LMFDB - Embedded newform 78.3.f.b.31.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,3,Mod(31,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("78.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	78.f (of order $4$, degree $2$, 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:	$2.12534606201$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.564373557504.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 86x^{6} + 2523x^{4} - 28394x^{2} + 113569 $ x^8 - 86x^6 + 2523x^4 - 28394*x^2 + 113569
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.3
Root			$-5.82017 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	78.31
Dual form			78.3.f.b.73.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +1.73205 q^{3} -2.00000i q^{4} +(-6.68619 + 6.68619i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(5.62668 + 5.62668i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +1.73205 q^{3} -2.00000i q^{4} +(-6.68619 + 6.68619i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(5.62668 + 5.62668i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} -13.3724i q^{10} +(3.24201 + 3.24201i) q^{11} -3.46410i q^{12} +(-9.52361 + 8.84878i) q^{13} -11.2534 q^{14} +(-11.5808 + 11.5808i) q^{15} -4.00000 q^{16} -6.32516i q^{17} +(-3.00000 + 3.00000i) q^{18} +(18.0709 - 18.0709i) q^{19} +(13.3724 + 13.3724i) q^{20} +(9.74570 + 9.74570i) q^{21} -6.48402 q^{22} -1.41222i q^{23} +(3.46410 + 3.46410i) q^{24} -64.4104i q^{25} +(0.674835 - 18.3724i) q^{26} +5.19615 q^{27} +(11.2534 - 11.2534i) q^{28} +36.2987 q^{29} -23.1617i q^{30} +(1.74570 - 1.74570i) q^{31} +(4.00000 - 4.00000i) q^{32} +(5.61533 + 5.61533i) q^{33} +(6.32516 + 6.32516i) q^{34} -75.2422 q^{35} -6.00000i q^{36} +(21.9036 + 21.9036i) q^{37} +36.1417i q^{38} +(-16.4954 + 15.3265i) q^{39} -26.7448 q^{40} +(11.8770 - 11.8770i) q^{41} -19.4914 q^{42} +61.4729i q^{43} +(6.48402 - 6.48402i) q^{44} +(-20.0586 + 20.0586i) q^{45} +(1.41222 + 1.41222i) q^{46} +(-55.3193 - 55.3193i) q^{47} -6.92820 q^{48} +14.3191i q^{49} +(64.4104 + 64.4104i) q^{50} -10.9555i q^{51} +(17.6976 + 19.0472i) q^{52} +72.8699 q^{53} +(-5.19615 + 5.19615i) q^{54} -43.3534 q^{55} +22.5067i q^{56} +(31.2997 - 31.2997i) q^{57} +(-36.2987 + 36.2987i) q^{58} +(11.7015 + 11.7015i) q^{59} +(23.1617 + 23.1617i) q^{60} -82.0912 q^{61} +3.49141i q^{62} +(16.8801 + 16.8801i) q^{63} +8.00000i q^{64} +(4.51208 - 122.841i) q^{65} -11.2307 q^{66} +(-39.7211 + 39.7211i) q^{67} -12.6503 q^{68} -2.44604i q^{69} +(75.2422 - 75.2422i) q^{70} +(-58.0512 + 58.0512i) q^{71} +(6.00000 + 6.00000i) q^{72} +(61.8772 + 61.8772i) q^{73} -43.8073 q^{74} -111.562i q^{75} +(-36.1417 - 36.1417i) q^{76} +36.4835i q^{77} +(1.16885 - 31.8219i) q^{78} +124.369 q^{79} +(26.7448 - 26.7448i) q^{80} +9.00000 q^{81} +23.7540i q^{82} +(35.9076 - 35.9076i) q^{83} +(19.4914 - 19.4914i) q^{84} +(42.2913 + 42.2913i) q^{85} +(-61.4729 - 61.4729i) q^{86} +62.8712 q^{87} +12.9680i q^{88} +(-72.0966 - 72.0966i) q^{89} -40.1172i q^{90} +(-103.376 - 3.79708i) q^{91} -2.82445 q^{92} +(3.02365 - 3.02365i) q^{93} +110.639 q^{94} +241.651i q^{95} +(6.92820 - 6.92820i) q^{96} +(25.6429 - 25.6429i) q^{97} +(-14.3191 - 14.3191i) q^{98} +(9.72603 + 9.72603i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 4 q^{7} + 16 q^{8} + 24 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 4 * q^7 + 16 * q^8 + 24 * q^9	$ 8 q - 8 q^{2} + 4 q^{7} + 16 q^{8} + 24 q^{9} + 24 q^{11} - 36 q^{13} - 8 q^{14} - 12 q^{15} - 32 q^{16} - 24 q^{18} + 52 q^{19} + 12 q^{21} - 48 q^{22} + 32 q^{26} + 8 q^{28} - 168 q^{29} - 52 q^{31} + 32 q^{32} + 84 q^{33} + 24 q^{34} - 16 q^{37} - 48 q^{39} + 72 q^{41} - 24 q^{42} + 48 q^{44} - 48 q^{46} - 72 q^{47} + 160 q^{50} + 8 q^{52} + 144 q^{53} + 264 q^{55} - 60 q^{57} + 168 q^{58} - 48 q^{59} + 24 q^{60} - 72 q^{61} + 12 q^{63} + 48 q^{65} - 168 q^{66} - 116 q^{67} - 48 q^{68} - 432 q^{71} + 48 q^{72} - 128 q^{73} + 32 q^{74} - 104 q^{76} + 72 q^{78} + 240 q^{79} + 72 q^{81} + 144 q^{83} + 24 q^{84} - 48 q^{85} - 24 q^{86} + 192 q^{87} - 168 q^{89} - 20 q^{91} + 96 q^{92} + 12 q^{93} + 144 q^{94} + 224 q^{97} - 344 q^{98} + 72 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 + 4 * q^7 + 16 * q^8 + 24 * q^9 + 24 * q^11 - 36 * q^13 - 8 * q^14 - 12 * q^15 - 32 * q^16 - 24 * q^18 + 52 * q^19 + 12 * q^21 - 48 * q^22 + 32 * q^26 + 8 * q^28 - 168 * q^29 - 52 * q^31 + 32 * q^32 + 84 * q^33 + 24 * q^34 - 16 * q^37 - 48 * q^39 + 72 * q^41 - 24 * q^42 + 48 * q^44 - 48 * q^46 - 72 * q^47 + 160 * q^50 + 8 * q^52 + 144 * q^53 + 264 * q^55 - 60 * q^57 + 168 * q^58 - 48 * q^59 + 24 * q^60 - 72 * q^61 + 12 * q^63 + 48 * q^65 - 168 * q^66 - 116 * q^67 - 48 * q^68 - 432 * q^71 + 48 * q^72 - 128 * q^73 + 32 * q^74 - 104 * q^76 + 72 * q^78 + 240 * q^79 + 72 * q^81 + 144 * q^83 + 24 * q^84 - 48 * q^85 - 24 * q^86 + 192 * q^87 - 168 * q^89 - 20 * q^91 + 96 * q^92 + 12 * q^93 + 144 * q^94 + 224 * q^97 - 344 * q^98 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$		−	2.00000i		−	0.500000i
$5$	−6.68619	+	6.68619i	−1.33724	+	1.33724i	−0.438515	+	0.898724i	$0.644495\pi$
$5$	−6.68619	+	6.68619i	−1.33724	+	1.33724i	−0.898724	+	0.438515i	$0.855505\pi$
$6$	−1.73205	+	1.73205i	−0.288675	+	0.288675i
$7$	5.62668	+	5.62668i	0.803812	+	0.803812i	0.983689	−	0.179877i	$-0.0575700\pi$
$7$	5.62668	+	5.62668i	0.803812	+	0.803812i	−0.179877	+	0.983689i	$0.557570\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	3.00000			0.333333
$10$		−	13.3724i		−	1.33724i
$11$	3.24201	+	3.24201i	0.294728	+	0.294728i	0.838945	−	0.544217i	$-0.183173\pi$
$11$	3.24201	+	3.24201i	0.294728	+	0.294728i	−0.544217	+	0.838945i	$0.683173\pi$
$12$		−	3.46410i		−	0.288675i
$13$	−9.52361	+	8.84878i	−0.732585	+	0.680675i
$13$	−9.52361	+	8.84878i	−0.732585	+	0.680675i
$14$	−11.2534			−0.803812
$15$	−11.5808	+	11.5808i	−0.772055	+	0.772055i
$16$	−4.00000			−0.250000
$17$		−	6.32516i		−	0.372069i	−0.982543	−	0.186034i	$-0.940436\pi$
$17$		−	6.32516i		−	0.372069i	0.982543	−	0.186034i	$-0.0595635\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$	18.0709	−	18.0709i	0.951098	−	0.951098i	−0.0477605	−	0.998859i	$-0.515208\pi$
$19$	18.0709	−	18.0709i	0.951098	−	0.951098i	0.998859	+	0.0477605i	$0.0152084\pi$
$20$	13.3724	+	13.3724i	0.668619	+	0.668619i
$21$	9.74570	+	9.74570i	0.464081	+	0.464081i
$22$	−6.48402			−0.294728
$23$		−	1.41222i		−	0.0614010i	−0.999529	−	0.0307005i	$-0.990226\pi$
$23$		−	1.41222i		−	0.0614010i	0.999529	−	0.0307005i	$-0.00977381\pi$
$24$	3.46410	+	3.46410i	0.144338	+	0.144338i
$25$		−	64.4104i		−	2.57641i
$26$	0.674835	−	18.3724i	0.0259552	−	0.706630i
$27$	5.19615			0.192450
$28$	11.2534	−	11.2534i	0.401906	−	0.401906i
$29$	36.2987			1.25168			0.625840	−	0.779951i	$-0.284756\pi$
$29$	36.2987			1.25168			0.625840	+	0.779951i	$0.284756\pi$
$30$		−	23.1617i		−	0.772055i
$31$	1.74570	−	1.74570i	0.0563130	−	0.0563130i	−0.678389	−	0.734702i	$-0.737322\pi$
$31$	1.74570	−	1.74570i	0.0563130	−	0.0563130i	0.734702	+	0.678389i	$0.237322\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	5.61533	+	5.61533i	0.170161	+	0.170161i
$34$	6.32516	+	6.32516i	0.186034	+	0.186034i
$35$	−75.2422			−2.14978
$36$		−	6.00000i		−	0.166667i
$37$	21.9036	+	21.9036i	0.591990	+	0.591990i	0.938169	−	0.346179i	$-0.112521\pi$
$37$	21.9036	+	21.9036i	0.591990	+	0.591990i	−0.346179	+	0.938169i	$0.612521\pi$
$38$			36.1417i			0.951098i
$39$	−16.4954	+	15.3265i	−0.422958	+	0.392988i
$40$	−26.7448			−0.668619
$41$	11.8770	−	11.8770i	0.289683	−	0.289683i	−0.547272	−	0.836955i	$-0.684334\pi$
$41$	11.8770	−	11.8770i	0.289683	−	0.289683i	0.836955	+	0.547272i	$0.184334\pi$
$42$	−19.4914			−0.464081
$43$			61.4729i			1.42960i	0.699328	+	0.714801i	$0.253483\pi$
$43$			61.4729i			1.42960i	−0.699328	+	0.714801i	$0.746517\pi$
$44$	6.48402	−	6.48402i	0.147364	−	0.147364i
$45$	−20.0586	+	20.0586i	−0.445746	+	0.445746i
$46$	1.41222	+	1.41222i	0.0307005	+	0.0307005i
$47$	−55.3193	−	55.3193i	−1.17701	−	1.17701i	−0.980503	−	0.196504i	$-0.937041\pi$
$47$	−55.3193	−	55.3193i	−1.17701	−	1.17701i	−0.196504	−	0.980503i	$-0.562959\pi$
$48$	−6.92820			−0.144338
$49$			14.3191i			0.292228i
$50$	64.4104	+	64.4104i	1.28821	+	1.28821i
$51$		−	10.9555i		−	0.214814i
$52$	17.6976	+	19.0472i	0.340338	+	0.366293i
$53$	72.8699			1.37490			0.687452	−	0.726230i	$-0.258729\pi$
$53$	72.8699			1.37490			0.687452	+	0.726230i	$0.258729\pi$
$54$	−5.19615	+	5.19615i	−0.0962250	+	0.0962250i
$55$	−43.3534			−0.788244
$56$			22.5067i			0.401906i
$57$	31.2997	−	31.2997i	0.549117	−	0.549117i
$58$	−36.2987	+	36.2987i	−0.625840	+	0.625840i
$59$	11.7015	+	11.7015i	0.198330	+	0.198330i	0.799284	−	0.600954i	$-0.205212\pi$
$59$	11.7015	+	11.7015i	0.198330	+	0.198330i	−0.600954	+	0.799284i	$0.705212\pi$
$60$	23.1617	+	23.1617i	0.386028	+	0.386028i
$61$	−82.0912			−1.34576			−0.672879	−	0.739753i	$-0.734942\pi$
$61$	−82.0912			−1.34576			−0.672879	+	0.739753i	$0.734942\pi$
$62$			3.49141i			0.0563130i
$63$	16.8801	+	16.8801i	0.267937	+	0.267937i
$64$			8.00000i			0.125000i
$65$	4.51208	−	122.841i	0.0694166	−	1.88987i
$66$	−11.2307			−0.170161
$67$	−39.7211	+	39.7211i	−0.592853	+	0.592853i	−0.938401	−	0.345548i	$-0.887693\pi$
$67$	−39.7211	+	39.7211i	−0.592853	+	0.592853i	0.345548	+	0.938401i	$0.387693\pi$
$68$	−12.6503			−0.186034
$69$		−	2.44604i		−	0.0354499i
$70$	75.2422	−	75.2422i	1.07489	−	1.07489i
$71$	−58.0512	+	58.0512i	−0.817622	+	0.817622i	−0.985763	−	0.168141i	$-0.946224\pi$
$71$	−58.0512	+	58.0512i	−0.817622	+	0.817622i	0.168141	+	0.985763i	$0.446224\pi$
$72$	6.00000	+	6.00000i	0.0833333	+	0.0833333i
$73$	61.8772	+	61.8772i	0.847633	+	0.847633i	0.989837	−	0.142204i	$-0.0454191\pi$
$73$	61.8772	+	61.8772i	0.847633	+	0.847633i	−0.142204	+	0.989837i	$0.545419\pi$
$74$	−43.8073			−0.591990
$75$		−	111.562i		−	1.48749i
$76$	−36.1417	−	36.1417i	−0.475549	−	0.475549i
$77$			36.4835i			0.473812i
$78$	1.16885	−	31.8219i	0.0149852	−	0.407973i
$79$	124.369			1.57429			0.787143	−	0.616770i	$-0.211559\pi$
$79$	124.369			1.57429			0.787143	+	0.616770i	$0.211559\pi$
$80$	26.7448	−	26.7448i	0.334310	−	0.334310i
$81$	9.00000			0.111111
$82$			23.7540i			0.289683i
$83$	35.9076	−	35.9076i	0.432622	−	0.432622i	−0.456898	−	0.889519i	$-0.651039\pi$
$83$	35.9076	−	35.9076i	0.432622	−	0.432622i	0.889519	+	0.456898i	$0.151039\pi$
$84$	19.4914	−	19.4914i	0.232041	−	0.232041i
$85$	42.2913	+	42.2913i	0.497544	+	0.497544i
$86$	−61.4729	−	61.4729i	−0.714801	−	0.714801i
$87$	62.8712			0.722658
$88$			12.9680i			0.147364i
$89$	−72.0966	−	72.0966i	−0.810074	−	0.810074i	0.174571	−	0.984645i	$-0.444146\pi$
$89$	−72.0966	−	72.0966i	−0.810074	−	0.810074i	−0.984645	+	0.174571i	$0.944146\pi$
$90$		−	40.1172i		−	0.445746i
$91$	−103.376	−	3.79708i	−1.13600	−	0.0417262i
$92$	−2.82445			−0.0307005
$93$	3.02365	−	3.02365i	0.0325123	−	0.0325123i
$94$	110.639			1.17701
$95$			241.651i			2.54369i
$96$	6.92820	−	6.92820i	0.0721688	−	0.0721688i
$97$	25.6429	−	25.6429i	0.264360	−	0.264360i	−0.562463	−	0.826822i	$-0.690146\pi$
$97$	25.6429	−	25.6429i	0.264360	−	0.264360i	0.826822	+	0.562463i	$0.190146\pi$
$98$	−14.3191	−	14.3191i	−0.146114	−	0.146114i
$99$	9.72603	+	9.72603i	0.0982427	+	0.0982427i
$100$	−128.821			−1.28821
$101$		−	163.875i		−	1.62253i	−0.584680	−	0.811264i	$-0.698780\pi$
$101$		−	163.875i		−	1.62253i	0.584680	−	0.811264i	$-0.301220\pi$
$102$	10.9555	+	10.9555i	0.107407	+	0.107407i
$103$		−	92.6975i		−	0.899976i	−0.893035	−	0.449988i	$-0.851428\pi$
$103$		−	92.6975i		−	0.899976i	0.893035	−	0.449988i	$-0.148572\pi$
$104$	−36.7448	−	1.34967i	−0.353315	−	0.0129776i
$105$	−130.323			−1.24117
$106$	−72.8699	+	72.8699i	−0.687452	+	0.687452i
$107$	66.1931			0.618627			0.309314	−	0.950960i	$-0.399901\pi$
$107$	66.1931			0.618627			0.309314	+	0.950960i	$0.399901\pi$
$108$		−	10.3923i		−	0.0962250i
$109$	−28.3872	+	28.3872i	−0.260433	+	0.260433i	−0.825230	−	0.564797i	$-0.808954\pi$
$109$	−28.3872	+	28.3872i	−0.260433	+	0.260433i	0.564797	+	0.825230i	$0.308954\pi$
$110$	43.3534	−	43.3534i	0.394122	−	0.394122i
$111$	37.9382	+	37.9382i	0.341786	+	0.341786i
$112$	−22.5067	−	22.5067i	−0.200953	−	0.200953i
$113$	−1.67906			−0.0148590			−0.00742949	−	0.999972i	$-0.502365\pi$
$113$	−1.67906			−0.0148590			−0.00742949	+	0.999972i	$0.502365\pi$
$114$			62.5993i			0.549117i
$115$	9.44240	+	9.44240i	0.0821078	+	0.0821078i
$116$		−	72.5975i		−	0.625840i
$117$	−28.5708	+	26.5463i	−0.244195	+	0.226892i
$118$	−23.4029			−0.198330
$119$	35.5897	−	35.5897i	0.299073	−	0.299073i
$120$	−46.3233			−0.386028
$121$		−	99.9787i		−	0.826271i
$122$	82.0912	−	82.0912i	0.672879	−	0.672879i
$123$	20.5716	−	20.5716i	0.167249	−	0.167249i
$124$	−3.49141	−	3.49141i	−0.0281565	−	0.0281565i
$125$	263.505	+	263.505i	2.10804	+	2.10804i
$126$	−33.7601			−0.267937
$127$		−	11.1496i		−	0.0877922i	−0.999036	−	0.0438961i	$-0.986023\pi$
$127$		−	11.1496i		−	0.0877922i	0.999036	−	0.0438961i	$-0.0139771\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$			106.474i			0.825382i
$130$	118.329	+	127.353i	0.910225	+	0.979642i
$131$	−153.365			−1.17073			−0.585363	−	0.810771i	$-0.699048\pi$
$131$	−153.365			−1.17073			−0.585363	+	0.810771i	$0.699048\pi$
$132$	11.2307	−	11.2307i	0.0850807	−	0.0850807i
$133$	203.358			1.52901
$134$		−	79.4423i		−	0.592853i
$135$	−34.7425	+	34.7425i	−0.257352	+	0.257352i
$136$	12.6503	−	12.6503i	0.0930171	−	0.0930171i
$137$	71.5144	+	71.5144i	0.522003	+	0.522003i	0.918176	−	0.396173i	$-0.129662\pi$
$137$	71.5144	+	71.5144i	0.522003	+	0.522003i	−0.396173	+	0.918176i	$0.629662\pi$
$138$	2.44604	+	2.44604i	0.0177249	+	0.0177249i
$139$	−11.4626			−0.0824648			−0.0412324	−	0.999150i	$-0.513128\pi$
$139$	−11.4626			−0.0824648			−0.0412324	+	0.999150i	$0.513128\pi$
$140$			150.484i			1.07489i
$141$	−95.8159	−	95.8159i	−0.679545	−	0.679545i
$142$		−	116.102i		−	0.817622i
$143$	−59.5635	−	2.18782i	−0.416528	−	0.0152995i
$144$	−12.0000			−0.0833333
$145$	−242.700	+	242.700i	−1.67380	+	1.67380i
$146$	−123.754			−0.847633
$147$			24.8015i			0.168718i
$148$	43.8073	−	43.8073i	0.295995	−	0.295995i
$149$	−85.6612	+	85.6612i	−0.574907	+	0.574907i	−0.933496	−	0.358588i	$-0.883258\pi$
$149$	−85.6612	+	85.6612i	−0.574907	+	0.574907i	0.358588	+	0.933496i	$0.383258\pi$
$150$	111.562	+	111.562i	0.743747	+	0.743747i
$151$	−137.666	−	137.666i	−0.911696	−	0.911696i	0.0847101	−	0.996406i	$-0.473004\pi$
$151$	−137.666	−	137.666i	−0.911696	−	0.911696i	−0.996406	+	0.0847101i	$0.973004\pi$
$152$	72.2835			0.475549
$153$		−	18.9755i		−	0.124023i
$154$	−36.4835	−	36.4835i	−0.236906	−	0.236906i
$155$			23.3442i			0.150608i
$156$	30.6531	+	32.9908i	0.196494	+	0.211479i
$157$	−85.9128			−0.547215			−0.273608	−	0.961841i	$-0.588217\pi$
$157$	−85.9128			−0.547215			−0.273608	+	0.961841i	$0.588217\pi$
$158$	−124.369	+	124.369i	−0.787143	+	0.787143i
$159$	126.214			0.793801
$160$			53.4895i			0.334310i
$161$	7.94613	−	7.94613i	0.0493549	−	0.0493549i
$162$	−9.00000	+	9.00000i	−0.0555556	+	0.0555556i
$163$	−6.14308	−	6.14308i	−0.0376876	−	0.0376876i	0.688012	−	0.725699i	$-0.258484\pi$
$163$	−6.14308	−	6.14308i	−0.0376876	−	0.0376876i	−0.725699	+	0.688012i	$0.758484\pi$
$164$	−23.7540	−	23.7540i	−0.144842	−	0.144842i
$165$	−75.0903			−0.455093
$166$			71.8152i			0.432622i
$167$	78.9335	+	78.9335i	0.472656	+	0.472656i	0.902773	−	0.430117i	$-0.141528\pi$
$167$	78.9335	+	78.9335i	0.472656	+	0.472656i	−0.430117	+	0.902773i	$0.641528\pi$
$168$			38.9828i			0.232041i
$169$	12.3983	−	168.545i	0.0733629	−	0.997305i
$170$	−84.5826			−0.497544
$171$	54.2126	−	54.2126i	0.317033	−	0.317033i
$172$	122.946			0.714801
$173$		−	39.5270i		−	0.228480i	−0.993453	−	0.114240i	$-0.963557\pi$
$173$		−	39.5270i		−	0.228480i	0.993453	−	0.114240i	$-0.0364433\pi$
$174$	−62.8712	+	62.8712i	−0.361329	+	0.361329i
$175$	362.417	−	362.417i	2.07095	−	2.07095i
$176$	−12.9680	−	12.9680i	−0.0736820	−	0.0736820i
$177$	20.2675	+	20.2675i	0.114506	+	0.114506i
$178$	144.193			0.810074
$179$		−	121.026i		−	0.676121i	−0.941124	−	0.338060i	$-0.890229\pi$
$179$		−	121.026i		−	0.676121i	0.941124	−	0.338060i	$-0.109771\pi$
$180$	40.1172	+	40.1172i	0.222873	+	0.222873i
$181$		−	66.4761i		−	0.367271i	−0.982994	−	0.183636i	$-0.941213\pi$
$181$		−	66.4761i		−	0.367271i	0.982994	−	0.183636i	$-0.0587866\pi$
$182$	107.173	−	99.5785i	0.588861	−	0.547135i
$183$	−142.186			−0.776974
$184$	2.82445	−	2.82445i	0.0153502	−	0.0153502i
$185$	−292.904			−1.58326
$186$			6.04729i			0.0325123i
$187$	20.5062	−	20.5062i	0.109659	−	0.109659i
$188$	−110.639	+	110.639i	−0.588504	+	0.588504i
$189$	29.2371	+	29.2371i	0.154694	+	0.154694i
$190$	−241.651	−	241.651i	−1.27185	−	1.27185i
$191$	172.437			0.902812			0.451406	−	0.892319i	$-0.350923\pi$
$191$	172.437			0.902812			0.451406	+	0.892319i	$0.350923\pi$
$192$			13.8564i			0.0721688i
$193$	−149.980	−	149.980i	−0.777099	−	0.777099i	0.202238	−	0.979336i	$-0.435179\pi$
$193$	−149.980	−	149.980i	−0.777099	−	0.777099i	−0.979336	+	0.202238i	$0.935179\pi$
$194$			51.2857i			0.264360i
$195$	7.81515	−	212.767i	0.0400777	−	1.09112i
$196$	28.6383			0.146114
$197$	69.7219	−	69.7219i	0.353918	−	0.353918i	−0.507647	−	0.861565i	$-0.669485\pi$
$197$	69.7219	−	69.7219i	0.353918	−	0.353918i	0.861565	+	0.507647i	$0.169485\pi$
$198$	−19.4521			−0.0982427
$199$			130.571i			0.656133i	0.944655	+	0.328067i	$0.106397\pi$
$199$			130.571i			0.656133i	−0.944655	+	0.328067i	$0.893603\pi$
$200$	128.821	−	128.821i	0.644104	−	0.644104i
$201$	−68.7990	+	68.7990i	−0.342284	+	0.342284i
$202$	163.875	+	163.875i	0.811264	+	0.811264i
$203$	204.241	+	204.241i	1.00612	+	1.00612i
$204$	−21.9110			−0.107407
$205$			158.824i			0.774751i
$206$	92.6975	+	92.6975i	0.449988	+	0.449988i
$207$		−	4.23667i		−	0.0204670i
$208$	38.0944	−	35.3951i	0.183146	−	0.170169i
$209$	117.172			0.560631
$210$	130.323	−	130.323i	0.620587	−	0.620587i
$211$	−136.464			−0.646750			−0.323375	−	0.946271i	$-0.604817\pi$
$211$	−136.464			−0.646750			−0.323375	+	0.946271i	$0.604817\pi$
$212$		−	145.740i		−	0.687452i
$213$	−100.548	+	100.548i	−0.472055	+	0.472055i
$214$	−66.1931	+	66.1931i	−0.309314	+	0.309314i
$215$	−411.020	−	411.020i	−1.91172	−	1.91172i
$216$	10.3923	+	10.3923i	0.0481125	+	0.0481125i
$217$	19.6450			0.0905301
$218$		−	56.7743i		−	0.260433i
$219$	107.174	+	107.174i	0.489381	+	0.489381i
$220$			86.7068i			0.394122i
$221$	55.9700	+	60.2384i	0.253258	+	0.272572i
$222$	−75.8764			−0.341786
$223$	41.8068	−	41.8068i	0.187474	−	0.187474i	−0.607129	−	0.794603i	$-0.707679\pi$
$223$	41.8068	−	41.8068i	0.187474	−	0.187474i	0.794603	+	0.607129i	$0.207679\pi$
$224$	45.0135			0.200953
$225$		−	193.231i		−	0.858805i
$226$	1.67906	−	1.67906i	0.00742949	−	0.00742949i
$227$	−84.8089	+	84.8089i	−0.373607	+	0.373607i	−0.868789	−	0.495182i	$-0.835101\pi$
$227$	−84.8089	+	84.8089i	−0.373607	+	0.373607i	0.495182	+	0.868789i	$0.335101\pi$
$228$	−62.5993	−	62.5993i	−0.274558	−	0.274558i
$229$	−134.372	−	134.372i	−0.586777	−	0.586777i	0.349980	−	0.936757i	$-0.386188\pi$
$229$	−134.372	−	134.372i	−0.586777	−	0.586777i	−0.936757	+	0.349980i	$0.886188\pi$
$230$	−18.8848			−0.0821078
$231$			63.1913i			0.273556i
$232$	72.5975	+	72.5975i	0.312920	+	0.312920i
$233$		−	127.160i		−	0.545752i	−0.962049	−	0.272876i	$-0.912025\pi$
$233$		−	127.160i		−	0.545752i	0.962049	−	0.272876i	$-0.0879748\pi$
$234$	2.02451	−	55.1172i	0.00865173	−	0.235543i
$235$	739.752			3.14788
$236$	23.4029	−	23.4029i	0.0991649	−	0.0991649i
$237$	215.413			0.908914
$238$			71.1794i			0.299073i
$239$	−49.1093	+	49.1093i	−0.205478	+	0.205478i	−0.802342	−	0.596864i	$-0.796413\pi$
$239$	−49.1093	+	49.1093i	−0.205478	+	0.205478i	0.596864	+	0.802342i	$0.296413\pi$
$240$	46.3233	−	46.3233i	0.193014	−	0.193014i
$241$	−235.567	−	235.567i	−0.977456	−	0.977456i	0.0222957	−	0.999751i	$-0.492902\pi$
$241$	−235.567	−	235.567i	−0.977456	−	0.977456i	−0.999751	+	0.0222957i	$0.992902\pi$
$242$	99.9787	+	99.9787i	0.413135	+	0.413135i
$243$	15.5885			0.0641500
$244$			164.182i			0.672879i
$245$	−95.7406	−	95.7406i	−0.390778	−	0.390778i
$246$			41.1432i			0.167249i
$247$	−12.1949	+	332.005i	−0.0493719	+	1.34415i
$248$	6.98281			0.0281565
$249$	62.1938	−	62.1938i	0.249774	−	0.249774i
$250$	−527.011			−2.10804
$251$			284.858i			1.13489i	0.823411	+	0.567445i	$0.192068\pi$
$251$			284.858i			1.13489i	−0.823411	+	0.567445i	$0.807932\pi$
$252$	33.7601	−	33.7601i	0.133969	−	0.133969i
$253$	4.57844	−	4.57844i	0.0180966	−	0.0180966i
$254$	11.1496	+	11.1496i	0.0438961	+	0.0438961i
$255$	73.2506	+	73.2506i	0.287257	+	0.287257i
$256$	16.0000			0.0625000
$257$			308.122i			1.19892i	0.800405	+	0.599459i	$0.204618\pi$
$257$			308.122i			1.19892i	−0.800405	+	0.599459i	$0.795382\pi$
$258$	−106.474	−	106.474i	−0.412691	−	0.412691i
$259$			246.490i			0.951697i
$260$	−245.683	−	9.02416i	−0.944933	−	0.0347083i
$261$	108.896			0.417227
$262$	153.365	−	153.365i	0.585363	−	0.585363i
$263$	−353.459			−1.34395			−0.671976	−	0.740573i	$-0.734554\pi$
$263$	−353.459			−1.34395			−0.671976	+	0.740573i	$0.734554\pi$
$264$			22.4613i			0.0850807i
$265$	−487.222	+	487.222i	−1.83857	+	1.83857i
$266$	−203.358	+	203.358i	−0.764504	+	0.764504i
$267$	−124.875	−	124.875i	−0.467696	−	0.467696i
$268$	79.4423	+	79.4423i	0.296426	+	0.296426i
$269$	244.784			0.909979			0.454989	−	0.890497i	$-0.349643\pi$
$269$	244.784			0.909979			0.454989	+	0.890497i	$0.349643\pi$
$270$		−	69.4850i		−	0.257352i
$271$	9.62666	+	9.62666i	0.0355227	+	0.0355227i	0.724645	−	0.689122i	$-0.242004\pi$
$271$	9.62666	+	9.62666i	0.0355227	+	0.0355227i	−0.689122	+	0.724645i	$0.742004\pi$
$272$			25.3007i			0.0930171i
$273$	−179.052	−	6.57674i	−0.655867	−	0.0240906i
$274$	−143.029			−0.522003
$275$	208.819	−	208.819i	0.759342	−	0.759342i
$276$	−4.89208			−0.0177249
$277$			423.145i			1.52760i	0.645454	+	0.763800i	$0.276668\pi$
$277$			423.145i			1.52760i	−0.645454	+	0.763800i	$0.723332\pi$
$278$	11.4626	−	11.4626i	0.0412324	−	0.0412324i
$279$	5.23711	−	5.23711i	0.0187710	−	0.0187710i
$280$	−150.484	−	150.484i	−0.537444	−	0.537444i
$281$	−70.4865	−	70.4865i	−0.250842	−	0.250842i	0.570474	−	0.821316i	$-0.306760\pi$
$281$	−70.4865	−	70.4865i	−0.250842	−	0.250842i	−0.821316	+	0.570474i	$0.806760\pi$
$282$	191.632			0.679545
$283$			32.5791i			0.115120i	0.998342	+	0.0575602i	$0.0183321\pi$
$283$			32.5791i			0.115120i	−0.998342	+	0.0575602i	$0.981668\pi$
$284$	116.102	+	116.102i	0.408811	+	0.408811i
$285$			418.551i			1.46860i
$286$	61.7513	−	57.3756i	0.215914	−	0.200614i
$287$	133.656			0.465702
$288$	12.0000	−	12.0000i	0.0416667	−	0.0416667i
$289$	248.992			0.861565
$290$		−	485.401i		−	1.67380i
$291$	44.4148	−	44.4148i	0.152628	−	0.152628i
$292$	123.754	−	123.754i	0.423816	−	0.423816i
$293$	105.166	+	105.166i	0.358930	+	0.358930i	0.863418	−	0.504488i	$-0.168319\pi$
$293$	105.166	+	105.166i	0.358930	+	0.358930i	−0.504488	+	0.863418i	$0.668319\pi$
$294$	−24.8015	−	24.8015i	−0.0843588	−	0.0843588i
$295$	−156.476			−0.530428
$296$			87.6145i			0.295995i
$297$	16.8460	+	16.8460i	0.0567205	+	0.0567205i
$298$		−	171.322i		−	0.574907i
$299$	12.4964	+	13.4495i	0.0417941	+	0.0449815i
$300$	−223.124			−0.743747
$301$	−345.889	+	345.889i	−1.14913	+	1.14913i
$302$	275.332			0.911696
$303$		−	283.840i		−	0.936767i
$304$	−72.2835	+	72.2835i	−0.237775	+	0.237775i
$305$	548.878	−	548.878i	1.79960	−	1.79960i
$306$	18.9755	+	18.9755i	0.0620114	+	0.0620114i
$307$	−113.461	−	113.461i	−0.369579	−	0.369579i	0.497744	−	0.867324i	$-0.334162\pi$
$307$	−113.461	−	113.461i	−0.369579	−	0.369579i	−0.867324	+	0.497744i	$0.834162\pi$
$308$	72.9671			0.236906
$309$		−	160.557i		−	0.519601i
$310$	−23.3442	−	23.3442i	−0.0753039	−	0.0753039i
$311$			121.466i			0.390565i	0.980747	+	0.195283i	$0.0625624\pi$
$311$			121.466i			0.390565i	−0.980747	+	0.195283i	$0.937438\pi$
$312$	−63.6438	−	2.33770i	−0.203987	−	0.00749262i
$313$	337.489			1.07824			0.539120	−	0.842229i	$-0.318757\pi$
$313$	337.489			1.07824			0.539120	+	0.842229i	$0.318757\pi$
$314$	85.9128	−	85.9128i	0.273608	−	0.273608i
$315$	−225.727			−0.716592
$316$		−	248.737i		−	0.787143i
$317$	−68.6684	+	68.6684i	−0.216620	+	0.216620i	−0.807072	−	0.590453i	$-0.798949\pi$
$317$	−68.6684	+	68.6684i	−0.216620	+	0.216620i	0.590453	+	0.807072i	$0.298949\pi$
$318$	−126.214	+	126.214i	−0.396900	+	0.396900i
$319$	117.681	+	117.681i	0.368905	+	0.368905i
$320$	−53.4895	−	53.4895i	−0.167155	−	0.167155i
$321$	114.650			0.357165
$322$			15.8923i			0.0493549i
$323$	−114.301	−	114.301i	−0.353874	−	0.353874i
$324$		−	18.0000i		−	0.0555556i
$325$	569.953	+	613.419i	1.75370	+	1.88744i
$326$	12.2862			0.0376876
$327$	−49.1680	+	49.1680i	−0.150361	+	0.150361i
$328$	47.5080			0.144842
$329$		−	622.529i		−	1.89218i
$330$	75.0903	−	75.0903i	0.227546	−	0.227546i
$331$	−411.309	+	411.309i	−1.24262	+	1.24262i	−0.283716	+	0.958908i	$0.591567\pi$
$331$	−411.309	+	411.309i	−1.24262	+	1.24262i	−0.958908	+	0.283716i	$0.908433\pi$
$332$	−71.8152	−	71.8152i	−0.216311	−	0.216311i
$333$	65.7109	+	65.7109i	0.197330	+	0.197330i
$334$	−157.867			−0.472656
$335$		−	531.166i		−	1.58557i
$336$	−38.9828	−	38.9828i	−0.116020	−	0.116020i
$337$		−	599.641i		−	1.77935i	−0.456595	−	0.889675i	$-0.650931\pi$
$337$		−	599.641i		−	1.77935i	0.456595	−	0.889675i	$-0.349069\pi$
$338$	156.146	+	180.943i	0.461971	+	0.535334i
$339$	−2.90822			−0.00857883
$340$	84.5826	−	84.5826i	0.248772	−	0.248772i
$341$	11.3192			0.0331940
$342$			108.425i			0.317033i
$343$	195.138	−	195.138i	0.568916	−	0.568916i
$344$	−122.946	+	122.946i	−0.357401	+	0.357401i
$345$	16.3547	+	16.3547i	0.0474050	+	0.0474050i
$346$	39.5270	+	39.5270i	0.114240	+	0.114240i
$347$	29.0199			0.0836309			0.0418154	−	0.999125i	$-0.486686\pi$
$347$	29.0199			0.0836309			0.0418154	+	0.999125i	$0.486686\pi$
$348$		−	125.742i		−	0.361329i
$349$	−181.409	−	181.409i	−0.519796	−	0.519796i	0.397714	−	0.917510i	$-0.369804\pi$
$349$	−181.409	−	181.409i	−0.519796	−	0.519796i	−0.917510	+	0.397714i	$0.869804\pi$
$350$			724.834i			2.07095i
$351$	−49.4861	+	45.9796i	−0.140986	+	0.130996i
$352$	25.9361			0.0736820
$353$	237.844	−	237.844i	0.673779	−	0.673779i	−0.284806	−	0.958585i	$-0.591929\pi$
$353$	237.844	−	237.844i	0.673779	−	0.673779i	0.958585	+	0.284806i	$0.0919291\pi$
$354$	−40.5350			−0.114506
$355$		−	776.283i		−	2.18671i
$356$	−144.193	+	144.193i	−0.405037	+	0.405037i
$357$	61.6432	−	61.6432i	0.172670	−	0.172670i
$358$	121.026	+	121.026i	0.338060	+	0.338060i
$359$	−410.597	−	410.597i	−1.14372	−	1.14372i	−0.987763	−	0.155961i	$-0.950153\pi$
$359$	−410.597	−	410.597i	−1.14372	−	1.14372i	−0.155961	−	0.987763i	$-0.549847\pi$
$360$	−80.2343			−0.222873
$361$		−	292.113i		−	0.809176i
$362$	66.4761	+	66.4761i	0.183636	+	0.183636i
$363$		−	173.168i		−	0.477048i
$364$	−7.59417	+	206.751i	−0.0208631	+	0.567998i
$365$	−827.446			−2.26697
$366$	142.186	−	142.186i	0.388487	−	0.388487i
$367$	−181.634			−0.494915			−0.247457	−	0.968899i	$-0.579595\pi$
$367$	−181.634			−0.494915			−0.247457	+	0.968899i	$0.579595\pi$
$368$			5.64889i			0.0153502i
$369$	35.6310	−	35.6310i	0.0965610	−	0.0965610i
$370$	292.904	−	292.904i	0.791632	−	0.791632i
$371$	410.016	+	410.016i	1.10516	+	1.10516i
$372$	−6.04729	−	6.04729i	−0.0162562	−	0.0162562i
$373$	452.204			1.21234			0.606172	−	0.795334i	$-0.292704\pi$
$373$	452.204			1.21234			0.606172	+	0.795334i	$0.292704\pi$
$374$			41.0125i			0.109659i
$375$	456.405	+	456.405i	1.21708	+	1.21708i
$376$		−	221.277i		−	0.588504i
$377$	−345.695	+	321.199i	−0.916963	+	0.851988i
$378$	−58.4742			−0.154694
$379$	95.5018	−	95.5018i	0.251984	−	0.251984i	−0.569800	−	0.821784i	$-0.692979\pi$
$379$	95.5018	−	95.5018i	0.251984	−	0.251984i	0.821784	+	0.569800i	$0.192979\pi$
$380$	483.301			1.27185
$381$		−	19.3117i		−	0.0506869i
$382$	−172.437	+	172.437i	−0.451406	+	0.451406i
$383$	−356.616	+	356.616i	−0.931113	+	0.931113i	−0.997776	−	0.0666626i	$-0.978765\pi$
$383$	−356.616	+	356.616i	−0.931113	+	0.931113i	0.0666626	+	0.997776i	$0.478765\pi$
$384$	−13.8564	−	13.8564i	−0.0360844	−	0.0360844i
$385$	−243.936	−	243.936i	−0.633600	−	0.633600i
$386$	299.960			0.777099
$387$			184.419i			0.476534i
$388$	−51.2857	−	51.2857i	−0.132180	−	0.132180i
$389$			250.752i			0.644606i	0.946637	+	0.322303i	$0.104457\pi$
$389$			250.752i			0.644606i	−0.946637	+	0.322303i	$0.895543\pi$
$390$	204.952	+	220.583i	0.525519	+	0.565596i
$391$	−8.93254			−0.0228454
$392$	−28.6383	+	28.6383i	−0.0730569	+	0.0730569i
$393$	−265.636			−0.675919
$394$			139.444i			0.353918i
$395$	−831.553	+	831.553i	−2.10520	+	2.10520i
$396$	19.4521	−	19.4521i	0.0491214	−	0.0491214i
$397$	−265.933	−	265.933i	−0.669857	−	0.669857i	0.287826	−	0.957683i	$-0.407068\pi$
$397$	−265.933	−	265.933i	−0.669857	−	0.669857i	−0.957683	+	0.287826i	$0.907068\pi$
$398$	−130.571	−	130.571i	−0.328067	−	0.328067i
$399$	352.227			0.882773
$400$			257.641i			0.644104i
$401$	132.498	+	132.498i	0.330419	+	0.330419i	0.852746	−	0.522326i	$-0.174936\pi$
$401$	132.498	+	132.498i	0.330419	+	0.330419i	−0.522326	+	0.852746i	$0.674936\pi$
$402$		−	137.598i		−	0.342284i
$403$	−1.17806	+	32.0727i	−0.00292323	+	0.0795849i
$404$	−327.751			−0.811264
$405$	−60.1757	+	60.1757i	−0.148582	+	0.148582i
$406$	−408.483			−1.00612
$407$			142.024i			0.348952i
$408$	21.9110	−	21.9110i	0.0537035	−	0.0537035i
$409$	239.333	−	239.333i	0.585165	−	0.585165i	−0.351153	−	0.936318i	$-0.614210\pi$
$409$	239.333	−	239.333i	0.585165	−	0.585165i	0.936318	+	0.351153i	$0.114210\pi$
$410$	−158.824	−	158.824i	−0.387376	−	0.387376i
$411$	123.867	+	123.867i	0.301378	+	0.301378i
$412$	−185.395			−0.449988
$413$			131.681i			0.318840i
$414$	4.23667	+	4.23667i	0.0102335	+	0.0102335i
$415$			480.170i			1.15704i
$416$	−2.69934	+	73.4895i	−0.00648880	+	0.176658i
$417$	−19.8538			−0.0476111
$418$	−117.172	+	117.172i	−0.280315	+	0.280315i
$419$	573.772			1.36939			0.684693	−	0.728832i	$-0.259936\pi$
$419$	573.772			1.36939			0.684693	+	0.728832i	$0.259936\pi$
$420$			260.647i			0.620587i
$421$	362.028	−	362.028i	0.859924	−	0.859924i	−0.131405	−	0.991329i	$-0.541949\pi$
$421$	362.028	−	362.028i	0.859924	−	0.859924i	0.991329	+	0.131405i	$0.0419488\pi$
$422$	136.464	−	136.464i	0.323375	−	0.323375i
$423$	−165.958	−	165.958i	−0.392336	−	0.392336i
$424$	145.740	+	145.740i	0.343726	+	0.343726i
$425$	−407.406			−0.958603
$426$		−	201.095i		−	0.472055i
$427$	−461.901	−	461.901i	−1.08174	−	1.08174i
$428$		−	132.386i		−	0.309314i
$429$	−103.167	−	3.78942i	−0.240482	−	0.00883314i
$430$	822.040			1.91172
$431$	568.781	−	568.781i	1.31968	−	1.31968i	0.405650	−	0.914028i	$-0.367045\pi$
$431$	568.781	−	568.781i	1.31968	−	1.31968i	0.914028	−	0.405650i	$-0.132955\pi$
$432$	−20.7846			−0.0481125
$433$		−	1.71126i		−	0.00395211i	−0.999998	−	0.00197606i	$-0.999371\pi$
$433$		−	1.71126i		−	0.00395211i	0.999998	−	0.00197606i	$-0.000628999\pi$
$434$	−19.6450	+	19.6450i	−0.0452651	+	0.0452651i
$435$	−420.369	+	420.369i	−0.966366	+	0.966366i
$436$	56.7743	+	56.7743i	0.130216	+	0.130216i
$437$	−25.5201	−	25.5201i	−0.0583984	−	0.0583984i
$438$	−214.349			−0.489381
$439$			592.080i			1.34870i	0.738411	+	0.674351i	$0.235576\pi$
$439$			592.080i			1.34870i	−0.738411	+	0.674351i	$0.764424\pi$
$440$	−86.7068	−	86.7068i	−0.197061	−	0.197061i
$441$			42.9574i			0.0974092i
$442$	−116.208	−	4.26844i	−0.262915	−	0.00965711i
$443$	−120.401			−0.271785			−0.135893	−	0.990724i	$-0.543390\pi$
$443$	−120.401			−0.271785			−0.135893	+	0.990724i	$0.543390\pi$
$444$	75.8764	−	75.8764i	0.170893	−	0.170893i
$445$	964.103			2.16652
$446$			83.6135i			0.187474i
$447$	−148.370	+	148.370i	−0.331923	+	0.331923i
$448$	−45.0135	+	45.0135i	−0.100477	+	0.100477i
$449$	431.341	+	431.341i	0.960670	+	0.960670i	0.999255	−	0.0385850i	$-0.0122850\pi$
$449$	431.341	+	431.341i	0.960670	+	0.960670i	−0.0385850	+	0.999255i	$0.512285\pi$
$450$	193.231	+	193.231i	0.429402	+	0.429402i
$451$	77.0108			0.170756
$452$			3.35813i			0.00742949i
$453$	−238.445	−	238.445i	−0.526368	−	0.526368i
$454$		−	169.618i		−	0.373607i
$455$	716.577	−	665.801i	1.57490	−	1.46330i
$456$	125.199			0.274558
$457$	102.228	−	102.228i	0.223694	−	0.223694i	−0.586358	−	0.810052i	$-0.699439\pi$
$457$	102.228	−	102.228i	0.223694	−	0.223694i	0.810052	+	0.586358i	$0.199439\pi$
$458$	268.744			0.586777
$459$		−	32.8665i		−	0.0716046i
$460$	18.8848	−	18.8848i	0.0410539	−	0.0410539i
$461$	146.196	−	146.196i	0.317128	−	0.317128i	−0.530535	−	0.847663i	$-0.678009\pi$
$461$	146.196	−	146.196i	0.317128	−	0.317128i	0.847663	+	0.530535i	$0.178009\pi$
$462$	−63.1913	−	63.1913i	−0.136778	−	0.136778i
$463$	221.783	+	221.783i	0.479013	+	0.479013i	0.904816	−	0.425803i	$-0.140008\pi$
$463$	221.783	+	221.783i	0.479013	+	0.479013i	−0.425803	+	0.904816i	$0.640008\pi$
$464$	−145.195			−0.312920
$465$			40.4334i			0.0869535i
$466$	127.160	+	127.160i	0.272876	+	0.272876i
$467$			119.016i			0.254852i	0.991848	+	0.127426i	$0.0406716\pi$
$467$			119.016i			0.254852i	−0.991848	+	0.127426i	$0.959328\pi$
$468$	53.0927	+	57.1417i	0.113446	+	0.122098i
$469$	−446.996			−0.953084
$470$	−739.752	+	739.752i	−1.57394	+	1.57394i
$471$	−148.805			−0.315935
$472$			46.8058i			0.0991649i
$473$	−199.296	+	199.296i	−0.421344	+	0.421344i
$474$	−215.413	+	215.413i	−0.454457	+	0.454457i
$475$	−1163.95	−	1163.95i	−2.45042	−	2.45042i
$476$	−71.1794	−	71.1794i	−0.149537	−	0.149537i
$477$	218.610			0.458301
$478$		−	98.2186i		−	0.205478i
$479$	−53.4327	−	53.4327i	−0.111550	−	0.111550i	0.649128	−	0.760679i	$-0.275134\pi$
$479$	−53.4327	−	53.4327i	−0.111550	−	0.111550i	−0.760679	+	0.649128i	$0.775134\pi$
$480$			92.6466i			0.193014i
$481$	−402.422	−	14.7813i	−0.836636	−	0.0307304i
$482$	471.134			0.977456
$483$	13.7631	−	13.7631i	0.0284950	−	0.0284950i
$484$	−199.957			−0.413135
$485$			342.906i			0.707024i
$486$	−15.5885	+	15.5885i	−0.0320750	+	0.0320750i
$487$	−667.025	+	667.025i	−1.36966	+	1.36966i	−0.508743	+	0.860919i	$0.669890\pi$
$487$	−667.025	+	667.025i	−1.36966	+	1.36966i	−0.860919	+	0.508743i	$0.830110\pi$
$488$	−164.182	−	164.182i	−0.336439	−	0.336439i
$489$	−10.6401	−	10.6401i	−0.0217590	−	0.0217590i
$490$	191.481			0.390778
$491$			171.754i			0.349805i	0.984586	+	0.174902i	$0.0559610\pi$
$491$			171.754i			0.349805i	−0.984586	+	0.174902i	$0.944039\pi$
$492$	−41.1432	−	41.1432i	−0.0836243	−	0.0836243i
$493$		−	229.595i		−	0.465711i
$494$	−319.810	−	344.200i	−0.647389	−	0.696761i
$495$	−130.060			−0.262748
$496$	−6.98281	+	6.98281i	−0.0140782	+	0.0140782i
$497$	−653.271			−1.31443
$498$			124.388i			0.249774i
$499$	478.233	−	478.233i	0.958382	−	0.958382i	−0.0407860	−	0.999168i	$-0.512986\pi$
$499$	478.233	−	478.233i	0.958382	−	0.958382i	0.999168	+	0.0407860i	$0.0129862\pi$
$500$	527.011	−	527.011i	1.05402	−	1.05402i
$501$	136.717	+	136.717i	0.272888	+	0.272888i
$502$	−284.858	−	284.858i	−0.567445	−	0.567445i
$503$	−206.006			−0.409555			−0.204777	−	0.978809i	$-0.565647\pi$
$503$	−206.006			−0.409555			−0.204777	+	0.978809i	$0.565647\pi$
$504$			67.5202i			0.133969i
$505$	1095.70	+	1095.70i	2.16971	+	2.16971i
$506$			9.15688i			0.0180966i
$507$	21.4745	−	291.928i	0.0423561	−	0.575794i
$508$	−22.2992			−0.0438961
$509$	266.087	−	266.087i	0.522765	−	0.522765i	−0.395641	−	0.918405i	$-0.629477\pi$
$509$	266.087	−	266.087i	0.522765	−	0.522765i	0.918405	+	0.395641i	$0.129477\pi$
$510$	−146.501			−0.287257
$511$			696.327i			1.36267i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	93.8990	−	93.8990i	0.183039	−	0.183039i
$514$	−308.122	−	308.122i	−0.599459	−	0.599459i
$515$	619.793	+	619.793i	1.20348	+	1.20348i
$516$	212.948			0.412691
$517$		−	358.692i		−	0.693794i
$518$	−246.490	−	246.490i	−0.475849	−	0.475849i
$519$		−	68.4628i		−	0.131913i
$520$	254.707	−	236.659i	0.489821	−	0.455113i
$521$	325.685			0.625115			0.312557	−	0.949899i	$-0.398814\pi$
$521$	325.685			0.625115			0.312557	+	0.949899i	$0.398814\pi$
$522$	−108.896	+	108.896i	−0.208613	+	0.208613i
$523$	−429.290			−0.820823			−0.410411	−	0.911901i	$-0.634615\pi$
$523$	−429.290			−0.820823			−0.410411	+	0.911901i	$0.634615\pi$
$524$			306.730i			0.585363i
$525$	627.724	−	627.724i	1.19567	−	1.19567i
$526$	353.459	−	353.459i	0.671976	−	0.671976i
$527$	−11.0419	−	11.0419i	−0.0209523	−	0.0209523i
$528$	−22.4613	−	22.4613i	−0.0425403	−	0.0425403i
$529$	527.006			0.996230
$530$		−	974.444i		−	1.83857i
$531$	35.1044	+	35.1044i	0.0661099	+	0.0661099i
$532$		−	406.716i		−	0.764504i
$533$	−8.01502	+	218.209i	−0.0150376	+	0.409398i
$534$	249.750			0.467696
$535$	−442.580	+	442.580i	−0.827252	+	0.827252i
$536$	−158.885			−0.296426
$537$		−	209.623i		−	0.390359i
$538$	−244.784	+	244.784i	−0.454989	+	0.454989i
$539$	−46.4228	+	46.4228i	−0.0861277	+	0.0861277i
$540$	69.4850	+	69.4850i	0.128676	+	0.128676i
$541$	−499.273	−	499.273i	−0.922871	−	0.922871i	0.0743608	−	0.997231i	$-0.476308\pi$
$541$	−499.273	−	499.273i	−0.922871	−	0.922871i	−0.997231	+	0.0743608i	$0.976308\pi$
$542$	−19.2533			−0.0355227
$543$		−	115.140i		−	0.212044i
$544$	−25.3007	−	25.3007i	−0.0465086	−	0.0465086i
$545$		−	379.604i		−	0.696521i
$546$	185.629	−	172.475i	0.339979	−	0.315888i
$547$	669.395			1.22376			0.611878	−	0.790952i	$-0.290414\pi$
$547$	669.395			1.22376			0.611878	+	0.790952i	$0.290414\pi$
$548$	143.029	−	143.029i	0.261001	−	0.261001i
$549$	−246.274			−0.448586
$550$			417.638i			0.759342i
$551$	655.950	−	655.950i	1.19047	−	1.19047i
$552$	4.89208	−	4.89208i	0.00886247	−	0.00886247i
$553$	699.783	+	699.783i	1.26543	+	1.26543i
$554$	−423.145	−	423.145i	−0.763800	−	0.763800i
$555$	−507.324			−0.914098
$556$			22.9252i			0.0412324i
$557$	−629.221	−	629.221i	−1.12966	−	1.12966i	−0.990232	−	0.139429i	$-0.955473\pi$
$557$	−629.221	−	629.221i	−1.12966	−	1.12966i	−0.139429	−	0.990232i	$-0.544527\pi$
$558$			10.4742i			0.0187710i
$559$	−543.960	−	585.444i	−0.973095	−	1.04731i
$560$	300.969			0.537444
$561$	35.5179	−	35.5179i	0.0633117	−	0.0633117i
$562$	140.973			0.250842
$563$		−	339.462i		−	0.602951i	−0.953474	−	0.301476i	$-0.902521\pi$
$563$		−	339.462i		−	0.602951i	0.953474	−	0.301476i	$-0.0974792\pi$
$564$	−191.632	+	191.632i	−0.339773	+	0.339773i
$565$	11.2265	−	11.2265i	0.0198700	−	0.0198700i
$566$	−32.5791	−	32.5791i	−0.0575602	−	0.0575602i
$567$	50.6402	+	50.6402i	0.0893124	+	0.0893124i
$568$	−232.205			−0.408811
$569$			620.916i			1.09124i	0.838033	+	0.545620i	$0.183706\pi$
$569$			620.916i			1.09124i	−0.838033	+	0.545620i	$0.816294\pi$
$570$	−418.551	−	418.551i	−0.734300	−	0.734300i
$571$			415.214i			0.727170i	0.931561	+	0.363585i	$0.118447\pi$
$571$			415.214i			0.727170i	−0.931561	+	0.363585i	$0.881553\pi$
$572$	−4.37564	+	119.127i	−0.00764973	+	0.208264i
$573$	298.670			0.521239
$574$	−133.656	+	133.656i	−0.232851	+	0.232851i
$575$	−90.9618			−0.158194
$576$			24.0000i			0.0416667i
$577$	−96.9535	+	96.9535i	−0.168030	+	0.168030i	−0.786113	−	0.618083i	$-0.787910\pi$
$577$	−96.9535	+	96.9535i	−0.168030	+	0.168030i	0.618083	+	0.786113i	$0.287910\pi$
$578$	−248.992	+	248.992i	−0.430783	+	0.430783i
$579$	−259.773	−	259.773i	−0.448658	−	0.448658i
$580$	485.401	+	485.401i	0.836898	+	0.836898i
$581$	404.081			0.695493
$582$			88.8295i			0.152628i
$583$	236.245	+	236.245i	0.405223	+	0.405223i
$584$			247.509i			0.423816i
$585$	13.5362	−	368.524i	0.0231389	−	0.629956i
$586$	−210.333			−0.358930
$587$	−316.619	+	316.619i	−0.539385	+	0.539385i	−0.923348	−	0.383963i	$-0.874559\pi$
$587$	−316.619	+	316.619i	−0.539385	+	0.539385i	0.383963	+	0.923348i	$0.374559\pi$
$588$	49.6030			0.0843588
$589$		−	63.0927i		−	0.107118i
$590$	156.476	−	156.476i	0.265214	−	0.265214i
$591$	120.762	−	120.762i	0.204335	−	0.204335i
$592$	−87.6145	−	87.6145i	−0.147997	−	0.147997i
$593$	386.333	+	386.333i	0.651489	+	0.651489i	0.953352	−	0.301862i	$-0.0976082\pi$
$593$	386.333	+	386.333i	0.651489	+	0.651489i	−0.301862	+	0.953352i	$0.597608\pi$
$594$	−33.6920			−0.0567205
$595$			475.919i			0.799864i
$596$	171.322	+	171.322i	0.287454	+	0.287454i
$597$			226.155i			0.378819i
$598$	−25.9459	−	0.953017i	−0.0433878	−	0.00159367i
$599$	−672.298			−1.12237			−0.561184	−	0.827691i	$-0.689654\pi$
$599$	−672.298			−1.12237			−0.561184	+	0.827691i	$0.689654\pi$
$600$	223.124	−	223.124i	0.371873	−	0.371873i
$601$	−295.046			−0.490926			−0.245463	−	0.969406i	$-0.578940\pi$
$601$	−295.046			−0.490926			−0.245463	+	0.969406i	$0.578940\pi$
$602$		−	691.777i		−	1.14913i
$603$	−119.163	+	119.163i	−0.197618	+	0.197618i
$604$	−275.332	+	275.332i	−0.455848	+	0.455848i
$605$	668.477	+	668.477i	1.10492	+	1.10492i
$606$	283.840	+	283.840i	0.468383	+	0.468383i
$607$	−881.610			−1.45240			−0.726202	−	0.687481i	$-0.758716\pi$
$607$	−881.610			−1.45240			−0.726202	+	0.687481i	$0.758716\pi$
$608$		−	144.567i		−	0.237775i
$609$	353.757	+	353.757i	0.580881	+	0.580881i
$610$			1097.76i			1.79960i
$611$	1016.35	+	37.3314i	1.66342	+	0.0610989i
$612$	−37.9510			−0.0620114
$613$	126.761	−	126.761i	0.206788	−	0.206788i	−0.596113	−	0.802901i	$-0.703289\pi$
$613$	126.761	−	126.761i	0.206788	−	0.206788i	0.802901	+	0.596113i	$0.203289\pi$
$614$	226.922			0.369579
$615$			275.091i			0.447303i
$616$	−72.9671	+	72.9671i	−0.118453	+	0.118453i
$617$	279.330	−	279.330i	0.452723	−	0.452723i	−0.443534	−	0.896257i	$-0.646276\pi$
$617$	279.330	−	279.330i	0.452723	−	0.452723i	0.896257	+	0.443534i	$0.146276\pi$
$618$	160.557	+	160.557i	0.259801	+	0.259801i
$619$	171.746	+	171.746i	0.277458	+	0.277458i	0.832093	−	0.554636i	$-0.187142\pi$
$619$	171.746	+	171.746i	0.277458	+	0.277458i	−0.554636	+	0.832093i	$0.687142\pi$
$620$	46.6884			0.0753039
$621$		−	7.33813i		−	0.0118166i
$622$	−121.466	−	121.466i	−0.195283	−	0.195283i
$623$		−	811.329i		−	1.30229i
$624$	65.9815	−	61.3061i	0.105740	−	0.0982470i
$625$	−1913.44			−3.06150
$626$	−337.489	+	337.489i	−0.539120	+	0.539120i
$627$	202.948			0.323680
$628$			171.826i			0.273608i
$629$	138.544	−	138.544i	0.220261	−	0.220261i
$630$	225.727	−	225.727i	0.358296	−	0.358296i
$631$	871.640	+	871.640i	1.38136	+	1.38136i	0.842205	+	0.539158i	$0.181257\pi$
$631$	871.640	+	871.640i	1.38136	+	1.38136i	0.539158	+	0.842205i	$0.318743\pi$
$632$	248.737	+	248.737i	0.393572	+	0.393572i
$633$	−236.363			−0.373401
$634$		−	137.337i		−	0.216620i
$635$	74.5485	+	74.5485i	0.117399	+	0.117399i
$636$		−	252.429i		−	0.396900i
$637$	−126.707	−	136.370i	−0.198912	−	0.214082i
$638$	−235.362			−0.368905
$639$	−174.154	+	174.154i	−0.272541	+	0.272541i
$640$	106.979			0.167155
$641$			191.543i			0.298819i	0.988775	+	0.149410i	$0.0477373\pi$
$641$			191.543i			0.298819i	−0.988775	+	0.149410i	$0.952263\pi$
$642$	−114.650	+	114.650i	−0.178582	+	0.178582i
$643$	605.259	−	605.259i	0.941305	−	0.941305i	−0.0570658	−	0.998370i	$-0.518174\pi$
$643$	605.259	−	605.259i	0.941305	−	0.941305i	0.998370	+	0.0570658i	$0.0181745\pi$
$644$	−15.8923	−	15.8923i	−0.0246774	−	0.0246774i
$645$	−711.907	−	711.907i	−1.10373	−	1.10373i
$646$	228.602			0.353874
$647$			1095.12i			1.69261i	0.532695	+	0.846307i	$0.321179\pi$
$647$			1095.12i			1.69261i	−0.532695	+	0.846307i	$0.678821\pi$
$648$	18.0000	+	18.0000i	0.0277778	+	0.0277778i
$649$			75.8725i			0.116907i
$650$	−1183.37	−	43.4664i	−1.82057	−	0.0668713i
$651$	34.0262			0.0522676
$652$	−12.2862	+	12.2862i	−0.0188438	+	0.0188438i
$653$	−478.602			−0.732928			−0.366464	−	0.930432i	$-0.619432\pi$
$653$	−478.602			−0.732928			−0.366464	+	0.930432i	$0.619432\pi$
$654$		−	98.3360i		−	0.150361i
$655$	1025.43	−	1025.43i	1.56554	−	1.56554i
$656$	−47.5080	+	47.5080i	−0.0724208	+	0.0724208i
$657$	185.632	+	185.632i	0.282544	+	0.282544i
$658$	622.529	+	622.529i	0.946092	+	0.946092i
$659$	−763.931			−1.15923			−0.579614	−	0.814891i	$-0.696797\pi$
$659$	−763.931			−1.15923			−0.579614	+	0.814891i	$0.696797\pi$
$660$			150.181i			0.227546i
$661$	−509.962	−	509.962i	−0.771500	−	0.771500i	0.206869	−	0.978369i	$-0.433673\pi$
$661$	−509.962	−	509.962i	−0.771500	−	0.771500i	−0.978369	+	0.206869i	$0.933673\pi$
$662$		−	822.617i		−	1.24262i
$663$	96.9428	+	104.336i	0.146218	+	0.157370i
$664$	143.630			0.216311
$665$	−1359.69	+	1359.69i	−2.04465	+	2.04465i
$666$	−131.422			−0.197330
$667$		−	51.2619i		−	0.0768544i
$668$	157.867	−	157.867i	0.236328	−	0.236328i
$669$	72.4115	−	72.4115i	0.108238	−	0.108238i
$670$	531.166	+	531.166i	0.792786	+	0.792786i
$671$	−266.141	−	266.141i	−0.396633	−	0.396633i
$672$	77.9656			0.116020
$673$			799.106i			1.18738i	0.804694	+	0.593690i	$0.202329\pi$
$673$			799.106i			1.18738i	−0.804694	+	0.593690i	$0.797671\pi$
$674$	599.641	+	599.641i	0.889675	+	0.889675i
$675$		−	334.686i		−	0.495831i
$676$	−337.089	−	24.7967i	−0.498653	−	0.0366815i
$677$	−1175.81			−1.73679			−0.868395	−	0.495873i	$-0.834848\pi$
$677$	−1175.81			−1.73679			−0.868395	+	0.495873i	$0.834848\pi$
$678$	2.90822	−	2.90822i	0.00428942	−	0.00428942i
$679$	288.569			0.424991
$680$			169.165i			0.248772i
$681$	−146.893	+	146.893i	−0.215702	+	0.215702i
$682$	−11.3192	+	11.3192i	−0.0165970	+	0.0165970i
$683$	132.777	+	132.777i	0.194403	+	0.194403i	0.797596	−	0.603192i	$-0.206105\pi$
$683$	132.777	+	132.777i	0.194403	+	0.194403i	−0.603192	+	0.797596i	$0.706105\pi$
$684$	−108.425	−	108.425i	−0.158516	−	0.158516i
$685$	−956.318			−1.39608
$686$			390.276i			0.568916i
$687$	−232.739	−	232.739i	−0.338776	−	0.338776i
$688$		−	245.892i		−	0.357401i
$689$	−693.984	+	644.809i	−1.00723	+	0.935862i
$690$	−32.7094			−0.0474050
$691$	153.135	−	153.135i	0.221614	−	0.221614i	−0.587564	−	0.809178i	$-0.699913\pi$
$691$	153.135	−	153.135i	0.221614	−	0.221614i	0.809178	+	0.587564i	$0.199913\pi$
$692$	−79.0541			−0.114240
$693$			109.451i			0.157937i
$694$	−29.0199	+	29.0199i	−0.0418154	+	0.0418154i
$695$	76.6412	−	76.6412i	0.110275	−	0.110275i
$696$	125.742	+	125.742i	0.180665	+	0.180665i
$697$	−75.1240	−	75.1240i	−0.107782	−	0.107782i
$698$	362.817			0.519796
$699$		−	220.248i		−	0.315090i
$700$	−724.834	−	724.834i	−1.03548	−	1.03548i
$701$		−	1152.65i		−	1.64429i	−0.569278	−	0.822145i	$-0.692777\pi$
$701$		−	1152.65i		−	1.64429i	0.569278	−	0.822145i	$-0.307223\pi$
$702$	3.50655	−	95.4657i	0.00499508	−	0.135991i
$703$	791.635			1.12608
$704$	−25.9361	+	25.9361i	−0.0368410	+	0.0368410i
$705$	1281.29			1.81743
$706$			475.688i			0.673779i
$707$	922.074	−	922.074i	1.30421	−	1.30421i
$708$	40.5350	−	40.5350i	0.0572529	−	0.0572529i
$709$	224.566	+	224.566i	0.316737	+	0.316737i	0.847512	−	0.530776i	$-0.178099\pi$
$709$	224.566	+	224.566i	0.316737	+	0.316737i	−0.530776	+	0.847512i	$0.678099\pi$
$710$	776.283	+	776.283i	1.09336	+	1.09336i
$711$	373.106			0.524762
$712$		−	288.386i		−	0.405037i
$713$	−2.46532	−	2.46532i	−0.00345767	−	0.00345767i
$714$			123.286i			0.172670i
$715$	412.881	−	383.625i	0.577456	−	0.536538i
$716$	−242.051			−0.338060
$717$	−85.0598	+	85.0598i	−0.118633	+	0.118633i
$718$	821.194			1.14372
$719$		−	405.925i		−	0.564569i	−0.959331	−	0.282284i	$-0.908908\pi$
$719$		−	405.925i		−	0.564569i	0.959331	−	0.282284i	$-0.0910922\pi$
$720$	80.2343	−	80.2343i	0.111437	−	0.111437i
$721$	521.579	−	521.579i	0.723411	−	0.723411i
$722$	292.113	+	292.113i	0.404588	+	0.404588i
$723$	−408.014	−	408.014i	−0.564334	−	0.564334i
$724$	−132.952			−0.183636
$725$		−	2338.01i		−	3.22485i
$726$	173.168	+	173.168i	0.238524	+	0.238524i
$727$		−	116.566i		−	0.160339i	−0.996781	−	0.0801693i	$-0.974454\pi$
$727$		−	116.566i		−	0.160339i	0.996781	−	0.0801693i	$-0.0255461\pi$
$728$	−199.157	−	214.345i	−0.273567	−	0.294430i
$729$	27.0000			0.0370370
$730$	827.446	−	827.446i	1.13349	−	1.13349i
$731$	388.826			0.531910
$732$			284.372i			0.388487i
$733$	−489.770	+	489.770i	−0.668172	+	0.668172i	−0.957293	−	0.289121i	$-0.906637\pi$
$733$	−489.770	+	489.770i	−0.668172	+	0.668172i	0.289121	+	0.957293i	$0.406637\pi$
$734$	181.634	−	181.634i	0.247457	−	0.247457i
$735$	−165.828	−	165.828i	−0.225616	−	0.225616i
$736$	−5.64889	−	5.64889i	−0.00767512	−	0.00767512i
$737$	−257.553			−0.349461
$738$			71.2621i			0.0965610i
$739$	−124.487	−	124.487i	−0.168453	−	0.168453i	0.617846	−	0.786299i	$-0.288005\pi$
$739$	−124.487	−	124.487i	−0.168453	−	0.168453i	−0.786299	+	0.617846i	$0.788005\pi$
$740$			585.808i			0.791632i
$741$	−21.1221	+	575.049i	−0.0285049	+	0.776045i
$742$	−820.032			−1.10516
$743$	342.334	−	342.334i	0.460745	−	0.460745i	−0.438154	−	0.898900i	$-0.644368\pi$
$743$	342.334	−	342.334i	0.460745	−	0.460745i	0.898900	+	0.438154i	$0.144368\pi$
$744$	12.0946			0.0162562
$745$		−	1145.49i		−	1.53758i
$746$	−452.204	+	452.204i	−0.606172	+	0.606172i
$747$	107.723	−	107.723i	0.144207	−	0.144207i
$748$	−41.0125	−	41.0125i	−0.0548295	−	0.0548295i
$749$	372.448	+	372.448i	0.497260	+	0.497260i
$750$	−912.809			−1.21708
$751$		−	474.974i		−	0.632456i	−0.948683	−	0.316228i	$-0.897584\pi$
$751$		−	474.974i		−	0.632456i	0.948683	−	0.316228i	$-0.102416\pi$
$752$	221.277	+	221.277i	0.294252	+	0.294252i
$753$			493.388i			0.655229i
$754$	24.4957	−	666.894i	0.0324876	−	0.884475i
$755$	1840.92			2.43831
$756$	58.4742	−	58.4742i	0.0773468	−	0.0773468i
$757$	230.232			0.304137			0.152068	−	0.988370i	$-0.451407\pi$
$757$	230.232			0.304137			0.152068	+	0.988370i	$0.451407\pi$
$758$			191.004i			0.251984i
$759$	7.93009	−	7.93009i	0.0104481	−	0.0104481i
$760$	−483.301	+	483.301i	−0.635923	+	0.635923i
$761$	262.942	+	262.942i	0.345521	+	0.345521i	0.858438	−	0.512917i	$-0.171435\pi$
$761$	262.942	+	262.942i	0.345521	+	0.345521i	−0.512917	+	0.858438i	$0.671435\pi$
$762$	19.3117	+	19.3117i	0.0253434	+	0.0253434i
$763$	−319.451			−0.418678
$764$		−	344.874i		−	0.451406i
$765$	126.874	+	126.874i	0.165848	+	0.165848i
$766$		−	713.233i		−	0.931113i
$767$	−214.984	−	7.89655i	−0.280292	−	0.0102954i
$768$	27.7128			0.0360844
$769$	−571.952	+	571.952i	−0.743761	+	0.743761i	−0.973300	−	0.229538i	$-0.926278\pi$
$769$	−571.952	+	571.952i	−0.743761	+	0.743761i	0.229538	+	0.973300i	$0.426278\pi$
$770$	487.872			0.633600
$771$			533.683i			0.692196i
$772$	−299.960	+	299.960i	−0.388549	+	0.388549i
$773$	−880.087	+	880.087i	−1.13853	+	1.13853i	−0.149822	+	0.988713i	$0.547870\pi$
$773$	−880.087	+	880.087i	−1.13853	+	1.13853i	−0.988713	+	0.149822i	$0.952130\pi$
$774$	−184.419	−	184.419i	−0.238267	−	0.238267i
$775$	−112.441	−	112.441i	−0.145086	−	0.145086i
$776$	102.571			0.132180
$777$			426.933i			0.549463i
$778$	−250.752	−	250.752i	−0.322303	−	0.322303i
$779$		−	429.256i		−	0.551034i
$780$	−425.535	−	15.6303i	−0.545558	−	0.0200388i
$781$	−376.405			−0.481953
$782$	8.93254	−	8.93254i	0.0114227	−	0.0114227i
$783$	188.614			0.240886
$784$		−	57.2766i		−	0.0730569i
$785$	574.429	−	574.429i	0.731757	−	0.731757i
$786$	265.636	−	265.636i	0.337959	−	0.337959i
$787$	103.141	+	103.141i	0.131056	+	0.131056i	0.769592	−	0.638536i	$-0.220460\pi$
$787$	103.141	+	103.141i	0.131056	+	0.131056i	−0.638536	+	0.769592i	$0.720460\pi$
$788$	−139.444	−	139.444i	−0.176959	−	0.176959i
$789$	−612.209			−0.775930
$790$		−	1663.11i		−	2.10520i
$791$	−9.44756	−	9.44756i	−0.0119438	−	0.0119438i
$792$			38.9041i			0.0491214i
$793$	781.805	−	726.407i	0.985882	−	0.916024i
$794$	531.866			0.669857
$795$	−843.893	+	843.893i	−1.06150	+	1.06150i
$796$	261.141			0.328067
$797$			828.592i			1.03964i	0.854276	+	0.519819i	$0.174001\pi$
$797$			828.592i			1.03964i	−0.854276	+	0.519819i	$0.825999\pi$
$798$	−352.227	+	352.227i	−0.441387	+	0.441387i
$799$	−349.904	+	349.904i	−0.437927	+	0.437927i
$800$	−257.641	−	257.641i	−0.322052	−	0.322052i
$801$	−216.290	−	216.290i	−0.270025	−	0.270025i
$802$	−264.996			−0.330419
$803$			401.213i			0.499643i
$804$	137.598	+	137.598i	0.171142	+	0.171142i
$805$			106.259i			0.131998i
$806$	−30.8947	−	33.2508i	−0.0383308	−	0.0412541i
$807$	423.979			0.525376
$808$	327.751	−	327.751i	0.405632	−	0.405632i
$809$	−547.805			−0.677139			−0.338569	−	0.940941i	$-0.609943\pi$
$809$	−547.805			−0.677139			−0.338569	+	0.940941i	$0.609943\pi$
$810$		−	120.351i		−	0.148582i
$811$	−780.398	+	780.398i	−0.962267	+	0.962267i	−0.999314	−	0.0370467i	$-0.988205\pi$
$811$	−780.398	+	780.398i	−0.962267	+	0.962267i	0.0370467	+	0.999314i	$0.488205\pi$
$812$	408.483	−	408.483i	0.503058	−	0.503058i
$813$	16.6739	+	16.6739i	0.0205091	+	0.0205091i
$814$	−142.024	−	142.024i	−0.174476	−	0.174476i
$815$	82.1477			0.100795
$816$			43.8220i			0.0537035i
$817$	1110.87	+	1110.87i	1.35969	+	1.35969i
$818$			478.665i			0.585165i
$819$	−310.127	−	11.3913i	−0.378665	−	0.0139087i
$820$	317.648			0.387376
$821$	28.4402	−	28.4402i	0.0346409	−	0.0346409i	−0.689574	−	0.724215i	$-0.742202\pi$
$821$	28.4402	−	28.4402i	0.0346409	−	0.0346409i	0.724215	+	0.689574i	$0.242202\pi$
$822$	−247.733			−0.301378
$823$			330.594i			0.401694i	0.979623	+	0.200847i	$0.0643695\pi$
$823$			330.594i			0.401694i	−0.979623	+	0.200847i	$0.935631\pi$
$824$	185.395	−	185.395i	0.224994	−	0.224994i
$825$	361.685	−	361.685i	0.438406	−	0.438406i
$826$	−131.681	−	131.681i	−0.159420	−	0.159420i
$827$	−961.770	−	961.770i	−1.16296	−	1.16296i	−0.983824	−	0.179139i	$-0.942669\pi$
$827$	−961.770	−	961.770i	−1.16296	−	1.16296i	−0.179139	−	0.983824i	$-0.557331\pi$
$828$	−8.47334			−0.0102335
$829$		−	1155.15i		−	1.39343i	−0.717349	−	0.696714i	$-0.754645\pi$
$829$		−	1155.15i		−	1.39343i	0.717349	−	0.696714i	$-0.245355\pi$
$830$	−480.170	−	480.170i	−0.578518	−	0.578518i
$831$			732.909i			0.881960i
$832$	−70.7902	−	76.1889i	−0.0850844	−	0.0915732i
$833$	90.5710			0.108729
$834$	19.8538	−	19.8538i	0.0238055	−	0.0238055i
$835$	−1055.53			−1.26411
$836$		−	234.344i		−	0.280315i
$837$	9.07094	−	9.07094i	0.0108374	−	0.0108374i
$838$	−573.772	+	573.772i	−0.684693	+	0.684693i
$839$	−764.570	−	764.570i	−0.911288	−	0.911288i	0.0850859	−	0.996374i	$-0.472884\pi$
$839$	−764.570	−	764.570i	−0.911288	−	0.911288i	−0.996374	+	0.0850859i	$0.972884\pi$
$840$	−260.647	−	260.647i	−0.310294	−	0.310294i
$841$	476.598			0.566704
$842$			724.056i			0.859924i
$843$	−122.086	−	122.086i	−0.144824	−	0.144824i
$844$			272.928i			0.323375i
$845$	1044.02	+	1209.82i	1.23553	+	1.43174i
$846$	331.916			0.392336
$847$	562.549	−	562.549i	0.664166	−	0.664166i
$848$	−291.480			−0.343726
$849$			56.4286i			0.0664648i
$850$	407.406	−	407.406i	0.479301	−	0.479301i
$851$	30.9328	−	30.9328i	0.0363488	−	0.0363488i
$852$	201.095	+	201.095i	0.236027	+	0.236027i
$853$	1004.33	+	1004.33i	1.17741	+	1.17741i	0.980402	+	0.197007i	$0.0631223\pi$
$853$	1004.33	+	1004.33i	1.17741	+	1.17741i	0.197007	+	0.980402i	$0.436878\pi$
$854$	923.803			1.08174
$855$			724.952i			0.847897i
$856$	132.386	+	132.386i	0.154657	+	0.154657i
$857$			232.425i			0.271208i	0.990763	+	0.135604i	$0.0432974\pi$
$857$			232.425i			0.271208i	−0.990763	+	0.135604i	$0.956703\pi$
$858$	106.956	−	99.3775i	0.124658	−	0.115825i
$859$	−306.012			−0.356242			−0.178121	−	0.984009i	$-0.557002\pi$
$859$	−306.012			−0.356242			−0.178121	+	0.984009i	$0.557002\pi$
$860$	−822.040	+	822.040i	−0.955860	+	0.955860i
$861$	231.500			0.268873
$862$			1137.56i			1.31968i
$863$	180.768	−	180.768i	0.209464	−	0.209464i	−0.594575	−	0.804040i	$-0.702680\pi$
$863$	180.768	−	180.768i	0.209464	−	0.209464i	0.804040	+	0.594575i	$0.202680\pi$
$864$	20.7846	−	20.7846i	0.0240563	−	0.0240563i
$865$	264.285	+	264.285i	0.305532	+	0.305532i
$866$	1.71126	+	1.71126i	0.00197606	+	0.00197606i
$867$	431.267			0.497425
$868$		−	39.2901i		−	0.0452651i
$869$	403.204	+	403.204i	0.463986	+	0.463986i
$870$		−	840.739i		−	0.966366i
$871$	26.8052	−	729.772i	0.0307752	−	0.837855i
$872$	−113.549			−0.130216
$873$	76.9286	−	76.9286i	0.0881198	−	0.0881198i
$874$	51.0402			0.0583984
$875$			2965.32i			3.38894i
$876$	214.349	−	214.349i	0.244691	−	0.244691i
$877$	−549.466	+	549.466i	−0.626529	+	0.626529i	−0.947193	−	0.320664i	$-0.896094\pi$
$877$	−549.466	+	549.466i	−0.626529	+	0.626529i	0.320664	+	0.947193i	$0.396094\pi$
$878$	−592.080	−	592.080i	−0.674351	−	0.674351i
$879$	182.154	+	182.154i	0.207228	+	0.207228i
$880$	173.414			0.197061
$881$		−	339.367i		−	0.385206i	−0.981277	−	0.192603i	$-0.938307\pi$
$881$		−	339.367i		−	0.385206i	0.981277	−	0.192603i	$-0.0616930\pi$
$882$	−42.9574	−	42.9574i	−0.0487046	−	0.0487046i
$883$			39.1957i			0.0443892i	0.999754	+	0.0221946i	$0.00706534\pi$
$883$			39.1957i			0.0443892i	−0.999754	+	0.0221946i	$0.992935\pi$
$884$	120.477	−	111.940i	0.136286	−	0.126629i
$885$	−271.025			−0.306243
$886$	120.401	−	120.401i	0.135893	−	0.135893i
$887$	−618.112			−0.696857			−0.348428	−	0.937335i	$-0.613285\pi$
$887$	−618.112			−0.696857			−0.348428	+	0.937335i	$0.613285\pi$
$888$			151.753i			0.170893i
$889$	62.7353	−	62.7353i	0.0705684	−	0.0705684i
$890$	−964.103	+	964.103i	−1.08326	+	1.08326i
$891$	29.1781	+	29.1781i	0.0327476	+	0.0327476i
$892$	−83.6135	−	83.6135i	−0.0937372	−	0.0937372i
$893$	−1999.34			−2.23890
$894$		−	296.739i		−	0.331923i
$895$	809.201	+	809.201i	0.904135	+	0.904135i
$896$		−	90.0269i		−	0.100477i
$897$	21.6445	+	23.2951i	0.0241298	+	0.0259701i
$898$	−862.682			−0.960670
$899$	63.3668	−	63.3668i	0.0704859	−	0.0704859i
$900$	−386.462			−0.429402
$901$		−	460.914i		−	0.511558i
$902$	−77.0108	+	77.0108i	−0.0853778	+	0.0853778i
$903$	−599.097	+	599.097i	−0.663452	+	0.663452i
$904$	−3.35813	−	3.35813i	−0.00371474	−	0.00371474i
$905$	444.472	+	444.472i	0.491129	+	0.491129i
$906$	476.889			0.526368
$907$		−	373.862i		−	0.412197i	−0.978531	−	0.206098i	$-0.933923\pi$
$907$		−	373.862i		−	0.412197i	0.978531	−	0.206098i	$-0.0660767\pi$
$908$	169.618	+	169.618i	0.186804	+	0.186804i
$909$		−	491.626i		−	0.540842i
$910$	−50.7761	+	1382.38i	−0.0557979	+	1.51910i
$911$	−95.0881			−0.104378			−0.0521889	−	0.998637i	$-0.516620\pi$
$911$	−95.0881			−0.104378			−0.0521889	+	0.998637i	$0.516620\pi$
$912$	−125.199	+	125.199i	−0.137279	+	0.137279i
$913$	232.826			0.255012
$914$			204.456i			0.223694i
$915$	950.684	−	950.684i	1.03900	−	1.03900i
$916$	−268.744	+	268.744i	−0.293388	+	0.293388i
$917$	−862.937	−	862.937i	−0.941044	−	0.941044i
$918$	32.8665	+	32.8665i	0.0358023	+	0.0358023i
$919$	124.977			0.135992			0.0679961	−	0.997686i	$-0.478339\pi$
$919$	124.977			0.135992			0.0679961	+	0.997686i	$0.478339\pi$
$920$			37.7696i			0.0410539i
$921$	−196.520	−	196.520i	−0.213377	−	0.213377i
$922$			292.392i			0.317128i
$923$	39.1750	−	1066.54i	0.0424431	−	1.15551i
$924$	126.383			0.136778
$925$	1410.82	−	1410.82i	1.52521	−	1.52521i
$926$	−443.566			−0.479013
$927$		−	278.092i		−	0.299992i
$928$	145.195	−	145.195i	0.156460	−	0.156460i
$929$	−340.230	+	340.230i	−0.366233	+	0.366233i	−0.866101	−	0.499869i	$-0.833382\pi$
$929$	−340.230	+	340.230i	−0.366233	+	0.366233i	0.499869	+	0.866101i	$0.333382\pi$
$930$	−40.4334	−	40.4334i	−0.0434767	−	0.0434767i
$931$	258.759	+	258.759i	0.277937	+	0.277937i
$932$	−254.320			−0.272876
$933$			210.385i			0.225493i
$934$	−119.016	−	119.016i	−0.127426	−	0.127426i
$935$			274.217i			0.293281i
$936$	−110.234	−	4.04901i	−0.117772	−	0.00432587i
$937$	236.029			0.251899			0.125949	−	0.992037i	$-0.459802\pi$
$937$	236.029			0.251899			0.125949	+	0.992037i	$0.459802\pi$
$938$	446.996	−	446.996i	0.476542	−	0.476542i
$939$	584.548			0.622522
$940$		−	1479.50i		−	1.57394i
$941$	−311.733	+	311.733i	−0.331278	+	0.331278i	−0.853072	−	0.521793i	$-0.825263\pi$
$941$	−311.733	+	311.733i	−0.331278	+	0.331278i	0.521793	+	0.853072i	$0.325263\pi$
$942$	148.805	−	148.805i	0.157967	−	0.157967i
$943$	−16.7730	−	16.7730i	−0.0177868	−	0.0177868i
$944$	−46.8058	−	46.8058i	−0.0495824	−	0.0495824i
$945$	−390.970			−0.413725
$946$		−	398.592i		−	0.421344i
$947$	466.397	+	466.397i	0.492499	+	0.492499i	0.909093	−	0.416594i	$-0.136776\pi$
$947$	466.397	+	466.397i	0.492499	+	0.492499i	−0.416594	+	0.909093i	$0.636776\pi$
$948$		−	430.825i		−	0.454457i
$949$	−1136.83	−	41.7569i	−1.19793	−	0.0440009i
$950$	2327.90			2.45042
$951$	−118.937	+	118.937i	−0.125065	+	0.125065i
$952$	142.359			0.149537
$953$		−	1594.49i		−	1.67313i	−0.547869	−	0.836564i	$-0.684561\pi$
$953$		−	1594.49i		−	1.67313i	0.547869	−	0.836564i	$-0.315439\pi$
$954$	−218.610	+	218.610i	−0.229151	+	0.229151i
$955$	−1152.95	+	1152.95i	−1.20728	+	1.20728i
$956$	98.2186	+	98.2186i	0.102739	+	0.102739i
$957$	203.829	+	203.829i	0.212988	+	0.212988i
$958$	106.865			0.111550
$959$			804.778i			0.839184i
$960$	−92.6466	−	92.6466i	−0.0965069	−	0.0965069i
$961$			954.905i			0.993658i
$962$	417.203	−	387.641i	0.433683	−	0.402953i
$963$	198.579			0.206209
$964$	−471.134	+	471.134i	−0.488728	+	0.488728i
$965$	2005.59			2.07833
$966$			27.5262i			0.0284950i
$967$	915.706	−	915.706i	0.946956	−	0.946956i	−0.0517064	−	0.998662i	$-0.516466\pi$
$967$	915.706	−	915.706i	0.946956	−	0.946956i	0.998662	+	0.0517064i	$0.0164660\pi$
$968$	199.957	−	199.957i	0.206568	−	0.206568i
$969$	−197.976	−	197.976i	−0.204309	−	0.204309i
$970$	−342.906	−	342.906i	−0.353512	−	0.353512i
$971$	168.061			0.173080			0.0865399	−	0.996248i	$-0.472419\pi$
$971$	168.061			0.173080			0.0865399	+	0.996248i	$0.472419\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	−64.4964	−	64.4964i	−0.0662862	−	0.0662862i
$974$		−	1334.05i		−	1.36966i
$975$	987.187	+	1062.47i	1.01250	+	1.08972i
$976$	328.365			0.336439
$977$	976.935	−	976.935i	0.999933	−	0.999933i	−6.69043e−5	−	1.00000i	$-0.500021\pi$
$977$	976.935	−	976.935i	0.999933	−	0.999933i	1.00000		6.69043e-5i	$2.12963e-5\pi$
$978$	21.2803			0.0217590
$979$		−	467.475i		−	0.477503i
$980$	−191.481	+	191.481i	−0.195389	+	0.195389i
$981$	−85.1615	+	85.1615i	−0.0868109	+	0.0868109i
$982$	−171.754	−	171.754i	−0.174902	−	0.174902i
$983$	−709.988	−	709.988i	−0.722266	−	0.722266i	0.246800	−	0.969066i	$-0.420621\pi$
$983$	−709.988	−	709.988i	−0.722266	−	0.722266i	−0.969066	+	0.246800i	$0.920621\pi$
$984$	82.2863			0.0836243
$985$			932.348i			0.946546i
$986$	229.595	+	229.595i	0.232855	+	0.232855i
$987$		−	1078.25i		−	1.09245i
$988$	664.010	+	24.3897i	0.672075	+	0.0246859i
$989$	86.8135			0.0877790
$990$	130.060	−	130.060i	0.131374	−	0.131374i
$991$	−1261.42			−1.27288			−0.636438	−	0.771328i	$-0.719593\pi$
$991$	−1261.42			−1.27288			−0.636438	+	0.771328i	$0.719593\pi$
$992$		−	13.9656i		−	0.0140782i
$993$	−712.407	+	712.407i	−0.717429	+	0.717429i
$994$	653.271	−	653.271i	0.657215	−	0.657215i
$995$	−873.020	−	873.020i	−0.877407	−	0.877407i
$996$	−124.388	−	124.388i	−0.124887	−	0.124887i
$997$	−162.659			−0.163148			−0.0815740	−	0.996667i	$-0.525995\pi$
$997$	−162.659			−0.163148			−0.0815740	+	0.996667i	$0.525995\pi$
$998$			956.465i			0.958382i
$999$	113.815	+	113.815i	0.113929	+	0.113929i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.3.f.b.31.3	✓	8
3.2	odd	2		234.3.i.e.109.4		8
4.3	odd	2		624.3.ba.c.577.1		8
13.5	odd	4		1014.3.f.i.775.4		8
13.8	odd	4	inner	78.3.f.b.73.3	yes	8
13.12	even	2		1014.3.f.i.577.4		8
39.8	even	4		234.3.i.e.73.4		8
52.47	even	4		624.3.ba.c.385.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.f.b.31.3	✓	8	1.1	even	1	trivial
78.3.f.b.73.3	yes	8	13.8	odd	4	inner
234.3.i.e.73.4		8	39.8	even	4
234.3.i.e.109.4		8	3.2	odd	2
624.3.ba.c.385.1		8	52.47	even	4
624.3.ba.c.577.1		8	4.3	odd	2
1014.3.f.i.577.4		8	13.12	even	2
1014.3.f.i.775.4		8	13.5	odd	4

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:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	78.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +1.73205 q^{3} -2.00000i q^{4} +(-6.68619 + 6.68619i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(5.62668 + 5.62668i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +1.73205 q^{3} -2.00000i q^{4} +(-6.68619 + 6.68619i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(5.62668 + 5.62668i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} -13.3724i q^{10} +(3.24201 + 3.24201i) q^{11} -3.46410i q^{12} +(-9.52361 + 8.84878i) q^{13} -11.2534 q^{14} +(-11.5808 + 11.5808i) q^{15} -4.00000 q^{16} -6.32516i q^{17} +(-3.00000 + 3.00000i) q^{18} +(18.0709 - 18.0709i) q^{19} +(13.3724 + 13.3724i) q^{20} +(9.74570 + 9.74570i) q^{21} -6.48402 q^{22} -1.41222i q^{23} +(3.46410 + 3.46410i) q^{24} -64.4104i q^{25} +(0.674835 - 18.3724i) q^{26} +5.19615 q^{27} +(11.2534 - 11.2534i) q^{28} +36.2987 q^{29} -23.1617i q^{30} +(1.74570 - 1.74570i) q^{31} +(4.00000 - 4.00000i) q^{32} +(5.61533 + 5.61533i) q^{33} +(6.32516 + 6.32516i) q^{34} -75.2422 q^{35} -6.00000i q^{36} +(21.9036 + 21.9036i) q^{37} +36.1417i q^{38} +(-16.4954 + 15.3265i) q^{39} -26.7448 q^{40} +(11.8770 - 11.8770i) q^{41} -19.4914 q^{42} +61.4729i q^{43} +(6.48402 - 6.48402i) q^{44} +(-20.0586 + 20.0586i) q^{45} +(1.41222 + 1.41222i) q^{46} +(-55.3193 - 55.3193i) q^{47} -6.92820 q^{48} +14.3191i q^{49} +(64.4104 + 64.4104i) q^{50} -10.9555i q^{51} +(17.6976 + 19.0472i) q^{52} +72.8699 q^{53} +(-5.19615 + 5.19615i) q^{54} -43.3534 q^{55} +22.5067i q^{56} +(31.2997 - 31.2997i) q^{57} +(-36.2987 + 36.2987i) q^{58} +(11.7015 + 11.7015i) q^{59} +(23.1617 + 23.1617i) q^{60} -82.0912 q^{61} +3.49141i q^{62} +(16.8801 + 16.8801i) q^{63} +8.00000i q^{64} +(4.51208 - 122.841i) q^{65} -11.2307 q^{66} +(-39.7211 + 39.7211i) q^{67} -12.6503 q^{68} -2.44604i q^{69} +(75.2422 - 75.2422i) q^{70} +(-58.0512 + 58.0512i) q^{71} +(6.00000 + 6.00000i) q^{72} +(61.8772 + 61.8772i) q^{73} -43.8073 q^{74} -111.562i q^{75} +(-36.1417 - 36.1417i) q^{76} +36.4835i q^{77} +(1.16885 - 31.8219i) q^{78} +124.369 q^{79} +(26.7448 - 26.7448i) q^{80} +9.00000 q^{81} +23.7540i q^{82} +(35.9076 - 35.9076i) q^{83} +(19.4914 - 19.4914i) q^{84} +(42.2913 + 42.2913i) q^{85} +(-61.4729 - 61.4729i) q^{86} +62.8712 q^{87} +12.9680i q^{88} +(-72.0966 - 72.0966i) q^{89} -40.1172i q^{90} +(-103.376 - 3.79708i) q^{91} -2.82445 q^{92} +(3.02365 - 3.02365i) q^{93} +110.639 q^{94} +241.651i q^{95} +(6.92820 - 6.92820i) q^{96} +(25.6429 - 25.6429i) q^{97} +(-14.3191 - 14.3191i) q^{98} +(9.72603 + 9.72603i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 4 q^{7} + 16 q^{8} + 24 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 4 * q^7 + 16 * q^8 + 24 * q^9	\( 8 q - 8 q^{2} + 4 q^{7} + 16 q^{8} + 24 q^{9} + 24 q^{11} - 36 q^{13} - 8 q^{14} - 12 q^{15} - 32 q^{16} - 24 q^{18} + 52 q^{19} + 12 q^{21} - 48 q^{22} + 32 q^{26} + 8 q^{28} - 168 q^{29} - 52 q^{31} + 32 q^{32} + 84 q^{33} + 24 q^{34} - 16 q^{37} - 48 q^{39} + 72 q^{41} - 24 q^{42} + 48 q^{44} - 48 q^{46} - 72 q^{47} + 160 q^{50} + 8 q^{52} + 144 q^{53} + 264 q^{55} - 60 q^{57} + 168 q^{58} - 48 q^{59} + 24 q^{60} - 72 q^{61} + 12 q^{63} + 48 q^{65} - 168 q^{66} - 116 q^{67} - 48 q^{68} - 432 q^{71} + 48 q^{72} - 128 q^{73} + 32 q^{74} - 104 q^{76} + 72 q^{78} + 240 q^{79} + 72 q^{81} + 144 q^{83} + 24 q^{84} - 48 q^{85} - 24 q^{86} + 192 q^{87} - 168 q^{89} - 20 q^{91} + 96 q^{92} + 12 q^{93} + 144 q^{94} + 224 q^{97} - 344 q^{98} + 72 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 4 * q^7 + 16 * q^8 + 24 * q^9 + 24 * q^11 - 36 * q^13 - 8 * q^14 - 12 * q^15 - 32 * q^16 - 24 * q^18 + 52 * q^19 + 12 * q^21 - 48 * q^22 + 32 * q^26 + 8 * q^28 - 168 * q^29 - 52 * q^31 + 32 * q^32 + 84 * q^33 + 24 * q^34 - 16 * q^37 - 48 * q^39 + 72 * q^41 - 24 * q^42 + 48 * q^44 - 48 * q^46 - 72 * q^47 + 160 * q^50 + 8 * q^52 + 144 * q^53 + 264 * q^55 - 60 * q^57 + 168 * q^58 - 48 * q^59 + 24 * q^60 - 72 * q^61 + 12 * q^63 + 48 * q^65 - 168 * q^66 - 116 * q^67 - 48 * q^68 - 432 * q^71 + 48 * q^72 - 128 * q^73 + 32 * q^74 - 104 * q^76 + 72 * q^78 + 240 * q^79 + 72 * q^81 + 144 * q^83 + 24 * q^84 - 48 * q^85 - 24 * q^86 + 192 * q^87 - 168 * q^89 - 20 * q^91 + 96 * q^92 + 12 * q^93 + 144 * q^94 + 224 * q^97 - 344 * q^98 + 72 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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