LMFDB - Embedded newform 648.2.t.a.613.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [648,2,Mod(37,648)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(648, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 14]))

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

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

chi := DirichletCharacter("648.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.t (of order $18$, degree $6$, 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:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			613.16
Character	$\chi$	$=$	648.613
Dual form			648.2.t.a.37.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.138542 - 1.40741i) q^{2} +(-1.96161 + 0.389971i) q^{4} +(-0.608623 + 1.67218i) q^{5} +(0.408085 - 2.31436i) q^{7} +(0.820615 + 2.70677i) q^{8} +O(q^{10})$	\(q+(-0.138542 - 1.40741i) q^{2} +(-1.96161 + 0.389971i) q^{4} +(-0.608623 + 1.67218i) q^{5} +(0.408085 - 2.31436i) q^{7} +(0.820615 + 2.70677i) q^{8} +(2.43776 + 0.624915i) q^{10} +(0.860398 + 2.36392i) q^{11} +(0.359719 + 0.428697i) q^{13} +(-3.31380 - 0.253707i) q^{14} +(3.69585 - 1.52994i) q^{16} +(-1.49770 - 2.59409i) q^{17} +(6.64437 + 3.83613i) q^{19} +(0.541781 - 3.51751i) q^{20} +(3.20781 - 1.53844i) q^{22} +(1.12812 + 6.39788i) q^{23} +(1.40447 + 1.17849i) q^{25} +(0.553516 - 0.565665i) q^{26} +(0.102031 + 4.69903i) q^{28} +(5.22169 - 6.22297i) q^{29} +(-0.643875 - 3.65160i) q^{31} +(-2.66529 - 4.98961i) q^{32} +(-3.44345 + 2.46726i) q^{34} +(3.62166 + 2.09096i) q^{35} +(4.07450 - 2.35241i) q^{37} +(4.47848 - 9.88282i) q^{38} +(-5.02564 - 0.275186i) q^{40} +(5.67863 - 4.76494i) q^{41} +(0.928888 + 2.55210i) q^{43} +(-2.60963 - 4.30157i) q^{44} +(8.84815 - 2.47410i) q^{46} +(-0.0919295 + 0.521358i) q^{47} +(1.38810 + 0.505226i) q^{49} +(1.46404 - 2.13994i) q^{50} +(-0.872809 - 0.700657i) q^{52} +6.39371i q^{53} -4.47656 q^{55} +(6.59933 - 0.794612i) q^{56} +(-9.48170 - 6.48692i) q^{58} +(-2.87131 + 7.88886i) q^{59} +(0.716954 + 0.126418i) q^{61} +(-5.05009 + 1.41210i) q^{62} +(-6.65318 + 4.44243i) q^{64} +(-0.935790 + 0.340600i) q^{65} +(3.68574 + 4.39249i) q^{67} +(3.94952 + 4.50453i) q^{68} +(2.44110 - 5.38685i) q^{70} +(-7.38597 - 12.7929i) q^{71} +(-5.98642 + 10.3688i) q^{73} +(-3.87530 - 5.40859i) q^{74} +(-14.5296 - 4.93388i) q^{76} +(5.82210 - 1.02659i) q^{77} +(-8.94860 - 7.50876i) q^{79} +(0.308962 + 7.11126i) q^{80} +(-7.49296 - 7.33203i) q^{82} +(-4.81848 + 5.74244i) q^{83} +(5.24930 - 0.925594i) q^{85} +(3.46316 - 1.66090i) q^{86} +(-5.69254 + 4.26877i) q^{88} +(1.16774 - 2.02259i) q^{89} +(1.13896 - 0.657577i) q^{91} +(-4.70792 - 12.1102i) q^{92} +(0.746501 + 0.0571526i) q^{94} +(-10.4586 + 8.77580i) q^{95} +(13.8915 - 5.05610i) q^{97} +(0.518751 - 2.02362i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8}+O(q^{10}) $ 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8	$ 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40} + 24 q^{41} - 21 q^{44} - 3 q^{46} + 12 q^{47} - 12 q^{49} + 99 q^{50} - 33 q^{52} - 24 q^{55} - 99 q^{56} + 21 q^{58} + 36 q^{62} - 3 q^{64} + 12 q^{65} - 75 q^{68} + 9 q^{70} + 90 q^{71} - 6 q^{73} - 9 q^{74} - 18 q^{76} - 12 q^{79} - 78 q^{80} - 12 q^{82} + 30 q^{86} - 30 q^{88} + 6 q^{89} - 111 q^{92} - 33 q^{94} + 42 q^{95} - 12 q^{97} - 54 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$	−0.138542	−	1.40741i	−0.0979640	−	0.995190i
$2$	−0.138542	−	1.40741i	−0.0979640	−	0.995190i
$3$		0			0
$3$		0			0
$4$	−1.96161	+	0.389971i	−0.980806	+	0.194986i
$5$	−0.608623	+	1.67218i	−0.272184	+	0.747820i	0.726006	+	0.687688i	$0.241374\pi$
$5$	−0.608623	+	1.67218i	−0.272184	+	0.747820i	−0.998190	+	0.0601320i	$0.980848\pi$
$6$		0			0
$7$	0.408085	−	2.31436i	0.154242	−	0.874748i	−0.805234	−	0.592957i	$-0.797960\pi$
$7$	0.408085	−	2.31436i	0.154242	−	0.874748i	0.959476	−	0.281791i	$-0.0909284\pi$
$8$	0.820615	+	2.70677i	0.290131	+	0.956987i
$9$		0			0
$10$	2.43776	+	0.624915i	0.770887	+	0.197616i
$11$	0.860398	+	2.36392i	0.259420	+	0.712750i	0.999203	+	0.0399051i	$0.0127056\pi$
$11$	0.860398	+	2.36392i	0.259420	+	0.712750i	−0.739784	+	0.672845i	$0.765072\pi$
$12$		0			0
$13$	0.359719	+	0.428697i	0.0997682	+	0.118899i	0.813618	−	0.581399i	$-0.197495\pi$
$13$	0.359719	+	0.428697i	0.0997682	+	0.118899i	−0.713850	+	0.700299i	$0.753050\pi$
$14$	−3.31380	−	0.253707i	−0.885650	−	0.0678060i
$15$		0			0
$16$	3.69585	−	1.52994i	0.923961	−	0.382486i
$17$	−1.49770	−	2.59409i	−0.363245	−	0.629158i	0.625248	−	0.780426i	$-0.284998\pi$
$17$	−1.49770	−	2.59409i	−0.363245	−	0.629158i	−0.988493	+	0.151268i	$0.951664\pi$
$18$		0			0
$19$	6.64437	+	3.83613i	1.52432	+	0.880068i	0.999585	+	0.0288032i	$0.00916963\pi$
$19$	6.64437	+	3.83613i	1.52432	+	0.880068i	0.524737	+	0.851264i	$0.324164\pi$
$20$	0.541781	−	3.51751i	0.121146	−	0.786539i
$21$		0			0
$22$	3.20781	−	1.53844i	0.683908	−	0.327996i
$23$	1.12812	+	6.39788i	0.235229	+	1.33405i	0.842131	+	0.539273i	$0.181301\pi$
$23$	1.12812	+	6.39788i	0.235229	+	1.33405i	−0.606902	+	0.794777i	$0.707588\pi$
$24$		0			0
$25$	1.40447	+	1.17849i	0.280894	+	0.235698i
$26$	0.553516	−	0.565665i	0.108553	−	0.110936i
$27$		0			0
$28$	0.102031	+	4.69903i	0.0192820	+	0.888033i
$29$	5.22169	−	6.22297i	0.969643	−	1.15558i	−0.0181545	−	0.999835i	$-0.505779\pi$
$29$	5.22169	−	6.22297i	0.969643	−	1.15558i	0.987798	−	0.155741i	$-0.0497765\pi$
$30$		0			0
$31$	−0.643875	−	3.65160i	−0.115643	−	0.655846i	−0.986430	−	0.164184i	$-0.947501\pi$
$31$	−0.643875	−	3.65160i	−0.115643	−	0.655846i	0.870786	−	0.491662i	$-0.163610\pi$
$32$	−2.66529	−	4.98961i	−0.471161	−	0.882047i
$33$		0			0
$34$	−3.44345	+	2.46726i	−0.590547	+	0.423132i
$35$	3.62166	+	2.09096i	0.612172	+	0.353438i
$36$		0			0
$37$	4.07450	−	2.35241i	0.669843	−	0.386734i	−0.126174	−	0.992008i	$-0.540270\pi$
$37$	4.07450	−	2.35241i	0.669843	−	0.386734i	0.796017	+	0.605274i	$0.206936\pi$
$38$	4.47848	−	9.88282i	0.726506	−	1.60320i
$39$		0			0
$40$	−5.02564	−	0.275186i	−0.794623	−	0.0435107i
$41$	5.67863	−	4.76494i	0.886853	−	0.744158i	−0.0807232	−	0.996737i	$-0.525723\pi$
$41$	5.67863	−	4.76494i	0.886853	−	0.744158i	0.967576	+	0.252578i	$0.0812785\pi$
$42$		0			0
$43$	0.928888	+	2.55210i	0.141654	+	0.389191i	0.990150	−	0.140011i	$-0.0447136\pi$
$43$	0.928888	+	2.55210i	0.141654	+	0.389191i	−0.848496	+	0.529202i	$0.822491\pi$
$44$	−2.60963	−	4.30157i	−0.393416	−	0.648486i
$45$		0			0
$46$	8.84815	−	2.47410i	1.30459	−	0.364786i
$47$	−0.0919295	+	0.521358i	−0.0134093	+	0.0760479i	−0.990778	−	0.135495i	$-0.956738\pi$
$47$	−0.0919295	+	0.521358i	−0.0134093	+	0.0760479i	0.977369	+	0.211543i	$0.0678487\pi$
$48$		0			0
$49$	1.38810	+	0.505226i	0.198300	+	0.0721751i
$50$	1.46404	−	2.13994i	0.207047	−	0.302633i
$51$		0			0
$52$	−0.872809	−	0.700657i	−0.121037	−	0.0971636i
$53$			6.39371i			0.878244i	0.898427	+	0.439122i	$0.144710\pi$
$53$			6.39371i			0.878244i	−0.898427	+	0.439122i	$0.855290\pi$
$54$		0			0
$55$	−4.47656			−0.603619
$56$	6.59933	−	0.794612i	0.881872	−	0.106184i
$57$		0			0
$58$	−9.48170	−	6.48692i	−1.24501	−	0.851775i
$59$	−2.87131	+	7.88886i	−0.373813	+	1.02704i	0.600061	+	0.799954i	$0.295143\pi$
$59$	−2.87131	+	7.88886i	−0.373813	+	1.02704i	−0.973874	+	0.227088i	$0.927079\pi$
$60$		0			0
$61$	0.716954	+	0.126418i	0.0917966	+	0.0161862i	0.219358	−	0.975644i	$-0.429604\pi$
$61$	0.716954	+	0.126418i	0.0917966	+	0.0161862i	−0.127561	+	0.991831i	$0.540715\pi$
$62$	−5.05009	+	1.41210i	−0.641363	+	0.179336i
$63$		0			0
$64$	−6.65318	+	4.44243i	−0.831648	+	0.555304i
$65$	−0.935790	+	0.340600i	−0.116070	+	0.0422462i
$66$		0			0
$67$	3.68574	+	4.39249i	0.450285	+	0.536628i	0.942660	−	0.333755i	$-0.108316\pi$
$67$	3.68574	+	4.39249i	0.450285	+	0.536628i	−0.492375	+	0.870383i	$0.663871\pi$
$68$	3.94952	+	4.50453i	0.478949	+	0.546255i
$69$		0			0
$70$	2.44110	−	5.38685i	0.291767	−	0.643851i
$71$	−7.38597	−	12.7929i	−0.876553	−	1.51823i	−0.855099	−	0.518465i	$-0.826504\pi$
$71$	−7.38597	−	12.7929i	−0.876553	−	1.51823i	−0.0214546	−	0.999770i	$-0.506830\pi$
$72$		0			0
$73$	−5.98642	+	10.3688i	−0.700657	+	1.21357i	0.267579	+	0.963536i	$0.413776\pi$
$73$	−5.98642	+	10.3688i	−0.700657	+	1.21357i	−0.968236	+	0.250038i	$0.919557\pi$
$74$	−3.87530	−	5.40859i	−0.450495	−	0.628735i
$75$		0			0
$76$	−14.5296	−	4.93388i	−1.66666	−	0.565955i
$77$	5.82210	−	1.02659i	0.663490	−	0.116991i
$78$		0			0
$79$	−8.94860	−	7.50876i	−1.00680	−	0.844802i	−0.0188843	−	0.999822i	$-0.506011\pi$
$79$	−8.94860	−	7.50876i	−1.00680	−	0.844802i	−0.987911	+	0.155020i	$0.950456\pi$
$80$	0.308962	+	7.11126i	0.0345430	+	0.795064i
$81$		0			0
$82$	−7.49296	−	7.33203i	−0.827458	−	0.809687i
$83$	−4.81848	+	5.74244i	−0.528897	+	0.630315i	−0.962660	−	0.270712i	$-0.912741\pi$
$83$	−4.81848	+	5.74244i	−0.528897	+	0.630315i	0.433764	+	0.901027i	$0.357185\pi$
$84$		0			0
$85$	5.24930	−	0.925594i	0.569367	−	0.100395i
$86$	3.46316	−	1.66090i	0.373442	−	0.179099i
$87$		0			0
$88$	−5.69254	+	4.26877i	−0.606826	+	0.455052i
$89$	1.16774	−	2.02259i	0.123780	−	0.214394i	−0.797475	−	0.603352i	$-0.793832\pi$
$89$	1.16774	−	2.02259i	0.123780	−	0.214394i	0.921255	+	0.388958i	$0.127165\pi$
$90$		0			0
$91$	1.13896	−	0.657577i	0.119395	−	0.0689328i
$92$	−4.70792	−	12.1102i	−0.490834	−	1.26258i
$93$		0			0
$94$	0.746501	+	0.0571526i	0.0769957	+	0.00589484i
$95$	−10.4586	+	8.77580i	−1.07303	+	0.900378i
$96$		0			0
$97$	13.8915	−	5.05610i	1.41047	−	0.513369i	0.479202	−	0.877705i	$-0.340926\pi$
$97$	13.8915	−	5.05610i	1.41047	−	0.513369i	0.931268	+	0.364336i	$0.118704\pi$
$98$	0.518751	−	2.02362i	0.0524017	−	0.204416i
$99$		0			0
$100$	−3.21460	−	1.76404i	−0.321460	−	0.176404i
$101$	−12.0747	−	2.12910i	−1.20148	−	0.211853i	−0.463142	−	0.886284i	$-0.653278\pi$
$101$	−12.0747	−	2.12910i	−1.20148	−	0.211853i	−0.738338	+	0.674431i	$0.764389\pi$
$102$		0			0
$103$	10.8828	+	3.96103i	1.07232	+	0.390292i	0.817043	−	0.576576i	$-0.195612\pi$
$103$	10.8828	+	3.96103i	1.07232	+	0.390292i	0.255276	+	0.966868i	$0.417834\pi$
$104$	−0.865191	+	1.32547i	−0.0848390	+	0.129973i
$105$		0			0
$106$	8.99858	−	0.885798i	0.874020	−	0.0860363i
$107$			3.95255i			0.382107i	0.981580	+	0.191054i	$0.0611904\pi$
$107$			3.95255i			0.382107i	−0.981580	+	0.191054i	$0.938810\pi$
$108$		0			0
$109$			5.12938i			0.491305i	0.969358	+	0.245653i	$0.0790023\pi$
$109$			5.12938i			0.491305i	−0.969358	+	0.245653i	$0.920998\pi$
$110$	0.620191	+	6.30035i	0.0591329	+	0.600715i
$111$		0			0
$112$	−2.03263	−	9.17788i	−0.192065	−	0.867228i
$113$	9.37151	+	3.41095i	0.881597	+	0.320875i	0.742854	−	0.669453i	$-0.233472\pi$
$113$	9.37151	+	3.41095i	0.881597	+	0.320875i	0.138743	+	0.990328i	$0.455694\pi$
$114$		0			0
$115$	−11.3850	−	2.00748i	−1.06165	−	0.187198i
$116$	−7.81615	+	14.2434i	−0.725712	+	1.32246i
$117$		0			0
$118$	11.5007	+	2.94818i	1.05872	+	0.271402i
$119$	−6.61485	+	2.40761i	−0.606382	+	0.220705i
$120$		0			0
$121$	3.57864	−	3.00283i	0.325331	−	0.272985i
$122$	0.0785944	−	1.02656i	0.00711560	−	0.0929407i
$123$		0			0
$124$	2.68705	+	6.91192i	0.241304	+	0.620709i
$125$	−10.5309	+	6.08000i	−0.941909	+	0.543812i
$126$		0			0
$127$	−10.0971	+	17.4887i	−0.895973	+	1.55187i	−0.0633763	+	0.997990i	$0.520187\pi$
$127$	−10.0971	+	17.4887i	−0.895973	+	1.55187i	−0.832596	+	0.553880i	$0.813147\pi$
$128$	7.17407	+	8.74830i	0.634104	+	0.773248i
$129$		0			0
$130$	0.609010	+	1.26985i	0.0534137	+	0.111374i
$131$	13.3484	−	2.35368i	1.16625	−	0.205642i	0.443192	−	0.896427i	$-0.353846\pi$
$131$	13.3484	−	2.35368i	1.16625	−	0.205642i	0.723060	+	0.690785i	$0.242735\pi$
$132$		0			0
$133$	11.5897	−	13.8120i	1.00495	−	1.19765i
$134$	5.67141	−	5.79589i	0.489935	−	0.500689i
$135$		0			0
$136$	5.79256	−	6.18266i	0.496708	−	0.530159i
$137$	−6.18657	−	5.19115i	−0.528555	−	0.443510i	0.339047	−	0.940769i	$-0.389895\pi$
$137$	−6.18657	−	5.19115i	−0.528555	−	0.443510i	−0.867602	+	0.497259i	$0.834340\pi$
$138$		0			0
$139$	−18.8808	+	3.32919i	−1.60145	+	0.282378i	−0.901814	−	0.432124i	$-0.857764\pi$
$139$	−18.8808	+	3.32919i	−1.60145	+	0.282378i	−0.699633	+	0.714502i	$0.746653\pi$
$140$	−7.91970	−	2.68932i	−0.669337	−	0.227289i
$141$		0			0
$142$	−16.9816	+	12.1674i	−1.42506	+	1.02107i
$143$	−0.703905	+	1.21920i	−0.0588635	+	0.101955i
$144$		0			0
$145$	7.22786	+	12.5190i	0.600241	+	1.03965i
$146$	15.4225	+	6.98884i	1.27638	+	0.578400i
$147$		0			0
$148$	−7.07521	+	6.20346i	−0.581579	+	0.509921i
$149$	−0.614187	−	0.731960i	−0.0503162	−	0.0599645i	0.740299	−	0.672277i	$-0.234684\pi$
$149$	−0.614187	−	0.731960i	−0.0503162	−	0.0599645i	−0.790616	+	0.612313i	$0.790239\pi$
$150$		0			0
$151$	−1.04563	+	0.380578i	−0.0850921	+	0.0309710i	−0.384215	−	0.923243i	$-0.625528\pi$
$151$	−1.04563	+	0.380578i	−0.0850921	+	0.0309710i	0.299123	+	0.954214i	$0.403306\pi$
$152$	−4.93103	+	21.1327i	−0.399960	+	1.71409i
$153$		0			0
$154$	−2.25144	−	8.05186i	−0.181426	−	0.648837i
$155$	6.49799	+	1.14577i	0.521931	+	0.0920306i
$156$		0			0
$157$	2.45899	−	6.75603i	0.196249	−	0.539190i	−0.802065	−	0.597237i	$-0.796265\pi$
$157$	2.45899	−	6.75603i	0.196249	−	0.539190i	0.998314	+	0.0580471i	$0.0184873\pi$
$158$	−9.32816	+	13.6346i	−0.742109	+	1.08471i
$159$		0			0
$160$	9.96567	−	1.42004i	0.787855	−	0.112264i
$161$	15.2674			1.20324
$162$		0			0
$163$		−	0.783193i		−	0.0613444i	−0.999529	−	0.0306722i	$-0.990235\pi$
$163$		−	0.783193i		−	0.0613444i	0.999529	−	0.0306722i	$-0.00976480\pi$
$164$	−9.28109	+	11.5615i	−0.724731	+	0.902798i
$165$		0			0
$166$	8.74953	+	5.98601i	0.679096	+	0.464605i
$167$	13.3409	+	4.85570i	1.03235	+	0.375745i	0.801976	−	0.597356i	$-0.203782\pi$
$167$	13.3409	+	4.85570i	1.03235	+	0.375745i	0.230376	+	0.973102i	$0.426004\pi$
$168$		0			0
$169$	2.20304	−	12.4941i	0.169465	−	0.961083i
$170$	−2.02994	−	7.25969i	−0.155689	−	0.556793i
$171$		0			0
$172$	−2.81736	−	4.64399i	−0.214822	−	0.354101i
$173$	−4.11676	−	11.3107i	−0.312991	−	0.859937i	−0.992049	−	0.125852i	$-0.959834\pi$
$173$	−4.11676	−	11.3107i	−0.312991	−	0.859937i	0.679058	−	0.734085i	$-0.262389\pi$
$174$		0			0
$175$	3.30060	−	2.76953i	0.249502	−	0.209357i
$176$	6.79657	+	7.42033i	0.512311	+	0.559329i
$177$		0			0
$178$	−3.00839	−	1.36328i	−0.225488	−	0.102182i
$179$	6.41741	−	3.70509i	0.479660	−	0.276932i	−0.240615	−	0.970621i	$-0.577349\pi$
$179$	6.41741	−	3.70509i	0.479660	−	0.276932i	0.720275	+	0.693689i	$0.244016\pi$
$180$		0			0
$181$	−12.0116	−	6.93490i	−0.892815	−	0.515467i	−0.0179527	−	0.999839i	$-0.505715\pi$
$181$	−12.0116	−	6.93490i	−0.892815	−	0.515467i	−0.874862	+	0.484372i	$0.839048\pi$
$182$	−1.08327	−	1.51188i	−0.0802977	−	0.112068i
$183$		0			0
$184$	−16.3918	+	8.30375i	−1.20842	+	0.612161i
$185$	1.45382	+	8.24501i	0.106887	+	0.606185i
$186$		0			0
$187$	4.84361	−	5.77239i	0.354200	−	0.422119i
$188$	−0.0229845	−	1.05855i	−0.00167632	−	0.0772029i
$189$		0			0
$190$	13.8001	+	13.5037i	1.00117	+	0.979663i
$191$	6.35332	+	5.33107i	0.459710	+	0.385743i	0.843024	−	0.537875i	$-0.180773\pi$
$191$	6.35332	+	5.33107i	0.459710	+	0.385743i	−0.383314	+	0.923618i	$0.625217\pi$
$192$		0			0
$193$	1.66122	+	9.42126i	0.119577	+	0.678157i	0.984382	+	0.176048i	$0.0563314\pi$
$193$	1.66122	+	9.42126i	0.119577	+	0.678157i	−0.864804	+	0.502109i	$0.832558\pi$
$194$	−9.04056	−	18.8506i	−0.649075	−	1.35339i
$195$		0			0
$196$	−2.91993	−	0.449740i	−0.208566	−	0.0321243i
$197$	−12.5364	−	7.23789i	−0.893181	−	0.515678i	−0.0181995	−	0.999834i	$-0.505793\pi$
$197$	−12.5364	−	7.23789i	−0.893181	−	0.515678i	−0.874982	+	0.484156i	$0.839127\pi$
$198$		0			0
$199$	−13.2319	−	22.9183i	−0.937983	−	1.62463i	−0.769225	−	0.638977i	$-0.779358\pi$
$199$	−13.2319	−	22.9183i	−0.937983	−	1.62463i	−0.168758	−	0.985658i	$-0.553976\pi$
$200$	−2.03737	+	4.76866i	−0.144064	+	0.337195i
$201$		0			0
$202$	−1.32366	+	17.2891i	−0.0931325	+	1.21645i
$203$	−12.2713	−	14.6244i	−0.861278	−	1.02643i
$204$		0			0
$205$	4.51167	+	12.3957i	0.315109	+	0.865755i
$206$	4.06707	−	15.8654i	0.283366	−	1.10540i
$207$		0			0
$208$	1.98535	+	1.03405i	0.137659	+	0.0716982i
$209$	−3.35151	+	19.0074i	−0.231829	+	1.31477i
$210$		0			0
$211$	−6.13970	+	16.8687i	−0.422674	+	1.16129i	0.527496	+	0.849558i	$0.323131\pi$
$211$	−6.13970	+	16.8687i	−0.422674	+	1.16129i	−0.950170	+	0.311731i	$0.899091\pi$
$212$	−2.49336	−	12.5420i	−0.171245	−	0.861387i
$213$		0			0
$214$	5.56286	−	0.547594i	0.380269	−	0.0374327i
$215$	−4.83290			−0.329601
$216$		0			0
$217$	−8.71388			−0.591537
$218$	7.21915	−	0.710634i	0.488942	−	0.0481302i
$219$		0			0
$220$	8.78127	−	1.74573i	0.592033	−	0.117697i
$221$	0.573326	−	1.57520i	0.0385661	−	0.105959i
$222$		0			0
$223$	−3.13816	+	17.7974i	−0.210147	+	1.19180i	0.678985	+	0.734152i	$0.262420\pi$
$223$	−3.13816	+	17.7974i	−0.210147	+	1.19180i	−0.889132	+	0.457651i	$0.848691\pi$
$224$	−12.6354	+	4.13227i	−0.844241	+	0.276099i
$225$		0			0
$226$	3.50226	−	13.6621i	0.232967	−	0.908791i
$227$	2.07372	+	5.69750i	0.137638	+	0.378156i	0.989292	−	0.145947i	$-0.0466229\pi$
$227$	2.07372	+	5.69750i	0.137638	+	0.378156i	−0.851655	+	0.524103i	$0.824401\pi$
$228$		0			0
$229$	−14.8939	−	17.7498i	−0.984215	−	1.17294i	−0.984932	−	0.172942i	$-0.944673\pi$
$229$	−14.8939	−	17.7498i	−0.984215	−	1.17294i	0.000716763	−	1.00000i	$-0.499772\pi$
$230$	−1.24805	+	16.3015i	−0.0822940	+	1.07489i
$231$		0			0
$232$	21.1291	+	9.02724i	1.38720	+	0.592667i
$233$	−4.63643	−	8.03053i	−0.303742	−	0.526097i	0.673238	−	0.739426i	$-0.264903\pi$
$233$	−4.63643	−	8.03053i	−0.303742	−	0.526097i	−0.976981	+	0.213328i	$0.931570\pi$
$234$		0			0
$235$	−0.815853	−	0.471033i	−0.0532204	−	0.0307268i
$236$	2.55597	−	16.5946i	0.166380	−	1.08022i
$237$		0			0
$238$	4.30493	+	8.97626i	0.279047	+	0.581844i
$239$	1.63200	+	9.25552i	0.105565	+	0.598690i	0.990993	+	0.133913i	$0.0427543\pi$
$239$	1.63200	+	9.25552i	0.105565	+	0.598690i	−0.885428	+	0.464777i	$0.846135\pi$
$240$		0			0
$241$	−20.4723	−	17.1783i	−1.31873	−	1.10655i	−0.986572	−	0.163328i	$-0.947777\pi$
$241$	−20.4723	−	17.1783i	−1.31873	−	1.10655i	−0.332163	−	0.943222i	$-0.607778\pi$
$242$	−4.72201	−	4.62060i	−0.303543	−	0.297023i
$243$		0			0
$244$	−1.45569	+	0.0316075i	−0.0931907	+	0.00202347i
$245$	−1.68965	+	2.01365i	−0.107948	+	0.128647i
$246$		0			0
$247$	0.745572	+	4.22835i	0.0474396	+	0.269043i
$248$	9.35565	−	4.73938i	0.594084	−	0.300951i
$249$		0			0
$250$	10.0160	+	13.9789i	0.633469	+	0.884105i
$251$	0.101849	+	0.0588028i	0.00642868	+	0.00371160i	0.503211	−	0.864164i	$-0.332152\pi$
$251$	0.101849	+	0.0588028i	0.00642868	+	0.00371160i	−0.496782	+	0.867875i	$0.665485\pi$
$252$		0			0
$253$	−14.1535	+	8.17150i	−0.889821	+	0.513738i
$254$	26.0126	+	11.7879i	1.63218	+	0.739636i
$255$		0			0
$256$	11.3185	−	11.3089i	0.707409	−	0.706804i
$257$	7.73634	−	6.49156i	0.482580	−	0.404932i	−0.368778	−	0.929517i	$-0.620224\pi$
$257$	7.73634	−	6.49156i	0.482580	−	0.404932i	0.851358	+	0.524585i	$0.175779\pi$
$258$		0			0
$259$	−3.78160	−	10.3899i	−0.234977	−	0.645594i
$260$	1.70283	−	1.03306i	0.105605	−	0.0640674i
$261$		0			0
$262$	−5.16190	−	18.4606i	−0.318903	−	1.14050i
$263$	1.42729	−	8.09455i	0.0880104	−	0.499132i	−0.908656	−	0.417546i	$-0.862890\pi$
$263$	1.42729	−	8.09455i	0.0880104	−	0.499132i	0.996666	−	0.0815860i	$-0.0259985\pi$
$264$		0			0
$265$	−10.6914	−	3.89136i	−0.656769	−	0.239044i
$266$	−21.0448	−	14.3979i	−1.29034	−	0.882790i
$267$		0			0
$268$	−8.94293	−	7.17903i	−0.546277	−	0.438529i
$269$		−	16.5496i		−	1.00905i	−0.863398	−	0.504524i	$-0.831668\pi$
$269$		−	16.5496i		−	1.00905i	0.863398	−	0.504524i	$-0.168332\pi$
$270$		0			0
$271$	8.76275			0.532299			0.266150	−	0.963932i	$-0.414249\pi$
$271$	8.76275			0.532299			0.266150	+	0.963932i	$0.414249\pi$
$272$	−9.50406	−	7.29595i	−0.576268	−	0.442382i
$273$		0			0
$274$	−6.44898	+	9.42624i	−0.389597	+	0.569460i
$275$	−1.57746	+	4.33403i	−0.0951242	+	0.261352i
$276$		0			0
$277$	5.89916	+	1.04018i	0.354446	+	0.0624985i	0.348036	−	0.937481i	$-0.386849\pi$
$277$	5.89916	+	1.04018i	0.354446	+	0.0624985i	0.00640991	+	0.999979i	$0.497960\pi$
$278$	7.30132	+	26.1118i	0.437904	+	1.56608i
$279$		0			0
$280$	−2.68777	+	11.5189i	−0.160625	+	0.688384i
$281$	−10.4464	+	3.80217i	−0.623179	+	0.226819i	−0.634260	−	0.773120i	$-0.718695\pi$
$281$	−10.4464	+	3.80217i	−0.623179	+	0.226819i	0.0110807	+	0.999939i	$0.496473\pi$
$282$		0			0
$283$	8.16295	+	9.72822i	0.485237	+	0.578283i	0.951999	−	0.306100i	$-0.0990242\pi$
$283$	8.16295	+	9.72822i	0.485237	+	0.578283i	−0.466763	+	0.884383i	$0.654580\pi$
$284$	19.4773	+	22.2143i	1.15576	+	1.31818i
$285$		0			0
$286$	1.81343	+	0.821773i	0.107231	+	0.0485925i
$287$	−8.71044	−	15.0869i	−0.514161	−	0.890553i
$288$		0			0
$289$	4.01381	−	6.95213i	0.236107	−	0.408949i
$290$	16.6181	−	11.9070i	0.975846	−	0.699202i
$291$		0			0
$292$	7.69950	−	22.6740i	0.450579	−	1.32690i
$293$	26.3005	−	4.63749i	1.53649	−	0.270925i	0.659601	−	0.751616i	$-0.270725\pi$
$293$	26.3005	−	4.63749i	1.53649	−	0.270925i	0.876890	+	0.480691i	$0.159614\pi$
$294$		0			0
$295$	−11.4440	−	9.60268i	−0.666297	−	0.559089i
$296$	9.71103	+	9.09829i	0.564442	+	0.528828i
$297$		0			0
$298$	−0.945078	+	0.965822i	−0.0547469	+	0.0559485i
$299$	−2.33694	+	2.78506i	−0.135149	+	0.161064i
$300$		0			0
$301$	6.28555	−	1.10831i	0.362293	−	0.0638821i
$302$	0.680493	+	1.41890i	0.0391580	+	0.0816488i
$303$		0			0
$304$	30.4256	+	4.01222i	1.74503	+	0.230117i
$305$	−0.647748	+	1.12193i	−0.0370900	+	0.0642417i
$306$		0			0
$307$	−4.31774	+	2.49285i	−0.246426	+	0.142274i	−0.618127	−	0.786078i	$-0.712108\pi$
$307$	−4.31774	+	2.49285i	−0.246426	+	0.142274i	0.371700	+	0.928353i	$0.378775\pi$
$308$	−11.0204	+	4.28423i	−0.627943	+	0.244116i
$309$		0			0
$310$	0.712327	−	9.30408i	0.0404574	−	0.528436i
$311$	12.4172	−	10.4193i	0.704116	−	0.590824i	−0.218825	−	0.975764i	$-0.570222\pi$
$311$	12.4172	−	10.4193i	0.704116	−	0.590824i	0.922941	+	0.384940i	$0.125778\pi$
$312$		0			0
$313$	12.8980	−	4.69448i	0.729037	−	0.265348i	0.0492798	−	0.998785i	$-0.484307\pi$
$313$	12.8980	−	4.69448i	0.729037	−	0.265348i	0.679757	+	0.733437i	$0.262085\pi$
$314$	−9.84919	−	2.52482i	−0.555822	−	0.142484i
$315$		0			0
$316$	20.4819	+	11.2396i	1.15220	+	0.632276i
$317$	5.48493	+	0.967141i	0.308064	+	0.0543200i	0.325543	−	0.945527i	$-0.394453\pi$
$317$	5.48493	+	0.967141i	0.308064	+	0.0543200i	−0.0174789	+	0.999847i	$0.505564\pi$
$318$		0			0
$319$	19.2033	+	6.98945i	1.07518	+	0.391334i
$320$	−3.37925	−	13.8291i	−0.188906	−	0.773068i
$321$		0			0
$322$	−2.11517	−	21.4875i	−0.117874	−	1.19745i
$323$		−	22.9814i		−	1.27872i
$324$		0			0
$325$			1.02602i			0.0569132i
$326$	−1.10227	+	0.108505i	−0.0610494	+	0.00600954i
$327$		0			0
$328$	17.5576	+	11.4606i	0.969454	+	0.632803i
$329$	1.16910	+	0.425517i	0.0644545	+	0.0234595i
$330$		0			0
$331$	−22.7828	−	4.01723i	−1.25226	−	0.220807i	−0.492097	−	0.870541i	$-0.663769\pi$
$331$	−22.7828	−	4.01723i	−1.25226	−	0.220807i	−0.760162	+	0.649734i	$0.774880\pi$
$332$	7.21260	−	13.1435i	0.395843	−	0.721344i
$333$		0			0
$334$	4.98569	−	19.4489i	0.272805	−	1.06420i
$335$	−9.58825	+	3.48984i	−0.523862	+	0.190670i
$336$		0			0
$337$	3.50303	−	2.93939i	0.190822	−	0.160119i	−0.542371	−	0.840139i	$-0.682473\pi$
$337$	3.50303	−	2.93939i	0.190822	−	0.160119i	0.733194	+	0.680020i	$0.238029\pi$
$338$	−17.8895	−	1.36963i	−0.973062	−	0.0744982i
$339$		0			0
$340$	−9.93614	+	3.86273i	−0.538863	+	0.209486i
$341$	8.07811	−	4.66390i	0.437454	−	0.252564i
$342$		0			0
$343$	9.96098	−	17.2529i	0.537842	−	0.931570i
$344$	−6.14568	+	4.60857i	−0.331353	+	0.248478i
$345$		0			0
$346$	−15.3485	+	7.36098i	−0.825138	+	0.395729i
$347$	−17.5663	+	3.09741i	−0.943008	+	0.166278i	−0.623956	−	0.781459i	$-0.714476\pi$
$347$	−17.5663	+	3.09741i	−0.943008	+	0.166278i	−0.319052	+	0.947737i	$0.603364\pi$
$348$		0			0
$349$	−11.1052	+	13.2347i	−0.594449	+	0.708436i	−0.976454	−	0.215724i	$-0.930789\pi$
$349$	−11.1052	+	13.2347i	−0.594449	+	0.708436i	0.382006	+	0.924160i	$0.375233\pi$
$350$	−4.35514	−	4.26160i	−0.232792	−	0.227792i
$351$		0			0
$352$	9.50185	−	10.5936i	0.506450	−	0.564640i
$353$	−21.4608	−	18.0078i	−1.14225	−	0.958458i	−0.142736	−	0.989761i	$-0.545590\pi$
$353$	−21.4608	−	18.0078i	−1.14225	−	0.958458i	−0.999510	+	0.0313029i	$0.990034\pi$
$354$		0			0
$355$	25.8872	−	4.56461i	1.37395	−	0.242265i
$356$	−1.50190	+	4.42291i	−0.0796008	+	0.234414i
$357$		0			0
$358$	−6.10367	−	8.51863i	−0.322589	−	0.450223i
$359$	11.9164	−	20.6398i	0.628922	−	1.08932i	−0.358846	−	0.933397i	$-0.616830\pi$
$359$	11.9164	−	20.6398i	0.628922	−	1.08932i	0.987768	−	0.155928i	$-0.0498369\pi$
$360$		0			0
$361$	19.9317	+	34.5228i	1.04904	+	1.81699i
$362$	−8.09614	+	17.8660i	−0.425524	+	0.939018i
$363$		0			0
$364$	−1.97776	+	1.73407i	−0.103663	+	0.0908900i
$365$	−13.6950	−	16.3210i	−0.716827	−	0.854281i
$366$		0			0
$367$	−0.313629	+	0.114152i	−0.0163713	+	0.00595866i	−0.350193	−	0.936678i	$-0.613884\pi$
$367$	−0.313629	+	0.114152i	−0.0163713	+	0.00595866i	0.333822	+	0.942636i	$0.391662\pi$
$368$	13.9577	+	21.9196i	0.727598	+	1.14264i
$369$		0			0
$370$	11.4027	−	3.18840i	0.592799	−	0.165757i
$371$	14.7974	+	2.60918i	0.768242	+	0.135462i
$372$		0			0
$373$	1.23868	−	3.40324i	0.0641364	−	0.176213i	−0.903485	−	0.428620i	$-0.859000\pi$
$373$	1.23868	−	3.40324i	0.0641364	−	0.176213i	0.967621	+	0.252407i	$0.0812221\pi$
$374$	−8.79516	−	6.01723i	−0.454787	−	0.311143i
$375$		0			0
$376$	−1.48663	+	0.179003i	−0.0766673	+	0.00923136i
$377$	4.54611			0.234137
$378$		0			0
$379$		−	31.7219i		−	1.62944i	−0.579852	−	0.814722i	$-0.696890\pi$
$379$		−	31.7219i		−	1.62944i	0.579852	−	0.814722i	$-0.303110\pi$
$380$	17.0934	−	21.2933i	0.876873	−	1.09232i
$381$		0			0
$382$	6.62280	−	9.68031i	0.338852	−	0.495288i
$383$	−15.3087	−	5.57190i	−0.782237	−	0.284711i	−0.0801320	−	0.996784i	$-0.525534\pi$
$383$	−15.3087	−	5.57190i	−0.782237	−	0.284711i	−0.702105	+	0.712073i	$0.747756\pi$
$384$		0			0
$385$	−1.82681	+	10.3604i	−0.0931031	+	0.528014i
$386$	13.0294	−	3.64326i	0.663181	−	0.185437i
$387$		0			0
$388$	−25.2780	+	15.3354i	−1.28330	+	0.778536i
$389$	0.814629	+	2.23818i	0.0413034	+	0.113480i	0.958630	−	0.284656i	$-0.0918794\pi$
$389$	0.814629	+	2.23818i	0.0413034	+	0.113480i	−0.917326	+	0.398136i	$0.869657\pi$
$390$		0			0
$391$	14.9071	−	12.5085i	0.753883	−	0.632583i
$392$	−0.228436	+	4.17185i	−0.0115377	+	0.210710i
$393$		0			0
$394$	−8.44987	+	18.6466i	−0.425698	+	0.939403i
$395$	18.0023	−	10.3936i	0.905794	−	0.522960i
$396$		0			0
$397$	−14.7658	−	8.52506i	−0.741076	−	0.427860i	0.0813844	−	0.996683i	$-0.474066\pi$
$397$	−14.7658	−	8.52506i	−0.741076	−	0.427860i	−0.822460	+	0.568822i	$0.807399\pi$
$398$	−30.4223	+	21.7978i	−1.52493	+	1.09263i
$399$		0			0
$400$	6.99372	+	2.20676i	0.349686	+	0.110338i
$401$	−6.89131	−	39.0826i	−0.344136	−	1.95169i	−0.304629	−	0.952471i	$-0.598532\pi$
$401$	−6.89131	−	39.0826i	−0.344136	−	1.95169i	−0.0395068	−	0.999219i	$-0.512579\pi$
$402$		0			0
$403$	1.33381	−	1.58958i	0.0664420	−	0.0791825i
$404$	24.5162	−	0.532325i	1.21973	−	0.0264841i
$405$		0			0
$406$	−18.8824	+	19.2969i	−0.937120	+	0.957689i
$407$	9.06661	+	7.60779i	0.449415	+	0.377104i
$408$		0			0
$409$	−1.68450	−	9.55328i	−0.0832932	−	0.472379i	−0.997712	−	0.0676096i	$-0.978463\pi$
$409$	−1.68450	−	9.55328i	−0.0832932	−	0.472379i	0.914419	−	0.404770i	$-0.132648\pi$
$410$	16.8208	−	8.06711i	0.830721	−	0.398406i
$411$		0			0
$412$	−22.8926	−	3.52602i	−1.12784	−	0.173714i
$413$	17.0860	+	9.86459i	0.840745	+	0.485405i
$414$		0			0
$415$	−6.66974	−	11.5523i	−0.327405	−	0.567081i
$416$	1.18027	−	2.93746i	0.0578677	−	0.144021i
$417$		0			0
$418$	27.2155	+	2.08364i	1.33115	+	0.101914i
$419$	−21.3004	−	25.3848i	−1.04059	−	1.24013i	−0.970122	−	0.242616i	$-0.921995\pi$
$419$	−21.3004	−	25.3848i	−1.04059	−	1.24013i	−0.0704699	−	0.997514i	$-0.522450\pi$
$420$		0			0
$421$	10.7589	+	29.5598i	0.524355	+	1.44065i	0.865627	+	0.500690i	$0.166920\pi$
$421$	10.7589	+	29.5598i	0.524355	+	1.44065i	−0.341271	+	0.939965i	$0.610857\pi$
$422$	24.5918	+	6.30406i	1.19711	+	0.306877i
$423$		0			0
$424$	−17.3063	+	5.24678i	−0.840468	+	0.254806i
$425$	0.953635	−	5.40833i	0.0462581	−	0.262343i
$426$		0			0
$427$	0.585156	−	1.60770i	0.0283177	−	0.0778022i
$428$	−1.54138	−	7.75337i	−0.0745054	−	0.374773i
$429$		0			0
$430$	0.669560	+	6.80188i	0.0322890	+	0.328016i
$431$	−9.66850			−0.465715			−0.232858	−	0.972511i	$-0.574808\pi$
$431$	−9.66850			−0.465715			−0.232858	+	0.972511i	$0.574808\pi$
$432$		0			0
$433$	−20.0283			−0.962501			−0.481250	−	0.876583i	$-0.659817\pi$
$433$	−20.0283			−0.962501			−0.481250	+	0.876583i	$0.659817\pi$
$434$	1.20724	+	12.2640i	0.0579493	+	0.588692i
$435$		0			0
$436$	−2.00031	−	10.0619i	−0.0957974	−	0.481875i
$437$	−17.0474	+	46.8374i	−0.815489	+	2.24054i
$438$		0			0
$439$	0.0379532	−	0.215244i	0.00181141	−	0.0102730i	−0.983889	−	0.178782i	$-0.942784\pi$
$439$	0.0379532	−	0.215244i	0.00181141	−	0.0102730i	0.985700	+	0.168509i	$0.0538953\pi$
$440$	−3.67353	−	12.1170i	−0.175129	−	0.577655i
$441$		0			0
$442$	−2.29638	−	0.588674i	−0.109228	−	0.0280004i
$443$	−3.15720	−	8.67435i	−0.150003	−	0.412131i	0.841819	−	0.539761i	$-0.181485\pi$
$443$	−3.15720	−	8.67435i	−0.150003	−	0.412131i	−0.991822	+	0.127630i	$0.959263\pi$
$444$		0			0
$445$	2.67141	+	3.18366i	0.126637	+	0.150920i
$446$	25.4830	+	1.95100i	1.20666	+	0.0923824i
$447$		0			0
$448$	7.56634	+	17.2108i	0.357476	+	0.813133i
$449$	20.7878	+	36.0055i	0.981036	+	1.69920i	0.658375	+	0.752690i	$0.271244\pi$
$449$	20.7878	+	36.0055i	0.981036	+	1.69920i	0.322661	+	0.946514i	$0.395422\pi$
$450$		0			0
$451$	16.1498	+	9.32411i	0.760466	+	0.439055i
$452$	−19.7134	−	3.03634i	−0.927242	−	0.142818i
$453$		0			0
$454$	7.73142	−	3.70792i	0.362854	−	0.174021i
$455$	0.406390	+	2.30475i	0.0190519	+	0.108049i
$456$		0			0
$457$	1.23132	+	1.03320i	0.0575986	+	0.0483309i	0.671132	−	0.741337i	$-0.265808\pi$
$457$	1.23132	+	1.03320i	0.0575986	+	0.0483309i	−0.613534	+	0.789668i	$0.710253\pi$
$458$	−22.9179	+	23.4209i	−1.07088	+	1.09439i
$459$		0			0
$460$	23.1158	−	0.501917i	1.07778	−	0.0234020i
$461$	16.0349	−	19.1096i	0.746819	−	0.890024i	−0.250120	−	0.968215i	$-0.580470\pi$
$461$	16.0349	−	19.1096i	0.746819	−	0.890024i	0.996938	+	0.0781909i	$0.0249144\pi$
$462$		0			0
$463$	6.29923	+	35.7247i	0.292750	+	1.66027i	0.676208	+	0.736711i	$0.263622\pi$
$463$	6.29923	+	35.7247i	0.292750	+	1.66027i	−0.383458	+	0.923558i	$0.625267\pi$
$464$	9.77777	−	30.9880i	0.453921	−	1.43858i
$465$		0			0
$466$	−10.6599	+	7.63792i	−0.493811	+	0.353820i
$467$	−6.88704	−	3.97623i	−0.318694	−	0.183998i	0.332116	−	0.943238i	$-0.392237\pi$
$467$	−6.88704	−	3.97623i	−0.318694	−	0.183998i	−0.650810	+	0.759240i	$0.725571\pi$
$468$		0			0
$469$	11.6699	−	6.73763i	0.538867	−	0.311115i
$470$	−0.549907	+	1.21350i	−0.0253653	+	0.0559745i
$471$		0			0
$472$	−23.7096	−	1.29825i	−1.09132	−	0.0597568i
$473$	−5.23375	+	4.39164i	−0.240648	+	0.201928i
$474$		0			0
$475$	4.81097	+	13.2180i	0.220742	+	0.606485i
$476$	12.0369	−	7.30239i	0.551709	−	0.334705i
$477$		0			0
$478$	12.8002	−	3.57917i	0.585469	−	0.163707i
$479$	−2.84409	+	16.1296i	−0.129950	+	0.736982i	0.848294	+	0.529525i	$0.177630\pi$
$479$	−2.84409	+	16.1296i	−0.129950	+	0.736982i	−0.978244	+	0.207457i	$0.933481\pi$
$480$		0			0
$481$	2.47415	+	0.900516i	0.112811	+	0.0410600i
$482$	−21.3406	+	31.1928i	−0.972039	+	1.42079i
$483$		0			0
$484$	−5.84888	+	7.28596i	−0.265858	+	0.331180i
$485$			26.3063i			1.19451i
$486$		0			0
$487$	4.24111			0.192183			0.0960914	−	0.995373i	$-0.469366\pi$
$487$	4.24111			0.192183			0.0960914	+	0.995373i	$0.469366\pi$
$488$	0.246158	+	2.04437i	0.0111431	+	0.0925442i
$489$		0			0
$490$	3.06812	+	2.09906i	0.138604	+	0.0948260i
$491$	−4.31034	+	11.8426i	−0.194523	+	0.534447i	−0.998158	−	0.0606758i	$-0.980674\pi$
$491$	−4.31034	+	11.8426i	−0.194523	+	0.534447i	0.803635	+	0.595123i	$0.202897\pi$
$492$		0			0
$493$	−23.9634	−	4.22540i	−1.07926	−	0.190302i
$494$	5.84773	−	1.63513i	0.263102	−	0.0735679i
$495$		0			0
$496$	−7.96640	−	12.5106i	−0.357702	−	0.561744i
$497$	−32.6215	+	11.8732i	−1.46327	+	0.532588i
$498$		0			0
$499$	−10.4544	−	12.4591i	−0.468003	−	0.557744i	0.479479	−	0.877553i	$-0.340826\pi$
$499$	−10.4544	−	12.4591i	−0.468003	−	0.557744i	−0.947482	+	0.319809i	$0.896381\pi$
$500$	18.2865	−	16.0333i	0.817795	−	0.717032i
$501$		0			0
$502$	0.0686493	−	0.151491i	0.00306397	−	0.00676136i
$503$	17.8227	+	30.8698i	0.794674	+	1.37642i	0.923046	+	0.384690i	$0.125692\pi$
$503$	17.8227	+	30.8698i	0.794674	+	1.37642i	−0.128372	+	0.991726i	$0.540975\pi$
$504$		0			0
$505$	10.9092	−	18.8953i	0.485452	−	0.840828i
$506$	13.4615	+	18.7876i	0.598437	+	0.835213i
$507$		0			0
$508$	12.9865	−	38.2436i	0.576183	−	1.69679i
$509$	25.2257	−	4.44797i	1.11811	−	0.197153i	0.416099	−	0.909319i	$-0.363397\pi$
$509$	25.2257	−	4.44797i	1.11811	−	0.197153i	0.702010	+	0.712167i	$0.252286\pi$
$510$		0			0
$511$	21.5542	+	18.0861i	0.953500	+	0.800082i
$512$	−17.4843	−	14.3631i	−0.772705	−	0.634765i
$513$		0			0
$514$	−10.2081	−	9.98886i	−0.450260	−	0.440590i
$515$	−13.2471	+	15.7873i	−0.583737	+	0.695670i
$516$		0			0
$517$	−1.31155	+	0.231261i	−0.0576818	+	0.0101709i
$518$	−14.0989	+	6.76170i	−0.619470	+	0.297092i
$519$		0			0
$520$	−1.68985	−	2.25346i	−0.0741047	−	0.0988210i
$521$	−1.83496	+	3.17824i	−0.0803909	+	0.139241i	−0.903418	−	0.428761i	$-0.858950\pi$
$521$	−1.83496	+	3.17824i	−0.0803909	+	0.139241i	0.823027	+	0.568002i	$0.192284\pi$
$522$		0			0
$523$	6.27809	−	3.62466i	0.274522	−	0.158495i	−0.356419	−	0.934326i	$-0.616002\pi$
$523$	6.27809	−	3.62466i	0.274522	−	0.158495i	0.630941	+	0.775831i	$0.282669\pi$
$524$	−25.2665	+	9.82248i	−1.10377	+	0.429097i
$525$		0			0
$526$	−11.5901	−	0.887346i	−0.505353	−	0.0386901i
$527$	−8.50823	+	7.13925i	−0.370624	+	0.310991i
$528$		0			0
$529$	−18.0473	+	6.56866i	−0.784663	+	0.285594i
$530$	−3.99553	+	15.5863i	−0.173555	+	0.677027i
$531$		0			0
$532$	−17.3481	+	31.6135i	−0.752137	+	1.37062i
$533$	4.08543	+	0.720371i	0.176959	+	0.0312027i
$534$		0			0
$535$	−6.60936	−	2.40561i	−0.285747	−	0.104004i
$536$	−8.86488	+	13.5810i	−0.382905	+	0.586609i
$537$		0			0
$538$	−23.2921	+	2.29282i	−1.00419	+	0.0988503i
$539$			3.71605i			0.160062i
$540$		0			0
$541$			45.0694i			1.93768i	0.247679	+	0.968842i	$0.420332\pi$
$541$			45.0694i			1.93768i	−0.247679	+	0.968842i	$0.579668\pi$
$542$	−1.21401	−	12.3328i	−0.0521461	−	0.529739i
$543$		0			0
$544$	−8.95169	+	14.3869i	−0.383800	+	0.616834i
$545$	−8.57723	−	3.12186i	−0.367408	−	0.133726i
$546$		0			0
$547$	14.7500	+	2.60083i	0.630666	+	0.111203i	0.479839	−	0.877357i	$-0.340695\pi$
$547$	14.7500	+	2.60083i	0.630666	+	0.111203i	0.150827	+	0.988560i	$0.451806\pi$
$548$	14.1601	+	7.77044i	0.604888	+	0.331937i
$549$		0			0
$550$	6.31830	+	1.61969i	0.269413	+	0.0690636i
$551$	58.5669	−	21.3166i	2.49503	−	0.908118i
$552$		0			0
$553$	−21.0298	+	17.6461i	−0.894278	+	0.750389i
$554$	0.646682	−	8.44666i	0.0274749	−	0.358864i
$555$		0			0
$556$	35.7385	−	13.8935i	1.51565	−	0.589217i
$557$	−22.1699	+	12.7998i	−0.939368	+	0.542344i	−0.889762	−	0.456424i	$-0.849130\pi$
$557$	−22.1699	+	12.7998i	−0.939368	+	0.542344i	−0.0496059	+	0.998769i	$0.515797\pi$
$558$		0			0
$559$	−0.759937	+	1.31625i	−0.0321419	+	0.0556714i
$560$	16.5841	+	2.18695i	0.700808	+	0.0924155i
$561$		0			0
$562$	6.79848	+	14.1756i	0.286777	+	0.597962i
$563$	−8.77498	+	1.54727i	−0.369821	+	0.0652095i	−0.355470	−	0.934688i	$-0.615679\pi$
$563$	−8.77498	+	1.54727i	−0.369821	+	0.0652095i	−0.0143510	+	0.999897i	$0.504568\pi$
$564$		0			0
$565$	−11.4074	+	13.5948i	−0.479914	+	0.571939i
$566$	12.5607	−	12.8364i	0.527965	−	0.539554i
$567$		0			0
$568$	28.5663	−	30.4901i	1.19862	−	1.27934i
$569$	16.0670	+	13.4818i	0.673565	+	0.565188i	0.914118	−	0.405448i	$-0.132884\pi$
$569$	16.0670	+	13.4818i	0.673565	+	0.565188i	−0.240553	+	0.970636i	$0.577329\pi$
$570$		0			0
$571$	−1.19314	+	0.210382i	−0.0499312	+	0.00880422i	−0.198558	−	0.980089i	$-0.563626\pi$
$571$	−1.19314	+	0.210382i	−0.0499312	+	0.00880422i	0.148627	+	0.988893i	$0.452515\pi$
$572$	0.905336	−	2.66610i	0.0378540	−	0.111475i
$573$		0			0
$574$	−20.0267	+	14.3493i	−0.835900	+	0.598930i
$575$	−5.95542	+	10.3151i	−0.248358	+	0.430169i
$576$		0			0
$577$	−8.95106	−	15.5037i	−0.372638	−	0.645427i	0.617333	−	0.786702i	$-0.288213\pi$
$577$	−8.95106	−	15.5037i	−0.372638	−	0.645427i	−0.989970	+	0.141275i	$0.954880\pi$
$578$	−10.3406	−	4.68592i	−0.430111	−	0.194909i
$579$		0			0
$580$	−19.0603	−	21.7388i	−0.791437	−	0.902655i
$581$	11.3238	+	13.4951i	0.469788	+	0.559872i
$582$		0			0
$583$	−15.1142	+	5.50114i	−0.625968	+	0.227834i
$584$	−32.9784	−	7.69506i	−1.36466	−	0.318424i
$585$		0			0
$586$	−10.1706	−	36.3731i	−0.420143	−	1.50256i
$587$	−4.19636	−	0.739932i	−0.173202	−	0.0305402i	0.0863743	−	0.996263i	$-0.472472\pi$
$587$	−4.19636	−	0.739932i	−0.173202	−	0.0305402i	−0.259577	+	0.965723i	$0.583583\pi$
$588$		0			0
$589$	9.72984	−	26.7325i	0.400911	−	1.10149i
$590$	−11.9294	+	17.4368i	−0.491127	+	0.717863i
$591$		0			0
$592$	11.4597	−	14.9279i	0.470989	−	0.613533i
$593$	−14.8627			−0.610340			−0.305170	−	0.952298i	$-0.598713\pi$
$593$	−14.8627			−0.610340			−0.305170	+	0.952298i	$0.598713\pi$
$594$		0			0
$595$		−	12.5265i		−	0.513537i
$596$	1.49024	+	1.19631i	0.0610426	+	0.0490026i
$597$		0			0
$598$	4.24349	+	2.90319i	0.173529	+	0.118720i
$599$	−4.35844	−	1.58634i	−0.178081	−	0.0648162i	0.251441	−	0.967873i	$-0.419096\pi$
$599$	−4.35844	−	1.58634i	−0.178081	−	0.0648162i	−0.429522	+	0.903057i	$0.641318\pi$
$600$		0			0
$601$	2.59673	−	14.7268i	0.105923	−	0.600718i	−0.884925	−	0.465734i	$-0.845790\pi$
$601$	2.59673	−	14.7268i	0.105923	−	0.600718i	0.990848	−	0.134985i	$-0.0430985\pi$
$602$	−2.43066	−	8.69281i	−0.0990665	−	0.354292i
$603$		0			0
$604$	1.90270	−	1.15431i	0.0774200	−	0.0469683i
$605$	2.84323	+	7.81171i	0.115594	+	0.317591i
$606$		0			0
$607$	−13.7989	+	11.5786i	−0.560079	+	0.469962i	−0.878337	−	0.478042i	$-0.841347\pi$
$607$	−13.7989	+	11.5786i	−0.560079	+	0.469962i	0.318258	+	0.948004i	$0.396902\pi$
$608$	1.43162	−	43.3772i	0.0580600	−	1.75918i
$609$		0			0
$610$	1.66876	+	0.756213i	0.0675662	+	0.0306182i
$611$	−0.256573	+	0.148133i	−0.0103798	+	0.00599281i
$612$		0			0
$613$	−26.2514	−	15.1562i	−1.06028	−	0.612155i	−0.134772	−	0.990877i	$-0.543030\pi$
$613$	−26.2514	−	15.1562i	−1.06028	−	0.612155i	−0.925511	+	0.378722i	$0.876364\pi$
$614$	4.10665	+	5.73147i	0.165731	+	0.231303i
$615$		0			0
$616$	7.55645	+	14.9166i	0.304458	+	0.601008i
$617$	2.22018	+	12.5913i	0.0893810	+	0.506905i	0.996325	+	0.0856536i	$0.0272978\pi$
$617$	2.22018	+	12.5913i	0.0893810	+	0.506905i	−0.906944	+	0.421251i	$0.861591\pi$
$618$		0			0
$619$	11.8907	−	14.1707i	0.477926	−	0.569570i	−0.472178	−	0.881503i	$-0.656532\pi$
$619$	11.8907	−	14.1707i	0.477926	−	0.569570i	0.950104	+	0.311933i	$0.100977\pi$
$620$	−13.1934	+	0.286470i	−0.529858	+	0.0115049i
$621$		0			0
$622$	−16.3845	−	16.0326i	−0.656960	−	0.642850i
$623$	−4.20447	−	3.52797i	−0.168448	−	0.141345i
$624$		0			0
$625$	−2.16567	−	12.2821i	−0.0866269	−	0.491286i
$626$	−8.39398	−	17.5024i	−0.335491	−	0.699536i
$627$		0			0
$628$	−2.18894	+	14.2117i	−0.0873481	+	0.567107i
$629$	−12.2047	−	7.04640i	−0.486634	−	0.280958i
$630$		0			0
$631$	4.30167	+	7.45072i	0.171247	+	0.296608i	0.938856	−	0.344310i	$-0.111887\pi$
$631$	4.30167	+	7.45072i	0.171247	+	0.296608i	−0.767609	+	0.640918i	$0.778554\pi$
$632$	12.9811	−	30.3836i	0.516361	−	1.20859i
$633$		0			0
$634$	0.601272	−	7.85354i	0.0238796	−	0.311904i
$635$	−23.0989	−	27.5281i	−0.916650	−	1.09242i
$636$		0			0
$637$	0.282736	+	0.776812i	0.0112024	+	0.0307784i
$638$	7.17656	−	27.9953i	0.284123	−	1.10835i
$639$		0			0
$640$	−18.9950	+	6.67190i	−0.750843	+	0.263730i
$641$	1.04346	−	5.91773i	0.0412140	−	0.233736i	−0.957242	−	0.289289i	$-0.906581\pi$
$641$	1.04346	−	5.91773i	0.0412140	−	0.233736i	0.998456	+	0.0555530i	$0.0176922\pi$
$642$		0			0
$643$	8.03942	−	22.0881i	0.317044	−	0.871070i	−0.674143	−	0.738601i	$-0.735487\pi$
$643$	8.03942	−	22.0881i	0.317044	−	0.871070i	0.991187	−	0.132470i	$-0.0422908\pi$
$644$	−29.9487	+	5.95384i	−1.18014	+	0.234614i
$645$		0			0
$646$	−32.3443	+	3.18389i	−1.27257	+	0.125268i
$647$	10.6875			0.420169			0.210085	−	0.977683i	$-0.432626\pi$
$647$	10.6875			0.420169			0.210085	+	0.977683i	$0.432626\pi$
$648$		0			0
$649$	−21.1191			−0.828998
$650$	1.44403	−	0.142146i	0.0566394	−	0.00557544i
$651$		0			0
$652$	0.305423	+	1.53632i	0.0119613	+	0.0601670i
$653$	−7.40542	+	20.3462i	−0.289796	+	0.796209i	0.706298	+	0.707915i	$0.250364\pi$
$653$	−7.40542	+	20.3462i	−0.289796	+	0.796209i	−0.996094	+	0.0882946i	$0.971858\pi$
$654$		0			0
$655$	−4.18835	+	23.7533i	−0.163653	+	0.928120i
$656$	13.6973	−	26.2985i	0.534788	−	1.02678i
$657$		0			0
$658$	0.436908	−	1.70435i	0.0170324	−	0.0664426i
$659$	6.12164	+	16.8191i	0.238465	+	0.655177i	0.999975	+	0.00702451i	$0.00223599\pi$
$659$	6.12164	+	16.8191i	0.238465	+	0.655177i	−0.761510	+	0.648153i	$0.775542\pi$
$660$		0			0
$661$	15.6447	+	18.6447i	0.608510	+	0.725194i	0.979049	−	0.203623i	$-0.0652716\pi$
$661$	15.6447	+	18.6447i	0.608510	+	0.725194i	−0.370539	+	0.928817i	$0.620827\pi$
$662$	−2.49751	+	32.6214i	−0.0970687	+	1.26787i
$663$		0			0
$664$	−19.4976	−	8.33017i	−0.756652	−	0.323273i
$665$	16.0424	+	27.7863i	0.622098	+	1.07751i
$666$		0			0
$667$	45.7045	+	26.3875i	1.76968	+	1.02173i
$668$	−28.0633	−	4.32243i	−1.08580	−	0.167240i
$669$		0			0
$670$	6.24001	+	13.0111i	0.241073	+	0.502663i
$671$	0.318022	+	1.80359i	0.0122771	+	0.0696270i
$672$		0			0
$673$	7.83345	+	6.57304i	0.301957	+	0.253372i	0.781158	−	0.624333i	$-0.214629\pi$
$673$	7.83345	+	6.57304i	0.301957	+	0.253372i	−0.479201	+	0.877705i	$0.659074\pi$
$674$	−4.62225	−	4.52298i	−0.178042	−	0.174219i
$675$		0			0
$676$	0.550812	+	25.3677i	0.0211851	+	0.975679i
$677$	−18.4828	+	22.0270i	−0.710352	+	0.846565i	−0.993656	−	0.112465i	$-0.964125\pi$
$677$	−18.4828	+	22.0270i	−0.710352	+	0.846565i	0.283303	+	0.959030i	$0.408570\pi$
$678$		0			0
$679$	−6.03274	−	34.2133i	−0.231515	−	1.31299i
$680$	6.81302	+	13.4491i	0.261268	+	0.515749i
$681$		0			0
$682$	−7.68318	−	10.7231i	−0.294204	−	0.410608i
$683$	28.1049	+	16.2264i	1.07540	+	0.620885i	0.929653	−	0.368436i	$-0.120107\pi$
$683$	28.1049	+	16.2264i	1.07540	+	0.620885i	0.145751	+	0.989321i	$0.453440\pi$
$684$		0			0
$685$	12.4458	−	7.18559i	0.475530	−	0.274547i
$686$	−25.6620	−	11.6289i	−0.979778	−	0.443995i
$687$		0			0
$688$	7.33759	+	8.01101i	0.279743	+	0.305417i
$689$	−2.74096	+	2.29994i	−0.104422	+	0.0876208i
$690$		0			0
$691$	−9.17035	−	25.1953i	−0.348856	−	0.958475i	−0.982731	−	0.185039i	$-0.940759\pi$
$691$	−9.17035	−	25.1953i	−0.348856	−	0.958475i	0.633875	−	0.773436i	$-0.281463\pi$
$692$	12.4863	+	20.5818i	0.474659	+	0.782402i
$693$		0			0
$694$	6.79300	+	24.2939i	0.257859	+	0.922183i
$695$	5.92427	−	33.5982i	0.224721	−	1.27445i
$696$		0			0
$697$	−20.8655	−	7.59443i	−0.790338	−	0.287660i
$698$	20.1652	+	13.7960i	0.763263	+	0.522188i
$699$		0			0
$700$	−5.39445	+	6.71988i	−0.203891	+	0.253988i
$701$			26.7362i			1.00981i	0.863174	+	0.504907i	$0.168473\pi$
$701$			26.7362i			1.00981i	−0.863174	+	0.504907i	$0.831527\pi$
$702$		0			0
$703$	36.0966			1.36141
$704$	−16.2259	−	11.9054i	−0.611538	−	0.448700i
$705$		0			0
$706$	−22.3711	+	32.6991i	−0.841949	+	1.23065i
$707$	−9.85503	+	27.0765i	−0.370636	+	1.01832i
$708$		0			0
$709$	41.4005	+	7.30003i	1.55483	+	0.274158i	0.884012	−	0.467464i	$-0.154832\pi$
$709$	41.4005	+	7.30003i	1.55483	+	0.274158i	0.670817	+	0.741623i	$0.265943\pi$
$710$	−10.0108	−	35.8016i	−0.375697	−	1.34361i
$711$		0			0
$712$	6.43294	+	1.50104i	0.241084	+	0.0562538i
$713$	22.6361	−	8.23887i	0.847729	−	0.308548i
$714$		0			0
$715$	−1.61030	−	1.91908i	−0.0602219	−	0.0717697i
$716$	−11.1436	+	9.77056i	−0.416456	+	0.365143i
$717$		0			0
$718$	−30.6995	−	13.9118i	−1.14570	−	0.519182i
$719$	−7.75793	−	13.4371i	−0.289322	−	0.501121i	0.684326	−	0.729176i	$-0.260097\pi$
$719$	−7.75793	−	13.4371i	−0.289322	−	0.501121i	−0.973648	+	0.228056i	$0.926763\pi$
$720$		0			0
$721$	13.6084	−	23.5704i	0.506803	−	0.877809i
$722$	45.8263	−	32.8350i	1.70548	−	1.22199i
$723$		0			0
$724$	26.2665	+	8.91941i	0.976187	+	0.331487i
$725$	14.6674	−	2.58626i	0.544734	−	0.0960512i
$726$		0			0
$727$	−6.76072	−	5.67292i	−0.250741	−	0.210397i	0.508750	−	0.860914i	$-0.330108\pi$
$727$	−6.76072	−	5.67292i	−0.250741	−	0.210397i	−0.759491	+	0.650517i	$0.774552\pi$
$728$	2.71455	+	2.54327i	0.100608	+	0.0942600i
$729$		0			0
$730$	−21.0731	+	21.5356i	−0.779949	+	0.797068i
$731$	5.22917	−	6.23188i	0.193408	−	0.230494i
$732$		0			0
$733$	−17.4479	+	3.07653i	−0.644452	+	0.113634i	−0.486316	−	0.873783i	$-0.661660\pi$
$733$	−17.4479	+	3.07653i	−0.644452	+	0.113634i	−0.158136	+	0.987417i	$0.550549\pi$
$734$	0.204109	+	0.425590i	0.00753380	+	0.0157088i
$735$		0			0
$736$	28.9162	−	22.6811i	1.06586	−	0.836035i
$737$	−7.21231	+	12.4921i	−0.265669	+	0.460152i
$738$		0			0
$739$	−24.2476	+	13.9993i	−0.891961	+	0.514974i	−0.874583	−	0.484875i	$-0.838865\pi$
$739$	−24.2476	+	13.9993i	−0.891961	+	0.514974i	−0.0173774	+	0.999849i	$0.505532\pi$
$740$	−6.06714	−	15.6066i	−0.223033	−	0.573709i
$741$		0			0
$742$	1.62213	−	21.1875i	0.0595502	−	0.777817i
$743$	0.976314	−	0.819225i	0.0358175	−	0.0300544i	−0.624703	−	0.780862i	$-0.714780\pi$
$743$	0.976314	−	0.819225i	0.0358175	−	0.0300544i	0.660521	+	0.750808i	$0.270336\pi$
$744$		0			0
$745$	1.59778	−	0.581543i	0.0585379	−	0.0213061i
$746$	−4.96137	−	1.27184i	−0.181649	−	0.0465653i
$747$		0			0
$748$	−7.25021	+	13.2120i	−0.265094	+	0.483080i
$749$	9.14764	+	1.61298i	0.334247	+	0.0589368i
$750$		0			0
$751$	−8.98866	−	3.27161i	−0.328001	−	0.119383i	0.172771	−	0.984962i	$-0.444728\pi$
$751$	−8.98866	−	3.27161i	−0.328001	−	0.119383i	−0.500771	+	0.865580i	$0.666950\pi$
$752$	0.457892	+	2.06751i	0.0166976	+	0.0753942i
$753$		0			0
$754$	−0.629827	−	6.39824i	−0.0229369	−	0.233010i
$755$		−	1.98011i		−	0.0720634i
$756$		0			0
$757$			5.24463i			0.190619i	0.995448	+	0.0953096i	$0.0303841\pi$
$757$			5.24463i			0.190619i	−0.995448	+	0.0953096i	$0.969616\pi$
$758$	−44.6457	+	4.39481i	−1.62161	+	0.159627i
$759$		0			0
$760$	−32.3365	−	21.1074i	−1.17297	−	0.765647i
$761$	−27.2099	−	9.90361i	−0.986360	−	0.359006i	−0.202050	−	0.979375i	$-0.564760\pi$
$761$	−27.2099	−	9.90361i	−0.986360	−	0.359006i	−0.784310	+	0.620370i	$0.786983\pi$
$762$		0			0
$763$	11.8713	+	2.09322i	0.429768	+	0.0757797i
$764$	−14.5417	−	7.97988i	−0.526101	−	0.288702i
$765$		0			0
$766$	−5.72107	+	22.3176i	−0.206711	+	0.806366i
$767$	−4.41479	+	1.60685i	−0.159409	+	0.0580201i
$768$		0			0
$769$	−31.0584	+	26.0611i	−1.11999	+	0.939786i	−0.998604	−	0.0528190i	$-0.983179\pi$
$769$	−31.0584	+	26.0611i	−1.11999	+	0.939786i	−0.121389	+	0.992605i	$0.538735\pi$
$770$	14.8344	+	1.13573i	0.534595	+	0.0409289i
$771$		0			0
$772$	−6.93269	−	17.8330i	−0.249513	−	0.641825i
$773$	8.73768	−	5.04470i	0.314273	−	0.181445i	−0.334564	−	0.942373i	$-0.608589\pi$
$773$	8.73768	−	5.04470i	0.314273	−	0.181445i	0.648837	+	0.760928i	$0.275256\pi$
$774$		0			0
$775$	3.39906	−	5.88735i	0.122098	−	0.211480i
$776$	25.0853	+	33.4520i	0.900509	+	1.20086i
$777$		0			0
$778$	3.03717	−	1.45660i	0.108888	−	0.0522216i
$779$	56.0098	−	9.87604i	2.00676	−	0.353846i
$780$		0			0
$781$	23.8865	−	28.4668i	0.854726	−	1.01862i
$782$	−19.6699	−	19.2474i	−0.703393	−	0.688286i
$783$		0			0
$784$	5.90316	−	0.256473i	0.210827	−	0.00915977i
$785$	9.80068	+	8.22375i	0.349801	+	0.293518i
$786$		0			0
$787$	−14.0000	+	2.46858i	−0.499046	+	0.0879952i	−0.417505	−	0.908675i	$-0.637095\pi$
$787$	−14.0000	+	2.46858i	−0.499046	+	0.0879952i	−0.0815410	+	0.996670i	$0.525984\pi$
$788$	27.4141	+	9.30910i	0.976587	+	0.331623i
$789$		0			0
$790$	−17.1222	−	23.8967i	−0.609180	−	0.850206i
$791$	11.7186	−	20.2971i	0.416664	−	0.721683i
$792$		0			0
$793$	0.203707	+	0.352831i	0.00723385	+	0.0125294i
$794$	−9.95258	+	21.9627i	−0.353204	+	0.779426i
$795$		0			0
$796$	34.8933	+	39.7968i	1.23676	+	1.41056i
$797$	−14.0727	−	16.7712i	−0.498482	−	0.594068i	0.456871	−	0.889533i	$-0.348970\pi$
$797$	−14.0727	−	16.7712i	−0.498482	−	0.594068i	−0.955354	+	0.295465i	$0.904525\pi$
$798$		0			0
$799$	1.49013	−	0.542363i	0.0527170	−	0.0191874i
$800$	2.13689	−	10.1488i	0.0755504	−	0.358813i
$801$		0			0
$802$	−54.0505	+	15.1135i	−1.90859	+	0.533676i
$803$	−29.6617	−	5.23016i	−1.04674	−	0.184568i
$804$		0			0
$805$	−9.29208	+	25.5298i	−0.327503	+	0.899806i
$806$	−2.42198	−	1.65700i	−0.0853105	−	0.0583654i
$807$		0			0
$808$	−4.14572	−	34.4306i	−0.145846	−	1.21127i
$809$	−40.9197			−1.43866			−0.719331	−	0.694668i	$-0.755551\pi$
$809$	−40.9197			−1.43866			−0.719331	+	0.694668i	$0.755551\pi$
$810$		0			0
$811$		−	19.0286i		−	0.668185i	−0.942540	−	0.334093i	$-0.891570\pi$
$811$		−	19.0286i		−	0.668185i	0.942540	−	0.334093i	$-0.108430\pi$
$812$	29.7747	+	23.9019i	1.04489	+	0.838793i
$813$		0			0
$814$	9.45118	−	13.8144i	0.331264	−	0.484196i
$815$	1.30964	+	0.476669i	0.0458746	+	0.0166970i
$816$		0			0
$817$	−3.61830	+	20.5204i	−0.126588	+	0.717918i
$818$	−13.2120	+	3.69432i	−0.461947	+	0.129169i
$819$		0			0
$820$	−13.6841	−	22.5562i	−0.477871	−	0.787696i
$821$	−4.35542	−	11.9664i	−0.152005	−	0.417631i	0.840195	−	0.542284i	$-0.182440\pi$
$821$	−4.35542	−	11.9664i	−0.152005	−	0.417631i	−0.992200	+	0.124653i	$0.960218\pi$
$822$		0			0
$823$	11.3183	−	9.49719i	0.394531	−	0.331051i	−0.423844	−	0.905735i	$-0.639320\pi$
$823$	11.3183	−	9.49719i	0.394531	−	0.331051i	0.818375	+	0.574684i	$0.194875\pi$
$824$	−1.79096	+	32.7078i	−0.0623912	+	1.13943i
$825$		0			0
$826$	11.5164	−	25.4136i	0.400707	−	0.884253i
$827$	−18.0361	+	10.4132i	−0.627178	+	0.362101i	−0.779658	−	0.626205i	$-0.784607\pi$
$827$	−18.0361	+	10.4132i	−0.627178	+	0.362101i	0.152481	+	0.988306i	$0.451274\pi$
$828$		0			0
$829$	11.5499	+	6.66836i	0.401146	+	0.231602i	0.686978	−	0.726678i	$-0.258937\pi$
$829$	11.5499	+	6.66836i	0.401146	+	0.231602i	−0.285832	+	0.958280i	$0.592270\pi$
$830$	−15.3348	+	10.9875i	−0.532280	+	0.381383i
$831$		0			0
$832$	−4.29773	−	1.25417i	−0.148997	−	0.0434805i
$833$	−0.768348	−	4.35752i	−0.0266217	−	0.150979i
$834$		0			0
$835$	−16.2392	+	19.3531i	−0.561980	+	0.669742i
$836$	−0.837956	−	38.5921i	−0.0289813	−	1.33473i
$837$		0			0
$838$	−32.7759	+	33.4953i	−1.13222	+	1.15708i
$839$	9.48780	+	7.96121i	0.327555	+	0.274852i	0.791703	−	0.610906i	$-0.209195\pi$
$839$	9.48780	+	7.96121i	0.327555	+	0.274852i	−0.464148	+	0.885758i	$0.653639\pi$
$840$		0			0
$841$	−6.42348	−	36.4294i	−0.221499	−	1.25619i
$842$	40.1122	−	19.2374i	1.38236	−	0.662966i
$843$		0			0
$844$	5.46541	−	35.4841i	0.188127	−	1.22141i
$845$	19.5515	+	11.2881i	0.672592	+	0.388321i
$846$		0			0
$847$	−5.48927	−	9.50769i	−0.188613	−	0.326688i
$848$	9.78202	+	23.6302i	0.335916	+	0.811464i
$849$		0			0
$850$	−7.74386	−	0.592875i	−0.265612	−	0.0203355i
$851$	19.6470	+	23.4143i	0.673489	+	0.802633i
$852$		0			0
$853$	−8.85840	−	24.3382i	−0.303306	−	0.833326i	−0.993920	−	0.110103i	$-0.964882\pi$
$853$	−8.85840	−	24.3382i	−0.303306	−	0.833326i	0.690614	−	0.723223i	$-0.257340\pi$
$854$	−2.34377	−	0.600821i	−0.0802021	−	0.0205597i
$855$		0			0
$856$	−10.6986	+	3.24352i	−0.365672	+	0.110861i
$857$	−0.658395	+	3.73394i	−0.0224903	+	0.127549i	−0.993986	−	0.109509i	$-0.965072\pi$
$857$	−0.658395	+	3.73394i	−0.0224903	+	0.127549i	0.971495	+	0.237058i	$0.0761832\pi$
$858$		0			0
$859$	−12.7084	+	34.9159i	−0.433603	+	1.19132i	0.509982	+	0.860185i	$0.329652\pi$
$859$	−12.7084	+	34.9159i	−0.433603	+	1.19132i	−0.943585	+	0.331130i	$0.892570\pi$
$860$	9.48028	−	1.88469i	0.323275	−	0.0642674i
$861$		0			0
$862$	1.33949	+	13.6076i	0.0456233	+	0.463475i
$863$	−14.8041			−0.503936			−0.251968	−	0.967736i	$-0.581078\pi$
$863$	−14.8041			−0.503936			−0.251968	+	0.967736i	$0.581078\pi$
$864$		0			0
$865$	21.4190			0.728269
$866$	2.77477	+	28.1881i	0.0942904	+	0.957871i
$867$		0			0
$868$	17.0933	−	3.39816i	0.580183	−	0.115341i
$869$	10.0508	−	27.6143i	0.340950	−	0.936752i
$870$		0			0
$871$	−0.557216	+	3.16013i	−0.0188805	+	0.107077i
$872$	−13.8840	+	4.20925i	−0.470173	+	0.142543i
$873$		0			0
$874$	68.2813	+	17.5038i	2.30965	+	0.592075i
$875$	9.77385	+	26.8534i	0.330416	+	0.907811i
$876$		0			0
$877$	20.8616	+	24.8619i	0.704447	+	0.839527i	0.993022	−	0.117931i	$-0.0376260\pi$
$877$	20.8616	+	24.8619i	0.704447	+	0.839527i	−0.288575	+	0.957457i	$0.593182\pi$
$878$	−0.308194	−	0.0235956i	−0.0104011	−	0.000796311i
$879$		0			0
$880$	−16.5447	+	6.84888i	−0.557720	+	0.230876i
$881$	−9.60040	−	16.6284i	−0.323446	−	0.560224i	0.657751	−	0.753235i	$-0.271508\pi$
$881$	−9.60040	−	16.6284i	−0.323446	−	0.560224i	−0.981197	+	0.193011i	$0.938175\pi$
$882$		0			0
$883$	−2.82855	−	1.63307i	−0.0951884	−	0.0549571i	0.451650	−	0.892195i	$-0.350836\pi$
$883$	−2.82855	−	1.63307i	−0.0951884	−	0.0549571i	−0.546839	+	0.837238i	$0.684169\pi$
$884$	−0.510361	+	3.31351i	−0.0171653	+	0.111446i
$885$		0			0
$886$	−11.7710	+	5.64525i	−0.395453	+	0.189656i
$887$	−4.93246	−	27.9734i	−0.165616	−	0.939255i	−0.948427	−	0.316995i	$-0.897326\pi$
$887$	−4.93246	−	27.9734i	−0.165616	−	0.939255i	0.782811	−	0.622259i	$-0.213785\pi$
$888$		0			0
$889$	36.3547	+	30.5052i	1.21930	+	1.02311i
$890$	4.11062	−	4.20084i	0.137788	−	0.140812i
$891$		0			0
$892$	−0.784614	−	36.1354i	−0.0262708	−	1.20990i
$893$	−2.61081	+	3.11144i	−0.0873674	+	0.104120i
$894$		0			0
$895$	2.28979	+	12.9861i	0.0765393	+	0.434076i
$896$	23.1744	−	13.0334i	0.774202	−	0.435414i
$897$		0			0
$898$	47.7946	−	34.2452i	1.59493	−	1.14278i
$899$	−26.0859	−	15.0607i	−0.870013	−	0.502302i
$900$		0			0
$901$	16.5858	−	9.57584i	0.552555	−	0.319018i
$902$	10.8854	−	24.0212i	0.362445	−	0.799819i
$903$		0			0
$904$	−1.54225	+	28.1656i	−0.0512944	+	0.936773i
$905$	18.9069	−	15.8648i	0.628487	−	0.527363i
$906$		0			0
$907$	3.87326	+	10.6417i	0.128609	+	0.353351i	0.987239	−	0.159245i	$-0.0509059\pi$
$907$	3.87326	+	10.6417i	0.128609	+	0.353351i	−0.858630	+	0.512596i	$0.828684\pi$
$908$	−6.28969	−	10.3676i	−0.208731	−	0.344061i
$909$		0			0
$910$	3.18743	−	0.891263i	0.105662	−	0.0295451i
$911$	1.07530	−	6.09830i	0.0356261	−	0.202046i	−0.961799	−	0.273755i	$-0.911734\pi$
$911$	1.07530	−	6.09830i	0.0356261	−	0.202046i	0.997426	+	0.0717092i	$0.0228454\pi$
$912$		0			0
$913$	−17.7205	−	6.44973i	−0.586463	−	0.213455i
$914$	1.28354	−	1.87611i	0.0424559	−	0.0620562i
$915$		0			0
$916$	36.1379	+	29.0101i	1.19403	+	0.958521i
$917$		−	31.8535i		−	1.05190i
$918$		0			0
$919$	38.3693			1.26569			0.632844	−	0.774279i	$-0.281887\pi$
$919$	38.3693			1.26569			0.632844	+	0.774279i	$0.281887\pi$
$920$	−3.90891	−	32.4639i	−0.128873	−	1.07030i
$921$		0			0
$922$	−29.1166	−	19.9202i	−0.958904	−	0.656036i
$923$	2.82739	−	7.76819i	0.0930646	−	0.255693i
$924$		0			0
$925$	8.49480	+	1.49786i	0.279307	+	0.0492494i
$926$	49.4067	−	13.8150i	1.62360	−	0.453989i
$927$		0			0
$928$	−44.9675	−	9.46820i	−1.47613	−	0.310809i
$929$	24.3789	−	8.87320i	0.799846	−	0.291120i	0.0904233	−	0.995903i	$-0.471178\pi$
$929$	24.3789	−	8.87320i	0.799846	−	0.291120i	0.709423	+	0.704783i	$0.248956\pi$
$930$		0			0
$931$	7.28491	+	8.68182i	0.238753	+	0.284535i
$932$	12.2265	+	13.9447i	0.400494	+	0.456774i
$933$		0			0
$934$	−4.64205	+	10.2438i	−0.151893	+	0.335186i
$935$	6.70452	+	11.6126i	0.219261	+	0.379772i
$936$		0			0
$937$	9.82408	−	17.0158i	0.320939	−	0.555882i	−0.659743	−	0.751491i	$-0.729335\pi$
$937$	9.82408	−	17.0158i	0.320939	−	0.555882i	0.980682	+	0.195609i	$0.0626684\pi$
$938$	−11.0994	−	15.4909i	−0.362408	−	0.505797i
$939$		0			0
$940$	1.78408	+	0.605825i	0.0581901	+	0.0197598i
$941$	−13.6658	+	2.40964i	−0.445491	+	0.0785520i	−0.391894	−	0.920011i	$-0.628180\pi$
$941$	−13.6658	+	2.40964i	−0.445491	+	0.0785520i	−0.0535973	+	0.998563i	$0.517069\pi$
$942$		0			0
$943$	36.8917	+	30.9558i	1.20136	+	1.00806i
$944$	1.45760	+	33.5490i	0.0474407	+	1.09193i
$945$		0			0
$946$	6.90594	+	6.75761i	0.224531	+	0.219709i
$947$	22.0765	−	26.3098i	0.717391	−	0.854953i	−0.276984	−	0.960875i	$-0.589335\pi$
$947$	22.0765	−	26.3098i	0.717391	−	0.854953i	0.994375	+	0.105921i	$0.0337792\pi$
$948$		0			0
$949$	−6.59849	+	1.16349i	−0.214196	+	0.0377685i
$950$	17.9367	−	8.60227i	0.581943	−	0.279094i
$951$		0			0
$952$	−11.9451	−	15.9291i	−0.387142	−	0.516266i
$953$	−7.72473	+	13.3796i	−0.250228	+	0.433408i	−0.963589	−	0.267389i	$-0.913839\pi$
$953$	−7.72473	+	13.3796i	−0.250228	+	0.433408i	0.713360	+	0.700798i	$0.247172\pi$
$954$		0			0
$955$	−12.7813	+	7.37926i	−0.413592	+	0.238787i
$956$	−6.81073	−	17.5193i	−0.220275	−	0.566615i
$957$		0			0
$958$	23.0951	+	1.76817i	0.746168	+	0.0571271i
$959$	−14.5389	+	12.1996i	−0.469484	+	0.393944i
$960$		0			0
$961$	16.2109	−	5.90028i	0.522932	−	0.190332i
$962$	0.924623	−	3.60690i	0.0298110	−	0.116291i
$963$		0			0
$964$	46.8577	+	25.7135i	1.50918	+	0.828177i
$965$	−16.7651	−	2.95613i	−0.539687	−	0.0951613i
$966$		0			0
$967$	−23.1303	−	8.41874i	−0.743820	−	0.270728i	−0.0578171	−	0.998327i	$-0.518414\pi$
$967$	−23.1303	−	8.41874i	−0.743820	−	0.270728i	−0.686003	+	0.727599i	$0.740636\pi$
$968$	11.0647	+	7.22237i	0.355632	+	0.232136i
$969$		0			0
$970$	37.0238	−	3.64453i	1.18876	−	0.117019i
$971$		−	14.5202i		−	0.465977i	−0.972480	−	0.232988i	$-0.925150\pi$
$971$		−	14.5202i		−	0.465977i	0.972480	−	0.232988i	$-0.0748504\pi$
$972$		0			0
$973$			45.0556i			1.44442i
$974$	−0.587571	−	5.96898i	−0.0188270	−	0.191258i
$975$		0			0
$976$	2.84316	−	0.629677i	0.0910075	−	0.0201555i
$977$	−1.09977	−	0.400283i	−0.0351847	−	0.0128062i	0.324368	−	0.945931i	$-0.394848\pi$
$977$	−1.09977	−	0.400283i	−0.0351847	−	0.0128062i	−0.359553	+	0.933125i	$0.617071\pi$
$978$		0			0
$979$	5.78596	+	1.02022i	0.184920	+	0.0326064i
$980$	2.52918	−	4.60892i	0.0807917	−	0.147226i
$981$		0			0
$982$	17.2645	+	4.42573i	0.550933	+	0.141231i
$983$	10.8380	−	3.94472i	0.345679	−	0.125817i	−0.163345	−	0.986569i	$-0.552228\pi$
$983$	10.8380	−	3.94472i	0.345679	−	0.125817i	0.509025	+	0.860752i	$0.330006\pi$
$984$		0			0
$985$	19.7330	−	16.5579i	0.628745	−	0.527579i
$986$	−2.62693	+	34.3118i	−0.0836586	+	1.09271i
$987$		0			0
$988$	−3.11146	−	8.00363i	−0.0989886	−	0.254629i
$989$	−15.2801	+	8.82198i	−0.485879	+	0.280523i
$990$		0			0
$991$	−28.8387	+	49.9500i	−0.916091	+	1.58672i	−0.110794	+	0.993843i	$0.535339\pi$
$991$	−28.8387	+	49.9500i	−0.916091	+	1.58672i	−0.805297	+	0.592872i	$0.797994\pi$
$992$	−16.5039	+	12.9453i	−0.524001	+	0.411012i
$993$		0			0
$994$	21.2300	+	44.2669i	0.673374	+	1.40406i
$995$	46.3767	−	8.17746i	1.47024	−	0.259243i
$996$		0			0
$997$	−1.71942	+	2.04913i	−0.0544547	+	0.0648966i	−0.792584	−	0.609762i	$-0.791265\pi$
$997$	−1.71942	+	2.04913i	−0.0544547	+	0.0648966i	0.738130	+	0.674659i	$0.235709\pi$
$998$	−16.0867	+	16.4397i	−0.509214	+	0.520391i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.t.a.613.16		204
3.2	odd	2		216.2.t.a.205.19	yes	204
8.5	even	2	inner	648.2.t.a.613.1		204
12.11	even	2		864.2.bf.a.529.17		204
24.5	odd	2		216.2.t.a.205.34	yes	204
24.11	even	2		864.2.bf.a.529.18		204
27.5	odd	18		216.2.t.a.157.34	yes	204
27.22	even	9	inner	648.2.t.a.37.1		204
108.59	even	18		864.2.bf.a.49.18		204
216.5	odd	18		216.2.t.a.157.19	✓	204
216.59	even	18		864.2.bf.a.49.17		204
216.157	even	18	inner	648.2.t.a.37.16		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.19	✓	204	216.5	odd	18
216.2.t.a.157.34	yes	204	27.5	odd	18
216.2.t.a.205.19	yes	204	3.2	odd	2
216.2.t.a.205.34	yes	204	24.5	odd	2
648.2.t.a.37.1		204	27.22	even	9	inner
648.2.t.a.37.16		204	216.157	even	18	inner
648.2.t.a.613.1		204	8.5	even	2	inner
648.2.t.a.613.16		204	1.1	even	1	trivial
864.2.bf.a.49.17		204	216.59	even	18
864.2.bf.a.49.18		204	108.59	even	18
864.2.bf.a.529.17		204	12.11	even	2
864.2.bf.a.529.18		204	24.11	even	2

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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.t (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.138542 - 1.40741i) q^{2} +(-1.96161 + 0.389971i) q^{4} +(-0.608623 + 1.67218i) q^{5} +(0.408085 - 2.31436i) q^{7} +(0.820615 + 2.70677i) q^{8} +O(q^{10})\)	\(q+(-0.138542 - 1.40741i) q^{2} +(-1.96161 + 0.389971i) q^{4} +(-0.608623 + 1.67218i) q^{5} +(0.408085 - 2.31436i) q^{7} +(0.820615 + 2.70677i) q^{8} +(2.43776 + 0.624915i) q^{10} +(0.860398 + 2.36392i) q^{11} +(0.359719 + 0.428697i) q^{13} +(-3.31380 - 0.253707i) q^{14} +(3.69585 - 1.52994i) q^{16} +(-1.49770 - 2.59409i) q^{17} +(6.64437 + 3.83613i) q^{19} +(0.541781 - 3.51751i) q^{20} +(3.20781 - 1.53844i) q^{22} +(1.12812 + 6.39788i) q^{23} +(1.40447 + 1.17849i) q^{25} +(0.553516 - 0.565665i) q^{26} +(0.102031 + 4.69903i) q^{28} +(5.22169 - 6.22297i) q^{29} +(-0.643875 - 3.65160i) q^{31} +(-2.66529 - 4.98961i) q^{32} +(-3.44345 + 2.46726i) q^{34} +(3.62166 + 2.09096i) q^{35} +(4.07450 - 2.35241i) q^{37} +(4.47848 - 9.88282i) q^{38} +(-5.02564 - 0.275186i) q^{40} +(5.67863 - 4.76494i) q^{41} +(0.928888 + 2.55210i) q^{43} +(-2.60963 - 4.30157i) q^{44} +(8.84815 - 2.47410i) q^{46} +(-0.0919295 + 0.521358i) q^{47} +(1.38810 + 0.505226i) q^{49} +(1.46404 - 2.13994i) q^{50} +(-0.872809 - 0.700657i) q^{52} +6.39371i q^{53} -4.47656 q^{55} +(6.59933 - 0.794612i) q^{56} +(-9.48170 - 6.48692i) q^{58} +(-2.87131 + 7.88886i) q^{59} +(0.716954 + 0.126418i) q^{61} +(-5.05009 + 1.41210i) q^{62} +(-6.65318 + 4.44243i) q^{64} +(-0.935790 + 0.340600i) q^{65} +(3.68574 + 4.39249i) q^{67} +(3.94952 + 4.50453i) q^{68} +(2.44110 - 5.38685i) q^{70} +(-7.38597 - 12.7929i) q^{71} +(-5.98642 + 10.3688i) q^{73} +(-3.87530 - 5.40859i) q^{74} +(-14.5296 - 4.93388i) q^{76} +(5.82210 - 1.02659i) q^{77} +(-8.94860 - 7.50876i) q^{79} +(0.308962 + 7.11126i) q^{80} +(-7.49296 - 7.33203i) q^{82} +(-4.81848 + 5.74244i) q^{83} +(5.24930 - 0.925594i) q^{85} +(3.46316 - 1.66090i) q^{86} +(-5.69254 + 4.26877i) q^{88} +(1.16774 - 2.02259i) q^{89} +(1.13896 - 0.657577i) q^{91} +(-4.70792 - 12.1102i) q^{92} +(0.746501 + 0.0571526i) q^{94} +(-10.4586 + 8.77580i) q^{95} +(13.8915 - 5.05610i) q^{97} +(0.518751 - 2.02362i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8}+O(q^{10}) \) 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40} + 24 q^{41} - 21 q^{44} - 3 q^{46} + 12 q^{47} - 12 q^{49} + 99 q^{50} - 33 q^{52} - 24 q^{55} - 99 q^{56} + 21 q^{58} + 36 q^{62} - 3 q^{64} + 12 q^{65} - 75 q^{68} + 9 q^{70} + 90 q^{71} - 6 q^{73} - 9 q^{74} - 18 q^{76} - 12 q^{79} - 78 q^{80} - 12 q^{82} + 30 q^{86} - 30 q^{88} + 6 q^{89} - 111 q^{92} - 33 q^{94} + 42 q^{95} - 12 q^{97} - 54 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Introduction

L-functions

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