LMFDB - Embedded newform 354.6.a.i.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("354.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$56.7758722138$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 17732 x^{6} - 152272 x^{5} + 93277609 x^{4} + 1554240404 x^{3} - 156444406614 x^{2} + \cdots + 6279664243680 $ x^8 - 17732x^6 - 152272x^5 + 93277609x^4 + 1554240404x^3 - 156444406614x^2 - 3720609623076x + 6279664243680
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.58411$ 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)

$f(q)$	$=$	$q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +10.4159 q^{5} +36.0000 q^{6} +172.112 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +10.4159 q^{5} +36.0000 q^{6} +172.112 q^{7} +64.0000 q^{8} +81.0000 q^{9} +41.6636 q^{10} +483.226 q^{11} +144.000 q^{12} +1078.34 q^{13} +688.448 q^{14} +93.7430 q^{15} +256.000 q^{16} -62.0885 q^{17} +324.000 q^{18} -2883.03 q^{19} +166.654 q^{20} +1549.01 q^{21} +1932.90 q^{22} -2804.22 q^{23} +576.000 q^{24} -3016.51 q^{25} +4313.35 q^{26} +729.000 q^{27} +2753.79 q^{28} -3104.05 q^{29} +374.972 q^{30} +4063.82 q^{31} +1024.00 q^{32} +4349.03 q^{33} -248.354 q^{34} +1792.70 q^{35} +1296.00 q^{36} +7345.97 q^{37} -11532.1 q^{38} +9705.04 q^{39} +666.617 q^{40} +16308.3 q^{41} +6196.03 q^{42} -2508.10 q^{43} +7731.62 q^{44} +843.687 q^{45} -11216.9 q^{46} -15687.7 q^{47} +2304.00 q^{48} +12815.6 q^{49} -12066.0 q^{50} -558.796 q^{51} +17253.4 q^{52} -13858.5 q^{53} +2916.00 q^{54} +5033.23 q^{55} +11015.2 q^{56} -25947.3 q^{57} -12416.2 q^{58} +3481.00 q^{59} +1499.89 q^{60} +49512.0 q^{61} +16255.3 q^{62} +13941.1 q^{63} +4096.00 q^{64} +11231.8 q^{65} +17396.1 q^{66} -8771.31 q^{67} -993.416 q^{68} -25238.0 q^{69} +7170.80 q^{70} +59269.6 q^{71} +5184.00 q^{72} +21719.9 q^{73} +29383.9 q^{74} -27148.6 q^{75} -46128.5 q^{76} +83169.0 q^{77} +38820.1 q^{78} +1046.76 q^{79} +2666.47 q^{80} +6561.00 q^{81} +65233.2 q^{82} -57161.4 q^{83} +24784.1 q^{84} -646.707 q^{85} -10032.4 q^{86} -27936.5 q^{87} +30926.5 q^{88} -113104. q^{89} +3374.75 q^{90} +185595. q^{91} -44867.6 q^{92} +36574.4 q^{93} -62750.8 q^{94} -30029.4 q^{95} +9216.00 q^{96} -118378. q^{97} +51262.2 q^{98} +39141.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 32 q^{2} + 72 q^{3} + 128 q^{4} + 96 q^{5} + 288 q^{6} + 181 q^{7} + 512 q^{8} + 648 q^{9}+O(q^{10}) $ 8 * q + 32 * q^2 + 72 * q^3 + 128 * q^4 + 96 * q^5 + 288 * q^6 + 181 * q^7 + 512 * q^8 + 648 * q^9	\( 8 q + 32 q^{2} + 72 q^{3} + 128 q^{4} + 96 q^{5} + 288 q^{6} + 181 q^{7} + 512 q^{8} + 648 q^{9} + 384 q^{10} + 897 q^{11} + 1152 q^{12} + 1743 q^{13} + 724 q^{14} + 864 q^{15} + 2048 q^{16} + 1861 q^{17} + 2592 q^{18} + 3154 q^{19} + 1536 q^{20} + 1629 q^{21} + 3588 q^{22} + 3808 q^{23} + 4608 q^{24} + 11616 q^{25} + 6972 q^{26} + 5832 q^{27} + 2896 q^{28} + 328 q^{29} + 3456 q^{30} + 570 q^{31} + 8192 q^{32} + 8073 q^{33} + 7444 q^{34} + 36086 q^{35} + 10368 q^{36} + 12777 q^{37} + 12616 q^{38} + 15687 q^{39} + 6144 q^{40} + 20167 q^{41} + 6516 q^{42} + 24579 q^{43} + 14352 q^{44} + 7776 q^{45} + 15232 q^{46} + 20490 q^{47} + 18432 q^{48} + 59391 q^{49} + 46464 q^{50} + 16749 q^{51} + 27888 q^{52} + 13404 q^{53} + 23328 q^{54} - 34588 q^{55} + 11584 q^{56} + 28386 q^{57} + 1312 q^{58} + 27848 q^{59} + 13824 q^{60} + 94944 q^{61} + 2280 q^{62} + 14661 q^{63} + 32768 q^{64} + 54560 q^{65} + 32292 q^{66} + 28838 q^{67} + 29776 q^{68} + 34272 q^{69} + 144344 q^{70} + 14983 q^{71} + 41472 q^{72} + 69384 q^{73} + 51108 q^{74} + 104544 q^{75} + 50464 q^{76} - 22359 q^{77} + 62748 q^{78} - 49199 q^{79} + 24576 q^{80} + 52488 q^{81} + 80668 q^{82} + 3995 q^{83} + 26064 q^{84} - 142290 q^{85} + 98316 q^{86} + 2952 q^{87} + 57408 q^{88} + 28722 q^{89} + 31104 q^{90} + 20815 q^{91} + 60928 q^{92} + 5130 q^{93} + 81960 q^{94} + 208010 q^{95} + 73728 q^{96} + 204150 q^{97} + 237564 q^{98} + 72657 q^{99}+O(q^{100}) \) 8 * q + 32 * q^2 + 72 * q^3 + 128 * q^4 + 96 * q^5 + 288 * q^6 + 181 * q^7 + 512 * q^8 + 648 * q^9 + 384 * q^10 + 897 * q^11 + 1152 * q^12 + 1743 * q^13 + 724 * q^14 + 864 * q^15 + 2048 * q^16 + 1861 * q^17 + 2592 * q^18 + 3154 * q^19 + 1536 * q^20 + 1629 * q^21 + 3588 * q^22 + 3808 * q^23 + 4608 * q^24 + 11616 * q^25 + 6972 * q^26 + 5832 * q^27 + 2896 * q^28 + 328 * q^29 + 3456 * q^30 + 570 * q^31 + 8192 * q^32 + 8073 * q^33 + 7444 * q^34 + 36086 * q^35 + 10368 * q^36 + 12777 * q^37 + 12616 * q^38 + 15687 * q^39 + 6144 * q^40 + 20167 * q^41 + 6516 * q^42 + 24579 * q^43 + 14352 * q^44 + 7776 * q^45 + 15232 * q^46 + 20490 * q^47 + 18432 * q^48 + 59391 * q^49 + 46464 * q^50 + 16749 * q^51 + 27888 * q^52 + 13404 * q^53 + 23328 * q^54 - 34588 * q^55 + 11584 * q^56 + 28386 * q^57 + 1312 * q^58 + 27848 * q^59 + 13824 * q^60 + 94944 * q^61 + 2280 * q^62 + 14661 * q^63 + 32768 * q^64 + 54560 * q^65 + 32292 * q^66 + 28838 * q^67 + 29776 * q^68 + 34272 * q^69 + 144344 * q^70 + 14983 * q^71 + 41472 * q^72 + 69384 * q^73 + 51108 * q^74 + 104544 * q^75 + 50464 * q^76 - 22359 * q^77 + 62748 * q^78 - 49199 * q^79 + 24576 * q^80 + 52488 * q^81 + 80668 * q^82 + 3995 * q^83 + 26064 * q^84 - 142290 * q^85 + 98316 * q^86 + 2952 * q^87 + 57408 * q^88 + 28722 * q^89 + 31104 * q^90 + 20815 * q^91 + 60928 * q^92 + 5130 * q^93 + 81960 * q^94 + 208010 * q^95 + 73728 * q^96 + 204150 * q^97 + 237564 * q^98 + 72657 * 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
$5$	10.4159	0.186325	0.0931626	−	0.995651i	$-0.470302\pi$
$5$	10.4159	0.186325	0.0931626	+	0.995651i	$0.470302\pi$
$6$	36.0000	0.408248
$7$	172.112	1.32760	0.663798	−	0.747912i	$-0.268943\pi$
$7$	172.112	1.32760	0.663798	+	0.747912i	$0.268943\pi$
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	41.6636	0.131752
$11$	483.226	1.20412	0.602058	−	0.798452i	$-0.294347\pi$
$11$	483.226	1.20412	0.602058	+	0.798452i	$0.294347\pi$
$12$	144.000	0.288675
$13$	1078.34	1.76969	0.884843	−	0.465889i	$-0.154266\pi$
$13$	1078.34	1.76969	0.884843	+	0.465889i	$0.154266\pi$
$14$	688.448	0.938753
$15$	93.7430	0.107575
$16$	256.000	0.250000
$17$	−62.0885	−0.0521061	−0.0260531	−	0.999661i	$-0.508294\pi$
$17$	−62.0885	−0.0521061	−0.0260531	+	0.999661i	$0.508294\pi$
$18$	324.000	0.235702
$19$	−2883.03	−1.83217	−0.916084	−	0.400986i	$-0.868668\pi$
$19$	−2883.03	−1.83217	−0.916084	+	0.400986i	$0.868668\pi$
$20$	166.654	0.0931626
$21$	1549.01	0.766488
$22$	1932.90	0.851439
$23$	−2804.22	−1.10533	−0.552666	−	0.833403i	$-0.686390\pi$
$23$	−2804.22	−1.10533	−0.552666	+	0.833403i	$0.686390\pi$
$24$	576.000	0.204124
$25$	−3016.51	−0.965283
$26$	4313.35	1.25136
$27$	729.000	0.192450
$28$	2753.79	0.663798
$29$	−3104.05	−0.685384	−0.342692	−	0.939448i	$-0.611339\pi$
$29$	−3104.05	−0.685384	−0.342692	+	0.939448i	$0.611339\pi$
$30$	374.972	0.0760669
$31$	4063.82	0.759505	0.379752	−	0.925088i	$-0.376009\pi$
$31$	4063.82	0.759505	0.379752	+	0.925088i	$0.376009\pi$
$32$	1024.00	0.176777
$33$	4349.03	0.695197
$34$	−248.354	−0.0368446
$35$	1792.70	0.247365
$36$	1296.00	0.166667
$37$	7345.97	0.882155	0.441077	−	0.897469i	$-0.354596\pi$
$37$	7345.97	0.882155	0.441077	+	0.897469i	$0.354596\pi$
$38$	−11532.1	−1.29554
$39$	9705.04	1.02173
$40$	666.617	0.0658759
$41$	16308.3	1.51513	0.757563	−	0.652762i	$-0.226390\pi$
$41$	16308.3	1.51513	0.757563	+	0.652762i	$0.226390\pi$
$42$	6196.03	0.541989
$43$	−2508.10	−0.206859	−0.103429	−	0.994637i	$-0.532982\pi$
$43$	−2508.10	−0.206859	−0.103429	+	0.994637i	$0.532982\pi$
$44$	7731.62	0.602058
$45$	843.687	0.0621084
$46$	−11216.9	−0.781588
$47$	−15687.7	−1.03589	−0.517947	−	0.855413i	$-0.673303\pi$
$47$	−15687.7	−1.03589	−0.517947	+	0.855413i	$0.673303\pi$
$48$	2304.00	0.144338
$49$	12815.6	0.762513
$50$	−12066.0	−0.682558
$51$	−558.796	−0.0300835
$52$	17253.4	0.884843
$53$	−13858.5	−0.677684	−0.338842	−	0.940843i	$-0.610035\pi$
$53$	−13858.5	−0.677684	−0.338842	+	0.940843i	$0.610035\pi$
$54$	2916.00	0.136083
$55$	5033.23	0.224357
$56$	11015.2	0.469376
$57$	−25947.3	−1.05780
$58$	−12416.2	−0.484640
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	1499.89	0.0537874
$61$	49512.0	1.70367	0.851836	−	0.523809i	$-0.175489\pi$
$61$	49512.0	1.70367	0.851836	+	0.523809i	$0.175489\pi$
$62$	16255.3	0.537051
$63$	13941.1	0.442532
$64$	4096.00	0.125000
$65$	11231.8	0.329737
$66$	17396.1	0.491579
$67$	−8771.31	−0.238714	−0.119357	−	0.992851i	$-0.538083\pi$
$67$	−8771.31	−0.238714	−0.119357	+	0.992851i	$0.538083\pi$
$68$	−993.416	−0.0260531
$69$	−25238.0	−0.638164
$70$	7170.80	0.174913
$71$	59269.6	1.39536	0.697680	−	0.716410i	$-0.254216\pi$
$71$	59269.6	1.39536	0.697680	+	0.716410i	$0.254216\pi$
$72$	5184.00	0.117851
$73$	21719.9	0.477035	0.238517	−	0.971138i	$-0.423339\pi$
$73$	21719.9	0.477035	0.238517	+	0.971138i	$0.423339\pi$
$74$	29383.9	0.623778
$75$	−27148.6	−0.557306
$76$	−46128.5	−0.916084
$77$	83169.0	1.59858
$78$	38820.1	0.722471
$79$	1046.76	0.0188702	0.00943512	−	0.999955i	$-0.496997\pi$
$79$	1046.76	0.0188702	0.00943512	+	0.999955i	$0.496997\pi$
$80$	2666.47	0.0465813
$81$	6561.00	0.111111
$82$	65233.2	1.07136
$83$	−57161.4	−0.910768	−0.455384	−	0.890295i	$-0.650498\pi$
$83$	−57161.4	−0.910768	−0.455384	+	0.890295i	$0.650498\pi$
$84$	24784.1	0.383244
$85$	−646.707	−0.00970868
$86$	−10032.4	−0.146271
$87$	−27936.5	−0.395707
$88$	30926.5	0.425720
$89$	−113104.	−1.51357	−0.756785	−	0.653664i	$-0.773231\pi$
$89$	−113104.	−1.51357	−0.756785	+	0.653664i	$0.773231\pi$
$90$	3374.75	0.0439173
$91$	185595.	2.34943
$92$	−44867.6	−0.552666
$93$	36574.4	0.438500
$94$	−62750.8	−0.732487
$95$	−30029.4	−0.341379
$96$	9216.00	0.102062
$97$	−118378.	−1.27744	−0.638720	−	0.769440i	$-0.720536\pi$
$97$	−118378.	−1.27744	−0.638720	+	0.769440i	$0.720536\pi$
$98$	51262.2	0.539178
$99$	39141.3	0.401372
$100$	−48264.1	−0.482641
$101$	−87910.5	−0.857506	−0.428753	−	0.903422i	$-0.641047\pi$
$101$	−87910.5	−0.857506	−0.428753	+	0.903422i	$0.641047\pi$
$102$	−2235.18	−0.0212722
$103$	−142254.	−1.32121	−0.660606	−	0.750732i	$-0.729701\pi$
$103$	−142254.	−1.32121	−0.660606	+	0.750732i	$0.729701\pi$
$104$	69013.6	0.625678
$105$	16134.3	0.142816
$106$	−55434.1	−0.479195
$107$	164938.	1.39271	0.696357	−	0.717695i	$-0.254803\pi$
$107$	164938.	1.39271	0.696357	+	0.717695i	$0.254803\pi$
$108$	11664.0	0.0962250
$109$	27774.5	0.223914	0.111957	−	0.993713i	$-0.464288\pi$
$109$	27774.5	0.223914	0.111957	+	0.993713i	$0.464288\pi$
$110$	20132.9	0.158645
$111$	66113.7	0.509312
$112$	44060.7	0.331899
$113$	−46014.9	−0.339002	−0.169501	−	0.985530i	$-0.554216\pi$
$113$	−46014.9	−0.339002	−0.169501	+	0.985530i	$0.554216\pi$
$114$	−103789.	−0.747980
$115$	−29208.5	−0.205951
$116$	−49664.8	−0.342692
$117$	87345.3	0.589895
$118$	13924.0	0.0920575
$119$	−10686.2	−0.0691759
$120$	5999.55	0.0380335
$121$	72456.4	0.449897
$122$	198048.	1.20468
$123$	146775.	0.874758
$124$	65021.2	0.379752
$125$	−63969.3	−0.366182
$126$	55764.3	0.312918
$127$	349084.	1.92053	0.960264	−	0.279095i	$-0.0900343\pi$
$127$	349084.	1.92053	0.960264	+	0.279095i	$0.0900343\pi$
$128$	16384.0	0.0883883
$129$	−22572.9	−0.119430
$130$	44927.4	0.233159
$131$	74646.6	0.380042	0.190021	−	0.981780i	$-0.439144\pi$
$131$	74646.6	0.380042	0.190021	+	0.981780i	$0.439144\pi$
$132$	69584.6	0.347599
$133$	−496205.	−2.43238
$134$	−35085.2	−0.168796
$135$	7593.19	0.0358583
$136$	−3973.66	−0.0184223
$137$	46594.0	0.212094	0.106047	−	0.994361i	$-0.466181\pi$
$137$	46594.0	0.212094	0.106047	+	0.994361i	$0.466181\pi$
$138$	−100952.	−0.451250
$139$	−304634.	−1.33734	−0.668669	−	0.743560i	$-0.733136\pi$
$139$	−304634.	−1.33734	−0.668669	+	0.743560i	$0.733136\pi$
$140$	28683.2	0.123682
$141$	−141189.	−0.598073
$142$	237078.	0.986668
$143$	521081.	2.13091
$144$	20736.0	0.0833333
$145$	−32331.5	−0.127704
$146$	86879.4	0.337314
$147$	115340.	0.440237
$148$	117536.	0.441077
$149$	−112341.	−0.414547	−0.207273	−	0.978283i	$-0.566459\pi$
$149$	−112341.	−0.414547	−0.207273	+	0.978283i	$0.566459\pi$
$150$	−108594.	−0.394075
$151$	217345.	0.775724	0.387862	−	0.921717i	$-0.373214\pi$
$151$	217345.	0.775724	0.387862	+	0.921717i	$0.373214\pi$
$152$	−184514.	−0.647769
$153$	−5029.17	−0.0173687
$154$	332676.	1.13037
$155$	42328.3	0.141515
$156$	155281.	0.510864
$157$	27511.9	0.0890782	0.0445391	−	0.999008i	$-0.485818\pi$
$157$	27511.9	0.0890782	0.0445391	+	0.999008i	$0.485818\pi$
$158$	4187.02	0.0133433
$159$	−124727.	−0.391261
$160$	10665.9	0.0329379
$161$	−482641.	−1.46744
$162$	26244.0	0.0785674
$163$	−616020.	−1.81604	−0.908021	−	0.418925i	$-0.862407\pi$
$163$	−616020.	−1.81604	−0.908021	+	0.418925i	$0.862407\pi$
$164$	260933.	0.757563
$165$	45299.1	0.129533
$166$	−228646.	−0.644010
$167$	34100.9	0.0946182	0.0473091	−	0.998880i	$-0.484935\pi$
$167$	34100.9	0.0946182	0.0473091	+	0.998880i	$0.484935\pi$
$168$	99136.5	0.270995
$169$	791518.	2.13179
$170$	−2586.83	−0.00686507
$171$	−233526.	−0.610723
$172$	−40129.7	−0.103429
$173$	197054.	0.500576	0.250288	−	0.968171i	$-0.419475\pi$
$173$	197054.	0.500576	0.250288	+	0.968171i	$0.419475\pi$
$174$	−111746.	−0.279807
$175$	−519178.	−1.28151
$176$	123706.	0.301029
$177$	31329.0	0.0751646
$178$	−452415.	−1.07026
$179$	−598494.	−1.39613	−0.698067	−	0.716032i	$-0.745956\pi$
$179$	−598494.	−1.39613	−0.698067	+	0.716032i	$0.745956\pi$
$180$	13499.0	0.0310542
$181$	269841.	0.612227	0.306113	−	0.951995i	$-0.400971\pi$
$181$	269841.	0.612227	0.306113	+	0.951995i	$0.400971\pi$
$182$	742379.	1.66130
$183$	445608.	0.983615
$184$	−179470.	−0.390794
$185$	76514.8	0.164368
$186$	146298.	0.310067
$187$	−30002.8	−0.0627418
$188$	−251003.	−0.517947
$189$	125470.	0.255496
$190$	−120117.	−0.241391
$191$	149108.	0.295745	0.147873	−	0.989006i	$-0.452757\pi$
$191$	149108.	0.295745	0.147873	+	0.989006i	$0.452757\pi$
$192$	36864.0	0.0721688
$193$	−244695.	−0.472859	−0.236430	−	0.971649i	$-0.575977\pi$
$193$	−244695.	−0.472859	−0.236430	+	0.971649i	$0.575977\pi$
$194$	−473510.	−0.903286
$195$	101087.	0.190374
$196$	205049.	0.381256
$197$	20266.4	0.0372059	0.0186029	−	0.999827i	$-0.494078\pi$
$197$	20266.4	0.0372059	0.0186029	+	0.999827i	$0.494078\pi$
$198$	156565.	0.283813
$199$	−67312.8	−0.120494	−0.0602469	−	0.998184i	$-0.519189\pi$
$199$	−67312.8	−0.120494	−0.0602469	+	0.998184i	$0.519189\pi$
$200$	−193057.	−0.341279
$201$	−78941.8	−0.137821
$202$	−351642.	−0.606348
$203$	−534245.	−0.909913
$204$	−8940.74	−0.0150417
$205$	169865.	0.282306
$206$	−569018.	−0.934239
$207$	−227142.	−0.368444
$208$	276054.	0.442422
$209$	−1.39316e6	−2.20615
$210$	64537.2	0.100986
$211$	−591994.	−0.915401	−0.457700	−	0.889107i	$-0.651327\pi$
$211$	−591994.	−0.915401	−0.457700	+	0.889107i	$0.651327\pi$
$212$	−221736.	−0.338842
$213$	533426.	0.805611
$214$	659753.	0.984798
$215$	−26124.1	−0.0385430
$216$	46656.0	0.0680414
$217$	699433.	1.00832
$218$	111098.	0.158331
$219$	195479.	0.275416
$220$	80531.7	0.112179
$221$	−66952.3	−0.0922115
$222$	264455.	0.360138
$223$	1.23656e6	1.66515	0.832574	−	0.553914i	$-0.186866\pi$
$223$	1.23656e6	1.66515	0.832574	+	0.553914i	$0.186866\pi$
$224$	176243.	0.234688
$225$	−244337.	−0.321761
$226$	−184060.	−0.239711
$227$	−52773.7	−0.0679756	−0.0339878	−	0.999422i	$-0.510821\pi$
$227$	−52773.7	−0.0679756	−0.0339878	+	0.999422i	$0.510821\pi$
$228$	−415157.	−0.528902
$229$	711081.	0.896046	0.448023	−	0.894022i	$-0.352128\pi$
$229$	711081.	0.896046	0.448023	+	0.894022i	$0.352128\pi$
$230$	−116834.	−0.145630
$231$	748521.	0.922941
$232$	−198659.	−0.242320
$233$	−749801.	−0.904807	−0.452404	−	0.891813i	$-0.649433\pi$
$233$	−749801.	−0.904807	−0.452404	+	0.891813i	$0.649433\pi$
$234$	349381.	0.417119
$235$	−163402.	−0.193013
$236$	55696.0	0.0650945
$237$	9420.80	0.0108947
$238$	−42744.7	−0.0489147
$239$	−102384.	−0.115941	−0.0579706	−	0.998318i	$-0.518463\pi$
$239$	−102384.	−0.115941	−0.0579706	+	0.998318i	$0.518463\pi$
$240$	23998.2	0.0268937
$241$	32284.5	0.0358057	0.0179028	−	0.999840i	$-0.494301\pi$
$241$	32284.5	0.0358057	0.0179028	+	0.999840i	$0.494301\pi$
$242$	289826.	0.318125
$243$	59049.0	0.0641500
$244$	792192.	0.851836
$245$	133485.	0.142075
$246$	587098.	0.618548
$247$	−3.10888e6	−3.24236
$248$	260085.	0.268526
$249$	−514453.	−0.525832
$250$	−255877.	−0.258930
$251$	−1.09769e6	−1.09975	−0.549874	−	0.835247i	$-0.685324\pi$
$251$	−1.09769e6	−1.09975	−0.549874	+	0.835247i	$0.685324\pi$
$252$	223057.	0.221266
$253$	−1.35507e6	−1.33095
$254$	1.39634e6	1.35802
$255$	−5820.36	−0.00560531
$256$	65536.0	0.0625000
$257$	−1.02773e6	−0.970617	−0.485308	−	0.874343i	$-0.661293\pi$
$257$	−1.02773e6	−0.970617	−0.485308	+	0.874343i	$0.661293\pi$
$258$	−90291.7	−0.0844498
$259$	1.26433e6	1.17115
$260$	179710.	0.164869
$261$	−251428.	−0.228461
$262$	298586.	0.268730
$263$	1.00405e6	0.895089	0.447545	−	0.894262i	$-0.352299\pi$
$263$	1.00405e6	0.895089	0.447545	+	0.894262i	$0.352299\pi$
$264$	278338.	0.245789
$265$	−144349.	−0.126270
$266$	−1.98482e6	−1.71995
$267$	−1.01793e6	−0.873860
$268$	−140341.	−0.119357
$269$	−1638.22	−0.00138036	−0.000690178	−	1.00000i	$-0.500220\pi$
$269$	−1638.22	−0.00138036	−0.000690178		1.00000i	$0.500220\pi$
$270$	30372.7	0.0253556
$271$	−418252.	−0.345951	−0.172975	−	0.984926i	$-0.555338\pi$
$271$	−418252.	−0.345951	−0.172975	+	0.984926i	$0.555338\pi$
$272$	−15894.6	−0.0130265
$273$	1.67035e6	1.35644
$274$	186376.	0.149973
$275$	−1.45766e6	−1.16231
$276$	−403808.	−0.319082
$277$	−1.49364e6	−1.16963	−0.584814	−	0.811168i	$-0.698832\pi$
$277$	−1.49364e6	−1.16963	−0.584814	+	0.811168i	$0.698832\pi$
$278$	−1.21854e6	−0.945641
$279$	329170.	0.253168
$280$	114733.	0.0874566
$281$	289446.	0.218677	0.109338	−	0.994005i	$-0.465127\pi$
$281$	289446.	0.218677	0.109338	+	0.994005i	$0.465127\pi$
$282$	−564758.	−0.422902
$283$	538499.	0.399686	0.199843	−	0.979828i	$-0.435957\pi$
$283$	538499.	0.399686	0.199843	+	0.979828i	$0.435957\pi$
$284$	948314.	0.697680
$285$	−270264.	−0.197095
$286$	2.08432e6	1.50678
$287$	2.80685e6	2.01148
$288$	82944.0	0.0589256
$289$	−1.41600e6	−0.997285
$290$	−129326.	−0.0903005
$291$	−1.06540e6	−0.737530
$292$	347518.	0.238517
$293$	456567.	0.310696	0.155348	−	0.987860i	$-0.450350\pi$
$293$	456567.	0.310696	0.155348	+	0.987860i	$0.450350\pi$
$294$	461360.	0.311295
$295$	36257.7	0.0242575
$296$	470142.	0.311889
$297$	352272.	0.231732
$298$	−449365.	−0.293129
$299$	−3.02390e6	−1.95609
$300$	−434377.	−0.278653
$301$	−431675.	−0.274625
$302$	869380.	0.548520
$303$	−791194.	−0.495081
$304$	−738056.	−0.458042
$305$	515712.	0.317437
$306$	−20116.7	−0.0122815
$307$	2.28824e6	1.38566	0.692828	−	0.721103i	$-0.256364\pi$
$307$	2.28824e6	1.38566	0.692828	+	0.721103i	$0.256364\pi$
$308$	1.33070e6	0.799291
$309$	−1.28029e6	−0.762803
$310$	169313.	0.100066
$311$	−3.24389e6	−1.90180	−0.950901	−	0.309496i	$-0.899840\pi$
$311$	−3.24389e6	−1.90180	−0.950901	+	0.309496i	$0.899840\pi$
$312$	621122.	0.361236
$313$	−768001.	−0.443099	−0.221550	−	0.975149i	$-0.571111\pi$
$313$	−768001.	−0.443099	−0.221550	+	0.975149i	$0.571111\pi$
$314$	110048.	0.0629878
$315$	145209.	0.0824549
$316$	16748.1	0.00943512
$317$	−2.54166e6	−1.42059	−0.710296	−	0.703903i	$-0.751439\pi$
$317$	−2.54166e6	−1.42059	−0.710296	+	0.703903i	$0.751439\pi$
$318$	−498907.	−0.276663
$319$	−1.49996e6	−0.825282
$320$	42663.5	0.0232906
$321$	1.48444e6	0.804084
$322$	−1.93056e6	−1.03763
$323$	179003.	0.0954672
$324$	104976.	0.0555556
$325$	−3.25281e6	−1.70825
$326$	−2.46408e6	−1.28414
$327$	249971.	0.129277
$328$	1.04373e6	0.535678
$329$	−2.70004e6	−1.37525
$330$	181196.	0.0915935
$331$	750100.	0.376313	0.188157	−	0.982139i	$-0.439749\pi$
$331$	750100.	0.376313	0.188157	+	0.982139i	$0.439749\pi$
$332$	−914582.	−0.455384
$333$	595024.	0.294052
$334$	136404.	0.0669052
$335$	−91361.0	−0.0444784
$336$	396546.	0.191622
$337$	3.20784e6	1.53864	0.769322	−	0.638861i	$-0.220594\pi$
$337$	3.20784e6	1.53864	0.769322	+	0.638861i	$0.220594\pi$
$338$	3.16607e6	1.50740
$339$	−414134.	−0.195723
$340$	−10347.3	−0.00485434
$341$	1.96375e6	0.914533
$342$	−934102.	−0.431846
$343$	−686976.	−0.315287
$344$	−160519.	−0.0731357
$345$	−262876.	−0.118906
$346$	788216.	0.353961
$347$	−3.04843e6	−1.35910	−0.679551	−	0.733628i	$-0.737825\pi$
$347$	−3.04843e6	−1.35910	−0.679551	+	0.733628i	$0.737825\pi$
$348$	−446983.	−0.197853
$349$	828645.	0.364171	0.182085	−	0.983283i	$-0.441715\pi$
$349$	828645.	0.364171	0.182085	+	0.983283i	$0.441715\pi$
$350$	−2.07671e6	−0.906162
$351$	786108.	0.340576
$352$	494823.	0.212860
$353$	−651743.	−0.278381	−0.139191	−	0.990266i	$-0.544450\pi$
$353$	−651743.	−0.278381	−0.139191	+	0.990266i	$0.544450\pi$
$354$	125316.	0.0531494
$355$	617346.	0.259991
$356$	−1.80966e6	−0.756785
$357$	−96175.6	−0.0399387
$358$	−2.39398e6	−0.987216
$359$	−501693.	−0.205448	−0.102724	−	0.994710i	$-0.532756\pi$
$359$	−501693.	−0.205448	−0.102724	+	0.994710i	$0.532756\pi$
$360$	53996.0	0.0219586
$361$	5.83578e6	2.35684
$362$	1.07937e6	0.432910
$363$	652108.	0.259748
$364$	2.96952e6	1.17471
$365$	226232.	0.0888835
$366$	1.78243e6	0.695521
$367$	3.29486e6	1.27694	0.638472	−	0.769645i	$-0.279567\pi$
$367$	3.29486e6	1.27694	0.638472	+	0.769645i	$0.279567\pi$
$368$	−717881.	−0.276333
$369$	1.32097e6	0.505042
$370$	306059.	0.116225
$371$	−2.38522e6	−0.899691
$372$	585190.	0.219250
$373$	4.48623e6	1.66959	0.834793	−	0.550563i	$-0.185587\pi$
$373$	4.48623e6	1.66959	0.834793	+	0.550563i	$0.185587\pi$
$374$	−120011.	−0.0443652
$375$	−575724.	−0.211415
$376$	−1.00401e6	−0.366244
$377$	−3.34721e6	−1.21291
$378$	501879.	0.180663
$379$	2.37314e6	0.848645	0.424323	−	0.905511i	$-0.360512\pi$
$379$	2.37314e6	0.848645	0.424323	+	0.905511i	$0.360512\pi$
$380$	−480470.	−0.170690
$381$	3.14175e6	1.10882
$382$	596432.	0.209123
$383$	−1.22266e6	−0.425900	−0.212950	−	0.977063i	$-0.568307\pi$
$383$	−1.22266e6	−0.425900	−0.212950	+	0.977063i	$0.568307\pi$
$384$	147456.	0.0510310
$385$	866280.	0.297856
$386$	−978780.	−0.334362
$387$	−203156.	−0.0689530
$388$	−1.89404e6	−0.638720
$389$	−1.34442e6	−0.450466	−0.225233	−	0.974305i	$-0.572314\pi$
$389$	−1.34442e6	−0.450466	−0.225233	+	0.974305i	$0.572314\pi$
$390$	404346.	0.134615
$391$	174110.	0.0575946
$392$	820195.	0.269589
$393$	671819.	0.219417
$394$	81065.7	0.0263085
$395$	10902.9	0.00351600
$396$	626261.	0.200686
$397$	−2.86705e6	−0.912977	−0.456488	−	0.889729i	$-0.650893\pi$
$397$	−2.86705e6	−0.912977	−0.456488	+	0.889729i	$0.650893\pi$
$398$	−269251.	−0.0852020
$399$	−4.46584e6	−1.40434
$400$	−772226.	−0.241321
$401$	−5.51350e6	−1.71225	−0.856124	−	0.516771i	$-0.827134\pi$
$401$	−5.51350e6	−1.71225	−0.856124	+	0.516771i	$0.827134\pi$
$402$	−315767.	−0.0974545
$403$	4.38217e6	1.34409
$404$	−1.40657e6	−0.428753
$405$	68338.7	0.0207028
$406$	−2.13698e6	−0.643406
$407$	3.54976e6	1.06222
$408$	−35763.0	−0.0106361
$409$	−1.83260e6	−0.541699	−0.270850	−	0.962622i	$-0.587305\pi$
$409$	−1.83260e6	−0.541699	−0.270850	+	0.962622i	$0.587305\pi$
$410$	679462.	0.199621
$411$	419346.	0.122453
$412$	−2.27607e6	−0.660606
$413$	599122.	0.172838
$414$	−908568.	−0.260529
$415$	−595387.	−0.169699
$416$	1.10422e6	0.312839
$417$	−2.74171e6	−0.772113
$418$	−5.57262e6	−1.55998
$419$	1.00083e6	0.278501	0.139251	−	0.990257i	$-0.455531\pi$
$419$	1.00083e6	0.278501	0.139251	+	0.990257i	$0.455531\pi$
$420$	258149.	0.0714080
$421$	4.76541e6	1.31037	0.655187	−	0.755467i	$-0.272590\pi$
$421$	4.76541e6	1.31037	0.655187	+	0.755467i	$0.272590\pi$
$422$	−2.36798e6	−0.647286
$423$	−1.27070e6	−0.345298
$424$	−886946.	−0.239598
$425$	187290.	0.0502971
$426$	2.13371e6	0.569653
$427$	8.52161e6	2.26179
$428$	2.63901e6	0.696357
$429$	4.68973e6	1.23028
$430$	−104497.	−0.0272540
$431$	−4.35817e6	−1.13008	−0.565042	−	0.825062i	$-0.691140\pi$
$431$	−4.35817e6	−1.13008	−0.565042	+	0.825062i	$0.691140\pi$
$432$	186624.	0.0481125
$433$	−4.61965e6	−1.18410	−0.592051	−	0.805901i	$-0.701682\pi$
$433$	−4.61965e6	−1.18410	−0.592051	+	0.805901i	$0.701682\pi$
$434$	2.79773e6	0.712987
$435$	−290983.	−0.0737301
$436$	444393.	0.111957
$437$	8.08467e6	2.02516
$438$	781915.	0.194749
$439$	1.53118e6	0.379197	0.189599	−	0.981862i	$-0.439281\pi$
$439$	1.53118e6	0.379197	0.189599	+	0.981862i	$0.439281\pi$
$440$	322127.	0.0793223
$441$	1.03806e6	0.254171
$442$	−267809.	−0.0652033
$443$	−6.66069e6	−1.61254	−0.806269	−	0.591550i	$-0.798516\pi$
$443$	−6.66069e6	−1.61254	−0.806269	+	0.591550i	$0.798516\pi$
$444$	1.05782e6	0.254656
$445$	−1.17808e6	−0.282016
$446$	4.94624e6	1.17744
$447$	−1.01107e6	−0.239339
$448$	704971.	0.165950
$449$	6.32105e6	1.47970	0.739849	−	0.672773i	$-0.234897\pi$
$449$	6.32105e6	1.47970	0.739849	+	0.672773i	$0.234897\pi$
$450$	−977349.	−0.227519
$451$	7.88059e6	1.82439
$452$	−736238.	−0.169501
$453$	1.95611e6	0.447865
$454$	−211095.	−0.0480660
$455$	1.93314e6	0.437758
$456$	−1.66063e6	−0.373990
$457$	2.38220e6	0.533566	0.266783	−	0.963757i	$-0.414039\pi$
$457$	2.38220e6	0.533566	0.266783	+	0.963757i	$0.414039\pi$
$458$	2.84432e6	0.633600
$459$	−45262.5	−0.0100278
$460$	−467336.	−0.102976
$461$	−3.96018e6	−0.867885	−0.433943	−	0.900940i	$-0.642878\pi$
$461$	−3.96018e6	−0.867885	−0.433943	+	0.900940i	$0.642878\pi$
$462$	2.99408e6	0.652618
$463$	4.94681e6	1.07244	0.536219	−	0.844079i	$-0.319852\pi$
$463$	4.94681e6	1.07244	0.536219	+	0.844079i	$0.319852\pi$
$464$	−794637.	−0.171346
$465$	380955.	0.0817036
$466$	−2.99920e6	−0.639795
$467$	−9.35244e6	−1.98442	−0.992208	−	0.124596i	$-0.960237\pi$
$467$	−9.35244e6	−1.98442	−0.992208	+	0.124596i	$0.960237\pi$
$468$	1.39753e6	0.294948
$469$	−1.50965e6	−0.316916
$470$	−653606.	−0.136481
$471$	247607.	0.0514293
$472$	222784.	0.0460287
$473$	−1.21198e6	−0.249082
$474$	37683.2	0.00770374
$475$	8.69669e6	1.76856
$476$	−170979.	−0.0345879
$477$	−1.12254e6	−0.225895
$478$	−409536.	−0.0819828
$479$	−1.89798e6	−0.377967	−0.188984	−	0.981980i	$-0.560519\pi$
$479$	−1.89798e6	−0.377967	−0.188984	+	0.981980i	$0.560519\pi$
$480$	95992.9	0.0190167
$481$	7.92143e6	1.56114
$482$	129138.	0.0253184
$483$	−4.34377e6	−0.847225
$484$	1.15930e6	0.224949
$485$	−1.23301e6	−0.238019
$486$	236196.	0.0453609
$487$	6.12176e6	1.16964	0.584822	−	0.811162i	$-0.301164\pi$
$487$	6.12176e6	1.16964	0.584822	+	0.811162i	$0.301164\pi$
$488$	3.16877e6	0.602339
$489$	−5.54418e6	−1.04849
$490$	533942.	0.100462
$491$	5.89663e6	1.10383	0.551913	−	0.833902i	$-0.313898\pi$
$491$	5.89663e6	1.10383	0.551913	+	0.833902i	$0.313898\pi$
$492$	2.34839e6	0.437379
$493$	192726.	0.0357127
$494$	−1.24355e7	−2.29270
$495$	407692.	0.0747857
$496$	1.04034e6	0.189876
$497$	1.02010e7	1.85247
$498$	−2.05781e6	−0.371819
$499$	−2.15522e6	−0.387472	−0.193736	−	0.981054i	$-0.562060\pi$
$499$	−2.15522e6	−0.387472	−0.193736	+	0.981054i	$0.562060\pi$
$500$	−1.02351e6	−0.183091
$501$	306908.	0.0546279
$502$	−4.39074e6	−0.777640
$503$	−1.85411e6	−0.326750	−0.163375	−	0.986564i	$-0.552238\pi$
$503$	−1.85411e6	−0.326750	−0.163375	+	0.986564i	$0.552238\pi$
$504$	892229.	0.156459
$505$	−915666.	−0.159775
$506$	−5.42030e6	−0.941124
$507$	7.12366e6	1.23079
$508$	5.58534e6	0.960264
$509$	592566.	0.101378	0.0506888	−	0.998714i	$-0.483858\pi$
$509$	592566.	0.101378	0.0506888	+	0.998714i	$0.483858\pi$
$510$	−23281.4	−0.00396355
$511$	3.73825e6	0.633309
$512$	262144.	0.0441942
$513$	−2.10173e6	−0.352601
$514$	−4.11093e6	−0.686330
$515$	−1.48171e6	−0.246175
$516$	−361167.	−0.0597150
$517$	−7.58071e6	−1.24734
$518$	5.05732e6	0.828125
$519$	1.77349e6	0.289008
$520$	718838.	0.116580
$521$	6.15353e6	0.993185	0.496593	−	0.867984i	$-0.334584\pi$
$521$	6.15353e6	0.993185	0.496593	+	0.867984i	$0.334584\pi$
$522$	−1.00571e6	−0.161547
$523$	5.07329e6	0.811028	0.405514	−	0.914089i	$-0.367093\pi$
$523$	5.07329e6	0.811028	0.405514	+	0.914089i	$0.367093\pi$
$524$	1.19435e6	0.190021
$525$	−4.67260e6	−0.739878
$526$	4.01620e6	0.632924
$527$	−252317.	−0.0395748
$528$	1.11335e6	0.173799
$529$	1.42733e6	0.221761
$530$	−577396.	−0.0892861
$531$	281961.	0.0433963
$532$	−7.93927e6	−1.21619
$533$	1.75858e7	2.68130
$534$	−4.07174e6	−0.617912
$535$	1.71798e6	0.259498
$536$	−561364.	−0.0843980
$537$	−5.38644e6	−0.806058
$538$	−6552.87	−0.000976059 0
$539$	6.19281e6	0.918155
$540$	121491.	0.0179291
$541$	2.51845e6	0.369948	0.184974	−	0.982743i	$-0.440780\pi$
$541$	2.51845e6	0.369948	0.184974	+	0.982743i	$0.440780\pi$
$542$	−1.67301e6	−0.244624
$543$	2.42857e6	0.353469
$544$	−63578.6	−0.00921115
$545$	289297.	0.0417207
$546$	6.68141e6	0.959150
$547$	−1.32195e7	−1.88906	−0.944531	−	0.328423i	$-0.893483\pi$
$547$	−1.32195e7	−1.88906	−0.944531	+	0.328423i	$0.893483\pi$
$548$	745504.	0.106047
$549$	4.01047e6	0.567891
$550$	−5.83062e6	−0.821880
$551$	8.94908e6	1.25574
$552$	−1.61523e6	−0.225625
$553$	180159.	0.0250521
$554$	−5.97457e6	−0.827051
$555$	688633.	0.0948977
$556$	−4.87414e6	−0.668669
$557$	4.95748e6	0.677053	0.338527	−	0.940957i	$-0.390072\pi$
$557$	4.95748e6	0.677053	0.338527	+	0.940957i	$0.390072\pi$
$558$	1.31668e6	0.179017
$559$	−2.70458e6	−0.366075
$560$	458931.	0.0618412
$561$	−270025.	−0.0362240
$562$	1.15779e6	0.154628
$563$	1.26411e7	1.68079	0.840395	−	0.541974i	$-0.182323\pi$
$563$	1.26411e7	1.68079	0.840395	+	0.541974i	$0.182323\pi$
$564$	−2.25903e6	−0.299037
$565$	−479286.	−0.0631646
$566$	2.15400e6	0.282621
$567$	1.12923e6	0.147511
$568$	3.79325e6	0.493334
$569$	−4.80990e6	−0.622810	−0.311405	−	0.950277i	$-0.600800\pi$
$569$	−4.80990e6	−0.622810	−0.311405	+	0.950277i	$0.600800\pi$
$570$	−1.08106e6	−0.139367
$571$	−1.13155e7	−1.45239	−0.726197	−	0.687487i	$-0.758714\pi$
$571$	−1.13155e7	−1.45239	−0.726197	+	0.687487i	$0.758714\pi$
$572$	8.33729e6	1.06545
$573$	1.34197e6	0.170748
$574$	1.12274e7	1.42233
$575$	8.45897e6	1.06696
$576$	331776.	0.0416667
$577$	1.04770e6	0.131007	0.0655037	−	0.997852i	$-0.479135\pi$
$577$	1.04770e6	0.131007	0.0655037	+	0.997852i	$0.479135\pi$
$578$	−5.66401e6	−0.705187
$579$	−2.20226e6	−0.273005
$580$	−517303.	−0.0638521
$581$	−9.83816e6	−1.20913
$582$	−4.26159e6	−0.521512
$583$	−6.69680e6	−0.816011
$584$	1.39007e6	0.168657
$585$	909779.	0.109912
$586$	1.82627e6	0.219695
$587$	489874.	0.0586798	0.0293399	−	0.999569i	$-0.490659\pi$
$587$	489874.	0.0586798	0.0293399	+	0.999569i	$0.490659\pi$
$588$	1.84544e6	0.220118
$589$	−1.17161e7	−1.39154
$590$	145031.	0.0171526
$591$	182398.	0.0214808
$592$	1.88057e6	0.220539
$593$	1.68777e7	1.97095	0.985476	−	0.169815i	$-0.0543170\pi$
$593$	1.68777e7	1.97095	0.985476	+	0.169815i	$0.0543170\pi$
$594$	1.40909e6	0.163860
$595$	−111306.	−0.0128892
$596$	−1.79746e6	−0.207273
$597$	−605815.	−0.0695672
$598$	−1.20956e7	−1.38317
$599$	−1.02133e7	−1.16305	−0.581523	−	0.813530i	$-0.697543\pi$
$599$	−1.02133e7	−1.16305	−0.581523	+	0.813530i	$0.697543\pi$
$600$	−1.73751e6	−0.197038
$601$	9.95708e6	1.12447	0.562233	−	0.826979i	$-0.309943\pi$
$601$	9.95708e6	1.12447	0.562233	+	0.826979i	$0.309943\pi$
$602$	−1.72670e6	−0.194189
$603$	−710476.	−0.0795712
$604$	3.47752e6	0.387862
$605$	754698.	0.0838272
$606$	−3.16478e6	−0.350075
$607$	−1.06118e7	−1.16901	−0.584504	−	0.811391i	$-0.698711\pi$
$607$	−1.06118e7	−1.16901	−0.584504	+	0.811391i	$0.698711\pi$
$608$	−2.95222e6	−0.323885
$609$	−4.80820e6	−0.525339
$610$	2.06285e6	0.224462
$611$	−1.69166e7	−1.83321
$612$	−80466.7	−0.00868435
$613$	8.42572e6	0.905641	0.452820	−	0.891602i	$-0.350418\pi$
$613$	8.42572e6	0.905641	0.452820	+	0.891602i	$0.350418\pi$
$614$	9.15296e6	0.979807
$615$	1.52879e6	0.162989
$616$	5.32282e6	0.565184
$617$	1.61311e7	1.70589	0.852945	−	0.522000i	$-0.174814\pi$
$617$	1.61311e7	1.70589	0.852945	+	0.522000i	$0.174814\pi$
$618$	−5.12116e6	−0.539383
$619$	6.92102e6	0.726012	0.363006	−	0.931787i	$-0.381751\pi$
$619$	6.92102e6	0.726012	0.363006	+	0.931787i	$0.381751\pi$
$620$	677253.	0.0707574
$621$	−2.04428e6	−0.212721
$622$	−1.29756e7	−1.34478
$623$	−1.94665e7	−2.00941
$624$	2.48449e6	0.255432
$625$	8.76029e6	0.897054
$626$	−3.07201e6	−0.313319
$627$	−1.25384e7	−1.27372
$628$	440190.	0.0445391
$629$	−456100.	−0.0459657
$630$	580835.	0.0583044
$631$	−1.61031e7	−1.61004	−0.805020	−	0.593248i	$-0.797845\pi$
$631$	−1.61031e7	−1.61004	−0.805020	+	0.593248i	$0.797845\pi$
$632$	66992.3	0.00667164
$633$	−5.32795e6	−0.528507
$634$	−1.01666e7	−1.00451
$635$	3.63602e6	0.357843
$636$	−1.99563e6	−0.195631
$637$	1.38195e7	1.34941
$638$	−5.99983e6	−0.583563
$639$	4.80084e6	0.465120
$640$	170654.	0.0164690
$641$	990127.	0.0951801	0.0475900	−	0.998867i	$-0.484846\pi$
$641$	990127.	0.0951801	0.0475900	+	0.998867i	$0.484846\pi$
$642$	5.93778e6	0.568573
$643$	−873445.	−0.0833121	−0.0416560	−	0.999132i	$-0.513263\pi$
$643$	−873445.	−0.0833121	−0.0416560	+	0.999132i	$0.513263\pi$
$644$	−7.72225e6	−0.733718
$645$	−235117.	−0.0222528
$646$	716012.	0.0675055
$647$	−1.85825e7	−1.74519	−0.872597	−	0.488441i	$-0.837566\pi$
$647$	−1.85825e7	−1.74519	−0.872597	+	0.488441i	$0.837566\pi$
$648$	419904.	0.0392837
$649$	1.68211e6	0.156763
$650$	−1.30113e7	−1.20791
$651$	6.29490e6	0.582152
$652$	−9.85632e6	−0.908021
$653$	−5.32895e6	−0.489056	−0.244528	−	0.969642i	$-0.578633\pi$
$653$	−5.32895e6	−0.489056	−0.244528	+	0.969642i	$0.578633\pi$
$654$	999883.	0.0914124
$655$	777511.	0.0708114
$656$	4.17492e6	0.378781
$657$	1.75931e6	0.159012
$658$	−1.08002e7	−0.972447
$659$	−1.65290e7	−1.48263	−0.741317	−	0.671155i	$-0.765798\pi$
$659$	−1.65290e7	−1.48263	−0.741317	+	0.671155i	$0.765798\pi$
$660$	724785.	0.0647664
$661$	8.82173e6	0.785327	0.392663	−	0.919682i	$-0.371554\pi$
$661$	8.82173e6	0.785327	0.392663	+	0.919682i	$0.371554\pi$
$662$	3.00040e6	0.266094
$663$	−602571.	−0.0532383
$664$	−3.65833e6	−0.322005
$665$	−5.16841e6	−0.453214
$666$	2.38009e6	0.207926
$667$	8.70445e6	0.757577
$668$	545615.	0.0473091
$669$	1.11290e7	0.961373
$670$	−365444.	−0.0314510
$671$	2.39255e7	2.05142
$672$	1.58618e6	0.135497
$673$	−1.35962e7	−1.15713	−0.578564	−	0.815637i	$-0.696387\pi$
$673$	−1.35962e7	−1.15713	−0.578564	+	0.815637i	$0.696387\pi$
$674$	1.28314e7	1.08799
$675$	−2.19904e6	−0.185769
$676$	1.26643e7	1.06589
$677$	5.55500e6	0.465814	0.232907	−	0.972499i	$-0.425176\pi$
$677$	5.55500e6	0.465814	0.232907	+	0.972499i	$0.425176\pi$
$678$	−1.65654e6	−0.138397
$679$	−2.03742e7	−1.69592
$680$	−41389.2	−0.00343254
$681$	−474964.	−0.0392458
$682$	7.85498e6	0.646672
$683$	5.35587e6	0.439318	0.219659	−	0.975577i	$-0.429506\pi$
$683$	5.35587e6	0.439318	0.219659	+	0.975577i	$0.429506\pi$
$684$	−3.73641e6	−0.305361
$685$	485318.	0.0395185
$686$	−2.74790e6	−0.222942
$687$	6.39973e6	0.517332
$688$	−642075.	−0.0517147
$689$	−1.49442e7	−1.19929
$690$	−1.05151e6	−0.0840793
$691$	−1.28658e7	−1.02504	−0.512520	−	0.858676i	$-0.671288\pi$
$691$	−1.28658e7	−1.02504	−0.512520	+	0.858676i	$0.671288\pi$
$692$	3.15286e6	0.250288
$693$	6.73669e6	0.532860
$694$	−1.21937e7	−0.961030
$695$	−3.17303e6	−0.249180
$696$	−1.78793e6	−0.139903
$697$	−1.01256e6	−0.0789473
$698$	3.31458e6	0.257508
$699$	−6.74821e6	−0.522391
$700$	−8.30684e6	−0.640753
$701$	−1.32394e7	−1.01759	−0.508794	−	0.860888i	$-0.669908\pi$
$701$	−1.32394e7	−1.01759	−0.508794	+	0.860888i	$0.669908\pi$
$702$	3.14443e6	0.240824
$703$	−2.11787e7	−1.61626
$704$	1.97929e6	0.150515
$705$	−1.47061e6	−0.111436
$706$	−2.60697e6	−0.196845
$707$	−1.51305e7	−1.13842
$708$	501264.	0.0375823
$709$	−5.60098e6	−0.418454	−0.209227	−	0.977867i	$-0.567095\pi$
$709$	−5.60098e6	−0.418454	−0.209227	+	0.977867i	$0.567095\pi$
$710$	2.46938e6	0.183841
$711$	84787.2	0.00629008
$712$	−7.23865e6	−0.535128
$713$	−1.13959e7	−0.839506
$714$	−384702.	−0.0282409
$715$	5.42752e6	0.397042
$716$	−9.57590e6	−0.698067
$717$	−921457.	−0.0669387
$718$	−2.00677e6	−0.145274
$719$	2.41581e7	1.74277	0.871387	−	0.490596i	$-0.163221\pi$
$719$	2.41581e7	1.74277	0.871387	+	0.490596i	$0.163221\pi$
$720$	215984.	0.0155271
$721$	−2.44837e7	−1.75404
$722$	2.33431e7	1.66654
$723$	290561.	0.0206724
$724$	4.31746e6	0.306113
$725$	9.36340e6	0.661589
$726$	2.60843e6	0.183670
$727$	−1.54911e7	−1.08704	−0.543521	−	0.839396i	$-0.682909\pi$
$727$	−1.54911e7	−1.08704	−0.543521	+	0.839396i	$0.682909\pi$
$728$	1.18781e7	0.830649
$729$	531441.	0.0370370
$730$	904927.	0.0628501
$731$	155724.	0.0107786
$732$	7.12973e6	0.491808
$733$	4.68739e6	0.322234	0.161117	−	0.986935i	$-0.448490\pi$
$733$	4.68739e6	0.322234	0.161117	+	0.986935i	$0.448490\pi$
$734$	1.31794e7	0.902935
$735$	1.20137e6	0.0820272
$736$	−2.87153e6	−0.195397
$737$	−4.23852e6	−0.287439
$738$	5.28389e6	0.357119
$739$	1.89181e7	1.27428	0.637142	−	0.770747i	$-0.280117\pi$
$739$	1.89181e7	1.27428	0.637142	+	0.770747i	$0.280117\pi$
$740$	1.22424e6	0.0821838
$741$	−2.79799e7	−1.87198
$742$	−9.54087e6	−0.636178
$743$	−1.42791e6	−0.0948919	−0.0474459	−	0.998874i	$-0.515108\pi$
$743$	−1.42791e6	−0.0948919	−0.0474459	+	0.998874i	$0.515108\pi$
$744$	2.34076e6	0.155033
$745$	−1.17013e6	−0.0772405
$746$	1.79449e7	1.18058
$747$	−4.63007e6	−0.303589
$748$	−480044.	−0.0313709
$749$	2.83879e7	1.84896
$750$	−2.30289e6	−0.149493
$751$	−2.59496e7	−1.67892	−0.839462	−	0.543418i	$-0.817130\pi$
$751$	−2.59496e7	−1.67892	−0.839462	+	0.543418i	$0.817130\pi$
$752$	−4.01605e6	−0.258973
$753$	−9.87917e6	−0.634940
$754$	−1.33889e7	−0.857660
$755$	2.26384e6	0.144537
$756$	2.00751e6	0.127748
$757$	−1.21677e6	−0.0771737	−0.0385868	−	0.999255i	$-0.512286\pi$
$757$	−1.21677e6	−0.0771737	−0.0385868	+	0.999255i	$0.512286\pi$
$758$	9.49258e6	0.600083
$759$	−1.21957e7	−0.768424
$760$	−1.92188e6	−0.120696
$761$	−2.14369e7	−1.34184	−0.670920	−	0.741530i	$-0.734100\pi$
$761$	−2.14369e7	−1.34184	−0.670920	+	0.741530i	$0.734100\pi$
$762$	1.25670e7	0.784052
$763$	4.78033e6	0.297267
$764$	2.38573e6	0.147873
$765$	−52383.3	−0.00323623
$766$	−4.89063e6	−0.301157
$767$	3.75369e6	0.230393
$768$	589824.	0.0360844
$769$	1.60523e7	0.978860	0.489430	−	0.872043i	$-0.337205\pi$
$769$	1.60523e7	0.978860	0.489430	+	0.872043i	$0.337205\pi$
$770$	3.46512e6	0.210616
$771$	−9.24960e6	−0.560386
$772$	−3.91512e6	−0.236430
$773$	−7.79439e6	−0.469173	−0.234587	−	0.972095i	$-0.575374\pi$
$773$	−7.79439e6	−0.469173	−0.234587	+	0.972095i	$0.575374\pi$
$774$	−812626.	−0.0487571
$775$	−1.22586e7	−0.733137
$776$	−7.57617e6	−0.451643
$777$	1.13790e7	0.676161
$778$	−5.37770e6	−0.318528
$779$	−4.70173e7	−2.77597
$780$	1.61739e6	0.0951869
$781$	2.86406e7	1.68018
$782$	696440.	0.0407255
$783$	−2.26285e6	−0.131902
$784$	3.28078e6	0.190628
$785$	286561.	0.0165975
$786$	2.68728e6	0.155151
$787$	−8.19388e6	−0.471577	−0.235789	−	0.971804i	$-0.575767\pi$
$787$	−8.19388e6	−0.471577	−0.235789	+	0.971804i	$0.575767\pi$
$788$	324263.	0.0186029
$789$	9.03646e6	0.516780
$790$	43611.6	0.00248619
$791$	−7.91972e6	−0.450058
$792$	2.50504e6	0.141907
$793$	5.33906e7	3.01496
$794$	−1.14682e7	−0.645572
$795$	−1.29914e6	−0.0729018
$796$	−1.07700e6	−0.0602469
$797$	−1.88920e7	−1.05349	−0.526747	−	0.850022i	$-0.676588\pi$
$797$	−1.88920e7	−1.05349	−0.526747	+	0.850022i	$0.676588\pi$
$798$	−1.78634e7	−0.993015
$799$	974026.	0.0539764
$800$	−3.08891e6	−0.170640
$801$	−9.16141e6	−0.504523
$802$	−2.20540e7	−1.21074
$803$	1.04956e7	0.574405
$804$	−1.26307e6	−0.0689107
$805$	−5.02713e6	−0.273420
$806$	1.75287e7	0.950412
$807$	−14744.0	−0.000796949 0
$808$	−5.62627e6	−0.303174
$809$	−9.71745e6	−0.522012	−0.261006	−	0.965337i	$-0.584054\pi$
$809$	−9.71745e6	−0.522012	−0.261006	+	0.965337i	$0.584054\pi$
$810$	273355.	0.0146391
$811$	−2.09139e7	−1.11656	−0.558280	−	0.829653i	$-0.688538\pi$
$811$	−2.09139e7	−1.11656	−0.558280	+	0.829653i	$0.688538\pi$
$812$	−8.54791e6	−0.454957
$813$	−3.76426e6	−0.199735
$814$	1.41991e7	0.751101
$815$	−6.41640e6	−0.338374
$816$	−143052.	−0.00752087
$817$	7.23094e6	0.379001
$818$	−7.33038e6	−0.383039
$819$	1.50332e7	0.783143
$820$	2.71785e6	0.141153
$821$	3.20789e7	1.66097	0.830485	−	0.557042i	$-0.188064\pi$
$821$	3.20789e7	1.66097	0.830485	+	0.557042i	$0.188064\pi$
$822$	1.67738e6	0.0865871
$823$	2.96941e6	0.152817	0.0764083	−	0.997077i	$-0.475655\pi$
$823$	2.96941e6	0.152817	0.0764083	+	0.997077i	$0.475655\pi$
$824$	−9.10428e6	−0.467119
$825$	−1.31189e7	−0.671062
$826$	2.39649e6	0.122215
$827$	3.76525e7	1.91439	0.957194	−	0.289448i	$-0.0934716\pi$
$827$	3.76525e7	1.91439	0.957194	+	0.289448i	$0.0934716\pi$
$828$	−3.63427e6	−0.184222
$829$	2.72751e6	0.137841	0.0689207	−	0.997622i	$-0.478044\pi$
$829$	2.72751e6	0.137841	0.0689207	+	0.997622i	$0.478044\pi$
$830$	−2.38155e6	−0.119995
$831$	−1.34428e7	−0.675285
$832$	4.41687e6	0.221211
$833$	−795698.	−0.0397316
$834$	−1.09668e7	−0.545966
$835$	355191.	0.0176298
$836$	−2.22905e7	−1.10307
$837$	2.96253e6	0.146167
$838$	4.00334e6	0.196930
$839$	1.55659e7	0.763430	0.381715	−	0.924280i	$-0.375334\pi$
$839$	1.55659e7	0.763430	0.381715	+	0.924280i	$0.375334\pi$
$840$	1.03260e6	0.0504931
$841$	−1.08760e7	−0.530249
$842$	1.90616e7	0.926574
$843$	2.60502e6	0.126253
$844$	−9.47190e6	−0.457700
$845$	8.24437e6	0.397206
$846$	−5.08282e6	−0.244162
$847$	1.24706e7	0.597282
$848$	−3.54778e6	−0.169421
$849$	4.84650e6	0.230759
$850$	749162.	0.0355654
$851$	−2.05997e7	−0.975075
$852$	8.53482e6	0.402806
$853$	−4.49750e6	−0.211640	−0.105820	−	0.994385i	$-0.533747\pi$
$853$	−4.49750e6	−0.211640	−0.105820	+	0.994385i	$0.533747\pi$
$854$	3.40864e7	1.59933
$855$	−2.43238e6	−0.113793
$856$	1.05561e7	0.492399
$857$	1.81439e7	0.843877	0.421938	−	0.906624i	$-0.361350\pi$
$857$	1.81439e7	0.843877	0.421938	+	0.906624i	$0.361350\pi$
$858$	1.87589e7	0.869940
$859$	3.72027e7	1.72025	0.860125	−	0.510084i	$-0.170386\pi$
$859$	3.72027e7	1.72025	0.860125	+	0.510084i	$0.170386\pi$
$860$	−417986.	−0.0192715
$861$	2.52617e7	1.16133
$862$	−1.74327e7	−0.799090
$863$	2.77450e7	1.26811	0.634057	−	0.773286i	$-0.281389\pi$
$863$	2.77450e7	1.26811	0.634057	+	0.773286i	$0.281389\pi$
$864$	746496.	0.0340207
$865$	2.05249e6	0.0932699
$866$	−1.84786e7	−0.837286
$867$	−1.27440e7	−0.575783
$868$	1.11909e7	0.504158
$869$	505819.	0.0227220
$870$	−1.16393e6	−0.0521350
$871$	−9.45843e6	−0.422448
$872$	1.77757e6	0.0791654
$873$	−9.58859e6	−0.425813
$874$	3.23387e7	1.43200
$875$	−1.10099e7	−0.486141
$876$	3.12766e6	0.137708
$877$	3.53301e7	1.55112	0.775561	−	0.631272i	$-0.217467\pi$
$877$	3.53301e7	1.55112	0.775561	+	0.631272i	$0.217467\pi$
$878$	6.12472e6	0.268133
$879$	4.10910e6	0.179380
$880$	1.28851e6	0.0560893
$881$	−1.71386e7	−0.743934	−0.371967	−	0.928246i	$-0.621317\pi$
$881$	−1.71386e7	−0.743934	−0.371967	+	0.928246i	$0.621317\pi$
$882$	4.15224e6	0.179726
$883$	1.39596e7	0.602518	0.301259	−	0.953542i	$-0.402593\pi$
$883$	1.39596e7	0.602518	0.301259	+	0.953542i	$0.402593\pi$
$884$	−1.07124e6	−0.0461057
$885$	326319.	0.0140051
$886$	−2.66427e7	−1.14024
$887$	7.89342e6	0.336865	0.168433	−	0.985713i	$-0.446129\pi$
$887$	7.89342e6	0.336865	0.168433	+	0.985713i	$0.446129\pi$
$888$	4.23128e6	0.180069
$889$	6.00815e7	2.54969
$890$	−4.71231e6	−0.199415
$891$	3.17045e6	0.133791
$892$	1.97849e7	0.832574
$893$	4.52282e7	1.89793
$894$	−4.04429e6	−0.169238
$895$	−6.23385e6	−0.260135
$896$	2.81988e6	0.117344
$897$	−2.72151e7	−1.12935
$898$	2.52842e7	1.04630
$899$	−1.26143e7	−0.520552
$900$	−3.90940e6	−0.160880
$901$	860455.	0.0353115
$902$	3.15224e7	1.29004
$903$	−3.88507e6	−0.158555
$904$	−2.94495e6	−0.119855
$905$	2.81064e6	0.114073
$906$	7.82442e6	0.316688
$907$	−4.02294e7	−1.62377	−0.811887	−	0.583814i	$-0.801560\pi$
$907$	−4.02294e7	−1.62377	−0.811887	+	0.583814i	$0.801560\pi$
$908$	−844380.	−0.0339878
$909$	−7.12075e6	−0.285835
$910$	7.73254e6	0.309541
$911$	1.76236e7	0.703555	0.351778	−	0.936084i	$-0.385577\pi$
$911$	1.76236e7	0.703555	0.351778	+	0.936084i	$0.385577\pi$
$912$	−6.64251e6	−0.264451
$913$	−2.76219e7	−1.09667
$914$	9.52881e6	0.377288
$915$	4.64140e6	0.183272
$916$	1.13773e7	0.448023
$917$	1.28476e7	0.504542
$918$	−181050.	−0.00709074
$919$	3.74427e7	1.46244	0.731220	−	0.682142i	$-0.238951\pi$
$919$	3.74427e7	1.46244	0.731220	+	0.682142i	$0.238951\pi$
$920$	−1.86934e6	−0.0728148
$921$	2.05942e7	0.800009
$922$	−1.58407e7	−0.613688
$923$	6.39126e7	2.46935
$924$	1.19763e7	0.461471
$925$	−2.21592e7	−0.851529
$926$	1.97872e7	0.758329
$927$	−1.15226e7	−0.440404
$928$	−3.17855e6	−0.121160
$929$	2.67438e7	1.01668	0.508339	−	0.861157i	$-0.330260\pi$
$929$	2.67438e7	1.01668	0.508339	+	0.861157i	$0.330260\pi$
$930$	1.52382e6	0.0577732
$931$	−3.69477e7	−1.39705
$932$	−1.19968e7	−0.452404
$933$	−2.91950e7	−1.09801
$934$	−3.74097e7	−1.40319
$935$	−312506.	−0.0116904
$936$	5.59010e6	0.208559
$937$	1.31471e7	0.489193	0.244596	−	0.969625i	$-0.421345\pi$
$937$	1.31471e7	0.489193	0.244596	+	0.969625i	$0.421345\pi$
$938$	−6.03859e6	−0.224093
$939$	−6.91201e6	−0.255824
$940$	−2.61442e6	−0.0965065
$941$	2.75043e7	1.01257	0.506287	−	0.862365i	$-0.331018\pi$
$941$	2.75043e7	1.01257	0.506287	+	0.862365i	$0.331018\pi$
$942$	990428.	0.0363660
$943$	−4.57321e7	−1.67472
$944$	891136.	0.0325472
$945$	1.30688e6	0.0476053
$946$	−4.84792e6	−0.176128
$947$	−5.22540e7	−1.89341	−0.946705	−	0.322103i	$-0.895610\pi$
$947$	−5.22540e7	−1.89341	−0.946705	+	0.322103i	$0.895610\pi$
$948$	150733.	0.00544737
$949$	2.34213e7	0.844201
$950$	3.47868e7	1.25056
$951$	−2.28750e7	−0.820180
$952$	−683915.	−0.0244574
$953$	−115833.	−0.00413141	−0.00206570	−	0.999998i	$-0.500658\pi$
$953$	−115833.	−0.00413141	−0.00206570	+	0.999998i	$0.500658\pi$
$954$	−4.49016e6	−0.159732
$955$	1.55309e6	0.0551047
$956$	−1.63815e6	−0.0579706
$957$	−1.34996e7	−0.476477
$958$	−7.59194e6	−0.267263
$959$	8.01939e6	0.281575
$960$	383971.	0.0134469
$961$	−1.21145e7	−0.423152
$962$	3.16857e7	1.10389
$963$	1.33600e7	0.464238
$964$	516552.	0.0179028
$965$	−2.54872e6	−0.0881056
$966$	−1.73751e7	−0.599078
$967$	773505.	0.0266009	0.0133005	−	0.999912i	$-0.495766\pi$
$967$	773505.	0.0266009	0.0133005	+	0.999912i	$0.495766\pi$
$968$	4.63721e6	0.159063
$969$	1.61103e6	0.0551180
$970$	−4.93203e6	−0.168305
$971$	−2.68625e7	−0.914321	−0.457161	−	0.889384i	$-0.651134\pi$
$971$	−2.68625e7	−0.914321	−0.457161	+	0.889384i	$0.651134\pi$
$972$	944784.	0.0320750
$973$	−5.24312e7	−1.77545
$974$	2.44870e7	0.827063
$975$	−2.92753e7	−0.986257
$976$	1.26751e7	0.425918
$977$	9.24308e6	0.309799	0.154900	−	0.987930i	$-0.450495\pi$
$977$	9.24308e6	0.309799	0.154900	+	0.987930i	$0.450495\pi$
$978$	−2.21767e7	−0.741396
$979$	−5.46547e7	−1.82251
$980$	2.13577e6	0.0710377
$981$	2.24974e6	0.0746379
$982$	2.35865e7	0.780522
$983$	−3.03918e7	−1.00317	−0.501583	−	0.865110i	$-0.667249\pi$
$983$	−3.03918e7	−1.00317	−0.501583	+	0.865110i	$0.667249\pi$
$984$	9.39357e6	0.309274
$985$	211093.	0.00693239
$986$	770903.	0.0252527
$987$	−2.43004e7	−0.794000
$988$	−4.97421e7	−1.62118
$989$	7.03328e6	0.228648
$990$	1.63077e6	0.0528815
$991$	2.08155e7	0.673291	0.336645	−	0.941632i	$-0.390708\pi$
$991$	2.08155e7	0.673291	0.336645	+	0.941632i	$0.390708\pi$
$992$	4.16135e6	0.134263
$993$	6.75090e6	0.217265
$994$	4.08041e7	1.30990
$995$	−701123.	−0.0224510
$996$	−8.23124e6	−0.262916
$997$	2.74896e7	0.875851	0.437925	−	0.899011i	$-0.355713\pi$
$997$	2.74896e7	0.875851	0.437925	+	0.899011i	$0.355713\pi$
$998$	−8.62088e6	−0.273984
$999$	5.35521e6	0.169771

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.a.i.1.4	✓	8
3.2	odd	2		1062.6.a.k.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.a.i.1.4	✓	8	1.1	even	1	trivial
1062.6.a.k.1.5		8	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)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +10.4159 q^{5} +36.0000 q^{6} +172.112 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +10.4159 q^{5} +36.0000 q^{6} +172.112 q^{7} +64.0000 q^{8} +81.0000 q^{9} +41.6636 q^{10} +483.226 q^{11} +144.000 q^{12} +1078.34 q^{13} +688.448 q^{14} +93.7430 q^{15} +256.000 q^{16} -62.0885 q^{17} +324.000 q^{18} -2883.03 q^{19} +166.654 q^{20} +1549.01 q^{21} +1932.90 q^{22} -2804.22 q^{23} +576.000 q^{24} -3016.51 q^{25} +4313.35 q^{26} +729.000 q^{27} +2753.79 q^{28} -3104.05 q^{29} +374.972 q^{30} +4063.82 q^{31} +1024.00 q^{32} +4349.03 q^{33} -248.354 q^{34} +1792.70 q^{35} +1296.00 q^{36} +7345.97 q^{37} -11532.1 q^{38} +9705.04 q^{39} +666.617 q^{40} +16308.3 q^{41} +6196.03 q^{42} -2508.10 q^{43} +7731.62 q^{44} +843.687 q^{45} -11216.9 q^{46} -15687.7 q^{47} +2304.00 q^{48} +12815.6 q^{49} -12066.0 q^{50} -558.796 q^{51} +17253.4 q^{52} -13858.5 q^{53} +2916.00 q^{54} +5033.23 q^{55} +11015.2 q^{56} -25947.3 q^{57} -12416.2 q^{58} +3481.00 q^{59} +1499.89 q^{60} +49512.0 q^{61} +16255.3 q^{62} +13941.1 q^{63} +4096.00 q^{64} +11231.8 q^{65} +17396.1 q^{66} -8771.31 q^{67} -993.416 q^{68} -25238.0 q^{69} +7170.80 q^{70} +59269.6 q^{71} +5184.00 q^{72} +21719.9 q^{73} +29383.9 q^{74} -27148.6 q^{75} -46128.5 q^{76} +83169.0 q^{77} +38820.1 q^{78} +1046.76 q^{79} +2666.47 q^{80} +6561.00 q^{81} +65233.2 q^{82} -57161.4 q^{83} +24784.1 q^{84} -646.707 q^{85} -10032.4 q^{86} -27936.5 q^{87} +30926.5 q^{88} -113104. q^{89} +3374.75 q^{90} +185595. q^{91} -44867.6 q^{92} +36574.4 q^{93} -62750.8 q^{94} -30029.4 q^{95} +9216.00 q^{96} -118378. q^{97} +51262.2 q^{98} +39141.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 32 q^{2} + 72 q^{3} + 128 q^{4} + 96 q^{5} + 288 q^{6} + 181 q^{7} + 512 q^{8} + 648 q^{9}+O(q^{10}) \) 8 * q + 32 * q^2 + 72 * q^3 + 128 * q^4 + 96 * q^5 + 288 * q^6 + 181 * q^7 + 512 * q^8 + 648 * q^9	\( 8 q + 32 q^{2} + 72 q^{3} + 128 q^{4} + 96 q^{5} + 288 q^{6} + 181 q^{7} + 512 q^{8} + 648 q^{9} + 384 q^{10} + 897 q^{11} + 1152 q^{12} + 1743 q^{13} + 724 q^{14} + 864 q^{15} + 2048 q^{16} + 1861 q^{17} + 2592 q^{18} + 3154 q^{19} + 1536 q^{20} + 1629 q^{21} + 3588 q^{22} + 3808 q^{23} + 4608 q^{24} + 11616 q^{25} + 6972 q^{26} + 5832 q^{27} + 2896 q^{28} + 328 q^{29} + 3456 q^{30} + 570 q^{31} + 8192 q^{32} + 8073 q^{33} + 7444 q^{34} + 36086 q^{35} + 10368 q^{36} + 12777 q^{37} + 12616 q^{38} + 15687 q^{39} + 6144 q^{40} + 20167 q^{41} + 6516 q^{42} + 24579 q^{43} + 14352 q^{44} + 7776 q^{45} + 15232 q^{46} + 20490 q^{47} + 18432 q^{48} + 59391 q^{49} + 46464 q^{50} + 16749 q^{51} + 27888 q^{52} + 13404 q^{53} + 23328 q^{54} - 34588 q^{55} + 11584 q^{56} + 28386 q^{57} + 1312 q^{58} + 27848 q^{59} + 13824 q^{60} + 94944 q^{61} + 2280 q^{62} + 14661 q^{63} + 32768 q^{64} + 54560 q^{65} + 32292 q^{66} + 28838 q^{67} + 29776 q^{68} + 34272 q^{69} + 144344 q^{70} + 14983 q^{71} + 41472 q^{72} + 69384 q^{73} + 51108 q^{74} + 104544 q^{75} + 50464 q^{76} - 22359 q^{77} + 62748 q^{78} - 49199 q^{79} + 24576 q^{80} + 52488 q^{81} + 80668 q^{82} + 3995 q^{83} + 26064 q^{84} - 142290 q^{85} + 98316 q^{86} + 2952 q^{87} + 57408 q^{88} + 28722 q^{89} + 31104 q^{90} + 20815 q^{91} + 60928 q^{92} + 5130 q^{93} + 81960 q^{94} + 208010 q^{95} + 73728 q^{96} + 204150 q^{97} + 237564 q^{98} + 72657 q^{99}+O(q^{100}) \) 8 * q + 32 * q^2 + 72 * q^3 + 128 * q^4 + 96 * q^5 + 288 * q^6 + 181 * q^7 + 512 * q^8 + 648 * q^9 + 384 * q^10 + 897 * q^11 + 1152 * q^12 + 1743 * q^13 + 724 * q^14 + 864 * q^15 + 2048 * q^16 + 1861 * q^17 + 2592 * q^18 + 3154 * q^19 + 1536 * q^20 + 1629 * q^21 + 3588 * q^22 + 3808 * q^23 + 4608 * q^24 + 11616 * q^25 + 6972 * q^26 + 5832 * q^27 + 2896 * q^28 + 328 * q^29 + 3456 * q^30 + 570 * q^31 + 8192 * q^32 + 8073 * q^33 + 7444 * q^34 + 36086 * q^35 + 10368 * q^36 + 12777 * q^37 + 12616 * q^38 + 15687 * q^39 + 6144 * q^40 + 20167 * q^41 + 6516 * q^42 + 24579 * q^43 + 14352 * q^44 + 7776 * q^45 + 15232 * q^46 + 20490 * q^47 + 18432 * q^48 + 59391 * q^49 + 46464 * q^50 + 16749 * q^51 + 27888 * q^52 + 13404 * q^53 + 23328 * q^54 - 34588 * q^55 + 11584 * q^56 + 28386 * q^57 + 1312 * q^58 + 27848 * q^59 + 13824 * q^60 + 94944 * q^61 + 2280 * q^62 + 14661 * q^63 + 32768 * q^64 + 54560 * q^65 + 32292 * q^66 + 28838 * q^67 + 29776 * q^68 + 34272 * q^69 + 144344 * q^70 + 14983 * q^71 + 41472 * q^72 + 69384 * q^73 + 51108 * q^74 + 104544 * q^75 + 50464 * q^76 - 22359 * q^77 + 62748 * q^78 - 49199 * q^79 + 24576 * q^80 + 52488 * q^81 + 80668 * q^82 + 3995 * q^83 + 26064 * q^84 - 142290 * q^85 + 98316 * q^86 + 2952 * q^87 + 57408 * q^88 + 28722 * q^89 + 31104 * q^90 + 20815 * q^91 + 60928 * q^92 + 5130 * q^93 + 81960 * q^94 + 208010 * q^95 + 73728 * q^96 + 204150 * q^97 + 237564 * q^98 + 72657 * q^99

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