LMFDB - Embedded newform 60.5.c.a.31.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,5,Mod(31,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

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

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

chi := DirichletCharacter("60.31");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	60.c (of order $2$, degree $1$, 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:	$6.20219778503$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 9 x^{14} + 18 x^{13} + 263 x^{12} - 444 x^{11} - 1732 x^{10} - 832 x^{9} + \cdots + 16777216 $ x^16 - 4x^15 - 9x^14 + 18x^13 + 263x^12 - 444x^11 - 1732x^10 - 832x^9 + 25296x^8 - 6656x^7 - 110848x^6 - 227328x^5 + 1077248x^4 + 589824x^3 - 2359296x^2 - 8388608*x + 16777216
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{4}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			31.9
Root			$2.77114 + 0.566380i$ of defining polynomial
Character	$\chi$	$=$	60.31
Dual form			60.5.c.a.31.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.264404 - 3.99125i) q^{2} +5.19615i q^{3} +(-15.8602 - 2.11060i) q^{4} -11.1803 q^{5} +(20.7392 + 1.37388i) q^{6} +29.5855i q^{7} +(-12.6174 + 62.7439i) q^{8} -27.0000 q^{9} +O(q^{10})$	\(q+(0.264404 - 3.99125i) q^{2} +5.19615i q^{3} +(-15.8602 - 2.11060i) q^{4} -11.1803 q^{5} +(20.7392 + 1.37388i) q^{6} +29.5855i q^{7} +(-12.6174 + 62.7439i) q^{8} -27.0000 q^{9} +(-2.95612 + 44.6236i) q^{10} +210.571i q^{11} +(10.9670 - 82.4119i) q^{12} -135.726 q^{13} +(118.083 + 7.82252i) q^{14} -58.0948i q^{15} +(247.091 + 66.9491i) q^{16} -7.65200 q^{17} +(-7.13890 + 107.764i) q^{18} -166.741i q^{19} +(177.322 + 23.5973i) q^{20} -153.731 q^{21} +(840.442 + 55.6758i) q^{22} +405.405i q^{23} +(-326.027 - 65.5622i) q^{24} +125.000 q^{25} +(-35.8866 + 541.718i) q^{26} -140.296i q^{27} +(62.4433 - 469.231i) q^{28} -1646.13 q^{29} +(-231.871 - 15.3605i) q^{30} -1179.57i q^{31} +(332.543 - 968.500i) q^{32} -1094.16 q^{33} +(-2.02322 + 30.5410i) q^{34} -330.776i q^{35} +(428.225 + 56.9863i) q^{36} +605.018 q^{37} +(-665.506 - 44.0870i) q^{38} -705.255i q^{39} +(141.067 - 701.498i) q^{40} -1498.18 q^{41} +(-40.6470 + 613.578i) q^{42} +1511.90i q^{43} +(444.432 - 3339.69i) q^{44} +301.869 q^{45} +(1618.07 + 107.191i) q^{46} +1880.00i q^{47} +(-347.878 + 1283.92i) q^{48} +1525.70 q^{49} +(33.0505 - 498.906i) q^{50} -39.7609i q^{51} +(2152.65 + 286.465i) q^{52} +4955.24 q^{53} +(-559.957 - 37.0948i) q^{54} -2354.26i q^{55} +(-1856.31 - 373.293i) q^{56} +866.413 q^{57} +(-435.242 + 6570.10i) q^{58} -500.976i q^{59} +(-122.615 + 921.393i) q^{60} -928.887 q^{61} +(-4707.95 - 311.882i) q^{62} -798.809i q^{63} +(-3777.60 - 1583.34i) q^{64} +1517.47 q^{65} +(-289.300 + 4367.06i) q^{66} +3041.07i q^{67} +(121.362 + 16.1503i) q^{68} -2106.55 q^{69} +(-1320.21 - 87.4584i) q^{70} +6963.76i q^{71} +(340.671 - 1694.09i) q^{72} +7810.56 q^{73} +(159.969 - 2414.78i) q^{74} +649.519i q^{75} +(-351.925 + 2644.55i) q^{76} -6229.85 q^{77} +(-2814.85 - 186.472i) q^{78} -9433.20i q^{79} +(-2762.56 - 748.514i) q^{80} +729.000 q^{81} +(-396.124 + 5979.61i) q^{82} +9487.99i q^{83} +(2438.20 + 324.465i) q^{84} +85.5519 q^{85} +(6034.36 + 399.751i) q^{86} -8553.52i q^{87} +(-13212.1 - 2656.87i) q^{88} +13795.1 q^{89} +(79.8154 - 1204.84i) q^{90} -4015.54i q^{91} +(855.649 - 6429.79i) q^{92} +6129.21 q^{93} +(7503.57 + 497.080i) q^{94} +1864.22i q^{95} +(5032.47 + 1727.94i) q^{96} -7695.33 q^{97} +(403.400 - 6089.45i) q^{98} -5685.42i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{2} + 26 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9}+O(q^{10}) $ 16 * q - 12 * q^2 + 26 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9	$ 16 q - 12 q^{2} + 26 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9} + 50 q^{10} - 352 q^{13} - 804 q^{14} - 190 q^{16} + 324 q^{18} + 600 q^{20} + 288 q^{21} + 436 q^{22} - 1998 q^{24} + 2000 q^{25} - 852 q^{26} - 1156 q^{28} - 3456 q^{29} + 7668 q^{32} + 4772 q^{34} - 702 q^{36} + 9376 q^{37} - 1320 q^{38} + 550 q^{40} + 1248 q^{41} - 324 q^{42} - 6420 q^{44} - 1112 q^{46} - 4176 q^{48} - 3952 q^{49} - 1500 q^{50} + 12704 q^{52} - 5184 q^{53} - 486 q^{54} - 2604 q^{56} - 11232 q^{57} + 12708 q^{58} + 3150 q^{60} - 3808 q^{61} - 16152 q^{62} - 11902 q^{64} + 2400 q^{65} - 2916 q^{66} - 12312 q^{68} + 9792 q^{69} - 17100 q^{70} + 4860 q^{72} + 11040 q^{73} + 30516 q^{74} - 5160 q^{76} - 27456 q^{77} - 3600 q^{78} + 10800 q^{80} + 11664 q^{81} - 54040 q^{82} - 2052 q^{84} - 11200 q^{85} + 39768 q^{86} - 7220 q^{88} + 7584 q^{89} - 1350 q^{90} + 28848 q^{92} + 19872 q^{93} + 49776 q^{94} + 18882 q^{96} - 14496 q^{97} + 23940 q^{98}+O(q^{100}) $ 16 * q - 12 * q^2 + 26 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9 + 50 * q^10 - 352 * q^13 - 804 * q^14 - 190 * q^16 + 324 * q^18 + 600 * q^20 + 288 * q^21 + 436 * q^22 - 1998 * q^24 + 2000 * q^25 - 852 * q^26 - 1156 * q^28 - 3456 * q^29 + 7668 * q^32 + 4772 * q^34 - 702 * q^36 + 9376 * q^37 - 1320 * q^38 + 550 * q^40 + 1248 * q^41 - 324 * q^42 - 6420 * q^44 - 1112 * q^46 - 4176 * q^48 - 3952 * q^49 - 1500 * q^50 + 12704 * q^52 - 5184 * q^53 - 486 * q^54 - 2604 * q^56 - 11232 * q^57 + 12708 * q^58 + 3150 * q^60 - 3808 * q^61 - 16152 * q^62 - 11902 * q^64 + 2400 * q^65 - 2916 * q^66 - 12312 * q^68 + 9792 * q^69 - 17100 * q^70 + 4860 * q^72 + 11040 * q^73 + 30516 * q^74 - 5160 * q^76 - 27456 * q^77 - 3600 * q^78 + 10800 * q^80 + 11664 * q^81 - 54040 * q^82 - 2052 * q^84 - 11200 * q^85 + 39768 * q^86 - 7220 * q^88 + 7584 * q^89 - 1350 * q^90 + 28848 * q^92 + 19872 * q^93 + 49776 * q^94 + 18882 * q^96 - 14496 * q^97 + 23940 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	0.264404	−	3.99125i	0.0661009	−	0.997813i
$2$	0.264404	−	3.99125i	0.0661009	−	0.997813i
$3$			5.19615i			0.577350i
$3$			5.19615i			0.577350i
$4$	−15.8602	−	2.11060i	−0.991261	−	0.131913i
$5$	−11.1803			−0.447214
$5$	−11.1803			−0.447214
$6$	20.7392	+	1.37388i	0.576088	+	0.0381634i
$7$			29.5855i			0.603786i	0.953342	+	0.301893i	$0.0976185\pi$
$7$			29.5855i			0.603786i	−0.953342	+	0.301893i	$0.902382\pi$
$8$	−12.6174	+	62.7439i	−0.197148	+	0.980374i
$9$	−27.0000			−0.333333
$10$	−2.95612	+	44.6236i	−0.0295612	+	0.446236i
$11$			210.571i			1.74026i	0.492825	+	0.870128i	$0.335964\pi$
$11$			210.571i			1.74026i	−0.492825	+	0.870128i	$0.664036\pi$
$12$	10.9670	−	82.4119i	0.0761599	−	0.572305i
$13$	−135.726			−0.803115			−0.401558	−	0.915834i	$-0.631531\pi$
$13$	−135.726			−0.803115			−0.401558	+	0.915834i	$0.631531\pi$
$14$	118.083	+	7.82252i	0.602465	+	0.0399108i
$15$		−	58.0948i		−	0.258199i
$16$	247.091	+	66.9491i	0.965198	+	0.261520i
$17$	−7.65200			−0.0264775			−0.0132387	−	0.999912i	$-0.504214\pi$
$17$	−7.65200			−0.0264775			−0.0132387	+	0.999912i	$0.504214\pi$
$18$	−7.13890	+	107.764i	−0.0220336	+	0.332604i
$19$		−	166.741i		−	0.461887i	−0.972967	−	0.230943i	$-0.925819\pi$
$19$		−	166.741i		−	0.461887i	0.972967	−	0.230943i	$-0.0741812\pi$
$20$	177.322	+	23.5973i	0.443306	+	0.0589932i
$21$	−153.731			−0.348596
$22$	840.442	+	55.6758i	1.73645	+	0.115033i
$23$			405.405i			0.766361i	0.923674	+	0.383180i	$0.125171\pi$
$23$			405.405i			0.766361i	−0.923674	+	0.383180i	$0.874829\pi$
$24$	−326.027	−	65.5622i	−0.566019	−	0.113823i
$25$	125.000			0.200000
$26$	−35.8866	+	541.718i	−0.0530867	+	0.801359i
$27$		−	140.296i		−	0.192450i
$28$	62.4433	−	469.231i	0.0796470	−	0.598509i
$29$	−1646.13			−1.95734			−0.978672	−	0.205431i	$-0.934140\pi$
$29$	−1646.13			−1.95734			−0.978672	+	0.205431i	$0.934140\pi$
$30$	−231.871	−	15.3605i	−0.257634	−	0.0170672i
$31$		−	1179.57i		−	1.22744i	−0.789525	−	0.613718i	$-0.789673\pi$
$31$		−	1179.57i		−	1.22744i	0.789525	−	0.613718i	$-0.210327\pi$
$32$	332.543	−	968.500i	0.324749	−	0.945800i
$33$	−1094.16			−1.00474
$34$	−2.02322	+	30.5410i	−0.00175019	+	0.0264196i
$35$		−	330.776i		−	0.270021i
$36$	428.225	+	56.9863i	0.330420	+	0.0439709i
$37$	605.018			0.441941			0.220971	−	0.975280i	$-0.429077\pi$
$37$	605.018			0.441941			0.220971	+	0.975280i	$0.429077\pi$
$38$	−665.506	−	44.0870i	−0.460877	−	0.0305312i
$39$		−	705.255i		−	0.463679i
$40$	141.067	−	701.498i	0.0881671	−	0.438437i
$41$	−1498.18			−0.891243			−0.445621	−	0.895222i	$-0.647017\pi$
$41$	−1498.18			−0.891243			−0.445621	+	0.895222i	$0.647017\pi$
$42$	−40.6470	+	613.578i	−0.0230425	+	0.347833i
$43$			1511.90i			0.817683i	0.912605	+	0.408842i	$0.134067\pi$
$43$			1511.90i			0.817683i	−0.912605	+	0.408842i	$0.865933\pi$
$44$	444.432	−	3339.69i	0.229562	−	1.72505i
$45$	301.869			0.149071
$46$	1618.07	+	107.191i	0.764685	+	0.0506572i
$47$			1880.00i			0.851066i	0.904943	+	0.425533i	$0.139913\pi$
$47$			1880.00i			0.851066i	−0.904943	+	0.425533i	$0.860087\pi$
$48$	−347.878	+	1283.92i	−0.150989	+	0.557257i
$49$	1525.70			0.635443
$50$	33.0505	−	498.906i	0.0132202	−	0.199563i
$51$		−	39.7609i		−	0.0152868i
$52$	2152.65	+	286.465i	0.796097	+	0.105941i
$53$	4955.24			1.76406			0.882029	−	0.471194i	$-0.156177\pi$
$53$	4955.24			1.76406			0.882029	+	0.471194i	$0.156177\pi$
$54$	−559.957	−	37.0948i	−0.192029	−	0.0127211i
$55$		−	2354.26i		−	0.778266i
$56$	−1856.31	−	373.293i	−0.591936	−	0.119035i
$57$	866.413			0.266671
$58$	−435.242	+	6570.10i	−0.129382	+	1.95306i
$59$		−	500.976i		−	0.143917i	−0.997408	−	0.0719587i	$-0.977075\pi$
$59$		−	500.976i		−	0.143917i	0.997408	−	0.0719587i	$-0.0229250\pi$
$60$	−122.615	+	921.393i	−0.0340597	+	0.255943i
$61$	−928.887			−0.249634			−0.124817	−	0.992180i	$-0.539834\pi$
$61$	−928.887			−0.249634			−0.124817	+	0.992180i	$0.539834\pi$
$62$	−4707.95	−	311.882i	−1.22475	−	0.0811347i
$63$		−	798.809i		−	0.201262i
$64$	−3777.60	−	1583.34i	−0.922266	−	0.386557i
$65$	1517.47			0.359164
$66$	−289.300	+	4367.06i	−0.0664141	+	1.00254i
$67$			3041.07i			0.677450i	0.940885	+	0.338725i	$0.109996\pi$
$67$			3041.07i			0.677450i	−0.940885	+	0.338725i	$0.890004\pi$
$68$	121.362	+	16.1503i	0.0262461	+	0.00349272i
$69$	−2106.55			−0.442459
$70$	−1320.21	−	87.4584i	−0.269431	−	0.0178487i
$71$			6963.76i			1.38143i	0.723129	+	0.690713i	$0.242703\pi$
$71$			6963.76i			1.38143i	−0.723129	+	0.690713i	$0.757297\pi$
$72$	340.671	−	1694.09i	0.0657159	−	0.326791i
$73$	7810.56			1.46567			0.732835	−	0.680406i	$-0.238197\pi$
$73$	7810.56			1.46567			0.732835	+	0.680406i	$0.238197\pi$
$74$	159.969	−	2414.78i	0.0292127	−	0.440975i
$75$			649.519i			0.115470i
$76$	−351.925	+	2644.55i	−0.0609288	+	0.457851i
$77$	−6229.85			−1.05074
$78$	−2814.85	−	186.472i	−0.462665	−	0.0306496i
$79$		−	9433.20i		−	1.51149i	−0.654867	−	0.755744i	$-0.727275\pi$
$79$		−	9433.20i		−	1.51149i	0.654867	−	0.755744i	$-0.272725\pi$
$80$	−2762.56	−	748.514i	−0.431650	−	0.116955i
$81$	729.000			0.111111
$82$	−396.124	+	5979.61i	−0.0589120	+	0.889293i
$83$			9487.99i			1.37727i	0.725110	+	0.688633i	$0.241789\pi$
$83$			9487.99i			1.37727i	−0.725110	+	0.688633i	$0.758211\pi$
$84$	2438.20	+	324.465i	0.345550	+	0.0459842i
$85$	85.5519			0.0118411
$86$	6034.36	+	399.751i	0.815895	+	0.0540496i
$87$		−	8553.52i		−	1.13007i
$88$	−13212.1	−	2656.87i	−1.70610	−	0.343087i
$89$	13795.1			1.74159			0.870794	−	0.491648i	$-0.163605\pi$
$89$	13795.1			1.74159			0.870794	+	0.491648i	$0.163605\pi$
$90$	79.8154	−	1204.84i	0.00985375	−	0.148745i
$91$		−	4015.54i		−	0.484909i
$92$	855.649	−	6429.79i	0.101093	−	0.759664i
$93$	6129.21			0.708661
$94$	7503.57	+	497.080i	0.849204	+	0.0562562i
$95$			1864.22i			0.206562i
$96$	5032.47	+	1727.94i	0.546058	+	0.187494i
$97$	−7695.33			−0.817869			−0.408934	−	0.912564i	$-0.634100\pi$
$97$	−7695.33			−0.817869			−0.408934	+	0.912564i	$0.634100\pi$
$98$	403.400	−	6089.45i	0.0420034	−	0.634053i
$99$		−	5685.42i		−	0.580085i
$100$	−1982.52	−	263.826i	−0.198252	−	0.0263826i
$101$	−4743.34			−0.464988			−0.232494	−	0.972598i	$-0.574689\pi$
$101$	−4743.34			−0.464988			−0.232494	+	0.972598i	$0.574689\pi$
$102$	−158.696	−	10.5129i	−0.0152534	−	0.00101047i
$103$		−	549.159i		−	0.0517635i	−0.999665	−	0.0258818i	$-0.991761\pi$
$103$		−	549.159i		−	0.0517635i	0.999665	−	0.0258818i	$-0.00823934\pi$
$104$	1712.52	−	8516.01i	0.158332	−	0.787353i
$105$	1718.76			0.155897
$106$	1310.18	−	19777.6i	0.116606	−	1.76020i
$107$			1692.83i			0.147859i	0.997263	+	0.0739293i	$0.0235539\pi$
$107$			1692.83i			0.147859i	−0.997263	+	0.0739293i	$0.976446\pi$
$108$	−296.110	+	2225.12i	−0.0253866	+	0.190768i
$109$	−15885.9			−1.33708			−0.668542	−	0.743674i	$-0.733081\pi$
$109$	−15885.9			−1.33708			−0.668542	+	0.743674i	$0.733081\pi$
$110$	−9396.43	−	622.474i	−0.776564	−	0.0514441i
$111$			3143.76i			0.255155i
$112$	−1980.72	+	7310.30i	−0.157902	+	0.582773i
$113$	8839.42			0.692256			0.346128	−	0.938187i	$-0.387496\pi$
$113$	8839.42			0.692256			0.346128	+	0.938187i	$0.387496\pi$
$114$	229.083	−	3458.07i	0.0176272	−	0.266087i
$115$		−	4532.56i		−	0.342727i
$116$	26107.8	+	3474.32i	1.94024	+	0.258199i
$117$	3664.61			0.267705
$118$	−1999.52	−	132.460i	−0.143603	−	0.00951308i
$119$		−	226.388i		−	0.0159867i
$120$	3645.09	+	733.007i	0.253131	+	0.0509033i
$121$	−29699.2			−2.02849
$122$	−245.601	+	3707.42i	−0.0165010	+	0.249088i
$123$		−	7784.76i		−	0.514559i
$124$	−2489.60	+	18708.1i	−0.161915	+	1.21671i
$125$	−1397.54			−0.0894427
$126$	−3188.25	−	211.208i	−0.200822	−	0.0133036i
$127$			2789.62i			0.172957i	0.996254	+	0.0864784i	$0.0275614\pi$
$127$			2789.62i			0.172957i	−0.996254	+	0.0864784i	$0.972439\pi$
$128$	−7318.30	+	14658.7i	−0.446674	+	0.894697i
$129$	−7856.04			−0.472090
$130$	401.224	−	6056.60i	0.0237411	−	0.358379i
$131$			11818.8i			0.688701i	0.938841	+	0.344350i	$0.111901\pi$
$131$			11818.8i			0.688701i	−0.938841	+	0.344350i	$0.888099\pi$
$132$	17353.6	+	2309.34i	0.995957	+	0.132538i
$133$	4933.12			0.278881
$134$	12137.7	+	804.071i	0.675969	+	0.0447801i
$135$			1568.56i			0.0860663i
$136$	96.5486	−	480.116i	0.00521997	−	0.0259578i
$137$	−29908.7			−1.59352			−0.796759	−	0.604297i	$-0.793454\pi$
$137$	−29908.7			−1.59352			−0.796759	+	0.604297i	$0.793454\pi$
$138$	−556.978	+	8407.75i	−0.0292469	+	0.441491i
$139$			23947.7i			1.23947i	0.784812	+	0.619733i	$0.212759\pi$
$139$			23947.7i			1.23947i	−0.784812	+	0.619733i	$0.787241\pi$
$140$	−698.137	+	5246.17i	−0.0356192	+	0.267662i
$141$	−9768.79			−0.491363
$142$	27794.1	+	1841.25i	1.37840	+	0.0913135i
$143$		−	28580.1i		−	1.39763i
$144$	−6671.45	−	1807.63i	−0.321733	−	0.0871733i
$145$	18404.2			0.875350
$146$	2065.14	−	31173.9i	0.0968822	−	1.46246i
$147$			7927.76i			0.366873i
$148$	−9595.69	−	1276.95i	−0.438079	−	0.0582977i
$149$	−4438.67			−0.199931			−0.0999656	−	0.994991i	$-0.531873\pi$
$149$	−4438.67			−0.199931			−0.0999656	+	0.994991i	$0.531873\pi$
$150$	2592.39	+	171.735i	0.115218	+	0.00763268i
$151$		−	7753.12i		−	0.340034i	−0.985441	−	0.170017i	$-0.945618\pi$
$151$		−	7753.12i		−	0.340034i	0.985441	−	0.170017i	$-0.0543823\pi$
$152$	10462.0	+	2103.85i	0.452822	+	0.0910599i
$153$	206.604			0.00882583
$154$	−1647.20	+	24864.9i	−0.0694550	+	1.04844i
$155$			13188.0i			0.548926i
$156$	−1488.51	+	11185.5i	−0.0611651	+	0.459627i
$157$	29000.7			1.17655			0.588273	−	0.808662i	$-0.299808\pi$
$157$	29000.7			1.17655			0.588273	+	0.808662i	$0.299808\pi$
$158$	−37650.3	−	2494.17i	−1.50818	−	0.0999108i
$159$			25748.2i			1.01848i
$160$	−3717.94	+	10828.2i	−0.145232	+	0.422975i
$161$	−11994.1			−0.462718
$162$	192.750	−	2909.62i	0.00734455	−	0.110868i
$163$			14916.0i			0.561406i	0.959795	+	0.280703i	$0.0905676\pi$
$163$			14916.0i			0.561406i	−0.959795	+	0.280703i	$0.909432\pi$
$164$	23761.4	+	3162.06i	0.883454	+	0.117566i
$165$	12233.1			0.449332
$166$	37868.9	+	2508.66i	1.37425	+	0.0910386i
$167$		−	26694.7i		−	0.957178i	−0.878039	−	0.478589i	$-0.841148\pi$
$167$		−	26694.7i		−	0.957178i	0.878039	−	0.478589i	$-0.158852\pi$
$168$	1939.69	−	9645.67i	0.0687248	−	0.341754i
$169$	−10139.3			−0.355006
$170$	22.6203	−	341.459i	0.000782708	−	0.0118152i
$171$			4502.01i			0.153962i
$172$	3191.01	−	23979.0i	0.107863	−	0.810538i
$173$	41306.9			1.38016			0.690082	−	0.723731i	$-0.257574\pi$
$173$	41306.9			1.38016			0.690082	+	0.723731i	$0.257574\pi$
$174$	−34139.2	−	2261.58i	−1.12760	−	0.0746989i
$175$			3698.19i			0.120757i
$176$	−14097.5	+	52030.1i	−0.455112	+	1.67969i
$177$	2603.15			0.0830907
$178$	3647.48	−	55059.8i	0.115121	−	1.73778i
$179$			30792.3i			0.961029i	0.876987	+	0.480515i	$0.159550\pi$
$179$			30792.3i			0.961029i	−0.876987	+	0.480515i	$0.840450\pi$
$180$	−4787.70	−	637.126i	−0.147769	−	0.0196644i
$181$	−5864.01			−0.178994			−0.0894968	−	0.995987i	$-0.528526\pi$
$181$	−5864.01			−0.178994			−0.0894968	+	0.995987i	$0.528526\pi$
$182$	−16027.0	−	1061.72i	−0.483849	−	0.0320530i
$183$		−	4826.64i		−	0.144126i
$184$	−25436.7	−	5115.17i	−0.751320	−	0.151086i
$185$	−6764.31			−0.197642
$186$	1620.59	−	24463.2i	0.0468432	−	0.707111i
$187$		−	1611.29i		−	0.0460776i
$188$	3967.94	−	29817.2i	0.112266	−	0.843629i
$189$	4150.73			0.116199
$190$	7440.58	+	492.908i	0.206110	+	0.0136540i
$191$		−	69081.5i		−	1.89363i	−0.321777	−	0.946815i	$-0.604280\pi$
$191$		−	69081.5i		−	1.89363i	0.321777	−	0.946815i	$-0.395720\pi$
$192$	8227.26	−	19629.0i	0.223179	−	0.532470i
$193$	38834.2			1.04256			0.521279	−	0.853387i	$-0.325455\pi$
$193$	38834.2			1.04256			0.521279	+	0.853387i	$0.325455\pi$
$194$	−2034.67	+	30714.0i	−0.0540619	+	0.816080i
$195$			7884.99i			0.207363i
$196$	−24197.8	−	3220.14i	−0.629890	−	0.0838230i
$197$	−26569.0			−0.684608			−0.342304	−	0.939589i	$-0.611207\pi$
$197$	−26569.0			−0.684608			−0.342304	+	0.939589i	$0.611207\pi$
$198$	−22691.9	−	1503.25i	−0.578817	−	0.0383442i
$199$		−	59241.5i		−	1.49596i	−0.663721	−	0.747980i	$-0.731024\pi$
$199$		−	59241.5i		−	1.49596i	0.663721	−	0.747980i	$-0.268976\pi$
$200$	−1577.18	+	7842.99i	−0.0394295	+	0.196075i
$201$	−15801.9			−0.391126
$202$	−1254.16	+	18931.9i	−0.0307361	+	0.463971i
$203$		−	48701.4i		−	1.18182i
$204$	−83.9196	+	630.616i	−0.00201652	+	0.0151532i
$205$	16750.1			0.398576
$206$	−2191.83	−	145.200i	−0.0516503	−	0.00342162i
$207$		−	10945.9i		−	0.255454i
$208$	−33536.7	−	9086.77i	−0.775165	−	0.210031i
$209$	35110.9			0.803802
$210$	454.447	−	6860.01i	0.0103049	−	0.155556i
$211$			52946.2i			1.18924i	0.804007	+	0.594620i	$0.202698\pi$
$211$			52946.2i			1.18924i	−0.804007	+	0.594620i	$0.797302\pi$
$212$	−78591.0	−	10458.6i	−1.74864	−	0.232702i
$213$	−36184.8			−0.797566
$214$	6756.52	+	447.591i	0.147535	+	0.00977359i
$215$		−	16903.5i		−	0.365679i
$216$	8802.73	+	1770.18i	0.188673	+	0.0379411i
$217$	34898.1			0.741109
$218$	−4200.29	+	63404.6i	−0.0883825	+	1.33416i
$219$			40584.8i			0.846205i
$220$	−4968.90	+	37338.9i	−0.102663	+	0.771465i
$221$	1038.58			0.0212645
$222$	12547.6	+	831.223i	0.254597	+	0.0168660i
$223$			12221.6i			0.245764i	0.992421	+	0.122882i	$0.0392137\pi$
$223$			12221.6i			0.245764i	−0.992421	+	0.122882i	$0.960786\pi$
$224$	28653.5	+	9838.44i	0.571061	+	0.196079i
$225$	−3375.00			−0.0666667
$226$	2337.17	−	35280.3i	0.0457588	−	0.690742i
$227$			52981.1i			1.02818i	0.857736	+	0.514090i	$0.171870\pi$
$227$			52981.1i			1.02818i	−0.857736	+	0.514090i	$0.828130\pi$
$228$	−13741.5	−	1828.65i	−0.264340	−	0.0351772i
$229$	26289.4			0.501315			0.250657	−	0.968076i	$-0.419353\pi$
$229$	26289.4			0.501315			0.250657	+	0.968076i	$0.419353\pi$
$230$	−18090.6	−	1198.43i	−0.341977	−	0.0226546i
$231$		−	32371.2i		−	0.606646i
$232$	20769.9	−	103284.i	0.385885	−	1.91893i
$233$	37894.8			0.698020			0.349010	−	0.937119i	$-0.386518\pi$
$233$	37894.8			0.698020			0.349010	+	0.937119i	$0.386518\pi$
$234$	968.938	−	14626.4i	0.0176956	−	0.267120i
$235$		−	21019.1i		−	0.380608i
$236$	−1057.36	+	7945.58i	−0.0189845	+	0.142660i
$237$	49016.3			0.872658
$238$	−903.572	−	59.8579i	−0.0159518	−	0.00105674i
$239$			7490.41i			0.131132i	0.997848	+	0.0655662i	$0.0208853\pi$
$239$			7490.41i			0.131132i	−0.997848	+	0.0655662i	$0.979115\pi$
$240$	3889.39	−	14354.7i	0.0675242	−	0.249213i
$241$	76034.4			1.30911			0.654555	−	0.756014i	$-0.272856\pi$
$241$	76034.4			1.30911			0.654555	+	0.756014i	$0.272856\pi$
$242$	−7852.57	+	118537.i	−0.134085	+	2.02406i
$243$			3788.00i			0.0641500i
$244$	14732.3	+	1960.51i	0.247452	+	0.0329299i
$245$	−17057.8			−0.284179
$246$	−31071.0	−	2058.32i	−0.513434	−	0.0340128i
$247$			22631.2i			0.370948i
$248$	74010.6	+	14883.1i	1.20335	+	0.241986i
$249$	−49301.0			−0.795165
$250$	−369.516	+	5577.94i	−0.00591225	+	0.0892471i
$251$		−	40829.4i		−	0.648076i	−0.946044	−	0.324038i	$-0.894959\pi$
$251$		−	40829.4i		−	0.648076i	0.946044	−	0.324038i	$-0.105041\pi$
$252$	−1685.97	+	12669.2i	−0.0265490	+	0.199503i
$253$	−85366.5			−1.33366
$254$	11134.1	+	737.587i	0.172579	+	0.0114326i
$255$			444.541i			0.00683646i
$256$	56571.6	+	33085.0i	0.863215	+	0.504837i
$257$	−89298.5			−1.35200			−0.676002	−	0.736900i	$-0.736289\pi$
$257$	−89298.5			−1.35200			−0.676002	+	0.736900i	$0.736289\pi$
$258$	−2077.17	+	31355.5i	−0.0312056	+	0.471057i
$259$			17899.8i			0.266838i
$260$	−24067.3	−	3202.77i	−0.356025	−	0.0473783i
$261$	44445.4			0.652448
$262$	47171.8	+	3124.93i	0.687195	+	0.0455238i
$263$		−	9881.37i		−	0.142858i	−0.997446	−	0.0714292i	$-0.977244\pi$
$263$		−	9881.37i		−	0.142858i	0.997446	−	0.0714292i	$-0.0227560\pi$
$264$	13805.5	−	68651.8i	0.198082	−	0.985018i
$265$	−55401.3			−0.788911
$266$	1304.34	−	19689.3i	0.0184343	−	0.278271i
$267$			71681.5i			1.00551i
$268$	6418.50	−	48232.0i	0.0893643	−	0.671530i
$269$	106250.			1.46833			0.734163	−	0.678974i	$-0.237575\pi$
$269$	106250.			1.46833			0.734163	+	0.678974i	$0.237575\pi$
$270$	6260.51	+	414.733i	0.0858781	+	0.00568906i
$271$			64500.8i			0.878267i	0.898422	+	0.439133i	$0.144714\pi$
$271$			64500.8i			0.878267i	−0.898422	+	0.439133i	$0.855286\pi$
$272$	−1890.74	−	512.294i	−0.0255560	−	0.00692440i
$273$	20865.3			0.279963
$274$	−7907.98	+	119373.i	−0.105333	+	1.59003i
$275$			26321.4i			0.348051i
$276$	33410.2	+	4446.08i	0.438592	+	0.0583659i
$277$	−99154.8			−1.29227			−0.646136	−	0.763222i	$-0.723616\pi$
$277$	−99154.8			−1.29227			−0.646136	+	0.763222i	$0.723616\pi$
$278$	95581.5	+	6331.87i	1.23676	+	0.0819299i
$279$			31848.3i			0.409146i
$280$	20754.2	+	4173.55i	0.264722	+	0.0532340i
$281$	−53023.5			−0.671515			−0.335758	−	0.941948i	$-0.608992\pi$
$281$	−53023.5			−0.671515			−0.335758	+	0.941948i	$0.608992\pi$
$282$	−2582.90	+	38989.7i	−0.0324796	+	0.490288i
$283$			135026.i			1.68596i	0.537949	+	0.842978i	$0.319199\pi$
$283$			135026.i			1.68596i	−0.537949	+	0.842978i	$0.680801\pi$
$284$	14697.8	−	110447.i	0.182228	−	1.36935i
$285$	−9686.79			−0.119259
$286$	−114070.	−	7556.68i	−1.39457	−	0.0923844i
$287$		−	44324.4i		−	0.538120i
$288$	−8978.65	+	26149.5i	−0.108250	+	0.315267i
$289$	−83462.4			−0.999299
$290$	4866.15	−	73456.0i	0.0578615	−	0.873436i
$291$		−	39986.1i		−	0.472197i
$292$	−123877.	−	16485.0i	−1.45286	−	0.193341i
$293$	−133739.			−1.55784			−0.778922	−	0.627120i	$-0.784233\pi$
$293$	−133739.			−1.55784			−0.778922	+	0.627120i	$0.784233\pi$
$294$	31641.7	+	2096.13i	0.366071	+	0.0242507i
$295$			5601.09i			0.0643618i
$296$	−7633.78	+	37961.2i	−0.0871277	+	0.433268i
$297$	29542.3			0.334913
$298$	−1173.60	+	17715.9i	−0.0132156	+	0.199494i
$299$		−	55024.2i		−	0.615476i
$300$	1370.88	−	10301.5i	0.0152320	−	0.114461i
$301$	−44730.2			−0.493706
$302$	−30944.7	−	2049.96i	−0.339291	−	0.0224766i
$303$		−	24647.1i		−	0.268461i
$304$	11163.2	−	41200.2i	0.120793	−	0.445812i
$305$	10385.3			0.111640
$306$	54.6269	−	824.608i	0.000583396	−	0.00880653i
$307$		−	125386.i		−	1.33037i	−0.746678	−	0.665185i	$-0.768353\pi$
$307$		−	125386.i		−	1.33037i	0.746678	−	0.665185i	$-0.231647\pi$
$308$	98806.5	+	13148.7i	1.04156	+	0.138606i
$309$	2853.51			0.0298857
$310$	52636.4	+	3486.95i	0.547726	+	0.0362845i
$311$			34537.2i			0.357080i	0.983933	+	0.178540i	$0.0571375\pi$
$311$			34537.2i			0.357080i	−0.983933	+	0.178540i	$0.942863\pi$
$312$	44250.5	+	8898.52i	0.454579	+	0.0914131i
$313$	−16667.3			−0.170129			−0.0850644	−	0.996375i	$-0.527110\pi$
$313$	−16667.3			−0.170129			−0.0850644	+	0.996375i	$0.527110\pi$
$314$	7667.89	−	115749.i	0.0777708	−	1.17397i
$315$			8930.95i			0.0900071i
$316$	−19909.7	+	149612.i	−0.199385	+	1.49828i
$317$	73762.0			0.734030			0.367015	−	0.930215i	$-0.380380\pi$
$317$	73762.0			0.734030			0.367015	+	0.930215i	$0.380380\pi$
$318$	102768.	+	6807.92i	1.01625	+	0.0673225i
$319$		−	346626.i		−	3.40628i
$320$	42234.9	+	17702.2i	0.412450	+	0.172873i
$321$	−8796.21			−0.0853661
$322$	−3171.29	+	47871.5i	−0.0305861	+	0.461706i
$323$			1275.90i			0.0122296i
$324$	−11562.1	−	1538.63i	−0.110140	−	0.0146570i
$325$	−16965.8			−0.160623
$326$	59533.5	+	3943.85i	0.560178	+	0.0371095i
$327$		−	82545.6i		−	0.771966i
$328$	18903.2	−	94001.6i	0.175706	−	0.873751i
$329$	−55620.9			−0.513861
$330$	3234.47	−	48825.3i	0.0297013	−	0.448350i
$331$			122804.i			1.12088i	0.828196	+	0.560438i	$0.189367\pi$
$331$			122804.i			1.12088i	−0.828196	+	0.560438i	$0.810633\pi$
$332$	20025.4	−	150481.i	0.181679	−	1.36523i
$333$	−16335.5			−0.147314
$334$	−106545.	−	7058.19i	−0.955085	−	0.0632704i
$335$		−	34000.2i		−	0.302965i
$336$	−37985.4	−	10292.1i	−0.336464	−	0.0911648i
$337$	93476.4			0.823081			0.411540	−	0.911392i	$-0.364991\pi$
$337$	93476.4			0.823081			0.411540	+	0.911392i	$0.364991\pi$
$338$	−2680.88	+	40468.6i	−0.0234662	+	0.354230i
$339$			45931.0i			0.399674i
$340$	−1356.87	−	180.566i	−0.0117376	−	0.00156199i
$341$	248383.			2.13605
$342$	17968.7	+	1190.35i	0.153626	+	0.0101771i
$343$			116173.i			0.987457i
$344$	−94862.3	−	19076.3i	−0.801635	−	0.161204i
$345$	23551.9			0.197873
$346$	10921.7	−	164866.i	0.0912302	−	1.37715i
$347$			16526.2i			0.137251i	0.997643	+	0.0686253i	$0.0218613\pi$
$347$			16526.2i			0.137251i	−0.997643	+	0.0686253i	$0.978139\pi$
$348$	−18053.1	+	135660.i	−0.149071	+	1.12020i
$349$	−78324.9			−0.643056			−0.321528	−	0.946900i	$-0.604196\pi$
$349$	−78324.9			−0.643056			−0.321528	+	0.946900i	$0.604196\pi$
$350$	14760.4	+	977.815i	0.120493	+	0.00798216i
$351$			19041.9i			0.154560i
$352$	203938.	+	70023.8i	1.64594	+	0.565146i
$353$	−89837.2			−0.720953			−0.360476	−	0.932768i	$-0.617386\pi$
$353$	−89837.2			−0.720953			−0.360476	+	0.932768i	$0.617386\pi$
$354$	688.283	−	10389.8i	0.00549238	−	0.0829090i
$355$		−	77857.3i		−	0.617792i
$356$	−218793.	−	29116.0i	−1.72637	−	0.229738i
$357$	1176.35			0.00922995
$358$	122900.	+	8141.61i	0.958928	+	0.0635250i
$359$			152507.i			1.18332i	0.806188	+	0.591659i	$0.201527\pi$
$359$			152507.i			1.18332i	−0.806188	+	0.591659i	$0.798473\pi$
$360$	−3808.82	+	18940.5i	−0.0293890	+	0.146146i
$361$	102518.			0.786660
$362$	−1550.47	+	23404.8i	−0.0118317	+	0.178602i
$363$		−	154321.i		−	1.17115i
$364$	−8475.21	+	63687.1i	−0.0639657	+	0.480672i
$365$	−87324.7			−0.655468
$366$	−19264.3	−	1276.18i	−0.143811	−	0.00952687i
$367$			110809.i			0.822700i	0.911477	+	0.411350i	$0.134943\pi$
$367$			110809.i			0.822700i	−0.911477	+	0.411350i	$0.865057\pi$
$368$	−27141.5	+	100172.i	−0.200419	+	0.739690i
$369$	40450.8			0.297081
$370$	−1788.51	+	26998.0i	−0.0130643	+	0.197210i
$371$			146603.i			1.06511i
$372$	−97210.3	−	12936.3i	−0.702468	−	0.0934814i
$373$	−146097.			−1.05009			−0.525043	−	0.851076i	$-0.675951\pi$
$373$	−146097.			−1.05009			−0.525043	+	0.851076i	$0.675951\pi$
$374$	−6431.06	−	426.031i	−0.0459769	−	0.00304577i
$375$		−	7261.84i		−	0.0516398i
$376$	−117959.	−	23720.8i	−0.834363	−	0.167786i
$377$	223423.			1.57197
$378$	1097.47	−	16566.6i	0.00768084	−	0.115944i
$379$		−	193663.i		−	1.34824i	−0.738620	−	0.674122i	$-0.764522\pi$
$379$		−	193663.i		−	1.34824i	0.738620	−	0.674122i	$-0.235478\pi$
$380$	3934.64	−	29566.9i	0.0272482	−	0.204757i
$381$	−14495.3			−0.0998567
$382$	−275722.	−	18265.4i	−1.88949	−	0.125171i
$383$			144521.i			0.985223i	0.870249	+	0.492612i	$0.163958\pi$
$383$			144521.i			0.985223i	−0.870249	+	0.492612i	$0.836042\pi$
$384$	−76168.9	−	38027.0i	−0.516553	−	0.257887i
$385$	69651.8			0.469906
$386$	10267.9	−	154997.i	0.0689140	−	1.04028i
$387$		−	40821.2i		−	0.272561i
$388$	122049.	+	16241.8i	0.810722	+	0.107887i
$389$	−111547.			−0.737153			−0.368577	−	0.929597i	$-0.620155\pi$
$389$	−111547.			−0.737153			−0.368577	+	0.929597i	$0.620155\pi$
$390$	31471.0	+	2084.82i	0.206910	+	0.0137069i
$391$		−	3102.16i		−	0.0202913i
$392$	−19250.4	+	95728.3i	−0.125276	+	0.622971i
$393$	−61412.3			−0.397622
$394$	−7024.93	+	106043.i	−0.0452533	+	0.683111i
$395$			105466.i			0.675958i
$396$	−11999.7	+	90171.8i	−0.0765207	+	0.575016i
$397$	151266.			0.959756			0.479878	−	0.877335i	$-0.340681\pi$
$397$	151266.			0.959756			0.479878	+	0.877335i	$0.340681\pi$
$398$	−236448.	−	15663.7i	−1.49269	−	0.0988844i
$399$			25633.3i			0.161012i
$400$	30886.3	+	8368.64i	0.193040	+	0.0523040i
$401$	79502.4			0.494415			0.247207	−	0.968963i	$-0.420487\pi$
$401$	79502.4			0.494415			0.247207	+	0.968963i	$0.420487\pi$
$402$	−4178.08	+	63069.3i	−0.0258538	+	0.390271i
$403$			160098.i			0.985773i
$404$	75230.3	+	10011.3i	0.460925	+	0.0613379i
$405$	−8150.47			−0.0496904
$406$	−194380.	−	12876.8i	−1.17923	−	0.0781191i
$407$			127399.i			0.769091i
$408$	2494.76	+	501.681i	0.0149868	+	0.00301375i
$409$	294406.			1.75995			0.879975	−	0.475020i	$-0.157559\pi$
$409$	294406.			1.75995			0.879975	+	0.475020i	$0.157559\pi$
$410$	4428.80	−	66854.1i	0.0263462	−	0.397704i
$411$		−	155410.i		−	0.920018i
$412$	−1159.06	+	8709.76i	−0.00682827	+	0.0513112i
$413$	14821.6			0.0868953
$414$	−43688.0	−	2894.15i	−0.254895	−	0.0168857i
$415$		−	106079.i		−	0.615932i
$416$	−45134.8	+	131451.i	−0.260811	+	0.759587i
$417$	−124436.			−0.715607
$418$	9283.44	−	140136.i	0.0531321	−	0.802044i
$419$			250549.i			1.42713i	0.700587	+	0.713567i	$0.252921\pi$
$419$			250549.i			1.42713i	−0.700587	+	0.713567i	$0.747079\pi$
$420$	−27259.9	−	3627.63i	−0.154534	−	0.0205648i
$421$	171788.			0.969234			0.484617	−	0.874726i	$-0.338959\pi$
$421$	171788.			0.969234			0.484617	+	0.874726i	$0.338959\pi$
$422$	211322.	+	13999.2i	1.18664	+	0.0786099i
$423$		−	50760.1i		−	0.283689i
$424$	−62522.5	+	310911.i	−0.347780	+	1.72944i
$425$	−956.499			−0.00529550
$426$	−9567.39	+	144423.i	−0.0527199	+	0.795822i
$427$		−	27481.6i		−	0.150725i
$428$	3572.90	−	26848.6i	0.0195044	−	0.146566i
$429$	148506.			0.806920
$430$	−67466.2	−	4469.35i	−0.364879	−	0.0241717i
$431$		−	142972.i		−	0.769658i	−0.922988	−	0.384829i	$-0.874260\pi$
$431$		−	142972.i		−	0.769658i	0.922988	−	0.384829i	$-0.125740\pi$
$432$	9392.70	−	34665.9i	0.0503296	−	0.185752i
$433$	77884.1			0.415406			0.207703	−	0.978192i	$-0.433401\pi$
$433$	77884.1			0.415406			0.207703	+	0.978192i	$0.433401\pi$
$434$	9227.18	−	139287.i	0.0489880	−	0.739488i
$435$			95631.3i			0.505384i
$436$	251953.	+	33528.8i	1.32540	+	0.176379i
$437$	67597.7			0.353972
$438$	161984.	+	10730.8i	0.844354	+	0.0559350i
$439$			45863.6i			0.237979i	0.992895	+	0.118990i	$0.0379655\pi$
$439$			45863.6i			0.237979i	−0.992895	+	0.118990i	$0.962034\pi$
$440$	147715.	+	29704.7i	0.762992	+	0.153433i
$441$	−41193.8			−0.211814
$442$	274.604	−	4145.23i	0.00140560	−	0.0212180i
$443$		−	178266.i		−	0.908367i	−0.890908	−	0.454184i	$-0.849931\pi$
$443$		−	178266.i		−	0.908367i	0.890908	−	0.454184i	$-0.150069\pi$
$444$	6635.24	−	49860.7i	0.0336582	−	0.252925i
$445$	−154234.			−0.778862
$446$	48779.6	+	3231.44i	0.245227	+	0.0162453i
$447$		−	23064.0i		−	0.115430i
$448$	46843.8	−	111762.i	0.233397	−	0.556851i
$449$	−72533.3			−0.359786			−0.179893	−	0.983686i	$-0.557575\pi$
$449$	−72533.3			−0.359786			−0.179893	+	0.983686i	$0.557575\pi$
$450$	−892.363	+	13470.5i	−0.00440673	+	0.0665209i
$451$		−	315473.i		−	1.55099i
$452$	−140195.	−	18656.5i	−0.686207	−	0.0913174i
$453$	40286.4			0.196319
$454$	211461.	+	14008.4i	1.02593	+	0.0679637i
$455$			44895.1i			0.216858i
$456$	−10931.9	+	54362.1i	−0.0525734	+	0.261437i
$457$	−21324.1			−0.102103			−0.0510514	−	0.998696i	$-0.516257\pi$
$457$	−21324.1			−0.102103			−0.0510514	+	0.998696i	$0.516257\pi$
$458$	6951.03	−	104928.i	0.0331374	−	0.500218i
$459$			1073.55i			0.00509560i
$460$	−9566.45	+	71887.3i	−0.0452101	+	0.339732i
$461$	−24839.5			−0.116880			−0.0584401	−	0.998291i	$-0.518613\pi$
$461$	−24839.5			−0.116880			−0.0584401	+	0.998291i	$0.518613\pi$
$462$	−129202.	−	8559.08i	−0.605319	−	0.0400999i
$463$		−	64668.0i		−	0.301667i	−0.988559	−	0.150833i	$-0.951804\pi$
$463$		−	64668.0i		−	0.301667i	0.988559	−	0.150833i	$-0.0481957\pi$
$464$	−406742.	−	110207.i	−1.88922	−	0.511884i
$465$	−68526.6			−0.316923
$466$	10019.5	−	151248.i	0.0461398	−	0.696493i
$467$		−	172892.i		−	0.792761i	−0.918086	−	0.396381i	$-0.870266\pi$
$467$		−	172892.i		−	0.792761i	0.918086	−	0.396381i	$-0.129734\pi$
$468$	−58121.4	−	7734.55i	−0.265366	−	0.0353137i
$469$	−89971.7			−0.409035
$470$	−83892.5	−	5557.53i	−0.379776	−	0.0251586i
$471$			150692.i			0.679279i
$472$	31433.2	+	6321.04i	0.141093	+	0.0283730i
$473$	−318362.			−1.42298
$474$	12960.1	−	195637.i	0.0576835	−	0.870750i
$475$		−	20842.6i		−	0.0923774i
$476$	−477.816	+	3590.56i	−0.00210885	+	0.0158470i
$477$	−133792.			−0.588020
$478$	29896.1	+	1980.49i	0.130846	+	0.00866797i
$479$		−	19930.4i		−	0.0868652i	−0.999056	−	0.0434326i	$-0.986171\pi$
$479$		−	19930.4i		−	0.0868652i	0.999056	−	0.0434326i	$-0.0138294\pi$
$480$	−56264.7	−	19319.0i	−0.244205	−	0.0838497i
$481$	−82116.9			−0.354930
$482$	20103.8	−	303473.i	0.0865334	−	1.30625i
$483$		−	62323.2i		−	0.267150i
$484$	471034.	+	62683.2i	2.01077	+	0.267584i
$485$	86036.4			0.365762
$486$	15118.8	+	1001.56i	0.0640097	+	0.00424038i
$487$			110147.i			0.464426i	0.972665	+	0.232213i	$0.0745966\pi$
$487$			110147.i			0.464426i	−0.972665	+	0.232213i	$0.925403\pi$
$488$	11720.2	−	58282.0i	0.0492147	−	0.244734i
$489$	−77505.8			−0.324128
$490$	−4510.15	+	68082.1i	−0.0187845	+	0.283557i
$491$		−	164562.i		−	0.682599i	−0.939955	−	0.341300i	$-0.889133\pi$
$491$		−	164562.i		−	0.682599i	0.939955	−	0.341300i	$-0.110867\pi$
$492$	−16430.6	+	123468.i	−0.0678769	+	0.510063i
$493$	12596.1			0.0518255
$494$	90326.8	+	5983.77i	0.370137	+	0.0245200i
$495$			63564.9i			0.259422i
$496$	78971.0	−	291460.i	0.320999	−	1.18472i
$497$	−206026.			−0.834085
$498$	−13035.4	+	196773.i	−0.0525612	+	0.793426i
$499$			104374.i			0.419169i	0.977791	+	0.209585i	$0.0672112\pi$
$499$			104374.i			0.419169i	−0.977791	+	0.209585i	$0.932789\pi$
$500$	22165.3	+	2949.66i	0.0886611	+	0.0117986i
$501$	138710.			0.552627
$502$	−162960.	−	10795.5i	−0.646658	−	0.0428384i
$503$		−	177345.i		−	0.700945i	−0.936573	−	0.350472i	$-0.886021\pi$
$503$		−	177345.i		−	0.700945i	0.936573	−	0.350472i	$-0.113979\pi$
$504$	50120.4	+	10078.9i	0.197312	+	0.0396783i
$505$	53032.2			0.207949
$506$	−22571.2	+	340719.i	−0.0881565	+	1.33075i
$507$		−	52685.5i		−	0.204963i
$508$	5887.79	−	44243.9i	0.0228152	−	0.171445i
$509$	68651.6			0.264981			0.132491	−	0.991184i	$-0.457703\pi$
$509$	68651.6			0.264981			0.132491	+	0.991184i	$0.457703\pi$
$510$	1774.27	+	117.538i	0.00682151	+	0.000451896i
$511$			231079.i			0.884951i
$512$	147008.	−	217044.i	0.560792	−	0.827956i
$513$	−23393.1			−0.0888902
$514$	−23610.9	+	356413.i	−0.0893687	+	1.34905i
$515$			6139.79i			0.0231494i
$516$	124598.	+	16581.0i	0.467964	+	0.0622747i
$517$	−395874.			−1.48107
$518$	71442.4	+	4732.76i	0.266254	+	0.0176382i
$519$			214637.i			0.796838i
$520$	−19146.6	+	95211.9i	−0.0708083	+	0.352115i
$521$	−371672.			−1.36926			−0.684628	−	0.728893i	$-0.740035\pi$
$521$	−371672.			−1.36926			−0.684628	+	0.728893i	$0.740035\pi$
$522$	11751.5	−	177393.i	0.0431274	−	0.651021i
$523$		−	247920.i		−	0.906376i	−0.891415	−	0.453188i	$-0.850287\pi$
$523$		−	247920.i		−	0.906376i	0.891415	−	0.453188i	$-0.149713\pi$
$524$	24944.8	−	187448.i	0.0908484	−	0.682683i
$525$	−19216.3			−0.0697192
$526$	−39439.1	−	2612.67i	−0.142546	−	0.00944308i
$527$			9026.04i			0.0324994i
$528$	−270357.	−	73253.0i	−0.969771	−	0.262759i
$529$	115488.			0.412691
$530$	−14648.3	+	221120.i	−0.0521478	+	0.787186i
$531$			13526.4i			0.0479725i
$532$	−78240.2	−	10411.9i	−0.276444	−	0.0367879i
$533$	203342.			0.715770
$534$	286099.	+	18952.9i	1.00331	+	0.0664649i
$535$		−	18926.4i		−	0.0661243i
$536$	−190809.	−	38370.6i	−0.664154	−	0.133558i
$537$	−160002.			−0.554851
$538$	28092.8	−	424069.i	0.0970577	−	1.46511i
$539$			321268.i			1.10583i
$540$	3310.61	−	24877.6i	0.0113532	−	0.0853142i
$541$	−283935.			−0.970119			−0.485059	−	0.874481i	$-0.661202\pi$
$541$	−283935.			−0.970119			−0.485059	+	0.874481i	$0.661202\pi$
$542$	257439.	+	17054.3i	0.876346	+	0.0580543i
$543$		−	30470.3i		−	0.103342i
$544$	−2544.61	+	7410.95i	−0.00859853	+	0.0250424i
$545$	177610.			0.597962
$546$	5516.87	−	83278.8i	0.0185058	−	0.279350i
$547$			573141.i			1.91552i	0.287567	+	0.957761i	$0.407154\pi$
$547$			573141.i			1.91552i	−0.287567	+	0.957761i	$0.592846\pi$
$548$	474358.	+	63125.5i	1.57959	+	0.210205i
$549$	25080.0			0.0832113
$550$	105055.	+	6959.47i	0.347290	+	0.0230065i
$551$			274477.i			0.904071i
$552$	26579.2	−	132173.i	0.0872296	−	0.433775i
$553$	279086.			0.912615
$554$	−26216.9	+	395752.i	−0.0854204	+	1.28945i
$555$		−	35148.4i		−	0.114109i
$556$	50544.2	−	379815.i	0.163501	−	1.22864i
$557$	148550.			0.478810			0.239405	−	0.970920i	$-0.423048\pi$
$557$	148550.			0.478810			0.239405	+	0.970920i	$0.423048\pi$
$558$	127115.	+	8420.81i	0.408251	+	0.0270449i
$559$		−	205204.i		−	0.656694i
$560$	22145.2	−	81731.7i	0.0706160	−	0.260624i
$561$	8372.50			0.0266029
$562$	−14019.6	+	211630.i	−0.0443878	+	0.670047i
$563$		−	518103.i		−	1.63455i	−0.576246	−	0.817277i	$-0.695483\pi$
$563$		−	518103.i		−	1.63455i	0.576246	−	0.817277i	$-0.304517\pi$
$564$	154935.	+	20618.0i	0.487069	+	0.0648171i
$565$	−98827.7			−0.309586
$566$	538925.	+	35701.5i	1.68227	+	0.111443i
$567$			21567.8i			0.0670873i
$568$	−436934.	−	87864.9i	−1.35431	−	0.272345i
$569$	−250898.			−0.774948			−0.387474	−	0.921881i	$-0.626652\pi$
$569$	−250898.			−0.774948			−0.387474	+	0.921881i	$0.626652\pi$
$570$	−2561.22	+	38662.4i	−0.00788311	+	0.118998i
$571$		−	379446.i		−	1.16380i	−0.813261	−	0.581899i	$-0.802310\pi$
$571$		−	379446.i		−	1.16380i	0.813261	−	0.581899i	$-0.197690\pi$
$572$	−60321.2	+	453285.i	−0.184365	+	1.38541i
$573$	358958.			1.09329
$574$	−176910.	−	11719.5i	−0.536943	−	0.0355702i
$575$			50675.6i			0.153272i
$576$	101995.	+	42750.1i	0.307422	+	0.128852i
$577$	−84917.5			−0.255062			−0.127531	−	0.991835i	$-0.540705\pi$
$577$	−84917.5			−0.255062			−0.127531	+	0.991835i	$0.540705\pi$
$578$	−22067.8	+	333120.i	−0.0660546	+	0.997113i
$579$			201788.i			0.601921i
$580$	−291895.	−	38844.1i	−0.867701	−	0.115470i
$581$	−280707.			−0.831574
$582$	−159595.	−	10572.5i	−0.471164	−	0.0312127i
$583$			1.04343e6i			3.06991i
$584$	−98549.3	+	490065.i	−0.288953	+	1.43690i
$585$	−40971.6			−0.119721
$586$	−35361.2	+	533788.i	−0.102975	+	1.55444i
$587$		−	540757.i		−	1.56937i	−0.619893	−	0.784686i	$-0.712824\pi$
$587$		−	540757.i		−	1.56937i	0.619893	−	0.784686i	$-0.287176\pi$
$588$	16732.4	−	125736.i	0.0483952	−	0.363667i
$589$	−196682.			−0.566937
$590$	22355.3	+	1480.95i	0.0642210	+	0.00425438i
$591$		−	138056.i		−	0.395259i
$592$	149494.	+	40505.4i	0.426561	+	0.115577i
$593$	304664.			0.866386			0.433193	−	0.901301i	$-0.357387\pi$
$593$	304664.			0.866386			0.433193	+	0.901301i	$0.357387\pi$
$594$	7811.10	−	117911.i	0.0221380	−	0.334180i
$595$			2531.10i			0.00714948i
$596$	70398.2	+	9368.28i	0.198184	+	0.0263735i
$597$	307828.			0.863693
$598$	−219615.	−	14548.6i	−0.614130	−	0.0406835i
$599$		−	148036.i		−	0.412584i	−0.978490	−	0.206292i	$-0.933860\pi$
$599$		−	148036.i		−	0.412584i	0.978490	−	0.206292i	$-0.0661397\pi$
$600$	−40753.4	−	8195.27i	−0.113204	−	0.0227646i
$601$	−149586.			−0.414134			−0.207067	−	0.978327i	$-0.566392\pi$
$601$	−149586.			−0.414134			−0.207067	+	0.978327i	$0.566392\pi$
$602$	−11826.8	+	178530.i	−0.0326344	+	0.492626i
$603$		−	82109.0i		−	0.225817i
$604$	−16363.8	+	122966.i	−0.0448549	+	0.337063i
$605$	332047.			0.907169
$606$	−98372.9	−	6516.79i	−0.267874	−	0.0177455i
$607$		−	220755.i		−	0.599147i	−0.954073	−	0.299574i	$-0.903156\pi$
$607$		−	220755.i		−	0.599147i	0.954073	−	0.299574i	$-0.0968445\pi$
$608$	−161489.	−	55448.5i	−0.436853	−	0.149997i
$609$	253060.			0.682322
$610$	2745.91	−	41450.2i	0.00737948	−	0.111395i
$611$		−	255166.i		−	0.683504i
$612$	−3276.78	−	436.059i	−0.00874871	−	0.00116424i
$613$	−15013.9			−0.0399551			−0.0199776	−	0.999800i	$-0.506359\pi$
$613$	−15013.9			−0.0399551			−0.0199776	+	0.999800i	$0.506359\pi$
$614$	−500447.	−	33152.6i	−1.32746	−	0.0879387i
$615$			87036.3i			0.230118i
$616$	78604.8	−	390885.i	0.207151	−	1.03012i
$617$	537682.			1.41239			0.706196	−	0.708016i	$-0.250410\pi$
$617$	537682.			1.41239			0.706196	+	0.708016i	$0.250410\pi$
$618$	754.480	−	11389.1i	0.00197547	−	0.0298203i
$619$		−	22215.9i		−	0.0579806i	−0.999580	−	0.0289903i	$-0.990771\pi$
$619$		−	22215.9i		−	0.0579806i	0.999580	−	0.0289903i	$-0.00922919\pi$
$620$	27834.6	−	209163.i	0.0724104	−	0.544129i
$621$	56876.7			0.147486
$622$	137847.	+	9131.76i	0.356299	+	0.0236034i
$623$			408135.i			1.05155i
$624$	47216.2	−	174262.i	0.121261	−	0.447542i
$625$	15625.0			0.0400000
$626$	−4406.91	+	66523.6i	−0.0112457	+	0.169757i
$627$			182441.i			0.464075i
$628$	−459956.	−	61209.0i	−1.16626	−	0.155201i
$629$	−4629.59			−0.0117015
$630$	35645.7	+	2361.38i	0.0898102	+	0.00594955i
$631$			356750.i			0.895994i	0.894035	+	0.447997i	$0.147863\pi$
$631$			356750.i			0.895994i	−0.894035	+	0.447997i	$0.852137\pi$
$632$	591876.	+	119023.i	1.48182	+	0.297986i
$633$	−275116.			−0.686608
$634$	19502.9	−	294403.i	0.0485201	−	0.732425i
$635$		−	31188.9i		−	0.0773487i
$636$	54344.2	−	408371.i	0.134350	−	1.00958i
$637$	−207078.			−0.510334
$638$	−1.38347e6	−	91649.3i	−3.39883	−	0.225158i
$639$		−	188022.i		−	0.460475i
$640$	81821.1	−	163889.i	0.199759	−	0.400121i
$641$	41392.0			0.100740			0.0503698	−	0.998731i	$-0.483960\pi$
$641$	41392.0			0.100740			0.0503698	+	0.998731i	$0.483960\pi$
$642$	−2325.75	+	35107.9i	−0.00564278	+	0.0851794i
$643$		−	342725.i		−	0.828940i	−0.910063	−	0.414470i	$-0.863967\pi$
$643$		−	342725.i		−	0.828940i	0.910063	−	0.414470i	$-0.136033\pi$
$644$	190229.	+	25314.8i	0.458674	+	0.0610384i
$645$	87833.2			0.211125
$646$	5092.45	+	337.354i	0.0122029	+	0.000808389i
$647$			300662.i			0.718240i	0.933291	+	0.359120i	$0.116923\pi$
$647$			300662.i			0.718240i	−0.933291	+	0.359120i	$0.883077\pi$
$648$	−9198.12	+	45740.3i	−0.0219053	+	0.108930i
$649$	105491.			0.250453
$650$	−4485.82	+	67714.8i	−0.0106173	+	0.160272i
$651$			181336.i			0.427879i
$652$	31481.8	−	236571.i	0.0740567	−	0.556500i
$653$	127668.			0.299402			0.149701	−	0.988731i	$-0.452169\pi$
$653$	127668.			0.299402			0.149701	+	0.988731i	$0.452169\pi$
$654$	−329460.	−	21825.4i	−0.770278	−	0.0510277i
$655$		−	132138.i		−	0.307996i
$656$	−370186.	−	100302.i	−0.860226	−	0.233078i
$657$	−210885.			−0.488557
$658$	−14706.4	+	221997.i	−0.0339667	+	0.512738i
$659$		−	387877.i		−	0.893147i	−0.894747	−	0.446574i	$-0.852644\pi$
$659$		−	387877.i		−	0.893147i	0.894747	−	0.446574i	$-0.147356\pi$
$660$	−194019.	−	25819.2i	−0.445406	−	0.0592727i
$661$	116256.			0.266079			0.133040	−	0.991111i	$-0.457526\pi$
$661$	116256.			0.266079			0.133040	+	0.991111i	$0.457526\pi$
$662$	490143.	+	32469.9i	1.11842	+	0.0740910i
$663$			5396.61i			0.0122771i
$664$	−595314.	−	119714.i	−1.35024	−	0.271525i
$665$	−55154.0			−0.124719
$666$	−4319.16	+	65199.0i	−0.00973758	+	0.146992i
$667$		−	667347.i		−	1.50003i
$668$	−56342.0	+	423384.i	−0.126264	+	0.948814i
$669$	−63505.4			−0.141892
$670$	−135704.	−	8989.79i	−0.302302	−	0.0200263i
$671$		−	195597.i		−	0.434427i
$672$	−51122.0	+	148888.i	−0.113206	+	0.329702i
$673$	764966.			1.68893			0.844466	−	0.535609i	$-0.179918\pi$
$673$	764966.			1.68893			0.844466	+	0.535609i	$0.179918\pi$
$674$	24715.5	−	373088.i	0.0544064	−	0.821281i
$675$		−	17537.0i		−	0.0384900i
$676$	160812.	+	21400.1i	0.351904	+	0.0468298i
$677$	303589.			0.662382			0.331191	−	0.943564i	$-0.392550\pi$
$677$	303589.			0.662382			0.331191	+	0.943564i	$0.392550\pi$
$678$	183322.	+	12144.3i	0.398800	+	0.0264188i
$679$		−	227670.i		−	0.493818i
$680$	−1079.45	+	5367.86i	−0.00233444	+	0.0116087i
$681$	−275298.			−0.593621
$682$	65673.3	−	991357.i	0.141195	−	2.13138i
$683$		−	541205.i		−	1.16017i	−0.814557	−	0.580083i	$-0.803020\pi$
$683$		−	541205.i		−	1.16017i	0.814557	−	0.580083i	$-0.196980\pi$
$684$	9501.96	−	71402.7i	0.0203096	−	0.152617i
$685$	334390.			0.712643
$686$	463677.	+	30716.7i	0.985297	+	0.0652718i
$687$			136604.i			0.289434i
$688$	−101220.	+	373576.i	−0.213841	+	0.789226i
$689$	−672557.			−1.41674
$690$	6227.21	−	94001.5i	0.0130796	−	0.197441i
$691$			902741.i			1.89063i	0.326155	+	0.945316i	$0.394247\pi$
$691$			902741.i			1.89063i	−0.326155	+	0.945316i	$0.605753\pi$
$692$	−655136.	−	87182.6i	−1.36810	−	0.182061i
$693$	168206.			0.350247
$694$	65960.3	+	4369.59i	0.136950	+	0.00907240i
$695$		−	267744.i		−	0.554306i
$696$	536681.	+	107924.i	1.10789	+	0.222791i
$697$	11464.1			0.0235979
$698$	−20709.4	+	312614.i	−0.0425066	+	0.641650i
$699$			196907.i			0.403002i
$700$	7805.41	−	58653.9i	0.0159294	−	0.119702i
$701$	16867.4			0.0343251			0.0171625	−	0.999853i	$-0.494537\pi$
$701$	16867.4			0.0343251			0.0171625	+	0.999853i	$0.494537\pi$
$702$	76001.0	+	5034.75i	0.154222	+	0.0102165i
$703$		−	100881.i		−	0.204127i
$704$	333405.	−	795453.i	0.672708	−	1.60498i
$705$	109218.			0.219744
$706$	−23753.3	+	358563.i	−0.0476556	+	0.719376i
$707$		−	140334.i		−	0.280753i
$708$	−41286.4	−	5494.22i	−0.0823646	−	0.0109607i
$709$	231636.			0.460801			0.230400	−	0.973096i	$-0.425996\pi$
$709$	231636.			0.460801			0.230400	+	0.973096i	$0.425996\pi$
$710$	−310748.	−	20585.8i	−0.616441	−	0.0408366i
$711$			254696.i			0.503829i
$712$	−174059.	+	865560.i	−0.343350	+	1.70741i
$713$	478202.			0.940659
$714$	311.031	−	4695.10i	0.000610108	−	0.00920976i
$715$			319535.i			0.625037i
$716$	64990.5	−	488372.i	0.126772	−	0.952631i
$717$	−38921.3			−0.0757093
$718$	608695.	+	40323.5i	1.18073	+	0.0782185i
$719$		−	283759.i		−	0.548898i	−0.961602	−	0.274449i	$-0.911504\pi$
$719$		−	283759.i		−	0.548898i	0.961602	−	0.274449i	$-0.0884955\pi$
$720$	74589.1	+	20209.9i	0.143883	+	0.0389851i
$721$	16247.2			0.0312541
$722$	27106.2	−	409177.i	0.0519990	−	0.784940i
$723$			395087.i			0.755815i
$724$	93004.3	+	12376.6i	0.177430	+	0.0236116i
$725$	−205766.			−0.391469
$726$	−615935.	−	40803.1i	−1.16859	−	0.0774142i
$727$			70775.4i			0.133910i	0.997756	+	0.0669551i	$0.0213284\pi$
$727$			70775.4i			0.133910i	−0.997756	+	0.0669551i	$0.978672\pi$
$728$	251950.	+	50665.8i	0.475393	+	0.0955987i
$729$	−19683.0			−0.0370370
$730$	−23089.0	+	348535.i	−0.0433270	+	0.654034i
$731$		−	11569.0i		−	0.0216502i
$732$	−10187.1	+	76551.4i	−0.0190121	+	0.142867i
$733$	−195503.			−0.363870			−0.181935	−	0.983311i	$-0.558236\pi$
$733$	−195503.			−0.363870			−0.181935	+	0.983311i	$0.558236\pi$
$734$	442265.	+	29298.2i	0.820901	+	0.0543813i
$735$		−	88635.0i		−	0.164071i
$736$	392634.	+	134814.i	0.724824	+	0.248875i
$737$	−640362.			−1.17894
$738$	10695.4	−	161449.i	0.0196373	−	0.296431i
$739$		−	193327.i		−	0.354001i	−0.984211	−	0.177000i	$-0.943361\pi$
$739$		−	193327.i		−	0.354001i	0.984211	−	0.177000i	$-0.0566394\pi$
$740$	107283.	+	14276.8i	0.195915	+	0.0260715i
$741$	−117595.			−0.214167
$742$	585131.	+	38762.5i	1.06278	+	0.0704050i
$743$			592034.i			1.07243i	0.844082	+	0.536215i	$0.180146\pi$
$743$			592034.i			1.07243i	−0.844082	+	0.536215i	$0.819854\pi$
$744$	−77334.9	+	384571.i	−0.139711	+	0.694753i
$745$	49625.9			0.0894120
$746$	−38628.7	+	583111.i	−0.0694117	+	1.04779i
$747$		−	256176.i		−	0.459089i
$748$	−3400.79	+	25555.3i	−0.00607823	+	0.0456750i
$749$	−50083.3			−0.0892749
$750$	−28983.8	−	1920.06i	−0.0515268	−	0.00341344i
$751$			488630.i			0.866363i	0.901307	+	0.433181i	$0.142609\pi$
$751$			488630.i			0.866363i	−0.901307	+	0.433181i	$0.857391\pi$
$752$	−125865.	+	464532.i	−0.222571	+	0.821447i
$753$	212156.			0.374167
$754$	59073.8	−	891737.i	0.103909	−	1.56853i
$755$			86682.6i			0.152068i
$756$	−65831.3	−	8760.55i	−0.115183	−	0.0153281i
$757$	−123002.			−0.214645			−0.107323	−	0.994224i	$-0.534228\pi$
$757$	−123002.			−0.214645			−0.107323	+	0.994224i	$0.534228\pi$
$758$	−772959.	−	51205.3i	−1.34530	−	0.0891203i
$759$		−	443577.i		−	0.769991i
$760$	−116969.	−	23521.7i	−0.202508	−	0.0407232i
$761$	186320.			0.321729			0.160865	−	0.986976i	$-0.448572\pi$
$761$	186320.			0.321729			0.160865	+	0.986976i	$0.448572\pi$
$762$	−3832.61	+	57854.4i	−0.00660062	+	0.0996383i
$763$		−	469992.i		−	0.807313i
$764$	−145804.	+	1.09565e6i	−0.249794	+	1.87708i
$765$	−2309.90			−0.00394703
$766$	576821.	+	38212.0i	0.983069	+	0.0651242i
$767$			67995.8i			0.115582i
$768$	−171915.	+	293955.i	−0.291468	+	0.498377i
$769$	305968.			0.517396			0.258698	−	0.965958i	$-0.416707\pi$
$769$	305968.			0.517396			0.258698	+	0.965958i	$0.416707\pi$
$770$	18416.2	−	277998.i	0.0310612	−	0.468878i
$771$		−	464009.i		−	0.780580i
$772$	−615918.	−	81963.6i	−1.03345	−	0.137527i
$773$	−453241.			−0.758526			−0.379263	−	0.925289i	$-0.623822\pi$
$773$	−453241.			−0.758526			−0.379263	+	0.925289i	$0.623822\pi$
$774$	−162928.	−	10793.3i	−0.271965	−	0.0180165i
$775$		−	147446.i		−	0.245487i
$776$	97095.4	−	482835.i	0.161241	−	0.801817i
$777$	−93009.9			−0.154059
$778$	−29493.4	+	445211.i	−0.0487265	+	0.735541i
$779$			249808.i			0.411653i
$780$	16642.1	−	125057.i	0.0273539	−	0.205551i
$781$	−1.46637e6			−2.40403
$782$	−12381.5	−	820.222i	−0.0202469	−	0.00134127i
$783$			230945.i			0.376691i
$784$	376986.	+	102144.i	0.613328	+	0.166181i
$785$	−324237.			−0.526167
$786$	−16237.6	+	245112.i	−0.0262832	+	0.396752i
$787$			590772.i			0.953829i	0.878950	+	0.476915i	$0.158245\pi$
$787$			590772.i			0.953829i	−0.878950	+	0.476915i	$0.841755\pi$
$788$	421389.	+	56076.6i	0.678626	+	0.0903086i
$789$	51345.1			0.0824794
$790$	420943.	+	27885.7i	0.674480	+	0.0446815i
$791$			261519.i			0.417974i
$792$	356725.	+	71735.4i	0.568701	+	0.114362i
$793$	126075.			0.200485
$794$	39995.4	−	603742.i	0.0634408	−	0.957657i
$795$		−	287874.i		−	0.455478i
$796$	−125035.	+	939581.i	−0.197336	+	1.48289i
$797$	−709741.			−1.11734			−0.558668	−	0.829392i	$-0.688687\pi$
$797$	−709741.			−1.11734			−0.558668	+	0.829392i	$0.688687\pi$
$798$	102309.	+	6777.53i	0.160660	+	0.0106430i
$799$		−	14385.8i		−	0.0225341i
$800$	41567.8	−	121062.i	0.0649497	−	0.189160i
$801$	−372468.			−0.580529
$802$	21020.7	−	317314.i	0.0326813	−	0.493334i
$803$			1.64468e6i			2.55064i
$804$	250621.	+	33351.5i	0.387708	+	0.0515945i
$805$	134098.			0.206934
$806$	638993.	+	42330.6i	0.983617	+	0.0651605i
$807$			552089.i			0.847738i
$808$	59848.9	−	297616.i	0.0916713	−	0.455862i
$809$	165063.			0.252204			0.126102	−	0.992017i	$-0.459753\pi$
$809$	165063.			0.252204			0.126102	+	0.992017i	$0.459753\pi$
$810$	−2155.01	+	32530.6i	−0.00328458	+	0.0495817i
$811$		−	1.10477e6i		−	1.67969i	−0.542823	−	0.839847i	$-0.682644\pi$
$811$		−	1.10477e6i		−	1.67969i	0.542823	−	0.839847i	$-0.317356\pi$
$812$	−102789.	+	772414.i	−0.155897	+	1.17149i
$813$	−335156.			−0.507068
$814$	508482.	+	33684.8i	0.767409	+	0.0508377i
$815$		−	166766.i		−	0.251069i
$816$	2661.96	−	9824.56i	0.00399780	−	0.0147548i
$817$	252095.			0.377677
$818$	77842.1	−	1.17505e6i	0.116334	−	1.75610i
$819$			108419.i			0.161636i
$820$	−265660.	−	35352.9i	−0.395093	−	0.0525772i
$821$	−479717.			−0.711703			−0.355851	−	0.934543i	$-0.615809\pi$
$821$	−479717.			−0.711703			−0.355851	+	0.934543i	$0.615809\pi$
$822$	−620282.	−	41091.1i	−0.918006	−	0.0608141i
$823$			462067.i			0.682190i	0.940029	+	0.341095i	$0.110798\pi$
$823$			462067.i			0.682190i	−0.940029	+	0.341095i	$0.889202\pi$
$824$	34456.4	+	6928.99i	0.0507476	+	0.0102051i
$825$	−136770.			−0.200948
$826$	3918.90	−	59156.9i	0.00574386	−	0.0867052i
$827$			986535.i			1.44245i	0.692699	+	0.721226i	$0.256421\pi$
$827$			986535.i			1.44245i	−0.692699	+	0.721226i	$0.743579\pi$
$828$	−23102.5	+	173604.i	−0.0336976	+	0.253221i
$829$	−919939.			−1.33860			−0.669298	−	0.742994i	$-0.733405\pi$
$829$	−919939.			−1.33860			−0.669298	+	0.742994i	$0.733405\pi$
$830$	−423388.	−	28047.7i	−0.614585	−	0.0407137i
$831$		−	515223.i		−	0.746094i
$832$	512720.	+	214901.i	0.740686	+	0.310449i
$833$	−11674.6			−0.0168249
$834$	−32901.4	+	496656.i	−0.0473023	+	0.714041i
$835$			298456.i			0.428063i
$836$	−556865.	−	74105.1i	−0.796778	−	0.106032i
$837$	−165489.			−0.236220
$838$	1.00000e6	+	66246.1i	1.42401	+	0.0943349i
$839$		−	913352.i		−	1.29752i	−0.760993	−	0.648760i	$-0.775288\pi$
$839$		−	913352.i		−	1.29752i	0.760993	−	0.648760i	$-0.224712\pi$
$840$	−21686.4	+	107842.i	−0.0307347	+	0.152837i
$841$	2.00245e6			2.83119
$842$	45421.4	−	685649.i	0.0640673	−	0.967114i
$843$		−	275518.i		−	0.387699i
$844$	111748.	−	839736.i	0.156876	−	1.17885i
$845$	113361.			0.158764
$846$	−202596.	−	13421.2i	−0.283068	−	0.0187521i
$847$		−	878664.i		−	1.22477i
$848$	1.22439e6	+	331749.i	1.70267	+	0.461337i
$849$	−701618.			−0.973387
$850$	−252.902	+	3817.63i	−0.000350037	+	0.00528392i
$851$			245277.i			0.338687i
$852$	573897.	+	76371.8i	0.790597	+	0.105209i
$853$	514313.			0.706854			0.353427	−	0.935462i	$-0.385016\pi$
$853$	514313.			0.706854			0.353427	+	0.935462i	$0.385016\pi$
$854$	−109686.	−	7266.24i	−0.150396	−	0.00996309i
$855$		−	50334.0i		−	0.0688540i
$856$	−106215.	−	21359.2i	−0.144957	−	0.0291499i
$857$	−415272.			−0.565420			−0.282710	−	0.959205i	$-0.591233\pi$
$857$	−415272.			−0.565420			−0.282710	+	0.959205i	$0.591233\pi$
$858$	39265.6	−	592726.i	0.0533382	−	0.805155i
$859$			516118.i			0.699459i	0.936851	+	0.349730i	$0.113727\pi$
$859$			516118.i			0.699459i	−0.936851	+	0.349730i	$0.886273\pi$
$860$	−35676.6	+	268093.i	−0.0482377	+	0.362484i
$861$	230316.			0.310683
$862$	−570639.	−	37802.4i	−0.767975	−	0.0508751i
$863$		−	535169.i		−	0.718570i	−0.933228	−	0.359285i	$-0.883021\pi$
$863$		−	535169.i		−	0.718570i	0.933228	−	0.359285i	$-0.116979\pi$
$864$	−135877.	−	46654.4i	−0.182019	−	0.0624979i
$865$	−461826.			−0.617228
$866$	20592.9	−	310855.i	0.0274587	−	0.414498i
$867$		−	433684.i		−	0.576946i
$868$	−553490.	−	73656.0i	−0.734632	−	0.0977617i
$869$	1.98636e6			2.63038
$870$	381688.	+	25285.3i	0.504279	+	0.0334063i
$871$		−	412754.i		−	0.544071i
$872$	200439.	−	996744.i	0.263603	−	1.31084i
$873$	207774.			0.272623
$874$	17873.1	−	269799.i	0.0233979	−	0.353198i
$875$		−	41347.0i		−	0.0540042i
$876$	85658.5	−	643683.i	0.111625	−	0.838810i
$877$	70986.4			0.0922945			0.0461473	−	0.998935i	$-0.485306\pi$
$877$	70986.4			0.0922945			0.0461473	+	0.998935i	$0.485306\pi$
$878$	183053.	+	12126.5i	0.237459	+	0.0157307i
$879$		−	694930.i		−	0.899422i
$880$	157615.	−	581715.i	0.203532	−	0.751181i
$881$	−348009.			−0.448372			−0.224186	−	0.974546i	$-0.571972\pi$
$881$	−348009.			−0.448372			−0.224186	+	0.974546i	$0.571972\pi$
$882$	−10891.8	+	164415.i	−0.0140011	+	0.211351i
$883$		−	1.32985e6i		−	1.70562i	−0.522222	−	0.852810i	$-0.674897\pi$
$883$		−	1.32985e6i		−	1.70562i	0.522222	−	0.852810i	$-0.325103\pi$
$884$	−16472.0	−	2192.03i	−0.0210787	−	0.00280506i
$885$	−29104.1			−0.0371593
$886$	−711505.	−	47134.3i	−0.906381	−	0.0600439i
$887$			633096.i			0.804678i	0.915491	+	0.402339i	$0.131803\pi$
$887$			633096.i			0.804678i	−0.915491	+	0.402339i	$0.868197\pi$
$888$	−197252.	−	39666.3i	−0.250147	−	0.0503032i
$889$	−82532.4			−0.104429
$890$	−40780.1	+	615587.i	−0.0514835	+	0.777158i
$891$			153506.i			0.193362i
$892$	25795.0	−	193837.i	0.0324195	−	0.243617i
$893$	313474.			0.393096
$894$	−92054.3	−	6098.21i	−0.115178	−	0.00763005i
$895$		−	344269.i		−	0.429785i
$896$	−433685.	−	216516.i	−0.540205	−	0.269695i
$897$	285914.			0.355345
$898$	−19178.1	+	289499.i	−0.0237822	+	0.359000i
$899$			1.94171e6i			2.40251i
$900$	53528.1	+	7123.29i	0.0660841	+	0.00879418i
$901$	−37917.5			−0.0467079
$902$	−1.25913e6	−	83412.3i	−1.54760	−	0.102522i
$903$		−	232425.i		−	0.285041i
$904$	−111531.	+	554620.i	−0.136477	+	0.678670i
$905$	65561.7			0.0800484
$906$	10651.9	−	160793.i	0.0129769	−	0.195890i
$907$		−	375984.i		−	0.457041i	−0.973539	−	0.228520i	$-0.926611\pi$
$907$		−	375984.i		−	0.457041i	0.973539	−	0.228520i	$-0.0733887\pi$
$908$	111822.	−	840290.i	0.135630	−	1.01920i
$909$	128070.			0.154996
$910$	179187.	+	11870.4i	0.216384	+	0.0143345i
$911$			265425.i			0.319819i	0.987132	+	0.159910i	$0.0511203\pi$
$911$			265425.i			0.319819i	−0.987132	+	0.159910i	$0.948880\pi$
$912$	214082.	+	58005.6i	0.257390	+	0.0697397i
$913$	−1.99790e6			−2.39680
$914$	−5638.16	+	85109.7i	−0.00674909	+	0.101879i
$915$			53963.5i			0.0644552i
$916$	−416955.	−	55486.6i	−0.496934	−	0.0661298i
$917$	−349665.			−0.415828
$918$	4284.79	+	283.849i	0.00508445	+	0.000336824i
$919$			283610.i			0.335808i	0.985803	+	0.167904i	$0.0536999\pi$
$919$			283610.i			0.335808i	−0.985803	+	0.167904i	$0.946300\pi$
$920$	284391.	+	57189.4i	0.336000	+	0.0675678i
$921$	651525.			0.768090
$922$	−6567.66	+	99140.7i	−0.00772589	+	0.116625i
$923$		−	945167.i		−	1.10944i
$924$	−68322.9	+	513414.i	−0.0800244	+	0.601345i
$925$	75627.2			0.0883883
$926$	−258106.	−	17098.5i	−0.301007	−	0.0199405i
$927$			14827.3i			0.0172545i
$928$	−547407.	+	1.59427e6i	−0.635644	+	1.85126i
$929$	871065.			1.00930			0.504649	−	0.863325i	$-0.331622\pi$
$929$	871065.			1.00930			0.504649	+	0.863325i	$0.331622\pi$
$930$	−18118.7	+	273507.i	−0.0209489	+	0.316230i
$931$		−	254397.i		−	0.293503i
$932$	−601018.	−	79980.9i	−0.691920	−	0.0920777i
$933$	−179460.			−0.206160
$934$	−690057.	−	45713.4i	−0.791027	−	0.0524023i
$935$			18014.8i			0.0206065i
$936$	−46238.1	+	229932.i	−0.0527774	+	0.262451i
$937$	981541.			1.11797			0.558984	−	0.829178i	$-0.311191\pi$
$937$	981541.			1.11797			0.558984	+	0.829178i	$0.311191\pi$
$938$	−23788.9	+	359100.i	−0.0270376	+	0.408140i
$939$		−	86606.0i		−	0.0982239i
$940$	−44363.0	+	333367.i	−0.0502071	+	0.377282i
$941$	1.53969e6			1.73882			0.869409	−	0.494094i	$-0.164500\pi$
$941$	1.53969e6			1.73882			0.869409	+	0.494094i	$0.164500\pi$
$942$	601449.	+	39843.5i	0.677793	+	0.0449010i
$943$		−	607369.i		−	0.683013i
$944$	33539.9	−	123787.i	0.0376373	−	0.138909i
$945$	−46406.6			−0.0519656
$946$	−84176.0	+	1.27066e6i	−0.0940602	+	1.41987i
$947$			100610.i			0.112187i	0.998426	+	0.0560933i	$0.0178644\pi$
$947$			100610.i			0.112187i	−0.998426	+	0.0560933i	$0.982136\pi$
$948$	−777408.	−	103454.i	−0.865032	−	0.115115i
$949$	−1.06010e6			−1.17710
$950$	−83188.3	−	5510.87i	−0.0921754	−	0.00610623i
$951$			383279.i			0.423793i
$952$	14204.5	+	2856.44i	0.0156730	+	0.00315175i
$953$	−1.47750e6			−1.62683			−0.813415	−	0.581683i	$-0.802394\pi$
$953$	−1.47750e6			−1.62683			−0.813415	+	0.581683i	$0.802394\pi$
$954$	−35375.0	+	533996.i	−0.0388687	+	0.586734i
$955$			772355.i			0.846857i
$956$	15809.3	−	118799.i	0.0172980	−	0.129986i
$957$	1.80112e6			1.96662
$958$	−79547.4	−	5269.68i	−0.0866752	−	0.00574187i
$959$		−	884865.i		−	0.962143i
$960$	−91983.5	+	219459.i	−0.0998085	+	0.238128i
$961$	−467856.			−0.506600
$962$	−21712.0	+	327749.i	−0.0234612	+	0.354154i
$963$		−	45706.5i		−	0.0492862i
$964$	−1.20592e6	−	160479.i	−1.29767	−	0.172688i
$965$	−434180.			−0.466246
$966$	−248748.	−	16478.5i	−0.266566	−	0.0176589i
$967$		−	768191.i		−	0.821517i	−0.911744	−	0.410758i	$-0.865264\pi$
$967$		−	768191.i		−	0.821517i	0.911744	−	0.410758i	$-0.134736\pi$
$968$	374727.	−	1.86344e6i	0.399912	−	1.98868i
$969$	−6629.79			−0.00706077
$970$	22748.3	−	343393.i	0.0241772	−	0.364962i
$971$		−	458094.i		−	0.485866i	−0.970043	−	0.242933i	$-0.921891\pi$
$971$		−	458094.i		−	0.485866i	0.970043	−	0.242933i	$-0.0781094\pi$
$972$	7994.96	−	60078.3i	0.00846221	−	0.0635894i
$973$	−708506.			−0.748372
$974$	439626.	+	29123.4i	0.463410	+	0.0306990i
$975$		−	88156.9i		−	0.0927357i
$976$	−229519.	−	62188.2i	−0.240946	−	0.0652842i
$977$	905743.			0.948890			0.474445	−	0.880285i	$-0.342649\pi$
$977$	905743.			0.948890			0.474445	+	0.880285i	$0.342649\pi$
$978$	−20492.8	+	309345.i	−0.0214252	+	0.323419i
$979$			2.90485e6i			3.03081i
$980$	270540.	+	36002.3i	0.281695	+	0.0374868i
$981$	428919.			0.445695
$982$	−656807.	−	43510.7i	−0.681106	−	0.0451205i
$983$			776569.i			0.803661i	0.915714	+	0.401830i	$0.131626\pi$
$983$			776569.i			0.803661i	−0.915714	+	0.401830i	$0.868374\pi$
$984$	488447.	+	98223.8i	0.504460	+	0.101444i
$985$	297050.			0.306166
$986$	3330.47	−	50274.4i	0.00342572	−	0.0517122i
$987$		−	289015.i		−	0.296678i
$988$	47765.5	−	358935.i	0.0489328	−	0.367707i
$989$	−612930.			−0.626640
$990$	253704.	+	16806.8i	0.258855	+	0.0171480i
$991$		−	1.06325e6i		−	1.08265i	−0.840812	−	0.541327i	$-0.817922\pi$
$991$		−	1.06325e6i		−	1.08265i	0.840812	−	0.541327i	$-0.182078\pi$
$992$	−1.14241e6	−	392256.i	−1.16091	−	0.398608i
$993$	−638110.			−0.647138
$994$	−54474.2	+	822304.i	−0.0551338	+	0.832261i
$995$			662340.i			0.669014i
$996$	781923.	+	104055.i	0.788216	+	0.104892i
$997$	1.19772e6			1.20494			0.602470	−	0.798141i	$-0.294183\pi$
$997$	1.19772e6			1.20494			0.602470	+	0.798141i	$0.294183\pi$
$998$	416581.	+	27596.8i	0.418252	+	0.0277075i
$999$		−	84881.7i		−	0.0850517i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.5.c.a.31.9	✓	16
3.2	odd	2		180.5.c.c.91.8		16
4.3	odd	2	inner	60.5.c.a.31.10	yes	16
5.2	odd	4		300.5.f.b.199.32		32
5.3	odd	4		300.5.f.b.199.1		32
5.4	even	2		300.5.c.d.151.8		16
8.3	odd	2		960.5.e.f.511.13		16
8.5	even	2		960.5.e.f.511.8		16
12.11	even	2		180.5.c.c.91.7		16
20.3	even	4		300.5.f.b.199.31		32
20.7	even	4		300.5.f.b.199.2		32
20.19	odd	2		300.5.c.d.151.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.c.a.31.9	✓	16	1.1	even	1	trivial
60.5.c.a.31.10	yes	16	4.3	odd	2	inner
180.5.c.c.91.7		16	12.11	even	2
180.5.c.c.91.8		16	3.2	odd	2
300.5.c.d.151.7		16	20.19	odd	2
300.5.c.d.151.8		16	5.4	even	2
300.5.f.b.199.1		32	5.3	odd	4
300.5.f.b.199.2		32	20.7	even	4
300.5.f.b.199.31		32	20.3	even	4
300.5.f.b.199.32		32	5.2	odd	4
960.5.e.f.511.8		16	8.5	even	2
960.5.e.f.511.13		16	8.3	odd	2

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	60.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.264404 - 3.99125i) q^{2} +5.19615i q^{3} +(-15.8602 - 2.11060i) q^{4} -11.1803 q^{5} +(20.7392 + 1.37388i) q^{6} +29.5855i q^{7} +(-12.6174 + 62.7439i) q^{8} -27.0000 q^{9} +O(q^{10})\)	\(q+(0.264404 - 3.99125i) q^{2} +5.19615i q^{3} +(-15.8602 - 2.11060i) q^{4} -11.1803 q^{5} +(20.7392 + 1.37388i) q^{6} +29.5855i q^{7} +(-12.6174 + 62.7439i) q^{8} -27.0000 q^{9} +(-2.95612 + 44.6236i) q^{10} +210.571i q^{11} +(10.9670 - 82.4119i) q^{12} -135.726 q^{13} +(118.083 + 7.82252i) q^{14} -58.0948i q^{15} +(247.091 + 66.9491i) q^{16} -7.65200 q^{17} +(-7.13890 + 107.764i) q^{18} -166.741i q^{19} +(177.322 + 23.5973i) q^{20} -153.731 q^{21} +(840.442 + 55.6758i) q^{22} +405.405i q^{23} +(-326.027 - 65.5622i) q^{24} +125.000 q^{25} +(-35.8866 + 541.718i) q^{26} -140.296i q^{27} +(62.4433 - 469.231i) q^{28} -1646.13 q^{29} +(-231.871 - 15.3605i) q^{30} -1179.57i q^{31} +(332.543 - 968.500i) q^{32} -1094.16 q^{33} +(-2.02322 + 30.5410i) q^{34} -330.776i q^{35} +(428.225 + 56.9863i) q^{36} +605.018 q^{37} +(-665.506 - 44.0870i) q^{38} -705.255i q^{39} +(141.067 - 701.498i) q^{40} -1498.18 q^{41} +(-40.6470 + 613.578i) q^{42} +1511.90i q^{43} +(444.432 - 3339.69i) q^{44} +301.869 q^{45} +(1618.07 + 107.191i) q^{46} +1880.00i q^{47} +(-347.878 + 1283.92i) q^{48} +1525.70 q^{49} +(33.0505 - 498.906i) q^{50} -39.7609i q^{51} +(2152.65 + 286.465i) q^{52} +4955.24 q^{53} +(-559.957 - 37.0948i) q^{54} -2354.26i q^{55} +(-1856.31 - 373.293i) q^{56} +866.413 q^{57} +(-435.242 + 6570.10i) q^{58} -500.976i q^{59} +(-122.615 + 921.393i) q^{60} -928.887 q^{61} +(-4707.95 - 311.882i) q^{62} -798.809i q^{63} +(-3777.60 - 1583.34i) q^{64} +1517.47 q^{65} +(-289.300 + 4367.06i) q^{66} +3041.07i q^{67} +(121.362 + 16.1503i) q^{68} -2106.55 q^{69} +(-1320.21 - 87.4584i) q^{70} +6963.76i q^{71} +(340.671 - 1694.09i) q^{72} +7810.56 q^{73} +(159.969 - 2414.78i) q^{74} +649.519i q^{75} +(-351.925 + 2644.55i) q^{76} -6229.85 q^{77} +(-2814.85 - 186.472i) q^{78} -9433.20i q^{79} +(-2762.56 - 748.514i) q^{80} +729.000 q^{81} +(-396.124 + 5979.61i) q^{82} +9487.99i q^{83} +(2438.20 + 324.465i) q^{84} +85.5519 q^{85} +(6034.36 + 399.751i) q^{86} -8553.52i q^{87} +(-13212.1 - 2656.87i) q^{88} +13795.1 q^{89} +(79.8154 - 1204.84i) q^{90} -4015.54i q^{91} +(855.649 - 6429.79i) q^{92} +6129.21 q^{93} +(7503.57 + 497.080i) q^{94} +1864.22i q^{95} +(5032.47 + 1727.94i) q^{96} -7695.33 q^{97} +(403.400 - 6089.45i) q^{98} -5685.42i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{2} + 26 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9}+O(q^{10}) \) 16 * q - 12 * q^2 + 26 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9	\( 16 q - 12 q^{2} + 26 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9} + 50 q^{10} - 352 q^{13} - 804 q^{14} - 190 q^{16} + 324 q^{18} + 600 q^{20} + 288 q^{21} + 436 q^{22} - 1998 q^{24} + 2000 q^{25} - 852 q^{26} - 1156 q^{28} - 3456 q^{29} + 7668 q^{32} + 4772 q^{34} - 702 q^{36} + 9376 q^{37} - 1320 q^{38} + 550 q^{40} + 1248 q^{41} - 324 q^{42} - 6420 q^{44} - 1112 q^{46} - 4176 q^{48} - 3952 q^{49} - 1500 q^{50} + 12704 q^{52} - 5184 q^{53} - 486 q^{54} - 2604 q^{56} - 11232 q^{57} + 12708 q^{58} + 3150 q^{60} - 3808 q^{61} - 16152 q^{62} - 11902 q^{64} + 2400 q^{65} - 2916 q^{66} - 12312 q^{68} + 9792 q^{69} - 17100 q^{70} + 4860 q^{72} + 11040 q^{73} + 30516 q^{74} - 5160 q^{76} - 27456 q^{77} - 3600 q^{78} + 10800 q^{80} + 11664 q^{81} - 54040 q^{82} - 2052 q^{84} - 11200 q^{85} + 39768 q^{86} - 7220 q^{88} + 7584 q^{89} - 1350 q^{90} + 28848 q^{92} + 19872 q^{93} + 49776 q^{94} + 18882 q^{96} - 14496 q^{97} + 23940 q^{98}+O(q^{100}) \) 16 * q - 12 * q^2 + 26 * q^4 + 18 * q^6 - 180 * q^8 - 432 * q^9 + 50 * q^10 - 352 * q^13 - 804 * q^14 - 190 * q^16 + 324 * q^18 + 600 * q^20 + 288 * q^21 + 436 * q^22 - 1998 * q^24 + 2000 * q^25 - 852 * q^26 - 1156 * q^28 - 3456 * q^29 + 7668 * q^32 + 4772 * q^34 - 702 * q^36 + 9376 * q^37 - 1320 * q^38 + 550 * q^40 + 1248 * q^41 - 324 * q^42 - 6420 * q^44 - 1112 * q^46 - 4176 * q^48 - 3952 * q^49 - 1500 * q^50 + 12704 * q^52 - 5184 * q^53 - 486 * q^54 - 2604 * q^56 - 11232 * q^57 + 12708 * q^58 + 3150 * q^60 - 3808 * q^61 - 16152 * q^62 - 11902 * q^64 + 2400 * q^65 - 2916 * q^66 - 12312 * q^68 + 9792 * q^69 - 17100 * q^70 + 4860 * q^72 + 11040 * q^73 + 30516 * q^74 - 5160 * q^76 - 27456 * q^77 - 3600 * q^78 + 10800 * q^80 + 11664 * q^81 - 54040 * q^82 - 2052 * q^84 - 11200 * q^85 + 39768 * q^86 - 7220 * q^88 + 7584 * q^89 - 1350 * q^90 + 28848 * q^92 + 19872 * q^93 + 49776 * q^94 + 18882 * q^96 - 14496 * q^97 + 23940 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more