LMFDB - Embedded newform 825.2.k.j.518.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(518,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("825.518");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.k (of order $4$, degree $2$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 8 x^{14} + 19 x^{12} - 80 x^{11} + 168 x^{10} + 28 x^{9} + 119 x^{8} - 432 x^{7} + \cdots + 16 $ x^16 - 4x^15 + 8x^14 + 19x^12 - 80x^11 + 168x^10 + 28x^9 + 119x^8 - 432x^7 + 784x^6 + 84x^5 + 169x^4 - 420x^3 + 392x^2 - 112x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			518.2
Root			$-1.14633 - 1.14633i$ of defining polynomial
Character	$\chi$	$=$	825.518
Dual form			825.2.k.j.782.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.14633 - 1.14633i) q^{2} +(0.582649 - 1.63111i) q^{3} +0.628149i q^{4} +(-2.53770 + 1.20188i) q^{6} +(0.201884 - 0.201884i) q^{7} +(-1.57260 + 1.57260i) q^{8} +(-2.32104 - 1.90073i) q^{9} -1.00000i q^{11} +(1.02458 + 0.365990i) q^{12} +(-1.02066 - 1.02066i) q^{13} -0.462851 q^{14} +4.86173 q^{16} +(-2.87911 - 2.87911i) q^{17} +(0.481818 + 4.83954i) q^{18} +0.281435i q^{19} +(-0.211667 - 0.446922i) q^{21} +(-1.14633 + 1.14633i) q^{22} +(-5.22177 + 5.22177i) q^{23} +(1.64881 + 3.48135i) q^{24} +2.34002i q^{26} +(-4.45265 + 2.67842i) q^{27} +(0.126813 + 0.126813i) q^{28} -9.71095 q^{29} +4.46829 q^{31} +(-2.42796 - 2.42796i) q^{32} +(-1.63111 - 0.582649i) q^{33} +6.60083i q^{34} +(1.19394 - 1.45796i) q^{36} +(-2.37906 + 2.37906i) q^{37} +(0.322618 - 0.322618i) q^{38} +(-2.25949 + 1.07012i) q^{39} -9.00173i q^{41} +(-0.269680 + 0.754962i) q^{42} +(-1.84728 - 1.84728i) q^{43} +0.628149 q^{44} +11.9718 q^{46} +(3.98588 + 3.98588i) q^{47} +(2.83268 - 7.93001i) q^{48} +6.91849i q^{49} +(-6.37366 + 3.01864i) q^{51} +(0.641125 - 0.641125i) q^{52} +(4.75830 - 4.75830i) q^{53} +(8.17456 + 2.03386i) q^{54} +0.634963i q^{56} +(0.459052 + 0.163978i) q^{57} +(11.1320 + 11.1320i) q^{58} -2.68228 q^{59} -9.46983 q^{61} +(-5.12214 - 5.12214i) q^{62} +(-0.852307 + 0.0848544i) q^{63} -4.15697i q^{64} +(1.20188 + 2.53770i) q^{66} +(6.27596 - 6.27596i) q^{67} +(1.80851 - 1.80851i) q^{68} +(5.47482 + 11.5597i) q^{69} -0.679177i q^{71} +(6.63914 - 0.660982i) q^{72} +(5.74145 + 5.74145i) q^{73} +5.45437 q^{74} -0.176783 q^{76} +(-0.201884 - 0.201884i) q^{77} +(3.81683 + 1.36341i) q^{78} -12.5134i q^{79} +(1.77446 + 8.82334i) q^{81} +(-10.3190 + 10.3190i) q^{82} +(-4.93065 + 4.93065i) q^{83} +(0.280734 - 0.132959i) q^{84} +4.23518i q^{86} +(-5.65807 + 15.8396i) q^{87} +(1.57260 + 1.57260i) q^{88} +2.97979 q^{89} -0.412109 q^{91} +(-3.28005 - 3.28005i) q^{92} +(2.60345 - 7.28828i) q^{93} -9.13826i q^{94} +(-5.37491 + 2.54562i) q^{96} +(11.4137 - 11.4137i) q^{97} +(7.93087 - 7.93087i) q^{98} +(-1.90073 + 2.32104i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 2 q^{3} - 4 q^{6} - 8 q^{7} - 16 q^{8} + 6 q^{9} + 4 q^{12} - 24 q^{14} - 4 q^{16} - 8 q^{17} + 32 q^{18} - 8 q^{21} + 4 q^{22} - 14 q^{23} + 12 q^{24} + 20 q^{27} - 8 q^{28} - 16 q^{29}+ \cdots - 4 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 + 2 * q^3 - 4 * q^6 - 8 * q^7 - 16 * q^8 + 6 * q^9 + 4 * q^12 - 24 * q^14 - 4 * q^16 - 8 * q^17 + 32 * q^18 - 8 * q^21 + 4 * q^22 - 14 * q^23 + 12 * q^24 + 20 * q^27 - 8 * q^28 - 16 * q^29 + 8 * q^31 - 28 * q^32 - 4 * q^33 + 44 * q^36 + 6 * q^37 - 24 * q^38 + 24 * q^39 + 60 * q^42 - 16 * q^43 + 12 * q^44 - 32 * q^46 - 48 * q^47 + 48 * q^48 - 8 * q^51 - 36 * q^52 + 4 * q^53 + 4 * q^54 + 8 * q^57 + 12 * q^58 - 68 * q^59 - 8 * q^61 - 48 * q^62 + 12 * q^63 + 8 * q^66 - 6 * q^67 - 24 * q^68 + 12 * q^69 + 8 * q^72 + 8 * q^74 + 16 * q^76 + 8 * q^77 + 48 * q^78 + 2 * q^81 - 12 * q^82 + 8 * q^83 + 52 * q^84 + 36 * q^87 + 16 * q^88 + 32 * q^89 - 56 * q^91 - 20 * q^92 - 28 * q^93 + 80 * q^96 - 18 * q^97 - 16 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.14633	−	1.14633i	−0.810578	−	0.810578i	0.174142	−	0.984721i	$-0.444285\pi$
$2$	−1.14633	−	1.14633i	−0.810578	−	0.810578i	−0.984721	+	0.174142i	$0.944285\pi$
$3$	0.582649	−	1.63111i	0.336392	−	0.941722i
$3$	0.582649	−	1.63111i	0.336392	−	0.941722i
$4$			0.628149i			0.314074i
$5$		0			0
$5$		0			0
$6$	−2.53770	+	1.20188i	−1.03601	+	0.490667i
$7$	0.201884	−	0.201884i	0.0763049	−	0.0763049i	−0.667924	−	0.744229i	$-0.732817\pi$
$7$	0.201884	−	0.201884i	0.0763049	−	0.0763049i	0.744229	+	0.667924i	$0.232817\pi$
$8$	−1.57260	+	1.57260i	−0.555996	+	0.555996i
$9$	−2.32104	−	1.90073i	−0.773680	−	0.633576i
$10$		0			0
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	1.02458	+	0.365990i	0.295771	+	0.105652i
$13$	−1.02066	−	1.02066i	−0.283079	−	0.283079i	0.551256	−	0.834336i	$-0.314149\pi$
$13$	−1.02066	−	1.02066i	−0.283079	−	0.283079i	−0.834336	+	0.551256i	$0.814149\pi$
$14$	−0.462851			−0.123702
$15$		0			0
$16$	4.86173			1.21543
$17$	−2.87911	−	2.87911i	−0.698287	−	0.698287i	0.265754	−	0.964041i	$-0.414379\pi$
$17$	−2.87911	−	2.87911i	−0.698287	−	0.698287i	−0.964041	+	0.265754i	$0.914379\pi$
$18$	0.481818	+	4.83954i	0.113566	+	1.14069i
$19$			0.281435i			0.0645657i	0.999479	+	0.0322828i	$0.0102777\pi$
$19$			0.281435i			0.0645657i	−0.999479	+	0.0322828i	$0.989722\pi$
$20$		0			0
$21$	−0.211667	−	0.446922i	−0.0461896	−	0.0975264i
$22$	−1.14633	+	1.14633i	−0.244399	+	0.244399i
$23$	−5.22177	+	5.22177i	−1.08881	+	1.08881i	−0.0931634	+	0.995651i	$0.529698\pi$
$23$	−5.22177	+	5.22177i	−1.08881	+	1.08881i	−0.995651	+	0.0931634i	$0.970302\pi$
$24$	1.64881	+	3.48135i	0.336561	+	0.710627i
$25$		0			0
$26$			2.34002i			0.458916i
$27$	−4.45265	+	2.67842i	−0.856913	+	0.515462i
$28$	0.126813	+	0.126813i	0.0239654	+	0.0239654i
$29$	−9.71095			−1.80328			−0.901639	−	0.432490i	$-0.857635\pi$
$29$	−9.71095			−1.80328			−0.901639	+	0.432490i	$0.857635\pi$
$30$		0			0
$31$	4.46829			0.802529			0.401265	−	0.915962i	$-0.368571\pi$
$31$	4.46829			0.802529			0.401265	+	0.915962i	$0.368571\pi$
$32$	−2.42796	−	2.42796i	−0.429206	−	0.429206i
$33$	−1.63111	−	0.582649i	−0.283940	−	0.101426i
$34$			6.60083i			1.13203i
$35$		0			0
$36$	1.19394	−	1.45796i	0.198990	−	0.242993i
$37$	−2.37906	+	2.37906i	−0.391114	+	0.391114i	−0.875085	−	0.483970i	$-0.839194\pi$
$37$	−2.37906	+	2.37906i	−0.391114	+	0.391114i	0.483970	+	0.875085i	$0.339194\pi$
$38$	0.322618	−	0.322618i	0.0523355	−	0.0523355i
$39$	−2.25949	+	1.07012i	−0.361808	+	0.171356i
$40$		0			0
$41$		−	9.00173i		−	1.40583i	−0.711272	−	0.702917i	$-0.751881\pi$
$41$		−	9.00173i		−	1.40583i	0.711272	−	0.702917i	$-0.248119\pi$
$42$	−0.269680	+	0.754962i	−0.0416125	+	0.116493i
$43$	−1.84728	−	1.84728i	−0.281707	−	0.281707i	0.552083	−	0.833789i	$-0.313833\pi$
$43$	−1.84728	−	1.84728i	−0.281707	−	0.281707i	−0.833789	+	0.552083i	$0.813833\pi$
$44$	0.628149			0.0946970
$45$		0			0
$46$	11.9718			1.76514
$47$	3.98588	+	3.98588i	0.581400	+	0.581400i	0.935288	−	0.353888i	$-0.115141\pi$
$47$	3.98588	+	3.98588i	0.581400	+	0.581400i	−0.353888	+	0.935288i	$0.615141\pi$
$48$	2.83268	−	7.93001i	0.408862	−	1.14460i
$49$			6.91849i			0.988355i
$50$		0			0
$51$	−6.37366	+	3.01864i	−0.892490	+	0.422694i
$52$	0.641125	−	0.641125i	0.0889080	−	0.0889080i
$53$	4.75830	−	4.75830i	0.653603	−	0.653603i	−0.300256	−	0.953859i	$-0.597072\pi$
$53$	4.75830	−	4.75830i	0.653603	−	0.653603i	0.953859	+	0.300256i	$0.0970720\pi$
$54$	8.17456	+	2.03386i	1.11242	+	0.276773i
$55$		0			0
$56$			0.634963i			0.0848505i
$57$	0.459052	+	0.163978i	0.0608029	+	0.0217194i
$58$	11.1320	+	11.1320i	1.46170	+	1.46170i
$59$	−2.68228			−0.349203			−0.174602	−	0.984639i	$-0.555864\pi$
$59$	−2.68228			−0.349203			−0.174602	+	0.984639i	$0.555864\pi$
$60$		0			0
$61$	−9.46983			−1.21249			−0.606244	−	0.795279i	$-0.707324\pi$
$61$	−9.46983			−1.21249			−0.606244	+	0.795279i	$0.707324\pi$
$62$	−5.12214	−	5.12214i	−0.650513	−	0.650513i
$63$	−0.852307	+	0.0848544i	−0.107381	+	0.0106907i
$64$		−	4.15697i		−	0.519622i
$65$		0			0
$66$	1.20188	+	2.53770i	0.147942	+	0.312369i
$67$	6.27596	−	6.27596i	0.766731	−	0.766731i	−0.210799	−	0.977529i	$-0.567607\pi$
$67$	6.27596	−	6.27596i	0.766731	−	0.766731i	0.977529	+	0.210799i	$0.0676065\pi$
$68$	1.80851	−	1.80851i	0.219314	−	0.219314i
$69$	5.47482	+	11.5597i	0.659091	+	1.39163i
$70$		0			0
$71$		−	0.679177i		−	0.0806035i	−0.999188	−	0.0403017i	$-0.987168\pi$
$71$		−	0.679177i		−	0.0806035i	0.999188	−	0.0403017i	$-0.0128319\pi$
$72$	6.63914	−	0.660982i	0.782430	−	0.0778975i
$73$	5.74145	+	5.74145i	0.671986	+	0.671986i	0.958174	−	0.286188i	$-0.0923881\pi$
$73$	5.74145	+	5.74145i	0.671986	+	0.671986i	−0.286188	+	0.958174i	$0.592388\pi$
$74$	5.45437			0.634058
$75$		0			0
$76$	−0.176783			−0.0202784
$77$	−0.201884	−	0.201884i	−0.0230068	−	0.0230068i
$78$	3.81683	+	1.36341i	0.432171	+	0.154376i
$79$		−	12.5134i		−	1.40786i	−0.710267	−	0.703932i	$-0.751426\pi$
$79$		−	12.5134i		−	1.40786i	0.710267	−	0.703932i	$-0.248574\pi$
$80$		0			0
$81$	1.77446	+	8.82334i	0.197163	+	0.980371i
$82$	−10.3190	+	10.3190i	−1.13954	+	1.13954i
$83$	−4.93065	+	4.93065i	−0.541209	+	0.541209i	−0.923883	−	0.382674i	$-0.875003\pi$
$83$	−4.93065	+	4.93065i	−0.541209	+	0.541209i	0.382674	+	0.923883i	$0.375003\pi$
$84$	0.280734	−	0.132959i	0.0306305	−	0.0145070i
$85$		0			0
$86$			4.23518i			0.456691i
$87$	−5.65807	+	15.8396i	−0.606609	+	1.69819i
$88$	1.57260	+	1.57260i	0.167639	+	0.167639i
$89$	2.97979			0.315857			0.157928	−	0.987451i	$-0.449519\pi$
$89$	2.97979			0.315857			0.157928	+	0.987451i	$0.449519\pi$
$90$		0			0
$91$	−0.412109			−0.0432007
$92$	−3.28005	−	3.28005i	−0.341969	−	0.341969i
$93$	2.60345	−	7.28828i	0.269965	−	0.755759i
$94$		−	9.13826i		−	0.942540i
$95$		0			0
$96$	−5.37491	+	2.54562i	−0.548574	+	0.259811i
$97$	11.4137	−	11.4137i	1.15889	−	1.15889i	0.174172	−	0.984715i	$-0.444275\pi$
$97$	11.4137	−	11.4137i	1.15889	−	1.15889i	0.984715	−	0.174172i	$-0.0557250\pi$
$98$	7.93087	−	7.93087i	0.801139	−	0.801139i
$99$	−1.90073	+	2.32104i	−0.191030	+	0.233273i
$100$		0			0
$101$			16.8528i			1.67692i	0.544965	+	0.838458i	$0.316543\pi$
$101$			16.8528i			1.67692i	−0.544965	+	0.838458i	$0.683457\pi$
$102$	10.7667	+	3.84596i	1.06606	+	0.380807i
$103$	−4.78866	−	4.78866i	−0.471841	−	0.471841i	0.430669	−	0.902510i	$-0.358278\pi$
$103$	−4.78866	−	4.78866i	−0.471841	−	0.471841i	−0.902510	+	0.430669i	$0.858278\pi$
$104$	3.21016			0.314782
$105$		0			0
$106$	−10.9092			−1.05959
$107$	−0.547413	−	0.547413i	−0.0529204	−	0.0529204i	0.680151	−	0.733072i	$-0.261914\pi$
$107$	−0.547413	−	0.547413i	−0.0529204	−	0.0529204i	−0.733072	+	0.680151i	$0.761914\pi$
$108$	−1.68244	−	2.79692i	−0.161893	−	0.269134i
$109$		−	0.251236i		−	0.0240641i	−0.999928	−	0.0120320i	$-0.996170\pi$
$109$		−	0.251236i		−	0.0240641i	0.999928	−	0.0120320i	$-0.00383001\pi$
$110$		0			0
$111$	2.49435	+	5.26666i	0.236753	+	0.499889i
$112$	0.981504	−	0.981504i	0.0927434	−	0.0927434i
$113$	−2.40152	+	2.40152i	−0.225916	+	0.225916i	−0.810984	−	0.585068i	$-0.801068\pi$
$113$	−2.40152	+	2.40152i	−0.225916	+	0.225916i	0.585068	+	0.810984i	$0.301068\pi$
$114$	−0.338252	−	0.714198i	−0.0316802	−	0.0668908i
$115$		0			0
$116$		−	6.09992i		−	0.566363i
$117$	0.428996	+	4.30898i	0.0396607	+	0.398365i
$118$	3.07478	+	3.07478i	0.283057	+	0.283057i
$119$	−1.16249			−0.106565
$120$		0			0
$121$	−1.00000			−0.0909091
$122$	10.8556	+	10.8556i	0.982816	+	0.982816i
$123$	−14.6828	−	5.24485i	−1.32390	−	0.472912i
$124$			2.80675i			0.252054i
$125$		0			0
$126$	1.07430	+	0.879755i	0.0957060	+	0.0783748i
$127$	−2.88720	+	2.88720i	−0.256198	+	0.256198i	−0.823506	−	0.567308i	$-0.807985\pi$
$127$	−2.88720	+	2.88720i	−0.256198	+	0.256198i	0.567308	+	0.823506i	$0.307985\pi$
$128$	−9.62118	+	9.62118i	−0.850400	+	0.850400i
$129$	−4.08942	+	1.93680i	−0.360054	+	0.170525i
$130$		0			0
$131$		−	17.2568i		−	1.50774i	−0.657026	−	0.753868i	$-0.728186\pi$
$131$		−	17.2568i		−	1.50774i	0.657026	−	0.753868i	$-0.271814\pi$
$132$	0.365990	−	1.02458i	0.0318553	−	0.0891782i
$133$	0.0568172	+	0.0568172i	0.00492668	+	0.00492668i
$134$	−14.3887			−1.24299
$135$		0			0
$136$	9.05535			0.776490
$137$	−14.3666	−	14.3666i	−1.22742	−	1.22742i	−0.964936	−	0.262485i	$-0.915458\pi$
$137$	−14.3666	−	14.3666i	−1.22742	−	1.22742i	−0.262485	−	0.964936i	$-0.584542\pi$
$138$	6.97532	−	19.5272i	0.593779	−	1.66227i
$139$			3.60234i			0.305547i	0.988261	+	0.152773i	$0.0488205\pi$
$139$			3.60234i			0.305547i	−0.988261	+	0.152773i	$0.951180\pi$
$140$		0			0
$141$	8.82377	−	4.17904i	0.743095	−	0.351938i
$142$	−0.778561	+	0.778561i	−0.0653354	+	0.0653354i
$143$	−1.02066	+	1.02066i	−0.0853517	+	0.0853517i
$144$	−11.2843	−	9.24082i	−0.940356	−	0.770068i
$145$		0			0
$146$		−	13.1632i		−	1.08939i
$147$	11.2848	+	4.03105i	0.930756	+	0.332475i
$148$	−1.49440	−	1.49440i	−0.122839	−	0.122839i
$149$	11.6538			0.954716			0.477358	−	0.878709i	$-0.341594\pi$
$149$	11.6538			0.954716			0.477358	+	0.878709i	$0.341594\pi$
$150$		0			0
$151$	−16.7356			−1.36192			−0.680961	−	0.732319i	$-0.738438\pi$
$151$	−16.7356			−1.36192			−0.680961	+	0.732319i	$0.738438\pi$
$152$	−0.442584	−	0.442584i	−0.0358983	−	0.0358983i
$153$	1.21013	+	12.1549i	0.0978330	+	0.982669i
$154$			0.462851i			0.0372976i
$155$		0			0
$156$	−0.672195	−	1.41930i	−0.0538186	−	0.113635i
$157$	−8.98141	+	8.98141i	−0.716794	+	0.716794i	−0.967947	−	0.251153i	$-0.919190\pi$
$157$	−8.98141	+	8.98141i	−0.716794	+	0.716794i	0.251153	+	0.967947i	$0.419190\pi$
$158$	−14.3445	+	14.3445i	−1.14118	+	1.14118i
$159$	−4.98890	−	10.5337i	−0.395645	−	0.835379i
$160$		0			0
$161$			2.10838i			0.166164i
$162$	8.08034	−	12.1486i	0.634851	−	0.954483i
$163$	−12.8794	−	12.8794i	−1.00879	−	1.00879i	−0.999961	−	0.00882847i	$-0.997190\pi$
$163$	−12.8794	−	12.8794i	−1.00879	−	1.00879i	−0.00882847	−	0.999961i	$-0.502810\pi$
$164$	5.65442			0.441536
$165$		0			0
$166$	11.3043			0.877385
$167$	1.49091	+	1.49091i	0.115370	+	0.115370i	0.762435	−	0.647065i	$-0.224004\pi$
$167$	1.49091	+	1.49091i	0.115370	+	0.115370i	−0.647065	+	0.762435i	$0.724004\pi$
$168$	1.03570	+	0.369961i	0.0799056	+	0.0285431i
$169$		−	10.9165i		−	0.839732i
$170$		0			0
$171$	0.534932	−	0.653223i	0.0409073	−	0.0499532i
$172$	1.16036	−	1.16036i	0.0884769	−	0.0884769i
$173$	12.3165	−	12.3165i	0.936404	−	0.936404i	−0.0616917	−	0.998095i	$-0.519650\pi$
$173$	12.3165	−	12.3165i	0.936404	−	0.936404i	0.998095	+	0.0616917i	$0.0196495\pi$
$174$	24.6435	−	11.6714i	1.86822	−	0.884809i
$175$		0			0
$176$		−	4.86173i		−	0.366466i
$177$	−1.56283	+	4.37510i	−0.117469	+	0.328852i
$178$	−3.41582	−	3.41582i	−0.256027	−	0.256027i
$179$	20.3135			1.51830			0.759151	−	0.650915i	$-0.225615\pi$
$179$	20.3135			1.51830			0.759151	+	0.650915i	$0.225615\pi$
$180$		0			0
$181$	−14.0192			−1.04204			−0.521020	−	0.853544i	$-0.674448\pi$
$181$	−14.0192			−1.04204			−0.521020	+	0.853544i	$0.674448\pi$
$182$	0.472413	+	0.472413i	0.0350176	+	0.0350176i
$183$	−5.51758	+	15.4463i	−0.407871	+	1.14183i
$184$		−	16.4235i		−	1.21075i
$185$		0			0
$186$	−11.3392	+	5.37037i	−0.831430	+	0.393775i
$187$	−2.87911	+	2.87911i	−0.210541	+	0.210541i
$188$	−2.50372	+	2.50372i	−0.182603	+	0.182603i
$189$	−0.358189	+	1.43965i	−0.0260544	+	0.104719i
$190$		0			0
$191$		−	18.9839i		−	1.37363i	−0.726832	−	0.686815i	$-0.759008\pi$
$191$		−	18.9839i		−	1.37363i	0.726832	−	0.686815i	$-0.240992\pi$
$192$	−6.78048	−	2.42205i	−0.489339	−	0.174797i
$193$	0.749286	+	0.749286i	0.0539348	+	0.0539348i	0.733560	−	0.679625i	$-0.237857\pi$
$193$	0.749286	+	0.749286i	0.0539348	+	0.0539348i	−0.679625	+	0.733560i	$0.737857\pi$
$194$	−26.1678			−1.87874
$195$		0			0
$196$	−4.34584			−0.310417
$197$	−0.218136	−	0.218136i	−0.0155416	−	0.0155416i	0.699293	−	0.714835i	$-0.253498\pi$
$197$	−0.218136	−	0.218136i	−0.0155416	−	0.0155416i	−0.714835	+	0.699293i	$0.753498\pi$
$198$	4.83954	−	0.481818i	0.343931	−	0.0342413i
$199$		−	2.62375i		−	0.185993i	−0.995666	−	0.0929964i	$-0.970355\pi$
$199$		−	2.62375i		−	0.185993i	0.995666	−	0.0929964i	$-0.0296445\pi$
$200$		0			0
$201$	−6.58010	−	13.8935i	−0.464125	−	0.979969i
$202$	19.3189	−	19.3189i	1.35927	−	1.35927i
$203$	−1.96048	+	1.96048i	−0.137599	+	0.137599i
$204$	−1.89615	−	4.00360i	−0.132757	−	0.280308i
$205$		0			0
$206$			10.9788i			0.764928i
$207$	22.0451	−	2.19478i	1.53224	−	0.152548i
$208$	−4.96216	−	4.96216i	−0.344064	−	0.344064i
$209$	0.281435			0.0194673
$210$		0			0
$211$	−10.1379			−0.697919			−0.348959	−	0.937138i	$-0.613465\pi$
$211$	−10.1379			−0.697919			−0.348959	+	0.937138i	$0.613465\pi$
$212$	2.98892	+	2.98892i	0.205280	+	0.205280i
$213$	−1.10781	−	0.395721i	−0.0759060	−	0.0271144i
$214$			1.25503i			0.0857923i
$215$		0			0
$216$	2.79015	−	11.2143i	0.189846	−	0.763035i
$217$	0.902076	−	0.902076i	0.0612369	−	0.0612369i
$218$	−0.288000	+	0.288000i	−0.0195058	+	0.0195058i
$219$	12.7102	−	6.01969i	0.858875	−	0.406773i
$220$		0			0
$221$			5.87717i			0.395341i
$222$	3.17798	−	8.89668i	0.213292	−	0.597106i
$223$	−15.2100	−	15.2100i	−1.01854	−	1.01854i	−0.999825	−	0.0187139i	$-0.994043\pi$
$223$	−15.2100	−	15.2100i	−1.01854	−	1.01854i	−0.0187139	−	0.999825i	$-0.505957\pi$
$224$	−0.980330			−0.0655011
$225$		0			0
$226$	5.50587			0.366245
$227$	−9.77054	−	9.77054i	−0.648494	−	0.648494i	0.304135	−	0.952629i	$-0.401633\pi$
$227$	−9.77054	−	9.77054i	−0.648494	−	0.648494i	−0.952629	+	0.304135i	$0.901633\pi$
$228$	−0.103002	+	0.288353i	−0.00682150	+	0.0190966i
$229$			19.5023i			1.28875i	0.764711	+	0.644373i	$0.222882\pi$
$229$			19.5023i			1.28875i	−0.764711	+	0.644373i	$0.777118\pi$
$230$		0			0
$231$	−0.446922	+	0.211667i	−0.0294053	+	0.0139267i
$232$	15.2714	−	15.2714i	1.00262	−	1.00262i
$233$	10.3725	−	10.3725i	0.679522	−	0.679522i	−0.280370	−	0.959892i	$-0.590457\pi$
$233$	10.3725	−	10.3725i	0.679522	−	0.679522i	0.959892	+	0.280370i	$0.0904570\pi$
$234$	4.44775	−	5.43129i	0.290758	−	0.355054i
$235$		0			0
$236$		−	1.68487i		−	0.109676i
$237$	−20.4107	−	7.29090i	−1.32582	−	0.473595i
$238$	1.33260	+	1.33260i	0.0863796	+	0.0863796i
$239$	−26.0494			−1.68499			−0.842497	−	0.538701i	$-0.818915\pi$
$239$	−26.0494			−1.68499			−0.842497	+	0.538701i	$0.818915\pi$
$240$		0			0
$241$	2.19788			0.141578			0.0707890	−	0.997491i	$-0.477448\pi$
$241$	2.19788			0.141578			0.0707890	+	0.997491i	$0.477448\pi$
$242$	1.14633	+	1.14633i	0.0736889	+	0.0736889i
$243$	15.4257	+	2.24656i	0.989561	+	0.144117i
$244$		−	5.94846i		−	0.380811i
$245$		0			0
$246$	10.8190	+	22.8437i	0.689796	+	1.45646i
$247$	0.287249	−	0.287249i	0.0182772	−	0.0182772i
$248$	−7.02682	+	7.02682i	−0.446203	+	0.446203i
$249$	5.16960	+	10.9153i	0.327610	+	0.691727i
$250$		0			0
$251$		−	3.44023i		−	0.217145i	−0.994089	−	0.108573i	$-0.965372\pi$
$251$		−	3.44023i		−	0.217145i	0.994089	−	0.108573i	$-0.0346280\pi$
$252$	−0.0533012	−	0.535376i	−0.00335766	−	0.0337255i
$253$	5.22177	+	5.22177i	0.328290	+	0.328290i
$254$	6.61938			0.415337
$255$		0			0
$256$	13.7442			0.859010
$257$	−11.6741	−	11.6741i	−0.728213	−	0.728213i	0.242051	−	0.970264i	$-0.422180\pi$
$257$	−11.6741	−	11.6741i	−0.728213	−	0.728213i	−0.970264	+	0.242051i	$0.922180\pi$
$258$	6.90804	+	2.46762i	0.430076	+	0.153627i
$259$			0.960586i			0.0596879i
$260$		0			0
$261$	22.5395	+	18.4579i	1.39516	+	1.14251i
$262$	−19.7820	+	19.7820i	−1.22214	+	1.22214i
$263$	15.9766	−	15.9766i	0.985158	−	0.985158i	−0.0147331	−	0.999891i	$-0.504690\pi$
$263$	15.9766	−	15.9766i	0.985158	−	0.985158i	0.999891	+	0.0147331i	$0.00468987\pi$
$264$	3.48135	−	1.64881i	0.214262	−	0.101477i
$265$		0			0
$266$		−	0.130263i		−	0.00798692i
$267$	1.73617	−	4.86036i	0.106252	−	0.297449i
$268$	3.94224	+	3.94224i	0.240810	+	0.240810i
$269$	1.98520			0.121040			0.0605200	−	0.998167i	$-0.480724\pi$
$269$	1.98520			0.121040			0.0605200	+	0.998167i	$0.480724\pi$
$270$		0			0
$271$	−16.7391			−1.01683			−0.508413	−	0.861113i	$-0.669768\pi$
$271$	−16.7391			−1.01683			−0.508413	+	0.861113i	$0.669768\pi$
$272$	−13.9974	−	13.9974i	−0.848720	−	0.848720i
$273$	−0.240114	+	0.672195i	−0.0145324	+	0.0406831i
$274$			32.9377i			1.98984i
$275$		0			0
$276$	−7.26123	+	3.43900i	−0.437075	+	0.207004i
$277$	15.6387	−	15.6387i	0.939637	−	0.939637i	−0.0586420	−	0.998279i	$-0.518677\pi$
$277$	15.6387	−	15.6387i	0.939637	−	0.939637i	0.998279	+	0.0586420i	$0.0186770\pi$
$278$	4.12948	−	4.12948i	0.247670	−	0.247670i
$279$	−10.3711	−	8.49301i	−0.620901	−	0.508463i
$280$		0			0
$281$		−	11.1500i		−	0.665153i	−0.943076	−	0.332577i	$-0.892082\pi$
$281$		−	11.1500i		−	0.665153i	0.943076	−	0.332577i	$-0.107918\pi$
$282$	−14.9055	−	5.32440i	−0.887610	−	0.317063i
$283$	−9.74142	−	9.74142i	−0.579068	−	0.579068i	0.355579	−	0.934646i	$-0.384284\pi$
$283$	−9.74142	−	9.74142i	−0.579068	−	0.579068i	−0.934646	+	0.355579i	$0.884284\pi$
$284$	0.426624			0.0253155
$285$		0			0
$286$	2.34002			0.138368
$287$	−1.81730	−	1.81730i	−0.107272	−	0.107272i
$288$	1.02050	+	10.2503i	0.0601336	+	0.604003i
$289$		−	0.421449i		−	0.0247911i
$290$		0			0
$291$	−11.9668	−	25.2672i	−0.701509	−	1.48119i
$292$	−3.60648	+	3.60648i	−0.211053	+	0.211053i
$293$	−3.70667	+	3.70667i	−0.216546	+	0.216546i	−0.807041	−	0.590495i	$-0.798932\pi$
$293$	−3.70667	+	3.70667i	−0.216546	+	0.216546i	0.590495	+	0.807041i	$0.298932\pi$
$294$	−8.31522	−	17.5570i	−0.484953	−	1.02395i
$295$		0			0
$296$		−	7.48259i		−	0.434916i
$297$	2.67842	+	4.45265i	0.155418	+	0.258369i
$298$	−13.3591	−	13.3591i	−0.773872	−	0.773872i
$299$	10.6593			0.616442
$300$		0			0
$301$	−0.745870			−0.0429912
$302$	19.1845	+	19.1845i	1.10395	+	1.10395i
$303$	27.4888	+	9.81926i	1.57919	+	0.564102i
$304$			1.36826i			0.0784751i
$305$		0			0
$306$	12.5464	−	15.3208i	0.717229	−	0.875831i
$307$	−5.20688	+	5.20688i	−0.297172	+	0.297172i	−0.839905	−	0.542733i	$-0.817390\pi$
$307$	−5.20688	+	5.20688i	−0.297172	+	0.297172i	0.542733	+	0.839905i	$0.317390\pi$
$308$	0.126813	−	0.126813i	0.00722585	−	0.00722585i
$309$	−10.6009	+	5.02073i	−0.603067	+	0.285619i
$310$		0			0
$311$			22.2889i			1.26389i	0.775013	+	0.631945i	$0.217743\pi$
$311$			22.2889i			1.26389i	−0.775013	+	0.631945i	$0.782257\pi$
$312$	1.87040	−	5.23613i	0.105890	−	0.296437i
$313$	8.76264	+	8.76264i	0.495293	+	0.495293i	0.909969	−	0.414676i	$-0.136105\pi$
$313$	8.76264	+	8.76264i	0.495293	+	0.495293i	−0.414676	+	0.909969i	$0.636105\pi$
$314$	20.5913			1.16204
$315$		0			0
$316$	7.86026			0.442174
$317$	18.4371	+	18.4371i	1.03553	+	1.03553i	0.999345	+	0.0361858i	$0.0115208\pi$
$317$	18.4371	+	18.4371i	1.03553	+	1.03553i	0.0361858	+	0.999345i	$0.488479\pi$
$318$	−6.35622	+	17.7941i	−0.356439	+	0.997842i
$319$			9.71095i			0.543709i
$320$		0			0
$321$	−1.21184	+	0.573942i	−0.0676384	+	0.0320343i
$322$	2.41690	−	2.41690i	0.134689	−	0.134689i
$323$	0.810283	−	0.810283i	0.0450853	−	0.0450853i
$324$	−5.54237	+	1.11463i	−0.307909	+	0.0619238i
$325$		0			0
$326$			29.5280i			1.63541i
$327$	−0.409794	−	0.146382i	−0.0226617	−	0.00809496i
$328$	14.1561	+	14.1561i	0.781639	+	0.781639i
$329$	1.60937			0.0887273
$330$		0			0
$331$	−0.848055			−0.0466133			−0.0233067	−	0.999728i	$-0.507419\pi$
$331$	−0.848055			−0.0466133			−0.0233067	+	0.999728i	$0.507419\pi$
$332$	−3.09718	−	3.09718i	−0.169980	−	0.169980i
$333$	10.0438	−	0.999948i	0.550398	−	0.0547968i
$334$		−	3.41815i		−	0.187033i
$335$		0			0
$336$	−1.02907	−	2.17281i	−0.0561403	−	0.118537i
$337$	−24.8680	+	24.8680i	−1.35465	+	1.35465i	−0.474264	+	0.880383i	$0.657286\pi$
$337$	−24.8680	+	24.8680i	−1.35465	+	1.35465i	−0.880383	+	0.474264i	$0.842714\pi$
$338$	−12.5139	+	12.5139i	−0.680669	+	0.680669i
$339$	2.51790	+	5.31639i	0.136754	+	0.288747i
$340$		0			0
$341$		−	4.46829i		−	0.241972i
$342$	−1.36202	+	0.135600i	−0.0736495	+	0.00733243i
$343$	2.80992	+	2.80992i	0.151721	+	0.151721i
$344$	5.81003			0.313256
$345$		0			0
$346$	−28.2375			−1.51806
$347$	7.84495	+	7.84495i	0.421139	+	0.421139i	0.885596	−	0.464457i	$-0.153750\pi$
$347$	7.84495	+	7.84495i	0.421139	+	0.421139i	−0.464457	+	0.885596i	$0.653750\pi$
$348$	−9.94964	−	3.55411i	−0.533357	−	0.190520i
$349$			3.21032i			0.171845i	0.996302	+	0.0859223i	$0.0273837\pi$
$349$			3.21032i			0.171845i	−0.996302	+	0.0859223i	$0.972616\pi$
$350$		0			0
$351$	7.27838	+	1.81088i	0.388491	+	0.0966577i
$352$	−2.42796	+	2.42796i	−0.129410	+	0.129410i
$353$	−2.32761	+	2.32761i	−0.123886	+	0.123886i	−0.766331	−	0.642445i	$-0.777920\pi$
$353$	−2.32761	+	2.32761i	−0.123886	+	0.123886i	0.642445	+	0.766331i	$0.277920\pi$
$354$	6.80683	−	3.22379i	0.361779	−	0.171343i
$355$		0			0
$356$			1.87175i			0.0992024i
$357$	−0.677324	+	1.89615i	−0.0358478	+	0.100355i
$358$	−23.2860	−	23.2860i	−1.23070	−	1.23070i
$359$	−11.6869			−0.616811			−0.308406	−	0.951255i	$-0.599795\pi$
$359$	−11.6869			−0.616811			−0.308406	+	0.951255i	$0.599795\pi$
$360$		0			0
$361$	18.9208			0.995831
$362$	16.0707	+	16.0707i	0.844655	+	0.844655i
$363$	−0.582649	+	1.63111i	−0.0305811	+	0.0856111i
$364$		−	0.258865i		−	0.0135682i
$365$		0			0
$366$	24.0316	−	11.3816i	1.25615	−	0.594927i
$367$	6.60685	−	6.60685i	0.344875	−	0.344875i	−0.513321	−	0.858196i	$-0.671585\pi$
$367$	6.60685	−	6.60685i	0.344875	−	0.344875i	0.858196	+	0.513321i	$0.171585\pi$
$368$	−25.3868	+	25.3868i	−1.32338	+	1.32338i
$369$	−17.1098	+	20.8934i	−0.890703	+	1.08767i
$370$		0			0
$371$		−	1.92125i		−	0.0997463i
$372$	4.57812	+	1.63535i	0.237365	+	0.0847890i
$373$	12.6827	+	12.6827i	0.656683	+	0.656683i	0.954594	−	0.297911i	$-0.0962898\pi$
$373$	12.6827	+	12.6827i	0.656683	+	0.656683i	−0.297911	+	0.954594i	$0.596290\pi$
$374$	6.60083			0.341321
$375$		0			0
$376$	−12.5363			−0.646512
$377$	9.91155	+	9.91155i	0.510471	+	0.510471i
$378$	2.06091	−	1.23971i	0.106002	−	0.0637638i
$379$		−	6.12762i		−	0.314755i	−0.987539	−	0.157377i	$-0.949696\pi$
$379$		−	6.12762i		−	0.314755i	0.987539	−	0.157377i	$-0.0503039\pi$
$380$		0			0
$381$	3.02712	+	6.39157i	0.155084	+	0.327450i
$382$	−21.7619	+	21.7619i	−1.11343	+	1.11343i
$383$	20.8849	−	20.8849i	1.06717	−	1.06717i	0.0695907	−	0.997576i	$-0.477831\pi$
$383$	20.8849	−	20.8849i	1.06717	−	1.06717i	0.997576	−	0.0695907i	$-0.0221693\pi$
$384$	10.0874	+	21.2990i	0.514772	+	1.08691i
$385$		0			0
$386$		−	1.71786i		−	0.0874367i
$387$	0.776434	+	7.79877i	0.0394684	+	0.396434i
$388$	7.16951	+	7.16951i	0.363977	+	0.363977i
$389$	−17.8685			−0.905968			−0.452984	−	0.891519i	$-0.649640\pi$
$389$	−17.8685			−0.905968			−0.452984	+	0.891519i	$0.649640\pi$
$390$		0			0
$391$	30.0681			1.52061
$392$	−10.8800	−	10.8800i	−0.549522	−	0.549522i
$393$	−28.1478	−	10.0547i	−1.41987	−	0.507191i
$394$			0.500113i			0.0251953i
$395$		0			0
$396$	−1.45796	−	1.19394i	−0.0732652	−	0.0599977i
$397$	−10.2866	+	10.2866i	−0.516271	+	0.516271i	−0.916441	−	0.400170i	$-0.868951\pi$
$397$	−10.2866	+	10.2866i	−0.516271	+	0.516271i	0.400170	+	0.916441i	$0.368951\pi$
$398$	−3.00769	+	3.00769i	−0.150762	+	0.150762i
$399$	0.125780	−	0.0595707i	0.00629686	−	0.00298226i
$400$		0			0
$401$			23.5884i			1.17795i	0.808151	+	0.588975i	$0.200468\pi$
$401$			23.5884i			1.17795i	−0.808151	+	0.588975i	$0.799532\pi$
$402$	−8.38353	+	23.4695i	−0.418132	+	1.17055i
$403$	−4.56060	−	4.56060i	−0.227180	−	0.227180i
$404$	−10.5861			−0.526677
$405$		0			0
$406$	4.49473			0.223069
$407$	2.37906	+	2.37906i	0.117925	+	0.117925i
$408$	5.27609	−	14.7703i	0.261205	−	0.731238i
$409$			12.6076i			0.623405i	0.950180	+	0.311703i	$0.100899\pi$
$409$			12.6076i			0.623405i	−0.950180	+	0.311703i	$0.899101\pi$
$410$		0			0
$411$	−31.8042	+	15.0628i	−1.56878	+	0.742994i
$412$	3.00799	−	3.00799i	0.148193	−	0.148193i
$413$	−0.541509	+	0.541509i	−0.0266459	+	0.0266459i
$414$	−27.7869	−	22.7550i	−1.36565	−	1.11835i
$415$		0			0
$416$			4.95622i			0.242999i
$417$	5.87582	+	2.09890i	0.287740	+	0.102784i
$418$	−0.322618	−	0.322618i	−0.0157798	−	0.0157798i
$419$	33.5948			1.64121			0.820606	−	0.571495i	$-0.193636\pi$
$419$	33.5948			1.64121			0.820606	+	0.571495i	$0.193636\pi$
$420$		0			0
$421$	−11.1669			−0.544240			−0.272120	−	0.962263i	$-0.587725\pi$
$421$	−11.1669			−0.544240			−0.272120	+	0.962263i	$0.587725\pi$
$422$	11.6213	+	11.6213i	0.565718	+	0.565718i
$423$	−1.67532	−	16.8274i	−0.0814566	−	0.818178i
$424$			14.9658i			0.726802i
$425$		0			0
$426$	0.816292	+	1.72355i	0.0395495	+	0.0835061i
$427$	−1.91181	+	1.91181i	−0.0925187	+	0.0925187i
$428$	0.343857	−	0.343857i	0.0166209	−	0.0166209i
$429$	1.07012	+	2.25949i	0.0516659	+	0.109089i
$430$		0			0
$431$			3.65334i			0.175975i	0.996122	+	0.0879875i	$0.0280436\pi$
$431$			3.65334i			0.175975i	−0.996122	+	0.0879875i	$0.971956\pi$
$432$	−21.6476	+	13.0217i	−1.04152	+	0.626508i
$433$	−3.56615	−	3.56615i	−0.171378	−	0.171378i	0.616207	−	0.787585i	$-0.288669\pi$
$433$	−3.56615	−	3.56615i	−0.171378	−	0.171378i	−0.787585	+	0.616207i	$0.788669\pi$
$434$	−2.06816			−0.0992747
$435$		0			0
$436$	0.157814			0.00755790
$437$	−1.46959	−	1.46959i	−0.0703000	−	0.0703000i
$438$	−21.4706	−	7.66952i	−1.02591	−	0.366464i
$439$		−	34.7868i		−	1.66028i	−0.557552	−	0.830142i	$-0.688259\pi$
$439$		−	34.7868i		−	1.66028i	0.557552	−	0.830142i	$-0.311741\pi$
$440$		0			0
$441$	13.1502	−	16.0581i	0.626198	−	0.764671i
$442$	6.73718	−	6.73718i	0.320455	−	0.320455i
$443$	10.4616	−	10.4616i	0.497045	−	0.497045i	−0.413472	−	0.910517i	$-0.635684\pi$
$443$	10.4616	−	10.4616i	0.497045	−	0.497045i	0.910517	+	0.413472i	$0.135684\pi$
$444$	−3.30824	+	1.56682i	−0.157002	+	0.0743581i
$445$		0			0
$446$			34.8714i			1.65121i
$447$	6.79007	−	19.0086i	0.321159	−	0.899077i
$448$	−0.839226	−	0.839226i	−0.0396497	−	0.0396497i
$449$	18.1102			0.854671			0.427335	−	0.904093i	$-0.359452\pi$
$449$	18.1102			0.854671			0.427335	+	0.904093i	$0.359452\pi$
$450$		0			0
$451$	−9.00173			−0.423875
$452$	−1.50851	−	1.50851i	−0.0709544	−	0.0709544i
$453$	−9.75097	+	27.2976i	−0.458140	+	1.28255i
$454$			22.4005i			1.05131i
$455$		0			0
$456$	−0.979774	+	0.464032i	−0.0458821	+	0.0217303i
$457$	4.07759	−	4.07759i	0.190742	−	0.190742i	−0.605275	−	0.796016i	$-0.706937\pi$
$457$	4.07759	−	4.07759i	0.190742	−	0.190742i	0.796016	+	0.605275i	$0.206937\pi$
$458$	22.3561	−	22.3561i	1.04463	−	1.04463i
$459$	20.5311	+	5.10821i	0.958311	+	0.238431i
$460$		0			0
$461$		−	22.5889i		−	1.05207i	−0.850462	−	0.526036i	$-0.823678\pi$
$461$		−	22.5889i		−	1.05207i	0.850462	−	0.526036i	$-0.176322\pi$
$462$	0.754962	+	0.269680i	0.0351240	+	0.0125466i
$463$	4.81057	+	4.81057i	0.223566	+	0.223566i	0.809998	−	0.586432i	$-0.199468\pi$
$463$	4.81057	+	4.81057i	0.223566	+	0.223566i	−0.586432	+	0.809998i	$0.699468\pi$
$464$	−47.2120			−2.19176
$465$		0			0
$466$	−23.7805			−1.10161
$467$	−4.10549	−	4.10549i	−0.189979	−	0.189979i	0.605708	−	0.795687i	$-0.292890\pi$
$467$	−4.10549	−	4.10549i	−0.189979	−	0.189979i	−0.795687	+	0.605708i	$0.792890\pi$
$468$	−2.70668	+	0.269473i	−0.125116	+	0.0124564i
$469$		−	2.53403i		−	0.117011i
$470$		0			0
$471$	9.41666	+	19.8827i	0.433897	+	0.916145i
$472$	4.21814	−	4.21814i	0.194156	−	0.194156i
$473$	−1.84728	+	1.84728i	−0.0849378	+	0.0849378i
$474$	15.0396	+	31.7552i	0.690793	+	1.45856i
$475$		0			0
$476$		−	0.730218i		−	0.0334695i
$477$	−20.0885	+	1.99998i	−0.919787	+	0.0915726i
$478$	29.8612	+	29.8612i	1.36582	+	1.36582i
$479$	−5.74056			−0.262293			−0.131146	−	0.991363i	$-0.541866\pi$
$479$	−5.74056			−0.262293			−0.131146	+	0.991363i	$0.541866\pi$
$480$		0			0
$481$	4.85640			0.221433
$482$	−2.51950	−	2.51950i	−0.114760	−	0.114760i
$483$	3.43900	+	1.22845i	0.156480	+	0.0558962i
$484$		−	0.628149i		−	0.0285522i
$485$		0			0
$486$	−15.1077	−	20.2583i	−0.685299	−	0.918934i
$487$	−15.2791	+	15.2791i	−0.692361	+	0.692361i	−0.962751	−	0.270390i	$-0.912847\pi$
$487$	−15.2791	+	15.2791i	−0.692361	+	0.692361i	0.270390	+	0.962751i	$0.412847\pi$
$488$	14.8922	−	14.8922i	0.674139	−	0.674139i
$489$	−28.5118	+	13.5035i	−1.28935	+	0.610650i
$490$		0			0
$491$			9.79503i			0.442043i	0.975269	+	0.221022i	$0.0709392\pi$
$491$			9.79503i			0.442043i	−0.975269	+	0.221022i	$0.929061\pi$
$492$	3.29454	−	9.22299i	0.148529	−	0.415804i
$493$	27.9589	+	27.9589i	1.25920	+	1.25920i
$494$	−0.658565			−0.0296302
$495$		0			0
$496$	21.7236			0.975419
$497$	−0.137115	−	0.137115i	−0.00615044	−	0.00615044i
$498$	6.58644	−	18.4386i	0.295146	−	0.826253i
$499$		−	0.929617i		−	0.0416154i	−0.999783	−	0.0208077i	$-0.993376\pi$
$499$		−	0.929617i		−	0.0416154i	0.999783	−	0.0208077i	$-0.00662377\pi$
$500$		0			0
$501$	3.30051	−	1.56316i	0.147456	−	0.0698368i
$502$	−3.94364	+	3.94364i	−0.176013	+	0.176013i
$503$	−6.49027	+	6.49027i	−0.289387	+	0.289387i	−0.836838	−	0.547451i	$-0.815598\pi$
$503$	−6.49027	+	6.49027i	−0.289387	+	0.289387i	0.547451	+	0.836838i	$0.315598\pi$
$504$	1.20689	−	1.47378i	0.0537593	−	0.0656472i
$505$		0			0
$506$		−	11.9718i		−	0.532209i
$507$	−17.8060	−	6.36049i	−0.790794	−	0.282479i
$508$	−1.81359	−	1.81359i	−0.0804651	−	0.0804651i
$509$	13.0970			0.580515			0.290257	−	0.956949i	$-0.406259\pi$
$509$	13.0970			0.580515			0.290257	+	0.956949i	$0.406259\pi$
$510$		0			0
$511$	2.31821			0.102552
$512$	3.48700	+	3.48700i	0.154105	+	0.154105i
$513$	−0.753801	−	1.25313i	−0.0332811	−	0.0553271i
$514$			26.7649i			1.18055i
$515$		0			0
$516$	−1.21660	−	2.56876i	−0.0535577	−	0.113084i
$517$	3.98588	−	3.98588i	0.175299	−	0.175299i
$518$	1.10115	−	1.10115i	0.0483817	−	0.0483817i
$519$	−12.9133	−	27.2657i	−0.566833	−	1.19683i
$520$		0			0
$521$		−	3.26098i		−	0.142866i	−0.997445	−	0.0714330i	$-0.977243\pi$
$521$		−	3.26098i		−	0.142866i	0.997445	−	0.0714330i	$-0.0227572\pi$
$522$	−4.67891	−	46.9966i	−0.204790	−	2.05698i
$523$	17.8320	+	17.8320i	0.779737	+	0.779737i	0.979786	−	0.200049i	$-0.0641100\pi$
$523$	17.8320	+	17.8320i	0.779737	+	0.779737i	−0.200049	+	0.979786i	$0.564110\pi$
$524$	10.8399			0.473541
$525$		0			0
$526$	−36.6289			−1.59710
$527$	−12.8647	−	12.8647i	−0.560396	−	0.560396i
$528$	−7.93001	−	2.83268i	−0.345109	−	0.123276i
$529$		−	31.5338i		−	1.37103i
$530$		0			0
$531$	6.22569	+	5.09829i	0.270172	+	0.221247i
$532$	−0.0356897	+	0.0356897i	−0.00154734	+	0.00154734i
$533$	−9.18768	+	9.18768i	−0.397963	+	0.397963i
$534$	−7.56180	+	3.58136i	−0.327231	+	0.154980i
$535$		0			0
$536$			19.7391i			0.852599i
$537$	11.8356	−	33.1335i	0.510745	−	1.42982i
$538$	−2.27570	−	2.27570i	−0.0981124	−	0.0981124i
$539$	6.91849			0.298000
$540$		0			0
$541$	29.4057			1.26425			0.632125	−	0.774866i	$-0.282183\pi$
$541$	29.4057			1.26425			0.632125	+	0.774866i	$0.282183\pi$
$542$	19.1885	+	19.1885i	0.824218	+	0.824218i
$543$	−8.16828	+	22.8669i	−0.350534	+	0.981312i
$544$			13.9807i			0.599418i
$545$		0			0
$546$	1.04581	−	0.495307i	0.0447564	−	0.0211972i
$547$	6.91991	−	6.91991i	0.295874	−	0.295874i	−0.543521	−	0.839395i	$-0.682909\pi$
$547$	6.91991	−	6.91991i	0.295874	−	0.295874i	0.839395	+	0.543521i	$0.182909\pi$
$548$	9.02436	−	9.02436i	0.385501	−	0.385501i
$549$	21.9799	+	17.9996i	0.938078	+	0.768203i
$550$		0			0
$551$		−	2.73300i		−	0.116430i
$552$	−26.7885	−	9.56911i	−1.14019	−	0.407288i
$553$	−2.52625	−	2.52625i	−0.107427	−	0.107427i
$554$	−35.8542			−1.52330
$555$		0			0
$556$	−2.26281			−0.0959644
$557$	3.53461	+	3.53461i	0.149766	+	0.149766i	0.778014	−	0.628247i	$-0.216227\pi$
$557$	3.53461	+	3.53461i	0.149766	+	0.149766i	−0.628247	+	0.778014i	$0.716227\pi$
$558$	2.15290	+	21.6245i	0.0911397	+	0.915438i
$559$			3.77087i			0.159491i
$560$		0			0
$561$	3.01864	+	6.37366i	0.127447	+	0.269096i
$562$	−12.7816	+	12.7816i	−0.539159	+	0.539159i
$563$	−11.1629	+	11.1629i	−0.470458	+	0.470458i	−0.902063	−	0.431605i	$-0.857948\pi$
$563$	−11.1629	+	11.1629i	−0.470458	+	0.470458i	0.431605	+	0.902063i	$0.357948\pi$
$564$	2.62506	+	5.54264i	0.110535	+	0.233387i
$565$		0			0
$566$			22.3338i			0.938759i
$567$	2.13953	+	1.42305i	0.0898516	+	0.0597626i
$568$	1.06807	+	1.06807i	0.0448152	+	0.0448152i
$569$	11.5279			0.483275			0.241637	−	0.970367i	$-0.422316\pi$
$569$	11.5279			0.483275			0.241637	+	0.970367i	$0.422316\pi$
$570$		0			0
$571$	37.5721			1.57234			0.786172	−	0.618008i	$-0.212060\pi$
$571$	37.5721			1.57234			0.786172	+	0.618008i	$0.212060\pi$
$572$	−0.641125	−	0.641125i	−0.0268068	−	0.0268068i
$573$	−30.9649	−	11.0610i	−1.29358	−	0.462079i
$574$			4.16646i			0.173905i
$575$		0			0
$576$	−7.90127	+	9.64850i	−0.329220	+	0.402021i
$577$	9.80937	−	9.80937i	0.408369	−	0.408369i	−0.472800	−	0.881170i	$-0.656757\pi$
$577$	9.80937	−	9.80937i	0.408369	−	0.408369i	0.881170	+	0.472800i	$0.156757\pi$
$578$	−0.483120	+	0.483120i	−0.0200951	+	0.0200951i
$579$	1.65874	−	0.785598i	0.0689348	−	0.0326483i
$580$		0			0
$581$			1.99084i			0.0825939i
$582$	−15.2466	+	42.6826i	−0.631993	+	1.76925i
$583$	−4.75830	−	4.75830i	−0.197069	−	0.197069i
$584$	−18.0580			−0.747243
$585$		0			0
$586$	8.49813			0.351055
$587$	−28.3158	−	28.3158i	−1.16872	−	1.16872i	−0.982510	−	0.186209i	$-0.940380\pi$
$587$	−28.3158	−	28.3158i	−1.16872	−	1.16872i	−0.186209	−	0.982510i	$-0.559620\pi$
$588$	−2.53210	+	7.08854i	−0.104422	+	0.292326i
$589$			1.25754i			0.0518158i
$590$		0			0
$591$	−0.482901	+	0.228708i	−0.0198639	+	0.00940778i
$592$	−11.5663	+	11.5663i	−0.475373	+	0.475373i
$593$	22.0674	−	22.0674i	0.906199	−	0.906199i	−0.0897641	−	0.995963i	$-0.528611\pi$
$593$	22.0674	−	22.0674i	0.906199	−	0.906199i	0.995963	+	0.0897641i	$0.0286113\pi$
$594$	2.03386	−	8.17456i	0.0834501	−	0.335406i
$595$		0			0
$596$			7.32031i			0.299852i
$597$	−4.27963	−	1.52873i	−0.175154	−	0.0625666i
$598$	−12.2191	−	12.2191i	−0.499674	−	0.499674i
$599$	13.7723			0.562721			0.281361	−	0.959602i	$-0.409214\pi$
$599$	13.7723			0.562721			0.281361	+	0.959602i	$0.409214\pi$
$600$		0			0
$601$	47.6415			1.94334			0.971669	−	0.236346i	$-0.0759500\pi$
$601$	47.6415			1.94334			0.971669	+	0.236346i	$0.0759500\pi$
$602$	0.855014	+	0.855014i	0.0348478	+	0.0348478i
$603$	−26.4957	+	2.63787i	−1.07899	+	0.107422i
$604$		−	10.5124i		−	0.427745i
$605$		0			0
$606$	−20.2551	−	42.7674i	−0.822808	−	1.73731i
$607$	24.2606	−	24.2606i	0.984709	−	0.984709i	−0.0151761	−	0.999885i	$-0.504831\pi$
$607$	24.2606	−	24.2606i	0.984709	−	0.984709i	0.999885	+	0.0151761i	$0.00483087\pi$
$608$	0.683312	−	0.683312i	0.0277120	−	0.0277120i
$609$	2.05549	+	4.34004i	0.0832927	+	0.175867i
$610$		0			0
$611$		−	8.13643i		−	0.329165i
$612$	−7.63511	+	0.760140i	−0.308631	+	0.0307268i
$613$	−2.32722	−	2.32722i	−0.0939954	−	0.0939954i	0.658546	−	0.752541i	$-0.271172\pi$
$613$	−2.32722	−	2.32722i	−0.0939954	−	0.0939954i	−0.752541	+	0.658546i	$0.771172\pi$
$614$	11.9376			0.481763
$615$		0			0
$616$	0.634963			0.0255834
$617$	14.3887	+	14.3887i	0.579267	+	0.579267i	0.934701	−	0.355434i	$-0.115667\pi$
$617$	14.3887	+	14.3887i	0.579267	+	0.579267i	−0.355434	+	0.934701i	$0.615667\pi$
$618$	17.9076	+	6.39677i	0.720349	+	0.257316i
$619$		−	0.383560i		−	0.0154166i	−0.999970	−	0.00770829i	$-0.997546\pi$
$619$		−	0.383560i		−	0.0154166i	0.999970	−	0.00770829i	$-0.00245365\pi$
$620$		0			0
$621$	9.26463	−	37.2368i	0.371777	−	1.49426i
$622$	25.5505	−	25.5505i	1.02448	−	1.02448i
$623$	0.601571	−	0.601571i	0.0241014	−	0.0241014i
$624$	−10.9850	+	5.20263i	−0.439753	+	0.208272i
$625$		0			0
$626$		−	20.0898i		−	0.802948i
$627$	0.163978	−	0.459052i	0.00654864	−	0.0183328i
$628$	−5.64166	−	5.64166i	−0.225127	−	0.225127i
$629$	13.6991			0.546220
$630$		0			0
$631$	15.5344			0.618416			0.309208	−	0.950994i	$-0.399936\pi$
$631$	15.5344			0.618416			0.309208	+	0.950994i	$0.399936\pi$
$632$	19.6785	+	19.6785i	0.782768	+	0.782768i
$633$	−5.90681	+	16.5360i	−0.234774	+	0.657245i
$634$		−	42.2700i		−	1.67876i
$635$		0			0
$636$	6.61675	−	3.13377i	0.262371	−	0.124262i
$637$	7.06140	−	7.06140i	0.279783	−	0.279783i
$638$	11.1320	−	11.1320i	0.440718	−	0.440718i
$639$	−1.29093	+	1.57640i	−0.0510684	+	0.0623613i
$640$		0			0
$641$		−	30.7396i		−	1.21414i	−0.794648	−	0.607071i	$-0.792344\pi$
$641$		−	30.7396i		−	1.21414i	0.794648	−	0.607071i	$-0.207656\pi$
$642$	2.04710	+	0.731243i	0.0807925	+	0.0288599i
$643$	−5.50784	−	5.50784i	−0.217208	−	0.217208i	0.590113	−	0.807321i	$-0.299083\pi$
$643$	−5.50784	−	5.50784i	−0.217208	−	0.217208i	−0.807321	+	0.590113i	$0.799083\pi$
$644$	−1.32438			−0.0521878
$645$		0			0
$646$	−1.85770			−0.0730904
$647$	1.83127	+	1.83127i	0.0719945	+	0.0719945i	0.742187	−	0.670193i	$-0.233789\pi$
$647$	1.83127	+	1.83127i	0.0719945	+	0.0719945i	−0.670193	+	0.742187i	$0.733789\pi$
$648$	−16.6661	−	11.0850i	−0.654704	−	0.435461i
$649$			2.68228i			0.105289i
$650$		0			0
$651$	−0.945793	−	1.99698i	−0.0370685	−	0.0782678i
$652$	8.09015	−	8.09015i	0.316835	−	0.316835i
$653$	−2.26241	+	2.26241i	−0.0885350	+	0.0885350i	−0.749987	−	0.661452i	$-0.769940\pi$
$653$	−2.26241	+	2.26241i	−0.0885350	+	0.0885350i	0.661452	+	0.749987i	$0.269940\pi$
$654$	0.301957	+	0.637562i	0.0118074	+	0.0249306i
$655$		0			0
$656$		−	43.7639i		−	1.70870i
$657$	−2.41321	−	24.2391i	−0.0941481	−	0.945656i
$658$	−1.84487	−	1.84487i	−0.0719204	−	0.0719204i
$659$	−21.4513			−0.835624			−0.417812	−	0.908534i	$-0.637203\pi$
$659$	−21.4513			−0.835624			−0.417812	+	0.908534i	$0.637203\pi$
$660$		0			0
$661$	−23.6158			−0.918548			−0.459274	−	0.888295i	$-0.651890\pi$
$661$	−23.6158			−0.918548			−0.459274	+	0.888295i	$0.651890\pi$
$662$	0.972152	+	0.972152i	0.0377837	+	0.0377837i
$663$	9.58631	+	3.42433i	0.372302	+	0.132990i
$664$		−	15.5078i		−	0.601821i
$665$		0			0
$666$	−12.6598	−	10.3673i	−0.490558	−	0.401724i
$667$	50.7083	−	50.7083i	1.96343	−	1.96343i
$668$	−0.936511	+	0.936511i	−0.0362347	+	0.0362347i
$669$	−33.6713	+	15.9471i	−1.30181	+	0.616552i
$670$		0			0
$671$			9.46983i			0.365579i
$672$	−0.571188	+	1.59903i	−0.0220341	+	0.0616838i
$673$	−5.74356	−	5.74356i	−0.221398	−	0.221398i	0.587689	−	0.809087i	$-0.300038\pi$
$673$	−5.74356	−	5.74356i	−0.221398	−	0.221398i	−0.809087	+	0.587689i	$0.800038\pi$
$674$	57.0139			2.19609
$675$		0			0
$676$	6.85719			0.263738
$677$	1.13494	+	1.13494i	0.0436194	+	0.0436194i	0.728580	−	0.684961i	$-0.240181\pi$
$677$	1.13494	+	1.13494i	0.0436194	+	0.0436194i	−0.684961	+	0.728580i	$0.740181\pi$
$678$	3.20799	−	8.98069i	0.123202	−	0.344901i
$679$		−	4.60849i		−	0.176858i
$680$		0			0
$681$	−21.6296	+	10.2440i	−0.828849	+	0.392552i
$682$	−5.12214	+	5.12214i	−0.196137	+	0.196137i
$683$	−1.61763	+	1.61763i	−0.0618968	+	0.0618968i	−0.737378	−	0.675481i	$-0.763936\pi$
$683$	−1.61763	+	1.61763i	−0.0618968	+	0.0618968i	0.675481	+	0.737378i	$0.263936\pi$
$684$	0.410321	+	0.336017i	0.0156890	+	0.0128479i
$685$		0			0
$686$		−	6.44219i		−	0.245964i
$687$	31.8104	+	11.3630i	1.21364	+	0.433524i
$688$	−8.98095	−	8.98095i	−0.342395	−	0.342395i
$689$	−9.71319			−0.370043
$690$		0			0
$691$	−26.3783			−1.00348			−0.501739	−	0.865019i	$-0.667306\pi$
$691$	−26.3783			−1.00348			−0.501739	+	0.865019i	$0.667306\pi$
$692$	7.73657	+	7.73657i	0.294100	+	0.294100i
$693$	0.0848544	+	0.852307i	0.00322335	+	0.0323765i
$694$		−	17.9858i		−	0.682732i
$695$		0			0
$696$	−16.0115	−	33.8072i	−0.606913	−	1.28146i
$697$	−25.9170	+	25.9170i	−0.981675	+	0.981675i
$698$	3.68009	−	3.68009i	0.139293	−	0.139293i
$699$	−10.8751	−	22.9621i	−0.411335	−	0.868507i
$700$		0			0
$701$		−	11.2314i		−	0.424205i	−0.977247	−	0.212102i	$-0.931969\pi$
$701$		−	11.2314i		−	0.424205i	0.977247	−	0.212102i	$-0.0680310\pi$
$702$	−6.26756	−	10.4193i	−0.236554	−	0.393251i
$703$	−0.669550	−	0.669550i	−0.0252526	−	0.0252526i
$704$	−4.15697			−0.156672
$705$		0			0
$706$	5.33641			0.200839
$707$	3.40231	+	3.40231i	0.127957	+	0.127957i
$708$	−2.74821	−	0.981688i	−0.103284	−	0.0368941i
$709$		−	13.2746i		−	0.498538i	−0.968434	−	0.249269i	$-0.919810\pi$
$709$		−	13.2746i		−	0.498538i	0.968434	−	0.249269i	$-0.0801903\pi$
$710$		0			0
$711$	−23.7845	+	29.0441i	−0.891989	+	1.08924i
$712$	−4.68600	+	4.68600i	−0.175615	+	0.175615i
$713$	−23.3324	+	23.3324i	−0.873805	+	0.873805i
$714$	2.95006	−	1.39718i	0.110403	−	0.0522882i
$715$		0			0
$716$			12.7599i			0.476859i
$717$	−15.1776	+	42.4894i	−0.566819	+	1.58680i
$718$	13.3971	+	13.3971i	0.499974	+	0.499974i
$719$	45.9916			1.71520			0.857600	−	0.514318i	$-0.171955\pi$
$719$	45.9916			1.71520			0.857600	+	0.514318i	$0.171955\pi$
$720$		0			0
$721$	−1.93351			−0.0720076
$722$	−21.6895	−	21.6895i	−0.807199	−	0.807199i
$723$	1.28059	−	3.58499i	0.0476257	−	0.133327i
$724$		−	8.80615i		−	0.327278i
$725$		0			0
$726$	2.53770	−	1.20188i	0.0941829	−	0.0446061i
$727$	5.64032	−	5.64032i	0.209188	−	0.209188i	−0.594734	−	0.803922i	$-0.702743\pi$
$727$	5.64032	−	5.64032i	0.209188	−	0.209188i	0.803922	+	0.594734i	$0.202743\pi$
$728$	0.648080	−	0.648080i	0.0240194	−	0.0240194i
$729$	12.6522	−	23.8521i	0.468598	−	0.883411i
$730$		0			0
$731$			10.6370i			0.393424i
$732$	−9.70259	−	3.46586i	−0.358618	−	0.128102i
$733$	−33.8431	−	33.8431i	−1.25002	−	1.25002i	−0.955709	−	0.294313i	$-0.904909\pi$
$733$	−33.8431	−	33.8431i	−1.25002	−	1.25002i	−0.294313	−	0.955709i	$-0.595091\pi$
$734$	−15.1473			−0.559096
$735$		0			0
$736$	25.3565			0.934651
$737$	−6.27596	−	6.27596i	−0.231178	−	0.231178i
$738$	43.5643	−	4.33719i	1.60362	−	0.159654i
$739$		−	5.33288i		−	0.196173i	−0.995178	−	0.0980866i	$-0.968728\pi$
$739$		−	5.33288i		−	0.196173i	0.995178	−	0.0980866i	$-0.0312722\pi$
$740$		0			0
$741$	−0.301169	−	0.635900i	−0.0110637	−	0.0233604i
$742$	−2.20239	+	2.20239i	−0.0808522	+	0.0808522i
$743$	−28.7768	+	28.7768i	−1.05572	+	1.05572i	−0.0573664	+	0.998353i	$0.518270\pi$
$743$	−28.7768	+	28.7768i	−1.05572	+	1.05572i	−0.998353	+	0.0573664i	$0.981730\pi$
$744$	7.36735	+	15.5557i	0.270100	+	0.570299i
$745$		0			0
$746$		−	29.0770i		−	1.06459i
$747$	20.8161	−	2.07242i	0.761620	−	0.0758258i
$748$	−1.80851	−	1.80851i	−0.0661256	−	0.0661256i
$749$	−0.221028			−0.00807618
$750$		0			0
$751$	14.4158			0.526040			0.263020	−	0.964790i	$-0.415281\pi$
$751$	14.4158			0.526040			0.263020	+	0.964790i	$0.415281\pi$
$752$	19.3782	+	19.3782i	0.706652	+	0.706652i
$753$	−5.61140	−	2.00445i	−0.204491	−	0.0730461i
$754$		−	22.7238i		−	0.827553i
$755$		0			0
$756$	−0.904312	−	0.224996i	−0.0328895	−	0.00818301i
$757$	−28.9382	+	28.9382i	−1.05178	+	1.05178i	−0.0531933	+	0.998584i	$0.516940\pi$
$757$	−28.9382	+	28.9382i	−1.05178	+	1.05178i	−0.998584	+	0.0531933i	$0.983060\pi$
$758$	−7.02428	+	7.02428i	−0.255133	+	0.255133i
$759$	11.5597	−	5.47482i	0.419592	−	0.198724i
$760$		0			0
$761$			18.7778i			0.680696i	0.940299	+	0.340348i	$0.110545\pi$
$761$			18.7778i			0.680696i	−0.940299	+	0.340348i	$0.889455\pi$
$762$	3.85677	−	10.7969i	0.139716	−	0.391132i
$763$	−0.0507205	−	0.0507205i	−0.00183621	−	0.00183621i
$764$	11.9247			0.431422
$765$		0			0
$766$	−47.8819			−1.73004
$767$	2.73769	+	2.73769i	0.0988523	+	0.0988523i
$768$	8.00801	−	22.4182i	0.288964	−	0.808948i
$769$		−	0.107567i		−	0.00387895i	−0.999998	−	0.00193948i	$-0.999383\pi$
$769$		−	0.107567i		−	0.00387895i	0.999998	−	0.00193948i	$-0.000617355\pi$
$770$		0			0
$771$	−25.8437	+	12.2399i	−0.930740	+	0.440809i
$772$	−0.470663	+	0.470663i	−0.0169395	+	0.0169395i
$773$	4.72647	−	4.72647i	0.169999	−	0.169999i	−0.616980	−	0.786979i	$-0.711644\pi$
$773$	4.72647	−	4.72647i	0.169999	−	0.169999i	0.786979	+	0.616980i	$0.211644\pi$
$774$	8.04992	−	9.83002i	0.289348	−	0.353333i
$775$		0			0
$776$			35.8983i			1.28867i
$777$	1.56682	+	0.559684i	0.0562094	+	0.0200786i
$778$	20.4832	+	20.4832i	0.734358	+	0.734358i
$779$	2.53340			0.0907686
$780$		0			0
$781$	−0.679177			−0.0243029
$782$	−34.4680	−	34.4680i	−1.23257	−	1.23257i
$783$	43.2394	−	26.0100i	1.54525	−	0.929521i
$784$			33.6358i			1.20128i
$785$		0			0
$786$	20.7407	+	43.7927i	0.739797	+	1.56203i
$787$	20.3978	−	20.3978i	0.727103	−	0.727103i	−0.242939	−	0.970042i	$-0.578111\pi$
$787$	20.3978	−	20.3978i	0.727103	−	0.727103i	0.970042	+	0.242939i	$0.0781115\pi$
$788$	0.137022	−	0.137022i	0.00488121	−	0.00488121i
$789$	−16.7508	−	35.3683i	−0.596346	−	1.25914i
$790$		0			0
$791$			0.969657i			0.0344770i
$792$	−0.660982	−	6.63914i	−0.0234870	−	0.235911i
$793$	9.66545	+	9.66545i	0.343230	+	0.343230i
$794$	23.5838			0.836957
$795$		0			0
$796$	1.64811			0.0584156
$797$	15.7865	+	15.7865i	0.559186	+	0.559186i	0.929076	−	0.369889i	$-0.120604\pi$
$797$	15.7865	+	15.7865i	0.559186	+	0.559186i	−0.369889	+	0.929076i	$0.620604\pi$
$798$	−0.212473	−	0.0758974i	−0.00752145	−	0.00268674i
$799$		−	22.9515i		−	0.811967i
$800$		0			0
$801$	−6.91620	−	5.66376i	−0.244372	−	0.200119i
$802$	27.0401	−	27.0401i	0.954821	−	0.954821i
$803$	5.74145	−	5.74145i	0.202611	−	0.202611i
$804$	8.72716	−	4.13328i	0.307783	−	0.145770i
$805$		0			0
$806$			10.4559i			0.368294i
$807$	1.15668	−	3.23808i	0.0407169	−	0.113986i
$808$	−26.5026	−	26.5026i	−0.932360	−	0.932360i
$809$	−47.1778			−1.65868			−0.829341	−	0.558742i	$-0.811284\pi$
$809$	−47.1778			−1.65868			−0.829341	+	0.558742i	$0.811284\pi$
$810$		0			0
$811$	−42.0723			−1.47736			−0.738680	−	0.674057i	$-0.764550\pi$
$811$	−42.0723			−1.47736			−0.738680	+	0.674057i	$0.764550\pi$
$812$	−1.23148	−	1.23148i	−0.0432163	−	0.0432163i
$813$	−9.75300	+	27.3033i	−0.342053	+	0.957568i
$814$		−	5.45437i		−	0.191176i
$815$		0			0
$816$	−30.9870	+	14.6758i	−1.08476	+	0.513755i
$817$	0.519888	−	0.519888i	0.0181886	−	0.0181886i
$818$	14.4525	−	14.4525i	0.505319	−	0.505319i
$819$	0.956521	+	0.783306i	0.0334235	+	0.0273709i
$820$		0			0
$821$			44.0134i			1.53608i	0.640403	+	0.768039i	$0.278767\pi$
$821$			44.0134i			1.53608i	−0.640403	+	0.768039i	$0.721233\pi$
$822$	53.7251	+	19.1911i	1.87388	+	0.669368i
$823$	12.1320	+	12.1320i	0.422896	+	0.422896i	0.886200	−	0.463303i	$-0.153336\pi$
$823$	12.1320	+	12.1320i	0.422896	+	0.422896i	−0.463303	+	0.886200i	$0.653336\pi$
$824$	15.0613			0.524684
$825$		0			0
$826$	1.24150			0.0431972
$827$	−14.5719	−	14.5719i	−0.506716	−	0.506716i	0.406801	−	0.913517i	$-0.366644\pi$
$827$	−14.5719	−	14.5719i	−0.506716	−	0.506716i	−0.913517	+	0.406801i	$0.866644\pi$
$828$	1.37865	+	13.8476i	0.0479113	+	0.481237i
$829$			34.3317i			1.19239i	0.802840	+	0.596195i	$0.203321\pi$
$829$			34.3317i			1.19239i	−0.802840	+	0.596195i	$0.796679\pi$
$830$		0			0
$831$	−16.3966	−	34.6203i	−0.568790	−	1.20096i
$832$	−4.24284	+	4.24284i	−0.147094	+	0.147094i
$833$	19.9191	−	19.9191i	0.690155	−	0.690155i
$834$	−4.32960	−	9.14167i	−0.149922	−	0.316550i
$835$		0			0
$836$			0.176783i			0.00611417i
$837$	−19.8957	+	11.9680i	−0.687697	+	0.413673i
$838$	−38.5107	−	38.5107i	−1.33033	−	1.33033i
$839$	7.37612			0.254652			0.127326	−	0.991861i	$-0.459361\pi$
$839$	7.37612			0.254652			0.127326	+	0.991861i	$0.459361\pi$
$840$		0			0
$841$	65.3025			2.25181
$842$	12.8009	+	12.8009i	0.441149	+	0.441149i
$843$	−18.1869	−	6.49653i	−0.626389	−	0.223752i
$844$		−	6.36808i		−	0.219198i
$845$		0			0
$846$	−17.3694	+	21.2103i	−0.597171	+	0.729225i
$847$	−0.201884	+	0.201884i	−0.00693681	+	0.00693681i
$848$	23.1336	−	23.1336i	0.794410	−	0.794410i
$849$	−21.5652	+	10.2135i	−0.740115	+	0.350527i
$850$		0			0
$851$		−	24.8458i		−	0.851702i
$852$	0.248572	−	0.695871i	0.00851593	−	0.0238401i
$853$	22.1377	+	22.1377i	0.757980	+	0.757980i	0.975955	−	0.217974i	$-0.0699449\pi$
$853$	22.1377	+	22.1377i	0.757980	+	0.757980i	−0.217974	+	0.975955i	$0.569945\pi$
$854$	4.38312			0.149987
$855$		0			0
$856$	1.72172			0.0588471
$857$	8.67169	+	8.67169i	0.296219	+	0.296219i	0.839531	−	0.543312i	$-0.182830\pi$
$857$	8.67169	+	8.67169i	0.296219	+	0.296219i	−0.543312	+	0.839531i	$0.682830\pi$
$858$	1.36341	−	3.81683i	0.0465461	−	0.130305i
$859$			15.3607i			0.524101i	0.965054	+	0.262050i	$0.0843987\pi$
$859$			15.3607i			0.524101i	−0.965054	+	0.262050i	$0.915601\pi$
$860$		0			0
$861$	−4.02307	+	1.90537i	−0.137106	+	0.0649350i
$862$	4.18793	−	4.18793i	0.142642	−	0.142642i
$863$	25.8970	−	25.8970i	0.881543	−	0.881543i	−0.112149	−	0.993691i	$-0.535773\pi$
$863$	25.8970	−	25.8970i	0.881543	−	0.881543i	0.993691	+	0.112149i	$0.0357732\pi$
$864$	17.3139	+	4.30775i	0.589031	+	0.146553i
$865$		0			0
$866$			8.17597i			0.277831i
$867$	−0.687429	−	0.245556i	−0.0233463	−	0.00833953i
$868$	0.566638	+	0.566638i	0.0192329	+	0.0192329i
$869$	−12.5134			−0.424487
$870$		0			0
$871$	−12.8112			−0.434091
$872$	0.395093	+	0.395093i	0.0133795	+	0.0133795i
$873$	−48.1861	+	4.79733i	−1.63085	+	0.162365i
$874$			3.36927i			0.113967i
$875$		0			0
$876$	3.78126	+	7.98388i	0.127757	+	0.269750i
$877$	−11.3433	+	11.3433i	−0.383037	+	0.383037i	−0.872195	−	0.489158i	$-0.837304\pi$
$877$	−11.3433	+	11.3433i	−0.383037	+	0.383037i	0.489158	+	0.872195i	$0.337304\pi$
$878$	−39.8772	+	39.8772i	−1.34579	+	1.34579i
$879$	3.88630	+	8.20566i	0.131082	+	0.276770i
$880$		0			0
$881$			45.7437i			1.54115i	0.637352	+	0.770573i	$0.280030\pi$
$881$			45.7437i			1.54115i	−0.637352	+	0.770573i	$0.719970\pi$
$882$	−33.4823	+	3.33345i	−1.12741	+	0.112243i
$883$	−33.5492	−	33.5492i	−1.12902	−	1.12902i	−0.990337	−	0.138685i	$-0.955713\pi$
$883$	−33.5492	−	33.5492i	−1.12902	−	1.12902i	−0.138685	−	0.990337i	$-0.544287\pi$
$884$	−3.69174			−0.124167
$885$		0			0
$886$	−23.9849			−0.805788
$887$	41.1834	+	41.1834i	1.38280	+	1.38280i	0.839601	+	0.543204i	$0.182789\pi$
$887$	41.1834	+	41.1834i	1.38280	+	1.38280i	0.543204	+	0.839601i	$0.317211\pi$
$888$	−12.2049	−	4.35972i	−0.409570	−	0.146303i
$889$			1.16576i			0.0390983i
$890$		0			0
$891$	8.82334	−	1.77446i	0.295593	−	0.0594468i
$892$	9.55416	−	9.55416i	0.319897	−	0.319897i
$893$	−1.12177	+	1.12177i	−0.0375384	+	0.0375384i
$894$	−29.5738	+	14.0065i	−0.989097	+	0.468448i
$895$		0			0
$896$			3.88472i			0.129779i
$897$	6.21061	−	17.3865i	0.207366	−	0.580517i
$898$	−20.7602	−	20.7602i	−0.692778	−	0.692778i
$899$	−43.3914			−1.44718
$900$		0			0
$901$	−27.3994			−0.912805
$902$	10.3190	+	10.3190i	0.343584	+	0.343584i
$903$	−0.434580	+	1.21660i	−0.0144619	+	0.0404858i
$904$		−	7.55324i		−	0.251217i
$905$		0			0
$906$	42.4699	−	20.1142i	1.41097	−	0.668251i
$907$	−40.3742	+	40.3742i	−1.34060	+	1.34060i	−0.445143	+	0.895459i	$0.646847\pi$
$907$	−40.3742	+	40.3742i	−1.34060	+	1.34060i	−0.895459	+	0.445143i	$0.853153\pi$
$908$	6.13735	−	6.13735i	0.203675	−	0.203675i
$909$	32.0326	−	39.1161i	1.06245	−	1.29740i
$910$		0			0
$911$			3.96308i			0.131303i	0.997843	+	0.0656514i	$0.0209125\pi$
$911$			3.96308i			0.131303i	−0.997843	+	0.0656514i	$0.979087\pi$
$912$	2.23178	+	0.797215i	0.0739018	+	0.0263984i
$913$	4.93065	+	4.93065i	0.163181	+	0.163181i
$914$	−9.34853			−0.309222
$915$		0			0
$916$	−12.2503			−0.404762
$917$	−3.48388	−	3.48388i	−0.115048	−	0.115048i
$918$	−17.6798	−	29.3912i	−0.583519	−	0.970053i
$919$			7.06389i			0.233016i	0.993190	+	0.116508i	$0.0371701\pi$
$919$			7.06389i			0.233016i	−0.993190	+	0.116508i	$0.962830\pi$
$920$		0			0
$921$	5.45921	+	11.5268i	0.179887	+	0.379820i
$922$	−25.8944	+	25.8944i	−0.852787	+	0.852787i
$923$	−0.693207	+	0.693207i	−0.0228172	+	0.0228172i
$924$	−0.132959	−	0.280734i	−0.00437402	−	0.00923546i
$925$		0			0
$926$		−	11.0290i		−	0.362436i
$927$	2.01274	+	20.2166i	0.0661070	+	0.664001i
$928$	23.5778	+	23.5778i	0.773978	+	0.773978i
$929$	5.42663			0.178042			0.0890210	−	0.996030i	$-0.471626\pi$
$929$	5.42663			0.178042			0.0890210	+	0.996030i	$0.471626\pi$
$930$		0			0
$931$	−1.94711			−0.0638138
$932$	6.51545	+	6.51545i	0.213421	+	0.213421i
$933$	36.3557	+	12.9866i	1.19023	+	0.425163i
$934$			9.41249i			0.307986i
$935$		0			0
$936$	−7.45092	−	6.10165i	−0.243541	−	0.199439i
$937$	−29.0081	+	29.0081i	−0.947653	+	0.947653i	−0.998696	−	0.0510439i	$-0.983745\pi$
$937$	−29.0081	+	29.0081i	−0.947653	+	0.947653i	0.0510439	+	0.998696i	$0.483745\pi$
$938$	−2.90484	+	2.90484i	−0.0948463	+	0.0948463i
$939$	19.3984	−	9.18729i	0.633042	−	0.299816i
$940$		0			0
$941$			17.7369i			0.578208i	0.957298	+	0.289104i	$0.0933573\pi$
$941$			17.7369i			0.578208i	−0.957298	+	0.289104i	$0.906643\pi$
$942$	11.9975	−	33.5867i	0.390900	−	1.09431i
$943$	47.0050	+	47.0050i	1.53069	+	1.53069i
$944$	−13.0405			−0.424433
$945$		0			0
$946$	4.23518			0.137697
$947$	14.6533	+	14.6533i	0.476169	+	0.476169i	0.903904	−	0.427735i	$-0.140688\pi$
$947$	14.6533	+	14.6533i	0.476169	+	0.476169i	−0.427735	+	0.903904i	$0.640688\pi$
$948$	4.57977	−	12.8209i	0.148744	−	0.416405i
$949$		−	11.7201i		−	0.380451i
$950$		0			0
$951$	40.8153	−	19.3306i	1.32353	−	0.626838i
$952$	1.82813	−	1.82813i	0.0592500	−	0.0592500i
$953$	−11.7199	+	11.7199i	−0.379646	+	0.379646i	−0.870975	−	0.491328i	$-0.836512\pi$
$953$	−11.7199	+	11.7199i	−0.379646	+	0.379646i	0.491328	+	0.870975i	$0.336512\pi$
$954$	25.3206	+	20.7354i	0.819786	+	0.671333i
$955$		0			0
$956$		−	16.3629i		−	0.529213i
$957$	15.8396	+	5.65807i	0.512022	+	0.182899i
$958$	6.58058	+	6.58058i	0.212609	+	0.212609i
$959$	−5.80077			−0.187317
$960$		0			0
$961$	−11.0344			−0.355947
$962$	−5.56704	−	5.56704i	−0.179489	−	0.179489i
$963$	0.230085	+	2.31105i	0.00741438	+	0.0744726i
$964$			1.38060i			0.0444660i
$965$		0			0
$966$	−2.53403	−	5.35044i	−0.0815311	−	0.172148i
$967$	21.1658	−	21.1658i	0.680647	−	0.680647i	−0.279499	−	0.960146i	$-0.590168\pi$
$967$	21.1658	−	21.1658i	0.680647	−	0.680647i	0.960146	+	0.279499i	$0.0901685\pi$
$968$	1.57260	−	1.57260i	0.0505451	−	0.0505451i
$969$	−0.849551	−	1.79377i	−0.0272915	−	0.0576242i
$970$		0			0
$971$		−	15.3244i		−	0.491783i	−0.969297	−	0.245891i	$-0.920919\pi$
$971$		−	15.3244i		−	0.491783i	0.969297	−	0.245891i	$-0.0790807\pi$
$972$	−1.41117	+	9.68965i	−0.0452634	+	0.310796i
$973$	0.727255	+	0.727255i	0.0233147	+	0.0233147i
$974$	35.0297			1.12243
$975$		0			0
$976$	−46.0397			−1.47370
$977$	9.31965	+	9.31965i	0.298162	+	0.298162i	0.840294	−	0.542132i	$-0.182383\pi$
$977$	9.31965	+	9.31965i	0.298162	+	0.298162i	−0.542132	+	0.840294i	$0.682383\pi$
$978$	48.1635	+	17.2045i	1.54010	+	0.550138i
$979$		−	2.97979i		−	0.0952344i
$980$		0			0
$981$	−0.477532	+	0.583129i	−0.0152464	+	0.0186179i
$982$	11.2283	−	11.2283i	0.358311	−	0.358311i
$983$	22.0174	−	22.0174i	0.702247	−	0.702247i	−0.262645	−	0.964892i	$-0.584595\pi$
$983$	22.0174	−	22.0174i	0.702247	−	0.702247i	0.964892	+	0.262645i	$0.0845949\pi$
$984$	31.3381	−	14.8421i	0.999024	−	0.473149i
$985$		0			0
$986$		−	64.1003i		−	2.04137i
$987$	0.937696	−	2.62506i	0.0298472	−	0.0835565i
$988$	0.180435	+	0.180435i	0.00574040	+	0.00574040i
$989$	19.2921			0.613453
$990$		0			0
$991$	−1.02170			−0.0324553			−0.0162276	−	0.999868i	$-0.505166\pi$
$991$	−1.02170			−0.0324553			−0.0162276	+	0.999868i	$0.505166\pi$
$992$	−10.8488	−	10.8488i	−0.344450	−	0.344450i
$993$	−0.494118	+	1.38327i	−0.0156804	+	0.0438968i
$994$			0.314358i			0.00997083i
$995$		0			0
$996$	−6.85641	+	3.24728i	−0.217254	+	0.102894i
$997$	23.8372	−	23.8372i	0.754932	−	0.754932i	−0.220464	−	0.975395i	$-0.570757\pi$
$997$	23.8372	−	23.8372i	0.754932	−	0.754932i	0.975395	+	0.220464i	$0.0707570\pi$
$998$	−1.06565	+	1.06565i	−0.0337325	+	0.0337325i
$999$	4.22100	−	16.9652i	0.133546	−	0.536755i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.k.j.518.2		16
3.2	odd	2		825.2.k.i.518.7		16
5.2	odd	4		825.2.k.i.782.7		16
5.3	odd	4		165.2.k.d.122.2	yes	16
5.4	even	2		165.2.k.c.23.7	✓	16
15.2	even	4	inner	825.2.k.j.782.2		16
15.8	even	4		165.2.k.c.122.7	yes	16
15.14	odd	2		165.2.k.d.23.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.k.c.23.7	✓	16	5.4	even	2
165.2.k.c.122.7	yes	16	15.8	even	4
165.2.k.d.23.2	yes	16	15.14	odd	2
165.2.k.d.122.2	yes	16	5.3	odd	4
825.2.k.i.518.7		16	3.2	odd	2
825.2.k.i.782.7		16	5.2	odd	4
825.2.k.j.518.2		16	1.1	even	1	trivial
825.2.k.j.782.2		16	15.2	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14633 - 1.14633i) q^{2} +(0.582649 - 1.63111i) q^{3} +0.628149i q^{4} +(-2.53770 + 1.20188i) q^{6} +(0.201884 - 0.201884i) q^{7} +(-1.57260 + 1.57260i) q^{8} +(-2.32104 - 1.90073i) q^{9} -1.00000i q^{11} +(1.02458 + 0.365990i) q^{12} +(-1.02066 - 1.02066i) q^{13} -0.462851 q^{14} +4.86173 q^{16} +(-2.87911 - 2.87911i) q^{17} +(0.481818 + 4.83954i) q^{18} +0.281435i q^{19} +(-0.211667 - 0.446922i) q^{21} +(-1.14633 + 1.14633i) q^{22} +(-5.22177 + 5.22177i) q^{23} +(1.64881 + 3.48135i) q^{24} +2.34002i q^{26} +(-4.45265 + 2.67842i) q^{27} +(0.126813 + 0.126813i) q^{28} -9.71095 q^{29} +4.46829 q^{31} +(-2.42796 - 2.42796i) q^{32} +(-1.63111 - 0.582649i) q^{33} +6.60083i q^{34} +(1.19394 - 1.45796i) q^{36} +(-2.37906 + 2.37906i) q^{37} +(0.322618 - 0.322618i) q^{38} +(-2.25949 + 1.07012i) q^{39} -9.00173i q^{41} +(-0.269680 + 0.754962i) q^{42} +(-1.84728 - 1.84728i) q^{43} +0.628149 q^{44} +11.9718 q^{46} +(3.98588 + 3.98588i) q^{47} +(2.83268 - 7.93001i) q^{48} +6.91849i q^{49} +(-6.37366 + 3.01864i) q^{51} +(0.641125 - 0.641125i) q^{52} +(4.75830 - 4.75830i) q^{53} +(8.17456 + 2.03386i) q^{54} +0.634963i q^{56} +(0.459052 + 0.163978i) q^{57} +(11.1320 + 11.1320i) q^{58} -2.68228 q^{59} -9.46983 q^{61} +(-5.12214 - 5.12214i) q^{62} +(-0.852307 + 0.0848544i) q^{63} -4.15697i q^{64} +(1.20188 + 2.53770i) q^{66} +(6.27596 - 6.27596i) q^{67} +(1.80851 - 1.80851i) q^{68} +(5.47482 + 11.5597i) q^{69} -0.679177i q^{71} +(6.63914 - 0.660982i) q^{72} +(5.74145 + 5.74145i) q^{73} +5.45437 q^{74} -0.176783 q^{76} +(-0.201884 - 0.201884i) q^{77} +(3.81683 + 1.36341i) q^{78} -12.5134i q^{79} +(1.77446 + 8.82334i) q^{81} +(-10.3190 + 10.3190i) q^{82} +(-4.93065 + 4.93065i) q^{83} +(0.280734 - 0.132959i) q^{84} +4.23518i q^{86} +(-5.65807 + 15.8396i) q^{87} +(1.57260 + 1.57260i) q^{88} +2.97979 q^{89} -0.412109 q^{91} +(-3.28005 - 3.28005i) q^{92} +(2.60345 - 7.28828i) q^{93} -9.13826i q^{94} +(-5.37491 + 2.54562i) q^{96} +(11.4137 - 11.4137i) q^{97} +(7.93087 - 7.93087i) q^{98} +(-1.90073 + 2.32104i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 2 q^{3} - 4 q^{6} - 8 q^{7} - 16 q^{8} + 6 q^{9} + 4 q^{12} - 24 q^{14} - 4 q^{16} - 8 q^{17} + 32 q^{18} - 8 q^{21} + 4 q^{22} - 14 q^{23} + 12 q^{24} + 20 q^{27} - 8 q^{28} - 16 q^{29}+ \cdots - 4 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 2 * q^3 - 4 * q^6 - 8 * q^7 - 16 * q^8 + 6 * q^9 + 4 * q^12 - 24 * q^14 - 4 * q^16 - 8 * q^17 + 32 * q^18 - 8 * q^21 + 4 * q^22 - 14 * q^23 + 12 * q^24 + 20 * q^27 - 8 * q^28 - 16 * q^29 + 8 * q^31 - 28 * q^32 - 4 * q^33 + 44 * q^36 + 6 * q^37 - 24 * q^38 + 24 * q^39 + 60 * q^42 - 16 * q^43 + 12 * q^44 - 32 * q^46 - 48 * q^47 + 48 * q^48 - 8 * q^51 - 36 * q^52 + 4 * q^53 + 4 * q^54 + 8 * q^57 + 12 * q^58 - 68 * q^59 - 8 * q^61 - 48 * q^62 + 12 * q^63 + 8 * q^66 - 6 * q^67 - 24 * q^68 + 12 * q^69 + 8 * q^72 + 8 * q^74 + 16 * q^76 + 8 * q^77 + 48 * q^78 + 2 * q^81 - 12 * q^82 + 8 * q^83 + 52 * q^84 + 36 * q^87 + 16 * q^88 + 32 * q^89 - 56 * q^91 - 20 * q^92 - 28 * q^93 + 80 * q^96 - 18 * q^97 - 16 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more