LMFDB - Embedded newform 690.6.a.g.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,6,Mod(1,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("690.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	690.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:	$110.664835671$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 1159x^{2} - 10254x - 22896 $ x^4 - 1159x^2 - 10254x - 22896
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-4.15675$ of defining polynomial
Character	$\chi$	$=$	690.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +85.4075 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +85.4075 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -556.905 q^{11} +144.000 q^{12} +644.303 q^{13} -341.630 q^{14} +225.000 q^{15} +256.000 q^{16} -1506.76 q^{17} -324.000 q^{18} +981.374 q^{19} +400.000 q^{20} +768.668 q^{21} +2227.62 q^{22} -529.000 q^{23} -576.000 q^{24} +625.000 q^{25} -2577.21 q^{26} +729.000 q^{27} +1366.52 q^{28} -6354.71 q^{29} -900.000 q^{30} +2719.31 q^{31} -1024.00 q^{32} -5012.14 q^{33} +6027.06 q^{34} +2135.19 q^{35} +1296.00 q^{36} -6118.43 q^{37} -3925.49 q^{38} +5798.73 q^{39} -1600.00 q^{40} -3170.63 q^{41} -3074.67 q^{42} +3334.83 q^{43} -8910.48 q^{44} +2025.00 q^{45} +2116.00 q^{46} -15691.7 q^{47} +2304.00 q^{48} -9512.56 q^{49} -2500.00 q^{50} -13560.9 q^{51} +10308.8 q^{52} -20567.4 q^{53} -2916.00 q^{54} -13922.6 q^{55} -5466.08 q^{56} +8832.36 q^{57} +25418.8 q^{58} -1559.76 q^{59} +3600.00 q^{60} -2163.08 q^{61} -10877.3 q^{62} +6918.01 q^{63} +4096.00 q^{64} +16107.6 q^{65} +20048.6 q^{66} -5051.46 q^{67} -24108.2 q^{68} -4761.00 q^{69} -8540.75 q^{70} +42344.2 q^{71} -5184.00 q^{72} -20845.0 q^{73} +24473.7 q^{74} +5625.00 q^{75} +15702.0 q^{76} -47563.9 q^{77} -23194.9 q^{78} -9707.44 q^{79} +6400.00 q^{80} +6561.00 q^{81} +12682.5 q^{82} +7745.37 q^{83} +12298.7 q^{84} -37669.1 q^{85} -13339.3 q^{86} -57192.3 q^{87} +35641.9 q^{88} -49454.1 q^{89} -8100.00 q^{90} +55028.3 q^{91} -8464.00 q^{92} +24473.8 q^{93} +62766.7 q^{94} +24534.3 q^{95} -9216.00 q^{96} -128461. q^{97} +38050.2 q^{98} -45109.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} + 25 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) $ 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 + 100 * q^5 - 144 * q^6 + 25 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} + 25 q^{7} - 256 q^{8} + 324 q^{9} - 400 q^{10} - 730 q^{11} + 576 q^{12} - 828 q^{13} - 100 q^{14} + 900 q^{15} + 1024 q^{16} - 179 q^{17} - 1296 q^{18} + 1568 q^{19} + 1600 q^{20} + 225 q^{21} + 2920 q^{22} - 2116 q^{23} - 2304 q^{24} + 2500 q^{25} + 3312 q^{26} + 2916 q^{27} + 400 q^{28} - 1917 q^{29} - 3600 q^{30} - 6331 q^{31} - 4096 q^{32} - 6570 q^{33} + 716 q^{34} + 625 q^{35} + 5184 q^{36} + 10127 q^{37} - 6272 q^{38} - 7452 q^{39} - 6400 q^{40} - 14527 q^{41} - 900 q^{42} - 18052 q^{43} - 11680 q^{44} + 8100 q^{45} + 8464 q^{46} - 13208 q^{47} + 9216 q^{48} - 52681 q^{49} - 10000 q^{50} - 1611 q^{51} - 13248 q^{52} - 39327 q^{53} - 11664 q^{54} - 18250 q^{55} - 1600 q^{56} + 14112 q^{57} + 7668 q^{58} - 43301 q^{59} + 14400 q^{60} - 25154 q^{61} + 25324 q^{62} + 2025 q^{63} + 16384 q^{64} - 20700 q^{65} + 26280 q^{66} - 15827 q^{67} - 2864 q^{68} - 19044 q^{69} - 2500 q^{70} - 20999 q^{71} - 20736 q^{72} - 35844 q^{73} - 40508 q^{74} + 22500 q^{75} + 25088 q^{76} - 16142 q^{77} + 29808 q^{78} - 100414 q^{79} + 25600 q^{80} + 26244 q^{81} + 58108 q^{82} - 140015 q^{83} + 3600 q^{84} - 4475 q^{85} + 72208 q^{86} - 17253 q^{87} + 46720 q^{88} - 26030 q^{89} - 32400 q^{90} + 34190 q^{91} - 33856 q^{92} - 56979 q^{93} + 52832 q^{94} + 39200 q^{95} - 36864 q^{96} - 16946 q^{97} + 210724 q^{98} - 59130 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 + 100 * q^5 - 144 * q^6 + 25 * q^7 - 256 * q^8 + 324 * q^9 - 400 * q^10 - 730 * q^11 + 576 * q^12 - 828 * q^13 - 100 * q^14 + 900 * q^15 + 1024 * q^16 - 179 * q^17 - 1296 * q^18 + 1568 * q^19 + 1600 * q^20 + 225 * q^21 + 2920 * q^22 - 2116 * q^23 - 2304 * q^24 + 2500 * q^25 + 3312 * q^26 + 2916 * q^27 + 400 * q^28 - 1917 * q^29 - 3600 * q^30 - 6331 * q^31 - 4096 * q^32 - 6570 * q^33 + 716 * q^34 + 625 * q^35 + 5184 * q^36 + 10127 * q^37 - 6272 * q^38 - 7452 * q^39 - 6400 * q^40 - 14527 * q^41 - 900 * q^42 - 18052 * q^43 - 11680 * q^44 + 8100 * q^45 + 8464 * q^46 - 13208 * q^47 + 9216 * q^48 - 52681 * q^49 - 10000 * q^50 - 1611 * q^51 - 13248 * q^52 - 39327 * q^53 - 11664 * q^54 - 18250 * q^55 - 1600 * q^56 + 14112 * q^57 + 7668 * q^58 - 43301 * q^59 + 14400 * q^60 - 25154 * q^61 + 25324 * q^62 + 2025 * q^63 + 16384 * q^64 - 20700 * q^65 + 26280 * q^66 - 15827 * q^67 - 2864 * q^68 - 19044 * q^69 - 2500 * q^70 - 20999 * q^71 - 20736 * q^72 - 35844 * q^73 - 40508 * q^74 + 22500 * q^75 + 25088 * q^76 - 16142 * q^77 + 29808 * q^78 - 100414 * q^79 + 25600 * q^80 + 26244 * q^81 + 58108 * q^82 - 140015 * q^83 + 3600 * q^84 - 4475 * q^85 + 72208 * q^86 - 17253 * q^87 + 46720 * q^88 - 26030 * q^89 - 32400 * q^90 + 34190 * q^91 - 33856 * q^92 - 56979 * q^93 + 52832 * q^94 + 39200 * q^95 - 36864 * q^96 - 16946 * q^97 + 210724 * q^98 - 59130 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	16.0000	0.500000
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−36.0000	−0.408248
$7$	85.4075	0.658796	0.329398	−	0.944191i	$-0.393154\pi$
$7$	85.4075	0.658796	0.329398	+	0.944191i	$0.393154\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−100.000	−0.316228
$11$	−556.905	−1.38771	−0.693856	−	0.720114i	$-0.744090\pi$
$11$	−556.905	−1.38771	−0.693856	+	0.720114i	$0.744090\pi$
$12$	144.000	0.288675
$13$	644.303	1.05738	0.528691	−	0.848815i	$-0.322683\pi$
$13$	644.303	1.05738	0.528691	+	0.848815i	$0.322683\pi$
$14$	−341.630	−0.465839
$15$	225.000	0.258199
$16$	256.000	0.250000
$17$	−1506.76	−1.26451	−0.632256	−	0.774760i	$-0.717871\pi$
$17$	−1506.76	−1.26451	−0.632256	+	0.774760i	$0.717871\pi$
$18$	−324.000	−0.235702
$19$	981.374	0.623664	0.311832	−	0.950137i	$-0.399057\pi$
$19$	981.374	0.623664	0.311832	+	0.950137i	$0.399057\pi$
$20$	400.000	0.223607
$21$	768.668	0.380356
$22$	2227.62	0.981261
$23$	−529.000	−0.208514
$23$	−529.000	−0.208514
$24$	−576.000	−0.204124
$25$	625.000	0.200000
$26$	−2577.21	−0.747682
$27$	729.000	0.192450
$28$	1366.52	0.329398
$29$	−6354.71	−1.40314	−0.701569	−	0.712601i	$-0.747517\pi$
$29$	−6354.71	−1.40314	−0.701569	+	0.712601i	$0.747517\pi$
$30$	−900.000	−0.182574
$31$	2719.31	0.508224	0.254112	−	0.967175i	$-0.418217\pi$
$31$	2719.31	0.508224	0.254112	+	0.967175i	$0.418217\pi$
$32$	−1024.00	−0.176777
$33$	−5012.14	−0.801196
$34$	6027.06	0.894145
$35$	2135.19	0.294623
$36$	1296.00	0.166667
$37$	−6118.43	−0.734744	−0.367372	−	0.930074i	$-0.619742\pi$
$37$	−6118.43	−0.734744	−0.367372	+	0.930074i	$0.619742\pi$
$38$	−3925.49	−0.440997
$39$	5798.73	0.610480
$40$	−1600.00	−0.158114
$41$	−3170.63	−0.294568	−0.147284	−	0.989094i	$-0.547053\pi$
$41$	−3170.63	−0.294568	−0.147284	+	0.989094i	$0.547053\pi$
$42$	−3074.67	−0.268952
$43$	3334.83	0.275044	0.137522	−	0.990499i	$-0.456086\pi$
$43$	3334.83	0.275044	0.137522	+	0.990499i	$0.456086\pi$
$44$	−8910.48	−0.693856
$45$	2025.00	0.149071
$46$	2116.00	0.147442
$47$	−15691.7	−1.03616	−0.518078	−	0.855334i	$-0.673352\pi$
$47$	−15691.7	−1.03616	−0.518078	+	0.855334i	$0.673352\pi$
$48$	2304.00	0.144338
$49$	−9512.56	−0.565988
$50$	−2500.00	−0.141421
$51$	−13560.9	−0.730066
$52$	10308.8	0.528691
$53$	−20567.4	−1.00575	−0.502874	−	0.864360i	$-0.667724\pi$
$53$	−20567.4	−1.00575	−0.502874	+	0.864360i	$0.667724\pi$
$54$	−2916.00	−0.136083
$55$	−13922.6	−0.620604
$56$	−5466.08	−0.232920
$57$	8832.36	0.360072
$58$	25418.8	0.992168
$59$	−1559.76	−0.0583349	−0.0291675	−	0.999575i	$-0.509286\pi$
$59$	−1559.76	−0.0583349	−0.0291675	+	0.999575i	$0.509286\pi$
$60$	3600.00	0.129099
$61$	−2163.08	−0.0744300	−0.0372150	−	0.999307i	$-0.511849\pi$
$61$	−2163.08	−0.0744300	−0.0372150	+	0.999307i	$0.511849\pi$
$62$	−10877.3	−0.359369
$63$	6918.01	0.219599
$64$	4096.00	0.125000
$65$	16107.6	0.472875
$66$	20048.6	0.566531
$67$	−5051.46	−0.137477	−0.0687385	−	0.997635i	$-0.521897\pi$
$67$	−5051.46	−0.137477	−0.0687385	+	0.997635i	$0.521897\pi$
$68$	−24108.2	−0.632256
$69$	−4761.00	−0.120386
$70$	−8540.75	−0.208330
$71$	42344.2	0.996892	0.498446	−	0.866921i	$-0.333904\pi$
$71$	42344.2	0.996892	0.498446	+	0.866921i	$0.333904\pi$
$72$	−5184.00	−0.117851
$73$	−20845.0	−0.457819	−0.228910	−	0.973448i	$-0.573516\pi$
$73$	−20845.0	−0.457819	−0.228910	+	0.973448i	$0.573516\pi$
$74$	24473.7	0.519542
$75$	5625.00	0.115470
$76$	15702.0	0.311832
$77$	−47563.9	−0.914219
$78$	−23194.9	−0.431674
$79$	−9707.44	−0.175000	−0.0874998	−	0.996165i	$-0.527888\pi$
$79$	−9707.44	−0.175000	−0.0874998	+	0.996165i	$0.527888\pi$
$80$	6400.00	0.111803
$81$	6561.00	0.111111
$82$	12682.5	0.208291
$83$	7745.37	0.123409	0.0617045	−	0.998094i	$-0.480346\pi$
$83$	7745.37	0.123409	0.0617045	+	0.998094i	$0.480346\pi$
$84$	12298.7	0.190178
$85$	−37669.1	−0.565507
$86$	−13339.3	−0.194485
$87$	−57192.3	−0.810102
$88$	35641.9	0.490630
$89$	−49454.1	−0.661801	−0.330900	−	0.943666i	$-0.607352\pi$
$89$	−49454.1	−0.661801	−0.330900	+	0.943666i	$0.607352\pi$
$90$	−8100.00	−0.105409
$91$	55028.3	0.696599
$92$	−8464.00	−0.104257
$93$	24473.8	0.293423
$94$	62766.7	0.732673
$95$	24534.3	0.278911
$96$	−9216.00	−0.102062
$97$	−128461.	−1.38625	−0.693126	−	0.720817i	$-0.743767\pi$
$97$	−128461.	−1.38625	−0.693126	+	0.720817i	$0.743767\pi$
$98$	38050.2	0.400214
$99$	−45109.3	−0.462571
$100$	10000.0	0.100000
$101$	82111.1	0.800937	0.400469	−	0.916310i	$-0.368847\pi$
$101$	82111.1	0.800937	0.400469	+	0.916310i	$0.368847\pi$
$102$	54243.5	0.516235
$103$	−20423.8	−0.189689	−0.0948446	−	0.995492i	$-0.530235\pi$
$103$	−20423.8	−0.189689	−0.0948446	+	0.995492i	$0.530235\pi$
$104$	−41235.4	−0.373841
$105$	19216.7	0.170100
$106$	82269.5	0.711171
$107$	−27536.9	−0.232517	−0.116259	−	0.993219i	$-0.537090\pi$
$107$	−27536.9	−0.232517	−0.116259	+	0.993219i	$0.537090\pi$
$108$	11664.0	0.0962250
$109$	81221.2	0.654792	0.327396	−	0.944887i	$-0.393829\pi$
$109$	81221.2	0.654792	0.327396	+	0.944887i	$0.393829\pi$
$110$	55690.5	0.438833
$111$	−55065.9	−0.424204
$112$	21864.3	0.164699
$113$	124535.	0.917475	0.458738	−	0.888572i	$-0.348302\pi$
$113$	124535.	0.917475	0.458738	+	0.888572i	$0.348302\pi$
$114$	−35329.4	−0.254610
$115$	−13225.0	−0.0932505
$116$	−101675.	−0.701569
$117$	52188.5	0.352461
$118$	6239.05	0.0412490
$119$	−128689.	−0.833056
$120$	−14400.0	−0.0912871
$121$	149092.	0.925745
$122$	8652.32	0.0526300
$123$	−28535.6	−0.170069
$124$	43509.0	0.254112
$125$	15625.0	0.0894427
$126$	−27672.0	−0.155280
$127$	−37736.6	−0.207612	−0.103806	−	0.994598i	$-0.533102\pi$
$127$	−37736.6	−0.207612	−0.103806	+	0.994598i	$0.533102\pi$
$128$	−16384.0	−0.0883883
$129$	30013.4	0.158797
$130$	−64430.3	−0.334373
$131$	73787.0	0.375666	0.187833	−	0.982201i	$-0.439854\pi$
$131$	73787.0	0.375666	0.187833	+	0.982201i	$0.439854\pi$
$132$	−80194.3	−0.400598
$133$	83816.7	0.410867
$134$	20205.8	0.0972109
$135$	18225.0	0.0860663
$136$	96432.9	0.447073
$137$	315705.	1.43708	0.718539	−	0.695487i	$-0.244811\pi$
$137$	315705.	1.43708	0.718539	+	0.695487i	$0.244811\pi$
$138$	19044.0	0.0851257
$139$	−421123.	−1.84873	−0.924363	−	0.381515i	$-0.875403\pi$
$139$	−421123.	−1.84873	−0.924363	+	0.381515i	$0.875403\pi$
$140$	34163.0	0.147311
$141$	−141225.	−0.598225
$142$	−169377.	−0.704909
$143$	−358815.	−1.46734
$144$	20736.0	0.0833333
$145$	−158868.	−0.627502
$146$	83379.9	0.323727
$147$	−85613.0	−0.326773
$148$	−97894.9	−0.367372
$149$	−22212.7	−0.0819665	−0.0409832	−	0.999160i	$-0.513049\pi$
$149$	−22212.7	−0.0819665	−0.0409832	+	0.999160i	$0.513049\pi$
$150$	−22500.0	−0.0816497
$151$	181105.	0.646382	0.323191	−	0.946334i	$-0.395244\pi$
$151$	181105.	0.646382	0.323191	+	0.946334i	$0.395244\pi$
$152$	−62807.9	−0.220498
$153$	−122048.	−0.421504
$154$	190255.	0.646451
$155$	67982.9	0.227285
$156$	92779.6	0.305240
$157$	2669.87	0.00864453	0.00432226	−	0.999991i	$-0.498624\pi$
$157$	2669.87	0.00864453	0.00432226	+	0.999991i	$0.498624\pi$
$158$	38829.8	0.123743
$159$	−185106.	−0.580669
$160$	−25600.0	−0.0790569
$161$	−45180.6	−0.137368
$162$	−26244.0	−0.0785674
$163$	−236868.	−0.698293	−0.349146	−	0.937068i	$-0.613528\pi$
$163$	−236868.	−0.698293	−0.349146	+	0.937068i	$0.613528\pi$
$164$	−50730.0	−0.147284
$165$	−125304.	−0.358306
$166$	−30981.5	−0.0872634
$167$	−101091.	−0.280493	−0.140246	−	0.990117i	$-0.544789\pi$
$167$	−101091.	−0.280493	−0.140246	+	0.990117i	$0.544789\pi$
$168$	−49194.7	−0.134476
$169$	43833.3	0.118056
$170$	150676.	0.399874
$171$	79491.3	0.207888
$172$	53357.2	0.137522
$173$	−172989.	−0.439443	−0.219722	−	0.975563i	$-0.570515\pi$
$173$	−172989.	−0.439443	−0.219722	+	0.975563i	$0.570515\pi$
$174$	228769.	0.572829
$175$	53379.7	0.131759
$176$	−142568.	−0.346928
$177$	−14037.9	−0.0336797
$178$	197816.	0.467964
$179$	−65764.9	−0.153413	−0.0767064	−	0.997054i	$-0.524440\pi$
$179$	−65764.9	−0.153413	−0.0767064	+	0.997054i	$0.524440\pi$
$180$	32400.0	0.0745356
$181$	729835.	1.65588	0.827939	−	0.560819i	$-0.189513\pi$
$181$	729835.	1.65588	0.827939	+	0.560819i	$0.189513\pi$
$182$	−220113.	−0.492570
$183$	−19467.7	−0.0429722
$184$	33856.0	0.0737210
$185$	−152961.	−0.328587
$186$	−97895.3	−0.207482
$187$	839124.	1.75478
$188$	−251067.	−0.518078
$189$	62262.1	0.126785
$190$	−98137.4	−0.197220
$191$	256844.	0.509431	0.254716	−	0.967016i	$-0.418018\pi$
$191$	256844.	0.509431	0.254716	+	0.967016i	$0.418018\pi$
$192$	36864.0	0.0721688
$193$	−182415.	−0.352506	−0.176253	−	0.984345i	$-0.556398\pi$
$193$	−182415.	−0.352506	−0.176253	+	0.984345i	$0.556398\pi$
$194$	513844.	0.980228
$195$	144968.	0.273015
$196$	−152201.	−0.282994
$197$	−444855.	−0.816682	−0.408341	−	0.912829i	$-0.633893\pi$
$197$	−444855.	−0.816682	−0.408341	+	0.912829i	$0.633893\pi$
$198$	180437.	0.327087
$199$	−524097.	−0.938164	−0.469082	−	0.883155i	$-0.655415\pi$
$199$	−524097.	−0.938164	−0.469082	+	0.883155i	$0.655415\pi$
$200$	−40000.0	−0.0707107
$201$	−45463.1	−0.0793724
$202$	−328444.	−0.566348
$203$	−542740.	−0.924382
$204$	−216974.	−0.365033
$205$	−79265.7	−0.131735
$206$	81695.0	0.134130
$207$	−42849.0	−0.0695048
$208$	164942.	0.264345
$209$	−546532.	−0.865465
$210$	−76866.8	−0.120279
$211$	−292362.	−0.452079	−0.226039	−	0.974118i	$-0.572578\pi$
$211$	−292362.	−0.452079	−0.226039	+	0.974118i	$0.572578\pi$
$212$	−329078.	−0.502874
$213$	381098.	0.575556
$214$	110148.	0.164415
$215$	83370.7	0.123003
$216$	−46656.0	−0.0680414
$217$	232250.	0.334816
$218$	−324885.	−0.463008
$219$	−187605.	−0.264322
$220$	−222762.	−0.310302
$221$	−970813.	−1.33707
$222$	220264.	0.299958
$223$	40424.6	0.0544357	0.0272178	−	0.999630i	$-0.491335\pi$
$223$	40424.6	0.0544357	0.0272178	+	0.999630i	$0.491335\pi$
$224$	−87457.3	−0.116460
$225$	50625.0	0.0666667
$226$	−498139.	−0.648753
$227$	−536794.	−0.691421	−0.345711	−	0.938341i	$-0.612362\pi$
$227$	−536794.	−0.691421	−0.345711	+	0.938341i	$0.612362\pi$
$228$	141318.	0.180036
$229$	−1.06661e6	−1.34406	−0.672030	−	0.740524i	$-0.734577\pi$
$229$	−1.06661e6	−1.34406	−0.672030	+	0.740524i	$0.734577\pi$
$230$	52900.0	0.0659380
$231$	−428075.	−0.527825
$232$	406701.	0.496084
$233$	8350.72	0.0100771	0.00503854	−	0.999987i	$-0.498396\pi$
$233$	8350.72	0.0100771	0.00503854	+	0.999987i	$0.498396\pi$
$234$	−208754.	−0.249227
$235$	−392292.	−0.463383
$236$	−24956.2	−0.0291675
$237$	−87367.0	−0.101036
$238$	514756.	0.589059
$239$	−1.53306e6	−1.73606	−0.868031	−	0.496509i	$-0.834615\pi$
$239$	−1.53306e6	−1.73606	−0.868031	+	0.496509i	$0.834615\pi$
$240$	57600.0	0.0645497
$241$	−1.57363e6	−1.74526	−0.872629	−	0.488384i	$-0.837586\pi$
$241$	−1.57363e6	−1.74526	−0.872629	+	0.488384i	$0.837586\pi$
$242$	−596368.	−0.654600
$243$	59049.0	0.0641500
$244$	−34609.3	−0.0372150
$245$	−237814.	−0.253117
$246$	114143.	0.120257
$247$	632302.	0.659450
$248$	−174036.	−0.179684
$249$	69708.3	0.0712502
$250$	−62500.0	−0.0632456
$251$	−1.70561e6	−1.70882	−0.854410	−	0.519599i	$-0.826081\pi$
$251$	−1.70561e6	−1.70882	−0.854410	+	0.519599i	$0.826081\pi$
$252$	110688.	0.109799
$253$	294603.	0.289358
$254$	150946.	0.146804
$255$	−339022.	−0.326496
$256$	65536.0	0.0625000
$257$	−699946.	−0.661046	−0.330523	−	0.943798i	$-0.607225\pi$
$257$	−699946.	−0.661046	−0.330523	+	0.943798i	$0.607225\pi$
$258$	−120054.	−0.112286
$259$	−522560.	−0.484046
$260$	257721.	0.236438
$261$	−514731.	−0.467713
$262$	−295148.	−0.265636
$263$	537641.	0.479295	0.239647	−	0.970860i	$-0.422968\pi$
$263$	537641.	0.479295	0.239647	+	0.970860i	$0.422968\pi$
$264$	320777.	0.283266
$265$	−514184.	−0.449784
$266$	−335267.	−0.290527
$267$	−445087.	−0.382091
$268$	−80823.4	−0.0687385
$269$	−102571.	−0.0864256	−0.0432128	−	0.999066i	$-0.513759\pi$
$269$	−102571.	−0.0864256	−0.0432128	+	0.999066i	$0.513759\pi$
$270$	−72900.0	−0.0608581
$271$	−506055.	−0.418576	−0.209288	−	0.977854i	$-0.567115\pi$
$271$	−506055.	−0.418576	−0.209288	+	0.977854i	$0.567115\pi$
$272$	−385732.	−0.316128
$273$	495255.	0.402182
$274$	−1.26282e6	−1.01617
$275$	−348066.	−0.277542
$276$	−76176.0	−0.0601929
$277$	−913661.	−0.715460	−0.357730	−	0.933825i	$-0.616449\pi$
$277$	−913661.	−0.715460	−0.357730	+	0.933825i	$0.616449\pi$
$278$	1.68449e6	1.30725
$279$	220264.	0.169408
$280$	−136652.	−0.104165
$281$	−1.17769e6	−0.889741	−0.444870	−	0.895595i	$-0.646750\pi$
$281$	−1.17769e6	−0.889741	−0.444870	+	0.895595i	$0.646750\pi$
$282$	564901.	0.423009
$283$	484592.	0.359675	0.179837	−	0.983696i	$-0.442443\pi$
$283$	484592.	0.359675	0.179837	+	0.983696i	$0.442443\pi$
$284$	677507.	0.498446
$285$	220809.	0.161029
$286$	1.43526e6	1.03757
$287$	−270795.	−0.194060
$288$	−82944.0	−0.0589256
$289$	850481.	0.598991
$290$	635471.	0.443711
$291$	−1.15615e6	−0.800353
$292$	−333519.	−0.228910
$293$	136026.	0.0925662	0.0462831	−	0.998928i	$-0.485262\pi$
$293$	136026.	0.0925662	0.0462831	+	0.998928i	$0.485262\pi$
$294$	342452.	0.231064
$295$	−38994.1	−0.0260882
$296$	391580.	0.259771
$297$	−405984.	−0.267065
$298$	88850.9	0.0579590
$299$	−340836.	−0.220479
$300$	90000.0	0.0577350
$301$	284819.	0.181198
$302$	−724422.	−0.457061
$303$	739000.	0.462421
$304$	251232.	0.155916
$305$	−54077.0	−0.0332861
$306$	488192.	0.298048
$307$	246009.	0.148972	0.0744861	−	0.997222i	$-0.476268\pi$
$307$	246009.	0.148972	0.0744861	+	0.997222i	$0.476268\pi$
$308$	−761022.	−0.457110
$309$	−183814.	−0.109517
$310$	−271931.	−0.160715
$311$	−968224.	−0.567643	−0.283821	−	0.958877i	$-0.591602\pi$
$311$	−968224.	−0.567643	−0.283821	+	0.958877i	$0.591602\pi$
$312$	−371118.	−0.215837
$313$	1.64323e6	0.948065	0.474032	−	0.880507i	$-0.342798\pi$
$313$	1.64323e6	0.948065	0.474032	+	0.880507i	$0.342798\pi$
$314$	−10679.5	−0.00611260
$315$	172950.	0.0982075
$316$	−155319.	−0.0874998
$317$	−828436.	−0.463032	−0.231516	−	0.972831i	$-0.574368\pi$
$317$	−828436.	−0.463032	−0.231516	+	0.972831i	$0.574368\pi$
$318$	740425.	0.410595
$319$	3.53897e6	1.94715
$320$	102400.	0.0559017
$321$	−247832.	−0.134244
$322$	180722.	0.0971342
$323$	−1.47870e6	−0.788630
$324$	104976.	0.0555556
$325$	402689.	0.211476
$326$	947472.	0.493767
$327$	730991.	0.378044
$328$	202920.	0.104145
$329$	−1.34019e6	−0.682615
$330$	501214.	0.253360
$331$	−2.06811e6	−1.03754	−0.518768	−	0.854915i	$-0.673609\pi$
$331$	−2.06811e6	−1.03754	−0.518768	+	0.854915i	$0.673609\pi$
$332$	123926.	0.0617045
$333$	−495593.	−0.244915
$334$	404364.	0.198338
$335$	−126286.	−0.0614816
$336$	196779.	0.0950890
$337$	−1.12485e6	−0.539533	−0.269766	−	0.962926i	$-0.586947\pi$
$337$	−1.12485e6	−0.539533	−0.269766	+	0.962926i	$0.586947\pi$
$338$	−175333.	−0.0834780
$339$	1.12081e6	0.529705
$340$	−602706.	−0.282753
$341$	−1.51440e6	−0.705269
$342$	−317965.	−0.146999
$343$	−2.24789e6	−1.03167
$344$	−213429.	−0.0972427
$345$	−119025.	−0.0538382
$346$	691955.	0.310733
$347$	−2.27887e6	−1.01600	−0.508002	−	0.861356i	$-0.669616\pi$
$347$	−2.27887e6	−1.01600	−0.508002	+	0.861356i	$0.669616\pi$
$348$	−915078.	−0.405051
$349$	1.99934e6	0.878666	0.439333	−	0.898324i	$-0.355215\pi$
$349$	1.99934e6	0.878666	0.439333	+	0.898324i	$0.355215\pi$
$350$	−213519.	−0.0931678
$351$	469697.	0.203493
$352$	570271.	0.245315
$353$	2.71596e6	1.16008	0.580039	−	0.814589i	$-0.303037\pi$
$353$	2.71596e6	1.16008	0.580039	+	0.814589i	$0.303037\pi$
$354$	56151.5	0.0238151
$355$	1.05860e6	0.445823
$356$	−791266.	−0.330900
$357$	−1.15820e6	−0.480965
$358$	263060.	0.108479
$359$	3.37503e6	1.38211	0.691054	−	0.722804i	$-0.257147\pi$
$359$	3.37503e6	1.38211	0.691054	+	0.722804i	$0.257147\pi$
$360$	−129600.	−0.0527046
$361$	−1.51301e6	−0.611044
$362$	−2.91934e6	−1.17088
$363$	1.34183e6	0.534479
$364$	880453.	0.348299
$365$	−521124.	−0.204743
$366$	77870.9	0.0303859
$367$	1.26957e6	0.492031	0.246015	−	0.969266i	$-0.420879\pi$
$367$	1.26957e6	0.492031	0.246015	+	0.969266i	$0.420879\pi$
$368$	−135424.	−0.0521286
$369$	−256821.	−0.0981893
$370$	611843.	0.232346
$371$	−1.75661e6	−0.662582
$372$	391581.	0.146712
$373$	1.85893e6	0.691815	0.345908	−	0.938269i	$-0.387571\pi$
$373$	1.85893e6	0.691815	0.345908	+	0.938269i	$0.387571\pi$
$374$	−3.35650e6	−1.24082
$375$	140625.	0.0516398
$376$	1.00427e6	0.366336
$377$	−4.09436e6	−1.48365
$378$	−249048.	−0.0896508
$379$	1.97555e6	0.706465	0.353233	−	0.935536i	$-0.385082\pi$
$379$	1.97555e6	0.706465	0.353233	+	0.935536i	$0.385082\pi$
$380$	392549.	0.139455
$381$	−339629.	−0.119865
$382$	−1.02737e6	−0.360222
$383$	340472.	0.118600	0.0592999	−	0.998240i	$-0.481113\pi$
$383$	340472.	0.118600	0.0592999	+	0.998240i	$0.481113\pi$
$384$	−147456.	−0.0510310
$385$	−1.18910e6	−0.408851
$386$	729659.	0.249259
$387$	270121.	0.0916813
$388$	−2.05538e6	−0.693126
$389$	2.38826e6	0.800215	0.400108	−	0.916468i	$-0.368973\pi$
$389$	2.38826e6	0.800215	0.400108	+	0.916468i	$0.368973\pi$
$390$	−579873.	−0.193051
$391$	797078.	0.263669
$392$	608804.	0.200107
$393$	664083.	0.216891
$394$	1.77942e6	0.577482
$395$	−242686.	−0.0782622
$396$	−721749.	−0.231285
$397$	−2.41837e6	−0.770098	−0.385049	−	0.922896i	$-0.625815\pi$
$397$	−2.41837e6	−0.770098	−0.385049	+	0.922896i	$0.625815\pi$
$398$	2.09639e6	0.663382
$399$	754350.	0.237214
$400$	160000.	0.0500000
$401$	2.27103e6	0.705280	0.352640	−	0.935759i	$-0.385284\pi$
$401$	2.27103e6	0.705280	0.352640	+	0.935759i	$0.385284\pi$
$402$	181853.	0.0561247
$403$	1.75206e6	0.537387
$404$	1.31378e6	0.400469
$405$	164025.	0.0496904
$406$	2.17096e6	0.653637
$407$	3.40738e6	1.01961
$408$	867896.	0.258117
$409$	−1.55937e6	−0.460935	−0.230468	−	0.973080i	$-0.574026\pi$
$409$	−1.55937e6	−0.460935	−0.230468	+	0.973080i	$0.574026\pi$
$410$	317063.	0.0931505
$411$	2.84135e6	0.829698
$412$	−326780.	−0.0948446
$413$	−133216.	−0.0384308
$414$	171396.	0.0491473
$415$	193634.	0.0551902
$416$	−659766.	−0.186920
$417$	−3.79011e6	−1.06736
$418$	2.18613e6	0.611976
$419$	1.81633e6	0.505429	0.252715	−	0.967541i	$-0.418677\pi$
$419$	1.81633e6	0.505429	0.252715	+	0.967541i	$0.418677\pi$
$420$	307467.	0.0850502
$421$	5.37832e6	1.47891	0.739455	−	0.673206i	$-0.235083\pi$
$421$	5.37832e6	1.47891	0.739455	+	0.673206i	$0.235083\pi$
$422$	1.16945e6	0.319668
$423$	−1.27103e6	−0.345385
$424$	1.31631e6	0.355585
$425$	−941728.	−0.252902
$426$	−1.52439e6	−0.406979
$427$	−184743.	−0.0490342
$428$	−440590.	−0.116259
$429$	−3.22934e6	−0.847170
$430$	−333483.	−0.0869765
$431$	861121.	0.223291	0.111645	−	0.993748i	$-0.464388\pi$
$431$	861121.	0.223291	0.111645	+	0.993748i	$0.464388\pi$
$432$	186624.	0.0481125
$433$	3.57774e6	0.917041	0.458521	−	0.888684i	$-0.348379\pi$
$433$	3.57774e6	0.917041	0.458521	+	0.888684i	$0.348379\pi$
$434$	−929000.	−0.236751
$435$	−1.42981e6	−0.362289
$436$	1.29954e6	0.327396
$437$	−519147.	−0.130043
$438$	750419.	0.186904
$439$	2.83691e6	0.702562	0.351281	−	0.936270i	$-0.385746\pi$
$439$	2.83691e6	0.702562	0.351281	+	0.936270i	$0.385746\pi$
$440$	891048.	0.219417
$441$	−770517.	−0.188663
$442$	3.88325e6	0.945452
$443$	401367.	0.0971700	0.0485850	−	0.998819i	$-0.484529\pi$
$443$	401367.	0.0971700	0.0485850	+	0.998819i	$0.484529\pi$
$444$	−881054.	−0.212102
$445$	−1.23635e6	−0.295966
$446$	−161698.	−0.0384918
$447$	−199915.	−0.0473234
$448$	349829.	0.0823495
$449$	−7.62227e6	−1.78430	−0.892151	−	0.451736i	$-0.850805\pi$
$449$	−7.62227e6	−1.78430	−0.892151	+	0.451736i	$0.850805\pi$
$450$	−202500.	−0.0471405
$451$	1.76574e6	0.408775
$452$	1.99256e6	0.458738
$453$	1.62995e6	0.373189
$454$	2.14717e6	0.488909
$455$	1.37571e6	0.311528
$456$	−565271.	−0.127305
$457$	3.56828e6	0.799224	0.399612	−	0.916684i	$-0.369145\pi$
$457$	3.56828e6	0.799224	0.399612	+	0.916684i	$0.369145\pi$
$458$	4.26646e6	0.950394
$459$	−1.09843e6	−0.243355
$460$	−211600.	−0.0466252
$461$	1.76974e6	0.387843	0.193922	−	0.981017i	$-0.437879\pi$
$461$	1.76974e6	0.387843	0.193922	+	0.981017i	$0.437879\pi$
$462$	1.71230e6	0.373228
$463$	−1.88325e6	−0.408277	−0.204138	−	0.978942i	$-0.565439\pi$
$463$	−1.88325e6	−0.408277	−0.204138	+	0.978942i	$0.565439\pi$
$464$	−1.62680e6	−0.350785
$465$	611846.	0.131223
$466$	−33402.9	−0.00712557
$467$	4.90746e6	1.04127	0.520637	−	0.853778i	$-0.325695\pi$
$467$	4.90746e6	1.04127	0.520637	+	0.853778i	$0.325695\pi$
$468$	835017.	0.176230
$469$	−431433.	−0.0905693
$470$	1.56917e6	0.327661
$471$	24028.8	0.00499092
$472$	99824.9	0.0206245
$473$	−1.85718e6	−0.381682
$474$	349468.	0.0714433
$475$	613358.	0.124733
$476$	−2.05902e6	−0.416528
$477$	−1.66596e6	−0.335249
$478$	6.13225e6	1.22758
$479$	1.25181e6	0.249286	0.124643	−	0.992202i	$-0.460221\pi$
$479$	1.25181e6	0.249286	0.124643	+	0.992202i	$0.460221\pi$
$480$	−230400.	−0.0456435
$481$	−3.94212e6	−0.776904
$482$	6.29451e6	1.23408
$483$	−406625.	−0.0793097
$484$	2.38547e6	0.462872
$485$	−3.21153e6	−0.619951
$486$	−236196.	−0.0453609
$487$	1.53182e6	0.292674	0.146337	−	0.989235i	$-0.453252\pi$
$487$	1.53182e6	0.292674	0.146337	+	0.989235i	$0.453252\pi$
$488$	138437.	0.0263150
$489$	−2.13181e6	−0.403159
$490$	951256.	0.178981
$491$	−2.77389e6	−0.519260	−0.259630	−	0.965708i	$-0.583601\pi$
$491$	−2.77389e6	−0.519260	−0.259630	+	0.965708i	$0.583601\pi$
$492$	−456570.	−0.0850344
$493$	9.57504e6	1.77428
$494$	−2.52921e6	−0.466302
$495$	−1.12773e6	−0.206868
$496$	696145.	0.127056
$497$	3.61651e6	0.656748
$498$	−278833.	−0.0503815
$499$	−965538.	−0.173587	−0.0867937	−	0.996226i	$-0.527662\pi$
$499$	−965538.	−0.173587	−0.0867937	+	0.996226i	$0.527662\pi$
$500$	250000.	0.0447214
$501$	−909820.	−0.161943
$502$	6.82246e6	1.20832
$503$	5.55511e6	0.978977	0.489489	−	0.872010i	$-0.337184\pi$
$503$	5.55511e6	0.978977	0.489489	+	0.872010i	$0.337184\pi$
$504$	−442753.	−0.0776399
$505$	2.05278e6	0.358190
$506$	−1.17841e6	−0.204607
$507$	394499.	0.0681595
$508$	−603785.	−0.103806
$509$	880255.	0.150596	0.0752981	−	0.997161i	$-0.476009\pi$
$509$	880255.	0.150596	0.0752981	+	0.997161i	$0.476009\pi$
$510$	1.35609e6	0.230867
$511$	−1.78032e6	−0.301610
$512$	−262144.	−0.0441942
$513$	715421.	0.120024
$514$	2.79978e6	0.467430
$515$	−510594.	−0.0848316
$516$	480215.	0.0793984
$517$	8.73878e6	1.43789
$518$	2.09024e6	0.342272
$519$	−1.55690e6	−0.253713
$520$	−1.03088e6	−0.167187
$521$	−7.92961e6	−1.27984	−0.639922	−	0.768440i	$-0.721034\pi$
$521$	−7.92961e6	−1.27984	−0.639922	+	0.768440i	$0.721034\pi$
$522$	2.05892e6	0.330723
$523$	311239.	0.0497554	0.0248777	−	0.999691i	$-0.492080\pi$
$523$	311239.	0.0497554	0.0248777	+	0.999691i	$0.492080\pi$
$524$	1.18059e6	0.187833
$525$	480417.	0.0760712
$526$	−2.15056e6	−0.338913
$527$	−4.09737e6	−0.642655
$528$	−1.28311e6	−0.200299
$529$	279841.	0.0434783
$530$	2.05674e6	0.318045
$531$	−126341.	−0.0194450
$532$	1.34107e6	0.205434
$533$	−2.04284e6	−0.311471
$534$	1.78035e6	0.270179
$535$	−688422.	−0.103985
$536$	323293.	0.0486054
$537$	−591884.	−0.0885730
$538$	410283.	0.0611122
$539$	5.29759e6	0.785428
$540$	291600.	0.0430331
$541$	−1.49988e6	−0.220325	−0.110163	−	0.993914i	$-0.535137\pi$
$541$	−1.49988e6	−0.220325	−0.110163	+	0.993914i	$0.535137\pi$
$542$	2.02422e6	0.295978
$543$	6.56851e6	0.956021
$544$	1.54293e6	0.223536
$545$	2.03053e6	0.292832
$546$	−1.98102e6	−0.284385
$547$	−6.65051e6	−0.950357	−0.475179	−	0.879889i	$-0.657617\pi$
$547$	−6.65051e6	−0.950357	−0.475179	+	0.879889i	$0.657617\pi$
$548$	5.05128e6	0.718539
$549$	−175210.	−0.0248100
$550$	1.39226e6	0.196252
$551$	−6.23634e6	−0.875086
$552$	304704.	0.0425628
$553$	−829089.	−0.115289
$554$	3.65464e6	0.505907
$555$	−1.37665e6	−0.189710
$556$	−6.73798e6	−0.924363
$557$	−5.48392e6	−0.748950	−0.374475	−	0.927237i	$-0.622177\pi$
$557$	−5.48392e6	−0.748950	−0.374475	+	0.927237i	$0.622177\pi$
$558$	−881058.	−0.119790
$559$	2.14864e6	0.290826
$560$	546608.	0.0736556
$561$	7.55212e6	1.01312
$562$	4.71074e6	0.629142
$563$	−5.67910e6	−0.755107	−0.377553	−	0.925988i	$-0.623235\pi$
$563$	−5.67910e6	−0.755107	−0.377553	+	0.925988i	$0.623235\pi$
$564$	−2.25960e6	−0.299112
$565$	3.11337e6	0.410307
$566$	−1.93837e6	−0.254329
$567$	560359.	0.0731996
$568$	−2.71003e6	−0.352454
$569$	1.02362e7	1.32543	0.662715	−	0.748872i	$-0.269404\pi$
$569$	1.02362e7	1.32543	0.662715	+	0.748872i	$0.269404\pi$
$570$	−883236.	−0.113865
$571$	−1.37412e7	−1.76374	−0.881868	−	0.471496i	$-0.843714\pi$
$571$	−1.37412e7	−1.76374	−0.881868	+	0.471496i	$0.843714\pi$
$572$	−5.74105e6	−0.733671
$573$	2.31159e6	0.294120
$574$	1.08318e6	0.137221
$575$	−330625.	−0.0417029
$576$	331776.	0.0416667
$577$	−2.18964e6	−0.273800	−0.136900	−	0.990585i	$-0.543714\pi$
$577$	−2.18964e6	−0.273800	−0.136900	+	0.990585i	$0.543714\pi$
$578$	−3.40192e6	−0.423550
$579$	−1.64173e6	−0.203519
$580$	−2.54188e6	−0.313751
$581$	661513.	0.0813014
$582$	4.62460e6	0.565935
$583$	1.14541e7	1.39569
$584$	1.33408e6	0.161864
$585$	1.30471e6	0.157625
$586$	−544103.	−0.0654542
$587$	5.71673e6	0.684782	0.342391	−	0.939558i	$-0.388763\pi$
$587$	5.71673e6	0.684782	0.342391	+	0.939558i	$0.388763\pi$
$588$	−1.36981e6	−0.163387
$589$	2.66866e6	0.316961
$590$	155976.	0.0184471
$591$	−4.00370e6	−0.471512
$592$	−1.56632e6	−0.183686
$593$	979657.	0.114403	0.0572015	−	0.998363i	$-0.481782\pi$
$593$	979657.	0.114403	0.0572015	+	0.998363i	$0.481782\pi$
$594$	1.62393e6	0.188844
$595$	−3.21722e6	−0.372554
$596$	−355404.	−0.0409832
$597$	−4.71687e6	−0.541649
$598$	1.36335e6	0.155902
$599$	9.45355e6	1.07653	0.538267	−	0.842774i	$-0.319079\pi$
$599$	9.45355e6	1.07653	0.538267	+	0.842774i	$0.319079\pi$
$600$	−360000.	−0.0408248
$601$	3.45418e6	0.390084	0.195042	−	0.980795i	$-0.437516\pi$
$601$	3.45418e6	0.390084	0.195042	+	0.980795i	$0.437516\pi$
$602$	−1.13928e6	−0.128126
$603$	−409168.	−0.0458256
$604$	2.89769e6	0.323191
$605$	3.72730e6	0.414006
$606$	−2.95600e6	−0.326981
$607$	9.27837e6	1.02212	0.511058	−	0.859546i	$-0.329254\pi$
$607$	9.27837e6	1.02212	0.511058	+	0.859546i	$0.329254\pi$
$608$	−1.00493e6	−0.110249
$609$	−4.88466e6	−0.533692
$610$	216308.	0.0235368
$611$	−1.01102e7	−1.09561
$612$	−1.95277e6	−0.210752
$613$	1.42679e7	1.53359	0.766796	−	0.641891i	$-0.221850\pi$
$613$	1.42679e7	1.53359	0.766796	+	0.641891i	$0.221850\pi$
$614$	−984036.	−0.105339
$615$	−713391.	−0.0760571
$616$	3.04409e6	0.323225
$617$	1.55008e7	1.63923	0.819616	−	0.572913i	$-0.194187\pi$
$617$	1.55008e7	1.63923	0.819616	+	0.572913i	$0.194187\pi$
$618$	735255.	0.0774403
$619$	−1.64419e7	−1.72475	−0.862373	−	0.506274i	$-0.831023\pi$
$619$	−1.64419e7	−1.72475	−0.862373	+	0.506274i	$0.831023\pi$
$620$	1.08773e6	0.113642
$621$	−385641.	−0.0401286
$622$	3.87290e6	0.401384
$623$	−4.22375e6	−0.435992
$624$	1.48447e6	0.152620
$625$	390625.	0.0400000
$626$	−6.57293e6	−0.670383
$627$	−4.91879e6	−0.499677
$628$	42717.9	0.00432226
$629$	9.21903e6	0.929092
$630$	−691801.	−0.0694432
$631$	8.51877e6	0.851733	0.425866	−	0.904786i	$-0.359969\pi$
$631$	8.51877e6	0.851733	0.425866	+	0.904786i	$0.359969\pi$
$632$	621276.	0.0618717
$633$	−2.63125e6	−0.261008
$634$	3.31374e6	0.327413
$635$	−943414.	−0.0928470
$636$	−2.96170e6	−0.290334
$637$	−6.12897e6	−0.598465
$638$	−1.41559e7	−1.37684
$639$	3.42988e6	0.332297
$640$	−409600.	−0.0395285
$641$	−1.85520e7	−1.78338	−0.891692	−	0.452642i	$-0.850481\pi$
$641$	−1.85520e7	−1.78338	−0.891692	+	0.452642i	$0.850481\pi$
$642$	991328.	0.0949249
$643$	−8.89971e6	−0.848885	−0.424442	−	0.905455i	$-0.639530\pi$
$643$	−8.89971e6	−0.848885	−0.424442	+	0.905455i	$0.639530\pi$
$644$	−722889.	−0.0686842
$645$	750336.	0.0710161
$646$	5.91479e6	0.557646
$647$	−3.34124e6	−0.313796	−0.156898	−	0.987615i	$-0.550149\pi$
$647$	−3.34124e6	−0.313796	−0.156898	+	0.987615i	$0.550149\pi$
$648$	−419904.	−0.0392837
$649$	868640.	0.0809521
$650$	−1.61076e6	−0.149536
$651$	2.09025e6	0.193306
$652$	−3.78989e6	−0.349146
$653$	1.78336e7	1.63665	0.818327	−	0.574753i	$-0.194902\pi$
$653$	1.78336e7	1.63665	0.818327	+	0.574753i	$0.194902\pi$
$654$	−2.92396e6	−0.267318
$655$	1.84467e6	0.168003
$656$	−811680.	−0.0736420
$657$	−1.68844e6	−0.152606
$658$	5.36075e6	0.482682
$659$	1.47454e7	1.32264	0.661322	−	0.750102i	$-0.269996\pi$
$659$	1.47454e7	1.32264	0.661322	+	0.750102i	$0.269996\pi$
$660$	−2.00486e6	−0.179153
$661$	−561309.	−0.0499687	−0.0249844	−	0.999688i	$-0.507954\pi$
$661$	−561309.	−0.0499687	−0.0249844	+	0.999688i	$0.507954\pi$
$662$	8.27243e6	0.733649
$663$	−8.73731e6	−0.771959
$664$	−495704.	−0.0436317
$665$	2.09542e6	0.183745
$666$	1.98237e6	0.173181
$667$	3.36164e6	0.292575
$668$	−1.61746e6	−0.140246
$669$	363821.	0.0314284
$670$	505146.	0.0434740
$671$	1.20463e6	0.103287
$672$	−787116.	−0.0672381
$673$	1.38819e7	1.18144	0.590718	−	0.806878i	$-0.298844\pi$
$673$	1.38819e7	1.18144	0.590718	+	0.806878i	$0.298844\pi$
$674$	4.49938e6	0.381507
$675$	455625.	0.0384900
$676$	701332.	0.0590279
$677$	1.43945e7	1.20705	0.603526	−	0.797343i	$-0.293762\pi$
$677$	1.43945e7	1.20705	0.603526	+	0.797343i	$0.293762\pi$
$678$	−4.48325e6	−0.374558
$679$	−1.09715e7	−0.913257
$680$	2.41082e6	0.199937
$681$	−4.83114e6	−0.399192
$682$	6.05760e6	0.498700
$683$	−2.20966e7	−1.81248	−0.906240	−	0.422763i	$-0.861060\pi$
$683$	−2.20966e7	−1.81248	−0.906240	+	0.422763i	$0.861060\pi$
$684$	1.27186e6	0.103944
$685$	7.89263e6	0.642681
$686$	8.99155e6	0.729498
$687$	−9.59953e6	−0.775993
$688$	853716.	0.0687610
$689$	−1.32516e7	−1.06346
$690$	476100.	0.0380693
$691$	−8.84013e6	−0.704309	−0.352155	−	0.935942i	$-0.614551\pi$
$691$	−8.84013e6	−0.704309	−0.352155	+	0.935942i	$0.614551\pi$
$692$	−2.76782e6	−0.219722
$693$	−3.85267e6	−0.304740
$694$	9.11546e6	0.718423
$695$	−1.05281e7	−0.826775
$696$	3.66031e6	0.286414
$697$	4.77739e6	0.372485
$698$	−7.99737e6	−0.621311
$699$	75156.5	0.00581800
$700$	854075.	0.0658796
$701$	−3.46261e6	−0.266139	−0.133069	−	0.991107i	$-0.542483\pi$
$701$	−3.46261e6	−0.266139	−0.133069	+	0.991107i	$0.542483\pi$
$702$	−1.87879e6	−0.143891
$703$	−6.00447e6	−0.458233
$704$	−2.28108e6	−0.173464
$705$	−3.53063e6	−0.267534
$706$	−1.08639e7	−0.820299
$707$	7.01291e6	0.527654
$708$	−224606.	−0.0168398
$709$	−1.82665e7	−1.36471	−0.682356	−	0.731020i	$-0.739044\pi$
$709$	−1.82665e7	−1.36471	−0.682356	+	0.731020i	$0.739044\pi$
$710$	−4.23442e6	−0.315245
$711$	−786303.	−0.0583332
$712$	3.16506e6	0.233982
$713$	−1.43852e6	−0.105972
$714$	4.63280e6	0.340094
$715$	−8.97039e6	−0.656215
$716$	−1.05224e6	−0.0767064
$717$	−1.37976e7	−1.00232
$718$	−1.35001e7	−0.977297
$719$	−4.36123e6	−0.314621	−0.157310	−	0.987549i	$-0.550282\pi$
$719$	−4.36123e6	−0.314621	−0.157310	+	0.987549i	$0.550282\pi$
$720$	518400.	0.0372678
$721$	−1.74434e6	−0.124966
$722$	6.05202e6	0.432073
$723$	−1.41627e7	−1.00762
$724$	1.16774e7	0.827939
$725$	−3.97169e6	−0.280628
$726$	−5.36732e6	−0.377934
$727$	−8.96627e6	−0.629181	−0.314591	−	0.949227i	$-0.601867\pi$
$727$	−8.96627e6	−0.629181	−0.314591	+	0.949227i	$0.601867\pi$
$728$	−3.52181e6	−0.246285
$729$	531441.	0.0370370
$730$	2.08450e6	0.144775
$731$	−5.02480e6	−0.347796
$732$	−311484.	−0.0214861
$733$	2.44166e7	1.67852	0.839259	−	0.543731i	$-0.182989\pi$
$733$	2.44166e7	1.67852	0.839259	+	0.543731i	$0.182989\pi$
$734$	−5.07829e6	−0.347918
$735$	−2.14033e6	−0.146137
$736$	541696.	0.0368605
$737$	2.81318e6	0.190778
$738$	1.02728e6	0.0694303
$739$	393147.	0.0264816	0.0132408	−	0.999912i	$-0.495785\pi$
$739$	393147.	0.0264816	0.0132408	+	0.999912i	$0.495785\pi$
$740$	−2.44737e6	−0.164294
$741$	5.69072e6	0.380734
$742$	7.02643e6	0.468517
$743$	2.03200e6	0.135037	0.0675185	−	0.997718i	$-0.478492\pi$
$743$	2.03200e6	0.135037	0.0675185	+	0.997718i	$0.478492\pi$
$744$	−1.56633e6	−0.103741
$745$	−555318.	−0.0366565
$746$	−7.43570e6	−0.489187
$747$	627375.	0.0411363
$748$	1.34260e7	0.877389
$749$	−2.35186e6	−0.153182
$750$	−562500.	−0.0365148
$751$	−1.15862e7	−0.749621	−0.374811	−	0.927101i	$-0.622292\pi$
$751$	−1.15862e7	−0.749621	−0.374811	+	0.927101i	$0.622292\pi$
$752$	−4.01707e6	−0.259039
$753$	−1.53505e7	−0.986588
$754$	1.63774e7	1.04910
$755$	4.52764e6	0.289071
$756$	996193.	0.0633927
$757$	5.27498e6	0.334565	0.167283	−	0.985909i	$-0.446501\pi$
$757$	5.27498e6	0.334565	0.167283	+	0.985909i	$0.446501\pi$
$758$	−7.90221e6	−0.499546
$759$	2.65142e6	0.167061
$760$	−1.57020e6	−0.0986099
$761$	−2.85251e7	−1.78552	−0.892762	−	0.450528i	$-0.851236\pi$
$761$	−2.85251e7	−1.78552	−0.892762	+	0.450528i	$0.851236\pi$
$762$	1.35852e6	0.0847574
$763$	6.93690e6	0.431374
$764$	4.10950e6	0.254716
$765$	−3.05120e6	−0.188502
$766$	−1.36189e6	−0.0838627
$767$	−1.00496e6	−0.0616823
$768$	589824.	0.0360844
$769$	−1.45597e7	−0.887841	−0.443920	−	0.896066i	$-0.646413\pi$
$769$	−1.45597e7	−0.887841	−0.443920	+	0.896066i	$0.646413\pi$
$770$	4.75639e6	0.289102
$771$	−6.29951e6	−0.381655
$772$	−2.91863e6	−0.176253
$773$	−1.95783e7	−1.17849	−0.589246	−	0.807954i	$-0.700575\pi$
$773$	−1.95783e7	−1.17849	−0.589246	+	0.807954i	$0.700575\pi$
$774$	−1.08048e6	−0.0648285
$775$	1.69957e6	0.101645
$776$	8.22151e6	0.490114
$777$	−4.70304e6	−0.279464
$778$	−9.55302e6	−0.565838
$779$	−3.11157e6	−0.183711
$780$	2.31949e6	0.136507
$781$	−2.35817e7	−1.38340
$782$	−3.18831e6	−0.186442
$783$	−4.63258e6	−0.270034
$784$	−2.43521e6	−0.141497
$785$	66746.8	0.00386595
$786$	−2.65633e6	−0.153365
$787$	558524.	0.0321444	0.0160722	−	0.999871i	$-0.494884\pi$
$787$	558524.	0.0321444	0.0160722	+	0.999871i	$0.494884\pi$
$788$	−7.11769e6	−0.408341
$789$	4.83877e6	0.276721
$790$	970744.	0.0553398
$791$	1.06362e7	0.604429
$792$	2.88700e6	0.163543
$793$	−1.39368e6	−0.0787009
$794$	9.67347e6	0.544542
$795$	−4.62766e6	−0.259683
$796$	−8.38555e6	−0.469082
$797$	−6.55051e6	−0.365283	−0.182641	−	0.983180i	$-0.558465\pi$
$797$	−6.55051e6	−0.365283	−0.182641	+	0.983180i	$0.558465\pi$
$798$	−3.01740e6	−0.167736
$799$	2.36437e7	1.31023
$800$	−640000.	−0.0353553
$801$	−4.00578e6	−0.220600
$802$	−9.08411e6	−0.498708
$803$	1.16087e7	0.635321
$804$	−727410.	−0.0396862
$805$	−1.12951e6	−0.0614331
$806$	−7.00825e6	−0.379990
$807$	−923136.	−0.0498979
$808$	−5.25511e6	−0.283174
$809$	−2.85798e7	−1.53528	−0.767640	−	0.640881i	$-0.778569\pi$
$809$	−2.85798e7	−1.53528	−0.767640	+	0.640881i	$0.778569\pi$
$810$	−656100.	−0.0351364
$811$	3.07438e7	1.64137	0.820684	−	0.571382i	$-0.193593\pi$
$811$	3.07438e7	1.64137	0.820684	+	0.571382i	$0.193593\pi$
$812$	−8.68383e6	−0.462191
$813$	−4.55449e6	−0.241665
$814$	−1.36295e7	−0.720975
$815$	−5.92170e6	−0.312286
$816$	−3.47158e6	−0.182517
$817$	3.27271e6	0.171535
$818$	6.23746e6	0.325930
$819$	4.45729e6	0.232200
$820$	−1.26825e6	−0.0658674
$821$	2.62365e7	1.35846	0.679232	−	0.733924i	$-0.262313\pi$
$821$	2.62365e7	1.35846	0.679232	+	0.733924i	$0.262313\pi$
$822$	−1.13654e7	−0.586685
$823$	−5.19831e6	−0.267524	−0.133762	−	0.991013i	$-0.542706\pi$
$823$	−5.19831e6	−0.267524	−0.133762	+	0.991013i	$0.542706\pi$
$824$	1.30712e6	0.0670652
$825$	−3.13259e6	−0.160239
$826$	532862.	0.0271747
$827$	2.94859e7	1.49917	0.749584	−	0.661909i	$-0.230254\pi$
$827$	2.94859e7	1.49917	0.749584	+	0.661909i	$0.230254\pi$
$828$	−685584.	−0.0347524
$829$	2.87618e7	1.45355	0.726776	−	0.686875i	$-0.241018\pi$
$829$	2.87618e7	1.45355	0.726776	+	0.686875i	$0.241018\pi$
$830$	−774537.	−0.0390254
$831$	−8.22295e6	−0.413071
$832$	2.63906e6	0.132173
$833$	1.43332e7	0.715698
$834$	1.51604e7	0.754739
$835$	−2.52728e6	−0.125440
$836$	−8.74451e6	−0.432733
$837$	1.98238e6	0.0978078
$838$	−7.26533e6	−0.357393
$839$	−1.40451e7	−0.688843	−0.344422	−	0.938815i	$-0.611925\pi$
$839$	−1.40451e7	−0.688843	−0.344422	+	0.938815i	$0.611925\pi$
$840$	−1.22987e6	−0.0601396
$841$	1.98711e7	0.968797
$842$	−2.15133e7	−1.04575
$843$	−1.05992e7	−0.513692
$844$	−4.67778e6	−0.226039
$845$	1.09583e6	0.0527961
$846$	5.08411e6	0.244224
$847$	1.27336e7	0.609877
$848$	−5.26525e6	−0.251437
$849$	4.36133e6	0.207658
$850$	3.76691e6	0.178829
$851$	3.23665e6	0.153205
$852$	6.09756e6	0.287778
$853$	3.23615e7	1.52285	0.761423	−	0.648256i	$-0.224501\pi$
$853$	3.23615e7	1.52285	0.761423	+	0.648256i	$0.224501\pi$
$854$	738973.	0.0346724
$855$	1.98728e6	0.0929703
$856$	1.76236e6	0.0822073
$857$	3.01807e7	1.40371	0.701854	−	0.712321i	$-0.252356\pi$
$857$	3.01807e7	1.40371	0.701854	+	0.712321i	$0.252356\pi$
$858$	1.29174e7	0.599039
$859$	3.65930e7	1.69206	0.846029	−	0.533137i	$-0.178987\pi$
$859$	3.65930e7	1.69206	0.846029	+	0.533137i	$0.178987\pi$
$860$	1.33393e6	0.0615017
$861$	−2.43716e6	−0.112041
$862$	−3.44448e6	−0.157890
$863$	9.00395e6	0.411534	0.205767	−	0.978601i	$-0.434031\pi$
$863$	9.00395e6	0.411534	0.205767	+	0.978601i	$0.434031\pi$
$864$	−746496.	−0.0340207
$865$	−4.32472e6	−0.196525
$866$	−1.43110e7	−0.648446
$867$	7.65433e6	0.345827
$868$	3.71600e6	0.167408
$869$	5.40612e6	0.242849
$870$	5.71923e6	0.256177
$871$	−3.25467e6	−0.145366
$872$	−5.19816e6	−0.231504
$873$	−1.04053e7	−0.462084
$874$	2.07659e6	0.0919542
$875$	1.33449e6	0.0589245
$876$	−3.00168e6	−0.132161
$877$	−8.92047e6	−0.391641	−0.195821	−	0.980640i	$-0.562737\pi$
$877$	−8.92047e6	−0.391641	−0.195821	+	0.980640i	$0.562737\pi$
$878$	−1.13476e7	−0.496786
$879$	1.22423e6	0.0534431
$880$	−3.56419e6	−0.155151
$881$	−2.58410e7	−1.12168	−0.560841	−	0.827923i	$-0.689522\pi$
$881$	−2.58410e7	−1.12168	−0.560841	+	0.827923i	$0.689522\pi$
$882$	3.08207e6	0.133405
$883$	1.03464e7	0.446568	0.223284	−	0.974753i	$-0.428322\pi$
$883$	1.03464e7	0.446568	0.223284	+	0.974753i	$0.428322\pi$
$884$	−1.55330e7	−0.668536
$885$	−350947.	−0.0150620
$886$	−1.60547e6	−0.0687096
$887$	2.95857e7	1.26262	0.631310	−	0.775531i	$-0.282518\pi$
$887$	2.95857e7	1.26262	0.631310	+	0.775531i	$0.282518\pi$
$888$	3.52422e6	0.149979
$889$	−3.22299e6	−0.136774
$890$	4.94541e6	0.209280
$891$	−3.65385e6	−0.154190
$892$	646794.	0.0272178
$893$	−1.53994e7	−0.646212
$894$	799658.	0.0334627
$895$	−1.64412e6	−0.0686083
$896$	−1.39932e6	−0.0582299
$897$	−3.06753e6	−0.127294
$898$	3.04891e7	1.26169
$899$	−1.72804e7	−0.713109
$900$	810000.	0.0333333
$901$	3.09902e7	1.27178
$902$	−7.06295e6	−0.289048
$903$	2.56337e6	0.104615
$904$	−7.97022e6	−0.324376
$905$	1.82459e7	0.740531
$906$	−6.51980e6	−0.263884
$907$	3.24431e7	1.30949	0.654747	−	0.755848i	$-0.272775\pi$
$907$	3.24431e7	1.30949	0.654747	+	0.755848i	$0.272775\pi$
$908$	−8.58870e6	−0.345711
$909$	6.65100e6	0.266979
$910$	−5.50283e6	−0.220284
$911$	1.37590e7	0.549275	0.274637	−	0.961548i	$-0.411442\pi$
$911$	1.37590e7	0.549275	0.274637	+	0.961548i	$0.411442\pi$
$912$	2.26108e6	0.0900181
$913$	−4.31344e6	−0.171256
$914$	−1.42731e7	−0.565137
$915$	−486693.	−0.0192177
$916$	−1.70658e7	−0.672030
$917$	6.30196e6	0.247487
$918$	4.39372e6	0.172078
$919$	−4.87349e7	−1.90349	−0.951746	−	0.306888i	$-0.900712\pi$
$919$	−4.87349e7	−1.90349	−0.951746	+	0.306888i	$0.900712\pi$
$920$	846400.	0.0329690
$921$	2.21408e6	0.0860091
$922$	−7.07895e6	−0.274247
$923$	2.72825e7	1.05409
$924$	−6.84920e6	−0.263912
$925$	−3.82402e6	−0.146949
$926$	7.53299e6	0.288695
$927$	−1.65432e6	−0.0632297
$928$	6.50722e6	0.248042
$929$	−324032.	−0.0123182	−0.00615912	−	0.999981i	$-0.501961\pi$
$929$	−324032.	−0.0123182	−0.00615912	+	0.999981i	$0.501961\pi$
$930$	−2.44738e6	−0.0927886
$931$	−9.33537e6	−0.352986
$932$	133612.	0.00503854
$933$	−8.71402e6	−0.327729
$934$	−1.96298e7	−0.736291
$935$	2.09781e7	0.784761
$936$	−3.34007e6	−0.124614
$937$	−4.10422e6	−0.152715	−0.0763576	−	0.997080i	$-0.524329\pi$
$937$	−4.10422e6	−0.152715	−0.0763576	+	0.997080i	$0.524329\pi$
$938$	1.72573e6	0.0640421
$939$	1.47891e7	0.547365
$940$	−6.27667e6	−0.231691
$941$	−1.18382e7	−0.435823	−0.217911	−	0.975969i	$-0.569924\pi$
$941$	−1.18382e7	−0.435823	−0.217911	+	0.975969i	$0.569924\pi$
$942$	−96115.4	−0.00352911
$943$	1.67726e6	0.0614217
$944$	−399299.	−0.0145837
$945$	1.55655e6	0.0567001
$946$	7.42873e6	0.269890
$947$	−1.20772e7	−0.437616	−0.218808	−	0.975768i	$-0.570217\pi$
$947$	−1.20772e7	−0.437616	−0.218808	+	0.975768i	$0.570217\pi$
$948$	−1.39787e6	−0.0505180
$949$	−1.34305e7	−0.484090
$950$	−2.45343e6	−0.0881993
$951$	−7.45592e6	−0.267331
$952$	8.23609e6	0.294530
$953$	−4.72805e6	−0.168636	−0.0843180	−	0.996439i	$-0.526871\pi$
$953$	−4.72805e6	−0.168636	−0.0843180	+	0.996439i	$0.526871\pi$
$954$	6.66383e6	0.237057
$955$	6.42109e6	0.227825
$956$	−2.45290e7	−0.868031
$957$	3.18507e7	1.12419
$958$	−5.00723e6	−0.176272
$959$	2.69636e7	0.946742
$960$	921600.	0.0322749
$961$	−2.12345e7	−0.741708
$962$	1.57685e7	0.549354
$963$	−2.23049e6	−0.0775058
$964$	−2.51780e7	−0.872629
$965$	−4.56037e6	−0.157645
$966$	1.62650e6	0.0560804
$967$	−4.82568e7	−1.65956	−0.829778	−	0.558093i	$-0.811533\pi$
$967$	−4.82568e7	−1.65956	−0.829778	+	0.558093i	$0.811533\pi$
$968$	−9.54189e6	−0.327300
$969$	−1.33083e7	−0.455316
$970$	1.28461e7	0.438371
$971$	9.07608e6	0.308923	0.154462	−	0.987999i	$-0.450636\pi$
$971$	9.07608e6	0.308923	0.154462	+	0.987999i	$0.450636\pi$
$972$	944784.	0.0320750
$973$	−3.59671e7	−1.21793
$974$	−6.12727e6	−0.206952
$975$	3.62420e6	0.122096
$976$	−553749.	−0.0186075
$977$	−3.34629e7	−1.12157	−0.560786	−	0.827961i	$-0.689501\pi$
$977$	−3.34629e7	−1.12157	−0.560786	+	0.827961i	$0.689501\pi$
$978$	8.52725e6	0.285077
$979$	2.75412e7	0.918389
$980$	−3.80502e6	−0.126559
$981$	6.57892e6	0.218264
$982$	1.10955e7	0.367172
$983$	4.24521e7	1.40125	0.700624	−	0.713531i	$-0.252905\pi$
$983$	4.24521e7	1.40125	0.700624	+	0.713531i	$0.252905\pi$
$984$	1.82628e6	0.0601284
$985$	−1.11214e7	−0.365232
$986$	−3.83002e7	−1.25461
$987$	−1.20617e7	−0.394108
$988$	1.01168e7	0.329725
$989$	−1.76412e6	−0.0573506
$990$	4.51093e6	0.146278
$991$	−3.00484e7	−0.971936	−0.485968	−	0.873976i	$-0.661533\pi$
$991$	−3.00484e7	−0.971936	−0.485968	+	0.873976i	$0.661533\pi$
$992$	−2.78458e6	−0.0898422
$993$	−1.86130e7	−0.599022
$994$	−1.44660e7	−0.464391
$995$	−1.31024e7	−0.419560
$996$	1.11533e6	0.0356251
$997$	−1.17839e7	−0.375451	−0.187725	−	0.982222i	$-0.560111\pi$
$997$	−1.17839e7	−0.375451	−0.187725	+	0.982222i	$0.560111\pi$
$998$	3.86215e6	0.122745
$999$	−4.46034e6	−0.141401

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.6.a.g.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.6.a.g.1.4	✓	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	690.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +85.4075 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +85.4075 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -556.905 q^{11} +144.000 q^{12} +644.303 q^{13} -341.630 q^{14} +225.000 q^{15} +256.000 q^{16} -1506.76 q^{17} -324.000 q^{18} +981.374 q^{19} +400.000 q^{20} +768.668 q^{21} +2227.62 q^{22} -529.000 q^{23} -576.000 q^{24} +625.000 q^{25} -2577.21 q^{26} +729.000 q^{27} +1366.52 q^{28} -6354.71 q^{29} -900.000 q^{30} +2719.31 q^{31} -1024.00 q^{32} -5012.14 q^{33} +6027.06 q^{34} +2135.19 q^{35} +1296.00 q^{36} -6118.43 q^{37} -3925.49 q^{38} +5798.73 q^{39} -1600.00 q^{40} -3170.63 q^{41} -3074.67 q^{42} +3334.83 q^{43} -8910.48 q^{44} +2025.00 q^{45} +2116.00 q^{46} -15691.7 q^{47} +2304.00 q^{48} -9512.56 q^{49} -2500.00 q^{50} -13560.9 q^{51} +10308.8 q^{52} -20567.4 q^{53} -2916.00 q^{54} -13922.6 q^{55} -5466.08 q^{56} +8832.36 q^{57} +25418.8 q^{58} -1559.76 q^{59} +3600.00 q^{60} -2163.08 q^{61} -10877.3 q^{62} +6918.01 q^{63} +4096.00 q^{64} +16107.6 q^{65} +20048.6 q^{66} -5051.46 q^{67} -24108.2 q^{68} -4761.00 q^{69} -8540.75 q^{70} +42344.2 q^{71} -5184.00 q^{72} -20845.0 q^{73} +24473.7 q^{74} +5625.00 q^{75} +15702.0 q^{76} -47563.9 q^{77} -23194.9 q^{78} -9707.44 q^{79} +6400.00 q^{80} +6561.00 q^{81} +12682.5 q^{82} +7745.37 q^{83} +12298.7 q^{84} -37669.1 q^{85} -13339.3 q^{86} -57192.3 q^{87} +35641.9 q^{88} -49454.1 q^{89} -8100.00 q^{90} +55028.3 q^{91} -8464.00 q^{92} +24473.8 q^{93} +62766.7 q^{94} +24534.3 q^{95} -9216.00 q^{96} -128461. q^{97} +38050.2 q^{98} -45109.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} + 25 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 + 100 * q^5 - 144 * q^6 + 25 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} + 25 q^{7} - 256 q^{8} + 324 q^{9} - 400 q^{10} - 730 q^{11} + 576 q^{12} - 828 q^{13} - 100 q^{14} + 900 q^{15} + 1024 q^{16} - 179 q^{17} - 1296 q^{18} + 1568 q^{19} + 1600 q^{20} + 225 q^{21} + 2920 q^{22} - 2116 q^{23} - 2304 q^{24} + 2500 q^{25} + 3312 q^{26} + 2916 q^{27} + 400 q^{28} - 1917 q^{29} - 3600 q^{30} - 6331 q^{31} - 4096 q^{32} - 6570 q^{33} + 716 q^{34} + 625 q^{35} + 5184 q^{36} + 10127 q^{37} - 6272 q^{38} - 7452 q^{39} - 6400 q^{40} - 14527 q^{41} - 900 q^{42} - 18052 q^{43} - 11680 q^{44} + 8100 q^{45} + 8464 q^{46} - 13208 q^{47} + 9216 q^{48} - 52681 q^{49} - 10000 q^{50} - 1611 q^{51} - 13248 q^{52} - 39327 q^{53} - 11664 q^{54} - 18250 q^{55} - 1600 q^{56} + 14112 q^{57} + 7668 q^{58} - 43301 q^{59} + 14400 q^{60} - 25154 q^{61} + 25324 q^{62} + 2025 q^{63} + 16384 q^{64} - 20700 q^{65} + 26280 q^{66} - 15827 q^{67} - 2864 q^{68} - 19044 q^{69} - 2500 q^{70} - 20999 q^{71} - 20736 q^{72} - 35844 q^{73} - 40508 q^{74} + 22500 q^{75} + 25088 q^{76} - 16142 q^{77} + 29808 q^{78} - 100414 q^{79} + 25600 q^{80} + 26244 q^{81} + 58108 q^{82} - 140015 q^{83} + 3600 q^{84} - 4475 q^{85} + 72208 q^{86} - 17253 q^{87} + 46720 q^{88} - 26030 q^{89} - 32400 q^{90} + 34190 q^{91} - 33856 q^{92} - 56979 q^{93} + 52832 q^{94} + 39200 q^{95} - 36864 q^{96} - 16946 q^{97} + 210724 q^{98} - 59130 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 + 100 * q^5 - 144 * q^6 + 25 * q^7 - 256 * q^8 + 324 * q^9 - 400 * q^10 - 730 * q^11 + 576 * q^12 - 828 * q^13 - 100 * q^14 + 900 * q^15 + 1024 * q^16 - 179 * q^17 - 1296 * q^18 + 1568 * q^19 + 1600 * q^20 + 225 * q^21 + 2920 * q^22 - 2116 * q^23 - 2304 * q^24 + 2500 * q^25 + 3312 * q^26 + 2916 * q^27 + 400 * q^28 - 1917 * q^29 - 3600 * q^30 - 6331 * q^31 - 4096 * q^32 - 6570 * q^33 + 716 * q^34 + 625 * q^35 + 5184 * q^36 + 10127 * q^37 - 6272 * q^38 - 7452 * q^39 - 6400 * q^40 - 14527 * q^41 - 900 * q^42 - 18052 * q^43 - 11680 * q^44 + 8100 * q^45 + 8464 * q^46 - 13208 * q^47 + 9216 * q^48 - 52681 * q^49 - 10000 * q^50 - 1611 * q^51 - 13248 * q^52 - 39327 * q^53 - 11664 * q^54 - 18250 * q^55 - 1600 * q^56 + 14112 * q^57 + 7668 * q^58 - 43301 * q^59 + 14400 * q^60 - 25154 * q^61 + 25324 * q^62 + 2025 * q^63 + 16384 * q^64 - 20700 * q^65 + 26280 * q^66 - 15827 * q^67 - 2864 * q^68 - 19044 * q^69 - 2500 * q^70 - 20999 * q^71 - 20736 * q^72 - 35844 * q^73 - 40508 * q^74 + 22500 * q^75 + 25088 * q^76 - 16142 * q^77 + 29808 * q^78 - 100414 * q^79 + 25600 * q^80 + 26244 * q^81 + 58108 * q^82 - 140015 * q^83 + 3600 * q^84 - 4475 * q^85 + 72208 * q^86 - 17253 * q^87 + 46720 * q^88 - 26030 * q^89 - 32400 * q^90 + 34190 * q^91 - 33856 * q^92 - 56979 * q^93 + 52832 * q^94 + 39200 * q^95 - 36864 * q^96 - 16946 * q^97 + 210724 * q^98 - 59130 * q^99

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