LMFDB - Embedded newform 43.6.a.a.1.6

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			1.6
Root			$5.65705$ 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)

$f(q)$	$=$	$q+3.65705 q^{2} +7.84314 q^{3} -18.6260 q^{4} -107.102 q^{5} +28.6827 q^{6} -25.5214 q^{7} -185.142 q^{8} -181.485 q^{9} +O(q^{10})$	\(q+3.65705 q^{2} +7.84314 q^{3} -18.6260 q^{4} -107.102 q^{5} +28.6827 q^{6} -25.5214 q^{7} -185.142 q^{8} -181.485 q^{9} -391.677 q^{10} +512.073 q^{11} -146.086 q^{12} +862.516 q^{13} -93.3331 q^{14} -840.016 q^{15} -81.0406 q^{16} -1521.49 q^{17} -663.700 q^{18} -1543.11 q^{19} +1994.88 q^{20} -200.168 q^{21} +1872.67 q^{22} -3126.31 q^{23} -1452.09 q^{24} +8345.85 q^{25} +3154.26 q^{26} -3329.30 q^{27} +475.362 q^{28} -947.120 q^{29} -3071.98 q^{30} +339.499 q^{31} +5628.17 q^{32} +4016.26 q^{33} -5564.17 q^{34} +2733.40 q^{35} +3380.34 q^{36} -7448.67 q^{37} -5643.25 q^{38} +6764.84 q^{39} +19829.1 q^{40} +5116.45 q^{41} -732.024 q^{42} -1849.00 q^{43} -9537.86 q^{44} +19437.4 q^{45} -11433.1 q^{46} -17159.9 q^{47} -635.613 q^{48} -16155.7 q^{49} +30521.2 q^{50} -11933.3 q^{51} -16065.2 q^{52} +18090.4 q^{53} -12175.4 q^{54} -54844.0 q^{55} +4725.08 q^{56} -12102.9 q^{57} -3463.66 q^{58} +17031.6 q^{59} +15646.1 q^{60} +10664.9 q^{61} +1241.56 q^{62} +4631.76 q^{63} +23175.8 q^{64} -92377.3 q^{65} +14687.6 q^{66} -8799.60 q^{67} +28339.3 q^{68} -24520.1 q^{69} +9996.16 q^{70} -77057.3 q^{71} +33600.5 q^{72} -7964.75 q^{73} -27240.1 q^{74} +65457.6 q^{75} +28742.0 q^{76} -13068.8 q^{77} +24739.3 q^{78} +68997.0 q^{79} +8679.62 q^{80} +17988.8 q^{81} +18711.1 q^{82} +40813.4 q^{83} +3728.33 q^{84} +162955. q^{85} -6761.88 q^{86} -7428.39 q^{87} -94806.0 q^{88} -83692.1 q^{89} +71083.6 q^{90} -22012.6 q^{91} +58230.7 q^{92} +2662.74 q^{93} -62754.7 q^{94} +165271. q^{95} +44142.5 q^{96} +159824. q^{97} -59082.0 q^{98} -92933.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	3.65705	0.646481	0.323241	−	0.946317i	$-0.395228\pi$
$2$	3.65705	0.646481	0.323241	+	0.946317i	$0.395228\pi$
$3$	7.84314	0.503138	0.251569	−	0.967839i	$-0.419054\pi$
$3$	7.84314	0.503138	0.251569	+	0.967839i	$0.419054\pi$
$4$	−18.6260	−0.582062
$5$	−107.102	−1.91590	−0.957950	−	0.286936i	$-0.907363\pi$
$5$	−107.102	−1.91590	−0.957950	+	0.286936i	$0.907363\pi$
$6$	28.6827	0.325269
$7$	−25.5214	−0.196861	−0.0984305	−	0.995144i	$-0.531382\pi$
$7$	−25.5214	−0.196861	−0.0984305	+	0.995144i	$0.531382\pi$
$8$	−185.142	−1.02277
$9$	−181.485	−0.746853
$10$	−391.677	−1.23859
$11$	512.073	1.27600	0.637999	−	0.770037i	$-0.279762\pi$
$11$	512.073	1.27600	0.637999	+	0.770037i	$0.279762\pi$
$12$	−146.086	−0.292857
$13$	862.516	1.41550	0.707749	−	0.706464i	$-0.249711\pi$
$13$	862.516	1.41550	0.707749	+	0.706464i	$0.249711\pi$
$14$	−93.3331	−0.127267
$15$	−840.016	−0.963961
$16$	−81.0406	−0.0791413
$17$	−1521.49	−1.27687	−0.638435	−	0.769675i	$-0.720418\pi$
$17$	−1521.49	−1.27687	−0.638435	+	0.769675i	$0.720418\pi$
$18$	−663.700	−0.482826
$19$	−1543.11	−0.980650	−0.490325	−	0.871540i	$-0.663122\pi$
$19$	−1543.11	−0.980650	−0.490325	+	0.871540i	$0.663122\pi$
$20$	1994.88	1.11517
$21$	−200.168	−0.0990481
$22$	1872.67	0.824908
$23$	−3126.31	−1.23229	−0.616145	−	0.787633i	$-0.711306\pi$
$23$	−3126.31	−1.23229	−0.616145	+	0.787633i	$0.711306\pi$
$24$	−1452.09	−0.514596
$25$	8345.85	2.67067
$26$	3154.26	0.915092
$27$	−3329.30	−0.878907
$28$	475.362	0.114585
$29$	−947.120	−0.209127	−0.104563	−	0.994518i	$-0.533345\pi$
$29$	−947.120	−0.209127	−0.104563	+	0.994518i	$0.533345\pi$
$30$	−3071.98	−0.623183
$31$	339.499	0.0634504	0.0317252	−	0.999497i	$-0.489900\pi$
$31$	339.499	0.0634504	0.0317252	+	0.999497i	$0.489900\pi$
$32$	5628.17	0.971610
$33$	4016.26	0.642002
$34$	−5564.17	−0.825473
$35$	2733.40	0.377166
$36$	3380.34	0.434715
$37$	−7448.67	−0.894488	−0.447244	−	0.894412i	$-0.647594\pi$
$37$	−7448.67	−0.894488	−0.447244	+	0.894412i	$0.647594\pi$
$38$	−5643.25	−0.633972
$39$	6764.84	0.712190
$40$	19829.1	1.95953
$41$	5116.45	0.475345	0.237672	−	0.971345i	$-0.423616\pi$
$41$	5116.45	0.475345	0.237672	+	0.971345i	$0.423616\pi$
$42$	−732.024	−0.0640328
$43$	−1849.00	−0.152499
$43$	−1849.00	−0.152499
$44$	−9537.86	−0.742710
$45$	19437.4	1.43089
$46$	−11433.1	−0.796652
$47$	−17159.9	−1.13311	−0.566553	−	0.824025i	$-0.691724\pi$
$47$	−17159.9	−1.13311	−0.566553	+	0.824025i	$0.691724\pi$
$48$	−635.613	−0.0398189
$49$	−16155.7	−0.961246
$50$	30521.2	1.72654
$51$	−11933.3	−0.642442
$52$	−16065.2	−0.823907
$53$	18090.4	0.884623	0.442312	−	0.896861i	$-0.354159\pi$
$53$	18090.4	0.884623	0.442312	+	0.896861i	$0.354159\pi$
$54$	−12175.4	−0.568197
$55$	−54844.0	−2.44468
$56$	4725.08	0.201344
$57$	−12102.9	−0.493402
$58$	−3463.66	−0.135197
$59$	17031.6	0.636980	0.318490	−	0.947926i	$-0.396824\pi$
$59$	17031.6	0.636980	0.318490	+	0.947926i	$0.396824\pi$
$60$	15646.1	0.561085
$61$	10664.9	0.366972	0.183486	−	0.983022i	$-0.441262\pi$
$61$	10664.9	0.366972	0.183486	+	0.983022i	$0.441262\pi$
$62$	1241.56	0.0410195
$63$	4631.76	0.147026
$64$	23175.8	0.707269
$65$	−92377.3	−2.71195
$66$	14687.6	0.415042
$67$	−8799.60	−0.239484	−0.119742	−	0.992805i	$-0.538207\pi$
$67$	−8799.60	−0.239484	−0.119742	+	0.992805i	$0.538207\pi$
$68$	28339.3	0.743218
$69$	−24520.1	−0.620011
$70$	9996.16	0.243831
$71$	−77057.3	−1.81413	−0.907064	−	0.420992i	$-0.861682\pi$
$71$	−77057.3	−1.81413	−0.907064	+	0.420992i	$0.861682\pi$
$72$	33600.5	0.763861
$73$	−7964.75	−0.174930	−0.0874652	−	0.996168i	$-0.527877\pi$
$73$	−7964.75	−0.174930	−0.0874652	+	0.996168i	$0.527877\pi$
$74$	−27240.1	−0.578269
$75$	65457.6	1.34371
$76$	28742.0	0.570800
$77$	−13068.8	−0.251194
$78$	24739.3	0.460417
$79$	68997.0	1.24383	0.621917	−	0.783083i	$-0.286354\pi$
$79$	68997.0	1.24383	0.621917	+	0.783083i	$0.286354\pi$
$80$	8679.62	0.151627
$81$	17988.8	0.304641
$82$	18711.1	0.307301
$83$	40813.4	0.650290	0.325145	−	0.945664i	$-0.394587\pi$
$83$	40813.4	0.650290	0.325145	+	0.945664i	$0.394587\pi$
$84$	3728.33	0.0576522
$85$	162955.	2.44636
$86$	−6761.88	−0.0985874
$87$	−7428.39	−0.105220
$88$	−94806.0	−1.30506
$89$	−83692.1	−1.11998	−0.559989	−	0.828500i	$-0.689195\pi$
$89$	−83692.1	−1.11998	−0.559989	+	0.828500i	$0.689195\pi$
$90$	71083.6	0.925046
$91$	−22012.6	−0.278656
$92$	58230.7	0.717269
$93$	2662.74	0.0319243
$94$	−62754.7	−0.732532
$95$	165271.	1.87883
$96$	44142.5	0.488853
$97$	159824.	1.72469	0.862346	−	0.506320i	$-0.168994\pi$
$97$	159824.	1.72469	0.862346	+	0.506320i	$0.168994\pi$
$98$	−59082.0	−0.621427
$99$	−92933.6	−0.952982
$100$	−155450.	−1.55450
$101$	−168968.	−1.64817	−0.824085	−	0.566466i	$-0.808310\pi$
$101$	−168968.	−1.64817	−0.824085	+	0.566466i	$0.808310\pi$
$102$	−43640.5	−0.415326
$103$	−145084.	−1.34749	−0.673747	−	0.738962i	$-0.735316\pi$
$103$	−145084.	−1.34749	−0.673747	+	0.738962i	$0.735316\pi$
$104$	−159688.	−1.44773
$105$	21438.4	0.189766
$106$	66157.5	0.571892
$107$	72693.1	0.613810	0.306905	−	0.951740i	$-0.400707\pi$
$107$	72693.1	0.613810	0.306905	+	0.951740i	$0.400707\pi$
$108$	62011.4	0.511579
$109$	−3254.39	−0.0262364	−0.0131182	−	0.999914i	$-0.504176\pi$
$109$	−3254.39	−0.0262364	−0.0131182	+	0.999914i	$0.504176\pi$
$110$	−200567.	−1.58044
$111$	−58420.9	−0.450050
$112$	2068.27	0.0155798
$113$	116394.	0.857503	0.428752	−	0.903422i	$-0.358954\pi$
$113$	116394.	0.857503	0.428752	+	0.903422i	$0.358954\pi$
$114$	−44260.8	−0.318975
$115$	334834.	2.36094
$116$	17641.0	0.121725
$117$	−156534.	−1.05717
$118$	62285.4	0.411795
$119$	38830.6	0.251366
$120$	155522.	0.985914
$121$	101167.	0.628170
$122$	39002.1	0.237240
$123$	40129.0	0.239164
$124$	−6323.50	−0.0369321
$125$	−559163.	−3.20084
$126$	16938.6	0.0950496
$127$	−6451.01	−0.0354910	−0.0177455	−	0.999843i	$-0.505649\pi$
$127$	−6451.01	−0.0354910	−0.0177455	+	0.999843i	$0.505649\pi$
$128$	−95346.3	−0.514374
$129$	−14502.0	−0.0767278
$130$	−337828.	−1.75322
$131$	−48048.9	−0.244628	−0.122314	−	0.992491i	$-0.539031\pi$
$131$	−48048.9	−0.244628	−0.122314	+	0.992491i	$0.539031\pi$
$132$	−74806.8	−0.373685
$133$	39382.5	0.193052
$134$	−32180.6	−0.154822
$135$	356574.	1.68390
$136$	281691.	1.30595
$137$	−103084.	−0.469233	−0.234616	−	0.972088i	$-0.575383\pi$
$137$	−103084.	−0.469233	−0.234616	+	0.972088i	$0.575383\pi$
$138$	−89671.2	−0.400826
$139$	219626.	0.964156	0.482078	−	0.876128i	$-0.339882\pi$
$139$	219626.	0.964156	0.482078	+	0.876128i	$0.339882\pi$
$140$	−50912.2	−0.219534
$141$	−134588.	−0.570109
$142$	−281802.	−1.17280
$143$	441671.	1.80617
$144$	14707.7	0.0591069
$145$	101438.	0.400666
$146$	−29127.5	−0.113089
$147$	−126711.	−0.483639
$148$	138739.	0.520648
$149$	−335627.	−1.23849	−0.619243	−	0.785200i	$-0.712560\pi$
$149$	−335627.	−1.23849	−0.619243	+	0.785200i	$0.712560\pi$
$150$	239382.	0.868686
$151$	−84920.3	−0.303088	−0.151544	−	0.988450i	$-0.548425\pi$
$151$	−84920.3	−0.303088	−0.151544	+	0.988450i	$0.548425\pi$
$152$	285695.	1.00298
$153$	276128.	0.953634
$154$	−47793.3	−0.162392
$155$	−36361.0	−0.121565
$156$	−126002.	−0.414539
$157$	313767.	1.01592	0.507958	−	0.861382i	$-0.330401\pi$
$157$	313767.	1.01592	0.507958	+	0.861382i	$0.330401\pi$
$158$	252325.	0.804115
$159$	141885.	0.445087
$160$	−602788.	−1.86151
$161$	79787.9	0.242590
$162$	65785.8	0.196945
$163$	239642.	0.706469	0.353235	−	0.935535i	$-0.385082\pi$
$163$	239642.	0.706469	0.353235	+	0.935535i	$0.385082\pi$
$164$	−95298.9	−0.276680
$165$	−430149.	−1.23001
$166$	149257.	0.420400
$167$	−506675.	−1.40585	−0.702923	−	0.711266i	$-0.748122\pi$
$167$	−506675.	−1.40585	−0.702923	+	0.711266i	$0.748122\pi$
$168$	37059.4	0.101304
$169$	372641.	1.00363
$170$	595933.	1.58152
$171$	280052.	0.732401
$172$	34439.5	0.0887637
$173$	−427174.	−1.08515	−0.542575	−	0.840007i	$-0.682551\pi$
$173$	−427174.	−1.08515	−0.542575	+	0.840007i	$0.682551\pi$
$174$	−27166.0	−0.0680225
$175$	−212998.	−0.525751
$176$	−41498.7	−0.100984
$177$	133581.	0.320489
$178$	−306066.	−0.724044
$179$	11674.9	0.0272345	0.0136172	−	0.999907i	$-0.495665\pi$
$179$	11674.9	0.0272345	0.0136172	+	0.999907i	$0.495665\pi$
$180$	−362041.	−0.832870
$181$	71691.3	0.162656	0.0813280	−	0.996687i	$-0.474084\pi$
$181$	71691.3	0.162656	0.0813280	+	0.996687i	$0.474084\pi$
$182$	−80501.3	−0.180146
$183$	83646.4	0.184637
$184$	578811.	1.26035
$185$	797768.	1.71375
$186$	9737.76	0.0206384
$187$	−779114.	−1.62928
$188$	319621.	0.659539
$189$	84968.3	0.173023
$190$	604403.	1.21463
$191$	212639.	0.421755	0.210877	−	0.977513i	$-0.432368\pi$
$191$	212639.	0.421755	0.210877	+	0.977513i	$0.432368\pi$
$192$	181771.	0.355853
$193$	−137469.	−0.265651	−0.132825	−	0.991139i	$-0.542405\pi$
$193$	−137469.	−0.265651	−0.132825	+	0.991139i	$0.542405\pi$
$194$	584483.	1.11498
$195$	−724528.	−1.36448
$196$	300915.	0.559505
$197$	−28517.3	−0.0523531	−0.0261766	−	0.999657i	$-0.508333\pi$
$197$	−28517.3	−0.0523531	−0.0261766	+	0.999657i	$0.508333\pi$
$198$	−339863.	−0.616085
$199$	−353575.	−0.632921	−0.316460	−	0.948606i	$-0.602494\pi$
$199$	−353575.	−0.632921	−0.316460	+	0.948606i	$0.602494\pi$
$200$	−1.54516e6	−2.73149
$201$	−69016.5	−0.120493
$202$	−617926.	−1.06551
$203$	24171.8	0.0411689
$204$	222269.	0.373941
$205$	−547982.	−0.910713
$206$	−530580.	−0.871130
$207$	567379.	0.920339
$208$	−69898.9	−0.112024
$209$	−790187.	−1.25131
$210$	78401.3	0.122680
$211$	327840.	0.506939	0.253469	−	0.967343i	$-0.418428\pi$
$211$	327840.	0.506939	0.253469	+	0.967343i	$0.418428\pi$
$212$	−336952.	−0.514906
$213$	−604371.	−0.912756
$214$	265842.	0.396816
$215$	198032.	0.292172
$216$	616392.	0.898923
$217$	−8664.49	−0.0124909
$218$	−11901.5	−0.0169613
$219$	−62468.7	−0.0880140
$220$	1.02152e6	1.42296
$221$	−1.31231e6	−1.80741
$222$	−213648.	−0.290949
$223$	247951.	0.333890	0.166945	−	0.985966i	$-0.446610\pi$
$223$	247951.	0.333890	0.166945	+	0.985966i	$0.446610\pi$
$224$	−143639.	−0.191272
$225$	−1.51465e6	−1.99460
$226$	425660.	0.554359
$227$	−868910.	−1.11921	−0.559603	−	0.828761i	$-0.689046\pi$
$227$	−868910.	−1.11921	−0.559603	+	0.828761i	$0.689046\pi$
$228$	225428.	0.287191
$229$	238721.	0.300817	0.150408	−	0.988624i	$-0.451941\pi$
$229$	238721.	0.300817	0.150408	+	0.988624i	$0.451941\pi$
$230$	1.22451e6	1.52631
$231$	−102501.	−0.126385
$232$	175351.	0.213889
$233$	507726.	0.612688	0.306344	−	0.951921i	$-0.400894\pi$
$233$	507726.	0.612688	0.306344	+	0.951921i	$0.400894\pi$
$234$	−572452.	−0.683439
$235$	1.83786e6	2.17092
$236$	−317231.	−0.370762
$237$	541153.	0.625819
$238$	142005.	0.162503
$239$	143880.	0.162932	0.0814660	−	0.996676i	$-0.474040\pi$
$239$	143880.	0.162932	0.0814660	+	0.996676i	$0.474040\pi$
$240$	68075.4	0.0762891
$241$	398237.	0.441671	0.220835	−	0.975311i	$-0.429122\pi$
$241$	398237.	0.441671	0.220835	+	0.975311i	$0.429122\pi$
$242$	369974.	0.406100
$243$	950107.	1.03218
$244$	−198645.	−0.213600
$245$	1.73030e6	1.84165
$246$	146754.	0.154615
$247$	−1.33096e6	−1.38811
$248$	−62855.4	−0.0648953
$249$	320105.	0.327185
$250$	−2.04489e6	−2.06928
$251$	1.65625e6	1.65937	0.829684	−	0.558233i	$-0.188520\pi$
$251$	1.65625e6	1.65937	0.829684	+	0.558233i	$0.188520\pi$
$252$	−86271.1	−0.0855784
$253$	−1.60090e6	−1.57240
$254$	−23591.7	−0.0229443
$255$	1.27808e6	1.23085
$256$	−1.09031e6	−1.03980
$257$	32691.4	0.0308746	0.0154373	−	0.999881i	$-0.495086\pi$
$257$	32691.4	0.0308746	0.0154373	+	0.999881i	$0.495086\pi$
$258$	−53034.4	−0.0496030
$259$	190101.	0.176090
$260$	1.72062e6	1.57852
$261$	171888.	0.156187
$262$	−175717.	−0.158147
$263$	1.02727e6	0.915791	0.457895	−	0.889006i	$-0.348603\pi$
$263$	1.02727e6	0.915791	0.457895	+	0.889006i	$0.348603\pi$
$264$	−743577.	−0.656623
$265$	−1.93752e6	−1.69485
$266$	144024.	0.124804
$267$	−656409.	−0.563503
$268$	163901.	0.139394
$269$	−1.88917e6	−1.59180	−0.795902	−	0.605426i	$-0.793003\pi$
$269$	−1.88917e6	−1.59180	−0.795902	+	0.605426i	$0.793003\pi$
$270$	1.30401e6	1.08861
$271$	605259.	0.500631	0.250316	−	0.968164i	$-0.419466\pi$
$271$	605259.	0.500631	0.250316	+	0.968164i	$0.419466\pi$
$272$	123303.	0.101053
$273$	−172648.	−0.140202
$274$	−376982.	−0.303350
$275$	4.27368e6	3.40777
$276$	456711.	0.360885
$277$	−1.16555e6	−0.912710	−0.456355	−	0.889798i	$-0.650845\pi$
$277$	−1.16555e6	−0.912710	−0.456355	+	0.889798i	$0.650845\pi$
$278$	803184.	0.623309
$279$	−61614.0	−0.0473881
$280$	−506066.	−0.385755
$281$	938873.	0.709318	0.354659	−	0.934996i	$-0.384597\pi$
$281$	938873.	0.709318	0.354659	+	0.934996i	$0.384597\pi$
$282$	−492194.	−0.368564
$283$	−2.54537e6	−1.88923	−0.944616	−	0.328179i	$-0.893565\pi$
$283$	−2.54537e6	−1.88923	−0.944616	+	0.328179i	$0.893565\pi$
$284$	1.43527e6	1.05594
$285$	1.29624e6	0.945309
$286$	1.61521e6	1.16766
$287$	−130579.	−0.0935768
$288$	−1.02143e6	−0.725649
$289$	895076.	0.630399
$290$	370965.	0.259023
$291$	1.25352e6	0.867757
$292$	148351.	0.101820
$293$	−1.61560e6	−1.09942	−0.549712	−	0.835354i	$-0.685263\pi$
$293$	−1.61560e6	−1.09942	−0.549712	+	0.835354i	$0.685263\pi$
$294$	−463389.	−0.312663
$295$	−1.82412e6	−1.22039
$296$	1.37906e6	0.914858
$297$	−1.70484e6	−1.12148
$298$	−1.22740e6	−0.800657
$299$	−2.69650e6	−1.74430
$300$	−1.21921e6	−0.782126
$301$	47189.1	0.0300210
$302$	−310558.	−0.195941
$303$	−1.32524e6	−0.829257
$304$	125055.	0.0776099
$305$	−1.14223e6	−0.703081
$306$	1.00981e6	0.616506
$307$	−1.49055e6	−0.902613	−0.451307	−	0.892369i	$-0.649042\pi$
$307$	−1.49055e6	−0.902613	−0.451307	+	0.892369i	$0.649042\pi$
$308$	243420.	0.146211
$309$	−1.13792e6	−0.677975
$310$	−132974.	−0.0785892
$311$	−754959.	−0.442611	−0.221305	−	0.975205i	$-0.571032\pi$
$311$	−754959.	−0.442611	−0.221305	+	0.975205i	$0.571032\pi$
$312$	−1.25245e6	−0.728409
$313$	1.31681e6	0.759735	0.379867	−	0.925041i	$-0.375970\pi$
$313$	1.31681e6	0.759735	0.379867	+	0.925041i	$0.375970\pi$
$314$	1.14746e6	0.656770
$315$	−496071.	−0.281687
$316$	−1.28514e6	−0.723988
$317$	−2.19577e6	−1.22727	−0.613633	−	0.789591i	$-0.710293\pi$
$317$	−2.19577e6	−1.22727	−0.613633	+	0.789591i	$0.710293\pi$
$318$	518882.	0.287740
$319$	−484994.	−0.266845
$320$	−2.48217e6	−1.35506
$321$	570142.	0.308831
$322$	291788.	0.156830
$323$	2.34783e6	1.25216
$324$	−335059.	−0.177320
$325$	7.19843e6	3.78033
$326$	876381.	0.456719
$327$	−25524.7	−0.0132005
$328$	−947268.	−0.486170
$329$	437946.	0.223065
$330$	−1.57308e6	−0.795179
$331$	727999.	0.365225	0.182613	−	0.983185i	$-0.441545\pi$
$331$	727999.	0.365225	0.182613	+	0.983185i	$0.441545\pi$
$332$	−760190.	−0.378509
$333$	1.35182e6	0.668050
$334$	−1.85293e6	−0.908853
$335$	942455.	0.458827
$336$	16221.7	0.00783879
$337$	626937.	0.300711	0.150355	−	0.988632i	$-0.451958\pi$
$337$	626937.	0.300711	0.150355	+	0.988632i	$0.451958\pi$
$338$	1.36277e6	0.648829
$339$	912897.	0.431442
$340$	−3.03519e6	−1.42393
$341$	173848.	0.0809625
$342$	1.02417e6	0.473484
$343$	841254.	0.386093
$344$	342327.	0.155971
$345$	2.62615e6	1.18788
$346$	−1.56220e6	−0.701529
$347$	−3.30393e6	−1.47302	−0.736508	−	0.676428i	$-0.763527\pi$
$347$	−3.30393e6	−1.47302	−0.736508	+	0.676428i	$0.763527\pi$
$348$	138361.	0.0612444
$349$	−2.93486e6	−1.28980	−0.644902	−	0.764265i	$-0.723102\pi$
$349$	−2.93486e6	−1.28980	−0.644902	+	0.764265i	$0.723102\pi$
$350$	−778943.	−0.339888
$351$	−2.87157e6	−1.24409
$352$	2.88203e6	1.23977
$353$	633691.	0.270670	0.135335	−	0.990800i	$-0.456789\pi$
$353$	633691.	0.270670	0.135335	+	0.990800i	$0.456789\pi$
$354$	488513.	0.207190
$355$	8.25300e6	3.47569
$356$	1.55885e6	0.651897
$357$	304554.	0.126472
$358$	42695.6	0.0176066
$359$	3.08062e6	1.26154	0.630771	−	0.775969i	$-0.282739\pi$
$359$	3.08062e6	1.26154	0.630771	+	0.775969i	$0.282739\pi$
$360$	−3.59868e6	−1.46348
$361$	−94896.2	−0.0383249
$362$	262179.	0.105154
$363$	793470.	0.316056
$364$	410007.	0.162195
$365$	853042.	0.335149
$366$	305899.	0.119364
$367$	−1.32881e6	−0.514988	−0.257494	−	0.966280i	$-0.582897\pi$
$367$	−1.32881e6	−0.514988	−0.257494	+	0.966280i	$0.582897\pi$
$368$	253358.	0.0975250
$369$	−928559.	−0.355012
$370$	2.91748e6	1.10791
$371$	−461692.	−0.174148
$372$	−49596.1	−0.0185819
$373$	−1.91319e6	−0.712011	−0.356006	−	0.934484i	$-0.615862\pi$
$373$	−1.91319e6	−0.712011	−0.356006	+	0.934484i	$0.615862\pi$
$374$	−2.84926e6	−1.05330
$375$	−4.38560e6	−1.61046
$376$	3.17702e6	1.15891
$377$	−816906.	−0.296019
$378$	310733.	0.111856
$379$	703691.	0.251642	0.125821	−	0.992053i	$-0.459843\pi$
$379$	703691.	0.251642	0.125821	+	0.992053i	$0.459843\pi$
$380$	−3.07833e6	−1.09359
$381$	−50596.2	−0.0178569
$382$	777632.	0.272656
$383$	1.73748e6	0.605234	0.302617	−	0.953112i	$-0.402140\pi$
$383$	1.73748e6	0.605234	0.302617	+	0.953112i	$0.402140\pi$
$384$	−747815.	−0.258801
$385$	1.39970e6	0.481263
$386$	−502731.	−0.171738
$387$	335566.	0.113894
$388$	−2.97687e6	−1.00388
$389$	3.93096e6	1.31712	0.658559	−	0.752529i	$-0.271166\pi$
$389$	3.93096e6	1.31712	0.658559	+	0.752529i	$0.271166\pi$
$390$	−2.64963e6	−0.882113
$391$	4.75666e6	1.57347
$392$	2.99109e6	0.983136
$393$	−376854.	−0.123081
$394$	−104289.	−0.0338453
$395$	−7.38971e6	−2.38306
$396$	1.73098e6	0.554695
$397$	3.99784e6	1.27306	0.636530	−	0.771252i	$-0.280369\pi$
$397$	3.99784e6	1.27306	0.636530	+	0.771252i	$0.280369\pi$
$398$	−1.29304e6	−0.409171
$399$	308882.	0.0971316
$400$	−676353.	−0.211360
$401$	4.39985e6	1.36640	0.683198	−	0.730233i	$-0.260588\pi$
$401$	4.39985e6	1.36640	0.683198	+	0.730233i	$0.260588\pi$
$402$	−252397.	−0.0778966
$403$	292823.	0.0898138
$404$	3.14721e6	0.959338
$405$	−1.92663e6	−0.583662
$406$	88397.6	0.0266149
$407$	−3.81426e6	−1.14136
$408$	2.20934e6	0.657072
$409$	−1.64907e6	−0.487451	−0.243726	−	0.969844i	$-0.578370\pi$
$409$	−1.64907e6	−0.487451	−0.243726	+	0.969844i	$0.578370\pi$
$410$	−2.00400e6	−0.588759
$411$	−808499.	−0.236089
$412$	2.70234e6	0.784326
$413$	−434671.	−0.125396
$414$	2.07493e6	0.594982
$415$	−4.37120e6	−1.24589
$416$	4.85439e6	1.37531
$417$	1.72256e6	0.485103
$418$	−2.88975e6	−0.808947
$419$	−5.93011e6	−1.65017	−0.825083	−	0.565012i	$-0.808871\pi$
$419$	−5.93011e6	−1.65017	−0.825083	+	0.565012i	$0.808871\pi$
$420$	−399311.	−0.110456
$421$	4.85544e6	1.33513	0.667565	−	0.744552i	$-0.267337\pi$
$421$	4.85544e6	1.33513	0.667565	+	0.744552i	$0.267337\pi$
$422$	1.19893e6	0.327726
$423$	3.11427e6	0.846264
$424$	−3.34929e6	−0.904769
$425$	−1.26981e7	−3.41010
$426$	−2.21022e6	−0.590080
$427$	−272184.	−0.0722424
$428$	−1.35398e6	−0.357275
$429$	3.46409e6	0.908752
$430$	724212.	0.188884
$431$	2.59168e6	0.672029	0.336015	−	0.941857i	$-0.390921\pi$
$431$	2.59168e6	0.672029	0.336015	+	0.941857i	$0.390921\pi$
$432$	269808.	0.0695578
$433$	−5.08691e6	−1.30387	−0.651934	−	0.758275i	$-0.726042\pi$
$433$	−5.08691e6	−1.30387	−0.651934	+	0.758275i	$0.726042\pi$
$434$	−31686.5	−0.00807513
$435$	795596.	0.201590
$436$	60616.3	0.0152712
$437$	4.82426e6	1.20845
$438$	−228451.	−0.0568994
$439$	−5.71552e6	−1.41545	−0.707725	−	0.706488i	$-0.750278\pi$
$439$	−5.71552e6	−1.41545	−0.707725	+	0.706488i	$0.750278\pi$
$440$	1.01539e7	2.50036
$441$	2.93201e6	0.717909
$442$	−4.79918e6	−1.16845
$443$	−4.81790e6	−1.16640	−0.583201	−	0.812328i	$-0.698200\pi$
$443$	−4.81790e6	−1.16640	−0.583201	+	0.812328i	$0.698200\pi$
$444$	1.08815e6	0.261957
$445$	8.96359e6	2.14576
$446$	906769.	0.215854
$447$	−2.63237e6	−0.623128
$448$	−591479.	−0.139234
$449$	−2.36680e6	−0.554046	−0.277023	−	0.960863i	$-0.589348\pi$
$449$	−2.36680e6	−0.554046	−0.277023	+	0.960863i	$0.589348\pi$
$450$	−5.53914e6	−1.28947
$451$	2.61999e6	0.606539
$452$	−2.16796e6	−0.499120
$453$	−666042.	−0.152495
$454$	−3.17765e6	−0.723546
$455$	2.35760e6	0.533877
$456$	2.24074e6	0.504638
$457$	1.78378e6	0.399531	0.199766	−	0.979844i	$-0.435982\pi$
$457$	1.78378e6	0.399531	0.199766	+	0.979844i	$0.435982\pi$
$458$	873015.	0.194472
$459$	5.06549e6	1.12225
$460$	−6.23662e6	−1.37422
$461$	−4.26575e6	−0.934852	−0.467426	−	0.884032i	$-0.654819\pi$
$461$	−4.26575e6	−0.934852	−0.467426	+	0.884032i	$0.654819\pi$
$462$	−374850.	−0.0817056
$463$	−2.33897e6	−0.507074	−0.253537	−	0.967326i	$-0.581594\pi$
$463$	−2.33897e6	−0.507074	−0.253537	+	0.967326i	$0.581594\pi$
$464$	76755.2	0.0165506
$465$	−285185.	−0.0611637
$466$	1.85678e6	0.396091
$467$	−6.84641e6	−1.45268	−0.726342	−	0.687334i	$-0.758781\pi$
$467$	−6.84641e6	−1.45268	−0.726342	+	0.687334i	$0.758781\pi$
$468$	2.91560e6	0.615337
$469$	224578.	0.0471450
$470$	6.72116e6	1.40346
$471$	2.46091e6	0.511145
$472$	−3.15326e6	−0.651486
$473$	−946822.	−0.194588
$474$	1.97902e6	0.404580
$475$	−1.28786e7	−2.61899
$476$	−723258.	−0.146311
$477$	−3.28314e6	−0.660683
$478$	526177.	0.105332
$479$	9.12451e6	1.81707	0.908533	−	0.417814i	$-0.137203\pi$
$479$	9.12451e6	1.81707	0.908533	+	0.417814i	$0.137203\pi$
$480$	−4.72775e6	−0.936594
$481$	−6.42460e6	−1.26614
$482$	1.45637e6	0.285532
$483$	625788.	0.122056
$484$	−1.88434e6	−0.365634
$485$	−1.71174e7	−3.30434
$486$	3.47459e6	0.667287
$487$	2.68151e6	0.512338	0.256169	−	0.966632i	$-0.417540\pi$
$487$	2.68151e6	0.512338	0.256169	+	0.966632i	$0.417540\pi$
$488$	−1.97452e6	−0.375329
$489$	1.87954e6	0.355451
$490$	6.32781e6	1.19059
$491$	4.83155e6	0.904446	0.452223	−	0.891905i	$-0.350631\pi$
$491$	4.83155e6	0.904446	0.452223	+	0.891905i	$0.350631\pi$
$492$	−747442.	−0.139208
$493$	1.44103e6	0.267028
$494$	−4.86739e6	−0.897385
$495$	9.95338e6	1.82582
$496$	−27513.2	−0.00502154
$497$	1.96661e6	0.357131
$498$	1.17064e6	0.211519
$499$	8.26537e6	1.48597	0.742987	−	0.669306i	$-0.233409\pi$
$499$	8.26537e6	1.48597	0.742987	+	0.669306i	$0.233409\pi$
$500$	1.04150e7	1.86309
$501$	−3.97392e6	−0.707334
$502$	6.05701e6	1.07275
$503$	−1.06078e7	−1.86941	−0.934703	−	0.355429i	$-0.884335\pi$
$503$	−1.06078e7	−1.86941	−0.934703	+	0.355429i	$0.884335\pi$
$504$	−857532.	−0.150374
$505$	1.80969e7	3.15773
$506$	−5.85457e6	−1.01653
$507$	2.92268e6	0.504965
$508$	120157.	0.0206580
$509$	−1.89756e6	−0.324639	−0.162320	−	0.986738i	$-0.551898\pi$
$509$	−1.89756e6	−0.324639	−0.162320	+	0.986738i	$0.551898\pi$
$510$	4.67399e6	0.795724
$511$	203272.	0.0344370
$512$	−936238.	−0.157838
$513$	5.13749e6	0.861901
$514$	119554.	0.0199598
$515$	1.55388e7	2.58166
$516$	270113.	0.0446603
$517$	−8.78713e6	−1.44584
$518$	695207.	0.113839
$519$	−3.35039e6	−0.545980
$520$	1.71029e7	2.77371
$521$	−1.76155e6	−0.284316	−0.142158	−	0.989844i	$-0.545404\pi$
$521$	−1.76155e6	−0.284316	−0.142158	+	0.989844i	$0.545404\pi$
$522$	628604.	0.100972
$523$	−7.12167e6	−1.13849	−0.569243	−	0.822170i	$-0.692764\pi$
$523$	−7.12167e6	−1.13849	−0.569243	+	0.822170i	$0.692764\pi$
$524$	894959.	0.142388
$525$	−1.67057e6	−0.264525
$526$	3.75679e6	0.592041
$527$	−516544.	−0.0810179
$528$	−325480.	−0.0508089
$529$	3.33749e6	0.518538
$530$	−7.08560e6	−1.09569
$531$	−3.09099e6	−0.475730
$532$	−733538.	−0.112368
$533$	4.41302e6	0.672849
$534$	−2.40052e6	−0.364294
$535$	−7.78558e6	−1.17600
$536$	1.62917e6	0.244937
$537$	91567.6	0.0137027
$538$	−6.90877e6	−1.02907
$539$	−8.27287e6	−1.22655
$540$	−6.64155e6	−0.980133
$541$	6.26443e6	0.920214	0.460107	−	0.887864i	$-0.347811\pi$
$541$	6.26443e6	0.920214	0.460107	+	0.887864i	$0.347811\pi$
$542$	2.21346e6	0.323649
$543$	562285.	0.0818383
$544$	−8.56320e6	−1.24062
$545$	348552.	0.0502663
$546$	−631383.	−0.0906382
$547$	−3.19734e6	−0.456899	−0.228449	−	0.973556i	$-0.573366\pi$
$547$	−3.19734e6	−0.456899	−0.228449	+	0.973556i	$0.573366\pi$
$548$	1.92003e6	0.273123
$549$	−1.93552e6	−0.274074
$550$	1.56291e7	2.20306
$551$	1.46151e6	0.205080
$552$	4.53969e6	0.634131
$553$	−1.76090e6	−0.244862
$554$	−4.26248e6	−0.590049
$555$	6.25700e6	0.862251
$556$	−4.09076e6	−0.561199
$557$	1.13299e7	1.54735	0.773677	−	0.633581i	$-0.218416\pi$
$557$	1.13299e7	1.54735	0.773677	+	0.633581i	$0.218416\pi$
$558$	−225326.	−0.0306355
$559$	−1.59479e6	−0.215861
$560$	−221516.	−0.0298494
$561$	−6.11070e6	−0.819754
$562$	3.43350e6	0.458561
$563$	−4.20790e6	−0.559492	−0.279746	−	0.960074i	$-0.590250\pi$
$563$	−4.20790e6	−0.559492	−0.279746	+	0.960074i	$0.590250\pi$
$564$	2.50683e6	0.331839
$565$	−1.24661e7	−1.64289
$566$	−9.30855e6	−1.22135
$567$	−459099.	−0.0599720
$568$	1.42665e7	1.85544
$569$	−3.28836e6	−0.425794	−0.212897	−	0.977075i	$-0.568290\pi$
$569$	−3.28836e6	−0.425794	−0.212897	+	0.977075i	$0.568290\pi$
$570$	4.74042e6	0.611124
$571$	−2.54135e6	−0.326192	−0.163096	−	0.986610i	$-0.552148\pi$
$571$	−2.54135e6	−0.326192	−0.163096	+	0.986610i	$0.552148\pi$
$572$	−8.22656e6	−1.05130
$573$	1.66776e6	0.212201
$574$	−477534.	−0.0604956
$575$	−2.60917e7	−3.29104
$576$	−4.20606e6	−0.528225
$577$	−1.69533e6	−0.211990	−0.105995	−	0.994367i	$-0.533803\pi$
$577$	−1.69533e6	−0.211990	−0.105995	+	0.994367i	$0.533803\pi$
$578$	3.27334e6	0.407541
$579$	−1.07819e6	−0.133659
$580$	−1.88939e6	−0.233213
$581$	−1.04161e6	−0.128017
$582$	4.58418e6	0.560988
$583$	9.26360e6	1.12878
$584$	1.47461e6	0.178914
$585$	1.67651e7	2.02543
$586$	−5.90834e6	−0.710757
$587$	6.20781e6	0.743607	0.371803	−	0.928311i	$-0.378740\pi$
$587$	6.20781e6	0.743607	0.371803	+	0.928311i	$0.378740\pi$
$588$	2.36012e6	0.281508
$589$	−523886.	−0.0622226
$590$	−6.67090e6	−0.788959
$591$	−223665.	−0.0263408
$592$	603645.	0.0707909
$593$	3.01403e6	0.351974	0.175987	−	0.984393i	$-0.443688\pi$
$593$	3.01403e6	0.351974	0.175987	+	0.984393i	$0.443688\pi$
$594$	−6.23469e6	−0.725018
$595$	−4.15884e6	−0.481592
$596$	6.25138e6	0.720876
$597$	−2.77314e6	−0.318446
$598$	−9.86122e6	−1.12766
$599$	1.21463e7	1.38317	0.691586	−	0.722294i	$-0.256912\pi$
$599$	1.21463e7	1.38317	0.691586	+	0.722294i	$0.256912\pi$
$600$	−1.21189e7	−1.37432
$601$	1.68363e6	0.190134	0.0950671	−	0.995471i	$-0.469693\pi$
$601$	1.68363e6	0.190134	0.0950671	+	0.995471i	$0.469693\pi$
$602$	172573.	0.0194080
$603$	1.59700e6	0.178859
$604$	1.58173e6	0.176416
$605$	−1.08352e7	−1.20351
$606$	−4.84648e6	−0.536099
$607$	−5.11718e6	−0.563714	−0.281857	−	0.959456i	$-0.590950\pi$
$607$	−5.11718e6	−0.563714	−0.281857	+	0.959456i	$0.590950\pi$
$608$	−8.68491e6	−0.952810
$609$	189583.	0.0207136
$610$	−4.17720e6	−0.454528
$611$	−1.48007e7	−1.60391
$612$	−5.14316e6	−0.555075
$613$	4.10152e6	0.440853	0.220426	−	0.975404i	$-0.429255\pi$
$613$	4.10152e6	0.440853	0.220426	+	0.975404i	$0.429255\pi$
$614$	−5.45103e6	−0.583522
$615$	−4.29790e6	−0.458214
$616$	2.41958e6	0.256915
$617$	1.52311e7	1.61071	0.805355	−	0.592792i	$-0.201975\pi$
$617$	1.52311e7	1.61071	0.805355	+	0.592792i	$0.201975\pi$
$618$	−4.16141e6	−0.438298
$619$	5.27961e6	0.553829	0.276914	−	0.960895i	$-0.410688\pi$
$619$	5.27961e6	0.553829	0.276914	+	0.960895i	$0.410688\pi$
$620$	677260.	0.0707581
$621$	1.04084e7	1.08307
$622$	−2.76092e6	−0.286140
$623$	2.13594e6	0.220480
$624$	−548227.	−0.0563636
$625$	3.38068e7	3.46181
$626$	4.81564e6	0.491154
$627$	−6.19754e6	−0.629580
$628$	−5.84421e6	−0.591326
$629$	1.13331e7	1.14215
$630$	−1.81416e6	−0.182105
$631$	−1.84888e7	−1.84857	−0.924283	−	0.381709i	$-0.875336\pi$
$631$	−1.84888e7	−1.84857	−0.924283	+	0.381709i	$0.875336\pi$
$632$	−1.27742e7	−1.27216
$633$	2.57129e6	0.255060
$634$	−8.03004e6	−0.793404
$635$	690917.	0.0679973
$636$	−2.64276e6	−0.259068
$637$	−1.39345e7	−1.36064
$638$	−1.77365e6	−0.172511
$639$	1.39848e7	1.35489
$640$	1.02118e7	0.985489
$641$	−3.87212e6	−0.372223	−0.186112	−	0.982529i	$-0.559589\pi$
$641$	−3.87212e6	−0.372223	−0.186112	+	0.982529i	$0.559589\pi$
$642$	2.08504e6	0.199653
$643$	3.24879e6	0.309880	0.154940	−	0.987924i	$-0.450482\pi$
$643$	3.24879e6	0.309880	0.154940	+	0.987924i	$0.450482\pi$
$644$	−1.48613e6	−0.141202
$645$	1.55319e6	0.147003
$646$	8.58615e6	0.809500
$647$	1.85942e7	1.74629	0.873147	−	0.487456i	$-0.162075\pi$
$647$	1.85942e7	1.74629	0.873147	+	0.487456i	$0.162075\pi$
$648$	−3.33047e6	−0.311579
$649$	8.72142e6	0.812785
$650$	2.63250e7	2.44391
$651$	−67956.8	−0.00628464
$652$	−4.46356e6	−0.411209
$653$	9.77909e6	0.897461	0.448730	−	0.893667i	$-0.351876\pi$
$653$	9.77909e6	0.897461	0.448730	+	0.893667i	$0.351876\pi$
$654$	−93345.0	−0.00853388
$655$	5.14614e6	0.468682
$656$	−414640.	−0.0376194
$657$	1.44548e6	0.130647
$658$	1.60159e6	0.144207
$659$	1.92292e7	1.72484	0.862418	−	0.506196i	$-0.168949\pi$
$659$	1.92292e7	1.72484	0.862418	+	0.506196i	$0.168949\pi$
$660$	8.01196e6	0.715944
$661$	−1.39614e7	−1.24287	−0.621434	−	0.783467i	$-0.713449\pi$
$661$	−1.39614e7	−1.24287	−0.621434	+	0.783467i	$0.713449\pi$
$662$	2.66233e6	0.236111
$663$	−1.02926e7	−0.909374
$664$	−7.55626e6	−0.665099
$665$	−4.21794e6	−0.369868
$666$	4.94368e6	0.431882
$667$	2.96099e6	0.257705
$668$	9.43732e6	0.818290
$669$	1.94471e6	0.167993
$670$	3.44660e6	0.296623
$671$	5.46121e6	0.468255
$672$	−1.12658e6	−0.0962362
$673$	1.13333e7	0.964537	0.482269	−	0.876023i	$-0.339813\pi$
$673$	1.13333e7	0.964537	0.482269	+	0.876023i	$0.339813\pi$
$674$	2.29274e6	0.194404
$675$	−2.77858e7	−2.34727
$676$	−6.94082e6	−0.584176
$677$	−9.84009e6	−0.825140	−0.412570	−	0.910926i	$-0.635369\pi$
$677$	−9.84009e6	−0.825140	−0.412570	+	0.910926i	$0.635369\pi$
$678$	3.33851e6	0.278919
$679$	−4.07892e6	−0.339524
$680$	−3.01697e7	−2.50207
$681$	−6.81498e6	−0.563115
$682$	635771.	0.0523407
$683$	4282.68	0.000351288 0	0.000175644	−	1.00000i	$-0.499944\pi$
$683$	4282.68	0.000351288 0	0.000175644		1.00000i	$0.499944\pi$
$684$	−5.21625e6	−0.426303
$685$	1.10405e7	0.899003
$686$	3.07651e6	0.249602
$687$	1.87232e6	0.151352
$688$	149844.	0.0120689
$689$	1.56033e7	1.25218
$690$	9.60397e6	0.767941
$691$	5.24701e6	0.418039	0.209019	−	0.977911i	$-0.432973\pi$
$691$	5.24701e6	0.418039	0.209019	+	0.977911i	$0.432973\pi$
$692$	7.95655e6	0.631625
$693$	2.37180e6	0.187605
$694$	−1.20826e7	−0.952277
$695$	−2.35224e7	−1.84723
$696$	1.37531e6	0.107616
$697$	−7.78462e6	−0.606954
$698$	−1.07329e7	−0.833834
$699$	3.98217e6	0.308267
$700$	3.96730e6	0.306020
$701$	−3.73379e6	−0.286982	−0.143491	−	0.989652i	$-0.545833\pi$
$701$	−3.73379e6	−0.286982	−0.143491	+	0.989652i	$0.545833\pi$
$702$	−1.05015e7	−0.804281
$703$	1.14942e7	0.877180
$704$	1.18677e7	0.902473
$705$	1.44146e7	1.09227
$706$	2.31744e6	0.174983
$707$	4.31231e6	0.324461
$708$	−2.48808e6	−0.186544
$709$	−1.21242e7	−0.905810	−0.452905	−	0.891559i	$-0.649612\pi$
$709$	−1.21242e7	−0.905810	−0.452905	+	0.891559i	$0.649612\pi$
$710$	3.01816e7	2.24697
$711$	−1.25219e7	−0.928960
$712$	1.54949e7	1.14548
$713$	−1.06138e6	−0.0781892
$714$	1.11377e6	0.0817615
$715$	−4.73039e7	−3.46044
$716$	−217456.	−0.0158522
$717$	1.12847e6	0.0819772
$718$	1.12660e7	0.815563
$719$	1.59176e7	1.14830	0.574149	−	0.818751i	$-0.305333\pi$
$719$	1.59176e7	1.14830	0.574149	+	0.818751i	$0.305333\pi$
$720$	−1.57522e6	−0.113243
$721$	3.70275e6	0.265269
$722$	−347040.	−0.0247763
$723$	3.12342e6	0.222221
$724$	−1.33532e6	−0.0946759
$725$	−7.90452e6	−0.558509
$726$	2.90176e6	0.204324
$727$	−633198.	−0.0444328	−0.0222164	−	0.999753i	$-0.507072\pi$
$727$	−633198.	−0.0444328	−0.0222164	+	0.999753i	$0.507072\pi$
$728$	4.07546e6	0.285002
$729$	3.08055e6	0.214689
$730$	3.11961e6	0.216668
$731$	2.81324e6	0.194721
$732$	−1.55800e6	−0.107470
$733$	−2.64288e7	−1.81684	−0.908421	−	0.418057i	$-0.862711\pi$
$733$	−2.64288e7	−1.81684	−0.908421	+	0.418057i	$0.862711\pi$
$734$	−4.85952e6	−0.332930
$735$	1.35710e7	0.926603
$736$	−1.75954e7	−1.19730
$737$	−4.50603e6	−0.305581
$738$	−3.39579e6	−0.229509
$739$	2.15407e6	0.145094	0.0725470	−	0.997365i	$-0.476887\pi$
$739$	2.15407e6	0.145094	0.0725470	+	0.997365i	$0.476887\pi$
$740$	−1.48592e7	−0.997508
$741$	−1.04389e7	−0.698409
$742$	−1.68843e6	−0.112583
$743$	1.76951e7	1.17593	0.587964	−	0.808887i	$-0.299930\pi$
$743$	1.76951e7	1.17593	0.587964	+	0.808887i	$0.299930\pi$
$744$	−492984.	−0.0326513
$745$	3.59463e7	2.37281
$746$	−6.99664e6	−0.460302
$747$	−7.40702e6	−0.485671
$748$	1.45118e7	0.948345
$749$	−1.85523e6	−0.120835
$750$	−1.60383e7	−1.04113
$751$	2.58345e7	1.67148	0.835739	−	0.549127i	$-0.185040\pi$
$751$	2.58345e7	1.67148	0.835739	+	0.549127i	$0.185040\pi$
$752$	1.39065e6	0.0896755
$753$	1.29902e7	0.834891
$754$	−2.98747e6	−0.191370
$755$	9.09514e6	0.580687
$756$	−1.58262e6	−0.100710
$757$	−2.47558e7	−1.57013	−0.785067	−	0.619411i	$-0.787371\pi$
$757$	−2.47558e7	−1.57013	−0.785067	+	0.619411i	$0.787371\pi$
$758$	2.57343e6	0.162682
$759$	−1.25561e7	−0.791133
$760$	−3.05985e7	−1.92161
$761$	−1.12818e7	−0.706183	−0.353092	−	0.935589i	$-0.614870\pi$
$761$	−1.12818e7	−0.706183	−0.353092	+	0.935589i	$0.614870\pi$
$762$	−185033.	−0.0115441
$763$	83056.7	0.00516492
$764$	−3.96062e6	−0.245488
$765$	−2.95739e7	−1.82707
$766$	6.35406e6	0.391272
$767$	1.46900e7	0.901643
$768$	−8.55146e6	−0.523163
$769$	−1.45315e7	−0.886124	−0.443062	−	0.896491i	$-0.646108\pi$
$769$	−1.45315e7	−0.886124	−0.443062	+	0.896491i	$0.646108\pi$
$770$	5.11876e6	0.311127
$771$	256403.	0.0155341
$772$	2.56050e6	0.154625
$773$	−5.49667e6	−0.330865	−0.165433	−	0.986221i	$-0.552902\pi$
$773$	−5.49667e6	−0.330865	−0.165433	+	0.986221i	$0.552902\pi$
$774$	1.22718e6	0.0736303
$775$	2.83341e6	0.169455
$776$	−2.95900e7	−1.76397
$777$	1.49099e6	0.0885974
$778$	1.43757e7	0.851492
$779$	−7.89526e6	−0.466147
$780$	1.34950e7	0.794215
$781$	−3.94590e7	−2.31482
$782$	1.73953e7	1.01722
$783$	3.15324e6	0.183803
$784$	1.30926e6	0.0760742
$785$	−3.36050e7	−1.94639
$786$	−1.37817e6	−0.0795697
$787$	1.62860e7	0.937297	0.468649	−	0.883385i	$-0.344741\pi$
$787$	1.62860e7	0.937297	0.468649	+	0.883385i	$0.344741\pi$
$788$	531163.	0.0304728
$789$	8.05704e6	0.460769
$790$	−2.70245e7	−1.54060
$791$	−2.97055e6	−0.168809
$792$	1.72059e7	0.974685
$793$	9.19866e6	0.519447
$794$	1.46203e7	0.823009
$795$	−1.51962e7	−0.852742
$796$	6.58569e6	0.368399
$797$	1.65610e7	0.923506	0.461753	−	0.887009i	$-0.347221\pi$
$797$	1.65610e7	0.923506	0.461753	+	0.887009i	$0.347221\pi$
$798$	1.12960e6	0.0627937
$799$	2.61087e7	1.44683
$800$	4.69718e7	2.59485
$801$	1.51889e7	0.836458
$802$	1.60905e7	0.883350
$803$	−4.07853e6	−0.223211
$804$	1.28550e6	0.0701346
$805$	−8.54545e6	−0.464778
$806$	1.07087e6	0.0580629
$807$	−1.48170e7	−0.800896
$808$	3.12831e7	1.68571
$809$	−1.93881e7	−1.04151	−0.520756	−	0.853706i	$-0.674350\pi$
$809$	−1.93881e7	−1.04151	−0.520756	+	0.853706i	$0.674350\pi$
$810$	−7.04580e6	−0.377327
$811$	1.99327e7	1.06418	0.532089	−	0.846688i	$-0.321407\pi$
$811$	1.99327e7	1.06418	0.532089	+	0.846688i	$0.321407\pi$
$812$	−450224.	−0.0239629
$813$	4.74713e6	0.251886
$814$	−1.39489e7	−0.737870
$815$	−2.56661e7	−1.35352
$816$	967079.	0.0508436
$817$	2.85322e6	0.149548
$818$	−6.03074e6	−0.315128
$819$	3.99497e6	0.208115
$820$	1.02067e7	0.530092
$821$	−2.97106e7	−1.53834	−0.769172	−	0.639041i	$-0.779331\pi$
$821$	−2.97106e7	−1.53834	−0.769172	+	0.639041i	$0.779331\pi$
$822$	−2.95672e6	−0.152627
$823$	−3.70742e6	−0.190797	−0.0953987	−	0.995439i	$-0.530413\pi$
$823$	−3.70742e6	−0.190797	−0.0953987	+	0.995439i	$0.530413\pi$
$824$	2.68611e7	1.37818
$825$	3.35191e7	1.71458
$826$	−1.58961e6	−0.0810664
$827$	−5.42093e6	−0.275620	−0.137810	−	0.990459i	$-0.544006\pi$
$827$	−5.42093e6	−0.275620	−0.137810	+	0.990459i	$0.544006\pi$
$828$	−1.05680e7	−0.535694
$829$	−3.24596e7	−1.64043	−0.820214	−	0.572056i	$-0.806146\pi$
$829$	−3.24596e7	−1.64043	−0.820214	+	0.572056i	$0.806146\pi$
$830$	−1.59857e7	−0.805445
$831$	−9.14159e6	−0.459218
$832$	1.99895e7	1.00114
$833$	2.45807e7	1.22739
$834$	6.29948e6	0.313610
$835$	5.42659e7	2.69346
$836$	1.47180e7	0.728339
$837$	−1.13029e6	−0.0557670
$838$	−2.16867e7	−1.06680
$839$	−6.99699e6	−0.343168	−0.171584	−	0.985170i	$-0.554888\pi$
$839$	−6.99699e6	−0.343168	−0.171584	+	0.985170i	$0.554888\pi$
$840$	−3.96914e6	−0.194088
$841$	−1.96141e7	−0.956266
$842$	1.77566e7	0.863136
$843$	7.36371e6	0.356885
$844$	−6.10634e6	−0.295070
$845$	−3.99107e7	−1.92286
$846$	1.13891e7	0.547094
$847$	−2.58194e6	−0.123662
$848$	−1.46606e6	−0.0700102
$849$	−1.99637e7	−0.950543
$850$	−4.64377e7	−2.20457
$851$	2.32869e7	1.10227
$852$	1.12570e7	0.531281
$853$	−5.68399e6	−0.267474	−0.133737	−	0.991017i	$-0.542698\pi$
$853$	−5.68399e6	−0.267474	−0.133737	+	0.991017i	$0.542698\pi$
$854$	−995389.	−0.0467033
$855$	−2.99942e7	−1.40321
$856$	−1.34585e7	−0.627788
$857$	−8.71203e6	−0.405198	−0.202599	−	0.979262i	$-0.564939\pi$
$857$	−8.71203e6	−0.405198	−0.202599	+	0.979262i	$0.564939\pi$
$858$	1.26683e7	0.587491
$859$	1.41568e7	0.654609	0.327304	−	0.944919i	$-0.393860\pi$
$859$	1.41568e7	0.654609	0.327304	+	0.944919i	$0.393860\pi$
$860$	−3.68854e6	−0.170062
$861$	−1.02415e6	−0.0470820
$862$	9.47790e6	0.434454
$863$	9.82195e6	0.448922	0.224461	−	0.974483i	$-0.427938\pi$
$863$	9.82195e6	0.448922	0.224461	+	0.974483i	$0.427938\pi$
$864$	−1.87378e7	−0.853955
$865$	4.57513e7	2.07904
$866$	−1.86031e7	−0.842927
$867$	7.02021e6	0.317177
$868$	161385.	0.00727048
$869$	3.53315e7	1.58713
$870$	2.90953e6	0.130324
$871$	−7.58980e6	−0.338988
$872$	602524.	0.0268339
$873$	−2.90056e7	−1.28809
$874$	1.76426e7	0.781237
$875$	1.42706e7	0.630120
$876$	1.16354e6	0.0512297
$877$	2.13034e7	0.935298	0.467649	−	0.883914i	$-0.345101\pi$
$877$	2.13034e7	0.935298	0.467649	+	0.883914i	$0.345101\pi$
$878$	−2.09019e7	−0.915061
$879$	−1.26714e7	−0.553162
$880$	4.44460e6	0.193475
$881$	3.10088e7	1.34600	0.673000	−	0.739642i	$-0.265005\pi$
$881$	3.10088e7	1.34600	0.673000	+	0.739642i	$0.265005\pi$
$882$	1.07225e7	0.464114
$883$	−2.21207e7	−0.954766	−0.477383	−	0.878695i	$-0.658415\pi$
$883$	−2.21207e7	−0.954766	−0.477383	+	0.878695i	$0.658415\pi$
$884$	2.44431e7	1.05202
$885$	−1.43068e7	−0.614024
$886$	−1.76193e7	−0.754057
$887$	4.29991e7	1.83506	0.917530	−	0.397666i	$-0.130180\pi$
$887$	4.29991e7	1.83506	0.917530	+	0.397666i	$0.130180\pi$
$888$	1.08162e7	0.460299
$889$	164639.	0.00698680
$890$	3.27803e7	1.38720
$891$	9.21156e6	0.388722
$892$	−4.61833e6	−0.194345
$893$	2.64797e7	1.11118
$894$	−9.62669e6	−0.402841
$895$	−1.25040e6	−0.0521786
$896$	2.43337e6	0.101260
$897$	−2.11490e7	−0.877624
$898$	−8.65551e6	−0.358181
$899$	−321546.	−0.0132692
$900$	2.82118e7	1.16098
$901$	−2.75244e7	−1.12955
$902$	9.58144e6	0.392116
$903$	370111.	0.0151047
$904$	−2.15494e7	−0.877031
$905$	−7.67828e6	−0.311632
$906$	−2.43575e6	−0.0985852
$907$	3.34186e7	1.34887	0.674435	−	0.738334i	$-0.264387\pi$
$907$	3.34186e7	1.34887	0.674435	+	0.738334i	$0.264387\pi$
$908$	1.61843e7	0.651448
$909$	3.06653e7	1.23094
$910$	8.62185e6	0.345141
$911$	−3.77821e7	−1.50831	−0.754155	−	0.656697i	$-0.771953\pi$
$911$	−3.77821e7	−1.50831	−0.754155	+	0.656697i	$0.771953\pi$
$912$	980824.	0.0390485
$913$	2.08994e7	0.829769
$914$	6.52337e6	0.258289
$915$	−8.95869e6	−0.353746
$916$	−4.44642e6	−0.175094
$917$	1.22628e6	0.0481576
$918$	1.85248e7	0.725514
$919$	3.71228e7	1.44995	0.724973	−	0.688777i	$-0.241852\pi$
$919$	3.71228e7	1.44995	0.724973	+	0.688777i	$0.241852\pi$
$920$	−6.19918e7	−2.41471
$921$	−1.16906e7	−0.454139
$922$	−1.56000e7	−0.604364
$923$	−6.64632e7	−2.56789
$924$	1.90917e6	0.0735641
$925$	−6.21655e7	−2.38888
$926$	−8.55371e6	−0.327814
$927$	2.63306e7	1.00638
$928$	−5.33055e6	−0.203190
$929$	4.73143e6	0.179868	0.0899339	−	0.995948i	$-0.471334\pi$
$929$	4.73143e6	0.179868	0.0899339	+	0.995948i	$0.471334\pi$
$930$	−1.04293e6	−0.0395412
$931$	2.49300e7	0.942646
$932$	−9.45690e6	−0.356623
$933$	−5.92124e6	−0.222694
$934$	−2.50377e7	−0.939132
$935$	8.34447e7	3.12154
$936$	2.89810e7	1.08124
$937$	−1.74328e7	−0.648660	−0.324330	−	0.945944i	$-0.605139\pi$
$937$	−1.74328e7	−0.648660	−0.324330	+	0.945944i	$0.605139\pi$
$938$	821293.	0.0304783
$939$	1.03279e7	0.382251
$940$	−3.42320e7	−1.26361
$941$	3.82735e7	1.40904	0.704521	−	0.709683i	$-0.251162\pi$
$941$	3.82735e7	1.40904	0.704521	+	0.709683i	$0.251162\pi$
$942$	8.99968e6	0.330446
$943$	−1.59956e7	−0.585762
$944$	−1.38025e6	−0.0504114
$945$	−9.10028e6	−0.331494
$946$	−3.46258e6	−0.125797
$947$	−1.65041e7	−0.598021	−0.299011	−	0.954250i	$-0.596657\pi$
$947$	−1.65041e7	−0.598021	−0.299011	+	0.954250i	$0.596657\pi$
$948$	−1.00795e7	−0.364266
$949$	−6.86973e6	−0.247613
$950$	−4.70977e7	−1.69313
$951$	−1.72217e7	−0.617484
$952$	−7.18916e6	−0.257090
$953$	−2.15575e7	−0.768894	−0.384447	−	0.923147i	$-0.625608\pi$
$953$	−2.15575e7	−0.768894	−0.384447	+	0.923147i	$0.625608\pi$
$954$	−1.20066e7	−0.427119
$955$	−2.27741e7	−0.808040
$956$	−2.67991e6	−0.0948365
$957$	−3.80388e6	−0.134260
$958$	3.33688e7	1.17470
$959$	2.63084e6	0.0923736
$960$	−1.94680e7	−0.681779
$961$	−2.85139e7	−0.995974
$962$	−2.34951e7	−0.818539
$963$	−1.31927e7	−0.458425
$964$	−7.41755e6	−0.257080
$965$	1.47232e7	0.508960
$966$	2.28854e6	0.0789069
$967$	−3.38528e7	−1.16420	−0.582101	−	0.813116i	$-0.697769\pi$
$967$	−3.38528e7	−1.16420	−0.582101	+	0.813116i	$0.697769\pi$
$968$	−1.87303e7	−0.642476
$969$	1.84144e7	0.630011
$970$	−6.25993e7	−2.13619
$971$	1.12966e7	0.384502	0.192251	−	0.981346i	$-0.438421\pi$
$971$	1.12966e7	0.384502	0.192251	+	0.981346i	$0.438421\pi$
$972$	−1.76967e7	−0.600795
$973$	−5.60517e6	−0.189805
$974$	9.80641e6	0.331217
$975$	5.64583e7	1.90202
$976$	−864291.	−0.0290426
$977$	−2.28369e7	−0.765423	−0.382711	−	0.923868i	$-0.625010\pi$
$977$	−2.28369e7	−0.765423	−0.382711	+	0.923868i	$0.625010\pi$
$978$	6.87358e6	0.229793
$979$	−4.28564e7	−1.42909
$980$	−3.22286e7	−1.07196
$981$	590624.	0.0195947
$982$	1.76692e7	0.584707
$983$	1.60143e7	0.528598	0.264299	−	0.964441i	$-0.414860\pi$
$983$	1.60143e7	0.528598	0.264299	+	0.964441i	$0.414860\pi$
$984$	−7.42955e6	−0.244610
$985$	3.05426e6	0.100303
$986$	5.26993e6	0.172629
$987$	3.43487e6	0.112232
$988$	2.47905e7	0.807965
$989$	5.78055e6	0.187922
$990$	3.64000e7	1.18036
$991$	1.70581e7	0.551755	0.275878	−	0.961193i	$-0.411032\pi$
$991$	1.70581e7	0.551755	0.275878	+	0.961193i	$0.411032\pi$
$992$	1.91076e6	0.0616490
$993$	5.70980e6	0.183759
$994$	7.19200e6	0.230879
$995$	3.78687e7	1.21261
$996$	−5.96227e6	−0.190442
$997$	−2.65006e7	−0.844341	−0.422171	−	0.906516i	$-0.638732\pi$
$997$	−2.65006e7	−0.844341	−0.422171	+	0.906516i	$0.638732\pi$
$998$	3.02269e7	0.960653
$999$	2.47988e7	0.786172

Twists

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

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

\(f(q)\)	\(=\)	\(q+3.65705 q^{2} +7.84314 q^{3} -18.6260 q^{4} -107.102 q^{5} +28.6827 q^{6} -25.5214 q^{7} -185.142 q^{8} -181.485 q^{9} +O(q^{10})\)	\(q+3.65705 q^{2} +7.84314 q^{3} -18.6260 q^{4} -107.102 q^{5} +28.6827 q^{6} -25.5214 q^{7} -185.142 q^{8} -181.485 q^{9} -391.677 q^{10} +512.073 q^{11} -146.086 q^{12} +862.516 q^{13} -93.3331 q^{14} -840.016 q^{15} -81.0406 q^{16} -1521.49 q^{17} -663.700 q^{18} -1543.11 q^{19} +1994.88 q^{20} -200.168 q^{21} +1872.67 q^{22} -3126.31 q^{23} -1452.09 q^{24} +8345.85 q^{25} +3154.26 q^{26} -3329.30 q^{27} +475.362 q^{28} -947.120 q^{29} -3071.98 q^{30} +339.499 q^{31} +5628.17 q^{32} +4016.26 q^{33} -5564.17 q^{34} +2733.40 q^{35} +3380.34 q^{36} -7448.67 q^{37} -5643.25 q^{38} +6764.84 q^{39} +19829.1 q^{40} +5116.45 q^{41} -732.024 q^{42} -1849.00 q^{43} -9537.86 q^{44} +19437.4 q^{45} -11433.1 q^{46} -17159.9 q^{47} -635.613 q^{48} -16155.7 q^{49} +30521.2 q^{50} -11933.3 q^{51} -16065.2 q^{52} +18090.4 q^{53} -12175.4 q^{54} -54844.0 q^{55} +4725.08 q^{56} -12102.9 q^{57} -3463.66 q^{58} +17031.6 q^{59} +15646.1 q^{60} +10664.9 q^{61} +1241.56 q^{62} +4631.76 q^{63} +23175.8 q^{64} -92377.3 q^{65} +14687.6 q^{66} -8799.60 q^{67} +28339.3 q^{68} -24520.1 q^{69} +9996.16 q^{70} -77057.3 q^{71} +33600.5 q^{72} -7964.75 q^{73} -27240.1 q^{74} +65457.6 q^{75} +28742.0 q^{76} -13068.8 q^{77} +24739.3 q^{78} +68997.0 q^{79} +8679.62 q^{80} +17988.8 q^{81} +18711.1 q^{82} +40813.4 q^{83} +3728.33 q^{84} +162955. q^{85} -6761.88 q^{86} -7428.39 q^{87} -94806.0 q^{88} -83692.1 q^{89} +71083.6 q^{90} -22012.6 q^{91} +58230.7 q^{92} +2662.74 q^{93} -62754.7 q^{94} +165271. q^{95} +44142.5 q^{96} +159824. q^{97} -59082.0 q^{98} -92933.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{2} - 26 q^{3} + 122 q^{4} - 212 q^{5} - 69 q^{6} - 136 q^{7} - 666 q^{8} + 546 q^{9}+O(q^{10}) \) 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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