LMFDB - Embedded newform 525.3.o.l.451.3

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			451.3
Root			$-0.336732 - 0.583237i$ of defining polynomial
Character	$\chi$	$=$	525.451
Dual form			525.3.o.l.376.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.336732 + 0.583237i) q^{2} +(1.50000 + 0.866025i) q^{3} +(1.77322 - 3.07131i) q^{4} +1.16647i q^{6} +(6.82455 + 1.55742i) q^{7} +5.08226 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.336732 + 0.583237i) q^{2} +(1.50000 + 0.866025i) q^{3} +(1.77322 - 3.07131i) q^{4} +1.16647i q^{6} +(6.82455 + 1.55742i) q^{7} +5.08226 q^{8} +(1.50000 + 2.59808i) q^{9} +(0.0223800 - 0.0387632i) q^{11} +(5.31967 - 3.07131i) q^{12} +23.0010i q^{13} +(1.38970 + 4.50476i) q^{14} +(-5.38154 - 9.32109i) q^{16} +(8.16292 + 4.71286i) q^{17} +(-1.01020 + 1.74971i) q^{18} +(0.991050 - 0.572183i) q^{19} +(8.88806 + 8.24636i) q^{21} +0.0301442 q^{22} +(-22.1202 - 38.3133i) q^{23} +(7.62339 + 4.40136i) q^{24} +(-13.4150 + 7.74518i) q^{26} +5.19615i q^{27} +(16.8848 - 18.1987i) q^{28} +53.0004 q^{29} +(19.5690 + 11.2982i) q^{31} +(13.7888 - 23.8829i) q^{32} +(0.0671399 - 0.0387632i) q^{33} +6.34788i q^{34} +10.6393 q^{36} +(21.1418 + 36.6186i) q^{37} +(0.667436 + 0.385344i) q^{38} +(-19.9195 + 34.5015i) q^{39} -38.2787i q^{41} +(-1.81669 + 7.96065i) q^{42} -76.5222 q^{43} +(-0.0793693 - 0.137472i) q^{44} +(14.8971 - 25.8026i) q^{46} +(23.5070 - 13.5718i) q^{47} -18.6422i q^{48} +(44.1489 + 21.2574i) q^{49} +(8.16292 + 14.1386i) q^{51} +(70.6434 + 40.7860i) q^{52} +(9.49388 - 16.4439i) q^{53} +(-3.03059 + 1.74971i) q^{54} +(34.6841 + 7.91521i) q^{56} +1.98210 q^{57} +(17.8469 + 30.9118i) q^{58} +(-4.21731 - 2.43486i) q^{59} +(-33.6432 + 19.4239i) q^{61} +15.2178i q^{62} +(6.19052 + 20.0668i) q^{63} -24.4798 q^{64} +(0.0452163 + 0.0261056i) q^{66} +(-3.50439 + 6.06978i) q^{67} +(28.9494 - 16.7139i) q^{68} -76.6266i q^{69} -46.8735 q^{71} +(7.62339 + 13.2041i) q^{72} +(-72.3956 - 41.7976i) q^{73} +(-14.2382 + 24.6613i) q^{74} -4.05843i q^{76} +(0.213104 - 0.229686i) q^{77} -26.8301 q^{78} +(-10.2397 - 17.7357i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(22.3256 - 12.8897i) q^{82} +125.683i q^{83} +(41.0877 - 12.6754i) q^{84} +(-25.7674 - 44.6305i) q^{86} +(79.5006 + 45.8997i) q^{87} +(0.113741 - 0.197005i) q^{88} +(40.4455 - 23.3512i) q^{89} +(-35.8223 + 156.972i) q^{91} -156.896 q^{92} +(19.5690 + 33.8945i) q^{93} +(15.8311 + 9.14010i) q^{94} +(41.3663 - 23.8829i) q^{96} +3.11494i q^{97} +(2.46826 + 32.9073i) q^{98} +0.134280 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 $

$2$	0.336732	+	0.583237i	0.168366	+	0.291618i	0.937845	−	0.347053i	$-0.112818\pi$
$2$	0.336732	+	0.583237i	0.168366	+	0.291618i	−0.769480	+	0.638671i	$0.779484\pi$
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$4$	1.77322	−	3.07131i	0.443306	−	0.767828i
$5$		0			0
$5$		0			0
$6$			1.16647i			0.194412i
$7$	6.82455	+	1.55742i	0.974935	+	0.222489i
$7$	6.82455	+	1.55742i	0.974935	+	0.222489i
$8$	5.08226			0.635282
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	0.0223800	−	0.0387632i	0.00203454	−	0.00352393i	−0.865006	−	0.501761i	$-0.832686\pi$
$11$	0.0223800	−	0.0387632i	0.00203454	−	0.00352393i	0.867041	+	0.498237i	$0.166019\pi$
$12$	5.31967	−	3.07131i	0.443306	−	0.255943i
$13$			23.0010i			1.76931i	0.466246	+	0.884655i	$0.345606\pi$
$13$			23.0010i			1.76931i	−0.466246	+	0.884655i	$0.654394\pi$
$14$	1.38970	+	4.50476i	0.0992641	+	0.321768i
$15$		0			0
$16$	−5.38154	−	9.32109i	−0.336346	−	0.582568i
$17$	8.16292	+	4.71286i	0.480172	+	0.277227i	0.720488	−	0.693467i	$-0.243918\pi$
$17$	8.16292	+	4.71286i	0.480172	+	0.277227i	−0.240316	+	0.970695i	$0.577251\pi$
$18$	−1.01020	+	1.74971i	−0.0561220	+	0.0972061i
$19$	0.991050	−	0.572183i	0.0521605	−	0.0301149i	−0.473693	−	0.880690i	$-0.657079\pi$
$19$	0.991050	−	0.572183i	0.0521605	−	0.0301149i	0.525853	+	0.850575i	$0.323746\pi$
$20$		0			0
$21$	8.88806	+	8.24636i	0.423241	+	0.392684i
$22$	0.0301442			0.00137019
$23$	−22.1202	−	38.3133i	−0.961748	−	1.66580i	−0.718110	−	0.695929i	$-0.754993\pi$
$23$	−22.1202	−	38.3133i	−0.961748	−	1.66580i	−0.243637	−	0.969866i	$-0.578341\pi$
$24$	7.62339	+	4.40136i	0.317641	+	0.183390i
$25$		0			0
$26$	−13.4150	+	7.74518i	−0.515963	+	0.297891i
$27$			5.19615i			0.192450i
$28$	16.8848	−	18.1987i	0.603028	−	0.649952i
$29$	53.0004			1.82760			0.913799	−	0.406166i	$-0.133134\pi$
$29$	53.0004			1.82760			0.913799	+	0.406166i	$0.133134\pi$
$30$		0			0
$31$	19.5690	+	11.2982i	0.631258	+	0.364457i	0.781239	−	0.624232i	$-0.214588\pi$
$31$	19.5690	+	11.2982i	0.631258	+	0.364457i	−0.149981	+	0.988689i	$0.547921\pi$
$32$	13.7888	−	23.8829i	0.430899	−	0.746340i
$33$	0.0671399	−	0.0387632i	0.00203454	−	0.00117464i
$34$			6.34788i			0.186702i
$35$		0			0
$36$	10.6393			0.295537
$37$	21.1418	+	36.6186i	0.571400	+	0.989693i	0.996423	+	0.0845106i	$0.0269327\pi$
$37$	21.1418	+	36.6186i	0.571400	+	0.989693i	−0.425023	+	0.905183i	$0.639734\pi$
$38$	0.667436	+	0.385344i	0.0175641	+	0.0101406i
$39$	−19.9195	+	34.5015i	−0.510756	+	0.884655i
$40$		0			0
$41$		−	38.2787i		−	0.933628i	−0.884356	−	0.466814i	$-0.845402\pi$
$41$		−	38.2787i		−	0.933628i	0.884356	−	0.466814i	$-0.154598\pi$
$42$	−1.81669	+	7.96065i	−0.0432545	+	0.189539i
$43$	−76.5222			−1.77959			−0.889793	−	0.456365i	$-0.849151\pi$
$43$	−76.5222			−1.77959			−0.889793	+	0.456365i	$0.849151\pi$
$44$	−0.0793693	−	0.137472i	−0.00180385	−	0.00312436i
$45$		0			0
$46$	14.8971	−	25.8026i	0.323851	−	0.560926i
$47$	23.5070	−	13.5718i	0.500149	−	0.288761i	−0.228626	−	0.973514i	$-0.573423\pi$
$47$	23.5070	−	13.5718i	0.500149	−	0.288761i	0.728775	+	0.684753i	$0.240090\pi$
$48$		−	18.6422i		−	0.388379i
$49$	44.1489	+	21.2574i	0.900998	+	0.433824i
$50$		0			0
$51$	8.16292	+	14.1386i	0.160057	+	0.277227i
$52$	70.6434	+	40.7860i	1.35853	+	0.784345i
$53$	9.49388	−	16.4439i	0.179130	−	0.310262i	−0.762453	−	0.647044i	$-0.776005\pi$
$53$	9.49388	−	16.4439i	0.179130	−	0.310262i	0.941583	+	0.336782i	$0.109338\pi$
$54$	−3.03059	+	1.74971i	−0.0561220	+	0.0324020i
$55$		0			0
$56$	34.6841	+	7.91521i	0.619359	+	0.141343i
$57$	1.98210			0.0347737
$58$	17.8469	+	30.9118i	0.307705	+	0.532961i
$59$	−4.21731	−	2.43486i	−0.0714798	−	0.0412689i	0.463834	−	0.885922i	$-0.346473\pi$
$59$	−4.21731	−	2.43486i	−0.0714798	−	0.0412689i	−0.535314	+	0.844653i	$0.679807\pi$
$60$		0			0
$61$	−33.6432	+	19.4239i	−0.551528	+	0.318425i	−0.749738	−	0.661735i	$-0.769821\pi$
$61$	−33.6432	+	19.4239i	−0.551528	+	0.318425i	0.198210	+	0.980160i	$0.436487\pi$
$62$			15.2178i			0.245449i
$63$	6.19052	+	20.0668i	0.0982623	+	0.318521i
$64$	−24.4798			−0.382497
$65$		0			0
$66$	0.0452163	+	0.0261056i	0.000685095	+	0.000395540i
$67$	−3.50439	+	6.06978i	−0.0523043	+	0.0905938i	−0.890992	−	0.454019i	$-0.849990\pi$
$67$	−3.50439	+	6.06978i	−0.0523043	+	0.0905938i	0.838688	+	0.544612i	$0.183323\pi$
$68$	28.9494	−	16.7139i	0.425726	−	0.245793i
$69$		−	76.6266i		−	1.11053i
$70$		0			0
$71$	−46.8735			−0.660190			−0.330095	−	0.943948i	$-0.607081\pi$
$71$	−46.8735			−0.660190			−0.330095	+	0.943948i	$0.607081\pi$
$72$	7.62339	+	13.2041i	0.105880	+	0.183390i
$73$	−72.3956	−	41.7976i	−0.991720	−	0.572570i	−0.0859319	−	0.996301i	$-0.527387\pi$
$73$	−72.3956	−	41.7976i	−0.991720	−	0.572570i	−0.905788	+	0.423731i	$0.860720\pi$
$74$	−14.2382	+	24.6613i	−0.192408	+	0.333261i
$75$		0			0
$76$		−	4.05843i		−	0.0534004i
$77$	0.213104	−	0.229686i	0.00276758	−	0.00298294i
$78$	−26.8301			−0.343975
$79$	−10.2397	−	17.7357i	−0.129617	−	0.224502i	0.793912	−	0.608033i	$-0.208041\pi$
$79$	−10.2397	−	17.7357i	−0.129617	−	0.224502i	−0.923528	+	0.383531i	$0.874708\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	22.3256	−	12.8897i	0.272263	−	0.157191i
$83$			125.683i			1.51425i	0.653271	+	0.757124i	$0.273396\pi$
$83$			125.683i			1.51425i	−0.653271	+	0.757124i	$0.726604\pi$
$84$	41.0877	−	12.6754i	0.489139	−	0.150897i
$85$		0			0
$86$	−25.7674	−	44.6305i	−0.299621	−	0.518960i
$87$	79.5006	+	45.8997i	0.913799	+	0.527582i
$88$	0.113741	−	0.197005i	0.00129251	−	0.00223869i
$89$	40.4455	−	23.3512i	0.454444	−	0.262373i	−0.255261	−	0.966872i	$-0.582162\pi$
$89$	40.4455	−	23.3512i	0.454444	−	0.262373i	0.709705	+	0.704499i	$0.248828\pi$
$90$		0			0
$91$	−35.8223	+	156.972i	−0.393651	+	1.72496i
$92$	−156.896			−1.70539
$93$	19.5690	+	33.8945i	0.210419	+	0.364457i
$94$	15.8311	+	9.14010i	0.168416	+	0.0972351i
$95$		0			0
$96$	41.3663	−	23.8829i	0.430899	−	0.248780i
$97$			3.11494i			0.0321128i	0.999871	+	0.0160564i	$0.00511112\pi$
$97$			3.11494i			0.0321128i	−0.999871	+	0.0160564i	$0.994889\pi$
$98$	2.46826	+	32.9073i	0.0251863	+	0.335789i
$99$	0.134280			0.00135636
$100$		0			0
$101$	−77.4555	−	44.7189i	−0.766886	−	0.442762i	0.0648768	−	0.997893i	$-0.479335\pi$
$101$	−77.4555	−	44.7189i	−0.766886	−	0.442762i	−0.831763	+	0.555132i	$0.812668\pi$
$102$	−5.49743	+	9.52183i	−0.0538964	+	0.0933512i
$103$	79.1385	−	45.6906i	0.768335	−	0.443598i	−0.0639453	−	0.997953i	$-0.520368\pi$
$103$	79.1385	−	45.6906i	0.768335	−	0.443598i	0.832280	+	0.554355i	$0.187035\pi$
$104$			116.897i			1.12401i
$105$		0			0
$106$	12.7876			0.120637
$107$	−52.5515	−	91.0219i	−0.491136	−	0.850672i	0.508812	−	0.860877i	$-0.330085\pi$
$107$	−52.5515	−	91.0219i	−0.491136	−	0.850672i	−0.999948	+	0.0102057i	$0.996751\pi$
$108$	15.9590	+	9.21394i	0.147769	+	0.0853143i
$109$	−27.8507	+	48.2388i	−0.255511	+	0.442558i	−0.965034	−	0.262124i	$-0.915577\pi$
$109$	−27.8507	+	48.2388i	−0.255511	+	0.442558i	0.709523	+	0.704682i	$0.248910\pi$
$110$		0			0
$111$			73.2373i			0.659795i
$112$	−22.2097	−	71.9936i	−0.198301	−	0.642800i
$113$	5.25425			0.0464978			0.0232489	−	0.999730i	$-0.492599\pi$
$113$	5.25425			0.0464978			0.0232489	+	0.999730i	$0.492599\pi$
$114$	0.667436	+	1.15603i	0.00585470	+	0.0101406i
$115$		0			0
$116$	93.9815	−	162.781i	0.810185	−	1.40328i
$117$	−59.7584	+	34.5015i	−0.510756	+	0.294885i
$118$		−	3.27958i		−	0.0277931i
$119$	48.3683	+	44.8763i	0.406457	+	0.377111i
$120$		0			0
$121$	60.4990	+	104.787i	0.499992	+	0.866011i
$122$	−22.6575	−	13.0813i	−0.185717	−	0.107224i
$123$	33.1504	−	57.4181i	0.269515	−	0.466814i
$124$	69.4005	−	40.0684i	0.559681	−	0.323132i
$125$		0			0
$126$	−9.61916	+	10.3677i	−0.0763425	+	0.0822832i
$127$	5.54989			0.0436999			0.0218500	−	0.999761i	$-0.493044\pi$
$127$	5.54989			0.0436999			0.0218500	+	0.999761i	$0.493044\pi$
$128$	−63.3983	−	109.809i	−0.495299	−	0.857883i
$129$	−114.783	−	66.2701i	−0.889793	−	0.513722i
$130$		0			0
$131$	−144.212	+	83.2606i	−1.10085	+	0.635577i	−0.936445	−	0.350815i	$-0.885904\pi$
$131$	−144.212	+	83.2606i	−1.10085	+	0.635577i	−0.164407	+	0.986393i	$0.552571\pi$
$132$		−	0.274943i		−	0.00208290i
$133$	7.65460	−	2.36141i	0.0575534	−	0.0177550i
$134$	−4.72016			−0.0352251
$135$		0			0
$136$	41.4861	+	23.9520i	0.305045	+	0.176118i
$137$	36.4731	−	63.1733i	0.266227	−	0.461119i	−0.701657	−	0.712515i	$-0.747556\pi$
$137$	36.4731	−	63.1733i	0.266227	−	0.461119i	0.967884	+	0.251395i	$0.0808895\pi$
$138$	44.6914	−	25.8026i	0.323851	−	0.186975i
$139$		−	114.994i		−	0.827292i	−0.910438	−	0.413646i	$-0.864255\pi$
$139$		−	114.994i		−	0.827292i	0.910438	−	0.413646i	$-0.135745\pi$
$140$		0			0
$141$	47.0140			0.333433
$142$	−15.7838	−	27.3383i	−0.111153	−	0.192523i
$143$	0.891594	+	0.514762i	0.00623492	+	0.00359973i
$144$	16.1446	−	27.9633i	0.112115	−	0.194189i
$145$		0			0
$146$		−	56.2983i		−	0.385605i
$147$	47.8139	+	70.1201i	0.325265	+	0.477008i
$148$	149.956			1.01322
$149$	−36.3729	−	62.9997i	−0.244113	−	0.422817i	0.717769	−	0.696282i	$-0.245164\pi$
$149$	−36.3729	−	62.9997i	−0.244113	−	0.422817i	−0.961882	+	0.273465i	$0.911830\pi$
$150$		0			0
$151$	63.5643	−	110.097i	0.420956	−	0.729117i	−0.575078	−	0.818099i	$-0.695028\pi$
$151$	63.5643	−	110.097i	0.420956	−	0.729117i	0.996033	+	0.0889823i	$0.0283615\pi$
$152$	5.03677	−	2.90798i	0.0331366	−	0.0191315i
$153$			28.2772i			0.184818i
$154$	0.205720	+	0.0469471i	0.00133585	+	0.000304851i
$155$		0			0
$156$	70.6434	+	122.358i	0.452842	+	0.784345i
$157$	−130.826	−	75.5327i	−0.833290	−	0.481100i	0.0216880	−	0.999765i	$-0.493096\pi$
$157$	−130.826	−	75.5327i	−0.833290	−	0.481100i	−0.854978	+	0.518665i	$0.826429\pi$
$158$	6.89607	−	11.9443i	0.0436460	−	0.0755971i
$159$	28.4816	−	16.4439i	0.179130	−	0.103421i
$160$		0			0
$161$	−91.2904	−	295.921i	−0.567021	−	1.83802i
$162$	−6.06117			−0.0374146
$163$	−29.9639	−	51.8990i	−0.183828	−	0.318399i	0.759353	−	0.650679i	$-0.225515\pi$
$163$	−29.9639	−	51.8990i	−0.183828	−	0.318399i	−0.943181	+	0.332280i	$0.892182\pi$
$164$	−117.566	−	67.8768i	−0.716866	−	0.413883i
$165$		0			0
$166$	−73.3027	+	42.3213i	−0.441582	+	0.254948i
$167$		−	224.089i		−	1.34185i	−0.741526	−	0.670924i	$-0.765898\pi$
$167$		−	224.089i		−	1.34185i	0.741526	−	0.670924i	$-0.234102\pi$
$168$	45.1714	+	41.9101i	0.268877	+	0.249465i
$169$	−360.047			−2.13046
$170$		0			0
$171$	2.97315	+	1.71655i	0.0173868	+	0.0100383i
$172$	−135.691	+	235.024i	−0.788901	+	1.36642i
$173$	−165.080	+	95.3092i	−0.954221	+	0.550920i	−0.894390	−	0.447288i	$-0.852390\pi$
$173$	−165.080	+	95.3092i	−0.954221	+	0.550920i	−0.0598317	+	0.998208i	$0.519056\pi$
$174$			61.8235i			0.355307i
$175$		0			0
$176$	−0.481754			−0.00273724
$177$	−4.21731	−	7.30459i	−0.0238266	−	0.0412689i
$178$	27.2386	+	15.7262i	0.153026	+	0.0883494i
$179$	−108.931	+	188.674i	−0.608553	+	1.05404i	0.382926	+	0.923779i	$0.374916\pi$
$179$	−108.931	+	188.674i	−0.608553	+	1.05404i	−0.991479	+	0.130265i	$0.958417\pi$
$180$		0			0
$181$		−	39.0804i		−	0.215914i	−0.994156	−	0.107957i	$-0.965569\pi$
$181$		−	39.0804i		−	0.215914i	0.994156	−	0.107957i	$-0.0344309\pi$
$182$	−103.614	+	31.9645i	−0.569308	+	0.175629i
$183$	−67.2865			−0.367686
$184$	−112.421	−	194.718i	−0.610981	−	1.05825i
$185$		0			0
$186$	−13.1790	+	22.8267i	−0.0708549	+	0.122724i
$187$	0.365372	−	0.210947i	0.00195386	−	0.00112806i
$188$		−	96.2632i		−	0.512038i
$189$	−8.09259	+	35.4614i	−0.0428179	+	0.187626i
$190$		0			0
$191$	−94.7586	−	164.127i	−0.496118	−	0.859302i	0.503872	−	0.863778i	$-0.331908\pi$
$191$	−94.7586	−	164.127i	−0.496118	−	0.859302i	−0.999990	+	0.00447651i	$0.998575\pi$
$192$	−36.7197	−	21.2001i	−0.191249	−	0.110417i
$193$	−136.570	+	236.547i	−0.707619	+	1.22563i	0.258119	+	0.966113i	$0.416897\pi$
$193$	−136.570	+	236.547i	−0.707619	+	1.22563i	−0.965738	+	0.259519i	$0.916436\pi$
$194$	−1.81675	+	1.04890i	−0.00936467	+	0.00540669i
$195$		0			0
$196$	143.574	−	97.9010i	0.732520	−	0.499495i
$197$	−198.898			−1.00963			−0.504817	−	0.863226i	$-0.668440\pi$
$197$	−198.898			−1.00963			−0.504817	+	0.863226i	$0.668440\pi$
$198$	0.0452163	+	0.0783168i	0.000228365	+	0.000395540i
$199$	33.2334	+	19.1873i	0.167002	+	0.0964185i	0.581171	−	0.813781i	$-0.302595\pi$
$199$	33.2334	+	19.1873i	0.167002	+	0.0964185i	−0.414170	+	0.910200i	$0.635928\pi$
$200$		0			0
$201$	−10.5132	+	6.06978i	−0.0523043	+	0.0301979i
$202$		−	60.2331i		−	0.298184i
$203$	361.704	+	82.5438i	1.78179	+	0.406620i
$204$	57.8987			0.283817
$205$		0			0
$206$	53.2969	+	30.7710i	0.258723	+	0.149374i
$207$	66.3606	−	114.940i	0.320583	−	0.555265i
$208$	214.395	−	123.781i	1.03074	−	0.595100i
$209$		−	0.0512217i		−	0.000245080i
$210$		0			0
$211$	−127.283			−0.603238			−0.301619	−	0.953429i	$-0.597527\pi$
$211$	−127.283			−0.603238			−0.301619	+	0.953429i	$0.597527\pi$
$212$	−33.6695	−	58.3173i	−0.158819	−	0.275082i
$213$	−70.3102	−	40.5936i	−0.330095	−	0.190580i
$214$	35.3915	−	61.2999i	0.165381	−	0.286448i
$215$		0			0
$216$			26.4082i			0.122260i
$217$	115.954	+	107.582i	0.534349	+	0.495770i
$218$	−37.5129			−0.172077
$219$	−72.3956	−	125.393i	−0.330573	−	0.572570i
$220$		0			0
$221$	−108.401	+	187.756i	−0.490501	+	0.849573i
$222$	−42.7147	+	24.6613i	−0.192408	+	0.111087i
$223$			293.558i			1.31641i	0.752841	+	0.658203i	$0.228683\pi$
$223$			293.558i			1.31641i	−0.752841	+	0.658203i	$0.771317\pi$
$224$	131.298	−	141.515i	0.586151	−	0.631763i
$225$		0			0
$226$	1.76927	+	3.06447i	0.00782864	+	0.0135596i
$227$	−186.611	−	107.740i	−0.822077	−	0.474626i	0.0290554	−	0.999578i	$-0.490750\pi$
$227$	−186.611	−	107.740i	−0.822077	−	0.474626i	−0.851132	+	0.524952i	$0.824083\pi$
$228$	3.51471	−	6.08765i	0.0154154	−	0.0267002i
$229$	124.938	−	72.1332i	0.545582	−	0.314992i	−0.201756	−	0.979436i	$-0.564665\pi$
$229$	124.938	−	72.1332i	0.545582	−	0.314992i	0.747338	+	0.664444i	$0.231332\pi$
$230$		0			0
$231$	0.518570	−	0.159976i	0.00224489	−	0.000692539i
$232$	269.361			1.16104
$233$	−143.216	−	248.058i	−0.614662	−	1.06463i	−0.990444	−	0.137918i	$-0.955959\pi$
$233$	−143.216	−	248.058i	−0.614662	−	1.06463i	0.375781	−	0.926708i	$-0.377374\pi$
$234$	−40.2451	−	23.2355i	−0.171988	−	0.0992971i
$235$		0			0
$236$	−14.9565	+	8.63511i	−0.0633748	+	0.0365895i
$237$		−	35.4714i		−	0.149668i
$238$	−9.88632	+	43.3214i	−0.0415392	+	0.182023i
$239$	−413.420			−1.72979			−0.864895	−	0.501954i	$-0.832615\pi$
$239$	−413.420			−1.72979			−0.864895	+	0.501954i	$0.832615\pi$
$240$		0			0
$241$	256.252	+	147.947i	1.06329	+	0.613890i	0.926340	−	0.376689i	$-0.122937\pi$
$241$	256.252	+	147.947i	1.06329	+	0.613890i	0.136948	+	0.990578i	$0.456271\pi$
$242$	−40.7439	+	70.5705i	−0.168363	+	0.291613i
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$			137.772i			0.564639i
$245$		0			0
$246$	44.6511			0.181509
$247$	13.1608	+	22.7952i	0.0532826	+	0.0922881i
$248$	99.4547	+	57.4202i	0.401027	+	0.231533i
$249$	−108.844	+	188.524i	−0.437126	+	0.757124i
$250$		0			0
$251$			311.712i			1.24188i	0.783858	+	0.620940i	$0.213249\pi$
$251$			311.712i			1.24188i	−0.783858	+	0.620940i	$0.786751\pi$
$252$	72.6087	+	16.5699i	0.288130	+	0.0657537i
$253$	−1.98020			−0.00782686
$254$	1.86882	+	3.23690i	0.00735758	+	0.0127437i
$255$		0			0
$256$	−6.26320	+	10.8482i	−0.0244656	+	0.0423757i
$257$	125.335	−	72.3619i	0.487683	−	0.281564i	−0.235930	−	0.971770i	$-0.575814\pi$
$257$	125.335	−	72.3619i	0.487683	−	0.281564i	0.723613	+	0.690206i	$0.242480\pi$
$258$		−	89.2610i		−	0.345973i
$259$	87.2525	+	282.832i	0.336882	+	1.09202i
$260$		0			0
$261$	79.5006	+	137.699i	0.304600	+	0.527582i
$262$	−97.1213	−	56.0730i	−0.370692	−	0.214019i
$263$	−114.833	+	198.896i	−0.436626	+	0.756258i	−0.997427	−	0.0716928i	$-0.977160\pi$
$263$	−114.833	+	198.896i	−0.436626	+	0.756258i	0.560801	+	0.827950i	$0.310493\pi$
$264$	0.341222	−	0.197005i	0.00129251	−	0.000746230i
$265$		0			0
$266$	3.95481	+	3.66928i	0.0148677	+	0.0137943i
$267$	80.8910			0.302962
$268$	12.4281	+	21.5262i	0.0463736	+	0.0803215i
$269$	367.508	+	212.181i	1.36620	+	0.788776i	0.990440	−	0.137941i	$-0.0440485\pi$
$269$	367.508	+	212.181i	1.36620	+	0.788776i	0.375760	+	0.926717i	$0.377382\pi$
$270$		0			0
$271$	252.710	−	145.902i	0.932509	−	0.538385i	0.0449051	−	0.998991i	$-0.485701\pi$
$271$	252.710	−	145.902i	0.932509	−	0.538385i	0.887604	+	0.460607i	$0.152368\pi$
$272$		−	101.450i		−	0.372977i
$273$	−189.675	+	204.434i	−0.694779	+	0.748844i
$274$	49.1267			0.179294
$275$		0			0
$276$	−235.344	−	135.876i	−0.852697	−	0.492305i
$277$	−101.450	+	175.717i	−0.366247	+	0.634358i	−0.988975	−	0.148080i	$-0.952691\pi$
$277$	−101.450	+	175.717i	−0.366247	+	0.634358i	0.622729	+	0.782438i	$0.286024\pi$
$278$	67.0684	−	38.7220i	0.241253	−	0.139288i
$279$			67.7890i			0.242971i
$280$		0			0
$281$	254.325			0.905071			0.452536	−	0.891746i	$-0.350520\pi$
$281$	254.325			0.905071			0.452536	+	0.891746i	$0.350520\pi$
$282$	15.8311	+	27.4203i	0.0561387	+	0.0972351i
$283$	−384.259	−	221.852i	−1.35781	−	0.783930i	−0.368478	−	0.929636i	$-0.620121\pi$
$283$	−384.259	−	221.852i	−1.35781	−	0.783930i	−0.989328	+	0.145706i	$0.953454\pi$
$284$	−83.1172	+	143.963i	−0.292666	+	0.506912i
$285$		0			0
$286$			0.693347i			0.00242429i
$287$	59.6161	−	261.235i	0.207722	−	0.910227i
$288$	82.7327			0.287266
$289$	−100.078	−	173.340i	−0.346290	−	0.599792i
$290$		0			0
$291$	−2.69761	+	4.67241i	−0.00927015	+	0.0160564i
$292$	−256.747	+	148.233i	−0.879270	+	0.507647i
$293$		−	223.513i		−	0.762845i	−0.924401	−	0.381422i	$-0.875434\pi$
$293$		−	223.513i		−	0.762845i	0.924401	−	0.381422i	$-0.124566\pi$
$294$	−24.7962	+	51.4985i	−0.0843406	+	0.175165i
$295$		0			0
$296$	107.448	+	186.105i	0.363000	+	0.628734i
$297$	0.201420	+	0.116290i	0.000678180	+	0.000391548i
$298$	24.4958	−	42.4280i	0.0822007	−	0.142376i
$299$	881.245	−	508.787i	2.94731	−	1.70163i
$300$		0			0
$301$	−522.229	−	119.177i	−1.73498	−	0.395937i
$302$	85.6165			0.283498
$303$	−77.4555	−	134.157i	−0.255629	−	0.442762i
$304$	−10.6667	−	6.15845i	−0.0350880	−	0.0202580i
$305$		0			0
$306$	−16.4923	+	9.52183i	−0.0538964	+	0.0311171i
$307$		−	47.3887i		−	0.154361i	−0.997017	−	0.0771803i	$-0.975408\pi$
$307$		−	47.3887i		−	0.154361i	0.997017	−	0.0771803i	$-0.0245917\pi$
$308$	−0.327559	−	1.06179i	−0.00106350	−	0.00344738i
$309$	158.277			0.512223
$310$		0			0
$311$	−313.595	−	181.054i	−1.00834	−	0.582167i	−0.0976367	−	0.995222i	$-0.531128\pi$
$311$	−313.595	−	181.054i	−1.00834	−	0.582167i	−0.910706	+	0.413055i	$0.864462\pi$
$312$	−101.236	+	175.346i	−0.324474	+	0.562005i
$313$	340.880	−	196.807i	1.08907	−	0.628777i	0.155744	−	0.987797i	$-0.450222\pi$
$313$	340.880	−	196.807i	1.08907	−	0.628777i	0.933330	+	0.359020i	$0.116889\pi$
$314$		−	101.737i		−	0.324003i
$315$		0			0
$316$	−72.6291			−0.229839
$317$	288.788	+	500.196i	0.911004	+	1.57791i	0.812648	+	0.582754i	$0.198025\pi$
$317$	288.788	+	500.196i	0.911004	+	1.57791i	0.0983557	+	0.995151i	$0.468642\pi$
$318$	19.1813	+	11.0744i	0.0603187	+	0.0348250i
$319$	1.18615	−	2.05446i	0.00371833	−	0.00644033i
$320$		0			0
$321$		−	182.044i		−	0.567114i
$322$	141.852	−	152.890i	0.440533	−	0.474814i
$323$	10.7865			0.0333947
$324$	15.9590	+	27.6418i	0.0492562	+	0.0853143i
$325$		0			0
$326$	20.1796	−	34.9521i	0.0619006	−	0.107215i
$327$	−83.5521	+	48.2388i	−0.255511	+	0.147519i
$328$		−	194.542i		−	0.593117i
$329$	181.562	−	56.0109i	0.551859	−	0.170246i
$330$		0			0
$331$	91.7974	+	158.998i	0.277333	+	0.480356i	0.970721	−	0.240209i	$-0.0772160\pi$
$331$	91.7974	+	158.998i	0.277333	+	0.480356i	−0.693388	+	0.720565i	$0.743883\pi$
$332$	386.011	+	222.863i	1.16268	+	0.671275i
$333$	−63.4254	+	109.856i	−0.190467	+	0.329898i
$334$	130.697	−	75.4578i	0.391307	−	0.225921i
$335$		0			0
$336$	29.0337	−	127.224i	0.0864099	−	0.378644i
$337$	205.885			0.610934			0.305467	−	0.952203i	$-0.401187\pi$
$337$	205.885			0.610934			0.305467	+	0.952203i	$0.401187\pi$
$338$	−121.239	−	209.993i	−0.358696	−	0.621280i
$339$	7.88138	+	4.55032i	0.0232489	+	0.0134228i
$340$		0			0
$341$	0.875907	−	0.505705i	0.00256864	−	0.00148301i
$342$			2.31207i			0.00676043i
$343$	268.190	+	213.830i	0.781894	+	0.623412i
$344$	−388.905			−1.13054
$345$		0			0
$346$	−111.176	−	64.1872i	−0.321317	−	0.185512i
$347$	99.7256	−	172.730i	0.287394	−	0.497780i	−0.685793	−	0.727796i	$-0.740545\pi$
$347$	99.7256	−	172.730i	0.287394	−	0.497780i	0.973187	+	0.230016i	$0.0738779\pi$
$348$	281.944	−	162.781i	0.810185	−	0.467761i
$349$			391.231i			1.12101i	0.828152	+	0.560503i	$0.189392\pi$
$349$			391.231i			1.12101i	−0.828152	+	0.560503i	$0.810608\pi$
$350$		0			0
$351$	−119.517			−0.340504
$352$	−0.617185	−	1.06900i	−0.00175337	−	0.00303692i
$353$	81.1020	+	46.8243i	0.229751	+	0.132647i	0.610457	−	0.792049i	$-0.290986\pi$
$353$	81.1020	+	46.8243i	0.229751	+	0.132647i	−0.380706	+	0.924696i	$0.624319\pi$
$354$	2.84020	−	4.91937i	0.00802317	−	0.0138965i
$355$		0			0
$356$		−	165.628i		−	0.465246i
$357$	33.6885	+	109.203i	0.0943656	+	0.305890i
$358$	−146.722			−0.409838
$359$	−73.8759	−	127.957i	−0.205782	−	0.356426i	0.744599	−	0.667512i	$-0.232641\pi$
$359$	−73.8759	−	127.957i	−0.205782	−	0.356426i	−0.950382	+	0.311086i	$0.899307\pi$
$360$		0			0
$361$	−179.845	+	311.501i	−0.498186	+	0.862884i
$362$	22.7931	−	13.1596i	0.0629644	−	0.0363525i
$363$			209.575i			0.577341i
$364$	418.588	+	388.367i	1.14997	+	1.06694i
$365$		0			0
$366$	−22.6575	−	39.2439i	−0.0619057	−	0.107224i
$367$	71.5485	+	41.3085i	0.194955	+	0.112557i	0.594300	−	0.804243i	$-0.297429\pi$
$367$	71.5485	+	41.3085i	0.194955	+	0.112557i	−0.399345	+	0.916801i	$0.630762\pi$
$368$	−238.081	+	412.369i	−0.646960	+	1.12057i
$369$	99.4511	−	57.4181i	0.269515	−	0.155605i
$370$		0			0
$371$	90.4014	−	97.4361i	0.243670	−	0.262631i
$372$	138.801			0.373121
$373$	−171.325	−	296.744i	−0.459318	−	0.795561i	0.539607	−	0.841917i	$-0.318573\pi$
$373$	−171.325	−	296.744i	−0.459318	−	0.795561i	−0.998925	+	0.0463554i	$0.985239\pi$
$374$	0.246064	+	0.142065i	0.000657926	+	0.000379854i
$375$		0			0
$376$	119.469	−	68.9752i	0.317736	−	0.183445i
$377$			1219.06i			3.23359i
$378$	−23.4074	+	7.22108i	−0.0619244	+	0.0191034i
$379$	355.679			0.938467			0.469233	−	0.883074i	$-0.344530\pi$
$379$	355.679			0.938467			0.469233	+	0.883074i	$0.344530\pi$
$380$		0			0
$381$	8.32483	+	4.80635i	0.0218500	+	0.0126151i
$382$	63.8164	−	110.533i	0.167059	−	0.289354i
$383$	144.616	−	83.4939i	0.377586	−	0.218000i	−0.299181	−	0.954196i	$-0.596714\pi$
$383$	144.616	−	83.4939i	0.377586	−	0.218000i	0.676768	+	0.736197i	$0.263380\pi$
$384$		−	219.618i		−	0.571922i
$385$		0			0
$386$	−183.950			−0.476556
$387$	−114.783	−	198.810i	−0.296598	−	0.513722i
$388$	9.56695	+	5.52348i	0.0246571	+	0.0142358i
$389$	−79.6452	+	137.950i	−0.204744	+	0.354626i	−0.950051	−	0.312095i	$-0.898969\pi$
$389$	−79.6452	+	137.950i	−0.204744	+	0.354626i	0.745307	+	0.666721i	$0.232303\pi$
$390$		0			0
$391$		−	416.998i		−	1.06649i
$392$	224.376	+	108.035i	0.572388	+	0.275601i
$393$	−288.423			−0.733901
$394$	−66.9753	−	116.005i	−0.169988	−	0.294428i
$395$		0			0
$396$	0.238108	−	0.412415i	0.000601283	−	0.00104145i
$397$	510.352	−	294.652i	1.28552	−	0.742196i	0.307669	−	0.951494i	$-0.400451\pi$
$397$	510.352	−	294.652i	1.28552	−	0.742196i	0.977852	+	0.209298i	$0.0671178\pi$
$398$			25.8439i			0.0649344i
$399$	13.5269	+	3.08696i	0.0339021	+	0.00773675i
$400$		0			0
$401$	83.1535	+	144.026i	0.207365	+	0.359167i	0.950884	−	0.309548i	$-0.100178\pi$
$401$	83.1535	+	144.026i	0.207365	+	0.359167i	−0.743518	+	0.668716i	$0.766844\pi$
$402$	−7.08024	−	4.08778i	−0.0176125	−	0.0101686i
$403$	−259.870	+	450.107i	−0.644838	+	1.11689i
$404$	−274.692	+	158.593i	−0.679930	+	0.392558i
$405$		0			0
$406$	73.6545	+	238.754i	0.181415	+	0.588064i
$407$	1.89261			0.00465014
$408$	41.4861	+	71.8560i	0.101682	+	0.176118i
$409$	−189.742	−	109.548i	−0.463917	−	0.267843i	0.249773	−	0.968304i	$-0.419644\pi$
$409$	−189.742	−	109.548i	−0.463917	−	0.267843i	−0.713690	+	0.700462i	$0.752977\pi$
$410$		0			0
$411$	109.419	−	63.1733i	0.266227	−	0.153706i
$412$		−	324.079i		−	0.786599i
$413$	−24.9891	−	23.1850i	−0.0605063	−	0.0561379i
$414$	89.3829			0.215901
$415$		0			0
$416$	549.331	+	317.156i	1.32051	+	0.762395i
$417$	99.5873	−	172.490i	0.238819	−	0.413646i
$418$	0.0298744	−	0.0172480i	7.14698e−5	−	4.12631e-5i
$419$			554.704i			1.32388i	0.749558	+	0.661938i	$0.230266\pi$
$419$			554.704i			1.32388i	−0.749558	+	0.661938i	$0.769734\pi$
$420$		0			0
$421$	642.342			1.52575			0.762876	−	0.646545i	$-0.223787\pi$
$421$	642.342			1.52575			0.762876	+	0.646545i	$0.223787\pi$
$422$	−42.8603	−	74.2362i	−0.101565	−	0.175915i
$423$	70.5210	+	40.7153i	0.166716	+	0.0962537i
$424$	48.2503	−	83.5720i	0.113798	−	0.197104i
$425$		0			0
$426$		−	54.6767i		−	0.128349i
$427$	−259.851	+	80.1629i	−0.608550	+	0.187735i
$428$	−372.742			−0.870893
$429$	0.891594	+	1.54429i	0.00207831	+	0.00359973i
$430$		0			0
$431$	−37.6661	+	65.2395i	−0.0873923	+	0.151368i	−0.906408	−	0.422403i	$-0.861187\pi$
$431$	−37.6661	+	65.2395i	−0.0873923	+	0.151368i	0.819016	+	0.573771i	$0.194520\pi$
$432$	48.4338	−	27.9633i	0.112115	−	0.0647298i
$433$		−	353.064i		−	0.815391i	−0.913118	−	0.407695i	$-0.866333\pi$
$433$		−	353.064i		−	0.815391i	0.913118	−	0.407695i	$-0.133667\pi$
$434$	−23.7005	+	103.855i	−0.0546095	+	0.239297i
$435$		0			0
$436$	98.7710	+	171.076i	0.226539	+	0.392377i
$437$	−43.8444	−	25.3136i	−0.100331	−	0.0579259i
$438$	48.7558	−	84.4475i	0.111315	−	0.192802i
$439$	−235.512	+	135.973i	−0.536473	+	0.309733i	−0.743648	−	0.668571i	$-0.766906\pi$
$439$	−235.512	+	135.973i	−0.536473	+	0.309733i	0.207175	+	0.978304i	$0.433573\pi$
$440$		0			0
$441$	10.9951	+	146.588i	0.0249321	+	0.332400i
$442$	−146.008			−0.330335
$443$	−55.1204	−	95.4714i	−0.124425	−	0.215511i	0.797083	−	0.603870i	$-0.206375\pi$
$443$	−55.1204	−	95.4714i	−0.124425	−	0.215511i	−0.921508	+	0.388359i	$0.873042\pi$
$444$	224.935	+	129.866i	0.506610	+	0.292491i
$445$		0			0
$446$	−171.214	+	98.8504i	−0.383888	+	0.221638i
$447$		−	125.999i		−	0.281878i
$448$	−167.064	−	38.1253i	−0.372910	−	0.0851012i
$449$	59.1007			0.131627			0.0658137	−	0.997832i	$-0.479036\pi$
$449$	59.1007			0.131627			0.0658137	+	0.997832i	$0.479036\pi$
$450$		0			0
$451$	−1.48381	−	0.856677i	−0.00329004	−	0.00189950i
$452$	9.31696	−	16.1375i	0.0206127	−	0.0357023i
$453$	190.693	−	110.097i	0.420956	−	0.243039i
$454$		−	145.118i		−	0.319643i
$455$		0			0
$456$	10.0735			0.0220911
$457$	−102.638	−	177.775i	−0.224592	−	0.389004i	0.731605	−	0.681729i	$-0.238772\pi$
$457$	−102.638	−	177.775i	−0.224592	−	0.389004i	−0.956197	+	0.292724i	$0.905438\pi$
$458$	84.1414	+	48.5791i	0.183715	+	0.106068i
$459$	−24.4888	+	42.4158i	−0.0533524	+	0.0924091i
$460$		0			0
$461$			466.172i			1.01122i	0.862762	+	0.505610i	$0.168732\pi$
$461$			466.172i			1.01122i	−0.862762	+	0.505610i	$0.831268\pi$
$462$	0.267923	+	0.248580i	0.000579920	+	0.000538051i
$463$	−191.705			−0.414051			−0.207025	−	0.978336i	$-0.566378\pi$
$463$	−191.705			−0.414051			−0.207025	+	0.978336i	$0.566378\pi$
$464$	−285.223	−	494.021i	−0.614706	−	1.06470i
$465$		0			0
$466$	96.4510	−	167.058i	0.206976	−	0.358493i
$467$	730.261	−	421.617i	1.56373	−	0.902819i	0.566855	−	0.823818i	$-0.308160\pi$
$467$	730.261	−	421.617i	1.56373	−	0.902819i	0.996874	−	0.0790015i	$-0.0251732\pi$
$468$			244.716i			0.522897i
$469$	−33.3691	+	35.9657i	−0.0711494	+	0.0766859i
$470$		0			0
$471$	−130.826	−	226.598i	−0.277763	−	0.481100i
$472$	−21.4334	−	12.3746i	−0.0454098	−	0.0262174i
$473$	−1.71256	+	2.96625i	−0.00362064	+	0.00627113i
$474$	20.6882	−	11.9443i	0.0436460	−	0.0251990i
$475$		0			0
$476$	223.597	−	68.9786i	0.469741	−	0.144913i
$477$	56.9633			0.119420
$478$	−139.212	−	241.121i	−0.291237	−	0.504438i
$479$	−246.540	−	142.340i	−0.514698	−	0.297161i	0.220065	−	0.975485i	$-0.429373\pi$
$479$	−246.540	−	142.340i	−0.514698	−	0.297161i	−0.734763	+	0.678324i	$0.762707\pi$
$480$		0			0
$481$	−842.267	+	486.283i	−1.75107	+	1.01098i
$482$			199.274i			0.413432i
$483$	119.340	−	522.942i	0.247080	−	1.08270i
$484$	429.113			0.886597
$485$		0			0
$486$	−9.09176	−	5.24913i	−0.0187073	−	0.0108007i
$487$	−97.8228	+	169.434i	−0.200868	+	0.347914i	−0.948808	−	0.315852i	$-0.897710\pi$
$487$	−97.8228	+	169.434i	−0.200868	+	0.347914i	0.747940	+	0.663766i	$0.231043\pi$
$488$	−170.984	+	98.7174i	−0.350376	+	0.202290i
$489$		−	103.798i		−	0.212266i
$490$		0			0
$491$	745.464			1.51826			0.759128	−	0.650941i	$-0.225625\pi$
$491$	745.464			1.51826			0.759128	+	0.650941i	$0.225625\pi$
$492$	−117.566	−	203.630i	−0.238955	−	0.413883i
$493$	432.638	+	249.784i	0.877562	+	0.506660i
$494$	−8.86332	+	15.3517i	−0.0179419	+	0.0310763i
$495$		0			0
$496$		−	243.206i		−	0.490335i
$497$	−319.890	−	73.0017i	−0.643642	−	0.146885i
$498$	−146.605			−0.294388
$499$	−45.9747	−	79.6306i	−0.0921337	−	0.159580i	0.816275	−	0.577663i	$-0.196035\pi$
$499$	−45.9747	−	79.6306i	−0.0921337	−	0.159580i	−0.908409	+	0.418083i	$0.862702\pi$
$500$		0			0
$501$	194.066	−	336.133i	0.387358	−	0.670924i
$502$	−181.802	+	104.963i	−0.362155	+	0.209090i
$503$			672.220i			1.33642i	0.743972	+	0.668211i	$0.232940\pi$
$503$			672.220i			1.33642i	−0.743972	+	0.668211i	$0.767060\pi$
$504$	31.4618	+	101.985i	0.0624243	+	0.202351i
$505$		0			0
$506$	−0.666795	−	1.15492i	−0.00131778	−	0.00228246i
$507$	−540.071	−	311.810i	−1.06523	−	0.615010i
$508$	9.84119	−	17.0454i	0.0193724	−	0.0335540i
$509$	282.238	−	162.950i	0.554495	−	0.320138i	−0.196438	−	0.980516i	$-0.562937\pi$
$509$	282.238	−	162.950i	0.554495	−	0.320138i	0.750933	+	0.660378i	$0.229604\pi$
$510$		0			0
$511$	−428.970	−	398.000i	−0.839473	−	0.778865i
$512$	−515.622			−1.00707
$513$	2.97315	+	5.14965i	0.00579561	+	0.0100383i
$514$	84.4082	+	48.7331i	0.164218	+	0.0948115i
$515$		0			0
$516$	−407.073	+	235.024i	−0.788901	+	0.455472i
$517$		−	1.21494i		−	0.00234999i
$518$	−135.577	+	146.127i	−0.261733	+	0.282099i
$519$	−330.161			−0.636148
$520$		0			0
$521$	515.449	+	297.595i	0.989346	+	0.571199i	0.905079	−	0.425244i	$-0.139812\pi$
$521$	515.449	+	297.595i	0.989346	+	0.571199i	0.0842672	+	0.996443i	$0.473145\pi$
$522$	−53.5407	+	92.7353i	−0.102568	+	0.177654i
$523$	43.6490	−	25.2007i	0.0834588	−	0.0481850i	−0.457690	−	0.889112i	$-0.651323\pi$
$523$	43.6490	−	25.2007i	0.0834588	−	0.0481850i	0.541149	+	0.840927i	$0.317990\pi$
$524$			590.559i			1.12702i
$525$		0			0
$526$	−154.671			−0.294051
$527$	106.494	+	184.452i	0.202075	+	0.350004i
$528$	−0.722631	−	0.417211i	−0.00136862	−	0.000790173i
$529$	−714.106	+	1236.87i	−1.34992	+	2.33812i
$530$		0			0
$531$		−	14.6092i		−	0.0275126i
$532$	6.32068	−	27.6970i	0.0118810	−	0.0520620i
$533$	880.451			1.65188
$534$	27.2386	+	47.1786i	0.0510085	+	0.0883494i
$535$		0			0
$536$	−17.8102	+	30.8482i	−0.0332280	+	0.0575526i
$537$	−326.793	+	188.674i	−0.608553	+	0.351348i
$538$			285.792i			0.531212i
$539$	1.81205	−	1.23561i	0.00336188	−	0.00229242i
$540$		0			0
$541$	−468.381	−	811.260i	−0.865769	−	1.49956i	−0.866282	−	0.499556i	$-0.833497\pi$
$541$	−468.381	−	811.260i	−0.865769	−	1.49956i	0.000512769	−	1.00000i	$-0.499837\pi$
$542$	170.191	+	98.2598i	0.314006	+	0.181291i
$543$	33.8446	−	58.6206i	0.0623290	−	0.107957i
$544$	225.113	−	129.969i	0.413812	−	0.238914i
$545$		0			0
$546$	−183.103	−	41.7857i	−0.335354	−	0.0765306i
$547$	3.89041			0.00711227			0.00355613	−	0.999994i	$-0.498868\pi$
$547$	3.89041			0.00711227			0.00355613	+	0.999994i	$0.498868\pi$
$548$	−129.350	−	224.041i	−0.236040	−	0.408834i
$549$	−100.930	−	58.2718i	−0.183843	−	0.106142i
$550$		0			0
$551$	52.5260	−	30.3259i	0.0953285	−	0.0550379i
$552$		−	389.436i		−	0.705500i
$553$	−42.2594	−	136.986i	−0.0764185	−	0.247714i
$554$	−136.646			−0.246654
$555$		0			0
$556$	−353.181	−	203.909i	−0.635218	−	0.366743i
$557$	193.381	−	334.945i	0.347183	−	0.601338i	−0.638565	−	0.769568i	$-0.720472\pi$
$557$	193.381	−	334.945i	0.347183	−	0.601338i	0.985748	+	0.168230i	$0.0538051\pi$
$558$	−39.5370	+	22.8267i	−0.0708549	+	0.0409081i
$559$		−	1760.09i		−	3.14864i
$560$		0			0
$561$	0.730743			0.00130257
$562$	85.6393	+	148.332i	0.152383	+	0.263935i
$563$	105.001	+	60.6226i	0.186503	+	0.107678i	0.590345	−	0.807151i	$-0.298992\pi$
$563$	105.001	+	60.6226i	0.186503	+	0.107678i	−0.403841	+	0.914829i	$0.632325\pi$
$564$	83.3663	−	144.395i	0.147813	−	0.256019i
$565$		0			0
$566$		−	298.819i		−	0.527948i
$567$	−42.8493	+	46.1837i	−0.0755720	+	0.0814527i
$568$	−238.223			−0.419407
$569$	−204.955	−	354.993i	−0.360202	−	0.623889i	0.627792	−	0.778381i	$-0.283959\pi$
$569$	−204.955	−	354.993i	−0.360202	−	0.623889i	−0.987994	+	0.154493i	$0.950626\pi$
$570$		0			0
$571$	287.861	−	498.591i	0.504136	−	0.873188i	−0.495853	−	0.868406i	$-0.665145\pi$
$571$	287.861	−	498.591i	0.504136	−	0.873188i	0.999989	−	0.00478199i	$-0.00152216\pi$
$572$	3.16199	−	1.82558i	0.00552796	−	0.00319157i
$573$		−	328.253i		−	0.572868i
$574$	172.436	−	53.1959i	0.300412	−	0.0926758i
$575$		0			0
$576$	−36.7197	−	63.6004i	−0.0637495	−	0.110417i
$577$	202.254	+	116.772i	0.350527	+	0.202377i	0.664917	−	0.746917i	$-0.268467\pi$
$577$	202.254	+	116.772i	0.350527	+	0.202377i	−0.314390	+	0.949294i	$0.601800\pi$
$578$	67.3988	−	116.738i	0.116607	−	0.201969i
$579$	−409.711	+	236.547i	−0.707619	+	0.408544i
$580$		0			0
$581$	−195.741	+	857.727i	−0.336903	+	1.47629i
$582$	−3.63349			−0.00624311
$583$	−0.424945	−	0.736027i	−0.000728894	−	0.00126248i
$584$	−367.933	−	212.426i	−0.630022	−	0.363743i
$585$		0			0
$586$	130.361	−	75.2641i	0.222459	−	0.128437i
$587$			606.882i			1.03387i	0.856024	+	0.516935i	$0.172927\pi$
$587$			606.882i			1.03387i	−0.856024	+	0.516935i	$0.827073\pi$
$588$	300.146	−	22.5128i	0.510452	−	0.0382872i
$589$	25.8585			0.0439024
$590$		0			0
$591$	−298.347	−	172.251i	−0.504817	−	0.291456i
$592$	227.551	−	394.129i	0.384376	−	0.665759i
$593$	701.998	−	405.299i	1.18381	−	0.683472i	0.226915	−	0.973914i	$-0.427136\pi$
$593$	701.998	−	405.299i	1.18381	−	0.683472i	0.956892	+	0.290443i	$0.0938026\pi$
$594$			0.156634i			0.000263693i
$595$		0			0
$596$	−257.989			−0.432867
$597$	33.2334	+	57.5619i	0.0556673	+	0.0964185i
$598$	593.487	+	342.650i	0.992453	+	0.572993i
$599$	511.389	−	885.752i	0.853738	−	1.47872i	−0.0240732	−	0.999710i	$-0.507663\pi$
$599$	511.389	−	885.752i	0.853738	−	1.47872i	0.877811	−	0.479007i	$-0.159003\pi$
$600$		0			0
$601$		−	147.884i		−	0.246063i	−0.992403	−	0.123032i	$-0.960738\pi$
$601$		−	147.884i		−	0.246063i	0.992403	−	0.123032i	$-0.0392617\pi$
$602$	−106.343	−	344.714i	−0.176649	−	0.572614i
$603$	−21.0263			−0.0348696
$604$	−225.427	−	390.452i	−0.373224	−	0.646443i
$605$		0			0
$606$	52.1634	−	90.3497i	0.0860783	−	0.149092i
$607$	−815.490	+	470.823i	−1.34348	+	0.775656i	−0.987316	−	0.158769i	$-0.949248\pi$
$607$	−815.490	+	470.823i	−1.34348	+	0.775656i	−0.356160	+	0.934425i	$0.615914\pi$
$608$		−	31.5588i		−	0.0519060i
$609$	471.070	+	437.060i	0.773514	+	0.717669i
$610$		0			0
$611$	312.165	+	540.685i	0.510908	+	0.884919i
$612$	86.8481	+	50.1418i	0.141909	+	0.0819310i
$613$	180.068	−	311.886i	0.293748	−	0.508786i	−0.680945	−	0.732335i	$-0.738431\pi$
$613$	180.068	−	311.886i	0.293748	−	0.508786i	0.974693	+	0.223548i	$0.0717640\pi$
$614$	27.6388	−	15.9573i	0.0450144	−	0.0259891i
$615$		0			0
$616$	1.08305	−	1.16733i	0.00175819	−	0.00189501i
$617$	−769.687			−1.24747			−0.623734	−	0.781637i	$-0.714385\pi$
$617$	−769.687			−1.24747			−0.623734	+	0.781637i	$0.714385\pi$
$618$	53.2969	+	92.3129i	0.0862409	+	0.149374i
$619$	−853.542	−	492.793i	−1.37890	−	0.796111i	−0.386877	−	0.922131i	$-0.626446\pi$
$619$	−853.542	−	492.793i	−1.37890	−	0.796111i	−0.992028	+	0.126020i	$0.959780\pi$
$620$		0			0
$621$	199.082	−	114.940i	0.320583	−	0.185088i
$622$		−	243.866i		−	0.392068i
$623$	312.390	−	96.3709i	0.501428	−	0.154688i
$624$	428.790			0.687163
$625$		0			0
$626$	229.570	+	132.542i	0.366726	+	0.211729i
$627$	0.0443593	−	0.0768326i	7.07485e−5	−	0.000122540i
$628$	−463.969	+	267.873i	−0.738804	+	0.426549i
$629$			398.554i			0.633630i
$630$		0			0
$631$	−89.7688			−0.142264			−0.0711322	−	0.997467i	$-0.522661\pi$
$631$	−89.7688			−0.142264			−0.0711322	+	0.997467i	$0.522661\pi$
$632$	−52.0408	−	90.1373i	−0.0823431	−	0.142622i
$633$	−190.925	−	110.230i	−0.301619	−	0.174140i
$634$	−194.488	+	336.864i	−0.306764	+	0.531331i
$635$		0			0
$636$		−	116.635i		−	0.183388i
$637$	−488.941	+	1015.47i	−0.767569	+	1.59414i
$638$	1.59765			0.00250416
$639$	−70.3102	−	121.781i	−0.110032	−	0.190580i
$640$		0			0
$641$	214.166	−	370.947i	0.334113	−	0.578701i	−0.649201	−	0.760617i	$-0.724897\pi$
$641$	214.166	−	370.947i	0.334113	−	0.578701i	0.983314	+	0.181916i	$0.0582300\pi$
$642$	106.175	−	61.2999i	0.165381	−	0.0954827i
$643$			111.498i			0.173403i	0.996234	+	0.0867015i	$0.0276326\pi$
$643$			111.498i			0.173403i	−0.996234	+	0.0867015i	$0.972367\pi$
$644$	−1070.75	−	244.353i	−1.66265	−	0.379431i
$645$		0			0
$646$	3.63215	+	6.29107i	0.00562253	+	0.00973850i
$647$	250.033	+	144.357i	0.386450	+	0.223117i	0.680621	−	0.732636i	$-0.261710\pi$
$647$	250.033	+	144.357i	0.386450	+	0.223117i	−0.294171	+	0.955753i	$0.595043\pi$
$648$	−22.8702	+	39.6123i	−0.0352934	+	0.0611300i
$649$	−0.188766	+	0.108984i	−0.000290857	+	0.000167926i
$650$		0			0
$651$	80.7616	+	261.792i	0.124058	+	0.402138i
$652$	−212.531			−0.325967
$653$	426.848	+	739.322i	0.653672	+	1.13219i	0.982225	+	0.187707i	$0.0601056\pi$
$653$	426.848	+	739.322i	0.653672	+	1.13219i	−0.328553	+	0.944485i	$0.606561\pi$
$654$	−56.2693	−	32.4871i	−0.0860387	−	0.0496744i
$655$		0			0
$656$	−356.800	+	205.998i	−0.543902	+	0.314022i
$657$		−	250.786i		−	0.381713i
$658$	93.8052	+	87.0327i	0.142561	+	0.132269i
$659$	−288.693			−0.438077			−0.219039	−	0.975716i	$-0.570292\pi$
$659$	−288.693			−0.438077			−0.219039	+	0.975716i	$0.570292\pi$
$660$		0			0
$661$	182.367	+	105.289i	0.275895	+	0.159288i	0.631564	−	0.775324i	$-0.282413\pi$
$661$	182.367	+	105.289i	0.275895	+	0.159288i	−0.355668	+	0.934612i	$0.615747\pi$
$662$	−61.8222	+	107.079i	−0.0933870	+	0.161751i
$663$	−325.202	+	187.756i	−0.490501	+	0.283191i
$664$			638.751i			0.961974i
$665$		0			0
$666$	−85.4293			−0.128272
$667$	−1172.38	−	2030.62i	−1.75769	−	3.04441i
$668$	−688.246	−	397.359i	−1.03031	−	0.594849i
$669$	−254.229	+	440.338i	−0.380013	+	0.658203i
$670$		0			0
$671$			1.73883i			0.00259140i
$672$	319.502	−	98.5650i	0.475450	−	0.146674i
$673$	−760.139			−1.12948			−0.564739	−	0.825269i	$-0.691023\pi$
$673$	−760.139			−1.12948			−0.564739	+	0.825269i	$0.691023\pi$
$674$	69.3279	+	120.080i	0.102860	+	0.178160i
$675$		0			0
$676$	−638.444	+	1105.82i	−0.944444	+	1.63583i
$677$	−163.263	+	94.2600i	−0.241157	+	0.139232i	−0.615708	−	0.787974i	$-0.711130\pi$
$677$	−163.263	+	94.2600i	−0.241157	+	0.139232i	0.374552	+	0.927206i	$0.377797\pi$
$678$			6.12894i			0.00903974i
$679$	−4.85126	+	21.2580i	−0.00714472	+	0.0313079i
$680$		0			0
$681$	−186.611	−	323.220i	−0.274026	−	0.474626i
$682$	0.589892	+	0.340574i	0.000864944	+	0.000499375i
$683$	260.243	−	450.754i	0.381029	−	0.659962i	−0.610181	−	0.792262i	$-0.708903\pi$
$683$	260.243	−	450.754i	0.381029	−	0.659962i	0.991210	+	0.132301i	$0.0422364\pi$
$684$	10.5441	−	6.08765i	0.0154154	−	0.00890007i
$685$		0			0
$686$	−34.4057	+	228.421i	−0.0501541	+	0.332976i
$687$	249.877			0.363721
$688$	411.807	+	713.270i	0.598556	+	1.03673i
$689$	378.226	+	218.369i	0.548949	+	0.316936i
$690$		0			0
$691$	590.615	−	340.991i	0.854724	−	0.493475i	−0.00751772	−	0.999972i	$-0.502393\pi$
$691$	590.615	−	340.991i	0.854724	−	0.493475i	0.862242	+	0.506496i	$0.169060\pi$
$692$			676.018i			0.976904i
$693$	0.916398	+	0.209130i	0.00132236	+	0.000301775i
$694$	134.323			0.193549
$695$		0			0
$696$	404.042	+	233.274i	0.580520	+	0.335164i
$697$	180.403	−	312.466i	0.258827	−	0.448302i
$698$	−228.180	+	131.740i	−0.326906	+	0.188739i
$699$		−	496.116i		−	0.709751i
$700$		0			0
$701$	−946.473			−1.35018			−0.675088	−	0.737737i	$-0.735894\pi$
$701$	−946.473			−1.35018			−0.675088	+	0.737737i	$0.735894\pi$
$702$	−40.2451	−	69.7066i	−0.0573292	−	0.0992971i
$703$	41.9051	+	24.1939i	0.0596090	+	0.0344153i
$704$	−0.547857	+	0.948916i	−0.000778206	+	0.00134789i
$705$		0			0
$706$			63.0689i			0.0893327i
$707$	−458.952	−	425.817i	−0.649155	−	0.602287i
$708$	−29.9129			−0.0422499
$709$	504.785	+	874.313i	0.711967	+	1.23316i	0.964118	+	0.265475i	$0.0855289\pi$
$709$	504.785	+	874.313i	0.711967	+	1.23316i	−0.252150	+	0.967688i	$0.581138\pi$
$710$		0			0
$711$	30.7191	−	53.2071i	0.0432055	−	0.0748341i
$712$	205.554	−	118.677i	0.288700	−	0.166681i
$713$		−	999.671i		−	1.40206i
$714$	−52.3470	+	56.4204i	−0.0733151	+	0.0790201i
$715$		0			0
$716$	386.318	+	669.122i	0.539550	+	0.934528i
$717$	−620.129	−	358.032i	−0.864895	−	0.499347i
$718$	49.7527	−	86.1742i	0.0692935	−	0.120020i
$719$	783.382	−	452.286i	1.08954	−	0.629049i	0.156089	−	0.987743i	$-0.450111\pi$
$719$	783.382	−	452.286i	1.08954	−	0.629049i	0.933455	+	0.358694i	$0.116778\pi$
$720$		0			0
$721$	611.244	−	188.566i	0.847773	−	0.261534i
$722$	−242.238			−0.335510
$723$	256.252	+	443.842i	0.354429	+	0.613890i
$724$	−120.028	−	69.2983i	−0.165785	−	0.0957159i
$725$		0			0
$726$	−122.232	+	70.5705i	−0.168363	+	0.0972045i
$727$		−	535.515i		−	0.736609i	−0.929705	−	0.368304i	$-0.879938\pi$
$727$		−	535.515i		−	0.736609i	0.929705	−	0.368304i	$-0.120062\pi$
$728$	−182.058	+	797.770i	−0.250080	+	1.09584i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−624.644	−	360.639i	−0.854507	−	0.493350i
$732$	−119.314	+	206.658i	−0.162997	+	0.282319i
$733$	652.583	−	376.769i	0.890290	−	0.514009i	0.0162527	−	0.999868i	$-0.494826\pi$
$733$	652.583	−	376.769i	0.890290	−	0.514009i	0.874037	+	0.485859i	$0.161493\pi$
$734$			55.6396i			0.0758033i
$735$		0			0
$736$	−1220.04			−1.65767
$737$	0.156856	+	0.271683i	0.000212831	+	0.000368634i
$738$	66.9767	+	38.6690i	0.0907543	+	0.0523970i
$739$	546.157	−	945.972i	0.739049	−	1.28007i	−0.213875	−	0.976861i	$-0.568609\pi$
$739$	546.157	−	945.972i	0.739049	−	1.28007i	0.952924	−	0.303209i	$-0.0980580\pi$
$740$		0			0
$741$			45.5903i			0.0615254i
$742$	87.2693	+	19.9156i	0.117614	+	0.0268404i
$743$	362.303			0.487622			0.243811	−	0.969823i	$-0.421602\pi$
$743$	362.303			0.487622			0.243811	+	0.969823i	$0.421602\pi$
$744$	99.4547	+	172.261i	0.133676	+	0.231533i
$745$		0			0
$746$	115.381	−	199.847i	0.154667	−	0.267891i
$747$	−326.533	+	188.524i	−0.437126	+	0.252375i
$748$		−	1.49623i		−	0.00200030i
$749$	−216.881	−	703.028i	−0.289561	−	0.938622i
$750$		0			0
$751$	336.270	+	582.437i	0.447763	+	0.775548i	0.998240	−	0.0593020i	$-0.0188875\pi$
$751$	336.270	+	582.437i	0.447763	+	0.775548i	−0.550477	+	0.834850i	$0.685554\pi$
$752$	−253.008	−	146.074i	−0.336446	−	0.194247i
$753$	−269.950	+	467.568i	−0.358500	+	0.620940i
$754$	−711.002	+	410.497i	−0.942974	+	0.544426i
$755$		0			0
$756$	94.5630	+	87.7358i	0.125083	+	0.116053i
$757$	368.166			0.486349			0.243174	−	0.969983i	$-0.421811\pi$
$757$	368.166			0.486349			0.243174	+	0.969983i	$0.421811\pi$
$758$	119.768	+	207.445i	0.158006	+	0.273674i
$759$	−2.97029	−	1.71490i	−0.00391343	−	0.00225942i
$760$		0			0
$761$	565.660	−	326.584i	0.743312	−	0.429151i	−0.0799606	−	0.996798i	$-0.525479\pi$
$761$	565.660	−	326.584i	0.743312	−	0.429151i	0.823272	+	0.567647i	$0.192146\pi$
$762$			6.47380i			0.00849580i
$763$	−265.197	+	285.833i	−0.347571	+	0.374617i
$764$	−672.113			−0.879728
$765$		0			0
$766$	97.3933	+	56.2301i	0.127145	+	0.0734074i
$767$	56.0043	−	97.0024i	0.0730174	−	0.126470i
$768$	−18.7896	+	10.8482i	−0.0244656	+	0.0141252i
$769$			1393.19i			1.81170i	0.423602	+	0.905848i	$0.360765\pi$
$769$			1393.19i			1.81170i	−0.423602	+	0.905848i	$0.639235\pi$
$770$		0			0
$771$	250.669			0.325122
$772$	484.340	+	838.901i	0.627383	+	1.08666i
$773$	−1129.82	−	652.302i	−1.46160	−	0.843858i	−0.462519	−	0.886609i	$-0.653054\pi$
$773$	−1129.82	−	652.302i	−1.46160	−	0.843858i	−0.999086	+	0.0427514i	$0.986388\pi$
$774$	77.3023	−	133.892i	0.0998738	−	0.172987i
$775$		0			0
$776$			15.8309i			0.0204007i
$777$	−114.061	+	499.811i	−0.146797	+	0.643258i
$778$	−107.276			−0.137887
$779$	−21.9024	−	37.9362i	−0.0281161	−	0.0486985i
$780$		0			0
$781$	−1.04903	+	1.81697i	−0.00134318	+	0.00232646i
$782$	243.208	−	140.416i	0.311008	−	0.179561i
$783$			275.398i			0.351722i
$784$	−39.4469	−	525.913i	−0.0503149	−	0.670808i
$785$		0			0
$786$	−97.1213	−	168.219i	−0.123564	−	0.214019i
$787$	−182.275	−	105.237i	−0.231607	−	0.133719i	0.379706	−	0.925107i	$-0.376025\pi$
$787$	−182.275	−	105.237i	−0.231607	−	0.133719i	−0.611313	+	0.791389i	$0.709358\pi$
$788$	−352.691	+	610.878i	−0.447577	+	0.775226i
$789$	−344.498	+	198.896i	−0.436626	+	0.252086i
$790$		0			0
$791$	35.8579	+	8.18308i	0.0453323	+	0.0103452i
$792$	0.682444			0.000861672
$793$	−446.770	−	773.829i	−0.563393	−	0.975825i
$794$	343.703	+	198.437i	0.432876	+	0.249921i
$795$		0			0
$796$	117.860	−	68.0467i	0.148066	−	0.0854858i
$797$			254.794i			0.319691i	0.987142	+	0.159845i	$0.0510996\pi$
$797$			254.794i			0.319691i	−0.987142	+	0.159845i	$0.948900\pi$
$798$	2.75452	+	8.92888i	0.00345178	+	0.0111891i
$799$	255.848			0.320210
$800$		0			0
$801$	121.336	+	70.0536i	0.151481	+	0.0874577i
$802$	−56.0009	+	96.9964i	−0.0698265	+	0.120943i
$803$	−3.24042	+	1.87086i	−0.00403539	+	0.00232983i
$804$			43.0523i			0.0535477i
$805$		0			0
$806$	−350.025			−0.434275
$807$	367.508	+	636.542i	0.455400	+	0.788776i
$808$	−393.649	−	227.273i	−0.487189	−	0.281279i
$809$	114.683	−	198.637i	0.141759	−	0.245533i	−0.786400	−	0.617717i	$-0.788058\pi$
$809$	114.683	−	198.637i	0.141759	−	0.245533i	0.928159	+	0.372184i	$0.121391\pi$
$810$		0			0
$811$			1108.59i			1.36694i	0.729978	+	0.683470i	$0.239530\pi$
$811$			1108.59i			1.36694i	−0.729978	+	0.683470i	$0.760470\pi$
$812$	894.899	−	964.536i	1.10209	−	1.18785i
$813$	505.420			0.621673
$814$	0.637302	+	1.10384i	0.000782926	+	0.00135607i
$815$		0			0
$816$	87.8581	−	152.175i	0.107669	−	0.186489i
$817$	−75.8373	+	43.7847i	−0.0928241	+	0.0535920i
$818$		−	147.553i		−	0.180382i
$819$	−461.558	+	142.388i	−0.563562	+	0.173856i
$820$		0			0
$821$	−433.762	−	751.297i	−0.528333	−	0.915100i	−0.999454	−	0.0330318i	$-0.989484\pi$
$821$	−433.762	−	751.297i	−0.528333	−	0.915100i	0.471121	−	0.882069i	$-0.343850\pi$
$822$	73.6900	+	42.5449i	0.0896472	+	0.0517578i
$823$	492.440	−	852.931i	0.598348	−	1.03637i	−0.394718	−	0.918802i	$-0.629158\pi$
$823$	492.440	−	852.931i	0.598348	−	1.03637i	0.993065	−	0.117566i	$-0.0375091\pi$
$824$	402.202	−	232.212i	0.488110	−	0.281810i
$825$		0			0
$826$	5.10769	−	22.3817i	0.00618364	−	0.0270964i
$827$	767.641			0.928224			0.464112	−	0.885777i	$-0.346374\pi$
$827$	767.641			0.928224			0.464112	+	0.885777i	$0.346374\pi$
$828$	−235.344	−	407.628i	−0.284232	−	0.492305i
$829$	−153.578	−	88.6684i	−0.185257	−	0.106958i	0.404503	−	0.914537i	$-0.367444\pi$
$829$	−153.578	−	88.6684i	−0.185257	−	0.106958i	−0.589760	+	0.807578i	$0.700778\pi$
$830$		0			0
$831$	−304.351	+	175.717i	−0.366247	+	0.211453i
$832$		−	563.061i		−	0.676756i
$833$	260.201	+	381.590i	0.312366	+	0.458091i
$834$	134.137			0.160836
$835$		0			0
$836$	−0.157318	−	0.0908275i	−0.000188179	−	0.000108645i
$837$	−58.7070	+	101.684i	−0.0701398	+	0.121486i
$838$	−323.524	+	186.787i	−0.386067	+	0.222896i
$839$			15.9176i			0.0189721i	0.999955	+	0.00948606i	$0.00301955\pi$
$839$			15.9176i			0.0189721i	−0.999955	+	0.00948606i	$0.996980\pi$
$840$		0			0
$841$	1968.04			2.34012
$842$	216.297	+	374.637i	0.256885	+	0.444937i
$843$	381.488	+	220.252i	0.452536	+	0.261272i
$844$	−225.701	+	390.926i	−0.267419	+	0.463183i
$845$		0			0
$846$			54.8406i			0.0648234i
$847$	249.680	+	809.348i	0.294782	+	0.955547i
$848$	−204.367			−0.240998
$849$	−384.259	−	665.556i	−0.452602	−	0.783930i
$850$		0			0
$851$	935.321	−	1620.02i	1.09908	−	1.90367i
$852$	−249.351	+	143.963i	−0.292666	+	0.168971i
$853$			694.629i			0.814336i	0.913353	+	0.407168i	$0.133484\pi$
$853$			694.629i			0.814336i	−0.913353	+	0.407168i	$0.866516\pi$
$854$	−134.254	−	124.561i	−0.157206	−	0.145856i
$855$		0			0
$856$	−267.080	−	462.597i	−0.312010	−	0.540417i
$857$	1301.17	+	751.232i	1.51829	+	0.876583i	0.999769	+	0.0215161i	$0.00684933\pi$
$857$	1301.17	+	751.232i	1.51829	+	0.876583i	0.518518	+	0.855067i	$0.326484\pi$
$858$	−0.600456	+	1.04002i	−0.000699832	+	0.00121214i
$859$	−254.436	+	146.898i	−0.296200	+	0.171011i	−0.640734	−	0.767763i	$-0.721370\pi$
$859$	−254.436	+	146.898i	−0.296200	+	0.171011i	0.344535	+	0.938774i	$0.388037\pi$
$860$		0			0
$861$	315.660	−	340.224i	0.366621	−	0.395149i
$862$	−50.7334			−0.0588555
$863$	−129.059	−	223.537i	−0.149547	−	0.259023i	0.781513	−	0.623889i	$-0.214448\pi$
$863$	−129.059	−	223.537i	−0.149547	−	0.259023i	−0.931060	+	0.364866i	$0.881115\pi$
$864$	124.099	+	71.6486i	0.143633	+	0.0829266i
$865$		0			0
$866$	205.920	−	118.888i	0.237783	−	0.137284i
$867$		−	346.680i		−	0.399861i
$868$	536.030	−	165.363i	0.617546	−	0.190510i
$869$	−0.916657			−0.00105484
$870$		0			0
$871$	−139.611	−	80.6046i	−0.160288	−	0.0925426i
$872$	−141.544	+	245.162i	−0.162322	+	0.281149i
$873$	−8.09284	+	4.67241i	−0.00927015	+	0.00535213i
$874$		−	34.0956i		−	0.0390109i
$875$		0			0
$876$	−513.494			−0.586180
$877$	668.747	+	1158.30i	0.762539	+	1.32076i	0.941538	+	0.336907i	$0.109381\pi$
$877$	668.747	+	1158.30i	0.762539	+	1.32076i	−0.178999	+	0.983849i	$0.557286\pi$
$878$	−158.609	−	91.5727i	−0.180648	−	0.104297i
$879$	193.568	−	335.270i	0.220214	−	0.381422i
$880$		0			0
$881$			606.188i			0.688069i	0.938957	+	0.344034i	$0.111794\pi$
$881$			606.188i			0.688069i	−0.938957	+	0.344034i	$0.888206\pi$
$882$	−81.7932	+	55.7736i	−0.0927361	+	0.0632354i
$883$	862.650			0.976953			0.488477	−	0.872577i	$-0.337553\pi$
$883$	862.650			0.976953			0.488477	+	0.872577i	$0.337553\pi$
$884$	384.437	+	665.865i	0.434884	+	0.753241i
$885$		0			0
$886$	37.1216	−	64.2965i	0.0418980	−	0.0725694i
$887$	799.662	−	461.685i	0.901536	−	0.520502i	0.0238378	−	0.999716i	$-0.492411\pi$
$887$	799.662	−	461.685i	0.901536	−	0.520502i	0.877698	+	0.479214i	$0.159078\pi$
$888$			372.211i			0.419156i
$889$	37.8755	+	8.64351i	0.0426046	+	0.00972273i
$890$		0			0
$891$	0.201420	+	0.348869i	0.000226060	+	0.000391548i
$892$	901.610	+	520.545i	1.01077	+	0.583570i
$893$	15.5311	−	26.9006i	0.0173920	−	0.0301239i
$894$	73.4874	−	42.4280i	0.0822007	−	0.0474586i
$895$		0			0
$896$	−261.646	−	848.134i	−0.292015	−	0.946579i
$897$	1762.49			1.96487
$898$	19.9011	+	34.4697i	0.0221616	+	0.0383850i
$899$	1037.16	+	598.807i	1.15369	+	0.666082i
$900$		0			0
$901$	154.996	−	89.4867i	0.172026	−	0.0993193i
$902$		−	1.15388i		−	0.00127925i
$903$	−680.133	−	631.029i	−0.753193	−	0.698814i
$904$	26.7035			0.0295392
$905$		0			0
$906$	128.425	+	74.1461i	0.141749	+	0.0818389i
$907$	−47.3567	+	82.0242i	−0.0522125	+	0.0904346i	−0.890950	−	0.454101i	$-0.849961\pi$
$907$	−47.3567	+	82.0242i	−0.0522125	+	0.0904346i	0.838738	+	0.544535i	$0.183294\pi$
$908$	−661.807	+	382.095i	−0.728863	+	0.420809i
$909$		−	268.314i		−	0.295174i
$910$		0			0
$911$	−556.948			−0.611359			−0.305679	−	0.952134i	$-0.598884\pi$
$911$	−556.948			−0.611359			−0.305679	+	0.952134i	$0.598884\pi$
$912$	−10.6667	−	18.4753i	−0.0116960	−	0.0202580i
$913$	4.87186	+	2.81277i	0.00533610	+	0.00308080i
$914$	69.1233	−	119.725i	0.0756272	−	0.130990i
$915$		0			0
$916$		−	511.633i		−	0.558551i
$917$	−1113.85	+	343.618i	−1.21467	+	0.374720i
$918$	−32.9846			−0.0359309
$919$	478.581	+	828.926i	0.520762	+	0.901987i	0.999709	+	0.0241428i	$0.00768562\pi$
$919$	478.581	+	828.926i	0.520762	+	0.901987i	−0.478946	+	0.877844i	$0.658981\pi$
$920$		0			0
$921$	41.0398	−	71.0831i	0.0445601	−	0.0771803i
$922$	−271.889	+	156.975i	−0.294890	+	0.170255i
$923$		−	1078.14i		−	1.16808i
$924$	0.428202	−	1.87636i	0.000463422	−	0.00203070i
$925$		0			0
$926$	−64.5533	−	111.810i	−0.0697120	−	0.120745i
$927$	237.416	+	137.072i	0.256112	+	0.147866i
$928$	730.811	−	1265.80i	0.787511	−	1.36401i
$929$	−990.414	+	571.816i	−1.06611	+	0.615517i	−0.927115	−	0.374776i	$-0.877720\pi$
$929$	−990.414	+	571.816i	−1.06611	+	0.615517i	−0.138992	+	0.990294i	$0.544386\pi$
$930$		0			0
$931$	55.9169	−	4.19412i	0.0600611	−	0.00450497i
$932$	−1015.82			−1.08993
$933$	−313.595	−	543.162i	−0.336114	−	0.582167i
$934$	491.804	+	283.943i	0.526557	+	0.304008i
$935$		0			0
$936$	−303.708	+	175.346i	−0.324474	+	0.187335i
$937$		−	578.660i		−	0.617567i	−0.951132	−	0.308783i	$-0.900078\pi$
$937$		−	578.660i		−	0.617567i	0.951132	−	0.308783i	$-0.0999218\pi$
$938$	−32.2129	−	7.35127i	−0.0343422	−	0.00783717i
$939$	681.760			0.726049
$940$		0			0
$941$	−1086.18	−	627.108i	−1.15428	−	0.666427i	−0.204357	−	0.978896i	$-0.565510\pi$
$941$	−1086.18	−	627.108i	−1.15428	−	0.666427i	−0.949928	+	0.312470i	$0.898844\pi$
$942$	88.1069	−	152.606i	0.0935317	−	0.162002i
$943$	−1466.59	+	846.733i	−1.55523	+	0.897915i
$944$			52.4132i			0.0555225i
$945$		0			0
$946$	−2.30670			−0.00243837
$947$	−878.012	−	1520.76i	−0.927151	−	1.60587i	−0.788065	−	0.615592i	$-0.788917\pi$
$947$	−878.012	−	1520.76i	−0.927151	−	1.60587i	−0.139086	−	0.990280i	$-0.544417\pi$
$948$	−108.944	−	62.8987i	−0.114920	−	0.0663488i
$949$	961.388	−	1665.17i	1.01305	−	1.75466i
$950$		0			0
$951$			1000.39i			1.05194i
$952$	245.820	+	228.073i	0.258215	+	0.239572i
$953$	1048.32			1.10002			0.550011	−	0.835157i	$-0.314624\pi$
$953$	1048.32			1.10002			0.550011	+	0.835157i	$0.314624\pi$
$954$	19.1813	+	33.2231i	0.0201062	+	0.0348250i
$955$		0			0
$956$	−733.085	+	1269.74i	−0.766826	+	1.32818i
$957$	3.55844	−	2.05446i	0.00371833	−	0.00214678i
$958$		−	191.722i		−	0.200127i
$959$	347.300	−	374.325i	0.362148	−	0.390329i
$960$		0			0
$961$	−225.203	−	390.062i	−0.234342	−	0.405892i
$962$	−567.236	−	327.494i	−0.589642	−	0.340430i
$963$	157.655	−	273.066i	0.163712	−	0.283557i
$964$	908.785	−	524.688i	0.942723	−	0.544282i
$965$		0			0
$966$	345.184	−	106.488i	0.357334	−	0.110236i
$967$	1770.86			1.83130			0.915648	−	0.401982i	$-0.131679\pi$
$967$	1770.86			1.83130			0.915648	+	0.401982i	$0.131679\pi$
$968$	307.471	+	532.556i	0.317636	+	0.550161i
$969$	16.1797	+	9.34137i	0.0166973	+	0.00964022i
$970$		0			0
$971$	834.000	−	481.510i	0.858908	−	0.495891i	−0.00473848	−	0.999989i	$-0.501508\pi$
$971$	834.000	−	481.510i	0.858908	−	0.495891i	0.863646	+	0.504098i	$0.168175\pi$
$972$			55.2836i			0.0568762i
$973$	179.093	−	784.779i	0.184063	−	0.806556i
$974$	−131.760			−0.135277
$975$		0			0
$976$	362.105	+	209.061i	0.371009	+	0.214202i
$977$	−269.150	+	466.182i	−0.275487	+	0.477157i	−0.970258	−	0.242074i	$-0.922172\pi$
$977$	−269.150	+	466.182i	−0.275487	+	0.477157i	0.694771	+	0.719231i	$0.255506\pi$
$978$	60.5388	−	34.9521i	0.0619006	−	0.0357383i
$979$		−	2.09040i		−	0.00213524i
$980$		0			0
$981$	−167.104			−0.170341
$982$	251.021	+	434.782i	0.255623	+	0.442751i
$983$	586.233	+	338.462i	0.596371	+	0.344315i	0.767613	−	0.640914i	$-0.221444\pi$
$983$	586.233	+	338.462i	0.596371	+	0.344315i	−0.171241	+	0.985229i	$0.554778\pi$
$984$	168.479	−	291.814i	0.171218	−	0.296559i
$985$		0			0
$986$			336.440i			0.341217i
$987$	320.849	+	73.2206i	0.325075	+	0.0741850i
$988$	93.3481			0.0944819
$989$	1692.69	+	2931.82i	1.71151	+	2.96443i
$990$		0			0
$991$	−584.900	+	1013.08i	−0.590212	+	1.02228i	0.403992	+	0.914763i	$0.367622\pi$
$991$	−584.900	+	1013.08i	−0.590212	+	1.02228i	−0.994204	+	0.107514i	$0.965711\pi$
$992$	539.666	−	311.576i	0.544018	−	0.314089i
$993$			317.995i			0.320237i
$994$	−65.1400	−	211.154i	−0.0655332	−	0.212428i
$995$		0			0
$996$	386.011	+	668.590i	0.387561	+	0.671275i
$997$	−523.016	−	301.963i	−0.524590	−	0.302872i	0.214221	−	0.976785i	$-0.431279\pi$
$997$	−523.016	−	301.963i	−0.524590	−	0.302872i	−0.738810	+	0.673913i	$0.764612\pi$
$998$	30.9623	−	53.6283i	0.0310244	−	0.0537358i
$999$	−190.276	+	109.856i	−0.190467	+	0.109966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.o.l.451.3		8
5.2	odd	4		525.3.s.h.199.4		16
5.3	odd	4		525.3.s.h.199.5		16
5.4	even	2		105.3.n.a.31.2	✓	8
7.5	odd	6	inner	525.3.o.l.376.3		8
15.14	odd	2		315.3.w.a.136.3		8
35.4	even	6		735.3.h.a.391.6		8
35.12	even	12		525.3.s.h.124.5		16
35.19	odd	6		105.3.n.a.61.2	yes	8
35.24	odd	6		735.3.h.a.391.5		8
35.33	even	12		525.3.s.h.124.4		16
105.89	even	6		315.3.w.a.271.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.n.a.31.2	✓	8	5.4	even	2
105.3.n.a.61.2	yes	8	35.19	odd	6
315.3.w.a.136.3		8	15.14	odd	2
315.3.w.a.271.3		8	105.89	even	6
525.3.o.l.376.3		8	7.5	odd	6	inner
525.3.o.l.451.3		8	1.1	even	1	trivial
525.3.s.h.124.4		16	35.33	even	12
525.3.s.h.124.5		16	35.12	even	12
525.3.s.h.199.4		16	5.2	odd	4
525.3.s.h.199.5		16	5.3	odd	4
735.3.h.a.391.5		8	35.24	odd	6
735.3.h.a.391.6		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)

\(f(q)\)	\(=\)	\(q+(0.336732 + 0.583237i) q^{2} +(1.50000 + 0.866025i) q^{3} +(1.77322 - 3.07131i) q^{4} +1.16647i q^{6} +(6.82455 + 1.55742i) q^{7} +5.08226 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.336732 + 0.583237i) q^{2} +(1.50000 + 0.866025i) q^{3} +(1.77322 - 3.07131i) q^{4} +1.16647i q^{6} +(6.82455 + 1.55742i) q^{7} +5.08226 q^{8} +(1.50000 + 2.59808i) q^{9} +(0.0223800 - 0.0387632i) q^{11} +(5.31967 - 3.07131i) q^{12} +23.0010i q^{13} +(1.38970 + 4.50476i) q^{14} +(-5.38154 - 9.32109i) q^{16} +(8.16292 + 4.71286i) q^{17} +(-1.01020 + 1.74971i) q^{18} +(0.991050 - 0.572183i) q^{19} +(8.88806 + 8.24636i) q^{21} +0.0301442 q^{22} +(-22.1202 - 38.3133i) q^{23} +(7.62339 + 4.40136i) q^{24} +(-13.4150 + 7.74518i) q^{26} +5.19615i q^{27} +(16.8848 - 18.1987i) q^{28} +53.0004 q^{29} +(19.5690 + 11.2982i) q^{31} +(13.7888 - 23.8829i) q^{32} +(0.0671399 - 0.0387632i) q^{33} +6.34788i q^{34} +10.6393 q^{36} +(21.1418 + 36.6186i) q^{37} +(0.667436 + 0.385344i) q^{38} +(-19.9195 + 34.5015i) q^{39} -38.2787i q^{41} +(-1.81669 + 7.96065i) q^{42} -76.5222 q^{43} +(-0.0793693 - 0.137472i) q^{44} +(14.8971 - 25.8026i) q^{46} +(23.5070 - 13.5718i) q^{47} -18.6422i q^{48} +(44.1489 + 21.2574i) q^{49} +(8.16292 + 14.1386i) q^{51} +(70.6434 + 40.7860i) q^{52} +(9.49388 - 16.4439i) q^{53} +(-3.03059 + 1.74971i) q^{54} +(34.6841 + 7.91521i) q^{56} +1.98210 q^{57} +(17.8469 + 30.9118i) q^{58} +(-4.21731 - 2.43486i) q^{59} +(-33.6432 + 19.4239i) q^{61} +15.2178i q^{62} +(6.19052 + 20.0668i) q^{63} -24.4798 q^{64} +(0.0452163 + 0.0261056i) q^{66} +(-3.50439 + 6.06978i) q^{67} +(28.9494 - 16.7139i) q^{68} -76.6266i q^{69} -46.8735 q^{71} +(7.62339 + 13.2041i) q^{72} +(-72.3956 - 41.7976i) q^{73} +(-14.2382 + 24.6613i) q^{74} -4.05843i q^{76} +(0.213104 - 0.229686i) q^{77} -26.8301 q^{78} +(-10.2397 - 17.7357i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(22.3256 - 12.8897i) q^{82} +125.683i q^{83} +(41.0877 - 12.6754i) q^{84} +(-25.7674 - 44.6305i) q^{86} +(79.5006 + 45.8997i) q^{87} +(0.113741 - 0.197005i) q^{88} +(40.4455 - 23.3512i) q^{89} +(-35.8223 + 156.972i) q^{91} -156.896 q^{92} +(19.5690 + 33.8945i) q^{93} +(15.8311 + 9.14010i) q^{94} +(41.3663 - 23.8829i) q^{96} +3.11494i q^{97} +(2.46826 + 32.9073i) q^{98} +0.134280 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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