LMFDB - Embedded newform 230.6.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,6,Mod(1,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, 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("230.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	230.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:	$36.8882785570$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 1168x^{4} - 2857x^{3} + 297325x^{2} + 680040x - 8930700 $ x^6 - x^5 - 1168x^4 - 2857x^3 + 297325x^2 + 680040x - 8930700
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$16.9517$ of defining polynomial
Character	$\chi$	$=$	230.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.00000 q^{2} -14.9517 q^{3} +16.0000 q^{4} +25.0000 q^{5} -59.8068 q^{6} +52.9827 q^{7} +64.0000 q^{8} -19.4468 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} -14.9517 q^{3} +16.0000 q^{4} +25.0000 q^{5} -59.8068 q^{6} +52.9827 q^{7} +64.0000 q^{8} -19.4468 q^{9} +100.000 q^{10} +300.681 q^{11} -239.227 q^{12} +55.9240 q^{13} +211.931 q^{14} -373.792 q^{15} +256.000 q^{16} -731.263 q^{17} -77.7874 q^{18} -543.758 q^{19} +400.000 q^{20} -792.181 q^{21} +1202.72 q^{22} +529.000 q^{23} -956.908 q^{24} +625.000 q^{25} +223.696 q^{26} +3924.02 q^{27} +847.723 q^{28} +6819.44 q^{29} -1495.17 q^{30} -4841.76 q^{31} +1024.00 q^{32} -4495.69 q^{33} -2925.05 q^{34} +1324.57 q^{35} -311.149 q^{36} +8983.83 q^{37} -2175.03 q^{38} -836.159 q^{39} +1600.00 q^{40} +14766.2 q^{41} -3168.72 q^{42} +23713.0 q^{43} +4810.89 q^{44} -486.171 q^{45} +2116.00 q^{46} -24259.8 q^{47} -3827.63 q^{48} -13999.8 q^{49} +2500.00 q^{50} +10933.6 q^{51} +894.784 q^{52} +19458.4 q^{53} +15696.1 q^{54} +7517.02 q^{55} +3390.89 q^{56} +8130.10 q^{57} +27277.8 q^{58} +28756.7 q^{59} -5980.68 q^{60} +31474.3 q^{61} -19367.0 q^{62} -1030.35 q^{63} +4096.00 q^{64} +1398.10 q^{65} -17982.7 q^{66} +9158.23 q^{67} -11700.2 q^{68} -7909.45 q^{69} +5298.27 q^{70} +75461.4 q^{71} -1244.60 q^{72} +25985.0 q^{73} +35935.3 q^{74} -9344.81 q^{75} -8700.12 q^{76} +15930.9 q^{77} -3344.63 q^{78} -29366.0 q^{79} +6400.00 q^{80} -53945.2 q^{81} +59064.7 q^{82} +50096.9 q^{83} -12674.9 q^{84} -18281.6 q^{85} +94851.8 q^{86} -101962. q^{87} +19243.6 q^{88} -44595.7 q^{89} -1944.68 q^{90} +2963.00 q^{91} +8464.00 q^{92} +72392.5 q^{93} -97039.3 q^{94} -13593.9 q^{95} -15310.5 q^{96} -55634.3 q^{97} -55999.4 q^{98} -5847.29 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 24 q^{2} + 11 q^{3} + 96 q^{4} + 150 q^{5} + 44 q^{6} + 366 q^{7} + 384 q^{8} + 899 q^{9}+O(q^{10}) $ 6 * q + 24 * q^2 + 11 * q^3 + 96 * q^4 + 150 * q^5 + 44 * q^6 + 366 * q^7 + 384 * q^8 + 899 * q^9	\( 6 q + 24 q^{2} + 11 q^{3} + 96 q^{4} + 150 q^{5} + 44 q^{6} + 366 q^{7} + 384 q^{8} + 899 q^{9} + 600 q^{10} + 151 q^{11} + 176 q^{12} + 463 q^{13} + 1464 q^{14} + 275 q^{15} + 1536 q^{16} + 644 q^{17} + 3596 q^{18} + 3431 q^{19} + 2400 q^{20} - 3846 q^{21} + 604 q^{22} + 3174 q^{23} + 704 q^{24} + 3750 q^{25} + 1852 q^{26} - 3364 q^{27} + 5856 q^{28} + 5973 q^{29} + 1100 q^{30} + 10262 q^{31} + 6144 q^{32} + 23025 q^{33} + 2576 q^{34} + 9150 q^{35} + 14384 q^{36} + 17207 q^{37} + 13724 q^{38} + 14136 q^{39} + 9600 q^{40} + 784 q^{41} - 15384 q^{42} + 13452 q^{43} + 2416 q^{44} + 22475 q^{45} + 12696 q^{46} + 24572 q^{47} + 2816 q^{48} + 28050 q^{49} + 15000 q^{50} + 26125 q^{51} + 7408 q^{52} + 17563 q^{53} - 13456 q^{54} + 3775 q^{55} + 23424 q^{56} - 41798 q^{57} + 23892 q^{58} + 62911 q^{59} + 4400 q^{60} + 32851 q^{61} + 41048 q^{62} + 138693 q^{63} + 24576 q^{64} + 11575 q^{65} + 92100 q^{66} + 54177 q^{67} + 10304 q^{68} + 5819 q^{69} + 36600 q^{70} - 14368 q^{71} + 57536 q^{72} + 33276 q^{73} + 68828 q^{74} + 6875 q^{75} + 54896 q^{76} - 143678 q^{77} + 56544 q^{78} + 74296 q^{79} + 38400 q^{80} + 150834 q^{81} + 3136 q^{82} + 65145 q^{83} - 61536 q^{84} + 16100 q^{85} + 53808 q^{86} - 790 q^{87} + 9664 q^{88} - 67562 q^{89} + 89900 q^{90} - 89487 q^{91} + 50784 q^{92} - 209450 q^{93} + 98288 q^{94} + 85775 q^{95} + 11264 q^{96} - 13201 q^{97} + 112200 q^{98} - 355951 q^{99}+O(q^{100}) \) 6 * q + 24 * q^2 + 11 * q^3 + 96 * q^4 + 150 * q^5 + 44 * q^6 + 366 * q^7 + 384 * q^8 + 899 * q^9 + 600 * q^10 + 151 * q^11 + 176 * q^12 + 463 * q^13 + 1464 * q^14 + 275 * q^15 + 1536 * q^16 + 644 * q^17 + 3596 * q^18 + 3431 * q^19 + 2400 * q^20 - 3846 * q^21 + 604 * q^22 + 3174 * q^23 + 704 * q^24 + 3750 * q^25 + 1852 * q^26 - 3364 * q^27 + 5856 * q^28 + 5973 * q^29 + 1100 * q^30 + 10262 * q^31 + 6144 * q^32 + 23025 * q^33 + 2576 * q^34 + 9150 * q^35 + 14384 * q^36 + 17207 * q^37 + 13724 * q^38 + 14136 * q^39 + 9600 * q^40 + 784 * q^41 - 15384 * q^42 + 13452 * q^43 + 2416 * q^44 + 22475 * q^45 + 12696 * q^46 + 24572 * q^47 + 2816 * q^48 + 28050 * q^49 + 15000 * q^50 + 26125 * q^51 + 7408 * q^52 + 17563 * q^53 - 13456 * q^54 + 3775 * q^55 + 23424 * q^56 - 41798 * q^57 + 23892 * q^58 + 62911 * q^59 + 4400 * q^60 + 32851 * q^61 + 41048 * q^62 + 138693 * q^63 + 24576 * q^64 + 11575 * q^65 + 92100 * q^66 + 54177 * q^67 + 10304 * q^68 + 5819 * q^69 + 36600 * q^70 - 14368 * q^71 + 57536 * q^72 + 33276 * q^73 + 68828 * q^74 + 6875 * q^75 + 54896 * q^76 - 143678 * q^77 + 56544 * q^78 + 74296 * q^79 + 38400 * q^80 + 150834 * q^81 + 3136 * q^82 + 65145 * q^83 - 61536 * q^84 + 16100 * q^85 + 53808 * q^86 - 790 * q^87 + 9664 * q^88 - 67562 * q^89 + 89900 * q^90 - 89487 * q^91 + 50784 * q^92 - 209450 * q^93 + 98288 * q^94 + 85775 * q^95 + 11264 * q^96 - 13201 * q^97 + 112200 * q^98 - 355951 * 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
$3$	−14.9517	−0.959152	−0.479576	−	0.877500i	$-0.659209\pi$
$3$	−14.9517	−0.959152	−0.479576	+	0.877500i	$0.659209\pi$
$4$	16.0000	0.500000
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−59.8068	−0.678223
$7$	52.9827	0.408685	0.204342	−	0.978899i	$-0.434494\pi$
$7$	52.9827	0.408685	0.204342	+	0.978899i	$0.434494\pi$
$8$	64.0000	0.353553
$9$	−19.4468	−0.0800282
$10$	100.000	0.316228
$11$	300.681	0.749245	0.374622	−	0.927177i	$-0.377772\pi$
$11$	300.681	0.749245	0.374622	+	0.927177i	$0.377772\pi$
$12$	−239.227	−0.479576
$13$	55.9240	0.0917783	0.0458891	−	0.998947i	$-0.485388\pi$
$13$	55.9240	0.0917783	0.0458891	+	0.998947i	$0.485388\pi$
$14$	211.931	0.288984
$15$	−373.792	−0.428946
$16$	256.000	0.250000
$17$	−731.263	−0.613693	−0.306847	−	0.951759i	$-0.599274\pi$
$17$	−731.263	−0.613693	−0.306847	+	0.951759i	$0.599274\pi$
$18$	−77.7874	−0.0565885
$19$	−543.758	−0.345558	−0.172779	−	0.984961i	$-0.555275\pi$
$19$	−543.758	−0.345558	−0.172779	+	0.984961i	$0.555275\pi$
$20$	400.000	0.223607
$21$	−792.181	−0.391991
$22$	1202.72	0.529796
$23$	529.000	0.208514
$23$	529.000	0.208514
$24$	−956.908	−0.339111
$25$	625.000	0.200000
$26$	223.696	0.0648970
$27$	3924.02	1.03591
$28$	847.723	0.204342
$29$	6819.44	1.50575	0.752877	−	0.658162i	$-0.228666\pi$
$29$	6819.44	1.50575	0.752877	+	0.658162i	$0.228666\pi$
$30$	−1495.17	−0.303310
$31$	−4841.76	−0.904897	−0.452448	−	0.891791i	$-0.649449\pi$
$31$	−4841.76	−0.904897	−0.452448	+	0.891791i	$0.649449\pi$
$32$	1024.00	0.176777
$33$	−4495.69	−0.718639
$34$	−2925.05	−0.433947
$35$	1324.57	0.182769
$36$	−311.149	−0.0400141
$37$	8983.83	1.07884	0.539420	−	0.842037i	$-0.318643\pi$
$37$	8983.83	1.07884	0.539420	+	0.842037i	$0.318643\pi$
$38$	−2175.03	−0.244347
$39$	−836.159	−0.0880293
$40$	1600.00	0.158114
$41$	14766.2	1.37186	0.685928	−	0.727669i	$-0.259396\pi$
$41$	14766.2	1.37186	0.685928	+	0.727669i	$0.259396\pi$
$42$	−3168.72	−0.277179
$43$	23713.0	1.95576	0.977878	−	0.209176i	$-0.0670782\pi$
$43$	23713.0	1.95576	0.977878	+	0.209176i	$0.0670782\pi$
$44$	4810.89	0.374622
$45$	−486.171	−0.0357897
$46$	2116.00	0.147442
$47$	−24259.8	−1.60193	−0.800964	−	0.598712i	$-0.795679\pi$
$47$	−24259.8	−1.60193	−0.800964	+	0.598712i	$0.795679\pi$
$48$	−3827.63	−0.239788
$49$	−13999.8	−0.832977
$50$	2500.00	0.141421
$51$	10933.6	0.588625
$52$	894.784	0.0458891
$53$	19458.4	0.951517	0.475759	−	0.879576i	$-0.342174\pi$
$53$	19458.4	0.951517	0.475759	+	0.879576i	$0.342174\pi$
$54$	15696.1	0.732500
$55$	7517.02	0.335072
$56$	3390.89	0.144492
$57$	8130.10	0.331443
$58$	27277.8	1.06473
$59$	28756.7	1.07550	0.537748	−	0.843106i	$-0.319275\pi$
$59$	28756.7	1.07550	0.537748	+	0.843106i	$0.319275\pi$
$60$	−5980.68	−0.214473
$61$	31474.3	1.08301	0.541504	−	0.840698i	$-0.317855\pi$
$61$	31474.3	1.08301	0.541504	+	0.840698i	$0.317855\pi$
$62$	−19367.0	−0.639859
$63$	−1030.35	−0.0327063
$64$	4096.00	0.125000
$65$	1398.10	0.0410445
$66$	−17982.7	−0.508155
$67$	9158.23	0.249244	0.124622	−	0.992204i	$-0.460228\pi$
$67$	9158.23	0.249244	0.124622	+	0.992204i	$0.460228\pi$
$68$	−11700.2	−0.306847
$69$	−7909.45	−0.199997
$70$	5298.27	0.129238
$71$	75461.4	1.77656	0.888278	−	0.459307i	$-0.151902\pi$
$71$	75461.4	1.77656	0.888278	+	0.459307i	$0.151902\pi$
$72$	−1244.60	−0.0282942
$73$	25985.0	0.570710	0.285355	−	0.958422i	$-0.407889\pi$
$73$	25985.0	0.570710	0.285355	+	0.958422i	$0.407889\pi$
$74$	35935.3	0.762856
$75$	−9344.81	−0.191830
$76$	−8700.12	−0.172779
$77$	15930.9	0.306205
$78$	−3344.63	−0.0622461
$79$	−29366.0	−0.529391	−0.264696	−	0.964332i	$-0.585271\pi$
$79$	−29366.0	−0.529391	−0.264696	+	0.964332i	$0.585271\pi$
$80$	6400.00	0.111803
$81$	−53945.2	−0.913567
$82$	59064.7	0.970049
$83$	50096.9	0.798207	0.399103	−	0.916906i	$-0.369321\pi$
$83$	50096.9	0.798207	0.399103	+	0.916906i	$0.369321\pi$
$84$	−12674.9	−0.195995
$85$	−18281.6	−0.274452
$86$	94851.8	1.38293
$87$	−101962.	−1.44425
$88$	19243.6	0.264898
$89$	−44595.7	−0.596784	−0.298392	−	0.954443i	$-0.596450\pi$
$89$	−44595.7	−0.596784	−0.298392	+	0.954443i	$0.596450\pi$
$90$	−1944.68	−0.0253071
$91$	2963.00	0.0375084
$92$	8464.00	0.104257
$93$	72392.5	0.867933
$94$	−97039.3	−1.13273
$95$	−13593.9	−0.154538
$96$	−15310.5	−0.169556
$97$	−55634.3	−0.600362	−0.300181	−	0.953882i	$-0.597047\pi$
$97$	−55634.3	−0.600362	−0.300181	+	0.953882i	$0.597047\pi$
$98$	−55999.4	−0.589003
$99$	−5847.29	−0.0599607
$100$	10000.0	0.100000
$101$	−135640.	−1.32307	−0.661536	−	0.749914i	$-0.730095\pi$
$101$	−135640.	−1.32307	−0.661536	+	0.749914i	$0.730095\pi$
$102$	43734.5	0.416221
$103$	61222.3	0.568613	0.284307	−	0.958733i	$-0.408237\pi$
$103$	61222.3	0.568613	0.284307	+	0.958733i	$0.408237\pi$
$104$	3579.14	0.0324485
$105$	−19804.5	−0.175304
$106$	77833.4	0.672824
$107$	−91079.0	−0.769058	−0.384529	−	0.923113i	$-0.625636\pi$
$107$	−91079.0	−0.769058	−0.384529	+	0.923113i	$0.625636\pi$
$108$	62784.4	0.517955
$109$	−181113.	−1.46010	−0.730052	−	0.683392i	$-0.760504\pi$
$109$	−181113.	−1.46010	−0.730052	+	0.683392i	$0.760504\pi$
$110$	30068.1	0.236932
$111$	−134324.	−1.03477
$112$	13563.6	0.102171
$113$	72837.3	0.536609	0.268304	−	0.963334i	$-0.413537\pi$
$113$	72837.3	0.536609	0.268304	+	0.963334i	$0.413537\pi$
$114$	32520.4	0.234365
$115$	13225.0	0.0932505
$116$	109111.	0.752877
$117$	−1087.55	−0.00734485
$118$	115027.	0.760490
$119$	−38744.3	−0.250807
$120$	−23922.7	−0.151655
$121$	−70642.1	−0.438632
$122$	125897.	0.765803
$123$	−220779.	−1.31582
$124$	−77468.2	−0.452448
$125$	15625.0	0.0894427
$126$	−4121.38	−0.0231268
$127$	211246.	1.16220	0.581099	−	0.813833i	$-0.302623\pi$
$127$	211246.	1.16220	0.581099	+	0.813833i	$0.302623\pi$
$128$	16384.0	0.0883883
$129$	−354549.	−1.87587
$130$	5592.40	0.0290228
$131$	−18759.0	−0.0955059	−0.0477530	−	0.998859i	$-0.515206\pi$
$131$	−18759.0	−0.0955059	−0.0477530	+	0.998859i	$0.515206\pi$
$132$	−71931.0	−0.359320
$133$	−28809.7	−0.141224
$134$	36632.9	0.176242
$135$	98100.6	0.463273
$136$	−46800.8	−0.216973
$137$	−98962.6	−0.450474	−0.225237	−	0.974304i	$-0.572316\pi$
$137$	−98962.6	−0.450474	−0.225237	+	0.974304i	$0.572316\pi$
$138$	−31637.8	−0.141419
$139$	151657.	0.665774	0.332887	−	0.942967i	$-0.391977\pi$
$139$	151657.	0.665774	0.332887	+	0.942967i	$0.391977\pi$
$140$	21193.1	0.0913847
$141$	362726.	1.53649
$142$	301845.	1.25621
$143$	16815.3	0.0687644
$144$	−4978.39	−0.0200070
$145$	170486.	0.673393
$146$	103940.	0.403553
$147$	209321.	0.798951
$148$	143741.	0.539420
$149$	−319208.	−1.17790	−0.588950	−	0.808170i	$-0.700458\pi$
$149$	−319208.	−1.17790	−0.588950	+	0.808170i	$0.700458\pi$
$150$	−37379.2	−0.135645
$151$	443214.	1.58187	0.790935	−	0.611900i	$-0.209594\pi$
$151$	443214.	1.58187	0.790935	+	0.611900i	$0.209594\pi$
$152$	−34800.5	−0.122173
$153$	14220.8	0.0491128
$154$	63723.4	0.216520
$155$	−121044.	−0.404682
$156$	−13378.5	−0.0440146
$157$	−434520.	−1.40689	−0.703446	−	0.710748i	$-0.748356\pi$
$157$	−434520.	−1.40689	−0.703446	+	0.710748i	$0.748356\pi$
$158$	−117464.	−0.374336
$159$	−290935.	−0.912649
$160$	25600.0	0.0790569
$161$	28027.8	0.0852167
$162$	−215781.	−0.645990
$163$	−53359.0	−0.157303	−0.0786517	−	0.996902i	$-0.525062\pi$
$163$	−53359.0	−0.157303	−0.0786517	+	0.996902i	$0.525062\pi$
$164$	236259.	0.685928
$165$	−112392.	−0.321385
$166$	200388.	0.564417
$167$	645914.	1.79219	0.896093	−	0.443865i	$-0.146393\pi$
$167$	645914.	1.79219	0.896093	+	0.443865i	$0.146393\pi$
$168$	−50699.6	−0.138590
$169$	−368166.	−0.991577
$170$	−73126.3	−0.194067
$171$	10574.4	0.0276544
$172$	379407.	0.977878
$173$	240494.	0.610928	0.305464	−	0.952204i	$-0.401188\pi$
$173$	240494.	0.610928	0.305464	+	0.952204i	$0.401188\pi$
$174$	−407849.	−1.02124
$175$	33114.2	0.0817370
$176$	76974.2	0.187311
$177$	−429961.	−1.03156
$178$	−178383.	−0.421990
$179$	23095.1	0.0538749	0.0269375	−	0.999637i	$-0.491424\pi$
$179$	23095.1	0.0538749	0.0269375	+	0.999637i	$0.491424\pi$
$180$	−7778.74	−0.0178948
$181$	−682533.	−1.54856	−0.774278	−	0.632845i	$-0.781887\pi$
$181$	−682533.	−1.54856	−0.774278	+	0.632845i	$0.781887\pi$
$182$	11852.0	0.0265224
$183$	−470595.	−1.03877
$184$	33856.0	0.0737210
$185$	224596.	0.482472
$186$	289570.	0.613721
$187$	−219877.	−0.459807
$188$	−388157.	−0.800964
$189$	207905.	0.423361
$190$	−54375.8	−0.109275
$191$	−642237.	−1.27383	−0.636915	−	0.770934i	$-0.719790\pi$
$191$	−642237.	−1.27383	−0.636915	+	0.770934i	$0.719790\pi$
$192$	−61242.1	−0.119894
$193$	−181282.	−0.350317	−0.175159	−	0.984540i	$-0.556044\pi$
$193$	−181282.	−0.350317	−0.175159	+	0.984540i	$0.556044\pi$
$194$	−222537.	−0.424520
$195$	−20904.0	−0.0393679
$196$	−223997.	−0.416488
$197$	−519512.	−0.953739	−0.476870	−	0.878974i	$-0.658229\pi$
$197$	−519512.	−0.953739	−0.476870	+	0.878974i	$0.658229\pi$
$198$	−23389.2	−0.0423986
$199$	−643748.	−1.15235	−0.576173	−	0.817328i	$-0.695455\pi$
$199$	−643748.	−1.15235	−0.576173	+	0.817328i	$0.695455\pi$
$200$	40000.0	0.0707107
$201$	−136931.	−0.239063
$202$	−542559.	−0.935553
$203$	361312.	0.615379
$204$	174938.	0.294313
$205$	369155.	0.613513
$206$	244889.	0.402070
$207$	−10287.4	−0.0166870
$208$	14316.5	0.0229446
$209$	−163497.	−0.258908
$210$	−79218.1	−0.123958
$211$	714590.	1.10497	0.552486	−	0.833522i	$-0.313679\pi$
$211$	714590.	1.10497	0.552486	+	0.833522i	$0.313679\pi$
$212$	311334.	0.475759
$213$	−1.12828e6	−1.70399
$214$	−364316.	−0.543806
$215$	592824.	0.874641
$216$	251138.	0.366250
$217$	−256529.	−0.369818
$218$	−724452.	−1.03245
$219$	−388520.	−0.547397
$220$	120272.	0.167536
$221$	−40895.2	−0.0563237
$222$	−537294.	−0.731694
$223$	68929.6	0.0928204	0.0464102	−	0.998922i	$-0.485222\pi$
$223$	68929.6	0.0928204	0.0464102	+	0.998922i	$0.485222\pi$
$224$	54254.2	0.0722460
$225$	−12154.3	−0.0160056
$226$	291349.	0.379440
$227$	655952.	0.844904	0.422452	−	0.906385i	$-0.361170\pi$
$227$	655952.	0.844904	0.422452	+	0.906385i	$0.361170\pi$
$228$	130082.	0.165721
$229$	374972.	0.472510	0.236255	−	0.971691i	$-0.424080\pi$
$229$	374972.	0.472510	0.236255	+	0.971691i	$0.424080\pi$
$230$	52900.0	0.0659380
$231$	−238193.	−0.293697
$232$	436444.	0.532364
$233$	−110929.	−0.133861	−0.0669304	−	0.997758i	$-0.521321\pi$
$233$	−110929.	−0.133861	−0.0669304	+	0.997758i	$0.521321\pi$
$234$	−4350.18	−0.00519359
$235$	−606496.	−0.716404
$236$	460107.	0.537748
$237$	439071.	0.507767
$238$	−154977.	−0.177348
$239$	−590537.	−0.668733	−0.334366	−	0.942443i	$-0.608522\pi$
$239$	−590537.	−0.668733	−0.334366	+	0.942443i	$0.608522\pi$
$240$	−95690.8	−0.107236
$241$	1.25394e6	1.39070	0.695351	−	0.718670i	$-0.255249\pi$
$241$	1.25394e6	1.39070	0.695351	+	0.718670i	$0.255249\pi$
$242$	−282569.	−0.310160
$243$	−146965.	−0.159661
$244$	503589.	0.541504
$245$	−349996.	−0.372518
$246$	−883118.	−0.930424
$247$	−30409.1	−0.0317147
$248$	−309873.	−0.319929
$249$	−749033.	−0.765601
$250$	62500.0	0.0632456
$251$	429490.	0.430298	0.215149	−	0.976581i	$-0.430976\pi$
$251$	429490.	0.430298	0.215149	+	0.976581i	$0.430976\pi$
$252$	−16485.5	−0.0163532
$253$	159060.	0.156228
$254$	844985.	0.821798
$255$	273341.	0.263241
$256$	65536.0	0.0625000
$257$	−866297.	−0.818152	−0.409076	−	0.912500i	$-0.634149\pi$
$257$	−866297.	−0.818152	−0.409076	+	0.912500i	$0.634149\pi$
$258$	−1.41820e6	−1.32644
$259$	475987.	0.440906
$260$	22369.6	0.0205222
$261$	−132617.	−0.120503
$262$	−75035.8	−0.0675329
$263$	1.52425e6	1.35884	0.679418	−	0.733751i	$-0.262232\pi$
$263$	1.52425e6	1.35884	0.679418	+	0.733751i	$0.262232\pi$
$264$	−287724.	−0.254077
$265$	486459.	0.425531
$266$	−115239.	−0.0998608
$267$	666781.	0.572407
$268$	146532.	0.124622
$269$	1.29881e6	1.09437	0.547186	−	0.837011i	$-0.315699\pi$
$269$	1.29881e6	1.09437	0.547186	+	0.837011i	$0.315699\pi$
$270$	392402.	0.327584
$271$	−1.22302e6	−1.01161	−0.505803	−	0.862649i	$-0.668804\pi$
$271$	−1.22302e6	−1.01161	−0.505803	+	0.862649i	$0.668804\pi$
$272$	−187203.	−0.153423
$273$	−44301.9	−0.0359762
$274$	−395850.	−0.318533
$275$	187925.	0.149849
$276$	−126551.	−0.0999985
$277$	1.79383e6	1.40470	0.702349	−	0.711833i	$-0.252135\pi$
$277$	1.79383e6	1.40470	0.702349	+	0.711833i	$0.252135\pi$
$278$	606630.	0.470773
$279$	94156.9	0.0724172
$280$	84772.3	0.0646188
$281$	−1.38365e6	−1.04535	−0.522673	−	0.852533i	$-0.675065\pi$
$281$	−1.38365e6	−1.04535	−0.522673	+	0.852533i	$0.675065\pi$
$282$	1.45090e6	1.08646
$283$	28278.7	0.0209891	0.0104945	−	0.999945i	$-0.496659\pi$
$283$	28278.7	0.0209891	0.0104945	+	0.999945i	$0.496659\pi$
$284$	1.20738e6	0.888278
$285$	203252.	0.148226
$286$	67261.1	0.0486238
$287$	782352.	0.560657
$288$	−19913.6	−0.0141471
$289$	−885111.	−0.623380
$290$	681944.	0.476161
$291$	831827.	0.575838
$292$	415760.	0.285355
$293$	−1.67966e6	−1.14301	−0.571507	−	0.820597i	$-0.693641\pi$
$293$	−1.67966e6	−1.14301	−0.571507	+	0.820597i	$0.693641\pi$
$294$	837285.	0.564944
$295$	718917.	0.480976
$296$	574965.	0.381428
$297$	1.17988e6	0.776151
$298$	−1.27683e6	−0.832901
$299$	29583.8	0.0191371
$300$	−149517.	−0.0959152
$301$	1.25638e6	0.799288
$302$	1.77286e6	1.11855
$303$	2.02804e6	1.26903
$304$	−139202.	−0.0863896
$305$	786858.	0.484336
$306$	56883.0	0.0347280
$307$	−818323.	−0.495540	−0.247770	−	0.968819i	$-0.579698\pi$
$307$	−818323.	−0.495540	−0.247770	+	0.968819i	$0.579698\pi$
$308$	254894.	0.153103
$309$	−915378.	−0.545386
$310$	−484176.	−0.286153
$311$	1.65986e6	0.973132	0.486566	−	0.873644i	$-0.338249\pi$
$311$	1.65986e6	0.973132	0.486566	+	0.873644i	$0.338249\pi$
$312$	−53514.2	−0.0311231
$313$	1.89720e6	1.09459	0.547296	−	0.836939i	$-0.315657\pi$
$313$	1.89720e6	1.09459	0.547296	+	0.836939i	$0.315657\pi$
$314$	−1.73808e6	−0.994823
$315$	−25758.6	−0.0146267
$316$	−469856.	−0.264696
$317$	1.95427e6	1.09229	0.546144	−	0.837692i	$-0.316095\pi$
$317$	1.95427e6	1.09229	0.546144	+	0.837692i	$0.316095\pi$
$318$	−1.16374e6	−0.645340
$319$	2.05047e6	1.12818
$320$	102400.	0.0559017
$321$	1.36179e6	0.737643
$322$	112111.	0.0602573
$323$	397630.	0.212067
$324$	−863124.	−0.456784
$325$	34952.5	0.0183557
$326$	−213436.	−0.111230
$327$	2.70795e6	1.40046
$328$	945036.	0.485025
$329$	−1.28535e6	−0.654684
$330$	−449569.	−0.227254
$331$	−2.99756e6	−1.50383	−0.751914	−	0.659262i	$-0.770869\pi$
$331$	−2.99756e6	−1.50383	−0.751914	+	0.659262i	$0.770869\pi$
$332$	801550.	0.399103
$333$	−174707.	−0.0863376
$334$	2.58365e6	1.26727
$335$	228956.	0.111465
$336$	−202798.	−0.0979977
$337$	1.67098e6	0.801489	0.400744	−	0.916190i	$-0.368752\pi$
$337$	1.67098e6	0.801489	0.400744	+	0.916190i	$0.368752\pi$
$338$	−1.47266e6	−0.701151
$339$	−1.08904e6	−0.514689
$340$	−292505.	−0.137226
$341$	−1.45582e6	−0.677989
$342$	42297.5	0.0195546
$343$	−1.63223e6	−0.749110
$344$	1.51763e6	0.691464
$345$	−197736.	−0.0894414
$346$	961978.	0.431991
$347$	2.80782e6	1.25183	0.625916	−	0.779891i	$-0.284725\pi$
$347$	2.80782e6	1.25183	0.625916	+	0.779891i	$0.284725\pi$
$348$	−1.63140e6	−0.722123
$349$	−1.15660e6	−0.508300	−0.254150	−	0.967165i	$-0.581796\pi$
$349$	−1.15660e6	−0.508300	−0.254150	+	0.967165i	$0.581796\pi$
$350$	132457.	0.0577968
$351$	219447.	0.0950741
$352$	307897.	0.132449
$353$	−2.52329e6	−1.07778	−0.538890	−	0.842376i	$-0.681156\pi$
$353$	−2.52329e6	−1.07778	−0.538890	+	0.842376i	$0.681156\pi$
$354$	−1.71984e6	−0.729425
$355$	1.88653e6	0.794500
$356$	−713530.	−0.298392
$357$	579293.	0.240562
$358$	92380.3	0.0380953
$359$	−850399.	−0.348247	−0.174123	−	0.984724i	$-0.555709\pi$
$359$	−850399.	−0.348247	−0.174123	+	0.984724i	$0.555709\pi$
$360$	−31114.9	−0.0126536
$361$	−2.18043e6	−0.880589
$362$	−2.73013e6	−1.09500
$363$	1.05622e6	0.420715
$364$	47408.0	0.0187542
$365$	649625.	0.255229
$366$	−1.88238e6	−0.734521
$367$	1.54181e6	0.597537	0.298769	−	0.954326i	$-0.403424\pi$
$367$	1.54181e6	0.597537	0.298769	+	0.954326i	$0.403424\pi$
$368$	135424.	0.0521286
$369$	−287156.	−0.109787
$370$	898383.	0.341159
$371$	1.03096e6	0.388871
$372$	1.15828e6	0.433967
$373$	4.69554e6	1.74749	0.873743	−	0.486388i	$-0.161686\pi$
$373$	4.69554e6	1.74749	0.873743	+	0.486388i	$0.161686\pi$
$374$	−879507.	−0.325132
$375$	−233620.	−0.0857891
$376$	−1.55263e6	−0.566367
$377$	381371.	0.138195
$378$	831621.	0.299362
$379$	−922010.	−0.329714	−0.164857	−	0.986317i	$-0.552716\pi$
$379$	−922010.	−0.329714	−0.164857	+	0.986317i	$0.552716\pi$
$380$	−217503.	−0.0772692
$381$	−3.15849e6	−1.11472
$382$	−2.56895e6	−0.900734
$383$	−4.04430e6	−1.40879	−0.704395	−	0.709809i	$-0.748781\pi$
$383$	−4.04430e6	−1.40879	−0.704395	+	0.709809i	$0.748781\pi$
$384$	−244969.	−0.0847778
$385$	398272.	0.136939
$386$	−725129.	−0.247712
$387$	−461142.	−0.156516
$388$	−890148.	−0.300181
$389$	4.73384e6	1.58613	0.793067	−	0.609134i	$-0.208483\pi$
$389$	4.73384e6	1.58613	0.793067	+	0.609134i	$0.208483\pi$
$390$	−83615.9	−0.0278373
$391$	−386838.	−0.127964
$392$	−895990.	−0.294502
$393$	280478.	0.0916047
$394$	−2.07805e6	−0.674396
$395$	−734150.	−0.236751
$396$	−93556.6	−0.0299803
$397$	−1.13445e6	−0.361251	−0.180626	−	0.983552i	$-0.557812\pi$
$397$	−1.13445e6	−0.361251	−0.180626	+	0.983552i	$0.557812\pi$
$398$	−2.57499e6	−0.814832
$399$	430754.	0.135456
$400$	160000.	0.0500000
$401$	827013.	0.256833	0.128417	−	0.991720i	$-0.459010\pi$
$401$	827013.	0.256833	0.128417	+	0.991720i	$0.459010\pi$
$402$	−547724.	−0.169043
$403$	−270771.	−0.0830499
$404$	−2.17023e6	−0.661536
$405$	−1.34863e6	−0.408560
$406$	1.44525e6	0.435139
$407$	2.70126e6	0.808316
$408$	699752.	0.208110
$409$	−6.62311e6	−1.95773	−0.978867	−	0.204497i	$-0.934444\pi$
$409$	−6.62311e6	−1.95773	−0.978867	+	0.204497i	$0.934444\pi$
$410$	1.47662e6	0.433819
$411$	1.47966e6	0.432073
$412$	979557.	0.284307
$413$	1.52361e6	0.439539
$414$	−41149.5	−0.0117995
$415$	1.25242e6	0.356969
$416$	57266.2	0.0162243
$417$	−2.26754e6	−0.638578
$418$	−653990.	−0.183075
$419$	−6.71096e6	−1.86745	−0.933726	−	0.357988i	$-0.883463\pi$
$419$	−6.71096e6	−1.86745	−0.933726	+	0.357988i	$0.883463\pi$
$420$	−316872.	−0.0876518
$421$	−3.03910e6	−0.835680	−0.417840	−	0.908521i	$-0.637213\pi$
$421$	−3.03910e6	−0.835680	−0.417840	+	0.908521i	$0.637213\pi$
$422$	2.85836e6	0.781333
$423$	471777.	0.128199
$424$	1.24534e6	0.336412
$425$	−457040.	−0.122739
$426$	−4.51310e6	−1.20490
$427$	1.66759e6	0.442609
$428$	−1.45726e6	−0.384529
$429$	−251417.	−0.0659555
$430$	2.37130e6	0.618464
$431$	−4.19538e6	−1.08787	−0.543936	−	0.839127i	$-0.683067\pi$
$431$	−4.19538e6	−1.08787	−0.543936	+	0.839127i	$0.683067\pi$
$432$	1.00455e6	0.258978
$433$	3.46154e6	0.887258	0.443629	−	0.896211i	$-0.353691\pi$
$433$	3.46154e6	0.887258	0.443629	+	0.896211i	$0.353691\pi$
$434$	−1.02612e6	−0.261501
$435$	−2.54906e6	−0.645886
$436$	−2.89781e6	−0.730052
$437$	−287648.	−0.0720539
$438$	−1.55408e6	−0.387068
$439$	4.18208e6	1.03569	0.517847	−	0.855474i	$-0.326734\pi$
$439$	4.18208e6	1.03569	0.517847	+	0.855474i	$0.326734\pi$
$440$	481089.	0.118466
$441$	272253.	0.0666616
$442$	−163581.	−0.0398269
$443$	3.52414e6	0.853187	0.426593	−	0.904444i	$-0.359714\pi$
$443$	3.52414e6	0.853187	0.426593	+	0.904444i	$0.359714\pi$
$444$	−2.14918e6	−0.517386
$445$	−1.11489e6	−0.266890
$446$	275718.	0.0656339
$447$	4.77270e6	1.12978
$448$	217017.	0.0510856
$449$	−4.61174e6	−1.07957	−0.539783	−	0.841804i	$-0.681494\pi$
$449$	−4.61174e6	−1.07957	−0.539783	+	0.841804i	$0.681494\pi$
$450$	−48617.1	−0.0113177
$451$	4.43991e6	1.02786
$452$	1.16540e6	0.268304
$453$	−6.62680e6	−1.51725
$454$	2.62381e6	0.597437
$455$	74075.1	0.0167743
$456$	520326.	0.117183
$457$	3.35381e6	0.751187	0.375593	−	0.926785i	$-0.377439\pi$
$457$	3.35381e6	0.751187	0.375593	+	0.926785i	$0.377439\pi$
$458$	1.49989e6	0.334115
$459$	−2.86950e6	−0.635732
$460$	211600.	0.0466252
$461$	2.00124e6	0.438578	0.219289	−	0.975660i	$-0.429626\pi$
$461$	2.00124e6	0.438578	0.219289	+	0.975660i	$0.429626\pi$
$462$	−952773.	−0.207675
$463$	−5.32941e6	−1.15539	−0.577693	−	0.816254i	$-0.696047\pi$
$463$	−5.32941e6	−1.15539	−0.577693	+	0.816254i	$0.696047\pi$
$464$	1.74578e6	0.376438
$465$	1.80981e6	0.388152
$466$	−443714.	−0.0946539
$467$	−4.91986e6	−1.04390	−0.521952	−	0.852975i	$-0.674796\pi$
$467$	−4.91986e6	−1.04390	−0.521952	+	0.852975i	$0.674796\pi$
$468$	−17400.7	−0.00367242
$469$	485227.	0.101862
$470$	−2.42598e6	−0.506574
$471$	6.49681e6	1.34942
$472$	1.84043e6	0.380245
$473$	7.13003e6	1.46534
$474$	1.75628e6	0.359045
$475$	−339848.	−0.0691117
$476$	−619908.	−0.125404
$477$	−378404.	−0.0761482
$478$	−2.36215e6	−0.472865
$479$	−1.60883e6	−0.320385	−0.160193	−	0.987086i	$-0.551212\pi$
$479$	−1.60883e6	−0.320385	−0.160193	+	0.987086i	$0.551212\pi$
$480$	−382763.	−0.0758276
$481$	502412.	0.0990141
$482$	5.01576e6	0.983375
$483$	−419063.	−0.0817357
$484$	−1.13027e6	−0.219316
$485$	−1.39086e6	−0.268490
$486$	−587861.	−0.112897
$487$	7.03311e6	1.34377	0.671886	−	0.740655i	$-0.265485\pi$
$487$	7.03311e6	1.34377	0.671886	+	0.740655i	$0.265485\pi$
$488$	2.01436e6	0.382901
$489$	797807.	0.150878
$490$	−1.39998e6	−0.263410
$491$	−5.98047e6	−1.11952	−0.559759	−	0.828655i	$-0.689106\pi$
$491$	−5.98047e6	−1.11952	−0.559759	+	0.828655i	$0.689106\pi$
$492$	−3.53247e6	−0.657909
$493$	−4.98681e6	−0.924071
$494$	−121636.	−0.0224257
$495$	−146182.	−0.0268152
$496$	−1.23949e6	−0.226224
$497$	3.99814e6	0.726051
$498$	−2.99613e6	−0.541362
$499$	−9.04633e6	−1.62638	−0.813188	−	0.582000i	$-0.802270\pi$
$499$	−9.04633e6	−1.62638	−0.813188	+	0.582000i	$0.802270\pi$
$500$	250000.	0.0447214
$501$	−9.65750e6	−1.71898
$502$	1.71796e6	0.304266
$503$	2.09077e6	0.368456	0.184228	−	0.982884i	$-0.441021\pi$
$503$	2.09077e6	0.368456	0.184228	+	0.982884i	$0.441021\pi$
$504$	−65942.1	−0.0115634
$505$	−3.39099e6	−0.591696
$506$	636240.	0.110470
$507$	5.50470e6	0.951072
$508$	3.37994e6	0.581099
$509$	−6.02388e6	−1.03058	−0.515290	−	0.857016i	$-0.672316\pi$
$509$	−6.02388e6	−1.03058	−0.515290	+	0.857016i	$0.672316\pi$
$510$	1.09336e6	0.186140
$511$	1.37675e6	0.233241
$512$	262144.	0.0441942
$513$	−2.13372e6	−0.357968
$514$	−3.46519e6	−0.578521
$515$	1.53056e6	0.254291
$516$	−5.67278e6	−0.937933
$517$	−7.29446e6	−1.20024
$518$	1.90395e6	0.311768
$519$	−3.59580e6	−0.585972
$520$	89478.4	0.0145114
$521$	−110767.	−0.0178780	−0.00893898	−	0.999960i	$-0.502845\pi$
$521$	−110767.	−0.0178780	−0.00893898	+	0.999960i	$0.502845\pi$
$522$	−530467.	−0.0852083
$523$	−2.57191e6	−0.411151	−0.205576	−	0.978641i	$-0.565907\pi$
$523$	−2.57191e6	−0.411151	−0.205576	+	0.978641i	$0.565907\pi$
$524$	−300143.	−0.0477530
$525$	−495113.	−0.0783982
$526$	6.09700e6	0.960842
$527$	3.54060e6	0.555329
$528$	−1.15090e6	−0.179660
$529$	279841.	0.0434783
$530$	1.94584e6	0.300896
$531$	−559227.	−0.0860699
$532$	−460956.	−0.0706122
$533$	825784.	0.125907
$534$	2.66712e6	0.404753
$535$	−2.27698e6	−0.343933
$536$	586127.	0.0881210
$537$	−345311.	−0.0516742
$538$	5.19524e6	0.773838
$539$	−4.20948e6	−0.624103
$540$	1.56961e6	0.231637
$541$	9.44630e6	1.38761	0.693807	−	0.720161i	$-0.255932\pi$
$541$	9.44630e6	1.38761	0.693807	+	0.720161i	$0.255932\pi$
$542$	−4.89210e6	−0.715314
$543$	1.02050e7	1.48530
$544$	−748814.	−0.108487
$545$	−4.52783e6	−0.652978
$546$	−177208.	−0.0254390
$547$	−1.97650e6	−0.282442	−0.141221	−	0.989978i	$-0.545103\pi$
$547$	−1.97650e6	−0.282442	−0.141221	+	0.989978i	$0.545103\pi$
$548$	−1.58340e6	−0.225237
$549$	−612076.	−0.0866712
$550$	751702.	0.105959
$551$	−3.70812e6	−0.520326
$552$	−506205.	−0.0707096
$553$	−1.55589e6	−0.216354
$554$	7.17534e6	0.993272
$555$	−3.35809e6	−0.462764
$556$	2.42652e6	0.332887
$557$	−2.85979e6	−0.390567	−0.195284	−	0.980747i	$-0.562563\pi$
$557$	−2.85979e6	−0.390567	−0.195284	+	0.980747i	$0.562563\pi$
$558$	376628.	0.0512067
$559$	1.32612e6	0.179496
$560$	339089.	0.0456924
$561$	3.28753e6	0.441024
$562$	−5.53459e6	−0.739171
$563$	−6.90282e6	−0.917816	−0.458908	−	0.888484i	$-0.651759\pi$
$563$	−6.90282e6	−0.917816	−0.458908	+	0.888484i	$0.651759\pi$
$564$	5.80361e6	0.768246
$565$	1.82093e6	0.239979
$566$	113115.	0.0148415
$567$	−2.85816e6	−0.373361
$568$	4.82953e6	0.628107
$569$	−9.90057e6	−1.28198	−0.640988	−	0.767551i	$-0.721475\pi$
$569$	−9.90057e6	−1.28198	−0.640988	+	0.767551i	$0.721475\pi$
$570$	813010.	0.104811
$571$	7.64220e6	0.980908	0.490454	−	0.871467i	$-0.336831\pi$
$571$	7.64220e6	0.980908	0.490454	+	0.871467i	$0.336831\pi$
$572$	269044.	0.0343822
$573$	9.60253e6	1.22180
$574$	3.12941e6	0.396444
$575$	330625.	0.0417029
$576$	−79654.3	−0.0100035
$577$	−7.00875e6	−0.876397	−0.438198	−	0.898878i	$-0.644383\pi$
$577$	−7.00875e6	−0.876397	−0.438198	+	0.898878i	$0.644383\pi$
$578$	−3.54044e6	−0.440797
$579$	2.71048e6	0.336008
$580$	2.72778e6	0.336697
$581$	2.65427e6	0.326215
$582$	3.32731e6	0.407179
$583$	5.85075e6	0.712919
$584$	1.66304e6	0.201776
$585$	−27188.6	−0.00328472
$586$	−6.71862e6	−0.808233
$587$	−2.70812e6	−0.324394	−0.162197	−	0.986758i	$-0.551858\pi$
$587$	−2.70812e6	−0.324394	−0.162197	+	0.986758i	$0.551858\pi$
$588$	3.34914e6	0.399475
$589$	2.63274e6	0.312695
$590$	2.87567e6	0.340102
$591$	7.76758e6	0.914781
$592$	2.29986e6	0.269710
$593$	−1.03876e7	−1.21305	−0.606525	−	0.795065i	$-0.707437\pi$
$593$	−1.03876e7	−1.21305	−0.606525	+	0.795065i	$0.707437\pi$
$594$	4.71951e6	0.548822
$595$	−968607.	−0.112164
$596$	−5.10733e6	−0.588950
$597$	9.62512e6	1.10527
$598$	118335.	0.0135320
$599$	6.91543e6	0.787503	0.393752	−	0.919217i	$-0.371177\pi$
$599$	6.91543e6	0.787503	0.393752	+	0.919217i	$0.371177\pi$
$600$	−598068.	−0.0678223
$601$	2.35952e6	0.266463	0.133232	−	0.991085i	$-0.457465\pi$
$601$	2.35952e6	0.266463	0.133232	+	0.991085i	$0.457465\pi$
$602$	5.02550e6	0.565182
$603$	−178099.	−0.0199465
$604$	7.09142e6	0.790935
$605$	−1.76605e6	−0.196162
$606$	8.11217e6	0.897337
$607$	7.65871e6	0.843691	0.421846	−	0.906668i	$-0.361382\pi$
$607$	7.65871e6	0.843691	0.421846	+	0.906668i	$0.361382\pi$
$608$	−556808.	−0.0610867
$609$	−5.40223e6	−0.590242
$610$	3.14743e6	0.342477
$611$	−1.35671e6	−0.147022
$612$	227532.	0.0245564
$613$	7.37062e6	0.792233	0.396117	−	0.918200i	$-0.370358\pi$
$613$	7.37062e6	0.792233	0.396117	+	0.918200i	$0.370358\pi$
$614$	−3.27329e6	−0.350400
$615$	−5.51949e6	−0.588452
$616$	1.01958e6	0.108260
$617$	−2.90103e6	−0.306788	−0.153394	−	0.988165i	$-0.549020\pi$
$617$	−2.90103e6	−0.306788	−0.153394	+	0.988165i	$0.549020\pi$
$618$	−3.66151e6	−0.385646
$619$	−576144.	−0.0604372	−0.0302186	−	0.999543i	$-0.509620\pi$
$619$	−576144.	−0.0604372	−0.0302186	+	0.999543i	$0.509620\pi$
$620$	−1.93670e6	−0.202341
$621$	2.07581e6	0.216002
$622$	6.63946e6	0.688108
$623$	−2.36280e6	−0.243897
$624$	−214057.	−0.0220073
$625$	390625.	0.0400000
$626$	7.58880e6	0.773994
$627$	2.44456e6	0.248332
$628$	−6.95233e6	−0.703446
$629$	−6.56955e6	−0.662077
$630$	−103035.	−0.0103426
$631$	1.41972e7	1.41948	0.709741	−	0.704463i	$-0.248812\pi$
$631$	1.41972e7	1.41948	0.709741	+	0.704463i	$0.248812\pi$
$632$	−1.87942e6	−0.187168
$633$	−1.06843e7	−1.05983
$634$	7.81709e6	0.772364
$635$	5.28116e6	0.519750
$636$	−4.65497e6	−0.456325
$637$	−782927.	−0.0764492
$638$	8.20190e6	0.797742
$639$	−1.46749e6	−0.142174
$640$	409600.	0.0395285
$641$	−1.03808e7	−0.997898	−0.498949	−	0.866631i	$-0.666280\pi$
$641$	−1.03808e7	−0.997898	−0.498949	+	0.866631i	$0.666280\pi$
$642$	5.44714e6	0.521592
$643$	1.67906e7	1.60154	0.800772	−	0.598970i	$-0.204423\pi$
$643$	1.67906e7	1.60154	0.800772	+	0.598970i	$0.204423\pi$
$644$	448445.	0.0426084
$645$	−8.86372e6	−0.838913
$646$	1.59052e6	0.149954
$647$	−1.13700e6	−0.106782	−0.0533910	−	0.998574i	$-0.517003\pi$
$647$	−1.13700e6	−0.106782	−0.0533910	+	0.998574i	$0.517003\pi$
$648$	−3.45250e6	−0.322995
$649$	8.64658e6	0.805810
$650$	139810.	0.0129794
$651$	3.83555e6	0.354711
$652$	−853743.	−0.0786517
$653$	−8.36939e6	−0.768088	−0.384044	−	0.923315i	$-0.625469\pi$
$653$	−8.36939e6	−0.768088	−0.384044	+	0.923315i	$0.625469\pi$
$654$	1.08318e7	0.990275
$655$	−468974.	−0.0427115
$656$	3.78014e6	0.342964
$657$	−505326.	−0.0456729
$658$	−5.14140e6	−0.462931
$659$	4.08206e6	0.366156	0.183078	−	0.983098i	$-0.441394\pi$
$659$	4.08206e6	0.366156	0.183078	+	0.983098i	$0.441394\pi$
$660$	−1.79827e6	−0.160693
$661$	193452.	0.0172215	0.00861073	−	0.999963i	$-0.497259\pi$
$661$	193452.	0.0172215	0.00861073	+	0.999963i	$0.497259\pi$
$662$	−1.19902e7	−1.06337
$663$	611452.	0.0540230
$664$	3.20620e6	0.282209
$665$	−720243.	−0.0631575
$666$	−698829.	−0.0610499
$667$	3.60749e6	0.313971
$668$	1.03346e7	0.896093
$669$	−1.03061e6	−0.0890288
$670$	915823.	0.0788178
$671$	9.46372e6	0.811439
$672$	−811193.	−0.0692948
$673$	6.30678e6	0.536748	0.268374	−	0.963315i	$-0.413514\pi$
$673$	6.30678e6	0.536748	0.268374	+	0.963315i	$0.413514\pi$
$674$	6.68393e6	0.566738
$675$	2.45252e6	0.207182
$676$	−5.89065e6	−0.495788
$677$	−6.91759e6	−0.580074	−0.290037	−	0.957015i	$-0.593668\pi$
$677$	−6.91759e6	−0.580074	−0.290037	+	0.957015i	$0.593668\pi$
$678$	−4.35616e6	−0.363940
$679$	−2.94765e6	−0.245359
$680$	−1.17002e6	−0.0970334
$681$	−9.80759e6	−0.810391
$682$	−5.82329e6	−0.479411
$683$	9.68782e6	0.794647	0.397323	−	0.917679i	$-0.369939\pi$
$683$	9.68782e6	0.794647	0.397323	+	0.917679i	$0.369939\pi$
$684$	169190.	0.0138272
$685$	−2.47406e6	−0.201458
$686$	−6.52891e6	−0.529701
$687$	−5.60647e6	−0.453208
$688$	6.07052e6	0.488939
$689$	1.08819e6	0.0873286
$690$	−790945.	−0.0632446
$691$	3.29950e6	0.262877	0.131438	−	0.991324i	$-0.458040\pi$
$691$	3.29950e6	0.262877	0.131438	+	0.991324i	$0.458040\pi$
$692$	3.84791e6	0.305464
$693$	−309805.	−0.0245050
$694$	1.12313e7	0.885178
$695$	3.79144e6	0.297743
$696$	−6.52558e6	−0.510618
$697$	−1.07980e7	−0.841899
$698$	−4.62640e6	−0.359422
$699$	1.65857e6	0.128393
$700$	529827.	0.0408685
$701$	−6.61904e6	−0.508744	−0.254372	−	0.967106i	$-0.581869\pi$
$701$	−6.61904e6	−0.508744	−0.254372	+	0.967106i	$0.581869\pi$
$702$	877789.	0.0672275
$703$	−4.88503e6	−0.372802
$704$	1.23159e6	0.0936556
$705$	9.06814e6	0.687140
$706$	−1.00932e7	−0.762106
$707$	−7.18655e6	−0.540719
$708$	−6.87938e6	−0.515782
$709$	5.40699e6	0.403961	0.201981	−	0.979390i	$-0.435262\pi$
$709$	5.40699e6	0.403961	0.201981	+	0.979390i	$0.435262\pi$
$710$	7.54614e6	0.561796
$711$	571076.	0.0423662
$712$	−2.85412e6	−0.210995
$713$	−2.56129e6	−0.188684
$714$	2.31717e6	0.170103
$715$	420382.	0.0307524
$716$	369521.	0.0269375
$717$	8.82953e6	0.641416
$718$	−3.40160e6	−0.246248
$719$	−2.56780e7	−1.85242	−0.926209	−	0.377011i	$-0.876952\pi$
$719$	−2.56780e7	−1.85242	−0.926209	+	0.377011i	$0.876952\pi$
$720$	−124460.	−0.00894742
$721$	3.24372e6	0.232384
$722$	−8.72171e6	−0.622671
$723$	−1.87485e7	−1.33389
$724$	−1.09205e7	−0.774278
$725$	4.26215e6	0.301151
$726$	4.22488e6	0.297490
$727$	5.16688e6	0.362570	0.181285	−	0.983431i	$-0.441974\pi$
$727$	5.16688e6	0.362570	0.181285	+	0.983431i	$0.441974\pi$
$728$	189632.	0.0132612
$729$	1.53061e7	1.06671
$730$	2.59850e6	0.180474
$731$	−1.73404e7	−1.20023
$732$	−7.52951e6	−0.519385
$733$	1.22580e7	0.842674	0.421337	−	0.906904i	$-0.361561\pi$
$733$	1.22580e7	0.842674	0.421337	+	0.906904i	$0.361561\pi$
$734$	6.16723e6	0.422523
$735$	5.23303e6	0.357302
$736$	541696.	0.0368605
$737$	2.75370e6	0.186745
$738$	−1.14862e6	−0.0776312
$739$	6.69587e6	0.451020	0.225510	−	0.974241i	$-0.427595\pi$
$739$	6.69587e6	0.451020	0.225510	+	0.974241i	$0.427595\pi$
$740$	3.59353e6	0.241236
$741$	454668.	0.0304193
$742$	4.12382e6	0.274973
$743$	−1.34464e7	−0.893581	−0.446790	−	0.894639i	$-0.647433\pi$
$743$	−1.34464e7	−0.893581	−0.446790	+	0.894639i	$0.647433\pi$
$744$	4.63312e6	0.306861
$745$	−7.98020e6	−0.526773
$746$	1.87822e7	1.23566
$747$	−974226.	−0.0638790
$748$	−3.51803e6	−0.229903
$749$	−4.82561e6	−0.314302
$750$	−934481.	−0.0606621
$751$	2.61692e7	1.69313	0.846565	−	0.532286i	$-0.178667\pi$
$751$	2.61692e7	1.69313	0.846565	+	0.532286i	$0.178667\pi$
$752$	−6.21052e6	−0.400482
$753$	−6.42161e6	−0.412721
$754$	1.52548e6	0.0977190
$755$	1.10803e7	0.707434
$756$	3.32648e6	0.211681
$757$	−7.67157e6	−0.486569	−0.243285	−	0.969955i	$-0.578225\pi$
$757$	−7.67157e6	−0.486569	−0.243285	+	0.969955i	$0.578225\pi$
$758$	−3.68804e6	−0.233143
$759$	−2.37822e6	−0.149847
$760$	−870012.	−0.0546376
$761$	−4.07579e6	−0.255123	−0.127562	−	0.991831i	$-0.540715\pi$
$761$	−4.07579e6	−0.255123	−0.127562	+	0.991831i	$0.540715\pi$
$762$	−1.26340e7	−0.788229
$763$	−9.59585e6	−0.596722
$764$	−1.02758e7	−0.636915
$765$	355519.	0.0219639
$766$	−1.61772e7	−0.996164
$767$	1.60819e6	0.0987071
$768$	−979874.	−0.0599470
$769$	2.25401e7	1.37448	0.687241	−	0.726429i	$-0.258822\pi$
$769$	2.25401e7	1.37448	0.687241	+	0.726429i	$0.258822\pi$
$770$	1.59309e6	0.0968306
$771$	1.29526e7	0.784731
$772$	−2.90051e6	−0.175159
$773$	2.85857e6	0.172068	0.0860341	−	0.996292i	$-0.472581\pi$
$773$	2.85857e6	0.172068	0.0860341	+	0.996292i	$0.472581\pi$
$774$	−1.84457e6	−0.110673
$775$	−3.02610e6	−0.180979
$776$	−3.56059e6	−0.212260
$777$	−7.11682e6	−0.422896
$778$	1.89354e7	1.12157
$779$	−8.02923e6	−0.474056
$780$	−334463.	−0.0196839
$781$	2.26898e7	1.33107
$782$	−1.54735e6	−0.0904842
$783$	2.67597e7	1.55983
$784$	−3.58396e6	−0.208244
$785$	−1.08630e7	−0.629182
$786$	1.12191e6	0.0647743
$787$	8.83438e6	0.508440	0.254220	−	0.967146i	$-0.418181\pi$
$787$	8.83438e6	0.508440	0.254220	+	0.967146i	$0.418181\pi$
$788$	−8.31219e6	−0.476870
$789$	−2.27901e7	−1.30333
$790$	−2.93660e6	−0.167408
$791$	3.85911e6	0.219304
$792$	−374227.	−0.0211993
$793$	1.76017e6	0.0993967
$794$	−4.53780e6	−0.255443
$795$	−7.27339e6	−0.408149
$796$	−1.03000e7	−0.576173
$797$	−3.15917e7	−1.76168	−0.880839	−	0.473415i	$-0.843021\pi$
$797$	−3.15917e7	−1.76168	−0.880839	+	0.473415i	$0.843021\pi$
$798$	1.72302e6	0.0957816
$799$	1.77403e7	0.983093
$800$	640000.	0.0353553
$801$	867245.	0.0477596
$802$	3.30805e6	0.181609
$803$	7.81318e6	0.427601
$804$	−2.19090e6	−0.119531
$805$	700696.	0.0381101
$806$	−1.08308e6	−0.0587251
$807$	−1.94194e7	−1.04967
$808$	−8.68094e6	−0.467776
$809$	1.62256e7	0.871625	0.435812	−	0.900038i	$-0.356461\pi$
$809$	1.62256e7	0.871625	0.435812	+	0.900038i	$0.356461\pi$
$810$	−5.39452e6	−0.288895
$811$	7.27121e6	0.388199	0.194100	−	0.980982i	$-0.437821\pi$
$811$	7.27121e6	0.388199	0.194100	+	0.980982i	$0.437821\pi$
$812$	5.78100e6	0.307689
$813$	1.82863e7	0.970284
$814$	1.08051e7	0.571566
$815$	−1.33397e6	−0.0703483
$816$	2.79901e6	0.147156
$817$	−1.28941e7	−0.675828
$818$	−2.64924e7	−1.38433
$819$	−57621.0	−0.00300173
$820$	5.90647e6	0.306756
$821$	−2.29777e7	−1.18973	−0.594865	−	0.803825i	$-0.702795\pi$
$821$	−2.29777e7	−1.18973	−0.594865	+	0.803825i	$0.702795\pi$
$822$	5.91863e6	0.305522
$823$	−3.58281e6	−0.184384	−0.0921922	−	0.995741i	$-0.529387\pi$
$823$	−3.58281e6	−0.184384	−0.0921922	+	0.995741i	$0.529387\pi$
$824$	3.91823e6	0.201035
$825$	−2.80980e6	−0.143728
$826$	6.09442e6	0.310801
$827$	−1.78787e7	−0.909020	−0.454510	−	0.890742i	$-0.650186\pi$
$827$	−1.78787e7	−0.909020	−0.454510	+	0.890742i	$0.650186\pi$
$828$	−164598.	−0.00834351
$829$	5.44878e6	0.275368	0.137684	−	0.990476i	$-0.456034\pi$
$829$	5.44878e6	0.275368	0.137684	+	0.990476i	$0.456034\pi$
$830$	5.00969e6	0.252415
$831$	−2.68209e7	−1.34732
$832$	229065.	0.0114723
$833$	1.02376e7	0.511192
$834$	−9.07014e6	−0.451543
$835$	1.61478e7	0.801490
$836$	−2.61596e6	−0.129454
$837$	−1.89992e7	−0.937392
$838$	−2.68438e7	−1.32049
$839$	7.26039e6	0.356086	0.178043	−	0.984023i	$-0.443023\pi$
$839$	7.26039e6	0.356086	0.178043	+	0.984023i	$0.443023\pi$
$840$	−1.26749e6	−0.0619792
$841$	2.59936e7	1.26729
$842$	−1.21564e7	−0.590915
$843$	2.06879e7	1.00264
$844$	1.14334e7	0.552486
$845$	−9.20414e6	−0.443447
$846$	1.88711e6	0.0906506
$847$	−3.74281e6	−0.179262
$848$	4.98134e6	0.237879
$849$	−422814.	−0.0201317
$850$	−1.82816e6	−0.0867894
$851$	4.75245e6	0.224954
$852$	−1.80524e7	−0.851993
$853$	−4.75995e6	−0.223991	−0.111995	−	0.993709i	$-0.535724\pi$
$853$	−4.75995e6	−0.223991	−0.111995	+	0.993709i	$0.535724\pi$
$854$	6.67037e6	0.312972
$855$	264359.	0.0123674
$856$	−5.82906e6	−0.271903
$857$	−5.35221e6	−0.248932	−0.124466	−	0.992224i	$-0.539722\pi$
$857$	−5.35221e6	−0.248932	−0.124466	+	0.992224i	$0.539722\pi$
$858$	−1.00567e6	−0.0466376
$859$	3.08612e6	0.142702	0.0713510	−	0.997451i	$-0.477269\pi$
$859$	3.08612e6	0.142702	0.0713510	+	0.997451i	$0.477269\pi$
$860$	9.48518e6	0.437320
$861$	−1.16975e7	−0.537755
$862$	−1.67815e7	−0.769242
$863$	−3.48666e6	−0.159361	−0.0796807	−	0.996820i	$-0.525390\pi$
$863$	−3.48666e6	−0.159361	−0.0796807	+	0.996820i	$0.525390\pi$
$864$	4.01820e6	0.183125
$865$	6.01236e6	0.273215
$866$	1.38462e7	0.627386
$867$	1.32339e7	0.597916
$868$	−4.10447e6	−0.184909
$869$	−8.82978e6	−0.396644
$870$	−1.01962e7	−0.456711
$871$	512165.	0.0228752
$872$	−1.15912e7	−0.516225
$873$	1.08191e6	0.0480459
$874$	−1.15059e6	−0.0509498
$875$	827854.	0.0365539
$876$	−6.21631e6	−0.273699
$877$	−4.39790e7	−1.93084	−0.965421	−	0.260696i	$-0.916048\pi$
$877$	−4.39790e7	−1.93084	−0.965421	+	0.260696i	$0.916048\pi$
$878$	1.67283e7	0.732346
$879$	2.51137e7	1.09632
$880$	1.92436e6	0.0837681
$881$	−6.47613e6	−0.281110	−0.140555	−	0.990073i	$-0.544889\pi$
$881$	−6.47613e6	−0.281110	−0.140555	+	0.990073i	$0.544889\pi$
$882$	1.08901e6	0.0471369
$883$	3.38855e7	1.46256	0.731278	−	0.682079i	$-0.238924\pi$
$883$	3.38855e7	1.46256	0.731278	+	0.682079i	$0.238924\pi$
$884$	−654323.	−0.0281619
$885$	−1.07490e7	−0.461329
$886$	1.40966e7	0.603294
$887$	−2.04703e7	−0.873605	−0.436802	−	0.899558i	$-0.643889\pi$
$887$	−2.04703e7	−0.873605	−0.436802	+	0.899558i	$0.643889\pi$
$888$	−8.59670e6	−0.365847
$889$	1.11924e7	0.474973
$890$	−4.45957e6	−0.188720
$891$	−1.62203e7	−0.684486
$892$	1.10287e6	0.0464102
$893$	1.31915e7	0.553560
$894$	1.90908e7	0.798878
$895$	577377.	0.0240936
$896$	868068.	0.0361230
$897$	−442328.	−0.0183554
$898$	−1.84470e7	−0.763368
$899$	−3.30181e7	−1.36255
$900$	−194468.	−0.00800282
$901$	−1.42292e7	−0.583940
$902$	1.77596e7	0.726804
$903$	−1.87849e7	−0.766638
$904$	4.66159e6	0.189720
$905$	−1.70633e7	−0.692536
$906$	−2.65072e7	−1.07286
$907$	2.13343e7	0.861112	0.430556	−	0.902564i	$-0.358317\pi$
$907$	2.13343e7	0.861112	0.430556	+	0.902564i	$0.358317\pi$
$908$	1.04952e7	0.422452
$909$	2.63776e6	0.105883
$910$	296300.	0.0118612
$911$	2.13158e7	0.850955	0.425477	−	0.904969i	$-0.360106\pi$
$911$	2.13158e7	0.850955	0.425477	+	0.904969i	$0.360106\pi$
$912$	2.08130e6	0.0828607
$913$	1.50632e7	0.598052
$914$	1.34152e7	0.531169
$915$	−1.17649e7	−0.464552
$916$	5.99956e6	0.236255
$917$	−993899.	−0.0390318
$918$	−1.14780e7	−0.449530
$919$	4.27746e7	1.67070	0.835348	−	0.549721i	$-0.185266\pi$
$919$	4.27746e7	1.67070	0.835348	+	0.549721i	$0.185266\pi$
$920$	846400.	0.0329690
$921$	1.22353e7	0.475298
$922$	8.00496e6	0.310121
$923$	4.22010e6	0.163049
$924$	−3.81109e6	−0.146849
$925$	5.61490e6	0.215768
$926$	−2.13177e7	−0.816981
$927$	−1.19058e6	−0.0455051
$928$	6.98311e6	0.266182
$929$	2.18331e6	0.0829996	0.0414998	−	0.999139i	$-0.486786\pi$
$929$	2.18331e6	0.0829996	0.0414998	+	0.999139i	$0.486786\pi$
$930$	7.23925e6	0.274465
$931$	7.61252e6	0.287842
$932$	−1.77486e6	−0.0669304
$933$	−2.48178e7	−0.933381
$934$	−1.96795e7	−0.738152
$935$	−5.49692e6	−0.205632
$936$	−69602.9	−0.00259680
$937$	−3.53802e7	−1.31647	−0.658235	−	0.752813i	$-0.728697\pi$
$937$	−3.53802e7	−1.31647	−0.658235	+	0.752813i	$0.728697\pi$
$938$	1.94091e6	0.0720275
$939$	−2.83664e7	−1.04988
$940$	−9.70393e6	−0.358202
$941$	2.25497e7	0.830168	0.415084	−	0.909783i	$-0.363752\pi$
$941$	2.25497e7	0.830168	0.415084	+	0.909783i	$0.363752\pi$
$942$	2.59873e7	0.954186
$943$	7.81131e6	0.286052
$944$	7.36171e6	0.268874
$945$	5.19763e6	0.189333
$946$	2.85201e7	1.03615
$947$	−2.75310e7	−0.997579	−0.498790	−	0.866723i	$-0.666222\pi$
$947$	−2.75310e7	−0.997579	−0.498790	+	0.866723i	$0.666222\pi$
$948$	7.02514e6	0.253883
$949$	1.45318e6	0.0523788
$950$	−1.35939e6	−0.0488693
$951$	−2.92197e7	−1.04767
$952$	−2.47963e6	−0.0886738
$953$	4.72507e7	1.68529	0.842647	−	0.538467i	$-0.180996\pi$
$953$	4.72507e7	1.68529	0.842647	+	0.538467i	$0.180996\pi$
$954$	−1.51361e6	−0.0538449
$955$	−1.60559e7	−0.569674
$956$	−9.44860e6	−0.334366
$957$	−3.06581e7	−1.08209
$958$	−6.43534e6	−0.226547
$959$	−5.24330e6	−0.184102
$960$	−1.53105e6	−0.0536182
$961$	−5.18651e6	−0.181162
$962$	2.00965e6	0.0700136
$963$	1.77120e6	0.0615463
$964$	2.00630e7	0.695351
$965$	−4.53205e6	−0.156667
$966$	−1.67625e6	−0.0577959
$967$	2.69753e7	0.927684	0.463842	−	0.885918i	$-0.346471\pi$
$967$	2.69753e7	0.927684	0.463842	+	0.885918i	$0.346471\pi$
$968$	−4.52110e6	−0.155080
$969$	−5.94524e6	−0.203404
$970$	−5.56343e6	−0.189851
$971$	1.95756e7	0.666296	0.333148	−	0.942875i	$-0.391889\pi$
$971$	1.95756e7	0.666296	0.333148	+	0.942875i	$0.391889\pi$
$972$	−2.35145e6	−0.0798306
$973$	8.03521e6	0.272092
$974$	2.81325e7	0.950190
$975$	−522599.	−0.0176059
$976$	8.05743e6	0.270752
$977$	2.21273e7	0.741638	0.370819	−	0.928705i	$-0.379077\pi$
$977$	2.21273e7	0.741638	0.370819	+	0.928705i	$0.379077\pi$
$978$	3.19123e6	0.106687
$979$	−1.34091e7	−0.447138
$980$	−5.59994e6	−0.186259
$981$	3.52208e6	0.116849
$982$	−2.39219e7	−0.791619
$983$	2.41757e7	0.797987	0.398993	−	0.916954i	$-0.369360\pi$
$983$	2.41757e7	0.797987	0.398993	+	0.916954i	$0.369360\pi$
$984$	−1.41299e7	−0.465212
$985$	−1.29878e7	−0.426525
$986$	−1.99472e7	−0.653417
$987$	1.92182e7	0.627941
$988$	−486546.	−0.0158574
$989$	1.25442e7	0.407803
$990$	−584729.	−0.0189612
$991$	2.41528e7	0.781238	0.390619	−	0.920552i	$-0.372261\pi$
$991$	2.41528e7	0.781238	0.390619	+	0.920552i	$0.372261\pi$
$992$	−4.95796e6	−0.159965
$993$	4.48186e7	1.44240
$994$	1.59926e7	0.513396
$995$	−1.60937e7	−0.515345
$996$	−1.19845e7	−0.382801
$997$	3.92482e7	1.25049	0.625247	−	0.780427i	$-0.284998\pi$
$997$	3.92482e7	1.25049	0.625247	+	0.780427i	$0.284998\pi$
$998$	−3.61853e7	−1.15002
$999$	3.52528e7	1.11758

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.6.a.h.1.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.a.h.1.2	✓	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	230.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} -14.9517 q^{3} +16.0000 q^{4} +25.0000 q^{5} -59.8068 q^{6} +52.9827 q^{7} +64.0000 q^{8} -19.4468 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} -14.9517 q^{3} +16.0000 q^{4} +25.0000 q^{5} -59.8068 q^{6} +52.9827 q^{7} +64.0000 q^{8} -19.4468 q^{9} +100.000 q^{10} +300.681 q^{11} -239.227 q^{12} +55.9240 q^{13} +211.931 q^{14} -373.792 q^{15} +256.000 q^{16} -731.263 q^{17} -77.7874 q^{18} -543.758 q^{19} +400.000 q^{20} -792.181 q^{21} +1202.72 q^{22} +529.000 q^{23} -956.908 q^{24} +625.000 q^{25} +223.696 q^{26} +3924.02 q^{27} +847.723 q^{28} +6819.44 q^{29} -1495.17 q^{30} -4841.76 q^{31} +1024.00 q^{32} -4495.69 q^{33} -2925.05 q^{34} +1324.57 q^{35} -311.149 q^{36} +8983.83 q^{37} -2175.03 q^{38} -836.159 q^{39} +1600.00 q^{40} +14766.2 q^{41} -3168.72 q^{42} +23713.0 q^{43} +4810.89 q^{44} -486.171 q^{45} +2116.00 q^{46} -24259.8 q^{47} -3827.63 q^{48} -13999.8 q^{49} +2500.00 q^{50} +10933.6 q^{51} +894.784 q^{52} +19458.4 q^{53} +15696.1 q^{54} +7517.02 q^{55} +3390.89 q^{56} +8130.10 q^{57} +27277.8 q^{58} +28756.7 q^{59} -5980.68 q^{60} +31474.3 q^{61} -19367.0 q^{62} -1030.35 q^{63} +4096.00 q^{64} +1398.10 q^{65} -17982.7 q^{66} +9158.23 q^{67} -11700.2 q^{68} -7909.45 q^{69} +5298.27 q^{70} +75461.4 q^{71} -1244.60 q^{72} +25985.0 q^{73} +35935.3 q^{74} -9344.81 q^{75} -8700.12 q^{76} +15930.9 q^{77} -3344.63 q^{78} -29366.0 q^{79} +6400.00 q^{80} -53945.2 q^{81} +59064.7 q^{82} +50096.9 q^{83} -12674.9 q^{84} -18281.6 q^{85} +94851.8 q^{86} -101962. q^{87} +19243.6 q^{88} -44595.7 q^{89} -1944.68 q^{90} +2963.00 q^{91} +8464.00 q^{92} +72392.5 q^{93} -97039.3 q^{94} -13593.9 q^{95} -15310.5 q^{96} -55634.3 q^{97} -55999.4 q^{98} -5847.29 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 24 q^{2} + 11 q^{3} + 96 q^{4} + 150 q^{5} + 44 q^{6} + 366 q^{7} + 384 q^{8} + 899 q^{9}+O(q^{10}) \) 6 * q + 24 * q^2 + 11 * q^3 + 96 * q^4 + 150 * q^5 + 44 * q^6 + 366 * q^7 + 384 * q^8 + 899 * q^9	\( 6 q + 24 q^{2} + 11 q^{3} + 96 q^{4} + 150 q^{5} + 44 q^{6} + 366 q^{7} + 384 q^{8} + 899 q^{9} + 600 q^{10} + 151 q^{11} + 176 q^{12} + 463 q^{13} + 1464 q^{14} + 275 q^{15} + 1536 q^{16} + 644 q^{17} + 3596 q^{18} + 3431 q^{19} + 2400 q^{20} - 3846 q^{21} + 604 q^{22} + 3174 q^{23} + 704 q^{24} + 3750 q^{25} + 1852 q^{26} - 3364 q^{27} + 5856 q^{28} + 5973 q^{29} + 1100 q^{30} + 10262 q^{31} + 6144 q^{32} + 23025 q^{33} + 2576 q^{34} + 9150 q^{35} + 14384 q^{36} + 17207 q^{37} + 13724 q^{38} + 14136 q^{39} + 9600 q^{40} + 784 q^{41} - 15384 q^{42} + 13452 q^{43} + 2416 q^{44} + 22475 q^{45} + 12696 q^{46} + 24572 q^{47} + 2816 q^{48} + 28050 q^{49} + 15000 q^{50} + 26125 q^{51} + 7408 q^{52} + 17563 q^{53} - 13456 q^{54} + 3775 q^{55} + 23424 q^{56} - 41798 q^{57} + 23892 q^{58} + 62911 q^{59} + 4400 q^{60} + 32851 q^{61} + 41048 q^{62} + 138693 q^{63} + 24576 q^{64} + 11575 q^{65} + 92100 q^{66} + 54177 q^{67} + 10304 q^{68} + 5819 q^{69} + 36600 q^{70} - 14368 q^{71} + 57536 q^{72} + 33276 q^{73} + 68828 q^{74} + 6875 q^{75} + 54896 q^{76} - 143678 q^{77} + 56544 q^{78} + 74296 q^{79} + 38400 q^{80} + 150834 q^{81} + 3136 q^{82} + 65145 q^{83} - 61536 q^{84} + 16100 q^{85} + 53808 q^{86} - 790 q^{87} + 9664 q^{88} - 67562 q^{89} + 89900 q^{90} - 89487 q^{91} + 50784 q^{92} - 209450 q^{93} + 98288 q^{94} + 85775 q^{95} + 11264 q^{96} - 13201 q^{97} + 112200 q^{98} - 355951 q^{99}+O(q^{100}) \) 6 * q + 24 * q^2 + 11 * q^3 + 96 * q^4 + 150 * q^5 + 44 * q^6 + 366 * q^7 + 384 * q^8 + 899 * q^9 + 600 * q^10 + 151 * q^11 + 176 * q^12 + 463 * q^13 + 1464 * q^14 + 275 * q^15 + 1536 * q^16 + 644 * q^17 + 3596 * q^18 + 3431 * q^19 + 2400 * q^20 - 3846 * q^21 + 604 * q^22 + 3174 * q^23 + 704 * q^24 + 3750 * q^25 + 1852 * q^26 - 3364 * q^27 + 5856 * q^28 + 5973 * q^29 + 1100 * q^30 + 10262 * q^31 + 6144 * q^32 + 23025 * q^33 + 2576 * q^34 + 9150 * q^35 + 14384 * q^36 + 17207 * q^37 + 13724 * q^38 + 14136 * q^39 + 9600 * q^40 + 784 * q^41 - 15384 * q^42 + 13452 * q^43 + 2416 * q^44 + 22475 * q^45 + 12696 * q^46 + 24572 * q^47 + 2816 * q^48 + 28050 * q^49 + 15000 * q^50 + 26125 * q^51 + 7408 * q^52 + 17563 * q^53 - 13456 * q^54 + 3775 * q^55 + 23424 * q^56 - 41798 * q^57 + 23892 * q^58 + 62911 * q^59 + 4400 * q^60 + 32851 * q^61 + 41048 * q^62 + 138693 * q^63 + 24576 * q^64 + 11575 * q^65 + 92100 * q^66 + 54177 * q^67 + 10304 * q^68 + 5819 * q^69 + 36600 * q^70 - 14368 * q^71 + 57536 * q^72 + 33276 * q^73 + 68828 * q^74 + 6875 * q^75 + 54896 * q^76 - 143678 * q^77 + 56544 * q^78 + 74296 * q^79 + 38400 * q^80 + 150834 * q^81 + 3136 * q^82 + 65145 * q^83 - 61536 * q^84 + 16100 * q^85 + 53808 * q^86 - 790 * q^87 + 9664 * q^88 - 67562 * q^89 + 89900 * q^90 - 89487 * q^91 + 50784 * q^92 - 209450 * q^93 + 98288 * q^94 + 85775 * q^95 + 11264 * q^96 - 13201 * q^97 + 112200 * q^98 - 355951 * q^99

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