LMFDB - Embedded newform 675.2.r.a.46.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(46,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 18]))

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

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

chi := DirichletCharacter("675.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			46.14
Character	$\chi$	$=$	675.46
Dual form			675.2.r.a.631.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.110043 + 0.122216i) q^{2} +(0.206230 - 1.96215i) q^{4} +(2.06082 + 0.867759i) q^{5} +(2.06663 - 3.57951i) q^{7} +(0.528597 - 0.384048i) q^{8} +O(q^{10})$	\(q+(0.110043 + 0.122216i) q^{2} +(0.206230 - 1.96215i) q^{4} +(2.06082 + 0.867759i) q^{5} +(2.06663 - 3.57951i) q^{7} +(0.528597 - 0.384048i) q^{8} +(0.120726 + 0.347356i) q^{10} +(0.239690 + 0.266203i) q^{11} +(1.23537 - 1.37202i) q^{13} +(0.664892 - 0.141327i) q^{14} +(-3.75457 - 0.798059i) q^{16} +(-3.22940 + 2.34629i) q^{17} +(-0.0599095 + 0.0435268i) q^{19} +(2.12767 - 3.86468i) q^{20} +(-0.00615783 + 0.0585878i) q^{22} +(-4.28234 + 0.910239i) q^{23} +(3.49399 + 3.57660i) q^{25} +0.303627 q^{26} +(-6.59733 - 4.79324i) q^{28} +(5.93713 - 2.64338i) q^{29} +(-4.95171 - 2.20464i) q^{31} +(-0.969013 - 1.67838i) q^{32} +(-0.642128 - 0.136489i) q^{34} +(7.36512 - 5.58341i) q^{35} +(2.37480 + 7.30889i) q^{37} +(-0.0119123 - 0.00253204i) q^{38} +(1.42261 - 0.332761i) q^{40} +(-3.14813 + 3.49635i) q^{41} +(1.55061 - 2.68574i) q^{43} +(0.571760 - 0.415408i) q^{44} +(-0.582489 - 0.423203i) q^{46} +(11.8169 - 5.26122i) q^{47} +(-5.04195 - 8.73292i) q^{49} +(-0.0526256 + 0.820601i) q^{50} +(-2.43733 - 2.70693i) q^{52} +(-1.53179 - 1.11291i) q^{53} +(0.262959 + 0.756591i) q^{55} +(-0.282290 - 2.68581i) q^{56} +(0.976404 + 0.434723i) q^{58} +(-3.31117 + 3.67743i) q^{59} +(6.08932 + 6.76288i) q^{61} +(-0.275461 - 0.847783i) q^{62} +(-2.27380 + 6.99805i) q^{64} +(3.73647 - 1.75549i) q^{65} +(13.1648 + 5.86135i) q^{67} +(3.93777 + 6.82042i) q^{68} +(1.49286 + 0.285716i) q^{70} +(-10.8652 - 7.89400i) q^{71} +(4.15877 - 12.7994i) q^{73} +(-0.631930 + 1.09453i) q^{74} +(0.0730507 + 0.126528i) q^{76} +(1.44823 - 0.307831i) q^{77} +(-5.47332 + 2.43688i) q^{79} +(-7.04499 - 4.90273i) q^{80} -0.773739 q^{82} +(-0.301668 - 2.87018i) q^{83} +(-8.69124 + 2.03296i) q^{85} +(0.498874 - 0.106039i) q^{86} +(0.228934 + 0.0486615i) q^{88} +(-2.21408 + 6.81425i) q^{89} +(-2.35810 - 7.25750i) q^{91} +(0.902876 + 8.59029i) q^{92} +(1.94338 + 0.865246i) q^{94} +(-0.161234 + 0.0377140i) q^{95} +(9.65762 - 4.29985i) q^{97} +(0.512465 - 1.57721i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	0.110043	+	0.122216i	0.0778125	+	0.0864195i	0.780794	−	0.624789i	$-0.214815\pi$
$2$	0.110043	+	0.122216i	0.0778125	+	0.0864195i	−0.702981	+	0.711208i	$0.748148\pi$
$3$		0			0
$3$		0			0
$4$	0.206230	−	1.96215i	0.103115	−	0.981073i
$5$	2.06082	+	0.867759i	0.921628	+	0.388074i
$5$	2.06082	+	0.867759i	0.921628	+	0.388074i
$6$		0			0
$7$	2.06663	−	3.57951i	0.781114	−	1.35293i	−0.150179	−	0.988659i	$-0.547985\pi$
$7$	2.06663	−	3.57951i	0.781114	−	1.35293i	0.931293	−	0.364271i	$-0.118682\pi$
$8$	0.528597	−	0.384048i	0.186887	−	0.135782i
$9$		0			0
$10$	0.120726	+	0.347356i	0.0381771	+	0.109844i
$11$	0.239690	+	0.266203i	0.0722693	+	0.0802632i	0.778195	−	0.628023i	$-0.216135\pi$
$11$	0.239690	+	0.266203i	0.0722693	+	0.0802632i	−0.705926	+	0.708286i	$0.749469\pi$
$12$		0			0
$13$	1.23537	−	1.37202i	0.342631	−	0.380530i	−0.547060	−	0.837093i	$-0.684253\pi$
$13$	1.23537	−	1.37202i	0.342631	−	0.380530i	0.889691	+	0.456563i	$0.150920\pi$
$14$	0.664892	−	0.141327i	0.177700	−	0.0377713i
$15$		0			0
$16$	−3.75457	−	0.798059i	−0.938644	−	0.199515i
$17$	−3.22940	+	2.34629i	−0.783244	+	0.569060i	−0.905951	−	0.423383i	$-0.860843\pi$
$17$	−3.22940	+	2.34629i	−0.783244	+	0.569060i	0.122707	+	0.992443i	$0.460843\pi$
$18$		0			0
$19$	−0.0599095	+	0.0435268i	−0.0137442	+	0.00998573i	−0.594636	−	0.803995i	$-0.702704\pi$
$19$	−0.0599095	+	0.0435268i	−0.0137442	+	0.00998573i	0.580892	+	0.813981i	$0.302704\pi$
$20$	2.12767	−	3.86468i	0.475762	−	0.864168i
$21$		0			0
$22$	−0.00615783	+	0.0585878i	−0.00131285	+	0.0124910i
$23$	−4.28234	+	0.910239i	−0.892929	+	0.189798i	−0.631455	−	0.775413i	$-0.717542\pi$
$23$	−4.28234	+	0.910239i	−0.892929	+	0.189798i	−0.261474	+	0.965210i	$0.584209\pi$
$24$		0			0
$25$	3.49399	+	3.57660i	0.698798	+	0.715319i
$26$	0.303627			0.0595462
$27$		0			0
$28$	−6.59733	−	4.79324i	−1.24678	−	0.905837i
$29$	5.93713	−	2.64338i	1.10250	−	0.490863i	0.226906	−	0.973917i	$-0.427139\pi$
$29$	5.93713	−	2.64338i	1.10250	−	0.490863i	0.875591	+	0.483054i	$0.160472\pi$
$30$		0			0
$31$	−4.95171	−	2.20464i	−0.889353	−	0.395966i	−0.0893776	−	0.995998i	$-0.528488\pi$
$31$	−4.95171	−	2.20464i	−0.889353	−	0.395966i	−0.799976	+	0.600032i	$0.795154\pi$
$32$	−0.969013	−	1.67838i	−0.171299	−	0.296698i
$33$		0			0
$34$	−0.642128	−	0.136489i	−0.110124	−	0.0234076i
$35$	7.36512	−	5.58341i	1.24493	−	0.943768i
$36$		0			0
$37$	2.37480	+	7.30889i	0.390415	+	1.20157i	0.932475	+	0.361235i	$0.117645\pi$
$37$	2.37480	+	7.30889i	0.390415	+	1.20157i	−0.542060	+	0.840340i	$0.682355\pi$
$38$	−0.0119123	−	0.00253204i	−0.00193243	−	0.000410751i
$39$		0			0
$40$	1.42261	−	0.332761i	0.224934	−	0.0526141i
$41$	−3.14813	+	3.49635i	−0.491655	+	0.546038i	−0.937004	−	0.349319i	$-0.886413\pi$
$41$	−3.14813	+	3.49635i	−0.491655	+	0.546038i	0.445349	+	0.895357i	$0.353080\pi$
$42$		0			0
$43$	1.55061	−	2.68574i	0.236466	−	0.409571i	−0.723232	−	0.690605i	$-0.757344\pi$
$43$	1.55061	−	2.68574i	0.236466	−	0.409571i	0.959698	+	0.281034i	$0.0906775\pi$
$44$	0.571760	−	0.415408i	0.0861961	−	0.0626252i
$45$		0			0
$46$	−0.582489	−	0.423203i	−0.0858833	−	0.0623979i
$47$	11.8169	−	5.26122i	1.72367	−	0.767428i	0.726934	−	0.686707i	$-0.240945\pi$
$47$	11.8169	−	5.26122i	1.72367	−	0.767428i	0.996737	−	0.0807203i	$-0.0257221\pi$
$48$		0			0
$49$	−5.04195	−	8.73292i	−0.720279	−	1.24756i
$50$	−0.0526256	+	0.820601i	−0.00744238	+	0.116051i
$51$		0			0
$52$	−2.43733	−	2.70693i	−0.337997	−	0.375384i
$53$	−1.53179	−	1.11291i	−0.210408	−	0.152870i	0.477590	−	0.878583i	$-0.341510\pi$
$53$	−1.53179	−	1.11291i	−0.210408	−	0.152870i	−0.687998	+	0.725712i	$0.741510\pi$
$54$		0			0
$55$	0.262959	+	0.756591i	0.0354574	+	0.102019i
$56$	−0.282290	−	2.68581i	−0.0377225	−	0.358906i
$57$		0			0
$58$	0.976404	+	0.434723i	0.128208	+	0.0570820i
$59$	−3.31117	+	3.67743i	−0.431078	+	0.478760i	−0.919074	−	0.394086i	$-0.871061\pi$
$59$	−3.31117	+	3.67743i	−0.431078	+	0.478760i	0.487996	+	0.872846i	$0.337728\pi$
$60$		0			0
$61$	6.08932	+	6.76288i	0.779658	+	0.865898i	0.993832	−	0.110898i	$-0.0353726\pi$
$61$	6.08932	+	6.76288i	0.779658	+	0.865898i	−0.214174	+	0.976796i	$0.568706\pi$
$62$	−0.275461	−	0.847783i	−0.0349836	−	0.107669i
$63$		0			0
$64$	−2.27380	+	6.99805i	−0.284226	+	0.874756i
$65$	3.73647	−	1.75549i	0.463452	−	0.217741i
$66$		0			0
$67$	13.1648	+	5.86135i	1.60834	+	0.716078i	0.997153	−	0.0754107i	$-0.0240268\pi$
$67$	13.1648	+	5.86135i	1.60834	+	0.716078i	0.611184	+	0.791488i	$0.290693\pi$
$68$	3.93777	+	6.82042i	0.477525	+	0.827098i
$69$		0			0
$70$	1.49286	+	0.285716i	0.178431	+	0.0341496i
$71$	−10.8652	−	7.89400i	−1.28946	−	0.936845i	−0.289662	−	0.957129i	$-0.593543\pi$
$71$	−10.8652	−	7.89400i	−1.28946	−	0.936845i	−0.999794	+	0.0202841i	$0.993543\pi$
$72$		0			0
$73$	4.15877	−	12.7994i	0.486747	−	1.49805i	−0.342688	−	0.939449i	$-0.611337\pi$
$73$	4.15877	−	12.7994i	0.486747	−	1.49805i	0.829435	−	0.558603i	$-0.188663\pi$
$74$	−0.631930	+	1.09453i	−0.0734603	+	0.127237i
$75$		0			0
$76$	0.0730507	+	0.126528i	0.00837950	+	0.0145137i
$77$	1.44823	−	0.307831i	0.165041	−	0.0350806i
$78$		0			0
$79$	−5.47332	+	2.43688i	−0.615797	+	0.274170i	−0.690837	−	0.723010i	$-0.742758\pi$
$79$	−5.47332	+	2.43688i	−0.615797	+	0.274170i	0.0750407	+	0.997180i	$0.476091\pi$
$80$	−7.04499	−	4.90273i	−0.787654	−	0.548141i
$81$		0			0
$82$	−0.773739			−0.0854452
$83$	−0.301668	−	2.87018i	−0.0331123	−	0.315043i	−0.998524	−	0.0543124i	$-0.982703\pi$
$83$	−0.301668	−	2.87018i	−0.0331123	−	0.315043i	0.965412	−	0.260730i	$-0.0839633\pi$
$84$		0			0
$85$	−8.69124	+	2.03296i	−0.942697	+	0.220506i
$86$	0.498874	−	0.106039i	0.0537949	−	0.0114345i
$87$		0			0
$88$	0.228934	+	0.0486615i	0.0244045	+	0.00518733i
$89$	−2.21408	+	6.81425i	−0.234692	+	0.722309i	0.762470	+	0.647024i	$0.223987\pi$
$89$	−2.21408	+	6.81425i	−0.234692	+	0.722309i	−0.997162	+	0.0752851i	$0.976013\pi$
$90$		0			0
$91$	−2.35810	−	7.25750i	−0.247196	−	0.760792i
$92$	0.902876	+	8.59029i	0.0941313	+	0.895600i
$93$		0			0
$94$	1.94338	+	0.865246i	0.200444	+	0.0892434i
$95$	−0.161234	+	0.0377140i	−0.0165422	+	0.00386938i
$96$		0			0
$97$	9.65762	−	4.29985i	0.980583	−	0.436584i	0.147095	−	0.989122i	$-0.453008\pi$
$97$	9.65762	−	4.29985i	0.980583	−	0.436584i	0.833487	+	0.552539i	$0.186341\pi$
$98$	0.512465	−	1.57721i	0.0517668	−	0.159322i
$99$		0			0
$100$	7.73837	−	6.11811i	0.773837	−	0.611811i
$101$	−8.75862	+	15.1704i	−0.871516	+	1.50951i	−0.0110870	+	0.999939i	$0.503529\pi$
$101$	−8.75862	+	15.1704i	−0.871516	+	1.50951i	−0.860429	+	0.509571i	$0.829804\pi$
$102$		0			0
$103$	−1.25065	+	11.8991i	−0.123230	+	1.17245i	0.741761	+	0.670665i	$0.233991\pi$
$103$	−1.25065	+	11.8991i	−0.123230	+	1.17245i	−0.864990	+	0.501788i	$0.832676\pi$
$104$	0.126092	−	1.19969i	0.0123644	−	0.117639i
$105$		0			0
$106$	−0.0325485	−	0.309678i	−0.00316138	−	0.0300786i
$107$	8.49063			0.820820			0.410410	−	0.911901i	$-0.365386\pi$
$107$	8.49063			0.820820			0.410410	+	0.911901i	$0.365386\pi$
$108$		0			0
$109$	2.49526	+	7.67961i	0.239002	+	0.735573i	0.996565	+	0.0828110i	$0.0263898\pi$
$109$	2.49526	+	7.67961i	0.239002	+	0.735573i	−0.757563	+	0.652762i	$0.773610\pi$
$110$	−0.0635303	+	0.115396i	−0.00605738	+	0.0110025i
$111$		0			0
$112$	−10.6160	+	11.7903i	−1.00312	+	1.11407i
$113$	−5.95046	+	6.60865i	−0.559772	+	0.621690i	−0.954897	−	0.296938i	$-0.904035\pi$
$113$	−5.95046	+	6.60865i	−0.559772	+	0.621690i	0.395125	+	0.918627i	$0.370701\pi$
$114$		0			0
$115$	−9.61501	−	1.84020i	−0.896604	−	0.171599i
$116$	−3.96228	−	12.1946i	−0.367889	−	1.13224i
$117$		0			0
$118$	−0.813812			−0.0749175
$119$	1.72461	+	16.4086i	0.158095	+	1.50417i
$120$		0			0
$121$	1.13640	−	10.8121i	0.103309	−	0.982921i
$122$	−0.156439	+	1.48842i	−0.0141634	+	0.134755i
$123$		0			0
$124$	−5.34702	+	9.26131i	−0.480177	+	0.831691i
$125$	4.09687	+	10.4027i	0.366435	+	0.930444i
$126$		0			0
$127$	−1.00273	+	3.08608i	−0.0889778	+	0.273845i	−0.985637	−	0.168875i	$-0.945987\pi$
$127$	−1.00273	+	3.08608i	−0.0889778	+	0.273845i	0.896660	+	0.442720i	$0.145987\pi$
$128$	−4.64644	+	2.06873i	−0.410691	+	0.182851i
$129$		0			0
$130$	0.625722	+	0.263475i	0.0548794	+	0.0231083i
$131$	7.86032	+	3.49964i	0.686759	+	0.305765i	0.720290	−	0.693673i	$-0.244009\pi$
$131$	7.86032	+	3.49964i	0.686759	+	0.305765i	−0.0335311	+	0.999438i	$0.510675\pi$
$132$		0			0
$133$	0.0319938	+	0.304401i	0.00277421	+	0.0263949i
$134$	0.732352	+	2.25395i	0.0632656	+	0.194711i
$135$		0			0
$136$	−0.805959	+	2.48049i	−0.0691105	+	0.212700i
$137$	−5.60580	−	1.19155i	−0.478936	−	0.101801i	−0.0378831	−	0.999282i	$-0.512061\pi$
$137$	−5.60580	−	1.19155i	−0.478936	−	0.101801i	−0.441053	+	0.897481i	$0.645395\pi$
$138$		0			0
$139$	−16.2222	+	3.44813i	−1.37595	+	0.292466i	−0.835767	−	0.549084i	$-0.814977\pi$
$139$	−16.2222	+	3.44813i	−1.37595	+	0.292466i	−0.540179	+	0.841550i	$0.681643\pi$
$140$	−9.43655	−	15.6029i	−0.797534	−	1.31869i
$141$		0			0
$142$	−0.230869	−	2.19657i	−0.0193741	−	0.184332i
$143$	0.661343			0.0553043
$144$		0			0
$145$	14.5292	−	0.295542i	1.20658	−	0.0245434i
$146$	2.02193	−	0.900220i	0.167336	−	0.0745028i
$147$		0			0
$148$	14.8309	−	3.15240i	1.21909	−	0.259126i
$149$	3.50472	+	6.07035i	0.287118	+	0.497302i	0.973120	−	0.230297i	$-0.0739696\pi$
$149$	3.50472	+	6.07035i	0.287118	+	0.497302i	−0.686003	+	0.727599i	$0.740636\pi$
$150$		0			0
$151$	2.35416	−	4.07752i	0.191579	−	0.331824i	−0.754195	−	0.656651i	$-0.771973\pi$
$151$	2.35416	−	4.07752i	0.191579	−	0.331824i	0.945774	+	0.324827i	$0.105306\pi$
$152$	−0.0149516	+	0.0460162i	−0.00121273	+	0.00373241i
$153$		0			0
$154$	0.196990	+	0.143122i	0.0158739	+	0.0115331i
$155$	−8.29150	−	8.84027i	−0.665989	−	0.710068i
$156$		0			0
$157$	8.51816	+	14.7539i	0.679823	+	1.17749i	0.975034	+	0.222057i	$0.0712770\pi$
$157$	8.51816	+	14.7539i	0.679823	+	1.17749i	−0.295210	+	0.955432i	$0.595390\pi$
$158$	−0.900128	−	0.400763i	−0.0716104	−	0.0318830i
$159$		0			0
$160$	−0.540535	−	4.29971i	−0.0427331	−	0.339922i
$161$	−5.59181	+	17.2098i	−0.440696	+	1.35632i
$162$		0			0
$163$	0.313473	+	0.964770i	0.0245531	+	0.0755666i	0.962582	−	0.270990i	$-0.0873509\pi$
$163$	0.313473	+	0.964770i	0.0245531	+	0.0755666i	−0.938029	+	0.346556i	$0.887351\pi$
$164$	6.21111	+	6.89813i	0.485006	+	0.538654i
$165$		0			0
$166$	0.317584	−	0.352713i	0.0246493	−	0.0273758i
$167$	−3.50153	−	1.55898i	−0.270956	−	0.120637i	0.266761	−	0.963763i	$-0.414047\pi$
$167$	−3.50153	−	1.55898i	−0.270956	−	0.120637i	−0.537717	+	0.843125i	$0.680713\pi$
$168$		0			0
$169$	1.00258	+	9.53887i	0.0771212	+	0.733760i
$170$	−1.20487	−	0.838491i	−0.0924096	−	0.0643094i
$171$		0			0
$172$	−4.95002	−	3.59640i	−0.377436	−	0.274223i
$173$	−14.8429	−	16.4847i	−1.12849	−	1.25331i	−0.963701	−	0.266982i	$-0.913974\pi$
$173$	−14.8429	−	16.4847i	−1.12849	−	1.25331i	−0.164785	−	0.986329i	$-0.552693\pi$
$174$		0			0
$175$	20.0233	−	5.11527i	1.51362	−	0.386678i
$176$	−0.687489	−	1.19077i	−0.0518215	−	0.0897574i
$177$		0			0
$178$	−1.07645	+	0.479268i	−0.0806836	+	0.0359227i
$179$	−11.8426	−	8.60413i	−0.885156	−	0.643103i	0.0494548	−	0.998776i	$-0.484252\pi$
$179$	−11.8426	−	8.60413i	−0.885156	−	0.643103i	−0.934610	+	0.355673i	$0.884252\pi$
$180$		0			0
$181$	−13.9341	+	10.1237i	−1.03571	+	0.752489i	−0.969444	−	0.245313i	$-0.921109\pi$
$181$	−13.9341	+	10.1237i	−1.03571	+	0.752489i	−0.0662678	+	0.997802i	$0.521109\pi$
$182$	0.627486	−	1.08684i	0.0465123	−	0.0805617i
$183$		0			0
$184$	−1.91405	+	2.12577i	−0.141106	+	0.156714i
$185$	−1.44831	+	17.1231i	−0.106482	+	1.25892i
$186$		0			0
$187$	−1.39865	−	0.297291i	−0.102279	−	0.0217401i
$188$	−7.88628	−	24.2715i	−0.575166	−	1.77018i
$189$		0			0
$190$	−0.0223519	−	0.0155551i	−0.00162158	−	0.00112848i
$191$	0.569688	+	0.121091i	0.0412212	+	0.00876184i	0.228476	−	0.973550i	$-0.426626\pi$
$191$	0.569688	+	0.121091i	0.0412212	+	0.00876184i	−0.187255	+	0.982311i	$0.559959\pi$
$192$		0			0
$193$	−4.64632	−	8.04765i	−0.334449	−	0.579283i	0.648930	−	0.760848i	$-0.275217\pi$
$193$	−4.64632	−	8.04765i	−0.334449	−	0.579283i	−0.983379	+	0.181565i	$0.941884\pi$
$194$	1.58827	+	0.707142i	0.114031	+	0.0507698i
$195$		0			0
$196$	−18.1751	+	8.09205i	−1.29822	+	0.578004i
$197$	3.47512	+	2.52482i	0.247592	+	0.179886i	0.704659	−	0.709546i	$-0.251100\pi$
$197$	3.47512	+	2.52482i	0.247592	+	0.179886i	−0.457067	+	0.889432i	$0.651100\pi$
$198$		0			0
$199$	−3.20175			−0.226966			−0.113483	−	0.993540i	$-0.536201\pi$
$199$	−3.20175			−0.226966			−0.113483	+	0.993540i	$0.536201\pi$
$200$	3.22050	+	0.548719i	0.227723	+	0.0388003i
$201$		0			0
$202$	−2.81789	+	0.598961i	−0.198266	+	0.0421427i
$203$	2.80785	−	26.7149i	0.197073	−	1.87502i
$204$		0			0
$205$	−9.52172	+	4.47354i	−0.665026	+	0.312446i
$206$	−1.59188	+	1.15657i	−0.110912	+	0.0805820i
$207$		0			0
$208$	−5.73325	+	4.16545i	−0.397529	+	0.288822i
$209$	−0.0259467	−	0.00551514i	−0.00179477	−	0.000381490i
$210$		0			0
$211$	7.09956	−	1.50906i	0.488754	−	0.103888i	0.0430586	−	0.999073i	$-0.486290\pi$
$211$	7.09956	−	1.50906i	0.488754	−	0.103888i	0.445695	+	0.895185i	$0.352956\pi$
$212$	−2.49960	+	2.77608i	−0.171673	+	0.190662i
$213$		0			0
$214$	0.934339	+	1.03769i	0.0638701	+	0.0709349i
$215$	5.52611	−	4.18927i	0.376877	−	0.285706i
$216$		0			0
$217$	−18.1249	+	13.1685i	−1.23040	+	0.893938i
$218$	−0.663982	+	1.15005i	−0.0449705	+	0.0778912i
$219$		0			0
$220$	1.53877	−	0.359933i	0.103744	−	0.0242667i
$221$	−0.770345	+	7.32935i	−0.0518190	+	0.493025i
$222$		0			0
$223$	−0.398119	−	0.442156i	−0.0266600	−	0.0296090i	0.729667	−	0.683802i	$-0.239675\pi$
$223$	−0.398119	−	0.442156i	−0.0266600	−	0.0296090i	−0.756327	+	0.654193i	$0.773008\pi$
$224$	−8.01038			−0.535216
$225$		0			0
$226$	−1.46249			−0.0972834
$227$	6.17937	+	6.86289i	0.410139	+	0.455506i	0.912454	−	0.409179i	$-0.134185\pi$
$227$	6.17937	+	6.86289i	0.410139	+	0.455506i	−0.502315	+	0.864685i	$0.667518\pi$
$228$		0			0
$229$	−0.272928	+	2.59673i	−0.0180356	+	0.171597i	−0.999832	−	0.0183402i	$-0.994162\pi$
$229$	−0.272928	+	2.59673i	−0.0180356	+	0.171597i	0.981796	+	0.189937i	$0.0608285\pi$
$230$	−0.833169	−	1.37761i	−0.0549375	−	0.0908367i
$231$		0			0
$232$	2.12316	−	3.67742i	0.139392	−	0.241435i
$233$	−5.35177	+	3.88829i	−0.350606	+	0.254730i	−0.749123	−	0.662431i	$-0.769525\pi$
$233$	−5.35177	+	3.88829i	−0.350606	+	0.254730i	0.398517	+	0.917161i	$0.369525\pi$
$234$		0			0
$235$	28.9180	−	0.588229i	1.88640	−	0.0383718i
$236$	6.53279	+	7.25539i	0.425248	+	0.472286i
$237$		0			0
$238$	−1.81561	+	2.01644i	−0.117688	+	0.130706i
$239$	16.1587	−	3.43464i	1.04522	−	0.222168i	0.346861	−	0.937917i	$-0.387248\pi$
$239$	16.1587	−	3.43464i	1.04522	−	0.222168i	0.698358	+	0.715748i	$0.253914\pi$
$240$		0			0
$241$	−7.35486	−	1.56332i	−0.473768	−	0.100703i	−0.0351616	−	0.999382i	$-0.511195\pi$
$241$	−7.35486	−	1.56332i	−0.473768	−	0.100703i	−0.438607	+	0.898679i	$0.644528\pi$
$242$	1.44646	−	1.05092i	0.0929823	−	0.0675556i
$243$		0			0
$244$	14.5256	−	10.5534i	0.929903	−	0.675614i
$245$	−2.81250	−	22.3722i	−0.179684	−	1.42931i
$246$		0			0
$247$	−0.0142909	+	0.135969i	−0.000909308	+	0.00865148i
$248$	−3.46415	+	0.736327i	−0.219974	+	0.0467568i
$249$		0			0
$250$	−0.820536	+	1.64545i	−0.0518953	+	0.104067i
$251$	19.2136			1.21275			0.606377	−	0.795177i	$-0.292622\pi$
$251$	19.2136			1.21275			0.606377	+	0.795177i	$0.292622\pi$
$252$		0			0
$253$	−1.26874	−	0.921796i	−0.0797652	−	0.0579528i
$254$	−0.487511	+	0.217054i	−0.0305892	+	0.0136192i
$255$		0			0
$256$	12.6799	+	5.64547i	0.792496	+	0.352842i
$257$	9.44838	+	16.3651i	0.589374	+	1.02083i	0.994315	+	0.106483i	$0.0339588\pi$
$257$	9.44838	+	16.3651i	0.589374	+	1.02083i	−0.404941	+	0.914343i	$0.632708\pi$
$258$		0			0
$259$	31.0701	+	6.60416i	1.93060	+	0.410363i
$260$	−2.67395	−	7.69353i	−0.165831	−	0.477132i
$261$		0			0
$262$	0.437266	+	1.34577i	0.0270144	+	0.0831417i
$263$	15.8269	+	3.36410i	0.975926	+	0.207439i	0.668156	−	0.744021i	$-0.267084\pi$
$263$	15.8269	+	3.36410i	0.975926	+	0.207439i	0.307770	+	0.951461i	$0.400417\pi$
$264$		0			0
$265$	−2.19101	−	3.62274i	−0.134593	−	0.222543i
$266$	−0.0336818	+	0.0374075i	−0.00206517	+	0.00229360i
$267$		0			0
$268$	14.2158	−	24.6225i	0.868368	−	1.50406i
$269$	1.72574	−	1.25382i	0.105220	−	0.0764469i	−0.533931	−	0.845528i	$-0.679286\pi$
$269$	1.72574	−	1.25382i	0.105220	−	0.0764469i	0.639151	+	0.769081i	$0.279286\pi$
$270$		0			0
$271$	−13.1625	−	9.56310i	−0.799563	−	0.580917i	0.111223	−	0.993796i	$-0.464523\pi$
$271$	−13.1625	−	9.56310i	−0.799563	−	0.580917i	−0.910786	+	0.412879i	$0.864523\pi$
$272$	13.9975	−	6.23209i	0.848723	−	0.377876i
$273$		0			0
$274$	−0.471256	−	0.816239i	−0.0284696	−	0.0493108i
$275$	−0.114626	+	1.78739i	−0.00691221	+	0.107783i
$276$		0			0
$277$	−5.70183	−	6.33252i	−0.342590	−	0.380484i	0.547087	−	0.837076i	$-0.315737\pi$
$277$	−5.70183	−	6.33252i	−0.342590	−	0.380484i	−0.889676	+	0.456591i	$0.849070\pi$
$278$	−2.20656	−	1.60316i	−0.132341	−	0.0961511i
$279$		0			0
$280$	1.74888	−	5.77993i	0.104516	−	0.345417i
$281$	−0.868414	−	8.26241i	−0.0518052	−	0.492894i	−0.989405	−	0.145179i	$-0.953624\pi$
$281$	−0.868414	−	8.26241i	−0.0518052	−	0.492894i	0.937600	−	0.347715i	$-0.113042\pi$
$282$		0			0
$283$	4.78188	+	2.12903i	0.284253	+	0.126558i	0.543911	−	0.839143i	$-0.316943\pi$
$283$	4.78188	+	2.12903i	0.284253	+	0.126558i	−0.259657	+	0.965701i	$0.583610\pi$
$284$	−17.7299	+	19.6910i	−1.05208	+	1.16845i
$285$		0			0
$286$	0.0727764	+	0.0808264i	0.00430336	+	0.00477937i
$287$	6.00921	+	18.4944i	0.354712	+	1.09169i
$288$		0			0
$289$	−0.329378	+	1.01372i	−0.0193752	+	0.0596307i
$290$	1.63496	+	1.74317i	0.0960083	+	0.102363i
$291$		0			0
$292$	−24.2566	−	10.7997i	−1.41951	−	0.632006i
$293$	10.1972	+	17.6621i	0.595728	+	1.03183i	0.993444	+	0.114323i	$0.0364698\pi$
$293$	10.1972	+	17.6621i	0.595728	+	1.03183i	−0.397715	+	0.917509i	$0.630197\pi$
$294$		0			0
$295$	−10.0149	+	4.70523i	−0.583088	+	0.273949i
$296$	4.06228	+	2.95142i	0.236115	+	0.171548i
$297$		0			0
$298$	−0.356220	+	1.09633i	−0.0206353	+	0.0635089i
$299$	−4.04142	+	6.99994i	−0.233721	+	0.404817i
$300$		0			0
$301$	−6.40909	−	11.1009i	−0.369414	−	0.639843i
$302$	0.757397	−	0.160990i	0.0435833	−	0.00926392i
$303$		0			0
$304$	0.259671	−	0.115613i	0.0148932	−	0.00663087i
$305$	6.68047	+	19.2212i	0.382523	+	1.10060i
$306$		0			0
$307$	8.63664			0.492919			0.246459	−	0.969153i	$-0.420733\pi$
$307$	8.63664			0.492919			0.246459	+	0.969153i	$0.420733\pi$
$308$	−0.305341	−	2.90512i	−0.0173984	−	0.165535i
$309$		0			0
$310$	0.167994	−	1.98617i	0.00954143	−	0.112807i
$311$	−13.1734	+	2.80008i	−0.746992	+	0.158778i	−0.565654	−	0.824643i	$-0.691376\pi$
$311$	−13.1734	+	2.80008i	−0.746992	+	0.158778i	−0.181338	+	0.983421i	$0.558043\pi$
$312$		0			0
$313$	7.14512	+	1.51874i	0.403866	+	0.0858443i	0.405366	−	0.914155i	$-0.367144\pi$
$313$	7.14512	+	1.51874i	0.403866	+	0.0858443i	−0.00150004	+	0.999999i	$0.500477\pi$
$314$	−0.865788	+	2.66462i	−0.0488593	+	0.150373i
$315$		0			0
$316$	3.65275	+	11.2420i	0.205483	+	0.632413i
$317$	−2.42838	−	23.1045i	−0.136391	−	1.29768i	−0.821908	−	0.569620i	$-0.807090\pi$
$317$	−2.42838	−	23.1045i	−0.136391	−	1.29768i	0.685517	−	0.728057i	$-0.259576\pi$
$318$		0			0
$319$	2.12675	+	0.946889i	0.119075	+	0.0530156i
$320$	−10.7585	+	12.4486i	−0.601420	+	0.695900i
$321$		0			0
$322$	−2.71865	+	1.21042i	−0.151505	+	0.0674542i
$323$	0.0913448	−	0.281131i	0.00508256	−	0.0156425i
$324$		0			0
$325$	9.22354	−	0.375392i	0.511630	−	0.0208230i
$326$	−0.0834143	+	0.144478i	−0.00461989	+	0.00800189i
$327$		0			0
$328$	−0.321324	+	3.05719i	−0.0177421	+	0.168805i
$329$	5.58858	−	53.1718i	0.308108	−	2.93145i
$330$		0			0
$331$	−2.81073	−	26.7423i	−0.154492	−	1.46989i	−0.747267	−	0.664524i	$-0.768634\pi$
$331$	−2.81073	−	26.7423i	−0.154492	−	1.46989i	0.592775	−	0.805368i	$-0.298032\pi$
$332$	−5.69392			−0.312494
$333$		0			0
$334$	−0.194788	−	0.599497i	−0.0106583	−	0.0328030i
$335$	22.0441	+	23.5031i	1.20440	+	1.28411i
$336$		0			0
$337$	5.77004	−	6.40828i	0.314314	−	0.349081i	−0.565200	−	0.824954i	$-0.691201\pi$
$337$	5.77004	−	6.40828i	0.314314	−	0.349081i	0.879514	+	0.475873i	$0.157868\pi$
$338$	−1.05547	+	1.17222i	−0.0574102	+	0.0637604i
$339$		0			0
$340$	2.19657	+	17.4727i	0.119126	+	0.947592i
$341$	−0.599994	−	1.84659i	−0.0324915	−	0.0999986i
$342$		0			0
$343$	−12.7466			−0.688251
$344$	−0.211804	−	2.01518i	−0.0114197	−	0.108651i
$345$		0			0
$346$	0.381326	−	3.62808i	0.0205002	−	0.195047i
$347$	3.67108	−	34.9280i	0.197074	−	1.87503i	−0.233330	−	0.972398i	$-0.574962\pi$
$347$	3.67108	−	34.9280i	0.197074	−	1.87503i	0.430404	−	0.902636i	$-0.358371\pi$
$348$		0			0
$349$	10.5156	−	18.2135i	0.562886	−	0.974946i	−0.434357	−	0.900741i	$-0.643025\pi$
$349$	10.5156	−	18.2135i	0.562886	−	0.974946i	0.997243	−	0.0742057i	$-0.0236421\pi$
$350$	2.82860	+	1.88426i	0.151195	+	0.100718i
$351$		0			0
$352$	0.214527	−	0.660245i	0.0114343	−	0.0351912i
$353$	−17.9989	+	8.01363i	−0.957985	+	0.426523i	−0.825337	−	0.564641i	$-0.809015\pi$
$353$	−17.9989	+	8.01363i	−0.957985	+	0.426523i	−0.132649	+	0.991163i	$0.542348\pi$
$354$		0			0
$355$	−15.5411	−	25.6965i	−0.824835	−	1.36383i
$356$	12.9139	+	5.74966i	0.684438	+	0.304731i
$357$		0			0
$358$	−0.251638	−	2.39418i	−0.0132995	−	0.126536i
$359$	0.938606	+	2.88873i	0.0495377	+	0.152461i	0.972765	−	0.231792i	$-0.0744589\pi$
$359$	0.938606	+	2.88873i	0.0495377	+	0.152461i	−0.923228	+	0.384253i	$0.874459\pi$
$360$		0			0
$361$	−5.86963	+	18.0649i	−0.308928	+	0.950782i
$362$	−2.77063	−	0.588915i	−0.145621	−	0.0309527i
$363$		0			0
$364$	−14.7266	+	3.13023i	−0.771882	+	0.164069i
$365$	19.6773	−	22.7684i	1.02995	−	1.19175i
$366$		0			0
$367$	0.759260	+	7.22388i	0.0396330	+	0.377083i	0.996303	+	0.0859088i	$0.0273794\pi$
$367$	0.759260	+	7.22388i	0.0396330	+	0.377083i	−0.956670	+	0.291175i	$0.905954\pi$
$368$	16.8048			0.876010
$369$		0			0
$370$	−2.25209	+	1.70728i	−0.117080	+	0.0887572i
$371$	−7.14934	+	3.18309i	−0.371175	+	0.165258i
$372$		0			0
$373$	−10.3292	+	2.19554i	−0.534825	+	0.113681i	−0.467404	−	0.884044i	$-0.654810\pi$
$373$	−10.3292	+	2.19554i	−0.534825	+	0.113681i	−0.0674212	+	0.997725i	$0.521477\pi$
$374$	−0.117578	−	0.203651i	−0.00607983	−	0.0105306i
$375$		0			0
$376$	4.22581	−	7.31932i	0.217930	−	0.377465i
$377$	3.70779	−	11.4114i	0.190961	−	0.587718i
$378$		0			0
$379$	−28.5159	−	20.7180i	−1.46476	−	1.06421i	−0.982090	−	0.188412i	$-0.939666\pi$
$379$	−28.5159	−	20.7180i	−1.46476	−	1.06421i	−0.482673	−	0.875801i	$-0.660334\pi$
$380$	0.0407492	+	0.324142i	0.00209039	+	0.0166281i
$381$		0			0
$382$	0.0478913	+	0.0829501i	0.00245033	+	0.00424410i
$383$	5.70095	+	2.53823i	0.291305	+	0.129697i	0.547186	−	0.837011i	$-0.315699\pi$
$383$	5.70095	+	2.53823i	0.291305	+	0.129697i	−0.255881	+	0.966708i	$0.582366\pi$
$384$		0			0
$385$	3.25167	+	0.622330i	0.165720	+	0.0317169i
$386$	0.472253	−	1.45344i	0.0240370	−	0.0739784i
$387$		0			0
$388$	−6.44524	−	19.8364i	−0.327208	−	1.00704i
$389$	−19.0702	−	21.1796i	−0.966899	−	1.07385i	−0.997235	−	0.0743103i	$-0.976324\pi$
$389$	−19.0702	−	21.1796i	−0.966899	−	1.07385i	0.0303363	−	0.999540i	$-0.490342\pi$
$390$		0			0
$391$	11.6937	−	12.9872i	0.591375	−	0.656788i
$392$	−6.01902	−	2.67984i	−0.304006	−	0.135352i
$393$		0			0
$394$	0.0738414	+	0.702554i	0.00372008	+	0.0353942i
$395$	−13.3942	+	0.272455i	−0.673934	+	0.0137087i
$396$		0			0
$397$	−4.87063	−	3.53872i	−0.244450	−	0.177603i	0.458814	−	0.888533i	$-0.348275\pi$
$397$	−4.87063	−	3.53872i	−0.244450	−	0.177603i	−0.703263	+	0.710929i	$0.748275\pi$
$398$	−0.352332	−	0.391304i	−0.0176608	−	0.0196143i
$399$		0			0
$400$	−10.2641	−	16.2170i	−0.513205	−	0.810851i
$401$	−13.2682	−	22.9812i	−0.662583	−	1.14763i	−0.979934	−	0.199320i	$-0.936127\pi$
$401$	−13.2682	−	22.9812i	−0.662583	−	1.14763i	0.317351	−	0.948308i	$-0.397207\pi$
$402$		0			0
$403$	−9.14202	+	4.07029i	−0.455396	+	0.202756i
$404$	27.9602	+	20.3143i	1.39107	+	1.01067i
$405$		0			0
$406$	3.57397	−	2.59664i	0.177373	−	0.128869i
$407$	−1.37643	+	2.38405i	−0.0682272	+	0.118173i
$408$		0			0
$409$	−18.2716	+	20.2927i	−0.903475	+	1.00341i	0.0964928	+	0.995334i	$0.469238\pi$
$409$	−18.2716	+	20.2927i	−0.903475	+	1.00341i	−0.999967	+	0.00807647i	$0.997429\pi$
$410$	−1.59454	−	0.671419i	−0.0787487	−	0.0331590i
$411$		0			0
$412$	23.0898	+	4.90790i	1.13755	+	0.241795i
$413$	6.32043	+	19.4523i	0.311008	+	0.957184i
$414$		0			0
$415$	1.86894	−	6.17670i	0.0917425	−	0.303202i
$416$	−3.49986	−	0.743918i	−0.171595	−	0.0364736i
$417$		0			0
$418$	−0.00218123	−	0.00377800i	−0.000106687	−	0.000184788i
$419$	10.8046	+	4.81054i	0.527841	+	0.235010i	0.653314	−	0.757087i	$-0.273378\pi$
$419$	10.8046	+	4.81054i	0.527841	+	0.235010i	−0.125473	+	0.992097i	$0.540045\pi$
$420$		0			0
$421$	1.67084	−	0.743904i	0.0814316	−	0.0362557i	−0.365617	−	0.930766i	$-0.619142\pi$
$421$	1.67084	−	0.743904i	0.0814316	−	0.0362557i	0.447048	+	0.894510i	$0.352475\pi$
$422$	0.965691	+	0.701616i	0.0470091	+	0.0341541i
$423$		0			0
$424$	−1.23711			−0.0600795
$425$	−19.6752	−	3.35233i	−0.954389	−	0.162612i
$426$		0			0
$427$	36.7922	−	7.82043i	1.78050	−	0.378457i
$428$	1.75102	−	16.6599i	0.0846388	−	0.805285i
$429$		0			0
$430$	1.12011	+	0.214375i	0.0540163	+	0.0103381i
$431$	−28.5016	+	20.7076i	−1.37288	+	0.997452i	−0.375369	+	0.926876i	$0.622484\pi$
$431$	−28.5016	+	20.7076i	−1.37288	+	0.997452i	−0.997506	+	0.0705766i	$0.977516\pi$
$432$		0			0
$433$	3.17805	−	2.30899i	0.152727	−	0.110963i	−0.508797	−	0.860886i	$-0.669910\pi$
$433$	3.17805	−	2.30899i	0.152727	−	0.110963i	0.661525	+	0.749923i	$0.269910\pi$
$434$	−3.60393	−	0.766039i	−0.172994	−	0.0367711i
$435$		0			0
$436$	15.5831	−	3.31229i	0.746295	−	0.158630i
$437$	0.216933	−	0.240928i	0.0103773	−	0.0115252i
$438$		0			0
$439$	12.9252	+	14.3549i	0.616887	+	0.685123i	0.967925	−	0.251238i	$-0.0808378\pi$
$439$	12.9252	+	14.3549i	0.616887	+	0.685123i	−0.351038	+	0.936361i	$0.614171\pi$
$440$	0.429567	+	0.298943i	0.0204788	+	0.0142515i
$441$		0			0
$442$	−0.980532	+	0.712398i	−0.0466392	+	0.0338853i
$443$	2.24077	−	3.88113i	0.106462	−	0.184398i	−0.807872	−	0.589357i	$-0.799381\pi$
$443$	2.24077	−	3.88113i	0.106462	−	0.184398i	0.914335	+	0.404959i	$0.132714\pi$
$444$		0			0
$445$	−10.4760	+	12.1217i	−0.496608	+	0.574623i
$446$	0.0102280	−	0.0973128i	0.000484309	−	0.00460790i
$447$		0			0
$448$	20.3505	+	22.6015i	0.961471	+	1.06782i
$449$	11.2399			0.530445			0.265222	−	0.964187i	$-0.414555\pi$
$449$	11.2399			0.530445			0.265222	+	0.964187i	$0.414555\pi$
$450$		0			0
$451$	−1.68531			−0.0793583
$452$	11.7400	+	13.0386i	0.552202	+	0.613283i
$453$		0			0
$454$	−0.158753	+	1.51043i	−0.00745064	+	0.0708881i
$455$	1.43812	−	17.0027i	0.0674203	−	0.797098i
$456$		0			0
$457$	7.48417	−	12.9630i	0.350095	−	0.606381i	−0.636171	−	0.771548i	$-0.719483\pi$
$457$	7.48417	−	12.9630i	0.350095	−	0.606381i	0.986266	+	0.165166i	$0.0528161\pi$
$458$	−0.347396	+	0.252398i	−0.0162327	+	0.0117938i
$459$		0			0
$460$	−5.59363	+	18.4866i	−0.260805	+	0.861940i
$461$	−20.1758	−	22.4075i	−0.939679	−	1.04362i	−0.998970	−	0.0453786i	$-0.985551\pi$
$461$	−20.1758	−	22.4075i	−0.939679	−	1.04362i	0.0592908	−	0.998241i	$-0.481116\pi$
$462$		0			0
$463$	−18.4989	+	20.5451i	−0.859718	+	0.954814i	−0.999374	−	0.0353863i	$-0.988734\pi$
$463$	−18.4989	+	20.5451i	−0.859718	+	0.954814i	0.139655	+	0.990200i	$0.455401\pi$
$464$	−24.4010	+	5.18658i	−1.13279	+	0.240781i
$465$		0			0
$466$	−1.06414	−	0.226189i	−0.0492952	−	0.0104780i
$467$	23.9054	−	17.3683i	1.10621	−	0.803709i	0.124147	−	0.992264i	$-0.460380\pi$
$467$	23.9054	−	17.3683i	1.10621	−	0.803709i	0.982063	+	0.188555i	$0.0603805\pi$
$468$		0			0
$469$	48.1876	−	35.0103i	2.22510	−	1.61663i
$470$	3.25413	+	3.46950i	0.150102	+	0.160036i
$471$		0			0
$472$	−0.337965	+	3.21552i	−0.0155561	+	0.148007i
$473$	1.08662	−	0.230968i	0.0499627	−	0.0106199i
$474$		0			0
$475$	−0.365001	−	0.0621900i	−0.0167474	−	0.00285347i
$476$	32.5517			1.49201
$477$		0			0
$478$	2.19793	+	1.59689i	0.100531	+	0.0730399i
$479$	12.2428	−	5.45085i	0.559389	−	0.249056i	−0.107510	−	0.994204i	$-0.534288\pi$
$479$	12.2428	−	5.45085i	0.559389	−	0.249056i	0.666899	+	0.745148i	$0.267621\pi$
$480$		0			0
$481$	12.9617	+	5.77093i	0.591003	+	0.263132i
$482$	−0.618292	−	1.07091i	−0.0281624	−	0.0487788i
$483$		0			0
$484$	−20.9806	−	4.45957i	−0.953664	−	0.202708i
$485$	23.6339	−	0.480743i	1.07316	−	0.0218294i
$486$		0			0
$487$	0.825534	+	2.54073i	0.0374085	+	0.115132i	0.968017	−	0.250885i	$-0.0807215\pi$
$487$	0.825534	+	2.54073i	0.0374085	+	0.115132i	−0.930608	+	0.366016i	$0.880721\pi$
$488$	5.81607	+	1.23624i	0.263281	+	0.0559621i
$489$		0			0
$490$	2.42474	−	2.80565i	0.109538	−	0.126746i
$491$	11.9826	−	13.3080i	0.540767	−	0.600582i	−0.409388	−	0.912360i	$-0.634258\pi$
$491$	11.9826	−	13.3080i	0.540767	−	0.600582i	0.950155	+	0.311778i	$0.100925\pi$
$492$		0			0
$493$	−12.9712	+	22.4668i	−0.584193	+	1.01185i
$494$	−0.0181901	+	0.0132159i	−0.000818413	+	0.000594612i
$495$		0			0
$496$	16.8321	+	12.2293i	0.755785	+	0.549110i
$497$	−50.7110	+	22.5780i	−2.27470	+	1.01276i
$498$		0			0
$499$	−10.2734	−	17.7940i	−0.459899	−	0.796568i	0.539057	−	0.842270i	$-0.318781\pi$
$499$	−10.2734	−	17.7940i	−0.459899	−	0.796568i	−0.998955	+	0.0457019i	$0.985448\pi$
$500$	21.2565	−	5.89331i	0.950618	−	0.263557i
$501$		0			0
$502$	2.11433	+	2.34821i	0.0943674	+	0.104806i
$503$	32.2593	+	23.4377i	1.43837	+	1.04504i	0.988380	+	0.152003i	$0.0485724\pi$
$503$	32.2593	+	23.4377i	1.43837	+	1.04504i	0.449990	+	0.893034i	$0.351428\pi$
$504$		0			0
$505$	−31.2142	+	23.6631i	−1.38901	+	1.05299i
$506$	−0.0269590	−	0.256498i	−0.00119847	−	0.0114027i
$507$		0			0
$508$	5.84855	+	2.60394i	0.259487	+	0.115531i
$509$	−13.2868	+	14.7564i	−0.588925	+	0.654068i	−0.961780	−	0.273822i	$-0.911712\pi$
$509$	−13.2868	+	14.7564i	−0.588925	+	0.654068i	0.372855	+	0.927890i	$0.378379\pi$
$510$		0			0
$511$	−37.2209	−	41.3380i	−1.64655	−	1.82868i
$512$	3.84880	+	11.8454i	0.170094	+	0.523497i
$513$		0			0
$514$	−0.960336	+	2.95561i	−0.0423586	+	0.130366i
$515$	−12.9029	+	23.4367i	−0.568570	+	1.03274i
$516$		0			0
$517$	4.23295	+	1.88463i	0.186165	+	0.0828859i
$518$	2.61193	+	4.52400i	0.114762	+	0.198773i
$519$		0			0
$520$	1.30089	−	2.36293i	0.0570480	−	0.103621i
$521$	−8.76012	−	6.36460i	−0.383788	−	0.278838i	0.379117	−	0.925349i	$-0.376228\pi$
$521$	−8.76012	−	6.36460i	−0.383788	−	0.278838i	−0.762905	+	0.646510i	$0.776228\pi$
$522$		0			0
$523$	4.62026	−	14.2197i	0.202030	−	0.621785i	−0.797792	−	0.602932i	$-0.793999\pi$
$523$	4.62026	−	14.2197i	0.202030	−	0.621785i	0.999822	−	0.0188521i	$-0.00600116\pi$
$524$	8.48783	−	14.7014i	0.370793	−	0.642232i
$525$		0			0
$526$	1.33050	+	2.30449i	0.0580124	+	0.100480i
$527$	21.1638	−	4.49850i	0.921909	−	0.195958i
$528$		0			0
$529$	−3.50166	+	1.55904i	−0.152246	+	0.0677844i
$530$	0.201649	−	0.666436i	0.00875908	−	0.0289481i
$531$		0			0
$532$	0.603877			0.0261814
$533$	0.907952	+	8.63858i	0.0393278	+	0.374179i
$534$		0			0
$535$	17.4977	+	7.36782i	0.756491	+	0.318539i
$536$	9.20991	−	1.95763i	0.397808	−	0.0845566i
$537$		0			0
$538$	0.343143	+	0.0729373i	0.0147939	+	0.00314455i
$539$	1.11622	−	3.43538i	0.0480791	−	0.147972i
$540$		0			0
$541$	11.4490	+	35.2363i	0.492230	+	1.51493i	0.821230	+	0.570597i	$0.193288\pi$
$541$	11.4490	+	35.2363i	0.492230	+	1.51493i	−0.329000	+	0.944330i	$0.606712\pi$
$542$	−0.279684	−	2.66102i	−0.0120135	−	0.114300i
$543$		0			0
$544$	7.06730	+	3.14656i	0.303008	+	0.134908i
$545$	−1.52177	+	17.9916i	−0.0651854	+	0.770675i
$546$		0			0
$547$	−19.4966	+	8.68045i	−0.833615	+	0.371149i	−0.778742	−	0.627344i	$-0.784142\pi$
$547$	−19.4966	+	8.68045i	−0.833615	+	0.371149i	−0.0548729	+	0.998493i	$0.517475\pi$
$548$	−3.49408	+	10.7537i	−0.149260	+	0.459374i
$549$		0			0
$550$	−0.231060	+	0.182681i	−0.00985245	+	0.00778955i
$551$	−0.240632	+	0.416787i	−0.0102513	+	0.0177557i
$552$		0			0
$553$	−2.58850	+	24.6280i	−0.110074	+	1.04729i
$554$	0.146484	−	1.39371i	0.00622352	−	0.0592129i
$555$		0			0
$556$	3.42023	+	32.5414i	0.145050	+	1.38006i
$557$	−38.6947			−1.63955			−0.819773	−	0.572689i	$-0.805900\pi$
$557$	−38.6947			−1.63955			−0.819773	+	0.572689i	$0.805900\pi$
$558$		0			0
$559$	−1.76930	−	5.44535i	−0.0748335	−	0.230314i
$560$	−32.1088	+	15.0855i	−1.35684	+	0.637479i
$561$		0			0
$562$	0.914232	−	1.01536i	0.0385646	−	0.0428303i
$563$	−9.13347	+	10.1437i	−0.384930	+	0.427508i	−0.904205	−	0.427100i	$-0.859535\pi$
$563$	−9.13347	+	10.1437i	−0.384930	+	0.427508i	0.519275	+	0.854607i	$0.326202\pi$
$564$		0			0
$565$	−17.9976	+	8.45570i	−0.757163	+	0.355734i
$566$	0.266014	+	0.818707i	0.0111814	+	0.0344128i
$567$		0			0
$568$	−8.77496			−0.368189
$569$	2.42745	+	23.0956i	0.101764	+	0.968218i	0.919624	+	0.392801i	$0.128494\pi$
$569$	2.42745	+	23.0956i	0.101764	+	0.968218i	−0.817860	+	0.575417i	$0.804840\pi$
$570$		0			0
$571$	−2.66000	+	25.3082i	−0.111317	+	1.05911i	0.786151	+	0.618035i	$0.212071\pi$
$571$	−2.66000	+	25.3082i	−0.111317	+	1.05911i	−0.897468	+	0.441079i	$0.854596\pi$
$572$	0.136389	−	1.29765i	0.00570269	−	0.0542575i
$573$		0			0
$574$	−1.59904	+	2.76961i	−0.0667425	+	0.115601i
$575$	−18.2180	−	12.1358i	−0.759743	−	0.506099i
$576$		0			0
$577$	9.47834	−	29.1713i	0.394588	−	1.21442i	−0.534693	−	0.845046i	$-0.679573\pi$
$577$	9.47834	−	29.1713i	0.394588	−	1.21442i	0.929282	−	0.369372i	$-0.120427\pi$
$578$	−0.160139	+	0.0712983i	−0.00666089	+	0.00296562i
$579$		0			0
$580$	2.41645	−	28.5693i	0.100338	−	1.18628i
$581$	−10.8973	−	4.85178i	−0.452095	−	0.201286i
$582$		0			0
$583$	−0.0708951	−	0.674522i	−0.00293618	−	0.0279359i
$584$	−2.71726	−	8.36287i	−0.112441	−	0.346058i
$585$		0			0
$586$	−1.03645	+	3.18986i	−0.0428153	+	0.131772i
$587$	−14.4830	−	3.07845i	−0.597777	−	0.127061i	−0.100921	−	0.994894i	$-0.532179\pi$
$587$	−14.4830	−	3.07845i	−0.597777	−	0.127061i	−0.496856	+	0.867833i	$0.665512\pi$
$588$		0			0
$589$	0.392615	−	0.0834530i	0.0161774	−	0.00343862i
$590$	−1.67712	−	0.706193i	−0.0690460	−	0.0290735i
$591$		0			0
$592$	−3.08345	−	29.3370i	−0.126729	−	1.20574i
$593$	−29.3262			−1.20428			−0.602140	−	0.798390i	$-0.705685\pi$
$593$	−29.3262			−1.20428			−0.602140	+	0.798390i	$0.705685\pi$
$594$		0			0
$595$	−10.6846	+	35.3118i	−0.438026	+	1.44764i
$596$	12.6337	−	5.62488i	0.517496	−	0.230404i
$597$		0			0
$598$	−1.30023	+	0.276373i	−0.0531705	+	0.0113017i
$599$	−2.03948	−	3.53249i	−0.0833310	−	0.144334i	0.821348	−	0.570428i	$-0.193223\pi$
$599$	−2.03948	−	3.53249i	−0.0833310	−	0.144334i	−0.904679	+	0.426094i	$0.859889\pi$
$600$		0			0
$601$	−8.15219	+	14.1200i	−0.332535	+	0.575967i	−0.983008	−	0.183562i	$-0.941237\pi$
$601$	−8.15219	+	14.1200i	−0.332535	+	0.575967i	0.650474	+	0.759529i	$0.274570\pi$
$602$	0.651421	−	2.00487i	0.0265500	−	0.0817124i
$603$		0			0
$604$	−7.51520	−	5.46011i	−0.305789	−	0.222169i
$605$	11.7242	−	21.2958i	0.476658	−	0.865796i
$606$		0			0
$607$	9.93751	+	17.2123i	0.403351	+	0.698625i	0.994128	−	0.108210i	$-0.0345120\pi$
$607$	9.93751	+	17.2123i	0.403351	+	0.698625i	−0.590777	+	0.806835i	$0.701179\pi$
$608$	0.131107	+	0.0583728i	0.00531711	+	0.00236733i
$609$		0			0
$610$	−1.61398	+	2.93162i	−0.0653483	+	0.118698i
$611$	7.37976	−	22.7126i	0.298553	−	0.918852i
$612$		0			0
$613$	1.01670	+	3.12907i	0.0410639	+	0.126382i	0.969487	−	0.245143i	$-0.0788350\pi$
$613$	1.01670	+	3.12907i	0.0410639	+	0.126382i	−0.928423	+	0.371525i	$0.878835\pi$
$614$	0.950406	+	1.05553i	0.0383552	+	0.0425978i
$615$		0			0
$616$	0.647308	−	0.718908i	0.0260808	−	0.0289656i
$617$	−40.1863	−	17.8921i	−1.61784	−	0.720308i	−0.619912	−	0.784671i	$-0.712832\pi$
$617$	−40.1863	−	17.8921i	−1.61784	−	0.720308i	−0.997927	+	0.0643626i	$0.979499\pi$
$618$		0			0
$619$	1.18396	+	11.2646i	0.0475873	+	0.452763i	0.992207	+	0.124597i	$0.0397638\pi$
$619$	1.18396	+	11.2646i	0.0475873	+	0.452763i	−0.944620	+	0.328166i	$0.893570\pi$
$620$	−19.0559	+	14.4460i	−0.765302	+	0.580166i
$621$		0			0
$622$	−1.79186	−	1.30186i	−0.0718469	−	0.0521998i
$623$	19.8160	+	22.0079i	0.793912	+	0.881728i
$624$		0			0
$625$	−0.584094	+	24.9932i	−0.0233638	+	0.999727i
$626$	0.600659	+	1.04037i	0.0240072	+	0.0415817i
$627$		0			0
$628$	30.7060	−	13.6712i	1.22530	−	0.545540i
$629$	−24.8180	−	18.0313i	−0.989559	−	0.718956i
$630$		0			0
$631$	19.7944	−	14.3815i	0.788005	−	0.572519i	−0.119366	−	0.992850i	$-0.538086\pi$
$631$	19.7944	−	14.3815i	0.788005	−	0.572519i	0.907371	+	0.420331i	$0.138086\pi$
$632$	−1.95730	+	3.39015i	−0.0778573	+	0.134853i
$633$		0			0
$634$	2.55650	−	2.83928i	0.101532	−	0.112762i
$635$	−4.74442	+	5.48974i	−0.188277	+	0.217854i
$636$		0			0
$637$	−18.2104	−	3.87074i	−0.721523	−	0.153364i
$638$	0.118310	+	0.364121i	0.00468394	+	0.0144157i
$639$		0			0
$640$	−11.3706	+	0.231293i	−0.449464	+	0.00914267i
$641$	28.6247	+	6.08438i	1.13061	+	0.240318i	0.734978	−	0.678091i	$-0.237192\pi$
$641$	28.6247	+	6.08438i	1.13061	+	0.240318i	0.395631	+	0.918409i	$0.370526\pi$
$642$		0			0
$643$	−3.57430	−	6.19087i	−0.140957	−	0.244144i	0.786900	−	0.617080i	$-0.211685\pi$
$643$	−3.57430	−	6.19087i	−0.140957	−	0.244144i	−0.927857	+	0.372936i	$0.878351\pi$
$644$	32.6150	+	14.5211i	1.28521	+	0.572213i
$645$		0			0
$646$	0.0444105	−	0.0197728i	0.00174731	−	0.000777951i
$647$	−25.5288	−	18.5478i	−1.00364	−	0.729188i	−0.0407758	−	0.999168i	$-0.512983\pi$
$647$	−25.5288	−	18.5478i	−1.00364	−	0.729188i	−0.962866	+	0.269980i	$0.912983\pi$
$648$		0			0
$649$	−1.77260			−0.0695805
$650$	1.06087	+	1.08595i	0.0416107	+	0.0425945i
$651$		0			0
$652$	1.95767	−	0.416115i	0.0766681	−	0.0162963i
$653$	−0.244296	+	2.32432i	−0.00956003	+	0.0909576i	−0.998262	−	0.0589403i	$-0.981228\pi$
$653$	−0.244296	+	2.32432i	−0.00956003	+	0.0909576i	0.988701	+	0.149898i	$0.0478945\pi$
$654$		0			0
$655$	13.1619	+	14.0330i	0.514277	+	0.548315i
$656$	14.6102	−	10.6149i	0.570431	−	0.414443i
$657$		0			0
$658$	7.11341	−	5.16819i	0.277309	−	0.201477i
$659$	−41.8091	−	8.88679i	−1.62865	−	0.346180i	−0.699142	−	0.714983i	$-0.746435\pi$
$659$	−41.8091	−	8.88679i	−1.62865	−	0.346180i	−0.929508	+	0.368802i	$0.879768\pi$
$660$		0			0
$661$	−5.59291	+	1.18881i	−0.217539	+	0.0462393i	−0.315392	−	0.948962i	$-0.602136\pi$
$661$	−5.59291	+	1.18881i	−0.217539	+	0.0462393i	0.0978528	+	0.995201i	$0.468803\pi$
$662$	2.95903	−	3.28634i	0.115006	−	0.127727i
$663$		0			0
$664$	−1.26175	−	1.40131i	−0.0489652	−	0.0543814i
$665$	−0.198213	+	0.655079i	−0.00768637	+	0.0254029i
$666$		0			0
$667$	−23.0187	+	16.7240i	−0.891287	+	0.647558i
$668$	−3.78106	+	6.54900i	−0.146294	+	0.253388i
$669$		0			0
$670$	−0.446636	+	5.28050i	−0.0172550	+	0.204003i
$671$	−0.340747	+	3.24199i	−0.0131544	+	0.125156i
$672$		0			0
$673$	−1.32261	−	1.46890i	−0.0509827	−	0.0566221i	0.717114	−	0.696956i	$-0.245463\pi$
$673$	−1.32261	−	1.46890i	−0.0509827	−	0.0566221i	−0.768097	+	0.640334i	$0.778796\pi$
$674$	1.41815			0.0546250
$675$		0			0
$676$	18.9234			0.727824
$677$	6.94407	+	7.71217i	0.266882	+	0.296403i	0.861659	−	0.507488i	$-0.169426\pi$
$677$	6.94407	+	7.71217i	0.266882	+	0.296403i	−0.594776	+	0.803891i	$0.702759\pi$
$678$		0			0
$679$	4.56739	−	43.4558i	0.175280	−	1.66768i
$680$	−3.81341	+	4.41247i	−0.146237	+	0.169210i
$681$		0			0
$682$	0.159657	−	0.276534i	0.00611358	−	0.0105890i
$683$	−19.2932	+	14.0174i	−0.738235	+	0.536359i	−0.892158	−	0.451724i	$-0.850809\pi$
$683$	−19.2932	+	14.0174i	−0.738235	+	0.536359i	0.153923	+	0.988083i	$0.450809\pi$
$684$		0			0
$685$	−10.5186	−	7.32006i	−0.401894	−	0.279685i
$686$	−1.40268	−	1.55783i	−0.0535545	−	0.0594783i
$687$		0			0
$688$	−7.96526	+	8.84632i	−0.303673	+	0.337263i
$689$	−3.41927	+	0.726789i	−0.130264	+	0.0276884i
$690$		0			0
$691$	1.00613	+	0.213859i	0.0382748	+	0.00813556i	0.227009	−	0.973893i	$-0.427105\pi$
$691$	1.00613	+	0.213859i	0.0382748	+	0.00813556i	−0.188734	+	0.982028i	$0.560439\pi$
$692$	−35.4065	+	25.7243i	−1.34595	+	0.977893i
$693$		0			0
$694$	4.67273	−	3.39494i	0.177374	−	0.128870i
$695$	−36.4232	−	6.97095i	−1.38161	−	0.264423i
$696$		0			0
$697$	1.96309	−	18.6775i	0.0743573	−	0.707462i
$698$	3.38314	−	0.719110i	0.128054	−	0.0272187i
$699$		0			0
$700$	−5.90750	−	40.3435i	−0.223283	−	1.52484i
$701$	−14.7743			−0.558019			−0.279009	−	0.960288i	$-0.590006\pi$
$701$	−14.7743			−0.558019			−0.279009	+	0.960288i	$0.590006\pi$
$702$		0			0
$703$	−0.460406	−	0.334504i	−0.0173645	−	0.0126161i
$704$	−2.40791	+	1.07207i	−0.0907516	+	0.0404052i
$705$		0			0
$706$	−2.96005	−	1.31790i	−0.111403	−	0.0495999i
$707$	36.2017	+	62.7032i	1.36151	+	2.35820i
$708$		0			0
$709$	11.5131	+	2.44719i	0.432384	+	0.0919062i	0.418962	−	0.908004i	$-0.362394\pi$
$709$	11.5131	+	2.44719i	0.432384	+	0.0919062i	0.0134224	+	0.999910i	$0.495727\pi$
$710$	1.43032	−	4.72709i	0.0536788	−	0.177405i
$711$		0			0
$712$	1.44664	+	4.45231i	0.0542152	+	0.166857i
$713$	23.2117	+	4.93379i	0.869283	+	0.184772i
$714$		0			0
$715$	1.36291	+	0.573886i	0.0509700	+	0.0214621i
$716$	−19.3249	+	21.4624i	−0.722204	+	0.802089i
$717$		0			0
$718$	−0.249761	+	0.432599i	−0.00932099	+	0.0161444i
$719$	37.9326	−	27.5596i	1.41465	−	1.02780i	0.422019	−	0.906587i	$-0.361321\pi$
$719$	37.9326	−	27.5596i	1.41465	−	1.02780i	0.992626	−	0.121213i	$-0.0386785\pi$
$720$		0			0
$721$	40.0084	+	29.0678i	1.48999	+	1.08254i
$722$	−2.85372	+	1.27056i	−0.106205	+	0.0472853i
$723$		0			0
$724$	16.9905	+	29.4285i	0.631449	+	1.09370i
$725$	30.1985	+	11.9988i	1.12155	+	0.445623i
$726$		0			0
$727$	−21.0528	−	23.3815i	−0.780806	−	0.867173i	0.213142	−	0.977021i	$-0.431630\pi$
$727$	−21.0528	−	23.3815i	−0.780806	−	0.867173i	−0.993948	+	0.109848i	$0.964964\pi$
$728$	−4.03371	−	2.93066i	−0.149499	−	0.108618i
$729$		0			0
$730$	4.94801	−	0.100649i	0.183134	−	0.00372518i
$731$	1.29399	+	12.3115i	0.0478600	+	0.455357i
$732$		0			0
$733$	−41.4138	−	18.4386i	−1.52965	−	0.681045i	−0.542388	−	0.840128i	$-0.682480\pi$
$733$	−41.4138	−	18.4386i	−1.52965	−	0.681045i	−0.987265	+	0.159083i	$0.949146\pi$
$734$	−0.799319	+	0.887734i	−0.0295034	+	0.0327669i
$735$		0			0
$736$	5.67737	+	6.30535i	0.209271	+	0.232418i
$737$	1.59517	+	4.90942i	0.0587587	+	0.180841i
$738$		0			0
$739$	12.0961	−	37.2280i	0.444963	−	1.36945i	−0.437562	−	0.899188i	$-0.644158\pi$
$739$	12.0961	−	37.2280i	0.444963	−	1.36945i	0.882524	−	0.470267i	$-0.155842\pi$
$740$	33.2993	+	6.37309i	1.22411	+	0.234279i
$741$		0			0
$742$	−1.17576	−	0.523483i	−0.0431636	−	0.0192177i
$743$	−24.2958	−	42.0815i	−0.891325	−	1.54382i	−0.838288	−	0.545228i	$-0.816443\pi$
$743$	−24.2958	−	42.0815i	−0.891325	−	1.54382i	−0.0530375	−	0.998593i	$-0.516890\pi$
$744$		0			0
$745$	1.95500	+	15.5512i	0.0716258	+	0.569750i
$746$	−1.40499	−	1.02078i	−0.0514403	−	0.0373735i
$747$		0			0
$748$	−0.871772	+	2.68304i	−0.0318751	+	0.0981016i
$749$	17.5470	−	30.3923i	0.641154	−	1.11051i
$750$		0			0
$751$	9.62073	+	16.6636i	0.351066	+	0.608063i	0.986436	−	0.164144i	$-0.0524861\pi$
$751$	9.62073	+	16.6636i	0.351066	+	0.608063i	−0.635371	+	0.772207i	$0.719153\pi$
$752$	−48.5662	+	10.3231i	−1.77103	+	0.376443i
$753$		0			0
$754$	1.80267	−	0.802601i	0.0656494	−	0.0292290i
$755$	8.38982	−	6.36021i	0.305337	−	0.231472i
$756$		0			0
$757$	−21.2374			−0.771886			−0.385943	−	0.922523i	$-0.626124\pi$
$757$	−21.2374			−0.771886			−0.385943	+	0.922523i	$0.626124\pi$
$758$	−0.605923	−	5.76497i	−0.0220081	−	0.209393i
$759$		0			0
$760$	−0.0707436	+	0.0818570i	−0.00256614	+	0.00296926i
$761$	33.1709	−	7.05068i	1.20244	−	0.255587i	0.437221	−	0.899354i	$-0.355963\pi$
$761$	33.1709	−	7.05068i	1.20244	−	0.255587i	0.765221	+	0.643767i	$0.222629\pi$
$762$		0			0
$763$	32.6460	+	6.93913i	1.18187	+	0.251213i
$764$	0.355085	−	1.09284i	0.0128465	−	0.0395375i
$765$		0			0
$766$	0.317141	+	0.976061i	0.0114588	+	0.0352665i
$767$	0.954975	+	9.08598i	0.0344822	+	0.328076i
$768$		0			0
$769$	32.2891	+	14.3760i	1.16437	+	0.518413i	0.895631	−	0.444799i	$-0.146725\pi$
$769$	32.2891	+	14.3760i	1.16437	+	0.518413i	0.268744	+	0.963212i	$0.413391\pi$
$770$	0.281767	+	0.465888i	0.0101542	+	0.0167894i
$771$		0			0
$772$	−16.7489	+	7.45708i	−0.602805	+	0.268386i
$773$	−2.89307	+	8.90395i	−0.104056	+	0.320253i	−0.989508	−	0.144479i	$-0.953849\pi$
$773$	−2.89307	+	8.90395i	−0.104056	+	0.320253i	0.885451	+	0.464732i	$0.153849\pi$
$774$		0			0
$775$	−9.41610	−	25.4133i	−0.338236	−	0.912872i
$776$	3.45364	−	5.98188i	0.123978	−	0.214737i
$777$		0			0
$778$	0.489929	−	4.66136i	0.0175648	−	0.167118i
$779$	0.0364178	−	0.346492i	0.00130480	−	0.0124144i
$780$		0			0
$781$	−0.502866	−	4.78445i	−0.0179940	−	0.171201i
$782$	2.87405			0.102776
$783$		0			0
$784$	11.9610	+	36.8122i	0.427178	+	1.31472i
$785$	4.75161	+	37.7969i	0.169592	+	1.34903i
$786$		0			0
$787$	6.25098	−	6.94241i	0.222823	−	0.247470i	−0.621360	−	0.783525i	$-0.713419\pi$
$787$	6.25098	−	6.94241i	0.222823	−	0.247470i	0.844183	+	0.536055i	$0.180086\pi$
$788$	5.67074	−	6.29800i	0.202012	−	0.224357i
$789$		0			0
$790$	−1.50724	−	1.60700i	−0.0536252	−	0.0571744i
$791$	11.3584	+	34.9574i	0.403857	+	1.24294i
$792$		0			0
$793$	16.8014			0.596635
$794$	−0.103494	−	0.984680i	−0.00367287	−	0.0349450i
$795$		0			0
$796$	−0.660296	+	6.28230i	−0.0234036	+	0.222670i
$797$	−0.912195	+	8.67896i	−0.0323116	+	0.307424i	0.966416	+	0.256985i	$0.0827290\pi$
$797$	−0.912195	+	8.67896i	−0.0323116	+	0.307424i	−0.998727	+	0.0504398i	$0.983938\pi$
$798$		0			0
$799$	−25.8171	+	44.7165i	−0.913342	+	1.58196i
$800$	2.61717	−	9.33001i	0.0925308	−	0.329866i
$801$		0			0
$802$	1.34859	−	4.15052i	0.0476202	−	0.146560i
$803$	4.40405	−	1.96081i	0.155415	−	0.0691954i
$804$		0			0
$805$	−26.4577	+	30.6141i	−0.932512	+	1.07900i
$806$	−1.50347	−	0.669389i	−0.0529576	−	0.0235782i
$807$		0			0
$808$	1.19638	+	11.3827i	0.0420883	+	0.400444i
$809$	1.28747	+	3.96244i	0.0452652	+	0.139312i	0.971135	−	0.238531i	$-0.0766659\pi$
$809$	1.28747	+	3.96244i	0.0452652	+	0.139312i	−0.925870	+	0.377843i	$0.876666\pi$
$810$		0			0
$811$	−7.66159	+	23.5800i	−0.269035	+	0.828004i	0.721701	+	0.692205i	$0.243360\pi$
$811$	−7.66159	+	23.5800i	−0.269035	+	0.828004i	−0.990736	+	0.135800i	$0.956640\pi$
$812$	−51.8395	−	11.0188i	−1.81921	−	0.386685i
$813$		0			0
$814$	−0.442836	+	0.0941277i	−0.0155214	+	0.00329917i
$815$	−0.191176	+	2.26024i	−0.00669660	+	0.0791727i
$816$		0			0
$817$	0.0240052	+	0.228394i	0.000839835	+	0.00799050i
$818$	−4.49076			−0.157016
$819$		0			0
$820$	6.81408	+	19.6056i	0.237958	+	0.684657i
$821$	26.1661	−	11.6499i	0.913204	−	0.406584i	0.104314	−	0.994544i	$-0.466735\pi$
$821$	26.1661	−	11.6499i	0.913204	−	0.406584i	0.808890	+	0.587960i	$0.200069\pi$
$822$		0			0
$823$	−42.8413	+	9.10620i	−1.49335	+	0.317422i	−0.880983	−	0.473149i	$-0.843117\pi$
$823$	−42.8413	+	9.10620i	−1.49335	+	0.317422i	−0.612371	+	0.790571i	$0.709784\pi$
$824$	3.90874	+	6.77013i	0.136167	+	0.235849i
$825$		0			0
$826$	−1.68185	+	2.91305i	−0.0585191	+	0.101358i
$827$	8.39488	−	25.8368i	0.291919	−	0.898433i	−0.692320	−	0.721590i	$-0.743411\pi$
$827$	8.39488	−	25.8368i	0.291919	−	0.898433i	0.984239	−	0.176843i	$-0.0565885\pi$
$828$		0			0
$829$	−24.7627	−	17.9912i	−0.860045	−	0.624859i	0.0678520	−	0.997695i	$-0.478385\pi$
$829$	−24.7627	−	17.9912i	−0.860045	−	0.624859i	−0.927897	+	0.372836i	$0.878385\pi$
$830$	0.960554	−	0.451292i	0.0333413	−	0.0156646i
$831$		0			0
$832$	6.79247	+	11.7649i	0.235487	+	0.407875i
$833$	36.7725	+	16.3722i	1.27409	+	0.567261i
$834$		0			0
$835$	−5.86321	−	6.25126i	−0.202905	−	0.216334i
$836$	−0.0161725	+	0.0497738i	−0.000559337	+	0.00172146i
$837$		0			0
$838$	0.601058	+	1.84987i	0.0207632	+	0.0639025i
$839$	−28.0673	−	31.1719i	−0.968990	−	1.07617i	−0.997065	−	0.0765661i	$-0.975604\pi$
$839$	−28.0673	−	31.1719i	−0.968990	−	1.07617i	0.0280749	−	0.999606i	$-0.491062\pi$
$840$		0			0
$841$	8.85722	−	9.83694i	0.305422	−	0.339205i
$842$	0.274781	+	0.122341i	0.00946959	+	0.00421613i
$843$		0			0
$844$	−1.49685	−	14.2416i	−0.0515237	−	0.490216i
$845$	−6.21131	+	20.5279i	−0.213676	+	0.706182i
$846$		0			0
$847$	−36.3536	−	26.4125i	−1.24913	−	0.907543i
$848$	4.86306	+	5.40097i	0.166998	+	0.185470i
$849$		0			0
$850$	−1.75542	−	2.77352i	−0.0602105	−	0.0951311i
$851$	−16.8226	−	29.1375i	−0.576670	−	0.998821i
$852$		0			0
$853$	21.1852	−	9.43224i	0.725366	−	0.322954i	−0.0106265	−	0.999944i	$-0.503383\pi$
$853$	21.1852	−	9.43224i	0.725366	−	0.322954i	0.735992	+	0.676990i	$0.236716\pi$
$854$	5.00452	+	3.63600i	0.171251	+	0.124421i
$855$		0			0
$856$	4.48812	−	3.26081i	0.153401	−	0.111452i
$857$	13.5979	−	23.5523i	0.464496	−	0.804532i	−0.534682	−	0.845053i	$-0.679569\pi$
$857$	13.5979	−	23.5523i	0.464496	−	0.804532i	0.999179	+	0.0405217i	$0.0129020\pi$
$858$		0			0
$859$	−1.90895	+	2.12010i	−0.0651326	+	0.0723370i	−0.774830	−	0.632169i	$-0.782165\pi$
$859$	−1.90895	+	2.12010i	−0.0651326	+	0.0723370i	0.709698	+	0.704506i	$0.248831\pi$
$860$	−7.08031	−	11.7070i	−0.241437	−	0.399205i
$861$		0			0
$862$	−5.66722	−	1.20460i	−0.193026	−	0.0410290i
$863$	−7.66135	−	23.5792i	−0.260795	−	0.802646i	−0.992632	−	0.121166i	$-0.961337\pi$
$863$	−7.66135	−	23.5792i	−0.260795	−	0.802646i	0.731837	−	0.681480i	$-0.238663\pi$
$864$		0			0
$865$	−16.2839	−	46.8522i	−0.553668	−	1.59302i
$866$	0.631918	+	0.134318i	0.0214735	+	0.00456432i
$867$		0			0
$868$	22.1007	+	38.2795i	0.750146	+	1.29929i
$869$	−1.96061	−	0.872918i	−0.0665090	−	0.0296117i
$870$		0			0
$871$	24.3053	−	10.8214i	0.823554	−	0.366670i
$872$	4.26832	+	3.10112i	0.144544	+	0.105017i
$873$		0			0
$874$	0.0533172			0.00180348
$875$	45.7033	+	6.83372i	1.54505	+	0.231022i
$876$		0			0
$877$	24.9580	−	5.30498i	0.842771	−	0.179136i	0.233756	−	0.972295i	$-0.424898\pi$
$877$	24.9580	−	5.30498i	0.842771	−	0.179136i	0.609015	+	0.793159i	$0.291565\pi$
$878$	−0.332059	+	3.15933i	−0.0112064	+	0.106622i
$879$		0			0
$880$	−0.383496	−	3.05053i	−0.0129276	−	0.102834i
$881$	12.7368	−	9.25380i	0.429112	−	0.311768i	−0.352181	−	0.935932i	$-0.614560\pi$
$881$	12.7368	−	9.25380i	0.429112	−	0.311768i	0.781294	+	0.624163i	$0.214560\pi$
$882$		0			0
$883$	3.13548	−	2.27806i	0.105517	−	0.0766627i	−0.533775	−	0.845626i	$-0.679227\pi$
$883$	3.13548	−	2.27806i	0.105517	−	0.0766627i	0.639293	+	0.768964i	$0.279227\pi$
$884$	14.2224	+	3.02306i	0.478350	+	0.101676i
$885$		0			0
$886$	0.720918	−	0.153236i	0.0242197	−	0.00514806i
$887$	3.41528	−	3.79305i	0.114674	−	0.127358i	−0.683075	−	0.730349i	$-0.739358\pi$
$887$	3.41528	−	3.79305i	0.114674	−	0.127358i	0.797748	+	0.602990i	$0.206024\pi$
$888$		0			0
$889$	8.97440	+	9.96708i	0.300992	+	0.334285i
$890$	−2.63427	+	0.0535844i	−0.0883009	+	0.00179615i
$891$		0			0
$892$	−0.949679	+	0.689982i	−0.0317976	+	0.0231023i
$893$	−0.478940	+	0.829548i	−0.0160271	+	0.0277598i
$894$		0			0
$895$	−16.9391	−	28.0081i	−0.566213	−	0.936208i
$896$	−2.19745	+	20.9073i	−0.0734115	+	0.698464i
$897$		0			0
$898$	1.23688	+	1.37369i	0.0412752	+	0.0458408i
$899$	−35.2266			−1.17487
$900$		0			0
$901$	7.55799			0.251793
$902$	−0.185458	−	0.205972i	−0.00617507	−	0.00685811i
$903$		0			0
$904$	−0.607353	+	5.77857i	−0.0202002	+	0.192193i
$905$	−37.5006	+	8.77174i	−1.24656	+	0.291582i
$906$		0			0
$907$	−6.09501	+	10.5569i	−0.202382	+	0.350535i	−0.949295	−	0.314386i	$-0.898201\pi$
$907$	−6.09501	+	10.5569i	−0.202382	+	0.350535i	0.746914	+	0.664921i	$0.231535\pi$
$908$	14.7404	−	10.7095i	0.489176	−	0.355407i
$909$		0			0
$910$	2.23625	−	1.69527i	0.0741310	−	0.0561978i
$911$	2.43329	+	2.70244i	0.0806184	+	0.0895358i	0.782104	−	0.623147i	$-0.214146\pi$
$911$	2.43329	+	2.70244i	0.0806184	+	0.0895358i	−0.701486	+	0.712683i	$0.747480\pi$
$912$		0			0
$913$	0.691743	−	0.768258i	0.0228933	−	0.0254256i
$914$	2.40786	−	0.511806i	0.0796449	−	0.0169291i
$915$		0			0
$916$	5.03889	+	1.07105i	0.166489	+	0.0353884i
$917$	28.7714	−	20.9036i	0.950115	−	0.690299i
$918$		0			0
$919$	19.4901	−	14.1604i	0.642919	−	0.467108i	−0.217933	−	0.975964i	$-0.569931\pi$
$919$	19.4901	−	14.1604i	0.642919	−	0.467108i	0.860852	+	0.508856i	$0.169931\pi$
$920$	−5.78919	+	2.71991i	−0.190864	+	0.0896726i
$921$		0			0
$922$	0.518331	−	4.93159i	0.0170703	−	0.162413i
$923$	−24.2532	+	5.15518i	−0.798305	+	0.169685i
$924$		0			0
$925$	−17.8434	+	34.0309i	−0.586688	+	1.11893i
$926$	−4.54663			−0.149411
$927$		0			0
$928$	−10.1897	−	7.40328i	−0.334495	−	0.243025i
$929$	14.7933	−	6.58640i	0.485352	−	0.216093i	−0.149447	−	0.988770i	$-0.547749\pi$
$929$	14.7933	−	6.58640i	0.485352	−	0.216093i	0.634799	+	0.772677i	$0.281083\pi$
$930$		0			0
$931$	0.682176	+	0.303724i	0.0223574	+	0.00995416i
$932$	6.52569	+	11.3028i	0.213756	+	0.370236i
$933$		0			0
$934$	4.75331	+	1.01035i	0.155533	+	0.0330596i
$935$	−2.62439	−	1.82635i	−0.0858266	−	0.0597281i
$936$		0			0
$937$	6.74493	+	20.7587i	0.220347	+	0.678159i	0.998731	+	0.0503697i	$0.0160399\pi$
$937$	6.74493	+	20.7587i	0.220347	+	0.678159i	−0.778384	+	0.627789i	$0.783960\pi$
$938$	9.58155	+	2.03662i	0.312849	+	0.0664980i
$939$		0			0
$940$	4.80956	−	56.8626i	0.156871	−	1.85465i
$941$	15.0308	−	16.6934i	0.489991	−	0.544190i	−0.446545	−	0.894761i	$-0.647346\pi$
$941$	15.0308	−	16.6934i	0.489991	−	0.544190i	0.936536	+	0.350571i	$0.114012\pi$
$942$		0			0
$943$	10.2988	−	17.8381i	0.335376	−	0.580888i
$944$	15.3668	−	11.1647i	0.500148	−	0.363379i
$945$		0			0
$946$	0.147803	+	0.107385i	0.00480549	+	0.00349139i
$947$	38.8398	−	17.2926i	1.26212	−	0.561934i	0.336966	−	0.941517i	$-0.390599\pi$
$947$	38.8398	−	17.2926i	1.26212	−	0.561934i	0.925158	+	0.379583i	$0.123933\pi$
$948$		0			0
$949$	−12.4234	−	21.5179i	−0.403279	−	0.698500i
$950$	−0.0325654	−	0.0514524i	−0.00105656	−	0.00166934i
$951$		0			0
$952$	7.21332	+	8.01120i	0.233785	+	0.259645i
$953$	22.8049	+	16.5687i	0.738722	+	0.536713i	0.892311	−	0.451422i	$-0.149083\pi$
$953$	22.8049	+	16.5687i	0.738722	+	0.536713i	−0.153588	+	0.988135i	$0.549083\pi$
$954$		0			0
$955$	1.06895	+	0.743900i	0.0345904	+	0.0240720i
$956$	−3.40685	−	32.4140i	−0.110185	−	1.04834i
$957$		0			0
$958$	2.01342	+	0.896433i	0.0650507	+	0.0289624i
$959$	−15.8503	+	17.6035i	−0.511833	+	0.568448i
$960$		0			0
$961$	−1.08407	−	1.20398i	−0.0349699	−	0.0388380i
$962$	0.721055	+	2.21918i	0.0232477	+	0.0715492i
$963$		0			0
$964$	−4.58426	+	14.1089i	−0.147649	+	0.454417i
$965$	−2.59181	−	20.6167i	−0.0834333	−	0.663674i
$966$		0			0
$967$	−3.03887	−	1.35299i	−0.0977235	−	0.0435093i	0.357293	−	0.933992i	$-0.383700\pi$
$967$	−3.03887	−	1.35299i	−0.0977235	−	0.0435093i	−0.455016	+	0.890483i	$0.650367\pi$
$968$	−3.55168	−	6.15169i	−0.114155	−	0.197723i
$969$		0			0
$970$	2.65951	+	2.83553i	0.0853917	+	0.0910433i
$971$	31.5894	+	22.9510i	1.01375	+	0.736534i	0.964993	−	0.262277i	$-0.0844734\pi$
$971$	31.5894	+	22.9510i	1.01375	+	0.736534i	0.0487589	+	0.998811i	$0.484473\pi$
$972$		0			0
$973$	−21.1826	+	65.1935i	−0.679085	+	2.09001i
$974$	−0.219673	+	0.380484i	−0.00703877	+	0.0121915i
$975$		0			0
$976$	−17.4656	−	30.2514i	−0.559061	−	0.968323i
$977$	24.3820	−	5.18256i	0.780050	−	0.165805i	0.199357	−	0.979927i	$-0.436115\pi$
$977$	24.3820	−	5.18256i	0.780050	−	0.165805i	0.580694	+	0.814122i	$0.302781\pi$
$978$		0			0
$979$	−2.34467	+	1.04391i	−0.0749359	+	0.0333636i
$980$	−44.4775	+	0.904730i	−1.42078	+	0.0289005i
$981$		0			0
$982$	2.94505			0.0939804
$983$	−4.20083	−	39.9683i	−0.133986	−	1.27479i	−0.830408	−	0.557157i	$-0.811892\pi$
$983$	−4.20083	−	39.9683i	−0.133986	−	1.27479i	0.696422	−	0.717633i	$-0.254774\pi$
$984$		0			0
$985$	4.97067	+	8.21878i	0.158379	+	0.261872i
$986$	−4.17319	+	0.887038i	−0.132901	+	0.0282491i
$987$		0			0
$988$	0.263843	+	0.0560816i	0.00839397	+	0.00178419i
$989$	−4.19558	+	12.9127i	−0.133412	+	0.410599i
$990$		0			0
$991$	−13.0513	−	40.1678i	−0.414588	−	1.27597i	−0.912619	−	0.408812i	$-0.865943\pi$
$991$	−13.0513	−	40.1678i	−0.414588	−	1.27597i	0.498030	−	0.867160i	$-0.334057\pi$
$992$	1.09804	+	10.4472i	0.0348629	+	0.331698i
$993$		0			0
$994$	−8.33979	−	3.71312i	−0.264522	−	0.117773i
$995$	−6.59824	−	2.77835i	−0.209178	−	0.0880795i
$996$		0			0
$997$	43.7314	−	19.4705i	1.38499	−	0.616637i	0.427213	−	0.904151i	$-0.359496\pi$
$997$	43.7314	−	19.4705i	1.38499	−	0.616637i	0.957776	+	0.287514i	$0.0928289\pi$
$998$	1.04419	−	3.21368i	0.0330531	−	0.101727i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.46.14		224
3.2	odd	2		225.2.q.a.196.15	yes	224
9.4	even	3	inner	675.2.r.a.496.15		224
9.5	odd	6		225.2.q.a.121.14	yes	224
25.6	even	5	inner	675.2.r.a.181.15		224
75.56	odd	10		225.2.q.a.106.14	yes	224
225.31	even	15	inner	675.2.r.a.631.14		224
225.131	odd	30		225.2.q.a.31.15	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.15	✓	224	225.131	odd	30
225.2.q.a.106.14	yes	224	75.56	odd	10
225.2.q.a.121.14	yes	224	9.5	odd	6
225.2.q.a.196.15	yes	224	3.2	odd	2
675.2.r.a.46.14		224	1.1	even	1	trivial
675.2.r.a.181.15		224	25.6	even	5	inner
675.2.r.a.496.15		224	9.4	even	3	inner
675.2.r.a.631.14		224	225.31	even	15	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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.110043 + 0.122216i) q^{2} +(0.206230 - 1.96215i) q^{4} +(2.06082 + 0.867759i) q^{5} +(2.06663 - 3.57951i) q^{7} +(0.528597 - 0.384048i) q^{8} +O(q^{10})\)	\(q+(0.110043 + 0.122216i) q^{2} +(0.206230 - 1.96215i) q^{4} +(2.06082 + 0.867759i) q^{5} +(2.06663 - 3.57951i) q^{7} +(0.528597 - 0.384048i) q^{8} +(0.120726 + 0.347356i) q^{10} +(0.239690 + 0.266203i) q^{11} +(1.23537 - 1.37202i) q^{13} +(0.664892 - 0.141327i) q^{14} +(-3.75457 - 0.798059i) q^{16} +(-3.22940 + 2.34629i) q^{17} +(-0.0599095 + 0.0435268i) q^{19} +(2.12767 - 3.86468i) q^{20} +(-0.00615783 + 0.0585878i) q^{22} +(-4.28234 + 0.910239i) q^{23} +(3.49399 + 3.57660i) q^{25} +0.303627 q^{26} +(-6.59733 - 4.79324i) q^{28} +(5.93713 - 2.64338i) q^{29} +(-4.95171 - 2.20464i) q^{31} +(-0.969013 - 1.67838i) q^{32} +(-0.642128 - 0.136489i) q^{34} +(7.36512 - 5.58341i) q^{35} +(2.37480 + 7.30889i) q^{37} +(-0.0119123 - 0.00253204i) q^{38} +(1.42261 - 0.332761i) q^{40} +(-3.14813 + 3.49635i) q^{41} +(1.55061 - 2.68574i) q^{43} +(0.571760 - 0.415408i) q^{44} +(-0.582489 - 0.423203i) q^{46} +(11.8169 - 5.26122i) q^{47} +(-5.04195 - 8.73292i) q^{49} +(-0.0526256 + 0.820601i) q^{50} +(-2.43733 - 2.70693i) q^{52} +(-1.53179 - 1.11291i) q^{53} +(0.262959 + 0.756591i) q^{55} +(-0.282290 - 2.68581i) q^{56} +(0.976404 + 0.434723i) q^{58} +(-3.31117 + 3.67743i) q^{59} +(6.08932 + 6.76288i) q^{61} +(-0.275461 - 0.847783i) q^{62} +(-2.27380 + 6.99805i) q^{64} +(3.73647 - 1.75549i) q^{65} +(13.1648 + 5.86135i) q^{67} +(3.93777 + 6.82042i) q^{68} +(1.49286 + 0.285716i) q^{70} +(-10.8652 - 7.89400i) q^{71} +(4.15877 - 12.7994i) q^{73} +(-0.631930 + 1.09453i) q^{74} +(0.0730507 + 0.126528i) q^{76} +(1.44823 - 0.307831i) q^{77} +(-5.47332 + 2.43688i) q^{79} +(-7.04499 - 4.90273i) q^{80} -0.773739 q^{82} +(-0.301668 - 2.87018i) q^{83} +(-8.69124 + 2.03296i) q^{85} +(0.498874 - 0.106039i) q^{86} +(0.228934 + 0.0486615i) q^{88} +(-2.21408 + 6.81425i) q^{89} +(-2.35810 - 7.25750i) q^{91} +(0.902876 + 8.59029i) q^{92} +(1.94338 + 0.865246i) q^{94} +(-0.161234 + 0.0377140i) q^{95} +(9.65762 - 4.29985i) q^{97} +(0.512465 - 1.57721i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

L-functions

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