LMFDB - Embedded newform 230.6.a.g.1.4

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:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 772x^{3} - 255x^{2} + 13416x + 10080 $ x^5 - 772x^3 - 255x^2 + 13416*x + 10080
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			1.4
Root			$4.40191$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} +5.40191 q^{3} +16.0000 q^{4} -25.0000 q^{5} -21.6076 q^{6} -140.289 q^{7} -64.0000 q^{8} -213.819 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +5.40191 q^{3} +16.0000 q^{4} -25.0000 q^{5} -21.6076 q^{6} -140.289 q^{7} -64.0000 q^{8} -213.819 q^{9} +100.000 q^{10} -585.979 q^{11} +86.4305 q^{12} -238.483 q^{13} +561.154 q^{14} -135.048 q^{15} +256.000 q^{16} +2090.75 q^{17} +855.278 q^{18} -732.649 q^{19} -400.000 q^{20} -757.826 q^{21} +2343.92 q^{22} +529.000 q^{23} -345.722 q^{24} +625.000 q^{25} +953.931 q^{26} -2467.70 q^{27} -2244.62 q^{28} +3924.22 q^{29} +540.191 q^{30} +292.998 q^{31} -1024.00 q^{32} -3165.41 q^{33} -8363.01 q^{34} +3507.21 q^{35} -3421.11 q^{36} +5132.28 q^{37} +2930.59 q^{38} -1288.26 q^{39} +1600.00 q^{40} +10511.8 q^{41} +3031.30 q^{42} +2424.70 q^{43} -9375.67 q^{44} +5345.48 q^{45} -2116.00 q^{46} -23539.3 q^{47} +1382.89 q^{48} +2873.87 q^{49} -2500.00 q^{50} +11294.1 q^{51} -3815.72 q^{52} -22763.9 q^{53} +9870.79 q^{54} +14649.5 q^{55} +8978.46 q^{56} -3957.70 q^{57} -15696.9 q^{58} -263.242 q^{59} -2160.76 q^{60} +47683.4 q^{61} -1171.99 q^{62} +29996.4 q^{63} +4096.00 q^{64} +5962.07 q^{65} +12661.6 q^{66} -9969.94 q^{67} +33452.0 q^{68} +2857.61 q^{69} -14028.9 q^{70} +17061.3 q^{71} +13684.4 q^{72} +43830.1 q^{73} -20529.1 q^{74} +3376.19 q^{75} -11722.4 q^{76} +82206.1 q^{77} +5153.05 q^{78} +90142.5 q^{79} -6400.00 q^{80} +38627.8 q^{81} -42047.1 q^{82} +42021.0 q^{83} -12125.2 q^{84} -52268.8 q^{85} -9698.81 q^{86} +21198.3 q^{87} +37502.7 q^{88} -88102.8 q^{89} -21381.9 q^{90} +33456.4 q^{91} +8464.00 q^{92} +1582.75 q^{93} +94157.3 q^{94} +18316.2 q^{95} -5531.55 q^{96} +45440.7 q^{97} -11495.5 q^{98} +125294. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 20 q^{2} + 5 q^{3} + 80 q^{4} - 125 q^{5} - 20 q^{6} + 130 q^{7} - 320 q^{8} + 334 q^{9}+O(q^{10}) $ 5 * q - 20 * q^2 + 5 * q^3 + 80 * q^4 - 125 * q^5 - 20 * q^6 + 130 * q^7 - 320 * q^8 + 334 * q^9	\( 5 q - 20 q^{2} + 5 q^{3} + 80 q^{4} - 125 q^{5} - 20 q^{6} + 130 q^{7} - 320 q^{8} + 334 q^{9} + 500 q^{10} + 81 q^{11} + 80 q^{12} - 753 q^{13} - 520 q^{14} - 125 q^{15} + 1280 q^{16} - 1780 q^{17} - 1336 q^{18} + 1933 q^{19} - 2000 q^{20} - 2526 q^{21} - 324 q^{22} + 2645 q^{23} - 320 q^{24} + 3125 q^{25} + 3012 q^{26} + 2972 q^{27} + 2080 q^{28} + 3527 q^{29} + 500 q^{30} + 1816 q^{31} - 5120 q^{32} - 21947 q^{33} + 7120 q^{34} - 3250 q^{35} + 5344 q^{36} + 11683 q^{37} - 7732 q^{38} + 12580 q^{39} + 8000 q^{40} - 9602 q^{41} + 10104 q^{42} - 2232 q^{43} + 1296 q^{44} - 8350 q^{45} - 10580 q^{46} - 14552 q^{47} + 1280 q^{48} + 25889 q^{49} - 12500 q^{50} + 31351 q^{51} - 12048 q^{52} - 23069 q^{53} - 11888 q^{54} - 2025 q^{55} - 8320 q^{56} + 95210 q^{57} - 14108 q^{58} + 43917 q^{59} - 2000 q^{60} + 107483 q^{61} - 7264 q^{62} + 119033 q^{63} + 20480 q^{64} + 18825 q^{65} + 87788 q^{66} + 133125 q^{67} - 28480 q^{68} + 2645 q^{69} + 13000 q^{70} + 103326 q^{71} - 21376 q^{72} + 125870 q^{73} - 46732 q^{74} + 3125 q^{75} + 30928 q^{76} + 110422 q^{77} - 50320 q^{78} + 274892 q^{79} - 32000 q^{80} + 316657 q^{81} + 38408 q^{82} + 106201 q^{83} - 40416 q^{84} + 44500 q^{85} + 8928 q^{86} + 23782 q^{87} - 5184 q^{88} + 57800 q^{89} + 33400 q^{90} + 272163 q^{91} + 42320 q^{92} + 198110 q^{93} + 58208 q^{94} - 48325 q^{95} - 5120 q^{96} - 24935 q^{97} - 103556 q^{98} + 362547 q^{99}+O(q^{100}) \) 5 * q - 20 * q^2 + 5 * q^3 + 80 * q^4 - 125 * q^5 - 20 * q^6 + 130 * q^7 - 320 * q^8 + 334 * q^9 + 500 * q^10 + 81 * q^11 + 80 * q^12 - 753 * q^13 - 520 * q^14 - 125 * q^15 + 1280 * q^16 - 1780 * q^17 - 1336 * q^18 + 1933 * q^19 - 2000 * q^20 - 2526 * q^21 - 324 * q^22 + 2645 * q^23 - 320 * q^24 + 3125 * q^25 + 3012 * q^26 + 2972 * q^27 + 2080 * q^28 + 3527 * q^29 + 500 * q^30 + 1816 * q^31 - 5120 * q^32 - 21947 * q^33 + 7120 * q^34 - 3250 * q^35 + 5344 * q^36 + 11683 * q^37 - 7732 * q^38 + 12580 * q^39 + 8000 * q^40 - 9602 * q^41 + 10104 * q^42 - 2232 * q^43 + 1296 * q^44 - 8350 * q^45 - 10580 * q^46 - 14552 * q^47 + 1280 * q^48 + 25889 * q^49 - 12500 * q^50 + 31351 * q^51 - 12048 * q^52 - 23069 * q^53 - 11888 * q^54 - 2025 * q^55 - 8320 * q^56 + 95210 * q^57 - 14108 * q^58 + 43917 * q^59 - 2000 * q^60 + 107483 * q^61 - 7264 * q^62 + 119033 * q^63 + 20480 * q^64 + 18825 * q^65 + 87788 * q^66 + 133125 * q^67 - 28480 * q^68 + 2645 * q^69 + 13000 * q^70 + 103326 * q^71 - 21376 * q^72 + 125870 * q^73 - 46732 * q^74 + 3125 * q^75 + 30928 * q^76 + 110422 * q^77 - 50320 * q^78 + 274892 * q^79 - 32000 * q^80 + 316657 * q^81 + 38408 * q^82 + 106201 * q^83 - 40416 * q^84 + 44500 * q^85 + 8928 * q^86 + 23782 * q^87 - 5184 * q^88 + 57800 * q^89 + 33400 * q^90 + 272163 * q^91 + 42320 * q^92 + 198110 * q^93 + 58208 * q^94 - 48325 * q^95 - 5120 * q^96 - 24935 * q^97 - 103556 * q^98 + 362547 * 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
$3$	5.40191	0.346533	0.173266	−	0.984875i	$-0.444568\pi$
$3$	5.40191	0.346533	0.173266	+	0.984875i	$0.444568\pi$
$4$	16.0000	0.500000
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−21.6076	−0.245036
$7$	−140.289	−1.08212	−0.541062	−	0.840983i	$-0.681978\pi$
$7$	−140.289	−1.08212	−0.541062	+	0.840983i	$0.681978\pi$
$8$	−64.0000	−0.353553
$9$	−213.819	−0.879915
$10$	100.000	0.316228
$11$	−585.979	−1.46016	−0.730080	−	0.683362i	$-0.760517\pi$
$11$	−585.979	−1.46016	−0.730080	+	0.683362i	$0.760517\pi$
$12$	86.4305	0.173266
$13$	−238.483	−0.391380	−0.195690	−	0.980666i	$-0.562695\pi$
$13$	−238.483	−0.391380	−0.195690	+	0.980666i	$0.562695\pi$
$14$	561.154	0.765177
$15$	−135.048	−0.154974
$16$	256.000	0.250000
$17$	2090.75	1.75461	0.877304	−	0.479934i	$-0.159340\pi$
$17$	2090.75	1.75461	0.877304	+	0.479934i	$0.159340\pi$
$18$	855.278	0.622194
$19$	−732.649	−0.465599	−0.232799	−	0.972525i	$-0.574789\pi$
$19$	−732.649	−0.465599	−0.232799	+	0.972525i	$0.574789\pi$
$20$	−400.000	−0.223607
$21$	−757.826	−0.374991
$22$	2343.92	1.03249
$23$	529.000	0.208514
$23$	529.000	0.208514
$24$	−345.722	−0.122518
$25$	625.000	0.200000
$26$	953.931	0.276747
$27$	−2467.70	−0.651452
$28$	−2244.62	−0.541062
$29$	3924.22	0.866480	0.433240	−	0.901279i	$-0.357370\pi$
$29$	3924.22	0.866480	0.433240	+	0.901279i	$0.357370\pi$
$30$	540.191	0.109583
$31$	292.998	0.0547597	0.0273798	−	0.999625i	$-0.491284\pi$
$31$	292.998	0.0547597	0.0273798	+	0.999625i	$0.491284\pi$
$32$	−1024.00	−0.176777
$33$	−3165.41	−0.505993
$34$	−8363.01	−1.24070
$35$	3507.21	0.483941
$36$	−3421.11	−0.439958
$37$	5132.28	0.616319	0.308160	−	0.951335i	$-0.400287\pi$
$37$	5132.28	0.616319	0.308160	+	0.951335i	$0.400287\pi$
$38$	2930.59	0.329228
$39$	−1288.26	−0.135626
$40$	1600.00	0.158114
$41$	10511.8	0.976599	0.488300	−	0.872676i	$-0.337617\pi$
$41$	10511.8	0.976599	0.488300	+	0.872676i	$0.337617\pi$
$42$	3031.30	0.265159
$43$	2424.70	0.199980	0.0999902	−	0.994988i	$-0.468119\pi$
$43$	2424.70	0.199980	0.0999902	+	0.994988i	$0.468119\pi$
$44$	−9375.67	−0.730080
$45$	5345.48	0.393510
$46$	−2116.00	−0.147442
$47$	−23539.3	−1.55435	−0.777176	−	0.629283i	$-0.783349\pi$
$47$	−23539.3	−1.55435	−0.777176	+	0.629283i	$0.783349\pi$
$48$	1382.89	0.0866332
$49$	2873.87	0.170992
$50$	−2500.00	−0.141421
$51$	11294.1	0.608029
$52$	−3815.72	−0.195690
$53$	−22763.9	−1.11316	−0.556580	−	0.830794i	$-0.687887\pi$
$53$	−22763.9	−1.11316	−0.556580	+	0.830794i	$0.687887\pi$
$54$	9870.79	0.460646
$55$	14649.5	0.653003
$56$	8978.46	0.382589
$57$	−3957.70	−0.161345
$58$	−15696.9	−0.612694
$59$	−263.242	−0.00984523	−0.00492261	−	0.999988i	$-0.501567\pi$
$59$	−263.242	−0.00984523	−0.00492261	+	0.999988i	$0.501567\pi$
$60$	−2160.76	−0.0774870
$61$	47683.4	1.64075	0.820375	−	0.571827i	$-0.193765\pi$
$61$	47683.4	1.64075	0.820375	+	0.571827i	$0.193765\pi$
$62$	−1171.99	−0.0387209
$63$	29996.4	0.952177
$64$	4096.00	0.125000
$65$	5962.07	0.175030
$66$	12661.6	0.357791
$67$	−9969.94	−0.271335	−0.135667	−	0.990754i	$-0.543318\pi$
$67$	−9969.94	−0.271335	−0.135667	+	0.990754i	$0.543318\pi$
$68$	33452.0	0.877304
$69$	2857.61	0.0722570
$70$	−14028.9	−0.342198
$71$	17061.3	0.401668	0.200834	−	0.979625i	$-0.435635\pi$
$71$	17061.3	0.401668	0.200834	+	0.979625i	$0.435635\pi$
$72$	13684.4	0.311097
$73$	43830.1	0.962644	0.481322	−	0.876544i	$-0.340157\pi$
$73$	43830.1	0.962644	0.481322	+	0.876544i	$0.340157\pi$
$74$	−20529.1	−0.435804
$75$	3376.19	0.0693065
$76$	−11722.4	−0.232799
$77$	82206.1	1.58007
$78$	5153.05	0.0959020
$79$	90142.5	1.62503	0.812516	−	0.582940i	$-0.198098\pi$
$79$	90142.5	1.62503	0.812516	+	0.582940i	$0.198098\pi$
$80$	−6400.00	−0.111803
$81$	38627.8	0.654166
$82$	−42047.1	−0.690560
$83$	42021.0	0.669532	0.334766	−	0.942301i	$-0.391343\pi$
$83$	42021.0	0.669532	0.334766	+	0.942301i	$0.391343\pi$
$84$	−12125.2	−0.187496
$85$	−52268.8	−0.784685
$86$	−9698.81	−0.141407
$87$	21198.3	0.300264
$88$	37502.7	0.516245
$89$	−88102.8	−1.17900	−0.589501	−	0.807767i	$-0.700676\pi$
$89$	−88102.8	−1.17900	−0.589501	+	0.807767i	$0.700676\pi$
$90$	−21381.9	−0.278254
$91$	33456.4	0.423522
$92$	8464.00	0.104257
$93$	1582.75	0.0189760
$94$	94157.3	1.09909
$95$	18316.2	0.208222
$96$	−5531.55	−0.0612589
$97$	45440.7	0.490361	0.245180	−	0.969477i	$-0.421153\pi$
$97$	45440.7	0.490361	0.245180	+	0.969477i	$0.421153\pi$
$98$	−11495.5	−0.120910
$99$	125294.	1.28482
$100$	10000.0	0.100000
$101$	85003.7	0.829152	0.414576	−	0.910015i	$-0.363930\pi$
$101$	85003.7	0.829152	0.414576	+	0.910015i	$0.363930\pi$
$102$	−45176.2	−0.429942
$103$	−87971.0	−0.817046	−0.408523	−	0.912748i	$-0.633956\pi$
$103$	−87971.0	−0.817046	−0.408523	+	0.912748i	$0.633956\pi$
$104$	15262.9	0.138374
$105$	18945.6	0.167701
$106$	91055.8	0.787123
$107$	76481.6	0.645799	0.322900	−	0.946433i	$-0.395342\pi$
$107$	76481.6	0.645799	0.322900	+	0.946433i	$0.395342\pi$
$108$	−39483.1	−0.325726
$109$	22318.1	0.179925	0.0899624	−	0.995945i	$-0.471325\pi$
$109$	22318.1	0.179925	0.0899624	+	0.995945i	$0.471325\pi$
$110$	−58597.9	−0.461743
$111$	27724.1	0.213575
$112$	−35913.9	−0.270531
$113$	−199393.	−1.46897	−0.734487	−	0.678623i	$-0.762577\pi$
$113$	−199393.	−1.46897	−0.734487	+	0.678623i	$0.762577\pi$
$114$	15830.8	0.114088
$115$	−13225.0	−0.0932505
$116$	62787.6	0.433240
$117$	50992.2	0.344381
$118$	1052.97	0.00696163
$119$	−293309.	−1.89870
$120$	8643.05	0.0547916
$121$	182321.	1.13207
$122$	−190733.	−1.16018
$123$	56783.6	0.338423
$124$	4687.97	0.0273798
$125$	−15625.0	−0.0894427
$126$	−119986.	−0.673291
$127$	−13583.4	−0.0747306	−0.0373653	−	0.999302i	$-0.511897\pi$
$127$	−13583.4	−0.0747306	−0.0373653	+	0.999302i	$0.511897\pi$
$128$	−16384.0	−0.0883883
$129$	13098.0	0.0692997
$130$	−23848.3	−0.123765
$131$	129991.	0.661812	0.330906	−	0.943664i	$-0.392646\pi$
$131$	129991.	0.661812	0.330906	+	0.943664i	$0.392646\pi$
$132$	−50646.5	−0.252997
$133$	102782.	0.503836
$134$	39879.8	0.191863
$135$	61692.4	0.291338
$136$	−133808.	−0.620348
$137$	−19997.6	−0.0910281	−0.0455141	−	0.998964i	$-0.514493\pi$
$137$	−19997.6	−0.0910281	−0.0455141	+	0.998964i	$0.514493\pi$
$138$	−11430.4	−0.0510934
$139$	−168322.	−0.738929	−0.369464	−	0.929245i	$-0.620459\pi$
$139$	−168322.	−0.738929	−0.369464	+	0.929245i	$0.620459\pi$
$140$	56115.4	0.241970
$141$	−127157.	−0.538634
$142$	−68245.3	−0.284022
$143$	139746.	0.571477
$144$	−54737.8	−0.219979
$145$	−98105.6	−0.387502
$146$	−175320.	−0.680692
$147$	15524.4	0.0592544
$148$	82116.4	0.308160
$149$	63098.7	0.232839	0.116419	−	0.993200i	$-0.462858\pi$
$149$	63098.7	0.232839	0.116419	+	0.993200i	$0.462858\pi$
$150$	−13504.8	−0.0490071
$151$	−317247.	−1.13228	−0.566142	−	0.824308i	$-0.691565\pi$
$151$	−317247.	−1.13228	−0.566142	+	0.824308i	$0.691565\pi$
$152$	46889.5	0.164614
$153$	−447043.	−1.54391
$154$	−328825.	−1.11728
$155$	−7324.96	−0.0244893
$156$	−20612.2	−0.0678130
$157$	−215751.	−0.698559	−0.349280	−	0.937019i	$-0.613574\pi$
$157$	−215751.	−0.698559	−0.349280	+	0.937019i	$0.613574\pi$
$158$	−360570.	−1.14907
$159$	−122969.	−0.385746
$160$	25600.0	0.0790569
$161$	−74212.6	−0.225638
$162$	−154511.	−0.462565
$163$	609956.	1.79816	0.899082	−	0.437779i	$-0.144235\pi$
$163$	609956.	1.79816	0.899082	+	0.437779i	$0.144235\pi$
$164$	168188.	0.488300
$165$	79135.1	0.226287
$166$	−168084.	−0.473430
$167$	−405550.	−1.12526	−0.562630	−	0.826709i	$-0.690210\pi$
$167$	−405550.	−1.12526	−0.562630	+	0.826709i	$0.690210\pi$
$168$	48500.8	0.132579
$169$	−314419.	−0.846822
$170$	209075.	0.554856
$171$	156654.	0.409687
$172$	38795.2	0.0999902
$173$	316263.	0.803403	0.401701	−	0.915771i	$-0.368419\pi$
$173$	316263.	0.803403	0.401701	+	0.915771i	$0.368419\pi$
$174$	−84793.2	−0.212318
$175$	−87680.3	−0.216425
$176$	−150011.	−0.365040
$177$	−1422.01	−0.00341169
$178$	352411.	0.833681
$179$	110128.	0.256900	0.128450	−	0.991716i	$-0.459000\pi$
$179$	110128.	0.256900	0.128450	+	0.991716i	$0.459000\pi$
$180$	85527.8	0.196755
$181$	408874.	0.927668	0.463834	−	0.885922i	$-0.346473\pi$
$181$	408874.	0.927668	0.463834	+	0.885922i	$0.346473\pi$
$182$	−133826.	−0.299475
$183$	257581.	0.568573
$184$	−33856.0	−0.0737210
$185$	−128307.	−0.275626
$186$	−6331.00	−0.0134181
$187$	−1.22514e6	−2.56201
$188$	−376629.	−0.777176
$189$	346189.	0.704952
$190$	−73264.9	−0.147235
$191$	523485.	1.03830	0.519148	−	0.854685i	$-0.326249\pi$
$191$	523485.	1.03830	0.519148	+	0.854685i	$0.326249\pi$
$192$	22126.2	0.0433166
$193$	463129.	0.894971	0.447485	−	0.894291i	$-0.352320\pi$
$193$	463129.	0.894971	0.447485	+	0.894291i	$0.352320\pi$
$194$	−181763.	−0.346737
$195$	32206.5	0.0606538
$196$	45981.9	0.0854961
$197$	−647480.	−1.18867	−0.594334	−	0.804218i	$-0.702584\pi$
$197$	−647480.	−1.18867	−0.594334	+	0.804218i	$0.702584\pi$
$198$	−501175.	−0.908503
$199$	637164.	1.14056	0.570280	−	0.821450i	$-0.306835\pi$
$199$	637164.	1.14056	0.570280	+	0.821450i	$0.306835\pi$
$200$	−40000.0	−0.0707107
$201$	−53856.7	−0.0940264
$202$	−340015.	−0.586299
$203$	−550523.	−0.937639
$204$	180705.	0.304015
$205$	−262794.	−0.436748
$206$	351884.	0.577739
$207$	−113110.	−0.183475
$208$	−61051.6	−0.0978450
$209$	429317.	0.679849
$210$	−75782.6	−0.118583
$211$	−238284.	−0.368459	−0.184230	−	0.982883i	$-0.558979\pi$
$211$	−238284.	−0.368459	−0.184230	+	0.982883i	$0.558979\pi$
$212$	−364223.	−0.556580
$213$	92163.7	0.139191
$214$	−305926.	−0.456649
$215$	−60617.6	−0.0894339
$216$	157933.	0.230323
$217$	−41104.3	−0.0592567
$218$	−89272.4	−0.127226
$219$	236766.	0.333587
$220$	234392.	0.326502
$221$	−498608.	−0.686719
$222$	−110896.	−0.151020
$223$	930645.	1.25320	0.626602	−	0.779339i	$-0.284445\pi$
$223$	930645.	1.25320	0.626602	+	0.779339i	$0.284445\pi$
$224$	143655.	0.191294
$225$	−133637.	−0.175983
$226$	797572.	1.03872
$227$	−717013.	−0.923554	−0.461777	−	0.886996i	$-0.652788\pi$
$227$	−717013.	−0.923554	−0.461777	+	0.886996i	$0.652788\pi$
$228$	−63323.2	−0.0806726
$229$	381612.	0.480876	0.240438	−	0.970665i	$-0.422709\pi$
$229$	381612.	0.480876	0.240438	+	0.970665i	$0.422709\pi$
$230$	52900.0	0.0659380
$231$	444070.	0.547547
$232$	−251150.	−0.306347
$233$	−1.47920e6	−1.78500	−0.892500	−	0.451048i	$-0.851050\pi$
$233$	−1.47920e6	−1.78500	−0.892500	+	0.451048i	$0.851050\pi$
$234$	−203969.	−0.243514
$235$	588483.	0.695128
$236$	−4211.88	−0.00492261
$237$	486941.	0.563126
$238$	1.17323e6	1.34259
$239$	18751.8	0.0212348	0.0106174	−	0.999944i	$-0.496620\pi$
$239$	18751.8	0.0212348	0.0106174	+	0.999944i	$0.496620\pi$
$240$	−34572.2	−0.0387435
$241$	1.42975e6	1.58569	0.792843	−	0.609425i	$-0.208600\pi$
$241$	1.42975e6	1.58569	0.792843	+	0.609425i	$0.208600\pi$
$242$	−729282.	−0.800493
$243$	808314.	0.878142
$244$	762934.	0.820375
$245$	−71846.6	−0.0764700
$246$	−227135.	−0.239302
$247$	174724.	0.182226
$248$	−18751.9	−0.0193605
$249$	226994.	0.232014
$250$	62500.0	0.0632456
$251$	1.08095e6	1.08298	0.541491	−	0.840707i	$-0.317860\pi$
$251$	1.08095e6	1.08298	0.541491	+	0.840707i	$0.317860\pi$
$252$	479942.	0.476089
$253$	−309983.	−0.304464
$254$	54333.5	0.0528425
$255$	−282351.	−0.271919
$256$	65536.0	0.0625000
$257$	−468038.	−0.442027	−0.221013	−	0.975271i	$-0.570936\pi$
$257$	−468038.	−0.442027	−0.221013	+	0.975271i	$0.570936\pi$
$258$	−52392.1	−0.0490023
$259$	−719999.	−0.666934
$260$	95393.1	0.0875152
$261$	−839075.	−0.762429
$262$	−519963.	−0.467972
$263$	−1.03524e6	−0.922896	−0.461448	−	0.887167i	$-0.652670\pi$
$263$	−1.03524e6	−0.922896	−0.461448	+	0.887167i	$0.652670\pi$
$264$	202586.	0.178896
$265$	569099.	0.497821
$266$	−411129.	−0.356266
$267$	−475923.	−0.408563
$268$	−159519.	−0.135667
$269$	572226.	0.482155	0.241078	−	0.970506i	$-0.422499\pi$
$269$	572226.	0.482155	0.241078	+	0.970506i	$0.422499\pi$
$270$	−246770.	−0.206007
$271$	637924.	0.527650	0.263825	−	0.964571i	$-0.415016\pi$
$271$	637924.	0.527650	0.263825	+	0.964571i	$0.415016\pi$
$272$	535233.	0.438652
$273$	180728.	0.146764
$274$	79990.2	0.0643666
$275$	−366237.	−0.292032
$276$	45721.8	0.0361285
$277$	1.19267e6	0.933941	0.466971	−	0.884273i	$-0.345345\pi$
$277$	1.19267e6	0.933941	0.466971	+	0.884273i	$0.345345\pi$
$278$	673286.	0.522502
$279$	−62648.7	−0.0481839
$280$	−224462.	−0.171099
$281$	54582.3	0.0412369	0.0206184	−	0.999787i	$-0.493436\pi$
$281$	54582.3	0.0412369	0.0206184	+	0.999787i	$0.493436\pi$
$282$	508629.	0.380872
$283$	1.47904e6	1.09777	0.548887	−	0.835897i	$-0.315052\pi$
$283$	1.47904e6	1.09777	0.548887	+	0.835897i	$0.315052\pi$
$284$	272981.	0.200834
$285$	98942.5	0.0721557
$286$	−558984.	−0.404096
$287$	−1.47468e6	−1.05680
$288$	218951.	0.155548
$289$	2.95139e6	2.07865
$290$	392422.	0.274005
$291$	245467.	0.169926
$292$	701282.	0.481322
$293$	−1.25534e6	−0.854264	−0.427132	−	0.904189i	$-0.640476\pi$
$293$	−1.25534e6	−0.854264	−0.427132	+	0.904189i	$0.640476\pi$
$294$	−62097.4	−0.0418992
$295$	6581.06	0.00440292
$296$	−328466.	−0.217902
$297$	1.44602e6	0.951224
$298$	−252395.	−0.164642
$299$	−126157.	−0.0816084
$300$	54019.1	0.0346533
$301$	−340158.	−0.216403
$302$	1.26899e6	0.800645
$303$	459182.	0.287328
$304$	−187558.	−0.116400
$305$	−1.19208e6	−0.733765
$306$	1.78817e6	1.09171
$307$	−2.47061e6	−1.49609	−0.748046	−	0.663647i	$-0.769008\pi$
$307$	−2.47061e6	−1.49609	−0.748046	+	0.663647i	$0.769008\pi$
$308$	1.31530e6	0.790037
$309$	−475212.	−0.283133
$310$	29299.8	0.0173165
$311$	−1.28274e6	−0.752037	−0.376018	−	0.926612i	$-0.622707\pi$
$311$	−1.28274e6	−0.752037	−0.376018	+	0.926612i	$0.622707\pi$
$312$	82448.8	0.0479510
$313$	1.80637e6	1.04219	0.521093	−	0.853500i	$-0.325524\pi$
$313$	1.80637e6	1.04219	0.521093	+	0.853500i	$0.325524\pi$
$314$	863003.	0.493956
$315$	−749910.	−0.425827
$316$	1.44228e6	0.812516
$317$	−1.27196e6	−0.710927	−0.355463	−	0.934690i	$-0.615677\pi$
$317$	−1.27196e6	−0.710927	−0.355463	+	0.934690i	$0.615677\pi$
$318$	491875.	0.272764
$319$	−2.29951e6	−1.26520
$320$	−102400.	−0.0559017
$321$	413146.	0.223790
$322$	296850.	0.159550
$323$	−1.53179e6	−0.816944
$324$	618045.	0.327083
$325$	−149052.	−0.0782760
$326$	−2.43982e6	−1.27149
$327$	120560.	0.0623498
$328$	−672754.	−0.345280
$329$	3.30230e6	1.68200
$330$	−316541.	−0.160009
$331$	−3.51562e6	−1.76373	−0.881864	−	0.471503i	$-0.843712\pi$
$331$	−3.51562e6	−1.76373	−0.881864	+	0.471503i	$0.843712\pi$
$332$	672336.	0.334766
$333$	−1.09738e6	−0.542309
$334$	1.62220e6	0.795679
$335$	249249.	0.121345
$336$	−194003.	−0.0937478
$337$	−864668.	−0.414739	−0.207369	−	0.978263i	$-0.566490\pi$
$337$	−864668.	−0.414739	−0.207369	+	0.978263i	$0.566490\pi$
$338$	1.25768e6	0.598793
$339$	−1.07710e6	−0.509047
$340$	−836301.	−0.392342
$341$	−171691.	−0.0799579
$342$	−626618.	−0.289693
$343$	1.95466e6	0.897089
$344$	−155181.	−0.0707037
$345$	−71440.2	−0.0323143
$346$	−1.26505e6	−0.568092
$347$	−28061.3	−0.0125108	−0.00625539	−	0.999980i	$-0.501991\pi$
$347$	−28061.3	−0.0125108	−0.00625539	+	0.999980i	$0.501991\pi$
$348$	339173.	0.150132
$349$	1.28173e6	0.563292	0.281646	−	0.959518i	$-0.409120\pi$
$349$	1.28173e6	0.563292	0.281646	+	0.959518i	$0.409120\pi$
$350$	350721.	0.153035
$351$	588503.	0.254965
$352$	600043.	0.258122
$353$	3.70382e6	1.58203	0.791013	−	0.611800i	$-0.209554\pi$
$353$	3.70382e6	1.58203	0.791013	+	0.611800i	$0.209554\pi$
$354$	5688.04	0.00241243
$355$	−426533.	−0.179631
$356$	−1.40965e6	−0.589501
$357$	−1.58443e6	−0.657963
$358$	−440510.	−0.181656
$359$	1.83577e6	0.751767	0.375883	−	0.926667i	$-0.377339\pi$
$359$	1.83577e6	0.751767	0.375883	+	0.926667i	$0.377339\pi$
$360$	−342111.	−0.139127
$361$	−1.93932e6	−0.783218
$362$	−1.63549e6	−0.655961
$363$	984879.	0.392298
$364$	535302.	0.211761
$365$	−1.09575e6	−0.430507
$366$	−1.03032e6	−0.402042
$367$	−1.88815e6	−0.731763	−0.365881	−	0.930661i	$-0.619232\pi$
$367$	−1.88815e6	−0.731763	−0.365881	+	0.930661i	$0.619232\pi$
$368$	135424.	0.0521286
$369$	−2.24762e6	−0.859325
$370$	513228.	0.194897
$371$	3.19352e6	1.20458
$372$	25324.0	0.00948801
$373$	−1.69444e6	−0.630600	−0.315300	−	0.948992i	$-0.602105\pi$
$373$	−1.69444e6	−0.630600	−0.315300	+	0.948992i	$0.602105\pi$
$374$	4.90055e6	1.81161
$375$	−84404.8	−0.0309948
$376$	1.50652e6	0.549547
$377$	−935859.	−0.339123
$378$	−1.38476e6	−0.498476
$379$	2.28364e6	0.816638	0.408319	−	0.912839i	$-0.366115\pi$
$379$	2.28364e6	0.816638	0.408319	+	0.912839i	$0.366115\pi$
$380$	293059.	0.104111
$381$	−73376.1	−0.0258966
$382$	−2.09394e6	−0.734186
$383$	−2.65602e6	−0.925197	−0.462598	−	0.886568i	$-0.653083\pi$
$383$	−2.65602e6	−0.925197	−0.462598	+	0.886568i	$0.653083\pi$
$384$	−88504.9	−0.0306294
$385$	−2.05515e6	−0.706631
$386$	−1.85252e6	−0.632840
$387$	−518448.	−0.175966
$388$	727051.	0.245180
$389$	4.44643e6	1.48983	0.744916	−	0.667159i	$-0.232490\pi$
$389$	4.44643e6	1.48983	0.744916	+	0.667159i	$0.232490\pi$
$390$	−128826.	−0.0428887
$391$	1.10601e6	0.365861
$392$	−183927.	−0.0604549
$393$	702199.	0.229339
$394$	2.58992e6	0.840516
$395$	−2.25356e6	−0.726736
$396$	2.00470e6	0.642408
$397$	5.73344e6	1.82574	0.912871	−	0.408248i	$-0.133860\pi$
$397$	5.73344e6	1.82574	0.912871	+	0.408248i	$0.133860\pi$
$398$	−2.54865e6	−0.806498
$399$	555220.	0.174595
$400$	160000.	0.0500000
$401$	2.68773e6	0.834689	0.417345	−	0.908748i	$-0.362961\pi$
$401$	2.68773e6	0.834689	0.417345	+	0.908748i	$0.362961\pi$
$402$	215427.	0.0664867
$403$	−69875.0	−0.0214318
$404$	1.36006e6	0.414576
$405$	−965696.	−0.292552
$406$	2.20209e6	0.663011
$407$	−3.00741e6	−0.899925
$408$	−722819.	−0.214971
$409$	−1.55452e6	−0.459501	−0.229751	−	0.973250i	$-0.573791\pi$
$409$	−1.55452e6	−0.459501	−0.229751	+	0.973250i	$0.573791\pi$
$410$	1.05118e6	0.308828
$411$	−108025.	−0.0315442
$412$	−1.40754e6	−0.408523
$413$	36929.9	0.0106538
$414$	452442.	0.129736
$415$	−1.05052e6	−0.299424
$416$	244206.	0.0691869
$417$	−909258.	−0.256063
$418$	−1.71727e6	−0.480726
$419$	−1.12253e6	−0.312364	−0.156182	−	0.987728i	$-0.549919\pi$
$419$	−1.12253e6	−0.312364	−0.156182	+	0.987728i	$0.549919\pi$
$420$	303130.	0.0838506
$421$	617549.	0.169811	0.0849056	−	0.996389i	$-0.472941\pi$
$421$	617549.	0.169811	0.0849056	+	0.996389i	$0.472941\pi$
$422$	953137.	0.260540
$423$	5.03317e6	1.36770
$424$	1.45689e6	0.393562
$425$	1.30672e6	0.350922
$426$	−368655.	−0.0984229
$427$	−6.68943e6	−1.77549
$428$	1.22371e6	0.322900
$429$	754895.	0.198036
$430$	242470.	0.0632393
$431$	3.55233e6	0.921130	0.460565	−	0.887626i	$-0.347647\pi$
$431$	3.55233e6	0.921130	0.460565	+	0.887626i	$0.347647\pi$
$432$	−631730.	−0.162863
$433$	5.87329e6	1.50543	0.752717	−	0.658344i	$-0.228743\pi$
$433$	5.87329e6	1.50543	0.752717	+	0.658344i	$0.228743\pi$
$434$	164417.	0.0419008
$435$	−529957.	−0.134282
$436$	357090.	0.0899624
$437$	−387571.	−0.0970840
$438$	−947065.	−0.235882
$439$	−1.43952e6	−0.356498	−0.178249	−	0.983985i	$-0.557043\pi$
$439$	−1.43952e6	−0.356498	−0.178249	+	0.983985i	$0.557043\pi$
$440$	−937567.	−0.230872
$441$	−614488.	−0.150459
$442$	1.99443e6	0.485583
$443$	−6.91813e6	−1.67486	−0.837432	−	0.546542i	$-0.815944\pi$
$443$	−6.91813e6	−1.67486	−0.837432	+	0.546542i	$0.815944\pi$
$444$	443585.	0.106787
$445$	2.20257e6	0.527266
$446$	−3.72258e6	−0.886149
$447$	340854.	0.0806862
$448$	−574622.	−0.135265
$449$	−6.78928e6	−1.58931	−0.794654	−	0.607063i	$-0.792348\pi$
$449$	−6.78928e6	−1.58931	−0.794654	+	0.607063i	$0.792348\pi$
$450$	534548.	0.124439
$451$	−6.15968e6	−1.42599
$452$	−3.19029e6	−0.734487
$453$	−1.71374e6	−0.392373
$454$	2.86805e6	0.653051
$455$	−836410.	−0.189405
$456$	253293.	0.0570441
$457$	−6.82189e6	−1.52797	−0.763984	−	0.645236i	$-0.776759\pi$
$457$	−6.82189e6	−1.52797	−0.763984	+	0.645236i	$0.776759\pi$
$458$	−1.52645e6	−0.340031
$459$	−5.15934e6	−1.14304
$460$	−211600.	−0.0466252
$461$	431457.	0.0945552	0.0472776	−	0.998882i	$-0.484945\pi$
$461$	431457.	0.0945552	0.0472776	+	0.998882i	$0.484945\pi$
$462$	−1.77628e6	−0.387174
$463$	−174449.	−0.0378195	−0.0189098	−	0.999821i	$-0.506020\pi$
$463$	−174449.	−0.0378195	−0.0189098	+	0.999821i	$0.506020\pi$
$464$	1.00460e6	0.216620
$465$	−39568.7	−0.00848633
$466$	5.91681e6	1.26219
$467$	4.76836e6	1.01176	0.505879	−	0.862605i	$-0.331168\pi$
$467$	4.76836e6	1.01176	0.505879	+	0.862605i	$0.331168\pi$
$468$	815876.	0.172191
$469$	1.39867e6	0.293618
$470$	−2.35393e6	−0.491529
$471$	−1.16547e6	−0.242073
$472$	16847.5	0.00348081
$473$	−1.42083e6	−0.292003
$474$	−1.94777e6	−0.398190
$475$	−457905.	−0.0931197
$476$	−4.69294e6	−0.949352
$477$	4.86737e6	0.979487
$478$	−75007.1	−0.0150152
$479$	−6.16515e6	−1.22774	−0.613868	−	0.789409i	$-0.710387\pi$
$479$	−6.16515e6	−1.22774	−0.613868	+	0.789409i	$0.710387\pi$
$480$	138289.	0.0273958
$481$	−1.22396e6	−0.241215
$482$	−5.71900e6	−1.12125
$483$	−400890.	−0.0781911
$484$	2.91713e6	0.566034
$485$	−1.13602e6	−0.219296
$486$	−3.23326e6	−0.620940
$487$	3.18391e6	0.608329	0.304165	−	0.952619i	$-0.401623\pi$
$487$	3.18391e6	0.608329	0.304165	+	0.952619i	$0.401623\pi$
$488$	−3.05173e6	−0.580092
$489$	3.29493e6	0.623123
$490$	287387.	0.0540725
$491$	−8.90645e6	−1.66725	−0.833625	−	0.552331i	$-0.813738\pi$
$491$	−8.90645e6	−1.66725	−0.833625	+	0.552331i	$0.813738\pi$
$492$	908538.	0.169212
$493$	8.20458e6	1.52033
$494$	−698896.	−0.128853
$495$	−3.13234e6	−0.574588
$496$	75007.6	0.0136899
$497$	−2.39351e6	−0.434654
$498$	−907974.	−0.164059
$499$	−2.31592e6	−0.416363	−0.208181	−	0.978090i	$-0.566754\pi$
$499$	−2.31592e6	−0.416363	−0.208181	+	0.978090i	$0.566754\pi$
$500$	−250000.	−0.0447214
$501$	−2.19074e6	−0.389939
$502$	−4.32380e6	−0.765783
$503$	6.67301e6	1.17598	0.587992	−	0.808866i	$-0.299919\pi$
$503$	6.67301e6	1.17598	0.587992	+	0.808866i	$0.299919\pi$
$504$	−1.91977e6	−0.336645
$505$	−2.12509e6	−0.370808
$506$	1.23993e6	0.215289
$507$	−1.69846e6	−0.293451
$508$	−217334.	−0.0373653
$509$	−485108.	−0.0829936	−0.0414968	−	0.999139i	$-0.513213\pi$
$509$	−485108.	−0.0829936	−0.0414968	+	0.999139i	$0.513213\pi$
$510$	1.12941e6	0.192276
$511$	−6.14886e6	−1.04170
$512$	−262144.	−0.0441942
$513$	1.80795e6	0.303315
$514$	1.87215e6	0.312560
$515$	2.19928e6	0.365394
$516$	209568.	0.0346499
$517$	1.37936e7	2.26960
$518$	2.88000e6	0.471593
$519$	1.70842e6	0.278405
$520$	−381572.	−0.0618826
$521$	9.10686e6	1.46985	0.734927	−	0.678146i	$-0.237216\pi$
$521$	9.10686e6	1.46985	0.734927	+	0.678146i	$0.237216\pi$
$522$	3.35630e6	0.539119
$523$	−1.23811e6	−0.197927	−0.0989634	−	0.995091i	$-0.531553\pi$
$523$	−1.23811e6	−0.197927	−0.0989634	+	0.995091i	$0.531553\pi$
$524$	2.07985e6	0.330906
$525$	−473641.	−0.0749982
$526$	4.14097e6	0.652586
$527$	612587.	0.0960818
$528$	−810344.	−0.126498
$529$	279841.	0.0434783
$530$	−2.27639e6	−0.352012
$531$	56286.3	0.00866296
$532$	1.64452e6	0.251918
$533$	−2.50688e6	−0.382221
$534$	1.90369e6	0.288898
$535$	−1.91204e6	−0.288810
$536$	638076.	0.0959314
$537$	594899.	0.0890241
$538$	−2.28890e6	−0.340935
$539$	−1.68403e6	−0.249676
$540$	987079.	0.145669
$541$	1.25423e7	1.84240	0.921202	−	0.389084i	$-0.127208\pi$
$541$	1.25423e7	1.84240	0.921202	+	0.389084i	$0.127208\pi$
$542$	−2.55170e6	−0.373105
$543$	2.20870e6	0.321467
$544$	−2.14093e6	−0.310174
$545$	−557953.	−0.0804648
$546$	−722913.	−0.103778
$547$	6.74184e6	0.963408	0.481704	−	0.876334i	$-0.340018\pi$
$547$	6.74184e6	0.963408	0.481704	+	0.876334i	$0.340018\pi$
$548$	−319961.	−0.0455141
$549$	−1.01956e7	−1.44372
$550$	1.46495e6	0.206498
$551$	−2.87508e6	−0.403432
$552$	−182887.	−0.0255467
$553$	−1.26460e7	−1.75848
$554$	−4.77066e6	−0.660396
$555$	−693102.	−0.0955135
$556$	−2.69314e6	−0.369464
$557$	−2.98727e6	−0.407978	−0.203989	−	0.978973i	$-0.565391\pi$
$557$	−2.98727e6	−0.407978	−0.203989	+	0.978973i	$0.565391\pi$
$558$	250595.	0.0340711
$559$	−578250.	−0.0782683
$560$	897846.	0.120985
$561$	−6.61808e6	−0.887820
$562$	−218329.	−0.0291589
$563$	5.71442e6	0.759803	0.379901	−	0.925027i	$-0.375958\pi$
$563$	5.71442e6	0.759803	0.379901	+	0.925027i	$0.375958\pi$
$564$	−2.03452e6	−0.269317
$565$	4.98483e6	0.656945
$566$	−5.91615e6	−0.776243
$567$	−5.41904e6	−0.707889
$568$	−1.09193e6	−0.142011
$569$	5.16575e6	0.668887	0.334444	−	0.942416i	$-0.391452\pi$
$569$	5.16575e6	0.668887	0.334444	+	0.942416i	$0.391452\pi$
$570$	−395770.	−0.0510218
$571$	−4.70272e6	−0.603613	−0.301807	−	0.953369i	$-0.597590\pi$
$571$	−4.70272e6	−0.603613	−0.301807	+	0.953369i	$0.597590\pi$
$572$	2.23593e6	0.285739
$573$	2.82782e6	0.359803
$574$	5.89872e6	0.747271
$575$	330625.	0.0417029
$576$	−875804.	−0.109989
$577$	−5.79118e6	−0.724148	−0.362074	−	0.932149i	$-0.617931\pi$
$577$	−5.79118e6	−0.724148	−0.362074	+	0.932149i	$0.617931\pi$
$578$	−1.18056e7	−1.46983
$579$	2.50178e6	0.310136
$580$	−1.56969e6	−0.193751
$581$	−5.89506e6	−0.724516
$582$	−981866.	−0.120156
$583$	1.33392e7	1.62539
$584$	−2.80513e6	−0.340346
$585$	−1.27481e6	−0.154012
$586$	5.02136e6	0.604056
$587$	−1.01917e7	−1.22082	−0.610409	−	0.792086i	$-0.708995\pi$
$587$	−1.01917e7	−1.22082	−0.610409	+	0.792086i	$0.708995\pi$
$588$	248390.	0.0296272
$589$	−214665.	−0.0254960
$590$	−26324.2	−0.00311333
$591$	−3.49763e6	−0.411912
$592$	1.31386e6	0.154080
$593$	8.27685e6	0.966559	0.483279	−	0.875466i	$-0.339445\pi$
$593$	8.27685e6	0.966559	0.483279	+	0.875466i	$0.339445\pi$
$594$	−5.78408e6	−0.672617
$595$	7.33271e6	0.849126
$596$	1.00958e6	0.116419
$597$	3.44190e6	0.395241
$598$	504629.	0.0577058
$599$	1.19995e7	1.36646	0.683229	−	0.730204i	$-0.260575\pi$
$599$	1.19995e7	1.36646	0.683229	+	0.730204i	$0.260575\pi$
$600$	−216076.	−0.0245036
$601$	1.47157e7	1.66186	0.830930	−	0.556377i	$-0.187809\pi$
$601$	1.47157e7	1.66186	0.830930	+	0.556377i	$0.187809\pi$
$602$	1.36063e6	0.153020
$603$	2.13177e6	0.238752
$604$	−5.07595e6	−0.566142
$605$	−4.55801e6	−0.506276
$606$	−1.83673e6	−0.203172
$607$	1.29045e7	1.42158	0.710789	−	0.703406i	$-0.248338\pi$
$607$	1.29045e7	1.42158	0.710789	+	0.703406i	$0.248338\pi$
$608$	750232.	0.0823070
$609$	−2.97388e6	−0.324922
$610$	4.76834e6	0.518850
$611$	5.61372e6	0.608342
$612$	−7.15269e6	−0.771953
$613$	1.48559e7	1.59679	0.798393	−	0.602137i	$-0.205684\pi$
$613$	1.48559e7	1.59679	0.798393	+	0.602137i	$0.205684\pi$
$614$	9.88244e6	1.05790
$615$	−1.41959e6	−0.151348
$616$	−5.26119e6	−0.558641
$617$	−1.23814e7	−1.30935	−0.654674	−	0.755911i	$-0.727194\pi$
$617$	−1.23814e7	−1.30935	−0.654674	+	0.755911i	$0.727194\pi$
$618$	1.90085e6	0.200205
$619$	1.43316e7	1.50338	0.751688	−	0.659519i	$-0.229240\pi$
$619$	1.43316e7	1.50338	0.751688	+	0.659519i	$0.229240\pi$
$620$	−117199.	−0.0122446
$621$	−1.30541e6	−0.135837
$622$	5.13098e6	0.531770
$623$	1.23598e7	1.27583
$624$	−329795.	−0.0339065
$625$	390625.	0.0400000
$626$	−7.22547e6	−0.736937
$627$	2.31913e6	0.235590
$628$	−3.45201e6	−0.349280
$629$	1.07303e7	1.08140
$630$	2.99964e6	0.301105
$631$	1.58139e7	1.58112	0.790562	−	0.612382i	$-0.209789\pi$
$631$	1.58139e7	1.58112	0.790562	+	0.612382i	$0.209789\pi$
$632$	−5.76912e6	−0.574535
$633$	−1.28719e6	−0.127683
$634$	5.08783e6	0.502701
$635$	339584.	0.0334205
$636$	−1.96750e6	−0.192873
$637$	−685367.	−0.0669229
$638$	9.19805e6	0.894631
$639$	−3.64804e6	−0.353434
$640$	409600.	0.0395285
$641$	7.52556e6	0.723426	0.361713	−	0.932290i	$-0.382192\pi$
$641$	7.52556e6	0.723426	0.361713	+	0.932290i	$0.382192\pi$
$642$	−1.65259e6	−0.158244
$643$	−7.41685e6	−0.707444	−0.353722	−	0.935351i	$-0.615084\pi$
$643$	−7.41685e6	−0.707444	−0.353722	+	0.935351i	$0.615084\pi$
$644$	−1.18740e6	−0.112819
$645$	−327450.	−0.0309918
$646$	6.12715e6	0.577666
$647$	−5.93274e6	−0.557179	−0.278589	−	0.960410i	$-0.589867\pi$
$647$	−5.93274e6	−0.557179	−0.278589	+	0.960410i	$0.589867\pi$
$648$	−2.47218e6	−0.231283
$649$	154255.	0.0143756
$650$	596207.	0.0553495
$651$	−222042.	−0.0205344
$652$	9.75930e6	0.899082
$653$	1.24637e7	1.14384	0.571920	−	0.820309i	$-0.306199\pi$
$653$	1.24637e7	1.14384	0.571920	+	0.820309i	$0.306199\pi$
$654$	−482242.	−0.0440880
$655$	−3.24977e6	−0.295971
$656$	2.69101e6	0.244150
$657$	−9.37173e6	−0.847045
$658$	−1.32092e7	−1.18936
$659$	−1.40720e7	−1.26224	−0.631119	−	0.775686i	$-0.717404\pi$
$659$	−1.40720e7	−1.26224	−0.631119	+	0.775686i	$0.717404\pi$
$660$	1.26616e6	0.113143
$661$	1.03910e6	0.0925024	0.0462512	−	0.998930i	$-0.485273\pi$
$661$	1.03910e6	0.0925024	0.0462512	+	0.998930i	$0.485273\pi$
$662$	1.40625e7	1.24714
$663$	−2.69344e6	−0.237970
$664$	−2.68934e6	−0.236715
$665$	−2.56955e6	−0.225322
$666$	4.38952e6	0.383470
$667$	2.07591e6	0.180674
$668$	−6.48879e6	−0.562630
$669$	5.02726e6	0.434276
$670$	−996994.	−0.0858036
$671$	−2.79415e7	−2.39576
$672$	776014.	0.0662897
$673$	4.73197e6	0.402721	0.201360	−	0.979517i	$-0.435464\pi$
$673$	4.73197e6	0.402721	0.201360	+	0.979517i	$0.435464\pi$
$674$	3.45867e6	0.293265
$675$	−1.54231e6	−0.130290
$676$	−5.03070e6	−0.423411
$677$	1.74191e7	1.46067	0.730337	−	0.683088i	$-0.239363\pi$
$677$	1.74191e7	1.46067	0.730337	+	0.683088i	$0.239363\pi$
$678$	4.30841e6	0.359951
$679$	−6.37481e6	−0.530631
$680$	3.34520e6	0.277428
$681$	−3.87324e6	−0.320042
$682$	686764.	0.0565388
$683$	−702223.	−0.0576001	−0.0288000	−	0.999585i	$-0.509169\pi$
$683$	−702223.	−0.0576001	−0.0288000	+	0.999585i	$0.509169\pi$
$684$	2.50647e6	0.204844
$685$	499939.	0.0407090
$686$	−7.81863e6	−0.634338
$687$	2.06143e6	0.166639
$688$	620724.	0.0499951
$689$	5.42881e6	0.435669
$690$	285761.	0.0228497
$691$	1.70344e7	1.35716	0.678580	−	0.734526i	$-0.262596\pi$
$691$	1.70344e7	1.35716	0.678580	+	0.734526i	$0.262596\pi$
$692$	5.06021e6	0.401701
$693$	−1.75773e7	−1.39033
$694$	112245.	0.00884646
$695$	4.20804e6	0.330459
$696$	−1.35669e6	−0.106159
$697$	2.19775e7	1.71355
$698$	−5.12692e6	−0.398307
$699$	−7.99052e6	−0.618560
$700$	−1.40289e6	−0.108212
$701$	2.33424e7	1.79412	0.897058	−	0.441913i	$-0.145700\pi$
$701$	2.33424e7	1.79412	0.897058	+	0.441913i	$0.145700\pi$
$702$	−2.35401e6	−0.180288
$703$	−3.76016e6	−0.286957
$704$	−2.40017e6	−0.182520
$705$	3.17893e6	0.240884
$706$	−1.48153e7	−1.11866
$707$	−1.19250e7	−0.897246
$708$	−22752.2	−0.00170585
$709$	−1.36791e7	−1.02198	−0.510988	−	0.859588i	$-0.670720\pi$
$709$	−1.36791e7	−1.02198	−0.510988	+	0.859588i	$0.670720\pi$
$710$	1.70613e6	0.127019
$711$	−1.92742e7	−1.42989
$712$	5.63858e6	0.416840
$713$	154996.	0.0114182
$714$	6.33770e6	0.465250
$715$	−3.49365e6	−0.255572
$716$	1.76204e6	0.128450
$717$	101295.	0.00735854
$718$	−7.34309e6	−0.531579
$719$	−2.61009e6	−0.188293	−0.0941464	−	0.995558i	$-0.530012\pi$
$719$	−2.61009e6	−0.188293	−0.0941464	+	0.995558i	$0.530012\pi$
$720$	1.36844e6	0.0983775
$721$	1.23413e7	0.884145
$722$	7.75730e6	0.553819
$723$	7.72338e6	0.549492
$724$	6.54198e6	0.463834
$725$	2.45264e6	0.173296
$726$	−3.93952e6	−0.277397
$727$	6.01306e6	0.421949	0.210974	−	0.977492i	$-0.432336\pi$
$727$	6.01306e6	0.421949	0.210974	+	0.977492i	$0.432336\pi$
$728$	−2.14121e6	−0.149737
$729$	−5.02012e6	−0.349861
$730$	4.38301e6	0.304415
$731$	5.06945e6	0.350887
$732$	4.12130e6	0.284287
$733$	1.43313e7	0.985203	0.492601	−	0.870255i	$-0.336046\pi$
$733$	1.43313e7	0.985203	0.492601	+	0.870255i	$0.336046\pi$
$734$	7.55258e6	0.517435
$735$	−388109.	−0.0264994
$736$	−541696.	−0.0368605
$737$	5.84218e6	0.396192
$738$	8.99048e6	0.607634
$739$	9.35533e6	0.630156	0.315078	−	0.949066i	$-0.397969\pi$
$739$	9.35533e6	0.630156	0.315078	+	0.949066i	$0.397969\pi$
$740$	−2.05291e6	−0.137813
$741$	943843.	0.0631473
$742$	−1.27741e7	−0.851765
$743$	−2.09044e7	−1.38920	−0.694602	−	0.719394i	$-0.744420\pi$
$743$	−2.09044e7	−1.38920	−0.694602	+	0.719394i	$0.744420\pi$
$744$	−101296.	−0.00670903
$745$	−1.57747e6	−0.104129
$746$	6.77776e6	0.445902
$747$	−8.98490e6	−0.589131
$748$	−1.96022e7	−1.28100
$749$	−1.07295e7	−0.698835
$750$	337619.	0.0219166
$751$	2.62219e7	1.69654	0.848269	−	0.529565i	$-0.177645\pi$
$751$	2.62219e7	1.69654	0.848269	+	0.529565i	$0.177645\pi$
$752$	−6.02607e6	−0.388588
$753$	5.83919e6	0.375288
$754$	3.74344e6	0.239796
$755$	7.93118e6	0.506373
$756$	5.53903e6	0.352476
$757$	1.40893e7	0.893616	0.446808	−	0.894630i	$-0.352561\pi$
$757$	1.40893e7	0.893616	0.446808	+	0.894630i	$0.352561\pi$
$758$	−9.13456e6	−0.577450
$759$	−1.67450e6	−0.105507
$760$	−1.17224e6	−0.0736176
$761$	9.56035e6	0.598428	0.299214	−	0.954186i	$-0.403276\pi$
$761$	9.56035e6	0.598428	0.299214	+	0.954186i	$0.403276\pi$
$762$	293505.	0.0183116
$763$	−3.13097e6	−0.194701
$764$	8.37576e6	0.519148
$765$	1.11761e7	0.690456
$766$	1.06241e7	0.654213
$767$	62778.8	0.00385322
$768$	354019.	0.0216583
$769$	−1.33276e7	−0.812714	−0.406357	−	0.913714i	$-0.633201\pi$
$769$	−1.33276e7	−0.812714	−0.406357	+	0.913714i	$0.633201\pi$
$770$	8.22061e6	0.499663
$771$	−2.52830e6	−0.153177
$772$	7.41006e6	0.447485
$773$	1.05693e7	0.636204	0.318102	−	0.948056i	$-0.396955\pi$
$773$	1.05693e7	0.636204	0.318102	+	0.948056i	$0.396955\pi$
$774$	2.07379e6	0.124427
$775$	183124.	0.0109519
$776$	−2.90820e6	−0.173369
$777$	−3.88937e6	−0.231114
$778$	−1.77857e7	−1.05347
$779$	−7.70144e6	−0.454703
$780$	515305.	0.0303269
$781$	−9.99758e6	−0.586499
$782$	−4.42403e6	−0.258703
$783$	−9.68379e6	−0.564470
$784$	735710.	0.0427480
$785$	5.39377e6	0.312405
$786$	−2.80879e6	−0.162167
$787$	−1.33233e7	−0.766785	−0.383393	−	0.923586i	$-0.625244\pi$
$787$	−1.33233e7	−0.766785	−0.383393	+	0.923586i	$0.625244\pi$
$788$	−1.03597e7	−0.594334
$789$	−5.59229e6	−0.319814
$790$	9.01425e6	0.513880
$791$	2.79726e7	1.58961
$792$	−8.01880e6	−0.454251
$793$	−1.13717e7	−0.642156
$794$	−2.29338e7	−1.29099
$795$	3.07422e6	0.172511
$796$	1.01946e7	0.570280
$797$	1.73442e7	0.967182	0.483591	−	0.875294i	$-0.339332\pi$
$797$	1.73442e7	0.967182	0.483591	+	0.875294i	$0.339332\pi$
$798$	−2.22088e6	−0.123458
$799$	−4.92149e7	−2.72728
$800$	−640000.	−0.0353553
$801$	1.88381e7	1.03742
$802$	−1.07509e7	−0.590215
$803$	−2.56835e7	−1.40561
$804$	−861708.	−0.0470132
$805$	1.85532e6	0.100909
$806$	279500.	0.0151546
$807$	3.09111e6	0.167082
$808$	−5.44024e6	−0.293150
$809$	−2.26761e7	−1.21814	−0.609071	−	0.793116i	$-0.708458\pi$
$809$	−2.26761e7	−1.21814	−0.609071	+	0.793116i	$0.708458\pi$
$810$	3.86278e6	0.206865
$811$	−2.76306e7	−1.47516	−0.737579	−	0.675261i	$-0.764031\pi$
$811$	−2.76306e7	−1.47516	−0.737579	+	0.675261i	$0.764031\pi$
$812$	−8.80837e6	−0.468819
$813$	3.44601e6	0.182848
$814$	1.20296e7	0.636343
$815$	−1.52489e7	−0.804164
$816$	2.89128e6	0.152007
$817$	−1.77645e6	−0.0931106
$818$	6.21806e6	0.324917
$819$	−7.15362e6	−0.372663
$820$	−4.20471e6	−0.218374
$821$	3.60028e7	1.86414	0.932069	−	0.362282i	$-0.118002\pi$
$821$	3.60028e7	1.86414	0.932069	+	0.362282i	$0.118002\pi$
$822$	432100.	0.0223051
$823$	441065.	0.0226988	0.0113494	−	0.999936i	$-0.496387\pi$
$823$	441065.	0.0226988	0.0113494	+	0.999936i	$0.496387\pi$
$824$	5.63015e6	0.288869
$825$	−1.97838e6	−0.101199
$826$	−147720.	−0.00753334
$827$	−9.53561e6	−0.484825	−0.242412	−	0.970173i	$-0.577939\pi$
$827$	−9.53561e6	−0.484825	−0.242412	+	0.970173i	$0.577939\pi$
$828$	−1.80977e6	−0.0917375
$829$	−3.62368e7	−1.83132	−0.915659	−	0.401957i	$-0.868330\pi$
$829$	−3.62368e7	−1.83132	−0.915659	+	0.401957i	$0.868330\pi$
$830$	4.20210e6	0.211724
$831$	6.44267e6	0.323641
$832$	−976825.	−0.0489225
$833$	6.00854e6	0.300024
$834$	3.63703e6	0.181064
$835$	1.01387e7	0.503231
$836$	6.86907e6	0.339924
$837$	−723031.	−0.0356733
$838$	4.49010e6	0.220875
$839$	−2.42487e7	−1.18928	−0.594639	−	0.803993i	$-0.702705\pi$
$839$	−2.42487e7	−1.18928	−0.594639	+	0.803993i	$0.702705\pi$
$840$	−1.21252e6	−0.0592913
$841$	−5.11163e6	−0.249212
$842$	−2.47020e6	−0.120075
$843$	294848.	0.0142899
$844$	−3.81255e6	−0.184230
$845$	7.86047e6	0.378710
$846$	−2.01327e7	−0.967109
$847$	−2.55775e7	−1.22504
$848$	−5.82757e6	−0.278290
$849$	7.98962e6	0.380414
$850$	−5.22688e6	−0.248139
$851$	2.71497e6	0.128511
$852$	1.47462e6	0.0695955
$853$	−3.12932e7	−1.47258	−0.736288	−	0.676668i	$-0.763423\pi$
$853$	−3.12932e7	−1.47258	−0.736288	+	0.676668i	$0.763423\pi$
$854$	2.67577e7	1.25546
$855$	−3.91636e6	−0.183218
$856$	−4.89482e6	−0.228324
$857$	2.86581e7	1.33289	0.666447	−	0.745552i	$-0.267814\pi$
$857$	2.86581e7	1.33289	0.666447	+	0.745552i	$0.267814\pi$
$858$	−3.01958e6	−0.140032
$859$	3.07779e7	1.42317	0.711583	−	0.702602i	$-0.247979\pi$
$859$	3.07779e7	1.42317	0.711583	+	0.702602i	$0.247979\pi$
$860$	−969881.	−0.0447170
$861$	−7.96609e6	−0.366216
$862$	−1.42093e7	−0.651337
$863$	−3.95038e7	−1.80556	−0.902779	−	0.430104i	$-0.858477\pi$
$863$	−3.95038e7	−1.80556	−0.902779	+	0.430104i	$0.858477\pi$
$864$	2.52692e6	0.115162
$865$	−7.90658e6	−0.359293
$866$	−2.34932e7	−1.06450
$867$	1.59431e7	0.720321
$868$	−657669.	−0.0296284
$869$	−5.28216e7	−2.37281
$870$	2.11983e6	0.0949517
$871$	2.37766e6	0.106195
$872$	−1.42836e6	−0.0636130
$873$	−9.71610e6	−0.431476
$874$	1.55028e6	0.0686488
$875$	2.19201e6	0.0967881
$876$	3.78826e6	0.166794
$877$	1.37496e7	0.603660	0.301830	−	0.953362i	$-0.402402\pi$
$877$	1.37496e7	0.603660	0.301830	+	0.953362i	$0.402402\pi$
$878$	5.75809e6	0.252082
$879$	−6.78123e6	−0.296030
$880$	3.75027e6	0.163251
$881$	−1.05440e7	−0.457683	−0.228841	−	0.973464i	$-0.573494\pi$
$881$	−1.05440e7	−0.457683	−0.228841	+	0.973464i	$0.573494\pi$
$882$	2.45795e6	0.106390
$883$	3.01365e7	1.30074	0.650371	−	0.759617i	$-0.274614\pi$
$883$	3.01365e7	1.30074	0.650371	+	0.759617i	$0.274614\pi$
$884$	−7.97773e6	−0.343359
$885$	35550.3	0.00152576
$886$	2.76725e7	1.18431
$887$	2.39926e6	0.102393	0.0511964	−	0.998689i	$-0.483697\pi$
$887$	2.39926e6	0.102393	0.0511964	+	0.998689i	$0.483697\pi$
$888$	−1.77434e6	−0.0755101
$889$	1.90559e6	0.0808677
$890$	−8.81028e6	−0.372833
$891$	−2.26351e7	−0.955187
$892$	1.48903e7	0.626602
$893$	1.72461e7	0.723705
$894$	−1.36341e6	−0.0570537
$895$	−2.75319e6	−0.114889
$896$	2.29849e6	0.0956471
$897$	−681491.	−0.0282800
$898$	2.71571e7	1.12381
$899$	1.14979e6	0.0474482
$900$	−2.13819e6	−0.0879915
$901$	−4.75938e7	−1.95316
$902$	2.46387e7	1.00833
$903$	−1.83750e6	−0.0749909
$904$	1.27612e7	0.519360
$905$	−1.02218e7	−0.414866
$906$	6.85496e6	0.277450
$907$	1.47912e7	0.597013	0.298507	−	0.954408i	$-0.403511\pi$
$907$	1.47912e7	0.597013	0.298507	+	0.954408i	$0.403511\pi$
$908$	−1.14722e7	−0.461777
$909$	−1.81754e7	−0.729584
$910$	3.34564e6	0.133929
$911$	−4.23139e7	−1.68922	−0.844611	−	0.535381i	$-0.820168\pi$
$911$	−4.23139e7	−1.68922	−0.844611	+	0.535381i	$0.820168\pi$
$912$	−1.01317e6	−0.0403363
$913$	−2.46234e7	−0.977623
$914$	2.72875e7	1.08044
$915$	−6.43953e6	−0.254274
$916$	6.10579e6	0.240438
$917$	−1.82362e7	−0.716162
$918$	2.06374e7	0.808254
$919$	−4.25844e7	−1.66327	−0.831633	−	0.555326i	$-0.812593\pi$
$919$	−4.25844e7	−1.66327	−0.831633	+	0.555326i	$0.812593\pi$
$920$	846400.	0.0329690
$921$	−1.33460e7	−0.518444
$922$	−1.72583e6	−0.0668606
$923$	−4.06883e6	−0.157205
$924$	7.10512e6	0.273774
$925$	3.20767e6	0.123264
$926$	697796.	0.0267425
$927$	1.88099e7	0.718931
$928$	−4.01840e6	−0.153173
$929$	3.02898e7	1.15148	0.575742	−	0.817632i	$-0.304713\pi$
$929$	3.02898e7	1.15148	0.575742	+	0.817632i	$0.304713\pi$
$930$	158275.	0.00600074
$931$	−2.10553e6	−0.0796137
$932$	−2.36673e7	−0.892500
$933$	−6.92926e6	−0.260605
$934$	−1.90734e7	−0.715421
$935$	3.06284e7	1.14577
$936$	−3.26350e6	−0.121757
$937$	−4.39864e7	−1.63670	−0.818351	−	0.574718i	$-0.805112\pi$
$937$	−4.39864e7	−1.63670	−0.818351	+	0.574718i	$0.805112\pi$
$938$	−5.59467e6	−0.207619
$939$	9.75783e6	0.361152
$940$	9.41573e6	0.347564
$941$	−3.61032e7	−1.32914	−0.664571	−	0.747225i	$-0.731386\pi$
$941$	−3.61032e7	−1.32914	−0.664571	+	0.747225i	$0.731386\pi$
$942$	4.66186e6	0.171172
$943$	5.56073e6	0.203635
$944$	−67390.0	−0.00246131
$945$	−8.65474e6	−0.315264
$946$	5.68330e6	0.206478
$947$	2.03243e7	0.736445	0.368223	−	0.929738i	$-0.379966\pi$
$947$	2.03243e7	0.736445	0.368223	+	0.929738i	$0.379966\pi$
$948$	7.79106e6	0.281563
$949$	−1.04527e7	−0.376759
$950$	1.83162e6	0.0658456
$951$	−6.87100e6	−0.246359
$952$	1.87717e7	0.671293
$953$	−2.72809e6	−0.0973029	−0.0486515	−	0.998816i	$-0.515492\pi$
$953$	−2.72809e6	−0.0973029	−0.0486515	+	0.998816i	$0.515492\pi$
$954$	−1.94695e7	−0.692602
$955$	−1.30871e7	−0.464340
$956$	300028.	0.0106174
$957$	−1.24218e7	−0.438433
$958$	2.46606e7	0.868140
$959$	2.80543e6	0.0985037
$960$	−553155.	−0.0193718
$961$	−2.85433e7	−0.997001
$962$	4.89584e6	0.170565
$963$	−1.63532e7	−0.568248
$964$	2.28760e7	0.792843
$965$	−1.15782e7	−0.400243
$966$	1.60356e6	0.0552894
$967$	3.94894e7	1.35805	0.679023	−	0.734117i	$-0.262403\pi$
$967$	3.94894e7	1.35805	0.679023	+	0.734117i	$0.262403\pi$
$968$	−1.16685e7	−0.400246
$969$	−8.27457e6	−0.283098
$970$	4.54407e6	0.155066
$971$	5.82812e7	1.98372	0.991861	−	0.127326i	$-0.0406395\pi$
$971$	5.82812e7	1.98372	0.991861	+	0.127326i	$0.0406395\pi$
$972$	1.29330e7	0.439071
$973$	2.36136e7	0.799613
$974$	−1.27357e7	−0.430154
$975$	−805164.	−0.0271252
$976$	1.22069e7	0.410187
$977$	−1.95461e7	−0.655124	−0.327562	−	0.944830i	$-0.606227\pi$
$977$	−1.95461e7	−0.655124	−0.327562	+	0.944830i	$0.606227\pi$
$978$	−1.31797e7	−0.440614
$979$	5.16264e7	1.72153
$980$	−1.14955e6	−0.0382350
$981$	−4.77204e6	−0.158319
$982$	3.56258e7	1.17892
$983$	5.67096e7	1.87186	0.935929	−	0.352189i	$-0.114563\pi$
$983$	5.67096e7	1.87186	0.935929	+	0.352189i	$0.114563\pi$
$984$	−3.63415e6	−0.119651
$985$	1.61870e7	0.531589
$986$	−3.28183e7	−1.07504
$987$	1.78387e7	0.582869
$988$	2.79559e6	0.0911130
$989$	1.28267e6	0.0416988
$990$	1.25294e7	0.406295
$991$	2.48052e7	0.802342	0.401171	−	0.916003i	$-0.368603\pi$
$991$	2.48052e7	0.802342	0.401171	+	0.916003i	$0.368603\pi$
$992$	−300030.	−0.00968023
$993$	−1.89910e7	−0.611189
$994$	9.57403e6	0.307347
$995$	−1.59291e7	−0.510074
$996$	3.63190e6	0.116007
$997$	1.88830e7	0.601636	0.300818	−	0.953682i	$-0.402740\pi$
$997$	1.88830e7	0.601636	0.300818	+	0.953682i	$0.402740\pi$
$998$	9.26368e6	0.294413
$999$	−1.26649e7	−0.401502

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.6.a.g.1.4	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.a.g.1.4	✓	5	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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +5.40191 q^{3} +16.0000 q^{4} -25.0000 q^{5} -21.6076 q^{6} -140.289 q^{7} -64.0000 q^{8} -213.819 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +5.40191 q^{3} +16.0000 q^{4} -25.0000 q^{5} -21.6076 q^{6} -140.289 q^{7} -64.0000 q^{8} -213.819 q^{9} +100.000 q^{10} -585.979 q^{11} +86.4305 q^{12} -238.483 q^{13} +561.154 q^{14} -135.048 q^{15} +256.000 q^{16} +2090.75 q^{17} +855.278 q^{18} -732.649 q^{19} -400.000 q^{20} -757.826 q^{21} +2343.92 q^{22} +529.000 q^{23} -345.722 q^{24} +625.000 q^{25} +953.931 q^{26} -2467.70 q^{27} -2244.62 q^{28} +3924.22 q^{29} +540.191 q^{30} +292.998 q^{31} -1024.00 q^{32} -3165.41 q^{33} -8363.01 q^{34} +3507.21 q^{35} -3421.11 q^{36} +5132.28 q^{37} +2930.59 q^{38} -1288.26 q^{39} +1600.00 q^{40} +10511.8 q^{41} +3031.30 q^{42} +2424.70 q^{43} -9375.67 q^{44} +5345.48 q^{45} -2116.00 q^{46} -23539.3 q^{47} +1382.89 q^{48} +2873.87 q^{49} -2500.00 q^{50} +11294.1 q^{51} -3815.72 q^{52} -22763.9 q^{53} +9870.79 q^{54} +14649.5 q^{55} +8978.46 q^{56} -3957.70 q^{57} -15696.9 q^{58} -263.242 q^{59} -2160.76 q^{60} +47683.4 q^{61} -1171.99 q^{62} +29996.4 q^{63} +4096.00 q^{64} +5962.07 q^{65} +12661.6 q^{66} -9969.94 q^{67} +33452.0 q^{68} +2857.61 q^{69} -14028.9 q^{70} +17061.3 q^{71} +13684.4 q^{72} +43830.1 q^{73} -20529.1 q^{74} +3376.19 q^{75} -11722.4 q^{76} +82206.1 q^{77} +5153.05 q^{78} +90142.5 q^{79} -6400.00 q^{80} +38627.8 q^{81} -42047.1 q^{82} +42021.0 q^{83} -12125.2 q^{84} -52268.8 q^{85} -9698.81 q^{86} +21198.3 q^{87} +37502.7 q^{88} -88102.8 q^{89} -21381.9 q^{90} +33456.4 q^{91} +8464.00 q^{92} +1582.75 q^{93} +94157.3 q^{94} +18316.2 q^{95} -5531.55 q^{96} +45440.7 q^{97} -11495.5 q^{98} +125294. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 20 q^{2} + 5 q^{3} + 80 q^{4} - 125 q^{5} - 20 q^{6} + 130 q^{7} - 320 q^{8} + 334 q^{9}+O(q^{10}) \) 5 * q - 20 * q^2 + 5 * q^3 + 80 * q^4 - 125 * q^5 - 20 * q^6 + 130 * q^7 - 320 * q^8 + 334 * q^9	\( 5 q - 20 q^{2} + 5 q^{3} + 80 q^{4} - 125 q^{5} - 20 q^{6} + 130 q^{7} - 320 q^{8} + 334 q^{9} + 500 q^{10} + 81 q^{11} + 80 q^{12} - 753 q^{13} - 520 q^{14} - 125 q^{15} + 1280 q^{16} - 1780 q^{17} - 1336 q^{18} + 1933 q^{19} - 2000 q^{20} - 2526 q^{21} - 324 q^{22} + 2645 q^{23} - 320 q^{24} + 3125 q^{25} + 3012 q^{26} + 2972 q^{27} + 2080 q^{28} + 3527 q^{29} + 500 q^{30} + 1816 q^{31} - 5120 q^{32} - 21947 q^{33} + 7120 q^{34} - 3250 q^{35} + 5344 q^{36} + 11683 q^{37} - 7732 q^{38} + 12580 q^{39} + 8000 q^{40} - 9602 q^{41} + 10104 q^{42} - 2232 q^{43} + 1296 q^{44} - 8350 q^{45} - 10580 q^{46} - 14552 q^{47} + 1280 q^{48} + 25889 q^{49} - 12500 q^{50} + 31351 q^{51} - 12048 q^{52} - 23069 q^{53} - 11888 q^{54} - 2025 q^{55} - 8320 q^{56} + 95210 q^{57} - 14108 q^{58} + 43917 q^{59} - 2000 q^{60} + 107483 q^{61} - 7264 q^{62} + 119033 q^{63} + 20480 q^{64} + 18825 q^{65} + 87788 q^{66} + 133125 q^{67} - 28480 q^{68} + 2645 q^{69} + 13000 q^{70} + 103326 q^{71} - 21376 q^{72} + 125870 q^{73} - 46732 q^{74} + 3125 q^{75} + 30928 q^{76} + 110422 q^{77} - 50320 q^{78} + 274892 q^{79} - 32000 q^{80} + 316657 q^{81} + 38408 q^{82} + 106201 q^{83} - 40416 q^{84} + 44500 q^{85} + 8928 q^{86} + 23782 q^{87} - 5184 q^{88} + 57800 q^{89} + 33400 q^{90} + 272163 q^{91} + 42320 q^{92} + 198110 q^{93} + 58208 q^{94} - 48325 q^{95} - 5120 q^{96} - 24935 q^{97} - 103556 q^{98} + 362547 q^{99}+O(q^{100}) \) 5 * q - 20 * q^2 + 5 * q^3 + 80 * q^4 - 125 * q^5 - 20 * q^6 + 130 * q^7 - 320 * q^8 + 334 * q^9 + 500 * q^10 + 81 * q^11 + 80 * q^12 - 753 * q^13 - 520 * q^14 - 125 * q^15 + 1280 * q^16 - 1780 * q^17 - 1336 * q^18 + 1933 * q^19 - 2000 * q^20 - 2526 * q^21 - 324 * q^22 + 2645 * q^23 - 320 * q^24 + 3125 * q^25 + 3012 * q^26 + 2972 * q^27 + 2080 * q^28 + 3527 * q^29 + 500 * q^30 + 1816 * q^31 - 5120 * q^32 - 21947 * q^33 + 7120 * q^34 - 3250 * q^35 + 5344 * q^36 + 11683 * q^37 - 7732 * q^38 + 12580 * q^39 + 8000 * q^40 - 9602 * q^41 + 10104 * q^42 - 2232 * q^43 + 1296 * q^44 - 8350 * q^45 - 10580 * q^46 - 14552 * q^47 + 1280 * q^48 + 25889 * q^49 - 12500 * q^50 + 31351 * q^51 - 12048 * q^52 - 23069 * q^53 - 11888 * q^54 - 2025 * q^55 - 8320 * q^56 + 95210 * q^57 - 14108 * q^58 + 43917 * q^59 - 2000 * q^60 + 107483 * q^61 - 7264 * q^62 + 119033 * q^63 + 20480 * q^64 + 18825 * q^65 + 87788 * q^66 + 133125 * q^67 - 28480 * q^68 + 2645 * q^69 + 13000 * q^70 + 103326 * q^71 - 21376 * q^72 + 125870 * q^73 - 46732 * q^74 + 3125 * q^75 + 30928 * q^76 + 110422 * q^77 - 50320 * q^78 + 274892 * q^79 - 32000 * q^80 + 316657 * q^81 + 38408 * q^82 + 106201 * q^83 - 40416 * q^84 + 44500 * q^85 + 8928 * q^86 + 23782 * q^87 - 5184 * q^88 + 57800 * q^89 + 33400 * q^90 + 272163 * q^91 + 42320 * q^92 + 198110 * q^93 + 58208 * q^94 - 48325 * q^95 - 5120 * q^96 - 24935 * q^97 - 103556 * q^98 + 362547 * q^99

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