LMFDB - Embedded newform 196.2.j.a.111.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,2,Mod(27,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 1]))

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

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

chi := DirichletCharacter("196.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	196.j (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.56506787962$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			111.4
Character	$\chi$	$=$	196.111
Dual form			196.2.j.a.83.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33971 + 0.452975i) q^{2} +(0.470328 + 0.589772i) q^{3} +(1.58963 - 1.21371i) q^{4} +(0.701998 - 0.559824i) q^{5} +(-0.897253 - 0.577075i) q^{6} +(0.938659 - 2.47364i) q^{7} +(-1.57985 + 2.34607i) q^{8} +(0.540940 - 2.37001i) q^{9} +O(q^{10})$	\(q+(-1.33971 + 0.452975i) q^{2} +(0.470328 + 0.589772i) q^{3} +(1.58963 - 1.21371i) q^{4} +(0.701998 - 0.559824i) q^{5} +(-0.897253 - 0.577075i) q^{6} +(0.938659 - 2.47364i) q^{7} +(-1.57985 + 2.34607i) q^{8} +(0.540940 - 2.37001i) q^{9} +(-0.686884 + 1.06799i) q^{10} +(0.406550 - 0.0927925i) q^{11} +(1.46346 + 0.366677i) q^{12} +(0.0704045 - 0.0160694i) q^{13} +(-0.137027 + 3.73915i) q^{14} +(0.660338 + 0.150718i) q^{15} +(1.05383 - 3.85869i) q^{16} +(-1.30432 + 2.70845i) q^{17} +(0.348856 + 3.42015i) q^{18} +7.07149 q^{19} +(0.436451 - 1.74193i) q^{20} +(1.90036 - 0.609829i) q^{21} +(-0.502625 + 0.308472i) q^{22} +(-0.339993 - 0.706003i) q^{23} +(-2.12670 + 0.171670i) q^{24} +(-0.933207 + 4.08865i) q^{25} +(-0.0870424 + 0.0534197i) q^{26} +(3.69112 - 1.77755i) q^{27} +(-1.51017 - 5.07143i) q^{28} +(4.62837 + 2.22890i) q^{29} +(-0.952931 + 0.0971991i) q^{30} -2.54266 q^{31} +(0.336071 + 5.64686i) q^{32} +(0.245938 + 0.196129i) q^{33} +(0.520546 - 4.21935i) q^{34} +(-0.725871 - 2.26198i) q^{35} +(-2.01661 - 4.42398i) q^{36} +(-7.13701 - 3.43700i) q^{37} +(-9.47372 + 3.20321i) q^{38} +(0.0425905 + 0.0339648i) q^{39} +(0.204336 + 2.53138i) q^{40} +(-5.37941 + 4.28994i) q^{41} +(-2.26969 + 1.67781i) q^{42} +(-3.75265 - 2.99264i) q^{43} +(0.533640 - 0.640939i) q^{44} +(-0.947052 - 1.96657i) q^{45} +(0.775292 + 0.791828i) q^{46} +(0.549665 + 2.40824i) q^{47} +(2.77139 - 1.19333i) q^{48} +(-5.23784 - 4.64382i) q^{49} +(-0.601833 - 5.90031i) q^{50} +(-2.21083 + 0.504606i) q^{51} +(0.0924134 - 0.110995i) q^{52} +(-5.53554 + 2.66578i) q^{53} +(-4.13983 + 4.05338i) q^{54} +(0.233450 - 0.292737i) q^{55} +(4.32041 + 6.11016i) q^{56} +(3.32592 + 4.17057i) q^{57} +(-7.21029 - 0.889541i) q^{58} +(-6.25588 + 7.84462i) q^{59} +(1.23262 - 0.561872i) q^{60} +(5.42920 - 11.2738i) q^{61} +(3.40641 - 1.15176i) q^{62} +(-5.35481 - 3.56272i) q^{63} +(-3.00813 - 7.41291i) q^{64} +(0.0404278 - 0.0506948i) q^{65} +(-0.418327 - 0.151352i) q^{66} +10.3163i q^{67} +(1.21388 + 5.88848i) q^{68} +(0.256473 - 0.532571i) q^{69} +(1.99707 + 2.70158i) q^{70} +(-3.56667 - 7.40627i) q^{71} +(4.70562 + 5.01335i) q^{72} +(11.0764 + 2.52812i) q^{73} +(11.1184 + 1.37169i) q^{74} +(-2.85029 + 1.37262i) q^{75} +(11.2410 - 8.58272i) q^{76} +(0.152077 - 1.09276i) q^{77} +(-0.0724439 - 0.0262104i) q^{78} +8.93692i q^{79} +(-1.42040 - 3.29875i) q^{80} +(-3.78628 - 1.82337i) q^{81} +(5.26360 - 8.18400i) q^{82} +(0.295384 - 1.29416i) q^{83} +(2.28072 - 3.27589i) q^{84} +(0.600626 + 2.63151i) q^{85} +(6.38304 + 2.30940i) q^{86} +(0.862303 + 3.77800i) q^{87} +(-0.424592 + 1.10040i) q^{88} +(3.97228 + 0.906646i) q^{89} +(2.15958 + 2.20564i) q^{90} +(0.0263359 - 0.189239i) q^{91} +(-1.39734 - 0.709628i) q^{92} +(-1.19588 - 1.49959i) q^{93} +(-1.82726 - 2.97735i) q^{94} +(4.96417 - 3.95879i) q^{95} +(-3.17230 + 2.85408i) q^{96} +12.4755i q^{97} +(9.12070 + 3.84874i) q^{98} -1.01372i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9}+O(q^{10}) $ 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9	$ 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9} - 7 q^{10} - 42 q^{12} - 14 q^{13} + 21 q^{14} - 13 q^{16} - 14 q^{17} - 12 q^{18} - 7 q^{20} - 14 q^{21} + 3 q^{22} + 35 q^{24} - 7 q^{26} + 42 q^{28} - 30 q^{29} - 4 q^{30} - 5 q^{32} - 14 q^{33} + 77 q^{34} - 11 q^{36} + 10 q^{37} - 21 q^{38} - 63 q^{40} - 14 q^{41} - 7 q^{42} - 55 q^{44} - 14 q^{45} - 19 q^{46} - 132 q^{50} - 7 q^{52} - 2 q^{53} + 14 q^{54} - 70 q^{56} - 64 q^{57} - 3 q^{58} - 107 q^{60} + 14 q^{61} - 21 q^{62} - 11 q^{64} - 22 q^{65} + 161 q^{66} - 70 q^{69} - 77 q^{70} + 114 q^{72} - 14 q^{73} + 5 q^{74} + 70 q^{76} - 42 q^{77} + 61 q^{78} + 92 q^{81} - 42 q^{82} + 70 q^{84} - 6 q^{85} + 47 q^{86} + 65 q^{88} - 14 q^{89} + 112 q^{90} - 70 q^{92} - 48 q^{93} - 28 q^{94} + 238 q^{96} + 105 q^{98}+O(q^{100}) $ 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9 - 7 * q^10 - 42 * q^12 - 14 * q^13 + 21 * q^14 - 13 * q^16 - 14 * q^17 - 12 * q^18 - 7 * q^20 - 14 * q^21 + 3 * q^22 + 35 * q^24 - 7 * q^26 + 42 * q^28 - 30 * q^29 - 4 * q^30 - 5 * q^32 - 14 * q^33 + 77 * q^34 - 11 * q^36 + 10 * q^37 - 21 * q^38 - 63 * q^40 - 14 * q^41 - 7 * q^42 - 55 * q^44 - 14 * q^45 - 19 * q^46 - 132 * q^50 - 7 * q^52 - 2 * q^53 + 14 * q^54 - 70 * q^56 - 64 * q^57 - 3 * q^58 - 107 * q^60 + 14 * q^61 - 21 * q^62 - 11 * q^64 - 22 * q^65 + 161 * q^66 - 70 * q^69 - 77 * q^70 + 114 * q^72 - 14 * q^73 + 5 * q^74 + 70 * q^76 - 42 * q^77 + 61 * q^78 + 92 * q^81 - 42 * q^82 + 70 * q^84 - 6 * q^85 + 47 * q^86 + 65 * q^88 - 14 * q^89 + 112 * q^90 - 70 * q^92 - 48 * q^93 - 28 * q^94 + 238 * q^96 + 105 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{11}{14}\right)$

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 $

$2$	−1.33971	+	0.452975i	−0.947316	+	0.320302i
$2$	−1.33971	+	0.452975i	−0.947316	+	0.320302i
$3$	0.470328	+	0.589772i	0.271544	+	0.340505i	0.898841	−	0.438275i	$-0.144410\pi$
$3$	0.470328	+	0.589772i	0.271544	+	0.340505i	−0.627297	+	0.778780i	$0.715839\pi$
$4$	1.58963	−	1.21371i	0.794813	−	0.606854i
$5$	0.701998	−	0.559824i	0.313943	−	0.250361i	−0.453823	−	0.891092i	$-0.649940\pi$
$5$	0.701998	−	0.559824i	0.313943	−	0.250361i	0.767765	+	0.640731i	$0.221369\pi$
$6$	−0.897253	−	0.577075i	−0.366302	−	0.235590i
$7$	0.938659	−	2.47364i	0.354780	−	0.934950i
$7$	0.938659	−	2.47364i	0.354780	−	0.934950i
$8$	−1.57985	+	2.34607i	−0.558563	+	0.829462i
$9$	0.540940	−	2.37001i	0.180313	−	0.790004i
$10$	−0.686884	+	1.06799i	−0.217212	+	0.337727i
$11$	0.406550	−	0.0927925i	0.122580	−	0.0279780i	−0.160791	−	0.986988i	$-0.551405\pi$
$11$	0.406550	−	0.0927925i	0.122580	−	0.0279780i	0.283371	+	0.959010i	$0.408547\pi$
$12$	1.46346	+	0.366677i	0.422464	+	0.105851i
$13$	0.0704045	−	0.0160694i	0.0195267	−	0.00445684i	−0.212746	−	0.977107i	$-0.568241\pi$
$13$	0.0704045	−	0.0160694i	0.0195267	−	0.00445684i	0.232273	+	0.972651i	$0.425384\pi$
$14$	−0.137027	+	3.73915i	−0.0366221	+	0.999329i
$15$	0.660338	+	0.150718i	0.170499	+	0.0389152i
$16$	1.05383	−	3.85869i	0.263457	−	0.964671i
$17$	−1.30432	+	2.70845i	−0.316344	+	0.656895i	−0.997140	−	0.0755781i	$-0.975920\pi$
$17$	−1.30432	+	2.70845i	−0.316344	+	0.656895i	0.680796	+	0.732473i	$0.261634\pi$
$18$	0.348856	+	3.42015i	0.0822262	+	0.806137i
$19$	7.07149			1.62231			0.811156	−	0.584830i	$-0.198839\pi$
$19$	7.07149			1.62231			0.811156	+	0.584830i	$0.198839\pi$
$20$	0.436451	−	1.74193i	0.0975934	−	0.389508i
$21$	1.90036	−	0.609829i	0.414694	−	0.133076i
$22$	−0.502625	+	0.308472i	−0.107160	+	0.0657664i
$23$	−0.339993	−	0.706003i	−0.0708934	−	0.147212i	0.862510	−	0.506039i	$-0.168891\pi$
$23$	−0.339993	−	0.706003i	−0.0708934	−	0.147212i	−0.933404	+	0.358828i	$0.883177\pi$
$24$	−2.12670	+	0.171670i	−0.434110	+	0.0350419i
$25$	−0.933207	+	4.08865i	−0.186641	+	0.817730i
$26$	−0.0870424	+	0.0534197i	−0.0170704	+	0.0104765i
$27$	3.69112	−	1.77755i	0.710356	−	0.342089i
$28$	−1.51017	−	5.07143i	−0.285394	−	0.958410i
$29$	4.62837	+	2.22890i	0.859466	+	0.413897i	0.811082	−	0.584932i	$-0.198879\pi$
$29$	4.62837	+	2.22890i	0.859466	+	0.413897i	0.0483835	+	0.998829i	$0.484593\pi$
$30$	−0.952931	+	0.0971991i	−0.173981	+	0.0177461i
$31$	−2.54266			−0.456675			−0.228337	−	0.973582i	$-0.573329\pi$
$31$	−2.54266			−0.456675			−0.228337	+	0.973582i	$0.573329\pi$
$32$	0.336071	+	5.64686i	0.0594095	+	0.998234i
$33$	0.245938	+	0.196129i	0.0428124	+	0.0341417i
$34$	0.520546	−	4.21935i	0.0892728	−	0.723612i
$35$	−0.725871	−	2.26198i	−0.122695	−	0.382344i
$36$	−2.01661	−	4.42398i	−0.336102	−	0.737329i
$37$	−7.13701	−	3.43700i	−1.17332	−	0.565040i	−0.257360	−	0.966316i	$-0.582853\pi$
$37$	−7.13701	−	3.43700i	−1.17332	−	0.565040i	−0.915957	+	0.401276i	$0.868567\pi$
$38$	−9.47372	+	3.20321i	−1.53684	+	0.519629i
$39$	0.0425905	+	0.0339648i	0.00681993	+	0.00543871i
$40$	0.204336	+	2.53138i	0.0323084	+	0.400246i
$41$	−5.37941	+	4.28994i	−0.840123	+	0.669976i	−0.945916	−	0.324413i	$-0.894833\pi$
$41$	−5.37941	+	4.28994i	−0.840123	+	0.669976i	0.105793	+	0.994388i	$0.466262\pi$
$42$	−2.26969	+	1.67781i	−0.350221	+	0.258892i
$43$	−3.75265	−	2.99264i	−0.572274	−	0.456373i	0.294096	−	0.955776i	$-0.404981\pi$
$43$	−3.75265	−	2.99264i	−0.572274	−	0.456373i	−0.866370	+	0.499403i	$0.833553\pi$
$44$	0.533640	−	0.640939i	0.0804493	−	0.0966252i
$45$	−0.947052	−	1.96657i	−0.141178	−	0.293159i
$46$	0.775292	+	0.791828i	0.114311	+	0.116749i
$47$	0.549665	+	2.40824i	0.0801768	+	0.351278i	0.999065	−	0.0432413i	$-0.0137684\pi$
$47$	0.549665	+	2.40824i	0.0801768	+	0.351278i	−0.918888	+	0.394519i	$0.870911\pi$
$48$	2.77139	−	1.19333i	0.400016	−	0.172242i
$49$	−5.23784	−	4.64382i	−0.748263	−	0.663403i
$50$	−0.601833	−	5.90031i	−0.0851120	−	0.834430i
$51$	−2.21083	+	0.504606i	−0.309577	+	0.0706590i
$52$	0.0924134	−	0.110995i	0.0128154	−	0.0153922i
$53$	−5.53554	+	2.66578i	−0.760365	+	0.366172i	−0.773546	−	0.633741i	$-0.781519\pi$
$53$	−5.53554	+	2.66578i	−0.760365	+	0.366172i	0.0131807	+	0.999913i	$0.495804\pi$
$54$	−4.13983	+	4.05338i	−0.563359	+	0.551595i
$55$	0.233450	−	0.292737i	0.0314784	−	0.0394726i
$56$	4.32041	+	6.11016i	0.577339	+	0.816504i
$57$	3.32592	+	4.17057i	0.440529	+	0.552405i
$58$	−7.21029	−	0.889541i	−0.946757	−	0.116802i
$59$	−6.25588	+	7.84462i	−0.814446	+	1.02128i	0.184813	+	0.982774i	$0.440832\pi$
$59$	−6.25588	+	7.84462i	−0.814446	+	1.02128i	−0.999258	+	0.0385089i	$0.987739\pi$
$60$	1.23262	−	0.561872i	0.159130	−	0.0725374i
$61$	5.42920	−	11.2738i	0.695137	−	1.44347i	−0.191732	−	0.981447i	$-0.561410\pi$
$61$	5.42920	−	11.2738i	0.695137	−	1.44347i	0.886869	−	0.462020i	$-0.152875\pi$
$62$	3.40641	−	1.15176i	0.432615	−	0.146274i
$63$	−5.35481	−	3.56272i	−0.674642	−	0.448861i
$64$	−3.00813	−	7.41291i	−0.376016	−	0.926613i
$65$	0.0404278	−	0.0506948i	0.00501445	−	0.00628792i
$66$	−0.418327	−	0.151352i	−0.0514925	−	0.0186301i
$67$			10.3163i			1.26033i	0.776460	+	0.630166i	$0.217013\pi$
$67$			10.3163i			1.26033i	−0.776460	+	0.630166i	$0.782987\pi$
$68$	1.21388	+	5.88848i	0.147205	+	0.714084i
$69$	0.256473	−	0.532571i	0.0308757	−	0.0641140i
$70$	1.99707	+	2.70158i	0.238696	+	0.322901i
$71$	−3.56667	−	7.40627i	−0.423286	−	0.878962i	−0.998155	−	0.0607168i	$-0.980661\pi$
$71$	−3.56667	−	7.40627i	−0.423286	−	0.878962i	0.574869	−	0.818245i	$-0.305053\pi$
$72$	4.70562	+	5.01335i	0.554562	+	0.590830i
$73$	11.0764	+	2.52812i	1.29639	+	0.295894i	0.814412	−	0.580287i	$-0.197060\pi$
$73$	11.0764	+	2.52812i	1.29639	+	0.295894i	0.481983	+	0.876181i	$0.339917\pi$
$74$	11.1184	+	1.37169i	1.29249	+	0.159455i
$75$	−2.85029	+	1.37262i	−0.329123	+	0.158497i
$76$	11.2410	−	8.58272i	1.28943	−	0.984506i
$77$	0.152077	−	1.09276i	0.0173307	−	0.124532i
$78$	−0.0724439	−	0.0262104i	−0.00820266	−	0.00296774i
$79$			8.93692i			1.00548i	0.864437	+	0.502741i	$0.167675\pi$
$79$			8.93692i			1.00548i	−0.864437	+	0.502741i	$0.832325\pi$
$80$	−1.42040	−	3.29875i	−0.158806	−	0.368811i
$81$	−3.78628	−	1.82337i	−0.420697	−	0.202597i
$82$	5.26360	−	8.18400i	0.581267	−	0.903771i
$83$	0.295384	−	1.29416i	0.0324226	−	0.142053i	−0.956126	−	0.292956i	$-0.905361\pi$
$83$	0.295384	−	1.29416i	0.0324226	−	0.142053i	0.988549	+	0.150903i	$0.0482182\pi$
$84$	2.28072	−	3.27589i	0.248847	−	0.357429i
$85$	0.600626	+	2.63151i	0.0651470	+	0.285428i
$86$	6.38304	+	2.30940i	0.688301	+	0.249029i
$87$	0.862303	+	3.77800i	0.0924486	+	0.405044i
$88$	−0.424592	+	1.10040i	−0.0452617	+	0.117303i
$89$	3.97228	+	0.906646i	0.421060	+	0.0961043i	0.427801	−	0.903873i	$-0.359288\pi$
$89$	3.97228	+	0.906646i	0.421060	+	0.0961043i	−0.00674054	+	0.999977i	$0.502146\pi$
$90$	2.15958	+	2.20564i	0.227640	+	0.232495i
$91$	0.0263359	−	0.189239i	0.00276075	−	0.0198377i
$92$	−1.39734	−	0.709628i	−0.145683	−	0.0739839i
$93$	−1.19588	−	1.49959i	−0.124007	−	0.155500i
$94$	−1.82726	−	2.97735i	−0.188468	−	0.307090i
$95$	4.96417	−	3.95879i	0.509313	−	0.406164i
$96$	−3.17230	+	2.85408i	−0.323771	+	0.291293i
$97$			12.4755i			1.26670i	0.773866	+	0.633349i	$0.218320\pi$
$97$			12.4755i			1.26670i	−0.773866	+	0.633349i	$0.781680\pi$
$98$	9.12070	+	3.84874i	0.921330	+	0.388782i
$99$		−	1.01372i		−	0.101883i
$100$	3.47897	+	7.63207i	0.347897	+	0.763207i
$101$	10.9604	−	8.74065i	1.09060	−	0.869727i	0.0984984	−	0.995137i	$-0.468596\pi$
$101$	10.9604	−	8.74065i	1.09060	−	0.869727i	0.992105	+	0.125410i	$0.0400246\pi$
$102$	2.73328	−	1.67747i	0.270635	−	0.166095i
$103$	2.98595	+	3.74426i	0.294214	+	0.368933i	0.906865	−	0.421420i	$-0.138468\pi$
$103$	2.98595	+	3.74426i	0.294214	+	0.368933i	−0.612651	+	0.790353i	$0.709897\pi$
$104$	−0.0735289	+	0.190561i	−0.00721010	+	0.0186861i
$105$	0.992655	−	1.49197i	0.0968732	−	0.145601i
$106$	6.20847	−	6.07882i	0.603020	−	0.590427i
$107$	−11.8175	−	2.69727i	−1.14244	−	0.260755i	−0.390896	−	0.920435i	$-0.627835\pi$
$107$	−11.8175	−	2.69727i	−1.14244	−	0.260755i	−0.751547	+	0.659680i	$0.770692\pi$
$108$	3.71007	−	7.30557i	0.357002	−	0.702979i
$109$	−1.69934	−	7.44530i	−0.162767	−	0.713130i	−0.988768	−	0.149460i	$-0.952246\pi$
$109$	−1.69934	−	7.44530i	−0.162767	−	0.713130i	0.826000	−	0.563669i	$-0.190611\pi$
$110$	−0.180152	+	0.497929i	−0.0171768	+	0.0474756i
$111$	−1.32968	−	5.82573i	−0.126208	−	0.552954i
$112$	−8.55583	−	6.22878i	−0.808450	−	0.588565i
$113$	−0.152605	+	0.668607i	−0.0143559	+	0.0628972i	−0.981598	−	0.190957i	$-0.938841\pi$
$113$	−0.152605	+	0.668607i	−0.0143559	+	0.0628972i	0.967243	+	0.253854i	$0.0816982\pi$
$114$	−6.34492	−	4.08078i	−0.594256	−	0.382200i
$115$	−0.633912	−	0.305276i	−0.0591126	−	0.0284671i
$116$	10.0626	−	2.07436i	0.934290	−	0.192599i
$117$		−	0.175552i		−	0.0162298i
$118$	4.82762	−	13.3432i	0.444418	−	1.22835i
$119$	5.47543	+	5.76873i	0.501932	+	0.528819i
$120$	−1.39683	+	1.31109i	−0.127513	+	0.119686i
$121$	−9.75398	+	4.69727i	−0.886726	+	0.427025i
$122$	−2.16676	+	17.5629i	−0.196169	+	1.59007i
$123$	−5.06017	−	1.15495i	−0.456260	−	0.104138i
$124$	−4.04187	+	3.08604i	−0.362971	+	0.277135i
$125$	3.58171	+	7.43750i	0.320358	+	0.665231i
$126$	8.78770	+	2.34741i	0.782870	+	0.209124i
$127$	−5.69720	+	11.8304i	−0.505545	+	1.04977i	0.479511	+	0.877536i	$0.340814\pi$
$127$	−5.69720	+	11.8304i	−0.505545	+	1.04977i	−0.985055	+	0.172238i	$0.944900\pi$
$128$	7.38787	+	8.56851i	0.653002	+	0.757357i
$129$		−	3.62073i		−	0.318788i
$130$	−0.0311978	+	0.0862290i	−0.00273623	+	0.00756278i
$131$	3.04776	−	3.82177i	0.266284	−	0.333910i	−0.630655	−	0.776063i	$-0.717214\pi$
$131$	3.04776	−	3.82177i	0.266284	−	0.333910i	0.896939	+	0.442153i	$0.145785\pi$
$132$	0.628994	+	0.0132751i	0.0547469	+	0.00115544i
$133$	6.63772	−	17.4924i	0.575563	−	1.51678i
$134$	−4.67301	−	13.8208i	−0.403687	−	1.19393i
$135$	1.59604	−	3.31421i	0.137365	−	0.285242i
$136$	−4.29358	−	7.33898i	−0.368172	−	0.629312i
$137$	−11.9611	+	14.9987i	−1.02191	+	1.28143i	−0.0629073	+	0.998019i	$0.520037\pi$
$137$	−11.9611	+	14.9987i	−1.02191	+	1.28143i	−0.958999	+	0.283410i	$0.908534\pi$
$138$	−0.102357	+	0.829665i	−0.00871317	+	0.0706257i
$139$	10.7518	+	13.4823i	0.911957	+	1.14356i	0.989204	+	0.146546i	$0.0468156\pi$
$139$	10.7518	+	13.4823i	0.911957	+	1.14356i	−0.0772468	+	0.997012i	$0.524613\pi$
$140$	−3.89924	−	2.71470i	−0.329546	−	0.229434i
$141$	−1.16179	+	1.45684i	−0.0978403	+	0.122688i
$142$	8.13315	+	8.30661i	0.682519	+	0.697075i
$143$	0.0271319	−	0.0130660i	0.00226888	−	0.00109264i
$144$	−8.57507	−	4.58490i	−0.714589	−	0.382075i
$145$	4.49690	−	1.02639i	0.373447	−	0.0852368i
$146$	−15.9843	+	1.63040i	−1.32287	+	0.134933i
$147$	0.275294	−	5.27325i	0.0227059	−	0.434930i
$148$	−15.5167	+	3.19869i	−1.27546	+	0.262931i
$149$	−2.30729	−	10.1089i	−0.189020	−	0.828153i	−0.977134	−	0.212623i	$-0.931799\pi$
$149$	−2.30729	−	10.1089i	−0.189020	−	0.828153i	0.788114	−	0.615529i	$-0.211058\pi$
$150$	3.19678	−	3.13002i	0.261016	−	0.255565i
$151$	0.0266286	+	0.0552948i	0.00216700	+	0.00449983i	0.902050	−	0.431632i	$-0.142062\pi$
$151$	0.0266286	+	0.0552948i	0.00216700	+	0.00449983i	−0.899883	+	0.436132i	$0.856348\pi$
$152$	−11.1719	+	16.5902i	−0.906162	+	1.34565i
$153$	5.71349	+	4.55636i	0.461909	+	0.368360i
$154$	0.291256	+	1.53287i	0.0234701	+	0.123522i
$155$	−1.78494	+	1.42344i	−0.143370	+	0.114334i
$156$	0.108926	+	0.00229891i	0.00872108	+	0.000184060i
$157$	7.50286	+	5.98333i	0.598794	+	0.477522i	0.875359	−	0.483473i	$-0.160625\pi$
$157$	7.50286	+	5.98333i	0.598794	+	0.477522i	−0.276566	+	0.960995i	$0.589196\pi$
$158$	−4.04821	−	11.9729i	−0.322058	−	0.952509i
$159$	−4.17572	−	2.01092i	−0.331156	−	0.159476i
$160$	3.39717	+	3.77594i	0.268570	+	0.298515i
$161$	−2.06554	+	0.178326i	−0.162787	+	0.0140541i
$162$	5.89844	+	0.727697i	0.463425	+	0.0571733i
$163$	−5.57334	−	4.44459i	−0.436537	−	0.348127i	0.380431	−	0.924809i	$-0.375776\pi$
$163$	−5.57334	−	4.44459i	−0.436537	−	0.348127i	−0.816968	+	0.576682i	$0.804347\pi$
$164$	−3.34453	+	13.3484i	−0.261164	+	1.04234i
$165$	0.282446			0.0219884
$166$	0.190496	+	1.86760i	0.0147853	+	0.144954i
$167$	−19.2852	−	9.28724i	−1.49233	−	0.718669i	−0.502990	−	0.864292i	$-0.667767\pi$
$167$	−19.2852	−	9.28724i	−1.49233	−	0.718669i	−0.989340	+	0.145623i	$0.953481\pi$
$168$	−1.57159	+	5.42184i	−0.121251	+	0.418304i
$169$	−11.7079	+	5.63823i	−0.900607	+	0.433710i
$170$	−1.99667	−	3.25339i	−0.153138	−	0.249523i
$171$	3.82525	−	16.7595i	0.292524	−	1.28163i
$172$	−9.59750	−	0.202557i	−0.731803	−	0.0154449i
$173$	4.84437	+	10.0594i	0.368310	+	0.764805i	0.999945	−	0.0104615i	$-0.00333006\pi$
$173$	4.84437	+	10.0594i	0.368310	+	0.764805i	−0.631635	+	0.775266i	$0.717616\pi$
$174$	−2.86657	−	4.67081i	−0.217314	−	0.354093i
$175$	9.23790	+	6.14627i	0.698320	+	0.464614i
$176$	0.0703766	−	1.66654i	0.00530484	−	0.125620i
$177$	−7.56885			−0.568910
$178$	−5.73237	+	0.584703i	−0.429659	+	0.0438254i
$179$	2.97622	−	6.18018i	0.222453	−	0.461929i	−0.759635	−	0.650349i	$-0.774623\pi$
$179$	2.97622	−	6.18018i	0.222453	−	0.461929i	0.982088	+	0.188421i	$0.0603368\pi$
$180$	−3.89231	−	1.97667i	−0.290115	−	0.147333i
$181$	−4.10373	−	0.936649i	−0.305028	−	0.0696206i	0.0672674	−	0.997735i	$-0.478572\pi$
$181$	−4.10373	−	0.936649i	−0.305028	−	0.0696206i	−0.372295	+	0.928114i	$0.621429\pi$
$182$	0.0504384	+	0.265455i	0.00373874	+	0.0196768i
$183$	9.20250	−	2.10041i	0.680269	−	0.155267i
$184$	2.19347	+	0.317732i	0.161705	+	0.0234235i
$185$	−6.93428	+	1.58270i	−0.509819	+	0.116363i
$186$	2.28141	+	1.46730i	0.167281	+	0.107588i
$187$	−0.278948	+	1.22215i	−0.0203987	+	0.0893726i
$188$	3.79666	+	3.16107i	0.276900	+	0.230545i
$189$	−0.932323	−	10.7990i	−0.0678165	−	0.785513i
$190$	−4.85729	+	7.55227i	−0.352385	+	0.547899i
$191$	21.3388	−	17.0171i	1.54402	−	1.23131i	0.673494	−	0.739193i	$-0.264793\pi$
$191$	21.3388	−	17.0171i	1.54402	−	1.23131i	0.870526	−	0.492122i	$-0.163779\pi$
$192$	2.95712	−	5.26060i	0.213412	−	0.379651i
$193$	−10.3202	−	12.9411i	−0.742866	−	0.931524i	0.256521	−	0.966539i	$-0.417424\pi$
$193$	−10.3202	−	12.9411i	−0.742866	−	0.931524i	−0.999387	+	0.0350147i	$0.988852\pi$
$194$	−5.65111	−	16.7135i	−0.405726	−	1.19996i
$195$	0.0489127			0.00350271
$196$	−13.9624	−	1.02473i	−0.997318	−	0.0731951i
$197$	5.99663			0.427242			0.213621	−	0.976917i	$-0.431474\pi$
$197$	5.99663			0.427242			0.213621	+	0.976917i	$0.431474\pi$
$198$	0.459192	+	1.35809i	0.0326334	+	0.0965154i
$199$	10.2193	+	12.8146i	0.724425	+	0.908400i	0.998579	−	0.0532859i	$-0.0169695\pi$
$199$	10.2193	+	12.8146i	0.724425	+	0.908400i	−0.274155	+	0.961686i	$0.588398\pi$
$200$	−8.11794	−	8.64884i	−0.574025	−	0.611565i
$201$	−6.08425	+	4.85202i	−0.429150	+	0.342235i
$202$	−10.7245	+	16.6747i	−0.754570	+	1.17323i
$203$	9.85797	−	9.35675i	0.691894	−	0.656715i
$204$	−2.90194	+	3.48543i	−0.203177	+	0.244029i
$205$	−1.37472	+	6.02305i	−0.0960148	+	0.420668i
$206$	−5.69635	−	3.66365i	−0.396884	−	0.255259i
$207$	−1.85715	+	0.423882i	−0.129081	+	0.0294619i
$208$	0.0121875	−	0.288603i	0.000845051	−	0.0200110i
$209$	2.87492	−	0.656181i	0.198862	−	0.0453890i
$210$	−0.654041	+	2.44845i	−0.0451331	+	0.168959i
$211$	15.6255	+	3.56641i	1.07570	+	0.245522i	0.723445	−	0.690382i	$-0.242557\pi$
$211$	15.6255	+	3.56641i	1.07570	+	0.245522i	0.352256	+	0.935904i	$0.385415\pi$
$212$	−5.56397	+	10.9561i	−0.382135	+	0.752469i
$213$	2.69051	−	5.58690i	0.184351	−	0.382808i
$214$	17.0538	−	1.73949i	1.16577	−	0.118909i
$215$	−4.30970			−0.293919
$216$	−1.66116	+	11.4679i	−0.113028	+	0.780291i
$217$	−2.38669	+	6.28963i	−0.162019	+	0.426968i
$218$	5.64915	+	9.20475i	0.382609	+	0.623424i
$219$	3.71853	+	7.72160i	0.251275	+	0.521777i
$220$	0.0158011	−	0.748683i	0.00106531	−	0.0504762i
$221$	−0.0483069	+	0.211647i	−0.00324948	+	0.0142369i
$222$	4.42030	+	7.20245i	0.296671	+	0.483397i
$223$	3.62551	−	1.74595i	0.242782	−	0.116918i	−0.308537	−	0.951212i	$-0.599839\pi$
$223$	3.62551	−	1.74595i	0.242782	−	0.116918i	0.551318	+	0.834295i	$0.314125\pi$
$224$	14.2838	+	4.46916i	0.954376	+	0.298608i
$225$	9.18533	+	4.42342i	0.612356	+	0.294895i
$226$	−0.0984163	−	0.964863i	−0.00654655	−	0.0641817i
$227$	21.1949			1.40676			0.703378	−	0.710816i	$-0.251674\pi$
$227$	21.1949			1.40676			0.703378	+	0.710816i	$0.251674\pi$
$228$	10.3488	+	2.59296i	0.685367	+	0.171723i
$229$	−14.3732	−	11.4623i	−0.949810	−	0.757448i	0.0203801	−	0.999792i	$-0.493512\pi$
$229$	−14.3732	−	11.4623i	−0.949810	−	0.757448i	−0.970190	+	0.242344i	$0.922084\pi$
$230$	0.987538	+	0.121834i	0.0651163	+	0.00803347i
$231$	0.716006	−	0.424266i	0.0471098	−	0.0279146i
$232$	−12.5413	+	7.33715i	−0.823378	+	0.481707i
$233$	7.37493	+	3.55158i	0.483148	+	0.232672i	0.659570	−	0.751643i	$-0.270738\pi$
$233$	7.37493	+	3.55158i	0.483148	+	0.232672i	−0.176423	+	0.984315i	$0.556453\pi$
$234$	0.0795207	+	0.235188i	0.00519843	+	0.0153747i
$235$	1.73405	+	1.38286i	0.113117	+	0.0902080i
$236$	−0.423430	+	20.0628i	−0.0275630	+	1.30598i
$237$	−5.27075	+	4.20328i	−0.342372	+	0.273033i
$238$	−9.94856	−	5.24817i	−0.644869	−	0.340189i
$239$	−8.17046	−	6.51572i	−0.528503	−	0.421467i	0.322546	−	0.946554i	$-0.395461\pi$
$239$	−8.17046	−	6.51572i	−0.528503	−	0.421467i	−0.851049	+	0.525087i	$0.824033\pi$
$240$	1.27745	−	2.38921i	0.0824593	−	0.154223i
$241$	9.20491	+	19.1142i	0.592940	+	1.23125i	0.954307	+	0.298829i	$0.0965960\pi$
$241$	9.20491	+	19.1142i	0.592940	+	1.23125i	−0.361367	+	0.932424i	$0.617690\pi$
$242$	10.9397	−	10.7113i	0.703232	−	0.688547i
$243$	−3.44031	−	15.0730i	−0.220696	−	0.966931i
$244$	−5.05276	−	24.5107i	−0.323470	−	1.56913i
$245$	−6.27667	−	0.327679i	−0.401002	−	0.0209346i
$246$	7.30231	−	0.744837i	0.465578	−	0.0474891i
$247$	0.497865	−	0.113634i	0.0316784	−	0.00723038i
$248$	4.01702	−	5.96526i	0.255081	−	0.378794i
$249$	0.902188	−	0.434471i	0.0571738	−	0.0275335i
$250$	−8.16745	−	8.34164i	−0.516555	−	0.527572i
$251$	−4.35853	+	5.46543i	−0.275108	+	0.344975i	−0.900121	−	0.435640i	$-0.856522\pi$
$251$	−4.35853	+	5.46543i	−0.275108	+	0.344975i	0.625013	+	0.780614i	$0.285094\pi$
$252$	−12.8363	+	0.835771i	−0.808608	+	0.0526486i
$253$	−0.203736	−	0.255477i	−0.0128088	−	0.0160617i
$254$	2.27371	−	18.4299i	0.142666	−	1.15639i
$255$	−1.26950	+	1.59191i	−0.0794994	+	0.0996891i
$256$	−13.7789	−	8.13277i	−0.861181	−	0.508298i
$257$	11.7963	−	24.4954i	0.735836	−	1.52798i	−0.109643	−	0.993971i	$-0.534971\pi$
$257$	11.7963	−	24.4954i	0.735836	−	1.52798i	0.845479	−	0.534008i	$-0.179315\pi$
$258$	1.64010	+	4.85072i	0.102108	+	0.301992i
$259$	−15.2011	+	14.4283i	−0.944553	+	0.896528i
$260$	0.00273636	−	0.129653i	0.000169702	−	0.00804076i
$261$	7.78619	−	9.76358i	0.481953	−	0.604350i
$262$	−2.35194	+	6.50061i	−0.145303	+	0.401609i
$263$		−	13.8027i		−	0.851113i	−0.904932	−	0.425557i	$-0.860078\pi$
$263$		−	13.8027i		−	0.851113i	0.904932	−	0.425557i	$-0.139922\pi$
$264$	−0.848680	+	0.267134i	−0.0522327	+	0.0164410i
$265$	−2.39357	+	4.97030i	−0.147036	+	0.305323i
$266$	−0.968988	+	26.4413i	−0.0594124	+	1.62122i
$267$	1.33356	+	2.76916i	0.0816123	+	0.169470i
$268$	12.5209	+	16.3990i	0.764837	+	1.00173i
$269$	4.52148	+	1.03200i	0.275679	+	0.0629220i	0.358125	−	0.933674i	$-0.383416\pi$
$269$	4.52148	+	1.03200i	0.275679	+	0.0629220i	−0.0824459	+	0.996596i	$0.526273\pi$
$270$	−0.636969	+	5.16304i	−0.0387647	+	0.314212i
$271$	−14.3127	+	6.89261i	−0.869432	+	0.418696i	−0.814753	−	0.579808i	$-0.803128\pi$
$271$	−14.3127	+	6.89261i	−0.869432	+	0.418696i	−0.0546783	+	0.998504i	$0.517413\pi$
$272$	9.07652	+	7.88719i	0.550345	+	0.478231i
$273$	0.123995	−	0.0734724i	0.00750450	−	0.00444675i
$274$	9.23030	−	25.5120i	0.557623	−	1.54124i
$275$			1.74884i			0.105459i
$276$	−0.238690	−	1.15787i	−0.0143674	−	0.0696957i
$277$	24.0701	+	11.5916i	1.44624	+	0.696470i	0.981937	−	0.189209i	$-0.0605923\pi$
$277$	24.0701	+	11.5916i	1.44624	+	0.696470i	0.464298	+	0.885679i	$0.346307\pi$
$278$	−20.5114	−	13.1921i	−1.23019	−	0.791209i
$279$	−1.37542	+	6.02612i	−0.0823445	+	0.360775i
$280$	6.45354	+	1.87065i	0.385673	+	0.111793i
$281$	2.51382	+	11.0138i	0.149962	+	0.657027i	0.992894	+	0.119006i	$0.0379708\pi$
$281$	2.51382	+	11.0138i	0.149962	+	0.657027i	−0.842931	+	0.538021i	$0.819172\pi$
$282$	0.896545	−	2.47800i	0.0533885	−	0.147563i
$283$	−4.32781	−	18.9614i	−0.257262	−	1.12714i	−0.924165	−	0.381993i	$-0.875238\pi$
$283$	−4.32781	−	18.9614i	−0.257262	−	1.12714i	0.666904	−	0.745144i	$-0.267619\pi$
$284$	−14.6587	−	7.44430i	−0.869835	−	0.441738i
$285$	4.66957	+	1.06580i	0.276602	+	0.0631325i
$286$	−0.0304302	+	0.0297947i	−0.00179937	+	0.00176180i
$287$	5.56235	+	17.3335i	0.328335	+	1.02317i
$288$	13.5649	+	2.25812i	0.799321	+	0.133061i
$289$	4.96489	+	6.22577i	0.292052	+	0.366222i
$290$	−5.55959	+	3.41204i	−0.326471	+	0.200362i
$291$	−7.35772	+	5.86759i	−0.431317	+	0.343964i
$292$	20.6757	−	9.42475i	1.20996	−	0.551542i
$293$		−	18.1872i		−	1.06251i	−0.847212	−	0.531254i	$-0.821721\pi$
$293$		−	18.1872i		−	1.06251i	0.847212	−	0.531254i	$-0.178279\pi$
$294$	2.01984	+	7.18931i	0.117799	+	0.419289i
$295$			9.00910i			0.524530i
$296$	19.3389	−	11.3140i	1.12405	−	0.657612i
$297$	1.33568	−	1.06517i	0.0775041	−	0.0618075i
$298$	7.67017	+	12.4978i	0.444321	+	0.723978i
$299$	−0.0352821	−	0.0442423i	−0.00204041	−	0.00255860i
$300$	−2.86492	+	5.64137i	−0.165406	+	0.325705i
$301$	−10.9252	+	6.47366i	−0.629717	+	0.373135i
$302$	−0.0607217	−	0.0620168i	−0.00349414	−	0.00356866i
$303$	10.3100	+	2.35319i	0.592293	+	0.135187i
$304$	7.45212	−	27.2867i	0.427409	−	1.56500i
$305$	−2.50009	−	10.9536i	−0.143155	−	0.627202i
$306$	−9.71832	−	3.51611i	−0.555559	−	0.201003i
$307$	−1.10214	−	4.82878i	−0.0629023	−	0.275593i	0.933690	−	0.358083i	$-0.116570\pi$
$307$	−1.10214	−	4.82878i	−0.0629023	−	0.275593i	−0.996592	+	0.0824907i	$0.973713\pi$
$308$	−1.08455	−	1.92166i	−0.0617979	−	0.109497i
$309$	−0.803887	+	3.52206i	−0.0457315	+	0.200363i
$310$	1.74651	−	2.71553i	0.0991951	−	0.154232i
$311$	−28.7608	−	13.8505i	−1.63088	−	0.785389i	−0.999954	−	0.00954398i	$-0.996962\pi$
$311$	−28.7608	−	13.8505i	−1.63088	−	0.785389i	−0.630923	−	0.775845i	$-0.717324\pi$
$312$	−0.146971	+	0.0462610i	−0.00832057	+	0.00261902i
$313$		−	1.48340i		−	0.0838468i	−0.999121	−	0.0419234i	$-0.986651\pi$
$313$		−	1.48340i		−	0.0838468i	0.999121	−	0.0419234i	$-0.0133485\pi$
$314$	−12.7619	−	4.61730i	−0.720198	−	0.260569i
$315$	−5.75356	+	0.496728i	−0.324177	+	0.0279875i
$316$	10.8468	+	14.2064i	0.610181	+	0.799171i
$317$	−2.38613	+	1.14910i	−0.134019	+	0.0645400i	−0.499691	−	0.866204i	$-0.666553\pi$
$317$	−2.38613	+	1.14910i	−0.134019	+	0.0645400i	0.365673	+	0.930744i	$0.380839\pi$
$318$	6.50513	+	0.802545i	0.364790	+	0.0450045i
$319$	2.08849	+	0.476684i	0.116933	+	0.0266892i
$320$	−6.26162	−	3.51982i	−0.350035	−	0.196764i
$321$	−3.96733	−	8.23824i	−0.221435	−	0.459814i
$322$	2.68644	−	1.17454i	0.149709	−	0.0654547i
$323$	−9.22348	+	19.1528i	−0.513208	+	1.06569i
$324$	−8.23181	+	1.69695i	−0.457323	+	0.0942749i
$325$			0.302855i			0.0167994i
$326$	9.47992	+	3.42986i	0.525044	+	0.189962i
$327$	3.59178	−	4.50395i	0.198626	−	0.249069i
$328$	−1.56583	−	19.3980i	−0.0864584	−	1.07107i
$329$	6.47307	+	0.900839i	0.356872	+	0.0496649i
$330$	−0.378395	+	0.127941i	−0.0208300	+	0.00704293i
$331$	−0.330449	+	0.686185i	−0.0181631	+	0.0377161i	−0.909853	−	0.414931i	$-0.863806\pi$
$331$	−0.330449	+	0.686185i	−0.0181631	+	0.0377161i	0.891690	+	0.452647i	$0.149520\pi$
$332$	−1.10118	−	2.41574i	−0.0604353	−	0.132581i
$333$	−12.0064	+	15.0556i	−0.657948	+	0.825041i
$334$	30.0433	+	3.70648i	1.64390	+	0.202810i
$335$	5.77530	+	7.24199i	0.315538	+	0.395672i
$336$	−0.350483	−	7.97556i	−0.0191204	−	0.435103i
$337$	10.2210	−	12.8168i	0.556776	−	0.698175i	−0.421182	−	0.906976i	$-0.638385\pi$
$337$	10.2210	−	12.8168i	0.556776	−	0.698175i	0.977958	+	0.208801i	$0.0669561\pi$
$338$	13.1312	−	12.8570i	0.714241	−	0.699326i
$339$	−0.466100	+	0.224462i	−0.0253151	+	0.0121911i
$340$	4.14866	+	3.45414i	0.224993	+	0.187327i
$341$	−1.03372	+	0.235939i	−0.0559790	+	0.0127768i
$342$	2.46693	+	24.1856i	0.133397	+	1.30781i
$343$	−16.4037	+	8.59759i	−0.885717	+	0.464226i
$344$	12.9496	−	4.07606i	0.698195	−	0.219767i
$345$	−0.118103	−	0.517443i	−0.00635845	−	0.0278582i
$346$	−11.0467	−	11.2823i	−0.593875	−	0.606541i
$347$	−6.57185	−	13.6466i	−0.352796	−	0.732588i	0.646751	−	0.762701i	$-0.276127\pi$
$347$	−6.57185	−	13.6466i	−0.352796	−	0.732588i	−0.999546	+	0.0301137i	$0.990413\pi$
$348$	5.95613	+	4.95902i	0.319282	+	0.265831i
$349$	−11.1313	−	8.87693i	−0.595846	−	0.475171i	0.278525	−	0.960429i	$-0.410154\pi$
$349$	−11.1313	−	8.87693i	−0.595846	−	0.475171i	−0.874371	+	0.485258i	$0.838726\pi$
$350$	−15.1602	−	4.04966i	−0.810346	−	0.216463i
$351$	0.231307	−	0.184461i	0.0123463	−	0.00984581i
$352$	0.660616	+	2.26455i	0.0352110	+	0.120701i
$353$	−25.5541	−	20.3787i	−1.36011	−	1.08465i	−0.987663	−	0.156594i	$-0.949949\pi$
$353$	−25.5541	−	20.3787i	−1.36011	−	1.08465i	−0.372443	−	0.928055i	$-0.621480\pi$
$354$	10.1400	−	3.42850i	0.538937	−	0.182223i
$355$	−6.65000	−	3.20247i	−0.352946	−	0.169970i
$356$	7.41484	−	3.37995i	0.392986	−	0.179137i
$357$	−0.826994	+	5.94245i	−0.0437691	+	0.314508i
$358$	−1.18779	+	9.62779i	−0.0627766	+	0.508844i
$359$	7.56955	+	6.03652i	0.399506	+	0.318595i	0.802550	−	0.596585i	$-0.203476\pi$
$359$	7.56955	+	6.03652i	0.399506	+	0.318595i	−0.403044	+	0.915181i	$0.632048\pi$
$360$	6.10993	+	0.885044i	0.322022	+	0.0466459i
$361$	31.0060			1.63189
$362$	5.92207	−	0.604053i	0.311257	−	0.0317483i
$363$	−7.35789	−	3.54337i	−0.386189	−	0.185979i
$364$	−0.187817	−	0.332784i	−0.00984429	−	0.0174426i
$365$	9.19091	−	4.42611i	0.481074	−	0.231673i
$366$	−11.3772	+	6.98244i	−0.594697	+	0.364978i
$367$	2.28021	−	9.99026i	0.119026	−	0.521487i	−0.879900	−	0.475159i	$-0.842391\pi$
$367$	2.28021	−	9.99026i	0.119026	−	0.521487i	0.998926	−	0.0463287i	$-0.0147522\pi$
$368$	−3.08253	+	0.567921i	−0.160688	+	0.0296050i
$369$	7.25726	+	15.0699i	0.377798	+	0.784506i
$370$	8.57298	−	5.26142i	0.445688	−	0.273528i
$371$	1.39820	+	16.1952i	0.0725908	+	0.840814i
$372$	−3.72107	−	0.932335i	−0.192928	−	0.0483393i
$373$	−3.75925			−0.194647			−0.0973233	−	0.995253i	$-0.531028\pi$
$373$	−3.75925			−0.194647			−0.0973233	+	0.995253i	$0.531028\pi$
$374$	−0.179896	−	1.76368i	−0.00930219	−	0.0911978i
$375$	−2.70185	+	5.61046i	−0.139523	+	0.289723i
$376$	−6.51829	−	2.51511i	−0.336155	−	0.129707i
$377$	0.361675	+	0.0825499i	0.0186272	+	0.00425154i
$378$	6.14073	+	14.0452i	0.315845	+	0.722407i
$379$	29.7964	−	6.80084i	1.53054	−	0.349336i	0.627406	−	0.778693i	$-0.284117\pi$
$379$	29.7964	−	6.80084i	1.53054	−	0.349336i	0.903135	+	0.429357i	$0.141260\pi$
$380$	3.08636	−	12.3181i	0.158327	−	0.631903i
$381$	−9.65677	+	2.20409i	−0.494731	+	0.112919i
$382$	−20.8794	+	32.4639i	−1.06828	+	1.66100i
$383$	−5.84418	+	25.6050i	−0.298624	+	1.30836i	0.573554	+	0.819168i	$0.305564\pi$
$383$	−5.84418	+	25.6050i	−0.298624	+	1.30836i	−0.872178	+	0.489189i	$0.837293\pi$
$384$	−1.57875	+	8.38717i	−0.0805653	+	0.428006i
$385$	−0.504997	−	0.852252i	−0.0257371	−	0.0434348i
$386$	19.6881	+	12.6625i	1.00210	+	0.644506i
$387$	−9.12254	+	7.27499i	−0.463725	+	0.369808i
$388$	15.1416	+	19.8314i	0.768701	+	1.00679i
$389$	−4.36161	−	5.46929i	−0.221142	−	0.277304i	0.658868	−	0.752259i	$-0.271036\pi$
$389$	−4.36161	−	5.46929i	−0.221142	−	0.277304i	−0.880010	+	0.474955i	$0.842464\pi$
$390$	−0.0655287	+	0.0221563i	−0.00331817	+	0.00112193i
$391$	2.35563			0.119129
$392$	19.1698	−	4.95181i	0.968219	−	0.250104i
$393$	3.68742			0.186006
$394$	−8.03372	+	2.71632i	−0.404733	+	0.136846i
$395$	5.00311	+	6.27370i	0.251734	+	0.315664i
$396$	−1.23036	−	1.61144i	−0.0618282	−	0.0809781i
$397$	−8.09339	+	6.45427i	−0.406196	+	0.323930i	−0.805183	−	0.593026i	$-0.797933\pi$
$397$	−8.09339	+	6.45427i	−0.406196	+	0.323930i	0.398988	+	0.916956i	$0.369362\pi$
$398$	−19.4955	−	12.5387i	−0.977221	−	0.628507i
$399$	13.4384	−	4.31240i	0.672762	−	0.215890i
$400$	14.7934	+	7.90968i	0.739668	+	0.395484i
$401$	1.95429	−	8.56232i	0.0975927	−	0.427582i	−0.902402	−	0.430896i	$-0.858198\pi$
$401$	1.95429	−	8.56232i	0.0975927	−	0.427582i	0.999995	+	0.00331389i	$0.00105485\pi$
$402$	5.95326	−	9.25630i	0.296921	−	0.461662i
$403$	−0.179014	+	0.0408589i	−0.00891735	+	0.00203533i
$404$	6.81439	−	27.1971i	0.339029	−	1.35311i
$405$	−3.67873	+	0.839645i	−0.182797	+	0.0417223i
$406$	−8.96841	+	17.0007i	−0.445095	+	0.843732i
$407$	−3.22048	−	0.735054i	−0.159633	−	0.0364353i
$408$	2.30894	−	5.98396i	0.114309	−	0.296250i
$409$	−10.1190	+	21.0123i	−0.500351	+	1.03899i	0.485942	+	0.873991i	$0.338476\pi$
$409$	−10.1190	+	21.0123i	−0.500351	+	1.03899i	−0.986294	+	0.164999i	$0.947238\pi$
$410$	−0.886570	−	8.69184i	−0.0437845	−	0.429259i
$411$	−14.4715			−0.713826
$412$	9.29098	+	2.32791i	0.457734	+	0.114688i
$413$	13.5327	+	22.8382i	0.665899	+	1.12380i
$414$	2.29603	−	1.40912i	0.112844	−	0.0692545i
$415$	−0.517145	−	1.07386i	−0.0253856	−	0.0527138i
$416$	0.114402	+	0.392164i	0.00560904	+	0.0192274i
$417$	−2.89464	+	12.6822i	−0.141751	+	0.621052i
$418$	−3.55431	+	2.18136i	−0.173847	+	0.106694i
$419$	−21.6233	+	10.4132i	−1.05637	+	0.508720i	−0.879689	−	0.475549i	$-0.842250\pi$
$419$	−21.6233	+	10.4132i	−1.05637	+	0.508720i	−0.176678	+	0.984269i	$0.556535\pi$
$420$	−0.232864	−	3.57647i	−0.0113626	−	0.174514i
$421$	−26.5389	−	12.7805i	−1.29343	−	0.622882i	−0.344622	−	0.938741i	$-0.611993\pi$
$421$	−26.5389	−	12.7805i	−1.29343	−	0.622882i	−0.948806	+	0.315859i	$0.897707\pi$
$422$	−22.5490	+	2.30001i	−1.09767	+	0.111963i
$423$	6.00489			0.291968
$424$	2.49124	−	17.1983i	0.120985	−	0.835224i
$425$	−9.85669	−	7.86045i	−0.478120	−	0.381288i
$426$	−1.07376	+	8.70353i	−0.0520240	+	0.421688i
$427$	−22.7913	−	24.0122i	−1.10295	−	1.16203i
$428$	−22.0591	+	10.0554i	−1.06627	+	0.486044i
$429$	0.0204668	+	0.00985631i	0.000988149	+	0.000475867i
$430$	5.77374	−	1.95219i	0.278434	−	0.0941430i
$431$	−12.3711	−	9.86566i	−0.595897	−	0.475212i	0.278491	−	0.960439i	$-0.410166\pi$
$431$	−12.3711	−	9.86566i	−0.595897	−	0.475212i	−0.874388	+	0.485227i	$0.838737\pi$
$432$	−2.96920	−	16.1161i	−0.142856	−	0.775385i
$433$	9.11835	−	7.27164i	0.438200	−	0.349453i	−0.379407	−	0.925230i	$-0.623872\pi$
$433$	9.11835	−	7.27164i	0.438200	−	0.349453i	0.817607	+	0.575777i	$0.195300\pi$
$434$	0.348413	−	9.50737i	0.0167244	−	0.456368i
$435$	2.72035	+	2.16941i	0.130431	+	0.104015i
$436$	−11.7377	−	9.77274i	−0.562135	−	0.468029i
$437$	−2.40426	−	4.99249i	−0.115011	−	0.238823i
$438$	−8.47943	−	8.66027i	−0.405163	−	0.413804i
$439$	−0.427086	−	1.87119i	−0.0203837	−	0.0893069i	0.963713	−	0.266941i	$-0.0860128\pi$
$439$	−0.427086	−	1.87119i	−0.0203837	−	0.0893069i	−0.984097	+	0.177634i	$0.943156\pi$
$440$	0.317966	+	1.01017i	0.0151584	+	0.0481581i
$441$	−13.8393	+	9.90171i	−0.659012	+	0.471510i
$442$	−0.0311535	−	0.305426i	−0.00148182	−	0.0145276i
$443$	15.8880	−	3.62634i	0.754863	−	0.172292i	0.172262	−	0.985051i	$-0.444892\pi$
$443$	15.8880	−	3.62634i	0.754863	−	0.172292i	0.582601	+	0.812759i	$0.302035\pi$
$444$	−9.18444	−	7.64689i	−0.435874	−	0.362905i
$445$	3.29609	−	1.58731i	0.156250	−	0.0752459i
$446$	−4.06624	+	3.98133i	−0.192542	+	0.188521i
$447$	4.87676	−	6.11527i	0.230663	−	0.289242i
$448$	−21.1605	+	0.482845i	−0.999740	+	0.0228123i
$449$	−22.8747	−	28.6840i	−1.07953	−	1.35368i	−0.931102	−	0.364759i	$-0.881151\pi$
$449$	−22.8747	−	28.6840i	−1.07953	−	1.35368i	−0.148424	−	0.988924i	$-0.547420\pi$
$450$	−14.3094	−	1.76536i	−0.674549	−	0.0832199i
$451$	−1.78893	+	2.24324i	−0.0842373	+	0.105630i
$452$	0.568908	+	1.24805i	0.0267592	+	0.0587035i
$453$	−0.0200872	+	0.0417115i	−0.000943779	+	0.00195978i
$454$	−28.3950	+	9.60077i	−1.33264	+	0.450587i
$455$	−0.0874531	−	0.147589i	−0.00409987	−	0.00691909i
$456$	−15.0389	+	1.21396i	−0.704262	+	0.0568489i
$457$	−6.61337	+	8.29291i	−0.309361	+	0.387926i	−0.912070	−	0.410035i	$-0.865516\pi$
$457$	−6.61337	+	8.29291i	−0.309361	+	0.387926i	0.602709	+	0.797961i	$0.294088\pi$
$458$	24.4480	+	8.84536i	1.14238	+	0.413317i
$459$			12.3157i			0.574847i
$460$	−1.37820	+	0.284109i	−0.0642588	+	0.0132467i
$461$	4.76737	−	9.89954i	0.222038	−	0.461067i	−0.759957	−	0.649974i	$-0.774780\pi$
$461$	4.76737	−	9.89954i	0.222038	−	0.461067i	0.981995	+	0.188906i	$0.0604942\pi$
$462$	−0.767057	+	0.892725i	−0.0356867	+	0.0415333i
$463$	−14.8579	−	30.8528i	−0.690507	−	1.43385i	−0.890929	−	0.454142i	$-0.849946\pi$
$463$	−14.8579	−	30.8528i	−0.690507	−	1.43385i	0.200423	−	0.979710i	$-0.435768\pi$
$464$	13.4781	−	15.5105i	0.625707	−	0.720058i
$465$	−1.67901	−	0.383224i	−0.0778623	−	0.0177716i
$466$	−11.4890	−	1.41741i	−0.532219	−	0.0656604i
$467$	13.7753	−	6.63382i	0.637444	−	0.306977i	−0.0871062	−	0.996199i	$-0.527762\pi$
$467$	13.7753	−	6.63382i	0.637444	−	0.306977i	0.724550	+	0.689222i	$0.242048\pi$
$468$	−0.213069	−	0.279062i	−0.00984911	−	0.0128997i
$469$	25.5188	+	9.68345i	1.17835	+	0.447140i
$470$	−2.94953	−	1.06715i	−0.136051	−	0.0492237i
$471$			7.23911i			0.333560i
$472$	−8.52069	−	27.0701i	−0.392197	−	1.24600i
$473$	−1.80334	−	0.868441i	−0.0829175	−	0.0399310i
$474$	5.15727	−	8.01868i	0.236881	−	0.368310i
$475$	−6.59917	+	28.9128i	−0.302791	+	1.32661i
$476$	15.7054	+	2.52456i	0.719858	+	0.115713i
$477$	3.32353	+	14.5613i	0.152174	+	0.666717i
$478$	13.8975	+	5.02814i	0.635656	+	0.229982i
$479$	6.49214	+	28.4439i	0.296633	+	1.29964i	0.875105	+	0.483933i	$0.160792\pi$
$479$	6.49214	+	28.4439i	0.296633	+	1.29964i	−0.578471	+	0.815703i	$0.696351\pi$
$480$	−0.629162	+	3.77949i	−0.0287172	+	0.172509i
$481$	−0.557708	−	0.127293i	−0.0254293	−	0.00580407i
$482$	−20.9901	−	21.4378i	−0.956074	−	0.976465i
$483$	−1.07665	−	1.13432i	−0.0489893	−	0.0516136i
$484$	−9.80408	+	19.3054i	−0.445640	+	0.877518i
$485$	6.98411	+	8.75779i	0.317132	+	0.397671i
$486$	11.4367	+	18.6350i	0.518778	+	0.845300i
$487$	10.3993	−	8.29316i	0.471237	−	0.375799i	−0.358884	−	0.933382i	$-0.616843\pi$
$487$	10.3993	−	8.29316i	0.471237	−	0.375799i	0.830121	+	0.557583i	$0.188271\pi$
$488$	17.8719	+	30.5483i	0.809024	+	1.38286i
$489$		−	5.37741i		−	0.243175i
$490$	8.55733	−	2.40418i	0.386581	−	0.108610i
$491$			17.4012i			0.785306i	0.919687	+	0.392653i	$0.128443\pi$
$491$			17.4012i			0.785306i	−0.919687	+	0.392653i	$0.871557\pi$
$492$	−9.44556	+	4.30563i	−0.425839	+	0.194113i
$493$	−12.0737	+	9.62848i	−0.543774	+	0.433645i
$494$	−0.615519	+	0.377757i	−0.0276935	+	0.0169961i
$495$	−0.567508	−	0.711632i	−0.0255076	−	0.0319855i
$496$	−2.67952	+	9.81131i	−0.120314	+	0.440541i
$497$	−21.6684	+	1.87072i	−0.971959	+	0.0839131i
$498$	−1.01186	+	0.990732i	−0.0453426	+	0.0443958i
$499$	−19.4764	−	4.44536i	−0.871882	−	0.199001i	−0.236905	−	0.971533i	$-0.576133\pi$
$499$	−19.4764	−	4.44536i	−0.871882	−	0.199001i	−0.634977	+	0.772531i	$0.718990\pi$
$500$	14.7205	+	7.47570i	0.658323	+	0.334324i
$501$	−3.59299	−	15.7419i	−0.160523	−	0.703296i
$502$	3.36345	−	9.29637i	0.150118	−	0.414917i
$503$	−8.21716	−	36.0017i	−0.366385	−	1.60524i	−0.736625	−	0.676301i	$-0.763582\pi$
$503$	−8.21716	−	36.0017i	−0.366385	−	1.60524i	0.370241	−	0.928936i	$-0.379275\pi$
$504$	16.8182	−	6.93419i	0.749143	−	0.308874i
$505$	2.80097	−	12.2718i	0.124641	−	0.546089i
$506$	0.388671	+	0.249977i	0.0172785	+	0.0111128i
$507$	−8.83182	−	4.25318i	−0.392235	−	0.188890i
$508$	5.30218	+	25.7206i	0.235246	+	1.14117i
$509$			39.8681i			1.76712i	0.468317	+	0.883560i	$0.344860\pi$
$509$			39.8681i			1.76712i	−0.468317	+	0.883560i	$0.655140\pi$
$510$	0.979667	−	2.70774i	0.0433804	−	0.119901i
$511$	16.6506	−	25.0260i	0.736580	−	1.10709i
$512$	22.1436	+	4.65402i	0.978619	+	0.205681i
$513$	26.1017	−	12.5699i	1.15242	−	0.554975i
$514$	−4.70785	+	38.1601i	−0.207654	+	1.68317i
$515$	4.19226	+	0.956856i	0.184733	+	0.0421641i
$516$	−4.39451	−	5.75561i	−0.193457	−	0.253377i
$517$	0.446933	+	0.928065i	0.0196561	+	0.0408163i
$518$	13.8294	−	26.2154i	0.607630	−	1.15184i
$519$	−3.65433	+	7.58830i	−0.160407	+	0.333090i
$520$	0.0550639	+	0.174937i	0.00241471	+	0.00767149i
$521$		−	22.1676i		−	0.971181i	−0.874186	−	0.485591i	$-0.838605\pi$
$521$		−	22.1676i		−	0.971181i	0.874186	−	0.485591i	$-0.161395\pi$
$522$	−6.00855	+	16.6073i	−0.262987	+	0.726881i
$523$	16.4332	−	20.6066i	0.718574	−	0.901064i	−0.279682	−	0.960093i	$-0.590229\pi$
$523$	16.4332	−	20.6066i	0.718574	−	0.901064i	0.998256	+	0.0590291i	$0.0188005\pi$
$524$	0.206288	−	9.77428i	0.00901174	−	0.426991i
$525$	0.719941	+	8.33902i	0.0314208	+	0.363945i
$526$	6.25230	+	18.4916i	0.272613	+	0.806273i
$527$	3.31644	−	6.88665i	0.144466	−	0.299987i
$528$	1.01598	−	0.742312i	0.0442147	−	0.0323050i
$529$	13.9574	−	17.5021i	0.606844	−	0.760959i
$530$	0.955258	−	7.74297i	0.0414938	−	0.336333i
$531$	15.2078	+	19.0700i	0.659962	+	0.827566i
$532$	−10.6791	−	35.8626i	−0.462998	−	1.55484i
$533$	−0.309798	+	0.388475i	−0.0134189	+	0.0168267i
$534$	−3.04093	−	3.10579i	−0.131594	−	0.134401i
$535$	−9.80587	+	4.72226i	−0.423945	+	0.204161i
$536$	−24.2027	−	16.2982i	−1.04540	−	0.703974i
$537$	5.04470	−	1.15142i	0.217695	−	0.0496874i
$538$	−6.52492	+	0.665544i	−0.281309	+	0.0286936i
$539$	−2.56036	−	1.40191i	−0.110282	−	0.0603847i
$540$	−1.48538	−	7.20549i	−0.0639204	−	0.310075i
$541$	5.67668	+	24.8712i	0.244060	+	1.06930i	0.937282	+	0.348572i	$0.113333\pi$
$541$	5.67668	+	24.8712i	0.244060	+	1.06930i	−0.693222	+	0.720724i	$0.743810\pi$
$542$	16.0526	−	15.7174i	0.689517	−	0.675118i
$543$	−1.37769	−	2.86080i	−0.0591222	−	0.122769i
$544$	−15.7326	−	6.45508i	−0.674529	−	0.276759i
$545$	−5.36099	−	4.27525i	−0.229640	−	0.183132i
$546$	−0.132835	+	0.154598i	−0.00568483	+	0.00661618i
$547$	9.53754	−	7.60594i	0.407796	−	0.325206i	−0.398015	−	0.917379i	$-0.630301\pi$
$547$	9.53754	−	7.60594i	0.407796	−	0.325206i	0.805811	+	0.592172i	$0.201730\pi$
$548$	−0.809590	+	38.3597i	−0.0345840	+	1.63865i
$549$	−23.7823	−	18.9657i	−1.01500	−	0.809437i
$550$	−0.792180	−	2.34293i	−0.0337787	−	0.0999028i
$551$	32.7294	+	15.7617i	1.39432	+	0.671470i
$552$	0.844262	+	1.44309i	0.0359342	+	0.0614219i
$553$	22.1068	+	8.38872i	0.940076	+	0.356725i
$554$	−37.4976	−	4.62612i	−1.59312	−	0.196545i
$555$	−4.19482	−	3.34526i	−0.178060	−	0.141998i
$556$	33.4550	+	8.38234i	1.41881	+	0.355490i
$557$	29.9024			1.26701			0.633503	−	0.773740i	$-0.281616\pi$
$557$	29.9024			1.26701			0.633503	+	0.773740i	$0.281616\pi$
$558$	−0.887022	−	8.69627i	−0.0375506	−	0.368142i
$559$	−0.312293	−	0.150393i	−0.0132086	−	0.00636093i
$560$	−9.49320	+	0.417175i	−0.401161	+	0.0176288i
$561$	−0.851988	+	0.410296i	−0.0359710	+	0.0173227i
$562$	−8.35676	−	13.6165i	−0.352508	−	0.574379i
$563$	5.19380	−	22.7555i	0.218893	−	0.959031i	−0.739405	−	0.673261i	$-0.764893\pi$
$563$	5.19380	−	22.7555i	0.218893	−	0.959031i	0.958298	−	0.285771i	$-0.0922496\pi$
$564$	−0.0786360	+	3.72590i	−0.00331117	+	0.156889i
$565$	0.267174	+	0.554792i	0.0112401	+	0.0233403i
$566$	14.3870	+	23.4423i	0.604732	+	0.985353i
$567$	−8.06440	+	7.65438i	−0.338673	+	0.321454i
$568$	23.0105	+	3.33314i	0.965498	+	0.139856i
$569$	36.2215			1.51848			0.759242	−	0.650809i	$-0.225570\pi$
$569$	36.2215			1.51848			0.759242	+	0.650809i	$0.225570\pi$
$570$	−6.73864	+	0.687343i	−0.282251	+	0.0287896i
$571$	−8.21485	+	17.0583i	−0.343781	+	0.713868i	−0.999141	−	0.0414487i	$-0.986803\pi$
$571$	−8.21485	+	17.0583i	−0.343781	+	0.713868i	0.655360	+	0.755317i	$0.272517\pi$
$572$	0.0272712	−	0.0537003i	0.00114027	−	0.00224532i
$573$	20.0724	+	4.58140i	0.838538	+	0.191391i
$574$	−15.3036	−	20.7023i	−0.638759	−	0.864095i
$575$	3.20388	−	0.731265i	0.133611	−	0.0304958i
$576$	−19.1959	+	3.11936i	−0.799829	+	0.129973i
$577$	13.5434	−	3.09119i	0.563818	−	0.128688i	0.0688938	−	0.997624i	$-0.478053\pi$
$577$	13.5434	−	3.09119i	0.563818	−	0.128688i	0.494924	+	0.868936i	$0.335196\pi$
$578$	−9.47161	−	6.09174i	−0.393967	−	0.253383i
$579$	2.77844	−	12.1732i	0.115468	−	0.505899i
$580$	5.90265	−	7.08949i	0.245094	−	0.294375i
$581$	−2.92403	−	1.94545i	−0.121309	−	0.0807109i
$582$	7.19931	−	11.1937i	0.298421	−	0.463994i
$583$	−2.00311	+	1.59743i	−0.0829604	+	0.0661587i
$584$	−23.4302	+	21.9920i	−0.969550	+	0.910035i
$585$	−0.0982783	−	0.123237i	−0.00406331	−	0.00509523i
$586$	8.23836	+	24.3655i	0.340324	+	1.00653i
$587$	43.2157			1.78370			0.891851	−	0.452330i	$-0.149407\pi$
$587$	43.2157			1.78370			0.891851	+	0.452330i	$0.149407\pi$
$588$	−5.96257	−	8.71662i	−0.245892	−	0.359468i
$589$	−17.9804			−0.740868
$590$	−4.08090	−	12.0695i	−0.168008	−	0.496895i
$591$	2.82038	+	3.53665i	0.116015	+	0.145478i
$592$	−20.7835	+	23.9175i	−0.854196	+	0.983002i
$593$	−36.8648	+	29.3987i	−1.51385	+	1.20726i	−0.600814	+	0.799389i	$0.705157\pi$
$593$	−36.8648	+	29.3987i	−1.51385	+	1.20726i	−0.913040	+	0.407869i	$0.866272\pi$
$594$	−1.30693	+	2.03205i	−0.0536238	+	0.0833759i
$595$	7.07321	+	0.984359i	0.289974	+	0.0403548i
$596$	−15.9370	−	13.2690i	−0.652804	−	0.543519i
$597$	−2.75127	+	12.0541i	−0.112602	+	0.493341i
$598$	0.0673083	+	0.0432898i	0.00275244	+	0.00177025i
$599$	32.2430	−	7.35926i	1.31741	−	0.300691i	0.494659	−	0.869087i	$-0.335293\pi$
$599$	32.2430	−	7.35926i	1.31741	−	0.300691i	0.822755	+	0.568396i	$0.192436\pi$
$600$	1.28275	−	8.85553i	0.0523682	−	0.361525i
$601$	4.29972	−	0.981383i	0.175389	−	0.0400315i	−0.133924	−	0.990992i	$-0.542758\pi$
$601$	4.29972	−	0.981383i	0.175389	−	0.0400315i	0.309314	+	0.950960i	$0.399901\pi$
$602$	11.7041	−	13.6216i	0.477025	−	0.555177i
$603$	24.4497	+	5.58047i	0.995667	+	0.227254i
$604$	0.109441	+	0.0555788i	0.00445310	+	0.00226147i
$605$	−4.21763	+	8.75799i	−0.171471	+	0.356063i
$606$	−14.8783	+	1.51759i	−0.604389	+	0.0616479i
$607$	19.3206			0.784199			0.392100	−	0.919923i	$-0.371749\pi$
$607$	19.3206			0.784199			0.392100	+	0.919923i	$0.371749\pi$
$608$	2.37652	+	39.9317i	0.0963807	+	1.61945i
$609$	10.1548	+	1.41322i	0.411495	+	0.0572665i
$610$	8.31110	+	13.5421i	0.336507	+	0.548305i
$611$	0.0773977	+	0.160718i	0.00313118	+	0.00650196i
$612$	14.6124	+	0.308398i	0.590672	+	0.0124663i
$613$	3.97479	−	17.4147i	0.160540	−	0.703373i	−0.829016	−	0.559225i	$-0.811099\pi$
$613$	3.97479	−	17.4147i	0.160540	−	0.703373i	0.989556	−	0.144148i	$-0.0460441\pi$
$614$	3.66386	+	5.96990i	0.147861	+	0.240926i
$615$	−4.19880	+	2.02204i	−0.169312	+	0.0815363i
$616$	2.32344	+	2.08319i	0.0936141	+	0.0839340i
$617$	−14.9436	−	7.19648i	−0.601608	−	0.289719i	0.108183	−	0.994131i	$-0.465497\pi$
$617$	−14.9436	−	7.19648i	−0.601608	−	0.289719i	−0.709792	+	0.704412i	$0.751211\pi$
$618$	−0.518433	−	5.08267i	−0.0208544	−	0.204455i
$619$	39.5914			1.59131			0.795657	−	0.605748i	$-0.207126\pi$
$619$	39.5914			1.59131			0.795657	+	0.605748i	$0.207126\pi$
$620$	−1.10974	+	4.42913i	−0.0445684	+	0.177878i
$621$	−2.50991	−	2.00158i	−0.100719	−	0.0803208i
$622$	44.8050	+	5.52764i	1.79652	+	0.221638i
$623$	5.97133	−	8.97497i	0.239236	−	0.359574i
$624$	0.175942	−	0.128550i	0.00704333	−	0.00514613i
$625$	−12.2143	−	5.88212i	−0.488574	−	0.235285i
$626$	0.671944	+	1.98732i	0.0268563	+	0.0794293i
$627$	1.73915	+	1.38693i	0.0694550	+	0.0553885i
$628$	19.1888	+	0.404983i	0.765715	+	0.0161606i
$629$	18.6179	−	14.8473i	0.742344	−	0.591999i
$630$	7.48308	−	3.27169i	0.298133	−	0.130347i
$631$	−28.2461	−	22.5255i	−1.12446	−	0.896726i	−0.128974	−	0.991648i	$-0.541168\pi$
$631$	−28.2461	−	22.5255i	−1.12446	−	0.896726i	−0.995485	+	0.0949224i	$0.969740\pi$
$632$	−20.9667	−	14.1190i	−0.834010	−	0.561625i
$633$	5.24572	+	10.8929i	0.208499	+	0.432952i
$634$	2.67620	−	2.62032i	0.106286	−	0.104066i
$635$	2.62350	+	11.4943i	0.104110	+	0.456138i
$636$	−9.07850	+	1.87149i	−0.359986	+	0.0742094i
$637$	−0.443391	−	0.242777i	−0.0175678	−	0.00961917i
$638$	−3.01389	+	0.307417i	−0.119321	+	0.0121708i
$639$	−19.4823	+	4.44671i	−0.770707	+	0.175909i
$640$	9.98313	+	1.87917i	0.394618	+	0.0742805i
$641$	14.8442	−	7.14861i	0.586312	−	0.282353i	−0.117117	−	0.993118i	$-0.537365\pi$
$641$	14.8442	−	7.14861i	0.586312	−	0.282353i	0.703430	+	0.710765i	$0.251651\pi$
$642$	9.04678	+	9.23973i	0.357048	+	0.364663i
$643$	18.5192	−	23.2223i	0.730325	−	0.915799i	−0.268548	−	0.963266i	$-0.586544\pi$
$643$	18.5192	−	23.2223i	0.730325	−	0.915799i	0.998873	+	0.0474678i	$0.0151152\pi$
$644$	−3.06700	+	2.79043i	−0.120857	+	0.109958i
$645$	−2.02697	−	2.54174i	−0.0798120	−	0.100081i
$646$	3.68103	−	29.8371i	0.144828	−	1.17392i
$647$	−30.3485	+	38.0558i	−1.19312	+	1.49613i	−0.369273	+	0.929321i	$0.620393\pi$
$647$	−30.3485	+	38.0558i	−1.19312	+	1.49613i	−0.823850	+	0.566808i	$0.808178\pi$
$648$	10.2595	−	6.00222i	0.403033	−	0.235789i
$649$	−1.81541	+	3.76973i	−0.0712610	+	0.147975i
$650$	−0.137186	−	0.405737i	−0.00538088	−	0.0159143i
$651$	−4.83197	+	1.55059i	−0.189380	+	0.0607722i
$652$	−14.2540	−	0.300833i	−0.558228	−	0.0117815i
$653$	−1.65427	+	2.07440i	−0.0647368	+	0.0811774i	−0.813146	−	0.582060i	$-0.802247\pi$
$653$	−1.65427	+	2.07440i	−0.0647368	+	0.0811774i	0.748409	+	0.663238i	$0.230818\pi$
$654$	−2.77175	+	7.66096i	−0.108384	+	0.299567i
$655$		−	4.38908i		−	0.171496i
$656$	10.8846	+	25.2783i	0.424970	+	0.986952i
$657$	11.9833	−	24.8836i	0.467514	−	0.970803i
$658$	−9.08008	+	1.72528i	−0.353978	+	0.0672585i
$659$	−13.9113	−	28.8872i	−0.541909	−	1.12529i	−0.974643	−	0.223764i	$-0.928166\pi$
$659$	−13.9113	−	28.8872i	−0.541909	−	1.12529i	0.432735	−	0.901521i	$-0.357549\pi$
$660$	0.448984	−	0.342807i	0.0174767	−	0.0133437i
$661$	7.49465	+	1.71060i	0.291508	+	0.0665348i	0.365774	−	0.930704i	$-0.380804\pi$
$661$	7.49465	+	1.71060i	0.291508	+	0.0665348i	−0.0742661	+	0.997238i	$0.523661\pi$
$662$	0.131880	−	1.06897i	0.00512567	−	0.0415468i
$663$	−0.147543	+	0.0710531i	−0.00573011	+	0.00275948i
$664$	2.56954	+	2.73758i	0.0997173	+	0.106239i
$665$	−5.13299	−	15.9956i	−0.199049	−	0.620281i
$666$	9.26528	−	25.6087i	0.359022	−	0.992316i
$667$		−	4.02545i		−	0.155866i
$668$	−41.9282	+	8.64330i	−1.62225	+	0.334419i
$669$	2.73489	+	1.31705i	0.105737	+	0.0509202i
$670$	−11.0176	−	7.08608i	−0.425649	−	0.273759i
$671$	1.16111	−	5.08717i	0.0448243	−	0.196388i
$672$	4.08228	+	10.5262i	0.157477	+	0.406055i
$673$	−6.95028	−	30.4512i	−0.267914	−	1.17381i	−0.912436	−	0.409220i	$-0.865801\pi$
$673$	−6.95028	−	30.4512i	−0.267914	−	1.17381i	0.644522	−	0.764586i	$-0.277056\pi$
$674$	−7.88752	+	21.8006i	−0.303816	+	0.839729i
$675$	3.82319	+	16.7505i	0.147155	+	0.644727i
$676$	−11.7680	+	23.1726i	−0.452616	+	0.891255i
$677$	−2.67823	−	0.611288i	−0.102933	−	0.0234937i	0.170744	−	0.985315i	$-0.445383\pi$
$677$	−2.67823	−	0.611288i	−0.102933	−	0.0234937i	−0.273677	+	0.961822i	$0.588240\pi$
$678$	0.522762	−	0.511845i	0.0200765	−	0.0196573i
$679$	30.8600	+	11.7103i	1.18430	+	0.449399i
$680$	−7.12263	−	2.74829i	−0.273140	−	0.105392i
$681$	9.96856	+	12.5002i	0.381996	+	0.479008i
$682$	1.27800	−	0.784338i	0.0489373	−	0.0300339i
$683$	−20.0308	+	15.9740i	−0.766457	+	0.611229i	−0.926680	−	0.375852i	$-0.877350\pi$
$683$	−20.0308	+	15.9740i	−0.766457	+	0.611229i	0.160223	+	0.987081i	$0.448779\pi$
$684$	−14.2604	−	31.2841i	−0.545261	−	1.19618i
$685$			17.2252i			0.658141i
$686$	18.0816	−	18.9487i	0.690360	−	0.723466i
$687$		−	13.8680i		−	0.529096i
$688$	−15.5023	+	11.3266i	−0.591019	+	0.431822i
$689$	−0.346890	+	0.276635i	−0.0132154	+	0.0105390i
$690$	0.392612	+	0.639724i	0.0149465	+	0.0243539i
$691$	−23.5923	−	29.5838i	−0.897494	−	1.12542i	−0.991533	−	0.129854i	$-0.958549\pi$
$691$	−23.5923	−	29.5838i	−0.897494	−	1.12542i	0.0940389	−	0.995569i	$-0.470022\pi$
$692$	19.9100	+	10.1111i	0.756863	+	0.384366i
$693$	−2.50759	−	0.951541i	−0.0952556	−	0.0361461i
$694$	14.9859	+	15.3055i	0.568858	+	0.580990i
$695$	15.0955	+	3.44545i	0.572605	+	0.130693i
$696$	−10.2258	−	3.94566i	−0.387607	−	0.149560i
$697$	−4.60260	−	20.1653i	−0.174336	−	0.763815i
$698$	18.9337	+	6.85027i	0.716652	+	0.259286i
$699$	1.37401	+	6.01994i	0.0519699	+	0.227695i
$700$	22.1446	−	1.44184i	0.836987	−	0.0544964i
$701$	−4.21036	+	18.4468i	−0.159023	+	0.696725i	0.831053	+	0.556193i	$0.187738\pi$
$701$	−4.21036	+	18.4468i	−0.159023	+	0.696725i	−0.990076	+	0.140532i	$0.955119\pi$
$702$	−0.226327	+	0.351900i	−0.00854217	+	0.0132816i
$703$	−50.4693	−	24.3047i	−1.90349	−	0.916670i
$704$	−1.91082	−	2.73459i	−0.0720166	−	0.103064i
$705$			1.67310i			0.0630124i
$706$	43.4660	+	15.7261i	1.63586	+	0.591860i
$707$	−11.3332	−	35.3167i	−0.426227	−	1.32822i
$708$	−12.0317	+	9.18638i	−0.452177	+	0.345245i
$709$	−12.1149	+	5.83424i	−0.454985	+	0.219109i	−0.647317	−	0.762221i	$-0.724109\pi$
$709$	−12.1149	+	5.83424i	−0.454985	+	0.219109i	0.192332	+	0.981330i	$0.438395\pi$
$710$	10.3597	+	1.27809i	0.388792	+	0.0479657i
$711$	21.1806	+	4.83434i	0.794335	+	0.181302i
$712$	−8.40267	+	7.88688i	−0.314903	+	0.295573i
$713$	0.864485	+	1.79512i	0.0323752	+	0.0672278i
$714$	−1.58385	−	8.33575i	−0.0592743	−	0.311957i
$715$	0.0117318	−	0.0243614i	0.000438746	−	0.000911065i
$716$	−2.76986	−	13.4364i	−0.103514	−	0.502144i
$717$		−	7.88323i		−	0.294405i
$718$	−12.8754	−	4.65834i	−0.480505	−	0.173848i
$719$	−27.3330	+	34.2744i	−1.01935	+	1.27822i	−0.0593423	+	0.998238i	$0.518900\pi$
$719$	−27.3330	+	34.2744i	−1.01935	+	1.27822i	−0.960005	+	0.279983i	$0.909671\pi$
$720$	−8.58642	+	1.58195i	−0.319997	+	0.0589557i
$721$	12.0648	−	3.87159i	0.449315	−	0.144186i
$722$	−41.5389	+	14.0449i	−1.54592	+	0.522699i
$723$	−6.94369	+	14.4187i	−0.258239	+	0.536238i
$724$	−7.66022	+	3.49181i	−0.284690	+	0.129772i
$725$	−13.4324	+	16.8437i	−0.498868	+	0.625561i
$726$	11.4625	+	1.41414i	0.425412	+	0.0524836i
$727$	−12.8273	−	16.0849i	−0.475737	−	0.596555i	0.484829	−	0.874609i	$-0.338882\pi$
$727$	−12.8273	−	16.0849i	−0.475737	−	0.596555i	−0.960565	+	0.278054i	$0.910311\pi$
$728$	0.402363	+	0.360757i	0.0149126	+	0.0133705i
$729$	−0.589008	+	0.738592i	−0.0218151	+	0.0273553i
$730$	−10.3082	+	10.0929i	−0.381524	+	0.373556i
$731$	13.0001	−	6.26050i	0.480825	−	0.231553i
$732$	12.0793	−	14.5080i	0.446462	−	0.536232i
$733$	−44.2709	+	10.1045i	−1.63518	+	0.373220i	−0.938803	−	0.344454i	$-0.888064\pi$
$733$	−44.2709	+	10.1045i	−1.63518	+	0.373220i	−0.696379	+	0.717674i	$0.745207\pi$
$734$	1.47053	+	14.4169i	0.0542781	+	0.532137i
$735$	−2.75884	−	3.85593i	−0.101761	−	0.142228i
$736$	3.87244	−	2.15716i	0.142740	−	0.0795140i
$737$	0.957271	+	4.19408i	0.0352615	+	0.154491i
$738$	−16.5489	−	16.9018i	−0.609173	−	0.622165i
$739$	18.9640	+	39.3792i	0.697603	+	1.44859i	0.884659	+	0.466238i	$0.154391\pi$
$739$	18.9640	+	39.3792i	0.697603	+	1.44859i	−0.187056	+	0.982349i	$0.559895\pi$
$740$	−9.10198	+	10.9321i	−0.334595	+	0.401872i
$741$	0.301178	+	0.240181i	0.0110641	+	0.00882329i
$742$	−9.20921	−	21.0635i	−0.338081	−	0.773265i
$743$	−27.3585	+	21.8177i	−1.00369	+	0.800412i	−0.979937	−	0.199306i	$-0.936131\pi$
$743$	−27.3585	+	21.8177i	−1.00369	+	0.800412i	−0.0237478	+	0.999718i	$0.507560\pi$
$744$	5.40746	−	0.436497i	0.198247	−	0.0160028i
$745$	−7.27892	−	5.80474i	−0.266679	−	0.212669i
$746$	5.03629	−	1.70285i	0.184392	−	0.0623457i
$747$	−2.90739	−	1.40013i	−0.106376	−	0.0512280i
$748$	1.03991	+	2.28133i	0.0380229	+	0.0834135i
$749$	−17.7647	+	26.7005i	−0.649108	+	0.975616i
$750$	1.07829	−	8.74024i	0.0393737	−	0.319149i
$751$	−9.37349	−	7.47511i	−0.342044	−	0.272771i	0.437368	−	0.899282i	$-0.355911\pi$
$751$	−9.37349	−	7.47511i	−0.342044	−	0.272771i	−0.779412	+	0.626512i	$0.784482\pi$
$752$	9.87188	+	0.416882i	0.359991	+	0.0152021i
$753$	−5.27330			−0.192170
$754$	−0.521931	+	0.0532371i	−0.0190076	+	0.00193878i
$755$	0.0496486	+	0.0239095i	0.00180690	+	0.000870156i
$756$	−14.5889	−	16.0348i	−0.530593	−	0.583182i
$757$	9.99027	−	4.81106i	0.363103	−	0.174861i	−0.243432	−	0.969918i	$-0.578273\pi$
$757$	9.99027	−	4.81106i	0.363103	−	0.174861i	0.606535	+	0.795057i	$0.292559\pi$
$758$	−36.8379	+	22.6082i	−1.33801	+	0.821166i
$759$	0.0548505	−	0.240316i	0.00199095	−	0.00872291i
$760$	1.44496	+	17.9006i	0.0524142	+	0.649324i
$761$	7.16016	+	14.8682i	0.259556	+	0.538973i	0.989500	−	0.144534i	$-0.0461683\pi$
$761$	7.16016	+	14.8682i	0.259556	+	0.538973i	−0.729944	+	0.683507i	$0.760454\pi$
$762$	11.9388	−	7.32712i	0.432498	−	0.265433i
$763$	−20.0121	−	2.78503i	−0.724487	−	0.100825i
$764$	13.2669	−	52.9499i	0.479980	−	1.91566i
$765$	6.56162			0.237236
$766$	−3.76896	−	36.9505i	−0.136178	−	1.33508i
$767$	−0.314384	+	0.652825i	−0.0113517	+

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.j (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33971 + 0.452975i) q^{2} +(0.470328 + 0.589772i) q^{3} +(1.58963 - 1.21371i) q^{4} +(0.701998 - 0.559824i) q^{5} +(-0.897253 - 0.577075i) q^{6} +(0.938659 - 2.47364i) q^{7} +(-1.57985 + 2.34607i) q^{8} +(0.540940 - 2.37001i) q^{9} +O(q^{10})\)	\(q+(-1.33971 + 0.452975i) q^{2} +(0.470328 + 0.589772i) q^{3} +(1.58963 - 1.21371i) q^{4} +(0.701998 - 0.559824i) q^{5} +(-0.897253 - 0.577075i) q^{6} +(0.938659 - 2.47364i) q^{7} +(-1.57985 + 2.34607i) q^{8} +(0.540940 - 2.37001i) q^{9} +(-0.686884 + 1.06799i) q^{10} +(0.406550 - 0.0927925i) q^{11} +(1.46346 + 0.366677i) q^{12} +(0.0704045 - 0.0160694i) q^{13} +(-0.137027 + 3.73915i) q^{14} +(0.660338 + 0.150718i) q^{15} +(1.05383 - 3.85869i) q^{16} +(-1.30432 + 2.70845i) q^{17} +(0.348856 + 3.42015i) q^{18} +7.07149 q^{19} +(0.436451 - 1.74193i) q^{20} +(1.90036 - 0.609829i) q^{21} +(-0.502625 + 0.308472i) q^{22} +(-0.339993 - 0.706003i) q^{23} +(-2.12670 + 0.171670i) q^{24} +(-0.933207 + 4.08865i) q^{25} +(-0.0870424 + 0.0534197i) q^{26} +(3.69112 - 1.77755i) q^{27} +(-1.51017 - 5.07143i) q^{28} +(4.62837 + 2.22890i) q^{29} +(-0.952931 + 0.0971991i) q^{30} -2.54266 q^{31} +(0.336071 + 5.64686i) q^{32} +(0.245938 + 0.196129i) q^{33} +(0.520546 - 4.21935i) q^{34} +(-0.725871 - 2.26198i) q^{35} +(-2.01661 - 4.42398i) q^{36} +(-7.13701 - 3.43700i) q^{37} +(-9.47372 + 3.20321i) q^{38} +(0.0425905 + 0.0339648i) q^{39} +(0.204336 + 2.53138i) q^{40} +(-5.37941 + 4.28994i) q^{41} +(-2.26969 + 1.67781i) q^{42} +(-3.75265 - 2.99264i) q^{43} +(0.533640 - 0.640939i) q^{44} +(-0.947052 - 1.96657i) q^{45} +(0.775292 + 0.791828i) q^{46} +(0.549665 + 2.40824i) q^{47} +(2.77139 - 1.19333i) q^{48} +(-5.23784 - 4.64382i) q^{49} +(-0.601833 - 5.90031i) q^{50} +(-2.21083 + 0.504606i) q^{51} +(0.0924134 - 0.110995i) q^{52} +(-5.53554 + 2.66578i) q^{53} +(-4.13983 + 4.05338i) q^{54} +(0.233450 - 0.292737i) q^{55} +(4.32041 + 6.11016i) q^{56} +(3.32592 + 4.17057i) q^{57} +(-7.21029 - 0.889541i) q^{58} +(-6.25588 + 7.84462i) q^{59} +(1.23262 - 0.561872i) q^{60} +(5.42920 - 11.2738i) q^{61} +(3.40641 - 1.15176i) q^{62} +(-5.35481 - 3.56272i) q^{63} +(-3.00813 - 7.41291i) q^{64} +(0.0404278 - 0.0506948i) q^{65} +(-0.418327 - 0.151352i) q^{66} +10.3163i q^{67} +(1.21388 + 5.88848i) q^{68} +(0.256473 - 0.532571i) q^{69} +(1.99707 + 2.70158i) q^{70} +(-3.56667 - 7.40627i) q^{71} +(4.70562 + 5.01335i) q^{72} +(11.0764 + 2.52812i) q^{73} +(11.1184 + 1.37169i) q^{74} +(-2.85029 + 1.37262i) q^{75} +(11.2410 - 8.58272i) q^{76} +(0.152077 - 1.09276i) q^{77} +(-0.0724439 - 0.0262104i) q^{78} +8.93692i q^{79} +(-1.42040 - 3.29875i) q^{80} +(-3.78628 - 1.82337i) q^{81} +(5.26360 - 8.18400i) q^{82} +(0.295384 - 1.29416i) q^{83} +(2.28072 - 3.27589i) q^{84} +(0.600626 + 2.63151i) q^{85} +(6.38304 + 2.30940i) q^{86} +(0.862303 + 3.77800i) q^{87} +(-0.424592 + 1.10040i) q^{88} +(3.97228 + 0.906646i) q^{89} +(2.15958 + 2.20564i) q^{90} +(0.0263359 - 0.189239i) q^{91} +(-1.39734 - 0.709628i) q^{92} +(-1.19588 - 1.49959i) q^{93} +(-1.82726 - 2.97735i) q^{94} +(4.96417 - 3.95879i) q^{95} +(-3.17230 + 2.85408i) q^{96} +12.4755i q^{97} +(9.12070 + 3.84874i) q^{98} -1.01372i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9}+O(q^{10}) \) 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9	\( 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9} - 7 q^{10} - 42 q^{12} - 14 q^{13} + 21 q^{14} - 13 q^{16} - 14 q^{17} - 12 q^{18} - 7 q^{20} - 14 q^{21} + 3 q^{22} + 35 q^{24} - 7 q^{26} + 42 q^{28} - 30 q^{29} - 4 q^{30} - 5 q^{32} - 14 q^{33} + 77 q^{34} - 11 q^{36} + 10 q^{37} - 21 q^{38} - 63 q^{40} - 14 q^{41} - 7 q^{42} - 55 q^{44} - 14 q^{45} - 19 q^{46} - 132 q^{50} - 7 q^{52} - 2 q^{53} + 14 q^{54} - 70 q^{56} - 64 q^{57} - 3 q^{58} - 107 q^{60} + 14 q^{61} - 21 q^{62} - 11 q^{64} - 22 q^{65} + 161 q^{66} - 70 q^{69} - 77 q^{70} + 114 q^{72} - 14 q^{73} + 5 q^{74} + 70 q^{76} - 42 q^{77} + 61 q^{78} + 92 q^{81} - 42 q^{82} + 70 q^{84} - 6 q^{85} + 47 q^{86} + 65 q^{88} - 14 q^{89} + 112 q^{90} - 70 q^{92} - 48 q^{93} - 28 q^{94} + 238 q^{96} + 105 q^{98}+O(q^{100}) \) 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9 - 7 * q^10 - 42 * q^12 - 14 * q^13 + 21 * q^14 - 13 * q^16 - 14 * q^17 - 12 * q^18 - 7 * q^20 - 14 * q^21 + 3 * q^22 + 35 * q^24 - 7 * q^26 + 42 * q^28 - 30 * q^29 - 4 * q^30 - 5 * q^32 - 14 * q^33 + 77 * q^34 - 11 * q^36 + 10 * q^37 - 21 * q^38 - 63 * q^40 - 14 * q^41 - 7 * q^42 - 55 * q^44 - 14 * q^45 - 19 * q^46 - 132 * q^50 - 7 * q^52 - 2 * q^53 + 14 * q^54 - 70 * q^56 - 64 * q^57 - 3 * q^58 - 107 * q^60 + 14 * q^61 - 21 * q^62 - 11 * q^64 - 22 * q^65 + 161 * q^66 - 70 * q^69 - 77 * q^70 + 114 * q^72 - 14 * q^73 + 5 * q^74 + 70 * q^76 - 42 * q^77 + 61 * q^78 + 92 * q^81 - 42 * q^82 + 70 * q^84 - 6 * q^85 + 47 * q^86 + 65 * q^88 - 14 * q^89 + 112 * q^90 - 70 * q^92 - 48 * q^93 - 28 * q^94 + 238 * q^96 + 105 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more