LMFDB - Embedded newform 418.2.f.b.115.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(115,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("418.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			115.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	418.115
Dual form			418.2.f.b.229.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(0.881966 - 2.71441i) q^{5} +(1.30902 - 0.951057i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.927051 - 2.85317i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(0.881966 - 2.71441i) q^{5} +(1.30902 - 0.951057i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.927051 - 2.85317i) q^{9} +2.85410 q^{10} +(-3.04508 - 1.31433i) q^{11} +(-2.00000 - 6.15537i) q^{13} +(1.30902 + 0.951057i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-2.19098 + 6.74315i) q^{17} +(2.42705 - 1.76336i) q^{18} +(-0.809017 - 0.587785i) q^{19} +(0.881966 + 2.71441i) q^{20} +(0.309017 - 3.30220i) q^{22} +7.85410 q^{23} +(-2.54508 - 1.84911i) q^{25} +(5.23607 - 3.80423i) q^{26} +(-0.500000 + 1.53884i) q^{28} +(2.61803 - 1.90211i) q^{29} +(2.38197 + 7.33094i) q^{31} +1.00000 q^{32} -7.09017 q^{34} +(-1.42705 - 4.39201i) q^{35} +(2.42705 + 1.76336i) q^{36} +(3.85410 - 2.80017i) q^{37} +(0.309017 - 0.951057i) q^{38} +(-2.30902 + 1.67760i) q^{40} +(-1.23607 - 0.898056i) q^{41} +0.618034 q^{43} +(3.23607 - 0.726543i) q^{44} -8.56231 q^{45} +(2.42705 + 7.46969i) q^{46} +(7.59017 + 5.51458i) q^{47} +(-1.35410 + 4.16750i) q^{49} +(0.972136 - 2.99193i) q^{50} +(5.23607 + 3.80423i) q^{52} +(0.618034 + 1.90211i) q^{53} +(-6.25329 + 7.10642i) q^{55} -1.61803 q^{56} +(2.61803 + 1.90211i) q^{58} +(8.09017 - 5.87785i) q^{59} +(-0.336881 + 1.03681i) q^{61} +(-6.23607 + 4.53077i) q^{62} +(-3.92705 - 2.85317i) q^{63} +(0.309017 + 0.951057i) q^{64} -18.4721 q^{65} -8.00000 q^{67} +(-2.19098 - 6.74315i) q^{68} +(3.73607 - 2.71441i) q^{70} +(-0.145898 + 0.449028i) q^{71} +(-0.927051 + 2.85317i) q^{72} +(-0.381966 + 0.277515i) q^{73} +(3.85410 + 2.80017i) q^{74} +1.00000 q^{76} +(-5.23607 + 1.17557i) q^{77} +(-3.70820 - 11.4127i) q^{79} +(-2.30902 - 1.67760i) q^{80} +(-7.28115 + 5.29007i) q^{81} +(0.472136 - 1.45309i) q^{82} +(-0.881966 + 2.71441i) q^{83} +(16.3713 + 11.8945i) q^{85} +(0.190983 + 0.587785i) q^{86} +(1.69098 + 2.85317i) q^{88} +8.18034 q^{89} +(-2.64590 - 8.14324i) q^{90} +(-8.47214 - 6.15537i) q^{91} +(-6.35410 + 4.61653i) q^{92} +(-2.89919 + 8.92278i) q^{94} +(-2.30902 + 1.67760i) q^{95} +(-5.09017 - 15.6659i) q^{97} -4.38197 q^{98} +(-0.927051 + 9.90659i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - q^{4} + 8 q^{5} + 3 q^{7} - q^{8} + 3 q^{9}+O(q^{10}) $ 4 * q - q^2 - q^4 + 8 * q^5 + 3 * q^7 - q^8 + 3 * q^9	$ 4 q - q^{2} - q^{4} + 8 q^{5} + 3 q^{7} - q^{8} + 3 q^{9} - 2 q^{10} - q^{11} - 8 q^{13} + 3 q^{14} - q^{16} - 11 q^{17} + 3 q^{18} - q^{19} + 8 q^{20} - q^{22} + 18 q^{23} + q^{25} + 12 q^{26} - 2 q^{28} + 6 q^{29} + 14 q^{31} + 4 q^{32} - 6 q^{34} + q^{35} + 3 q^{36} + 2 q^{37} - q^{38} - 7 q^{40} + 4 q^{41} - 2 q^{43} + 4 q^{44} + 6 q^{45} + 3 q^{46} + 8 q^{47} + 8 q^{49} - 14 q^{50} + 12 q^{52} - 2 q^{53} + 13 q^{55} - 2 q^{56} + 6 q^{58} + 10 q^{59} - 17 q^{61} - 16 q^{62} - 9 q^{63} - q^{64} - 56 q^{65} - 32 q^{67} - 11 q^{68} + 6 q^{70} - 14 q^{71} + 3 q^{72} - 6 q^{73} + 2 q^{74} + 4 q^{76} - 12 q^{77} + 12 q^{79} - 7 q^{80} - 9 q^{81} - 16 q^{82} - 8 q^{83} + 23 q^{85} + 3 q^{86} + 9 q^{88} - 12 q^{89} - 24 q^{90} - 16 q^{91} - 12 q^{92} + 13 q^{94} - 7 q^{95} + 2 q^{97} - 22 q^{98} + 3 q^{99}+O(q^{100}) $ 4 * q - q^2 - q^4 + 8 * q^5 + 3 * q^7 - q^8 + 3 * q^9 - 2 * q^10 - q^11 - 8 * q^13 + 3 * q^14 - q^16 - 11 * q^17 + 3 * q^18 - q^19 + 8 * q^20 - q^22 + 18 * q^23 + q^25 + 12 * q^26 - 2 * q^28 + 6 * q^29 + 14 * q^31 + 4 * q^32 - 6 * q^34 + q^35 + 3 * q^36 + 2 * q^37 - q^38 - 7 * q^40 + 4 * q^41 - 2 * q^43 + 4 * q^44 + 6 * q^45 + 3 * q^46 + 8 * q^47 + 8 * q^49 - 14 * q^50 + 12 * q^52 - 2 * q^53 + 13 * q^55 - 2 * q^56 + 6 * q^58 + 10 * q^59 - 17 * q^61 - 16 * q^62 - 9 * q^63 - q^64 - 56 * q^65 - 32 * q^67 - 11 * q^68 + 6 * q^70 - 14 * q^71 + 3 * q^72 - 6 * q^73 + 2 * q^74 + 4 * q^76 - 12 * q^77 + 12 * q^79 - 7 * q^80 - 9 * q^81 - 16 * q^82 - 8 * q^83 + 23 * q^85 + 3 * q^86 + 9 * q^88 - 12 * q^89 - 24 * q^90 - 16 * q^91 - 12 * q^92 + 13 * q^94 - 7 * q^95 + 2 * q^97 - 22 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$3$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	0.881966	−	2.71441i	0.394427	−	1.21392i	−0.534980	−	0.844865i	$-0.679681\pi$
$5$	0.881966	−	2.71441i	0.394427	−	1.21392i	0.929407	−	0.369057i	$-0.120319\pi$
$6$		0			0
$7$	1.30902	−	0.951057i	0.494762	−	0.359466i	−0.312251	−	0.950000i	$-0.601083\pi$
$7$	1.30902	−	0.951057i	0.494762	−	0.359466i	0.807013	+	0.590534i	$0.201083\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	−0.927051	−	2.85317i	−0.309017	−	0.951057i
$10$	2.85410			0.902546
$11$	−3.04508	−	1.31433i	−0.918128	−	0.396285i
$11$	−3.04508	−	1.31433i	−0.918128	−	0.396285i
$12$		0			0
$13$	−2.00000	−	6.15537i	−0.554700	−	1.70719i	−0.696734	−	0.717330i	$-0.745364\pi$
$13$	−2.00000	−	6.15537i	−0.554700	−	1.70719i	0.142034	−	0.989862i	$-0.454636\pi$
$14$	1.30902	+	0.951057i	0.349850	+	0.254181i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−2.19098	+	6.74315i	−0.531391	+	1.63545i	0.219928	+	0.975516i	$0.429418\pi$
$17$	−2.19098	+	6.74315i	−0.531391	+	1.63545i	−0.751320	+	0.659939i	$0.770582\pi$
$18$	2.42705	−	1.76336i	0.572061	−	0.415627i
$19$	−0.809017	−	0.587785i	−0.185601	−	0.134847i
$19$	−0.809017	−	0.587785i	−0.185601	−	0.134847i
$20$	0.881966	+	2.71441i	0.197214	+	0.606961i
$21$		0			0
$22$	0.309017	−	3.30220i	0.0658826	−	0.704031i
$23$	7.85410			1.63769			0.818847	−	0.574012i	$-0.194614\pi$
$23$	7.85410			1.63769			0.818847	+	0.574012i	$0.194614\pi$
$24$		0			0
$25$	−2.54508	−	1.84911i	−0.509017	−	0.369822i
$26$	5.23607	−	3.80423i	1.02688	−	0.746070i
$27$		0			0
$28$	−0.500000	+	1.53884i	−0.0944911	+	0.290814i
$29$	2.61803	−	1.90211i	0.486157	−	0.353214i	−0.317548	−	0.948242i	$-0.602859\pi$
$29$	2.61803	−	1.90211i	0.486157	−	0.353214i	0.803704	+	0.595029i	$0.202859\pi$
$30$		0			0
$31$	2.38197	+	7.33094i	0.427814	+	1.31668i	0.900274	+	0.435323i	$0.143366\pi$
$31$	2.38197	+	7.33094i	0.427814	+	1.31668i	−0.472460	+	0.881352i	$0.656634\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−7.09017			−1.21595
$35$	−1.42705	−	4.39201i	−0.241216	−	0.742385i
$36$	2.42705	+	1.76336i	0.404508	+	0.293893i
$37$	3.85410	−	2.80017i	0.633610	−	0.460345i	−0.224039	−	0.974580i	$-0.571924\pi$
$37$	3.85410	−	2.80017i	0.633610	−	0.460345i	0.857649	+	0.514235i	$0.171924\pi$
$38$	0.309017	−	0.951057i	0.0501292	−	0.154282i
$39$		0			0
$40$	−2.30902	+	1.67760i	−0.365088	+	0.265252i
$41$	−1.23607	−	0.898056i	−0.193041	−	0.140253i	0.487066	−	0.873365i	$-0.338067\pi$
$41$	−1.23607	−	0.898056i	−0.193041	−	0.140253i	−0.680108	+	0.733112i	$0.738067\pi$
$42$		0			0
$43$	0.618034			0.0942493			0.0471246	−	0.998889i	$-0.484994\pi$
$43$	0.618034			0.0942493			0.0471246	+	0.998889i	$0.484994\pi$
$44$	3.23607	−	0.726543i	0.487856	−	0.109530i
$45$	−8.56231			−1.27639
$46$	2.42705	+	7.46969i	0.357849	+	1.10135i
$47$	7.59017	+	5.51458i	1.10714	+	0.804384i	0.982211	−	0.187781i	$-0.0601296\pi$
$47$	7.59017	+	5.51458i	1.10714	+	0.804384i	0.124929	+	0.992166i	$0.460130\pi$
$48$		0			0
$49$	−1.35410	+	4.16750i	−0.193443	+	0.595357i
$50$	0.972136	−	2.99193i	0.137481	−	0.423122i
$51$		0			0
$52$	5.23607	+	3.80423i	0.726112	+	0.527551i
$53$	0.618034	+	1.90211i	0.0848935	+	0.261275i	0.984488	−	0.175450i	$-0.0561381\pi$
$53$	0.618034	+	1.90211i	0.0848935	+	0.261275i	−0.899595	+	0.436726i	$0.856138\pi$
$54$		0			0
$55$	−6.25329	+	7.10642i	−0.843193	+	0.958230i
$56$	−1.61803			−0.216219
$57$		0			0
$58$	2.61803	+	1.90211i	0.343765	+	0.249760i
$59$	8.09017	−	5.87785i	1.05325	−	0.765231i	0.0804226	−	0.996761i	$-0.474373\pi$
$59$	8.09017	−	5.87785i	1.05325	−	0.765231i	0.972828	+	0.231530i	$0.0743730\pi$
$60$		0			0
$61$	−0.336881	+	1.03681i	−0.0431332	+	0.132750i	−0.970304	−	0.241888i	$-0.922233\pi$
$61$	−0.336881	+	1.03681i	−0.0431332	+	0.132750i	0.927171	+	0.374639i	$0.122233\pi$
$62$	−6.23607	+	4.53077i	−0.791981	+	0.575408i
$63$	−3.92705	−	2.85317i	−0.494762	−	0.359466i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−18.4721			−2.29119
$66$		0			0
$67$	−8.00000			−0.977356			−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000			−0.977356			−0.488678	+	0.872464i	$0.662521\pi$
$68$	−2.19098	−	6.74315i	−0.265696	−	0.817727i
$69$		0			0
$70$	3.73607	−	2.71441i	0.446546	−	0.324434i
$71$	−0.145898	+	0.449028i	−0.0173149	+	0.0532898i	−0.959341	−	0.282251i	$-0.908919\pi$
$71$	−0.145898	+	0.449028i	−0.0173149	+	0.0532898i	0.942026	+	0.335541i	$0.108919\pi$
$72$	−0.927051	+	2.85317i	−0.109254	+	0.336249i
$73$	−0.381966	+	0.277515i	−0.0447057	+	0.0324806i	−0.609914	−	0.792468i	$-0.708796\pi$
$73$	−0.381966	+	0.277515i	−0.0447057	+	0.0324806i	0.565208	+	0.824948i	$0.308796\pi$
$74$	3.85410	+	2.80017i	0.448030	+	0.325513i
$75$		0			0
$76$	1.00000			0.114708
$77$	−5.23607	+	1.17557i	−0.596705	+	0.133969i
$78$		0			0
$79$	−3.70820	−	11.4127i	−0.417206	−	1.28403i	−0.910263	−	0.414030i	$-0.864121\pi$
$79$	−3.70820	−	11.4127i	−0.417206	−	1.28403i	0.493058	−	0.869997i	$-0.335879\pi$
$80$	−2.30902	−	1.67760i	−0.258156	−	0.187561i
$81$	−7.28115	+	5.29007i	−0.809017	+	0.587785i
$82$	0.472136	−	1.45309i	0.0521387	−	0.160466i
$83$	−0.881966	+	2.71441i	−0.0968083	+	0.297945i	−0.987721	−	0.156230i	$-0.950066\pi$
$83$	−0.881966	+	2.71441i	−0.0968083	+	0.297945i	0.890912	+	0.454175i	$0.150066\pi$
$84$		0			0
$85$	16.3713	+	11.8945i	1.77572	+	1.29014i
$86$	0.190983	+	0.587785i	0.0205942	+	0.0633825i
$87$		0			0
$88$	1.69098	+	2.85317i	0.180259	+	0.304149i
$89$	8.18034			0.867114			0.433557	−	0.901126i	$-0.357258\pi$
$89$	8.18034			0.867114			0.433557	+	0.901126i	$0.357258\pi$
$90$	−2.64590	−	8.14324i	−0.278902	−	0.858373i
$91$	−8.47214	−	6.15537i	−0.888121	−	0.645258i
$92$	−6.35410	+	4.61653i	−0.662461	+	0.481306i
$93$		0			0
$94$	−2.89919	+	8.92278i	−0.299028	+	0.920314i
$95$	−2.30902	+	1.67760i	−0.236900	+	0.172118i
$96$		0			0
$97$	−5.09017	−	15.6659i	−0.516828	−	1.59063i	−0.779930	−	0.625866i	$-0.784746\pi$
$97$	−5.09017	−	15.6659i	−0.516828	−	1.59063i	0.263102	−	0.964768i	$-0.415254\pi$
$98$	−4.38197			−0.442645
$99$	−0.927051	+	9.90659i	−0.0931721	+	0.995650i
$100$	3.14590			0.314590
$101$	1.11803	+	3.44095i	0.111249	+	0.342388i	0.991146	−	0.132776i	$-0.0423890\pi$
$101$	1.11803	+	3.44095i	0.111249	+	0.342388i	−0.879898	+	0.475163i	$0.842389\pi$
$102$		0			0
$103$	15.7082	−	11.4127i	1.54778	−	1.12452i	0.602562	−	0.798072i	$-0.294147\pi$
$103$	15.7082	−	11.4127i	1.54778	−	1.12452i	0.945214	−	0.326452i	$-0.105853\pi$
$104$	−2.00000	+	6.15537i	−0.196116	+	0.603583i
$105$		0			0
$106$	−1.61803	+	1.17557i	−0.157157	+	0.114182i
$107$	3.85410	+	2.80017i	0.372590	+	0.270703i	0.758284	−	0.651924i	$-0.226038\pi$
$107$	3.85410	+	2.80017i	0.372590	+	0.270703i	−0.385694	+	0.922627i	$0.626038\pi$
$108$		0			0
$109$	−11.7082			−1.12144			−0.560721	−	0.828005i	$-0.689476\pi$
$109$	−11.7082			−1.12144			−0.560721	+	0.828005i	$0.689476\pi$
$110$	−8.69098	−	3.75123i	−0.828653	−	0.357665i
$111$		0			0
$112$	−0.500000	−	1.53884i	−0.0472456	−	0.145407i
$113$	0.236068	+	0.171513i	0.0222074	+	0.0161346i	0.598834	−	0.800873i	$-0.295631\pi$
$113$	0.236068	+	0.171513i	0.0222074	+	0.0161346i	−0.576626	+	0.817008i	$0.695631\pi$
$114$		0			0
$115$	6.92705	−	21.3193i	0.645951	−	1.98803i
$116$	−1.00000	+	3.07768i	−0.0928477	+	0.285756i
$117$	−15.7082	+	11.4127i	−1.45222	+	1.05510i
$118$	8.09017	+	5.87785i	0.744761	+	0.541100i
$119$	3.54508	+	10.9106i	0.324977	+	1.00018i
$120$		0			0
$121$	7.54508	+	8.00448i	0.685917	+	0.727680i
$122$	−1.09017			−0.0986993
$123$		0			0
$124$	−6.23607	−	4.53077i	−0.560015	−	0.406875i
$125$	4.28115	−	3.11044i	0.382918	−	0.278206i
$126$	1.50000	−	4.61653i	0.133631	−	0.411273i
$127$	−0.236068	+	0.726543i	−0.0209476	+	0.0644702i	−0.960984	−	0.276604i	$-0.910791\pi$
$127$	−0.236068	+	0.726543i	−0.0209476	+	0.0644702i	0.940036	+	0.341075i	$0.110791\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$		0			0
$130$	−5.70820	−	17.5680i	−0.500643	−	1.54082i
$131$	9.32624			0.814837			0.407419	−	0.913242i	$-0.366429\pi$
$131$	9.32624			0.814837			0.407419	+	0.913242i	$0.366429\pi$
$132$		0			0
$133$	−1.61803			−0.140301
$134$	−2.47214	−	7.60845i	−0.213560	−	0.657270i
$135$		0			0
$136$	5.73607	−	4.16750i	0.491864	−	0.357360i
$137$	−4.44427	+	13.6781i	−0.379700	+	1.16860i	0.560553	+	0.828119i	$0.310589\pi$
$137$	−4.44427	+	13.6781i	−0.379700	+	1.16860i	−0.940253	+	0.340477i	$0.889411\pi$
$138$		0			0
$139$	2.97214	−	2.15938i	0.252093	−	0.183156i	−0.454561	−	0.890716i	$-0.650204\pi$
$139$	2.97214	−	2.15938i	0.252093	−	0.183156i	0.706654	+	0.707559i	$0.250204\pi$
$140$	3.73607	+	2.71441i	0.315755	+	0.229410i
$141$		0			0
$142$	−0.472136			−0.0396208
$143$	−2.00000	+	21.3723i	−0.167248	+	1.78724i
$144$	−3.00000			−0.250000
$145$	−2.85410	−	8.78402i	−0.237020	−	0.729473i
$146$	−0.381966	−	0.277515i	−0.0316117	−	0.0229673i
$147$		0			0
$148$	−1.47214	+	4.53077i	−0.121009	+	0.372427i
$149$	−4.14590	+	12.7598i	−0.339645	+	1.04532i	0.624743	+	0.780830i	$0.285204\pi$
$149$	−4.14590	+	12.7598i	−0.339645	+	1.04532i	−0.964388	+	0.264490i	$0.914796\pi$
$150$		0			0
$151$	−6.61803	−	4.80828i	−0.538568	−	0.391293i	0.284985	−	0.958532i	$-0.408011\pi$
$151$	−6.61803	−	4.80828i	−0.538568	−	0.391293i	−0.823553	+	0.567239i	$0.808011\pi$
$152$	0.309017	+	0.951057i	0.0250646	+	0.0771409i
$153$	21.2705			1.71962
$154$	−2.73607	−	4.61653i	−0.220479	−	0.372010i
$155$	22.0000			1.76708
$156$		0			0
$157$	−16.6353	−	12.0862i	−1.32764	−	0.964585i	−0.999803	−	0.0198504i	$-0.993681\pi$
$157$	−16.6353	−	12.0862i	−1.32764	−	0.964585i	−0.327835	−	0.944735i	$-0.606319\pi$
$158$	9.70820	−	7.05342i	0.772343	−	0.561140i
$159$		0			0
$160$	0.881966	−	2.71441i	0.0697255	−	0.214593i
$161$	10.2812	−	7.46969i	0.810268	−	0.588694i
$162$	−7.28115	−	5.29007i	−0.572061	−	0.415627i
$163$	4.29837	+	13.2290i	0.336675	+	1.03618i	0.965891	+	0.258948i	$0.0833758\pi$
$163$	4.29837	+	13.2290i	0.336675	+	1.03618i	−0.629217	+	0.777230i	$0.716624\pi$
$164$	1.52786			0.119306
$165$		0			0
$166$	−2.85410			−0.221521
$167$	2.47214	+	7.60845i	0.191300	+	0.588760i	1.00000		0.000538710i	$0.000171477\pi$
$167$	2.47214	+	7.60845i	0.191300	+	0.588760i	−0.808700	+	0.588221i	$0.799829\pi$
$168$		0			0
$169$	−23.3713	+	16.9803i	−1.79779	+	1.30617i
$170$	−6.25329	+	19.2456i	−0.479605	+	1.47607i
$171$	−0.927051	+	2.85317i	−0.0708934	+	0.218187i
$172$	−0.500000	+	0.363271i	−0.0381246	+	0.0276992i
$173$	−6.00000	−	4.35926i	−0.456172	−	0.331428i	0.335856	−	0.941913i	$-0.390974\pi$
$173$	−6.00000	−	4.35926i	−0.456172	−	0.331428i	−0.792028	+	0.610485i	$0.790974\pi$
$174$		0			0
$175$	−5.09017			−0.384781
$176$	−2.19098	+	2.48990i	−0.165152	+	0.187683i
$177$		0			0
$178$	2.52786	+	7.77997i	0.189471	+	0.583133i
$179$	−2.23607	−	1.62460i	−0.167132	−	0.121428i	0.501075	−	0.865404i	$-0.332938\pi$
$179$	−2.23607	−	1.62460i	−0.167132	−	0.121428i	−0.668207	+	0.743975i	$0.732938\pi$
$180$	6.92705	−	5.03280i	0.516312	−	0.375123i
$181$	5.76393	−	17.7396i	0.428430	−	1.31857i	−0.471242	−	0.882004i	$-0.656194\pi$
$181$	5.76393	−	17.7396i	0.428430	−	1.31857i	0.899672	−	0.436567i	$-0.143806\pi$
$182$	3.23607	−	9.95959i	0.239873	−	0.738254i
$183$		0			0
$184$	−6.35410	−	4.61653i	−0.468431	−	0.340335i
$185$	−4.20163	−	12.9313i	−0.308910	−	0.950726i
$186$		0			0
$187$	15.5344	−	17.6538i	1.13599	−	1.29097i
$188$	−9.38197			−0.684250
$189$		0			0
$190$	−2.30902	−	1.67760i	−0.167514	−	0.121706i
$191$	8.54508	−	6.20837i	0.618301	−	0.449222i	−0.234027	−	0.972230i	$-0.575190\pi$
$191$	8.54508	−	6.20837i	0.618301	−	0.449222i	0.852328	+	0.523008i	$0.175190\pi$
$192$		0			0
$193$	0.618034	−	1.90211i	0.0444871	−	0.136917i	−0.926346	−	0.376674i	$-0.877068\pi$
$193$	0.618034	−	1.90211i	0.0444871	−	0.136917i	0.970833	+	0.239757i	$0.0770677\pi$
$194$	13.3262	−	9.68208i	0.956768	−	0.695133i
$195$		0			0
$196$	−1.35410	−	4.16750i	−0.0967216	−	0.297678i
$197$	16.4721			1.17359			0.586796	−	0.809735i	$-0.300389\pi$
$197$	16.4721			1.17359			0.586796	+	0.809735i	$0.300389\pi$
$198$	−9.70820	+	2.17963i	−0.689932	+	0.154899i
$199$	2.38197			0.168853			0.0844265	−	0.996430i	$-0.473094\pi$
$199$	2.38197			0.168853			0.0844265	+	0.996430i	$0.473094\pi$
$200$	0.972136	+	2.99193i	0.0687404	+	0.211561i
$201$		0			0
$202$	−2.92705	+	2.12663i	−0.205947	+	0.149629i
$203$	1.61803	−	4.97980i	0.113564	−	0.349513i
$204$		0			0
$205$	−3.52786	+	2.56314i	−0.246397	+	0.179018i
$206$	15.7082	+	11.4127i	1.09444	+	0.795159i
$207$	−7.28115	−	22.4091i	−0.506075	−	1.55754i
$208$	−6.47214			−0.448762
$209$	1.69098	+	2.85317i	0.116968	+	0.197358i
$210$		0			0
$211$	7.14590	+	21.9928i	0.491944	+	1.51405i	0.821666	+	0.569970i	$0.193045\pi$
$211$	7.14590	+	21.9928i	0.491944	+	1.51405i	−0.329722	+	0.944078i	$0.606955\pi$
$212$	−1.61803	−	1.17557i	−0.111127	−	0.0807385i
$213$		0			0
$214$	−1.47214	+	4.53077i	−0.100633	+	0.309717i
$215$	0.545085	−	1.67760i	0.0371745	−	0.114411i
$216$		0			0
$217$	10.0902	+	7.33094i	0.684965	+	0.497656i
$218$	−3.61803	−	11.1352i	−0.245044	−	0.754168i
$219$		0			0
$220$	0.881966	−	9.42481i	0.0594621	−	0.635420i
$221$	45.8885			3.08680
$222$		0			0
$223$	3.61803	+	2.62866i	0.242281	+	0.176028i	0.702299	−	0.711882i	$-0.252157\pi$
$223$	3.61803	+	2.62866i	0.242281	+	0.176028i	−0.460018	+	0.887910i	$0.652157\pi$
$224$	1.30902	−	0.951057i	0.0874624	−	0.0635451i
$225$	−2.91641	+	8.97578i	−0.194427	+	0.598385i
$226$	−0.0901699	+	0.277515i	−0.00599802	+	0.0184600i
$227$	−16.5623	+	12.0332i	−1.09928	+	0.798673i	−0.980942	−	0.194301i	$-0.937756\pi$
$227$	−16.5623	+	12.0332i	−1.09928	+	0.798673i	−0.118337	+	0.992974i	$0.537756\pi$
$228$		0			0
$229$	6.04508	+	18.6049i	0.399470	+	1.22944i	0.925425	+	0.378931i	$0.123708\pi$
$229$	6.04508	+	18.6049i	0.399470	+	1.22944i	−0.525954	+	0.850513i	$0.676292\pi$
$230$	22.4164			1.47809
$231$		0			0
$232$	−3.23607			−0.212458
$233$	−6.20820	−	19.1069i	−0.406713	−	1.25173i	−0.919456	−	0.393192i	$-0.871371\pi$
$233$	−6.20820	−	19.1069i	−0.406713	−	1.25173i	0.512743	−	0.858542i	$-0.328629\pi$
$234$	−15.7082	−	11.4127i	−1.02688	−	0.746070i
$235$	21.6631	−	15.7392i	1.41315	−	1.02671i
$236$	−3.09017	+	9.51057i	−0.201153	+	0.619085i
$237$		0			0
$238$	−9.28115	+	6.74315i	−0.601608	+	0.437094i
$239$	7.11803	+	5.17155i	0.460427	+	0.334520i	0.793699	−	0.608311i	$-0.208153\pi$
$239$	7.11803	+	5.17155i	0.460427	+	0.334520i	−0.333272	+	0.942831i	$0.608153\pi$
$240$		0			0
$241$	26.9443			1.73563			0.867817	−	0.496885i	$-0.165523\pi$
$241$	26.9443			1.73563			0.867817	+	0.496885i	$0.165523\pi$
$242$	−5.28115	+	9.64932i	−0.339485	+	0.620282i
$243$		0			0
$244$	−0.336881	−	1.03681i	−0.0215666	−	0.0663752i
$245$	10.1180	+	7.35118i	0.646417	+	0.469650i
$246$		0			0
$247$	−2.00000	+	6.15537i	−0.127257	+	0.391657i
$248$	2.38197	−	7.33094i	0.151255	−	0.465515i
$249$		0			0
$250$	4.28115	+	3.11044i	0.270764	+	0.196721i
$251$	−2.37132	−	7.29818i	−0.149677	−	0.460657i	0.847906	−	0.530146i	$-0.177863\pi$
$251$	−2.37132	−	7.29818i	−0.149677	−	0.460657i	−0.997583	+	0.0694893i	$0.977863\pi$
$252$	4.85410			0.305780
$253$	−23.9164	−	10.3229i	−1.50361	−	0.648993i
$254$	−0.763932			−0.0479334
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−6.23607	+	4.53077i	−0.388995	+	0.282622i	−0.765044	−	0.643978i	$-0.777283\pi$
$257$	−6.23607	+	4.53077i	−0.388995	+	0.282622i	0.376048	+	0.926600i	$0.377283\pi$
$258$		0			0
$259$	2.38197	−	7.33094i	0.148008	−	0.455522i
$260$	14.9443	−	10.8576i	0.926804	−	0.673363i
$261$	−7.85410	−	5.70634i	−0.486157	−	0.353214i
$262$	2.88197	+	8.86978i	0.178048	+	0.547977i
$263$	−10.4721			−0.645740			−0.322870	−	0.946443i	$-0.604648\pi$
$263$	−10.4721			−0.645740			−0.322870	+	0.946443i	$0.604648\pi$
$264$		0			0
$265$	5.70820			0.350652
$266$	−0.500000	−	1.53884i	−0.0306570	−	0.0943524i
$267$		0			0
$268$	6.47214	−	4.70228i	0.395349	−	0.287238i
$269$	−8.76393	+	26.9726i	−0.534346	+	1.64455i	0.210711	+	0.977548i	$0.432422\pi$
$269$	−8.76393	+	26.9726i	−0.534346	+	1.64455i	−0.745057	+	0.667001i	$0.767578\pi$
$270$		0			0
$271$	2.35410	−	1.71036i	0.143002	−	0.103897i	−0.513984	−	0.857800i	$-0.671831\pi$
$271$	2.35410	−	1.71036i	0.143002	−	0.103897i	0.656986	+	0.753903i	$0.271831\pi$
$272$	5.73607	+	4.16750i	0.347800	+	0.252692i
$273$		0			0
$274$	−14.3820			−0.868846
$275$	5.31966	+	8.97578i	0.320788	+	0.541260i
$276$		0			0
$277$	−6.79837	−	20.9232i	−0.408475	−	1.25716i	−0.917959	−	0.396676i	$-0.870164\pi$
$277$	−6.79837	−	20.9232i	−0.408475	−	1.25716i	0.509484	−	0.860480i	$-0.329836\pi$
$278$	2.97214	+	2.15938i	0.178257	+	0.129511i
$279$	18.7082	−	13.5923i	1.12003	−	0.813750i
$280$	−1.42705	+	4.39201i	−0.0852826	+	0.262473i
$281$	−5.90983	+	18.1886i	−0.352551	+	1.08504i	0.604865	+	0.796328i	$0.293227\pi$
$281$	−5.90983	+	18.1886i	−0.352551	+	1.08504i	−0.957416	+	0.288712i	$0.906773\pi$
$282$		0			0
$283$	5.07295	+	3.68571i	0.301556	+	0.219093i	0.728265	−	0.685296i	$-0.240327\pi$
$283$	5.07295	+	3.68571i	0.301556	+	0.219093i	−0.426709	+	0.904389i	$0.640327\pi$
$284$	−0.145898	−	0.449028i	−0.00865746	−	0.0266449i
$285$		0			0
$286$	−20.9443	+	4.70228i	−1.23846	+	0.278052i
$287$	−2.47214			−0.145926
$288$	−0.927051	−	2.85317i	−0.0546270	−	0.168125i
$289$	−26.9164	−	19.5559i	−1.58332	−	1.15035i
$290$	7.47214	−	5.42882i	0.438779	−	0.318792i
$291$		0			0
$292$	0.145898	−	0.449028i	0.00853804	−	0.0262774i
$293$	−9.47214	+	6.88191i	−0.553368	+	0.402045i	−0.829026	−	0.559210i	$-0.811104\pi$
$293$	−9.47214	+	6.88191i	−0.553368	+	0.402045i	0.275658	+	0.961256i	$0.411104\pi$
$294$		0			0
$295$	−8.81966	−	27.1441i	−0.513500	−	1.58039i
$296$	−4.76393			−0.276898
$297$		0			0
$298$	−13.4164			−0.777192
$299$	−15.7082	−	48.3449i	−0.908429	−	2.79586i
$300$		0			0
$301$	0.809017	−	0.587785i	0.0466310	−	0.0338794i
$302$	2.52786	−	7.77997i	0.145462	−	0.447687i
$303$		0			0
$304$	−0.809017	+	0.587785i	−0.0464003	+	0.0337118i
$305$	2.51722	+	1.82887i	0.144136	+	0.104721i
$306$	6.57295	+	20.2295i	0.375750	+	1.15644i
$307$	7.41641			0.423277			0.211638	−	0.977348i	$-0.432120\pi$
$307$	7.41641			0.423277			0.211638	+	0.977348i	$0.432120\pi$
$308$	3.54508	−	4.02874i	0.202000	−	0.229559i
$309$		0			0
$310$	6.79837	+	20.9232i	0.386122	+	1.18836i
$311$	14.2984	+	10.3884i	0.810786	+	0.589071i	0.914059	−	0.405582i	$-0.132931\pi$
$311$	14.2984	+	10.3884i	0.810786	+	0.589071i	−0.103272	+	0.994653i	$0.532931\pi$
$312$		0			0
$313$	8.66312	−	26.6623i	0.489668	−	1.50704i	−0.335435	−	0.942063i	$-0.608883\pi$
$313$	8.66312	−	26.6623i	0.489668	−	1.50704i	0.825104	−	0.564981i	$-0.191117\pi$
$314$	6.35410	−	19.5559i	0.358583	−	1.10360i
$315$	−11.2082	+	8.14324i	−0.631511	+	0.458819i
$316$	9.70820	+	7.05342i	0.546129	+	0.396786i
$317$	−3.52786	−	10.8576i	−0.198145	−	0.609826i	−0.999925	−	0.0122082i	$-0.996114\pi$
$317$	−3.52786	−	10.8576i	−0.198145	−	0.609826i	0.801781	−	0.597618i	$-0.203886\pi$
$318$		0			0
$319$	−10.4721	+	2.35114i	−0.586327	+	0.131639i
$320$	2.85410			0.159549
$321$		0			0
$322$	10.2812	+	7.46969i	0.572946	+	0.416270i
$323$	5.73607	−	4.16750i	0.319163	−	0.231886i
$324$	2.78115	−	8.55951i	0.154508	−	0.475528i
$325$	−6.29180	+	19.3642i	−0.349006	+	1.07413i
$326$	−11.2533	+	8.17599i	−0.623262	+	0.452826i
$327$		0			0
$328$	0.472136	+	1.45309i	0.0260693	+	0.0802332i
$329$	15.1803			0.836919
$330$		0			0
$331$	−7.52786			−0.413769			−0.206884	−	0.978365i	$-0.566332\pi$
$331$	−7.52786			−0.413769			−0.206884	+	0.978365i	$0.566332\pi$
$332$	−0.881966	−	2.71441i	−0.0484042	−	0.148973i
$333$	−11.5623	−	8.40051i	−0.633610	−	0.460345i
$334$	−6.47214	+	4.70228i	−0.354140	+	0.257297i
$335$	−7.05573	+	21.7153i	−0.385496	+	1.18643i
$336$		0			0
$337$	−13.4721	+	9.78808i	−0.733874	+	0.533191i	−0.890787	−	0.454422i	$-0.849846\pi$
$337$	−13.4721	+	9.78808i	−0.733874	+	0.533191i	0.156913	+	0.987612i	$0.449846\pi$
$338$	−23.3713	−	16.9803i	−1.27123	−	0.923604i
$339$		0			0
$340$	−20.2361			−1.09745
$341$	2.38197	−	25.4540i	0.128991	−	1.37841i
$342$	−3.00000			−0.162221
$343$	5.69098	+	17.5150i	0.307284	+	0.945724i
$344$	−0.500000	−	0.363271i	−0.0269582	−	0.0195863i
$345$		0			0
$346$	2.29180	−	7.05342i	0.123208	−	0.379194i
$347$	−10.5729	+	32.5402i	−0.567586	+	1.74685i	0.0925556	+	0.995708i	$0.470496\pi$
$347$	−10.5729	+	32.5402i	−0.567586	+	1.74685i	−0.660141	+	0.751141i	$0.729504\pi$
$348$		0			0
$349$	1.83688	+	1.33457i	0.0983260	+	0.0714380i	0.635862	−	0.771803i	$-0.280645\pi$
$349$	1.83688	+	1.33457i	0.0983260	+	0.0714380i	−0.537536	+	0.843241i	$0.680645\pi$
$350$	−1.57295	−	4.84104i	−0.0840777	−	0.258764i
$351$		0			0
$352$	−3.04508	−	1.31433i	−0.162304	−	0.0700539i
$353$	−7.32624			−0.389936			−0.194968	−	0.980810i	$-0.562460\pi$
$353$	−7.32624			−0.389936			−0.194968	+	0.980810i	$0.562460\pi$
$354$		0			0
$355$	1.09017	+	0.792055i	0.0578602	+	0.0420379i
$356$	−6.61803	+	4.80828i	−0.350755	+	0.254838i
$357$		0			0
$358$	0.854102	−	2.62866i	0.0451407	−	0.138929i
$359$	−28.5344	+	20.7315i	−1.50599	+	1.09417i	−0.538073	+	0.842899i	$0.680847\pi$
$359$	−28.5344	+	20.7315i	−1.50599	+	1.09417i	−0.967918	+	0.251267i	$0.919153\pi$
$360$	6.92705	+	5.03280i	0.365088	+	0.265252i
$361$	0.309017	+	0.951057i	0.0162641	+	0.0500556i
$362$	18.6525			0.980352
$363$		0			0
$364$	10.4721			0.548889
$365$	0.416408	+	1.28157i	0.0217958	+	0.0670805i
$366$		0			0
$367$	−20.8713	+	15.1639i	−1.08947	+	0.791549i	−0.979310	−	0.202364i	$-0.935138\pi$
$367$	−20.8713	+	15.1639i	−1.08947	+	0.791549i	−0.110164	+	0.993913i	$0.535138\pi$
$368$	2.42705	−	7.46969i	0.126519	−	0.389385i
$369$	−1.41641	+	4.35926i	−0.0737352	+	0.226934i
$370$	11.0000	−	7.99197i	0.571863	−	0.415483i
$371$	2.61803	+	1.90211i	0.135922	+	0.0987528i
$372$		0			0
$373$	−23.5967			−1.22179			−0.610897	−	0.791710i	$-0.709191\pi$
$373$	−23.5967			−1.22179			−0.610897	+	0.791710i	$0.709191\pi$
$374$	21.5902	+	9.31881i	1.11640	+	0.481864i
$375$		0			0
$376$	−2.89919	−	8.92278i	−0.149514	−	0.460157i
$377$	−16.9443	−	12.3107i	−0.872674	−	0.634035i
$378$		0			0
$379$	3.23607	−	9.95959i	0.166226	−	0.511590i	−0.832899	−	0.553425i	$-0.813320\pi$
$379$	3.23607	−	9.95959i	0.166226	−	0.511590i	0.999125	+	0.0418353i	$0.0133205\pi$
$380$	0.881966	−	2.71441i	0.0452439	−	0.139246i
$381$		0			0
$382$	8.54508	+	6.20837i	0.437205	+	0.317648i
$383$	2.94427	+	9.06154i	0.150445	+	0.463023i	0.997671	−	0.0682102i	$-0.0217288\pi$
$383$	2.94427	+	9.06154i	0.150445	+	0.463023i	−0.847226	+	0.531233i	$0.821729\pi$
$384$		0			0
$385$	−1.42705	+	15.2497i	−0.0727293	+	0.777195i
$386$	2.00000			0.101797
$387$	−0.572949	−	1.76336i	−0.0291246	−	0.0896364i
$388$	13.3262	+	9.68208i	0.676537	+	0.491533i
$389$	−4.35410	+	3.16344i	−0.220762	+	0.160393i	−0.692669	−	0.721255i	$-0.743566\pi$
$389$	−4.35410	+	3.16344i	−0.220762	+	0.160393i	0.471908	+	0.881648i	$0.343566\pi$
$390$		0			0
$391$	−17.2082	+	52.9614i	−0.870256	+	2.67837i
$392$	3.54508	−	2.57565i	0.179054	−	0.130090i
$393$		0			0
$394$	5.09017	+	15.6659i	0.256439	+	0.789238i
$395$	−34.2492			−1.72327
$396$	−5.07295	−	8.55951i	−0.254925	−	0.430131i
$397$	−16.7984			−0.843086			−0.421543	−	0.906808i	$-0.638511\pi$
$397$	−16.7984			−0.843086			−0.421543	+	0.906808i	$0.638511\pi$
$398$	0.736068	+	2.26538i	0.0368958	+	0.113553i
$399$		0			0
$400$	−2.54508	+	1.84911i	−0.127254	+	0.0924556i
$401$	7.23607	−	22.2703i	0.361352	−	1.11213i	−0.590882	−	0.806758i	$-0.701220\pi$
$401$	7.23607	−	22.2703i	0.361352	−	1.11213i	0.952234	−	0.305369i	$-0.0987798\pi$
$402$		0			0
$403$	40.3607	−	29.3238i	2.01051	−	1.46072i
$404$	−2.92705	−	2.12663i	−0.145626	−	0.105804i
$405$	7.93769	+	24.4297i	0.394427	+	1.21392i
$406$	5.23607			0.259862
$407$	−15.4164	+	3.46120i	−0.764163	+	0.171565i
$408$		0			0
$409$	3.18034	+	9.78808i	0.157258	+	0.483989i	0.998383	−	0.0568514i	$-0.0181061\pi$
$409$	3.18034	+	9.78808i	0.157258	+	0.483989i	−0.841125	+	0.540841i	$0.818106\pi$
$410$	−3.52786	−	2.56314i	−0.174229	−	0.126585i
$411$		0			0
$412$	−6.00000	+	18.4661i	−0.295599	+	0.909760i
$413$	5.00000	−	15.3884i	0.246034	−	0.757215i
$414$	19.0623	−	13.8496i	0.936861	−	0.680670i
$415$	6.59017	+	4.78804i	0.323499	+	0.235036i
$416$	−2.00000	−	6.15537i	−0.0980581	−	0.301792i
$417$		0			0
$418$	−2.19098	+	2.48990i	−0.107164	+	0.121785i
$419$	28.3262			1.38383			0.691914	−	0.721980i	$-0.256768\pi$
$419$	28.3262			1.38383			0.691914	+	0.721980i	$0.256768\pi$
$420$		0			0
$421$	23.6525	+	17.1845i	1.15275	+	0.837523i	0.988844	−	0.148953i	$-0.0475903\pi$
$421$	23.6525	+	17.1845i	1.15275	+	0.837523i	0.163907	+	0.986476i	$0.447590\pi$
$422$	−18.7082	+	13.5923i	−0.910701	+	0.661663i
$423$	8.69756	−	26.7683i	0.422890	−	1.30152i
$424$	0.618034	−	1.90211i	0.0300144	−	0.0923748i
$425$	18.0451	−	13.1105i	0.875315	−	0.635954i
$426$		0			0
$427$	0.545085	+	1.67760i	0.0263785	+	0.0811847i
$428$	−4.76393			−0.230273
$429$		0			0
$430$	1.76393			0.0850644
$431$	2.43769	+	7.50245i	0.117420	+	0.361380i	0.992444	−	0.122698i	$-0.0391548\pi$
$431$	2.43769	+	7.50245i	0.117420	+	0.361380i	−0.875024	+	0.484079i	$0.839155\pi$
$432$		0			0
$433$	−24.7082	+	17.9516i	−1.18740	+	0.862697i	−0.992987	−	0.118223i	$-0.962280\pi$
$433$	−24.7082	+	17.9516i	−1.18740	+	0.862697i	−0.194413	+	0.980920i	$0.562280\pi$
$434$	−3.85410	+	11.8617i	−0.185003	+	0.569380i
$435$		0			0
$436$	9.47214	−	6.88191i	0.453633	−	0.329584i
$437$	−6.35410	−	4.61653i	−0.303958	−	0.220838i
$438$		0			0
$439$	8.36068			0.399033			0.199517	−	0.979894i	$-0.436063\pi$
$439$	8.36068			0.399033			0.199517	+	0.979894i	$0.436063\pi$
$440$	9.23607	−	2.07363i	0.440312	−	0.0988563i
$441$	13.1459			0.625995
$442$	14.1803	+	43.6426i	0.674490	+	2.07587i
$443$	0.309017	+	0.224514i	0.0146818	+	0.0106670i	0.595102	−	0.803650i	$-0.297112\pi$
$443$	0.309017	+	0.224514i	0.0146818	+	0.0106670i	−0.580420	+	0.814317i	$0.697112\pi$
$444$		0			0
$445$	7.21478	−	22.2048i	0.342013	−	1.05261i
$446$	−1.38197	+	4.25325i	−0.0654380	+	0.201397i
$447$		0			0
$448$	1.30902	+	0.951057i	0.0618452	+	0.0449332i
$449$	−4.65248	−	14.3188i	−0.219564	−	0.675748i	−0.998798	−	0.0490153i	$-0.984392\pi$
$449$	−4.65248	−	14.3188i	−0.219564	−	0.675748i	0.779234	−	0.626733i	$-0.215608\pi$
$450$	−9.43769			−0.444897
$451$	2.58359	+	4.35926i	0.121657	+	0.205269i
$452$	−0.291796			−0.0137249
$453$		0			0
$454$	−16.5623	−	12.0332i	−0.777308	−	0.564747i
$455$	−24.1803	+	17.5680i	−1.13359	+	0.823603i
$456$		0			0
$457$	−1.91641	+	5.89810i	−0.0896458	+	0.275901i	−0.985821	−	0.167798i	$-0.946334\pi$
$457$	−1.91641	+	5.89810i	−0.0896458	+	0.275901i	0.896176	+	0.443700i	$0.146334\pi$
$458$	−15.8262	+	11.4984i	−0.739512	+	0.537287i
$459$		0			0
$460$	6.92705	+	21.3193i	0.322975	+	0.994016i
$461$	27.6180			1.28630			0.643150	−	0.765740i	$-0.277627\pi$
$461$	27.6180			1.28630			0.643150	+	0.765740i	$0.277627\pi$
$462$		0			0
$463$	−11.1459			−0.517994			−0.258997	−	0.965878i	$-0.583392\pi$
$463$	−11.1459			−0.517994			−0.258997	+	0.965878i	$0.583392\pi$
$464$	−1.00000	−	3.07768i	−0.0464238	−	0.142878i
$465$		0			0
$466$	16.2533	−	11.8087i	0.752919	−	0.547028i
$467$	3.35410	−	10.3229i	0.155209	−	0.477685i	−0.842973	−	0.537956i	$-0.819197\pi$
$467$	3.35410	−	10.3229i	0.155209	−	0.477685i	0.998182	+	0.0602711i	$0.0191965\pi$
$468$	6.00000	−	18.4661i	0.277350	−	0.853596i
$469$	−10.4721	+	7.60845i	−0.483558	+	0.351326i
$470$	21.6631	+	15.7392i	0.999245	+	0.725994i
$471$		0			0
$472$	−10.0000			−0.460287
$473$	−1.88197	−	0.812299i	−0.0865329	−	0.0373496i
$474$		0			0
$475$	0.972136	+	2.99193i	0.0446047	+	0.137279i
$476$	−9.28115	−	6.74315i	−0.425401	−	0.309072i
$477$	4.85410	−	3.52671i	0.222254	−	0.161477i
$478$	−2.71885	+	8.36775i	−0.124357	+	0.382732i
$479$	−1.10081	+	3.38795i	−0.0502974	+	0.154800i	−0.973050	−	0.230592i	$-0.925934\pi$
$479$	−1.10081	+	3.38795i	−0.0502974	+	0.154800i	0.922753	+	0.385392i	$0.125934\pi$
$480$		0			0
$481$	−24.9443	−	18.1231i	−1.13736	−	0.826341i
$482$	8.32624	+	25.6255i	0.379250	+	1.16721i
$483$		0			0
$484$	−10.8090	−	2.04087i	−0.491319	−	0.0927668i
$485$	−47.0132			−2.13476
$486$		0			0
$487$	1.14590	+	0.832544i	0.0519256	+	0.0377262i	0.613445	−	0.789737i	$-0.289783\pi$
$487$	1.14590	+	0.832544i	0.0519256	+	0.0377262i	−0.561520	+	0.827463i	$0.689783\pi$
$488$	0.881966	−	0.640786i	0.0399247	−	0.0290070i
$489$		0			0
$490$	−3.86475	+	11.8945i	−0.174591	+	0.537337i
$491$	12.4894	−	9.07405i	0.563637	−	0.409506i	−0.269151	−	0.963098i	$-0.586743\pi$
$491$	12.4894	−	9.07405i	0.563637	−	0.409506i	0.832788	+	0.553592i	$0.186743\pi$
$492$		0			0
$493$	7.09017	+	21.8213i	0.319325	+	0.982782i
$494$	−6.47214			−0.291195
$495$	26.0729	+	11.2537i	1.17189	+	0.505815i
$496$	7.70820			0.346109
$497$	0.236068	+	0.726543i	0.0105891	+	0.0325899i
$498$		0			0
$499$	−8.30902	+	6.03685i	−0.371963	+	0.270247i	−0.758024	−	0.652226i	$-0.773835\pi$
$499$	−8.30902	+	6.03685i	−0.371963	+	0.270247i	0.386062	+	0.922473i	$0.373835\pi$
$500$	−1.63525	+	5.03280i	−0.0731308	+	0.225074i
$501$		0			0
$502$	6.20820	−	4.51052i	0.277086	−	0.201315i
$503$	−0.472136	−	0.343027i	−0.0210515	−	0.0152948i	0.577210	−	0.816596i	$-0.304142\pi$
$503$	−0.472136	−	0.343027i	−0.0210515	−	0.0152948i	−0.598261	+	0.801301i	$0.704142\pi$
$504$	1.50000	+	4.61653i	0.0668153	+	0.205636i
$505$	10.3262			0.459512
$506$	2.42705	−	25.9358i	0.107896	−	1.15299i
$507$		0			0
$508$	−0.236068	−	0.726543i	−0.0104738	−	0.0322351i
$509$	−4.09017	−	2.97168i	−0.181294	−	0.131718i	0.493437	−	0.869781i	$-0.335740\pi$
$509$	−4.09017	−	2.97168i	−0.181294	−	0.131718i	−0.674731	+	0.738064i	$0.735740\pi$
$510$		0			0
$511$	−0.236068	+	0.726543i	−0.0104430	+	0.0321403i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$		0			0
$514$	−6.23607	−	4.53077i	−0.275061	−	0.199844i
$515$	−17.1246	−	52.7041i	−0.754601	−	2.32242i
$516$		0			0
$517$	−15.8647	−	26.7683i	−0.697731	−	1.17727i
$518$	7.70820			0.338679
$519$		0			0
$520$	14.9443	+	10.8576i	0.655350	+	0.476139i
$521$	−6.23607	+	4.53077i	−0.273207	+	0.198497i	−0.715949	−	0.698152i	$-0.754006\pi$
$521$	−6.23607	+	4.53077i	−0.273207	+	0.198497i	0.442742	+	0.896649i	$0.354006\pi$
$522$	3.00000	−	9.23305i	0.131306	−	0.404120i
$523$	−3.18034	+	9.78808i	−0.139067	+	0.428003i	−0.996200	−	0.0870910i	$-0.972243\pi$
$523$	−3.18034	+	9.78808i	−0.139067	+	0.428003i	0.857134	+	0.515094i	$0.172243\pi$
$524$	−7.54508	+	5.48183i	−0.329609	+	0.239475i
$525$		0			0
$526$	−3.23607	−	9.95959i	−0.141099	−	0.434259i
$527$	−54.6525			−2.38070
$528$		0			0
$529$	38.6869			1.68204
$530$	1.76393	+	5.42882i	0.0766203	+	0.235813i
$531$	−24.2705	−	17.6336i	−1.05325	−	0.765231i
$532$	1.30902	−	0.951057i	0.0567531	−	0.0412335i
$533$	−3.05573	+	9.40456i	−0.132358	+	0.407357i
$534$		0			0
$535$	11.0000	−	7.99197i	0.475571	−	0.345523i
$536$	6.47214	+	4.70228i	0.279554	+	0.203108i
$537$		0			0
$538$	−28.3607			−1.22272
$539$	9.60081	−	10.9106i	0.413536	−	0.469955i
$540$		0			0
$541$	6.24671	+	19.2254i	0.268567	+	0.826565i	0.990850	+	0.134967i	$0.0430928\pi$
$541$	6.24671	+	19.2254i	0.268567	+	0.826565i	−0.722283	+	0.691598i	$0.756907\pi$
$542$	2.35410	+	1.71036i	0.101117	+	0.0734660i
$543$		0			0
$544$	−2.19098	+	6.74315i	−0.0939376	+	0.289110i
$545$	−10.3262	+	31.7809i	−0.442327	+	1.36134i
$546$		0			0
$547$	−25.2705	−	18.3601i	−1.08049	−	0.785021i	−0.102721	−	0.994710i	$-0.532755\pi$
$547$	−25.2705	−	18.3601i	−1.08049	−	0.785021i	−0.977768	+	0.209689i	$0.932755\pi$
$548$	−4.44427	−	13.6781i	−0.189850	−	0.584298i
$549$	3.27051			0.139582
$550$	−6.89261	+	7.83297i	−0.293902	+	0.333999i
$551$	−3.23607			−0.137861
$552$		0			0
$553$	−15.7082	−	11.4127i	−0.667981	−	0.485316i
$554$	17.7984	−	12.9313i	0.756180	−	0.549397i
$555$		0			0
$556$	−1.13525	+	3.49396i	−0.0481455	+	0.148177i
$557$	31.4336	−	22.8379i	1.33189	−	0.967672i	0.332185	−	0.943214i	$-0.392214\pi$
$557$	31.4336	−	22.8379i	1.33189	−	0.967672i	0.999701	−	0.0244572i	$-0.00778574\pi$
$558$	18.7082	+	13.5923i	0.791981	+	0.575408i
$559$	−1.23607	−	3.80423i	−0.0522801	−	0.160902i
$560$	−4.61803			−0.195148
$561$		0			0
$562$	−19.1246			−0.806723
$563$	2.14590	+	6.60440i	0.0904388	+	0.278342i	0.986038	−	0.166520i	$-0.0532529\pi$
$563$	2.14590	+	6.60440i	0.0904388	+	0.278342i	−0.895599	+	0.444862i	$0.853253\pi$
$564$		0			0
$565$	0.673762	−	0.489517i	0.0283454	−	0.0205941i
$566$	−1.93769	+	5.96361i	−0.0814474	+	0.250669i
$567$	−4.50000	+	13.8496i	−0.188982	+	0.581628i
$568$	0.381966	−	0.277515i	0.0160269	−	0.0116443i
$569$	13.0902	+	9.51057i	0.548768	+	0.398704i	0.827331	−	0.561714i	$-0.189858\pi$
$569$	13.0902	+	9.51057i	0.548768	+	0.398704i	−0.278563	+	0.960418i	$0.589858\pi$
$570$		0			0
$571$	−13.5066			−0.565233			−0.282616	−	0.959233i	$-0.591202\pi$
$571$	−13.5066			−0.565233			−0.282616	+	0.959233i	$0.591202\pi$
$572$	−10.9443	−	18.4661i	−0.457603	−	0.772106i
$573$		0			0
$574$	−0.763932	−	2.35114i	−0.0318859	−	0.0981347i
$575$	−19.9894	−	14.5231i	−0.833614	−	0.605656i
$576$	2.42705	−	1.76336i	0.101127	−	0.0734732i
$577$	7.27051	−	22.3763i	0.302675	−	0.931539i	−0.677859	−	0.735192i	$-0.737092\pi$
$577$	7.27051	−	22.3763i	0.302675	−	0.931539i	0.980534	−	0.196347i	$-0.0629079\pi$
$578$	10.2812	−	31.6421i	0.427640	−	1.31614i
$579$		0			0
$580$	7.47214	+	5.42882i	0.310264	+	0.225420i
$581$	1.42705	+	4.39201i	0.0592041	+	0.182211i
$582$		0			0
$583$	0.618034	−	6.60440i	0.0255964	−	0.273526i
$584$	0.472136			0.0195371
$585$	17.1246	+	52.7041i	0.708016	+	2.17905i
$586$	−9.47214	−	6.88191i	−0.391290	−	0.284289i
$587$	27.4164	−	19.9192i	1.13160	−	0.822153i	0.145670	−	0.989333i	$-0.453466\pi$
$587$	27.4164	−	19.9192i	1.13160	−	0.822153i	0.985926	+	0.167180i	$0.0534662\pi$
$588$		0			0
$589$	2.38197	−	7.33094i	0.0981472	−	0.302066i
$590$	23.0902	−	16.7760i	0.950607	−	0.690657i
$591$		0			0
$592$	−1.47214	−	4.53077i	−0.0605044	−	0.186213i
$593$	43.0902			1.76950			0.884751	−	0.466065i	$-0.154329\pi$
$593$	43.0902			1.76950			0.884751	+	0.466065i	$0.154329\pi$
$594$		0			0
$595$	32.7426			1.34232
$596$	−4.14590	−	12.7598i	−0.169823	−	0.522660i
$597$		0			0
$598$	41.1246	−	29.8788i	1.68171	−	1.22183i
$599$	−7.76393	+	23.8949i	−0.317226	+	0.976320i	0.657603	+	0.753365i	$0.271570\pi$
$599$	−7.76393	+	23.8949i	−0.317226	+	0.976320i	−0.974829	+	0.222956i	$0.928430\pi$
$600$		0			0
$601$	29.1803	−	21.2008i	1.19029	−	0.864797i	0.196996	−	0.980404i	$-0.436881\pi$
$601$	29.1803	−	21.2008i	1.19029	−	0.864797i	0.993295	+	0.115607i	$0.0368814\pi$
$602$	0.809017	+	0.587785i	0.0329731	+	0.0239563i
$603$	7.41641	+	22.8254i	0.302019	+	0.929520i
$604$	8.18034			0.332853
$605$	28.3820	−	13.4208i	1.15389	−	0.545633i
$606$		0			0
$607$	−14.0344	−	43.1936i	−0.569640	−	1.75317i	−0.653744	−	0.756716i	$-0.726803\pi$
$607$	−14.0344	−	43.1936i	−0.569640	−	1.75317i	0.0841034	−	0.996457i	$-0.473197\pi$
$608$	−0.809017	−	0.587785i	−0.0328100	−	0.0238378i
$609$		0			0
$610$	−0.961493	+	2.95917i	−0.0389297	+	0.119813i
$611$	18.7639	−	57.7494i	0.759107	−	2.33629i
$612$	−17.2082	+	12.5025i	−0.695600	+	0.505383i
$613$	−28.2984	−	20.5600i	−1.14296	−	0.830409i	−0.155432	−	0.987847i	$-0.549677\pi$
$613$	−28.2984	−	20.5600i	−1.14296	−	0.830409i	−0.987529	+	0.157437i	$0.949677\pi$
$614$	2.29180	+	7.05342i	0.0924894	+	0.284653i
$615$		0			0
$616$	4.92705	+	2.12663i	0.198517	+	0.0856842i
$617$	13.0557			0.525604			0.262802	−	0.964850i	$-0.415353\pi$
$617$	13.0557			0.525604			0.262802	+	0.964850i	$0.415353\pi$
$618$		0			0
$619$	32.4443	+	23.5721i	1.30405	+	0.947444i	0.999986	−	0.00520878i	$-0.00165801\pi$
$619$	32.4443	+	23.5721i	1.30405	+	0.947444i	0.304059	+	0.952653i	$0.401658\pi$
$620$	−17.7984	+	12.9313i	−0.714800	+	0.519333i
$621$		0			0
$622$	−5.46149	+	16.8087i	−0.218986	+	0.673969i
$623$	10.7082	−	7.77997i	0.429015	−	0.311698i
$624$		0			0
$625$	−9.52786	−	29.3238i	−0.381115	−	1.17295i
$626$	28.0344			1.12048
$627$		0			0
$628$	20.5623			0.820525
$629$	10.4377	+	32.1239i	0.416178	+	1.28086i
$630$	−11.2082	−	8.14324i	−0.446546	−	0.324434i
$631$	−21.4164	+	15.5599i	−0.852574	+	0.619431i	−0.925854	−	0.377880i	$-0.876653\pi$
$631$	−21.4164	+	15.5599i	−0.852574	+	0.619431i	0.0732807	+	0.997311i	$0.476653\pi$
$632$	−3.70820	+	11.4127i	−0.147504	+	0.453972i
$633$		0			0
$634$	9.23607	−	6.71040i	0.366811	−	0.266504i
$635$	1.76393	+	1.28157i	0.0699995	+	0.0508576i
$636$		0			0
$637$	28.3607			1.12369
$638$	−5.47214	−	9.23305i	−0.216644	−	0.365540i
$639$	1.41641			0.0560322
$640$	0.881966	+	2.71441i	0.0348628	+	0.107297i
$641$	20.6525	+	15.0049i	0.815724	+	0.592658i	0.915484	−	0.402353i	$-0.131808\pi$
$641$	20.6525	+	15.0049i	0.815724	+	0.592658i	−0.0997606	+	0.995011i	$0.531808\pi$
$642$		0			0
$643$	−14.9336	+	45.9610i	−0.588925	+	1.81252i	−0.00602273	+	0.999982i	$0.501917\pi$
$643$	−14.9336	+	45.9610i	−0.588925	+	1.81252i	−0.582902	+	0.812542i	$0.698083\pi$
$644$	−3.92705	+	12.0862i	−0.154747	+	0.476264i
$645$		0			0
$646$	5.73607	+	4.16750i	0.225683	+	0.163968i
$647$	−7.52786	−	23.1684i	−0.295951	−	0.910843i	−0.982900	−	0.184138i	$-0.941051\pi$
$647$	−7.52786	−	23.1684i	−0.295951	−	0.910843i	0.686950	−	0.726705i	$-0.258949\pi$
$648$	9.00000			0.353553
$649$	−32.3607	+	7.26543i	−1.27027	+	0.285193i
$650$	−20.3607			−0.798612
$651$		0			0
$652$	−11.2533	−	8.17599i	−0.440713	−	0.320197i
$653$	7.59017	−	5.51458i	0.297026	−	0.215802i	−0.429283	−	0.903170i	$-0.641234\pi$
$653$	7.59017	−	5.51458i	0.297026	−	0.215802i	0.726310	+	0.687368i	$0.241234\pi$
$654$		0			0
$655$	8.22542	−	25.3153i	0.321394	−	0.989149i
$656$	−1.23607	+	0.898056i	−0.0482603	+	0.0350632i
$657$	1.14590	+	0.832544i	0.0447057	+	0.0324806i
$658$	4.69098	+	14.4374i	0.182874	+	0.562827i
$659$	−21.3050			−0.829923			−0.414962	−	0.909839i	$-0.636205\pi$
$659$	−21.3050			−0.829923			−0.414962	+	0.909839i	$0.636205\pi$
$660$		0			0
$661$	10.9443			0.425683			0.212841	−	0.977087i	$-0.431728\pi$
$661$	10.9443			0.425683			0.212841	+	0.977087i	$0.431728\pi$
$662$	−2.32624	−	7.15942i	−0.0904118	−	0.278259i
$663$		0			0
$664$	2.30902	−	1.67760i	0.0896072	−	0.0651035i
$665$	−1.42705	+	4.39201i	−0.0553387	+	0.170315i
$666$	4.41641	−	13.5923i	0.171132	−	0.526691i
$667$	20.5623	−	14.9394i	0.796176	−	0.578455i
$668$	−6.47214	−	4.70228i	−0.250414	−	0.181937i
$669$		0			0
$670$	−22.8328			−0.882109
$671$	2.38854	−	2.71441i	0.0922087	−	0.104789i
$672$		0			0
$673$	−8.23607	−	25.3480i	−0.317477	−	0.977094i	−0.974723	−	0.223418i	$-0.928279\pi$
$673$	−8.23607	−	25.3480i	−0.317477	−	0.977094i	0.657246	−	0.753676i	$-0.271721\pi$
$674$	−13.4721	−	9.78808i	−0.518927	−	0.377023i
$675$		0			0
$676$	8.92705	−	27.4746i	0.343348	−	1.05672i
$677$	−4.34752	+	13.3803i	−0.167089	+	0.514247i	−0.999184	−	0.0403860i	$-0.987141\pi$
$677$	−4.34752	+	13.3803i	−0.167089	+	0.514247i	0.832095	+	0.554633i	$0.187141\pi$
$678$		0			0
$679$	−21.5623	−	15.6659i	−0.827485	−	0.601203i
$680$	−6.25329	−	19.2456i	−0.239803	−	0.738037i
$681$		0			0
$682$	24.9443	−	5.60034i	0.955166	−	0.214448i
$683$	−36.8328			−1.40937			−0.704684	−	0.709521i	$-0.748911\pi$
$683$	−36.8328			−1.40937			−0.704684	+	0.709521i	$0.748911\pi$
$684$	−0.927051	−	2.85317i	−0.0354467	−	0.109094i
$685$	33.2082	+	24.1272i	1.26882	+	0.921852i
$686$	−14.8992	+	10.8249i	−0.568854	+	0.413296i
$687$		0			0
$688$	0.190983	−	0.587785i	0.00728116	−	0.0224091i
$689$	10.4721	−	7.60845i	0.398957	−	0.289859i
$690$		0			0
$691$	2.29837	+	7.07367i	0.0874343	+	0.269095i	0.985208	−	0.171362i	$-0.0548166\pi$
$691$	2.29837	+	7.07367i	0.0874343	+	0.269095i	−0.897774	+	0.440456i	$0.854817\pi$
$692$	7.41641			0.281930
$693$	8.20820	+	13.8496i	0.311804	+	0.526102i
$694$	−34.2148			−1.29878
$695$	−3.24013	−	9.97210i	−0.122905	−	0.378263i
$696$		0			0
$697$	8.76393	−	6.36737i	0.331958	−	0.241181i
$698$	−0.701626	+	2.15938i	−0.0265569	+	0.0817339i
$699$		0			0
$700$	4.11803	−	2.99193i	0.155647	−	0.113084i
$701$	−22.2984	−	16.2007i	−0.842198	−	0.611893i	0.0807858	−	0.996731i	$-0.474257\pi$
$701$	−22.2984	−	16.2007i	−0.842198	−	0.611893i	−0.922984	+	0.384839i	$0.874257\pi$
$702$		0			0
$703$	−4.76393			−0.179675
$704$	0.309017	−	3.30220i	0.0116465	−	0.124456i
$705$		0			0
$706$	−2.26393	−	6.96767i	−0.0852042	−	0.262232i
$707$	4.73607	+	3.44095i	0.178118	+	0.129410i
$708$		0			0
$709$	9.88197	−	30.4136i	0.371125	−	1.14221i	−0.574931	−	0.818202i	$-0.694971\pi$
$709$	9.88197	−	30.4136i	0.371125	−	1.14221i	0.946056	−	0.324003i	$-0.105029\pi$
$710$	−0.416408	+	1.28157i	−0.0156275	+	0.0480965i
$711$	−29.1246	+	21.1603i	−1.09226	+	0.793572i
$712$	−6.61803	−	4.80828i	−0.248021	−	0.180198i
$713$	18.7082	+	57.5779i	0.700628	+	2.15631i
$714$		0			0
$715$	56.2492	+	24.2784i	2.10360	+	0.907962i
$716$	2.76393			0.103293
$717$		0			0
$718$	−28.5344	−	20.7315i	−1.06490	−	0.773692i
$719$	−39.4894	+	28.6907i	−1.47270	+	1.06998i	−0.492886	+	0.870094i	$0.664058\pi$
$719$	−39.4894	+	28.6907i	−1.47270	+	1.06998i	−0.979819	+	0.199888i	$0.935942\pi$
$720$	−2.64590	+	8.14324i	−0.0986068	+	0.303481i
$721$	9.70820	−	29.8788i	0.361552	−	1.11274i
$722$	−0.809017	+	0.587785i	−0.0301085	+	0.0218751i
$723$		0			0
$724$	5.76393	+	17.7396i	0.214215	+	0.659286i
$725$	−10.1803			−0.378088
$726$		0			0
$727$	−37.0902			−1.37560			−0.687799	−	0.725901i	$-0.741423\pi$
$727$	−37.0902			−1.37560			−0.687799	+	0.725901i	$0.741423\pi$
$728$	3.23607	+	9.95959i	0.119937	+	0.369127i
$729$	21.8435	+	15.8702i	0.809017	+	0.587785i
$730$	−1.09017	+	0.792055i	−0.0403490	+	0.0293153i
$731$	−1.35410	+	4.16750i	−0.0500833	+	0.154140i
$732$		0			0
$733$	14.9271	−	10.8451i	0.551343	−	0.400574i	−0.276937	−	0.960888i	$-0.589319\pi$
$733$	14.9271	−	10.8451i	0.551343	−	0.400574i	0.828280	+	0.560314i	$0.189319\pi$
$734$	−20.8713	−	15.1639i	−0.770375	−	0.559710i
$735$		0			0
$736$	7.85410			0.289506
$737$	24.3607	+	10.5146i	0.897337	+	0.387311i
$738$	−4.58359			−0.168724
$739$	2.17376	+	6.69015i	0.0799631	+	0.246101i	0.983044	−	0.183369i	$-0.0587003\pi$
$739$	2.17376	+	6.69015i	0.0799631	+	0.246101i	−0.903081	+	0.429470i	$0.858700\pi$
$740$	11.0000	+	7.99197i	0.404368	+	0.293791i
$741$		0			0
$742$	−1.00000	+	3.07768i	−0.0367112	+	0.112985i
$743$	5.03444	−	15.4944i	0.184696	−	0.568435i	−0.815247	−	0.579113i	$-0.803399\pi$
$743$	5.03444	−	15.4944i	0.184696	−	0.568435i	0.999943	+	0.0106780i	$0.00339897\pi$
$744$		0			0
$745$	30.9787	+	22.5074i	1.13497	+	0.824606i
$746$	−7.29180	−	22.4418i	−0.266972	−	0.821654i
$747$	8.56231			0.313278
$748$	−2.19098	+	23.4131i	−0.0801103	+	0.856069i
$749$	7.70820			0.281652
$750$		0			0
$751$	23.2705	+	16.9070i	0.849153	+	0.616946i	0.924912	−	0.380180i	$-0.124138\pi$
$751$	23.2705	+	16.9070i	0.849153	+	0.616946i	−0.0757594	+	0.997126i	$0.524138\pi$
$752$	7.59017	−	5.51458i	0.276785	−	0.201096i
$753$		0			0
$754$	6.47214	−	19.9192i	0.235701	−	0.725414i
$755$	−18.8885	+	13.7233i	−0.687424	+	0.499443i
$756$		0			0
$757$	4.72949	+	14.5559i	0.171896	+	0.529042i	0.999478	−	0.0323028i	$-0.0102841\pi$
$757$	4.72949	+	14.5559i	0.171896	+	0.529042i	−0.827582	+	0.561345i	$0.810284\pi$
$758$	10.4721			0.380365
$759$		0			0
$760$	2.85410			0.103529
$761$	−6.61803	−	20.3682i	−0.239904	−	0.738347i	−0.996433	−	0.0843876i	$-0.973107\pi$
$761$	−6.61803	−	20.3682i	−0.239904	−	0.738347i	0.756529	−	0.653960i	$-0.226893\pi$
$762$		0			0
$763$	−15.3262	+	11.1352i	−0.554847	+	0.403120i
$764$	−3.26393	+	10.0453i	−0.118085	+	0.363428i
$765$	18.7599	−	57.7369i	0.678264	−	2.08748i
$766$	−7.70820	+	5.60034i	−0.278509	+	0.202348i
$767$	−52.3607	−	38.0423i	−1.89063	−	1.37363i
$768$		0			0
$769$	10.7426			0.387390			0.193695	−	0.981062i	$-0.437953\pi$
$769$	10.7426			0.387390			0.193695	+	0.981062i	$0.437953\pi$
$770$	−14.9443	+	3.35520i	−0.538554	+	0.120913i
$771$		0			0
$772$	0.618034	+	1.90211i	0.0222435	+	0.0684585i
$773$	0.291796	+	0.212002i	0.0104952	+	0.00762519i	0.593020	−	0.805187i	$-0.297935\pi$
$773$	0.291796	+	0.212002i	0.0104952	+	0.00762519i	−0.582525	+	0.812813i	$0.697935\pi$
$774$	1.50000	−	1.08981i	0.0539164	−	0.0391725i
$775$	7.49342	−	23.0624i	0.269172	−	0.828425i
$776$	−5.09017	+	15.6659i	−0.182726	+	0.562374i
$777$		0			0
$778$	−4.35410	−	3.16344i	−0.156102	−	0.113415i
$779$	0.472136	+	1.45309i	0.0169160	+	0.0520622i
$780$		0			0
$781$	1.03444	−	1.17557i	0.0370152	−	0.0420652i
$782$	−55.6869			−1.99136
$783$		0			0
$784$	3.54508	+	2.57565i	0.126610	+	0.0919877i
$785$	−47.4787	+	34.4953i	−1.69459	+	1.23119i
$786$		0			0
$787$	−6.50658	+	20.0252i	−0.231934	+	0.713821i	0.765579	+	0.643342i	$0.222453\pi$
$787$	−6.50658	+	20.0252i	−0.231934	+	0.713821i	−0.997513	+	0.0704787i	$0.977547\pi$
$788$	−13.3262	+	9.68208i	−0.474728	+	0.344910i
$789$		0			0
$790$	−10.5836	−	32.5729i	−0.376547	−	1.15889i
$791$	0.472136			0.0167872
$792$	6.57295	−	7.46969i	0.233560	−	0.265424i
$793$	7.05573			0.250556
$794$	−5.19098	−	15.9762i	−0.184221	−	0.566974i
$795$		0			0
$796$	−1.92705	+	1.40008i	−0.0683025	+	0.0496247i
$797$	4.14590	−	12.7598i	0.146855	−	0.451974i	−0.850390	−	0.526153i	$-0.823634\pi$
$797$	4.14590	−	12.7598i	0.146855	−	0.451974i	0.997245	+	0.0741795i	$0.0236338\pi$
$798$		0			0
$799$	−53.8156	+	39.0993i	−1.90386	+	1.38323i
$800$	−2.54508	−	1.84911i	−0.0899823	−	0.0653760i
$801$	−7.58359	−	23.3399i	−0.267953	−	0.824675i
$802$	23.4164			0.826862
$803$	1.52786	−	0.343027i	0.0539172	−	0.0121052i
$804$		0			0
$805$	−11.2082	−	34.4953i	−0.395037	−	1.21580i
$806$	40.3607	+	29.3238i	1.42164	+	1.03289i
$807$		0			0
$808$	1.11803	−	3.44095i	0.0393323	−	0.121052i
$809$	1.61146	−	4.95955i	0.0566558	−	0.174369i	−0.918724	−	0.394900i	$-0.870779\pi$
$809$	1.61146	−	4.95955i	0.0566558	−	0.174369i	0.975380	+	0.220532i	$0.0707792\pi$
$810$	−20.7812	+	15.0984i	−0.730175	+	0.530503i
$811$	12.7639	+	9.27354i	0.448202	+	0.325638i	0.788886	−	0.614540i	$-0.210658\pi$
$811$	12.7639	+	9.27354i	0.448202	+	0.325638i	−0.340683	+	0.940178i	$0.610658\pi$
$812$	1.61803	+	4.97980i	0.0567819	+	0.174757i
$813$		0			0
$814$	−8.05573	−	13.5923i	−0.282353	−	0.476410i
$815$	39.7001			1.39063
$816$		0			0
$817$	−0.500000	−	0.363271i	−0.0174928	−	0.0127093i
$818$	−8.32624	+	6.04937i	−0.291120	+	0.211511i
$819$	−9.70820	+	29.8788i	−0.339232	+	1.04405i
$820$	1.34752	−	4.14725i	0.0470576	−	0.144828i
$821$	−31.5344	+	22.9111i	−1.10056	+	0.799603i	−0.981151	−	0.193242i	$-0.938100\pi$
$821$	−31.5344	+	22.9111i	−1.10056	+	0.799603i	−0.119408	+	0.992845i	$0.538100\pi$
$822$		0			0
$823$	−0.972136	−	2.99193i	−0.0338865	−	0.104292i	0.932683	−	0.360698i	$-0.117462\pi$
$823$	−0.972136	−	2.99193i	−0.0338865	−	0.104292i	−0.966569	+	0.256406i	$0.917462\pi$
$824$	−19.4164			−0.676403
$825$		0			0
$826$	16.1803			0.562986
$827$	0.965558	+	2.97168i	0.0335757	+	0.103336i	0.966440	−	0.256893i	$-0.0826988\pi$
$827$	0.965558	+	2.97168i	0.0335757	+	0.103336i	−0.932864	+	0.360228i	$0.882699\pi$
$828$	19.0623	+	13.8496i	0.662461	+	0.481306i
$829$	35.6525	−	25.9030i	1.23826	−	0.899650i	0.240780	−	0.970580i	$-0.422597\pi$
$829$	35.6525	−	25.9030i	1.23826	−	0.899650i	0.997481	+	0.0709299i	$0.0225967\pi$
$830$	−2.51722	+	7.74721i	−0.0873740	+	0.268910i
$831$		0			0
$832$	5.23607	−	3.80423i	0.181528	−	0.131888i
$833$	−25.1353	−	18.2618i	−0.870885	−	0.632735i
$834$		0			0
$835$	22.8328			0.790162
$836$	−3.04508	−	1.31433i	−0.105316	−	0.0454570i
$837$		0			0
$838$	8.75329	+	26.9399i	0.302377	+	0.930622i
$839$	12.2361	+	8.89002i	0.422436	+	0.306918i	0.778617	−	0.627499i	$-0.215921\pi$
$839$	12.2361	+	8.89002i	0.422436	+	0.306918i	−0.356181	+	0.934417i	$0.615921\pi$
$840$		0			0
$841$	−5.72542	+	17.6210i	−0.197428	+	0.607622i
$842$	−9.03444	+	27.8052i	−0.311347	+	0.958229i
$843$		0			0
$844$	−18.7082	−	13.5923i	−0.643963	−	0.467866i
$845$	25.4787	+	78.4154i	0.876494	+	2.69757i
$846$	28.1459			0.967676
$847$	17.4894	+	3.30220i	0.600941	+	0.113465i
$848$	2.00000			0.0686803
$849$		0			0
$850$	18.0451	+	13.1105i	0.618941	+	0.449687i
$851$	30.2705	−	21.9928i	1.03766	−	0.753904i
$852$		0			0
$853$	−5.75329	+	17.7068i	−0.196989	+	0.606269i	0.802959	+	0.596035i	$0.203258\pi$
$853$	−5.75329	+	17.7068i	−0.196989	+	0.606269i	−0.999948	+	0.0102348i	$0.996742\pi$
$854$	−1.42705	+	1.03681i	−0.0488327	+	0.0354790i
$855$	6.92705	+	5.03280i	0.236900	+	0.172118i
$856$	−1.47214	−	4.53077i	−0.0503166	−	0.154858i
$857$	−20.8328			−0.711635			−0.355818	−	0.934555i	$-0.615798\pi$
$857$	−20.8328			−0.711635			−0.355818	+	0.934555i	$0.615798\pi$
$858$		0			0
$859$	40.6869			1.38822			0.694110	−	0.719869i	$-0.255798\pi$
$859$	40.6869			1.38822			0.694110	+	0.719869i	$0.255798\pi$
$860$	0.545085	+	1.67760i	0.0185872	+	0.0572057i
$861$		0			0
$862$	−6.38197	+	4.63677i	−0.217371	+	0.157929i
$863$	−11.2361	+	34.5811i	−0.382480	+	1.17715i	0.555812	+	0.831308i	$0.312408\pi$
$863$	−11.2361	+	34.5811i	−0.382480	+	1.17715i	−0.938292	+	0.345845i	$0.887592\pi$
$864$		0			0
$865$	−17.1246	+	12.4418i	−0.582254	+	0.423032i
$866$	−24.7082	−	17.9516i	−0.839619	−	0.610019i
$867$		0			0
$868$	−12.4721			−0.423332
$869$	−3.70820	+	39.6264i	−0.125792	+	1.34423i
$870$		0			0
$871$	16.0000	+	49.2429i	0.542139	+	1.66853i
$872$	9.47214	+	6.88191i	0.320767	+	0.233051i
$873$	−39.9787	+	29.0462i	−1.35307	+	0.983066i
$874$	2.42705	−	7.46969i	0.0820962	−	0.252666i
$875$	2.64590	−	8.14324i	0.0894477	−	0.275292i
$876$		0			0
$877$	39.3607	+	28.5972i	1.32912	+	0.965659i	0.999770	+	0.0214497i	$0.00682818\pi$
$877$	39.3607	+	28.5972i	1.32912	+	0.965659i	0.329346	+	0.944209i	$0.393172\pi$
$878$	2.58359	+	7.95148i	0.0871920	+	0.268349i
$879$		0			0
$880$	4.82624	+	8.14324i	0.162692	+	0.274508i
$881$	6.94427			0.233958			0.116979	−	0.993134i	$-0.462679\pi$
$881$	6.94427			0.233958			0.116979	+	0.993134i	$0.462679\pi$
$882$	4.06231	+	12.5025i	0.136785	+	0.420981i
$883$	26.1976	+	19.0336i	0.881618	+	0.640533i	0.933679	−	0.358111i	$-0.116579\pi$
$883$	26.1976	+	19.0336i	0.881618	+	0.640533i	−0.0520610	+	0.998644i	$0.516579\pi$
$884$	−37.1246	+	26.9726i	−1.24864	+	0.907187i
$885$		0			0
$886$	−0.118034	+	0.363271i	−0.00396543	+	0.0122043i
$887$	−17.0344	+	12.3762i	−0.571961	+	0.415554i	−0.835817	−	0.549008i	$-0.815006\pi$
$887$	−17.0344	+	12.3762i	−0.571961	+	0.415554i	0.263856	+	0.964562i	$0.415006\pi$
$888$		0			0
$889$	0.381966	+	1.17557i	0.0128107	+	0.0394274i
$890$	23.3475			0.782611
$891$	29.1246	−	6.53888i	0.975711	−	0.219061i
$892$	−4.47214			−0.149738
$893$	−2.89919	−	8.92278i	−0.0970176	−	0.298589i
$894$		0			0
$895$	−6.38197	+	4.63677i	−0.213326	+	0.154990i
$896$	−0.500000	+	1.53884i	−0.0167038	+	0.0514091i
$897$		0			0
$898$	12.1803	−	8.84953i	0.406463	−	0.295313i
$899$	20.1803	+	14.6619i	0.673052	+	0.489001i
$900$	−2.91641	−	8.97578i	−0.0972136	−	0.299193i
$901$	−14.1803			−0.472416
$902$	−3.34752	+	3.80423i	−0.111460	+	0.126667i
$903$		0			0
$904$	−0.0901699	−	0.277515i	−0.00299901	−	0.00923000i
$905$	−43.0689	−	31.2914i	−1.43166	−	1.04016i
$906$		0			0
$907$	8.12461	−	25.0050i	0.269773	−	0.830277i	−0.720782	−	0.693162i	$-0.756217\pi$
$907$	8.12461	−	25.0050i	0.269773	−	0.830277i	0.990555	−	0.137115i	$-0.0437830\pi$
$908$	6.32624	−	19.4702i	0.209944	−	0.646140i
$909$	8.78115	−	6.37988i	0.291252	−	0.211607i
$910$	−24.1803	−	17.5680i	−0.801570	−	0.582375i
$911$	−3.70820	−	11.4127i	−0.122858	−	0.378119i	0.870647	−	0.491909i	$-0.163701\pi$
$911$	−3.70820	−	11.4127i	−0.122858	−	0.378119i	−0.993505	+	0.113790i	$0.963701\pi$
$912$		0			0
$913$	6.25329	−	7.10642i	0.206954	−	0.235188i
$914$	−6.20163			−0.205132
$915$		0			0
$916$	−15.8262	−	11.4984i	−0.522914	−	0.379919i
$917$	12.2082	−	8.86978i	0.403150	−	0.292906i
$918$		0			0
$919$	3.26393	−	10.0453i	0.107667	−	0.331366i	−0.882680	−	0.469974i	$-0.844263\pi$
$919$	3.26393	−	10.0453i	0.107667	−	0.331366i	0.990347	+	0.138609i	$0.0442631\pi$
$920$	−18.1353	+	13.1760i	−0.597902	+	0.434401i
$921$		0			0
$922$	8.53444	+	26.2663i	0.281067	+	0.865035i
$923$	3.05573			0.100581
$924$		0			0
$925$	−14.9868			−0.492764
$926$	−3.44427	−	10.6004i	−0.113186	−	0.348350i
$927$	−47.1246	−	34.2380i	−1.54778	−	1.12452i
$928$	2.61803	−	1.90211i	0.0859412	−	0.0624399i
$929$	−2.39261	+	7.36369i	−0.0784990	+	0.241595i	−0.982603	−	0.185717i	$-0.940539\pi$
$929$	−2.39261	+	7.36369i	−0.0784990	+	0.241595i	0.904104	+	0.427312i	$0.140539\pi$
$930$		0			0
$931$	3.54508	−	2.57565i	0.116185	−	0.0844137i
$932$	16.2533	+	11.8087i	0.532394	+	0.386807i
$933$		0			0
$934$	10.8541			0.355157
$935$	−34.2188	−	57.7369i	−1.11908	−	1.88820i
$936$	19.4164			0.634645
$937$	0.864745	+	2.66141i	0.0282500	+	0.0869445i	0.964187	−	0.265222i	$-0.0854452\pi$
$937$	0.864745	+	2.66141i	0.0282500	+	0.0869445i	−0.935937	+	0.352166i	$0.885445\pi$
$938$	−10.4721	−	7.60845i	−0.341927	−	0.248425i
$939$		0			0
$940$	−8.27458	+	25.4665i	−0.269887	+	0.830626i
$941$	15.4721	−	47.6183i	0.504377	−	1.55231i	−0.297438	−	0.954741i	$-0.596132\pi$
$941$	15.4721	−	47.6183i	0.504377	−	1.55231i	0.801815	−	0.597572i	$-0.203868\pi$
$942$		0			0
$943$	−9.70820	−	7.05342i	−0.316143	−	0.229691i
$944$	−3.09017	−	9.51057i	−0.100576	−	0.309543i
$945$		0			0
$946$	0.190983	−	2.04087i	0.00620939	−	0.0663544i
$947$	−20.9656			−0.681289			−0.340645	−	0.940192i	$-0.610645\pi$
$947$	−20.9656			−0.681289			−0.340645	+	0.940192i	$0.610645\pi$
$948$		0			0
$949$	2.47214	+	1.79611i	0.0802489	+	0.0583043i
$950$	−2.54508	+	1.84911i	−0.0825735	+	0.0599931i
$951$		0			0
$952$	3.54508	−	10.9106i	0.114897	−	0.353616i
$953$	2.47214	−	1.79611i	0.0800803	−	0.0581818i	−0.547025	−	0.837116i	$-0.684240\pi$
$953$	2.47214	−	1.79611i	0.0800803	−	0.0581818i	0.627105	+	0.778935i	$0.284240\pi$
$954$	4.85410	+	3.52671i	0.157157	+	0.114182i
$955$	−9.31559	−	28.6705i	−0.301446	−	0.927754i
$956$	−8.79837			−0.284560
$957$		0			0
$958$	−3.56231			−0.115093
$959$	7.19098	+	22.1316i	0.232209	+	0.714666i
$960$		0			0
$961$	−22.9894	+	16.7027i	−0.741592	+	0.538798i
$962$	9.52786	−	29.3238i	0.307191	−	0.945436i
$963$	4.41641	−	13.5923i	0.142317	−	0.438006i
$964$	−21.7984	+	15.8374i	−0.702078	+	0.510090i
$965$	−4.61803	−	3.35520i	−0.148660	−	0.108008i
$966$		0			0
$967$	−24.7984			−0.797462			−0.398731	−	0.917068i	$-0.630549\pi$
$967$	−24.7984			−0.797462			−0.398731	+	0.917068i	$0.630549\pi$
$968$	−1.39919	−	10.9106i	−0.0449716	−	0.350682i
$969$		0			0
$970$	−14.5279	−	44.7122i	−0.466462	−	1.43562i
$971$	−19.0902	−	13.8698i	−0.612633	−	0.445104i	0.237708	−	0.971337i	$-0.423604\pi$
$971$	−19.0902	−	13.8698i	−0.612633	−	0.445104i	−0.850340	+	0.526233i	$0.823604\pi$
$972$		0			0
$973$	1.83688	−	5.65334i	0.0588877	−	0.181238i
$974$	−0.437694	+	1.34708i	−0.0140246	+	0.0431634i
$975$		0			0
$976$	0.881966	+	0.640786i	0.0282310	+	0.0205111i
$977$	7.00000	+	21.5438i	0.223950	+	0.689247i	0.998397	+	0.0566075i	$0.0180284\pi$
$977$	7.00000	+	21.5438i	0.223950	+	0.689247i	−0.774447	+	0.632639i	$0.781972\pi$
$978$		0			0
$979$	−24.9098	−	10.7516i	−0.796122	−	0.343624i
$980$	−12.5066			−0.399508
$981$	10.8541	+	33.4055i	0.346545	+	1.06656i
$982$	12.4894	+	9.07405i	0.398551	+	0.289565i
$983$	39.2705	−	28.5317i	1.25253	−	0.910020i	0.254169	−	0.967160i	$-0.418198\pi$
$983$	39.2705	−	28.5317i	1.25253	−	0.910020i	0.998366	+	0.0571402i	$0.0181982\pi$
$984$		0			0
$985$	14.5279	−	44.7122i	0.462896	−	1.42465i
$986$	−18.5623	+	13.4863i	−0.591144	+	0.429491i
$987$		0			0
$988$	−2.00000	−	6.15537i	−0.0636285	−	0.195828i
$989$	4.85410			0.154351
$990$	−2.64590	+	28.2744i	−0.0840922	+	0.898620i
$991$	−26.2918			−0.835186			−0.417593	−	0.908634i	$-0.637126\pi$
$991$	−26.2918			−0.835186			−0.417593	+	0.908634i	$0.637126\pi$
$992$	2.38197	+	7.33094i	0.0756275	+	0.232758i
$993$		0			0
$994$	−0.618034	+	0.449028i	−0.0196028	+	0.0142423i
$995$	2.10081	−	6.46564i	0.0666003	−	0.204974i
$996$		0			0
$997$	−28.3435	+	20.5927i	−0.897646	+	0.652178i	−0.937860	−	0.347013i	$-0.887196\pi$
$997$	−28.3435	+	20.5927i	−0.897646	+	0.652178i	0.0402140	+	0.999191i	$0.487196\pi$
$998$	−8.30902	−	6.03685i	−0.263017	−	0.191093i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.f.b.115.1	✓	4
11.3	even	5		4598.2.a.bh.1.2		2
11.8	odd	10		4598.2.a.z.1.2		2
11.9	even	5	inner	418.2.f.b.229.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.b.115.1	✓	4	1.1	even	1	trivial
418.2.f.b.229.1	yes	4	11.9	even	5	inner
4598.2.a.z.1.2		2	11.8	odd	10
4598.2.a.bh.1.2		2	11.3	even	5

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(0.881966 - 2.71441i) q^{5} +(1.30902 - 0.951057i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.927051 - 2.85317i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(0.881966 - 2.71441i) q^{5} +(1.30902 - 0.951057i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.927051 - 2.85317i) q^{9} +2.85410 q^{10} +(-3.04508 - 1.31433i) q^{11} +(-2.00000 - 6.15537i) q^{13} +(1.30902 + 0.951057i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-2.19098 + 6.74315i) q^{17} +(2.42705 - 1.76336i) q^{18} +(-0.809017 - 0.587785i) q^{19} +(0.881966 + 2.71441i) q^{20} +(0.309017 - 3.30220i) q^{22} +7.85410 q^{23} +(-2.54508 - 1.84911i) q^{25} +(5.23607 - 3.80423i) q^{26} +(-0.500000 + 1.53884i) q^{28} +(2.61803 - 1.90211i) q^{29} +(2.38197 + 7.33094i) q^{31} +1.00000 q^{32} -7.09017 q^{34} +(-1.42705 - 4.39201i) q^{35} +(2.42705 + 1.76336i) q^{36} +(3.85410 - 2.80017i) q^{37} +(0.309017 - 0.951057i) q^{38} +(-2.30902 + 1.67760i) q^{40} +(-1.23607 - 0.898056i) q^{41} +0.618034 q^{43} +(3.23607 - 0.726543i) q^{44} -8.56231 q^{45} +(2.42705 + 7.46969i) q^{46} +(7.59017 + 5.51458i) q^{47} +(-1.35410 + 4.16750i) q^{49} +(0.972136 - 2.99193i) q^{50} +(5.23607 + 3.80423i) q^{52} +(0.618034 + 1.90211i) q^{53} +(-6.25329 + 7.10642i) q^{55} -1.61803 q^{56} +(2.61803 + 1.90211i) q^{58} +(8.09017 - 5.87785i) q^{59} +(-0.336881 + 1.03681i) q^{61} +(-6.23607 + 4.53077i) q^{62} +(-3.92705 - 2.85317i) q^{63} +(0.309017 + 0.951057i) q^{64} -18.4721 q^{65} -8.00000 q^{67} +(-2.19098 - 6.74315i) q^{68} +(3.73607 - 2.71441i) q^{70} +(-0.145898 + 0.449028i) q^{71} +(-0.927051 + 2.85317i) q^{72} +(-0.381966 + 0.277515i) q^{73} +(3.85410 + 2.80017i) q^{74} +1.00000 q^{76} +(-5.23607 + 1.17557i) q^{77} +(-3.70820 - 11.4127i) q^{79} +(-2.30902 - 1.67760i) q^{80} +(-7.28115 + 5.29007i) q^{81} +(0.472136 - 1.45309i) q^{82} +(-0.881966 + 2.71441i) q^{83} +(16.3713 + 11.8945i) q^{85} +(0.190983 + 0.587785i) q^{86} +(1.69098 + 2.85317i) q^{88} +8.18034 q^{89} +(-2.64590 - 8.14324i) q^{90} +(-8.47214 - 6.15537i) q^{91} +(-6.35410 + 4.61653i) q^{92} +(-2.89919 + 8.92278i) q^{94} +(-2.30902 + 1.67760i) q^{95} +(-5.09017 - 15.6659i) q^{97} -4.38197 q^{98} +(-0.927051 + 9.90659i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{4} + 8 q^{5} + 3 q^{7} - q^{8} + 3 q^{9}+O(q^{10}) \) 4 * q - q^2 - q^4 + 8 * q^5 + 3 * q^7 - q^8 + 3 * q^9	\( 4 q - q^{2} - q^{4} + 8 q^{5} + 3 q^{7} - q^{8} + 3 q^{9} - 2 q^{10} - q^{11} - 8 q^{13} + 3 q^{14} - q^{16} - 11 q^{17} + 3 q^{18} - q^{19} + 8 q^{20} - q^{22} + 18 q^{23} + q^{25} + 12 q^{26} - 2 q^{28} + 6 q^{29} + 14 q^{31} + 4 q^{32} - 6 q^{34} + q^{35} + 3 q^{36} + 2 q^{37} - q^{38} - 7 q^{40} + 4 q^{41} - 2 q^{43} + 4 q^{44} + 6 q^{45} + 3 q^{46} + 8 q^{47} + 8 q^{49} - 14 q^{50} + 12 q^{52} - 2 q^{53} + 13 q^{55} - 2 q^{56} + 6 q^{58} + 10 q^{59} - 17 q^{61} - 16 q^{62} - 9 q^{63} - q^{64} - 56 q^{65} - 32 q^{67} - 11 q^{68} + 6 q^{70} - 14 q^{71} + 3 q^{72} - 6 q^{73} + 2 q^{74} + 4 q^{76} - 12 q^{77} + 12 q^{79} - 7 q^{80} - 9 q^{81} - 16 q^{82} - 8 q^{83} + 23 q^{85} + 3 q^{86} + 9 q^{88} - 12 q^{89} - 24 q^{90} - 16 q^{91} - 12 q^{92} + 13 q^{94} - 7 q^{95} + 2 q^{97} - 22 q^{98} + 3 q^{99}+O(q^{100}) \) 4 * q - q^2 - q^4 + 8 * q^5 + 3 * q^7 - q^8 + 3 * q^9 - 2 * q^10 - q^11 - 8 * q^13 + 3 * q^14 - q^16 - 11 * q^17 + 3 * q^18 - q^19 + 8 * q^20 - q^22 + 18 * q^23 + q^25 + 12 * q^26 - 2 * q^28 + 6 * q^29 + 14 * q^31 + 4 * q^32 - 6 * q^34 + q^35 + 3 * q^36 + 2 * q^37 - q^38 - 7 * q^40 + 4 * q^41 - 2 * q^43 + 4 * q^44 + 6 * q^45 + 3 * q^46 + 8 * q^47 + 8 * q^49 - 14 * q^50 + 12 * q^52 - 2 * q^53 + 13 * q^55 - 2 * q^56 + 6 * q^58 + 10 * q^59 - 17 * q^61 - 16 * q^62 - 9 * q^63 - q^64 - 56 * q^65 - 32 * q^67 - 11 * q^68 + 6 * q^70 - 14 * q^71 + 3 * q^72 - 6 * q^73 + 2 * q^74 + 4 * q^76 - 12 * q^77 + 12 * q^79 - 7 * q^80 - 9 * q^81 - 16 * q^82 - 8 * q^83 + 23 * q^85 + 3 * q^86 + 9 * q^88 - 12 * q^89 - 24 * q^90 - 16 * q^91 - 12 * q^92 + 13 * q^94 - 7 * q^95 + 2 * q^97 - 22 * q^98 + 3 * q^99

Introduction

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