LMFDB - Embedded newform 547.6.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,6,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, 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("547.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	547.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:	$87.7299494377$
Analytic rank:	$0$
Dimension:	$117$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.0439 q^{2} -17.9614 q^{3} +68.8790 q^{4} -103.266 q^{5} +180.402 q^{6} -120.875 q^{7} -370.407 q^{8} +79.6121 q^{9} +O(q^{10})$	\(q-10.0439 q^{2} -17.9614 q^{3} +68.8790 q^{4} -103.266 q^{5} +180.402 q^{6} -120.875 q^{7} -370.407 q^{8} +79.6121 q^{9} +1037.19 q^{10} +294.108 q^{11} -1237.16 q^{12} +378.094 q^{13} +1214.05 q^{14} +1854.80 q^{15} +1516.19 q^{16} +1557.34 q^{17} -799.612 q^{18} -975.898 q^{19} -7112.86 q^{20} +2171.08 q^{21} -2953.97 q^{22} -2566.07 q^{23} +6653.04 q^{24} +7538.86 q^{25} -3797.52 q^{26} +2934.68 q^{27} -8325.74 q^{28} +3065.72 q^{29} -18629.4 q^{30} -7599.06 q^{31} -3375.34 q^{32} -5282.58 q^{33} -15641.7 q^{34} +12482.3 q^{35} +5483.60 q^{36} +9439.81 q^{37} +9801.77 q^{38} -6791.09 q^{39} +38250.5 q^{40} +3683.22 q^{41} -21806.0 q^{42} -8168.17 q^{43} +20257.8 q^{44} -8221.22 q^{45} +25773.2 q^{46} -847.038 q^{47} -27232.9 q^{48} -2196.28 q^{49} -75719.2 q^{50} -27972.0 q^{51} +26042.7 q^{52} +30985.1 q^{53} -29475.5 q^{54} -30371.3 q^{55} +44772.9 q^{56} +17528.5 q^{57} -30791.7 q^{58} +13093.9 q^{59} +127757. q^{60} -47679.6 q^{61} +76323.9 q^{62} -9623.10 q^{63} -14616.6 q^{64} -39044.2 q^{65} +53057.5 q^{66} -49634.5 q^{67} +107268. q^{68} +46090.2 q^{69} -125370. q^{70} -8465.02 q^{71} -29488.9 q^{72} +25511.3 q^{73} -94812.0 q^{74} -135408. q^{75} -67218.8 q^{76} -35550.2 q^{77} +68208.7 q^{78} -36431.1 q^{79} -156571. q^{80} -72056.7 q^{81} -36993.7 q^{82} -121696. q^{83} +149542. q^{84} -160820. q^{85} +82039.9 q^{86} -55064.7 q^{87} -108940. q^{88} +24381.9 q^{89} +82572.7 q^{90} -45702.0 q^{91} -176748. q^{92} +136490. q^{93} +8507.53 q^{94} +100777. q^{95} +60625.9 q^{96} +36687.2 q^{97} +22059.1 q^{98} +23414.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9}+O(q^{10}) $ 117 * q + 24 * q^2 + 100 * q^3 + 1962 * q^4 + 749 * q^5 + 306 * q^6 + 393 * q^7 + 1152 * q^8 + 10671 * q^9	\( 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9} + 850 q^{10} + 1798 q^{11} + 5361 q^{12} + 4419 q^{13} + 3847 q^{14} + 1913 q^{15} + 34722 q^{16} + 15252 q^{17} + 2367 q^{18} + 1052 q^{19} + 23568 q^{20} + 9212 q^{21} + 9176 q^{22} + 18178 q^{23} + 15983 q^{24} + 84312 q^{25} + 21552 q^{26} + 30883 q^{27} + 23528 q^{28} + 43620 q^{29} + 23582 q^{30} + 13127 q^{31} + 49108 q^{32} + 39222 q^{33} + 32097 q^{34} + 52467 q^{35} + 217244 q^{36} + 56152 q^{37} + 76245 q^{38} + 28595 q^{39} + 20368 q^{40} + 46679 q^{41} + 78924 q^{42} + 39058 q^{43} + 78528 q^{44} + 185770 q^{45} + 41430 q^{46} + 150268 q^{47} + 180930 q^{48} + 323802 q^{49} + 91604 q^{50} + 43367 q^{51} + 136030 q^{52} + 297398 q^{53} + 116761 q^{54} + 94579 q^{55} + 173545 q^{56} + 164740 q^{57} + 87844 q^{58} + 135778 q^{59} + 114650 q^{60} + 166976 q^{61} + 229394 q^{62} + 147179 q^{63} + 630138 q^{64} + 216626 q^{65} + 82380 q^{66} + 133444 q^{67} + 634057 q^{68} + 232986 q^{69} + 30943 q^{70} + 126787 q^{71} + 78583 q^{72} + 241702 q^{73} + 242589 q^{74} + 374853 q^{75} + 90228 q^{76} + 766693 q^{77} + 82537 q^{78} + 117230 q^{79} + 730509 q^{80} + 1051409 q^{81} + 468130 q^{82} + 368467 q^{83} + 234191 q^{84} + 261997 q^{85} + 230487 q^{86} + 214239 q^{87} + 247415 q^{88} + 494902 q^{89} + 41821 q^{90} + 259647 q^{91} + 663682 q^{92} + 767344 q^{93} + 373605 q^{94} + 426186 q^{95} + 474162 q^{96} + 733038 q^{97} + 461746 q^{98} + 334651 q^{99}+O(q^{100}) \) 117 * q + 24 * q^2 + 100 * q^3 + 1962 * q^4 + 749 * q^5 + 306 * q^6 + 393 * q^7 + 1152 * q^8 + 10671 * q^9 + 850 * q^10 + 1798 * q^11 + 5361 * q^12 + 4419 * q^13 + 3847 * q^14 + 1913 * q^15 + 34722 * q^16 + 15252 * q^17 + 2367 * q^18 + 1052 * q^19 + 23568 * q^20 + 9212 * q^21 + 9176 * q^22 + 18178 * q^23 + 15983 * q^24 + 84312 * q^25 + 21552 * q^26 + 30883 * q^27 + 23528 * q^28 + 43620 * q^29 + 23582 * q^30 + 13127 * q^31 + 49108 * q^32 + 39222 * q^33 + 32097 * q^34 + 52467 * q^35 + 217244 * q^36 + 56152 * q^37 + 76245 * q^38 + 28595 * q^39 + 20368 * q^40 + 46679 * q^41 + 78924 * q^42 + 39058 * q^43 + 78528 * q^44 + 185770 * q^45 + 41430 * q^46 + 150268 * q^47 + 180930 * q^48 + 323802 * q^49 + 91604 * q^50 + 43367 * q^51 + 136030 * q^52 + 297398 * q^53 + 116761 * q^54 + 94579 * q^55 + 173545 * q^56 + 164740 * q^57 + 87844 * q^58 + 135778 * q^59 + 114650 * q^60 + 166976 * q^61 + 229394 * q^62 + 147179 * q^63 + 630138 * q^64 + 216626 * q^65 + 82380 * q^66 + 133444 * q^67 + 634057 * q^68 + 232986 * q^69 + 30943 * q^70 + 126787 * q^71 + 78583 * q^72 + 241702 * q^73 + 242589 * q^74 + 374853 * q^75 + 90228 * q^76 + 766693 * q^77 + 82537 * q^78 + 117230 * q^79 + 730509 * q^80 + 1051409 * q^81 + 468130 * q^82 + 368467 * q^83 + 234191 * q^84 + 261997 * q^85 + 230487 * q^86 + 214239 * q^87 + 247415 * q^88 + 494902 * q^89 + 41821 * q^90 + 259647 * q^91 + 663682 * q^92 + 767344 * q^93 + 373605 * q^94 + 426186 * q^95 + 474162 * q^96 + 733038 * q^97 + 461746 * q^98 + 334651 * 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 $

$2$	−10.0439	−1.77552	−0.887760	−	0.460307i	$-0.847739\pi$
$2$	−10.0439	−1.77552	−0.887760	+	0.460307i	$0.847739\pi$
$3$	−17.9614	−1.15222	−0.576112	−	0.817371i	$-0.695431\pi$
$3$	−17.9614	−1.15222	−0.576112	+	0.817371i	$0.695431\pi$
$4$	68.8790	2.15247
$5$	−103.266	−1.84728	−0.923639	−	0.383264i	$-0.874800\pi$
$5$	−103.266	−1.84728	−0.923639	+	0.383264i	$0.874800\pi$
$6$	180.402	2.04580
$7$	−120.875	−0.932375	−0.466188	−	0.884686i	$-0.654373\pi$
$7$	−120.875	−0.932375	−0.466188	+	0.884686i	$0.654373\pi$
$8$	−370.407	−2.04623
$9$	79.6121	0.327622
$10$	1037.19	3.27988
$11$	294.108	0.732866	0.366433	−	0.930444i	$-0.380579\pi$
$11$	294.108	0.732866	0.366433	+	0.930444i	$0.380579\pi$
$12$	−1237.16	−2.48013
$13$	378.094	0.620499	0.310249	−	0.950655i	$-0.399587\pi$
$13$	378.094	0.620499	0.310249	+	0.950655i	$0.399587\pi$
$14$	1214.05	1.65545
$15$	1854.80	2.12848
$16$	1516.19	1.48065
$17$	1557.34	1.30695	0.653477	−	0.756947i	$-0.273310\pi$
$17$	1557.34	1.30695	0.653477	+	0.756947i	$0.273310\pi$
$18$	−799.612	−0.581699
$19$	−975.898	−0.620184	−0.310092	−	0.950707i	$-0.600360\pi$
$19$	−975.898	−0.620184	−0.310092	+	0.950707i	$0.600360\pi$
$20$	−7112.86	−3.97621
$21$	2171.08	1.07431
$22$	−2953.97	−1.30122
$23$	−2566.07	−1.01146	−0.505730	−	0.862692i	$-0.668777\pi$
$23$	−2566.07	−1.01146	−0.505730	+	0.862692i	$0.668777\pi$
$24$	6653.04	2.35772
$25$	7538.86	2.41243
$26$	−3797.52	−1.10171
$27$	2934.68	0.774731
$28$	−8325.74	−2.00691
$29$	3065.72	0.676921	0.338460	−	0.940981i	$-0.390094\pi$
$29$	3065.72	0.676921	0.338460	+	0.940981i	$0.390094\pi$
$30$	−18629.4	−3.77916
$31$	−7599.06	−1.42022	−0.710110	−	0.704090i	$-0.751355\pi$
$31$	−7599.06	−1.42022	−0.710110	+	0.704090i	$0.751355\pi$
$32$	−3375.34	−0.582697
$33$	−5282.58	−0.844426
$34$	−15641.7	−2.32052
$35$	12482.3	1.72236
$36$	5483.60	0.705196
$37$	9439.81	1.13360	0.566799	−	0.823856i	$-0.308182\pi$
$37$	9439.81	1.13360	0.566799	+	0.823856i	$0.308182\pi$
$38$	9801.77	1.10115
$39$	−6791.09	−0.714954
$40$	38250.5	3.77996
$41$	3683.22	0.342191	0.171095	−	0.985254i	$-0.445269\pi$
$41$	3683.22	0.342191	0.171095	+	0.985254i	$0.445269\pi$
$42$	−21806.0	−1.90745
$43$	−8168.17	−0.673680	−0.336840	−	0.941562i	$-0.609358\pi$
$43$	−8168.17	−0.673680	−0.336840	+	0.941562i	$0.609358\pi$
$44$	20257.8	1.57747
$45$	−8221.22	−0.605208
$46$	25773.2	1.79587
$47$	−847.038	−0.0559317	−0.0279659	−	0.999609i	$-0.508903\pi$
$47$	−847.038	−0.0559317	−0.0279659	+	0.999609i	$0.508903\pi$
$48$	−27232.9	−1.70604
$49$	−2196.28	−0.130677
$50$	−75719.2	−4.28332
$51$	−27972.0	−1.50590
$52$	26042.7	1.33560
$53$	30985.1	1.51517	0.757587	−	0.652734i	$-0.226378\pi$
$53$	30985.1	1.51517	0.757587	+	0.652734i	$0.226378\pi$
$54$	−29475.5	−1.37555
$55$	−30371.3	−1.35381
$56$	44772.9	1.90785
$57$	17528.5	0.714591
$58$	−30791.7	−1.20189
$59$	13093.9	0.489710	0.244855	−	0.969560i	$-0.421260\pi$
$59$	13093.9	0.489710	0.244855	+	0.969560i	$0.421260\pi$
$60$	127757.	4.58148
$61$	−47679.6	−1.64062	−0.820310	−	0.571918i	$-0.806199\pi$
$61$	−47679.6	−1.64062	−0.820310	+	0.571918i	$0.806199\pi$
$62$	76323.9	2.52163
$63$	−9623.10	−0.305466
$64$	−14616.6	−0.446063
$65$	−39044.2	−1.14623
$66$	53057.5	1.49929
$67$	−49634.5	−1.35082	−0.675409	−	0.737443i	$-0.736033\pi$
$67$	−49634.5	−1.35082	−0.675409	+	0.737443i	$0.736033\pi$
$68$	107268.	2.81318
$69$	46090.2	1.16543
$70$	−125370.	−3.05808
$71$	−8465.02	−0.199288	−0.0996442	−	0.995023i	$-0.531770\pi$
$71$	−8465.02	−0.199288	−0.0996442	+	0.995023i	$0.531770\pi$
$72$	−29488.9	−0.670390
$73$	25511.3	0.560305	0.280153	−	0.959955i	$-0.409615\pi$
$73$	25511.3	0.560305	0.280153	+	0.959955i	$0.409615\pi$
$74$	−94812.0	−2.01272
$75$	−135408.	−2.77967
$76$	−67218.8	−1.33493
$77$	−35550.2	−0.683306
$78$	68208.7	1.26941
$79$	−36431.1	−0.656757	−0.328379	−	0.944546i	$-0.606502\pi$
$79$	−36431.1	−0.656757	−0.328379	+	0.944546i	$0.606502\pi$
$80$	−156571.	−2.73518
$81$	−72056.7	−1.22029
$82$	−36993.7	−0.607566
$83$	−121696.	−1.93901	−0.969505	−	0.245073i	$-0.921188\pi$
$83$	−121696.	−1.93901	−0.969505	+	0.245073i	$0.921188\pi$
$84$	149542.	2.31241
$85$	−160820.	−2.41431
$86$	82039.9	1.19613
$87$	−55064.7	−0.779965
$88$	−108940.	−1.49961
$89$	24381.9	0.326282	0.163141	−	0.986603i	$-0.447837\pi$
$89$	24381.9	0.326282	0.163141	+	0.986603i	$0.447837\pi$
$90$	82572.7	1.07456
$91$	−45702.0	−0.578538
$92$	−176748.	−2.17714
$93$	136490.	1.63641
$94$	8507.53	0.0993079
$95$	100777.	1.14565
$96$	60625.9	0.671398
$97$	36687.2	0.395900	0.197950	−	0.980212i	$-0.436572\pi$
$97$	36687.2	0.395900	0.197950	+	0.980212i	$0.436572\pi$
$98$	22059.1	0.232019
$99$	23414.5	0.240103
$100$	519269.	5.19269
$101$	−46613.9	−0.454686	−0.227343	−	0.973815i	$-0.573004\pi$
$101$	−46613.9	−0.454686	−0.227343	+	0.973815i	$0.573004\pi$
$102$	280946.	2.67376
$103$	141196.	1.31138	0.655692	−	0.755029i	$-0.272377\pi$
$103$	141196.	1.31138	0.655692	+	0.755029i	$0.272377\pi$
$104$	−140049.	−1.26968
$105$	−224199.	−1.98454
$106$	−311209.	−2.69022
$107$	−151325.	−1.27777	−0.638885	−	0.769303i	$-0.720604\pi$
$107$	−151325.	−1.27777	−0.638885	+	0.769303i	$0.720604\pi$
$108$	202138.	1.66758
$109$	−84943.2	−0.684798	−0.342399	−	0.939555i	$-0.611239\pi$
$109$	−84943.2	−0.684798	−0.342399	+	0.939555i	$0.611239\pi$
$110$	305045.	2.40371
$111$	−169552.	−1.30616
$112$	−183269.	−1.38052
$113$	232476.	1.71270	0.856351	−	0.516393i	$-0.172726\pi$
$113$	232476.	1.71270	0.856351	+	0.516393i	$0.172726\pi$
$114$	−176054.	−1.26877
$115$	264988.	1.86845
$116$	211164.	1.45705
$117$	30100.8	0.203289
$118$	−131513.	−0.869489
$119$	−188243.	−1.21857
$120$	−687032.	−4.35536
$121$	−74551.8	−0.462908
$122$	478887.	2.91295
$123$	−66155.8	−0.394280
$124$	−523416.	−3.05698
$125$	−455801.	−2.60916
$126$	96653.0	0.542362
$127$	−313645.	−1.72555	−0.862777	−	0.505585i	$-0.831277\pi$
$127$	−313645.	−1.72555	−0.862777	+	0.505585i	$0.831277\pi$
$128$	254818.	1.37469
$129$	146712.	0.776231
$130$	392154.	2.03516
$131$	−79339.6	−0.403935	−0.201968	−	0.979392i	$-0.564734\pi$
$131$	−79339.6	−0.403935	−0.201968	+	0.979392i	$0.564734\pi$
$132$	−363859.	−1.81760
$133$	117961.	0.578244
$134$	498522.	2.39840
$135$	−303052.	−1.43114
$136$	−576849.	−2.67433
$137$	−56064.1	−0.255202	−0.127601	−	0.991826i	$-0.540728\pi$
$137$	−56064.1	−0.255202	−0.127601	+	0.991826i	$0.540728\pi$
$138$	−462924.	−2.06924
$139$	22975.6	0.100863	0.0504314	−	0.998728i	$-0.483940\pi$
$139$	22975.6	0.100863	0.0504314	+	0.998728i	$0.483940\pi$
$140$	859765.	3.70732
$141$	15214.0	0.0644459
$142$	85021.4	0.353840
$143$	111200.	0.454742
$144$	120707.	0.485094
$145$	−316585.	−1.25046
$146$	−256231.	−0.994833
$147$	39448.3	0.150569
$148$	650204.	2.44003
$149$	274915.	1.01445	0.507227	−	0.861812i	$-0.330670\pi$
$149$	274915.	1.01445	0.507227	+	0.861812i	$0.330670\pi$
$150$	1.36002e6	4.93535
$151$	226673.	0.809017	0.404508	−	0.914534i	$-0.367443\pi$
$151$	226673.	0.809017	0.404508	+	0.914534i	$0.367443\pi$
$152$	361480.	1.26904
$153$	123983.	0.428187
$154$	357061.	1.21322
$155$	784725.	2.62354
$156$	−467764.	−1.53892
$157$	400227.	1.29586	0.647929	−	0.761700i	$-0.275635\pi$
$157$	400227.	1.29586	0.647929	+	0.761700i	$0.275635\pi$
$158$	365909.	1.16608
$159$	−556535.	−1.74582
$160$	348558.	1.07640
$161$	310173.	0.943061
$162$	723727.	2.16664
$163$	−358253.	−1.05614	−0.528069	−	0.849201i	$-0.677084\pi$
$163$	−358253.	−1.05614	−0.528069	+	0.849201i	$0.677084\pi$
$164$	253697.	0.736554
$165$	545511.	1.55989
$166$	1.22229e6	3.44275
$167$	177391.	0.492198	0.246099	−	0.969245i	$-0.420851\pi$
$167$	177391.	0.492198	0.246099	+	0.969245i	$0.420851\pi$
$168$	−804184.	−2.19828
$169$	−228338.	−0.614981
$170$	1.61525e6	4.28665
$171$	−77693.3	−0.203186
$172$	−562616.	−1.45008
$173$	567900.	1.44264	0.721318	−	0.692604i	$-0.243537\pi$
$173$	567900.	1.44264	0.721318	+	0.692604i	$0.243537\pi$
$174$	553062.	1.38484
$175$	−911258.	−2.24929
$176$	445922.	1.08512
$177$	−235185.	−0.564256
$178$	−244889.	−0.579320
$179$	−347021.	−0.809511	−0.404756	−	0.914425i	$-0.632643\pi$
$179$	−347021.	−0.809511	−0.404756	+	0.914425i	$0.632643\pi$
$180$	−566269.	−1.30269
$181$	195461.	0.443470	0.221735	−	0.975107i	$-0.428828\pi$
$181$	195461.	0.443470	0.221735	+	0.975107i	$0.428828\pi$
$182$	459024.	1.02720
$183$	856393.	1.89036
$184$	950491.	2.06968
$185$	−974811.	−2.09407
$186$	−1.37088e6	−2.90548
$187$	458024.	0.957821
$188$	−58343.1	−0.120391
$189$	−354728.	−0.722340
$190$	−1.01219e6	−2.03413
$191$	−77147.8	−0.153017	−0.0765085	−	0.997069i	$-0.524377\pi$
$191$	−77147.8	−0.153017	−0.0765085	+	0.997069i	$0.524377\pi$
$192$	262534.	0.513965
$193$	455103.	0.879461	0.439731	−	0.898130i	$-0.355074\pi$
$193$	455103.	0.879461	0.439731	+	0.898130i	$0.355074\pi$
$194$	−368481.	−0.702928
$195$	701289.	1.32072
$196$	−151278.	−0.281277
$197$	−654790.	−1.20209	−0.601045	−	0.799215i	$-0.705249\pi$
$197$	−654790.	−1.20209	−0.601045	+	0.799215i	$0.705249\pi$
$198$	−235172.	−0.426307
$199$	250904.	0.449133	0.224566	−	0.974459i	$-0.427903\pi$
$199$	250904.	0.449133	0.224566	+	0.974459i	$0.427903\pi$
$200$	−2.79245e6	−4.93640
$201$	891506.	1.55645
$202$	468183.	0.807304
$203$	−370569.	−0.631144
$204$	−1.92668e6	−3.24141
$205$	−380351.	−0.632121
$206$	−1.41815e6	−2.32839
$207$	−204290.	−0.331377
$208$	573261.	0.918743
$209$	−287019.	−0.454511
$210$	2.25182e6	3.52359
$211$	567566.	0.877628	0.438814	−	0.898578i	$-0.355399\pi$
$211$	567566.	0.877628	0.438814	+	0.898578i	$0.355399\pi$
$212$	2.13422e6	3.26137
$213$	152044.	0.229625
$214$	1.51989e6	2.26870
$215$	843494.	1.24447
$216$	−1.08703e6	−1.58528
$217$	918535.	1.32418
$218$	853157.	1.21587
$219$	−458218.	−0.645597
$220$	−2.09194e6	−2.91403
$221$	588819.	0.810963
$222$	1.70296e6	2.31911
$223$	214671.	0.289075	0.144537	−	0.989499i	$-0.453831\pi$
$223$	214671.	0.289075	0.144537	+	0.989499i	$0.453831\pi$
$224$	407994.	0.543292
$225$	600184.	0.790366
$226$	−2.33496e6	−3.04094
$227$	220847.	0.284463	0.142232	−	0.989833i	$-0.454572\pi$
$227$	220847.	0.284463	0.142232	+	0.989833i	$0.454572\pi$
$228$	1.20734e6	1.53813
$229$	−1.08448e6	−1.36657	−0.683285	−	0.730152i	$-0.739449\pi$
$229$	−1.08448e6	−1.36657	−0.683285	+	0.730152i	$0.739449\pi$
$230$	−2.66150e6	−3.31747
$231$	638531.	0.787322
$232$	−1.13557e6	−1.38514
$233$	−636818.	−0.768468	−0.384234	−	0.923236i	$-0.625534\pi$
$233$	−636818.	−0.768468	−0.384234	+	0.923236i	$0.625534\pi$
$234$	−302328.	−0.360943
$235$	87470.2	0.103321
$236$	901894.	1.05408
$237$	654354.	0.756732
$238$	1.89068e6	2.16360
$239$	−58636.2	−0.0664004	−0.0332002	−	0.999449i	$-0.510570\pi$
$239$	−58636.2	−0.0664004	−0.0332002	+	0.999449i	$0.510570\pi$
$240$	2.81223e6	3.15154
$241$	−1.38686e6	−1.53812	−0.769060	−	0.639177i	$-0.779275\pi$
$241$	−1.38686e6	−1.53812	−0.769060	+	0.639177i	$0.779275\pi$
$242$	748787.	0.821902
$243$	581113.	0.631313
$244$	−3.28412e6	−3.53139
$245$	226801.	0.241396
$246$	664459.	0.700053
$247$	−368981.	−0.384823
$248$	2.81475e6	2.90610
$249$	2.18583e6	2.23417
$250$	4.57800e6	4.63261
$251$	−367793.	−0.368485	−0.184242	−	0.982881i	$-0.558983\pi$
$251$	−367793.	−0.368485	−0.184242	+	0.982881i	$0.558983\pi$
$252$	−662829.	−0.657507
$253$	−754701.	−0.741265
$254$	3.15020e6	3.06375
$255$	2.88855e6	2.78182
$256$	−2.09162e6	−1.99473
$257$	1.63611e6	1.54518	0.772589	−	0.634906i	$-0.218961\pi$
$257$	1.63611e6	1.54518	0.772589	+	0.634906i	$0.218961\pi$
$258$	−1.47355e6	−1.37821
$259$	−1.14103e6	−1.05694
$260$	−2.68932e6	−2.46723
$261$	244069.	0.221774
$262$	796875.	0.717194
$263$	1.83628e6	1.63701	0.818503	−	0.574502i	$-0.194804\pi$
$263$	1.83628e6	1.63701	0.818503	+	0.574502i	$0.194804\pi$
$264$	1.95671e6	1.72789
$265$	−3.19970e6	−2.79895
$266$	−1.18479e6	−1.02668
$267$	−437934.	−0.375950
$268$	−3.41878e6	−2.90759
$269$	−1.67110e6	−1.40806	−0.704031	−	0.710169i	$-0.748619\pi$
$269$	−1.67110e6	−1.40806	−0.704031	+	0.710169i	$0.748619\pi$
$270$	3.04381e6	2.54102
$271$	949104.	0.785038	0.392519	−	0.919744i	$-0.371604\pi$
$271$	949104.	0.785038	0.392519	+	0.919744i	$0.371604\pi$
$272$	2.36122e6	1.93514
$273$	820872.	0.666605
$274$	563100.	0.453116
$275$	2.21723e6	1.76799
$276$	3.17465e6	2.50855
$277$	−877518.	−0.687158	−0.343579	−	0.939124i	$-0.611639\pi$
$277$	−877518.	−0.687158	−0.343579	+	0.939124i	$0.611639\pi$
$278$	−230764.	−0.179084
$279$	−604978.	−0.465295
$280$	−4.62352e6	−3.52434
$281$	−754132.	−0.569747	−0.284873	−	0.958565i	$-0.591952\pi$
$281$	−754132.	−0.569747	−0.284873	+	0.958565i	$0.591952\pi$
$282$	−152807.	−0.114425
$283$	−1.08569e6	−0.805821	−0.402911	−	0.915239i	$-0.632001\pi$
$283$	−1.08569e6	−0.805821	−0.402911	+	0.915239i	$0.632001\pi$
$284$	−583062.	−0.428962
$285$	−1.81010e6	−1.32005
$286$	−1.11688e6	−0.807404
$287$	−445209.	−0.319050
$288$	−268718.	−0.190904
$289$	1.00544e6	0.708128
$290$	3.17973e6	2.22022
$291$	−658954.	−0.456166
$292$	1.75719e6	1.20604
$293$	1.71040e6	1.16393	0.581967	−	0.813213i	$-0.302283\pi$
$293$	1.71040e6	1.16393	0.581967	+	0.813213i	$0.302283\pi$
$294$	−396213.	−0.267338
$295$	−1.35215e6	−0.904630
$296$	−3.49657e6	−2.31960
$297$	863110.	0.567774
$298$	−2.76120e6	−1.80118
$299$	−970215.	−0.627610
$300$	−9.32680e6	−5.98314
$301$	987326.	0.628123
$302$	−2.27667e6	−1.43642
$303$	837250.	0.523901
$304$	−1.47964e6	−0.918276
$305$	4.92368e6	3.03068
$306$	−1.24527e6	−0.760254
$307$	299283.	0.181233	0.0906164	−	0.995886i	$-0.471116\pi$
$307$	299283.	0.181233	0.0906164	+	0.995886i	$0.471116\pi$
$308$	−2.44866e6	−1.47079
$309$	−2.53608e6	−1.51101
$310$	−7.88166e6	−4.65815
$311$	2.85590e6	1.67433	0.837166	−	0.546949i	$-0.184211\pi$
$311$	2.85590e6	1.67433	0.837166	+	0.546949i	$0.184211\pi$
$312$	2.51547e6	1.46296
$313$	−1.74887e6	−1.00902	−0.504508	−	0.863407i	$-0.668326\pi$
$313$	−1.74887e6	−1.00902	−0.504508	+	0.863407i	$0.668326\pi$
$314$	−4.01983e6	−2.30082
$315$	993738.	0.564281
$316$	−2.50934e6	−1.41365
$317$	−1.76734e6	−0.987807	−0.493904	−	0.869517i	$-0.664430\pi$
$317$	−1.76734e6	−0.987807	−0.493904	+	0.869517i	$0.664430\pi$
$318$	5.58976e6	3.09974
$319$	901652.	0.496092
$320$	1.50940e6	0.824002
$321$	2.71802e6	1.47228
$322$	−3.11533e6	−1.67442
$323$	−1.51980e6	−0.810551
$324$	−4.96319e6	−2.62663
$325$	2.85039e6	1.49691
$326$	3.59824e6	1.87519
$327$	1.52570e6	0.789041
$328$	−1.36429e6	−0.700201
$329$	102386.	0.0521494
$330$	−5.47903e6	−2.76961
$331$	85888.1	0.0430887	0.0215443	−	0.999768i	$-0.493142\pi$
$331$	85888.1	0.0430887	0.0215443	+	0.999768i	$0.493142\pi$
$332$	−8.38227e6	−4.17366
$333$	751523.	0.371391
$334$	−1.78169e6	−0.873908
$335$	5.12556e6	2.49534
$336$	3.29177e6	1.59067
$337$	−3.73576e6	−1.79186	−0.895931	−	0.444193i	$-0.853491\pi$
$337$	−3.73576e6	−1.79186	−0.895931	+	0.444193i	$0.853491\pi$
$338$	2.29340e6	1.09191
$339$	−4.17560e6	−1.97342
$340$	−1.10771e7	−5.19672
$341$	−2.23494e6	−1.04083
$342$	780340.	0.360760
$343$	2.29702e6	1.05421
$344$	3.02555e6	1.37851
$345$	−4.75955e6	−2.15287
$346$	−5.70390e6	−2.56143
$347$	−428165.	−0.190892	−0.0954459	−	0.995435i	$-0.530428\pi$
$347$	−428165.	−0.190892	−0.0954459	+	0.995435i	$0.530428\pi$
$348$	−3.79280e6	−1.67885
$349$	−1.25502e6	−0.551554	−0.275777	−	0.961222i	$-0.588935\pi$
$349$	−1.25502e6	−0.551554	−0.275777	+	0.961222i	$0.588935\pi$
$350$	9.15254e6	3.99366
$351$	1.10958e6	0.480719
$352$	−992713.	−0.427039
$353$	−4.21415e6	−1.80000	−0.900002	−	0.435886i	$-0.856435\pi$
$353$	−4.21415e6	−1.80000	−0.900002	+	0.435886i	$0.856435\pi$
$354$	2.36216e6	1.00185
$355$	874148.	0.368141
$356$	1.67940e6	0.702312
$357$	3.38110e6	1.40407
$358$	3.48543e6	1.43730
$359$	−3.59355e6	−1.47159	−0.735797	−	0.677202i	$-0.763192\pi$
$359$	−3.59355e6	−1.47159	−0.735797	+	0.677202i	$0.763192\pi$
$360$	3.04520e6	1.23840
$361$	−1.52372e6	−0.615372
$362$	−1.96319e6	−0.787390
$363$	1.33905e6	0.533374
$364$	−3.14791e6	−1.24528
$365$	−2.63444e6	−1.03504
$366$	−8.60149e6	−3.35638
$367$	171311.	0.0663928	0.0331964	−	0.999449i	$-0.489431\pi$
$367$	171311.	0.0663928	0.0331964	+	0.999449i	$0.489431\pi$
$368$	−3.89065e6	−1.49762
$369$	293229.	0.112109
$370$	9.79086e6	3.71806
$371$	−3.74531e6	−1.41271
$372$	9.40129e6	3.52233
$373$	4.64805e6	1.72981	0.864906	−	0.501934i	$-0.167378\pi$
$373$	4.64805e6	1.72981	0.864906	+	0.501934i	$0.167378\pi$
$374$	−4.60033e6	−1.70063
$375$	8.18683e6	3.00634
$376$	313749.	0.114449
$377$	1.15913e6	0.420029
$378$	3.56284e6	1.28253
$379$	−189196.	−0.0676571	−0.0338285	−	0.999428i	$-0.510770\pi$
$379$	−189196.	−0.0676571	−0.0338285	+	0.999428i	$0.510770\pi$
$380$	6.94142e6	2.46598
$381$	5.63350e6	1.98823
$382$	774861.	0.271685
$383$	−1.07039e6	−0.372861	−0.186431	−	0.982468i	$-0.559692\pi$
$383$	−1.07039e6	−0.372861	−0.186431	+	0.982468i	$0.559692\pi$
$384$	−4.57689e6	−1.58395
$385$	3.67112e6	1.26226
$386$	−4.57099e6	−1.56150
$387$	−650286.	−0.220712
$388$	2.52698e6	0.852162
$389$	798189.	0.267443	0.133722	−	0.991019i	$-0.457307\pi$
$389$	798189.	0.267443	0.133722	+	0.991019i	$0.457307\pi$
$390$	−7.04364e6	−2.34496
$391$	−3.99624e6	−1.32193
$392$	813519.	0.267395
$393$	1.42505e6	0.465424
$394$	6.57662e6	2.13433
$395$	3.76209e6	1.21321
$396$	1.61277e6	0.516814
$397$	5.52099e6	1.75809	0.879044	−	0.476741i	$-0.158182\pi$
$397$	5.52099e6	1.75809	0.879044	+	0.476741i	$0.158182\pi$
$398$	−2.52004e6	−0.797444
$399$	−2.11875e6	−0.666267
$400$	1.14303e7	3.57198
$401$	2.97310e6	0.923312	0.461656	−	0.887059i	$-0.347255\pi$
$401$	2.97310e6	0.923312	0.461656	+	0.887059i	$0.347255\pi$
$402$	−8.95416e6	−2.76350
$403$	−2.87316e6	−0.881245
$404$	−3.21072e6	−0.978697
$405$	7.44100e6	2.25421
$406$	3.72194e6	1.12061
$407$	2.77632e6	0.830775
$408$	1.03610e7	3.08143
$409$	−641458.	−0.189609	−0.0948047	−	0.995496i	$-0.530223\pi$
$409$	−641458.	−0.189609	−0.0948047	+	0.995496i	$0.530223\pi$
$410$	3.82019e6	1.12234
$411$	1.00699e6	0.294050
$412$	9.72545e6	2.82271
$413$	−1.58272e6	−0.456593
$414$	2.05186e6	0.588366
$415$	1.25670e7	3.58189
$416$	−1.27620e6	−0.361563
$417$	−412675.	−0.116217
$418$	2.88277e6	0.806993
$419$	956404.	0.266138	0.133069	−	0.991107i	$-0.457517\pi$
$419$	956404.	0.266138	0.133069	+	0.991107i	$0.457517\pi$
$420$	−1.54426e7	−4.27166
$421$	−2.11646e6	−0.581975	−0.290987	−	0.956727i	$-0.593984\pi$
$421$	−2.11646e6	−0.581975	−0.290987	+	0.956727i	$0.593984\pi$
$422$	−5.70055e6	−1.55824
$423$	−67434.5	−0.0183245
$424$	−1.14771e7	−3.10040
$425$	1.17405e7	3.15294
$426$	−1.52710e6	−0.407704
$427$	5.76327e6	1.52967
$428$	−1.04231e7	−2.75036
$429$	−1.99731e6	−0.523965
$430$	−8.47193e6	−2.20959
$431$	3.54105e6	0.918204	0.459102	−	0.888383i	$-0.348171\pi$
$431$	3.54105e6	0.918204	0.459102	+	0.888383i	$0.348171\pi$
$432$	4.44952e6	1.14711
$433$	−1.88089e6	−0.482108	−0.241054	−	0.970512i	$-0.577493\pi$
$433$	−1.88089e6	−0.482108	−0.241054	+	0.970512i	$0.577493\pi$
$434$	−9.22564e6	−2.35110
$435$	5.68631e6	1.44081
$436$	−5.85080e6	−1.47401
$437$	2.50422e6	0.627291
$438$	4.60227e6	1.14627
$439$	−2.21172e6	−0.547733	−0.273866	−	0.961768i	$-0.588303\pi$
$439$	−2.21172e6	−0.547733	−0.273866	+	0.961768i	$0.588303\pi$
$440$	1.12497e7	2.77020
$441$	−174851.	−0.0428125
$442$	−5.91401e6	−1.43988
$443$	−4.23952e6	−1.02638	−0.513189	−	0.858276i	$-0.671536\pi$
$443$	−4.23952e6	−1.02638	−0.513189	+	0.858276i	$0.671536\pi$
$444$	−1.16786e7	−2.81147
$445$	−2.51782e6	−0.602733
$446$	−2.15612e6	−0.513258
$447$	−4.93786e6	−1.16888
$448$	1.76678e6	0.415898
$449$	−2.86211e6	−0.669994	−0.334997	−	0.942219i	$-0.608735\pi$
$449$	−2.86211e6	−0.669994	−0.334997	+	0.942219i	$0.608735\pi$
$450$	−6.02816e6	−1.40331
$451$	1.08326e6	0.250780
$452$	1.60127e7	3.68654
$453$	−4.07137e6	−0.932169
$454$	−2.21815e6	−0.505070
$455$	4.71946e6	1.06872
$456$	−6.49268e6	−1.46222
$457$	−4.01910e6	−0.900198	−0.450099	−	0.892979i	$-0.648611\pi$
$457$	−4.01910e6	−0.900198	−0.450099	+	0.892979i	$0.648611\pi$
$458$	1.08923e7	2.42637
$459$	4.57028e6	1.01254
$460$	1.82521e7	4.02178
$461$	−1.25933e6	−0.275986	−0.137993	−	0.990433i	$-0.544065\pi$
$461$	−1.25933e6	−0.275986	−0.137993	+	0.990433i	$0.544065\pi$
$462$	−6.41332e6	−1.39791
$463$	−6.49804e6	−1.40874	−0.704369	−	0.709834i	$-0.748770\pi$
$463$	−6.49804e6	−1.40874	−0.704369	+	0.709834i	$0.748770\pi$
$464$	4.64821e6	1.00228
$465$	−1.40948e7	−3.02291
$466$	6.39611e6	1.36443
$467$	−1.65780e6	−0.351754	−0.175877	−	0.984412i	$-0.556276\pi$
$467$	−1.65780e6	−0.351754	−0.175877	+	0.984412i	$0.556276\pi$
$468$	2.07331e6	0.437573
$469$	5.99957e6	1.25947
$470$	−878538.	−0.183449
$471$	−7.18865e6	−1.49312
$472$	−4.85007e6	−1.00206
$473$	−2.40232e6	−0.493717
$474$	−6.57224e6	−1.34359
$475$	−7.35715e6	−1.49615
$476$	−1.29660e7	−2.62294
$477$	2.46679e6	0.496404
$478$	588933.	0.117895
$479$	−7.03379e6	−1.40072	−0.700359	−	0.713791i	$-0.746977\pi$
$479$	−7.03379e6	−1.40072	−0.700359	+	0.713791i	$0.746977\pi$
$480$	−6.26059e6	−1.24026
$481$	3.56913e6	0.703396
$482$	1.39294e7	2.73096
$483$	−5.57115e6	−1.08662
$484$	−5.13505e6	−0.996395
$485$	−3.78854e6	−0.731337
$486$	−5.83661e6	−1.12091
$487$	−5.11747e6	−0.977761	−0.488880	−	0.872351i	$-0.662595\pi$
$487$	−5.11747e6	−0.977761	−0.488880	+	0.872351i	$0.662595\pi$
$488$	1.76609e7	3.35709
$489$	6.43473e6	1.21691
$490$	−2.27796e6	−0.428603
$491$	−5.06861e6	−0.948823	−0.474412	−	0.880303i	$-0.657339\pi$
$491$	−5.06861e6	−0.948823	−0.474412	+	0.880303i	$0.657339\pi$
$492$	−4.55675e6	−0.848676
$493$	4.77436e6	0.884704
$494$	3.70599e6	0.683261
$495$	−2.41792e6	−0.443537
$496$	−1.15216e7	−2.10285
$497$	1.02321e6	0.185812
$498$	−2.19541e7	−3.96682
$499$	3.37518e6	0.606799	0.303400	−	0.952863i	$-0.401878\pi$
$499$	3.37518e6	0.606799	0.303400	+	0.952863i	$0.401878\pi$
$500$	−3.13951e7	−5.61613
$501$	−3.18619e6	−0.567123
$502$	3.69406e6	0.654251
$503$	2.61545e6	0.460921	0.230461	−	0.973082i	$-0.425977\pi$
$503$	2.61545e6	0.460921	0.230461	+	0.973082i	$0.425977\pi$
$504$	3.56447e6	0.625055
$505$	4.81362e6	0.839931
$506$	7.58010e6	1.31613
$507$	4.10128e6	0.708597
$508$	−2.16035e7	−3.71420
$509$	5.30873e6	0.908230	0.454115	−	0.890943i	$-0.349956\pi$
$509$	5.30873e6	0.908230	0.454115	+	0.890943i	$0.349956\pi$
$510$	−2.90122e7	−4.93918
$511$	−3.08367e6	−0.522415
$512$	1.28538e7	2.16698
$513$	−2.86394e6	−0.480475
$514$	−1.64328e7	−2.74349
$515$	−1.45808e7	−2.42249
$516$	1.01054e7	1.67081
$517$	−249120.	−0.0409905
$518$	1.14604e7	1.87661
$519$	−1.02003e7	−1.66224
$520$	1.44623e7	2.34546
$521$	1.02256e7	1.65042	0.825208	−	0.564829i	$-0.191058\pi$
$521$	1.02256e7	1.65042	0.825208	+	0.564829i	$0.191058\pi$
$522$	−2.45139e6	−0.393764
$523$	8.91876e6	1.42577	0.712886	−	0.701280i	$-0.247388\pi$
$523$	8.91876e6	1.42577	0.712886	+	0.701280i	$0.247388\pi$
$524$	−5.46483e6	−0.869458
$525$	1.63675e7	2.59169
$526$	−1.84434e7	−2.90654
$527$	−1.18343e7	−1.85616
$528$	−8.00939e6	−1.25030
$529$	148375.	0.0230527
$530$	3.21373e7	4.96959
$531$	1.04243e6	0.160440
$532$	8.12506e6	1.24465
$533$	1.39260e6	0.212329
$534$	4.39854e6	0.667507
$535$	1.56268e7	2.36039
$536$	1.83850e7	2.76409
$537$	6.23298e6	0.932739
$538$	1.67843e7	2.50004
$539$	−645943.	−0.0957684
$540$	−2.08739e7	−3.08049
$541$	1.48286e6	0.217825	0.108913	−	0.994051i	$-0.465263\pi$
$541$	1.48286e6	0.217825	0.108913	+	0.994051i	$0.465263\pi$
$542$	−9.53266e6	−1.39385
$543$	−3.51076e6	−0.510978
$544$	−5.25654e6	−0.761558
$545$	8.77174e6	1.26501
$546$	−8.24472e6	−1.18357
$547$	299209.	0.0427569
$547$	299209.	0.0427569
$548$	−3.86164e6	−0.549314
$549$	−3.79588e6	−0.537503
$550$	−2.22696e7	−3.13910
$551$	−2.99183e6	−0.419815
$552$	−1.70722e7	−2.38474
$553$	4.40360e6	0.612344
$554$	8.81366e6	1.22006
$555$	1.75090e7	2.41284
$556$	1.58254e6	0.217104
$557$	1.20776e7	1.64946	0.824729	−	0.565529i	$-0.191328\pi$
$557$	1.20776e7	1.64946	0.824729	+	0.565529i	$0.191328\pi$
$558$	6.07631e6	0.826141
$559$	−3.08833e6	−0.418018
$560$	1.89254e7	2.55021
$561$	−8.22676e6	−1.10363
$562$	7.57439e6	1.01160
$563$	−5.23506e6	−0.696067	−0.348033	−	0.937482i	$-0.613150\pi$
$563$	−5.23506e6	−0.696067	−0.348033	+	0.937482i	$0.613150\pi$
$564$	1.04792e6	0.138718
$565$	−2.40069e7	−3.16384
$566$	1.09045e7	1.43075
$567$	8.70983e6	1.13776
$568$	3.13550e6	0.407790
$569$	−8.37646e6	−1.08463	−0.542313	−	0.840177i	$-0.682451\pi$
$569$	−8.37646e6	−1.08463	−0.542313	+	0.840177i	$0.682451\pi$
$570$	1.81803e7	2.34377
$571$	5.64690e6	0.724803	0.362401	−	0.932022i	$-0.381957\pi$
$571$	5.64690e6	0.724803	0.362401	+	0.932022i	$0.381957\pi$
$572$	7.65935e6	0.978818
$573$	1.38568e6	0.176310
$574$	4.47161e6	0.566479
$575$	−1.93452e7	−2.44008
$576$	−1.16366e6	−0.146140
$577$	−3.76306e6	−0.470545	−0.235273	−	0.971929i	$-0.575598\pi$
$577$	−3.76306e6	−0.470545	−0.235273	+	0.971929i	$0.575598\pi$
$578$	−1.00985e7	−1.25729
$579$	−8.17430e6	−1.01334
$580$	−2.18060e7	−2.69158
$581$	1.47099e7	1.80788
$582$	6.61844e6	0.809931
$583$	9.11294e6	1.11042
$584$	−9.44955e6	−1.14651
$585$	−3.10839e6	−0.375531
$586$	−1.71790e7	−2.06659
$587$	−1.38000e7	−1.65305	−0.826523	−	0.562903i	$-0.809684\pi$
$587$	−1.38000e7	−1.65305	−0.826523	+	0.562903i	$0.809684\pi$
$588$	2.71716e6	0.324095
$589$	7.41591e6	0.880798
$590$	1.35808e7	1.60619
$591$	1.17610e7	1.38508
$592$	1.43125e7	1.67846
$593$	−1.49481e7	−1.74561	−0.872807	−	0.488066i	$-0.837702\pi$
$593$	−1.49481e7	−1.74561	−0.872807	+	0.488066i	$0.837702\pi$
$594$	−8.66895e6	−1.00809
$595$	1.94391e7	2.25104
$596$	1.89359e7	2.18358
$597$	−4.50659e6	−0.517502
$598$	9.74469e6	1.11433
$599$	−5.36238e6	−0.610647	−0.305324	−	0.952249i	$-0.598765\pi$
$599$	−5.36238e6	−0.610647	−0.305324	+	0.952249i	$0.598765\pi$
$600$	5.01563e7	5.68784
$601$	1.08778e7	1.22844	0.614221	−	0.789134i	$-0.289470\pi$
$601$	1.08778e7	1.22844	0.614221	+	0.789134i	$0.289470\pi$
$602$	−9.91656e6	−1.11524
$603$	−3.95151e6	−0.442558
$604$	1.56130e7	1.74138
$605$	7.69866e6	0.855119
$606$	−8.40922e6	−0.930195
$607$	5.53009e6	0.609201	0.304601	−	0.952480i	$-0.401477\pi$
$607$	5.53009e6	0.609201	0.304601	+	0.952480i	$0.401477\pi$
$608$	3.29399e6	0.361379
$609$	6.65593e6	0.727220
$610$	−4.94527e7	−5.38103
$611$	−320260.	−0.0347056
$612$	8.53981e6	0.921658
$613$	−8.70296e6	−0.935440	−0.467720	−	0.883877i	$-0.654924\pi$
$613$	−8.70296e6	−0.935440	−0.467720	+	0.883877i	$0.654924\pi$
$614$	−3.00596e6	−0.321782
$615$	6.83164e6	0.728345
$616$	1.31680e7	1.39820
$617$	−1.36184e7	−1.44017	−0.720083	−	0.693887i	$-0.755897\pi$
$617$	−1.36184e7	−1.44017	−0.720083	+	0.693887i	$0.755897\pi$
$618$	2.54720e7	2.68282
$619$	1.36838e7	1.43542	0.717712	−	0.696340i	$-0.245190\pi$
$619$	1.36838e7	1.43542	0.717712	+	0.696340i	$0.245190\pi$
$620$	5.40510e7	5.64709
$621$	−7.53059e6	−0.783610
$622$	−2.86842e7	−2.97281
$623$	−2.94716e6	−0.304217
$624$	−1.02966e7	−1.05860
$625$	2.35098e7	2.40740
$626$	1.75654e7	1.79153
$627$	5.15526e6	0.523699
$628$	2.75673e7	2.78930
$629$	1.47010e7	1.48156
$630$	−9.98096e6	−1.00189
$631$	−1.16466e7	−1.16446	−0.582232	−	0.813023i	$-0.697820\pi$
$631$	−1.16466e7	−1.16446	−0.582232	+	0.813023i	$0.697820\pi$
$632$	1.34943e7	1.34388
$633$	−1.01943e7	−1.01122
$634$	1.77509e7	1.75387
$635$	3.23888e7	3.18758
$636$	−3.83336e7	−3.75783
$637$	−830400.	−0.0810847
$638$	−9.05606e6	−0.880821
$639$	−673918.	−0.0652912
$640$	−2.63140e7	−2.53943
$641$	−2.65889e6	−0.255597	−0.127798	−	0.991800i	$-0.540791\pi$
$641$	−2.65889e6	−0.255597	−0.127798	+	0.991800i	$0.540791\pi$
$642$	−2.72994e7	−2.61406
$643$	3.87074e6	0.369204	0.184602	−	0.982813i	$-0.440900\pi$
$643$	3.87074e6	0.369204	0.184602	+	0.982813i	$0.440900\pi$
$644$	2.13644e7	2.02991
$645$	−1.51503e7	−1.43391
$646$	1.52647e7	1.43915
$647$	7.86143e6	0.738314	0.369157	−	0.929367i	$-0.379647\pi$
$647$	7.86143e6	0.738314	0.369157	+	0.929367i	$0.379647\pi$
$648$	2.66903e7	2.49699
$649$	3.85101e6	0.358891
$650$	−2.86289e7	−2.65780
$651$	−1.64982e7	−1.52575
$652$	−2.46761e7	−2.27331
$653$	−8.49492e6	−0.779608	−0.389804	−	0.920898i	$-0.627457\pi$
$653$	−8.49492e6	−0.779608	−0.389804	+	0.920898i	$0.627457\pi$
$654$	−1.53239e7	−1.40096
$655$	8.19307e6	0.746180
$656$	5.58446e6	0.506665
$657$	2.03100e6	0.183568
$658$	−1.02835e6	−0.0925922
$659$	−5.55392e6	−0.498180	−0.249090	−	0.968480i	$-0.580131\pi$
$659$	−5.55392e6	−0.498180	−0.249090	+	0.968480i	$0.580131\pi$
$660$	3.75743e7	3.35761
$661$	−1.98363e7	−1.76586	−0.882931	−	0.469503i	$-0.844433\pi$
$661$	−1.98363e7	−1.76586	−0.882931	+	0.469503i	$0.844433\pi$
$662$	−862648.	−0.0765048
$663$	−1.05760e7	−0.934412
$664$	4.50770e7	3.96766
$665$	−1.21814e7	−1.06818
$666$	−7.54819e6	−0.659412
$667$	−7.86686e6	−0.684679
$668$	1.22185e7	1.05944
$669$	−3.85579e6	−0.333079
$670$	−5.14804e7	−4.43052
$671$	−1.40229e7	−1.20235
$672$	−7.32814e6	−0.625995
$673$	−3.18347e6	−0.270934	−0.135467	−	0.990782i	$-0.543253\pi$
$673$	−3.18347e6	−0.270934	−0.135467	+	0.990782i	$0.543253\pi$
$674$	3.75215e7	3.18149
$675$	2.21241e7	1.86899
$676$	−1.57277e7	−1.32373
$677$	1.83494e7	1.53869	0.769344	−	0.638835i	$-0.220583\pi$
$677$	1.83494e7	1.53869	0.769344	+	0.638835i	$0.220583\pi$
$678$	4.19391e7	3.50384
$679$	−4.43456e6	−0.369127
$680$	5.95688e7	4.94023
$681$	−3.96672e6	−0.327766
$682$	2.24474e7	1.84802
$683$	1.64911e7	1.35269	0.676346	−	0.736584i	$-0.263562\pi$
$683$	1.64911e7	1.35269	0.676346	+	0.736584i	$0.263562\pi$
$684$	−5.35143e6	−0.437351
$685$	5.78952e6	0.471429
$686$	−2.30709e7	−1.87178
$687$	1.94787e7	1.57459
$688$	−1.23845e7	−0.997487
$689$	1.17153e7	0.940164
$690$	4.78042e7	3.82247
$691$	−1.14414e7	−0.911556	−0.455778	−	0.890093i	$-0.650639\pi$
$691$	−1.14414e7	−0.911556	−0.455778	+	0.890093i	$0.650639\pi$
$692$	3.91164e7	3.10523
$693$	−2.83023e6	−0.223866
$694$	4.30043e6	0.338932
$695$	−2.37260e6	−0.186321
$696$	2.03964e7	1.59599
$697$	5.73601e6	0.447227
$698$	1.26053e7	0.979295
$699$	1.14381e7	0.885448
$700$	−6.27665e7	−4.84153
$701$	−7.31063e6	−0.561901	−0.280950	−	0.959722i	$-0.590650\pi$
$701$	−7.31063e6	−0.561901	−0.280950	+	0.959722i	$0.590650\pi$
$702$	−1.11445e7	−0.853527
$703$	−9.21228e6	−0.703038
$704$	−4.29885e6	−0.326904
$705$	−1.57109e6	−0.119050
$706$	4.23263e7	3.19594
$707$	5.63444e6	0.423938
$708$	−1.61993e7	−1.21454
$709$	−2.32717e7	−1.73865	−0.869327	−	0.494237i	$-0.835447\pi$
$709$	−2.32717e7	−1.73865	−0.869327	+	0.494237i	$0.835447\pi$
$710$	−8.77982e6	−0.653641
$711$	−2.90036e6	−0.215168
$712$	−9.03124e6	−0.667648
$713$	1.94997e7	1.43650
$714$	−3.39593e7	−2.49295
$715$	−1.14832e7	−0.840035
$716$	−2.39024e7	−1.74245
$717$	1.05319e6	0.0765082
$718$	3.60931e7	2.61284
$719$	1.33862e7	0.965682	0.482841	−	0.875708i	$-0.339605\pi$
$719$	1.33862e7	0.965682	0.482841	+	0.875708i	$0.339605\pi$
$720$	−1.24649e7	−0.896104
$721$	−1.70671e7	−1.22270
$722$	1.53041e7	1.09261
$723$	2.49100e7	1.77226
$724$	1.34632e7	0.954556
$725$	2.31120e7	1.63303
$726$	−1.34493e7	−0.947016
$727$	1.95071e6	0.136885	0.0684425	−	0.997655i	$-0.478197\pi$
$727$	1.95071e6	0.136885	0.0684425	+	0.997655i	$0.478197\pi$
$728$	1.69283e7	1.18382
$729$	7.07217e6	0.492872
$730$	2.64600e7	1.83773
$731$	−1.27206e7	−0.880469
$732$	5.89875e7	4.06895
$733$	8.41812e6	0.578702	0.289351	−	0.957223i	$-0.406561\pi$
$733$	8.41812e6	0.578702	0.289351	+	0.957223i	$0.406561\pi$
$734$	−1.72063e6	−0.117882
$735$	−4.07367e6	−0.278142
$736$	8.66137e6	0.589375
$737$	−1.45979e7	−0.989969
$738$	−2.94515e6	−0.199052
$739$	1.92463e7	1.29639	0.648196	−	0.761473i	$-0.275524\pi$
$739$	1.92463e7	1.29639	0.648196	+	0.761473i	$0.275524\pi$
$740$	−6.71440e7	−4.50742
$741$	6.62741e6	0.443403
$742$	3.76174e7	2.50830
$743$	−2.29549e6	−0.152547	−0.0762733	−	0.997087i	$-0.524302\pi$
$743$	−2.29549e6	−0.152547	−0.0762733	+	0.997087i	$0.524302\pi$
$744$	−5.05568e7	−3.34848
$745$	−2.83893e7	−1.87398
$746$	−4.66844e7	−3.07131
$747$	−9.68845e6	−0.635262
$748$	3.15483e7	2.06168
$749$	1.82914e7	1.19136
$750$	−8.22273e7	−5.33781
$751$	1.71530e7	1.10979	0.554894	−	0.831921i	$-0.312759\pi$
$751$	1.71530e7	1.10979	0.554894	+	0.831921i	$0.312759\pi$
$752$	−1.28427e6	−0.0828155
$753$	6.60608e6	0.424577
$754$	−1.16421e7	−0.745769
$755$	−2.34076e7	−1.49448
$756$	−2.44333e7	−1.55481
$757$	3.04782e7	1.93308	0.966540	−	0.256515i	$-0.0825743\pi$
$757$	3.04782e7	1.93308	0.966540	+	0.256515i	$0.0825743\pi$
$758$	1.90025e6	0.120126
$759$	1.35555e7	0.854104
$760$	−3.73285e7	−2.34427
$761$	−1.64124e7	−1.02733	−0.513664	−	0.857991i	$-0.671712\pi$
$761$	−1.64124e7	−1.02733	−0.513664	+	0.857991i	$0.671712\pi$
$762$	−5.65820e7	−3.53013
$763$	1.02675e7	0.638488
$764$	−5.31386e6	−0.329364
$765$	−1.28032e7	−0.790979
$766$	1.07509e7	0.662022
$767$	4.95072e6	0.303864
$768$	3.75685e7	2.29837
$769$	−1.91600e7	−1.16837	−0.584185	−	0.811620i	$-0.698586\pi$
$769$	−1.91600e7	−1.16837	−0.584185	+	0.811620i	$0.698586\pi$
$770$	−3.68722e7	−2.24116
$771$	−2.93868e7	−1.78039
$772$	3.13471e7	1.89301
$773$	1.95043e7	1.17404	0.587018	−	0.809574i	$-0.300302\pi$
$773$	1.95043e7	1.17404	0.587018	+	0.809574i	$0.300302\pi$
$774$	6.53137e6	0.391879
$775$	−5.72883e7	−3.42619
$776$	−1.35892e7	−0.810102
$777$	2.04946e7	1.21783
$778$	−8.01689e6	−0.474850
$779$	−3.59445e6	−0.212221
$780$	4.83041e7	2.84280
$781$	−2.48963e6	−0.146052
$782$	4.01376e7	2.34712
$783$	8.99690e6	0.524431
$784$	−3.32998e6	−0.193487
$785$	−4.13299e7	−2.39381
$786$	−1.43130e7	−0.826369
$787$	−2.22559e7	−1.28088	−0.640439	−	0.768009i	$-0.721248\pi$
$787$	−2.22559e7	−1.28088	−0.640439	+	0.768009i	$0.721248\pi$
$788$	−4.51013e7	−2.58746
$789$	−3.29822e7	−1.88620
$790$	−3.77859e7	−2.15408
$791$	−2.81005e7	−1.59688
$792$	−8.67291e6	−0.491306
$793$	−1.80274e7	−1.01800
$794$	−5.54520e7	−3.12152
$795$	5.74712e7	3.22502
$796$	1.72820e7	0.966745
$797$	1.83386e7	1.02263	0.511316	−	0.859393i	$-0.329158\pi$
$797$	1.83386e7	1.02263	0.511316	+	0.859393i	$0.329158\pi$
$798$	2.12804e7	1.18297
$799$	−1.31912e6	−0.0731002
$800$	−2.54462e7	−1.40572
$801$	1.94110e6	0.106897
$802$	−2.98614e7	−1.63936
$803$	7.50305e6	0.410628
$804$	6.14060e7	3.35020
$805$	−3.20303e7	−1.74209
$806$	2.88576e7	1.56467
$807$	3.00153e7	1.62240
$808$	1.72661e7	0.930392
$809$	3.65188e7	1.96175	0.980877	−	0.194627i	$-0.0623497\pi$
$809$	3.65188e7	1.96175	0.980877	+	0.194627i	$0.0623497\pi$
$810$	−7.47363e7	−4.00239
$811$	1.92393e7	1.02716	0.513579	−	0.858042i	$-0.328319\pi$
$811$	1.92393e7	1.02716	0.513579	+	0.858042i	$0.328319\pi$
$812$	−2.55244e7	−1.35852
$813$	−1.70472e7	−0.904540
$814$	−2.78849e7	−1.47506
$815$	3.69953e7	1.95098
$816$	−4.24108e7	−2.22972
$817$	7.97130e6	0.417805
$818$	6.44271e6	0.336655
$819$	−3.63843e6	−0.189542
$820$	−2.61982e7	−1.36062
$821$	1.55514e7	0.805215	0.402608	−	0.915373i	$-0.368104\pi$
$821$	1.55514e7	0.805215	0.402608	+	0.915373i	$0.368104\pi$
$822$	−1.01141e7	−0.522091
$823$	−1.38166e7	−0.711051	−0.355526	−	0.934667i	$-0.615698\pi$
$823$	−1.38166e7	−0.711051	−0.355526	+	0.934667i	$0.615698\pi$
$824$	−5.23001e7	−2.68339
$825$	−3.98246e7	−2.03712
$826$	1.58966e7	0.810690
$827$	1.08169e7	0.549968	0.274984	−	0.961449i	$-0.411327\pi$
$827$	1.08169e7	0.549968	0.274984	+	0.961449i	$0.411327\pi$
$828$	−1.40713e7	−0.713278
$829$	2.86230e7	1.44653	0.723267	−	0.690569i	$-0.242640\pi$
$829$	2.86230e7	1.44653	0.723267	+	0.690569i	$0.242640\pi$
$830$	−1.26221e8	−6.35971
$831$	1.57615e7	0.791760
$832$	−5.52644e6	−0.276781
$833$	−3.42035e6	−0.170788
$834$	4.14485e6	0.206345
$835$	−1.83184e7	−0.909227
$836$	−1.97696e7	−0.978321
$837$	−2.23008e7	−1.10029
$838$	−9.60598e6	−0.472532
$839$	−1.86791e7	−0.916116	−0.458058	−	0.888922i	$-0.651455\pi$
$839$	−1.86791e7	−0.916116	−0.458058	+	0.888922i	$0.651455\pi$
$840$	8.30449e7	4.06083
$841$	−1.11125e7	−0.541778
$842$	2.12574e7	1.03331
$843$	1.35453e7	0.656476
$844$	3.90934e7	1.88907
$845$	2.35796e7	1.13604
$846$	677302.	0.0325354
$847$	9.01143e6	0.431604
$848$	4.69792e7	2.24345
$849$	1.95005e7	0.928487
$850$	−1.17920e8	−5.59810
$851$	−2.42232e7	−1.14659
$852$	1.04726e7	0.494261
$853$	2.79936e7	1.31730	0.658652	−	0.752448i	$-0.271127\pi$
$853$	2.79936e7	1.31730	0.658652	+	0.752448i	$0.271127\pi$
$854$	−5.78854e7	−2.71597
$855$	8.02307e6	0.375340
$856$	5.60520e7	2.61461
$857$	−6.89480e6	−0.320678	−0.160339	−	0.987062i	$-0.551259\pi$
$857$	−6.89480e6	−0.320678	−0.160339	+	0.987062i	$0.551259\pi$
$858$	2.00607e7	0.930310
$859$	−1.18070e7	−0.545957	−0.272978	−	0.962020i	$-0.588009\pi$
$859$	−1.18070e7	−0.545957	−0.272978	+	0.962020i	$0.588009\pi$
$860$	5.80990e7	2.67869
$861$	7.99657e6	0.367617
$862$	−3.55658e7	−1.63029
$863$	−3.36955e7	−1.54008	−0.770042	−	0.637993i	$-0.779765\pi$
$863$	−3.36955e7	−1.54008	−0.770042	+	0.637993i	$0.779765\pi$
$864$	−9.90554e6	−0.451433
$865$	−5.86447e7	−2.66495
$866$	1.88914e7	0.855992
$867$	−1.80591e7	−0.815922
$868$	6.32678e7	2.85025
$869$	−1.07147e7	−0.481315
$870$	−5.71124e7	−2.55819
$871$	−1.87665e7	−0.838181
$872$	3.14636e7	1.40125
$873$	2.92075e6	0.129705
$874$	−2.51520e7	−1.11377
$875$	5.50949e7	2.43271
$876$	−3.15616e7	−1.38963
$877$	−2.17343e7	−0.954215	−0.477107	−	0.878845i	$-0.658315\pi$
$877$	−2.17343e7	−0.954215	−0.477107	+	0.878845i	$0.658315\pi$
$878$	2.22142e7	0.972510
$879$	−3.07211e7	−1.34111
$880$	−4.60486e7	−2.00452
$881$	9.23692e6	0.400947	0.200474	−	0.979699i	$-0.435752\pi$
$881$	9.23692e6	0.400947	0.200474	+	0.979699i	$0.435752\pi$
$882$	1.75617e6	0.0760145
$883$	2.77406e7	1.19733	0.598666	−	0.800999i	$-0.295698\pi$
$883$	2.77406e7	1.19733	0.598666	+	0.800999i	$0.295698\pi$
$884$	4.05573e7	1.74557
$885$	2.42866e7	1.04234
$886$	4.25811e7	1.82235
$887$	1.15027e7	0.490899	0.245450	−	0.969409i	$-0.421064\pi$
$887$	1.15027e7	0.490899	0.245450	+	0.969409i	$0.421064\pi$
$888$	6.28034e7	2.67270
$889$	3.79117e7	1.60886
$890$	2.52886e7	1.07016
$891$	−2.11924e7	−0.894306
$892$	1.47863e7	0.622225
$893$	826622.	0.0346879
$894$	4.95951e7	2.07537
$895$	3.58354e7	1.49539
$896$	−3.08011e7	−1.28173
$897$	1.74264e7	0.723148
$898$	2.87467e7	1.18959
$899$	−2.32966e7	−0.961377
$900$	4.13401e7	1.70124
$901$	4.82542e7	1.98026
$902$	−1.08801e7	−0.445264
$903$	−1.77338e7	−0.723739
$904$	−8.61108e7	−3.50458
$905$	−2.01845e7	−0.819213
$906$	4.08922e7	1.65508
$907$	3.48268e7	1.40571	0.702854	−	0.711334i	$-0.251909\pi$
$907$	3.48268e7	1.40571	0.702854	+	0.711334i	$0.251909\pi$
$908$	1.52117e7	0.612298
$909$	−3.71103e6	−0.148965
$910$	−4.74016e7	−1.89753
$911$	4.91635e7	1.96267	0.981334	−	0.192309i	$-0.0615975\pi$
$911$	4.91635e7	1.96267	0.981334	+	0.192309i	$0.0615975\pi$
$912$	2.65765e7	1.05806
$913$	−3.57916e7	−1.42103
$914$	4.03672e7	1.59832
$915$	−8.84363e7	−3.49203
$916$	−7.46977e7	−2.94150
$917$	9.59015e6	0.376619
$918$	−4.59032e7	−1.79778
$919$	−4.03449e7	−1.57580	−0.787898	−	0.615806i	$-0.788830\pi$
$919$	−4.03449e7	−1.57580	−0.787898	+	0.615806i	$0.788830\pi$
$920$	−9.81534e7	−3.82328
$921$	−5.37555e6	−0.208821
$922$	1.26485e7	0.490019
$923$	−3.20057e6	−0.123658
$924$	4.39814e7	1.69469
$925$	7.11654e7	2.73473
$926$	6.52654e7	2.50124
$927$	1.12409e7	0.429638
$928$	−1.03479e7	−0.394440
$929$	1.07020e7	0.406842	0.203421	−	0.979091i	$-0.434794\pi$
$929$	1.07020e7	0.406842	0.203421	+	0.979091i	$0.434794\pi$
$930$	1.41566e8	5.36724
$931$	2.14335e6	0.0810435
$932$	−4.38634e7	−1.65410
$933$	−5.12959e7	−1.92921
$934$	1.66507e7	0.624546
$935$	−4.72983e7	−1.76936
$936$	−1.11496e7	−0.415976
$937$	−8.59893e6	−0.319960	−0.159980	−	0.987120i	$-0.551143\pi$
$937$	−8.59893e6	−0.319960	−0.159980	+	0.987120i	$0.551143\pi$
$938$	−6.02588e7	−2.23621
$939$	3.14122e7	1.16261
$940$	6.02486e6	0.222396
$941$	−3.88926e6	−0.143184	−0.0715918	−	0.997434i	$-0.522808\pi$
$941$	−3.88926e6	−0.143184	−0.0715918	+	0.997434i	$0.522808\pi$
$942$	7.22017e7	2.65106
$943$	−9.45140e6	−0.346112
$944$	1.98528e7	0.725090
$945$	3.66314e7	1.33436
$946$	2.41286e7	0.876604
$947$	−2.78493e7	−1.00911	−0.504556	−	0.863379i	$-0.668344\pi$
$947$	−2.78493e7	−1.00911	−0.504556	+	0.863379i	$0.668344\pi$
$948$	4.50713e7	1.62884
$949$	9.64564e6	0.347669
$950$	7.38942e7	2.65645
$951$	3.17439e7	1.13818
$952$	6.97265e7	2.49348
$953$	−3.07223e7	−1.09578	−0.547888	−	0.836552i	$-0.684568\pi$
$953$	−3.07223e7	−1.09578	−0.547888	+	0.836552i	$0.684568\pi$
$954$	−2.47760e7	−0.881376
$955$	7.96674e6	0.282665
$956$	−4.03880e6	−0.142925
$957$	−1.61949e7	−0.571610
$958$	7.06464e7	2.48700
$959$	6.77674e6	0.237944
$960$	−2.71109e7	−0.949435
$961$	2.91166e7	1.01703
$962$	−3.58478e7	−1.24889
$963$	−1.20473e7	−0.418625
$964$	−9.55256e7	−3.31076
$965$	−4.69967e7	−1.62461
$966$	5.59558e7	1.92931
$967$	6.99194e6	0.240454	0.120227	−	0.992746i	$-0.461638\pi$
$967$	6.99194e6	0.240454	0.120227	+	0.992746i	$0.461638\pi$
$968$	2.76145e7	0.947216
$969$	2.72978e7	0.933937
$970$	3.80515e7	1.29850
$971$	−1.87874e7	−0.639466	−0.319733	−	0.947508i	$-0.603593\pi$
$971$	−1.87874e7	−0.639466	−0.319733	+	0.947508i	$0.603593\pi$
$972$	4.00264e7	1.35888
$973$	−2.77718e6	−0.0940419
$974$	5.13991e7	1.73603
$975$	−5.11971e7	−1.72478
$976$	−7.22913e7	−2.42919
$977$	2.84347e7	0.953043	0.476521	−	0.879163i	$-0.341897\pi$
$977$	2.84347e7	0.953043	0.476521	+	0.879163i	$0.341897\pi$
$978$	−6.46295e7	−2.16065
$979$	7.17091e6	0.239121
$980$	1.56218e7	0.519597
$981$	−6.76251e6	−0.224355
$982$	5.09084e7	1.68465
$983$	−2.62539e7	−0.866583	−0.433291	−	0.901254i	$-0.642648\pi$
$983$	−2.62539e7	−0.866583	−0.433291	+	0.901254i	$0.642648\pi$
$984$	2.45046e7	0.806789
$985$	6.76175e7	2.22059
$986$	−4.79530e7	−1.57081
$987$	−1.83899e6	−0.0600878
$988$	−2.54150e7	−0.828320
$989$	2.09601e7	0.681401
$990$	2.42853e7	0.787508
$991$	−5.72251e7	−1.85098	−0.925492	−	0.378768i	$-0.876348\pi$
$991$	−5.72251e7	−1.85098	−0.925492	+	0.378768i	$0.876348\pi$
$992$	2.56494e7	0.827559
$993$	−1.54267e6	−0.0496478
$994$	−1.02769e7	−0.329912
$995$	−2.59098e7	−0.829673
$996$	1.50557e8	4.80899
$997$	3.39527e7	1.08177	0.540887	−	0.841095i	$-0.318089\pi$
$997$	3.39527e7	1.08177	0.540887	+	0.841095i	$0.318089\pi$
$998$	−3.38998e7	−1.07738
$999$	2.77028e7	0.878233

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.6.a.b.1.7	✓	117

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.6.a.b.1.7	✓	117	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-10.0439 q^{2} -17.9614 q^{3} +68.8790 q^{4} -103.266 q^{5} +180.402 q^{6} -120.875 q^{7} -370.407 q^{8} +79.6121 q^{9} +O(q^{10})\)	\(q-10.0439 q^{2} -17.9614 q^{3} +68.8790 q^{4} -103.266 q^{5} +180.402 q^{6} -120.875 q^{7} -370.407 q^{8} +79.6121 q^{9} +1037.19 q^{10} +294.108 q^{11} -1237.16 q^{12} +378.094 q^{13} +1214.05 q^{14} +1854.80 q^{15} +1516.19 q^{16} +1557.34 q^{17} -799.612 q^{18} -975.898 q^{19} -7112.86 q^{20} +2171.08 q^{21} -2953.97 q^{22} -2566.07 q^{23} +6653.04 q^{24} +7538.86 q^{25} -3797.52 q^{26} +2934.68 q^{27} -8325.74 q^{28} +3065.72 q^{29} -18629.4 q^{30} -7599.06 q^{31} -3375.34 q^{32} -5282.58 q^{33} -15641.7 q^{34} +12482.3 q^{35} +5483.60 q^{36} +9439.81 q^{37} +9801.77 q^{38} -6791.09 q^{39} +38250.5 q^{40} +3683.22 q^{41} -21806.0 q^{42} -8168.17 q^{43} +20257.8 q^{44} -8221.22 q^{45} +25773.2 q^{46} -847.038 q^{47} -27232.9 q^{48} -2196.28 q^{49} -75719.2 q^{50} -27972.0 q^{51} +26042.7 q^{52} +30985.1 q^{53} -29475.5 q^{54} -30371.3 q^{55} +44772.9 q^{56} +17528.5 q^{57} -30791.7 q^{58} +13093.9 q^{59} +127757. q^{60} -47679.6 q^{61} +76323.9 q^{62} -9623.10 q^{63} -14616.6 q^{64} -39044.2 q^{65} +53057.5 q^{66} -49634.5 q^{67} +107268. q^{68} +46090.2 q^{69} -125370. q^{70} -8465.02 q^{71} -29488.9 q^{72} +25511.3 q^{73} -94812.0 q^{74} -135408. q^{75} -67218.8 q^{76} -35550.2 q^{77} +68208.7 q^{78} -36431.1 q^{79} -156571. q^{80} -72056.7 q^{81} -36993.7 q^{82} -121696. q^{83} +149542. q^{84} -160820. q^{85} +82039.9 q^{86} -55064.7 q^{87} -108940. q^{88} +24381.9 q^{89} +82572.7 q^{90} -45702.0 q^{91} -176748. q^{92} +136490. q^{93} +8507.53 q^{94} +100777. q^{95} +60625.9 q^{96} +36687.2 q^{97} +22059.1 q^{98} +23414.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9}+O(q^{10}) \) 117 * q + 24 * q^2 + 100 * q^3 + 1962 * q^4 + 749 * q^5 + 306 * q^6 + 393 * q^7 + 1152 * q^8 + 10671 * q^9	\( 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9} + 850 q^{10} + 1798 q^{11} + 5361 q^{12} + 4419 q^{13} + 3847 q^{14} + 1913 q^{15} + 34722 q^{16} + 15252 q^{17} + 2367 q^{18} + 1052 q^{19} + 23568 q^{20} + 9212 q^{21} + 9176 q^{22} + 18178 q^{23} + 15983 q^{24} + 84312 q^{25} + 21552 q^{26} + 30883 q^{27} + 23528 q^{28} + 43620 q^{29} + 23582 q^{30} + 13127 q^{31} + 49108 q^{32} + 39222 q^{33} + 32097 q^{34} + 52467 q^{35} + 217244 q^{36} + 56152 q^{37} + 76245 q^{38} + 28595 q^{39} + 20368 q^{40} + 46679 q^{41} + 78924 q^{42} + 39058 q^{43} + 78528 q^{44} + 185770 q^{45} + 41430 q^{46} + 150268 q^{47} + 180930 q^{48} + 323802 q^{49} + 91604 q^{50} + 43367 q^{51} + 136030 q^{52} + 297398 q^{53} + 116761 q^{54} + 94579 q^{55} + 173545 q^{56} + 164740 q^{57} + 87844 q^{58} + 135778 q^{59} + 114650 q^{60} + 166976 q^{61} + 229394 q^{62} + 147179 q^{63} + 630138 q^{64} + 216626 q^{65} + 82380 q^{66} + 133444 q^{67} + 634057 q^{68} + 232986 q^{69} + 30943 q^{70} + 126787 q^{71} + 78583 q^{72} + 241702 q^{73} + 242589 q^{74} + 374853 q^{75} + 90228 q^{76} + 766693 q^{77} + 82537 q^{78} + 117230 q^{79} + 730509 q^{80} + 1051409 q^{81} + 468130 q^{82} + 368467 q^{83} + 234191 q^{84} + 261997 q^{85} + 230487 q^{86} + 214239 q^{87} + 247415 q^{88} + 494902 q^{89} + 41821 q^{90} + 259647 q^{91} + 663682 q^{92} + 767344 q^{93} + 373605 q^{94} + 426186 q^{95} + 474162 q^{96} + 733038 q^{97} + 461746 q^{98} + 334651 q^{99}+O(q^{100}) \) 117 * q + 24 * q^2 + 100 * q^3 + 1962 * q^4 + 749 * q^5 + 306 * q^6 + 393 * q^7 + 1152 * q^8 + 10671 * q^9 + 850 * q^10 + 1798 * q^11 + 5361 * q^12 + 4419 * q^13 + 3847 * q^14 + 1913 * q^15 + 34722 * q^16 + 15252 * q^17 + 2367 * q^18 + 1052 * q^19 + 23568 * q^20 + 9212 * q^21 + 9176 * q^22 + 18178 * q^23 + 15983 * q^24 + 84312 * q^25 + 21552 * q^26 + 30883 * q^27 + 23528 * q^28 + 43620 * q^29 + 23582 * q^30 + 13127 * q^31 + 49108 * q^32 + 39222 * q^33 + 32097 * q^34 + 52467 * q^35 + 217244 * q^36 + 56152 * q^37 + 76245 * q^38 + 28595 * q^39 + 20368 * q^40 + 46679 * q^41 + 78924 * q^42 + 39058 * q^43 + 78528 * q^44 + 185770 * q^45 + 41430 * q^46 + 150268 * q^47 + 180930 * q^48 + 323802 * q^49 + 91604 * q^50 + 43367 * q^51 + 136030 * q^52 + 297398 * q^53 + 116761 * q^54 + 94579 * q^55 + 173545 * q^56 + 164740 * q^57 + 87844 * q^58 + 135778 * q^59 + 114650 * q^60 + 166976 * q^61 + 229394 * q^62 + 147179 * q^63 + 630138 * q^64 + 216626 * q^65 + 82380 * q^66 + 133444 * q^67 + 634057 * q^68 + 232986 * q^69 + 30943 * q^70 + 126787 * q^71 + 78583 * q^72 + 241702 * q^73 + 242589 * q^74 + 374853 * q^75 + 90228 * q^76 + 766693 * q^77 + 82537 * q^78 + 117230 * q^79 + 730509 * q^80 + 1051409 * q^81 + 468130 * q^82 + 368467 * q^83 + 234191 * q^84 + 261997 * q^85 + 230487 * q^86 + 214239 * q^87 + 247415 * q^88 + 494902 * q^89 + 41821 * q^90 + 259647 * q^91 + 663682 * q^92 + 767344 * q^93 + 373605 * q^94 + 426186 * q^95 + 474162 * q^96 + 733038 * q^97 + 461746 * q^98 + 334651 * q^99

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