LMFDB - Embedded newform 207.2.i.d.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(55,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("207.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.i (of order $11$, degree $10$, 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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 7 x^{19} + 24 x^{18} - 70 x^{17} + 209 x^{16} - 527 x^{15} + 1115 x^{14} - 2187 x^{13} + \cdots + 529 $ x^20 - 7x^19 + 24x^18 - 70x^17 + 209x^16 - 527x^15 + 1115x^14 - 2187x^13 + 4165x^12 - 7040x^11 + 10649x^10 - 13519x^9 + 15111x^8 - 12101x^7 + 8244x^6 - 2837x^5 + 1859x^4 - 1730x^3 + 1957x^2 - 1656*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 69)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			127.1
Root			$0.124087 + 0.863041i$ of defining polynomial
Character	$\chi$	$=$	207.127
Dual form			207.2.i.d.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19300 + 0.766692i) q^{2} +(0.00459227 - 0.0100557i) q^{4} +(-0.815022 + 0.239312i) q^{5} +(-3.31578 - 3.82661i) q^{7} +(-0.401407 - 2.79185i) q^{8} +O(q^{10})$	\(q+(-1.19300 + 0.766692i) q^{2} +(0.00459227 - 0.0100557i) q^{4} +(-0.815022 + 0.239312i) q^{5} +(-3.31578 - 3.82661i) q^{7} +(-0.401407 - 2.79185i) q^{8} +(0.788839 - 0.910368i) q^{10} +(1.24362 + 0.799227i) q^{11} +(-0.666743 + 0.769463i) q^{13} +(6.88954 + 2.02295i) q^{14} +(2.63384 + 3.03962i) q^{16} +(-2.37590 - 5.20249i) q^{17} +(1.89731 - 4.15452i) q^{19} +(-0.00133636 + 0.00929457i) q^{20} -2.09640 q^{22} +(-4.33154 - 2.05857i) q^{23} +(-3.59928 + 2.31312i) q^{25} +(0.205481 - 1.42915i) q^{26} +(-0.0537061 + 0.0157695i) q^{28} +(1.19571 + 2.61825i) q^{29} +(-0.751167 - 5.22448i) q^{31} +(-0.0600008 - 0.0176178i) q^{32} +(6.82314 + 4.38497i) q^{34} +(3.61819 + 2.32527i) q^{35} +(0.443467 + 0.130214i) q^{37} +(0.921759 + 6.41098i) q^{38} +(0.995278 + 2.17935i) q^{40} +(-6.61755 + 1.94309i) q^{41} +(-0.690297 + 4.80112i) q^{43} +(0.0137478 - 0.00883519i) q^{44} +(6.74580 - 0.865089i) q^{46} -4.11922 q^{47} +(-2.65237 + 18.4477i) q^{49} +(2.52048 - 5.51907i) q^{50} +(0.00467560 + 0.0102381i) q^{52} +(1.84980 + 2.13478i) q^{53} +(-1.20484 - 0.353774i) q^{55} +(-9.35234 + 10.7932i) q^{56} +(-3.43387 - 2.20681i) q^{58} +(1.38652 - 1.60013i) q^{59} +(-1.39065 - 9.67215i) q^{61} +(4.90170 + 5.65687i) q^{62} +(-7.63305 + 2.24127i) q^{64} +(0.359269 - 0.786689i) q^{65} +(-4.61302 + 2.96461i) q^{67} -0.0632253 q^{68} -6.09924 q^{70} +(10.6456 - 6.84151i) q^{71} +(0.730756 - 1.60013i) q^{73} +(-0.628889 + 0.184658i) q^{74} +(-0.0330636 - 0.0381574i) q^{76} +(-1.06524 - 7.40892i) q^{77} +(1.53299 - 1.76917i) q^{79} +(-2.87405 - 1.84704i) q^{80} +(6.40496 - 7.39172i) q^{82} +(15.7737 + 4.63157i) q^{83} +(3.18143 + 3.67156i) q^{85} +(-2.85746 - 6.25696i) q^{86} +(1.73212 - 3.79282i) q^{88} +(-1.44953 + 10.0817i) q^{89} +5.15521 q^{91} +(-0.0405920 + 0.0341030i) q^{92} +(4.91421 - 3.15817i) q^{94} +(-0.552119 + 3.84008i) q^{95} +(10.8134 - 3.17511i) q^{97} +(-10.9794 - 24.0415i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8}+O(q^{10}) $ 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 10 * q^8	$ 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8} - 18 q^{10} + 16 q^{11} + 14 q^{13} + 22 q^{14} - 8 q^{16} - 11 q^{17} - 11 q^{19} - 57 q^{20} + 26 q^{22} - 4 q^{25} + 14 q^{26} - 14 q^{28} - 12 q^{29} + 41 q^{31} + 46 q^{32} - 3 q^{34} + 26 q^{35} - 18 q^{37} - 70 q^{38} - 13 q^{40} - 10 q^{43} + 3 q^{44} - 24 q^{46} - 18 q^{47} - 10 q^{49} - 33 q^{50} + 61 q^{52} + 20 q^{53} - 17 q^{55} - 6 q^{56} - 37 q^{58} - 40 q^{59} - 12 q^{61} + 89 q^{62} - 2 q^{64} + 51 q^{65} - 47 q^{67} + 12 q^{68} + 32 q^{70} + 47 q^{71} + 39 q^{73} + 50 q^{74} - 39 q^{76} - 22 q^{77} - 2 q^{79} - 12 q^{80} + 26 q^{82} + 52 q^{83} + 35 q^{85} - 34 q^{86} + 30 q^{88} - 36 q^{89} + 8 q^{91} + 19 q^{92} + 21 q^{94} - 89 q^{95} - 85 q^{98}+O(q^{100}) $ 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 10 * q^8 - 18 * q^10 + 16 * q^11 + 14 * q^13 + 22 * q^14 - 8 * q^16 - 11 * q^17 - 11 * q^19 - 57 * q^20 + 26 * q^22 - 4 * q^25 + 14 * q^26 - 14 * q^28 - 12 * q^29 + 41 * q^31 + 46 * q^32 - 3 * q^34 + 26 * q^35 - 18 * q^37 - 70 * q^38 - 13 * q^40 - 10 * q^43 + 3 * q^44 - 24 * q^46 - 18 * q^47 - 10 * q^49 - 33 * q^50 + 61 * q^52 + 20 * q^53 - 17 * q^55 - 6 * q^56 - 37 * q^58 - 40 * q^59 - 12 * q^61 + 89 * q^62 - 2 * q^64 + 51 * q^65 - 47 * q^67 + 12 * q^68 + 32 * q^70 + 47 * q^71 + 39 * q^73 + 50 * q^74 - 39 * q^76 - 22 * q^77 - 2 * q^79 - 12 * q^80 + 26 * q^82 + 52 * q^83 + 35 * q^85 - 34 * q^86 + 30 * q^88 - 36 * q^89 + 8 * q^91 + 19 * q^92 + 21 * q^94 - 89 * q^95 - 85 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.19300	+	0.766692i	−0.843575	+	0.542133i	−0.889565	−	0.456809i	$-0.848992\pi$
$2$	−1.19300	+	0.766692i	−0.843575	+	0.542133i	0.0459895	+	0.998942i	$0.485356\pi$
$3$		0			0
$3$		0			0
$4$	0.00459227	−	0.0100557i	0.00229614	−	0.00502784i
$5$	−0.815022	+	0.239312i	−0.364489	+	0.107024i	−0.458848	−	0.888515i	$-0.651738\pi$
$5$	−0.815022	+	0.239312i	−0.364489	+	0.107024i	0.0943595	+	0.995538i	$0.469920\pi$
$6$		0			0
$7$	−3.31578	−	3.82661i	−1.25325	−	1.44632i	−0.846155	−	0.532937i	$-0.821088\pi$
$7$	−3.31578	−	3.82661i	−1.25325	−	1.44632i	−0.407092	−	0.913387i	$-0.633457\pi$
$8$	−0.401407	−	2.79185i	−0.141919	−	0.987067i
$9$		0			0
$10$	0.788839	−	0.910368i	0.249453	−	0.287884i
$11$	1.24362	+	0.799227i	0.374966	+	0.240976i	0.714527	−	0.699608i	$-0.246642\pi$
$11$	1.24362	+	0.799227i	0.374966	+	0.240976i	−0.339561	+	0.940584i	$0.610278\pi$
$12$		0			0
$13$	−0.666743	+	0.769463i	−0.184921	+	0.213411i	−0.840639	−	0.541595i	$-0.817821\pi$
$13$	−0.666743	+	0.769463i	−0.184921	+	0.213411i	0.655718	+	0.755006i	$0.272366\pi$
$14$	6.88954	+	2.02295i	1.84131	+	0.540657i
$15$		0			0
$16$	2.63384	+	3.03962i	0.658460	+	0.759904i
$17$	−2.37590	−	5.20249i	−0.576240	−	1.26179i	−0.943408	−	0.331635i	$-0.892400\pi$
$17$	−2.37590	−	5.20249i	−0.576240	−	1.26179i	0.367168	−	0.930155i	$-0.380327\pi$
$18$		0			0
$19$	1.89731	−	4.15452i	0.435272	−	0.953113i	−0.557170	−	0.830399i	$-0.688113\pi$
$19$	1.89731	−	4.15452i	0.435272	−	0.953113i	0.992442	−	0.122715i	$-0.0391599\pi$
$20$	−0.00133636	+	0.00929457i	−0.000298819	+	0.00207833i
$21$		0			0
$22$	−2.09640			−0.446953
$23$	−4.33154	−	2.05857i	−0.903189	−	0.429242i
$23$	−4.33154	−	2.05857i	−0.903189	−	0.429242i
$24$		0			0
$25$	−3.59928	+	2.31312i	−0.719856	+	0.462623i
$26$	0.205481	−	1.42915i	0.0402982	−	0.280280i
$27$		0			0
$28$	−0.0537061	+	0.0157695i	−0.0101495	+	0.00298016i
$29$	1.19571	+	2.61825i	0.222039	+	0.486197i	0.987566	−	0.157207i	$-0.0502490\pi$
$29$	1.19571	+	2.61825i	0.222039	+	0.486197i	−0.765527	+	0.643404i	$0.777522\pi$
$30$		0			0
$31$	−0.751167	−	5.22448i	−0.134913	−	0.938344i	−0.939021	−	0.343860i	$-0.888265\pi$
$31$	−0.751167	−	5.22448i	−0.134913	−	0.938344i	0.804107	−	0.594484i	$-0.202644\pi$
$32$	−0.0600008	−	0.0176178i	−0.0106067	−	0.00311442i
$33$		0			0
$34$	6.82314	+	4.38497i	1.17016	+	0.752016i
$35$	3.61819	+	2.32527i	0.611585	+	0.393042i
$36$		0			0
$37$	0.443467	+	0.130214i	0.0729056	+	0.0214070i	0.317982	−	0.948097i	$-0.396995\pi$
$37$	0.443467	+	0.130214i	0.0729056	+	0.0214070i	−0.245076	+	0.969504i	$0.578813\pi$
$38$	0.921759	+	6.41098i	0.149529	+	1.04000i
$39$		0			0
$40$	0.995278	+	2.17935i	0.157367	+	0.344586i
$41$	−6.61755	+	1.94309i	−1.03349	+	0.303460i	−0.754128	−	0.656727i	$-0.771940\pi$
$41$	−6.61755	+	1.94309i	−1.03349	+	0.303460i	−0.279360	+	0.960186i	$0.590122\pi$
$42$		0			0
$43$	−0.690297	+	4.80112i	−0.105269	+	0.732164i	0.867001	+	0.498306i	$0.166044\pi$
$43$	−0.690297	+	4.80112i	−0.105269	+	0.732164i	−0.972271	+	0.233859i	$0.924865\pi$
$44$	0.0137478	−	0.00883519i	0.00207256	−	0.00133195i
$45$		0			0
$46$	6.74580	−	0.865089i	0.994615	−	0.127550i
$47$	−4.11922			−0.600850			−0.300425	−	0.953805i	$-0.597129\pi$
$47$	−4.11922			−0.600850			−0.300425	+	0.953805i	$0.597129\pi$
$48$		0			0
$49$	−2.65237	+	18.4477i	−0.378911	+	2.63538i
$50$	2.52048	−	5.51907i	0.356449	−	0.780515i
$51$		0			0
$52$	0.00467560	+	0.0102381i	0.000648389	+	0.00141977i
$53$	1.84980	+	2.13478i	0.254090	+	0.293235i	0.868436	−	0.495801i	$-0.165126\pi$
$53$	1.84980	+	2.13478i	0.254090	+	0.293235i	−0.614346	+	0.789037i	$0.710580\pi$
$54$		0			0
$55$	−1.20484	−	0.353774i	−0.162461	−	0.0477029i
$56$	−9.35234	+	10.7932i	−1.24976	+	1.44230i
$57$		0			0
$58$	−3.43387	−	2.20681i	−0.450889	−	0.289769i
$59$	1.38652	−	1.60013i	0.180510	−	0.208320i	−0.658282	−	0.752771i	$-0.728717\pi$
$59$	1.38652	−	1.60013i	0.180510	−	0.208320i	0.838792	+	0.544452i	$0.183262\pi$
$60$		0			0
$61$	−1.39065	−	9.67215i	−0.178054	−	1.23839i	−0.861259	−	0.508166i	$-0.830324\pi$
$61$	−1.39065	−	9.67215i	−0.178054	−	1.23839i	0.683205	−	0.730226i	$-0.260585\pi$
$62$	4.90170	+	5.65687i	0.622517	+	0.718423i
$63$		0			0
$64$	−7.63305	+	2.24127i	−0.954131	+	0.280158i
$65$	0.359269	−	0.786689i	0.0445618	−	0.0975767i
$66$		0			0
$67$	−4.61302	+	2.96461i	−0.563571	+	0.362185i	−0.791195	−	0.611564i	$-0.790541\pi$
$67$	−4.61302	+	2.96461i	−0.563571	+	0.362185i	0.227624	+	0.973749i	$0.426904\pi$
$68$	−0.0632253			−0.00766719
$69$		0			0
$70$	−6.09924			−0.728999
$71$	10.6456	−	6.84151i	1.26340	−	0.811938i	0.274654	−	0.961543i	$-0.411437\pi$
$71$	10.6456	−	6.84151i	1.26340	−	0.811938i	0.988746	+	0.149606i	$0.0478004\pi$
$72$		0			0
$73$	0.730756	−	1.60013i	0.0855285	−	0.187281i	−0.862035	−	0.506849i	$-0.830810\pi$
$73$	0.730756	−	1.60013i	0.0855285	−	0.187281i	0.947564	+	0.319567i	$0.103538\pi$
$74$	−0.628889	+	0.184658i	−0.0731068	+	0.0214661i
$75$		0			0
$76$	−0.0330636	−	0.0381574i	−0.00379265	−	0.00437695i
$77$	−1.06524	−	7.40892i	−0.121396	−	0.844325i
$78$		0			0
$79$	1.53299	−	1.76917i	0.172475	−	0.199047i	−0.662930	−	0.748681i	$-0.730687\pi$
$79$	1.53299	−	1.76917i	0.172475	−	0.199047i	0.835405	+	0.549634i	$0.185233\pi$
$80$	−2.87405	−	1.84704i	−0.321329	−	0.206506i
$81$		0			0
$82$	6.40496	−	7.39172i	0.707310	−	0.816279i
$83$	15.7737	+	4.63157i	1.73139	+	0.508381i	0.987186	−	0.159576i	$-0.0510128\pi$
$83$	15.7737	+	4.63157i	1.73139	+	0.508381i	0.744200	+	0.667957i	$0.232831\pi$
$84$		0			0
$85$	3.18143	+	3.67156i	0.345074	+	0.398237i
$86$	−2.85746	−	6.25696i	−0.308128	−	0.674706i
$87$		0			0
$88$	1.73212	−	3.79282i	0.184645	−	0.404316i
$89$	−1.44953	+	10.0817i	−0.153650	+	1.06866i	0.756386	+	0.654126i	$0.226963\pi$
$89$	−1.44953	+	10.0817i	−0.153650	+	1.06866i	−0.910035	+	0.414531i	$0.863946\pi$
$90$		0			0
$91$	5.15521			0.540413
$92$	−0.0405920	+	0.0341030i	−0.00423200	+	0.00355549i
$93$		0			0
$94$	4.91421	−	3.15817i	0.506862	−	0.325741i
$95$	−0.552119	+	3.84008i	−0.0566463	+	0.393983i
$96$		0			0
$97$	10.8134	−	3.17511i	1.09794	−	0.322384i	0.317905	−	0.948122i	$-0.397021\pi$
$97$	10.8134	−	3.17511i	1.09794	−	0.322384i	0.780033	+	0.625739i	$0.215202\pi$
$98$	−10.9794	−	24.0415i	−1.10909	−	2.42856i
$99$		0			0
$100$	0.00673107	+	0.0468156i	0.000673107	+	0.00468156i
$101$	−14.5621	−	4.27583i	−1.44899	−	0.425461i	−0.539781	−	0.841806i	$-0.681493\pi$
$101$	−14.5621	−	4.27583i	−1.44899	−	0.425461i	−0.909207	+	0.416344i	$0.863311\pi$
$102$		0			0
$103$	−4.99950	−	3.21299i	−0.492616	−	0.316585i	0.270641	−	0.962680i	$-0.412764\pi$
$103$	−4.99950	−	3.21299i	−0.492616	−	0.316585i	−0.763257	+	0.646095i	$0.776401\pi$
$104$	2.41586	+	1.55258i	0.236894	+	0.152243i
$105$		0			0
$106$	−3.84353	−	1.12856i	−0.373316	−	0.109616i
$107$	−2.71431	−	18.8784i	−0.262402	−	1.82505i	−0.514667	−	0.857390i	$-0.672085\pi$
$107$	−2.71431	−	18.8784i	−0.262402	−	1.82505i	0.252265	−	0.967658i	$-0.418825\pi$
$108$		0			0
$109$	−2.74559	−	6.01201i	−0.262980	−	0.575846i	0.731372	−	0.681979i	$-0.238880\pi$
$109$	−2.74559	−	6.01201i	−0.262980	−	0.575846i	−0.994352	+	0.106133i	$0.966153\pi$
$110$	1.70861	−	0.501693i	0.162909	−	0.0478345i
$111$		0			0
$112$	2.89819	−	20.1574i	0.273854	−	1.90469i
$113$	0.827237	−	0.531633i	0.0778199	−	0.0500118i	−0.501152	−	0.865359i	$-0.667090\pi$
$113$	0.827237	−	0.531633i	0.0778199	−	0.0500118i	0.578972	+	0.815347i	$0.303454\pi$
$114$		0			0
$115$	4.02294	+	0.641192i	0.375141	+	0.0597915i
$116$	0.0318193			0.00295435
$117$		0			0
$118$	−0.427307	+	2.97199i	−0.0393368	+	0.273594i
$119$	−12.0300	+	26.3420i	−1.10279	+	2.41476i
$120$		0			0
$121$	−3.66173	−	8.01808i	−0.332885	−	0.728916i
$122$	9.07460	+	10.4726i	0.821575	+	0.948148i
$123$		0			0
$124$	−0.0559852	−	0.0164387i	−0.00502762	−	0.00147624i
$125$	5.16122	−	5.95637i	0.461634	−	0.532754i
$126$		0			0
$127$	4.50364	+	2.89432i	0.399634	+	0.256829i	0.724986	−	0.688764i	$-0.241846\pi$
$127$	4.50364	+	2.89432i	0.399634	+	0.256829i	−0.325352	+	0.945593i	$0.605483\pi$
$128$	7.46974	−	8.62053i	0.660238	−	0.761955i
$129$		0			0
$130$	0.174542	+	1.21396i	0.0153083	+	0.106472i
$131$	5.98133	+	6.90282i	0.522591	+	0.603102i	0.954278	−	0.298922i	$-0.0966269\pi$
$131$	5.98133	+	6.90282i	0.522591	+	0.603102i	−0.431687	+	0.902024i	$0.642081\pi$
$132$		0			0
$133$	−22.1888	+	6.51522i	−1.92401	+	0.564941i
$134$	3.23037	−	7.07353i	0.279062	−	0.611060i
$135$		0			0
$136$	−13.5709	+	8.72146i	−1.16369	+	0.747859i
$137$	5.65456			0.483102			0.241551	−	0.970388i	$-0.422344\pi$
$137$	5.65456			0.483102			0.241551	+	0.970388i	$0.422344\pi$
$138$		0			0
$139$	15.8561			1.34490			0.672448	−	0.740144i	$-0.265243\pi$
$139$	15.8561			1.34490			0.672448	+	0.740144i	$0.265243\pi$
$140$	0.0399978	−	0.0257050i	0.00338043	−	0.00217247i
$141$		0			0
$142$	−7.45482	+	16.3238i	−0.625594	+	1.36986i
$143$	−1.44415	+	0.424042i	−0.120766	+	0.0354601i
$144$		0			0
$145$	−1.60111	−	1.84778i	−0.132965	−	0.153450i
$146$	0.355020	+	2.46922i	0.0293816	+	0.204354i
$147$		0			0
$148$	0.00334591	−	0.00386139i	0.000275032	−	0.000317404i
$149$	−0.354287	−	0.227686i	−0.0290243	−	0.0186528i	0.526048	−	0.850455i	$-0.323673\pi$
$149$	−0.354287	−	0.227686i	−0.0290243	−	0.0186528i	−0.555073	+	0.831802i	$0.687309\pi$
$150$		0			0
$151$	14.1704	−	16.3535i	1.15317	−	1.33083i	0.218282	−	0.975886i	$-0.429955\pi$
$151$	14.1704	−	16.3535i	1.15317	−	1.33083i	0.934888	−	0.354943i	$-0.115500\pi$
$152$	−12.3604	−	3.62934i	−1.00256	−	0.294378i
$153$		0			0
$154$	6.95119	+	8.02210i	0.560143	+	0.646439i
$155$	1.86250	+	4.07830i	0.149599	+	0.327577i
$156$		0			0
$157$	0.748985	−	1.64005i	0.0597755	−	0.130890i	−0.877387	−	0.479784i	$-0.840715\pi$
$157$	0.748985	−	1.64005i	0.0597755	−	0.130890i	0.937162	+	0.348893i	$0.113442\pi$
$158$	−0.472447	+	3.28594i	−0.0375859	+	0.261415i
$159$		0			0
$160$	0.0531181			0.00419936
$161$	6.48508	+	23.4009i	0.511096	+	1.84425i
$162$		0			0
$163$	−10.3871	+	6.67541i	−0.813584	+	0.522859i	−0.880023	−	0.474932i	$-0.842473\pi$
$163$	−10.3871	+	6.67541i	−0.813584	+	0.522859i	0.0664385	+	0.997791i	$0.478836\pi$
$164$	−0.0108505	+	0.0754671i	−0.000847284	+	0.00589299i
$165$		0			0
$166$	−22.3689	+	6.56810i	−1.73616	+	0.509784i
$167$	−5.59891	−	12.2599i	−0.433257	−	0.948700i	−0.992787	−	0.119890i	$-0.961746\pi$
$167$	−5.59891	−	12.2599i	−0.433257	−	0.948700i	0.559531	−	0.828810i	$-0.310981\pi$
$168$		0			0
$169$	1.70257	+	11.8416i	0.130967	+	0.910893i
$170$	−6.61038	−	1.94098i	−0.506993	−	0.148867i
$171$		0			0
$172$	0.0451085	+	0.0289895i	0.00343949	+	0.00221043i
$173$	2.37257	+	1.52476i	0.180383	+	0.115925i	0.627716	−	0.778442i	$-0.283990\pi$
$173$	2.37257	+	1.52476i	0.180383	+	0.115925i	−0.447333	+	0.894367i	$0.647626\pi$
$174$		0			0
$175$	20.7858	+	6.10326i	1.57126	+	0.461363i
$176$	0.846160	+	5.88517i	0.0637817	+	0.443611i
$177$		0			0
$178$	−6.00027	−	13.1388i	−0.449739	−	0.984791i
$179$	5.30129	−	1.55660i	0.396237	−	0.116346i	−0.0775429	−	0.996989i	$-0.524707\pi$
$179$	5.30129	−	1.55660i	0.396237	−	0.116346i	0.473780	+	0.880643i	$0.342889\pi$
$180$		0			0
$181$	−1.69164	+	11.7656i	−0.125739	+	0.874532i	0.825131	+	0.564941i	$0.191101\pi$
$181$	−1.69164	+	11.7656i	−0.125739	+	0.874532i	−0.950870	+	0.309591i	$0.899808\pi$
$182$	−6.15014	+	3.95246i	−0.455879	+	0.292976i
$183$		0			0
$184$	−4.00851	+	12.9193i	−0.295511	+	0.952426i
$185$	−0.392597			−0.0288643
$186$		0			0
$187$	1.20325	−	8.36881i	0.0879906	−	0.611988i
$188$	−0.0189166	+	0.0414215i	−0.00137963	+	0.00302098i
$189$		0			0
$190$	−2.28548	−	5.00450i	−0.165806	−	0.363064i
$191$	−11.3856	−	13.1397i	−0.823833	−	0.950754i	0.175599	−	0.984462i	$-0.443814\pi$
$191$	−11.3856	−	13.1397i	−0.823833	−	0.950754i	−0.999432	+	0.0337081i	$0.989268\pi$
$192$		0			0
$193$	9.99854	+	2.93584i	0.719711	+	0.211326i	0.621023	−	0.783792i	$-0.286717\pi$
$193$	9.99854	+	2.93584i	0.719711	+	0.211326i	0.0986878	+	0.995118i	$0.468535\pi$
$194$	−10.4661	+	12.0785i	−0.751419	+	0.867183i
$195$		0			0
$196$	0.173323	+	0.111388i	0.0123802	+	0.00795629i
$197$	−6.83086	+	7.88323i	−0.486679	+	0.561657i	−0.944975	−	0.327142i	$-0.893914\pi$
$197$	−6.83086	+	7.88323i	−0.486679	+	0.561657i	0.458296	+	0.888799i	$0.348460\pi$
$198$		0			0
$199$	−0.654831	−	4.55445i	−0.0464197	−	0.322856i	−0.999779	−	0.0210186i	$-0.993309\pi$
$199$	−0.654831	−	4.55445i	−0.0464197	−	0.322856i	0.953359	−	0.301838i	$-0.0976000\pi$
$200$	7.90264	+	9.12013i	0.558801	+	0.644891i
$201$		0			0
$202$	20.6508	−	6.06363i	1.45299	−	0.426635i
$203$	6.05430	−	13.2571i	0.424929	−	0.930464i
$204$		0			0
$205$	4.92845	−	3.16732i	0.344218	−	0.221215i
$206$	8.42776			0.587190
$207$		0			0
$208$	−4.09497			−0.283935
$209$	5.67994	−	3.65028i	0.392890	−	0.252495i
$210$		0			0
$211$	−0.220488	+	0.482801i	−0.0151790	+	0.0332374i	−0.917070	−	0.398727i	$-0.869452\pi$
$211$	−0.220488	+	0.482801i	−0.0151790	+	0.0332374i	0.901891	+	0.431964i	$0.142179\pi$
$212$	0.0299615	−	0.00879748i	0.00205776	−	0.000604214i
$213$		0			0
$214$	17.7121	+	20.4409i	1.21077	+	1.39731i
$215$	−0.586359	−	4.07822i	−0.0399893	−	0.278132i
$216$		0			0
$217$	−17.5014	+	20.1976i	−1.18807	+	1.37111i
$218$	7.88484	+	5.06728i	0.534029	+	0.343199i
$219$		0			0
$220$	−0.00909040	+	0.0104909i	−0.000612875	+	0.000707295i
$221$	5.58724	+	1.64056i	0.375838	+	0.110356i
$222$		0			0
$223$	2.15754	+	2.48993i	0.144479	+	0.166738i	0.823377	−	0.567495i	$-0.192087\pi$
$223$	2.15754	+	2.48993i	0.144479	+	0.166738i	−0.678897	+	0.734233i	$0.737542\pi$
$224$	0.131533	+	0.288017i	0.00878841	+	0.0192439i
$225$		0			0
$226$	−0.579291	+	1.26847i	−0.0385339	+	0.0843774i
$227$	1.85262	−	12.8852i	0.122963	−	0.855224i	−0.831208	−	0.555961i	$-0.812350\pi$
$227$	1.85262	−	12.8852i	0.122963	−	0.855224i	0.954171	−	0.299263i	$-0.0967407\pi$
$228$		0			0
$229$	−4.91857			−0.325028			−0.162514	−	0.986706i	$-0.551960\pi$
$229$	−4.91857			−0.325028			−0.162514	+	0.986706i	$0.551960\pi$
$230$	−5.29095	+	2.31942i	−0.348875	+	0.152938i
$231$		0			0
$232$	6.82978	−	4.38923i	0.448397	−	0.288167i
$233$	−2.36668	+	16.4606i	−0.155047	+	1.07837i	0.752552	+	0.658533i	$0.228823\pi$
$233$	−2.36668	+	16.4606i	−0.155047	+	1.07837i	−0.907598	+	0.419839i	$0.862086\pi$
$234$		0			0
$235$	3.35725	−	0.985779i	0.219003	−	0.0643051i
$236$	−0.00972312	−	0.0212907i	−0.000632921	−	0.00138590i
$237$		0			0
$238$	−5.84446	−	40.6491i	−0.378840	−	2.63489i
$239$	−8.83233	−	2.59341i	−0.571316	−	0.167753i	−0.0167008	−	0.999861i	$-0.505316\pi$
$239$	−8.83233	−	2.59341i	−0.571316	−	0.167753i	−0.554615	+	0.832107i	$0.687134\pi$
$240$		0			0
$241$	2.27184	+	1.46002i	0.146342	+	0.0940482i	0.611763	−	0.791041i	$-0.290461\pi$
$241$	2.27184	+	1.46002i	0.146342	+	0.0940482i	−0.465421	+	0.885089i	$0.654097\pi$
$242$	10.5158	+	6.75811i	0.675983	+	0.434428i
$243$		0			0
$244$	−0.103646	−	0.0304333i	−0.00663527	−	0.00194829i
$245$	−2.25300	−	15.6700i	−0.143939	−	1.00112i
$246$		0			0
$247$	1.93173	+	4.22991i	0.122913	+	0.269143i
$248$	−14.2844	+	4.19428i	−0.907062	+	0.266337i
$249$		0			0
$250$	−1.59062	+	11.0630i	−0.100600	+	0.699685i
$251$	7.62163	−	4.89812i	0.481073	−	0.309167i	−0.277533	−	0.960716i	$-0.589517\pi$
$251$	7.62163	−	4.89812i	0.481073	−	0.309167i	0.758606	+	0.651549i	$0.225881\pi$
$252$		0			0
$253$	−3.74154	−	6.02198i	−0.235228	−	0.378598i
$254$	−7.59188			−0.476357
$255$		0			0
$256$	−0.0377567	+	0.262603i	−0.00235979	+	0.0164127i
$257$	8.48884	−	18.5880i	0.529519	−	1.15949i	−0.436189	−	0.899855i	$-0.643672\pi$
$257$	8.48884	−	18.5880i	0.529519	−	1.15949i	0.965708	−	0.259630i	$-0.0836007\pi$
$258$		0			0
$259$	−0.972162	−	2.12874i	−0.0604072	−	0.132273i
$260$	−0.00626082	−	0.00722537i	−0.000388280	−	0.000448099i
$261$		0			0
$262$	−12.4280	−	3.64920i	−0.767806	−	0.225448i
$263$	−2.03326	+	2.34650i	−0.125376	+	0.144692i	−0.814967	−	0.579508i	$-0.803245\pi$
$263$	−2.03326	+	2.34650i	−0.125376	+	0.144692i	0.689591	+	0.724199i	$0.257790\pi$
$264$		0			0
$265$	−2.01851	−	1.29722i	−0.123996	−	0.0796873i
$266$	21.4760	−	24.7846i	1.31678	−	1.51964i
$267$		0			0
$268$	0.00862689	+	0.0600013i	0.000526971	+	0.00366516i
$269$	2.49938	+	2.88444i	0.152390	+	0.175868i	0.826812	−	0.562479i	$-0.190152\pi$
$269$	2.49938	+	2.88444i	0.152390	+	0.175868i	−0.674421	+	0.738347i	$0.735607\pi$
$270$		0			0
$271$	1.90222	−	0.558543i	0.115552	−	0.0339291i	−0.223445	−	0.974716i	$-0.571730\pi$
$271$	1.90222	−	0.558543i	0.115552	−	0.0339291i	0.338997	+	0.940787i	$0.389912\pi$
$272$	9.55583	−	20.9243i	0.579407	−	1.26872i
$273$		0			0
$274$	−6.74587	+	4.33531i	−0.407533	+	0.261905i
$275$	−6.32485			−0.381403
$276$		0			0
$277$	−14.5994			−0.877195			−0.438598	−	0.898684i	$-0.644525\pi$
$277$	−14.5994			−0.877195			−0.438598	+	0.898684i	$0.644525\pi$
$278$	−18.9163	+	12.1567i	−1.13452	+	0.729113i
$279$		0			0
$280$	5.03943	−	11.0348i	0.301163	−	0.659456i
$281$	−13.8332	+	4.06180i	−0.825221	+	0.242307i	−0.666963	−	0.745091i	$-0.732406\pi$
$281$	−13.8332	+	4.06180i	−0.825221	+	0.242307i	−0.158258	+	0.987398i	$0.550588\pi$
$282$		0			0
$283$	−9.70517	−	11.2004i	−0.576913	−	0.665793i	0.390025	−	0.920804i	$-0.372466\pi$
$283$	−9.70517	−	11.2004i	−0.576913	−	0.665793i	−0.966938	+	0.255011i	$0.917921\pi$
$284$	−0.0199085	−	0.138467i	−0.00118135	−	0.00821648i
$285$		0			0
$286$	1.39776	−	1.61310i	0.0826512	−	0.0953846i
$287$	29.3778	+	18.8800i	1.73412	+	1.11445i
$288$		0			0
$289$	−10.2884	+	11.8734i	−0.605199	+	0.698437i
$290$	3.32680	+	0.976836i	0.195356	+	0.0573618i
$291$		0			0
$292$	−0.0127346	−	0.0146965i	−0.000745235	−	0.000860047i
$293$	4.54987	+	9.96282i	0.265806	+	0.582034i	0.994726	−	0.102564i	$-0.0327047\pi$
$293$	4.54987	+	9.96282i	0.265806	+	0.582034i	−0.728920	+	0.684599i	$0.759977\pi$
$294$		0			0
$295$	−0.747116	+	1.63595i	−0.0434987	+	0.0952490i
$296$	0.185526	−	1.29036i	0.0107835	−	0.0750008i
$297$		0			0
$298$	0.597228			0.0345965
$299$	4.47202	−	1.96042i	0.258624	−	0.113374i
$300$		0			0
$301$	20.6609	−	13.2780i	1.19088	−	0.765329i
$302$	−4.36712	+	30.3740i	−0.251299	+	1.74783i
$303$		0			0
$304$	17.6254	−	5.17527i	1.01088	−	0.296822i
$305$	3.44807	+	7.55022i	0.197436	+	0.432324i
$306$		0			0
$307$	1.79661	+	12.4957i	0.102538	+	0.713166i	0.974630	+	0.223824i	$0.0718539\pi$
$307$	1.79661	+	12.4957i	0.102538	+	0.713166i	−0.872092	+	0.489342i	$0.837237\pi$
$308$	−0.0793936	−	0.0233121i	−0.00452387	−	0.00132833i
$309$		0			0
$310$	−5.34875	−	3.43743i	−0.303789	−	0.195233i
$311$	−24.9256	−	16.0187i	−1.41340	−	0.908336i	−0.413401	−	0.910549i	$-0.635659\pi$
$311$	−24.9256	−	16.0187i	−1.41340	−	0.908336i	−0.999998	+	0.00221286i	$0.999296\pi$
$312$		0			0
$313$	1.44883	+	0.425416i	0.0818929	+	0.0240459i	0.322422	−	0.946596i	$-0.395503\pi$
$313$	1.44883	+	0.425416i	0.0818929	+	0.0240459i	−0.240529	+	0.970642i	$0.577321\pi$
$314$	0.363876	+	2.53081i	0.0205347	+	0.142822i
$315$		0			0
$316$	−0.0107502	−	0.0235398i	−0.000604749	−	0.00132422i
$317$	−12.6824	+	3.72389i	−0.712314	+	0.209154i	−0.617761	−	0.786366i	$-0.711960\pi$
$317$	−12.6824	+	3.72389i	−0.712314	+	0.209154i	−0.0945527	+	0.995520i	$0.530142\pi$
$318$		0			0
$319$	−0.605560	+	4.21176i	−0.0339048	+	0.235813i
$320$	5.68474	−	3.65336i	0.317787	−	0.204229i
$321$		0			0
$322$	−25.6780	−	22.9451i	−1.43098	−	1.27868i
$323$	−26.1217			−1.45345
$324$		0			0
$325$	0.619938	−	4.31176i	0.0343880	−	0.239174i
$326$	7.27384	−	15.9275i	0.402860	−	0.882141i
$327$		0			0
$328$	8.08114	+	17.6952i	0.446206	+	0.977056i
$329$	13.6584	+	15.7627i	0.753014	+	0.869024i
$330$		0			0
$331$	−29.1836	−	8.56908i	−1.60408	−	0.470999i	−0.647399	−	0.762152i	$-0.724143\pi$
$331$	−29.1836	−	8.56908i	−1.60408	−	0.470999i	−0.956677	+	0.291153i	$0.905961\pi$
$332$	0.119011	−	0.137345i	0.00653155	−	0.00753781i
$333$		0			0
$334$	16.0790	+	10.3334i	0.879806	+	0.565417i
$335$	3.05025	−	3.52017i	0.166653	−	0.192328i
$336$		0			0
$337$	−0.133717	−	0.930023i	−0.00728403	−	0.0506616i	0.985855	−	0.167599i	$-0.0536014\pi$
$337$	−0.133717	−	0.930023i	−0.00728403	−	0.0506616i	−0.993139	+	0.116937i	$0.962692\pi$
$338$	−11.1100	−	12.8216i	−0.604305	−	0.697406i
$339$		0			0
$340$	0.0515300	−	0.0151306i	0.00279461	−	0.000820570i
$341$	3.24138	−	7.09763i	0.175531	−	0.384358i
$342$		0			0
$343$	49.5699	−	31.8567i	2.67653	−	1.72010i
$344$	13.6811			0.737635
$345$		0			0
$346$	−3.99948			−0.215013
$347$	−23.4665	+	15.0810i	−1.25975	+	0.809589i	−0.988249	−	0.152850i	$-0.951155\pi$
$347$	−23.4665	+	15.0810i	−1.25975	+	0.809589i	−0.271496	+	0.962439i	$0.587519\pi$
$348$		0			0
$349$	9.10101	−	19.9284i	0.487166	−	1.06674i	−0.493265	−	0.869879i	$-0.664197\pi$
$349$	9.10101	−	19.9284i	0.487166	−	1.06674i	0.980431	−	0.196865i	$-0.0630761\pi$
$350$	−29.4767	+	8.65514i	−1.57560	+	0.462637i
$351$		0			0
$352$	−0.0605377	−	0.0698642i	−0.00322667	−	0.00372378i
$353$	−2.48373	−	17.2747i	−0.132195	−	0.919440i	−0.942684	−	0.333686i	$-0.891708\pi$
$353$	−2.48373	−	17.2747i	−0.132195	−	0.919440i	0.810489	−	0.585754i	$-0.199201\pi$
$354$		0			0
$355$	−7.03913	+	8.12359i	−0.373598	+	0.431156i
$356$	0.0947215	+	0.0608738i	0.00502023	+	0.00322631i
$357$		0			0
$358$	−5.13098	+	5.92147i	−0.271181	+	0.312959i
$359$	15.4036	+	4.52289i	0.812968	+	0.238709i	0.661686	−	0.749781i	$-0.269841\pi$
$359$	15.4036	+	4.52289i	0.812968	+	0.238709i	0.151283	+	0.988491i	$0.451660\pi$
$360$		0			0
$361$	−1.21794	−	1.40557i	−0.0641019	−	0.0739775i
$362$	−7.00249	−	15.3333i	−0.368043	−	0.805901i
$363$		0			0
$364$	0.0236741	−	0.0518391i	0.00124086	−	0.00271711i
$365$	−0.212651	+	1.47902i	−0.0111307	+	0.0774155i
$366$		0			0
$367$	12.0449			0.628736			0.314368	−	0.949301i	$-0.398207\pi$
$367$	12.0449			0.628736			0.314368	+	0.949301i	$0.398207\pi$
$368$	−5.15133	−	18.5882i	−0.268531	−	0.968976i
$369$		0			0
$370$	0.468367	−	0.301001i	0.0243492	−	0.0156483i
$371$	2.03546	−	14.1569i	0.105676	−	0.734992i
$372$		0			0
$373$	−16.2747	+	4.77868i	−0.842671	+	0.247431i	−0.674452	−	0.738319i	$-0.735620\pi$
$373$	−16.2747	+	4.77868i	−0.842671	+	0.247431i	−0.168220	+	0.985750i	$0.553802\pi$
$374$	4.98082	+	10.9065i	0.257552	+	0.563961i
$375$		0			0
$376$	1.65348	+	11.5002i	0.0852719	+	0.593079i
$377$	−2.81188	−	0.825642i	−0.144819	−	0.0425227i
$378$		0			0
$379$	−5.55732	−	3.57147i	−0.285460	−	0.183454i	0.390072	−	0.920784i	$-0.372450\pi$
$379$	−5.55732	−	3.57147i	−0.285460	−	0.183454i	−0.675533	+	0.737330i	$0.736086\pi$
$380$	0.0360790	+	0.0231866i	0.00185082	+	0.00118945i
$381$		0			0
$382$	23.6570	+	6.94634i	1.21040	+	0.355405i
$383$	1.65497	+	11.5106i	0.0845650	+	0.588163i	0.987408	+	0.158193i	$0.0505668\pi$
$383$	1.65497	+	11.5106i	0.0845650	+	0.588163i	−0.902843	+	0.429970i	$0.858524\pi$
$384$		0			0
$385$	2.64124	+	5.78351i	0.134610	+	0.294755i
$386$	−14.1791	+	4.16336i	−0.721697	+	0.211909i
$387$		0			0
$388$	0.0177304	−	0.123317i	0.000900122	−	0.00626049i
$389$	14.0012	−	8.99802i	0.709889	−	0.456218i	−0.135218	−	0.990816i	$-0.543173\pi$
$389$	14.0012	−	8.99802i	0.709889	−	0.456218i	0.845106	+	0.534598i	$0.179537\pi$
$390$		0			0
$391$	−0.418406	+	27.4258i	−0.0211597	+	1.38698i
$392$	52.5677			2.65507
$393$		0			0
$394$	2.10518	−	14.6418i	0.106057	−	0.737645i
$395$	−0.826039	+	1.80877i	−0.0415625	+	0.0910093i
$396$		0			0
$397$	−12.9047	−	28.2572i	−0.647666	−	1.41819i	−0.893582	−	0.448899i	$-0.851816\pi$
$397$	−12.9047	−	28.2572i	−0.647666	−	1.41819i	0.245916	−	0.969291i	$-0.420911\pi$
$398$	4.27307	+	4.93138i	0.214189	+	0.247188i
$399$		0			0
$400$	−16.5109	−	4.84804i	−0.825545	−	0.242402i
$401$	10.6369	−	12.2757i	0.531183	−	0.613018i	−0.425212	−	0.905094i	$-0.639801\pi$
$401$	10.6369	−	12.2757i	0.531183	−	0.613018i	0.956395	+	0.292076i	$0.0943460\pi$
$402$		0			0
$403$	4.52088	+	2.90539i	0.225201	+	0.144728i
$404$	−0.109870	+	0.126796i	−0.00546622	+	0.00630836i
$405$		0			0
$406$	2.94133	+	20.4574i	0.145976	+	1.01528i
$407$	0.447436	+	0.516368i	0.0221786	+	0.0255954i
$408$		0			0
$409$	5.43103	−	1.59469i	0.268547	−	0.0788525i	−0.144687	−	0.989478i	$-0.546217\pi$
$409$	5.43103	−	1.59469i	0.268547	−	0.0788525i	0.413234	+	0.910625i	$0.364399\pi$
$410$	−3.45126	+	7.55720i	−0.170445	+	0.373223i
$411$		0			0
$412$	−0.0552678	+	0.0355185i	−0.00272285	+	0.00174987i
$413$	−10.7205			−0.527521
$414$		0			0
$415$	−13.9643			−0.685479
$416$	0.0535614	−	0.0344218i	0.00262606	−	0.00168767i
$417$		0			0
$418$	−3.97751	+	8.70953i	−0.194546	+	0.425997i
$419$	15.7427	−	4.62248i	0.769083	−	0.225823i	0.126425	−	0.991976i	$-0.459650\pi$
$419$	15.7427	−	4.62248i	0.769083	−	0.225823i	0.642658	+	0.766153i	$0.277832\pi$
$420$		0			0
$421$	−2.07761	−	2.39769i	−0.101256	−	0.116856i	0.702859	−	0.711329i	$-0.251906\pi$
$421$	−2.07761	−	2.39769i	−0.101256	−	0.116856i	−0.804116	+	0.594473i	$0.797361\pi$
$422$	−0.107118	−	0.745025i	−0.00521444	−	0.0362672i
$423$		0			0
$424$	5.21747	−	6.02128i	0.253383	−	0.292419i
$425$	20.5855	+	13.2295i	0.998542	+	0.641724i
$426$		0			0
$427$	−32.4005	+	37.3922i	−1.56797	+	1.80954i
$428$	−0.202300	−	0.0594007i	−0.00977855	−	0.00287124i
$429$		0			0
$430$	3.82626	+	4.41574i	0.184519	+	0.212946i
$431$	10.3239	+	22.6063i	0.497286	+	1.08891i	0.977342	+	0.211667i	$0.0678893\pi$
$431$	10.3239	+	22.6063i	0.497286	+	1.08891i	−0.480055	+	0.877238i	$0.659383\pi$
$432$		0			0
$433$	6.37355	−	13.9561i	0.306293	−	0.670689i	−0.692415	−	0.721499i	$-0.743453\pi$
$433$	6.37355	−	13.9561i	0.306293	−	0.670689i	0.998708	+	0.0508108i	$0.0161805\pi$
$434$	5.39368	−	37.5138i	0.258905	−	1.80072i
$435$		0			0
$436$	−0.0730633			−0.00349910
$437$	−16.7707	+	14.0898i	−0.802250	+	0.674004i
$438$		0			0
$439$	−21.5080	+	13.8224i	−1.02652	+	0.659705i	−0.941618	−	0.336684i	$-0.890695\pi$
$439$	−21.5080	+	13.8224i	−1.02652	+	0.659705i	−0.0849034	+	0.996389i	$0.527058\pi$
$440$	−0.504050	+	3.50575i	−0.0240297	+	0.167130i
$441$		0			0
$442$	−7.92335	+	2.32651i	−0.376876	+	0.110661i
$443$	9.94096	+	21.7677i	0.472309	+	1.03421i	0.984507	+	0.175345i	$0.0561041\pi$
$443$	9.94096	+	21.7677i	0.472309	+	1.03421i	−0.512198	+	0.858867i	$0.671169\pi$
$444$		0			0
$445$	−1.23127	−	8.56369i	−0.0583679	−	0.405958i
$446$	−4.48294	−	1.31631i	−0.212273	−	0.0623291i
$447$		0			0
$448$	33.8860	+	21.7772i	1.60096	+	1.02888i
$449$	−6.80003	−	4.37012i	−0.320913	−	0.206239i	0.370259	−	0.928929i	$-0.379269\pi$
$449$	−6.80003	−	4.37012i	−0.320913	−	0.206239i	−0.691172	+	0.722690i	$0.742905\pi$
$450$		0			0
$451$	−9.78271	−	2.87246i	−0.460650	−	0.135259i
$452$	−0.00154703	−	0.0107598i	−7.27661e−5	−	0.000506099i
$453$		0			0
$454$	7.66885	+	16.7924i	0.359917	+	0.788108i
$455$	−4.20161	+	1.23370i	−0.196974	+	0.0578369i
$456$		0			0
$457$	−3.23464	+	22.4974i	−0.151310	+	1.05238i	0.762717	+	0.646732i	$0.223865\pi$
$457$	−3.23464	+	22.4974i	−0.151310	+	1.05238i	−0.914027	+	0.405653i	$0.867044\pi$
$458$	5.86783	−	3.77102i	0.274186	−	0.176208i
$459$		0			0
$460$	0.0249221	−	0.0375089i	0.00116200	−	0.00174886i
$461$	7.53588			0.350981			0.175490	−	0.984481i	$-0.443849\pi$
$461$	7.53588			0.350981			0.175490	+	0.984481i	$0.443849\pi$
$462$		0			0
$463$	3.26986	−	22.7424i	0.151963	−	1.05693i	−0.760961	−	0.648798i	$-0.775272\pi$
$463$	3.26986	−	22.7424i	0.151963	−	1.05693i	0.912924	−	0.408129i	$-0.133819\pi$
$464$	−4.80915	+	10.5306i	−0.223259	+	0.488869i
$465$		0			0
$466$	−9.79679	−	21.4520i	−0.453828	−	0.993744i
$467$	−7.33848	−	8.46906i	−0.339584	−	0.391901i	0.560112	−	0.828417i	$-0.310758\pi$
$467$	−7.33848	−	8.46906i	−0.339584	−	0.391901i	−0.899697	+	0.436515i	$0.856212\pi$
$468$		0			0
$469$	26.6402	+	7.82226i	1.23013	+	0.361199i
$470$	−3.24940	+	3.75001i	−0.149884	+	0.172975i
$471$		0			0
$472$	−5.02389	−	3.22866i	−0.231243	−	0.148611i
$473$	−4.69566	+	5.41908i	−0.215907	+	0.249170i
$474$		0			0
$475$	2.78096	+	19.3420i	0.127599	+	0.887471i
$476$	0.209641	+	0.241939i	0.00960889	+	0.0110892i
$477$		0			0
$478$	12.5253	−	3.67775i	0.572893	−	0.168216i
$479$	8.61197	−	18.8576i	0.393491	−	0.861625i	−0.604398	−	0.796683i	$-0.706586\pi$
$479$	8.61197	−	18.8576i	0.393491	−	0.861625i	0.997889	−	0.0649427i	$-0.0206865\pi$
$480$		0			0
$481$	−0.395874	+	0.254413i	−0.0180503	+	0.0116002i
$482$	−3.82968			−0.174437
$483$		0			0
$484$	−0.0974428			−0.00442922
$485$	−8.05334	+	5.17557i	−0.365683	+	0.235010i
$486$		0			0
$487$	−10.4365	+	22.8528i	−0.472924	+	1.03556i	0.511425	+	0.859328i	$0.329118\pi$
$487$	−10.4365	+	22.8528i	−0.472924	+	1.03556i	−0.984349	+	0.176231i	$0.943609\pi$
$488$	−26.4450	+	7.76494i	−1.19711	+	0.351502i
$489$		0			0
$490$	14.7019	+	16.9669i	0.664163	+	0.766485i
$491$	2.46426	+	17.1393i	0.111211	+	0.773486i	0.966745	+	0.255741i	$0.0823194\pi$
$491$	2.46426	+	17.1393i	0.111211	+	0.773486i	−0.855535	+	0.517745i	$0.826771\pi$
$492$		0			0
$493$	10.7805	−	12.4414i	0.485530	−	0.560332i
$494$	−5.54759	−	3.56522i	−0.249598	−	0.160407i
$495$		0			0
$496$	13.9019	−	16.0437i	0.624216	−	0.720384i
$497$	−61.4782	−	18.0516i	−2.75768	−	0.809727i
$498$		0			0
$499$	−25.3979	−	29.3107i	−1.13697	−	1.31213i	−0.943632	−	0.330996i	$-0.892615\pi$
$499$	−25.3979	−	29.3107i	−1.13697	−	1.31213i	−0.193334	−	0.981133i	$-0.561930\pi$
$500$	−0.0361936	−	0.0792528i	−0.00161862	−	0.00354429i
$501$		0			0
$502$	−5.33722	+	11.6869i	−0.238212	+	0.521611i
$503$	−2.39704	+	16.6718i	−0.106879	+	0.743357i	0.863949	+	0.503579i	$0.167984\pi$
$503$	−2.39704	+	16.6718i	−0.106879	+	0.743357i	−0.970828	+	0.239778i	$0.922925\pi$
$504$		0			0
$505$	12.8917			0.573674
$506$	9.08064	+	4.31559i	0.403683	+	0.191851i
$507$		0			0
$508$	0.0497862	−	0.0319957i	0.00220891	−	0.00141958i
$509$	3.46573	−	24.1047i	0.153616	−	1.06842i	−0.756478	−	0.654020i	$-0.773081\pi$
$509$	3.46573	−	24.1047i	0.153616	−	1.06842i	0.910094	−	0.414403i	$-0.136010\pi$
$510$		0			0
$511$	−8.54612	+	2.50937i	−0.378058	+	0.111008i
$512$	9.32066	+	20.4094i	0.411919	+	0.901976i
$513$		0			0
$514$	4.12409	+	28.6837i	0.181906	+	1.26518i
$515$	4.84361	+	1.42221i	0.213435	+	0.0626702i
$516$		0			0
$517$	−5.12275	−	3.29219i	−0.225299	−	0.144791i
$518$	2.79187	+	1.79423i	0.122668	+	0.0788338i
$519$		0			0
$520$	−2.34053	−	0.687241i	−0.102639	−	0.0301375i
$521$	3.92388	+	27.2912i	0.171908	+	1.19565i	0.874848	+	0.484398i	$0.160961\pi$
$521$	3.92388	+	27.2912i	0.171908	+	1.19565i	−0.702940	+	0.711249i	$0.748130\pi$
$522$		0			0
$523$	−8.81501	−	19.3022i	−0.385454	−	0.844026i	−0.998540	−	0.0540101i	$-0.982800\pi$
$523$	−8.81501	−	19.3022i	−0.385454	−	0.844026i	0.613087	−	0.790016i	$-0.289928\pi$
$524$	0.0968803	−	0.0284466i	0.00423224	−	0.00124270i
$525$		0			0
$526$	0.626622	−	4.35825i	0.0273220	−	0.190029i
$527$	−25.3956	+	16.3208i	−1.10625	+	0.710944i
$528$		0			0
$529$	14.5245	+	17.8336i	0.631502	+	0.775374i
$530$	3.40264			0.147801
$531$		0			0
$532$	−0.0363821	+	0.253043i	−0.00157736	+	0.0109708i
$533$	2.91708	−	6.38750i	0.126353	−	0.276673i
$534$		0			0
$535$	6.73006	+	14.7368i	0.290966	+	0.637126i
$536$	10.1284	+	11.6888i	0.437482	+	0.504881i
$537$		0			0
$538$	−5.19323	−	1.52487i	−0.223896	−	0.0657418i
$539$	−18.0424	+	20.8221i	−0.777143	+	0.896870i
$540$		0			0
$541$	10.7003	+	6.87668i	0.460043	+	0.295652i	0.750060	−	0.661370i	$-0.230025\pi$
$541$	10.7003	+	6.87668i	0.460043	+	0.295652i	−0.290017	+	0.957022i	$0.593661\pi$
$542$	−1.84111	+	2.12476i	−0.0790826	+	0.0912661i
$543$		0			0
$544$	0.0508992	+	0.354012i	0.00218229	+	0.0151781i
$545$	3.67646	+	4.24287i	0.157482	+	0.181744i
$546$		0			0
$547$	24.5840	−	7.21851i	1.05114	−	0.308641i	0.289860	−	0.957069i	$-0.406391\pi$
$547$	24.5840	−	7.21851i	1.05114	−	0.308641i	0.761276	+	0.648428i	$0.224573\pi$
$548$	0.0259673	−	0.0568604i	0.00110927	−	0.00242896i
$549$		0			0
$550$	7.54551	−	4.84921i	0.321742	−	0.206771i
$551$	13.1462			0.560047
$552$		0			0
$553$	−11.8530			−0.504040
$554$	17.4171	−	11.1933i	0.739980	−	0.475556i
$555$		0			0
$556$	0.0728155	−	0.159444i	0.00308806	−	0.00676192i
$557$	31.1901	−	9.15824i	1.32157	−	0.388047i	0.456509	−	0.889719i	$-0.349100\pi$
$557$	31.1901	−	9.15824i	1.32157	−	0.388047i	0.865058	+	0.501672i	$0.167281\pi$
$558$		0			0
$559$	−3.23404	−	3.73228i	−0.136785	−	0.157858i
$560$	2.46181	+	17.1223i	0.104031	+	0.723548i
$561$		0			0
$562$	13.3888	−	15.4515i	0.564774	−	0.651784i
$563$	−25.9719	−	16.6911i	−1.09458	−	0.703446i	−0.136703	−	0.990612i	$-0.543650\pi$
$563$	−25.9719	−	16.6911i	−1.09458	−	0.703446i	−0.957881	+	0.287166i	$0.907287\pi$
$564$		0			0
$565$	−0.546990	+	0.631260i	−0.0230120	+	0.0265573i
$566$	20.1655	+	5.92111i	0.847618	+	0.248883i
$567$		0			0
$568$	−23.3737	−	26.9746i	−0.980737	−	1.13183i
$569$	−9.52698	−	20.8612i	−0.399392	−	0.874546i	−0.997332	−	0.0730050i	$-0.976741\pi$
$569$	−9.52698	−	20.8612i	−0.399392	−	0.874546i	0.597940	−	0.801541i	$-0.295986\pi$
$570$		0			0
$571$	5.27646	−	11.5538i	0.220813	−	0.483513i	−0.766511	−	0.642231i	$-0.778009\pi$
$571$	5.27646	−	11.5538i	0.220813	−	0.483513i	0.987324	+	0.158718i	$0.0507362\pi$
$572$	−0.00236792	+	0.0164692i	−9.90077e−5	+	0.000688613i
$573$		0			0
$574$	−49.5227			−2.06704
$575$	20.3521	−	2.60998i	0.848743	−	0.108844i
$576$		0			0
$577$	9.24594	−	5.94200i	0.384913	−	0.247369i	−0.333846	−	0.942628i	$-0.608347\pi$
$577$	9.24594	−	5.94200i	0.384913	−	0.247369i	0.718760	+	0.695259i	$0.244710\pi$
$578$	3.17074	−	22.0530i	0.131885	−	0.917282i
$579$		0			0
$580$	−0.0259334	+	0.00761474i	−0.00107683	+	0.000316185i
$581$	−34.5788	−	75.7170i	−1.43457	−	3.14127i
$582$		0			0
$583$	0.594276	+	4.13328i	0.0246124	+	0.171183i
$584$	−4.76066	−	1.39786i	−0.196997	−	0.0578437i
$585$		0			0
$586$	−13.0664	−	8.39726i	−0.539768	−	0.346888i
$587$	17.4816	+	11.2348i	0.721544	+	0.463708i	0.849174	−	0.528114i	$-0.177101\pi$
$587$	17.4816	+	11.2348i	0.721544	+	0.463708i	−0.127630	+	0.991822i	$0.540737\pi$
$588$		0			0
$589$	−23.1304	−	6.79170i	−0.953072	−	0.279847i
$590$	−0.362967	−	2.52449i	−0.0149431	−	0.103932i
$591$		0			0
$592$	0.772223	+	1.69093i	0.0317382	+	0.0694969i
$593$	30.3177	−	8.90209i	1.24500	−	0.365565i	0.408109	−	0.912933i	$-0.366188\pi$
$593$	30.3177	−	8.90209i	1.24500	−	0.365565i	0.836892	+	0.547368i	$0.184370\pi$
$594$		0			0
$595$	3.50074	−	24.3482i	0.143516	−	0.998178i
$596$	−0.00391652	+	0.00251699i	−0.000160427	+	0.000103100i
$597$		0			0
$598$	−3.83207	+	5.76744i	−0.156705	+	0.235848i
$599$	−21.9650			−0.897466			−0.448733	−	0.893666i	$-0.648125\pi$
$599$	−21.9650			−0.897466			−0.448733	+	0.893666i	$0.648125\pi$
$600$		0			0
$601$	3.04007	−	21.1441i	0.124007	−	0.862487i	−0.828937	−	0.559342i	$-0.811054\pi$
$601$	3.04007	−	21.1441i	0.124007	−	0.862487i	0.952944	−	0.303146i	$-0.0980369\pi$
$602$	−14.4683	+	31.6811i	−0.589683	+	1.29123i
$603$		0			0
$604$	−0.0993711	−	0.217592i	−0.00404335	−	0.00885371i
$605$	4.90321	+	5.65861i	0.199344	+	0.230055i
$606$		0			0
$607$	5.65071	+	1.65920i	0.229355	+	0.0673448i	0.394391	−	0.918943i	$-0.370956\pi$
$607$	5.65071	+	1.65920i	0.229355	+	0.0673448i	−0.165035	+	0.986288i	$0.552774\pi$
$608$	−0.187034	+	0.215848i	−0.00758522	+	0.00875381i
$609$		0			0
$610$	−9.90222	−	6.36377i	−0.400929	−	0.257662i
$611$	2.74646	−	3.16959i	0.111110	−	0.128228i
$612$		0			0
$613$	−0.720390	−	5.01042i	−0.0290963	−	0.202369i	0.970088	−	0.242754i	$-0.0780507\pi$
$613$	−0.720390	−	5.01042i	−0.0290963	−	0.202369i	−0.999184	+	0.0403847i	$0.987142\pi$
$614$	−11.7237	−	13.5298i	−0.473129	−	0.546020i
$615$		0			0
$616$	−20.2570	+	5.94799i	−0.816177	+	0.239651i
$617$	3.34228	−	7.31857i	0.134555	−	0.294634i	−0.830346	−	0.557248i	$-0.811857\pi$
$617$	3.34228	−	7.31857i	0.134555	−	0.294634i	0.964901	+	0.262614i	$0.0845845\pi$
$618$		0			0
$619$	−6.01077	+	3.86289i	−0.241593	+	0.155263i	−0.655835	−	0.754904i	$-0.727683\pi$
$619$	−6.01077	+	3.86289i	−0.241593	+	0.155263i	0.414242	+	0.910167i	$0.364047\pi$
$620$	0.0495631			0.00199050
$621$		0			0
$622$	42.0175			1.68475
$623$	43.3850	−	27.8819i	1.73819	−	1.11706i
$624$		0			0
$625$	6.10562	−	13.3695i	0.244225	−	0.534778i
$626$	−2.05461	+	0.603289i	−0.0821189	+	0.0241123i
$627$		0			0
$628$	−0.0130522	−	0.0150631i	−0.000520841	−	0.000601083i
$629$	−0.376197	−	2.61651i	−0.0150000	−	0.104327i
$630$		0			0
$631$	−25.0399	+	28.8976i	−0.996823	+	1.15040i	−0.00820264	+	0.999966i	$0.502611\pi$
$631$	−25.0399	+	28.8976i	−0.996823	+	1.15040i	−0.988621	+	0.150429i	$0.951934\pi$
$632$	−5.55460	−	3.56972i	−0.220950	−	0.141996i
$633$		0			0
$634$	12.2750	−	14.1661i	0.487501	−	0.562606i
$635$	−4.36321	−	1.28115i	−0.173149	−	0.0508411i
$636$		0			0
$637$	−12.4263	−	14.3408i	−0.492350	−	0.568202i
$638$	−2.50669	−	5.48889i	−0.0992409	−	0.217307i
$639$		0			0
$640$	−4.02500	+	8.81352i	−0.159102	+	0.348385i
$641$	−4.60792	+	32.0488i	−0.182002	+	1.26585i	0.670020	+	0.742343i	$0.266286\pi$
$641$	−4.60792	+	32.0488i	−0.182002	+	1.26585i	−0.852021	+	0.523507i	$0.824623\pi$
$642$		0			0
$643$	35.7909			1.41146			0.705728	−	0.708483i	$-0.250620\pi$
$643$	35.7909			1.41146			0.705728	+	0.708483i	$0.250620\pi$
$644$	0.265093	+	0.0422516i	0.0104461	+	0.00166495i
$645$		0			0
$646$	31.1630	−	20.0273i	1.22609	−	0.787962i
$647$	−0.635729	+	4.42159i	−0.0249931	+	0.173831i	−0.998495	−	0.0548497i	$-0.982532\pi$
$647$	−0.635729	+	4.42159i	−0.0249931	+	0.173831i	0.973502	+	0.228681i	$0.0734411\pi$
$648$		0			0
$649$	3.00318	−	0.881814i	0.117885	−	0.0346142i
$650$	2.56621	+	5.61922i	0.100655	+	0.220404i
$651$		0			0
$652$	0.0194252	+	0.135105i	0.000760748	+	0.00529112i
$653$	20.4224	+	5.99656i	0.799191	+	0.234664i	0.655733	−	0.754993i	$-0.272360\pi$
$653$	20.4224	+	5.99656i	0.799191	+	0.234664i	0.143458	+	0.989656i	$0.454178\pi$
$654$		0			0
$655$	−6.52684	−	4.19454i	−0.255025	−	0.163894i
$656$	−23.3358	−	14.9970i	−0.911111	−	0.585536i
$657$		0			0
$658$	−28.3796	−	8.33299i	−1.10635	−	0.324854i
$659$	−6.55101	−	45.5632i	−0.255191	−	1.77489i	−0.565986	−	0.824415i	$-0.691504\pi$
$659$	−6.55101	−	45.5632i	−0.255191	−	1.77489i	0.310795	−	0.950477i	$-0.399405\pi$
$660$		0			0
$661$	13.7426	+	30.0922i	0.534527	+	1.17045i	0.963641	+	0.267200i	$0.0860986\pi$
$661$	13.7426	+	30.0922i	0.534527	+	1.17045i	−0.429114	+	0.903250i	$0.641174\pi$
$662$	41.3857	−	12.1519i	1.60850	−	0.472299i
$663$		0			0
$664$	6.59897	−	45.8968i	0.256090	−	1.78114i
$665$	16.5252	−	10.6201i	0.640819	−	0.411830i
$666$		0			0
$667$	0.210571	−	13.8025i	0.00815333	−	0.534436i
$668$	−0.148993			−0.00576472
$669$		0			0
$670$	−0.940044	+	6.53815i	−0.0363171	+	0.252591i
$671$	6.00081	−	13.1399i	0.231659	−	0.507262i
$672$		0			0
$673$	17.1613	+	37.5779i	0.661518	+	1.44852i	0.881101	+	0.472928i	$0.156803\pi$
$673$	17.1613	+	37.5779i	0.661518	+	1.44852i	−0.219583	+	0.975594i	$0.570470\pi$
$674$	0.872565	+	1.00699i	0.0336099	+	0.0387879i
$675$		0			0
$676$	0.126894	+	0.0372594i	0.00488054	+	0.00143306i
$677$	19.6629	−	22.6922i	0.755707	−	0.872132i	−0.239402	−	0.970921i	$-0.576951\pi$
$677$	19.6629	−	22.6922i	0.755707	−	0.872132i	0.995108	+	0.0987884i	$0.0314967\pi$
$678$		0			0
$679$	−48.0049	−	30.8509i	−1.84226	−	1.18395i
$680$	8.97339	−	10.3558i	0.344114	−	0.397129i
$681$		0			0
$682$	1.57474	+	10.9526i	0.0603000	+	0.419396i
$683$	−26.4965	−	30.5786i	−1.01386	−	1.17006i	−0.985364	−	0.170464i	$-0.945473\pi$
$683$	−26.4965	−	30.5786i	−1.01386	−	1.17006i	−0.0284968	−	0.999594i	$-0.509072\pi$
$684$		0			0
$685$	−4.60859	+	1.35320i	−0.176085	+	0.0517033i
$686$	−34.7125	+	76.0097i	−1.32533	+	2.90206i
$687$		0			0
$688$	−16.4117	+	10.5472i	−0.625690	+	0.402107i
$689$	−2.87598			−0.109566
$690$		0			0
$691$	3.24119			0.123301			0.0616503	−	0.998098i	$-0.480364\pi$
$691$	3.24119			0.123301			0.0616503	+	0.998098i	$0.480364\pi$
$692$	0.0262279	−	0.0168556i	0.000997035	−	0.000640756i
$693$		0			0
$694$	16.4329	−	35.9831i	0.623785	−	1.36590i
$695$	−12.9231	+	3.79455i	−0.490200	+	0.143936i
$696$		0			0
$697$	25.8315	+	29.8112i	0.978439	+	1.12918i
$698$	4.42150	+	30.7522i	0.167356	+	1.16399i
$699$		0			0
$700$	0.156826	−	0.180987i	0.00592748	−	0.00684068i
$701$	−25.0443	−	16.0950i	−0.945909	−	0.607899i	−0.0258443	−	0.999666i	$-0.508227\pi$
$701$	−25.0443	−	16.0950i	−0.945909	−	0.607899i	−0.920064	+	0.391767i	$0.871864\pi$
$702$		0			0
$703$	1.38237	−	1.59534i	0.0521371	−	0.0601694i
$704$	−11.2839	−	3.31325i	−0.425278	−	0.124873i
$705$		0			0
$706$	16.2074	+	18.7044i	0.609975	+	0.703949i
$707$	31.9229	+	69.9014i	1.20058	+	2.62891i
$708$		0			0
$709$	13.2698	−	29.0568i	0.498357	−	1.09125i	−0.478643	−	0.878010i	$-0.658871\pi$
$709$	13.2698	−	29.0568i	0.498357	−	1.09125i	0.977000	−	0.213240i	$-0.0684016\pi$
$710$	2.16936	−	15.0883i	0.0814148	−	0.566252i
$711$		0			0
$712$	28.7284			1.07664
$713$	−7.50126	+	24.1764i	−0.280925	+	0.905413i
$714$		0			0
$715$	1.07554	−	0.691206i	0.0402228	−	0.0258496i
$716$	0.00869230	−	0.0604563i	0.000324847	−	0.00225936i
$717$		0			0
$718$	−21.8440	+	6.41399i	−0.815212	+	0.239368i
$719$	4.83459	+	10.5863i	0.180300	+	0.394801i	0.978104	−	0.208115i	$-0.0667327\pi$
$719$	4.83459	+	10.5863i	0.180300	+	0.394801i	−0.797805	+	0.602916i	$0.794005\pi$
$720$		0			0
$721$	4.28240	+	29.7847i	0.159485	+	1.10924i
$722$	2.53063	+	0.743061i	0.0941804	+	0.0276539i
$723$		0			0
$724$	0.110543	+	0.0710416i	0.00410829	+	0.00264024i
$725$	−10.3600	−	6.65798i	−0.384761	−	0.247271i
$726$		0			0
$727$	−34.5960	−	10.1583i	−1.28309	−	0.376751i	−0.432053	−	0.901848i	$-0.642211\pi$
$727$	−34.5960	−	10.1583i	−1.28309	−	0.376751i	−0.851042	+	0.525098i	$0.824029\pi$
$728$	−2.06934	−	14.3926i	−0.0766948	−	0.533424i
$729$		0			0
$730$	−0.880262	−	1.92750i	−0.0325799	−	0.0713401i
$731$	26.6179	−	7.81571i	0.984498	−	0.289075i
$732$		0			0
$733$	−0.233177	+	1.62178i	−0.00861260	+	0.0599019i	−0.993674	−	0.112299i	$-0.964179\pi$
$733$	−0.233177	+	1.62178i	−0.00861260	+	0.0599019i	0.985062	+	0.172201i	$0.0550877\pi$
$734$	−14.3695	+	9.23469i	−0.530387	+	0.340859i
$735$		0			0
$736$	0.223629	+	0.199829i	0.00824306	+	0.00736578i
$737$	−8.10626			−0.298598
$738$		0			0
$739$	−5.12916	+	35.6741i	−0.188679	+	1.31229i	0.646753	+	0.762700i	$0.276127\pi$
$739$	−5.12916	+	35.6741i	−0.188679	+	1.31229i	−0.835432	+	0.549594i	$0.814782\pi$
$740$	−0.00180291	+	0.00394783i	−6.62764e−5	+	0.000145125i
$741$		0			0
$742$	8.42572	+	18.4497i	0.309318	+	0.677312i
$743$	−17.4000	−	20.0806i	−0.638343	−	0.736687i	0.340738	−	0.940158i	$-0.389323\pi$
$743$	−17.4000	−	20.0806i	−0.638343	−	0.736687i	−0.979081	+	0.203471i	$0.934778\pi$
$744$		0			0
$745$	0.343239	+	0.100784i	0.0125753	+	0.00369245i
$746$	15.7519	−	18.1786i	0.576716	−	0.665566i
$747$		0			0
$748$	−0.0786284	−	0.0505314i	−0.00287494	−	0.00184761i
$749$	−63.2405	+	72.9834i	−2.31076	+	2.66675i
$750$		0			0
$751$	−4.41579	−	30.7125i	−0.161134	−	1.12071i	−0.896500	−	0.443044i	$-0.853899\pi$
$751$	−4.41579	−	30.7125i	−0.161134	−	1.12071i	0.735366	−	0.677671i	$-0.237010\pi$
$752$	−10.8494	−	12.5208i	−0.395636	−	0.456588i
$753$		0			0
$754$	3.98757	−	1.17086i	0.145219	−	0.0426401i
$755$	−7.63559	+	16.7196i	−0.277887	+	0.608489i
$756$		0			0
$757$	−9.14398	+	5.87648i	−0.332344	+	0.213584i	−0.696160	−	0.717886i	$-0.745110\pi$
$757$	−9.14398	+	5.87648i	−0.332344	+	0.213584i	0.363817	+	0.931471i	$0.381473\pi$
$758$	9.36808			0.340264
$759$		0			0
$760$	10.9425			0.396927
$761$	−14.3975	+	9.25274i	−0.521911	+	0.335412i	−0.774927	−	0.632050i	$-0.782214\pi$
$761$	−14.3975	+	9.25274i	−0.521911	+	0.335412i	0.253017	+	0.967462i	$0.418577\pi$
$762$		0			0
$763$	−13.9019	+	30.4408i	−0.503281	+	1.10203i
$764$	−0.184414	+	0.0541488i	−0.00667186	+	0.00195904i
$765$		0			0
$766$	−10.7994	−	12.4632i	−0.390199	−	0.450314i
$767$	0.306788	+	2.13376i	0.0110775	+	0.0770455i
$768$		0			0
$769$	18.3252	−	21.1484i	0.660823	−	0.762630i	−0.322088	−	0.946710i	$-0.604385\pi$
$769$	18.3252	−	21.1484i	0.660823	−	0.762630i	0.982911	+	0.184079i	$0.0589303\pi$
$770$	−7.58516	−	4.87468i	−0.273350	−	0.175671i
$771$		0			0
$772$	0.0754378	−	0.0870599i	0.00271507	−	0.00313335i
$773$	10.3412	+	3.03645i	0.371947	+	0.109213i	0.462363	−	0.886691i	$-0.347002\pi$
$773$	10.3412	+	3.03645i	0.371947	+	0.109213i	−0.0904164	+	0.995904i	$0.528820\pi$
$774$		0			0
$775$	14.7885	+	17.0668i	0.531218	+	0.613058i
$776$	−13.2050	−	28.9149i	−0.474032	−	1.03799i
$777$		0			0
$778$	−9.80465	+	21.4692i	−0.351514	+	0.769708i
$779$	−4.48292	+	31.1794i	−0.160617	+	1.11712i
$780$		0			0
$781$	18.7070			0.669390
$782$	−20.5280	−	33.0396i	−0.734078	−	1.18149i
$783$		0			0
$784$	−63.0597	+	40.5260i	−2.25213	+	1.44736i
$785$	−0.217956	+	1.51592i	−0.00777918	+	0.0541054i
$786$		0			0
$787$	31.6859	−	9.30382i	1.12948	−	0.331646i	0.336977	−	0.941513i	$-0.390595\pi$
$787$	31.6859	−	9.30382i	1.12948	−	0.331646i	0.792504	+	0.609867i	$0.208777\pi$
$788$	0.0479020	+	0.104891i	0.00170644	+	0.00373658i
$789$		0			0
$790$	−0.401311	−	2.79118i	−0.0142780	−	0.0993056i
$791$	−4.77729	−	1.40274i	−0.169861	−	0.0498756i
$792$		0			0
$793$	8.36957	+	5.37879i	0.297212	+	0.191007i
$794$	37.0598	+	23.8169i	1.31520	+	0.845229i
$795$		0			0
$796$	−0.0488052	−	0.0143305i	−0.00172985	−	0.000507931i
$797$	7.33853	+	51.0406i	0.259944	+	1.80795i	0.533177	+	0.846004i	$0.320998\pi$
$797$	7.33853	+	51.0406i	0.259944	+	1.80795i	−0.273233	+	0.961948i	$0.588093\pi$
$798$		0			0
$799$	9.78685	+	21.4302i	0.346234	+	0.758146i
$800$	0.256712	−	0.0753773i	0.00907613	−	0.00266499i
$801$		0			0
$802$	−3.27815	+	22.8001i	−0.115756	+	0.805098i
$803$	2.18765	−	1.40592i	0.0772007	−	0.0496139i
$804$		0			0
$805$	−10.8856	−	17.5203i	−0.383667	−	0.617510i
$806$	−7.62093			−0.268436
$807$		0			0
$808$	−6.09212	+	42.3716i	−0.214320	+	1.49063i
$809$	2.73121	−	5.98051i	0.0960241	−	0.210263i	−0.855524	−	0.517763i	$-0.826765\pi$
$809$	2.73121	−	5.98051i	0.0960241	−	0.210263i	0.951548	+	0.307499i	$0.0994922\pi$
$810$		0			0
$811$	3.36425	+	7.36668i	0.118135	+	0.258679i	0.959457	−	0.281855i	$-0.0909496\pi$
$811$	3.36425	+	7.36668i	0.118135	+	0.258679i	−0.841322	+	0.540534i	$0.818222\pi$
$812$	−0.105506	−	0.121760i	−0.00370253	−	0.00427294i
$813$		0			0
$814$	−0.929684	−	0.272980i	−0.0325854	−	0.00956794i
$815$	6.86824	−	7.92638i	0.240584	−	0.277649i
$816$		0			0
$817$	18.6367	+	11.9771i	0.652015	+	0.419024i
$818$	−5.25655	+	6.06639i	−0.183791	+	0.212106i
$819$		0			0
$820$	−0.00921676	−	0.0641040i	−0.000321863	−	0.00223861i
$821$	34.3452	+	39.6365i	1.19866	+	1.38332i	0.903897	+	0.427751i	$0.140694\pi$
$821$	34.3452	+	39.6365i	1.19866	+	1.38332i	0.294759	+	0.955572i	$0.404761\pi$
$822$		0			0
$823$	−7.33469	+	2.15366i	−0.255671	+	0.0750718i	−0.407056	−	0.913403i	$-0.633445\pi$
$823$	−7.33469	+	2.15366i	−0.255671	+	0.0750718i	0.151385	+	0.988475i	$0.451627\pi$
$824$	−6.96333	+	15.2476i	−0.242579	+	0.531174i
$825$		0			0
$826$	12.7895	−	8.21932i	0.445004	−	0.285987i
$827$	10.4045			0.361800			0.180900	−	0.983501i	$-0.442099\pi$
$827$	10.4045			0.361800			0.180900	+	0.983501i	$0.442099\pi$
$828$		0			0
$829$	35.0711			1.21807			0.609035	−	0.793144i	$-0.291557\pi$
$829$	35.0711			1.21807			0.609035	+	0.793144i	$0.291557\pi$
$830$	16.6593	−	10.7063i	0.578253	−	0.371621i
$831$		0			0
$832$	3.36471	−	7.36770i	0.116650	−	0.255429i
$833$	102.276	−	30.0308i	3.54364	−	1.04051i
$834$		0			0
$835$	7.49717	+	8.65220i	0.259450	+	0.299422i
$836$	−0.0106222	−	0.0738787i	−0.000367375	−	0.00255515i
$837$		0			0
$838$	−15.2370	+	17.5844i	−0.526353	+	0.607444i
$839$	−13.9538	−	8.96757i	−0.481739	−	0.309595i	0.277137	−	0.960831i	$-0.410615\pi$
$839$	−13.9538	−	8.96757i	−0.481739	−	0.309595i	−0.758875	+	0.651236i	$0.774251\pi$
$840$		0			0
$841$	13.5655	−	15.6554i	0.467775	−	0.539841i
$842$	4.31686	+	1.26754i	0.148769	+	0.0436825i
$843$		0			0
$844$	0.00384234	+	0.00443430i	0.000132259	+	0.000152635i
$845$	−4.22147	−	9.24372i	−0.145223	−	0.317994i
$846$		0			0
$847$	−18.5406	+	40.5982i	−0.637062	+	1.39497i
$848$	−1.61684	+	11.2454i	−0.0555225	+	0.386167i
$849$		0			0
$850$	−34.7013			−1.19025
$851$	−1.65284	−	1.47694i	−0.0566588	−	0.0506288i
$852$		0			0
$853$	−22.8625	+	14.6928i	−0.782798	+	0.503073i	−0.869961	−	0.493121i	$-0.835856\pi$
$853$	−22.8625	+	14.6928i	−0.782798	+	0.503073i	0.0871634	+	0.996194i	$0.472220\pi$
$854$	9.98539	−	69.4499i	0.341693	−	2.37653i
$855$		0			0
$856$	−51.6162	+	15.1559i	−1.76421	+	0.518017i
$857$	8.47480	+	18.5572i	0.289494	+	0.633903i	0.997373	−	0.0724301i	$-0.0230754\pi$
$857$	8.47480	+	18.5572i	0.289494	+	0.633903i	−0.707880	+	0.706333i	$0.750348\pi$
$858$		0			0
$859$	−1.36466	−	9.49141i	−0.0465616	−	0.323843i	−0.999768	−	0.0215237i	$-0.993148\pi$
$859$	−1.36466	−	9.49141i	−0.0465616	−	0.323843i	0.953207	−	0.302319i	$-0.0977608\pi$
$860$	−0.0437019	−	0.0128320i	−0.00149022	−	0.000437569i
$861$		0			0
$862$	−29.6484	−	19.0539i	−1.00983	−	0.648978i
$863$	17.3869	+	11.1739i	0.591858	+	0.380364i	0.802015	−	0.597303i	$-0.203761\pi$
$863$	17.3869	+	11.1739i	0.591858	+	0.380364i	−0.210157	+	0.977668i	$0.567398\pi$
$864$		0			0
$865$	−2.29858	−	0.674925i	−0.0781542	−	0.0229481i
$866$	3.09643	+	21.5361i	0.105221	+	0.731828i
$867$		0			0
$868$	0.122730	+	0.268741i	0.00416572	+	0.00912166i
$869$	3.32043	−	0.974966i	0.112638	−	0.0330735i
$870$		0			0
$871$	0.794545	−	5.52618i	0.0269221	−	0.187248i
$872$	−15.6825	+	10.0785i	−0.531077	+	0.341302i
$873$		0			0
$874$	9.20483	−	29.6669i	0.311358	−	1.00350i
$875$	−39.9062			−1.34908
$876$		0			0
$877$	7.02177	−	48.8375i	0.237108	−	1.64912i	−0.429026	−	0.903292i	$-0.641143\pi$
$877$	7.02177	−	48.8375i	0.237108	−	1.64912i	0.666134	−	0.745832i	$-0.267948\pi$
$878$	15.0615	−	32.9800i	0.508300	−	1.11302i
$879$		0			0
$880$	−2.09803	−	4.59405i	−0.0707246	−	0.154865i
$881$	−18.2842	−	21.1011i	−0.616012	−	0.710916i	0.358933	−	0.933363i	$-0.383141\pi$
$881$	−18.2842	−	21.1011i	−0.616012	−	0.710916i	−0.974945	+	0.222448i	$0.928595\pi$
$882$		0			0
$883$	5.40832	+	1.58802i	0.182004	+	0.0534413i	0.371465	−	0.928447i	$-0.378856\pi$
$883$	5.40832	+	1.58802i	0.182004	+	0.0534413i	−0.189460	+	0.981888i	$0.560674\pi$
$884$	0.0421550	−	0.0486495i	0.00141783	−	0.00163626i
$885$		0			0
$886$	−28.5486	−	18.3471i	−0.959109	−	0.616382i
$887$	−11.4361	+	13.1979i	−0.383986	+	0.443143i	−0.914532	−	0.404513i	$-0.867441\pi$
$887$	−11.4361	+	13.1979i	−0.383986	+	0.443143i	0.530547	+	0.847656i	$0.321987\pi$
$888$		0			0
$889$	−3.85766	−	26.8306i	−0.129382	−	0.899870i
$890$	8.03461	+	9.27243i	0.269321	+	0.310813i
$891$		0			0
$892$	0.0349459	−	0.0102610i	0.00117008	−	0.000343565i
$893$	−7.81543	+	17.1134i	−0.261533	+	0.572678i
$894$		0			0
$895$	−3.94815	+	2.53732i	−0.131972	+	0.0848133i
$896$	−57.7555			−1.92947
$897$		0			0
$898$	11.4629			0.382523
$899$	12.7808	−	8.21372i	0.426264	−	0.273943i
$900$		0			0
$901$	6.71126	−	14.6956i	0.223584	−	0.489581i
$902$	13.8730	−	4.07349i	0.461921	−	0.135632i
$903$		0			0
$904$	−1.81630	−	2.09612i	−0.0604091	−	0.0697158i
$905$	−1.43693	−	9.99408i	−0.0477652	−	0.332214i
$906$		0			0
$907$	24.0798	−	27.7896i	0.799558	−	0.922739i	−0.198799	−	0.980040i	$-0.563704\pi$
$907$	24.0798	−	27.7896i	0.799558	−	0.922739i	0.998357	+	0.0573012i	$0.0182495\pi$
$908$	−0.121062	−	0.0778019i	−0.00401759	−	0.00258195i
$909$		0			0
$910$	4.06663	−	4.69314i	0.134808	−	0.155576i
$911$	13.1586	+	3.86373i	0.435965	+	0.128011i	0.492348	−	0.870398i	$-0.336139\pi$
$911$	13.1586	+	3.86373i	0.435965	+	0.128011i	−0.0563831	+	0.998409i	$0.517957\pi$
$912$		0			0
$913$	15.9148	+	18.3667i	0.526703	+	0.607848i
$914$	−13.3897	−	29.3193i	−0.442891	−	0.969796i
$915$		0			0
$916$	−0.0225874	+	0.0494595i	−0.000746308	+	0.00163419i
$917$	6.58166	−	45.7764i	0.217346	−	1.51167i
$918$		0			0
$919$	−14.1731			−0.467528			−0.233764	−	0.972293i	$-0.575104\pi$
$919$	−14.1731			−0.467528			−0.233764	+	0.972293i	$0.575104\pi$
$920$	0.175273	−	11.4888i	0.00577858	−	0.378775i
$921$		0			0
$922$	−8.99027	+	5.77770i	−0.296079	+	0.190278i
$923$	−1.83359	+	12.7529i	−0.0603534	+	0.419767i
$924$		0			0
$925$	−1.89736	+	0.557116i	−0.0623849	+	0.0183179i
$926$	13.5355	+	29.6385i	0.444803	+	0.973982i
$927$		0			0
$928$	−0.0256160	−	0.178163i	−0.000840885	−	0.00584848i
$929$	13.2089	+	3.87848i	0.433370	+	0.127249i	0.491139	−	0.871081i	$-0.336581\pi$
$929$	13.2089	+	3.87848i	0.433370	+	0.127249i	−0.0577694	+	0.998330i	$0.518399\pi$
$930$		0			0
$931$	71.6089	+	46.0202i	2.34689	+	1.50825i
$932$	0.154654	+	0.0993903i	0.00506587	+	0.00325564i
$933$		0			0
$934$	15.2479	+	4.47720i	0.498928	+	0.146498i
$935$	1.02208	+	7.10872i	0.0334256	+	0.232480i
$936$		0			0
$937$	−0.974836	−	2.13459i	−0.0318465	−	0.0697341i	0.893040	−	0.449977i	$-0.148568\pi$
$937$	−0.974836	−	2.13459i	−0.0318465	−	0.0697341i	−0.924887	+	0.380243i	$0.875840\pi$
$938$	−37.7789	+	11.0929i	−1.23352	+	0.362195i
$939$		0			0
$940$	0.00550475	−	0.0382864i	0.000179545	−	0.00124876i
$941$	43.2829	−	27.8162i	1.41098	−	0.906783i	0.410993	−	0.911638i	$-0.365182\pi$
$941$	43.2829	−	27.8162i	1.41098	−	0.906783i	0.999988	+	0.00485554i	$0.00154557\pi$
$942$		0			0
$943$	32.6642	+	5.20615i	1.06369	+	0.169536i
$944$	8.51567			0.277161
$945$		0			0
$946$	1.44714	−	10.0651i	0.0470505	−	0.327243i
$947$	−14.6846	+	32.1547i	−0.477184	+	1.04489i	0.506044	+	0.862508i	$0.331107\pi$
$947$	−14.6846	+	32.1547i	−0.477184	+	1.04489i	−0.983228	+	0.182380i	$0.941620\pi$
$948$		0			0
$949$	0.744016	+	1.62917i	0.0241518	+	0.0528850i
$950$	−18.1470	−	20.9428i	−0.588766	−	0.679473i
$951$		0			0
$952$	78.3716	+	23.0120i	2.54004	+	0.745823i
$953$	−7.01592	+	8.09680i	−0.227268	+	0.262281i	−0.857919	−	0.513786i	$-0.828243\pi$
$953$	−7.01592	+	8.09680i	−0.227268	+	0.262281i	0.630651	+	0.776067i	$0.282788\pi$
$954$		0			0
$955$	12.4240	+	7.98441i	0.402031	+	0.258370i
$956$	−0.0666389	+	0.0769054i	−0.00215526	+	0.00248730i
$957$		0			0
$958$	4.18391	+	29.0997i	0.135176	+	0.940170i
$959$	−18.7493	−	21.6378i	−0.605446	−	0.698722i
$960$		0			0
$961$	3.01336	−	0.884803i	0.0972053	−	0.0285420i
$962$	0.277220	−	0.607026i	0.00893792	−	0.0195713i
$963$		0			0
$964$	0.0251144	−	0.0161400i	0.000808880	−	0.000519835i
$965$	−8.85161			−0.284943
$966$		0			0
$967$	−44.9115			−1.44426			−0.722128	−	0.691759i	$-0.756836\pi$
$967$	−44.9115			−1.44426			−0.722128	+	0.691759i	$0.756836\pi$
$968$	−20.9154	+	13.4415i	−0.672247	+	0.432027i
$969$		0			0
$970$	5.63954	−	12.3489i	0.181075	−	0.396498i
$971$	−27.5680	+	8.09469i	−0.884699	+	0.259771i	−0.692355	−	0.721557i	$-0.743427\pi$
$971$	−27.5680	+	8.09469i	−0.884699	+	0.259771i	−0.192343	+	0.981328i	$0.561609\pi$
$972$		0			0
$973$	−52.5753	−	60.6752i	−1.68549	−	1.94516i
$974$	−5.07033	−	35.2649i	−0.162464	−	1.12996i
$975$		0			0
$976$	25.7369	−	29.7019i	0.823818	−	0.950736i
$977$	−35.7057	−	22.9466i	−1.14233	−	0.734128i	−0.174229	−	0.984705i	$-0.555743\pi$
$977$	−35.7057	−	22.9466i	−1.14233	−	0.734128i	−0.968097	+	0.250577i	$0.919380\pi$
$978$		0			0
$979$	−9.86023	+	11.3793i	−0.315134	+	0.363684i
$980$	−0.167919	−	0.0493054i	−0.00536397	−	0.00157500i
$981$		0			0
$982$	−16.0804	−	18.5578i	−0.513147	−	0.592203i
$983$	−0.256325	−	0.561274i	−0.00817550	−	0.0179018i	0.905500	−	0.424346i	$-0.139496\pi$
$983$	−0.256325	−	0.561274i	−0.00817550	−	0.0179018i	−0.913676	+	0.406444i	$0.866769\pi$
$984$		0			0
$985$	3.68075	−	8.05971i	0.117278	−	0.256804i
$986$	−3.32241	+	23.1078i	−0.105807	+	0.735904i
$987$		0			0
$988$	0.0514056			0.00163543
$989$	12.8735	−	19.3752i	0.409354	−	0.616097i
$990$		0			0
$991$	−11.8686	+	7.62752i	−0.377020	+	0.242296i	−0.715402	−	0.698713i	$-0.753757\pi$
$991$	−11.8686	+	7.62752i	−0.377020	+	0.242296i	0.338382	+	0.941009i	$0.390120\pi$
$992$	−0.0469734	+	0.326707i	−0.00149141	+	0.0103730i
$993$		0			0
$994$	87.1833	−	25.5993i	2.76529	−	0.811962i
$995$	1.62363	+	3.55526i	0.0514727	+	0.112709i
$996$		0			0
$997$	−7.79322	−	54.2030i	−0.246814	−	1.71663i	−0.616403	−	0.787431i	$-0.711411\pi$
$997$	−7.79322	−	54.2030i	−0.246814	−	1.71663i	0.369589	−	0.929195i	$-0.379498\pi$
$998$	52.7719	+	15.4952i	1.67047	+	0.490493i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.i.d.127.1		20
3.2	odd	2		69.2.e.c.58.2	yes	20
23.2	even	11	inner	207.2.i.d.163.1		20
23.5	odd	22		4761.2.a.bu.1.3		10
23.18	even	11		4761.2.a.bt.1.3		10
69.2	odd	22		69.2.e.c.25.2	✓	20
69.5	even	22		1587.2.a.t.1.8		10
69.41	odd	22		1587.2.a.u.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.c.25.2	✓	20	69.2	odd	22
69.2.e.c.58.2	yes	20	3.2	odd	2
207.2.i.d.127.1		20	1.1	even	1	trivial
207.2.i.d.163.1		20	23.2	even	11	inner
1587.2.a.t.1.8		10	69.5	even	22
1587.2.a.u.1.8		10	69.41	odd	22
4761.2.a.bt.1.3		10	23.18	even	11
4761.2.a.bu.1.3		10	23.5	odd	22

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19300 + 0.766692i) q^{2} +(0.00459227 - 0.0100557i) q^{4} +(-0.815022 + 0.239312i) q^{5} +(-3.31578 - 3.82661i) q^{7} +(-0.401407 - 2.79185i) q^{8} +O(q^{10})\)	\(q+(-1.19300 + 0.766692i) q^{2} +(0.00459227 - 0.0100557i) q^{4} +(-0.815022 + 0.239312i) q^{5} +(-3.31578 - 3.82661i) q^{7} +(-0.401407 - 2.79185i) q^{8} +(0.788839 - 0.910368i) q^{10} +(1.24362 + 0.799227i) q^{11} +(-0.666743 + 0.769463i) q^{13} +(6.88954 + 2.02295i) q^{14} +(2.63384 + 3.03962i) q^{16} +(-2.37590 - 5.20249i) q^{17} +(1.89731 - 4.15452i) q^{19} +(-0.00133636 + 0.00929457i) q^{20} -2.09640 q^{22} +(-4.33154 - 2.05857i) q^{23} +(-3.59928 + 2.31312i) q^{25} +(0.205481 - 1.42915i) q^{26} +(-0.0537061 + 0.0157695i) q^{28} +(1.19571 + 2.61825i) q^{29} +(-0.751167 - 5.22448i) q^{31} +(-0.0600008 - 0.0176178i) q^{32} +(6.82314 + 4.38497i) q^{34} +(3.61819 + 2.32527i) q^{35} +(0.443467 + 0.130214i) q^{37} +(0.921759 + 6.41098i) q^{38} +(0.995278 + 2.17935i) q^{40} +(-6.61755 + 1.94309i) q^{41} +(-0.690297 + 4.80112i) q^{43} +(0.0137478 - 0.00883519i) q^{44} +(6.74580 - 0.865089i) q^{46} -4.11922 q^{47} +(-2.65237 + 18.4477i) q^{49} +(2.52048 - 5.51907i) q^{50} +(0.00467560 + 0.0102381i) q^{52} +(1.84980 + 2.13478i) q^{53} +(-1.20484 - 0.353774i) q^{55} +(-9.35234 + 10.7932i) q^{56} +(-3.43387 - 2.20681i) q^{58} +(1.38652 - 1.60013i) q^{59} +(-1.39065 - 9.67215i) q^{61} +(4.90170 + 5.65687i) q^{62} +(-7.63305 + 2.24127i) q^{64} +(0.359269 - 0.786689i) q^{65} +(-4.61302 + 2.96461i) q^{67} -0.0632253 q^{68} -6.09924 q^{70} +(10.6456 - 6.84151i) q^{71} +(0.730756 - 1.60013i) q^{73} +(-0.628889 + 0.184658i) q^{74} +(-0.0330636 - 0.0381574i) q^{76} +(-1.06524 - 7.40892i) q^{77} +(1.53299 - 1.76917i) q^{79} +(-2.87405 - 1.84704i) q^{80} +(6.40496 - 7.39172i) q^{82} +(15.7737 + 4.63157i) q^{83} +(3.18143 + 3.67156i) q^{85} +(-2.85746 - 6.25696i) q^{86} +(1.73212 - 3.79282i) q^{88} +(-1.44953 + 10.0817i) q^{89} +5.15521 q^{91} +(-0.0405920 + 0.0341030i) q^{92} +(4.91421 - 3.15817i) q^{94} +(-0.552119 + 3.84008i) q^{95} +(10.8134 - 3.17511i) q^{97} +(-10.9794 - 24.0415i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8}+O(q^{10}) \) 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 10 * q^8	\( 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8} - 18 q^{10} + 16 q^{11} + 14 q^{13} + 22 q^{14} - 8 q^{16} - 11 q^{17} - 11 q^{19} - 57 q^{20} + 26 q^{22} - 4 q^{25} + 14 q^{26} - 14 q^{28} - 12 q^{29} + 41 q^{31} + 46 q^{32} - 3 q^{34} + 26 q^{35} - 18 q^{37} - 70 q^{38} - 13 q^{40} - 10 q^{43} + 3 q^{44} - 24 q^{46} - 18 q^{47} - 10 q^{49} - 33 q^{50} + 61 q^{52} + 20 q^{53} - 17 q^{55} - 6 q^{56} - 37 q^{58} - 40 q^{59} - 12 q^{61} + 89 q^{62} - 2 q^{64} + 51 q^{65} - 47 q^{67} + 12 q^{68} + 32 q^{70} + 47 q^{71} + 39 q^{73} + 50 q^{74} - 39 q^{76} - 22 q^{77} - 2 q^{79} - 12 q^{80} + 26 q^{82} + 52 q^{83} + 35 q^{85} - 34 q^{86} + 30 q^{88} - 36 q^{89} + 8 q^{91} + 19 q^{92} + 21 q^{94} - 89 q^{95} - 85 q^{98}+O(q^{100}) \) 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 10 * q^8 - 18 * q^10 + 16 * q^11 + 14 * q^13 + 22 * q^14 - 8 * q^16 - 11 * q^17 - 11 * q^19 - 57 * q^20 + 26 * q^22 - 4 * q^25 + 14 * q^26 - 14 * q^28 - 12 * q^29 + 41 * q^31 + 46 * q^32 - 3 * q^34 + 26 * q^35 - 18 * q^37 - 70 * q^38 - 13 * q^40 - 10 * q^43 + 3 * q^44 - 24 * q^46 - 18 * q^47 - 10 * q^49 - 33 * q^50 + 61 * q^52 + 20 * q^53 - 17 * q^55 - 6 * q^56 - 37 * q^58 - 40 * q^59 - 12 * q^61 + 89 * q^62 - 2 * q^64 + 51 * q^65 - 47 * q^67 + 12 * q^68 + 32 * q^70 + 47 * q^71 + 39 * q^73 + 50 * q^74 - 39 * q^76 - 22 * q^77 - 2 * q^79 - 12 * q^80 + 26 * q^82 + 52 * q^83 + 35 * q^85 - 34 * q^86 + 30 * q^88 - 36 * q^89 + 8 * q^91 + 19 * q^92 + 21 * q^94 - 89 * q^95 - 85 * q^98

Introduction

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