LMFDB - Embedded newform 275.2.h.d.201.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(26,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("275.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.h (of order $5$, degree $4$, 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:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 7x^{14} + 25x^{12} + 57x^{10} + 194x^{8} + 303x^{6} + 235x^{4} + 33x^{2} + 121 $ x^16 + 7x^14 + 25x^12 + 57x^10 + 194x^8 + 303x^6 + 235x^4 + 33*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.3
Root			$-0.381325 - 1.17360i$ of defining polynomial
Character	$\chi$	$=$	275.201
Dual form			275.2.h.d.26.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.998322 - 0.725323i) q^{2} +(0.112477 + 0.346168i) q^{3} +(-0.147481 + 0.453901i) q^{4} +(0.363371 + 0.264005i) q^{6} +(-0.798988 + 2.45903i) q^{7} +(0.944641 + 2.90731i) q^{8} +(2.31987 - 1.68548i) q^{9} +(3.12020 + 1.12443i) q^{11} -0.173714 q^{12} +(2.23232 - 1.62187i) q^{13} +(0.985946 + 3.03443i) q^{14} +(2.27957 + 1.65620i) q^{16} +(-3.11572 - 2.26370i) q^{17} +(1.09346 - 3.36531i) q^{18} +(-0.0857804 - 0.264005i) q^{19} -0.941105 q^{21} +(3.93054 - 1.14061i) q^{22} -8.40180 q^{23} +(-0.900166 + 0.654009i) q^{24} +(1.05219 - 3.23830i) q^{26} +(1.72780 + 1.25532i) q^{27} +(-0.998322 - 0.725323i) q^{28} +(1.02689 - 3.16043i) q^{29} +(-0.456498 + 0.331666i) q^{31} -2.63682 q^{32} +(-0.0382919 + 1.20659i) q^{33} -4.75241 q^{34} +(0.422906 + 1.30157i) q^{36} +(-0.161487 + 0.497006i) q^{37} +(-0.277125 - 0.201343i) q^{38} +(0.812523 + 0.590333i) q^{39} +(-1.57966 - 4.86168i) q^{41} +(-0.939526 + 0.682605i) q^{42} +2.54457 q^{43} +(-0.970553 + 1.25043i) q^{44} +(-8.38769 + 6.09402i) q^{46} +(-1.52184 - 4.68373i) q^{47} +(-0.316926 + 0.975398i) q^{48} +(0.254663 + 0.185023i) q^{49} +(0.433175 - 1.33318i) q^{51} +(0.406945 + 1.25245i) q^{52} +(7.05533 - 5.12599i) q^{53} +2.63541 q^{54} -7.90392 q^{56} +(0.0817417 - 0.0593888i) q^{57} +(-1.26717 - 3.89995i) q^{58} +(2.31987 - 7.13983i) q^{59} +(-11.4711 - 8.33424i) q^{61} +(-0.215168 + 0.662218i) q^{62} +(2.29111 + 7.05132i) q^{63} +(-7.19153 + 5.22495i) q^{64} +(0.836937 + 1.23233i) q^{66} +3.20618 q^{67} +(1.48701 - 1.08037i) q^{68} +(-0.945006 - 2.90843i) q^{69} +(6.79655 + 4.93798i) q^{71} +(7.09166 + 5.15239i) q^{72} +(-4.02812 + 12.3973i) q^{73} +(0.199274 + 0.613302i) q^{74} +0.132483 q^{76} +(-5.25802 + 6.77427i) q^{77} +1.23934 q^{78} +(-7.85090 + 5.70401i) q^{79} +(2.41812 - 7.44221i) q^{81} +(-5.10330 - 3.70776i) q^{82} +(-2.66732 - 1.93792i) q^{83} +(0.138796 - 0.427169i) q^{84} +(2.54030 - 1.84564i) q^{86} +1.20954 q^{87} +(-0.321596 + 10.1336i) q^{88} +2.48823 q^{89} +(2.20464 + 6.78519i) q^{91} +(1.23911 - 3.81359i) q^{92} +(-0.166157 - 0.120720i) q^{93} +(-4.91650 - 3.57205i) q^{94} +(-0.296581 - 0.912781i) q^{96} +(8.81946 - 6.40771i) q^{97} +0.388437 q^{98} +(9.13367 - 2.65051i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 18 q^{6} - 2 q^{9} - 6 q^{11} + 12 q^{14} + 16 q^{16} - 6 q^{19} + 8 q^{21} - 6 q^{24} + 40 q^{26} - 2 q^{29} + 8 q^{31} + 16 q^{34} + 10 q^{36} - 30 q^{39} - 52 q^{41} - 4 q^{44} - 62 q^{46}+ \cdots + 72 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 - 18 * q^6 - 2 * q^9 - 6 * q^11 + 12 * q^14 + 16 * q^16 - 6 * q^19 + 8 * q^21 - 6 * q^24 + 40 * q^26 - 2 * q^29 + 8 * q^31 + 16 * q^34 + 10 * q^36 - 30 * q^39 - 52 * q^41 - 4 * q^44 - 62 * q^46 + 10 * q^49 - 42 * q^51 + 40 * q^54 - 20 * q^56 - 2 * q^59 - 40 * q^61 + 8 * q^64 + 58 * q^66 - 26 * q^69 + 36 * q^71 - 48 * q^74 + 56 * q^76 - 38 * q^79 + 68 * q^81 - 12 * q^84 + 22 * q^86 - 24 * q^89 - 20 * q^91 - 14 * q^94 - 86 * q^96 + 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.998322	−	0.725323i	0.705920	−	0.512881i	−0.175935	−	0.984402i	$-0.556295\pi$
$2$	0.998322	−	0.725323i	0.705920	−	0.512881i	0.881855	+	0.471521i	$0.156295\pi$
$3$	0.112477	+	0.346168i	0.0649385	+	0.199860i	0.978261	−	0.207376i	$-0.0664925\pi$
$3$	0.112477	+	0.346168i	0.0649385	+	0.199860i	−0.913323	+	0.407236i	$0.866492\pi$
$4$	−0.147481	+	0.453901i	−0.0737407	+	0.226951i
$5$		0			0
$5$		0			0
$6$	0.363371	+	0.264005i	0.148346	+	0.107780i
$7$	−0.798988	+	2.45903i	−0.301989	+	0.929427i	0.678795	+	0.734328i	$0.262503\pi$
$7$	−0.798988	+	2.45903i	−0.301989	+	0.929427i	−0.980784	+	0.195099i	$0.937497\pi$
$8$	0.944641	+	2.90731i	0.333981	+	1.02789i
$9$	2.31987	−	1.68548i	0.773290	−	0.561828i
$10$		0			0
$11$	3.12020	+	1.12443i	0.940776	+	0.339029i
$11$	3.12020	+	1.12443i	0.940776	+	0.339029i
$12$	−0.173714			−0.0501470
$13$	2.23232	−	1.62187i	0.619133	−	0.449826i	−0.233486	−	0.972360i	$-0.575013\pi$
$13$	2.23232	−	1.62187i	0.619133	−	0.449826i	0.852619	+	0.522534i	$0.175013\pi$
$14$	0.985946	+	3.03443i	0.263505	+	0.810985i
$15$		0			0
$16$	2.27957	+	1.65620i	0.569892	+	0.414051i
$17$	−3.11572	−	2.26370i	−0.755673	−	0.549028i	0.141907	−	0.989880i	$-0.454677\pi$
$17$	−3.11572	−	2.26370i	−0.755673	−	0.549028i	−0.897580	+	0.440852i	$0.854677\pi$
$18$	1.09346	−	3.36531i	0.257730	−	0.793211i
$19$	−0.0857804	−	0.264005i	−0.0196794	−	0.0605669i	0.940735	−	0.339144i	$-0.110137\pi$
$19$	−0.0857804	−	0.264005i	−0.0196794	−	0.0605669i	−0.960414	+	0.278577i	$0.910137\pi$
$20$		0			0
$21$	−0.941105			−0.205366
$22$	3.93054	−	1.14061i	0.837994	−	0.243179i
$23$	−8.40180			−1.75190			−0.875948	−	0.482406i	$-0.839763\pi$
$23$	−8.40180			−1.75190			−0.875948	+	0.482406i	$0.839763\pi$
$24$	−0.900166	+	0.654009i	−0.183746	+	0.133499i
$25$		0			0
$26$	1.05219	−	3.23830i	0.206351	−	0.635083i
$27$	1.72780	+	1.25532i	0.332514	+	0.241586i
$28$	−0.998322	−	0.725323i	−0.188665	−	0.137073i
$29$	1.02689	−	3.16043i	0.190688	−	0.586877i	−0.809312	−	0.587379i	$-0.800160\pi$
$29$	1.02689	−	3.16043i	0.190688	−	0.586877i	1.00000		0.000502126i	$0.000159832\pi$
$30$		0			0
$31$	−0.456498	+	0.331666i	−0.0819895	+	0.0595689i	−0.628025	−	0.778193i	$-0.716136\pi$
$31$	−0.456498	+	0.331666i	−0.0819895	+	0.0595689i	0.546035	+	0.837762i	$0.316136\pi$
$32$	−2.63682			−0.466128
$33$	−0.0382919	+	1.20659i	−0.00666576	+	0.210040i
$34$	−4.75241			−0.815031
$35$		0			0
$36$	0.422906	+	1.30157i	0.0704843	+	0.216928i
$37$	−0.161487	+	0.497006i	−0.0265483	+	0.0817073i	−0.963453	−	0.267878i	$-0.913678\pi$
$37$	−0.161487	+	0.497006i	−0.0265483	+	0.0817073i	0.936905	+	0.349585i	$0.113678\pi$
$38$	−0.277125	−	0.201343i	−0.0449556	−	0.0326622i
$39$	0.812523	+	0.590333i	0.130108	+	0.0945289i
$40$		0			0
$41$	−1.57966	−	4.86168i	−0.246701	−	0.759267i	−0.995352	−	0.0963031i	$-0.969298\pi$
$41$	−1.57966	−	4.86168i	−0.246701	−	0.759267i	0.748651	−	0.662964i	$-0.230702\pi$
$42$	−0.939526	+	0.682605i	−0.144972	+	0.105328i
$43$	2.54457			0.388043			0.194022	−	0.980997i	$-0.437847\pi$
$43$	2.54457			0.388043			0.194022	+	0.980997i	$0.437847\pi$
$44$	−0.970553	+	1.25043i	−0.146316	+	0.188509i
$45$		0			0
$46$	−8.38769	+	6.09402i	−1.23670	+	0.898514i
$47$	−1.52184	−	4.68373i	−0.221983	−	0.683193i	−0.998584	−	0.0532000i	$-0.983058\pi$
$47$	−1.52184	−	4.68373i	−0.221983	−	0.683193i	0.776601	−	0.629993i	$-0.216942\pi$
$48$	−0.316926	+	0.975398i	−0.0457443	+	0.140787i
$49$	0.254663	+	0.185023i	0.0363804	+	0.0264319i
$50$		0			0
$51$	0.433175	−	1.33318i	0.0606566	−	0.186682i
$52$	0.406945	+	1.25245i	0.0564331	+	0.173683i
$53$	7.05533	−	5.12599i	0.969123	−	0.704109i	0.0138718	−	0.999904i	$-0.495584\pi$
$53$	7.05533	−	5.12599i	0.969123	−	0.704109i	0.955252	+	0.295794i	$0.0955843\pi$
$54$	2.63541			0.358633
$55$		0			0
$56$	−7.90392			−1.05621
$57$	0.0817417	−	0.0593888i	0.0108269	−	0.00786624i
$58$	−1.26717	−	3.89995i	−0.166388	−	0.512088i
$59$	2.31987	−	7.13983i	0.302021	−	0.929526i	−0.678751	−	0.734369i	$-0.737478\pi$
$59$	2.31987	−	7.13983i	0.302021	−	0.929526i	0.980772	−	0.195157i	$-0.0625217\pi$
$60$		0			0
$61$	−11.4711	−	8.33424i	−1.46872	−	1.06709i	−0.980981	−	0.194103i	$-0.937820\pi$
$61$	−11.4711	−	8.33424i	−1.46872	−	1.06709i	−0.487743	−	0.872987i	$-0.662180\pi$
$62$	−0.215168	+	0.662218i	−0.0273263	+	0.0841017i
$63$	2.29111	+	7.05132i	0.288653	+	0.888382i
$64$	−7.19153	+	5.22495i	−0.898942	+	0.653119i
$65$		0			0
$66$	0.836937	+	1.23233i	0.103020	+	0.151690i
$67$	3.20618			0.391698			0.195849	−	0.980634i	$-0.437254\pi$
$67$	3.20618			0.391698			0.195849	+	0.980634i	$0.437254\pi$
$68$	1.48701	−	1.08037i	0.180326	−	0.131015i
$69$	−0.945006	−	2.90843i	−0.113765	−	0.350134i
$70$		0			0
$71$	6.79655	+	4.93798i	0.806602	+	0.586030i	0.912843	−	0.408310i	$-0.133882\pi$
$71$	6.79655	+	4.93798i	0.806602	+	0.586030i	−0.106242	+	0.994340i	$0.533882\pi$
$72$	7.09166	+	5.15239i	0.835761	+	0.607216i
$73$	−4.02812	+	12.3973i	−0.471455	+	1.45099i	0.379224	+	0.925305i	$0.376191\pi$
$73$	−4.02812	+	12.3973i	−0.471455	+	1.45099i	−0.850679	+	0.525685i	$0.823809\pi$
$74$	0.199274	+	0.613302i	0.0231651	+	0.0712949i
$75$		0			0
$76$	0.132483			0.0151969
$77$	−5.25802	+	6.77427i	−0.599206	+	0.771999i
$78$	1.23934			0.140328
$79$	−7.85090	+	5.70401i	−0.883295	+	0.641752i	−0.934121	−	0.356956i	$-0.883815\pi$
$79$	−7.85090	+	5.70401i	−0.883295	+	0.641752i	0.0508259	+	0.998708i	$0.483815\pi$
$80$		0			0
$81$	2.41812	−	7.44221i	0.268680	−	0.826912i
$82$	−5.10330	−	3.70776i	−0.563565	−	0.409454i
$83$	−2.66732	−	1.93792i	−0.292776	−	0.212715i	0.431694	−	0.902020i	$-0.357916\pi$
$83$	−2.66732	−	1.93792i	−0.292776	−	0.212715i	−0.724471	+	0.689305i	$0.757916\pi$
$84$	0.138796	−	0.427169i	0.0151438	−	0.0466079i
$85$		0			0
$86$	2.54030	−	1.84564i	0.273928	−	0.199020i
$87$	1.20954			0.129676
$88$	−0.321596	+	10.1336i	−0.0342823	+	1.08024i
$89$	2.48823			0.263752			0.131876	−	0.991266i	$-0.457900\pi$
$89$	2.48823			0.263752			0.131876	+	0.991266i	$0.457900\pi$
$90$		0			0
$91$	2.20464	+	6.78519i	0.231109	+	0.711281i
$92$	1.23911	−	3.81359i	0.129186	−	0.397594i
$93$	−0.166157	−	0.120720i	−0.0172297	−	0.0125181i
$94$	−4.91650	−	3.57205i	−0.507099	−	0.368429i
$95$		0			0
$96$	−0.296581	−	0.912781i	−0.0302696	−	0.0931604i
$97$	8.81946	−	6.40771i	0.895480	−	0.650605i	−0.0418208	−	0.999125i	$-0.513316\pi$
$97$	8.81946	−	6.40771i	0.895480	−	0.650605i	0.937301	+	0.348521i	$0.113316\pi$
$98$	0.388437			0.0392380
$99$	9.13367	−	2.65051i	0.917969	−	0.266387i
$100$		0			0
$101$	−11.1954	+	8.13391i	−1.11398	+	0.809355i	−0.983286	−	0.182068i	$-0.941721\pi$
$101$	−11.1954	+	8.13391i	−1.11398	+	0.809355i	−0.130695	+	0.991423i	$0.541721\pi$
$102$	−0.534535	−	1.64513i	−0.0529269	−	0.162892i
$103$	4.13771	−	12.7346i	0.407700	−	1.25477i	−0.510919	−	0.859629i	$-0.670695\pi$
$103$	4.13771	−	12.7346i	0.407700	−	1.25477i	0.918619	−	0.395144i	$-0.129305\pi$
$104$	6.82402	+	4.95794i	0.669150	+	0.486166i
$105$		0			0
$106$	3.32548	−	10.2348i	0.322999	−	0.994090i
$107$	3.17033	+	9.75728i	0.306488	+	0.943272i	0.979118	+	0.203293i	$0.0651644\pi$
$107$	3.17033	+	9.75728i	0.306488	+	0.943272i	−0.672630	+	0.739979i	$0.734836\pi$
$108$	−0.824608	+	0.599112i	−0.0793479	+	0.0576496i
$109$	−4.94262			−0.473417			−0.236708	−	0.971581i	$-0.576069\pi$
$109$	−4.94262			−0.473417			−0.236708	+	0.971581i	$0.576069\pi$
$110$		0			0
$111$	−0.190211			−0.0180540
$112$	−5.89401	+	4.28225i	−0.556931	+	0.404634i
$113$	−3.06671	−	9.43836i	−0.288492	−	0.887886i	−0.985330	−	0.170658i	$-0.945411\pi$
$113$	−3.06671	−	9.43836i	−0.288492	−	0.887886i	0.696839	−	0.717228i	$-0.254589\pi$
$114$	0.0385284	−	0.118578i	0.00360852	−	0.0111059i
$115$		0			0
$116$	1.28308	+	0.932209i	0.119131	+	0.0865534i
$117$	2.44504	−	7.52506i	0.226044	−	0.695692i
$118$	−2.86270	−	8.81050i	−0.263533	−	0.811072i
$119$	8.05594	−	5.85298i	0.738487	−	0.536542i
$120$		0			0
$121$	8.47131	+	7.01690i	0.770119	+	0.637900i
$122$	−17.4969			−1.58409
$123$	1.50528	−	1.09365i	0.135727	−	0.0986113i
$124$	−0.0832183	−	0.256120i	−0.00747323	−	0.0230002i
$125$		0			0
$126$	7.40175	+	5.37769i	0.659400	+	0.479082i
$127$	−9.00901	−	6.54543i	−0.799420	−	0.580813i	0.111324	−	0.993784i	$-0.464491\pi$
$127$	−9.00901	−	6.54543i	−0.799420	−	0.580813i	−0.910744	+	0.412972i	$0.864491\pi$
$128$	−1.76004	+	5.41684i	−0.155567	+	0.478786i
$129$	0.286205	+	0.880848i	0.0251989	+	0.0775544i
$130$		0			0
$131$	10.1649			0.888114			0.444057	−	0.895999i	$-0.353539\pi$
$131$	10.1649			0.888114			0.444057	+	0.895999i	$0.353539\pi$
$132$	−0.542023	−	0.195330i	−0.0471771	−	0.0170013i
$133$	0.717734			0.0622354
$134$	3.20080	−	2.32552i	0.276507	−	0.200894i
$135$		0			0
$136$	3.63804	−	11.1967i	0.311959	−	0.960112i
$137$	3.51604	+	2.55455i	0.300395	+	0.218250i	0.727764	−	0.685827i	$-0.240559\pi$
$137$	3.51604	+	2.55455i	0.300395	+	0.218250i	−0.427369	+	0.904077i	$0.640559\pi$
$138$	−3.05297	−	2.21811i	−0.259886	−	0.188818i
$139$	−2.56560	+	7.89611i	−0.217612	+	0.669739i	0.781346	+	0.624098i	$0.214533\pi$
$139$	−2.56560	+	7.89611i	−0.217612	+	0.669739i	−0.998958	+	0.0456418i	$0.985467\pi$
$140$		0			0
$141$	1.45019	−	1.05362i	0.122128	−	0.0887310i
$142$	10.3668			0.869960
$143$	8.78896	−	2.55048i	0.734969	−	0.213282i
$144$	8.07981			0.673318
$145$		0			0
$146$	4.97067	+	15.2981i	0.411375	+	1.26608i
$147$	−0.0354054	+	0.108967i	−0.00292019	+	0.00898743i
$148$	−0.201775	−	0.146598i	−0.0165858	−	0.0120503i
$149$	−6.84987	−	4.97672i	−0.561163	−	0.407709i	0.270721	−	0.962658i	$-0.412738\pi$
$149$	−6.84987	−	4.97672i	−0.561163	−	0.407709i	−0.831884	+	0.554949i	$0.812738\pi$
$150$		0			0
$151$	3.43080	+	10.5589i	0.279195	+	0.859273i	0.988079	+	0.153948i	$0.0491988\pi$
$151$	3.43080	+	10.5589i	0.279195	+	0.859273i	−0.708884	+	0.705325i	$0.750801\pi$
$152$	0.686511	−	0.498780i	0.0556834	−	0.0404564i
$153$	−11.0435			−0.892814
$154$	−0.335658	+	10.5767i	−0.0270481	+	0.852291i
$155$		0			0
$156$	−0.387785	+	0.281742i	−0.0310476	+	0.0225574i
$157$	4.25400	+	13.0925i	0.339506	+	1.04489i	0.964459	+	0.264231i	$0.0851181\pi$
$157$	4.25400	+	13.0925i	0.339506	+	1.04489i	−0.624953	+	0.780662i	$0.714882\pi$
$158$	−3.70047	+	11.3889i	−0.294394	+	0.906051i
$159$	2.56801	+	1.86577i	0.203657	+	0.147965i
$160$		0			0
$161$	6.71293	−	20.6603i	0.529053	−	1.62826i
$162$	−2.98395	−	9.18364i	−0.234441	−	0.721535i
$163$	−7.23337	+	5.25535i	−0.566561	+	0.411631i	−0.833854	−	0.551985i	$-0.813871\pi$
$163$	−7.23337	+	5.25535i	−0.566561	+	0.411631i	0.267293	+	0.963615i	$0.413871\pi$
$164$	2.43969			0.190508
$165$		0			0
$166$	−4.06846			−0.315774
$167$	13.6871	−	9.94425i	1.05914	−	0.769509i	0.0852095	−	0.996363i	$-0.472844\pi$
$167$	13.6871	−	9.94425i	1.05914	−	0.769509i	0.973929	+	0.226854i	$0.0728440\pi$
$168$	−0.889007	−	2.73608i	−0.0685883	−	0.211093i
$169$	−1.66446	+	5.12268i	−0.128035	+	0.394052i
$170$		0			0
$171$	−0.643975	−	0.467875i	−0.0492460	−	0.0357793i
$172$	−0.375277	+	1.15498i	−0.0286146	+	0.0880667i
$173$	1.04445	+	3.21447i	0.0794077	+	0.244392i	0.982878	−	0.184260i	$-0.0589888\pi$
$173$	1.04445	+	3.21447i	0.0794077	+	0.244392i	−0.903470	+	0.428652i	$0.858989\pi$
$174$	1.20751	−	0.877307i	0.0915410	−	0.0665085i
$175$		0			0
$176$	5.25043	+	7.73091i	0.395766	+	0.582739i
$177$	2.73251			0.205388
$178$	2.48405	−	1.80477i	0.186188	−	0.135273i
$179$	4.27183	+	13.1473i	0.319291	+	0.982678i	0.973952	+	0.226755i	$0.0728116\pi$
$179$	4.27183	+	13.1473i	0.319291	+	0.982678i	−0.654660	+	0.755923i	$0.727188\pi$
$180$		0			0
$181$	2.10264	+	1.52766i	0.156288	+	0.113550i	0.663181	−	0.748459i	$-0.269206\pi$
$181$	2.10264	+	1.52766i	0.156288	+	0.113550i	−0.506893	+	0.862009i	$0.669206\pi$
$182$	7.12240	+	5.17473i	0.527947	+	0.383576i
$183$	1.59481	−	4.90833i	0.117892	−	0.362834i
$184$	−7.93668	−	24.4266i	−0.585100	−	1.80075i
$185$		0			0
$186$	−0.253440			−0.0185831
$187$	−7.17629	−	10.5666i	−0.524782	−	0.772708i
$188$	2.35039			0.171420
$189$	−4.46735	+	3.24572i	−0.324952	+	0.236091i
$190$		0			0
$191$	0.685498	−	2.10975i	0.0496009	−	0.152656i	−0.923188	−	0.384348i	$-0.874426\pi$
$191$	0.685498	−	2.10975i	0.0496009	−	0.152656i	0.972789	+	0.231692i	$0.0744262\pi$
$192$	−2.61759	−	1.90179i	−0.188908	−	0.137250i
$193$	8.47564	+	6.15791i	0.610090	+	0.443256i	0.849446	−	0.527676i	$-0.176936\pi$
$193$	8.47564	+	6.15791i	0.610090	+	0.443256i	−0.239356	+	0.970932i	$0.576936\pi$
$194$	4.15700	−	12.7939i	0.298455	−	0.918550i
$195$		0			0
$196$	−0.121540	+	0.0883042i	−0.00868145	+	0.00630744i
$197$	−1.32667			−0.0945210			−0.0472605	−	0.998883i	$-0.515049\pi$
$197$	−1.32667			−0.0945210			−0.0472605	+	0.998883i	$0.515049\pi$
$198$	7.19586	−	9.27093i	0.511388	−	0.658856i
$199$	−5.20321			−0.368846			−0.184423	−	0.982847i	$-0.559042\pi$
$199$	−5.20321			−0.368846			−0.184423	+	0.982847i	$0.559042\pi$
$200$		0			0
$201$	0.360621	+	1.10988i	0.0254362	+	0.0782847i
$202$	−5.27687	+	16.2405i	−0.371279	+	1.14268i
$203$	6.95113	+	5.05029i	0.487873	+	0.354461i
$204$	0.541245	+	0.393237i	0.0378947	+	0.0275321i
$205$		0			0
$206$	−5.10590	−	15.7144i	−0.355745	−	1.09487i
$207$	−19.4911	+	14.1611i	−1.35472	+	0.984264i
$208$	7.77487			0.539090
$209$	0.0292033	−	0.920202i	0.00202004	−	0.0636517i
$210$		0			0
$211$	−15.3038	+	11.1189i	−1.05356	+	0.765454i	−0.972886	−	0.231287i	$-0.925706\pi$
$211$	−15.3038	+	11.1189i	−1.05356	+	0.765454i	−0.0806716	+	0.996741i	$0.525706\pi$
$212$	1.28617	+	3.95841i	0.0883342	+	0.271865i
$213$	−0.944916	+	2.90815i	−0.0647446	+	0.199263i
$214$	10.2422	+	7.44139i	0.700142	+	0.508683i
$215$		0			0
$216$	−2.01744	+	6.20905i	−0.137270	+	0.422473i
$217$	−0.450839	−	1.38754i	−0.0306050	−	0.0941924i
$218$	−4.93432	+	3.58499i	−0.334194	+	0.242806i
$219$	−4.74460			−0.320611
$220$		0			0
$221$	−10.6267			−0.714829
$222$	−0.189892	+	0.137964i	−0.0127447	+	0.00925956i
$223$	6.75890	+	20.8018i	0.452610	+	1.39299i	0.873919	+	0.486072i	$0.161571\pi$
$223$	6.75890	+	20.8018i	0.452610	+	1.39299i	−0.421309	+	0.906917i	$0.638429\pi$
$224$	2.10679	−	6.48402i	0.140766	−	0.433232i
$225$		0			0
$226$	−9.90742	−	7.19816i	−0.659032	−	0.478815i
$227$	−0.753584	+	2.31929i	−0.0500171	+	0.153937i	−0.972945	−	0.231035i	$-0.925789\pi$
$227$	−0.753584	+	2.31929i	−0.0500171	+	0.153937i	0.922928	+	0.384972i	$0.125789\pi$
$228$	0.0149013	+	0.0458614i	0.000986860	+	0.00303724i
$229$	−5.90678	+	4.29153i	−0.390331	+	0.283592i	−0.765591	−	0.643327i	$-0.777553\pi$
$229$	−5.90678	+	4.29153i	−0.390331	+	0.283592i	0.375260	+	0.926920i	$0.377553\pi$
$230$		0			0
$231$	−2.93644	−	1.05821i	−0.193203	−	0.0696250i
$232$	10.1584			0.666930
$233$	−3.60685	+	2.62053i	−0.236292	+	0.171676i	−0.699630	−	0.714505i	$-0.746652\pi$
$233$	−3.60685	+	2.62053i	−0.236292	+	0.171676i	0.463338	+	0.886182i	$0.346652\pi$
$234$	−3.01717	−	9.28588i	−0.197238	−	0.607037i
$235$		0			0
$236$	2.89864	+	2.10598i	0.188685	+	0.137088i
$237$	−2.85759	−	2.07616i	−0.185620	−	0.134861i
$238$	3.79711	−	11.6863i	0.246130	−	0.757511i
$239$	7.47040	+	22.9915i	0.483220	+	1.48720i	0.834542	+	0.550944i	$0.185732\pi$
$239$	7.47040	+	22.9915i	0.483220	+	1.48720i	−0.351322	+	0.936255i	$0.614268\pi$
$240$		0			0
$241$	−12.0393			−0.775522			−0.387761	−	0.921760i	$-0.626751\pi$
$241$	−12.0393			−0.775522			−0.387761	+	0.921760i	$0.626751\pi$
$242$	13.5466	+	0.860691i	0.870809	+	0.0553273i
$243$	9.25525			0.593725
$244$	5.47470	−	3.97760i	0.350482	−	0.254640i
$245$		0			0
$246$	0.709506	−	2.18363i	0.0452364	−	0.139223i
$247$	−0.619671	−	0.450217i	−0.0394287	−	0.0286466i
$248$	−1.39548	−	1.01388i	−0.0886131	−	0.0643812i
$249$	0.370835	−	1.14131i	0.0235007	−	0.0723277i
$250$		0			0
$251$	0.433947	−	0.315281i	0.0273905	−	0.0199004i	−0.574006	−	0.818851i	$-0.694611\pi$
$251$	0.433947	−	0.315281i	0.0273905	−	0.0199004i	0.601396	+	0.798951i	$0.294611\pi$
$252$	−3.53850			−0.222904
$253$	−26.2153	−	9.44724i	−1.64814	−	0.593943i
$254$	−13.7414			−0.862214
$255$		0			0
$256$	−3.32196	−	10.2240i	−0.207623	−	0.638997i
$257$	7.32987	−	22.5590i	0.457224	−	1.40719i	−0.411279	−	0.911509i	$-0.634918\pi$
$257$	7.32987	−	22.5590i	0.457224	−	1.40719i	0.868504	−	0.495683i	$-0.165082\pi$
$258$	0.924624	+	0.671779i	0.0575646	+	0.0418231i
$259$	−1.09313	−	0.794203i	−0.0679236	−	0.0493494i
$260$		0			0
$261$	−2.94461	−	9.06258i	−0.182267	−	0.560960i
$262$	10.1479	−	7.37286i	0.626937	−	0.455497i
$263$	−4.97643			−0.306860			−0.153430	−	0.988160i	$-0.549032\pi$
$263$	−4.97643			−0.306860			−0.153430	+	0.988160i	$0.549032\pi$
$264$	−3.54409	+	1.02846i	−0.218123	+	0.0632976i
$265$		0			0
$266$	0.716529	−	0.520589i	0.0439332	−	0.0319194i
$267$	0.279868	+	0.861345i	0.0171276	+	0.0527134i
$268$	−0.472852	+	1.45529i	−0.0288841	+	0.0888960i
$269$	−23.3034	−	16.9309i	−1.42083	−	1.03230i	−0.991633	−	0.129087i	$-0.958795\pi$
$269$	−23.3034	−	16.9309i	−1.42083	−	1.03230i	−0.429201	−	0.903209i	$-0.641205\pi$
$270$		0			0
$271$	−4.96782	+	15.2894i	−0.301773	+	0.928763i	0.679088	+	0.734057i	$0.262375\pi$
$271$	−4.96782	+	15.2894i	−0.301773	+	0.928763i	−0.980862	+	0.194706i	$0.937625\pi$
$272$	−3.35334	−	10.3205i	−0.203326	−	0.625774i
$273$	−2.10084	+	1.52635i	−0.127149	+	0.0923790i
$274$	5.36301			0.323992
$275$		0			0
$276$	1.45951			0.0878522
$277$	−14.5654	+	10.5824i	−0.875148	+	0.635832i	−0.931963	−	0.362552i	$-0.881905\pi$
$277$	−14.5654	+	10.5824i	−0.875148	+	0.635832i	0.0568151	+	0.998385i	$0.481905\pi$
$278$	3.16594	+	9.74375i	0.189880	+	0.584391i
$279$	−0.500000	+	1.53884i	−0.0299342	+	0.0921280i
$280$		0			0
$281$	−11.0957	−	8.06146i	−0.661911	−	0.480907i	0.205397	−	0.978679i	$-0.434152\pi$
$281$	−11.0957	−	8.06146i	−0.661911	−	0.480907i	−0.867308	+	0.497772i	$0.834152\pi$
$282$	0.683536	−	2.10371i	0.0407040	−	0.125274i
$283$	−6.33621	−	19.5009i	−0.376649	−	1.15921i	−0.942360	−	0.334602i	$-0.891398\pi$
$283$	−6.33621	−	19.5009i	−0.376649	−	1.15921i	0.565711	−	0.824604i	$-0.308602\pi$
$284$	−3.24372	+	2.35670i	−0.192479	+	0.139844i
$285$		0			0
$286$	6.92428	−	8.92103i	0.409441	−	0.527512i
$287$	13.2172			0.780184
$288$	−6.11708	+	4.44432i	−0.360452	+	0.261884i
$289$	−0.669933	−	2.06184i	−0.0394078	−	0.121285i
$290$		0			0
$291$	3.21013	+	2.33229i	0.188181	+	0.136721i
$292$	−5.03306	−	3.65673i	−0.294538	−	0.213994i
$293$	6.92608	−	21.3163i	0.404626	−	1.24531i	−0.516581	−	0.856238i	$-0.672796\pi$
$293$	6.92608	−	21.3163i	0.404626	−	1.24531i	0.921207	−	0.389073i	$-0.127204\pi$
$294$	0.0436901	+	0.134464i	0.00254806	+	0.00784212i
$295$		0			0
$296$	−1.59750			−0.0928525
$297$	3.97955	+	5.85963i	0.230917	+	0.340010i
$298$	−10.4481			−0.605242
$299$	−18.7555	+	13.6266i	−1.08466	+	0.788049i
$300$		0			0
$301$	−2.03308	+	6.25718i	−0.117185	+	0.360658i
$302$	11.0837	+	8.05276i	0.637794	+	0.463384i
$303$	−4.07492	−	2.96060i	−0.234098	−	0.170082i
$304$	0.241704	−	0.743887i	0.0138627	−	0.0426649i
$305$		0			0
$306$	−11.0250	+	8.01010i	−0.630255	+	0.457907i
$307$	−20.3044			−1.15883			−0.579416	−	0.815032i	$-0.696719\pi$
$307$	−20.3044			−1.15883			−0.579416	+	0.815032i	$0.696719\pi$
$308$	−2.29939	−	3.38570i	−0.131020	−	0.192918i
$309$	4.87369			0.277254
$310$		0			0
$311$	−2.70662	−	8.33012i	−0.153478	−	0.472358i	0.844525	−	0.535516i	$-0.179883\pi$
$311$	−2.70662	−	8.33012i	−0.153478	−	0.472358i	−0.998004	+	0.0631580i	$0.979883\pi$
$312$	−0.948735	+	2.91991i	−0.0537116	+	0.165307i
$313$	−1.40060	−	1.01759i	−0.0791664	−	0.0575177i	0.547498	−	0.836807i	$-0.315580\pi$
$313$	−1.40060	−	1.01759i	−0.0791664	−	0.0575177i	−0.626664	+	0.779289i	$0.715580\pi$
$314$	13.7431	+	9.98497i	0.775570	+	0.563485i
$315$		0			0
$316$	−1.43120	−	4.40477i	−0.0805111	−	0.247788i
$317$	−14.1387	+	10.2724i	−0.794109	+	0.576954i	−0.909180	−	0.416403i	$-0.863290\pi$
$317$	−14.1387	+	10.2724i	−0.794109	+	0.576954i	0.115071	+	0.993357i	$0.463290\pi$
$318$	3.91699			0.219654
$319$	6.75777	−	8.70651i	0.378363	−	0.487471i
$320$		0			0
$321$	−3.02107	+	2.19493i	−0.168619	+	0.122509i
$322$	−8.28372	−	25.4947i	−0.461633	−	1.42076i
$323$	−0.330361	+	1.01675i	−0.0183818	+	0.0565733i
$324$	3.02140	+	2.19518i	0.167856	+	0.121954i
$325$		0			0
$326$	−3.40940	+	10.4931i	−0.188829	+	0.581157i
$327$	−0.555929	−	1.71097i	−0.0307430	−	0.0946171i
$328$	12.6422	−	9.18509i	0.698048	−	0.507162i
$329$	12.7334			0.702014
$330$		0			0
$331$	12.6193			0.693620			0.346810	−	0.937935i	$-0.387265\pi$
$331$	12.6193			0.693620			0.346810	+	0.937935i	$0.387265\pi$
$332$	1.27301	−	0.924893i	0.0698653	−	0.0507601i
$333$	0.463067	+	1.42517i	0.0253759	+	0.0780990i
$334$	6.45132	−	19.8551i	0.353000	−	1.08642i
$335$		0			0
$336$	−2.14531	−	1.55866i	−0.117036	−	0.0850320i
$337$	−3.66490	+	11.2794i	−0.199640	+	0.614428i	0.800251	+	0.599665i	$0.204699\pi$
$337$	−3.66490	+	11.2794i	−0.199640	+	0.614428i	−0.999891	+	0.0147629i	$0.995301\pi$
$338$	2.05393	+	6.32135i	0.111719	+	0.343836i
$339$	2.92232	−	2.12319i	0.158719	−	0.115316i
$340$		0			0
$341$	−1.79730	+	0.521562i	−0.0973294	+	0.0282442i
$342$	−0.982255			−0.0531143
$343$	−15.3009	+	11.1167i	−0.826171	+	0.600248i
$344$	2.40371	+	7.39785i	0.129599	+	0.398865i
$345$		0			0
$346$	3.37422	+	2.45152i	0.181399	+	0.131794i
$347$	18.0444	+	13.1100i	0.968672	+	0.703781i	0.955148	−	0.296127i	$-0.0956953\pi$
$347$	18.0444	+	13.1100i	0.968672	+	0.703781i	0.0135232	+	0.999909i	$0.495695\pi$
$348$	−0.178385	+	0.549011i	−0.00956242	+	0.0294301i
$349$	4.93434	+	15.1863i	0.264129	+	0.812906i	0.991893	+	0.127078i	$0.0405599\pi$
$349$	4.93434	+	15.1863i	0.264129	+	0.812906i	−0.727763	+	0.685828i	$0.759440\pi$
$350$		0			0
$351$	5.89295			0.314542
$352$	−8.22740	−	2.96492i	−0.438522	−	0.158031i
$353$	24.1406			1.28488			0.642439	−	0.766337i	$-0.277923\pi$
$353$	24.1406			1.28488			0.642439	+	0.766337i	$0.277923\pi$
$354$	2.72792	−	1.98195i	0.144987	−	0.105340i
$355$		0			0
$356$	−0.366968	+	1.12941i	−0.0194492	+	0.0598586i
$357$	2.93222	+	2.13038i	0.155189	+	0.112752i
$358$	13.8007	+	10.0268i	0.729391	+	0.529934i
$359$	6.29726	−	19.3810i	0.332357	−	1.02289i	−0.635653	−	0.771975i	$-0.719269\pi$
$359$	6.29726	−	19.3810i	0.332357	−	1.02289i	0.968010	−	0.250913i	$-0.0807309\pi$
$360$		0			0
$361$	15.3090	−	11.1226i	0.805736	−	0.585401i
$362$	3.20716			0.168564
$363$	−1.47620	+	3.72173i	−0.0774804	+	0.195340i
$364$	−3.40495			−0.178468
$365$		0			0
$366$	−1.96799	−	6.05685i	−0.102869	−	0.316597i
$367$	−1.67002	+	5.13979i	−0.0871744	+	0.268295i	−0.985135	−	0.171780i	$-0.945048\pi$
$367$	−1.67002	+	5.13979i	−0.0871744	+	0.268295i	0.897961	+	0.440075i	$0.145048\pi$
$368$	−19.1525	−	13.9151i	−0.998392	−	0.725374i
$369$	−11.8589	−	8.61599i	−0.617349	−	0.448530i
$370$		0			0
$371$	6.96786	+	21.4449i	0.361753	+	1.11336i
$372$	0.0793003	−	0.0576150i	0.00411153	−	0.00298720i
$373$	17.0982			0.885311			0.442656	−	0.896692i	$-0.354036\pi$
$373$	17.0982			0.885311			0.442656	+	0.896692i	$0.354036\pi$
$374$	−14.8285	−	5.34375i	−0.766761	−	0.276319i
$375$		0			0
$376$	12.1795	−	8.84889i	0.628108	−	0.456347i
$377$	−2.83348	−	8.72055i	−0.145932	−	0.449131i
$378$	−2.10566	+	6.48055i	−0.108303	+	0.333323i
$379$	6.95104	+	5.05023i	0.357051	+	0.259413i	0.751821	−	0.659367i	$-0.229176\pi$
$379$	6.95104	+	5.05023i	0.357051	+	0.259413i	−0.394770	+	0.918780i	$0.629176\pi$
$380$		0			0
$381$	1.25251	−	3.85484i	0.0641681	−	0.197489i
$382$	−0.845900	−	2.60341i	−0.0432800	−	0.133202i
$383$	−7.82286	+	5.68364i	−0.399729	+	0.290420i	−0.769431	−	0.638730i	$-0.779460\pi$
$383$	−7.82286	+	5.68364i	−0.399729	+	0.290420i	0.369701	+	0.929151i	$0.379460\pi$
$384$	−2.07310			−0.105792
$385$		0			0
$386$	12.9279			0.658012
$387$	5.90307	−	4.28883i	0.300070	−	0.218014i
$388$	1.60776	+	4.94818i	0.0816217	+	0.251206i
$389$	−8.45759	+	26.0298i	−0.428817	+	1.31976i	0.470475	+	0.882414i	$0.344083\pi$
$389$	−8.45759	+	26.0298i	−0.428817	+	1.31976i	−0.899292	+	0.437350i	$0.855917\pi$
$390$		0			0
$391$	26.1776	+	19.0192i	1.32386	+	0.961840i
$392$	−0.297354	+	0.915163i	−0.0150187	+	0.0462227i
$393$	1.14332	+	3.51877i	0.0576727	+	0.177498i
$394$	−1.32444	+	0.962262i	−0.0667243	+	0.0484780i
$395$		0			0
$396$	−0.143975	+	4.53669i	−0.00723503	+	0.227977i
$397$	10.6518			0.534596			0.267298	−	0.963614i	$-0.413869\pi$
$397$	10.6518			0.534596			0.267298	+	0.963614i	$0.413869\pi$
$398$	−5.19448	+	3.77401i	−0.260376	+	0.189174i
$399$	0.0807283	+	0.248456i	0.00404147	+	0.0124384i
$400$		0			0
$401$	−11.0953	−	8.06124i	−0.554075	−	0.402559i	0.275210	−	0.961384i	$-0.411252\pi$
$401$	−11.0953	−	8.06124i	−0.554075	−	0.402559i	−0.829286	+	0.558825i	$0.811252\pi$
$402$	1.16504	+	0.846448i	0.0581067	+	0.0422170i
$403$	−0.481129	+	1.48076i	−0.0239668	+	0.0737621i
$404$	−2.04088	−	6.28119i	−0.101538	−	0.312501i
$405$		0			0
$406$	10.6026			0.526196
$407$	−1.06272	+	1.36918i	−0.0526771	+	0.0678676i
$408$	4.28514			0.212146
$409$	18.0478	−	13.1125i	0.892408	−	0.648372i	−0.0440970	−	0.999027i	$-0.514041\pi$
$409$	18.0478	−	13.1125i	0.892408	−	0.648372i	0.936505	+	0.350655i	$0.114041\pi$
$410$		0			0
$411$	−0.488831	+	1.50447i	−0.0241123	+	0.0742099i
$412$	5.16999	+	3.75622i	0.254707	+	0.185056i
$413$	15.7035	+	11.4093i	0.772719	+	0.561413i
$414$	−9.18699	+	28.2747i	−0.451516	+	1.38962i
$415$		0			0
$416$	−5.88621	+	4.27658i	−0.288595	+	0.209677i
$417$	−3.02195			−0.147986
$418$	−0.638290	−	0.939840i	−0.0312198	−	0.0459691i
$419$	−0.510725			−0.0249506			−0.0124753	−	0.999922i	$-0.503971\pi$
$419$	−0.510725			−0.0249506			−0.0124753	+	0.999922i	$0.503971\pi$
$420$		0			0
$421$	4.08365	+	12.5682i	0.199025	+	0.612536i	0.999906	+	0.0137124i	$0.00436492\pi$
$421$	4.08365	+	12.5682i	0.199025	+	0.612536i	−0.800881	+	0.598824i	$0.795635\pi$
$422$	−7.21335	+	22.2004i	−0.351140	+	1.08070i
$423$	−11.4248	−	8.30062i	−0.555494	−	0.403590i
$424$	21.5676	+	15.6698i	1.04741	+	0.760991i
$425$		0			0
$426$	1.16602	+	3.58864i	0.0564939	+	0.173870i
$427$	29.6594	−	21.5488i	1.43532	−	1.04282i
$428$	−4.89641			−0.236677
$429$	1.87145	+	2.75558i	0.0903543	+	0.133041i
$430$		0			0
$431$	23.7902	−	17.2846i	1.14594	−	0.832571i	0.158000	−	0.987439i	$-0.449495\pi$
$431$	23.7902	−	17.2846i	1.14594	−	0.832571i	0.987935	+	0.154868i	$0.0494952\pi$
$432$	1.85957	+	5.72316i	0.0894685	+	0.275356i
$433$	−3.15708	+	9.71650i	−0.151720	+	0.466945i	−0.997814	−	0.0660883i	$-0.978948\pi$
$433$	−3.15708	+	9.71650i	−0.151720	+	0.466945i	0.846094	+	0.533034i	$0.178948\pi$
$434$	−1.45650	−	1.05821i	−0.0699142	−	0.0507956i
$435$		0			0
$436$	0.728944	−	2.24346i	0.0349101	−	0.107442i
$437$	0.720709	+	2.21811i	0.0344762	+	0.106107i
$438$	−4.73664	+	3.44137i	−0.226325	+	0.164435i
$439$	−1.53306			−0.0731691			−0.0365846	−	0.999331i	$-0.511648\pi$
$439$	−1.53306			−0.0731691			−0.0365846	+	0.999331i	$0.511648\pi$
$440$		0			0
$441$	0.902638			0.0429827
$442$	−10.6089	+	7.70779i	−0.504612	+	0.366622i
$443$	1.04835	+	3.22650i	0.0498088	+	0.153296i	0.972867	−	0.231364i	$-0.0743188\pi$
$443$	1.04835	+	3.22650i	0.0498088	+	0.153296i	−0.923058	+	0.384660i	$0.874319\pi$
$444$	0.0280526	−	0.0863370i	0.00133132	−	0.00409737i
$445$		0			0
$446$	21.8356	+	15.8645i	1.03394	+	0.751204i
$447$	0.952329	−	2.93097i	0.0450436	−	0.138630i
$448$	−7.10238	−	21.8589i	−0.335556	−	1.03274i
$449$	26.1718	−	19.0149i	1.23512	−	0.897368i	0.237858	−	0.971300i	$-0.423555\pi$
$449$	26.1718	−	19.0149i	1.23512	−	0.897368i	0.997263	+	0.0739317i	$0.0235547\pi$
$450$		0			0
$451$	0.537783	−	16.9456i	0.0253232	−	0.797939i
$452$	4.73637			0.222780
$453$	−3.26927	+	2.37527i	−0.153604	+	0.111600i
$454$	0.929918	+	2.86199i	0.0436432	+	0.134320i
$455$		0			0
$456$	0.249878	+	0.181547i	0.0117016	+	0.00850171i
$457$	−9.84814	−	7.15509i	−0.460676	−	0.334701i	0.333120	−	0.942884i	$-0.391899\pi$
$457$	−9.84814	−	7.15509i	−0.460676	−	0.334701i	−0.793797	+	0.608183i	$0.791899\pi$
$458$	−2.78412	+	8.56865i	−0.130094	+	0.400387i
$459$	−2.54166	−	7.82243i	−0.118635	−	0.365120i
$460$		0			0
$461$	−16.5699			−0.771739			−0.385869	−	0.922553i	$-0.626098\pi$
$461$	−16.5699			−0.771739			−0.385869	+	0.922553i	$0.626098\pi$
$462$	−3.69905	+	1.07343i	−0.172095	+	0.0499407i
$463$	14.6302			0.679924			0.339962	−	0.940439i	$-0.389586\pi$
$463$	14.6302			0.679924			0.339962	+	0.940439i	$0.389586\pi$
$464$	7.57517	−	5.50368i	0.351669	−	0.255502i
$465$		0			0
$466$	−1.70006	+	5.23226i	−0.0787539	+	0.242380i
$467$	−24.6632	−	17.9188i	−1.14128	−	0.829185i	−0.153979	−	0.988074i	$-0.549209\pi$
$467$	−24.6632	−	17.9188i	−1.14128	−	0.829185i	−0.987296	+	0.158889i	$0.949209\pi$
$468$	3.05504	+	2.21961i	0.141219	+	0.102602i
$469$	−2.56170	+	7.88411i	−0.118288	+	0.364054i
$470$		0			0
$471$	−4.05372	+	2.94520i	−0.186785	+	0.135707i
$472$	22.9491			1.05632
$473$	7.93957	+	2.86120i	0.365062	+	0.131558i
$474$	−4.35868			−0.200201
$475$		0			0
$476$	1.46857	+	4.51981i	0.0673120	+	0.207165i
$477$	7.72766	−	23.7833i	0.353825	−	1.08896i
$478$	24.1342	+	17.5345i	1.10387	+	0.802009i
$479$	−11.3257	−	8.22857i	−0.517482	−	0.375973i	0.298172	−	0.954512i	$-0.403623\pi$
$479$	−11.3257	−	8.22857i	−0.517482	−	0.375973i	−0.815655	+	0.578539i	$0.803623\pi$
$480$		0			0
$481$	0.445590	+	1.37138i	0.0203172	+	0.0625298i
$482$	−12.0191	+	8.73241i	−0.547456	+	0.397750i
$483$	7.90697			0.359780
$484$	−4.43434	+	2.81027i	−0.201561	+	0.127740i
$485$		0			0
$486$	9.23972	−	6.71305i	0.419122	−	0.304510i
$487$	10.5471	+	32.4606i	0.477934	+	1.47093i	0.841960	+	0.539541i	$0.181402\pi$
$487$	10.5471	+	32.4606i	0.477934	+	1.47093i	−0.364026	+	0.931389i	$0.618598\pi$
$488$	13.3941	−	41.2229i	0.606324	−	1.86607i
$489$	−2.63282	−	1.91285i	−0.119060	−	0.0865022i
$490$		0			0
$491$	−0.987097	+	3.03797i	−0.0445470	+	0.137102i	−0.970856	−	0.239662i	$-0.922963\pi$
$491$	−0.987097	+	3.03797i	−0.0445470	+	0.137102i	0.926309	+	0.376764i	$0.122963\pi$
$492$	0.274409	+	0.844543i	0.0123713	+	0.0380750i
$493$	−10.3538	+	7.52244i	−0.466310	+	0.338794i
$494$	−0.945184			−0.0425258
$495$		0			0
$496$	−1.58993			−0.0713898
$497$	−17.5730	+	12.7675i	−0.788257	+	0.572702i
$498$	−0.457607	−	1.40837i	−0.0205059	−	0.0631106i
$499$	2.01742	−	6.20897i	0.0903120	−	0.277952i	−0.895692	−	0.444676i	$-0.853319\pi$
$499$	2.01742	−	6.20897i	0.0903120	−	0.277952i	0.986004	+	0.166724i	$0.0533189\pi$
$500$		0			0
$501$	4.98186	+	3.61953i	0.222573	+	0.161709i
$502$	0.204538	−	0.629504i	0.00912898	−	0.0280961i
$503$	0.310213	+	0.954737i	0.0138317	+	0.0425696i	0.957734	−	0.287655i	$-0.0928756\pi$
$503$	0.310213	+	0.954737i	0.0138317	+	0.0425696i	−0.943902	+	0.330224i	$0.892876\pi$
$504$	−18.3361	+	13.3219i	−0.816753	+	0.593406i
$505$		0			0
$506$	−33.0236	+	9.58317i	−1.46808	+	0.426024i
$507$	−1.96052			−0.0870697
$508$	4.29964	−	3.12387i	0.190766	−	0.138599i
$509$	−1.32074	−	4.06483i	−0.0585409	−	0.180170i	0.917510	−	0.397713i	$-0.130196\pi$
$509$	−1.32074	−	4.06483i	−0.0585409	−	0.180170i	−0.976051	+	0.217542i	$0.930196\pi$
$510$		0			0
$511$	−27.2669	−	19.8105i	−1.20621	−	0.876366i
$512$	−19.9477	−	14.4929i	−0.881574	−	0.640501i
$513$	0.183199	−	0.563828i	0.00808842	−	0.0248936i
$514$	−9.04501	−	27.8377i	−0.398958	−	1.22787i
$515$		0			0
$516$	−0.442028			−0.0194592
$517$	0.518099	−	16.3254i	0.0227860	−	0.717990i
$518$	−1.66735			−0.0732590
$519$	−0.995271	+	0.723107i	−0.0436875	+	0.0317409i
$520$		0			0
$521$	−3.05561	+	9.40421i	−0.133869	+	0.412006i	−0.995412	−	0.0956779i	$-0.969498\pi$
$521$	−3.05561	+	9.40421i	−0.133869	+	0.412006i	0.861544	+	0.507684i	$0.169498\pi$
$522$	−9.51297	−	6.91158i	−0.416371	−	0.302512i
$523$	−35.7318	−	25.9607i	−1.56244	−	1.13518i	−0.933970	−	0.357351i	$-0.883680\pi$
$523$	−35.7318	−	25.9607i	−1.56244	−	1.13518i	−0.628474	−	0.777831i	$-0.716320\pi$
$524$	−1.49914	+	4.61387i	−0.0654901	+	0.201558i
$525$		0			0
$526$	−4.96808	+	3.60952i	−0.216619	+	0.157383i
$527$	2.17311			0.0946623
$528$	−2.08564	+	2.68708i	−0.0907659	+	0.116940i
$529$	47.5902			2.06914
$530$		0			0
$531$	−6.65227	−	20.4736i	−0.288684	−	0.888477i
$532$	−0.105852	+	0.325780i	−0.00458928	+	0.0141244i
$533$	−11.4113	−	8.29081i	−0.494279	−	0.359115i
$534$	0.904152	+	0.656905i	0.0391265	+	0.0284270i
$535$		0			0
$536$	3.02869	+	9.32135i	0.130820	+	0.402621i
$537$	−4.07070	+	2.95754i	−0.175664	+	0.127627i
$538$	−35.5447			−1.53244
$539$	0.586552	+	0.863660i	0.0252646	+	0.0372005i
$540$		0			0
$541$	17.2074	−	12.5019i	0.739805	−	0.537499i	−0.152845	−	0.988250i	$-0.548844\pi$
$541$	17.2074	−	12.5019i	0.739805	−	0.537499i	0.892650	+	0.450751i	$0.148844\pi$
$542$	6.13026	+	18.8670i	0.263317	+	0.810406i
$543$	−0.292328	+	0.899692i	−0.0125450	+	0.0386095i
$544$	8.21558	+	5.96897i	0.352240	+	0.255918i
$545$		0			0
$546$	−0.990219	+	3.04758i	−0.0423775	+	0.130424i
$547$	1.27746	+	3.93160i	0.0546201	+	0.168103i	0.974645	−	0.223756i	$-0.0718319\pi$
$547$	1.27746	+	3.93160i	0.0546201	+	0.168103i	−0.920025	+	0.391859i	$0.871832\pi$
$548$	−1.67806	+	1.21919i	−0.0716834	+	0.0520810i
$549$	−40.6587			−1.73527
$550$		0			0
$551$	−0.922455			−0.0392979
$552$	7.56301	−	5.49485i	0.321903	−	0.233876i
$553$	−7.75358	−	23.8631i	−0.329716	−	1.01476i
$554$	−6.86529	+	21.1292i	−0.291678	+	0.897694i
$555$		0			0
$556$	−3.20568	−	2.32906i	−0.135951	−	0.0987742i
$557$	9.78568	−	30.1172i	0.414633	−	1.27611i	−0.497947	−	0.867208i	$-0.665912\pi$
$557$	9.78568	−	30.1172i	0.414633	−	1.27611i	0.912579	−	0.408900i	$-0.134088\pi$
$558$	0.616997	+	1.89892i	0.0261196	+	0.0803877i
$559$	5.68028	−	4.12697i	0.240250	−	0.174552i
$560$		0			0
$561$	2.85066	−	3.67270i	0.120355	−	0.155061i
$562$	−16.9242			−0.713904
$563$	10.3123	−	7.49233i	0.434612	−	0.315764i	−0.348879	−	0.937168i	$-0.613437\pi$
$563$	10.3123	−	7.49233i	0.434612	−	0.315764i	0.783490	+	0.621404i	$0.213437\pi$
$564$	0.264365	+	0.813631i	0.0111318	+	0.0342600i
$565$		0			0
$566$	−20.4700	−	14.8723i	−0.860419	−	0.625131i
$567$	16.3686	+	11.8925i	0.687416	+	0.499437i
$568$	−7.93592	+	24.4243i	−0.332984	+	1.02482i
$569$	4.83153	+	14.8699i	0.202548	+	0.623380i	0.999805	+	0.0197396i	$0.00628372\pi$
$569$	4.83153	+	14.8699i	0.202548	+	0.623380i	−0.797257	+	0.603640i	$0.793716\pi$
$570$		0			0
$571$	−3.61999			−0.151492			−0.0757460	−	0.997127i	$-0.524134\pi$
$571$	−3.61999			−0.151492			−0.0757460	+	0.997127i	$0.524134\pi$
$572$	−0.138541	+	4.36547i	−0.00579271	+	0.182529i
$573$	0.807429			0.0337308
$574$	13.1950	−	9.58671i	0.550748	−	0.400142i
$575$		0			0
$576$	−7.87684	+	24.2424i	−0.328202	+	1.01010i
$577$	19.2831	+	14.0100i	0.802765	+	0.583243i	0.911724	−	0.410803i	$-0.134752\pi$
$577$	19.2831	+	14.0100i	0.802765	+	0.583243i	−0.108959	+	0.994046i	$0.534752\pi$
$578$	−2.16431	−	1.57246i	−0.0900234	−	0.0654058i
$579$	−1.17836	+	3.62661i	−0.0489709	+	0.150717i
$580$		0			0
$581$	6.89657	−	5.01065i	0.286118	−	0.207877i
$582$	4.89641			0.202963
$583$	27.7779	−	8.06090i	1.15044	−	0.333848i
$584$	−39.8478			−1.64891
$585$		0			0
$586$	−8.54674	−	26.3042i	−0.353063	−	1.08661i
$587$	−0.385338	+	1.18595i	−0.0159046	+	0.0489493i	−0.958694	−	0.284440i	$-0.908192\pi$
$587$	−0.385338	+	1.18595i	−0.0159046	+	0.0489493i	0.942789	+	0.333389i	$0.108192\pi$
$588$	−0.0442385	−	0.0321412i	−0.00182436	−	0.00132548i
$589$	0.126720	+	0.0920674i	0.00522140	+	0.00379357i
$590$		0			0
$591$	−0.149219	−	0.459249i	−0.00613805	−	0.0188910i
$592$	−1.19126	+	0.865504i	−0.0489606	+	0.0355720i
$593$	−18.5288			−0.760886			−0.380443	−	0.924804i	$-0.624228\pi$
$593$	−18.5288			−0.760886			−0.380443	+	0.924804i	$0.624228\pi$
$594$	8.22300	+	2.96333i	0.337394	+	0.121587i
$595$		0			0
$596$	3.26917	−	2.37519i	0.133910	−	0.0972915i
$597$	−0.585240	−	1.80118i	−0.0239523	−	0.0737176i
$598$	−8.84026	+	27.2075i	−0.361505	+	1.11260i
$599$	−27.3738	−	19.8882i	−1.11846	−	0.812611i	−0.134488	−	0.990915i	$-0.542939\pi$
$599$	−27.3738	−	19.8882i	−1.11846	−	0.812611i	−0.983975	+	0.178304i	$0.942939\pi$
$600$		0			0
$601$	−6.58286	+	20.2600i	−0.268520	+	0.826421i	0.722341	+	0.691537i	$0.243066\pi$
$601$	−6.58286	+	20.2600i	−0.268520	+	0.826421i	−0.990861	+	0.134884i	$0.956934\pi$
$602$	2.50881	+	7.72132i	0.102251	+	0.314698i
$603$	7.43793	−	5.40397i	0.302896	−	0.220067i
$604$	−5.29869			−0.215601
$605$		0			0
$606$	−6.21547			−0.252486
$607$	30.3059	−	22.0185i	1.23008	−	0.893704i	0.233182	−	0.972433i	$-0.425086\pi$
$607$	30.3059	−	22.0185i	1.23008	−	0.893704i	0.996896	+	0.0787287i	$0.0250861\pi$
$608$	0.226187	+	0.696133i	0.00917310	+	0.0282319i
$609$	−0.966407	+	2.97430i	−0.0391608	+	0.120525i
$610$		0			0
$611$	−10.9936	−	7.98734i	−0.444755	−	0.323133i
$612$	1.62871	−	5.01266i	0.0658367	−	0.202625i
$613$	6.18180	+	19.0256i	0.249680	+	0.768437i	0.994831	+	0.101541i	$0.0323774\pi$
$613$	6.18180	+	19.0256i	0.249680	+	0.768437i	−0.745151	+	0.666896i	$0.767623\pi$
$614$	−20.2703	+	14.7272i	−0.818043	+	0.594343i
$615$		0			0
$616$	−24.6618	−	8.88741i	−0.993652	−	0.358084i
$617$	−34.7932			−1.40072			−0.700360	−	0.713790i	$-0.746977\pi$
$617$	−34.7932			−1.40072			−0.700360	+	0.713790i	$0.746977\pi$
$618$	4.86551	−	3.53500i	0.195719	−	0.142198i
$619$	−14.2407	−	43.8285i	−0.572384	−	1.76162i	−0.644920	−	0.764250i	$-0.723109\pi$
$619$	−14.2407	−	43.8285i	−0.572384	−	1.76162i	0.0725362	−	0.997366i	$-0.476891\pi$
$620$		0			0
$621$	−14.5166	−	10.5469i	−0.582530	−	0.423233i
$622$	−8.74411	−	6.35297i	−0.350607	−	0.254731i
$623$	−1.98807	+	6.11864i	−0.0796502	+	0.245138i
$624$	0.874492	+	2.69141i	0.0350077	+	0.107743i
$625$		0			0
$626$	−2.13633			−0.0853849
$627$	0.321829	−	0.0933921i	0.0128526	−	0.00372972i
$628$	−6.57008			−0.262175
$629$	1.62822	−	1.18297i	0.0649214	−	0.0471682i
$630$		0			0
$631$	−6.34658	+	19.5328i	−0.252653	+	0.777587i	0.741629	+	0.670810i	$0.234053\pi$
$631$	−6.34658	+	19.5328i	−0.252653	+	0.777587i	−0.994283	+	0.106778i	$0.965947\pi$
$632$	−23.9996	−	17.4367i	−0.954653	−	0.693596i
$633$	−5.57031	−	4.04707i	−0.221400	−	0.160857i
$634$	−6.66419	+	20.5103i	−0.264669	+	0.814567i
$635$		0			0
$636$	−1.22561	+	0.890458i	−0.0485986	+	0.0353090i
$637$	0.868571			0.0344140
$638$	0.431399	−	13.5935i	0.0170793	−	0.538171i
$639$	24.0900			0.952985
$640$		0			0
$641$	4.91631	+	15.1309i	0.194183	+	0.597633i	0.999985	+	0.00544856i	$0.00173434\pi$
$641$	4.91631	+	15.1309i	0.194183	+	0.597633i	−0.805802	+	0.592185i	$0.798266\pi$
$642$	−1.42396	+	4.38250i	−0.0561992	+	0.172963i
$643$	34.2246	+	24.8656i	1.34968	+	0.980603i	0.999027	+	0.0440996i	$0.0140419\pi$
$643$	34.2246	+	24.8656i	1.34968	+	0.980603i	0.350658	+	0.936504i	$0.385958\pi$
$644$	8.38769	+	6.09402i	0.330521	+	0.240138i
$645$		0			0
$646$	0.407663	+	1.25466i	0.0160393	+	0.0493639i
$647$	−6.05866	+	4.40187i	−0.238190	+	0.173055i	−0.700477	−	0.713675i	$-0.747029\pi$
$647$	−6.05866	+	4.40187i	−0.238190	+	0.173055i	0.462286	+	0.886731i	$0.347029\pi$
$648$	23.9210			0.939707
$649$	15.2667	−	19.6692i	0.599271	−	0.772082i
$650$		0			0
$651$	0.429613	−	0.312132i	0.0168379	−	0.0122334i
$652$	−1.31862	−	4.05830i	−0.0516412	−	0.158935i
$653$	−5.08959	+	15.6641i	−0.199171	+	0.612985i	0.800732	+	0.599023i	$0.204444\pi$
$653$	−5.08959	+	15.6641i	−0.199171	+	0.612985i	−0.999903	+	0.0139618i	$0.995556\pi$
$654$	−1.79601	−	1.30487i	−0.0702294	−	0.0510246i
$655$		0			0
$656$	4.45100	−	13.6988i	0.173782	−	0.534847i
$657$	11.5507	+	35.5494i	0.450635	+	1.38691i
$658$	12.7120	−	9.23581i	0.495566	−	0.360050i
$659$	23.7359			0.924619			0.462310	−	0.886719i	$-0.347021\pi$
$659$	23.7359			0.924619			0.462310	+	0.886719i	$0.347021\pi$
$660$		0			0
$661$	13.4183			0.521911			0.260956	−	0.965351i	$-0.415962\pi$
$661$	13.4183			0.521911			0.260956	+	0.965351i	$0.415962\pi$
$662$	12.5981	−	9.15308i	0.489640	−	0.355745i
$663$	−1.19526	−	3.67862i	−0.0464199	−	0.142866i
$664$	3.11447	−	9.58536i	0.120865	−	0.371984i
$665$		0			0
$666$	1.49600	+	1.08691i	0.0579688	+	0.0421168i
$667$	−8.62768	+	26.5533i	−0.334065	+	1.02815i
$668$	2.49512	+	7.67918i	0.0965389	+	0.297116i
$669$	−6.44068	+	4.67943i	−0.249011	+	0.180917i
$670$		0			0
$671$	−26.4209	−	38.9030i	−1.01997	−	1.50183i
$672$	2.48152			0.0957268
$673$	39.0650	−	28.3824i	1.50585	−	1.09406i	0.537867	−	0.843030i	$-0.319230\pi$
$673$	39.0650	−	28.3824i	1.50585	−	1.09406i	0.967979	−	0.251031i	$-0.0807697\pi$
$674$	4.52246	+	13.9187i	0.174199	+	0.536128i
$675$		0			0
$676$	−2.07971	−	1.51100i	−0.0799889	−	0.0581154i
$677$	19.7107	+	14.3206i	0.757543	+	0.550387i	0.898156	−	0.439678i	$-0.144907\pi$
$677$	19.7107	+	14.3206i	0.757543	+	0.550387i	−0.140613	+	0.990065i	$0.544907\pi$
$678$	1.37742	−	4.23926i	0.0528994	−	0.162808i
$679$	8.71013	+	26.8070i	0.334264	+	1.02876i
$680$		0			0
$681$	−0.887625			−0.0340139
$682$	−1.41598	+	1.82431i	−0.0542209	+	0.0698565i
$683$	−38.9856			−1.49174			−0.745871	−	0.666090i	$-0.767966\pi$
$683$	−38.9856			−1.49174			−0.745871	+	0.666090i	$0.767966\pi$
$684$	0.307344	−	0.223298i	0.0117516	−	0.00853802i
$685$		0			0
$686$	−7.21198	+	22.1962i	−0.275355	+	0.847454i
$687$	−2.14996	−	1.56204i	−0.0820263	−	0.0595956i
$688$	5.80053	+	4.21433i	0.221143	+	0.160670i
$689$	7.43600	−	22.8857i	0.283289	−	0.871875i
$690$		0			0
$691$	−4.78820	+	3.47883i	−0.182152	+	0.132341i	−0.675125	−	0.737704i	$-0.735910\pi$
$691$	−4.78820	+	3.47883i	−0.182152	+	0.132341i	0.492973	+	0.870045i	$0.335910\pi$
$692$	−1.61309			−0.0613205
$693$	−0.779993	+	24.5777i	−0.0296295	+	0.933630i
$694$	27.5230			1.04476
$695$		0			0
$696$	1.14258	+	3.51650i	0.0433094	+	0.133293i
$697$	−6.08364	+	18.7235i	−0.230434	+	0.709203i
$698$	15.9411	+	11.5819i	0.603378	+	0.438380i
$699$	−1.31283	−	0.953826i	−0.0496557	−	0.0360770i
$700$		0			0
$701$	3.69808	+	11.3815i	0.139675	+	0.429874i	0.996288	−	0.0860851i	$-0.0274357\pi$
$701$	3.69808	+	11.3815i	0.139675	+	0.429874i	−0.856613	+	0.515959i	$0.827436\pi$
$702$	5.88306	−	4.27429i	0.222042	−	0.161323i
$703$	0.145064			0.00547120
$704$	−28.3141	+	8.21652i	−1.06713	+	0.309672i
$705$		0			0
$706$	24.1001	−	17.5098i	0.907021	−	0.658989i
$707$	−11.0566	−	34.0287i	−0.415826	−	1.27978i
$708$	−0.402994	+	1.24029i	−0.0151455	+	0.0466129i
$709$	−5.50819	−	4.00194i	−0.206865	−	0.150296i	0.479529	−	0.877526i	$-0.340807\pi$
$709$	−5.50819	−	4.00194i	−0.206865	−	0.150296i	−0.686394	+	0.727230i	$0.740807\pi$
$710$		0			0
$711$	−8.59904	+	26.4651i	−0.322489	+	0.992520i
$712$	2.35048	+	7.23405i	0.0880881	+	0.271107i
$713$	3.83541	−	2.78659i	0.143637	−	0.104358i
$714$	4.47251			0.167380
$715$		0			0
$716$	−6.59761			−0.246564
$717$	−7.11868	+	5.17202i	−0.265852	+	0.193153i
$718$	−7.77077	−	23.9160i	−0.290003	−	0.892537i
$719$	−2.86277	+	8.81069i	−0.106763	+	0.328583i	−0.990140	−	0.140080i	$-0.955264\pi$
$719$	−2.86277	+	8.81069i	−0.106763	+	0.328583i	0.883377	+	0.468663i	$0.155264\pi$
$720$		0			0
$721$	28.0087	+	20.3495i	1.04310	+	0.757855i
$722$	7.21579	−	22.2079i	0.268544	−	0.826493i
$723$	−1.35414	−	4.16763i	−0.0503612	−	0.154996i
$724$	−1.00351	+	0.729090i	−0.0372950	+	0.0270964i
$725$		0			0
$726$	1.22574	+	4.78621i	0.0454913	+	0.177633i
$727$	−19.4121			−0.719956			−0.359978	−	0.932961i	$-0.617216\pi$
$727$	−19.4121			−0.719956			−0.359978	+	0.932961i	$0.617216\pi$
$728$	−17.6440	+	12.8191i	−0.653931	+	0.475109i
$729$	−6.21336	−	19.1228i	−0.230125	−	0.708250i
$730$		0			0
$731$	−7.92817	−	5.76015i	−0.293234	−	0.213047i
$732$	1.99269	+	1.44778i	0.0736521	+	0.0535114i
$733$	−3.57287	+	10.9962i	−0.131967	+	0.406152i	−0.995106	−	0.0988140i	$-0.968495\pi$
$733$	−3.57287	+	10.9962i	−0.131967	+	0.406152i	0.863139	+	0.504966i	$0.168495\pi$
$734$	2.06079	+	6.34247i	0.0760653	+	0.234105i
$735$		0			0
$736$	22.1540			0.816608
$737$	10.0039	+	3.60513i	0.368500	+	0.132797i
$738$	−18.0884			−0.665842
$739$	−7.36801	+	5.35317i	−0.271037	+	0.196920i	−0.714998	−	0.699126i	$-0.753573\pi$
$739$	−7.36801	+	5.35317i	−0.271037	+	0.196920i	0.443962	+	0.896046i	$0.353573\pi$
$740$		0			0
$741$	0.0861521	−	0.265149i	0.00316488	−	0.00974049i
$742$	22.5106	+	16.3549i	0.826391	+	0.600409i
$743$	0.0591398	+	0.0429676i	0.00216963	+	0.00157633i	0.588870	−	0.808228i	$-0.299573\pi$
$743$	0.0591398	+	0.0429676i	0.00216963	+	0.00157633i	−0.586700	+	0.809804i	$0.699573\pi$
$744$	0.194012	−	0.597108i	0.00711283	−	0.0218910i
$745$		0			0
$746$	17.0695	−	12.4017i	0.624959	−	0.454059i
$747$	−9.45417			−0.345910
$748$	5.85457	−	1.69895i	0.214064	−	0.0621197i
$749$	−26.5265			−0.969258
$750$		0			0
$751$	−11.9045	−	36.6384i	−0.434403	−	1.33695i	−0.893697	−	0.448670i	$-0.851898\pi$
$751$	−11.9045	−	36.6384i	−0.434403	−	1.33695i	0.459295	−	0.888284i	$-0.348102\pi$
$752$	4.28808	−	13.1974i	0.156370	−	0.481258i
$753$	0.157949	+	0.114757i	0.00575598	+	0.00418197i
$754$	−9.15394	−	6.65073i	−0.333367	−	0.242205i
$755$		0			0
$756$	−0.814385	−	2.50642i	−0.0296189	−	0.0911576i
$757$	22.7833	−	16.5530i	0.828073	−	0.601630i	−0.0909407	−	0.995856i	$-0.528987\pi$
$757$	22.7833	−	16.5530i	0.828073	−	0.601630i	0.919013	+	0.394226i	$0.128987\pi$
$758$	10.6024			0.385097
$759$	0.321721	−	10.1375i	0.0116777	−	0.367967i
$760$		0			0
$761$	23.8575	−	17.3335i	0.864832	−	0.628337i	−0.0643631	−	0.997927i	$-0.520502\pi$
$761$	23.8575	−	17.3335i	0.864832	−	0.628337i	0.929195	+	0.369589i	$0.120502\pi$
$762$	−1.54559	−	4.75684i	−0.0559909	−	0.172322i
$763$	3.94909	−	12.1541i	0.142967	−	0.440006i
$764$	0.856518	+	0.622297i	0.0309877	+	0.0225139i
$765$		0			0
$766$	−3.68725	+	11.3482i	−0.133226	+	0.410027i
$767$	−6.40120	−	19.7009i	−0.231134	−	0.711357i
$768$	3.16556	−	2.29991i	0.114227	−	0.0829910i
$769$	8.42410			0.303781			0.151890	−	0.988397i	$-0.451464\pi$
$769$	8.42410			0.303781			0.151890	+	0.988397i	$0.451464\pi$
$770$		0			0
$771$	8.63364			0.310933
$772$	−4.04508	+	2.93892i	−0.145586	+	0.105774i
$773$	−0.277338	−	0.853557i	−0.00997514	−	0.0307003i	0.945945	−	0.324327i	$-0.105138\pi$
$773$	−0.277338	−	0.853557i	−0.00997514	−	0.0307003i	−0.955920	+	0.293627i	$0.905138\pi$
$774$	2.78238	−	8.56327i	0.100010	−	0.307800i
$775$		0			0
$776$	26.9604	+	19.5879i	0.967822	+	0.703164i
$777$	0.151976	−	0.467735i	0.00545212	−	0.0167799i
$778$	10.4366	+	32.1206i	0.374171	+	1.15158i
$779$	−1.14800	+	0.834074i	−0.0411315	+	0.0298838i
$780$		0			0
$781$	15.6542	+	23.0497i	0.560150	+	0.824785i
$782$	39.9287			1.42785
$783$	5.74159	−	4.17151i	0.205188	−	0.149077i
$784$	0.274085	+	0.843546i	0.00978874	+	0.0301267i
$785$		0			0
$786$	3.69364	+	2.68359i	0.131748	+	0.0957205i
$787$	−30.5814	−	22.2187i	−1.09011	−	0.792010i	−0.110691	−	0.993855i	$-0.535306\pi$
$787$	−30.5814	−	22.2187i	−1.09011	−	0.792010i	−0.979418	+	0.201844i	$0.935306\pi$
$788$	0.195659	−	0.602175i	0.00697005	−	0.0214516i
$789$	−0.559733	−	1.72268i	−0.0199270	−	0.0613290i
$790$		0			0
$791$	25.6595			0.912346
$792$	16.3339	+	24.0506i	0.580400	+	0.854601i
$793$	−39.1242			−1.38934
$794$	10.6339	−	7.72596i	0.377382	−	0.274184i
$795$		0			0
$796$	0.767377	−	2.36174i	0.0271990	−	0.0837098i
$797$	12.2894	+	8.92880i	0.435314	+	0.316274i	0.783770	−	0.621051i	$-0.213294\pi$
$797$	12.2894	+	8.92880i	0.435314	+	0.316274i	−0.348456	+	0.937325i	$0.613294\pi$
$798$	0.260804	+	0.189485i	0.00923236	+	0.00670770i
$799$	−5.86096	+	18.0382i	−0.207346	+	0.638145i
$800$		0			0
$801$	5.77237	−	4.19387i	0.203957	−	0.148183i
$802$	−16.9237			−0.597598
$803$	−26.5084	+	34.1526i	−0.935461	+	1.20522i
$804$	−0.556959			−0.0196424
$805$		0			0
$806$	0.593711	+	1.82725i	0.0209126	+	0.0643623i
$807$	3.23985	−	9.97122i	0.114048	−	0.351004i
$808$	−34.2234	−	24.8647i	−1.20397	−	0.874739i
$809$	32.1268	+	23.3415i	1.12952	+	0.820643i	0.985625	−	0.168951i	$-0.0540379\pi$
$809$	32.1268	+	23.3415i	1.12952	+	0.820643i	0.143893	+	0.989593i	$0.454038\pi$
$810$		0			0
$811$	2.72454	+	8.38527i	0.0956715	+	0.294447i	0.987428	−	0.158069i	$-0.0505268\pi$
$811$	2.72454	+	8.38527i	0.0956715	+	0.294447i	−0.891757	+	0.452515i	$0.850527\pi$
$812$	−3.31749	+	2.41030i	−0.116421	+	0.0845850i
$813$	−5.85145			−0.205219
$814$	−0.0678414	+	2.13770i	−0.00237784	+	0.0749262i
$815$		0			0
$816$	3.19546	−	2.32164i	0.111864	−	0.0812736i
$817$	−0.218274	−	0.671779i	−0.00763645	−	0.0235026i
$818$	8.50673	−	26.1810i	0.297431	−	0.915398i
$819$	16.5508	+	12.0249i	0.578332	+	0.420183i
$820$		0			0
$821$	−2.60214	+	8.00856i	−0.0908153	+	0.279501i	−0.986141	−	0.165912i	$-0.946943\pi$
$821$	−2.60214	+	8.00856i	−0.0908153	+	0.279501i	0.895325	+	0.445413i	$0.146943\pi$
$822$	0.603214	+	1.85650i	0.0210395	+	0.0647530i
$823$	19.3388	−	14.0504i	0.674107	−	0.489767i	−0.197291	−	0.980345i	$-0.563214\pi$
$823$	19.3388	−	14.0504i	0.674107	−	0.489767i	0.871397	+	0.490578i	$0.163214\pi$
$824$	40.9319			1.42593
$825$		0			0
$826$	23.9526			0.833416
$827$	−38.4379	+	27.9268i	−1.33662	+	0.971109i	−0.337055	+	0.941485i	$0.609431\pi$
$827$	−38.4379	+	27.9268i	−1.33662	+	0.971109i	−0.999561	+	0.0296239i	$0.990569\pi$
$828$	−3.55317	−	10.9355i	−0.123481	−	0.380036i
$829$	−8.71437	+	26.8201i	−0.302663	+	0.931500i	0.677876	+	0.735176i	$0.262900\pi$
$829$	−8.71437	+	26.8201i	−0.302663	+	0.931500i	−0.980539	+	0.196324i	$0.937100\pi$
$830$		0			0
$831$	−5.30154	−	3.85179i	−0.183908	−	0.133617i
$832$	−7.57956	+	23.3275i	−0.262774	+	0.808735i
$833$	−0.374620	−	1.15296i	−0.0129798	−	0.0399477i
$834$	−3.01688	+	2.19189i	−0.104466	+	0.0758990i
$835$		0			0
$836$	0.413374	+	0.148968i	0.0142968	+	0.00515217i
$837$	−1.20508			−0.0416537
$838$	−0.509868	+	0.370441i	−0.0176131	+	0.0127967i
$839$	6.90363	+	21.2472i	0.238340	+	0.733535i	0.996661	+	0.0816534i	$0.0260200\pi$
$839$	6.90363	+	21.2472i	0.238340	+	0.733535i	−0.758321	+	0.651881i	$0.773980\pi$
$840$		0			0
$841$	14.5277	+	10.5550i	0.500954	+	0.363965i
$842$	13.1928	+	9.58513i	0.454654	+	0.330325i
$843$	1.54262	−	4.74768i	0.0531305	−	0.163519i
$844$	−2.78984	−	8.58624i	−0.0960302	−	0.295551i
$845$		0			0
$846$	−17.4263			−0.599128
$847$	−24.0233	+	15.2248i	−0.825449	+	0.523130i
$848$	24.5728			0.843833
$849$	6.03789	−	4.38679i	0.207220	−	0.150554i
$850$		0			0
$851$	1.35678	−	4.17574i	0.0465098	−	0.143143i
$852$	−1.18066	−	0.857797i	−0.0404486	−	0.0293876i
$853$	−6.59563	−	4.79201i	−0.225830	−	0.164075i	0.469117	−	0.883136i	$-0.344572\pi$
$853$	−6.59563	−	4.79201i	−0.225830	−	0.164075i	−0.694947	+	0.719061i	$0.744572\pi$
$854$	13.9798	−	43.0254i	0.478378	−	1.47230i
$855$		0			0
$856$	−25.3726	+	18.4343i	−0.867217	+	0.630070i
$857$	−4.42433			−0.151132			−0.0755662	−	0.997141i	$-0.524076\pi$
$857$	−4.42433			−0.151132			−0.0755662	+	0.997141i	$0.524076\pi$
$858$	3.86699	+	1.39355i	0.132017	+	0.0475752i
$859$	2.90501			0.0991176			0.0495588	−	0.998771i	$-0.484218\pi$
$859$	2.90501			0.0991176			0.0495588	+	0.998771i	$0.484218\pi$
$860$		0			0
$861$	1.48662	+	4.57535i	0.0506640	+	0.155928i
$862$	11.2134	−	34.5112i	0.381929	−	1.17546i
$863$	−14.3277	−	10.4097i	−0.487722	−	0.354351i	0.316586	−	0.948564i	$-0.397464\pi$
$863$	−14.3277	−	10.4097i	−0.487722	−	0.354351i	−0.804308	+	0.594213i	$0.797464\pi$
$864$	−4.55588	−	3.31004i	−0.154994	−	0.112610i
$865$		0			0
$866$	3.89582	+	11.9901i	0.132385	+	0.407440i
$867$	0.638391	−	0.463818i	0.0216809	−	0.0157521i
$868$	0.696297			0.0236339
$869$	−30.9102	+	8.96987i	−1.04856	+	0.304282i
$870$		0			0
$871$	7.15721	−	5.20002i	0.242513	−	0.176196i
$872$	−4.66900	−	14.3697i	−0.158112	−	0.486619i
$873$	9.65990	−	29.7301i	0.326938	−	1.00621i
$874$	2.32835	+	1.69164i	0.0787576	+	0.0572207i
$875$		0			0
$876$	0.699741	−	2.15358i	0.0236421	−	0.0727628i
$877$	−15.8772	−	48.8651i	−0.536136	−	1.65006i	−0.741181	−	0.671305i	$-0.765734\pi$
$877$	−15.8772	−	48.8651i	−0.536136	−	1.65006i	0.205045	−	0.978753i	$-0.434266\pi$
$878$	−1.53049	+	1.11197i	−0.0516516	+	0.0375270i
$879$	8.15803			0.275164
$880$		0			0
$881$	33.6727			1.13446			0.567231	−	0.823559i	$-0.308015\pi$
$881$	33.6727			1.13446			0.567231	+	0.823559i	$0.308015\pi$
$882$	0.901123	−	0.654704i	0.0303424	−	0.0220450i
$883$	4.29860	+	13.2297i	0.144660	+	0.445216i	0.996967	−	0.0778247i	$-0.0247974\pi$
$883$	4.29860	+	13.2297i	0.144660	+	0.445216i	−0.852308	+	0.523041i	$0.824797\pi$
$884$	1.56724	−	4.82347i	0.0527120	−	0.162231i
$885$		0			0
$886$	3.38685	+	2.46069i	0.113783	+	0.0826685i
$887$	−13.8133	+	42.5128i	−0.463804	+	1.42744i	0.396677	+	0.917958i	$0.370163\pi$
$887$	−13.8133	+	42.5128i	−0.463804	+	1.42744i	−0.860481	+	0.509483i	$0.829837\pi$
$888$	−0.179681	−	0.553001i	−0.00602970	−	0.0185575i
$889$	23.2935	−	16.9237i	0.781239	−	0.567603i
$890$		0			0
$891$	15.9133	−	20.5022i	0.533115	−	0.686849i
$892$	−10.4388			−0.349516
$893$	−1.10598	+	0.803545i	−0.0370104	+	0.0268896i
$894$	−1.17517	−	3.61680i	−0.0393035	−	0.120964i
$895$		0			0
$896$	−11.9139	−	8.65598i	−0.398017	−	0.289176i
$897$	−6.82665	−	4.95985i	−0.227935	−	0.165605i
$898$	12.3359	−	37.9660i	0.411654	−	1.26694i
$899$	0.579434	+	1.78331i	0.0193252	+	0.0594768i
$900$		0			0
$901$	−33.5861			−1.11892
$902$	−11.7542	−	17.3073i	−0.391372	−	0.576269i
$903$	−2.39471			−0.0796909
$904$	24.5433	−	17.8317i	0.816297	−	0.593074i
$905$		0			0
$906$	−1.54095	+	4.74256i	−0.0511947	+	0.157561i
$907$	18.4440	+	13.4003i	0.612421	+	0.444950i	0.850266	−	0.526353i	$-0.176441\pi$
$907$	18.4440	+	13.4003i	0.612421	+	0.444950i	−0.237845	+	0.971303i	$0.576441\pi$
$908$	−0.941591	−	0.684106i	−0.0312478	−	0.0227028i
$909$	−12.2622	+	37.7392i	−0.406712	+	1.25173i
$910$		0			0
$911$	−30.3887	+	22.0787i	−1.00682	+	0.731499i	−0.963540	−	0.267564i	$-0.913781\pi$
$911$	−30.3887	+	22.0787i	−1.00682	+	0.731499i	−0.0432817	+	0.999063i	$0.513781\pi$
$912$	0.284696			0.00942722
$913$	−6.14352	−	9.04593i	−0.203321	−	0.299376i
$914$	−15.0214			−0.496863
$915$		0			0
$916$	−1.07679	−	3.31402i	−0.0355781	−	0.109498i
$917$	−8.12165	+	24.9959i	−0.268201	+	0.825437i
$918$	−8.21118	−	5.96577i	−0.271009	−	0.196900i
$919$	−32.1280	−	23.3424i	−1.05981	−	0.769994i	−0.0857538	−	0.996316i	$-0.527330\pi$
$919$	−32.1280	−	23.3424i	−1.05981	−	0.769994i	−0.974053	+	0.226322i	$0.927330\pi$
$920$		0			0
$921$	−2.28377	−	7.02872i	−0.0752528	−	0.231604i
$922$	−16.5421	+	12.0186i	−0.544786	+	0.395810i
$923$	23.1808			0.763005
$924$	0.913392	−	1.17679i	0.0300484	−	0.0387134i
$925$		0			0
$926$	14.6057	−	10.6116i	0.479972	−	0.348720i
$927$	−11.8649	−	36.5165i	−0.389696	−	1.19936i
$928$	−2.70771	+	8.33348i	−0.0888850	+	0.273560i
$929$	−16.7708	−	12.1847i	−0.550231	−	0.399766i	0.277640	−	0.960685i	$-0.410448\pi$
$929$	−16.7708	−	12.1847i	−0.550231	−	0.399766i	−0.827871	+	0.560919i	$0.810448\pi$
$930$		0			0
$931$	0.0270020	−	0.0831035i	0.000884954	−	0.00272361i
$932$	−0.657518	−	2.02363i	−0.0215377	−	0.0662862i
$933$	2.57919	−	1.87389i	0.0844388	−	0.0613484i
$934$	−37.6187			−1.23092
$935$		0			0
$936$	24.1874			0.790588
$937$	45.1841	−	32.8282i	1.47610	−	1.07245i	0.497312	−	0.867572i	$-0.334320\pi$
$937$	45.1841	−	32.8282i	1.47610	−	1.07245i	0.978788	−	0.204877i	$-0.0656795\pi$
$938$	3.16112	+	9.72893i	0.103214	+	0.317661i
$939$	0.194723	−	0.599297i	0.00635455	−	0.0195573i
$940$		0			0
$941$	10.8120	+	7.85541i	0.352462	+	0.256079i	0.749901	−	0.661550i	$-0.230101\pi$
$941$	10.8120	+	7.85541i	0.352462	+	0.256079i	−0.397439	+	0.917629i	$0.630101\pi$
$942$	−1.91069	+	5.88051i	−0.0622537	+	0.191597i
$943$	13.2720	+	40.8469i	0.432194	+	1.33016i
$944$	17.1133	−	12.4336i	0.556991	−	0.404678i
$945$		0			0
$946$	10.0015	−	2.90236i	0.325178	−	0.0943639i
$947$	42.2245			1.37211			0.686055	−	0.727550i	$-0.259341\pi$
$947$	42.2245			1.37211			0.686055	+	0.727550i	$0.259341\pi$
$948$	1.36381	−	0.990868i	0.0442946	−	0.0321819i
$949$	11.1148	+	34.2077i	0.360800	+	1.11043i
$950$		0			0
$951$	−5.14624	−	3.73896i	−0.166878	−	0.121244i
$952$	24.6264	+	17.8921i	0.798146	+	0.579887i
$953$	−4.54837	+	13.9985i	−0.147336	+	0.453454i	−0.997304	−	0.0733803i	$-0.976621\pi$
$953$	−4.54837	+	13.9985i	−0.147336	+	0.453454i	0.849968	+	0.526835i	$0.176621\pi$
$954$	−9.53588	−	29.3484i	−0.308735	−	0.950190i
$955$		0			0
$956$	−11.5376			−0.373154
$957$	3.77401	+	1.36004i	0.121996	+	0.0439640i
$958$	−17.2750			−0.558131
$959$	−9.09100	+	6.60500i	−0.293564	+	0.213286i
$960$		0			0
$961$	−9.48114	+	29.1799i	−0.305843	+	0.941288i
$962$	1.43954	+	1.04589i	0.0464126	+	0.0337207i
$963$	23.8005	+	17.2921i	0.766960	+	0.557229i
$964$	1.77558	−	5.46467i	0.0571875	−	0.176005i
$965$		0			0
$966$	7.89370	−	5.73511i	0.253976	−	0.184524i
$967$	32.2786			1.03801			0.519005	−	0.854771i	$-0.326303\pi$
$967$	32.2786			1.03801			0.519005	+	0.854771i	$0.326303\pi$
$968$	−12.3979	+	31.2571i	−0.398485	+	1.00464i
$969$	−0.389123			−0.0125004
$970$		0			0
$971$	−13.2262	−	40.7060i	−0.424448	−	1.30632i	−0.903522	−	0.428542i	$-0.859027\pi$
$971$	−13.2262	−	40.7060i	−0.424448	−	1.30632i	0.479074	−	0.877775i	$-0.340973\pi$
$972$	−1.36498	+	4.20097i	−0.0437817	+	0.134746i
$973$	−17.3669	−	12.6178i	−0.556757	−	0.404508i
$974$	34.0738	+	24.7561i	1.09179	+	0.793235i
$975$		0			0
$976$	−12.3460	−	37.9970i	−0.395185	−	1.21625i
$977$	9.86772	−	7.16932i	0.315696	−	0.229367i	−0.418640	−	0.908152i	$-0.637493\pi$
$977$	9.86772	−	7.16932i	0.315696	−	0.229367i	0.734337	+	0.678785i	$0.237493\pi$
$978$	−4.01584			−0.128412
$979$	7.76378	+	2.79784i	0.248131	+	0.0894195i
$980$		0			0
$981$	−11.4662	+	8.33070i	−0.366088	+	0.265979i
$982$	1.21807	+	3.74884i	0.0388702	+	0.119630i
$983$	−4.34697	+	13.3786i	−0.138647	+	0.426711i	−0.996139	−	0.0877853i	$-0.972021\pi$
$983$	−4.34697	+	13.3786i	−0.138647	+	0.426711i	0.857493	+	0.514496i	$0.172021\pi$
$984$	4.60153	+	3.34321i	0.146692	+	0.106578i
$985$		0			0
$986$	−4.88018	+	15.0196i	−0.155416	+	0.478323i
$987$	1.43221	+	4.40788i	0.0455877	+	0.140305i
$988$	0.295744	−	0.214871i	0.00940887	−	0.00683595i
$989$	−21.3790			−0.679811
$990$		0			0
$991$	−22.9455			−0.728887			−0.364444	−	0.931225i	$-0.618741\pi$
$991$	−22.9455			−0.728887			−0.364444	+	0.931225i	$0.618741\pi$
$992$	1.20370	−	0.874542i	0.0382176	−	0.0277667i
$993$	1.41938	+	4.36840i	0.0450426	+	0.138627i
$994$	−8.28292	+	25.4922i	−0.262718	+	0.808564i
$995$		0			0
$996$	0.463351	+	0.336645i	0.0146819	+	0.0106670i
$997$	−1.12311	+	3.45659i	−0.0355694	+	0.109471i	−0.967265	−	0.253769i	$-0.918330\pi$
$997$	−1.12311	+	3.45659i	−0.0355694	+	0.109471i	0.931695	+	0.363240i	$0.118330\pi$
$998$	−2.48948	−	7.66183i	−0.0788031	−	0.242531i
$999$	−0.902916	+	0.656007i	−0.0285670	+	0.0207551i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.h.d.201.3		16
5.2	odd	4		55.2.j.a.14.3	yes	16
5.3	odd	4		55.2.j.a.14.2	yes	16
5.4	even	2	inner	275.2.h.d.201.2		16
11.2	odd	10		3025.2.a.bk.1.6		8
11.4	even	5	inner	275.2.h.d.26.3		16
11.9	even	5		3025.2.a.bl.1.3		8
15.2	even	4		495.2.ba.a.289.2		16
15.8	even	4		495.2.ba.a.289.3		16
20.3	even	4		880.2.cd.c.289.3		16
20.7	even	4		880.2.cd.c.289.2		16
55.2	even	20		605.2.b.f.364.6		8
55.3	odd	20		605.2.j.h.269.2		16
55.4	even	10	inner	275.2.h.d.26.2		16
55.7	even	20		605.2.j.d.444.3		16
55.8	even	20		605.2.j.g.269.3		16
55.9	even	10		3025.2.a.bl.1.6		8
55.13	even	20		605.2.b.f.364.3		8
55.17	even	20		605.2.j.g.9.3		16
55.18	even	20		605.2.j.d.444.2		16
55.24	odd	10		3025.2.a.bk.1.3		8
55.27	odd	20		605.2.j.h.9.2		16
55.28	even	20		605.2.j.g.9.2		16
55.32	even	4		605.2.j.d.124.2		16
55.37	odd	20		55.2.j.a.4.2	✓	16
55.38	odd	20		605.2.j.h.9.3		16
55.42	odd	20		605.2.b.g.364.3		8
55.43	even	4		605.2.j.d.124.3		16
55.47	odd	20		605.2.j.h.269.3		16
55.48	odd	20		55.2.j.a.4.3	yes	16
55.52	even	20		605.2.j.g.269.2		16
55.53	odd	20		605.2.b.g.364.6		8
165.92	even	20		495.2.ba.a.334.3		16
165.158	even	20		495.2.ba.a.334.2		16
220.103	even	20		880.2.cd.c.609.2		16
220.147	even	20		880.2.cd.c.609.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.4.2	✓	16	55.37	odd	20
55.2.j.a.4.3	yes	16	55.48	odd	20
55.2.j.a.14.2	yes	16	5.3	odd	4
55.2.j.a.14.3	yes	16	5.2	odd	4
275.2.h.d.26.2		16	55.4	even	10	inner
275.2.h.d.26.3		16	11.4	even	5	inner
275.2.h.d.201.2		16	5.4	even	2	inner
275.2.h.d.201.3		16	1.1	even	1	trivial
495.2.ba.a.289.2		16	15.2	even	4
495.2.ba.a.289.3		16	15.8	even	4
495.2.ba.a.334.2		16	165.158	even	20
495.2.ba.a.334.3		16	165.92	even	20
605.2.b.f.364.3		8	55.13	even	20
605.2.b.f.364.6		8	55.2	even	20
605.2.b.g.364.3		8	55.42	odd	20
605.2.b.g.364.6		8	55.53	odd	20
605.2.j.d.124.2		16	55.32	even	4
605.2.j.d.124.3		16	55.43	even	4
605.2.j.d.444.2		16	55.18	even	20
605.2.j.d.444.3		16	55.7	even	20
605.2.j.g.9.2		16	55.28	even	20
605.2.j.g.9.3		16	55.17	even	20
605.2.j.g.269.2		16	55.52	even	20
605.2.j.g.269.3		16	55.8	even	20
605.2.j.h.9.2		16	55.27	odd	20
605.2.j.h.9.3		16	55.38	odd	20
605.2.j.h.269.2		16	55.3	odd	20
605.2.j.h.269.3		16	55.47	odd	20
880.2.cd.c.289.2		16	20.7	even	4
880.2.cd.c.289.3		16	20.3	even	4
880.2.cd.c.609.2		16	220.103	even	20
880.2.cd.c.609.3		16	220.147	even	20
3025.2.a.bk.1.3		8	55.24	odd	10
3025.2.a.bk.1.6		8	11.2	odd	10
3025.2.a.bl.1.3		8	11.9	even	5
3025.2.a.bl.1.6		8	55.9	even	10

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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.998322 - 0.725323i) q^{2} +(0.112477 + 0.346168i) q^{3} +(-0.147481 + 0.453901i) q^{4} +(0.363371 + 0.264005i) q^{6} +(-0.798988 + 2.45903i) q^{7} +(0.944641 + 2.90731i) q^{8} +(2.31987 - 1.68548i) q^{9} +(3.12020 + 1.12443i) q^{11} -0.173714 q^{12} +(2.23232 - 1.62187i) q^{13} +(0.985946 + 3.03443i) q^{14} +(2.27957 + 1.65620i) q^{16} +(-3.11572 - 2.26370i) q^{17} +(1.09346 - 3.36531i) q^{18} +(-0.0857804 - 0.264005i) q^{19} -0.941105 q^{21} +(3.93054 - 1.14061i) q^{22} -8.40180 q^{23} +(-0.900166 + 0.654009i) q^{24} +(1.05219 - 3.23830i) q^{26} +(1.72780 + 1.25532i) q^{27} +(-0.998322 - 0.725323i) q^{28} +(1.02689 - 3.16043i) q^{29} +(-0.456498 + 0.331666i) q^{31} -2.63682 q^{32} +(-0.0382919 + 1.20659i) q^{33} -4.75241 q^{34} +(0.422906 + 1.30157i) q^{36} +(-0.161487 + 0.497006i) q^{37} +(-0.277125 - 0.201343i) q^{38} +(0.812523 + 0.590333i) q^{39} +(-1.57966 - 4.86168i) q^{41} +(-0.939526 + 0.682605i) q^{42} +2.54457 q^{43} +(-0.970553 + 1.25043i) q^{44} +(-8.38769 + 6.09402i) q^{46} +(-1.52184 - 4.68373i) q^{47} +(-0.316926 + 0.975398i) q^{48} +(0.254663 + 0.185023i) q^{49} +(0.433175 - 1.33318i) q^{51} +(0.406945 + 1.25245i) q^{52} +(7.05533 - 5.12599i) q^{53} +2.63541 q^{54} -7.90392 q^{56} +(0.0817417 - 0.0593888i) q^{57} +(-1.26717 - 3.89995i) q^{58} +(2.31987 - 7.13983i) q^{59} +(-11.4711 - 8.33424i) q^{61} +(-0.215168 + 0.662218i) q^{62} +(2.29111 + 7.05132i) q^{63} +(-7.19153 + 5.22495i) q^{64} +(0.836937 + 1.23233i) q^{66} +3.20618 q^{67} +(1.48701 - 1.08037i) q^{68} +(-0.945006 - 2.90843i) q^{69} +(6.79655 + 4.93798i) q^{71} +(7.09166 + 5.15239i) q^{72} +(-4.02812 + 12.3973i) q^{73} +(0.199274 + 0.613302i) q^{74} +0.132483 q^{76} +(-5.25802 + 6.77427i) q^{77} +1.23934 q^{78} +(-7.85090 + 5.70401i) q^{79} +(2.41812 - 7.44221i) q^{81} +(-5.10330 - 3.70776i) q^{82} +(-2.66732 - 1.93792i) q^{83} +(0.138796 - 0.427169i) q^{84} +(2.54030 - 1.84564i) q^{86} +1.20954 q^{87} +(-0.321596 + 10.1336i) q^{88} +2.48823 q^{89} +(2.20464 + 6.78519i) q^{91} +(1.23911 - 3.81359i) q^{92} +(-0.166157 - 0.120720i) q^{93} +(-4.91650 - 3.57205i) q^{94} +(-0.296581 - 0.912781i) q^{96} +(8.81946 - 6.40771i) q^{97} +0.388437 q^{98} +(9.13367 - 2.65051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 18 q^{6} - 2 q^{9} - 6 q^{11} + 12 q^{14} + 16 q^{16} - 6 q^{19} + 8 q^{21} - 6 q^{24} + 40 q^{26} - 2 q^{29} + 8 q^{31} + 16 q^{34} + 10 q^{36} - 30 q^{39} - 52 q^{41} - 4 q^{44} - 62 q^{46}+ \cdots + 72 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 - 18 * q^6 - 2 * q^9 - 6 * q^11 + 12 * q^14 + 16 * q^16 - 6 * q^19 + 8 * q^21 - 6 * q^24 + 40 * q^26 - 2 * q^29 + 8 * q^31 + 16 * q^34 + 10 * q^36 - 30 * q^39 - 52 * q^41 - 4 * q^44 - 62 * q^46 + 10 * q^49 - 42 * q^51 + 40 * q^54 - 20 * q^56 - 2 * q^59 - 40 * q^61 + 8 * q^64 + 58 * q^66 - 26 * q^69 + 36 * q^71 - 48 * q^74 + 56 * q^76 - 38 * q^79 + 68 * q^81 - 12 * q^84 + 22 * q^86 - 24 * q^89 - 20 * q^91 - 14 * q^94 - 86 * q^96 + 72 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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