LMFDB - Embedded newform 475.2.e.g.201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(26,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("475.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 6x^{10} + 29x^{8} + 40x^{6} + 43x^{4} + 7x^{2} + 1 $ x^12 + 6x^10 + 29x^8 + 40x^6 + 43x^4 + 7*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.1
Root			$0.203566 - 0.352587i$ of defining polynomial
Character	$\chi$	$=$	475.201
Dual form			475.2.e.g.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22810 + 2.12713i) q^{2} +(-0.780522 + 1.35190i) q^{3} +(-2.01647 - 3.49262i) q^{4} +(-1.91712 - 3.32055i) q^{6} +4.50527 q^{7} +4.99330 q^{8} +(0.281570 + 0.487693i) q^{9} +O(q^{10})$	\(q+(-1.22810 + 2.12713i) q^{2} +(-0.780522 + 1.35190i) q^{3} +(-2.01647 - 3.49262i) q^{4} +(-1.91712 - 3.32055i) q^{6} +4.50527 q^{7} +4.99330 q^{8} +(0.281570 + 0.487693i) q^{9} +2.19869 q^{11} +6.29559 q^{12} +(1.87925 + 3.25495i) q^{13} +(-5.53293 + 9.58332i) q^{14} +(-2.09935 + 3.63617i) q^{16} +(-0.332943 + 0.576674i) q^{17} -1.38318 q^{18} +(3.79804 - 2.13891i) q^{19} +(-3.51647 + 6.09070i) q^{21} +(-2.70022 + 4.67691i) q^{22} +(0.244013 + 0.422643i) q^{23} +(-3.89738 + 6.75046i) q^{24} -9.23163 q^{26} -5.56222 q^{27} +(-9.08474 - 15.7352i) q^{28} +(-1.79804 - 3.11429i) q^{29} +6.83424 q^{31} +(-0.163119 - 0.282531i) q^{32} +(-1.71613 + 2.97242i) q^{33} +(-0.817776 - 1.41643i) q^{34} +(1.13555 - 1.96683i) q^{36} -3.01171 q^{37} +(-0.114636 + 10.7057i) q^{38} -5.86718 q^{39} +(-0.0362063 + 0.0627112i) q^{41} +(-8.63716 - 14.9600i) q^{42} +(-0.210271 + 0.364199i) q^{43} +(-4.43359 - 7.67920i) q^{44} -1.19869 q^{46} +(-2.51139 - 4.34986i) q^{47} +(-3.27717 - 5.67623i) q^{48} +13.2975 q^{49} +(-0.519739 - 0.900215i) q^{51} +(7.57888 - 13.1270i) q^{52} +(-1.30900 - 2.26725i) q^{53} +(6.83097 - 11.8316i) q^{54} +22.4962 q^{56} +(-0.0728572 + 6.80405i) q^{57} +8.83269 q^{58} +(-6.26783 + 10.8562i) q^{59} +(-3.53293 - 6.11922i) q^{61} +(-8.39315 + 14.5374i) q^{62} +(1.26855 + 2.19719i) q^{63} -7.59607 q^{64} +(-4.21516 - 7.30087i) q^{66} +(-2.86334 - 4.95944i) q^{67} +2.68548 q^{68} -0.761831 q^{69} +(-3.48626 + 6.03838i) q^{71} +(1.40596 + 2.43520i) q^{72} +(1.47882 - 2.56139i) q^{73} +(3.69869 - 6.40632i) q^{74} +(-15.1290 - 8.95208i) q^{76} +9.90571 q^{77} +(7.20549 - 12.4803i) q^{78} +(-5.66849 + 9.81811i) q^{79} +(3.49673 - 6.05651i) q^{81} +(-0.0889301 - 0.154031i) q^{82} -15.6999 q^{83} +28.3634 q^{84} +(-0.516467 - 0.894547i) q^{86} +5.61363 q^{87} +10.9787 q^{88} +(0.668486 + 1.15785i) q^{89} +(8.46652 + 14.6644i) q^{91} +(0.984089 - 1.70449i) q^{92} +(-5.33428 + 9.23924i) q^{93} +12.3370 q^{94} +0.509273 q^{96} +(-2.19319 + 3.79871i) q^{97} +(-16.3307 + 28.2856i) q^{98} +(0.619085 + 1.07229i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{4} - 12 q^{6} - 8 q^{9}+O(q^{10}) $ 12 * q - 2 * q^4 - 12 * q^6 - 8 * q^9	$ 12 q - 2 q^{4} - 12 q^{6} - 8 q^{9} + 4 q^{11} - 22 q^{14} - 14 q^{16} + 12 q^{19} - 20 q^{21} - 2 q^{24} - 44 q^{26} + 12 q^{29} + 60 q^{31} - 10 q^{34} + 14 q^{36} - 4 q^{39} - 12 q^{41} - 20 q^{44} + 8 q^{46} + 4 q^{49} - 40 q^{51} + 4 q^{54} + 92 q^{56} - 20 q^{59} + 2 q^{61} - 24 q^{64} - 6 q^{66} + 36 q^{69} + 2 q^{71} + 22 q^{74} - 70 q^{76} - 24 q^{79} - 14 q^{81} + 96 q^{84} + 16 q^{86} - 36 q^{89} + 24 q^{91} + 60 q^{94} + 52 q^{96} + 30 q^{99}+O(q^{100}) $ 12 * q - 2 * q^4 - 12 * q^6 - 8 * q^9 + 4 * q^11 - 22 * q^14 - 14 * q^16 + 12 * q^19 - 20 * q^21 - 2 * q^24 - 44 * q^26 + 12 * q^29 + 60 * q^31 - 10 * q^34 + 14 * q^36 - 4 * q^39 - 12 * q^41 - 20 * q^44 + 8 * q^46 + 4 * q^49 - 40 * q^51 + 4 * q^54 + 92 * q^56 - 20 * q^59 + 2 * q^61 - 24 * q^64 - 6 * q^66 + 36 * q^69 + 2 * q^71 + 22 * q^74 - 70 * q^76 - 24 * q^79 - 14 * q^81 + 96 * q^84 + 16 * q^86 - 36 * q^89 + 24 * q^91 + 60 * q^94 + 52 * q^96 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.22810	+	2.12713i	−0.868399	+	1.50411i	−0.00476685	+	0.999989i	$0.501517\pi$
$2$	−1.22810	+	2.12713i	−0.868399	+	1.50411i	−0.863632	+	0.504123i	$0.831816\pi$
$3$	−0.780522	+	1.35190i	−0.450635	+	0.780522i	−0.998426	−	0.0560930i	$-0.982136\pi$
$3$	−0.780522	+	1.35190i	−0.450635	+	0.780522i	0.547791	+	0.836615i	$0.315469\pi$
$4$	−2.01647	−	3.49262i	−1.00823	−	1.74631i
$5$		0			0
$5$		0			0
$6$	−1.91712	−	3.32055i	−0.782662	−	1.35561i
$7$	4.50527			1.70283			0.851417	−	0.524490i	$-0.175744\pi$
$7$	4.50527			1.70283			0.851417	+	0.524490i	$0.175744\pi$
$8$	4.99330			1.76540
$9$	0.281570	+	0.487693i	0.0938566	+	0.162564i
$10$		0			0
$11$	2.19869			0.662930			0.331465	−	0.943467i	$-0.392457\pi$
$11$	2.19869			0.662930			0.331465	+	0.943467i	$0.392457\pi$
$12$	6.29559			1.81738
$13$	1.87925	+	3.25495i	0.521209	+	0.902761i	0.999696	+	0.0246661i	$0.00785227\pi$
$13$	1.87925	+	3.25495i	0.521209	+	0.902761i	−0.478486	+	0.878095i	$0.658814\pi$
$14$	−5.53293	+	9.58332i	−1.47874	+	2.56125i
$15$		0			0
$16$	−2.09935	+	3.63617i	−0.524836	+	0.909043i
$17$	−0.332943	+	0.576674i	−0.0807506	+	0.139864i	−0.903573	−	0.428435i	$-0.859065\pi$
$17$	−0.332943	+	0.576674i	−0.0807506	+	0.139864i	0.822822	+	0.568299i	$0.192398\pi$
$18$	−1.38318			−0.326020
$19$	3.79804	−	2.13891i	0.871329	−	0.490699i
$19$	3.79804	−	2.13891i	0.871329	−	0.490699i
$20$		0			0
$21$	−3.51647	+	6.09070i	−0.767356	+	1.32910i
$22$	−2.70022	+	4.67691i	−0.575688	+	0.997121i
$23$	0.244013	+	0.422643i	0.0508802	+	0.0881272i	0.890344	−	0.455289i	$-0.150464\pi$
$23$	0.244013	+	0.422643i	0.0508802	+	0.0881272i	−0.839464	+	0.543416i	$0.817131\pi$
$24$	−3.89738	+	6.75046i	−0.795550	+	1.37793i
$25$		0			0
$26$	−9.23163			−1.81047
$27$	−5.56222			−1.07045
$28$	−9.08474	−	15.7352i	−1.71685	−	2.97368i
$29$	−1.79804	−	3.11429i	−0.333887	−	0.578309i	0.649383	−	0.760461i	$-0.275027\pi$
$29$	−1.79804	−	3.11429i	−0.333887	−	0.578309i	−0.983270	+	0.182152i	$0.941694\pi$
$30$		0			0
$31$	6.83424			1.22747			0.613733	−	0.789514i	$-0.289667\pi$
$31$	6.83424			1.22747			0.613733	+	0.789514i	$0.289667\pi$
$32$	−0.163119	−	0.282531i	−0.0288357	−	0.0499449i
$33$	−1.71613	+	2.97242i	−0.298739	+	0.517432i
$34$	−0.817776	−	1.41643i	−0.140247	−	0.242916i
$35$		0			0
$36$	1.13555	−	1.96683i	0.189259	−	0.327806i
$37$	−3.01171			−0.495123			−0.247561	−	0.968872i	$-0.579629\pi$
$37$	−3.01171			−0.495123			−0.247561	+	0.968872i	$0.579629\pi$
$38$	−0.114636	+	10.7057i	−0.0185964	+	1.73670i
$39$	−5.86718			−0.939500
$40$		0			0
$41$	−0.0362063	+	0.0627112i	−0.00565448	+	0.00979384i	−0.868839	−	0.495095i	$-0.835133\pi$
$41$	−0.0362063	+	0.0627112i	−0.00565448	+	0.00979384i	0.863184	+	0.504889i	$0.168467\pi$
$42$	−8.63716	−	14.9600i	−1.33274	−	2.30838i
$43$	−0.210271	+	0.364199i	−0.0320660	+	0.0555399i	−0.881613	−	0.471973i	$-0.843542\pi$
$43$	−0.210271	+	0.364199i	−0.0320660	+	0.0555399i	0.849547	+	0.527513i	$0.176875\pi$
$44$	−4.43359	−	7.67920i	−0.668389	−	1.15768i
$45$		0			0
$46$	−1.19869			−0.176737
$47$	−2.51139	−	4.34986i	−0.366324	−	0.634492i	0.622664	−	0.782490i	$-0.286050\pi$
$47$	−2.51139	−	4.34986i	−0.366324	−	0.634492i	−0.988988	+	0.147998i	$0.952717\pi$
$48$	−3.27717	−	5.67623i	−0.473019	−	0.819293i
$49$	13.2975			1.89964
$50$		0			0
$51$	−0.519739	−	0.900215i	−0.0727780	−	0.126055i
$52$	7.57888	−	13.1270i	1.05100	−	1.82039i
$53$	−1.30900	−	2.26725i	−0.179804	−	0.311430i	0.762009	−	0.647566i	$-0.224213\pi$
$53$	−1.30900	−	2.26725i	−0.179804	−	0.311430i	−0.941813	+	0.336136i	$0.890880\pi$
$54$	6.83097	−	11.8316i	0.929577	−	1.61008i
$55$		0			0
$56$	22.4962			3.00618
$57$	−0.0728572	+	6.80405i	−0.00965017	+	0.901218i
$58$	8.83269			1.15979
$59$	−6.26783	+	10.8562i	−0.816002	+	1.41336i	0.0926038	+	0.995703i	$0.470481\pi$
$59$	−6.26783	+	10.8562i	−0.816002	+	1.41336i	−0.908606	+	0.417654i	$0.862852\pi$
$60$		0			0
$61$	−3.53293	−	6.11922i	−0.452346	−	0.783486i	0.546185	−	0.837664i	$-0.316079\pi$
$61$	−3.53293	−	6.11922i	−0.452346	−	0.783486i	−0.998531	+	0.0541782i	$0.982746\pi$
$62$	−8.39315	+	14.5374i	−1.06593	+	1.84625i
$63$	1.26855	+	2.19719i	0.159822	+	0.276820i
$64$	−7.59607			−0.949509
$65$		0			0
$66$	−4.21516	−	7.30087i	−0.518850	−	0.898675i
$67$	−2.86334	−	4.95944i	−0.349812	−	0.605892i	0.636404	−	0.771356i	$-0.280421\pi$
$67$	−2.86334	−	4.95944i	−0.349812	−	0.605892i	−0.986216	+	0.165464i	$0.947088\pi$
$68$	2.68548			0.325662
$69$	−0.761831			−0.0917136
$70$		0			0
$71$	−3.48626	+	6.03838i	−0.413743	+	0.716624i	−0.995296	−	0.0968847i	$-0.969112\pi$
$71$	−3.48626	+	6.03838i	−0.413743	+	0.716624i	0.581552	+	0.813509i	$0.302446\pi$
$72$	1.40596	+	2.43520i	0.165694	+	0.286991i
$73$	1.47882	−	2.56139i	0.173083	−	0.299788i	−0.766413	−	0.642348i	$-0.777961\pi$
$73$	1.47882	−	2.56139i	0.173083	−	0.299788i	0.939496	+	0.342560i	$0.111294\pi$
$74$	3.69869	−	6.40632i	0.429964	−	0.744720i
$75$		0			0
$76$	−15.1290	−	8.95208i	−1.73542	−	1.02687i
$77$	9.90571			1.12886
$78$	7.20549	−	12.4803i	0.815861	−	1.41311i
$79$	−5.66849	+	9.81811i	−0.637755	+	1.10462i	0.348170	+	0.937431i	$0.386803\pi$
$79$	−5.66849	+	9.81811i	−0.637755	+	1.10462i	−0.985924	+	0.167192i	$0.946530\pi$
$80$		0			0
$81$	3.49673	−	6.05651i	0.388525	−	0.672946i
$82$	−0.0889301	−	0.154031i	−0.00982068	−	0.0170099i
$83$	−15.6999			−1.72328			−0.861642	−	0.507517i	$-0.830564\pi$
$83$	−15.6999			−1.72328			−0.861642	+	0.507517i	$0.830564\pi$
$84$	28.3634			3.09470
$85$		0			0
$86$	−0.516467	−	0.894547i	−0.0556921	−	0.0964615i
$87$	5.61363			0.601845
$88$	10.9787			1.17034
$89$	0.668486	+	1.15785i	0.0708594	+	0.122732i	0.899278	−	0.437377i	$-0.144092\pi$
$89$	0.668486	+	1.15785i	0.0708594	+	0.122732i	−0.828419	+	0.560109i	$0.810759\pi$
$90$		0			0
$91$	8.46652	+	14.6644i	0.887533	+	1.53725i
$92$	0.984089	−	1.70449i	0.102598	−	0.177706i
$93$	−5.33428	+	9.23924i	−0.553139	+	0.958065i
$94$	12.3370			1.27246
$95$		0			0
$96$	0.509273			0.0519775
$97$	−2.19319	+	3.79871i	−0.222685	+	0.385701i	−0.955622	−	0.294595i	$-0.904815\pi$
$97$	−2.19319	+	3.79871i	−0.222685	+	0.385701i	0.732938	+	0.680296i	$0.238149\pi$
$98$	−16.3307	+	28.2856i	−1.64965	+	2.85727i
$99$	0.619085	+	1.07229i	0.0622204	+	0.107769i
$100$		0			0
$101$	5.28430	+	9.15267i	0.525807	+	0.910725i	0.999548	+	0.0300608i	$0.00957008\pi$
$101$	5.28430	+	9.15267i	0.525807	+	0.910725i	−0.473741	+	0.880664i	$0.657097\pi$
$102$	2.55317			0.252801
$103$	5.75615			0.567171			0.283585	−	0.958947i	$-0.408476\pi$
$103$	5.75615			0.567171			0.283585	+	0.958947i	$0.408476\pi$
$104$	9.38364	+	16.2529i	0.920142	+	1.59373i
$105$		0			0
$106$	6.43032			0.624568
$107$	−1.30229			−0.125897			−0.0629486	−	0.998017i	$-0.520050\pi$
$107$	−1.30229			−0.125897			−0.0629486	+	0.998017i	$0.520050\pi$
$108$	11.2160	+	19.4267i	1.07926	+	1.86934i
$109$	6.01647	−	10.4208i	0.576273	−	0.998134i	−0.419629	−	0.907696i	$-0.637840\pi$
$109$	6.01647	−	10.4208i	0.576273	−	0.998134i	0.995902	−	0.0904385i	$-0.0288269\pi$
$110$		0			0
$111$	2.35071	−	4.07155i	0.223120	−	0.386454i
$112$	−9.45813	+	16.3820i	−0.893709	+	1.54795i
$113$	7.74626			0.728707			0.364353	−	0.931261i	$-0.381290\pi$
$113$	7.74626			0.728707			0.364353	+	0.931261i	$0.381290\pi$
$114$	−14.3836	−	8.51104i	−1.34715	−	0.797132i
$115$		0			0
$116$	−7.25136	+	12.5597i	−0.673272	+	1.16614i
$117$	−1.05828	+	1.83299i	−0.0978378	+	0.169460i
$118$	−15.3951	−	26.6650i	−1.41723	−	2.45472i
$119$	−1.50000	+	2.59808i	−0.137505	+	0.238165i
$120$		0			0
$121$	−6.16576			−0.560523
$122$	17.3552			1.57127
$123$	−0.0565197	−	0.0978950i	−0.00509621	−	0.00882689i
$124$	−13.7810	−	23.8694i	−1.23757	−	2.14354i
$125$		0			0
$126$	−6.23163			−0.555157
$127$	1.96818	+	3.40898i	0.174647	+	0.302498i	0.940039	−	0.341066i	$-0.110788\pi$
$127$	1.96818	+	3.40898i	0.174647	+	0.302498i	−0.765392	+	0.643565i	$0.777455\pi$
$128$	9.65499	−	16.7229i	0.853389	−	1.47811i
$129$	−0.328242	−	0.568531i	−0.0289001	−	0.0500564i
$130$		0			0
$131$	8.16248	−	14.1378i	0.713160	−	1.23523i	−0.250505	−	0.968115i	$-0.580597\pi$
$131$	8.16248	−	14.1378i	0.713160	−	1.23523i	0.963665	−	0.267114i	$-0.0860699\pi$
$132$	13.8421			1.20480
$133$	17.1112	−	9.63635i	1.48373	−	0.835578i
$134$	14.0659			1.21511
$135$		0			0
$136$	−1.66248	+	2.87951i	−0.142557	+	0.246916i
$137$	8.21529	+	14.2293i	0.701879	+	1.21569i	0.967806	+	0.251697i	$0.0809887\pi$
$137$	8.21529	+	14.2293i	0.701879	+	1.21569i	−0.265927	+	0.963993i	$0.585678\pi$
$138$	0.935605	−	1.62052i	0.0796440	−	0.137947i
$139$	1.33424	+	2.31098i	0.113169	+	0.196015i	0.917046	−	0.398781i	$-0.130567\pi$
$139$	1.33424	+	2.31098i	0.113169	+	0.196015i	−0.803877	+	0.594795i	$0.797233\pi$
$140$		0			0
$141$	7.84079			0.660313
$142$	−8.56297	−	14.8315i	−0.718588	−	1.24463i
$143$	4.13188	+	7.15663i	0.345526	+	0.598468i
$144$	−2.36445			−0.197037
$145$		0			0
$146$	3.63228	+	6.29129i	0.300610	+	0.520671i
$147$	−10.3790	+	17.9769i	−0.856045	+	1.48271i
$148$	6.07302	+	10.5188i	0.499199	+	0.864639i
$149$	8.98299	−	15.5590i	0.735915	−	1.27464i	−0.218405	−	0.975858i	$-0.570085\pi$
$149$	8.98299	−	15.5590i	0.735915	−	1.27464i	0.954321	−	0.298784i	$-0.0965812\pi$
$150$		0			0
$151$	−12.7344			−1.03631			−0.518154	−	0.855288i	$-0.673380\pi$
$151$	−12.7344			−1.03631			−0.518154	+	0.855288i	$0.673380\pi$
$152$	18.9647	−	10.6802i	1.53824	−	0.866278i
$153$	−0.374987			−0.0303159
$154$	−12.1652	+	21.0708i	−0.980301	+	1.69793i
$155$		0			0
$156$	11.8310	+	20.4918i	0.947236	+	1.64066i
$157$	10.0270	−	17.3674i	0.800245	−	1.38607i	−0.119209	−	0.992869i	$-0.538036\pi$
$157$	10.0270	−	17.3674i	0.800245	−	1.38607i	0.919454	−	0.393197i	$-0.128631\pi$
$158$	−13.9230	−	24.1153i	−1.10765	−	1.91851i
$159$	4.08680			0.324104
$160$		0			0
$161$	1.09935	+	1.90412i	0.0866406	+	0.150066i
$162$	8.58867	+	14.8760i	0.674790	+	1.16877i
$163$	−14.2331			−1.11482			−0.557412	−	0.830236i	$-0.688206\pi$
$163$	−14.2331			−1.11482			−0.557412	+	0.830236i	$0.688206\pi$
$164$	0.292035			0.0228041
$165$		0			0
$166$	19.2810	−	33.3957i	1.49650	−	2.59201i
$167$	−2.80815	−	4.86386i	−0.217301	−	0.376376i	0.736681	−	0.676241i	$-0.236392\pi$
$167$	−2.80815	−	4.86386i	−0.217301	−	0.376376i	−0.953982	+	0.299864i	$0.903059\pi$
$168$	−17.5588	+	30.4127i	−1.35469	+	2.34639i
$169$	−0.563139	+	0.975386i	−0.0433184	+	0.0750297i
$170$		0			0
$171$	2.11254	+	1.25002i	0.161550	+	0.0955918i
$172$	1.69601			0.129320
$173$	5.34524	−	9.25824i	0.406391	−	0.703891i	−0.588091	−	0.808795i	$-0.700120\pi$
$173$	5.34524	−	9.25824i	0.406391	−	0.703891i	0.994482	+	0.104904i	$0.0334536\pi$
$174$	−6.89411	+	11.9409i	−0.522641	+	0.905241i
$175$		0			0
$176$	−4.61581	+	7.99482i	−0.347930	+	0.602632i
$177$	−9.78437	−	16.9470i	−0.735438	−	1.27382i
$178$	−3.28388			−0.246137
$179$	7.68942			0.574734			0.287367	−	0.957821i	$-0.407220\pi$
$179$	7.68942			0.574734			0.287367	+	0.957821i	$0.407220\pi$
$180$		0			0
$181$	3.06314	+	5.30551i	0.227681	+	0.394356i	0.957121	−	0.289690i	$-0.0935522\pi$
$181$	3.06314	+	5.30551i	0.227681	+	0.394356i	−0.729439	+	0.684046i	$0.760219\pi$
$182$	−41.5910			−3.08293
$183$	11.0301			0.815371
$184$	1.21843	+	2.11038i	0.0898239	+	0.155580i
$185$		0			0
$186$	−13.1021	−	22.6935i	−0.960691	−	1.66397i
$187$	−0.732039	+	1.26793i	−0.0535320	+	0.0927201i
$188$	−10.1283	+	17.5427i	−0.738680	+	1.27943i
$189$	−25.0593			−1.82280
$190$		0			0
$191$	5.85517			0.423666			0.211833	−	0.977306i	$-0.432057\pi$
$191$	5.85517			0.423666			0.211833	+	0.977306i	$0.432057\pi$
$192$	5.92891	−	10.2692i	0.427882	−	0.741113i
$193$	−1.29559	+	2.24402i	−0.0932584	+	0.161528i	−0.908880	−	0.417057i	$-0.863062\pi$
$193$	−1.29559	+	2.24402i	−0.0932584	+	0.161528i	0.815622	+	0.578585i	$0.196395\pi$
$194$	−5.38692	−	9.33041i	−0.386758	−	0.669885i
$195$		0			0
$196$	−26.8140	−	46.4431i	−1.91528	−	3.31737i
$197$	−19.8628			−1.41517			−0.707584	−	0.706629i	$-0.750215\pi$
$197$	−19.8628			−1.41517			−0.707584	+	0.706629i	$0.750215\pi$
$198$	−3.04120			−0.216128
$199$	6.38092	+	11.0521i	0.452331	+	0.783460i	0.998530	−	0.0541948i	$-0.0172592\pi$
$199$	6.38092	+	11.0521i	0.452331	+	0.783460i	−0.546199	+	0.837655i	$0.683926\pi$
$200$		0			0
$201$	8.93959			0.630550
$202$	−25.9586			−1.82644
$203$	−8.10065	−	14.0307i	−0.568554	−	0.984765i
$204$	−2.09607	+	3.63051i	−0.146755	+	0.254186i
$205$		0			0
$206$	−7.06914	+	12.2441i	−0.492530	+	0.853088i
$207$	−0.137413	+	0.238007i	−0.00955089	+	0.0165426i
$208$	−15.7808			−1.09420
$209$	8.35071	−	4.70279i	0.577631	−	0.325299i
$210$		0			0
$211$	−6.92759	+	11.9989i	−0.476915	+	0.826041i	−0.999650	−	0.0264545i	$-0.991578\pi$
$211$	−6.92759	+	11.9989i	−0.476915	+	0.826041i	0.522735	+	0.852495i	$0.324912\pi$
$212$	−5.27909	+	9.14366i	−0.362570	+	0.627989i
$213$	−5.44221	−	9.42619i	−0.372894	−	0.645872i
$214$	1.59935	−	2.77015i	0.109329	−	0.189363i
$215$		0			0
$216$	−27.7738			−1.88977
$217$	30.7901			2.09017
$218$	14.7777	+	25.5957i	1.00087	+	1.73356i
$219$	2.30850	+	3.99844i	0.155994	+	0.270190i
$220$		0			0
$221$	−2.50273			−0.168352
$222$	5.77382	+	10.0006i	0.387514	+	0.671193i
$223$	10.8480	−	18.7893i	0.726437	−	1.25823i	−0.231943	−	0.972729i	$-0.574508\pi$
$223$	10.8480	−	18.7893i	0.726437	−	1.25823i	0.958380	−	0.285496i	$-0.0921584\pi$
$224$	−0.734898	−	1.27288i	−0.0491024	−	0.0850479i
$225$		0			0
$226$	−9.51320	+	16.4773i	−0.632808	+	1.09606i
$227$	−8.19628			−0.544006			−0.272003	−	0.962296i	$-0.587686\pi$
$227$	−8.19628			−0.544006			−0.272003	+	0.962296i	$0.587686\pi$
$228$	23.9109	−	13.4657i	1.58354	−	0.891786i
$229$	−16.6619			−1.10105			−0.550526	−	0.834818i	$-0.685573\pi$
$229$	−16.6619			−1.10105			−0.550526	+	0.834818i	$0.685573\pi$
$230$		0			0
$231$	−7.73163	+	13.3916i	−0.508704	+	0.881101i
$232$	−8.97814	−	15.5506i	−0.589444	−	1.02095i
$233$	6.10677	−	10.5772i	0.400068	−	0.692937i	−0.593666	−	0.804711i	$-0.702320\pi$
$233$	6.10677	−	10.5772i	0.400068	−	0.692937i	0.993734	+	0.111774i	$0.0356533\pi$
$234$	−2.59935	−	4.50220i	−0.169925	−	0.294318i
$235$		0			0
$236$	50.5555			3.29088
$237$	−8.84876	−	15.3265i	−0.574789	−	0.995563i
$238$	−3.68430	−	6.38140i	−0.238818	−	0.413645i
$239$	2.03948			0.131923			0.0659614	−	0.997822i	$-0.478989\pi$
$239$	2.03948			0.131923			0.0659614	+	0.997822i	$0.478989\pi$
$240$		0			0
$241$	−8.76183	−	15.1759i	−0.564399	−	0.977568i	−0.997105	−	0.0760330i	$-0.975775\pi$
$241$	−8.76183	−	15.1759i	−0.564399	−	0.977568i	0.432706	−	0.901535i	$-0.357559\pi$
$242$	7.57218	−	13.1154i	0.486758	−	0.843089i
$243$	−2.88478	−	4.99659i	−0.185059	−	0.320531i
$244$	−14.2481	+	24.6784i	−0.912141	+	1.57987i
$245$		0			0
$246$	0.277648			0.0177022
$247$	14.0995	+	8.34289i	0.897129	+	0.530846i
$248$	34.1254			2.16697
$249$	12.2541	−	21.2247i	0.776572	−	1.34506i
$250$		0			0
$251$	1.66903	+	2.89084i	0.105348	+	0.182468i	0.913880	−	0.405984i	$-0.133071\pi$
$251$	1.66903	+	2.89084i	0.105348	+	0.182468i	−0.808532	+	0.588452i	$0.799738\pi$
$252$	5.11597	−	8.86112i	0.322276	−	0.558198i
$253$	0.536509	+	0.929261i	0.0337301	+	0.0584222i
$254$	−9.66849			−0.606655
$255$		0			0
$256$	16.1185	+	27.9181i	1.00741	+	1.74488i
$257$	−13.7922	−	23.8889i	−0.860337	−	1.49015i	−0.871604	−	0.490210i	$-0.836920\pi$
$257$	−13.7922	−	23.8889i	−0.860337	−	1.49015i	0.0112676	−	0.999937i	$-0.496413\pi$
$258$	1.61246			0.100387
$259$	−13.5686			−0.843112
$260$		0			0
$261$	1.01255	−	1.75378i	0.0626750	−	0.108556i
$262$	20.0487	+	34.7254i	1.23861	+	2.14534i
$263$	−6.81310	+	11.8006i	−0.420114	+	0.727658i	−0.995950	−	0.0899066i	$-0.971343\pi$
$263$	−6.81310	+	11.8006i	−0.420114	+	0.727658i	0.575837	+	0.817565i	$0.304676\pi$
$264$	−8.56914	+	14.8422i	−0.527394	+	0.913473i
$265$		0			0
$266$	−0.516467	+	48.2322i	−0.0316666	+	2.95731i
$267$	−2.08707			−0.127727
$268$	−11.5476	+	20.0011i	−0.705385	+	1.22176i
$269$	1.80404	−	3.12469i	0.109994	−	0.190515i	−0.805773	−	0.592224i	$-0.798250\pi$
$269$	1.80404	−	3.12469i	0.109994	−	0.190515i	0.915768	+	0.401708i	$0.131583\pi$
$270$		0			0
$271$	−5.28157	+	9.14795i	−0.320833	+	0.555698i	−0.980660	−	0.195719i	$-0.937296\pi$
$271$	−5.28157	+	9.14795i	−0.320833	+	0.555698i	0.659828	+	0.751417i	$0.270629\pi$
$272$	−1.39793	−	2.42128i	−0.0847617	−	0.146812i
$273$	−26.4332			−1.59981
$274$	−40.3568			−2.43804
$275$		0			0
$276$	1.53621	+	2.66079i	0.0924688	+	0.160161i
$277$	6.73487			0.404659			0.202330	−	0.979317i	$-0.435149\pi$
$277$	6.73487			0.404659			0.202330	+	0.979317i	$0.435149\pi$
$278$	−6.55434			−0.393103
$279$	1.92432	+	3.33301i	0.115206	+	0.199542i
$280$		0			0
$281$	−11.7152	−	20.2912i	−0.698868	−	1.21047i	−0.968859	−	0.247612i	$-0.920354\pi$
$281$	−11.7152	−	20.2912i	−0.698868	−	1.21047i	0.269992	−	0.962863i	$-0.412979\pi$
$282$	−9.62928	+	16.6784i	−0.573415	+	0.993185i
$283$	−7.34157	+	12.7160i	−0.436411	+	0.755886i	−0.997410	−	0.0719306i	$-0.977084\pi$
$283$	−7.34157	+	12.7160i	−0.436411	+	0.755886i	0.560999	+	0.827817i	$0.310417\pi$
$284$	28.1197			1.66860
$285$		0			0
$286$	−20.2975			−1.20022
$287$	−0.163119	+	0.282531i	−0.00962863	+	0.0166773i
$288$	0.0918589	−	0.159104i	0.00541284	−	0.00937531i
$289$	8.27830	+	14.3384i	0.486959	+	0.843437i
$290$		0			0
$291$	−3.42367	−	5.92996i	−0.200699	−	0.347621i
$292$	−11.9280			−0.698031
$293$	18.1855			1.06241			0.531206	−	0.847243i	$-0.321739\pi$
$293$	18.1855			1.06241			0.531206	+	0.847243i	$0.321739\pi$
$294$	−25.4929	−	44.1550i	−1.48678	−	2.57517i
$295$		0			0
$296$	−15.0384			−0.874089
$297$	−12.2296			−0.709634
$298$	22.0641	+	38.2161i	1.27814	+	2.21380i
$299$	−0.917122	+	1.58850i	−0.0530385	+	0.0918654i
$300$		0			0
$301$	−0.947326	+	1.64082i	−0.0546030	+	0.0945752i
$302$	15.6391	−	27.0877i	0.899928	−	1.55872i
$303$	−16.4981			−0.947788
$304$	−0.195962	+	18.3006i	−0.0112392	+	1.04961i
$305$		0			0
$306$	0.460522	−	0.797647i	0.0263263	−	0.0455985i
$307$	14.6901	−	25.4439i	0.838406	−	1.45216i	−0.0528200	−	0.998604i	$-0.516821\pi$
$307$	14.6901	−	25.4439i	0.838406	−	1.45216i	0.891226	−	0.453559i	$-0.149846\pi$
$308$	−19.9745	−	34.5969i	−1.13815	−	1.97134i
$309$	−4.49281	+	7.78177i	−0.255587	+	0.442689i
$310$		0			0
$311$	−0.193232			−0.0109572			−0.00547859	−	0.999985i	$-0.501744\pi$
$311$	−0.193232			−0.0109572			−0.00547859	+	0.999985i	$0.501744\pi$
$312$	−29.2966			−1.65859
$313$	−10.6377	−	18.4251i	−0.601281	−	1.04145i	−0.992627	−	0.121206i	$-0.961324\pi$
$313$	−10.6377	−	18.4251i	−0.601281	−	1.04145i	0.391346	−	0.920243i	$-0.372009\pi$
$314$	24.6285	+	42.6578i	1.38986	+	2.40732i
$315$		0			0
$316$	45.7213			2.57202
$317$	9.58506	+	16.6018i	0.538351	+	0.932451i	0.998993	+	0.0448649i	$0.0142857\pi$
$317$	9.58506	+	16.6018i	0.538351	+	0.932451i	−0.460642	+	0.887586i	$0.652381\pi$
$318$	−5.01901	+	8.69317i	−0.281452	+	0.487489i
$319$	−3.95333	−	6.84736i	−0.221344	−	0.383379i
$320$		0			0
$321$	1.01647	−	1.76057i	0.0567337	−	0.0982656i
$322$	−5.40043			−0.300954
$323$	−0.0310783	+	2.90236i	−0.00172924	+	0.161492i
$324$	−28.2042			−1.56690
$325$		0			0
$326$	17.4797	−	30.2758i	0.968112	−	1.67682i
$327$	9.39197	+	16.2674i	0.519377	+	0.899588i
$328$	−0.180789	+	0.313136i	−0.00998240	+	0.0172900i
$329$	−11.3145	−	19.5973i	−0.623789	−	1.08043i
$330$		0			0
$331$	−20.6070			−1.13266			−0.566331	−	0.824178i	$-0.691638\pi$
$331$	−20.6070			−1.13266			−0.566331	+	0.824178i	$0.691638\pi$
$332$	31.6583	+	54.8337i	1.73747	+	3.00939i
$333$	−0.848007	−	1.46879i	−0.0464705	−	0.0804893i
$334$	13.7948			0.754816
$335$		0			0
$336$	−14.7646	−	25.5730i	−0.805473	−	1.39512i
$337$	−5.10368	+	8.83982i	−0.278015	+	0.481536i	−0.970891	−	0.239520i	$-0.923010\pi$
$337$	−5.10368	+	8.83982i	−0.278015	+	0.481536i	0.692876	+	0.721056i	$0.256343\pi$
$338$	−1.38318	−	2.39575i	−0.0752353	−	0.130311i
$339$	−6.04613	+	10.4722i	−0.328381	+	0.568772i
$340$		0			0
$341$	15.0264			0.813725
$342$	−5.25339	+	2.95850i	−0.284071	+	0.159977i
$343$	28.3719			1.53194
$344$	−1.04994	+	1.81856i	−0.0566092	+	0.0980500i
$345$		0			0
$346$	13.1290	+	22.7401i	0.705820	+	1.22252i
$347$	2.72055	−	4.71213i	0.146047	−	0.252960i	−0.783716	−	0.621119i	$-0.786678\pi$
$347$	2.72055	−	4.71213i	0.146047	−	0.252960i	0.929763	+	0.368159i	$0.120012\pi$
$348$	−11.3197	−	19.6063i	−0.606800	−	1.05101i
$349$	−1.55114			−0.0830304			−0.0415152	−	0.999138i	$-0.513219\pi$
$349$	−1.55114			−0.0830304			−0.0415152	+	0.999138i	$0.513219\pi$
$350$		0			0
$351$	−10.4528	−	18.1048i	−0.557928	−	0.966360i
$352$	−0.358649	−	0.621199i	−0.0191161	−	0.0331100i
$353$	32.9335			1.75287			0.876437	−	0.481517i	$-0.159914\pi$
$353$	32.9335			1.75287			0.876437	+	0.481517i	$0.159914\pi$
$354$	48.0648			2.55461
$355$		0			0
$356$	2.69596	−	4.66954i	0.142886	−	0.247485i
$357$	−2.34157	−	4.05571i	−0.123929	−	0.214651i
$358$	−9.44339	+	16.3564i	−0.499098	+	0.864464i
$359$	1.74864	−	3.02873i	0.0922894	−	0.159850i	−0.816185	−	0.577791i	$-0.803915\pi$
$359$	1.74864	−	3.02873i	0.0922894	−	0.159850i	0.908474	+	0.417941i	$0.137248\pi$
$360$		0			0
$361$	9.85017	−	16.2473i	0.518430	−	0.855120i
$362$	−15.0474			−0.790873
$363$	4.81251	−	8.33551i	0.252591	−	0.437501i
$364$	34.1449	−	59.1408i	1.78968	−	3.09982i
$365$		0			0
$366$	−13.5461	+	23.4626i	−0.708068	+	1.22641i
$367$	9.75196	+	16.8909i	0.509048	+	0.881697i	0.999945	+	0.0104794i	$0.00333575\pi$
$367$	9.75196	+	16.8909i	0.509048	+	0.881697i	−0.490897	+	0.871218i	$0.663331\pi$
$368$	−2.04907			−0.106815
$369$	−0.0407784			−0.00212284
$370$		0			0
$371$	−5.89738	−	10.2146i	−0.306177	−	0.530314i
$372$	43.0256			2.23077
$373$	−23.5158			−1.21760			−0.608802	−	0.793322i	$-0.708350\pi$
$373$	−23.5158			−1.21760			−0.608802	+	0.793322i	$0.708350\pi$
$374$	−1.79804	−	3.11429i	−0.0929743	−	0.161036i
$375$		0			0
$376$	−12.5401	−	21.7201i	−0.646708	−	1.12013i
$377$	6.75791	−	11.7050i	0.348050	−	0.602841i
$378$	30.7754	−	53.3046i	1.58292	−	2.74169i
$379$	−7.05148			−0.362210			−0.181105	−	0.983464i	$-0.557967\pi$
$379$	−7.05148			−0.362210			−0.181105	+	0.983464i	$0.557967\pi$
$380$		0			0
$381$	−6.14483			−0.314809
$382$	−7.19075	+	12.4547i	−0.367911	+	0.637240i
$383$	1.54204	−	2.67090i	0.0787947	−	0.136476i	−0.823935	−	0.566684i	$-0.808226\pi$
$383$	1.54204	−	2.67090i	0.0787947	−	0.136476i	0.902730	+	0.430207i	$0.141560\pi$
$384$	15.0719	+	26.1052i	0.769133	+	1.33218i
$385$		0			0
$386$	−3.18222	−	5.51177i	−0.161971	−	0.280542i
$387$	−0.236823			−0.0120384
$388$	17.6900			0.898072
$389$	−4.69542	−	8.13270i	−0.238067	−	0.412345i	0.722092	−	0.691797i	$-0.243181\pi$
$389$	−4.69542	−	8.13270i	−0.238067	−	0.412345i	−0.960160	+	0.279452i	$0.909847\pi$
$390$		0			0
$391$	−0.324970			−0.0164344
$392$	66.3984			3.35362
$393$	12.7420	+	22.0698i	0.642749	+	1.11327i
$394$	24.3936	−	42.2509i	1.22893	−	2.12857i
$395$		0			0
$396$	2.49673	−	4.32446i	0.125465	−	0.217312i
$397$	−13.3797	+	23.1744i	−0.671510	+	1.16309i	0.305966	+	0.952042i	$0.401021\pi$
$397$	−13.3797	+	23.1744i	−0.671510	+	1.16309i	−0.977476	+	0.211047i	$0.932313\pi$
$398$	−31.3456			−1.57122
$399$	−0.328242	+	30.6541i	−0.0164326	+	1.53462i
$400$		0			0
$401$	12.5851	−	21.7980i	0.628468	−	1.08854i	−0.359391	−	0.933187i	$-0.617016\pi$
$401$	12.5851	−	21.7980i	0.628468	−	1.08854i	0.987859	−	0.155352i	$-0.0496511\pi$
$402$	−10.9787	+	19.0157i	−0.547569	+	0.948417i
$403$	12.8432	+	22.2451i	0.639767	+	1.10811i
$404$	21.3112	−	36.9121i	1.06027	−	1.83645i
$405$		0			0
$406$	39.7937			1.97493
$407$	−6.62183			−0.328232
$408$	−2.59521	−	4.49504i	−0.128482	−	0.222538i
$409$	14.1608	+	24.5271i	0.700204	+	1.21279i	0.968395	+	0.249423i	$0.0802410\pi$
$409$	14.1608	+	24.5271i	0.700204	+	1.21279i	−0.268191	+	0.963366i	$0.586426\pi$
$410$		0			0
$411$	−25.6489			−1.26516
$412$	−11.6071	−	20.1041i	−0.571840	−	0.990457i
$413$	−28.2383	+	48.9102i	−1.38952	+	2.40671i
$414$	−0.337515	−	0.584593i	−0.0165880	−	0.0287312i
$415$		0			0
$416$	0.613083	−	1.06189i	0.0300589	−	0.0520635i
$417$	−4.16563			−0.203992
$418$	−0.252049	+	23.5386i	−0.0123281	+	1.15131i
$419$	13.0449			0.637287			0.318643	−	0.947875i	$-0.396773\pi$
$419$	13.0449			0.637287			0.318643	+	0.947875i	$0.396773\pi$
$420$		0			0
$421$	−1.66248	+	2.87951i	−0.0810246	+	0.140339i	−0.903690	−	0.428187i	$-0.859153\pi$
$421$	−1.66248	+	2.87951i	−0.0810246	+	0.140339i	0.822666	+	0.568525i	$0.192486\pi$
$422$	−17.0156	−	29.4718i	−0.828305	−	1.43467i
$423$	1.41426	−	2.44958i	0.0687638	−	0.119102i
$424$	−6.53621	−	11.3210i	−0.317426	−	0.549798i
$425$		0			0
$426$	26.7344			1.29528
$427$	−15.9168	−	27.5688i	−0.770270	−	1.33415i
$428$	2.62603	+	4.54841i	0.126934	+	0.219856i
$429$	−12.9001			−0.622823
$430$		0			0
$431$	−0.0242034	−	0.0419216i	−0.00116584	−	0.00201929i	0.865442	−	0.501009i	$-0.167038\pi$
$431$	−0.0242034	−	0.0419216i	−0.00116584	−	0.00201929i	−0.866608	+	0.498990i	$0.833704\pi$
$432$	11.6770	−	20.2252i	0.561811	−	0.973085i
$433$	−4.78436	−	8.28676i	−0.229922	−	0.398236i	0.727863	−	0.685723i	$-0.240514\pi$
$433$	−4.78436	−	8.28676i	−0.229922	−	0.398236i	−0.957785	+	0.287486i	$0.907180\pi$
$434$	−37.8134	+	65.4948i	−1.81510	+	3.14385i
$435$		0			0
$436$	−48.5280			−2.32407
$437$	1.83076	+	1.08329i	0.0875773	+	0.0518209i
$438$	−11.3403			−0.541861
$439$	11.1257	−	19.2703i	0.531002	−	0.919723i	−0.468343	−	0.883547i	$-0.655149\pi$
$439$	11.1257	−	19.2703i	0.531002	−	0.919723i	0.999345	−	0.0361764i	$-0.0115178\pi$
$440$		0			0
$441$	3.74417	+	6.48509i	0.178294	+	0.308814i
$442$	3.07361	−	5.32364i	0.146197	−	0.253220i
$443$	10.0579	+	17.4207i	0.477863	+	0.827684i	0.999678	−	0.0253753i	$-0.00807806\pi$
$443$	10.0579	+	17.4207i	0.477863	+	0.827684i	−0.521815	+	0.853059i	$0.674745\pi$
$444$	−18.9605			−0.899827
$445$		0			0
$446$	26.6449	+	46.1504i	1.26167	+	2.18528i
$447$	14.0229	+	24.2883i	0.663258	+	1.14880i
$448$	−34.2224			−1.61686
$449$	−12.4973			−0.589783			−0.294891	−	0.955531i	$-0.595283\pi$
$449$	−12.4973			−0.589783			−0.294891	+	0.955531i	$0.595283\pi$
$450$		0			0
$451$	−0.0796065	+	0.137883i	−0.00374852	+	0.00649263i
$452$	−15.6201	−	27.0548i	−0.734707	−	1.27255i
$453$	9.93945	−	17.2156i	0.466996	−	0.808861i
$454$	10.0659	−	17.4346i	0.472415	−	0.818246i
$455$		0			0
$456$	−0.363798	+	33.9746i	−0.0170364	+	1.59101i
$457$	28.3179			1.32465			0.662327	−	0.749215i	$-0.269569\pi$
$457$	28.3179			1.32465			0.662327	+	0.749215i	$0.269569\pi$
$458$	20.4626	−	35.4422i	0.956153	−	1.65610i
$459$	1.85190	−	3.20759i	0.0864394	−	0.149717i
$460$		0			0
$461$	−2.65976	+	4.60683i	−0.123877	+	0.214562i	−0.921293	−	0.388868i	$-0.872866\pi$
$461$	−2.65976	+	4.60683i	−0.123877	+	0.214562i	0.797416	+	0.603430i	$0.206200\pi$
$462$	−18.9904	−	32.8924i	−0.883515	−	1.53029i
$463$	17.9327			0.833401			0.416701	−	0.909044i	$-0.363186\pi$
$463$	17.9327			0.833401			0.416701	+	0.909044i	$0.363186\pi$
$464$	15.0988			0.700944
$465$		0			0
$466$	14.9995	+	25.9798i	0.694836	+	1.20349i
$467$	−28.7791			−1.33174			−0.665868	−	0.746069i	$-0.731939\pi$
$467$	−28.7791			−1.33174			−0.665868	+	0.746069i	$0.731939\pi$
$468$	8.53593			0.394574
$469$	−12.9001	−	22.3436i	−0.595672	−	1.03173i
$470$		0			0
$471$	15.6527	+	27.1112i	0.721237	+	1.24922i
$472$	−31.2972	+	54.2083i	−1.44057	+	2.49514i
$473$	−0.462320	+	0.800762i	−0.0212575	+	0.0368191i
$474$	43.4687			1.99658
$475$		0			0
$476$	12.0988			0.554548
$477$	0.737147	−	1.27678i	0.0337516	−	0.0584595i
$478$	−2.50469	+	4.33824i	−0.114562	+	0.198427i
$479$	4.02574	+	6.97279i	0.183941	+	0.318595i	0.943219	−	0.332171i	$-0.107781\pi$
$479$	4.02574	+	6.97279i	0.183941	+	0.318595i	−0.759278	+	0.650766i	$0.774448\pi$
$480$		0			0
$481$	−5.65976	−	9.80298i	−0.258063	−	0.446978i
$482$	43.0417			1.96049
$483$	−3.43226			−0.156173
$484$	12.4330	+	21.5347i	0.565138	+	0.978849i
$485$		0			0
$486$	14.1712			0.642819
$487$	−1.09761			−0.0497376			−0.0248688	−	0.999691i	$-0.507917\pi$
$487$	−1.09761			−0.0497376			−0.0248688	+	0.999691i	$0.507917\pi$
$488$	−17.6410	−	30.5551i	−0.798571	−	1.38316i
$489$	11.1093	−	19.2418i	0.502379	−	0.870145i
$490$		0			0
$491$	−6.55267	+	11.3496i	−0.295718	+	0.512199i	−0.975152	−	0.221538i	$-0.928892\pi$
$491$	−6.55267	+	11.3496i	−0.295718	+	0.512199i	0.679434	+	0.733737i	$0.262226\pi$
$492$	−0.227940	+	0.394804i	−0.0102763	+	0.0177991i
$493$	2.39458			0.107846
$494$	−35.0621	+	19.7456i	−1.57752	+	0.888395i
$495$		0			0
$496$	−14.3474	+	24.8505i	−0.644219	+	1.11582i
$497$	−15.7066	+	27.2046i	−0.704536	+	1.22029i
$498$	30.0985	+	52.1322i	1.34875	+	2.33610i
$499$	−12.0703	+	20.9064i	−0.540342	+	0.935900i	0.458542	+	0.888673i	$0.348372\pi$
$499$	−12.0703	+	20.9064i	−0.540342	+	0.935900i	−0.998884	+	0.0472275i	$0.984961\pi$
$500$		0			0
$501$	8.76729			0.391694
$502$	−8.19895			−0.365937
$503$	−9.48090	−	16.4214i	−0.422733	−	0.732194i	0.573473	−	0.819224i	$-0.305596\pi$
$503$	−9.48090	−	16.4214i	−0.422733	−	0.732194i	−0.996206	+	0.0870300i	$0.972262\pi$
$504$	6.33424	+	10.9712i	0.282150	+	0.488697i
$505$		0			0
$506$	−2.63555			−0.117165
$507$	−0.879086	−	1.52262i	−0.0390416	−	0.0676220i
$508$	7.93753	−	13.7482i	0.352171	−	0.609978i
$509$	−10.9803	−	19.0184i	−0.486692	−	0.842974i	0.513191	−	0.858274i	$-0.328463\pi$
$509$	−10.9803	−	19.0184i	−0.486692	−	0.842974i	−0.999883	+	0.0152997i	$0.995130\pi$
$510$		0			0
$511$	6.66248	−	11.5398i	0.294731	−	0.510489i
$512$	−40.5609			−1.79255
$513$	−21.1255	+	11.8971i	−0.932714	+	0.525268i
$514$	67.7531			2.98846
$515$		0			0
$516$	−1.32378	+	2.29285i	−0.0582761	+	0.100937i
$517$	−5.52177	−	9.56399i	−0.242847	−	0.420624i
$518$	16.6636	−	28.8622i	0.732157	−	1.26813i
$519$	8.34417	+	14.4525i	0.366268	+	0.634395i
$520$		0			0
$521$	6.56968			0.287823			0.143912	−	0.989591i	$-0.454032\pi$
$521$	6.56968			0.287823			0.143912	+	0.989591i	$0.454032\pi$
$522$	2.48702	+	4.30764i	0.108854	+	0.188540i
$523$	2.09889	+	3.63538i	0.0917779	+	0.158964i	0.908259	−	0.418408i	$-0.137412\pi$
$523$	2.09889	+	3.63538i	0.0917779	+	0.158964i	−0.816481	+	0.577372i	$0.804078\pi$
$524$	−65.8375			−2.87613
$525$		0			0
$526$	−16.7344	−	28.9848i	−0.729653	−	1.26380i
$527$	−2.27541	+	3.94113i	−0.0991186	+	0.171678i
$528$	−7.20549	−	12.4803i	−0.313579	−	0.543134i
$529$	11.3809	−	19.7123i	0.494822	−	0.857058i
$530$		0			0
$531$	−7.05933			−0.306349
$532$	−68.1603	−	40.3316i	−2.95513	−	1.74860i
$533$	−0.272162			−0.0117887
$534$	2.56314	−	4.43949i	0.110918	−	0.192115i
$535$		0			0
$536$	−14.2975	−	24.7640i	−0.617558	−	1.06964i
$537$	−6.00176	+	10.3954i	−0.258995	+	0.448593i
$538$	4.43108	+	7.67486i	0.191038	+	0.330887i
$539$	29.2371			1.25933
$540$		0			0
$541$	2.31505	+	4.00978i	0.0995316	+	0.172394i	0.911491	−	0.411320i	$-0.134932\pi$
$541$	2.31505	+	4.00978i	0.0995316	+	0.172394i	−0.811959	+	0.583714i	$0.801599\pi$
$542$	−12.9726	−	22.4692i	−0.557221	−	0.965136i
$543$	−9.56340			−0.410405
$544$	0.217238			0.00931400
$545$		0			0
$546$	32.4627	−	56.2271i	1.38928	−	2.40630i
$547$	−19.0199	−	32.9435i	−0.813233	−	1.40856i	−0.910590	−	0.413312i	$-0.864372\pi$
$547$	−19.0199	−	32.9435i	−0.813233	−	1.40856i	0.0973563	−	0.995250i	$-0.468961\pi$
$548$	33.1317	−	57.3858i	1.41532	−	2.45140i
$549$	1.98953	−	3.44597i	0.0849113	−	0.147071i
$550$		0			0
$551$	−13.4902	−	7.98236i	−0.574701	−	0.340060i
$552$	−3.80405			−0.161911
$553$	−25.5381	+	44.2333i	−1.08599	+	1.88099i
$554$	−8.27110	+	14.3260i	−0.351406	+	0.608652i
$555$		0			0
$556$	5.38092	−	9.32002i	0.228202	−	0.395257i
$557$	18.2153	+	31.5498i	0.771807	+	1.33681i	0.936572	+	0.350476i	$0.113980\pi$
$557$	18.2153	+	31.5498i	0.771807	+	1.33681i	−0.164765	+	0.986333i	$0.552687\pi$
$558$	−9.45302			−0.400178
$559$	−1.58060			−0.0668523
$560$		0			0
$561$	−1.14275	−	1.97929i	−0.0482468	−	0.0835659i
$562$	57.5496			2.42758
$563$	−20.6856			−0.871795			−0.435897	−	0.899996i	$-0.643569\pi$
$563$	−20.6856			−0.871795			−0.435897	+	0.899996i	$0.643569\pi$
$564$	−15.8107	−	27.3849i	−0.665750	−	1.15311i
$565$		0			0
$566$	−18.0324	−	31.2330i	−0.757958	−	1.31282i
$567$	15.7537	−	27.2862i	0.661594	−	1.14591i
$568$	−17.4080	+	30.1515i	−0.730422	+	1.26513i
$569$	−27.1132			−1.13664			−0.568322	−	0.822806i	$-0.692407\pi$
$569$	−27.1132			−1.13664			−0.568322	+	0.822806i	$0.692407\pi$
$570$		0			0
$571$	46.4687			1.94466			0.972328	−	0.233622i	$-0.0750578\pi$
$571$	46.4687			1.94466			0.972328	+	0.233622i	$0.0750578\pi$
$572$	16.6636	−	28.8622i	0.696741	−	1.20679i
$573$	−4.57009	+	7.91564i	−0.190918	+	0.330680i
$574$	−0.400654	−	0.693954i	−0.0167230	−	0.0289651i
$575$		0			0
$576$	−2.13882	−	3.70455i	−0.0891177	−	0.154356i
$577$	−18.0398			−0.751008			−0.375504	−	0.926821i	$-0.622530\pi$
$577$	−18.0398			−0.751008			−0.375504	+	0.926821i	$0.622530\pi$
$578$	−40.6664			−1.69150
$579$	−2.02247	−	3.50302i	−0.0840509	−	0.145580i
$580$		0			0
$581$	−70.7322			−2.93447
$582$	16.8184			0.697147
$583$	−2.87808	−	4.98497i	−0.119198	−	0.206457i
$584$	7.38419	−	12.7898i	0.305560	−	0.529245i
$585$		0			0
$586$	−22.3337	+	38.6831i	−0.922597	+	1.59798i
$587$	13.0168	−	22.5458i	0.537262	−	0.930565i	−0.461788	−	0.886990i	$-0.652792\pi$
$587$	13.0168	−	22.5458i	0.537262	−	0.930565i	0.999050	−	0.0435750i	$-0.0138747\pi$
$588$	83.7156			3.45237
$589$	25.9567	−	14.6178i	1.06953	−	0.602316i
$590$		0			0
$591$	15.5034	−	26.8526i	0.637724	−	1.10457i
$592$	6.32263	−	10.9511i	0.259858	−	0.450088i
$593$	−9.07803	−	15.7236i	−0.372790	−	0.645691i	0.617203	−	0.786804i	$-0.288266\pi$
$593$	−9.07803	−	15.7236i	−0.372790	−	0.645691i	−0.989994	+	0.141112i	$0.954932\pi$
$594$	15.0192	−	26.0140i	0.616245	−	1.06737i
$595$		0			0
$596$	−72.4556			−2.96790
$597$	−19.9218			−0.815345
$598$	−2.25264	−	3.90168i	−0.0921172	−	0.159552i
$599$	−20.0357	−	34.7028i	−0.818635	−	1.41792i	−0.906688	−	0.421802i	$-0.861398\pi$
$599$	−20.0357	−	34.7028i	−0.818635	−	1.41792i	0.0880531	−	0.996116i	$-0.471935\pi$
$600$		0			0
$601$	15.0473			0.613793			0.306897	−	0.951743i	$-0.400709\pi$
$601$	15.0473			0.613793			0.306897	+	0.951743i	$0.400709\pi$
$602$	−2.32683	−	4.03018i	−0.0948344	−	0.164258i
$603$	1.61246	−	2.79286i	0.0656643	−	0.113734i
$604$	25.6784	+	44.4763i	1.04484	+	1.80972i
$605$		0			0
$606$	20.2613	−	35.0936i	0.823059	−	1.42558i
$607$	29.3860			1.19274			0.596370	−	0.802709i	$-0.296609\pi$
$607$	29.3860			1.19274			0.596370	+	0.802709i	$0.296609\pi$
$608$	−1.22384	−	0.724166i	−0.0496333	−	0.0293688i
$609$	25.2910			1.02484
$610$		0			0
$611$	9.43905	−	16.3489i	0.381863	−	0.661406i
$612$	0.756148	+	1.30969i	0.0305655	+	0.0529410i
$613$	−17.3539	+	30.0578i	−0.700917	+	1.21402i	0.267229	+	0.963633i	$0.413892\pi$
$613$	−17.3539	+	30.0578i	−0.700917	+	1.21402i	−0.968145	+	0.250390i	$0.919441\pi$
$614$	36.0818	+	62.4955i	1.45614	+	2.52211i
$615$		0			0
$616$	49.4622			1.99289
$617$	5.36376	+	9.29031i	0.215937	+	0.374014i	0.953562	−	0.301197i	$-0.0973861\pi$
$617$	5.36376	+	9.29031i	0.215937	+	0.374014i	−0.737625	+	0.675210i	$0.764053\pi$
$618$	−11.0352	−	19.1136i	−0.443903	−	0.768862i
$619$	−36.1437			−1.45274			−0.726370	−	0.687304i	$-0.758794\pi$
$619$	−36.1437			−1.45274			−0.726370	+	0.687304i	$0.758794\pi$
$620$		0			0
$621$	−1.35725	−	2.35083i	−0.0544647	−	0.0943357i
$622$	0.237309	−	0.411031i	0.00951521	−	0.0164808i
$623$	3.01171	+	5.21644i	0.120662	+	0.208992i
$624$	12.3172	−	21.3341i	0.493084	−	0.854046i
$625$		0			0
$626$	52.2569			2.08861
$627$	−0.160191	+	14.9600i	−0.00639739	+	0.597445i
$628$	−80.8768			−3.22734
$629$	1.00273	−	1.73678i	0.0399814	−	0.0692499i
$630$		0			0
$631$	15.7882	+	27.3460i	0.628519	+	1.08863i	0.987849	+	0.155417i	$0.0496720\pi$
$631$	15.7882	+	27.3460i	0.628519	+	1.08863i	−0.359330	+	0.933211i	$0.616995\pi$
$632$	−28.3045	+	49.0248i	−1.12589	+	1.95010i
$633$	−10.8143	−	18.7309i	−0.429829	−	0.744485i
$634$	−47.0857			−1.87001
$635$		0			0
$636$	−8.24090	−	14.2737i	−0.326773	−	0.565987i
$637$	24.9893	+	43.2827i	0.990111	+	1.71492i
$638$	19.4204			0.768859
$639$	−3.92650			−0.155330
$640$		0			0
$641$	−9.91331	+	17.1704i	−0.391552	+	0.678188i	−0.992654	−	0.120984i	$-0.961395\pi$
$641$	−9.91331	+	17.1704i	−0.391552	+	0.678188i	0.601102	+	0.799172i	$0.294728\pi$
$642$	2.49665	+	4.32432i	0.0985349	+	0.170667i
$643$	6.72843	−	11.6540i	0.265343	−	0.459588i	−0.702310	−	0.711871i	$-0.747848\pi$
$643$	6.72843	−	11.6540i	0.265343	−	0.459588i	0.967654	+	0.252283i	$0.0811814\pi$
$644$	4.43359	−	7.67920i	0.174708	−	0.302603i
$645$		0			0
$646$	−6.13555	−	3.63051i	−0.241400	−	0.142840i
$647$	−4.19511			−0.164927			−0.0824634	−	0.996594i	$-0.526279\pi$
$647$	−4.19511			−0.164927			−0.0824634	+	0.996594i	$0.526279\pi$
$648$	17.4602	−	30.2420i	0.685902	−	1.18802i
$649$	−13.7810	+	23.8694i	−0.540953	+	0.936957i
$650$		0			0
$651$	−24.0324	+	41.6253i	−0.941904	+	1.63143i
$652$	28.7006	+	49.7109i	1.12400	+	1.94683i
$653$	12.1680			0.476170			0.238085	−	0.971244i	$-0.423480\pi$
$653$	12.1680			0.476170			0.238085	+	0.971244i	$0.423480\pi$
$654$	−46.1372			−1.80411
$655$		0			0
$656$	−0.152019	−	0.263305i	−0.00593535	−	0.0102803i
$657$	1.66556			0.0649798
$658$	55.5814			2.16679
$659$	−4.12236	−	7.14013i	−0.160584	−	0.278140i	0.774494	−	0.632581i	$-0.218004\pi$
$659$	−4.12236	−	7.14013i	−0.160584	−	0.278140i	−0.935078	+	0.354441i	$0.884671\pi$
$660$		0			0
$661$	−10.5599	−	18.2902i	−0.410731	−	0.711407i	0.584239	−	0.811582i	$-0.301393\pi$
$661$	−10.5599	−	18.2902i	−0.410731	−	0.711407i	−0.994970	+	0.100175i	$0.968060\pi$
$662$	25.3075	−	43.8338i	0.983603	−	1.70365i
$663$	1.95344	−	3.38345i	0.0758652	−	0.131402i
$664$	−78.3941			−3.04228
$665$		0			0
$666$	4.16576			0.161420
$667$	0.877489	−	1.51986i	0.0339765	−	0.0588490i
$668$	−11.3251	+	19.6156i	−0.438180	+	0.758951i
$669$	16.9342	+	29.3310i	0.654716	+	1.13400i
$670$		0			0
$671$	−7.76783	−	13.4543i	−0.299874	−	0.519397i
$672$	2.29442			0.0885090
$673$	30.2802			1.16722			0.583608	−	0.812036i	$-0.301641\pi$
$673$	30.2802			1.16722			0.583608	+	0.812036i	$0.301641\pi$
$674$	−12.5357	−	21.7124i	−0.482856	−	0.836331i
$675$		0			0
$676$	4.54221			0.174700
$677$	−49.9003			−1.91783			−0.958913	−	0.283701i	$-0.908438\pi$
$677$	−49.9003			−1.91783			−0.958913	+	0.283701i	$0.908438\pi$
$678$	−14.8505	−	25.7219i	−0.570331	−	0.987842i
$679$	−9.88092	+	17.1142i	−0.379195	+	0.656785i
$680$		0			0
$681$	6.39738	−	11.0806i	0.245148	−	0.424609i
$682$	−18.4539	+	31.9632i	−0.706638	+	1.22393i
$683$	−3.11357			−0.119137			−0.0595687	−	0.998224i	$-0.518973\pi$
$683$	−3.11357			−0.119137			−0.0595687	+	0.998224i	$0.518973\pi$
$684$	0.105997	−	9.89894i	0.00405290	−	0.378496i
$685$		0			0
$686$	−34.8436	+	60.3509i	−1.33034	+	2.30421i
$687$	13.0050	−	22.5254i	0.496172	−	0.859396i
$688$	−0.882861	−	1.52916i	−0.0336588	−	0.0582987i
$689$	4.91985	−	8.52143i	0.187431	−	0.324641i
$690$		0			0
$691$	−30.2831			−1.15202			−0.576012	−	0.817441i	$-0.695392\pi$
$691$	−30.2831			−1.15202			−0.576012	+	0.817441i	$0.695392\pi$
$692$	−43.1140			−1.63895
$693$	2.78915	+	4.83094i	0.105951	+	0.183512i
$694$	6.68222	+	11.5740i	0.253654	+	0.439341i
$695$		0			0
$696$	28.0305			1.06250
$697$	−0.0241093	−	0.0417585i	−0.000913204	−	0.00158172i
$698$	1.90495	−	3.29948i	0.0721035	−	0.124887i
$699$	9.53293	+	16.5115i	0.360569	+	0.624523i
$700$		0			0
$701$	−22.2849	+	38.5987i	−0.841691	+	1.45785i	0.0467733	+	0.998906i	$0.485106\pi$
$701$	−22.2849	+	38.5987i	−0.841691	+	1.45785i	−0.888464	+	0.458946i	$0.848227\pi$
$702$	51.3483			1.93802
$703$	−11.4386	+	6.44177i	−0.431415	+	0.242956i
$704$	−16.7014			−0.629458
$705$		0			0
$706$	−40.4457	+	70.0540i	−1.52219	+	2.63652i
$707$	23.8072	+	41.2353i	0.895363	+	1.55081i
$708$	−39.4597	+	68.3462i	−1.48299	+	2.56861i
$709$	−4.67176	−	8.09172i	−0.175452	−	0.303891i	0.764866	−	0.644190i	$-0.222805\pi$
$709$	−4.67176	−	8.09172i	−0.175452	−	0.303891i	−0.940317	+	0.340299i	$0.889472\pi$
$710$		0			0
$711$	−6.38429			−0.239430
$712$	3.33795	+	5.78150i	0.125095	+	0.216671i
$713$	1.66764	+	2.88844i	0.0624538	+	0.108173i
$714$	11.5027			0.430479
$715$		0			0
$716$	−15.5055	−	26.8562i	−0.579466	−	1.00366i
$717$	−1.59186	+	2.75718i	−0.0594490	+	0.102969i
$718$	4.29500	+	7.43916i	0.160288	+	0.277627i
$719$	−12.6987	+	21.9948i	−0.473581	+	0.820267i	−0.999543	−	0.0302417i	$-0.990372\pi$
$719$	−12.6987	+	21.9948i	−0.473581	+	0.820267i	0.525961	+	0.850508i	$0.323706\pi$
$720$		0			0
$721$	25.9330			0.965797
$722$	22.4631	+	40.9059i	0.835992	+	1.52236i
$723$	27.3552			1.01735
$724$	12.3534	−	21.3968i	0.459112	−	0.795205i
$725$		0			0
$726$	11.8205	+	20.4737i	0.438700	+	0.759851i
$727$	−15.7189	+	27.2259i	−0.582980	+	1.00975i	0.412143	+	0.911119i	$0.364780\pi$
$727$	−15.7189	+	27.2259i	−0.582980	+	1.00975i	−0.995124	+	0.0986328i	$0.968553\pi$
$728$	42.2759	+	73.2240i	1.56685	+	2.71386i
$729$	29.9869			1.11063
$730$		0			0
$731$	−0.140016	−	0.242515i	−0.00517869	−	0.00896975i
$732$	−22.2419	−	38.5241i	−0.822085	−	1.42389i
$733$	25.3946			0.937971			0.468985	−	0.883206i	$-0.344620\pi$
$733$	25.3946			0.937971			0.468985	+	0.883206i	$0.344620\pi$
$734$	−47.9056			−1.76823
$735$		0			0
$736$	0.0796065	−	0.137883i	0.00293434	−	0.00508242i
$737$	−6.29559	−	10.9043i	−0.231901	−	0.401664i
$738$	0.0500800	−	0.0867411i	0.00184347	−	0.00319299i
$739$	−17.7541	+	30.7510i	−0.653095	+	1.13119i	0.329273	+	0.944235i	$0.393196\pi$
$739$	−17.7541	+	30.7510i	−0.653095	+	1.13119i	−0.982368	+	0.186959i	$0.940137\pi$
$740$		0			0
$741$	−22.2838	+	12.5493i	−0.818614	+	0.461011i
$742$	28.9703			1.06353
$743$	8.55493	−	14.8176i	0.313850	−	0.543604i	−0.665342	−	0.746538i	$-0.731714\pi$
$743$	8.55493	−	14.8176i	0.313850	−	0.543604i	0.979192	+	0.202934i	$0.0650477\pi$
$744$	−26.6357	+	46.1343i	−0.976511	+	1.69137i
$745$		0			0
$746$	28.8798	−	50.0213i	1.05737	−	1.83141i
$747$	−4.42060	−	7.65671i	−0.161741	−	0.280144i
$748$	5.90453			0.215891
$749$	−5.86718			−0.214382
$750$		0			0
$751$	3.72562	+	6.45297i	0.135950	+	0.235472i	0.925960	−	0.377622i	$-0.123258\pi$
$751$	3.72562	+	6.45297i	0.135950	+	0.235472i	−0.790010	+	0.613094i	$0.789925\pi$
$752$	21.0891			0.769041
$753$	−5.21086			−0.189894
$754$	16.5988	+	28.7500i	0.604493	+	1.04701i
$755$		0			0
$756$	50.5313	+	87.5228i	1.83781	+	3.18317i
$757$	26.8838	−	46.5640i	0.977107	−	1.69240i	0.304306	−	0.952574i	$-0.401575\pi$
$757$	26.8838	−	46.5640i	0.977107	−	1.69240i	0.672801	−	0.739824i	$-0.265091\pi$
$758$	8.65994	−	14.9994i	0.314543	−	0.544804i
$759$	−1.67503			−0.0607997
$760$		0			0
$761$	23.3939			0.848029			0.424014	−	0.905655i	$-0.360621\pi$
$761$	23.3939			0.848029			0.424014	+	0.905655i	$0.360621\pi$
$762$	7.54647	−	13.0709i	0.273380	−	0.473508i
$763$	27.1058	−	46.9487i	0.981297	−	1.69966i
$764$	−11.8068	−	20.4499i	−0.427154	−	0.739852i
$765$		0			0
$766$	3.78757	+	6.56027i	0.136851	+	0.237032i
$767$	−47.1152			−1.70123
$768$	−50.3235			−1.81589
$769$	6.62236	+	11.4703i	0.238808	+	0.413628i	0.960373	−	0.278719i	$-0.0899099\pi$
$769$	6.62236	+	11.4703i	0.238808	+	0.413628i	−0.721564	+	0.692347i	$0.756577\pi$
$770$		0			0
$771$	43.0606			1.55079
$772$	10.4500			0.376105
$773$	−8.90262	−	15.4198i	−0.320205	−	0.554611i	0.660325	−	0.750980i	$-0.270418\pi$
$773$	−8.90262	−	15.4198i	−0.320205	−	0.554611i	−0.980530	+	0.196369i	$0.937085\pi$
$774$	0.290843	−	0.503755i	0.0104541	−	0.0181071i
$775$		0			0
$776$	−10.9512	+	18.9681i	−0.393127	+	0.680916i
$777$	10.5906	−	18.3434i	0.379935	−	0.658068i
$778$	23.0658			0.826949
$779$	−0.00337965	+	0.315621i	−0.000121088	+	0.0113083i
$780$		0			0
$781$	−7.66521	+	13.2765i	−0.274283	+	0.475072i
$782$	0.399096	−	0.691255i	0.0142716	−	0.0247192i
$783$	10.0011	+	17.3224i	0.357409	+	0.619051i
$784$	−27.9160	+	48.3520i	−0.997001	+	1.72686i
$785$		0			0
$786$	−62.5939			−2.23265
$787$	43.5779			1.55339			0.776693	−	0.629880i	$-0.216896\pi$
$787$	43.5779			1.55339			0.776693	+	0.629880i	$0.216896\pi$
$788$	40.0527	+	69.3734i	1.42682	+	2.47132i
$789$	−10.6356	−	18.4213i	−0.378636	−	0.655816i
$790$		0			0
$791$	34.8990			1.24087
$792$	3.09128	+	5.35425i	0.109844	+	0.190255i
$793$	13.2785	−	22.9991i	0.471534	−	0.816721i
$794$	−32.8634	−	56.9210i	−1.16628	−	2.02005i
$795$		0			0
$796$	25.7338	−	44.5723i	0.912111	−	1.57982i
$797$	16.1311			0.571395			0.285697	−	0.958320i	$-0.407775\pi$
$797$	16.1311			0.571395			0.285697	+	0.958320i	$0.407775\pi$
$798$	−64.8023	−	38.3446i	−2.29398	−	1.35738i
$799$	3.34460			0.118323
$800$		0			0
$801$	−0.376451	+	0.652032i	−0.0133012	+	0.0230384i
$802$	30.9115	+	53.5403i	1.09152	+	1.89057i
$803$	3.25147	−	5.63170i	0.114742	−	0.198739i
$804$	−18.0264	−	31.2226i	−0.635742	−	1.10114i
$805$		0			0
$806$	−63.0912			−2.22229
$807$	2.81618	+	4.87777i	0.0991344	+	0.171706i
$808$	26.3861	+	45.7021i	0.928259	+	1.60779i
$809$	28.7134			1.00951			0.504755	−	0.863263i	$-0.331583\pi$
$809$	28.7134			1.00951			0.504755	+	0.863263i	$0.331583\pi$
$810$		0			0
$811$	−10.7711	−	18.6561i	−0.378225	−	0.655104i	0.612579	−	0.790409i	$-0.290132\pi$
$811$	−10.7711	−	18.6561i	−0.378225	−	0.655104i	−0.990804	+	0.135305i	$0.956799\pi$
$812$	−32.6694	+	56.5850i	−1.14647	+	1.98575i
$813$	−8.24477	−	14.2804i	−0.289157	−	0.500834i
$814$	8.13228	−	14.0855i	0.285036	−	0.493697i
$815$		0			0
$816$	4.36445			0.152786
$817$	−0.0196275	+	1.83299i	−0.000686680	+	0.0641282i
$818$	−69.5634			−2.43223
$819$	−4.76783	+	8.25813i	−0.166602	+	0.288562i
$820$		0			0
$821$	−16.6602	−	28.8563i	−0.581445	−	1.00709i	−0.995308	−	0.0967536i	$-0.969154\pi$
$821$	−16.6602	−	28.8563i	−0.581445	−	1.00709i	0.413863	−	0.910339i	$-0.364179\pi$
$822$	31.4994	−	54.5586i	1.09867	−	1.90295i
$823$	18.6195	+	32.2499i	0.649035	+	1.12416i	0.983354	+	0.181701i	$0.0581604\pi$
$823$	18.6195	+	32.2499i	0.649035	+	1.12416i	−0.334319	+	0.942460i	$0.608506\pi$
$824$	28.7422			1.00128
$825$		0			0
$826$	−69.3590	−	120.133i	−2.41331	−	4.17997i
$827$	14.5256	+	25.1591i	0.505105	+	0.874868i	0.999983	+	0.00590503i	$0.00187964\pi$
$827$	14.5256	+	25.1591i	0.505105	+	0.874868i	−0.494877	+	0.868963i	$0.664787\pi$
$828$	1.10836			0.0385181
$829$	34.5380			1.19956			0.599778	−	0.800166i	$-0.295256\pi$
$829$	34.5380			1.19956			0.599778	+	0.800166i	$0.295256\pi$
$830$		0			0
$831$	−5.25672	+	9.10490i	−0.182353	+	0.315845i
$832$	−14.2749	−	24.7249i	−0.494893	−	0.857180i
$833$	−4.42731	+	7.66832i	−0.153397	+	0.265692i
$834$	5.11581	−	8.86085i	0.177146	−	0.306826i
$835$		0			0
$836$	−33.2640	−	19.6829i	−1.15046	−	0.680746i
$837$	−38.0136			−1.31394
$838$	−16.0205	+	27.7483i	−0.553419	+	0.958550i
$839$	22.3622	−	38.7324i	0.772028	−	1.33719i	−0.164422	−	0.986390i	$-0.552576\pi$
$839$	22.3622	−	38.7324i	0.772028	−	1.33719i	0.936450	−	0.350801i	$-0.114091\pi$
$840$		0			0
$841$	8.03413	−	13.9155i	0.277039	−	0.479845i
$842$	−4.08340	−	7.07266i	−0.140723	−	0.243740i
$843$	36.5758			1.25974
$844$	55.8770			1.92337
$845$		0			0
$846$	3.47372	+	6.01665i	0.119429	+	0.206857i
$847$	−27.7784			−0.954478
$848$	10.9921			0.377471
$849$	−11.4605	−	19.8502i	−0.393324	−	0.681257i
$850$		0			0
$851$	−0.734898	−	1.27288i	−0.0251920	−	0.0436338i
$852$	−21.9481	+	38.0152i	−0.751929	+	1.30238i
$853$	8.13013	−	14.0818i	0.278370	−	0.482152i	−0.692610	−	0.721313i	$-0.743539\pi$
$853$	8.13013	−	14.0818i	0.278370	−	0.482152i	0.970980	+	0.239161i	$0.0768724\pi$
$854$	78.1900			2.67561
$855$		0			0
$856$	−6.50273			−0.222259
$857$	8.31896	−	14.4089i	0.284170	−	0.492197i	−0.688237	−	0.725485i	$-0.741615\pi$
$857$	8.31896	−	14.4089i	0.284170	−	0.492197i	0.972408	+	0.233288i	$0.0749486\pi$
$858$	15.8426	−	27.4403i	0.540859	−	0.936795i
$859$	−20.1362	−	34.8769i	−0.687038	−	1.18999i	−0.972792	−	0.231682i	$-0.925577\pi$
$859$	−20.1362	−	34.8769i	−0.687038	−	1.18999i	0.285753	−	0.958303i	$-0.407756\pi$
$860$		0			0
$861$	−0.254637	−	0.441044i	−0.00867799	−	0.0150307i
$862$	0.118897			0.00404965
$863$	−32.9634			−1.12209			−0.561044	−	0.827786i	$-0.689600\pi$
$863$	−32.9634			−1.12209			−0.561044	+	0.827786i	$0.689600\pi$
$864$	0.907306	+	1.57150i	0.0308672	+	0.0534635i
$865$		0			0
$866$	23.5027			0.798655
$867$	−25.8456			−0.877762
$868$	−62.0873	−	107.538i	−2.10738	−	3.65009i
$869$	−12.4633	+	21.5870i	−0.422787	+	0.732288i
$870$		0			0
$871$	10.7618	−	18.6400i	0.364651	−	0.631594i
$872$	30.0420	−	52.0343i	1.01735	−	1.76210i
$873$	−2.47014			−0.0836016
$874$	−4.55267	+	2.56389i	−0.153996	+	0.0867248i
$875$		0			0
$876$	9.31004	−	16.1255i	0.314557	−	0.544829i
$877$	−0.106600	+	0.184636i	−0.00359962	+	0.00623472i	−0.867820	−	0.496879i	$-0.834479\pi$
$877$	−0.106600	+	0.184636i	−0.00359962	+	0.00623472i	0.864220	+	0.503114i	$0.167812\pi$
$878$	27.3271	+	47.3319i	0.922244	+	1.59737i
$879$	−14.1942	+	24.5851i	−0.478759	+	0.829236i
$880$		0			0
$881$	51.8661			1.74741			0.873707	−	0.486453i	$-0.161710\pi$
$881$	51.8661			1.74741			0.873707	+	0.486453i	$0.161710\pi$
$882$	−18.3929			−0.619321
$883$	−20.8225	−	36.0657i	−0.700734	−	1.21371i	−0.968209	−	0.250142i	$-0.919523\pi$
$883$	−20.8225	−	36.0657i	−0.700734	−	1.21371i	0.267475	−	0.963565i	$-0.413811\pi$
$884$	5.04667	+	8.74109i	0.169738	+	0.293995i
$885$		0			0
$886$	−49.4083			−1.65990
$887$	−2.04663	−	3.54486i	−0.0687190	−	0.119025i	0.829619	−	0.558330i	$-0.188558\pi$
$887$	−2.04663	−	3.54486i	−0.0687190	−	0.119025i	−0.898338	+	0.439306i	$0.855225\pi$
$888$	11.7378	−	20.3305i	0.393895	−	0.682246i
$889$	8.86718	+	15.3584i	0.297396	+	0.515104i
$890$		0			0
$891$	7.68823	−	13.3164i	0.257565	−	0.446116i
$892$	−87.4987			−2.92967
$893$	−18.8423	−	11.1493i	−0.630533	−	0.373097i
$894$	−68.8859			−2.30389
$895$		0			0
$896$	43.4984	−	75.3414i	1.45318	−	2.51698i
$897$	−1.43167	−	2.47972i	−0.0478020	−	0.0827955i
$898$	15.3479	−	26.5834i	0.512167	−	0.887099i
$899$	−12.2882	−	21.2838i	−0.409835	−	0.709855i
$900$		0			0
$901$	1.74328			0.0580772
$902$	−0.195530	−	0.338668i	−0.00651043	−	0.0112764i
$903$	−1.47882	−	2.56139i	−0.0492120	−	0.0852377i
$904$	38.6794			1.28646
$905$		0			0
$906$	24.4133	+	42.2851i	0.811078	+	1.40483i
$907$	−4.20363	+	7.28090i	−0.139579	+	0.241758i	−0.927337	−	0.374226i	$-0.877908\pi$
$907$	−4.20363	+	7.28090i	−0.139579	+	0.241758i	0.787758	+	0.615985i	$0.211242\pi$
$908$	16.5275	+	28.6265i	0.548486	+	0.950005i
$909$	−2.97580	+	5.15423i	−0.0987009	+	0.170955i
$910$		0			0
$911$	8.87918			0.294180			0.147090	−	0.989123i	$-0.453009\pi$
$911$	8.87918			0.294180			0.147090	+	0.989123i	$0.453009\pi$
$912$	−24.5877	−	14.5490i	−0.814181	−	0.481764i
$913$	−34.5192			−1.14242
$914$	−34.7772	+	60.2359i	−1.15033	+	1.99243i
$915$		0			0
$916$	33.5983	+	58.1939i	1.11012	+	1.92278i
$917$	36.7742	−	63.6948i	1.21439	−	2.10339i
$918$	4.54865	+	7.87849i	0.150128	+	0.260029i
$919$	−45.9834			−1.51685			−0.758427	−	0.651758i	$-0.774032\pi$
$919$	−45.9834			−1.51685			−0.758427	+	0.651758i	$0.774032\pi$
$920$		0			0
$921$	22.9319	+	39.7191i	0.755630	+	1.30879i
$922$	−6.53290	−	11.3153i	−0.215150	−	0.372650i
$923$	−26.2062			−0.862587
$924$	62.3623			2.05157
$925$		0			0
$926$	−22.0231	+	38.1452i	−0.723725	+	1.25353i
$927$	1.62076	+	2.80724i	0.0532327	+	0.0922017i
$928$	−0.586589	+	1.01600i	−0.0192557	+	0.0333519i
$929$	11.0889	−	19.2065i	0.363814	−	0.630145i	−0.624771	−	0.780808i	$-0.714808\pi$
$929$	11.0889	−	19.2065i	0.363814	−	0.630145i	0.988585	+	0.150663i	$0.0481409\pi$
$930$		0			0
$931$	50.5044	−	28.4421i	1.65521	−	0.932152i
$932$	−49.2564			−1.61345
$933$	0.150822	−	0.261231i	0.00493769	−	0.00855233i
$934$	35.3436	−	61.2170i	1.15648	−	2.00308i
$935$		0			0
$936$	−5.28430	+	9.15267i	−0.172723	+	0.299165i
$937$	−17.1637	−	29.7284i	−0.560714	−	0.971186i	−0.997434	−	0.0715882i	$-0.977193\pi$
$937$	−17.1637	−	29.7284i	−0.560714	−	0.971186i	0.436720	−	0.899598i	$-0.356140\pi$
$938$	63.3706			2.06912
$939$	33.2120			1.08383
$940$		0			0
$941$	−16.8606	−	29.2035i	−0.549641	−	0.952006i	−0.998299	−	0.0583025i	$-0.981431\pi$
$941$	−16.8606	−	29.2035i	−0.549641	−	0.952006i	0.448658	−	0.893704i	$-0.351902\pi$
$942$	−76.8923			−2.50529
$943$	−0.0353393			−0.00115080
$944$	−26.3167	−	45.5818i	−0.856535	−	1.48356i
$945$		0			0
$946$	−1.13555	−	1.96683i	−0.0369200	−	0.0639473i
$947$	11.0732	−	19.1794i	0.359832	−	0.623248i	−0.628100	−	0.778132i	$-0.716167\pi$
$947$	11.0732	−	19.1794i	0.359832	−	0.623248i	0.987933	+	0.154885i	$0.0495006\pi$
$948$	−35.6865	+	61.8108i	−1.15904	+	2.00752i
$949$	11.1163			0.360849
$950$		0			0
$951$	−29.9254			−0.970398
$952$	−7.48995	+	12.9730i	−0.242751	+	0.420457i
$953$	18.6484	−	32.2999i	0.604079	−	1.04630i	−0.388117	−	0.921610i	$-0.626874\pi$
$953$	18.6484	−	32.2999i	0.604079	−	1.04630i	0.992196	−	0.124686i	$-0.0397924\pi$
$954$	1.81058	+	3.13602i	0.0586198	+	0.101532i
$955$		0			0
$956$	−4.11254	−	7.12313i	−0.133009	−	0.230378i
$957$	12.3426			0.398981
$958$	−19.7761			−0.638936
$959$	37.0121	+	64.1069i	1.19518	+	2.07012i
$960$		0			0
$961$	15.7069			0.506674
$962$	27.8030			0.896405
$963$	−0.366686	−	0.635118i	−0.0118163	−	0.0204664i
$964$	−35.3359	+	61.2036i	−1.13809	+	1.97123i
$965$		0			0
$966$	4.21516	−	7.30087i	0.135621	−	0.234902i
$967$	9.33679	−	16.1718i	0.300251	−	0.520050i	−0.675942	−	0.736955i	$-0.736263\pi$
$967$	9.33679	−	16.1718i	0.300251	−	0.520050i	0.976193	+	0.216905i	$0.0695963\pi$
$968$	−30.7875			−0.989547
$969$	−3.89946	−	2.30738i	−0.125269	−	0.0741236i
$970$		0			0
$971$	−14.2903	+	24.7515i	−0.458598	+	0.794314i	−0.998887	−	0.0471649i	$-0.984981\pi$
$971$	−14.2903	+	24.7515i	−0.458598	+	0.794314i	0.540290	+	0.841479i	$0.318315\pi$
$972$	−11.6341	+	20.1509i	−0.373165	+	0.646341i
$973$	6.01113	+	10.4116i	0.192708	+	0.333780i
$974$	1.34798	−	2.33477i	0.0431921	−	0.0748109i
$975$		0			0
$976$	29.6674			0.949630
$977$	58.1909			1.86169			0.930846	−	0.365411i	$-0.119072\pi$
$977$	58.1909			1.86169			0.930846	+	0.365411i	$0.119072\pi$
$978$	27.2866	+	47.2618i	0.872530	+	1.51127i
$979$	1.46980	+	2.54576i	0.0469749	+	0.0813628i
$980$		0			0
$981$	6.77622			0.216348
$982$	−16.0947	−	27.8768i	−0.513602	−	0.889586i
$983$	−24.0363	+	41.6320i	−0.766638	+	1.32786i	0.172738	+	0.984968i	$0.444738\pi$
$983$	−24.0363	+	41.6320i	−0.766638	+	1.32786i	−0.939376	+	0.342888i	$0.888595\pi$
$984$	−0.282220	−	0.488819i	−0.00899684	−	0.0155830i
$985$		0			0
$986$	−2.94078	+	5.09359i	−0.0936536	+	0.162213i
$987$	35.3249			1.12440
$988$	0.707444	−	66.0674i	0.0225068	−	2.10188i
$989$	−0.205235			−0.00652609
$990$		0			0
$991$	−19.1976	+	33.2512i	−0.609832	+	1.05626i	0.381436	+	0.924395i	$0.375430\pi$
$991$	−19.1976	+	33.2512i	−0.609832	+	1.05626i	−0.991268	+	0.131865i	$0.957904\pi$
$992$	−1.11480	−	1.93089i	−0.0353949	−	0.0613057i
$993$	16.0842	−	27.8587i	0.510417	−	0.884069i
$994$	−38.5785	−	66.8200i	−1.22364	−	2.11940i
$995$		0			0
$996$	−98.8399			−3.13186
$997$	−18.9109	−	32.7546i	−0.598914	−	1.03735i	−0.992982	−	0.118268i	$-0.962266\pi$
$997$	−18.9109	−	32.7546i	−0.598914	−	1.03735i	0.394068	−	0.919081i	$-0.371067\pi$
$998$	−29.6472	−	51.3504i	−0.938465	−	1.62547i
$999$	16.7518			0.530004

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.e.g.201.1		12
5.2	odd	4		95.2.i.b.49.1	✓	12
5.3	odd	4		95.2.i.b.49.6	yes	12
5.4	even	2	inner	475.2.e.g.201.6		12
15.2	even	4		855.2.be.d.334.6		12
15.8	even	4		855.2.be.d.334.1		12
19.7	even	3	inner	475.2.e.g.26.1		12
19.8	odd	6		9025.2.a.bt.1.1		6
19.11	even	3		9025.2.a.bu.1.6		6
95.7	odd	12		95.2.i.b.64.6	yes	12
95.8	even	12		1805.2.b.g.1084.6		6
95.27	even	12		1805.2.b.g.1084.1		6
95.49	even	6		9025.2.a.bu.1.1		6
95.64	even	6	inner	475.2.e.g.26.6		12
95.68	odd	12		1805.2.b.f.1084.1		6
95.83	odd	12		95.2.i.b.64.1	yes	12
95.84	odd	6		9025.2.a.bt.1.6		6
95.87	odd	12		1805.2.b.f.1084.6		6
285.83	even	12		855.2.be.d.64.6		12
285.197	even	12		855.2.be.d.64.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.i.b.49.1	✓	12	5.2	odd	4
95.2.i.b.49.6	yes	12	5.3	odd	4
95.2.i.b.64.1	yes	12	95.83	odd	12
95.2.i.b.64.6	yes	12	95.7	odd	12
475.2.e.g.26.1		12	19.7	even	3	inner
475.2.e.g.26.6		12	95.64	even	6	inner
475.2.e.g.201.1		12	1.1	even	1	trivial
475.2.e.g.201.6		12	5.4	even	2	inner
855.2.be.d.64.1		12	285.197	even	12
855.2.be.d.64.6		12	285.83	even	12
855.2.be.d.334.1		12	15.8	even	4
855.2.be.d.334.6		12	15.2	even	4
1805.2.b.f.1084.1		6	95.68	odd	12
1805.2.b.f.1084.6		6	95.87	odd	12
1805.2.b.g.1084.1		6	95.27	even	12
1805.2.b.g.1084.6		6	95.8	even	12
9025.2.a.bt.1.1		6	19.8	odd	6
9025.2.a.bt.1.6		6	95.84	odd	6
9025.2.a.bu.1.1		6	95.49	even	6
9025.2.a.bu.1.6		6	19.11	even	3

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22810 + 2.12713i) q^{2} +(-0.780522 + 1.35190i) q^{3} +(-2.01647 - 3.49262i) q^{4} +(-1.91712 - 3.32055i) q^{6} +4.50527 q^{7} +4.99330 q^{8} +(0.281570 + 0.487693i) q^{9} +O(q^{10})\)	\(q+(-1.22810 + 2.12713i) q^{2} +(-0.780522 + 1.35190i) q^{3} +(-2.01647 - 3.49262i) q^{4} +(-1.91712 - 3.32055i) q^{6} +4.50527 q^{7} +4.99330 q^{8} +(0.281570 + 0.487693i) q^{9} +2.19869 q^{11} +6.29559 q^{12} +(1.87925 + 3.25495i) q^{13} +(-5.53293 + 9.58332i) q^{14} +(-2.09935 + 3.63617i) q^{16} +(-0.332943 + 0.576674i) q^{17} -1.38318 q^{18} +(3.79804 - 2.13891i) q^{19} +(-3.51647 + 6.09070i) q^{21} +(-2.70022 + 4.67691i) q^{22} +(0.244013 + 0.422643i) q^{23} +(-3.89738 + 6.75046i) q^{24} -9.23163 q^{26} -5.56222 q^{27} +(-9.08474 - 15.7352i) q^{28} +(-1.79804 - 3.11429i) q^{29} +6.83424 q^{31} +(-0.163119 - 0.282531i) q^{32} +(-1.71613 + 2.97242i) q^{33} +(-0.817776 - 1.41643i) q^{34} +(1.13555 - 1.96683i) q^{36} -3.01171 q^{37} +(-0.114636 + 10.7057i) q^{38} -5.86718 q^{39} +(-0.0362063 + 0.0627112i) q^{41} +(-8.63716 - 14.9600i) q^{42} +(-0.210271 + 0.364199i) q^{43} +(-4.43359 - 7.67920i) q^{44} -1.19869 q^{46} +(-2.51139 - 4.34986i) q^{47} +(-3.27717 - 5.67623i) q^{48} +13.2975 q^{49} +(-0.519739 - 0.900215i) q^{51} +(7.57888 - 13.1270i) q^{52} +(-1.30900 - 2.26725i) q^{53} +(6.83097 - 11.8316i) q^{54} +22.4962 q^{56} +(-0.0728572 + 6.80405i) q^{57} +8.83269 q^{58} +(-6.26783 + 10.8562i) q^{59} +(-3.53293 - 6.11922i) q^{61} +(-8.39315 + 14.5374i) q^{62} +(1.26855 + 2.19719i) q^{63} -7.59607 q^{64} +(-4.21516 - 7.30087i) q^{66} +(-2.86334 - 4.95944i) q^{67} +2.68548 q^{68} -0.761831 q^{69} +(-3.48626 + 6.03838i) q^{71} +(1.40596 + 2.43520i) q^{72} +(1.47882 - 2.56139i) q^{73} +(3.69869 - 6.40632i) q^{74} +(-15.1290 - 8.95208i) q^{76} +9.90571 q^{77} +(7.20549 - 12.4803i) q^{78} +(-5.66849 + 9.81811i) q^{79} +(3.49673 - 6.05651i) q^{81} +(-0.0889301 - 0.154031i) q^{82} -15.6999 q^{83} +28.3634 q^{84} +(-0.516467 - 0.894547i) q^{86} +5.61363 q^{87} +10.9787 q^{88} +(0.668486 + 1.15785i) q^{89} +(8.46652 + 14.6644i) q^{91} +(0.984089 - 1.70449i) q^{92} +(-5.33428 + 9.23924i) q^{93} +12.3370 q^{94} +0.509273 q^{96} +(-2.19319 + 3.79871i) q^{97} +(-16.3307 + 28.2856i) q^{98} +(0.619085 + 1.07229i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{4} - 12 q^{6} - 8 q^{9}+O(q^{10}) \) 12 * q - 2 * q^4 - 12 * q^6 - 8 * q^9	\( 12 q - 2 q^{4} - 12 q^{6} - 8 q^{9} + 4 q^{11} - 22 q^{14} - 14 q^{16} + 12 q^{19} - 20 q^{21} - 2 q^{24} - 44 q^{26} + 12 q^{29} + 60 q^{31} - 10 q^{34} + 14 q^{36} - 4 q^{39} - 12 q^{41} - 20 q^{44} + 8 q^{46} + 4 q^{49} - 40 q^{51} + 4 q^{54} + 92 q^{56} - 20 q^{59} + 2 q^{61} - 24 q^{64} - 6 q^{66} + 36 q^{69} + 2 q^{71} + 22 q^{74} - 70 q^{76} - 24 q^{79} - 14 q^{81} + 96 q^{84} + 16 q^{86} - 36 q^{89} + 24 q^{91} + 60 q^{94} + 52 q^{96} + 30 q^{99}+O(q^{100}) \) 12 * q - 2 * q^4 - 12 * q^6 - 8 * q^9 + 4 * q^11 - 22 * q^14 - 14 * q^16 + 12 * q^19 - 20 * q^21 - 2 * q^24 - 44 * q^26 + 12 * q^29 + 60 * q^31 - 10 * q^34 + 14 * q^36 - 4 * q^39 - 12 * q^41 - 20 * q^44 + 8 * q^46 + 4 * q^49 - 40 * q^51 + 4 * q^54 + 92 * q^56 - 20 * q^59 + 2 * q^61 - 24 * q^64 - 6 * q^66 + 36 * q^69 + 2 * q^71 + 22 * q^74 - 70 * q^76 - 24 * q^79 - 14 * q^81 + 96 * q^84 + 16 * q^86 - 36 * q^89 + 24 * q^91 + 60 * q^94 + 52 * q^96 + 30 * q^99

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