LMFDB - Embedded newform 968.2.c.h.485.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(485,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("968.485");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.c (of order $2$, degree $1$, 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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} - 2 x^{16} - 2 x^{15} - 4 x^{14} - 4 x^{13} + 12 x^{12} + 16 x^{11} + 32 x^{9} + \cdots + 1024 $ x^20 - x^18 - 2x^16 - 2x^15 - 4x^14 - 4x^13 + 12x^12 + 16x^11 + 32x^9 + 48x^8 - 32x^7 - 64x^6 - 64x^5 - 128x^4 - 256*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			485.6
Root			$-1.07012 - 0.924577i$ of defining polynomial
Character	$\chi$	$=$	968.485
Dual form			968.2.c.h.485.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07012 + 0.924577i) q^{2} -0.321222i q^{3} +(0.290315 - 1.97882i) q^{4} +1.28733i q^{5} +(0.296994 + 0.343746i) q^{6} -3.30669 q^{7} +(1.51890 + 2.38599i) q^{8} +2.89682 q^{9} +O(q^{10})$	\(q+(-1.07012 + 0.924577i) q^{2} -0.321222i q^{3} +(0.290315 - 1.97882i) q^{4} +1.28733i q^{5} +(0.296994 + 0.343746i) q^{6} -3.30669 q^{7} +(1.51890 + 2.38599i) q^{8} +2.89682 q^{9} +(-1.19023 - 1.37759i) q^{10} +(-0.635639 - 0.0932556i) q^{12} -3.08618i q^{13} +(3.53855 - 3.05728i) q^{14} +0.413517 q^{15} +(-3.83143 - 1.14896i) q^{16} -3.19795 q^{17} +(-3.09994 + 2.67833i) q^{18} -4.71799i q^{19} +(2.54738 + 0.373730i) q^{20} +1.06218i q^{21} -3.47634 q^{23} +(0.766432 - 0.487902i) q^{24} +3.34279 q^{25} +(2.85341 + 3.30259i) q^{26} -1.89419i q^{27} +(-0.959982 + 6.54333i) q^{28} +6.19081i q^{29} +(-0.442513 + 0.382328i) q^{30} -2.67961 q^{31} +(5.16240 - 2.31293i) q^{32} +(3.42219 - 2.95675i) q^{34} -4.25678i q^{35} +(0.840991 - 5.73227i) q^{36} -7.84394i q^{37} +(4.36214 + 5.04882i) q^{38} -0.991349 q^{39} +(-3.07155 + 1.95531i) q^{40} +5.18518 q^{41} +(-0.982066 - 1.13666i) q^{42} -2.37086i q^{43} +3.72915i q^{45} +(3.72010 - 3.21414i) q^{46} +3.19353 q^{47} +(-0.369072 + 1.23074i) q^{48} +3.93417 q^{49} +(-3.57719 + 3.09067i) q^{50} +1.02725i q^{51} +(-6.10699 - 0.895967i) q^{52} -4.72284i q^{53} +(1.75132 + 2.02701i) q^{54} +(-5.02251 - 7.88972i) q^{56} -1.51552 q^{57} +(-5.72388 - 6.62491i) q^{58} -14.1440i q^{59} +(0.120050 - 0.818274i) q^{60} -15.5658i q^{61} +(2.86751 - 2.47751i) q^{62} -9.57886 q^{63} +(-3.38591 + 7.24815i) q^{64} +3.97292 q^{65} -4.70162i q^{67} +(-0.928413 + 6.32815i) q^{68} +1.11668i q^{69} +(3.93572 + 4.55527i) q^{70} -9.17365 q^{71} +(4.39996 + 6.91178i) q^{72} -0.939086 q^{73} +(7.25233 + 8.39396i) q^{74} -1.07378i q^{75} +(-9.33604 - 1.36970i) q^{76} +(1.06086 - 0.916578i) q^{78} +9.56575 q^{79} +(1.47909 - 4.93230i) q^{80} +8.08200 q^{81} +(-5.54877 + 4.79410i) q^{82} +1.27824i q^{83} +(2.10186 + 0.308367i) q^{84} -4.11680i q^{85} +(2.19204 + 2.53711i) q^{86} +1.98862 q^{87} +15.3866 q^{89} +(-3.44788 - 3.99063i) q^{90} +10.2050i q^{91} +(-1.00924 + 6.87904i) q^{92} +0.860749i q^{93} +(-3.41746 + 2.95266i) q^{94} +6.07359 q^{95} +(-0.742962 - 1.65827i) q^{96} -13.9642 q^{97} +(-4.21004 + 3.63744i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{4} - q^{6} + 10 q^{7} - 10 q^{9}+O(q^{10}) $ 20 * q + 2 * q^4 - q^6 + 10 * q^7 - 10 * q^9	$ 20 q + 2 q^{4} - q^{6} + 10 q^{7} - 10 q^{9} - 10 q^{10} - 3 q^{12} - 4 q^{14} - 4 q^{15} + 10 q^{16} + 2 q^{17} - 5 q^{18} - 16 q^{20} - 4 q^{23} + 15 q^{24} - 2 q^{25} + 30 q^{26} - 14 q^{28} + 16 q^{30} + 2 q^{31} + 10 q^{32} + 5 q^{34} + 9 q^{36} + 21 q^{38} + 28 q^{39} + 10 q^{40} - 2 q^{41} - 20 q^{42} + 24 q^{46} + 2 q^{47} - 41 q^{48} - 2 q^{49} - 22 q^{50} - 20 q^{52} + 54 q^{54} - 16 q^{56} + 22 q^{57} + 12 q^{58} - 48 q^{60} + 4 q^{62} - 30 q^{63} + 38 q^{64} - 18 q^{65} - 21 q^{68} - 44 q^{70} - 34 q^{71} + 57 q^{72} + 2 q^{73} - 28 q^{74} - 67 q^{76} - 6 q^{78} - 58 q^{79} + 28 q^{80} - 12 q^{81} - 23 q^{82} - 44 q^{84} + 25 q^{86} + 34 q^{87} - 8 q^{89} - 42 q^{90} + 68 q^{92} + 60 q^{94} - 92 q^{95} + 35 q^{96} + 10 q^{97} - 72 q^{98}+O(q^{100}) $ 20 * q + 2 * q^4 - q^6 + 10 * q^7 - 10 * q^9 - 10 * q^10 - 3 * q^12 - 4 * q^14 - 4 * q^15 + 10 * q^16 + 2 * q^17 - 5 * q^18 - 16 * q^20 - 4 * q^23 + 15 * q^24 - 2 * q^25 + 30 * q^26 - 14 * q^28 + 16 * q^30 + 2 * q^31 + 10 * q^32 + 5 * q^34 + 9 * q^36 + 21 * q^38 + 28 * q^39 + 10 * q^40 - 2 * q^41 - 20 * q^42 + 24 * q^46 + 2 * q^47 - 41 * q^48 - 2 * q^49 - 22 * q^50 - 20 * q^52 + 54 * q^54 - 16 * q^56 + 22 * q^57 + 12 * q^58 - 48 * q^60 + 4 * q^62 - 30 * q^63 + 38 * q^64 - 18 * q^65 - 21 * q^68 - 44 * q^70 - 34 * q^71 + 57 * q^72 + 2 * q^73 - 28 * q^74 - 67 * q^76 - 6 * q^78 - 58 * q^79 + 28 * q^80 - 12 * q^81 - 23 * q^82 - 44 * q^84 + 25 * q^86 + 34 * q^87 - 8 * q^89 - 42 * q^90 + 68 * q^92 + 60 * q^94 - 92 * q^95 + 35 * q^96 + 10 * q^97 - 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.07012	+	0.924577i	−0.756689	+	0.653775i
$2$	−1.07012	+	0.924577i	−0.756689	+	0.653775i
$3$		−	0.321222i		−	0.185457i	−0.995691	−	0.0927287i	$-0.970441\pi$
$3$		−	0.321222i		−	0.185457i	0.995691	−	0.0927287i	$-0.0295589\pi$
$4$	0.290315	−	1.97882i	0.145158	−	0.989409i
$5$			1.28733i			0.575709i	0.957674	+	0.287855i	$0.0929420\pi$
$5$			1.28733i			0.575709i	−0.957674	+	0.287855i	$0.907058\pi$
$6$	0.296994	+	0.343746i	0.121247	+	0.140334i
$7$	−3.30669			−1.24981			−0.624905	−	0.780701i	$-0.714862\pi$
$7$	−3.30669			−1.24981			−0.624905	+	0.780701i	$0.714862\pi$
$8$	1.51890	+	2.38599i	0.537011	+	0.843575i
$9$	2.89682			0.965606
$10$	−1.19023	−	1.37759i	−0.376384	−	0.435633i
$11$		0			0
$11$		0			0
$12$	−0.635639	−	0.0932556i	−0.183493	−	0.0269206i
$13$		−	3.08618i		−	0.855953i	−0.903790	−	0.427977i	$-0.859227\pi$
$13$		−	3.08618i		−	0.855953i	0.903790	−	0.427977i	$-0.140773\pi$
$14$	3.53855	−	3.05728i	0.945718	−	0.817094i
$15$	0.413517			0.106770
$16$	−3.83143	−	1.14896i	−0.957858	−	0.287241i
$17$	−3.19795			−0.775616			−0.387808	−	0.921740i	$-0.626768\pi$
$17$	−3.19795			−0.775616			−0.387808	+	0.921740i	$0.626768\pi$
$18$	−3.09994	+	2.67833i	−0.730663	+	0.631288i
$19$		−	4.71799i		−	1.08238i	−0.840900	−	0.541190i	$-0.817974\pi$
$19$		−	4.71799i		−	1.08238i	0.840900	−	0.541190i	$-0.182026\pi$
$20$	2.54738	+	0.373730i	0.569612	+	0.0835687i
$21$			1.06218i			0.231786i
$22$		0			0
$23$	−3.47634			−0.724867			−0.362433	−	0.932010i	$-0.618054\pi$
$23$	−3.47634			−0.724867			−0.362433	+	0.932010i	$0.618054\pi$
$24$	0.766432	−	0.487902i	0.156447	−	0.0995926i
$25$	3.34279			0.668559
$26$	2.85341	+	3.30259i	0.559600	+	0.647691i
$27$		−	1.89419i		−	0.364536i
$28$	−0.959982	+	6.54333i	−0.181420	+	1.23657i
$29$			6.19081i			1.14960i	0.818292	+	0.574802i	$0.194921\pi$
$29$			6.19081i			1.14960i	−0.818292	+	0.574802i	$0.805079\pi$
$30$	−0.442513	+	0.382328i	−0.0807914	+	0.0698032i
$31$	−2.67961			−0.481272			−0.240636	−	0.970615i	$-0.577356\pi$
$31$	−2.67961			−0.481272			−0.240636	+	0.970615i	$0.577356\pi$
$32$	5.16240	−	2.31293i	0.912592	−	0.408872i
$33$		0			0
$34$	3.42219	−	2.95675i	0.586900	−	0.507078i
$35$		−	4.25678i		−	0.719527i
$36$	0.840991	−	5.73227i	0.140165	−	0.955378i
$37$		−	7.84394i		−	1.28954i	−0.764378	−	0.644768i	$-0.776954\pi$
$37$		−	7.84394i		−	1.28954i	0.764378	−	0.644768i	$-0.223046\pi$
$38$	4.36214	+	5.04882i	0.707633	+	0.819026i
$39$	−0.991349			−0.158743
$40$	−3.07155	+	1.95531i	−0.485654	+	0.309162i
$41$	5.18518			0.809789			0.404895	−	0.914363i	$-0.367308\pi$
$41$	5.18518			0.809789			0.404895	+	0.914363i	$0.367308\pi$
$42$	−0.982066	−	1.13666i	−0.151536	−	0.175390i
$43$		−	2.37086i		−	0.361553i	−0.983524	−	0.180776i	$-0.942139\pi$
$43$		−	2.37086i		−	0.361553i	0.983524	−	0.180776i	$-0.0578610\pi$
$44$		0			0
$45$			3.72915i			0.555908i
$46$	3.72010	−	3.21414i	0.548499	−	0.473900i
$47$	3.19353			0.465824			0.232912	−	0.972498i	$-0.425175\pi$
$47$	3.19353			0.465824			0.232912	+	0.972498i	$0.425175\pi$
$48$	−0.369072	+	1.23074i	−0.0532709	+	0.177642i
$49$	3.93417			0.562024
$50$	−3.57719	+	3.09067i	−0.505891	+	0.437087i
$51$			1.02725i			0.143844i
$52$	−6.10699	−	0.895967i	−0.846887	−	0.124248i
$53$		−	4.72284i		−	0.648732i	−0.945932	−	0.324366i	$-0.894849\pi$
$53$		−	4.72284i		−	0.648732i	0.945932	−	0.324366i	$-0.105151\pi$
$54$	1.75132	+	2.02701i	0.238324	+	0.275841i
$55$		0			0
$56$	−5.02251	−	7.88972i	−0.671161	−	1.05431i
$57$	−1.51552			−0.200736
$58$	−5.72388	−	6.62491i	−0.751582	−	0.869894i
$59$		−	14.1440i		−	1.84139i	−0.390284	−	0.920695i	$-0.627623\pi$
$59$		−	14.1440i		−	1.84139i	0.390284	−	0.920695i	$-0.372377\pi$
$60$	0.120050	−	0.818274i	0.0154984	−	0.105639i
$61$		−	15.5658i		−	1.99300i	−0.0835917	−	0.996500i	$-0.526639\pi$
$61$		−	15.5658i		−	1.99300i	0.0835917	−	0.996500i	$-0.473361\pi$
$62$	2.86751	−	2.47751i	0.364174	−	0.314644i
$63$	−9.57886			−1.20682
$64$	−3.38591	+	7.24815i	−0.423239	+	0.906018i
$65$	3.97292			0.492780
$66$		0			0
$67$		−	4.70162i		−	0.574395i	−0.957871	−	0.287197i	$-0.907276\pi$
$67$		−	4.70162i		−	0.574395i	0.957871	−	0.287197i	$-0.0927236\pi$
$68$	−0.928413	+	6.32815i	−0.112587	+	0.767401i
$69$			1.11668i			0.134432i
$70$	3.93572	+	4.55527i	0.470409	+	0.544459i
$71$	−9.17365			−1.08871			−0.544356	−	0.838854i	$-0.683226\pi$
$71$	−9.17365			−1.08871			−0.544356	+	0.838854i	$0.683226\pi$
$72$	4.39996	+	6.91178i	0.518541	+	0.814561i
$73$	−0.939086			−0.109912			−0.0549558	−	0.998489i	$-0.517502\pi$
$73$	−0.939086			−0.109912			−0.0549558	+	0.998489i	$0.517502\pi$
$74$	7.25233	+	8.39396i	0.843066	+	0.975778i
$75$		−	1.07378i		−	0.123989i
$76$	−9.33604	−	1.36970i	−1.07092	−	0.157116i
$77$		0			0
$78$	1.06086	−	0.916578i	0.120119	−	0.103782i
$79$	9.56575			1.07623			0.538116	−	0.842871i	$-0.319136\pi$
$79$	9.56575			1.07623			0.538116	+	0.842871i	$0.319136\pi$
$80$	1.47909	−	4.93230i	0.165367	−	0.551448i
$81$	8.08200			0.898000
$82$	−5.54877	+	4.79410i	−0.612759	+	0.529419i
$83$			1.27824i			0.140306i	0.997536	+	0.0701528i	$0.0223487\pi$
$83$			1.27824i			0.140306i	−0.997536	+	0.0701528i	$0.977651\pi$
$84$	2.10186	+	0.308367i	0.229332	+	0.0336456i
$85$		−	4.11680i		−	0.446529i
$86$	2.19204	+	2.53711i	0.236374	+	0.273583i
$87$	1.98862			0.213203
$88$		0			0
$89$	15.3866			1.63098			0.815489	−	0.578773i	$-0.196468\pi$
$89$	15.3866			1.63098			0.815489	+	0.578773i	$0.196468\pi$
$90$	−3.44788	−	3.99063i	−0.363439	−	0.420650i
$91$			10.2050i			1.06978i
$92$	−1.00924	+	6.87904i	−0.105220	+	0.717190i
$93$			0.860749i			0.0892555i
$94$	−3.41746	+	2.95266i	−0.352484	+	0.304544i
$95$	6.07359			0.623137
$96$	−0.742962	−	1.65827i	−0.0758283	−	0.169247i
$97$	−13.9642			−1.41785			−0.708924	−	0.705285i	$-0.750819\pi$
$97$	−13.9642			−1.41785			−0.708924	+	0.705285i	$0.750819\pi$
$98$	−4.21004	+	3.63744i	−0.425278	+	0.367437i
$99$		0			0
$100$	0.970465	−	6.61478i	0.0970465	−	0.661478i
$101$		−	11.0160i		−	1.09614i	−0.836433	−	0.548069i	$-0.815363\pi$
$101$		−	11.0160i		−	1.09614i	0.836433	−	0.548069i	$-0.184637\pi$
$102$	−0.949771	−	1.09928i	−0.0940413	−	0.108845i
$103$	−10.8978			−1.07379			−0.536897	−	0.843648i	$-0.680404\pi$
$103$	−10.8978			−1.07379			−0.536897	+	0.843648i	$0.680404\pi$
$104$	7.36361	−	4.68759i	0.722061	−	0.459656i
$105$	−1.36737			−0.133442
$106$	4.36663	+	5.05401i	0.424125	+	0.490889i
$107$		−	14.4930i		−	1.40109i	−0.713609	−	0.700544i	$-0.752941\pi$
$107$		−	14.4930i		−	1.40109i	0.713609	−	0.700544i	$-0.247059\pi$
$108$	−3.74825	−	0.549911i	−0.360675	−	0.0529152i
$109$		−	1.96781i		−	0.188482i	−0.995549	−	0.0942411i	$-0.969958\pi$
$109$		−	1.96781i		−	0.188482i	0.995549	−	0.0942411i	$-0.0300424\pi$
$110$		0			0
$111$	−2.51964			−0.239154
$112$	12.6693	+	3.79926i	1.19714	+	0.358996i
$113$	−6.34757			−0.597129			−0.298565	−	0.954389i	$-0.596508\pi$
$113$	−6.34757			−0.597129			−0.298565	+	0.954389i	$0.596508\pi$
$114$	1.62179	−	1.40121i	0.151894	−	0.131236i
$115$		−	4.47518i		−	0.417313i
$116$	12.2505	+	1.79729i	1.13743	+	0.166874i
$117$		−	8.94011i		−	0.826513i
$118$	13.0772	+	15.1358i	1.20385	+	1.39336i
$119$	10.5746			0.969372
$120$	0.628089	+	0.986647i	0.0573364	+	0.0900682i
$121$		0			0
$122$	14.3918	+	16.6573i	1.30297	+	1.50808i
$123$		−	1.66559i		−	0.150181i
$124$	−0.777933	+	5.30246i	−0.0698604	+	0.476175i
$125$			10.7399i			0.960605i
$126$	10.2505	−	8.85639i	0.913190	−	0.788990i
$127$	16.7029			1.48215			0.741073	−	0.671425i	$-0.234317\pi$
$127$	16.7029			1.48215			0.741073	+	0.671425i	$0.234317\pi$
$128$	−3.07813	−	10.8869i	−0.272071	−	0.962277i
$129$	−0.761572			−0.0670526
$130$	−4.25150	+	3.67327i	−0.372882	+	0.322167i
$131$			9.29813i			0.812381i	0.913788	+	0.406191i	$0.133143\pi$
$131$			9.29813i			0.812381i	−0.913788	+	0.406191i	$0.866857\pi$
$132$		0			0
$133$			15.6009i			1.35277i
$134$	4.34701	+	5.03130i	0.375525	+	0.434638i
$135$	2.43843			0.209867
$136$	−4.85735	−	7.63027i	−0.416514	−	0.654290i
$137$	9.06748			0.774687			0.387344	−	0.921935i	$-0.373393\pi$
$137$	9.06748			0.774687			0.387344	+	0.921935i	$0.373393\pi$
$138$	−1.03245	−	1.19498i	−0.0878882	−	0.101723i
$139$		−	0.233509i		−	0.0198059i	−0.999951	−	0.00990297i	$-0.996848\pi$
$139$		−	0.233509i		−	0.0198059i	0.999951	−	0.00990297i	$-0.00315226\pi$
$140$	−8.42339	−	1.23581i	−0.711906	−	0.104445i
$141$		−	1.02583i		−	0.0863905i
$142$	9.81691	−	8.48174i	0.823817	−	0.711772i
$143$		0			0
$144$	−11.0990	−	3.32833i	−0.924913	−	0.277361i
$145$	−7.96959			−0.661838
$146$	1.00493	−	0.868257i	0.0831690	−	0.0718575i
$147$		−	1.26374i		−	0.104232i
$148$	−15.5217	−	2.27722i	−1.27588	−	0.187186i
$149$		−	2.28997i		−	0.187601i	−0.995591	−	0.0938006i	$-0.970098\pi$
$149$		−	2.28997i		−	0.187601i	0.995591	−	0.0938006i	$-0.0299016\pi$
$150$	0.992790	+	1.14907i	0.0810610	+	0.0938213i
$151$	3.79592			0.308907			0.154454	−	0.988000i	$-0.450638\pi$
$151$	3.79592			0.308907			0.154454	+	0.988000i	$0.450638\pi$
$152$	11.2571	−	7.16613i	0.913070	−	0.581250i
$153$	−9.26386			−0.748939
$154$		0			0
$155$		−	3.44953i		−	0.277073i
$156$	−0.287804	+	1.96170i	−0.0230427	+	0.157062i
$157$			12.1538i			0.969981i	0.874519	+	0.484991i	$0.161177\pi$
$157$			12.1538i			0.969981i	−0.874519	+	0.484991i	$0.838823\pi$
$158$	−10.2365	+	8.84427i	−0.814373	+	0.703612i
$159$	−1.51708			−0.120312
$160$	2.97749	+	6.64569i	0.235391	+	0.525388i
$161$	11.4952			0.905946
$162$	−8.64871	+	7.47243i	−0.679507	+	0.587089i
$163$			8.28822i			0.649183i	0.945854	+	0.324592i	$0.105227\pi$
$163$			8.28822i			0.649183i	−0.945854	+	0.324592i	$0.894773\pi$
$164$	1.50534	−	10.2605i	0.117547	−	0.801212i
$165$		0			0
$166$	−1.18183	−	1.36788i	−0.0917282	−	0.106168i
$167$	−8.92881			−0.690932			−0.345466	−	0.938431i	$-0.612279\pi$
$167$	−8.92881			−0.690932			−0.345466	+	0.938431i	$0.612279\pi$
$168$	−2.53435	+	1.61334i	−0.195529	+	0.124472i
$169$	3.47548			0.267344
$170$	3.80629	+	4.40547i	0.291929	+	0.337884i
$171$		−	13.6671i		−	1.04515i
$172$	−4.69150	−	0.688297i	−0.357723	−	0.0524822i
$173$			8.50496i			0.646620i	0.946293	+	0.323310i	$0.104796\pi$
$173$			8.50496i			0.646620i	−0.946293	+	0.323310i	$0.895204\pi$
$174$	−2.12807	+	1.83863i	−0.161328	+	0.139386i
$175$	−11.0536			−0.835571
$176$		0			0
$177$	−4.54335			−0.341499
$178$	−16.4655	+	14.2261i	−1.23414	+	1.06629i
$179$			2.94347i			0.220005i	0.993931	+	0.110003i	$0.0350859\pi$
$179$			2.94347i			0.220005i	−0.993931	+	0.110003i	$0.964914\pi$
$180$	7.37930	+	1.08263i	0.550020	+	0.0806944i
$181$			21.2709i			1.58105i	0.612429	+	0.790526i	$0.290192\pi$
$181$			21.2709i			1.58105i	−0.612429	+	0.790526i	$0.709808\pi$
$182$	−9.43534	−	10.9206i	−0.699394	−	0.809490i
$183$	−5.00008			−0.369617
$184$	−5.28020	−	8.29452i	−0.389261	−	0.611480i
$185$	10.0977			0.742398
$186$	−0.795829	−	0.921105i	−0.0583530	−	0.0675387i
$187$		0			0
$188$	0.927131	−	6.31941i	0.0676179	−	0.460890i
$189$			6.26347i			0.455601i
$190$	−6.49947	+	5.61550i	−0.471521	+	0.407391i
$191$	−5.15586			−0.373065			−0.186533	−	0.982449i	$-0.559725\pi$
$191$	−5.15586			−0.373065			−0.186533	+	0.982449i	$0.559725\pi$
$192$	2.32826	+	1.08763i	0.168028	+	0.0784928i
$193$	−27.0169			−1.94472			−0.972361	−	0.233482i	$-0.924988\pi$
$193$	−27.0169			−1.94472			−0.972361	+	0.233482i	$0.924988\pi$
$194$	14.9434	−	12.9110i	1.07287	−	0.926952i
$195$		−	1.27619i		−	0.0913897i
$196$	1.14215	−	7.78500i	0.0815822	−	0.556072i
$197$			6.68220i			0.476087i	0.971254	+	0.238044i	$0.0765061\pi$
$197$			6.68220i			0.476087i	−0.971254	+	0.238044i	$0.923494\pi$
$198$		0			0
$199$	−14.2586			−1.01076			−0.505382	−	0.862896i	$-0.668648\pi$
$199$	−14.2586			−1.01076			−0.505382	+	0.862896i	$0.668648\pi$
$200$	5.07736	+	7.97588i	0.359023	+	0.563980i
$201$	−1.51026			−0.106526
$202$	10.1852	+	11.7885i	0.716627	+	0.829436i
$203$		−	20.4711i		−	1.43679i
$204$	2.03274	+	0.298226i	0.142320	+	0.0208800i
$205$			6.67501i			0.466203i
$206$	11.6620	−	10.0759i	0.812528	−	0.702019i
$207$	−10.0703			−0.699936
$208$	−3.54591	+	11.8245i	−0.245864	+	0.819882i
$209$		0			0
$210$	1.46325	−	1.26424i	0.100974	−	0.0872407i
$211$			19.3294i			1.33069i	0.746535	+	0.665346i	$0.231716\pi$
$211$			19.3294i			1.33069i	−0.746535	+	0.665346i	$0.768284\pi$
$212$	−9.34564	−	1.37111i	−0.641861	−	0.0941685i
$213$			2.94678i			0.201910i
$214$	13.3999	+	15.5092i	0.915996	+	1.06019i
$215$	3.05207			0.208149
$216$	4.51951	−	2.87707i	0.307514	−	0.195760i
$217$	8.86063			0.601499
$218$	1.81939	+	2.10579i	0.123225	+	0.142622i
$219$			0.301655i			0.0203839i
$220$		0			0
$221$			9.86944i			0.663891i
$222$	2.69632	−	2.32960i	0.180965	−	0.156353i
$223$	−13.6844			−0.916378			−0.458189	−	0.888855i	$-0.651502\pi$
$223$	−13.6844			−0.916378			−0.458189	+	0.888855i	$0.651502\pi$
$224$	−17.0704	+	7.64812i	−1.14057	+	0.511012i
$225$	9.68346			0.645564
$226$	6.79267	−	5.86882i	0.451842	−	0.390388i
$227$		−	11.8877i		−	0.789016i	−0.918893	−	0.394508i	$-0.870915\pi$
$227$		−	11.8877i		−	0.789016i	0.918893	−	0.394508i	$-0.129085\pi$
$228$	−0.439979	+	2.99894i	−0.0291383	+	0.198609i
$229$		−	0.217689i		−	0.0143853i	−0.999974	−	0.00719264i	$-0.997710\pi$
$229$		−	0.217689i		−	0.0143853i	0.999974	−	0.00719264i	$-0.00228951\pi$
$230$	4.13765	+	4.78898i	0.272828	+	0.315776i
$231$		0			0
$232$	−14.7712	+	9.40320i	−0.969778	+	0.617350i
$233$	−3.67905			−0.241023			−0.120511	−	0.992712i	$-0.538453\pi$
$233$	−3.67905			−0.241023			−0.120511	+	0.992712i	$0.538453\pi$
$234$	8.26581	+	9.56699i	0.540353	+	0.625414i
$235$			4.11111i			0.268179i
$236$	−27.9883	−	4.10622i	−1.82189	−	0.267292i
$237$		−	3.07273i		−	0.199595i
$238$	−11.3161	+	9.77703i	−0.733514	+	0.633751i
$239$	−20.0477			−1.29678			−0.648388	−	0.761310i	$-0.724556\pi$
$239$	−20.0477			−1.29678			−0.648388	+	0.761310i	$0.724556\pi$
$240$	−1.58436	−	0.475115i	−0.102270	−	0.0306686i
$241$	14.4772			0.932561			0.466280	−	0.884637i	$-0.345594\pi$
$241$	14.4772			0.932561			0.466280	+	0.884637i	$0.345594\pi$
$242$		0			0
$243$		−	8.27867i		−	0.531077i
$244$	−30.8019	−	4.51900i	−1.97189	−	0.289299i
$245$			5.06456i			0.323563i
$246$	1.53997	+	1.78238i	0.0981848	+	0.113641i
$247$	−14.5606			−0.926467
$248$	−4.07005	−	6.39353i	−0.258449	−	0.405990i
$249$	0.410600			0.0260207
$250$	−9.92985	−	11.4930i	−0.628019	−	0.726880i
$251$		−	21.6387i		−	1.36582i	−0.730502	−	0.682910i	$-0.760714\pi$
$251$		−	21.6387i		−	1.36582i	0.730502	−	0.682910i	$-0.239286\pi$
$252$	−2.78089	+	18.9548i	−0.175180	+	1.19404i
$253$		0			0
$254$	−17.8741	+	15.4431i	−1.12152	+	0.968989i
$255$	−1.32240			−0.0828122
$256$	13.3598	+	8.80435i	0.834986	+	0.550272i
$257$	−8.50900			−0.530777			−0.265388	−	0.964142i	$-0.585500\pi$
$257$	−8.50900			−0.530777			−0.265388	+	0.964142i	$0.585500\pi$
$258$	0.814973	−	0.704131i	0.0507380	−	0.0438373i
$259$			25.9375i			1.61167i
$260$	1.15340	−	7.86168i	0.0715309	−	0.487561i
$261$			17.9336i			1.11006i
$262$	−8.59683	−	9.95011i	−0.531114	−	0.614720i
$263$	9.34658			0.576335			0.288167	−	0.957580i	$-0.406954\pi$
$263$	9.34658			0.576335			0.288167	+	0.957580i	$0.406954\pi$
$264$		0			0
$265$	6.07983			0.373481
$266$	−14.4242	−	16.6948i	−0.884407	−	1.02363i
$267$		−	4.94251i		−	0.302477i
$268$	−9.30365	−	1.36495i	−0.568311	−	0.0833778i
$269$		−	12.2303i		−	0.745692i	−0.927893	−	0.372846i	$-0.878382\pi$
$269$		−	12.2303i		−	0.745692i	0.927893	−	0.372846i	$-0.121618\pi$
$270$	−2.60942	+	2.25452i	−0.158804	+	0.137206i
$271$	−24.6688			−1.49852			−0.749262	−	0.662274i	$-0.769592\pi$
$271$	−24.6688			−1.49852			−0.749262	+	0.662274i	$0.769592\pi$
$272$	12.2527	+	3.67432i	0.742930	+	0.222788i
$273$	3.27808			0.198398
$274$	−9.70329	+	8.38358i	−0.586197	+	0.506471i
$275$		0			0
$276$	2.20970	+	0.324188i	0.133008	+	0.0195138i
$277$			8.05153i			0.483769i	0.970305	+	0.241885i	$0.0777656\pi$
$277$			8.05153i			0.483769i	−0.970305	+	0.241885i	$0.922234\pi$
$278$	0.215897	+	0.249882i	0.0129486	+	0.0149869i
$279$	−7.76234			−0.464719
$280$	10.1566	−	6.46561i	0.606975	−	0.386394i
$281$	13.2894			0.792778			0.396389	−	0.918083i	$-0.370263\pi$
$281$	13.2894			0.792778			0.396389	+	0.918083i	$0.370263\pi$
$282$	0.948459	+	1.09776i	0.0564799	+	0.0653708i
$283$		−	0.345924i		−	0.0205630i	−0.999947	−	0.0102815i	$-0.996727\pi$
$283$		−	0.345924i		−	0.0205630i	0.999947	−	0.0102815i	$-0.00327277\pi$
$284$	−2.66325	+	18.1530i	−0.158035	+	1.07718i
$285$		−	1.95097i		−	0.115565i
$286$		0			0
$287$	−17.1458			−1.01208
$288$	14.9545	−	6.70013i	0.881204	−	0.394809i
$289$	−6.77314			−0.398420
$290$	8.52842	−	7.36850i	0.500806	−	0.432693i
$291$			4.48560i			0.262950i
$292$	−0.272631	+	1.85828i	−0.0159545	+	0.108748i
$293$			3.82936i			0.223713i	0.993724	+	0.111857i	$0.0356798\pi$
$293$			3.82936i			0.223713i	−0.993724	+	0.111857i	$0.964320\pi$
$294$	1.16843	+	1.35235i	0.0681439	+	0.0788709i
$295$	18.2079			1.06010
$296$	18.7156	−	11.9141i	1.08782	−	0.692495i
$297$		0			0
$298$	2.11725	+	2.45054i	0.122649	+	0.141956i
$299$			10.7286i			0.620452i
$300$	−2.12481	−	0.311734i	−0.122676	−	0.0179980i
$301$			7.83969i			0.451872i
$302$	−4.06209	+	3.50962i	−0.233747	+	0.201956i
$303$	−3.53859			−0.203287
$304$	−5.42079	+	18.0767i	−0.310904	+	1.03677i
$305$	20.0383			1.14739
$306$	9.91345	−	8.56515i	0.566714	−	0.489637i
$307$		−	23.7376i		−	1.35478i	−0.735626	−	0.677388i	$-0.763112\pi$
$307$		−	23.7376i		−	1.35478i	0.735626	−	0.677388i	$-0.236888\pi$
$308$		0			0
$309$			3.50061i			0.199143i
$310$	3.18936	+	3.69141i	0.181143	+	0.209658i
$311$	8.82141			0.500216			0.250108	−	0.968218i	$-0.419534\pi$
$311$	8.82141			0.500216			0.250108	+	0.968218i	$0.419534\pi$
$312$	−1.50576	−	2.36535i	−0.0852466	−	0.133912i
$313$	−3.21543			−0.181747			−0.0908733	−	0.995862i	$-0.528966\pi$
$313$	−3.21543			−0.181747			−0.0908733	+	0.995862i	$0.528966\pi$
$314$	−11.2371	−	13.0061i	−0.634149	−	0.733974i
$315$		−	12.3311i		−	0.694779i
$316$	2.77709	−	18.9289i	0.156223	−	1.06483i
$317$			9.23560i			0.518723i	0.965780	+	0.259362i	$0.0835121\pi$
$317$			9.23560i			0.518723i	−0.965780	+	0.259362i	$0.916488\pi$
$318$	1.62346	−	1.40266i	0.0910390	−	0.0786571i
$319$		0			0
$320$	−9.33072	−	4.35877i	−0.521603	−	0.243663i
$321$	−4.65546			−0.259842
$322$	−12.3012	+	10.6282i	−0.685520	+	0.592284i
$323$			15.0879i			0.839512i
$324$	2.34633	−	15.9928i	0.130352	−	0.888488i
$325$		−	10.3165i		−	0.572255i
$326$	−7.66309	−	8.86939i	−0.424419	−	0.491230i
$327$	−0.632103			−0.0349554
$328$	7.87575	+	12.3718i	0.434865	+	0.683118i
$329$	−10.5600			−0.582191
$330$		0			0
$331$		−	4.00167i		−	0.219952i	−0.993934	−	0.109976i	$-0.964923\pi$
$331$		−	4.00167i		−	0.219952i	0.993934	−	0.109976i	$-0.0350774\pi$
$332$	2.52941	+	0.371094i	0.138819	+	0.0203664i
$333$		−	22.7225i		−	1.24518i
$334$	9.55490	−	8.25537i	0.522821	−	0.451714i
$335$	6.05252			0.330684
$336$	1.22040	−	4.06967i	0.0665785	−	0.222019i
$337$	2.35879			0.128492			0.0642459	−	0.997934i	$-0.479536\pi$
$337$	2.35879			0.128492			0.0642459	+	0.997934i	$0.479536\pi$
$338$	−3.71918	+	3.21334i	−0.202297	+	0.174783i
$339$			2.03898i			0.110742i
$340$	−8.14639	−	1.19517i	−0.441800	−	0.0648172i
$341$		0			0
$342$	12.6363	+	14.6255i	0.683294	+	0.790856i
$343$	10.1377			0.547386
$344$	5.65685	−	3.60109i	0.304997	−	0.194158i
$345$	−1.43752			−0.0773937
$346$	−7.86349	−	9.10133i	−0.422744	−	0.489290i
$347$			23.9187i			1.28402i	0.766695	+	0.642012i	$0.221900\pi$
$347$			23.9187i			1.28402i	−0.766695	+	0.642012i	$0.778100\pi$
$348$	0.577328	−	3.93512i	0.0309480	−	0.210945i
$349$		−	2.12274i		−	0.113628i	−0.998385	−	0.0568139i	$-0.981906\pi$
$349$		−	2.12274i		−	0.113628i	0.998385	−	0.0568139i	$-0.0180942\pi$
$350$	11.8286	−	10.2199i	0.632268	−	0.546275i
$351$	−5.84580			−0.312026
$352$		0			0
$353$	5.11533			0.272262			0.136131	−	0.990691i	$-0.456533\pi$
$353$	5.11533			0.272262			0.136131	+	0.990691i	$0.456533\pi$
$354$	4.86193	−	4.20068i	0.258409	−	0.223263i
$355$		−	11.8095i		−	0.626782i
$356$	4.46697	−	30.4473i	0.236749	−	1.61370i
$357$		−	3.39679i		−	0.179777i
$358$	−2.72146	−	3.14986i	−0.143834	−	0.166476i
$359$	28.9715			1.52906			0.764528	−	0.644591i	$-0.222972\pi$
$359$	28.9715			1.52906			0.764528	+	0.644591i	$0.222972\pi$
$360$	−8.89771	+	5.66418i	−0.468950	+	0.298529i
$361$	−3.25941			−0.171548
$362$	−19.6665	−	22.7624i	−1.03365	−	1.19636i
$363$		0			0
$364$	20.1939	+	2.96268i	1.05845	+	0.155287i
$365$		−	1.20891i		−	0.0632772i
$366$	5.35069	−	4.62296i	0.279685	−	0.241646i
$367$	29.6944			1.55004			0.775019	−	0.631938i	$-0.217740\pi$
$367$	29.6944			1.55004			0.775019	+	0.631938i	$0.217740\pi$
$368$	13.3194	+	3.99418i	0.694320	+	0.208211i
$369$	15.0205			0.781937
$370$	−10.8058	+	9.33611i	−0.561765	+	0.485361i
$371$			15.6170i			0.810792i
$372$	1.70327	+	0.249889i	0.0883102	+	0.0129561i
$373$		−	4.07522i		−	0.211007i	−0.994419	−	0.105504i	$-0.966355\pi$
$373$		−	4.07522i		−	0.211007i	0.994419	−	0.105504i	$-0.0336454\pi$
$374$		0			0
$375$	3.44988			0.178151
$376$	4.85064	+	7.61973i	0.250153	+	0.392958i
$377$	19.1060			0.984008
$378$	−5.79106	−	6.70267i	−0.297860	−	0.344748i
$379$			29.1300i			1.49631i	0.663526	+	0.748154i	$0.269059\pi$
$379$			29.1300i			1.49631i	−0.663526	+	0.748154i	$0.730941\pi$
$380$	1.76326	−	12.0185i	0.0904531	−	0.616537i
$381$		−	5.36534i		−	0.274875i
$382$	5.51739	−	4.76699i	0.282294	−	0.243900i
$383$	−18.8174			−0.961524			−0.480762	−	0.876851i	$-0.659640\pi$
$383$	−18.8174			−0.961524			−0.480762	+	0.876851i	$0.659640\pi$
$384$	−3.49712	+	0.988764i	−0.178461	+	0.0504576i
$385$		0			0
$386$	28.9114	−	24.9792i	1.47155	−	1.27141i
$387$		−	6.86795i		−	0.349117i
$388$	−4.05402	+	27.6326i	−0.205811	+	1.40283i
$389$			27.0108i			1.36950i	0.728778	+	0.684750i	$0.240089\pi$
$389$			27.0108i			1.36950i	−0.728778	+	0.684750i	$0.759911\pi$
$390$	1.17993	+	1.36568i	0.0597483	+	0.0691536i
$391$	11.1171			0.562218
$392$	5.97559	+	9.38690i	0.301813	+	0.474110i
$393$	2.98676			0.150662
$394$	−6.17821	−	7.15076i	−0.311254	−	0.360250i
$395$			12.3142i			0.619596i
$396$		0			0
$397$		−	28.1281i		−	1.41171i	−0.708358	−	0.705854i	$-0.750564\pi$
$397$		−	28.1281i		−	1.41171i	0.708358	−	0.705854i	$-0.249436\pi$
$398$	15.2584	−	13.1831i	0.764834	−	0.660811i
$399$	5.01135			0.250881
$400$	−12.8077	−	3.84074i	−0.640385	−	0.192037i
$401$	−8.33290			−0.416125			−0.208063	−	0.978115i	$-0.566716\pi$
$401$	−8.33290			−0.416125			−0.208063	+	0.978115i	$0.566716\pi$
$402$	1.61616	−	1.39635i	0.0806069	−	0.0696438i
$403$			8.26977i			0.411947i
$404$	−21.7987	−	3.19813i	−1.08453	−	0.159113i
$405$			10.4042i			0.516987i
$406$	18.9271	+	21.9065i	0.939335	+	1.08720i
$407$		0			0
$408$	−2.45101	+	1.56028i	−0.121343	+	0.0772456i
$409$	4.14774			0.205093			0.102546	−	0.994728i	$-0.467301\pi$
$409$	4.14774			0.205093			0.102546	+	0.994728i	$0.467301\pi$
$410$	−6.17156	−	7.14307i	−0.304792	−	0.352771i
$411$		−	2.91267i		−	0.143671i
$412$	−3.16380	+	21.5648i	−0.155869	+	1.06242i
$413$			46.7697i			2.30139i
$414$	10.7765	−	9.31078i	0.529634	−	0.457600i
$415$	−1.64552			−0.0807752
$416$	−7.13812	−	15.9321i	−0.349975	−	0.781136i
$417$	−0.0750080			−0.00367316
$418$		0			0
$419$		−	7.25457i		−	0.354409i	−0.984174	−	0.177204i	$-0.943295\pi$
$419$		−	7.25457i		−	0.354409i	0.984174	−	0.177204i	$-0.0567054\pi$
$420$	−0.396969	+	2.70577i	−0.0193701	+	0.132028i
$421$		−	35.1980i		−	1.71545i	−0.514111	−	0.857724i	$-0.671878\pi$
$421$		−	35.1980i		−	1.71545i	0.514111	−	0.857724i	$-0.328122\pi$
$422$	−17.8715	−	20.6848i	−0.869973	−	1.00692i
$423$	9.25107			0.449802
$424$	11.2687	−	7.17351i	0.547255	−	0.348376i
$425$	−10.6901			−0.518545
$426$	−2.72452	−	3.15340i	−0.132003	−	0.152783i
$427$			51.4713i			2.49087i
$428$	−28.6789	−	4.20753i	−1.38625	−	0.203379i
$429$		0			0
$430$	−3.26608	+	2.82187i	−0.157504	+	0.136083i
$431$	13.5078			0.650648			0.325324	−	0.945603i	$-0.394527\pi$
$431$	13.5078			0.650648			0.325324	+	0.945603i	$0.394527\pi$
$432$	−2.17635	+	7.25745i	−0.104710	+	0.349174i
$433$	14.5538			0.699412			0.349706	−	0.936859i	$-0.386281\pi$
$433$	14.5538			0.699412			0.349706	+	0.936859i	$0.386281\pi$
$434$	−9.48195	+	8.19234i	−0.455148	+	0.393245i
$435$			2.56000i			0.122743i
$436$	−3.89394	−	0.571286i	−0.186486	−	0.0273596i
$437$			16.4013i			0.784582i
$438$	−0.278903	−	0.322807i	−0.0133265	−	0.0154243i
$439$	8.11893			0.387495			0.193748	−	0.981051i	$-0.437936\pi$
$439$	8.11893			0.387495			0.193748	+	0.981051i	$0.437936\pi$
$440$		0			0
$441$	11.3966			0.542694
$442$	−9.12506	−	10.5615i	−0.434035	−	0.502359i
$443$			4.06209i			0.192996i	0.995333	+	0.0964979i	$0.0307641\pi$
$443$			4.06209i			0.192996i	−0.995333	+	0.0964979i	$0.969236\pi$
$444$	−0.731492	+	4.98592i	−0.0347151	+	0.236621i
$445$			19.8076i			0.938969i
$446$	14.6440	−	12.6523i	0.693414	−	0.599105i
$447$	−0.735586			−0.0347920
$448$	11.1961	−	23.9673i	0.528968	−	1.13235i
$449$	−8.28691			−0.391083			−0.195542	−	0.980695i	$-0.562646\pi$
$449$	−8.28691			−0.391083			−0.195542	+	0.980695i	$0.562646\pi$
$450$	−10.3625	+	8.95310i	−0.488491	+	0.422053i
$451$		0			0
$452$	−1.84280	+	12.5607i	−0.0866780	+	0.590805i
$453$		−	1.21933i		−	0.0572892i
$454$	10.9911	+	12.7213i	0.515838	+	0.597040i
$455$	−13.1372			−0.615881
$456$	−2.30192	−	3.61602i	−0.107797	−	0.169336i
$457$	−9.82837			−0.459752			−0.229876	−	0.973220i	$-0.573832\pi$
$457$	−9.82837			−0.459752			−0.229876	+	0.973220i	$0.573832\pi$
$458$	0.201270	+	0.232953i	0.00940473	+	0.0108852i
$459$			6.05750i			0.282740i
$460$	−8.85556	−	1.29921i	−0.412893	−	0.0605762i
$461$			24.4759i			1.13996i	0.821660	+	0.569978i	$0.193048\pi$
$461$			24.4759i			1.13996i	−0.821660	+	0.569978i	$0.806952\pi$
$462$		0			0
$463$	20.2431			0.940778			0.470389	−	0.882459i	$-0.344114\pi$
$463$	20.2431			0.940778			0.470389	+	0.882459i	$0.344114\pi$
$464$	7.11301	−	23.7197i	0.330213	−	1.10116i
$465$	−1.10806			−0.0513853
$466$	3.93703	−	3.40157i	0.182379	−	0.157575i
$467$		−	24.3857i		−	1.12844i	−0.825625	−	0.564219i	$-0.809178\pi$
$467$		−	24.3857i		−	1.12844i	0.825625	−	0.564219i	$-0.190822\pi$
$468$	−17.6908	−	2.59545i	−0.817759	−	0.119975i
$469$			15.5468i			0.717884i
$470$	−3.80104	−	4.39938i	−0.175329	−	0.202928i
$471$	3.90407			0.179890
$472$	33.7474	−	21.4832i	1.55335	−	0.988846i
$473$		0			0
$474$	2.84097	+	3.28819i	0.130490	+	0.151031i
$475$		−	15.7713i		−	0.723635i
$476$	3.06997	−	20.9252i	0.140712	−	0.959105i
$477$		−	13.6812i		−	0.626419i
$478$	21.4534	−	18.5356i	0.981256	−	0.847799i
$479$	−1.72894			−0.0789975			−0.0394987	−	0.999220i	$-0.512576\pi$
$479$	−1.72894			−0.0789975			−0.0394987	+	0.999220i	$0.512576\pi$
$480$	2.13474	−	0.956434i	0.0974370	−	0.0436550i
$481$	−24.2078			−1.10378
$482$	−15.4924	+	13.3853i	−0.705659	+	0.609684i
$483$		−	3.69250i		−	0.168014i
$484$		0			0
$485$		−	17.9764i		−	0.816268i
$486$	7.65426	+	8.85917i	0.347204	+	0.401860i
$487$	−2.65499			−0.120309			−0.0601545	−	0.998189i	$-0.519159\pi$
$487$	−2.65499			−0.120309			−0.0601545	+	0.998189i	$0.519159\pi$
$488$	37.1399	−	23.6429i	1.68125	−	1.07026i
$489$	2.66235			0.120396
$490$	−4.68257	−	5.41969i	−0.211537	−	0.244836i
$491$			29.3090i			1.32270i	0.750079	+	0.661348i	$0.230015\pi$
$491$			29.3090i			1.32270i	−0.750079	+	0.661348i	$0.769985\pi$
$492$	−3.29590	−	0.483547i	−0.148591	−	0.0218000i
$493$		−	19.7979i		−	0.891652i
$494$	15.5816	−	13.4624i	0.701048	−	0.605701i
$495$		0			0
$496$	10.2668	+	3.07877i	0.460991	+	0.138241i
$497$	30.3344			1.36068
$498$	−0.439391	+	0.379631i	−0.0196896	+	0.0170117i
$499$		−	8.05488i		−	0.360586i	−0.983613	−	0.180293i	$-0.942295\pi$
$499$		−	8.05488i		−	0.360586i	0.983613	−	0.180293i	$-0.0577046\pi$
$500$	21.2523	+	3.11796i	0.950431	+	0.139439i
$501$			2.86813i			0.128138i
$502$	20.0066	+	23.1560i	0.892939	+	1.03350i
$503$	30.0379			1.33932			0.669661	−	0.742667i	$-0.266439\pi$
$503$	30.0379			1.33932			0.669661	+	0.742667i	$0.266439\pi$
$504$	−14.5493	−	22.8551i	−0.648077	−	1.01805i
$505$	14.1812			0.631057
$506$		0			0
$507$		−	1.11640i		−	0.0495810i
$508$	4.84912	−	33.0520i	0.215145	−	1.46645i
$509$			2.76641i			0.122619i	0.998119	+	0.0613095i	$0.0195277\pi$
$509$			2.76641i			0.122619i	−0.998119	+	0.0613095i	$0.980472\pi$
$510$	1.41513	−	1.22266i	0.0626631	−	0.0541405i
$511$	3.10526			0.137369
$512$	−22.4369	+	2.93042i	−0.991578	+	0.129508i
$513$	−8.93674			−0.394567
$514$	9.10565	−	7.86722i	0.401633	−	0.347008i
$515$		−	14.0290i		−	0.618193i
$516$	−0.221096	+	1.50701i	−0.00973321	+	0.0663425i
$517$		0			0
$518$	−23.9812	−	27.7562i	−1.05367	−	1.21954i
$519$	2.73198			0.119920
$520$	6.03445	+	9.47936i	0.264628	+	0.415697i
$521$	12.0184			0.526536			0.263268	−	0.964723i	$-0.415200\pi$
$521$	12.0184			0.526536			0.263268	+	0.964723i	$0.415200\pi$
$522$	−16.5810	−	19.1912i	−0.725732	−	0.839974i
$523$		−	5.32522i		−	0.232856i	−0.993199	−	0.116428i	$-0.962856\pi$
$523$		−	5.32522i		−	0.232856i	0.993199	−	0.116428i	$-0.0371444\pi$
$524$	18.3993	+	2.69939i	0.803777	+	0.117923i
$525$			3.55065i			0.154963i
$526$	−10.0020	+	8.64163i	−0.436106	+	0.376793i
$527$	8.56925			0.373283
$528$		0			0
$529$	−10.9151			−0.474568
$530$	−6.50615	+	5.62127i	−0.282609	+	0.244173i
$531$		−	40.9725i		−	1.77806i
$532$	30.8713	+	4.52918i	1.33844	+	0.196365i
$533$		−	16.0024i		−	0.693141i
$534$	4.56973	+	5.28908i	0.197752	+	0.228881i
$535$	18.6572			0.806620
$536$	11.2180	−	7.14128i	0.484545	−	0.308456i
$537$	0.945505			0.0408016
$538$	11.3078	+	13.0879i	0.487515	+	0.564257i
$539$		0			0
$540$	0.707915	−	4.82521i	0.0304638	−	0.207644i
$541$		−	9.71132i		−	0.417522i	−0.977967	−	0.208761i	$-0.933057\pi$
$541$		−	9.71132i		−	0.417522i	0.977967	−	0.208761i	$-0.0669431\pi$
$542$	26.3986	−	22.8082i	1.13392	−	0.979697i
$543$	6.83266			0.293218
$544$	−16.5091	+	7.39661i	−0.707821	+	0.317127i
$545$	2.53321			0.108511
$546$	−3.50794	+	3.03084i	−0.150126	+	0.129708i
$547$			20.6628i			0.883476i	0.897144	+	0.441738i	$0.145638\pi$
$547$			20.6628i			0.883476i	−0.897144	+	0.441738i	$0.854362\pi$
$548$	2.63243	−	17.9429i	0.112452	−	0.766482i
$549$		−	45.0914i		−	1.92445i
$550$		0			0
$551$	29.2082			1.24431
$552$	−2.66438	+	1.69611i	−0.113403	+	0.0721914i
$553$	−31.6309			−1.34508
$554$	−7.44426	−	8.61611i	−0.316276	−	0.366063i
$555$		−	3.24360i		−	0.137683i
$556$	−0.462071	−	0.0677911i	−0.0195962	−	0.00287499i
$557$		−	26.5466i		−	1.12482i	−0.826860	−	0.562408i	$-0.809875\pi$
$557$		−	26.5466i		−	1.12482i	0.826860	−	0.562408i	$-0.190125\pi$
$558$	8.30664	−	7.17688i	0.351648	−	0.303822i
$559$	−7.31691			−0.309472
$560$	−4.89088	+	16.3096i	−0.206677	+	0.689205i
$561$		0			0
$562$	−14.2212	+	12.2871i	−0.599887	+	0.518298i
$563$			13.5955i			0.572982i	0.958083	+	0.286491i	$0.0924888\pi$
$563$			13.5955i			0.572982i	−0.958083	+	0.286491i	$0.907511\pi$
$564$	−2.02993	−	0.297814i	−0.0854755	−	0.0125402i
$565$		−	8.17139i		−	0.343773i
$566$	0.319833	+	0.370180i	0.0134436	+	0.0155598i
$567$	−26.7246			−1.12233
$568$	−13.9338	−	21.8883i	−0.584650	−	0.918411i
$569$	−24.4670			−1.02571			−0.512854	−	0.858476i	$-0.671412\pi$
$569$	−24.4670			−1.02571			−0.512854	+	0.858476i	$0.671412\pi$
$570$	1.80382	+	2.08777i	0.0755537	+	0.0874471i
$571$		−	12.1063i		−	0.506634i	−0.967383	−	0.253317i	$-0.918478\pi$
$571$		−	12.1063i		−	0.506634i	0.967383	−	0.253317i	$-0.0815216\pi$
$572$		0			0
$573$			1.65617i			0.0691877i
$574$	18.3480	−	15.8526i	0.765832	−	0.661674i
$575$	−11.6207			−0.484616
$576$	−9.80836	+	20.9965i	−0.408682	+	0.874856i
$577$	−2.33364			−0.0971505			−0.0485753	−	0.998820i	$-0.515468\pi$
$577$	−2.33364			−0.0971505			−0.0485753	+	0.998820i	$0.515468\pi$
$578$	7.24808	−	6.26229i	0.301480	−	0.260477i
$579$			8.67843i			0.360663i
$580$	−2.31369	+	15.7704i	−0.0960709	+	0.654828i
$581$		−	4.22675i		−	0.175355i
$582$	−4.14728	−	4.80013i	−0.171910	−	0.198972i
$583$		0			0
$584$	−1.42637	−	2.24065i	−0.0590238	−	0.0927188i
$585$	11.5088			0.475831
$586$	−3.54053	−	4.09787i	−0.146258	−	0.169282i
$587$			24.2039i			0.999001i	0.866314	+	0.499500i	$0.166483\pi$
$587$			24.2039i			0.999001i	−0.866314	+	0.499500i	$0.833517\pi$
$588$	−2.50071	−	0.366883i	−0.103128	−	0.0151300i
$589$			12.6424i			0.520920i
$590$	−19.4846	+	16.8346i	−0.802170	+	0.693070i
$591$	2.14647			0.0882939
$592$	−9.01240	+	30.0535i	−0.370407	+	1.23519i
$593$	−27.1495			−1.11490			−0.557448	−	0.830212i	$-0.688220\pi$
$593$	−27.1495			−1.11490			−0.557448	+	0.830212i	$0.688220\pi$
$594$		0			0
$595$			13.6130i			0.558077i
$596$	−4.53142	−	0.664812i	−0.185614	−	0.0272318i
$597$			4.58016i			0.187454i
$598$	−9.91943	−	11.4809i	−0.405636	−	0.469490i
$599$	7.01855			0.286770			0.143385	−	0.989667i	$-0.454201\pi$
$599$	7.01855			0.286770			0.143385	+	0.989667i	$0.454201\pi$
$600$	2.56202	−	1.63096i	0.104594	−	0.0665835i
$601$	2.81601			0.114867			0.0574337	−	0.998349i	$-0.481708\pi$
$601$	2.81601			0.114867			0.0574337	+	0.998349i	$0.481708\pi$
$602$	−7.24839	−	8.38941i	−0.295423	−	0.341927i
$603$		−	13.6197i		−	0.554639i
$604$	1.10201	−	7.51143i	0.0448403	−	0.305636i
$605$		0			0
$606$	3.78672	−	3.27170i	0.153825	−	0.132904i
$607$	−36.1882			−1.46884			−0.734418	−	0.678698i	$-0.762545\pi$
$607$	−36.1882			−1.46884			−0.734418	+	0.678698i	$0.762545\pi$
$608$	−10.9124	−	24.3561i	−0.442555	−	0.987772i
$609$	−6.57575			−0.266463
$610$	−21.4434	+	18.5269i	−0.868217	+	0.750134i
$611$		−	9.85581i		−	0.398723i
$612$	−2.68944	+	18.3315i	−0.108714	+	0.741007i
$613$		−	31.2100i		−	1.26056i	−0.776369	−	0.630279i	$-0.782940\pi$
$613$		−	31.2100i		−	1.26056i	0.776369	−	0.630279i	$-0.217060\pi$
$614$	21.9472	+	25.4021i	0.885718	+	1.02514i
$615$	2.14416			0.0864608
$616$		0			0
$617$	−34.6326			−1.39426			−0.697129	−	0.716946i	$-0.745539\pi$
$617$	−34.6326			−1.39426			−0.697129	+	0.716946i	$0.745539\pi$
$618$	−3.23659	−	3.74608i	−0.130195	−	0.150689i
$619$		−	15.8975i		−	0.638974i	−0.947591	−	0.319487i	$-0.896489\pi$
$619$		−	15.8975i		−	0.638974i	0.947591	−	0.319487i	$-0.103511\pi$
$620$	−6.82599	−	1.00145i	−0.274138	−	0.0402193i
$621$			6.58483i			0.264240i
$622$	−9.43997	+	8.15607i	−0.378508	+	0.327029i
$623$	−50.8787			−2.03841
$624$	3.79829	+	1.13902i	0.152053	+	0.0455974i
$625$	2.88824			0.115530
$626$	3.44089	−	2.97291i	0.137526	−	0.118821i
$627$		0			0
$628$	24.0502	+	3.52844i	0.959708	+	0.140800i
$629$			25.0845i			1.00018i
$630$	11.4011	+	13.1958i	0.454229	+	0.525732i
$631$	−14.6113			−0.581667			−0.290834	−	0.956774i	$-0.593933\pi$
$631$	−14.6113			−0.581667			−0.290834	+	0.956774i	$0.593933\pi$
$632$	14.5294	+	22.8238i	0.577948	+	0.907882i
$633$	6.20903			0.246787
$634$	−8.53902	−	9.88321i	−0.339128	−	0.392512i
$635$			21.5021i			0.853285i
$636$	−0.440431	+	3.00202i	−0.0174642	+	0.119038i
$637$		−	12.1416i		−	0.481066i
$638$		0			0
$639$	−26.5744			−1.05127
$640$	14.0150	−	3.96256i	0.553992	−	0.156634i
$641$	29.6286			1.17026			0.585130	−	0.810940i	$-0.301043\pi$
$641$	29.6286			1.17026			0.585130	+	0.810940i	$0.301043\pi$
$642$	4.98190	−	4.30433i	0.196620	−	0.169878i
$643$			29.5335i			1.16469i	0.812943	+	0.582344i	$0.197864\pi$
$643$			29.5335i			1.16469i	−0.812943	+	0.582344i	$0.802136\pi$
$644$	3.33722	−	22.7468i	0.131505	−	0.896350i
$645$		−	0.980390i		−	0.0386028i
$646$	−13.9499	−	16.1458i	−0.548851	−	0.635250i
$647$	7.18758			0.282573			0.141286	−	0.989969i	$-0.454876\pi$
$647$	7.18758			0.282573			0.141286	+	0.989969i	$0.454876\pi$
$648$	12.2757	+	19.2836i	0.482235	+	0.757530i
$649$		0			0
$650$	9.53837	+	11.0399i	0.374126	+	0.433019i
$651$		−	2.84623i		−	0.111552i
$652$	16.4009	+	2.40620i	0.642307	+	0.0942340i
$653$		−	28.4975i		−	1.11520i	−0.830111	−	0.557598i	$-0.811723\pi$
$653$		−	28.4975i		−	1.11520i	0.830111	−	0.557598i	$-0.188277\pi$
$654$	0.676427	−	0.584428i	0.0264504	−	0.0228530i
$655$	−11.9697			−0.467695
$656$	−19.8667	−	5.95758i	−0.775663	−	0.232604i
$657$	−2.72036			−0.106131
$658$	11.3005	−	9.76353i	0.440538	−	0.380622i
$659$			26.9704i			1.05062i	0.850912	+	0.525308i	$0.176050\pi$
$659$			26.9704i			1.05062i	−0.850912	+	0.525308i	$0.823950\pi$
$660$		0			0
$661$		−	40.1424i		−	1.56136i	−0.624931	−	0.780680i	$-0.714873\pi$
$661$		−	40.1424i		−	1.56136i	0.624931	−	0.780680i	$-0.285127\pi$
$662$	3.69985	+	4.28227i	0.143799	+	0.166435i
$663$	3.17028			0.123123
$664$	−3.04988	+	1.94152i	−0.118358	+	0.0753456i
$665$	−20.0834			−0.778802
$666$	21.0087	+	24.3158i	0.814069	+	0.942217i
$667$		−	21.5214i		−	0.833310i
$668$	−2.59217	+	17.6685i	−0.100294	+	0.683614i
$669$			4.39574i			0.169949i
$670$	−6.47692	+	5.59602i	−0.250225	+	0.216193i
$671$		0			0
$672$	2.45674	+	5.48339i	0.0947709	+	0.211526i
$673$	−19.5859			−0.754982			−0.377491	−	0.926013i	$-0.623213\pi$
$673$	−19.5859			−0.754982			−0.377491	+	0.926013i	$0.623213\pi$
$674$	−2.52419	+	2.18089i	−0.0972283	+	0.0840046i
$675$		−	6.33187i		−	0.243714i
$676$	1.00898	−	6.87733i	0.0388071	−	0.264513i
$677$			14.2527i			0.547777i	0.961761	+	0.273889i	$0.0883099\pi$
$677$			14.2527i			0.547777i	−0.961761	+	0.273889i	$0.911690\pi$
$678$	−1.88519	−	2.18195i	−0.0724004	−	0.0837974i
$679$	46.1751			1.77204
$680$	9.82264	−	6.25298i	0.376681	−	0.239791i
$681$	−3.81859			−0.146329
$682$		0			0
$683$			11.2957i			0.432218i	0.976369	+	0.216109i	$0.0693367\pi$
$683$			11.2957i			0.432218i	−0.976369	+	0.216109i	$0.930663\pi$
$684$	−27.0448	−	3.96778i	−1.03408	−	0.151712i
$685$			11.6728i			0.445995i
$686$	−10.8486	+	9.37312i	−0.414201	+	0.357867i
$687$	−0.0699264			−0.00266786
$688$	−2.72403	+	9.08379i	−0.103853	+	0.346316i
$689$	−14.5756			−0.555284
$690$	1.53832	−	1.32910i	0.0585630	−	0.0505980i
$691$		−	8.58370i		−	0.326539i	−0.986581	−	0.163270i	$-0.947796\pi$
$691$		−	8.58370i		−	0.326539i	0.986581	−	0.163270i	$-0.0522041\pi$
$692$	16.8298	+	2.46912i	0.639771	+	0.0938619i
$693$		0			0
$694$	−22.1147	−	25.5959i	−0.839462	−	0.971607i
$695$	0.300602			0.0114025
$696$	3.02051	+	4.74484i	0.114492	+	0.179853i
$697$	−16.5819			−0.628085
$698$	1.96264	+	2.27159i	0.0742869	+	0.0859809i
$699$			1.18179i			0.0446995i
$700$	−3.20902	+	21.8730i	−0.121290	+	0.826721i
$701$		−	25.6358i		−	0.968252i	−0.874998	−	0.484126i	$-0.839138\pi$
$701$		−	25.6358i		−	0.968252i	0.874998	−	0.484126i	$-0.160862\pi$
$702$	6.25571	−	5.40489i	0.236107	−	0.203995i
$703$	−37.0076			−1.39577
$704$		0			0
$705$	1.32058			0.0497358
$706$	−5.47402	+	4.72952i	−0.206017	+	0.177998i
$707$			36.4266i			1.36996i
$708$	−1.31901	+	8.99046i	−0.0495712	+	0.337882i
$709$		−	29.7950i		−	1.11898i	−0.828838	−	0.559488i	$-0.810998\pi$
$709$		−	29.7950i		−	1.11898i	0.828838	−	0.559488i	$-0.189002\pi$
$710$	10.9188	+	12.6376i	0.409774	+	0.474279i
$711$	27.7102			1.03921
$712$	23.3707	+	36.7123i	0.875852	+	1.37585i
$713$	9.31524			0.348859
$714$	3.14059	+	3.63498i	0.117534	+	0.136036i
$715$		0			0
$716$	5.82458	+	0.854534i	0.217675	+	0.0319354i
$717$			6.43974i			0.240497i
$718$	−31.0030	+	26.7863i	−1.15702	+	0.999657i
$719$	43.5670			1.62477			0.812387	−	0.583118i	$-0.198168\pi$
$719$	43.5670			1.62477			0.812387	+	0.583118i	$0.198168\pi$
$720$	4.28465	−	14.2880i	0.159679	−	0.532481i
$721$	36.0356			1.34204
$722$	3.48797	−	3.01358i	0.129809	−	0.112154i
$723$		−	4.65040i		−	0.172950i
$724$	42.0912	+	6.17526i	1.56431	+	0.229502i
$725$			20.6946i			0.768578i
$726$		0			0
$727$	51.1659			1.89764			0.948819	−	0.315820i	$-0.102280\pi$
$727$	51.1659			1.89764			0.948819	+	0.315820i	$0.102280\pi$
$728$	−24.3491	+	15.5004i	−0.902439	+	0.574483i
$729$	21.5867			0.799508
$730$	1.11773	+	1.29368i	0.0413690	+	0.0478812i
$731$			7.58188i			0.280426i
$732$	−1.45160	+	9.89425i	−0.0536527	+	0.365702i
$733$			17.3837i			0.642082i	0.947065	+	0.321041i	$0.104033\pi$
$733$			17.3837i			0.642082i	−0.947065	+	0.321041i	$0.895967\pi$
$734$	−31.7766	+	27.4548i	−1.17290	+	1.01338i
$735$	1.62685			0.0600071
$736$	−17.9463	+	8.04052i	−0.661508	+	0.296377i
$737$		0			0
$738$	−16.0738	+	13.8876i	−0.591683	+	0.511210i
$739$		−	10.3923i		−	0.382286i	−0.981562	−	0.191143i	$-0.938781\pi$
$739$		−	10.3923i		−	0.382286i	0.981562	−	0.191143i	$-0.0612195\pi$
$740$	2.93152	−	19.9815i	0.107765	−	0.734535i
$741$			4.67717i			0.171820i
$742$	−14.4391	−	16.7120i	−0.530075	−	0.613518i
$743$	−12.5580			−0.460707			−0.230353	−	0.973107i	$-0.573988\pi$
$743$	−12.5580			−0.460707			−0.230353	+	0.973107i	$0.573988\pi$
$744$	−2.05374	+	1.30739i	−0.0752938	+	0.0479312i
$745$	2.94793			0.108004
$746$	3.76786	+	4.36098i	0.137951	+	0.159667i
$747$			3.70284i			0.135480i
$748$		0			0
$749$			47.9237i			1.75109i
$750$	−3.69179	+	3.18968i	−0.134805	+	0.116471i
$751$	40.6689			1.48403			0.742014	−	0.670384i	$-0.233871\pi$
$751$	40.6689			1.48403			0.742014	+	0.670384i	$0.233871\pi$
$752$	−12.2358	−	3.66924i	−0.446193	−	0.133804i
$753$	−6.95081			−0.253302
$754$	−20.4457	+	17.6649i	−0.744588	+	0.643319i
$755$			4.88658i			0.177841i
$756$	12.3943	+	1.81838i	0.450775	+	0.0661340i
$757$			35.9968i			1.30832i	0.756354	+	0.654162i	$0.226979\pi$
$757$			35.9968i			1.30832i	−0.756354	+	0.654162i	$0.773021\pi$
$758$	−26.9329	−	31.1726i	−0.978247	−	1.13224i
$759$		0			0
$760$	9.22514	+	14.4915i	0.334631	+	0.525663i
$761$	−23.3625			−0.846890			−0.423445	−	0.905922i	$-0.639179\pi$
$761$	−23.3625			−0.846890			−0.423445	+	0.905922i	$0.639179\pi$
$762$	4.96067	+	5.74156i	0.179706	+	0.207995i
$763$			6.50693i			0.235567i
$764$	−1.49683	+	10.2025i	−0.0541533	+	0.369114i
$765$		−	11.9256i		−	0.431171i
$766$	20.1369	−	17.3981i	0.727575	−	0.628620i
$767$	−43.6509			−1.57614
$768$	2.82815	−	4.29145i	0.102052	−	0.154854i
$769$	8.08790			0.291657			0.145829	−	0.989310i	$-0.453415\pi$
$769$	8.08790			0.291657			0.145829	+	0.989310i	$0.453415\pi$
$770$		0			0
$771$			2.73327i			0.0984365i
$772$	−7.84344	+	53.4616i	−0.282291	+	1.92412i
$773$			27.9261i			1.00443i	0.864742	+	0.502216i	$0.167482\pi$
$773$			27.9261i			1.00443i	−0.864742	+	0.502216i	$0.832518\pi$
$774$	6.34994	+	7.34953i	0.228244	+	0.264173i
$775$	−8.95739			−0.321759
$776$	−21.2101	−	33.3184i	−0.761399	−	1.19606i
$777$	8.33167			0.298897
$778$	−24.9735	−	28.9048i	−0.895345	−	1.03629i
$779$		−	24.4636i		−	0.876500i
$780$	−2.52534	−	0.370497i	−0.0904218	−	0.0132659i
$781$		0			0
$782$	−11.8967	+	10.2787i	−0.425425	+	0.367564i
$783$	11.7265			0.419072
$784$	−15.0735	−	4.52021i	−0.538340	−	0.161436i
$785$	−15.6459			−0.558427
$786$	−3.19619	+	2.76149i	−0.114004	+	0.0984990i
$787$		−	33.0205i		−	1.17705i	−0.808478	−	0.588527i	$-0.799708\pi$
$787$		−	33.0205i		−	1.17705i	0.808478	−	0.588527i	$-0.200292\pi$
$788$	13.2229	+	1.93995i	0.471045	+	0.0691077i
$789$		−	3.00232i		−	0.106886i
$790$	−11.3855	−	13.1777i	−0.405076	−	0.468842i
$791$	20.9894			0.746298
$792$		0			0
$793$	−48.0390			−1.70591
$794$	26.0066	+	30.1004i	0.922938	+	1.06822i
$795$		−	1.95297i		−	0.0692649i
$796$	−4.13948	+	28.2151i	−0.146720	+	1.00006i
$797$		−	25.9022i		−	0.917504i	−0.888564	−	0.458752i	$-0.848297\pi$
$797$		−	25.9022i		−	0.917504i	0.888564	−	0.458752i	$-0.151703\pi$
$798$	−5.36275	+	4.63338i	−0.189839	+	0.164020i
$799$	−10.2127			−0.361300
$800$	17.2568	−	7.73164i	0.610121	−	0.273355i
$801$	44.5722			1.57488
$802$	8.91721	−	7.70441i	0.314878	−	0.272052i
$803$		0			0
$804$	−0.438453	+	2.98853i	−0.0154630	+	0.105397i
$805$			14.7980i			0.521561i
$806$	−7.64604	−	8.84965i	−0.269320	−	0.311716i
$807$	−3.92863			−0.138294
$808$	26.2842	−	16.7322i	0.924675	−	0.588638i
$809$	−6.52260			−0.229322			−0.114661	−	0.993405i	$-0.536578\pi$
$809$	−6.52260			−0.229322			−0.114661	+	0.993405i	$0.536578\pi$
$810$	−9.61944	−	11.1337i	−0.337993	−	0.391198i
$811$		−	25.5743i		−	0.898035i	−0.893523	−	0.449018i	$-0.851774\pi$
$811$		−	25.5743i		−	0.898035i	0.893523	−	0.449018i	$-0.148226\pi$
$812$	−40.5085	−	5.94307i	−1.42157	−	0.208561i
$813$			7.92416i			0.277912i
$814$		0			0
$815$	−10.6696			−0.373741
$816$	1.18027	−	3.93584i	0.0413177	−	0.137782i
$817$	−11.1857			−0.391338
$818$	−4.43858	+	3.83490i	−0.155191	+	0.134084i
$819$			29.5621i			1.03298i
$820$	13.2086	+	1.93786i	0.461265	+	0.0676730i
$821$			14.1096i			0.492429i	0.969215	+	0.246215i	$0.0791868\pi$
$821$			14.1096i			0.492429i	−0.969215	+	0.246215i	$0.920813\pi$
$822$	2.69299	+	3.11691i	0.0939287	+	0.108715i
$823$	22.9254			0.799128			0.399564	−	0.916705i	$-0.369161\pi$
$823$	22.9254			0.799128			0.399564	+	0.916705i	$0.369161\pi$
$824$	−16.5526	−	26.0021i	−0.576639	−	0.905826i
$825$		0			0
$826$	−43.2422	−	50.0492i	−1.50459	−	1.74143i
$827$		−	40.9219i		−	1.42299i	−0.702690	−	0.711496i	$-0.748018\pi$
$827$		−	40.9219i		−	1.42299i	0.702690	−	0.711496i	$-0.251982\pi$
$828$	−2.92357	+	19.9273i	−0.101601	+	0.692522i
$829$		−	2.56458i		−	0.0890716i	−0.999008	−	0.0445358i	$-0.985819\pi$
$829$		−	2.56458i		−	0.0890716i	0.999008	−	0.0445358i	$-0.0141809\pi$
$830$	1.76090	−	1.52141i	0.0611217	−	0.0528088i
$831$	2.58633			0.0897186
$832$	22.3691	+	10.4495i	0.775509	+	0.362273i
$833$	−12.5813			−0.435915
$834$	0.0802676	−	0.0693507i	0.00277944	−	0.00240142i
$835$		−	11.4943i		−	0.397776i
$836$		0			0
$837$			5.07568i			0.175441i
$838$	6.70740	+	7.76326i	0.231703	+	0.268177i
$839$	−42.0345			−1.45119			−0.725595	−	0.688122i	$-0.758436\pi$
$839$	−42.0345			−1.45119			−0.725595	+	0.688122i	$0.758436\pi$
$840$	−2.07689	−	3.26253i	−0.0716596	−	0.112568i
$841$	−9.32614			−0.321591
$842$	32.5433	+	37.6661i	1.12152	+	1.29806i
$843$		−	4.26884i		−	0.147027i
$844$	38.2494	+	5.61163i	1.31660	+	0.193160i
$845$			4.47407i			0.153913i
$846$	−9.89975	+	8.55332i	−0.340361	+	0.294069i
$847$		0			0
$848$	−5.42637	+	18.0953i	−0.186342	+	0.621394i
$849$	−0.111118			−0.00381357
$850$	11.4397	−	9.88379i	0.392377	−	0.339011i
$851$			27.2682i			0.934742i
$852$	5.83113	+	0.855494i	0.199771	+	0.0293088i
$853$		−	20.4281i		−	0.699446i	−0.936853	−	0.349723i	$-0.886276\pi$
$853$		−	20.4281i		−	0.699446i	0.936853	−	0.349723i	$-0.113724\pi$
$854$	−47.5892	−	55.0805i	−1.62847	−	1.88482i
$855$	17.5941			0.601704
$856$	34.5801	−	22.0133i	1.18192	−	0.752400i
$857$	51.9575			1.77483			0.887417	−	0.460968i	$-0.152498\pi$
$857$	51.9575			1.77483			0.887417	+	0.460968i	$0.152498\pi$
$858$		0			0
$859$			44.6566i			1.52366i	0.647775	+	0.761832i	$0.275700\pi$
$859$			44.6566i			1.52366i	−0.647775	+	0.761832i	$0.724300\pi$
$860$	0.886062	−	6.03948i	0.0302145	−	0.205945i
$861$			5.50759i			0.187698i
$862$	−14.4550	+	12.4890i	−0.492338	+	0.425377i
$863$	50.4467			1.71723			0.858613	−	0.512624i	$-0.171327\pi$
$863$	50.4467			1.71723			0.858613	+	0.512624i	$0.171327\pi$
$864$	−4.38111	−	9.77854i	−0.149048	−	0.332673i
$865$	−10.9486			−0.372265
$866$	−15.5743	+	13.4561i	−0.529238	+	0.457258i
$867$			2.17568i			0.0738900i
$868$	2.57238	−	17.5336i	0.0873122	−	0.595128i
$869$		0			0
$870$	−2.36692	−	2.73951i	−0.0802461	−	0.0928782i
$871$	−14.5101			−0.491655
$872$	4.69518	−	2.98890i	0.158999	−	0.101217i
$873$	−40.4517			−1.36908
$874$	−15.1643	−	17.5514i	−0.512940	−	0.593685i
$875$		−	35.5134i		−	1.20057i
$876$	0.596919	+	0.0875750i	0.0201680	+	0.00295889i
$877$			18.0407i			0.609190i	0.952482	+	0.304595i	$0.0985211\pi$
$877$			18.0407i			0.609190i	−0.952482	+	0.304595i	$0.901479\pi$
$878$	−8.68824	+	7.50658i	−0.293214	+	0.253335i
$879$	1.23007			0.0414893
$880$		0			0
$881$	3.97122			0.133794			0.0668969	−	0.997760i	$-0.478690\pi$
$881$	3.97122			0.133794			0.0668969	+	0.997760i	$0.478690\pi$
$882$	−12.1957	+	10.5370i	−0.410651	+	0.354799i
$883$			49.5141i			1.66628i	0.553059	+	0.833142i	$0.313460\pi$
$883$			49.5141i			1.66628i	−0.553059	+	0.833142i	$0.686540\pi$
$884$	19.5298	+	2.86525i	0.656859	+	0.0963689i
$885$		−	5.84877i		−	0.196604i
$886$	−3.75572	−	4.34693i	−0.126176	−	0.146038i
$887$	33.4482			1.12308			0.561541	−	0.827449i	$-0.310209\pi$
$887$	33.4482			1.12308			0.561541	+	0.827449i	$0.310209\pi$
$888$	−3.82708	−	6.01185i	−0.128428	−	0.201744i
$889$	−55.2313			−1.85240
$890$	−18.3136	−	21.1965i	−0.613874	−	0.710508i
$891$		0			0
$892$	−3.97281	+	27.0790i	−0.133019	+	0.906673i
$893$		−	15.0670i		−	0.504199i
$894$	0.787166	−	0.680106i	0.0263268	−	0.0227461i
$895$	−3.78920			−0.126659
$896$	10.1784	+	35.9996i	0.340037	+	1.20266i
$897$	3.44626			0.115067
$898$	8.86799	−	7.66188i	0.295929	−	0.255680i
$899$		−	16.5890i		−	0.553273i
$900$	2.81126	−	19.1618i	0.0937086	−	0.638727i
$901$			15.1034i			0.503167i
$902$		0			0
$903$	2.51828			0.0838030
$904$	−9.64130	−	15.1453i	−0.320665	−	0.503724i
$905$	−27.3825			−0.910226
$906$	1.12737	+	1.30483i	0.0374542	+	0.0433501i
$907$			6.94962i			0.230759i	0.993322	+	0.115379i	$0.0368083\pi$
$907$			6.94962i			0.230759i	−0.993322	+	0.115379i	$0.963192\pi$
$908$	−23.5236	−	3.45119i	−0.780659	−	0.114532i
$909$		−	31.9115i		−	1.05844i
$910$	14.0584	−	12.1464i	0.466031	−	0.402648i
$911$	−42.4273			−1.40568			−0.702840	−	0.711348i	$-0.748085\pi$
$911$	−42.4273			−1.40568			−0.702840	+	0.711348i	$0.748085\pi$
$912$	5.80661	+	1.74128i	0.192276	+	0.0576594i
$913$		0			0
$914$	10.5175	−	9.08708i	0.347889	−	0.300574i
$915$		−	6.43673i		−	0.212792i
$916$	−0.430766	−	0.0631984i	−0.0142329	−	0.00208813i
$917$		−	30.7460i		−	1.01532i
$918$	−5.60063	−	6.48226i	−0.184848	−	0.213946i
$919$	3.22452			0.106367			0.0531836	−	0.998585i	$-0.483063\pi$
$919$	3.22452			0.106367			0.0531836	+	0.998585i	$0.483063\pi$
$920$	10.6777	−	6.79733i	0.352035	−	0.224101i
$921$	−7.62503			−0.251253
$922$	−22.6298	−	26.1921i	−0.745274	−	0.862592i
$923$			28.3116i			0.931886i
$924$		0			0
$925$		−	26.2207i		−	0.862131i
$926$	−21.6626	+	18.7163i	−0.711877	+	0.615057i
$927$	−31.5690			−1.03686
$928$	14.3189	+	31.9594i	0.470041	+	1.04912i
$929$	−23.9207			−0.784813			−0.392406	−	0.919792i	$-0.628357\pi$
$929$	−23.9207			−0.784813			−0.392406	+	0.919792i	$0.628357\pi$
$930$	1.18576	−	1.02449i	0.0388827	−	0.0335944i
$931$		−	18.5614i		−	0.608324i
$932$	−1.06809	+	7.28017i	−0.0349863	+	0.238470i
$933$		−	2.83363i		−	0.0927688i
$934$	22.5465	+	26.0957i	0.737743	+	0.853876i
$935$		0			0
$936$	21.3310	−	13.5791i	0.697226	−	0.443846i
$937$	24.2049			0.790739			0.395370	−	0.918522i	$-0.370617\pi$
$937$	24.2049			0.790739			0.395370	+	0.918522i	$0.370617\pi$
$938$	−14.3742	−	16.6369i	−0.469334	−	0.543215i
$939$			1.03286i			0.0337063i
$940$	8.13513	+	1.19352i	0.265339	+	0.0389283i
$941$		−	2.24680i		−	0.0732434i	−0.999329	−	0.0366217i	$-0.988340\pi$
$941$		−	2.24680i		−	0.0732434i	0.999329	−	0.0366217i	$-0.0116597\pi$
$942$	−4.17783	+	3.60961i	−0.136121	+	0.117608i
$943$	−18.0254			−0.586989
$944$	−16.2509	+	54.1917i	−0.528922	+	1.76379i
$945$	−8.06313			−0.262294
$946$		0			0
$947$			26.7519i			0.869321i	0.900594	+	0.434660i	$0.143132\pi$
$947$			26.7519i			0.869321i	−0.900594	+	0.434660i	$0.856868\pi$
$948$	−6.08036	−	0.892060i	−0.197481	−	0.0289728i
$949$			2.89819i			0.0940792i
$950$	14.5817	+	16.8771i	0.473094	+	0.547567i
$951$	2.96668			0.0962010
$952$	16.0617	+	25.2309i	0.520563	+	0.817738i
$953$	33.9853			1.10089			0.550445	−	0.834871i	$-0.314458\pi$
$953$	33.9853			1.10089			0.550445	+	0.834871i	$0.314458\pi$
$954$	12.6493	+	14.6405i	0.409537	+	0.474005i
$955$		−	6.63727i		−	0.214777i
$956$	−5.82015	+	39.6707i	−0.188237	+	1.28304i
$957$		0			0
$958$	1.85018	−	1.59854i	0.0597766	−	0.0516466i
$959$	−29.9833			−0.968211
$960$	−1.40013	+	2.99723i	−0.0451890	+	0.0967352i
$961$	−23.8197			−0.768377
$962$	25.9053	−	22.3820i	0.835221	−	0.721625i
$963$		−	41.9835i		−	1.35290i
$964$	4.20296	−	28.6478i	0.135368	−	0.922683i
$965$		−	34.7796i		−	1.11959i
$966$	3.41400	+	3.95141i	0.109843	+	0.127135i
$967$	3.94526			0.126871			0.0634356	−	0.997986i	$-0.479794\pi$
$967$	3.94526			0.126871			0.0634356	+	0.997986i	$0.479794\pi$
$968$		0			0
$969$	4.84655			0.155694
$970$	16.6206	+	19.2370i	0.533655	+	0.617661i
$971$			16.7355i			0.537067i	0.963270	+	0.268534i	$0.0865390\pi$
$971$			16.7355i			0.537067i	−0.963270	+	0.268534i	$0.913461\pi$
$972$	−16.3820	−	2.40343i	−0.525452	−	0.0770899i
$973$			0.772139i			0.0247537i
$974$	2.84116	−	2.45474i	0.0910366	−	0.0786550i
$975$	−3.31387			−0.106129
$976$	−17.8846	+	59.6394i	−0.572471	+	1.90901i
$977$	6.85898			0.219438			0.109719	−	0.993963i	$-0.465005\pi$
$977$	6.85898			0.219438			0.109719	+	0.993963i	$0.465005\pi$
$978$	−2.84904	+	2.46155i	−0.0911023	+	0.0787117i
$979$		0			0
$980$	10.0218	+	1.47032i	0.320136	+	0.0469676i
$981$		−	5.70039i		−	0.181999i
$982$	−27.0984	−	31.3641i	−0.864745	−	1.00087i
$983$	1.73756			0.0554196			0.0277098	−	0.999616i	$-0.491179\pi$
$983$	1.73756			0.0554196			0.0277098	+	0.999616i	$0.491179\pi$
$984$	3.97409	−	2.52986i	0.126689	−	0.0806490i
$985$	−8.60217			−0.274088
$986$	18.3047	+	21.1861i	0.582939	+	0.674703i
$987$			3.39210i			0.107972i
$988$	−4.22716	+	28.8127i	−0.134484	+	0.916655i
$989$			8.24192i			0.262078i
$990$		0			0
$991$	17.5645			0.557956			0.278978	−	0.960298i	$-0.410004\pi$
$991$	17.5645			0.557956			0.278978	+	0.960298i	$0.410004\pi$
$992$	−13.8332	+	6.19775i	−0.439205	+	0.196779i
$993$	−1.28542			−0.0407917
$994$	−32.4614	+	28.0465i	−1.02961	+	0.889580i
$995$		−	18.3554i		−	0.581906i
$996$	0.119203	−	0.812502i	0.00377711	−	0.0257451i
$997$		−	50.0422i		−	1.58485i	−0.609967	−	0.792427i	$-0.708817\pi$
$997$		−	50.0422i		−	1.58485i	0.609967	−	0.792427i	$-0.291183\pi$
$998$	7.44736	+	8.61969i	0.235742	+	0.272852i
$999$	−14.8579			−0.470083

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.c.h.485.6		20
4.3	odd	2		3872.2.c.h.1937.11		20
8.3	odd	2		3872.2.c.h.1937.10		20
8.5	even	2	inner	968.2.c.h.485.5		20
11.2	odd	10		968.2.o.d.565.1		40
11.3	even	5		88.2.o.a.53.7	yes	40
11.4	even	5		88.2.o.a.5.2	✓	40
11.5	even	5		968.2.o.j.245.5		40
11.6	odd	10		968.2.o.d.245.6		40
11.7	odd	10		968.2.o.i.269.9		40
11.8	odd	10		968.2.o.i.493.4		40
11.9	even	5		968.2.o.j.565.10		40
11.10	odd	2		968.2.c.i.485.15		20
33.14	odd	10		792.2.br.b.757.4		40
33.26	odd	10		792.2.br.b.181.9		40
44.3	odd	10		352.2.w.a.273.5		40
44.15	odd	10		352.2.w.a.49.6		40
44.43	even	2		3872.2.c.i.1937.11		20
88.3	odd	10		352.2.w.a.273.6		40
88.5	even	10		968.2.o.j.245.10		40
88.13	odd	10		968.2.o.d.565.6		40
88.21	odd	2		968.2.c.i.485.16		20
88.29	odd	10		968.2.o.i.269.4		40
88.37	even	10		88.2.o.a.5.7	yes	40
88.43	even	2		3872.2.c.i.1937.10		20
88.53	even	10		968.2.o.j.565.5		40
88.59	odd	10		352.2.w.a.49.5		40
88.61	odd	10		968.2.o.d.245.1		40
88.69	even	10		88.2.o.a.53.2	yes	40
88.85	odd	10		968.2.o.i.493.9		40
264.125	odd	10		792.2.br.b.181.4		40
264.245	odd	10		792.2.br.b.757.9		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.o.a.5.2	✓	40	11.4	even	5
88.2.o.a.5.7	yes	40	88.37	even	10
88.2.o.a.53.2	yes	40	88.69	even	10
88.2.o.a.53.7	yes	40	11.3	even	5
352.2.w.a.49.5		40	88.59	odd	10
352.2.w.a.49.6		40	44.15	odd	10
352.2.w.a.273.5		40	44.3	odd	10
352.2.w.a.273.6		40	88.3	odd	10
792.2.br.b.181.4		40	264.125	odd	10
792.2.br.b.181.9		40	33.26	odd	10
792.2.br.b.757.4		40	33.14	odd	10
792.2.br.b.757.9		40	264.245	odd	10
968.2.c.h.485.5		20	8.5	even	2	inner
968.2.c.h.485.6		20	1.1	even	1	trivial
968.2.c.i.485.15		20	11.10	odd	2
968.2.c.i.485.16		20	88.21	odd	2
968.2.o.d.245.1		40	88.61	odd	10
968.2.o.d.245.6		40	11.6	odd	10
968.2.o.d.565.1		40	11.2	odd	10
968.2.o.d.565.6		40	88.13	odd	10
968.2.o.i.269.4		40	88.29	odd	10
968.2.o.i.269.9		40	11.7	odd	10
968.2.o.i.493.4		40	11.8	odd	10
968.2.o.i.493.9		40	88.85	odd	10
968.2.o.j.245.5		40	11.5	even	5
968.2.o.j.245.10		40	88.5	even	10
968.2.o.j.565.5		40	88.53	even	10
968.2.o.j.565.10		40	11.9	even	5
3872.2.c.h.1937.10		20	8.3	odd	2
3872.2.c.h.1937.11		20	4.3	odd	2
3872.2.c.i.1937.10		20	88.43	even	2
3872.2.c.i.1937.11		20	44.43	even	2

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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07012 + 0.924577i) q^{2} -0.321222i q^{3} +(0.290315 - 1.97882i) q^{4} +1.28733i q^{5} +(0.296994 + 0.343746i) q^{6} -3.30669 q^{7} +(1.51890 + 2.38599i) q^{8} +2.89682 q^{9} +O(q^{10})\)	\(q+(-1.07012 + 0.924577i) q^{2} -0.321222i q^{3} +(0.290315 - 1.97882i) q^{4} +1.28733i q^{5} +(0.296994 + 0.343746i) q^{6} -3.30669 q^{7} +(1.51890 + 2.38599i) q^{8} +2.89682 q^{9} +(-1.19023 - 1.37759i) q^{10} +(-0.635639 - 0.0932556i) q^{12} -3.08618i q^{13} +(3.53855 - 3.05728i) q^{14} +0.413517 q^{15} +(-3.83143 - 1.14896i) q^{16} -3.19795 q^{17} +(-3.09994 + 2.67833i) q^{18} -4.71799i q^{19} +(2.54738 + 0.373730i) q^{20} +1.06218i q^{21} -3.47634 q^{23} +(0.766432 - 0.487902i) q^{24} +3.34279 q^{25} +(2.85341 + 3.30259i) q^{26} -1.89419i q^{27} +(-0.959982 + 6.54333i) q^{28} +6.19081i q^{29} +(-0.442513 + 0.382328i) q^{30} -2.67961 q^{31} +(5.16240 - 2.31293i) q^{32} +(3.42219 - 2.95675i) q^{34} -4.25678i q^{35} +(0.840991 - 5.73227i) q^{36} -7.84394i q^{37} +(4.36214 + 5.04882i) q^{38} -0.991349 q^{39} +(-3.07155 + 1.95531i) q^{40} +5.18518 q^{41} +(-0.982066 - 1.13666i) q^{42} -2.37086i q^{43} +3.72915i q^{45} +(3.72010 - 3.21414i) q^{46} +3.19353 q^{47} +(-0.369072 + 1.23074i) q^{48} +3.93417 q^{49} +(-3.57719 + 3.09067i) q^{50} +1.02725i q^{51} +(-6.10699 - 0.895967i) q^{52} -4.72284i q^{53} +(1.75132 + 2.02701i) q^{54} +(-5.02251 - 7.88972i) q^{56} -1.51552 q^{57} +(-5.72388 - 6.62491i) q^{58} -14.1440i q^{59} +(0.120050 - 0.818274i) q^{60} -15.5658i q^{61} +(2.86751 - 2.47751i) q^{62} -9.57886 q^{63} +(-3.38591 + 7.24815i) q^{64} +3.97292 q^{65} -4.70162i q^{67} +(-0.928413 + 6.32815i) q^{68} +1.11668i q^{69} +(3.93572 + 4.55527i) q^{70} -9.17365 q^{71} +(4.39996 + 6.91178i) q^{72} -0.939086 q^{73} +(7.25233 + 8.39396i) q^{74} -1.07378i q^{75} +(-9.33604 - 1.36970i) q^{76} +(1.06086 - 0.916578i) q^{78} +9.56575 q^{79} +(1.47909 - 4.93230i) q^{80} +8.08200 q^{81} +(-5.54877 + 4.79410i) q^{82} +1.27824i q^{83} +(2.10186 + 0.308367i) q^{84} -4.11680i q^{85} +(2.19204 + 2.53711i) q^{86} +1.98862 q^{87} +15.3866 q^{89} +(-3.44788 - 3.99063i) q^{90} +10.2050i q^{91} +(-1.00924 + 6.87904i) q^{92} +0.860749i q^{93} +(-3.41746 + 2.95266i) q^{94} +6.07359 q^{95} +(-0.742962 - 1.65827i) q^{96} -13.9642 q^{97} +(-4.21004 + 3.63744i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{4} - q^{6} + 10 q^{7} - 10 q^{9}+O(q^{10}) \) 20 * q + 2 * q^4 - q^6 + 10 * q^7 - 10 * q^9	\( 20 q + 2 q^{4} - q^{6} + 10 q^{7} - 10 q^{9} - 10 q^{10} - 3 q^{12} - 4 q^{14} - 4 q^{15} + 10 q^{16} + 2 q^{17} - 5 q^{18} - 16 q^{20} - 4 q^{23} + 15 q^{24} - 2 q^{25} + 30 q^{26} - 14 q^{28} + 16 q^{30} + 2 q^{31} + 10 q^{32} + 5 q^{34} + 9 q^{36} + 21 q^{38} + 28 q^{39} + 10 q^{40} - 2 q^{41} - 20 q^{42} + 24 q^{46} + 2 q^{47} - 41 q^{48} - 2 q^{49} - 22 q^{50} - 20 q^{52} + 54 q^{54} - 16 q^{56} + 22 q^{57} + 12 q^{58} - 48 q^{60} + 4 q^{62} - 30 q^{63} + 38 q^{64} - 18 q^{65} - 21 q^{68} - 44 q^{70} - 34 q^{71} + 57 q^{72} + 2 q^{73} - 28 q^{74} - 67 q^{76} - 6 q^{78} - 58 q^{79} + 28 q^{80} - 12 q^{81} - 23 q^{82} - 44 q^{84} + 25 q^{86} + 34 q^{87} - 8 q^{89} - 42 q^{90} + 68 q^{92} + 60 q^{94} - 92 q^{95} + 35 q^{96} + 10 q^{97} - 72 q^{98}+O(q^{100}) \) 20 * q + 2 * q^4 - q^6 + 10 * q^7 - 10 * q^9 - 10 * q^10 - 3 * q^12 - 4 * q^14 - 4 * q^15 + 10 * q^16 + 2 * q^17 - 5 * q^18 - 16 * q^20 - 4 * q^23 + 15 * q^24 - 2 * q^25 + 30 * q^26 - 14 * q^28 + 16 * q^30 + 2 * q^31 + 10 * q^32 + 5 * q^34 + 9 * q^36 + 21 * q^38 + 28 * q^39 + 10 * q^40 - 2 * q^41 - 20 * q^42 + 24 * q^46 + 2 * q^47 - 41 * q^48 - 2 * q^49 - 22 * q^50 - 20 * q^52 + 54 * q^54 - 16 * q^56 + 22 * q^57 + 12 * q^58 - 48 * q^60 + 4 * q^62 - 30 * q^63 + 38 * q^64 - 18 * q^65 - 21 * q^68 - 44 * q^70 - 34 * q^71 + 57 * q^72 + 2 * q^73 - 28 * q^74 - 67 * q^76 - 6 * q^78 - 58 * q^79 + 28 * q^80 - 12 * q^81 - 23 * q^82 - 44 * q^84 + 25 * q^86 + 34 * q^87 - 8 * q^89 - 42 * q^90 + 68 * q^92 + 60 * q^94 - 92 * q^95 + 35 * q^96 + 10 * q^97 - 72 * q^98

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