LMFDB - Embedded newform 43.6.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,6,Mod(1,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("43.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	43.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:	$6.89650425196$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 173x^{6} + 462x^{5} + 9118x^{4} - 14192x^{3} - 167688x^{2} + 106368x + 681984 $ x^8 - 4x^7 - 173x^6 + 462x^5 + 9118x^4 - 14192x^3 - 167688x^2 + 106368*x + 681984
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-5.06235$ of defining polynomial
Character	$\chi$	$=$	43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.06235 q^{2} -9.19190 q^{3} +17.8767 q^{4} +73.4416 q^{5} +64.9164 q^{6} -4.24720 q^{7} +99.7434 q^{8} -158.509 q^{9} +O(q^{10})$	\(q-7.06235 q^{2} -9.19190 q^{3} +17.8767 q^{4} +73.4416 q^{5} +64.9164 q^{6} -4.24720 q^{7} +99.7434 q^{8} -158.509 q^{9} -518.670 q^{10} -99.8962 q^{11} -164.321 q^{12} -441.198 q^{13} +29.9952 q^{14} -675.068 q^{15} -1276.48 q^{16} -1032.37 q^{17} +1119.45 q^{18} +402.714 q^{19} +1312.90 q^{20} +39.0398 q^{21} +705.502 q^{22} -3450.72 q^{23} -916.832 q^{24} +2268.67 q^{25} +3115.89 q^{26} +3690.63 q^{27} -75.9260 q^{28} -4268.03 q^{29} +4767.56 q^{30} +3774.65 q^{31} +5823.14 q^{32} +918.236 q^{33} +7290.94 q^{34} -311.921 q^{35} -2833.62 q^{36} -7574.57 q^{37} -2844.11 q^{38} +4055.45 q^{39} +7325.32 q^{40} -14105.9 q^{41} -275.713 q^{42} -1849.00 q^{43} -1785.82 q^{44} -11641.2 q^{45} +24370.2 q^{46} -13498.9 q^{47} +11733.3 q^{48} -16789.0 q^{49} -16022.1 q^{50} +9489.43 q^{51} -7887.18 q^{52} -11768.5 q^{53} -26064.5 q^{54} -7336.54 q^{55} -423.630 q^{56} -3701.71 q^{57} +30142.3 q^{58} +23905.8 q^{59} -12068.0 q^{60} +44667.8 q^{61} -26657.9 q^{62} +673.219 q^{63} -277.722 q^{64} -32402.3 q^{65} -6484.90 q^{66} +39220.3 q^{67} -18455.4 q^{68} +31718.7 q^{69} +2202.89 q^{70} +6594.36 q^{71} -15810.2 q^{72} -36343.7 q^{73} +53494.2 q^{74} -20853.3 q^{75} +7199.21 q^{76} +424.279 q^{77} -28641.0 q^{78} +61839.8 q^{79} -93746.6 q^{80} +4593.79 q^{81} +99620.6 q^{82} -64688.9 q^{83} +697.904 q^{84} -75818.8 q^{85} +13058.3 q^{86} +39231.3 q^{87} -9963.99 q^{88} +29521.4 q^{89} +82213.8 q^{90} +1873.86 q^{91} -61687.6 q^{92} -34696.2 q^{93} +95333.8 q^{94} +29576.0 q^{95} -53525.7 q^{96} +19309.4 q^{97} +118569. q^{98} +15834.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{2} - 26 q^{3} + 122 q^{4} - 212 q^{5} - 69 q^{6} - 136 q^{7} - 666 q^{8} + 546 q^{9}+O(q^{10}) $ 8 * q - 12 * q^2 - 26 * q^3 + 122 * q^4 - 212 * q^5 - 69 * q^6 - 136 * q^7 - 666 * q^8 + 546 * q^9	\( 8 q - 12 q^{2} - 26 q^{3} + 122 q^{4} - 212 q^{5} - 69 q^{6} - 136 q^{7} - 666 q^{8} + 546 q^{9} - 617 q^{10} - 532 q^{11} - 4195 q^{12} - 2492 q^{13} - 4240 q^{14} - 1780 q^{15} + 1882 q^{16} - 2534 q^{17} - 3711 q^{18} - 1678 q^{19} - 2607 q^{20} - 2256 q^{21} + 11502 q^{22} - 2488 q^{23} + 19953 q^{24} + 4378 q^{25} + 4586 q^{26} - 8960 q^{27} + 18640 q^{28} - 4360 q^{29} + 25092 q^{30} + 5704 q^{31} - 18294 q^{32} - 12852 q^{33} + 30007 q^{34} + 5640 q^{35} + 67969 q^{36} - 3772 q^{37} - 6559 q^{38} + 11120 q^{39} + 14869 q^{40} - 10698 q^{41} + 78698 q^{42} - 14792 q^{43} - 356 q^{44} - 44912 q^{45} - 19389 q^{46} - 77864 q^{47} - 118727 q^{48} + 7188 q^{49} + 26877 q^{50} - 80246 q^{51} - 60736 q^{52} - 62352 q^{53} + 61026 q^{54} - 49552 q^{55} - 144528 q^{56} - 808 q^{57} + 52951 q^{58} - 26224 q^{59} + 101500 q^{60} - 82540 q^{61} - 9023 q^{62} - 61768 q^{63} + 153858 q^{64} - 5000 q^{65} - 48516 q^{66} + 27784 q^{67} + 40507 q^{68} - 93776 q^{69} + 185910 q^{70} - 9504 q^{71} - 186687 q^{72} + 14260 q^{73} - 15239 q^{74} + 167420 q^{75} + 1279 q^{76} - 218140 q^{77} + 264170 q^{78} + 160248 q^{79} - 1291 q^{80} + 161076 q^{81} - 47781 q^{82} - 77176 q^{83} + 16382 q^{84} + 141096 q^{85} + 22188 q^{86} + 268136 q^{87} + 129544 q^{88} - 265692 q^{89} + 48990 q^{90} + 401148 q^{91} + 190391 q^{92} - 123860 q^{93} + 248737 q^{94} + 135884 q^{95} + 950817 q^{96} + 144742 q^{97} - 292244 q^{98} + 239516 q^{99}+O(q^{100}) \) 8 * q - 12 * q^2 - 26 * q^3 + 122 * q^4 - 212 * q^5 - 69 * q^6 - 136 * q^7 - 666 * q^8 + 546 * q^9 - 617 * q^10 - 532 * q^11 - 4195 * q^12 - 2492 * q^13 - 4240 * q^14 - 1780 * q^15 + 1882 * q^16 - 2534 * q^17 - 3711 * q^18 - 1678 * q^19 - 2607 * q^20 - 2256 * q^21 + 11502 * q^22 - 2488 * q^23 + 19953 * q^24 + 4378 * q^25 + 4586 * q^26 - 8960 * q^27 + 18640 * q^28 - 4360 * q^29 + 25092 * q^30 + 5704 * q^31 - 18294 * q^32 - 12852 * q^33 + 30007 * q^34 + 5640 * q^35 + 67969 * q^36 - 3772 * q^37 - 6559 * q^38 + 11120 * q^39 + 14869 * q^40 - 10698 * q^41 + 78698 * q^42 - 14792 * q^43 - 356 * q^44 - 44912 * q^45 - 19389 * q^46 - 77864 * q^47 - 118727 * q^48 + 7188 * q^49 + 26877 * q^50 - 80246 * q^51 - 60736 * q^52 - 62352 * q^53 + 61026 * q^54 - 49552 * q^55 - 144528 * q^56 - 808 * q^57 + 52951 * q^58 - 26224 * q^59 + 101500 * q^60 - 82540 * q^61 - 9023 * q^62 - 61768 * q^63 + 153858 * q^64 - 5000 * q^65 - 48516 * q^66 + 27784 * q^67 + 40507 * q^68 - 93776 * q^69 + 185910 * q^70 - 9504 * q^71 - 186687 * q^72 + 14260 * q^73 - 15239 * q^74 + 167420 * q^75 + 1279 * q^76 - 218140 * q^77 + 264170 * q^78 + 160248 * q^79 - 1291 * q^80 + 161076 * q^81 - 47781 * q^82 - 77176 * q^83 + 16382 * q^84 + 141096 * q^85 + 22188 * q^86 + 268136 * q^87 + 129544 * q^88 - 265692 * q^89 + 48990 * q^90 + 401148 * q^91 + 190391 * q^92 - 123860 * q^93 + 248737 * q^94 + 135884 * q^95 + 950817 * q^96 + 144742 * q^97 - 292244 * q^98 + 239516 * 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 $

$2$	−7.06235	−1.24846	−0.624229	−	0.781241i	$-0.714587\pi$
$2$	−7.06235	−1.24846	−0.624229	+	0.781241i	$0.714587\pi$
$3$	−9.19190	−0.589661	−0.294830	−	0.955550i	$-0.595263\pi$
$3$	−9.19190	−0.589661	−0.294830	+	0.955550i	$0.595263\pi$
$4$	17.8767	0.558648
$5$	73.4416	1.31376	0.656881	−	0.753994i	$-0.271875\pi$
$5$	73.4416	1.31376	0.656881	+	0.753994i	$0.271875\pi$
$6$	64.9164	0.736167
$7$	−4.24720	−0.0327610	−0.0163805	−	0.999866i	$-0.505214\pi$
$7$	−4.24720	−0.0327610	−0.0163805	+	0.999866i	$0.505214\pi$
$8$	99.7434	0.551010
$9$	−158.509	−0.652300
$10$	−518.670	−1.64018
$11$	−99.8962	−0.248924	−0.124462	−	0.992224i	$-0.539721\pi$
$11$	−99.8962	−0.248924	−0.124462	+	0.992224i	$0.539721\pi$
$12$	−164.321	−0.329413
$13$	−441.198	−0.724061	−0.362031	−	0.932166i	$-0.617916\pi$
$13$	−441.198	−0.724061	−0.362031	+	0.932166i	$0.617916\pi$
$14$	29.9952	0.0409008
$15$	−675.068	−0.774674
$16$	−1276.48	−1.24656
$17$	−1032.37	−0.866388	−0.433194	−	0.901301i	$-0.642614\pi$
$17$	−1032.37	−0.866388	−0.433194	+	0.901301i	$0.642614\pi$
$18$	1119.45	0.814370
$19$	402.714	0.255925	0.127963	−	0.991779i	$-0.459156\pi$
$19$	402.714	0.255925	0.127963	+	0.991779i	$0.459156\pi$
$20$	1312.90	0.733931
$21$	39.0398	0.0193179
$22$	705.502	0.310772
$23$	−3450.72	−1.36016	−0.680080	−	0.733138i	$-0.738055\pi$
$23$	−3450.72	−1.36016	−0.680080	+	0.733138i	$0.738055\pi$
$24$	−916.832	−0.324909
$25$	2268.67	0.725973
$26$	3115.89	0.903960
$27$	3690.63	0.974296
$28$	−75.9260	−0.0183019
$29$	−4268.03	−0.942394	−0.471197	−	0.882028i	$-0.656178\pi$
$29$	−4268.03	−0.942394	−0.471197	+	0.882028i	$0.656178\pi$
$30$	4767.56	0.967148
$31$	3774.65	0.705460	0.352730	−	0.935725i	$-0.385253\pi$
$31$	3774.65	0.705460	0.352730	+	0.935725i	$0.385253\pi$
$32$	5823.14	1.00527
$33$	918.236	0.146781
$34$	7290.94	1.08165
$35$	−311.921	−0.0430402
$36$	−2833.62	−0.364406
$37$	−7574.57	−0.909606	−0.454803	−	0.890592i	$-0.650290\pi$
$37$	−7574.57	−0.909606	−0.454803	+	0.890592i	$0.650290\pi$
$38$	−2844.11	−0.319512
$39$	4055.45	0.426950
$40$	7325.32	0.723896
$41$	−14105.9	−1.31051	−0.655255	−	0.755408i	$-0.727439\pi$
$41$	−14105.9	−1.31051	−0.655255	+	0.755408i	$0.727439\pi$
$42$	−275.713	−0.0241176
$43$	−1849.00	−0.152499
$43$	−1849.00	−0.152499
$44$	−1785.82	−0.139061
$45$	−11641.2	−0.856968
$46$	24370.2	1.69810
$47$	−13498.9	−0.891360	−0.445680	−	0.895192i	$-0.647038\pi$
$47$	−13498.9	−0.891360	−0.445680	+	0.895192i	$0.647038\pi$
$48$	11733.3	0.735048
$49$	−16789.0	−0.998927
$50$	−16022.1	−0.906347
$51$	9489.43	0.510875
$52$	−7887.18	−0.404495
$53$	−11768.5	−0.575479	−0.287740	−	0.957709i	$-0.592904\pi$
$53$	−11768.5	−0.575479	−0.287740	+	0.957709i	$0.592904\pi$
$54$	−26064.5	−1.21637
$55$	−7336.54	−0.327028
$56$	−423.630	−0.0180517
$57$	−3701.71	−0.150909
$58$	30142.3	1.17654
$59$	23905.8	0.894075	0.447037	−	0.894515i	$-0.352479\pi$
$59$	23905.8	0.894075	0.447037	+	0.894515i	$0.352479\pi$
$60$	−12068.0	−0.432770
$61$	44667.8	1.53699	0.768493	−	0.639858i	$-0.221007\pi$
$61$	44667.8	1.53699	0.768493	+	0.639858i	$0.221007\pi$
$62$	−26657.9	−0.880737
$63$	673.219	0.0213700
$64$	−277.722	−0.00847541
$65$	−32402.3	−0.951245
$66$	−6484.90	−0.183250
$67$	39220.3	1.06739	0.533696	−	0.845677i	$-0.320803\pi$
$67$	39220.3	1.06739	0.533696	+	0.845677i	$0.320803\pi$
$68$	−18455.4	−0.484006
$69$	31718.7	0.802033
$70$	2202.89	0.0537339
$71$	6594.36	0.155248	0.0776241	−	0.996983i	$-0.475267\pi$
$71$	6594.36	0.155248	0.0776241	+	0.996983i	$0.475267\pi$
$72$	−15810.2	−0.359424
$73$	−36343.7	−0.798219	−0.399109	−	0.916903i	$-0.630681\pi$
$73$	−36343.7	−0.798219	−0.399109	+	0.916903i	$0.630681\pi$
$74$	53494.2	1.13561
$75$	−20853.3	−0.428078
$76$	7199.21	0.142972
$77$	424.279	0.00815502
$78$	−28641.0	−0.533030
$79$	61839.8	1.11481	0.557405	−	0.830241i	$-0.311797\pi$
$79$	61839.8	1.11481	0.557405	+	0.830241i	$0.311797\pi$
$80$	−93746.6	−1.63768
$81$	4593.79	0.0777962
$82$	99620.6	1.63612
$83$	−64688.9	−1.03071	−0.515353	−	0.856978i	$-0.672339\pi$
$83$	−64688.9	−1.03071	−0.515353	+	0.856978i	$0.672339\pi$
$84$	697.904	0.0107919
$85$	−75818.8	−1.13823
$86$	13058.3	0.190388
$87$	39231.3	0.555692
$88$	−9963.99	−0.137160
$89$	29521.4	0.395059	0.197529	−	0.980297i	$-0.436708\pi$
$89$	29521.4	0.395059	0.197529	+	0.980297i	$0.436708\pi$
$90$	82213.8	1.06989
$91$	1873.86	0.0237210
$92$	−61687.6	−0.759850
$93$	−34696.2	−0.415982
$94$	95333.8	1.11283
$95$	29576.0	0.336225
$96$	−53525.7	−0.592767
$97$	19309.4	0.208372	0.104186	−	0.994558i	$-0.466776\pi$
$97$	19309.4	0.208372	0.104186	+	0.994558i	$0.466776\pi$
$98$	118569.	1.24712
$99$	15834.4	0.162373
$100$	40556.3	0.405563
$101$	175754.	1.71436	0.857178	−	0.515020i	$-0.172216\pi$
$101$	175754.	1.71436	0.857178	+	0.515020i	$0.172216\pi$
$102$	−67017.6	−0.637806
$103$	−23109.9	−0.214637	−0.107319	−	0.994225i	$-0.534227\pi$
$103$	−23109.9	−0.214637	−0.107319	+	0.994225i	$0.534227\pi$
$104$	−44006.6	−0.398965
$105$	2867.15	0.0253791
$106$	83112.9	0.718462
$107$	−120952.	−1.02130	−0.510651	−	0.859788i	$-0.670595\pi$
$107$	−120952.	−1.02130	−0.510651	+	0.859788i	$0.670595\pi$
$108$	65976.4	0.544288
$109$	2739.65	0.0220866	0.0110433	−	0.999939i	$-0.496485\pi$
$109$	2739.65	0.0220866	0.0110433	+	0.999939i	$0.496485\pi$
$110$	51813.2	0.408280
$111$	69624.7	0.536359
$112$	5421.46	0.0408386
$113$	−151540.	−1.11643	−0.558215	−	0.829697i	$-0.688513\pi$
$113$	−151540.	−1.11643	−0.558215	+	0.829697i	$0.688513\pi$
$114$	26142.7	0.188404
$115$	−253426.	−1.78693
$116$	−76298.4	−0.526466
$117$	69933.9	0.472305
$118$	−168831.	−1.11621
$119$	4384.68	0.0283838
$120$	−67333.6	−0.426853
$121$	−151072.	−0.938037
$122$	−315460.	−1.91886
$123$	129660.	0.772756
$124$	67478.4	0.394104
$125$	−62890.5	−0.360006
$126$	−4754.51	−0.0266796
$127$	−250657.	−1.37902	−0.689509	−	0.724277i	$-0.742174\pi$
$127$	−250657.	−1.37902	−0.689509	+	0.724277i	$0.742174\pi$
$128$	−184379.	−0.994687
$129$	16995.8	0.0899224
$130$	228836.	1.18759
$131$	97219.0	0.494963	0.247482	−	0.968893i	$-0.420397\pi$
$131$	97219.0	0.494963	0.247482	+	0.968893i	$0.420397\pi$
$132$	16415.1	0.0819988
$133$	−1710.41	−0.00838437
$134$	−276987.	−1.33259
$135$	271046.	1.27999
$136$	−102972.	−0.477388
$137$	198985.	0.905770	0.452885	−	0.891569i	$-0.350395\pi$
$137$	198985.	0.905770	0.452885	+	0.891569i	$0.350395\pi$
$138$	−224008.	−1.00130
$139$	402794.	1.76826	0.884130	−	0.467241i	$-0.154752\pi$
$139$	402794.	1.76826	0.884130	+	0.467241i	$0.154752\pi$
$140$	−5576.13	−0.0240443
$141$	124080.	0.525600
$142$	−46571.6	−0.193821
$143$	44074.0	0.180236
$144$	202333.	0.813132
$145$	−313451.	−1.23808
$146$	256672.	0.996542
$147$	154322.	0.589028
$148$	−135408.	−0.508150
$149$	−423748.	−1.56366	−0.781830	−	0.623492i	$-0.785713\pi$
$149$	−423748.	−1.56366	−0.781830	+	0.623492i	$0.785713\pi$
$150$	147274.	0.534437
$151$	178324.	0.636454	0.318227	−	0.948015i	$-0.396913\pi$
$151$	178324.	0.636454	0.318227	+	0.948015i	$0.396913\pi$
$152$	40168.1	0.141017
$153$	163640.	0.565145
$154$	−2996.41	−0.0101812
$155$	277216.	0.926807
$156$	72498.1	0.238515
$157$	326875.	1.05836	0.529180	−	0.848510i	$-0.322500\pi$
$157$	326875.	1.05836	0.529180	+	0.848510i	$0.322500\pi$
$158$	−436734.	−1.39179
$159$	108174.	0.339337
$160$	427660.	1.32068
$161$	14655.9	0.0445603
$162$	−32442.9	−0.0971253
$163$	−8888.26	−0.0262028	−0.0131014	−	0.999914i	$-0.504170\pi$
$163$	−8888.26	−0.0262028	−0.0131014	+	0.999914i	$0.504170\pi$
$164$	−252167.	−0.732114
$165$	67436.7	0.192835
$166$	456856.	1.28679
$167$	308667.	0.856443	0.428222	−	0.903674i	$-0.359140\pi$
$167$	308667.	0.856443	0.428222	+	0.903674i	$0.359140\pi$
$168$	3893.97	0.0106443
$169$	−176637.	−0.475736
$170$	535458.	1.42103
$171$	−63833.8	−0.166940
$172$	−33054.1	−0.0851930
$173$	365702.	0.928993	0.464497	−	0.885575i	$-0.346235\pi$
$173$	365702.	0.928993	0.464497	+	0.885575i	$0.346235\pi$
$174$	−277065.	−0.693759
$175$	−9635.48	−0.0237836
$176$	127515.	0.310299
$177$	−219740.	−0.527201
$178$	−208490.	−0.493214
$179$	−545317.	−1.27209	−0.636043	−	0.771653i	$-0.719430\pi$
$179$	−545317.	−1.27209	−0.636043	+	0.771653i	$0.719430\pi$
$180$	−208106.	−0.478743
$181$	74018.5	0.167936	0.0839681	−	0.996468i	$-0.473241\pi$
$181$	74018.5	0.167936	0.0839681	+	0.996468i	$0.473241\pi$
$182$	−13233.8	−0.0296147
$183$	−410582.	−0.906301
$184$	−344187.	−0.749462
$185$	−556288.	−1.19501
$186$	245037.	0.519336
$187$	103130.	0.215665
$188$	−241316.	−0.497956
$189$	−15674.8	−0.0319190
$190$	−208876.	−0.419763
$191$	334841.	0.664133	0.332066	−	0.943256i	$-0.392254\pi$
$191$	334841.	0.664133	0.332066	+	0.943256i	$0.392254\pi$
$192$	2552.79	0.00499761
$193$	−815493.	−1.57589	−0.787947	−	0.615743i	$-0.788856\pi$
$193$	−815493.	−1.57589	−0.787947	+	0.615743i	$0.788856\pi$
$194$	−136370.	−0.260144
$195$	297839.	0.560911
$196$	−300132.	−0.558048
$197$	621397.	1.14078	0.570392	−	0.821373i	$-0.306791\pi$
$197$	621397.	1.14078	0.570392	+	0.821373i	$0.306791\pi$
$198$	−111828.	−0.202716
$199$	106834.	0.191239	0.0956196	−	0.995418i	$-0.469517\pi$
$199$	106834.	0.191239	0.0956196	+	0.995418i	$0.469517\pi$
$200$	226285.	0.400018
$201$	−360509.	−0.629399
$202$	−1.24123e6	−2.14030
$203$	18127.2	0.0308738
$204$	169640.	0.285399
$205$	−1.03596e6	−1.72170
$206$	163210.	0.267966
$207$	546970.	0.887233
$208$	563180.	0.902586
$209$	−40229.6	−0.0637060
$210$	−20248.8	−0.0316848
$211$	907859.	1.40382	0.701912	−	0.712264i	$-0.252330\pi$
$211$	907859.	1.40382	0.701912	+	0.712264i	$0.252330\pi$
$212$	−210381.	−0.321490
$213$	−60614.7	−0.0915437
$214$	854205.	1.27505
$215$	−135793.	−0.200347
$216$	368116.	0.536847
$217$	−16031.7	−0.0231116
$218$	−19348.4	−0.0275742
$219$	334067.	0.470678
$220$	−131153.	−0.182693
$221$	455479.	0.627318
$222$	−491713.	−0.669622
$223$	618351.	0.832670	0.416335	−	0.909211i	$-0.363314\pi$
$223$	618351.	0.832670	0.416335	+	0.909211i	$0.363314\pi$
$224$	−24732.0	−0.0329336
$225$	−359604.	−0.473553
$226$	1.07023e6	1.39382
$227$	−1.34766e6	−1.73586	−0.867930	−	0.496687i	$-0.834550\pi$
$227$	−1.34766e6	−1.73586	−0.867930	+	0.496687i	$0.834550\pi$
$228$	−66174.4	−0.0843050
$229$	−949751.	−1.19680	−0.598399	−	0.801198i	$-0.704196\pi$
$229$	−949751.	−1.19680	−0.598399	+	0.801198i	$0.704196\pi$
$230$	1.78978e6	2.23091
$231$	−3899.93	−0.00480869
$232$	−425708.	−0.519268
$233$	−1.12504e6	−1.35762	−0.678808	−	0.734316i	$-0.737503\pi$
$233$	−1.12504e6	−1.35762	−0.678808	+	0.734316i	$0.737503\pi$
$234$	−493897.	−0.589653
$235$	−991380.	−1.17104
$236$	427358.	0.499473
$237$	−568425.	−0.657359
$238$	−30966.1	−0.0354359
$239$	−1.03632e6	−1.17354	−0.586770	−	0.809754i	$-0.699601\pi$
$239$	−1.03632e6	−1.17354	−0.586770	+	0.809754i	$0.699601\pi$
$240$	861709.	0.965678
$241$	1.48417e6	1.64605	0.823024	−	0.568007i	$-0.192285\pi$
$241$	1.48417e6	1.64605	0.823024	+	0.568007i	$0.192285\pi$
$242$	1.06692e6	1.17110
$243$	−939049.	−1.02017
$244$	798514.	0.858634
$245$	−1.23301e6	−1.31235
$246$	−915702.	−0.964754
$247$	−177677.	−0.185305
$248$	376496.	0.388715
$249$	594614.	0.607767
$250$	444155.	0.449453
$251$	305796.	0.306371	0.153186	−	0.988197i	$-0.451047\pi$
$251$	305796.	0.306371	0.153186	+	0.988197i	$0.451047\pi$
$252$	12035.0	0.0119383
$253$	344714.	0.338577
$254$	1.77023e6	1.72165
$255$	696918.	0.671168
$256$	1.31104e6	1.25030
$257$	260456.	0.245981	0.122990	−	0.992408i	$-0.460752\pi$
$257$	260456.	0.245981	0.122990	+	0.992408i	$0.460752\pi$
$258$	−120030.	−0.112264
$259$	32170.7	0.0297996
$260$	−579247.	−0.531411
$261$	676521.	0.614724
$262$	−686594.	−0.617941
$263$	1.72190e6	1.53504	0.767518	−	0.641027i	$-0.221491\pi$
$263$	1.72190e6	1.53504	0.767518	+	0.641027i	$0.221491\pi$
$264$	91588.0	0.0808777
$265$	−864294.	−0.756043
$266$	12079.5	0.0104675
$267$	−271358.	−0.232951
$268$	701130.	0.596296
$269$	−1.49611e6	−1.26062	−0.630309	−	0.776344i	$-0.717072\pi$
$269$	−1.49611e6	−1.26062	−0.630309	+	0.776344i	$0.717072\pi$
$270$	−1.91422e6	−1.59802
$271$	−765101.	−0.632842	−0.316421	−	0.948619i	$-0.602481\pi$
$271$	−765101.	−0.632842	−0.316421	+	0.948619i	$0.602481\pi$
$272$	1.31780e6	1.08000
$273$	−17224.3	−0.0139873
$274$	−1.40530e6	−1.13082
$275$	−226631.	−0.180712
$276$	567026.	0.448054
$277$	1.42971e6	1.11956	0.559782	−	0.828640i	$-0.310885\pi$
$277$	1.42971e6	1.11956	0.559782	+	0.828640i	$0.310885\pi$
$278$	−2.84467e6	−2.20760
$279$	−598316.	−0.460172
$280$	−31112.1	−0.0237156
$281$	1.57486e6	1.18981	0.594903	−	0.803798i	$-0.297191\pi$
$281$	1.57486e6	1.18981	0.594903	+	0.803798i	$0.297191\pi$
$282$	−876299.	−0.656190
$283$	2.26651e6	1.68225	0.841126	−	0.540839i	$-0.181893\pi$
$283$	2.26651e6	1.68225	0.841126	+	0.540839i	$0.181893\pi$
$284$	117886.	0.0867291
$285$	−271859.	−0.198259
$286$	−311266.	−0.225018
$287$	59910.5	0.0429337
$288$	−923020.	−0.655737
$289$	−354072.	−0.249372
$290$	2.21370e6	1.54569
$291$	−177490.	−0.122869
$292$	−649706.	−0.445923
$293$	−1.71741e6	−1.16871	−0.584353	−	0.811500i	$-0.698652\pi$
$293$	−1.71741e6	−1.16871	−0.584353	+	0.811500i	$0.698652\pi$
$294$	−1.08988e6	−0.735376
$295$	1.75568e6	1.17460
$296$	−755513.	−0.501202
$297$	−368680.	−0.242526
$298$	2.99266e6	1.95216
$299$	1.52245e6	0.984839
$300$	−372790.	−0.239145
$301$	7853.07	0.00499601
$302$	−1.25939e6	−0.794586
$303$	−1.61551e6	−1.01089
$304$	−514056.	−0.319026
$305$	3.28048e6	2.01924
$306$	−1.15568e6	−0.705560
$307$	1.74721e6	1.05804	0.529018	−	0.848611i	$-0.322560\pi$
$307$	1.74721e6	1.05804	0.529018	+	0.848611i	$0.322560\pi$
$308$	7584.72	0.00455578
$309$	212424.	0.126563
$310$	−1.95780e6	−1.15708
$311$	1.69074e6	0.991234	0.495617	−	0.868541i	$-0.334942\pi$
$311$	1.69074e6	0.991234	0.495617	+	0.868541i	$0.334942\pi$
$312$	404504.	0.235254
$313$	−2.25813e6	−1.30283	−0.651414	−	0.758722i	$-0.725824\pi$
$313$	−2.25813e6	−1.30283	−0.651414	+	0.758722i	$0.725824\pi$
$314$	−2.30851e6	−1.32132
$315$	49442.3	0.0280752
$316$	1.10549e6	0.622786
$317$	−1.35062e6	−0.754895	−0.377448	−	0.926031i	$-0.623198\pi$
$317$	−1.35062e6	−0.754895	−0.377448	+	0.926031i	$0.623198\pi$
$318$	−763965.	−0.423649
$319$	426360.	0.234585
$320$	−20396.4	−0.0111347
$321$	1.11178e6	0.602221
$322$	−103505.	−0.0556316
$323$	−415749.	−0.221730
$324$	82121.9	0.0434607
$325$	−1.00093e6	−0.525649
$326$	62771.9	0.0327131
$327$	−25182.6	−0.0130236
$328$	−1.40697e6	−0.722104
$329$	57332.5	0.0292019
$330$	−476261.	−0.240747
$331$	−3.34400e6	−1.67763	−0.838814	−	0.544418i	$-0.816751\pi$
$331$	−3.34400e6	−1.67763	−0.838814	+	0.544418i	$0.816751\pi$
$332$	−1.15643e6	−0.575801
$333$	1.20064e6	0.593337
$334$	−2.17991e6	−1.06923
$335$	2.88040e6	1.40230
$336$	−49833.5	−0.0240809
$337$	−2.71414e6	−1.30184	−0.650920	−	0.759146i	$-0.725617\pi$
$337$	−2.71414e6	−1.30184	−0.650920	+	0.759146i	$0.725617\pi$
$338$	1.24747e6	0.593936
$339$	1.39294e6	0.658314
$340$	−1.35539e6	−0.635869
$341$	−377073.	−0.175606
$342$	450817.	0.208418
$343$	142689.	0.0654869
$344$	−184426.	−0.0840282
$345$	2.32947e6	1.05368
$346$	−2.58272e6	−1.15981
$347$	−2.38384e6	−1.06280	−0.531402	−	0.847120i	$-0.678335\pi$
$347$	−2.38384e6	−1.06280	−0.531402	+	0.847120i	$0.678335\pi$
$348$	701327.	0.310436
$349$	−1.95869e6	−0.860799	−0.430400	−	0.902638i	$-0.641627\pi$
$349$	−1.95869e6	−0.860799	−0.430400	+	0.902638i	$0.641627\pi$
$350$	68049.1	0.0296929
$351$	−1.62830e6	−0.705450
$352$	−581709.	−0.250236
$353$	3.44654e6	1.47213	0.736066	−	0.676910i	$-0.236681\pi$
$353$	3.44654e6	1.47213	0.736066	+	0.676910i	$0.236681\pi$
$354$	1.55188e6	0.658188
$355$	484300.	0.203959
$356$	527746.	0.220699
$357$	−40303.5	−0.0167368
$358$	3.85122e6	1.58815
$359$	2.13197e6	0.873063	0.436531	−	0.899689i	$-0.356207\pi$
$359$	2.13197e6	0.873063	0.436531	+	0.899689i	$0.356207\pi$
$360$	−1.16113e6	−0.472198
$361$	−2.31392e6	−0.934502
$362$	−522745.	−0.209661
$363$	1.38864e6	0.553123
$364$	33498.4	0.0132517
$365$	−2.66914e6	−1.04867
$366$	2.89967e6	1.13148
$367$	2.28364e6	0.885039	0.442520	−	0.896759i	$-0.354085\pi$
$367$	2.28364e6	0.885039	0.442520	+	0.896759i	$0.354085\pi$
$368$	4.40477e6	1.69552
$369$	2.23591e6	0.854846
$370$	3.92870e6	1.49192
$371$	49983.0	0.0188533
$372$	−620254.	−0.232387
$373$	1.36046e6	0.506305	0.253153	−	0.967426i	$-0.418532\pi$
$373$	1.36046e6	0.506305	0.253153	+	0.967426i	$0.418532\pi$
$374$	−728338.	−0.269249
$375$	578083.	0.212282
$376$	−1.34643e6	−0.491148
$377$	1.88305e6	0.682350
$378$	110701.	0.0398495
$379$	−2.30799e6	−0.825345	−0.412672	−	0.910880i	$-0.635405\pi$
$379$	−2.30799e6	−0.825345	−0.412672	+	0.910880i	$0.635405\pi$
$380$	528722.	0.187831
$381$	2.30401e6	0.813153
$382$	−2.36476e6	−0.829142
$383$	−4.86524e6	−1.69476	−0.847378	−	0.530990i	$-0.821820\pi$
$383$	−4.86524e6	−1.69476	−0.847378	+	0.530990i	$0.821820\pi$
$384$	1.69479e6	0.586528
$385$	31159.7	0.0107138
$386$	5.75929e6	1.96744
$387$	293083.	0.0994749
$388$	345189.	0.116407
$389$	2.31012e6	0.774034	0.387017	−	0.922073i	$-0.373506\pi$
$389$	2.31012e6	0.774034	0.387017	+	0.922073i	$0.373506\pi$
$390$	−2.10344e6	−0.700274
$391$	3.56241e6	1.17843
$392$	−1.67459e6	−0.550418
$393$	−893627.	−0.291860
$394$	−4.38852e6	−1.42422
$395$	4.54161e6	1.46459
$396$	283068.	0.0907095
$397$	−2.01533e6	−0.641756	−0.320878	−	0.947120i	$-0.603978\pi$
$397$	−2.01533e6	−0.641756	−0.320878	+	0.947120i	$0.603978\pi$
$398$	−754499.	−0.238754
$399$	15721.9	0.00494393
$400$	−2.89590e6	−0.904969
$401$	1.08183e6	0.335967	0.167984	−	0.985790i	$-0.446274\pi$
$401$	1.08183e6	0.335967	0.167984	+	0.985790i	$0.446274\pi$
$402$	2.54604e6	0.785778
$403$	−1.66537e6	−0.510796
$404$	3.14190e6	0.957721
$405$	337375.	0.102206
$406$	−128020.	−0.0385446
$407$	756671.	0.226423
$408$	946508.	0.281497
$409$	3.27121e6	0.966942	0.483471	−	0.875360i	$-0.339376\pi$
$409$	3.27121e6	0.966942	0.483471	+	0.875360i	$0.339376\pi$
$410$	7.31629e6	2.14947
$411$	−1.82905e6	−0.534097
$412$	−413130.	−0.119907
$413$	−101533.	−0.0292908
$414$	−3.86289e6	−1.10767
$415$	−4.75086e6	−1.35410
$416$	−2.56916e6	−0.727876
$417$	−3.70244e6	−1.04267
$418$	284116.	0.0795343
$419$	−6.28944e6	−1.75016	−0.875078	−	0.483982i	$-0.839190\pi$
$419$	−6.28944e6	−1.75016	−0.875078	+	0.483982i	$0.839190\pi$
$420$	51255.2	0.0141780
$421$	−2.93720e6	−0.807661	−0.403830	−	0.914834i	$-0.632321\pi$
$421$	−2.93720e6	−0.807661	−0.403830	+	0.914834i	$0.632321\pi$
$422$	−6.41162e6	−1.75261
$423$	2.13970e6	0.581435
$424$	−1.17383e6	−0.317095
$425$	−2.34210e6	−0.628974
$426$	428082.	0.114289
$427$	−189713.	−0.0503533
$428$	−2.16223e6	−0.570548
$429$	−405124.	−0.106278
$430$	959021.	0.250125
$431$	−4.86878e6	−1.26249	−0.631243	−	0.775585i	$-0.717455\pi$
$431$	−4.86878e6	−1.26249	−0.631243	+	0.775585i	$0.717455\pi$
$432$	−4.71101e6	−1.21452
$433$	3.51734e6	0.901560	0.450780	−	0.892635i	$-0.351146\pi$
$433$	3.51734e6	0.901560	0.450780	+	0.892635i	$0.351146\pi$
$434$	113221.	0.0288539
$435$	2.88121e6	0.730048
$436$	48976.0	0.0123386
$437$	−1.38965e6	−0.348099
$438$	−2.35930e6	−0.587622
$439$	672313.	0.166498	0.0832492	−	0.996529i	$-0.473470\pi$
$439$	672313.	0.166498	0.0832492	+	0.996529i	$0.473470\pi$
$440$	−731771.	−0.180195
$441$	2.66120e6	0.651600
$442$	−3.21675e6	−0.783180
$443$	−5.61023e6	−1.35822	−0.679112	−	0.734035i	$-0.737635\pi$
$443$	−5.61023e6	−1.35822	−0.679112	+	0.734035i	$0.737635\pi$
$444$	1.24466e6	0.299636
$445$	2.16810e6	0.519014
$446$	−4.36701e6	−1.03955
$447$	3.89505e6	0.922028
$448$	1179.54	0.000277663 0
$449$	−3.59210e6	−0.840877	−0.420438	−	0.907321i	$-0.638124\pi$
$449$	−3.59210e6	−0.840877	−0.420438	+	0.907321i	$0.638124\pi$
$450$	2.53965e6	0.591211
$451$	1.40912e6	0.326218
$452$	−2.70904e6	−0.623691
$453$	−1.63914e6	−0.375292
$454$	9.51762e6	2.16715
$455$	137619.	0.0311638
$456$	−369221.	−0.0831523
$457$	3.48791e6	0.781222	0.390611	−	0.920556i	$-0.372264\pi$
$457$	3.48791e6	0.781222	0.390611	+	0.920556i	$0.372264\pi$
$458$	6.70747e6	1.49415
$459$	−3.81009e6	−0.844119
$460$	−4.53043e6	−0.998263
$461$	−3.41573e6	−0.748568	−0.374284	−	0.927314i	$-0.622112\pi$
$461$	−3.41573e6	−0.748568	−0.374284	+	0.927314i	$0.622112\pi$
$462$	27542.7	0.00600345
$463$	−2.10091e6	−0.455465	−0.227732	−	0.973724i	$-0.573131\pi$
$463$	−2.10091e6	−0.455465	−0.227732	+	0.973724i	$0.573131\pi$
$464$	5.44804e6	1.17475
$465$	−2.54814e6	−0.546502
$466$	7.94540e6	1.69493
$467$	−3.63285e6	−0.770824	−0.385412	−	0.922745i	$-0.625941\pi$
$467$	−3.63285e6	−0.770824	−0.385412	+	0.922745i	$0.625941\pi$
$468$	1.25019e6	0.263852
$469$	−166576.	−0.0349688
$470$	7.00147e6	1.46199
$471$	−3.00461e6	−0.624073
$472$	2.38445e6	0.492644
$473$	184708.	0.0379606
$474$	4.01442e6	0.820685
$475$	913624.	0.185795
$476$	78383.6	0.0158565
$477$	1.86541e6	0.375385
$478$	7.31883e6	1.46512
$479$	−9.20955e6	−1.83400	−0.917000	−	0.398887i	$-0.869397\pi$
$479$	−9.20955e6	−1.83400	−0.917000	+	0.398887i	$0.869397\pi$
$480$	−3.93101e6	−0.778756
$481$	3.34188e6	0.658611
$482$	−1.04818e7	−2.05502
$483$	−134716.	−0.0262754
$484$	−2.70067e6	−0.524032
$485$	1.41811e6	0.273752
$486$	6.63189e6	1.27364
$487$	1.50007e6	0.286609	0.143304	−	0.989679i	$-0.454227\pi$
$487$	1.50007e6	0.286609	0.143304	+	0.989679i	$0.454227\pi$
$488$	4.45532e6	0.846895
$489$	81700.0	0.0154508
$490$	8.70793e6	1.63842
$491$	2.98959e6	0.559639	0.279819	−	0.960053i	$-0.409725\pi$
$491$	2.98959e6	0.559639	0.279819	+	0.960053i	$0.409725\pi$
$492$	2.31789e6	0.431699
$493$	4.40618e6	0.816478
$494$	1.25481e6	0.231346
$495$	1.16291e6	0.213320
$496$	−4.81826e6	−0.879398
$497$	−28007.6	−0.00508609
$498$	−4.19937e6	−0.758771
$499$	5.69652e6	1.02414	0.512069	−	0.858944i	$-0.328879\pi$
$499$	5.69652e6	1.02414	0.512069	+	0.858944i	$0.328879\pi$
$500$	−1.12428e6	−0.201117
$501$	−2.83723e6	−0.505011
$502$	−2.15964e6	−0.382491
$503$	−510777.	−0.0900143	−0.0450072	−	0.998987i	$-0.514331\pi$
$503$	−510777.	−0.0900143	−0.0450072	+	0.998987i	$0.514331\pi$
$504$	67149.2	0.0117751
$505$	1.29076e7	2.25226
$506$	−2.43449e6	−0.422699
$507$	1.62363e6	0.280522
$508$	−4.48092e6	−0.770386
$509$	−6.63405e6	−1.13497	−0.567485	−	0.823384i	$-0.692083\pi$
$509$	−6.63405e6	−1.13497	−0.567485	+	0.823384i	$0.692083\pi$
$510$	−4.92188e6	−0.837926
$511$	154359.	0.0261505
$512$	−3.35886e6	−0.566261
$513$	1.48627e6	0.249347
$514$	−1.83943e6	−0.307097
$515$	−1.69723e6	−0.281983
$516$	303830.	0.0502349
$517$	1.34849e6	0.221881
$518$	−227201.	−0.0372036
$519$	−3.36150e6	−0.547791
$520$	−3.23192e6	−0.524145
$521$	8.23919e6	1.32981	0.664906	−	0.746927i	$-0.268472\pi$
$521$	8.23919e6	1.32981	0.664906	+	0.746927i	$0.268472\pi$
$522$	−4.77782e6	−0.767457
$523$	−2.19556e6	−0.350987	−0.175494	−	0.984481i	$-0.556152\pi$
$523$	−2.19556e6	−0.350987	−0.175494	+	0.984481i	$0.556152\pi$
$524$	1.73796e6	0.276510
$525$	88568.3	0.0140243
$526$	−1.21607e7	−1.91643
$527$	−3.89683e6	−0.611202
$528$	−1.17211e6	−0.182971
$529$	5.47112e6	0.850036
$530$	6.10394e6	0.943888
$531$	−3.78929e6	−0.583205
$532$	−30576.5	−0.00468391
$533$	6.22349e6	0.948890
$534$	1.91642e6	0.290829
$535$	−8.88291e6	−1.34175
$536$	3.91197e6	0.588143
$537$	5.01250e6	0.750099
$538$	1.05661e7	1.57383
$539$	1.67715e6	0.248657
$540$	4.84541e6	0.715066
$541$	1.11926e7	1.64414	0.822071	−	0.569384i	$-0.192818\pi$
$541$	1.11926e7	1.64414	0.822071	+	0.569384i	$0.192818\pi$
$542$	5.40341e6	0.790077
$543$	−680371.	−0.0990253
$544$	−6.01162e6	−0.870953
$545$	201205.	0.0290166
$546$	121644.	0.0174626
$547$	−9.83831e6	−1.40589	−0.702946	−	0.711243i	$-0.748133\pi$
$547$	−9.83831e6	−1.40589	−0.702946	+	0.711243i	$0.748133\pi$
$548$	3.55719e6	0.506006
$549$	−7.08025e6	−1.00258
$550$	1.60055e6	0.225612
$551$	−1.71880e6	−0.241182
$552$	3.16373e6	0.441928
$553$	−262646.	−0.0365223
$554$	−1.00971e7	−1.39773
$555$	5.11335e6	0.704649
$556$	7.20064e6	0.987834
$557$	−2.90233e6	−0.396378	−0.198189	−	0.980164i	$-0.563506\pi$
$557$	−2.90233e6	−0.396378	−0.198189	+	0.980164i	$0.563506\pi$
$558$	4.22551e6	0.574505
$559$	815775.	0.110418
$560$	398160.	0.0536523
$561$	−947958.	−0.127169
$562$	−1.11222e7	−1.48542
$563$	−1.18464e7	−1.57513	−0.787566	−	0.616231i	$-0.788659\pi$
$563$	−1.18464e7	−1.57513	−0.787566	+	0.616231i	$0.788659\pi$
$564$	2.21815e6	0.293625
$565$	−1.11293e7	−1.46672
$566$	−1.60069e7	−2.10022
$567$	−19510.7	−0.00254868
$568$	657744.	0.0855433
$569$	1.03184e7	1.33608	0.668038	−	0.744127i	$-0.267134\pi$
$569$	1.03184e7	1.33608	0.668038	+	0.744127i	$0.267134\pi$
$570$	1.91996e6	0.247518
$571$	8.69974e6	1.11665	0.558323	−	0.829623i	$-0.311445\pi$
$571$	8.69974e6	1.11665	0.558323	+	0.829623i	$0.311445\pi$
$572$	787899.	0.100689
$573$	−3.07782e6	−0.391613
$574$	−423109.	−0.0536009
$575$	−7.82853e6	−0.987440
$576$	44021.5	0.00552851
$577$	6.13956e6	0.767711	0.383856	−	0.923393i	$-0.374596\pi$
$577$	6.13956e6	0.767711	0.383856	+	0.923393i	$0.374596\pi$
$578$	2.50058e6	0.311330
$579$	7.49593e6	0.929243
$580$	−5.60347e6	−0.691652
$581$	274747.	0.0337670
$582$	1.25350e6	0.153397
$583$	1.17562e6	0.143251
$584$	−3.62504e6	−0.439826
$585$	5.13605e6	0.620497
$586$	1.21289e7	1.45908
$587$	8.63572e6	1.03443	0.517217	−	0.855854i	$-0.326968\pi$
$587$	8.63572e6	1.03443	0.517217	+	0.855854i	$0.326968\pi$
$588$	2.75878e6	0.329059
$589$	1.52010e6	0.180545
$590$	−1.23992e7	−1.46644
$591$	−5.71182e6	−0.672675
$592$	9.66877e6	1.13388
$593$	919244.	0.107348	0.0536740	−	0.998559i	$-0.482907\pi$
$593$	919244.	0.107348	0.0536740	+	0.998559i	$0.482907\pi$
$594$	2.60375e6	0.302784
$595$	322017.	0.0372895
$596$	−7.57523e6	−0.873535
$597$	−982008.	−0.112766
$598$	−1.07521e7	−1.22953
$599$	−9.70062e6	−1.10467	−0.552335	−	0.833622i	$-0.686263\pi$
$599$	−9.70062e6	−1.10467	−0.552335	+	0.833622i	$0.686263\pi$
$600$	−2.07998e6	−0.235875
$601$	−3.39087e6	−0.382935	−0.191467	−	0.981499i	$-0.561325\pi$
$601$	−3.39087e6	−0.382935	−0.191467	+	0.981499i	$0.561325\pi$
$602$	−55461.1	−0.00623731
$603$	−6.21677e6	−0.696260
$604$	3.18785e6	0.355554
$605$	−1.10949e7	−1.23236
$606$	1.14093e7	1.26205
$607$	7.75122e6	0.853883	0.426942	−	0.904279i	$-0.359591\pi$
$607$	7.75122e6	0.853883	0.426942	+	0.904279i	$0.359591\pi$
$608$	2.34506e6	0.257274
$609$	−166623.	−0.0182051
$610$	−2.31679e7	−2.52093
$611$	5.95568e6	0.645399
$612$	2.92534e6	0.315717
$613$	5.02322e6	0.539922	0.269961	−	0.962871i	$-0.412989\pi$
$613$	5.02322e6	0.539922	0.269961	+	0.962871i	$0.412989\pi$
$614$	−1.23394e7	−1.32091
$615$	9.52242e6	1.01522
$616$	42319.1	0.00449350
$617$	8.22276e6	0.869571	0.434785	−	0.900534i	$-0.356824\pi$
$617$	8.22276e6	0.869571	0.434785	+	0.900534i	$0.356824\pi$
$618$	−1.50021e6	−0.158009
$619$	4.78837e6	0.502297	0.251149	−	0.967949i	$-0.419192\pi$
$619$	4.78837e6	0.502297	0.251149	+	0.967949i	$0.419192\pi$
$620$	4.95572e6	0.517759
$621$	−1.27353e7	−1.32520
$622$	−1.19406e7	−1.23751
$623$	−125383.	−0.0129425
$624$	−5.17669e6	−0.532219
$625$	−1.17084e7	−1.19894
$626$	1.59477e7	1.62653
$627$	369787.	0.0375649
$628$	5.84346e6	0.591250
$629$	7.81974e6	0.788072
$630$	−349179.	−0.0350507
$631$	1.36662e7	1.36639	0.683195	−	0.730236i	$-0.260590\pi$
$631$	1.36662e7	1.36639	0.683195	+	0.730236i	$0.260590\pi$
$632$	6.16812e6	0.614271
$633$	−8.34495e6	−0.827779
$634$	9.53858e6	0.942455
$635$	−1.84086e7	−1.81170
$636$	1.93380e6	0.189570
$637$	7.40726e6	0.723284
$638$	−3.01110e6	−0.292869
$639$	−1.04526e6	−0.101268
$640$	−1.35411e7	−1.30678
$641$	−1.44535e7	−1.38940	−0.694701	−	0.719299i	$-0.744463\pi$
$641$	−1.44535e7	−1.38940	−0.694701	+	0.719299i	$0.744463\pi$
$642$	−7.85177e6	−0.751848
$643$	−155911.	−0.0148713	−0.00743564	−	0.999972i	$-0.502367\pi$
$643$	−155911.	−0.0148713	−0.00743564	+	0.999972i	$0.502367\pi$
$644$	261999.	0.0248935
$645$	1.24820e6	0.118137
$646$	2.93617e6	0.276821
$647$	9.88750e6	0.928594	0.464297	−	0.885680i	$-0.346307\pi$
$647$	9.88750e6	0.928594	0.464297	+	0.885680i	$0.346307\pi$
$648$	458200.	0.0428665
$649$	−2.38810e6	−0.222557
$650$	7.06892e6	0.656251
$651$	147362.	0.0136280
$652$	−158893.	−0.0146381
$653$	−1.95289e7	−1.79224	−0.896119	−	0.443814i	$-0.853625\pi$
$653$	−1.95289e7	−1.79224	−0.896119	+	0.443814i	$0.853625\pi$
$654$	177848.	0.0162594
$655$	7.13992e6	0.650264
$656$	1.80058e7	1.63363
$657$	5.76080e6	0.520678
$658$	−404902.	−0.0364573
$659$	1.14663e7	1.02851	0.514257	−	0.857636i	$-0.328068\pi$
$659$	1.14663e7	1.02851	0.514257	+	0.857636i	$0.328068\pi$
$660$	1.20555e6	0.107727
$661$	−1.16475e7	−1.03688	−0.518442	−	0.855113i	$-0.673488\pi$
$661$	−1.16475e7	−1.03688	−0.518442	+	0.855113i	$0.673488\pi$
$662$	2.36165e7	2.09445
$663$	−4.18672e6	−0.369905
$664$	−6.45230e6	−0.567929
$665$	−125615.	−0.0110151
$666$	−8.47931e6	−0.740756
$667$	1.47278e7	1.28181
$668$	5.51795e6	0.478450
$669$	−5.68382e6	−0.490992
$670$	−2.03424e7	−1.75071
$671$	−4.46215e6	−0.382593
$672$	227334.	0.0194197
$673$	2.25271e6	0.191720	0.0958601	−	0.995395i	$-0.469440\pi$
$673$	2.25271e6	0.191720	0.0958601	+	0.995395i	$0.469440\pi$
$674$	1.91682e7	1.62529
$675$	8.37281e6	0.707313
$676$	−3.15770e6	−0.265769
$677$	−8.64928e6	−0.725284	−0.362642	−	0.931929i	$-0.618125\pi$
$677$	−8.64928e6	−0.725284	−0.362642	+	0.931929i	$0.618125\pi$
$678$	−9.83743e6	−0.821878
$679$	−82010.9	−0.00682649
$680$	−7.56242e6	−0.627175
$681$	1.23875e7	1.02357
$682$	2.66302e6	0.219237
$683$	1.98237e6	0.162605	0.0813024	−	0.996689i	$-0.474092\pi$
$683$	1.98237e6	0.162605	0.0813024	+	0.996689i	$0.474092\pi$
$684$	−1.14114e6	−0.0932607
$685$	1.46137e7	1.18997
$686$	−1.00772e6	−0.0817577
$687$	8.73002e6	0.705705
$688$	2.36021e6	0.190099
$689$	5.19222e6	0.416682
$690$	−1.64515e7	−1.31548
$691$	−2.17111e7	−1.72977	−0.864883	−	0.501973i	$-0.832607\pi$
$691$	−2.17111e7	−1.72977	−0.864883	+	0.501973i	$0.832607\pi$
$692$	6.53756e6	0.518980
$693$	−67252.1	−0.00531952
$694$	1.68355e7	1.32687
$695$	2.95818e7	2.32307
$696$	3.91306e6	0.306192
$697$	1.45625e7	1.13541
$698$	1.38329e7	1.07467
$699$	1.03412e7	0.800533
$700$	−172251.	−0.0132867
$701$	9.30126e6	0.714902	0.357451	−	0.933932i	$-0.383646\pi$
$701$	9.30126e6	0.714902	0.357451	+	0.933932i	$0.383646\pi$
$702$	1.14996e7	0.880725
$703$	−3.05039e6	−0.232791
$704$	27743.4	0.00210973
$705$	9.11266e6	0.690514
$706$	−2.43407e7	−1.83790
$707$	−746461.	−0.0561641
$708$	−3.92823e6	−0.294519
$709$	1.05795e7	0.790405	0.395203	−	0.918594i	$-0.370674\pi$
$709$	1.05795e7	0.790405	0.395203	+	0.918594i	$0.370674\pi$
$710$	−3.42029e6	−0.254635
$711$	−9.80217e6	−0.727190
$712$	2.94457e6	0.217681
$713$	−1.30253e7	−0.959539
$714$	284637.	0.0208952
$715$	3.23687e6	0.236788
$716$	−9.74849e6	−0.710648
$717$	9.52572e6	0.691990
$718$	−1.50567e7	−1.08998
$719$	−1.48644e7	−1.07232	−0.536161	−	0.844116i	$-0.680126\pi$
$719$	−1.48644e7	−1.07232	−0.536161	+	0.844116i	$0.680126\pi$
$720$	1.48597e7	1.06826
$721$	98152.5	0.00703175
$722$	1.63417e7	1.16669
$723$	−1.36424e7	−0.970610
$724$	1.32321e6	0.0938171
$725$	−9.68273e6	−0.684152
$726$	−9.80703e6	−0.690551
$727$	−1.59916e7	−1.12216	−0.561082	−	0.827760i	$-0.689615\pi$
$727$	−1.59916e7	−1.12216	−0.561082	+	0.827760i	$0.689615\pi$
$728$	186905.	0.0130705
$729$	7.51535e6	0.523758
$730$	1.88504e7	1.30922
$731$	1.90885e6	0.132123
$732$	−7.33986e6	−0.506303
$733$	−4.72246e6	−0.324645	−0.162322	−	0.986738i	$-0.551898\pi$
$733$	−4.72246e6	−0.324645	−0.162322	+	0.986738i	$0.551898\pi$
$734$	−1.61279e7	−1.10493
$735$	1.13337e7	0.773843
$736$	−2.00940e7	−1.36733
$737$	−3.91796e6	−0.265700
$738$	−1.57908e7	−1.06724
$739$	−6.65028e6	−0.447949	−0.223975	−	0.974595i	$-0.571903\pi$
$739$	−6.65028e6	−0.447949	−0.223975	+	0.974595i	$0.571903\pi$
$740$	−9.94461e6	−0.667588
$741$	1.63319e6	0.109267
$742$	−352997.	−0.0235376
$743$	275876.	0.0183334	0.00916668	−	0.999958i	$-0.497082\pi$
$743$	275876.	0.0183334	0.00916668	+	0.999958i	$0.497082\pi$
$744$	−3.46072e6	−0.229210
$745$	−3.11207e7	−2.05428
$746$	−9.60801e6	−0.632101
$747$	1.02538e7	0.672330
$748$	1.84362e6	0.120481
$749$	513708.	0.0334589
$750$	−4.08262e6	−0.265025
$751$	−1.13215e7	−0.732493	−0.366246	−	0.930518i	$-0.619357\pi$
$751$	−1.13215e7	−0.732493	−0.366246	+	0.930518i	$0.619357\pi$
$752$	1.72310e7	1.11113
$753$	−2.81085e6	−0.180655
$754$	−1.32987e7	−0.851886
$755$	1.30964e7	0.836150
$756$	−280215.	−0.0178315
$757$	8.10576e6	0.514108	0.257054	−	0.966397i	$-0.417248\pi$
$757$	8.10576e6	0.514108	0.257054	+	0.966397i	$0.417248\pi$
$758$	1.62998e7	1.03041
$759$	−3.16857e6	−0.199645
$760$	2.95001e6	0.185263
$761$	6.32095e6	0.395659	0.197829	−	0.980236i	$-0.436611\pi$
$761$	6.32095e6	0.395659	0.197829	+	0.980236i	$0.436611\pi$
$762$	−1.62717e7	−1.01519
$763$	−11635.9	−0.000723581 0
$764$	5.98586e6	0.371016
$765$	1.20180e7	0.742467
$766$	3.43600e7	2.11583
$767$	−1.05472e7	−0.647365
$768$	−1.20509e7	−0.737253
$769$	−9.40923e6	−0.573770	−0.286885	−	0.957965i	$-0.592620\pi$
$769$	−9.40923e6	−0.573770	−0.286885	+	0.957965i	$0.592620\pi$
$770$	−220061.	−0.0133757
$771$	−2.39408e6	−0.145045
$772$	−1.45783e7	−0.880370
$773$	−1.11136e7	−0.668969	−0.334484	−	0.942401i	$-0.608562\pi$
$773$	−1.11136e7	−0.668969	−0.334484	+	0.942401i	$0.608562\pi$
$774$	−2.06985e6	−0.124190
$775$	8.56342e6	0.512145
$776$	1.92599e6	0.114815
$777$	−295710.	−0.0175717
$778$	−1.63148e7	−0.966349
$779$	−5.68064e6	−0.335393
$780$	5.32438e6	0.313352
$781$	−658751.	−0.0386451
$782$	−2.51590e7	−1.47122
$783$	−1.57517e7	−0.918171
$784$	2.14307e7	1.24522
$785$	2.40062e7	1.39043
$786$	6.31110e6	0.364375
$787$	−1.18619e7	−0.682681	−0.341340	−	0.939940i	$-0.610881\pi$
$787$	−1.18619e7	−0.682681	−0.341340	+	0.939940i	$0.610881\pi$
$788$	1.11085e7	0.637296
$789$	−1.58275e7	−0.905151
$790$	−3.20744e7	−1.82849
$791$	643621.	0.0365754
$792$	1.57938e6	0.0894694
$793$	−1.97074e7	−1.11287
$794$	1.42330e7	0.801206
$795$	7.94450e6	0.445809
$796$	1.90984e6	0.106835
$797$	−1.05735e7	−0.589619	−0.294809	−	0.955556i	$-0.595256\pi$
$797$	−1.05735e7	−0.589619	−0.294809	+	0.955556i	$0.595256\pi$
$798$	−111033.	−0.00617230
$799$	1.39358e7	0.772264
$800$	1.32108e7	0.729798
$801$	−4.67941e6	−0.257697
$802$	−7.64024e6	−0.419441
$803$	3.63060e6	0.198696
$804$	−6.44472e6	−0.351612
$805$	1.07635e6	0.0585416
$806$	1.17614e7	0.637708
$807$	1.37521e7	0.743337
$808$	1.75303e7	0.944627
$809$	7.15527e6	0.384375	0.192187	−	0.981358i	$-0.438442\pi$
$809$	7.15527e6	0.384375	0.192187	+	0.981358i	$0.438442\pi$
$810$	−2.38266e6	−0.127600
$811$	−1.61605e7	−0.862783	−0.431391	−	0.902165i	$-0.641977\pi$
$811$	−1.61605e7	−0.862783	−0.431391	+	0.902165i	$0.641977\pi$
$812$	324054.	0.0172476
$813$	7.03273e6	0.373162
$814$	−5.34387e6	−0.282680
$815$	−652768.	−0.0344243
$816$	−1.21130e7	−0.636836
$817$	−744619.	−0.0390282
$818$	−2.31024e7	−1.20719
$819$	−297023.	−0.0154732
$820$	−1.85195e7	−0.961824
$821$	1.84687e7	0.956263	0.478131	−	0.878288i	$-0.341314\pi$
$821$	1.84687e7	0.956263	0.478131	+	0.878288i	$0.341314\pi$
$822$	1.29174e7	0.666798
$823$	−2.60022e7	−1.33817	−0.669084	−	0.743187i	$-0.733313\pi$
$823$	−2.60022e7	−1.33817	−0.669084	+	0.743187i	$0.733313\pi$
$824$	−2.30506e6	−0.118267
$825$	2.08317e6	0.106559
$826$	717060.	0.0365684
$827$	2.06980e7	1.05236	0.526181	−	0.850373i	$-0.323624\pi$
$827$	2.06980e7	1.05236	0.526181	+	0.850373i	$0.323624\pi$
$828$	9.77804e6	0.495651
$829$	−2.83384e7	−1.43215	−0.716075	−	0.698024i	$-0.754063\pi$
$829$	−2.83384e7	−1.43215	−0.716075	+	0.698024i	$0.754063\pi$
$830$	3.35522e7	1.69054
$831$	−1.31418e7	−0.660162
$832$	122530.	0.00613671
$833$	1.73324e7	0.865458
$834$	2.61479e7	1.30173
$835$	2.26690e7	1.12516
$836$	−719174.	−0.0355892
$837$	1.39308e7	0.687327
$838$	4.44182e7	2.18500
$839$	7.91413e6	0.388149	0.194074	−	0.980987i	$-0.437830\pi$
$839$	7.91413e6	0.388149	0.194074	+	0.980987i	$0.437830\pi$
$840$	285979.	0.0139842
$841$	−2.29508e6	−0.111894
$842$	2.07435e7	1.00833
$843$	−1.44760e7	−0.701582
$844$	1.62296e7	0.784243
$845$	−1.29725e7	−0.625004
$846$	−1.51113e7	−0.725897
$847$	641632.	0.0307311
$848$	1.50222e7	0.717370
$849$	−2.08335e7	−0.991958
$850$	1.65407e7	0.785248
$851$	2.61377e7	1.23721
$852$	−1.08359e6	−0.0511407
$853$	9.61170e6	0.452301	0.226151	−	0.974092i	$-0.427386\pi$
$853$	9.61170e6	0.452301	0.226151	+	0.974092i	$0.427386\pi$
$854$	1.33982e6	0.0628640
$855$	−4.68806e6	−0.219320
$856$	−1.20642e7	−0.562747
$857$	1.10987e7	0.516203	0.258101	−	0.966118i	$-0.416903\pi$
$857$	1.10987e7	0.516203	0.258101	+	0.966118i	$0.416903\pi$
$858$	2.86112e6	0.132684
$859$	2.13737e7	0.988316	0.494158	−	0.869372i	$-0.335476\pi$
$859$	2.13737e7	0.988316	0.494158	+	0.869372i	$0.335476\pi$
$860$	−2.42754e6	−0.111923
$861$	−550691.	−0.0253163
$862$	3.43850e7	1.57616
$863$	1.96904e7	0.899970	0.449985	−	0.893036i	$-0.351429\pi$
$863$	1.96904e7	0.899970	0.449985	+	0.893036i	$0.351429\pi$
$864$	2.14910e7	0.979430
$865$	2.68578e7	1.22048
$866$	−2.48407e7	−1.12556
$867$	3.25460e6	0.147045
$868$	−286594.	−0.0129112
$869$	−6.17756e6	−0.277503
$870$	−2.03481e7	−0.911434
$871$	−1.73039e7	−0.772857
$872$	273263.	0.0121700
$873$	−3.06071e6	−0.135921
$874$	9.81422e6	0.434587
$875$	267109.	0.0117942
$876$	5.97203e6	0.262943
$877$	−2.53046e7	−1.11096	−0.555482	−	0.831529i	$-0.687466\pi$
$877$	−2.53046e7	−1.11096	−0.555482	+	0.831529i	$0.687466\pi$
$878$	−4.74810e6	−0.207866
$879$	1.57863e7	0.689140
$880$	9.36493e6	0.407660
$881$	−2.55408e7	−1.10865	−0.554325	−	0.832301i	$-0.687023\pi$
$881$	−2.55408e7	−1.10865	−0.554325	+	0.832301i	$0.687023\pi$
$882$	−1.87943e7	−0.813496
$883$	−2.23540e7	−0.964836	−0.482418	−	0.875941i	$-0.660241\pi$
$883$	−2.23540e7	−0.964836	−0.482418	+	0.875941i	$0.660241\pi$
$884$	8.14247e6	0.350450
$885$	−1.61380e7	−0.692617
$886$	3.96214e7	1.69569
$887$	−2.77035e7	−1.18229	−0.591147	−	0.806564i	$-0.701325\pi$
$887$	−2.77035e7	−1.18229	−0.591147	+	0.806564i	$0.701325\pi$
$888$	6.94460e6	0.295539
$889$	1.06459e6	0.0451781
$890$	−1.53119e7	−0.647967
$891$	−458902.	−0.0193654
$892$	1.10541e7	0.465169
$893$	−5.43619e6	−0.228122
$894$	−2.75082e7	−1.15111
$895$	−4.00490e7	−1.67122
$896$	783095.	0.0325870
$897$	−1.39942e7	−0.580721
$898$	2.53686e7	1.04980
$899$	−1.61103e7	−0.664821
$900$	−6.42854e6	−0.264549
$901$	1.21494e7	0.498588
$902$	−9.95172e6	−0.407269
$903$	−72184.7	−0.00294595
$904$	−1.51151e7	−0.615164
$905$	5.43604e6	0.220628
$906$	1.15761e7	0.468536
$907$	−3.23111e7	−1.30417	−0.652083	−	0.758147i	$-0.726105\pi$
$907$	−3.23111e7	−1.30417	−0.652083	+	0.758147i	$0.726105\pi$
$908$	−2.40917e7	−0.969734
$909$	−2.78585e7	−1.11828
$910$	−971913.	−0.0389067
$911$	−4.47890e6	−0.178803	−0.0894016	−	0.995996i	$-0.528495\pi$
$911$	−4.47890e6	−0.178803	−0.0894016	+	0.995996i	$0.528495\pi$
$912$	4.72515e6	0.188117
$913$	6.46218e6	0.256568
$914$	−2.46328e7	−0.975323
$915$	−3.01538e7	−1.19066
$916$	−1.69784e7	−0.668589
$917$	−412909.	−0.0162155
$918$	2.69082e7	1.05385
$919$	2.96865e7	1.15950	0.579748	−	0.814796i	$-0.303151\pi$
$919$	2.96865e7	1.15950	0.579748	+	0.814796i	$0.303151\pi$
$920$	−2.52776e7	−0.984615
$921$	−1.60602e7	−0.623882
$922$	2.41231e7	0.934556
$923$	−2.90942e6	−0.112409
$924$	−69718.0	−0.00268637
$925$	−1.71842e7	−0.660350
$926$	1.48373e7	0.568629
$927$	3.66313e6	0.140008
$928$	−2.48533e7	−0.947359
$929$	3.16000e6	0.120129	0.0600645	−	0.998195i	$-0.480869\pi$
$929$	3.16000e6	0.120129	0.0600645	+	0.998195i	$0.480869\pi$
$930$	1.79959e7	0.682284
$931$	−6.76115e6	−0.255650
$932$	−2.01120e7	−0.758429
$933$	−1.55411e7	−0.584492
$934$	2.56564e7	0.962342
$935$	7.57401e6	0.283333
$936$	6.97544e6	0.260245
$937$	2.79689e7	1.04070	0.520351	−	0.853952i	$-0.325801\pi$
$937$	2.79689e7	1.04070	0.520351	+	0.853952i	$0.325801\pi$
$938$	1.17642e6	0.0436571
$939$	2.07565e7	0.768227
$940$	−1.77226e7	−0.654197
$941$	−1.65692e7	−0.609996	−0.304998	−	0.952353i	$-0.598656\pi$
$941$	−1.65692e7	−0.609996	−0.304998	+	0.952353i	$0.598656\pi$
$942$	2.12196e7	0.779129
$943$	4.86754e7	1.78250
$944$	−3.05153e7	−1.11452
$945$	−1.15119e6	−0.0419339
$946$	−1.30447e6	−0.0473922
$947$	4.16311e7	1.50849	0.754247	−	0.656591i	$-0.228002\pi$
$947$	4.16311e7	1.50849	0.754247	+	0.656591i	$0.228002\pi$
$948$	−1.01616e7	−0.367232
$949$	1.60348e7	0.577959
$950$	−6.45233e6	−0.231957
$951$	1.24148e7	0.445132
$952$	437343.	0.0156397
$953$	−8.44381e6	−0.301166	−0.150583	−	0.988597i	$-0.548115\pi$
$953$	−8.44381e6	−0.301166	−0.150583	+	0.988597i	$0.548115\pi$
$954$	−1.31741e7	−0.468653
$955$	2.45912e7	0.872513
$956$	−1.85260e7	−0.655595
$957$	−3.91906e6	−0.138325
$958$	6.50410e7	2.28967
$959$	−845127.	−0.0296740
$960$	187481.	0.00656568
$961$	−1.43812e7	−0.502326
$962$	−2.36015e7	−0.822248
$963$	1.91720e7	0.666195
$964$	2.65322e7	0.919561
$965$	−5.98911e7	−2.07035
$966$	951408.	0.0328038
$967$	−528314.	−0.0181688	−0.00908440	−	0.999959i	$-0.502892\pi$
$967$	−528314.	−0.0181688	−0.00908440	+	0.999959i	$0.502892\pi$
$968$	−1.50684e7	−0.516867
$969$	3.82153e6	0.130746
$970$	−1.00152e7	−0.341767
$971$	8.28089e6	0.281857	0.140929	−	0.990020i	$-0.454991\pi$
$971$	8.28089e6	0.281857	0.140929	+	0.990020i	$0.454991\pi$
$972$	−1.67871e7	−0.569916
$973$	−1.71075e6	−0.0579300
$974$	−1.05940e7	−0.357819
$975$	9.20046e6	0.309954
$976$	−5.70175e7	−1.91595
$977$	4.43148e7	1.48529	0.742647	−	0.669683i	$-0.233570\pi$
$977$	4.43148e7	1.48529	0.742647	+	0.669683i	$0.233570\pi$
$978$	−576993.	−0.0192896
$979$	−2.94908e6	−0.0983398
$980$	−2.20421e7	−0.733143
$981$	−434260.	−0.0144071
$982$	−2.11135e7	−0.698686
$983$	5.21770e7	1.72225	0.861123	−	0.508397i	$-0.169762\pi$
$983$	5.21770e7	1.72225	0.861123	+	0.508397i	$0.169762\pi$
$984$	1.29327e7	0.425796
$985$	4.56364e7	1.49872
$986$	−3.11180e7	−1.01934
$987$	−526994.	−0.0172192
$988$	−3.17628e6	−0.103520
$989$	6.38038e6	0.207423
$990$	−8.21285e6	−0.266321
$991$	2.44475e6	0.0790770	0.0395385	−	0.999218i	$-0.487411\pi$
$991$	2.44475e6	0.0790770	0.0395385	+	0.999218i	$0.487411\pi$
$992$	2.19803e7	0.709177
$993$	3.07377e7	0.989231
$994$	197799.	0.00634977
$995$	7.84606e6	0.251243
$996$	1.06298e7	0.339527
$997$	3.29791e7	1.05075	0.525376	−	0.850870i	$-0.323925\pi$
$997$	3.29791e7	1.05075	0.525376	+	0.850870i	$0.323925\pi$
$998$	−4.02308e7	−1.27859
$999$	−2.79549e7	−0.886226

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.a.a.1.3	✓	8
3.2	odd	2		387.6.a.c.1.6		8
4.3	odd	2		688.6.a.e.1.5		8
5.4	even	2		1075.6.a.a.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.a.a.1.3	✓	8	1.1	even	1	trivial
387.6.a.c.1.6		8	3.2	odd	2
688.6.a.e.1.5		8	4.3	odd	2
1075.6.a.a.1.6		8	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.a (trivial)

\(f(q)\)	\(=\)	\(q-7.06235 q^{2} -9.19190 q^{3} +17.8767 q^{4} +73.4416 q^{5} +64.9164 q^{6} -4.24720 q^{7} +99.7434 q^{8} -158.509 q^{9} +O(q^{10})\)	\(q-7.06235 q^{2} -9.19190 q^{3} +17.8767 q^{4} +73.4416 q^{5} +64.9164 q^{6} -4.24720 q^{7} +99.7434 q^{8} -158.509 q^{9} -518.670 q^{10} -99.8962 q^{11} -164.321 q^{12} -441.198 q^{13} +29.9952 q^{14} -675.068 q^{15} -1276.48 q^{16} -1032.37 q^{17} +1119.45 q^{18} +402.714 q^{19} +1312.90 q^{20} +39.0398 q^{21} +705.502 q^{22} -3450.72 q^{23} -916.832 q^{24} +2268.67 q^{25} +3115.89 q^{26} +3690.63 q^{27} -75.9260 q^{28} -4268.03 q^{29} +4767.56 q^{30} +3774.65 q^{31} +5823.14 q^{32} +918.236 q^{33} +7290.94 q^{34} -311.921 q^{35} -2833.62 q^{36} -7574.57 q^{37} -2844.11 q^{38} +4055.45 q^{39} +7325.32 q^{40} -14105.9 q^{41} -275.713 q^{42} -1849.00 q^{43} -1785.82 q^{44} -11641.2 q^{45} +24370.2 q^{46} -13498.9 q^{47} +11733.3 q^{48} -16789.0 q^{49} -16022.1 q^{50} +9489.43 q^{51} -7887.18 q^{52} -11768.5 q^{53} -26064.5 q^{54} -7336.54 q^{55} -423.630 q^{56} -3701.71 q^{57} +30142.3 q^{58} +23905.8 q^{59} -12068.0 q^{60} +44667.8 q^{61} -26657.9 q^{62} +673.219 q^{63} -277.722 q^{64} -32402.3 q^{65} -6484.90 q^{66} +39220.3 q^{67} -18455.4 q^{68} +31718.7 q^{69} +2202.89 q^{70} +6594.36 q^{71} -15810.2 q^{72} -36343.7 q^{73} +53494.2 q^{74} -20853.3 q^{75} +7199.21 q^{76} +424.279 q^{77} -28641.0 q^{78} +61839.8 q^{79} -93746.6 q^{80} +4593.79 q^{81} +99620.6 q^{82} -64688.9 q^{83} +697.904 q^{84} -75818.8 q^{85} +13058.3 q^{86} +39231.3 q^{87} -9963.99 q^{88} +29521.4 q^{89} +82213.8 q^{90} +1873.86 q^{91} -61687.6 q^{92} -34696.2 q^{93} +95333.8 q^{94} +29576.0 q^{95} -53525.7 q^{96} +19309.4 q^{97} +118569. q^{98} +15834.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{2} - 26 q^{3} + 122 q^{4} - 212 q^{5} - 69 q^{6} - 136 q^{7} - 666 q^{8} + 546 q^{9}+O(q^{10}) \) 8 * q - 12 * q^2 - 26 * q^3 + 122 * q^4 - 212 * q^5 - 69 * q^6 - 136 * q^7 - 666 * q^8 + 546 * q^9	\( 8 q - 12 q^{2} - 26 q^{3} + 122 q^{4} - 212 q^{5} - 69 q^{6} - 136 q^{7} - 666 q^{8} + 546 q^{9} - 617 q^{10} - 532 q^{11} - 4195 q^{12} - 2492 q^{13} - 4240 q^{14} - 1780 q^{15} + 1882 q^{16} - 2534 q^{17} - 3711 q^{18} - 1678 q^{19} - 2607 q^{20} - 2256 q^{21} + 11502 q^{22} - 2488 q^{23} + 19953 q^{24} + 4378 q^{25} + 4586 q^{26} - 8960 q^{27} + 18640 q^{28} - 4360 q^{29} + 25092 q^{30} + 5704 q^{31} - 18294 q^{32} - 12852 q^{33} + 30007 q^{34} + 5640 q^{35} + 67969 q^{36} - 3772 q^{37} - 6559 q^{38} + 11120 q^{39} + 14869 q^{40} - 10698 q^{41} + 78698 q^{42} - 14792 q^{43} - 356 q^{44} - 44912 q^{45} - 19389 q^{46} - 77864 q^{47} - 118727 q^{48} + 7188 q^{49} + 26877 q^{50} - 80246 q^{51} - 60736 q^{52} - 62352 q^{53} + 61026 q^{54} - 49552 q^{55} - 144528 q^{56} - 808 q^{57} + 52951 q^{58} - 26224 q^{59} + 101500 q^{60} - 82540 q^{61} - 9023 q^{62} - 61768 q^{63} + 153858 q^{64} - 5000 q^{65} - 48516 q^{66} + 27784 q^{67} + 40507 q^{68} - 93776 q^{69} + 185910 q^{70} - 9504 q^{71} - 186687 q^{72} + 14260 q^{73} - 15239 q^{74} + 167420 q^{75} + 1279 q^{76} - 218140 q^{77} + 264170 q^{78} + 160248 q^{79} - 1291 q^{80} + 161076 q^{81} - 47781 q^{82} - 77176 q^{83} + 16382 q^{84} + 141096 q^{85} + 22188 q^{86} + 268136 q^{87} + 129544 q^{88} - 265692 q^{89} + 48990 q^{90} + 401148 q^{91} + 190391 q^{92} - 123860 q^{93} + 248737 q^{94} + 135884 q^{95} + 950817 q^{96} + 144742 q^{97} - 292244 q^{98} + 239516 q^{99}+O(q^{100}) \) 8 * q - 12 * q^2 - 26 * q^3 + 122 * q^4 - 212 * q^5 - 69 * q^6 - 136 * q^7 - 666 * q^8 + 546 * q^9 - 617 * q^10 - 532 * q^11 - 4195 * q^12 - 2492 * q^13 - 4240 * q^14 - 1780 * q^15 + 1882 * q^16 - 2534 * q^17 - 3711 * q^18 - 1678 * q^19 - 2607 * q^20 - 2256 * q^21 + 11502 * q^22 - 2488 * q^23 + 19953 * q^24 + 4378 * q^25 + 4586 * q^26 - 8960 * q^27 + 18640 * q^28 - 4360 * q^29 + 25092 * q^30 + 5704 * q^31 - 18294 * q^32 - 12852 * q^33 + 30007 * q^34 + 5640 * q^35 + 67969 * q^36 - 3772 * q^37 - 6559 * q^38 + 11120 * q^39 + 14869 * q^40 - 10698 * q^41 + 78698 * q^42 - 14792 * q^43 - 356 * q^44 - 44912 * q^45 - 19389 * q^46 - 77864 * q^47 - 118727 * q^48 + 7188 * q^49 + 26877 * q^50 - 80246 * q^51 - 60736 * q^52 - 62352 * q^53 + 61026 * q^54 - 49552 * q^55 - 144528 * q^56 - 808 * q^57 + 52951 * q^58 - 26224 * q^59 + 101500 * q^60 - 82540 * q^61 - 9023 * q^62 - 61768 * q^63 + 153858 * q^64 - 5000 * q^65 - 48516 * q^66 + 27784 * q^67 + 40507 * q^68 - 93776 * q^69 + 185910 * q^70 - 9504 * q^71 - 186687 * q^72 + 14260 * q^73 - 15239 * q^74 + 167420 * q^75 + 1279 * q^76 - 218140 * q^77 + 264170 * q^78 + 160248 * q^79 - 1291 * q^80 + 161076 * q^81 - 47781 * q^82 - 77176 * q^83 + 16382 * q^84 + 141096 * q^85 + 22188 * q^86 + 268136 * q^87 + 129544 * q^88 - 265692 * q^89 + 48990 * q^90 + 401148 * q^91 + 190391 * q^92 - 123860 * q^93 + 248737 * q^94 + 135884 * q^95 + 950817 * q^96 + 144742 * q^97 - 292244 * q^98 + 239516 * q^99

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