LMFDB - Embedded newform 605.2.j.c.269.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(9,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("605.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.j (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.484000000.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + 16x^{4} - 66x^{2} + 121 $ x^8 - x^6 + 16x^4 - 66x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{10}]$

Embedding invariants

Embedding label			269.2
Root			$1.46782 + 0.476925i$ of defining polynomial
Character	$\chi$	$=$	605.269
Dual form			605.2.j.c.9.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.37499 - 0.771681i) q^{2} +(3.42705 - 2.48990i) q^{4} +(0.690983 - 2.12663i) q^{5} +(1.81433 + 2.49721i) q^{7} +(3.28216 - 4.51750i) q^{8} +(0.927051 + 2.85317i) q^{9} +O(q^{10})$	\(q+(2.37499 - 0.771681i) q^{2} +(3.42705 - 2.48990i) q^{4} +(0.690983 - 2.12663i) q^{5} +(1.81433 + 2.49721i) q^{7} +(3.28216 - 4.51750i) q^{8} +(0.927051 + 2.85317i) q^{9} -5.58394i q^{10} +(-1.81433 + 0.589512i) q^{13} +(6.23607 + 4.53077i) q^{14} +(1.69098 - 5.20431i) q^{16} +(-7.68563 - 2.49721i) q^{17} +(4.40347 + 6.06086i) q^{18} +(-2.92705 - 9.00854i) q^{20} +(-4.04508 - 2.93893i) q^{25} +(-3.85410 + 2.80017i) q^{26} +(12.4356 + 4.04057i) q^{28} +(-2.76393 - 8.50651i) q^{31} -2.49721i q^{32} -20.1803 q^{34} +(6.56431 - 2.13287i) q^{35} +(10.2812 + 7.46969i) q^{36} +(-7.33912 - 10.1014i) q^{40} +13.0756i q^{43} +6.70820 q^{45} +(-0.781153 + 2.40414i) q^{49} +(-11.8749 - 3.85840i) q^{50} +(-4.74998 + 6.53779i) q^{52} +17.2361 q^{56} +(3.23607 - 2.35114i) q^{59} +(-13.1286 - 18.0700i) q^{62} +(-5.44299 + 7.49164i) q^{63} +(1.45492 + 4.47777i) q^{64} +4.26575i q^{65} +(-32.5568 + 10.5784i) q^{68} +(13.9443 - 10.1311i) q^{70} +(2.47214 - 7.60845i) q^{71} +(15.9319 + 5.17659i) q^{72} +(6.99262 + 9.62451i) q^{73} +(-9.89919 - 7.19218i) q^{80} +(-7.28115 + 5.29007i) q^{81} +(0.693013 + 0.225173i) q^{83} +(-10.6213 + 14.6189i) q^{85} +(10.0902 + 31.0543i) q^{86} +13.4164 q^{89} +(15.9319 - 5.17659i) q^{90} +(-4.76393 - 3.46120i) q^{91} +6.31261i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 14 q^{4} + 10 q^{5} - 6 q^{9}+O(q^{10}) $ 8 * q + 14 * q^4 + 10 * q^5 - 6 * q^9	$ 8 q + 14 q^{4} + 10 q^{5} - 6 q^{9} + 32 q^{14} + 18 q^{16} - 10 q^{20} - 10 q^{25} - 4 q^{26} - 40 q^{31} - 72 q^{34} + 42 q^{36} + 34 q^{49} + 120 q^{56} + 8 q^{59} + 34 q^{64} + 40 q^{70} - 16 q^{71} - 30 q^{80} - 18 q^{81} + 36 q^{86} - 56 q^{91}+O(q^{100}) $ 8 * q + 14 * q^4 + 10 * q^5 - 6 * q^9 + 32 * q^14 + 18 * q^16 - 10 * q^20 - 10 * q^25 - 4 * q^26 - 40 * q^31 - 72 * q^34 + 42 * q^36 + 34 * q^49 + 120 * q^56 + 8 * q^59 + 34 * q^64 + 40 * q^70 - 16 * q^71 - 30 * q^80 - 18 * q^81 + 36 * q^86 - 56 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	2.37499	−	0.771681i	1.67937	−	0.545661i	0.694582	−	0.719413i	$-0.255589\pi$
$2$	2.37499	−	0.771681i	1.67937	−	0.545661i	0.984789	+	0.173753i	$0.0555893\pi$
$3$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$3$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$4$	3.42705	−	2.48990i	1.71353	−	1.24495i
$5$	0.690983	−	2.12663i	0.309017	−	0.951057i
$5$	0.690983	−	2.12663i	0.309017	−	0.951057i
$6$		0			0
$7$	1.81433	+	2.49721i	0.685753	+	0.943857i	0.999985	−	0.00548867i	$-0.00174711\pi$
$7$	1.81433	+	2.49721i	0.685753	+	0.943857i	−0.314232	+	0.949346i	$0.601747\pi$
$8$	3.28216	−	4.51750i	1.16042	−	1.59718i
$9$	0.927051	+	2.85317i	0.309017	+	0.951057i
$10$		−	5.58394i		−	1.76580i
$11$		0			0
$11$		0			0
$12$		0			0
$13$	−1.81433	+	0.589512i	−0.503205	+	0.163501i	−0.549610	−	0.835422i	$-0.685224\pi$
$13$	−1.81433	+	0.589512i	−0.503205	+	0.163501i	0.0464049	+	0.998923i	$0.485224\pi$
$14$	6.23607	+	4.53077i	1.66666	+	1.21090i
$15$		0			0
$16$	1.69098	−	5.20431i	0.422746	−	1.30108i
$17$	−7.68563	−	2.49721i	−1.86404	−	0.605663i	−0.993539	−	0.113495i	$-0.963796\pi$
$17$	−7.68563	−	2.49721i	−1.86404	−	0.605663i	−0.870500	−	0.492168i	$-0.836204\pi$
$18$	4.40347	+	6.06086i	1.03791	+	1.42856i
$19$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$19$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$20$	−2.92705	−	9.00854i	−0.654508	−	2.01437i
$21$		0			0
$22$		0			0
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$		0			0
$25$	−4.04508	−	2.93893i	−0.809017	−	0.587785i
$26$	−3.85410	+	2.80017i	−0.755852	+	0.549158i
$27$		0			0
$28$	12.4356	+	4.04057i	2.35011	+	0.763597i
$29$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$29$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$30$		0			0
$31$	−2.76393	−	8.50651i	−0.496417	−	1.52781i	−0.814737	−	0.579831i	$-0.803119\pi$
$31$	−2.76393	−	8.50651i	−0.496417	−	1.52781i	0.318320	−	0.947983i	$-0.396881\pi$
$32$		−	2.49721i		−	0.441449i
$33$		0			0
$34$	−20.1803			−3.46090
$35$	6.56431	−	2.13287i	1.10957	−	0.360521i
$36$	10.2812	+	7.46969i	1.71353	+	1.24495i
$37$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$37$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$38$		0			0
$39$		0			0
$40$	−7.33912	−	10.1014i	−1.16042	−	1.59718i
$41$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$41$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$42$		0			0
$43$			13.0756i			1.99401i	0.0773627	+	0.997003i	$0.475350\pi$
$43$			13.0756i			1.99401i	−0.0773627	+	0.997003i	$0.524650\pi$
$44$		0			0
$45$	6.70820			1.00000
$46$		0			0
$47$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$47$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$48$		0			0
$49$	−0.781153	+	2.40414i	−0.111593	+	0.343449i
$50$	−11.8749	−	3.85840i	−1.67937	−	0.545661i
$51$		0			0
$52$	−4.74998	+	6.53779i	−0.658704	+	0.906628i
$53$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$53$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$54$		0			0
$55$		0			0
$56$	17.2361			2.30327
$57$		0			0
$58$		0			0
$59$	3.23607	−	2.35114i	0.421300	−	0.306092i	−0.356861	−	0.934158i	$-0.616153\pi$
$59$	3.23607	−	2.35114i	0.421300	−	0.306092i	0.778161	+	0.628065i	$0.216153\pi$
$60$		0			0
$61$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$61$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$62$	−13.1286	−	18.0700i	−1.66734	−	2.29489i
$63$	−5.44299	+	7.49164i	−0.685753	+	0.943857i
$64$	1.45492	+	4.47777i	0.181864	+	0.559721i
$65$			4.26575i			0.529101i
$66$		0			0
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$	−32.5568	+	10.5784i	−3.94810	+	1.28281i
$69$		0			0
$70$	13.9443	−	10.1311i	1.66666	−	1.21090i
$71$	2.47214	−	7.60845i	0.293389	−	0.902957i	−0.690369	−	0.723457i	$-0.742552\pi$
$71$	2.47214	−	7.60845i	0.293389	−	0.902957i	0.983758	−	0.179500i	$-0.0574480\pi$
$72$	15.9319	+	5.17659i	1.87759	+	0.610067i
$73$	6.99262	+	9.62451i	0.818424	+	1.12646i	0.989969	+	0.141287i	$0.0451242\pi$
$73$	6.99262	+	9.62451i	0.818424	+	1.12646i	−0.171545	+	0.985176i	$0.554876\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$79$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$80$	−9.89919	−	7.19218i	−1.10676	−	0.804110i
$81$	−7.28115	+	5.29007i	−0.809017	+	0.587785i
$82$		0			0
$83$	0.693013	+	0.225173i	0.0760680	+	0.0247160i	0.346804	−	0.937938i	$-0.387267\pi$
$83$	0.693013	+	0.225173i	0.0760680	+	0.0247160i	−0.270736	+	0.962654i	$0.587267\pi$
$84$		0			0
$85$	−10.6213	+	14.6189i	−1.15204	+	1.58565i
$86$	10.0902	+	31.0543i	1.08805	+	3.34868i
$87$		0			0
$88$		0			0
$89$	13.4164			1.42214			0.711068	−	0.703123i	$-0.248212\pi$
$89$	13.4164			1.42214			0.711068	+	0.703123i	$0.248212\pi$
$90$	15.9319	−	5.17659i	1.67937	−	0.545661i
$91$	−4.76393	−	3.46120i	−0.499396	−	0.362832i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$97$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$98$			6.31261i			0.637670i
$99$		0			0
$100$	−21.1803			−2.11803
$101$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$101$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$102$		0			0
$103$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$103$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$104$	−3.29180	+	10.1311i	−0.322787	+	0.993437i
$105$		0			0
$106$		0			0
$107$	11.3143	−	15.5728i	1.09379	−	1.50548i	0.250430	−	0.968135i	$-0.419428\pi$
$107$	11.3143	−	15.5728i	1.09379	−	1.50548i	0.843364	−	0.537343i	$-0.180572\pi$
$108$		0			0
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$		0			0
$112$	16.0643	−	5.21960i	1.51793	−	0.493206i
$113$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$113$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−3.36395	−	4.63009i	−0.310998	−	0.428052i
$118$	5.87130	−	8.08115i	0.540497	−	0.743930i
$119$	−7.70820	−	23.7234i	−0.706610	−	2.17472i
$120$		0			0
$121$		0			0
$122$		0			0
$123$		0			0
$124$	−30.6525	−	22.2703i	−2.75267	−	1.99993i
$125$	−9.04508	+	6.57164i	−0.809017	+	0.587785i
$126$	−7.14590	+	21.9928i	−0.636607	+	1.95928i
$127$	−16.0643	−	5.21960i	−1.42547	−	0.463164i	−0.508137	−	0.861276i	$-0.669666\pi$
$127$	−16.0643	−	5.21960i	−1.42547	−	0.463164i	−0.917337	+	0.398112i	$0.869666\pi$
$128$	9.84647	+	13.5525i	0.870313	+	1.19788i
$129$		0			0
$130$	3.29180	+	10.1311i	0.288710	+	0.888557i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−36.5066	+	26.5236i	−3.13041	+	2.27438i
$137$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$137$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$138$		0			0
$139$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$139$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$140$	17.1856	−	23.6539i	1.45245	−	1.99912i
$141$		0			0
$142$		−	19.9777i		−	1.67649i
$143$		0			0
$144$	16.4164			1.36803
$145$		0			0
$146$	24.0344	+	17.4620i	1.98910	+	1.44517i
$147$		0			0
$148$		0			0
$149$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$149$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$150$		0			0
$151$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$151$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$152$		0			0
$153$		−	24.2434i		−	1.95997i
$154$		0			0
$155$	−20.0000			−1.60644
$156$		0			0
$157$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$157$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$158$		0			0
$159$		0			0
$160$	−5.31064	−	1.72553i	−0.419843	−	0.136415i
$161$		0			0
$162$	−13.2104	+	18.1826i	−1.03791	+	1.42856i
$163$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$163$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$164$		0			0
$165$		0			0
$166$	1.81966			0.141233
$167$	−10.1930	+	3.31190i	−0.788756	+	0.256282i	−0.675574	−	0.737292i	$-0.736104\pi$
$167$	−10.1930	+	3.31190i	−0.788756	+	0.256282i	−0.113182	+	0.993574i	$0.536104\pi$
$168$		0			0
$169$	−7.57295	+	5.50207i	−0.582535	+	0.423236i
$170$	−13.9443	+	42.9161i	−1.06948	+	3.29151i
$171$		0			0
$172$	32.5568	+	44.8107i	2.48244	+	3.41678i
$173$	6.13600	−	8.44549i	0.466512	−	0.642098i	−0.509331	−	0.860570i	$-0.670107\pi$
$173$	6.13600	−	8.44549i	0.466512	−	0.642098i	0.975843	+	0.218472i	$0.0701072\pi$
$174$		0			0
$175$		−	15.4336i		−	1.16667i
$176$		0			0
$177$		0			0
$178$	31.8638	−	10.3532i	2.38830	−	0.776004i
$179$	−14.4721	−	10.5146i	−1.08170	−	0.785900i	−0.103720	−	0.994607i	$-0.533075\pi$
$179$	−14.4721	−	10.5146i	−1.08170	−	0.785900i	−0.977978	+	0.208707i	$0.933075\pi$
$180$	22.9894	−	16.7027i	1.71353	−	1.24495i
$181$	1.38197	−	4.25325i	0.102721	−	0.316142i	−0.886468	−	0.462790i	$-0.846848\pi$
$181$	1.38197	−	4.25325i	0.102721	−	0.316142i	0.989189	+	0.146648i	$0.0468485\pi$
$182$	−13.9852	−	4.54408i	−1.03665	−	0.336829i
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	21.7082	−	15.7719i	1.57075	−	1.14122i	0.644317	−	0.764758i	$-0.277142\pi$
$191$	21.7082	−	15.7719i	1.57075	−	1.14122i	0.926433	−	0.376459i	$-0.122858\pi$
$192$		0			0
$193$	19.4282	+	6.31261i	1.39847	+	0.454392i	0.908697	−	0.417456i	$-0.137078\pi$
$193$	19.4282	+	6.31261i	1.39847	+	0.454392i	0.489777	+	0.871848i	$0.337078\pi$
$194$		0			0
$195$		0			0
$196$	3.30902	+	10.1841i	0.236358	+	0.727436i
$197$			21.8854i			1.55927i	0.626234	+	0.779635i	$0.284595\pi$
$197$			21.8854i			1.55927i	−0.626234	+	0.779635i	$0.715405\pi$
$198$		0			0
$199$	24.0000			1.70131			0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000			1.70131			0.850657	+	0.525720i	$0.176204\pi$
$200$	−26.5532	+	8.62766i	−1.87759	+	0.610067i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$			10.4392i			0.723828i
$209$		0			0
$210$		0			0
$211$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$211$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$212$		0			0
$213$		0			0
$214$	14.8541	−	45.7162i	1.01541	−	3.12510i
$215$	27.8069	+	9.03500i	1.89641	+	0.616182i
$216$		0			0
$217$	16.2279	−	22.3357i	1.10162	−	1.51625i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	15.4164			1.03702
$222$		0			0
$223$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$223$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$224$	6.23607	−	4.53077i	0.416665	−	0.302725i
$225$	4.63525	−	14.2658i	0.309017	−	0.951057i
$226$		0			0
$227$	−14.9430	−	20.5672i	−0.991799	−	1.36509i	−0.930224	−	0.366991i	$-0.880388\pi$
$227$	−14.9430	−	20.5672i	−0.991799	−	1.36509i	−0.0615740	−	0.998103i	$-0.519612\pi$
$228$		0			0
$229$	1.85410	+	5.70634i	0.122523	+	0.377086i	0.993442	−	0.114341i	$-0.0364756\pi$
$229$	1.85410	+	5.70634i	0.122523	+	0.377086i	−0.870919	+	0.491426i	$0.836476\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	14.9430	−	4.85526i	0.978945	−	0.318079i	0.224524	−	0.974469i	$-0.427917\pi$
$233$	14.9430	−	4.85526i	0.978945	−	0.318079i	0.754422	+	0.656390i	$0.227917\pi$
$234$	−11.5623	−	8.40051i	−0.755852	−	0.549158i
$235$		0			0
$236$	5.23607	−	16.1150i	0.340839	−	1.04899i
$237$		0			0
$238$	−36.6138	−	50.3946i	−2.37332	−	3.26660i
$239$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$239$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$240$		0			0
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	4.57295	+	3.32244i	0.292155	+	0.212263i
$246$		0			0
$247$		0			0
$248$	−47.4998	−	15.4336i	−3.01624	−	0.980036i
$249$		0			0
$250$	−16.4108	+	22.5875i	−1.03791	+	1.42856i
$251$	8.65248	+	26.6296i	0.546139	+	1.68084i	0.718265	+	0.695769i	$0.244936\pi$
$251$	8.65248	+	26.6296i	0.546139	+	1.68084i	−0.172126	+	0.985075i	$0.555064\pi$
$252$			39.2267i			2.47105i
$253$		0			0
$254$	−42.1803			−2.64663
$255$		0			0
$256$	26.2254	+	19.0539i	1.63909	+	1.19087i
$257$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$257$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$258$		0			0
$259$		0			0
$260$	10.6213	+	14.6189i	0.658704	+	0.906628i
$261$		0			0
$262$		0			0
$263$		−	4.54408i		−	0.280200i	−0.990137	−	0.140100i	$-0.955258\pi$
$263$		−	4.54408i		−	0.280200i	0.990137	−	0.140100i	$-0.0447424\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−4.32624	+	13.3148i	−0.263775	+	0.811817i	0.728198	+	0.685367i	$0.240358\pi$
$269$	−4.32624	+	13.3148i	−0.263775	+	0.811817i	−0.991973	+	0.126450i	$0.959642\pi$
$270$		0			0
$271$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$271$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$272$	−25.9925	+	35.7757i	−1.57603	+	2.16922i
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−28.9282	+	9.39934i	−1.73813	+	0.564751i	−0.994584	−	0.103938i	$-0.966856\pi$
$277$	−28.9282	+	9.39934i	−1.73813	+	0.564751i	−0.743542	+	0.668689i	$0.766856\pi$
$278$		0			0
$279$	21.7082	−	15.7719i	1.29964	−	0.944241i
$280$	11.9098	−	36.6547i	0.711748	−	2.19054i
$281$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$281$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$282$		0			0
$283$	−15.7996	+	21.7462i	−0.939186	+	1.29268i	0.0169800	+	0.999856i	$0.494595\pi$
$283$	−15.7996	+	21.7462i	−0.939186	+	1.29268i	−0.956167	+	0.292823i	$0.905405\pi$
$284$	−10.4721	−	32.2299i	−0.621407	−	1.91249i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	7.12497	−	2.31504i	0.419843	−	0.136415i
$289$	39.0795	+	28.3929i	2.29880	+	1.67017i
$290$		0			0
$291$		0			0
$292$	47.9281	+	15.5728i	2.80478	+	0.911328i
$293$	−20.1212	−	27.6945i	−1.17550	−	1.61793i	−0.596906	−	0.802311i	$-0.703603\pi$
$293$	−20.1212	−	27.6945i	−1.17550	−	1.61793i	−0.578589	−	0.815619i	$-0.696397\pi$
$294$		0			0
$295$	−2.76393	−	8.50651i	−0.160922	−	0.495268i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−32.6525	+	23.7234i	−1.88206	+	1.36739i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$	−18.7082	−	57.5779i	−1.06948	−	3.29151i
$307$		−	33.0533i		−	1.88645i	−0.332155	−	0.943225i	$-0.607776\pi$
$307$		−	33.0533i		−	1.88645i	0.332155	−	0.943225i	$-0.392224\pi$
$308$		0			0
$309$		0			0
$310$	−47.4998	+	15.4336i	−2.69781	+	0.876571i
$311$	−25.8885	−	18.8091i	−1.46800	−	1.06657i	−0.981186	−	0.193065i	$-0.938157\pi$
$311$	−25.8885	−	18.8091i	−1.46800	−	1.06657i	−0.486819	−	0.873503i	$-0.661843\pi$
$312$		0			0
$313$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$313$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$314$		0			0
$315$	12.1709	+	16.7518i	0.685753	+	0.943857i
$316$		0			0
$317$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$317$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$318$		0			0
$319$		0			0
$320$	10.5279			0.588525
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−11.7812	+	36.2587i	−0.654508	+	2.01437i
$325$	9.07165	+	2.94756i	0.503205	+	0.163501i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−35.7771			−1.96649			−0.983243	−	0.182298i	$-0.941646\pi$
$331$	−35.7771			−1.96649			−0.983243	+	0.182298i	$0.941646\pi$
$332$	2.93565	−	0.953850i	0.161115	−	0.0523493i
$333$		0			0
$334$	−21.6525	+	15.7314i	−1.18477	+	0.860786i
$335$		0			0
$336$		0			0
$337$	−9.76467	−	13.4399i	−0.531915	−	0.732119i	0.455506	−	0.890233i	$-0.349459\pi$
$337$	−9.76467	−	13.4399i	−0.531915	−	0.732119i	−0.987421	+	0.158114i	$0.949459\pi$
$338$	−13.7398	+	18.9113i	−0.747348	+	1.02864i
$339$		0			0
$340$			76.5457i			4.15128i
$341$		0			0
$342$		0			0
$343$	13.1286	−	4.26575i	0.708879	−	0.230329i
$344$	59.0689	+	42.9161i	3.18478	+	2.31388i
$345$		0			0
$346$	8.05573	−	24.7930i	0.433079	−	1.33288i
$347$	11.0496	+	3.59023i	0.593173	+	0.192733i	0.590193	−	0.807262i	$-0.299052\pi$
$347$	11.0496	+	3.59023i	0.593173	+	0.192733i	0.00297954	+	0.999996i	$0.499052\pi$
$348$		0			0
$349$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$349$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$350$	−11.9098	−	36.6547i	−0.636607	−	1.95928i
$351$		0			0
$352$		0			0
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$		0			0
$355$	−14.4721	−	10.5146i	−0.768101	−	0.558058i
$356$	45.9787	−	33.4055i	2.43687	−	1.77049i
$357$		0			0
$358$	−42.4851	−	13.8042i	−2.24541	−	0.729577i
$359$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$359$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$360$	22.0174	−	30.3043i	1.16042	−	1.59718i
$361$	−5.87132	−	18.0701i	−0.309017	−	0.951057i
$362$		−	11.1679i		−	0.586970i
$363$		0			0
$364$	−24.9443			−1.30744
$365$	25.2995	−	8.22031i	1.32424	−	0.430271i
$366$		0			0
$367$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$367$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		−	6.62379i		−	0.342967i	−0.985187	−	0.171484i	$-0.945144\pi$
$373$		−	6.62379i		−	0.342967i	0.985187	−	0.171484i	$-0.0548560\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−11.1246	+	34.2380i	−0.571433	+	1.75869i	0.0765833	+	0.997063i	$0.475599\pi$
$379$	−11.1246	+	34.2380i	−0.571433	+	1.75869i	−0.648016	+	0.761627i	$0.724401\pi$
$380$		0			0
$381$		0			0
$382$	39.3859	−	54.2100i	2.01516	−	2.77362i
$383$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$383$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$384$		0			0
$385$		0			0
$386$	51.0132			2.59650
$387$	−37.3068	+	12.1217i	−1.89641	+	0.616182i
$388$		0			0
$389$	21.0344	−	15.2824i	1.06649	−	0.774849i	0.0912107	−	0.995832i	$-0.470926\pi$
$389$	21.0344	−	15.2824i	1.06649	−	0.774849i	0.975278	+	0.220982i	$0.0709263\pi$
$390$		0			0
$391$		0			0
$392$	8.29684	+	11.4196i	0.419054	+	0.576778i
$393$		0			0
$394$	16.8885	+	51.9776i	0.850833	+	2.61859i
$395$		0			0
$396$		0			0
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$	56.9998	−	18.5203i	2.85714	−	0.928341i
$399$		0			0
$400$	−22.1353	+	16.0822i	−1.10676	+	0.804110i
$401$	1.38197	−	4.25325i	0.0690121	−	0.212397i	−0.910603	−	0.413283i	$-0.864382\pi$
$401$	1.38197	−	4.25325i	0.0690121	−	0.212397i	0.979615	+	0.200886i	$0.0643820\pi$
$402$		0			0
$403$	10.0294	+	13.8042i	0.499599	+	0.687639i
$404$		0			0
$405$	6.21885	+	19.1396i	0.309017	+	0.951057i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$409$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	11.7426	+	3.81540i	0.577815	+	0.187744i
$414$		0			0
$415$	0.957720	−	1.31819i	0.0470126	−	0.0647073i
$416$	1.47214	+	4.53077i	0.0721774	+	0.222139i
$417$		0			0
$418$		0			0
$419$	−35.7771			−1.74783			−0.873913	−	0.486083i	$-0.838425\pi$
$419$	−35.7771			−1.74783			−0.873913	+	0.486083i	$0.838425\pi$
$420$		0			0
$421$	25.3262	+	18.4006i	1.23433	+	0.896790i	0.997207	−	0.0746909i	$-0.0237970\pi$
$421$	25.3262	+	18.4006i	1.23433	+	0.896790i	0.237119	+	0.971481i	$0.423797\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	23.7499	+	32.6889i	1.15204	+	1.58565i
$426$		0			0
$427$		0			0
$428$		−	81.5402i		−	3.94139i
$429$		0			0
$430$	73.0132			3.52101
$431$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$431$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$432$		0			0
$433$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$433$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$434$	21.3050	−	65.5699i	1.02267	−	3.14746i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$		0			0
$441$	−7.58359			−0.361123
$442$	36.6138	−	11.8965i	1.74154	−	0.565861i
$443$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$443$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$444$		0			0
$445$	9.27051	−	28.5317i	0.439464	−	1.35253i
$446$		0			0
$447$		0			0
$448$	−8.54224	+	11.7574i	−0.403583	+	0.555484i
$449$	12.4377	+	38.2793i	0.586971	+	1.80651i	0.591207	+	0.806520i	$0.298652\pi$
$449$	12.4377	+	38.2793i	0.586971	+	1.80651i	−0.00423548	+	0.999991i	$0.501348\pi$
$450$		−	37.4582i		−	1.76580i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−51.3607	−	37.3157i	−2.41048	−	1.75131i
$455$	−10.6525	+	7.73948i	−0.499396	+	0.362832i
$456$		0			0
$457$	−34.7995	−	11.3070i	−1.62785	−	0.528921i	−0.654075	−	0.756430i	$-0.726942\pi$
$457$	−34.7995	−	11.3070i	−1.62785	−	0.528921i	−0.973776	+	0.227509i	$0.926942\pi$
$458$	8.80695	+	12.1217i	0.411522	+	0.566411i
$459$		0			0
$460$		0			0
$461$		0			0			−	1.00000i	$-0.5\pi$
$461$		0			0				1.00000i	$0.5\pi$
$462$		0			0
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$		0			0
$465$		0			0
$466$	31.7426	−	23.0624i	1.47045	−	1.06834i
$467$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$467$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$468$	−23.0569	−	7.49164i	−1.06580	−	0.346301i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		−	22.3357i		−	1.02809i
$473$		0			0
$474$		0			0
$475$		0			0
$476$	−85.4853	−	62.1087i	−3.91821	−	2.84675i
$477$		0			0
$478$		0			0
$479$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$479$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$		0			0
$486$		0			0
$487$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$487$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$488$		0			0
$489$		0			0
$490$	13.4246	+	4.36191i	0.606460	+	0.197051i
$491$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$491$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−48.9443			−2.19766
$497$	23.4852	−	7.63080i	1.05345	−	0.342288i
$498$		0			0
$499$	3.23607	−	2.35114i	0.144866	−	0.105252i	−0.512992	−	0.858394i	$-0.671463\pi$
$499$	3.23607	−	2.35114i	0.144866	−	0.105252i	0.657858	+	0.753142i	$0.271463\pi$
$500$	−14.6353	+	45.0427i	−0.654508	+	2.01437i
$501$		0			0
$502$	41.0991	+	56.5680i	1.83434	+	2.52475i
$503$	21.6709	−	29.8274i	0.966256	−	1.32994i	0.0223402	−	0.999750i	$-0.492888\pi$
$503$	21.6709	−	29.8274i	0.966256	−	1.32994i	0.943916	−	0.330187i	$-0.107112\pi$
$504$	15.9787	+	49.1774i	0.711748	+	2.19054i
$505$		0			0
$506$		0			0
$507$		0			0
$508$	−68.0493	+	22.1106i	−3.01920	+	0.980998i
$509$	27.5066	+	19.9847i	1.21921	+	0.885806i	0.996034	−	0.0889725i	$-0.0283583\pi$
$509$	27.5066	+	19.9847i	1.21921	+	0.885806i	0.223174	+	0.974779i	$0.428358\pi$
$510$		0			0
$511$	−11.3475	+	34.9241i	−0.501985	+	1.54495i
$512$	45.1248	+	14.6619i	1.99425	+	0.647972i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	19.2705	+	14.0008i	0.845068	+	0.613978i
$521$	−18.0902	+	13.1433i	−0.792545	+	0.575817i	−0.908718	−	0.417412i	$-0.862937\pi$
$521$	−18.0902	+	13.1433i	−0.792545	+	0.575817i	0.116173	+	0.993229i	$0.462937\pi$
$522$		0			0
$523$	−43.1781	−	14.0294i	−1.88805	−	0.613464i	−0.981534	−	0.191286i	$-0.938734\pi$
$523$	−43.1781	−	14.0294i	−1.88805	−	0.613464i	−0.906513	−	0.422178i	$-0.861266\pi$
$524$		0			0
$525$		0			0
$526$	−3.50658	−	10.7921i	−0.152894	−	0.470560i
$527$			72.2800i			3.14857i
$528$		0			0
$529$	23.0000			1.00000
$530$		0			0
$531$	9.70820	+	7.05342i	0.421300	+	0.306092i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−25.2995	−	34.8218i	−1.09379	−	1.50548i
$536$		0			0
$537$		0			0
$538$			34.9610i			1.50727i
$539$		0			0
$540$		0			0
$541$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$541$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$542$		0			0
$543$		0			0
$544$	−6.23607	+	19.1926i	−0.267369	+	0.822878i
$545$		0			0
$546$		0			0
$547$	4.91358	−	6.76296i	0.210089	−	0.289163i	−0.690948	−	0.722904i	$-0.742807\pi$
$547$	4.91358	−	6.76296i	0.210089	−	0.289163i	0.901038	+	0.433741i	$0.142807\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−61.4508	+	44.6467i	−2.61080	+	1.89685i
$555$		0			0
$556$		0			0
$557$	13.3933	+	18.4343i	0.567494	+	0.781088i	0.992255	−	0.124217i	$-0.0396420\pi$
$557$	13.3933	+	18.4343i	0.567494	+	0.781088i	−0.424762	+	0.905305i	$0.639642\pi$
$558$	39.3859	−	54.2100i	1.66734	−	2.29489i
$559$	−7.70820	−	23.7234i	−0.326022	−	1.00339i
$560$		−	37.7694i		−	1.59605i
$561$		0			0
$562$		0			0
$563$	16.9209	−	5.49793i	0.713130	−	0.231710i	0.0700880	−	0.997541i	$-0.477672\pi$
$563$	16.9209	−	5.49793i	0.713130	−	0.231710i	0.643042	+	0.765831i	$0.277672\pi$
$564$		0			0
$565$		0			0
$566$	−20.7426	+	63.8393i	−0.871878	+	2.68337i
$567$	−26.4208	−	8.58465i	−1.10957	−	0.360521i
$568$	−26.2572	−	36.1400i	−1.10173	−	1.51640i
$569$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$569$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$570$		0			0
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−11.4271	+	8.30224i	−0.476127	+	0.345927i
$577$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$577$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$578$	114.724	+	37.2760i	4.77188	+	1.55048i
$579$		0			0
$580$		0			0
$581$	0.695048	+	2.13914i	0.0288355	+	0.0887464i
$582$		0			0
$583$		0			0
$584$	66.4296			2.74887
$585$	−12.1709	+	3.95457i	−0.503205	+	0.163501i
$586$	−69.1591	−	50.2470i	−2.85693	−	2.07568i
$587$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$587$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$588$		0			0
$589$		0			0
$590$	−13.1286	−	18.0700i	−0.540497	−	0.743930i
$591$		0			0
$592$		0			0
$593$			32.7749i			1.34591i	0.739686	+	0.672953i	$0.234974\pi$
$593$			32.7749i			1.34591i	−0.739686	+	0.672953i	$0.765026\pi$
$594$		0			0
$595$	−55.7771			−2.28664
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−13.8197	+	42.5325i	−0.564656	+	1.73783i	0.104315	+	0.994544i	$0.466735\pi$
$599$	−13.8197	+	42.5325i	−0.564656	+	1.73783i	−0.668971	+	0.743288i	$0.733265\pi$
$600$		0			0
$601$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$601$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$602$	−59.2424	+	81.5402i	−2.41454	+	3.32333i
$603$		0			0
$604$		0			0
$605$		0			0
$606$		0			0
$607$	23.3216	−	7.57764i	0.946594	−	0.307567i	0.205263	−	0.978707i	$-0.434195\pi$
$607$	23.3216	−	7.57764i	0.946594	−	0.307567i	0.741331	+	0.671140i	$0.234195\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−60.3637	−	83.0835i	−2.44006	−	3.35845i
$613$	−27.3786	+	37.6834i	−1.10581	+	1.52202i	−0.278360	+	0.960477i	$0.589791\pi$
$613$	−27.3786	+	37.6834i	−1.10581	+	1.52202i	−0.827450	+	0.561539i	$0.810209\pi$
$614$	−25.5066	−	78.5012i	−1.02936	−	3.16805i
$615$		0			0
$616$		0			0
$617$		0			0		1.00000			$0$
$617$		0			0		−1.00000			$\pi$
$618$		0			0
$619$	−14.4721	−	10.5146i	−0.581684	−	0.422618i	0.257647	−	0.966239i	$-0.417053\pi$
$619$	−14.4721	−	10.5146i	−0.581684	−	0.422618i	−0.839331	+	0.543621i	$0.817053\pi$
$620$	−68.5410	+	49.7980i	−2.75267	+	1.99993i
$621$		0			0
$622$	−75.9997	−	24.6938i	−3.04731	−	0.990131i
$623$	24.3418	+	33.5036i	0.975234	+	1.34229i
$624$		0			0
$625$	7.72542	+	23.7764i	0.309017	+	0.951057i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	41.8328	+	30.3933i	1.66666	+	1.21090i
$631$	38.8328	−	28.2137i	1.54591	−	1.12317i	0.599421	−	0.800434i	$-0.295398\pi$
$631$	38.8328	−	28.2137i	1.54591	−	1.12317i	0.946489	−	0.322735i	$-0.104602\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−22.2003	+	30.5561i	−0.880991	+	1.21258i
$636$		0			0
$637$		−	4.82241i		−	0.191071i
$638$		0			0
$639$	24.0000			0.949425
$640$	35.6248	−	11.5752i	1.40820	−	0.457551i
$641$	25.3262	+	18.4006i	1.00033	+	0.726780i	0.962158	−	0.272492i	$-0.0878478\pi$
$641$	25.3262	+	18.4006i	1.00033	+	0.726780i	0.0381681	+	0.999271i	$0.487848\pi$
$642$		0			0
$643$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$643$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$647$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$648$			50.2554i			1.97422i
$649$		0			0
$650$	23.8197			0.934284
$651$		0			0
$652$		0			0
$653$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$653$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−20.9778	+	28.8735i	−0.818424	+	1.12646i
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	−42.0000			−1.63361			−0.816805	−	0.576913i	$-0.804257\pi$
$661$	−42.0000			−1.63361			−0.816805	+	0.576913i	$0.804257\pi$
$662$	−84.9702	+	27.6085i	−3.30246	+	1.07303i
$663$		0			0
$664$	3.29180	−	2.39163i	0.127746	−	0.0928132i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−26.6855	+	36.7295i	−1.03249	+	1.42111i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−45.6855	+	14.8441i	−1.76105	+	0.572198i	−0.997308	−	0.0733287i	$-0.976638\pi$
$673$	−45.6855	+	14.8441i	−1.76105	+	0.572198i	−0.763737	+	0.645527i	$0.776638\pi$
$674$	−33.5623	−	24.3844i	−1.29277	−	0.939254i
$675$		0			0
$676$	−12.2533	+	37.7117i	−0.471280	+	1.45045i
$677$	2.67094	+	0.867842i	0.102653	+	0.0333539i	0.359893	−	0.932994i	$-0.382813\pi$
$677$	2.67094	+	0.867842i	0.102653	+	0.0333539i	−0.257240	+	0.966347i	$0.582813\pi$
$678$		0			0
$679$		0			0
$680$	31.1803	+	95.9632i	1.19571	+	3.68002i
$681$		0			0
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$		0			0
$685$		0			0
$686$	27.8885	−	20.2622i	1.06479	−	0.773615i
$687$		0			0
$688$	68.0493	+	22.1106i	2.59436	+	0.842958i
$689$		0			0
$690$		0			0
$691$	8.65248	+	26.6296i	0.329156	+	1.01304i	0.969530	+	0.244974i	$0.0787794\pi$
$691$	8.65248	+	26.6296i	0.329156	+	1.01304i	−0.640374	+	0.768063i	$0.721221\pi$
$692$		−	44.2211i		−	1.68104i
$693$		0			0
$694$	29.0132			1.10132
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−38.4281	−	52.8918i	−1.45245	−	1.99912i
$701$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$701$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	1.38197	−	4.25325i	0.0519008	−	0.159734i	−0.921747	−	0.387793i	$-0.873238\pi$
$709$	1.38197	−	4.25325i	0.0519008	−	0.159734i	0.973647	+	0.228058i	$0.0732377\pi$
$710$	−42.4851	−	13.8042i	−1.59444	−	0.518064i
$711$		0			0
$712$	44.0347	−	60.6086i	1.65027	−	2.27140i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−75.7771			−2.83192
$717$		0			0
$718$		0			0
$719$	21.7082	−	15.7719i	0.809579	−	0.588194i	−0.104129	−	0.994564i	$-0.533206\pi$
$719$	21.7082	−	15.7719i	0.809579	−	0.588194i	0.913709	+	0.406370i	$0.133206\pi$
$720$	11.3435	−	34.9116i	0.422746	−	1.30108i
$721$		0			0
$722$	−27.8887	−	38.3855i	−1.03791	−	1.42856i
$723$		0			0
$724$	−5.85410	−	18.0171i	−0.217566	−	0.669599i
$725$		0			0
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$	−31.2719	+	10.1609i	−1.15901	+	0.376587i
$729$	−21.8435	−	15.8702i	−0.809017	−	0.587785i
$730$	53.7426	−	39.0463i	1.98910	−	1.44517i
$731$	32.6525	−	100.494i	1.20770	−	3.71690i
$732$		0			0
$733$	17.3492	+	23.8791i	0.640807	+	0.881995i	0.998658	−	0.0517836i	$-0.0164906\pi$
$733$	17.3492	+	23.8791i	0.640807	+	0.881995i	−0.357852	+	0.933778i	$0.616491\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$739$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	17.4503	+	5.66994i	0.640189	+	0.208010i	0.611083	−	0.791566i	$-0.290734\pi$
$743$	17.4503	+	5.66994i	0.640189	+	0.208010i	0.0291059	+	0.999576i	$0.490734\pi$
$744$		0			0
$745$		0			0
$746$	−5.11146	−	15.7314i	−0.187144	−	0.575969i
$747$			2.18603i			0.0799827i
$748$		0			0
$749$	59.4164			2.17103
$750$		0			0
$751$	−25.8885	−	18.8091i	−0.944686	−	0.686355i	0.00485778	−	0.999988i	$-0.498454\pi$
$751$	−25.8885	−	18.8091i	−0.944686	−	0.686355i	−0.949544	+	0.313633i	$0.898454\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$757$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$758$			89.8996i			3.26530i
$759$		0			0
$760$		0			0
$761$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$761$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$762$		0			0
$763$		0			0
$764$	35.1246	−	108.102i	1.27076	−	3.91101i
$765$	−51.5568	−	16.7518i	−1.86404	−	0.605663i
$766$		0			0
$767$	−4.48527	+	6.17345i	−0.161954	+	0.222910i
$768$		0			0
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$		0			0
$772$	82.2993	−	26.7407i	2.96202	−	0.962417i
$773$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$773$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$774$	−79.2492	+	57.5779i	−2.84855	+	2.06960i
$775$	−13.8197	+	42.5325i	−0.496417	+	1.52781i
$776$		0			0
$777$		0			0
$778$	38.1634	−	52.5275i	1.36823	−	1.88320i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	11.1910	+	8.13073i	0.399678	+	0.290383i
$785$		0			0
$786$		0			0
$787$	44.5641	+	14.4798i	1.58854	+	0.516148i	0.964239	−	0.265035i	$-0.0853836\pi$
$787$	44.5641	+	14.4798i	1.58854	+	0.516148i	0.624302	+	0.781183i	$0.285384\pi$
$788$	54.4924	+	75.0024i	1.94121	+	2.67185i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	82.2492	−	59.7576i	2.91525	−	2.11805i
$797$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$797$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$798$		0			0
$799$		0			0
$800$	−7.33912	+	10.1014i	−0.259477	+	0.357140i
$801$	12.4377	+	38.2793i	0.439464	+	1.35253i
$802$		−	11.1679i		−	0.394351i
$803$		0			0
$804$		0			0
$805$		0			0
$806$	34.4721	+	25.0455i	1.21423	+	0.882189i
$807$		0			0
$808$		0			0
$809$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$809$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$810$	29.5394	+	40.6575i	1.03791	+	1.42856i
$811$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$811$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	5.45898	−	16.8010i	0.190752	−	0.587075i
$820$		0			0
$821$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$821$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$822$		0			0
$823$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$823$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$824$		0			0
$825$		0			0
$826$	30.8328			1.07281
$827$	50.4354	−	16.3875i	1.75381	−	0.569848i	0.757283	−	0.653087i	$-0.226527\pi$
$827$	50.4354	−	16.3875i	1.75381	−	0.569848i	0.996530	+	0.0832391i	$0.0265265\pi$
$828$		0			0
$829$	−18.0902	+	13.1433i	−0.628298	+	0.456485i	−0.855810	−	0.517290i	$-0.826941\pi$
$829$	−18.0902	+	13.1433i	−0.628298	+	0.456485i	0.227512	+	0.973775i	$0.426941\pi$
$830$	1.25735	−	3.86974i	0.0436434	−	0.134321i
$831$		0			0
$832$	−5.27939	−	7.26646i	−0.183030	−	0.251919i
$833$	12.0073	−	16.5266i	0.416028	−	0.572614i
$834$		0			0
$835$			23.9651i			0.829347i
$836$		0			0
$837$		0			0
$838$	−84.9702	+	27.6085i	−2.93525	+	0.953720i
$839$	45.3050	+	32.9160i	1.56410	+	1.13639i	0.932544	+	0.361056i	$0.117584\pi$
$839$	45.3050	+	32.9160i	1.56410	+	1.13639i	0.631556	+	0.775330i	$0.282416\pi$
$840$		0			0
$841$	−8.96149	+	27.5806i	−0.309017	+	0.951057i
$842$	74.3489	+	24.1574i	2.56223	+	0.832520i
$843$		0			0
$844$		0			0
$845$	6.46807	+	19.9067i	0.222508	+	0.684810i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$	81.6312	+	59.3085i	2.79993	+	2.03427i
$851$		0			0
$852$		0			0
$853$	−18.0422	−	5.86227i	−0.617753	−	0.200720i	−0.0166106	−	0.999862i	$-0.505288\pi$
$853$	−18.0422	−	5.86227i	−0.617753	−	0.200720i	−0.601142	+	0.799142i	$0.705288\pi$
$854$		0			0
$855$		0			0
$856$	−33.2148	−	102.225i	−1.13526	−	3.49396i
$857$		−	52.7526i		−	1.80200i	−0.433824	−	0.900998i	$-0.642836\pi$
$857$		−	52.7526i		−	1.80200i	0.433824	−	0.900998i	$-0.357164\pi$
$858$		0			0
$859$	−35.7771			−1.22070			−0.610349	−	0.792132i	$-0.708971\pi$
$859$	−35.7771			−1.22070			−0.610349	+	0.792132i	$0.708971\pi$
$860$	117.792	−	38.2729i	4.01667	−	1.30509i
$861$		0			0
$862$		0			0
$863$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$863$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$864$		0			0
$865$	−13.7205	−	18.8847i	−0.466512	−	0.642098i
$866$		0			0
$867$		0			0
$868$		−	116.951i		−	3.96959i
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−32.8216	−	10.6644i	−1.10957	−	0.360521i
$876$		0			0
$877$	22.8933	−	31.5099i	0.773051	−	1.06401i	−0.222964	−	0.974827i	$-0.571573\pi$
$877$	22.8933	−	31.5099i	0.773051	−	1.06401i	0.996015	−	0.0891871i	$-0.0284269\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	2.00000			0.0673817			0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000			0.0673817			0.0336909	+	0.999432i	$0.489274\pi$
$882$	−18.0110	+	5.85211i	−0.606460	+	0.197051i
$883$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$883$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$884$	52.8328	−	38.3853i	1.77696	−	1.29104i
$885$		0			0
$886$		0			0
$887$	8.21504	+	11.3070i	0.275834	+	0.379653i	0.924348	−	0.381549i	$-0.124609\pi$
$887$	8.21504	+	11.3070i	0.275834	+	0.379653i	−0.648514	+	0.761202i	$0.724609\pi$
$888$		0			0
$889$	−16.1115	−	49.5860i	−0.540361	−	1.66306i
$890$		−	74.9164i		−	2.51120i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−32.3607	+	23.5114i	−1.08170	+	0.785900i
$896$	−15.9787	+	49.1774i	−0.533811	+	1.64290i
$897$		0			0
$898$	59.0788	+	81.3150i	1.97148	+	2.71352i
$899$		0			0
$900$	−19.6353	−	60.4311i	−0.654508	−	2.01437i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−8.09017	−	5.87785i	−0.268926	−	0.195386i
$906$		0			0
$907$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$907$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$908$	−102.421	−	33.2784i	−3.39894	−	1.10438i
$909$		0			0
$910$	−19.3271	+	26.6015i	−0.640688	+	0.881831i
$911$	−2.76393	−	8.50651i	−0.0915732	−	0.281833i	0.894772	−	0.446523i	$-0.147338\pi$
$911$	−2.76393	−	8.50651i	−0.0915732	−	0.281833i	−0.986345	+	0.164690i	$0.947338\pi$
$912$		0			0
$913$		0			0
$914$	−91.3738			−3.02238
$915$		0			0
$916$	20.5623	+	14.9394i	0.679398	+	0.493611i
$917$		0			0
$918$		0			0
$919$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$919$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			15.2616i			0.502342i
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−4.32624	+	13.3148i	−0.141939	+	0.436844i	−0.996605	−	0.0823350i	$-0.973762\pi$
$929$	−4.32624	+	13.3148i	−0.141939	+	0.436844i	0.854665	+	0.519179i	$0.173762\pi$
$930$		0			0
$931$		0			0
$932$	39.1212	−	53.8456i	1.28146	−	1.76377i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−31.9574			−1.04456
$937$	8.54224	−	2.77554i	0.279063	−	0.0906730i	−0.166142	−	0.986102i	$-0.553131\pi$
$937$	8.54224	−	2.77554i	0.279063	−	0.0906730i	0.445205	+	0.895429i	$0.353131\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$941$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$942$		0			0
$943$		0			0
$944$	−6.76393	−	20.8172i	−0.220147	−	0.677544i
$945$		0			0
$946$		0			0
$947$		0			0		1.00000			$0$
$947$		0			0		−1.00000			$\pi$
$948$		0			0
$949$	−18.3607	−	13.3398i	−0.596013	−	0.433029i
$950$		0			0
$951$		0			0
$952$	−132.470	−	43.0421i	−4.29338	−	1.39500i
$953$	−30.4778	−	41.9491i	−0.987273	−	1.35886i	−0.932818	−	0.360348i	$-0.882658\pi$
$953$	−30.4778	−	41.9491i	−0.987273	−	1.35886i	−0.0544552	−	0.998516i	$-0.517342\pi$
$954$		0			0
$955$	−18.5410	−	57.0634i	−0.599973	−	1.84653i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−39.6418	+	28.8015i	−1.27877	+	0.929080i
$962$		0			0
$963$	54.9207	+	17.8448i	1.76980	+	0.575041i
$964$		0			0
$965$	26.8491	−	36.9547i	0.864305	−	1.18961i
$966$		0			0
$967$		−	61.5625i		−	1.97972i	−0.142063	−	0.989858i	$-0.545374\pi$
$967$		−	61.5625i		−	1.97972i	0.142063	−	0.989858i	$-0.454626\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−14.4721	−	10.5146i	−0.464433	−	0.337430i	0.330835	−	0.943689i	$-0.392670\pi$
$971$	−14.4721	−	10.5146i	−0.464433	−	0.337430i	−0.795268	+	0.606258i	$0.792670\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$977$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$978$		0			0
$979$		0			0
$980$	23.9443			0.764872
$981$		0			0
$982$		0			0
$983$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$983$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$984$		0			0
$985$	46.5421	+	15.1224i	1.48295	+	0.481841i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	62.6099			1.98887			0.994435	−	0.105356i	$-0.0335982\pi$
$991$	62.6099			1.98887			0.994435	+	0.105356i	$0.0335982\pi$
$992$	−21.2426	+	6.90212i	−0.674452	+	0.219143i
$993$		0			0
$994$	49.8885	−	36.2461i	1.58237	−	1.14966i
$995$	16.5836	−	51.0390i	0.525735	−	1.61805i
$996$		0			0
$997$	34.1065	+	46.9435i	1.08016	+	1.48672i	0.859342	+	0.511402i	$0.170874\pi$
$997$	34.1065	+	46.9435i	1.08016	+	1.48672i	0.220821	+	0.975314i	$0.429126\pi$
$998$	5.87130	−	8.08115i	0.185853	−	0.255804i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.j.c.269.2		8
5.4	even	2	inner	605.2.j.c.269.1		8
11.2	odd	10	inner	605.2.j.c.9.2		8
11.3	even	5		605.2.b.b.364.1	✓	4
11.4	even	5		605.2.j.a.124.2		8
11.5	even	5		605.2.j.a.444.1		8
11.6	odd	10		605.2.j.a.444.2		8
11.7	odd	10		605.2.j.a.124.1		8
11.8	odd	10		605.2.b.b.364.4	yes	4
11.9	even	5	inner	605.2.j.c.9.1		8
11.10	odd	2	inner	605.2.j.c.269.1		8
55.3	odd	20		3025.2.a.bb.1.1		4
55.4	even	10		605.2.j.a.124.1		8
55.8	even	20		3025.2.a.bb.1.4		4
55.9	even	10	inner	605.2.j.c.9.2		8
55.14	even	10		605.2.b.b.364.4	yes	4
55.19	odd	10		605.2.b.b.364.1	✓	4
55.24	odd	10	inner	605.2.j.c.9.1		8
55.29	odd	10		605.2.j.a.124.2		8
55.39	odd	10		605.2.j.a.444.1		8
55.47	odd	20		3025.2.a.bb.1.4		4
55.49	even	10		605.2.j.a.444.2		8
55.52	even	20		3025.2.a.bb.1.1		4
55.54	odd	2	CM	605.2.j.c.269.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.b.b.364.1	✓	4	11.3	even	5
605.2.b.b.364.1	✓	4	55.19	odd	10
605.2.b.b.364.4	yes	4	11.8	odd	10
605.2.b.b.364.4	yes	4	55.14	even	10
605.2.j.a.124.1		8	11.7	odd	10
605.2.j.a.124.1		8	55.4	even	10
605.2.j.a.124.2		8	11.4	even	5
605.2.j.a.124.2		8	55.29	odd	10
605.2.j.a.444.1		8	11.5	even	5
605.2.j.a.444.1		8	55.39	odd	10
605.2.j.a.444.2		8	11.6	odd	10
605.2.j.a.444.2		8	55.49	even	10
605.2.j.c.9.1		8	11.9	even	5	inner
605.2.j.c.9.1		8	55.24	odd	10	inner
605.2.j.c.9.2		8	11.2	odd	10	inner
605.2.j.c.9.2		8	55.9	even	10	inner
605.2.j.c.269.1		8	5.4	even	2	inner
605.2.j.c.269.1		8	11.10	odd	2	inner
605.2.j.c.269.2		8	1.1	even	1	trivial
605.2.j.c.269.2		8	55.54	odd	2	CM
3025.2.a.bb.1.1		4	55.3	odd	20
3025.2.a.bb.1.1		4	55.52	even	20
3025.2.a.bb.1.4		4	55.8	even	20
3025.2.a.bb.1.4		4	55.47	odd	20

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.j (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.37499 - 0.771681i) q^{2} +(3.42705 - 2.48990i) q^{4} +(0.690983 - 2.12663i) q^{5} +(1.81433 + 2.49721i) q^{7} +(3.28216 - 4.51750i) q^{8} +(0.927051 + 2.85317i) q^{9} +O(q^{10})\)	\(q+(2.37499 - 0.771681i) q^{2} +(3.42705 - 2.48990i) q^{4} +(0.690983 - 2.12663i) q^{5} +(1.81433 + 2.49721i) q^{7} +(3.28216 - 4.51750i) q^{8} +(0.927051 + 2.85317i) q^{9} -5.58394i q^{10} +(-1.81433 + 0.589512i) q^{13} +(6.23607 + 4.53077i) q^{14} +(1.69098 - 5.20431i) q^{16} +(-7.68563 - 2.49721i) q^{17} +(4.40347 + 6.06086i) q^{18} +(-2.92705 - 9.00854i) q^{20} +(-4.04508 - 2.93893i) q^{25} +(-3.85410 + 2.80017i) q^{26} +(12.4356 + 4.04057i) q^{28} +(-2.76393 - 8.50651i) q^{31} -2.49721i q^{32} -20.1803 q^{34} +(6.56431 - 2.13287i) q^{35} +(10.2812 + 7.46969i) q^{36} +(-7.33912 - 10.1014i) q^{40} +13.0756i q^{43} +6.70820 q^{45} +(-0.781153 + 2.40414i) q^{49} +(-11.8749 - 3.85840i) q^{50} +(-4.74998 + 6.53779i) q^{52} +17.2361 q^{56} +(3.23607 - 2.35114i) q^{59} +(-13.1286 - 18.0700i) q^{62} +(-5.44299 + 7.49164i) q^{63} +(1.45492 + 4.47777i) q^{64} +4.26575i q^{65} +(-32.5568 + 10.5784i) q^{68} +(13.9443 - 10.1311i) q^{70} +(2.47214 - 7.60845i) q^{71} +(15.9319 + 5.17659i) q^{72} +(6.99262 + 9.62451i) q^{73} +(-9.89919 - 7.19218i) q^{80} +(-7.28115 + 5.29007i) q^{81} +(0.693013 + 0.225173i) q^{83} +(-10.6213 + 14.6189i) q^{85} +(10.0902 + 31.0543i) q^{86} +13.4164 q^{89} +(15.9319 - 5.17659i) q^{90} +(-4.76393 - 3.46120i) q^{91} +6.31261i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 14 q^{4} + 10 q^{5} - 6 q^{9}+O(q^{10}) \) 8 * q + 14 * q^4 + 10 * q^5 - 6 * q^9	\( 8 q + 14 q^{4} + 10 q^{5} - 6 q^{9} + 32 q^{14} + 18 q^{16} - 10 q^{20} - 10 q^{25} - 4 q^{26} - 40 q^{31} - 72 q^{34} + 42 q^{36} + 34 q^{49} + 120 q^{56} + 8 q^{59} + 34 q^{64} + 40 q^{70} - 16 q^{71} - 30 q^{80} - 18 q^{81} + 36 q^{86} - 56 q^{91}+O(q^{100}) \) 8 * q + 14 * q^4 + 10 * q^5 - 6 * q^9 + 32 * q^14 + 18 * q^16 - 10 * q^20 - 10 * q^25 - 4 * q^26 - 40 * q^31 - 72 * q^34 + 42 * q^36 + 34 * q^49 + 120 * q^56 + 8 * q^59 + 34 * q^64 + 40 * q^70 - 16 * q^71 - 30 * q^80 - 18 * q^81 + 36 * q^86 - 56 * q^91

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