LMFDB - Embedded newform 425.2.c.b.424.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(424,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("425.424");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.c (of order $2$, degree $1$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			424.1
Root			$-0.854638 - 0.854638i$ of defining polynomial
Character	$\chi$	$=$	425.424
Dual form			425.2.c.b.424.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.17009i q^{2} -0.539189 q^{3} -2.70928 q^{4} +1.17009i q^{6} +4.87936 q^{7} +1.53919i q^{8} -2.70928 q^{9} -3.17009i q^{11} +1.46081 q^{12} -2.63090i q^{13} -10.5886i q^{14} -2.07838 q^{16} +(-2.53919 - 3.24846i) q^{17} +5.87936i q^{18} -1.07838 q^{19} -2.63090 q^{21} -6.87936 q^{22} +5.21953 q^{23} -0.829914i q^{24} -5.70928 q^{26} +3.07838 q^{27} -13.2195 q^{28} +2.92162i q^{29} +4.09171i q^{31} +7.58864i q^{32} +1.70928i q^{33} +(-7.04945 + 5.51026i) q^{34} +7.34017 q^{36} -5.26180 q^{37} +2.34017i q^{38} +1.41855i q^{39} -5.60197i q^{41} +5.70928i q^{42} -3.36910i q^{43} +8.58864i q^{44} -11.3268i q^{46} -6.78765i q^{47} +1.12064 q^{48} +16.8082 q^{49} +(1.36910 + 1.75154i) q^{51} +7.12783i q^{52} -3.75872i q^{53} -6.68035i q^{54} +7.51026i q^{56} +0.581449 q^{57} +6.34017 q^{58} +2.34017 q^{59} +12.2557i q^{61} +8.87936 q^{62} -13.2195 q^{63} +12.3112 q^{64} +3.70928 q^{66} +10.2062i q^{67} +(6.87936 + 8.80098i) q^{68} -2.81432 q^{69} +4.06505i q^{71} -4.17009i q^{72} +11.0784 q^{73} +11.4186i q^{74} +2.92162 q^{76} -15.4680i q^{77} +3.07838 q^{78} -6.92881i q^{79} +6.46800 q^{81} -12.1568 q^{82} -8.23287i q^{83} +7.12783 q^{84} -7.31124 q^{86} -1.57531i q^{87} +4.87936 q^{88} -7.15449 q^{89} -12.8371i q^{91} -14.1412 q^{92} -2.20620i q^{93} -14.7298 q^{94} -4.09171i q^{96} +8.18342 q^{97} -36.4752i q^{98} +8.58864i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{4} + 4 q^{7} - 2 q^{9} + 12 q^{12} - 6 q^{16} - 12 q^{17} - 8 q^{21} - 16 q^{22} - 16 q^{23} - 20 q^{26} + 12 q^{27} - 32 q^{28} - 6 q^{34} + 22 q^{36} - 16 q^{37} + 32 q^{48} + 14 q^{49} + 16 q^{51}+ \cdots + 40 q^{97}+O(q^{100}) $ 6 * q - 2 * q^4 + 4 * q^7 - 2 * q^9 + 12 * q^12 - 6 * q^16 - 12 * q^17 - 8 * q^21 - 16 * q^22 - 16 * q^23 - 20 * q^26 + 12 * q^27 - 32 * q^28 - 6 * q^34 + 22 * q^36 - 16 * q^37 + 32 * q^48 + 14 * q^49 + 16 * q^51 + 32 * q^57 + 16 * q^58 - 8 * q^59 + 28 * q^62 - 32 * q^63 + 22 * q^64 + 8 * q^66 + 16 * q^68 + 60 * q^73 + 24 * q^76 + 12 * q^78 - 26 * q^81 - 60 * q^82 + 8 * q^86 + 4 * q^88 - 4 * q^89 - 44 * q^92 - 8 * q^94 + 40 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	2.17009i		−	1.53448i	−0.641358	−	0.767241i	$-0.721629\pi$
$2$		−	2.17009i		−	1.53448i	0.641358	−	0.767241i	$-0.278371\pi$
$3$	−0.539189			−0.311301			−0.155650	−	0.987812i	$-0.549747\pi$
$3$	−0.539189			−0.311301			−0.155650	+	0.987812i	$0.549747\pi$
$4$	−2.70928			−1.35464
$5$		0			0
$5$		0			0
$6$			1.17009i			0.477686i
$7$	4.87936			1.84423			0.922113	−	0.386921i	$-0.126462\pi$
$7$	4.87936			1.84423			0.922113	+	0.386921i	$0.126462\pi$
$8$			1.53919i			0.544185i
$9$	−2.70928			−0.903092
$10$		0			0
$11$		−	3.17009i		−	0.955817i	−0.878410	−	0.477909i	$-0.841395\pi$
$11$		−	3.17009i		−	0.955817i	0.878410	−	0.477909i	$-0.158605\pi$
$12$	1.46081			0.421700
$13$		−	2.63090i		−	0.729680i	−0.931070	−	0.364840i	$-0.881124\pi$
$13$		−	2.63090i		−	0.729680i	0.931070	−	0.364840i	$-0.118876\pi$
$14$		−	10.5886i		−	2.82993i
$15$		0			0
$16$	−2.07838			−0.519594
$17$	−2.53919	−	3.24846i	−0.615844	−	0.787868i
$17$	−2.53919	−	3.24846i	−0.615844	−	0.787868i
$18$			5.87936i			1.38578i
$19$	−1.07838			−0.247397			−0.123698	−	0.992320i	$-0.539476\pi$
$19$	−1.07838			−0.247397			−0.123698	+	0.992320i	$0.539476\pi$
$20$		0			0
$21$	−2.63090			−0.574109
$22$	−6.87936			−1.46668
$23$	5.21953			1.08835			0.544174	−	0.838972i	$-0.316843\pi$
$23$	5.21953			1.08835			0.544174	+	0.838972i	$0.316843\pi$
$24$		−	0.829914i		−	0.169405i
$25$		0			0
$26$	−5.70928			−1.11968
$27$	3.07838			0.592434
$28$	−13.2195			−2.49826
$29$			2.92162i			0.542532i	0.962504	+	0.271266i	$0.0874422\pi$
$29$			2.92162i			0.542532i	−0.962504	+	0.271266i	$0.912558\pi$
$30$		0			0
$31$			4.09171i			0.734893i	0.930045	+	0.367446i	$0.119768\pi$
$31$			4.09171i			0.734893i	−0.930045	+	0.367446i	$0.880232\pi$
$32$			7.58864i			1.34149i
$33$			1.70928i			0.297547i
$34$	−7.04945	+	5.51026i	−1.20897	+	0.945002i
$35$		0			0
$36$	7.34017			1.22336
$37$	−5.26180			−0.865034			−0.432517	−	0.901626i	$-0.642374\pi$
$37$	−5.26180			−0.865034			−0.432517	+	0.901626i	$0.642374\pi$
$38$			2.34017i			0.379626i
$39$			1.41855i			0.227150i
$40$		0			0
$41$		−	5.60197i		−	0.874880i	−0.899247	−	0.437440i	$-0.855885\pi$
$41$		−	5.60197i		−	0.874880i	0.899247	−	0.437440i	$-0.144115\pi$
$42$			5.70928i			0.880960i
$43$		−	3.36910i		−	0.513783i	−0.966440	−	0.256892i	$-0.917302\pi$
$43$		−	3.36910i		−	0.513783i	0.966440	−	0.256892i	$-0.0826984\pi$
$44$			8.58864i			1.29479i
$45$		0			0
$46$		−	11.3268i		−	1.67005i
$47$		−	6.78765i		−	0.990081i	−0.868870	−	0.495040i	$-0.835153\pi$
$47$		−	6.78765i		−	0.990081i	0.868870	−	0.495040i	$-0.164847\pi$
$48$	1.12064			0.161750
$49$	16.8082			2.40117
$50$		0			0
$51$	1.36910	+	1.75154i	0.191713	+	0.245264i
$52$			7.12783i			0.988452i
$53$		−	3.75872i		−	0.516300i	−0.966105	−	0.258150i	$-0.916887\pi$
$53$		−	3.75872i		−	0.516300i	0.966105	−	0.258150i	$-0.0831129\pi$
$54$		−	6.68035i		−	0.909080i
$55$		0			0
$56$			7.51026i			1.00360i
$57$	0.581449			0.0770148
$58$	6.34017			0.832505
$59$	2.34017			0.304665			0.152332	−	0.988329i	$-0.451322\pi$
$59$	2.34017			0.304665			0.152332	+	0.988329i	$0.451322\pi$
$60$		0			0
$61$			12.2557i			1.56918i	0.620018	+	0.784588i	$0.287125\pi$
$61$			12.2557i			1.56918i	−0.620018	+	0.784588i	$0.712875\pi$
$62$	8.87936			1.12768
$63$	−13.2195			−1.66550
$64$	12.3112			1.53891
$65$		0			0
$66$	3.70928			0.456580
$67$			10.2062i			1.24689i	0.781869	+	0.623443i	$0.214267\pi$
$67$			10.2062i			1.24689i	−0.781869	+	0.623443i	$0.785733\pi$
$68$	6.87936	+	8.80098i	0.834245	+	1.06728i
$69$	−2.81432			−0.338804
$70$		0			0
$71$			4.06505i			0.482432i	0.970471	+	0.241216i	$0.0775463\pi$
$71$			4.06505i			0.482432i	−0.970471	+	0.241216i	$0.922454\pi$
$72$		−	4.17009i		−	0.491449i
$73$	11.0784			1.29663			0.648313	−	0.761374i	$-0.275475\pi$
$73$	11.0784			1.29663			0.648313	+	0.761374i	$0.275475\pi$
$74$			11.4186i			1.32738i
$75$		0			0
$76$	2.92162			0.335133
$77$		−	15.4680i		−	1.76274i
$78$	3.07838			0.348558
$79$		−	6.92881i		−	0.779552i	−0.920910	−	0.389776i	$-0.872552\pi$
$79$		−	6.92881i		−	0.779552i	0.920910	−	0.389776i	$-0.127448\pi$
$80$		0			0
$81$	6.46800			0.718667
$82$	−12.1568			−1.34249
$83$		−	8.23287i		−	0.903674i	−0.892100	−	0.451837i	$-0.850769\pi$
$83$		−	8.23287i		−	0.903674i	0.892100	−	0.451837i	$-0.149231\pi$
$84$	7.12783			0.777710
$85$		0			0
$86$	−7.31124			−0.788392
$87$		−	1.57531i		−	0.168891i
$88$	4.87936			0.520142
$89$	−7.15449			−0.758374			−0.379187	−	0.925320i	$-0.623796\pi$
$89$	−7.15449			−0.758374			−0.379187	+	0.925320i	$0.623796\pi$
$90$		0			0
$91$		−	12.8371i		−	1.34569i
$92$	−14.1412			−1.47432
$93$		−	2.20620i		−	0.228773i
$94$	−14.7298			−1.51926
$95$		0			0
$96$		−	4.09171i		−	0.417608i
$97$	8.18342			0.830900			0.415450	−	0.909616i	$-0.363624\pi$
$97$	8.18342			0.830900			0.415450	+	0.909616i	$0.363624\pi$
$98$		−	36.4752i		−	3.68455i
$99$			8.58864i			0.863191i
$100$		0			0
$101$	−2.47414			−0.246186			−0.123093	−	0.992395i	$-0.539281\pi$
$101$	−2.47414			−0.246186			−0.123093	+	0.992395i	$0.539281\pi$
$102$	3.80098	−	2.97107i	0.376354	−	0.294180i
$103$			19.6514i			1.93631i	0.250348	+	0.968156i	$0.419455\pi$
$103$			19.6514i			1.93631i	−0.250348	+	0.968156i	$0.580545\pi$
$104$	4.04945			0.397081
$105$		0			0
$106$	−8.15676			−0.792254
$107$	12.6381			1.22177			0.610885	−	0.791719i	$-0.290814\pi$
$107$	12.6381			1.22177			0.610885	+	0.791719i	$0.290814\pi$
$108$	−8.34017			−0.802534
$109$			8.15676i			0.781275i	0.920544	+	0.390638i	$0.127745\pi$
$109$			8.15676i			0.781275i	−0.920544	+	0.390638i	$0.872255\pi$
$110$		0			0
$111$	2.83710			0.269286
$112$	−10.1412			−0.958249
$113$	17.0205			1.60116			0.800578	−	0.599229i	$-0.204526\pi$
$113$	17.0205			1.60116			0.800578	+	0.599229i	$0.204526\pi$
$114$		−	1.26180i		−	0.118178i
$115$		0			0
$116$		−	7.91548i		−	0.734934i
$117$			7.12783i			0.658968i
$118$		−	5.07838i		−	0.467503i
$119$	−12.3896	−	15.8504i	−1.13575	−	1.45301i
$120$		0			0
$121$	0.950552			0.0864138
$122$	26.5958			2.40787
$123$			3.02052i			0.272351i
$124$		−	11.0856i		−	0.995513i
$125$		0			0
$126$			28.6875i			2.55569i
$127$		−	8.04945i		−	0.714273i	−0.934052	−	0.357137i	$-0.883753\pi$
$127$		−	8.04945i		−	0.714273i	0.934052	−	0.357137i	$-0.116247\pi$
$128$		−	11.5392i		−	1.01993i
$129$			1.81658i			0.159941i
$130$		0			0
$131$			11.6937i			1.02168i	0.859675	+	0.510841i	$0.170666\pi$
$131$			11.6937i			1.02168i	−0.859675	+	0.510841i	$0.829334\pi$
$132$		−	4.63090i		−	0.403068i
$133$	−5.26180			−0.456256
$134$	22.1483			1.91333
$135$		0			0
$136$	5.00000	−	3.90829i	0.428746	−	0.335133i
$137$			1.95055i			0.166647i	0.996523	+	0.0833234i	$0.0265535\pi$
$137$			1.95055i			0.166647i	−0.996523	+	0.0833234i	$0.973447\pi$
$138$			6.10731i			0.519889i
$139$			2.00719i			0.170247i	0.996370	+	0.0851237i	$0.0271286\pi$
$139$			2.00719i			0.170247i	−0.996370	+	0.0851237i	$0.972871\pi$
$140$		0			0
$141$			3.65983i			0.308213i
$142$	8.82150			0.740284
$143$	−8.34017			−0.697440
$144$	5.63090			0.469241
$145$		0			0
$146$		−	24.0410i		−	1.98965i
$147$	−9.06278			−0.747485
$148$	14.2557			1.17181
$149$	14.2823			1.17005			0.585026	−	0.811014i	$-0.301084\pi$
$149$	14.2823			1.17005			0.585026	+	0.811014i	$0.301084\pi$
$150$		0			0
$151$	12.8638			1.04684			0.523419	−	0.852075i	$-0.324656\pi$
$151$	12.8638			1.04684			0.523419	+	0.852075i	$0.324656\pi$
$152$		−	1.65983i		−	0.134630i
$153$	6.87936	+	8.80098i	0.556163	+	0.711517i
$154$	−33.5669			−2.70490
$155$		0			0
$156$		−	3.84324i		−	0.307706i
$157$			3.75872i			0.299979i	0.988688	+	0.149989i	$0.0479240\pi$
$157$			3.75872i			0.299979i	−0.988688	+	0.149989i	$0.952076\pi$
$158$	−15.0361			−1.19621
$159$			2.02666i			0.160725i
$160$		0			0
$161$	25.4680			2.00716
$162$		−	14.0361i		−	1.10278i
$163$	−8.69594			−0.681119			−0.340559	−	0.940223i	$-0.610616\pi$
$163$	−8.69594			−0.681119			−0.340559	+	0.940223i	$0.610616\pi$
$164$			15.1773i			1.18515i
$165$		0			0
$166$	−17.8660			−1.38667
$167$	−1.37629			−0.106501			−0.0532503	−	0.998581i	$-0.516958\pi$
$167$	−1.37629			−0.106501			−0.0532503	+	0.998581i	$0.516958\pi$
$168$		−	4.04945i		−	0.312422i
$169$	6.07838			0.467568
$170$		0			0
$171$	2.92162			0.223422
$172$			9.12783i			0.695990i
$173$	−17.3607			−1.31991			−0.659954	−	0.751306i	$-0.729424\pi$
$173$	−17.3607			−1.31991			−0.659954	+	0.751306i	$0.729424\pi$
$174$	−3.41855			−0.259160
$175$		0			0
$176$			6.58864i			0.496637i
$177$	−1.26180			−0.0948423
$178$			15.5259i			1.16371i
$179$	−6.83710			−0.511029			−0.255514	−	0.966805i	$-0.582245\pi$
$179$	−6.83710			−0.511029			−0.255514	+	0.966805i	$0.582245\pi$
$180$		0			0
$181$			15.0205i			1.11647i	0.829684	+	0.558233i	$0.188521\pi$
$181$			15.0205i			1.11647i	−0.829684	+	0.558233i	$0.811479\pi$
$182$	−27.8576			−2.06494
$183$		−	6.60811i		−	0.488486i
$184$			8.03385i			0.592263i
$185$		0			0
$186$	−4.78765			−0.351048
$187$	−10.2979	+	8.04945i	−0.753058	+	0.588634i
$188$			18.3896i			1.34120i
$189$	15.0205			1.09258
$190$		0			0
$191$	−24.2823			−1.75701			−0.878503	−	0.477736i	$-0.841457\pi$
$191$	−24.2823			−1.75701			−0.878503	+	0.477736i	$0.841457\pi$
$192$	−6.63809			−0.479063
$193$	−11.8576			−0.853530			−0.426765	−	0.904363i	$-0.640347\pi$
$193$	−11.8576			−0.853530			−0.426765	+	0.904363i	$0.640347\pi$
$194$		−	17.7587i		−	1.27500i
$195$		0			0
$196$	−45.5380			−3.25271
$197$	18.2557			1.30066			0.650331	−	0.759651i	$-0.274630\pi$
$197$	18.2557			1.30066			0.650331	+	0.759651i	$0.274630\pi$
$198$	18.6381			1.32455
$199$		−	3.72487i		−	0.264049i	−0.991246	−	0.132025i	$-0.957852\pi$
$199$		−	3.72487i		−	0.264049i	0.991246	−	0.132025i	$-0.0421478\pi$
$200$		0			0
$201$		−	5.50307i		−	0.388157i
$202$			5.36910i			0.377769i
$203$			14.2557i			1.00055i
$204$	−3.70928	−	4.74539i	−0.259701	−	0.332244i
$205$		0			0
$206$	42.6453			2.97124
$207$	−14.1412			−0.982878
$208$			5.46800i			0.379138i
$209$			3.41855i			0.236466i
$210$		0			0
$211$		−	22.2485i		−	1.53165i	−0.643051	−	0.765824i	$-0.722332\pi$
$211$		−	22.2485i		−	1.53165i	0.643051	−	0.765824i	$-0.277668\pi$
$212$			10.1834i			0.699400i
$213$		−	2.19183i		−	0.150182i
$214$		−	27.4257i		−	1.87478i
$215$		0			0
$216$			4.73820i			0.322394i
$217$			19.9649i			1.35531i
$218$	17.7009			1.19885
$219$	−5.97334			−0.403641
$220$		0			0
$221$	−8.54638	+	6.68035i	−0.574892	+	0.449369i
$222$		−	6.15676i		−	0.413214i
$223$			2.19183i			0.146776i	0.997303	+	0.0733878i	$0.0233811\pi$
$223$			2.19183i			0.146776i	−0.997303	+	0.0733878i	$0.976619\pi$
$224$			37.0277i			2.47402i
$225$		0			0
$226$		−	36.9360i		−	2.45695i
$227$	−9.55971			−0.634500			−0.317250	−	0.948342i	$-0.602759\pi$
$227$	−9.55971			−0.634500			−0.317250	+	0.948342i	$0.602759\pi$
$228$	−1.57531			−0.104327
$229$	−7.36910			−0.486964			−0.243482	−	0.969905i	$-0.578290\pi$
$229$	−7.36910			−0.486964			−0.243482	+	0.969905i	$0.578290\pi$
$230$		0			0
$231$			8.34017i			0.548743i
$232$	−4.49693			−0.295238
$233$	9.44521			0.618776			0.309388	−	0.950936i	$-0.399876\pi$
$233$	9.44521			0.618776			0.309388	+	0.950936i	$0.399876\pi$
$234$	15.4680			1.01117
$235$		0			0
$236$	−6.34017			−0.412710
$237$			3.73594i			0.242675i
$238$	−34.3968	+	26.8865i	−2.22961	+	1.74280i
$239$	−6.25565			−0.404644			−0.202322	−	0.979319i	$-0.564849\pi$
$239$	−6.25565			−0.404644			−0.202322	+	0.979319i	$0.564849\pi$
$240$		0			0
$241$		−	2.49693i		−	0.160841i	−0.996761	−	0.0804207i	$-0.974374\pi$
$241$		−	2.49693i		−	0.160841i	0.996761	−	0.0804207i	$-0.0256264\pi$
$242$		−	2.06278i		−	0.132600i
$243$	−12.7226			−0.816156
$244$		−	33.2039i		−	2.12566i
$245$		0			0
$246$	6.55479			0.417918
$247$			2.83710i			0.180520i
$248$	−6.29791			−0.399918
$249$			4.43907i			0.281315i
$250$		0			0
$251$	−11.8166			−0.745856			−0.372928	−	0.927860i	$-0.621646\pi$
$251$	−11.8166			−0.745856			−0.372928	+	0.927860i	$0.621646\pi$
$252$	35.8154			2.25616
$253$		−	16.5464i		−	1.04026i
$254$	−17.4680			−1.09604
$255$		0			0
$256$	−0.418551			−0.0261594
$257$			14.9444i			0.932207i	0.884730	+	0.466103i	$0.154342\pi$
$257$			14.9444i			0.932207i	−0.884730	+	0.466103i	$0.845658\pi$
$258$	3.94214			0.245427
$259$	−25.6742			−1.59532
$260$		0			0
$261$		−	7.91548i		−	0.489956i
$262$	25.3763			1.56775
$263$			12.9444i			0.798186i	0.916910	+	0.399093i	$0.130675\pi$
$263$			12.9444i			0.798186i	−0.916910	+	0.399093i	$0.869325\pi$
$264$	−2.63090			−0.161921
$265$		0			0
$266$			11.4186i			0.700116i
$267$	3.85762			0.236083
$268$		−	27.6514i		−	1.68908i
$269$			7.47641i			0.455845i	0.973679	+	0.227922i	$0.0731932\pi$
$269$			7.47641i			0.455845i	−0.973679	+	0.227922i	$0.926807\pi$
$270$		0			0
$271$	−2.15676			−0.131014			−0.0655068	−	0.997852i	$-0.520866\pi$
$271$	−2.15676			−0.131014			−0.0655068	+	0.997852i	$0.520866\pi$
$272$	5.27739	+	6.75154i	0.319989	+	0.409372i
$273$			6.92162i			0.418916i
$274$	4.23287			0.255717
$275$		0			0
$276$	7.62475			0.458956
$277$	−12.1568			−0.730429			−0.365214	−	0.930923i	$-0.619004\pi$
$277$	−12.1568			−0.730429			−0.365214	+	0.930923i	$0.619004\pi$
$278$	4.35577			0.261242
$279$		−	11.0856i		−	0.663675i
$280$		0			0
$281$	13.1194			0.782639			0.391319	−	0.920255i	$-0.372019\pi$
$281$	13.1194			0.782639			0.391319	+	0.920255i	$0.372019\pi$
$282$	7.94214			0.472948
$283$	−13.9577			−0.829701			−0.414851	−	0.909889i	$-0.636166\pi$
$283$	−13.9577			−0.829701			−0.414851	+	0.909889i	$0.636166\pi$
$284$		−	11.0133i		−	0.653521i
$285$		0			0
$286$			18.0989i			1.07021i
$287$		−	27.3340i		−	1.61348i
$288$		−	20.5597i		−	1.21149i
$289$	−4.10504	+	16.4969i	−0.241473	+	0.970408i
$290$		0			0
$291$	−4.41241			−0.258660
$292$	−30.0144			−1.75646
$293$		−	4.73820i		−	0.276809i	−0.990376	−	0.138404i	$-0.955803\pi$
$293$		−	4.73820i		−	0.276809i	0.990376	−	0.138404i	$-0.0441974\pi$
$294$			19.6670i			1.14700i
$295$		0			0
$296$		−	8.09890i		−	0.470739i
$297$		−	9.75872i		−	0.566259i
$298$		−	30.9939i		−	1.79543i
$299$		−	13.7321i		−	0.794146i
$300$		0			0
$301$		−	16.4391i		−	0.947532i
$302$		−	27.9155i		−	1.60636i
$303$	1.33403			0.0766380
$304$	2.24128			0.128546
$305$		0			0
$306$	19.0989	−	14.9288i	1.09181	−	0.853423i
$307$		−	21.5936i		−	1.23241i	−0.787586	−	0.616205i	$-0.788669\pi$
$307$		−	21.5936i		−	1.23241i	0.787586	−	0.616205i	$-0.211331\pi$
$308$			41.9071i			2.38788i
$309$		−	10.5958i		−	0.602775i
$310$		0			0
$311$			24.2628i			1.37582i	0.725796	+	0.687910i	$0.241472\pi$
$311$			24.2628i			1.37582i	−0.725796	+	0.687910i	$0.758528\pi$
$312$	−2.18342			−0.123612
$313$	4.07223			0.230176			0.115088	−	0.993355i	$-0.463285\pi$
$313$	4.07223			0.230176			0.115088	+	0.993355i	$0.463285\pi$
$314$	8.15676			0.460312
$315$		0			0
$316$			18.7721i			1.05601i
$317$	−8.05786			−0.452574			−0.226287	−	0.974061i	$-0.572659\pi$
$317$	−8.05786			−0.452574			−0.226287	+	0.974061i	$0.572659\pi$
$318$	4.39803			0.246629
$319$	9.26180			0.518561
$320$		0			0
$321$	−6.81432			−0.380338
$322$		−	55.2678i		−	3.07995i
$323$	2.73820	+	3.50307i	0.152358	+	0.194916i
$324$	−17.5236			−0.973533
$325$		0			0
$326$			18.8710i			1.04517i
$327$		−	4.39803i		−	0.243212i
$328$	8.62249			0.476097
$329$		−	33.1194i		−	1.82593i
$330$		0			0
$331$	−10.0722			−0.553620			−0.276810	−	0.960925i	$-0.589277\pi$
$331$	−10.0722			−0.553620			−0.276810	+	0.960925i	$0.589277\pi$
$332$			22.3051i			1.22415i
$333$	14.2557			0.781205
$334$			2.98667i			0.163423i
$335$		0			0
$336$	5.46800			0.298304
$337$	11.2351			0.612017			0.306008	−	0.952029i	$-0.401006\pi$
$337$	11.2351			0.612017			0.306008	+	0.952029i	$0.401006\pi$
$338$		−	13.1906i		−	0.717474i
$339$	−9.17727			−0.498441
$340$		0			0
$341$	12.9711			0.702423
$342$		−	6.34017i		−	0.342837i
$343$	47.8576			2.58407
$344$	5.18568			0.279593
$345$		0			0
$346$			37.6742i			2.02538i
$347$	8.74927			0.469685			0.234843	−	0.972033i	$-0.424543\pi$
$347$	8.74927			0.469685			0.234843	+	0.972033i	$0.424543\pi$
$348$			4.26794i			0.228786i
$349$	26.9093			1.44042			0.720212	−	0.693754i	$-0.244045\pi$
$349$	26.9093			1.44042			0.720212	+	0.693754i	$0.244045\pi$
$350$		0			0
$351$		−	8.09890i		−	0.432287i
$352$	24.0566			1.28222
$353$		−	18.3135i		−	0.974730i	−0.873198	−	0.487365i	$-0.837958\pi$
$353$		−	18.3135i		−	0.974730i	0.873198	−	0.487365i	$-0.162042\pi$
$354$			2.73820i			0.145534i
$355$		0			0
$356$	19.3835			1.02732
$357$	6.68035	+	8.54638i	0.353561	+	0.452322i
$358$			14.8371i			0.784165i
$359$	9.57531			0.505365			0.252683	−	0.967549i	$-0.418687\pi$
$359$	9.57531			0.505365			0.252683	+	0.967549i	$0.418687\pi$
$360$		0			0
$361$	−17.8371			−0.938795
$362$	32.5958			1.71320
$363$	−0.512527			−0.0269007
$364$			34.7792i			1.82293i
$365$		0			0
$366$	−14.3402			−0.749573
$367$	−12.1145			−0.632371			−0.316186	−	0.948697i	$-0.602402\pi$
$367$	−12.1145			−0.632371			−0.316186	+	0.948697i	$0.602402\pi$
$368$	−10.8482			−0.565500
$369$			15.1773i			0.790097i
$370$		0			0
$371$		−	18.3402i		−	0.952174i
$372$			5.97721i			0.309904i
$373$		−	30.4619i		−	1.57726i	−0.614871	−	0.788628i	$-0.710792\pi$
$373$		−	30.4619i		−	1.57726i	0.614871	−	0.788628i	$-0.289208\pi$
$374$	17.4680	+	22.3474i	0.903249	+	1.15555i
$375$		0			0
$376$	10.4475			0.538788
$377$	7.68649			0.395874
$378$		−	32.5958i		−	1.67655i
$379$			0.986669i			0.0506818i	0.999679	+	0.0253409i	$0.00806712\pi$
$379$			0.986669i			0.0506818i	−0.999679	+	0.0253409i	$0.991933\pi$
$380$		0			0
$381$			4.34017i			0.222354i
$382$			52.6947i			2.69610i
$383$			24.9588i			1.27533i	0.770312	+	0.637667i	$0.220100\pi$
$383$			24.9588i			1.27533i	−0.770312	+	0.637667i	$0.779900\pi$
$384$			6.22180i			0.317505i
$385$		0			0
$386$			25.7321i			1.30973i
$387$			9.12783i			0.463993i
$388$	−22.1711			−1.12557
$389$	−33.8082			−1.71414			−0.857071	−	0.515198i	$-0.827718\pi$
$389$	−33.8082			−1.71414			−0.857071	+	0.515198i	$0.827718\pi$
$390$		0			0
$391$	−13.2534	−	16.9555i	−0.670252	−	0.857475i
$392$			25.8710i			1.30668i
$393$		−	6.30510i		−	0.318050i
$394$		−	39.6163i		−	1.99584i
$395$		0			0
$396$		−	23.2690i		−	1.16931i
$397$	−28.5236			−1.43156			−0.715779	−	0.698327i	$-0.753928\pi$
$397$	−28.5236			−1.43156			−0.715779	+	0.698327i	$0.753928\pi$
$398$	−8.08330			−0.405179
$399$	2.83710			0.142033
$400$		0			0
$401$		−	33.0928i		−	1.65257i	−0.563250	−	0.826287i	$-0.690449\pi$
$401$		−	33.0928i		−	1.65257i	0.563250	−	0.826287i	$-0.309551\pi$
$402$	−11.9421			−0.595620
$403$	10.7649			0.536236
$404$	6.70313			0.333493
$405$		0			0
$406$	30.9360			1.53533
$407$			16.6803i			0.826814i
$408$	−2.69594	+	2.10731i	−0.133469	+	0.104327i
$409$	30.1978			1.49318			0.746592	−	0.665282i	$-0.231689\pi$
$409$	30.1978			1.49318			0.746592	+	0.665282i	$0.231689\pi$
$410$		0			0
$411$		−	1.05172i		−	0.0518773i
$412$		−	53.2411i		−	2.62300i
$413$	11.4186			0.561870
$414$			30.6875i			1.50821i
$415$		0			0
$416$	19.9649			0.978861
$417$		−	1.08225i		−	0.0529982i
$418$	7.41855			0.362853
$419$		−	18.1639i		−	0.887367i	−0.896184	−	0.443683i	$-0.853671\pi$
$419$		−	18.1639i		−	0.887367i	0.896184	−	0.443683i	$-0.146329\pi$
$420$		0			0
$421$	0.760991			0.0370884			0.0185442	−	0.999828i	$-0.494097\pi$
$421$	0.760991			0.0370884			0.0185442	+	0.999828i	$0.494097\pi$
$422$	−48.2811			−2.35029
$423$			18.3896i			0.894134i
$424$	5.78539			0.280963
$425$		0			0
$426$	−4.75646			−0.230451
$427$			59.7998i			2.89391i
$428$	−34.2401			−1.65506
$429$	4.49693			0.217114
$430$		0			0
$431$			6.34736i			0.305742i	0.988246	+	0.152871i	$0.0488518\pi$
$431$			6.34736i			0.305742i	−0.988246	+	0.152871i	$0.951148\pi$
$432$	−6.39803			−0.307825
$433$		−	3.62475i		−	0.174195i	−0.996200	−	0.0870973i	$-0.972241\pi$
$433$		−	3.62475i		−	0.174195i	0.996200	−	0.0870973i	$-0.0277591\pi$
$434$	43.3256			2.07970
$435$		0			0
$436$		−	22.0989i		−	1.05835i
$437$	−5.62863			−0.269254
$438$			12.9627i			0.619380i
$439$			6.40522i			0.305704i	0.988249	+	0.152852i	$0.0488459\pi$
$439$			6.40522i			0.305704i	−0.988249	+	0.152852i	$0.951154\pi$
$440$		0			0
$441$	−45.5380			−2.16847
$442$	14.4969	+	18.5464i	0.689549	+	0.882161i
$443$		−	27.4824i		−	1.30573i	−0.757476	−	0.652864i	$-0.773568\pi$
$443$		−	27.4824i		−	1.30573i	0.757476	−	0.652864i	$-0.226432\pi$
$444$	−7.68649			−0.364785
$445$		0			0
$446$	4.75646			0.225225
$447$	−7.70086			−0.364238
$448$	60.0710			2.83809
$449$			28.7526i			1.35692i	0.734638	+	0.678459i	$0.237352\pi$
$449$			28.7526i			1.35692i	−0.734638	+	0.678459i	$0.762648\pi$
$450$		0			0
$451$	−17.7587			−0.836226
$452$	−46.1133			−2.16899
$453$	−6.93600			−0.325882
$454$			20.7454i			0.973630i
$455$		0			0
$456$			0.894960i			0.0419104i
$457$		−	31.4101i		−	1.46930i	−0.678444	−	0.734652i	$-0.737345\pi$
$457$		−	31.4101i		−	1.46930i	0.678444	−	0.734652i	$-0.262655\pi$
$458$			15.9916i			0.747238i
$459$	−7.81658	−	10.0000i	−0.364847	−	0.466760i
$460$		0			0
$461$	−7.75872			−0.361360			−0.180680	−	0.983542i	$-0.557830\pi$
$461$	−7.75872			−0.361360			−0.180680	+	0.983542i	$0.557830\pi$
$462$	18.0989			0.842037
$463$		−	24.2329i		−	1.12620i	−0.826390	−	0.563098i	$-0.809609\pi$
$463$		−	24.2329i		−	1.12620i	0.826390	−	0.563098i	$-0.190391\pi$
$464$		−	6.07223i		−	0.281896i
$465$		0			0
$466$		−	20.4969i		−	0.949502i
$467$		−	12.3174i		−	0.569981i	−0.958530	−	0.284990i	$-0.908010\pi$
$467$		−	12.3174i		−	0.569981i	0.958530	−	0.284990i	$-0.0919904\pi$
$468$		−	19.3112i		−	0.892663i
$469$			49.7998i			2.29954i
$470$		0			0
$471$		−	2.02666i		−	0.0933837i
$472$			3.60197i			0.165794i
$473$	−10.6803			−0.491083
$474$	8.10731			0.372381
$475$		0			0
$476$	33.5669	+	42.9432i	1.53854	+	1.96830i
$477$			10.1834i			0.466267i
$478$			13.5753i			0.620920i
$479$		−	2.14957i		−	0.0982162i	−0.998793	−	0.0491081i	$-0.984362\pi$
$479$		−	2.14957i		−	0.0982162i	0.998793	−	0.0491081i	$-0.0156379\pi$
$480$		0			0
$481$			13.8432i			0.631198i
$482$	−5.41855			−0.246808
$483$	−13.7321			−0.624830
$484$	−2.57531			−0.117059
$485$		0			0
$486$			27.6092i			1.25238i
$487$	40.0833			1.81635			0.908174	−	0.418593i	$-0.137477\pi$
$487$	40.0833			1.81635			0.908174	+	0.418593i	$0.137477\pi$
$488$	−18.8638			−0.853922
$489$	4.68876			0.212033
$490$		0			0
$491$	−2.25565			−0.101796			−0.0508981	−	0.998704i	$-0.516208\pi$
$491$	−2.25565			−0.101796			−0.0508981	+	0.998704i	$0.516208\pi$
$492$		−	8.18342i		−	0.368937i
$493$	9.49079	−	7.41855i	0.427443	−	0.334115i
$494$	6.15676			0.277006
$495$		0			0
$496$		−	8.50412i		−	0.381846i
$497$			19.8348i			0.889714i
$498$	9.63317			0.431672
$499$			42.5452i			1.90458i	0.305190	+	0.952291i	$0.401280\pi$
$499$			42.5452i			1.90458i	−0.305190	+	0.952291i	$0.598720\pi$
$500$		0			0
$501$	0.742080			0.0331537
$502$			25.6430i			1.14450i
$503$	−9.55971			−0.426246			−0.213123	−	0.977025i	$-0.568364\pi$
$503$	−9.55971			−0.426246			−0.213123	+	0.977025i	$0.568364\pi$
$504$		−	20.3474i		−	0.906343i
$505$		0			0
$506$	−35.9071			−1.59626
$507$	−3.27739			−0.145554
$508$			21.8082i			0.967581i
$509$	−28.3545			−1.25679			−0.628397	−	0.777893i	$-0.716288\pi$
$509$	−28.3545			−1.25679			−0.628397	+	0.777893i	$0.716288\pi$
$510$		0			0
$511$	54.0554			2.39127
$512$		−	22.1701i		−	0.979789i
$513$	−3.31965			−0.146566
$514$	32.4307			1.43046
$515$		0			0
$516$		−	4.92162i		−	0.216662i
$517$	−21.5174			−0.946336
$518$			55.7152i			2.44799i
$519$	9.36069			0.410889
$520$		0			0
$521$			15.1050i			0.661764i	0.943672	+	0.330882i	$0.107346\pi$
$521$			15.1050i			0.661764i	−0.943672	+	0.330882i	$0.892654\pi$
$522$	−17.1773			−0.751829
$523$			10.8865i			0.476036i	0.971261	+	0.238018i	$0.0764977\pi$
$523$			10.8865i			0.476036i	−0.971261	+	0.238018i	$0.923502\pi$
$524$		−	31.6814i		−	1.38401i
$525$		0			0
$526$	28.0905			1.22480
$527$	13.2918	−	10.3896i	0.578999	−	0.452579i
$528$		−	3.55252i		−	0.154604i
$529$	4.24354			0.184502
$530$		0			0
$531$	−6.34017			−0.275140
$532$	14.2557			0.618061
$533$	−14.7382			−0.638383
$534$		−	8.37137i		−	0.362265i
$535$		0			0
$536$	−15.7093			−0.678537
$537$	3.68649			0.159084
$538$	16.2245			0.699486
$539$		−	53.2834i		−	2.29508i
$540$		0			0
$541$			6.86830i			0.295291i	0.989040	+	0.147646i	$0.0471695\pi$
$541$			6.86830i			0.295291i	−0.989040	+	0.147646i	$0.952830\pi$
$542$			4.68035i			0.201038i
$543$		−	8.09890i		−	0.347557i
$544$	24.6514	−	19.2690i	1.05692	−	0.826151i
$545$		0			0
$546$	15.0205			0.642819
$547$	5.89988			0.252261			0.126130	−	0.992014i	$-0.459744\pi$
$547$	5.89988			0.252261			0.126130	+	0.992014i	$0.459744\pi$
$548$		−	5.28458i		−	0.225746i
$549$		−	33.2039i		−	1.41711i
$550$		0			0
$551$		−	3.15061i		−	0.134221i
$552$		−	4.33176i		−	0.184372i
$553$		−	33.8082i		−	1.43767i
$554$			26.3812i			1.12083i
$555$		0			0
$556$		−	5.43802i		−	0.230624i
$557$		−	17.7359i		−	0.751496i	−0.926722	−	0.375748i	$-0.877386\pi$
$557$		−	17.7359i		−	0.751496i	0.926722	−	0.375748i	$-0.122614\pi$
$558$	−24.0566			−1.01840
$559$	−8.86376			−0.374897
$560$		0			0
$561$	5.55252	−	4.34017i	0.234428	−	0.183242i
$562$		−	28.4703i		−	1.20095i
$563$			38.8020i			1.63531i	0.575708	+	0.817655i	$0.304726\pi$
$563$			38.8020i			1.63531i	−0.575708	+	0.817655i	$0.695274\pi$
$564$		−	9.91548i		−	0.417517i
$565$		0			0
$566$			30.2895i			1.27316i
$567$	31.5597			1.32538
$568$	−6.25687			−0.262533
$569$	−12.1568			−0.509638			−0.254819	−	0.966989i	$-0.582016\pi$
$569$	−12.1568			−0.509638			−0.254819	+	0.966989i	$0.582016\pi$
$570$		0			0
$571$		−	15.4569i		−	0.646853i	−0.946253	−	0.323426i	$-0.895165\pi$
$571$		−	15.4569i		−	0.646853i	0.946253	−	0.323426i	$-0.104835\pi$
$572$	22.5958			0.944779
$573$	13.0928			0.546958
$574$	−59.3172			−2.47585
$575$		0			0
$576$	−33.3545			−1.38977
$577$		−	2.36296i		−	0.0983713i	−0.998790	−	0.0491856i	$-0.984337\pi$
$577$		−	2.36296i		−	0.0983713i	0.998790	−	0.0491856i	$-0.0156626\pi$
$578$	35.7998	+	8.90829i	1.48907	+	0.370536i
$579$	6.39350			0.265705
$580$		0			0
$581$		−	40.1711i		−	1.66658i
$582$			9.57531i			0.396909i
$583$	−11.9155			−0.493489
$584$			17.0517i			0.705605i
$585$		0			0
$586$	−10.2823			−0.424758
$587$		−	3.65142i		−	0.150710i	−0.997157	−	0.0753550i	$-0.975991\pi$
$587$		−	3.65142i		−	0.150710i	0.997157	−	0.0753550i	$-0.0240090\pi$
$588$	24.5536			1.01257
$589$		−	4.41241i		−	0.181810i
$590$		0			0
$591$	−9.84324			−0.404897
$592$	10.9360			0.449467
$593$			1.38735i			0.0569718i	0.999594	+	0.0284859i	$0.00906857\pi$
$593$			1.38735i			0.0569718i	−0.999594	+	0.0284859i	$0.990931\pi$
$594$	−21.1773			−0.868914
$595$		0			0
$596$	−38.6947			−1.58500
$597$			2.00841i			0.0821988i
$598$	−29.7998			−1.21860
$599$	0.451356			0.0184419			0.00922095	−	0.999957i	$-0.497065\pi$
$599$	0.451356			0.0184419			0.00922095	+	0.999957i	$0.497065\pi$
$600$		0			0
$601$			22.1301i			0.902705i	0.892346	+	0.451353i	$0.149058\pi$
$601$			22.1301i			0.902705i	−0.892346	+	0.451353i	$0.850942\pi$
$602$	−35.6742			−1.45397
$603$		−	27.6514i		−	1.12605i
$604$	−34.8515			−1.41809
$605$		0			0
$606$		−	2.89496i		−	0.117600i
$607$	−10.2667			−0.416713			−0.208357	−	0.978053i	$-0.566811\pi$
$607$	−10.2667			−0.416713			−0.208357	+	0.978053i	$0.566811\pi$
$608$		−	8.18342i		−	0.331881i
$609$		−	7.68649i		−	0.311472i
$610$		0			0
$611$	−17.8576			−0.722442
$612$	−18.6381	−	23.8443i	−0.753400	−	0.963848i
$613$			9.05172i			0.365595i	0.983151	+	0.182798i	$0.0585153\pi$
$613$			9.05172i			0.365595i	−0.983151	+	0.182798i	$0.941485\pi$
$614$	−46.8599			−1.89111
$615$		0			0
$616$	23.8082			0.959259
$617$	−17.8166			−0.717269			−0.358634	−	0.933478i	$-0.616757\pi$
$617$	−17.8166			−0.717269			−0.358634	+	0.933478i	$0.616757\pi$
$618$	−22.9939			−0.924949
$619$		−	38.3884i		−	1.54296i	−0.636254	−	0.771480i	$-0.719517\pi$
$619$		−	38.3884i		−	1.54296i	0.636254	−	0.771480i	$-0.280483\pi$
$620$		0			0
$621$	16.0677			0.644775
$622$	52.6525			2.11117
$623$	−34.9093			−1.39861
$624$		−	2.94828i		−	0.118026i
$625$		0			0
$626$		−	8.83710i		−	0.353202i
$627$		−	1.84324i		−	0.0736121i
$628$		−	10.1834i		−	0.406363i
$629$	13.3607	+	17.0928i	0.532726	+	0.681533i
$630$		0			0
$631$	−27.4863			−1.09421			−0.547105	−	0.837064i	$-0.684270\pi$
$631$	−27.4863			−1.09421			−0.547105	+	0.837064i	$0.684270\pi$
$632$	10.6647			0.424221
$633$			11.9961i			0.476803i
$634$			17.4863i			0.694468i
$635$		0			0
$636$		−	5.49079i		−	0.217724i
$637$		−	44.2206i		−	1.75208i
$638$		−	20.0989i		−	0.795723i
$639$		−	11.0133i		−	0.435681i
$640$		0			0
$641$			9.79976i			0.387067i	0.981094	+	0.193534i	$0.0619949\pi$
$641$			9.79976i			0.387067i	−0.981094	+	0.193534i	$0.938005\pi$
$642$			14.7877i			0.583622i
$643$	16.9372			0.667939			0.333969	−	0.942584i	$-0.391612\pi$
$643$	16.9372			0.667939			0.333969	+	0.942584i	$0.391612\pi$
$644$	−68.9998			−2.71897
$645$		0			0
$646$	7.60197	−	5.94214i	0.299095	−	0.233790i
$647$		−	2.98545i		−	0.117370i	−0.998277	−	0.0586850i	$-0.981309\pi$
$647$		−	2.98545i		−	0.117370i	0.998277	−	0.0586850i	$-0.0186908\pi$
$648$			9.95547i			0.391088i
$649$		−	7.41855i		−	0.291204i
$650$		0			0
$651$		−	10.7649i		−	0.421908i
$652$	23.5597			0.922669
$653$	40.1978			1.57306			0.786531	−	0.617551i	$-0.211875\pi$
$653$	40.1978			1.57306			0.786531	+	0.617551i	$0.211875\pi$
$654$	−9.54411			−0.373204
$655$		0			0
$656$			11.6430i			0.454583i
$657$	−30.0144			−1.17097
$658$	−71.8720			−2.80186
$659$	−43.9832			−1.71334			−0.856671	−	0.515864i	$-0.827471\pi$
$659$	−43.9832			−1.71334			−0.856671	+	0.515864i	$0.827471\pi$
$660$		0			0
$661$	26.1133			1.01569			0.507844	−	0.861449i	$-0.330443\pi$
$661$	26.1133			1.01569			0.507844	+	0.861449i	$0.330443\pi$
$662$			21.8576i			0.849521i
$663$	4.60811	−	3.60197i	0.178964	−	0.139889i
$664$	12.6719			0.491766
$665$		0			0
$666$		−	30.9360i		−	1.19875i
$667$			15.2495i			0.590463i
$668$	3.72875			0.144270
$669$		−	1.18181i		−	0.0456914i
$670$		0			0
$671$	38.8515			1.49984
$672$		−	19.9649i		−	0.770164i
$673$	−13.3340			−0.513989			−0.256995	−	0.966413i	$-0.582732\pi$
$673$	−13.3340			−0.513989			−0.256995	+	0.966413i	$0.582732\pi$
$674$		−	24.3812i		−	0.939129i
$675$		0			0
$676$	−16.4680			−0.633385
$677$	26.5113			1.01891			0.509456	−	0.860497i	$-0.329847\pi$
$677$	26.5113			1.01891			0.509456	+	0.860497i	$0.329847\pi$
$678$			19.9155i			0.764849i
$679$	39.9299			1.53237
$680$		0			0
$681$	5.15449			0.197520
$682$		−	28.1483i		−	1.07786i
$683$	5.71646			0.218734			0.109367	−	0.994001i	$-0.465118\pi$
$683$	5.71646			0.218734			0.109367	+	0.994001i	$0.465118\pi$
$684$	−7.91548			−0.302656
$685$		0			0
$686$		−	103.855i		−	3.96521i
$687$	3.97334			0.151592
$688$			7.00227i			0.266959i
$689$	−9.88882			−0.376734
$690$		0			0
$691$		−	43.8504i		−	1.66815i	−0.551652	−	0.834075i	$-0.686002\pi$
$691$		−	43.8504i		−	1.66815i	0.551652	−	0.834075i	$-0.313998\pi$
$692$	47.0349			1.78800
$693$			41.9071i			1.59192i
$694$		−	18.9867i		−	0.720724i
$695$		0			0
$696$	2.42469			0.0919078
$697$	−18.1978	+	14.2245i	−0.689291	+	0.538790i
$698$		−	58.3956i		−	2.21031i
$699$	−5.09275			−0.192626
$700$		0			0
$701$	0.0806452			0.00304593			0.00152296	−	0.999999i	$-0.499515\pi$
$701$	0.0806452			0.00304593			0.00152296	+	0.999999i	$0.499515\pi$
$702$	−17.5753			−0.663337
$703$	5.67420			0.214007
$704$		−	39.0277i		−	1.47091i
$705$		0			0
$706$	−39.7419			−1.49571
$707$	−12.0722			−0.454023
$708$	3.41855			0.128477
$709$			10.8227i			0.406456i	0.979131	+	0.203228i	$0.0651433\pi$
$709$			10.8227i			0.406456i	−0.979131	+	0.203228i	$0.934857\pi$
$710$		0			0
$711$			18.7721i			0.704007i
$712$		−	11.0121i		−	0.412696i
$713$			21.3568i			0.799819i
$714$	18.5464	−	14.4969i	0.694081	−	0.542534i
$715$		0			0
$716$	18.5236			0.692259
$717$	3.37298			0.125966
$718$		−	20.7792i		−	0.775474i
$719$			43.7659i			1.63219i	0.577916	+	0.816097i	$0.303866\pi$
$719$			43.7659i			1.63219i	−0.577916	+	0.816097i	$0.696134\pi$
$720$		0			0
$721$			95.8864i			3.57100i
$722$			38.7081i			1.44056i
$723$			1.34632i			0.0500700i
$724$		−	40.6947i		−	1.51241i
$725$		0			0
$726$			1.11223i			0.0412786i
$727$		−	3.59809i		−	0.133446i	−0.997772	−	0.0667229i	$-0.978746\pi$
$727$		−	3.59809i		−	0.133446i	0.997772	−	0.0667229i	$-0.0212544\pi$
$728$	19.7587			0.732307
$729$	−12.5441			−0.464597
$730$		0			0
$731$	−10.9444	+	8.55479i	−0.404794	+	0.316410i
$732$			17.9032i			0.661721i
$733$			39.8264i			1.47102i	0.677513	+	0.735511i	$0.263058\pi$
$733$			39.8264i			1.47102i	−0.677513	+	0.735511i	$0.736942\pi$
$734$			26.2895i			0.970363i
$735$		0			0
$736$			39.6092i			1.46001i
$737$	32.3545			1.19180
$738$	32.9360			1.21239
$739$	−13.7587			−0.506123			−0.253061	−	0.967450i	$-0.581437\pi$
$739$	−13.7587			−0.506123			−0.253061	+	0.967450i	$0.581437\pi$
$740$		0			0
$741$		−	1.52973i		−	0.0561962i
$742$	−39.7998			−1.46110
$743$	−9.34963			−0.343005			−0.171502	−	0.985184i	$-0.554862\pi$
$743$	−9.34963			−0.343005			−0.171502	+	0.985184i	$0.554862\pi$
$744$	3.39576			0.124495
$745$		0			0
$746$	−66.1049			−2.42027
$747$			22.3051i			0.816101i
$748$	27.8999	−	21.8082i	1.02012	−	0.797386i
$749$	61.6658			2.25322
$750$		0			0
$751$			53.7392i			1.96097i	0.196586	+	0.980487i	$0.437014\pi$
$751$			53.7392i			1.96097i	−0.196586	+	0.980487i	$0.562986\pi$
$752$			14.1073i			0.514441i
$753$	6.37137			0.232186
$754$		−	16.6803i		−	0.607462i
$755$		0			0
$756$	−40.6947			−1.48005
$757$		−	41.5136i		−	1.50884i	−0.656394	−	0.754418i	$-0.727919\pi$
$757$		−	41.5136i		−	1.50884i	0.656394	−	0.754418i	$-0.272081\pi$
$758$	2.14116			0.0777703
$759$			8.92162i			0.323834i
$760$		0			0
$761$	−18.0372			−0.653847			−0.326923	−	0.945051i	$-0.606012\pi$
$761$	−18.0372			−0.653847			−0.326923	+	0.945051i	$0.606012\pi$
$762$	9.41855			0.341198
$763$			39.7998i			1.44085i
$764$	65.7875			2.38011
$765$		0			0
$766$	54.1627			1.95698
$767$		−	6.15676i		−	0.222308i
$768$	0.225678			0.00814345
$769$	23.0843			0.832443			0.416221	−	0.909263i	$-0.363354\pi$
$769$	23.0843			0.832443			0.416221	+	0.909263i	$0.363354\pi$
$770$		0			0
$771$		−	8.05786i		−	0.290197i
$772$	32.1256			1.15622
$773$			27.4101i			0.985874i	0.870065	+	0.492937i	$0.164077\pi$
$773$			27.4101i			0.985874i	−0.870065	+	0.492937i	$0.835923\pi$
$774$	19.8082			0.711990
$775$		0			0
$776$			12.5958i			0.452164i
$777$	13.8432			0.496624
$778$			73.3667i			2.63032i
$779$			6.04104i			0.216443i
$780$		0			0
$781$	12.8865			0.461117
$782$	−36.7948	+	28.7610i	−1.31578	+	1.02849i
$783$			8.99386i			0.321414i
$784$	−34.9337			−1.24763
$785$		0			0
$786$	−13.6826			−0.488043
$787$	−30.6069			−1.09102			−0.545509	−	0.838105i	$-0.683664\pi$
$787$	−30.6069			−1.09102			−0.545509	+	0.838105i	$0.683664\pi$
$788$	−49.4596			−1.76192
$789$		−	6.97948i		−	0.248476i
$790$		0			0
$791$	83.0493			2.95289
$792$	−13.2195			−0.469736
$793$	32.2434			1.14500
$794$			61.8987i			2.19670i
$795$		0			0
$796$			10.0917i			0.357691i
$797$			22.9770i			0.813888i	0.913453	+	0.406944i	$0.133406\pi$
$797$			22.9770i			0.813888i	−0.913453	+	0.406944i	$0.866594\pi$
$798$		−	6.15676i		−	0.217947i
$799$	−22.0494	+	17.2351i	−0.780053	+	0.609735i
$800$		0			0
$801$	19.3835			0.684882
$802$	−71.8141			−2.53585
$803$		−	35.1194i		−	1.23934i
$804$			14.9093i			0.525812i
$805$		0			0
$806$		−	23.3607i		−	0.822845i
$807$		−	4.03120i		−	0.141905i
$808$		−	3.80817i		−	0.133971i
$809$		−	42.7670i		−	1.50361i	−0.659388	−	0.751803i	$-0.729184\pi$
$809$		−	42.7670i		−	1.50361i	0.659388	−	0.751803i	$-0.270816\pi$
$810$		0			0
$811$			9.41136i			0.330478i	0.986254	+	0.165239i	$0.0528395\pi$
$811$			9.41136i			0.330478i	−0.986254	+	0.165239i	$0.947161\pi$
$812$		−	38.6225i		−	1.35538i
$813$	1.16290			0.0407846
$814$	36.1978			1.26873
$815$		0			0
$816$	−2.84551	−	3.64035i	−0.0996128	−	0.127438i
$817$			3.63317i			0.127108i
$818$		−	65.5318i		−	2.29127i
$819$			34.7792i			1.21529i
$820$		0			0
$821$		−	32.6681i		−	1.14012i	−0.821602	−	0.570062i	$-0.806919\pi$
$821$		−	32.6681i		−	1.14012i	0.821602	−	0.570062i	$-0.193081\pi$
$822$	−2.28231			−0.0796048
$823$	−15.9265			−0.555164			−0.277582	−	0.960702i	$-0.589533\pi$
$823$	−15.9265			−0.555164			−0.277582	+	0.960702i	$0.589533\pi$
$824$	−30.2472			−1.05371
$825$		0			0
$826$		−	24.7792i		−	0.862180i
$827$	6.01560			0.209183			0.104591	−	0.994515i	$-0.466647\pi$
$827$	6.01560			0.209183			0.104591	+	0.994515i	$0.466647\pi$
$828$	38.3123			1.33144
$829$	−11.0472			−0.383684			−0.191842	−	0.981426i	$-0.561446\pi$
$829$	−11.0472			−0.383684			−0.191842	+	0.981426i	$0.561446\pi$
$830$		0			0
$831$	6.55479			0.227383
$832$		−	32.3896i		−	1.12291i
$833$	−42.6791	−	54.6007i	−1.47874	−	1.89180i
$834$	−2.34858			−0.0813248
$835$		0			0
$836$		−	9.26180i		−	0.320326i
$837$			12.5958i			0.435375i
$838$	−39.4173			−1.36165
$839$			35.9805i			1.24219i	0.783737	+	0.621093i	$0.213311\pi$
$839$			35.9805i			1.24219i	−0.783737	+	0.621093i	$0.786689\pi$
$840$		0			0
$841$	20.4641			0.705659
$842$		−	1.65142i		−	0.0569116i
$843$	−7.07384			−0.243636
$844$			60.2772i			2.07483i
$845$		0			0
$846$	39.9071			1.37203
$847$	4.63809			0.159367
$848$			7.81205i			0.268267i
$849$	7.52586			0.258287
$850$		0			0
$851$	−27.4641			−0.941458
$852$			5.93827i			0.203442i
$853$	−28.7792			−0.985382			−0.492691	−	0.870204i	$-0.663987\pi$
$853$	−28.7792			−0.985382			−0.492691	+	0.870204i	$0.663987\pi$
$854$	129.771			4.44066
$855$		0			0
$856$			19.4524i			0.664869i
$857$	17.0661			0.582967			0.291483	−	0.956576i	$-0.405851\pi$
$857$	17.0661			0.582967			0.291483	+	0.956576i	$0.405851\pi$
$858$		−	9.75872i		−	0.333157i
$859$	18.9360			0.646088			0.323044	−	0.946384i	$-0.395294\pi$
$859$	18.9360			0.646088			0.323044	+	0.946384i	$0.395294\pi$
$860$		0			0
$861$			14.7382i			0.502277i
$862$	13.7743			0.469155
$863$		−	30.8332i		−	1.04958i	−0.851233	−	0.524788i	$-0.824145\pi$
$863$		−	30.8332i		−	1.04958i	0.851233	−	0.524788i	$-0.175855\pi$
$864$			23.3607i			0.794747i
$865$		0			0
$866$	−7.86603			−0.267299
$867$	2.21339	−	8.89496i	0.0751707	−	0.302089i
$868$		−	54.0905i		−	1.83595i
$869$	−21.9649			−0.745109
$870$		0			0
$871$	26.8515			0.909828
$872$	−12.5548			−0.425159
$873$	−22.1711			−0.750379
$874$			12.2146i			0.413165i
$875$		0			0
$876$	16.1834			0.546787
$877$	−4.30898			−0.145504			−0.0727519	−	0.997350i	$-0.523178\pi$
$877$	−4.30898			−0.145504			−0.0727519	+	0.997350i	$0.523178\pi$
$878$	13.8999			0.469098
$879$			2.55479i			0.0861708i
$880$		0			0
$881$		−	12.2245i		−	0.411852i	−0.978568	−	0.205926i	$-0.933979\pi$
$881$		−	12.2245i		−	0.411852i	0.978568	−	0.205926i	$-0.0660207\pi$
$882$			98.8213i			3.32749i
$883$			28.2329i			0.950112i	0.879956	+	0.475056i	$0.157572\pi$
$883$			28.2329i			0.950112i	−0.879956	+	0.475056i	$0.842428\pi$
$884$	23.1545	−	18.0989i	0.778770	−	0.608732i
$885$		0			0
$886$	−59.6391			−2.00362
$887$	−5.17396			−0.173725			−0.0868623	−	0.996220i	$-0.527684\pi$
$887$	−5.17396			−0.173725			−0.0868623	+	0.996220i	$0.527684\pi$
$888$			4.36683i			0.146541i
$889$		−	39.2762i		−	1.31728i
$890$		0			0
$891$		−	20.5041i		−	0.686914i
$892$		−	5.93827i		−	0.198828i
$893$			7.31965i			0.244943i
$894$			16.7115i			0.558918i
$895$		0			0
$896$		−	56.3039i		−	1.88098i
$897$			7.40417i			0.247218i
$898$	62.3956			2.08217
$899$	−11.9544			−0.398702
$900$		0			0
$901$	−12.2101	+	9.54411i	−0.406777	+	0.317960i
$902$			38.5380i			1.28317i
$903$			8.86376i			0.294968i
$904$			26.1978i			0.871326i
$905$		0			0
$906$			15.0517i			0.500060i
$907$	6.32457			0.210004			0.105002	−	0.994472i	$-0.466515\pi$
$907$	6.32457			0.210004			0.105002	+	0.994472i	$0.466515\pi$
$908$	25.8999			0.859518
$909$	6.70313			0.222329
$910$		0			0
$911$			27.6526i			0.916173i	0.888908	+	0.458086i	$0.151465\pi$
$911$			27.6526i			0.916173i	−0.888908	+	0.458086i	$0.848535\pi$
$912$	−1.20847			−0.0400165
$913$	−26.0989			−0.863747
$914$	−68.1627			−2.25462
$915$		0			0
$916$	19.9649			0.659660
$917$			57.0577i			1.88421i
$918$	−21.7009	+	16.9627i	−0.716235	+	0.559851i
$919$	47.5318			1.56793			0.783965	−	0.620805i	$-0.213194\pi$
$919$	47.5318			1.56793			0.783965	+	0.620805i	$0.213194\pi$
$920$		0			0
$921$			11.6430i			0.383650i
$922$			16.8371i			0.554500i
$923$	10.6947			0.352021
$924$		−	22.5958i		−	0.743348i
$925$		0			0
$926$	−52.5874			−1.72813
$927$		−	53.2411i		−	1.74867i
$928$	−22.1711			−0.727803
$929$			43.7875i			1.43662i	0.695723	+	0.718310i	$0.255084\pi$
$929$			43.7875i			1.43662i	−0.695723	+	0.718310i	$0.744916\pi$
$930$		0			0
$931$	−18.1256			−0.594041
$932$	−25.5897			−0.838218
$933$		−	13.0823i		−	0.428294i
$934$	−26.7298			−0.874626
$935$		0			0
$936$	−10.9711			−0.358601
$937$			14.2367i			0.465094i	0.972585	+	0.232547i	$0.0747060\pi$
$937$			14.2367i			0.465094i	−0.972585	+	0.232547i	$0.925294\pi$
$938$	108.070			3.52860
$939$	−2.19570			−0.0716541
$940$		0			0
$941$			35.2183i			1.14808i	0.818826	+	0.574042i	$0.194625\pi$
$941$			35.2183i			1.14808i	−0.818826	+	0.574042i	$0.805375\pi$
$942$	−4.39803			−0.143296
$943$		−	29.2397i		−	0.952175i
$944$	−4.86376			−0.158302
$945$		0			0
$946$			23.1773i			0.753558i
$947$	−49.1227			−1.59627			−0.798137	−	0.602476i	$-0.794181\pi$
$947$	−49.1227			−1.59627			−0.798137	+	0.602476i	$0.794181\pi$
$948$		−	10.1217i		−	0.328737i
$949$		−	29.1461i		−	0.946122i
$950$		0			0
$951$	4.34471			0.140887
$952$	24.3968	−	19.0700i	0.790705	−	0.618061i
$953$			17.0556i			0.552485i	0.961088	+	0.276242i	$0.0890893\pi$
$953$			17.0556i			0.552485i	−0.961088	+	0.276242i	$0.910911\pi$
$954$	22.0989			0.715478
$955$		0			0
$956$	16.9483			0.548147
$957$	−4.99386			−0.161428
$958$	−4.66475			−0.150711
$959$			9.51745i			0.307334i
$960$		0			0
$961$	14.2579			0.459933
$962$	30.0410			0.968562
$963$	−34.2401			−1.10337
$964$			6.76487i			0.217882i
$965$		0			0
$966$			29.7998i			0.958792i
$967$		−	25.1955i		−	0.810233i	−0.914265	−	0.405117i	$-0.867231\pi$
$967$		−	25.1955i		−	0.810233i	0.914265	−	0.405117i	$-0.132769\pi$
$968$			1.46308i			0.0470251i
$969$	−1.47641	−	1.88882i	−0.0474291	−	0.0606776i
$970$		0			0
$971$	1.67420			0.0537277			0.0268639	−	0.999639i	$-0.491448\pi$
$971$	1.67420			0.0537277			0.0268639	+	0.999639i	$0.491448\pi$
$972$	34.4690			1.10560
$973$			9.79380i			0.313975i
$974$		−	86.9842i		−	2.78715i
$975$		0			0
$976$		−	25.4719i		−	0.815335i
$977$		−	39.9109i		−	1.27686i	−0.769678	−	0.638432i	$-0.779583\pi$
$977$		−	39.9109i		−	1.27686i	0.769678	−	0.638432i	$-0.220417\pi$
$978$		−	10.1750i		−	0.325361i
$979$			22.6803i			0.724867i
$980$		0			0
$981$		−	22.0989i		−	0.705563i
$982$			4.89496i			0.156204i
$983$	−5.46081			−0.174173			−0.0870864	−	0.996201i	$-0.527756\pi$
$983$	−5.46081			−0.174173			−0.0870864	+	0.996201i	$0.527756\pi$
$984$	−4.64915			−0.148209
$985$		0			0
$986$	−16.0989	−	20.5958i	−0.512693	−	0.655905i
$987$			17.8576i			0.568414i
$988$		−	7.68649i		−	0.244540i
$989$		−	17.5851i		−	0.559175i
$990$		0			0
$991$		−	42.0749i		−	1.33655i	−0.743913	−	0.668276i	$-0.767032\pi$
$991$		−	42.0749i		−	1.33655i	0.743913	−	0.668276i	$-0.232968\pi$
$992$	−31.0505			−0.985854
$993$	5.43084			0.172342
$994$	43.0433			1.36525
$995$		0			0
$996$		−	12.0267i		−	0.381079i
$997$	54.6681			1.73135			0.865677	−	0.500602i	$-0.166888\pi$
$997$	54.6681			1.73135			0.865677	+	0.500602i	$0.166888\pi$
$998$	92.3267			2.92255
$999$	−16.1978			−0.512476

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.c.b.424.1		6
5.2	odd	4		425.2.d.c.101.6		6
5.3	odd	4		85.2.d.a.16.1	✓	6
5.4	even	2		425.2.c.a.424.6		6
15.8	even	4		765.2.g.b.271.5		6
17.16	even	2		425.2.c.a.424.1		6
20.3	even	4		1360.2.c.f.1121.4		6
85.13	odd	4		1445.2.a.j.1.3		3
85.33	odd	4		85.2.d.a.16.2	yes	6
85.38	odd	4		1445.2.a.k.1.3		3
85.47	odd	4		7225.2.a.q.1.1		3
85.67	odd	4		425.2.d.c.101.5		6
85.72	odd	4		7225.2.a.r.1.1		3
85.84	even	2	inner	425.2.c.b.424.6		6
255.203	even	4		765.2.g.b.271.6		6
340.203	even	4		1360.2.c.f.1121.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.d.a.16.1	✓	6	5.3	odd	4
85.2.d.a.16.2	yes	6	85.33	odd	4
425.2.c.a.424.1		6	17.16	even	2
425.2.c.a.424.6		6	5.4	even	2
425.2.c.b.424.1		6	1.1	even	1	trivial
425.2.c.b.424.6		6	85.84	even	2	inner
425.2.d.c.101.5		6	85.67	odd	4
425.2.d.c.101.6		6	5.2	odd	4
765.2.g.b.271.5		6	15.8	even	4
765.2.g.b.271.6		6	255.203	even	4
1360.2.c.f.1121.3		6	340.203	even	4
1360.2.c.f.1121.4		6	20.3	even	4
1445.2.a.j.1.3		3	85.13	odd	4
1445.2.a.k.1.3		3	85.38	odd	4
7225.2.a.q.1.1		3	85.47	odd	4
7225.2.a.r.1.1		3	85.72	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.17009i q^{2} -0.539189 q^{3} -2.70928 q^{4} +1.17009i q^{6} +4.87936 q^{7} +1.53919i q^{8} -2.70928 q^{9} -3.17009i q^{11} +1.46081 q^{12} -2.63090i q^{13} -10.5886i q^{14} -2.07838 q^{16} +(-2.53919 - 3.24846i) q^{17} +5.87936i q^{18} -1.07838 q^{19} -2.63090 q^{21} -6.87936 q^{22} +5.21953 q^{23} -0.829914i q^{24} -5.70928 q^{26} +3.07838 q^{27} -13.2195 q^{28} +2.92162i q^{29} +4.09171i q^{31} +7.58864i q^{32} +1.70928i q^{33} +(-7.04945 + 5.51026i) q^{34} +7.34017 q^{36} -5.26180 q^{37} +2.34017i q^{38} +1.41855i q^{39} -5.60197i q^{41} +5.70928i q^{42} -3.36910i q^{43} +8.58864i q^{44} -11.3268i q^{46} -6.78765i q^{47} +1.12064 q^{48} +16.8082 q^{49} +(1.36910 + 1.75154i) q^{51} +7.12783i q^{52} -3.75872i q^{53} -6.68035i q^{54} +7.51026i q^{56} +0.581449 q^{57} +6.34017 q^{58} +2.34017 q^{59} +12.2557i q^{61} +8.87936 q^{62} -13.2195 q^{63} +12.3112 q^{64} +3.70928 q^{66} +10.2062i q^{67} +(6.87936 + 8.80098i) q^{68} -2.81432 q^{69} +4.06505i q^{71} -4.17009i q^{72} +11.0784 q^{73} +11.4186i q^{74} +2.92162 q^{76} -15.4680i q^{77} +3.07838 q^{78} -6.92881i q^{79} +6.46800 q^{81} -12.1568 q^{82} -8.23287i q^{83} +7.12783 q^{84} -7.31124 q^{86} -1.57531i q^{87} +4.87936 q^{88} -7.15449 q^{89} -12.8371i q^{91} -14.1412 q^{92} -2.20620i q^{93} -14.7298 q^{94} -4.09171i q^{96} +8.18342 q^{97} -36.4752i q^{98} +8.58864i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{4} + 4 q^{7} - 2 q^{9} + 12 q^{12} - 6 q^{16} - 12 q^{17} - 8 q^{21} - 16 q^{22} - 16 q^{23} - 20 q^{26} + 12 q^{27} - 32 q^{28} - 6 q^{34} + 22 q^{36} - 16 q^{37} + 32 q^{48} + 14 q^{49} + 16 q^{51}+ \cdots + 40 q^{97}+O(q^{100}) \) 6 * q - 2 * q^4 + 4 * q^7 - 2 * q^9 + 12 * q^12 - 6 * q^16 - 12 * q^17 - 8 * q^21 - 16 * q^22 - 16 * q^23 - 20 * q^26 + 12 * q^27 - 32 * q^28 - 6 * q^34 + 22 * q^36 - 16 * q^37 + 32 * q^48 + 14 * q^49 + 16 * q^51 + 32 * q^57 + 16 * q^58 - 8 * q^59 + 28 * q^62 - 32 * q^63 + 22 * q^64 + 8 * q^66 + 16 * q^68 + 60 * q^73 + 24 * q^76 + 12 * q^78 - 26 * q^81 - 60 * q^82 + 8 * q^86 + 4 * q^88 - 4 * q^89 - 44 * q^92 - 8 * q^94 + 40 * q^97

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