LMFDB - Embedded newform 666.2.bj.c.469.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(289,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("666.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.bj (of order $18$, degree $6$, 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:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			469.1
Root			$-0.642788 - 0.766044i$ of defining polynomial
Character	$\chi$	$=$	666.469
Dual form			666.2.bj.c.595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.642788 - 0.766044i) q^{2} +(-0.173648 + 0.984808i) q^{4} +(1.45842 + 4.00698i) q^{5} +(-3.39364 + 1.23518i) q^{7} +(0.866025 - 0.500000i) q^{8} +O(q^{10})$	\(q+(-0.642788 - 0.766044i) q^{2} +(-0.173648 + 0.984808i) q^{4} +(1.45842 + 4.00698i) q^{5} +(-3.39364 + 1.23518i) q^{7} +(0.866025 - 0.500000i) q^{8} +(2.13207 - 3.69285i) q^{10} +(-1.05840 - 1.83321i) q^{11} +(2.84019 + 0.500802i) q^{13} +(3.12760 + 1.80572i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(-0.0263137 + 0.00463982i) q^{17} +(-2.07522 + 2.47315i) q^{19} +(-4.19936 + 0.740460i) q^{20} +(-0.723990 + 1.98915i) q^{22} +(-2.57421 - 1.48622i) q^{23} +(-10.0987 + 8.47380i) q^{25} +(-1.44200 - 2.49762i) q^{26} +(-0.627119 - 3.55657i) q^{28} +(-4.96493 + 2.86650i) q^{29} -6.76932i q^{31} +(0.342020 + 0.939693i) q^{32} +(0.0204685 + 0.0171751i) q^{34} +(-9.89872 - 11.7968i) q^{35} +(-4.49375 + 4.09954i) q^{37} +3.22847 q^{38} +(3.26652 + 2.74094i) q^{40} +(-0.259000 + 1.46886i) q^{41} +5.53737i q^{43} +(1.98915 - 0.723990i) q^{44} +(0.516159 + 2.92728i) q^{46} +(1.30654 - 2.26300i) q^{47} +(4.62880 - 3.88403i) q^{49} +(12.9826 + 2.28918i) q^{50} +(-0.986387 + 2.71008i) q^{52} +(1.79389 + 0.652924i) q^{53} +(5.80203 - 6.91459i) q^{55} +(-2.32139 + 2.76652i) q^{56} +(5.38726 + 1.96080i) q^{58} +(-1.92380 + 5.28560i) q^{59} +(-5.65366 - 0.996892i) q^{61} +(-5.18560 + 4.35124i) q^{62} +(0.500000 - 0.866025i) q^{64} +(2.13549 + 12.1110i) q^{65} +(-6.50406 + 2.36728i) q^{67} -0.0267197i q^{68} +(-2.67412 + 15.1657i) q^{70} +(7.10830 + 5.96457i) q^{71} +16.2707 q^{73} +(6.02896 + 0.807274i) q^{74} +(-2.07522 - 2.47315i) q^{76} +(5.85619 + 4.91392i) q^{77} +(-0.484006 - 1.32980i) q^{79} -4.26414i q^{80} +(1.29170 - 0.745761i) q^{82} +(0.294580 + 1.67065i) q^{83} +(-0.0569682 - 0.0986718i) q^{85} +(4.24187 - 3.55935i) q^{86} +(-1.83321 - 1.05840i) q^{88} +(-2.82882 + 7.77213i) q^{89} +(-10.2572 + 1.80861i) q^{91} +(1.91065 - 2.27702i) q^{92} +(-2.57339 + 0.453757i) q^{94} +(-12.9364 - 4.70847i) q^{95} +(5.65105 + 3.26264i) q^{97} +(-5.95067 - 1.04926i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{7}+O(q^{10}) $ 12 * q - 12 * q^7	$ 12 q - 12 q^{7} + 6 q^{10} + 6 q^{11} + 6 q^{13} + 18 q^{14} - 18 q^{19} - 18 q^{25} - 12 q^{26} - 6 q^{28} - 18 q^{29} + 12 q^{34} - 18 q^{35} + 30 q^{37} + 24 q^{38} + 12 q^{40} - 24 q^{41} - 6 q^{44} + 30 q^{46} - 6 q^{47} + 12 q^{49} + 36 q^{50} - 12 q^{52} + 12 q^{53} - 18 q^{55} + 6 q^{58} - 36 q^{61} + 6 q^{64} - 36 q^{65} - 30 q^{67} - 12 q^{70} - 12 q^{71} + 48 q^{74} - 18 q^{76} - 12 q^{77} + 6 q^{79} + 48 q^{83} + 18 q^{85} + 36 q^{86} - 36 q^{88} + 18 q^{89} - 6 q^{91} - 18 q^{92} + 36 q^{97} - 36 q^{98}+O(q^{100}) $ 12 * q - 12 * q^7 + 6 * q^10 + 6 * q^11 + 6 * q^13 + 18 * q^14 - 18 * q^19 - 18 * q^25 - 12 * q^26 - 6 * q^28 - 18 * q^29 + 12 * q^34 - 18 * q^35 + 30 * q^37 + 24 * q^38 + 12 * q^40 - 24 * q^41 - 6 * q^44 + 30 * q^46 - 6 * q^47 + 12 * q^49 + 36 * q^50 - 12 * q^52 + 12 * q^53 - 18 * q^55 + 6 * q^58 - 36 * q^61 + 6 * q^64 - 36 * q^65 - 30 * q^67 - 12 * q^70 - 12 * q^71 + 48 * q^74 - 18 * q^76 - 12 * q^77 + 6 * q^79 + 48 * q^83 + 18 * q^85 + 36 * q^86 - 36 * q^88 + 18 * q^89 - 6 * q^91 - 18 * q^92 + 36 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$1$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−0.642788	−	0.766044i	−0.454519	−	0.541675i
$2$	−0.642788	−	0.766044i	−0.454519	−	0.541675i
$3$		0			0
$3$		0			0
$4$	−0.173648	+	0.984808i	−0.0868241	+	0.492404i
$5$	1.45842	+	4.00698i	0.652226	+	1.79198i	0.609358	+	0.792895i	$0.291427\pi$
$5$	1.45842	+	4.00698i	0.652226	+	1.79198i	0.0428683	+	0.999081i	$0.486350\pi$
$6$		0			0
$7$	−3.39364	+	1.23518i	−1.28268	+	0.466856i	−0.891316	−	0.453382i	$-0.850217\pi$
$7$	−3.39364	+	1.23518i	−1.28268	+	0.466856i	−0.391359	+	0.920238i	$0.627995\pi$
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$		0			0
$10$	2.13207	−	3.69285i	0.674220	−	1.16778i
$11$	−1.05840	−	1.83321i	−0.319120	−	0.552733i	0.661184	−	0.750223i	$-0.270054\pi$
$11$	−1.05840	−	1.83321i	−0.319120	−	0.552733i	−0.980305	+	0.197491i	$0.936721\pi$
$12$		0			0
$13$	2.84019	+	0.500802i	0.787726	+	0.138897i	0.553019	−	0.833169i	$-0.313476\pi$
$13$	2.84019	+	0.500802i	0.787726	+	0.138897i	0.234707	+	0.972066i	$0.424587\pi$
$14$	3.12760	+	1.80572i	0.835885	+	0.482598i
$15$		0			0
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−0.0263137	+	0.00463982i	−0.00638202	+	0.00112532i	−0.176838	−	0.984240i	$-0.556587\pi$
$17$	−0.0263137	+	0.00463982i	−0.00638202	+	0.00112532i	0.170456	+	0.985365i	$0.445476\pi$
$18$		0			0
$19$	−2.07522	+	2.47315i	−0.476088	+	0.567380i	−0.949623	−	0.313395i	$-0.898534\pi$
$19$	−2.07522	+	2.47315i	−0.476088	+	0.567380i	0.473534	+	0.880775i	$0.342978\pi$
$20$	−4.19936	+	0.740460i	−0.939005	+	0.165572i
$21$		0			0
$22$	−0.723990	+	1.98915i	−0.154355	+	0.424087i
$23$	−2.57421	−	1.48622i	−0.536760	−	0.309899i	0.207005	−	0.978340i	$-0.433628\pi$
$23$	−2.57421	−	1.48622i	−0.536760	−	0.309899i	−0.743765	+	0.668441i	$0.766962\pi$
$24$		0			0
$25$	−10.0987	+	8.47380i	−2.01974	+	1.69476i
$26$	−1.44200	−	2.49762i	−0.282800	−	0.489823i
$27$		0			0
$28$	−0.627119	−	3.55657i	−0.118514	−	0.672129i
$29$	−4.96493	+	2.86650i	−0.921964	+	0.532296i	−0.884261	−	0.466993i	$-0.845337\pi$
$29$	−4.96493	+	2.86650i	−0.921964	+	0.532296i	−0.0377027	+	0.999289i	$0.512004\pi$
$30$		0			0
$31$		−	6.76932i		−	1.21581i	−0.794011	−	0.607903i	$-0.792011\pi$
$31$		−	6.76932i		−	1.21581i	0.794011	−	0.607903i	$-0.207989\pi$
$32$	0.342020	+	0.939693i	0.0604612	+	0.166116i
$33$		0			0
$34$	0.0204685	+	0.0171751i	0.00351031	+	0.00294550i
$35$	−9.89872	−	11.7968i	−1.67319	−	1.99403i
$36$		0			0
$37$	−4.49375	+	4.09954i	−0.738767	+	0.673961i
$37$	−4.49375	+	4.09954i	−0.738767	+	0.673961i
$38$	3.22847			0.523727
$39$		0			0
$40$	3.26652	+	2.74094i	0.516482	+	0.433380i
$41$	−0.259000	+	1.46886i	−0.0404490	+	0.229398i	−0.998330	−	0.0577674i	$-0.981602\pi$
$41$	−0.259000	+	1.46886i	−0.0404490	+	0.229398i	0.957881	+	0.287165i	$0.0927129\pi$
$42$		0			0
$43$			5.53737i			0.844441i	0.906493	+	0.422221i	$0.138749\pi$
$43$			5.53737i			0.844441i	−0.906493	+	0.422221i	$0.861251\pi$
$44$	1.98915	−	0.723990i	0.299875	−	0.109146i
$45$		0			0
$46$	0.516159	+	2.92728i	0.0761035	+	0.431605i
$47$	1.30654	−	2.26300i	0.190579	−	0.330092i	−0.754863	−	0.655882i	$-0.772297\pi$
$47$	1.30654	−	2.26300i	0.190579	−	0.330092i	0.945442	+	0.325790i	$0.105630\pi$
$48$		0			0
$49$	4.62880	−	3.88403i	0.661257	−	0.554861i
$50$	12.9826	+	2.28918i	1.83602	+	0.323740i
$51$		0			0
$52$	−0.986387	+	2.71008i	−0.136787	+	0.375820i
$53$	1.79389	+	0.652924i	0.246410	+	0.0896860i	0.462273	−	0.886738i	$-0.347034\pi$
$53$	1.79389	+	0.652924i	0.246410	+	0.0896860i	−0.215862	+	0.976424i	$0.569256\pi$
$54$		0			0
$55$	5.80203	−	6.91459i	0.782345	−	0.932363i
$56$	−2.32139	+	2.76652i	−0.310208	+	0.369692i
$57$		0			0
$58$	5.38726	+	1.96080i	0.707382	+	0.257466i
$59$	−1.92380	+	5.28560i	−0.250457	+	0.688126i	0.749210	+	0.662333i	$0.230433\pi$
$59$	−1.92380	+	5.28560i	−0.250457	+	0.688126i	−0.999667	+	0.0257935i	$0.991789\pi$
$60$		0			0
$61$	−5.65366	−	0.996892i	−0.723876	−	0.127639i	−0.200443	−	0.979705i	$-0.564238\pi$
$61$	−5.65366	−	0.996892i	−0.723876	−	0.127639i	−0.523434	+	0.852066i	$0.675349\pi$
$62$	−5.18560	+	4.35124i	−0.658572	+	0.552608i
$63$		0			0
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	2.13549	+	12.1110i	0.264875	+	1.50218i
$66$		0			0
$67$	−6.50406	+	2.36728i	−0.794597	+	0.289210i	−0.707246	−	0.706968i	$-0.750063\pi$
$67$	−6.50406	+	2.36728i	−0.794597	+	0.289210i	−0.0873516	+	0.996178i	$0.527840\pi$
$68$		−	0.0267197i		−	0.00324024i
$69$		0			0
$70$	−2.67412	+	15.1657i	−0.319619	+	1.81265i
$71$	7.10830	+	5.96457i	0.843600	+	0.707865i	0.958371	−	0.285527i	$-0.0921688\pi$
$71$	7.10830	+	5.96457i	0.843600	+	0.707865i	−0.114770	+	0.993392i	$0.536613\pi$
$72$		0			0
$73$	16.2707			1.90434			0.952169	−	0.305571i	$-0.0988473\pi$
$73$	16.2707			1.90434			0.952169	+	0.305571i	$0.0988473\pi$
$74$	6.02896	+	0.807274i	0.700852	+	0.0938437i
$75$		0			0
$76$	−2.07522	−	2.47315i	−0.238044	−	0.283690i
$77$	5.85619	+	4.91392i	0.667374	+	0.559993i
$78$		0			0
$79$	−0.484006	−	1.32980i	−0.0544549	−	0.149614i	0.909483	−	0.415742i	$-0.136478\pi$
$79$	−0.484006	−	1.32980i	−0.0544549	−	0.149614i	−0.963938	+	0.266128i	$0.914256\pi$
$80$		−	4.26414i		−	0.476745i
$81$		0			0
$82$	1.29170	−	0.745761i	0.142644	−	0.0823556i
$83$	0.294580	+	1.67065i	0.0323343	+	0.183377i	0.996697	−	0.0812054i	$-0.0258770\pi$
$83$	0.294580	+	1.67065i	0.0323343	+	0.183377i	−0.964363	+	0.264583i	$0.914766\pi$
$84$		0			0
$85$	−0.0569682	−	0.0986718i	−0.00617907	−	0.0107025i
$86$	4.24187	−	3.55935i	0.457413	−	0.383815i
$87$		0			0
$88$	−1.83321	−	1.05840i	−0.195421	−	0.112826i
$89$	−2.82882	+	7.77213i	−0.299855	+	0.823844i	0.694669	+	0.719330i	$0.255551\pi$
$89$	−2.82882	+	7.77213i	−0.299855	+	0.823844i	−0.994523	+	0.104514i	$0.966671\pi$
$90$		0			0
$91$	−10.2572	+	1.80861i	−1.07524	+	0.189594i
$92$	1.91065	−	2.27702i	0.199199	−	0.237396i
$93$		0			0
$94$	−2.57339	+	0.453757i	−0.265425	+	0.0468015i
$95$	−12.9364	−	4.70847i	−1.32725	−	0.483079i
$96$		0			0
$97$	5.65105	+	3.26264i	0.573777	+	0.331270i	0.758657	−	0.651491i	$-0.225856\pi$
$97$	5.65105	+	3.26264i	0.573777	+	0.331270i	−0.184879	+	0.982761i	$0.559189\pi$
$98$	−5.95067	−	1.04926i	−0.601109	−	0.105992i
$99$		0			0
$100$	−6.59144	−	11.4167i	−0.659144	−	1.14167i
$101$	8.29974	−	14.3756i	0.825855	−	1.43042i	−0.0754083	−	0.997153i	$-0.524026\pi$
$101$	8.29974	−	14.3756i	0.825855	−	1.43042i	0.901264	−	0.433271i	$-0.142641\pi$
$102$		0			0
$103$	1.64095	−	0.947403i	0.161688	−	0.0933504i	−0.416973	−	0.908919i	$-0.636909\pi$
$103$	1.64095	−	0.947403i	0.161688	−	0.0933504i	0.578660	+	0.815569i	$0.303576\pi$
$104$	2.71008	−	0.986387i	0.265745	−	0.0967232i
$105$		0			0
$106$	−0.652924	−	1.79389i	−0.0634176	−	0.174238i
$107$	−0.0663781	+	0.376449i	−0.00641702	+	0.0363927i	−0.987848	−	0.155422i	$-0.950326\pi$
$107$	−0.0663781	+	0.376449i	−0.00641702	+	0.0363927i	0.981431	+	0.191815i	$0.0614373\pi$
$108$		0			0
$109$	−0.620666	−	0.739681i	−0.0594490	−	0.0708485i	0.735500	−	0.677524i	$-0.236947\pi$
$109$	−0.620666	−	0.739681i	−0.0594490	−	0.0708485i	−0.794949	+	0.606676i	$0.792503\pi$
$110$	−9.02635			−0.860629
$111$		0			0
$112$	3.61144			0.341249
$113$	−1.21535	−	1.44839i	−0.114330	−	0.136254i	0.705844	−	0.708367i	$-0.250568\pi$
$113$	−1.21535	−	1.44839i	−0.114330	−	0.136254i	−0.820174	+	0.572114i	$0.806124\pi$
$114$		0			0
$115$	2.20098	−	12.4824i	0.205242	−	1.16399i
$116$	−1.96080	−	5.38726i	−0.182056	−	0.500195i
$117$		0			0
$118$	5.28560	−	1.92380i	0.486579	−	0.177100i
$119$	0.0835683	−	0.0482482i	0.00766070	−	0.00442291i
$120$		0			0
$121$	3.25957	−	5.64574i	0.296324	−	0.513249i
$122$	2.87044	+	4.97174i	0.259877	+	0.450120i
$123$		0			0
$124$	6.66648	+	1.17548i	0.598668	+	0.105561i
$125$	−30.2182	−	17.4465i	−2.70280	−	1.56046i
$126$		0			0
$127$	15.1426	+	5.51145i	1.34369	+	0.489062i	0.910972	−	0.412469i	$-0.135334\pi$
$127$	15.1426	+	5.51145i	1.34369	+	0.489062i	0.432715	+	0.901531i	$0.357556\pi$
$128$	−0.984808	+	0.173648i	−0.0870455	+	0.0153485i
$129$		0			0
$130$	7.90487	−	9.42065i	0.693303	−	0.826246i
$131$	0.810446	−	0.142903i	0.0708090	−	0.0124855i	−0.138131	−	0.990414i	$-0.544110\pi$
$131$	0.810446	−	0.142903i	0.0708090	−	0.0124855i	0.208940	+	0.977928i	$0.432999\pi$
$132$		0			0
$133$	3.98776	−	10.9563i	0.345782	−	0.950029i
$134$	5.99417	+	3.46074i	0.517818	+	0.298962i
$135$		0			0
$136$	−0.0204685	+	0.0171751i	−0.00175516	+	0.00147275i
$137$	8.67847	+	15.0316i	0.741452	+	1.28423i	0.951834	+	0.306613i	$0.0991957\pi$
$137$	8.67847	+	15.0316i	0.741452	+	1.28423i	−0.210382	+	0.977619i	$0.567471\pi$
$138$		0			0
$139$	1.60198	+	9.08528i	0.135878	+	0.770604i	0.974244	+	0.225496i	$0.0724002\pi$
$139$	1.60198	+	9.08528i	0.135878	+	0.770604i	−0.838366	+	0.545108i	$0.816489\pi$
$140$	13.3365	−	7.69983i	1.12714	−	0.650755i
$141$		0			0
$142$		−	9.27923i		−	0.778696i
$143$	−2.08799	−	5.73670i	−0.174606	−	0.479727i
$144$		0			0
$145$	−18.7270	−	15.7138i	−1.55519	−	1.30496i
$146$	−10.4586	−	12.4641i	−0.865559	−	1.03153i
$147$		0			0
$148$	−3.25693	−	5.13735i	−0.267718	−	0.422288i
$149$	7.73776			0.633902			0.316951	−	0.948442i	$-0.397341\pi$
$149$	7.73776			0.633902			0.316951	+	0.948442i	$0.397341\pi$
$150$		0			0
$151$	−9.68000	−	8.12248i	−0.787747	−	0.660998i	0.157440	−	0.987529i	$-0.449676\pi$
$151$	−9.68000	−	8.12248i	−0.787747	−	0.660998i	−0.945187	+	0.326530i	$0.894120\pi$
$152$	−0.560618	+	3.17942i	−0.0454721	+	0.257885i
$153$		0			0
$154$		−	7.64471i		−	0.616028i
$155$	27.1245	−	9.87253i	2.17870	−	0.792980i
$156$		0			0
$157$	2.26554	+	12.8485i	0.180810	+	1.02542i	0.931222	+	0.364453i	$0.118744\pi$
$157$	2.26554	+	12.8485i	0.180810	+	1.02542i	−0.750412	+	0.660971i	$0.770145\pi$
$158$	−0.707569	+	1.22555i	−0.0562912	+	0.0974992i
$159$		0			0
$160$	−3.26652	+	2.74094i	−0.258241	+	0.216690i
$161$	10.5717	+	1.86408i	0.833167	+	0.146910i
$162$		0			0
$163$	−8.63820	+	23.7332i	−0.676596	+	1.85893i	−0.200038	+	0.979788i	$0.564107\pi$
$163$	−8.63820	+	23.7332i	−0.676596	+	1.85893i	−0.476558	+	0.879143i	$0.658116\pi$
$164$	−1.40157	−	0.510131i	−0.109444	−	0.0398345i
$165$		0			0
$166$	1.09044	−	1.29953i	0.0846343	−	0.100863i
$167$	6.60851	−	7.87572i	0.511382	−	0.609441i	−0.447139	−	0.894465i	$-0.647557\pi$
$167$	6.60851	−	7.87572i	0.511382	−	0.609441i	0.958521	+	0.285023i	$0.0920014\pi$
$168$		0			0
$169$	−4.40014	−	1.60152i	−0.338472	−	0.123194i
$170$	−0.0389686	+	0.107065i	−0.00298875	+	0.00821153i
$171$		0			0
$172$	−5.45325	−	0.961555i	−0.415806	−	0.0733179i
$173$	−18.1222	+	15.2064i	−1.37781	+	1.15612i	−0.407792	+	0.913075i	$0.633701\pi$
$173$	−18.1222	+	15.2064i	−1.37781	+	1.15612i	−0.970016	+	0.243043i	$0.921854\pi$
$174$		0			0
$175$	23.8046	−	41.2307i	1.79946	−	3.11675i
$176$	0.367579	+	2.08465i	0.0277073	+	0.157136i
$177$		0			0
$178$	7.77213	−	2.82882i	0.582546	−	0.212029i
$179$			5.05746i			0.378013i	0.981976	+	0.189006i	$0.0605267\pi$
$179$			5.05746i			0.378013i	−0.981976	+	0.189006i	$0.939473\pi$
$180$		0			0
$181$	−0.181540	+	1.02956i	−0.0134938	+	0.0765269i	−0.990811	−	0.135254i	$-0.956815\pi$
$181$	−0.181540	+	1.02956i	−0.0134938	+	0.0765269i	0.977317	+	0.211781i	$0.0679262\pi$
$182$	7.97865	+	6.69488i	0.591417	+	0.496258i
$183$		0			0
$184$	−2.97244			−0.219131
$185$	−22.9806	−	12.0275i	−1.68956	−	0.884279i
$186$		0			0
$187$	0.0363563	+	0.0433277i	0.00265864	+	0.00316844i
$188$	2.00174	+	1.67966i	0.145992	+	0.122502i
$189$		0			0
$190$	4.70847	+	12.9364i	0.341588	+	0.938507i
$191$		−	13.4633i		−	0.974173i	−0.873354	−	0.487087i	$-0.838060\pi$
$191$		−	13.4633i		−	0.974173i	0.873354	−	0.487087i	$-0.161940\pi$
$192$		0			0
$193$	3.91641	−	2.26114i	0.281909	−	0.162760i	−0.352378	−	0.935858i	$-0.614627\pi$
$193$	3.91641	−	2.26114i	0.281909	−	0.162760i	0.634288	+	0.773097i	$0.281294\pi$
$194$	−1.13310	−	6.42614i	−0.0813519	−	0.461370i
$195$		0			0
$196$	3.02124	+	5.23293i	0.215803	+	0.373781i
$197$	9.47751	−	7.95257i	0.675245	−	0.566597i	−0.239368	−	0.970929i	$-0.576940\pi$
$197$	9.47751	−	7.95257i	0.675245	−	0.566597i	0.914613	+	0.404331i	$0.132496\pi$
$198$		0			0
$199$	−3.90547	−	2.25483i	−0.276852	−	0.159840i	0.355146	−	0.934811i	$-0.384431\pi$
$199$	−3.90547	−	2.25483i	−0.276852	−	0.159840i	−0.631997	+	0.774971i	$0.717765\pi$
$200$	−4.50881	+	12.3879i	−0.318821	+	0.875954i
$201$		0			0
$202$	−16.3473	+	2.88247i	−1.15019	+	0.202810i
$203$	13.3085	−	15.8605i	0.934075	−	1.11319i
$204$		0			0
$205$	−6.26344	+	1.10441i	−0.437457	+	0.0771356i
$206$	−1.78053	−	0.648062i	−0.124056	−	0.0451526i
$207$		0			0
$208$	−2.49762	−	1.44200i	−0.173179	−	0.0999848i
$209$	6.73022	+	1.18672i	0.465539	+	0.0820871i
$210$		0			0
$211$	8.12299	+	14.0694i	0.559209	+	0.968579i	0.997563	+	0.0697764i	$0.0222286\pi$
$211$	8.12299	+	14.0694i	0.559209	+	0.968579i	−0.438353	+	0.898803i	$0.644438\pi$
$212$	−0.954511	+	1.65326i	−0.0655561	+	0.113546i
$213$		0			0
$214$	0.331044	−	0.191128i	0.0226297	−	0.0130653i
$215$	−22.1881	+	8.07582i	−1.51322	+	0.550767i
$216$		0			0
$217$	8.36136	+	22.9726i	0.567606	+	1.55948i
$218$	−0.167672	+	0.950915i	−0.0113562	+	0.0644041i
$219$		0			0
$220$	5.80203	+	6.91459i	0.391173	+	0.466181i
$221$	−0.0770596			−0.00518359
$222$		0			0
$223$	−0.847777			−0.0567713			−0.0283857	−	0.999597i	$-0.509037\pi$
$223$	−0.847777			−0.0567713			−0.0283857	+	0.999597i	$0.509037\pi$
$224$	−2.32139	−	2.76652i	−0.155104	−	0.184846i
$225$		0			0
$226$	−0.328324	+	1.86202i	−0.0218398	+	0.123860i
$227$	4.14827	+	11.3973i	0.275331	+	0.756464i	0.997876	+	0.0651411i	$0.0207497\pi$
$227$	4.14827	+	11.3973i	0.275331	+	0.756464i	−0.722546	+	0.691323i	$0.757028\pi$
$228$		0			0
$229$	−12.4674	+	4.53775i	−0.823867	+	0.299863i	−0.719339	−	0.694659i	$-0.755555\pi$
$229$	−12.4674	+	4.53775i	−0.823867	+	0.299863i	−0.104528	+	0.994522i	$0.533333\pi$
$230$	−10.9768	+	6.33746i	−0.723788	+	0.417879i
$231$		0			0
$232$	−2.86650	+	4.96493i	−0.188195	+	0.325963i
$233$	2.15328	+	3.72960i	0.141066	+	0.244334i	0.927898	−	0.372833i	$-0.121614\pi$
$233$	2.15328	+	3.72960i	0.141066	+	0.244334i	−0.786832	+	0.617167i	$0.788280\pi$
$234$		0			0
$235$	10.9733	+	1.93489i	0.715818	+	0.126218i
$236$	−4.87123	−	2.81241i	−0.317090	−	0.183072i
$237$		0			0
$238$	−0.0906770	−	0.0330037i	−0.00587771	−	0.00213931i
$239$	14.0259	−	2.47315i	0.907262	−	0.159975i	0.299502	−	0.954096i	$-0.403179\pi$
$239$	14.0259	−	2.47315i	0.907262	−	0.159975i	0.607760	+	0.794121i	$0.292068\pi$
$240$		0			0
$241$	9.16681	−	10.9246i	0.590486	−	0.703714i	−0.385213	−	0.922828i	$-0.625872\pi$
$241$	9.16681	−	10.9246i	0.590486	−	0.703714i	0.975699	+	0.219114i	$0.0703166\pi$
$242$	−6.42010	+	1.13204i	−0.412699	+	0.0727700i
$243$		0			0
$244$	1.96349	−	5.39466i	0.125700	−	0.345357i
$245$	22.3140	+	12.8830i	1.42559	+	0.823063i
$246$		0			0
$247$	−7.13258	+	5.98494i	−0.453835	+	0.380813i
$248$	−3.38466	−	5.86241i	−0.214926	−	0.372263i
$249$		0			0
$250$	6.05910	+	34.3629i	0.383211	+	2.17330i
$251$	−21.3974	+	12.3538i	−1.35059	+	0.779764i	−0.988332	−	0.152314i	$-0.951328\pi$
$251$	−21.3974	+	12.3538i	−1.35059	+	0.779764i	−0.362258	+	0.932078i	$0.617994\pi$
$252$		0			0
$253$			6.29208i			0.395580i
$254$	−5.51145	−	15.1426i	−0.345819	−	0.950130i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	10.5496	+	12.5726i	0.658068	+	0.784255i	0.987107	−	0.160062i	$-0.0511693\pi$
$257$	10.5496	+	12.5726i	0.658068	+	0.784255i	−0.329039	+	0.944316i	$0.606725\pi$
$258$		0			0
$259$	10.1865	−	19.4630i	0.632956	−	1.20937i
$260$	−12.2978			−0.762676
$261$		0			0
$262$	−0.630415	−	0.528981i	−0.0389472	−	0.0326806i
$263$	4.88671	−	27.7139i	0.301327	−	1.70891i	−0.338980	−	0.940793i	$-0.610082\pi$
$263$	4.88671	−	27.7139i	0.301327	−	1.70891i	0.640308	−	0.768118i	$-0.278807\pi$
$264$		0			0
$265$			8.14034i			0.500057i
$266$	−10.9563	+	3.98776i	−0.671772	+	0.244505i
$267$		0			0
$268$	−1.20190	−	6.81632i	−0.0734178	−	0.416373i
$269$	11.5852	−	20.0661i	0.706359	−	1.22345i	−0.259840	−	0.965652i	$-0.583670\pi$
$269$	11.5852	−	20.0661i	0.706359	−	1.22345i	0.966199	−	0.257798i	$-0.0829969\pi$
$270$		0			0
$271$	8.12679	−	6.81919i	0.493667	−	0.414236i	−0.361671	−	0.932306i	$-0.617794\pi$
$271$	8.12679	−	6.81919i	0.493667	−	0.414236i	0.855338	+	0.518070i	$0.173349\pi$
$272$	0.0263137	+	0.00463982i	0.00159551	+	0.000281331i
$273$		0			0
$274$	5.93642	−	16.3102i	0.358632	−	0.985335i
$275$	26.2227	+	9.54428i	1.58129	+	0.575542i
$276$		0			0
$277$	15.4537	−	18.4170i	0.928521	−	1.10657i	−0.0655519	−	0.997849i	$-0.520881\pi$
$277$	15.4537	−	18.4170i	0.928521	−	1.10657i	0.994073	−	0.108719i	$-0.0346748\pi$
$278$	5.93000	−	7.06710i	0.355658	−	0.423856i
$279$		0			0
$280$	−14.4710	−	5.26700i	−0.864805	−	0.314763i
$281$	−4.35215	+	11.9574i	−0.259628	+	0.713321i	0.739563	+	0.673088i	$0.235032\pi$
$281$	−4.35215	+	11.9574i	−0.259628	+	0.713321i	−0.999190	+	0.0402335i	$0.987190\pi$
$282$		0			0
$283$	−0.253793	−	0.0447506i	−0.0150864	−	0.00266015i	0.166100	−	0.986109i	$-0.446883\pi$
$283$	−0.253793	−	0.0447506i	−0.0150864	−	0.00266015i	−0.181186	+	0.983449i	$0.557994\pi$
$284$	−7.10830	+	5.96457i	−0.421800	+	0.353932i
$285$		0			0
$286$	−3.05244	+	5.28697i	−0.180494	+	0.312625i
$287$	−0.935363	−	5.30471i	−0.0552127	−	0.313127i
$288$		0			0
$289$	−15.9741	+	5.81410i	−0.939653	+	0.342006i
$290$			24.4463i			1.43554i
$291$		0			0
$292$	−2.82537	+	16.0235i	−0.165342	+	0.937704i
$293$	6.87967	+	5.77273i	0.401914	+	0.337246i	0.821233	−	0.570593i	$-0.193287\pi$
$293$	6.87967	+	5.77273i	0.401914	+	0.337246i	−0.419319	+	0.907839i	$0.637731\pi$
$294$		0			0
$295$	−23.9850			−1.39646
$296$	−1.84193	+	5.79718i	−0.107060	+	0.336954i
$297$		0			0
$298$	−4.97374	−	5.92747i	−0.288121	−	0.343369i
$299$	−6.56694	−	5.51032i	−0.379776	−	0.318670i
$300$		0			0
$301$	−6.83967	−	18.7918i	−0.394232	−	1.08314i
$302$			12.6363i			0.727140i
$303$		0			0
$304$	2.79594	−	1.61424i	0.160358	−	0.0925828i
$305$	−4.25089	−	24.1080i	−0.243405	−	1.38042i
$306$		0			0
$307$	7.39912	+	12.8157i	0.422290	+	0.731428i	0.996163	−	0.0875163i	$-0.0278930\pi$
$307$	7.39912	+	12.8157i	0.422290	+	0.731428i	−0.573873	+	0.818944i	$0.694560\pi$
$308$	−5.85619	+	4.91392i	−0.333687	+	0.279997i
$309$		0			0
$310$	−24.9981	−	14.4327i	−1.41980	−	0.819721i
$311$	−9.13738	+	25.1047i	−0.518133	+	1.42356i	0.354441	+	0.935078i	$0.384671\pi$
$311$	−9.13738	+	25.1047i	−0.518133	+	1.42356i	−0.872574	+	0.488481i	$0.837551\pi$
$312$		0			0
$313$	9.37905	−	1.65378i	0.530135	−	0.0934772i	0.0978278	−	0.995203i	$-0.468811\pi$
$313$	9.37905	−	1.65378i	0.530135	−	0.0934772i	0.432308	+	0.901726i	$0.357699\pi$
$314$	8.38628	−	9.99438i	0.473265	−	0.564016i
$315$		0			0
$316$	1.39364	−	0.245736i	0.0783984	−	0.0138237i
$317$	−14.2417	−	5.18354i	−0.799891	−	0.291137i	−0.0904498	−	0.995901i	$-0.528830\pi$
$317$	−14.2417	−	5.18354i	−0.799891	−	0.291137i	−0.709441	+	0.704764i	$0.751053\pi$
$318$		0			0
$319$	10.5098	+	6.06783i	0.588435	+	0.339733i
$320$	4.19936	+	0.740460i	0.234751	+	0.0413930i
$321$		0			0
$322$	−5.36739	−	9.29660i	−0.299113	−	0.518079i
$323$	0.0431318	−	0.0747066i	0.00239992	−	0.00415678i
$324$		0			0
$325$	−32.9258	+	19.0097i	−1.82640	+	1.05447i
$326$	23.7332	−	8.63820i	1.31446	−	0.478425i
$327$		0			0
$328$	0.510131	+	1.40157i	0.0281673	+	0.0773889i
$329$	−1.63872	+	9.29362i	−0.0903453	+	0.512374i
$330$		0			0
$331$	1.32812	+	1.58279i	0.0729998	+	0.0869978i	0.801308	−	0.598252i	$-0.204138\pi$
$331$	1.32812	+	1.58279i	0.0729998	+	0.0869978i	−0.728309	+	0.685249i	$0.759693\pi$
$332$	−1.69642			−0.0931030
$333$		0			0
$334$	−10.2810			−0.562552
$335$	−18.9713	−	22.6091i	−1.03651	−	1.23527i
$336$		0			0
$337$	−2.41835	+	13.7152i	−0.131736	+	0.747112i	0.845341	+	0.534227i	$0.179397\pi$
$337$	−2.41835	+	13.7152i	−0.131736	+	0.747112i	−0.977077	+	0.212885i	$0.931714\pi$
$338$	1.60152	+	4.40014i	0.0871112	+	0.239336i
$339$		0			0
$340$	0.107065	−	0.0389686i	0.00580643	−	0.00211337i
$341$	−12.4096	+	7.16467i	−0.672016	+	0.387989i
$342$		0			0
$343$	1.72903	−	2.99477i	0.0933588	−	0.161702i
$344$	2.76869	+	4.79551i	0.149278	+	0.258556i
$345$		0			0
$346$	23.2975	+	4.10798i	1.25248	+	0.220846i
$347$	17.5037	+	10.1058i	0.939647	+	0.542505i	0.889850	−	0.456254i	$-0.150809\pi$
$347$	17.5037	+	10.1058i	0.939647	+	0.542505i	0.0497972	+	0.998759i	$0.484143\pi$
$348$		0			0
$349$	−10.3271	−	3.75877i	−0.552799	−	0.201202i	0.0504906	−	0.998725i	$-0.483922\pi$
$349$	−10.3271	−	3.75877i	−0.552799	−	0.201202i	−0.603290	+	0.797522i	$0.706144\pi$
$350$	−46.8859	+	8.26724i	−2.50615	+	0.441903i
$351$		0			0
$352$	1.36066	−	1.62157i	0.0725232	−	0.0864298i
$353$	4.29024	−	0.756485i	0.228346	−	0.0402636i	−0.0583041	−	0.998299i	$-0.518569\pi$
$353$	4.29024	−	0.756485i	0.228346	−	0.0402636i	0.286650	+	0.958035i	$0.407458\pi$
$354$		0			0
$355$	−13.5330	+	37.1817i	−0.718259	+	1.97340i
$356$	−7.16283	−	4.13546i	−0.379629	−	0.219179i
$357$		0			0
$358$	3.87424	−	3.25088i	0.204760	−	0.171814i
$359$	3.84332	+	6.65683i	0.202843	+	0.351334i	0.949443	−	0.313939i	$-0.101649\pi$
$359$	3.84332	+	6.65683i	0.202843	+	0.351334i	−0.746600	+	0.665273i	$0.768315\pi$
$360$		0			0
$361$	1.48938	+	8.44667i	0.0783882	+	0.444562i
$362$	0.905384	−	0.522724i	0.0475859	−	0.0274737i
$363$		0			0
$364$		−	10.4154i		−	0.545915i
$365$	23.7295	+	65.1963i	1.24206	+	3.41253i
$366$		0			0
$367$	15.8706	+	13.3170i	0.828440	+	0.695143i	0.954932	−	0.296824i	$-0.0959275\pi$
$367$	15.8706	+	13.3170i	0.828440	+	0.695143i	−0.126492	+	0.991968i	$0.540372\pi$
$368$	1.91065	+	2.27702i	0.0995995	+	0.118698i
$369$		0			0
$370$	5.55803	+	25.3353i	0.288948	+	1.31712i
$371$	−6.89431			−0.357935
$372$		0			0
$373$	11.9553	+	10.0317i	0.619023	+	0.519422i	0.897496	−	0.441022i	$-0.145384\pi$
$373$	11.9553	+	10.0317i	0.619023	+	0.519422i	−0.278473	+	0.960444i	$0.589828\pi$
$374$	0.00982160	−	0.0557011i	0.000507863	−	0.00288023i
$375$		0			0
$376$		−	2.61309i		−	0.134760i
$377$	−15.5369	+	5.65496i	−0.800190	+	0.291245i
$378$		0			0
$379$	−4.37193	−	24.7944i	−0.224571	−	1.27360i	−0.863504	−	0.504342i	$-0.831735\pi$
$379$	−4.37193	−	24.7944i	−0.224571	−	1.27360i	0.638933	−	0.769262i	$-0.279376\pi$
$380$	6.88333	−	11.9223i	0.353107	−	0.611600i
$381$		0			0
$382$	−10.3135	+	8.65407i	−0.527685	+	0.442781i
$383$	29.7545	+	5.24652i	1.52038	+	0.268085i	0.870584	−	0.492020i	$-0.163741\pi$
$383$	29.7545	+	5.24652i	1.52038	+	0.268085i	0.649801	+	0.760105i	$0.274852\pi$
$384$		0			0
$385$	−11.1492	+	30.6322i	−0.568216	+	1.56116i
$386$	−4.24956	−	1.54671i	−0.216297	−	0.0787255i
$387$		0			0
$388$	−4.19436	+	4.99865i	−0.212937	+	0.253768i
$389$	−16.0701	+	19.1516i	−0.814786	+	0.971024i	−0.999932	−	0.0116872i	$-0.996280\pi$
$389$	−16.0701	+	19.1516i	−0.814786	+	0.971024i	0.185146	+	0.982711i	$0.440724\pi$
$390$		0			0
$391$	0.0746329	+	0.0271642i	0.00377435	+	0.00137375i
$392$	2.06665	−	5.67806i	0.104381	−	0.286786i
$393$		0			0
$394$	−12.1841	−	2.14838i	−0.613824	−	0.108234i
$395$	4.62258	−	3.87881i	0.232587	−	0.195164i
$396$		0			0
$397$	−6.83681	+	11.8417i	−0.343130	+	0.594318i	−0.985012	−	0.172485i	$-0.944820\pi$
$397$	−6.83681	+	11.8417i	−0.343130	+	0.594318i	0.641882	+	0.766803i	$0.278154\pi$
$398$	0.783093	+	4.44114i	0.0392529	+	0.222614i
$399$		0			0
$400$	12.3879	−	4.50881i	0.619393	−	0.225441i
$401$		−	1.62020i		−	0.0809089i	−0.999181	−	0.0404544i	$-0.987119\pi$
$401$		−	1.62020i		−	0.0809089i	0.999181	−	0.0404544i	$-0.0128806\pi$
$402$		0			0
$403$	3.39009	−	19.2261i	0.168872	−	0.957723i
$404$	12.7159	+	10.6699i	0.632642	+	0.530850i
$405$		0			0
$406$	−20.7044			−1.02754
$407$	12.2715	+	3.89900i	0.608276	+	0.193266i
$408$		0			0
$409$	−5.86780	−	6.99297i	−0.290144	−	0.345780i	0.601208	−	0.799093i	$-0.294686\pi$
$409$	−5.86780	−	6.99297i	−0.290144	−	0.345780i	−0.891351	+	0.453313i	$0.850242\pi$
$410$	4.87209	+	4.08817i	0.240615	+	0.201900i
$411$		0			0
$412$	0.648062	+	1.78053i	0.0319277	+	0.0877206i
$413$		−	20.3137i		−	0.999570i
$414$		0			0
$415$	−6.26462	+	3.61688i	−0.307518	+	0.177546i
$416$	0.500802	+	2.84019i	0.0245538	+	0.139252i
$417$		0			0
$418$	−3.41702	−	5.91846i	−0.167132	−	0.289481i
$419$	−10.9146	+	9.15844i	−0.533213	+	0.447419i	−0.869209	−	0.494444i	$-0.835372\pi$
$419$	−10.9146	+	9.15844i	−0.533213	+	0.447419i	0.335996	+	0.941863i	$0.390927\pi$
$420$		0			0
$421$	29.2667	+	16.8971i	1.42637	+	0.823516i	0.996832	−	0.0795325i	$-0.0253427\pi$
$421$	29.2667	+	16.8971i	1.42637	+	0.823516i	0.429539	+	0.903048i	$0.358676\pi$
$422$	5.55645	−	15.2662i	0.270484	−	0.743148i
$423$		0			0
$424$	1.88002	−	0.331498i	0.0913018	−	0.0160990i
$425$	0.226417	−	0.269833i	0.0109828	−	0.0130888i
$426$		0			0
$427$	20.4178	−	3.60021i	0.988087	−	0.174226i
$428$	−0.359204	−	0.130739i	−0.0173628	−	0.00631953i
$429$		0			0
$430$	20.4487	+	11.8061i	0.986124	+	0.569339i
$431$	−38.2487	−	6.74428i	−1.84238	−	0.324861i	−0.859787	−	0.510652i	$-0.829404\pi$
$431$	−38.2487	−	6.74428i	−1.84238	−	0.324861i	−0.982589	+	0.185791i	$0.940515\pi$
$432$		0			0
$433$	−9.05610	−	15.6856i	−0.435208	−	0.753803i	0.562104	−	0.827066i	$-0.309992\pi$
$433$	−9.05610	−	15.6856i	−0.435208	−	0.753803i	−0.997313	+	0.0732633i	$0.976659\pi$
$434$	12.2235	−	21.1717i	0.586746	−	1.01627i
$435$		0			0
$436$	0.836221	−	0.482792i	0.0400477	−	0.0231216i
$437$	9.01771	−	3.28218i	0.431376	−	0.157008i
$438$		0			0
$439$	−4.90855	−	13.4861i	−0.234273	−	0.643659i	−1.00000		0.000493184i	$-0.999843\pi$
$439$	−4.90855	−	13.4861i	−0.234273	−	0.643659i	0.765727	−	0.643165i	$-0.222379\pi$
$440$	1.56741	−	8.88922i	0.0747233	−	0.423777i
$441$		0			0
$442$	0.0495330	+	0.0590311i	0.00235604	+	0.00280782i
$443$	−5.43539			−0.258243			−0.129121	−	0.991629i	$-0.541216\pi$
$443$	−5.43539			−0.258243			−0.129121	+	0.991629i	$0.541216\pi$
$444$		0			0
$445$	−35.2684			−1.67188
$446$	0.544940	+	0.649435i	0.0258037	+	0.0307516i
$447$		0			0
$448$	−0.627119	+	3.55657i	−0.0296286	+	0.168032i
$449$	0.0445442	+	0.122384i	0.00210217	+	0.00577566i	0.940739	−	0.339131i	$-0.110133\pi$
$449$	0.0445442	+	0.122384i	0.00210217	+	0.00577566i	−0.938637	+	0.344906i	$0.887911\pi$
$450$		0			0
$451$	2.96686	−	1.07985i	0.139704	−	0.0508480i
$452$	1.63743	−	0.945373i	0.0770184	−	0.0444666i
$453$		0			0
$454$	6.06437	−	10.5038i	0.284615	−	0.492968i
$455$	−22.2063	−	38.4625i	−1.04105	−	1.80315i
$456$		0			0
$457$	27.8381	+	4.90861i	1.30221	+	0.229615i	0.781386	−	0.624048i	$-0.214513\pi$
$457$	27.8381	+	4.90861i	1.30221	+	0.229615i	0.520825	+	0.853663i	$0.325624\pi$
$458$	11.4900	+	6.63375i	0.536892	+	0.309975i
$459$		0			0
$460$	11.9105	+	4.33508i	0.555331	+	0.202124i
$461$	7.89127	−	1.39144i	0.367533	−	0.0648060i	0.0131684	−	0.999913i	$-0.495808\pi$
$461$	7.89127	−	1.39144i	0.367533	−	0.0648060i	0.354365	+	0.935107i	$0.384697\pi$
$462$		0			0
$463$	−22.0020	+	26.2210i	−1.02252	+	1.21859i	−0.0469535	+	0.998897i	$0.514951\pi$
$463$	−22.0020	+	26.2210i	−1.02252	+	1.21859i	−0.975568	+	0.219697i	$0.929493\pi$
$464$	5.64591	−	0.995526i	0.262105	−	0.0462161i
$465$		0			0
$466$	1.47293	−	4.04685i	0.0682323	−	0.187467i
$467$	17.7860	+	10.2688i	0.823040	+	0.475182i	0.851464	−	0.524414i	$-0.175715\pi$
$467$	17.7860	+	10.2688i	0.823040	+	0.475182i	−0.0284236	+	0.999596i	$0.509049\pi$
$468$		0			0
$469$	19.1484	−	16.0674i	0.884191	−	0.741925i
$470$	−5.57128	−	9.64974i	−0.256984	−	0.445109i
$471$		0			0
$472$	0.976739	+	5.53936i	0.0449581	+	0.254970i
$473$	10.1512	−	5.86077i	0.466750	−	0.269479i
$474$		0			0
$475$		−	42.5606i		−	1.95281i
$476$	0.0330037	+	0.0906770i	0.00151272	+	0.00415617i
$477$		0			0
$478$	−10.9102	−	9.15478i	−0.499023	−	0.418730i
$479$	4.04948	+	4.82598i	0.185025	+	0.220505i	0.850582	−	0.525843i	$-0.176250\pi$
$479$	4.04948	+	4.82598i	0.185025	+	0.220505i	−0.665556	+	0.746348i	$0.731806\pi$
$480$		0			0
$481$	−14.8161	+	9.39299i	−0.675558	+	0.428284i
$482$	−14.2610			−0.649572
$483$		0			0
$484$	4.99395	+	4.19042i	0.226998	+	0.190474i
$485$	−4.83170	+	27.4019i	−0.219396	+	1.24426i
$486$		0			0
$487$		−	27.5903i		−	1.25024i	−0.780530	−	0.625118i	$-0.785051\pi$
$487$		−	27.5903i		−	1.25024i	0.780530	−	0.625118i	$-0.214949\pi$
$488$	−5.39466	+	1.96349i	−0.244205	+	0.0888832i
$489$		0			0
$490$	−4.47421	−	25.3745i	−0.202124	−	1.14630i
$491$	16.5100	−	28.5962i	0.745088	−	1.29053i	−0.205066	−	0.978748i	$-0.565741\pi$
$491$	16.5100	−	28.5962i	0.745088	−	1.29053i	0.950154	−	0.311781i	$-0.100926\pi$
$492$		0			0
$493$	0.117346	−	0.0984648i	0.00528499	−	0.00443463i
$494$	9.16946	+	1.61682i	0.412554	+	0.0727443i
$495$		0			0
$496$	−2.31524	+	6.36108i	−0.103958	+	0.285621i
$497$	−31.4904	−	11.4616i	−1.41254	−	0.514121i
$498$		0			0
$499$	13.5539	−	16.1529i	0.606756	−	0.723103i	−0.371977	−	0.928242i	$-0.621320\pi$
$499$	13.5539	−	16.1529i	0.606756	−	0.723103i	0.978733	+	0.205139i	$0.0657645\pi$
$500$	22.4288	−	26.7296i	1.00305	−	1.19538i
$501$		0			0
$502$	23.2175	+	8.45048i	1.03625	+	0.377164i
$503$	−6.03817	+	16.5897i	−0.269229	+	0.739700i	0.729234	+	0.684265i	$0.239877\pi$
$503$	−6.03817	+	16.5897i	−0.269229	+	0.739700i	−0.998462	+	0.0554349i	$0.982345\pi$
$504$		0			0
$505$	69.7072	+	12.2913i	3.10193	+	0.546954i
$506$	4.82002	−	4.04447i	0.214276	−	0.179799i
$507$		0			0
$508$	−8.05720	+	13.9555i	−0.357480	+	0.619174i
$509$	−7.26094	−	41.1788i	−0.321835	−	1.82522i	−0.531039	−	0.847347i	$-0.678198\pi$
$509$	−7.26094	−	41.1788i	−0.321835	−	1.82522i	0.209203	−	0.977872i	$-0.432913\pi$
$510$		0			0
$511$	−55.2168	+	20.0973i	−2.44265	+	0.889051i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	2.84997	−	16.1630i	0.125707	−	0.712918i
$515$	6.18942	+	5.19354i	0.272738	+	0.228855i
$516$		0			0
$517$	−5.53139			−0.243270
$518$	−21.4572	+	4.70727i	−0.942777	+	0.206826i
$519$		0			0
$520$	7.90487	+	9.42065i	0.346651	+	0.413123i
$521$	−27.5629	−	23.1280i	−1.20755	−	1.01326i	−0.999382	−	0.0351633i	$-0.988805\pi$
$521$	−27.5629	−	23.1280i	−1.20755	−	1.01326i	−0.208170	−	0.978093i	$-0.566751\pi$
$522$		0			0
$523$	−11.2216	−	30.8312i	−0.490688	−	1.34815i	−0.900052	−	0.435783i	$-0.856471\pi$
$523$	−11.2216	−	30.8312i	−0.490688	−	1.34815i	0.409363	−	0.912371i	$-0.365751\pi$
$524$			0.822948i			0.0359507i
$525$		0			0
$526$	−24.3712	+	14.0707i	−1.06263	+	0.613512i
$527$	0.0314085	+	0.178126i	0.00136817	+	0.00775930i
$528$		0			0
$529$	−7.08229	−	12.2669i	−0.307926	−	0.533343i
$530$	6.23586	−	5.23251i	0.270868	−	0.227286i
$531$		0			0
$532$	10.0974	+	5.82971i	0.437776	+	0.252750i
$533$	−1.47122	+	4.04214i	−0.0637255	+	0.175085i
$534$		0			0
$535$	−1.60523	+	0.283046i	−0.0694002	+	0.0122371i
$536$	−4.44904	+	5.30216i	−0.192169	+	0.229018i
$537$		0			0
$538$	−22.8183	+	4.02348i	−0.983766	+	0.173465i
$539$	−12.0194	−	4.37469i	−0.517710	−	0.188431i
$540$		0			0
$541$	32.4941	+	18.7605i	1.39703	+	0.806576i	0.994080	−	0.108646i	$-0.0346516\pi$
$541$	32.4941	+	18.7605i	1.39703	+	0.806576i	0.402950	+	0.915222i	$0.367985\pi$
$542$	−10.4476	−	1.84219i	−0.448763	−	0.0791290i
$543$		0			0
$544$	−0.0133598	−	0.0231399i	−0.000572798	−	0.000992116i
$545$	2.05869	−	3.56576i	0.0881847	−	0.152740i
$546$		0			0
$547$	−22.5841	+	13.0389i	−0.965627	+	0.557505i	−0.897900	−	0.440199i	$-0.854908\pi$
$547$	−22.5841	+	13.0389i	−0.965627	+	0.557505i	−0.0677265	+	0.997704i	$0.521575\pi$
$548$	−16.3102	+	5.93642i	−0.696737	+	0.253591i
$549$		0			0
$550$	−9.54428	−	26.2227i	−0.406969	−	1.11814i
$551$	3.21403	−	18.2276i	0.136922	−	0.776524i
$552$		0			0
$553$	3.28508	+	3.91501i	0.139696	+	0.166483i
$554$	−24.0416			−1.02143
$555$		0			0
$556$	−9.22544			−0.391246
$557$	4.18253	+	4.98455i	0.177220	+	0.211202i	0.847341	−	0.531050i	$-0.178202\pi$
$557$	4.18253	+	4.98455i	0.177220	+	0.211202i	−0.670121	+	0.742252i	$0.733758\pi$
$558$		0			0
$559$	−2.77313	+	15.7272i	−0.117291	+	0.665189i
$560$	5.26700	+	14.4710i	0.222571	+	0.611509i
$561$		0			0
$562$	11.9574	−	4.35215i	0.504394	−	0.183585i
$563$	33.5577	−	19.3746i	1.41429	−	0.816540i	0.418500	−	0.908217i	$-0.362556\pi$
$563$	33.5577	−	19.3746i	1.41429	−	0.816540i	0.995789	+	0.0916766i	$0.0292226\pi$
$564$		0			0
$565$	4.03120	−	6.98224i	0.169594	−	0.293745i
$566$	0.128854	+	0.223182i	0.00541615	+	0.00938104i
$567$		0			0
$568$	9.13826	+	1.61132i	0.383433	+	0.0676095i
$569$	−11.1846	−	6.45744i	−0.468883	−	0.270710i	0.246889	−	0.969044i	$-0.420592\pi$
$569$	−11.1846	−	6.45744i	−0.468883	−	0.270710i	−0.715772	+	0.698334i	$0.753925\pi$
$570$		0			0
$571$	−2.81875	−	1.02594i	−0.117961	−	0.0429343i	0.282365	−	0.959307i	$-0.408881\pi$
$571$	−2.81875	−	1.02594i	−0.117961	−	0.0429343i	−0.400326	+	0.916373i	$0.631103\pi$
$572$	6.01212	−	1.06010i	0.251380	−	0.0443250i
$573$		0			0
$574$	−3.46240	+	4.12633i	−0.144518	+	0.172230i
$575$	38.5901	−	6.80447i	1.60932	−	0.283766i
$576$		0			0
$577$	9.86791	−	27.1119i	0.410806	−	1.12868i	−0.545957	−	0.837813i	$-0.683834\pi$
$577$	9.86791	−	27.1119i	0.410806	−	1.12868i	0.956763	−	0.290868i	$-0.0939440\pi$
$578$	14.7218	+	8.49964i	0.612347	+	0.353539i
$579$		0			0
$580$	18.7270	−	15.7138i	0.777595	−	0.652480i
$581$	−3.06325	−	5.30571i	−0.127085	−	0.220118i
$582$		0			0
$583$	−0.701717	−	3.97964i	−0.0290622	−	0.164820i
$584$	14.0908	−	8.13534i	0.583082	−	0.336643i
$585$		0			0
$586$		−	8.98077i		−	0.370992i
$587$	−8.30296	−	22.8122i	−0.342700	−	0.941560i	−0.984608	−	0.174778i	$-0.944079\pi$
$587$	−8.30296	−	22.8122i	−0.342700	−	0.941560i	0.641908	−	0.766782i	$-0.278143\pi$
$588$		0			0
$589$	16.7416	+	14.0478i	0.689824	+	0.578831i
$590$	15.4173	+	18.3736i	0.634719	+	0.756428i
$591$		0			0
$592$	5.62487	−	2.31536i	0.231181	−	0.0951606i
$593$	−12.0052			−0.492995			−0.246497	−	0.969143i	$-0.579280\pi$
$593$	−12.0052			−0.492995			−0.246497	+	0.969143i	$0.579280\pi$
$594$		0			0
$595$	0.315207	+	0.264490i	0.0129222	+	0.0108431i
$596$	−1.34365	+	7.62021i	−0.0550380	+	0.312136i
$597$		0			0
$598$			8.57253i			0.350557i
$599$	−17.9026	+	6.51602i	−0.731481	+	0.266237i	−0.680792	−	0.732477i	$-0.738364\pi$
$599$	−17.9026	+	6.51602i	−0.731481	+	0.266237i	−0.0506895	+	0.998714i	$0.516142\pi$
$600$		0			0
$601$	−3.95300	−	22.4186i	−0.161246	−	0.914472i	−0.952851	−	0.303439i	$-0.901865\pi$
$601$	−3.95300	−	22.4186i	−0.161246	−	0.914472i	0.791605	−	0.611033i	$-0.209246\pi$
$602$	−9.99893	+	17.3187i	−0.407526	+	0.705856i
$603$		0			0
$604$	9.68000	−	8.12248i	0.393874	−	0.330499i
$605$	27.3762	+	4.82716i	1.11300	+	0.196252i
$606$		0			0
$607$	−6.70527	+	18.4226i	−0.272159	+	0.747750i	0.726034	+	0.687658i	$0.241361\pi$
$607$	−6.70527	+	18.4226i	−0.272159	+	0.747750i	−0.998193	+	0.0600911i	$0.980861\pi$
$608$	−3.03377	−	1.10420i	−0.123036	−	0.0447813i
$609$		0			0
$610$	−15.7354	+	18.7527i	−0.637106	+	0.759274i
$611$	4.84414	−	5.77302i	0.195973	−	0.233551i
$612$		0			0
$613$	2.38568	+	0.868317i	0.0963568	+	0.0350710i	0.389749	−	0.920921i	$-0.372562\pi$
$613$	2.38568	+	0.868317i	0.0963568	+	0.0350710i	−0.293392	+	0.955992i	$0.594784\pi$
$614$	5.06130	−	13.9058i	0.204257	−	0.561192i
$615$		0			0
$616$	7.52857	+	1.32749i	0.303335	+	0.0534861i
$617$	14.5342	−	12.1956i	0.585124	−	0.490977i	−0.301502	−	0.953466i	$-0.597488\pi$
$617$	14.5342	−	12.1956i	0.585124	−	0.490977i	0.886625	+	0.462489i	$0.153043\pi$
$618$		0			0
$619$	−1.25679	+	2.17683i	−0.0505147	+	0.0874940i	−0.890177	−	0.455615i	$-0.849420\pi$
$619$	−1.25679	+	2.17683i	−0.0505147	+	0.0874940i	0.839662	+	0.543109i	$0.182753\pi$
$620$	5.01241	+	28.4268i	0.201303	+	1.14165i
$621$		0			0
$622$	25.1047	−	9.13738i	1.00661	−	0.366376i
$623$		−	29.8699i		−	1.19671i
$624$		0			0
$625$	14.3909	−	81.6150i	0.575637	−	3.26460i
$626$	−7.29561	−	6.12174i	−0.291591	−	0.244674i
$627$		0			0
$628$	−13.0467			−0.520621
$629$	0.0992261	−	0.128724i	0.00395640	−	0.00513258i
$630$		0			0
$631$	−4.27007	−	5.08887i	−0.169989	−	0.202585i	0.674324	−	0.738436i	$-0.264435\pi$
$631$	−4.27007	−	5.08887i	−0.169989	−	0.202585i	−0.844313	+	0.535851i	$0.819991\pi$
$632$	−1.08406	−	0.909634i	−0.0431216	−	0.0361833i
$633$		0			0
$634$	5.18354	+	14.2417i	0.205865	+	0.565609i
$635$			68.7140i			2.72683i
$636$		0			0
$637$	15.0918	−	8.71325i	0.597958	−	0.345231i
$638$	−2.10733	−	11.9513i	−0.0834301	−	0.473156i
$639$		0			0
$640$	−2.13207	−	3.69285i	−0.0842775	−	0.145973i
$641$	−6.30793	+	5.29298i	−0.249148	+	0.209060i	−0.758805	−	0.651317i	$-0.774217\pi$
$641$	−6.30793	+	5.29298i	−0.249148	+	0.209060i	0.509657	+	0.860378i	$0.329772\pi$
$642$		0			0
$643$	−12.3142	−	7.10959i	−0.485623	−	0.280375i	0.237134	−	0.971477i	$-0.423792\pi$
$643$	−12.3142	−	7.10959i	−0.485623	−	0.280375i	−0.722757	+	0.691102i	$0.757125\pi$
$644$	−3.67151	+	10.0874i	−0.144678	+	0.397499i
$645$		0			0
$646$	−0.0849532	+	0.0149795i	−0.00334244	+	0.000589362i
$647$	−25.6313	+	30.5462i	−1.00767	+	1.20089i	−0.0281389	+	0.999604i	$0.508958\pi$
$647$	−25.6313	+	30.5462i	−1.00767	+	1.20089i	−0.979532	+	0.201291i	$0.935486\pi$
$648$		0			0
$649$	11.7258	−	2.06757i	0.460276	−	0.0811591i
$650$	35.7266	+	13.0034i	1.40131	+	0.510036i
$651$		0			0
$652$	−21.8727	−	12.6282i	−0.856600	−	0.494558i
$653$	−7.99174	−	1.40916i	−0.312741	−	0.0551447i	0.0150747	−	0.999886i	$-0.495201\pi$
$653$	−7.99174	−	1.40916i	−0.312741	−	0.0551447i	−0.327816	+	0.944742i	$0.606313\pi$
$654$		0			0
$655$	1.75458	+	3.03903i	0.0685572	+	0.118745i
$656$	0.745761	−	1.29170i	0.0291171	−	0.0504323i
$657$		0			0
$658$	8.17267	−	4.71850i	0.318604	−	0.183946i
$659$	−26.3535	+	9.59188i	−1.02659	+	0.373647i	−0.799780	−	0.600293i	$-0.795050\pi$
$659$	−26.3535	+	9.59188i	−1.02659	+	0.373647i	−0.226806	+	0.973940i	$0.572828\pi$
$660$		0			0
$661$	−1.54764	−	4.25209i	−0.0601961	−	0.165387i	0.905949	−	0.423387i	$-0.139159\pi$
$661$	−1.54764	−	4.25209i	−0.0601961	−	0.165387i	−0.966145	+	0.258000i	$0.916937\pi$
$662$	0.358788	−	2.03479i	0.0139447	−	0.0790844i
$663$		0			0
$664$	1.09044	+	1.29953i	0.0423171	+	0.0504316i
$665$	49.7174			1.92796
$666$		0			0
$667$	17.0410			0.659831
$668$	6.60851	+	7.87572i	0.255691	+	0.304721i
$669$		0			0
$670$	−5.12508	+	29.0658i	−0.197999	+	1.12291i
$671$	4.15633	+	11.4194i	0.160454	+	0.440842i
$672$		0			0
$673$	−9.85346	+	3.58637i	−0.379823	+	0.138244i	−0.524874	−	0.851180i	$-0.675888\pi$
$673$	−9.85346	+	3.58637i	−0.379823	+	0.138244i	0.145051	+	0.989424i	$0.453665\pi$
$674$	12.0609	−	6.96337i	0.464569	−	0.268219i
$675$		0			0
$676$	2.34127	−	4.05519i	0.0900487	−	0.155969i
$677$	13.4277	+	23.2574i	0.516067	+	0.893853i	0.999826	+	0.0186525i	$0.00593760\pi$
$677$	13.4277	+	23.2574i	0.516067	+	0.893853i	−0.483760	+	0.875201i	$0.660729\pi$
$678$		0			0
$679$	−23.2076	−	4.09212i	−0.890625	−	0.157041i
$680$	−0.0986718	−	0.0569682i	−0.00378389	−	0.00218463i
$681$		0			0
$682$	13.4652	+	4.90092i	0.515608	+	0.187666i
$683$	−17.6006	+	3.10346i	−0.673469	+	0.118751i	−0.499916	−	0.866074i	$-0.666636\pi$
$683$	−17.6006	+	3.10346i	−0.673469	+	0.118751i	−0.173553	+	0.984825i	$0.555525\pi$
$684$		0			0
$685$	−47.5743	+	56.6968i	−1.81772	+	2.16627i
$686$	−3.40552	+	0.600485i	−0.130023	+	0.0229266i
$687$		0			0
$688$	1.89389	−	5.20343i	0.0722040	−	0.198379i
$689$	4.76801	+	2.75281i	0.181647	+	0.104874i
$690$		0			0
$691$	16.1699	−	13.5682i	0.615133	−	0.516158i	−0.281137	−	0.959668i	$-0.590711\pi$
$691$	16.1699	−	13.5682i	0.615133	−	0.516158i	0.896269	+	0.443510i	$0.146267\pi$
$692$	−11.8284	−	20.4875i	−0.449650	−	0.778817i
$693$		0			0
$694$	−3.50969	−	19.9044i	−0.133226	−	0.755563i
$695$	−34.0682	+	19.6693i	−1.29228	+	0.746098i
$696$		0			0
$697$		−	0.0398530i		−	0.00150954i
$698$	3.75877	+	10.3271i	0.142272	+	0.390888i
$699$		0			0
$700$	36.4707	+	30.6026i	1.37846	+	1.15667i
$701$	−2.94056	−	3.50442i	−0.111063	−	0.132360i	0.707649	−	0.706564i	$-0.249756\pi$
$701$	−2.94056	−	3.50442i	−0.111063	−	0.132360i	−0.818712	+	0.574204i	$0.805312\pi$
$702$		0			0
$703$	−0.813275	−	19.6212i	−0.0306733	−	0.740027i
$704$	−2.11681			−0.0797801
$705$		0			0
$706$	−3.33721	−	2.80025i	−0.125598	−	0.105389i
$707$	−10.4099	+	59.0372i	−0.391503	+	2.22032i
$708$		0			0
$709$		−	4.67695i		−	0.175647i	−0.996136	−	0.0878233i	$-0.972009\pi$
$709$		−	4.67695i		−	0.175647i	0.996136	−	0.0878233i	$-0.0279911\pi$
$710$	37.1817	−	13.5330i	1.39540	−	0.507886i
$711$		0			0
$712$	1.43623	+	8.14527i	0.0538251	+	0.305257i
$713$	−10.0607	+	17.4257i	−0.376777	+	0.652596i
$714$		0			0
$715$	19.9417	−	16.7331i	0.745777	−	0.625781i
$716$	−4.98063	−	0.878219i	−0.186135	−	0.0328206i
$717$		0			0
$718$	2.62899	−	7.22308i	0.0981129	−	0.269563i
$719$	43.2845	+	15.7543i	1.61424	+	0.587535i	0.982272	−	0.187460i	$-0.0600255\pi$
$719$	43.2845	+	15.7543i	1.61424	+	0.587535i	0.631967	+	0.774995i	$0.282248\pi$
$720$		0			0
$721$	−4.39857	+	5.24202i	−0.163811	+	0.195223i
$722$	5.51317	−	6.57034i	0.205179	−	0.244523i
$723$		0			0
$724$	−0.982399	−	0.357564i	−0.0365106	−	0.0132888i
$725$	25.8490	−	71.0196i	0.960009	−	2.63760i
$726$		0			0
$727$	−42.9014	−	7.56467i	−1.59112	−	0.280558i	−0.693213	−	0.720733i	$-0.743805\pi$
$727$	−42.9014	−	7.56467i	−1.59112	−	0.280558i	−0.897912	+	0.440175i	$0.854916\pi$
$728$	−7.97865	+	6.69488i	−0.295708	+	0.248129i
$729$		0			0
$730$	34.6902	−	60.0852i	1.28394	−	2.22385i
$731$	−0.0256924	−	0.145709i	−0.000950269	−	0.00538924i
$732$		0			0
$733$	26.1238	−	9.50828i	0.964904	−	0.351196i	0.188950	−	0.981987i	$-0.439491\pi$
$733$	26.1238	−	9.50828i	0.964904	−	0.351196i	0.775953	+	0.630790i	$0.217269\pi$
$734$		−	20.7176i		−	0.764702i
$735$		0			0
$736$	0.516159	−	2.92728i	0.0190259	−	0.107901i
$737$	11.2236	+	9.41775i	0.413428	+	0.346907i
$738$		0			0
$739$	26.4463			0.972843			0.486421	−	0.873724i	$-0.338302\pi$
$739$	26.4463			0.972843			0.486421	+	0.873724i	$0.338302\pi$
$740$	15.8353	−	20.5429i	0.582117	−	0.755171i
$741$		0			0
$742$	4.43158	+	5.28135i	0.162688	+	0.193884i
$743$	−31.0557	−	26.0589i	−1.13932	−	0.956007i	−0.139908	−	0.990165i	$-0.544681\pi$
$743$	−31.0557	−	26.0589i	−1.13932	−	0.956007i	−0.999416	+	0.0341578i	$0.989125\pi$
$744$		0			0
$745$	11.2849	+	31.0051i	0.413447	+	1.13594i
$746$		−	15.6066i		−	0.571397i
$747$		0			0
$748$	−0.0489827	+	0.0282802i	−0.00179098	+	0.00103403i
$749$	−0.239720	−	1.35952i	−0.00875919	−	0.0496759i
$750$		0			0
$751$	−5.14164	−	8.90559i	−0.187621	−	0.324969i	0.756835	−	0.653605i	$-0.226744\pi$
$751$	−5.14164	−	8.90559i	−0.187621	−	0.324969i	−0.944457	+	0.328636i	$0.893411\pi$
$752$	−2.00174	+	1.67966i	−0.0729959	+	0.0612509i
$753$		0			0
$754$	14.3189	+	8.26700i	0.521462	+	0.301066i
$755$	18.4291	−	50.6336i	0.670704	−	1.84274i
$756$		0			0
$757$	−34.9139	+	6.15626i	−1.26897	+	0.223753i	−0.767289	−	0.641301i	$-0.778395\pi$
$757$	−34.9139	+	6.15626i	−1.26897	+	0.223753i	−0.501678	+	0.865054i	$0.667284\pi$
$758$	−16.1834	+	19.2866i	−0.587808	+	0.700522i
$759$		0			0
$760$	−13.5575	+	2.39055i	−0.491782	+	0.0867145i
$761$	4.68947	+	1.70683i	0.169993	+	0.0618725i	0.425615	−	0.904904i	$-0.360058\pi$
$761$	4.68947	+	1.70683i	0.169993	+	0.0618725i	−0.255622	+	0.966777i	$0.582280\pi$
$762$		0			0
$763$	3.01996	+	1.74357i	0.109330	+	0.0631216i
$764$	13.2588	+	2.33788i	0.479687	+	0.0845817i
$765$		0			0
$766$	−15.1068	−	26.1657i	−0.545829	−	0.945404i
$767$	−8.11099	+	14.0486i	−0.292871	+	0.507267i
$768$		0			0
$769$	−30.5000	+	17.6092i	−1.09986	+	0.635004i	−0.936184	−	0.351511i	$-0.885668\pi$
$769$	−30.5000	+	17.6092i	−1.09986	+	0.635004i	−0.163675	+	0.986514i	$0.552335\pi$
$770$	30.6322	−	11.1492i	1.10391	−	0.401789i
$771$		0			0
$772$	1.54671	+	4.24956i	0.0556674	+	0.152945i
$773$	1.86072	−	10.5527i	0.0669255	−	0.379553i	−0.932887	−	0.360170i	$-0.882719\pi$
$773$	1.86072	−	10.5527i	0.0669255	−	0.379553i	0.999812	−	0.0193832i	$-0.00617025\pi$
$774$		0			0
$775$	57.3619	+	68.3612i	2.06050	+	2.45561i
$776$	6.52527			0.234244
$777$		0			0
$778$	25.0006			0.896316
$779$	−3.09524	−	3.68876i	−0.110898	−	0.132164i
$780$		0			0
$781$	3.41085	−	19.3439i	0.122050	−	0.692180i
$782$	−0.0271642	−	0.0746329i	−0.000971389	−	0.00266887i
$783$		0			0
$784$	−5.67806	+	2.06665i	−0.202788	+	0.0738088i
$785$	−48.1797	+	27.8166i	−1.71961	+	0.992815i
$786$		0			0
$787$	−13.6101	+	23.5734i	−0.485149	+	0.840302i	−0.999854	−	0.0170648i	$-0.994568\pi$
$787$	−13.6101	+	23.5734i	−0.485149	+	0.840302i	0.514706	+	0.857367i	$0.327901\pi$
$788$	6.18600	+	10.7145i	0.220367	+	0.381687i
$789$		0			0
$790$	−5.94267	−	1.04785i	−0.211431	−	0.0372810i
$791$	5.91349	+	3.41415i	0.210259	+	0.121393i
$792$		0			0
$793$	−15.5582	−	5.66272i	−0.552488	−	0.201089i
$794$	13.4659	−	2.37440i	0.477887	−	0.0842643i
$795$		0			0
$796$	2.89875	−	3.45459i	0.102743	−	0.122445i
$797$	−3.05954	+	0.539479i	−0.108374	+	0.0191093i	−0.227572	−	0.973761i	$-0.573079\pi$
$797$	−3.05954	+	0.539479i	−0.108374	+	0.0191093i	0.119198	+	0.992871i	$0.461968\pi$
$798$		0			0
$799$	−0.0238801	+	0.0656101i	−0.000844818	+	0.00232112i
$800$	−11.4167	−	6.59144i	−0.403642	−	0.233043i
$801$		0			0
$802$	−1.24114	+	1.04144i	−0.0438263	+	0.0367747i
$803$	−17.2209	−	29.8275i	−0.607713	−	1.05259i
$804$		0			0
$805$	7.94868	+	45.0792i	0.280154	+	1.58883i
$806$	−16.9072	+	9.76137i	−0.595530	+	0.343830i
$807$		0			0
$808$		−	16.5995i		−	0.583968i
$809$	1.77678	+	4.88167i	0.0624684	+	0.171630i	0.967000	−	0.254776i	$-0.0820017\pi$
$809$	1.77678	+	4.88167i	0.0624684	+	0.171630i	−0.904532	+	0.426406i	$0.859779\pi$
$810$		0			0
$811$	24.4994	+	20.5574i	0.860289	+	0.721868i	0.962030	−	0.272942i	$-0.0879969\pi$
$811$	24.4994	+	20.5574i	0.860289	+	0.721868i	−0.101741	+	0.994811i	$0.532441\pi$
$812$	13.3085	+	15.8605i	0.467037	+	0.556593i
$813$		0			0
$814$	−4.90116	−	11.9067i	−0.171786	−	0.417331i
$815$	−107.697			−3.77245
$816$		0			0
$817$	−13.6948	−	11.4913i	−0.479119	−	0.402029i
$818$	−1.58518	+	8.98998i	−0.0554244	+	0.314327i
$819$		0			0
$820$		−	6.36006i		−	0.222103i
$821$	7.04269	−	2.56333i	0.245792	−	0.0894608i	−0.216187	−	0.976352i	$-0.569362\pi$
$821$	7.04269	−	2.56333i	0.245792	−	0.0894608i	0.461978	+	0.886891i	$0.347140\pi$
$822$		0			0
$823$	−7.11013	−	40.3235i	−0.247843	−	1.40559i	−0.813795	−	0.581152i	$-0.802602\pi$
$823$	−7.11013	−	40.3235i	−0.247843	−	1.40559i	0.565952	−	0.824438i	$-0.308509\pi$
$824$	0.947403	−	1.64095i	0.0330043	−	0.0571652i
$825$		0			0
$826$	−15.5612	+	13.0574i	−0.541442	+	0.454324i
$827$	−43.1556	−	7.60950i	−1.50067	−	0.264608i	−0.637865	−	0.770148i	$-0.720182\pi$
$827$	−43.1556	−	7.60950i	−1.50067	−	0.264608i	−0.862803	+	0.505540i	$0.831293\pi$
$828$		0			0
$829$	12.4487	−	34.2026i	0.432362	−	1.18790i	−0.511997	−	0.858987i	$-0.671094\pi$
$829$	12.4487	−	34.2026i	0.432362	−	1.18790i	0.944359	−	0.328917i	$-0.106684\pi$
$830$	6.79751	+	2.47409i	0.235945	+	0.0858770i
$831$		0			0
$832$	1.85380	−	2.20927i	0.0642690	−	0.0765928i
$833$	−0.103780	+	0.123680i	−0.00359576	+	0.00428526i
$834$		0			0
$835$	41.1958	+	14.9941i	1.42564	+	0.518891i
$836$	−2.33738	+	6.42190i	−0.0808400	+	0.222106i
$837$		0			0
$838$	14.0315	+	2.47414i	0.484711	+	0.0854677i
$839$	−16.9323	+	14.2079i	−0.584567	+	0.490510i	−0.886443	−	0.462837i	$-0.846832\pi$
$839$	−16.9323	+	14.2079i	−0.584567	+	0.490510i	0.301876	+	0.953347i	$0.402387\pi$
$840$		0			0
$841$	1.93366	−	3.34920i	0.0666780	−	0.115490i
$842$	−5.86831	−	33.2809i	−0.202235	−	1.14693i
$843$		0			0
$844$	−15.2662	+	5.55645i	−0.525485	+	0.191261i
$845$		−	19.9670i		−	0.686885i
$846$		0			0
$847$	−4.08828	+	23.1858i	−0.140475	+	0.796672i
$848$	−1.46240	−	1.22710i	−0.0502189	−	0.0421386i
$849$		0			0
$850$	−0.352242			−0.0120818
$851$	17.6607	−	3.87439i	0.605400	−	0.132812i
$852$		0			0
$853$	26.8496	+	31.9982i	0.919314	+	1.09560i	0.995140	+	0.0984751i	$0.0313965\pi$
$853$	26.8496	+	31.9982i	0.919314	+	1.09560i	−0.0758251	+	0.997121i	$0.524159\pi$
$854$	−15.8822	−	13.3268i	−0.543479	−	0.456033i
$855$		0			0
$856$	0.130739	+	0.359204i	0.00446858	+	0.0122773i
$857$		−	2.80039i		−	0.0956595i	−0.998856	−	0.0478297i	$-0.984770\pi$
$857$		−	2.80039i		−	0.0956595i	0.998856	−	0.0478297i	$-0.0152305\pi$
$858$		0			0
$859$	−29.0965	+	16.7988i	−0.992758	+	0.573169i	−0.906098	−	0.423069i	$-0.860953\pi$
$859$	−29.0965	+	16.7988i	−0.992758	+	0.573169i	−0.0866605	+	0.996238i	$0.527620\pi$
$860$	−4.10020	−	23.2534i	−0.139816	−	0.792935i
$861$		0			0
$862$	19.4194	+	33.6354i	0.661427	+	1.14563i
$863$	19.4640	−	16.3322i	0.662561	−	0.555955i	−0.248292	−	0.968685i	$-0.579869\pi$
$863$	19.4640	−	16.3322i	0.662561	−	0.555955i	0.910853	+	0.412730i	$0.135425\pi$
$864$		0			0
$865$	−87.3614	−	50.4381i	−2.97038	−	1.71495i
$866$	−6.19474	+	17.0199i	−0.210506	+	0.578360i
$867$		0			0
$868$	−24.0756	+	4.24517i	−0.817178	+	0.144091i
$869$	−1.92552	+	2.29474i	−0.0653187	+	0.0778438i
$870$		0			0
$871$	−19.6583	+	3.46629i	−0.666096	+	0.117451i
$872$	−0.907352	−	0.330249i	−0.0307268	−	0.0111837i
$873$		0			0
$874$	−8.31077	−	4.79822i	−0.281116	−	0.162302i
$875$	124.099	+	21.8821i	4.19532	+	0.739749i
$876$		0			0
$877$	−10.5898	−	18.3420i	−0.357591	−	0.619367i	0.629966	−	0.776622i	$-0.283069\pi$
$877$	−10.5898	−	18.3420i	−0.357591	−	0.619367i	−0.987558	+	0.157256i	$0.949735\pi$
$878$	−7.17583	+	12.4289i	−0.242172	+	0.419455i
$879$		0			0
$880$	−7.81705	+	4.51318i	−0.263513	+	0.152139i
$881$	−13.6304	+	4.96105i	−0.459219	+	0.167142i	−0.561262	−	0.827638i	$-0.689684\pi$
$881$	−13.6304	+	4.96105i	−0.459219	+	0.167142i	0.102044	+	0.994780i	$0.467462\pi$
$882$		0			0
$883$	12.7053	+	34.9074i	0.427566	+	1.17473i	0.947285	+	0.320391i	$0.103814\pi$
$883$	12.7053	+	34.9074i	0.427566	+	1.17473i	−0.519719	+	0.854337i	$0.673963\pi$
$884$	0.0133813	−	0.0758889i	0.000450060	−	0.00255242i
$885$		0			0
$886$	3.49380	+	4.16375i	0.117376	+	0.139884i
$887$	−2.08616			−0.0700464			−0.0350232	−	0.999386i	$-0.511151\pi$
$887$	−2.08616			−0.0700464			−0.0350232	+	0.999386i	$0.511151\pi$
$888$		0			0
$889$	−58.1961			−1.95183
$890$	22.6701	+	27.0172i	0.759903	+	0.905617i
$891$		0			0
$892$	0.147215	−	0.834897i	0.00492912	−	0.0279544i
$893$	2.88537	+	7.92750i	0.0965554	+	0.265284i
$894$		0			0
$895$	−20.2652	+	7.37591i	−0.677390	+	0.246550i
$896$	3.12760	−	1.80572i	0.104486	−	0.0603248i
$897$		0			0
$898$	0.0651192	−	0.112790i	0.00217306	−	0.00376384i
$899$	19.4043	+	33.6092i	0.647169	+	1.12093i
$900$		0			0
$901$	−0.0502335	−	0.00885753i	−0.00167352	−	0.000295087i
$902$	−2.73427	−	1.57863i	−0.0910412	−	0.0525627i
$903$		0			0
$904$	−1.77672	−	0.646673i	−0.0590928	−	0.0215080i
$905$	−4.39021	+	0.774112i	−0.145935	+	0.0257323i
$906$		0			0
$907$	6.67576	−	7.95586i	0.221665	−	0.264170i	−0.643739	−	0.765245i	$-0.722618\pi$
$907$	6.67576	−	7.95586i	0.221665	−	0.264170i	0.865404	+	0.501075i	$0.167062\pi$
$908$	−11.9445	+	2.10613i	−0.396391	+	0.0698945i
$909$		0			0
$910$	−15.1900	+	41.7343i	−0.503545	+	1.38348i
$911$	5.79035	+	3.34306i	0.191843	+	0.110761i	0.592845	−	0.805317i	$-0.298005\pi$
$911$	5.79035	+	3.34306i	0.191843	+	0.110761i	−0.401002	+	0.916077i	$0.631338\pi$
$912$		0			0
$913$	2.75086	−	2.30824i	0.0910400	−	0.0763916i
$914$	−14.1338	−	24.4804i	−0.467504	−	0.809740i
$915$		0			0
$916$	−2.30388	−	13.0659i	−0.0761223	−	0.431711i
$917$	−2.57385	+	1.48601i	−0.0849960	+	0.0490725i
$918$		0			0
$919$			48.7881i			1.60937i	0.593702	+	0.804685i	$0.297666\pi$
$919$			48.7881i			1.60937i	−0.593702	+	0.804685i	$0.702334\pi$
$920$	−4.33508	−	11.9105i	−0.142923	−	0.392678i
$921$		0			0
$922$	−6.13832	−	5.15066i	−0.202155	−	0.169628i
$923$	17.2018	+	20.5004i	0.566206	+	0.674778i
$924$		0			0
$925$	10.6422	−	79.4790i	0.349914	−	2.61325i
$926$	34.2291			1.12484
$927$		0			0
$928$	−4.39174	−	3.68510i	−0.144166	−	0.120969i
$929$	4.20149	−	23.8278i	0.137846	−	0.781765i	−0.834989	−	0.550267i	$-0.814526\pi$
$929$	4.20149	−	23.8278i	0.137846	−	0.781765i	0.972835	−	0.231499i	$-0.0743628\pi$
$930$		0			0
$931$			19.5079i			0.639347i
$932$	−4.04685	+	1.47293i	−0.132559	+	0.0482475i
$933$		0			0
$934$	−3.56631	−	20.2255i	−0.116693	−	0.661800i
$935$	−0.120591	+	0.208869i	−0.00394373	+	0.00683075i
$936$		0			0
$937$	−44.8844	+	37.6625i	−1.46631	+	1.23038i	−0.546828	+	0.837245i	$0.684165\pi$
$937$	−44.8844	+	37.6625i	−1.46631	+	1.23038i	−0.919481	+	0.393134i	$0.871391\pi$
$938$	−24.6167	−	4.34059i	−0.803764	−	0.141725i
$939$		0			0
$940$	−3.81098	+	10.4706i	−0.124300	+	0.341513i
$941$	−44.2420	−	16.1028i	−1.44225	−	0.524936i	−0.501834	−	0.864964i	$-0.667341\pi$
$941$	−44.2420	−	16.1028i	−1.44225	−	0.524936i	−0.940415	+	0.340028i	$0.889563\pi$
$942$		0			0
$943$	2.84978	−	3.39623i	0.0928015	−	0.110597i
$944$	3.61556	−	4.30886i	0.117677	−	0.140241i
$945$		0			0
$946$	−11.0146	−	4.00900i	−0.358117	−	0.130344i
$947$	−6.54191	+	17.9738i	−0.212584	+	0.584068i	−0.999454	−	0.0330502i	$-0.989478\pi$
$947$	−6.54191	+	17.9738i	−0.212584	+	0.584068i	0.786870	+	0.617119i	$0.211700\pi$
$948$		0			0
$949$	46.2118	+	8.14838i	1.50010	+	0.264508i
$950$	−32.6033	+	27.3574i	−1.05779	+	0.887591i
$951$		0			0
$952$	0.0482482	−	0.0835683i	0.00156373	−	0.00270847i
$953$	−0.149089	−	0.845526i	−0.00482947	−	0.0273893i	0.982298	−	0.187326i	$-0.0599821\pi$
$953$	−0.149089	−	0.845526i	−0.00482947	−	0.0273893i	−0.987127	+	0.159937i	$0.948871\pi$
$954$		0			0
$955$	53.9473	−	19.6352i	1.74569	−	0.635381i
$956$			14.2423i			0.460629i
$957$		0			0
$958$	1.09396	−	6.20416i	0.0353443	−	0.200447i
$959$	−48.0183	−	40.2922i	−1.55059	−	1.30110i
$960$		0			0
$961$	−14.8237			−0.478185
$962$	16.7191	+	5.31212i	0.539045	+	0.171270i
$963$		0			0
$964$	9.16681	+	10.9246i	0.295243	+	0.351857i
$965$	14.7721	+	12.3953i	0.475532	+	0.399018i
$966$		0			0
$967$	20.6459	+	56.7241i	0.663927	+	1.82412i	0.558160	+	0.829733i	$0.311507\pi$
$967$	20.6459	+	56.7241i	0.663927	+	1.82412i	0.105766	+	0.994391i	$0.466270\pi$
$968$		−	6.51914i		−	0.209533i
$969$		0			0
$970$	24.0969	−	13.9123i	0.773704	−	0.446698i
$971$	6.14330	+	34.8404i	0.197148	+	1.11808i	0.909327	+	0.416083i	$0.136597\pi$
$971$	6.14330	+	34.8404i	0.197148	+	1.11808i	−0.712179	+	0.701998i	$0.752291\pi$
$972$		0			0
$973$	−16.6585	−	28.8534i	−0.534048	−	0.924999i
$974$	−21.1354	+	17.7347i	−0.677222	+	0.568256i
$975$		0			0
$976$	4.97174	+	2.87044i	0.159142	+	0.0918804i
$977$	11.7238	−	32.2109i	0.375078	−	1.03052i	−0.598292	−	0.801278i	$-0.704154\pi$
$977$	11.7238	−	32.2109i	0.375078	−	1.03052i	0.973370	−	0.229240i	$-0.0736241\pi$
$978$		0			0
$979$	17.2420	−	3.04022i	0.551055	−	0.0971659i
$980$	−16.5620	+	19.7379i	−0.529054	+	0.630503i
$981$		0			0
$982$	−32.5184	+	5.73388i	−1.03770	+	0.182975i
$983$	15.2535	+	5.55182i	0.486511	+	0.177076i	0.573617	−	0.819123i	$-0.305540\pi$
$983$	15.2535	+	5.55182i	0.486511	+	0.177076i	−0.0871061	+	0.996199i	$0.527762\pi$
$984$		0			0
$985$	45.6880	+	26.3780i	1.45574	+	0.840473i
$986$	−0.150857	−	0.0266001i	−0.00480426	−	0.000847120i
$987$		0			0
$988$	−4.65546	−	8.06349i	−0.148110	−	0.256534i
$989$	8.22976	−	14.2544i	0.261691	−	0.453263i
$990$		0			0
$991$	−2.92903	+	1.69107i	−0.0930436	+	0.0537187i	−0.545800	−	0.837916i	$-0.683774\pi$
$991$	−2.92903	+	1.69107i	−0.0930436	+	0.0537187i	0.452756	+	0.891634i	$0.350441\pi$
$992$	6.36108	−	2.31524i	0.201965	−	0.0735091i
$993$		0			0
$994$	11.4616	+	31.4904i	0.363538	+	0.998814i
$995$	3.33922	−	18.9376i	0.105860	−	0.600364i
$996$		0			0
$997$	−25.7715	−	30.7132i	−0.816190	−	0.972698i	0.183757	−	0.982972i	$-0.441174\pi$
$997$	−25.7715	−	30.7132i	−0.816190	−	0.972698i	−0.999947	+	0.0102738i	$0.996730\pi$
$998$	−21.0861			−0.667469
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bj.c.469.1		12
3.2	odd	2		74.2.h.a.25.2	yes	12
12.11	even	2		592.2.bq.b.321.1		12
37.3	even	18	inner	666.2.bj.c.595.1		12
111.59	even	36		2738.2.a.s.1.1		6
111.77	odd	18		74.2.h.a.3.2	✓	12
111.89	even	36		2738.2.a.r.1.2		6
444.299	even	18		592.2.bq.b.225.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.h.a.3.2	✓	12	111.77	odd	18
74.2.h.a.25.2	yes	12	3.2	odd	2
592.2.bq.b.225.1		12	444.299	even	18
592.2.bq.b.321.1		12	12.11	even	2
666.2.bj.c.469.1		12	1.1	even	1	trivial
666.2.bj.c.595.1		12	37.3	even	18	inner
2738.2.a.r.1.2		6	111.89	even	36
2738.2.a.s.1.1		6	111.59	even	36

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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.bj (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.642788 - 0.766044i) q^{2} +(-0.173648 + 0.984808i) q^{4} +(1.45842 + 4.00698i) q^{5} +(-3.39364 + 1.23518i) q^{7} +(0.866025 - 0.500000i) q^{8} +O(q^{10})\)	\(q+(-0.642788 - 0.766044i) q^{2} +(-0.173648 + 0.984808i) q^{4} +(1.45842 + 4.00698i) q^{5} +(-3.39364 + 1.23518i) q^{7} +(0.866025 - 0.500000i) q^{8} +(2.13207 - 3.69285i) q^{10} +(-1.05840 - 1.83321i) q^{11} +(2.84019 + 0.500802i) q^{13} +(3.12760 + 1.80572i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(-0.0263137 + 0.00463982i) q^{17} +(-2.07522 + 2.47315i) q^{19} +(-4.19936 + 0.740460i) q^{20} +(-0.723990 + 1.98915i) q^{22} +(-2.57421 - 1.48622i) q^{23} +(-10.0987 + 8.47380i) q^{25} +(-1.44200 - 2.49762i) q^{26} +(-0.627119 - 3.55657i) q^{28} +(-4.96493 + 2.86650i) q^{29} -6.76932i q^{31} +(0.342020 + 0.939693i) q^{32} +(0.0204685 + 0.0171751i) q^{34} +(-9.89872 - 11.7968i) q^{35} +(-4.49375 + 4.09954i) q^{37} +3.22847 q^{38} +(3.26652 + 2.74094i) q^{40} +(-0.259000 + 1.46886i) q^{41} +5.53737i q^{43} +(1.98915 - 0.723990i) q^{44} +(0.516159 + 2.92728i) q^{46} +(1.30654 - 2.26300i) q^{47} +(4.62880 - 3.88403i) q^{49} +(12.9826 + 2.28918i) q^{50} +(-0.986387 + 2.71008i) q^{52} +(1.79389 + 0.652924i) q^{53} +(5.80203 - 6.91459i) q^{55} +(-2.32139 + 2.76652i) q^{56} +(5.38726 + 1.96080i) q^{58} +(-1.92380 + 5.28560i) q^{59} +(-5.65366 - 0.996892i) q^{61} +(-5.18560 + 4.35124i) q^{62} +(0.500000 - 0.866025i) q^{64} +(2.13549 + 12.1110i) q^{65} +(-6.50406 + 2.36728i) q^{67} -0.0267197i q^{68} +(-2.67412 + 15.1657i) q^{70} +(7.10830 + 5.96457i) q^{71} +16.2707 q^{73} +(6.02896 + 0.807274i) q^{74} +(-2.07522 - 2.47315i) q^{76} +(5.85619 + 4.91392i) q^{77} +(-0.484006 - 1.32980i) q^{79} -4.26414i q^{80} +(1.29170 - 0.745761i) q^{82} +(0.294580 + 1.67065i) q^{83} +(-0.0569682 - 0.0986718i) q^{85} +(4.24187 - 3.55935i) q^{86} +(-1.83321 - 1.05840i) q^{88} +(-2.82882 + 7.77213i) q^{89} +(-10.2572 + 1.80861i) q^{91} +(1.91065 - 2.27702i) q^{92} +(-2.57339 + 0.453757i) q^{94} +(-12.9364 - 4.70847i) q^{95} +(5.65105 + 3.26264i) q^{97} +(-5.95067 - 1.04926i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{7}+O(q^{10}) \) 12 * q - 12 * q^7	\( 12 q - 12 q^{7} + 6 q^{10} + 6 q^{11} + 6 q^{13} + 18 q^{14} - 18 q^{19} - 18 q^{25} - 12 q^{26} - 6 q^{28} - 18 q^{29} + 12 q^{34} - 18 q^{35} + 30 q^{37} + 24 q^{38} + 12 q^{40} - 24 q^{41} - 6 q^{44} + 30 q^{46} - 6 q^{47} + 12 q^{49} + 36 q^{50} - 12 q^{52} + 12 q^{53} - 18 q^{55} + 6 q^{58} - 36 q^{61} + 6 q^{64} - 36 q^{65} - 30 q^{67} - 12 q^{70} - 12 q^{71} + 48 q^{74} - 18 q^{76} - 12 q^{77} + 6 q^{79} + 48 q^{83} + 18 q^{85} + 36 q^{86} - 36 q^{88} + 18 q^{89} - 6 q^{91} - 18 q^{92} + 36 q^{97} - 36 q^{98}+O(q^{100}) \) 12 * q - 12 * q^7 + 6 * q^10 + 6 * q^11 + 6 * q^13 + 18 * q^14 - 18 * q^19 - 18 * q^25 - 12 * q^26 - 6 * q^28 - 18 * q^29 + 12 * q^34 - 18 * q^35 + 30 * q^37 + 24 * q^38 + 12 * q^40 - 24 * q^41 - 6 * q^44 + 30 * q^46 - 6 * q^47 + 12 * q^49 + 36 * q^50 - 12 * q^52 + 12 * q^53 - 18 * q^55 + 6 * q^58 - 36 * q^61 + 6 * q^64 - 36 * q^65 - 30 * q^67 - 12 * q^70 - 12 * q^71 + 48 * q^74 - 18 * q^76 - 12 * q^77 + 6 * q^79 + 48 * q^83 + 18 * q^85 + 36 * q^86 - 36 * q^88 + 18 * q^89 - 6 * q^91 - 18 * q^92 + 36 * q^97 - 36 * q^98

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