LMFDB - Embedded newform 230.6.a.h.1.1

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			1.1
Root			$31.1755$ 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)

$f(q)$	$=$	$q+4.00000 q^{2} -29.1755 q^{3} +16.0000 q^{4} +25.0000 q^{5} -116.702 q^{6} +213.932 q^{7} +64.0000 q^{8} +608.209 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} -29.1755 q^{3} +16.0000 q^{4} +25.0000 q^{5} -116.702 q^{6} +213.932 q^{7} +64.0000 q^{8} +608.209 q^{9} +100.000 q^{10} -716.172 q^{11} -466.808 q^{12} -369.244 q^{13} +855.727 q^{14} -729.387 q^{15} +256.000 q^{16} -684.439 q^{17} +2432.83 q^{18} +1921.58 q^{19} +400.000 q^{20} -6241.56 q^{21} -2864.69 q^{22} +529.000 q^{23} -1867.23 q^{24} +625.000 q^{25} -1476.98 q^{26} -10655.1 q^{27} +3422.91 q^{28} -1816.40 q^{29} -2917.55 q^{30} +7880.24 q^{31} +1024.00 q^{32} +20894.7 q^{33} -2737.76 q^{34} +5348.29 q^{35} +9731.34 q^{36} +6902.52 q^{37} +7686.34 q^{38} +10772.9 q^{39} +1600.00 q^{40} -7120.74 q^{41} -24966.2 q^{42} +3354.45 q^{43} -11458.8 q^{44} +15205.2 q^{45} +2116.00 q^{46} +21115.3 q^{47} -7468.92 q^{48} +28959.8 q^{49} +2500.00 q^{50} +19968.8 q^{51} -5907.90 q^{52} -8397.00 q^{53} -42620.6 q^{54} -17904.3 q^{55} +13691.6 q^{56} -56063.2 q^{57} -7265.61 q^{58} +31048.5 q^{59} -11670.2 q^{60} +12612.8 q^{61} +31521.0 q^{62} +130115. q^{63} +4096.00 q^{64} -9231.09 q^{65} +83578.7 q^{66} +40749.9 q^{67} -10951.0 q^{68} -15433.8 q^{69} +21393.2 q^{70} -57020.8 q^{71} +38925.4 q^{72} +25150.5 q^{73} +27610.1 q^{74} -18234.7 q^{75} +30745.4 q^{76} -153212. q^{77} +43091.5 q^{78} +93643.8 q^{79} +6400.00 q^{80} +163074. q^{81} -28483.0 q^{82} +33134.2 q^{83} -99865.0 q^{84} -17111.0 q^{85} +13417.8 q^{86} +52994.4 q^{87} -45835.0 q^{88} -92472.8 q^{89} +60820.9 q^{90} -78992.9 q^{91} +8464.00 q^{92} -229910. q^{93} +84461.3 q^{94} +48039.6 q^{95} -29875.7 q^{96} +81079.6 q^{97} +115839. q^{98} -435582. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−29.1755	−1.87161	−0.935804	−	0.352521i	$-0.885325\pi$
$3$	−29.1755	−1.87161	−0.935804	+	0.352521i	$0.885325\pi$
$4$	16.0000	0.500000
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−116.702	−1.32343
$7$	213.932	1.65017	0.825087	−	0.565005i	$-0.191126\pi$
$7$	213.932	1.65017	0.825087	+	0.565005i	$0.191126\pi$
$8$	64.0000	0.353553
$9$	608.209	2.50292
$10$	100.000	0.316228
$11$	−716.172	−1.78458	−0.892290	−	0.451463i	$-0.850902\pi$
$11$	−716.172	−1.78458	−0.892290	+	0.451463i	$0.850902\pi$
$12$	−466.808	−0.935804
$13$	−369.244	−0.605975	−0.302988	−	0.952995i	$-0.597984\pi$
$13$	−369.244	−0.605975	−0.302988	+	0.952995i	$0.597984\pi$
$14$	855.727	1.16685
$15$	−729.387	−0.837009
$16$	256.000	0.250000
$17$	−684.439	−0.574398	−0.287199	−	0.957871i	$-0.592724\pi$
$17$	−684.439	−0.574398	−0.287199	+	0.957871i	$0.592724\pi$
$18$	2432.83	1.76983
$19$	1921.58	1.22117	0.610584	−	0.791951i	$-0.290935\pi$
$19$	1921.58	1.22117	0.610584	+	0.791951i	$0.290935\pi$
$20$	400.000	0.223607
$21$	−6241.56	−3.08848
$22$	−2864.69	−1.26189
$23$	529.000	0.208514
$23$	529.000	0.208514
$24$	−1867.23	−0.661713
$25$	625.000	0.200000
$26$	−1476.98	−0.428489
$27$	−10655.1	−2.81287
$28$	3422.91	0.825087
$29$	−1816.40	−0.401067	−0.200534	−	0.979687i	$-0.564268\pi$
$29$	−1816.40	−0.401067	−0.200534	+	0.979687i	$0.564268\pi$
$30$	−2917.55	−0.591854
$31$	7880.24	1.47277	0.736386	−	0.676562i	$-0.236531\pi$
$31$	7880.24	1.47277	0.736386	+	0.676562i	$0.236531\pi$
$32$	1024.00	0.176777
$33$	20894.7	3.34003
$34$	−2737.76	−0.406160
$35$	5348.29	0.737981
$36$	9731.34	1.25146
$37$	6902.52	0.828902	0.414451	−	0.910072i	$-0.363974\pi$
$37$	6902.52	0.828902	0.414451	+	0.910072i	$0.363974\pi$
$38$	7686.34	0.863496
$39$	10772.9	1.13415
$40$	1600.00	0.158114
$41$	−7120.74	−0.661554	−0.330777	−	0.943709i	$-0.607311\pi$
$41$	−7120.74	−0.661554	−0.330777	+	0.943709i	$0.607311\pi$
$42$	−24966.2	−2.18389
$43$	3354.45	0.276663	0.138331	−	0.990386i	$-0.455826\pi$
$43$	3354.45	0.276663	0.138331	+	0.990386i	$0.455826\pi$
$44$	−11458.8	−0.892290
$45$	15205.2	1.11934
$46$	2116.00	0.147442
$47$	21115.3	1.39429	0.697145	−	0.716930i	$-0.254453\pi$
$47$	21115.3	1.39429	0.697145	+	0.716930i	$0.254453\pi$
$48$	−7468.92	−0.467902
$49$	28959.8	1.72308
$50$	2500.00	0.141421
$51$	19968.8	1.07505
$52$	−5907.90	−0.302988
$53$	−8397.00	−0.410615	−0.205307	−	0.978698i	$-0.565819\pi$
$53$	−8397.00	−0.410615	−0.205307	+	0.978698i	$0.565819\pi$
$54$	−42620.6	−1.98900
$55$	−17904.3	−0.798088
$56$	13691.6	0.583425
$57$	−56063.2	−2.28555
$58$	−7265.61	−0.283597
$59$	31048.5	1.16121	0.580604	−	0.814186i	$-0.302816\pi$
$59$	31048.5	1.16121	0.580604	+	0.814186i	$0.302816\pi$
$60$	−11670.2	−0.418504
$61$	12612.8	0.433998	0.216999	−	0.976172i	$-0.430373\pi$
$61$	12612.8	0.433998	0.216999	+	0.976172i	$0.430373\pi$
$62$	31521.0	1.04141
$63$	130115.	4.13025
$64$	4096.00	0.125000
$65$	−9231.09	−0.271000
$66$	83578.7	2.36176
$67$	40749.9	1.10902	0.554511	−	0.832177i	$-0.312905\pi$
$67$	40749.9	1.10902	0.554511	+	0.832177i	$0.312905\pi$
$68$	−10951.0	−0.287199
$69$	−15433.8	−0.390257
$70$	21393.2	0.521831
$71$	−57020.8	−1.34242	−0.671208	−	0.741269i	$-0.734224\pi$
$71$	−57020.8	−1.34242	−0.671208	+	0.741269i	$0.734224\pi$
$72$	38925.4	0.884915
$73$	25150.5	0.552381	0.276191	−	0.961103i	$-0.410928\pi$
$73$	25150.5	0.552381	0.276191	+	0.961103i	$0.410928\pi$
$74$	27610.1	0.586122
$75$	−18234.7	−0.374322
$76$	30745.4	0.610584
$77$	−153212.	−2.94487
$78$	43091.5	0.801964
$79$	93643.8	1.68815	0.844076	−	0.536224i	$-0.180150\pi$
$79$	93643.8	1.68815	0.844076	+	0.536224i	$0.180150\pi$
$80$	6400.00	0.111803
$81$	163074.	2.76167
$82$	−28483.0	−0.467790
$83$	33134.2	0.527935	0.263968	−	0.964532i	$-0.414969\pi$
$83$	33134.2	0.527935	0.263968	+	0.964532i	$0.414969\pi$
$84$	−99865.0	−1.54424
$85$	−17111.0	−0.256878
$86$	13417.8	0.195630
$87$	52994.4	0.750641
$88$	−45835.0	−0.630944
$89$	−92472.8	−1.23748	−0.618741	−	0.785595i	$-0.712357\pi$
$89$	−92472.8	−1.23748	−0.618741	+	0.785595i	$0.712357\pi$
$90$	60820.9	0.791492
$91$	−78992.9	−0.999965
$92$	8464.00	0.104257
$93$	−229910.	−2.75645
$94$	84461.3	0.985912
$95$	48039.6	0.546123
$96$	−29875.7	−0.330857
$97$	81079.6	0.874948	0.437474	−	0.899231i	$-0.355873\pi$
$97$	81079.6	0.874948	0.437474	+	0.899231i	$0.355873\pi$
$98$	115839.	1.21840
$99$	−435582.	−4.46665
$100$	10000.0	0.100000
$101$	−29023.0	−0.283099	−0.141550	−	0.989931i	$-0.545208\pi$
$101$	−29023.0	−0.283099	−0.141550	+	0.989931i	$0.545208\pi$
$102$	79875.4	0.760173
$103$	−92435.8	−0.858513	−0.429257	−	0.903183i	$-0.641224\pi$
$103$	−92435.8	−0.858513	−0.429257	+	0.903183i	$0.641224\pi$
$104$	−23631.6	−0.214245
$105$	−156039.	−1.38121
$106$	−33588.0	−0.290348
$107$	148154.	1.25099	0.625496	−	0.780227i	$-0.284897\pi$
$107$	148154.	1.25099	0.625496	+	0.780227i	$0.284897\pi$
$108$	−170482.	−1.40644
$109$	−86116.5	−0.694257	−0.347128	−	0.937818i	$-0.612843\pi$
$109$	−86116.5	−0.694257	−0.347128	+	0.937818i	$0.612843\pi$
$110$	−71617.2	−0.564334
$111$	−201384.	−1.55138
$112$	54766.5	0.412544
$113$	257100.	1.89411	0.947055	−	0.321072i	$-0.104043\pi$
$113$	257100.	1.89411	0.947055	+	0.321072i	$0.104043\pi$
$114$	−224253.	−1.61613
$115$	13225.0	0.0932505
$116$	−29062.4	−0.200534
$117$	−224577.	−1.51671
$118$	124194.	0.821099
$119$	−146423.	−0.947857
$120$	−46680.8	−0.295927
$121$	351852.	2.18472
$122$	50451.2	0.306883
$123$	207751.	1.23817
$124$	126084.	0.736386
$125$	15625.0	0.0894427
$126$	520460.	2.92053
$127$	197587.	1.08705	0.543524	−	0.839394i	$-0.317090\pi$
$127$	197587.	1.08705	0.543524	+	0.839394i	$0.317090\pi$
$128$	16384.0	0.0883883
$129$	−97867.7	−0.517804
$130$	−36924.4	−0.191626
$131$	−312029.	−1.58861	−0.794304	−	0.607520i	$-0.792164\pi$
$131$	−312029.	−1.58861	−0.794304	+	0.607520i	$0.792164\pi$
$132$	334315.	1.67002
$133$	411088.	2.01514
$134$	163000.	0.784197
$135$	−266378.	−1.25795
$136$	−43804.1	−0.203080
$137$	313009.	1.42481	0.712404	−	0.701770i	$-0.247607\pi$
$137$	313009.	1.42481	0.712404	+	0.701770i	$0.247607\pi$
$138$	−61735.3	−0.275954
$139$	−114160.	−0.501163	−0.250581	−	0.968096i	$-0.580622\pi$
$139$	−114160.	−0.501163	−0.250581	+	0.968096i	$0.580622\pi$
$140$	85572.7	0.368990
$141$	−616050.	−2.60956
$142$	−228083.	−0.949232
$143$	264442.	1.08141
$144$	155701.	0.625729
$145$	−45410.1	−0.179363
$146$	100602.	0.390592
$147$	−844915.	−3.22493
$148$	110440.	0.414451
$149$	−15463.5	−0.0570615	−0.0285307	−	0.999593i	$-0.509083\pi$
$149$	−15463.5	−0.0570615	−0.0285307	+	0.999593i	$0.509083\pi$
$150$	−72938.7	−0.264685
$151$	164761.	0.588047	0.294023	−	0.955798i	$-0.405006\pi$
$151$	164761.	0.588047	0.294023	+	0.955798i	$0.405006\pi$
$152$	122981.	0.431748
$153$	−416282.	−1.43767
$154$	−612848.	−2.08234
$155$	197006.	0.658643
$156$	172366.	0.567074
$157$	−80478.9	−0.260575	−0.130288	−	0.991476i	$-0.541590\pi$
$157$	−80478.9	−0.260575	−0.130288	+	0.991476i	$0.541590\pi$
$158$	374575.	1.19370
$159$	244986.	0.768510
$160$	25600.0	0.0790569
$161$	113170.	0.344085
$162$	652296.	1.95280
$163$	622070.	1.83388	0.916938	−	0.399029i	$-0.130653\pi$
$163$	622070.	1.83388	0.916938	+	0.399029i	$0.130653\pi$
$164$	−113932.	−0.330777
$165$	522367.	1.49371
$166$	132537.	0.373307
$167$	−51808.2	−0.143750	−0.0718749	−	0.997414i	$-0.522898\pi$
$167$	−51808.2	−0.143750	−0.0718749	+	0.997414i	$0.522898\pi$
$168$	−399460.	−1.09194
$169$	−234952.	−0.632794
$170$	−68443.9	−0.181640
$171$	1.16872e6	3.05648
$172$	53671.2	0.138331
$173$	−1246.01	−0.00316523	−0.00158261	−	0.999999i	$-0.500504\pi$
$173$	−1246.01	−0.00316523	−0.00158261	+	0.999999i	$0.500504\pi$
$174$	211978.	0.530783
$175$	133707.	0.330035
$176$	−183340.	−0.446145
$177$	−905854.	−2.17333
$178$	−369891.	−0.875032
$179$	362931.	0.846626	0.423313	−	0.905983i	$-0.360867\pi$
$179$	362931.	0.846626	0.423313	+	0.905983i	$0.360867\pi$
$180$	243283.	0.559669
$181$	−518723.	−1.17690	−0.588449	−	0.808534i	$-0.700261\pi$
$181$	−518723.	−1.17690	−0.588449	+	0.808534i	$0.700261\pi$
$182$	−315972.	−0.707082
$183$	−367985.	−0.812273
$184$	33856.0	0.0737210
$185$	172563.	0.370696
$186$	−919639.	−1.94910
$187$	490177.	1.02506
$188$	337845.	0.697145
$189$	−2.27947e6	−4.64173
$190$	192158.	0.386167
$191$	297203.	0.589482	0.294741	−	0.955577i	$-0.404767\pi$
$191$	297203.	0.589482	0.294741	+	0.955577i	$0.404767\pi$
$192$	−119503.	−0.233951
$193$	−738170.	−1.42647	−0.713236	−	0.700924i	$-0.752771\pi$
$193$	−738170.	−1.42647	−0.713236	+	0.700924i	$0.752771\pi$
$194$	324318.	0.618681
$195$	269322.	0.507206
$196$	463356.	0.861539
$197$	218979.	0.402009	0.201005	−	0.979590i	$-0.435579\pi$
$197$	218979.	0.402009	0.201005	+	0.979590i	$0.435579\pi$
$198$	−1.74233e6	−3.15840
$199$	−493991.	−0.884272	−0.442136	−	0.896948i	$-0.645779\pi$
$199$	−493991.	−0.884272	−0.442136	+	0.896948i	$0.645779\pi$
$200$	40000.0	0.0707107
$201$	−1.18890e6	−2.07565
$202$	−116092.	−0.200181
$203$	−388586.	−0.661831
$204$	319502.	0.537524
$205$	−178019.	−0.295856
$206$	−369743.	−0.607060
$207$	321742.	0.521894
$208$	−94526.4	−0.151494
$209$	−1.37619e6	−2.17927
$210$	−624156.	−0.976663
$211$	−161946.	−0.250417	−0.125209	−	0.992130i	$-0.539960\pi$
$211$	−161946.	−0.250417	−0.125209	+	0.992130i	$0.539960\pi$
$212$	−134352.	−0.205307
$213$	1.66361e6	2.51248
$214$	592617.	0.884585
$215$	83861.3	0.123727
$216$	−681929.	−0.994500
$217$	1.68583e6	2.43033
$218$	−344466.	−0.490914
$219$	−733777.	−1.03384
$220$	−286469.	−0.399044
$221$	252725.	0.348071
$222$	−805537.	−1.09699
$223$	−570792.	−0.768627	−0.384313	−	0.923203i	$-0.625562\pi$
$223$	−570792.	−0.768627	−0.384313	+	0.923203i	$0.625562\pi$
$224$	219066.	0.291712
$225$	380130.	0.500583
$226$	1.02840e6	1.33934
$227$	−1.11444e6	−1.43546	−0.717731	−	0.696320i	$-0.754819\pi$
$227$	−1.11444e6	−1.43546	−0.717731	+	0.696320i	$0.754819\pi$
$228$	−897011.	−1.14277
$229$	−1.03370e6	−1.30259	−0.651294	−	0.758826i	$-0.725773\pi$
$229$	−1.03370e6	−1.30259	−0.651294	+	0.758826i	$0.725773\pi$
$230$	52900.0	0.0659380
$231$	4.47003e6	5.51164
$232$	−116250.	−0.141799
$233$	386040.	0.465846	0.232923	−	0.972495i	$-0.425171\pi$
$233$	386040.	0.465846	0.232923	+	0.972495i	$0.425171\pi$
$234$	−898309.	−1.07247
$235$	527883.	0.623545
$236$	496776.	0.580604
$237$	−2.73210e6	−3.15956
$238$	−585693.	−0.670236
$239$	1.72992e6	1.95898	0.979490	−	0.201492i	$-0.0645791\pi$
$239$	1.72992e6	1.95898	0.979490	+	0.201492i	$0.0645791\pi$
$240$	−186723.	−0.209252
$241$	−438715.	−0.486564	−0.243282	−	0.969956i	$-0.578224\pi$
$241$	−438715.	−0.486564	−0.243282	+	0.969956i	$0.578224\pi$
$242$	1.40741e6	1.54483
$243$	−2.16857e6	−2.35590
$244$	201805.	0.216999
$245$	723994.	0.770584
$246$	831004.	0.875519
$247$	−709533.	−0.739998
$248$	504336.	0.520703
$249$	−966705.	−0.988088
$250$	62500.0	0.0632456
$251$	−1.51846e6	−1.52131	−0.760656	−	0.649156i	$-0.775122\pi$
$251$	−1.51846e6	−1.52131	−0.760656	+	0.649156i	$0.775122\pi$
$252$	2.08184e6	2.06512
$253$	−378855.	−0.372110
$254$	790347.	0.768658
$255$	499221.	0.480776
$256$	65536.0	0.0625000
$257$	1.08879e6	1.02828	0.514139	−	0.857707i	$-0.328111\pi$
$257$	1.08879e6	1.02828	0.514139	+	0.857707i	$0.328111\pi$
$258$	−391471.	−0.366143
$259$	1.47667e6	1.36783
$260$	−147698.	−0.135500
$261$	−1.10475e6	−1.00384
$262$	−1.24812e6	−1.12332
$263$	−804734.	−0.717403	−0.358701	−	0.933452i	$-0.616780\pi$
$263$	−804734.	−0.717403	−0.358701	+	0.933452i	$0.616780\pi$
$264$	1.33726e6	1.18088
$265$	−209925.	−0.183632
$266$	1.64435e6	1.42492
$267$	2.69794e6	2.31608
$268$	651999.	0.554511
$269$	1.83054e6	1.54240	0.771202	−	0.636591i	$-0.219656\pi$
$269$	1.83054e6	1.54240	0.771202	+	0.636591i	$0.219656\pi$
$270$	−1.06551e6	−0.889508
$271$	789211.	0.652784	0.326392	−	0.945234i	$-0.394167\pi$
$271$	789211.	0.652784	0.326392	+	0.945234i	$0.394167\pi$
$272$	−175216.	−0.143599
$273$	2.30466e6	1.87154
$274$	1.25204e6	1.00749
$275$	−447608.	−0.356916
$276$	−246941.	−0.195129
$277$	−1.98507e6	−1.55445	−0.777226	−	0.629222i	$-0.783374\pi$
$277$	−1.98507e6	−1.55445	−0.777226	+	0.629222i	$0.783374\pi$
$278$	−456642.	−0.354376
$279$	4.79283e6	3.68622
$280$	342291.	0.260916
$281$	−1.60506e6	−1.21262	−0.606311	−	0.795228i	$-0.707351\pi$
$281$	−1.60506e6	−1.21262	−0.606311	+	0.795228i	$0.707351\pi$
$282$	−2.46420e6	−1.84524
$283$	−1.18298e6	−0.878037	−0.439019	−	0.898478i	$-0.644674\pi$
$283$	−1.18298e6	−0.878037	−0.439019	+	0.898478i	$0.644674\pi$
$284$	−912332.	−0.671208
$285$	−1.40158e6	−1.02213
$286$	1.05777e6	0.764673
$287$	−1.52335e6	−1.09168
$288$	622806.	0.442457
$289$	−951400.	−0.670067
$290$	−181640.	−0.126829
$291$	−2.36554e6	−1.63756
$292$	402407.	0.276191
$293$	−535263.	−0.364249	−0.182124	−	0.983275i	$-0.558297\pi$
$293$	−535263.	−0.364249	−0.182124	+	0.983275i	$0.558297\pi$
$294$	−3.37966e6	−2.28037
$295$	776212.	0.519308
$296$	441761.	0.293061
$297$	7.63092e6	5.01979
$298$	−61854.1	−0.0403486
$299$	−195330.	−0.126355
$300$	−291755.	−0.187161
$301$	717624.	0.456542
$302$	659044.	0.415812
$303$	846760.	0.529851
$304$	491926.	0.305292
$305$	315320.	0.194090
$306$	−1.66513e6	−1.01659
$307$	2.17632e6	1.31788	0.658941	−	0.752195i	$-0.271005\pi$
$307$	2.17632e6	1.31788	0.658941	+	0.752195i	$0.271005\pi$
$308$	−2.45139e6	−1.47243
$309$	2.69686e6	1.60680
$310$	788024.	0.465731
$311$	−978290.	−0.573544	−0.286772	−	0.957999i	$-0.592582\pi$
$311$	−978290.	−0.573544	−0.286772	+	0.957999i	$0.592582\pi$
$312$	689463.	0.400982
$313$	−1.05360e6	−0.607873	−0.303937	−	0.952692i	$-0.598301\pi$
$313$	−1.05360e6	−0.607873	−0.303937	+	0.952692i	$0.598301\pi$
$314$	−321915.	−0.184254
$315$	3.25288e6	1.84710
$316$	1.49830e6	0.844076
$317$	−259370.	−0.144968	−0.0724838	−	0.997370i	$-0.523093\pi$
$317$	−259370.	−0.144968	−0.0724838	+	0.997370i	$0.523093\pi$
$318$	979946.	0.543418
$319$	1.30086e6	0.715736
$320$	102400.	0.0559017
$321$	−4.32247e6	−2.34137
$322$	452679.	0.243305
$323$	−1.31521e6	−0.701436
$324$	2.60919e6	1.38084
$325$	−230777.	−0.121195
$326$	2.48828e6	1.29675
$327$	2.51249e6	1.29938
$328$	−455727.	−0.233895
$329$	4.51724e6	2.30082
$330$	2.08947e6	1.05621
$331$	693796.	0.348066	0.174033	−	0.984740i	$-0.444320\pi$
$331$	693796.	0.348066	0.174033	+	0.984740i	$0.444320\pi$
$332$	530147.	0.263968
$333$	4.19817e6	2.07467
$334$	−207233.	−0.101646
$335$	1.01875e6	0.495970
$336$	−1.59784e6	−0.772120
$337$	−2.10147e6	−1.00797	−0.503985	−	0.863712i	$-0.668133\pi$
$337$	−2.10147e6	−1.00797	−0.503985	+	0.863712i	$0.668133\pi$
$338$	−939808.	−0.447453
$339$	−7.50100e6	−3.54503
$340$	−273776.	−0.128439
$341$	−5.64361e6	−2.62828
$342$	4.67490e6	2.16126
$343$	2.59986e6	1.19320
$344$	214685.	0.0978150
$345$	−385846.	−0.174528
$346$	−4984.02	−0.00223815
$347$	563539.	0.251247	0.125623	−	0.992078i	$-0.459907\pi$
$347$	563539.	0.251247	0.125623	+	0.992078i	$0.459907\pi$
$348$	847911.	0.375320
$349$	1.10434e6	0.485333	0.242666	−	0.970110i	$-0.421978\pi$
$349$	1.10434e6	0.485333	0.242666	+	0.970110i	$0.421978\pi$
$350$	534829.	0.233370
$351$	3.93434e6	1.70453
$352$	−733360.	−0.315472
$353$	847917.	0.362174	0.181087	−	0.983467i	$-0.442039\pi$
$353$	847917.	0.362174	0.181087	+	0.983467i	$0.442039\pi$
$354$	−3.62342e6	−1.53677
$355$	−1.42552e6	−0.600347
$356$	−1.47956e6	−0.618741
$357$	4.27197e6	1.77402
$358$	1.45172e6	0.598655
$359$	1.20028e6	0.491528	0.245764	−	0.969330i	$-0.420961\pi$
$359$	1.20028e6	0.491528	0.245764	+	0.969330i	$0.420961\pi$
$360$	973134.	0.395746
$361$	1.21639e6	0.491252
$362$	−2.07489e6	−0.832192
$363$	−1.02654e7	−4.08895
$364$	−1.26389e6	−0.499982
$365$	628762.	0.247032
$366$	−1.47194e6	−0.574364
$367$	4.57649e6	1.77365	0.886824	−	0.462107i	$-0.152906\pi$
$367$	4.57649e6	1.77365	0.886824	+	0.462107i	$0.152906\pi$
$368$	135424.	0.0521286
$369$	−4.33090e6	−1.65582
$370$	690252.	0.262122
$371$	−1.79638e6	−0.677586
$372$	−3.67856e6	−1.37823
$373$	925019.	0.344254	0.172127	−	0.985075i	$-0.444936\pi$
$373$	925019.	0.344254	0.172127	+	0.985075i	$0.444936\pi$
$374$	1.96071e6	0.724826
$375$	−455867.	−0.167402
$376$	1.35138e6	0.492956
$377$	670695.	0.243037
$378$	−9.11789e6	−3.28220
$379$	−3.89803e6	−1.39395	−0.696975	−	0.717095i	$-0.745471\pi$
$379$	−3.89803e6	−1.39395	−0.696975	+	0.717095i	$0.745471\pi$
$380$	768634.	0.273062
$381$	−5.76469e6	−2.03453
$382$	1.18881e6	0.416827
$383$	2.05608e6	0.716214	0.358107	−	0.933681i	$-0.383422\pi$
$383$	2.05608e6	0.716214	0.358107	+	0.933681i	$0.383422\pi$
$384$	−478011.	−0.165428
$385$	−3.83030e6	−1.31698
$386$	−2.95268e6	−1.00867
$387$	2.04021e6	0.692463
$388$	1.29727e6	0.437474
$389$	−2.66376e6	−0.892525	−0.446262	−	0.894902i	$-0.647245\pi$
$389$	−2.66376e6	−0.892525	−0.446262	+	0.894902i	$0.647245\pi$
$390$	1.07729e6	0.358649
$391$	−362068.	−0.119770
$392$	1.85342e6	0.609200
$393$	9.10360e6	2.97325
$394$	875915.	0.284264
$395$	2.34110e6	0.754964
$396$	−6.96932e6	−2.23333
$397$	975796.	0.310730	0.155365	−	0.987857i	$-0.450345\pi$
$397$	975796.	0.310730	0.155365	+	0.987857i	$0.450345\pi$
$398$	−1.97596e6	−0.625275
$399$	−1.19937e7	−3.77155
$400$	160000.	0.0500000
$401$	4.05673e6	1.25984	0.629919	−	0.776661i	$-0.283088\pi$
$401$	4.05673e6	1.25984	0.629919	+	0.776661i	$0.283088\pi$
$402$	−4.75560e6	−1.46771
$403$	−2.90973e6	−0.892463
$404$	−464368.	−0.141550
$405$	4.07685e6	1.23506
$406$	−1.55434e6	−0.467985
$407$	−4.94339e6	−1.47924
$408$	1.27801e6	0.380087
$409$	−5.45235e6	−1.61167	−0.805833	−	0.592143i	$-0.798282\pi$
$409$	−5.45235e6	−1.61167	−0.805833	+	0.592143i	$0.798282\pi$
$410$	−712074.	−0.209202
$411$	−9.13220e6	−2.66668
$412$	−1.47897e6	−0.429257
$413$	6.64225e6	1.91620
$414$	1.28697e6	0.369035
$415$	828354.	0.236100
$416$	−378106.	−0.107122
$417$	3.33069e6	0.937980
$418$	−5.50474e6	−1.54098
$419$	4.86784e6	1.35457	0.677285	−	0.735721i	$-0.263157\pi$
$419$	4.86784e6	1.35457	0.677285	+	0.735721i	$0.263157\pi$
$420$	−2.49662e6	−0.690605
$421$	1.57556e6	0.433240	0.216620	−	0.976256i	$-0.430497\pi$
$421$	1.57556e6	0.433240	0.216620	+	0.976256i	$0.430497\pi$
$422$	−647785.	−0.177072
$423$	1.28425e7	3.48979
$424$	−537408.	−0.145174
$425$	−427775.	−0.114880
$426$	6.65443e6	1.77659
$427$	2.69828e6	0.716172
$428$	2.37047e6	0.625496
$429$	−7.71523e6	−2.02398
$430$	335445.	0.0874884
$431$	−3.85287e6	−0.999059	−0.499529	−	0.866297i	$-0.666494\pi$
$431$	−3.85287e6	−0.999059	−0.499529	+	0.866297i	$0.666494\pi$
$432$	−2.72772e6	−0.703218
$433$	−294956.	−0.0756027	−0.0378013	−	0.999285i	$-0.512035\pi$
$433$	−294956.	−0.0756027	−0.0378013	+	0.999285i	$0.512035\pi$
$434$	6.74333e6	1.71850
$435$	1.32486e6	0.335697
$436$	−1.37786e6	−0.347128
$437$	1.01652e6	0.254631
$438$	−2.93511e6	−0.731036
$439$	−2.77147e6	−0.686355	−0.343178	−	0.939271i	$-0.611503\pi$
$439$	−2.77147e6	−0.686355	−0.343178	+	0.939271i	$0.611503\pi$
$440$	−1.14588e6	−0.282167
$441$	1.76136e7	4.31272
$442$	1.01090e6	0.246123
$443$	−3.88732e6	−0.941111	−0.470555	−	0.882370i	$-0.655946\pi$
$443$	−3.88732e6	−0.941111	−0.470555	+	0.882370i	$0.655946\pi$
$444$	−3.22215e6	−0.775690
$445$	−2.31182e6	−0.553419
$446$	−2.28317e6	−0.543501
$447$	451156.	0.106797
$448$	876264.	0.206272
$449$	2.50011e6	0.585252	0.292626	−	0.956227i	$-0.405471\pi$
$449$	2.50011e6	0.585252	0.292626	+	0.956227i	$0.405471\pi$
$450$	1.52052e6	0.353966
$451$	5.09968e6	1.18060
$452$	4.11359e6	0.947055
$453$	−4.80698e6	−1.10059
$454$	−4.45776e6	−1.01503
$455$	−1.97482e6	−0.447198
$456$	−3.58804e6	−0.808063
$457$	4.85463e6	1.08734	0.543671	−	0.839299i	$-0.317034\pi$
$457$	4.85463e6	1.08734	0.543671	+	0.839299i	$0.317034\pi$
$458$	−4.13481e6	−0.921069
$459$	7.29280e6	1.61571
$460$	211600.	0.0466252
$461$	8.23478e6	1.80468	0.902339	−	0.431026i	$-0.141848\pi$
$461$	8.23478e6	1.80468	0.902339	+	0.431026i	$0.141848\pi$
$462$	1.78801e7	3.89732
$463$	−4.31435e6	−0.935327	−0.467663	−	0.883907i	$-0.654904\pi$
$463$	−4.31435e6	−0.935327	−0.467663	+	0.883907i	$0.654904\pi$
$464$	−464999.	−0.100267
$465$	−5.74775e6	−1.23272
$466$	1.54416e6	0.329403
$467$	2.44071e6	0.517874	0.258937	−	0.965894i	$-0.416628\pi$
$467$	2.44071e6	0.517874	0.258937	+	0.965894i	$0.416628\pi$
$468$	−3.59324e6	−0.758353
$469$	8.71770e6	1.83008
$470$	2.11153e6	0.440913
$471$	2.34801e6	0.487694
$472$	1.98710e6	0.410549
$473$	−2.40237e6	−0.493726
$474$	−1.09284e7	−2.23414
$475$	1.20099e6	0.244234
$476$	−2.34277e6	−0.473928
$477$	−5.10713e6	−1.02773
$478$	6.91966e6	1.38521
$479$	7.09804e6	1.41351	0.706756	−	0.707457i	$-0.250158\pi$
$479$	7.09804e6	1.41351	0.706756	+	0.707457i	$0.250158\pi$
$480$	−746892.	−0.147964
$481$	−2.54871e6	−0.502294
$482$	−1.75486e6	−0.344052
$483$	−3.30178e6	−0.643993
$484$	5.62963e6	1.09236
$485$	2.02699e6	0.391288
$486$	−8.67427e6	−1.66587
$487$	741794.	0.141730	0.0708648	−	0.997486i	$-0.477424\pi$
$487$	741794.	0.141730	0.0708648	+	0.997486i	$0.477424\pi$
$488$	807220.	0.153441
$489$	−1.81492e7	−3.43230
$490$	2.89598e6	0.544885
$491$	4.06281e6	0.760540	0.380270	−	0.924875i	$-0.375831\pi$
$491$	4.06281e6	0.760540	0.380270	+	0.924875i	$0.375831\pi$
$492$	3.32402e6	0.619085
$493$	1.24322e6	0.230372
$494$	−2.83813e6	−0.523257
$495$	−1.08896e7	−1.99755
$496$	2.01734e6	0.368193
$497$	−1.21985e7	−2.21522
$498$	−3.86682e6	−0.698684
$499$	−2.59650e6	−0.466806	−0.233403	−	0.972380i	$-0.574986\pi$
$499$	−2.59650e6	−0.466806	−0.233403	+	0.972380i	$0.574986\pi$
$500$	250000.	0.0447214
$501$	1.51153e6	0.269043
$502$	−6.07383e6	−1.07573
$503$	−6.60181e6	−1.16344	−0.581719	−	0.813390i	$-0.697620\pi$
$503$	−6.60181e6	−1.16344	−0.581719	+	0.813390i	$0.697620\pi$
$504$	8.32737e6	1.46026
$505$	−725575.	−0.126606
$506$	−1.51542e6	−0.263122
$507$	6.85484e6	1.18434
$508$	3.16139e6	0.543524
$509$	−1.11276e7	−1.90373	−0.951865	−	0.306516i	$-0.900837\pi$
$509$	−1.11276e7	−1.90373	−0.951865	+	0.306516i	$0.900837\pi$
$510$	1.99688e6	0.339960
$511$	5.38048e6	0.911525
$512$	262144.	0.0441942
$513$	−2.04748e7	−3.43499
$514$	4.35515e6	0.727103
$515$	−2.31089e6	−0.383939
$516$	−1.56588e6	−0.258902
$517$	−1.51222e7	−2.48822
$518$	5.90667e6	0.967204
$519$	36352.8	0.00592406
$520$	−590790.	−0.0958131
$521$	−1.61904e6	−0.261314	−0.130657	−	0.991428i	$-0.541709\pi$
$521$	−1.61904e6	−0.261314	−0.130657	+	0.991428i	$0.541709\pi$
$522$	−4.41901e6	−0.709821
$523$	−1.38182e6	−0.220901	−0.110450	−	0.993882i	$-0.535229\pi$
$523$	−1.38182e6	−0.220901	−0.110450	+	0.993882i	$0.535229\pi$
$524$	−4.99247e6	−0.794304
$525$	−3.90097e6	−0.617696
$526$	−3.21894e6	−0.507280
$527$	−5.39355e6	−0.845956
$528$	5.34904e6	0.835008
$529$	279841.	0.0434783
$530$	−839700.	−0.129848
$531$	1.88840e7	2.90641
$532$	6.57741e6	1.00757
$533$	2.62929e6	0.400886
$534$	1.07918e7	1.63772
$535$	3.70386e6	0.559461
$536$	2.60800e6	0.392098
$537$	−1.05887e7	−1.58455
$538$	7.32215e6	1.09064
$539$	−2.07402e7	−3.07497
$540$	−4.26206e6	−0.628977
$541$	−6.37501e6	−0.936457	−0.468229	−	0.883607i	$-0.655108\pi$
$541$	−6.37501e6	−0.936457	−0.468229	+	0.883607i	$0.655108\pi$
$542$	3.15684e6	0.461588
$543$	1.51340e7	2.20269
$544$	−700866.	−0.101540
$545$	−2.15291e6	−0.310481
$546$	9.21863e6	1.32338
$547$	1.14042e6	0.162966	0.0814830	−	0.996675i	$-0.474034\pi$
$547$	1.14042e6	0.162966	0.0814830	+	0.996675i	$0.474034\pi$
$548$	5.00815e6	0.712404
$549$	7.67122e6	1.08626
$550$	−1.79043e6	−0.252378
$551$	−3.49037e6	−0.489771
$552$	−987765.	−0.137977
$553$	2.00334e7	2.78574
$554$	−7.94029e6	−1.09916
$555$	−5.03461e6	−0.693798
$556$	−1.82657e6	−0.250581
$557$	−4.79968e6	−0.655502	−0.327751	−	0.944764i	$-0.606291\pi$
$557$	−4.79968e6	−0.655502	−0.327751	+	0.944764i	$0.606291\pi$
$558$	1.91713e7	2.60655
$559$	−1.23861e6	−0.167651
$560$	1.36916e6	0.184495
$561$	−1.43011e7	−1.91851
$562$	−6.42024e6	−0.857453
$563$	−1.13256e7	−1.50588	−0.752938	−	0.658091i	$-0.771364\pi$
$563$	−1.13256e7	−1.50588	−0.752938	+	0.658091i	$0.771364\pi$
$564$	−9.85680e6	−1.30478
$565$	6.42749e6	0.847072
$566$	−4.73194e6	−0.620866
$567$	3.48867e7	4.55725
$568$	−3.64933e6	−0.474616
$569$	−1.43234e7	−1.85466	−0.927331	−	0.374241i	$-0.877903\pi$
$569$	−1.43234e7	−1.85466	−0.927331	+	0.374241i	$0.877903\pi$
$570$	−5.60632e6	−0.722754
$571$	4.70280e6	0.603623	0.301812	−	0.953368i	$-0.402409\pi$
$571$	4.70280e6	0.603623	0.301812	+	0.953368i	$0.402409\pi$
$572$	4.23107e6	0.540705
$573$	−8.67105e6	−1.10328
$574$	−6.09341e6	−0.771935
$575$	330625.	0.0417029
$576$	2.49122e6	0.312865
$577$	−8.21610e6	−1.02737	−0.513684	−	0.857979i	$-0.671720\pi$
$577$	−8.21610e6	−1.02737	−0.513684	+	0.857979i	$0.671720\pi$
$578$	−3.80560e6	−0.473809
$579$	2.15365e7	2.66980
$580$	−726561.	−0.0896814
$581$	7.08845e6	0.871186
$582$	−9.46214e6	−1.15793
$583$	6.01370e6	0.732774
$584$	1.60963e6	0.195296
$585$	−5.61443e6	−0.678291
$586$	−2.14105e6	−0.257563
$587$	570301.	0.0683138	0.0341569	−	0.999416i	$-0.489125\pi$
$587$	570301.	0.0683138	0.0341569	+	0.999416i	$0.489125\pi$
$588$	−1.35186e7	−1.61246
$589$	1.51426e7	1.79850
$590$	3.10485e6	0.367206
$591$	−6.38881e6	−0.752404
$592$	1.76704e6	0.207226
$593$	1.44969e6	0.169293	0.0846463	−	0.996411i	$-0.473024\pi$
$593$	1.44969e6	0.169293	0.0846463	+	0.996411i	$0.473024\pi$
$594$	3.05237e7	3.54953
$595$	−3.66058e6	−0.423894
$596$	−247416.	−0.0285307
$597$	1.44124e7	1.65501
$598$	−781320.	−0.0893462
$599$	−4.92365e6	−0.560687	−0.280343	−	0.959900i	$-0.590448\pi$
$599$	−4.92365e6	−0.560687	−0.280343	+	0.959900i	$0.590448\pi$
$600$	−1.16702e6	−0.132343
$601$	−7.06073e6	−0.797377	−0.398688	−	0.917086i	$-0.630535\pi$
$601$	−7.06073e6	−0.797377	−0.398688	+	0.917086i	$0.630535\pi$
$602$	2.87049e6	0.322824
$603$	2.47845e7	2.77579
$604$	2.63618e6	0.294023
$605$	8.79630e6	0.977038
$606$	3.38704e6	0.374661
$607$	−1.15131e7	−1.26830	−0.634149	−	0.773211i	$-0.718650\pi$
$607$	−1.15131e7	−1.26830	−0.634149	+	0.773211i	$0.718650\pi$
$608$	1.96770e6	0.215874
$609$	1.13372e7	1.23869
$610$	1.26128e6	0.137242
$611$	−7.79670e6	−0.844905
$612$	−6.66051e6	−0.718835
$613$	1.08921e7	1.17075	0.585373	−	0.810764i	$-0.300948\pi$
$613$	1.08921e7	1.17075	0.585373	+	0.810764i	$0.300948\pi$
$614$	8.70527e6	0.931883
$615$	5.19378e6	0.553727
$616$	−9.80556e6	−1.04117
$617$	−6.67438e6	−0.705827	−0.352913	−	0.935656i	$-0.614809\pi$
$617$	−6.67438e6	−0.705827	−0.352913	+	0.935656i	$0.614809\pi$
$618$	1.07874e7	1.13618
$619$	−6.00300e6	−0.629712	−0.314856	−	0.949140i	$-0.601956\pi$
$619$	−6.00300e6	−0.629712	−0.314856	+	0.949140i	$0.601956\pi$
$620$	3.15210e6	0.329322
$621$	−5.63657e6	−0.586524
$622$	−3.91316e6	−0.405557
$623$	−1.97829e7	−2.04206
$624$	2.75785e6	0.283537
$625$	390625.	0.0400000
$626$	−4.21438e6	−0.429831
$627$	4.01509e7	4.07874
$628$	−1.28766e6	−0.130288
$629$	−4.72435e6	−0.476119
$630$	1.30115e7	1.30610
$631$	1.83793e7	1.83762	0.918809	−	0.394703i	$-0.129152\pi$
$631$	1.83793e7	1.83762	0.918809	+	0.394703i	$0.129152\pi$
$632$	5.99320e6	0.596852
$633$	4.72486e6	0.468683
$634$	−1.03748e6	−0.102508
$635$	4.93967e6	0.486142
$636$	3.91978e6	0.384255
$637$	−1.06932e7	−1.04414
$638$	5.20343e6	0.506102
$639$	−3.46805e7	−3.35996
$640$	409600.	0.0395285
$641$	1.49976e7	1.44171	0.720854	−	0.693087i	$-0.243750\pi$
$641$	1.49976e7	1.44171	0.720854	+	0.693087i	$0.243750\pi$
$642$	−1.72899e7	−1.65560
$643$	407997.	0.0389161	0.0194581	−	0.999811i	$-0.493806\pi$
$643$	407997.	0.0389161	0.0194581	+	0.999811i	$0.493806\pi$
$644$	1.81072e6	0.172043
$645$	−2.44669e6	−0.231569
$646$	−5.26083e6	−0.495990
$647$	−8.16721e6	−0.767032	−0.383516	−	0.923534i	$-0.625287\pi$
$647$	−8.16721e6	−0.767032	−0.383516	+	0.923534i	$0.625287\pi$
$648$	1.04367e7	0.976399
$649$	−2.22361e7	−2.07227
$650$	−923109.	−0.0856978
$651$	−4.91850e7	−4.54863
$652$	9.95311e6	0.916938
$653$	1.73922e7	1.59614	0.798071	−	0.602563i	$-0.205854\pi$
$653$	1.73922e7	1.59614	0.798071	+	0.602563i	$0.205854\pi$
$654$	1.00500e7	0.918798
$655$	−7.80073e6	−0.710447
$656$	−1.82291e6	−0.165389
$657$	1.52967e7	1.38256
$658$	1.80689e7	1.62693
$659$	−1.43284e7	−1.28524	−0.642620	−	0.766185i	$-0.722153\pi$
$659$	−1.43284e7	−1.28524	−0.642620	+	0.766185i	$0.722153\pi$
$660$	8.35787e6	0.746854
$661$	−1.39550e6	−0.124230	−0.0621148	−	0.998069i	$-0.519784\pi$
$661$	−1.39550e6	−0.124230	−0.0621148	+	0.998069i	$0.519784\pi$
$662$	2.77519e6	0.246120
$663$	−7.37337e6	−0.651452
$664$	2.12059e6	0.186653
$665$	1.02772e7	0.901199
$666$	1.67927e7	1.46702
$667$	−960877.	−0.0836283
$668$	−828931.	−0.0718749
$669$	1.66531e7	1.43857
$670$	4.07499e6	0.350703
$671$	−9.03295e6	−0.774503
$672$	−6.39136e6	−0.545971
$673$	−1.28083e7	−1.09007	−0.545033	−	0.838415i	$-0.683483\pi$
$673$	−1.28083e7	−1.09007	−0.545033	+	0.838415i	$0.683483\pi$
$674$	−8.40587e6	−0.712743
$675$	−6.65946e6	−0.562574
$676$	−3.75923e6	−0.316397
$677$	1.99426e7	1.67229	0.836143	−	0.548512i	$-0.184805\pi$
$677$	1.99426e7	1.67229	0.836143	+	0.548512i	$0.184805\pi$
$678$	−3.00040e7	−2.50672
$679$	1.73455e7	1.44382
$680$	−1.09510e6	−0.0908202
$681$	3.25143e7	2.68662
$682$	−2.25744e7	−1.85847
$683$	−9.77674e6	−0.801941	−0.400970	−	0.916091i	$-0.631327\pi$
$683$	−9.77674e6	−0.801941	−0.400970	+	0.916091i	$0.631327\pi$
$684$	1.86996e7	1.52824
$685$	7.82524e6	0.637193
$686$	1.03994e7	0.843723
$687$	3.01588e7	2.43793
$688$	858740.	0.0691656
$689$	3.10054e6	0.248822
$690$	−1.54338e6	−0.123410
$691$	1.17348e7	0.934936	0.467468	−	0.884010i	$-0.345166\pi$
$691$	1.17348e7	0.934936	0.467468	+	0.884010i	$0.345166\pi$
$692$	−19936.1	−0.00158261
$693$	−9.31848e7	−7.37076
$694$	2.25416e6	0.177658
$695$	−2.85401e6	−0.224127
$696$	3.39164e6	0.265392
$697$	4.87372e6	0.379995
$698$	4.41736e6	0.343182
$699$	−1.12629e7	−0.871881
$700$	2.13932e6	0.165017
$701$	−4.53981e6	−0.348934	−0.174467	−	0.984663i	$-0.555820\pi$
$701$	−4.53981e6	−0.348934	−0.174467	+	0.984663i	$0.555820\pi$
$702$	1.57374e7	1.20528
$703$	1.32638e7	1.01223
$704$	−2.93344e6	−0.223072
$705$	−1.54012e7	−1.16703
$706$	3.39167e6	0.256095
$707$	−6.20894e6	−0.467163
$708$	−1.44937e7	−1.08666
$709$	1.35220e7	1.01024	0.505122	−	0.863048i	$-0.331448\pi$
$709$	1.35220e7	1.01024	0.505122	+	0.863048i	$0.331448\pi$
$710$	−5.70208e6	−0.424509
$711$	5.69550e7	4.22530
$712$	−5.91826e6	−0.437516
$713$	4.16865e6	0.307094
$714$	1.70879e7	1.25442
$715$	6.61105e6	0.483622
$716$	5.80690e6	0.423313
$717$	−5.04711e7	−3.66644
$718$	4.80114e6	0.347562
$719$	−1.81588e6	−0.130998	−0.0654991	−	0.997853i	$-0.520864\pi$
$719$	−1.81588e6	−0.130998	−0.0654991	+	0.997853i	$0.520864\pi$
$720$	3.89254e6	0.279835
$721$	−1.97749e7	−1.41670
$722$	4.86556e6	0.347368
$723$	1.27997e7	0.910656
$724$	−8.29956e6	−0.588449
$725$	−1.13525e6	−0.0802135
$726$	−4.10618e7	−2.89132
$727$	1.11475e7	0.782242	0.391121	−	0.920339i	$-0.372087\pi$
$727$	1.11475e7	0.782242	0.391121	+	0.920339i	$0.372087\pi$
$728$	−5.05555e6	−0.353541
$729$	2.36420e7	1.64765
$730$	2.51505e6	0.174678
$731$	−2.29592e6	−0.158914
$732$	−5.88776e6	−0.406137
$733$	1.45612e7	1.00101	0.500505	−	0.865734i	$-0.333148\pi$
$733$	1.45612e7	1.00101	0.500505	+	0.865734i	$0.333148\pi$
$734$	1.83060e7	1.25416
$735$	−2.11229e7	−1.44223
$736$	541696.	0.0368605
$737$	−2.91840e7	−1.97914
$738$	−1.73236e7	−1.17084
$739$	2.14723e7	1.44633	0.723166	−	0.690674i	$-0.242686\pi$
$739$	2.14723e7	1.44633	0.723166	+	0.690674i	$0.242686\pi$
$740$	2.76101e6	0.185348
$741$	2.07010e7	1.38499
$742$	−7.18554e6	−0.479126
$743$	−20357.8	−0.00135288	−0.000676440	−	1.00000i	$-0.500215\pi$
$743$	−20357.8	−0.00135288	−0.000676440		1.00000i	$0.500215\pi$
$744$	−1.47142e7	−0.974552
$745$	−386588.	−0.0255187
$746$	3.70008e6	0.243424
$747$	2.01525e7	1.32138
$748$	7.84282e6	0.512529
$749$	3.16949e7	2.06436
$750$	−1.82347e6	−0.118371
$751$	1.05430e7	0.682125	0.341062	−	0.940041i	$-0.389213\pi$
$751$	1.05430e7	0.682125	0.341062	+	0.940041i	$0.389213\pi$
$752$	5.40552e6	0.348573
$753$	4.43017e7	2.84730
$754$	2.68278e6	0.171853
$755$	4.11902e6	0.262983
$756$	−3.64715e7	−2.32086
$757$	1.99658e7	1.26633	0.633165	−	0.774017i	$-0.281755\pi$
$757$	1.99658e7	1.26633	0.633165	+	0.774017i	$0.281755\pi$
$758$	−1.55921e7	−0.985672
$759$	1.10533e7	0.696445
$760$	3.07454e6	0.193084
$761$	−2.54467e7	−1.59283	−0.796414	−	0.604751i	$-0.793273\pi$
$761$	−2.54467e7	−1.59283	−0.796414	+	0.604751i	$0.793273\pi$
$762$	−2.30587e7	−1.43863
$763$	−1.84230e7	−1.14564
$764$	4.75526e6	0.294741
$765$	−1.04070e7	−0.642945
$766$	8.22431e6	0.506440
$767$	−1.14645e7	−0.703664
$768$	−1.91204e6	−0.116975
$769$	−955.655	−5.82754e−5 0	−2.91377e−5	−	1.00000i	$-0.500009\pi$
$769$	−955.655	−5.82754e−5 0	−2.91377e−5		1.00000i	$0.500009\pi$
$770$	−1.53212e7	−0.931249
$771$	−3.17659e7	−1.92453
$772$	−1.18107e7	−0.713236
$773$	−963607.	−0.0580031	−0.0290015	−	0.999579i	$-0.509233\pi$
$773$	−963607.	−0.0580031	−0.0290015	+	0.999579i	$0.509233\pi$
$774$	8.16083e6	0.489646
$775$	4.92515e6	0.294554
$776$	5.18909e6	0.309341
$777$	−4.30825e7	−2.56005
$778$	−1.06550e7	−0.631110
$779$	−1.36831e7	−0.807869
$780$	4.30915e6	0.253603
$781$	4.08367e7	2.39565
$782$	−1.44827e6	−0.0846903
$783$	1.93540e7	1.12815
$784$	7.41370e6	0.430769
$785$	−2.01197e6	−0.116533
$786$	3.64144e7	2.10241
$787$	−3.02876e7	−1.74312	−0.871561	−	0.490286i	$-0.836892\pi$
$787$	−3.02876e7	−1.74312	−0.871561	+	0.490286i	$0.836892\pi$
$788$	3.50366e6	0.201005
$789$	2.34785e7	1.34270
$790$	9.36438e6	0.533840
$791$	5.50017e7	3.12561
$792$	−2.78773e7	−1.57920
$793$	−4.65720e6	−0.262992
$794$	3.90318e6	0.219719
$795$	6.12466e6	0.343688
$796$	−7.90385e6	−0.442136
$797$	2.80237e6	0.156272	0.0781358	−	0.996943i	$-0.475103\pi$
$797$	2.80237e6	0.156272	0.0781358	+	0.996943i	$0.475103\pi$
$798$	−4.79747e7	−2.66689
$799$	−1.44522e7	−0.800877
$800$	640000.	0.0353553
$801$	−5.62428e7	−3.09732
$802$	1.62269e7	0.890840
$803$	−1.80121e7	−0.985768
$804$	−1.90224e7	−1.03783
$805$	2.82925e6	0.153880
$806$	−1.16389e7	−0.631067
$807$	−5.34068e7	−2.88678
$808$	−1.85747e6	−0.100091
$809$	7.23428e6	0.388619	0.194309	−	0.980940i	$-0.437753\pi$
$809$	7.23428e6	0.388619	0.194309	+	0.980940i	$0.437753\pi$
$810$	1.63074e7	0.873318
$811$	563246.	0.0300709	0.0150354	−	0.999887i	$-0.495214\pi$
$811$	563246.	0.0300709	0.0150354	+	0.999887i	$0.495214\pi$
$812$	−6.21738e6	−0.330916
$813$	−2.30256e7	−1.22176
$814$	−1.97736e7	−1.04598
$815$	1.55517e7	0.820134
$816$	5.11202e6	0.268762
$817$	6.44586e6	0.337852
$818$	−2.18094e7	−1.13962
$819$	−4.80442e7	−2.50283
$820$	−2.84830e6	−0.147928
$821$	−1.53666e7	−0.795645	−0.397822	−	0.917462i	$-0.630234\pi$
$821$	−1.53666e7	−0.795645	−0.397822	+	0.917462i	$0.630234\pi$
$822$	−3.65288e7	−1.88563
$823$	2.71941e7	1.39950	0.699752	−	0.714386i	$-0.253294\pi$
$823$	2.71941e7	1.39950	0.699752	+	0.714386i	$0.253294\pi$
$824$	−5.91589e6	−0.303530
$825$	1.30592e7	0.668007
$826$	2.65690e7	1.35496
$827$	−2.57168e7	−1.30753	−0.653767	−	0.756696i	$-0.726812\pi$
$827$	−2.57168e7	−1.30753	−0.653767	+	0.756696i	$0.726812\pi$
$828$	5.14788e6	0.260947
$829$	3.60565e7	1.82220	0.911102	−	0.412182i	$-0.135233\pi$
$829$	3.60565e7	1.82220	0.911102	+	0.412182i	$0.135233\pi$
$830$	3.31342e6	0.166948
$831$	5.79155e7	2.90932
$832$	−1.51242e6	−0.0757469
$833$	−1.98212e7	−0.989732
$834$	1.33227e7	0.663252
$835$	−1.29521e6	−0.0642869
$836$	−2.20190e7	−1.08964
$837$	−8.39651e7	−4.14271
$838$	1.94714e7	0.957825
$839$	−3.34048e7	−1.63834	−0.819170	−	0.573551i	$-0.805565\pi$
$839$	−3.34048e7	−1.63834	−0.819170	+	0.573551i	$0.805565\pi$
$840$	−9.98650e6	−0.488332
$841$	−1.72118e7	−0.839145
$842$	6.30222e6	0.306347
$843$	4.68284e7	2.26955
$844$	−2.59114e6	−0.125209
$845$	−5.87380e6	−0.282994
$846$	5.13701e7	2.46766
$847$	7.52723e7	3.60518
$848$	−2.14963e6	−0.102654
$849$	3.45141e7	1.64334
$850$	−1.71110e6	−0.0812321
$851$	3.65143e6	0.172838
$852$	2.66177e7	1.25624
$853$	965665.	0.0454416	0.0227208	−	0.999742i	$-0.492767\pi$
$853$	965665.	0.0454416	0.0227208	+	0.999742i	$0.492767\pi$
$854$	1.07931e7	0.506410
$855$	2.92181e7	1.36690
$856$	9.48187e6	0.442293
$857$	−6.70544e6	−0.311871	−0.155936	−	0.987767i	$-0.549839\pi$
$857$	−6.70544e6	−0.311871	−0.155936	+	0.987767i	$0.549839\pi$
$858$	−3.08609e7	−1.43117
$859$	2.86018e6	0.132255	0.0661273	−	0.997811i	$-0.478936\pi$
$859$	2.86018e6	0.132255	0.0661273	+	0.997811i	$0.478936\pi$
$860$	1.34178e6	0.0618636
$861$	4.44445e7	2.04320
$862$	−1.54115e7	−0.706441
$863$	6.50882e6	0.297492	0.148746	−	0.988875i	$-0.452476\pi$
$863$	6.50882e6	0.297492	0.148746	+	0.988875i	$0.452476\pi$
$864$	−1.09109e7	−0.497250
$865$	−31150.1	−0.00141553
$866$	−1.17982e6	−0.0534592
$867$	2.77575e7	1.25410
$868$	2.69733e7	1.21517
$869$	−6.70651e7	−3.01264
$870$	5.29944e6	0.237373
$871$	−1.50467e7	−0.672040
$872$	−5.51146e6	−0.245457
$873$	4.93133e7	2.18992
$874$	4.06607e6	0.180051
$875$	3.34268e6	0.147596
$876$	−1.17404e7	−0.516920
$877$	−2.94213e7	−1.29170	−0.645852	−	0.763462i	$-0.723498\pi$
$877$	−2.94213e7	−1.29170	−0.645852	+	0.763462i	$0.723498\pi$
$878$	−1.10859e7	−0.485326
$879$	1.56166e7	0.681731
$880$	−4.58350e6	−0.199522
$881$	−3.81275e6	−0.165500	−0.0827501	−	0.996570i	$-0.526370\pi$
$881$	−3.81275e6	−0.165500	−0.0827501	+	0.996570i	$0.526370\pi$
$882$	7.04543e7	3.04955
$883$	1.00351e7	0.433133	0.216567	−	0.976268i	$-0.430514\pi$
$883$	1.00351e7	0.433133	0.216567	+	0.976268i	$0.430514\pi$
$884$	4.04360e6	0.174035
$885$	−2.26464e7	−0.971942
$886$	−1.55493e7	−0.665466
$887$	−3.13243e6	−0.133682	−0.0668409	−	0.997764i	$-0.521292\pi$
$887$	−3.13243e6	−0.133682	−0.0668409	+	0.997764i	$0.521292\pi$
$888$	−1.28886e7	−0.548496
$889$	4.22700e7	1.79382
$890$	−9.24728e6	−0.391326
$891$	−1.16789e8	−4.92843
$892$	−9.13267e6	−0.384313
$893$	4.05749e7	1.70266
$894$	1.80462e6	0.0755167
$895$	9.07328e6	0.378623
$896$	3.50506e6	0.145856
$897$	5.69885e6	0.236486
$898$	1.00004e7	0.413836
$899$	−1.43137e7	−0.590680
$900$	6.08209e6	0.250292
$901$	5.74724e6	0.235856
$902$	2.03987e7	0.834808
$903$	−2.09370e7	−0.854467
$904$	1.64544e7	0.669669
$905$	−1.29681e7	−0.526325
$906$	−1.92279e7	−0.778237
$907$	3.78997e6	0.152974	0.0764871	−	0.997071i	$-0.475630\pi$
$907$	3.78997e6	0.152974	0.0764871	+	0.997071i	$0.475630\pi$
$908$	−1.78310e7	−0.717731
$909$	−1.76520e7	−0.708574
$910$	−7.89929e6	−0.316217
$911$	−4.32711e7	−1.72744	−0.863718	−	0.503976i	$-0.831870\pi$
$911$	−4.32711e7	−1.72744	−0.863718	+	0.503976i	$0.831870\pi$
$912$	−1.43522e7	−0.571387
$913$	−2.37298e7	−0.942143
$914$	1.94185e7	0.768867
$915$	−9.19962e6	−0.363260
$916$	−1.65392e7	−0.651294
$917$	−6.67529e7	−2.62148
$918$	2.91712e7	1.14248
$919$	−6.53511e6	−0.255249	−0.127625	−	0.991823i	$-0.540735\pi$
$919$	−6.53511e6	−0.255249	−0.127625	+	0.991823i	$0.540735\pi$
$920$	846400.	0.0329690
$921$	−6.34951e7	−2.46656
$922$	3.29391e7	1.27610
$923$	2.10546e7	0.813471
$924$	7.15205e7	2.75582
$925$	4.31407e6	0.165780
$926$	−1.72574e7	−0.661376
$927$	−5.62202e7	−2.14879
$928$	−1.86000e6	−0.0708993
$929$	−1.71699e7	−0.652722	−0.326361	−	0.945245i	$-0.605822\pi$
$929$	−1.71699e7	−0.652722	−0.326361	+	0.945245i	$0.605822\pi$
$930$	−2.29910e7	−0.871666
$931$	5.56486e7	2.10417
$932$	6.17664e6	0.232923
$933$	2.85421e7	1.07345
$934$	9.76285e6	0.366192
$935$	1.22544e7	0.458420
$936$	−1.43729e7	−0.536236
$937$	1.10426e7	0.410887	0.205443	−	0.978669i	$-0.434136\pi$
$937$	1.10426e7	0.410887	0.205443	+	0.978669i	$0.434136\pi$
$938$	3.48708e7	1.29406
$939$	3.07392e7	1.13770
$940$	8.44613e6	0.311773
$941$	−5.10876e6	−0.188080	−0.0940398	−	0.995568i	$-0.529978\pi$
$941$	−5.10876e6	−0.188080	−0.0940398	+	0.995568i	$0.529978\pi$
$942$	9.39204e6	0.344852
$943$	−3.76687e6	−0.137944
$944$	7.94841e6	0.290302
$945$	−5.69868e7	−2.07584
$946$	−9.60946e6	−0.349117
$947$	3.32941e7	1.20640	0.603202	−	0.797588i	$-0.293891\pi$
$947$	3.32941e7	1.20640	0.603202	+	0.797588i	$0.293891\pi$
$948$	−4.37136e7	−1.57978
$949$	−9.28665e6	−0.334729
$950$	4.80396e6	0.172699
$951$	7.56724e6	0.271323
$952$	−9.37109e6	−0.335118
$953$	−735976.	−0.0262501	−0.0131251	−	0.999914i	$-0.504178\pi$
$953$	−735976.	−0.0262501	−0.0131251	+	0.999914i	$0.504178\pi$
$954$	−2.04285e7	−0.726718
$955$	7.43009e6	0.263624
$956$	2.76786e7	0.979490
$957$	−3.79531e7	−1.33958
$958$	2.83921e7	0.999504
$959$	6.69626e7	2.35118
$960$	−2.98757e6	−0.104626
$961$	3.34691e7	1.16906
$962$	−1.01948e7	−0.355176
$963$	9.01087e7	3.13113
$964$	−7.01943e6	−0.243282
$965$	−1.84543e7	−0.637938
$966$	−1.32071e7	−0.455372
$967$	3.66782e7	1.26137	0.630684	−	0.776040i	$-0.282775\pi$
$967$	3.66782e7	1.26137	0.630684	+	0.776040i	$0.282775\pi$
$968$	2.25185e7	0.772416
$969$	3.83718e7	1.31281
$970$	8.10796e6	0.276683
$971$	3.93365e7	1.33890	0.669449	−	0.742858i	$-0.266530\pi$
$971$	3.93365e7	1.33890	0.669449	+	0.742858i	$0.266530\pi$
$972$	−3.46971e7	−1.17795
$973$	−2.44225e7	−0.827006
$974$	2.96718e6	0.100218
$975$	6.73304e6	0.226830
$976$	3.22888e6	0.108499
$977$	5.41378e7	1.81453	0.907265	−	0.420559i	$-0.138166\pi$
$977$	5.41378e7	1.81453	0.907265	+	0.420559i	$0.138166\pi$
$978$	−7.25967e7	−2.42700
$979$	6.62265e7	2.20839
$980$	1.15839e7	0.385292
$981$	−5.23768e7	−1.73767
$982$	1.62512e7	0.537783
$983$	2.66237e7	0.878789	0.439395	−	0.898294i	$-0.355193\pi$
$983$	2.66237e7	0.878789	0.439395	+	0.898294i	$0.355193\pi$
$984$	1.32961e7	0.437759
$985$	5.47447e6	0.179784
$986$	4.97287e6	0.162898
$987$	−1.31793e8	−4.30624
$988$	−1.13525e7	−0.369999
$989$	1.77451e6	0.0576881
$990$	−4.35582e7	−1.41248
$991$	−4.14887e6	−0.134198	−0.0670989	−	0.997746i	$-0.521374\pi$
$991$	−4.14887e6	−0.134198	−0.0670989	+	0.997746i	$0.521374\pi$
$992$	8.06937e6	0.260352
$993$	−2.02418e7	−0.651444
$994$	−4.87942e7	−1.56640
$995$	−1.23498e7	−0.395459
$996$	−1.54673e7	−0.494044
$997$	4.09554e6	0.130489	0.0652444	−	0.997869i	$-0.479217\pi$
$997$	4.09554e6	0.130489	0.0652444	+	0.997869i	$0.479217\pi$
$998$	−1.03860e7	−0.330081
$999$	−7.35473e7	−2.33159

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.a.h.1.1	✓	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)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} -29.1755 q^{3} +16.0000 q^{4} +25.0000 q^{5} -116.702 q^{6} +213.932 q^{7} +64.0000 q^{8} +608.209 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} -29.1755 q^{3} +16.0000 q^{4} +25.0000 q^{5} -116.702 q^{6} +213.932 q^{7} +64.0000 q^{8} +608.209 q^{9} +100.000 q^{10} -716.172 q^{11} -466.808 q^{12} -369.244 q^{13} +855.727 q^{14} -729.387 q^{15} +256.000 q^{16} -684.439 q^{17} +2432.83 q^{18} +1921.58 q^{19} +400.000 q^{20} -6241.56 q^{21} -2864.69 q^{22} +529.000 q^{23} -1867.23 q^{24} +625.000 q^{25} -1476.98 q^{26} -10655.1 q^{27} +3422.91 q^{28} -1816.40 q^{29} -2917.55 q^{30} +7880.24 q^{31} +1024.00 q^{32} +20894.7 q^{33} -2737.76 q^{34} +5348.29 q^{35} +9731.34 q^{36} +6902.52 q^{37} +7686.34 q^{38} +10772.9 q^{39} +1600.00 q^{40} -7120.74 q^{41} -24966.2 q^{42} +3354.45 q^{43} -11458.8 q^{44} +15205.2 q^{45} +2116.00 q^{46} +21115.3 q^{47} -7468.92 q^{48} +28959.8 q^{49} +2500.00 q^{50} +19968.8 q^{51} -5907.90 q^{52} -8397.00 q^{53} -42620.6 q^{54} -17904.3 q^{55} +13691.6 q^{56} -56063.2 q^{57} -7265.61 q^{58} +31048.5 q^{59} -11670.2 q^{60} +12612.8 q^{61} +31521.0 q^{62} +130115. q^{63} +4096.00 q^{64} -9231.09 q^{65} +83578.7 q^{66} +40749.9 q^{67} -10951.0 q^{68} -15433.8 q^{69} +21393.2 q^{70} -57020.8 q^{71} +38925.4 q^{72} +25150.5 q^{73} +27610.1 q^{74} -18234.7 q^{75} +30745.4 q^{76} -153212. q^{77} +43091.5 q^{78} +93643.8 q^{79} +6400.00 q^{80} +163074. q^{81} -28483.0 q^{82} +33134.2 q^{83} -99865.0 q^{84} -17111.0 q^{85} +13417.8 q^{86} +52994.4 q^{87} -45835.0 q^{88} -92472.8 q^{89} +60820.9 q^{90} -78992.9 q^{91} +8464.00 q^{92} -229910. q^{93} +84461.3 q^{94} +48039.6 q^{95} -29875.7 q^{96} +81079.6 q^{97} +115839. q^{98} -435582. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 24 q^{2} + 11 q^{3} + 96 q^{4} + 150 q^{5} + 44 q^{6} + 366 q^{7} + 384 q^{8} + 899 q^{9}+O(q^{10}) \) 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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