LMFDB - Embedded newform 27.5.f.a.2.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,5,Mod(2,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("27.2");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	27.f (of order $18$, degree $6$, minimal)

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:	no
Analytic conductor:	$2.79098900326$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			2.2
Character	$\chi$	$=$	27.2
Dual form			27.5.f.a.14.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.19782 - 1.09284i) q^{2} +(-7.35835 + 5.18216i) q^{3} +(22.1836 + 8.07418i) q^{4} +(-7.06026 - 8.41408i) q^{5} +(51.2690 - 24.0766i) q^{6} +(62.3269 - 22.6852i) q^{7} +(-41.4621 - 23.9381i) q^{8} +(27.2905 - 76.2642i) q^{9} +O(q^{10})$	\(q+(-6.19782 - 1.09284i) q^{2} +(-7.35835 + 5.18216i) q^{3} +(22.1836 + 8.07418i) q^{4} +(-7.06026 - 8.41408i) q^{5} +(51.2690 - 24.0766i) q^{6} +(62.3269 - 22.6852i) q^{7} +(-41.4621 - 23.9381i) q^{8} +(27.2905 - 76.2642i) q^{9} +(34.5629 + 59.8648i) q^{10} +(18.2440 - 21.7424i) q^{11} +(-205.077 + 55.5464i) q^{12} +(38.7578 + 219.806i) q^{13} +(-411.083 + 72.4850i) q^{14} +(95.5549 + 25.3264i) q^{15} +(-58.5343 - 49.1161i) q^{16} +(287.497 - 165.987i) q^{17} +(-252.487 + 442.848i) q^{18} +(283.914 - 491.754i) q^{19} +(-88.6853 - 243.661i) q^{20} +(-341.065 + 489.913i) q^{21} +(-136.834 + 114.818i) q^{22} +(-50.3714 + 138.394i) q^{23} +(429.144 - 38.7178i) q^{24} +(87.5805 - 496.694i) q^{25} -1404.68i q^{26} +(194.400 + 702.602i) q^{27} +1565.80 q^{28} +(1292.76 + 227.949i) q^{29} +(-564.555 - 261.395i) q^{30} +(-1356.31 - 493.655i) q^{31} +(801.497 + 955.187i) q^{32} +(-21.5734 + 254.531i) q^{33} +(-1963.25 + 714.566i) q^{34} +(-630.919 - 364.261i) q^{35} +(1221.17 - 1471.47i) q^{36} +(630.312 + 1091.73i) q^{37} +(-2297.06 + 2737.53i) q^{38} +(-1424.26 - 1416.56i) q^{39} +(91.3153 + 517.875i) q^{40} +(264.956 - 46.7189i) q^{41} +(2649.26 - 2663.66i) q^{42} +(184.572 + 154.874i) q^{43} +(580.271 - 335.020i) q^{44} +(-834.371 + 308.820i) q^{45} +(463.437 - 802.696i) q^{46} +(-458.931 - 1260.90i) q^{47} +(685.242 + 58.0794i) q^{48} +(1530.76 - 1284.46i) q^{49} +(-1085.62 + 2982.71i) q^{50} +(-1255.34 + 2711.24i) q^{51} +(-914.968 + 5189.04i) q^{52} -1318.19i q^{53} +(-437.022 - 4567.05i) q^{54} -311.750 q^{55} +(-3127.25 - 551.418i) q^{56} +(459.206 + 5089.78i) q^{57} +(-7763.20 - 2825.58i) q^{58} +(893.408 + 1064.72i) q^{59} +(1915.27 + 1333.36i) q^{60} +(2681.63 - 976.034i) q^{61} +(7866.66 + 4541.82i) q^{62} +(-29.1303 - 5372.40i) q^{63} +(-3312.38 - 5737.21i) q^{64} +(1575.83 - 1878.00i) q^{65} +(411.871 - 1553.96i) q^{66} +(252.937 + 1434.48i) q^{67} +(7717.94 - 1360.88i) q^{68} +(-346.531 - 1279.39i) q^{69} +(3512.24 + 2947.12i) q^{70} +(-880.106 + 508.129i) q^{71} +(-2957.14 + 2508.79i) q^{72} +(-1701.39 + 2946.89i) q^{73} +(-2713.47 - 7455.20i) q^{74} +(1929.50 + 4108.70i) q^{75} +(10268.8 - 8616.51i) q^{76} +(643.865 - 1769.01i) q^{77} +(7279.26 + 10336.1i) q^{78} +(250.938 - 1423.14i) q^{79} +839.284i q^{80} +(-5071.46 - 4162.58i) q^{81} -1693.21 q^{82} +(-9629.68 - 1697.97i) q^{83} +(-11521.7 + 8114.23i) q^{84} +(-3426.43 - 1247.12i) q^{85} +(-974.689 - 1161.59i) q^{86} +(-10693.9 + 5021.97i) q^{87} +(-1276.91 + 464.756i) q^{88} +(-10139.4 - 5854.01i) q^{89} +(5508.78 - 1002.17i) q^{90} +(7402.00 + 12820.6i) q^{91} +(-2234.84 + 2663.38i) q^{92} +(12538.4 - 3396.10i) q^{93} +(1466.40 + 8316.39i) q^{94} +(-6142.16 + 1083.03i) q^{95} +(-10847.6 - 2875.11i) q^{96} +(4082.19 + 3425.36i) q^{97} +(-10891.1 + 6287.97i) q^{98} +(-1160.28 - 1984.73i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 3 q^{5} + 90 q^{6} - 6 q^{7} - 9 q^{8} - 108 q^{9}+O(q^{10}) $ 66 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 3 * q^5 + 90 * q^6 - 6 * q^7 - 9 * q^8 - 108 * q^9	\( 66 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 3 q^{5} + 90 q^{6} - 6 q^{7} - 9 q^{8} - 108 q^{9} - 3 q^{10} - 492 q^{11} - 339 q^{12} - 6 q^{13} + 1137 q^{14} + 1017 q^{15} - 54 q^{16} - 9 q^{17} + 603 q^{18} - 3 q^{19} - 2487 q^{20} - 2784 q^{21} + 1002 q^{22} - 2724 q^{23} - 3312 q^{24} + 435 q^{25} + 1368 q^{27} - 12 q^{28} + 5016 q^{29} + 10773 q^{30} - 1671 q^{31} + 10224 q^{32} + 2925 q^{33} - 342 q^{34} - 2682 q^{35} - 7704 q^{36} - 3 q^{37} - 6564 q^{38} - 1983 q^{39} - 1113 q^{40} + 5754 q^{41} + 8694 q^{42} - 1266 q^{43} - 4545 q^{44} - 7029 q^{45} - 3 q^{46} - 9159 q^{47} - 28383 q^{48} + 5898 q^{49} - 34977 q^{50} - 14814 q^{51} + 2871 q^{52} + 13878 q^{54} - 12 q^{55} + 39243 q^{56} + 15792 q^{57} - 12291 q^{58} + 24762 q^{59} + 50670 q^{60} - 8358 q^{61} + 38304 q^{62} + 21609 q^{63} + 6141 q^{64} + 23727 q^{65} + 11349 q^{66} + 15996 q^{67} - 43533 q^{68} - 26847 q^{69} - 7251 q^{70} - 19773 q^{71} - 77580 q^{72} + 6108 q^{73} - 74847 q^{74} - 49155 q^{75} - 28614 q^{76} - 33909 q^{77} - 9108 q^{78} - 5658 q^{79} - 12600 q^{81} - 12 q^{82} + 18813 q^{83} + 82356 q^{84} + 24219 q^{85} + 96474 q^{86} + 84555 q^{87} + 36042 q^{88} + 110232 q^{89} + 153540 q^{90} - 6042 q^{91} + 73545 q^{92} + 1293 q^{93} + 2631 q^{94} - 65163 q^{95} - 152226 q^{96} - 3696 q^{97} - 259938 q^{98} - 162405 q^{99}+O(q^{100}) \) 66 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 3 * q^5 + 90 * q^6 - 6 * q^7 - 9 * q^8 - 108 * q^9 - 3 * q^10 - 492 * q^11 - 339 * q^12 - 6 * q^13 + 1137 * q^14 + 1017 * q^15 - 54 * q^16 - 9 * q^17 + 603 * q^18 - 3 * q^19 - 2487 * q^20 - 2784 * q^21 + 1002 * q^22 - 2724 * q^23 - 3312 * q^24 + 435 * q^25 + 1368 * q^27 - 12 * q^28 + 5016 * q^29 + 10773 * q^30 - 1671 * q^31 + 10224 * q^32 + 2925 * q^33 - 342 * q^34 - 2682 * q^35 - 7704 * q^36 - 3 * q^37 - 6564 * q^38 - 1983 * q^39 - 1113 * q^40 + 5754 * q^41 + 8694 * q^42 - 1266 * q^43 - 4545 * q^44 - 7029 * q^45 - 3 * q^46 - 9159 * q^47 - 28383 * q^48 + 5898 * q^49 - 34977 * q^50 - 14814 * q^51 + 2871 * q^52 + 13878 * q^54 - 12 * q^55 + 39243 * q^56 + 15792 * q^57 - 12291 * q^58 + 24762 * q^59 + 50670 * q^60 - 8358 * q^61 + 38304 * q^62 + 21609 * q^63 + 6141 * q^64 + 23727 * q^65 + 11349 * q^66 + 15996 * q^67 - 43533 * q^68 - 26847 * q^69 - 7251 * q^70 - 19773 * q^71 - 77580 * q^72 + 6108 * q^73 - 74847 * q^74 - 49155 * q^75 - 28614 * q^76 - 33909 * q^77 - 9108 * q^78 - 5658 * q^79 - 12600 * q^81 - 12 * q^82 + 18813 * q^83 + 82356 * q^84 + 24219 * q^85 + 96474 * q^86 + 84555 * q^87 + 36042 * q^88 + 110232 * q^89 + 153540 * q^90 - 6042 * q^91 + 73545 * q^92 + 1293 * q^93 + 2631 * q^94 - 65163 * q^95 - 152226 * q^96 - 3696 * q^97 - 259938 * q^98 - 162405 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	−6.19782	−	1.09284i	−1.54946	−	0.273211i	−0.667524	−	0.744588i	$-0.732646\pi$
$2$	−6.19782	−	1.09284i	−1.54946	−	0.273211i	−0.881932	+	0.471377i	$0.843757\pi$
$3$	−7.35835	+	5.18216i	−0.817594	+	0.575795i
$3$	−7.35835	+	5.18216i	−0.817594	+	0.575795i
$4$	22.1836	+	8.07418i	1.38648	+	0.504637i
$5$	−7.06026	−	8.41408i	−0.282410	−	0.336563i	0.606127	−	0.795368i	$-0.292722\pi$
$5$	−7.06026	−	8.41408i	−0.282410	−	0.336563i	−0.888537	+	0.458804i	$0.848278\pi$
$6$	51.2690	−	24.0766i	1.42414	−	0.668794i
$7$	62.3269	−	22.6852i	1.27198	−	0.462962i	0.384207	−	0.923247i	$-0.374475\pi$
$7$	62.3269	−	22.6852i	1.27198	−	0.462962i	0.887771	+	0.460285i	$0.152253\pi$
$8$	−41.4621	−	23.9381i	−0.647845	−	0.374033i
$9$	27.2905	−	76.2642i	0.336920	−	0.941533i
$10$	34.5629	+	59.8648i	0.345629	+	0.598648i
$11$	18.2440	−	21.7424i	0.150777	−	0.179689i	−0.685369	−	0.728196i	$-0.740359\pi$
$11$	18.2440	−	21.7424i	0.150777	−	0.179689i	0.836146	+	0.548507i	$0.184804\pi$
$12$	−205.077	+	55.5464i	−1.42414	+	0.385739i
$13$	38.7578	+	219.806i	0.229336	+	1.30063i	0.854220	+	0.519912i	$0.174035\pi$
$13$	38.7578	+	219.806i	0.229336	+	1.30063i	−0.624884	+	0.780718i	$0.714854\pi$
$14$	−411.083	+	72.4850i	−2.09736	+	0.369821i
$15$	95.5549	+	25.3264i	0.424688	+	0.112562i
$16$	−58.5343	−	49.1161i	−0.228649	−	0.191860i
$17$	287.497	−	165.987i	0.994800	−	0.574348i	0.0880945	−	0.996112i	$-0.471922\pi$
$17$	287.497	−	165.987i	0.994800	−	0.574348i	0.906706	+	0.421764i	$0.138589\pi$
$18$	−252.487	+	442.848i	−0.779280	+	1.36681i
$19$	283.914	−	491.754i	0.786466	−	1.36220i	−0.141654	−	0.989916i	$-0.545242\pi$
$19$	283.914	−	491.754i	0.786466	−	1.36220i	0.928120	−	0.372282i	$-0.121425\pi$
$20$	−88.6853	−	243.661i	−0.221713	−	0.609152i
$21$	−341.065	+	489.913i	−0.773391	+	1.11091i
$22$	−136.834	+	114.818i	−0.282716	+	0.237227i
$23$	−50.3714	+	138.394i	−0.0952201	+	0.261615i	−0.978154	−	0.207883i	$-0.933343\pi$
$23$	−50.3714	+	138.394i	−0.0952201	+	0.261615i	0.882934	+	0.469498i	$0.155565\pi$
$24$	429.144	−	38.7178i	0.745041	−	0.0672184i
$25$	87.5805	−	496.694i	0.140129	−	0.794710i
$26$		−	1404.68i		−	2.07793i
$27$	194.400	+	702.602i	0.266667	+	0.963789i
$28$	1565.80			1.99720
$29$	1292.76	+	227.949i	1.53717	+	0.271045i	0.877156	−	0.480205i	$-0.159438\pi$
$29$	1292.76	+	227.949i	1.53717	+	0.271045i	0.660017	+	0.751251i	$0.270549\pi$
$30$	−564.555	−	261.395i	−0.627283	−	0.290439i
$31$	−1356.31	−	493.655i	−1.41135	−	0.513689i	−0.479823	−	0.877365i	$-0.659299\pi$
$31$	−1356.31	−	493.655i	−1.41135	−	0.513689i	−0.931525	+	0.363677i	$0.881521\pi$
$32$	801.497	+	955.187i	0.782712	+	0.932800i
$33$	−21.5734	+	254.531i	−0.0198103	+	0.233730i
$34$	−1963.25	+	714.566i	−1.69832	+	0.618137i
$35$	−630.919	−	364.261i	−0.515036	−	0.297356i
$36$	1221.17	−	1471.47i	0.942264	−	1.13539i
$37$	630.312	+	1091.73i	0.460418	+	0.797467i	0.998982	−	0.0451175i	$-0.0143662\pi$
$37$	630.312	+	1091.73i	0.460418	+	0.797467i	−0.538564	+	0.842585i	$0.681033\pi$
$38$	−2297.06	+	2737.53i	−1.59076	+	1.89580i
$39$	−1424.26	−	1416.56i	−0.936400	−	0.931336i
$40$	91.3153	+	517.875i	0.0570721	+	0.323672i
$41$	264.956	−	46.7189i	0.157618	−	0.0277924i	−0.0942821	−	0.995546i	$-0.530056\pi$
$41$	264.956	−	46.7189i	0.157618	−	0.0277924i	0.251900	+	0.967753i	$0.418944\pi$
$42$	2649.26	−	2663.66i	1.50185	−	1.51001i
$43$	184.572	+	154.874i	0.0998224	+	0.0837609i	0.691333	−	0.722536i	$-0.257024\pi$
$43$	184.572	+	154.874i	0.0998224	+	0.0837609i	−0.591511	+	0.806297i	$0.701468\pi$
$44$	580.271	−	335.020i	0.299727	−	0.173047i
$45$	−834.371	+	308.820i	−0.412035	+	0.152504i
$46$	463.437	−	802.696i	0.219015	−	0.379346i
$47$	−458.931	−	1260.90i	−0.207755	−	0.570802i	0.791426	−	0.611265i	$-0.209339\pi$
$47$	−458.931	−	1260.90i	−0.207755	−	0.570802i	−0.999181	+	0.0404627i	$0.987117\pi$
$48$	685.242	+	58.0794i	0.297414	+	0.0252081i
$49$	1530.76	−	1284.46i	0.637551	−	0.534968i
$50$	−1085.62	+	2982.71i	−0.434247	+	1.19308i
$51$	−1255.34	+	2711.24i	−0.482636	+	1.04238i
$52$	−914.968	+	5189.04i	−0.338376	+	1.91902i
$53$		−	1318.19i		−	0.469274i	−0.972083	−	0.234637i	$-0.924610\pi$
$53$		−	1318.19i		−	0.469274i	0.972083	−	0.234637i	$-0.0753902\pi$
$54$	−437.022	−	4567.05i	−0.149870	−	1.56620i
$55$	−311.750			−0.103058
$56$	−3127.25	−	551.418i	−0.997208	−	0.175835i
$57$	459.206	+	5089.78i	0.141338	+	1.56657i
$58$	−7763.20	−	2825.58i	−2.30773	−	0.839945i
$59$	893.408	+	1064.72i	0.256653	+	0.305867i	0.878950	−	0.476915i	$-0.158245\pi$
$59$	893.408	+	1064.72i	0.256653	+	0.305867i	−0.622297	+	0.782781i	$0.713800\pi$
$60$	1915.27	+	1333.36i	0.532018	+	0.370378i
$61$	2681.63	−	976.034i	0.720675	−	0.262304i	0.0444625	−	0.999011i	$-0.485842\pi$
$61$	2681.63	−	976.034i	0.720675	−	0.262304i	0.676212	+	0.736707i	$0.263620\pi$
$62$	7866.66	+	4541.82i	2.04648	+	1.18153i
$63$	−29.1303	−	5372.40i	−0.00733947	−	1.35359i
$64$	−3312.38	−	5737.21i	−0.808687	−	1.40069i
$65$	1575.83	−	1878.00i	0.372977	−	0.444497i
$66$	411.871	−	1553.96i	0.0945527	−	0.356741i
$67$	252.937	+	1434.48i	0.0563460	+	0.319554i	0.999933	−	0.0115704i	$-0.00368306\pi$
$67$	252.937	+	1434.48i	0.0563460	+	0.319554i	−0.943587	+	0.331125i	$0.892572\pi$
$68$	7717.94	−	1360.88i	1.66911	−	0.294308i
$69$	−346.531	−	1279.39i	−0.0727853	−	0.268722i
$70$	3512.24	+	2947.12i	0.716785	+	0.601454i
$71$	−880.106	+	508.129i	−0.174590	+	0.100799i	−0.584748	−	0.811215i	$-0.698807\pi$
$71$	−880.106	+	508.129i	−0.174590	+	0.100799i	0.410159	+	0.912014i	$0.365473\pi$
$72$	−2957.14	+	2508.79i	−0.570437	+	0.483948i
$73$	−1701.39	+	2946.89i	−0.319270	+	0.552992i	−0.980336	−	0.197336i	$-0.936771\pi$
$73$	−1701.39	+	2946.89i	−0.319270	+	0.552992i	0.661066	+	0.750328i	$0.270104\pi$
$74$	−2713.47	−	7455.20i	−0.495521	−	1.36143i
$75$	1929.50	+	4108.70i	0.343022	+	0.730436i
$76$	10268.8	−	8616.51i	1.77783	−	1.49178i
$77$	643.865	−	1769.01i	0.108596	−	0.298365i
$78$	7279.26	+	10336.1i	1.19646	+	1.69890i
$79$	250.938	−	1423.14i	0.0402079	−	0.228030i	−0.958082	−	0.286496i	$-0.907510\pi$
$79$	250.938	−	1423.14i	0.0402079	−	0.228030i	0.998289	+	0.0584653i	$0.0186207\pi$
$80$			839.284i			0.131138i
$81$	−5071.46	−	4162.58i	−0.772970	−	0.634443i
$82$	−1693.21			−0.251816
$83$	−9629.68	−	1697.97i	−1.39783	−	0.246476i	−0.576581	−	0.817040i	$-0.695614\pi$
$83$	−9629.68	−	1697.97i	−1.39783	−	0.246476i	−0.821253	+	0.570564i	$0.806725\pi$
$84$	−11521.7	+	8114.23i	−1.63290	+	1.14998i
$85$	−3426.43	−	1247.12i	−0.474246	−	0.172612i
$86$	−974.689	−	1161.59i	−0.131786	−	0.157056i
$87$	−10693.9	+	5021.97i	−1.41285	+	0.663492i
$88$	−1276.91	+	464.756i	−0.164890	+	0.0600150i
$89$	−10139.4	−	5854.01i	−1.28007	−	0.739050i	−0.303210	−	0.952924i	$-0.598059\pi$
$89$	−10139.4	−	5854.01i	−1.28007	−	0.739050i	−0.976861	+	0.213874i	$0.931392\pi$
$90$	5508.78	−	1002.17i	0.680096	−	0.123725i
$91$	7402.00	+	12820.6i	0.893853	+	1.54820i
$92$	−2234.84	+	2663.38i	−0.264041	+	0.314672i
$93$	12538.4	−	3396.10i	1.44969	−	0.392659i
$94$	1466.40	+	8316.39i	0.165958	+	0.941194i
$95$	−6142.16	+	1083.03i	−0.680572	+	0.120003i
$96$	−10847.6	−	2875.11i	−1.17704	−	0.311970i
$97$	4082.19	+	3425.36i	0.433860	+	0.364052i	0.833406	−	0.552662i	$-0.186388\pi$
$97$	4082.19	+	3425.36i	0.433860	+	0.364052i	−0.399546	+	0.916713i	$0.630832\pi$
$98$	−10891.1	+	6287.97i	−1.13402	+	0.654724i
$99$	−1160.28	−	1984.73i	−0.118384	−	0.202503i
$100$	5953.25	−	10311.3i	0.595325	−	1.03113i
$101$	5579.65	+	15330.0i	0.546971	+	1.50279i	0.837780	+	0.546009i	$0.183853\pi$
$101$	5579.65	+	15330.0i	0.546971	+	1.50279i	−0.290809	+	0.956781i	$0.593924\pi$
$102$	10743.3	−	15431.9i	1.03261	−	1.48327i
$103$	5565.88	−	4670.32i	0.524637	−	0.440223i	−0.341608	−	0.939843i	$-0.610971\pi$
$103$	5565.88	−	4670.32i	0.524637	−	0.440223i	0.866245	+	0.499620i	$0.166527\pi$
$104$	3654.78	−	10041.4i	0.337905	−	0.928386i
$105$	6530.18	−	589.160i	0.592306	−	0.0534386i
$106$	−1440.58	+	8169.92i	−0.128211	+	0.727120i
$107$		−	20589.5i		−	1.79836i	−0.437575	−	0.899182i	$-0.644163\pi$
$107$		−	20589.5i		−	1.79836i	0.437575	−	0.899182i	$-0.355837\pi$
$108$	−1360.44	+	17155.9i	−0.116636	+	1.47084i
$109$	6506.21			0.547614			0.273807	−	0.961785i	$-0.411717\pi$
$109$	6506.21			0.547614			0.273807	+	0.961785i	$0.411717\pi$
$110$	1932.17	+	340.694i	0.159684	+	0.0281565i
$111$	−10295.6	−	4766.97i	−0.835613	−	0.386898i
$112$	−4762.47	−	1733.40i	−0.379661	−	0.138185i
$113$	3348.18	+	3990.21i	0.262212	+	0.312492i	0.881047	−	0.473029i	$-0.156839\pi$
$113$	3348.18	+	3990.21i	0.262212	+	0.312492i	−0.618835	+	0.785521i	$0.712395\pi$
$114$	2716.26	−	32047.4i	0.209007	−	2.46594i
$115$	1520.10	−	553.270i	0.114941	−	0.0418352i
$116$	26837.7	+	15494.7i	1.99448	+	1.15151i
$117$	17821.1	+	3042.80i	1.30185	+	0.222280i
$118$	−4373.61	−	7575.31i	−0.314106	−	0.544047i
$119$	14153.4	−	16867.4i	0.999463	−	1.19111i
$120$	−3355.64	−	3337.49i	−0.233030	−	0.231770i
$121$	2402.50	+	13625.2i	0.164094	+	0.930622i
$122$	−17686.9	+	3118.68i	−1.18832	+	0.209533i
$123$	−1707.54	+	1716.82i	−0.112865	+	0.113479i
$124$	−26101.9	−	21902.1i	−1.69758	−	1.42444i
$125$	−10742.7	+	6202.31i	−0.687534	+	0.396948i
$126$	−5690.65	+	33329.1i	−0.358444	+	2.09934i
$127$	−8010.15	+	13874.0i	−0.496630	+	0.860189i	−0.999992	−	0.00388641i	$-0.998763\pi$
$127$	−8010.15	+	13874.0i	−0.496630	+	0.860189i	0.503362	+	0.864076i	$0.332096\pi$
$128$	7436.20	+	20430.8i	0.453869	+	1.24700i
$129$	−2160.72	−	183.137i	−0.129843	−	0.0110052i
$130$	−11819.1	+	9917.38i	−0.699354	+	0.586827i
$131$	−3109.27	+	8542.66i	−0.181183	+	0.497795i	−0.996722	−	0.0809069i	$-0.974218\pi$
$131$	−3109.27	+	8542.66i	−0.181183	+	0.497795i	0.815539	+	0.578702i	$0.196441\pi$
$132$	−2533.71	+	5472.25i	−0.145415	+	0.314064i
$133$	6539.99	−	37090.1i	0.369721	−	2.09679i
$134$		−	9167.07i		−	0.510530i
$135$	4539.24	−	6596.25i	0.249067	−	0.361934i
$136$	−15893.6			−0.859302
$137$	31865.7	+	5618.77i	1.69778	+	0.299365i	0.936918	−	0.349548i	$-0.113665\pi$
$137$	31865.7	+	5618.77i	1.69778	+	0.299365i	0.760863	+	0.648913i	$0.224776\pi$
$138$	749.568	+	8308.12i	0.0393598	+	0.436259i
$139$	92.1216	+	33.5295i	0.00476795	+	0.00173539i	0.344403	−	0.938822i	$-0.388081\pi$
$139$	92.1216	+	33.5295i	0.00476795	+	0.00173539i	−0.339635	+	0.940557i	$0.610304\pi$
$140$	−11055.0	−	13174.8i	−0.564029	−	0.672183i
$141$	9911.17	+	6899.90i	0.498525	+	0.347060i
$142$	6010.05	−	2187.48i	0.298058	−	0.108484i
$143$	5486.21	+	3167.47i	0.268288	+	0.154896i
$144$	−5343.23	+	3123.66i	−0.257679	+	0.150640i
$145$	−7209.25	−	12486.8i	−0.342890	−	0.593902i
$146$	13765.4	−	16405.0i	0.645778	−	0.769608i
$147$	−4607.59	+	17384.1i	−0.213225	+	0.804486i
$148$	5167.77	+	29307.9i	0.235928	+	1.33801i
$149$	−748.137	+	131.917i	−0.0336983	+	0.00594193i	−0.190472	−	0.981693i	$-0.561002\pi$
$149$	−748.137	+	131.917i	−0.0336983	+	0.00594193i	0.156774	+	0.987635i	$0.449891\pi$
$150$	−7468.51	−	27573.6i	−0.331934	−	1.22550i
$151$	−10700.5	−	8978.81i	−0.469301	−	0.393790i	0.377238	−	0.926116i	$-0.376874\pi$
$151$	−10700.5	−	8978.81i	−0.469301	−	0.393790i	−0.846540	+	0.532326i	$0.821318\pi$
$152$	−23543.3	+	13592.8i	−1.01902	+	0.588329i
$153$	−4812.89	−	26455.6i	−0.205600	−	1.13015i
$154$	−5923.81	+	10260.3i	−0.249781	+	0.432634i
$155$	5422.21	+	14897.4i	0.225690	+	0.620079i
$156$	−20157.8	−	42924.3i	−0.828311	−	1.76382i
$157$	−18051.3	+	15146.9i	−0.732336	+	0.614503i	−0.930767	−	0.365612i	$-0.880860\pi$
$157$	−18051.3	+	15146.9i	−0.732336	+	0.614503i	0.198431	+	0.980115i	$0.436415\pi$
$158$	−3110.53	+	8546.12i	−0.124601	+	0.342338i
$159$	6831.07	+	9699.71i	0.270206	+	0.383676i
$160$	2378.25	−	13487.7i	0.0929004	−	0.526865i
$161$			9768.38i			0.376852i
$162$	26882.9	+	31341.2i	1.02435	+	1.19423i
$163$	−11897.4			−0.447791			−0.223895	−	0.974613i	$-0.571877\pi$
$163$	−11897.4			−0.447791			−0.223895	+	0.974613i	$0.571877\pi$
$164$	6254.91	+	1102.91i	0.232559	+	0.0410065i
$165$	2293.96	−	1615.54i	0.0842594	−	0.0593402i
$166$	57827.4	+	21047.5i	2.09854	+	0.763807i
$167$	−11583.2	−	13804.3i	−0.415332	−	0.494974i	0.517299	−	0.855805i	$-0.326938\pi$
$167$	−11583.2	−	13804.3i	−0.415332	−	0.494974i	−0.932631	+	0.360831i	$0.882493\pi$
$168$	25868.9	−	12148.4i	0.916556	−	0.430426i
$169$	−19974.1	+	7269.98i	−0.699349	+	0.254542i
$170$	19873.5	+	11474.0i	0.687664	+	0.397023i
$171$	−29755.0	−	35072.7i	−1.01758	−	1.19944i
$172$	2843.99	+	4925.93i	0.0961327	+	0.166507i
$173$	−28468.3	+	33927.2i	−0.951196	+	1.13359i	0.0397341	+	0.999210i	$0.487349\pi$
$173$	−28468.3	+	33927.2i	−0.951196	+	1.13359i	−0.990930	+	0.134381i	$0.957096\pi$
$174$	71766.9	−	19438.6i	2.37042	−	0.642046i
$175$	−5808.95	−	32944.2i	−0.189680	−	1.07573i
$176$	−2135.80	+	376.599i	−0.0689502	+	0.0121578i
$177$	−12091.6	−	3204.81i	−0.385954	−	0.102295i
$178$	56445.0	+	47363.0i	1.78150	+	1.49485i
$179$	−23089.5	+	13330.7i	−0.720625	+	0.416053i	−0.814983	−	0.579485i	$-0.803254\pi$
$179$	−23089.5	+	13330.7i	−0.720625	+	0.416053i	0.0943579	+	0.995538i	$0.469920\pi$
$180$	−21002.9	+	113.882i	−0.648237	+	0.00351488i
$181$	−1292.58	+	2238.81i	−0.0394547	+	0.0683375i	−0.885078	−	0.465442i	$-0.845895\pi$
$181$	−1292.58	+	2238.81i	−0.0394547	+	0.0683375i	0.845624	+	0.533779i	$0.179229\pi$
$182$	−31865.3	−	87549.3i	−0.962001	−	2.64308i
$183$	−14674.4	+	21078.6i	−0.438186	+	0.629419i
$184$	5401.41	−	4532.32i	0.159541	−	0.133871i
$185$	4735.77	−	13011.4i	0.138372	−	0.380173i
$186$	−81422.0	+	7345.99i	−2.35351	+	0.212336i
$187$	1636.16	−	9279.14i	0.0467890	−	0.265353i
$188$		−	31676.9i		−	0.896245i
$189$	28055.0	+	39381.0i	0.785392	+	1.10246i
$190$	39251.6			1.08730
$191$	10928.8	+	1927.04i	0.299574	+	0.0528230i	0.321415	−	0.946938i	$-0.395842\pi$
$191$	10928.8	+	1927.04i	0.299574	+	0.0528230i	−0.0218407	+	0.999761i	$0.506953\pi$
$192$	54104.8	+	25051.1i	1.46769	+	0.679555i
$193$	8390.83	+	3054.01i	0.225263	+	0.0819892i	0.452186	−	0.891924i	$-0.350644\pi$
$193$	8390.83	+	3054.01i	0.225263	+	0.0819892i	−0.226923	+	0.973913i	$0.572867\pi$
$194$	−21557.3	−	25691.0i	−0.572784	−	0.682617i
$195$	−1863.41	+	21985.2i	−0.0490048	+	0.578177i
$196$	44328.8	−	16134.4i	1.15391	−	0.419990i
$197$	−9119.33	−	5265.05i	−0.234980	−	0.135666i	0.377888	−	0.925852i	$-0.376651\pi$
$197$	−9119.33	−	5265.05i	−0.234980	−	0.135666i	−0.612867	+	0.790186i	$0.709984\pi$
$198$	5022.20	+	13569.0i	0.128104	+	0.346112i
$199$	13293.1	+	23024.3i	0.335675	+	0.581406i	0.983614	−	0.180286i	$-0.0577023\pi$
$199$	13293.1	+	23024.3i	0.335675	+	0.581406i	−0.647939	+	0.761692i	$0.724369\pi$
$200$	−15521.2	+	18497.4i	−0.388030	+	0.462436i
$201$	−9294.89	−	9244.63i	−0.230066	−	0.228822i
$202$	−17828.4	−	101110.i	−0.436929	−	2.47795i
$203$	85745.0	−	15119.2i	2.08073	−	0.366890i
$204$	−49739.0	+	50009.4i	−1.19519	+	1.20169i
$205$	−2263.76	−	1899.52i	−0.0538669	−	0.0451997i
$206$	−39600.3	+	22863.2i	−0.933176	+	0.538769i
$207$	9179.87	+	7618.39i	0.214238	+	0.177796i
$208$	8527.37	−	14769.8i	0.197101	−	0.341388i
$209$	−5512.16	−	15144.5i	−0.126191	−	0.346708i
$210$	−41116.8	−	3484.95i	−0.932353	−	0.0790239i
$211$	27035.8	−	22685.8i	0.607260	−	0.509552i	−0.286510	−	0.958077i	$-0.592495\pi$
$211$	27035.8	−	22685.8i	0.607260	−	0.509552i	0.893770	+	0.448525i	$0.148051\pi$
$212$	10643.3	−	29242.3i	0.236813	−	0.650638i
$213$	3842.92	−	8299.84i	0.0847036	−	0.182941i
$214$	−22501.1	+	127610.i	−0.491333	+	2.78649i
$215$		−	2646.45i		−	0.0572515i
$216$	8758.77	−	33784.9i	0.187731	−	0.724128i
$217$	−95733.0			−2.03302
$218$	−40324.3	−	7110.27i	−0.848505	−	0.149614i
$219$	−2751.85	−	30501.1i	−0.0573767	−	0.635957i
$220$	−6915.75	−	2517.13i	−0.142887	−	0.0520067i
$221$	47627.7	+	56760.4i	0.975158	+	1.16215i
$222$	58600.7	+	40796.3i	1.18904	+	0.827780i
$223$	−40539.8	+	14755.3i	−0.815214	+	0.296714i	−0.715776	−	0.698330i	$-0.753927\pi$
$223$	−40539.8	+	14755.3i	−0.815214	+	0.296714i	−0.0994383	+	0.995044i	$0.531705\pi$
$224$	71623.5	+	41351.8i	1.42744	+	0.824135i
$225$	−35489.8	−	20234.3i	−0.701034	−	0.399690i
$226$	−16390.8	−	28389.7i	−0.320910	−	0.555832i
$227$	−34396.1	+	40991.7i	−0.667509	+	0.795507i	−0.988443	−	0.151595i	$-0.951559\pi$
$227$	−34396.1	+	40991.7i	−0.667509	+	0.795507i	0.320933	+	0.947102i	$0.396003\pi$
$228$	−30909.0	+	116618.i	−0.594586	+	2.24334i
$229$	−10270.1	−	58244.6i	−0.195841	−	1.11067i	−0.911216	−	0.411929i	$-0.864855\pi$
$229$	−10270.1	−	58244.6i	−0.195841	−	1.11067i	0.715375	−	0.698741i	$-0.246256\pi$
$230$	−10025.9	+	1767.84i	−0.189526	+	0.0334186i
$231$	4429.48	+	16353.6i	0.0830096	+	0.306470i
$232$	−48144.0	−	40397.6i	−0.894470	−	0.750550i
$233$	12167.6	−	7024.97i	0.224126	−	0.129399i	−0.383733	−	0.923444i	$-0.625362\pi$
$233$	12167.6	−	7024.97i	0.224126	−	0.129399i	0.607859	+	0.794045i	$0.292028\pi$
$234$	−107127.	−	38334.4i	−1.95644	−	0.700095i
$235$	−7369.17	+	12763.8i	−0.133439	+	0.231123i
$236$	11222.3	+	30832.9i	0.201492	+	0.553593i
$237$	5528.44	+	11772.3i	0.0984250	+	0.209588i
$238$	−106154.	+	89073.5i	−1.87405	+	1.57251i
$239$	20692.1	−	56851.1i	0.362250	−	0.995274i	−0.615982	−	0.787760i	$-0.711241\pi$
$239$	20692.1	−	56851.1i	0.362250	−	0.995274i	0.978232	−	0.207514i	$-0.0665372\pi$
$240$	−4349.30	−	6175.74i	−0.0755087	−	0.107218i
$241$	9558.73	−	54210.2i	0.164576	−	0.933356i	−0.784925	−	0.619591i	$-0.787298\pi$
$241$	9558.73	−	54210.2i	0.164576	−	0.933356i	0.949501	−	0.313765i	$-0.101590\pi$
$242$		−	87072.4i		−	1.48679i
$243$	58888.7	+	4348.62i	0.997285	+	0.0736443i
$244$	67369.0			1.13157
$245$	−21615.1	−	3811.33i	−0.360102	−	0.0634956i
$246$	12459.2	−	8774.47i	0.205883	−	0.144994i
$247$	119094.	+	43346.8i	1.95208	+	0.710499i
$248$	44418.1	+	52935.4i	0.722198	+	0.860682i
$249$	79657.7	−	37408.2i	1.28478	−	0.603349i
$250$	73359.7	−	26700.7i	1.17375	−	0.427212i
$251$	−2594.71	−	1498.06i	−0.0411852	−	0.0237783i	0.479266	−	0.877670i	$-0.340903\pi$
$251$	−2594.71	−	1498.06i	−0.0411852	−	0.0237783i	−0.520451	+	0.853891i	$0.674236\pi$
$252$	42731.6	−	119415.i	0.672896	−	1.88043i
$253$	2090.05	+	3620.07i	0.0326524	+	0.0565556i
$254$	64807.6	−	77234.7i	1.00452	−	1.19714i
$255$	31675.6	−	8579.56i	0.487130	−	0.131943i
$256$	−5354.54	−	30367.1i	−0.0817038	−	0.463365i
$257$	−106120.	+	18711.8i	−1.60669	+	0.283302i	−0.903786	−	0.427985i	$-0.859223\pi$
$257$	−106120.	+	18711.8i	−1.60669	+	0.283302i	−0.702901	+	0.711288i	$0.748112\pi$
$258$	13191.6	+	3496.39i	0.198180	+	0.0525267i
$259$	64051.5	+	53745.6i	0.954839	+	0.801205i
$260$	50121.0	−	28937.3i	0.741434	−	0.428067i
$261$	52664.5	−	92370.7i	0.773102	−	1.35598i
$262$	28606.5	−	49548.0i	0.416738	−	0.721811i
$263$	−11348.9	−	31180.8i	−0.164075	−	0.450791i	0.830223	−	0.557431i	$-0.188213\pi$
$263$	−11348.9	−	31180.8i	−0.164075	−	0.450791i	−0.994298	+	0.106640i	$0.965991\pi$
$264$	6987.49	−	10037.0i	0.100257	−	0.144011i
$265$	−11091.4	+	9306.77i	−0.157941	+	0.132528i
$266$	−81067.4	+	222731.i	−1.14573	+	3.14787i
$267$	104946.	−	9468.35i	1.47212	−	0.132816i
$268$	−5971.18	+	33864.2i	−0.0831362	+	0.471489i
$269$			68153.7i			0.941857i	0.882171	+	0.470928i	$0.156081\pi$
$269$			68153.7i			0.941857i	−0.882171	+	0.470928i	$0.843919\pi$
$270$	−35342.1	+	35921.7i	−0.484802	+	0.492753i
$271$	82407.6			1.12209			0.561046	−	0.827784i	$-0.310399\pi$
$271$	82407.6			1.12209			0.561046	+	0.827784i	$0.310399\pi$
$272$	−24981.0	−	4404.83i	−0.337655	−	0.0595376i
$273$	−120905.	−	55980.4i	−1.62225	−	0.751122i
$274$	−191357.	−	69648.4i	−2.54885	−	0.927705i
$275$	−9201.49	−	10965.9i	−0.121673	−	0.145004i
$276$	2642.69	−	31179.4i	0.0346919	−	0.409307i
$277$	−132172.	+	48106.5i	−1.72258	+	0.626966i	−0.998058	−	0.0622896i	$-0.980160\pi$
$277$	−132172.	+	48106.5i	−1.72258	+	0.626966i	−0.724518	+	0.689256i	$0.757938\pi$
$278$	−534.311	−	308.485i	−0.00691361	−	0.00399157i
$279$	−74662.5	+	89965.5i	−0.959166	+	1.15576i
$280$	17439.5	+	30206.1i	0.222442	+	0.385281i
$281$	−34857.1	+	41541.1i	−0.441448	+	0.526097i	−0.940189	−	0.340654i	$-0.889351\pi$
$281$	−34857.1	+	41541.1i	−0.441448	+	0.526097i	0.498741	+	0.866751i	$0.333796\pi$
$282$	−53887.1	−	53595.8i	−0.677621	−	0.673957i
$283$	27319.8	+	154938.i	0.341118	+	1.93458i	0.355491	+	0.934680i	$0.384314\pi$
$283$	27319.8	+	154938.i	0.341118	+	1.93458i	−0.0143731	+	0.999897i	$0.504575\pi$
$284$	−23626.7	+	4166.02i	−0.292932	+	0.0516517i
$285$	39583.7	−	39798.9i	0.487334	−	0.489984i
$286$	−30541.0	−	25627.0i	−0.373381	−	0.313304i
$287$	15454.1	−	8922.42i	0.187620	−	0.108323i
$288$	94719.9	−	35058.0i	1.14197	−	0.422671i
$289$	13342.6	−	23110.1i	0.159752	−	0.276698i
$290$	31035.6	+	85269.5i	0.369032	+	1.01391i
$291$	−47788.9	−	4050.47i	−0.564340	−	0.0478321i
$292$	−61536.7	+	51635.5i	−0.721720	+	0.605595i
$293$	30733.6	−	84439.9i	0.357996	−	0.983586i	−0.621728	−	0.783234i	$-0.713569\pi$
$293$	30733.6	−	84439.9i	0.357996	−	0.983586i	0.979724	−	0.200353i	$-0.0642089\pi$
$294$	47555.1	−	102708.i	0.550178	−	1.18826i
$295$	2650.97	−	15034.4i	0.0304622	−	0.172760i
$296$		−	60354.0i		−	0.688847i
$297$	18822.9	+	8591.58i	0.213390	+	0.0974002i
$298$	4780.99			0.0538375
$299$	−32372.2	−	5708.10i	−0.362102	−	0.0638483i
$300$	9628.85	+	106725.i	0.106987	+	1.18583i
$301$	15017.1	+	5465.79i	0.165750	+	0.0603281i
$302$	56507.6	+	67343.1i	0.619574	+	0.738379i
$303$	−120499.	−	83888.5i	−1.31250	−	0.913729i
$304$	−40771.7	+	14839.7i	−0.441176	+	0.160575i
$305$	−27145.4	−	15672.4i	−0.291808	−	0.168475i
$306$	917.585	+	169227.i	0.00979949	+	1.80729i
$307$	−15111.7	−	26174.3i	−0.160338	−	0.277714i	0.774652	−	0.632388i	$-0.217925\pi$
$307$	−15111.7	−	26174.3i	−0.160338	−	0.277714i	−0.934990	+	0.354674i	$0.884592\pi$
$308$	28566.6	−	34044.3i	0.301132	−	0.358875i
$309$	−16753.3	+	63209.1i	−0.175462	+	0.662007i
$310$	−17325.4	−	98257.1i	−0.180285	−	1.02245i
$311$	20942.7	−	3692.77i	0.216527	−	0.0381796i	−0.0643321	−	0.997929i	$-0.520492\pi$
$311$	20942.7	−	3692.77i	0.216527	−	0.0381796i	0.280859	+	0.959749i	$0.409381\pi$
$312$	25143.1	+	92827.9i	0.258291	+	0.953606i
$313$	−48381.3	−	40596.7i	−0.493843	−	0.414384i	0.361558	−	0.932350i	$-0.382245\pi$
$313$	−48381.3	−	40596.7i	−0.493843	−	0.414384i	−0.855401	+	0.517966i	$0.826689\pi$
$314$	128432.	−	74150.4i	1.30261	−	0.752063i
$315$	−44998.2	+	38175.6i	−0.453497	+	0.384738i
$316$	17057.4	−	29544.3i	0.170820	−	0.295869i
$317$	50318.9	+	138250.i	0.500741	+	1.37577i	0.890553	+	0.454879i	$0.150318\pi$
$317$	50318.9	+	138250.i	0.500741	+	1.37577i	−0.389813	+	0.920894i	$0.627460\pi$
$318$	−31737.5	−	67582.4i	−0.313848	−	0.668312i
$319$	28541.4	−	23949.0i	0.280474	−	0.235346i
$320$	−24887.1	+	68376.8i	−0.243038	+	0.667743i
$321$	106698.	+	151504.i	1.03549	+	1.47033i
$322$	10675.3	−	60542.7i	0.102960	−	0.583916i
$323$		−	188504.i		−	1.80682i
$324$	−78893.9	−	133289.i	−0.751542	−	1.26971i
$325$	112571.			1.06576
$326$	73737.7	+	13002.0i	0.693832	+	0.122341i
$327$	−47874.9	+	33716.2i	−0.447726	+	0.315314i
$328$	−12104.0	−	4405.50i	−0.112507	−	0.0409494i
$329$	−57207.5	−	68177.3i	−0.528520	−	0.629866i
$330$	−15983.1	+	7505.87i	−0.146769	+	0.0689244i
$331$	13320.8	−	4848.39i	0.121584	−	0.0442529i	−0.280512	−	0.959851i	$-0.590504\pi$
$331$	13320.8	−	4848.39i	0.121584	−	0.0442529i	0.402096	+	0.915598i	$0.368282\pi$
$332$	−199912.	−	115419.i	−1.81368	−	1.04713i
$333$	100462.	−	18276.3i	0.905966	−	0.164816i
$334$	56704.7	+	98215.4i	0.508307	+	0.880413i
$335$	10284.0	−	12256.0i	0.0916375	−	0.109209i
$336$	44026.6	−	11924.9i	0.389975	−	0.105627i
$337$	−8248.02	−	46776.8i	−0.0726256	−	0.411880i	−0.999347	−	0.0361312i	$-0.988497\pi$
$337$	−8248.02	−	46776.8i	−0.0726256	−	0.411880i	0.926721	−	0.375749i	$-0.122615\pi$
$338$	131741.	−	23229.5i	1.15315	−	0.203332i
$339$	−45315.0	−	12010.5i	−0.394314	−	0.104511i
$340$	−65941.2	−	55331.2i	−0.570426	−	0.478644i
$341$	−35477.7	+	20483.1i	−0.305103	+	0.176151i
$342$	146087.	+	249892.i	1.24900	+	2.13649i
$343$	−13356.1	+	23133.5i	−0.113525	+	0.196631i
$344$	−3945.33	−	10839.7i	−0.0333400	−	0.0916010i
$345$	−8318.27	+	11948.5i	−0.0698867	+	0.100387i
$346$	213519.	−	179164.i	1.78355	−	1.49657i
$347$	48527.4	−	133328.i	0.403021	−	1.10729i	−0.557765	−	0.829999i	$-0.688341\pi$
$347$	48527.4	−	133328.i	0.403021	−	1.10729i	0.960786	−	0.277292i	$-0.0894370\pi$
$348$	−277777.	+	25061.4i	−2.29371	+	0.206941i
$349$	−11095.9	+	62927.9i	−0.0910985	+	0.516645i	0.904775	+	0.425890i	$0.140039\pi$
$349$	−11095.9	+	62927.9i	−0.0910985	+	0.516645i	−0.995873	+	0.0907548i	$0.971072\pi$
$350$			210530.i			1.71862i
$351$	−146902.	+	69961.6i	−1.19238	+	0.567866i
$352$	35390.6			0.285629
$353$	−82029.3	−	14464.0i	−0.658293	−	0.116075i	−0.165484	−	0.986212i	$-0.552919\pi$
$353$	−82029.3	−	14464.0i	−0.658293	−	0.116075i	−0.492809	+	0.870138i	$0.664030\pi$
$354$	71439.0	+	33077.1i	0.570071	+	0.263949i
$355$	10489.2	+	3817.76i	0.0832312	+	0.0302937i
$356$	−177663.	−	211731.i	−1.40184	−	1.67065i
$357$	−16736.3	+	197461.i	−0.131318	+	1.54933i
$358$	157673.	−	57388.4i	1.23025	−	0.447773i
$359$	24583.0	+	14193.0i	0.190742	+	0.110125i	0.592330	−	0.805696i	$-0.298208\pi$
$359$	24583.0	+	14193.0i	0.190742	+	0.110125i	−0.401588	+	0.915820i	$0.631542\pi$
$360$	41987.4	+	7168.98i	0.323976	+	0.0553162i
$361$	−96053.9	−	166370.i	−0.737056	−	1.27662i
$362$	10457.8	−	12463.1i	0.0798039	−	0.0951066i
$363$	−88286.5	−	87809.1i	−0.670009	−	0.666386i
$364$	60687.1	+	344173.i	0.458029	+	2.59761i
$365$	36807.6	−	6490.18i	0.276282	−	0.0487159i
$366$	113985.	−	114605.i	0.850914	−	0.855540i
$367$	148368.	+	124495.i	1.10156	+	0.924316i	0.997529	−	0.0702587i	$-0.0223825\pi$
$367$	148368.	+	124495.i	1.10156	+	0.924316i	0.104028	+	0.994574i	$0.466827\pi$
$368$	9745.84	−	5626.76i	0.0719654	−	0.0415492i
$369$	3667.81	−	21481.7i	0.0269373	−	0.157767i
$370$	−43570.9	+	75467.0i	−0.318268	+	0.551256i
$371$	−29903.4	−	82158.8i	−0.217256	−	0.596907i
$372$	305567.	+	25899.1i	2.20811	+	0.187154i
$373$	89100.8	−	74764.4i	0.640418	−	0.537375i	−0.263728	−	0.964597i	$-0.584952\pi$
$373$	89100.8	−	74764.4i	0.640418	−	0.537375i	0.904147	+	0.427222i	$0.140508\pi$
$374$	−20281.3	+	55722.4i	−0.144995	+	0.398370i
$375$	46907.3	−	101309.i	0.333563	−	0.720421i
$376$	−11155.4	+	63265.6i	−0.0789061	+	0.447499i
$377$			292992.i			2.06145i
$378$	−130843.	−	274737.i	−0.915726	−	1.92279i
$379$	−162689.			−1.13261			−0.566303	−	0.824197i	$-0.691627\pi$
$379$	−162689.			−1.13261			−0.566303	+	0.824197i	$0.691627\pi$
$380$	−145000.	−	25567.4i	−1.00416	−	0.177060i
$381$	−12955.7	−	143600.i	−0.0892506	−	0.989243i
$382$	−65628.7	−	23886.9i	−0.449745	−	0.163694i
$383$	66642.3	+	79421.2i	0.454310	+	0.541425i	0.943771	−	0.330600i	$-0.107251\pi$
$383$	66642.3	+	79421.2i	0.454310	+	0.541425i	−0.489461	+	0.872025i	$0.662807\pi$
$384$	−160594.	−	111801.i	−1.08910	−	0.758201i
$385$	−19430.4	+	7072.09i	−0.131087	+	0.0477119i
$386$	−48667.4	−	28098.1i	−0.326635	−	0.188583i
$387$	16848.4	−	9849.61i	0.112496	−	0.0657654i
$388$	62900.8	+	108947.i	0.417823	+	0.723691i
$389$	174142.	−	207534.i	1.15081	−	1.37148i	0.233964	−	0.972245i	$-0.424830\pi$
$389$	174142.	−	207534.i	1.15081	−	1.37148i	0.916847	−	0.399238i	$-0.130725\pi$
$390$	35575.4	−	134224.i	0.233895	−	0.882471i
$391$	8489.97	+	48149.0i	0.0555332	+	0.314944i
$392$	−94216.0	+	16612.8i	−0.613130	+	0.108111i
$393$	−21390.3	−	78972.6i	−0.138494	−	0.511318i
$394$	50766.1	+	42597.8i	0.327025	+	0.274407i
$395$	−13746.1	+	7936.31i	−0.0881018	+	0.0508656i
$396$	−9714.11	−	53396.8i	−0.0619459	−	0.340506i
$397$	−30297.8	+	52477.3i	−0.192234	+	0.332959i	−0.945990	−	0.324195i	$-0.894907\pi$
$397$	−30297.8	+	52477.3i	−0.192234	+	0.332959i	0.753756	+	0.657154i	$0.228240\pi$
$398$	−57226.2	−	157228.i	−0.361267	−	0.992573i
$399$	144083.	+	306813.i	0.905040	+	1.92721i
$400$	−29522.1	+	24772.0i	−0.184513	+	0.154825i
$401$	−32918.4	+	90442.5i	−0.204715	+	0.562450i	−0.998982	−	0.0451196i	$-0.985633\pi$
$401$	−32918.4	+	90442.5i	−0.204715	+	0.562450i	0.794267	+	0.607569i	$0.207855\pi$
$402$	47505.2	+	67454.5i	0.293960	+	0.417406i
$403$	55941.1	−	317258.i	0.344446	−	1.95345i
$404$			385125.i			2.35961i
$405$	781.479	+	72060.5i	0.00476439	+	0.439326i
$406$	−547955.			−3.32425
$407$	35236.3	+	6213.11i	0.212717	+	0.0375077i
$408$	116951.	−	82363.4i	0.702560	−	0.494782i
$409$	−118507.	−	43133.1i	−0.708432	−	0.257848i	−0.0374253	−	0.999299i	$-0.511916\pi$
$409$	−118507.	−	43133.1i	−0.708432	−	0.257848i	−0.671007	+	0.741451i	$0.734138\pi$
$410$	11954.5	+	14246.8i	0.0711153	+	0.0847520i
$411$	−263596.	+	123788.i	−1.56047	+	0.732815i
$412$	161180.	−	58664.9i	0.949550	−	0.345608i
$413$	79836.7	+	46093.8i	0.468061	+	0.270235i
$414$	−48569.5	−	57249.6i	−0.283376	−	0.334020i
$415$	53701.1	+	93013.1i	0.311808	+	0.540067i
$416$	−178892.	+	213195.i	−1.03372	+	1.23194i
$417$	−851.618	+	230.667i	−0.00489748	+	0.00132652i
$418$	17612.8	+	99887.1i	0.100804	+	0.571685i
$419$	−169373.	+	29865.1i	−0.964755	+	0.170112i	−0.633768	−	0.773523i	$-0.718493\pi$
$419$	−169373.	+	29865.1i	−0.964755	+	0.170112i	−0.330987	+	0.943635i	$0.607382\pi$
$420$	149620.	+	39656.1i	0.848187	+	0.224808i
$421$	178528.	+	149803.i	1.00726	+	0.845193i	0.987974	−	0.154621i	$-0.0494157\pi$
$421$	178528.	+	149803.i	1.00726	+	0.845193i	0.0192879	+	0.999814i	$0.493860\pi$
$422$	−192355.	+	111056.i	−1.08014	+	0.623618i
$423$	−108686.	+	589.320i	−0.607426	+	0.00329360i
$424$	−31555.1	+	54655.0i	−0.175524	+	0.304017i
$425$	−57265.3	−	157335.i	−0.317040	−	0.871060i
$426$	−32888.2	+	47241.2i	−0.181226	+	0.260317i
$427$	144996.	−	121666.i	0.795246	−	0.667290i
$428$	166243.	−	456749.i	0.907520	−	2.49339i
$429$	−56783.8	+	5123.10i	−0.308539	+	0.0278367i
$430$	−2892.16	+	16402.2i	−0.0156417	+	0.0887087i
$431$		−	155134.i		−	0.835126i	−0.908648	−	0.417563i	$-0.862884\pi$
$431$		−	155134.i		−	0.835126i	0.908648	−	0.417563i	$-0.137116\pi$
$432$	23130.0	−	50674.4i	0.123939	−	0.271532i
$433$	−3126.89			−0.0166777			−0.00833887	−	0.999965i	$-0.502654\pi$
$433$	−3126.89			−0.0166777			−0.00833887	+	0.999965i	$0.502654\pi$
$434$	593336.	+	104621.i	3.15008	+	0.555444i
$435$	117757.	+	54522.7i	0.622310	+	0.288137i
$436$	144331.	+	52532.3i	0.759255	+	0.276346i
$437$	53754.8	+	64062.4i	0.281484	+	0.335460i
$438$	−16277.5	+	192048.i	−0.0848476	+	1.00106i
$439$	−242506.	+	88264.8i	−1.25833	+	0.457993i	−0.883207	−	0.468984i	$-0.844620\pi$
$439$	−242506.	+	88264.8i	−1.25833	+	0.457993i	−0.375118	+	0.926977i	$0.622398\pi$
$440$	12925.8	+	7462.71i	0.0667655	+	0.0385471i
$441$	−56183.1	−	151796.i	−0.288887	−	0.780517i
$442$	−233158.	−	403841.i	−1.19345	−	2.06712i
$443$	−150984.	+	179936.i	−0.769351	+	0.916877i	−0.998400	−	0.0565377i	$-0.981994\pi$
$443$	−150984.	+	179936.i	−0.769351	+	0.916877i	0.229049	+	0.973415i	$0.426438\pi$
$444$	−189904.	−	188877.i	−0.963315	−	0.958106i
$445$	22330.9	+	126645.i	0.112768	+	0.639540i
$446$	267384.	−	47147.0i	1.34420	−	0.237019i
$447$	4821.44	−	4847.65i	0.0241302	−	0.0242614i
$448$	−336600.	−	282441.i	−1.67710	−	1.40725i
$449$	188149.	−	108628.i	0.933274	−	0.538826i	0.0454285	−	0.998968i	$-0.485535\pi$
$449$	188149.	−	108628.i	0.933274	−	0.538826i	0.887846	+	0.460142i	$0.152201\pi$
$450$	197847.	+	164193.i	0.977021	+	0.810831i
$451$	3818.09	−	6613.12i	0.0187712	−	0.0325127i
$452$	42057.2	+	115551.i	0.205856	+	0.565585i
$453$	125268.	+	10617.4i	0.610440	+	0.0517394i
$454$	257978.	−	216470.i	1.25162	−	1.05023i
$455$	55613.9	−	152798.i	0.268634	−	0.738065i
$456$	102800.	−	222025.i	0.494384	−	1.06776i
$457$	13225.3	−	75004.7i	0.0633249	−	0.359133i	−0.936636	−	0.350304i	$-0.886078\pi$
$457$	13225.3	−	75004.7i	0.0633249	−	0.359133i	0.999961	−	0.00882954i	$-0.00281057\pi$
$458$			372213.i			1.77444i
$459$	172512.	+	169728.i	0.818830	+	0.805618i
$460$	38188.5			0.180475
$461$	179478.	+	31646.8i	0.844519	+	0.148912i	0.579135	−	0.815231i	$-0.303390\pi$
$461$	179478.	+	31646.8i	0.844519	+	0.148912i	0.265384	+	0.964143i	$0.414501\pi$
$462$	−9581.24	−	106197.i	−0.0448888	−	0.497541i
$463$	−302626.	−	110147.i	−1.41171	−	0.513819i	−0.480076	−	0.877227i	$-0.659391\pi$
$463$	−302626.	−	110147.i	−1.41171	−	0.513819i	−0.931630	+	0.363408i	$0.881613\pi$
$464$	−64474.9	−	76838.2i	−0.299471	−	0.356896i
$465$	−117099.	−	81521.5i	−0.541562	−	0.377022i
$466$	−83089.8	+	30242.2i	−0.382627	+	0.139265i
$467$	−23093.6	−	13333.1i	−0.105891	−	0.0611359i	0.446119	−	0.894973i	$-0.352806\pi$
$467$	−23093.6	−	13333.1i	−0.105891	−	0.0611359i	−0.552010	+	0.833837i	$0.686139\pi$
$468$	370768.	+	211391.i	1.69282	+	0.965150i
$469$	48306.2	+	83668.8i	0.219612	+	0.380380i
$470$	59621.6	−	71054.3i	0.269903	−	0.321658i
$471$	54334.6	−	205001.i	0.244926	−	0.924089i
$472$	−11555.1	−	65532.1i	−0.0518667	−	0.294151i
$473$	6734.66	−	1187.50i	0.0301019	−	0.00530777i
$474$	−21399.0	−	79004.6i	−0.0952436	−	0.351638i
$475$	−219386.	−	184086.i	−0.972346	−	0.815895i
$476$	450164.	−	259902.i	1.98681	−	1.14709i
$477$	−100531.	−	35974.1i	−0.441837	−	0.158108i
$478$	−190375.	+	329740.i	−0.833210	+	1.44316i
$479$	47067.5	+	129317.i	0.205140	+	0.563617i	0.999011	−	0.0444692i	$-0.0141596\pi$
$479$	47067.5	+	129317.i	0.205140	+	0.563617i	−0.793871	+	0.608086i	$0.791937\pi$
$480$	52395.5	+	111572.i	0.227411	+	0.484253i
$481$	−215540.	+	180860.i	−0.931619	+	0.781721i
$482$	−118487.	+	325539.i	−0.510006	+	1.40123i
$483$	−50621.3	−	71879.1i	−0.216990	−	0.308112i
$484$	−56716.5	+	321655.i	−0.242113	+	1.37309i
$485$		−	58531.8i		−	0.248833i
$486$	−360229.	−	91308.1i	−1.52513	−	0.386578i
$487$	327215.			1.37967			0.689834	−	0.723967i	$-0.257683\pi$
$487$	327215.			1.37967			0.689834	+	0.723967i	$0.257683\pi$
$488$	−134550.	−	23724.9i	−0.564996	−	0.0996241i
$489$	87544.9	−	61654.0i	0.366111	−	0.257836i
$490$	129801.	+	47243.9i	0.540614	+	0.196767i
$491$	238624.	+	284382.i	0.989810	+	1.17961i	0.983735	+	0.179629i	$0.0574896\pi$
$491$	238624.	+	284382.i	0.989810	+	1.17961i	0.00607590	+	0.999982i	$0.498066\pi$
$492$	−51741.3	+	24298.3i	−0.213750	+	0.100380i
$493$	409502.	−	149047.i	1.68485	−	0.613237i
$494$	−690755.	−	398808.i	−2.83055	−	1.63422i
$495$	−8507.81	+	23775.4i	−0.0347222	+	0.0970323i
$496$	55143.9	+	95512.1i	0.224148	+	0.388235i
$497$	−43327.3	+	51635.5i	−0.175408	+	0.209043i
$498$	−534586.	+	144796.i	−2.15555	+	0.583847i
$499$	−24139.4	−	136901.i	−0.0969449	−	0.549802i	−0.994134	−	0.108155i	$-0.965506\pi$
$499$	−24139.4	−	136901.i	−0.0969449	−	0.549802i	0.897189	−	0.441646i	$-0.145605\pi$
$500$	−288391.	+	50851.2i	−1.15357	+	0.203405i
$501$	156769.	+	41551.0i	0.624576	+	0.165541i
$502$	14444.4	+	12120.3i	0.0573182	+	0.0480957i
$503$	−105718.	+	61036.5i	−0.417844	+	0.241243i	−0.694155	−	0.719826i	$-0.744222\pi$
$503$	−105718.	+	61036.5i	−0.417844	+	0.241243i	0.276310	+	0.961068i	$0.410888\pi$
$504$	−127398.	+	223448.i	−0.501534	+	0.879663i
$505$	89593.8	−	155181.i	0.351314	−	0.608493i
$506$	−8997.57	−	24720.6i	−0.0351418	−	0.0965514i
$507$	109302.	−	157004.i	0.425219	−	0.610794i
$508$	−289716.	+	243100.i	−1.12265	+	0.942015i
$509$	−67757.9	+	186163.i	−0.261532	+	0.718552i	0.737533	+	0.675311i	$0.235991\pi$
$509$	−67757.9	+	186163.i	−0.261532	+	0.718552i	−0.999065	+	0.0432413i	$0.986232\pi$
$510$	−205696.	+	18558.1i	−0.790834	+	0.0713500i
$511$	−39191.7	+	222267.i	−0.150090	+	0.851203i
$512$		−	153810.i		−	0.586739i
$513$	400700.	+	103882.i	1.52260	+	0.394734i
$514$	678163.			2.56689
$515$	−78593.0	−	13858.1i	−0.296326	−	0.0522502i
$516$	−46454.0	−	21508.7i	−0.174471	−	0.0807821i
$517$	−35787.8	−	13025.7i	−0.133892	−	0.0487326i
$518$	−338245.	−	403104.i	−1.26058	−	1.50230i
$519$	33663.6	−	397176.i	0.124976	−	1.47451i
$520$	−110293.	+	40143.4i	−0.407888	+	0.148459i
$521$	−330879.	−	191033.i	−1.21897	−	0.703773i	−0.254273	−	0.967132i	$-0.581836\pi$
$521$	−330879.	−	191033.i	−1.21897	−	0.703773i	−0.964698	+	0.263359i	$0.915170\pi$
$522$	−427352.	+	514943.i	−1.56836	+	1.88981i
$523$	187042.	+	323966.i	0.683811	+	1.18440i	0.973809	+	0.227368i	$0.0730120\pi$
$523$	187042.	+	323966.i	0.683811	+	1.18440i	−0.289998	+	0.957027i	$0.593655\pi$
$524$	−137950.	+	164402.i	−0.502411	+	0.598750i
$525$	213466.	+	212312.i	0.774480	+	0.770292i
$526$	36262.6	+	205656.i	0.131065	+	0.743308i
$527$	−471874.	+	83204.2i	−1.69905	+	0.299588i
$528$	13764.4	−	13839.2i	0.0493729	−	0.0496413i
$529$	197755.	+	165936.i	0.706669	+	0.592966i
$530$	78913.2	−	45560.6i	0.280930	−	0.162195i
$531$	105582.	−	39078.2i	0.374455	−	0.138594i
$532$	444553.	−	769989.i	1.57073	−	2.72058i
$533$	20538.2	+	56428.4i	0.0722951	+	0.198629i
$534$	−660784.	−	56006.4i	−2.31727	−	0.196406i
$535$	−173241.	+	145367.i	−0.605263	+	0.507876i
$536$	23851.5	−	65531.3i	0.0830205	−	0.228097i
$537$	100819.	−	217746.i	0.349617	−	0.755095i
$538$	74481.3	−	422405.i	0.257326	−	1.45937i
$539$		−	56716.1i		−	0.195222i
$540$	153956.	−	109678.i	0.527971	−	0.376125i
$541$	−179687.			−0.613936			−0.306968	−	0.951720i	$-0.599314\pi$
$541$	−179687.			−0.613936			−0.306968	+	0.951720i	$0.599314\pi$
$542$	−510748.	−	90058.6i	−1.73863	−	0.306568i
$543$	−2090.63	−	23172.2i	−0.00709050	−	0.0785902i
$544$	388977.	+	141576.i	1.31439	+	0.478400i
$545$	−45935.5	−	54743.8i	−0.154652	−	0.184307i
$546$	688170.	+	479087.i	2.30840	+	1.60705i
$547$	−188810.	+	68721.1i	−0.631030	+	0.229676i	−0.637679	−	0.770302i	$-0.720106\pi$
$547$	−188810.	+	68721.1i	−0.631030	+	0.229676i	0.00664982	+	0.999978i	$0.497883\pi$
$548$	661529.	+	381934.i	2.20286	+	1.27182i
$549$	−1253.34	−	231149.i	−0.00415838	−	0.766915i
$550$	45045.2	+	78020.5i	0.148910	+	0.257919i
$551$	479128.	−	571003.i	1.57815	−	1.88077i
$552$	−16258.2	+	61341.3i	−0.0533575	+	0.201314i
$553$	−16643.9	−	94392.4i	−0.0544259	−	0.308665i
$554$	871749.	−	153713.i	2.84035	−	0.500830i
$555$	32579.8	+	120284.i	0.105770	+	0.390501i
$556$	1772.87	+	1487.61i	0.00573492	+	0.00481217i
$557$	51655.6	−	29823.4i	0.166497	−	0.0961272i	−0.414436	−	0.910079i	$-0.636021\pi$
$557$	51655.6	−	29823.4i	0.166497	−	0.0961272i	0.580933	+	0.813951i	$0.302688\pi$
$558$	561063.	−	475996.i	1.80195	−	1.52874i
$559$	−26888.7	+	46572.6i	−0.0860490	+	0.149041i
$560$	19039.3	+	52310.0i	0.0607120	+	0.166805i
$561$	36046.5	+	76758.0i	0.114535	+	0.243892i
$562$	261436.	−	219371.i	0.827739	−	0.694556i
$563$	−207044.	+	568850.i	−0.653201	+	1.79465i	−0.0476268	+	0.998865i	$0.515166\pi$
$563$	−207044.	+	568850.i	−0.653201	+	1.79465i	−0.605574	+	0.795789i	$0.707056\pi$
$564$	164155.	+	233090.i	0.516054	+	0.732765i
$565$	9934.94	−	56343.8i	0.0311220	−	0.176502i
$566$		−	990137.i		−	3.09074i
$567$	−410517.	−	144394.i	−1.27692	−	0.449142i
$568$	48654.7			0.150809
$569$	174871.	+	30834.4i	0.540122	+	0.0952381i	0.437053	−	0.899436i	$-0.356022\pi$
$569$	174871.	+	30834.4i	0.540122	+	0.0952381i	0.103070	+	0.994674i	$0.467133\pi$
$570$	−288827.	+	203408.i	−0.888972	+	0.626064i
$571$	10666.5	+	3882.28i	0.0327151	+	0.0119073i	0.358326	−	0.933597i	$-0.383348\pi$
$571$	10666.5	+	3882.28i	0.0327151	+	0.0119073i	−0.325611	+	0.945504i	$0.605570\pi$
$572$	96129.5	+	114563.i	0.293809	+	0.350147i
$573$	−90403.9	+	42454.8i	−0.275345	+	0.129306i
$574$	−105533.	+	38410.7i	−0.320304	+	0.116581i
$575$	64328.1	+	37139.8i	0.194565	+	0.112332i
$576$	−527941.	+	96044.6i	−1.59126	+	0.289486i
$577$	−111023.	−	192298.i	−0.333474	−	0.577593i	0.649717	−	0.760176i	$-0.274888\pi$
$577$	−111023.	−	192298.i	−0.333474	−	0.577593i	−0.983190	+	0.182583i	$0.941554\pi$
$578$	−107951.	+	128651.i	−0.323125	+	0.385085i
$579$	−77569.0	+	21010.1i	−0.231383	+	0.0626717i
$580$	−59106.8	−	335211.i	−0.175704	−	0.996467i
$581$	−638707.	+	112621.i	−1.89212	+	0.333633i
$582$	291761.	+	77329.9i	0.861352	+	0.228298i
$583$	−28660.6	−	24049.1i	−0.0843235	−	0.0707558i
$584$	141086.	−	81456.2i	0.413675	−	0.238835i
$585$	−100219.	−	171431.i	−0.292845	−	0.500931i
$586$	−282761.	+	489757.i	−0.823426	+	1.42622i
$587$	−6758.00	−	18567.4i	−0.0196129	−	0.0538860i	0.929500	−	0.368823i	$-0.120239\pi$
$587$	−6758.00	−	18567.4i	−0.0196129	−	0.0538860i	−0.949113	+	0.314937i	$0.898017\pi$
$588$	−242576.	+	348441.i	−0.701605	+	1.00780i
$589$	−627831.	+	526813.i	−1.80972	+	1.51854i
$590$	−32860.5	+	90283.6i	−0.0943997	+	0.259361i
$591$	94387.4	−	8515.74i	0.270234	−	0.0243808i
$592$	16726.8	−	94862.2i	0.0477275	−	0.270676i
$593$			550403.i			1.56521i	0.622521	+	0.782603i	$0.286108\pi$
$593$			550403.i			1.56521i	−0.622521	+	0.782603i	$0.713892\pi$
$594$	−107272.	−	73819.6i	−0.304027	−	0.209218i
$595$	−241850.			−0.683144
$596$	−17661.5	−	3114.20i	−0.0497205	−	0.00876707i
$597$	−217130.	−	100534.i	−0.609217	−	0.282074i
$598$	194399.	+	70755.6i	0.543617	+	0.197860i
$599$	128103.	+	152667.i	0.357031	+	0.425493i	0.914425	−	0.404755i	$-0.132643\pi$
$599$	128103.	+	152667.i	0.357031	+	0.425493i	−0.557394	+	0.830248i	$0.688199\pi$
$600$	18353.7	−	216544.i	0.0509825	−	0.601511i
$601$	133684.	−	48657.0i	0.370110	−	0.134709i	−0.150268	−	0.988645i	$-0.548014\pi$
$601$	133684.	−	48657.0i	0.370110	−	0.134709i	0.520377	+	0.853936i	$0.325791\pi$
$602$	−87100.2	−	50287.3i	−0.240340	−	0.138760i
$603$	116302.	+	19857.6i	0.319855	+	0.0546125i
$604$	−164880.	−	285581.i	−0.451954	−	0.782808i
$605$	97681.6	−	116412.i	0.266871	−	0.318045i
$606$	655156.	+	651613.i	1.78402	+	1.77437i
$607$	−90199.7	−	511548.i	−0.244809	−	1.38838i	−0.820936	−	0.571021i	$-0.806548\pi$
$607$	−90199.7	−	511548.i	−0.244809	−	1.38838i	0.576127	−	0.817361i	$-0.304564\pi$
$608$	697273.	−	122948.i	1.88624	−	0.332594i
$609$	−552592.	+	555596.i	−1.48994	+	1.49804i
$610$	151115.	+	126801.i	0.406114	+	0.340770i
$611$	259367.	−	149746.i	0.694757	−	0.401118i
$612$	106840.	−	625742.i	0.285254	−	1.67068i
$613$	164250.	−	284490.i	0.437104	−	0.757087i	−0.560360	−	0.828249i	$-0.689337\pi$
$613$	164250.	−	284490.i	0.437104	−	0.757087i	0.997465	+	0.0711618i	$0.0226707\pi$
$614$	65055.4	+	178738.i	0.172563	+	0.474112i
$615$	26501.1	+	2246.17i	0.0700670	+	0.00593870i
$616$	−69042.7	+	57933.7i	−0.181952	+	0.152676i
$617$	200393.	−	550576.i	0.526396	−	1.44626i	−0.336889	−	0.941544i	$-0.609375\pi$
$617$	200393.	−	550576.i	0.526396	−	1.44626i	0.863285	−	0.504717i	$-0.168403\pi$
$618$	172912.	−	373450.i	0.452738	−	0.977813i
$619$	−5535.97	+	31396.1i	−0.0144482	+	0.0819396i	−0.991179	−	0.132528i	$-0.957691\pi$
$619$	−5535.97	+	31396.1i	−0.0144482	+	0.0819396i	0.976731	+	0.214468i	$0.0688017\pi$
$620$			374258.i			0.973617i
$621$	−107028.	−	8487.22i	−0.277534	−	0.0220081i
$622$	−133835.			−0.345930
$623$	−764760.	−	134848.i	−1.97038	−	0.347430i
$624$	13792.3	+	152872.i	0.0354214	+	0.392607i
$625$	−168179.	−	61212.2i	−0.430538	−	0.156703i
$626$	255493.	+	304485.i	0.651974	+	0.776993i
$627$	119042.	+	82873.9i	0.302806	+	0.210806i
$628$	−522743.	+	190263.i	−1.32547	+	0.482431i
$629$	362426.	+	209247.i	0.916048	+	0.528880i
$630$	320611.	−	187430.i	0.807788	−	0.472235i
$631$	−25960.6	−	44965.1i	−0.0652013	−	0.112932i	0.831582	−	0.555402i	$-0.187436\pi$
$631$	−25960.6	−	44965.1i	−0.0652013	−	0.112932i	−0.896783	+	0.442470i	$0.854102\pi$
$632$	−44471.7	+	52999.3i	−0.111340	+	0.132689i
$633$	−81377.9	+	307034.i	−0.203095	+	0.766264i
$634$	−160782.	−	911840.i	−0.399999	−	2.26851i
$635$	173291.	−	30555.8i	0.429762	−	0.0757786i
$636$	73220.8	+	270330.i	0.181017	+	0.668314i
$637$	341661.	+	286688.i	0.842009	+	0.706530i
$638$	−203067.	+	117241.i	−0.498882	+	0.288030i
$639$	14733.5	+	80987.7i	0.0360832	+	0.198343i
$640$	119405.	−	206815.i	0.291516	−	0.504920i
$641$	−16727.5	−	45958.4i	−0.0407113	−	0.111853i	0.917671	−	0.397341i	$-0.130067\pi$
$641$	−16727.5	−	45958.4i	−0.0407113	−	0.111853i	−0.958383	+	0.285487i	$0.907845\pi$
$642$	−495724.	−	1.05560e6i	−1.20273	−	2.56112i
$643$	99454.3	−	83452.1i	0.240548	−	0.201844i	−0.514542	−	0.857465i	$-0.672038\pi$
$643$	99454.3	−	83452.1i	0.240548	−	0.201844i	0.755089	+	0.655622i	$0.227593\pi$
$644$	−78871.7	+	216698.i	−0.190173	+	0.522497i
$645$	13714.3	+	19473.5i	0.0329651	+	0.0468085i
$646$	−206005.	+	1.16831e6i	−0.493643	+	2.79959i
$647$		−	219579.i		−	0.524544i	−0.964994	−	0.262272i	$-0.915528\pi$
$647$		−	219579.i		−	0.524544i	0.964994	−	0.262272i	$-0.0844717\pi$
$648$	110629.	+	293990.i	0.263462	+	0.700137i
$649$	39448.9			0.0936582
$650$	−697694.	−	123022.i	−1.65135	−	0.291177i
$651$	704437.	−	496103.i	1.66219	−	1.17060i
$652$	−263927.	−	96061.5i	−0.620852	−	0.225972i
$653$	−12945.7	−	15428.1i	−0.0303598	−	0.0361814i	0.750651	−	0.660699i	$-0.229740\pi$
$653$	−12945.7	−	15428.1i	−0.0303598	−	0.0361814i	−0.781011	+	0.624518i	$0.785296\pi$
$654$	333567.	−	156647.i	0.779879	−	0.366241i
$655$	93830.9	−	34151.7i	0.218707	−	0.0796030i
$656$	−17803.7	−	10279.0i	−0.0413716	−	0.0238859i
$657$	178311.	+	210177.i	0.413092	+	0.486917i
$658$	280055.	+	485070.i	0.646832	+	1.12035i
$659$	−482438.	+	574947.i	−1.11089	+	1.32391i	−0.169904	+	0.985461i	$0.554346\pi$
$659$	−482438.	+	574947.i	−1.11089	+	1.32391i	−0.940986	+	0.338446i	$0.890099\pi$
$660$	63932.6	−	17316.6i	0.146769	−	0.0397534i
$661$	−28440.2	−	161292.i	−0.0650923	−	0.369157i	−0.999902	−	0.0140075i	$-0.995541\pi$
$661$	−28440.2	−	161292.i	−0.0650923	−	0.369157i	0.934810	−	0.355149i	$-0.115570\pi$
$662$	−87858.8	+	15491.9i	−0.200479	+	0.0353499i
$663$	−644602.	−	170849.i	−1.46644	−	0.388674i
$664$	358620.	+	300918.i	0.813390	+	0.682515i
$665$	−358254.	+	206838.i	−0.810116	+	0.467721i
$666$	−642617.	+	3484.41i	−1.44878	+	0.00785562i
$667$	−96665.2	+	167429.i	−0.217279	+	0.376339i
$668$	−145499.	−	399755.i	−0.326067	−	0.895862i
$669$	221842.	−	318658.i	0.495668	−	0.711988i
$670$	−77132.5	+	64721.8i	−0.171826	+	0.144179i
$671$	27702.4	−	76111.9i	0.0615280	−	0.169047i
$672$	−741322.	+	66882.9i	−1.64160	+	0.148107i
$673$	−84265.1	+	477891.i	−0.186045	+	1.05511i	0.738561	+	0.674187i	$0.235506\pi$
$673$	−84265.1	+	477891.i	−0.186045	+	1.05511i	−0.924606	+	0.380926i	$0.875605\pi$
$674$			298928.i			0.658032i
$675$	366004.	−	35023.0i	0.803300	−	0.0768679i
$676$	−501798.			−1.09808
$677$	744551.	+	131284.i	1.62449	+	0.286441i	0.910436	−	0.413650i	$-0.135746\pi$
$677$	744551.	+	131284.i	1.62449	+	0.286441i	0.714053	+	0.700091i	$0.246857\pi$
$678$	267729.	+	123961.i	0.582419	+	0.269667i
$679$	332135.	+	120887.i	0.720402	+	0.262205i
$680$	112213.	+	133730.i	0.242676	+	0.289210i
$681$	40673.1	−	479877.i	0.0877028	−	1.03475i
$682$	242269.	−	88178.9i	0.520871	−	0.189581i
$683$	331391.	+	191329.i	0.710393	+	0.410146i	0.811207	−	0.584760i	$-0.198811\pi$
$683$	331391.	+	191329.i	0.710393	+	0.410146i	−0.100813	+	0.994905i	$0.532144\pi$
$684$	−376892.	−	1.01829e6i	−0.805572	−	2.17650i
$685$	−177703.	−	307790.i	−0.378716	−	0.655955i
$686$	108060.	−	128781.i	0.229624	−	0.273655i
$687$	377404.	+	375363.i	0.799636	+	0.795312i
$688$	−3196.96	−	18130.9i	−0.00675399	−	0.0383038i
$689$	289747.	−	51090.2i	0.610352	−	0.107621i
$690$	64613.1	−	64964.3i	0.135713	−	0.136451i
$691$	−569224.	−	477636.i	−1.19214	−	1.00032i	−0.999820	−	0.0189914i	$-0.993954\pi$
$691$	−569224.	−	477636.i	−1.19214	−	1.00032i	−0.192320	−	0.981332i	$-0.561601\pi$
$692$	−905466.	+	522771.i	−1.89086	+	1.09169i
$693$	−117340.	−	97380.9i	−0.244332	−	0.202772i
$694$	−446471.	+	773310.i	−0.926988	+	1.60559i
$695$	−368.282	−	1011.85i	−0.000762449	−	0.00209481i
$696$	563606.	+	47769.9i	1.16348	+	0.0986133i
$697$	68419.5	−	57410.8i	0.140836	−	0.118176i
$698$	137541.	−	377890.i	0.282306	−	0.775630i
$699$	−53128.9	+	114747.i	−0.108737	+	0.234847i
$700$	137134.	−	777724.i	0.279865	−	1.58719i
$701$		−	357201.i		−	0.726902i	−0.931613	−	0.363451i	$-0.881598\pi$
$701$		−	357201.i		−	0.726902i	0.931613	−	0.363451i	$-0.118402\pi$
$702$	986929.	−	273069.i	2.00268	−	0.554113i
$703$	715818.			1.44841
$704$	−185172.	−	32650.8i	−0.373620	−	0.0658792i
$705$	−11919.0	−	132108.i	−0.0239806	−	0.265798i
$706$	492596.	+	179290.i	0.988284	+	0.359706i
$707$	695525.	+	828894.i	1.39147	+	1.65829i
$708$	−242358.	−	168724.i	−0.483495	−	0.336597i
$709$	121993.	−	44401.9i	0.242685	−	0.0883301i	−0.217814	−	0.975990i	$-0.569893\pi$
$709$	121993.	−	44401.9i	0.242685	−	0.0883301i	0.460499	+	0.887660i	$0.347670\pi$
$710$	−60838.1	−	35124.9i	−0.120687	−	0.0696784i
$711$	−101686.	−	57975.7i	−0.201151	−	0.114685i
$712$	280268.	+	485439.i	0.552859	+	0.957579i
$713$	136638.	−	162839.i	0.268777	−	0.320316i
$714$	319523.	−	1.20554e6i	0.626765	−	2.36475i
$715$	−12082.7	−	68524.6i	−0.0236349	−	0.134040i
$716$	−619845.	+	109295.i	−1.20909	+	0.213194i
$717$	142351.	+	525559.i	0.276900	+	1.02231i
$718$	−136850.	−	114831.i	−0.265459	−	0.222746i
$719$	667081.	−	385139.i	1.29039	−	0.745007i	0.311666	−	0.950192i	$-0.399113\pi$
$719$	667081.	−	385139.i	1.29039	−	0.745007i	0.978723	+	0.205185i	$0.0657796\pi$
$720$	64007.3	+	22904.5i	0.123471	+	0.0441831i
$721$	240957.	−	417350.i	0.463521	−	0.802841i
$722$	413509.	+	1.13611e6i	0.793250	+	2.17944i
$723$	210590.	+	448433.i	0.402866	+	0.857868i
$724$	−46750.6	+	39228.4i	−0.0891887	+	0.0748382i
$725$	226442.	−	622143.i	0.430804	−	1.18363i
$726$	451223.	+	640709.i	0.856086	+	1.21559i
$727$	−72177.6	+	409339.i	−0.136563	+	0.774488i	0.837195	+	0.546904i	$0.184194\pi$
$727$	−72177.6	+	409339.i	−0.136563	+	0.774488i	−0.973758	+	0.227584i	$0.926917\pi$
$728$		−	708760.i		−	1.33732i
$729$	−455858.	+	273172.i	−0.857778	+	0.514020i
$730$	−235220.			−0.441396
$731$	78770.8	+	13889.4i	0.147411	+	0.0259926i
$732$	−495724.	+	349117.i	−0.925163	+	0.651551i
$733$	79575.9	+	28963.2i	0.148106	+	0.0539063i	0.415010	−	0.909817i	$-0.363778\pi$
$733$	79575.9	+	28963.2i	0.148106	+	0.0539063i	−0.266903	+	0.963723i	$0.586000\pi$
$734$	−783502.	−	933742.i	−1.45428	−	1.73314i
$735$	178802.	−	83967.8i	0.330977	−	0.155431i
$736$	−172565.	+	62808.6i	−0.318565	+	0.115948i
$737$	35803.6	+	20671.2i	0.0659161	+	0.0380567i
$738$	−46208.6	+	129131.i	−0.0848418	+	0.237093i
$739$	−343960.	−	595756.i	−0.629824	−	1.09089i	−0.987587	−	0.157074i	$-0.949794\pi$
$739$	−343960.	−	595756.i	−0.629824	−	1.09089i	0.357763	−	0.933812i	$-0.383540\pi$
$740$	210113.	−	250403.i	0.383698	−	0.457274i
$741$	−1.10097e6	+	298205.i	−2.00511	+	0.543098i
$742$	95549.1	+	541886.i	0.173548	+	0.984237i
$743$	−23488.6	+	4141.68i	−0.0425481	+	0.00750238i	−0.194882	−	0.980827i	$-0.562432\pi$
$743$	−23488.6	+	4141.68i	−0.0425481	+	0.00750238i	0.152334	+	0.988329i	$0.451321\pi$
$744$	−601163.	−	159336.i	−1.08604	−	0.287850i
$745$	6392.00	+	5363.52i	0.0115166	+	0.00966357i
$746$	−633937.	+	366004.i	−1.13912	+	0.657669i
$747$	−392293.	+	688061.i	−0.703024	+	1.23306i
$748$	111218.	−	192634.i	0.198779	−	0.344295i
$749$	−467075.	−	1.28328e6i	−0.832574	−	2.28748i
$750$	−401439.	+	576635.i	−0.713668	+	1.02513i
$751$	806672.	−	676878.i	1.43027	−	1.20014i	0.484712	−	0.874674i	$-0.338924\pi$
$751$	806672.	−	676878.i	1.43027	−	1.20014i	0.945555	−	0.325462i	$-0.105520\pi$
$752$	−35067.4	+	96346.9i	−0.0620109	+	0.170373i
$753$	26855.9	−	2422.97i	0.0473642	−	0.00427325i
$754$	320195.	−	1.81591e6i	0.563211	−	3.19413i
$755$			153428.i			0.269160i
$756$	304392.	+	1.10014e6i	0.532586	+	1.92488i
$757$	7573.14			0.0132155			0.00660776	−	0.999978i	$-0.497897\pi$
$757$	7573.14			0.0132155			0.00660776	+	0.999978i	$0.497897\pi$
$758$	1.00832e6	+	177793.i	1.75492	+	0.309441i
$759$	−34139.0	−	15806.8i	−0.0592608	−	0.0274384i
$760$	280593.	+	102127.i	0.485790	+	0.176813i
$761$	−559188.	−	666414.i	−0.965580	−	1.15073i	−0.988534	−	0.150997i	$-0.951752\pi$
$761$	−559188.	−	666414.i	−0.965580	−	1.15073i	0.0229542	−	0.999737i	$-0.492693\pi$
$762$	−76634.6	+	904163.i	−0.131982	+	1.55717i
$763$	405512.	−	147594.i	0.696554	−	0.253525i
$764$	226881.	+	130990.i	0.388697	+	0.224414i
$765$	−188620.	+	227279.i	−0.322303	+	0.388362i
$766$	−326242.	−	565068.i	−0.556010	−	0.963037i
$767$	−199406.	+	237643.i	−0.338959	+	0.403956i
$768$	196768.	+	195704.i	0.333604	+	0.331800i
$769$	139267.	+	789822.i	0.235502	+	1.33560i	0.841553	+	0.540175i	$0.181642\pi$
$769$	139267.	+	789822.i	0.235502	+	1.33560i	−0.606051	+	0.795426i	$0.707247\pi$
$770$	128155.	−	22597.2i	0.216149	−	0.0381130i
$771$	683900.	−	687619.i	1.15049	−	1.15675i
$772$	161481.	+	135498.i	0.270948	+	0.227352i
$773$	−728698.	+	420714.i	−1.21952	+	0.704090i	−0.964815	−	0.262929i	$-0.915312\pi$
$773$	−728698.	+	420714.i	−1.21952	+	0.704090i	−0.254705	+	0.967019i	$0.581978\pi$
$774$	−115187.	+	42633.5i	−0.192275	+	0.0711655i
$775$	−363981.	+	630434.i	−0.606004	+	1.04963i
$776$	−87259.2	−	239743.i	−0.144906	−	0.398127i
$777$	−749832.	−	63553.8i	−1.24200	−	0.105269i
$778$	−1.30610e6	+	1.09595e6i	−2.15784	+	1.81064i
$779$	52250.6	−	143557.i	0.0861026	−	0.236565i
$780$	−218849.	+	472666.i	−0.359713	+	0.776899i
$781$	−5008.73	+	28405.9i	−0.00821156	+	0.0465701i
$782$		−	307697.i		−	0.503165i
$783$	91155.5	+	952611.i	0.148682	+	1.55379i
$784$	−152689.			−0.248414
$785$	254894.	+	44944.7i	0.413638	+	0.0729356i
$786$	46268.5	+	512835.i	0.0748929	+	0.830103i
$787$	−372205.	−	135472.i	−0.600943	−	0.218725i	0.0235926	−	0.999722i	$-0.492490\pi$
$787$	−372205.	−	135472.i	−0.600943	−	0.218725i	−0.624536	+	0.780996i	$0.714712\pi$
$788$	−159789.	−	190429.i	−0.257332	−	0.306677i
$789$	245093.	+	170627.i	0.393710	+	0.274091i
$790$	93869.0	−	34165.5i	0.150407	−	0.0547436i
$791$	299201.	+	172744.i	0.478200	+	0.276089i
$792$	596.801	+	110066.i	0.000951435	+	0.175470i
$793$	318473.	+	551611.i	0.506437	+	0.877175i
$794$	245130.	−	292134.i	0.388826	−	0.463384i
$795$	33385.0	−	125960.i	0.0528223	−	0.199295i
$796$	108986.	+	618093.i	0.172007	+	0.975500i
$797$	−1.05154e6	+	185415.i	−1.65542	+	0.291896i	−0.921802	−	0.387661i	$-0.873283\pi$
$797$	−1.05154e6	+	185415.i	−1.65542	+	0.291896i	−0.733623	+	0.679557i	$0.762172\pi$
$798$	−557704.	−	2.05904e6i	−0.875786	−	3.23339i
$799$	−341234.	−	286330.i	−0.534514	−	0.448511i
$800$	544631.	−	314443.i	0.850986	−	0.491317i
$801$	−723162.	+	613518.i	−1.12712	+	0.956229i
$802$	302862.	−	524572.i	0.470864	−	0.815561i
$803$	33032.3	+	90755.4i	0.0512280	+	0.140748i
$804$	−131552.	−	280128.i	−0.203509	−	0.433356i
$805$	82192.0	−	68967.3i	0.126835	−	0.106427i
$806$	−693426.	+	1.90517e6i	−1.06741	+	2.93268i
$807$	−353183.	−	501499.i	−0.542317	−	0.770057i
$808$	135627.	−	769178.i	0.207741	−	1.17816i
$809$		−	689350.i		−	1.05328i	−0.850089	−	0.526639i	$-0.823452\pi$
$809$		−	689350.i		−	1.05328i	0.850089	−	0.526639i	$-0.176548\pi$
$810$	73907.4	−	447473.i	0.112647	−	0.682019i
$811$	−693300.			−1.05409			−0.527047	−	0.849836i	$-0.676701\pi$
$811$	−693300.			−1.05409			−0.527047	+	0.849836i	$0.676701\pi$
$812$	2.02421e6	+	356923.i	3.07004	+	0.541331i
$813$	−606384.	+	427049.i	−0.917416	+	0.646095i
$814$	−211599.	−	77015.6i	−0.319348	−	0.116233i
$815$	83998.4	+	100105.i	0.126461	+	0.150710i
$816$	206646.	−	97043.4i	0.310346	−	0.145742i
$817$	128562.	−	46792.8i	0.192606	−	0.0701028i
$818$	687349.	+	396841.i	1.02724	+	0.593076i
$819$	1.17976e6	−	214626.i	1.75884	−	0.319973i
$820$	−34881.3	−	60416.2i	−0.0518758	−	0.0898516i
$821$	−180372.	+	214959.i	−0.267599	+	0.318911i	−0.883064	−	0.469252i	$-0.844524\pi$
$821$	−180372.	+	214959.i	−0.267599	+	0.318911i	0.615466	+	0.788164i	$0.288968\pi$
$822$	1.76900e6	−	479147.i	2.61809	−	0.709128i
$823$	132869.	+	753539.i	0.196167	+	1.11252i	0.910748	+	0.412963i	$0.135506\pi$
$823$	132869.	+	753539.i	0.196167	+	1.11252i	−0.714581	+	0.699553i	$0.753383\pi$
$824$	−342572.	+	60404.6i	−0.504542	+	0.0889643i
$825$	124535.	+	33007.4i	0.182971	+	0.0484957i
$826$	−444441.	−	372930.i	−0.651409	−	0.546597i
$827$	−320685.	+	185148.i	−0.468886	+	0.270712i	−0.715773	−	0.698333i	$-0.753926\pi$
$827$	−320685.	+	185148.i	−0.468886	+	0.270712i	0.246887	+	0.969044i	$0.420592\pi$
$828$	142131.	+	243124.i	0.207313	+	0.354623i
$829$	138822.	−	240446.i	0.201999	−	0.349872i	−0.747174	−	0.664629i	$-0.768590\pi$
$829$	138822.	−	240446.i	0.201999	−	0.349872i	0.949172	+	0.314757i	$0.101923\pi$
$830$	−231181.	−	635166.i	−0.335580	−	0.922000i
$831$	723269.	−	1.03892e6i	1.04736	−	1.50445i
$832$	1.13270e6	−	950444.i	1.63631	−	1.37303i
$833$	226886.	−	623364.i	0.326977	−	0.898363i
$834$	5530.26	−	498.947i	0.00795085	−	0.000717335i
$835$	−34370.4	+	194924.i	−0.0492959	+	0.279571i
$836$		−	380467.i		−	0.544383i
$837$	83177.3	−	1.04891e6i	0.118728	−	1.49723i
$838$	1.08238e6			1.54132
$839$	−290551.	−	51232.0i	−0.412761	−	0.0727808i	−0.0365880	−	0.999330i	$-0.511649\pi$
$839$	−290551.	−	51232.0i	−0.412761	−	0.0727808i	−0.376173	+	0.926550i	$0.622760\pi$
$840$	−284858.	−	131893.i	−0.403711	−	0.186923i
$841$	954648.	+	347463.i	1.34974	+	0.491266i
$842$	−942775.	−	1.12356e6i	−1.32979	−	1.58478i
$843$	41218.3	−	486309.i	0.0580010	−	0.684317i
$844$	782922.	−	284960.i	1.09909	−	0.400037i
$845$	202193.	+	116736.i	0.283173	+	0.163490i
$846$	674262.	+	115124.i	0.942080	+	0.160852i
$847$	458831.	+	794718.i	0.639566	+	1.10776i
$848$	−64744.4	+	77159.3i	−0.0900348	+	0.107299i
$849$	−1.00394e6	−	998514.i	−1.39282	−	1.38528i
$850$	182978.	+	1.03772e6i	0.253256	+	1.43629i
$851$	−182839.	+	32239.5i	−0.252470	+	0.0445174i
$852$	152264.	−	153092.i	0.209758	−	0.210899i
$853$	−302369.	−	253718.i	−0.415565	−	0.348701i	0.410908	−	0.911677i	$-0.365212\pi$
$853$	−302369.	−	253718.i	−0.415565	−	0.348701i	−0.826473	+	0.562976i	$0.809656\pi$
$854$	−1.03162e6	+	595609.i	−1.41451	+	0.816667i
$855$	−85026.5	+	497984.i	−0.116311	+	0.681213i
$856$	−492874.	+	853682.i	−0.672648	+	1.16506i
$857$	159679.	+	438714.i	0.217413	+	0.597338i	0.999672	−	0.0256160i	$-0.00815472\pi$
$857$	159679.	+	438714.i	0.217413	+	0.597338i	−0.782259	+	0.622954i	$0.785933\pi$
$858$	357535.	+	30303.7i	0.485672	+	0.0411644i
$859$	−35253.9	+	29581.5i	−0.0477772	+	0.0400898i	−0.666364	−	0.745627i	$-0.732150\pi$
$859$	−35253.9	+	29581.5i	−0.0477772	+	0.0400898i	0.618586	+	0.785717i	$0.287706\pi$
$860$	21367.9	−	58707.9i	0.0288912	−	0.0793779i
$861$	−67479.2	+	145740.i	−0.0910256	+	0.196595i
$862$	−169537.	+	961492.i	−0.228166	+	1.29399i
$863$			489117.i			0.656737i	0.944550	+	0.328369i	$0.106499\pi$
$863$			489117.i			0.656737i	−0.944550	+	0.328369i	$0.893501\pi$
$864$	−515306.	+	748822.i	−0.690299	+	1.00312i
$865$	486460.			0.650153
$866$	19379.9	+	3417.21i	0.0258414	+	0.00455654i
$867$	21580.5	+	239195.i	0.0287093	+	0.318211i
$868$	−2.12371e6	−	772966.i	−2.81874	−	1.02594i
$869$	−26364.3	−	31419.8i	−0.0349122	−	0.0416067i
$870$	−670251.	−	466612.i	−0.885521	−	0.616477i
$871$	−305504.	+	111194.i	−0.402699	+	0.146571i
$872$	−269761.	−	155747.i	−0.354769	−	0.204826i
$873$	372637.	−	217845.i	0.488943	−	0.285837i
$874$	−263152.	−	455793.i	−0.344496	−	0.596685i
$875$	−528861.	+	630272.i	−0.690757	+	0.823212i
$876$	185226.	−	698845.i	0.241375	−	0.910694i
$877$	110165.	+	624775.i	0.143233	+	0.812315i	0.968769	+	0.247966i	$0.0797620\pi$
$877$	110165.	+	624775.i	0.143233	+	0.812315i	−0.825536	+	0.564350i	$0.809127\pi$
$878$	1.59947e6	−	282029.i	2.07485	−	0.365852i
$879$	211432.	+	780605.i	0.273649	+	1.01031i
$880$	18248.0	+	15311.9i	0.0235641	+	0.0197726i
$881$	329154.	−	190037.i	0.424079	−	0.244842i	−0.272742	−	0.962087i	$-0.587930\pi$
$881$	329154.	−	190037.i	0.424079	−	0.244842i	0.696821	+	0.717245i	$0.254597\pi$
$882$	182324.	+	1.00220e6i	0.234372	+	1.28830i
$883$	669958.	−	1.16040e6i	0.859263	−	1.48829i	−0.0133692	−	0.999911i	$-0.504256\pi$
$883$	669958.	−	1.16040e6i	0.859263	−	1.48829i	0.872633	−	0.488377i	$-0.162411\pi$
$884$	598261.	+	1.64371e6i	0.765572	+	2.10339i
$885$	58403.9	+	124366.i	0.0745685	+	0.158787i
$886$	1.13242e6	−	950211.i	1.44258	−	1.21047i
$887$	225118.	−	618507.i	0.286130	−	0.786135i	−0.710469	−	0.703729i	$-0.751517\pi$
$887$	225118.	−	618507.i	0.286130	−	0.786135i	0.996599	−	0.0824068i	$-0.0262607\pi$
$888$	312764.	+	444106.i	0.396635	+	0.563197i
$889$	−184515.	+	1.04644e6i	−0.233468	+	1.32406i
$890$		−	809328.i		−	1.02175i
$891$	−183028.	+	34323.3i	−0.230549	+	0.0432349i
$892$	−1.01846e6			−1.28001
$893$	−750350.	−	132307.i	−0.940938	−	0.165913i
$894$	−35180.1	+	24775.8i	−0.0440172	+	0.0309994i
$895$	275184.	+	100159.i	0.343540	+	0.125038i
$896$	926951.	+	1.10470e6i	1.15462	+	1.37603i
$897$	267786.	−	125756.i	0.332816	−	0.156294i
$898$	−1.28483e6	+	467639.i	−1.59328	+	0.579907i
$899$	−1.64085e6	−	947347.i	−2.03025	−	1.17217i
$900$	−623918.	−	735421.i	−0.770269	−	0.907928i
$901$	−218802.	−	378976.i	−0.269527	−	0.466834i
$902$	−30891.0	+	36814.4i	−0.0379681	+	0.0452486i
$903$	−138826.	+	37601.9i	−0.170253	+	0.0461142i
$904$	−43304.5	−	245592.i	−0.0529902	−	0.300523i
$905$	27963.4	−	4930.70i	0.0341423	−	0.00602021i
$906$	−764785.	−	202703.i	−0.931715	−	0.246947i
$907$	−458046.	−	384346.i	−0.556794	−	0.467205i	0.320440	−	0.947269i	$-0.396169\pi$
$907$	−458046.	−	384346.i	−0.556794	−	0.467205i	−0.877234	+	0.480063i	$0.840614\pi$
$908$	−1.09400e6	+	631624.i	−1.32693	+	0.766102i
$909$	1.32140e6	−	7164.91i	1.59921	−	0.00867127i
$910$	−511670.	+	886238.i	−0.617884	+	1.07021i
$911$	223451.	+	613928.i	0.269244	+	0.739742i	0.998461	+	0.0554595i	$0.0176624\pi$
$911$	223451.	+	613928.i	0.269244	+	0.739742i	−0.729217	+	0.684283i	$0.760115\pi$
$912$	223111.	−	320481.i	0.268244	−	0.385312i
$913$	−212602.	+	178394.i	−0.255050	+	0.214013i
$914$	−163937.	+	450412.i	−0.196238	+	0.539160i
$915$	280962.	−	25348.8i	0.335588	−	0.0302771i
$916$	242450.	−	1.37500e6i	0.288955	−	1.63875i
$917$			602972.i			0.717065i
$918$	−883712.	−	1.24048e6i	−1.04864	−	1.47198i
$919$	−1.18656e6			−1.40495			−0.702473	−	0.711710i	$-0.747921\pi$
$919$	−1.18656e6			−1.40495			−0.702473	+	0.711710i	$0.747921\pi$
$920$	−76270.7	−	13448.6i	−0.0901118	−	0.0158891i
$921$	246836.	+	114288.i	0.290998	+	0.134735i
$922$	−1.07779e6	−	392283.i	−1.26786	−	0.461464i
$923$	−145801.	−	173759.i	−0.171142	−	0.203959i
$924$	−33779.8	+	398546.i	−0.0395651	+	0.466804i
$925$	597460.	−	217458.i	0.698273	−	0.254151i
$926$	1.75525e6	+	1.01339e6i	2.04700	+	1.18183i
$927$	−204283.	−	551933.i	−0.237724	−	0.642283i
$928$	818412.	+	1.41753e6i	0.950333	+	1.64603i
$929$	480817.	−	573015.i	0.557119	−	0.663949i	−0.411815	−	0.911267i	$-0.635105\pi$
$929$	480817.	−	573015.i	0.557119	−	0.663949i	0.968934	+	0.247319i	$0.0795495\pi$
$930$	636670.	+	633227.i	0.736120	+	0.732139i
$931$	−197033.	−	1.11743e6i	−0.227322	−	1.28920i
$932$	326643.	−	57595.9i	0.376046	−	0.0663070i
$933$	−134967.	+	135701.i	−0.155048	+	0.155891i
$934$	128559.	+	107874.i	0.147370	+	0.123658i
$935$	−89627.2	+	51746.3i	−0.102522	+	0.0591911i
$936$	−666060.	−	552764.i	−0.760259	−	0.630940i
$937$	−340190.	+	589226.i	−0.387474	+	0.671124i	−0.992109	−	0.125378i	$-0.959986\pi$
$937$	−340190.	+	589226.i	−0.387474	+	0.671124i	0.604635	+	0.796502i	$0.293319\pi$
$938$	−207956.	−	571355.i	−0.236356	−	0.649383i
$939$	566385.	+	48005.4i	0.642363	+	0.0544451i
$940$	−266532.	+	223647.i	−0.301643	+	0.253109i
$941$	90092.8	−	247528.i	0.101745	−	0.279541i	−0.878367	−	0.477986i	$-0.841367\pi$
$941$	90092.8	−	247528.i	0.101745	−	0.279541i	0.980112	+	0.198445i	$0.0635892\pi$
$942$	−560790.	+	1.21118e6i	−0.631973	+	1.36492i
$943$	−6880.59	+	39021.8i	−0.00773753	+	0.0438817i
$944$		−	106203.i		−	0.119177i
$945$	133280.	−	514097.i	0.149246	−	0.575681i
$946$	−43038.0			−0.0480917
$947$	−1.01479e6	−	178935.i	−1.13156	−	0.199525i	−0.423649	−	0.905826i	$-0.639251\pi$
$947$	−1.01479e6	−	178935.i	−1.13156	−	0.199525i	−0.707911	+	0.706302i	$0.750362\pi$
$948$	27588.8	+	305791.i	0.0306984	+	0.340258i
$949$	−713688.	−	259761.i	−0.792457	−	0.288431i
$950$	1.15854e6	+	1.38069e6i	1.28370	+	1.52985i
$951$	−1.08670e6	−	756532.i	−1.20157	−	0.836500i
$952$	−990602.	+	360550.i	−1.09301	+	0.397824i
$953$	1.32645e6	+	765824.i	1.46051	+	0.843225i	0.999035	−	0.0439291i	$-0.0139876\pi$
$953$	1.32645e6	+	765824.i	1.46051	+	0.843225i	0.461474	+	0.887154i	$0.347321\pi$
$954$	583758.	+	332826.i	0.641411	+	0.365696i
$955$	−60945.7	−	105561.i	−0.0668246	−	0.115744i
$956$	918052.	−	1.09409e6i	1.00450	−	1.19712i
$957$	−85909.5	+	324131.i	−0.0938031	+	0.353913i
$958$	−150393.	−	852921.i	−0.163869	−	0.929347i
$959$	2.11355e6	−	372676.i	2.29814	−	0.405223i
$960$	−171211.	−	632110.i	−0.185776	−	0.685883i
$961$	888412.	+	745466.i	0.961983	+	0.807200i
$962$	1.53353e6	−	885385.i	1.65708	−	0.956714i
$963$	−1.57024e6	−	561897.i	−1.69322	−	0.605905i
$964$	649751.	−	1.12540e6i	0.699186	−	1.21103i
$965$	−33544.7	−	92163.3i	−0.0360221	−	0.0989700i
$966$	235189.	+	500815.i	0.252036	+	0.536690i
$967$	670376.	−	562512.i	0.716912	−	0.601560i	−0.209617	−	0.977783i	$-0.567222\pi$
$967$	670376.	−	562512.i	0.716912	−	0.601560i	0.926529	+	0.376223i	$0.122777\pi$
$968$	226550.	−	622442.i	0.241776	−	0.664275i
$969$	976856.	+	1.38708e6i	1.04036	+	1.47725i
$970$	−63966.1	+	362770.i	−0.0679839	+	0.385556i
$971$			836356.i			0.887059i	0.896260	+	0.443530i	$0.146274\pi$
$971$			836356.i			0.887059i	−0.896260	+	0.443530i	$0.853726\pi$
$972$	1.27125e6	+	571946.i	1.34555	+	0.605372i
$973$	6502.28			0.00686816
$974$	−2.02802e6	−	357594.i	−2.13774	−	0.376940i
$975$	−828335.	+	583360.i	−0.871359	+	0.613659i
$976$	−204906.	−	74579.8i	−0.215107	−	0.0782927i
$977$	160169.	+	190882.i	0.167799	+	0.199975i	0.843391	−	0.537301i	$-0.180556\pi$
$977$	160169.	+	190882.i	0.167799	+	0.199975i	−0.675591	+	0.737276i	$0.736112\pi$
$978$	−609966.	+	286448.i	−0.637717	+	0.299480i
$979$	−312265.	+	113655.i	−0.325805	+	0.118583i
$980$	−448728.	−	259073.i	−0.467231	−	0.269756i
$981$	177558.	−	496191.i	0.184502	−	0.515597i
$982$	−1.16817e6	−	2.02333e6i	−1.21139	−	2.09818i
$983$	449001.	−	535098.i	0.464665	−	0.553766i	−0.481922	−	0.876214i	$-0.660061\pi$
$983$	449001.	−	535098.i	0.464665	−	0.553766i	0.946587	+	0.322448i	$0.104506\pi$
$984$	111895.	−	30307.7i	0.115564	−	0.0313013i
$985$	20084.2	+	113903.i	0.0207006	+	0.117399i
$986$	−2.70091e6	+	476243.i	−2.77815	+	0.489863i
$987$	774258.	+	205214.i	0.794788	+	0.210655i
$988$	2.29196e6	+	1.92318e6i	2.34797	+	1.97018i
$989$	−30730.8	+	17742.4i	−0.0314182	+	0.0181393i
$990$	78712.7	−	138058.i	0.0803109	−	0.140861i
$991$	−684350.	+	1.18533e6i	−0.696836	+	1.20696i	0.272722	+	0.962093i	$0.412076\pi$
$991$	−684350.	+	1.18533e6i	−0.696836	+	1.20696i	−0.969558	+	0.244863i	$0.921257\pi$
$992$	−615543.	−	1.69119e6i	−0.625511	−	1.71858i
$993$	−72894.2	+	104707.i	−0.0739256	+	0.106188i
$994$	324965.	−	272678.i	0.328900	−	0.275980i
$995$	99875.7	−	274406.i	0.100882	−	0.277171i
$996$	2.06914e6	−	186680.i	2.08579	−	0.188182i
$997$	−4282.13	+	24285.2i	−0.00430794	+	0.0244315i	−0.986886	−	0.161419i	$-0.948393\pi$
$997$	−4282.13	+	24285.2i	−0.00430794	+	0.0244315i	0.982578	+	0.185851i	$0.0595040\pi$
$998$			874870.i			0.878380i
$999$	−644521.	+	655091.i	−0.645812	+	0.656403i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.5.f.a.2.2	✓	66
3.2	odd	2		81.5.f.a.8.10		66
27.13	even	9		81.5.f.a.71.10		66
27.14	odd	18	inner	27.5.f.a.14.2	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.f.a.2.2	✓	66	1.1	even	1	trivial
27.5.f.a.14.2	yes	66	27.14	odd	18	inner
81.5.f.a.8.10		66	3.2	odd	2
81.5.f.a.71.10		66	27.13	even	9

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.19782 - 1.09284i) q^{2} +(-7.35835 + 5.18216i) q^{3} +(22.1836 + 8.07418i) q^{4} +(-7.06026 - 8.41408i) q^{5} +(51.2690 - 24.0766i) q^{6} +(62.3269 - 22.6852i) q^{7} +(-41.4621 - 23.9381i) q^{8} +(27.2905 - 76.2642i) q^{9} +O(q^{10})\)	\(q+(-6.19782 - 1.09284i) q^{2} +(-7.35835 + 5.18216i) q^{3} +(22.1836 + 8.07418i) q^{4} +(-7.06026 - 8.41408i) q^{5} +(51.2690 - 24.0766i) q^{6} +(62.3269 - 22.6852i) q^{7} +(-41.4621 - 23.9381i) q^{8} +(27.2905 - 76.2642i) q^{9} +(34.5629 + 59.8648i) q^{10} +(18.2440 - 21.7424i) q^{11} +(-205.077 + 55.5464i) q^{12} +(38.7578 + 219.806i) q^{13} +(-411.083 + 72.4850i) q^{14} +(95.5549 + 25.3264i) q^{15} +(-58.5343 - 49.1161i) q^{16} +(287.497 - 165.987i) q^{17} +(-252.487 + 442.848i) q^{18} +(283.914 - 491.754i) q^{19} +(-88.6853 - 243.661i) q^{20} +(-341.065 + 489.913i) q^{21} +(-136.834 + 114.818i) q^{22} +(-50.3714 + 138.394i) q^{23} +(429.144 - 38.7178i) q^{24} +(87.5805 - 496.694i) q^{25} -1404.68i q^{26} +(194.400 + 702.602i) q^{27} +1565.80 q^{28} +(1292.76 + 227.949i) q^{29} +(-564.555 - 261.395i) q^{30} +(-1356.31 - 493.655i) q^{31} +(801.497 + 955.187i) q^{32} +(-21.5734 + 254.531i) q^{33} +(-1963.25 + 714.566i) q^{34} +(-630.919 - 364.261i) q^{35} +(1221.17 - 1471.47i) q^{36} +(630.312 + 1091.73i) q^{37} +(-2297.06 + 2737.53i) q^{38} +(-1424.26 - 1416.56i) q^{39} +(91.3153 + 517.875i) q^{40} +(264.956 - 46.7189i) q^{41} +(2649.26 - 2663.66i) q^{42} +(184.572 + 154.874i) q^{43} +(580.271 - 335.020i) q^{44} +(-834.371 + 308.820i) q^{45} +(463.437 - 802.696i) q^{46} +(-458.931 - 1260.90i) q^{47} +(685.242 + 58.0794i) q^{48} +(1530.76 - 1284.46i) q^{49} +(-1085.62 + 2982.71i) q^{50} +(-1255.34 + 2711.24i) q^{51} +(-914.968 + 5189.04i) q^{52} -1318.19i q^{53} +(-437.022 - 4567.05i) q^{54} -311.750 q^{55} +(-3127.25 - 551.418i) q^{56} +(459.206 + 5089.78i) q^{57} +(-7763.20 - 2825.58i) q^{58} +(893.408 + 1064.72i) q^{59} +(1915.27 + 1333.36i) q^{60} +(2681.63 - 976.034i) q^{61} +(7866.66 + 4541.82i) q^{62} +(-29.1303 - 5372.40i) q^{63} +(-3312.38 - 5737.21i) q^{64} +(1575.83 - 1878.00i) q^{65} +(411.871 - 1553.96i) q^{66} +(252.937 + 1434.48i) q^{67} +(7717.94 - 1360.88i) q^{68} +(-346.531 - 1279.39i) q^{69} +(3512.24 + 2947.12i) q^{70} +(-880.106 + 508.129i) q^{71} +(-2957.14 + 2508.79i) q^{72} +(-1701.39 + 2946.89i) q^{73} +(-2713.47 - 7455.20i) q^{74} +(1929.50 + 4108.70i) q^{75} +(10268.8 - 8616.51i) q^{76} +(643.865 - 1769.01i) q^{77} +(7279.26 + 10336.1i) q^{78} +(250.938 - 1423.14i) q^{79} +839.284i q^{80} +(-5071.46 - 4162.58i) q^{81} -1693.21 q^{82} +(-9629.68 - 1697.97i) q^{83} +(-11521.7 + 8114.23i) q^{84} +(-3426.43 - 1247.12i) q^{85} +(-974.689 - 1161.59i) q^{86} +(-10693.9 + 5021.97i) q^{87} +(-1276.91 + 464.756i) q^{88} +(-10139.4 - 5854.01i) q^{89} +(5508.78 - 1002.17i) q^{90} +(7402.00 + 12820.6i) q^{91} +(-2234.84 + 2663.38i) q^{92} +(12538.4 - 3396.10i) q^{93} +(1466.40 + 8316.39i) q^{94} +(-6142.16 + 1083.03i) q^{95} +(-10847.6 - 2875.11i) q^{96} +(4082.19 + 3425.36i) q^{97} +(-10891.1 + 6287.97i) q^{98} +(-1160.28 - 1984.73i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 3 q^{5} + 90 q^{6} - 6 q^{7} - 9 q^{8} - 108 q^{9}+O(q^{10}) \) 66 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 3 * q^5 + 90 * q^6 - 6 * q^7 - 9 * q^8 - 108 * q^9	\( 66 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 3 q^{5} + 90 q^{6} - 6 q^{7} - 9 q^{8} - 108 q^{9} - 3 q^{10} - 492 q^{11} - 339 q^{12} - 6 q^{13} + 1137 q^{14} + 1017 q^{15} - 54 q^{16} - 9 q^{17} + 603 q^{18} - 3 q^{19} - 2487 q^{20} - 2784 q^{21} + 1002 q^{22} - 2724 q^{23} - 3312 q^{24} + 435 q^{25} + 1368 q^{27} - 12 q^{28} + 5016 q^{29} + 10773 q^{30} - 1671 q^{31} + 10224 q^{32} + 2925 q^{33} - 342 q^{34} - 2682 q^{35} - 7704 q^{36} - 3 q^{37} - 6564 q^{38} - 1983 q^{39} - 1113 q^{40} + 5754 q^{41} + 8694 q^{42} - 1266 q^{43} - 4545 q^{44} - 7029 q^{45} - 3 q^{46} - 9159 q^{47} - 28383 q^{48} + 5898 q^{49} - 34977 q^{50} - 14814 q^{51} + 2871 q^{52} + 13878 q^{54} - 12 q^{55} + 39243 q^{56} + 15792 q^{57} - 12291 q^{58} + 24762 q^{59} + 50670 q^{60} - 8358 q^{61} + 38304 q^{62} + 21609 q^{63} + 6141 q^{64} + 23727 q^{65} + 11349 q^{66} + 15996 q^{67} - 43533 q^{68} - 26847 q^{69} - 7251 q^{70} - 19773 q^{71} - 77580 q^{72} + 6108 q^{73} - 74847 q^{74} - 49155 q^{75} - 28614 q^{76} - 33909 q^{77} - 9108 q^{78} - 5658 q^{79} - 12600 q^{81} - 12 q^{82} + 18813 q^{83} + 82356 q^{84} + 24219 q^{85} + 96474 q^{86} + 84555 q^{87} + 36042 q^{88} + 110232 q^{89} + 153540 q^{90} - 6042 q^{91} + 73545 q^{92} + 1293 q^{93} + 2631 q^{94} - 65163 q^{95} - 152226 q^{96} - 3696 q^{97} - 259938 q^{98} - 162405 q^{99}+O(q^{100}) \) 66 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 3 * q^5 + 90 * q^6 - 6 * q^7 - 9 * q^8 - 108 * q^9 - 3 * q^10 - 492 * q^11 - 339 * q^12 - 6 * q^13 + 1137 * q^14 + 1017 * q^15 - 54 * q^16 - 9 * q^17 + 603 * q^18 - 3 * q^19 - 2487 * q^20 - 2784 * q^21 + 1002 * q^22 - 2724 * q^23 - 3312 * q^24 + 435 * q^25 + 1368 * q^27 - 12 * q^28 + 5016 * q^29 + 10773 * q^30 - 1671 * q^31 + 10224 * q^32 + 2925 * q^33 - 342 * q^34 - 2682 * q^35 - 7704 * q^36 - 3 * q^37 - 6564 * q^38 - 1983 * q^39 - 1113 * q^40 + 5754 * q^41 + 8694 * q^42 - 1266 * q^43 - 4545 * q^44 - 7029 * q^45 - 3 * q^46 - 9159 * q^47 - 28383 * q^48 + 5898 * q^49 - 34977 * q^50 - 14814 * q^51 + 2871 * q^52 + 13878 * q^54 - 12 * q^55 + 39243 * q^56 + 15792 * q^57 - 12291 * q^58 + 24762 * q^59 + 50670 * q^60 - 8358 * q^61 + 38304 * q^62 + 21609 * q^63 + 6141 * q^64 + 23727 * q^65 + 11349 * q^66 + 15996 * q^67 - 43533 * q^68 - 26847 * q^69 - 7251 * q^70 - 19773 * q^71 - 77580 * q^72 + 6108 * q^73 - 74847 * q^74 - 49155 * q^75 - 28614 * q^76 - 33909 * q^77 - 9108 * q^78 - 5658 * q^79 - 12600 * q^81 - 12 * q^82 + 18813 * q^83 + 82356 * q^84 + 24219 * q^85 + 96474 * q^86 + 84555 * q^87 + 36042 * q^88 + 110232 * q^89 + 153540 * q^90 - 6042 * q^91 + 73545 * q^92 + 1293 * q^93 + 2631 * q^94 - 65163 * q^95 - 152226 * q^96 - 3696 * q^97 - 259938 * q^98 - 162405 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more