LMFDB - Embedded newform 671.2.f.a.538.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(538,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("671.538");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$60$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			538.12
Character	$\chi$	$=$	671.538
Dual form			671.2.f.a.560.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31077 - 1.31077i) q^{2} -1.31199i q^{3} +1.43623i q^{4} +0.632792i q^{5} +(-1.71972 + 1.71972i) q^{6} +(2.27656 + 2.27656i) q^{7} +(-0.738974 + 0.738974i) q^{8} +1.27868 q^{9} +O(q^{10})$	\(q+(-1.31077 - 1.31077i) q^{2} -1.31199i q^{3} +1.43623i q^{4} +0.632792i q^{5} +(-1.71972 + 1.71972i) q^{6} +(2.27656 + 2.27656i) q^{7} +(-0.738974 + 0.738974i) q^{8} +1.27868 q^{9} +(0.829444 - 0.829444i) q^{10} +(-3.31432 - 0.123721i) q^{11} +1.88432 q^{12} -2.23007i q^{13} -5.96808i q^{14} +0.830218 q^{15} +4.80971 q^{16} +(-1.39968 + 1.39968i) q^{17} +(-1.67605 - 1.67605i) q^{18} +1.05573 q^{19} -0.908834 q^{20} +(2.98682 - 2.98682i) q^{21} +(4.18213 + 4.50647i) q^{22} +(5.68099 - 5.68099i) q^{23} +(0.969528 + 0.969528i) q^{24} +4.59957 q^{25} +(-2.92311 + 2.92311i) q^{26} -5.61359i q^{27} +(-3.26966 + 3.26966i) q^{28} +(5.50074 - 5.50074i) q^{29} +(-1.08822 - 1.08822i) q^{30} +(-2.52003 - 2.52003i) q^{31} +(-4.82646 - 4.82646i) q^{32} +(-0.162321 + 4.34836i) q^{33} +3.66930 q^{34} +(-1.44059 + 1.44059i) q^{35} +1.83647i q^{36} +(3.40424 + 3.40424i) q^{37} +(-1.38382 - 1.38382i) q^{38} -2.92584 q^{39} +(-0.467617 - 0.467617i) q^{40} +0.588200 q^{41} -7.83007 q^{42} +(5.74665 - 5.74665i) q^{43} +(0.177691 - 4.76011i) q^{44} +0.809137i q^{45} -14.8929 q^{46} -7.94842 q^{47} -6.31029i q^{48} +3.36543i q^{49} +(-6.02898 - 6.02898i) q^{50} +(1.83636 + 1.83636i) q^{51} +3.20290 q^{52} +(-3.58343 + 3.58343i) q^{53} +(-7.35812 + 7.35812i) q^{54} +(0.0782895 - 2.09727i) q^{55} -3.36464 q^{56} -1.38511i q^{57} -14.4204 q^{58} +(2.44367 + 2.44367i) q^{59} +1.19238i q^{60} +(-5.56181 - 5.48327i) q^{61} +6.60635i q^{62} +(2.91098 + 2.91098i) q^{63} +3.03334i q^{64} +1.41117 q^{65} +(5.91245 - 5.48692i) q^{66} +(6.48385 + 6.48385i) q^{67} +(-2.01025 - 2.01025i) q^{68} +(-7.45342 - 7.45342i) q^{69} +3.77655 q^{70} +(7.96951 + 7.96951i) q^{71} +(-0.944911 + 0.944911i) q^{72} +2.25311i q^{73} -8.92434i q^{74} -6.03460i q^{75} +1.51627i q^{76} +(-7.26357 - 7.82689i) q^{77} +(3.83510 + 3.83510i) q^{78} +(4.51038 + 4.51038i) q^{79} +3.04354i q^{80} -3.52895 q^{81} +(-0.770994 - 0.770994i) q^{82} -4.27880i q^{83} +(4.28976 + 4.28976i) q^{84} +(-0.885704 - 0.885704i) q^{85} -15.0651 q^{86} +(-7.21692 - 7.21692i) q^{87} +(2.54062 - 2.35777i) q^{88} +(-0.478541 - 0.478541i) q^{89} +(1.06059 - 1.06059i) q^{90} +(5.07689 - 5.07689i) q^{91} +(8.15920 + 8.15920i) q^{92} +(-3.30626 + 3.30626i) q^{93} +(10.4185 + 10.4185i) q^{94} +0.668058i q^{95} +(-6.33228 + 6.33228i) q^{96} -5.83972i q^{97} +(4.41130 - 4.41130i) q^{98} +(-4.23794 - 0.158199i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 120 q^{9}+O(q^{10}) $ 120 * q - 120 * q^9	$ 120 q - 120 q^{9} - 4 q^{11} + 16 q^{12} + 16 q^{15} - 148 q^{16} + 56 q^{20} - 4 q^{22} - 4 q^{23} - 104 q^{25} + 40 q^{26} - 2 q^{33} - 8 q^{34} - 12 q^{37} + 20 q^{38} + 16 q^{42} - 10 q^{44} - 4 q^{53} + 50 q^{55} - 24 q^{56} + 64 q^{58} - 56 q^{67} + 68 q^{69} + 144 q^{70} - 12 q^{71} - 64 q^{77} + 84 q^{78} + 72 q^{81} + 40 q^{82} - 80 q^{86} + 4 q^{89} - 4 q^{91} + 4 q^{92} + 64 q^{93} + 24 q^{99}+O(q^{100}) $ 120 * q - 120 * q^9 - 4 * q^11 + 16 * q^12 + 16 * q^15 - 148 * q^16 + 56 * q^20 - 4 * q^22 - 4 * q^23 - 104 * q^25 + 40 * q^26 - 2 * q^33 - 8 * q^34 - 12 * q^37 + 20 * q^38 + 16 * q^42 - 10 * q^44 - 4 * q^53 + 50 * q^55 - 24 * q^56 + 64 * q^58 - 56 * q^67 + 68 * q^69 + 144 * q^70 - 12 * q^71 - 64 * q^77 + 84 * q^78 + 72 * q^81 + 40 * q^82 - 80 * q^86 + 4 * q^89 - 4 * q^91 + 4 * q^92 + 64 * q^93 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/671\mathbb{Z}\right)^\times$.

$n$	$123$	$551$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.31077	−	1.31077i	−0.926853	−	0.926853i	0.0706480	−	0.997501i	$-0.477493\pi$
$2$	−1.31077	−	1.31077i	−0.926853	−	0.926853i	−0.997501	+	0.0706480i	$0.977493\pi$
$3$		−	1.31199i		−	0.757479i	−0.925503	−	0.378739i	$-0.876358\pi$
$3$		−	1.31199i		−	0.757479i	0.925503	−	0.378739i	$-0.123642\pi$
$4$			1.43623i			0.718114i
$5$			0.632792i			0.282993i	0.989939	+	0.141497i	$0.0451914\pi$
$5$			0.632792i			0.282993i	−0.989939	+	0.141497i	$0.954809\pi$
$6$	−1.71972	+	1.71972i	−0.702072	+	0.702072i
$7$	2.27656	+	2.27656i	0.860458	+	0.860458i	0.991391	−	0.130933i	$-0.0417974\pi$
$7$	2.27656	+	2.27656i	0.860458	+	0.860458i	−0.130933	+	0.991391i	$0.541797\pi$
$8$	−0.738974	+	0.738974i	−0.261267	+	0.261267i
$9$	1.27868			0.426226
$10$	0.829444	−	0.829444i	0.262293	−	0.262293i
$11$	−3.31432	−	0.123721i	−0.999304	−	0.0373032i
$11$	−3.31432	−	0.123721i	−0.999304	−	0.0373032i
$12$	1.88432			0.543956
$13$		−	2.23007i		−	0.618511i	−0.950979	−	0.309256i	$-0.899920\pi$
$13$		−	2.23007i		−	0.618511i	0.950979	−	0.309256i	$-0.100080\pi$
$14$		−	5.96808i		−	1.59504i
$15$	0.830218			0.214361
$16$	4.80971			1.20243
$17$	−1.39968	+	1.39968i	−0.339471	+	0.339471i	−0.856168	−	0.516697i	$-0.827161\pi$
$17$	−1.39968	+	1.39968i	−0.339471	+	0.339471i	0.516697	+	0.856168i	$0.327161\pi$
$18$	−1.67605	−	1.67605i	−0.395049	−	0.395049i
$19$	1.05573			0.242201			0.121101	−	0.992640i	$-0.461358\pi$
$19$	1.05573			0.242201			0.121101	+	0.992640i	$0.461358\pi$
$20$	−0.908834			−0.203221
$21$	2.98682	−	2.98682i	0.651779	−	0.651779i
$22$	4.18213	+	4.50647i	0.891634	+	0.960783i
$23$	5.68099	−	5.68099i	1.18457	−	1.18457i	0.206021	−	0.978547i	$-0.433948\pi$
$23$	5.68099	−	5.68099i	1.18457	−	1.18457i	0.978547	−	0.206021i	$-0.0660517\pi$
$24$	0.969528	+	0.969528i	0.197904	+	0.197904i
$25$	4.59957			0.919915
$26$	−2.92311	+	2.92311i	−0.573269	+	0.573269i
$27$		−	5.61359i		−	1.08034i
$28$	−3.26966	+	3.26966i	−0.617907	+	0.617907i
$29$	5.50074	−	5.50074i	1.02146	−	1.02146i	0.0216970	−	0.999765i	$-0.493093\pi$
$29$	5.50074	−	5.50074i	1.02146	−	1.02146i	0.999765	−	0.0216970i	$-0.00690691\pi$
$30$	−1.08822	−	1.08822i	−0.198682	−	0.198682i
$31$	−2.52003	−	2.52003i	−0.452611	−	0.452611i	0.443610	−	0.896220i	$-0.353698\pi$
$31$	−2.52003	−	2.52003i	−0.452611	−	0.452611i	−0.896220	+	0.443610i	$0.853698\pi$
$32$	−4.82646	−	4.82646i	−0.853206	−	0.853206i
$33$	−0.162321	+	4.34836i	−0.0282564	+	0.756951i
$34$	3.66930			0.629280
$35$	−1.44059	+	1.44059i	−0.243504	+	0.243504i
$36$			1.83647i			0.306079i
$37$	3.40424	+	3.40424i	0.559653	+	0.559653i	0.929209	−	0.369555i	$-0.120490\pi$
$37$	3.40424	+	3.40424i	0.559653	+	0.559653i	−0.369555	+	0.929209i	$0.620490\pi$
$38$	−1.38382	−	1.38382i	−0.224485	−	0.224485i
$39$	−2.92584			−0.468509
$40$	−0.467617	−	0.467617i	−0.0739368	−	0.0739368i
$41$	0.588200			0.0918614			0.0459307	−	0.998945i	$-0.485375\pi$
$41$	0.588200			0.0918614			0.0459307	+	0.998945i	$0.485375\pi$
$42$	−7.83007			−1.20821
$43$	5.74665	−	5.74665i	0.876356	−	0.876356i	−0.116800	−	0.993156i	$-0.537264\pi$
$43$	5.74665	−	5.74665i	0.876356	−	0.876356i	0.993156	+	0.116800i	$0.0372635\pi$
$44$	0.177691	−	4.76011i	0.0267880	−	0.717614i
$45$			0.809137i			0.120619i
$46$	−14.8929			−2.19584
$47$	−7.94842			−1.15940			−0.579698	−	0.814831i	$-0.696830\pi$
$47$	−7.94842			−1.15940			−0.579698	+	0.814831i	$0.696830\pi$
$48$		−	6.31029i		−	0.910812i
$49$			3.36543i			0.480776i
$50$	−6.02898	−	6.02898i	−0.852626	−	0.852626i
$51$	1.83636	+	1.83636i	0.257142	+	0.257142i
$52$	3.20290			0.444162
$53$	−3.58343	+	3.58343i	−0.492222	+	0.492222i	−0.909006	−	0.416784i	$-0.863157\pi$
$53$	−3.58343	+	3.58343i	−0.492222	+	0.492222i	0.416784	+	0.909006i	$0.363157\pi$
$54$	−7.35812	+	7.35812i	−1.00131	+	1.00131i
$55$	0.0782895	−	2.09727i	0.0105566	−	0.282796i
$56$	−3.36464			−0.449618
$57$		−	1.38511i		−	0.183462i
$58$	−14.4204			−1.89349
$59$	2.44367	+	2.44367i	0.318138	+	0.318138i	0.848052	−	0.529913i	$-0.177776\pi$
$59$	2.44367	+	2.44367i	0.318138	+	0.318138i	−0.529913	+	0.848052i	$0.677776\pi$
$60$			1.19238i			0.153936i
$61$	−5.56181	−	5.48327i	−0.712117	−	0.702061i
$61$	−5.56181	−	5.48327i	−0.712117	−	0.702061i
$62$			6.60635i			0.839007i
$63$	2.91098	+	2.91098i	0.366750	+	0.366750i
$64$			3.03334i			0.379167i
$65$	1.41117			0.175035
$66$	5.91245	−	5.48692i	0.727772	−	0.675393i
$67$	6.48385	+	6.48385i	0.792128	+	0.792128i	0.981840	−	0.189712i	$-0.0607553\pi$
$67$	6.48385	+	6.48385i	0.792128	+	0.792128i	−0.189712	+	0.981840i	$0.560755\pi$
$68$	−2.01025	−	2.01025i	−0.243779	−	0.243779i
$69$	−7.45342	−	7.45342i	−0.897286	−	0.897286i
$70$	3.77655			0.451385
$71$	7.96951	+	7.96951i	0.945806	+	0.945806i	0.998605	−	0.0527987i	$-0.0168142\pi$
$71$	7.96951	+	7.96951i	0.945806	+	0.945806i	−0.0527987	+	0.998605i	$0.516814\pi$
$72$	−0.944911	+	0.944911i	−0.111359	+	0.111359i
$73$			2.25311i			0.263707i	0.991269	+	0.131853i	$0.0420928\pi$
$73$			2.25311i			0.263707i	−0.991269	+	0.131853i	$0.957907\pi$
$74$		−	8.92434i		−	1.03743i
$75$		−	6.03460i		−	0.696816i
$76$			1.51627i			0.173928i
$77$	−7.26357	−	7.82689i	−0.827761	−	0.891957i
$78$	3.83510	+	3.83510i	0.434239	+	0.434239i
$79$	4.51038	+	4.51038i	0.507457	+	0.507457i	0.913745	−	0.406288i	$-0.133177\pi$
$79$	4.51038	+	4.51038i	0.507457	+	0.507457i	−0.406288	+	0.913745i	$0.633177\pi$
$80$			3.04354i			0.340279i
$81$	−3.52895			−0.392105
$82$	−0.770994	−	0.770994i	−0.0851420	−	0.0851420i
$83$		−	4.27880i		−	0.469659i	−0.972037	−	0.234829i	$-0.924547\pi$
$83$		−	4.27880i		−	0.469659i	0.972037	−	0.234829i	$-0.0754532\pi$
$84$	4.28976	+	4.28976i	0.468051	+	0.468051i
$85$	−0.885704	−	0.885704i	−0.0960680	−	0.0960680i
$86$	−15.0651			−1.62451
$87$	−7.21692	−	7.21692i	−0.773735	−	0.773735i
$88$	2.54062	−	2.35777i	0.270831	−	0.251339i
$89$	−0.478541	−	0.478541i	−0.0507253	−	0.0507253i	0.681289	−	0.732014i	$-0.261420\pi$
$89$	−0.478541	−	0.478541i	−0.0507253	−	0.0507253i	−0.732014	+	0.681289i	$0.761420\pi$
$90$	1.06059	−	1.06059i	0.111796	−	0.111796i
$91$	5.07689	−	5.07689i	0.532203	−	0.532203i
$92$	8.15920	+	8.15920i	0.850656	+	0.850656i
$93$	−3.30626	+	3.30626i	−0.342843	+	0.342843i
$94$	10.4185	+	10.4185i	1.07459	+	1.07459i
$95$			0.668058i			0.0685413i
$96$	−6.33228	+	6.33228i	−0.646285	+	0.646285i
$97$		−	5.83972i		−	0.592933i	−0.955043	−	0.296467i	$-0.904192\pi$
$97$		−	5.83972i		−	0.592933i	0.955043	−	0.296467i	$-0.0958084\pi$
$98$	4.41130	−	4.41130i	0.445609	−	0.445609i
$99$	−4.23794	−	0.158199i	−0.425929	−	0.0158996i
$100$			6.60604i			0.660604i
$101$	−4.50732	−	4.50732i	−0.448495	−	0.448495i	0.446359	−	0.894854i	$-0.352720\pi$
$101$	−4.50732	−	4.50732i	−0.448495	−	0.448495i	−0.894854	+	0.446359i	$0.852720\pi$
$102$		−	4.81409i		−	0.476666i
$103$	−14.5157			−1.43028			−0.715138	−	0.698984i	$-0.753636\pi$
$103$	−14.5157			−1.43028			−0.715138	+	0.698984i	$0.753636\pi$
$104$	1.64797	+	1.64797i	0.161597	+	0.161597i
$105$	1.89004	+	1.89004i	0.184449	+	0.184449i
$106$	9.39409			0.912434
$107$	−5.56106			−0.537608			−0.268804	−	0.963195i	$-0.586628\pi$
$107$	−5.56106			−0.537608			−0.268804	+	0.963195i	$0.586628\pi$
$108$	8.06239			0.775804
$109$	16.3192			1.56309			0.781547	−	0.623846i	$-0.214431\pi$
$109$	16.3192			1.56309			0.781547	+	0.623846i	$0.214431\pi$
$110$	−2.85166	+	2.64642i	−0.271895	+	0.252326i
$111$	4.46633	−	4.46633i	0.423926	−	0.423926i
$112$	10.9496	+	10.9496i	1.03464	+	1.03464i
$113$			5.69736i			0.535963i	0.963424	+	0.267981i	$0.0863566\pi$
$113$			5.69736i			0.535963i	−0.963424	+	0.267981i	$0.913643\pi$
$114$	−1.81556	+	1.81556i	−0.170043	+	0.170043i
$115$	3.59489	+	3.59489i	0.335225	+	0.335225i
$116$	7.90032	+	7.90032i	0.733526	+	0.733526i
$117$		−	2.85155i		−	0.263626i
$118$		−	6.40616i		−	0.589735i
$119$	−6.37288			−0.584201
$120$	−0.613510	+	0.613510i	−0.0560055	+	0.0560055i
$121$	10.9694	+	0.820100i	0.997217	+	0.0745545i
$122$	0.102946	+	14.4775i	0.00932030	+	1.31074i
$123$		−	0.771713i		−	0.0695830i
$124$	3.61934	−	3.61934i	0.325026	−	0.325026i
$125$			6.07453i			0.543323i
$126$		−	7.63125i		−	0.679846i
$127$	−8.81320			−0.782045			−0.391022	−	0.920381i	$-0.627878\pi$
$127$	−8.81320			−0.782045			−0.391022	+	0.920381i	$0.627878\pi$
$128$	−5.67692	+	5.67692i	−0.501774	+	0.501774i
$129$	−7.53956	−	7.53956i	−0.663821	−	0.663821i
$130$	−1.84972	−	1.84972i	−0.162231	−	0.162231i
$131$		−	11.4433i		−	0.999806i	−0.866081	−	0.499903i	$-0.833369\pi$
$131$		−	11.4433i		−	0.999806i	0.866081	−	0.499903i	$-0.166631\pi$
$132$	−6.24523	−	0.233129i	−0.543577	−	0.0202913i
$133$	2.40343	+	2.40343i	0.208404	+	0.208404i
$134$		−	16.9977i		−	1.46837i
$135$	3.55224			0.305728
$136$		−	2.06865i		−	0.177385i
$137$	10.4554			0.893261			0.446630	−	0.894719i	$-0.352624\pi$
$137$	10.4554			0.893261			0.446630	+	0.894719i	$0.352624\pi$
$138$			19.5394i			1.66330i
$139$	5.13905	−	5.13905i	0.435889	−	0.435889i	−0.454737	−	0.890626i	$-0.650267\pi$
$139$	5.13905	−	5.13905i	0.435889	−	0.435889i	0.890626	+	0.454737i	$0.150267\pi$
$140$	−2.06901	−	2.06901i	−0.174863	−	0.174863i
$141$			10.4283i			0.878218i
$142$		−	20.8924i		−	1.75325i
$143$	−0.275907	+	7.39117i	−0.0230725	+	0.618081i
$144$	6.15006			0.512505
$145$	3.48082	+	3.48082i	0.289067	+	0.289067i
$146$	2.95331	−	2.95331i	0.244417	−	0.244417i
$147$	4.41542			0.364177
$148$	−4.88926	+	4.88926i	−0.401895	+	0.401895i
$149$	14.4824			1.18645			0.593224	−	0.805038i	$-0.297855\pi$
$149$	14.4824			1.18645			0.593224	+	0.805038i	$0.297855\pi$
$150$	−7.90997	+	7.90997i	−0.645846	+	0.645846i
$151$	−1.77606	+	1.77606i	−0.144534	+	0.144534i	−0.775671	−	0.631137i	$-0.782588\pi$
$151$	−1.77606	+	1.77606i	−0.144534	+	0.144534i	0.631137	+	0.775671i	$0.282588\pi$
$152$	−0.780158	+	0.780158i	−0.0632792	+	0.0632792i
$153$	−1.78973	+	1.78973i	−0.144691	+	0.144691i
$154$	−0.738376	+	19.7801i	−0.0595000	+	1.59393i
$155$	1.59465	−	1.59465i	0.128086	−	0.128086i
$156$		−	4.20217i		−	0.336443i
$157$	13.1787	+	13.1787i	1.05178	+	1.05178i	0.998584	+	0.0531945i	$0.0169403\pi$
$157$	13.1787	+	13.1787i	1.05178	+	1.05178i	0.0531945	+	0.998584i	$0.483060\pi$
$158$		−	11.8241i		−	0.940676i
$159$	4.70143	+	4.70143i	0.372847	+	0.372847i
$160$	3.05415	−	3.05415i	0.241451	−	0.241451i
$161$	25.8662			2.03854
$162$	4.62563	+	4.62563i	0.363424	+	0.363424i
$163$		−	10.9730i		−	0.859474i	−0.902954	−	0.429737i	$-0.858606\pi$
$163$		−	10.9730i		−	0.859474i	0.902954	−	0.429737i	$-0.141394\pi$
$164$			0.844789i			0.0659669i
$165$	−2.75160	−	0.102715i	−0.214212	−	0.00799637i
$166$	−5.60851	+	5.60851i	−0.435305	+	0.435305i
$167$	−6.48754			−0.502021			−0.251011	−	0.967984i	$-0.580763\pi$
$167$	−6.48754			−0.502021			−0.251011	+	0.967984i	$0.580763\pi$
$168$			4.41437i			0.340576i
$169$	8.02677			0.617444
$170$			2.32190i			0.178082i
$171$	1.34994			0.103232
$172$	8.25350	+	8.25350i	0.629323	+	0.629323i
$173$	11.6813	+	11.6813i	0.888115	+	0.888115i	0.994342	−	0.106227i	$-0.0338771\pi$
$173$	11.6813	+	11.6813i	0.888115	+	0.888115i	−0.106227	+	0.994342i	$0.533877\pi$
$174$			18.9194i			1.43428i
$175$	10.4712	+	10.4712i	0.791548	+	0.791548i
$176$	−15.9409	−	0.595060i	−1.20159	−	0.0448544i
$177$	3.20607	−	3.20607i	0.240983	−	0.240983i
$178$			1.25451i			0.0940298i
$179$	−12.6004			−0.941799			−0.470900	−	0.882187i	$-0.656071\pi$
$179$	−12.6004			−0.941799			−0.470900	+	0.882187i	$0.656071\pi$
$180$	−1.16211			−0.0866183
$181$	12.1206	+	12.1206i	0.900916	+	0.900916i	0.995515	−	0.0945990i	$-0.0301569\pi$
$181$	12.1206	+	12.1206i	0.900916	+	0.900916i	−0.0945990	+	0.995515i	$0.530157\pi$
$182$	−13.3093			−0.986548
$183$	−7.19401	+	7.29705i	−0.531796	+	0.539413i
$184$			8.39622i			0.618977i
$185$	−2.15418	+	2.15418i	−0.158378	+	0.158378i
$186$	8.66747			0.635530
$187$	4.81214	−	4.46580i	0.351898	−	0.326572i
$188$		−	11.4157i		−	0.832579i
$189$	12.7797	−	12.7797i	0.929584	−	0.929584i
$190$	0.875670	−	0.875670i	0.0635278	−	0.0635278i
$191$	0.169335	+	0.169335i	0.0122526	+	0.0122526i	0.713207	−	0.700954i	$-0.247242\pi$
$191$	0.169335	+	0.169335i	0.0122526	+	0.0122526i	−0.700954	+	0.713207i	$0.747242\pi$
$192$	3.97971			0.287211
$193$	−18.1011	+	18.1011i	−1.30294	+	1.30294i	−0.376545	+	0.926398i	$0.622888\pi$
$193$	−18.1011	+	18.1011i	−1.30294	+	1.30294i	−0.926398	+	0.376545i	$0.877112\pi$
$194$	−7.65452	+	7.65452i	−0.549562	+	0.549562i
$195$		−	1.85145i		−	0.132585i
$196$	−4.83352			−0.345252
$197$	−25.6781			−1.82949			−0.914744	−	0.404033i	$-0.867608\pi$
$197$	−25.6781			−1.82949			−0.914744	+	0.404033i	$0.867608\pi$
$198$	5.34760	+	5.76233i	0.380037	+	0.409511i
$199$	−20.5327			−1.45553			−0.727764	−	0.685828i	$-0.759440\pi$
$199$	−20.5327			−1.45553			−0.727764	+	0.685828i	$0.759440\pi$
$200$	−3.39897	+	3.39897i	−0.240343	+	0.240343i
$201$	8.50676	−	8.50676i	0.600020	−	0.600020i
$202$			11.8161i			0.831378i
$203$	25.0455			1.75785
$204$	−2.63744	+	2.63744i	−0.184657	+	0.184657i
$205$			0.372208i			0.0259961i
$206$	19.0267	+	19.0267i	1.32566	+	1.32566i
$207$	7.26416	−	7.26416i	0.504894	−	0.504894i
$208$		−	10.7260i		−	0.743714i
$209$	−3.49903	−	0.130616i	−0.242033	−	0.00903489i
$210$		−	4.95481i		−	0.341914i
$211$	−2.70047	+	2.70047i	−0.185908	+	0.185908i	−0.793925	−	0.608016i	$-0.791966\pi$
$211$	−2.70047	+	2.70047i	−0.185908	+	0.185908i	0.608016	+	0.793925i	$0.291966\pi$
$212$	−5.14662	−	5.14662i	−0.353471	−	0.353471i
$213$	10.4559	−	10.4559i	0.716428	−	0.716428i
$214$	7.28926	+	7.28926i	0.498283	+	0.498283i
$215$	3.63644	+	3.63644i	0.248003	+	0.248003i
$216$	4.14830	+	4.14830i	0.282256	+	0.282256i
$217$		−	11.4740i		−	0.778905i
$218$	−21.3907	−	21.3907i	−1.44876	−	1.44876i
$219$	2.95606			0.199752
$220$	3.01216	+	0.112442i	0.203080	+	0.00758081i
$221$	3.12138	+	3.12138i	0.209967	+	0.209967i
$222$	−11.7087			−0.785834
$223$	−17.6242	+	17.6242i	−1.18020	+	1.18020i	−0.200509	+	0.979692i	$0.564260\pi$
$223$	−17.6242	+	17.6242i	−1.18020	+	1.18020i	−0.979692	+	0.200509i	$0.935740\pi$
$224$		−	21.9754i		−	1.46830i
$225$	5.88137			0.392092
$226$	7.46792	−	7.46792i	0.496759	−	0.496759i
$227$	2.01154	+	2.01154i	0.133510	+	0.133510i	0.770704	−	0.637193i	$-0.219905\pi$
$227$	2.01154	+	2.01154i	0.133510	+	0.133510i	−0.637193	+	0.770704i	$0.719905\pi$
$228$	1.98933			0.131747
$229$		−	25.5203i		−	1.68643i	−0.537578	−	0.843214i	$-0.680661\pi$
$229$		−	25.5203i		−	1.68643i	0.537578	−	0.843214i	$-0.319339\pi$
$230$		−	9.42413i		−	0.621409i
$231$	−10.2688	+	9.52975i	−0.675638	+	0.627011i
$232$			8.12981i			0.533748i
$233$	−8.67368	−	8.67368i	−0.568232	−	0.568232i	0.363401	−	0.931633i	$-0.381615\pi$
$233$	−8.67368	−	8.67368i	−0.568232	−	0.568232i	−0.931633	+	0.363401i	$0.881615\pi$
$234$	−3.73772	+	3.73772i	−0.244342	+	0.244342i
$235$		−	5.02970i		−	0.328101i
$236$	−3.50966	+	3.50966i	−0.228460	+	0.228460i
$237$	5.91758	−	5.91758i	0.384388	−	0.384388i
$238$	8.35337	+	8.35337i	0.541469	+	0.541469i
$239$		−	19.4141i		−	1.25579i	−0.778297	−	0.627897i	$-0.783916\pi$
$239$		−	19.4141i		−	1.25579i	0.778297	−	0.627897i	$-0.216084\pi$
$240$	3.99310			0.257754
$241$			22.1513i			1.42689i	0.700712	+	0.713444i	$0.252866\pi$
$241$			22.1513i			1.42689i	−0.700712	+	0.713444i	$0.747134\pi$
$242$	−13.3034	−	15.4533i	−0.855173	−	0.993375i
$243$		−	12.2108i		−	0.783324i
$244$	7.87523	−	7.98803i	0.504160	−	0.511381i
$245$	−2.12962			−0.136056
$246$	−1.01154	+	1.01154i	−0.0644933	+	0.0644933i
$247$		−	2.35436i		−	0.149804i
$248$	3.72447			0.236504
$249$	−5.61374			−0.355757
$250$	7.96231	−	7.96231i	0.503581	−	0.503581i
$251$	13.1791	−	13.1791i	0.831859	−	0.831859i	−0.155912	−	0.987771i	$-0.549832\pi$
$251$	13.1791	−	13.1791i	0.831859	−	0.831859i	0.987771	+	0.155912i	$0.0498316\pi$
$252$	−4.18084	+	4.18084i	−0.263368	+	0.263368i
$253$	−19.5315	+	18.1258i	−1.22793	+	1.13956i
$254$	11.5521	+	11.5521i	0.724841	+	0.724841i
$255$	−1.16204	+	1.16204i	−0.0727695	+	0.0727695i
$256$	20.9489			1.30931
$257$	−18.9725			−1.18347			−0.591737	−	0.806131i	$-0.701558\pi$
$257$	−18.9725			−1.18347			−0.591737	+	0.806131i	$0.701558\pi$
$258$			19.7652i			1.23053i
$259$			15.4999i			0.963117i
$260$			2.02677i			0.125695i
$261$	7.03367	−	7.03367i	0.435374	−	0.435374i
$262$	−14.9995	+	14.9995i	−0.926674	+	0.926674i
$263$	−0.139622			−0.00860946			−0.00430473	−	0.999991i	$-0.501370\pi$
$263$	−0.139622			−0.00860946			−0.00430473	+	0.999991i	$0.501370\pi$
$264$	−3.09337	−	3.33327i	−0.190384	−	0.205149i
$265$	−2.26756	−	2.26756i	−0.139295	−	0.139295i
$266$		−	6.30069i		−	0.386320i
$267$	−0.627842	+	0.627842i	−0.0384233	+	0.0384233i
$268$	−9.31229	+	9.31229i	−0.568838	+	0.568838i
$269$	8.18725			0.499185			0.249593	−	0.968351i	$-0.419703\pi$
$269$	8.18725			0.499185			0.249593	+	0.968351i	$0.419703\pi$
$270$	−4.65616	−	4.65616i	−0.283365	−	0.283365i
$271$	1.98050			0.120307			0.0601533	−	0.998189i	$-0.480841\pi$
$271$	1.98050			0.120307			0.0601533	+	0.998189i	$0.480841\pi$
$272$	−6.73203	+	6.73203i	−0.408189	+	0.408189i
$273$	−6.66084	−	6.66084i	−0.403132	−	0.403132i
$274$	−13.7045	−	13.7045i	−0.827922	−	0.827922i
$275$	−15.2444	−	0.569063i	−0.919275	−	0.0343158i
$276$	10.7048	−	10.7048i	0.644353	−	0.644353i
$277$	−22.6894	−	22.6894i	−1.36328	−	1.36328i	−0.869707	−	0.493568i	$-0.835692\pi$
$277$	−22.6894	−	22.6894i	−1.36328	−	1.36328i	−0.493568	−	0.869707i	$-0.664308\pi$
$278$	−13.4722			−0.808009
$279$	−3.22231	−	3.22231i	−0.192914	−	0.192914i
$280$		−	2.12912i		−	0.127239i
$281$	−5.67885	+	5.67885i	−0.338772	+	0.338772i	−0.855905	−	0.517133i	$-0.826999\pi$
$281$	−5.67885	+	5.67885i	−0.338772	+	0.338772i	0.517133	+	0.855905i	$0.326999\pi$
$282$	13.6690	−	13.6690i	0.813979	−	0.813979i
$283$	−7.54161			−0.448302			−0.224151	−	0.974554i	$-0.571961\pi$
$283$	−7.54161			−0.448302			−0.224151	+	0.974554i	$0.571961\pi$
$284$	−11.4460	+	11.4460i	−0.679197	+	0.679197i
$285$	0.876487			0.0519186
$286$	10.0498	−	9.32647i	0.594255	−	0.551486i
$287$	1.33907	+	1.33907i	0.0790428	+	0.0790428i
$288$	−6.17149	−	6.17149i	−0.363659	−	0.363659i
$289$			13.0818i			0.769519i
$290$		−	9.12511i		−	0.535845i
$291$	−7.66166			−0.449134
$292$	−3.23598			−0.189371
$293$	3.53842			0.206717			0.103358	−	0.994644i	$-0.467041\pi$
$293$	3.53842			0.206717			0.103358	+	0.994644i	$0.467041\pi$
$294$	−5.78759	−	5.78759i	−0.337539	−	0.337539i
$295$	−1.54633	+	1.54633i	−0.0900310	+	0.0900310i
$296$	−5.03129			−0.292438
$297$	−0.694518	+	18.6052i	−0.0403000	+	1.07958i
$298$	−18.9831	−	18.9831i	−1.09966	−	1.09966i
$299$	−12.6690	−	12.6690i	−0.732669	−	0.732669i
$300$	8.66707			0.500393
$301$	26.1652			1.50813
$302$	4.65601			0.267923
$303$	−5.91356	+	5.91356i	−0.339725	+	0.339725i
$304$	5.07775			0.291229
$305$	3.46977	−	3.51947i	0.198679	−	0.201524i
$306$	4.69185			0.268215
$307$	−19.5561	−	19.5561i	−1.11613	−	1.11613i	−0.992304	−	0.123822i	$-0.960485\pi$
$307$	−19.5561	−	19.5561i	−1.11613	−	1.11613i	−0.123822	−	0.992304i	$-0.539515\pi$
$308$	11.2412	−	10.4322i	0.640527	−	0.594427i
$309$			19.0445i			1.08340i
$310$	−4.18045			−0.237433
$311$	20.7787	+	20.7787i	1.17825	+	1.17825i	0.980189	+	0.198063i	$0.0634651\pi$
$311$	20.7787	+	20.7787i	1.17825	+	1.17825i	0.198063	+	0.980189i	$0.436535\pi$
$312$	2.16212	−	2.16212i	0.122406	−	0.122406i
$313$	0.489007	+	0.489007i	0.0276403	+	0.0276403i	0.720792	−	0.693152i	$-0.243778\pi$
$313$	0.489007	+	0.489007i	0.0276403	+	0.0276403i	−0.693152	+	0.720792i	$0.743778\pi$
$314$		−	34.5486i		−	1.94969i
$315$	−1.84205	+	1.84205i	−0.103788	+	0.103788i
$316$	−6.47793	+	6.47793i	−0.364412	+	0.364412i
$317$	10.6083			0.595820			0.297910	−	0.954594i	$-0.403711\pi$
$317$	10.6083			0.595820			0.297910	+	0.954594i	$0.403711\pi$
$318$		−	12.3250i		−	0.691150i
$319$	−18.9117	+	17.5506i	−1.05885	+	0.982647i
$320$	−1.91947			−0.107302
$321$			7.29606i			0.407226i
$322$	−33.9046	−	33.9046i	−1.88943	−	1.88943i
$323$	−1.47768	+	1.47768i	−0.0822203	+	0.0822203i
$324$		−	5.06837i		−	0.281576i
$325$		−	10.2574i		−	0.568978i
$326$	−14.3831	+	14.3831i	−0.796606	+	0.796606i
$327$		−	21.4106i		−	1.18401i
$328$	−0.434665	+	0.434665i	−0.0240003	+	0.0240003i
$329$	−18.0950	−	18.0950i	−0.997612	−	0.997612i
$330$	3.47208	+	3.74135i	0.191132	+	0.205955i
$331$	−0.171787	+	0.171787i	−0.00944226	+	0.00944226i	−0.711812	−	0.702370i	$-0.752125\pi$
$331$	−0.171787	+	0.171787i	−0.00944226	+	0.00944226i	0.702370	+	0.711812i	$0.252125\pi$
$332$	6.14533			0.337269
$333$	4.35293	+	4.35293i	0.238539	+	0.238539i
$334$	8.50367	+	8.50367i	0.465300	+	0.465300i
$335$	−4.10293	+	4.10293i	−0.224167	+	0.224167i
$336$	14.3657	−	14.3657i	0.783716	−	0.783716i
$337$	3.73348	+	3.73348i	0.203375	+	0.203375i	0.801445	−	0.598069i	$-0.204065\pi$
$337$	3.73348	+	3.73348i	0.203375	+	0.203375i	−0.598069	+	0.801445i	$0.704065\pi$
$338$	−10.5212	−	10.5212i	−0.572280	−	0.572280i
$339$	7.47489			0.405980
$340$	1.27207	−	1.27207i	0.0689878	−	0.0689878i
$341$	8.04039	+	8.66395i	0.435412	+	0.469179i
$342$	−1.76946	−	1.76946i	−0.0956814	−	0.0956814i
$343$	8.27431	−	8.27431i	0.446771	−	0.446771i
$344$			8.49326i			0.457926i
$345$	4.71646	−	4.71646i	0.253926	−	0.253926i
$346$		−	30.6230i		−	1.64630i
$347$		−	6.64600i		−	0.356776i	−0.983960	−	0.178388i	$-0.942912\pi$
$347$		−	6.64600i		−	0.356776i	0.983960	−	0.178388i	$-0.0570882\pi$
$348$	10.3651	−	10.3651i	0.555630	−	0.555630i
$349$	18.3021	+	18.3021i	0.979691	+	0.979691i	0.999798	−	0.0201069i	$-0.00640065\pi$
$349$	18.3021	+	18.3021i	0.979691	+	0.979691i	−0.0201069	+	0.999798i	$0.506401\pi$
$350$		−	27.4506i		−	1.46730i
$351$	−12.5187			−0.668200
$352$	15.3993	+	16.5936i	0.820785	+	0.884439i
$353$			29.6380i			1.57747i	0.614731	+	0.788737i	$0.289264\pi$
$353$			29.6380i			1.57747i	−0.614731	+	0.788737i	$0.710736\pi$
$354$	−8.40483			−0.446712
$355$	−5.04304	+	5.04304i	−0.267657	+	0.267657i
$356$	0.687295	−	0.687295i	0.0364265	−	0.0364265i
$357$			8.36117i			0.442520i
$358$	16.5162	+	16.5162i	0.872910	+	0.872910i
$359$	−7.11495	+	7.11495i	−0.375513	+	0.375513i	−0.869480	−	0.493967i	$-0.835546\pi$
$359$	−7.11495	+	7.11495i	−0.375513	+	0.375513i	0.493967	+	0.869480i	$0.335546\pi$
$360$	−0.597932	−	0.597932i	−0.0315138	−	0.0315138i
$361$	−17.8854			−0.941339
$362$		−	31.7746i		−	1.67003i
$363$	1.07596	−	14.3917i	0.0564735	−	0.755371i
$364$	7.29158	+	7.29158i	0.382182	+	0.382182i
$365$	−1.42575			−0.0746272
$366$	18.9944	−	0.135064i	0.992854	−	0.00705993i
$367$	−13.2971			−0.694103			−0.347052	−	0.937846i	$-0.612817\pi$
$367$	−13.2971			−0.694103			−0.347052	+	0.937846i	$0.612817\pi$
$368$	27.3239	−	27.3239i	1.42436	−	1.42436i
$369$	0.752118			0.0391537
$370$	5.64725			0.293587
$371$	−16.3158			−0.847072
$372$	−4.74854	−	4.74854i	−0.246200	−	0.246200i
$373$	11.6483	+	11.6483i	0.603124	+	0.603124i	0.941140	−	0.338016i	$-0.109756\pi$
$373$	11.6483	+	11.6483i	0.603124	+	0.603124i	−0.338016	+	0.941140i	$0.609756\pi$
$374$	−12.1612	−	0.453969i	−0.628842	−	0.0234742i
$375$	7.96974			0.411556
$376$	5.87368	−	5.87368i	0.302912	−	0.302912i
$377$	−12.2671	−	12.2671i	−0.631786	−	0.631786i
$378$	−33.5024			−1.72318
$379$	1.74503			0.0896364			0.0448182	−	0.998995i	$-0.485729\pi$
$379$	1.74503			0.0896364			0.0448182	+	0.998995i	$0.485729\pi$
$380$	−0.959484			−0.0492205
$381$			11.5628i			0.592382i
$382$		−	0.443917i		−	0.0227128i
$383$	11.1056	+	11.1056i	0.567468	+	0.567468i	0.931418	−	0.363950i	$-0.118572\pi$
$383$	11.1056	+	11.1056i	0.567468	+	0.567468i	−0.363950	+	0.931418i	$0.618572\pi$
$384$	7.44807	+	7.44807i	0.380083	+	0.380083i
$385$	4.95279	−	4.59633i	0.252418	−	0.234251i
$386$	47.4526			2.41527
$387$	7.34812	−	7.34812i	0.373526	−	0.373526i
$388$	8.38716			0.425794
$389$	5.69684	−	5.69684i	0.288841	−	0.288841i	−0.547781	−	0.836622i	$-0.684527\pi$
$389$	5.69684	−	5.69684i	0.288841	−	0.288841i	0.836622	+	0.547781i	$0.184527\pi$
$390$	−2.42682	+	2.42682i	−0.122887	+	0.122887i
$391$			15.9031i			0.804254i
$392$	−2.48697	−	2.48697i	−0.125611	−	0.125611i
$393$	−15.0135			−0.757332
$394$	33.6580	+	33.6580i	1.69567	+	1.69567i
$395$	−2.85413	+	2.85413i	−0.143607	+	0.143607i
$396$	0.227210	−	6.08665i	0.0114177	−	0.305866i
$397$	−19.1329	−	19.1329i	−0.960252	−	0.960252i	0.0389874	−	0.999240i	$-0.487587\pi$
$397$	−19.1329	−	19.1329i	−0.960252	−	0.960252i	−0.999240	+	0.0389874i	$0.987587\pi$
$398$	26.9137	+	26.9137i	1.34906	+	1.34906i
$399$	3.15328	−	3.15328i	0.157862	−	0.157862i
$400$	22.1226			1.10613
$401$	−14.4766	−	14.4766i	−0.722924	−	0.722924i	0.246275	−	0.969200i	$-0.420793\pi$
$401$	−14.4766	−	14.4766i	−0.722924	−	0.722924i	−0.969200	+	0.246275i	$0.920793\pi$
$402$	−22.3008			−1.11226
$403$	−5.61985	+	5.61985i	−0.279945	+	0.279945i
$404$	6.47353	−	6.47353i	0.322070	−	0.322070i
$405$		−	2.23309i		−	0.110963i
$406$	−32.8289	−	32.8289i	−1.62927	−	1.62927i
$407$	−10.8616	−	11.7039i	−0.538387	−	0.580141i
$408$	−2.71405			−0.134365
$409$	6.70168	−	6.70168i	0.331377	−	0.331377i	−0.521733	−	0.853109i	$-0.674714\pi$
$409$	6.70168	−	6.70168i	0.331377	−	0.331377i	0.853109	+	0.521733i	$0.174714\pi$
$410$	0.487879	−	0.487879i	0.0240946	−	0.0240946i
$411$		−	13.7173i		−	0.676626i
$412$		−	20.8479i		−	1.02710i
$413$			11.1263i			0.547489i
$414$	−19.0433			−0.935926
$415$	2.70759			0.132910
$416$	−10.7634	+	10.7634i	−0.527718	+	0.527718i
$417$	−6.74239	−	6.74239i	−0.330176	−	0.330176i
$418$	4.41521	+	4.75762i	0.215955	+	0.232703i
$419$	−8.07339	+	8.07339i	−0.394411	+	0.394411i	−0.876256	−	0.481845i	$-0.839967\pi$
$419$	−8.07339	+	8.07339i	−0.394411	+	0.394411i	0.481845	+	0.876256i	$0.339967\pi$
$420$	−2.71453	+	2.71453i	−0.132455	+	0.132455i
$421$	−11.4104	+	11.4104i	−0.556110	+	0.556110i	−0.928198	−	0.372088i	$-0.878642\pi$
$421$	−11.4104	+	11.4104i	−0.556110	+	0.556110i	0.372088	+	0.928198i	$0.378642\pi$
$422$	7.07939			0.344619
$423$	−10.1635			−0.494165
$424$		−	5.29612i		−	0.257202i
$425$	−6.43791	+	6.43791i	−0.312285	+	0.312285i
$426$	−27.4106			−1.32805
$427$	−0.178798	−	25.1448i	−0.00865264	−	1.21684i
$428$		−	7.98695i		−	0.386064i
$429$	9.69716	+	0.361987i	0.468183	+	0.0174769i
$430$		−	9.53305i		−	0.459724i
$431$	−0.733282			−0.0353209			−0.0176605	−	0.999844i	$-0.505622\pi$
$431$	−0.733282			−0.0353209			−0.0176605	+	0.999844i	$0.505622\pi$
$432$		−	26.9997i		−	1.29902i
$433$	5.05798	+	5.05798i	0.243071	+	0.243071i	0.818119	−	0.575048i	$-0.195017\pi$
$433$	5.05798	+	5.05798i	0.243071	+	0.243071i	−0.575048	+	0.818119i	$0.695017\pi$
$434$	−15.0397	+	15.0397i	−0.721930	+	0.721930i
$435$	4.56681	−	4.56681i	0.218962	−	0.218962i
$436$			23.4381i			1.12248i
$437$	5.99760	−	5.99760i	0.286904	−	0.286904i
$438$	−3.87471	−	3.87471i	−0.185141	−	0.185141i
$439$			19.2410i			0.918322i	0.888353	+	0.459161i	$0.151850\pi$
$439$			19.2410i			0.918322i	−0.888353	+	0.459161i	$0.848150\pi$
$440$	1.49198	+	1.60769i	0.0711272	+	0.0766434i
$441$			4.30330i			0.204919i
$442$		−	8.18281i		−	0.389217i
$443$	−21.9347			−1.04215			−0.521074	−	0.853512i	$-0.674468\pi$
$443$	−21.9347			−1.04215			−0.521074	+	0.853512i	$0.674468\pi$
$444$	6.41467	+	6.41467i	0.304427	+	0.304427i
$445$	0.302817	−	0.302817i	0.0143549	−	0.0143549i
$446$	46.2024			2.18775
$447$		−	19.0008i		−	0.898709i
$448$	−6.90556	+	6.90556i	−0.326257	+	0.326257i
$449$	−10.6536			−0.502773			−0.251386	−	0.967887i	$-0.580886\pi$
$449$	−10.6536			−0.502773			−0.251386	+	0.967887i	$0.580886\pi$
$450$	−7.70912	−	7.70912i	−0.363411	−	0.363411i
$451$	−1.94948	−	0.0727725i	−0.0917974	−	0.00342672i
$452$	−8.18271			−0.384882
$453$	2.33018	+	2.33018i	0.109481	+	0.109481i
$454$		−	5.27332i		−	0.247489i
$455$	3.21262	+	3.21262i	0.150610	+	0.150610i
$456$	1.02356	+	1.02356i	0.0479326	+	0.0479326i
$457$	21.3128	+	21.3128i	0.996973	+	0.996973i	0.999995	−	0.00302238i	$-0.000962054\pi$
$457$	21.3128	+	21.3128i	0.996973	+	0.996973i	−0.00302238	+	0.999995i	$0.500962\pi$
$458$	−33.4512	+	33.4512i	−1.56307	+	1.56307i
$459$	7.85720	+	7.85720i	0.366743	+	0.366743i
$460$	−5.16308	+	5.16308i	−0.240730	+	0.240730i
$461$			21.9573i			1.02265i	0.859387	+	0.511326i	$0.170845\pi$
$461$			21.9573i			1.02265i	−0.859387	+	0.511326i	$0.829155\pi$
$462$	25.9513	+	0.968742i	1.20737	+	0.0450700i
$463$			17.8335i			0.828794i	0.910096	+	0.414397i	$0.136008\pi$
$463$			17.8335i			0.828794i	−0.910096	+	0.414397i	$0.863992\pi$
$464$	26.4569	−	26.4569i	1.22823	−	1.22823i
$465$	−2.09217	−	2.09217i	−0.0970222	−	0.0970222i
$466$			22.7384i			1.05334i
$467$	5.62965	−	5.62965i	0.260509	−	0.260509i	−0.564752	−	0.825261i	$-0.691028\pi$
$467$	5.62965	−	5.62965i	0.260509	−	0.260509i	0.825261	+	0.564752i	$0.191028\pi$
$468$	4.09547			0.189313
$469$			29.5217i			1.36319i
$470$	−6.59277	+	6.59277i	−0.304102	+	0.304102i
$471$	17.2904	−	17.2904i	0.796700	−	0.796700i
$472$	−3.61161			−0.166238
$473$	−19.7572	+	18.3352i	−0.908437	+	0.843055i
$474$	−15.5131			−0.712542
$475$	4.85591			0.222805
$476$		−	9.15291i		−	0.419523i
$477$	−4.58205	+	4.58205i	−0.209798	+	0.209798i
$478$	−25.4474	+	25.4474i	−1.16394	+	1.16394i
$479$	36.7558			1.67942			0.839708	−	0.543038i	$-0.182726\pi$
$479$	36.7558			1.67942			0.839708	+	0.543038i	$0.182726\pi$
$480$	−4.00701	−	4.00701i	−0.182894	−	0.182894i
$481$	7.59171	−	7.59171i	0.346152	−	0.346152i
$482$	29.0352	−	29.0352i	1.32252	−	1.32252i
$483$		−	33.9363i		−	1.54415i
$484$	−1.17785	+	15.7545i	−0.0535386	+	0.716115i
$485$	3.69533			0.167796
$486$	−16.0056	+	16.0056i	−0.726027	+	0.726027i
$487$		−	18.2291i		−	0.826038i	−0.910722	−	0.413019i	$-0.864474\pi$
$487$		−	18.2291i		−	0.826038i	0.910722	−	0.413019i	$-0.135526\pi$
$488$	8.16203	−	0.0580381i	0.369478	−	0.00262726i
$489$	−14.3965			−0.651033
$490$	2.79144	+	2.79144i	0.126104	+	0.126104i
$491$	4.92633			0.222322			0.111161	−	0.993802i	$-0.464543\pi$
$491$	4.92633			0.222322			0.111161	+	0.993802i	$0.464543\pi$
$492$	1.10836			0.0499685
$493$			15.3985i			0.693513i
$494$	−3.08602	+	3.08602i	−0.138847	+	0.138847i
$495$	0.100107	−	2.68174i	0.00449948	−	0.120535i
$496$	−12.1206	−	12.1206i	−0.544231	−	0.544231i
$497$			36.2861i			1.62765i
$498$	7.35832	+	7.35832i	0.329734	+	0.329734i
$499$	−7.85854	−	7.85854i	−0.351797	−	0.351797i	0.508981	−	0.860778i	$-0.330022\pi$
$499$	−7.85854	−	7.85854i	−0.351797	−	0.351797i	−0.860778	+	0.508981i	$0.830022\pi$
$500$	−8.72442			−0.390168
$501$			8.51160i			0.380270i
$502$	−34.5496			−1.54202
$503$			3.90385i			0.174064i	0.996206	+	0.0870320i	$0.0277382\pi$
$503$			3.90385i			0.174064i	−0.996206	+	0.0870320i	$0.972262\pi$
$504$	−4.30229			−0.191639
$505$	2.85219	−	2.85219i	0.126921	−	0.126921i
$506$	49.3599	+	1.84257i	2.19431	+	0.0819120i
$507$		−	10.5311i		−	0.467700i
$508$		−	12.6578i		−	0.561597i
$509$	14.6650	+	14.6650i	0.650013	+	0.650013i	0.952996	−	0.302983i	$-0.0979826\pi$
$509$	14.6650	+	14.6650i	0.650013	+	0.650013i	−0.302983	+	0.952996i	$0.597983\pi$
$510$	3.04632			0.134893
$511$	−5.12933	+	5.12933i	−0.226908	+	0.226908i
$512$	−16.1054	−	16.1054i	−0.711763	−	0.711763i
$513$		−	5.92644i		−	0.261659i
$514$	24.8686	+	24.8686i	1.09691	+	1.09691i
$515$		−	9.18543i		−	0.404758i
$516$	10.8285	−	10.8285i	0.476699	−	0.476699i
$517$	26.3436	+	0.983385i	1.15859	+	0.0432492i
$518$	20.3168	−	20.3168i	0.892668	−	0.892668i
$519$	15.3258	−	15.3258i	0.672728	−	0.672728i
$520$	−1.04282	+	1.04282i	−0.0457307	+	0.0457307i
$521$	−18.2350	+	18.2350i	−0.798888	+	0.798888i	−0.982920	−	0.184032i	$-0.941085\pi$
$521$	−18.2350	+	18.2350i	−0.798888	+	0.798888i	0.184032	+	0.982920i	$0.441085\pi$
$522$	−18.4390			−0.807055
$523$	−10.6577	+	10.6577i	−0.466027	+	0.466027i	−0.900625	−	0.434598i	$-0.856890\pi$
$523$	−10.6577	+	10.6577i	−0.466027	+	0.466027i	0.434598	+	0.900625i	$0.356890\pi$
$524$	16.4352			0.717975
$525$	13.7381	−	13.7381i	0.599581	−	0.599581i
$526$	0.183012	+	0.183012i	0.00797971	+	0.00797971i
$527$	7.05444			0.307296
$528$	−0.780714	+	20.9143i	−0.0339762	+	0.910178i
$529$		−	41.5474i		−	1.80641i
$530$			5.94450i			0.258213i
$531$	3.12466	+	3.12466i	0.135599	+	0.135599i
$532$	−3.45188	+	3.45188i	−0.149658	+	0.149658i
$533$		−	1.31173i		−	0.0568173i
$534$	1.64591			0.0712256
$535$		−	3.51899i		−	0.152139i
$536$	−9.58280			−0.413914
$537$			16.5316i			0.713393i
$538$	−10.7316	−	10.7316i	−0.462672	−	0.462672i
$539$	0.416374	−	11.1541i	0.0179345	−	0.480441i
$540$			5.10182i			0.219547i
$541$	1.89315	+	1.89315i	0.0813930	+	0.0813930i	0.746631	−	0.665238i	$-0.231670\pi$
$541$	1.89315	+	1.89315i	0.0813930	+	0.0813930i	−0.665238	+	0.746631i	$0.731670\pi$
$542$	−2.59597	−	2.59597i	−0.111507	−	0.111507i
$543$	15.9021	−	15.9021i	0.682425	−	0.682425i
$544$	13.5110			0.579278
$545$			10.3266i			0.442345i
$546$			17.4616i			0.747289i
$547$	−18.4104	+	18.4104i	−0.787171	+	0.787171i	−0.981030	−	0.193858i	$-0.937900\pi$
$547$	−18.4104	+	18.4104i	−0.787171	+	0.787171i	0.193858	+	0.981030i	$0.437900\pi$
$548$			15.0163i			0.641463i
$549$	−7.11177	−	7.01134i	−0.303523	−	0.299237i
$550$	19.2360	+	20.7278i	0.820227	+	0.883838i
$551$	5.80730	−	5.80730i	0.247399	−	0.247399i
$552$	11.0158			0.468862
$553$			20.5363i			0.873291i
$554$			59.4812i			2.52711i
$555$	2.82626	+	2.82626i	0.119968	+	0.119968i
$556$	7.38085	+	7.38085i	0.313018	+	0.313018i
$557$	−31.8583	+	31.8583i	−1.34988	+	1.34988i	−0.464094	+	0.885786i	$0.653620\pi$
$557$	−31.8583	+	31.8583i	−1.34988	+	1.34988i	−0.885786	+	0.464094i	$0.846380\pi$
$558$			8.44739i			0.357607i
$559$	−12.8155	−	12.8155i	−0.542036	−	0.542036i
$560$	−6.92880	+	6.92880i	−0.292795	+	0.292795i
$561$	−5.85909	−	6.31348i	−0.247371	−	0.266555i
$562$	14.8873			0.627983
$563$	−32.1321			−1.35420			−0.677102	−	0.735889i	$-0.736765\pi$
$563$	−32.1321			−1.35420			−0.677102	+	0.735889i	$0.736765\pi$
$564$	−14.9774			−0.630661
$565$	−3.60525			−0.151674
$566$	9.88531	+	9.88531i	0.415511	+	0.415511i
$567$	−8.03385	−	8.03385i	−0.337390	−	0.337390i
$568$	−11.7785			−0.494216
$569$		−	30.5655i		−	1.28137i	−0.767802	−	0.640687i	$-0.778650\pi$
$569$		−	30.5655i		−	1.28137i	0.767802	−	0.640687i	$-0.221350\pi$
$570$	−1.14887	−	1.14887i	−0.0481209	−	0.0481209i
$571$			41.4665i			1.73532i	0.497158	+	0.867660i	$0.334377\pi$
$571$			41.4665i			1.73532i	−0.497158	+	0.867660i	$0.665623\pi$
$572$	−10.6154	−	0.396265i	−0.443853	−	0.0165687i
$573$	0.222165	−	0.222165i	0.00928109	−	0.00928109i
$574$		−	3.51042i		−	0.146522i
$575$	26.1301	−	26.1301i	1.08970	−	1.08970i
$576$			3.87866i			0.161611i
$577$	−11.0429	−	11.0429i	−0.459723	−	0.459723i	0.438841	−	0.898565i	$-0.355389\pi$
$577$	−11.0429	−	11.0429i	−0.459723	−	0.459723i	−0.898565	+	0.438841i	$0.855389\pi$
$578$	17.1472	−	17.1472i	0.713231	−	0.713231i
$579$	23.7484	+	23.7484i	0.986952	+	0.986952i
$580$	−4.99926	+	4.99926i	−0.207583	+	0.207583i
$581$	9.74092	−	9.74092i	0.404122	−	0.404122i
$582$	10.0427	+	10.0427i	0.416282	+	0.416282i
$583$	12.3200	−	11.4333i	0.510240	−	0.473518i
$584$	−1.66499	−	1.66499i	−0.0688978	−	0.0688978i
$585$	1.80444			0.0746043
$586$	−4.63806	−	4.63806i	−0.191596	−	0.191596i
$587$	−28.5163	−	28.5163i	−1.17699	−	1.17699i	−0.980507	−	0.196487i	$-0.937047\pi$
$587$	−28.5163	−	28.5163i	−1.17699	−	1.17699i	−0.196487	−	0.980507i	$-0.562953\pi$
$588$			6.34154i			0.261521i
$589$	−2.66047	−	2.66047i	−0.109623	−	0.109623i
$590$	4.05377			0.166891
$591$			33.6894i			1.38580i
$592$	16.3734	+	16.3734i	0.672942	+	0.672942i
$593$	23.9206	+	23.9206i	0.982301	+	0.982301i	0.999846	−	0.0175450i	$-0.00558504\pi$
$593$	23.9206	+	23.9206i	0.982301	+	0.982301i	−0.0175450	+	0.999846i	$0.505585\pi$
$594$	25.2975	−	23.4768i	1.03797	−	0.963264i
$595$		−	4.03271i		−	0.165325i
$596$			20.8001i			0.852005i
$597$			26.9388i			1.10253i
$598$			33.2124i			1.35815i
$599$	−7.81381	+	7.81381i	−0.319263	+	0.319263i	−0.848484	−	0.529221i	$-0.822484\pi$
$599$	−7.81381	+	7.81381i	−0.319263	+	0.319263i	0.529221	+	0.848484i	$0.322484\pi$
$600$	4.45942	+	4.45942i	0.182055	+	0.182055i
$601$	29.8748			1.21862			0.609309	−	0.792933i	$-0.291447\pi$
$601$	29.8748			1.21862			0.609309	+	0.792933i	$0.291447\pi$
$602$	−34.2965	−	34.2965i	−1.39782	−	1.39782i
$603$	8.29076	+	8.29076i	0.337626	+	0.337626i
$604$	−2.55083	−	2.55083i	−0.103792	−	0.103792i
$605$	−0.518953	+	6.94134i	−0.0210984	+	0.282206i
$606$	15.5026			0.629751
$607$		−	24.2102i		−	0.982662i	−0.870973	−	0.491331i	$-0.836511\pi$
$607$		−	24.2102i		−	0.982662i	0.870973	−	0.491331i	$-0.163489\pi$
$608$	−5.09544	−	5.09544i	−0.206648	−	0.206648i
$609$		−	32.8595i		−	1.33153i
$610$	−9.16128	+	0.0651435i	−0.370929	+	0.00263758i
$611$			17.7256i			0.717100i
$612$	−2.57047	−	2.57047i	−0.103905	−	0.103905i
$613$	34.2258			1.38237			0.691183	−	0.722680i	$-0.257090\pi$
$613$	34.2258			1.38237			0.691183	+	0.722680i	$0.257090\pi$
$614$			51.2671i			2.06897i
$615$	0.488334			0.0196915
$616$	11.1515	+	0.416275i	0.449305	+	0.0167722i
$617$	−8.45860	+	8.45860i	−0.340530	+	0.340530i	−0.856567	−	0.516036i	$-0.827407\pi$
$617$	−8.45860	+	8.45860i	−0.340530	+	0.340530i	0.516036	+	0.856567i	$0.327407\pi$
$618$	24.9629	−	24.9629i	1.00416	−	1.00416i
$619$	−38.3974			−1.54332			−0.771661	−	0.636034i	$-0.780574\pi$
$619$	−38.3974			−1.54332			−0.771661	+	0.636034i	$0.780574\pi$
$620$	2.29029	+	2.29029i	0.0919801	+	0.0919801i
$621$	−31.8908	−	31.8908i	−1.27973	−	1.27973i
$622$		−	54.4722i		−	2.18413i
$623$		−	2.17885i		−	0.0872940i
$624$	−14.0724			−0.563348
$625$	19.1540			0.766158
$626$		−	1.28195i		−	0.0512370i
$627$	−0.171367	+	4.59069i	−0.00684373	+	0.183335i
$628$	−18.9277	+	18.9277i	−0.755297	+	0.755297i
$629$	−9.52966			−0.379972
$630$	4.82900			0.192392
$631$	−9.67575	−	9.67575i	−0.385186	−	0.385186i	0.487781	−	0.872966i	$-0.337807\pi$
$631$	−9.67575	−	9.67575i	−0.385186	−	0.385186i	−0.872966	+	0.487781i	$0.837807\pi$
$632$	−6.66611			−0.265163
$633$	3.54300	+	3.54300i	0.140821	+	0.140821i
$634$	−13.9050	−	13.9050i	−0.552238	−	0.552238i
$635$		−	5.57692i		−	0.221313i
$636$	−6.75232	+	6.75232i	−0.267747	+	0.267747i
$637$	7.50516			0.297365
$638$	47.7937	+	1.78410i	1.89217	+	0.0706333i
$639$	10.1904	+	10.1904i	0.403127	+	0.403127i
$640$	−3.59231	−	3.59231i	−0.141999	−	0.141999i
$641$	28.0157	+	28.0157i	1.10655	+	1.10655i	0.993600	+	0.112955i	$0.0360315\pi$
$641$	28.0157	+	28.0157i	1.10655	+	1.10655i	0.112955	+	0.993600i	$0.463969\pi$
$642$	9.56345	−	9.56345i	0.377439	−	0.377439i
$643$	20.7743	−	20.7743i	0.819257	−	0.819257i	−0.166743	−	0.986000i	$-0.553325\pi$
$643$	20.7743	−	20.7743i	0.819257	−	0.819257i	0.986000	+	0.166743i	$0.0533251\pi$
$644$			37.1498i			1.46391i
$645$	4.77097	−	4.77097i	0.187857	−	0.187857i
$646$	3.87379			0.152412
$647$	17.0158	+	17.0158i	0.668962	+	0.668962i	0.957476	−	0.288514i	$-0.0931612\pi$
$647$	17.0158	+	17.0158i	0.668962	+	0.668962i	−0.288514	+	0.957476i	$0.593161\pi$
$648$	2.60780	−	2.60780i	0.102444	−	0.102444i
$649$	−7.79675	−	8.40142i	−0.306049	−	0.329784i
$650$	−13.4451	+	13.4451i	−0.527359	+	0.527359i
$651$	−15.0538			−0.590004
$652$	15.7598			0.617200
$653$	13.7707	+	13.7707i	0.538890	+	0.538890i	0.923203	−	0.384313i	$-0.125562\pi$
$653$	13.7707	+	13.7707i	0.538890	+	0.538890i	−0.384313	+	0.923203i	$0.625562\pi$
$654$	−28.0644	+	28.0644i	−1.09740	+	1.09740i
$655$	7.24124			0.282938
$656$	2.82907			0.110457
$657$			2.88100i			0.112399i
$658$			47.4368i			1.84928i
$659$	18.9368			0.737675			0.368837	−	0.929494i	$-0.379756\pi$
$659$	18.9368			0.737675			0.368837	+	0.929494i	$0.379756\pi$
$660$	0.147522	−	3.95193i	0.00574230	−	0.153829i
$661$	−30.4152	+	30.4152i	−1.18301	+	1.18301i	−0.204054	+	0.978960i	$0.565412\pi$
$661$	−30.4152	+	30.4152i	−1.18301	+	1.18301i	−0.978960	+	0.204054i	$0.934588\pi$
$662$	0.450346			0.0175032
$663$	4.09522	−	4.09522i	0.159045	−	0.159045i
$664$	3.16192	+	3.16192i	0.122706	+	0.122706i
$665$	−1.52087	+	1.52087i	−0.0589769	+	0.0589769i
$666$		−	11.4114i		−	0.442181i
$667$		−	62.4993i		−	2.41998i
$668$		−	9.31759i		−	0.360509i
$669$	23.1227	+	23.1227i	0.893977	+	0.893977i
$670$	10.7560			0.415540
$671$	17.7552	+	18.8614i	0.685432	+	0.728137i
$672$	−28.8316			−1.11220
$673$	10.3594	+	10.3594i	0.399325	+	0.399325i	0.877995	−	0.478670i	$-0.158881\pi$
$673$	10.3594	+	10.3594i	0.399325	+	0.399325i	−0.478670	+	0.877995i	$0.658881\pi$
$674$		−	9.78745i		−	0.376998i
$675$		−	25.8201i		−	0.993817i
$676$			11.5283i			0.443395i
$677$	17.6378	−	17.6378i	0.677878	−	0.677878i	−0.281642	−	0.959520i	$-0.590879\pi$
$677$	17.6378	−	17.6378i	0.677878	−	0.677878i	0.959520	+	0.281642i	$0.0908791\pi$
$678$	−9.79785	−	9.79785i	−0.376284	−	0.376284i
$679$	13.2944	−	13.2944i	0.510194	−	0.510194i
$680$	1.30902			0.0501988
$681$	2.63912	−	2.63912i	0.101131	−	0.101131i
$682$	0.817343	−	21.8955i	0.0312977	−	0.838423i
$683$	28.2274			1.08009			0.540046	−	0.841635i	$-0.318407\pi$
$683$	28.2274			1.08009			0.540046	+	0.841635i	$0.318407\pi$
$684$			1.93882i			0.0741327i
$685$			6.61606i			0.252787i
$686$	−21.6914			−0.828182
$687$	−33.4824			−1.27743
$688$	27.6397	−	27.6397i	1.05375	−	1.05375i
$689$	7.99131	+	7.99131i	0.304445	+	0.304445i
$690$	−12.3644			−0.470704
$691$	−26.1839			−0.996081			−0.498041	−	0.867154i	$-0.665947\pi$
$691$	−26.1839			−0.996081			−0.498041	+	0.867154i	$0.665947\pi$
$692$	−16.7770	+	16.7770i	−0.637768	+	0.637768i
$693$	−9.28777	−	10.0081i	−0.352813	−	0.380175i
$694$	−8.71136	+	8.71136i	−0.330679	+	0.330679i
$695$	3.25195	+	3.25195i	0.123354	+	0.123354i
$696$	10.6662			0.404303
$697$	−0.823289	+	0.823289i	−0.0311843	+	0.0311843i
$698$		−	47.9797i		−	1.81606i
$699$	−11.3798	+	11.3798i	−0.430423	+	0.430423i
$700$	−15.0390	+	15.0390i	−0.568422	+	0.568422i
$701$	22.3856	+	22.3856i	0.845491	+	0.845491i	0.989567	−	0.144076i	$-0.0460210\pi$
$701$	22.3856	+	22.3856i	0.845491	+	0.845491i	−0.144076	+	0.989567i	$0.546021\pi$
$702$	16.4091	+	16.4091i	0.619323	+	0.619323i
$703$	3.59396	+	3.59396i	0.135549	+	0.135549i
$704$	0.375287	−	10.0534i	0.0141441	−	0.378903i
$705$	−6.59892			−0.248530
$706$	38.8486	−	38.8486i	1.46209	−	1.46209i
$707$		−	20.5223i		−	0.771822i
$708$	4.60465	+	4.60465i	0.173053	+	0.173053i
$709$	−37.4028	−	37.4028i	−1.40469	−	1.40469i	−0.784256	−	0.620437i	$-0.786955\pi$
$709$	−37.4028	−	37.4028i	−1.40469	−	1.40469i	−0.620437	−	0.784256i	$-0.713045\pi$
$710$	13.2205			0.496157
$711$	5.76732	+	5.76732i	0.216291	+	0.216291i
$712$	0.707260			0.0265057
$713$	−28.6325			−1.07230
$714$	10.9596	−	10.9596i	0.410151	−	0.410151i
$715$	−4.67708	−	0.174592i	−0.174913	−	0.00652935i
$716$		−	18.0971i		−	0.676319i
$717$	−25.4711			−0.951237
$718$	18.6521			0.696091
$719$			4.76005i			0.177520i	0.996053	+	0.0887600i	$0.0282904\pi$
$719$			4.76005i			0.177520i	−0.996053	+	0.0887600i	$0.971710\pi$
$720$			3.89171i			0.145036i
$721$	−33.0458	−	33.0458i	−1.23069	−	1.23069i
$722$	23.4437	+	23.4437i	0.872483	+	0.872483i
$723$	29.0623			1.08084
$724$	−17.4079	+	17.4079i	−0.646961	+	0.646961i
$725$	25.3011	−	25.3011i	0.939658	−	0.939658i
$726$	−20.2746	+	17.4539i	−0.752460	+	0.647775i
$727$	−40.1719			−1.48989			−0.744947	−	0.667124i	$-0.767525\pi$
$727$	−40.1719			−1.48989			−0.744947	+	0.667124i	$0.767525\pi$
$728$			7.50339i			0.278094i
$729$	−26.6073			−0.985457
$730$	1.86883	+	1.86883i	0.0691684	+	0.0691684i
$731$			16.0869i			0.594995i
$732$	−10.4802	−	10.3322i	−0.387360	−	0.381890i
$733$		−	15.9673i		−	0.589766i	−0.955533	−	0.294883i	$-0.904719\pi$
$733$		−	15.9673i		−	0.589766i	0.955533	−	0.294883i	$-0.0952807\pi$
$734$	17.4294	+	17.4294i	0.643332	+	0.643332i
$735$			2.79404i			0.103060i
$736$	−54.8382			−2.02136
$737$	−20.6873	−	22.2917i	−0.762028	−	0.821126i
$738$	−0.985853	−	0.985853i	−0.0362897	−	0.0362897i
$739$	−15.3262	−	15.3262i	−0.563782	−	0.563782i	0.366598	−	0.930380i	$-0.380523\pi$
$739$	−15.3262	−	15.3262i	−0.563782	−	0.563782i	−0.930380	+	0.366598i	$0.880523\pi$
$740$	−3.09389	−	3.09389i	−0.113734	−	0.113734i
$741$	−3.08890			−0.113474
$742$	21.3862	+	21.3862i	0.785111	+	0.785111i
$743$	−15.8660	+	15.8660i	−0.582067	+	0.582067i	−0.935471	−	0.353404i	$-0.885024\pi$
$743$	−15.8660	+	15.8660i	−0.582067	+	0.582067i	0.353404	+	0.935471i	$0.385024\pi$
$744$		−	4.88648i		−	0.179147i
$745$			9.16437i			0.335757i
$746$		−	30.5363i		−	1.11802i
$747$		−	5.47120i		−	0.200181i
$748$	6.41390	+	6.91132i	0.234516	+	0.252703i
$749$	−12.6601	−	12.6601i	−0.462589	−	0.462589i
$750$	−10.4465	−	10.4465i	−0.381452	−	0.381452i
$751$		−	20.9355i		−	0.763947i	−0.924173	−	0.381973i	$-0.875245\pi$
$751$		−	20.9355i		−	0.763947i	0.924173	−	0.381973i	$-0.124755\pi$
$752$	−38.2296			−1.39409
$753$	−17.2909	−	17.2909i	−0.630116	−	0.630116i
$754$			32.1585i			1.17115i
$755$	−1.12388	−	1.12388i	−0.0409021	−	0.0409021i
$756$	18.3545	+	18.3545i	0.667547	+	0.667547i
$757$	−13.6114			−0.494714			−0.247357	−	0.968924i	$-0.579562\pi$
$757$	−13.6114			−0.494714			−0.247357	+	0.968924i	$0.579562\pi$
$758$	−2.28734	−	2.28734i	−0.0830798	−	0.0830798i
$759$	23.7808	+	25.6251i	0.863190	+	0.930133i
$760$	−0.493678	−	0.493678i	−0.0179076	−	0.0179076i
$761$	−28.8481	+	28.8481i	−1.04574	+	1.04574i	−0.0468411	+	0.998902i	$0.514915\pi$
$761$	−28.8481	+	28.8481i	−1.04574	+	1.04574i	−0.998902	+	0.0468411i	$0.985085\pi$
$762$	15.1562	−	15.1562i	0.549051	−	0.549051i
$763$	37.1516	+	37.1516i	1.34498	+	1.34498i
$764$	−0.243203	+	0.243203i	−0.00879877	+	0.00879877i
$765$	−1.13253	−	1.13253i	−0.0409467	−	0.0409467i
$766$		−	29.1137i		−	1.05192i
$767$	5.44956	−	5.44956i	0.196772	−	0.196772i
$768$		−	27.4848i		−	0.991773i
$769$	5.26595	−	5.26595i	0.189895	−	0.189895i	−0.605756	−	0.795651i	$-0.707129\pi$
$769$	5.26595	−	5.26595i	0.189895	−	0.189895i	0.795651	+	0.605756i	$0.207129\pi$
$770$	−12.5167	−	0.467238i	−0.451070	−	0.0168381i
$771$			24.8918i			0.896456i
$772$	−25.9973	−	25.9973i	−0.935662	−	0.935662i
$773$		−	33.0089i		−	1.18725i	−0.804742	−	0.593624i	$-0.797696\pi$
$773$		−	33.0089i		−	1.18725i	0.804742	−	0.593624i	$-0.202304\pi$
$774$	−19.2634			−0.692407
$775$	−11.5911	−	11.5911i	−0.416363	−	0.416363i
$776$	4.31540	+	4.31540i	0.154914	+	0.154914i
$777$	20.3357			0.729540
$778$	−14.9345			−0.535427
$779$	0.620981			0.0222489
$780$	2.65910			0.0952111
$781$	−25.4275	−	27.3995i	−0.909867	−	0.980430i
$782$	20.8453	−	20.8453i	0.745425	−	0.745425i
$783$	−30.8789	−	30.8789i	−1.10352	−	1.10352i
$784$			16.1867i			0.578097i
$785$	−8.33941	+	8.33941i	−0.297646	+	0.297646i
$786$	19.6793	+	19.6793i	0.701936	+	0.701936i
$787$	−12.9204	−	12.9204i	−0.460563	−	0.460563i	0.438277	−	0.898840i	$-0.355589\pi$
$787$	−12.9204	−	12.9204i	−0.460563	−	0.460563i	−0.898840	+	0.438277i	$0.855589\pi$
$788$		−	36.8796i		−	1.31378i
$789$			0.183183i			0.00652148i
$790$	7.48221			0.266205
$791$	−12.9704	+	12.9704i	−0.461174	+	0.461174i
$792$	3.24864	−	3.01483i	0.115435	−	0.107127i
$793$	−12.2281	+	12.4033i	−0.434233	+	0.440452i
$794$			50.1576i			1.78003i
$795$	−2.97503	+	2.97503i	−0.105513	+	0.105513i
$796$		−	29.4897i		−	1.04523i
$797$			30.5407i			1.08181i	0.841084	+	0.540904i	$0.181918\pi$
$797$			30.5407i			1.08181i	−0.841084	+	0.540904i	$0.818082\pi$
$798$	−8.26645			−0.292629
$799$	11.1252	−	11.1252i	0.393582	−	0.393582i
$800$	−22.1997	−	22.1997i	−0.784877	−	0.784877i
$801$	−0.611901	−	0.611901i	−0.0216204	−	0.0216204i
$802$			37.9508i			1.34009i
$803$	0.278756	−	7.46752i	0.00983710	−	0.263523i
$804$	12.2176	+	12.2176i	0.430883	+	0.430883i
$805$			16.3679i			0.576894i
$806$	14.7326			0.518935
$807$		−	10.7416i		−	0.378122i
$808$	6.66158			0.234354
$809$			11.3509i			0.399075i	0.979890	+	0.199538i	$0.0639440\pi$
$809$			11.3509i			0.399075i	−0.979890	+	0.199538i	$0.936056\pi$
$810$	−2.92706	+	2.92706i	−0.102847	+	0.102847i
$811$	−23.4798	−	23.4798i	−0.824487	−	0.824487i	0.162261	−	0.986748i	$-0.448121\pi$
$811$	−23.4798	−	23.4798i	−0.824487	−	0.824487i	−0.986748	+	0.162261i	$0.948121\pi$
$812$			35.9710i			1.26234i
$813$		−	2.59839i		−	0.0911297i
$814$	−1.10413	+	29.5781i	−0.0386996	+	1.03671i
$815$	6.94365			0.243225
$816$	8.83236	+	8.83236i	0.309194	+	0.309194i
$817$	6.06692	−	6.06692i	0.212255	−	0.212255i
$818$	−17.5687			−0.614275
$819$	6.49171	−	6.49171i	0.226839	−	0.226839i
$820$	−0.534576			−0.0186682
$821$	29.3364	−	29.3364i	1.02385	−	1.02385i	0.0241394	−	0.999709i	$-0.492315\pi$
$821$	29.3364	−	29.3364i	1.02385	−	1.02385i	0.999709	−	0.0241394i	$-0.00768454\pi$
$822$	−17.9802	+	17.9802i	−0.627133	+	0.627133i
$823$	−1.98048	+	1.98048i	−0.0690351	+	0.0690351i	−0.740781	−	0.671746i	$-0.765545\pi$
$823$	−1.98048	+	1.98048i	−0.0690351	+	0.0690351i	0.671746	+	0.740781i	$0.265545\pi$
$824$	10.7267	−	10.7267i	0.373684	−	0.373684i
$825$	−0.746606	+	20.0006i	−0.0259935	+	0.696331i
$826$	14.5840	−	14.5840i	0.507442	−	0.507442i
$827$			6.75802i			0.234999i	0.993073	+	0.117500i	$0.0374879\pi$
$827$			6.75802i			0.234999i	−0.993073	+	0.117500i	$0.962512\pi$
$828$	10.4330	+	10.4330i	0.362572	+	0.362572i
$829$			22.4997i			0.781447i	0.920508	+	0.390723i	$0.127775\pi$
$829$			22.4997i			0.781447i	−0.920508	+	0.390723i	$0.872225\pi$
$830$	−3.54902	−	3.54902i	−0.123188	−	0.123188i
$831$	−29.7683	+	29.7683i	−1.03265	+	1.03265i
$832$	6.76456			0.234519
$833$	−4.71051	−	4.71051i	−0.163209	−	0.163209i
$834$			17.6754i			0.612050i
$835$		−	4.10527i		−	0.142069i
$836$	0.187594	−	5.02540i	0.00648808	−	0.173807i
$837$	−14.1464	+	14.1464i	−0.488971	+	0.488971i
$838$	21.1647			0.731122
$839$			28.4661i			0.982758i	0.870946	+	0.491379i	$0.163507\pi$
$839$			28.4661i			0.982758i	−0.870946	+	0.491379i	$0.836493\pi$
$840$	−2.79338			−0.0963808
$841$		−	31.5163i		−	1.08677i
$842$	29.9128			1.03086
$843$	7.45060	+	7.45060i	0.256612	+	0.256612i
$844$	−3.87849	−	3.87849i	−0.133503	−	0.133503i
$845$			5.07928i			0.174732i
$846$	13.3220	+	13.3220i	0.458018	+	0.458018i
$847$	23.1054	+	26.8394i	0.793912	+	0.922214i
$848$	−17.2352	+	17.2352i	−0.591860	+	0.591860i
$849$			9.89453i			0.339580i
$850$	16.8772			0.578884
$851$	38.6789			1.32590
$852$	15.0171	+	15.0171i	0.514477	+	0.514477i
$853$	−35.4408			−1.21347			−0.606734	−	0.794905i	$-0.707521\pi$
$853$	−35.4408			−1.21347			−0.606734	+	0.794905i	$0.707521\pi$
$854$	−32.7246	+	33.1933i	−1.11981	+	1.13585i
$855$			0.854231i			0.0292141i
$856$	4.10948	−	4.10948i	0.140459	−	0.140459i
$857$	9.46293			0.323247			0.161624	−	0.986852i	$-0.448327\pi$
$857$	9.46293			0.323247			0.161624	+	0.986852i	$0.448327\pi$
$858$	−12.2362	−	13.1852i	−0.417739	−	0.450136i
$859$		−	35.4707i		−	1.21025i	−0.796132	−	0.605123i	$-0.793124\pi$
$859$		−	35.4707i		−	1.21025i	0.796132	−	0.605123i	$-0.206876\pi$
$860$	−5.22275	+	5.22275i	−0.178094	+	0.178094i
$861$	1.75685	−	1.75685i	0.0598733	−	0.0598733i
$862$	0.961162	+	0.961162i	0.0327373	+	0.0327373i
$863$	−1.90860			−0.0649695			−0.0324847	−	0.999472i	$-0.510342\pi$
$863$	−1.90860			−0.0649695			−0.0324847	+	0.999472i	$0.510342\pi$
$864$	−27.0938	+	27.0938i	−0.921749	+	0.921749i
$865$	−7.39185	+	7.39185i	−0.251330	+	0.251330i
$866$		−	13.2597i		−	0.450583i
$867$	17.1632			0.582894
$868$	16.4793			0.559342
$869$	−14.3908	−	15.5068i	−0.488174	−	0.526034i
$870$	−11.9721			−0.405891
$871$	14.4595	−	14.4595i	0.489940	−	0.489940i
$872$	−12.0595	+	12.0595i	−0.408385	+	0.408385i
$873$		−	7.46712i		−	0.252724i
$874$	−15.7229			−0.531836
$875$	−13.8290	+	13.8290i	−0.467507	+	0.467507i
$876$			4.24558i			0.143445i
$877$	8.01901	+	8.01901i	0.270783	+	0.270783i	0.829415	−	0.558633i	$-0.188674\pi$
$877$	8.01901	+	8.01901i	0.270783	+	0.270783i	−0.558633	+	0.829415i	$0.688674\pi$
$878$	25.2205	−	25.2205i	0.851150	−	0.851150i
$879$		−	4.64238i		−	0.156584i
$880$	0.376550	−	10.0873i	0.0126935	−	0.340042i
$881$		−	11.3556i		−	0.382581i	−0.981533	−	0.191290i	$-0.938733\pi$
$881$		−	11.3556i		−	0.382581i	0.981533	−	0.191290i	$-0.0612672\pi$
$882$	5.64063	−	5.64063i	0.189930	−	0.189930i
$883$	16.4017	+	16.4017i	0.551962	+	0.551962i	0.927007	−	0.375044i	$-0.122373\pi$
$883$	16.4017	+	16.4017i	0.551962	+	0.551962i	−0.375044	+	0.927007i	$0.622373\pi$
$884$	−4.48301	+	4.48301i	−0.150780	+	0.150780i
$885$	2.02878	+	2.02878i	0.0681965	+	0.0681965i
$886$	28.7513	+	28.7513i	0.965918	+	0.965918i
$887$	32.2226	+	32.2226i	1.08193	+	1.08193i	0.996329	+	0.0856010i	$0.0272810\pi$
$887$	32.2226	+	32.2226i	1.08193	+	1.08193i	0.0856010	+	0.996329i	$0.472719\pi$
$888$			6.60101i			0.221515i
$889$	−20.0638	−	20.0638i	−0.672917	−	0.672917i
$890$	−0.793847			−0.0266098
$891$	11.6960	+	0.436604i	0.391832	+	0.0146268i
$892$	−25.3123	−	25.3123i	−0.847519	−	0.847519i
$893$	−8.39139			−0.280807
$894$	−24.9057	+	24.9057i	−0.832971	+	0.832971i
$895$		−	7.97344i		−	0.266523i
$896$	−25.8477			−0.863510
$897$	−16.6217	+	16.6217i	−0.554981	+	0.554981i
$898$	13.9644	+	13.9644i	0.465996	+	0.465996i
$899$	−27.7240			−0.924649
$900$			8.44700i			0.281567i
$901$		−	10.0313i		−	0.334190i
$902$	2.45993	+	2.65070i	0.0819067	+	0.0882588i
$903$		−	34.3285i		−	1.14238i
$904$	−4.21021	−	4.21021i	−0.140029	−	0.140029i
$905$	−7.66981	+	7.66981i	−0.254953	+	0.254953i
$906$		−	6.10864i		−	0.202946i
$907$	−12.7151	+	12.7151i	−0.422197	+	0.422197i	−0.885959	−	0.463763i	$-0.846499\pi$
$907$	−12.7151	+	12.7151i	−0.422197	+	0.422197i	0.463763	+	0.885959i	$0.346499\pi$
$908$	−2.88903	+	2.88903i	−0.0958758	+	0.0958758i
$909$	−5.76341	−	5.76341i	−0.191160	−	0.191160i
$910$		−	8.42200i		−	0.279186i
$911$	37.7006			1.24908			0.624539	−	0.780994i	$-0.285287\pi$
$911$	37.7006			1.24908			0.624539	+	0.780994i	$0.285287\pi$
$912$		−	6.66197i		−	0.220600i
$913$	−0.529376	+	14.1813i	−0.0175198	+	0.469332i
$914$		−	55.8724i		−	1.84810i
$915$	−4.61751	−	4.55231i	−0.152650	−	0.150495i
$916$	36.6529			1.21105
$917$	26.0514	−	26.0514i	0.860291	−	0.860291i
$918$		−	20.5979i		−	0.679834i
$919$	0.242260			0.00799143			0.00399572	−	0.999992i	$-0.498728\pi$
$919$	0.242260			0.00799143			0.00399572	+	0.999992i	$0.498728\pi$
$920$	−5.31306			−0.175166
$921$	−25.6575	+	25.6575i	−0.845442	+	0.845442i
$922$	28.7809	−	28.7809i	0.947848	−	0.947848i
$923$	17.7726	−	17.7726i	0.584992	−	0.584992i
$924$	−13.6869	−	14.7484i	−0.450266	−	0.485185i
$925$	15.6581	+	15.6581i	0.514834	+	0.514834i
$926$	23.3756	−	23.3756i	0.768171	−	0.768171i
$927$	−18.5609			−0.609621
$928$	−53.0982			−1.74303
$929$		−	29.2581i		−	0.959926i	−0.877289	−	0.479963i	$-0.840650\pi$
$929$		−	29.2581i		−	0.959926i	0.877289	−	0.479963i	$-0.159350\pi$
$930$			5.48471i			0.179851i
$931$			3.55299i			0.116444i
$932$	12.4574	−	12.4574i	0.408055	−	0.408055i
$933$	27.2615	−	27.2615i	0.892501	−	0.892501i
$934$	−14.7583			−0.482908
$935$	2.82592	+	3.04508i	0.0924175	+	0.0995848i
$936$	2.10722	+	2.10722i	0.0688767	+	0.0688767i
$937$			25.7579i			0.841475i	0.907182	+	0.420737i	$0.138229\pi$
$937$			25.7579i			0.841475i	−0.907182	+	0.420737i	$0.861771\pi$
$938$	38.6961	−	38.6961i	1.26347	−	1.26347i
$939$	0.641573	−	0.641573i	0.0209370	−	0.0209370i
$940$	7.22379			0.235614
$941$	−24.1141	−	24.1141i	−0.786097	−	0.786097i	0.194755	−	0.980852i	$-0.437609\pi$
$941$	−24.1141	−	24.1141i	−0.786097	−	0.786097i	−0.980852	+	0.194755i	$0.937609\pi$
$942$	−45.3274			−1.47685
$943$	3.34156	−	3.34156i	0.108816	−	0.108816i
$944$	11.7533	+	11.7533i	0.382538	+	0.382538i
$945$	8.08687	+	8.08687i	0.263066	+	0.263066i
$946$	49.9304	+	1.86386i	1.62338	+	0.0605993i
$947$	−6.27732	+	6.27732i	−0.203986	+	0.203986i	−0.801705	−	0.597720i	$-0.796074\pi$
$947$	−6.27732	+	6.27732i	−0.203986	+	0.203986i	0.597720	+	0.801705i	$0.296074\pi$
$948$	8.49899	+	8.49899i	0.276034	+	0.276034i
$949$	5.02460			0.163105
$950$	−6.36498	−	6.36498i	−0.206507	−	0.206507i
$951$		−	13.9180i		−	0.451321i
$952$	4.70940	−	4.70940i	0.152632	−	0.152632i
$953$	11.2197	−	11.2197i	0.363443	−	0.363443i	−0.501636	−	0.865079i	$-0.667268\pi$
$953$	11.2197	−	11.2197i	0.363443	−	0.363443i	0.865079	+	0.501636i	$0.167268\pi$
$954$	12.0120			0.388903
$955$	−0.107154	+	0.107154i	−0.00346741	+	0.00346741i
$956$	27.8831			0.901803
$957$	23.0263	+	24.8121i	0.744334	+	0.802060i
$958$	−48.1784	−	48.1784i	−1.55657	−	1.55657i
$959$	23.8022	+	23.8022i	0.768613	+	0.768613i
$960$			2.51833i			0.0812787i
$961$		−	18.2989i		−	0.590287i
$962$	−19.9019			−0.641664
$963$	−7.11080			−0.229142
$964$	−31.8143			−1.02467
$965$	−11.4542	−	11.4542i	−0.368724	−	0.368724i
$966$	−44.4826	+	44.4826i	−1.43120	+	1.43120i
$967$	−31.2182			−1.00391			−0.501955	−	0.864894i	$-0.667386\pi$
$967$	−31.2182			−1.00391			−0.501955	+	0.864894i	$0.667386\pi$
$968$	−8.71213	+	7.50006i	−0.280018	+	0.241061i
$969$	1.93870	+	1.93870i	0.0622802	+	0.0622802i
$970$	−4.84372	−	4.84372i	−0.155522	−	0.155522i
$971$	−19.8944			−0.638440			−0.319220	−	0.947681i	$-0.603421\pi$
$971$	−19.8944			−0.638440			−0.319220	+	0.947681i	$0.603421\pi$
$972$	17.5375			0.562516
$973$	23.3987			0.750128
$974$	−23.8941	+	23.8941i	−0.765616	+	0.765616i
$975$	−13.4576			−0.430989
$976$	−26.7507	−	26.3729i	−0.856268	−	0.844177i
$977$	21.8738			0.699805			0.349903	−	0.936786i	$-0.386215\pi$
$977$	21.8738			0.699805			0.349903	+	0.936786i	$0.386215\pi$
$978$	18.8705	+	18.8705i	0.603412	+	0.603412i
$979$	1.52683	+	1.64524i	0.0487978	+	0.0525822i
$980$		−	3.05862i		−	0.0977039i
$981$	20.8670			0.666231
$982$	−6.45728	−	6.45728i	−0.206060	−	0.206060i
$983$	8.41754	−	8.41754i	0.268478	−	0.268478i	−0.560009	−	0.828487i	$-0.689202\pi$
$983$	8.41754	−	8.41754i	0.268478	−	0.268478i	0.828487	+	0.560009i	$0.189202\pi$
$984$	0.570276	+	0.570276i	0.0181797	+	0.0181797i
$985$		−	16.2489i		−	0.517733i
$986$	20.1839	−	20.1839i	0.642785	−	0.642785i
$987$	−23.7405	+	23.7405i	−0.755670	+	0.755670i
$988$	3.38140			0.107577
$989$		−	65.2934i		−	2.07621i
$990$	−3.64635	+	3.38392i	−0.115889	+	0.107548i
$991$	−41.7575			−1.32647			−0.663235	−	0.748411i	$-0.730817\pi$
$991$	−41.7575			−1.32647			−0.663235	+	0.748411i	$0.730817\pi$
$992$			24.3256i			0.772340i
$993$	0.225383	+	0.225383i	0.00715231	+	0.00715231i
$994$	47.5627	−	47.5627i	1.50860	−	1.50860i
$995$		−	12.9930i		−	0.411905i
$996$		−	8.06262i		−	0.255474i
$997$	3.03733	−	3.03733i	0.0961932	−	0.0961932i	−0.657373	−	0.753566i	$-0.728332\pi$
$997$	3.03733	−	3.03733i	0.0961932	−	0.0961932i	0.753566	+	0.657373i	$0.228332\pi$
$998$			20.6015i			0.652128i
$999$	19.1100	−	19.1100i	0.604614	−	0.604614i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.f.a.538.12	✓	120
11.10	odd	2	inner	671.2.f.a.538.49	yes	120
61.11	odd	4	inner	671.2.f.a.560.49	yes	120
671.560	even	4	inner	671.2.f.a.560.12	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.f.a.538.12	✓	120	1.1	even	1	trivial
671.2.f.a.538.49	yes	120	11.10	odd	2	inner
671.2.f.a.560.12	yes	120	671.560	even	4	inner
671.2.f.a.560.49	yes	120	61.11	odd	4	inner

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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31077 - 1.31077i) q^{2} -1.31199i q^{3} +1.43623i q^{4} +0.632792i q^{5} +(-1.71972 + 1.71972i) q^{6} +(2.27656 + 2.27656i) q^{7} +(-0.738974 + 0.738974i) q^{8} +1.27868 q^{9} +O(q^{10})\)	\(q+(-1.31077 - 1.31077i) q^{2} -1.31199i q^{3} +1.43623i q^{4} +0.632792i q^{5} +(-1.71972 + 1.71972i) q^{6} +(2.27656 + 2.27656i) q^{7} +(-0.738974 + 0.738974i) q^{8} +1.27868 q^{9} +(0.829444 - 0.829444i) q^{10} +(-3.31432 - 0.123721i) q^{11} +1.88432 q^{12} -2.23007i q^{13} -5.96808i q^{14} +0.830218 q^{15} +4.80971 q^{16} +(-1.39968 + 1.39968i) q^{17} +(-1.67605 - 1.67605i) q^{18} +1.05573 q^{19} -0.908834 q^{20} +(2.98682 - 2.98682i) q^{21} +(4.18213 + 4.50647i) q^{22} +(5.68099 - 5.68099i) q^{23} +(0.969528 + 0.969528i) q^{24} +4.59957 q^{25} +(-2.92311 + 2.92311i) q^{26} -5.61359i q^{27} +(-3.26966 + 3.26966i) q^{28} +(5.50074 - 5.50074i) q^{29} +(-1.08822 - 1.08822i) q^{30} +(-2.52003 - 2.52003i) q^{31} +(-4.82646 - 4.82646i) q^{32} +(-0.162321 + 4.34836i) q^{33} +3.66930 q^{34} +(-1.44059 + 1.44059i) q^{35} +1.83647i q^{36} +(3.40424 + 3.40424i) q^{37} +(-1.38382 - 1.38382i) q^{38} -2.92584 q^{39} +(-0.467617 - 0.467617i) q^{40} +0.588200 q^{41} -7.83007 q^{42} +(5.74665 - 5.74665i) q^{43} +(0.177691 - 4.76011i) q^{44} +0.809137i q^{45} -14.8929 q^{46} -7.94842 q^{47} -6.31029i q^{48} +3.36543i q^{49} +(-6.02898 - 6.02898i) q^{50} +(1.83636 + 1.83636i) q^{51} +3.20290 q^{52} +(-3.58343 + 3.58343i) q^{53} +(-7.35812 + 7.35812i) q^{54} +(0.0782895 - 2.09727i) q^{55} -3.36464 q^{56} -1.38511i q^{57} -14.4204 q^{58} +(2.44367 + 2.44367i) q^{59} +1.19238i q^{60} +(-5.56181 - 5.48327i) q^{61} +6.60635i q^{62} +(2.91098 + 2.91098i) q^{63} +3.03334i q^{64} +1.41117 q^{65} +(5.91245 - 5.48692i) q^{66} +(6.48385 + 6.48385i) q^{67} +(-2.01025 - 2.01025i) q^{68} +(-7.45342 - 7.45342i) q^{69} +3.77655 q^{70} +(7.96951 + 7.96951i) q^{71} +(-0.944911 + 0.944911i) q^{72} +2.25311i q^{73} -8.92434i q^{74} -6.03460i q^{75} +1.51627i q^{76} +(-7.26357 - 7.82689i) q^{77} +(3.83510 + 3.83510i) q^{78} +(4.51038 + 4.51038i) q^{79} +3.04354i q^{80} -3.52895 q^{81} +(-0.770994 - 0.770994i) q^{82} -4.27880i q^{83} +(4.28976 + 4.28976i) q^{84} +(-0.885704 - 0.885704i) q^{85} -15.0651 q^{86} +(-7.21692 - 7.21692i) q^{87} +(2.54062 - 2.35777i) q^{88} +(-0.478541 - 0.478541i) q^{89} +(1.06059 - 1.06059i) q^{90} +(5.07689 - 5.07689i) q^{91} +(8.15920 + 8.15920i) q^{92} +(-3.30626 + 3.30626i) q^{93} +(10.4185 + 10.4185i) q^{94} +0.668058i q^{95} +(-6.33228 + 6.33228i) q^{96} -5.83972i q^{97} +(4.41130 - 4.41130i) q^{98} +(-4.23794 - 0.158199i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 120 q^{9}+O(q^{10}) \) 120 * q - 120 * q^9	\( 120 q - 120 q^{9} - 4 q^{11} + 16 q^{12} + 16 q^{15} - 148 q^{16} + 56 q^{20} - 4 q^{22} - 4 q^{23} - 104 q^{25} + 40 q^{26} - 2 q^{33} - 8 q^{34} - 12 q^{37} + 20 q^{38} + 16 q^{42} - 10 q^{44} - 4 q^{53} + 50 q^{55} - 24 q^{56} + 64 q^{58} - 56 q^{67} + 68 q^{69} + 144 q^{70} - 12 q^{71} - 64 q^{77} + 84 q^{78} + 72 q^{81} + 40 q^{82} - 80 q^{86} + 4 q^{89} - 4 q^{91} + 4 q^{92} + 64 q^{93} + 24 q^{99}+O(q^{100}) \) 120 * q - 120 * q^9 - 4 * q^11 + 16 * q^12 + 16 * q^15 - 148 * q^16 + 56 * q^20 - 4 * q^22 - 4 * q^23 - 104 * q^25 + 40 * q^26 - 2 * q^33 - 8 * q^34 - 12 * q^37 + 20 * q^38 + 16 * q^42 - 10 * q^44 - 4 * q^53 + 50 * q^55 - 24 * q^56 + 64 * q^58 - 56 * q^67 + 68 * q^69 + 144 * q^70 - 12 * q^71 - 64 * q^77 + 84 * q^78 + 72 * q^81 + 40 * q^82 - 80 * q^86 + 4 * q^89 - 4 * q^91 + 4 * q^92 + 64 * q^93 + 24 * q^99

Introduction

L-functions

Modular forms

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Database

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