LMFDB - Embedded newform 547.6.a.b.1.5

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			1.5
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)

$f(q)$	$=$	$q-10.6726 q^{2} -19.1230 q^{3} +81.9040 q^{4} -34.6115 q^{5} +204.092 q^{6} +2.13984 q^{7} -532.605 q^{8} +122.689 q^{9} +O(q^{10})$	\(q-10.6726 q^{2} -19.1230 q^{3} +81.9040 q^{4} -34.6115 q^{5} +204.092 q^{6} +2.13984 q^{7} -532.605 q^{8} +122.689 q^{9} +369.394 q^{10} +130.415 q^{11} -1566.25 q^{12} -217.527 q^{13} -22.8377 q^{14} +661.877 q^{15} +3063.34 q^{16} -87.7116 q^{17} -1309.41 q^{18} -2948.65 q^{19} -2834.82 q^{20} -40.9203 q^{21} -1391.86 q^{22} +3893.56 q^{23} +10185.0 q^{24} -1927.04 q^{25} +2321.57 q^{26} +2300.70 q^{27} +175.262 q^{28} -2139.03 q^{29} -7063.93 q^{30} +6371.54 q^{31} -15650.4 q^{32} -2493.92 q^{33} +936.109 q^{34} -74.0633 q^{35} +10048.7 q^{36} -4957.69 q^{37} +31469.7 q^{38} +4159.77 q^{39} +18434.3 q^{40} +1091.96 q^{41} +436.725 q^{42} +20492.8 q^{43} +10681.5 q^{44} -4246.47 q^{45} -41554.3 q^{46} +11422.7 q^{47} -58580.2 q^{48} -16802.4 q^{49} +20566.5 q^{50} +1677.31 q^{51} -17816.3 q^{52} -25759.1 q^{53} -24554.4 q^{54} -4513.85 q^{55} -1139.69 q^{56} +56387.0 q^{57} +22828.9 q^{58} -24976.9 q^{59} +54210.3 q^{60} +7753.49 q^{61} -68000.8 q^{62} +262.536 q^{63} +69003.1 q^{64} +7528.94 q^{65} +26616.5 q^{66} -1877.05 q^{67} -7183.93 q^{68} -74456.6 q^{69} +790.447 q^{70} -6941.62 q^{71} -65344.9 q^{72} -64769.7 q^{73} +52911.3 q^{74} +36850.8 q^{75} -241506. q^{76} +279.067 q^{77} -44395.4 q^{78} -55905.2 q^{79} -106027. q^{80} -73809.8 q^{81} -11654.0 q^{82} -91302.5 q^{83} -3351.53 q^{84} +3035.83 q^{85} -218711. q^{86} +40904.6 q^{87} -69459.4 q^{88} -90405.5 q^{89} +45320.8 q^{90} -465.474 q^{91} +318898. q^{92} -121843. q^{93} -121909. q^{94} +102057. q^{95} +299282. q^{96} -34465.1 q^{97} +179325. q^{98} +16000.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−10.6726	−1.88666	−0.943332	−	0.331851i	$-0.892327\pi$
$2$	−10.6726	−1.88666	−0.943332	+	0.331851i	$0.892327\pi$
$3$	−19.1230	−1.22674	−0.613371	−	0.789795i	$-0.710187\pi$
$3$	−19.1230	−1.22674	−0.613371	+	0.789795i	$0.710187\pi$
$4$	81.9040	2.55950
$5$	−34.6115	−0.619150	−0.309575	−	0.950875i	$-0.600187\pi$
$5$	−34.6115	−0.619150	−0.309575	+	0.950875i	$0.600187\pi$
$6$	204.092	2.31445
$7$	2.13984	0.0165058	0.00825291	−	0.999966i	$-0.497373\pi$
$7$	2.13984	0.0165058	0.00825291	+	0.999966i	$0.497373\pi$
$8$	−532.605	−2.94225
$9$	122.689	0.504894
$10$	369.394	1.16813
$11$	130.415	0.324971	0.162485	−	0.986711i	$-0.448049\pi$
$11$	130.415	0.324971	0.162485	+	0.986711i	$0.448049\pi$
$12$	−1566.25	−3.13984
$13$	−217.527	−0.356989	−0.178494	−	0.983941i	$-0.557123\pi$
$13$	−217.527	−0.356989	−0.178494	+	0.983941i	$0.557123\pi$
$14$	−22.8377	−0.0311409
$15$	661.877	0.759537
$16$	3063.34	2.99154
$17$	−87.7116	−0.0736097	−0.0368048	−	0.999322i	$-0.511718\pi$
$17$	−87.7116	−0.0736097	−0.0368048	+	0.999322i	$0.511718\pi$
$18$	−1309.41	−0.952566
$19$	−2948.65	−1.87387	−0.936934	−	0.349506i	$-0.886349\pi$
$19$	−2948.65	−1.87387	−0.936934	+	0.349506i	$0.886349\pi$
$20$	−2834.82	−1.58471
$21$	−40.9203	−0.0202484
$22$	−1391.86	−0.613110
$23$	3893.56	1.53471	0.767357	−	0.641221i	$-0.221572\pi$
$23$	3893.56	1.53471	0.767357	+	0.641221i	$0.221572\pi$
$24$	10185.0	3.60938
$25$	−1927.04	−0.616653
$26$	2321.57	0.673517
$27$	2300.70	0.607367
$28$	175.262	0.0422467
$29$	−2139.03	−0.472304	−0.236152	−	0.971716i	$-0.575886\pi$
$29$	−2139.03	−0.472304	−0.236152	+	0.971716i	$0.575886\pi$
$30$	−7063.93	−1.43299
$31$	6371.54	1.19080	0.595402	−	0.803428i	$-0.296993\pi$
$31$	6371.54	1.19080	0.595402	+	0.803428i	$0.296993\pi$
$32$	−15650.4	−2.70178
$33$	−2493.92	−0.398655
$34$	936.109	0.138877
$35$	−74.0633	−0.0102196
$36$	10048.7	1.29228
$37$	−4957.69	−0.595354	−0.297677	−	0.954667i	$-0.596212\pi$
$37$	−4957.69	−0.595354	−0.297677	+	0.954667i	$0.596212\pi$
$38$	31469.7	3.53536
$39$	4159.77	0.437933
$40$	18434.3	1.82170
$41$	1091.96	0.101448	0.0507242	−	0.998713i	$-0.483847\pi$
$41$	1091.96	0.101448	0.0507242	+	0.998713i	$0.483847\pi$
$42$	436.725	0.0382019
$43$	20492.8	1.69017	0.845084	−	0.534634i	$-0.179550\pi$
$43$	20492.8	1.69017	0.845084	+	0.534634i	$0.179550\pi$
$44$	10681.5	0.831763
$45$	−4246.47	−0.312605
$46$	−41554.3	−2.89549
$47$	11422.7	0.754264	0.377132	−	0.926160i	$-0.376910\pi$
$47$	11422.7	0.754264	0.377132	+	0.926160i	$0.376910\pi$
$48$	−58580.2	−3.66985
$49$	−16802.4	−0.999728
$50$	20566.5	1.16342
$51$	1677.31	0.0903000
$52$	−17816.3	−0.913712
$53$	−25759.1	−1.25962	−0.629812	−	0.776748i	$-0.716868\pi$
$53$	−25759.1	−1.25962	−0.629812	+	0.776748i	$0.716868\pi$
$54$	−24554.4	−1.14590
$55$	−4513.85	−0.201206
$56$	−1139.69	−0.0485643
$57$	56387.0	2.29875
$58$	22828.9	0.891078
$59$	−24976.9	−0.934131	−0.467066	−	0.884223i	$-0.654689\pi$
$59$	−24976.9	−0.934131	−0.467066	+	0.884223i	$0.654689\pi$
$60$	54210.3	1.94403
$61$	7753.49	0.266792	0.133396	−	0.991063i	$-0.457412\pi$
$61$	7753.49	0.266792	0.133396	+	0.991063i	$0.457412\pi$
$62$	−68000.8	−2.24665
$63$	262.536	0.00833370
$64$	69003.1	2.10581
$65$	7528.94	0.221030
$66$	26616.5	0.752128
$67$	−1877.05	−0.0510846	−0.0255423	−	0.999674i	$-0.508131\pi$
$67$	−1877.05	−0.0510846	−0.0255423	+	0.999674i	$0.508131\pi$
$68$	−7183.93	−0.188404
$69$	−74456.6	−1.88270
$70$	790.447	0.0192809
$71$	−6941.62	−0.163424	−0.0817118	−	0.996656i	$-0.526039\pi$
$71$	−6941.62	−0.163424	−0.0817118	+	0.996656i	$0.526039\pi$
$72$	−65344.9	−1.48553
$73$	−64769.7	−1.42254	−0.711270	−	0.702919i	$-0.751880\pi$
$73$	−64769.7	−1.42254	−0.711270	+	0.702919i	$0.751880\pi$
$74$	52911.3	1.12323
$75$	36850.8	0.756474
$76$	−241506.	−4.79617
$77$	279.067	0.00536391
$78$	−44395.4	−0.826232
$79$	−55905.2	−1.00782	−0.503911	−	0.863755i	$-0.668106\pi$
$79$	−55905.2	−1.00782	−0.503911	+	0.863755i	$0.668106\pi$
$80$	−106027.	−1.85221
$81$	−73809.8	−1.24998
$82$	−11654.0	−0.191399
$83$	−91302.5	−1.45475	−0.727374	−	0.686242i	$-0.759259\pi$
$83$	−91302.5	−1.45475	−0.727374	+	0.686242i	$0.759259\pi$
$84$	−3351.53	−0.0518257
$85$	3035.83	0.0455754
$86$	−218711.	−3.18878
$87$	40904.6	0.579394
$88$	−69459.4	−0.956146
$89$	−90405.5	−1.20982	−0.604909	−	0.796295i	$-0.706790\pi$
$89$	−90405.5	−1.20982	−0.604909	+	0.796295i	$0.706790\pi$
$90$	45320.8	0.589781
$91$	−465.474	−0.00589239
$92$	318898.	3.92810
$93$	−121843.	−1.46081
$94$	−121909.	−1.42304
$95$	102057.	1.16021
$96$	299282.	3.31438
$97$	−34465.1	−0.371921	−0.185960	−	0.982557i	$-0.559540\pi$
$97$	−34465.1	−0.371921	−0.185960	+	0.982557i	$0.559540\pi$
$98$	179325.	1.88615
$99$	16000.5	0.164076
$100$	−157832.	−1.57832
$101$	121154.	1.18177	0.590886	−	0.806755i	$-0.298778\pi$
$101$	121154.	1.18177	0.590886	+	0.806755i	$0.298778\pi$
$102$	−17901.2	−0.170366
$103$	−133714.	−1.24189	−0.620944	−	0.783855i	$-0.713251\pi$
$103$	−133714.	−1.24189	−0.620944	+	0.783855i	$0.713251\pi$
$104$	115856.	1.05035
$105$	1416.31	0.0125368
$106$	274916.	2.37649
$107$	193843.	1.63678	0.818389	−	0.574664i	$-0.194867\pi$
$107$	193843.	1.63678	0.818389	+	0.574664i	$0.194867\pi$
$108$	188437.	1.55455
$109$	−181796.	−1.46561	−0.732803	−	0.680441i	$-0.761788\pi$
$109$	−181796.	−1.46561	−0.732803	+	0.680441i	$0.761788\pi$
$110$	48174.4	0.379607
$111$	94805.9	0.730345
$112$	6555.07	0.0493778
$113$	10467.1	0.0771136	0.0385568	−	0.999256i	$-0.487724\pi$
$113$	10467.1	0.0771136	0.0385568	+	0.999256i	$0.487724\pi$
$114$	−601795.	−4.33697
$115$	−134762.	−0.950218
$116$	−175195.	−1.20886
$117$	−26688.2	−0.180242
$118$	266568.	1.76239
$119$	−187.689	−0.00121499
$120$	−352519.	−2.23475
$121$	−144043.	−0.894394
$122$	−82749.8	−0.503347
$123$	−20881.5	−0.124451
$124$	521855.	3.04786
$125$	174859.	1.00095
$126$	−2801.94	−0.0157229
$127$	−226980.	−1.24876	−0.624378	−	0.781123i	$-0.714647\pi$
$127$	−226980.	−1.24876	−0.624378	+	0.781123i	$0.714647\pi$
$128$	−235629.	−1.27117
$129$	−391884.	−2.07340
$130$	−80353.2	−0.417008
$131$	35837.4	0.182456	0.0912281	−	0.995830i	$-0.470921\pi$
$131$	35837.4	0.182456	0.0912281	+	0.995830i	$0.470921\pi$
$132$	−204262.	−1.02036
$133$	−6309.65	−0.0309297
$134$	20033.0	0.0963794
$135$	−79630.8	−0.376051
$136$	46715.6	0.216578
$137$	295756.	1.34627	0.673135	−	0.739519i	$-0.264947\pi$
$137$	295756.	1.34627	0.673135	+	0.739519i	$0.264947\pi$
$138$	794644.	3.55201
$139$	92858.6	0.407648	0.203824	−	0.979008i	$-0.434663\pi$
$139$	92858.6	0.407648	0.203824	+	0.979008i	$0.434663\pi$
$140$	−6066.08	−0.0261570
$141$	−218436.	−0.925287
$142$	74085.0	0.308325
$143$	−28368.6	−0.116011
$144$	375839.	1.51041
$145$	74035.0	0.292427
$146$	691259.	2.68385
$147$	321313.	1.22641
$148$	−406055.	−1.52381
$149$	−249560.	−0.920894	−0.460447	−	0.887687i	$-0.652311\pi$
$149$	−249560.	−0.920894	−0.460447	+	0.887687i	$0.652311\pi$
$150$	−393293.	−1.42721
$151$	−182641.	−0.651862	−0.325931	−	0.945394i	$-0.605678\pi$
$151$	−182641.	−0.651862	−0.325931	+	0.945394i	$0.605678\pi$
$152$	1.57046e6	5.51339
$153$	−10761.3	−0.0371651
$154$	−2978.36	−0.0101199
$155$	−220529.	−0.737286
$156$	340701.	1.12089
$157$	568376.	1.84029	0.920145	−	0.391577i	$-0.128070\pi$
$157$	568376.	1.84029	0.920145	+	0.391577i	$0.128070\pi$
$158$	596653.	1.90142
$159$	492591.	1.54523
$160$	541684.	1.67281
$161$	8331.61	0.0253317
$162$	787742.	2.35828
$163$	−440678.	−1.29913	−0.649565	−	0.760306i	$-0.725049\pi$
$163$	−440678.	−1.29913	−0.649565	+	0.760306i	$0.725049\pi$
$164$	89435.5	0.259657
$165$	86318.3	0.246827
$166$	974434.	2.74462
$167$	−468359.	−1.29954	−0.649768	−	0.760133i	$-0.725134\pi$
$167$	−468359.	−1.29954	−0.649768	+	0.760133i	$0.725134\pi$
$168$	21794.3	0.0595758
$169$	−323975.	−0.872559
$170$	−32400.2	−0.0859855
$171$	−361768.	−0.946105
$172$	1.67844e6	4.32598
$173$	392121.	0.996104	0.498052	−	0.867147i	$-0.334049\pi$
$173$	392121.	0.996104	0.498052	+	0.867147i	$0.334049\pi$
$174$	−436558.	−1.09312
$175$	−4123.57	−0.0101784
$176$	399504.	0.972163
$177$	477633.	1.14594
$178$	964860.	2.28252
$179$	−14867.1	−0.0346811	−0.0173405	−	0.999850i	$-0.505520\pi$
$179$	−14867.1	−0.0346811	−0.0173405	+	0.999850i	$0.505520\pi$
$180$	−347803.	−0.800113
$181$	−116418.	−0.264133	−0.132066	−	0.991241i	$-0.542161\pi$
$181$	−116418.	−0.264133	−0.132066	+	0.991241i	$0.542161\pi$
$182$	4967.80	0.0111170
$183$	−148270.	−0.327285
$184$	−2.07373e6	−4.51551
$185$	171593.	0.368613
$186$	1.30038e6	2.75606
$187$	−11438.9	−0.0239210
$188$	935563.	1.93054
$189$	4923.14	0.0100251
$190$	−1.08921e6	−2.18892
$191$	374463.	0.742720	0.371360	−	0.928489i	$-0.378892\pi$
$191$	374463.	0.742720	0.371360	+	0.928489i	$0.378892\pi$
$192$	−1.31955e6	−2.58328
$193$	−305518.	−0.590395	−0.295198	−	0.955436i	$-0.595386\pi$
$193$	−305518.	−0.590395	−0.295198	+	0.955436i	$0.595386\pi$
$194$	367832.	0.701689
$195$	−143976.	−0.271146
$196$	−1.37619e6	−2.55880
$197$	472627.	0.867666	0.433833	−	0.900993i	$-0.357161\pi$
$197$	472627.	0.867666	0.433833	+	0.900993i	$0.357161\pi$
$198$	−170766.	−0.309556
$199$	−499750.	−0.894582	−0.447291	−	0.894388i	$-0.647611\pi$
$199$	−499750.	−0.894582	−0.447291	+	0.894388i	$0.647611\pi$
$200$	1.02635e6	1.81435
$201$	35894.9	0.0626675
$202$	−1.29302e6	−2.22961
$203$	−4577.18	−0.00779576
$204$	137378.	0.231123
$205$	−37794.2	−0.0628118
$206$	1.42707e6	2.34302
$207$	477698.	0.774868
$208$	−666358.	−1.06795
$209$	−384547.	−0.608952
$210$	−15115.7	−0.0236527
$211$	−19481.4	−0.0301242	−0.0150621	−	0.999887i	$-0.504795\pi$
$211$	−19481.4	−0.0301242	−0.0150621	+	0.999887i	$0.504795\pi$
$212$	−2.10977e6	−3.22401
$213$	132745.	0.200479
$214$	−2.06880e6	−3.08805
$215$	−709287.	−1.04647
$216$	−1.22536e6	−1.78703
$217$	13634.1	0.0196552
$218$	1.94023e6	2.76511
$219$	1.23859e6	1.74509
$220$	−369702.	−0.514986
$221$	19079.6	0.0262778
$222$	−1.01182e6	−1.37792
$223$	−330984.	−0.445702	−0.222851	−	0.974852i	$-0.571536\pi$
$223$	−330984.	−0.445702	−0.222851	+	0.974852i	$0.571536\pi$
$224$	−33489.4	−0.0445951
$225$	−236427.	−0.311345
$226$	−111711.	−0.145487
$227$	1.32547e6	1.70728	0.853641	−	0.520862i	$-0.174389\pi$
$227$	1.32547e6	1.70728	0.853641	+	0.520862i	$0.174389\pi$
$228$	4.61832e6	5.88365
$229$	666740.	0.840171	0.420085	−	0.907485i	$-0.362000\pi$
$229$	666740.	0.840171	0.420085	+	0.907485i	$0.362000\pi$
$230$	1.43826e6	1.79274
$231$	−5336.60	−0.00658013
$232$	1.13926e6	1.38964
$233$	−336702.	−0.406309	−0.203154	−	0.979147i	$-0.565119\pi$
$233$	−336702.	−0.406309	−0.203154	+	0.979147i	$0.565119\pi$
$234$	284832.	0.340055
$235$	−395356.	−0.467002
$236$	−2.04571e6	−2.39091
$237$	1.06907e6	1.23634
$238$	2003.13	0.00229227
$239$	−1.00622e6	−1.13946	−0.569731	−	0.821831i	$-0.692953\pi$
$239$	−1.00622e6	−1.13946	−0.569731	+	0.821831i	$0.692953\pi$
$240$	2.02755e6	2.27219
$241$	500785.	0.555404	0.277702	−	0.960667i	$-0.410427\pi$
$241$	500785.	0.555404	0.277702	+	0.960667i	$0.410427\pi$
$242$	1.53731e6	1.68742
$243$	852395.	0.926031
$244$	635042.	0.682854
$245$	581558.	0.618981
$246$	222859.	0.234797
$247$	641410.	0.668950
$248$	−3.39351e6	−3.50365
$249$	1.74598e6	1.78460
$250$	−1.86620e6	−1.88846
$251$	−999909.	−1.00179	−0.500894	−	0.865508i	$-0.666996\pi$
$251$	−999909.	−1.00179	−0.500894	+	0.865508i	$0.666996\pi$
$252$	21502.8	0.0213301
$253$	507777.	0.498737
$254$	2.42246e6	2.35598
$255$	−58054.3	−0.0559093
$256$	306675.	0.292468
$257$	114230.	0.107882	0.0539408	−	0.998544i	$-0.482822\pi$
$257$	114230.	0.107882	0.0539408	+	0.998544i	$0.482822\pi$
$258$	4.18241e6	3.91181
$259$	−10608.7	−0.00982680
$260$	616650.	0.565725
$261$	−262436.	−0.238463
$262$	−382478.	−0.344234
$263$	940940.	0.838827	0.419414	−	0.907795i	$-0.362236\pi$
$263$	940940.	0.838827	0.419414	+	0.907795i	$0.362236\pi$
$264$	1.32827e6	1.17294
$265$	891561.	0.779896
$266$	67340.3	0.0583540
$267$	1.72882e6	1.48413
$268$	−153738.	−0.130751
$269$	710127.	0.598350	0.299175	−	0.954198i	$-0.403289\pi$
$269$	710127.	0.598350	0.299175	+	0.954198i	$0.403289\pi$
$270$	849866.	0.709482
$271$	−7701.70	−0.00637035	−0.00318518	−	0.999995i	$-0.501014\pi$
$271$	−7701.70	−0.00637035	−0.00318518	+	0.999995i	$0.501014\pi$
$272$	−268690.	−0.220206
$273$	8901.25	0.00722844
$274$	−3.15648e6	−2.53996
$275$	−251314.	−0.200394
$276$	−6.09829e6	−4.81876
$277$	−802981.	−0.628790	−0.314395	−	0.949292i	$-0.601802\pi$
$277$	−802981.	−0.628790	−0.314395	+	0.949292i	$0.601802\pi$
$278$	−991041.	−0.769095
$279$	781720.	0.601230
$280$	39446.5	0.0300686
$281$	−2.41331e6	−1.82326	−0.911628	−	0.411016i	$-0.865174\pi$
$281$	−2.41331e6	−1.82326	−0.911628	+	0.411016i	$0.865174\pi$
$282$	2.33128e6	1.74570
$283$	803323.	0.596244	0.298122	−	0.954528i	$-0.403640\pi$
$283$	803323.	0.596244	0.298122	+	0.954528i	$0.403640\pi$
$284$	−568546.	−0.418283
$285$	−1.95164e6	−1.42327
$286$	302767.	0.218873
$287$	2336.61	0.00167449
$288$	−1.92013e6	−1.36411
$289$	−1.41216e6	−0.994582
$290$	−790145.	−0.551711
$291$	659076.	0.456250
$292$	−5.30489e6	−3.64099
$293$	−1.18938e6	−0.809379	−0.404689	−	0.914454i	$-0.632620\pi$
$293$	−1.18938e6	−0.809379	−0.404689	+	0.914454i	$0.632620\pi$
$294$	−3.42924e6	−2.31382
$295$	864488.	0.578368
$296$	2.64049e6	1.75168
$297$	300045.	0.197376
$298$	2.66345e6	1.73742
$299$	−846953.	−0.547875
$300$	3.01823e6	1.93620
$301$	43851.4	0.0278976
$302$	1.94925e6	1.22984
$303$	−2.31683e6	−1.44973
$304$	−9.03271e6	−5.60575
$305$	−268360.	−0.165184
$306$	114851.	0.0701181
$307$	631601.	0.382470	0.191235	−	0.981544i	$-0.438751\pi$
$307$	631601.	0.382470	0.191235	+	0.981544i	$0.438751\pi$
$308$	22856.7	0.0137289
$309$	2.55700e6	1.52348
$310$	2.35361e6	1.39101
$311$	−163361.	−0.0957742	−0.0478871	−	0.998853i	$-0.515249\pi$
$311$	−163361.	−0.0957742	−0.0478871	+	0.998853i	$0.515249\pi$
$312$	−2.21551e6	−1.28851
$313$	595221.	0.343414	0.171707	−	0.985148i	$-0.445072\pi$
$313$	595221.	0.343414	0.171707	+	0.985148i	$0.445072\pi$
$314$	−6.06604e6	−3.47201
$315$	−9086.78	−0.00515981
$316$	−4.57886e6	−2.57952
$317$	367545.	0.205429	0.102715	−	0.994711i	$-0.467247\pi$
$317$	367545.	0.205429	0.102715	+	0.994711i	$0.467247\pi$
$318$	−5.25722e6	−2.91533
$319$	−278960.	−0.153485
$320$	−2.38830e6	−1.30381
$321$	−3.70686e6	−2.00790
$322$	−88919.8	−0.0477924
$323$	258631.	0.137935
$324$	−6.04532e6	−3.19931
$325$	419183.	0.220138
$326$	4.70317e6	2.45102
$327$	3.47648e6	1.79792
$328$	−581580.	−0.298487
$329$	24442.8	0.0124497
$330$	−921239.	−0.465680
$331$	3.30469e6	1.65791	0.828954	−	0.559317i	$-0.188936\pi$
$331$	3.30469e6	1.65791	0.828954	+	0.559317i	$0.188936\pi$
$332$	−7.47804e6	−3.72343
$333$	−608256.	−0.300591
$334$	4.99861e6	2.45179
$335$	64967.7	0.0316290
$336$	−125353.	−0.0605738
$337$	−31583.4	−0.0151490	−0.00757450	−	0.999971i	$-0.502411\pi$
$337$	−31583.4	−0.0151490	−0.00757450	+	0.999971i	$0.502411\pi$
$338$	3.45765e6	1.64623
$339$	−200163.	−0.0945985
$340$	248647.	0.116650
$341$	830942.	0.386976
$342$	3.86100e6	1.78498
$343$	−71918.9	−0.0330071
$344$	−1.09145e7	−4.97290
$345$	2.57706e6	1.16567
$346$	−4.18494e6	−1.87931
$347$	1.50016e6	0.668828	0.334414	−	0.942426i	$-0.391462\pi$
$347$	1.50016e6	0.668828	0.334414	+	0.942426i	$0.391462\pi$
$348$	3.35025e6	1.48296
$349$	2.00496e6	0.881134	0.440567	−	0.897720i	$-0.354777\pi$
$349$	2.00496e6	0.881134	0.440567	+	0.897720i	$0.354777\pi$
$350$	44009.1	0.0192032
$351$	−500464.	−0.216823
$352$	−2.04104e6	−0.877999
$353$	701655.	0.299700	0.149850	−	0.988709i	$-0.452121\pi$
$353$	701655.	0.299700	0.149850	+	0.988709i	$0.452121\pi$
$354$	−5.09758e6	−2.16200
$355$	240260.	0.101184
$356$	−7.40457e6	−3.09653
$357$	3589.18	0.00149048
$358$	158670.	0.0654316
$359$	−2.33657e6	−0.956848	−0.478424	−	0.878129i	$-0.658792\pi$
$359$	−2.33657e6	−0.956848	−0.478424	+	0.878129i	$0.658792\pi$
$360$	2.26169e6	0.919764
$361$	6.21843e6	2.51138
$362$	1.24248e6	0.498330
$363$	2.75454e6	1.09719
$364$	−38124.1	−0.0150816
$365$	2.24178e6	0.880765
$366$	1.58242e6	0.617476
$367$	−2.22489e6	−0.862270	−0.431135	−	0.902287i	$-0.641887\pi$
$367$	−2.22489e6	−0.862270	−0.431135	+	0.902287i	$0.641887\pi$
$368$	1.19273e7	4.59116
$369$	133971.	0.0512207
$370$	−1.83134e6	−0.695449
$371$	−55120.4	−0.0207911
$372$	−9.97943e6	−3.73894
$373$	−2.80180e6	−1.04271	−0.521357	−	0.853339i	$-0.674574\pi$
$373$	−2.80180e6	−1.04271	−0.521357	+	0.853339i	$0.674574\pi$
$374$	122082.	0.0451309
$375$	−3.34383e6	−1.22791
$376$	−6.08377e6	−2.21923
$377$	465296.	0.168607
$378$	−52542.7	−0.0189140
$379$	477438.	0.170734	0.0853668	−	0.996350i	$-0.472794\pi$
$379$	477438.	0.170734	0.0853668	+	0.996350i	$0.472794\pi$
$380$	8.35890e6	2.96955
$381$	4.34053e6	1.53190
$382$	−3.99649e6	−1.40126
$383$	5.56550e6	1.93868	0.969342	−	0.245715i	$-0.0790227\pi$
$383$	5.56550e6	1.93868	0.969342	+	0.245715i	$0.0790227\pi$
$384$	4.50594e6	1.55940
$385$	−9658.93	−0.00332106
$386$	3.26066e6	1.11388
$387$	2.51425e6	0.853356
$388$	−2.82283e6	−0.951931
$389$	−984641.	−0.329916	−0.164958	−	0.986301i	$-0.552749\pi$
$389$	−984641.	−0.329916	−0.164958	+	0.986301i	$0.552749\pi$
$390$	1.53659e6	0.511561
$391$	−341510.	−0.112970
$392$	8.94905e6	2.94145
$393$	−685320.	−0.223827
$394$	−5.04415e6	−1.63699
$395$	1.93496e6	0.623994
$396$	1.31050e6	0.419952
$397$	−3.67174e6	−1.16922	−0.584609	−	0.811315i	$-0.698752\pi$
$397$	−3.67174e6	−1.16922	−0.584609	+	0.811315i	$0.698752\pi$
$398$	5.33362e6	1.68778
$399$	120659.	0.0379428
$400$	−5.90318e6	−1.84474
$401$	4.02084e6	1.24869	0.624346	−	0.781148i	$-0.285365\pi$
$401$	4.02084e6	1.24869	0.624346	+	0.781148i	$0.285365\pi$
$402$	−383091.	−0.118233
$403$	−1.38598e6	−0.425104
$404$	9.92299e6	3.02475
$405$	2.55467e6	0.773923
$406$	48850.4	0.0147080
$407$	−646555.	−0.193472
$408$	−893343.	−0.265685
$409$	4.08832e6	1.20847	0.604236	−	0.796805i	$-0.293478\pi$
$409$	4.08832e6	1.20847	0.604236	+	0.796805i	$0.293478\pi$
$410$	403362.	0.118505
$411$	−5.65575e6	−1.65153
$412$	−1.09517e7	−3.17861
$413$	−53446.6	−0.0154186
$414$	−5.09827e6	−1.46192
$415$	3.16012e6	0.900707
$416$	3.40438e6	0.964505
$417$	−1.77574e6	−0.500079
$418$	4.10410e6	1.14889
$419$	4.49613e6	1.25113	0.625566	−	0.780171i	$-0.284868\pi$
$419$	4.49613e6	1.25113	0.625566	+	0.780171i	$0.284868\pi$
$420$	116002.	0.0320879
$421$	2.56149e6	0.704347	0.352174	−	0.935935i	$-0.385443\pi$
$421$	2.56149e6	0.704347	0.352174	+	0.935935i	$0.385443\pi$
$422$	207917.	0.0568342
$423$	1.40144e6	0.380824
$424$	1.37194e7	3.70613
$425$	169024.	0.0453916
$426$	−1.41673e6	−0.378236
$427$	16591.3	0.00440362
$428$	1.58765e7	4.18934
$429$	542494.	0.142315
$430$	7.56992e6	1.97433
$431$	−1.90400e6	−0.493711	−0.246856	−	0.969052i	$-0.579397\pi$
$431$	−1.90400e6	−0.493711	−0.246856	+	0.969052i	$0.579397\pi$
$432$	7.04783e6	1.81696
$433$	−2.08484e6	−0.534382	−0.267191	−	0.963644i	$-0.586095\pi$
$433$	−2.08484e6	−0.534382	−0.267191	+	0.963644i	$0.586095\pi$
$434$	−145511.	−0.0370828
$435$	−1.41577e6	−0.358732
$436$	−1.48898e7	−3.75122
$437$	−1.14807e7	−2.87585
$438$	−1.32190e7	−3.29239
$439$	−2.76050e6	−0.683639	−0.341820	−	0.939766i	$-0.611043\pi$
$439$	−2.76050e6	−0.683639	−0.341820	+	0.939766i	$0.611043\pi$
$440$	2.40410e6	0.591998
$441$	−2.06148e6	−0.504757
$442$	−203629.	−0.0495774
$443$	1.86063e6	0.450454	0.225227	−	0.974306i	$-0.427688\pi$
$443$	1.86063e6	0.450454	0.225227	+	0.974306i	$0.427688\pi$
$444$	7.76498e6	1.86932
$445$	3.12907e6	0.749058
$446$	3.53245e6	0.840890
$447$	4.77234e6	1.12970
$448$	147656.	0.0347581
$449$	−7.04611e6	−1.64943	−0.824715	−	0.565549i	$-0.808664\pi$
$449$	−7.04611e6	−1.64943	−0.824715	+	0.565549i	$0.808664\pi$
$450$	2.52329e6	0.587403
$451$	142407.	0.0329678
$452$	857299.	0.197372
$453$	3.49264e6	0.799666
$454$	−1.41462e7	−3.22107
$455$	16110.8	0.00364827
$456$	−3.00320e7	−6.76351
$457$	6.10656e6	1.36775	0.683874	−	0.729600i	$-0.260294\pi$
$457$	6.10656e6	1.36775	0.683874	+	0.729600i	$0.260294\pi$
$458$	−7.11583e6	−1.58512
$459$	−201798.	−0.0447081
$460$	−1.10376e7	−2.43208
$461$	2.78801e6	0.611002	0.305501	−	0.952192i	$-0.401176\pi$
$461$	2.78801e6	0.611002	0.305501	+	0.952192i	$0.401176\pi$
$462$	56955.3	0.0124145
$463$	1.29138e6	0.279964	0.139982	−	0.990154i	$-0.455296\pi$
$463$	1.29138e6	0.279964	0.139982	+	0.990154i	$0.455296\pi$
$464$	−6.55256e6	−1.41292
$465$	4.21718e6	0.904460
$466$	3.59348e6	0.766568
$467$	−82782.1	−0.0175648	−0.00878242	−	0.999961i	$-0.502796\pi$
$467$	−82782.1	−0.0175648	−0.00878242	+	0.999961i	$0.502796\pi$
$468$	−2.18587e6	−0.461328
$469$	−4016.60	−0.000843193 0
$470$	4.21947e6	0.881077
$471$	−1.08691e7	−2.25756
$472$	1.33028e7	2.74845
$473$	2.67256e6	0.549255
$474$	−1.14098e7	−2.33255
$475$	5.68217e6	1.15553
$476$	−15372.5	−0.00310976
$477$	−3.16036e6	−0.635977
$478$	1.07390e7	2.14978
$479$	416882.	0.0830184	0.0415092	−	0.999138i	$-0.486783\pi$
$479$	416882.	0.0830184	0.0415092	+	0.999138i	$0.486783\pi$
$480$	−1.03586e7	−2.05210
$481$	1.07843e6	0.212534
$482$	−5.34467e6	−1.04786
$483$	−159325.	−0.0310754
$484$	−1.17977e7	−2.28920
$485$	1.19289e6	0.230275
$486$	−9.09726e6	−1.74711
$487$	6.48318e6	1.23870	0.619349	−	0.785115i	$-0.287396\pi$
$487$	6.48318e6	1.23870	0.619349	+	0.785115i	$0.287396\pi$
$488$	−4.12954e6	−0.784969
$489$	8.42709e6	1.59370
$490$	−6.20672e6	−1.16781
$491$	−5.71451e6	−1.06973	−0.534866	−	0.844937i	$-0.679638\pi$
$491$	−5.71451e6	−1.06973	−0.534866	+	0.844937i	$0.679638\pi$
$492$	−1.71028e6	−0.318532
$493$	187617.	0.0347661
$494$	−6.84550e6	−1.26208
$495$	−553801.	−0.101588
$496$	1.95182e7	3.56234
$497$	−14854.0	−0.00269744
$498$	−1.86341e7	−3.36694
$499$	5.11811e6	0.920150	0.460075	−	0.887880i	$-0.347823\pi$
$499$	5.11811e6	0.920150	0.460075	+	0.887880i	$0.347823\pi$
$500$	1.43216e7	2.56193
$501$	8.95644e6	1.59419
$502$	1.06716e7	1.89004
$503$	−6.08392e6	−1.07217	−0.536085	−	0.844164i	$-0.680097\pi$
$503$	−6.08392e6	−1.07217	−0.536085	+	0.844164i	$0.680097\pi$
$504$	−139828.	−0.0245198
$505$	−4.19332e6	−0.731694
$506$	−5.41929e6	−0.940949
$507$	6.19538e6	1.07040
$508$	−1.85905e7	−3.19619
$509$	−4.52354e6	−0.773898	−0.386949	−	0.922101i	$-0.626471\pi$
$509$	−4.52354e6	−0.773898	−0.386949	+	0.922101i	$0.626471\pi$
$510$	619589.	0.105482
$511$	−138597.	−0.0234802
$512$	4.26713e6	0.719385
$513$	−6.78396e6	−1.13812
$514$	−1.21913e6	−0.203536
$515$	4.62803e6	0.768915
$516$	−3.20968e7	−5.30686
$517$	1.48968e6	0.245114
$518$	113222.	0.0185399
$519$	−7.49853e6	−1.22196
$520$	−4.00995e6	−0.650325
$521$	6.40759e6	1.03419	0.517095	−	0.855928i	$-0.327013\pi$
$521$	6.40759e6	1.03419	0.517095	+	0.855928i	$0.327013\pi$
$522$	2.80087e6	0.449900
$523$	9.24113e6	1.47731	0.738654	−	0.674085i	$-0.235462\pi$
$523$	9.24113e6	1.47731	0.738654	+	0.674085i	$0.235462\pi$
$524$	2.93523e6	0.466997
$525$	78855.0	0.0124862
$526$	−1.00423e7	−1.58258
$527$	−558858.	−0.0876547
$528$	−7.63971e6	−1.19259
$529$	8.72346e6	1.35534
$530$	−9.51526e6	−1.47140
$531$	−3.06440e6	−0.471638
$532$	−516786.	−0.0791647
$533$	−237530.	−0.0362159
$534$	−1.84510e7	−2.80006
$535$	−6.70919e6	−1.01341
$536$	999727.	0.150304
$537$	284303.	0.0425447
$538$	−7.57889e6	−1.12889
$539$	−2.19128e6	−0.324882
$540$	−6.52208e6	−0.962503
$541$	−7.47491e6	−1.09803	−0.549013	−	0.835814i	$-0.684996\pi$
$541$	−7.47491e6	−1.09803	−0.549013	+	0.835814i	$0.684996\pi$
$542$	82197.0	0.0120187
$543$	2.22625e6	0.324023
$544$	1.37272e6	0.198877
$545$	6.29223e6	0.907430
$546$	−94999.3	−0.0136376
$547$	299209.	0.0427569
$547$	299209.	0.0427569
$548$	2.42236e7	3.44578
$549$	951270.	0.134702
$550$	2.68217e6	0.378077
$551$	6.30724e6	0.885034
$552$	3.96559e7	5.53937
$553$	−119628.	−0.0166349
$554$	8.56988e6	1.18632
$555$	−3.28138e6	−0.452193
$556$	7.60549e6	1.04337
$557$	−1.13727e7	−1.55319	−0.776596	−	0.629999i	$-0.783055\pi$
$557$	−1.13727e7	−1.55319	−0.776596	+	0.629999i	$0.783055\pi$
$558$	−8.34297e6	−1.13432
$559$	−4.45773e6	−0.603371
$560$	−226881.	−0.0305723
$561$	218746.	0.0293449
$562$	2.57563e7	3.43987
$563$	1.08127e6	0.143768	0.0718840	−	0.997413i	$-0.477099\pi$
$563$	1.08127e6	0.143768	0.0718840	+	0.997413i	$0.477099\pi$
$564$	−1.78908e7	−2.36827
$565$	−362283.	−0.0477449
$566$	−8.57353e6	−1.12491
$567$	−157942.	−0.0206319
$568$	3.69714e6	0.480834
$569$	−3.87061e6	−0.501186	−0.250593	−	0.968093i	$-0.580626\pi$
$569$	−3.87061e6	−0.501186	−0.250593	+	0.968093i	$0.580626\pi$
$570$	2.08291e7	2.68524
$571$	8.95301e6	1.14915	0.574577	−	0.818450i	$-0.305166\pi$
$571$	8.95301e6	1.14915	0.574577	+	0.818450i	$0.305166\pi$
$572$	−2.32351e6	−0.296930
$573$	−7.16086e6	−0.911126
$574$	−24937.7	−0.00315920
$575$	−7.50305e6	−0.946386
$576$	8.46595e6	1.06321
$577$	−4.45717e6	−0.557340	−0.278670	−	0.960387i	$-0.589893\pi$
$577$	−4.45717e6	−0.557340	−0.278670	+	0.960387i	$0.589893\pi$
$578$	1.50714e7	1.87644
$579$	5.84242e6	0.724263
$580$	6.06376e6	0.748466
$581$	−195373.	−0.0240118
$582$	−7.03404e6	−0.860791
$583$	−3.35936e6	−0.409341
$584$	3.44966e7	4.18547
$585$	923720.	0.111597
$586$	1.26938e7	1.52703
$587$	1.32036e7	1.58161	0.790803	−	0.612070i	$-0.209663\pi$
$587$	1.32036e7	1.58161	0.790803	+	0.612070i	$0.209663\pi$
$588$	2.63168e7	3.13899
$589$	−1.87874e7	−2.23141
$590$	−9.22632e6	−1.09119
$591$	−9.03805e6	−1.06440
$592$	−1.51871e7	−1.78102
$593$	8.62482e6	1.00719	0.503597	−	0.863939i	$-0.332010\pi$
$593$	8.62482e6	1.00719	0.503597	+	0.863939i	$0.332010\pi$
$594$	−3.20225e6	−0.372383
$595$	6496.21	0.000752260 0
$596$	−2.04400e7	−2.35703
$597$	9.55672e6	1.09742
$598$	9.03918e6	1.03366
$599$	−1.87380e6	−0.213381	−0.106690	−	0.994292i	$-0.534025\pi$
$599$	−1.87380e6	−0.213381	−0.106690	+	0.994292i	$0.534025\pi$
$600$	−1.96269e7	−2.22574
$601$	−6.19436e6	−0.699536	−0.349768	−	0.936836i	$-0.613740\pi$
$601$	−6.19436e6	−0.699536	−0.349768	+	0.936836i	$0.613740\pi$
$602$	−468007.	−0.0526334
$603$	−230294.	−0.0257923
$604$	−1.49590e7	−1.66844
$605$	4.98555e6	0.553764
$606$	2.47265e7	2.73515
$607$	−1.00895e7	−1.11147	−0.555735	−	0.831359i	$-0.687563\pi$
$607$	−1.00895e7	−1.11147	−0.555735	+	0.831359i	$0.687563\pi$
$608$	4.61475e7	5.06278
$609$	87529.5	0.00956338
$610$	2.86410e6	0.311647
$611$	−2.48474e6	−0.269264
$612$	−881392.	−0.0951241
$613$	1.77112e7	1.90369	0.951847	−	0.306573i	$-0.0991823\pi$
$613$	1.77112e7	1.90369	0.951847	+	0.306573i	$0.0991823\pi$
$614$	−6.74081e6	−0.721591
$615$	722740.	0.0770538
$616$	−148632.	−0.0157820
$617$	4.08149e6	0.431624	0.215812	−	0.976435i	$-0.430760\pi$
$617$	4.08149e6	0.431624	0.215812	+	0.976435i	$0.430760\pi$
$618$	−2.72898e7	−2.87429
$619$	3.56505e6	0.373972	0.186986	−	0.982363i	$-0.440128\pi$
$619$	3.56505e6	0.373972	0.186986	+	0.982363i	$0.440128\pi$
$620$	−1.80622e7	−1.88708
$621$	8.95792e6	0.932134
$622$	1.74349e6	0.180694
$623$	−193454.	−0.0199690
$624$	1.27428e7	1.31009
$625$	−30131.6	−0.00308548
$626$	−6.35255e6	−0.647906
$627$	7.35369e6	0.747027
$628$	4.65522e7	4.71022
$629$	434847.	0.0438238
$630$	96979.4	0.00973482
$631$	−1.39331e7	−1.39307	−0.696535	−	0.717523i	$-0.745276\pi$
$631$	−1.39331e7	−1.39307	−0.696535	+	0.717523i	$0.745276\pi$
$632$	2.97754e7	2.96527
$633$	372544.	0.0369546
$634$	−3.92265e6	−0.387576
$635$	7.85611e6	0.773167
$636$	4.03452e7	3.95502
$637$	3.65498e6	0.356891
$638$	2.97722e6	0.289574
$639$	−851662.	−0.0825117
$640$	8.15550e6	0.787047
$641$	708272.	0.0680855	0.0340428	−	0.999420i	$-0.489162\pi$
$641$	708272.	0.0680855	0.0340428	+	0.999420i	$0.489162\pi$
$642$	3.95617e7	3.78824
$643$	−1.69470e7	−1.61646	−0.808231	−	0.588866i	$-0.799575\pi$
$643$	−1.69470e7	−1.61646	−0.808231	+	0.588866i	$0.799575\pi$
$644$	682392.	0.0648365
$645$	1.35637e7	1.28374
$646$	−2.76026e6	−0.260237
$647$	1.01551e7	0.953725	0.476862	−	0.878978i	$-0.341774\pi$
$647$	1.01551e7	0.953725	0.476862	+	0.878978i	$0.341774\pi$
$648$	3.93115e7	3.67775
$649$	−3.25735e6	−0.303565
$650$	−4.47377e6	−0.415327
$651$	−260725.	−0.0241118
$652$	−3.60933e7	−3.32512
$653$	1.00983e7	0.926752	0.463376	−	0.886162i	$-0.346638\pi$
$653$	1.00983e7	0.926752	0.463376	+	0.886162i	$0.346638\pi$
$654$	−3.71030e7	−3.39207
$655$	−1.24039e6	−0.112968
$656$	3.34503e6	0.303487
$657$	−7.94654e6	−0.718232
$658$	−260867.	−0.0234885
$659$	1.72736e7	1.54942	0.774710	−	0.632317i	$-0.217896\pi$
$659$	1.72736e7	1.54942	0.774710	+	0.632317i	$0.217896\pi$
$660$	7.06982e6	0.631754
$661$	1.99120e7	1.77260	0.886299	−	0.463114i	$-0.153268\pi$
$661$	1.99120e7	1.77260	0.886299	+	0.463114i	$0.153268\pi$
$662$	−3.52695e7	−3.12791
$663$	−364860.	−0.0322361
$664$	4.86281e7	4.28023
$665$	218387.	0.0191501
$666$	6.49166e6	0.567114
$667$	−8.32843e6	−0.724850
$668$	−3.83605e7	−3.32616
$669$	6.32941e6	0.546761
$670$	−693373.	−0.0596733
$671$	1.01117e6	0.0866996
$672$	640418.	0.0547066
$673$	8.81639e6	0.750331	0.375166	−	0.926958i	$-0.377586\pi$
$673$	8.81639e6	0.750331	0.375166	+	0.926958i	$0.377586\pi$
$674$	337076.	0.0285811
$675$	−4.43355e6	−0.374535
$676$	−2.65349e7	−2.23332
$677$	8.33532e6	0.698957	0.349479	−	0.936944i	$-0.386359\pi$
$677$	8.33532e6	0.698957	0.349479	+	0.936944i	$0.386359\pi$
$678$	2.13625e6	0.178475
$679$	−73749.9	−0.00613885
$680$	−1.61690e6	−0.134094
$681$	−2.53470e7	−2.09439
$682$	−8.86829e6	−0.730095
$683$	−8.20735e6	−0.673211	−0.336606	−	0.941646i	$-0.609279\pi$
$683$	−8.20735e6	−0.673211	−0.336606	+	0.941646i	$0.609279\pi$
$684$	−2.96302e7	−2.42156
$685$	−1.02366e7	−0.833543
$686$	767561.	0.0622734
$687$	−1.27501e7	−1.03067
$688$	6.27763e7	5.05621
$689$	5.60329e6	0.449671
$690$	−2.75038e7	−2.19923
$691$	−1.14692e7	−0.913774	−0.456887	−	0.889525i	$-0.651036\pi$
$691$	−1.14692e7	−0.913774	−0.456887	+	0.889525i	$0.651036\pi$
$692$	3.21163e7	2.54953
$693$	34238.5	0.00270821
$694$	−1.60106e7	−1.26185
$695$	−3.21398e6	−0.252395
$696$	−2.17860e7	−1.70472
$697$	−95777.2	−0.00746758
$698$	−2.13981e7	−1.66240
$699$	6.43876e6	0.498436
$700$	−337737.	−0.0260515
$701$	−3.18606e6	−0.244883	−0.122441	−	0.992476i	$-0.539072\pi$
$701$	−3.18606e6	−0.244883	−0.122441	+	0.992476i	$0.539072\pi$
$702$	5.34125e6	0.409072
$703$	1.46185e7	1.11561
$704$	8.99901e6	0.684326
$705$	7.56040e6	0.572891
$706$	−7.48847e6	−0.565434
$707$	259250.	0.0195061
$708$	3.91200e7	2.93303
$709$	1.44919e7	1.08270	0.541351	−	0.840797i	$-0.317913\pi$
$709$	1.44919e7	1.08270	0.541351	+	0.840797i	$0.317913\pi$
$710$	−2.56420e6	−0.190900
$711$	−6.85897e6	−0.508844
$712$	4.81504e7	3.55959
$713$	2.48080e7	1.82754
$714$	−38305.8	−0.00281203
$715$	981883.	0.0718281
$716$	−1.21767e6	−0.0887663
$717$	1.92420e7	1.39783
$718$	2.49373e7	1.80525
$719$	1.75488e7	1.26598	0.632989	−	0.774161i	$-0.281828\pi$
$719$	1.75488e7	1.26598	0.632989	+	0.774161i	$0.281828\pi$
$720$	−1.30084e7	−0.935172
$721$	−286126.	−0.0204984
$722$	−6.63667e7	−4.73813
$723$	−9.57652e6	−0.681337
$724$	−9.53507e6	−0.676048
$725$	4.12199e6	0.291248
$726$	−2.93980e7	−2.07003
$727$	2.65445e7	1.86268	0.931340	−	0.364150i	$-0.118641\pi$
$727$	2.65445e7	1.86268	0.931340	+	0.364150i	$0.118641\pi$
$728$	247913.	0.0173369
$729$	1.63543e6	0.113976
$730$	−2.39256e7	−1.66171
$731$	−1.79746e6	−0.124413
$732$	−1.21439e7	−0.837685
$733$	−8.09473e6	−0.556471	−0.278235	−	0.960513i	$-0.589750\pi$
$733$	−8.09473e6	−0.556471	−0.278235	+	0.960513i	$0.589750\pi$
$734$	2.37453e7	1.62681
$735$	−1.11211e7	−0.759330
$736$	−6.09357e7	−4.14646
$737$	−244795.	−0.0166010
$738$	−1.42982e6	−0.0966363
$739$	−2.84205e6	−0.191435	−0.0957175	−	0.995409i	$-0.530515\pi$
$739$	−2.84205e6	−0.191435	−0.0957175	+	0.995409i	$0.530515\pi$
$740$	1.40542e7	0.943466
$741$	−1.22657e7	−0.820628
$742$	588277.	0.0392258
$743$	−1.26977e7	−0.843823	−0.421912	−	0.906637i	$-0.638641\pi$
$743$	−1.26977e7	−0.843823	−0.421912	+	0.906637i	$0.638641\pi$
$744$	6.48942e7	4.29807
$745$	8.63766e6	0.570171
$746$	2.99024e7	1.96725
$747$	−1.12018e7	−0.734494
$748$	−936889.	−0.0612258
$749$	414793.	0.0270164
$750$	3.56873e7	2.31665
$751$	−6.83610e6	−0.442291	−0.221146	−	0.975241i	$-0.570980\pi$
$751$	−6.83610e6	−0.442291	−0.221146	+	0.975241i	$0.570980\pi$
$752$	3.49915e7	2.25641
$753$	1.91213e7	1.22894
$754$	−4.96591e6	−0.318105
$755$	6.32148e6	0.403600
$756$	403225.	0.0256592
$757$	3.48820e6	0.221239	0.110619	−	0.993863i	$-0.464717\pi$
$757$	3.48820e6	0.221239	0.110619	+	0.993863i	$0.464717\pi$
$758$	−5.09550e6	−0.322117
$759$	−9.71022e6	−0.611821
$760$	−5.43562e7	−3.41362
$761$	9.22578e6	0.577486	0.288743	−	0.957407i	$-0.406763\pi$
$761$	9.22578e6	0.577486	0.288743	+	0.957407i	$0.406763\pi$
$762$	−4.63247e7	−2.89018
$763$	−389015.	−0.0241910
$764$	3.06700e7	1.90099
$765$	372464.	0.0230108
$766$	−5.93982e7	−3.65765
$767$	5.43314e6	0.333474
$768$	−5.86454e6	−0.358782
$769$	1.40893e7	0.859158	0.429579	−	0.903029i	$-0.358662\pi$
$769$	1.40893e7	0.859158	0.429579	+	0.903029i	$0.358662\pi$
$770$	103086.	0.00626573
$771$	−2.18442e6	−0.132343
$772$	−2.50231e7	−1.51112
$773$	−3.83987e6	−0.231136	−0.115568	−	0.993300i	$-0.536869\pi$
$773$	−3.83987e6	−0.231136	−0.115568	+	0.993300i	$0.536869\pi$
$774$	−2.68335e7	−1.61000
$775$	−1.22782e7	−0.734313
$776$	1.83563e7	1.09428
$777$	202870.	0.0120549
$778$	1.05087e7	0.622441
$779$	−3.21979e6	−0.190101
$780$	−1.17922e7	−0.693998
$781$	−905288.	−0.0531079
$782$	3.64480e6	0.213136
$783$	−4.92126e6	−0.286861
$784$	−5.14715e7	−2.99073
$785$	−1.96724e7	−1.13942
$786$	7.31413e6	0.422286
$787$	−1.27468e7	−0.733609	−0.366804	−	0.930298i	$-0.619548\pi$
$787$	−1.27468e7	−0.733609	−0.366804	+	0.930298i	$0.619548\pi$
$788$	3.87100e7	2.22079
$789$	−1.79936e7	−1.02902
$790$	−2.06511e7	−1.17727
$791$	22398.0	0.00127282
$792$	−8.52192e6	−0.482753
$793$	−1.68659e6	−0.0952417
$794$	3.91870e7	2.20592
$795$	−1.70493e7	−0.956730
$796$	−4.09315e7	−2.28968
$797$	−7.04206e6	−0.392694	−0.196347	−	0.980535i	$-0.562908\pi$
$797$	−7.04206e6	−0.392694	−0.196347	+	0.980535i	$0.562908\pi$
$798$	−1.28775e6	−0.0715853
$799$	−1.00190e6	−0.0555211
$800$	3.01589e7	1.66606
$801$	−1.10918e7	−0.610830
$802$	−4.29127e7	−2.35586
$803$	−8.44690e6	−0.462284
$804$	2.93994e6	0.160398
$805$	−288370.	−0.0156841
$806$	1.47920e7	0.802028
$807$	−1.35798e7	−0.734021
$808$	−6.45271e7	−3.47707
$809$	−1.05101e7	−0.564591	−0.282296	−	0.959327i	$-0.591096\pi$
$809$	−1.05101e7	−0.564591	−0.282296	+	0.959327i	$0.591096\pi$
$810$	−2.72649e7	−1.46013
$811$	−1.04187e7	−0.556241	−0.278121	−	0.960546i	$-0.589712\pi$
$811$	−1.04187e7	−0.556241	−0.278121	+	0.960546i	$0.589712\pi$
$812$	−374890.	−0.0199532
$813$	147280.	0.00781477
$814$	6.90041e6	0.365018
$815$	1.52525e7	0.804356
$816$	5.13817e6	0.270136
$817$	−6.04260e7	−3.16715
$818$	−4.36329e7	−2.27998
$819$	−57108.6	−0.00297503
$820$	−3.09550e6	−0.160767
$821$	1.65112e6	0.0854908	0.0427454	−	0.999086i	$-0.486390\pi$
$821$	1.65112e6	0.0854908	0.0427454	+	0.999086i	$0.486390\pi$
$822$	6.03614e7	3.11587
$823$	−2.30706e6	−0.118730	−0.0593648	−	0.998236i	$-0.518908\pi$
$823$	−2.30706e6	−0.118730	−0.0593648	+	0.998236i	$0.518908\pi$
$824$	7.12165e7	3.65395
$825$	4.80588e6	0.245832
$826$	570413.	0.0290897
$827$	−2.95902e7	−1.50447	−0.752237	−	0.658893i	$-0.771025\pi$
$827$	−2.95902e7	−1.50447	−0.752237	+	0.658893i	$0.771025\pi$
$828$	3.91254e7	1.98327
$829$	3.66039e7	1.84987	0.924936	−	0.380124i	$-0.124119\pi$
$829$	3.66039e7	1.84987	0.924936	+	0.380124i	$0.124119\pi$
$830$	−3.37267e7	−1.69933
$831$	1.53554e7	0.771363
$832$	−1.50100e7	−0.751750
$833$	1.47377e6	0.0735896
$834$	1.89517e7	0.943480
$835$	1.62106e7	0.804607
$836$	−3.14959e7	−1.55861
$837$	1.46590e7	0.723255
$838$	−4.79853e7	−2.36047
$839$	1.22873e6	0.0602633	0.0301317	−	0.999546i	$-0.490407\pi$
$839$	1.22873e6	0.0602633	0.0301317	+	0.999546i	$0.490407\pi$
$840$	−754335.	−0.0368864
$841$	−1.59357e7	−0.776929
$842$	−2.73377e7	−1.32887
$843$	4.61498e7	2.23666
$844$	−1.59561e6	−0.0771028
$845$	1.12133e7	0.540245
$846$	−1.49570e7	−0.718486
$847$	−308230.	−0.0147627
$848$	−7.89088e7	−3.76821
$849$	−1.53619e7	−0.731437
$850$	−1.80392e6	−0.0856388
$851$	−1.93031e7	−0.913697
$852$	1.08723e7	0.513125
$853$	−1.16916e7	−0.550176	−0.275088	−	0.961419i	$-0.588707\pi$
$853$	−1.16916e7	−0.550176	−0.275088	+	0.961419i	$0.588707\pi$
$854$	−177072.	−0.00830815
$855$	1.25213e7	0.585781
$856$	−1.03242e8	−4.81582
$857$	−2.39453e7	−1.11370	−0.556849	−	0.830614i	$-0.687990\pi$
$857$	−2.39453e7	−1.11370	−0.556849	+	0.830614i	$0.687990\pi$
$858$	−5.78981e6	−0.268501
$859$	3.57936e7	1.65509	0.827546	−	0.561398i	$-0.189736\pi$
$859$	3.57936e7	1.65509	0.827546	+	0.561398i	$0.189736\pi$
$860$	−5.80934e7	−2.67843
$861$	−44683.1	−0.00205416
$862$	2.03206e7	0.931467
$863$	−2.14151e7	−0.978796	−0.489398	−	0.872060i	$-0.662784\pi$
$863$	−2.14151e7	−0.978796	−0.489398	+	0.872060i	$0.662784\pi$
$864$	−3.60069e7	−1.64097
$865$	−1.35719e7	−0.616738
$866$	2.22506e7	1.00820
$867$	2.70048e7	1.22009
$868$	1.11669e6	0.0503075
$869$	−7.29085e6	−0.327513
$870$	1.51099e7	0.676807
$871$	408309.	0.0182366
$872$	9.68252e7	4.31218
$873$	−4.22850e6	−0.187781
$874$	1.22529e8	5.42576
$875$	374171.	0.0165215
$876$	1.01446e8	4.46655
$877$	−2.47762e7	−1.08777	−0.543884	−	0.839161i	$-0.683047\pi$
$877$	−2.47762e7	−1.08777	−0.543884	+	0.839161i	$0.683047\pi$
$878$	2.94617e7	1.28980
$879$	2.27445e7	0.992898
$880$	−1.38274e7	−0.601915
$881$	−2.80671e7	−1.21831	−0.609154	−	0.793052i	$-0.708491\pi$
$881$	−2.80671e7	−1.21831	−0.609154	+	0.793052i	$0.708491\pi$
$882$	2.20013e7	0.952306
$883$	2.16189e7	0.933109	0.466555	−	0.884492i	$-0.345495\pi$
$883$	2.16189e7	0.933109	0.466555	+	0.884492i	$0.345495\pi$
$884$	1.56270e6	0.0672581
$885$	−1.65316e7	−0.709507
$886$	−1.98577e7	−0.849855
$887$	−2.73249e7	−1.16614	−0.583069	−	0.812422i	$-0.698148\pi$
$887$	−2.73249e7	−1.16614	−0.583069	+	0.812422i	$0.698148\pi$
$888$	−5.04941e7	−2.14886
$889$	−485701.	−0.0206117
$890$	−3.33953e7	−1.41322
$891$	−9.62587e6	−0.406206
$892$	−2.71089e7	−1.14078
$893$	−3.36815e7	−1.41339
$894$	−5.09332e7	−2.13136
$895$	514572.	0.0214728
$896$	−504210.	−0.0209818
$897$	1.61963e7	0.672101
$898$	7.52002e7	3.11192
$899$	−1.36289e7	−0.562421
$900$	−1.93644e7	−0.796887
$901$	2.25937e6	0.0927204
$902$	−1.51985e6	−0.0621991
$903$	−838570.	−0.0342231
$904$	−5.57484e6	−0.226888
$905$	4.02939e6	0.163538
$906$	−3.72755e7	−1.50870
$907$	3.63965e6	0.146907	0.0734534	−	0.997299i	$-0.476598\pi$
$907$	3.63965e6	0.146907	0.0734534	+	0.997299i	$0.476598\pi$
$908$	1.08561e8	4.36979
$909$	1.48643e7	0.596670
$910$	−171943.	−0.00688307
$911$	3.73528e7	1.49117	0.745586	−	0.666410i	$-0.232170\pi$
$911$	3.73528e7	1.49117	0.745586	+	0.666410i	$0.232170\pi$
$912$	1.72733e8	6.87681
$913$	−1.19072e7	−0.472750
$914$	−6.51728e7	−2.58048
$915$	5.13185e6	0.202638
$916$	5.46087e7	2.15042
$917$	76686.6	0.00301159
$918$	2.15371e6	0.0843491
$919$	−2.32685e7	−0.908822	−0.454411	−	0.890792i	$-0.650150\pi$
$919$	−2.32685e7	−0.908822	−0.454411	+	0.890792i	$0.650150\pi$
$920$	7.17749e7	2.79578
$921$	−1.20781e7	−0.469191
$922$	−2.97553e7	−1.15276
$923$	1.50999e6	0.0583404
$924$	−437089.	−0.0168418
$925$	9.55367e6	0.367127
$926$	−1.37824e7	−0.528198
$927$	−1.64052e7	−0.627022
$928$	3.34766e7	1.27606
$929$	2.21463e7	0.841904	0.420952	−	0.907083i	$-0.361696\pi$
$929$	2.21463e7	0.841904	0.420952	+	0.907083i	$0.361696\pi$
$930$	−4.50082e7	−1.70641
$931$	4.95444e7	1.87336
$932$	−2.75773e7	−1.03995
$933$	3.12396e6	0.117490
$934$	883499.	0.0331390
$935$	395917.	0.0148107
$936$	1.42143e7	0.530316
$937$	−8.15991e6	−0.303624	−0.151812	−	0.988409i	$-0.548511\pi$
$937$	−8.15991e6	−0.303624	−0.151812	+	0.988409i	$0.548511\pi$
$938$	42867.5	0.00159082
$939$	−1.13824e7	−0.421280
$940$	−3.23813e7	−1.19529
$941$	2.85064e7	1.04947	0.524733	−	0.851267i	$-0.324165\pi$
$941$	2.85064e7	1.04947	0.524733	+	0.851267i	$0.324165\pi$
$942$	1.16001e8	4.25926
$943$	4.25159e6	0.155694
$944$	−7.65126e7	−2.79449
$945$	−170398.	−0.00620703
$946$	−2.85231e7	−1.03626
$947$	−2.95167e7	−1.06953	−0.534765	−	0.845001i	$-0.679600\pi$
$947$	−2.95167e7	−1.06953	−0.534765	+	0.845001i	$0.679600\pi$
$948$	8.75615e7	3.16441
$949$	1.40891e7	0.507831
$950$	−6.06434e7	−2.18009
$951$	−7.02857e6	−0.252009
$952$	99964.1	0.00357480
$953$	3.36231e7	1.19924	0.599618	−	0.800286i	$-0.295319\pi$
$953$	3.36231e7	1.19924	0.599618	+	0.800286i	$0.295319\pi$
$954$	3.37292e7	1.19987
$955$	−1.29607e7	−0.459855
$956$	−8.24138e7	−2.91646
$957$	5.33456e6	0.188286
$958$	−4.44921e6	−0.156628
$959$	632872.	0.0222213
$960$	4.56716e7	1.59944
$961$	1.19674e7	0.418015
$962$	−1.15096e7	−0.400981
$963$	2.37824e7	0.826400
$964$	4.10163e7	1.42156
$965$	1.05744e7	0.365543
$966$	1.70041e6	0.0586289
$967$	−2.86360e7	−0.984795	−0.492398	−	0.870370i	$-0.663879\pi$
$967$	−2.86360e7	−0.984795	−0.492398	+	0.870370i	$0.663879\pi$
$968$	7.67180e7	2.63153
$969$	−4.94580e6	−0.169210
$970$	−1.27312e7	−0.434451
$971$	−4.29383e7	−1.46149	−0.730746	−	0.682650i	$-0.760828\pi$
$971$	−4.29383e7	−1.46149	−0.730746	+	0.682650i	$0.760828\pi$
$972$	6.98146e7	2.37018
$973$	198703.	0.00672856
$974$	−6.91923e7	−2.33701
$975$	−8.01604e6	−0.270053
$976$	2.37516e7	0.798119
$977$	1.53355e7	0.513998	0.256999	−	0.966412i	$-0.417266\pi$
$977$	1.53355e7	0.513998	0.256999	+	0.966412i	$0.417266\pi$
$978$	−8.99388e7	−3.00677
$979$	−1.17902e7	−0.393155
$980$	4.76319e7	1.58428
$981$	−2.23044e7	−0.739976
$982$	6.09885e7	2.01822
$983$	−3.40582e7	−1.12418	−0.562092	−	0.827075i	$-0.690003\pi$
$983$	−3.40582e7	−1.12418	−0.562092	+	0.827075i	$0.690003\pi$
$984$	1.11216e7	0.366166
$985$	−1.63583e7	−0.537216
$986$	−2.00236e6	−0.0655919
$987$	−467419.	−0.0152726
$988$	5.25341e7	1.71218
$989$	7.97899e7	2.59392
$990$	5.91048e6	0.191662
$991$	2.09306e7	0.677013	0.338507	−	0.940964i	$-0.390078\pi$
$991$	2.09306e7	0.677013	0.338507	+	0.940964i	$0.390078\pi$
$992$	−9.97171e7	−3.21729
$993$	−6.31956e7	−2.03382
$994$	158530.	0.00508916
$995$	1.72971e7	0.553880
$996$	1.43003e8	4.56768
$997$	−3.14074e7	−1.00068	−0.500339	−	0.865830i	$-0.666791\pi$
$997$	−3.14074e7	−1.00068	−0.500339	+	0.865830i	$0.666791\pi$
$998$	−5.46235e7	−1.73601
$999$	−1.14062e7	−0.361598

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.6.a.b.1.5	✓	117

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.6.a.b.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-10.6726 q^{2} -19.1230 q^{3} +81.9040 q^{4} -34.6115 q^{5} +204.092 q^{6} +2.13984 q^{7} -532.605 q^{8} +122.689 q^{9} +O(q^{10})\)	\(q-10.6726 q^{2} -19.1230 q^{3} +81.9040 q^{4} -34.6115 q^{5} +204.092 q^{6} +2.13984 q^{7} -532.605 q^{8} +122.689 q^{9} +369.394 q^{10} +130.415 q^{11} -1566.25 q^{12} -217.527 q^{13} -22.8377 q^{14} +661.877 q^{15} +3063.34 q^{16} -87.7116 q^{17} -1309.41 q^{18} -2948.65 q^{19} -2834.82 q^{20} -40.9203 q^{21} -1391.86 q^{22} +3893.56 q^{23} +10185.0 q^{24} -1927.04 q^{25} +2321.57 q^{26} +2300.70 q^{27} +175.262 q^{28} -2139.03 q^{29} -7063.93 q^{30} +6371.54 q^{31} -15650.4 q^{32} -2493.92 q^{33} +936.109 q^{34} -74.0633 q^{35} +10048.7 q^{36} -4957.69 q^{37} +31469.7 q^{38} +4159.77 q^{39} +18434.3 q^{40} +1091.96 q^{41} +436.725 q^{42} +20492.8 q^{43} +10681.5 q^{44} -4246.47 q^{45} -41554.3 q^{46} +11422.7 q^{47} -58580.2 q^{48} -16802.4 q^{49} +20566.5 q^{50} +1677.31 q^{51} -17816.3 q^{52} -25759.1 q^{53} -24554.4 q^{54} -4513.85 q^{55} -1139.69 q^{56} +56387.0 q^{57} +22828.9 q^{58} -24976.9 q^{59} +54210.3 q^{60} +7753.49 q^{61} -68000.8 q^{62} +262.536 q^{63} +69003.1 q^{64} +7528.94 q^{65} +26616.5 q^{66} -1877.05 q^{67} -7183.93 q^{68} -74456.6 q^{69} +790.447 q^{70} -6941.62 q^{71} -65344.9 q^{72} -64769.7 q^{73} +52911.3 q^{74} +36850.8 q^{75} -241506. q^{76} +279.067 q^{77} -44395.4 q^{78} -55905.2 q^{79} -106027. q^{80} -73809.8 q^{81} -11654.0 q^{82} -91302.5 q^{83} -3351.53 q^{84} +3035.83 q^{85} -218711. q^{86} +40904.6 q^{87} -69459.4 q^{88} -90405.5 q^{89} +45320.8 q^{90} -465.474 q^{91} +318898. q^{92} -121843. q^{93} -121909. q^{94} +102057. q^{95} +299282. q^{96} -34465.1 q^{97} +179325. q^{98} +16000.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9}+O(q^{10}) \) 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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