LMFDB - Embedded newform 547.6.a.b.1.16

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			1.16
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)

$f(q)$	$=$	$q-9.01126 q^{2} -22.0309 q^{3} +49.2028 q^{4} -64.3778 q^{5} +198.526 q^{6} +52.1292 q^{7} -155.019 q^{8} +242.362 q^{9} +O(q^{10})$	\(q-9.01126 q^{2} -22.0309 q^{3} +49.2028 q^{4} -64.3778 q^{5} +198.526 q^{6} +52.1292 q^{7} -155.019 q^{8} +242.362 q^{9} +580.125 q^{10} -266.294 q^{11} -1083.98 q^{12} -747.757 q^{13} -469.750 q^{14} +1418.30 q^{15} -177.572 q^{16} +453.099 q^{17} -2183.98 q^{18} +2642.38 q^{19} -3167.57 q^{20} -1148.46 q^{21} +2399.65 q^{22} +4094.41 q^{23} +3415.22 q^{24} +1019.50 q^{25} +6738.24 q^{26} +14.0622 q^{27} +2564.91 q^{28} +1837.94 q^{29} -12780.7 q^{30} -4171.87 q^{31} +6560.76 q^{32} +5866.71 q^{33} -4082.99 q^{34} -3355.96 q^{35} +11924.9 q^{36} +1614.37 q^{37} -23811.1 q^{38} +16473.8 q^{39} +9979.79 q^{40} +7793.39 q^{41} +10349.0 q^{42} +4992.68 q^{43} -13102.4 q^{44} -15602.7 q^{45} -36895.8 q^{46} -15546.1 q^{47} +3912.08 q^{48} -14089.5 q^{49} -9186.96 q^{50} -9982.19 q^{51} -36791.8 q^{52} -29241.1 q^{53} -126.718 q^{54} +17143.4 q^{55} -8081.03 q^{56} -58214.0 q^{57} -16562.2 q^{58} +44145.8 q^{59} +69784.5 q^{60} -42400.3 q^{61} +37593.8 q^{62} +12634.1 q^{63} -53438.4 q^{64} +48138.9 q^{65} -52866.5 q^{66} +18983.4 q^{67} +22293.7 q^{68} -90203.5 q^{69} +30241.5 q^{70} +870.255 q^{71} -37570.7 q^{72} +12322.8 q^{73} -14547.5 q^{74} -22460.5 q^{75} +130012. q^{76} -13881.7 q^{77} -148450. q^{78} -90496.7 q^{79} +11431.7 q^{80} -59203.7 q^{81} -70228.3 q^{82} +22533.7 q^{83} -56507.2 q^{84} -29169.5 q^{85} -44990.4 q^{86} -40491.6 q^{87} +41280.7 q^{88} +34756.7 q^{89} +140600. q^{90} -38980.0 q^{91} +201456. q^{92} +91910.2 q^{93} +140090. q^{94} -170110. q^{95} -144540. q^{96} -114596. q^{97} +126965. q^{98} -64539.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−9.01126	−1.59298	−0.796490	−	0.604651i	$-0.793313\pi$
$2$	−9.01126	−1.59298	−0.796490	+	0.604651i	$0.793313\pi$
$3$	−22.0309	−1.41328	−0.706642	−	0.707571i	$-0.749791\pi$
$3$	−22.0309	−1.41328	−0.706642	+	0.707571i	$0.749791\pi$
$4$	49.2028	1.53759
$5$	−64.3778	−1.15162	−0.575812	−	0.817582i	$-0.695314\pi$
$5$	−64.3778	−1.15162	−0.575812	+	0.817582i	$0.695314\pi$
$6$	198.526	2.25134
$7$	52.1292	0.402102	0.201051	−	0.979581i	$-0.435564\pi$
$7$	52.1292	0.402102	0.201051	+	0.979581i	$0.435564\pi$
$8$	−155.019	−0.856368
$9$	242.362	0.997373
$10$	580.125	1.83452
$11$	−266.294	−0.663560	−0.331780	−	0.943357i	$-0.607649\pi$
$11$	−266.294	−0.663560	−0.331780	+	0.943357i	$0.607649\pi$
$12$	−1083.98	−2.17305
$13$	−747.757	−1.22716	−0.613581	−	0.789631i	$-0.710272\pi$
$13$	−747.757	−1.22716	−0.613581	+	0.789631i	$0.710272\pi$
$14$	−469.750	−0.640541
$15$	1418.30	1.62757
$16$	−177.572	−0.173411
$17$	453.099	0.380251	0.190126	−	0.981760i	$-0.439110\pi$
$17$	453.099	0.380251	0.190126	+	0.981760i	$0.439110\pi$
$18$	−2183.98	−1.58880
$19$	2642.38	1.67923	0.839616	−	0.543180i	$-0.182780\pi$
$19$	2642.38	1.67923	0.839616	+	0.543180i	$0.182780\pi$
$20$	−3167.57	−1.77072
$21$	−1148.46	−0.568284
$22$	2399.65	1.05704
$23$	4094.41	1.61388	0.806940	−	0.590633i	$-0.201122\pi$
$23$	4094.41	1.61388	0.806940	+	0.590633i	$0.201122\pi$
$24$	3415.22	1.21029
$25$	1019.50	0.326239
$26$	6738.24	1.95485
$27$	14.0622	0.00371230
$28$	2564.91	0.618267
$29$	1837.94	0.405823	0.202912	−	0.979197i	$-0.434960\pi$
$29$	1837.94	0.405823	0.202912	+	0.979197i	$0.434960\pi$
$30$	−12780.7	−2.59269
$31$	−4171.87	−0.779698	−0.389849	−	0.920879i	$-0.627473\pi$
$31$	−4171.87	−0.779698	−0.389849	+	0.920879i	$0.627473\pi$
$32$	6560.76	1.13261
$33$	5866.71	0.937800
$34$	−4082.99	−0.605733
$35$	−3355.96	−0.463071
$36$	11924.9	1.53355
$37$	1614.37	0.193864	0.0969322	−	0.995291i	$-0.469097\pi$
$37$	1614.37	0.193864	0.0969322	+	0.995291i	$0.469097\pi$
$38$	−23811.1	−2.67499
$39$	16473.8	1.73433
$40$	9979.79	0.986214
$41$	7793.39	0.724047	0.362024	−	0.932169i	$-0.382086\pi$
$41$	7793.39	0.724047	0.362024	+	0.932169i	$0.382086\pi$
$42$	10349.0	0.905266
$43$	4992.68	0.411778	0.205889	−	0.978575i	$-0.433991\pi$
$43$	4992.68	0.411778	0.205889	+	0.978575i	$0.433991\pi$
$44$	−13102.4	−1.02028
$45$	−15602.7	−1.14860
$46$	−36895.8	−2.57088
$47$	−15546.1	−1.02654	−0.513272	−	0.858226i	$-0.671567\pi$
$47$	−15546.1	−1.02654	−0.513272	+	0.858226i	$0.671567\pi$
$48$	3912.08	0.245078
$49$	−14089.5	−0.838314
$50$	−9186.96	−0.519693
$51$	−9982.19	−0.537403
$52$	−36791.8	−1.88687
$53$	−29241.1	−1.42989	−0.714947	−	0.699179i	$-0.753549\pi$
$53$	−29241.1	−1.42989	−0.714947	+	0.699179i	$0.753549\pi$
$54$	−126.718	−0.00591362
$55$	17143.4	0.764172
$56$	−8081.03	−0.344347
$57$	−58214.0	−2.37323
$58$	−16562.2	−0.646469
$59$	44145.8	1.65105	0.825524	−	0.564368i	$-0.190880\pi$
$59$	44145.8	1.65105	0.825524	+	0.564368i	$0.190880\pi$
$60$	69784.5	2.50254
$61$	−42400.3	−1.45896	−0.729481	−	0.684001i	$-0.760238\pi$
$61$	−42400.3	−1.45896	−0.729481	+	0.684001i	$0.760238\pi$
$62$	37593.8	1.24204
$63$	12634.1	0.401046
$64$	−53438.4	−1.63081
$65$	48138.9	1.41323
$66$	−52866.5	−1.49390
$67$	18983.4	0.516639	0.258319	−	0.966060i	$-0.416831\pi$
$67$	18983.4	0.516639	0.258319	+	0.966060i	$0.416831\pi$
$68$	22293.7	0.584670
$69$	−90203.5	−2.28087
$70$	30241.5	0.737663
$71$	870.255	0.0204881	0.0102440	−	0.999948i	$-0.496739\pi$
$71$	870.255	0.0204881	0.0102440	+	0.999948i	$0.496739\pi$
$72$	−37570.7	−0.854118
$73$	12322.8	0.270646	0.135323	−	0.990802i	$-0.456793\pi$
$73$	12322.8	0.270646	0.135323	+	0.990802i	$0.456793\pi$
$74$	−14547.5	−0.308822
$75$	−22460.5	−0.461069
$76$	130012.	2.58197
$77$	−13881.7	−0.266819
$78$	−148450.	−2.76276
$79$	−90496.7	−1.63142	−0.815709	−	0.578463i	$-0.803653\pi$
$79$	−90496.7	−1.63142	−0.815709	+	0.578463i	$0.803653\pi$
$80$	11431.7	0.199704
$81$	−59203.7	−1.00262
$82$	−70228.3	−1.15339
$83$	22533.7	0.359035	0.179518	−	0.983755i	$-0.442546\pi$
$83$	22533.7	0.359035	0.179518	+	0.983755i	$0.442546\pi$
$84$	−56507.2	−0.873788
$85$	−29169.5	−0.437907
$86$	−44990.4	−0.655954
$87$	−40491.6	−0.573544
$88$	41280.7	0.568252
$89$	34756.7	0.465118	0.232559	−	0.972582i	$-0.425290\pi$
$89$	34756.7	0.465118	0.232559	+	0.972582i	$0.425290\pi$
$90$	140600.	1.82970
$91$	−38980.0	−0.493445
$92$	201456.	2.48148
$93$	91910.2	1.10194
$94$	140090.	1.63527
$95$	−170110.	−1.93385
$96$	−144540.	−1.60070
$97$	−114596.	−1.23663	−0.618313	−	0.785932i	$-0.712184\pi$
$97$	−114596.	−1.23663	−0.618313	+	0.785932i	$0.712184\pi$
$98$	126965.	1.33542
$99$	−64539.6	−0.661817
$100$	50162.2	0.501622
$101$	−29631.4	−0.289034	−0.144517	−	0.989502i	$-0.546163\pi$
$101$	−29631.4	−0.289034	−0.144517	+	0.989502i	$0.546163\pi$
$102$	89952.1	0.856073
$103$	−1795.17	−0.0166730	−0.00833649	−	0.999965i	$-0.502654\pi$
$103$	−1795.17	−0.0166730	−0.00833649	+	0.999965i	$0.502654\pi$
$104$	115917.	1.05090
$105$	73935.0	0.654450
$106$	263499.	2.27779
$107$	20147.0	0.170118	0.0850590	−	0.996376i	$-0.472892\pi$
$107$	20147.0	0.170118	0.0850590	+	0.996376i	$0.472892\pi$
$108$	691.899	0.00570799
$109$	48181.6	0.388432	0.194216	−	0.980959i	$-0.437784\pi$
$109$	48181.6	0.388432	0.194216	+	0.980959i	$0.437784\pi$
$110$	−154484.	−1.21731
$111$	−35566.0	−0.273986
$112$	−9256.71	−0.0697287
$113$	−259850.	−1.91437	−0.957185	−	0.289476i	$-0.906519\pi$
$113$	−259850.	−1.91437	−0.957185	+	0.289476i	$0.906519\pi$
$114$	524582.	3.78052
$115$	−263589.	−1.85858
$116$	90432.0	0.623989
$117$	−181228.	−1.22394
$118$	−397809.	−2.63009
$119$	23619.7	0.152900
$120$	−219864.	−1.39380
$121$	−90138.3	−0.559688
$122$	382080.	2.32410
$123$	−171696.	−1.02328
$124$	−205268.	−1.19885
$125$	135548.	0.775919
$126$	−113849.	−0.638858
$127$	268183.	1.47544	0.737721	−	0.675106i	$-0.235902\pi$
$127$	268183.	1.47544	0.737721	+	0.675106i	$0.235902\pi$
$128$	271603.	1.46524
$129$	−109993.	−0.581959
$130$	−433793.	−2.25125
$131$	−124100.	−0.631818	−0.315909	−	0.948789i	$-0.602309\pi$
$131$	−124100.	−0.631818	−0.315909	+	0.948789i	$0.602309\pi$
$132$	288659.	1.44195
$133$	137745.	0.675223
$134$	−171064.	−0.822995
$135$	−905.291	−0.00427518
$136$	−70239.0	−0.325635
$137$	−179094.	−0.815231	−0.407615	−	0.913154i	$-0.633640\pi$
$137$	−179094.	−0.815231	−0.407615	+	0.913154i	$0.633640\pi$
$138$	812848.	3.63339
$139$	−154429.	−0.677943	−0.338972	−	0.940797i	$-0.610079\pi$
$139$	−154429.	−0.677943	−0.338972	+	0.940797i	$0.610079\pi$
$140$	−165123.	−0.712012
$141$	342496.	1.45080
$142$	−7842.10	−0.0326371
$143$	199124.	0.814297
$144$	−43036.7	−0.172955
$145$	−118323.	−0.467356
$146$	−111044.	−0.431133
$147$	310406.	1.18478
$148$	79431.5	0.298084
$149$	286297.	1.05645	0.528227	−	0.849103i	$-0.322857\pi$
$149$	286297.	1.05645	0.528227	+	0.849103i	$0.322857\pi$
$150$	202397.	0.734474
$151$	−420312.	−1.50013	−0.750066	−	0.661363i	$-0.769978\pi$
$151$	−420312.	−1.50013	−0.750066	+	0.661363i	$0.769978\pi$
$152$	−409619.	−1.43804
$153$	109814.	0.379252
$154$	125092.	0.425037
$155$	268576.	0.897920
$156$	810557.	2.66669
$157$	−266471.	−0.862783	−0.431391	−	0.902165i	$-0.641977\pi$
$157$	−266471.	−0.862783	−0.431391	+	0.902165i	$0.641977\pi$
$158$	815489.	2.59882
$159$	644208.	2.02085
$160$	−422367.	−1.30434
$161$	213438.	0.648944
$162$	533500.	1.59715
$163$	613384.	1.80827	0.904135	−	0.427246i	$-0.140516\pi$
$163$	613384.	1.80827	0.904135	+	0.427246i	$0.140516\pi$
$164$	383457.	1.11329
$165$	−377686.	−1.07999
$166$	−203057.	−0.571937
$167$	563225.	1.56275	0.781377	−	0.624060i	$-0.214518\pi$
$167$	563225.	1.56275	0.781377	+	0.624060i	$0.214518\pi$
$168$	178033.	0.486661
$169$	187848.	0.505929
$170$	262854.	0.697577
$171$	640411.	1.67482
$172$	245654.	0.633145
$173$	636194.	1.61612	0.808061	−	0.589098i	$-0.200517\pi$
$173$	636194.	1.61612	0.808061	+	0.589098i	$0.200517\pi$
$174$	364880.	0.913645
$175$	53145.7	0.131182
$176$	47286.5	0.115068
$177$	−972573.	−2.33340
$178$	−313201.	−0.740924
$179$	344181.	0.802887	0.401443	−	0.915884i	$-0.368509\pi$
$179$	344181.	0.802887	0.401443	+	0.915884i	$0.368509\pi$
$180$	−767697.	−1.76607
$181$	−740458.	−1.67998	−0.839990	−	0.542602i	$-0.817439\pi$
$181$	−740458.	−1.67998	−0.839990	+	0.542602i	$0.817439\pi$
$182$	351259.	0.786048
$183$	934117.	2.06193
$184$	−634711.	−1.38208
$185$	−103929.	−0.223259
$186$	−828226.	−1.75536
$187$	−120658.	−0.252320
$188$	−764914.	−1.57840
$189$	733.050	0.00149272
$190$	1.53291e6	3.08058
$191$	−505974.	−1.00356	−0.501782	−	0.864994i	$-0.667322\pi$
$191$	−505974.	−1.00356	−0.501782	+	0.864994i	$0.667322\pi$
$192$	1.17730e6	2.30480
$193$	343724.	0.664228	0.332114	−	0.943239i	$-0.392238\pi$
$193$	343724.	0.664228	0.332114	+	0.943239i	$0.392238\pi$
$194$	1.03265e6	1.96992
$195$	−1.06055e6	−1.99730
$196$	−693245.	−1.28898
$197$	177038.	0.325013	0.162506	−	0.986708i	$-0.448042\pi$
$197$	177038.	0.325013	0.162506	+	0.986708i	$0.448042\pi$
$198$	581583.	1.05426
$199$	−88575.8	−0.158556	−0.0792780	−	0.996853i	$-0.525261\pi$
$199$	−88575.8	−0.158556	−0.0792780	+	0.996853i	$0.525261\pi$
$200$	−158042.	−0.279381
$201$	−418222.	−0.730157
$202$	267017.	0.460426
$203$	95810.6	0.163182
$204$	−491152.	−0.826305
$205$	−501721.	−0.833831
$206$	16176.8	0.0265597
$207$	992327.	1.60964
$208$	132781.	0.212803
$209$	−703650.	−1.11427
$210$	−666247.	−1.04253
$211$	45239.6	0.0699540	0.0349770	−	0.999388i	$-0.488864\pi$
$211$	45239.6	0.0699540	0.0349770	+	0.999388i	$0.488864\pi$
$212$	−1.43874e6	−2.19859
$213$	−19172.5	−0.0289555
$214$	−181550.	−0.270995
$215$	−321418.	−0.474213
$216$	−2179.91	−0.00317909
$217$	−217476.	−0.313518
$218$	−434177.	−0.618765
$219$	−271482.	−0.382499
$220$	843506.	1.17498
$221$	−338808.	−0.466630
$222$	320495.	0.436454
$223$	9983.78	0.0134441	0.00672207	−	0.999977i	$-0.497860\pi$
$223$	9983.78	0.0134441	0.00672207	+	0.999977i	$0.497860\pi$
$224$	342008.	0.455424
$225$	247087.	0.325382
$226$	2.34157e6	3.04956
$227$	−28315.0	−0.0364713	−0.0182357	−	0.999834i	$-0.505805\pi$
$227$	−28315.0	−0.0364713	−0.0182357	+	0.999834i	$0.505805\pi$
$228$	−2.86429e6	−3.64906
$229$	216893.	0.273311	0.136656	−	0.990619i	$-0.456365\pi$
$229$	216893.	0.273311	0.136656	+	0.990619i	$0.456365\pi$
$230$	2.37527e6	2.96069
$231$	305827.	0.377091
$232$	−284916.	−0.347534
$233$	−1.41549e6	−1.70812	−0.854058	−	0.520178i	$-0.825865\pi$
$233$	−1.41549e6	−1.70812	−0.854058	+	0.520178i	$0.825865\pi$
$234$	1.63309e6	1.94971
$235$	1.00083e6	1.18219
$236$	2.17210e6	2.53863
$237$	1.99373e6	2.30566
$238$	−212843.	−0.243566
$239$	1.50117e6	1.69995	0.849975	−	0.526822i	$-0.176617\pi$
$239$	1.50117e6	1.69995	0.849975	+	0.526822i	$0.176617\pi$
$240$	−251851.	−0.282238
$241$	−455608.	−0.505299	−0.252649	−	0.967558i	$-0.581302\pi$
$241$	−455608.	−0.505299	−0.252649	+	0.967558i	$0.581302\pi$
$242$	812259.	0.891572
$243$	1.30090e6	1.41327
$244$	−2.08621e6	−2.24328
$245$	907054.	0.965423
$246$	1.54719e6	1.63007
$247$	−1.97586e6	−2.06069
$248$	646720.	0.667708
$249$	−496438.	−0.507419
$250$	−1.22145e6	−1.23602
$251$	469647.	0.470530	0.235265	−	0.971931i	$-0.424404\pi$
$251$	469647.	0.470530	0.235265	+	0.971931i	$0.424404\pi$
$252$	621635.	0.616643
$253$	−1.09032e6	−1.07091
$254$	−2.41667e6	−2.35035
$255$	642631.	0.618887
$256$	−737458.	−0.703295
$257$	−1.38194e6	−1.30513	−0.652567	−	0.757731i	$-0.726308\pi$
$257$	−1.38194e6	−1.30513	−0.652567	+	0.757731i	$0.726308\pi$
$258$	991180.	0.927050
$259$	84155.8	0.0779533
$260$	2.36857e6	2.17297
$261$	445447.	0.404757
$262$	1.11829e6	1.00647
$263$	−991548.	−0.883943	−0.441972	−	0.897029i	$-0.645721\pi$
$263$	−991548.	−0.883943	−0.441972	+	0.897029i	$0.645721\pi$
$264$	−909453.	−0.803101
$265$	1.88248e6	1.64670
$266$	−1.24126e6	−1.07562
$267$	−765721.	−0.657344
$268$	934036.	0.794377
$269$	388857.	0.327649	0.163824	−	0.986490i	$-0.447617\pi$
$269$	388857.	0.327649	0.163824	+	0.986490i	$0.447617\pi$
$270$	8157.82	0.00681027
$271$	−165410.	−0.136816	−0.0684081	−	0.997657i	$-0.521792\pi$
$271$	−165410.	−0.136816	−0.0684081	+	0.997657i	$0.521792\pi$
$272$	−80457.8	−0.0659396
$273$	858766.	0.697378
$274$	1.61387e6	1.29865
$275$	−271487.	−0.216480
$276$	−4.43827e6	−3.50704
$277$	2.07271e6	1.62307	0.811537	−	0.584301i	$-0.198631\pi$
$277$	2.07271e6	1.62307	0.811537	+	0.584301i	$0.198631\pi$
$278$	1.39160e6	1.07995
$279$	−1.01110e6	−0.777650
$280$	520239.	0.396559
$281$	−1.35917e6	−1.02685	−0.513426	−	0.858134i	$-0.671624\pi$
$281$	−1.35917e6	−1.02685	−0.513426	+	0.858134i	$0.671624\pi$
$282$	−3.08632e6	−2.31110
$283$	540155.	0.400915	0.200457	−	0.979702i	$-0.435757\pi$
$283$	540155.	0.400915	0.200457	+	0.979702i	$0.435757\pi$
$284$	42819.0	0.0315022
$285$	3.74769e6	2.73307
$286$	−1.79435e6	−1.29716
$287$	406264.	0.291141
$288$	1.59008e6	1.12963
$289$	−1.21456e6	−0.855409
$290$	1.06624e6	0.744490
$291$	2.52465e6	1.74770
$292$	606315.	0.416141
$293$	1.76327e6	1.19991	0.599957	−	0.800033i	$-0.295184\pi$
$293$	1.76327e6	1.19991	0.599957	+	0.800033i	$0.295184\pi$
$294$	−2.79715e6	−1.88733
$295$	−2.84201e6	−1.90139
$296$	−250258.	−0.166019
$297$	−3744.68	−0.00246333
$298$	−2.57990e6	−1.68291
$299$	−3.06162e6	−1.98049
$300$	−1.10512e6	−0.708935
$301$	260265.	0.165577
$302$	3.78754e6	2.38968
$303$	652808.	0.408487
$304$	−469213.	−0.291197
$305$	2.72964e6	1.68018
$306$	−989561.	−0.604142
$307$	−2.55479e6	−1.54707	−0.773535	−	0.633753i	$-0.781513\pi$
$307$	−2.55479e6	−1.54707	−0.773535	+	0.633753i	$0.781513\pi$
$308$	−683020.	−0.410258
$309$	39549.3	0.0235637
$310$	−2.42021e6	−1.43037
$311$	−2.91869e6	−1.71114	−0.855572	−	0.517684i	$-0.826794\pi$
$311$	−2.91869e6	−1.71114	−0.855572	+	0.517684i	$0.826794\pi$
$312$	−2.55375e6	−1.48522
$313$	132854.	0.0766503	0.0383251	−	0.999265i	$-0.487798\pi$
$313$	132854.	0.0766503	0.0383251	+	0.999265i	$0.487798\pi$
$314$	2.40124e6	1.37440
$315$	−813357.	−0.461854
$316$	−4.45269e6	−2.50845
$317$	−770592.	−0.430702	−0.215351	−	0.976537i	$-0.569089\pi$
$317$	−770592.	−0.430702	−0.215351	+	0.976537i	$0.569089\pi$
$318$	−5.80513e6	−3.21917
$319$	−489434.	−0.269288
$320$	3.44025e6	1.87808
$321$	−443856.	−0.240425
$322$	−1.92335e6	−1.03376
$323$	1.19726e6	0.638530
$324$	−2.91299e6	−1.54162
$325$	−762337.	−0.400349
$326$	−5.52736e6	−2.88054
$327$	−1.06149e6	−0.548965
$328$	−1.20813e6	−0.620051
$329$	−810408.	−0.412775
$330$	3.40343e6	1.72041
$331$	−1.86898e6	−0.937637	−0.468818	−	0.883295i	$-0.655320\pi$
$331$	−1.86898e6	−0.937637	−0.468818	+	0.883295i	$0.655320\pi$
$332$	1.10872e6	0.552049
$333$	391261.	0.193355
$334$	−5.07536e6	−2.48944
$335$	−1.22211e6	−0.594974
$336$	203934.	0.0985465
$337$	81788.1	0.0392298	0.0196149	−	0.999808i	$-0.493756\pi$
$337$	81788.1	0.0392298	0.0196149	+	0.999808i	$0.493756\pi$
$338$	−1.69275e6	−0.805935
$339$	5.72473e6	2.70555
$340$	−1.43522e6	−0.673320
$341$	1.11095e6	0.517377
$342$	−5.77091e6	−2.66796
$343$	−1.61061e6	−0.739190
$344$	−773962.	−0.352633
$345$	5.80710e6	2.62671
$346$	−5.73291e6	−2.57445
$347$	−858835.	−0.382901	−0.191450	−	0.981502i	$-0.561319\pi$
$347$	−858835.	−0.382901	−0.191450	+	0.981502i	$0.561319\pi$
$348$	−1.99230e6	−0.881875
$349$	−1.81284e6	−0.796704	−0.398352	−	0.917233i	$-0.630418\pi$
$349$	−1.81284e6	−0.796704	−0.398352	+	0.917233i	$0.630418\pi$
$350$	−478909.	−0.208970
$351$	−10515.1	−0.00455560
$352$	−1.74709e6	−0.751553
$353$	2.92967e6	1.25136	0.625680	−	0.780080i	$-0.284822\pi$
$353$	2.92967e6	1.25136	0.625680	+	0.780080i	$0.284822\pi$
$354$	8.76411e6	3.71706
$355$	−56025.1	−0.0235946
$356$	1.71013e6	0.715160
$357$	−520364.	−0.216091
$358$	−3.10150e6	−1.27898
$359$	3.65909e6	1.49843	0.749217	−	0.662325i	$-0.230430\pi$
$359$	3.65909e6	1.49843	0.749217	+	0.662325i	$0.230430\pi$
$360$	2.41872e6	0.983624
$361$	4.50606e6	1.81982
$362$	6.67246e6	2.67618
$363$	1.98583e6	0.790998
$364$	−1.91793e6	−0.758715
$365$	−793312.	−0.311682
$366$	−8.41757e6	−3.28461
$367$	4.54708e6	1.76225	0.881125	−	0.472883i	$-0.156787\pi$
$367$	4.54708e6	1.76225	0.881125	+	0.472883i	$0.156787\pi$
$368$	−727053.	−0.279864
$369$	1.88882e6	0.722145
$370$	936535.	0.355648
$371$	−1.52432e6	−0.574963
$372$	4.52224e6	1.69432
$373$	2.67305e6	0.994800	0.497400	−	0.867521i	$-0.334288\pi$
$373$	2.67305e6	0.994800	0.497400	+	0.867521i	$0.334288\pi$
$374$	1.08728e6	0.401940
$375$	−2.98624e6	−1.09659
$376$	2.40995e6	0.879100
$377$	−1.37434e6	−0.498011
$378$	−6605.71	−0.00237788
$379$	1.41985e6	0.507742	0.253871	−	0.967238i	$-0.418296\pi$
$379$	1.41985e6	0.507742	0.253871	+	0.967238i	$0.418296\pi$
$380$	−8.36991e6	−2.97346
$381$	−5.90832e6	−2.08522
$382$	4.55946e6	1.59866
$383$	4.25949e6	1.48375	0.741874	−	0.670539i	$-0.233937\pi$
$383$	4.25949e6	1.48375	0.741874	+	0.670539i	$0.233937\pi$
$384$	−5.98367e6	−2.07081
$385$	893674.	0.307275
$386$	−3.09739e6	−1.05810
$387$	1.21004e6	0.410696
$388$	−5.63843e6	−1.90142
$389$	−1.35952e6	−0.455525	−0.227762	−	0.973717i	$-0.573141\pi$
$389$	−1.35952e6	−0.455525	−0.227762	+	0.973717i	$0.573141\pi$
$390$	9.55685e6	3.18166
$391$	1.85517e6	0.613680
$392$	2.18415e6	0.717905
$393$	2.73403e6	0.892939
$394$	−1.59533e6	−0.517739
$395$	5.82598e6	1.87878
$396$	−3.17553e6	−1.01760
$397$	1.29030e6	0.410879	0.205439	−	0.978670i	$-0.434138\pi$
$397$	1.29030e6	0.410879	0.205439	+	0.978670i	$0.434138\pi$
$398$	798180.	0.252577
$399$	−3.03465e6	−0.954282
$400$	−181035.	−0.0565734
$401$	3.13778e6	0.974455	0.487227	−	0.873275i	$-0.338008\pi$
$401$	3.13778e6	0.974455	0.487227	+	0.873275i	$0.338008\pi$
$402$	3.76870e6	1.16313
$403$	3.11955e6	0.956817
$404$	−1.45795e6	−0.444415
$405$	3.81140e6	1.15464
$406$	−863374.	−0.259946
$407$	−429897.	−0.128641
$408$	1.54743e6	0.460215
$409$	−4.56479e6	−1.34931	−0.674656	−	0.738133i	$-0.735708\pi$
$409$	−4.56479e6	−1.34931	−0.674656	+	0.738133i	$0.735708\pi$
$410$	4.52114e6	1.32828
$411$	3.94562e6	1.15215
$412$	−88327.5	−0.0256362
$413$	2.30129e6	0.663889
$414$	−8.94212e6	−2.56413
$415$	−1.45067e6	−0.413474
$416$	−4.90586e6	−1.38989
$417$	3.40222e6	0.958126
$418$	6.34078e6	1.77501
$419$	−892402.	−0.248328	−0.124164	−	0.992262i	$-0.539625\pi$
$419$	−892402.	−0.248328	−0.124164	+	0.992262i	$0.539625\pi$
$420$	3.63781e6	1.00628
$421$	983056.	0.270317	0.135158	−	0.990824i	$-0.456846\pi$
$421$	983056.	0.270317	0.135158	+	0.990824i	$0.456846\pi$
$422$	−407666.	−0.111435
$423$	−3.76779e6	−1.02385
$424$	4.53293e6	1.22452
$425$	461933.	0.124053
$426$	172769.	0.0461255
$427$	−2.21029e6	−0.586652
$428$	991288.	0.261571
$429$	−4.38688e6	−1.15083
$430$	2.89638e6	0.755413
$431$	−6.79217e6	−1.76123	−0.880614	−	0.473834i	$-0.842870\pi$
$431$	−6.79217e6	−1.76123	−0.880614	+	0.473834i	$0.842870\pi$
$432$	−2497.05	−0.000643752 0
$433$	3.29187e6	0.843767	0.421883	−	0.906650i	$-0.361369\pi$
$433$	3.29187e6	0.843767	0.421883	+	0.906650i	$0.361369\pi$
$434$	1.95974e6	0.499428
$435$	2.60676e6	0.660507
$436$	2.37067e6	0.597249
$437$	1.08190e7	2.71008
$438$	2.44639e6	0.609314
$439$	2.96096e6	0.733283	0.366641	−	0.930362i	$-0.380508\pi$
$439$	2.96096e6	0.733283	0.366641	+	0.930362i	$0.380508\pi$
$440$	−2.65756e6	−0.654413
$441$	−3.41477e6	−0.836112
$442$	3.05309e6	0.743333
$443$	499762.	0.120991	0.0604957	−	0.998168i	$-0.480732\pi$
$443$	499762.	0.120991	0.0604957	+	0.998168i	$0.480732\pi$
$444$	−1.74995e6	−0.421277
$445$	−2.23756e6	−0.535641
$446$	−89966.5	−0.0214163
$447$	−6.30738e6	−1.49307
$448$	−2.78570e6	−0.655753
$449$	−3.04363e6	−0.712485	−0.356243	−	0.934394i	$-0.615942\pi$
$449$	−3.04363e6	−0.712485	−0.356243	+	0.934394i	$0.615942\pi$
$450$	−2.22657e6	−0.518328
$451$	−2.07534e6	−0.480449
$452$	−1.27853e7	−2.94351
$453$	9.25986e6	2.12011
$454$	255154.	0.0580981
$455$	2.50945e6	0.568263
$456$	9.02429e6	2.03236
$457$	2.79591e6	0.626229	0.313115	−	0.949715i	$-0.398628\pi$
$457$	2.79591e6	0.626229	0.313115	+	0.949715i	$0.398628\pi$
$458$	−1.95448e6	−0.435380
$459$	6371.55	0.00141161
$460$	−1.29693e7	−2.85774
$461$	−34719.2	−0.00760881	−0.00380441	−	0.999993i	$-0.501211\pi$
$461$	−34719.2	−0.00760881	−0.00380441	+	0.999993i	$0.501211\pi$
$462$	−2.75589e6	−0.600699
$463$	−169775.	−0.0368062	−0.0184031	−	0.999831i	$-0.505858\pi$
$463$	−169775.	−0.0368062	−0.0184031	+	0.999831i	$0.505858\pi$
$464$	−326368.	−0.0703741
$465$	−5.91697e6	−1.26902
$466$	1.27554e7	2.72099
$467$	−4.31712e6	−0.916013	−0.458006	−	0.888949i	$-0.651436\pi$
$467$	−4.31712e6	−0.916013	−0.458006	+	0.888949i	$0.651436\pi$
$468$	−8.91692e6	−1.88192
$469$	989589.	0.207741
$470$	−9.01870e6	−1.88321
$471$	5.87061e6	1.21936
$472$	−6.84345e6	−1.41390
$473$	−1.32952e6	−0.273239
$474$	−1.79660e7	−3.67287
$475$	2.69390e6	0.547832
$476$	1.16216e6	0.235097
$477$	−7.08692e6	−1.42614
$478$	−1.35275e7	−2.70799
$479$	1.54575e6	0.307823	0.153912	−	0.988085i	$-0.450813\pi$
$479$	1.54575e6	0.307823	0.153912	+	0.988085i	$0.450813\pi$
$480$	9.30515e6	1.84340
$481$	−1.20716e6	−0.237903
$482$	4.10560e6	0.804932
$483$	−4.70224e6	−0.917143
$484$	−4.43506e6	−0.860569
$485$	7.37741e6	1.42413
$486$	−1.17227e7	−2.25132
$487$	−8.73971e6	−1.66984	−0.834919	−	0.550372i	$-0.814486\pi$
$487$	−8.73971e6	−1.66984	−0.834919	+	0.550372i	$0.814486\pi$
$488$	6.57285e6	1.24941
$489$	−1.35134e7	−2.55560
$490$	−8.17370e6	−1.53790
$491$	3.71065e6	0.694619	0.347310	−	0.937751i	$-0.387095\pi$
$491$	3.71065e6	0.694619	0.347310	+	0.937751i	$0.387095\pi$
$492$	−8.44791e6	−1.57339
$493$	832770.	0.154315
$494$	1.78050e7	3.28264
$495$	4.15491e6	0.762165
$496$	740809.	0.135208
$497$	45365.7	0.00823829
$498$	4.47354e6	0.808309
$499$	−4.00010e6	−0.719151	−0.359575	−	0.933116i	$-0.617078\pi$
$499$	−4.00010e6	−0.719151	−0.359575	+	0.933116i	$0.617078\pi$
$500$	6.66932e6	1.19304
$501$	−1.24084e7	−2.20862
$502$	−4.23211e6	−0.749545
$503$	4.62362e6	0.814821	0.407410	−	0.913245i	$-0.366432\pi$
$503$	4.62362e6	0.814821	0.407410	+	0.913245i	$0.366432\pi$
$504$	−1.95853e6	−0.343443
$505$	1.90761e6	0.332859
$506$	9.82513e6	1.70593
$507$	−4.13846e6	−0.715022
$508$	1.31954e7	2.26862
$509$	−66533.8	−0.0113828	−0.00569138	−	0.999984i	$-0.501812\pi$
$509$	−66533.8	−0.0113828	−0.00569138	+	0.999984i	$0.501812\pi$
$510$	−5.79092e6	−0.985875
$511$	642376.	0.108827
$512$	−2.04588e6	−0.344909
$513$	37157.6	0.00623381
$514$	1.24530e7	2.07905
$515$	115569.	0.0192010
$516$	−5.41199e6	−0.894814
$517$	4.13985e6	0.681174
$518$	−758350.	−0.124178
$519$	−1.40159e7	−2.28404
$520$	−7.46246e6	−1.21025
$521$	−1.04251e7	−1.68262	−0.841310	−	0.540553i	$-0.818215\pi$
$521$	−1.04251e7	−1.68262	−0.841310	+	0.540553i	$0.818215\pi$
$522$	−4.01404e6	−0.644771
$523$	3.66258e6	0.585509	0.292754	−	0.956188i	$-0.405428\pi$
$523$	3.66258e6	0.585509	0.292754	+	0.956188i	$0.405428\pi$
$524$	−6.10605e6	−0.971476
$525$	−1.17085e6	−0.185397
$526$	8.93510e6	1.40810
$527$	−1.89027e6	−0.296481
$528$	−1.04177e6	−0.162624
$529$	1.03278e7	1.60461
$530$	−1.69635e7	−2.62316
$531$	1.06993e7	1.64671
$532$	6.77745e6	1.03821
$533$	−5.82757e6	−0.888524
$534$	6.90012e6	1.04714
$535$	−1.29702e6	−0.195912
$536$	−2.94279e6	−0.442433
$537$	−7.58263e6	−1.13471
$538$	−3.50409e6	−0.521938
$539$	3.75197e6	0.556272
$540$	−44542.9	−0.00657346
$541$	5.17659e6	0.760415	0.380208	−	0.924901i	$-0.375853\pi$
$541$	5.17659e6	0.760415	0.380208	+	0.924901i	$0.375853\pi$
$542$	1.49055e6	0.217946
$543$	1.63130e7	2.37429
$544$	2.97267e6	0.430675
$545$	−3.10182e6	−0.447328
$546$	−7.73856e6	−1.11091
$547$	299209.	0.0427569
$547$	299209.	0.0427569
$548$	−8.81195e6	−1.25349
$549$	−1.02762e7	−1.45513
$550$	2.44644e6	0.344848
$551$	4.85654e6	0.681472
$552$	1.39833e7	1.95327
$553$	−4.71752e6	−0.655996
$554$	−1.86777e7	−2.58553
$555$	2.28966e6	0.315529
$556$	−7.59837e6	−1.04240
$557$	7.38151e6	1.00811	0.504054	−	0.863672i	$-0.331841\pi$
$557$	7.38151e6	1.00811	0.504054	+	0.863672i	$0.331841\pi$
$558$	9.11130e6	1.23878
$559$	−3.73332e6	−0.505318
$560$	595926.	0.0803013
$561$	2.65820e6	0.356599
$562$	1.22478e7	1.63576
$563$	1.07536e7	1.42982	0.714910	−	0.699217i	$-0.246468\pi$
$563$	1.07536e7	1.42982	0.714910	+	0.699217i	$0.246468\pi$
$564$	1.68518e7	2.23073
$565$	1.67285e7	2.20464
$566$	−4.86748e6	−0.638650
$567$	−3.08624e6	−0.403155
$568$	−134906.	−0.0175453
$569$	−5.71541e6	−0.740060	−0.370030	−	0.929020i	$-0.620653\pi$
$569$	−5.71541e6	−0.740060	−0.370030	+	0.929020i	$0.620653\pi$
$570$	−3.37714e7	−4.35373
$571$	−7.92615e6	−1.01735	−0.508677	−	0.860957i	$-0.669865\pi$
$571$	−7.92615e6	−1.01735	−0.508677	+	0.860957i	$0.669865\pi$
$572$	9.79744e6	1.25205
$573$	1.11471e7	1.41832
$574$	−3.66095e6	−0.463782
$575$	4.17424e6	0.526511
$576$	−1.29514e7	−1.62653
$577$	−2.43324e6	−0.304260	−0.152130	−	0.988361i	$-0.548613\pi$
$577$	−2.43324e6	−0.304260	−0.152130	+	0.988361i	$0.548613\pi$
$578$	1.09447e7	1.36265
$579$	−7.57257e6	−0.938743
$580$	−5.82181e6	−0.718602
$581$	1.17466e6	0.144369
$582$	−2.27502e7	−2.78406
$583$	7.78674e6	0.948821
$584$	−1.91026e6	−0.231772
$585$	1.16670e7	1.40952
$586$	−1.58893e7	−1.91144
$587$	−1.14213e7	−1.36811	−0.684055	−	0.729430i	$-0.739785\pi$
$587$	−1.14213e7	−1.36811	−0.684055	+	0.729430i	$0.739785\pi$
$588$	1.52728e7	1.82170
$589$	−1.10237e7	−1.30929
$590$	2.56101e7	3.02887
$591$	−3.90030e6	−0.459335
$592$	−286667.	−0.0336181
$593$	−5.01560e6	−0.585715	−0.292857	−	0.956156i	$-0.594606\pi$
$593$	−5.01560e6	−0.585715	−0.292857	+	0.956156i	$0.594606\pi$
$594$	33744.3	0.00392405
$595$	−1.52058e6	−0.176083
$596$	1.40866e7	1.62439
$597$	1.95141e6	0.224085
$598$	2.75891e7	3.15489
$599$	1.01747e7	1.15866	0.579329	−	0.815094i	$-0.303315\pi$
$599$	1.01747e7	1.15866	0.579329	+	0.815094i	$0.303315\pi$
$600$	3.48181e6	0.394845
$601$	1.65384e7	1.86770	0.933851	−	0.357662i	$-0.116426\pi$
$601$	1.65384e7	1.86770	0.933851	+	0.357662i	$0.116426\pi$
$602$	−2.34531e6	−0.263760
$603$	4.60085e6	0.515281
$604$	−2.06805e7	−2.30658
$605$	5.80290e6	0.644550
$606$	−5.88262e6	−0.650713
$607$	1.33772e7	1.47365	0.736824	−	0.676085i	$-0.236325\pi$
$607$	1.33772e7	1.47365	0.736824	+	0.676085i	$0.236325\pi$
$608$	1.73360e7	1.90191
$609$	−2.11080e6	−0.230623
$610$	−2.45975e7	−2.67649
$611$	1.16247e7	1.25974
$612$	5.40315e6	0.583134
$613$	−1.50274e7	−1.61523	−0.807613	−	0.589713i	$-0.799241\pi$
$613$	−1.50274e7	−1.61523	−0.807613	+	0.589713i	$0.799241\pi$
$614$	2.30219e7	2.46445
$615$	1.10534e7	1.17844
$616$	2.15193e6	0.228495
$617$	−1.00696e6	−0.106487	−0.0532436	−	0.998582i	$-0.516956\pi$
$617$	−1.00696e6	−0.106487	−0.0532436	+	0.998582i	$0.516956\pi$
$618$	−356389.	−0.0375364
$619$	−2.24550e6	−0.235551	−0.117776	−	0.993040i	$-0.537576\pi$
$619$	−2.24550e6	−0.235551	−0.117776	+	0.993040i	$0.537576\pi$
$620$	1.32147e7	1.38063
$621$	57576.2	0.00599121
$622$	2.63010e7	2.72582
$623$	1.81184e6	0.187025
$624$	−2.92529e6	−0.300751
$625$	−1.19122e7	−1.21981
$626$	−1.19718e6	−0.122102
$627$	1.55021e7	1.57478
$628$	−1.31111e7	−1.32660
$629$	731468.	0.0737172
$630$	7.32937e6	0.735725
$631$	−1.16490e7	−1.16471	−0.582353	−	0.812936i	$-0.697868\pi$
$631$	−1.16490e7	−1.16471	−0.582353	+	0.812936i	$0.697868\pi$
$632$	1.40287e7	1.39709
$633$	−996670.	−0.0988649
$634$	6.94401e6	0.686100
$635$	−1.72650e7	−1.69916
$636$	3.16969e7	3.10723
$637$	1.05356e7	1.02875
$638$	4.41042e6	0.428971
$639$	210917.	0.0204342
$640$	−1.74852e7	−1.68741
$641$	4.52887e6	0.435356	0.217678	−	0.976021i	$-0.430152\pi$
$641$	4.52887e6	0.435356	0.217678	+	0.976021i	$0.430152\pi$
$642$	3.99971e6	0.382993
$643$	−1.82495e7	−1.74070	−0.870349	−	0.492435i	$-0.836107\pi$
$643$	−1.82495e7	−1.74070	−0.870349	+	0.492435i	$0.836107\pi$
$644$	1.05018e7	0.997809
$645$	7.08113e6	0.670199
$646$	−1.07888e7	−1.01717
$647$	514684.	0.0483370	0.0241685	−	0.999708i	$-0.492306\pi$
$647$	514684.	0.0483370	0.0241685	+	0.999708i	$0.492306\pi$
$648$	9.17771e6	0.858611
$649$	−1.17558e7	−1.09557
$650$	6.86962e6	0.637748
$651$	4.79121e6	0.443090
$652$	3.01802e7	2.78038
$653$	1.70845e7	1.56791	0.783953	−	0.620821i	$-0.213201\pi$
$653$	1.70845e7	1.56791	0.783953	+	0.620821i	$0.213201\pi$
$654$	9.56532e6	0.874491
$655$	7.98926e6	0.727617
$656$	−1.38389e6	−0.125557
$657$	2.98657e6	0.269935
$658$	7.30280e6	0.657543
$659$	−340042.	−0.0305013	−0.0152507	−	0.999884i	$-0.504855\pi$
$659$	−340042.	−0.0305013	−0.0152507	+	0.999884i	$0.504855\pi$
$660$	−1.85832e7	−1.66058
$661$	2.39084e6	0.212837	0.106418	−	0.994321i	$-0.466062\pi$
$661$	2.39084e6	0.212837	0.106418	+	0.994321i	$0.466062\pi$
$662$	1.68419e7	1.49364
$663$	7.46425e6	0.659481
$664$	−3.49316e6	−0.307466
$665$	−8.86772e6	−0.777603
$666$	−3.52576e6	−0.308011
$667$	7.52529e6	0.654950
$668$	2.77122e7	2.40287
$669$	−219952.	−0.0190004
$670$	1.10127e7	0.947782
$671$	1.12910e7	0.968109
$672$	−7.53474e6	−0.643643
$673$	−1.41611e6	−0.120520	−0.0602600	−	0.998183i	$-0.519193\pi$
$673$	−1.41611e6	−0.120520	−0.0602600	+	0.998183i	$0.519193\pi$
$674$	−737014.	−0.0624922
$675$	14336.4	0.00121110
$676$	9.24265e6	0.777910
$677$	1.47725e7	1.23875	0.619375	−	0.785095i	$-0.287386\pi$
$677$	1.47725e7	1.23875	0.619375	+	0.785095i	$0.287386\pi$
$678$	−5.15870e7	−4.30989
$679$	−5.97378e6	−0.497250
$680$	4.52183e6	0.375009
$681$	623805.	0.0515444
$682$	−1.00110e7	−0.824171
$683$	−5.45073e6	−0.447099	−0.223549	−	0.974693i	$-0.571764\pi$
$683$	−5.45073e6	−0.447099	−0.223549	+	0.974693i	$0.571764\pi$
$684$	3.15100e7	2.57519
$685$	1.15297e7	0.938840
$686$	1.45137e7	1.17751
$687$	−4.77836e6	−0.386267
$688$	−886563.	−0.0714066
$689$	2.18652e7	1.75471
$690$	−5.23293e7	−4.18430
$691$	1.02810e7	0.819103	0.409551	−	0.912287i	$-0.365685\pi$
$691$	1.02810e7	0.819103	0.409551	+	0.912287i	$0.365685\pi$
$692$	3.13025e7	2.48493
$693$	−3.36440e6	−0.266118
$694$	7.73919e6	0.609953
$695$	9.94183e6	0.780736
$696$	6.27697e6	0.491165
$697$	3.53118e6	0.275320
$698$	1.63360e7	1.26913
$699$	3.11846e7	2.41405
$700$	2.61492e6	0.201703
$701$	−8.72842e6	−0.670874	−0.335437	−	0.942063i	$-0.608884\pi$
$701$	−8.72842e6	−0.670874	−0.335437	+	0.942063i	$0.608884\pi$
$702$	94754.2	0.00725698
$703$	4.26577e6	0.325544
$704$	1.42304e7	1.08214
$705$	−2.20491e7	−1.67078
$706$	−2.64000e7	−1.99339
$707$	−1.54466e6	−0.116221
$708$	−4.78533e7	−3.58781
$709$	−2.86095e6	−0.213744	−0.106872	−	0.994273i	$-0.534084\pi$
$709$	−2.86095e6	−0.213744	−0.106872	+	0.994273i	$0.534084\pi$
$710$	504857.	0.0375857
$711$	−2.19329e7	−1.62713
$712$	−5.38795e6	−0.398312
$713$	−1.70813e7	−1.25834
$714$	4.68913e6	0.344229
$715$	−1.28191e7	−0.937764
$716$	1.69347e7	1.23451
$717$	−3.30723e7	−2.40251
$718$	−3.29730e7	−2.38698
$719$	1.61818e7	1.16736	0.583679	−	0.811985i	$-0.301613\pi$
$719$	1.61818e7	1.16736	0.583679	+	0.811985i	$0.301613\pi$
$720$	2.77061e6	0.199179
$721$	−93580.9	−0.00670423
$722$	−4.06053e7	−2.89894
$723$	1.00375e7	0.714131
$724$	−3.64326e7	−2.58312
$725$	1.87378e6	0.132396
$726$	−1.78948e7	−1.26004
$727$	6.49927e6	0.456067	0.228033	−	0.973653i	$-0.426770\pi$
$727$	6.49927e6	0.456067	0.228033	+	0.973653i	$0.426770\pi$
$728$	6.04265e6	0.422570
$729$	−1.42734e7	−0.994740
$730$	7.14874e6	0.496504
$731$	2.26218e6	0.156579
$732$	4.59612e7	3.17040
$733$	1.96917e7	1.35370	0.676851	−	0.736120i	$-0.263344\pi$
$733$	1.96917e7	1.35370	0.676851	+	0.736120i	$0.263344\pi$
$734$	−4.09749e7	−2.80723
$735$	−1.99832e7	−1.36442
$736$	2.68624e7	1.82789
$737$	−5.05517e6	−0.342821
$738$	−1.70207e7	−1.15036
$739$	4.70094e6	0.316646	0.158323	−	0.987387i	$-0.449391\pi$
$739$	4.70094e6	0.316646	0.158323	+	0.987387i	$0.449391\pi$
$740$	−5.11362e6	−0.343281
$741$	4.35299e7	2.91234
$742$	1.37360e7	0.915905
$743$	−1.89537e7	−1.25957	−0.629785	−	0.776769i	$-0.716857\pi$
$743$	−1.89537e7	−1.25957	−0.629785	+	0.776769i	$0.716857\pi$
$744$	−1.42478e7	−0.943662
$745$	−1.84312e7	−1.21664
$746$	−2.40876e7	−1.58470
$747$	5.46131e6	0.358092
$748$	−5.93670e6	−0.387964
$749$	1.05025e6	0.0684048
$750$	2.69098e7	1.74685
$751$	−8.14855e6	−0.527206	−0.263603	−	0.964631i	$-0.584911\pi$
$751$	−8.14855e6	−0.527206	−0.263603	+	0.964631i	$0.584911\pi$
$752$	2.76056e6	0.178014
$753$	−1.03468e7	−0.664992
$754$	1.23845e7	0.793323
$755$	2.70587e7	1.72759
$756$	36068.1	0.00229519
$757$	−1.13972e7	−0.722869	−0.361435	−	0.932397i	$-0.617713\pi$
$757$	−1.13972e7	−0.722869	−0.361435	+	0.932397i	$0.617713\pi$
$758$	−1.27946e7	−0.808823
$759$	2.40207e7	1.51350
$760$	2.63704e7	1.65608
$761$	1.64626e7	1.03047	0.515237	−	0.857048i	$-0.327704\pi$
$761$	1.64626e7	1.03047	0.515237	+	0.857048i	$0.327704\pi$
$762$	5.32414e7	3.32171
$763$	2.51167e6	0.156189
$764$	−2.48953e7	−1.54307
$765$	−7.06957e6	−0.436756
$766$	−3.83833e7	−2.36358
$767$	−3.30103e7	−2.02610
$768$	1.62469e7	0.993956
$769$	1.01495e7	0.618909	0.309454	−	0.950914i	$-0.399854\pi$
$769$	1.01495e7	0.618909	0.309454	+	0.950914i	$0.399854\pi$
$770$	−8.05313e6	−0.489484
$771$	3.04453e7	1.84453
$772$	1.69122e7	1.02131
$773$	2.23981e7	1.34822	0.674112	−	0.738629i	$-0.264526\pi$
$773$	2.23981e7	1.34822	0.674112	+	0.738629i	$0.264526\pi$
$774$	−1.09039e7	−0.654231
$775$	−4.25321e6	−0.254368
$776$	1.77645e7	1.05901
$777$	−1.85403e6	−0.110170
$778$	1.22510e7	0.725642
$779$	2.05931e7	1.21584
$780$	−5.21818e7	−3.07102
$781$	−231744.	−0.0135951
$782$	−1.67174e7	−0.977580
$783$	25845.5	0.00150654
$784$	2.50191e6	0.145372
$785$	1.71548e7	0.993602
$786$	−2.46370e7	−1.42243
$787$	−7.44056e6	−0.428222	−0.214111	−	0.976809i	$-0.568685\pi$
$787$	−7.44056e6	−0.428222	−0.214111	+	0.976809i	$0.568685\pi$
$788$	8.71075e6	0.499736
$789$	2.18447e7	1.24926
$790$	−5.24994e7	−2.99286
$791$	−1.35458e7	−0.769772
$792$	1.00049e7	0.566759
$793$	3.17051e7	1.79038
$794$	−1.16272e7	−0.654522
$795$	−4.14727e7	−2.32726
$796$	−4.35818e6	−0.243794
$797$	−1.88569e7	−1.05154	−0.525768	−	0.850628i	$-0.676222\pi$
$797$	−1.88569e7	−1.05154	−0.525768	+	0.850628i	$0.676222\pi$
$798$	2.73460e7	1.52015
$799$	−7.04393e6	−0.390345
$800$	6.68869e6	0.369501
$801$	8.42368e6	0.463896
$802$	−2.82754e7	−1.55229
$803$	−3.28148e6	−0.179590
$804$	−2.05777e7	−1.12268
$805$	−1.37407e7	−0.747340
$806$	−2.81110e7	−1.52419
$807$	−8.56687e6	−0.463061
$808$	4.59344e6	0.247520
$809$	−1.97382e7	−1.06032	−0.530159	−	0.847898i	$-0.677868\pi$
$809$	−1.97382e7	−1.06032	−0.530159	+	0.847898i	$0.677868\pi$
$810$	−3.43455e7	−1.83932
$811$	−1.82602e6	−0.0974883	−0.0487441	−	0.998811i	$-0.515522\pi$
$811$	−1.82602e6	−0.0974883	−0.0487441	+	0.998811i	$0.515522\pi$
$812$	4.71415e6	0.250907
$813$	3.64413e6	0.193360
$814$	3.87392e6	0.204922
$815$	−3.94883e7	−2.08245
$816$	1.77256e6	0.0931914
$817$	1.31926e7	0.691471
$818$	4.11345e7	2.14943
$819$	−9.44726e6	−0.492148
$820$	−2.46861e7	−1.28209
$821$	4.05008e6	0.209703	0.104852	−	0.994488i	$-0.466563\pi$
$821$	4.05008e6	0.209703	0.104852	+	0.994488i	$0.466563\pi$
$822$	−3.55550e7	−1.83536
$823$	2.93199e7	1.50891	0.754454	−	0.656353i	$-0.227902\pi$
$823$	2.93199e7	1.50891	0.754454	+	0.656353i	$0.227902\pi$
$824$	278286.	0.0142782
$825$	5.98110e6	0.305947
$826$	−2.07375e7	−1.05756
$827$	−2.94006e7	−1.49483	−0.747416	−	0.664357i	$-0.768706\pi$
$827$	−2.94006e7	−1.49483	−0.747416	+	0.664357i	$0.768706\pi$
$828$	4.88253e7	2.47496
$829$	−2.02109e7	−1.02141	−0.510704	−	0.859757i	$-0.670615\pi$
$829$	−2.02109e7	−1.02141	−0.510704	+	0.859757i	$0.670615\pi$
$830$	1.30724e7	0.658656
$831$	−4.56636e7	−2.29387
$832$	3.99590e7	2.00127
$833$	−6.38396e6	−0.318770
$834$	−3.06583e7	−1.52628
$835$	−3.62592e7	−1.79971
$836$	−3.46216e7	−1.71329
$837$	−58665.6	−0.00289447
$838$	8.04167e6	0.395582
$839$	2.07555e7	1.01795	0.508977	−	0.860780i	$-0.330024\pi$
$839$	2.07555e7	1.01795	0.508977	+	0.860780i	$0.330024\pi$
$840$	−1.14613e7	−0.560450
$841$	−1.71331e7	−0.835307
$842$	−8.85858e6	−0.430610
$843$	2.99438e7	1.45124
$844$	2.22592e6	0.107560
$845$	−1.20932e7	−0.582640
$846$	3.39525e7	1.63097
$847$	−4.69884e6	−0.225052
$848$	5.19241e6	0.247959
$849$	−1.19001e7	−0.566607
$850$	−4.16260e6	−0.197614
$851$	6.60988e6	0.312874
$852$	−943343.	−0.0445216
$853$	2.14304e7	1.00846	0.504229	−	0.863570i	$-0.331777\pi$
$853$	2.14304e7	1.00846	0.504229	+	0.863570i	$0.331777\pi$
$854$	1.99175e7	0.934525
$855$	−4.12282e7	−1.92877
$856$	−3.12317e6	−0.145684
$857$	−2.27977e7	−1.06033	−0.530163	−	0.847896i	$-0.677869\pi$
$857$	−2.27977e7	−1.06033	−0.530163	+	0.847896i	$0.677869\pi$
$858$	3.95313e7	1.83325
$859$	−3.19779e6	−0.147865	−0.0739327	−	0.997263i	$-0.523555\pi$
$859$	−3.19779e6	−0.147865	−0.0739327	+	0.997263i	$0.523555\pi$
$860$	−1.58147e7	−0.729145
$861$	−8.95036e6	−0.411465
$862$	6.12060e7	2.80560
$863$	−1.42408e7	−0.650889	−0.325445	−	0.945561i	$-0.605514\pi$
$863$	−1.42408e7	−0.650889	−0.325445	+	0.945561i	$0.605514\pi$
$864$	92258.6	0.00420458
$865$	−4.09568e7	−1.86117
$866$	−2.96639e7	−1.34410
$867$	2.67578e7	1.20894
$868$	−1.07005e7	−0.482062
$869$	2.40988e7	1.08254
$870$	−2.34902e7	−1.05218
$871$	−1.41950e7	−0.634000
$872$	−7.46907e6	−0.332641
$873$	−2.77736e7	−1.23338
$874$	−9.74925e7	−4.31710
$875$	7.06599e6	0.311999
$876$	−1.33577e7	−0.588126
$877$	1.24434e7	0.546310	0.273155	−	0.961970i	$-0.411933\pi$
$877$	1.24434e7	0.546310	0.273155	+	0.961970i	$0.411933\pi$
$878$	−2.66820e7	−1.16811
$879$	−3.88465e7	−1.69582
$880$	−3.04420e6	−0.132516
$881$	9.86642e6	0.428272	0.214136	−	0.976804i	$-0.431306\pi$
$881$	9.86642e6	0.428272	0.214136	+	0.976804i	$0.431306\pi$
$882$	3.07713e7	1.33191
$883$	3.26046e7	1.40727	0.703634	−	0.710563i	$-0.251560\pi$
$883$	3.26046e7	1.40727	0.703634	+	0.710563i	$0.251560\pi$
$884$	−1.66703e7	−0.717485
$885$	6.26121e7	2.68720
$886$	−4.50349e6	−0.192737
$887$	1.75299e7	0.748117	0.374058	−	0.927405i	$-0.377966\pi$
$887$	1.75299e7	0.748117	0.374058	+	0.927405i	$0.377966\pi$
$888$	5.51342e6	0.234633
$889$	1.39802e7	0.593278
$890$	2.01632e7	0.853266
$891$	1.57656e7	0.665299
$892$	491230.	0.0206716
$893$	−4.10787e7	−1.72381
$894$	5.68375e7	2.37843
$895$	−2.21576e7	−0.924624
$896$	1.41585e7	0.589178
$897$	6.74504e7	2.79900
$898$	2.74269e7	1.13498
$899$	−7.66766e6	−0.316420
$900$	1.21574e7	0.500304
$901$	−1.32491e7	−0.543719
$902$	1.87014e7	0.765346
$903$	−5.73387e6	−0.234007
$904$	4.02817e7	1.63941
$905$	4.76690e7	1.93471
$906$	−8.34430e7	−3.37730
$907$	−3.65899e7	−1.47687	−0.738436	−	0.674324i	$-0.764435\pi$
$907$	−3.65899e7	−1.47687	−0.738436	+	0.674324i	$0.764435\pi$
$908$	−1.39318e6	−0.0560779
$909$	−7.18152e6	−0.288275
$910$	−2.26133e7	−0.905232
$911$	1.42907e7	0.570503	0.285251	−	0.958453i	$-0.407923\pi$
$911$	1.42907e7	0.570503	0.285251	+	0.958453i	$0.407923\pi$
$912$	1.03372e7	0.411544
$913$	−6.00060e6	−0.238242
$914$	−2.51947e7	−0.997571
$915$	−6.01364e7	−2.37457
$916$	1.06718e7	0.420240
$917$	−6.46922e6	−0.254055
$918$	−57415.7	−0.00224866
$919$	2.02508e7	0.790957	0.395478	−	0.918475i	$-0.370579\pi$
$919$	2.02508e7	0.790957	0.395478	+	0.918475i	$0.370579\pi$
$920$	4.08613e7	1.59163
$921$	5.62845e7	2.18645
$922$	312863.	0.0121207
$923$	−650740.	−0.0251422
$924$	1.50476e7	0.579811
$925$	1.64585e6	0.0632462
$926$	1.52989e6	0.0586317
$927$	−435081.	−0.0166292
$928$	1.20583e7	0.459639
$929$	−3.95892e7	−1.50500	−0.752501	−	0.658591i	$-0.771153\pi$
$929$	−3.95892e7	−1.50500	−0.752501	+	0.658591i	$0.771153\pi$
$930$	5.33194e7	2.02152
$931$	−3.72299e7	−1.40772
$932$	−6.96461e7	−2.62638
$933$	6.43014e7	2.41833
$934$	3.89027e7	1.45919
$935$	7.76768e6	0.290578
$936$	2.80938e7	1.04814
$937$	−3.76315e7	−1.40024	−0.700121	−	0.714024i	$-0.746871\pi$
$937$	−3.76315e7	−1.40024	−0.700121	+	0.714024i	$0.746871\pi$
$938$	−8.91745e6	−0.330928
$939$	−2.92690e6	−0.108329
$940$	4.92434e7	1.81773
$941$	5.11990e6	0.188490	0.0942448	−	0.995549i	$-0.469956\pi$
$941$	5.11990e6	0.188490	0.0942448	+	0.995549i	$0.469956\pi$
$942$	−5.29016e7	−1.94241
$943$	3.19093e7	1.16853
$944$	−7.83908e6	−0.286309
$945$	−47192.1	−0.00171906
$946$	1.19807e7	0.435265
$947$	7.06228e6	0.255900	0.127950	−	0.991781i	$-0.459160\pi$
$947$	7.06228e6	0.255900	0.127950	+	0.991781i	$0.459160\pi$
$948$	9.80970e7	3.54515
$949$	−9.21443e6	−0.332126
$950$	−2.42754e7	−0.872686
$951$	1.69769e7	0.608704
$952$	−3.66150e6	−0.130938
$953$	−1.11466e7	−0.397568	−0.198784	−	0.980043i	$-0.563699\pi$
$953$	−1.11466e7	−0.397568	−0.198784	+	0.980043i	$0.563699\pi$
$954$	6.38621e7	2.27181
$955$	3.25735e7	1.15573
$956$	7.38620e7	2.61382
$957$	1.07827e7	0.380581
$958$	−1.39292e7	−0.490357
$959$	−9.33605e6	−0.327806
$960$	−7.57918e7	−2.65427
$961$	−1.12247e7	−0.392071
$962$	1.08780e7	0.378975
$963$	4.88285e6	0.169671
$964$	−2.24172e7	−0.776942
$965$	−2.21282e7	−0.764941
$966$	4.23731e7	1.46099
$967$	−829399.	−0.0285231	−0.0142616	−	0.999898i	$-0.504540\pi$
$967$	−829399.	−0.0285231	−0.0142616	+	0.999898i	$0.504540\pi$
$968$	1.39732e7	0.479299
$969$	−2.63767e7	−0.902425
$970$	−6.64798e7	−2.26861
$971$	1.69916e7	0.578345	0.289173	−	0.957277i	$-0.406620\pi$
$971$	1.69916e7	0.578345	0.289173	+	0.957277i	$0.406620\pi$
$972$	6.40077e7	2.17303
$973$	−8.05029e6	−0.272602
$974$	7.87558e7	2.66002
$975$	1.67950e7	0.565807
$976$	7.52912e6	0.252999
$977$	2.23722e6	0.0749846	0.0374923	−	0.999297i	$-0.488063\pi$
$977$	2.23722e6	0.0749846	0.0374923	+	0.999297i	$0.488063\pi$
$978$	1.21773e8	4.07102
$979$	−9.25551e6	−0.308634
$980$	4.46296e7	1.48442
$981$	1.16774e7	0.387412
$982$	−3.34377e7	−1.10651
$983$	−5.23217e7	−1.72702	−0.863512	−	0.504328i	$-0.831740\pi$
$983$	−5.23217e7	−1.72702	−0.863512	+	0.504328i	$0.831740\pi$
$984$	2.66161e7	0.876308
$985$	−1.13973e7	−0.374293
$986$	−7.50431e6	−0.245821
$987$	1.78540e7	0.583369
$988$	−9.72177e7	−3.16850
$989$	2.04421e7	0.664560
$990$	−3.74410e7	−1.21411
$991$	−5.33682e7	−1.72623	−0.863115	−	0.505008i	$-0.831490\pi$
$991$	−5.33682e7	−1.72623	−0.863115	+	0.505008i	$0.831490\pi$
$992$	−2.73707e7	−0.883092
$993$	4.11753e7	1.32515
$994$	−408803.	−0.0131234
$995$	5.70232e6	0.182597
$996$	−2.44262e7	−0.780202
$997$	3.97108e7	1.26523	0.632616	−	0.774465i	$-0.281981\pi$
$997$	3.97108e7	1.26523	0.632616	+	0.774465i	$0.281981\pi$
$998$	3.60460e7	1.14559
$999$	22701.5	0.000719683 0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.6.a.b.1.16	✓	117

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.6.a.b.1.16	✓	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)

\(f(q)\)	\(=\)	\(q-9.01126 q^{2} -22.0309 q^{3} +49.2028 q^{4} -64.3778 q^{5} +198.526 q^{6} +52.1292 q^{7} -155.019 q^{8} +242.362 q^{9} +O(q^{10})\)	\(q-9.01126 q^{2} -22.0309 q^{3} +49.2028 q^{4} -64.3778 q^{5} +198.526 q^{6} +52.1292 q^{7} -155.019 q^{8} +242.362 q^{9} +580.125 q^{10} -266.294 q^{11} -1083.98 q^{12} -747.757 q^{13} -469.750 q^{14} +1418.30 q^{15} -177.572 q^{16} +453.099 q^{17} -2183.98 q^{18} +2642.38 q^{19} -3167.57 q^{20} -1148.46 q^{21} +2399.65 q^{22} +4094.41 q^{23} +3415.22 q^{24} +1019.50 q^{25} +6738.24 q^{26} +14.0622 q^{27} +2564.91 q^{28} +1837.94 q^{29} -12780.7 q^{30} -4171.87 q^{31} +6560.76 q^{32} +5866.71 q^{33} -4082.99 q^{34} -3355.96 q^{35} +11924.9 q^{36} +1614.37 q^{37} -23811.1 q^{38} +16473.8 q^{39} +9979.79 q^{40} +7793.39 q^{41} +10349.0 q^{42} +4992.68 q^{43} -13102.4 q^{44} -15602.7 q^{45} -36895.8 q^{46} -15546.1 q^{47} +3912.08 q^{48} -14089.5 q^{49} -9186.96 q^{50} -9982.19 q^{51} -36791.8 q^{52} -29241.1 q^{53} -126.718 q^{54} +17143.4 q^{55} -8081.03 q^{56} -58214.0 q^{57} -16562.2 q^{58} +44145.8 q^{59} +69784.5 q^{60} -42400.3 q^{61} +37593.8 q^{62} +12634.1 q^{63} -53438.4 q^{64} +48138.9 q^{65} -52866.5 q^{66} +18983.4 q^{67} +22293.7 q^{68} -90203.5 q^{69} +30241.5 q^{70} +870.255 q^{71} -37570.7 q^{72} +12322.8 q^{73} -14547.5 q^{74} -22460.5 q^{75} +130012. q^{76} -13881.7 q^{77} -148450. q^{78} -90496.7 q^{79} +11431.7 q^{80} -59203.7 q^{81} -70228.3 q^{82} +22533.7 q^{83} -56507.2 q^{84} -29169.5 q^{85} -44990.4 q^{86} -40491.6 q^{87} +41280.7 q^{88} +34756.7 q^{89} +140600. q^{90} -38980.0 q^{91} +201456. q^{92} +91910.2 q^{93} +140090. q^{94} -170110. q^{95} -144540. q^{96} -114596. q^{97} +126965. q^{98} -64539.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9}+O(q^{10}) \) 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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