LMFDB - Embedded newform 387.2.y.c.181.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(10,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("387.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.y (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 43)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			181.2
Character	$\chi$	$=$	387.181
Dual form			387.2.y.c.325.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11243 + 1.39495i) q^{2} +(-0.263330 + 1.15372i) q^{4} +(0.492700 + 0.335917i) q^{5} +(2.18154 - 3.77854i) q^{7} +(1.31271 - 0.632167i) q^{8} +O(q^{10})$	\(q+(1.11243 + 1.39495i) q^{2} +(-0.263330 + 1.15372i) q^{4} +(0.492700 + 0.335917i) q^{5} +(2.18154 - 3.77854i) q^{7} +(1.31271 - 0.632167i) q^{8} +(0.0795092 + 1.06098i) q^{10} +(0.452993 + 1.98469i) q^{11} +(-0.130264 + 1.73826i) q^{13} +(7.69769 - 1.16024i) q^{14} +(4.47454 + 2.15483i) q^{16} +(-1.21261 + 0.826746i) q^{17} +(-2.07906 + 0.641305i) q^{19} +(-0.517297 + 0.479982i) q^{20} +(-2.26462 + 2.83974i) q^{22} +(-1.99563 + 1.85167i) q^{23} +(-1.69679 - 4.32336i) q^{25} +(-2.56969 + 1.75199i) q^{26} +(3.78492 + 3.51189i) q^{28} +(-7.48963 + 1.12888i) q^{29} +(-0.208229 + 0.530558i) q^{31} +(1.32334 + 5.79793i) q^{32} +(-2.50222 - 0.771833i) q^{34} +(2.34412 - 1.12887i) q^{35} +(1.98083 + 3.43090i) q^{37} +(-3.20740 - 2.18677i) q^{38} +(0.859126 + 0.129492i) q^{40} +(-1.32534 - 1.66193i) q^{41} +(3.81986 + 5.32998i) q^{43} -2.40907 q^{44} +(-4.80299 - 0.723935i) q^{46} +(2.08348 - 9.12834i) q^{47} +(-6.01823 - 10.4239i) q^{49} +(4.14329 - 7.17639i) q^{50} +(-1.97117 - 0.608024i) q^{52} +(0.441351 + 5.88942i) q^{53} +(-0.443502 + 1.13002i) q^{55} +(0.475058 - 6.33921i) q^{56} +(-9.90645 - 9.19184i) q^{58} +(4.60418 + 2.21726i) q^{59} +(-3.57526 - 9.10961i) q^{61} +(-0.971743 + 0.299743i) q^{62} +(-0.422726 + 0.530082i) q^{64} +(-0.648092 + 0.812681i) q^{65} +(-0.506577 + 0.156258i) q^{67} +(-0.634519 - 1.61673i) q^{68} +(4.18239 + 2.01413i) q^{70} +(-3.91319 - 3.63091i) q^{71} +(-1.05058 + 14.0191i) q^{73} +(-2.58239 + 6.57982i) q^{74} +(-0.192410 - 2.56753i) q^{76} +(8.48745 + 2.61803i) q^{77} +(-1.82633 + 3.16330i) q^{79} +(1.48076 + 2.56476i) q^{80} +(0.843946 - 3.69757i) q^{82} +(-10.2305 - 1.54199i) q^{83} -0.875173 q^{85} +(-3.18571 + 11.2578i) q^{86} +(1.84930 + 2.31895i) q^{88} +(-5.97021 - 0.899865i) q^{89} +(6.28390 + 4.28429i) q^{91} +(-1.61081 - 2.79000i) q^{92} +(15.0513 - 7.24833i) q^{94} +(-1.23978 - 0.382420i) q^{95} +(-2.28198 - 9.99799i) q^{97} +(7.84589 - 19.9910i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8}+O(q^{10}) $ 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8	$ 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8} - 7 q^{10} + 4 q^{11} - 18 q^{14} - 10 q^{16} + 10 q^{17} + 10 q^{19} + 3 q^{20} - 3 q^{22} - 4 q^{23} - 2 q^{25} + 15 q^{26} + 20 q^{28} - 9 q^{29} + 40 q^{31} - 48 q^{32} - 42 q^{34} - 11 q^{35} - 19 q^{37} + 21 q^{38} - 97 q^{40} + 28 q^{41} - 8 q^{43} - 14 q^{44} - 61 q^{46} + 30 q^{47} + 6 q^{49} + 3 q^{50} - 8 q^{52} + 24 q^{53} + 14 q^{55} - 39 q^{56} + 64 q^{58} + q^{59} - 14 q^{61} - 33 q^{62} + 48 q^{64} - 38 q^{65} + 66 q^{67} - 66 q^{68} + 47 q^{70} + 33 q^{71} + 29 q^{73} + 40 q^{74} - 39 q^{76} + 27 q^{77} - 17 q^{79} - 8 q^{80} - 54 q^{82} + 23 q^{83} - 56 q^{85} + 45 q^{86} - 17 q^{88} + 19 q^{89} - 13 q^{91} + 18 q^{92} + 44 q^{94} - q^{95} - 31 q^{97} + 5 q^{98}+O(q^{100}) $ 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8 - 7 * q^10 + 4 * q^11 - 18 * q^14 - 10 * q^16 + 10 * q^17 + 10 * q^19 + 3 * q^20 - 3 * q^22 - 4 * q^23 - 2 * q^25 + 15 * q^26 + 20 * q^28 - 9 * q^29 + 40 * q^31 - 48 * q^32 - 42 * q^34 - 11 * q^35 - 19 * q^37 + 21 * q^38 - 97 * q^40 + 28 * q^41 - 8 * q^43 - 14 * q^44 - 61 * q^46 + 30 * q^47 + 6 * q^49 + 3 * q^50 - 8 * q^52 + 24 * q^53 + 14 * q^55 - 39 * q^56 + 64 * q^58 + q^59 - 14 * q^61 - 33 * q^62 + 48 * q^64 - 38 * q^65 + 66 * q^67 - 66 * q^68 + 47 * q^70 + 33 * q^71 + 29 * q^73 + 40 * q^74 - 39 * q^76 + 27 * q^77 - 17 * q^79 - 8 * q^80 - 54 * q^82 + 23 * q^83 - 56 * q^85 + 45 * q^86 - 17 * q^88 + 19 * q^89 - 13 * q^91 + 18 * q^92 + 44 * q^94 - q^95 - 31 * q^97 + 5 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{1}{21}\right)$	$1$

Coefficient data

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

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

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

$2$	1.11243	+	1.39495i	0.786610	+	0.986378i	0.999956	+	0.00940101i	$0.00299248\pi$
$2$	1.11243	+	1.39495i	0.786610	+	0.986378i	−0.213346	+	0.976977i	$0.568436\pi$
$3$		0			0
$3$		0			0
$4$	−0.263330	+	1.15372i	−0.131665	+	0.576861i
$5$	0.492700	+	0.335917i	0.220342	+	0.150227i	0.668461	−	0.743747i	$-0.266953\pi$
$5$	0.492700	+	0.335917i	0.220342	+	0.150227i	−0.448119	+	0.893974i	$0.647906\pi$
$6$		0			0
$7$	2.18154	−	3.77854i	0.824544	−	1.42815i	−0.0777227	−	0.996975i	$-0.524765\pi$
$7$	2.18154	−	3.77854i	0.824544	−	1.42815i	0.902267	−	0.431178i	$-0.141902\pi$
$8$	1.31271	−	0.632167i	0.464112	−	0.223505i
$9$		0			0
$10$	0.0795092	+	1.06098i	0.0251430	+	0.335510i
$11$	0.452993	+	1.98469i	0.136582	+	0.598407i	0.996171	+	0.0874207i	$0.0278624\pi$
$11$	0.452993	+	1.98469i	0.136582	+	0.598407i	−0.859589	+	0.510986i	$0.829280\pi$
$12$		0			0
$13$	−0.130264	+	1.73826i	−0.0361289	+	0.482106i	0.949566	+	0.313567i	$0.101524\pi$
$13$	−0.130264	+	1.73826i	−0.0361289	+	0.482106i	−0.985695	+	0.168539i	$0.946095\pi$
$14$	7.69769	−	1.16024i	2.05729	−	0.310087i
$15$		0			0
$16$	4.47454	+	2.15483i	1.11864	+	0.538706i
$17$	−1.21261	+	0.826746i	−0.294102	+	0.200515i	−0.701378	−	0.712790i	$-0.747431\pi$
$17$	−1.21261	+	0.826746i	−0.294102	+	0.200515i	0.407275	+	0.913305i	$0.366479\pi$
$18$		0			0
$19$	−2.07906	+	0.641305i	−0.476969	+	0.147125i	−0.523912	−	0.851772i	$-0.675528\pi$
$19$	−2.07906	+	0.641305i	−0.476969	+	0.147125i	0.0469436	+	0.998898i	$0.485052\pi$
$20$	−0.517297	+	0.479982i	−0.115671	+	0.107327i
$21$		0			0
$22$	−2.26462	+	2.83974i	−0.482818	+	0.605434i
$23$	−1.99563	+	1.85167i	−0.416117	+	0.386100i	−0.860260	−	0.509856i	$-0.829699\pi$
$23$	−1.99563	+	1.85167i	−0.416117	+	0.386100i	0.444143	+	0.895956i	$0.353508\pi$
$24$		0			0
$25$	−1.69679	−	4.32336i	−0.339358	−	0.864671i
$26$	−2.56969	+	1.75199i	−0.503958	+	0.343593i
$27$		0			0
$28$	3.78492	+	3.51189i	0.715283	+	0.663685i
$29$	−7.48963	+	1.12888i	−1.39079	+	0.209628i	−0.801355	−	0.598189i	$-0.795887\pi$
$29$	−7.48963	+	1.12888i	−1.39079	+	0.209628i	−0.589434	+	0.807817i	$0.700649\pi$
$30$		0			0
$31$	−0.208229	+	0.530558i	−0.0373990	+	0.0952911i	−0.948353	−	0.317217i	$-0.897252\pi$
$31$	−0.208229	+	0.530558i	−0.0373990	+	0.0952911i	0.910954	+	0.412508i	$0.135347\pi$
$32$	1.32334	+	5.79793i	0.233936	+	1.02494i
$33$		0			0
$34$	−2.50222	−	0.771833i	−0.429128	−	0.132368i
$35$	2.34412	−	1.12887i	0.396228	−	0.190813i
$36$		0			0
$37$	1.98083	+	3.43090i	0.325647	+	0.564037i	0.981643	−	0.190727i	$-0.0610846\pi$
$37$	1.98083	+	3.43090i	0.325647	+	0.564037i	−0.655996	+	0.754764i	$0.727751\pi$
$38$	−3.20740	−	2.18677i	−0.520310	−	0.354741i
$39$		0			0
$40$	0.859126	+	0.129492i	0.135840	+	0.0204746i
$41$	−1.32534	−	1.66193i	−0.206984	−	0.259549i	0.667494	−	0.744615i	$-0.267367\pi$
$41$	−1.32534	−	1.66193i	−0.206984	−	0.259549i	−0.874478	+	0.485066i	$0.838796\pi$
$42$		0			0
$43$	3.81986	+	5.32998i	0.582523	+	0.812814i
$43$	3.81986	+	5.32998i	0.582523	+	0.812814i
$44$	−2.40907			−0.363181
$45$		0			0
$46$	−4.80299	−	0.723935i	−0.708163	−	0.106738i
$47$	2.08348	−	9.12834i	0.303907	−	1.33151i	−0.560266	−	0.828312i	$-0.689301\pi$
$47$	2.08348	−	9.12834i	0.303907	−	1.33151i	0.864174	−	0.503193i	$-0.167842\pi$
$48$		0			0
$49$	−6.01823	−	10.4239i	−0.859747	−	1.48913i
$50$	4.14329	−	7.17639i	0.585950	−	1.01489i
$51$		0			0
$52$	−1.97117	−	0.608024i	−0.273351	−	0.0843178i
$53$	0.441351	+	5.88942i	0.0606242	+	0.808974i	0.941797	+	0.336181i	$0.109135\pi$
$53$	0.441351	+	5.88942i	0.0606242	+	0.808974i	−0.881173	+	0.472794i	$0.843246\pi$
$54$		0			0
$55$	−0.443502	+	1.13002i	−0.0598017	+	0.152372i
$56$	0.475058	−	6.33921i	0.0634823	−	0.847113i
$57$		0			0
$58$	−9.90645	−	9.19184i	−1.30078	−	1.20695i
$59$	4.60418	+	2.21726i	0.599413	+	0.288662i	0.708881	−	0.705328i	$-0.249200\pi$
$59$	4.60418	+	2.21726i	0.599413	+	0.288662i	−0.109468	+	0.993990i	$0.534915\pi$
$60$		0			0
$61$	−3.57526	−	9.10961i	−0.457765	−	1.16637i	−0.954433	−	0.298426i	$-0.903539\pi$
$61$	−3.57526	−	9.10961i	−0.457765	−	1.16637i	0.496668	−	0.867941i	$-0.334557\pi$
$62$	−0.971743	+	0.299743i	−0.123411	+	0.0380674i
$63$		0			0
$64$	−0.422726	+	0.530082i	−0.0528407	+	0.0662602i
$65$	−0.648092	+	0.812681i	−0.0803859	+	0.100801i
$66$		0			0
$67$	−0.506577	+	0.156258i	−0.0618882	+	0.0190900i	−0.325545	−	0.945527i	$-0.605548\pi$
$67$	−0.506577	+	0.156258i	−0.0618882	+	0.0190900i	0.263656	+	0.964617i	$0.415071\pi$
$68$	−0.634519	−	1.61673i	−0.0769467	−	0.196057i
$69$		0			0
$70$	4.18239	+	2.01413i	0.499891	+	0.240735i
$71$	−3.91319	−	3.63091i	−0.464410	−	0.430910i	0.412941	−	0.910758i	$-0.364501\pi$
$71$	−3.91319	−	3.63091i	−0.464410	−	0.430910i	−0.877352	+	0.479848i	$0.840692\pi$
$72$		0			0
$73$	−1.05058	+	14.0191i	−0.122961	+	1.64081i	0.505401	+	0.862885i	$0.331345\pi$
$73$	−1.05058	+	14.0191i	−0.122961	+	1.64081i	−0.628362	+	0.777921i	$0.716274\pi$
$74$	−2.58239	+	6.57982i	−0.300196	+	0.764888i
$75$		0			0
$76$	−0.192410	−	2.56753i	−0.0220709	−	0.294516i
$77$	8.48745	+	2.61803i	0.967234	+	0.298352i
$78$		0			0
$79$	−1.82633	+	3.16330i	−0.205478	+	0.355899i	−0.950285	−	0.311381i	$-0.899208\pi$
$79$	−1.82633	+	3.16330i	−0.205478	+	0.355899i	0.744807	+	0.667280i	$0.232542\pi$
$80$	1.48076	+	2.56476i	0.165554	+	0.286748i
$81$		0			0
$82$	0.843946	−	3.69757i	0.0931983	−	0.408328i
$83$	−10.2305	−	1.54199i	−1.12294	−	0.169256i	−0.438784	−	0.898592i	$-0.644591\pi$
$83$	−10.2305	−	1.54199i	−1.12294	−	0.169256i	−0.684155	+	0.729337i	$0.739829\pi$
$84$		0			0
$85$	−0.875173			−0.0949258
$86$	−3.18571	+	11.2578i	−0.343524	+	1.21396i
$87$		0			0
$88$	1.84930	+	2.31895i	0.197136	+	0.247201i
$89$	−5.97021	−	0.899865i	−0.632841	−	0.0953855i	−0.175215	−	0.984530i	$-0.556062\pi$
$89$	−5.97021	−	0.899865i	−0.632841	−	0.0953855i	−0.457626	+	0.889145i	$0.651300\pi$
$90$		0			0
$91$	6.28390	+	4.28429i	0.658731	+	0.449115i
$92$	−1.61081	−	2.79000i	−0.167938	−	0.290878i
$93$		0			0
$94$	15.0513	−	7.24833i	1.55242	−	0.747608i
$95$	−1.23978	−	0.382420i	−0.127198	−	0.0392355i
$96$		0			0
$97$	−2.28198	−	9.99799i	−0.231700	−	1.01514i	−0.948230	−	0.317586i	$-0.897128\pi$
$97$	−2.28198	−	9.99799i	−0.231700	−	1.01514i	0.716530	−	0.697556i	$-0.245729\pi$
$98$	7.84589	−	19.9910i	0.792554	−	2.01940i
$99$		0			0
$100$	5.43477	−	0.819160i	0.543477	−	0.0819160i
$101$	−8.19564	−	7.60445i	−0.815497	−	0.756671i	0.157492	−	0.987520i	$-0.449659\pi$
$101$	−8.19564	−	7.60445i	−0.815497	−	0.756671i	−0.972989	+	0.230849i	$0.925850\pi$
$102$		0			0
$103$	−0.115290	+	0.0786031i	−0.0113598	+	0.00774499i	−0.568987	−	0.822347i	$-0.692664\pi$
$103$	−0.115290	+	0.0786031i	−0.0113598	+	0.00774499i	0.557627	+	0.830092i	$0.311712\pi$
$104$	0.927870	+	2.36417i	0.0909851	+	0.231826i
$105$		0			0
$106$	−7.72447	+	7.16726i	−0.750267	+	0.696146i
$107$	−3.64662	+	4.57272i	−0.352533	+	0.442062i	−0.926203	−	0.377024i	$-0.876947\pi$
$107$	−3.64662	+	4.57272i	−0.352533	+	0.442062i	0.573671	+	0.819086i	$0.305519\pi$
$108$		0			0
$109$	−0.578145	+	0.536440i	−0.0553762	+	0.0513816i	−0.707375	−	0.706838i	$-0.750121\pi$
$109$	−0.578145	+	0.536440i	−0.0553762	+	0.0513816i	0.651999	+	0.758220i	$0.273931\pi$
$110$	−2.06969	+	0.638415i	−0.197337	+	0.0608705i
$111$		0			0
$112$	17.9035	−	12.2064i	1.69172	−	1.15340i
$113$	−5.42511	−	2.61260i	−0.510352	−	0.245772i	0.160942	−	0.986964i	$-0.448547\pi$
$113$	−5.42511	−	2.61260i	−0.510352	−	0.245772i	−0.671294	+	0.741191i	$0.734261\pi$
$114$		0			0
$115$	−1.60525	+	0.241953i	−0.149691	+	0.0225622i
$116$	0.669827	−	8.93822i	0.0621919	−	0.829893i
$117$		0			0
$118$	2.02889	+	8.88915i	0.186775	+	0.818313i
$119$	0.478526	+	6.38549i	0.0438664	+	0.585357i
$120$		0			0
$121$	6.17687	−	2.97462i	0.561533	−	0.270420i
$122$	8.73020	−	15.1211i	0.790395	−	1.36900i
$123$		0			0
$124$	−0.557284	−	0.379950i	−0.0500456	−	0.0341205i
$125$	1.27974	−	5.60692i	0.114464	−	0.501498i
$126$		0			0
$127$	−2.35751	−	2.95623i	−0.209195	−	0.262323i	0.666153	−	0.745815i	$-0.267940\pi$
$127$	−2.35751	−	2.95623i	−0.209195	−	0.262323i	−0.875349	+	0.483492i	$0.839368\pi$
$128$	10.6844			0.944374
$129$		0			0
$130$	−1.85461			−0.162660
$131$	10.8237	+	13.5725i	0.945669	+	1.18583i	0.982453	+	0.186508i	$0.0597170\pi$
$131$	10.8237	+	13.5725i	0.945669	+	1.18583i	−0.0367848	+	0.999323i	$0.511712\pi$
$132$		0			0
$133$	−2.11235	+	9.25483i	−0.183164	+	0.802496i
$134$	−0.781506	−	0.532822i	−0.0675118	−	0.0460288i
$135$		0			0
$136$	−1.06917	+	1.85185i	−0.0916803	+	0.158795i
$137$	2.80268	−	1.34970i	0.239449	−	0.115312i	−0.310311	−	0.950635i	$-0.600433\pi$
$137$	2.80268	−	1.34970i	0.239449	−	0.115312i	0.549760	+	0.835322i	$0.314719\pi$
$138$		0			0
$139$	0.390211	+	5.20700i	0.0330973	+	0.441652i	0.988995	+	0.147951i	$0.0472679\pi$
$139$	0.390211	+	5.20700i	0.0330973	+	0.441652i	−0.955897	+	0.293701i	$0.905113\pi$
$140$	0.685124	+	3.00173i	0.0579036	+	0.253692i
$141$		0			0
$142$	0.711766	−	9.49785i	0.0597301	−	0.797042i
$143$	−3.50891	+	0.528883i	−0.293430	+	0.0442275i
$144$		0			0
$145$	−4.06935	−	1.95969i	−0.337941	−	0.162744i
$146$	−20.7246	+	14.1298i	−1.71518	+	1.16939i
$147$		0			0
$148$	−4.47992	+	1.38187i	−0.368247	+	0.113589i
$149$	14.9269	−	13.8502i	1.22286	−	1.13465i	0.236229	−	0.971698i	$-0.424089\pi$
$149$	14.9269	−	13.8502i	1.22286	−	1.13465i	0.986634	−	0.162953i	$-0.0521019\pi$
$150$		0			0
$151$	−12.4488	+	15.6103i	−1.01307	+	1.27035i	−0.0506675	+	0.998716i	$0.516135\pi$
$151$	−12.4488	+	15.6103i	−1.01307	+	1.27035i	−0.962401	+	0.271632i	$0.912437\pi$
$152$	−2.32379	+	2.15616i	−0.188484	+	0.174887i
$153$		0			0
$154$	5.78971	+	14.7519i	0.466548	+	1.18875i
$155$	−0.280818	+	0.191458i	−0.0225558	+	0.0153783i
$156$		0			0
$157$	−12.6185	−	11.7083i	−1.00707	−	0.934423i	−0.00921861	−	0.999958i	$-0.502934\pi$
$157$	−12.6185	−	11.7083i	−1.00707	−	0.934423i	−0.997850	+	0.0655341i	$0.979125\pi$
$158$	−6.44432	+	0.971325i	−0.512682	+	0.0772744i
$159$		0			0
$160$	−1.29561	+	3.30117i	−0.102427	+	0.260980i
$161$	2.64307	+	11.5800i	0.208303	+	0.912636i
$162$		0			0
$163$	20.8543	+	6.43270i	1.63344	+	0.503848i	0.969737	−	0.244152i	$-0.0785095\pi$
$163$	20.8543	+	6.43270i	1.63344	+	0.503848i	0.663699	+	0.748000i	$0.268986\pi$
$164$	2.26641	−	1.09144i	0.176977	−	0.0852274i
$165$		0			0
$166$	−9.22972	−	15.9863i	−0.716365	−	1.24078i
$167$	−7.00644	−	4.77691i	−0.542175	−	0.369649i	0.261049	−	0.965325i	$-0.415931\pi$
$167$	−7.00644	−	4.77691i	−0.542175	−	0.369649i	−0.803224	+	0.595677i	$0.796884\pi$
$168$		0			0
$169$	9.85023	+	1.48468i	0.757710	+	0.114206i
$170$	−0.973572	−	1.22082i	−0.0746696	−	0.0936327i
$171$		0			0
$172$	−7.15520	+	3.00351i	−0.545579	+	0.229016i
$173$	11.0837			0.842677			0.421338	−	0.906904i	$-0.361561\pi$
$173$	11.0837			0.842677			0.421338	+	0.906904i	$0.361561\pi$
$174$		0			0
$175$	−20.0376	−	3.02018i	−1.51470	−	0.228304i
$176$	−2.24973	+	9.85670i	−0.169580	+	0.742977i
$177$		0			0
$178$	−5.38621	−	9.32918i	−0.403713	−	0.699252i
$179$	−7.70817	+	13.3509i	−0.576135	+	0.997896i	0.419782	+	0.907625i	$0.362107\pi$
$179$	−7.70817	+	13.3509i	−0.576135	+	0.997896i	−0.995917	+	0.0902708i	$0.971227\pi$
$180$		0			0
$181$	−3.06551	−	0.945583i	−0.227857	−	0.0702847i	0.178724	−	0.983899i	$-0.442803\pi$
$181$	−3.06551	−	0.945583i	−0.227857	−	0.0702847i	−0.406581	+	0.913615i	$0.633279\pi$
$182$	1.01406	+	13.5317i	0.0751672	+	1.00304i
$183$		0			0
$184$	−1.44911	+	3.69227i	−0.106830	+	0.272198i
$185$	−0.176543	+	2.35580i	−0.0129797	+	0.173202i
$186$		0			0
$187$	−2.19014	−	2.03215i	−0.160159	−	0.148606i
$188$	9.98293	+	4.80753i	0.728080	+	0.350625i
$189$		0			0
$190$	−0.845713	−	2.15484i	−0.0613545	−	0.156329i
$191$	5.09606	−	1.57193i	0.368738	−	0.113741i	−0.104848	−	0.994488i	$-0.533436\pi$
$191$	5.09606	−	1.57193i	0.368738	−	0.113741i	0.473586	+	0.880748i	$0.342959\pi$
$192$		0			0
$193$	−4.19096	+	5.25530i	−0.301672	+	0.378285i	−0.909444	−	0.415827i	$-0.863492\pi$
$193$	−4.19096	+	5.25530i	−0.301672	+	0.378285i	0.607772	+	0.794112i	$0.292064\pi$
$194$	11.4081	−	14.3054i	0.819057	−	1.02706i
$195$		0			0
$196$	13.6110	−	4.19845i	0.972217	−	0.299889i
$197$	1.77600	+	4.52518i	0.126535	+	0.322406i	0.980077	−	0.198618i	$-0.0636454\pi$
$197$	1.77600	+	4.52518i	0.126535	+	0.322406i	−0.853542	+	0.521024i	$0.825550\pi$
$198$		0			0
$199$	20.4216	+	9.83452i	1.44765	+	0.697151i	0.982185	−	0.187916i	$-0.0601734\pi$
$199$	20.4216	+	9.83452i	1.44765	+	0.697151i	0.465463	+	0.885067i	$0.345888\pi$
$200$	−4.96048	−	4.60265i	−0.350759	−	0.325456i
$201$		0			0
$202$	1.49070	−	19.8920i	0.104885	−	1.39959i
$203$	−12.0734	+	30.7625i	−0.847387	+	2.15911i
$204$		0			0
$205$	−0.0947264	−	1.26404i	−0.00661598	−	0.0882841i
$206$	−0.237899	−	0.0733822i	−0.0165752	−	0.00511278i
$207$		0			0
$208$	−4.32852	+	7.49721i	−0.300129	+	0.519838i
$209$	−2.21459	−	3.83578i	−0.153186	−	0.265327i
$210$		0			0
$211$	−4.22277	+	18.5012i	−0.290707	+	1.27367i	0.592836	+	0.805323i	$0.298008\pi$
$211$	−4.22277	+	18.5012i	−0.290707	+	1.27367i	−0.883543	+	0.468349i	$0.844849\pi$
$212$	−6.91098	−	1.04166i	−0.474648	−	0.0715417i
$213$		0			0
$214$	−10.4353			−0.713346
$215$	0.0916113	+	3.90923i	0.00624784	+	0.266608i
$216$		0			0
$217$	1.55047	+	1.94423i	0.105253	+	0.131983i
$218$	−1.39145	−	0.209728i	−0.0942412	−	0.0142046i
$219$		0			0
$220$	−1.18695	−	0.809247i	−0.0800239	−	0.0545594i
$221$	−1.27914	−	2.21553i	−0.0860441	−	0.149033i
$222$		0			0
$223$	−8.70607	+	4.19262i	−0.583002	+	0.280759i	−0.702048	−	0.712130i	$-0.747731\pi$
$223$	−8.70607	+	4.19262i	−0.583002	+	0.280759i	0.119046	+	0.992889i	$0.462016\pi$
$224$	24.7946	+	7.64812i	1.65666	+	0.511012i
$225$		0			0
$226$	−2.39064	−	10.4741i	−0.159023	−	0.696727i
$227$	6.45065	−	16.4360i	0.428144	−	1.09089i	−0.540258	−	0.841500i	$-0.681673\pi$
$227$	6.45065	−	16.4360i	0.428144	−	1.09089i	0.968402	−	0.249394i	$-0.0802316\pi$
$228$		0			0
$229$	0.234167	−	0.0352950i	0.0154742	−	0.00233236i	−0.141301	−	0.989967i	$-0.545128\pi$
$229$	0.234167	−	0.0352950i	0.0154742	−	0.00233236i	0.156775	+	0.987634i	$0.449890\pi$
$230$	−2.12325	−	1.97009i	−0.140003	−	0.129904i
$231$		0			0
$232$	−9.11805	+	6.21658i	−0.598629	+	0.408139i
$233$	−2.54575	−	6.48646i	−0.166777	−	0.424942i	0.822913	−	0.568168i	$-0.192348\pi$
$233$	−2.54575	−	6.48646i	−0.166777	−	0.424942i	−0.989690	+	0.143226i	$0.954252\pi$
$234$		0			0
$235$	4.09290	−	3.79765i	0.266991	−	0.247732i
$236$	−3.77052	+	4.72808i	−0.245440	+	0.307772i
$237$		0			0
$238$	−8.37510	+	7.77096i	−0.542877	+	0.503716i
$239$	28.2108	−	8.70187i	1.82480	−	0.562877i	0.824807	−	0.565414i	$-0.191284\pi$
$239$	28.2108	−	8.70187i	1.82480	−	0.562877i	0.999997	+	0.00253697i	$0.000807545\pi$
$240$		0			0
$241$	14.3617	−	9.79162i	0.925117	−	0.630734i	−0.00421050	−	0.999991i	$-0.501340\pi$
$241$	14.3617	−	9.79162i	0.925117	−	0.630734i	0.929327	+	0.369257i	$0.120388\pi$
$242$	11.0208	+	5.30734i	0.708444	+	0.341169i
$243$		0			0
$244$	11.4514	−	1.72603i	0.733103	−	0.110498i
$245$	0.536378	−	7.15746i	0.0342679	−	0.457274i
$246$		0			0
$247$	−0.843926	−	3.69748i	−0.0536977	−	0.235265i
$248$	0.0620578	+	0.828103i	0.00394067	+	0.0525846i
$249$		0			0
$250$	9.24500	−	4.45216i	0.584705	−	0.281579i
$251$	−9.78186	+	16.9427i	−0.617426	+	1.06941i	0.372528	+	0.928021i	$0.378491\pi$
$251$	−9.78186	+	16.9427i	−0.617426	+	1.06941i	−0.989954	+	0.141392i	$0.954842\pi$
$252$		0			0
$253$	−4.57900	−	3.12191i	−0.287879	−	0.196273i
$254$	1.50121	−	6.57722i	0.0941941	−	0.412691i
$255$		0			0
$256$	12.7311	+	15.9643i	0.795695	+	0.997770i
$257$	−21.9755			−1.37080			−0.685398	−	0.728168i	$-0.740372\pi$
$257$	−21.9755			−1.37080			−0.685398	+	0.728168i	$0.740372\pi$
$258$		0			0
$259$	17.2851			1.07404
$260$	−0.766947	−	0.961721i	−0.0475640	−	0.0596434i
$261$		0			0
$262$	−6.89225	+	30.1969i	−0.425805	+	1.86557i
$263$	17.5044	+	11.9343i	1.07937	+	0.735900i	0.966230	−	0.257679i	$-0.0829578\pi$
$263$	17.5044	+	11.9343i	1.07937	+	0.735900i	0.113137	+	0.993579i	$0.463910\pi$
$264$		0			0
$265$	−1.76090	+	3.04997i	−0.108171	+	0.187358i
$266$	−15.2599	+	7.34877i	−0.935643	+	0.450582i
$267$		0			0
$268$	−0.0468820	−	0.625596i	−0.00286377	−	0.0382144i
$269$	−0.540806	−	2.36943i	−0.0329735	−	0.144466i	0.955762	−	0.294143i	$-0.0950340\pi$
$269$	−0.540806	−	2.36943i	−0.0329735	−	0.144466i	−0.988735	+	0.149676i	$0.952177\pi$
$270$		0			0
$271$	1.48929	−	19.8731i	0.0904677	−	1.20721i	−0.748541	−	0.663089i	$-0.769245\pi$
$271$	1.48929	−	19.8731i	0.0904677	−	1.20721i	0.839008	−	0.544118i	$-0.183136\pi$
$272$	−7.20739	+	1.08634i	−0.437012	+	0.0658690i
$273$		0			0
$274$	5.00055	+	2.40814i	0.302094	+	0.145481i
$275$	7.81189	−	5.32606i	0.471075	−	0.321173i
$276$		0			0
$277$	14.3542	−	4.42768i	0.862460	−	0.266034i	0.168196	−	0.985754i	$-0.446206\pi$
$277$	14.3542	−	4.42768i	0.862460	−	0.266034i	0.694265	+	0.719720i	$0.255730\pi$
$278$	−6.82942	+	6.33677i	−0.409601	+	0.380054i
$279$		0			0
$280$	2.36351	−	2.96375i	0.141247	−	0.177118i
$281$	24.0279	−	22.2946i	1.43338	−	1.32998i	0.573793	−	0.819000i	$-0.305471\pi$
$281$	24.0279	−	22.2946i	1.43338	−	1.32998i	0.859590	−	0.510985i	$-0.170719\pi$
$282$		0			0
$283$	4.57856	+	11.6660i	0.272167	+	0.693470i	0.999970	+	0.00768433i	$0.00244602\pi$
$283$	4.57856	+	11.6660i	0.272167	+	0.693470i	−0.727804	+	0.685786i	$0.759459\pi$
$284$	5.21952	−	3.55861i	0.309722	−	0.211165i
$285$		0			0
$286$	−4.64120	−	4.30641i	−0.274440	−	0.254643i
$287$	−9.17094	+	1.38230i	−0.541344	+	0.0815944i
$288$		0			0
$289$	−5.42387	+	13.8198i	−0.319051	+	0.812930i
$290$	−1.79321	−	7.85656i	−0.105301	−	0.461353i
$291$		0			0
$292$	−15.8974	−	4.90371i	−0.930328	−	0.286968i
$293$	−6.61965	+	3.18786i	−0.386724	+	0.186237i	−0.617136	−	0.786857i	$-0.711707\pi$
$293$	−6.61965	+	3.18786i	−0.386724	+	0.186237i	0.230411	+	0.973093i	$0.425993\pi$
$294$		0			0
$295$	1.52366	+	2.63906i	0.0887112	+	0.153652i
$296$	4.76916	+	3.25156i	0.277202	+	0.188993i
$297$		0			0
$298$	35.9255	+	5.41490i	2.08111	+	0.313677i
$299$	−2.95872	−	3.71012i	−0.171107	−	0.214562i
$300$		0			0
$301$	28.4727	−	2.80591i	1.64114	−	0.161730i
$302$	−35.6240			−2.04993
$303$		0			0
$304$	−10.6847	−	1.61046i	−0.612812	−	0.0923665i
$305$	1.29854	−	5.68929i	0.0743544	−	0.325768i
$306$		0			0
$307$	−5.68990	−	9.85520i	−0.324740	−	0.562466i	0.656720	−	0.754135i	$-0.271943\pi$
$307$	−5.68990	−	9.85520i	−0.324740	−	0.562466i	−0.981460	+	0.191669i	$0.938610\pi$
$308$	−5.25548	+	9.10275i	−0.299459	+	0.518678i
$309$		0			0
$310$	−0.579466	−	0.178742i	−0.0329114	−	0.0101518i
$311$	−1.85648	−	24.7730i	−0.105271	−	1.40475i	−0.760511	−	0.649325i	$-0.775052\pi$
$311$	−1.85648	−	24.7730i	−0.105271	−	1.40475i	0.655240	−	0.755421i	$-0.272567\pi$
$312$		0			0
$313$	6.18554	−	15.7605i	0.349627	−	0.890836i	−0.642578	−	0.766221i	$-0.722135\pi$
$313$	6.18554	−	15.7605i	0.349627	−	0.890836i	0.992205	−	0.124616i	$-0.0397698\pi$
$314$	2.29517	−	30.6269i	0.129524	−	1.72838i
$315$		0			0
$316$	−3.16864	−	2.94007i	−0.178250	−	0.165392i
$317$	21.3116	+	10.2631i	1.19698	+	0.576435i	0.922813	−	0.385247i	$-0.125884\pi$
$317$	21.3116	+	10.2631i	1.19698	+	0.576435i	0.274166	+	0.961682i	$0.411598\pi$
$318$		0			0
$319$	−5.63322	−	14.3532i	−0.315400	−	0.803626i
$320$	−0.386340	+	0.119170i	−0.0215971	+	0.00666182i
$321$		0			0
$322$	−13.2133	+	16.5690i	−0.736350	+	0.923354i
$323$	1.99090	−	2.49651i	0.110777	−	0.138909i
$324$		0			0
$325$	7.73614	−	2.38628i	0.429124	−	0.132367i
$326$	14.2258	+	36.2467i	0.787892	+	2.00752i
$327$		0			0
$328$	−2.79040	−	1.34379i	−0.154074	−	0.0741982i
$329$	−29.9466	−	27.7864i	−1.65101	−	1.53191i
$330$		0			0
$331$	1.80682	−	24.1103i	0.0993117	−	1.32522i	−0.695570	−	0.718458i	$-0.744848\pi$
$331$	1.80682	−	24.1103i	0.0993117	−	1.32522i	0.794882	−	0.606764i	$-0.207533\pi$
$332$	4.47302	−	11.3971i	0.245489	−	0.625495i
$333$		0			0
$334$	−1.13066	−	15.0876i	−0.0618671	−	0.825558i
$335$	−0.302080	−	0.0931793i	−0.0165044	−	0.00509093i
$336$		0			0
$337$	7.76921	−	13.4567i	0.423216	−	0.733031i	−0.573036	−	0.819530i	$-0.694235\pi$
$337$	7.76921	−	13.4567i	0.423216	−	0.733031i	0.996252	+	0.0864989i	$0.0275679\pi$
$338$	8.88668	+	15.3922i	0.483372	+	0.837224i
$339$		0			0
$340$	0.230459	−	1.00971i	0.0124984	−	0.0547590i
$341$	−1.14732	−	0.172931i	−0.0621309	−	0.00936472i
$342$		0			0
$343$	−21.9745			−1.18651
$344$	8.38379	+	4.58192i	0.452024	+	0.247041i
$345$		0			0
$346$	12.3299	+	15.4612i	0.662858	+	0.831197i
$347$	−13.6421	−	2.05621i	−0.732346	−	0.110383i	−0.227726	−	0.973725i	$-0.573129\pi$
$347$	−13.6421	−	2.05621i	−0.732346	−	0.110383i	−0.504620	+	0.863342i	$0.668367\pi$
$348$		0			0
$349$	11.1033	+	7.57012i	0.594348	+	0.405219i	0.822796	−	0.568337i	$-0.192413\pi$
$349$	11.1033	+	7.57012i	0.594348	+	0.405219i	−0.228449	+	0.973556i	$0.573365\pi$
$350$	−18.0775	−	31.3112i	−0.966283	−	1.67365i
$351$		0			0
$352$	−10.9076	+	5.25284i	−0.581378	+	0.279977i
$353$	−7.28752	−	2.24790i	−0.387876	−	0.119644i	0.0946829	−	0.995507i	$-0.469816\pi$
$353$	−7.28752	−	2.24790i	−0.387876	−	0.119644i	−0.482559	+	0.875864i	$0.660292\pi$
$354$		0			0
$355$	−0.708343	−	3.10346i	−0.0375950	−	0.164714i
$356$	2.61033	−	6.65101i	0.138347	−	0.352503i
$357$		0			0
$358$	−27.1987	+	4.09954i	−1.43750	+	0.216668i
$359$	12.3345	+	11.4447i	0.650989	+	0.604029i	0.934939	−	0.354810i	$-0.115454\pi$
$359$	12.3345	+	11.4447i	0.650989	+	0.604029i	−0.283950	+	0.958839i	$0.591645\pi$
$360$		0			0
$361$	−11.7873	+	8.03646i	−0.620385	+	0.422972i
$362$	−2.09113	−	5.32812i	−0.109908	−	0.280040i
$363$		0			0
$364$	−6.59762	+	6.12169i	−0.345809	+	0.320864i
$365$	−5.22686	+	6.55427i	−0.273586	+	0.343066i
$366$		0			0
$367$	−0.0534689	+	0.0496119i	−0.00279105	+	0.00258972i	−0.681567	−	0.731756i	$-0.738701\pi$
$367$	−0.0534689	+	0.0496119i	−0.00279105	+	0.00258972i	0.678776	+	0.734345i	$0.262511\pi$
$368$	−12.9195	+	3.98515i	−0.673478	+	0.207740i
$369$		0			0
$370$	−3.48261	+	2.37441i	−0.181052	+	0.123439i
$371$	23.2162	+	11.1803i	1.20533	+	0.580455i
$372$		0			0
$373$	−25.4691	+	3.83884i	−1.31874	+	0.198768i	−0.770438	−	0.637514i	$-0.779963\pi$
$373$	−25.4691	+	3.83884i	−1.31874	+	0.198768i	−0.548299	+	0.836282i	$0.684725\pi$
$374$	0.398362	−	5.31577i	0.0205988	−	0.274872i
$375$		0			0
$376$	−3.03563	−	13.3000i	−0.156551	−	0.685893i
$377$	−0.986652	−	13.1660i	−0.0508152	−	0.678081i
$378$		0			0
$379$	14.4579	−	6.96257i	0.742654	−	0.357643i	−0.0239929	−	0.999712i	$-0.507638\pi$
$379$	14.4579	−	6.96257i	0.742654	−	0.357643i	0.766647	+	0.642069i	$0.221924\pi$
$380$	0.767677	−	1.32966i	0.0393810	−	0.0682099i
$381$		0			0
$382$	7.86178	+	5.36007i	0.402244	+	0.274245i
$383$	−5.36944	+	23.5250i	−0.274365	+	1.20207i	0.630437	+	0.776241i	$0.282876\pi$
$383$	−5.36944	+	23.5250i	−0.274365	+	1.20207i	−0.904802	+	0.425833i	$0.859981\pi$
$384$		0			0
$385$	3.30232	+	4.14098i	0.168302	+	0.211044i
$386$	−11.9930			−0.610430
$387$		0			0
$388$	12.1358			0.616103
$389$	−10.2266	−	12.8237i	−0.518507	−	0.650187i	0.451784	−	0.892127i	$-0.350788\pi$
$389$	−10.2266	−	12.8237i	−0.518507	−	0.650187i	−0.970291	+	0.241940i	$0.922216\pi$
$390$		0			0
$391$	0.889063	−	3.89524i	0.0449619	−	0.196991i
$392$	−14.4898	−	9.87898i	−0.731846	−	0.498964i
$393$		0			0
$394$	−4.33671	+	7.51140i	−0.218480	+	0.378419i
$395$	−1.96244	+	0.945061i	−0.0987410	+	0.0475512i
$396$		0			0
$397$	−0.575635	−	7.68131i	−0.0288903	−	0.385514i	−0.992842	−	0.119436i	$-0.961891\pi$
$397$	−0.575635	−	7.68131i	−0.0288903	−	0.385514i	0.963952	−	0.266078i	$-0.0857278\pi$
$398$	8.99903	+	39.4273i	0.451081	+	1.97631i
$399$		0			0
$400$	1.72371	−	23.0013i	0.0861856	−	1.15007i
$401$	1.39718	−	0.210591i	0.0697719	−	0.0105164i	−0.114064	−	0.993473i	$-0.536387\pi$
$401$	1.39718	−	0.210591i	0.0697719	−	0.0105164i	0.183835	+	0.982957i	$0.441149\pi$
$402$		0			0
$403$	−0.895123	−	0.431068i	−0.0445892	−	0.0214730i
$404$	10.9316	−	7.45302i	0.543866	−	0.370802i
$405$		0			0
$406$	−56.3430	+	17.3795i	−2.79626	+	0.862531i
$407$	−5.91198	+	5.48551i	−0.293046	+	0.271907i
$408$		0			0
$409$	−4.44166	+	5.56967i	−0.219626	+	0.275402i	−0.879423	−	0.476042i	$-0.842071\pi$
$409$	−4.44166	+	5.56967i	−0.219626	+	0.275402i	0.659796	+	0.751444i	$0.270642\pi$
$410$	1.65789	−	1.53830i	0.0818773	−	0.0759710i
$411$		0			0
$412$	−0.0603270	−	0.153711i	−0.00297210	−	0.00757278i
$413$	18.4222	−	12.5600i	0.906497	−	0.618039i
$414$		0			0
$415$	−4.52256	−	4.19632i	−0.222004	−	0.205989i
$416$	−10.2507	+	1.54504i	−0.502581	+	0.0757519i
$417$		0			0
$418$	2.88713	−	7.35629i	0.141214	−	0.359808i
$419$	3.05031	+	13.3643i	0.149018	+	0.652889i	0.993159	+	0.116769i	$0.0372536\pi$
$419$	3.05031	+	13.3643i	0.149018	+	0.652889i	−0.844142	+	0.536120i	$0.819889\pi$
$420$		0			0
$421$	−1.78387	−	0.550250i	−0.0869404	−	0.0268176i	0.250980	−	0.967992i	$-0.419247\pi$
$421$	−1.78387	−	0.550250i	−0.0869404	−	0.0268176i	−0.337920	+	0.941175i	$0.609723\pi$
$422$	−30.5057	+	14.6908i	−1.48500	+	0.715136i
$423$		0			0
$424$	4.30246	+	7.45208i	0.208946	+	0.361905i
$425$	5.63187	+	3.83975i	0.273186	+	0.186255i
$426$		0			0
$427$	−42.2206	−	6.36373i	−2.04320	−	0.307962i
$428$	−4.31539	−	5.41133i	−0.208592	−	0.261566i
$429$		0			0
$430$	−5.35127	+	4.47656i	−0.258061	+	0.215879i
$431$	23.8277			1.14774			0.573871	−	0.818946i	$-0.305441\pi$
$431$	23.8277			1.14774			0.573871	+	0.818946i	$0.305441\pi$
$432$		0			0
$433$	−39.6397	−	5.97472i	−1.90496	−	0.287127i	−0.912442	−	0.409206i	$-0.865806\pi$
$433$	−39.6397	−	5.97472i	−1.90496	−	0.287127i	−0.992520	+	0.122079i	$0.961044\pi$
$434$	−0.987305	+	4.32567i	−0.0473922	+	0.207639i
$435$		0			0
$436$	−0.466660	−	0.808279i	−0.0223490	−	0.0387096i
$437$	2.96154	−	5.12954i	0.141670	−	0.245379i
$438$		0			0
$439$	7.92185	+	2.44357i	0.378089	+	0.116625i	0.477974	−	0.878374i	$-0.341371\pi$
$439$	7.92185	+	2.44357i	0.378089	+	0.116625i	−0.0998848	+	0.994999i	$0.531847\pi$
$440$	0.132175	+	1.76376i	0.00630121	+	0.0840839i
$441$		0			0
$442$	1.66760	−	4.24897i	0.0793195	−	0.202103i
$443$	2.35373	−	31.4083i	0.111829	−	1.49225i	−0.605682	−	0.795706i	$-0.707100\pi$
$443$	2.35373	−	31.4083i	0.111829	−	1.49225i	0.717511	−	0.696547i	$-0.245281\pi$
$444$		0			0
$445$	−2.63924	−	2.44886i	−0.125112	−	0.116087i
$446$	−15.5334	−	7.48050i	−0.735529	−	0.354212i
$447$		0			0
$448$	1.08074	+	2.75368i	0.0510601	+	0.130099i
$449$	−14.7459	+	4.54851i	−0.695903	+	0.214658i	−0.622471	−	0.782643i	$-0.713871\pi$
$449$	−14.7459	+	4.54851i	−0.695903	+	0.214658i	−0.0734316	+	0.997300i	$0.523395\pi$
$450$		0			0
$451$	2.69804	−	3.38324i	0.127046	−	0.159310i
$452$	4.44281	−	5.57110i	0.208972	−	0.262043i
$453$		0			0
$454$	30.1033	−	9.28563i	1.41282	−	0.435796i
$455$	1.65691	+	4.22173i	0.0776771	+	0.197918i
$456$		0			0
$457$	8.36585	+	4.02878i	0.391338	+	0.188458i	0.619197	−	0.785236i	$-0.287458\pi$
$457$	8.36585	+	4.02878i	0.391338	+	0.188458i	−0.227859	+	0.973694i	$0.573173\pi$
$458$	0.309730	+	0.287387i	0.0144727	+	0.0134287i
$459$		0			0
$460$	0.143564	−	1.91573i	0.00669371	−	0.0893214i
$461$	7.64092	−	19.4688i	0.355873	−	0.906750i	−0.635068	−	0.772456i	$-0.719028\pi$
$461$	7.64092	−	19.4688i	0.355873	−	0.906750i	0.990942	−	0.134294i	$-0.0428767\pi$
$462$		0			0
$463$	0.163595	+	2.18303i	0.00760292	+	0.101454i	0.999714	−	0.0239064i	$-0.00761037\pi$
$463$	0.163595	+	2.18303i	0.00760292	+	0.101454i	−0.992111	+	0.125360i	$0.959991\pi$
$464$	−35.9452	−	11.0876i	−1.66871	−	0.514730i
$465$		0			0
$466$	6.21630	−	10.7669i	0.287965	−	0.498769i
$467$	−0.115483	−	0.200022i	−0.00534391	−	0.00925593i	0.863341	−	0.504621i	$-0.168368\pi$
$467$	−0.115483	−	0.200022i	−0.00534391	−	0.00925593i	−0.868685	+	0.495365i	$0.835034\pi$
$468$		0			0
$469$	−0.514690	+	2.25500i	−0.0237662	+	0.104126i
$470$	9.85061	+	1.48474i	0.454375	+	0.0684860i
$471$		0			0
$472$	7.44562			0.342713
$473$	−8.84799	+	9.99567i	−0.406831	+	0.459602i
$474$		0			0
$475$	6.30032	+	7.90035i	0.289079	+	0.362493i
$476$	−7.49309	−	1.12940i	−0.343445	−	0.0517660i
$477$		0			0
$478$	43.5213	+	29.6723i	1.99062	+	1.35718i
$479$	2.50477	+	4.33839i	0.114446	+	0.198226i	0.917558	−	0.397602i	$-0.130157\pi$
$479$	2.50477	+	4.33839i	0.114446	+	0.198226i	−0.803112	+	0.595828i	$0.796824\pi$
$480$		0			0
$481$	−6.22183	+	2.99627i	−0.283691	+	0.136618i
$482$	29.6352	+	9.14126i	1.34985	+	0.416373i
$483$		0			0
$484$	1.80534	+	7.90970i	0.0820607	+	0.359532i
$485$	2.23417	−	5.69256i	0.101448	−	0.258486i
$486$		0			0
$487$	12.8944	−	1.94351i	0.584299	−	0.0880689i	0.149761	−	0.988722i	$-0.452150\pi$
$487$	12.8944	−	1.94351i	0.584299	−	0.0880689i	0.434538	+	0.900653i	$0.356912\pi$
$488$	−10.4521	−	9.69810i	−0.473143	−	0.439012i
$489$		0			0
$490$	10.5810	−	7.21399i	0.478000	−	0.325895i
$491$	−9.25153	−	23.5725i	−0.417516	−	1.06381i	−0.972696	−	0.232083i	$-0.925446\pi$
$491$	−9.25153	−	23.5725i	−0.417516	−	1.06381i	0.555180	−	0.831730i	$-0.312649\pi$
$492$		0			0
$493$	8.14873	−	7.56092i	0.367000	−	0.340527i
$494$	4.21898	−	5.29044i	0.189821	−	0.238028i
$495$		0			0
$496$	−2.07499	+	1.92531i	−0.0931698	+	0.0864489i
$497$	−22.2563	+	6.86516i	−0.998332	+	0.307945i
$498$		0			0
$499$	7.17570	−	4.89231i	0.321228	−	0.219010i	−0.391960	−	0.919982i	$-0.628203\pi$
$499$	7.17570	−	4.89231i	0.321228	−	0.219010i	0.713188	+	0.700973i	$0.247250\pi$
$500$	6.13184	+	2.95294i	0.274224	+	0.132059i
$501$		0			0
$502$	−34.5158	+	5.20243i	−1.54052	+	0.232196i
$503$	−2.14991	+	28.6886i	−0.0958599	+	1.27916i	0.717153	+	0.696916i	$0.245445\pi$
$503$	−2.14991	+	28.6886i	−0.0958599	+	1.27916i	−0.813013	+	0.582246i	$0.802174\pi$
$504$		0			0
$505$	−1.48353	−	6.49976i	−0.0660162	−	0.289236i
$506$	−0.738934	−	9.86039i	−0.0328496	−	0.438348i
$507$		0			0
$508$	4.03147	−	1.94145i	0.178867	−	0.0861380i
$509$	13.2695	−	22.9835i	0.588162	−	1.01873i	−0.406311	−	0.913735i	$-0.633185\pi$
$509$	13.2695	−	22.9835i	0.588162	−	1.01873i	0.994473	−	0.104992i	$-0.0334816\pi$
$510$		0			0
$511$	50.6796	+	34.5528i	2.24193	+	1.52852i
$512$	−3.35188	+	14.6855i	−0.148133	+	0.649015i
$513$		0			0
$514$	−24.4464	−	30.6548i	−1.07828	−	1.35212i
$515$	−0.0832072			−0.00366655
$516$		0			0
$517$	19.0607			0.838290
$518$	19.2285	+	24.1118i	0.844852	+	1.05941i
$519$		0			0
$520$	−0.337005	+	1.47651i	−0.0147786	+	0.0647495i
$521$	29.4870	+	20.1039i	1.29185	+	0.880769i	0.997196	−	0.0748353i	$-0.0238431\pi$
$521$	29.4870	+	20.1039i	1.29185	+	0.880769i	0.294654	+	0.955604i	$0.404795\pi$
$522$		0			0
$523$	19.4445	−	33.6789i	0.850249	−	1.47267i	−0.0307344	−	0.999528i	$-0.509785\pi$
$523$	19.4445	−	33.6789i	0.850249	−	1.47267i	0.880983	−	0.473147i	$-0.156882\pi$
$524$	−18.5090	+	8.91349i	−0.808571	+	0.389387i
$525$		0			0
$526$	2.82476	+	37.6939i	0.123166	+	1.64353i
$527$	−0.186136	−	0.815515i	−0.00810821	−	0.0355244i
$528$		0			0
$529$	−1.16495	+	15.5452i	−0.0506501	+	0.675878i
$530$	−6.21344	+	0.936526i	−0.269895	+	0.0406801i
$531$		0			0
$532$	−10.1213	−	4.87414i	−0.438812	−	0.211321i
$533$	3.06150	−	2.08730i	0.132608	−	0.0904109i
$534$		0			0
$535$	−3.33275	+	1.02802i	−0.144087	+	0.0444450i
$536$	−0.566206	+	0.525362i	−0.0244564	+	0.0226922i
$537$		0			0
$538$	2.70362	−	3.39023i	0.116561	−	0.146163i
$539$	17.9620	−	16.6663i	0.773676	−	0.717866i
$540$		0			0
$541$	6.99876	+	17.8325i	0.300900	+	0.766681i	0.998728	+	0.0504159i	$0.0160547\pi$
$541$	6.99876	+	17.8325i	0.300900	+	0.766681i	−0.697828	+	0.716265i	$0.745850\pi$
$542$	29.3787	−	20.0301i	1.26192	−	0.860366i
$543$		0			0
$544$	−6.39812	−	5.93658i	−0.274317	−	0.254529i
$545$	−0.465051	+	0.0700951i	−0.0199206	+	0.00300255i
$546$		0			0
$547$	−0.882978	+	2.24979i	−0.0377534	+	0.0961942i	−0.948507	−	0.316756i	$-0.897406\pi$
$547$	−0.882978	+	2.24979i	−0.0377534	+	0.0961942i	0.910754	+	0.412950i	$0.135502\pi$
$548$	0.819149	+	3.58893i	0.0349923	+	0.153311i
$549$		0			0
$550$	16.1198	+	4.97230i	0.687350	+	0.212019i
$551$	14.8474	−	7.15014i	0.632521	−	0.304606i
$552$		0			0
$553$	7.96843	+	13.8017i	0.338852	+	0.586909i
$554$	22.1445	+	15.0979i	0.940830	+	0.641447i
$555$		0			0
$556$	−6.11019	−	0.920963i	−0.259130	−	0.0390575i
$557$	−1.65271	−	2.07243i	−0.0700274	−	0.0878116i	0.745584	−	0.666412i	$-0.232171\pi$
$557$	−1.65271	−	2.07243i	−0.0700274	−	0.0878116i	−0.815611	+	0.578600i	$0.803599\pi$
$558$		0			0
$559$	−9.76247	+	5.94559i	−0.412909	+	0.251472i
$560$	12.9214			0.546027
$561$		0			0
$562$	57.8293	+	8.71636i	2.43938	+	0.367678i
$563$	1.07396	−	4.70535i	0.0452622	−	0.198307i	−0.947242	−	0.320520i	$-0.896142\pi$
$563$	1.07396	−	4.70535i	0.0452622	−	0.198307i	0.992504	+	0.122214i	$0.0389993\pi$
$564$		0			0
$565$	−1.79534	−	3.10961i	−0.0755303	−	0.130822i
$566$	−11.1801	+	19.3645i	−0.469934	+	0.813950i
$567$		0			0
$568$	−7.43222	−	2.29254i	−0.311849	−	0.0961927i
$569$	−0.904422	−	12.0687i	−0.0379153	−	0.505945i	−0.983541	−	0.180687i	$-0.942168\pi$
$569$	−0.904422	−	12.0687i	−0.0379153	−	0.505945i	0.945625	−	0.325258i	$-0.105451\pi$
$570$		0			0
$571$	−10.2678	+	26.1619i	−0.429694	+	1.09484i	0.538052	+	0.842912i	$0.319160\pi$
$571$	−10.2678	+	26.1619i	−0.429694	+	1.09484i	−0.967746	+	0.251930i	$0.918935\pi$
$572$	0.313816	−	4.18758i	0.0131213	−	0.175092i
$573$		0			0
$574$	−12.1303	−	11.2553i	−0.506309	−	0.469786i
$575$	11.3916	+	5.48591i	0.475063	+	0.228778i
$576$		0			0
$577$	−8.48151	−	21.6105i	−0.353090	−	0.899659i	−0.991517	−	0.129976i	$-0.958510\pi$
$577$	−8.48151	−	21.6105i	−0.353090	−	0.899659i	0.638427	−	0.769682i	$-0.279585\pi$
$578$	−25.3116	+	7.80760i	−1.05282	+	0.324753i
$579$		0			0
$580$	3.33252	−	4.17885i	0.138375	−	0.173517i
$581$	−28.1446	+	35.2923i	−1.16764	+	1.46417i
$582$		0			0
$583$	−11.4887	+	3.54381i	−0.475815	+	0.146770i
$584$	7.48327	+	19.0671i	0.309660	+	0.789001i
$585$		0			0
$586$	−11.8108	−	5.68780i	−0.487901	−	0.234961i
$587$	25.3059	+	23.4805i	1.04449	+	0.969143i	0.999554	−	0.0298472i	$-0.00950208\pi$
$587$	25.3059	+	23.4805i	1.04449	+	0.969143i	0.0449330	+	0.998990i	$0.485693\pi$
$588$		0			0
$589$	0.0926704	−	1.23660i	0.00381842	−	0.0509532i
$590$	−1.98638	+	5.06122i	−0.0817781	+	0.208367i
$591$		0			0
$592$	1.47032	+	19.6201i	0.0604298	+	0.806380i
$593$	−25.9112	−	7.99254i	−1.06404	−	0.328214i	−0.287177	−	0.957878i	$-0.592717\pi$
$593$	−25.9112	−	7.99254i	−1.06404	−	0.328214i	−0.776868	+	0.629663i	$0.783193\pi$
$594$		0			0
$595$	−1.90922	+	3.30687i	−0.0782705	+	0.135569i
$596$	12.0486	+	20.8687i	0.493528	+	0.854816i
$597$		0			0
$598$	1.88404	−	8.25454i	0.0770443	−	0.337553i
$599$	7.61082	+	1.14715i	0.310970	+	0.0468711i	0.302673	−	0.953094i	$-0.402121\pi$
$599$	7.61082	+	1.14715i	0.310970	+	0.0468711i	0.00829658	+	0.999966i	$0.497359\pi$
$600$		0			0
$601$	−31.0119			−1.26500			−0.632500	−	0.774560i	$-0.717971\pi$
$601$	−31.0119			−1.26500			−0.632500	+	0.774560i	$0.717971\pi$
$602$	35.5881	+	36.5966i	1.45046	+	1.49156i
$603$		0			0
$604$	−14.7318	−	18.4731i	−0.599429	−	0.751660i
$605$	4.04256	+	0.609319i	0.164354	+	0.0247723i
$606$		0			0
$607$	3.94082	+	2.68680i	0.159953	+	0.109054i	0.640651	−	0.767832i	$-0.278664\pi$
$607$	3.94082	+	2.68680i	0.159953	+	0.109054i	−0.480698	+	0.876886i	$0.659617\pi$
$608$	−6.46954	−	11.2056i	−0.262374	−	0.454446i
$609$		0			0
$610$	9.38081	−	4.51756i	0.379818	−	0.182911i
$611$	15.5960	+	4.81073i	0.630947	+	0.194621i
$612$		0			0
$613$	7.62154	+	33.3922i	0.307831	+	1.34870i	0.858003	+	0.513645i	$0.171705\pi$
$613$	7.62154	+	33.3922i	0.307831	+	1.34870i	−0.550171	+	0.835052i	$0.685438\pi$
$614$	7.41786	−	18.9004i	0.299360	−	0.762758i
$615$		0			0
$616$	12.7966	−	1.92877i	0.515588	−	0.0777125i
$617$	16.7395	+	15.5320i	0.673908	+	0.625295i	0.941012	−	0.338372i	$-0.109876\pi$
$617$	16.7395	+	15.5320i	0.673908	+	0.625295i	−0.267104	+	0.963668i	$0.586067\pi$
$618$		0			0
$619$	13.4359	−	9.16045i	0.540035	−	0.368190i	−0.262372	−	0.964967i	$-0.584505\pi$
$619$	13.4359	−	9.16045i	0.540035	−	0.368190i	0.802407	+	0.596777i	$0.203552\pi$
$620$	−0.146942	−	0.374402i	−0.00590134	−	0.0150364i
$621$		0			0
$622$	32.4918	−	30.1480i	1.30280	−	1.20882i
$623$	−16.4244	+	20.5956i	−0.658031	+	0.825145i
$624$		0			0
$625$	−14.5090	+	13.4624i	−0.580359	+	0.538494i
$626$	28.8661	−	8.90401i	1.15372	−	0.355876i
$627$		0			0
$628$	16.8310	−	11.4752i	0.671628	−	0.457908i
$629$	−5.23847	−	2.52272i	−0.208872	−	0.100587i
$630$		0			0
$631$	1.89851	−	0.286155i	0.0755786	−	0.0113916i	−0.111144	−	0.993804i	$-0.535452\pi$
$631$	1.89851	−	0.286155i	0.0755786	−	0.0113916i	0.186723	+	0.982413i	$0.440213\pi$
$632$	−0.397707	+	5.30704i	−0.0158200	+	0.211103i
$633$		0			0
$634$	9.39123	+	41.1457i	0.372973	+	1.63410i
$635$	−0.168499	−	2.24846i	−0.00668667	−	0.0892274i
$636$		0			0
$637$	18.9034	−	9.10337i	0.748978	−	0.360689i
$638$	13.7554	−	23.8251i	0.544582	−	0.943243i
$639$		0			0
$640$	5.26419	+	3.58906i	0.208085	+	0.141870i
$641$	−6.59005	+	28.8729i	−0.260291	+	1.14041i	0.660645	+	0.750698i	$0.270283\pi$
$641$	−6.59005	+	28.8729i	−0.260291	+	1.14041i	−0.920937	+	0.389712i	$0.872574\pi$
$642$		0			0
$643$	−6.44594	−	8.08296i	−0.254203	−	0.318761i	0.638312	−	0.769778i	$-0.279633\pi$
$643$	−6.44594	−	8.08296i	−0.254203	−	0.318761i	−0.892515	+	0.451017i	$0.851061\pi$
$644$	−14.0562			−0.553890
$645$		0			0
$646$	5.69725			0.224155
$647$	−9.51303	−	11.9290i	−0.373996	−	0.468976i	0.558841	−	0.829275i	$-0.311246\pi$
$647$	−9.51303	−	11.9290i	−0.373996	−	0.468976i	−0.932837	+	0.360299i	$0.882675\pi$
$648$		0			0
$649$	−2.31491	+	10.1423i	−0.0908681	+	0.398119i
$650$	11.9347	+	8.13694i	0.468117	+	0.319157i
$651$		0			0
$652$	−12.9131	+	22.3662i	−0.505717	+	0.875927i
$653$	−1.77106	+	0.852898i	−0.0693070	+	0.0333765i	−0.468216	−	0.883614i	$-0.655103\pi$
$653$	−1.77106	+	0.852898i	−0.0693070	+	0.0333765i	0.398909	+	0.916990i	$0.369389\pi$
$654$		0			0
$655$	0.773602	+	10.3230i	0.0302271	+	0.403353i
$656$	−2.34914	−	10.2922i	−0.0917184	−	0.401845i
$657$		0			0
$658$	5.44695	−	72.6844i	0.212344	−	2.83353i
$659$	−29.3755	+	4.42764i	−1.14431	+	0.172476i	−0.693712	−	0.720252i	$-0.744026\pi$
$659$	−29.3755	+	4.42764i	−1.14431	+	0.172476i	−0.450594	+	0.892729i	$0.648788\pi$
$660$		0			0
$661$	10.6317	+	5.11995i	0.413525	+	0.199143i	0.629066	−	0.777352i	$-0.283437\pi$
$661$	10.6317	+	5.11995i	0.413525	+	0.199143i	−0.215542	+	0.976495i	$0.569152\pi$
$662$	35.6426	−	24.3007i	1.38529	−	0.944474i
$663$		0			0
$664$	−14.4044	+	4.44317i	−0.558999	+	0.172428i
$665$	−4.14961	+	3.85028i	−0.160915	+	0.149307i
$666$		0			0
$667$	12.8562	−	16.1212i	0.497794	−	0.624214i
$668$	7.35624	−	6.82559i	0.284621	−	0.264090i
$669$		0			0
$670$	−0.206064	−	0.525042i	−0.00796094	−	0.0202841i
$671$	16.4602	−	11.2224i	0.635439	−	0.433235i
$672$		0			0
$673$	−14.9166	−	13.8406i	−0.574993	−	0.533516i	0.338183	−	0.941080i	$-0.390188\pi$
$673$	−14.9166	−	13.8406i	−0.574993	−	0.533516i	−0.913176	+	0.407565i	$0.866378\pi$
$674$	27.4141	−	4.13201i	1.05595	−	0.159159i
$675$		0			0
$676$	−4.30677	+	10.9735i	−0.165645	+	0.422057i
$677$	−5.30533	−	23.2442i	−0.203900	−	0.893346i	−0.968534	−	0.248881i	$-0.919937\pi$
$677$	−5.30533	−	23.2442i	−0.203900	−	0.893346i	0.764634	−	0.644465i	$-0.222920\pi$
$678$		0			0
$679$	−42.7560	−	13.1885i	−1.64082	−	0.506127i
$680$	−1.14885	+	0.553255i	−0.0440562	+	0.0212164i
$681$		0			0
$682$	−1.03509	−	1.79283i	−0.0396356	−	0.0686509i
$683$	−29.2625	−	19.9508i	−1.11970	−	0.763398i	−0.145560	−	0.989349i	$-0.546498\pi$
$683$	−29.2625	−	19.9508i	−1.11970	−	0.763398i	−0.974138	+	0.225952i	$0.927451\pi$
$684$		0			0
$685$	1.83426	+	0.276471i	0.0700836	+	0.0105634i
$686$	−24.4451	−	30.6532i	−0.933320	−	1.17035i
$687$		0			0
$688$	5.60693	+	32.0803i	0.213762	+	1.22305i
$689$	−10.2948			−0.392202
$690$		0			0
$691$	−15.4237	−	2.32475i	−0.586746	−	0.0884377i	−0.151041	−	0.988527i	$-0.548263\pi$
$691$	−15.4237	−	2.32475i	−0.586746	−	0.0884377i	−0.435704	+	0.900090i	$0.643501\pi$
$692$	−2.91866	+	12.7875i	−0.110951	+	0.486107i
$693$		0			0
$694$	−12.3076	−	21.3174i	−0.467191	−	0.809198i
$695$	−1.55686	+	2.69657i	−0.0590552	+	0.102287i
$696$		0			0
$697$	2.98112	+	0.919554i	0.112918	+	0.0348306i
$698$	1.79179	+	23.9098i	0.0678204	+	0.905001i
$699$		0			0
$700$	8.76094	−	22.3225i	0.331132	−	0.843712i
$701$	−0.820522	+	10.9491i	−0.0309907	+	0.413542i	0.960036	+	0.279877i	$0.0902937\pi$
$701$	−0.820522	+	10.9491i	−0.0309907	+	0.413542i	−0.991027	+	0.133665i	$0.957325\pi$
$702$		0			0
$703$	−6.31852	−	5.86273i	−0.238308	−	0.221117i
$704$	−1.24354	−	0.598857i	−0.0468677	−	0.0225703i
$705$		0			0
$706$	−4.97118	−	12.6664i	−0.187093	−	0.476705i
$707$	−46.6128	+	14.3781i	−1.75305	+	0.540746i
$708$		0			0
$709$	20.7337	−	25.9992i	0.778670	−	0.976421i	−0.221329	−	0.975199i	$-0.571040\pi$
$709$	20.7337	−	25.9992i	0.778670	−	0.976421i	0.999999	−	0.00122191i	$-0.000388946\pi$
$710$	3.54118	−	4.44049i	0.132898	−	0.166649i
$711$		0			0
$712$	−8.40601	+	2.59291i	−0.315029	+	0.0971735i
$713$	−0.566873	−	1.44437i	−0.0212295	−	0.0540920i
$714$		0			0
$715$	−1.90650	−	0.918122i	−0.0712991	−	0.0343358i
$716$	−13.3735	−	12.4088i	−0.499791	−	0.463738i
$717$		0			0
$718$	−2.24350	+	29.9375i	−0.0837268	+	1.11726i
$719$	8.42223	−	21.4595i	0.314096	−	0.800304i	−0.683431	−	0.730015i	$-0.739513\pi$
$719$	8.42223	−	21.4595i	0.314096	−	0.800304i	0.997527	−	0.0702882i	$-0.0223919\pi$
$720$		0			0
$721$	0.0454960	+	0.607102i	0.00169436	+	0.0226096i
$722$	−24.3231	−	7.50268i	−0.905211	−	0.279221i
$723$		0			0
$724$	1.89818	−	3.28774i	0.0705453	−	0.122188i
$725$	17.5889	+	30.4649i	0.653235	+	1.13144i
$726$		0			0
$727$	−6.21668	+	27.2370i	−0.230564	+	1.01017i	0.718610	+	0.695413i	$0.244779\pi$
$727$	−6.21668	+	27.2370i	−0.230564	+	1.01017i	−0.949174	+	0.314753i	$0.898078\pi$
$728$	10.9573	+	1.65155i	0.406105	+	0.0612104i
$729$		0			0
$730$	−14.9574			−0.553599
$731$	−9.03855	−	3.30516i	−0.334303	−	0.122246i
$732$		0			0
$733$	4.22218	+	5.29445i	0.155950	+	0.195555i	0.853668	−	0.520817i	$-0.174373\pi$
$733$	4.22218	+	5.29445i	0.155950	+	0.195555i	−0.697718	+	0.716372i	$0.745801\pi$
$734$	−0.128687	−	0.0193964i	−0.00474991	−	0.000715934i
$735$		0			0
$736$	−13.3768	−	9.12011i	−0.493074	−	0.336172i
$737$	−0.539600	−	0.934614i	−0.0198764	−	0.0344269i
$738$		0			0
$739$	−13.6045	+	6.55159i	−0.500450	+	0.241004i	−0.667040	−	0.745022i	$-0.732439\pi$
$739$	−13.6045	+	6.55159i	−0.500450	+	0.241004i	0.166590	+	0.986026i	$0.446725\pi$
$740$	−2.67145	−	0.824033i	−0.0982045	−	0.0302921i
$741$		0			0
$742$	10.2305	+	44.8228i	0.375574	+	1.64550i
$743$	−9.34603	+	23.8133i	−0.342873	+	0.873626i	0.650586	+	0.759433i	$0.274523\pi$
$743$	−9.34603	+	23.8133i	−0.342873	+	0.873626i	−0.993459	+	0.114193i	$0.963572\pi$
$744$		0			0
$745$	12.0070	−	1.80976i	0.439903	−	0.0663046i
$746$	−33.6876	−	31.2576i	−1.23339	−	1.14442i
$747$		0			0
$748$	2.92127	−	1.99169i	0.106812	−	0.0728233i
$749$	9.32295	+	23.7545i	0.340653	+	0.867970i
$750$		0			0
$751$	−19.4680	+	18.0637i	−0.710398	+	0.659153i	−0.950190	−	0.311671i	$-0.899111\pi$
$751$	−19.4680	+	18.0637i	−0.710398	+	0.659153i	0.239792	+	0.970824i	$0.422921\pi$
$752$	28.9926	−	36.3556i	1.05725	−	1.32575i
$753$		0			0
$754$	17.2683	−	16.0226i	0.628873	−	0.583509i
$755$	−11.3773	+	3.50943i	−0.414062	+	0.127721i
$756$		0			0
$757$	−35.7878	+	24.3997i	−1.30073	+	0.886824i	−0.997807	−	0.0661909i	$-0.978915\pi$
$757$	−35.7878	+	24.3997i	−1.30073	+	0.886824i	−0.302924	+	0.953015i	$0.597963\pi$
$758$	25.7959	+	12.4227i	0.936951	+	0.451212i
$759$		0			0
$760$	−1.86922	+	0.281739i	−0.0678037	+	0.0102198i
$761$	2.59319	−	34.6036i	0.0940029	−	1.25438i	−0.728271	−	0.685289i	$-0.759676\pi$
$761$	2.59319	−	34.6036i	0.0940029	−	1.25438i	0.822274	−	0.569092i	$-0.192705\pi$
$762$		0			0
$763$	0.765713	+	3.35481i	0.0277207	+	0.121452i
$764$	0.471623	+	6.29337i	0.0170627	+	0.227686i
$765$		0			0
$766$	−38.7894	+	18.6800i	−1.40152	+	0.674935i
$767$	−4.45393	+	7.71443i	−0.160822	+	0.278552i
$768$		0			0
$769$	−12.9224	−	8.81031i	−0.465992	−	0.317708i	0.307462	−	0.951560i	$-0.400520\pi$
$769$	−12.9224	−	8.81031i	−0.465992	−	0.317708i	−0.773454	+	0.633852i	$0.781473\pi$
$770$	−2.10284	+	9.21314i	−0.0757810	+	0.332018i
$771$		0			0
$772$	−4.95955	−	6.21908i	−0.178498	−	0.223830i
$773$	−36.9024			−1.32729			−0.663643	−	0.748049i	$-0.730991\pi$
$773$	−36.9024			−1.32729			−0.663643	+	0.748049i	$0.730991\pi$
$774$		0			0
$775$	2.64711			0.0950871
$776$	−9.31597	−	11.6819i	−0.334424	−	0.419354i
$777$		0			0
$778$	6.51203	−	28.5310i	0.233467	−	1.02289i
$779$	3.82127	+	2.60530i	0.136911	+	0.0933444i
$780$		0			0
$781$	5.43359	−	9.41125i	0.194429	−	0.336761i
$782$	6.42269	−	3.09300i	0.229675	−	0.110606i
$783$		0			0
$784$	−4.46717	−	59.6103i	−0.159542	−	2.12894i
$785$	−2.28414	−	10.0074i	−0.0815243	−	0.357181i
$786$		0			0
$787$	−2.89420	+	38.6204i	−0.103167	+	1.37667i	0.669950	+	0.742406i	$0.266316\pi$
$787$	−2.89420	+	38.6204i	−0.103167	+	1.37667i	−0.773117	+	0.634263i	$0.781304\pi$
$788$	−5.68848	+	0.857400i	−0.202644	+	0.0305436i
$789$		0			0
$790$	−3.50140	−	1.68618i	−0.124574	−	0.0599917i
$791$	−21.7069	+	14.7995i	−0.771808	+	0.526210i
$792$		0			0
$793$	16.3006	−	5.02806i	0.578851	−	0.178552i
$794$	10.0747	−	9.34794i	0.357537	−	0.331746i
$795$		0			0
$796$	−16.7239	+	20.9711i	−0.592764	+	0.743302i
$797$	28.3808	−	26.3335i	1.00530	−	0.932782i	0.00755980	−	0.999971i	$-0.497594\pi$
$797$	28.3808	−	26.3335i	1.00530	−	0.932782i	0.997740	+	0.0671893i	$0.0214031\pi$
$798$		0			0
$799$	5.02036	+	12.7917i	0.177608	+	0.452537i
$800$	22.8211	−	15.5591i	0.806847	−	0.550099i
$801$		0			0
$802$	1.84804	+	1.71473i	0.0652565	+	0.0605492i
$803$	−28.2994	+	4.26544i	−0.998663	+	0.150524i
$804$		0			0
$805$	−2.58769	+	6.59334i	−0.0912042	+	0.232385i
$806$	−0.394447	−	1.72819i	−0.0138938	−	0.0608727i
$807$		0			0
$808$	−15.5658	−	4.80140i	−0.547602	−	0.168913i
$809$	−23.3522	+	11.2458i	−0.821018	+	0.395382i	−0.796739	−	0.604324i	$-0.793443\pi$
$809$	−23.3522	+	11.2458i	−0.821018	+	0.395382i	−0.0242795	+	0.999705i	$0.507729\pi$
$810$		0			0
$811$	−5.83095	−	10.0995i	−0.204752	−	0.354641i	0.745302	−	0.666728i	$-0.232306\pi$
$811$	−5.83095	−	10.0995i	−0.204752	−	0.354641i	−0.950054	+	0.312086i	$0.898972\pi$
$812$	−32.3121	−	22.0300i	−1.13393	−	0.773103i
$813$		0			0
$814$	−14.2287	−	2.14463i	−0.498716	−	0.0751693i
$815$	8.11406	+	10.1747i	0.284223	+	0.356404i
$816$		0			0
$817$	−11.3598	−	8.63165i	−0.397431	−	0.301983i
$818$	−12.7105			−0.444411
$819$		0			0
$820$	1.48329	+	0.223570i	0.0517988	+	0.00780741i
$821$	−1.54182	+	6.75515i	−0.0538099	+	0.235756i	−0.994680	−	0.103010i	$-0.967153\pi$
$821$	−1.54182	+	6.75515i	−0.0538099	+	0.235756i	0.940870	+	0.338767i	$0.110010\pi$
$822$		0			0
$823$	−1.10308	−	1.91060i	−0.0384511	−	0.0665993i	0.846159	−	0.532930i	$-0.178909\pi$
$823$	−1.10308	−	1.91060i	−0.0384511	−	0.0665993i	−0.884611	+	0.466331i	$0.845576\pi$
$824$	−0.101651	+	0.176065i	−0.00354119	+	0.00613352i
$825$		0			0
$826$	38.0141	+	11.7258i	1.32268	+	0.407993i
$827$	0.862574	+	11.5102i	0.0299946	+	0.400250i	0.991914	+	0.126915i	$0.0405077\pi$
$827$	0.862574	+	11.5102i	0.0299946	+	0.400250i	−0.961919	+	0.273335i	$0.911873\pi$
$828$		0			0
$829$	17.7959	−	45.3432i	0.618077	−	1.57483i	−0.187450	−	0.982274i	$-0.560022\pi$
$829$	17.7959	−	45.3432i	0.618077	−	1.57483i	0.805527	−	0.592559i	$-0.201882\pi$
$830$	0.822603	−	10.9769i	0.0285530	−	0.381013i
$831$		0			0
$832$	−0.866353	−	0.803858i	−0.0300354	−	0.0278688i
$833$	15.9157	+	7.66459i	0.551446	+	0.265562i
$834$		0			0
$835$	−1.84743	−	4.70716i	−0.0639328	−	0.162898i
$836$	5.00859	−	1.54495i	0.173226	−	0.0534331i
$837$		0			0
$838$	−15.2492	+	19.1219i	−0.526776	+	0.660557i
$839$	3.63297	−	4.55560i	0.125424	−	0.157277i	−0.715155	−	0.698966i	$-0.753644\pi$
$839$	3.63297	−	4.55560i	0.125424	−	0.157277i	0.840579	+	0.541690i	$0.182215\pi$
$840$		0			0
$841$	27.1085	−	8.36187i	0.934777	−	0.288340i
$842$	−1.21687	−	3.10052i	−0.0419359	−	0.106851i
$843$		0			0
$844$	−20.2332	−	9.74381i	−0.696456	−	0.335396i
$845$	4.35447	+	4.04036i	0.149798	+	0.138993i
$846$		0			0
$847$	2.23536	−	29.8288i	0.0768078	−	1.02493i
$848$	−10.7158	+	27.3035i	−0.367983	+	0.937606i
$849$		0			0
$850$	0.908841	+	12.1276i	0.0311730	+	0.415975i
$851$	−10.3059	−	3.17895i	−0.353282	−	0.108973i
$852$		0			0
$853$	−6.61073	+	11.4501i	−0.226347	+	0.392045i	−0.956723	−	0.291001i	$-0.906012\pi$
$853$	−6.61073	+	11.4501i	−0.226347	+	0.392045i	0.730376	+	0.683046i	$0.239345\pi$
$854$	−38.0905	−	65.9748i	−1.30343	−	2.25761i
$855$		0			0
$856$	−1.89623	+	8.30793i	−0.0648118	+	0.283959i
$857$	0.650028	+	0.0979759i	0.0222045	+	0.00334679i	0.160135	−	0.987095i	$-0.448807\pi$
$857$	0.650028	+	0.0979759i	0.0222045	+	0.00334679i	−0.137931	+	0.990442i	$0.544045\pi$
$858$		0			0
$859$	38.6154			1.31754			0.658771	−	0.752344i	$-0.271077\pi$
$859$	38.6154			1.31754			0.658771	+	0.752344i	$0.271077\pi$
$860$	−4.53430	−	0.923723i	−0.154618	−	0.0314987i
$861$		0			0
$862$	26.5068	+	33.2385i	0.902825	+	1.13211i
$863$	−16.3367	−	2.46236i	−0.556108	−	0.0838198i	−0.135026	−	0.990842i	$-0.543112\pi$
$863$	−16.3367	−	2.46236i	−0.556108	−	0.0838198i	−0.421083	+	0.907022i	$0.638350\pi$
$864$		0			0
$865$	5.46092	+	3.72319i	0.185677	+	0.126592i
$866$	−35.7621	−	61.9418i	−1.21525	−	2.10487i
$867$		0			0
$868$	−2.65139	+	1.27684i	−0.0899941	+	0.0433389i
$869$	−7.10549	−	2.19175i	−0.241037	−	0.0743501i
$870$		0			0
$871$	−0.205628	−	0.900916i	−0.00696745	−	0.0305264i
$872$	−0.419816	+	1.06967i	−0.0142168	+	0.0362237i
$873$		0			0
$874$	10.4500	−	1.57508i	0.353475	−	0.0532778i
$875$	−18.3942	−	17.0673i	−0.621836	−	0.576979i
$876$		0			0
$877$	−38.9124	+	26.5300i	−1.31398	+	0.895855i	−0.998589	−	0.0531078i	$-0.983087\pi$
$877$	−38.9124	+	26.5300i	−1.31398	+	0.895855i	−0.315389	+	0.948963i	$0.602135\pi$
$878$	5.40389	+	13.7689i	0.182372	+	0.464677i
$879$		0			0
$880$	−4.41947	+	4.10067i	−0.148980	+	0.138234i
$881$	−16.0354	+	20.1078i	−0.540246	+	0.677447i	−0.974770	−	0.223213i	$-0.928345\pi$
$881$	−16.0354	+	20.1078i	−0.540246	+	0.677447i	0.434523	+	0.900661i	$0.356917\pi$
$882$		0			0
$883$	5.99913	−	5.56638i	0.201887	−	0.187324i	−0.572750	−	0.819730i	$-0.694123\pi$
$883$	5.99913	−	5.56638i	0.201887	−	0.187324i	0.774637	+	0.632407i	$0.217933\pi$
$884$	2.89294	−	0.892355i	0.0973003	−	0.0300132i
$885$		0			0
$886$	46.4313	−	31.6563i	1.55989	−	1.06352i
$887$	25.8411	+	12.4444i	0.867658	+	0.417842i	0.814101	−	0.580723i	$-0.197230\pi$
$887$	25.8411	+	12.4444i	0.867658	+	0.417842i	0.0535564	+	0.998565i	$0.482944\pi$
$888$		0			0
$889$	−16.3132	+	2.45882i	−0.547128	+	0.0824662i
$890$	0.480049	−	6.40580i	0.0160913	−	0.214723i
$891$		0			0
$892$	−2.54456	−	11.1484i	−0.0851981	−	0.373277i
$893$	1.52236	+	20.3145i	0.0509439	+	0.679799i
$894$		0			0
$895$	−8.28261	+	3.98870i	−0.276857	+	0.133327i
$896$	23.3084	−	40.3713i	0.778678	−	1.34871i
$897$		0			0
$898$	−22.7488	−	15.5099i	−0.759138	−	0.517571i
$899$	0.960619	−	4.20875i	0.0320385	−	0.140370i
$900$		0			0
$901$	−5.40425	−	6.77671i	−0.180042	−	0.225765i
$902$	7.72083			0.257076
$903$		0			0
$904$	−8.77319			−0.291792
$905$	−1.19274	−	1.49564i	−0.0396479	−	0.0497169i
$906$		0			0
$907$	−2.08244	+	9.12375i	−0.0691461	+	0.302949i	−0.997662	−	0.0683442i	$-0.978228\pi$
$907$	−2.08244	+	9.12375i	−0.0691461	+	0.302949i	0.928516	+	0.371293i	$0.121086\pi$
$908$	17.2639	+	11.7703i	0.572923	+	0.390612i
$909$		0			0
$910$	−4.04590	+	7.00770i	−0.134120	+	0.232303i
$911$	−15.5906	+	7.50806i	−0.516541	+	0.248753i	−0.673945	−	0.738781i	$-0.735402\pi$
$911$	−15.5906	+	7.50806i	−0.516541	+	0.248753i	0.157404	+	0.987534i	$0.449687\pi$
$912$		0			0
$913$	−1.57394	−	21.0028i	−0.0520899	−	0.695092i
$914$	3.68652	+	16.1517i	0.121939	+	0.534250i
$915$		0			0
$916$	−0.0209425	+	0.279458i	−0.000691959	+	0.00923355i
$917$	74.8963	−	11.2888i	2.47329	−	0.372789i
$918$		0			0
$919$	32.5165	+	15.6591i	1.07262	+	0.516546i	0.884950	−	0.465686i	$-0.154192\pi$
$919$	32.5165	+	15.6591i	1.07262	+	0.516546i	0.187669	+	0.982232i	$0.439907\pi$
$920$	−1.95427	+	1.33240i	−0.0644305	+	0.0439280i
$921$		0			0
$922$	35.6579	−	10.9990i	1.17433	−	0.362233i
$923$	6.82121	−	6.32916i	0.224523	−	0.208327i
$924$		0			0
$925$	11.4720	−	14.3854i	0.377196	−	0.472988i
$926$	−2.86322	+	2.65668i	−0.0940913	+	0.0873040i
$927$		0			0
$928$	−16.4565	−	41.9304i	−0.540210	−	1.37643i
$929$	−11.9724	+	8.16266i	−0.392803	+	0.267808i	−0.743575	−	0.668652i	$-0.766871\pi$
$929$	−11.9724	+	8.16266i	−0.392803	+	0.267808i	0.350772	+	0.936461i	$0.385919\pi$
$930$		0			0
$931$	19.1971	+	17.8123i	0.629161	+	0.583776i
$932$	8.15395	−	1.22901i	0.267091	−	0.0402575i
$933$		0			0
$934$	0.150554	−	0.383605i	0.00492627	−	0.0125519i
$935$	−0.396447	−	1.73695i	−0.0129652	−	0.0568042i
$936$		0			0
$937$	10.8335	+	3.34170i	0.353916	+	0.109169i	0.466615	−	0.884461i	$-0.345473\pi$
$937$	10.8335	+	3.34170i	0.353916	+	0.109169i	−0.112699	+	0.993629i	$0.535950\pi$
$938$	−3.71817	+	1.79058i	−0.121403	+	0.0584644i
$939$		0			0
$940$	3.30366	+	5.72210i	0.107753	+	0.186634i
$941$	28.7723	+	19.6166i	0.937949	+	0.639483i	0.932758	−	0.360504i	$-0.117395\pi$
$941$	28.7723	+	19.6166i	0.937949	+	0.639483i	0.00519143	+	0.999987i	$0.498348\pi$
$942$		0			0
$943$	5.72223	+	0.862488i	0.186342	+	0.0280865i
$944$	15.8238	+	19.8424i	0.515021	+	0.645816i
$945$		0			0
$946$	−23.7863	−	1.22296i	−0.773358	−	0.0397620i
$947$	−34.7749			−1.13003			−0.565016	−	0.825080i	$-0.691130\pi$
$947$	−34.7749			−1.13003			−0.565016	+	0.825080i	$0.691130\pi$
$948$		0			0
$949$	−24.2319	−	3.65237i	−0.786600	−	0.118561i
$950$	−4.01189	+	17.5772i	−0.130163	+	0.570281i
$951$		0			0
$952$	4.66486	+	8.07977i	0.151189	+	0.261867i
$953$	3.94892	−	6.83974i	0.127918	−	0.221561i	−0.794952	−	0.606673i	$-0.792504\pi$
$953$	3.94892	−	6.83974i	0.127918	−	0.221561i	0.922870	+	0.385112i	$0.125837\pi$
$954$		0			0
$955$	3.03886	+	0.937364i	0.0983352	+	0.0303324i
$956$	2.61081	+	34.8389i	0.0844397	+	1.12677i
$957$		0			0
$958$	−3.26544	+	8.32020i	−0.105502	+	0.268814i
$959$	1.01427	−	13.5344i	0.0327523	−	0.437050i
$960$		0			0
$961$	22.4865	+	20.8644i	0.725370	+	0.673045i
$962$	−11.1010	−	5.34597i	−0.357911	−	0.172361i
$963$		0			0
$964$	7.51496	+	19.1478i	0.242041	+	0.616710i
$965$	−3.83023	+	1.18147i	−0.123299	+	0.0380328i
$966$		0			0
$967$	−2.09656	+	2.62900i	−0.0674208	+	0.0845429i	−0.814398	−	0.580306i	$-0.802933\pi$
$967$	−2.09656	+	2.62900i	−0.0674208	+	0.0845429i	0.746978	+	0.664849i	$0.231504\pi$
$968$	6.22796	−	7.80962i	0.200174	−	0.251011i
$969$		0			0
$970$	10.4262	−	3.21605i	0.334765	−	0.103261i
$971$	17.7430	+	45.2084i	0.569400	+	1.45081i	0.868065	+	0.496450i	$0.165363\pi$
$971$	17.7430	+	45.2084i	0.569400	+	1.45081i	−0.298665	+	0.954358i	$0.596541\pi$
$972$		0			0
$973$	20.5261	+	9.88485i	0.658037	+	0.316894i
$974$	17.0552	+	15.8249i	0.546485	+	0.507064i
$975$		0			0
$976$	3.63198	−	48.4654i	0.116257	−	1.55134i
$977$	−0.376939	+	0.960425i	−0.0120593	+	0.0307267i	−0.936777	−	0.349928i	$-0.886206\pi$
$977$	−0.376939	+	0.960425i	−0.0120593	+	0.0307267i	0.924717	+	0.380655i	$0.124301\pi$
$978$		0			0
$979$	−0.918509	−	12.2567i	−0.0293557	−	0.391724i
$980$	8.11648	+	2.50360i	0.259272	+	0.0799747i
$981$		0			0
$982$	22.5907	−	39.1283i	0.720899	−	1.24863i
$983$	−27.8010	−	48.1527i	−0.886713	−	1.53583i	−0.843738	−	0.536756i	$-0.819650\pi$
$983$	−27.8010	−	48.1527i	−0.886713	−	1.53583i	−0.0429752	−	0.999076i	$-0.513684\pi$
$984$		0			0
$985$	−0.645049	+	2.82614i	−0.0205530	+	0.0900484i
$986$	19.6120	+	2.95604i	0.624574	+	0.0941394i
$987$		0			0
$988$	4.48810			0.142785
$989$	−17.4924	−	3.56354i	−0.556226	−	0.113314i
$990$		0			0
$991$	−26.0171	−	32.6244i	−0.826461	−	1.03635i	−0.998684	−	0.0512909i	$-0.983666\pi$
$991$	−26.0171	−	32.6244i	−0.826461	−	1.03635i	0.172223	−	0.985058i	$-0.444905\pi$
$992$	−3.35170	−	0.505187i	−0.106416	−	0.0160397i
$993$		0			0
$994$	−34.3352	−	23.4094i	−1.08905	−	0.742500i
$995$	6.75813	+	11.7054i	0.214247	+	0.371087i
$996$		0			0
$997$	−15.0791	+	7.26169i	−0.477558	+	0.229980i	−0.657148	−	0.753762i	$-0.728237\pi$
$997$	−15.0791	+	7.26169i	−0.477558	+	0.229980i	0.179589	+	0.983742i	$0.442523\pi$
$998$	14.8070	+	4.56736i	0.468708	+	0.144577i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.y.c.181.2		36
3.2	odd	2		43.2.g.a.9.2	✓	36
12.11	even	2		688.2.bg.c.353.3		36
43.24	even	21	inner	387.2.y.c.325.2		36
129.14	odd	42		1849.2.a.n.1.5		18
129.29	even	42		1849.2.a.o.1.14		18
129.110	odd	42		43.2.g.a.24.2	yes	36
516.239	even	42		688.2.bg.c.497.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.9.2	✓	36	3.2	odd	2
43.2.g.a.24.2	yes	36	129.110	odd	42
387.2.y.c.181.2		36	1.1	even	1	trivial
387.2.y.c.325.2		36	43.24	even	21	inner
688.2.bg.c.353.3		36	12.11	even	2
688.2.bg.c.497.3		36	516.239	even	42
1849.2.a.n.1.5		18	129.14	odd	42
1849.2.a.o.1.14		18	129.29	even	42

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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.y (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11243 + 1.39495i) q^{2} +(-0.263330 + 1.15372i) q^{4} +(0.492700 + 0.335917i) q^{5} +(2.18154 - 3.77854i) q^{7} +(1.31271 - 0.632167i) q^{8} +O(q^{10})\)	\(q+(1.11243 + 1.39495i) q^{2} +(-0.263330 + 1.15372i) q^{4} +(0.492700 + 0.335917i) q^{5} +(2.18154 - 3.77854i) q^{7} +(1.31271 - 0.632167i) q^{8} +(0.0795092 + 1.06098i) q^{10} +(0.452993 + 1.98469i) q^{11} +(-0.130264 + 1.73826i) q^{13} +(7.69769 - 1.16024i) q^{14} +(4.47454 + 2.15483i) q^{16} +(-1.21261 + 0.826746i) q^{17} +(-2.07906 + 0.641305i) q^{19} +(-0.517297 + 0.479982i) q^{20} +(-2.26462 + 2.83974i) q^{22} +(-1.99563 + 1.85167i) q^{23} +(-1.69679 - 4.32336i) q^{25} +(-2.56969 + 1.75199i) q^{26} +(3.78492 + 3.51189i) q^{28} +(-7.48963 + 1.12888i) q^{29} +(-0.208229 + 0.530558i) q^{31} +(1.32334 + 5.79793i) q^{32} +(-2.50222 - 0.771833i) q^{34} +(2.34412 - 1.12887i) q^{35} +(1.98083 + 3.43090i) q^{37} +(-3.20740 - 2.18677i) q^{38} +(0.859126 + 0.129492i) q^{40} +(-1.32534 - 1.66193i) q^{41} +(3.81986 + 5.32998i) q^{43} -2.40907 q^{44} +(-4.80299 - 0.723935i) q^{46} +(2.08348 - 9.12834i) q^{47} +(-6.01823 - 10.4239i) q^{49} +(4.14329 - 7.17639i) q^{50} +(-1.97117 - 0.608024i) q^{52} +(0.441351 + 5.88942i) q^{53} +(-0.443502 + 1.13002i) q^{55} +(0.475058 - 6.33921i) q^{56} +(-9.90645 - 9.19184i) q^{58} +(4.60418 + 2.21726i) q^{59} +(-3.57526 - 9.10961i) q^{61} +(-0.971743 + 0.299743i) q^{62} +(-0.422726 + 0.530082i) q^{64} +(-0.648092 + 0.812681i) q^{65} +(-0.506577 + 0.156258i) q^{67} +(-0.634519 - 1.61673i) q^{68} +(4.18239 + 2.01413i) q^{70} +(-3.91319 - 3.63091i) q^{71} +(-1.05058 + 14.0191i) q^{73} +(-2.58239 + 6.57982i) q^{74} +(-0.192410 - 2.56753i) q^{76} +(8.48745 + 2.61803i) q^{77} +(-1.82633 + 3.16330i) q^{79} +(1.48076 + 2.56476i) q^{80} +(0.843946 - 3.69757i) q^{82} +(-10.2305 - 1.54199i) q^{83} -0.875173 q^{85} +(-3.18571 + 11.2578i) q^{86} +(1.84930 + 2.31895i) q^{88} +(-5.97021 - 0.899865i) q^{89} +(6.28390 + 4.28429i) q^{91} +(-1.61081 - 2.79000i) q^{92} +(15.0513 - 7.24833i) q^{94} +(-1.23978 - 0.382420i) q^{95} +(-2.28198 - 9.99799i) q^{97} +(7.84589 - 19.9910i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8}+O(q^{10}) \) 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8	\( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8} - 7 q^{10} + 4 q^{11} - 18 q^{14} - 10 q^{16} + 10 q^{17} + 10 q^{19} + 3 q^{20} - 3 q^{22} - 4 q^{23} - 2 q^{25} + 15 q^{26} + 20 q^{28} - 9 q^{29} + 40 q^{31} - 48 q^{32} - 42 q^{34} - 11 q^{35} - 19 q^{37} + 21 q^{38} - 97 q^{40} + 28 q^{41} - 8 q^{43} - 14 q^{44} - 61 q^{46} + 30 q^{47} + 6 q^{49} + 3 q^{50} - 8 q^{52} + 24 q^{53} + 14 q^{55} - 39 q^{56} + 64 q^{58} + q^{59} - 14 q^{61} - 33 q^{62} + 48 q^{64} - 38 q^{65} + 66 q^{67} - 66 q^{68} + 47 q^{70} + 33 q^{71} + 29 q^{73} + 40 q^{74} - 39 q^{76} + 27 q^{77} - 17 q^{79} - 8 q^{80} - 54 q^{82} + 23 q^{83} - 56 q^{85} + 45 q^{86} - 17 q^{88} + 19 q^{89} - 13 q^{91} + 18 q^{92} + 44 q^{94} - q^{95} - 31 q^{97} + 5 q^{98}+O(q^{100}) \) 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8 - 7 * q^10 + 4 * q^11 - 18 * q^14 - 10 * q^16 + 10 * q^17 + 10 * q^19 + 3 * q^20 - 3 * q^22 - 4 * q^23 - 2 * q^25 + 15 * q^26 + 20 * q^28 - 9 * q^29 + 40 * q^31 - 48 * q^32 - 42 * q^34 - 11 * q^35 - 19 * q^37 + 21 * q^38 - 97 * q^40 + 28 * q^41 - 8 * q^43 - 14 * q^44 - 61 * q^46 + 30 * q^47 + 6 * q^49 + 3 * q^50 - 8 * q^52 + 24 * q^53 + 14 * q^55 - 39 * q^56 + 64 * q^58 + q^59 - 14 * q^61 - 33 * q^62 + 48 * q^64 - 38 * q^65 + 66 * q^67 - 66 * q^68 + 47 * q^70 + 33 * q^71 + 29 * q^73 + 40 * q^74 - 39 * q^76 + 27 * q^77 - 17 * q^79 - 8 * q^80 - 54 * q^82 + 23 * q^83 - 56 * q^85 + 45 * q^86 - 17 * q^88 + 19 * q^89 - 13 * q^91 + 18 * q^92 + 44 * q^94 - q^95 - 31 * q^97 + 5 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more