LMFDB - Embedded newform 297.2.n.b.289.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(37,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 6]))

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

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

chi := DirichletCharacter("297.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.n (of order $15$, degree $8$, 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			289.8
Character	$\chi$	$=$	297.289
Dual form			297.2.n.b.37.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.161615 + 1.53767i) q^{2} +(-0.382004 + 0.0811974i) q^{4} +(0.0618842 - 0.588789i) q^{5} +(0.483079 + 0.536514i) q^{7} +(0.768973 + 2.36665i) q^{8} +0.915362 q^{10} +(2.56419 + 2.10355i) q^{11} +(-1.43880 - 0.640596i) q^{13} +(-0.746906 + 0.829524i) q^{14} +(-4.22840 + 1.88260i) q^{16} +(3.71501 + 2.69911i) q^{17} +(0.775200 + 2.38582i) q^{19} +(0.0241681 + 0.229944i) q^{20} +(-2.82014 + 4.28284i) q^{22} +(-2.22600 - 3.85554i) q^{23} +(4.54790 + 0.966685i) q^{25} +(0.752490 - 2.31593i) q^{26} +(-0.228102 - 0.165726i) q^{28} +(-4.66961 - 5.18613i) q^{29} +(-8.33906 - 3.71279i) q^{31} +(-1.08974 - 1.88749i) q^{32} +(-3.54993 + 6.14866i) q^{34} +(0.345788 - 0.251230i) q^{35} +(0.893583 - 2.75017i) q^{37} +(-3.54331 + 1.57758i) q^{38} +(1.44105 - 0.306304i) q^{40} +(0.772257 - 0.857678i) q^{41} +(2.10724 - 3.64985i) q^{43} +(-1.15033 - 0.595357i) q^{44} +(5.56879 - 4.04596i) q^{46} +(-0.222583 - 0.0473114i) q^{47} +(0.677218 - 6.44330i) q^{49} +(-0.751430 + 7.14938i) q^{50} +(0.601643 + 0.127883i) q^{52} +(-4.61430 + 3.35249i) q^{53} +(1.39723 - 1.37959i) q^{55} +(-0.898268 + 1.55585i) q^{56} +(7.21985 - 8.01846i) q^{58} +(6.97767 - 1.48315i) q^{59} +(4.16481 - 1.85429i) q^{61} +(4.36131 - 13.4227i) q^{62} +(-4.76295 + 3.46049i) q^{64} +(-0.466215 + 0.807507i) q^{65} +(4.04571 + 7.00738i) q^{67} +(-1.63831 - 0.729422i) q^{68} +(0.442192 + 0.491104i) q^{70} +(-9.95852 - 7.23528i) q^{71} +(4.78461 - 14.7255i) q^{73} +(4.37326 + 0.929564i) q^{74} +(-0.489852 - 0.848448i) q^{76} +(0.110128 + 2.39191i) q^{77} +(1.52816 + 14.5395i) q^{79} +(0.846785 + 2.60614i) q^{80} +(1.44363 + 1.04886i) q^{82} +(6.35188 - 2.82804i) q^{83} +(1.81911 - 2.02032i) q^{85} +(5.95281 + 2.65036i) q^{86} +(-3.00657 + 7.68613i) q^{88} -12.4803 q^{89} +(-0.351367 - 1.08140i) q^{91} +(1.16340 + 1.29209i) q^{92} +(0.0367764 - 0.349904i) q^{94} +(1.45272 - 0.308785i) q^{95} +(-1.48226 - 14.1028i) q^{97} +10.0171 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) $ 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	0.161615	+	1.53767i	0.114279	+	1.08729i	0.889919	+	0.456119i	$0.150761\pi$
$2$	0.161615	+	1.53767i	0.114279	+	1.08729i	−0.775640	+	0.631176i	$0.782573\pi$
$3$		0			0
$3$		0			0
$4$	−0.382004	+	0.0811974i	−0.191002	+	0.0405987i
$5$	0.0618842	−	0.588789i	0.0276755	−	0.263314i	−0.971931	−	0.235266i	$-0.924404\pi$
$5$	0.0618842	−	0.588789i	0.0276755	−	0.263314i	0.999607	−	0.0280487i	$-0.00892935\pi$
$6$		0			0
$7$	0.483079	+	0.536514i	0.182587	+	0.202783i	0.827489	−	0.561482i	$-0.189769\pi$
$7$	0.483079	+	0.536514i	0.182587	+	0.202783i	−0.644902	+	0.764265i	$0.723102\pi$
$8$	0.768973	+	2.36665i	0.271873	+	0.836739i
$9$		0			0
$10$	0.915362			0.289463
$11$	2.56419	+	2.10355i	0.773134	+	0.634243i
$11$	2.56419	+	2.10355i	0.773134	+	0.634243i
$12$		0			0
$13$	−1.43880	−	0.640596i	−0.399052	−	0.177669i	0.197391	−	0.980325i	$-0.436753\pi$
$13$	−1.43880	−	0.640596i	−0.399052	−	0.177669i	−0.596443	+	0.802656i	$0.703420\pi$
$14$	−0.746906	+	0.829524i	−0.199619	+	0.221699i
$15$		0			0
$16$	−4.22840	+	1.88260i	−1.05710	+	0.470651i
$17$	3.71501	+	2.69911i	0.901022	+	0.654631i	0.938728	−	0.344658i	$-0.112005\pi$
$17$	3.71501	+	2.69911i	0.901022	+	0.654631i	−0.0377065	+	0.999289i	$0.512005\pi$
$18$		0			0
$19$	0.775200	+	2.38582i	0.177843	+	0.547345i	0.999752	−	0.0222743i	$-0.00709072\pi$
$19$	0.775200	+	2.38582i	0.177843	+	0.547345i	−0.821909	+	0.569619i	$0.807091\pi$
$20$	0.0241681	+	0.229944i	0.00540416	+	0.0514171i
$21$		0			0
$22$	−2.82014	+	4.28284i	−0.601256	+	0.913105i
$23$	−2.22600	−	3.85554i	−0.464153	−	0.803937i	0.535010	−	0.844846i	$-0.320308\pi$
$23$	−2.22600	−	3.85554i	−0.464153	−	0.803937i	−0.999163	+	0.0409092i	$0.986975\pi$
$24$		0			0
$25$	4.54790	+	0.966685i	0.909579	+	0.193337i
$26$	0.752490	−	2.31593i	0.147576	−	0.454191i
$27$		0			0
$28$	−0.228102	−	0.165726i	−0.0431072	−	0.0313192i
$29$	−4.66961	−	5.18613i	−0.867125	−	0.963039i	0.132479	−	0.991186i	$-0.457706\pi$
$29$	−4.66961	−	5.18613i	−0.867125	−	0.963039i	−0.999604	+	0.0281463i	$0.991040\pi$
$30$		0			0
$31$	−8.33906	−	3.71279i	−1.49774	−	0.666837i	−0.515917	−	0.856638i	$-0.672549\pi$
$31$	−8.33906	−	3.71279i	−1.49774	−	0.666837i	−0.981822	+	0.189802i	$0.939216\pi$
$32$	−1.08974	−	1.88749i	−0.192641	−	0.333664i
$33$		0			0
$34$	−3.54993	+	6.14866i	−0.608808	+	1.05449i
$35$	0.345788	−	0.251230i	0.0584489	−	0.0424656i
$36$		0			0
$37$	0.893583	−	2.75017i	0.146904	−	0.452125i	−0.850347	−	0.526223i	$-0.823608\pi$
$37$	0.893583	−	2.75017i	0.146904	−	0.452125i	0.997251	+	0.0740981i	$0.0236078\pi$
$38$	−3.54331	+	1.57758i	−0.574801	+	0.255918i
$39$		0			0
$40$	1.44105	−	0.306304i	0.227850	−	0.0484309i
$41$	0.772257	−	0.857678i	0.120606	−	0.133947i	−0.679818	−	0.733381i	$-0.737941\pi$
$41$	0.772257	−	0.857678i	0.120606	−	0.133947i	0.800424	+	0.599434i	$0.204608\pi$
$42$		0			0
$43$	2.10724	−	3.64985i	0.321351	−	0.556596i	−0.659416	−	0.751778i	$-0.729196\pi$
$43$	2.10724	−	3.64985i	0.321351	−	0.556596i	0.980767	+	0.195182i	$0.0625297\pi$
$44$	−1.15033	−	0.595357i	−0.173419	−	0.0897534i
$45$		0			0
$46$	5.56879	−	4.04596i	0.821073	−	0.596544i
$47$	−0.222583	−	0.0473114i	−0.0324670	−	0.00690108i	0.191650	−	0.981463i	$-0.438616\pi$
$47$	−0.222583	−	0.0473114i	−0.0324670	−	0.00690108i	−0.224117	+	0.974562i	$0.571950\pi$
$48$		0			0
$49$	0.677218	−	6.44330i	0.0967454	−	0.920471i
$50$	−0.751430	+	7.14938i	−0.106268	+	1.01107i
$51$		0			0
$52$	0.601643	+	0.127883i	0.0834328	+	0.0177342i
$53$	−4.61430	+	3.35249i	−0.633823	+	0.460500i	−0.857723	−	0.514113i	$-0.828121\pi$
$53$	−4.61430	+	3.35249i	−0.633823	+	0.460500i	0.223899	+	0.974612i	$0.428121\pi$
$54$		0			0
$55$	1.39723	−	1.37959i	0.188402	−	0.186024i
$56$	−0.898268	+	1.55585i	−0.120036	+	0.207909i
$57$		0			0
$58$	7.21985	−	8.01846i	0.948013	−	1.05288i
$59$	6.97767	−	1.48315i	0.908415	−	0.193090i	0.270071	−	0.962841i	$-0.412953\pi$
$59$	6.97767	−	1.48315i	0.908415	−	0.193090i	0.638344	+	0.769751i	$0.279620\pi$
$60$		0			0
$61$	4.16481	−	1.85429i	0.533250	−	0.237418i	−0.122403	−	0.992480i	$-0.539060\pi$
$61$	4.16481	−	1.85429i	0.533250	−	0.237418i	0.655653	+	0.755062i	$0.272393\pi$
$62$	4.36131	−	13.4227i	0.553887	−	1.70469i
$63$		0			0
$64$	−4.76295	+	3.46049i	−0.595369	+	0.432561i
$65$	−0.466215	+	0.807507i	−0.0578268	+	0.100159i
$66$		0			0
$67$	4.04571	+	7.00738i	0.494262	+	0.856087i	0.999978	−	0.00661279i	$-0.00210493\pi$
$67$	4.04571	+	7.00738i	0.494262	+	0.856087i	−0.505716	+	0.862700i	$0.668772\pi$
$68$	−1.63831	−	0.729422i	−0.198674	−	0.0884554i
$69$		0			0
$70$	0.442192	+	0.491104i	0.0528521	+	0.0586982i
$71$	−9.95852	−	7.23528i	−1.18186	−	0.858670i	−0.189478	−	0.981885i	$-0.560680\pi$
$71$	−9.95852	−	7.23528i	−1.18186	−	0.858670i	−0.992380	+	0.123215i	$0.960680\pi$
$72$		0			0
$73$	4.78461	−	14.7255i	0.559996	−	1.72349i	−0.122373	−	0.992484i	$-0.539050\pi$
$73$	4.78461	−	14.7255i	0.559996	−	1.72349i	0.682370	−	0.731007i	$-0.260950\pi$
$74$	4.37326	+	0.929564i	0.508381	+	0.108060i
$75$		0			0
$76$	−0.489852	−	0.848448i	−0.0561899	−	0.0973237i
$77$	0.110128	+	2.39191i	0.0125502	+	0.272583i
$78$		0			0
$79$	1.52816	+	14.5395i	0.171931	+	1.63582i	0.651738	+	0.758444i	$0.274040\pi$
$79$	1.52816	+	14.5395i	0.171931	+	1.63582i	−0.479807	+	0.877374i	$0.659293\pi$
$80$	0.846785	+	2.60614i	0.0946734	+	0.291375i
$81$		0			0
$82$	1.44363	+	1.04886i	0.159422	+	0.115827i
$83$	6.35188	−	2.82804i	0.697210	−	0.310418i	−0.0273537	−	0.999626i	$-0.508708\pi$
$83$	6.35188	−	2.82804i	0.697210	−	0.310418i	0.724564	+	0.689208i	$0.242041\pi$
$84$		0			0
$85$	1.81911	−	2.02032i	0.197310	−	0.219135i
$86$	5.95281	+	2.65036i	0.641908	+	0.285796i
$87$		0			0
$88$	−3.00657	+	7.68613i	−0.320502	+	0.819344i
$89$	−12.4803			−1.32291			−0.661453	−	0.749986i	$-0.730060\pi$
$89$	−12.4803			−1.32291			−0.661453	+	0.749986i	$0.730060\pi$
$90$		0			0
$91$	−0.351367	−	1.08140i	−0.0368332	−	0.113361i
$92$	1.16340	+	1.29209i	0.121293	+	0.134709i
$93$		0			0
$94$	0.0367764	−	0.349904i	0.00379320	−	0.0360899i
$95$	1.45272	−	0.308785i	0.149046	−	0.0316806i
$96$		0			0
$97$	−1.48226	−	14.1028i	−0.150501	−	1.43192i	−0.765522	−	0.643410i	$-0.777519\pi$
$97$	−1.48226	−	14.1028i	−0.150501	−	1.43192i	0.615021	−	0.788511i	$-0.289148\pi$
$98$	10.0171			1.01188
$99$		0			0
$100$	−1.81581			−0.181581
$101$	−1.50192	−	14.2898i	−0.149447	−	1.42189i	−0.770159	−	0.637852i	$-0.779823\pi$
$101$	−1.50192	−	14.2898i	−0.149447	−	1.42189i	0.620712	−	0.784039i	$-0.286844\pi$
$102$		0			0
$103$	4.33207	−	0.920810i	0.426852	−	0.0907301i	0.0105237	−	0.999945i	$-0.496650\pi$
$103$	4.33207	−	0.920810i	0.426852	−	0.0907301i	0.416328	+	0.909214i	$0.363317\pi$
$104$	0.409670	−	3.89775i	0.0401714	−	0.382206i
$105$		0			0
$106$	−5.90075	−	6.55345i	−0.573132	−	0.636527i
$107$	4.86529	+	14.9738i	0.470345	+	1.44757i	0.852134	+	0.523324i	$0.175308\pi$
$107$	4.86529	+	14.9738i	0.470345	+	1.44757i	−0.381788	+	0.924250i	$0.624692\pi$
$108$		0			0
$109$	−13.6970			−1.31194			−0.655969	−	0.754788i	$-0.727740\pi$
$109$	−13.6970			−1.31194			−0.655969	+	0.754788i	$0.727740\pi$
$110$	2.34717	+	1.92551i	0.223794	+	0.183590i
$111$		0			0
$112$	−3.05269	−	1.35915i	−0.288452	−	0.128427i
$113$	−5.37321	+	5.96755i	−0.505469	+	0.561380i	−0.940831	−	0.338875i	$-0.889954\pi$
$113$	−5.37321	+	5.96755i	−0.505469	+	0.561380i	0.435363	+	0.900255i	$0.356620\pi$
$114$		0			0
$115$	−2.40786	+	1.07205i	−0.224534	+	0.0999688i
$116$	2.20491	+	1.60196i	0.204721	+	0.148738i
$117$		0			0
$118$	3.40829	+	10.4896i	0.313758	+	0.965648i
$119$	0.346533	+	3.29704i	0.0317666	+	0.302239i
$120$		0			0
$121$	2.15019	+	10.7878i	0.195472	+	0.980709i
$122$	3.52438	+	6.10441i	0.319083	+	0.552668i
$123$		0			0
$124$	3.48702	+	0.741190i	0.313144	+	0.0665608i
$125$	1.76536	−	5.43321i	0.157898	−	0.485961i
$126$		0			0
$127$	9.70522	+	7.05126i	0.861199	+	0.625698i	0.928211	−	0.372054i	$-0.121347\pi$
$127$	9.70522	+	7.05126i	0.861199	+	0.625698i	−0.0670118	+	0.997752i	$0.521347\pi$
$128$	−9.00756	−	10.0039i	−0.796163	−	0.884229i
$129$		0			0
$130$	−1.31702	−	0.586377i	−0.115511	−	0.0514287i
$131$	−3.44555	−	5.96786i	−0.301039	−	0.521414i	0.675333	−	0.737513i	$-0.264000\pi$
$131$	−3.44555	−	5.96786i	−0.301039	−	0.521414i	−0.976372	+	0.216099i	$0.930667\pi$
$132$		0			0
$133$	−0.905543	+	1.56845i	−0.0785205	+	0.136002i
$134$	−10.1212	+	7.35345i	−0.874335	+	0.635242i
$135$		0			0
$136$	−3.53112	+	10.8677i	−0.302791	+	0.931896i
$137$	−8.44714	+	3.76091i	−0.721688	+	0.321316i	−0.734507	−	0.678602i	$-0.762586\pi$
$137$	−8.44714	+	3.76091i	−0.721688	+	0.321316i	0.0128184	+	0.999918i	$0.495920\pi$
$138$		0			0
$139$	−21.1390	+	4.49324i	−1.79299	+	0.381112i	−0.979656	−	0.200685i	$-0.935683\pi$
$139$	−21.1390	+	4.49324i	−1.79299	+	0.381112i	−0.813334	+	0.581797i	$0.802350\pi$
$140$	−0.111693	+	0.124048i	−0.00943980	+	0.0104840i
$141$		0			0
$142$	9.51601	−	16.4822i	0.798566	−	1.38316i
$143$	−2.34184	−	4.66920i	−0.195835	−	0.390458i
$144$		0			0
$145$	−3.34251	+	2.42847i	−0.277580	+	0.201674i
$146$	23.4162	+	4.97727i	1.93794	+	0.411922i
$147$		0			0
$148$	−0.118046	+	1.12313i	−0.00970331	+	0.0923208i
$149$	−0.119835	+	1.14015i	−0.00981725	+	0.0934049i	−0.998333	−	0.0577107i	$-0.981620\pi$
$149$	−0.119835	+	1.14015i	−0.00981725	+	0.0934049i	0.988516	+	0.151116i	$0.0482866\pi$
$150$		0			0
$151$	−0.861396	−	0.183095i	−0.0700994	−	0.0149001i	0.172728	−	0.984969i	$-0.444742\pi$
$151$	−0.861396	−	0.183095i	−0.0700994	−	0.0149001i	−0.242828	+	0.970069i	$0.578075\pi$
$152$	−5.05031	+	3.66926i	−0.409634	+	0.297616i
$153$		0			0
$154$	−3.66015	+	0.555908i	−0.294944	+	0.0447963i
$155$	−2.70211	+	4.68018i	−0.217038	+	0.375921i
$156$		0			0
$157$	−6.54825	+	7.27257i	−0.522608	+	0.580415i	−0.945441	−	0.325793i	$-0.894369\pi$
$157$	−6.54825	+	7.27257i	−0.522608	+	0.580415i	0.422834	+	0.906207i	$0.361035\pi$
$158$	−22.1099	+	4.69960i	−1.75897	+	0.373880i
$159$		0			0
$160$	−1.17877	+	0.524822i	−0.0931899	+	0.0414908i
$161$	0.993219	−	3.05681i	0.0782766	−	0.240911i
$162$		0			0
$163$	−3.74555	+	2.72130i	−0.293374	+	0.213149i	−0.724730	−	0.689033i	$-0.758035\pi$
$163$	−3.74555	+	2.72130i	−0.293374	+	0.213149i	0.431355	+	0.902182i	$0.358035\pi$
$164$	−0.225364	+	0.390342i	−0.0175980	+	0.0304806i
$165$		0			0
$166$	5.37515	+	9.31002i	0.417192	+	0.722598i
$167$	15.5187	+	6.90939i	1.20088	+	0.534665i	0.906980	−	0.421173i	$-0.138381\pi$
$167$	15.5187	+	6.90939i	1.20088	+	0.534665i	0.293896	+	0.955837i	$0.405048\pi$
$168$		0			0
$169$	−7.03891	−	7.81750i	−0.541455	−	0.601346i
$170$	3.40058	+	2.47066i	0.260812	+	0.189491i
$171$		0			0
$172$	−0.508616	+	1.56536i	−0.0387816	+	0.119357i
$173$	−0.578140	−	0.122887i	−0.0439551	−	0.00934296i	0.185882	−	0.982572i	$-0.440486\pi$
$173$	−0.578140	−	0.122887i	−0.0439551	−	0.00934296i	−0.229837	+	0.973229i	$0.573819\pi$
$174$		0			0
$175$	1.67835	+	2.90699i	0.126872	+	0.219748i
$176$	−14.8026	−	4.06727i	−1.11579	−	0.306582i
$177$		0			0
$178$	−2.01700	−	19.1905i	−0.151181	−	1.43839i
$179$	2.97921	+	9.16907i	0.222677	+	0.685328i	0.998519	+	0.0544017i	$0.0173251\pi$
$179$	2.97921	+	9.16907i	0.222677	+	0.685328i	−0.775842	+	0.630927i	$0.782675\pi$
$180$		0			0
$181$	3.85243	+	2.79896i	0.286349	+	0.208045i	0.721682	−	0.692225i	$-0.243369\pi$
$181$	3.85243	+	2.79896i	0.286349	+	0.208045i	−0.435333	+	0.900270i	$0.643369\pi$
$182$	1.60604	−	0.715055i	0.119048	−	0.0530034i
$183$		0			0
$184$	7.41301	−	8.23298i	0.546494	−	0.606943i
$185$	−1.56397	−	0.696324i	−0.114985	−	0.0511947i
$186$		0			0
$187$	3.84830	+	14.7357i	0.281415	+	1.07758i
$188$	0.0888691			0.00648144
$189$		0			0
$190$	0.709589	+	2.18389i	0.0514790	+	0.158436i
$191$	3.47816	+	3.86289i	0.251671	+	0.279509i	0.855721	−	0.517438i	$-0.173114\pi$
$191$	3.47816	+	3.86289i	0.251671	+	0.279509i	−0.604050	+	0.796946i	$0.706447\pi$
$192$		0			0
$193$	−0.341604	+	3.25014i	−0.0245892	+	0.233950i	0.975324	+	0.220778i	$0.0708597\pi$
$193$	−0.341604	+	3.25014i	−0.0245892	+	0.233950i	−0.999913	+	0.0131723i	$0.995807\pi$
$194$	21.4458	−	4.55845i	1.53972	−	0.327278i
$195$		0			0
$196$	0.264479	+	2.51635i	0.0188914	+	0.179739i
$197$	22.4626			1.60039			0.800197	−	0.599737i	$-0.204728\pi$
$197$	22.4626			1.60039			0.800197	+	0.599737i	$0.204728\pi$
$198$		0			0
$199$	−20.8291			−1.47654			−0.738269	−	0.674507i	$-0.764356\pi$
$199$	−20.8291			−1.47654			−0.738269	+	0.674507i	$0.764356\pi$
$200$	1.20940	+	11.5067i	0.0855173	+	0.813643i
$201$		0			0
$202$	21.7303	−	4.61891i	1.52894	−	0.324985i
$203$	0.526637	−	5.01062i	0.0369627	−	0.351677i
$204$		0			0
$205$	−0.457201	−	0.507773i	−0.0319323	−	0.0354644i
$206$	2.11603	+	6.51246i	0.147431	+	0.453745i
$207$		0			0
$208$	7.28981			0.505457
$209$	−3.03092	+	7.74838i	−0.209653	+	0.535966i
$210$		0			0
$211$	3.09877	+	1.37966i	0.213328	+	0.0949797i	0.510619	−	0.859807i	$-0.329416\pi$
$211$	3.09877	+	1.37966i	0.213328	+	0.0949797i	−0.297291	+	0.954787i	$0.596083\pi$
$212$	1.49047	−	1.65533i	0.102366	−	0.113689i
$213$		0			0
$214$	−22.2384	+	9.90119i	−1.52019	+	0.676831i
$215$	−2.01858	−	1.46659i	−0.137666	−	0.100020i
$216$		0			0
$217$	−2.03646	−	6.26759i	−0.138244	−	0.425472i
$218$	−2.21365	−	21.0615i	−0.149927	−	1.42646i
$219$		0			0
$220$	−0.421727	+	0.640461i	−0.0284328	+	0.0431799i
$221$	−3.61612	−	6.26330i	−0.243247	−	0.421315i
$222$		0			0
$223$	10.7854	+	2.29252i	0.722246	+	0.153518i	0.554347	−	0.832286i	$-0.312968\pi$
$223$	10.7854	+	2.29252i	0.722246	+	0.153518i	0.167900	+	0.985804i	$0.446302\pi$
$224$	0.486232	−	1.49647i	0.0324877	−	0.0999870i
$225$		0			0
$226$	−10.0445	−	7.29775i	−0.668150	−	0.485439i
$227$	3.99263	+	4.43426i	0.265000	+	0.294312i	0.860929	−	0.508725i	$-0.169883\pi$
$227$	3.99263	+	4.43426i	0.265000	+	0.294312i	−0.595929	+	0.803037i	$0.703216\pi$
$228$		0			0
$229$	22.6109	+	10.0670i	1.49417	+	0.665246i	0.981171	−	0.193144i	$-0.0618683\pi$
$229$	22.6109	+	10.0670i	1.49417	+	0.665246i	0.512998	+	0.858390i	$0.328535\pi$
$230$	−2.03760	−	3.52922i	−0.134355	−	0.232710i
$231$		0			0
$232$	8.68297	−	15.0393i	0.570065	−	0.987381i
$233$	3.38850	−	2.46189i	0.221988	−	0.161284i	−0.471233	−	0.882009i	$-0.656191\pi$
$233$	3.38850	−	2.46189i	0.221988	−	0.161284i	0.693221	+	0.720725i	$0.256191\pi$
$234$		0			0
$235$	−0.0416308	+	0.128126i	−0.00271569	+	0.00835805i
$236$	−2.54507	+	1.13314i	−0.165670	+	0.0737610i
$237$		0			0
$238$	−5.01374	+	1.06570i	−0.324992	+	0.0690793i
$239$	4.93340	−	5.47909i	0.319115	−	0.354413i	−0.562150	−	0.827035i	$-0.690026\pi$
$239$	4.93340	−	5.47909i	0.319115	−	0.354413i	0.881265	+	0.472622i	$0.156692\pi$
$240$		0			0
$241$	4.41462	−	7.64634i	0.284371	−	0.492544i	−0.688086	−	0.725629i	$-0.741549\pi$
$241$	4.41462	−	7.64634i	0.284371	−	0.492544i	0.972456	+	0.233085i	$0.0748821\pi$
$242$	−16.2405	+	5.04975i	−1.04398	+	0.324610i
$243$		0			0
$244$	−1.44041	+	1.04652i	−0.0922129	+	0.0669966i
$245$	−3.75183	−	0.797476i	−0.239696	−	0.0509489i
$246$		0			0
$247$	0.412987	−	3.92931i	0.0262778	−	0.250016i
$248$	2.37438	−	22.5907i	0.150773	−	1.43451i
$249$		0			0
$250$	8.63977	+	1.83644i	0.546427	+	0.116147i
$251$	16.6439	−	12.0925i	1.05056	−	0.763274i	0.0782385	−	0.996935i	$-0.475070\pi$
$251$	16.6439	−	12.0925i	1.05056	−	0.763274i	0.972318	+	0.233661i	$0.0750704\pi$
$252$		0			0
$253$	2.40242	−	14.5689i	0.151039	−	0.915936i
$254$	−9.27397	+	16.0630i	−0.581901	+	1.00788i
$255$		0			0
$256$	6.04813	−	6.71713i	0.378008	−	0.419820i
$257$	−3.30847	+	0.703238i	−0.206377	+	0.0438668i	−0.309940	−	0.950756i	$-0.600309\pi$
$257$	−3.30847	+	0.703238i	−0.206377	+	0.0438668i	0.103563	+	0.994623i	$0.466976\pi$
$258$		0			0
$259$	1.90717	−	0.849129i	0.118506	−	0.0527623i
$260$	0.112528	−	0.346326i	0.00697871	−	0.0214783i
$261$		0			0
$262$	8.61973	−	6.26260i	0.532528	−	0.386905i
$263$	−7.14112	+	12.3688i	−0.440341	+	0.762692i	−0.997715	−	0.0675692i	$-0.978476\pi$
$263$	−7.14112	+	12.3688i	−0.440341	+	0.762692i	0.557374	+	0.830262i	$0.311809\pi$
$264$		0			0
$265$	1.68836	+	2.92432i	0.103715	+	0.179639i
$266$	−2.55810	−	1.13894i	−0.156847	−	0.0698328i
$267$		0			0
$268$	−2.11446	−	2.34834i	−0.129161	−	0.143448i
$269$	5.43693	+	3.95016i	0.331495	+	0.240845i	0.741065	−	0.671433i	$-0.234321\pi$
$269$	5.43693	+	3.95016i	0.331495	+	0.240845i	−0.409570	+	0.912279i	$0.634321\pi$
$270$		0			0
$271$	−1.23000	+	3.78554i	−0.0747170	+	0.229955i	−0.981439	−	0.191773i	$-0.938576\pi$
$271$	−1.23000	+	3.78554i	−0.0747170	+	0.229955i	0.906722	+	0.421728i	$0.138576\pi$
$272$	−20.7899	−	4.41903i	−1.26057	−	0.267943i
$273$		0			0
$274$	−7.14821	−	12.3811i	−0.431839	−	0.747968i
$275$	9.62822	+	12.0455i	0.580604	+	0.726370i
$276$		0			0
$277$	1.37267	+	13.0601i	0.0824756	+	0.784703i	0.955094	+	0.296301i	$0.0957533\pi$
$277$	1.37267	+	13.0601i	0.0824756	+	0.784703i	−0.872619	+	0.488402i	$0.837580\pi$
$278$	−10.3255	−	31.7786i	−0.619282	−	1.90595i
$279$		0			0
$280$	0.860476	+	0.625172i	0.0514233	+	0.0373612i
$281$	2.71128	−	1.20714i	0.161742	−	0.0720120i	−0.324269	−	0.945965i	$-0.605118\pi$
$281$	2.71128	−	1.20714i	0.161742	−	0.0720120i	0.486011	+	0.873953i	$0.338452\pi$
$282$		0			0
$283$	5.41512	−	6.01410i	0.321896	−	0.357501i	−0.560379	−	0.828236i	$-0.689345\pi$
$283$	5.41512	−	6.01410i	0.321896	−	0.357501i	0.882275	+	0.470735i	$0.156011\pi$
$284$	4.39168	+	1.95530i	0.260598	+	0.116026i
$285$		0			0
$286$	6.80119	−	4.35559i	0.402163	−	0.257551i
$287$	0.833217			0.0491833
$288$		0			0
$289$	1.26279	+	3.88648i	0.0742820	+	0.228616i
$290$	−4.27438	−	4.74718i	−0.251000	−	0.278764i
$291$		0			0
$292$	−0.632066	+	6.01370i	−0.0369888	+	0.351925i
$293$	−15.3722	+	3.26745i	−0.898051	+	0.190887i	−0.633736	−	0.773550i	$-0.718479\pi$
$293$	−15.3722	+	3.26745i	−0.898051	+	0.190887i	−0.264315	+	0.964436i	$0.585146\pi$
$294$		0			0
$295$	−0.441454	−	4.20016i	−0.0257025	−	0.244543i
$296$	7.19584			0.418249
$297$		0			0
$298$	−1.77254			−0.102681
$299$	0.732926	+	6.97333i	0.0423862	+	0.403278i
$300$		0			0
$301$	2.97616	−	0.632602i	0.171543	−	0.0364626i
$302$	0.142325	−	1.35413i	0.00818988	−	0.0779215i
$303$		0			0
$304$	−7.76941	−	8.62880i	−0.445606	−	0.494896i
$305$	−0.834052	−	2.56695i	−0.0477577	−	0.146983i
$306$		0			0
$307$	−3.51315			−0.200506			−0.100253	−	0.994962i	$-0.531965\pi$
$307$	−3.51315			−0.200506			−0.100253	+	0.994962i	$0.531965\pi$
$308$	−0.236286	−	0.904775i	−0.0134636	−	0.0515543i
$309$		0			0
$310$	−7.63326	−	3.39855i	−0.433540	−	0.193025i
$311$	−17.6212	+	19.5703i	−0.999205	+	1.10973i	−0.00524459	+	0.999986i	$0.501669\pi$
$311$	−17.6212	+	19.5703i	−0.999205	+	1.10973i	−0.993960	+	0.109743i	$0.964997\pi$
$312$		0			0
$313$	−2.24836	+	1.00104i	−0.127085	+	0.0565819i	−0.469294	−	0.883042i	$-0.655492\pi$
$313$	−2.24836	+	1.00104i	−0.127085	+	0.0565819i	0.342209	+	0.939624i	$0.388825\pi$
$314$	−12.2411	−	8.89367i	−0.690805	−	0.501899i
$315$		0			0
$316$	−1.76433	−	5.43005i	−0.0992513	−	0.305464i
$317$	−2.77075	−	26.3619i	−0.155621	−	1.48063i	−0.741892	−	0.670519i	$-0.766071\pi$
$317$	−2.77075	−	26.3619i	−0.155621	−	1.48063i	0.586271	−	0.810115i	$-0.300595\pi$
$318$		0			0
$319$	−1.06453	−	23.1210i	−0.0596023	−	1.29453i
$320$	1.74274	+	3.01852i	0.0974224	+	0.168741i
$321$		0			0
$322$	4.86088	+	1.03321i	0.270886	+	0.0575786i
$323$	−3.55972	+	10.9557i	−0.198068	+	0.609591i
$324$		0			0
$325$	−5.92427	−	4.30423i	−0.328619	−	0.238756i
$326$	−4.78980	−	5.31961i	−0.265282	−	0.294626i
$327$		0			0
$328$	2.62367	+	1.16813i	0.144868	+	0.0644994i
$329$	−0.0821419	−	0.142274i	−0.00452863	−	0.00784382i
$330$		0			0
$331$	−4.05198	+	7.01824i	−0.222717	+	0.385757i	−0.955632	−	0.294563i	$-0.904826\pi$
$331$	−4.05198	+	7.01824i	−0.222717	+	0.385757i	0.732915	+	0.680320i	$0.238159\pi$
$332$	−2.19681	+	1.59608i	−0.120566	+	0.0875962i
$333$		0			0
$334$	−8.11627	+	24.9793i	−0.444103	+	1.36681i
$335$	4.37623	−	1.94842i	0.239099	−	0.106454i
$336$		0			0
$337$	−24.1804	+	5.13971i	−1.31719	+	0.279978i	−0.812318	−	0.583215i	$-0.801794\pi$
$337$	−24.1804	+	5.13971i	−1.31719	+	0.279978i	−0.504874	+	0.863193i	$0.668461\pi$
$338$	10.8831	−	12.0869i	0.591964	−	0.657442i
$339$		0			0
$340$	−0.530861	+	0.919478i	−0.0287900	+	0.0498657i
$341$	−13.5730	−	27.0619i	−0.735017	−	1.46549i
$342$		0			0
$343$	7.87256	−	5.71975i	0.425078	−	0.308837i
$344$	10.2583	+	2.18048i	0.553092	+	0.117563i
$345$		0			0
$346$	0.0955236	−	0.908847i	0.00513538	−	0.0488599i
$347$	−0.216337	+	2.05831i	−0.0116136	+	0.110496i	−0.998793	−	0.0491192i	$-0.984359\pi$
$347$	−0.216337	+	2.05831i	−0.0116136	+	0.110496i	0.987179	+	0.159615i	$0.0510252\pi$
$348$		0			0
$349$	5.10032	+	1.08411i	0.273014	+	0.0580309i	0.342384	−	0.939560i	$-0.388766\pi$
$349$	5.10032	+	1.08411i	0.273014	+	0.0580309i	−0.0693701	+	0.997591i	$0.522099\pi$
$350$	−4.19874	+	3.05056i	−0.224432	+	0.163059i
$351$		0			0
$352$	1.17611	−	7.13221i	0.0626868	−	0.380148i
$353$	10.8363	−	18.7689i	0.576756	−	0.998970i	−0.419093	−	0.907943i	$-0.637652\pi$
$353$	10.8363	−	18.7689i	0.576756	−	0.998970i	0.995848	−	0.0910266i	$-0.0290148\pi$
$354$		0			0
$355$	−4.87633	+	5.41571i	−0.258809	+	0.287436i
$356$	4.76751	−	1.01337i	0.252678	−	0.0537083i
$357$		0			0
$358$	−13.6175	+	6.06290i	−0.719706	+	0.320434i
$359$	−2.70478	+	8.32446i	−0.142753	+	0.439348i	−0.996715	−	0.0809868i	$-0.974193\pi$
$359$	−2.70478	+	8.32446i	−0.142753	+	0.439348i	0.853962	+	0.520335i	$0.174193\pi$
$360$		0			0
$361$	10.2801	−	7.46894i	0.541059	−	0.393102i
$362$	−3.68125	+	6.37611i	−0.193482	+	0.335121i
$363$		0			0
$364$	0.222030	+	0.384567i	0.0116375	+	0.0201568i
$365$	−8.37413	−	3.72840i	−0.438322	−	0.195153i
$366$		0			0
$367$	−4.52749	−	5.02829i	−0.236333	−	0.262474i	0.613298	−	0.789851i	$-0.289842\pi$
$367$	−4.52749	−	5.02829i	−0.236333	−	0.262474i	−0.849631	+	0.527377i	$0.823176\pi$
$368$	16.6709	+	12.1121i	0.869029	+	0.631387i
$369$		0			0
$370$	0.817952	−	2.51740i	0.0425233	−	0.130873i
$371$	−4.02773	−	0.856121i	−0.209109	−	0.0444476i
$372$		0			0
$373$	10.9467	+	18.9602i	0.566797	+	0.981722i	0.996880	+	0.0789323i	$0.0251511\pi$
$373$	10.9467	+	18.9602i	0.566797	+	0.981722i	−0.430083	+	0.902790i	$0.641516\pi$
$374$	−22.0367	+	8.29892i	−1.13949	+	0.429127i
$375$		0			0
$376$	−0.0591903	−	0.563158i	−0.00305251	−	0.0290426i
$377$	3.39643	+	10.4531i	0.174925	+	0.538364i
$378$		0			0
$379$	27.3639	+	19.8810i	1.40559	+	1.02122i	0.993946	+	0.109873i	$0.0350445\pi$
$379$	27.3639	+	19.8810i	1.40559	+	1.02122i	0.411642	+	0.911346i	$0.364955\pi$
$380$	−0.529871	+	0.235914i	−0.0271818	+	0.0121021i
$381$		0			0
$382$	−5.37771	+	5.97255i	−0.275147	+	0.305582i
$383$	16.7854	+	7.47333i	0.857693	+	0.381869i	0.787982	−	0.615698i	$-0.211126\pi$
$383$	16.7854	+	7.47333i	0.857693	+	0.381869i	0.0697105	+	0.997567i	$0.477792\pi$
$384$		0			0
$385$	1.41514	+	0.0831793i	0.0721223	+	0.00423921i
$386$	−5.05284			−0.257183
$387$		0			0
$388$	1.71134	+	5.26696i	0.0868801	+	0.267390i
$389$	20.6136	+	22.8937i	1.04515	+	1.16076i	0.986714	+	0.162467i	$0.0519450\pi$
$389$	20.6136	+	22.8937i	1.04515	+	1.16076i	0.0584370	+	0.998291i	$0.481388\pi$
$390$		0			0
$391$	2.13694	−	20.3316i	0.108070	−	1.02821i
$392$	15.7698	−	3.35198i	0.796496	−	0.169300i
$393$		0			0
$394$	3.63030	+	34.5400i	0.182892	+	1.74010i
$395$	8.65524			0.435493
$396$		0			0
$397$	−8.29578			−0.416353			−0.208177	−	0.978091i	$-0.566753\pi$
$397$	−8.29578			−0.416353			−0.208177	+	0.978091i	$0.566753\pi$
$398$	−3.36630	−	32.0282i	−0.168738	−	1.60543i
$399$		0			0
$400$	−21.0502	+	4.47436i	−1.05251	+	0.223718i
$401$	−0.411175	+	3.91207i	−0.0205331	+	0.195360i	−0.999980	−	0.00634326i	$-0.997981\pi$
$401$	−0.411175	+	3.91207i	−0.0205331	+	0.195360i	0.979447	+	0.201703i	$0.0646475\pi$
$402$		0			0
$403$	9.61986	+	10.6839i	0.479199	+	0.532205i
$404$	1.73404	+	5.33682i	0.0862716	+	0.265517i
$405$		0			0
$406$	7.78977			0.386600
$407$	8.07642	−	5.17227i	0.400333	−	0.256380i
$408$		0			0
$409$	−2.28775	−	1.01857i	−0.113122	−	0.0503651i	0.349395	−	0.936975i	$-0.386387\pi$
$409$	−2.28775	−	1.01857i	−0.113122	−	0.0503651i	−0.462517	+	0.886610i	$0.653054\pi$
$410$	0.706895	−	0.785086i	0.0349110	−	0.0387726i
$411$		0			0
$412$	−1.58010	+	0.703506i	−0.0778460	+	0.0346593i
$413$	4.16650	+	3.02714i	0.205020	+	0.148956i
$414$		0			0
$415$	−1.27204	−	3.91493i	−0.0624419	−	0.192176i
$416$	0.358805	+	3.41381i	0.0175919	+	0.167376i
$417$		0			0
$418$	−12.4043	−	3.40829i	−0.606712	−	0.166705i
$419$	5.36970	+	9.30060i	0.262327	+	0.454364i	0.966860	−	0.255307i	$-0.0821767\pi$
$419$	5.36970	+	9.30060i	0.262327	+	0.454364i	−0.704533	+	0.709672i	$0.748843\pi$
$420$		0			0
$421$	−21.7026	−	4.61303i	−1.05772	−	0.224825i	−0.353958	−	0.935261i	$-0.615164\pi$
$421$	−21.7026	−	4.61303i	−1.05772	−	0.224825i	−0.703762	+	0.710436i	$0.748498\pi$
$422$	−1.62065	+	4.98785i	−0.0788920	+	0.242805i
$423$		0			0
$424$	−11.4825	−	8.34249i	−0.557637	−	0.405147i
$425$	14.2863	+	15.8665i	0.692986	+	0.769639i
$426$		0			0
$427$	3.00679	+	1.33871i	0.145509	+	0.0647847i
$428$	−3.07440	−	5.32501i	−0.148606	−	0.257394i
$429$		0			0
$430$	1.92889	−	3.34093i	0.0930192	−	0.161114i
$431$	−14.9330	+	10.8495i	−0.719297	+	0.522600i	−0.886160	−	0.463380i	$-0.846636\pi$
$431$	−14.9330	+	10.8495i	−0.719297	+	0.522600i	0.166862	+	0.985980i	$0.446636\pi$
$432$		0			0
$433$	4.67130	−	14.3768i	0.224488	−	0.690904i	−0.773855	−	0.633363i	$-0.781674\pi$
$433$	4.67130	−	14.3768i	0.224488	−	0.690904i	0.998343	−	0.0575408i	$-0.0183259\pi$
$434$	9.30835	−	4.14434i	0.446815	−	0.198935i
$435$		0			0
$436$	5.23232	−	1.11216i	0.250583	−	0.0532630i
$437$	7.47304	−	8.29965i	0.357484	−	0.397026i
$438$		0			0
$439$	−11.9777	+	20.7459i	−0.571663	+	0.990150i	0.424732	+	0.905319i	$0.360368\pi$
$439$	−11.9777	+	20.7459i	−0.571663	+	0.990150i	−0.996395	+	0.0848306i	$0.972965\pi$
$440$	4.33945	+	2.24589i	0.206875	+	0.107068i
$441$		0			0
$442$	9.04645	−	6.57263i	0.430296	−	0.312628i
$443$	24.9405	+	5.30127i	1.18496	+	0.251871i	0.757911	−	0.652358i	$-0.226220\pi$
$443$	24.9405	+	5.30127i	1.18496	+	0.251871i	0.427049	+	0.904229i	$0.359553\pi$
$444$		0			0
$445$	−0.772332	+	7.34825i	−0.0366120	+	0.348340i
$446$	−1.78203	+	16.9549i	−0.0843817	+	0.802838i
$447$		0			0
$448$	−4.15748	−	0.883700i	−0.196423	−	0.0417509i
$449$	−18.1886	+	13.2148i	−0.858375	+	0.623646i	−0.927442	−	0.373966i	$-0.877998\pi$
$449$	−18.1886	+	13.2148i	−0.858375	+	0.623646i	0.0690672	+	0.997612i	$0.477998\pi$
$450$		0			0
$451$	3.78438	−	0.574776i	0.178200	−	0.0270651i
$452$	1.56804	−	2.71592i	0.0737542	−	0.127746i
$453$		0			0
$454$	−6.17315	+	6.85598i	−0.289720	+	0.321767i
$455$	−0.658458	+	0.139959i	−0.0308690	+	0.00656140i
$456$		0			0
$457$	19.8144	−	8.82195i	0.926879	−	0.412673i	0.112926	−	0.993603i	$-0.463978\pi$
$457$	19.8144	−	8.82195i	0.926879	−	0.412673i	0.813953	+	0.580930i	$0.197311\pi$
$458$	−11.8254	+	36.3950i	−0.552566	+	1.70062i
$459$		0			0
$460$	0.832763	−	0.605037i	0.0388278	−	0.0282100i
$461$	−6.05182	+	10.4821i	−0.281861	+	0.488198i	−0.971843	−	0.235629i	$-0.924285\pi$
$461$	−6.05182	+	10.4821i	−0.281861	+	0.488198i	0.689982	+	0.723827i	$0.257618\pi$
$462$		0			0
$463$	−10.0154	−	17.3472i	−0.465455	−	0.806192i	0.533767	−	0.845632i	$-0.320776\pi$
$463$	−10.0154	−	17.3472i	−0.465455	−	0.806192i	−0.999222	+	0.0394398i	$0.987443\pi$
$464$	29.5084	+	13.1380i	1.36989	+	0.609915i
$465$		0			0
$466$	4.33320	+	4.81250i	0.200731	+	0.222935i
$467$	4.90871	+	3.56639i	0.227148	+	0.165033i	0.695538	−	0.718489i	$-0.255166\pi$
$467$	4.90871	+	3.56639i	0.227148	+	0.165033i	−0.468390	+	0.883522i	$0.655166\pi$
$468$		0			0
$469$	−1.80516	+	5.55570i	−0.0833543	+	0.256538i
$470$	−0.203744	−	0.0433071i	−0.00939801	−	0.00199761i
$471$		0			0
$472$	8.87574	+	15.3732i	0.408539	+	0.707610i
$473$	13.0810	−	4.92624i	0.601465	−	0.226509i
$474$		0			0
$475$	1.21919	+	11.5998i	0.0559404	+	0.532237i
$476$	−0.400088	−	1.23134i	−0.0183380	−	0.0564385i
$477$		0			0
$478$	9.22233	+	6.70041i	0.421819	+	0.306470i
$479$	−33.1369	+	14.7535i	−1.51406	+	0.674104i	−0.984695	−	0.174289i	$-0.944237\pi$
$479$	−33.1369	+	14.7535i	−1.51406	+	0.674104i	−0.529367	+	0.848393i	$0.677571\pi$
$480$		0			0
$481$	−3.04743	+	3.38452i	−0.138951	+	0.154321i
$482$	12.4710	+	5.55244i	0.568038	+	0.252907i
$483$		0			0
$484$	−1.69732	−	3.94639i	−0.0771510	−	0.179381i
$485$	−8.39529			−0.381211
$486$		0			0
$487$	−2.68379	−	8.25986i	−0.121614	−	0.374290i	0.871655	−	0.490120i	$-0.163047\pi$
$487$	−2.68379	−	8.25986i	−0.121614	−	0.374290i	−0.993269	+	0.115830i	$0.963047\pi$
$488$	7.59110	+	8.43077i	0.343633	+	0.381643i
$489$		0			0
$490$	0.619900	−	5.89795i	0.0280042	−	0.266442i
$491$	−32.4719	+	6.90211i	−1.46544	+	0.311488i	−0.870453	−	0.492251i	$-0.836174\pi$
$491$	−32.4719	+	6.90211i	−1.46544	+	0.311488i	−0.594982	+	0.803739i	$0.702841\pi$
$492$		0			0
$493$	−3.34970	−	31.8703i	−0.150863	−	1.43537i
$494$	6.10872			0.274844
$495$		0			0
$496$	42.2506			1.89711
$497$	−0.928921	−	8.83810i	−0.0416678	−	0.396443i
$498$		0			0
$499$	−20.4207	+	4.34055i	−0.914155	+	0.194310i	−0.640893	−	0.767630i	$-0.721436\pi$
$499$	−20.4207	+	4.34055i	−0.914155	+	0.194310i	−0.273262	+	0.961940i	$0.588103\pi$
$500$	−0.233210	+	2.21885i	−0.0104295	+	0.0992299i
$501$		0			0
$502$	21.2842	+	23.6385i	0.949961	+	1.05504i
$503$	−7.20593	−	22.1776i	−0.321297	−	0.988850i	−0.973085	−	0.230448i	$-0.925981\pi$
$503$	−7.20593	−	22.1776i	−0.321297	−	0.988850i	0.651788	−	0.758401i	$-0.274019\pi$
$504$		0			0
$505$	−8.50663			−0.378540
$506$	22.7903	+	1.33957i	1.01315	+	0.0595511i
$507$		0			0
$508$	−4.27998	−	1.90557i	−0.189893	−	0.0845459i
$509$	−4.33678	+	4.81648i	−0.192224	+	0.213487i	−0.831551	−	0.555449i	$-0.812547\pi$
$509$	−4.33678	+	4.81648i	−0.192224	+	0.213487i	0.639327	+	0.768935i	$0.279213\pi$
$510$		0			0
$511$	10.2118	−	4.54658i	0.451743	−	0.201129i
$512$	−10.4751	−	7.61063i	−0.462940	−	0.336346i
$513$		0			0
$514$	−1.61605	−	4.97368i	−0.0712807	−	0.219379i
$515$	−0.274076	−	2.60766i	−0.0120772	−	0.114907i
$516$		0			0
$517$	−0.471224	−	0.589529i	−0.0207244	−	0.0259275i
$518$	1.61390	+	2.79537i	0.0709109	+	0.122821i
$519$		0			0
$520$	−2.26960	−	0.482418i	−0.0995284	−	0.0211554i
$521$	10.2625	−	31.5848i	0.449610	−	1.38376i	−0.427738	−	0.903903i	$-0.640689\pi$
$521$	10.2625	−	31.5848i	0.449610	−	1.38376i	0.877348	−	0.479855i	$-0.159311\pi$
$522$		0			0
$523$	32.4728	+	23.5929i	1.41994	+	1.03164i	0.991782	+	0.127938i	$0.0408359\pi$
$523$	32.4728	+	23.5929i	1.41994	+	1.03164i	0.428154	+	0.903706i	$0.359164\pi$
$524$	1.80079	+	1.99998i	0.0786677	+	0.0873694i
$525$		0			0
$526$	−20.1732	−	8.98168i	−0.879593	−	0.391620i
$527$	−20.9585	−	36.3011i	−0.912965	−	1.58130i
$528$		0			0
$529$	1.58985	−	2.75370i	0.0691240	−	0.119726i
$530$	−4.22376	+	3.06874i	−0.183468	+	0.133298i
$531$		0			0
$532$	0.218567	−	0.672680i	0.00947608	−	0.0291644i
$533$	−1.66055	+	0.739324i	−0.0719264	+	0.0320237i
$534$		0			0
$535$	9.11750	−	1.93798i	0.394184	−	0.0837864i
$536$	−13.4730	+	14.9633i	−0.581945	+	0.646315i
$537$		0			0
$538$	−5.19534	+	8.99859i	−0.223987	+	0.387957i
$539$	15.2903	−	15.0973i	0.658599	−	0.650287i
$540$		0			0
$541$	−19.9410	+	14.4880i	−0.857332	+	0.622888i	−0.927158	−	0.374671i	$-0.877756\pi$
$541$	−19.9410	+	14.4880i	−0.857332	+	0.622888i	0.0698260	+	0.997559i	$0.477756\pi$
$542$	−6.01969	−	1.27952i	−0.258568	−	0.0549602i
$543$		0			0
$544$	1.04614	−	9.95337i	0.0448529	−	0.426747i
$545$	−0.847630	+	8.06466i	−0.0363085	+	0.345452i
$546$		0			0
$547$	−25.1583	−	5.34756i	−1.07569	−	0.228645i	−0.364186	−	0.931326i	$-0.618653\pi$
$547$	−25.1583	−	5.34756i	−1.07569	−	0.228645i	−0.711505	+	0.702681i	$0.751986\pi$
$548$	2.92147	−	2.12257i	0.124799	−	0.0906716i
$549$		0			0
$550$	−16.9659	+	16.7517i	−0.723427	+	0.714296i
$551$	8.75329	−	15.1611i	0.372902	−	0.645886i
$552$		0			0
$553$	−7.06240	+	7.84359i	−0.300324	+	0.333543i
$554$	−19.8602	+	4.22141i	−0.843778	+	0.179351i
$555$		0			0
$556$	7.71035	−	3.43287i	0.326992	−	0.145586i
$557$	−3.60979	+	11.1098i	−0.152952	+	0.470737i	−0.997948	−	0.0640357i	$-0.979603\pi$
$557$	−3.60979	+	11.1098i	−0.152952	+	0.470737i	0.844996	+	0.534773i	$0.179603\pi$
$558$		0			0
$559$	−5.36998	+	3.90152i	−0.227126	+	0.165017i
$560$	−0.989164	+	1.71328i	−0.0417998	+	0.0723994i
$561$		0			0
$562$	2.29436	+	3.97396i	0.0967819	+	0.167631i
$563$	−7.41991	−	3.30356i	−0.312712	−	0.139228i	0.244379	−	0.969680i	$-0.421416\pi$
$563$	−7.41991	−	3.30356i	−0.312712	−	0.139228i	−0.557091	+	0.830451i	$0.688083\pi$
$564$		0			0
$565$	3.18111	+	3.53298i	0.133830	+	0.148634i
$566$	10.1229	+	7.35468i	0.425495	+	0.309140i
$567$		0			0
$568$	9.46559	−	29.1321i	0.397167	−	1.22236i
$569$	−17.6131	−	3.74379i	−0.738381	−	0.156948i	−0.176657	−	0.984272i	$-0.556528\pi$
$569$	−17.6131	−	3.74379i	−0.738381	−	0.156948i	−0.561724	+	0.827325i	$0.689862\pi$
$570$		0			0
$571$	1.30322	+	2.25725i	0.0545382	+	0.0944629i	0.892006	−	0.452024i	$-0.149298\pi$
$571$	1.30322	+	2.25725i	0.0545382	+	0.0944629i	−0.837467	+	0.546487i	$0.815965\pi$
$572$	1.27372	+	1.59350i	0.0532569	+	0.0666276i
$573$		0			0
$574$	0.134661	+	1.28121i	0.00562063	+	0.0534767i
$575$	−6.39652	−	19.6865i	−0.266753	−	0.820982i
$576$		0			0
$577$	−28.4684	−	20.6835i	−1.18515	−	0.861064i	−0.192409	−	0.981315i	$-0.561630\pi$
$577$	−28.4684	−	20.6835i	−1.18515	−	0.861064i	−0.992744	+	0.120251i	$0.961630\pi$
$578$	−5.77202	+	2.56987i	−0.240084	+	0.106893i
$579$		0			0
$580$	1.07967	−	1.19909i	0.0448307	−	0.0497895i
$581$	4.58575	+	2.04171i	0.190249	+	0.0847042i
$582$		0			0
$583$	−18.8841	−	1.10997i	−0.782099	−	0.0459702i
$584$	38.5294			1.59436
$585$		0			0
$586$	−7.50863	−	23.1092i	−0.310179	−	0.954631i
$587$	−15.7596	−	17.5029i	−0.650470	−	0.722420i	0.324220	−	0.945982i	$-0.394898\pi$
$587$	−15.7596	−	17.5029i	−0.650470	−	0.722420i	−0.974690	+	0.223562i	$0.928232\pi$
$588$		0			0
$589$	2.39361	−	22.7737i	0.0986269	−	0.938372i
$590$	6.38709	−	1.35762i	0.262952	−	0.0558923i
$591$		0			0
$592$	1.39905	+	13.3111i	0.0575005	+	0.547081i
$593$	−13.1828			−0.541354			−0.270677	−	0.962670i	$-0.587248\pi$
$593$	−13.1828			−0.541354			−0.270677	+	0.962670i	$0.587248\pi$
$594$		0			0
$595$	1.96270			0.0804630
$596$	−0.0468001	−	0.445273i	−0.00191701	−	0.0182391i
$597$		0			0
$598$	−10.6042	+	2.25399i	−0.433638	+	0.0921726i
$599$	3.57659	−	34.0290i	0.146135	−	1.39039i	−0.638115	−	0.769941i	$-0.720285\pi$
$599$	3.57659	−	34.0290i	0.146135	−	1.39039i	0.784250	−	0.620445i	$-0.213048\pi$
$600$		0			0
$601$	19.4239	+	21.5724i	0.792316	+	0.879956i	0.995060	−	0.0992759i	$-0.0316526\pi$
$601$	19.4239	+	21.5724i	0.792316	+	0.879956i	−0.202744	+	0.979232i	$0.564986\pi$
$602$	1.45372	+	4.47410i	0.0592493	+	0.182351i
$603$		0			0
$604$	0.343924			0.0139941
$605$	6.48480	−	0.598412i	0.263645	−	0.0243289i
$606$		0			0
$607$	−2.88347	−	1.28380i	−0.117037	−	0.0521080i	0.347383	−	0.937723i	$-0.387070\pi$
$607$	−2.88347	−	1.28380i	−0.117037	−	0.0521080i	−0.464420	+	0.885615i	$0.653737\pi$
$608$	3.65844	−	4.06311i	0.148369	−	0.164781i
$609$		0			0
$610$	3.81231	−	1.69735i	0.154356	−	0.0687238i
$611$	0.289945	+	0.210657i	0.0117299	+	0.00852229i
$612$		0			0
$613$	10.4884	+	32.2798i	0.423620	+	1.30377i	0.904309	+	0.426878i	$0.140387\pi$
$613$	10.4884	+	32.2798i	0.423620	+	1.30377i	−0.480689	+	0.876891i	$0.659613\pi$
$614$	−0.567779	−	5.40206i	−0.0229137	−	0.218009i
$615$		0			0
$616$	−5.57613	+	2.09994i	−0.224669	+	0.0846091i
$617$	−10.8039	−	18.7129i	−0.434948	−	0.753351i	0.562344	−	0.826904i	$-0.309900\pi$
$617$	−10.8039	−	18.7129i	−0.434948	−	0.753351i	−0.997291	+	0.0735523i	$0.976566\pi$
$618$		0			0
$619$	−20.0643	−	4.26481i	−0.806454	−	0.171417i	−0.213803	−	0.976877i	$-0.568585\pi$
$619$	−20.0643	−	4.26481i	−0.806454	−	0.171417i	−0.592651	+	0.805460i	$0.701919\pi$
$620$	0.652196	−	2.00725i	0.0261928	−	0.0806132i
$621$		0			0
$622$	−32.9404	−	23.9326i	−1.32079	−	0.959611i
$623$	−6.02896	−	6.69584i	−0.241545	−	0.268263i
$624$		0			0
$625$	18.1479	+	8.07996i	0.725915	+	0.323198i
$626$	−1.90263	−	3.29545i	−0.0760444	−	0.131713i
$627$		0			0
$628$	1.91094	−	3.30985i	0.0762550	−	0.132078i
$629$	10.7427	−	7.80501i	0.428339	−	0.311206i
$630$		0			0
$631$	9.22863	−	28.4028i	0.367386	−	1.13070i	−0.581087	−	0.813841i	$-0.697372\pi$
$631$	9.22863	−	28.4028i	0.367386	−	1.13070i	0.948473	−	0.316857i	$-0.102628\pi$
$632$	−33.2348	+	14.7971i	−1.32201	+	0.588596i
$633$		0			0
$634$	40.0881	−	8.52098i	1.59210	−	0.338411i
$635$	4.75230	−	5.27796i	0.188589	−	0.209450i
$636$		0			0
$637$	−5.10193	+	8.83680i	−0.202146	+	0.350127i
$638$	35.3803	−	5.37360i	1.40072	−	0.212743i
$639$		0			0
$640$	−6.44762	+	4.68447i	−0.254864	+	0.185170i
$641$	−37.2870	−	7.92561i	−1.47275	−	0.313043i	−0.599523	−	0.800357i	$-0.704643\pi$
$641$	−37.2870	−	7.92561i	−1.47275	−	0.313043i	−0.873226	+	0.487315i	$0.837976\pi$
$642$		0			0
$643$	1.75871	−	16.7330i	0.0693566	−	0.659884i	−0.903518	−	0.428550i	$-0.859024\pi$
$643$	1.75871	−	16.7330i	0.0693566	−	0.659884i	0.972875	−	0.231333i	$-0.0743088\pi$
$644$	−0.131208	+	1.24836i	−0.00517032	+	0.0491923i
$645$		0			0
$646$	−17.4215	−	3.70306i	−0.685440	−	0.145695i
$647$	−16.9687	+	12.3285i	−0.667109	+	0.484683i	−0.869056	−	0.494713i	$-0.835273\pi$
$647$	−16.9687	+	12.3285i	−0.667109	+	0.484683i	0.201947	+	0.979396i	$0.435273\pi$
$648$		0			0
$649$	21.0120	+	10.8748i	0.824792	+	0.426872i
$650$	5.66102	−	9.80517i	0.222043	−	0.384591i
$651$		0			0
$652$	1.20985	−	1.34368i	0.0473815	−	0.0526225i
$653$	19.3345	−	4.10968i	0.756619	−	0.160824i	0.186577	−	0.982440i	$-0.440261\pi$
$653$	19.3345	−	4.10968i	0.756619	−	0.160824i	0.570041	+	0.821616i	$0.306927\pi$
$654$		0			0
$655$	−3.72703	+	1.65938i	−0.145627	+	0.0648374i
$656$	−1.65074	+	5.08046i	−0.0644506	+	0.198358i
$657$		0			0
$658$	0.205494	−	0.149300i	0.00801101	−	0.00582034i
$659$	−5.90277	+	10.2239i	−0.229939	+	0.398267i	−0.957790	−	0.287469i	$-0.907186\pi$
$659$	−5.90277	+	10.2239i	−0.229939	+	0.398267i	0.727851	+	0.685736i	$0.240519\pi$
$660$		0			0
$661$	−8.90382	−	15.4219i	−0.346318	−	0.599841i	0.639274	−	0.768979i	$-0.279235\pi$
$661$	−8.90382	−	15.4219i	−0.346318	−	0.599841i	−0.985592	+	0.169138i	$0.945902\pi$
$662$	−11.4466	−	5.09634i	−0.444884	−	0.198075i
$663$		0			0
$664$	11.5774	+	12.8580i	0.449291	+	0.498988i
$665$	0.867445	+	0.630235i	0.0336381	+	0.0244395i
$666$		0			0
$667$	−9.60079	+	29.5482i	−0.371744	+	1.14411i
$668$	−6.48925	−	1.37933i	−0.251076	−	0.0533679i
$669$		0			0
$670$	3.70329	+	6.41429i	0.143071	+	0.247806i
$671$	14.5800	+	4.00611i	0.562854	+	0.154654i
$672$		0			0
$673$	−2.05976	−	19.5973i	−0.0793980	−	0.755422i	−0.959704	−	0.281014i	$-0.909329\pi$
$673$	−2.05976	−	19.5973i	−0.0793980	−	0.755422i	0.880306	−	0.474407i	$-0.157338\pi$
$674$	−11.8111	−	36.3508i	−0.454946	−	1.40018i
$675$		0			0
$676$	3.32365	+	2.41477i	0.127833	+	0.0928760i
$677$	11.3407	−	5.04919i	0.435857	−	0.194056i	−0.177065	−	0.984199i	$-0.556660\pi$
$677$	11.3407	−	5.04919i	0.435857	−	0.194056i	0.612923	+	0.790143i	$0.289994\pi$
$678$		0			0
$679$	6.85029	−	7.60802i	0.262890	−	0.291969i
$680$	6.18025	+	2.75162i	0.237002	+	0.105520i
$681$		0			0
$682$	39.4186	−	25.2443i	1.50942	−	0.966654i
$683$	−2.02837			−0.0776135			−0.0388068	−	0.999247i	$-0.512356\pi$
$683$	−2.02837			−0.0776135			−0.0388068	+	0.999247i	$0.512356\pi$
$684$		0			0
$685$	1.69164	+	5.20632i	0.0646341	+	0.198923i
$686$	10.0674	+	11.1810i	0.384375	+	0.426891i
$687$		0			0
$688$	−2.03903	+	19.4001i	−0.0777374	+	0.739622i
$689$	8.78666	−	1.86766i	0.334745	−	0.0711523i
$690$		0			0
$691$	−0.244897	−	2.33004i	−0.00931631	−	0.0886387i	0.988876	−	0.148744i	$-0.0475230\pi$
$691$	−0.244897	−	2.33004i	−0.00931631	−	0.0886387i	−0.998192	+	0.0601053i	$0.980856\pi$
$692$	0.230830			0.00877483
$693$		0			0
$694$	−3.19995			−0.121469
$695$	1.33740	+	12.7245i	0.0507304	+	0.482667i
$696$		0			0
$697$	5.18391	−	1.10187i	0.196355	−	0.0417364i
$698$	−0.842705	+	8.01780i	−0.0318969	+	0.303478i
$699$		0			0
$700$	−0.877178	−	0.974205i	−0.0331542	−	0.0368215i
$701$	1.37008	+	4.21668i	0.0517473	+	0.159262i	0.973591	−	0.228301i	$-0.0733170\pi$
$701$	1.37008	+	4.21668i	0.0517473	+	0.159262i	−0.921843	+	0.387563i	$0.873317\pi$
$702$		0			0
$703$	7.25411			0.273594
$704$	−19.4924	−	1.14573i	−0.734649	−	0.0431812i
$705$		0			0
$706$	30.6117	+	13.6292i	1.15209	+	0.512942i
$707$	6.94114	−	7.70892i	0.261049	−	0.289924i
$708$		0			0
$709$	27.2990	−	12.1543i	1.02524	−	0.456465i	0.175952	−	0.984399i	$-0.443700\pi$
$709$	27.2990	−	12.1543i	1.02524	−	0.456465i	0.849286	+	0.527934i	$0.177033\pi$
$710$	−9.11565	−	6.62291i	−0.342104	−	0.248553i
$711$		0			0
$712$	−9.59699	−	29.5365i	−0.359662	−	1.10693i
$713$	4.24792	+	40.4163i	0.159086	+	1.51360i
$714$		0			0
$715$	−2.89409	+	1.08990i	−0.108233	+	0.0407600i
$716$	−1.88258	−	3.26072i	−0.0703551	−	0.121859i
$717$		0			0
$718$	−13.2374	−	2.81369i	−0.494014	−	0.105006i
$719$	6.68469	−	20.5734i	0.249297	−	0.767257i	−0.745603	−	0.666390i	$-0.767838\pi$
$719$	6.68469	−	20.5734i	0.249297	−	0.767257i	0.994900	−	0.100867i	$-0.0321616\pi$
$720$		0			0
$721$	2.58676	+	1.87939i	0.0963360	+	0.0699922i
$722$	13.1462	+	14.6003i	0.489250	+	0.543367i
$723$		0			0
$724$	−1.69891	−	0.756405i	−0.0631396	−	0.0281116i
$725$	−16.2235	−	28.1000i	−0.602527	−	1.04361i
$726$		0			0
$727$	6.22109	−	10.7752i	0.230727	−	0.399631i	−0.727295	−	0.686325i	$-0.759223\pi$
$727$	6.22109	−	10.7752i	0.230727	−	0.399631i	0.958022	+	0.286694i	$0.0925561\pi$
$728$	2.28910	−	1.66313i	0.0848396	−	0.0616396i
$729$		0			0
$730$	4.37965	−	13.4792i	0.162098	−	0.498887i
$731$	17.6798	−	7.87154i	0.653909	−	0.291139i
$732$		0			0
$733$	51.2082	−	10.8846i	1.89142	−	0.402033i	0.892609	−	0.450832i	$-0.148873\pi$
$733$	51.2082	−	10.8846i	1.89142	−	0.402033i	0.998809	+	0.0487988i	$0.0155393\pi$
$734$	7.00012	−	7.77442i	0.258379	−	0.286959i
$735$		0			0
$736$	−4.85153	+	8.40310i	−0.178830	+	0.309742i
$737$	−4.36635	+	26.4786i	−0.160837	+	0.975352i
$738$		0			0
$739$	37.7617	−	27.4355i	1.38909	−	1.00923i	0.393122	−	0.919486i	$-0.371395\pi$
$739$	37.7617	−	27.4355i	1.38909	−	1.00923i	0.995965	−	0.0897445i	$-0.0286051\pi$
$740$	0.653982	+	0.139008i	0.0240408	+	0.00511004i
$741$		0			0
$742$	0.665485	−	6.33167i	0.0244307	−	0.232443i
$743$	−2.28623	+	21.7521i	−0.0838738	+	0.798006i	0.869035	+	0.494750i	$0.164740\pi$
$743$	−2.28623	+	21.7521i	−0.0838738	+	0.798006i	−0.952909	+	0.303256i	$0.901926\pi$
$744$		0			0
$745$	0.663893	+	0.141115i	0.0243232	+	0.00517005i
$746$	−27.3853	+	19.8966i	−1.00265	+	0.728466i
$747$		0			0
$748$	−2.66657	−	5.31664i	−0.0974994	−	0.194395i
$749$	−5.68334	+	9.84384i	−0.207665	+	0.359686i
$750$		0			0
$751$	26.4923	−	29.4227i	0.966718	−	1.07365i	−0.0305318	−	0.999534i	$-0.509720\pi$
$751$	26.4923	−	29.4227i	0.966718	−	1.07365i	0.997250	−	0.0741152i	$-0.0236132\pi$
$752$	1.03024	−	0.218984i	0.0375689	−	0.00798551i
$753$		0			0
$754$	−15.5245	+	6.91196i	−0.565370	+	0.251719i
$755$	−0.161111	+	0.495850i	−0.00586344	+	0.0180458i
$756$		0			0
$757$	−18.7253	+	13.6047i	−0.680583	+	0.494472i	−0.873551	−	0.486733i	$-0.838189\pi$
$757$	−18.7253	+	13.6047i	−0.680583	+	0.494472i	0.192968	+	0.981205i	$0.438189\pi$
$758$	−26.1480	+	45.2896i	−0.949736	+	1.64499i
$759$		0			0
$760$	1.84789	+	3.20063i	0.0670299	+	0.116099i
$761$	13.6053	+	6.05747i	0.493192	+	0.219583i	0.638234	−	0.769842i	$-0.279665\pi$
$761$	13.6053	+	6.05747i	0.493192	+	0.219583i	−0.145042	+	0.989425i	$0.546332\pi$
$762$		0			0
$763$	−6.61675	−	7.34864i	−0.239542	−	0.266039i
$764$	−1.64233	−	1.19322i	−0.0594173	−	0.0431692i
$765$		0			0
$766$	−8.77872	+	27.0181i	−0.317188	+	0.976204i
$767$	−10.9896	−	2.33591i	−0.396811	−	0.0843447i
$768$		0			0
$769$	−10.8117	−	18.7264i	−0.389879	−	0.675290i	0.602554	−	0.798078i	$-0.294150\pi$
$769$	−10.8117	−	18.7264i	−0.389879	−	0.675290i	−0.992433	+	0.122788i	$0.960816\pi$
$770$	0.100807	+	2.18946i	0.00363282	+	0.0789026i
$771$		0			0
$772$	−0.133409	−	1.26930i	−0.00480151	−	0.0456833i
$773$	1.87664	+	5.77569i	0.0674979	+	0.207737i	0.979117	−	0.203300i	$-0.0651666\pi$
$773$	1.87664	+	5.77569i	0.0674979	+	0.207737i	−0.911619	+	0.411037i	$0.865167\pi$
$774$		0			0
$775$	−34.3361	−	24.9466i	−1.23339	−	0.896109i
$776$	32.2366	−	14.3527i	1.15723	−	0.515231i
$777$		0			0
$778$	−31.8714	+	35.3968i	−1.14265	+	1.26904i
$779$	2.64492	+	1.17759i	0.0947641	+	0.0421917i
$780$		0			0
$781$	−10.3158	−	39.5009i	−0.369129	−	1.41345i
$782$	31.6086			1.13032
$783$		0			0
$784$	9.26663	+	28.5197i	0.330951	+	1.01856i
$785$	3.87678	+	4.30560i	0.138368	+	0.153673i
$786$		0			0
$787$	−5.34719	+	50.8751i	−0.190607	+	1.81350i	0.313201	+	0.949687i	$0.398599\pi$
$787$	−5.34719	+	50.8751i	−0.190607	+	1.81350i	−0.503808	+	0.863816i	$0.668068\pi$
$788$	−8.58080	+	1.82391i	−0.305678	+	0.0649739i
$789$		0			0
$790$	1.39882	+	13.3089i	0.0497678	+	0.473509i
$791$	−5.79736			−0.206130
$792$		0			0
$793$	−7.18019			−0.254976
$794$	−1.34072	−	12.7561i	−0.0475805	−	0.452699i
$795$		0			0
$796$	7.95681	−	1.69127i	0.282022	−	0.0599455i
$797$	−2.64052	+	25.1228i	−0.0935319	+	0.889897i	0.842669	+	0.538432i	$0.180983\pi$
$797$	−2.64052	+	25.1228i	−0.0935319	+	0.889897i	−0.936201	+	0.351465i	$0.885684\pi$
$798$		0			0
$799$	−0.699198	−	0.776538i	−0.0247359	−	0.0274719i
$800$	−3.13143	−	9.63754i	−0.110713	−	0.340738i
$801$		0			0
$802$	−6.08192			−0.214760
$803$	43.2445	−	27.6944i	1.52606	−	0.977316i
$804$		0			0
$805$	−1.73835	−	0.773964i	−0.0612689	−	0.0272787i
$806$	−14.8736	+	16.5188i	−0.523901	+	0.581851i
$807$		0			0
$808$	32.6641	−	14.5430i	1.14912	−	0.511621i
$809$	41.5248	+	30.1696i	1.45994	+	1.06071i	0.983380	+	0.181561i	$0.0581150\pi$
$809$	41.5248	+	30.1696i	1.45994	+	1.06071i	0.476556	+	0.879144i	$0.341885\pi$
$810$		0			0
$811$	1.40476	+	4.32339i	0.0493276	+	0.151815i	0.972686	−	0.232124i	$-0.0745674\pi$
$811$	1.40476	+	4.32339i	0.0493276	+	0.151815i	−0.923359	+	0.383939i	$0.874567\pi$
$812$	0.205672	+	1.95684i	0.00721767	+	0.0686715i
$813$		0			0
$814$	9.25850	+	11.5829i	0.324510	+	0.405981i
$815$	1.37048	+	2.37375i	0.0480059	+	0.0831487i
$816$		0			0
$817$	10.3414	+	2.19814i	0.361800	+	0.0769030i
$818$	1.19649	−	3.68241i	0.0418342	−	0.128753i
$819$		0			0
$820$	0.215882	+	0.156848i	0.00753894	+	0.00547736i
$821$	−7.27599	−	8.08080i	−0.253934	−	0.282022i	0.602677	−	0.797985i	$-0.294101\pi$
$821$	−7.27599	−	8.08080i	−0.253934	−	0.282022i	−0.856611	+	0.515963i	$0.827434\pi$
$822$		0			0
$823$	−21.5744	−	9.60555i	−0.752037	−	0.334828i	−0.00533378	−	0.999986i	$-0.501698\pi$
$823$	−21.5744	−	9.60555i	−0.752037	−	0.334828i	−0.746703	+	0.665157i	$0.768364\pi$
$824$	5.51048	+	9.54444i	0.191967	+	0.332496i
$825$		0			0
$826$	−3.98136	+	6.89591i	−0.138529	+	0.239940i
$827$	−22.3321	+	16.2252i	−0.776564	+	0.564207i	−0.903946	−	0.427647i	$-0.859343\pi$
$827$	−22.3321	+	16.2252i	−0.776564	+	0.564207i	0.127382	+	0.991854i	$0.459343\pi$
$828$		0			0
$829$	−4.97546	+	15.3129i	−0.172805	+	0.531839i	−0.999526	−	0.0307727i	$-0.990203\pi$
$829$	−4.97546	+	15.3129i	−0.172805	+	0.531839i	0.826722	+	0.562611i	$0.190203\pi$
$830$	5.81427	−	2.58868i	0.201816	−	0.0898545i
$831$		0			0
$832$	9.06972	−	1.92783i	0.314436	−	0.0668354i
$833$	19.9070	−	22.1090i	0.689738	−	0.766032i
$834$		0			0
$835$	5.02854	−	8.70968i	0.174020	−	0.301411i
$836$	0.528675	−	3.20601i	0.0182846	−	0.110882i
$837$		0			0
$838$	−13.4334	+	9.75993i	−0.464049	+	0.337151i
$839$	−19.0073	−	4.04012i	−0.656205	−	0.139481i	−0.132236	−	0.991218i	$-0.542216\pi$
$839$	−19.0073	−	4.04012i	−0.656205	−	0.139481i	−0.523968	+	0.851738i	$0.675549\pi$
$840$		0			0
$841$	−2.05933	+	19.5932i	−0.0710114	+	0.675629i
$842$	3.58583	−	34.1169i	0.123576	−	1.17575i
$843$		0			0
$844$	−1.29577	−	0.275424i	−0.0446021	−	0.00948047i
$845$	−5.03845	+	3.66065i	−0.173328	+	0.125930i
$846$		0			0
$847$	−4.74909	+	6.36497i	−0.163181	+	0.218703i
$848$	13.1997	−	22.8626i	0.453280	−	0.785103i
$849$		0			0
$850$	−22.0885	+	24.5318i	−0.757631	+	0.841434i
$851$	−12.5925	+	2.67662i	−0.431666	+	0.0917533i
$852$		0			0
$853$	−18.0750	+	8.04749i	−0.618875	+	0.275541i	−0.692131	−	0.721772i	$-0.743328\pi$
$853$	−18.0750	+	8.04749i	−0.618875	+	0.275541i	0.0732555	+	0.997313i	$0.476661\pi$
$854$	−1.57255	+	4.83980i	−0.0538114	+	0.165614i
$855$		0			0
$856$	−31.6966	+	23.0289i	−1.08337	+	0.787112i
$857$	−2.17032	+	3.75911i	−0.0741369	+	0.128409i	−0.900711	−	0.434420i	$-0.856953\pi$
$857$	−2.17032	+	3.75911i	−0.0741369	+	0.128409i	0.826574	+	0.562828i	$0.190287\pi$
$858$		0			0
$859$	2.58967	+	4.48545i	0.0883586	+	0.153042i	0.906817	−	0.421524i	$-0.138505\pi$
$859$	2.58967	+	4.48545i	0.0883586	+	0.153042i	−0.818459	+	0.574565i	$0.805171\pi$
$860$	0.890190	+	0.396338i	0.0303552	+	0.0135150i
$861$		0			0
$862$	−19.0963	−	21.2085i	−0.650421	−	0.722366i
$863$	−2.17943	−	1.58345i	−0.0741886	−	0.0539011i	0.550073	−	0.835117i	$-0.314600\pi$
$863$	−2.17943	−	1.58345i	−0.0741886	−	0.0539011i	−0.624261	+	0.781216i	$0.714600\pi$
$864$		0			0
$865$	−0.108132	+	0.332797i	−0.00367661	+	0.0113155i
$866$	22.8616	+	4.85939i	0.776870	+	0.165129i
$867$		0			0
$868$	1.28685	+	2.22889i	0.0436785	+	0.0756534i
$869$	−26.6659	+	40.4966i	−0.904580	+	1.37375i
$870$		0			0
$871$	−1.33208	−	12.6739i	−0.0451358	−	0.429438i
$872$	−10.5326	−	32.4161i	−0.356680	−	1.09775i
$873$		0			0
$874$	13.9699	+	10.1497i	0.472538	+	0.343319i
$875$	3.76780	−	1.67753i	0.127375	−	0.0567109i
$876$		0			0
$877$	−13.9479	+	15.4907i	−0.470986	+	0.523083i	−0.931094	−	0.364780i	$-0.881144\pi$
$877$	−13.9479	+	15.4907i	−0.470986	+	0.523083i	0.460107	+	0.887863i	$0.347811\pi$
$878$	−33.8361	−	15.0648i	−1.14191	−	0.508413i
$879$		0			0
$880$	−3.31081	+	8.46389i	−0.111607	+	0.285318i
$881$	−11.5843			−0.390286			−0.195143	−	0.980775i	$-0.562517\pi$
$881$	−11.5843			−0.390286			−0.195143	+	0.980775i	$0.562517\pi$
$882$		0			0
$883$	4.75801	+	14.6437i	0.160120	+	0.492798i	0.998644	−	0.0520667i	$-0.0165808\pi$
$883$	4.75801	+	14.6437i	0.160120	+	0.492798i	−0.838524	+	0.544865i	$0.816581\pi$
$884$	1.88994	+	2.09899i	0.0635654	+	0.0705966i
$885$		0			0
$886$	−4.12082	+	39.2070i	−0.138442	+	1.31718i
$887$	−5.78081	+	1.22875i	−0.194101	+	0.0412574i	−0.303936	−	0.952692i	$-0.598301\pi$
$887$	−5.78081	+	1.22875i	−0.194101	+	0.0412574i	0.109835	+	0.993950i	$0.464968\pi$
$888$		0			0
$889$	0.905294	+	8.61330i	0.0303626	+	0.288881i
$890$	−11.4240			−0.382932
$891$		0			0
$892$	−4.30623			−0.144183
$893$	−0.0596696	−	0.567719i	−0.00199677	−	0.0189980i
$894$		0			0
$895$	5.58301	−	1.18671i	0.186619	−	0.0396672i
$896$	1.01587	−	9.66536i	0.0339378	−	0.322897i
$897$		0			0
$898$	−23.2596	−	25.8324i	−0.776182	−	0.862037i
$899$	19.6852	+	60.5847i	0.656537	+	2.02061i
$900$		0			0
$901$	−26.1909			−0.872546
$902$	1.49543	+	5.72622i	0.0497923	+	0.190662i
$903$		0			0
$904$	−18.2550	−	8.12764i	−0.607152	−	0.270321i
$905$	1.88640	−	2.09506i	0.0627060	−	0.0696421i
$906$		0			0
$907$	−6.75413	+	3.00713i	−0.224267	+	0.0998502i	−0.515795	−	0.856712i	$-0.672503\pi$
$907$	−6.75413	+	3.00713i	−0.224267	+	0.0998502i	0.291527	+	0.956562i	$0.405837\pi$
$908$	−1.88525	−	1.36971i	−0.0625642	−	0.0454556i
$909$		0			0
$910$	−0.321628	−	0.989869i	−0.0106619	−	0.0328138i
$911$	−1.48418	−	14.1210i	−0.0491730	−	0.467850i	−0.991206	−	0.132329i	$-0.957754\pi$
$911$	−1.48418	−	14.1210i	−0.0491730	−	0.467850i	0.942033	−	0.335521i	$-0.108912\pi$
$912$		0			0
$913$	22.2364	+	6.10983i	0.735917	+	0.202206i
$914$	16.7675	+	29.0422i	0.554620	+	0.960631i
$915$		0			0
$916$	−9.45485	−	2.00969i	−0.312397	−	0.0664021i
$917$	1.53737	−	4.73153i	0.0507684	−	0.156249i
$918$		0			0
$919$	33.6895	+	24.4769i	1.11132	+	0.807418i	0.982870	−	0.184299i	$-0.0590013\pi$
$919$	33.6895	+	24.4769i	1.11132	+	0.807418i	0.128445	+	0.991717i	$0.459001\pi$
$920$	−4.38874	−	4.87419i	−0.144692	−	0.160697i
$921$		0			0
$922$	−17.0960	−	7.61162i	−0.563026	−	0.250675i
$923$	9.69344	+	16.7895i	0.319063	+	0.552634i
$924$		0			0
$925$	6.72247	−	11.6437i	0.221033	−	0.382841i
$926$	25.0555	−	18.2039i	0.823376	−	0.598218i
$927$		0			0
$928$	−4.70008	+	14.4654i	−0.154288	+	0.474849i
$929$	31.1818	−	13.8830i	1.02304	−	0.455488i	0.174524	−	0.984653i	$-0.444161\pi$
$929$	31.1818	−	13.8830i	1.02304	−	0.455488i	0.848519	+	0.529165i	$0.177495\pi$
$930$		0			0
$931$	15.8975	−	3.37912i	0.521020	−	0.110746i
$932$	−1.09452	+	1.21559i	−0.0358522	+	0.0398179i
$933$		0			0
$934$	−4.69059	+	8.12434i	−0.153481	+	0.265837i
$935$	8.91439	−	1.35393i	0.291532	−	0.0442781i
$936$		0			0
$937$	−41.8118	+	30.3780i	−1.36593	+	0.992407i	−0.367889	+	0.929870i	$0.619919\pi$
$937$	−41.8118	+	30.3780i	−1.36593	+	0.992407i	−0.998043	+	0.0625376i	$0.980081\pi$
$938$	−8.83455	−	1.87784i	−0.288458	−	0.0613137i
$939$		0			0
$940$	0.00549959	−	0.0523251i	0.000179377	−	0.00170666i
$941$	1.88216	−	17.9075i	0.0613566	−	0.583769i	−0.920046	−	0.391810i	$-0.871849\pi$
$941$	1.88216	−	17.9075i	0.0613566	−	0.583769i	0.981403	−	0.191959i	$-0.0614842\pi$
$942$		0			0
$943$	−5.02586	−	1.06828i	−0.163664	−	0.0347880i
$944$	−26.7122	+	19.4075i	−0.869407	+	0.631661i
$945$		0			0
$946$	9.68901	+	19.3181i	0.315017	+	0.628084i
$947$	14.3151	−	24.7946i	0.465180	−	0.805715i	−0.534030	−	0.845466i	$-0.679323\pi$
$947$	14.3151	−	24.7946i	0.465180	−	0.805715i	0.999210	+	0.0397506i	$0.0126563\pi$
$948$		0			0
$949$	−16.3172	+	18.1221i	−0.529679	+	0.588268i
$950$	−17.6396	+	3.74942i	−0.572306	+	0.121647i
$951$		0			0
$952$	−7.53647	+	3.35545i	−0.244259	+	0.108751i
$953$	−5.15728	+	15.8725i	−0.167061	+	0.514160i	−0.999182	−	0.0404331i	$-0.987126\pi$
$953$	−5.15728	+	15.8725i	−0.167061	+	0.514160i	0.832121	+	0.554594i	$0.187126\pi$
$954$		0			0
$955$	2.48967	−	1.80885i	0.0805637	−	0.0585330i
$956$	−1.43969	+	2.49361i	−0.0465628	+	0.0806492i
$957$		0			0
$958$	−28.0414	−	48.5690i	−0.905975	−	1.56919i
$959$	−6.09842	−	2.71519i	−0.196928	−	0.0876781i
$960$		0			0
$961$	35.0121	+	38.8849i	1.12942	+	1.25435i
$962$	−5.69677	−	4.13895i	−0.183671	−	0.133445i
$963$		0			0
$964$	−1.06554	+	3.27939i	−0.0343187	+	0.105622i
$965$	1.89251	+	0.402265i	0.0609220	+	0.0129494i
$966$		0			0
$967$	−12.1597	−	21.0612i	−0.391029	−	0.677281i	0.601557	−	0.798830i	$-0.294547\pi$
$967$	−12.1597	−	21.0612i	−0.391029	−	0.677281i	−0.992585	+	0.121549i	$0.961214\pi$
$968$	−23.8776	+	13.3843i	−0.767454	+	0.430187i
$969$		0			0
$970$	−1.35681	−	12.9092i	−0.0435645	−	0.414488i
$971$	−2.33367	−	7.18229i	−0.0748910	−	0.230491i	0.906603	−	0.421985i	$-0.138667\pi$
$971$	−2.33367	−	7.18229i	−0.0748910	−	0.230491i	−0.981494	+	0.191495i	$0.938667\pi$
$972$		0			0
$973$	−12.6225	−	9.17079i	−0.404659	−	0.294002i
$974$	12.2672	−	5.46169i	0.393065	−	0.175004i
$975$		0			0
$976$	−14.1196	+	15.6814i	−0.451957	+	0.501949i
$977$	−1.85659	−	0.826605i	−0.0593974	−	0.0264454i	0.376823	−	0.926285i	$-0.377017\pi$
$977$	−1.85659	−	0.826605i	−0.0593974	−	0.0264454i	−0.436220	+	0.899840i	$0.643683\pi$
$978$		0			0
$979$	−32.0019	−	26.2528i	−1.02278	−	0.839044i
$980$	1.49797			0.0478508
$981$		0			0
$982$	−15.8611	−	48.8154i	−0.506148	−	1.55776i
$983$	−22.3755	−	24.8505i	−0.713666	−	0.792607i	0.271822	−	0.962347i	$-0.412374\pi$
$983$	−22.3755	−	24.8505i	−0.713666	−	0.792607i	−0.985489	+	0.169741i	$0.945707\pi$
$984$		0			0
$985$	1.39008	−	13.2257i	0.0442916	−	0.421407i
$986$	48.4645	−	10.3015i	1.54342	−	0.328065i
$987$		0			0
$988$	0.161287	+	1.53455i	0.00513123	+	0.0488204i
$989$	−18.7629			−0.596624
$990$		0			0
$991$	40.1009			1.27385			0.636923	−	0.770927i	$-0.280207\pi$
$991$	40.1009			1.27385			0.636923	+	0.770927i	$0.280207\pi$
$992$	2.07958	+	19.7859i	0.0660267	+	0.628202i
$993$		0			0
$994$	13.4399	−	2.85674i	0.426288	−	0.0906104i
$995$	−1.28899	+	12.2640i	−0.0408638	+	0.388793i
$996$		0			0
$997$	10.7931	+	11.9870i	0.341822	+	0.379632i	0.889405	−	0.457119i	$-0.151119\pi$
$997$	10.7931	+	11.9870i	0.341822	+	0.379632i	−0.547583	+	0.836751i	$0.684452\pi$
$998$	−9.97461	−	30.6987i	−0.315741	−	0.971750i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.n.b.289.8		72
3.2	odd	2		99.2.m.b.25.2	yes	72
9.2	odd	6		891.2.f.f.487.2		36
9.4	even	3	inner	297.2.n.b.91.2		72
9.5	odd	6		99.2.m.b.58.8	yes	72
9.7	even	3		891.2.f.e.487.8		36
11.4	even	5	inner	297.2.n.b.235.2		72
33.2	even	10		1089.2.e.o.727.15		36
33.20	odd	10		1089.2.e.p.727.4		36
33.26	odd	10		99.2.m.b.70.8	yes	72
99.2	even	30		9801.2.a.co.1.4		18
99.4	even	15	inner	297.2.n.b.37.8		72
99.20	odd	30		9801.2.a.cm.1.15		18
99.59	odd	30		99.2.m.b.4.2	✓	72
99.68	even	30		1089.2.e.o.364.15		36
99.70	even	15		891.2.f.e.730.8		36
99.79	odd	30		9801.2.a.cn.1.15		18
99.86	odd	30		1089.2.e.p.364.4		36
99.92	odd	30		891.2.f.f.730.2		36
99.97	even	15		9801.2.a.cp.1.4		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.2	✓	72	99.59	odd	30
99.2.m.b.25.2	yes	72	3.2	odd	2
99.2.m.b.58.8	yes	72	9.5	odd	6
99.2.m.b.70.8	yes	72	33.26	odd	10
297.2.n.b.37.8		72	99.4	even	15	inner
297.2.n.b.91.2		72	9.4	even	3	inner
297.2.n.b.235.2		72	11.4	even	5	inner
297.2.n.b.289.8		72	1.1	even	1	trivial
891.2.f.e.487.8		36	9.7	even	3
891.2.f.e.730.8		36	99.70	even	15
891.2.f.f.487.2		36	9.2	odd	6
891.2.f.f.730.2		36	99.92	odd	30
1089.2.e.o.364.15		36	99.68	even	30
1089.2.e.o.727.15		36	33.2	even	10
1089.2.e.p.364.4		36	99.86	odd	30
1089.2.e.p.727.4		36	33.20	odd	10
9801.2.a.cm.1.15		18	99.20	odd	30
9801.2.a.cn.1.15		18	99.79	odd	30
9801.2.a.co.1.4		18	99.2	even	30
9801.2.a.cp.1.4		18	99.97	even	15

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.161615 + 1.53767i) q^{2} +(-0.382004 + 0.0811974i) q^{4} +(0.0618842 - 0.588789i) q^{5} +(0.483079 + 0.536514i) q^{7} +(0.768973 + 2.36665i) q^{8} +0.915362 q^{10} +(2.56419 + 2.10355i) q^{11} +(-1.43880 - 0.640596i) q^{13} +(-0.746906 + 0.829524i) q^{14} +(-4.22840 + 1.88260i) q^{16} +(3.71501 + 2.69911i) q^{17} +(0.775200 + 2.38582i) q^{19} +(0.0241681 + 0.229944i) q^{20} +(-2.82014 + 4.28284i) q^{22} +(-2.22600 - 3.85554i) q^{23} +(4.54790 + 0.966685i) q^{25} +(0.752490 - 2.31593i) q^{26} +(-0.228102 - 0.165726i) q^{28} +(-4.66961 - 5.18613i) q^{29} +(-8.33906 - 3.71279i) q^{31} +(-1.08974 - 1.88749i) q^{32} +(-3.54993 + 6.14866i) q^{34} +(0.345788 - 0.251230i) q^{35} +(0.893583 - 2.75017i) q^{37} +(-3.54331 + 1.57758i) q^{38} +(1.44105 - 0.306304i) q^{40} +(0.772257 - 0.857678i) q^{41} +(2.10724 - 3.64985i) q^{43} +(-1.15033 - 0.595357i) q^{44} +(5.56879 - 4.04596i) q^{46} +(-0.222583 - 0.0473114i) q^{47} +(0.677218 - 6.44330i) q^{49} +(-0.751430 + 7.14938i) q^{50} +(0.601643 + 0.127883i) q^{52} +(-4.61430 + 3.35249i) q^{53} +(1.39723 - 1.37959i) q^{55} +(-0.898268 + 1.55585i) q^{56} +(7.21985 - 8.01846i) q^{58} +(6.97767 - 1.48315i) q^{59} +(4.16481 - 1.85429i) q^{61} +(4.36131 - 13.4227i) q^{62} +(-4.76295 + 3.46049i) q^{64} +(-0.466215 + 0.807507i) q^{65} +(4.04571 + 7.00738i) q^{67} +(-1.63831 - 0.729422i) q^{68} +(0.442192 + 0.491104i) q^{70} +(-9.95852 - 7.23528i) q^{71} +(4.78461 - 14.7255i) q^{73} +(4.37326 + 0.929564i) q^{74} +(-0.489852 - 0.848448i) q^{76} +(0.110128 + 2.39191i) q^{77} +(1.52816 + 14.5395i) q^{79} +(0.846785 + 2.60614i) q^{80} +(1.44363 + 1.04886i) q^{82} +(6.35188 - 2.82804i) q^{83} +(1.81911 - 2.02032i) q^{85} +(5.95281 + 2.65036i) q^{86} +(-3.00657 + 7.68613i) q^{88} -12.4803 q^{89} +(-0.351367 - 1.08140i) q^{91} +(1.16340 + 1.29209i) q^{92} +(0.0367764 - 0.349904i) q^{94} +(1.45272 - 0.308785i) q^{95} +(-1.48226 - 14.1028i) q^{97} +10.0171 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) \) 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Introduction

L-functions

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