LMFDB - Embedded newform 525.3.o.l.451.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,3,Mod(376,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("525.376");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	525.o (of order $6$, 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:	$14.3052138789$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.523596960000.16
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 13x^{6} - 2x^{5} + 91x^{4} - 50x^{3} + 190x^{2} + 100x + 100 $ x^8 - 2x^7 + 13x^6 - 2x^5 + 91x^4 - 50x^3 + 190x^2 + 100*x + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.4
Root			$-1.26021 - 2.18275i$ of defining polynomial
Character	$\chi$	$=$	525.451
Dual form			525.3.o.l.376.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26021 + 2.18275i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.17628 + 2.03737i) q^{4} +4.36551i q^{6} +(6.18050 - 3.28656i) q^{7} +4.15226 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.26021 + 2.18275i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.17628 + 2.03737i) q^{4} +4.36551i q^{6} +(6.18050 - 3.28656i) q^{7} +4.15226 q^{8} +(1.50000 + 2.59808i) q^{9} +(4.36036 - 7.55236i) q^{11} +(-3.52883 + 2.03737i) q^{12} -21.5286i q^{13} +(14.9625 + 9.34874i) q^{14} +(9.93785 + 17.2129i) q^{16} +(18.7862 + 10.8462i) q^{17} +(-3.78064 + 6.54826i) q^{18} +(-2.71590 + 1.56803i) q^{19} +(12.1170 + 0.422628i) q^{21} +21.9799 q^{22} +(2.05421 + 3.55799i) q^{23} +(6.22840 + 3.59597i) q^{24} +(46.9917 - 27.1307i) q^{26} +5.19615i q^{27} +(-0.574033 + 16.4579i) q^{28} -50.8583 q^{29} +(-33.9213 - 19.5845i) q^{31} +(-16.7431 + 28.9999i) q^{32} +(13.0811 - 7.55236i) q^{33} +54.6743i q^{34} -7.05767 q^{36} +(26.4906 + 45.8831i) q^{37} +(-6.84523 - 3.95209i) q^{38} +(18.6443 - 32.2929i) q^{39} +36.8122i q^{41} +(14.3475 + 26.9810i) q^{42} -17.6504 q^{43} +(10.2580 + 17.7674i) q^{44} +(-5.17748 + 8.96766i) q^{46} +(3.49804 - 2.01959i) q^{47} +34.4257i q^{48} +(27.3971 - 40.6251i) q^{49} +(18.7862 + 32.5387i) q^{51} +(43.8618 + 25.3236i) q^{52} +(2.22593 - 3.85542i) q^{53} +(-11.3419 + 6.54826i) q^{54} +(25.6631 - 13.6467i) q^{56} -5.43180 q^{57} +(-64.0923 - 111.011i) q^{58} +(81.5032 + 47.0559i) q^{59} +(-63.3781 + 36.5913i) q^{61} -98.7226i q^{62} +(17.8095 + 11.1276i) q^{63} -4.89677 q^{64} +(32.9699 + 19.0352i) q^{66} +(-50.2661 + 87.0635i) q^{67} +(-44.1956 + 25.5164i) q^{68} +7.11598i q^{69} -56.6975 q^{71} +(6.22840 + 10.7879i) q^{72} +(-64.8042 - 37.4147i) q^{73} +(-66.7676 + 115.645i) q^{74} -7.37773i q^{76} +(2.12789 - 61.0079i) q^{77} +93.9833 q^{78} +(-14.4903 - 25.0980i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-80.3519 + 46.3912i) q^{82} -21.1116i q^{83} +(-15.1140 + 24.1897i) q^{84} +(-22.2433 - 38.5266i) q^{86} +(-76.2875 - 44.0446i) q^{87} +(18.1054 - 31.3594i) q^{88} +(63.1066 - 36.4346i) q^{89} +(-70.7551 - 133.057i) q^{91} -9.66528 q^{92} +(-33.9213 - 58.7535i) q^{93} +(8.81655 + 5.09024i) q^{94} +(-50.2293 + 28.9999i) q^{96} -73.7985i q^{97} +(123.201 + 8.60469i) q^{98} +26.1622 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 12 q^{3} - 6 q^{4} + 16 q^{7} + 32 q^{8} + 12 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 12 * q^3 - 6 * q^4 + 16 * q^7 + 32 * q^8 + 12 * q^9	$ 8 q - 2 q^{2} + 12 q^{3} - 6 q^{4} + 16 q^{7} + 32 q^{8} + 12 q^{9} + 20 q^{11} - 18 q^{12} - 16 q^{14} - 2 q^{16} + 18 q^{17} + 6 q^{18} + 48 q^{21} + 16 q^{22} - 62 q^{23} + 48 q^{24} + 120 q^{26} + 120 q^{28} - 100 q^{29} - 126 q^{31} - 36 q^{32} + 60 q^{33} - 36 q^{36} + 80 q^{37} - 114 q^{38} - 12 q^{39} - 90 q^{42} - 352 q^{43} - 18 q^{44} - 82 q^{46} + 72 q^{47} + 38 q^{49} + 18 q^{51} + 48 q^{52} + 76 q^{53} + 18 q^{54} + 196 q^{56} + 40 q^{58} - 54 q^{59} - 396 q^{61} + 96 q^{63} - 4 q^{64} + 24 q^{66} - 184 q^{67} + 312 q^{68} + 164 q^{71} + 48 q^{72} - 348 q^{73} - 140 q^{74} - 152 q^{77} + 240 q^{78} - 206 q^{79} - 36 q^{81} - 204 q^{82} + 132 q^{84} + 178 q^{86} - 150 q^{87} - 124 q^{88} + 282 q^{89} - 114 q^{91} + 288 q^{92} - 126 q^{93} + 30 q^{94} - 108 q^{96} + 592 q^{98} + 120 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 + 12 * q^3 - 6 * q^4 + 16 * q^7 + 32 * q^8 + 12 * q^9 + 20 * q^11 - 18 * q^12 - 16 * q^14 - 2 * q^16 + 18 * q^17 + 6 * q^18 + 48 * q^21 + 16 * q^22 - 62 * q^23 + 48 * q^24 + 120 * q^26 + 120 * q^28 - 100 * q^29 - 126 * q^31 - 36 * q^32 + 60 * q^33 - 36 * q^36 + 80 * q^37 - 114 * q^38 - 12 * q^39 - 90 * q^42 - 352 * q^43 - 18 * q^44 - 82 * q^46 + 72 * q^47 + 38 * q^49 + 18 * q^51 + 48 * q^52 + 76 * q^53 + 18 * q^54 + 196 * q^56 + 40 * q^58 - 54 * q^59 - 396 * q^61 + 96 * q^63 - 4 * q^64 + 24 * q^66 - 184 * q^67 + 312 * q^68 + 164 * q^71 + 48 * q^72 - 348 * q^73 - 140 * q^74 - 152 * q^77 + 240 * q^78 - 206 * q^79 - 36 * q^81 - 204 * q^82 + 132 * q^84 + 178 * q^86 - 150 * q^87 - 124 * q^88 + 282 * q^89 - 114 * q^91 + 288 * q^92 - 126 * q^93 + 30 * q^94 - 108 * q^96 + 592 * q^98 + 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.26021	+	2.18275i	0.630107	+	1.09138i	0.987529	+	0.157434i	$0.0503223\pi$
$2$	1.26021	+	2.18275i	0.630107	+	1.09138i	−0.357423	+	0.933943i	$0.616344\pi$
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$4$	−1.17628	+	2.03737i	−0.294069	+	0.509343i
$5$		0			0
$5$		0			0
$6$			4.36551i			0.727585i
$7$	6.18050	−	3.28656i	0.882928	−	0.469508i
$7$	6.18050	−	3.28656i	0.882928	−	0.469508i
$8$	4.15226			0.519033
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	4.36036	−	7.55236i	0.396396	−	0.686579i	−0.596882	−	0.802329i	$-0.703594\pi$
$11$	4.36036	−	7.55236i	0.396396	−	0.686579i	0.993278	+	0.115750i	$0.0369273\pi$
$12$	−3.52883	+	2.03737i	−0.294069	+	0.169781i
$13$		−	21.5286i		−	1.65605i	−0.560693	−	0.828024i	$-0.689465\pi$
$13$		−	21.5286i		−	1.65605i	0.560693	−	0.828024i	$-0.310535\pi$
$14$	14.9625	+	9.34874i	1.06875	+	0.667767i
$15$		0			0
$16$	9.93785	+	17.2129i	0.621116	+	1.07580i
$17$	18.7862	+	10.8462i	1.10507	+	0.638013i	0.937548	−	0.347855i	$-0.113090\pi$
$17$	18.7862	+	10.8462i	1.10507	+	0.638013i	0.167523	+	0.985868i	$0.446423\pi$
$18$	−3.78064	+	6.54826i	−0.210036	+	0.363792i
$19$	−2.71590	+	1.56803i	−0.142942	+	0.0825276i	−0.569765	−	0.821807i	$-0.692966\pi$
$19$	−2.71590	+	1.56803i	−0.142942	+	0.0825276i	0.426823	+	0.904335i	$0.359633\pi$
$20$		0			0
$21$	12.1170	+	0.422628i	0.576999	+	0.0201251i
$22$	21.9799			0.999088
$23$	2.05421	+	3.55799i	0.0893134	+	0.154695i	0.907221	−	0.420654i	$-0.138199\pi$
$23$	2.05421	+	3.55799i	0.0893134	+	0.154695i	−0.817908	+	0.575349i	$0.804866\pi$
$24$	6.22840	+	3.59597i	0.259517	+	0.149832i
$25$		0			0
$26$	46.9917	−	27.1307i	1.80737	−	1.04349i
$27$			5.19615i			0.192450i
$28$	−0.574033	+	16.4579i	−0.0205012	+	0.587781i
$29$	−50.8583			−1.75373			−0.876867	−	0.480732i	$-0.840371\pi$
$29$	−50.8583			−1.75373			−0.876867	+	0.480732i	$0.840371\pi$
$30$		0			0
$31$	−33.9213	−	19.5845i	−1.09424	−	0.631758i	−0.159536	−	0.987192i	$-0.551000\pi$
$31$	−33.9213	−	19.5845i	−1.09424	−	0.631758i	−0.934701	+	0.355434i	$0.884333\pi$
$32$	−16.7431	+	28.9999i	−0.523222	+	0.906247i
$33$	13.0811	−	7.55236i	0.396396	−	0.228860i
$34$			54.6743i			1.60807i
$35$		0			0
$36$	−7.05767			−0.196046
$37$	26.4906	+	45.8831i	0.715962	+	1.24008i	0.962587	+	0.270972i	$0.0873451\pi$
$37$	26.4906	+	45.8831i	0.715962	+	1.24008i	−0.246625	+	0.969111i	$0.579322\pi$
$38$	−6.84523	−	3.95209i	−0.180138	−	0.104002i
$39$	18.6443	−	32.2929i	0.478060	−	0.828024i
$40$		0			0
$41$			36.8122i			0.897857i	0.893568	+	0.448929i	$0.148194\pi$
$41$			36.8122i			0.897857i	−0.893568	+	0.448929i	$0.851806\pi$
$42$	14.3475	+	26.9810i	0.341607	+	0.642405i
$43$	−17.6504			−0.410475			−0.205238	−	0.978712i	$-0.565797\pi$
$43$	−17.6504			−0.410475			−0.205238	+	0.978712i	$0.565797\pi$
$44$	10.2580	+	17.7674i	0.233136	+	0.403804i
$45$		0			0
$46$	−5.17748	+	8.96766i	−0.112554	+	0.194949i
$47$	3.49804	−	2.01959i	0.0744263	−	0.0429701i	−0.462325	−	0.886711i	$-0.652985\pi$
$47$	3.49804	−	2.01959i	0.0744263	−	0.0429701i	0.536751	+	0.843740i	$0.319651\pi$
$48$			34.4257i			0.717203i
$49$	27.3971	−	40.6251i	0.559124	−	0.829084i
$50$		0			0
$51$	18.7862	+	32.5387i	0.368357	+	0.638013i
$52$	43.8618	+	25.3236i	0.843496	+	0.486993i
$53$	2.22593	−	3.85542i	0.0419986	−	0.0727438i	−0.844262	−	0.535931i	$-0.819961\pi$
$53$	2.22593	−	3.85542i	0.0419986	−	0.0727438i	0.886261	+	0.463187i	$0.153294\pi$
$54$	−11.3419	+	6.54826i	−0.210036	+	0.121264i
$55$		0			0
$56$	25.6631	−	13.6467i	0.458269	−	0.243690i
$57$	−5.43180			−0.0952947
$58$	−64.0923	−	111.011i	−1.10504	−	1.91399i
$59$	81.5032	+	47.0559i	1.38141	+	0.797558i	0.992327	−	0.123644i	$-0.0394582\pi$
$59$	81.5032	+	47.0559i	1.38141	+	0.797558i	0.389084	+	0.921202i	$0.372792\pi$
$60$		0			0
$61$	−63.3781	+	36.5913i	−1.03898	+	0.599858i	−0.919546	−	0.392984i	$-0.871443\pi$
$61$	−63.3781	+	36.5913i	−1.03898	+	0.599858i	−0.119439	+	0.992842i	$0.538110\pi$
$62$		−	98.7226i		−	1.59230i
$63$	17.8095	+	11.1276i	0.282690	+	0.176628i
$64$	−4.89677			−0.0765121
$65$		0			0
$66$	32.9699	+	19.0352i	0.499544	+	0.288412i
$67$	−50.2661	+	87.0635i	−0.750241	+	1.29946i	0.197465	+	0.980310i	$0.436729\pi$
$67$	−50.2661	+	87.0635i	−0.750241	+	1.29946i	−0.947706	+	0.319145i	$0.896604\pi$
$68$	−44.1956	+	25.5164i	−0.649936	+	0.375241i
$69$			7.11598i			0.103130i
$70$		0			0
$71$	−56.6975			−0.798557			−0.399278	−	0.916830i	$-0.630739\pi$
$71$	−56.6975			−0.798557			−0.399278	+	0.916830i	$0.630739\pi$
$72$	6.22840	+	10.7879i	0.0865055	+	0.149832i
$73$	−64.8042	−	37.4147i	−0.887729	−	0.512531i	−0.0145299	−	0.999894i	$-0.504625\pi$
$73$	−64.8042	−	37.4147i	−0.887729	−	0.512531i	−0.873199	+	0.487364i	$0.837959\pi$
$74$	−66.7676	+	115.645i	−0.902266	+	1.56277i
$75$		0			0
$76$		−	7.37773i		−	0.0970754i
$77$	2.12789	−	61.0079i	0.0276350	−	0.792311i
$78$	93.9833			1.20491
$79$	−14.4903	−	25.0980i	−0.183422	−	0.317696i	0.759622	−	0.650365i	$-0.225384\pi$
$79$	−14.4903	−	25.0980i	−0.183422	−	0.317696i	−0.943044	+	0.332669i	$0.892051\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−80.3519	+	46.3912i	−0.979901	+	0.565746i
$83$		−	21.1116i		−	0.254357i	−0.991880	−	0.127179i	$-0.959408\pi$
$83$		−	21.1116i		−	0.254357i	0.991880	−	0.127179i	$-0.0405921\pi$
$84$	−15.1140	+	24.1897i	−0.179928	+	0.287973i
$85$		0			0
$86$	−22.2433	−	38.5266i	−0.258643	−	0.447983i
$87$	−76.2875	−	44.0446i	−0.876867	−	0.506260i
$88$	18.1054	−	31.3594i	0.205743	−	0.356357i
$89$	63.1066	−	36.4346i	0.709063	−	0.409378i	−0.101651	−	0.994820i	$-0.532412\pi$
$89$	63.1066	−	36.4346i	0.709063	−	0.409378i	0.810714	+	0.585442i	$0.199079\pi$
$90$		0			0
$91$	−70.7551	−	133.057i	−0.777528	−	1.46217i
$92$	−9.66528			−0.105057
$93$	−33.9213	−	58.7535i	−0.364746	−	0.631758i
$94$	8.81655	+	5.09024i	0.0937931	+	0.0541515i
$95$		0			0
$96$	−50.2293	+	28.9999i	−0.523222	+	0.302082i
$97$		−	73.7985i		−	0.760809i	−0.924820	−	0.380405i	$-0.875785\pi$
$97$		−	73.7985i		−	0.760809i	0.924820	−	0.380405i	$-0.124215\pi$
$98$	123.201	+	8.60469i	1.25715	+	0.0878030i
$99$	26.1622			0.264264
$100$		0			0
$101$	−92.6245	−	53.4768i	−0.917075	−	0.529473i	−0.0343741	−	0.999409i	$-0.510944\pi$
$101$	−92.6245	−	53.4768i	−0.917075	−	0.529473i	−0.882701	+	0.469936i	$0.844277\pi$
$102$	−47.3493	+	82.0114i	−0.464209	+	0.804033i
$103$	−18.6535	+	10.7696i	−0.181102	+	0.104559i	−0.587810	−	0.808999i	$-0.700010\pi$
$103$	−18.6535	+	10.7696i	−0.181102	+	0.104559i	0.406708	+	0.913558i	$0.366677\pi$
$104$		−	89.3925i		−	0.859543i
$105$		0			0
$106$	11.2206			0.105855
$107$	44.8184	+	77.6277i	0.418863	+	0.725492i	0.995825	−	0.0912785i	$-0.0290953\pi$
$107$	44.8184	+	77.6277i	0.418863	+	0.725492i	−0.576962	+	0.816771i	$0.695762\pi$
$108$	−10.5865	−	6.11212i	−0.0980232	−	0.0565937i
$109$	−13.6751	+	23.6859i	−0.125459	+	0.217302i	−0.921912	−	0.387398i	$-0.873374\pi$
$109$	−13.6751	+	23.6859i	−0.125459	+	0.217302i	0.796453	+	0.604700i	$0.206707\pi$
$110$		0			0
$111$			91.7661i			0.826722i
$112$	117.992	+	73.7227i	1.05350	+	0.658238i
$113$	92.3372			0.817144			0.408572	−	0.912726i	$-0.366027\pi$
$113$	92.3372			0.817144			0.408572	+	0.912726i	$0.366027\pi$
$114$	−6.84523	−	11.8563i	−0.0600459	−	0.104002i
$115$		0			0
$116$	59.8235	−	103.617i	0.515720	−	0.893253i
$117$	55.9330	−	32.2929i	0.478060	−	0.276008i
$118$			237.202i			2.01019i
$119$	151.755	+	5.29305i	1.27525	+	0.0444794i
$120$		0			0
$121$	22.4745	+	38.9270i	0.185740	+	0.321711i
$122$	−159.740	−	92.2258i	−1.30934	−	0.755949i
$123$	−31.8803	+	55.2182i	−0.259189	+	0.448929i
$124$	79.8019	−	46.0736i	0.643563	−	0.371562i
$125$		0			0
$126$	−1.84498	+	52.8968i	−0.0146427	+	0.419816i
$127$	−191.591			−1.50859			−0.754297	−	0.656534i	$-0.772022\pi$
$127$	−191.591			−1.50859			−0.754297	+	0.656534i	$0.772022\pi$
$128$	60.8015	+	105.311i	0.475011	+	0.822744i
$129$	−26.4757	−	15.2857i	−0.205238	−	0.118494i
$130$		0			0
$131$	50.9329	−	29.4062i	0.388801	−	0.224474i	−0.292839	−	0.956162i	$-0.594600\pi$
$131$	50.9329	−	29.4062i	0.388801	−	0.224474i	0.681641	+	0.731687i	$0.261267\pi$
$132$			35.5347i			0.269202i
$133$	−11.6322	+	18.6171i	−0.0874601	+	0.139978i
$134$	−253.384			−1.89093
$135$		0			0
$136$	78.0054	+	45.0364i	0.573569	+	0.331150i
$137$	82.9571	−	143.686i	0.605526	−	1.04880i	−0.386442	−	0.922314i	$-0.626296\pi$
$137$	82.9571	−	143.686i	0.605526	−	1.04880i	0.991968	−	0.126488i	$-0.0403706\pi$
$138$	−15.5324	+	8.96766i	−0.112554	+	0.0649831i
$139$		−	139.625i		−	1.00449i	−0.864724	−	0.502247i	$-0.832507\pi$
$139$		−	139.625i		−	1.00449i	0.864724	−	0.502247i	$-0.167493\pi$
$140$		0			0
$141$	6.99607			0.0496176
$142$	−71.4510	−	123.757i	−0.503176	−	0.871527i
$143$	−162.592	−	93.8725i	−1.13701	−	0.656451i
$144$	−29.8136	+	51.6386i	−0.207039	+	0.358601i
$145$		0			0
$146$		−	188.602i		−	1.29180i
$147$	76.2780	−	37.2111i	0.518898	−	0.253137i
$148$	−124.641			−0.842171
$149$	7.16861	+	12.4164i	0.0481115	+	0.0833315i	0.889078	−	0.457755i	$-0.151346\pi$
$149$	7.16861	+	12.4164i	0.0481115	+	0.0833315i	−0.840967	+	0.541087i	$0.818013\pi$
$150$		0			0
$151$	−106.187	+	183.922i	−0.703226	+	1.21802i	0.264102	+	0.964495i	$0.414925\pi$
$151$	−106.187	+	183.922i	−0.703226	+	1.21802i	−0.967328	+	0.253529i	$0.918409\pi$
$152$	−11.2771	+	6.51085i	−0.0741917	+	0.0428346i
$153$			65.0774i			0.425342i
$154$	135.847	−	72.2384i	0.882123	−	0.469080i
$155$		0			0
$156$	43.8618	+	75.9709i	0.281165	+	0.486993i
$157$	210.373	+	121.459i	1.33996	+	0.773624i	0.986801	−	0.161941i	$-0.0517753\pi$
$157$	210.373	+	121.459i	1.33996	+	0.773624i	0.353156	+	0.935565i	$0.385109\pi$
$158$	36.5218	−	63.2577i	0.231151	−	0.400365i
$159$	6.67778	−	3.85542i	0.0419986	−	0.0242479i
$160$		0			0
$161$	24.3896	+	15.2389i	0.151488	+	0.0946514i
$162$	−22.6838			−0.140024
$163$	6.61728	+	11.4615i	0.0405968	+	0.0703157i	0.885610	−	0.464430i	$-0.153741\pi$
$163$	6.61728	+	11.4615i	0.0405968	+	0.0703157i	−0.845013	+	0.534746i	$0.820407\pi$
$164$	−75.0001	−	43.3013i	−0.457318	−	0.264032i
$165$		0			0
$166$	46.0815	−	26.6052i	0.277600	−	0.160272i
$167$		−	212.616i		−	1.27315i	−0.771216	−	0.636574i	$-0.780351\pi$
$167$		−	212.616i		−	1.27315i	0.771216	−	0.636574i	$-0.219649\pi$
$168$	50.3129	+	1.75486i	0.299482	+	0.0104456i
$169$	−294.481			−1.74249
$170$		0			0
$171$	−8.14770	−	4.70408i	−0.0476474	−	0.0275092i
$172$	20.7618	−	35.9605i	0.120708	−	0.209073i
$173$	215.456	−	124.393i	1.24541	−	0.719037i	0.275219	−	0.961382i	$-0.411250\pi$
$173$	215.456	−	124.393i	1.24541	−	0.719037i	0.970190	+	0.242345i	$0.0779164\pi$
$174$		−	222.022i		−	1.27599i
$175$		0			0
$176$	173.330			0.984832
$177$	81.5032	+	141.168i	0.460470	+	0.797558i
$178$	159.056	+	91.8308i	0.893571	+	0.515903i
$179$	−27.6352	+	47.8655i	−0.154386	+	0.267405i	−0.932835	−	0.360303i	$-0.882673\pi$
$179$	−27.6352	+	47.8655i	−0.154386	+	0.267405i	0.778449	+	0.627708i	$0.216007\pi$
$180$		0			0
$181$			46.9001i			0.259117i	0.991572	+	0.129558i	$0.0413559\pi$
$181$			46.9001i			0.259117i	−0.991572	+	0.129558i	$0.958644\pi$
$182$	201.265	−	322.122i	1.10585	−	1.76990i
$183$	−126.756			−0.692656
$184$	8.52961	+	14.7737i	0.0463566	+	0.0802920i
$185$		0			0
$186$	85.4963	−	148.084i	0.459658	−	0.796150i
$187$	163.829	−	94.5869i	0.876093	−	0.505812i
$188$			9.50241i			0.0505447i
$189$	17.0775	+	32.1148i	0.0903569	+	0.169920i
$190$		0			0
$191$	10.0561	+	17.4177i	0.0526499	+	0.0911923i	0.891149	−	0.453710i	$-0.149900\pi$
$191$	10.0561	+	17.4177i	0.0526499	+	0.0911923i	−0.838499	+	0.544903i	$0.816567\pi$
$192$	−7.34516	−	4.24073i	−0.0382560	−	0.0220871i
$193$	14.3516	−	24.8578i	0.0743609	−	0.128797i	−0.826447	−	0.563014i	$-0.809642\pi$
$193$	14.3516	−	24.8578i	0.0743609	−	0.128797i	0.900808	+	0.434217i	$0.142975\pi$
$194$	161.084	−	93.0019i	0.830330	−	0.479391i
$195$		0			0
$196$	50.5420	+	103.604i	0.257867	+	0.528594i
$197$	−224.436			−1.13927			−0.569636	−	0.821897i	$-0.692916\pi$
$197$	−224.436			−1.13927			−0.569636	+	0.821897i	$0.692916\pi$
$198$	32.9699	+	57.1056i	0.166515	+	0.288412i
$199$	−275.447	−	159.030i	−1.38416	−	0.799144i	−0.391509	−	0.920174i	$-0.628047\pi$
$199$	−275.447	−	159.030i	−1.38416	−	0.799144i	−0.992649	+	0.121030i	$0.961380\pi$
$200$		0			0
$201$	−150.798	+	87.0635i	−0.750241	+	0.433152i
$202$		−	269.569i		−	1.33450i
$203$	−314.330	+	167.149i	−1.54842	+	0.823393i
$204$	−88.3913			−0.433290
$205$		0			0
$206$	−47.0148	−	27.1440i	−0.228227	−	0.131767i
$207$	−6.16262	+	10.6740i	−0.0297711	+	0.0515651i
$208$	370.569	−	213.948i	1.78158	−	1.02860i
$209$			27.3486i			0.130855i
$210$		0			0
$211$	285.317			1.35221			0.676107	−	0.736804i	$-0.263666\pi$
$211$	285.317			1.35221			0.676107	+	0.736804i	$0.263666\pi$
$212$	5.23662	+	9.07009i	0.0247010	+	0.0427835i
$213$	−85.0463	−	49.1015i	−0.399278	−	0.230523i
$214$	−112.961	+	195.655i	−0.527857	+	0.914276i
$215$		0			0
$216$			21.5758i			0.0998880i
$217$	−274.016	−	9.55740i	−1.26275	−	0.0440433i
$218$	−68.9341			−0.316211
$219$	−64.8042	−	112.244i	−0.295910	−	0.512531i
$220$		0			0
$221$	233.504	−	404.441i	1.05658	−	1.83005i
$222$	−200.303	+	115.645i	−0.902266	+	0.520923i
$223$		−	57.0977i		−	0.256044i	−0.991771	−	0.128022i	$-0.959137\pi$
$223$		−	57.0977i		−	0.256044i	0.991771	−	0.128022i	$-0.0408627\pi$
$224$	−8.17078	+	234.261i	−0.0364767	+	1.04581i
$225$		0			0
$226$	116.365	+	201.549i	0.514888	+	0.891812i
$227$	158.185	+	91.3279i	0.696848	+	0.402325i	0.806172	−	0.591681i	$-0.201535\pi$
$227$	158.185	+	91.3279i	0.696848	+	0.402325i	−0.109324	+	0.994006i	$0.534869\pi$
$228$	6.38930	−	11.0666i	0.0280233	−	0.0485377i
$229$	−14.5347	+	8.39159i	−0.0634702	+	0.0366445i	−0.531399	−	0.847121i	$-0.678334\pi$
$229$	−14.5347	+	8.39159i	−0.0634702	+	0.0366445i	0.467929	+	0.883766i	$0.345000\pi$
$230$		0			0
$231$	56.0263	−	89.6691i	0.242538	−	0.388178i
$232$	−211.177			−0.910246
$233$	−133.203	−	230.715i	−0.571688	−	0.990193i	−0.996393	−	0.0848612i	$-0.972955\pi$
$233$	−133.203	−	230.715i	−0.571688	−	0.990193i	0.424704	−	0.905332i	$-0.360378\pi$
$234$	140.975	+	81.3920i	0.602457	+	0.347829i
$235$		0			0
$236$	−191.741	+	110.702i	−0.812461	+	0.469075i
$237$		−	50.1960i		−	0.211797i
$238$	179.690	+	337.914i	0.755001	+	1.41981i
$239$	−39.7012			−0.166114			−0.0830568	−	0.996545i	$-0.526468\pi$
$239$	−39.7012			−0.166114			−0.0830568	+	0.996545i	$0.526468\pi$
$240$		0			0
$241$	72.1896	+	41.6787i	0.299542	+	0.172941i	0.642237	−	0.766506i	$-0.278006\pi$
$241$	72.1896	+	41.6787i	0.299542	+	0.172941i	−0.342695	+	0.939447i	$0.611340\pi$
$242$	−56.6454	+	98.1128i	−0.234072	+	0.405425i
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$		−	172.166i		−	0.705600i
$245$		0			0
$246$	−160.704			−0.653267
$247$	33.7574	+	58.4695i	0.136670	+	0.236719i
$248$	−140.850	−	81.3200i	−0.567945	−	0.327903i
$249$	18.2832	−	31.6675i	0.0734266	−	0.127179i
$250$		0			0
$251$		−	111.464i		−	0.444079i	−0.975038	−	0.222039i	$-0.928729\pi$
$251$		−	111.464i		−	0.444079i	0.975038	−	0.222039i	$-0.0712713\pi$
$252$	−43.6199	+	23.1954i	−0.173095	+	0.0920454i
$253$	35.8283			0.141614
$254$	−241.446	−	418.197i	−0.950575	−	1.64644i
$255$		0			0
$256$	−163.039	+	282.392i	−0.636872	+	1.10309i
$257$	193.043	−	111.454i	0.751141	−	0.433672i	−0.0749649	−	0.997186i	$-0.523884\pi$
$257$	193.043	−	111.454i	0.751141	−	0.433672i	0.826106	+	0.563515i	$0.190551\pi$
$258$		−	77.0531i		−	0.298656i
$259$	314.522	+	196.517i	1.21437	+	0.758754i
$260$		0			0
$261$	−76.2875	−	132.134i	−0.292289	−	0.506260i
$262$	128.373	+	74.1161i	0.489973	+	0.282886i
$263$	−213.250	+	369.360i	−0.810837	+	1.40441i	0.101442	+	0.994841i	$0.467654\pi$
$263$	−213.250	+	369.360i	−0.810837	+	1.40441i	−0.912279	+	0.409569i	$0.865679\pi$
$264$	54.3161	−	31.3594i	0.205743	−	0.118786i
$265$		0			0
$266$	−55.2957	−	1.92865i	−0.207879	−	0.00725058i
$267$	126.213			0.472709
$268$	−118.254	−	204.822i	−0.441246	−	0.764260i
$269$	−51.5210	−	29.7457i	−0.191528	−	0.110579i	0.401170	−	0.916004i	$-0.368604\pi$
$269$	−51.5210	−	29.7457i	−0.191528	−	0.110579i	−0.592698	+	0.805425i	$0.701937\pi$
$270$		0			0
$271$	−47.1819	+	27.2405i	−0.174103	+	0.100518i	−0.584519	−	0.811380i	$-0.698717\pi$
$271$	−47.1819	+	27.2405i	−0.174103	+	0.100518i	0.410416	+	0.911898i	$0.365383\pi$
$272$			431.153i			1.58512i
$273$	9.09858	−	260.862i	0.0333281	−	0.955538i
$274$	418.175			1.52618
$275$		0			0
$276$	−14.4979	−	8.37037i	−0.0525287	−	0.0303274i
$277$	−236.189	+	409.092i	−0.852669	+	1.47687i	0.0261222	+	0.999659i	$0.491684\pi$
$277$	−236.189	+	409.092i	−0.852669	+	1.47687i	−0.878791	+	0.477207i	$0.841649\pi$
$278$	304.766	−	175.957i	1.09628	−	0.632939i
$279$		−	117.507i		−	0.421172i
$280$		0			0
$281$	−534.544			−1.90229			−0.951146	−	0.308743i	$-0.900092\pi$
$281$	−534.544			−1.90229			−0.951146	+	0.308743i	$0.900092\pi$
$282$	8.81655	+	15.2707i	0.0312644	+	0.0541515i
$283$	387.352	+	223.638i	1.36873	+	0.790239i	0.990766	−	0.135580i	$-0.0432899\pi$
$283$	387.352	+	223.638i	1.36873	+	0.790239i	0.377967	+	0.925819i	$0.376623\pi$
$284$	66.6921	−	115.514i	0.234831	−	0.406740i
$285$		0			0
$286$		−	473.198i		−	1.65454i
$287$	120.985	+	227.517i	0.421552	+	0.792743i
$288$	−100.459			−0.348815
$289$	90.7814	+	157.238i	0.314122	+	0.544076i
$290$		0			0
$291$	63.9114	−	110.698i	0.219627	−	0.380405i
$292$	152.456	−	88.0202i	0.522108	−	0.301439i
$293$			504.200i			1.72082i	0.509604	+	0.860409i	$0.329792\pi$
$293$			504.200i			1.72082i	−0.509604	+	0.860409i	$0.670208\pi$
$294$	177.349	+	119.602i	0.603229	+	0.406810i
$295$		0			0
$296$	109.996	+	190.519i	0.371608	+	0.643644i
$297$	39.2432	+	22.6571i	0.132132	+	0.0762865i
$298$	−18.0680	+	31.2946i	−0.0606308	+	0.105016i
$299$	76.5986	−	44.2242i	0.256183	−	0.147907i
$300$		0			0
$301$	−109.088	+	58.0092i	−0.362420	+	0.192722i
$302$	−535.274			−1.77243
$303$	−92.6245	−	160.430i	−0.305692	−	0.529473i
$304$	−53.9804	−	31.1656i	−0.177567	−	0.102518i
$305$		0			0
$306$	−142.048	+	82.0114i	−0.464209	+	0.268011i
$307$		−	398.792i		−	1.29900i	−0.760363	−	0.649499i	$-0.774979\pi$
$307$		−	398.792i		−	1.29900i	0.760363	−	0.649499i	$-0.225021\pi$
$308$	121.793	+	76.0976i	0.395432	+	0.247070i
$309$	−37.3070			−0.120735
$310$		0			0
$311$	−207.085	−	119.561i	−0.665869	−	0.384440i	0.128640	−	0.991691i	$-0.458939\pi$
$311$	−207.085	−	119.561i	−0.665869	−	0.384440i	−0.794510	+	0.607252i	$0.792272\pi$
$312$	77.4162	−	134.089i	0.248129	−	0.429772i
$313$	−193.296	+	111.599i	−0.617559	+	0.356548i	−0.775918	−	0.630834i	$-0.782713\pi$
$313$	−193.296	+	111.599i	−0.617559	+	0.356548i	0.158359	+	0.987382i	$0.449380\pi$
$314$			612.257i			1.94986i
$315$		0			0
$316$	68.1786			0.215755
$317$	−143.007	−	247.695i	−0.451126	−	0.781373i	0.547330	−	0.836917i	$-0.315644\pi$
$317$	−143.007	−	247.695i	−0.451126	−	0.781373i	−0.998456	+	0.0555434i	$0.982311\pi$
$318$	16.8309	+	9.71731i	0.0529273	+	0.0305576i
$319$	−221.761	+	384.100i	−0.695174	+	1.20408i
$320$		0			0
$321$			155.255i			0.483662i
$322$	−2.52665	+	72.4407i	−0.00784675	+	0.224971i
$323$	−68.0286			−0.210615
$324$	−10.5865	−	18.3364i	−0.0326744	−	0.0565937i
$325$		0			0
$326$	−16.6784	+	28.8878i	−0.0511607	+	0.0886129i
$327$	−41.0252	+	23.6859i	−0.125459	+	0.0724340i
$328$			152.854i			0.466018i
$329$	14.9821	−	23.9786i	0.0455383	−	0.0728833i
$330$		0			0
$331$	−269.512	−	466.809i	−0.814236	−	1.41030i	−0.909875	−	0.414882i	$-0.863823\pi$
$331$	−269.512	−	466.809i	−0.814236	−	1.41030i	0.0956391	−	0.995416i	$-0.469511\pi$
$332$	43.0123	+	24.8332i	0.129555	+	0.0747987i
$333$	−79.4718	+	137.649i	−0.238654	+	0.413361i
$334$	464.088	−	267.941i	1.38948	−	0.802219i
$335$		0			0
$336$	113.142	+	212.768i	0.336733	+	0.633238i
$337$	−68.2484			−0.202518			−0.101259	−	0.994860i	$-0.532287\pi$
$337$	−68.2484			−0.202518			−0.101259	+	0.994860i	$0.532287\pi$
$338$	−371.109	−	642.780i	−1.09796	−	1.90172i
$339$	138.506	+	79.9664i	0.408572	+	0.235889i
$340$		0			0
$341$	−295.819	+	170.791i	−0.867503	+	0.500853i
$342$		−	23.7126i		−	0.0693350i
$343$	35.8105	−	341.126i	0.104404	−	0.994535i
$344$	−73.2893			−0.213050
$345$		0			0
$346$	543.041	+	313.525i	1.56948	+	0.906141i
$347$	190.947	−	330.731i	0.550281	−	0.953114i	−0.447973	−	0.894047i	$-0.647854\pi$
$347$	190.947	−	330.731i	0.550281	−	0.953114i	0.998254	−	0.0590672i	$-0.0188126\pi$
$348$	179.470	−	103.617i	0.515720	−	0.297751i
$349$			301.869i			0.864953i	0.901645	+	0.432477i	$0.142360\pi$
$349$			301.869i			0.864953i	−0.901645	+	0.432477i	$0.857640\pi$
$350$		0			0
$351$	111.866			0.318706
$352$	146.012	+	252.900i	0.414807	+	0.718466i
$353$	−110.891	−	64.0227i	−0.314138	−	0.181367i	0.334639	−	0.942346i	$-0.391386\pi$
$353$	−110.891	−	64.0227i	−0.314138	−	0.181367i	−0.648776	+	0.760979i	$0.724719\pi$
$354$	−205.423	+	355.803i	−0.580291	+	1.00509i
$355$		0			0
$356$			171.429i			0.481542i
$357$	223.048	+	139.363i	0.624786	+	0.390373i
$358$	−139.305			−0.389120
$359$	262.113	+	453.993i	0.730119	+	1.26460i	0.956832	+	0.290642i	$0.0938688\pi$
$359$	262.113	+	453.993i	0.730119	+	1.26460i	−0.226713	+	0.973962i	$0.572798\pi$
$360$		0			0
$361$	−175.583	+	304.118i	−0.486378	+	0.842432i
$362$	−102.371	+	59.1041i	−0.282794	+	0.163271i
$363$			77.8541i			0.214474i
$364$	354.315	+	12.3581i	0.973394	+	0.0339509i
$365$		0			0
$366$	−159.740	−	276.677i	−0.436448	−	0.755949i
$367$	−30.8202	−	17.7941i	−0.0839789	−	0.0484852i	0.457423	−	0.889249i	$-0.348773\pi$
$367$	−30.8202	−	17.7941i	−0.0839789	−	0.0484852i	−0.541401	+	0.840764i	$0.682106\pi$
$368$	−40.8288	+	70.7176i	−0.110948	+	0.192167i
$369$	−95.6408	+	55.2182i	−0.259189	+	0.149643i
$370$		0			0
$371$	1.08627	−	31.1441i	0.00292796	−	0.0839462i
$372$	159.604			0.429042
$373$	−133.546	−	231.308i	−0.358031	−	0.620128i	0.629601	−	0.776919i	$-0.283219\pi$
$373$	−133.546	−	231.308i	−0.358031	−	0.620128i	−0.987632	+	0.156791i	$0.949885\pi$
$374$	412.920	+	238.399i	1.10406	+	0.637432i
$375$		0			0
$376$	14.5248	−	8.38588i	0.0386297	−	0.0223029i
$377$			1094.91i			2.90427i
$378$	−48.5775	+	77.7474i	−0.128512	+	0.205681i
$379$	−125.687			−0.331627			−0.165813	−	0.986157i	$-0.553025\pi$
$379$	−125.687			−0.331627			−0.165813	+	0.986157i	$0.553025\pi$
$380$		0			0
$381$	−287.387	−	165.923i	−0.754297	−	0.435493i
$382$	−25.3457	+	43.9001i	−0.0663501	+	0.114922i
$383$	308.755	−	178.260i	0.806149	−	0.465430i	−0.0394677	−	0.999221i	$-0.512566\pi$
$383$	308.755	−	178.260i	0.806149	−	0.465430i	0.845617	+	0.533790i	$0.179233\pi$
$384$			210.622i			0.548496i
$385$		0			0
$386$	72.3446			0.187421
$387$	−26.4757	−	45.8572i	−0.0684126	−	0.118494i
$388$	150.355	+	86.8076i	0.387513	+	0.223731i
$389$	−223.316	+	386.795i	−0.574078	+	0.994332i	0.422064	+	0.906566i	$0.361306\pi$
$389$	−223.316	+	386.795i	−0.574078	+	0.994332i	−0.996141	+	0.0877654i	$0.972027\pi$
$390$		0			0
$391$			89.1216i			0.227933i
$392$	113.760	−	168.686i	0.290204	−	0.430322i
$393$	101.866			0.259201
$394$	−282.838	−	489.890i	−0.717863	−	1.24337i
$395$		0			0
$396$	−30.7740	+	53.3021i	−0.0777120	+	0.134601i
$397$	−525.089	+	303.160i	−1.32264	+	0.763627i	−0.984149	−	0.177342i	$-0.943250\pi$
$397$	−525.089	+	303.160i	−1.32264	+	0.763627i	−0.338492	+	0.940969i	$0.609917\pi$
$398$		−	801.645i		−	2.01418i
$399$	−33.5712	+	17.8519i	−0.0841384	+	0.0447417i
$400$		0			0
$401$	364.402	+	631.163i	0.908734	+	1.57397i	0.815826	+	0.578298i	$0.196283\pi$
$401$	364.402	+	631.163i	0.908734	+	1.57397i	0.0929080	+	0.995675i	$0.470384\pi$
$402$	−380.076	−	219.437i	−0.945464	−	0.545864i
$403$	−421.627	+	730.280i	−1.04622	+	1.81211i
$404$	217.904	−	125.807i	0.539367	−	0.311404i
$405$		0			0
$406$	−760.967	−	475.461i	−1.87430	−	1.17109i
$407$	462.034			1.13522
$408$	78.0054	+	135.109i	0.191190	+	0.331150i
$409$	−459.563	−	265.329i	−1.12363	−	0.648725i	−0.181301	−	0.983428i	$-0.558031\pi$
$409$	−459.563	−	265.329i	−1.12363	−	0.648725i	−0.942324	+	0.334702i	$0.891364\pi$
$410$		0			0
$411$	248.871	−	143.686i	0.605526	−	0.349601i
$412$		−	50.6722i		−	0.122991i
$413$	658.382	+	22.9637i	1.59415	+	0.0556021i
$414$	−31.0649			−0.0750360
$415$		0			0
$416$	624.328	+	360.456i	1.50079	+	0.866481i
$417$	120.919	−	209.437i	0.289973	−	0.502247i
$418$	−59.6953	+	34.4651i	−0.142812	+	0.0824524i
$419$		−	282.637i		−	0.674552i	−0.941406	−	0.337276i	$-0.890494\pi$
$419$		−	282.637i		−	0.674552i	0.941406	−	0.337276i	$-0.109506\pi$
$420$		0			0
$421$	440.590			1.04653			0.523267	−	0.852169i	$-0.324713\pi$
$421$	440.590			1.04653			0.523267	+	0.852169i	$0.324713\pi$
$422$	359.560	+	622.777i	0.852039	+	1.47577i
$423$	10.4941	+	6.05878i	0.0248088	+	0.0143234i
$424$	9.24264	−	16.0087i	0.0217987	−	0.0377564i
$425$		0			0
$426$		−	247.514i		−	0.581018i
$427$	−271.448	+	434.448i	−0.635710	+	1.01744i
$428$	−210.875			−0.492700
$429$	−162.592	−	281.617i	−0.379002	−	0.656451i
$430$		0			0
$431$	63.7174	−	110.362i	0.147836	−	0.256060i	−0.782591	−	0.622536i	$-0.786103\pi$
$431$	63.7174	−	110.362i	0.147836	−	0.256060i	0.930427	+	0.366476i	$0.119436\pi$
$432$	−89.4407	+	51.6386i	−0.207039	+	0.119534i
$433$		−	433.284i		−	1.00066i	−0.865836	−	0.500328i	$-0.833213\pi$
$433$		−	433.284i		−	1.00066i	0.865836	−	0.500328i	$-0.166787\pi$
$434$	−324.458	−	610.155i	−0.747599	−	1.40589i
$435$		0			0
$436$	−32.1714	−	55.7225i	−0.0737876	−	0.127804i
$437$	−11.1580	−	6.44210i	−0.0255333	−	0.0147416i
$438$	163.334	−	282.903i	0.372909	−	0.645898i
$439$	−54.7578	+	31.6144i	−0.124733	+	0.0720146i	−0.561068	−	0.827770i	$-0.689609\pi$
$439$	−54.7578	+	31.6144i	−0.124733	+	0.0720146i	0.436335	+	0.899784i	$0.356276\pi$
$440$		0			0
$441$	146.643	+	10.2419i	0.332523	+	0.0232244i
$442$	1177.06			2.66303
$443$	219.190	+	379.648i	0.494785	+	0.856992i	0.999982	−	0.00601155i	$-0.00191355\pi$
$443$	219.190	+	379.648i	0.494785	+	0.856992i	−0.505197	+	0.863004i	$0.668580\pi$
$444$	−186.962	−	107.942i	−0.421085	−	0.243114i
$445$		0			0
$446$	124.630	−	71.9553i	0.279440	−	0.161335i
$447$			24.8328i			0.0555544i
$448$	−30.2645	+	16.0935i	−0.0675547	+	0.0359231i
$449$	214.986			0.478810			0.239405	−	0.970920i	$-0.423048\pi$
$449$	214.986			0.478810			0.239405	+	0.970920i	$0.423048\pi$
$450$		0			0
$451$	278.019	+	160.514i	0.616450	+	0.355907i
$452$	−108.614	+	188.125i	−0.240297	+	0.416207i
$453$	−318.561	+	183.922i	−0.703226	+	0.406008i
$454$			460.371i			1.01403i
$455$		0			0
$456$	−22.5543			−0.0494611
$457$	−120.600	−	208.885i	−0.263894	−	0.457078i	0.703379	−	0.710815i	$-0.251674\pi$
$457$	−120.600	−	208.885i	−0.263894	−	0.457078i	−0.967273	+	0.253737i	$0.918340\pi$
$458$	−36.6336	−	21.1504i	−0.0799860	−	0.0461799i
$459$	−56.3587	+	97.6161i	−0.122786	+	0.212671i
$460$		0			0
$461$			343.383i			0.744865i	0.928059	+	0.372432i	$0.121476\pi$
$461$			343.383i			0.744865i	−0.928059	+	0.372432i	$0.878524\pi$
$462$	266.331	+	9.28933i	0.576473	+	0.0201068i
$463$	−74.7714			−0.161493			−0.0807467	−	0.996735i	$-0.525730\pi$
$463$	−74.7714			−0.161493			−0.0807467	+	0.996735i	$0.525730\pi$
$464$	−505.422	−	875.417i	−1.08927	−	1.88667i
$465$		0			0
$466$	335.730	−	581.501i	0.720450	−	1.24786i
$467$	308.470	−	178.095i	0.660535	−	0.381360i	−0.131946	−	0.991257i	$-0.542122\pi$
$467$	308.470	−	178.095i	0.660535	−	0.381360i	0.792481	+	0.609897i	$0.208789\pi$
$468$			151.942i			0.324662i
$469$	−24.5303	+	703.298i	−0.0523034	+	1.49957i
$470$		0			0
$471$	210.373	+	364.377i	0.446652	+	0.773624i
$472$	338.423	+	195.389i	0.716998	+	0.413959i
$473$	−76.9623	+	133.303i	−0.162711	+	0.281824i
$474$	109.565	−	63.2577i	0.231151	−	0.133455i
$475$		0			0
$476$	−189.290	+	302.955i	−0.397668	+	0.636461i
$477$	13.3556			0.0279991
$478$	−50.0319	−	86.6579i	−0.104669	−	0.181293i
$479$	323.678	+	186.876i	0.675737	+	0.390137i	0.798247	−	0.602330i	$-0.205761\pi$
$479$	323.678	+	186.876i	0.675737	+	0.390137i	−0.122510	+	0.992467i	$0.539094\pi$
$480$		0			0
$481$	987.799	−	570.306i	2.05364	−	1.18567i
$482$			210.096i			0.435884i
$483$	23.3871	+	43.9803i	0.0484205	+	0.0910565i
$484$	−105.745			−0.218482
$485$		0			0
$486$	−34.0258	−	19.6448i	−0.0700119	−	0.0404214i
$487$	388.781	−	673.389i	0.798319	−	1.38273i	−0.122391	−	0.992482i	$-0.539056\pi$
$487$	388.781	−	673.389i	0.798319	−	1.38273i	0.920710	−	0.390247i	$-0.127610\pi$
$488$	−263.162	+	151.937i	−0.539267	+	0.311346i
$489$			22.9229i			0.0468772i
$490$		0			0
$491$	458.794			0.934407			0.467203	−	0.884150i	$-0.345262\pi$
$491$	458.794			0.934407			0.467203	+	0.884150i	$0.345262\pi$
$492$	−75.0001	−	129.904i	−0.152439	−	0.264032i
$493$	−955.435	−	551.621i	−1.93800	−	1.11891i
$494$	−85.0831	+	147.368i	−0.172233	+	0.298316i
$495$		0			0
$496$		−	778.511i		−	1.56958i
$497$	−350.419	+	186.340i	−0.705068	+	0.374929i
$498$	92.1631			0.185066
$499$	−317.772	−	550.396i	−0.636817	−	1.10300i	−0.986127	−	0.165992i	$-0.946917\pi$
$499$	−317.772	−	550.396i	−0.636817	−	1.10300i	0.349310	−	0.937007i	$-0.386416\pi$
$500$		0			0
$501$	184.131	−	318.924i	0.367526	−	0.636574i
$502$	243.298	−	140.468i	0.484657	−	0.279817i
$503$			10.6561i			0.0211852i	0.999944	+	0.0105926i	$0.00337179\pi$
$503$			10.6561i			0.0211852i	−0.999944	+	0.0105926i	$0.996628\pi$
$504$	73.9496	+	46.2046i	0.146725	+	0.0916757i
$505$		0			0
$506$	45.1514	+	78.2045i	0.0892319	+	0.154554i
$507$	−441.722	−	255.028i	−0.871246	−	0.503014i
$508$	225.365	−	390.343i	0.443631	−	0.768392i
$509$	706.084	−	407.658i	1.38720	−	0.800899i	0.394200	−	0.919025i	$-0.371022\pi$
$509$	706.084	−	407.658i	1.38720	−	0.800899i	0.992999	+	0.118126i	$0.0376885\pi$
$510$		0			0
$511$	−523.488	−	18.2587i	−1.02444	−	0.0357313i
$512$	−335.445			−0.655167
$513$	−8.14770	−	14.1122i	−0.0158825	−	0.0275092i
$514$	486.552	+	280.911i	0.946599	+	0.546519i
$515$		0			0
$516$	62.2855	−	35.9605i	0.120708	−	0.0696909i
$517$		−	35.2246i		−	0.0681327i
$518$	−32.5832	+	934.179i	−0.0629019	+	1.80343i
$519$	430.911			0.830273
$520$		0			0
$521$	−383.930	−	221.662i	−0.736911	−	0.425456i	0.0840344	−	0.996463i	$-0.473219\pi$
$521$	−383.930	−	221.662i	−0.736911	−	0.425456i	−0.820945	+	0.571007i	$0.806553\pi$
$522$	192.277	−	333.034i	0.368347	−	0.637995i
$523$	549.148	−	317.051i	1.05000	−	0.606216i	0.127348	−	0.991858i	$-0.459354\pi$
$523$	549.148	−	317.051i	1.05000	−	0.606216i	0.922648	+	0.385642i	$0.126020\pi$
$524$			138.359i			0.264044i
$525$		0			0
$526$	−1074.96			−2.04366
$527$	−424.836	−	735.837i	−0.806140	−	1.39628i
$528$	259.996	+	150.109i	0.492416	+	0.284297i
$529$	256.060	−	443.510i	0.484046	−	0.838393i
$530$		0			0
$531$			282.335i			0.531705i
$532$	−24.2474	−	45.5980i	−0.0455777	−	0.0857106i
$533$	792.515			1.48689
$534$	159.056	+	275.492i	0.297857	+	0.515903i
$535$		0			0
$536$	−208.718	+	361.511i	−0.389400	+	0.674460i
$537$	−82.9055	+	47.8655i	−0.154386	+	0.0891351i
$538$		−	149.944i		−	0.278706i
$539$	−187.355	−	384.053i	−0.347597	−	0.712528i
$540$		0			0
$541$	87.5750	+	151.684i	0.161876	+	0.280378i	0.935542	−	0.353217i	$-0.114912\pi$
$541$	87.5750	+	151.684i	0.161876	+	0.280378i	−0.773665	+	0.633594i	$0.781579\pi$
$542$	−118.919	−	68.6577i	−0.219407	−	0.126675i
$543$	−40.6167	+	70.3501i	−0.0748005	+	0.129558i
$544$	−629.079	+	363.199i	−1.15640	+	0.667646i
$545$		0			0
$546$	580.864	−	308.882i	1.06385	−	0.565718i
$547$	773.543			1.41416			0.707078	−	0.707136i	$-0.250013\pi$
$547$	773.543			1.41416			0.707078	+	0.707136i	$0.250013\pi$
$548$	195.161	+	338.029i	0.356133	+	0.616841i
$549$	−190.134	−	109.774i	−0.346328	−	0.199953i
$550$		0			0
$551$	138.126	−	79.7471i	0.250682	−	0.144732i
$552$			29.5474i			0.0535280i
$553$	−172.043	−	107.495i	−0.311109	−	0.194385i
$554$	−1190.60			−2.14909
$555$		0			0
$556$	284.468	+	164.237i	0.511632	+	0.295391i
$557$	−378.264	+	655.173i	−0.679110	+	1.17625i	0.296140	+	0.955145i	$0.404301\pi$
$557$	−378.264	+	655.173i	−0.679110	+	1.17625i	−0.975249	+	0.221108i	$0.929033\pi$
$558$	256.489	−	148.084i	0.459658	−	0.265383i
$559$			379.989i			0.679766i
$560$		0			0
$561$	327.659			0.584062
$562$	−673.639	−	1166.78i	−1.19865	−	2.07612i
$563$	451.185	+	260.492i	0.801394	+	0.462685i	0.843958	−	0.536409i	$-0.180219\pi$
$563$	451.185	+	260.492i	0.801394	+	0.462685i	−0.0425646	+	0.999094i	$0.513553\pi$
$564$	−8.22933	+	14.2536i	−0.0145910	+	0.0252724i
$565$		0			0
$566$			1127.32i			1.99174i
$567$	−2.19604	+	62.9617i	−0.00387308	+	0.111044i
$568$	−235.423			−0.414477
$569$	91.5332	+	158.540i	0.160867	+	0.278629i	0.935180	−	0.354173i	$-0.115238\pi$
$569$	91.5332	+	158.540i	0.160867	+	0.278629i	−0.774313	+	0.632803i	$0.781904\pi$
$570$		0			0
$571$	−498.800	+	863.947i	−0.873555	+	1.51304i	−0.0152618	+	0.999884i	$0.504858\pi$
$571$	−498.800	+	863.947i	−0.873555	+	1.51304i	−0.858294	+	0.513159i	$0.828475\pi$
$572$	382.507	−	220.840i	0.668718	−	0.386084i
$573$			34.8355i			0.0607949i
$574$	−344.147	+	550.802i	−0.599560	+	0.959585i
$575$		0			0
$576$	−7.34516	−	12.7222i	−0.0127520	−	0.0220871i
$577$	−279.135	−	161.158i	−0.483769	−	0.279304i	0.238217	−	0.971212i	$-0.423437\pi$
$577$	−279.135	−	161.158i	−0.483769	−	0.279304i	−0.721986	+	0.691908i	$0.756770\pi$
$578$	−228.808	+	396.307i	−0.395861	+	0.685652i
$579$	43.0549	−	24.8578i	0.0743609	−	0.0429323i
$580$		0			0
$581$	−69.3847	−	130.480i	−0.119423	−	0.224579i
$582$	322.168			0.553553
$583$	−19.4117	−	33.6220i	−0.0332962	−	0.0576707i
$584$	−269.084	−	155.356i	−0.460761	−	0.266020i
$585$		0			0
$586$	−1100.54	+	635.400i	−1.87806	+	1.08430i
$587$			406.391i			0.692318i	0.938176	+	0.346159i	$0.112514\pi$
$587$			406.391i			0.692318i	−0.938176	+	0.346159i	$0.887486\pi$
$588$	−13.9111	+	199.177i	−0.0236583	+	0.338737i
$589$	122.836			0.208550
$590$		0			0
$591$	−336.655	−	194.368i	−0.569636	−	0.328879i
$592$	−526.519	+	911.958i	−0.889391	+	1.54047i
$593$	−333.688	+	192.655i	−0.562711	+	0.324881i	−0.754233	−	0.656607i	$-0.771991\pi$
$593$	−333.688	+	192.655i	−0.562711	+	0.324881i	0.191522	+	0.981488i	$0.438658\pi$
$594$			114.211i			0.192275i
$595$		0			0
$596$	−33.7291			−0.0565925
$597$	−275.447	−	477.089i	−0.461386	−	0.799144i
$598$	193.061	+	111.464i	0.322845	+	0.186395i
$599$	448.272	−	776.430i	0.748367	−	1.29621i	−0.200238	−	0.979747i	$-0.564171\pi$
$599$	448.272	−	776.430i	0.748367	−	1.29621i	0.948605	−	0.316463i	$-0.102495\pi$
$600$		0			0
$601$		−	599.296i		−	0.997166i	−0.866842	−	0.498583i	$-0.833854\pi$
$601$		−	599.296i		−	0.997166i	0.866842	−	0.498583i	$-0.166146\pi$
$602$	−264.095	−	165.009i	−0.438695	−	0.274102i
$603$	−301.597			−0.500161
$604$	−249.811	−	432.686i	−0.413595	−	0.716367i
$605$		0			0
$606$	233.453	−	404.353i	0.385237	−	0.667250i
$607$	426.925	−	246.485i	0.703336	−	0.406071i	−0.105253	−	0.994445i	$-0.533565\pi$
$607$	426.925	−	246.485i	0.703336	−	0.406071i	0.808589	+	0.588374i	$0.200232\pi$
$608$		−	105.014i		−	0.172721i
$609$	−616.249	−	21.4941i	−1.01190	−	0.0352941i
$610$		0			0
$611$	−43.4790	−	75.3079i	−0.0711604	−	0.123253i
$612$	−132.587	−	76.5491i	−0.216645	−	0.125080i
$613$	−70.4822	+	122.079i	−0.114979	+	0.199150i	−0.917771	−	0.397109i	$-0.870013\pi$
$613$	−70.4822	+	122.079i	−0.114979	+	0.199150i	0.802792	+	0.596259i	$0.203347\pi$
$614$	870.465	−	502.563i	1.41770	−	0.818507i
$615$		0			0
$616$	8.83557	−	253.321i	0.0143435	−	0.411236i
$617$	−61.9853			−0.100462			−0.0502312	−	0.998738i	$-0.515996\pi$
$617$	−61.9853			−0.100462			−0.0502312	+	0.998738i	$0.515996\pi$
$618$	−47.0148	−	81.4321i	−0.0760758	−	0.131767i
$619$	−549.456	−	317.228i	−0.887651	−	0.512485i	−0.0144774	−	0.999895i	$-0.504608\pi$
$619$	−549.456	−	317.228i	−0.887651	−	0.512485i	−0.873173	+	0.487410i	$0.837942\pi$
$620$		0			0
$621$	−18.4879	+	10.6740i	−0.0297711	+	0.0171884i
$622$		−	602.689i		−	0.968953i
$623$	270.286	−	432.588i	0.433845	−	0.694362i
$624$	741.138			1.18772
$625$		0			0
$626$	−487.188	−	281.278i	−0.778256	−	0.449326i
$627$	−23.6846	+	41.0229i	−0.0377745	+	0.0654273i
$628$	−494.914	+	285.739i	−0.788080	+	0.454998i
$629$			1149.29i			1.82717i
$630$		0			0
$631$	93.3216			0.147895			0.0739474	−	0.997262i	$-0.476440\pi$
$631$	93.3216			0.147895			0.0739474	+	0.997262i	$0.476440\pi$
$632$	−60.1677	−	104.213i	−0.0952020	−	0.164895i
$633$	427.976	+	247.092i	0.676107	+	0.390350i
$634$	360.439	−	624.298i	0.568515	−	0.984698i
$635$		0			0
$636$			18.1402i			0.0285223i
$637$	−874.603	−	589.821i	−1.37300	−	0.925935i
$638$	−1117.86			−1.75214
$639$	−85.0463	−	147.305i	−0.133093	−	0.230523i
$640$		0			0
$641$	−153.961	+	266.668i	−0.240188	+	0.416018i	−0.960768	−	0.277354i	$-0.910543\pi$
$641$	−153.961	+	266.668i	−0.240188	+	0.416018i	0.720579	+	0.693372i	$0.243876\pi$
$642$	−338.884	+	195.655i	−0.527857	+	0.304759i
$643$		−	296.519i		−	0.461150i	−0.973055	−	0.230575i	$-0.925939\pi$
$643$		−	296.519i		−	0.461150i	0.973055	−	0.230575i	$-0.0740607\pi$
$644$	−59.7362	+	31.7655i	−0.0927581	+	0.0493253i
$645$		0			0
$646$	−85.7306	−	148.490i	−0.132710	−	0.229860i
$647$	−203.727	−	117.622i	−0.314880	−	0.181796i	0.334228	−	0.942492i	$-0.391524\pi$
$647$	−203.727	−	117.622i	−0.314880	−	0.181796i	−0.649108	+	0.760696i	$0.724858\pi$
$648$	−18.6852	+	32.3637i	−0.0288352	+	0.0499440i
$649$	710.767	−	410.361i	1.09517	−	0.632298i
$650$		0			0
$651$	−402.748	−	251.641i	−0.618660	−	0.386546i
$652$	−31.1350			−0.0477531
$653$	148.823	+	257.769i	0.227906	+	0.394746i	0.957187	−	0.289469i	$-0.0934786\pi$
$653$	148.823	+	257.769i	0.227906	+	0.394746i	−0.729281	+	0.684214i	$0.760145\pi$
$654$	−103.401	−	59.6987i	−0.158106	−	0.0912823i
$655$		0			0
$656$	−633.643	+	365.834i	−0.965919	+	0.557673i
$657$		−	224.488i		−	0.341687i
$658$	71.2200	+	2.48408i	0.108237	+	0.00377519i
$659$	−127.740			−0.193839			−0.0969197	−	0.995292i	$-0.530899\pi$
$659$	−127.740			−0.193839			−0.0969197	+	0.995292i	$0.530899\pi$
$660$		0			0
$661$	−823.610	−	475.512i	−1.24601	−	0.719382i	−0.275696	−	0.961245i	$-0.588908\pi$
$661$	−823.610	−	475.512i	−1.24601	−	0.719382i	−0.970311	+	0.241863i	$0.922242\pi$
$662$	679.286	−	1176.56i	1.02611	−	1.77728i
$663$	700.513	−	404.441i	1.05658	−	0.610017i
$664$		−	87.6611i		−	0.132020i
$665$		0			0
$666$	−400.606			−0.601510
$667$	−104.474	−	180.953i	−0.156632	−	0.271295i
$668$	433.178	+	250.095i	0.648469	+	0.374394i
$669$	49.4481	−	85.6466i	0.0739134	−	0.128022i
$670$		0			0
$671$			638.206i			0.951126i
$672$	−215.132	+	344.316i	−0.320137	+	0.512374i
$673$	1003.39			1.49092			0.745460	−	0.666550i	$-0.232230\pi$
$673$	1003.39			1.49092			0.745460	+	0.666550i	$0.232230\pi$
$674$	−86.0076	−	148.970i	−0.127608	−	0.221023i
$675$		0			0
$676$	346.392	−	599.968i	0.512414	−	0.887526i
$677$	−408.603	+	235.907i	−0.603550	+	0.348460i	−0.770437	−	0.637516i	$-0.779962\pi$
$677$	−408.603	+	235.907i	−0.603550	+	0.348460i	0.166887	+	0.985976i	$0.446629\pi$
$678$			403.099i			0.594541i
$679$	−242.543	−	456.111i	−0.357206	−	0.671740i
$680$		0			0
$681$	158.185	+	273.984i	0.232283	+	0.402325i
$682$	−745.589	−	430.466i	−1.09324	−	0.631182i
$683$	208.614	−	361.330i	0.305438	−	0.529034i	−0.671921	−	0.740623i	$-0.734530\pi$
$683$	208.614	−	361.330i	0.305438	−	0.529034i	0.977359	+	0.211589i	$0.0678638\pi$
$684$	19.1679	−	11.0666i	0.0280233	−	0.0161792i
$685$		0			0
$686$	789.722	−	351.726i	1.15120	−	0.512719i
$687$	−29.0693			−0.0423134
$688$	−175.407	−	303.815i	−0.254953	−	0.441591i
$689$	−83.0019	−	47.9211i	−0.120467	−	0.0695517i
$690$		0			0
$691$	160.907	−	92.8995i	0.232860	−	0.134442i	−0.379030	−	0.925384i	$-0.623742\pi$
$691$	160.907	−	92.8995i	0.232860	−	0.134442i	0.611891	+	0.790942i	$0.290409\pi$
$692$			585.285i			0.845787i
$693$	161.695	−	85.9835i	0.233326	−	0.124074i
$694$	962.538			1.38694
$695$		0			0
$696$	−316.766	−	182.885i	−0.455123	−	0.262765i
$697$	−399.273	+	691.561i	−0.572845	+	0.992197i
$698$	−658.905	+	380.419i	−0.943990	+	0.545013i
$699$		−	461.430i		−	0.660129i
$700$		0			0
$701$	1034.80			1.47618			0.738089	−	0.674704i	$-0.235729\pi$
$701$	1034.80			1.47618			0.738089	+	0.674704i	$0.235729\pi$
$702$	140.975	+	244.176i	0.200819	+	0.347829i
$703$	−143.892	−	83.0759i	−0.204682	−	0.118173i
$704$	−21.3517	+	36.9822i	−0.0303291	+	0.0525316i
$705$		0			0
$706$		−	322.729i		−	0.457123i
$707$	−748.220	−	26.0971i	−1.05830	−	0.0369125i
$708$	−383.482			−0.541641
$709$	108.321	+	187.618i	0.152780	+	0.264623i	0.932248	−	0.361819i	$-0.117844\pi$
$709$	108.321	+	187.618i	0.152780	+	0.264623i	−0.779468	+	0.626442i	$0.784511\pi$
$710$		0			0
$711$	43.4710	−	75.2940i	0.0611406	−	0.105899i
$712$	262.035	−	151.286i	0.368027	−	0.212481i
$713$		−	160.923i		−	0.225698i
$714$	−23.1069	+	662.487i	−0.0323625	+	0.927854i
$715$		0			0
$716$	−65.0133	−	112.606i	−0.0908007	−	0.157271i
$717$	−59.5517	−	34.3822i	−0.0830568	−	0.0479529i
$718$	−660.636	+	1144.26i	−0.920106	+	1.59367i
$719$	0.325449	−	0.187898i	0.000452641	−	0.000261332i	−0.499774	−	0.866156i	$-0.666583\pi$
$719$	0.325449	−	0.187898i	0.000452641	−	0.000261332i	0.500226	+	0.865895i	$0.333250\pi$
$720$		0			0
$721$	−79.8930	+	127.867i	−0.110809	+	0.177347i
$722$	−885.086			−1.22588
$723$	72.1896	+	125.036i	0.0998473	+	0.172941i
$724$	−95.5530	−	55.1675i	−0.131979	−	0.0761983i
$725$		0			0
$726$	−169.936	+	98.1128i	−0.234072	+	0.135142i
$727$			174.857i			0.240518i	0.992743	+	0.120259i	$0.0383726\pi$
$727$			174.857i			0.240518i	−0.992743	+	0.120259i	$0.961627\pi$
$728$	−293.794	−	552.490i	−0.403563	−	0.758915i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−331.585	−	191.441i	−0.453605	−	0.261889i
$732$	149.100	−	258.249i	0.203689	−	0.352800i
$733$	738.210	−	426.206i	1.00711	−	0.581454i	0.0967645	−	0.995307i	$-0.469151\pi$
$733$	738.210	−	426.206i	1.00711	−	0.581454i	0.910344	+	0.413853i	$0.135817\pi$
$734$		−	89.6973i		−	0.122203i
$735$		0			0
$736$	−137.575			−0.186923
$737$	438.357	+	759.256i	0.594785	+	1.03020i
$738$	−241.056	−	139.174i	−0.326634	−	0.188582i
$739$	584.126	−	1011.74i	0.790428	−	1.36906i	−0.135275	−	0.990808i	$-0.543192\pi$
$739$	584.126	−	1011.74i	0.790428	−	1.36906i	0.925702	−	0.378253i	$-0.123475\pi$
$740$		0			0
$741$			116.939i			0.157813i
$742$	69.3488	−	36.8771i	0.0934619	−	0.0496996i
$743$	558.877			0.752190			0.376095	−	0.926581i	$-0.377267\pi$
$743$	558.877			0.752190			0.376095	+	0.926581i	$0.377267\pi$
$744$	−140.850	−	243.960i	−0.189315	−	0.327903i
$745$		0			0
$746$	336.592	−	582.995i	0.451196	−	0.781494i
$747$	54.8497	−	31.6675i	0.0734266	−	0.0423929i
$748$			445.042i			0.594976i
$749$	532.128	+	332.479i	0.710451	+	0.443898i
$750$		0			0
$751$	−630.654	−	1092.32i	−0.839752	−	1.45449i	−0.890102	−	0.455762i	$-0.849367\pi$
$751$	−630.654	−	1092.32i	−0.839752	−	1.45449i	0.0503493	−	0.998732i	$-0.483967\pi$
$752$	69.5260	+	40.1408i	0.0924547	+	0.0533788i
$753$	96.5304	−	167.196i	0.128194	−	0.222039i
$754$	−2389.92	+	1379.82i	−3.16965	+	1.83000i
$755$		0			0
$756$	−85.5177	−	2.98276i	−0.113119	−	0.00394546i
$757$	1269.13			1.67652			0.838262	−	0.545268i	$-0.183572\pi$
$757$	1269.13			1.67652			0.838262	+	0.545268i	$0.183572\pi$
$758$	−158.392	−	274.343i	−0.208960	−	0.361930i
$759$	53.7425	+	31.0282i	0.0708070	+	0.0408804i
$760$		0			0
$761$	−157.718	+	91.0585i	−0.207251	+	0.119656i	−0.600033	−	0.799975i	$-0.704846\pi$
$761$	−157.718	+	91.0585i	−0.207251	+	0.119656i	0.392782	+	0.919632i	$0.371513\pi$
$762$		−	836.394i		−	1.09763i
$763$	−6.67355	+	191.335i	−0.00874646	+	0.250766i
$764$	−47.3152			−0.0619309
$765$		0			0
$766$	778.195	+	449.291i	1.01592	+	0.586542i
$767$	1013.05	−	1754.65i	1.32079	−	2.28768i
$768$	−489.118	+	282.392i	−0.636872	+	0.367698i
$769$		−	810.237i		−	1.05362i	−0.849982	−	0.526812i	$-0.823387\pi$
$769$		−	810.237i		−	1.05362i	0.849982	−	0.526812i	$-0.176613\pi$
$770$		0			0
$771$	386.087			0.500761
$772$	33.7630	+	58.4793i	0.0437345	+	0.0757504i
$773$	−212.492	−	122.682i	−0.274893	−	0.158709i	0.356216	−	0.934404i	$-0.384067\pi$
$773$	−212.492	−	122.682i	−0.274893	−	0.158709i	−0.631109	+	0.775694i	$0.717400\pi$
$774$	66.7300	−	115.580i	0.0862144	−	0.149328i
$775$		0			0
$776$		−	306.431i		−	0.394885i
$777$	301.595	+	567.160i	0.388153	+	0.729936i
$778$	−1125.70			−1.44692
$779$	−57.7224	−	99.9781i	−0.0740981	−	0.128342i
$780$		0			0
$781$	−247.222	+	428.200i	−0.316545	+	0.548272i
$782$	−194.531	+	112.312i	−0.248760	+	0.143622i
$783$		−	264.268i		−	0.337506i
$784$	971.543	+	67.8553i	1.23921	+	0.0865501i
$785$		0			0
$786$	128.373	+	222.348i	0.163324	+	0.282886i
$787$	373.020	+	215.363i	0.473977	+	0.273651i	0.717903	−	0.696143i	$-0.245102\pi$
$787$	373.020	+	215.363i	0.473977	+	0.273651i	−0.243926	+	0.969794i	$0.578435\pi$
$788$	264.000	−	457.261i	0.335025	−	0.580280i
$789$	−639.750	+	369.360i	−0.810837	+	0.468137i
$790$		0			0
$791$	570.690	−	303.472i	0.721479	−	0.383656i
$792$	108.632			0.137162
$793$	787.761	+	1364.44i	0.993393	+	1.72061i
$794$	−1323.45	−	764.093i	−1.66681	−	0.962334i
$795$		0			0
$796$	648.005	−	374.126i	0.814077	−	0.470008i
$797$			1137.61i			1.42737i	0.700468	+	0.713684i	$0.252975\pi$
$797$			1137.61i			1.42737i	−0.700468	+	0.713684i	$0.747025\pi$
$798$	−81.2733	−	50.7805i	−0.101846	−	0.0636347i
$799$	87.6199			0.109662
$800$		0			0
$801$	189.320	+	109.304i	0.236354	+	0.136459i
$802$	−918.449	+	1590.80i	−1.14520	+	1.98354i
$803$	−565.139	+	326.283i	−0.703785	+	0.406330i
$804$		−	409.643i		−	0.509507i
$805$		0			0
$806$	−2125.36			−2.63692
$807$	−51.5210	−	89.2370i	−0.0638426	−	0.110579i
$808$	−384.602	−	222.050i	−0.475992	−	0.274814i
$809$	−455.336	+	788.665i	−0.562838	+	0.974864i	0.434409	+	0.900716i	$0.356957\pi$
$809$	−455.336	+	788.665i	−0.562838	+	0.974864i	−0.997247	+	0.0741482i	$0.976376\pi$
$810$		0			0
$811$			546.361i			0.673688i	0.941560	+	0.336844i	$0.109360\pi$
$811$			546.361i			0.673688i	−0.941560	+	0.336844i	$0.890640\pi$
$812$	29.1944	−	837.020i	0.0359537	−	1.03081i
$813$	−94.3638			−0.116069
$814$	582.262	+	1008.51i	0.715309	+	1.23895i
$815$		0			0
$816$	−373.389	+	646.729i	−0.457585	+	0.792560i
$817$	47.9368	−	27.6763i	0.0586742	−	0.0338756i
$818$		−	1337.48i		−	1.63507i
$819$	239.561	−	383.413i	0.292504	−	0.468148i
$820$		0			0
$821$	−322.150	−	557.980i	−0.392388	−	0.679635i	0.600376	−	0.799718i	$-0.295017\pi$
$821$	−322.150	−	557.980i	−0.392388	−	0.679635i	−0.992764	+	0.120082i	$0.961684\pi$
$822$	627.262	+	362.150i	0.763092	+	0.440572i
$823$	384.661	−	666.252i	0.467388	−	0.809540i	−0.531917	−	0.846796i	$-0.678528\pi$
$823$	384.661	−	666.252i	0.467388	−	0.809540i	0.999306	+	0.0372559i	$0.0118617\pi$
$824$	−77.4543	+	44.7183i	−0.0939980	+	0.0542697i
$825$		0			0
$826$	779.579	+	1466.03i	0.943800	+	1.77485i
$827$	−715.404			−0.865060			−0.432530	−	0.901620i	$-0.642379\pi$
$827$	−715.404			−0.865060			−0.432530	+	0.901620i	$0.642379\pi$
$828$	−14.4979	−	25.1111i	−0.0175096	−	0.0303274i
$829$	68.2973	+	39.4315i	0.0823852	+	0.0475651i	0.540627	−	0.841263i	$-0.318187\pi$
$829$	68.2973	+	39.4315i	0.0823852	+	0.0475651i	−0.458241	+	0.888828i	$0.651521\pi$
$830$		0			0
$831$	−708.568	+	409.092i	−0.852669	+	0.492289i
$832$			105.421i			0.126708i
$833$	955.317	−	466.038i	1.14684	−	0.559469i
$834$	609.533			0.730855
$835$		0			0
$836$	−55.7193	−	32.1696i	−0.0666499	−	0.0384803i
$837$	101.764	−	176.261i	0.121582	−	0.210586i
$838$	616.928	−	356.184i	0.736191	−	0.425040i
$839$		−	165.698i		−	0.197494i	−0.995113	−	0.0987471i	$-0.968517\pi$
$839$		−	165.698i		−	0.197494i	0.995113	−	0.0987471i	$-0.0314835\pi$
$840$		0			0
$841$	1745.57			2.07559
$842$	555.238	+	961.701i	0.659428	+	1.14216i
$843$	−801.816	−	462.929i	−0.951146	−	0.549144i
$844$	−335.612	+	581.297i	−0.397645	+	0.688741i
$845$		0			0
$846$			30.5414i			0.0361010i
$847$	266.840	+	166.724i	0.315041	+	0.196841i
$848$	88.4838			0.104344
$849$	387.352	+	670.913i	0.456245	+	0.790239i
$850$		0			0
$851$	−108.834	+	188.507i	−0.127890	+	0.221512i
$852$	200.076	−	115.514i	0.234831	−	0.135580i
$853$			1066.17i			1.24991i	0.780661	+	0.624955i	$0.214883\pi$
$853$			1066.17i			1.24991i	−0.780661	+	0.624955i	$0.785117\pi$
$854$	−1290.38	−	45.0070i	−1.51098	−	0.0527014i
$855$		0			0
$856$	186.098	+	322.331i	0.217404	+	0.376555i
$857$	−192.821	−	111.325i	−0.224995	−	0.129901i	0.383266	−	0.923638i	$-0.374799\pi$
$857$	−192.821	−	111.325i	−0.224995	−	0.129901i	−0.608261	+	0.793737i	$0.708133\pi$
$858$	409.801	−	709.796i	0.477624	−	0.827269i
$859$	1313.46	−	758.329i	1.52906	−	0.882805i	0.529661	−	0.848209i	$-0.322319\pi$
$859$	1313.46	−	758.329i	1.52906	−	0.882805i	0.999401	−	0.0345956i	$-0.0110143\pi$
$860$		0			0
$861$	−15.5578	+	446.052i	−0.0180695	+	0.518063i
$862$	321.190			0.372610
$863$	69.0180	+	119.543i	0.0799745	+	0.138520i	0.903239	−	0.429139i	$-0.141183\pi$
$863$	69.0180	+	119.543i	0.0799745	+	0.138520i	−0.823264	+	0.567658i	$0.807849\pi$
$864$	−150.688	−	86.9997i	−0.174407	−	0.100694i
$865$		0			0
$866$	945.752	−	546.030i	1.09209	−	0.630520i
$867$			314.476i			0.362717i
$868$	341.791	−	547.031i	0.393769	−	0.630221i
$869$	−252.732			−0.290831
$870$		0			0
$871$	1874.36	+	1082.16i	2.15196	+	1.24243i
$872$	−56.7825	+	98.3502i	−0.0651176	+	0.112787i
$873$	191.734	−	110.698i	0.219627	−	0.126802i
$874$		−	32.4737i		−	0.0371552i
$875$		0			0
$876$	304.911			0.348072
$877$	−308.810	−	534.875i	−0.352121	−	0.609892i	0.634500	−	0.772923i	$-0.281206\pi$
$877$	−308.810	−	534.875i	−0.352121	−	0.609892i	−0.986621	+	0.163031i	$0.947873\pi$
$878$	−138.013	−	79.6818i	−0.157190	−	0.0907538i
$879$	−436.650	+	756.300i	−0.496757	+	0.860409i
$880$		0			0
$881$			425.629i			0.483120i	0.970386	+	0.241560i	$0.0776591\pi$
$881$			425.629i			0.483120i	−0.970386	+	0.241560i	$0.922341\pi$
$882$	162.446	+	332.992i	0.184179	+	0.377542i
$883$	−295.270			−0.334394			−0.167197	−	0.985923i	$-0.553472\pi$
$883$	−295.270			−0.334394			−0.167197	+	0.985923i	$0.553472\pi$
$884$	549.332	+	951.471i	0.621416	+	1.07632i
$885$		0			0
$886$	−552.452	+	956.874i	−0.623535	+	1.07999i
$887$	1463.38	−	844.884i	1.64981	−	0.952519i	0.672665	−	0.739947i	$-0.265150\pi$
$887$	1463.38	−	844.884i	1.64981	−	0.952519i	0.977146	−	0.212571i	$-0.0681838\pi$
$888$			381.037i			0.429096i
$889$	−1184.13	+	629.676i	−1.33198	+	0.708297i
$890$		0			0
$891$	39.2432	+	67.9713i	0.0440440	+	0.0762865i
$892$	116.329	+	67.1628i	0.130414	+	0.0752946i
$893$	−6.33354	+	10.9700i	−0.00709244	+	0.0122845i
$894$	−54.2039	+	31.2946i	−0.0606308	+	0.0350052i
$895$		0			0
$896$	721.895	+	451.048i	0.805686	+	0.503402i
$897$	153.197			0.170788
$898$	270.928	+	469.261i	0.301702	+	0.522563i
$899$	1725.18	+	996.035i	1.91900	+	1.10794i
$900$		0			0
$901$	83.6336	−	48.2859i	0.0928230	−	0.0535914i
$902$			809.129i			0.897039i
$903$	−213.870	−	7.45956i	−0.236844	−	0.00826087i
$904$	383.409			0.424124
$905$		0			0
$906$	−802.911	−	463.561i	−0.886215	−	0.511657i
$907$	221.038	−	382.848i	0.243702	−	0.422104i	−0.718064	−	0.695977i	$-0.754972\pi$
$907$	221.038	−	382.848i	0.243702	−	0.422104i	0.961766	+	0.273873i	$0.0883048\pi$
$908$	−372.138	+	214.854i	−0.409843	+	0.236623i
$909$		−	320.861i		−	0.352982i
$910$		0			0
$911$	998.378			1.09591			0.547957	−	0.836507i	$-0.315406\pi$
$911$	998.378			1.09591			0.547957	+	0.836507i	$0.315406\pi$
$912$	−53.9804	−	93.4968i	−0.0591890	−	0.102518i
$913$	−159.443	−	92.0544i	−0.174636	−	0.100826i
$914$	303.963	−	526.479i	0.332563	−	0.576016i
$915$		0			0
$916$		−	39.4834i		−	0.0431041i
$917$	218.146	−	349.139i	0.237891	−	0.380740i
$918$	−284.096			−0.309473
$919$	−154.797	−	268.116i	−0.168441	−	0.291748i	0.769431	−	0.638730i	$-0.220540\pi$
$919$	−154.797	−	268.116i	−0.168441	−	0.291748i	−0.937872	+	0.346982i	$0.887206\pi$
$920$		0			0
$921$	345.364	−	598.188i	0.374988	−	0.649499i
$922$	−749.520	+	432.736i	−0.812928	+	0.469344i
$923$			1220.62i			1.32245i
$924$	116.787	+	219.622i	0.126393	+	0.237686i
$925$		0			0
$926$	−94.2280	−	163.208i	−0.101758	−	0.176250i
$927$	−55.9605	−	32.3088i	−0.0603674	−	0.0348531i
$928$	851.526	−	1474.89i	0.917593	−	1.58932i
$929$	−443.269	+	255.921i	−0.477146	+	0.275480i	−0.719226	−	0.694776i	$-0.755504\pi$
$929$	−443.269	+	255.921i	−0.477146	+	0.275480i	0.242080	+	0.970256i	$0.422170\pi$
$930$		0			0
$931$	−10.7064	+	153.293i	−0.0114999	+	0.164654i
$932$	626.737			0.672464
$933$	−207.085	−	358.682i	−0.221956	−	0.384440i
$934$	777.476	+	448.876i	0.832415	+	0.480595i
$935$		0			0
$936$	232.248	−	134.089i	0.248129	−	0.143257i
$937$			592.935i			0.632801i	0.948626	+	0.316401i	$0.102474\pi$
$937$			592.935i			0.632801i	−0.948626	+	0.316401i	$0.897526\pi$
$938$	−1566.04	+	832.762i	−1.66955	+	0.887807i
$939$	−386.592			−0.411706
$940$		0			0
$941$	−549.458	−	317.230i	−0.583909	−	0.337120i	0.178777	−	0.983890i	$-0.442786\pi$
$941$	−549.458	−	317.230i	−0.583909	−	0.337120i	−0.762685	+	0.646770i	$0.776119\pi$
$942$	−530.230	+	918.386i	−0.562877	+	0.974932i
$943$	−130.977	+	75.6198i	−0.138894	+	0.0801907i
$944$			1870.54i			1.98150i
$945$		0			0
$946$	−387.956			−0.410101
$947$	329.805	+	571.239i	0.348263	+	0.603209i	0.985941	−	0.167094i	$-0.0534384\pi$
$947$	329.805	+	571.239i	0.348263	+	0.603209i	−0.637678	+	0.770303i	$0.720105\pi$
$948$	102.268	+	59.0444i	0.107878	+	0.0622831i
$949$	−805.487	+	1395.14i	−0.848775	+	1.47012i
$950$		0			0
$951$		−	495.391i		−	0.520916i
$952$	630.127	+	21.9781i	0.661898	+	0.0230863i
$953$	615.571			0.645930			0.322965	−	0.946411i	$-0.395320\pi$
$953$	615.571			0.645930			0.322965	+	0.946411i	$0.395320\pi$
$954$	16.8309	+	29.1519i	0.0176424	+	0.0305576i
$955$		0			0
$956$	46.6996	−	80.8861i	0.0488489	−	0.0846088i
$957$	−665.282	+	384.100i	−0.695174	+	0.401359i
$958$			942.013i			0.983312i
$959$	40.4837	−	1160.69i	0.0422145	−	1.21032i
$960$		0			0
$961$	286.605	+	496.415i	0.298237	+	0.516561i
$962$	2489.68	+	1437.41i	2.58802	+	1.49419i
$963$	−134.455	+	232.883i	−0.139621	+	0.241831i
$964$	−169.830	+	98.0515i	−0.176172	+	0.101713i
$965$		0			0
$966$	−66.5255	+	106.473i	−0.0688669	+	0.110220i
$967$	−386.702			−0.399899			−0.199949	−	0.979806i	$-0.564078\pi$
$967$	−386.702			−0.399899			−0.199949	+	0.979806i	$0.564078\pi$
$968$	93.3202	+	161.635i	0.0964052	+	0.166979i
$969$	−102.043	−	58.9145i	−0.105307	−	0.0607993i
$970$		0			0
$971$	487.138	−	281.249i	0.501687	−	0.289649i	−0.227723	−	0.973726i	$-0.573128\pi$
$971$	487.138	−	281.249i	0.501687	−	0.289649i	0.729410	+	0.684077i	$0.239795\pi$
$972$		−	36.6727i		−	0.0377291i
$973$	−458.885	−	862.950i	−0.471619	−	0.886896i
$974$	1959.79			2.01211
$975$		0			0
$976$	−1259.68	−	727.279i	−1.29066	−	0.745163i
$977$	356.041	−	616.682i	0.364423	−	0.631199i	−0.624260	−	0.781216i	$-0.714600\pi$
$977$	356.041	−	616.682i	0.364423	−	0.631199i	0.988683	+	0.150017i	$0.0479329\pi$
$978$	−50.0351	+	28.8878i	−0.0511607	+	0.0295376i
$979$		−	635.472i		−	0.649103i
$980$		0			0
$981$	−82.0504			−0.0836396
$982$	578.178	+	1001.43i	0.588776	+	1.01979i
$983$	−1064.18	−	614.407i	−1.08259	−	0.625032i	−0.150995	−	0.988535i	$-0.548248\pi$
$983$	−1064.18	−	614.407i	−1.08259	−	0.625032i	−0.931593	+	0.363502i	$0.881581\pi$
$984$	−132.375	+	229.281i	−0.134528	+	0.233009i
$985$		0			0
$986$		−	2780.64i		−	2.82012i
$987$	43.2392	−	22.9930i	0.0438087	−	0.0232959i
$988$	−158.832			−0.160761
$989$	−36.2577	−	62.8001i	−0.0366609	−	0.0634986i
$990$		0			0
$991$	621.249	−	1076.04i	0.626892	−	1.08581i	−0.361280	−	0.932457i	$-0.617660\pi$
$991$	621.249	−	1076.04i	0.626892	−	1.08581i	0.988172	−	0.153351i	$-0.0490064\pi$
$992$	1135.90	−	655.811i	1.14506	−	0.661100i
$993$		−	933.617i		−	0.940199i
$994$	−848.337	−	530.050i	−0.853457	−	0.533250i
$995$		0			0
$996$	43.0123	+	74.4995i	0.0431850	+	0.0747987i
$997$	694.350	+	400.883i	0.696439	+	0.402089i	0.806020	−	0.591889i	$-0.201618\pi$
$997$	694.350	+	400.883i	0.696439	+	0.402089i	−0.109581	+	0.993978i	$0.534951\pi$
$998$	800.920	−	1387.23i	0.802525	−	1.39001i
$999$	−238.415	+	137.649i	−0.238654	+	0.137787i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.o.l.451.4		8
5.2	odd	4		525.3.s.h.199.2		16
5.3	odd	4		525.3.s.h.199.7		16
5.4	even	2		105.3.n.a.31.1	✓	8
7.5	odd	6	inner	525.3.o.l.376.4		8
15.14	odd	2		315.3.w.a.136.4		8
35.4	even	6		735.3.h.a.391.8		8
35.12	even	12		525.3.s.h.124.7		16
35.19	odd	6		105.3.n.a.61.1	yes	8
35.24	odd	6		735.3.h.a.391.7		8
35.33	even	12		525.3.s.h.124.2		16
105.89	even	6		315.3.w.a.271.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.n.a.31.1	✓	8	5.4	even	2
105.3.n.a.61.1	yes	8	35.19	odd	6
315.3.w.a.136.4		8	15.14	odd	2
315.3.w.a.271.4		8	105.89	even	6
525.3.o.l.376.4		8	7.5	odd	6	inner
525.3.o.l.451.4		8	1.1	even	1	trivial
525.3.s.h.124.2		16	35.33	even	12
525.3.s.h.124.7		16	35.12	even	12
525.3.s.h.199.2		16	5.2	odd	4
525.3.s.h.199.7		16	5.3	odd	4
735.3.h.a.391.7		8	35.24	odd	6
735.3.h.a.391.8		8	35.4	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26021 + 2.18275i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.17628 + 2.03737i) q^{4} +4.36551i q^{6} +(6.18050 - 3.28656i) q^{7} +4.15226 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.26021 + 2.18275i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.17628 + 2.03737i) q^{4} +4.36551i q^{6} +(6.18050 - 3.28656i) q^{7} +4.15226 q^{8} +(1.50000 + 2.59808i) q^{9} +(4.36036 - 7.55236i) q^{11} +(-3.52883 + 2.03737i) q^{12} -21.5286i q^{13} +(14.9625 + 9.34874i) q^{14} +(9.93785 + 17.2129i) q^{16} +(18.7862 + 10.8462i) q^{17} +(-3.78064 + 6.54826i) q^{18} +(-2.71590 + 1.56803i) q^{19} +(12.1170 + 0.422628i) q^{21} +21.9799 q^{22} +(2.05421 + 3.55799i) q^{23} +(6.22840 + 3.59597i) q^{24} +(46.9917 - 27.1307i) q^{26} +5.19615i q^{27} +(-0.574033 + 16.4579i) q^{28} -50.8583 q^{29} +(-33.9213 - 19.5845i) q^{31} +(-16.7431 + 28.9999i) q^{32} +(13.0811 - 7.55236i) q^{33} +54.6743i q^{34} -7.05767 q^{36} +(26.4906 + 45.8831i) q^{37} +(-6.84523 - 3.95209i) q^{38} +(18.6443 - 32.2929i) q^{39} +36.8122i q^{41} +(14.3475 + 26.9810i) q^{42} -17.6504 q^{43} +(10.2580 + 17.7674i) q^{44} +(-5.17748 + 8.96766i) q^{46} +(3.49804 - 2.01959i) q^{47} +34.4257i q^{48} +(27.3971 - 40.6251i) q^{49} +(18.7862 + 32.5387i) q^{51} +(43.8618 + 25.3236i) q^{52} +(2.22593 - 3.85542i) q^{53} +(-11.3419 + 6.54826i) q^{54} +(25.6631 - 13.6467i) q^{56} -5.43180 q^{57} +(-64.0923 - 111.011i) q^{58} +(81.5032 + 47.0559i) q^{59} +(-63.3781 + 36.5913i) q^{61} -98.7226i q^{62} +(17.8095 + 11.1276i) q^{63} -4.89677 q^{64} +(32.9699 + 19.0352i) q^{66} +(-50.2661 + 87.0635i) q^{67} +(-44.1956 + 25.5164i) q^{68} +7.11598i q^{69} -56.6975 q^{71} +(6.22840 + 10.7879i) q^{72} +(-64.8042 - 37.4147i) q^{73} +(-66.7676 + 115.645i) q^{74} -7.37773i q^{76} +(2.12789 - 61.0079i) q^{77} +93.9833 q^{78} +(-14.4903 - 25.0980i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-80.3519 + 46.3912i) q^{82} -21.1116i q^{83} +(-15.1140 + 24.1897i) q^{84} +(-22.2433 - 38.5266i) q^{86} +(-76.2875 - 44.0446i) q^{87} +(18.1054 - 31.3594i) q^{88} +(63.1066 - 36.4346i) q^{89} +(-70.7551 - 133.057i) q^{91} -9.66528 q^{92} +(-33.9213 - 58.7535i) q^{93} +(8.81655 + 5.09024i) q^{94} +(-50.2293 + 28.9999i) q^{96} -73.7985i q^{97} +(123.201 + 8.60469i) q^{98} +26.1622 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 12 q^{3} - 6 q^{4} + 16 q^{7} + 32 q^{8} + 12 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 12 * q^3 - 6 * q^4 + 16 * q^7 + 32 * q^8 + 12 * q^9	\( 8 q - 2 q^{2} + 12 q^{3} - 6 q^{4} + 16 q^{7} + 32 q^{8} + 12 q^{9} + 20 q^{11} - 18 q^{12} - 16 q^{14} - 2 q^{16} + 18 q^{17} + 6 q^{18} + 48 q^{21} + 16 q^{22} - 62 q^{23} + 48 q^{24} + 120 q^{26} + 120 q^{28} - 100 q^{29} - 126 q^{31} - 36 q^{32} + 60 q^{33} - 36 q^{36} + 80 q^{37} - 114 q^{38} - 12 q^{39} - 90 q^{42} - 352 q^{43} - 18 q^{44} - 82 q^{46} + 72 q^{47} + 38 q^{49} + 18 q^{51} + 48 q^{52} + 76 q^{53} + 18 q^{54} + 196 q^{56} + 40 q^{58} - 54 q^{59} - 396 q^{61} + 96 q^{63} - 4 q^{64} + 24 q^{66} - 184 q^{67} + 312 q^{68} + 164 q^{71} + 48 q^{72} - 348 q^{73} - 140 q^{74} - 152 q^{77} + 240 q^{78} - 206 q^{79} - 36 q^{81} - 204 q^{82} + 132 q^{84} + 178 q^{86} - 150 q^{87} - 124 q^{88} + 282 q^{89} - 114 q^{91} + 288 q^{92} - 126 q^{93} + 30 q^{94} - 108 q^{96} + 592 q^{98} + 120 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 12 * q^3 - 6 * q^4 + 16 * q^7 + 32 * q^8 + 12 * q^9 + 20 * q^11 - 18 * q^12 - 16 * q^14 - 2 * q^16 + 18 * q^17 + 6 * q^18 + 48 * q^21 + 16 * q^22 - 62 * q^23 + 48 * q^24 + 120 * q^26 + 120 * q^28 - 100 * q^29 - 126 * q^31 - 36 * q^32 + 60 * q^33 - 36 * q^36 + 80 * q^37 - 114 * q^38 - 12 * q^39 - 90 * q^42 - 352 * q^43 - 18 * q^44 - 82 * q^46 + 72 * q^47 + 38 * q^49 + 18 * q^51 + 48 * q^52 + 76 * q^53 + 18 * q^54 + 196 * q^56 + 40 * q^58 - 54 * q^59 - 396 * q^61 + 96 * q^63 - 4 * q^64 + 24 * q^66 - 184 * q^67 + 312 * q^68 + 164 * q^71 + 48 * q^72 - 348 * q^73 - 140 * q^74 - 152 * q^77 + 240 * q^78 - 206 * q^79 - 36 * q^81 - 204 * q^82 + 132 * q^84 + 178 * q^86 - 150 * q^87 - 124 * q^88 + 282 * q^89 - 114 * q^91 + 288 * q^92 - 126 * q^93 + 30 * q^94 - 108 * q^96 + 592 * q^98 + 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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