LMFDB - Embedded newform 675.2.y.a.19.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(19,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([20, 27]))

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

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

chi := DirichletCharacter("675.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.y (of order $30$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.11
Character	$\chi$	$=$	675.19
Dual form			675.2.y.a.604.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0965635 + 0.454296i) q^{2} +(1.63003 + 0.725736i) q^{4} +(1.56019 + 1.60181i) q^{5} +(-3.50662 - 2.02455i) q^{7} +(-1.03309 + 1.42192i) q^{8} +O(q^{10})$	\(q+(-0.0965635 + 0.454296i) q^{2} +(1.63003 + 0.725736i) q^{4} +(1.56019 + 1.60181i) q^{5} +(-3.50662 - 2.02455i) q^{7} +(-1.03309 + 1.42192i) q^{8} +(-0.878353 + 0.554113i) q^{10} +(-1.82260 - 0.387406i) q^{11} +(0.982729 + 4.62338i) q^{13} +(1.25836 - 1.39755i) q^{14} +(1.84163 + 2.04534i) q^{16} +(-3.46971 + 4.77564i) q^{17} +(5.24541 + 3.81101i) q^{19} +(1.38067 + 3.74329i) q^{20} +(0.351994 - 0.790591i) q^{22} +(1.57956 + 1.42225i) q^{23} +(-0.131589 + 4.99827i) q^{25} -2.19528 q^{26} +(-4.24661 - 5.84496i) q^{28} +(-0.378599 - 3.60213i) q^{29} +(0.631110 - 6.00461i) q^{31} +(-4.15127 + 2.39674i) q^{32} +(-1.83451 - 2.03742i) q^{34} +(-2.22807 - 8.77563i) q^{35} +(0.543266 + 0.176518i) q^{37} +(-2.23784 + 2.01496i) q^{38} +(-3.88947 + 0.563666i) q^{40} +(2.61445 - 0.555718i) q^{41} +(4.96950 + 2.86914i) q^{43} +(-2.68974 - 1.95421i) q^{44} +(-0.798649 + 0.580252i) q^{46} +(6.60369 - 0.694076i) q^{47} +(4.69760 + 8.13649i) q^{49} +(-2.25799 - 0.542431i) q^{50} +(-1.75347 + 8.24945i) q^{52} +(-5.27101 - 7.25492i) q^{53} +(-2.22306 - 3.52389i) q^{55} +(6.50141 - 2.89461i) q^{56} +(1.67299 + 0.175838i) q^{58} +(-3.07398 + 0.653395i) q^{59} +(-3.32301 - 0.706327i) q^{61} +(2.66693 + 0.866537i) q^{62} +(1.01303 + 3.11780i) q^{64} +(-5.87252 + 8.78751i) q^{65} +(-3.67467 - 0.386223i) q^{67} +(-9.12158 + 5.26635i) q^{68} +(4.20188 - 0.164796i) q^{70} +(10.4419 - 7.58650i) q^{71} +(-4.11174 + 1.33598i) q^{73} +(-0.132651 + 0.229758i) q^{74} +(5.78438 + 10.0188i) q^{76} +(5.60685 + 5.04843i) q^{77} +(-0.767436 - 7.30167i) q^{79} +(-0.402942 + 6.14107i) q^{80} +1.24139i q^{82} +(1.36572 + 3.06747i) q^{83} +(-13.0631 + 1.89312i) q^{85} +(-1.78331 + 1.98057i) q^{86} +(2.43377 - 2.19138i) q^{88} +(0.948463 + 2.91907i) q^{89} +(5.91420 - 18.2020i) q^{91} +(1.54256 + 3.46465i) q^{92} +(-0.322360 + 3.06705i) q^{94} +(2.07934 + 14.3481i) q^{95} +(6.32893 - 0.665198i) q^{97} +(-4.14999 + 1.34841i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8}+O(q^{10}) $ 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8	$ 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8} - 12 q^{10} - 5 q^{11} - 5 q^{13} + 23 q^{14} + 15 q^{16} + 20 q^{17} - 12 q^{19} + 17 q^{20} - 5 q^{22} + 5 q^{23} - 16 q^{25} - 72 q^{26} - 60 q^{28} + 15 q^{29} - 9 q^{31} - 7 q^{34} + 46 q^{35} - 20 q^{37} + 75 q^{38} - q^{40} - 13 q^{41} - 20 q^{44} - 4 q^{46} - 20 q^{47} + 56 q^{49} + 29 q^{50} - 15 q^{52} + 20 q^{53} - 44 q^{55} - 22 q^{56} - 5 q^{58} + 30 q^{59} - 3 q^{61} - 40 q^{62} - 12 q^{64} - 45 q^{65} + 10 q^{67} - 12 q^{70} + 106 q^{71} - 20 q^{73} - 82 q^{74} + 8 q^{76} + 115 q^{77} - 15 q^{79} + 22 q^{80} - 65 q^{83} - 21 q^{85} + 15 q^{86} - 5 q^{88} - 26 q^{89} - 54 q^{91} - 95 q^{92} + 41 q^{94} + 17 q^{95} - 5 q^{97} + 70 q^{98}+O(q^{100}) $ 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8 - 12 * q^10 - 5 * q^11 - 5 * q^13 + 23 * q^14 + 15 * q^16 + 20 * q^17 - 12 * q^19 + 17 * q^20 - 5 * q^22 + 5 * q^23 - 16 * q^25 - 72 * q^26 - 60 * q^28 + 15 * q^29 - 9 * q^31 - 7 * q^34 + 46 * q^35 - 20 * q^37 + 75 * q^38 - q^40 - 13 * q^41 - 20 * q^44 - 4 * q^46 - 20 * q^47 + 56 * q^49 + 29 * q^50 - 15 * q^52 + 20 * q^53 - 44 * q^55 - 22 * q^56 - 5 * q^58 + 30 * q^59 - 3 * q^61 - 40 * q^62 - 12 * q^64 - 45 * q^65 + 10 * q^67 - 12 * q^70 + 106 * q^71 - 20 * q^73 - 82 * q^74 + 8 * q^76 + 115 * q^77 - 15 * q^79 + 22 * q^80 - 65 * q^83 - 21 * q^85 + 15 * q^86 - 5 * q^88 - 26 * q^89 - 54 * q^91 - 95 * q^92 + 41 * q^94 + 17 * q^95 - 5 * q^97 + 70 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.0965635	+	0.454296i	−0.0682807	+	0.321236i	−0.999011	−	0.0444717i	$-0.985840\pi$
$2$	−0.0965635	+	0.454296i	−0.0682807	+	0.321236i	0.930730	+	0.365707i	$0.119173\pi$
$3$		0			0
$3$		0			0
$4$	1.63003	+	0.725736i	0.815015	+	0.362868i
$5$	1.56019	+	1.60181i	0.697740	+	0.716351i
$5$	1.56019	+	1.60181i	0.697740	+	0.716351i
$6$		0			0
$7$	−3.50662	−	2.02455i	−1.32538	−	0.765208i	−0.340798	−	0.940137i	$-0.610697\pi$
$7$	−3.50662	−	2.02455i	−1.32538	−	0.765208i	−0.984581	+	0.174929i	$0.944030\pi$
$8$	−1.03309	+	1.42192i	−0.365252	+	0.502726i
$9$		0			0
$10$	−0.878353	+	0.554113i	−0.277760	+	0.175226i
$11$	−1.82260	−	0.387406i	−0.549535	−	0.116807i	−0.0752273	−	0.997166i	$-0.523968\pi$
$11$	−1.82260	−	0.387406i	−0.549535	−	0.116807i	−0.474308	+	0.880359i	$0.657302\pi$
$12$		0			0
$13$	0.982729	+	4.62338i	0.272560	+	1.28229i	0.874997	+	0.484128i	$0.160863\pi$
$13$	0.982729	+	4.62338i	0.272560	+	1.28229i	−0.602437	+	0.798166i	$0.705804\pi$
$14$	1.25836	−	1.39755i	0.336310	−	0.373510i
$15$		0			0
$16$	1.84163	+	2.04534i	0.460408	+	0.511335i
$17$	−3.46971	+	4.77564i	−0.841527	+	1.15826i	0.144139	+	0.989557i	$0.453959\pi$
$17$	−3.46971	+	4.77564i	−0.841527	+	1.15826i	−0.985667	+	0.168705i	$0.946041\pi$
$18$		0			0
$19$	5.24541	+	3.81101i	1.20338	+	0.874306i	0.994613	−	0.103660i	$-0.0330554\pi$
$19$	5.24541	+	3.81101i	1.20338	+	0.874306i	0.208766	+	0.977966i	$0.433055\pi$
$20$	1.38067	+	3.74329i	0.308728	+	0.837025i
$21$		0			0
$22$	0.351994	−	0.790591i	0.0750453	−	0.168554i
$23$	1.57956	+	1.42225i	0.329362	+	0.296559i	0.817175	−	0.576389i	$-0.195539\pi$
$23$	1.57956	+	1.42225i	0.329362	+	0.296559i	−0.487813	+	0.872948i	$0.662205\pi$
$24$		0			0
$25$	−0.131589	+	4.99827i	−0.0263179	+	0.999654i
$26$	−2.19528			−0.430529
$27$		0			0
$28$	−4.24661	−	5.84496i	−0.802535	−	1.10459i
$29$	−0.378599	−	3.60213i	−0.0703041	−	0.668899i	−0.971751	−	0.236009i	$-0.924161\pi$
$29$	−0.378599	−	3.60213i	−0.0703041	−	0.668899i	0.901447	−	0.432890i	$-0.142506\pi$
$30$		0			0
$31$	0.631110	−	6.00461i	0.113351	−	1.07846i	−0.778971	−	0.627060i	$-0.784258\pi$
$31$	0.631110	−	6.00461i	0.113351	−	1.07846i	0.892322	−	0.451400i	$-0.149075\pi$
$32$	−4.15127	+	2.39674i	−0.733847	+	0.423687i
$33$		0			0
$34$	−1.83451	−	2.03742i	−0.314615	−	0.349415i
$35$	−2.22807	−	8.77563i	−0.376612	−	1.48335i
$36$		0			0
$37$	0.543266	+	0.176518i	0.0893124	+	0.0290194i	0.353332	−	0.935498i	$-0.385048\pi$
$37$	0.543266	+	0.176518i	0.0893124	+	0.0290194i	−0.264020	+	0.964517i	$0.585048\pi$
$38$	−2.23784	+	2.01496i	−0.363026	+	0.326870i
$39$		0			0
$40$	−3.88947	+	0.563666i	−0.614979	+	0.0891235i
$41$	2.61445	−	0.555718i	0.408308	−	0.0867885i	0.000821156	−	1.00000i	$-0.499739\pi$
$41$	2.61445	−	0.555718i	0.408308	−	0.0867885i	0.407487	+	0.913211i	$0.366405\pi$
$42$		0			0
$43$	4.96950	+	2.86914i	0.757841	+	0.437540i	0.828520	−	0.559959i	$-0.189183\pi$
$43$	4.96950	+	2.86914i	0.757841	+	0.437540i	−0.0706790	+	0.997499i	$0.522517\pi$
$44$	−2.68974	−	1.95421i	−0.405494	−	0.294608i
$45$		0			0
$46$	−0.798649	+	0.580252i	−0.117754	+	0.0855535i
$47$	6.60369	−	0.694076i	0.963248	−	0.101241i	0.390170	−	0.920743i	$-0.372416\pi$
$47$	6.60369	−	0.694076i	0.963248	−	0.101241i	0.573077	+	0.819501i	$0.305749\pi$
$48$		0			0
$49$	4.69760	+	8.13649i	0.671086	+	1.16236i
$50$	−2.25799	−	0.542431i	−0.319327	−	0.0767113i
$51$		0			0
$52$	−1.75347	+	8.24945i	−0.243163	+	1.14399i
$53$	−5.27101	−	7.25492i	−0.724029	−	0.996540i	−0.999380	−	0.0351968i	$-0.988794\pi$
$53$	−5.27101	−	7.25492i	−0.724029	−	0.996540i	0.275351	−	0.961344i	$-0.411206\pi$
$54$		0			0
$55$	−2.22306	−	3.52389i	−0.299757	−	0.475161i
$56$	6.50141	−	2.89461i	0.868787	−	0.386809i
$57$		0			0
$58$	1.67299	+	0.175838i	0.219674	+	0.0230887i
$59$	−3.07398	+	0.653395i	−0.400198	+	0.0850648i	−0.403614	−	0.914929i	$-0.632246\pi$
$59$	−3.07398	+	0.653395i	−0.400198	+	0.0850648i	0.00341568	+	0.999994i	$0.498913\pi$
$60$		0			0
$61$	−3.32301	−	0.706327i	−0.425468	−	0.0904359i	−0.00979878	−	0.999952i	$-0.503119\pi$
$61$	−3.32301	−	0.706327i	−0.425468	−	0.0904359i	−0.415669	+	0.909516i	$0.636452\pi$
$62$	2.66693	+	0.866537i	0.338700	+	0.110050i
$63$		0			0
$64$	1.01303	+	3.11780i	0.126629	+	0.389725i
$65$	−5.87252	+	8.78751i	−0.728397	+	1.08996i
$66$		0			0
$67$	−3.67467	−	0.386223i	−0.448932	−	0.0471847i	−0.122635	−	0.992452i	$-0.539134\pi$
$67$	−3.67467	−	0.386223i	−0.448932	−	0.0471847i	−0.326297	+	0.945267i	$0.605801\pi$
$68$	−9.12158	+	5.26635i	−1.10615	+	0.638638i
$69$		0			0
$70$	4.20188	−	0.164796i	0.502221	−	0.0196969i
$71$	10.4419	−	7.58650i	1.23923	−	0.900352i	0.241681	−	0.970356i	$-0.422301\pi$
$71$	10.4419	−	7.58650i	1.23923	−	0.900352i	0.997547	+	0.0700042i	$0.0223013\pi$
$72$		0			0
$73$	−4.11174	+	1.33598i	−0.481243	+	0.156365i	−0.539584	−	0.841931i	$-0.681419\pi$
$73$	−4.11174	+	1.33598i	−0.481243	+	0.156365i	0.0583419	+	0.998297i	$0.481419\pi$
$74$	−0.132651	+	0.229758i	−0.0154204	+	0.0267089i
$75$		0			0
$76$	5.78438	+	10.0188i	0.663514	+	1.14924i
$77$	5.60685	+	5.04843i	0.638960	+	0.575322i
$78$		0			0
$79$	−0.767436	−	7.30167i	−0.0863433	−	0.821502i	−0.948908	−	0.315554i	$-0.897810\pi$
$79$	−0.767436	−	7.30167i	−0.0863433	−	0.821502i	0.862564	−	0.505947i	$-0.168857\pi$
$80$	−0.402942	+	6.14107i	−0.0450503	+	0.686593i
$81$		0			0
$82$			1.24139i			0.137089i
$83$	1.36572	+	3.06747i	0.149908	+	0.336698i	0.972854	−	0.231422i	$-0.0743377\pi$
$83$	1.36572	+	3.06747i	0.149908	+	0.336698i	−0.822946	+	0.568120i	$0.807671\pi$
$84$		0			0
$85$	−13.0631	+	1.89312i	−1.41689	+	0.205337i
$86$	−1.78331	+	1.98057i	−0.192299	+	0.213570i
$87$		0			0
$88$	2.43377	−	2.19138i	0.259441	−	0.233601i
$89$	0.948463	+	2.91907i	0.100537	+	0.309421i	0.988657	−	0.150191i	$-0.0479887\pi$
$89$	0.948463	+	2.91907i	0.100537	+	0.309421i	−0.888120	+	0.459611i	$0.847989\pi$
$90$		0			0
$91$	5.91420	−	18.2020i	0.619976	−	1.90809i
$92$	1.54256	+	3.46465i	0.160823	+	0.361215i
$93$		0			0
$94$	−0.322360	+	3.06705i	−0.0332489	+	0.316342i
$95$	2.07934	+	14.3481i	0.213335	+	1.47208i
$96$		0			0
$97$	6.32893	−	0.665198i	0.642606	−	0.0675406i	0.222380	−	0.974960i	$-0.428617\pi$
$97$	6.32893	−	0.665198i	0.642606	−	0.0675406i	0.420226	+	0.907419i	$0.361951\pi$
$98$	−4.14999	+	1.34841i	−0.419212	+	0.136210i
$99$		0			0
$100$	−3.84192	+	8.05183i	−0.384192	+	0.805183i
$101$	1.56396	−	2.70886i	0.155620	−	0.269542i	−0.777665	−	0.628679i	$-0.783596\pi$
$101$	1.56396	−	2.70886i	0.155620	−	0.269542i	0.933285	+	0.359138i	$0.116929\pi$
$102$		0			0
$103$	5.65271	−	12.6962i	0.556978	−	1.25099i	−0.387333	−	0.921940i	$-0.626604\pi$
$103$	5.65271	−	12.6962i	0.556978	−	1.25099i	0.944311	−	0.329053i	$-0.106730\pi$
$104$	−7.58934	−	3.37899i	−0.744196	−	0.331337i
$105$		0			0
$106$	3.80487	−	1.69404i	0.369561	−	0.164539i
$107$		−	5.56325i		−	0.537820i	−0.963165	−	0.268910i	$-0.913337\pi$
$107$		−	5.56325i		−	0.537820i	0.963165	−	0.268910i	$-0.0866634\pi$
$108$		0			0
$109$	−3.74231	+	11.5176i	−0.358448	+	1.10319i	0.595535	+	0.803330i	$0.296940\pi$
$109$	−3.74231	+	11.5176i	−0.358448	+	1.10319i	−0.953983	+	0.299861i	$0.903060\pi$
$110$	1.81555	−	0.669648i	0.173106	−	0.0638484i
$111$		0			0
$112$	−2.31702	−	10.9007i	−0.218938	−	1.03002i
$113$	−3.13036	−	14.7272i	−0.294479	−	1.38542i	−0.837840	−	0.545916i	$-0.816182\pi$
$113$	−3.13036	−	14.7272i	−0.294479	−	1.38542i	0.543361	−	0.839499i	$-0.317152\pi$
$114$		0			0
$115$	0.186259	+	4.74914i	0.0173687	+	0.442860i
$116$	1.99707	−	6.14634i	0.185423	−	0.570674i
$117$		0			0
$118$		−	1.45959i		−	0.134366i
$119$	21.8355	−	9.72178i	2.00165	−	0.891194i
$120$		0			0
$121$	−6.87721	−	3.06193i	−0.625201	−	0.278357i
$122$	0.641763	−	1.44142i	0.0581025	−	0.130500i
$123$		0			0
$124$	5.38650	−	9.32969i	0.483722	−	0.837830i
$125$	−8.21158	+	7.58749i	−0.734466	+	0.678645i
$126$		0			0
$127$	5.86130	−	1.90445i	0.520107	−	0.168993i	−0.0371871	−	0.999308i	$-0.511840\pi$
$127$	5.86130	−	1.90445i	0.520107	−	0.168993i	0.557294	+	0.830315i	$0.311840\pi$
$128$	−11.0486	+	1.16126i	−0.976572	+	0.102642i
$129$		0			0
$130$	−3.42506	−	3.51642i	−0.300397	−	0.308410i
$131$	−1.54142	+	14.6657i	−0.134675	+	1.28134i	0.693329	+	0.720622i	$0.256143\pi$
$131$	−1.54142	+	14.6657i	−0.134675	+	1.28134i	−0.828003	+	0.560723i	$0.810523\pi$
$132$		0			0
$133$	−10.6781	−	23.9834i	−0.925907	−	2.07962i
$134$	0.530299	−	1.63209i	0.0458108	−	0.140991i
$135$		0			0
$136$	−3.20608	−	9.86731i	−0.274920	−	0.846115i
$137$	13.9071	−	12.5220i	1.18816	−	1.06983i	0.192082	−	0.981379i	$-0.438476\pi$
$137$	13.9071	−	12.5220i	1.18816	−	1.06983i	0.996081	−	0.0884480i	$-0.0281907\pi$
$138$		0			0
$139$	4.82305	−	5.35654i	0.409086	−	0.454336i	−0.503030	−	0.864269i	$-0.667781\pi$
$139$	4.82305	−	5.35654i	0.409086	−	0.454336i	0.912116	+	0.409933i	$0.134448\pi$
$140$	2.73698	−	15.9215i	0.231317	−	1.34562i
$141$		0			0
$142$	2.43820	+	5.47630i	0.204610	+	0.459561i
$143$		−	8.80729i		−	0.736502i
$144$		0			0
$145$	5.17924	−	6.22646i	0.430112	−	0.517080i
$146$	−0.209888	−	1.99695i	−0.0173705	−	0.165269i
$147$		0			0
$148$	0.757435	+	0.681998i	0.0622608	+	0.0560599i
$149$	9.63580	+	16.6897i	0.789395	+	1.36727i	0.926338	+	0.376694i	$0.122939\pi$
$149$	9.63580	+	16.6897i	0.789395	+	1.36727i	−0.136942	+	0.990579i	$0.543727\pi$
$150$		0			0
$151$	−0.968205	+	1.67698i	−0.0787914	+	0.136471i	−0.902729	−	0.430210i	$-0.858439\pi$
$151$	−0.968205	+	1.67698i	−0.0787914	+	0.136471i	0.823937	+	0.566681i	$0.191773\pi$
$152$	−10.8379	+	3.52146i	−0.879073	+	0.285628i
$153$		0			0
$154$	−2.83490	+	2.05967i	−0.228443	+	0.165973i
$155$	10.6029	−	8.35744i	0.851646	−	0.671286i
$156$		0			0
$157$	−14.0905	+	8.13514i	−1.12454	+	0.649255i	−0.942557	−	0.334046i	$-0.891586\pi$
$157$	−14.0905	+	8.13514i	−1.12454	+	0.649255i	−0.181986	+	0.983301i	$0.558253\pi$
$158$	3.39122	+	0.356432i	0.269791	+	0.0283562i
$159$		0			0
$160$	−10.3159	−	2.91017i	−0.815543	−	0.230069i
$161$	−2.65953	−	8.18519i	−0.209600	−	0.645083i
$162$		0			0
$163$	−13.1125	−	4.26053i	−1.02705	−	0.333710i	−0.253429	−	0.967354i	$-0.581558\pi$
$163$	−13.1125	−	4.26053i	−1.02705	−	0.333710i	−0.773625	+	0.633644i	$0.781558\pi$
$164$	4.66493	+	0.991562i	0.364270	+	0.0774280i
$165$		0			0
$166$	−1.52542	+	0.324237i	−0.118395	+	0.0251657i
$167$	5.84977	+	0.614836i	0.452669	+	0.0475774i	0.328120	−	0.944636i	$-0.393585\pi$
$167$	5.84977	+	0.614836i	0.452669	+	0.0475774i	0.124549	+	0.992213i	$0.460252\pi$
$168$		0			0
$169$	−8.53377	+	3.79948i	−0.656444	+	0.292268i
$170$	0.401382	−	6.11731i	0.0307846	−	0.469176i
$171$		0			0
$172$	6.01819	+	8.28333i	0.458883	+	0.631598i
$173$	2.74467	−	12.9127i	0.208673	−	0.981731i	−0.741727	−	0.670702i	$-0.765993\pi$
$173$	2.74467	−	12.9127i	0.208673	−	0.981731i	0.950400	−	0.311029i	$-0.100674\pi$
$174$		0			0
$175$	10.5807	−	17.2606i	0.799824	−	1.30478i
$176$	−2.56418	−	4.44130i	−0.193283	−	0.334775i
$177$		0			0
$178$	−1.41771	+	0.149007i	−0.106262	+	0.0111686i
$179$	2.71554	−	1.97295i	0.202969	−	0.147465i	−0.481658	−	0.876359i	$-0.659965\pi$
$179$	2.71554	−	1.97295i	0.202969	−	0.147465i	0.684627	+	0.728894i	$0.259965\pi$
$180$		0			0
$181$	14.3097	+	10.3966i	1.06363	+	0.772775i	0.974757	−	0.223267i	$-0.0716723\pi$
$181$	14.3097	+	10.3966i	1.06363	+	0.772775i	0.0888767	+	0.996043i	$0.471672\pi$
$182$	7.69801	+	4.44445i	0.570614	+	0.329444i
$183$		0			0
$184$	−3.65416	+	0.776715i	−0.269388	+	0.0572602i
$185$	0.564853	+	1.14561i	0.0415288	+	0.0842271i
$186$		0			0
$187$	8.17400	−	7.35990i	0.597742	−	0.538209i
$188$	11.2679	+	3.66118i	0.821799	+	0.267019i
$189$		0			0
$190$	−6.71905	−	0.440865i	−0.487451	−	0.0319837i
$191$	−9.29658	−	10.3249i	−0.672677	−	0.747083i	0.306103	−	0.951998i	$-0.400975\pi$
$191$	−9.29658	−	10.3249i	−0.672677	−	0.747083i	−0.978780	+	0.204915i	$0.934308\pi$
$192$		0			0
$193$	10.7694	−	6.21772i	0.775199	−	0.447561i	−0.0595271	−	0.998227i	$-0.518959\pi$
$193$	10.7694	−	6.21772i	0.775199	−	0.447561i	0.834726	+	0.550665i	$0.185626\pi$
$194$	−0.308948	+	2.93944i	−0.0221812	+	0.211040i
$195$		0			0
$196$	1.75229	+	16.6719i	0.125164	+	1.19085i
$197$	11.1313	+	15.3210i	0.793075	+	1.09157i	0.993718	+	0.111910i	$0.0356969\pi$
$197$	11.1313	+	15.3210i	0.793075	+	1.09157i	−0.200643	+	0.979664i	$0.564303\pi$
$198$		0			0
$199$	10.3369			0.732764			0.366382	−	0.930465i	$-0.380596\pi$
$199$	10.3369			0.732764			0.366382	+	0.930465i	$0.380596\pi$
$200$	−6.97121	−	5.35076i	−0.492939	−	0.378356i
$201$		0			0
$202$	1.07960	+	0.972078i	0.0759605	+	0.0683952i
$203$	−5.96509	+	13.3978i	−0.418667	+	0.940341i
$204$		0			0
$205$	4.96920	+	3.32082i	0.347064	+	0.231936i
$206$	5.22198	+	3.79399i	0.363833	+	0.264340i
$207$		0			0
$208$	−7.64655	+	10.5246i	−0.530193	+	0.729748i
$209$	−8.08388	−	8.97805i	−0.559173	−	0.621025i
$210$		0			0
$211$	4.80813	−	5.33997i	0.331005	−	0.367618i	−0.554552	−	0.832149i	$-0.687110\pi$
$211$	4.80813	−	5.33997i	0.331005	−	0.367618i	0.885557	+	0.464531i	$0.153777\pi$
$212$	−3.32675	−	15.6511i	−0.228482	−	1.07492i
$213$		0			0
$214$	2.52736	+	0.537207i	0.172767	+	0.0367227i
$215$	3.15756	+	12.4366i	0.215344	+	0.848169i
$216$		0			0
$217$	−14.3697	+	19.7782i	−0.975479	+	1.34263i
$218$	−4.87105	−	2.81230i	−0.329909	−	0.190473i
$219$		0			0
$220$	−1.06624	−	7.35740i	−0.0718861	−	0.496036i
$221$	−25.4894	−	11.3486i	−1.71460	−	0.763389i
$222$		0			0
$223$	−2.11689	+	9.95920i	−0.141758	+	0.666917i	0.848674	+	0.528916i	$0.177401\pi$
$223$	−2.11689	+	9.95920i	−0.141758	+	0.666917i	−0.990432	+	0.138002i	$0.955932\pi$
$224$	19.4092			1.29683
$225$		0			0
$226$	6.99277			0.465152
$227$	−4.64606	+	21.8580i	−0.308370	+	1.45077i	0.502011	+	0.864861i	$0.332594\pi$
$227$	−4.64606	+	21.8580i	−0.308370	+	1.45077i	−0.810380	+	0.585904i	$0.800740\pi$
$228$		0			0
$229$	13.5662	+	6.04008i	0.896483	+	0.399140i	0.802651	−	0.596448i	$-0.203422\pi$
$229$	13.5662	+	6.04008i	0.896483	+	0.399140i	0.0938311	+	0.995588i	$0.470089\pi$
$230$	−2.17550	−	0.373977i	−0.143448	−	0.0246593i
$231$		0			0
$232$	5.51308	+	3.18298i	0.361951	+	0.208973i
$233$	14.5947	−	20.0879i	0.956130	−	1.31600i	0.00738020	−	0.999973i	$-0.497651\pi$
$233$	14.5947	−	20.0879i	0.956130	−	1.31600i	0.948750	−	0.316028i	$-0.102349\pi$
$234$		0			0
$235$	11.4148	+	9.49497i	0.744621	+	0.619383i
$236$	−5.48488	−	1.16585i	−0.357035	−	0.0758901i
$237$		0			0
$238$	2.30805	+	10.8585i	0.149609	+	0.703854i
$239$	−1.64179	+	1.82339i	−0.106198	+	0.117945i	−0.793900	−	0.608048i	$-0.791953\pi$
$239$	−1.64179	+	1.82339i	−0.106198	+	0.117945i	0.687702	+	0.725993i	$0.258620\pi$
$240$		0			0
$241$	−5.42452	−	6.02454i	−0.349424	−	0.388075i	0.542654	−	0.839956i	$-0.317420\pi$
$241$	−5.42452	−	6.02454i	−0.349424	−	0.388075i	−0.892078	+	0.451882i	$0.850753\pi$
$242$	2.05511	−	2.82862i	0.132107	−	0.181830i
$243$		0			0
$244$	−4.90400	−	3.56296i	−0.313946	−	0.228095i
$245$	−5.70393	+	20.2192i	−0.364411	+	1.29176i
$246$		0			0
$247$	−12.4649	+	27.9967i	−0.793124	+	1.78139i
$248$	7.88611	+	7.10069i	0.500769	+	0.450894i
$249$		0			0
$250$	−2.65402	−	4.46316i	−0.167855	−	0.282275i
$251$	−19.6503			−1.24032			−0.620158	−	0.784477i	$-0.712931\pi$
$251$	−19.6503			−1.24032			−0.620158	+	0.784477i	$0.712931\pi$
$252$		0			0
$253$	−2.32793	−	3.20412i	−0.146356	−	0.201441i
$254$	0.299197	+	2.84667i	0.0187733	+	0.178616i
$255$		0			0
$256$	−0.145999	+	1.38909i	−0.00912496	+	0.0868182i
$257$	12.3103	−	7.10737i	0.767897	−	0.443345i	−0.0642270	−	0.997935i	$-0.520458\pi$
$257$	12.3103	−	7.10737i	0.767897	−	0.443345i	0.832124	+	0.554590i	$0.187125\pi$
$258$		0			0
$259$	−1.54766	−	1.71885i	−0.0961670	−	0.106804i
$260$	−15.9498	+	10.0620i	−0.989165	+	0.624019i
$261$		0			0
$262$	−6.51370	−	2.11643i	−0.402418	−	0.130753i
$263$	−9.08416	+	8.17941i	−0.560153	+	0.504364i	−0.899867	−	0.436165i	$-0.856336\pi$
$263$	−9.08416	+	8.17941i	−0.560153	+	0.504364i	0.339714	+	0.940529i	$0.389670\pi$
$264$		0			0
$265$	3.39721	−	19.7622i	0.208689	−	1.21399i
$266$	11.9267	−	2.53509i	0.731270	−	0.155436i
$267$		0			0
$268$	−5.70953	−	3.29640i	−0.348765	−	0.201359i
$269$	6.38448	+	4.63859i	0.389268	+	0.282820i	0.765156	−	0.643845i	$-0.222662\pi$
$269$	6.38448	+	4.63859i	0.389268	+	0.282820i	−0.375887	+	0.926665i	$0.622662\pi$
$270$		0			0
$271$	19.0810	−	13.8631i	1.15909	−	0.842126i	0.169424	−	0.985543i	$-0.445809\pi$
$271$	19.0810	−	13.8631i	1.15909	−	0.842126i	0.989662	+	0.143417i	$0.0458091\pi$
$272$	−16.1577	+	1.69825i	−0.979706	+	0.102971i
$273$		0			0
$274$	4.34577	+	7.52710i	0.262538	+	0.454729i
$275$	2.17619	−	9.05887i	0.131229	−	0.546270i
$276$		0			0
$277$	−0.174595	+	0.821403i	−0.0104904	+	0.0493533i	−0.983081	−	0.183169i	$-0.941364\pi$
$277$	−0.174595	+	0.821403i	−0.0104904	+	0.0493533i	0.972591	+	0.232522i	$0.0746978\pi$
$278$	1.96772	+	2.70834i	0.118016	+	0.162435i
$279$		0			0
$280$	14.7801	+	5.89786i	0.883278	+	0.352465i
$281$	−0.0622480	+	0.0277146i	−0.00371341	+	0.00165331i	−0.408593	−	0.912717i	$-0.633980\pi$
$281$	−0.0622480	+	0.0277146i	−0.00371341	+	0.00165331i	0.404879	+	0.914370i	$0.367314\pi$
$282$		0			0
$283$	−10.6982	−	1.12443i	−0.635942	−	0.0668402i	−0.218929	−	0.975741i	$-0.570256\pi$
$283$	−10.6982	−	1.12443i	−0.635942	−	0.0668402i	−0.417013	+	0.908900i	$0.636923\pi$
$284$	22.5264	−	4.78814i	1.33670	−	0.284124i
$285$		0			0
$286$	4.00111	+	0.850463i	0.236591	+	0.0502889i
$287$	−10.2930	−	3.34438i	−0.607574	−	0.197413i
$288$		0			0
$289$	−5.51459	−	16.9722i	−0.324388	−	0.998362i
$290$	2.32853	+	2.95415i	0.136736	+	0.173474i
$291$		0			0
$292$	−7.67183	−	0.806342i	−0.448960	−	0.0471876i
$293$	−1.64127	+	0.947588i	−0.0958840	+	0.0553587i	−0.547175	−	0.837018i	$-0.684297\pi$
$293$	−1.64127	+	0.947588i	−0.0958840	+	0.0553587i	0.451291	+	0.892377i	$0.350964\pi$
$294$		0			0
$295$	−5.84262	−	3.90451i	−0.340171	−	0.227329i
$296$	−0.812237	+	0.590125i	−0.0472103	+	0.0343003i
$297$		0			0
$298$	−8.51252	+	2.76589i	−0.493117	+	0.160224i
$299$	−5.02330	+	8.70061i	−0.290505	+	0.503169i
$300$		0			0
$301$	−11.6174	−	20.1220i	−0.669618	−	1.15981i
$302$	−0.668352	−	0.601786i	−0.0384593	−	0.0346289i
$303$		0			0
$304$	1.86530	+	17.7471i	0.106982	+	1.01787i
$305$	−4.05313	−	6.42483i	−0.232082	−	0.367885i
$306$		0			0
$307$		−	13.6228i		−	0.777492i	−0.921345	−	0.388746i	$-0.872908\pi$
$307$		−	13.6228i		−	0.777492i	0.921345	−	0.388746i	$-0.127092\pi$
$308$	5.47551	+	12.2982i	0.311996	+	0.700755i
$309$		0			0
$310$	2.77290	+	5.62388i	0.157490	+	0.319415i
$311$	8.73860	−	9.70520i	0.495521	−	0.550332i	−0.442564	−	0.896737i	$-0.645931\pi$
$311$	8.73860	−	9.70520i	0.495521	−	0.550332i	0.938085	+	0.346405i	$0.112598\pi$
$312$		0			0
$313$	0.854451	−	0.769352i	0.0482965	−	0.0434863i	−0.644629	−	0.764496i	$-0.722988\pi$
$313$	0.854451	−	0.769352i	0.0482965	−	0.0434863i	0.692925	+	0.721009i	$0.256321\pi$
$314$	−2.33513	−	7.18680i	−0.131779	−	0.405575i
$315$		0			0
$316$	4.04814	−	12.4589i	0.227726	−	0.700868i
$317$	−3.70021	−	8.31080i	−0.207824	−	0.466781i	0.779317	−	0.626630i	$-0.215566\pi$
$317$	−3.70021	−	8.31080i	−0.207824	−	0.466781i	−0.987142	+	0.159849i	$0.948899\pi$
$318$		0			0
$319$	−0.705451	+	6.71192i	−0.0394977	+	0.375795i
$320$	−3.41359	+	6.48706i	−0.190826	+	0.362638i
$321$		0			0
$322$	3.97531	−	0.417822i	0.221535	−	0.0232843i
$323$	−36.4000	+	11.8271i	−2.02535	+	0.658077i
$324$		0			0
$325$	−23.2382	+	4.30356i	−1.28902	+	0.238718i
$326$	3.20173	−	5.54556i	0.177328	−	0.307140i
$327$		0			0
$328$	−1.91077	+	4.29165i	−0.105504	+	0.236967i
$329$	−24.5619	−	10.9356i	−1.35414	−	0.602902i
$330$		0			0
$331$	−10.3351	+	4.60148i	−0.568068	+	0.252920i	−0.670612	−	0.741808i	$-0.733968\pi$
$331$	−10.3351	+	4.60148i	−0.568068	+	0.252920i	0.102544	+	0.994728i	$0.467302\pi$
$332$			5.99122i			0.328811i
$333$		0			0
$334$	−0.844192	+	2.59816i	−0.0461921	+	0.142165i
$335$	−5.11454	−	6.48870i	−0.279437	−	0.354516i
$336$		0			0
$337$	5.83345	+	27.4442i	0.317768	+	1.49498i	0.789780	+	0.613390i	$0.210195\pi$
$337$	5.83345	+	27.4442i	0.317768	+	1.49498i	−0.472012	+	0.881592i	$0.656472\pi$
$338$	−0.902037	−	4.24375i	−0.0490643	−	0.230829i
$339$		0			0
$340$	−22.6671	−	6.39452i	−1.22930	−	0.346791i
$341$	−3.47648	+	10.6995i	−0.188262	+	0.579411i
$342$		0			0
$343$		−	9.69843i		−	0.523666i
$344$	−9.21363	+	4.10217i	−0.496765	+	0.221174i
$345$		0			0
$346$	5.60113	+	2.49378i	0.301118	+	0.134067i
$347$	−2.92423	+	6.56793i	−0.156981	+	0.352585i	−0.974864	−	0.222799i	$-0.928481\pi$
$347$	−2.92423	+	6.56793i	−0.156981	+	0.352585i	0.817883	+	0.575384i	$0.195147\pi$
$348$		0			0
$349$	8.28967	−	14.3581i	0.443736	−	0.768573i	−0.554227	−	0.832365i	$-0.686986\pi$
$349$	8.28967	−	14.3581i	0.443736	−	0.768573i	0.997963	+	0.0637921i	$0.0203195\pi$
$350$	6.81972	+	6.47350i	0.364530	+	0.346023i
$351$		0			0
$352$	8.49461	−	2.76007i	0.452764	−	0.147112i
$353$	−1.48705	+	0.156295i	−0.0791476	+	0.00831875i	−0.144019	−	0.989575i	$-0.546003\pi$
$353$	−1.48705	+	0.156295i	−0.0791476	+	0.00831875i	0.0648719	+	0.997894i	$0.479336\pi$
$354$		0			0
$355$	28.4435	+	4.88956i	1.50963	+	0.259511i
$356$	−0.572451	+	5.44651i	−0.0303399	+	0.288664i
$357$		0			0
$358$	0.634082	+	1.42417i	0.0335123	+	0.0752698i
$359$	−8.44096	+	25.9786i	−0.445497	+	1.37110i	0.436441	+	0.899733i	$0.356239\pi$
$359$	−8.44096	+	25.9786i	−0.445497	+	1.37110i	−0.881938	+	0.471366i	$0.843761\pi$
$360$		0			0
$361$	7.11916	+	21.9105i	0.374693	+	1.15319i
$362$	−6.10494	+	5.49691i	−0.320869	+	0.288911i
$363$		0			0
$364$	22.8502	−	25.3777i	1.19768	−	1.33015i
$365$	−8.55510	−	4.50183i	−0.447795	−	0.235636i
$366$		0			0
$367$	0.492892	+	1.10705i	0.0257288	+	0.0577878i	0.925953	−	0.377639i	$-0.123264\pi$
$367$	0.492892	+	1.10705i	0.0257288	+	0.0577878i	−0.900224	+	0.435427i	$0.856597\pi$
$368$			5.85000i			0.304952i
$369$		0			0
$370$	−0.574991	+	0.145986i	−0.0298923	+	0.00758945i
$371$	3.79549	+	36.1117i	0.197052	+	1.87483i
$372$		0			0
$373$	9.39471	+	8.45904i	0.486440	+	0.437992i	0.875499	−	0.483221i	$-0.160533\pi$
$373$	9.39471	+	8.45904i	0.486440	+	0.437992i	−0.389059	+	0.921213i	$0.627200\pi$
$374$	2.55426	+	4.42411i	0.132078	+	0.228765i
$375$		0			0
$376$	−5.83528	+	10.1070i	−0.300931	+	0.521228i
$377$	16.2819	−	5.29032i	0.838563	−	0.272466i
$378$		0			0
$379$	−15.1480	+	11.0057i	−0.778100	+	0.565322i	−0.904408	−	0.426669i	$-0.859687\pi$
$379$	−15.1480	+	11.0057i	−0.778100	+	0.565322i	0.126308	+	0.991991i	$0.459687\pi$
$380$	−7.02353	+	24.8968i	−0.360299	+	1.27718i
$381$		0			0
$382$	5.58827	−	3.22639i	0.285921	−	0.165076i
$383$	31.2962	+	3.28936i	1.59916	+	0.168079i	0.861738	−	0.507354i	$-0.169376\pi$
$383$	31.2962	+	3.28936i	1.59916	+	0.168079i	0.737422	+	0.675432i	$0.236043\pi$
$384$		0			0
$385$	0.661149	+	16.8576i	0.0336953	+	0.859145i
$386$	1.78475	+	5.49290i	0.0908415	+	0.279581i
$387$		0			0
$388$	10.7991	+	3.50885i	0.548242	+	0.178135i
$389$	27.2918	+	5.80105i	1.38375	+	0.294125i	0.838844	−	0.544372i	$-0.183232\pi$
$389$	27.2918	+	5.80105i	1.38375	+	0.294125i	0.544906	+	0.838497i	$0.316565\pi$
$390$		0			0
$391$	−12.2728	+	2.60866i	−0.620660	+	0.131925i
$392$	−16.4225	−	1.72608i	−0.829462	−	0.0871800i
$393$		0			0
$394$	−8.03514	+	3.57747i	−0.404804	+	0.180231i
$395$	10.4985	−	12.6213i	0.528238	−	0.635047i
$396$		0			0
$397$	−11.9517	−	16.4501i	−0.599839	−	0.825607i	0.395855	−	0.918313i	$-0.370448\pi$
$397$	−11.9517	−	16.4501i	−0.599839	−	0.825607i	−0.995694	+	0.0927060i	$0.970448\pi$
$398$	−0.998168	+	4.69601i	−0.0500337	+	0.235390i
$399$		0			0
$400$	−10.4655	+	8.93583i	−0.523275	+	0.446791i
$401$	6.98104	+	12.0915i	0.348617	+	0.603822i	0.986004	−	0.166722i	$-0.0533182\pi$
$401$	6.98104	+	12.0915i	0.348617	+	0.603822i	−0.637387	+	0.770544i	$0.719985\pi$
$402$		0			0
$403$	28.3818	−	2.98305i	1.41380	−	0.148596i
$404$	4.51522	−	3.28050i	0.224641	−	0.163211i
$405$		0			0
$406$	−5.51055	−	4.00365i	−0.273484	−	0.198698i
$407$	−0.921774	−	0.532186i	−0.0456906	−	0.0263795i
$408$		0			0
$409$	−23.1708	+	4.92511i	−1.14572	+	0.243531i	−0.741386	−	0.671079i	$-0.765831\pi$
$409$	−23.1708	+	4.92511i	−1.14572	+	0.243531i	−0.404337	+	0.914610i	$0.632498\pi$
$410$	−1.98848	+	1.93681i	−0.0982038	+	0.0956525i
$411$		0			0
$412$	18.4282	−	16.5928i	0.907891	−	0.817469i
$413$	12.1021	+	3.93222i	0.595507	+	0.193492i
$414$		0			0
$415$	−2.78270	+	6.97347i	−0.136598	+	0.342314i
$416$	−15.1606	−	16.8375i	−0.743309	−	0.825528i
$417$		0			0
$418$	4.85930	−	2.80552i	0.237676	−	0.137222i
$419$	2.60301	−	24.7660i	0.127166	−	1.20990i	−0.725790	−	0.687916i	$-0.758526\pi$
$419$	2.60301	−	24.7660i	0.127166	−	1.20990i	0.852956	−	0.521983i	$-0.174808\pi$
$420$		0			0
$421$	2.97741	+	28.3281i	0.145110	+	1.38063i	0.788474	+	0.615068i	$0.210871\pi$
$421$	2.97741	+	28.3281i	0.145110	+	1.38063i	−0.643364	+	0.765560i	$0.722462\pi$
$422$	1.96163	+	2.69996i	0.0954908	+	0.131432i
$423$		0			0
$424$	15.7614			0.765440
$425$	−23.4134	−	17.9709i	−1.13571	−	0.871719i
$426$		0			0
$427$	10.2225	+	9.20442i	0.494703	+	0.445433i
$428$	4.03746	−	9.06827i	0.195158	−	0.438331i
$429$		0			0
$430$	−5.95480	+	0.233544i	−0.287166	+	0.0112625i
$431$	−13.5072	−	9.81357i	−0.650620	−	0.472703i	0.212863	−	0.977082i	$-0.431721\pi$
$431$	−13.5072	−	9.81357i	−0.650620	−	0.472703i	−0.863482	+	0.504379i	$0.831721\pi$
$432$		0			0
$433$	3.78305	−	5.20692i	0.181802	−	0.250229i	−0.708383	−	0.705828i	$-0.750575\pi$
$433$	3.78305	−	5.20692i	0.181802	−	0.250229i	0.890185	+	0.455599i	$0.150575\pi$
$434$	−7.59756	−	8.43795i	−0.364695	−	0.405034i
$435$		0			0
$436$	−14.4589	+	16.0582i	−0.692454	+	0.769048i
$437$	2.86526	+	13.4800i	0.137064	+	0.644836i
$438$		0			0
$439$	−23.3449	−	4.96212i	−1.11419	−	0.236829i	−0.386201	−	0.922415i	$-0.626213\pi$
$439$	−23.3449	−	4.96212i	−1.11419	−	0.236829i	−0.727992	+	0.685586i	$0.759546\pi$
$440$	7.30732	+	0.479464i	0.348363	+	0.0228576i
$441$		0			0
$442$	7.61696	−	10.4838i	0.362302	−	0.498666i
$443$	−2.17168	−	1.25382i	−0.103180	−	0.0595709i	0.447522	−	0.894273i	$-0.352307\pi$
$443$	−2.17168	−	1.25382i	−0.103180	−	0.0595709i	−0.550702	+	0.834702i	$0.685640\pi$
$444$		0			0
$445$	−3.19601	+	6.07357i	−0.151505	+	0.287915i
$446$	−4.32001	−	1.92339i	−0.204558	−	0.0910752i
$447$		0			0
$448$	2.75981	−	12.9839i	0.130389	−	0.613431i
$449$	−23.7372			−1.12023			−0.560115	−	0.828415i	$-0.689243\pi$
$449$	−23.7372			−1.12023			−0.560115	+	0.828415i	$0.689243\pi$
$450$		0			0
$451$	−4.98038			−0.234517
$452$	5.58547	−	26.2776i	0.262718	−	1.23599i
$453$		0			0
$454$	−9.48135	−	4.22137i	−0.444982	−	0.198119i
$455$	38.3835	−	18.9253i	1.79945	−	0.887231i
$456$		0			0
$457$	14.9064	+	8.60622i	0.697293	+	0.402582i	0.806338	−	0.591455i	$-0.201446\pi$
$457$	14.9064	+	8.60622i	0.697293	+	0.402582i	−0.109046	+	0.994037i	$0.534779\pi$
$458$	−4.05399	+	5.57983i	−0.189430	+	0.260729i
$459$		0			0
$460$	−3.14302	+	7.87642i	−0.146544	+	0.367240i
$461$	9.68848	+	2.05935i	0.451237	+	0.0959135i	0.427924	−	0.903815i	$-0.359245\pi$
$461$	9.68848	+	2.05935i	0.451237	+	0.0959135i	0.0233134	+	0.999728i	$0.492578\pi$
$462$		0			0
$463$	2.44622	+	11.5086i	0.113686	+	0.534849i	0.997724	+	0.0674341i	$0.0214812\pi$
$463$	2.44622	+	11.5086i	0.113686	+	0.534849i	−0.884038	+	0.467415i	$0.845185\pi$
$464$	6.67034	−	7.40816i	0.309663	−	0.343915i
$465$		0			0
$466$	7.71652	+	8.57006i	0.357461	+	0.397001i
$467$	1.47584	−	2.03131i	0.0682935	−	0.0939979i	−0.773504	−	0.633792i	$-0.781498\pi$
$467$	1.47584	−	2.03131i	0.0682935	−	0.0939979i	0.841797	+	0.539794i	$0.181498\pi$
$468$		0			0
$469$	12.1038	+	8.79389i	0.558899	+	0.406064i
$470$	−5.41578	+	4.26884i	−0.249811	+	0.196907i
$471$		0			0
$472$	2.24662	−	5.04598i	0.103409	−	0.232260i
$473$	−7.94589	−	7.15451i	−0.365352	−	0.328965i
$474$		0			0
$475$	−19.7387	+	25.7165i	−0.905673	+	1.17995i
$476$	42.6479			1.95476
$477$		0			0
$478$	−0.669821	−	0.921929i	−0.0306369	−	0.0421681i
$479$	−2.26299	−	21.5309i	−0.103399	−	0.983772i	−0.916062	−	0.401038i	$-0.868650\pi$
$479$	−2.26299	−	21.5309i	−0.103399	−	0.983772i	0.812663	−	0.582734i	$-0.198017\pi$
$480$		0			0
$481$	−0.282225	+	2.68520i	−0.0128684	+	0.122434i
$482$	3.26073	−	1.88259i	0.148522	−	0.0857494i
$483$		0			0
$484$	−8.98791	−	9.98208i	−0.408541	−	0.453731i
$485$	10.9399	+	9.09991i	0.496755	+	0.413206i
$486$		0			0
$487$	−29.7328	−	9.66076i	−1.34732	−	0.437771i	−0.455530	−	0.890220i	$-0.650550\pi$
$487$	−29.7328	−	9.66076i	−1.34732	−	0.437771i	−0.891790	+	0.452450i	$0.850550\pi$
$488$	4.43730	−	3.99537i	0.200867	−	0.180862i
$489$		0			0
$490$	−8.63469	−	4.54371i	−0.390075	−	0.205264i
$491$	−3.83028	+	0.814151i	−0.172858	+	0.0367421i	−0.293528	−	0.955951i	$-0.594829\pi$
$491$	−3.83028	+	0.814151i	−0.172858	+	0.0367421i	0.120669	+	0.992693i	$0.461496\pi$
$492$		0			0
$493$	18.5161	+	10.6903i	0.833923	+	0.481466i
$494$	−11.5151	−	8.36622i	−0.518090	−	0.376414i
$495$		0			0
$496$	13.4437	−	9.76745i	0.603642	−	0.438572i
$497$	−51.9751	+	5.46280i	−2.33140	+	0.245040i
$498$		0			0
$499$	2.80768	+	4.86304i	0.125689	+	0.217699i	0.922002	−	0.387185i	$-0.126553\pi$
$499$	2.80768	+	4.86304i	0.125689	+	0.217699i	−0.796313	+	0.604885i	$0.793219\pi$
$500$	−18.8916	+	6.40839i	−0.844860	+	0.286592i
$501$		0			0
$502$	1.89750	−	8.92705i	0.0846897	−	0.398434i
$503$	2.36398	+	3.25374i	0.105405	+	0.145077i	0.858461	−	0.512879i	$-0.171421\pi$
$503$	2.36398	+	3.25374i	0.105405	+	0.145077i	−0.753056	+	0.657956i	$0.771421\pi$
$504$		0			0
$505$	6.77916	−	1.72118i	0.301669	−	0.0765915i
$506$	1.68041	−	0.748167i	0.0747034	−	0.0332601i
$507$		0			0
$508$	10.9362	+	1.14944i	0.485217	+	0.0509984i
$509$	−31.6664	+	6.73091i	−1.40359	+	0.298342i	−0.846623	−	0.532193i	$-0.821368\pi$
$509$	−31.6664	+	6.73091i	−1.40359	+	0.298342i	−0.556967	+	0.830535i	$0.688035\pi$
$510$		0			0
$511$	17.1231	+	3.63962i	0.757481	+	0.161008i
$512$	−21.7485	−	7.06651i	−0.961157	−	0.312299i
$513$		0			0
$514$	2.04012	+	6.27884i	0.0899858	+	0.276948i
$515$	29.1562	−	10.7540i	1.28478	−	0.473876i
$516$		0			0
$517$	−12.3048	−	1.29329i	−0.541164	−	0.0568786i
$518$	0.930315	−	0.537117i	0.0408757	−	0.0235996i
$519$		0			0
$520$	−6.42834	−	17.4286i	−0.281901	−	0.764293i
$521$	8.27088	−	6.00915i	0.362354	−	0.263265i	−0.391679	−	0.920102i	$-0.628106\pi$
$521$	8.27088	−	6.00915i	0.362354	−	0.263265i	0.754033	+	0.656836i	$0.228106\pi$
$522$		0			0
$523$	1.54847	−	0.503129i	0.0677100	−	0.0220003i	−0.274966	−	0.961454i	$-0.588667\pi$
$523$	1.54847	−	0.503129i	0.0677100	−	0.0220003i	0.342676	+	0.939454i	$0.388667\pi$
$524$	−13.1560	+	22.7868i	−0.574721	+	0.995447i
$525$		0			0
$526$	−2.83867	−	4.91673i	−0.123772	−	0.214379i
$527$	26.4861	+	23.8482i	1.15375	+	1.03884i
$528$		0			0
$529$	−1.93192	−	18.3809i	−0.0839963	−	0.799172i
$530$	8.64986	+	3.45165i	0.375726	+	0.149930i
$531$		0			0
$532$		−	46.8431i		−	2.03091i
$533$	5.13858	+	11.5415i	0.222577	+	0.499916i
$534$		0			0
$535$	8.91127	−	8.67975i	0.385268	−	0.375258i
$536$	4.34544	−	4.82610i	0.187694	−	0.208456i
$537$		0			0
$538$	−2.72380	+	2.45252i	−0.117431	+	0.105736i
$539$	−5.40973	−	16.6495i	−0.233014	−	0.717143i
$540$		0			0
$541$	−12.1352	+	37.3483i	−0.521733	+	1.60573i	0.248955	+	0.968515i	$0.419913\pi$
$541$	−12.1352	+	37.3483i	−0.521733	+	1.60573i	−0.770688	+	0.637213i	$0.780087\pi$
$542$	4.45544	+	10.0071i	0.191377	+	0.429841i
$543$		0			0
$544$	2.95773	−	28.1409i	0.126812	−	1.20653i
$545$	−24.2878	+	11.9753i	−1.04038	+	0.512965i
$546$		0			0
$547$	4.75788	−	0.500073i	0.203432	−	0.0213816i	−0.00226422	−	0.999997i	$-0.500721\pi$
$547$	4.75788	−	0.500073i	0.203432	−	0.0213816i	0.205696	+	0.978616i	$0.434054\pi$
$548$	31.7567	−	10.3184i	1.35658	−	0.440779i
$549$		0			0
$550$	3.90527	+	1.86339i	0.166521	+	0.0794553i
$551$	11.7418	−	20.3375i	0.500219	−	0.866406i
$552$		0			0
$553$	−12.0915	+	27.1579i	−0.514182	+	1.15487i
$554$	−0.356301	−	0.158635i	−0.0151378	−	0.00673976i
$555$		0			0
$556$	11.7492	−	5.23106i	0.498275	−	0.221846i
$557$			16.0033i			0.678083i	0.940771	+	0.339041i	$0.110103\pi$
$557$			16.0033i			0.678083i	−0.940771	+	0.339041i	$0.889897\pi$
$558$		0			0
$559$	−8.38145	+	25.7954i	−0.354497	+	1.09103i
$560$	13.8459	−	20.7186i	0.585095	−	0.875522i
$561$		0			0
$562$	−0.00657974	−	0.0309552i	−0.000277550	−	0.00130577i
$563$	−7.14825	−	33.6299i	−0.301263	−	1.41733i	−0.824847	−	0.565356i	$-0.808739\pi$
$563$	−7.14825	−	33.6299i	−0.301263	−	1.41733i	0.523584	−	0.851974i	$-0.324595\pi$
$564$		0			0
$565$	18.7062	−	27.9915i	0.786974	−	1.17761i
$566$	1.54388	−	4.75157i	0.0648941	−	0.199723i
$567$		0			0
$568$			22.6851i			0.951847i
$569$	−36.9526	+	16.4523i	−1.54913	+	0.689718i	−0.990221	−	0.139510i	$-0.955447\pi$
$569$	−36.9526	+	16.4523i	−1.54913	+	0.689718i	−0.558911	+	0.829228i	$0.688781\pi$
$570$		0			0
$571$	−32.1413	−	14.3102i	−1.34507	−	0.598865i	−0.397265	−	0.917704i	$-0.630040\pi$
$571$	−32.1413	−	14.3102i	−1.34507	−	0.598865i	−0.947809	+	0.318839i	$0.896707\pi$
$572$	6.39177	−	14.3562i	0.267253	−	0.600261i
$573$		0			0
$574$	2.51326	−	4.35310i	0.104902	−	0.181695i
$575$	−7.31662	+	7.70793i	−0.305124	+	0.321443i
$576$		0			0
$577$	6.80821	−	2.21212i	0.283429	−	0.0920918i	−0.163852	−	0.986485i	$-0.552392\pi$
$577$	6.80821	−	2.21212i	0.283429	−	0.0920918i	0.447282	+	0.894393i	$0.352392\pi$
$578$	8.24289	−	0.866362i	0.342859	−	0.0360359i
$579$		0			0
$580$	12.9611	−	6.39057i	0.538180	−	0.265354i
$581$	1.42116	−	13.5214i	0.0589596	−	0.560963i
$582$		0			0
$583$	6.79635	+	15.2649i	0.281476	+	0.632206i
$584$	2.34812	−	7.22677i	0.0971659	−	0.299046i
$585$		0			0
$586$	−0.271998	−	0.837125i	−0.0112361	−	0.0345813i
$587$	28.6094	−	25.7600i	1.18084	−	1.06323i	0.184067	−	0.982914i	$-0.441074\pi$
$587$	28.6094	−	25.7600i	1.18084	−	1.06323i	0.996769	−	0.0803163i	$-0.0255930\pi$
$588$		0			0
$589$	26.1941	−	29.0915i	1.07931	−	1.19869i
$590$	2.33799	−	2.27724i	0.0962534	−	0.0937527i
$591$		0			0
$592$	0.639458	+	1.43625i	0.0262815	+	0.0590293i
$593$			28.9799i			1.19006i	0.803703	+	0.595031i	$0.202860\pi$
$593$			28.9799i			1.19006i	−0.803703	+	0.595031i	$0.797140\pi$
$594$		0			0
$595$	49.6400	+	19.8084i	2.03504	+	0.812066i
$596$	3.59433	+	34.1978i	0.147230	+	1.40080i
$597$		0			0
$598$	−3.46758	−	3.12222i	−0.141800	−	0.127677i
$599$	20.6451	+	35.7584i	0.843538	+	1.46105i	0.886885	+	0.461990i	$0.152864\pi$
$599$	20.6451	+	35.7584i	0.843538	+	1.46105i	−0.0433474	+	0.999060i	$0.513802\pi$
$600$		0			0
$601$	11.8674	−	20.5550i	0.484083	−	0.838457i	−0.515750	−	0.856739i	$-0.672487\pi$
$601$	11.8674	−	20.5550i	0.484083	−	0.838457i	0.999833	+	0.0182828i	$0.00581991\pi$
$602$	10.2632	−	3.33470i	0.418295	−	0.135912i
$603$		0			0
$604$	−2.79525	+	2.03087i	−0.113737	+	0.0826348i
$605$	−5.82515	−	15.7932i	−0.236826	−	0.642084i
$606$		0			0
$607$	36.1063	−	20.8460i	1.46551	−	0.846113i	0.466253	−	0.884651i	$-0.345603\pi$
$607$	36.1063	−	20.8460i	1.46551	−	0.846113i	0.999257	+	0.0385383i	$0.0122702\pi$
$608$	−30.9091	−	3.24867i	−1.25353	−	0.131751i
$609$		0			0
$610$	3.31016	−	1.22092i	0.134024	−	0.0494335i
$611$	9.69862	+	29.8493i	0.392364	+	1.20757i
$612$		0			0
$613$	−18.5851	−	6.03866i	−0.750645	−	0.243899i	−0.0913860	−	0.995816i	$-0.529130\pi$
$613$	−18.5851	−	6.03866i	−0.750645	−	0.243899i	−0.659259	+	0.751916i	$0.729130\pi$
$614$	6.18876	+	1.31546i	0.249758	+	0.0530877i
$615$		0			0
$616$	−12.9709	+	2.75704i	−0.522611	+	0.111084i
$617$	−45.5013	−	4.78238i	−1.83181	−	0.192531i	−0.875175	−	0.483806i	$-0.839254\pi$
$617$	−45.5013	−	4.78238i	−1.83181	−	0.192531i	−0.956639	+	0.291275i	$0.905921\pi$
$618$		0			0
$619$	−2.04196	+	0.909138i	−0.0820732	+	0.0365413i	−0.447363	−	0.894353i	$-0.647637\pi$
$619$	−2.04196	+	0.909138i	−0.0820732	+	0.0365413i	0.365289	+	0.930894i	$0.380970\pi$
$620$	23.3484	−	5.92798i	0.937693	−	0.238073i
$621$		0			0
$622$	3.56520	+	4.90708i	0.142952	+	0.196756i
$623$	2.58390	−	12.1563i	0.103522	−	0.487032i
$624$		0			0
$625$	−24.9654	−	1.31544i	−0.998615	−	0.0526175i
$626$	0.267004	+	0.462465i	0.0106716	+	0.0184838i
$627$		0			0
$628$	−28.8719	+	3.03456i	−1.15211	+	0.121092i
$629$	−2.72796	+	1.98198i	−0.108771	+	0.0790267i
$630$		0			0
$631$	−36.8770	−	26.7927i	−1.46805	−	1.06660i	−0.981173	−	0.193133i	$-0.938135\pi$
$631$	−36.8770	−	26.7927i	−1.46805	−	1.06660i	−0.486880	−	0.873469i	$-0.661865\pi$
$632$	11.1752	+	6.45203i	0.444527	+	0.256648i
$633$		0			0
$634$	4.13286	−	0.878468i	0.164137	−	0.0348884i
$635$	12.1953	+	6.41738i	0.483957	+	0.254666i
$636$		0			0
$637$	−33.0016	+	29.7148i	−1.30757	+	1.17734i
$638$	−2.98107	−	0.968610i	−0.118022	−	0.0383476i
$639$		0			0
$640$	−19.0982	−	15.8860i	−0.754921	−	0.627951i
$641$	15.1973	+	16.8783i	0.600258	+	0.666654i	0.964326	−	0.264719i	$-0.0852791\pi$
$641$	15.1973	+	16.8783i	0.600258	+	0.666654i	−0.364068	+	0.931372i	$0.618612\pi$
$642$		0			0
$643$	−16.0494	+	9.26613i	−0.632927	+	0.365421i	−0.781885	−	0.623423i	$-0.785742\pi$
$643$	−16.0494	+	9.26613i	−0.632927	+	0.365421i	0.148958	+	0.988844i	$0.452408\pi$
$644$	1.60518	−	15.2722i	0.0632528	−	0.601810i
$645$		0			0
$646$	−1.85808	−	17.6784i	−0.0731051	−	0.695549i
$647$	1.44181	+	1.98448i	0.0566833	+	0.0780179i	0.836418	−	0.548093i	$-0.184646\pi$
$647$	1.44181	+	1.98448i	0.0566833	+	0.0780179i	−0.779734	+	0.626111i	$0.784646\pi$
$648$		0			0
$649$	5.85577			0.229859
$650$	0.288875	−	10.9726i	0.0113306	−	0.430380i
$651$		0			0
$652$	−18.2818	−	16.4610i	−0.715972	−	0.644664i
$653$	1.12901	−	2.53580i	0.0441816	−	0.0992335i	−0.890106	−	0.455753i	$-0.849370\pi$
$653$	1.12901	−	2.53580i	0.0441816	−	0.0992335i	0.934288	+	0.356520i	$0.116037\pi$
$654$		0			0
$655$	−25.8965	+	20.4122i	−1.01186	+	0.797571i
$656$	5.95148	+	4.32400i	0.232366	+	0.168824i
$657$		0			0
$658$	7.33980	−	10.1024i	0.286135	−	0.393831i
$659$	−1.97616	−	2.19474i	−0.0769801	−	0.0854951i	0.703424	−	0.710770i	$-0.251653\pi$
$659$	−1.97616	−	2.19474i	−0.0769801	−	0.0854951i	−0.780404	+	0.625275i	$0.784987\pi$
$660$		0			0
$661$	16.7332	−	18.5841i	0.650845	−	0.722837i	−0.323916	−	0.946086i	$-0.605000\pi$
$661$	16.7332	−	18.5841i	0.650845	−	0.722837i	0.974762	+	0.223249i	$0.0716662\pi$
$662$	−1.09244	−	5.13952i	−0.0424589	−	0.199753i
$663$		0			0
$664$	−5.77262	−	1.22701i	−0.224021	−	0.0476171i
$665$	21.7569	−	54.5230i	0.843697	−	2.11431i
$666$		0			0
$667$	4.52509	−	6.22826i	0.175212	−	0.241159i
$668$	9.08910	+	5.24760i	0.351668	+	0.203036i
$669$		0			0
$670$	3.44167	−	1.69694i	0.132963	−	0.0655586i
$671$	5.78288	+	2.57471i	0.223246	+	0.0993954i
$672$		0			0
$673$	7.70518	−	36.2500i	0.297013	−	1.39733i	−0.536064	−	0.844177i	$-0.680089\pi$
$673$	7.70518	−	36.2500i	0.297013	−	1.39733i	0.833077	−	0.553158i	$-0.186577\pi$
$674$	−13.0311			−0.501939
$675$		0			0
$676$	−16.6677			−0.641067
$677$	2.64567	−	12.4469i	0.101681	−	0.478372i	−0.897612	−	0.440786i	$-0.854700\pi$
$677$	2.64567	−	12.4469i	0.101681	−	0.478372i	0.999293	−	0.0375863i	$-0.0119669\pi$
$678$		0			0
$679$	−23.5399	−	10.4806i	−0.903379	−	0.402210i
$680$	10.8034	−	20.5305i	0.414293	−	0.787307i
$681$		0			0
$682$	−4.52504	−	2.61254i	−0.173273	−	0.100039i
$683$	3.75589	−	5.16954i	0.143715	−	0.197807i	−0.731091	−	0.682280i	$-0.760989\pi$
$683$	3.75589	−	5.16954i	0.143715	−	0.197807i	0.874806	+	0.484473i	$0.160989\pi$
$684$		0			0
$685$	41.7556	+	2.73976i	1.59540	+	0.104681i
$686$	4.40596	+	0.936515i	0.168220	+	0.0357563i
$687$		0			0
$688$	3.28362	+	15.4482i	0.125187	+	0.588957i
$689$	28.3623	−	31.4995i	1.08052	−	1.20004i
$690$		0			0
$691$	−15.0401	−	16.7037i	−0.572153	−	0.635440i	0.385726	−	0.922613i	$-0.373951\pi$
$691$	−15.0401	−	16.7037i	−0.572153	−	0.635440i	−0.957879	+	0.287174i	$0.907284\pi$
$692$	13.8451	−	19.0561i	0.526311	−	0.724405i
$693$		0			0
$694$	−2.70141	−	1.96269i	−0.102544	−	0.0745026i
$695$	16.1051	−	0.631633i	0.610900	−	0.0239592i
$696$		0			0
$697$	−6.41745	+	14.4138i	−0.243078	+	0.545963i
$698$	5.72236	+	5.15244i	0.216594	+	0.195023i
$699$		0			0
$700$	29.7735	−	20.4566i	1.12533	−	0.773186i
$701$	−39.9079			−1.50730			−0.753651	−	0.657275i	$-0.771709\pi$
$701$	−39.9079			−1.50730			−0.753651	+	0.657275i	$0.771709\pi$
$702$		0			0
$703$	2.17694	+	2.99630i	0.0821049	+	0.113008i
$704$	−0.638504	−	6.07496i	−0.0240645	−	0.228959i
$705$		0			0
$706$	0.0725905	−	0.690652i	0.00273198	−	0.0259930i
$707$	−10.9684	+	6.33263i	−0.412511	+	0.238163i
$708$		0			0
$709$	8.98411	+	9.97786i	0.337405	+	0.374726i	0.887840	−	0.460151i	$-0.152205\pi$
$709$	8.98411	+	9.97786i	0.337405	+	0.374726i	−0.550435	+	0.834878i	$0.685538\pi$
$710$	−4.96791	+	12.4496i	−0.186443	+	0.467226i
$711$		0			0
$712$	−5.13054	−	1.66701i	−0.192275	−	0.0624740i
$713$	9.53692	−	8.58708i	0.357160	−	0.321589i
$714$		0			0
$715$	14.1076	−	13.7411i	0.527594	−	0.513887i
$716$	5.85825	−	1.24521i	0.218933	−	0.0465357i
$717$		0			0
$718$	−10.9869	−	6.34328i	−0.410027	−	0.236729i
$719$	32.3514	+	23.5047i	1.20650	+	0.876576i	0.994909	−	0.100781i	$-0.0321341\pi$
$719$	32.3514	+	23.5047i	1.20650	+	0.876576i	0.211595	+	0.977357i	$0.432134\pi$
$720$		0			0
$721$	−45.5260	+	33.0766i	−1.69548	+	1.23184i
$722$	−10.6413	+	1.11845i	−0.396028	+	0.0416243i
$723$		0			0
$724$	15.7801	+	27.3319i	0.586462	+	1.01578i
$725$	18.0542	−	1.41834i	0.670517	−	0.0526757i
$726$		0			0
$727$	8.23702	−	38.7521i	0.305494	−	1.43724i	−0.510849	−	0.859670i	$-0.670669\pi$
$727$	8.23702	−	38.7521i	0.305494	−	1.43724i	0.816343	−	0.577567i	$-0.195998\pi$
$728$	19.7720	+	27.2138i	0.732800	+	1.00861i
$729$		0			0
$730$	2.87127	−	3.45183i	0.106271	−	0.127758i
$731$	−30.9447	+	13.7775i	−1.14453	+	0.509577i
$732$		0			0
$733$	−5.95611	−	0.626012i	−0.219994	−	0.0231223i	−0.00610980	−	0.999981i	$-0.501945\pi$
$733$	−5.95611	−	0.626012i	−0.219994	−	0.0231223i	−0.213884	+	0.976859i	$0.568611\pi$
$734$	−0.550525	+	0.117018i	−0.0203203	+	0.00431921i
$735$		0			0
$736$	−9.96594	−	2.11833i	−0.367349	−	0.0780825i
$737$	6.54783	+	2.12752i	0.241192	+	0.0783682i
$738$		0			0
$739$	−11.4278	−	35.1713i	−0.420380	−	1.29380i	−0.907349	−	0.420377i	$-0.861898\pi$
$739$	−11.4278	−	35.1713i	−0.420380	−	1.29380i	0.486969	−	0.873419i	$-0.338102\pi$
$740$	0.0893153	+	2.27732i	0.00328329	+	0.0837158i
$741$		0			0
$742$	−16.7719	−	1.76280i	−0.615716	−	0.0647143i
$743$	0.698069	−	0.403030i	0.0256097	−	0.0147858i	−0.487141	−	0.873324i	$-0.661960\pi$
$743$	0.698069	−	0.403030i	0.0256097	−	0.0147858i	0.512750	+	0.858538i	$0.328627\pi$
$744$		0			0
$745$	−11.7000	+	41.4739i	−0.428655	+	1.51949i
$746$	−4.75009	+	3.45114i	−0.173913	+	0.126355i
$747$		0			0
$748$	18.6652	−	6.06470i	0.682468	−	0.221747i
$749$	−11.2631	+	19.5082i	−0.411544	+	0.712815i
$750$		0			0
$751$	−3.43319	−	5.94646i	−0.125279	−	0.216989i	0.796563	−	0.604555i	$-0.206649\pi$
$751$	−3.43319	−	5.94646i	−0.125279	−	0.216989i	−0.921842	+	0.387566i	$0.873316\pi$
$752$	13.5812	+	12.2286i	0.495255	+	0.445930i
$753$		0			0
$754$	0.831130	+	7.90767i	0.0302680	+	0.287980i
$755$	−4.19679	+	1.06553i	−0.152737	+	0.0387788i
$756$		0			0
$757$		−	45.6576i		−	1.65945i	−0.558169	−	0.829727i	$-0.688496\pi$
$757$		−	45.6576i		−	1.65945i	0.558169	−	0.829727i	$-0.311504\pi$
$758$	−3.53708	−	7.94441i	−0.128472	−	0.288554i
$759$		0			0
$760$	−22.5500	−	11.8662i	−0.817974	−	0.430431i
$761$	−3.15353	+	3.50235i	−0.114315	+	0.126960i	−0.797586	−	0.603205i	$-0.793890\pi$
$761$	−3.15353	+	3.50235i	−0.114315	+	0.126960i	0.683271	+	0.730165i	$0.260557\pi$
$762$		0			0
$763$	36.4409	−	32.8116i	1.31925	−	1.18786i
$764$	−7.66055	−	23.5768i	−0.277149	−	0.852977i
$765$		0			0
$766$	−4.51641	+	13.9001i	−0.163185	+	0.502231i
$767$	−6.04178	−	13.5701i	−0.218156	−	0.489987i
$768$		0			0
$769$	−0.0421959	+	0.401467i	−0.00152162	+	0.0144773i	−0.995256	−	0.0972871i	$-0.968984\pi$
$769$	−0.0421959	+	0.401467i	−0.00152162	+	0.0144773i	0.993735	+	0.111764i	$0.0356502\pi$
$770$	−7.72220	−	1.32748i	−0.278289	−	0.0478389i
$771$		0			0
$772$	22.0669	−	2.31932i	0.794205	−	0.0834743i
$773$	−6.50538	+	2.11373i	−0.233982	+	0.0760254i	−0.423661	−	0.905821i	$-0.639255\pi$
$773$	−6.50538	+	2.11373i	−0.233982	+	0.0760254i	0.189679	+	0.981846i	$0.439255\pi$
$774$		0			0
$775$	29.9296	+	3.94460i	1.07510	+	0.141694i
$776$	−5.59249	+	9.68647i	−0.200759	+	0.347724i
$777$		0			0
$778$	−5.27079	+	11.8384i	−0.188967	+	0.424427i
$779$	15.8317	+	7.04872i	0.567229	+	0.252546i
$780$		0			0
$781$	−21.9705	+	9.78190i	−0.786166	+	0.350024i
$782$		−	5.82736i		−	0.208386i
$783$		0			0
$784$	−7.99062	+	24.5926i	−0.285379	+	0.878307i
$785$	−35.0148	−	9.87787i	−1.24973	−	0.352556i
$786$		0			0
$787$	−8.22714	−	38.7056i	−0.293266	−	1.37971i	−0.840084	−	0.542456i	$-0.817495\pi$
$787$	−8.22714	−	38.7056i	−0.293266	−	1.37971i	0.546819	−	0.837251i	$-0.315839\pi$
$788$	7.02544	+	33.0521i	0.250271	+	1.17743i
$789$		0			0
$790$	4.72003	+	5.98819i	0.167931	+	0.213050i
$791$	−18.8389	+	57.9802i	−0.669834	+	2.06154i
$792$		0			0
$793$		−	16.0576i		−	0.570224i
$794$	8.62731	−	3.84113i	0.306172	−	0.136316i
$795$		0			0
$796$	16.8495	+	7.50187i	0.597214	+	0.265897i
$797$	−5.61517	+	12.6119i	−0.198899	+	0.446736i	−0.985267	−	0.171023i	$-0.945293\pi$
$797$	−5.61517	+	12.6119i	−0.198899	+	0.446736i	0.786367	+	0.617759i	$0.211959\pi$
$798$		0			0
$799$	−19.5982	+	33.9451i	−0.693335	+	1.20089i
$800$	−11.4333	−	21.0645i	−0.404227	−	0.744744i
$801$		0			0
$802$	−6.16724	+	2.00386i	−0.217773	+	0.0707587i
$803$	8.01163	−	0.842056i	0.282724	−	0.0297155i
$804$		0			0
$805$	8.96173	−	17.0305i	0.315860	−	0.600248i
$806$	−1.38546	+	13.1818i	−0.0488008	+	0.464309i
$807$		0			0
$808$	2.23608	+	5.02233i	0.0786651	+	0.176685i
$809$	−1.52661	+	4.69843i	−0.0536729	+	0.165188i	−0.974300	−	0.225255i	$-0.927678\pi$
$809$	−1.52661	+	4.69843i	−0.0536729	+	0.165188i	0.920627	+	0.390444i	$0.127678\pi$
$810$		0			0
$811$	−1.67486	−	5.15468i	−0.0588122	−	0.181005i	0.917334	−	0.398117i	$-0.130336\pi$
$811$	−1.67486	−	5.15468i	−0.0588122	−	0.181005i	−0.976147	+	0.217112i	$0.930336\pi$
$812$	−19.4465	+	17.5097i	−0.682440	+	0.614472i
$813$		0			0
$814$	0.330780	−	0.367368i	0.0115938	−	0.0128762i
$815$	−13.6336	−	27.6511i	−0.477563	−	0.968574i
$816$		0			0
$817$	15.1327	+	33.9886i	0.529426	+	1.18911i
$818$		−	11.0020i		−	0.384675i
$819$		0			0
$820$	5.68991	+	9.01936i	0.198700	+	0.314970i
$821$	−4.16163	−	39.5953i	−0.145242	−	1.38188i	−0.787934	−	0.615759i	$-0.788849\pi$
$821$	−4.16163	−	39.5953i	−0.145242	−	1.38188i	0.642692	−	0.766124i	$-0.277817\pi$
$822$		0			0
$823$	25.2639	+	22.7477i	0.880643	+	0.792935i	0.979348	−	0.202182i	$-0.0648032\pi$
$823$	25.2639	+	22.7477i	0.880643	+	0.792935i	−0.0987045	+	0.995117i	$0.531470\pi$
$824$	12.2133	+	21.1540i	0.425470	+	0.736935i
$825$		0			0
$826$	−2.95501	+	5.11823i	−0.102818	+	0.178086i
$827$	−35.5278	+	11.5437i	−1.23542	+	0.401413i	−0.852676	−	0.522440i	$-0.825022\pi$
$827$	−35.5278	+	11.5437i	−1.23542	+	0.401413i	−0.382746	+	0.923853i	$0.625022\pi$
$828$		0			0
$829$	−39.1531	+	28.4464i	−1.35984	+	0.987985i	−0.361390	+	0.932415i	$0.617698\pi$
$829$	−39.1531	+	28.4464i	−1.35984	+	0.987985i	−0.998455	+	0.0555699i	$0.982302\pi$
$830$	−2.89931	−	1.93755i	−0.100637	−	0.0672535i
$831$		0			0
$832$	−13.4192	+	7.74759i	−0.465228	+	0.268599i
$833$	−55.1562	−	5.79715i	−1.91105	−	0.200859i
$834$		0			0
$835$	8.14193	+	10.3295i	0.281763	+	0.357467i
$836$	−6.66127	−	20.5013i	−0.230385	−	0.709051i
$837$		0			0
$838$	10.9997	+	3.57403i	0.379980	+	0.123463i
$839$	5.28167	+	1.12265i	0.182344	+	0.0387583i	0.298178	−	0.954510i	$-0.403621\pi$
$839$	5.28167	+	1.12265i	0.182344	+	0.0387583i	−0.115835	+	0.993268i	$0.536954\pi$
$840$		0			0
$841$	15.5343	−	3.30191i	0.535665	−	0.113859i
$842$	−13.1569	−	1.38284i	−0.453415	−	0.0476558i
$843$		0			0
$844$	11.7128	−	5.21488i	0.403171	−	0.179503i
$845$	−19.4004	−	7.74156i	−0.667394	−	0.266318i
$846$		0			0
$847$	17.9167	+	24.6603i	0.615627	+	0.847337i
$848$	5.13152	−	24.1419i	0.176217	−	0.829036i
$849$		0			0
$850$	10.4250	−	8.90125i	0.357574	−	0.305310i
$851$	0.607072	+	1.05148i	0.0208102	+	0.0360443i
$852$		0			0
$853$	25.5618	−	2.68665i	0.875219	−	0.0919892i	0.343744	−	0.939063i	$-0.388305\pi$
$853$	25.5618	−	2.68665i	0.875219	−	0.0919892i	0.531475	+	0.847074i	$0.321638\pi$
$854$	−5.16865	+	3.75525i	−0.176868	+	0.128502i
$855$		0			0
$856$	7.91052	+	5.74733i	0.270376	+	0.196440i
$857$	6.75936	+	3.90252i	0.230895	+	0.133307i	0.610985	−	0.791642i	$-0.290774\pi$
$857$	6.75936	+	3.90252i	0.230895	+	0.133307i	−0.380090	+	0.924950i	$0.624107\pi$
$858$		0			0
$859$	0.578237	−	0.122908i	0.0197292	−	0.00419357i	−0.198037	−	0.980195i	$-0.563456\pi$
$859$	0.578237	−	0.122908i	0.0197292	−	0.00419357i	0.217766	+	0.976001i	$0.430123\pi$
$860$	−3.87877	+	22.5636i	−0.132265	+	0.769412i
$861$		0			0
$862$	5.76257	−	5.18864i	0.196274	−	0.176726i
$863$	−3.48431	−	1.13212i	−0.118607	−	0.0385379i	0.249112	−	0.968475i	$-0.419861\pi$
$863$	−3.48431	−	1.13212i	−0.118607	−	0.0385379i	−0.367719	+	0.929937i	$0.619861\pi$
$864$		0			0
$865$	24.9658	−	15.7498i	0.848864	−	0.535509i
$866$	2.00018	+	2.22142i	0.0679688	+	0.0754870i
$867$		0			0
$868$	−37.7768	+	21.8105i	−1.28223	+	0.740295i
$869$	−1.42998	+	13.6053i	−0.0485087	+	0.461529i
$870$		0			0
$871$	−1.82555	−	17.3689i	−0.0618564	−	0.588524i
$872$	−12.5111	−	17.2200i	−0.423679	−	0.583144i
$873$		0			0
$874$	−6.40058			−0.216503
$875$	44.1562	−	9.98171i	1.49275	−	0.337443i
$876$		0			0
$877$	25.7975	+	23.2282i	0.871121	+	0.784361i	0.977714	−	0.209942i	$-0.0673275\pi$
$877$	25.7975	+	23.2282i	0.871121	+	0.784361i	−0.106593	+	0.994303i	$0.533994\pi$
$878$	4.50854	−	10.1263i	0.152156	−	0.341748i
$879$		0			0
$880$	3.11349	−	11.0366i	0.104956	−	0.372044i
$881$	−2.77914	−	2.01917i	−0.0936317	−	0.0680274i	0.539984	−	0.841675i	$-0.318430\pi$
$881$	−2.77914	−	2.01917i	−0.0936317	−	0.0680274i	−0.633616	+	0.773648i	$0.718430\pi$
$882$		0			0
$883$	−27.9976	+	38.5354i	−0.942193	+	1.29682i	0.0127157	+	0.999919i	$0.495952\pi$
$883$	−27.9976	+	38.5354i	−0.942193	+	1.29682i	−0.954909	+	0.296899i	$0.904048\pi$
$884$	−33.3124	−	36.9971i	−1.12042	−	1.24435i
$885$		0			0
$886$	0.779312	−	0.865513i	0.0261815	−	0.0290775i
$887$	−10.4497	−	49.1621i	−0.350867	−	1.65070i	−0.700381	−	0.713769i	$-0.746987\pi$
$887$	−10.4497	−	49.1621i	−0.350867	−	1.65070i	0.349514	−	0.936931i	$-0.386347\pi$
$888$		0			0
$889$	−24.4090	−	5.18830i	−0.818653	−	0.174010i
$890$	−2.45058	−	2.03842i	−0.0821437	−	0.0683280i
$891$		0			0
$892$	−10.6784	+	14.6975i	−0.357538	+	0.492109i
$893$	37.2842	+	21.5260i	1.24767	+	0.720341i
$894$		0			0
$895$	7.39706	+	1.27158i	0.247256	+	0.0425044i
$896$	41.0945	+	18.2964i	1.37287	+	0.611241i
$897$		0			0
$898$	2.29215	−	10.7837i	0.0764901	−	0.359857i
$899$	−21.8683			−0.729350
$900$		0			0
$901$	52.9358			1.76355
$902$	0.480923	−	2.26257i	0.0160130	−	0.0753352i
$903$		0			0
$904$	24.1749	+	10.7633i	0.804044	+	0.357983i
$905$	5.67254	+	39.1422i	0.188561	+	1.30113i
$906$		0			0
$907$	−3.15602	−	1.82213i	−0.104794	−	0.0605029i	0.446687	−	0.894690i	$-0.352604\pi$
$907$	−3.15602	−	1.82213i	−0.104794	−	0.0605029i	−0.551481	+	0.834187i	$0.685937\pi$
$908$	−23.4364	+	32.2574i	−0.777763	+	1.07050i
$909$		0			0
$910$	4.89123	+	19.2649i	0.162143	+	0.638627i
$911$	16.4221	+	3.49062i	0.544087	+	0.115649i	0.471752	−	0.881731i	$-0.343622\pi$
$911$	16.4221	+	3.49062i	0.544087	+	0.115649i	0.0723347	+	0.997380i	$0.476955\pi$
$912$		0			0
$913$	−1.30082	−	6.11986i	−0.0430507	−	0.202538i
$914$	−5.34919	+	5.94087i	−0.176935	+	0.196507i
$915$		0			0
$916$	17.7299	+	19.6910i	0.585812	+	0.650610i
$917$	35.0966	−	48.3063i	1.15899	−	1.59521i
$918$		0			0
$919$	−32.5388	−	23.6408i	−1.07336	−	0.779839i	−0.0968443	−	0.995300i	$-0.530875\pi$
$919$	−32.5388	−	23.6408i	−1.07336	−	0.779839i	−0.976513	+	0.215460i	$0.930875\pi$
$920$	−6.94534	−	4.64144i	−0.228981	−	0.153024i
$921$		0			0
$922$	−1.87111	+	4.20258i	−0.0616216	+	0.138404i
$923$	45.3368	+	40.8215i	1.49228	+	1.34365i
$924$		0			0
$925$	−0.953772	+	2.69216i	−0.0313598	+	0.0885178i
$926$	−5.46451			−0.179575
$927$		0			0
$928$	10.2050	+	14.0460i	0.334996	+	0.461082i
$929$	4.96647	+	47.2528i	0.162944	+	1.55031i	0.704534	+	0.709670i	$0.251156\pi$
$929$	4.96647	+	47.2528i	0.162944	+	1.55031i	−0.541590	+	0.840643i	$0.682177\pi$
$930$		0			0
$931$	−6.36740	+	60.5818i	−0.208683	+	1.98549i
$932$	38.3683	−	22.1520i	1.25680	−	0.725611i
$933$		0			0
$934$	0.780305	+	0.866616i	0.0255324	+	0.0283566i
$935$	24.5422	+	1.61032i	0.802615	+	0.0526630i
$936$		0			0
$937$	−2.54682	−	0.827513i	−0.0832011	−	0.0270337i	0.267121	−	0.963663i	$-0.413928\pi$
$937$	−2.54682	−	0.827513i	−0.0832011	−	0.0270337i	−0.350322	+	0.936629i	$0.613928\pi$
$938$	−5.16381	+	4.64951i	−0.168604	+	0.151812i
$939$		0			0
$940$	11.7157	+	23.7612i	0.382123	+	0.775006i
$941$	−8.39236	+	1.78385i	−0.273583	+	0.0581519i	−0.342660	−	0.939459i	$-0.611328\pi$
$941$	−8.39236	+	1.78385i	−0.273583	+	0.0581519i	0.0690770	+	0.997611i	$0.477995\pi$
$942$		0			0
$943$	4.92005	+	2.84059i	0.160219	+	0.0925025i
$944$	−6.99756	−	5.08402i	−0.227751	−	0.165471i
$945$		0			0
$946$	4.01755	−	2.91892i	0.130622	−	0.0949022i
$947$	−0.363027	+	0.0381557i	−0.0117968	+	0.00123989i	−0.110425	−	0.993884i	$-0.535221\pi$
$947$	−0.363027	+	0.0381557i	−0.0117968	+	0.00123989i	0.0986282	+	0.995124i	$0.468555\pi$
$948$		0			0
$949$	−10.2175	−	17.6972i	−0.331674	−	0.574476i
$950$	−9.77684	−	11.4505i	−0.317203	−	0.371502i
$951$		0			0
$952$	−8.73434	+	41.0918i	−0.283082	+	1.33179i
$953$	−8.62730	−	11.8745i	−0.279466	−	0.384652i	0.646091	−	0.763260i	$-0.276403\pi$
$953$	−8.62730	−	11.8745i	−0.279466	−	0.384652i	−0.925557	+	0.378609i	$0.876403\pi$
$954$		0			0
$955$	2.03405	−	31.0002i	0.0658204	−	1.00314i
$956$	−3.99946	+	1.78068i	−0.129352	+	0.0575912i
$957$		0			0
$958$	9.99992	+	1.05103i	0.323083	+	0.0339574i
$959$	−74.1183	+	15.7543i	−2.39341	+	0.508734i
$960$		0			0
$961$	−5.33451	−	1.13388i	−0.172081	−	0.0365769i
$962$	−1.19262	−	0.387506i	−0.0384516	−	0.0124937i
$963$		0			0
$964$	−4.46991	−	13.7570i	−0.143966	−	0.443082i
$965$	26.7620	+	7.54969i	0.861498	+	0.243033i
$966$		0			0
$967$	42.7172	+	4.48976i	1.37369	+	0.144381i	0.762442	−	0.647056i	$-0.224000\pi$
$967$	42.7172	+	4.48976i	1.37369	+	0.144381i	0.611251	+	0.791437i	$0.290667\pi$
$968$	11.4586	−	6.61562i	0.368293	−	0.212634i
$969$		0			0
$970$	−5.19045	+	4.09122i	−0.166655	+	0.131361i
$971$	19.1945	−	13.9456i	0.615982	−	0.447537i	−0.235534	−	0.971866i	$-0.575684\pi$
$971$	19.1945	−	13.9456i	0.615982	−	0.447537i	0.851516	+	0.524329i	$0.175684\pi$
$972$		0			0
$973$	−27.7572	+	9.01886i	−0.889855	+	0.289131i
$974$	7.25994	−	12.5746i	0.232624	−	0.402916i
$975$		0			0
$976$	−4.67508	−	8.09747i	−0.149646	−	0.259194i
$977$	17.5182	+	15.7735i	0.560458	+	0.504638i	0.899963	−	0.435966i	$-0.143593\pi$
$977$	17.5182	+	15.7735i	0.560458	+	0.504638i	−0.339506	+	0.940604i	$0.610260\pi$
$978$		0			0
$979$	−0.597806	−	5.68774i	−0.0191060	−	0.181781i
$980$	−23.9714	+	28.8183i	−0.765737	+	0.920567i
$981$		0			0
$982$		−	1.81870i		−	0.0580370i
$983$	−9.89952	−	22.2347i	−0.315746	−	0.709176i	0.684049	−	0.729436i	$-0.260217\pi$
$983$	−9.89952	−	22.2347i	−0.315746	−	0.709176i	−0.999795	+	0.0202596i	$0.993551\pi$
$984$		0			0
$985$	−7.17424	+	41.7340i	−0.228590	+	1.32976i
$986$	−6.64453	+	7.37949i	−0.211605	+	0.235011i
$987$		0			0
$988$	−40.6364	+	36.5892i	−1.29282	+	1.16406i
$989$	3.76902	+	11.5998i	0.119848	+	0.368853i
$990$		0			0
$991$	9.23710	−	28.4289i	0.293426	−	0.903072i	−0.690320	−	0.723505i	$-0.742530\pi$
$991$	9.23710	−	28.4289i	0.293426	−	0.903072i	0.983746	−	0.179568i	$-0.0574699\pi$
$992$	11.7716	+	26.4394i	0.373747	+	0.839450i
$993$		0			0
$994$	2.53717	−	24.1396i	0.0804742	−	0.765661i
$995$	16.1276	+	16.5578i	0.511279	+	0.524916i
$996$		0			0
$997$	−29.0337	+	3.05156i	−0.919506	+	0.0966439i	−0.552441	−	0.833552i	$-0.686304\pi$
$997$	−29.0337	+	3.05156i	−0.919506	+	0.0966439i	−0.367064	+	0.930196i	$0.619637\pi$
$998$	−2.48038	+	0.805923i	−0.0785149	+	0.0255111i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.y.a.19.11		224
3.2	odd	2		225.2.u.a.169.18	yes	224
9.4	even	3	inner	675.2.y.a.469.11		224
9.5	odd	6		225.2.u.a.94.18	yes	224
25.4	even	10	inner	675.2.y.a.154.11		224
75.29	odd	10		225.2.u.a.79.18	yes	224
225.4	even	30	inner	675.2.y.a.604.11		224
225.104	odd	30		225.2.u.a.4.18	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.u.a.4.18	✓	224	225.104	odd	30
225.2.u.a.79.18	yes	224	75.29	odd	10
225.2.u.a.94.18	yes	224	9.5	odd	6
225.2.u.a.169.18	yes	224	3.2	odd	2
675.2.y.a.19.11		224	1.1	even	1	trivial
675.2.y.a.154.11		224	25.4	even	10	inner
675.2.y.a.469.11		224	9.4	even	3	inner
675.2.y.a.604.11		224	225.4	even	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.y (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0965635 + 0.454296i) q^{2} +(1.63003 + 0.725736i) q^{4} +(1.56019 + 1.60181i) q^{5} +(-3.50662 - 2.02455i) q^{7} +(-1.03309 + 1.42192i) q^{8} +O(q^{10})\)	\(q+(-0.0965635 + 0.454296i) q^{2} +(1.63003 + 0.725736i) q^{4} +(1.56019 + 1.60181i) q^{5} +(-3.50662 - 2.02455i) q^{7} +(-1.03309 + 1.42192i) q^{8} +(-0.878353 + 0.554113i) q^{10} +(-1.82260 - 0.387406i) q^{11} +(0.982729 + 4.62338i) q^{13} +(1.25836 - 1.39755i) q^{14} +(1.84163 + 2.04534i) q^{16} +(-3.46971 + 4.77564i) q^{17} +(5.24541 + 3.81101i) q^{19} +(1.38067 + 3.74329i) q^{20} +(0.351994 - 0.790591i) q^{22} +(1.57956 + 1.42225i) q^{23} +(-0.131589 + 4.99827i) q^{25} -2.19528 q^{26} +(-4.24661 - 5.84496i) q^{28} +(-0.378599 - 3.60213i) q^{29} +(0.631110 - 6.00461i) q^{31} +(-4.15127 + 2.39674i) q^{32} +(-1.83451 - 2.03742i) q^{34} +(-2.22807 - 8.77563i) q^{35} +(0.543266 + 0.176518i) q^{37} +(-2.23784 + 2.01496i) q^{38} +(-3.88947 + 0.563666i) q^{40} +(2.61445 - 0.555718i) q^{41} +(4.96950 + 2.86914i) q^{43} +(-2.68974 - 1.95421i) q^{44} +(-0.798649 + 0.580252i) q^{46} +(6.60369 - 0.694076i) q^{47} +(4.69760 + 8.13649i) q^{49} +(-2.25799 - 0.542431i) q^{50} +(-1.75347 + 8.24945i) q^{52} +(-5.27101 - 7.25492i) q^{53} +(-2.22306 - 3.52389i) q^{55} +(6.50141 - 2.89461i) q^{56} +(1.67299 + 0.175838i) q^{58} +(-3.07398 + 0.653395i) q^{59} +(-3.32301 - 0.706327i) q^{61} +(2.66693 + 0.866537i) q^{62} +(1.01303 + 3.11780i) q^{64} +(-5.87252 + 8.78751i) q^{65} +(-3.67467 - 0.386223i) q^{67} +(-9.12158 + 5.26635i) q^{68} +(4.20188 - 0.164796i) q^{70} +(10.4419 - 7.58650i) q^{71} +(-4.11174 + 1.33598i) q^{73} +(-0.132651 + 0.229758i) q^{74} +(5.78438 + 10.0188i) q^{76} +(5.60685 + 5.04843i) q^{77} +(-0.767436 - 7.30167i) q^{79} +(-0.402942 + 6.14107i) q^{80} +1.24139i q^{82} +(1.36572 + 3.06747i) q^{83} +(-13.0631 + 1.89312i) q^{85} +(-1.78331 + 1.98057i) q^{86} +(2.43377 - 2.19138i) q^{88} +(0.948463 + 2.91907i) q^{89} +(5.91420 - 18.2020i) q^{91} +(1.54256 + 3.46465i) q^{92} +(-0.322360 + 3.06705i) q^{94} +(2.07934 + 14.3481i) q^{95} +(6.32893 - 0.665198i) q^{97} +(-4.14999 + 1.34841i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8}+O(q^{10}) \) 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8	\( 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8} - 12 q^{10} - 5 q^{11} - 5 q^{13} + 23 q^{14} + 15 q^{16} + 20 q^{17} - 12 q^{19} + 17 q^{20} - 5 q^{22} + 5 q^{23} - 16 q^{25} - 72 q^{26} - 60 q^{28} + 15 q^{29} - 9 q^{31} - 7 q^{34} + 46 q^{35} - 20 q^{37} + 75 q^{38} - q^{40} - 13 q^{41} - 20 q^{44} - 4 q^{46} - 20 q^{47} + 56 q^{49} + 29 q^{50} - 15 q^{52} + 20 q^{53} - 44 q^{55} - 22 q^{56} - 5 q^{58} + 30 q^{59} - 3 q^{61} - 40 q^{62} - 12 q^{64} - 45 q^{65} + 10 q^{67} - 12 q^{70} + 106 q^{71} - 20 q^{73} - 82 q^{74} + 8 q^{76} + 115 q^{77} - 15 q^{79} + 22 q^{80} - 65 q^{83} - 21 q^{85} + 15 q^{86} - 5 q^{88} - 26 q^{89} - 54 q^{91} - 95 q^{92} + 41 q^{94} + 17 q^{95} - 5 q^{97} + 70 q^{98}+O(q^{100}) \) 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8 - 12 * q^10 - 5 * q^11 - 5 * q^13 + 23 * q^14 + 15 * q^16 + 20 * q^17 - 12 * q^19 + 17 * q^20 - 5 * q^22 + 5 * q^23 - 16 * q^25 - 72 * q^26 - 60 * q^28 + 15 * q^29 - 9 * q^31 - 7 * q^34 + 46 * q^35 - 20 * q^37 + 75 * q^38 - q^40 - 13 * q^41 - 20 * q^44 - 4 * q^46 - 20 * q^47 + 56 * q^49 + 29 * q^50 - 15 * q^52 + 20 * q^53 - 44 * q^55 - 22 * q^56 - 5 * q^58 + 30 * q^59 - 3 * q^61 - 40 * q^62 - 12 * q^64 - 45 * q^65 + 10 * q^67 - 12 * q^70 + 106 * q^71 - 20 * q^73 - 82 * q^74 + 8 * q^76 + 115 * q^77 - 15 * q^79 + 22 * q^80 - 65 * q^83 - 21 * q^85 + 15 * q^86 - 5 * q^88 - 26 * q^89 - 54 * q^91 - 95 * q^92 + 41 * q^94 + 17 * q^95 - 5 * q^97 + 70 * q^98

Introduction

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