
$548$	−3.53583e6	−0.502968
$549$	1.75723e6	0.248827
$550$	1.10018e6	0.155080
$551$	−2.52783e6	−0.354707
$552$	−496015.	−0.0692863
$553$	3.71448e6	0.516517
$554$	3.91803e6	0.542366
$555$	−1.01172e6	−0.139421
$556$	2.87123e6	0.393896
$557$	3.44585e6	0.470608	0.235304	−	0.971922i	$-0.424391\pi$
$557$	3.44585e6	0.470608	0.235304	+	0.971922i	$0.424391\pi$
$558$	−825009.	−0.112169
$559$	−5.97044e6	−0.808122
$560$	−2.16374e6	−0.291565
$561$	3.66016e6	0.491014
$562$	5.25556e6	0.701904
$563$	3.69005e6	0.490638	0.245319	−	0.969442i	$-0.421107\pi$
$563$	3.69005e6	0.490638	0.245319	+	0.969442i	$0.421107\pi$
$564$	−877668.	−0.116180
$565$	3.09255e6	0.407563
$566$	−8.48058e6	−1.11272
$567$	−1.17280e6	−0.153203
$568$	4.09345e6	0.532376
$569$	−1.21307e7	−1.57074	−0.785369	−	0.619028i	$-0.787527\pi$
$569$	−1.21307e7	−1.57074	−0.785369	+	0.619028i	$0.787527\pi$
$570$	−1.94084e6	−0.250209
$571$	−5.01150e6	−0.643247	−0.321623	−	0.946868i	$-0.604228\pi$
$571$	−5.01150e6	−0.643247	−0.321623	+	0.946868i	$0.604228\pi$
$572$	2.33006e6	0.297767
$573$	−3.06738e6	−0.390284
$574$	5.48342e6	0.694659
$575$	765771.	0.0965893
$576$	331776.	0.0416667
$577$	−9.51880e6	−1.19026	−0.595131	−	0.803628i	$-0.702900\pi$
$577$	−9.51880e6	−1.19026	−0.595131	+	0.803628i	$0.702900\pi$
$578$	1.23607e6	0.153895
$579$	5.28355e6	0.654982
$580$	1.67727e6	0.207030
$581$	1.53757e7	1.88971
$582$	−3.29811e6	−0.403606
$583$	4.94607e6	0.602682
$584$	1.53582e6	0.186341
$585$	−1.80329e6	−0.217859
$586$	7.68730e6	0.924761
$587$	−764235.	−0.0915444	−0.0457722	−	0.998952i	$-0.514575\pi$
$587$	−764235.	−0.0915444	−0.0457722	+	0.998952i	$0.514575\pi$
$588$	2.18099e6	0.260142
$589$	2.90329e6	0.344827
$590$	−658378.	−0.0778655
$591$	3.17175e6	0.373534
$592$	−608623.	−0.0713746
$593$	514802.	0.0601178	0.0300589	−	0.999548i	$-0.490431\pi$
$593$	514802.	0.0601178	0.0300589	+	0.999548i	$0.490431\pi$
$594$	−901911.	−0.104881
$595$	1.11134e7	1.28693
$596$	55997.7	0.00645735
$597$	−4.54721e6	−0.522167
$598$	1.62182e6	0.185460
$599$	−6.49565e6	−0.739700	−0.369850	−	0.929092i	$-0.620591\pi$
$599$	−6.49565e6	−0.739700	−0.369850	+	0.929092i	$0.620591\pi$
$600$	−512211.	−0.0580859
$601$	−938003.	−0.105930	−0.0529649	−	0.998596i	$-0.516867\pi$
$601$	−938003.	−0.105930	−0.0529649	+	0.998596i	$0.516867\pi$
$602$	−9.06673e6	−1.01967
$603$	5.17437e6	0.579514
$604$	982262.	0.109556
$605$	−3.09169e6	−0.343406
$606$	−4.25764e6	−0.470964
$607$	−4.84625e6	−0.533868	−0.266934	−	0.963715i	$-0.586011\pi$
$607$	−4.84625e6	−0.533868	−0.266934	+	0.963715i	$0.586011\pi$
$608$	−1.16755e6	−0.128091
$609$	−3.56672e6	−0.389696
$610$	4.10312e6	0.446467
$611$	2.86971e6	0.310982
$612$	−1.70407e6	−0.183911
$613$	−4.40666e6	−0.473650	−0.236825	−	0.971552i	$-0.576107\pi$
$613$	−4.40666e6	−0.473650	−0.236825	+	0.971552i	$0.576107\pi$
$614$	−9.39049e6	−1.00523
$615$	−3.26355e6	−0.347939
$616$	3.53843e6	0.375715
$617$	−1.50163e7	−1.58800	−0.794000	−	0.607918i	$-0.792005\pi$
$617$	−1.50163e7	−1.58800	−0.794000	+	0.607918i	$0.792005\pi$
$618$	−308600.	−0.0325031
$619$	1.26084e7	1.32262	0.661308	−	0.750115i	$-0.270002\pi$
$619$	1.26084e7	1.32262	0.661308	+	0.750115i	$0.270002\pi$
$620$	−1.92639e6	−0.201264
$621$	−627769.	−0.0653237
$622$	−4.55570e6	−0.472149
$623$	1.78253e7	1.83999
$624$	−1.08481e6	−0.111530
$625$	−6.19593e6	−0.634463
$626$	−1.34561e6	−0.137241
$627$	3.17391e6	0.322423
$628$	−8.54302e6	−0.864396
$629$	3.12601e6	0.315038
$630$	−2.73849e6	−0.274890
$631$	6.71505e6	0.671392	0.335696	−	0.941970i	$-0.391029\pi$
$631$	6.71505e6	0.671392	0.335696	+	0.941970i	$0.391029\pi$
$632$	−1.32991e6	−0.132444
$633$	7.12202e6	0.706471
$634$	1.00528e7	0.993261
$635$	−2.81016e6	−0.276564
$636$	−2.30275e6	−0.225737
$637$	−7.13118e6	−0.696326
$638$	−2.74289e6	−0.266782
$639$	5.18077e6	0.501929
$640$	774696.	0.0747620
$641$	−6.42217e6	−0.617357	−0.308679	−	0.951166i	$-0.599887\pi$
$641$	−6.42217e6	−0.617357	−0.308679	+	0.951166i	$0.599887\pi$
$642$	2.84085e6	0.272026
$643$	4.14521e6	0.395384	0.197692	−	0.980264i	$-0.436655\pi$
$643$	4.14521e6	0.395384	0.197692	+	0.980264i	$0.436655\pi$
$644$	2.46290e6	0.234009
$645$	5.39622e6	0.510729
$646$	5.99678e6	0.565375
$647$	8.50990e6	0.799215	0.399607	−	0.916686i	$-0.369146\pi$
$647$	8.50990e6	0.799215	0.399607	+	0.916686i	$0.369146\pi$
$648$	419904.	0.0392837
$649$	1.07666e6	0.100339
$650$	1.67477e6	0.155479
$651$	4.09647e6	0.378842
$652$	5.39400e6	0.496927
$653$	−9.39935e6	−0.862611	−0.431305	−	0.902206i	$-0.641947\pi$
$653$	−9.39935e6	−0.862611	−0.431305	+	0.902206i	$0.641947\pi$
$654$	−2.31829e6	−0.211945
$655$	9.77102e6	0.889891
$656$	−1.96326e6	−0.178122
$657$	1.94377e6	0.175684
$658$	4.35795e6	0.392389
$659$	−1.00196e6	−0.0898749	−0.0449374	−	0.998990i	$-0.514309\pi$
$659$	−1.00196e6	−0.0898749	−0.0449374	+	0.998990i	$0.514309\pi$
$660$	−2.10596e6	−0.188187
$661$	9.14517e6	0.814119	0.407060	−	0.913402i	$-0.366554\pi$
$661$	9.14517e6	0.814119	0.407060	+	0.913402i	$0.366554\pi$
$662$	−4.23547e6	−0.375627
$663$	5.57178e6	0.492278
$664$	−5.50505e6	−0.484552
$665$	9.63700e6	0.845060
$666$	−770288.	−0.0672926
$667$	−1.90917e6	−0.166161
$668$	1.70959e6	0.148235
$669$	−3.36834e6	−0.290971
$670$	1.20821e7	1.03982
$671$	−6.70995e6	−0.575325
$672$	−1.64739e6	−0.140726
$673$	685058.	0.0583028	0.0291514	−	0.999575i	$-0.490720\pi$
$673$	685058.	0.0583028	0.0291514	+	0.999575i	$0.490720\pi$
$674$	−5.67527e6	−0.481212
$675$	−648267.	−0.0547639
$676$	−2.39370e6	−0.201467
$677$	3.09466e6	0.259503	0.129751	−	0.991547i	$-0.458582\pi$
$677$	3.09466e6	0.259503	0.129751	+	0.991547i	$0.458582\pi$
$678$	2.35455e6	0.196713
$679$	1.63764e7	1.36315
$680$	−3.97899e6	−0.329990
$681$	−1.16490e6	−0.0962542
$682$	3.15028e6	0.259352
$683$	7.93576e6	0.650934	0.325467	−	0.945553i	$-0.394479\pi$
$683$	7.93576e6	0.650934	0.325467	+	0.945553i	$0.394479\pi$
$684$	−1.47768e6	−0.120765
$685$	−1.04492e7	−0.850857
$686$	1.18780e6	0.0963681
$687$	2.14336e6	0.173262
$688$	3.24621e6	0.261460
$689$	7.52928e6	0.604234
$690$	−1.46584e6	−0.117210
$691$	8.51058e6	0.678053	0.339027	−	0.940777i	$-0.389902\pi$
$691$	8.51058e6	0.678053	0.339027	+	0.940777i	$0.389902\pi$
$692$	5.01372e6	0.398011
$693$	4.47833e6	0.354228
$694$	1.19640e7	0.942927
$695$	8.48516e6	0.666343
$696$	1.27701e6	0.0999243
$697$	1.00837e7	0.786207
$698$	1.38704e7	1.07759
$699$	1.35276e6	0.104720
$700$	2.54332e6	0.196180
$701$	9.78614e6	0.752170	0.376085	−	0.926585i	$-0.377270\pi$
$701$	9.78614e6	0.752170	0.376085	+	0.926585i	$0.377270\pi$
$702$	−1.37296e6	−0.105151
$703$	2.71072e6	0.206869
$704$	−1.26688e6	−0.0963396
$705$	−2.59371e6	−0.196539
$706$	4.30708e6	0.325216
$707$	2.11408e7	1.59064
$708$	−501264.	−0.0375823
$709$	1.78512e7	1.33368	0.666842	−	0.745199i	$-0.267646\pi$
$709$	1.78512e7	1.33368	0.666842	+	0.745199i	$0.267646\pi$
$710$	1.20971e7	0.900606
$711$	−1.68317e6	−0.124869
$712$	−6.38208e6	−0.471805
$713$	2.19273e6	0.161533
$714$	8.46133e6	0.621145
$715$	6.88585e6	0.503724
$716$	−7.46741e6	−0.544361
$717$	4.08508e6	0.296758
$718$	−1.80373e6	−0.130575
$719$	−9.83691e6	−0.709637	−0.354819	−	0.934935i	$-0.615457\pi$
$719$	−9.83691e6	−0.709637	−0.354819	+	0.934935i	$0.615457\pi$
$720$	980474.	0.0704863
$721$	1.53231e6	0.109776
$722$	−4.70428e6	−0.335854
$723$	1.09181e7	0.776786
$724$	−3.82811e6	−0.271417
$725$	−1.97151e6	−0.139301
$726$	−2.35390e6	−0.165747
$727$	−1.89766e7	−1.33163	−0.665813	−	0.746119i	$-0.731915\pi$
$727$	−1.89766e7	−1.33163	−0.665813	+	0.746119i	$0.731915\pi$
$728$	5.38647e6	0.376683
$729$	531441.	0.0370370
$730$	4.53870e6	0.315227
$731$	−1.66732e7	−1.15405
$732$	3.12396e6	0.215490
$733$	7.51581e6	0.516673	0.258336	−	0.966055i	$-0.416826\pi$
$733$	7.51581e6	0.516673	0.258336	+	0.966055i	$0.416826\pi$
$734$	1.31690e7	0.902221
$735$	6.44533e6	0.440075
$736$	−881804.	−0.0600037
$737$	−1.97583e7	−1.33992
$738$	−2.48475e6	−0.167935
$739$	3.79806e6	0.255829	0.127915	−	0.991785i	$-0.459172\pi$
$739$	3.79806e6	0.255829	0.127915	+	0.991785i	$0.459172\pi$
$740$	−1.79862e6	−0.120742
$741$	4.83158e6	0.323254
$742$	1.14340e7	0.762409
$743$	1.46603e7	0.974253	0.487127	−	0.873331i	$-0.338045\pi$
$743$	1.46603e7	0.974253	0.487127	+	0.873331i	$0.338045\pi$
$744$	−1.46668e6	−0.0971412
$745$	165486.	0.0109237
$746$	−8.39686e6	−0.552420
$747$	−6.96732e6	−0.456840
$748$	6.50696e6	0.425230
$749$	−1.41059e7	−0.918745
$750$	−6.83311e6	−0.443573
$751$	7.86979e6	0.509171	0.254585	−	0.967050i	$-0.418061\pi$
$751$	7.86979e6	0.509171	0.254585	+	0.967050i	$0.418061\pi$
$752$	−1.56030e6	−0.100615
$753$	1.11860e7	0.718933
$754$	−4.17544e6	−0.267469
$755$	2.90281e6	0.185332
$756$	−2.08498e6	−0.132678
$757$	−5.06369e6	−0.321164	−0.160582	−	0.987022i	$-0.551337\pi$
$757$	−5.06369e6	−0.321164	−0.160582	+	0.987022i	$0.551337\pi$
$758$	−8.94183e6	−0.565267
$759$	2.39713e6	0.151038
$760$	−3.45038e6	−0.216687
$761$	−2.41432e7	−1.51124	−0.755620	−	0.655011i	$-0.772664\pi$
$761$	−2.41432e7	−1.51124	−0.755620	+	0.655011i	$0.772664\pi$
$762$	−2.13955e6	−0.133486
$763$	1.15112e7	0.715826
$764$	−5.45312e6	−0.337996
$765$	−5.03591e6	−0.311117
$766$	4.96869e6	0.305964
$767$	1.63898e6	0.100597
$768$	589824.	0.0360844
$769$	−1.49662e7	−0.912630	−0.456315	−	0.889818i	$-0.650831\pi$
$769$	−1.49662e7	−0.912630	−0.456315	+	0.889818i	$0.650831\pi$
$770$	1.04569e7	0.635587
$771$	−3.81141e6	−0.230914
$772$	9.39298e6	0.567231
$773$	−1.86986e7	−1.12554	−0.562768	−	0.826615i	$-0.690264\pi$
$773$	−1.86986e7	−1.12554	−0.562768	+	0.826615i	$0.690264\pi$
$774$	4.10848e6	0.246507
$775$	2.26433e6	0.135421
$776$	−5.86331e6	−0.349533
$777$	3.82477e6	0.227275
$778$	−2.03790e7	−1.20707
$779$	8.74407e6	0.516262
$780$	−3.20585e6	−0.188672
$781$	−1.97827e7	−1.16054
$782$	4.52912e6	0.264848
$783$	1.61622e6	0.0942096
$784$	3.87732e6	0.225290
$785$	−2.52466e7	−1.46227
$786$	7.43929e6	0.429512
$787$	−1.03489e7	−0.595601	−0.297801	−	0.954628i	$-0.596253\pi$
$787$	−1.03489e7	−0.595601	−0.297801	+	0.954628i	$0.596253\pi$
$788$	5.63867e6	0.323490
$789$	1.56265e7	0.893654
$790$	−3.93020e6	−0.224051
$791$	−1.16912e7	−0.664382
$792$	−1.60340e6	−0.0908298
$793$	−1.02144e7	−0.576806
$794$	−9.29946e6	−0.523487
$795$	−6.80514e6	−0.381873
$796$	−8.08393e6	−0.452210
$797$	2.47596e7	1.38070	0.690348	−	0.723477i	$-0.257457\pi$
$797$	2.47596e7	1.38070	0.690348	+	0.723477i	$0.257457\pi$
$798$	7.33725e6	0.407874
$799$	8.01400e6	0.444102
$800$	−910597.	−0.0503039
$801$	−8.07732e6	−0.444822
$802$	−1.08249e7	−0.594276
$803$	−7.42226e6	−0.406207
$804$	9.19888e6	0.501874
$805$	7.27843e6	0.395866
$806$	4.79560e6	0.260019
$807$	−4.62167e6	−0.249813
$808$	−7.56914e6	−0.407867
$809$	7.42824e6	0.399038	0.199519	−	0.979894i	$-0.436062\pi$
$809$	7.42824e6	0.399038	0.199519	+	0.979894i	$0.436062\pi$
$810$	1.24091e6	0.0664551
$811$	2.85258e7	1.52295	0.761474	−	0.648195i	$-0.224476\pi$
$811$	2.85258e7	1.52295	0.761474	+	0.648195i	$0.224476\pi$
$812$	−6.34083e6	−0.337486
$813$	−7.29695e6	−0.387182
$814$	2.94133e6	0.155591
$815$	1.59405e7	0.840637
$816$	−3.02945e6	−0.159272
$817$	−1.44582e7	−0.757805
$818$	−1.92302e7	−1.00485
$819$	6.81725e6	0.355140
$820$	−5.80187e6	−0.301324
$821$	−2.31696e7	−1.19967	−0.599833	−	0.800126i	$-0.704766\pi$
$821$	−2.31696e7	−1.19967	−0.599833	+	0.800126i	$0.704766\pi$
$822$	−7.95562e6	−0.410672
$823$	−2.27125e7	−1.16887	−0.584434	−	0.811441i	$-0.698683\pi$
$823$	−2.27125e7	−1.16887	−0.584434	+	0.811441i	$0.698683\pi$
$824$	−548622.	−0.0281485
$825$	2.47540e6	0.126622
$826$	2.48896e6	0.126931
$827$	3.47556e7	1.76710	0.883549	−	0.468338i	$-0.155147\pi$
$827$	3.47556e7	1.76710	0.883549	+	0.468338i	$0.155147\pi$
$828$	−1.11603e6	−0.0565720
$829$	1.00684e7	0.508829	0.254415	−	0.967095i	$-0.418117\pi$
$829$	1.00684e7	0.508829	0.254415	+	0.967095i	$0.418117\pi$
$830$	−1.62687e7	−0.819704
$831$	8.81556e6	0.442840
$832$	−1.92855e6	−0.0965876
$833$	−1.99147e7	−0.994399
$834$	6.46028e6	0.321615
$835$	5.05224e6	0.250765
$836$	5.64251e6	0.279227
$837$	−1.85627e6	−0.0915856
$838$	−1.38393e7	−0.680776
$839$	−5.98756e6	−0.293660	−0.146830	−	0.989162i	$-0.546907\pi$
$839$	−5.98756e6	−0.293660	−0.146830	+	0.989162i	$0.546907\pi$
$840$	−4.86842e6	−0.238062
$841$	−1.55959e7	−0.760363
$842$	1.00171e7	0.486926
$843$	1.18250e7	0.573102
$844$	1.26614e7	0.611822
$845$	−7.07393e6	−0.340815
$846$	−1.97475e6	−0.0948608
$847$	1.16880e7	0.559798
$848$	−4.09377e6	−0.195494
$849$	−1.90813e7	−0.908529
$850$	4.67701e6	0.222035
$851$	2.04729e6	0.0969073
$852$	9.21026e6	0.434683
$853$	8.84595e6	0.416267	0.208134	−	0.978100i	$-0.433261\pi$
$853$	8.84595e6	0.416267	0.208134	+	0.978100i	$0.433261\pi$
$854$	−1.55116e7	−0.727801
$855$	−4.36689e6	−0.204295
$856$	5.05040e6	0.235581
$857$	2.46533e7	1.14663	0.573315	−	0.819335i	$-0.305657\pi$
$857$	2.46533e7	1.14663	0.573315	+	0.819335i	$0.305657\pi$
$858$	5.24262e6	0.243126
$859$	3.44468e7	1.59282	0.796408	−	0.604759i	$-0.206731\pi$
$859$	3.44468e7	1.59282	0.796408	+	0.604759i	$0.206731\pi$
$860$	9.59329e6	0.442305
$861$	1.23377e7	0.567187
$862$	−2.46654e7	−1.13063
$863$	−1.65974e7	−0.758598	−0.379299	−	0.925274i	$-0.623835\pi$
$863$	−1.65974e7	−0.758598	−0.379299	+	0.925274i	$0.623835\pi$
$864$	746496.	0.0340207
$865$	1.48167e7	0.673304
$866$	−2.94062e7	−1.33243
$867$	2.78116e6	0.125655
$868$	7.28262e6	0.328087
$869$	6.42717e6	0.288716
$870$	3.77386e6	0.169039
$871$	−3.00775e7	−1.34337
$872$	−4.12140e6	−0.183550
$873$	−7.42075e6	−0.329543
$874$	3.92743e6	0.173912
$875$	3.39289e7	1.49813
$876$	3.45559e6	0.152147
$877$	−9.17873e6	−0.402980	−0.201490	−	0.979491i	$-0.564578\pi$
$877$	−9.17873e6	−0.402980	−0.201490	+	0.979491i	$0.564578\pi$
$878$	−1.50191e7	−0.657519
$879$	1.72964e7	0.755064
$880$	−3.74393e6	−0.162975
$881$	3.50967e7	1.52345	0.761723	−	0.647903i	$-0.224354\pi$
$881$	3.50967e7	1.52345	0.761723	+	0.647903i	$0.224354\pi$
$882$	4.90723e6	0.212405
$883$	−3.94643e7	−1.70335	−0.851673	−	0.524074i	$-0.824412\pi$
$883$	−3.94643e7	−1.70335	−0.851673	+	0.524074i	$0.824412\pi$
$884$	9.90539e6	0.426325
$885$	−1.48135e6	−0.0635769
$886$	1.89155e7	0.809530
$887$	−2.55290e7	−1.08950	−0.544748	−	0.838600i	$-0.683375\pi$
$887$	−2.55290e7	−1.08950	−0.544748	+	0.838600i	$0.683375\pi$
$888$	−1.36940e6	−0.0582771
$889$	1.06237e7	0.450837
$890$	−1.88605e7	−0.798139
$891$	−2.02930e6	−0.0856352
$892$	−5.98815e6	−0.251989
$893$	6.94935e6	0.291619
$894$	125995.	0.00527240
$895$	−2.20679e7	−0.920881
$896$	−2.92870e6	−0.121872
$897$	3.64909e6	0.151427
$898$	−7.80237e6	−0.322876
$899$	−5.64528e6	−0.232963
$900$	−1.15247e6	−0.0474269
$901$	2.10264e7	0.862886
$902$	9.48798e6	0.388291
$903$	−2.04001e7	−0.832557
$904$	4.18586e6	0.170359
$905$	−1.13129e7	−0.459149
$906$	2.21009e6	0.0894519
$907$	−1.55023e7	−0.625716	−0.312858	−	0.949800i	$-0.601286\pi$
$907$	−1.55023e7	−0.625716	−0.312858	+	0.949800i	$0.601286\pi$
$908$	−2.07093e6	−0.0833586
$909$	−9.57970e6	−0.384541
$910$	1.59182e7	0.637224
$911$	−1.90367e7	−0.759968	−0.379984	−	0.924993i	$-0.624070\pi$
$911$	−1.90367e7	−0.759968	−0.379984	+	0.924993i	$0.624070\pi$
$912$	−2.62699e6	−0.104586
$913$	2.66046e7	1.05628
$914$	−8.26834e6	−0.327380
$915$	9.23202e6	0.364539
$916$	3.81041e6	0.150049
$917$	−3.69388e7	−1.45064
$918$	−3.83415e6	−0.150163
$919$	−2.99644e7	−1.17035	−0.585176	−	0.810907i	$-0.698974\pi$
$919$	−2.99644e7	−1.17035	−0.585176	+	0.810907i	$0.698974\pi$
$920$	−2.60593e6	−0.101507
$921$	−2.11286e7	−0.820770
$922$	2.57034e7	0.995781
$923$	−3.01148e7	−1.16352
$924$	7.96147e6	0.306770
$925$	2.11414e6	0.0812419
$926$	5.20844e6	0.199609
$927$	−694350.	−0.0265387
$928$	2.27024e6	0.0865370
$929$	−1.70587e7	−0.648493	−0.324247	−	0.945973i	$-0.605111\pi$
$929$	−1.70587e7	−0.648493	−0.324247	+	0.945973i	$0.605111\pi$
$930$	−4.33438e6	−0.164331
$931$	−1.72690e7	−0.652971
$932$	2.40491e6	0.0906898
$933$	−1.02503e7	−0.385508
$934$	−1.66799e6	−0.0625643
$935$	1.92296e7	0.719350
$936$	−2.44082e6	−0.0910637
$937$	2.88643e7	1.07402	0.537010	−	0.843576i	$-0.319554\pi$
$937$	2.88643e7	1.07402	0.537010	+	0.843576i	$0.319554\pi$
$938$	−4.56759e7	−1.69504
$939$	−3.02762e6	−0.112057
$940$	−4.61104e6	−0.170208
$941$	−1.56280e7	−0.575348	−0.287674	−	0.957728i	$-0.592882\pi$
$941$	−1.56280e7	−0.575348	−0.287674	+	0.957728i	$0.592882\pi$
$942$	−1.92218e7	−0.705776
$943$	6.60404e6	0.241841
$944$	−891136.	−0.0325472
$945$	−6.16159e6	−0.224447
$946$	−1.56882e7	−0.569961
$947$	2.25474e7	0.816998	0.408499	−	0.912759i	$-0.366052\pi$
$947$	2.25474e7	0.816998	0.408499	+	0.912759i	$0.366052\pi$
$948$	−2.99231e6	−0.108140
$949$	−1.12987e7	−0.407253
$950$	4.05567e6	0.145799
$951$	2.26188e7	0.810994
$952$	1.50424e7	0.537927
$953$	1.72116e7	0.613889	0.306944	−	0.951727i	$-0.400693\pi$
$953$	1.72116e7	0.613889	0.306944	+	0.951727i	$0.400693\pi$
$954$	−5.18118e6	−0.184314
$955$	−1.61152e7	−0.571778
$956$	7.26236e6	0.257000
$957$	−6.17150e6	−0.217827
$958$	−2.41056e7	−0.848601
$959$	3.95026e7	1.38701
$960$	1.74307e6	0.0610429
$961$	−2.21454e7	−0.773526
$962$	4.47752e6	0.155991
$963$	6.39191e6	0.222108
$964$	1.94100e7	0.672716
$965$	2.77584e7	0.959569
$966$	5.54152e6	0.191067
$967$	−1.55199e7	−0.533731	−0.266865	−	0.963734i	$-0.585988\pi$
$967$	−1.55199e7	−0.533731	−0.266865	+	0.963734i	$0.585988\pi$
$968$	−4.18471e6	−0.143541
$969$	1.34928e7	0.461627
$970$	−1.73274e7	−0.591296
$971$	7.67859e6	0.261356	0.130678	−	0.991425i	$-0.458285\pi$
$971$	7.67859e6	0.261356	0.130678	+	0.991425i	$0.458285\pi$
$972$	944784.	0.0320750
$973$	−3.20777e7	−1.08623
$974$	−6.46577e6	−0.218385
$975$	3.76824e6	0.126948
$976$	5.55371e6	0.186620
$977$	−5.02866e7	−1.68545	−0.842724	−	0.538345i	$-0.819050\pi$
$977$	−5.02866e7	−1.68545	−0.842724	+	0.538345i	$0.819050\pi$
$978$	1.21365e7	0.405739
$979$	3.08432e7	1.02849
$980$	1.14584e7	0.381116
$981$	−5.21614e6	−0.173052
$982$	−1.35420e7	−0.448132
$983$	1.00238e7	0.330862	0.165431	−	0.986221i	$-0.447098\pi$
$983$	1.00238e7	0.330862	0.165431	+	0.986221i	$0.447098\pi$
$984$	−4.41733e6	−0.145436
$985$	1.66636e7	0.547239
$986$	−1.16604e7	−0.381963
$987$	9.80538e6	0.320385
$988$	8.58947e6	0.279946
$989$	−1.09196e7	−0.354992
$990$	−4.73841e6	−0.153654
$991$	2.08986e7	0.675979	0.337989	−	0.941150i	$-0.390253\pi$
$991$	2.08986e7	0.675979	0.337989	+	0.941150i	$0.390253\pi$
$992$	−2.60743e6	−0.0841268
$993$	−9.52982e6	−0.306698
$994$	−4.57324e7	−1.46811
$995$	−2.38899e7	−0.764990
$996$	−1.23864e7	−0.395635
$997$	−2.79797e7	−0.891468	−0.445734	−	0.895166i	$-0.647057\pi$
$997$	−2.79797e7	−0.891468	−0.445734	+	0.895166i	$0.647057\pi$
$998$	−2.95146e7	−0.938016
$999$	−1.73315e6	−0.0549442

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.a.b.1.4	✓	4
3.2	odd	2		1062.6.a.b.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.a.b.1.4	✓	4	1.1	even	1	trivial
1062.6.a.b.1.1		4	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)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +47.2837 q^{5} +36.0000 q^{6} -178.753 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +47.2837 q^{5} +36.0000 q^{6} -178.753 q^{7} +64.0000 q^{8} +81.0000 q^{9} +189.135 q^{10} -309.297 q^{11} +144.000 q^{12} -470.836 q^{13} -715.014 q^{14} +425.553 q^{15} +256.000 q^{16} -1314.87 q^{17} +324.000 q^{18} -1140.19 q^{19} +756.539 q^{20} -1608.78 q^{21} -1237.19 q^{22} -861.137 q^{23} +576.000 q^{24} -889.255 q^{25} -1883.35 q^{26} +729.000 q^{27} -2860.05 q^{28} +2217.03 q^{29} +1702.21 q^{30} -2546.32 q^{31} +1024.00 q^{32} -2783.68 q^{33} -5259.47 q^{34} -8452.11 q^{35} +1296.00 q^{36} -2377.43 q^{37} -4560.75 q^{38} -4237.53 q^{39} +3026.15 q^{40} -7668.97 q^{41} -6435.12 q^{42} +12680.5 q^{43} -4948.76 q^{44} +3829.98 q^{45} -3444.55 q^{46} -6094.92 q^{47} +2304.00 q^{48} +15145.8 q^{49} -3557.02 q^{50} -11833.8 q^{51} -7533.38 q^{52} -15991.3 q^{53} +2916.00 q^{54} -14624.7 q^{55} -11440.2 q^{56} -10261.7 q^{57} +8868.13 q^{58} -3481.00 q^{59} +6808.85 q^{60} +21694.2 q^{61} -10185.3 q^{62} -14479.0 q^{63} +4096.00 q^{64} -22262.9 q^{65} -11134.7 q^{66} +63881.1 q^{67} -21037.9 q^{68} -7750.23 q^{69} -33808.5 q^{70} +63960.2 q^{71} +5184.00 q^{72} +23997.2 q^{73} -9509.73 q^{74} -8003.30 q^{75} -18243.0 q^{76} +55288.0 q^{77} -16950.1 q^{78} -20779.9 q^{79} +12104.6 q^{80} +6561.00 q^{81} -30675.9 q^{82} -86016.3 q^{83} -25740.5 q^{84} -62171.7 q^{85} +50722.0 q^{86} +19953.3 q^{87} -19795.0 q^{88} -99720.0 q^{89} +15319.9 q^{90} +84163.6 q^{91} -13778.2 q^{92} -22916.9 q^{93} -24379.7 q^{94} -53912.3 q^{95} +9216.00 q^{96} -91614.2 q^{97} +60583.1 q^{98} -25053.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 16 q^{2} + 36 q^{3} + 64 q^{4} - 104 q^{5} + 144 q^{6} - 162 q^{7} + 256 q^{8} + 324 q^{9}+O(q^{10}) \) 4 * q + 16 * q^2 + 36 * q^3 + 64 * q^4 - 104 * q^5 + 144 * q^6 - 162 * q^7 + 256 * q^8 + 324 * q^9	\( 4 q + 16 q^{2} + 36 q^{3} + 64 q^{4} - 104 q^{5} + 144 q^{6} - 162 q^{7} + 256 q^{8} + 324 q^{9} - 416 q^{10} - 676 q^{11} + 576 q^{12} - 792 q^{13} - 648 q^{14} - 936 q^{15} + 1024 q^{16} - 2474 q^{17} + 1296 q^{18} - 4538 q^{19} - 1664 q^{20} - 1458 q^{21} - 2704 q^{22} - 1238 q^{23} + 2304 q^{24} - 832 q^{25} - 3168 q^{26} + 2916 q^{27} - 2592 q^{28} - 4958 q^{29} - 3744 q^{30} - 7138 q^{31} + 4096 q^{32} - 6084 q^{33} - 9896 q^{34} - 13554 q^{35} + 5184 q^{36} - 13570 q^{37} - 18152 q^{38} - 7128 q^{39} - 6656 q^{40} - 13826 q^{41} - 5832 q^{42} - 1236 q^{43} - 10816 q^{44} - 8424 q^{45} - 4952 q^{46} - 12410 q^{47} + 9216 q^{48} - 24622 q^{49} - 3328 q^{50} - 22266 q^{51} - 12672 q^{52} - 50904 q^{53} + 11664 q^{54} - 20872 q^{55} - 10368 q^{56} - 40842 q^{57} - 19832 q^{58} - 13924 q^{59} - 14976 q^{60} - 70622 q^{61} - 28552 q^{62} - 13122 q^{63} + 16384 q^{64} + 17460 q^{65} - 24336 q^{66} - 50012 q^{67} - 39584 q^{68} - 11142 q^{69} - 54216 q^{70} + 21192 q^{71} + 20736 q^{72} - 13358 q^{73} - 54280 q^{74} - 7488 q^{75} - 72608 q^{76} + 98658 q^{77} - 28512 q^{78} + 6464 q^{79} - 26624 q^{80} + 26244 q^{81} - 55304 q^{82} + 51506 q^{83} - 23328 q^{84} + 61786 q^{85} - 4944 q^{86} - 44622 q^{87} - 43264 q^{88} + 90738 q^{89} - 33696 q^{90} + 48870 q^{91} - 19808 q^{92} - 64242 q^{93} - 49640 q^{94} + 171394 q^{95} + 36864 q^{96} - 266068 q^{97} - 98488 q^{98} - 54756 q^{99}+O(q^{100}) \) 4 * q + 16 * q^2 + 36 * q^3 + 64 * q^4 - 104 * q^5 + 144 * q^6 - 162 * q^7 + 256 * q^8 + 324 * q^9 - 416 * q^10 - 676 * q^11 + 576 * q^12 - 792 * q^13 - 648 * q^14 - 936 * q^15 + 1024 * q^16 - 2474 * q^17 + 1296 * q^18 - 4538 * q^19 - 1664 * q^20 - 1458 * q^21 - 2704 * q^22 - 1238 * q^23 + 2304 * q^24 - 832 * q^25 - 3168 * q^26 + 2916 * q^27 - 2592 * q^28 - 4958 * q^29 - 3744 * q^30 - 7138 * q^31 + 4096 * q^32 - 6084 * q^33 - 9896 * q^34 - 13554 * q^35 + 5184 * q^36 - 13570 * q^37 - 18152 * q^38 - 7128 * q^39 - 6656 * q^40 - 13826 * q^41 - 5832 * q^42 - 1236 * q^43 - 10816 * q^44 - 8424 * q^45 - 4952 * q^46 - 12410 * q^47 + 9216 * q^48 - 24622 * q^49 - 3328 * q^50 - 22266 * q^51 - 12672 * q^52 - 50904 * q^53 + 11664 * q^54 - 20872 * q^55 - 10368 * q^56 - 40842 * q^57 - 19832 * q^58 - 13924 * q^59 - 14976 * q^60 - 70622 * q^61 - 28552 * q^62 - 13122 * q^63 + 16384 * q^64 + 17460 * q^65 - 24336 * q^66 - 50012 * q^67 - 39584 * q^68 - 11142 * q^69 - 54216 * q^70 + 21192 * q^71 + 20736 * q^72 - 13358 * q^73 - 54280 * q^74 - 7488 * q^75 - 72608 * q^76 + 98658 * q^77 - 28512 * q^78 + 6464 * q^79 - 26624 * q^80 + 26244 * q^81 - 55304 * q^82 + 51506 * q^83 - 23328 * q^84 + 61786 * q^85 - 4944 * q^86 - 44622 * q^87 - 43264 * q^88 + 90738 * q^89 - 33696 * q^90 + 48870 * q^91 - 19808 * q^92 - 64242 * q^93 - 49640 * q^94 + 171394 * q^95 + 36864 * q^96 - 266068 * q^97 - 98488 * q^98 - 54756 * q^99

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