LMFDB - Embedded newform 547.6.a.a.1.11

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:	$1$
Dimension:	$111$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-9.83916 q^{2} +24.1089 q^{3} +64.8091 q^{4} -28.9694 q^{5} -237.211 q^{6} +28.9470 q^{7} -322.814 q^{8} +338.239 q^{9} +O(q^{10})$	\(q-9.83916 q^{2} +24.1089 q^{3} +64.8091 q^{4} -28.9694 q^{5} -237.211 q^{6} +28.9470 q^{7} -322.814 q^{8} +338.239 q^{9} +285.035 q^{10} -366.088 q^{11} +1562.48 q^{12} +235.109 q^{13} -284.815 q^{14} -698.421 q^{15} +1102.33 q^{16} -1639.05 q^{17} -3327.98 q^{18} +1041.14 q^{19} -1877.48 q^{20} +697.881 q^{21} +3602.00 q^{22} +3367.66 q^{23} -7782.69 q^{24} -2285.77 q^{25} -2313.28 q^{26} +2296.10 q^{27} +1876.03 q^{28} +1435.26 q^{29} +6871.88 q^{30} +5763.11 q^{31} -515.933 q^{32} -8825.98 q^{33} +16126.9 q^{34} -838.580 q^{35} +21920.9 q^{36} +11736.8 q^{37} -10244.0 q^{38} +5668.22 q^{39} +9351.74 q^{40} -16218.3 q^{41} -6866.57 q^{42} -517.345 q^{43} -23725.8 q^{44} -9798.58 q^{45} -33134.9 q^{46} -24601.7 q^{47} +26575.9 q^{48} -15969.1 q^{49} +22490.1 q^{50} -39515.7 q^{51} +15237.2 q^{52} +15028.2 q^{53} -22591.7 q^{54} +10605.4 q^{55} -9344.51 q^{56} +25100.8 q^{57} -14121.8 q^{58} +3937.07 q^{59} -45264.0 q^{60} -36449.5 q^{61} -56704.2 q^{62} +9791.01 q^{63} -30198.1 q^{64} -6810.98 q^{65} +86840.2 q^{66} -47590.6 q^{67} -106225. q^{68} +81190.5 q^{69} +8250.92 q^{70} -32735.6 q^{71} -109188. q^{72} +44888.1 q^{73} -115480. q^{74} -55107.4 q^{75} +67475.6 q^{76} -10597.2 q^{77} -55770.5 q^{78} +62651.7 q^{79} -31933.8 q^{80} -26835.6 q^{81} +159575. q^{82} -8638.84 q^{83} +45229.0 q^{84} +47482.4 q^{85} +5090.24 q^{86} +34602.5 q^{87} +118178. q^{88} -91459.7 q^{89} +96409.8 q^{90} +6805.71 q^{91} +218255. q^{92} +138942. q^{93} +242060. q^{94} -30161.4 q^{95} -12438.6 q^{96} -60942.7 q^{97} +157122. q^{98} -123825. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 111 q - 28 q^{2} - 98 q^{3} + 1722 q^{4} - 801 q^{5} - 414 q^{6} - 587 q^{7} - 1344 q^{8} + 8241 q^{9}+O(q^{10}) $ 111 * q - 28 * q^2 - 98 * q^3 + 1722 * q^4 - 801 * q^5 - 414 * q^6 - 587 * q^7 - 1344 * q^8 + 8241 * q^9	\( 111 q - 28 q^{2} - 98 q^{3} + 1722 q^{4} - 801 q^{5} - 414 q^{6} - 587 q^{7} - 1344 q^{8} + 8241 q^{9} - 950 q^{10} - 1832 q^{11} - 4143 q^{12} - 4369 q^{13} - 4777 q^{14} - 3487 q^{15} + 26274 q^{16} - 13648 q^{17} - 10269 q^{18} - 5446 q^{19} - 26032 q^{20} - 8428 q^{21} - 8248 q^{22} - 24142 q^{23} - 18577 q^{24} + 58062 q^{25} - 17656 q^{26} - 33269 q^{27} - 23512 q^{28} - 33752 q^{29} - 12418 q^{30} - 13781 q^{31} - 44076 q^{32} - 39186 q^{33} - 7207 q^{34} - 30833 q^{35} + 120044 q^{36} - 61582 q^{37} - 91259 q^{38} - 20077 q^{39} - 66032 q^{40} - 54181 q^{41} - 69252 q^{42} - 38600 q^{43} - 95712 q^{44} - 190880 q^{45} - 9354 q^{46} - 83886 q^{47} - 173886 q^{48} + 194148 q^{49} - 70896 q^{50} - 60673 q^{51} - 145186 q^{52} - 286874 q^{53} - 116519 q^{54} - 74821 q^{55} - 240407 q^{56} - 95180 q^{57} - 66900 q^{58} - 135740 q^{59} - 144550 q^{60} - 227450 q^{61} - 308766 q^{62} - 249721 q^{63} + 347514 q^{64} - 290374 q^{65} - 178980 q^{66} - 91006 q^{67} - 521943 q^{68} - 414510 q^{69} - 165057 q^{70} - 236165 q^{71} - 527945 q^{72} - 184618 q^{73} - 206443 q^{74} - 243897 q^{75} - 221676 q^{76} - 751131 q^{77} - 306839 q^{78} - 107446 q^{79} - 856691 q^{80} + 382187 q^{81} - 244614 q^{82} - 499547 q^{83} - 330289 q^{84} - 287103 q^{85} - 272441 q^{86} - 391281 q^{87} - 588937 q^{88} - 740774 q^{89} - 687179 q^{90} - 237213 q^{91} - 1367678 q^{92} - 754880 q^{93} - 32851 q^{94} - 295814 q^{95} - 816078 q^{96} - 320770 q^{97} - 661922 q^{98} - 547439 q^{99}+O(q^{100}) \) 111 * q - 28 * q^2 - 98 * q^3 + 1722 * q^4 - 801 * q^5 - 414 * q^6 - 587 * q^7 - 1344 * q^8 + 8241 * q^9 - 950 * q^10 - 1832 * q^11 - 4143 * q^12 - 4369 * q^13 - 4777 * q^14 - 3487 * q^15 + 26274 * q^16 - 13648 * q^17 - 10269 * q^18 - 5446 * q^19 - 26032 * q^20 - 8428 * q^21 - 8248 * q^22 - 24142 * q^23 - 18577 * q^24 + 58062 * q^25 - 17656 * q^26 - 33269 * q^27 - 23512 * q^28 - 33752 * q^29 - 12418 * q^30 - 13781 * q^31 - 44076 * q^32 - 39186 * q^33 - 7207 * q^34 - 30833 * q^35 + 120044 * q^36 - 61582 * q^37 - 91259 * q^38 - 20077 * q^39 - 66032 * q^40 - 54181 * q^41 - 69252 * q^42 - 38600 * q^43 - 95712 * q^44 - 190880 * q^45 - 9354 * q^46 - 83886 * q^47 - 173886 * q^48 + 194148 * q^49 - 70896 * q^50 - 60673 * q^51 - 145186 * q^52 - 286874 * q^53 - 116519 * q^54 - 74821 * q^55 - 240407 * q^56 - 95180 * q^57 - 66900 * q^58 - 135740 * q^59 - 144550 * q^60 - 227450 * q^61 - 308766 * q^62 - 249721 * q^63 + 347514 * q^64 - 290374 * q^65 - 178980 * q^66 - 91006 * q^67 - 521943 * q^68 - 414510 * q^69 - 165057 * q^70 - 236165 * q^71 - 527945 * q^72 - 184618 * q^73 - 206443 * q^74 - 243897 * q^75 - 221676 * q^76 - 751131 * q^77 - 306839 * q^78 - 107446 * q^79 - 856691 * q^80 + 382187 * q^81 - 244614 * q^82 - 499547 * q^83 - 330289 * q^84 - 287103 * q^85 - 272441 * q^86 - 391281 * q^87 - 588937 * q^88 - 740774 * q^89 - 687179 * q^90 - 237213 * q^91 - 1367678 * q^92 - 754880 * q^93 - 32851 * q^94 - 295814 * q^95 - 816078 * q^96 - 320770 * q^97 - 661922 * q^98 - 547439 * 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 $

$2$	−9.83916	−1.73933	−0.869667	−	0.493638i	$-0.835667\pi$
$2$	−9.83916	−1.73933	−0.869667	+	0.493638i	$0.835667\pi$
$3$	24.1089	1.54659	0.773293	−	0.634049i	$-0.218608\pi$
$3$	24.1089	1.54659	0.773293	+	0.634049i	$0.218608\pi$
$4$	64.8091	2.02528
$5$	−28.9694	−0.518221	−0.259111	−	0.965848i	$-0.583429\pi$
$5$	−28.9694	−0.518221	−0.259111	+	0.965848i	$0.583429\pi$
$6$	−237.211	−2.69003
$7$	28.9470	0.223285	0.111642	−	0.993748i	$-0.464389\pi$
$7$	28.9470	0.223285	0.111642	+	0.993748i	$0.464389\pi$
$8$	−322.814	−1.78331
$9$	338.239	1.39193
$10$	285.035	0.901360
$11$	−366.088	−0.912229	−0.456114	−	0.889921i	$-0.650759\pi$
$11$	−366.088	−0.912229	−0.456114	+	0.889921i	$0.650759\pi$
$12$	1562.48	3.13228
$13$	235.109	0.385843	0.192922	−	0.981214i	$-0.438204\pi$
$13$	235.109	0.385843	0.192922	+	0.981214i	$0.438204\pi$
$14$	−284.815	−0.388367
$15$	−698.421	−0.801473
$16$	1102.33	1.07649
$17$	−1639.05	−1.37553	−0.687766	−	0.725933i	$-0.741408\pi$
$17$	−1639.05	−1.37553	−0.687766	+	0.725933i	$0.741408\pi$
$18$	−3327.98	−2.42103
$19$	1041.14	0.661648	0.330824	−	0.943693i	$-0.392673\pi$
$19$	1041.14	0.661648	0.330824	+	0.943693i	$0.392673\pi$
$20$	−1877.48	−1.04954
$21$	697.881	0.345329
$22$	3602.00	1.58667
$23$	3367.66	1.32742	0.663710	−	0.747990i	$-0.268981\pi$
$23$	3367.66	1.32742	0.663710	+	0.747990i	$0.268981\pi$
$24$	−7782.69	−2.75805
$25$	−2285.77	−0.731447
$26$	−2313.28	−0.671111
$27$	2296.10	0.606151
$28$	1876.03	0.452215
$29$	1435.26	0.316910	0.158455	−	0.987366i	$-0.449349\pi$
$29$	1435.26	0.316910	0.158455	+	0.987366i	$0.449349\pi$
$30$	6871.88	1.39403
$31$	5763.11	1.07709	0.538546	−	0.842596i	$-0.318974\pi$
$31$	5763.11	1.07709	0.538546	+	0.842596i	$0.318974\pi$
$32$	−515.933	−0.0890674
$33$	−8825.98	−1.41084
$34$	16126.9	2.39251
$35$	−838.580	−0.115711
$36$	21920.9	2.81905
$37$	11736.8	1.40944	0.704718	−	0.709488i	$-0.251074\pi$
$37$	11736.8	1.40944	0.704718	+	0.709488i	$0.251074\pi$
$38$	−10244.0	−1.15083
$39$	5668.22	0.596740
$40$	9351.74	0.924150
$41$	−16218.3	−1.50677	−0.753385	−	0.657580i	$-0.771580\pi$
$41$	−16218.3	−1.50677	−0.753385	+	0.657580i	$0.771580\pi$
$42$	−6866.57	−0.600643
$43$	−517.345	−0.0426687	−0.0213343	−	0.999772i	$-0.506791\pi$
$43$	−517.345	−0.0426687	−0.0213343	+	0.999772i	$0.506791\pi$
$44$	−23725.8	−1.84752
$45$	−9798.58	−0.721327
$46$	−33134.9	−2.30883
$47$	−24601.7	−1.62450	−0.812250	−	0.583309i	$-0.801758\pi$
$47$	−24601.7	−1.62450	−0.812250	+	0.583309i	$0.801758\pi$
$48$	26575.9	1.66489
$49$	−15969.1	−0.950144
$50$	22490.1	1.27223
$51$	−39515.7	−2.12738
$52$	15237.2	0.781442
$53$	15028.2	0.734879	0.367440	−	0.930047i	$-0.380234\pi$
$53$	15028.2	0.734879	0.367440	+	0.930047i	$0.380234\pi$
$54$	−22591.7	−1.05430
$55$	10605.4	0.472736
$56$	−9344.51	−0.398186
$57$	25100.8	1.02330
$58$	−14121.8	−0.551212
$59$	3937.07	0.147246	0.0736230	−	0.997286i	$-0.476544\pi$
$59$	3937.07	0.147246	0.0736230	+	0.997286i	$0.476544\pi$
$60$	−45264.0	−1.62321
$61$	−36449.5	−1.25420	−0.627099	−	0.778939i	$-0.715758\pi$
$61$	−36449.5	−1.25420	−0.627099	+	0.778939i	$0.715758\pi$
$62$	−56704.2	−1.87342
$63$	9791.01	0.310796
$64$	−30198.1	−0.921574
$65$	−6810.98	−0.199952
$66$	86840.2	2.45392
$67$	−47590.6	−1.29519	−0.647596	−	0.761984i	$-0.724225\pi$
$67$	−47590.6	−1.29519	−0.647596	+	0.761984i	$0.724225\pi$
$68$	−106225.	−2.78584
$69$	81190.5	2.05297
$70$	8250.92	0.201260
$71$	−32735.6	−0.770680	−0.385340	−	0.922775i	$-0.625916\pi$
$71$	−32735.6	−0.770680	−0.385340	+	0.922775i	$0.625916\pi$
$72$	−109188.	−2.48224
$73$	44888.1	0.985879	0.492940	−	0.870064i	$-0.335922\pi$
$73$	44888.1	0.985879	0.492940	+	0.870064i	$0.335922\pi$
$74$	−115480.	−2.45148
$75$	−55107.4	−1.13125
$76$	67475.6	1.34002
$77$	−10597.2	−0.203687
$78$	−55770.5	−1.03793
$79$	62651.7	1.12945	0.564723	−	0.825281i	$-0.308983\pi$
$79$	62651.7	1.12945	0.564723	+	0.825281i	$0.308983\pi$
$80$	−31933.8	−0.557861
$81$	−26835.6	−0.454464
$82$	159575.	2.62078
$83$	−8638.84	−0.137645	−0.0688224	−	0.997629i	$-0.521924\pi$
$83$	−8638.84	−0.137645	−0.0688224	+	0.997629i	$0.521924\pi$
$84$	45229.0	0.699390
$85$	47482.4	0.712829
$86$	5090.24	0.0742151
$87$	34602.5	0.490128
$88$	118178.	1.62679
$89$	−91459.7	−1.22393	−0.611963	−	0.790887i	$-0.709620\pi$
$89$	−91459.7	−1.22393	−0.611963	+	0.790887i	$0.709620\pi$
$90$	96409.8	1.25463
$91$	6805.71	0.0861530
$92$	218255.	2.68840
$93$	138942.	1.66581
$94$	242060.	2.82555
$95$	−30161.4	−0.342880
$96$	−12438.6	−0.137750
$97$	−60942.7	−0.657646	−0.328823	−	0.944392i	$-0.606652\pi$
$97$	−60942.7	−0.657646	−0.328823	+	0.944392i	$0.606652\pi$
$98$	157122.	1.65262
$99$	−123825.	−1.26976
$100$	−148139.	−1.48139
$101$	132701.	1.29441	0.647204	−	0.762317i	$-0.275938\pi$
$101$	132701.	1.29441	0.647204	+	0.762317i	$0.275938\pi$
$102$	388802.	3.70022
$103$	35233.6	0.327238	0.163619	−	0.986524i	$-0.447683\pi$
$103$	35233.6	0.327238	0.163619	+	0.986524i	$0.447683\pi$
$104$	−75896.5	−0.688079
$105$	−20217.2	−0.178957
$106$	−147864.	−1.27820
$107$	−112266.	−0.947960	−0.473980	−	0.880536i	$-0.657183\pi$
$107$	−112266.	−0.947960	−0.473980	+	0.880536i	$0.657183\pi$
$108$	148808.	1.22763
$109$	168146.	1.35557	0.677783	−	0.735262i	$-0.262941\pi$
$109$	168146.	1.35557	0.677783	+	0.735262i	$0.262941\pi$
$110$	−104348.	−0.822246
$111$	282961.	2.17981
$112$	31909.1	0.240364
$113$	−163162.	−1.20205	−0.601025	−	0.799230i	$-0.705241\pi$
$113$	−163162.	−1.20205	−0.601025	+	0.799230i	$0.705241\pi$
$114$	−246971.	−1.77985
$115$	−97559.1	−0.687897
$116$	93017.9	0.641833
$117$	79523.0	0.537066
$118$	−38737.5	−0.256110
$119$	−47445.7	−0.307135
$120$	225460.	1.42928
$121$	−27030.6	−0.167839
$122$	358632.	2.18147
$123$	−391006.	−2.33035
$124$	373502.	2.18142
$125$	156747.	0.897272
$126$	−96335.3	−0.540579
$127$	−230912.	−1.27039	−0.635195	−	0.772352i	$-0.719080\pi$
$127$	−230912.	−1.27039	−0.635195	+	0.772352i	$0.719080\pi$
$128$	313634.	1.69199
$129$	−12472.6	−0.0659908
$130$	67014.3	0.347784
$131$	203423.	1.03567	0.517837	−	0.855480i	$-0.326738\pi$
$131$	203423.	1.03567	0.517837	+	0.855480i	$0.326738\pi$
$132$	−572003.	−2.85735
$133$	30138.0	0.147736
$134$	468251.	2.25277
$135$	−66516.7	−0.314120
$136$	529109.	2.45300
$137$	11679.7	0.0531654	0.0265827	−	0.999647i	$-0.491537\pi$
$137$	11679.7	0.0531654	0.0265827	+	0.999647i	$0.491537\pi$
$138$	−798846.	−3.57080
$139$	−293445.	−1.28822	−0.644109	−	0.764934i	$-0.722772\pi$
$139$	−293445.	−1.28822	−0.644109	+	0.764934i	$0.722772\pi$
$140$	−54347.6	−0.234347
$141$	−593119.	−2.51243
$142$	322091.	1.34047
$143$	−86070.6	−0.351977
$144$	372850.	1.49840
$145$	−41578.7	−0.164229
$146$	−441661.	−1.71477
$147$	−384997.	−1.46948
$148$	760651.	2.85451
$149$	−519010.	−1.91518	−0.957591	−	0.288130i	$-0.906966\pi$
$149$	−519010.	−1.91518	−0.957591	+	0.288130i	$0.906966\pi$
$150$	542211.	1.96761
$151$	265030.	0.945915	0.472957	−	0.881085i	$-0.343186\pi$
$151$	265030.	0.945915	0.472957	+	0.881085i	$0.343186\pi$
$152$	−336096.	−1.17992
$153$	−554391.	−1.91464
$154$	104267.	0.354279
$155$	−166954.	−0.558171
$156$	367352.	1.20857
$157$	536688.	1.73769	0.868846	−	0.495082i	$-0.164862\pi$
$157$	536688.	1.73769	0.868846	+	0.495082i	$0.164862\pi$
$158$	−616440.	−1.96448
$159$	362312.	1.13655
$160$	14946.3	0.0461566
$161$	97483.7	0.296393
$162$	264040.	0.790464
$163$	−334067.	−0.984836	−0.492418	−	0.870359i	$-0.663887\pi$
$163$	−334067.	−0.984836	−0.492418	+	0.870359i	$0.663887\pi$
$164$	−1.05110e6	−3.05164
$165$	255684.	0.731127
$166$	84998.9	0.239410
$167$	354862.	0.984620	0.492310	−	0.870420i	$-0.336153\pi$
$167$	354862.	0.984620	0.492310	+	0.870420i	$0.336153\pi$
$168$	−225286.	−0.615830
$169$	−316017.	−0.851125
$170$	−467187.	−1.23985
$171$	352155.	0.920966
$172$	−33528.7	−0.0864162
$173$	−463269.	−1.17684	−0.588421	−	0.808554i	$-0.700250\pi$
$173$	−463269.	−1.17684	−0.588421	+	0.808554i	$0.700250\pi$
$174$	−340460.	−0.852497
$175$	−66166.3	−0.163321
$176$	−403549.	−0.982007
$177$	94918.4	0.227728
$178$	899887.	2.12882
$179$	−362212.	−0.844949	−0.422475	−	0.906375i	$-0.638838\pi$
$179$	−362212.	−0.844949	−0.422475	+	0.906375i	$0.638838\pi$
$180$	−635037.	−1.46089
$181$	−242613.	−0.550449	−0.275225	−	0.961380i	$-0.588752\pi$
$181$	−242613.	−0.550449	−0.275225	+	0.961380i	$0.588752\pi$
$182$	−66962.5	−0.149849
$183$	−878756.	−1.93973
$184$	−1.08713e6	−2.36720
$185$	−340008.	−0.730399
$186$	−1.36707e6	−2.89741
$187$	600037.	1.25480
$188$	−1.59441e6	−3.29008
$189$	66465.2	0.135344
$190$	296762.	0.596383
$191$	−458586.	−0.909573	−0.454786	−	0.890601i	$-0.650284\pi$
$191$	−458586.	−0.909573	−0.454786	+	0.890601i	$0.650284\pi$
$192$	−728044.	−1.42529
$193$	−238017.	−0.459954	−0.229977	−	0.973196i	$-0.573865\pi$
$193$	−238017.	−0.459954	−0.229977	+	0.973196i	$0.573865\pi$
$194$	599625.	1.14387
$195$	−164205.	−0.309243
$196$	−1.03494e6	−1.92431
$197$	201461.	0.369850	0.184925	−	0.982753i	$-0.440796\pi$
$197$	201461.	0.369850	0.184925	+	0.982753i	$0.440796\pi$
$198$	1.21834e6	2.20853
$199$	−113324.	−0.202856	−0.101428	−	0.994843i	$-0.532341\pi$
$199$	−113324.	−0.202856	−0.101428	+	0.994843i	$0.532341\pi$
$200$	737879.	1.30440
$201$	−1.14736e6	−2.00312
$202$	−1.30567e6	−2.25141
$203$	41546.6	0.0707612
$204$	−2.56098e6	−4.30854
$205$	469836.	0.780840
$206$	−346669.	−0.569176
$207$	1.13907e6	1.84767
$208$	259167.	0.415357
$209$	−381150.	−0.603574
$210$	198921.	0.311266
$211$	584530.	0.903860	0.451930	−	0.892053i	$-0.350736\pi$
$211$	584530.	0.903860	0.451930	+	0.892053i	$0.350736\pi$
$212$	973961.	1.48834
$213$	−789218.	−1.19192
$214$	1.10461e6	1.64882
$215$	14987.2	0.0221118
$216$	−741212.	−1.08096
$217$	166825.	0.240498
$218$	−1.65442e6	−2.35778
$219$	1.08220e6	1.52475
$220$	687324.	0.957425
$221$	−385356.	−0.530740
$222$	−2.78410e6	−3.79142
$223$	−591491.	−0.796501	−0.398250	−	0.917277i	$-0.630382\pi$
$223$	−591491.	−0.796501	−0.398250	+	0.917277i	$0.630382\pi$
$224$	−14934.7	−0.0198874
$225$	−773136.	−1.01812
$226$	1.60538e6	2.09077
$227$	1.06236e6	1.36837	0.684187	−	0.729306i	$-0.260157\pi$
$227$	1.06236e6	1.36837	0.684187	+	0.729306i	$0.260157\pi$
$228$	1.62676e6	2.07246
$229$	−282120.	−0.355505	−0.177753	−	0.984075i	$-0.556883\pi$
$229$	−282120.	−0.355505	−0.177753	+	0.984075i	$0.556883\pi$
$230$	959900.	1.19648
$231$	−255486.	−0.315019
$232$	−463322.	−0.565149
$233$	−1.10183e6	−1.32961	−0.664805	−	0.747017i	$-0.731485\pi$
$233$	−1.10183e6	−1.32961	−0.664805	+	0.747017i	$0.731485\pi$
$234$	−782439.	−0.934138
$235$	712697.	0.841851
$236$	255158.	0.298215
$237$	1.51046e6	1.74678
$238$	466826.	0.534211
$239$	−324487.	−0.367453	−0.183727	−	0.982977i	$-0.558816\pi$
$239$	−324487.	−0.367453	−0.183727	+	0.982977i	$0.558816\pi$
$240$	−769889.	−0.862780
$241$	211302.	0.234348	0.117174	−	0.993111i	$-0.462616\pi$
$241$	211302.	0.234348	0.117174	+	0.993111i	$0.462616\pi$
$242$	265958.	0.291928
$243$	−1.20493e6	−1.30902
$244$	−2.36226e6	−2.54011
$245$	462615.	0.492385
$246$	3.84717e6	4.05326
$247$	244782.	0.255292
$248$	−1.86041e6	−1.92079
$249$	−208273.	−0.212880
$250$	−1.54226e6	−1.56066
$251$	−29102.9	−0.0291576	−0.0145788	−	0.999894i	$-0.504641\pi$
$251$	−29102.9	−0.0291576	−0.0145788	+	0.999894i	$0.504641\pi$
$252$	634546.	0.629451
$253$	−1.23286e6	−1.21091
$254$	2.27198e6	2.20963
$255$	1.14475e6	1.10245
$256$	−2.11956e6	−2.02137
$257$	−66428.8	−0.0627370	−0.0313685	−	0.999508i	$-0.509987\pi$
$257$	−66428.8	−0.0627370	−0.0313685	+	0.999508i	$0.509987\pi$
$258$	122720.	0.114780
$259$	339746.	0.314706
$260$	−441413.	−0.404960
$261$	485461.	0.441116
$262$	−2.00152e6	−1.80138
$263$	−1.07978e6	−0.962604	−0.481302	−	0.876555i	$-0.659836\pi$
$263$	−1.07978e6	−0.962604	−0.481302	+	0.876555i	$0.659836\pi$
$264$	2.84915e6	2.51597
$265$	−435357.	−0.380830
$266$	−296533.	−0.256962
$267$	−2.20499e6	−1.89291
$268$	−3.08430e6	−2.62313
$269$	−1.55549e6	−1.31065	−0.655324	−	0.755348i	$-0.727468\pi$
$269$	−1.55549e6	−1.31065	−0.655324	+	0.755348i	$0.727468\pi$
$270$	654468.	0.546360
$271$	−1.62159e6	−1.34128	−0.670638	−	0.741785i	$-0.733979\pi$
$271$	−1.62159e6	−1.34128	−0.670638	+	0.741785i	$0.733979\pi$
$272$	−1.80677e6	−1.48075
$273$	164078.	0.133243
$274$	−114918.	−0.0924724
$275$	836794.	0.667247
$276$	5.26188e6	4.15785
$277$	−1.11127e6	−0.870200	−0.435100	−	0.900382i	$-0.643287\pi$
$277$	−1.11127e6	−0.870200	−0.435100	+	0.900382i	$0.643287\pi$
$278$	2.88725e6	2.24064
$279$	1.94931e6	1.49923
$280$	270705.	0.206349
$281$	1.22398e6	0.924716	0.462358	−	0.886693i	$-0.347003\pi$
$281$	1.22398e6	0.924716	0.462358	+	0.886693i	$0.347003\pi$
$282$	5.83579e6	4.36996
$283$	705255.	0.523456	0.261728	−	0.965142i	$-0.415708\pi$
$283$	705255.	0.523456	0.261728	+	0.965142i	$0.415708\pi$
$284$	−2.12156e6	−1.56085
$285$	−727157.	−0.530293
$286$	846863.	0.612206
$287$	−469473.	−0.336439
$288$	−174509.	−0.123975
$289$	1.26663e6	0.892086
$290$	409099.	0.285650
$291$	−1.46926e6	−1.01711
$292$	2.90915e6	1.99669
$293$	117043.	0.0796482	0.0398241	−	0.999207i	$-0.487320\pi$
$293$	117043.	0.0796482	0.0398241	+	0.999207i	$0.487320\pi$
$294$	3.78804e6	2.55592
$295$	−114055.	−0.0763059
$296$	−3.78880e6	−2.51346
$297$	−840574.	−0.552949
$298$	5.10662e6	3.33114
$299$	791767.	0.512176
$300$	−3.57146e6	−2.29109
$301$	−14975.6	−0.00952726
$302$	−2.60767e6	−1.64526
$303$	3.19928e6	2.00191
$304$	1.14768e6	0.712259
$305$	1.05592e6	0.649952
$306$	5.45474e6	3.33020
$307$	1.37296e6	0.831402	0.415701	−	0.909501i	$-0.363536\pi$
$307$	1.37296e6	0.831402	0.415701	+	0.909501i	$0.363536\pi$
$308$	−686793.	−0.412524
$309$	849442.	0.506101
$310$	1.64269e6	0.970847
$311$	−1.66459e6	−0.975903	−0.487951	−	0.872871i	$-0.662256\pi$
$311$	−1.66459e6	−0.975903	−0.487951	+	0.872871i	$0.662256\pi$
$312$	−1.82978e6	−1.06417
$313$	−891842.	−0.514549	−0.257275	−	0.966338i	$-0.582825\pi$
$313$	−891842.	−0.514549	−0.257275	+	0.966338i	$0.582825\pi$
$314$	−5.28056e6	−3.02243
$315$	−283640.	−0.161061
$316$	4.06040e6	2.28745
$317$	3.02740e6	1.69208	0.846042	−	0.533117i	$-0.178979\pi$
$317$	3.02740e6	1.69208	0.846042	+	0.533117i	$0.178979\pi$
$318$	−3.56485e6	−1.97685
$319$	−525432.	−0.289094
$320$	874823.	0.477579
$321$	−2.70662e6	−1.46610
$322$	−959158.	−0.515526
$323$	−1.70649e6	−0.910117
$324$	−1.73919e6	−0.920418
$325$	−537406.	−0.282224
$326$	3.28693e6	1.71296
$327$	4.05382e6	2.09650
$328$	5.23551e6	2.68704
$329$	−712146.	−0.362726
$330$	−2.51571e6	−1.27167
$331$	−1.38425e6	−0.694455	−0.347227	−	0.937781i	$-0.612877\pi$
$331$	−1.38425e6	−0.694455	−0.347227	+	0.937781i	$0.612877\pi$
$332$	−559875.	−0.278770
$333$	3.96984e6	1.96183
$334$	−3.49155e6	−1.71258
$335$	1.37867e6	0.671195
$336$	769294.	0.371744
$337$	167641.	0.0804091	0.0402046	−	0.999191i	$-0.487199\pi$
$337$	167641.	0.0804091	0.0402046	+	0.999191i	$0.487199\pi$
$338$	3.10934e6	1.48039
$339$	−3.93365e6	−1.85907
$340$	3.07729e6	1.44368
$341$	−2.10980e6	−0.982554
$342$	−3.46491e6	−1.60187
$343$	−948770.	−0.435437
$344$	167006.	0.0760915
$345$	−2.35204e6	−1.06389
$346$	4.55818e6	2.04692
$347$	−605517.	−0.269962	−0.134981	−	0.990848i	$-0.543097\pi$
$347$	−605517.	−0.269962	−0.134981	+	0.990848i	$0.543097\pi$
$348$	2.24256e6	0.992649
$349$	−2.79673e6	−1.22910	−0.614550	−	0.788878i	$-0.710662\pi$
$349$	−2.79673e6	−1.22910	−0.614550	+	0.788878i	$0.710662\pi$
$350$	651021.	0.284070
$351$	539833.	0.233879
$352$	188877.	0.0812498
$353$	−3.98792e6	−1.70337	−0.851687	−	0.524051i	$-0.824420\pi$
$353$	−3.98792e6	−1.70337	−0.851687	+	0.524051i	$0.824420\pi$
$354$	−933918.	−0.396096
$355$	948331.	0.399383
$356$	−5.92742e6	−2.47880
$357$	−1.14386e6	−0.475011
$358$	3.56386e6	1.46965
$359$	−2.73592e6	−1.12039	−0.560193	−	0.828362i	$-0.689273\pi$
$359$	−2.73592e6	−1.12039	−0.560193	+	0.828362i	$0.689273\pi$
$360$	3.16312e6	1.28635
$361$	−1.39212e6	−0.562222
$362$	2.38711e6	0.957415
$363$	−651677.	−0.259577
$364$	441072.	0.174484
$365$	−1.30038e6	−0.510903
$366$	8.64622e6	3.37383
$367$	−895601.	−0.347096	−0.173548	−	0.984825i	$-0.555523\pi$
$367$	−895601.	−0.347096	−0.173548	+	0.984825i	$0.555523\pi$
$368$	3.71226e6	1.42896
$369$	−5.48567e6	−2.09732
$370$	3.34540e6	1.27041
$371$	435021.	0.164087
$372$	9.00471e6	3.37375
$373$	718621.	0.267441	0.133720	−	0.991019i	$-0.457308\pi$
$373$	718621.	0.267441	0.133720	+	0.991019i	$0.457308\pi$
$374$	−5.90386e6	−2.18252
$375$	3.77900e6	1.38771
$376$	7.94176e6	2.89699
$377$	337443.	0.122278
$378$	−653962.	−0.235409
$379$	−934769.	−0.334277	−0.167138	−	0.985933i	$-0.553453\pi$
$379$	−934769.	−0.334277	−0.167138	+	0.985933i	$0.553453\pi$
$380$	−1.95473e6	−0.694429
$381$	−5.56703e6	−1.96477
$382$	4.51210e6	1.58205
$383$	−863841.	−0.300910	−0.150455	−	0.988617i	$-0.548074\pi$
$383$	−863841.	−0.300910	−0.150455	+	0.988617i	$0.548074\pi$
$384$	7.56137e6	2.61681
$385$	306994.	0.105555
$386$	2.34189e6	0.800013
$387$	−174986.	−0.0593917
$388$	−3.94964e6	−1.33192
$389$	2.06802e6	0.692918	0.346459	−	0.938065i	$-0.387384\pi$
$389$	2.06802e6	0.692918	0.346459	+	0.938065i	$0.387384\pi$
$390$	1.61564e6	0.537877
$391$	−5.51976e6	−1.82591
$392$	5.15504e6	1.69440
$393$	4.90431e6	1.60176
$394$	−1.98221e6	−0.643293
$395$	−1.81498e6	−0.585302
$396$	−8.02499e6	−2.57162
$397$	4.14437e6	1.31972	0.659860	−	0.751388i	$-0.270615\pi$
$397$	4.14437e6	1.31972	0.659860	+	0.751388i	$0.270615\pi$
$398$	1.11501e6	0.352834
$399$	726595.	0.228486
$400$	−2.51967e6	−0.787397
$401$	5.21342e6	1.61906	0.809528	−	0.587081i	$-0.199723\pi$
$401$	5.21342e6	1.61906	0.809528	+	0.587081i	$0.199723\pi$
$402$	1.12890e7	3.48410
$403$	1.35496e6	0.415589
$404$	8.60024e6	2.62154
$405$	777413.	0.235513
$406$	−408783.	−0.123077
$407$	−4.29670e6	−1.28573
$408$	1.27562e7	3.79378
$409$	−4.66400e6	−1.37864	−0.689320	−	0.724457i	$-0.742090\pi$
$409$	−4.66400e6	−1.37864	−0.689320	+	0.724457i	$0.742090\pi$
$410$	−4.62280e6	−1.35814
$411$	281584.	0.0822249
$412$	2.28345e6	0.662750
$413$	113967.	0.0328778
$414$	−1.12075e7	−3.21372
$415$	250262.	0.0713305
$416$	−121301.	−0.0343661
$417$	−7.07463e6	−1.99234
$418$	3.75020e6	1.04982
$419$	312838.	0.0870532	0.0435266	−	0.999052i	$-0.486141\pi$
$419$	312838.	0.0870532	0.0435266	+	0.999052i	$0.486141\pi$
$420$	−1.31026e6	−0.362438
$421$	4.29803e6	1.18185	0.590927	−	0.806725i	$-0.298762\pi$
$421$	4.29803e6	1.18185	0.590927	+	0.806725i	$0.298762\pi$
$422$	−5.75129e6	−1.57211
$423$	−8.32124e6	−2.26119
$424$	−4.85130e6	−1.31052
$425$	3.74650e6	1.00613
$426$	7.76525e6	2.07315
$427$	−1.05510e6	−0.280044
$428$	−7.27587e6	−1.91989
$429$	−2.07507e6	−0.544363
$430$	−147461.	−0.0384598
$431$	−4.46758e6	−1.15846	−0.579228	−	0.815166i	$-0.696646\pi$
$431$	−4.46758e6	−1.15846	−0.579228	+	0.815166i	$0.696646\pi$
$432$	2.53105e6	0.652517
$433$	889597.	0.228020	0.114010	−	0.993480i	$-0.463630\pi$
$433$	889597.	0.228020	0.114010	+	0.993480i	$0.463630\pi$
$434$	−1.64142e6	−0.418307
$435$	−1.00242e6	−0.253995
$436$	1.08974e7	2.74541
$437$	3.50622e6	0.878284
$438$	−1.06480e7	−2.65205
$439$	1.64263e6	0.406797	0.203399	−	0.979096i	$-0.434801\pi$
$439$	1.64263e6	0.406797	0.203399	+	0.979096i	$0.434801\pi$
$440$	−3.42356e6	−0.843036
$441$	−5.40136e6	−1.32253
$442$	3.79158e6	0.923134
$443$	−5.68708e6	−1.37683	−0.688415	−	0.725317i	$-0.741693\pi$
$443$	−5.68708e6	−1.37683	−0.688415	+	0.725317i	$0.741693\pi$
$444$	1.83385e7	4.41474
$445$	2.64954e6	0.634264
$446$	5.81978e6	1.38538
$447$	−1.25128e7	−2.96199
$448$	−874147.	−0.205773
$449$	−6.77253e6	−1.58539	−0.792693	−	0.609621i	$-0.791322\pi$
$449$	−6.77253e6	−1.58539	−0.792693	+	0.609621i	$0.791322\pi$
$450$	7.60701e6	1.77085
$451$	5.93734e6	1.37452
$452$	−1.05744e7	−2.43449
$453$	6.38957e6	1.46294
$454$	−1.04527e7	−2.38006
$455$	−197158.	−0.0446463
$456$	−8.10290e6	−1.82485
$457$	3.20128e6	0.717023	0.358511	−	0.933525i	$-0.383284\pi$
$457$	3.20128e6	0.717023	0.358511	+	0.933525i	$0.383284\pi$
$458$	2.77583e6	0.618342
$459$	−3.76342e6	−0.833780
$460$	−6.32272e6	−1.39319
$461$	5.66099e6	1.24062	0.620312	−	0.784356i	$-0.287006\pi$
$461$	5.66099e6	1.24062	0.620312	+	0.784356i	$0.287006\pi$
$462$	2.51377e6	0.547924
$463$	6.17937e6	1.33965	0.669826	−	0.742518i	$-0.266369\pi$
$463$	6.17937e6	1.33965	0.669826	+	0.742518i	$0.266369\pi$
$464$	1.58213e6	0.341151
$465$	−4.02508e6	−0.863260
$466$	1.08411e7	2.31264
$467$	7.77966e6	1.65070	0.825350	−	0.564621i	$-0.190978\pi$
$467$	7.77966e6	1.65070	0.825350	+	0.564621i	$0.190978\pi$
$468$	5.15381e6	1.08771
$469$	−1.37761e6	−0.289196
$470$	−7.01234e6	−1.46426
$471$	1.29390e7	2.68749
$472$	−1.27094e6	−0.262585
$473$	189394.	0.0389236
$474$	−1.48617e7	−3.03824
$475$	−2.37982e6	−0.483960
$476$	−3.07491e6	−0.622036
$477$	5.08310e6	1.02290
$478$	3.19268e6	0.639124
$479$	5.67268e6	1.12966	0.564832	−	0.825206i	$-0.308941\pi$
$479$	5.67268e6	1.12966	0.564832	+	0.825206i	$0.308941\pi$
$480$	360339.	0.0713851
$481$	2.75943e6	0.543821
$482$	−2.07904e6	−0.407610
$483$	2.35022e6	0.458397
$484$	−1.75183e6	−0.339921
$485$	1.76548e6	0.340806
$486$	1.18555e7	2.27682
$487$	−862815.	−0.164852	−0.0824262	−	0.996597i	$-0.526267\pi$
$487$	−862815.	−0.164852	−0.0824262	+	0.996597i	$0.526267\pi$
$488$	1.17664e7	2.23663
$489$	−8.05397e6	−1.52313
$490$	−4.55174e6	−0.856421
$491$	−9.38771e6	−1.75734	−0.878670	−	0.477430i	$-0.841568\pi$
$491$	−9.38771e6	−1.75734	−0.878670	+	0.477430i	$0.841568\pi$
$492$	−2.53408e7	−4.71962
$493$	−2.35247e6	−0.435919
$494$	−2.40845e6	−0.444039
$495$	3.58714e6	0.658015
$496$	6.35283e6	1.15948
$497$	−947598.	−0.172081
$498$	2.04923e6	0.370269
$499$	4.48321e6	0.806005	0.403002	−	0.915199i	$-0.367967\pi$
$499$	4.48321e6	0.806005	0.403002	+	0.915199i	$0.367967\pi$
$500$	1.01586e7	1.81723
$501$	8.55534e6	1.52280
$502$	286348.	0.0507149
$503$	−3.79842e6	−0.669396	−0.334698	−	0.942325i	$-0.608634\pi$
$503$	−3.79842e6	−0.669396	−0.334698	+	0.942325i	$0.608634\pi$
$504$	−3.16067e6	−0.554247
$505$	−3.84428e6	−0.670789
$506$	1.21303e7	2.10618
$507$	−7.61881e6	−1.31634
$508$	−1.49652e7	−2.57290
$509$	3.78758e6	0.647989	0.323995	−	0.946059i	$-0.394974\pi$
$509$	3.78758e6	0.647989	0.323995	+	0.946059i	$0.394974\pi$
$510$	−1.12634e7	−1.91753
$511$	1.29938e6	0.220132
$512$	1.08184e7	1.82384
$513$	2.39057e6	0.401059
$514$	653604.	0.109121
$515$	−1.02070e6	−0.169581
$516$	−808339.	−0.133650
$517$	9.00638e6	1.48192
$518$	−3.34281e6	−0.547378
$519$	−1.11689e7	−1.82009
$520$	2.19868e6	0.356577
$521$	−890262.	−0.143689	−0.0718445	−	0.997416i	$-0.522889\pi$
$521$	−890262.	−0.143689	−0.0718445	+	0.997416i	$0.522889\pi$
$522$	−4.77652e6	−0.767248
$523$	−1.23179e7	−1.96917	−0.984583	−	0.174920i	$-0.944033\pi$
$523$	−1.23179e7	−1.96917	−0.984583	+	0.174920i	$0.944033\pi$
$524$	1.31837e7	2.09753
$525$	−1.59520e6	−0.252590
$526$	1.06242e7	1.67429
$527$	−9.44603e6	−1.48157
$528$	−9.72912e6	−1.51876
$529$	4.90477e6	0.762043
$530$	4.28355e6	0.662390
$531$	1.33167e6	0.204956
$532$	1.95322e6	0.299207
$533$	−3.81308e6	−0.581377
$534$	2.16953e7	3.29240
$535$	3.25229e6	0.491253
$536$	1.53629e7	2.30973
$537$	−8.73254e6	−1.30679
$538$	1.53047e7	2.27966
$539$	5.84608e6	0.866749
$540$	−4.31088e6	−0.636183
$541$	7.97711e6	1.17180	0.585899	−	0.810384i	$-0.300742\pi$
$541$	7.97711e6	1.17180	0.585899	+	0.810384i	$0.300742\pi$
$542$	1.59551e7	2.33293
$543$	−5.84913e6	−0.851317
$544$	845641.	0.122515
$545$	−4.87110e6	−0.702483
$546$	−1.61439e6	−0.231754
$547$	−299209.	−0.0427569
$547$	−299209.	−0.0427569
$548$	756949.	0.107675
$549$	−1.23286e7	−1.74576
$550$	−8.23335e6	−1.16057
$551$	1.49431e6	0.209683
$552$	−2.62094e7	−3.66108
$553$	1.81358e6	0.252188
$554$	1.09339e7	1.51357
$555$	−8.19722e6	−1.12963
$556$	−1.90179e7	−2.60901
$557$	3.04434e6	0.415772	0.207886	−	0.978153i	$-0.433342\pi$
$557$	3.04434e6	0.415772	0.207886	+	0.978153i	$0.433342\pi$
$558$	−1.91795e7	−2.60767
$559$	−121632.	−0.0164634
$560$	−924389.	−0.124562
$561$	1.44662e7	1.94065
$562$	−1.20429e7	−1.60839
$563$	−4.49674e6	−0.597897	−0.298949	−	0.954269i	$-0.596636\pi$
$563$	−4.49674e6	−0.597897	−0.298949	+	0.954269i	$0.596636\pi$
$564$	−3.84395e7	−5.08839
$565$	4.72671e6	0.622928
$566$	−6.93911e6	−0.910464
$567$	−776812.	−0.101475
$568$	1.05675e7	1.37436
$569$	3.31447e6	0.429175	0.214587	−	0.976705i	$-0.431159\pi$
$569$	3.31447e6	0.429175	0.214587	+	0.976705i	$0.431159\pi$
$570$	7.15461e6	0.922357
$571$	1.43202e7	1.83806	0.919029	−	0.394189i	$-0.128975\pi$
$571$	1.43202e7	1.83806	0.919029	+	0.394189i	$0.128975\pi$
$572$	−5.57816e6	−0.712854
$573$	−1.10560e7	−1.40673
$574$	4.61922e6	0.585180
$575$	−7.69770e6	−0.970937
$576$	−1.02142e7	−1.28277
$577$	642771.	0.0803742	0.0401871	−	0.999192i	$-0.487205\pi$
$577$	642771.	0.0803742	0.0401871	+	0.999192i	$0.487205\pi$
$578$	−1.24626e7	−1.55164
$579$	−5.73832e6	−0.711358
$580$	−2.69468e6	−0.332611
$581$	−250069.	−0.0307340
$582$	1.44563e7	1.76909
$583$	−5.50163e6	−0.670378
$584$	−1.44905e7	−1.75813
$585$	−2.30374e6	−0.278319
$586$	−1.15160e6	−0.138535
$587$	−4.08745e6	−0.489618	−0.244809	−	0.969571i	$-0.578725\pi$
$587$	−4.08745e6	−0.489618	−0.244809	+	0.969571i	$0.578725\pi$
$588$	−2.49513e7	−2.97611
$589$	6.00023e6	0.712655
$590$	1.12220e6	0.132722
$591$	4.85701e6	0.572005
$592$	1.29378e7	1.51725
$593$	8.37207e6	0.977678	0.488839	−	0.872374i	$-0.337420\pi$
$593$	8.37207e6	0.977678	0.488839	+	0.872374i	$0.337420\pi$
$594$	8.27054e6	0.961762
$595$	1.37448e6	0.159164
$596$	−3.36366e7	−3.87879
$597$	−2.73210e6	−0.313734
$598$	−7.79032e6	−0.890845
$599$	−4.09144e6	−0.465917	−0.232959	−	0.972487i	$-0.574841\pi$
$599$	−4.09144e6	−0.465917	−0.232959	+	0.972487i	$0.574841\pi$
$600$	1.77894e7	2.01736
$601$	1.03575e7	1.16969	0.584844	−	0.811146i	$-0.301156\pi$
$601$	1.03575e7	1.16969	0.584844	+	0.811146i	$0.301156\pi$
$602$	147347.	0.0165711
$603$	−1.60970e7	−1.80281
$604$	1.71763e7	1.91575
$605$	783061.	0.0869775
$606$	−3.14782e7	−3.48200
$607$	1.41473e6	0.155849	0.0779243	−	0.996959i	$-0.475171\pi$
$607$	1.41473e6	0.155849	0.0779243	+	0.996959i	$0.475171\pi$
$608$	−537161.	−0.0589312
$609$	1.00164e6	0.109438
$610$	−1.03894e7	−1.13048
$611$	−5.78408e6	−0.626803
$612$	−3.59296e7	−3.87769
$613$	−5.69694e6	−0.612337	−0.306169	−	0.951977i	$-0.599047\pi$
$613$	−5.69694e6	−0.612337	−0.306169	+	0.951977i	$0.599047\pi$
$614$	−1.35087e7	−1.44609
$615$	1.13272e7	1.20764
$616$	3.42091e6	0.363237
$617$	1.19600e6	0.126479	0.0632393	−	0.997998i	$-0.479857\pi$
$617$	1.19600e6	0.126479	0.0632393	+	0.997998i	$0.479857\pi$
$618$	−8.35780e6	−0.880280
$619$	−2.56989e6	−0.269580	−0.134790	−	0.990874i	$-0.543036\pi$
$619$	−2.56989e6	−0.269580	−0.134790	+	0.990874i	$0.543036\pi$
$620$	−1.08201e7	−1.13046
$621$	7.73247e6	0.804617
$622$	1.63782e7	1.69742
$623$	−2.64749e6	−0.273284
$624$	6.24824e6	0.642386
$625$	2.60216e6	0.266462
$626$	8.77498e6	0.894973
$627$	−9.18911e6	−0.933479
$628$	3.47823e7	3.51932
$629$	−1.92372e7	−1.93872
$630$	2.79078e6	0.280139
$631$	−3.36876e6	−0.336819	−0.168409	−	0.985717i	$-0.553863\pi$
$631$	−3.36876e6	−0.336819	−0.168409	+	0.985717i	$0.553863\pi$
$632$	−2.02249e7	−2.01415
$633$	1.40924e7	1.39790
$634$	−2.97871e7	−2.94310
$635$	6.68939e6	0.658343
$636$	2.34811e7	2.30184
$637$	−3.75447e6	−0.366607
$638$	5.16981e6	0.502832
$639$	−1.10724e7	−1.07273
$640$	−9.08581e6	−0.876826
$641$	−3.05455e6	−0.293631	−0.146815	−	0.989164i	$-0.546902\pi$
$641$	−3.05455e6	−0.293631	−0.146815	+	0.989164i	$0.546902\pi$
$642$	2.66308e7	2.55004
$643$	1.56701e7	1.49467	0.747335	−	0.664447i	$-0.231333\pi$
$643$	1.56701e7	1.49467	0.747335	+	0.664447i	$0.231333\pi$
$644$	6.31783e6	0.600279
$645$	361325.	0.0341978
$646$	1.67904e7	1.58300
$647$	−39981.6	−0.00375491	−0.00187746	−	0.999998i	$-0.500598\pi$
$647$	−39981.6	−0.00375491	−0.00187746	+	0.999998i	$0.500598\pi$
$648$	8.66291e6	0.810450
$649$	−1.44131e6	−0.134322
$650$	5.28762e6	0.490882
$651$	4.02196e6	0.371951
$652$	−2.16505e7	−1.99457
$653$	1.44875e7	1.32957	0.664785	−	0.747035i	$-0.268523\pi$
$653$	1.44875e7	1.32957	0.664785	+	0.747035i	$0.268523\pi$
$654$	−3.98862e7	−3.64652
$655$	−5.89306e6	−0.536708
$656$	−1.78779e7	−1.62203
$657$	1.51829e7	1.37227
$658$	7.00692e6	0.630902
$659$	1.99975e7	1.79375	0.896875	−	0.442283i	$-0.145831\pi$
$659$	1.99975e7	1.79375	0.896875	+	0.442283i	$0.145831\pi$
$660$	1.65706e7	1.48074
$661$	4.91560e6	0.437596	0.218798	−	0.975770i	$-0.429786\pi$
$661$	4.91560e6	0.437596	0.218798	+	0.975770i	$0.429786\pi$
$662$	1.36198e7	1.20789
$663$	−9.29051e6	−0.820834
$664$	2.78874e6	0.245464
$665$	−873082.	−0.0765598
$666$	−3.90599e7	−3.41228
$667$	4.83347e6	0.420672
$668$	2.29983e7	1.99414
$669$	−1.42602e7	−1.23186
$670$	−1.35650e7	−1.16743
$671$	1.33437e7	1.14412
$672$	−360060.	−0.0307576
$673$	8.50497e6	0.723828	0.361914	−	0.932211i	$-0.382123\pi$
$673$	8.50497e6	0.723828	0.361914	+	0.932211i	$0.382123\pi$
$674$	−1.64945e6	−0.139858
$675$	−5.24836e6	−0.443367
$676$	−2.04808e7	−1.72377
$677$	−1.01497e7	−0.851105	−0.425553	−	0.904934i	$-0.639920\pi$
$677$	−1.01497e7	−0.851105	−0.425553	+	0.904934i	$0.639920\pi$
$678$	3.87038e7	3.23355
$679$	−1.76411e6	−0.146842
$680$	−1.53280e7	−1.27120
$681$	2.56122e7	2.11631
$682$	2.07587e7	1.70899
$683$	−1.59968e7	−1.31214	−0.656071	−	0.754699i	$-0.727783\pi$
$683$	−1.59968e7	−1.31214	−0.656071	+	0.754699i	$0.727783\pi$
$684$	2.28229e7	1.86522
$685$	−338354.	−0.0275514
$686$	9.33510e6	0.757371
$687$	−6.80161e6	−0.549819
$688$	−570284.	−0.0459325
$689$	3.53326e6	0.283548
$690$	2.31421e7	1.85046
$691$	−2.82045e6	−0.224710	−0.112355	−	0.993668i	$-0.535839\pi$
$691$	−2.82045e6	−0.224710	−0.112355	+	0.993668i	$0.535839\pi$
$692$	−3.00241e7	−2.38344
$693$	−3.58437e6	−0.283517
$694$	5.95778e6	0.469554
$695$	8.50093e6	0.667582
$696$	−1.11702e7	−0.874052
$697$	2.65827e7	2.07261
$698$	2.75175e7	2.13781
$699$	−2.65639e7	−2.05636
$700$	−4.28818e6	−0.330771
$701$	2.05238e7	1.57748	0.788739	−	0.614728i	$-0.210734\pi$
$701$	2.05238e7	1.57748	0.788739	+	0.614728i	$0.210734\pi$
$702$	−5.31151e6	−0.406794
$703$	1.22197e7	0.932550
$704$	1.10552e7	0.840686
$705$	1.71823e7	1.30199
$706$	3.92378e7	2.96274
$707$	3.84131e6	0.289022
$708$	6.15158e6	0.461215
$709$	−3.90535e6	−0.291773	−0.145886	−	0.989301i	$-0.546603\pi$
$709$	−3.90535e6	−0.291773	−0.145886	+	0.989301i	$0.546603\pi$
$710$	−9.33078e6	−0.694660
$711$	2.11912e7	1.57211
$712$	2.95245e7	2.18264
$713$	1.94082e7	1.42975
$714$	1.12547e7	0.826203
$715$	2.49342e6	0.182402
$716$	−2.34746e7	−1.71126
$717$	−7.82302e6	−0.568298
$718$	2.69192e7	1.94872
$719$	−165697.	−0.0119534	−0.00597671	−	0.999982i	$-0.501902\pi$
$719$	−165697.	−0.0119534	−0.00597671	+	0.999982i	$0.501902\pi$
$720$	−1.08012e7	−0.776502
$721$	1.01991e6	0.0730672
$722$	1.36973e7	0.977892
$723$	5.09427e6	0.362440
$724$	−1.57235e7	−1.11482
$725$	−3.28068e6	−0.231803
$726$	6.41196e6	0.451491
$727$	−1.84335e7	−1.29352	−0.646759	−	0.762695i	$-0.723876\pi$
$727$	−1.84335e7	−1.29352	−0.646759	+	0.762695i	$0.723876\pi$
$728$	−2.19698e6	−0.153638
$729$	−2.25284e7	−1.57005
$730$	1.27947e7	0.888632
$731$	847955.	0.0586921
$732$	−5.69514e7	−3.92850
$733$	2.38741e7	1.64122	0.820611	−	0.571487i	$-0.193633\pi$
$733$	2.38741e7	1.64122	0.820611	+	0.571487i	$0.193633\pi$
$734$	8.81197e6	0.603716
$735$	1.11531e7	0.761515
$736$	−1.73749e6	−0.118230
$737$	1.74223e7	1.18151
$738$	5.39744e7	3.64793
$739$	2.18067e7	1.46886	0.734429	−	0.678686i	$-0.237450\pi$
$739$	2.18067e7	1.46886	0.734429	+	0.678686i	$0.237450\pi$
$740$	−2.20356e7	−1.47927
$741$	5.90143e6	0.394832
$742$	−4.28024e6	−0.285403
$743$	8.33514e6	0.553912	0.276956	−	0.960883i	$-0.410674\pi$
$743$	8.33514e6	0.553912	0.276956	+	0.960883i	$0.410674\pi$
$744$	−4.48525e7	−2.97067
$745$	1.50354e7	0.992488
$746$	−7.07063e6	−0.465169
$747$	−2.92199e6	−0.191592
$748$	3.88879e7	2.54132
$749$	−3.24978e6	−0.211665
$750$	−3.71822e7	−2.41369
$751$	−1.26609e7	−0.819154	−0.409577	−	0.912276i	$-0.634324\pi$
$751$	−1.26609e7	−0.819154	−0.409577	+	0.912276i	$0.634324\pi$
$752$	−2.71191e7	−1.74876
$753$	−701640.	−0.0450948
$754$	−3.32015e6	−0.212682
$755$	−7.67776e6	−0.490193
$756$	4.30755e6	0.274111
$757$	−4.89791e6	−0.310650	−0.155325	−	0.987863i	$-0.549642\pi$
$757$	−4.89791e6	−0.310650	−0.155325	+	0.987863i	$0.549642\pi$
$758$	9.19734e6	0.581419
$759$	−2.97229e7	−1.87278
$760$	9.73651e6	0.611462
$761$	−2.60414e7	−1.63006	−0.815028	−	0.579422i	$-0.803278\pi$
$761$	−2.60414e7	−1.63006	−0.815028	+	0.579422i	$0.803278\pi$
$762$	5.47749e7	3.41739
$763$	4.86734e6	0.302677
$764$	−2.97206e7	−1.84214
$765$	1.60604e7	0.992207
$766$	8.49947e6	0.523384
$767$	925641.	0.0568139
$768$	−5.11002e7	−3.12622
$769$	6.33702e6	0.386429	0.193214	−	0.981157i	$-0.438109\pi$
$769$	6.33702e6	0.386429	0.193214	+	0.981157i	$0.438109\pi$
$770$	−3.02056e6	−0.183595
$771$	−1.60152e6	−0.0970281
$772$	−1.54256e7	−0.931537
$773$	2.03750e7	1.22645	0.613225	−	0.789909i	$-0.289872\pi$
$773$	2.03750e7	1.22645	0.613225	+	0.789909i	$0.289872\pi$
$774$	1.72172e6	0.103302
$775$	−1.31732e7	−0.787835
$776$	1.96732e7	1.17279
$777$	8.19089e6	0.486719
$778$	−2.03476e7	−1.20522
$779$	−1.68856e7	−0.996951
$780$	−1.06420e7	−0.626305
$781$	1.19841e7	0.703036
$782$	5.43099e7	3.17586
$783$	3.29550e6	0.192095
$784$	−1.76031e7	−1.02282
$785$	−1.55476e7	−0.900509
$786$	−4.82543e7	−2.78599
$787$	−4.48796e6	−0.258293	−0.129146	−	0.991626i	$-0.541224\pi$
$787$	−4.48796e6	−0.258293	−0.129146	+	0.991626i	$0.541224\pi$
$788$	1.30565e7	0.749052
$789$	−2.60324e7	−1.48875
$790$	1.78579e7	1.01804
$791$	−4.72305e6	−0.268400
$792$	3.99725e7	2.26437
$793$	−8.56960e6	−0.483924
$794$	−4.07771e7	−2.29544
$795$	−1.04960e7	−0.588986
$796$	−7.34440e6	−0.410841
$797$	−1.99222e7	−1.11094	−0.555472	−	0.831535i	$-0.687463\pi$
$797$	−1.99222e7	−1.11094	−0.555472	+	0.831535i	$0.687463\pi$
$798$	−7.14908e6	−0.397414
$799$	4.03234e7	2.23455
$800$	1.17931e6	0.0651481
$801$	−3.09352e7	−1.70362
$802$	−5.12957e7	−2.81608
$803$	−1.64330e7	−0.899347
$804$	−7.43591e7	−4.05690
$805$	−2.82405e6	−0.153597
$806$	−1.33317e7	−0.722847
$807$	−3.75011e7	−2.02703
$808$	−4.28378e7	−2.30833
$809$	−4.54230e6	−0.244008	−0.122004	−	0.992530i	$-0.538932\pi$
$809$	−4.54230e6	−0.244008	−0.122004	+	0.992530i	$0.538932\pi$
$810$	−7.64909e6	−0.409635
$811$	−1.00839e7	−0.538367	−0.269183	−	0.963089i	$-0.586754\pi$
$811$	−1.00839e7	−0.538367	−0.269183	+	0.963089i	$0.586754\pi$
$812$	2.69259e6	0.143311
$813$	−3.90948e7	−2.07440
$814$	4.22759e7	2.23631
$815$	9.67772e6	0.510363
$816$	−4.35593e7	−2.29010
$817$	−538631.	−0.0282316
$818$	4.58899e7	2.39791
$819$	2.30196e6	0.119919
$820$	3.04497e7	1.58142
$821$	2.54249e7	1.31644	0.658222	−	0.752824i	$-0.271309\pi$
$821$	2.54249e7	1.31644	0.658222	+	0.752824i	$0.271309\pi$
$822$	−2.77055e6	−0.143017
$823$	−2.24704e7	−1.15641	−0.578204	−	0.815892i	$-0.696246\pi$
$823$	−2.24704e7	−1.15641	−0.578204	+	0.815892i	$0.696246\pi$
$824$	−1.13739e7	−0.583567
$825$	2.01742e7	1.03195
$826$	−1.12134e6	−0.0571854
$827$	−1.46790e7	−0.746334	−0.373167	−	0.927764i	$-0.621728\pi$
$827$	−1.46790e7	−0.746334	−0.373167	+	0.927764i	$0.621728\pi$
$828$	7.38222e7	3.74206
$829$	1.83173e7	0.925709	0.462854	−	0.886434i	$-0.346825\pi$
$829$	1.83173e7	0.925709	0.462854	+	0.886434i	$0.346825\pi$
$830$	−2.46237e6	−0.124068
$831$	−2.67914e7	−1.34584
$832$	−7.09986e6	−0.355583
$833$	2.61741e7	1.30695
$834$	6.96084e7	3.46535
$835$	−1.02802e7	−0.510251
$836$	−2.47020e7	−1.22241
$837$	1.32327e7	0.652880
$838$	−3.07807e6	−0.151415
$839$	−872063.	−0.0427704	−0.0213852	−	0.999771i	$-0.506808\pi$
$839$	−872063.	−0.0427704	−0.0213852	+	0.999771i	$0.506808\pi$
$840$	6.52640e6	0.319136
$841$	−1.84512e7	−0.899568
$842$	−4.22890e7	−2.05564
$843$	2.95088e7	1.43015
$844$	3.78829e7	1.83057
$845$	9.15483e6	0.441071
$846$	8.18740e7	3.93296
$847$	−782456.	−0.0374758
$848$	1.65660e7	0.791092
$849$	1.70029e7	0.809569
$850$	−3.68624e7	−1.74999
$851$	3.95255e7	1.87091
$852$	−5.11485e7	−2.41398
$853$	−3.09176e7	−1.45490	−0.727451	−	0.686160i	$-0.759295\pi$
$853$	−3.09176e7	−1.45490	−0.727451	+	0.686160i	$0.759295\pi$
$854$	1.03813e7	0.487089
$855$	−1.02017e7	−0.477264
$856$	3.62411e7	1.69051
$857$	4.22278e6	0.196402	0.0982011	−	0.995167i	$-0.468691\pi$
$857$	4.22278e6	0.196402	0.0982011	+	0.995167i	$0.468691\pi$
$858$	2.04169e7	0.946830
$859$	1.45928e7	0.674772	0.337386	−	0.941366i	$-0.390457\pi$
$859$	1.45928e7	0.674772	0.337386	+	0.941366i	$0.390457\pi$
$860$	971306.	0.0447827
$861$	−1.13185e7	−0.520332
$862$	4.39573e7	2.01494
$863$	5.91376e6	0.270294	0.135147	−	0.990826i	$-0.456849\pi$
$863$	5.91376e6	0.270294	0.135147	+	0.990826i	$0.456849\pi$
$864$	−1.18463e6	−0.0539883
$865$	1.34207e7	0.609865
$866$	−8.75289e6	−0.396603
$867$	3.05372e7	1.37969
$868$	1.08118e7	0.487077
$869$	−2.29360e7	−1.03031
$870$	9.86293e6	0.441782
$871$	−1.11890e7	−0.499741
$872$	−5.42800e7	−2.41740
$873$	−2.06132e7	−0.915397
$874$	−3.44982e7	−1.52763
$875$	4.53736e6	0.200347
$876$	7.01365e7	3.08805
$877$	−1.45465e7	−0.638644	−0.319322	−	0.947646i	$-0.603455\pi$
$877$	−1.45465e7	−0.638644	−0.319322	+	0.947646i	$0.603455\pi$
$878$	−1.61621e7	−0.707557
$879$	2.82177e6	0.123183
$880$	1.16906e7	0.508897
$881$	−6.18947e6	−0.268666	−0.134333	−	0.990936i	$-0.542889\pi$
$881$	−6.18947e6	−0.268666	−0.134333	+	0.990936i	$0.542889\pi$
$882$	5.31448e7	2.30033
$883$	1.03115e7	0.445063	0.222531	−	0.974926i	$-0.428568\pi$
$883$	1.03115e7	0.445063	0.222531	+	0.974926i	$0.428568\pi$
$884$	−2.49746e7	−1.07490
$885$	−2.74973e6	−0.118014
$886$	5.59561e7	2.39477
$887$	4.25491e7	1.81585	0.907927	−	0.419128i	$-0.137664\pi$
$887$	4.25491e7	1.81585	0.907927	+	0.419128i	$0.137664\pi$
$888$	−9.13438e7	−3.88729
$889$	−6.68422e6	−0.283659
$890$	−2.60692e7	−1.10320
$891$	9.82420e6	0.414575
$892$	−3.83340e7	−1.61314
$893$	−2.56139e7	−1.07485
$894$	1.23115e8	5.15190
$895$	1.04931e7	0.437870
$896$	9.07878e6	0.377796
$897$	1.90886e7	0.792124
$898$	6.66360e7	2.75752
$899$	8.27156e6	0.341341
$900$	−5.01063e7	−2.06199
$901$	−2.46319e7	−1.01085
$902$	−5.84185e7	−2.39075
$903$	−361045.	−0.0147347
$904$	5.26709e7	2.14363
$905$	7.02836e6	0.285254
$906$	−6.28680e7	−2.54454
$907$	−3.44341e7	−1.38986	−0.694930	−	0.719077i	$-0.744565\pi$
$907$	−3.44341e7	−1.38986	−0.694930	+	0.719077i	$0.744565\pi$
$908$	6.88503e7	2.77135
$909$	4.48846e7	1.80172
$910$	1.93987e6	0.0776548
$911$	7.27786e6	0.290541	0.145271	−	0.989392i	$-0.453595\pi$
$911$	7.27786e6	0.290541	0.145271	+	0.989392i	$0.453595\pi$
$912$	2.76693e7	1.10157
$913$	3.16257e6	0.125564
$914$	−3.14979e7	−1.24714
$915$	2.54571e7	1.00521
$916$	−1.82840e7	−0.719999
$917$	5.88851e6	0.231250
$918$	3.70289e7	1.45022
$919$	−2.37526e7	−0.927732	−0.463866	−	0.885905i	$-0.653538\pi$
$919$	−2.37526e7	−0.927732	−0.463866	+	0.885905i	$0.653538\pi$
$920$	3.14934e7	1.22673
$921$	3.31005e7	1.28583
$922$	−5.56994e7	−2.15786
$923$	−7.69643e6	−0.297362
$924$	−1.65578e7	−0.638003
$925$	−2.68276e7	−1.03093
$926$	−6.07999e7	−2.33010
$927$	1.19174e7	0.455492
$928$	−740499.	−0.0282263
$929$	3.31291e7	1.25942	0.629709	−	0.776831i	$-0.283174\pi$
$929$	3.31291e7	1.25942	0.629709	+	0.776831i	$0.283174\pi$
$930$	3.96034e7	1.50150
$931$	−1.66261e7	−0.628661
$932$	−7.14085e7	−2.69284
$933$	−4.01314e7	−1.50932
$934$	−7.65453e7	−2.87112
$935$	−1.73827e7	−0.650263
$936$	−2.56711e7	−0.957757
$937$	3.16274e7	1.17683	0.588416	−	0.808558i	$-0.299752\pi$
$937$	3.16274e7	1.17683	0.588416	+	0.808558i	$0.299752\pi$
$938$	1.35545e7	0.503009
$939$	−2.15013e7	−0.795795
$940$	4.61892e7	1.70499
$941$	2.84342e7	1.04681	0.523403	−	0.852085i	$-0.324662\pi$
$941$	2.84342e7	1.04681	0.523403	+	0.852085i	$0.324662\pi$
$942$	−1.27308e8	−4.67444
$943$	−5.46178e7	−2.00012
$944$	4.33994e6	0.158509
$945$	−1.92546e6	−0.0701383
$946$	−1.86348e6	−0.0677011
$947$	3.59150e7	1.30137	0.650686	−	0.759347i	$-0.274481\pi$
$947$	3.59150e7	1.30137	0.650686	+	0.759347i	$0.274481\pi$
$948$	9.78918e7	3.53774
$949$	1.05536e7	0.380395
$950$	2.34154e7	0.841769
$951$	7.29873e7	2.61695
$952$	1.53161e7	0.547718
$953$	−4.24366e7	−1.51359	−0.756796	−	0.653651i	$-0.773236\pi$
$953$	−4.24366e7	−1.51359	−0.756796	+	0.653651i	$0.773236\pi$
$954$	−5.00135e7	−1.77916
$955$	1.32850e7	0.471360
$956$	−2.10297e7	−0.744198
$957$	−1.26676e7	−0.447109
$958$	−5.58144e7	−1.96486
$959$	338092.	0.0118710
$960$	2.10910e7	0.738617
$961$	4.58427e6	0.160126
$962$	−2.71505e7	−0.945887
$963$	−3.79728e7	−1.31949
$964$	1.36943e7	0.474622
$965$	6.89521e6	0.238358
$966$	−2.31242e7	−0.797305
$967$	−6.01995e6	−0.207027	−0.103513	−	0.994628i	$-0.533008\pi$
$967$	−6.01995e6	−0.207027	−0.103513	+	0.994628i	$0.533008\pi$
$968$	8.72585e6	0.299309
$969$	−4.11416e7	−1.40757
$970$	−1.73708e7	−0.592776
$971$	−4.21751e7	−1.43552	−0.717758	−	0.696292i	$-0.754832\pi$
$971$	−4.21751e7	−1.43552	−0.717758	+	0.696292i	$0.754832\pi$
$972$	−7.80903e7	−2.65113
$973$	−8.49436e6	−0.287639
$974$	8.48938e6	0.286733
$975$	−1.29563e7	−0.436484
$976$	−4.01792e7	−1.35014
$977$	−5.21316e7	−1.74729	−0.873644	−	0.486565i	$-0.838250\pi$
$977$	−5.21316e7	−1.74729	−0.873644	+	0.486565i	$0.838250\pi$
$978$	7.92443e7	2.64924
$979$	3.34823e7	1.11650
$980$	2.99817e7	0.997219
$981$	5.68736e7	1.88685
$982$	9.23672e7	3.05660
$983$	−1.63974e6	−0.0541241	−0.0270620	−	0.999634i	$-0.508615\pi$
$983$	−1.63974e6	−0.0541241	−0.0270620	+	0.999634i	$0.508615\pi$
$984$	1.26222e8	4.15574
$985$	−5.83622e6	−0.191664
$986$	2.31463e7	0.758210
$987$	−1.71690e7	−0.560988
$988$	1.58641e7	0.517040
$989$	−1.74224e6	−0.0566392
$990$	−3.52945e7	−1.14451
$991$	2.64974e7	0.857075	0.428538	−	0.903524i	$-0.359029\pi$
$991$	2.64974e7	0.857075	0.428538	+	0.903524i	$0.359029\pi$
$992$	−2.97338e6	−0.0959337
$993$	−3.33727e7	−1.07403
$994$	9.32357e6	0.299307
$995$	3.28292e6	0.105124
$996$	−1.34980e7	−0.431142
$997$	−4.71024e7	−1.50074	−0.750370	−	0.661018i	$-0.770125\pi$
$997$	−4.71024e7	−1.50074	−0.750370	+	0.661018i	$0.770125\pi$
$998$	−4.41110e7	−1.40191
$999$	2.69488e7	0.854331

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.6.a.a.1.11	✓	111

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.6.a.a.1.11	✓	111	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)

\(f(q)\)	\(=\)	\(q-9.83916 q^{2} +24.1089 q^{3} +64.8091 q^{4} -28.9694 q^{5} -237.211 q^{6} +28.9470 q^{7} -322.814 q^{8} +338.239 q^{9} +O(q^{10})\)	\(q-9.83916 q^{2} +24.1089 q^{3} +64.8091 q^{4} -28.9694 q^{5} -237.211 q^{6} +28.9470 q^{7} -322.814 q^{8} +338.239 q^{9} +285.035 q^{10} -366.088 q^{11} +1562.48 q^{12} +235.109 q^{13} -284.815 q^{14} -698.421 q^{15} +1102.33 q^{16} -1639.05 q^{17} -3327.98 q^{18} +1041.14 q^{19} -1877.48 q^{20} +697.881 q^{21} +3602.00 q^{22} +3367.66 q^{23} -7782.69 q^{24} -2285.77 q^{25} -2313.28 q^{26} +2296.10 q^{27} +1876.03 q^{28} +1435.26 q^{29} +6871.88 q^{30} +5763.11 q^{31} -515.933 q^{32} -8825.98 q^{33} +16126.9 q^{34} -838.580 q^{35} +21920.9 q^{36} +11736.8 q^{37} -10244.0 q^{38} +5668.22 q^{39} +9351.74 q^{40} -16218.3 q^{41} -6866.57 q^{42} -517.345 q^{43} -23725.8 q^{44} -9798.58 q^{45} -33134.9 q^{46} -24601.7 q^{47} +26575.9 q^{48} -15969.1 q^{49} +22490.1 q^{50} -39515.7 q^{51} +15237.2 q^{52} +15028.2 q^{53} -22591.7 q^{54} +10605.4 q^{55} -9344.51 q^{56} +25100.8 q^{57} -14121.8 q^{58} +3937.07 q^{59} -45264.0 q^{60} -36449.5 q^{61} -56704.2 q^{62} +9791.01 q^{63} -30198.1 q^{64} -6810.98 q^{65} +86840.2 q^{66} -47590.6 q^{67} -106225. q^{68} +81190.5 q^{69} +8250.92 q^{70} -32735.6 q^{71} -109188. q^{72} +44888.1 q^{73} -115480. q^{74} -55107.4 q^{75} +67475.6 q^{76} -10597.2 q^{77} -55770.5 q^{78} +62651.7 q^{79} -31933.8 q^{80} -26835.6 q^{81} +159575. q^{82} -8638.84 q^{83} +45229.0 q^{84} +47482.4 q^{85} +5090.24 q^{86} +34602.5 q^{87} +118178. q^{88} -91459.7 q^{89} +96409.8 q^{90} +6805.71 q^{91} +218255. q^{92} +138942. q^{93} +242060. q^{94} -30161.4 q^{95} -12438.6 q^{96} -60942.7 q^{97} +157122. q^{98} -123825. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 111 q - 28 q^{2} - 98 q^{3} + 1722 q^{4} - 801 q^{5} - 414 q^{6} - 587 q^{7} - 1344 q^{8} + 8241 q^{9}+O(q^{10}) \) 111 * q - 28 * q^2 - 98 * q^3 + 1722 * q^4 - 801 * q^5 - 414 * q^6 - 587 * q^7 - 1344 * q^8 + 8241 * q^9	\( 111 q - 28 q^{2} - 98 q^{3} + 1722 q^{4} - 801 q^{5} - 414 q^{6} - 587 q^{7} - 1344 q^{8} + 8241 q^{9} - 950 q^{10} - 1832 q^{11} - 4143 q^{12} - 4369 q^{13} - 4777 q^{14} - 3487 q^{15} + 26274 q^{16} - 13648 q^{17} - 10269 q^{18} - 5446 q^{19} - 26032 q^{20} - 8428 q^{21} - 8248 q^{22} - 24142 q^{23} - 18577 q^{24} + 58062 q^{25} - 17656 q^{26} - 33269 q^{27} - 23512 q^{28} - 33752 q^{29} - 12418 q^{30} - 13781 q^{31} - 44076 q^{32} - 39186 q^{33} - 7207 q^{34} - 30833 q^{35} + 120044 q^{36} - 61582 q^{37} - 91259 q^{38} - 20077 q^{39} - 66032 q^{40} - 54181 q^{41} - 69252 q^{42} - 38600 q^{43} - 95712 q^{44} - 190880 q^{45} - 9354 q^{46} - 83886 q^{47} - 173886 q^{48} + 194148 q^{49} - 70896 q^{50} - 60673 q^{51} - 145186 q^{52} - 286874 q^{53} - 116519 q^{54} - 74821 q^{55} - 240407 q^{56} - 95180 q^{57} - 66900 q^{58} - 135740 q^{59} - 144550 q^{60} - 227450 q^{61} - 308766 q^{62} - 249721 q^{63} + 347514 q^{64} - 290374 q^{65} - 178980 q^{66} - 91006 q^{67} - 521943 q^{68} - 414510 q^{69} - 165057 q^{70} - 236165 q^{71} - 527945 q^{72} - 184618 q^{73} - 206443 q^{74} - 243897 q^{75} - 221676 q^{76} - 751131 q^{77} - 306839 q^{78} - 107446 q^{79} - 856691 q^{80} + 382187 q^{81} - 244614 q^{82} - 499547 q^{83} - 330289 q^{84} - 287103 q^{85} - 272441 q^{86} - 391281 q^{87} - 588937 q^{88} - 740774 q^{89} - 687179 q^{90} - 237213 q^{91} - 1367678 q^{92} - 754880 q^{93} - 32851 q^{94} - 295814 q^{95} - 816078 q^{96} - 320770 q^{97} - 661922 q^{98} - 547439 q^{99}+O(q^{100}) \) 111 * q - 28 * q^2 - 98 * q^3 + 1722 * q^4 - 801 * q^5 - 414 * q^6 - 587 * q^7 - 1344 * q^8 + 8241 * q^9 - 950 * q^10 - 1832 * q^11 - 4143 * q^12 - 4369 * q^13 - 4777 * q^14 - 3487 * q^15 + 26274 * q^16 - 13648 * q^17 - 10269 * q^18 - 5446 * q^19 - 26032 * q^20 - 8428 * q^21 - 8248 * q^22 - 24142 * q^23 - 18577 * q^24 + 58062 * q^25 - 17656 * q^26 - 33269 * q^27 - 23512 * q^28 - 33752 * q^29 - 12418 * q^30 - 13781 * q^31 - 44076 * q^32 - 39186 * q^33 - 7207 * q^34 - 30833 * q^35 + 120044 * q^36 - 61582 * q^37 - 91259 * q^38 - 20077 * q^39 - 66032 * q^40 - 54181 * q^41 - 69252 * q^42 - 38600 * q^43 - 95712 * q^44 - 190880 * q^45 - 9354 * q^46 - 83886 * q^47 - 173886 * q^48 + 194148 * q^49 - 70896 * q^50 - 60673 * q^51 - 145186 * q^52 - 286874 * q^53 - 116519 * q^54 - 74821 * q^55 - 240407 * q^56 - 95180 * q^57 - 66900 * q^58 - 135740 * q^59 - 144550 * q^60 - 227450 * q^61 - 308766 * q^62 - 249721 * q^63 + 347514 * q^64 - 290374 * q^65 - 178980 * q^66 - 91006 * q^67 - 521943 * q^68 - 414510 * q^69 - 165057 * q^70 - 236165 * q^71 - 527945 * q^72 - 184618 * q^73 - 206443 * q^74 - 243897 * q^75 - 221676 * q^76 - 751131 * q^77 - 306839 * q^78 - 107446 * q^79 - 856691 * q^80 + 382187 * q^81 - 244614 * q^82 - 499547 * q^83 - 330289 * q^84 - 287103 * q^85 - 272441 * q^86 - 391281 * q^87 - 588937 * q^88 - 740774 * q^89 - 687179 * q^90 - 237213 * q^91 - 1367678 * q^92 - 754880 * q^93 - 32851 * q^94 - 295814 * q^95 - 816078 * q^96 - 320770 * q^97 - 661922 * q^98 - 547439 * q^99

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