LMFDB - Embedded newform 245.3.h.b.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,3,Mod(31,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("245.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	245.h (of order $6$, degree $2$, not 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:	$6.67576647683$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 25 $ x^4 - 5*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.1
Root			$1.93649 + 1.11803i$ of defining polynomial
Character	$\chi$	$=$	245.31
Dual form			245.3.h.b.166.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-3.87298 - 2.23607i) q^{3} +(1.50000 - 2.59808i) q^{4} +(1.93649 - 1.11803i) q^{5} -4.47214i q^{6} +7.00000 q^{8} +(5.50000 + 9.52628i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-3.87298 - 2.23607i) q^{3} +(1.50000 - 2.59808i) q^{4} +(1.93649 - 1.11803i) q^{5} -4.47214i q^{6} +7.00000 q^{8} +(5.50000 + 9.52628i) q^{9} +(1.93649 + 1.11803i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(-11.6190 + 6.70820i) q^{12} -13.4164i q^{13} -10.0000 q^{15} +(-2.50000 - 4.33013i) q^{16} +(-23.2379 - 13.4164i) q^{17} +(-5.50000 + 9.52628i) q^{18} +(-11.6190 + 6.70820i) q^{19} -6.70820i q^{20} -2.00000 q^{22} +(-13.0000 - 22.5167i) q^{23} +(-27.1109 - 15.6525i) q^{24} +(2.50000 - 4.33013i) q^{25} +(11.6190 - 6.70820i) q^{26} -8.94427i q^{27} -22.0000 q^{29} +(-5.00000 - 8.66025i) q^{30} +(46.4758 + 26.8328i) q^{31} +(16.5000 - 28.5788i) q^{32} +(7.74597 - 4.47214i) q^{33} -26.8328i q^{34} +33.0000 q^{36} +(-7.00000 - 12.1244i) q^{37} +(-11.6190 - 6.70820i) q^{38} +(-30.0000 + 51.9615i) q^{39} +(13.5554 - 7.82624i) q^{40} -26.8328i q^{41} -34.0000 q^{43} +(3.00000 + 5.19615i) q^{44} +(21.3014 + 12.2984i) q^{45} +(13.0000 - 22.5167i) q^{46} +(-23.2379 + 13.4164i) q^{47} +22.3607i q^{48} +5.00000 q^{50} +(60.0000 + 103.923i) q^{51} +(-34.8569 - 20.1246i) q^{52} +(17.0000 - 29.4449i) q^{53} +(7.74597 - 4.47214i) q^{54} +4.47214i q^{55} +60.0000 q^{57} +(-11.0000 - 19.0526i) q^{58} +(34.8569 + 20.1246i) q^{59} +(-15.0000 + 25.9808i) q^{60} +(81.3327 - 46.9574i) q^{61} +53.6656i q^{62} +13.0000 q^{64} +(-15.0000 - 25.9808i) q^{65} +(7.74597 + 4.47214i) q^{66} +(-7.00000 + 12.1244i) q^{67} +(-69.7137 + 40.2492i) q^{68} +116.276i q^{69} +62.0000 q^{71} +(38.5000 + 66.6840i) q^{72} +(46.4758 + 26.8328i) q^{73} +(7.00000 - 12.1244i) q^{74} +(-19.3649 + 11.1803i) q^{75} +40.2492i q^{76} -60.0000 q^{78} +(-19.0000 - 32.9090i) q^{79} +(-9.68246 - 5.59017i) q^{80} +(29.5000 - 51.0955i) q^{81} +(23.2379 - 13.4164i) q^{82} +40.2492i q^{83} -60.0000 q^{85} +(-17.0000 - 29.4449i) q^{86} +(85.2056 + 49.1935i) q^{87} +(-7.00000 + 12.1244i) q^{88} +(-23.2379 + 13.4164i) q^{89} +24.5967i q^{90} -78.0000 q^{92} +(-120.000 - 207.846i) q^{93} +(-23.2379 - 13.4164i) q^{94} +(-15.0000 + 25.9808i) q^{95} +(-127.808 + 73.7902i) q^{96} -26.8328i q^{97} -22.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 6 q^{4} + 28 q^{8} + 22 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 6 * q^4 + 28 * q^8 + 22 * q^9	$ 4 q + 2 q^{2} + 6 q^{4} + 28 q^{8} + 22 q^{9} - 4 q^{11} - 40 q^{15} - 10 q^{16} - 22 q^{18} - 8 q^{22} - 52 q^{23} + 10 q^{25} - 88 q^{29} - 20 q^{30} + 66 q^{32} + 132 q^{36} - 28 q^{37} - 120 q^{39} - 136 q^{43} + 12 q^{44} + 52 q^{46} + 20 q^{50} + 240 q^{51} + 68 q^{53} + 240 q^{57} - 44 q^{58} - 60 q^{60} + 52 q^{64} - 60 q^{65} - 28 q^{67} + 248 q^{71} + 154 q^{72} + 28 q^{74} - 240 q^{78} - 76 q^{79} + 118 q^{81} - 240 q^{85} - 68 q^{86} - 28 q^{88} - 312 q^{92} - 480 q^{93} - 60 q^{95} - 88 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 6 * q^4 + 28 * q^8 + 22 * q^9 - 4 * q^11 - 40 * q^15 - 10 * q^16 - 22 * q^18 - 8 * q^22 - 52 * q^23 + 10 * q^25 - 88 * q^29 - 20 * q^30 + 66 * q^32 + 132 * q^36 - 28 * q^37 - 120 * q^39 - 136 * q^43 + 12 * q^44 + 52 * q^46 + 20 * q^50 + 240 * q^51 + 68 * q^53 + 240 * q^57 - 44 * q^58 - 60 * q^60 + 52 * q^64 - 60 * q^65 - 28 * q^67 + 248 * q^71 + 154 * q^72 + 28 * q^74 - 240 * q^78 - 76 * q^79 + 118 * q^81 - 240 * q^85 - 68 * q^86 - 28 * q^88 - 312 * q^92 - 480 * q^93 - 60 * q^95 - 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.250000	+	0.433013i	0.963525	−	0.267617i	$-0.0862360\pi$
$2$	0.500000	+	0.866025i	0.250000	+	0.433013i	−0.713525	+	0.700629i	$0.752903\pi$
$3$	−3.87298	−	2.23607i	−1.29099	−	0.745356i	−0.312164	−	0.950028i	$-0.601054\pi$
$3$	−3.87298	−	2.23607i	−1.29099	−	0.745356i	−0.978831	+	0.204672i	$0.934387\pi$
$4$	1.50000	−	2.59808i	0.375000	−	0.649519i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$6$		−	4.47214i		−	0.745356i
$7$		0			0
$7$		0			0
$8$	7.00000			0.875000
$9$	5.50000	+	9.52628i	0.611111	+	1.05848i
$10$	1.93649	+	1.11803i	0.193649	+	0.111803i
$11$	−1.00000	+	1.73205i	−0.0909091	+	0.157459i	−0.907894	−	0.419200i	$-0.862311\pi$
$11$	−1.00000	+	1.73205i	−0.0909091	+	0.157459i	0.816985	+	0.576659i	$0.195644\pi$
$12$	−11.6190	+	6.70820i	−0.968246	+	0.559017i
$13$		−	13.4164i		−	1.03203i	−0.856579	−	0.516016i	$-0.827415\pi$
$13$		−	13.4164i		−	1.03203i	0.856579	−	0.516016i	$-0.172585\pi$
$14$		0			0
$15$	−10.0000			−0.666667
$16$	−2.50000	−	4.33013i	−0.156250	−	0.270633i
$17$	−23.2379	−	13.4164i	−1.36694	−	0.789200i	−0.376400	−	0.926457i	$-0.622838\pi$
$17$	−23.2379	−	13.4164i	−1.36694	−	0.789200i	−0.990535	+	0.137257i	$0.956171\pi$
$18$	−5.50000	+	9.52628i	−0.305556	+	0.529238i
$19$	−11.6190	+	6.70820i	−0.611524	+	0.353063i	−0.773562	−	0.633721i	$-0.781527\pi$
$19$	−11.6190	+	6.70820i	−0.611524	+	0.353063i	0.162038	+	0.986785i	$0.448193\pi$
$20$		−	6.70820i		−	0.335410i
$21$		0			0
$22$	−2.00000			−0.0909091
$23$	−13.0000	−	22.5167i	−0.565217	−	0.978985i	−0.997029	−	0.0770216i	$-0.975459\pi$
$23$	−13.0000	−	22.5167i	−0.565217	−	0.978985i	0.431812	−	0.901964i	$-0.357874\pi$
$24$	−27.1109	−	15.6525i	−1.12962	−	0.652186i
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	11.6190	−	6.70820i	0.446883	−	0.258008i
$27$		−	8.94427i		−	0.331269i
$28$		0			0
$29$	−22.0000			−0.758621			−0.379310	−	0.925270i	$-0.623839\pi$
$29$	−22.0000			−0.758621			−0.379310	+	0.925270i	$0.623839\pi$
$30$	−5.00000	−	8.66025i	−0.166667	−	0.288675i
$31$	46.4758	+	26.8328i	1.49922	+	0.865575i	1.00000		0.000900703i	$-0.000286703\pi$
$31$	46.4758	+	26.8328i	1.49922	+	0.865575i	0.499220	+	0.866475i	$0.333620\pi$
$32$	16.5000	−	28.5788i	0.515625	−	0.893089i
$33$	7.74597	−	4.47214i	0.234726	−	0.135519i
$34$		−	26.8328i		−	0.789200i
$35$		0			0
$36$	33.0000			0.916667
$37$	−7.00000	−	12.1244i	−0.189189	−	0.327685i	0.755791	−	0.654813i	$-0.227253\pi$
$37$	−7.00000	−	12.1244i	−0.189189	−	0.327685i	−0.944980	+	0.327128i	$0.893919\pi$
$38$	−11.6190	−	6.70820i	−0.305762	−	0.176532i
$39$	−30.0000	+	51.9615i	−0.769231	+	1.33235i
$40$	13.5554	−	7.82624i	0.338886	−	0.195656i
$41$		−	26.8328i		−	0.654459i	−0.944945	−	0.327229i	$-0.893885\pi$
$41$		−	26.8328i		−	0.654459i	0.944945	−	0.327229i	$-0.106115\pi$
$42$		0			0
$43$	−34.0000			−0.790698			−0.395349	−	0.918531i	$-0.629376\pi$
$43$	−34.0000			−0.790698			−0.395349	+	0.918531i	$0.629376\pi$
$44$	3.00000	+	5.19615i	0.0681818	+	0.118094i
$45$	21.3014	+	12.2984i	0.473365	+	0.273297i
$46$	13.0000	−	22.5167i	0.282609	−	0.489493i
$47$	−23.2379	+	13.4164i	−0.494423	+	0.285455i	−0.726408	−	0.687264i	$-0.758812\pi$
$47$	−23.2379	+	13.4164i	−0.494423	+	0.285455i	0.231984	+	0.972720i	$0.425478\pi$
$48$			22.3607i			0.465847i
$49$		0			0
$50$	5.00000			0.100000
$51$	60.0000	+	103.923i	1.17647	+	2.03771i
$52$	−34.8569	−	20.1246i	−0.670324	−	0.387012i
$53$	17.0000	−	29.4449i	0.320755	−	0.555563i	−0.659889	−	0.751363i	$-0.729397\pi$
$53$	17.0000	−	29.4449i	0.320755	−	0.555563i	0.980644	+	0.195799i	$0.0627301\pi$
$54$	7.74597	−	4.47214i	0.143444	−	0.0828173i
$55$			4.47214i			0.0813116i
$56$		0			0
$57$	60.0000			1.05263
$58$	−11.0000	−	19.0526i	−0.189655	−	0.328492i
$59$	34.8569	+	20.1246i	0.590794	+	0.341095i	0.765411	−	0.643541i	$-0.222536\pi$
$59$	34.8569	+	20.1246i	0.590794	+	0.341095i	−0.174617	+	0.984636i	$0.555869\pi$
$60$	−15.0000	+	25.9808i	−0.250000	+	0.433013i
$61$	81.3327	−	46.9574i	1.33332	−	0.769794i	0.347515	−	0.937674i	$-0.387026\pi$
$61$	81.3327	−	46.9574i	1.33332	−	0.769794i	0.985807	+	0.167881i	$0.0536923\pi$
$62$			53.6656i			0.865575i
$63$		0			0
$64$	13.0000			0.203125
$65$	−15.0000	−	25.9808i	−0.230769	−	0.399704i
$66$	7.74597	+	4.47214i	0.117363	+	0.0677596i
$67$	−7.00000	+	12.1244i	−0.104478	+	0.180961i	−0.913525	−	0.406783i	$-0.866650\pi$
$67$	−7.00000	+	12.1244i	−0.104478	+	0.180961i	0.809047	+	0.587744i	$0.199984\pi$
$68$	−69.7137	+	40.2492i	−1.02520	+	0.591900i
$69$			116.276i			1.68515i
$70$		0			0
$71$	62.0000			0.873239			0.436620	−	0.899646i	$-0.356176\pi$
$71$	62.0000			0.873239			0.436620	+	0.899646i	$0.356176\pi$
$72$	38.5000	+	66.6840i	0.534722	+	0.926166i
$73$	46.4758	+	26.8328i	0.636655	+	0.367573i	0.783325	−	0.621613i	$-0.213522\pi$
$73$	46.4758	+	26.8328i	0.636655	+	0.367573i	−0.146670	+	0.989185i	$0.546856\pi$
$74$	7.00000	−	12.1244i	0.0945946	−	0.163843i
$75$	−19.3649	+	11.1803i	−0.258199	+	0.149071i
$76$			40.2492i			0.529595i
$77$		0			0
$78$	−60.0000			−0.769231
$79$	−19.0000	−	32.9090i	−0.240506	−	0.416569i	0.720352	−	0.693608i	$-0.243980\pi$
$79$	−19.0000	−	32.9090i	−0.240506	−	0.416569i	−0.960859	+	0.277039i	$0.910647\pi$
$80$	−9.68246	−	5.59017i	−0.121031	−	0.0698771i
$81$	29.5000	−	51.0955i	0.364198	−	0.630809i
$82$	23.2379	−	13.4164i	0.283389	−	0.163615i
$83$			40.2492i			0.484930i	0.970160	+	0.242465i	$0.0779560\pi$
$83$			40.2492i			0.484930i	−0.970160	+	0.242465i	$0.922044\pi$
$84$		0			0
$85$	−60.0000			−0.705882
$86$	−17.0000	−	29.4449i	−0.197674	−	0.342382i
$87$	85.2056	+	49.1935i	0.979375	+	0.565442i
$88$	−7.00000	+	12.1244i	−0.0795455	+	0.137777i
$89$	−23.2379	+	13.4164i	−0.261100	+	0.150746i	−0.624836	−	0.780756i	$-0.714834\pi$
$89$	−23.2379	+	13.4164i	−0.261100	+	0.150746i	0.363736	+	0.931502i	$0.381501\pi$
$90$			24.5967i			0.273297i
$91$		0			0
$92$	−78.0000			−0.847826
$93$	−120.000	−	207.846i	−1.29032	−	2.23490i
$94$	−23.2379	−	13.4164i	−0.247212	−	0.142728i
$95$	−15.0000	+	25.9808i	−0.157895	+	0.273482i
$96$	−127.808	+	73.7902i	−1.33134	+	0.768648i
$97$		−	26.8328i		−	0.276627i	−0.990388	−	0.138313i	$-0.955832\pi$
$97$		−	26.8328i		−	0.276627i	0.990388	−	0.138313i	$-0.0441681\pi$
$98$		0			0
$99$	−22.0000			−0.222222
$100$	−7.50000	−	12.9904i	−0.0750000	−	0.129904i
$101$	−58.0948	−	33.5410i	−0.575196	−	0.332089i	0.184026	−	0.982921i	$-0.441087\pi$
$101$	−58.0948	−	33.5410i	−0.575196	−	0.332089i	−0.759222	+	0.650832i	$0.774420\pi$
$102$	−60.0000	+	103.923i	−0.588235	+	1.01885i
$103$	139.427	−	80.4984i	1.35366	−	0.781538i	0.364903	−	0.931045i	$-0.381102\pi$
$103$	139.427	−	80.4984i	1.35366	−	0.781538i	0.988761	+	0.149507i	$0.0477687\pi$
$104$		−	93.9149i		−	0.903027i
$105$		0			0
$106$	34.0000			0.320755
$107$	53.0000	+	91.7987i	0.495327	+	0.857932i	0.999985	−	0.00538742i	$-0.00171488\pi$
$107$	53.0000	+	91.7987i	0.495327	+	0.857932i	−0.504658	+	0.863319i	$0.668382\pi$
$108$	−23.2379	−	13.4164i	−0.215166	−	0.124226i
$109$	71.0000	−	122.976i	0.651376	−	1.12822i	−0.331413	−	0.943486i	$-0.607525\pi$
$109$	71.0000	−	122.976i	0.651376	−	1.12822i	0.982789	−	0.184731i	$-0.0591413\pi$
$110$	−3.87298	+	2.23607i	−0.0352089	+	0.0203279i
$111$			62.6099i			0.564053i
$112$		0			0
$113$	−34.0000			−0.300885			−0.150442	−	0.988619i	$-0.548070\pi$
$113$	−34.0000			−0.300885			−0.150442	+	0.988619i	$0.548070\pi$
$114$	30.0000	+	51.9615i	0.263158	+	0.455803i
$115$	−50.3488	−	29.0689i	−0.437816	−	0.252773i
$116$	−33.0000	+	57.1577i	−0.284483	+	0.492739i
$117$	127.808	−	73.7902i	1.09238	−	0.630686i
$118$			40.2492i			0.341095i
$119$		0			0
$120$	−70.0000			−0.583333
$121$	58.5000	+	101.325i	0.483471	+	0.837396i
$122$	81.3327	+	46.9574i	0.666661	+	0.384897i
$123$	−60.0000	+	103.923i	−0.487805	+	0.844903i
$124$	139.427	−	80.4984i	1.12441	−	0.649181i
$125$		−	11.1803i		−	0.0894427i
$126$		0			0
$127$	194.000			1.52756			0.763780	−	0.645477i	$-0.223341\pi$
$127$	194.000			1.52756			0.763780	+	0.645477i	$0.223341\pi$
$128$	−59.5000	−	103.057i	−0.464844	−	0.805133i
$129$	131.681	+	76.0263i	1.02079	+	0.589351i
$130$	15.0000	−	25.9808i	0.115385	−	0.199852i
$131$	−104.571	+	60.3738i	−0.798248	+	0.460869i	−0.842858	−	0.538136i	$-0.819129\pi$
$131$	−104.571	+	60.3738i	−0.798248	+	0.460869i	0.0446099	+	0.999004i	$0.485796\pi$
$132$		−	26.8328i		−	0.203279i
$133$		0			0
$134$	−14.0000			−0.104478
$135$	−10.0000	−	17.3205i	−0.0740741	−	0.128300i
$136$	−162.665	−	93.9149i	−1.19607	−	0.690550i
$137$	83.0000	−	143.760i	0.605839	−	1.04934i	−0.386079	−	0.922466i	$-0.626171\pi$
$137$	83.0000	−	143.760i	0.605839	−	1.04934i	0.991918	−	0.126879i	$-0.0404959\pi$
$138$	−100.698	+	58.1378i	−0.729693	+	0.421288i
$139$		−	93.9149i		−	0.675646i	−0.941210	−	0.337823i	$-0.890309\pi$
$139$		−	93.9149i		−	0.675646i	0.941210	−	0.337823i	$-0.109691\pi$
$140$		0			0
$141$	120.000			0.851064
$142$	31.0000	+	53.6936i	0.218310	+	0.378124i
$143$	23.2379	+	13.4164i	0.162503	+	0.0938210i
$144$	27.5000	−	47.6314i	0.190972	−	0.330774i
$145$	−42.6028	+	24.5967i	−0.293813	+	0.169633i
$146$			53.6656i			0.367573i
$147$		0			0
$148$	−42.0000			−0.283784
$149$	71.0000	+	122.976i	0.476510	+	0.825340i	0.999638	−	0.0269147i	$-0.00856824\pi$
$149$	71.0000	+	122.976i	0.476510	+	0.825340i	−0.523128	+	0.852254i	$0.675235\pi$
$150$	−19.3649	−	11.1803i	−0.129099	−	0.0745356i
$151$	−1.00000	+	1.73205i	−0.00662252	+	0.0114705i	−0.869318	−	0.494254i	$-0.835441\pi$
$151$	−1.00000	+	1.73205i	−0.00662252	+	0.0114705i	0.862695	+	0.505724i	$0.168775\pi$
$152$	−81.3327	+	46.9574i	−0.535083	+	0.308930i
$153$		−	295.161i		−	1.92916i
$154$		0			0
$155$	120.000			0.774194
$156$	90.0000	+	155.885i	0.576923	+	0.999260i
$157$	58.0948	+	33.5410i	0.370030	+	0.213637i	0.673472	−	0.739213i	$-0.264802\pi$
$157$	58.0948	+	33.5410i	0.370030	+	0.213637i	−0.303441	+	0.952850i	$0.598136\pi$
$158$	19.0000	−	32.9090i	0.120253	−	0.208285i
$159$	−131.681	+	76.0263i	−0.828185	+	0.478153i
$160$		−	73.7902i		−	0.461189i
$161$		0			0
$162$	59.0000			0.364198
$163$	17.0000	+	29.4449i	0.104294	+	0.180643i	0.913450	−	0.406952i	$-0.133408\pi$
$163$	17.0000	+	29.4449i	0.104294	+	0.180643i	−0.809155	+	0.587595i	$0.800075\pi$
$164$	−69.7137	−	40.2492i	−0.425084	−	0.245422i
$165$	10.0000	−	17.3205i	0.0606061	−	0.104973i
$166$	−34.8569	+	20.1246i	−0.209981	+	0.121233i
$167$		−	107.331i		−	0.642702i	−0.946960	−	0.321351i	$-0.895863\pi$
$167$		−	107.331i		−	0.642702i	0.946960	−	0.321351i	$-0.104137\pi$
$168$		0			0
$169$	−11.0000			−0.0650888
$170$	−30.0000	−	51.9615i	−0.176471	−	0.305656i
$171$	−127.808	−	73.7902i	−0.747418	−	0.431522i
$172$	−51.0000	+	88.3346i	−0.296512	+	0.513573i
$173$	127.808	−	73.7902i	0.738777	−	0.426533i	−0.0828474	−	0.996562i	$-0.526401\pi$
$173$	127.808	−	73.7902i	0.738777	−	0.426533i	0.821625	+	0.570029i	$0.193068\pi$
$174$			98.3870i			0.565442i
$175$		0			0
$176$	10.0000			0.0568182
$177$	−90.0000	−	155.885i	−0.508475	−	0.880704i
$178$	−23.2379	−	13.4164i	−0.130550	−	0.0753731i
$179$	−109.000	+	188.794i	−0.608939	+	1.05471i	0.382477	+	0.923965i	$0.375071\pi$
$179$	−109.000	+	188.794i	−0.608939	+	1.05471i	−0.991416	+	0.130748i	$0.958262\pi$
$180$	63.9042	−	36.8951i	0.355023	−	0.204973i
$181$		−	254.912i		−	1.40835i	−0.710025	−	0.704176i	$-0.751317\pi$
$181$		−	254.912i		−	1.40835i	0.710025	−	0.704176i	$-0.248683\pi$
$182$		0			0
$183$	−420.000			−2.29508
$184$	−91.0000	−	157.617i	−0.494565	−	0.856612i
$185$	−27.1109	−	15.6525i	−0.146545	−	0.0846080i
$186$	120.000	−	207.846i	0.645161	−	1.11745i
$187$	46.4758	−	26.8328i	0.248534	−	0.143491i
$188$			80.4984i			0.428183i
$189$		0			0
$190$	−30.0000			−0.157895
$191$	29.0000	+	50.2295i	0.151832	+	0.262982i	0.931901	−	0.362712i	$-0.118149\pi$
$191$	29.0000	+	50.2295i	0.151832	+	0.262982i	−0.780069	+	0.625694i	$0.784816\pi$
$192$	−50.3488	−	29.0689i	−0.262233	−	0.151400i
$193$	−103.000	+	178.401i	−0.533679	+	0.924359i	0.465547	+	0.885023i	$0.345858\pi$
$193$	−103.000	+	178.401i	−0.533679	+	0.924359i	−0.999226	+	0.0393357i	$0.987476\pi$
$194$	23.2379	−	13.4164i	0.119783	−	0.0691567i
$195$			134.164i			0.688021i
$196$		0			0
$197$	−226.000			−1.14721			−0.573604	−	0.819133i	$-0.694455\pi$
$197$	−226.000			−1.14721			−0.573604	+	0.819133i	$0.694455\pi$
$198$	−11.0000	−	19.0526i	−0.0555556	−	0.0962250i
$199$	−116.190	−	67.0820i	−0.583867	−	0.337096i	0.178802	−	0.983885i	$-0.442778\pi$
$199$	−116.190	−	67.0820i	−0.583867	−	0.337096i	−0.762669	+	0.646789i	$0.776111\pi$
$200$	17.5000	−	30.3109i	0.0875000	−	0.151554i
$201$	54.2218	−	31.3050i	0.269760	−	0.155746i
$202$		−	67.0820i		−	0.332089i
$203$		0			0
$204$	360.000			1.76471
$205$	−30.0000	−	51.9615i	−0.146341	−	0.253471i
$206$	139.427	+	80.4984i	0.676832	+	0.390769i
$207$	143.000	−	247.683i	0.690821	−	1.19654i
$208$	−58.0948	+	33.5410i	−0.279302	+	0.161255i
$209$		−	26.8328i		−	0.128387i
$210$		0			0
$211$	−118.000			−0.559242			−0.279621	−	0.960111i	$-0.590209\pi$
$211$	−118.000			−0.559242			−0.279621	+	0.960111i	$0.590209\pi$
$212$	−51.0000	−	88.3346i	−0.240566	−	0.416673i
$213$	−240.125	−	138.636i	−1.12735	−	0.650874i
$214$	−53.0000	+	91.7987i	−0.247664	+	0.428966i
$215$	−65.8407	+	38.0132i	−0.306236	+	0.176805i
$216$		−	62.6099i		−	0.289861i
$217$		0			0
$218$	142.000			0.651376
$219$	−120.000	−	207.846i	−0.547945	−	0.949069i
$220$	11.6190	+	6.70820i	0.0528134	+	0.0304918i
$221$	−180.000	+	311.769i	−0.814480	+	1.41072i
$222$	−54.2218	+	31.3050i	−0.244242	+	0.141013i
$223$			80.4984i			0.360980i	0.983577	+	0.180490i	$0.0577683\pi$
$223$			80.4984i			0.360980i	−0.983577	+	0.180490i	$0.942232\pi$
$224$		0			0
$225$	55.0000			0.244444
$226$	−17.0000	−	29.4449i	−0.0752212	−	0.130287i
$227$	−220.760	−	127.456i	−0.972511	−	0.561480i	−0.0725103	−	0.997368i	$-0.523101\pi$
$227$	−220.760	−	127.456i	−0.972511	−	0.561480i	−0.900001	+	0.435888i	$0.856434\pi$
$228$	90.0000	−	155.885i	0.394737	−	0.683704i
$229$	11.6190	−	6.70820i	0.0507378	−	0.0292935i	−0.474417	−	0.880300i	$-0.657341\pi$
$229$	11.6190	−	6.70820i	0.0507378	−	0.0292935i	0.525154	+	0.851007i	$0.324008\pi$
$230$		−	58.1378i		−	0.252773i
$231$		0			0
$232$	−154.000			−0.663793
$233$	107.000	+	185.329i	0.459227	+	0.795405i	0.998920	−	0.0464567i	$-0.0147930\pi$
$233$	107.000	+	185.329i	0.459227	+	0.795405i	−0.539693	+	0.841862i	$0.681460\pi$
$234$	127.808	+	73.7902i	0.546190	+	0.315343i
$235$	−30.0000	+	51.9615i	−0.127660	+	0.221113i
$236$	104.571	−	60.3738i	0.443096	−	0.255821i
$237$			169.941i			0.717051i
$238$		0			0
$239$	98.0000			0.410042			0.205021	−	0.978758i	$-0.434274\pi$
$239$	98.0000			0.410042			0.205021	+	0.978758i	$0.434274\pi$
$240$	25.0000	+	43.3013i	0.104167	+	0.180422i
$241$	139.427	+	80.4984i	0.578537	+	0.334018i	0.760552	−	0.649277i	$-0.224929\pi$
$241$	139.427	+	80.4984i	0.578537	+	0.334018i	−0.182015	+	0.983296i	$0.558262\pi$
$242$	−58.5000	+	101.325i	−0.241736	+	0.418698i
$243$	−298.220	+	172.177i	−1.22724	+	0.708548i
$244$		−	281.745i		−	1.15469i
$245$		0			0
$246$	−120.000			−0.487805
$247$	90.0000	+	155.885i	0.364372	+	0.631112i
$248$	325.331	+	187.830i	1.31182	+	0.757378i
$249$	90.0000	−	155.885i	0.361446	−	0.626042i
$250$	9.68246	−	5.59017i	0.0387298	−	0.0223607i
$251$			335.410i			1.33630i	0.744029	+	0.668148i	$0.232913\pi$
$251$			335.410i			1.33630i	−0.744029	+	0.668148i	$0.767087\pi$
$252$		0			0
$253$	52.0000			0.205534
$254$	97.0000	+	168.009i	0.381890	+	0.661452i
$255$	232.379	+	134.164i	0.911290	+	0.526134i
$256$	85.5000	−	148.090i	0.333984	−	0.578478i
$257$	−116.190	+	67.0820i	−0.452099	+	0.261020i	−0.708716	−	0.705494i	$-0.750725\pi$
$257$	−116.190	+	67.0820i	−0.452099	+	0.261020i	0.256617	+	0.966513i	$0.417392\pi$
$258$			152.053i			0.589351i
$259$		0			0
$260$	−90.0000			−0.346154
$261$	−121.000	−	209.578i	−0.463602	−	0.802981i
$262$	−104.571	−	60.3738i	−0.399124	−	0.230434i
$263$	17.0000	−	29.4449i	0.0646388	−	0.111958i	−0.831895	−	0.554933i	$-0.812744\pi$
$263$	17.0000	−	29.4449i	0.0646388	−	0.111958i	0.896534	+	0.442976i	$0.146077\pi$
$264$	54.2218	−	31.3050i	0.205385	−	0.118579i
$265$		−	76.0263i		−	0.286892i
$266$		0			0
$267$	120.000			0.449438
$268$	21.0000	+	36.3731i	0.0783582	+	0.135720i
$269$	−220.760	−	127.456i	−0.820669	−	0.473814i	0.0299779	−	0.999551i	$-0.490456\pi$
$269$	−220.760	−	127.456i	−0.820669	−	0.473814i	−0.850647	+	0.525737i	$0.823790\pi$
$270$	10.0000	−	17.3205i	0.0370370	−	0.0641500i
$271$	278.855	−	160.997i	1.02898	−	0.594084i	0.112291	−	0.993675i	$-0.464181\pi$
$271$	278.855	−	160.997i	1.02898	−	0.594084i	0.916694	+	0.399591i	$0.130848\pi$
$272$			134.164i			0.493250i
$273$		0			0
$274$	166.000			0.605839
$275$	5.00000	+	8.66025i	0.0181818	+	0.0314918i
$276$	302.093	+	174.413i	1.09454	+	0.631932i
$277$	−7.00000	+	12.1244i	−0.0252708	+	0.0437702i	−0.878384	−	0.477955i	$-0.841378\pi$
$277$	−7.00000	+	12.1244i	−0.0252708	+	0.0437702i	0.853113	+	0.521725i	$0.174711\pi$
$278$	81.3327	−	46.9574i	0.292563	−	0.168912i
$279$			590.322i			2.11585i
$280$		0			0
$281$	2.00000			0.00711744			0.00355872	−	0.999994i	$-0.498867\pi$
$281$	2.00000			0.00711744			0.00355872	+	0.999994i	$0.498867\pi$
$282$	60.0000	+	103.923i	0.212766	+	0.368521i
$283$	81.3327	+	46.9574i	0.287395	+	0.165927i	0.636766	−	0.771057i	$-0.280272\pi$
$283$	81.3327	+	46.9574i	0.287395	+	0.165927i	−0.349372	+	0.936984i	$0.613605\pi$
$284$	93.0000	−	161.081i	0.327465	−	0.567186i
$285$	116.190	−	67.0820i	0.407682	−	0.235376i
$286$			26.8328i			0.0938210i
$287$		0			0
$288$	363.000			1.26042
$289$	215.500	+	373.257i	0.745675	+	1.29155i
$290$	−42.6028	−	24.5967i	−0.146906	−	0.0848164i
$291$	−60.0000	+	103.923i	−0.206186	+	0.357124i
$292$	139.427	−	80.4984i	0.477491	−	0.275680i
$293$			335.410i			1.14474i	0.819994	+	0.572372i	$0.193977\pi$
$293$			335.410i			1.14474i	−0.819994	+	0.572372i	$0.806023\pi$
$294$		0			0
$295$	90.0000			0.305085
$296$	−49.0000	−	84.8705i	−0.165541	−	0.286725i
$297$	15.4919	+	8.94427i	0.0521614	+	0.0301154i
$298$	−71.0000	+	122.976i	−0.238255	+	0.412670i
$299$	−302.093	+	174.413i	−1.01034	+	0.583322i
$300$			67.0820i			0.223607i
$301$		0			0
$302$	−2.00000			−0.00662252
$303$	150.000	+	259.808i	0.495050	+	0.857451i
$304$	58.0948	+	33.5410i	0.191101	+	0.110332i
$305$	105.000	−	181.865i	0.344262	−	0.596280i
$306$	255.617	−	147.580i	0.835349	−	0.482289i
$307$			201.246i			0.655525i	0.944760	+	0.327762i	$0.106295\pi$
$307$			201.246i			0.655525i	−0.944760	+	0.327762i	$0.893705\pi$
$308$		0			0
$309$	−720.000			−2.33010
$310$	60.0000	+	103.923i	0.193548	+	0.335236i
$311$	441.520	+	254.912i	1.41968	+	0.819652i	0.996270	−	0.0862870i	$-0.0275002\pi$
$311$	441.520	+	254.912i	1.41968	+	0.819652i	0.423408	+	0.905939i	$0.360834\pi$
$312$	−210.000	+	363.731i	−0.673077	+	1.16580i
$313$	278.855	−	160.997i	0.890910	−	0.514367i	0.0166699	−	0.999861i	$-0.494694\pi$
$313$	278.855	−	160.997i	0.890910	−	0.514367i	0.874240	+	0.485494i	$0.161360\pi$
$314$			67.0820i			0.213637i
$315$		0			0
$316$	−114.000			−0.360759
$317$	−187.000	−	323.894i	−0.589905	−	1.02175i	−0.994244	−	0.107137i	$-0.965832\pi$
$317$	−187.000	−	323.894i	−0.589905	−	1.02175i	0.404339	−	0.914609i	$-0.367502\pi$
$318$	−131.681	−	76.0263i	−0.414093	−	0.239076i
$319$	22.0000	−	38.1051i	0.0689655	−	0.119452i
$320$	25.1744	−	14.5344i	0.0786700	−	0.0454201i
$321$		−	474.046i		−	1.47678i
$322$		0			0
$323$	360.000			1.11455
$324$	−88.5000	−	153.286i	−0.273148	−	0.473106i
$325$	−58.0948	−	33.5410i	−0.178753	−	0.103203i
$326$	−17.0000	+	29.4449i	−0.0521472	+	0.0903217i
$327$	−549.964	+	317.522i	−1.68185	+	0.971014i
$328$		−	187.830i		−	0.572652i
$329$		0			0
$330$	20.0000			0.0606061
$331$	−241.000	−	417.424i	−0.728097	−	1.26110i	−0.957687	−	0.287813i	$-0.907072\pi$
$331$	−241.000	−	417.424i	−0.728097	−	1.26110i	0.229590	−	0.973287i	$-0.426261\pi$
$332$	104.571	+	60.3738i	0.314972	+	0.181849i
$333$	77.0000	−	133.368i	0.231231	−	0.400504i
$334$	92.9516	−	53.6656i	0.278298	−	0.160676i
$335$			31.3050i			0.0934476i
$336$		0			0
$337$	494.000			1.46588			0.732938	−	0.680296i	$-0.238149\pi$
$337$	494.000			1.46588			0.732938	+	0.680296i	$0.238149\pi$
$338$	−5.50000	−	9.52628i	−0.0162722	−	0.0281843i
$339$	131.681	+	76.0263i	0.388441	+	0.224266i
$340$	−90.0000	+	155.885i	−0.264706	+	0.458484i
$341$	−92.9516	+	53.6656i	−0.272585	+	0.157377i
$342$		−	147.580i		−	0.431522i
$343$		0			0
$344$	−238.000			−0.691860
$345$	130.000	+	225.167i	0.376812	+	0.652657i
$346$	127.808	+	73.7902i	0.369389	+	0.213267i
$347$	173.000	−	299.645i	0.498559	−	0.863530i	−0.501440	−	0.865193i	$-0.667196\pi$
$347$	173.000	−	299.645i	0.498559	−	0.863530i	0.999999	+	0.00166304i	$0.000529361\pi$
$348$	255.617	−	147.580i	0.734531	−	0.424082i
$349$		−	335.410i		−	0.961061i	−0.876978	−	0.480530i	$-0.840444\pi$
$349$		−	335.410i		−	0.961061i	0.876978	−	0.480530i	$-0.159556\pi$
$350$		0			0
$351$	−120.000			−0.341880
$352$	33.0000	+	57.1577i	0.0937500	+	0.162380i
$353$	−23.2379	−	13.4164i	−0.0658297	−	0.0380068i	0.466724	−	0.884403i	$-0.345434\pi$
$353$	−23.2379	−	13.4164i	−0.0658297	−	0.0380068i	−0.532554	+	0.846396i	$0.678768\pi$
$354$	90.0000	−	155.885i	0.254237	−	0.440352i
$355$	120.062	−	69.3181i	0.338204	−	0.195262i
$356$			80.4984i			0.226119i
$357$		0			0
$358$	−218.000			−0.608939
$359$	−169.000	−	292.717i	−0.470752	−	0.815367i	0.528688	−	0.848816i	$-0.322684\pi$
$359$	−169.000	−	292.717i	−0.470752	−	0.815367i	−0.999440	+	0.0334495i	$0.989351\pi$
$360$	149.110	+	86.0886i	0.414194	+	0.239135i
$361$	−90.5000	+	156.751i	−0.250693	+	0.434212i
$362$	220.760	−	127.456i	0.609834	−	0.352088i
$363$		−	523.240i		−	1.44143i
$364$		0			0
$365$	120.000			0.328767
$366$	−210.000	−	363.731i	−0.573770	−	0.993800i
$367$	−255.617	−	147.580i	−0.696504	−	0.402127i	0.109540	−	0.993982i	$-0.465062\pi$
$367$	−255.617	−	147.580i	−0.696504	−	0.402127i	−0.806044	+	0.591856i	$0.798396\pi$
$368$	−65.0000	+	112.583i	−0.176630	+	0.305933i
$369$	255.617	−	147.580i	0.692729	−	0.399947i
$370$		−	31.3050i		−	0.0846080i
$371$		0			0
$372$	−720.000			−1.93548
$373$	−43.0000	−	74.4782i	−0.115282	−	0.199673i	0.802611	−	0.596503i	$-0.203444\pi$
$373$	−43.0000	−	74.4782i	−0.115282	−	0.199673i	−0.917892	+	0.396830i	$0.870110\pi$
$374$	46.4758	+	26.8328i	0.124267	+	0.0717455i
$375$	−25.0000	+	43.3013i	−0.0666667	+	0.115470i
$376$	−162.665	+	93.9149i	−0.432620	+	0.249774i
$377$			295.161i			0.782920i
$378$		0			0
$379$	−262.000			−0.691293			−0.345646	−	0.938365i	$-0.612340\pi$
$379$	−262.000			−0.691293			−0.345646	+	0.938365i	$0.612340\pi$
$380$	45.0000	+	77.9423i	0.118421	+	0.205111i
$381$	−751.359	−	433.797i	−1.97207	−	1.13858i
$382$	−29.0000	+	50.2295i	−0.0759162	+	0.131491i
$383$	−487.996	+	281.745i	−1.27414	+	0.735625i	−0.975765	−	0.218823i	$-0.929778\pi$
$383$	−487.996	+	281.745i	−1.27414	+	0.735625i	−0.298376	+	0.954448i	$0.596445\pi$
$384$			532.184i			1.38590i
$385$		0			0
$386$	−206.000			−0.533679
$387$	−187.000	−	323.894i	−0.483204	−	0.836934i
$388$	−69.7137	−	40.2492i	−0.179674	−	0.103735i
$389$	−349.000	+	604.486i	−0.897172	+	1.55395i	−0.0660793	+	0.997814i	$0.521049\pi$
$389$	−349.000	+	604.486i	−0.897172	+	1.55395i	−0.831093	+	0.556134i	$0.812284\pi$
$390$	−116.190	+	67.0820i	−0.297922	+	0.172005i
$391$			697.653i			1.78428i
$392$		0			0
$393$	540.000			1.37405
$394$	−113.000	−	195.722i	−0.286802	−	0.496756i
$395$	−73.5867	−	42.4853i	−0.186295	−	0.107558i
$396$	−33.0000	+	57.1577i	−0.0833333	+	0.144338i
$397$	267.236	−	154.289i	0.673138	−	0.388636i	−0.124126	−	0.992266i	$-0.539613\pi$
$397$	267.236	−	154.289i	0.673138	−	0.388636i	0.797265	+	0.603630i	$0.206280\pi$
$398$		−	134.164i		−	0.337096i
$399$		0			0
$400$	−25.0000			−0.0625000
$401$	269.000	+	465.922i	0.670823	+	1.16190i	0.977671	+	0.210141i	$0.0673923\pi$
$401$	269.000	+	465.922i	0.670823	+	1.16190i	−0.306848	+	0.951758i	$0.599274\pi$
$402$	54.2218	+	31.3050i	0.134880	+	0.0778730i
$403$	360.000	−	623.538i	0.893300	−	1.54724i
$404$	−174.284	+	100.623i	−0.431397	+	0.249067i
$405$		−	131.928i		−	0.325748i
$406$		0			0
$407$	28.0000			0.0687961
$408$	420.000	+	727.461i	1.02941	+	1.78299i
$409$	−255.617	−	147.580i	−0.624980	−	0.360832i	0.153825	−	0.988098i	$-0.450841\pi$
$409$	−255.617	−	147.580i	−0.624980	−	0.360832i	−0.778805	+	0.627266i	$0.784174\pi$
$410$	30.0000	−	51.9615i	0.0731707	−	0.126735i
$411$	−642.915	+	371.187i	−1.56427	+	0.903132i
$412$		−	482.991i		−	1.17231i
$413$		0			0
$414$	286.000			0.690821
$415$	45.0000	+	77.9423i	0.108434	+	0.187813i
$416$	−383.425	−	221.371i	−0.921696	−	0.532141i
$417$	−210.000	+	363.731i	−0.503597	+	0.872256i
$418$	23.2379	−	13.4164i	0.0555931	−	0.0320967i
$419$		−	818.401i		−	1.95322i	−0.215009	−	0.976612i	$-0.568978\pi$
$419$		−	818.401i		−	1.95322i	0.215009	−	0.976612i	$-0.431022\pi$
$420$		0			0
$421$	−118.000			−0.280285			−0.140143	−	0.990131i	$-0.544756\pi$
$421$	−118.000			−0.280285			−0.140143	+	0.990131i	$0.544756\pi$
$422$	−59.0000	−	102.191i	−0.139810	−	0.242159i
$423$	−255.617	−	147.580i	−0.604295	−	0.348890i
$424$	119.000	−	206.114i	0.280660	−	0.486118i
$425$	−116.190	+	67.0820i	−0.273387	+	0.157840i
$426$		−	277.272i		−	0.650874i
$427$		0			0
$428$	318.000			0.742991
$429$	−60.0000	−	103.923i	−0.139860	−	0.242245i
$430$	−65.8407	−	38.0132i	−0.153118	−	0.0884027i
$431$	359.000	−	621.806i	0.832947	−	1.44271i	−0.0627447	−	0.998030i	$-0.519985\pi$
$431$	359.000	−	621.806i	0.832947	−	1.44271i	0.895691	−	0.444676i	$-0.146681\pi$
$432$	−38.7298	+	22.3607i	−0.0896524	+	0.0517608i
$433$			509.823i			1.17742i	0.808344	+	0.588711i	$0.200364\pi$
$433$			509.823i			1.17742i	−0.808344	+	0.588711i	$0.799636\pi$
$434$		0			0
$435$	220.000			0.505747
$436$	−213.000	−	368.927i	−0.488532	−	0.846162i
$437$	302.093	+	174.413i	0.691288	+	0.399115i
$438$	120.000	−	207.846i	0.273973	−	0.474534i
$439$	−23.2379	+	13.4164i	−0.0529337	+	0.0305613i	−0.526233	−	0.850340i	$-0.676396\pi$
$439$	−23.2379	+	13.4164i	−0.0529337	+	0.0305613i	0.473300	+	0.880902i	$0.343063\pi$
$440$			31.3050i			0.0711476i
$441$		0			0
$442$	−360.000			−0.814480
$443$	317.000	+	549.060i	0.715576	+	1.23941i	0.962737	+	0.270439i	$0.0871689\pi$
$443$	317.000	+	549.060i	0.715576	+	1.23941i	−0.247161	+	0.968974i	$0.579498\pi$
$444$	162.665	+	93.9149i	0.366363	+	0.211520i
$445$	−30.0000	+	51.9615i	−0.0674157	+	0.116767i
$446$	−69.7137	+	40.2492i	−0.156309	+	0.0902449i
$447$		−	635.043i		−	1.42068i
$448$		0			0
$449$	338.000			0.752784			0.376392	−	0.926461i	$-0.377165\pi$
$449$	338.000			0.752784			0.376392	+	0.926461i	$0.377165\pi$
$450$	27.5000	+	47.6314i	0.0611111	+	0.105848i
$451$	46.4758	+	26.8328i	0.103051	+	0.0594963i
$452$	−51.0000	+	88.3346i	−0.112832	+	0.195431i
$453$	7.74597	−	4.47214i	0.0170993	−	0.00987226i
$454$		−	254.912i		−	0.561480i
$455$		0			0
$456$	420.000			0.921053
$457$	233.000	+	403.568i	0.509847	+	0.883081i	0.999935	+	0.0114077i	$0.00363126\pi$
$457$	233.000	+	403.568i	0.509847	+	0.883081i	−0.490088	+	0.871673i	$0.663035\pi$
$458$	11.6190	+	6.70820i	0.0253689	+	0.0146467i
$459$	−120.000	+	207.846i	−0.261438	+	0.452824i
$460$	−151.046	+	87.2067i	−0.328362	+	0.189580i
$461$		−	442.741i		−	0.960394i	−0.877161	−	0.480197i	$-0.840565\pi$
$461$		−	442.741i		−	0.960394i	0.877161	−	0.480197i	$-0.159435\pi$
$462$		0			0
$463$	206.000			0.444924			0.222462	−	0.974941i	$-0.428591\pi$
$463$	206.000			0.444924			0.222462	+	0.974941i	$0.428591\pi$
$464$	55.0000	+	95.2628i	0.118534	+	0.205308i
$465$	−464.758	−	268.328i	−0.999480	−	0.577050i
$466$	−107.000	+	185.329i	−0.229614	+	0.397703i
$467$	313.712	−	181.122i	0.671759	−	0.387840i	−0.124984	−	0.992159i	$-0.539888\pi$
$467$	313.712	−	181.122i	0.671759	−	0.387840i	0.796743	+	0.604318i	$0.206554\pi$
$468$		−	442.741i		−	0.946029i
$469$		0			0
$470$	−60.0000			−0.127660
$471$	−150.000	−	259.808i	−0.318471	−	0.551609i
$472$	243.998	+	140.872i	0.516945	+	0.298458i
$473$	34.0000	−	58.8897i	0.0718816	−	0.124503i
$474$	−147.173	+	84.9706i	−0.310492	+	0.179263i
$475$			67.0820i			0.141225i
$476$		0			0
$477$	374.000			0.784067
$478$	49.0000	+	84.8705i	0.102510	+	0.177553i
$479$	−185.903	−	107.331i	−0.388107	−	0.224074i	0.293233	−	0.956041i	$-0.405269\pi$
$479$	−185.903	−	107.331i	−0.388107	−	0.224074i	−0.681340	+	0.731967i	$0.738602\pi$
$480$	−165.000	+	285.788i	−0.343750	+	0.595392i
$481$	−162.665	+	93.9149i	−0.338181	+	0.195249i
$482$			160.997i			0.334018i
$483$		0			0
$484$	351.000			0.725207
$485$	−30.0000	−	51.9615i	−0.0618557	−	0.107137i
$486$	−298.220	−	172.177i	−0.613621	−	0.354274i
$487$	83.0000	−	143.760i	0.170431	−	0.295196i	−0.768139	−	0.640283i	$-0.778817\pi$
$487$	83.0000	−	143.760i	0.170431	−	0.295196i	0.938571	+	0.345087i	$0.112151\pi$
$488$	569.329	−	328.702i	1.16666	−	0.673570i
$489$		−	152.053i		−	0.310946i
$490$		0			0
$491$	−838.000			−1.70672			−0.853360	−	0.521321i	$-0.825439\pi$
$491$	−838.000			−1.70672			−0.853360	+	0.521321i	$0.825439\pi$
$492$	180.000	+	311.769i	0.365854	+	0.633677i
$493$	511.234	+	295.161i	1.03699	+	0.598704i
$494$	−90.0000	+	155.885i	−0.182186	+	0.315556i
$495$	−42.6028	+	24.5967i	−0.0860663	+	0.0496904i
$496$		−	268.328i		−	0.540984i
$497$		0			0
$498$	180.000			0.361446
$499$	131.000	+	226.899i	0.262525	+	0.454707i	0.966912	−	0.255109i	$-0.0821114\pi$
$499$	131.000	+	226.899i	0.262525	+	0.454707i	−0.704387	+	0.709816i	$0.748778\pi$
$500$	−29.0474	−	16.7705i	−0.0580948	−	0.0335410i
$501$	−240.000	+	415.692i	−0.479042	+	0.829725i
$502$	−290.474	+	167.705i	−0.578633	+	0.334074i
$503$			429.325i			0.853529i	0.904363	+	0.426764i	$0.140347\pi$
$503$			429.325i			0.853529i	−0.904363	+	0.426764i	$0.859653\pi$
$504$		0			0
$505$	−150.000			−0.297030
$506$	26.0000	+	45.0333i	0.0513834	+	0.0889987i
$507$	42.6028	+	24.5967i	0.0840292	+	0.0485143i
$508$	291.000	−	504.027i	0.572835	−	0.992179i
$509$	778.470	−	449.450i	1.52941	−	0.883005i	0.530023	−	0.847983i	$-0.322183\pi$
$509$	778.470	−	449.450i	1.52941	−	0.883005i	0.999387	−	0.0350222i	$-0.0111502\pi$
$510$			268.328i			0.526134i
$511$		0			0
$512$	−305.000			−0.595703
$513$	60.0000	+	103.923i	0.116959	+	0.202579i
$514$	−116.190	−	67.0820i	−0.226050	−	0.130510i
$515$	180.000	−	311.769i	0.349515	−	0.605377i
$516$	395.044	−	228.079i	0.765590	−	0.442013i
$517$		−	53.6656i		−	0.103802i
$518$		0			0
$519$	−660.000			−1.27168
$520$	−105.000	−	181.865i	−0.201923	−	0.349741i
$521$	−627.423	−	362.243i	−1.20427	−	0.695284i	−0.242766	−	0.970085i	$-0.578055\pi$
$521$	−627.423	−	362.243i	−1.20427	−	0.695284i	−0.961501	+	0.274801i	$0.911388\pi$
$522$	121.000	−	209.578i	0.231801	−	0.401491i
$523$	−453.139	+	261.620i	−0.866423	+	0.500229i	−0.866158	−	0.499771i	$-0.833418\pi$
$523$	−453.139	+	261.620i	−0.866423	+	0.500229i	−0.000264858		1.00000i	$0.500084\pi$
$524$			362.243i			0.691303i
$525$		0			0
$526$	34.0000			0.0646388
$527$	−720.000	−	1247.08i	−1.36622	−	2.36637i
$528$	−38.7298	−	22.3607i	−0.0733520	−	0.0423498i
$529$	−73.5000	+	127.306i	−0.138941	+	0.240654i
$530$	65.8407	−	38.0132i	0.124228	−	0.0717229i
$531$			442.741i			0.833788i
$532$		0			0
$533$	−360.000			−0.675422
$534$	60.0000	+	103.923i	0.112360	+	0.194612i
$535$	205.268	+	118.512i	0.383679	+	0.221517i
$536$	−49.0000	+	84.8705i	−0.0914179	+	0.158340i
$537$	844.310	−	487.463i	1.57227	−	0.907752i
$538$		−	254.912i		−	0.473814i
$539$		0			0
$540$	−60.0000			−0.111111
$541$	−421.000	−	729.193i	−0.778189	−	1.34786i	−0.932985	−	0.359916i	$-0.882805\pi$
$541$	−421.000	−	729.193i	−0.778189	−	1.34786i	0.154796	−	0.987946i	$-0.450528\pi$
$542$	278.855	+	160.997i	0.514492	+	0.297042i
$543$	−570.000	+	987.269i	−1.04972	+	1.81817i
$544$	−766.851	+	442.741i	−1.40965	+	0.813863i
$545$		−	317.522i		−	0.582609i
$546$		0			0
$547$	134.000			0.244973			0.122486	−	0.992470i	$-0.460913\pi$
$547$	134.000			0.244973			0.122486	+	0.992470i	$0.460913\pi$
$548$	−249.000	−	431.281i	−0.454380	−	0.787008i
$549$	894.659	+	516.532i	1.62962	+	0.940859i
$550$	−5.00000	+	8.66025i	−0.00909091	+	0.0157459i
$551$	255.617	−	147.580i	0.463915	−	0.267841i
$552$			813.929i			1.47451i
$553$		0			0
$554$	−14.0000			−0.0252708
$555$	70.0000	+	121.244i	0.126126	+	0.218457i
$556$	−243.998	−	140.872i	−0.438845	−	0.253367i
$557$	353.000	−	611.414i	0.633752	−	1.09769i	−0.353026	−	0.935614i	$-0.614847\pi$
$557$	353.000	−	611.414i	0.633752	−	1.09769i	0.986778	−	0.162077i	$-0.0518195\pi$
$558$	−511.234	+	295.161i	−0.916190	+	0.528962i
$559$			456.158i			0.816025i
$560$		0			0
$561$	−240.000			−0.427807
$562$	1.00000	+	1.73205i	0.00177936	+	0.00308194i
$563$	11.6190	+	6.70820i	0.0206376	+	0.0119151i	0.510283	−	0.860006i	$-0.329541\pi$
$563$	11.6190	+	6.70820i	0.0206376	+	0.0119151i	−0.489646	+	0.871921i	$0.662874\pi$
$564$	180.000	−	311.769i	0.319149	−	0.552782i
$565$	−65.8407	+	38.0132i	−0.116532	+	0.0672799i
$566$			93.9149i			0.165927i
$567$		0			0
$568$	434.000			0.764085
$569$	41.0000	+	71.0141i	0.0720562	+	0.124805i	0.899802	−	0.436298i	$-0.143711\pi$
$569$	41.0000	+	71.0141i	0.0720562	+	0.124805i	−0.827746	+	0.561103i	$0.810377\pi$
$570$	116.190	+	67.0820i	0.203841	+	0.117688i
$571$	59.0000	−	102.191i	0.103327	−	0.178968i	−0.809726	−	0.586808i	$-0.800384\pi$
$571$	59.0000	−	102.191i	0.103327	−	0.178968i	0.913054	+	0.407839i	$0.133718\pi$
$572$	69.7137	−	40.2492i	0.121877	−	0.0703658i
$573$		−	259.384i		−	0.452677i
$574$		0			0
$575$	−130.000			−0.226087
$576$	71.5000	+	123.842i	0.124132	+	0.215003i
$577$	766.851	+	442.741i	1.32903	+	0.767316i	0.985150	−	0.171697i	$-0.0549250\pi$
$577$	766.851	+	442.741i	1.32903	+	0.767316i	0.343881	+	0.939013i	$0.388258\pi$
$578$	−215.500	+	373.257i	−0.372837	+	0.645773i
$579$	797.835	−	460.630i	1.37795	−	0.795561i
$580$			147.580i			0.254449i
$581$		0			0
$582$	−120.000			−0.206186
$583$	34.0000	+	58.8897i	0.0583190	+	0.101012i
$584$	325.331	+	187.830i	0.557073	+	0.321626i
$585$	165.000	−	285.788i	0.282051	−	0.488527i
$586$	−290.474	+	167.705i	−0.495689	+	0.286186i
$587$		−	791.568i		−	1.34850i	−0.738504	−	0.674249i	$-0.764468\pi$
$587$		−	791.568i		−	1.34850i	0.738504	−	0.674249i	$-0.235532\pi$
$588$		0			0
$589$	−720.000			−1.22241
$590$	45.0000	+	77.9423i	0.0762712	+	0.132106i
$591$	875.294	+	505.351i	1.48104	+	0.855078i
$592$	−35.0000	+	60.6218i	−0.0591216	+	0.102402i
$593$	−116.190	+	67.0820i	−0.195935	+	0.113123i	−0.594758	−	0.803905i	$-0.702752\pi$
$593$	−116.190	+	67.0820i	−0.195935	+	0.113123i	0.398823	+	0.917028i	$0.369419\pi$
$594$			17.8885i			0.0301154i
$595$		0			0
$596$	426.000			0.714765
$597$	300.000	+	519.615i	0.502513	+	0.870377i
$598$	−302.093	−	174.413i	−0.505172	−	0.291661i
$599$	−199.000	+	344.678i	−0.332220	+	0.575423i	−0.982947	−	0.183890i	$-0.941131\pi$
$599$	−199.000	+	344.678i	−0.332220	+	0.575423i	0.650727	+	0.759312i	$0.274464\pi$
$600$	−135.554	+	78.2624i	−0.225924	+	0.130437i
$601$			134.164i			0.223235i	0.993751	+	0.111617i	$0.0356031\pi$
$601$			134.164i			0.223235i	−0.993751	+	0.111617i	$0.964397\pi$
$602$		0			0
$603$	−154.000			−0.255390
$604$	3.00000	+	5.19615i	0.00496689	+	0.00860290i
$605$	226.570	+	130.810i	0.374495	+	0.216215i
$606$	−150.000	+	259.808i	−0.247525	+	0.428725i
$607$	−813.327	+	469.574i	−1.33991	+	0.773598i	−0.986794	−	0.161980i	$-0.948212\pi$
$607$	−813.327	+	469.574i	−1.33991	+	0.773598i	−0.353118	+	0.935579i	$0.614879\pi$
$608$			442.741i			0.728193i
$609$		0			0
$610$	210.000			0.344262
$611$	180.000	+	311.769i	0.294599	+	0.510260i
$612$	−766.851	−	442.741i	−1.25302	−	0.723434i
$613$	−103.000	+	178.401i	−0.168026	+	0.291030i	−0.937726	−	0.347376i	$-0.887073\pi$
$613$	−103.000	+	178.401i	−0.168026	+	0.291030i	0.769700	+	0.638406i	$0.220406\pi$
$614$	−174.284	+	100.623i	−0.283851	+	0.163881i
$615$			268.328i			0.436306i
$616$		0			0
$617$	494.000			0.800648			0.400324	−	0.916374i	$-0.368898\pi$
$617$	494.000			0.800648			0.400324	+	0.916374i	$0.368898\pi$
$618$	−360.000	−	623.538i	−0.582524	−	1.00896i
$619$	−104.571	−	60.3738i	−0.168935	−	0.0975345i	0.413149	−	0.910664i	$-0.364429\pi$
$619$	−104.571	−	60.3738i	−0.168935	−	0.0975345i	−0.582083	+	0.813129i	$0.697762\pi$
$620$	180.000	−	311.769i	0.290323	−	0.502853i
$621$	−201.395	+	116.276i	−0.324308	+	0.187239i
$622$			509.823i			0.819652i
$623$		0			0
$624$	300.000			0.480769
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	278.855	+	160.997i	0.445455	+	0.257184i
$627$	−60.0000	+	103.923i	−0.0956938	+	0.165746i
$628$	174.284	−	100.623i	0.277523	−	0.160228i
$629$			375.659i			0.597233i
$630$		0			0
$631$	542.000			0.858954			0.429477	−	0.903078i	$-0.358698\pi$
$631$	542.000			0.858954			0.429477	+	0.903078i	$0.358698\pi$
$632$	−133.000	−	230.363i	−0.210443	−	0.364498i
$633$	457.012	+	263.856i	0.721978	+	0.416834i
$634$	187.000	−	323.894i	0.294953	−	0.510873i
$635$	375.679	−	216.899i	0.591621	−	0.341573i
$636$			456.158i			0.717229i
$637$		0			0
$638$	44.0000			0.0689655
$639$	341.000	+	590.629i	0.533646	+	0.924303i
$640$	−230.443	−	133.046i	−0.360066	−	0.207884i
$641$	149.000	−	258.076i	0.232449	−	0.402614i	−0.726079	−	0.687611i	$-0.758659\pi$
$641$	149.000	−	258.076i	0.232449	−	0.402614i	0.958528	+	0.284997i	$0.0919927\pi$
$642$	410.536	−	237.023i	0.639465	−	0.369195i
$643$			1006.23i			1.56490i	0.622714	+	0.782450i	$0.286030\pi$
$643$			1006.23i			1.56490i	−0.622714	+	0.782450i	$0.713970\pi$
$644$		0			0
$645$	340.000			0.527132
$646$	180.000	+	311.769i	0.278638	+	0.482615i
$647$	−557.710	−	321.994i	−0.861993	−	0.497672i	0.00268605	−	0.999996i	$-0.499145\pi$
$647$	−557.710	−	321.994i	−0.861993	−	0.497672i	−0.864679	+	0.502324i	$0.832478\pi$
$648$	206.500	−	357.668i	0.318673	−	0.551958i
$649$	−69.7137	+	40.2492i	−0.107417	+	0.0620173i
$650$		−	67.0820i		−	0.103203i
$651$		0			0
$652$	102.000			0.156442
$653$	77.0000	+	133.368i	0.117917	+	0.204239i	0.918942	−	0.394392i	$-0.129045\pi$
$653$	77.0000	+	133.368i	0.117917	+	0.204239i	−0.801025	+	0.598631i	$0.795712\pi$
$654$	−549.964	−	317.522i	−0.840923	−	0.485507i
$655$	−135.000	+	233.827i	−0.206107	+	0.356988i
$656$	−116.190	+	67.0820i	−0.177118	+	0.102259i
$657$			590.322i			0.898511i
$658$		0			0
$659$	338.000			0.512898			0.256449	−	0.966558i	$-0.417447\pi$
$659$	338.000			0.512898			0.256449	+	0.966558i	$0.417447\pi$
$660$	−30.0000	−	51.9615i	−0.0454545	−	0.0787296i
$661$	499.615	+	288.453i	0.755847	+	0.436388i	0.827803	−	0.561019i	$-0.189591\pi$
$661$	499.615	+	288.453i	0.755847	+	0.436388i	−0.0719557	+	0.997408i	$0.522924\pi$
$662$	241.000	−	417.424i	0.364048	−	0.630550i
$663$	1394.27	−	804.984i	2.10298	−	1.21415i
$664$			281.745i			0.424314i
$665$		0			0
$666$	154.000			0.231231
$667$	286.000	+	495.367i	0.428786	+	0.742678i
$668$	−278.855	−	160.997i	−0.417447	−	0.241013i
$669$	180.000	−	311.769i	0.269058	−	0.466023i
$670$	−27.1109	+	15.6525i	−0.0404640	+	0.0233619i
$671$			187.830i			0.279925i
$672$		0			0
$673$	−814.000			−1.20951			−0.604755	−	0.796412i	$-0.706729\pi$
$673$	−814.000			−1.20951			−0.604755	+	0.796412i	$0.706729\pi$
$674$	247.000	+	427.817i	0.366469	+	0.634743i
$675$	−38.7298	−	22.3607i	−0.0573775	−	0.0331269i
$676$	−16.5000	+	28.5788i	−0.0244083	+	0.0422764i
$677$	−592.566	+	342.118i	−0.875283	+	0.505345i	−0.869100	−	0.494636i	$-0.835301\pi$
$677$	−592.566	+	342.118i	−0.875283	+	0.505345i	−0.00618263	+	0.999981i	$0.501968\pi$
$678$			152.053i			0.224266i
$679$		0			0
$680$	−420.000			−0.617647
$681$	570.000	+	987.269i	0.837004	+	1.44973i
$682$	−92.9516	−	53.6656i	−0.136293	−	0.0786886i
$683$	−463.000	+	801.940i	−0.677892	+	1.17414i	0.297723	+	0.954652i	$0.403773\pi$
$683$	−463.000	+	801.940i	−0.677892	+	1.17414i	−0.975615	+	0.219490i	$0.929561\pi$
$684$	−383.425	+	221.371i	−0.560563	+	0.323641i
$685$		−	371.187i		−	0.541879i
$686$		0			0
$687$	−60.0000			−0.0873362
$688$	85.0000	+	147.224i	0.123547	+	0.213989i
$689$	−395.044	−	228.079i	−0.573359	−	0.331029i
$690$	−130.000	+	225.167i	−0.188406	+	0.326328i
$691$	499.615	−	288.453i	0.723032	−	0.417443i	−0.0928359	−	0.995681i	$-0.529593\pi$
$691$	499.615	−	288.453i	0.723032	−	0.417443i	0.815867	+	0.578239i	$0.196260\pi$
$692$		−	442.741i		−	0.639800i
$693$		0			0
$694$	346.000			0.498559
$695$	−105.000	−	181.865i	−0.151079	−	0.261677i
$696$	596.439	+	344.354i	0.856953	+	0.494762i
$697$	−360.000	+	623.538i	−0.516499	+	0.894603i
$698$	290.474	−	167.705i	0.416152	−	0.240265i
$699$		−	957.037i		−	1.36915i
$700$		0			0
$701$	362.000			0.516405			0.258203	−	0.966091i	$-0.416870\pi$
$701$	362.000			0.516405			0.258203	+	0.966091i	$0.416870\pi$
$702$	−60.0000	−	103.923i	−0.0854701	−	0.148039i
$703$	162.665	+	93.9149i	0.231387	+	0.133592i
$704$	−13.0000	+	22.5167i	−0.0184659	+	0.0319839i
$705$	232.379	−	134.164i	0.329616	−	0.190304i
$706$		−	26.8328i		−	0.0380068i
$707$		0			0
$708$	−540.000			−0.762712
$709$	−529.000	−	916.255i	−0.746121	−	1.29232i	−0.949669	−	0.313255i	$-0.898581\pi$
$709$	−529.000	−	916.255i	−0.746121	−	1.29232i	0.203548	−	0.979065i	$-0.434753\pi$
$710$	120.062	+	69.3181i	0.169102	+	0.0976311i
$711$	209.000	−	361.999i	0.293952	−	0.509140i
$712$	−162.665	+	93.9149i	−0.228463	+	0.131903i
$713$		−	1395.31i		−	1.95695i
$714$		0			0
$715$	60.0000			0.0839161
$716$	327.000	+	566.381i	0.456704	+	0.791034i
$717$	−379.552	−	219.135i	−0.529362	−	0.305627i
$718$	169.000	−	292.717i	0.235376	−	0.407683i
$719$	−418.282	+	241.495i	−0.581755	+	0.335877i	−0.761831	−	0.647776i	$-0.775699\pi$
$719$	−418.282	+	241.495i	−0.581755	+	0.335877i	0.180075	+	0.983653i	$0.442366\pi$
$720$		−	122.984i		−	0.170811i
$721$		0			0
$722$	−181.000			−0.250693
$723$	−360.000	−	623.538i	−0.497925	−	0.862432i
$724$	−662.280	−	382.368i	−0.914752	−	0.528132i
$725$	−55.0000	+	95.2628i	−0.0758621	+	0.131397i
$726$	453.139	−	261.620i	0.624158	−	0.360358i
$727$			1126.98i			1.55018i	0.631853	+	0.775088i	$0.282295\pi$
$727$			1126.98i			1.55018i	−0.631853	+	0.775088i	$0.717705\pi$
$728$		0			0
$729$	1009.00			1.38409
$730$	60.0000	+	103.923i	0.0821918	+	0.142360i
$731$	790.089	+	456.158i	1.08083	+	0.624019i
$732$	−630.000	+	1091.19i	−0.860656	+	1.49070i
$733$	−1127.04	+	650.696i	−1.53757	+	0.887716i	−0.538589	+	0.842569i	$0.681042\pi$
$733$	−1127.04	+	650.696i	−1.53757	+	0.887716i	−0.998980	+	0.0451472i	$0.985624\pi$
$734$		−	295.161i		−	0.402127i
$735$		0			0
$736$	−858.000			−1.16576
$737$	−14.0000	−	24.2487i	−0.0189959	−	0.0329019i
$738$	255.617	+	147.580i	0.346364	+	0.199974i
$739$	491.000	−	850.437i	0.664411	−	1.15079i	−0.315033	−	0.949081i	$-0.602016\pi$
$739$	491.000	−	850.437i	0.664411	−	1.15079i	0.979445	−	0.201714i	$-0.0646510\pi$
$740$	−81.3327	+	46.9574i	−0.109909	+	0.0634560i
$741$		−	804.984i		−	1.08635i
$742$		0			0
$743$	−694.000			−0.934051			−0.467026	−	0.884244i	$-0.654674\pi$
$743$	−694.000			−0.934051			−0.467026	+	0.884244i	$0.654674\pi$
$744$	−840.000	−	1454.92i	−1.12903	−	1.95554i
$745$	274.982	+	158.761i	0.369103	+	0.213102i
$746$	43.0000	−	74.4782i	0.0576408	−	0.0998367i
$747$	−383.425	+	221.371i	−0.513287	+	0.296346i
$748$		−	160.997i		−	0.215236i
$749$		0			0
$750$	−50.0000			−0.0666667
$751$	−121.000	−	209.578i	−0.161119	−	0.279065i	0.774152	−	0.633000i	$-0.218177\pi$
$751$	−121.000	−	209.578i	−0.161119	−	0.279065i	−0.935270	+	0.353935i	$0.884843\pi$
$752$	116.190	+	67.0820i	0.154507	+	0.0892048i
$753$	750.000	−	1299.04i	0.996016	−	1.72515i
$754$	−255.617	+	147.580i	−0.339014	+	0.195730i
$755$			4.47214i			0.00592336i
$756$		0			0
$757$	−106.000			−0.140026			−0.0700132	−	0.997546i	$-0.522304\pi$
$757$	−106.000			−0.140026			−0.0700132	+	0.997546i	$0.522304\pi$
$758$	−131.000	−	226.899i	−0.172823	−	0.299339i
$759$	−201.395	−	116.276i	−0.265343	−	0.153196i
$760$	−105.000	+	181.865i	−0.138158	+	0.239296i
$761$	952.754	−	550.073i	1.25198	−	0.722829i	0.280475	−	0.959861i	$-0.409508\pi$
$761$	952.754	−	550.073i	1.25198	−	0.722829i	0.971502	+	0.237033i	$0.0761748\pi$
$762$		−	867.594i		−	1.13858i
$763$		0			0
$764$	174.000			0.227749
$765$	−330.000	−	571.577i	−0.431373	−	0.747159i
$766$	−487.996	−	281.745i	−0.637070	−	0.367813i
$767$	270.000	−	467.654i	0.352021	−	0.609718i
$768$	−662.280	+	382.368i	−0.862344	+	0.497875i
$769$			1126.98i			1.46551i	0.680492	+	0.732756i	$0.261766\pi$
$769$			1126.98i			1.46551i	−0.680492	+	0.732756i	$0.738234\pi$
$770$		0			0
$771$	600.000			0.778210
$772$	309.000	+	535.204i	0.400259	+	0.693269i
$773$	−708.756	−	409.200i	−0.916890	−	0.529367i	−0.0342484	−	0.999413i	$-0.510904\pi$
$773$	−708.756	−	409.200i	−0.916890	−	0.529367i	−0.882642	+	0.470047i	$0.844237\pi$
$774$	187.000	−	323.894i	0.241602	−	0.418467i
$775$	232.379	−	134.164i	0.299844	−	0.173115i
$776$		−	187.830i		−	0.242049i
$777$		0			0
$778$	−698.000			−0.897172
$779$	180.000	+	311.769i	0.231065	+	0.400217i
$780$	348.569	+	201.246i	0.446883	+	0.258008i
$781$	−62.0000	+	107.387i	−0.0793854	+	0.137500i
$782$	−604.185	+	348.827i	−0.772616	+	0.446070i
$783$			196.774i			0.251308i
$784$		0			0
$785$	150.000			0.191083
$786$	270.000	+	467.654i	0.343511	+	0.594979i
$787$	−592.566	−	342.118i	−0.752943	−	0.434712i	0.0738130	−	0.997272i	$-0.476483\pi$
$787$	−592.566	−	342.118i	−0.752943	−	0.434712i	−0.826756	+	0.562560i	$0.809817\pi$
$788$	−339.000	+	587.165i	−0.430203	+	0.745134i
$789$	−131.681	+	76.0263i	−0.166897	+	0.0963578i
$790$		−	84.9706i		−	0.107558i
$791$		0			0
$792$	−154.000			−0.194444
$793$	−630.000	−	1091.19i	−0.794451	−	1.37603i
$794$	267.236	+	154.289i	0.336569	+	0.194318i
$795$	−170.000	+	294.449i	−0.213836	+	0.370376i
$796$	−348.569	+	201.246i	−0.437900	+	0.252822i
$797$			308.577i			0.387174i	0.981083	+	0.193587i	$0.0620121\pi$
$797$			308.577i			0.387174i	−0.981083	+	0.193587i	$0.937988\pi$
$798$		0			0
$799$	720.000			0.901126
$800$	−82.5000	−	142.894i	−0.103125	−	0.178618i
$801$	−255.617	−	147.580i	−0.319122	−	0.184245i
$802$	−269.000	+	465.922i	−0.335411	+	0.580950i
$803$	−92.9516	+	53.6656i	−0.115755	+	0.0668314i
$804$		−	187.830i		−	0.233619i
$805$		0			0
$806$	720.000			0.893300
$807$	570.000	+	987.269i	0.706320	+	1.22338i
$808$	−406.663	−	234.787i	−0.503296	−	0.290578i
$809$	−679.000	+	1176.06i	−0.839308	+	1.45372i	0.0511665	+	0.998690i	$0.483706\pi$
$809$	−679.000	+	1176.06i	−0.839308	+	1.45372i	−0.890474	+	0.455034i	$0.849627\pi$
$810$	114.253	−	65.9640i	0.141053	−	0.0814370i
$811$		−	308.577i		−	0.380490i	−0.981737	−	0.190245i	$-0.939072\pi$
$811$		−	308.577i		−	0.380490i	0.981737	−	0.190245i	$-0.0609282\pi$
$812$		0			0
$813$	−1440.00			−1.77122
$814$	14.0000	+	24.2487i	0.0171990	+	0.0297896i
$815$	65.8407	+	38.0132i	0.0807862	+	0.0466419i
$816$	300.000	−	519.615i	0.367647	−	0.636783i
$817$	395.044	−	228.079i	0.483530	−	0.279166i
$818$		−	295.161i		−	0.360832i
$819$		0			0
$820$	−180.000			−0.219512
$821$	−241.000	−	417.424i	−0.293544	−	0.508434i	0.681101	−	0.732190i	$-0.261502\pi$
$821$	−241.000	−	417.424i	−0.293544	−	0.508434i	−0.974645	+	0.223756i	$0.928168\pi$
$822$	−642.915	−	371.187i	−0.782135	−	0.451566i
$823$	−463.000	+	801.940i	−0.562576	+	0.974410i	0.434695	+	0.900578i	$0.356856\pi$
$823$	−463.000	+	801.940i	−0.562576	+	0.974410i	−0.997271	+	0.0738323i	$0.976477\pi$
$824$	975.992	−	563.489i	1.18446	−	0.683846i
$825$		−	44.7214i		−	0.0542077i
$826$		0			0
$827$	−226.000			−0.273277			−0.136638	−	0.990621i	$-0.543630\pi$
$827$	−226.000			−0.273277			−0.136638	+	0.990621i	$0.543630\pi$
$828$	−429.000	−	743.050i	−0.518116	−	0.897403i
$829$	1266.47	+	731.194i	1.52770	+	0.882020i	0.999458	+	0.0329276i	$0.0104831\pi$
$829$	1266.47	+	731.194i	1.52770	+	0.882020i	0.528245	+	0.849092i	$0.322850\pi$
$830$	−45.0000	+	77.9423i	−0.0542169	+	0.0939064i
$831$	54.2218	−	31.3050i	0.0652488	−	0.0376714i
$832$		−	174.413i		−	0.209631i
$833$		0			0
$834$	−420.000			−0.503597
$835$	−120.000	−	207.846i	−0.143713	−	0.248917i
$836$	−69.7137	−	40.2492i	−0.0833896	−	0.0481450i
$837$	240.000	−	415.692i	0.286738	−	0.496645i
$838$	708.756	−	409.200i	0.845771	−	0.488306i
$839$		−	831.817i		−	0.991439i	−0.868483	−	0.495719i	$-0.834904\pi$
$839$		−	831.817i		−	0.991439i	0.868483	−	0.495719i	$-0.165096\pi$
$840$		0			0
$841$	−357.000			−0.424495
$842$	−59.0000	−	102.191i	−0.0700713	−	0.121367i
$843$	−7.74597	−	4.47214i	−0.00918857	−	0.00530502i
$844$	−177.000	+	306.573i	−0.209716	+	0.363238i
$845$	−21.3014	+	12.2984i	−0.0252088	+	0.0145543i
$846$		−	295.161i		−	0.348890i
$847$		0			0
$848$	−170.000			−0.200472
$849$	−210.000	−	363.731i	−0.247350	−	0.428422i
$850$	−116.190	−	67.0820i	−0.136694	−	0.0789200i
$851$	−182.000	+	315.233i	−0.213866	+	0.370427i
$852$	−720.375	+	415.909i	−0.845510	+	0.488156i
$853$		−	40.2492i		−	0.0471855i	−0.999722	−	0.0235927i	$-0.992489\pi$
$853$		−	40.2492i		−	0.0471855i	0.999722	−	0.0235927i	$-0.00751050\pi$
$854$		0			0
$855$	−330.000			−0.385965
$856$	371.000	+	642.591i	0.433411	+	0.750690i
$857$	−232.379	−	134.164i	−0.271154	−	0.156551i	0.358258	−	0.933623i	$-0.383371\pi$
$857$	−232.379	−	134.164i	−0.271154	−	0.156551i	−0.629412	+	0.777072i	$0.716704\pi$
$858$	60.0000	−	103.923i	0.0699301	−	0.121122i
$859$	−267.236	+	154.289i	−0.311101	+	0.179614i	−0.647419	−	0.762134i	$-0.724152\pi$
$859$	−267.236	+	154.289i	−0.311101	+	0.179614i	0.336318	+	0.941748i	$0.390818\pi$
$860$			228.079i			0.265208i
$861$		0			0
$862$	718.000			0.832947
$863$	257.000	+	445.137i	0.297798	+	0.515802i	0.975632	−	0.219413i	$-0.0704144\pi$
$863$	257.000	+	445.137i	0.297798	+	0.515802i	−0.677834	+	0.735215i	$0.737081\pi$
$864$	−255.617	−	147.580i	−0.295853	−	0.170811i
$865$	165.000	−	285.788i	0.190751	−	0.330391i
$866$	−441.520	+	254.912i	−0.509838	+	0.294355i
$867$		−	1927.49i		−	2.22317i
$868$		0			0
$869$	76.0000			0.0874568
$870$	110.000	+	190.526i	0.126437	+	0.218995i
$871$	162.665	+	93.9149i	0.186757	+	0.107824i
$872$	497.000	−	860.829i	0.569954	−	0.987190i
$873$	255.617	−	147.580i	0.292803	−	0.169050i
$874$			348.827i			0.399115i
$875$		0			0
$876$	−720.000			−0.821918
$877$	653.000	+	1131.03i	0.744584	+	1.28966i	0.950389	+	0.311064i	$0.100685\pi$
$877$	653.000	+	1131.03i	0.744584	+	1.28966i	−0.205805	+	0.978593i	$0.565981\pi$
$878$	−23.2379	−	13.4164i	−0.0264669	−	0.0152806i
$879$	750.000	−	1299.04i	0.853242	−	1.47786i
$880$	19.3649	−	11.1803i	0.0220056	−	0.0127049i
$881$		−	1126.98i		−	1.27920i	−0.768706	−	0.639602i	$-0.779099\pi$
$881$		−	1126.98i		−	1.27920i	0.768706	−	0.639602i	$-0.220901\pi$
$882$		0			0
$883$	1526.00			1.72820			0.864100	−	0.503321i	$-0.167889\pi$
$883$	1526.00			1.72820			0.864100	+	0.503321i	$0.167889\pi$
$884$	540.000	+	935.307i	0.610860	+	1.05804i
$885$	−348.569	−	201.246i	−0.393863	−	0.227397i
$886$	−317.000	+	549.060i	−0.357788	+	0.619707i
$887$	1347.80	−	778.152i	1.51950	−	0.877285i	0.519766	−	0.854309i	$-0.326019\pi$
$887$	1347.80	−	778.152i	1.51950	−	0.877285i	0.999736	−	0.0229761i	$-0.00731417\pi$
$888$			438.269i			0.493547i
$889$		0			0
$890$	−60.0000			−0.0674157
$891$	59.0000	+	102.191i	0.0662177	+	0.114692i
$892$	209.141	+	120.748i	0.234463	+	0.135367i
$893$	180.000	−	311.769i	0.201568	−	0.349126i
$894$	549.964	−	317.522i	0.615172	−	0.355170i
$895$			487.463i			0.544651i
$896$		0			0
$897$	1560.00			1.73913
$898$	169.000	+	292.717i	0.188196	+	0.325965i
$899$	−1022.47	−	590.322i	−1.13734	−	0.656643i
$900$	82.5000	−	142.894i	0.0916667	−	0.158771i
$901$	−790.089	+	456.158i	−0.876902	+	0.506280i
$902$			53.6656i			0.0594963i
$903$		0			0
$904$	−238.000			−0.263274
$905$	−285.000	−	493.634i	−0.314917	−	0.545452i
$906$	7.74597	+	4.47214i	0.00854963	+	0.00493613i
$907$	−367.000	+	635.663i	−0.404631	+	0.700841i	−0.994278	−	0.106820i	$-0.965933\pi$
$907$	−367.000	+	635.663i	−0.404631	+	0.700841i	0.589648	+	0.807661i	$0.299267\pi$
$908$	−662.280	+	382.368i	−0.729383	+	0.421110i
$909$		−	737.902i		−	0.811774i
$910$		0			0
$911$	1202.00			1.31943			0.659715	−	0.751516i	$-0.270677\pi$
$911$	1202.00			1.31943			0.659715	+	0.751516i	$0.270677\pi$
$912$	−150.000	−	259.808i	−0.164474	−	0.284877i
$913$	−69.7137	−	40.2492i	−0.0763567	−	0.0440846i
$914$	−233.000	+	403.568i	−0.254923	+	0.441540i
$915$	−813.327	+	469.574i	−0.888881	+	0.513196i
$916$		−	40.2492i		−	0.0439402i
$917$		0			0
$918$	−240.000			−0.261438
$919$	641.000	+	1110.24i	0.697497	+	1.20810i	0.969332	+	0.245757i	$0.0790364\pi$
$919$	641.000	+	1110.24i	0.697497	+	1.20810i	−0.271834	+	0.962344i	$0.587630\pi$
$920$	−352.441	−	203.482i	−0.383089	−	0.221176i
$921$	450.000	−	779.423i	0.488599	−	0.846279i
$922$	383.425	−	221.371i	0.415863	−	0.240098i
$923$		−	831.817i		−	0.901210i
$924$		0			0
$925$	−70.0000			−0.0756757
$926$	103.000	+	178.401i	0.111231	+	0.192658i
$927$	1533.70	+	885.483i	1.65448	+	0.955214i
$928$	−363.000	+	628.734i	−0.391164	+	0.677516i
$929$	−975.992	+	563.489i	−1.05058	+	0.606554i	−0.922813	−	0.385249i	$-0.874115\pi$
$929$	−975.992	+	563.489i	−1.05058	+	0.606554i	−0.127771	+	0.991804i	$0.540782\pi$
$930$		−	536.656i		−	0.577050i
$931$		0			0
$932$	642.000			0.688841
$933$	−1140.00	−	1974.54i	−1.22186	−	2.11633i
$934$	313.712	+	181.122i	0.335880	+	0.193920i
$935$	60.0000	−	103.923i	0.0641711	−	0.111148i
$936$	894.659	−	516.532i	0.955832	−	0.551850i
$937$			214.663i			0.229096i	0.993418	+	0.114548i	$0.0365419\pi$
$937$			214.663i			0.229096i	−0.993418	+	0.114548i	$0.963458\pi$
$938$		0			0
$939$	−1440.00			−1.53355
$940$	90.0000	+	155.885i	0.0957447	+	0.165835i
$941$	−731.994	−	422.617i	−0.777889	−	0.449115i	0.0577924	−	0.998329i	$-0.481594\pi$
$941$	−731.994	−	422.617i	−0.777889	−	0.449115i	−0.835682	+	0.549214i	$0.814927\pi$
$942$	150.000	−	259.808i	0.159236	−	0.275804i
$943$	−604.185	+	348.827i	−0.640706	+	0.369912i
$944$		−	201.246i		−	0.213184i
$945$		0			0
$946$	68.0000			0.0718816
$947$	−367.000	−	635.663i	−0.387540	−	0.671238i	0.604578	−	0.796546i	$-0.293342\pi$
$947$	−367.000	−	635.663i	−0.387540	−	0.671238i	−0.992118	+	0.125307i	$0.960008\pi$
$948$	441.520	+	254.912i	0.465739	+	0.268894i
$949$	360.000	−	623.538i	0.379347	−	0.657048i
$950$	−58.0948	+	33.5410i	−0.0611524	+	0.0353063i
$951$			1672.58i			1.75876i
$952$		0			0
$953$	−934.000			−0.980063			−0.490031	−	0.871705i	$-0.663015\pi$
$953$	−934.000			−0.980063			−0.490031	+	0.871705i	$0.663015\pi$
$954$	187.000	+	323.894i	0.196017	+	0.339511i
$955$	112.317	+	64.8460i	0.117609	+	0.0679015i
$956$	147.000	−	254.611i	0.153766	−	0.266330i
$957$	−170.411	+	98.3870i	−0.178068	+	0.102808i
$958$		−	214.663i		−	0.224074i
$959$		0			0
$960$	−130.000			−0.135417
$961$	959.500	+	1661.90i	0.998439	+	1.72935i
$962$	−162.665	−	93.9149i	−0.169091	−	0.0976246i
$963$	−583.000	+	1009.79i	−0.605400	+	1.04858i
$964$	418.282	−	241.495i	0.433903	−	0.250514i
$965$			460.630i			0.477337i
$966$		0			0
$967$	314.000			0.324716			0.162358	−	0.986732i	$-0.448090\pi$
$967$	314.000			0.324716			0.162358	+	0.986732i	$0.448090\pi$
$968$	409.500	+	709.275i	0.423037	+	0.732722i
$969$	−1394.27	−	804.984i	−1.43888	−	0.830737i
$970$	30.0000	−	51.9615i	0.0309278	−	0.0535686i
$971$	−127.808	+	73.7902i	−0.131626	+	0.0759941i	−0.564367	−	0.825524i	$-0.690880\pi$
$971$	−127.808	+	73.7902i	−0.131626	+	0.0759941i	0.432741	+	0.901518i	$0.357546\pi$
$972$			1033.06i			1.06282i
$973$		0			0
$974$	166.000			0.170431
$975$	150.000	+	259.808i	0.153846	+	0.266469i
$976$	−406.663	−	234.787i	−0.416663	−	0.240561i
$977$	743.000	−	1286.91i	0.760491	−	1.31721i	−0.182106	−	0.983279i	$-0.558292\pi$
$977$	743.000	−	1286.91i	0.760491	−	1.31721i	0.942598	−	0.333931i	$-0.108375\pi$
$978$	131.681	−	76.0263i	0.134644	−	0.0777365i
$979$		−	53.6656i		−	0.0548168i
$980$		0			0
$981$	1562.00			1.59225
$982$	−419.000	−	725.729i	−0.426680	−	0.739032i
$983$	836.564	+	482.991i	0.851032	+	0.491344i	0.860999	−	0.508607i	$-0.169839\pi$
$983$	836.564	+	482.991i	0.851032	+	0.491344i	−0.00996696	+	0.999950i	$0.503173\pi$
$984$	−420.000	+	727.461i	−0.426829	+	0.739290i
$985$	−437.647	+	252.676i	−0.444312	+	0.256524i
$986$			590.322i			0.598704i
$987$		0			0
$988$	540.000			0.546559
$989$	442.000	+	765.566i	0.446916	+	0.774081i
$990$	−42.6028	−	24.5967i	−0.0430331	−	0.0248452i
$991$	29.0000	−	50.2295i	0.0292634	−	0.0506856i	−0.851023	−	0.525129i	$-0.824017\pi$
$991$	29.0000	−	50.2295i	0.0292634	−	0.0506856i	0.880286	+	0.474443i	$0.157351\pi$
$992$	1533.70	−	885.483i	1.54607	−	0.892624i
$993$			2155.57i			2.17076i
$994$		0			0
$995$	−300.000			−0.301508
$996$	−270.000	−	467.654i	−0.271084	−	0.469532i
$997$	546.091	+	315.286i	0.547734	+	0.316234i	0.748207	−	0.663465i	$-0.230915\pi$
$997$	546.091	+	315.286i	0.547734	+	0.316234i	−0.200474	+	0.979699i	$0.564248\pi$
$998$	−131.000	+	226.899i	−0.131263	+	0.227353i
$999$	−108.444	+	62.6099i	−0.108552	+	0.0626726i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.3.h.b.31.1		4
7.2	even	3	inner	245.3.h.b.166.2		4
7.3	odd	6		35.3.d.a.6.1	✓	2
7.4	even	3		35.3.d.a.6.2	yes	2
7.5	odd	6	inner	245.3.h.b.166.1		4
7.6	odd	2	inner	245.3.h.b.31.2		4
21.11	odd	6		315.3.h.b.181.1		2
21.17	even	6		315.3.h.b.181.2		2
28.3	even	6		560.3.f.a.321.2		2
28.11	odd	6		560.3.f.a.321.1		2
35.3	even	12		175.3.c.d.174.4		4
35.4	even	6		175.3.d.f.76.1		2
35.17	even	12		175.3.c.d.174.1		4
35.18	odd	12		175.3.c.d.174.3		4
35.24	odd	6		175.3.d.f.76.2		2
35.32	odd	12		175.3.c.d.174.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.3.d.a.6.1	✓	2	7.3	odd	6
35.3.d.a.6.2	yes	2	7.4	even	3
175.3.c.d.174.1		4	35.17	even	12
175.3.c.d.174.2		4	35.32	odd	12
175.3.c.d.174.3		4	35.18	odd	12
175.3.c.d.174.4		4	35.3	even	12
175.3.d.f.76.1		2	35.4	even	6
175.3.d.f.76.2		2	35.24	odd	6
245.3.h.b.31.1		4	1.1	even	1	trivial
245.3.h.b.31.2		4	7.6	odd	2	inner
245.3.h.b.166.1		4	7.5	odd	6	inner
245.3.h.b.166.2		4	7.2	even	3	inner
315.3.h.b.181.1		2	21.11	odd	6
315.3.h.b.181.2		2	21.17	even	6
560.3.f.a.321.1		2	28.11	odd	6
560.3.f.a.321.2		2	28.3	even	6

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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	245.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-3.87298 - 2.23607i) q^{3} +(1.50000 - 2.59808i) q^{4} +(1.93649 - 1.11803i) q^{5} -4.47214i q^{6} +7.00000 q^{8} +(5.50000 + 9.52628i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-3.87298 - 2.23607i) q^{3} +(1.50000 - 2.59808i) q^{4} +(1.93649 - 1.11803i) q^{5} -4.47214i q^{6} +7.00000 q^{8} +(5.50000 + 9.52628i) q^{9} +(1.93649 + 1.11803i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(-11.6190 + 6.70820i) q^{12} -13.4164i q^{13} -10.0000 q^{15} +(-2.50000 - 4.33013i) q^{16} +(-23.2379 - 13.4164i) q^{17} +(-5.50000 + 9.52628i) q^{18} +(-11.6190 + 6.70820i) q^{19} -6.70820i q^{20} -2.00000 q^{22} +(-13.0000 - 22.5167i) q^{23} +(-27.1109 - 15.6525i) q^{24} +(2.50000 - 4.33013i) q^{25} +(11.6190 - 6.70820i) q^{26} -8.94427i q^{27} -22.0000 q^{29} +(-5.00000 - 8.66025i) q^{30} +(46.4758 + 26.8328i) q^{31} +(16.5000 - 28.5788i) q^{32} +(7.74597 - 4.47214i) q^{33} -26.8328i q^{34} +33.0000 q^{36} +(-7.00000 - 12.1244i) q^{37} +(-11.6190 - 6.70820i) q^{38} +(-30.0000 + 51.9615i) q^{39} +(13.5554 - 7.82624i) q^{40} -26.8328i q^{41} -34.0000 q^{43} +(3.00000 + 5.19615i) q^{44} +(21.3014 + 12.2984i) q^{45} +(13.0000 - 22.5167i) q^{46} +(-23.2379 + 13.4164i) q^{47} +22.3607i q^{48} +5.00000 q^{50} +(60.0000 + 103.923i) q^{51} +(-34.8569 - 20.1246i) q^{52} +(17.0000 - 29.4449i) q^{53} +(7.74597 - 4.47214i) q^{54} +4.47214i q^{55} +60.0000 q^{57} +(-11.0000 - 19.0526i) q^{58} +(34.8569 + 20.1246i) q^{59} +(-15.0000 + 25.9808i) q^{60} +(81.3327 - 46.9574i) q^{61} +53.6656i q^{62} +13.0000 q^{64} +(-15.0000 - 25.9808i) q^{65} +(7.74597 + 4.47214i) q^{66} +(-7.00000 + 12.1244i) q^{67} +(-69.7137 + 40.2492i) q^{68} +116.276i q^{69} +62.0000 q^{71} +(38.5000 + 66.6840i) q^{72} +(46.4758 + 26.8328i) q^{73} +(7.00000 - 12.1244i) q^{74} +(-19.3649 + 11.1803i) q^{75} +40.2492i q^{76} -60.0000 q^{78} +(-19.0000 - 32.9090i) q^{79} +(-9.68246 - 5.59017i) q^{80} +(29.5000 - 51.0955i) q^{81} +(23.2379 - 13.4164i) q^{82} +40.2492i q^{83} -60.0000 q^{85} +(-17.0000 - 29.4449i) q^{86} +(85.2056 + 49.1935i) q^{87} +(-7.00000 + 12.1244i) q^{88} +(-23.2379 + 13.4164i) q^{89} +24.5967i q^{90} -78.0000 q^{92} +(-120.000 - 207.846i) q^{93} +(-23.2379 - 13.4164i) q^{94} +(-15.0000 + 25.9808i) q^{95} +(-127.808 + 73.7902i) q^{96} -26.8328i q^{97} -22.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 6 q^{4} + 28 q^{8} + 22 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 6 * q^4 + 28 * q^8 + 22 * q^9	\( 4 q + 2 q^{2} + 6 q^{4} + 28 q^{8} + 22 q^{9} - 4 q^{11} - 40 q^{15} - 10 q^{16} - 22 q^{18} - 8 q^{22} - 52 q^{23} + 10 q^{25} - 88 q^{29} - 20 q^{30} + 66 q^{32} + 132 q^{36} - 28 q^{37} - 120 q^{39} - 136 q^{43} + 12 q^{44} + 52 q^{46} + 20 q^{50} + 240 q^{51} + 68 q^{53} + 240 q^{57} - 44 q^{58} - 60 q^{60} + 52 q^{64} - 60 q^{65} - 28 q^{67} + 248 q^{71} + 154 q^{72} + 28 q^{74} - 240 q^{78} - 76 q^{79} + 118 q^{81} - 240 q^{85} - 68 q^{86} - 28 q^{88} - 312 q^{92} - 480 q^{93} - 60 q^{95} - 88 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 6 * q^4 + 28 * q^8 + 22 * q^9 - 4 * q^11 - 40 * q^15 - 10 * q^16 - 22 * q^18 - 8 * q^22 - 52 * q^23 + 10 * q^25 - 88 * q^29 - 20 * q^30 + 66 * q^32 + 132 * q^36 - 28 * q^37 - 120 * q^39 - 136 * q^43 + 12 * q^44 + 52 * q^46 + 20 * q^50 + 240 * q^51 + 68 * q^53 + 240 * q^57 - 44 * q^58 - 60 * q^60 + 52 * q^64 - 60 * q^65 - 28 * q^67 + 248 * q^71 + 154 * q^72 + 28 * q^74 - 240 * q^78 - 76 * q^79 + 118 * q^81 - 240 * q^85 - 68 * q^86 - 28 * q^88 - 312 * q^92 - 480 * q^93 - 60 * q^95 - 88 * q^99

Introduction

L-functions

Modular forms

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