LMFDB - Embedded newform 405.2.r.a.197.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(8,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 27]))

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

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

chi := DirichletCharacter("405.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.r (of order $36$, degree $12$, not 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:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			197.9
Character	$\chi$	$=$	405.197
Dual form			405.2.r.a.368.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.576956 - 0.0504771i) q^{2} +(-1.63929 + 0.289050i) q^{4} +(-2.18512 + 0.474625i) q^{5} +(2.78018 - 1.94671i) q^{7} +(-2.05006 + 0.549311i) q^{8} +O(q^{10})$	\(q+(0.576956 - 0.0504771i) q^{2} +(-1.63929 + 0.289050i) q^{4} +(-2.18512 + 0.474625i) q^{5} +(2.78018 - 1.94671i) q^{7} +(-2.05006 + 0.549311i) q^{8} +(-1.23676 + 0.384136i) q^{10} +(-1.55726 - 4.27854i) q^{11} +(0.357151 - 4.08225i) q^{13} +(1.50578 - 1.26350i) q^{14} +(1.97331 - 0.718227i) q^{16} +(-0.284890 - 0.0763360i) q^{17} +(-4.26213 - 2.46074i) q^{19} +(3.44484 - 1.40965i) q^{20} +(-1.11444 - 2.38992i) q^{22} +(-0.869642 + 1.24198i) q^{23} +(4.54946 - 2.07422i) q^{25} -2.37331i q^{26} +(-3.99482 + 3.99482i) q^{28} +(-5.57542 - 4.67834i) q^{29} +(0.591015 + 3.35181i) q^{31} +(4.94931 - 2.30790i) q^{32} +(-0.168222 - 0.0296621i) q^{34} +(-5.15107 + 5.57332i) q^{35} +(1.28961 - 4.81289i) q^{37} +(-2.58327 - 1.20460i) q^{38} +(4.21889 - 2.17331i) q^{40} +(2.42980 + 2.89573i) q^{41} +(-4.02865 + 8.63947i) q^{43} +(3.78950 + 6.56361i) q^{44} +(-0.439054 + 0.760463i) q^{46} +(-1.09911 - 1.56969i) q^{47} +(1.54562 - 4.24655i) q^{49} +(2.52014 - 1.42638i) q^{50} +(0.594504 + 6.79521i) q^{52} +(1.39575 + 1.39575i) q^{53} +(5.43349 + 8.60998i) q^{55} +(-4.63018 + 5.51804i) q^{56} +(-3.45292 - 2.41776i) q^{58} +(9.34637 + 3.40180i) q^{59} +(-0.249603 + 1.41557i) q^{61} +(0.510179 + 1.90402i) q^{62} +(-0.898191 + 0.518571i) q^{64} +(1.15712 + 9.08971i) q^{65} +(-9.46116 - 0.827744i) q^{67} +(0.489081 + 0.0427890i) q^{68} +(-2.69061 + 3.47557i) q^{70} +(-0.728237 + 0.420448i) q^{71} +(0.166069 + 0.619776i) q^{73} +(0.501107 - 2.84192i) q^{74} +(7.69812 + 2.80189i) q^{76} +(-12.6585 - 8.86359i) q^{77} +(9.56341 - 11.3972i) q^{79} +(-3.97103 + 2.50599i) q^{80} +(1.54806 + 1.54806i) q^{82} +(-0.830405 - 9.49158i) q^{83} +(0.658748 + 0.0315873i) q^{85} +(-1.88826 + 5.18795i) q^{86} +(5.54271 + 7.91582i) q^{88} +(6.19767 - 10.7347i) q^{89} +(-6.95400 - 12.0447i) q^{91} +(1.06660 - 2.28733i) q^{92} +(-0.713371 - 0.850162i) q^{94} +(10.4812 + 3.35409i) q^{95} +(-4.11255 - 1.91772i) q^{97} +(0.677399 - 2.52809i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	0.576956	−	0.0504771i	0.407969	−	0.0356927i	0.118676	−	0.992933i	$-0.462135\pi$
$2$	0.576956	−	0.0504771i	0.407969	−	0.0356927i	0.289294	+	0.957240i	$0.406580\pi$
$3$		0			0
$3$		0			0
$4$	−1.63929	+	0.289050i	−0.819643	+	0.144525i
$5$	−2.18512	+	0.474625i	−0.977214	+	0.212259i
$5$	−2.18512	+	0.474625i	−0.977214	+	0.212259i
$6$		0			0
$7$	2.78018	−	1.94671i	1.05081	−	0.735785i	0.0853543	−	0.996351i	$-0.472798\pi$
$7$	2.78018	−	1.94671i	1.05081	−	0.735785i	0.965456	+	0.260565i	$0.0839089\pi$
$8$	−2.05006	+	0.549311i	−0.724804	+	0.194211i
$9$		0			0
$10$	−1.23676	+	0.384136i	−0.391097	+	0.121474i
$11$	−1.55726	−	4.27854i	−0.469531	−	1.29003i	−0.918125	−	0.396291i	$-0.870297\pi$
$11$	−1.55726	−	4.27854i	−0.469531	−	1.29003i	0.448594	−	0.893736i	$-0.351925\pi$
$12$		0			0
$13$	0.357151	−	4.08225i	0.0990558	−	1.13221i	−0.770184	−	0.637822i	$-0.779835\pi$
$13$	0.357151	−	4.08225i	0.0990558	−	1.13221i	0.869239	−	0.494391i	$-0.164609\pi$
$14$	1.50578	−	1.26350i	0.402436	−	0.337684i
$15$		0			0
$16$	1.97331	−	0.718227i	0.493328	−	0.179557i
$17$	−0.284890	−	0.0763360i	−0.0690959	−	0.0185142i	0.224105	−	0.974565i	$-0.428054\pi$
$17$	−0.284890	−	0.0763360i	−0.0690959	−	0.0185142i	−0.293201	+	0.956051i	$0.594721\pi$
$18$		0			0
$19$	−4.26213	−	2.46074i	−0.977799	−	0.564532i	−0.0761939	−	0.997093i	$-0.524277\pi$
$19$	−4.26213	−	2.46074i	−0.977799	−	0.564532i	−0.901605	+	0.432561i	$0.857610\pi$
$20$	3.44484	−	1.40965i	0.770289	−	0.315208i
$21$		0			0
$22$	−1.11444	−	2.38992i	−0.237599	−	0.509533i
$23$	−0.869642	+	1.24198i	−0.181333	+	0.258970i	−0.899520	−	0.436880i	$-0.856083\pi$
$23$	−0.869642	+	1.24198i	−0.181333	+	0.258970i	0.718187	+	0.695850i	$0.244972\pi$
$24$		0			0
$25$	4.54946	−	2.07422i	0.909893	−	0.414844i
$26$		−	2.37331i		−	0.465444i
$27$		0			0
$28$	−3.99482	+	3.99482i	−0.754950	+	0.754950i
$29$	−5.57542	−	4.67834i	−1.03533	−	0.868745i	−0.0438548	−	0.999038i	$-0.513964\pi$
$29$	−5.57542	−	4.67834i	−1.03533	−	0.868745i	−0.991476	+	0.130293i	$0.958408\pi$
$30$		0			0
$31$	0.591015	+	3.35181i	0.106149	+	0.602003i	0.990755	+	0.135663i	$0.0433165\pi$
$31$	0.591015	+	3.35181i	0.106149	+	0.602003i	−0.884606	+	0.466340i	$0.845572\pi$
$32$	4.94931	−	2.30790i	0.874922	−	0.407983i
$33$		0			0
$34$	−0.168222	−	0.0296621i	−0.0288498	−	0.00508701i
$35$	−5.15107	+	5.57332i	−0.870690	+	0.942063i
$36$		0			0
$37$	1.28961	−	4.81289i	0.212011	−	0.791234i	−0.775187	−	0.631732i	$-0.782344\pi$
$37$	1.28961	−	4.81289i	0.212011	−	0.791234i	0.987198	−	0.159502i	$-0.0509890\pi$
$38$	−2.58327	−	1.20460i	−0.419062	−	0.195412i
$39$		0			0
$40$	4.21889	−	2.17331i	0.667066	−	0.343631i
$41$	2.42980	+	2.89573i	0.379472	+	0.452237i	0.921647	−	0.388028i	$-0.126844\pi$
$41$	2.42980	+	2.89573i	0.379472	+	0.452237i	−0.542176	+	0.840265i	$0.682399\pi$
$42$		0			0
$43$	−4.02865	+	8.63947i	−0.614364	+	1.31751i	0.315263	+	0.949004i	$0.397907\pi$
$43$	−4.02865	+	8.63947i	−0.614364	+	1.31751i	−0.929627	+	0.368503i	$0.879871\pi$
$44$	3.78950	+	6.56361i	0.571289	+	0.989502i
$45$		0			0
$46$	−0.439054	+	0.760463i	−0.0647349	+	0.112124i
$47$	−1.09911	−	1.56969i	−0.160322	−	0.228963i	0.730952	−	0.682429i	$-0.239076\pi$
$47$	−1.09911	−	1.56969i	−0.160322	−	0.228963i	−0.891274	+	0.453466i	$0.850187\pi$
$48$		0			0
$49$	1.54562	−	4.24655i	0.220802	−	0.606650i
$50$	2.52014	−	1.42638i	0.356401	−	0.201720i
$51$		0			0
$52$	0.594504	+	6.79521i	0.0824429	+	0.942327i
$53$	1.39575	+	1.39575i	0.191721	+	0.191721i	0.796439	−	0.604719i	$-0.206714\pi$
$53$	1.39575	+	1.39575i	0.191721	+	0.191721i	−0.604719	+	0.796439i	$0.706714\pi$
$54$		0			0
$55$	5.43349	+	8.60998i	0.732652	+	1.16097i
$56$	−4.63018	+	5.51804i	−0.618734	+	0.737379i
$57$		0			0
$58$	−3.45292	−	2.41776i	−0.453391	−	0.317468i
$59$	9.34637	+	3.40180i	1.21679	+	0.442877i	0.869055	−	0.494715i	$-0.164728\pi$
$59$	9.34637	+	3.40180i	1.21679	+	0.442877i	0.347738	+	0.937592i	$0.386950\pi$
$60$		0			0
$61$	−0.249603	+	1.41557i	−0.0319584	+	0.181245i	−0.996609	−	0.0822889i	$-0.973777\pi$
$61$	−0.249603	+	1.41557i	−0.0319584	+	0.181245i	0.964650	+	0.263534i	$0.0848881\pi$
$62$	0.510179	+	1.90402i	0.0647928	+	0.241810i
$63$		0			0
$64$	−0.898191	+	0.518571i	−0.112274	+	0.0648214i
$65$	1.15712	+	9.08971i	0.143523	+	1.12744i
$66$		0			0
$67$	−9.46116	−	0.827744i	−1.15586	−	0.101125i	−0.506943	−	0.861980i	$-0.669224\pi$
$67$	−9.46116	−	0.827744i	−1.15586	−	0.101125i	−0.648922	+	0.760855i	$0.724780\pi$
$68$	0.489081	+	0.0427890i	0.0593097	+	0.00518893i
$69$		0			0
$70$	−2.69061	+	3.47557i	−0.321590	+	0.415410i
$71$	−0.728237	+	0.420448i	−0.0864258	+	0.0498980i	−0.542590	−	0.839998i	$-0.682556\pi$
$71$	−0.728237	+	0.420448i	−0.0864258	+	0.0498980i	0.456164	+	0.889896i	$0.349223\pi$
$72$		0			0
$73$	0.166069	+	0.619776i	0.0194369	+	0.0725393i	0.974963	−	0.222367i	$-0.0713783\pi$
$73$	0.166069	+	0.619776i	0.0194369	+	0.0725393i	−0.955526	+	0.294906i	$0.904712\pi$
$74$	0.501107	−	2.84192i	0.0582526	−	0.330367i
$75$		0			0
$76$	7.69812	+	2.80189i	0.883035	+	0.321398i
$77$	−12.6585	−	8.86359i	−1.44257	−	1.01010i
$78$		0			0
$79$	9.56341	−	11.3972i	1.07597	−	1.28229i	0.118748	−	0.992924i	$-0.462112\pi$
$79$	9.56341	−	11.3972i	1.07597	−	1.28229i	0.957219	−	0.289364i	$-0.0934436\pi$
$80$	−3.97103	+	2.50599i	−0.443974	+	0.280178i
$81$		0			0
$82$	1.54806	+	1.54806i	0.170954	+	0.170954i
$83$	−0.830405	−	9.49158i	−0.0911488	−	1.04184i	−0.894720	−	0.446627i	$-0.852625\pi$
$83$	−0.830405	−	9.49158i	−0.0911488	−	1.04184i	0.803571	−	0.595209i	$-0.202931\pi$
$84$		0			0
$85$	0.658748	+	0.0315873i	0.0714513	+	0.00342612i
$86$	−1.88826	+	5.18795i	−0.203616	+	0.559431i
$87$		0			0
$88$	5.54271	+	7.91582i	0.590855	+	0.843829i
$89$	6.19767	−	10.7347i	0.656952	−	1.13787i	−0.324448	−	0.945903i	$-0.605179\pi$
$89$	6.19767	−	10.7347i	0.656952	−	1.13787i	0.981401	−	0.191971i	$-0.0614880\pi$
$90$		0			0
$91$	−6.95400	−	12.0447i	−0.728977	−	1.26263i
$92$	1.06660	−	2.28733i	0.111200	−	0.238470i
$93$		0			0
$94$	−0.713371	−	0.850162i	−0.0735786	−	0.0876876i
$95$	10.4812	+	3.35409i	1.07534	+	0.344123i
$96$		0			0
$97$	−4.11255	−	1.91772i	−0.417567	−	0.194715i	0.202468	−	0.979289i	$-0.435104\pi$
$97$	−4.11255	−	1.91772i	−0.417567	−	0.194715i	−0.620035	+	0.784574i	$0.712882\pi$
$98$	0.677399	−	2.52809i	0.0684277	−	0.255376i
$99$		0			0
$100$	−6.85831	+	4.71526i	−0.685831	+	0.471526i
$101$	8.64670	+	1.52465i	0.860378	+	0.151708i	0.586394	−	0.810026i	$-0.300547\pi$
$101$	8.64670	+	1.52465i	0.860378	+	0.151708i	0.273985	+	0.961734i	$0.411658\pi$
$102$		0			0
$103$	−2.78831	+	1.30021i	−0.274741	+	0.128114i	−0.555106	−	0.831780i	$-0.687322\pi$
$103$	−2.78831	+	1.30021i	−0.274741	+	0.128114i	0.280365	+	0.959893i	$0.409544\pi$
$104$	1.51025	+	8.56503i	0.148092	+	0.839871i
$105$		0			0
$106$	0.875738	+	0.734831i	0.0850592	+	0.0713731i
$107$	0.840083	−	0.840083i	0.0812138	−	0.0812138i	−0.665333	−	0.746547i	$-0.731710\pi$
$107$	0.840083	−	0.840083i	0.0812138	−	0.0812138i	0.746547	+	0.665333i	$0.231710\pi$
$108$		0			0
$109$			15.3404i			1.46935i	0.678422	+	0.734673i	$0.262664\pi$
$109$			15.3404i			1.46935i	−0.678422	+	0.734673i	$0.737336\pi$
$110$	3.56949	+	4.69331i	0.340338	+	0.447490i
$111$		0			0
$112$	4.08799	−	5.83826i	0.386279	−	0.551664i
$113$	−1.57466	−	3.37688i	−0.148132	−	0.317670i	0.818215	−	0.574912i	$-0.194964\pi$
$113$	−1.57466	−	3.37688i	−0.148132	−	0.317670i	−0.966347	+	0.257242i	$0.917186\pi$
$114$		0			0
$115$	1.31080	−	3.12662i	0.122232	−	0.291559i
$116$	10.4920	+	6.05755i	0.974156	+	0.562429i
$117$		0			0
$118$	5.56415	+	1.49091i	0.512222	+	0.137249i
$119$	−0.940649	+	0.342368i	−0.0862292	+	0.0313849i
$120$		0			0
$121$	−7.45432	+	6.25492i	−0.677665	+	0.568629i
$122$	−0.0725561	+	0.829320i	−0.00656892	+	0.0750831i
$123$		0			0
$124$	−1.93768	−	5.32374i	−0.174009	−	0.478086i
$125$	−8.95663	+	6.69170i	−0.801105	+	0.598523i
$126$		0			0
$127$	−17.0553	+	4.56996i	−1.51342	+	0.405518i	−0.917568	−	0.397579i	$-0.869850\pi$
$127$	−17.0553	+	4.56996i	−1.51342	+	0.405518i	−0.595847	+	0.803098i	$0.703184\pi$
$128$	−9.43875	+	6.60908i	−0.834275	+	0.584166i
$129$		0			0
$130$	1.12643	+	5.18595i	0.0987945	+	0.454838i
$131$	4.36693	−	0.770008i	0.381540	−	0.0672759i	0.0204113	−	0.999792i	$-0.493502\pi$
$131$	4.36693	−	0.770008i	0.381540	−	0.0672759i	0.361129	+	0.932516i	$0.382391\pi$
$132$		0			0
$133$	−16.6398	+	1.45580i	−1.44286	+	0.126234i
$134$	−5.50045			−0.475167
$135$		0			0
$136$	0.625972			0.0536767
$137$	17.1191	−	1.49772i	1.46258	−	0.127959i	0.672107	−	0.740454i	$-0.265390\pi$
$137$	17.1191	−	1.49772i	1.46258	−	0.127959i	0.790474	+	0.612495i	$0.209834\pi$
$138$		0			0
$139$	3.49278	−	0.615871i	0.296254	−	0.0522375i	−0.0235459	−	0.999723i	$-0.507496\pi$
$139$	3.49278	−	0.615871i	0.296254	−	0.0522375i	0.319799	+	0.947485i	$0.396384\pi$
$140$	6.83310	−	10.6252i	0.577503	−	0.897992i
$141$		0			0
$142$	−0.398938	+	0.279339i	−0.0334781	+	0.0234416i
$143$	−18.0222	+	4.82905i	−1.50710	+	0.403825i
$144$		0			0
$145$	14.4034	+	7.57647i	1.19614	+	0.629192i
$146$	0.127099	+	0.349201i	0.0105188	+	0.0289001i
$147$		0			0
$148$	−0.722872	+	8.26246i	−0.0594197	+	0.679170i
$149$	2.74544	−	2.30369i	0.224915	−	0.188726i	−0.523366	−	0.852108i	$-0.675324\pi$
$149$	2.74544	−	2.30369i	0.224915	−	0.188726i	0.748281	+	0.663382i	$0.230880\pi$
$150$		0			0
$151$	18.4206	−	6.70454i	1.49904	−	0.545607i	0.543231	−	0.839583i	$-0.317201\pi$
$151$	18.4206	−	6.70454i	1.49904	−	0.545607i	0.955813	+	0.293976i	$0.0949785\pi$
$152$	10.0893	+	2.70342i	0.818351	+	0.219276i
$153$		0			0
$154$	−7.75081	−	4.47493i	−0.624578	−	0.360600i
$155$	−2.88229	−	7.04359i	−0.231511	−	0.565755i
$156$		0			0
$157$	0.239187	+	0.512939i	0.0190892	+	0.0409370i	0.915621	−	0.402042i	$-0.131699\pi$
$157$	0.239187	+	0.512939i	0.0190892	+	0.0409370i	−0.896532	+	0.442979i	$0.853922\pi$
$158$	4.94237	−	7.05843i	0.393193	−	0.561538i
$159$		0			0
$160$	−9.71943	+	7.39209i	−0.768388	+	0.584396i
$161$			5.14586i			0.405551i
$162$		0			0
$163$	3.48997	−	3.48997i	0.273355	−	0.273355i	−0.557094	−	0.830449i	$-0.688084\pi$
$163$	3.48997	−	3.48997i	0.273355	−	0.273355i	0.830449	+	0.557094i	$0.188084\pi$
$164$	−4.82015	−	4.04459i	−0.376391	−	0.315829i
$165$		0			0
$166$	−0.958215	−	5.43431i	−0.0743719	−	0.421784i
$167$	−13.2832	+	6.19404i	−1.02788	+	0.479309i	−0.862039	−	0.506843i	$-0.830812\pi$
$167$	−13.2832	+	6.19404i	−1.02788	+	0.479309i	−0.165844	+	0.986152i	$0.553035\pi$
$168$		0			0
$169$	−3.73474	−	0.658535i	−0.287288	−	0.0506566i
$170$	0.381663	−	0.0150272i	0.0292722	−	0.00115253i
$171$		0			0
$172$	4.10687	−	15.3270i	0.313146	−	1.16868i
$173$	8.49331	+	3.96050i	0.645735	+	0.301111i	0.717759	−	0.696292i	$-0.245168\pi$
$173$	8.49331	+	3.96050i	0.645735	+	0.301111i	−0.0720241	+	0.997403i	$0.522946\pi$
$174$		0			0
$175$	8.61045	−	14.6232i	0.650889	−	1.10541i
$176$	−6.14592	−	7.32442i	−0.463266	−	0.552099i
$177$		0			0
$178$	3.03393	−	6.50628i	0.227403	−	0.487666i
$179$	−10.1322	−	17.5496i	−0.757320	−	1.31172i	−0.944213	−	0.329336i	$-0.893175\pi$
$179$	−10.1322	−	17.5496i	−0.757320	−	1.31172i	0.186893	−	0.982380i	$-0.440158\pi$
$180$		0			0
$181$	5.71685	−	9.90188i	0.424930	−	0.736001i	−0.571484	−	0.820613i	$-0.693632\pi$
$181$	5.71685	−	9.90188i	0.424930	−	0.736001i	0.996414	+	0.0846126i	$0.0269653\pi$
$182$	−4.62013	−	6.59823i	−0.342467	−	0.489094i
$183$		0			0
$184$	1.10058	−	3.02383i	0.0811361	−	0.222920i
$185$	−0.533632	+	11.1288i	−0.0392334	+	0.818206i
$186$		0			0
$187$	0.117041	+	1.33779i	0.00855889	+	0.0978286i
$188$	2.25547	+	2.25547i	0.164497	+	0.164497i
$189$		0			0
$190$	6.21648	+	1.40610i	0.450991	+	0.102010i
$191$	3.38340	−	4.03218i	0.244814	−	0.291758i	−0.629619	−	0.776904i	$-0.716789\pi$
$191$	3.38340	−	4.03218i	0.244814	−	0.291758i	0.874433	+	0.485146i	$0.161233\pi$
$192$		0			0
$193$	8.91213	+	6.24034i	0.641509	+	0.449189i	0.848530	−	0.529147i	$-0.177488\pi$
$193$	8.91213	+	6.24034i	0.641509	+	0.449189i	−0.207021	+	0.978336i	$0.566377\pi$
$194$	−2.46956	−	0.898848i	−0.177304	−	0.0645335i
$195$		0			0
$196$	−1.30624	+	7.40806i	−0.0933030	+	0.529147i
$197$	−2.41739	−	9.02182i	−0.172232	−	0.642778i	−0.997007	−	0.0773166i	$-0.975365\pi$
$197$	−2.41739	−	9.02182i	−0.172232	−	0.642778i	0.824775	−	0.565461i	$-0.191302\pi$
$198$		0			0
$199$	10.1326	−	5.85008i	0.718284	−	0.414701i	−0.0958368	−	0.995397i	$-0.530553\pi$
$199$	10.1326	−	5.85008i	0.718284	−	0.414701i	0.814121	+	0.580696i	$0.197219\pi$
$200$	−8.18726	+	6.75133i	−0.578927	+	0.477391i
$201$		0			0
$202$	5.06572	+	0.443193i	0.356423	+	0.0311830i
$203$	−24.6080	−	2.15293i	−1.72715	−	0.151106i
$204$		0			0
$205$	−6.68379	−	5.17426i	−0.466816	−	0.361386i
$206$	−1.54310	+	0.890911i	−0.107513	+	0.0620727i
$207$		0			0
$208$	−2.22721	−	8.31207i	−0.154429	−	0.576339i
$209$	−3.89112	+	22.0677i	−0.269155	+	1.52645i
$210$		0			0
$211$	−13.7093	−	4.98977i	−0.943786	−	0.343510i	−0.176126	−	0.984368i	$-0.556357\pi$
$211$	−13.7093	−	4.98977i	−0.943786	−	0.343510i	−0.767660	+	0.640858i	$0.778579\pi$
$212$	−2.69147	−	1.88459i	−0.184851	−	0.129434i
$213$		0			0
$214$	0.442286	−	0.527096i	0.0302340	−	0.0360315i
$215$	4.70257	−	20.7903i	0.320712	−	1.41789i
$216$		0			0
$217$	8.16812	+	8.16812i	0.554488	+	0.554488i
$218$	0.774340	+	8.85074i	0.0524449	+	0.599448i
$219$		0			0
$220$	−11.3958	−	12.5437i	−0.768302	−	0.845694i
$221$	−0.413372	+	1.13573i	−0.0278064	+	0.0763974i
$222$		0			0
$223$	−11.8646	−	16.9444i	−0.794514	−	1.13468i	−0.988132	−	0.153607i	$-0.950911\pi$
$223$	−11.8646	−	16.9444i	−0.794514	−	1.13468i	0.193618	−	0.981077i	$-0.437978\pi$
$224$	9.26718	−	16.0512i	0.619190	−	1.07247i
$225$		0			0
$226$	−1.07897	−	1.86883i	−0.0717718	−	0.124312i
$227$	4.17394	−	8.95104i	0.277034	−	0.594101i	−0.717728	−	0.696324i	$-0.754818\pi$
$227$	4.17394	−	8.95104i	0.277034	−	0.594101i	0.994762	+	0.102223i	$0.0325954\pi$
$228$		0			0
$229$	17.3346	+	20.6585i	1.14550	+	1.36515i	0.920475	+	0.390800i	$0.127802\pi$
$229$	17.3346	+	20.6585i	1.14550	+	1.36515i	0.225024	+	0.974353i	$0.427754\pi$
$230$	0.598449	−	1.87009i	0.0394605	−	0.123310i
$231$		0			0
$232$	13.9998	+	6.52821i	0.919131	+	0.428598i
$233$	1.67108	−	6.23657i	0.109476	−	0.408571i	−0.889338	−	0.457250i	$-0.848834\pi$
$233$	1.67108	−	6.23657i	0.109476	−	0.408571i	0.998814	+	0.0486789i	$0.0155011\pi$
$234$		0			0
$235$	3.14669	+	2.90829i	0.205268	+	0.189716i
$236$	−16.3047	−	2.87495i	−1.06134	−	0.187143i
$237$		0			0
$238$	−0.525432	+	0.245013i	−0.0340587	+	0.0158818i
$239$	2.94647	+	16.7103i	0.190591	+	1.08090i	0.918558	+	0.395286i	$0.129354\pi$
$239$	2.94647	+	16.7103i	0.190591	+	1.08090i	−0.727967	+	0.685612i	$0.759535\pi$
$240$		0			0
$241$	−3.88280	−	3.25805i	−0.250113	−	0.209870i	0.509108	−	0.860703i	$-0.329975\pi$
$241$	−3.88280	−	3.25805i	−0.250113	−	0.209870i	−0.759221	+	0.650833i	$0.774420\pi$
$242$	−3.98508	+	3.98508i	−0.256171	+	0.256171i
$243$		0			0
$244$		−	2.39267i		−	0.153175i
$245$	−1.36184	+	10.0128i	−0.0870045	+	0.639693i
$246$		0			0
$247$	−11.5676	+	16.5202i	−0.736028	+	1.05116i
$248$	−3.05280	−	6.54675i	−0.193853	−	0.415719i
$249$		0			0
$250$	−4.82980	+	4.31292i	−0.305464	+	0.272773i
$251$	7.62764	+	4.40382i	0.481452	+	0.277967i	0.721022	−	0.692913i	$-0.243673\pi$
$251$	7.62764	+	4.40382i	0.481452	+	0.277967i	−0.239569	+	0.970879i	$0.577006\pi$
$252$		0			0
$253$	6.66810	+	1.78671i	0.419220	+	0.112330i
$254$	−9.60949	+	3.49757i	−0.602953	+	0.219457i
$255$		0			0
$256$	−3.52314	+	2.95627i	−0.220196	+	0.184767i
$257$	−2.26790	+	25.9222i	−0.141468	+	1.61698i	0.511286	+	0.859411i	$0.329169\pi$
$257$	−2.26790	+	25.9222i	−0.141468	+	1.61698i	−0.652753	+	0.757571i	$0.726386\pi$
$258$		0			0
$259$	−5.78393	−	15.8912i	−0.359396	−	0.987432i
$260$	−4.52424	−	14.5662i	−0.280581	−	0.903355i
$261$		0			0
$262$	2.48066	−	0.664690i	0.153256	−	0.0410647i
$263$	4.72837	−	3.31084i	0.291564	−	0.204155i	−0.418638	−	0.908153i	$-0.637493\pi$
$263$	4.72837	−	3.31084i	0.291564	−	0.204155i	0.710202	+	0.703998i	$0.248604\pi$
$264$		0			0
$265$	−3.71232	−	2.38741i	−0.228046	−	0.146658i
$266$	−9.52696	+	1.67986i	−0.584136	+	0.102999i
$267$		0			0
$268$	15.7488	−	1.37784i	0.962011	−	0.0841651i
$269$	21.3254			1.30023			0.650116	−	0.759835i	$-0.274720\pi$
$269$	21.3254			1.30023			0.650116	+	0.759835i	$0.274720\pi$
$270$		0			0
$271$	13.8664			0.842325			0.421162	−	0.906985i	$-0.361622\pi$
$271$	13.8664			0.842325			0.421162	+	0.906985i	$0.361622\pi$
$272$	−0.617003	+	0.0539808i	−0.0374113	+	0.00327306i
$273$		0			0
$274$	9.80135	−	1.72824i	0.592121	−	0.104407i
$275$	−15.9593	−	16.2349i	−0.962383	−	0.979004i
$276$		0			0
$277$	−3.39790	+	2.37923i	−0.204160	+	0.142954i	−0.671185	−	0.741290i	$-0.734215\pi$
$277$	−3.39790	+	2.37923i	−0.204160	+	0.142954i	0.467025	+	0.884244i	$0.345326\pi$
$278$	1.98409	−	0.531636i	0.118998	−	0.0318854i
$279$		0			0
$280$	7.49849	−	14.2552i	0.448121	−	0.851908i
$281$	−4.59659	−	12.6290i	−0.274210	−	0.753385i	−0.997991	−	0.0633553i	$-0.979820\pi$
$281$	−4.59659	−	12.6290i	−0.274210	−	0.753385i	0.723781	−	0.690029i	$-0.242402\pi$
$282$		0			0
$283$	1.01502	−	11.6017i	0.0603367	−	0.689651i	−0.904443	−	0.426594i	$-0.859713\pi$
$283$	1.01502	−	11.6017i	0.0603367	−	0.689651i	0.964780	−	0.263058i	$-0.0847310\pi$
$284$	1.07226	−	0.899731i	0.0636268	−	0.0533892i
$285$		0			0
$286$	−10.1543	+	3.69586i	−0.600435	+	0.218541i
$287$	12.3924	+	3.32054i	0.731502	+	0.196005i
$288$		0			0
$289$	−14.6471	−	8.45651i	−0.861594	−	0.497441i
$290$	8.69257	+	3.64425i	0.510445	+	0.213998i
$291$		0			0
$292$	−0.451380	−	0.967988i	−0.0264150	−	0.0566472i
$293$	15.1248	−	21.6004i	0.883598	−	1.26191i	−0.0806060	−	0.996746i	$-0.525686\pi$
$293$	15.1248	−	21.6004i	0.883598	−	1.26191i	0.964204	−	0.265162i	$-0.0854256\pi$
$294$		0			0
$295$	−22.0375	−	2.99731i	−1.28307	−	0.174510i
$296$			10.5751i			0.614665i
$297$		0			0
$298$	1.46771	−	1.46771i	0.0850222	−	0.0850222i
$299$	4.75947	+	3.99367i	0.275248	+	0.230960i
$300$		0			0
$301$	5.61812	+	31.8619i	0.323823	+	1.83649i
$302$	10.2894	−	4.79804i	0.592090	−	0.276096i
$303$		0			0
$304$	−10.1779	−	1.79463i	−0.583741	−	0.102929i
$305$	−0.126452	−	3.21165i	−0.00724063	−	0.183899i
$306$		0			0
$307$	4.69578	−	17.5249i	0.268003	−	1.00020i	−0.692384	−	0.721529i	$-0.743440\pi$
$307$	4.69578	−	17.5249i	0.268003	−	1.00020i	0.960387	−	0.278670i	$-0.0898936\pi$
$308$	23.3129	+	10.8710i	1.32838	+	0.619433i
$309$		0			0
$310$	−2.01849	−	3.91835i	−0.114643	−	0.222547i
$311$	−11.0997	−	13.2281i	−0.629405	−	0.750095i	0.353252	−	0.935528i	$-0.385076\pi$
$311$	−11.0997	−	13.2281i	−0.629405	−	0.750095i	−0.982657	+	0.185433i	$0.940631\pi$
$312$		0			0
$313$	−6.31743	+	13.5478i	−0.357082	+	0.765766i	−1.00000		0.000169586i	$-0.999946\pi$
$313$	−6.31743	+	13.5478i	−0.357082	+	0.765766i	0.642918	+	0.765935i	$0.277724\pi$
$314$	0.163892	+	0.283870i	0.00924897	+	0.0160197i
$315$		0			0
$316$	−12.3828	+	21.4476i	−0.696586	+	1.20652i
$317$	8.90361	+	12.7157i	0.500077	+	0.714183i	0.987260	−	0.159116i	$-0.0508645\pi$
$317$	8.90361	+	12.7157i	0.500077	+	0.714183i	−0.487183	+	0.873300i	$0.661976\pi$
$318$		0			0
$319$	−11.3340	+	31.1400i	−0.634585	+	1.74351i
$320$	1.71653	−	1.55944i	0.0959567	−	0.0871754i
$321$		0			0
$322$	0.259748	+	2.96894i	0.0144752	+	0.165452i
$323$	1.02639	+	1.02639i	0.0571100	+	0.0571100i
$324$		0			0
$325$	−6.84264	−	19.3129i	−0.379562	−	1.07129i
$326$	1.83739	−	2.18972i	0.101764	−	0.121277i
$327$		0			0
$328$	−6.57189	−	4.60169i	−0.362872	−	0.254086i
$329$	−6.11145	−	2.22439i	−0.336935	−	0.122634i
$330$		0			0
$331$	0.733175	−	4.15804i	0.0402990	−	0.228547i	−0.958006	−	0.286749i	$-0.907426\pi$
$331$	0.733175	−	4.15804i	0.0402990	−	0.228547i	0.998305	+	0.0582018i	$0.0185367\pi$
$332$	4.10481	+	15.3194i	0.225281	+	0.840760i
$333$		0			0
$334$	−7.35114	+	4.24418i	−0.402237	+	0.232231i
$335$	21.0666	−	2.68178i	1.15099	−	0.146521i
$336$		0			0
$337$	−4.83165	−	0.422715i	−0.263197	−	0.0230267i	−0.0452064	−	0.998978i	$-0.514395\pi$
$337$	−4.83165	−	0.422715i	−0.263197	−	0.0230267i	−0.217990	+	0.975951i	$0.569950\pi$
$338$	−2.18802	−	0.191427i	−0.119013	−	0.0104123i
$339$		0			0
$340$	−1.08901	+	0.138631i	−0.0590597	+	0.00751830i
$341$	13.4205	−	7.74832i	0.726760	−	0.419595i
$342$		0			0
$343$	2.17930	+	8.13327i	0.117671	+	0.439155i
$344$	3.51321	−	19.9244i	0.189419	−	1.07425i
$345$		0			0
$346$	5.10018	+	1.85631i	0.274187	+	0.0997961i
$347$	−15.3139	−	10.7229i	−0.822092	−	0.575635i	0.0850901	−	0.996373i	$-0.472882\pi$
$347$	−15.3139	−	10.7229i	−0.822092	−	0.575635i	−0.907182	+	0.420738i	$0.861771\pi$
$348$		0			0
$349$	−5.80311	+	6.91588i	−0.310634	+	0.370199i	−0.898662	−	0.438641i	$-0.855460\pi$
$349$	−5.80311	+	6.91588i	−0.310634	+	0.370199i	0.588029	+	0.808840i	$0.299904\pi$
$350$	4.22971	−	8.87156i	0.226088	−	0.474205i
$351$		0			0
$352$	−17.5818	−	17.5818i	−0.937112	−	0.937112i
$353$	3.00095	+	34.3010i	0.159724	+	1.82566i	0.478794	+	0.877927i	$0.341074\pi$
$353$	3.00095	+	34.3010i	0.159724	+	1.82566i	−0.319069	+	0.947731i	$0.603370\pi$
$354$		0			0
$355$	1.39173	−	1.26437i	0.0738652	−	0.0671056i
$356$	−7.05689	+	19.3887i	−0.374015	+	1.02760i
$357$		0			0
$358$	−6.73171	−	9.61388i	−0.355782	−	0.508109i
$359$	−2.43212	+	4.21256i	−0.128363	+	0.222330i	−0.923042	−	0.384698i	$-0.874305\pi$
$359$	−2.43212	+	4.21256i	−0.128363	+	0.222330i	0.794680	+	0.607029i	$0.207639\pi$
$360$		0			0
$361$	2.61048	+	4.52148i	0.137394	+	0.237973i
$362$	2.79855	−	6.00152i	0.147089	−	0.315433i
$363$		0			0
$364$	14.8811	+	17.7346i	0.779982	+	0.929546i
$365$	−0.657040	−	1.27546i	−0.0343910	−	0.0667608i
$366$		0			0
$367$	16.1484	+	7.53013i	0.842941	+	0.393070i	0.795610	−	0.605810i	$-0.207151\pi$
$367$	16.1484	+	7.53013i	0.842941	+	0.393070i	0.0473310	+	0.998879i	$0.484928\pi$
$368$	−0.824053	+	3.07541i	−0.0429568	+	0.160317i
$369$		0			0
$370$	0.253868	+	6.44777i	0.0131980	+	0.335203i
$371$	6.59754	+	1.16332i	0.342527	+	0.0603968i
$372$		0			0
$373$	1.45346	−	0.677762i	0.0752575	−	0.0350932i	−0.384625	−	0.923073i	$-0.625669\pi$
$373$	1.45346	−	0.677762i	0.0752575	−	0.0350932i	0.459883	+	0.887980i	$0.347891\pi$
$374$	0.135055	+	0.765936i	0.00698353	+	0.0396056i
$375$		0			0
$376$	3.11548	+	2.61420i	0.160669	+	0.134817i
$377$	−21.0894	+	21.0894i	−1.08616	+	1.08616i
$378$		0			0
$379$			16.2538i			0.834901i	0.908700	+	0.417451i	$0.137076\pi$
$379$			16.2538i			0.834901i	−0.908700	+	0.417451i	$0.862924\pi$
$380$	−18.1511	−	2.46873i	−0.931133	−	0.126643i
$381$		0			0
$382$	1.74854	−	2.49717i	0.0894631	−	0.127767i
$383$	14.0616	+	30.1551i	0.718512	+	1.54085i	0.836578	+	0.547848i	$0.184553\pi$
$383$	14.0616	+	30.1551i	0.718512	+	1.54085i	−0.118066	+	0.993006i	$0.537669\pi$
$384$		0			0
$385$	31.8672	+	13.3599i	1.62410	+	0.680885i
$386$	5.45690	+	3.15054i	0.277749	+	0.160358i
$387$		0			0
$388$	7.29597	+	1.95495i	0.370397	+	0.0992475i
$389$	−11.1086	+	4.04319i	−0.563227	+	0.204998i	−0.607914	−	0.794003i	$-0.707993\pi$
$389$	−11.1086	+	4.04319i	−0.563227	+	0.204998i	0.0446865	+	0.999001i	$0.485771\pi$
$390$		0			0
$391$	0.342560	−	0.287442i	0.0173240	−	0.0145366i
$392$	−0.835926	+	9.55468i	−0.0422207	+	0.482584i
$393$		0			0
$394$	−1.85012	−	5.08317i	−0.0932078	−	0.256086i
$395$	−15.4878	+	29.4433i	−0.779273	+	1.48145i
$396$		0			0
$397$	12.4793	−	3.34381i	0.626317	−	0.167821i	0.0683192	−	0.997664i	$-0.478236\pi$
$397$	12.4793	−	3.34381i	0.626317	−	0.167821i	0.557998	+	0.829842i	$0.311570\pi$
$398$	5.55079	−	3.88671i	0.278236	−	0.194823i
$399$		0			0
$400$	7.48775	−	7.36063i	0.374387	−	0.368031i
$401$	7.99873	−	1.41039i	0.399437	−	0.0704316i	0.0296788	−	0.999559i	$-0.490552\pi$
$401$	7.99873	−	1.41039i	0.399437	−	0.0704316i	0.369758	+	0.929128i	$0.379440\pi$
$402$		0			0
$403$	13.8940	−	1.21557i	0.692111	−	0.0605519i
$404$	−14.6151			−0.727129
$405$		0			0
$406$	−14.3064			−0.710016
$407$	−22.6004	+	1.97728i	−1.12026	+	0.0980100i
$408$		0			0
$409$	21.0475	−	3.71124i	1.04073	−	0.183509i	0.372938	−	0.927856i	$-0.378350\pi$
$409$	21.0475	−	3.71124i	1.04073	−	0.183509i	0.667793	+	0.744347i	$0.267239\pi$
$410$	−4.11743	−	2.64794i	−0.203346	−	0.130772i
$411$		0			0
$412$	4.19501	−	2.93738i	0.206673	−	0.144714i
$413$	32.6069	−	8.73700i	1.60448	−	0.429919i
$414$		0			0
$415$	6.31947	+	20.3461i	0.310210	+	0.998749i
$416$	−7.65378	−	21.0286i	−0.375258	−	1.03101i
$417$		0			0
$418$	−1.13110	+	12.9285i	−0.0553237	+	0.632353i
$419$	2.15215	−	1.80587i	0.105139	−	0.0882223i	−0.588703	−	0.808350i	$-0.700361\pi$
$419$	2.15215	−	1.80587i	0.105139	−	0.0882223i	0.693842	+	0.720127i	$0.255917\pi$
$420$		0			0
$421$	−4.87917	+	1.77587i	−0.237796	+	0.0865507i	−0.458169	−	0.888865i	$-0.651495\pi$
$421$	−4.87917	+	1.77587i	−0.237796	+	0.0865507i	0.220373	+	0.975416i	$0.429272\pi$
$422$	−8.16152	−	2.18687i	−0.397297	−	0.106455i
$423$		0			0
$424$	−3.62806	−	2.09466i	−0.176194	−	0.101726i
$425$	−1.45443	+	0.243636i	−0.0705504	+	0.0118181i
$426$		0			0
$427$	2.06175	+	4.42144i	0.0997752	+	0.213969i
$428$	−1.13431	+	1.61996i	−0.0548289	+	0.0783038i
$429$		0			0
$430$	1.66374	−	12.2325i	0.0802325	−	0.589903i
$431$		−	12.2810i		−	0.591553i	−0.955257	−	0.295776i	$-0.904422\pi$
$431$		−	12.2810i		−	0.591553i	0.955257	−	0.295776i	$-0.0955783\pi$
$432$		0			0
$433$	10.5318	−	10.5318i	0.506127	−	0.506127i	−0.407209	−	0.913335i	$-0.633498\pi$
$433$	10.5318	−	10.5318i	0.506127	−	0.506127i	0.913335	+	0.407209i	$0.133498\pi$
$434$	5.12495	+	4.30034i	0.246005	+	0.206423i
$435$		0			0
$436$	−4.43415	−	25.1473i	−0.212357	−	1.20434i
$437$	6.76271	−	3.15350i	0.323504	−	0.150852i
$438$		0			0
$439$	−0.587913	−	0.103665i	−0.0280596	−	0.00494766i	0.159601	−	0.987182i	$-0.448979\pi$
$439$	−0.587913	−	0.103665i	−0.0280596	−	0.00494766i	−0.187660	+	0.982234i	$0.560090\pi$
$440$	−15.8685	−	14.6663i	−0.756502	−	0.699187i
$441$		0			0
$442$	−0.181169	+	0.676131i	−0.00861732	+	0.0321603i
$443$	−20.1220	−	9.38303i	−0.956024	−	0.445801i	−0.118956	−	0.992900i	$-0.537955\pi$
$443$	−20.1220	−	9.38303i	−0.956024	−	0.445801i	−0.837068	+	0.547098i	$0.815732\pi$
$444$		0			0
$445$	−8.44769	+	26.3981i	−0.400459	+	1.25139i
$446$	−7.70067	−	9.17730i	−0.364637	−	0.434558i
$447$		0			0
$448$	−1.48763	+	3.19024i	−0.0702840	+	0.150724i
$449$	2.87636	+	4.98200i	0.135744	+	0.235115i	0.925881	−	0.377814i	$-0.123324\pi$
$449$	2.87636	+	4.98200i	0.135744	+	0.235115i	−0.790137	+	0.612930i	$0.789991\pi$
$450$		0			0
$451$	8.60564	−	14.9054i	0.405224	−	0.701868i
$452$	3.55741	+	5.08051i	0.167327	+	0.238967i
$453$		0			0
$454$	1.95636	−	5.37504i	0.0918163	−	0.252263i
$455$	20.9120	+	23.0185i	0.980370	+	1.07912i
$456$		0			0
$457$	2.29810	+	26.2674i	0.107501	+	1.22874i	0.837941	+	0.545761i	$0.183759\pi$
$457$	2.29810	+	26.2674i	0.107501	+	1.22874i	−0.730440	+	0.682977i	$0.760685\pi$
$458$	11.0441	+	11.0441i	0.516055	+	0.516055i
$459$		0			0
$460$	−1.24502	+	5.50431i	−0.0580493	+	0.256640i
$461$	21.8021	−	25.9827i	1.01542	−	1.21013i	0.0379057	−	0.999281i	$-0.487931\pi$
$461$	21.8021	−	25.9827i	1.01542	−	1.21013i	0.977518	−	0.210853i	$-0.0676242\pi$
$462$		0			0
$463$	−14.3797	−	10.0688i	−0.668283	−	0.467937i	0.189546	−	0.981872i	$-0.439298\pi$
$463$	−14.3797	−	10.0688i	−0.668283	−	0.467937i	−0.857829	+	0.513935i	$0.828187\pi$
$464$	−14.3622	−	5.22740i	−0.666746	−	0.242676i
$465$		0			0
$466$	0.649338	−	3.68258i	0.0300800	−	0.170592i
$467$	−1.95125	−	7.28218i	−0.0902933	−	0.336979i	0.905971	−	0.423341i	$-0.139143\pi$
$467$	−1.95125	−	7.28218i	−0.0902933	−	0.336979i	−0.996264	+	0.0863616i	$0.972476\pi$
$468$		0			0
$469$	−27.9151	+	16.1168i	−1.28900	+	0.744205i
$470$	1.96231	+	1.51912i	0.0905144	+	0.0700718i
$471$		0			0
$472$	−21.0292	−	1.83982i	−0.967948	−	0.0846845i
$473$	43.2379	+	3.78283i	1.98808	+	0.173935i
$474$		0			0
$475$	−24.4945	−	2.35446i	−1.12388	−	0.108030i
$476$	1.44303	−	0.833134i	0.0661412	−	0.0381867i
$477$		0			0
$478$	2.54347	+	9.49236i	0.116336	+	0.434171i
$479$	−2.36842	+	13.4320i	−0.108216	+	0.613722i	0.881671	+	0.471864i	$0.156419\pi$
$479$	−2.36842	+	13.4320i	−0.108216	+	0.613722i	−0.989887	+	0.141858i	$0.954692\pi$
$480$		0			0
$481$	−19.1869	−	6.98344i	−0.874845	−	0.318418i
$482$	−2.40466	−	1.68376i	−0.109529	−	0.0766932i
$483$		0			0
$484$	10.4118	−	12.4083i	0.473262	−	0.564012i
$485$	9.89660	+	2.23851i	0.449382	+	0.101646i
$486$		0			0
$487$	17.1622	+	17.1622i	0.777696	+	0.777696i	0.979439	−	0.201743i	$-0.0646605\pi$
$487$	17.1622	+	17.1622i	0.777696	+	0.777696i	−0.201743	+	0.979439i	$0.564661\pi$
$488$	−0.265887	−	3.03910i	−0.0120361	−	0.137574i
$489$		0			0
$490$	−0.280303	+	5.84568i	−0.0126628	+	0.264081i
$491$	−12.1283	+	33.3223i	−0.547344	+	1.50382i	0.289938	+	0.957046i	$0.406365\pi$
$491$	−12.1283	+	33.3223i	−0.547344	+	1.50382i	−0.837282	+	0.546771i	$0.815857\pi$
$492$		0			0
$493$	1.23126	+	1.75842i	0.0554530	+	0.0791951i
$494$	−5.84009	+	10.1153i	−0.262758	+	0.455111i
$495$		0			0
$496$	3.57362	+	6.18969i	0.160460	+	0.277925i
$497$	−1.20614	+	2.58658i	−0.0541030	+	0.116024i
$498$		0			0
$499$	−25.8228	−	30.7744i	−1.15599	−	1.37765i	−0.913171	−	0.407578i	$-0.866374\pi$
$499$	−25.8228	−	30.7744i	−1.15599	−	1.37765i	−0.242815	−	0.970073i	$-0.578071\pi$
$500$	12.7482	−	13.5585i	0.570118	−	0.606355i
$501$		0			0
$502$	4.62310	+	2.15579i	0.206339	+	0.0962176i
$503$	1.01183	−	3.77620i	0.0451153	−	0.168372i	−0.939693	−	0.342020i	$-0.888889\pi$
$503$	1.01183	−	3.77620i	0.0451153	−	0.168372i	0.984808	+	0.173648i	$0.0555555\pi$
$504$		0			0
$505$	−19.6177	+	0.772406i	−0.872975	+	0.0343716i
$506$	3.93739	+	0.694268i	0.175038	+	0.0308640i
$507$		0			0
$508$	26.6376	−	12.4213i	1.18185	−	0.551107i
$509$	4.88932	+	27.7287i	0.216715	+	1.22905i	0.877905	+	0.478835i	$0.158941\pi$
$509$	4.88932	+	27.7287i	0.216715	+	1.22905i	−0.661190	+	0.750219i	$0.729948\pi$
$510$		0			0
$511$	1.66822	+	1.39980i	0.0737978	+	0.0619237i
$512$	14.4119	−	14.4119i	0.636923	−	0.636923i
$513$		0			0
$514$			15.0704i			0.664728i
$515$	5.47567	−	4.16451i	0.241287	−	0.183510i
$516$		0			0
$517$	−5.00438	+	7.14699i	−0.220092	+	0.314324i
$518$	−4.13921	−	8.87657i	−0.181867	−	0.390014i
$519$		0			0
$520$	−7.36524	−	17.9988i	−0.322987	−	0.789299i
$521$	−20.7682	−	11.9905i	−0.909872	−	0.525315i	−0.0294818	−	0.999565i	$-0.509386\pi$
$521$	−20.7682	−	11.9905i	−0.909872	−	0.525315i	−0.880390	+	0.474251i	$0.842719\pi$
$522$		0			0
$523$	−8.27760	−	2.21798i	−0.361954	−	0.0969853i	0.0732586	−	0.997313i	$-0.476660\pi$
$523$	−8.27760	−	2.21798i	−0.361954	−	0.0969853i	−0.435213	+	0.900328i	$0.643327\pi$
$524$	−6.93607	+	2.52452i	−0.303004	+	0.110284i
$525$		0			0
$526$	2.56094	−	2.14888i	0.111662	−	0.0936957i
$527$	0.0874898	−	1.00001i	0.00381111	−	0.0435612i
$528$		0			0
$529$	7.08023	+	19.4528i	0.307836	+	0.845773i
$530$	−2.26236	−	1.19004i	−0.0982705	−	0.0516922i
$531$		0			0
$532$	26.8566	−	7.19621i	1.16438	−	0.311995i
$533$	12.6889	−	8.88487i	0.549618	−	0.384846i
$534$		0			0
$535$	−1.43695	+	2.23440i	−0.0621249	+	0.0966016i
$536$	19.8506	−	3.50020i	0.857415	−	0.151185i
$537$		0			0
$538$	12.3038	−	1.07644i	0.530455	−	0.0464088i
$539$	−20.5759			−0.886268
$540$		0			0
$541$	−24.1490			−1.03825			−0.519123	−	0.854700i	$-0.673741\pi$
$541$	−24.1490			−1.03825			−0.519123	+	0.854700i	$0.673741\pi$
$542$	8.00031	−	0.699936i	0.343643	−	0.0300648i
$543$		0			0
$544$	−1.58618	+	0.279687i	−0.0680070	+	0.0119915i
$545$	−7.28094	−	33.5206i	−0.311881	−	1.43586i
$546$		0			0
$547$	−8.43453	+	5.90592i	−0.360634	+	0.252519i	−0.739825	−	0.672800i	$-0.765092\pi$
$547$	−8.43453	+	5.90592i	−0.360634	+	0.252519i	0.379190	+	0.925319i	$0.376203\pi$
$548$	−27.6301	+	7.40347i	−1.18030	+	0.316261i
$549$		0			0
$550$	−10.0273	−	8.56127i	−0.427566	−	0.365054i
$551$	12.2510	+	33.6593i	0.521910	+	1.43394i
$552$		0			0
$553$	4.40099	−	50.3035i	0.187149	−	2.13912i
$554$	−1.84034	+	1.54423i	−0.0781886	+	0.0656080i
$555$		0			0
$556$	−5.54764	+	2.01918i	−0.235272	+	0.0856322i
$557$	−0.0136213	−	0.00364981i	−0.000577152	−	0.000154647i	0.258530	−	0.966003i	$-0.416762\pi$
$557$	−0.0136213	−	0.00364981i	−0.000577152	−	0.000154647i	−0.259108	+	0.965848i	$0.583428\pi$
$558$		0			0
$559$	33.8297	+	19.5316i	1.43084	+	0.826098i
$560$	−6.16176	+	14.6975i	−0.260382	+	0.621084i
$561$		0			0
$562$	−3.28951	−	7.05437i	−0.138759	−	0.297571i
$563$	8.54312	−	12.2008i	0.360050	−	0.514204i	−0.597734	−	0.801695i	$-0.703932\pi$
$563$	8.54312	−	12.2008i	0.360050	−	0.514204i	0.957783	+	0.287490i	$0.0928210\pi$
$564$		0			0
$565$	5.04357	+	6.63150i	0.212185	+	0.278989i
$566$		−	6.74492i		−	0.283510i
$567$		0			0
$568$	1.26197	−	1.26197i	0.0529511	−	0.0529511i
$569$	−21.1007	−	17.7056i	−0.884589	−	0.742258i	0.0825286	−	0.996589i	$-0.473700\pi$
$569$	−21.1007	−	17.7056i	−0.884589	−	0.742258i	−0.967117	+	0.254331i	$0.918145\pi$
$570$		0			0
$571$	−3.36410	−	19.0788i	−0.140783	−	0.798421i	−0.970657	−	0.240470i	$-0.922699\pi$
$571$	−3.36410	−	19.0788i	−0.140783	−	0.798421i	0.829873	−	0.557952i	$-0.188413\pi$
$572$	28.1478	−	13.1255i	1.17692	−	0.548805i
$573$		0			0
$574$	7.31750	+	1.29027i	0.305426	+	0.0538549i
$575$	−1.38027	+	7.45416i	−0.0575613	+	0.310860i
$576$		0			0
$577$	−6.81468	+	25.4327i	−0.283699	+	1.05878i	0.666086	+	0.745875i	$0.267968\pi$
$577$	−6.81468	+	25.4327i	−0.283699	+	1.05878i	−0.949785	+	0.312904i	$0.898698\pi$
$578$	−8.87759	−	4.13969i	−0.369259	−	0.172188i
$579$		0			0
$580$	−25.8013	−	8.25670i	−1.07134	−	0.342841i
$581$	−20.7860	−	24.7718i	−0.862348	−	1.02771i
$582$		0			0
$583$	3.79821	−	8.14529i	0.157306	−	0.337344i
$584$	−0.680899	−	1.17935i	−0.0281758	−	0.0488020i
$585$		0			0
$586$	7.63599	−	13.2259i	0.315440	−	0.546358i
$587$	−11.8655	−	16.9456i	−0.489740	−	0.699421i	0.495882	−	0.868390i	$-0.334845\pi$
$587$	−11.8655	−	16.9456i	−0.489740	−	0.699421i	−0.985621	+	0.168969i	$0.945956\pi$
$588$		0			0
$589$	5.72896	−	15.7402i	0.236058	−	0.648563i
$590$	−12.8659	−	0.616929i	−0.529683	−	0.0253985i
$591$		0			0
$592$	−0.911944	−	10.4236i	−0.0374807	−	0.428406i
$593$	−25.1558	−	25.1558i	−1.03302	−	1.03302i	−0.999436	−	0.0335886i	$-0.989306\pi$
$593$	−25.1558	−	25.1558i	−1.03302	−	1.03302i	−0.0335886	−	0.999436i	$-0.510694\pi$
$594$		0			0
$595$	1.89293	−	1.19457i	0.0776026	−	0.0489726i
$596$	−3.83467	+	4.56998i	−0.157074	+	0.187194i
$597$		0			0
$598$	2.94760	+	2.06393i	0.120536	+	0.0844003i
$599$	22.0669	+	8.03169i	0.901629	+	0.328166i	0.750905	−	0.660410i	$-0.229617\pi$
$599$	22.0669	+	8.03169i	0.901629	+	0.328166i	0.150723	+	0.988576i	$0.451840\pi$
$600$		0			0
$601$	−0.359287	+	2.03762i	−0.0146556	+	0.0831161i	−0.991258	−	0.131935i	$-0.957881\pi$
$601$	−0.359287	+	2.03762i	−0.0146556	+	0.0831161i	0.976603	+	0.215052i	$0.0689920\pi$
$602$	4.84970	+	18.0993i	0.197659	+	0.737674i
$603$		0			0
$604$	−28.2586	+	16.3151i	−1.14983	+	0.663853i
$605$	13.3198	−	17.2057i	0.541527	−	0.699512i
$606$		0			0
$607$	27.2557	+	2.38456i	1.10627	+	0.0967864i	0.625623	−	0.780126i	$-0.284845\pi$
$607$	27.2557	+	2.38456i	1.10627	+	0.0967864i	0.480651	+	0.876912i	$0.340401\pi$
$608$	−26.7737	−	2.34240i	−1.08582	−	0.0949967i
$609$		0			0
$610$	−0.235072	−	1.84660i	−0.00951779	−	0.0747665i
$611$	−6.80042	+	3.92623i	−0.275116	+	0.158838i
$612$		0			0
$613$	−2.44513	−	9.12534i	−0.0987578	−	0.368569i	0.898805	−	0.438350i	$-0.144437\pi$
$613$	−2.44513	−	9.12534i	−0.0987578	−	0.368569i	−0.997562	+	0.0697805i	$0.977770\pi$
$614$	1.82465	−	10.3481i	0.0736370	−	0.417616i
$615$		0			0
$616$	30.8195	+	11.2174i	1.24175	+	0.451962i
$617$	−26.3513	−	18.4514i	−1.06086	−	0.742826i	−0.0933483	−	0.995634i	$-0.529757\pi$
$617$	−26.3513	−	18.4514i	−1.06086	−	0.742826i	−0.967516	+	0.252808i	$0.918646\pi$
$618$		0			0
$619$	19.6122	−	23.3729i	0.788279	−	0.939435i	−0.210996	−	0.977487i	$-0.567671\pi$
$619$	19.6122	−	23.3729i	0.788279	−	0.939435i	0.999276	+	0.0380520i	$0.0121153\pi$
$620$	6.76084	+	10.7133i	0.271522	+	0.430257i
$621$		0			0
$622$	−7.07174	−	7.07174i	−0.283551	−	0.283551i
$623$	−3.66660	−	41.9094i	−0.146899	−	1.67907i
$624$		0			0
$625$	16.3952	−	18.8732i	0.655809	−	0.754927i
$626$	−2.96103	+	8.13536i	−0.118346	+	0.325154i
$627$		0			0
$628$	−0.540361	−	0.771716i	−0.0215628	−	0.0307948i
$629$	−0.734793	+	1.27270i	−0.0292981	+	0.0507459i
$630$		0			0
$631$	−13.5982	−	23.5528i	−0.541338	−	0.937624i	−0.998828	−	0.0484094i	$-0.984585\pi$
$631$	−13.5982	−	23.5528i	−0.541338	−	0.937624i	0.457490	−	0.889215i	$-0.348749\pi$
$632$	−13.3449	+	28.6182i	−0.530832	+	1.13837i
$633$		0			0
$634$	5.77884	+	6.88695i	0.229507	+	0.273516i
$635$	35.0988	−	18.0808i	1.39286	−	0.717513i
$636$		0			0
$637$	−16.7835	−	7.82626i	−0.664985	−	0.310088i
$638$	−4.96739	+	18.5385i	−0.196661	+	0.733948i
$639$		0			0
$640$	17.4879	−	18.9215i	0.691271	−	0.747937i
$641$	−47.3771	−	8.35386i	−1.87128	−	0.329957i	−0.881459	−	0.472261i	$-0.843438\pi$
$641$	−47.3771	−	8.35386i	−1.87128	−	0.329957i	−0.989823	+	0.142304i	$0.954549\pi$
$642$		0			0
$643$	1.29754	−	0.605053i	0.0511700	−	0.0238610i	−0.396865	−	0.917877i	$-0.629902\pi$
$643$	1.29754	−	0.605053i	0.0511700	−	0.0238610i	0.448035	+	0.894016i	$0.352124\pi$
$644$	−1.48741	−	8.43554i	−0.0586123	−	0.332407i
$645$		0			0
$646$	0.643993	+	0.540374i	0.0253376	+	0.0212607i
$647$	3.76082	−	3.76082i	0.147853	−	0.147853i	−0.629305	−	0.777158i	$-0.716660\pi$
$647$	3.76082	−	3.76082i	0.147853	−	0.147853i	0.777158	+	0.629305i	$0.216660\pi$
$648$		0			0
$649$		−	45.2862i		−	1.77764i
$650$	−4.92276	−	10.7973i	−0.193087	−	0.423504i
$651$		0			0
$652$	−4.71228	+	6.72983i	−0.184547	+	0.263561i
$653$	14.6726	+	31.4655i	0.574184	+	1.23134i	0.952181	+	0.305535i	$0.0988353\pi$
$653$	14.6726	+	31.4655i	0.574184	+	1.23134i	−0.377997	+	0.925807i	$0.623387\pi$
$654$		0			0
$655$	−9.17678	+	3.75521i	−0.358567	+	0.146728i
$656$	6.87455	+	3.96902i	0.268406	+	0.154964i
$657$		0			0
$658$	−3.63832	−	0.974884i	−0.141836	−	0.0380049i
$659$	−29.5525	+	10.7562i	−1.15120	+	0.419003i	−0.845946	−	0.533268i	$-0.820964\pi$
$659$	−29.5525	+	10.7562i	−1.15120	+	0.419003i	−0.305254	+	0.952271i	$0.598742\pi$
$660$		0			0
$661$	18.2275	−	15.2947i	0.708967	−	0.594894i	−0.215342	−	0.976539i	$-0.569087\pi$
$661$	18.2275	−	15.2947i	0.708967	−	0.594894i	0.924309	+	0.381645i	$0.124642\pi$
$662$	0.213124	−	2.43602i	0.00828329	−	0.0946785i
$663$		0			0
$664$	6.91620	+	19.0021i	0.268401	+	0.737425i
$665$	35.6690	−	11.0788i	1.38318	−	0.429616i
$666$		0			0
$667$	10.6590	−	2.85607i	0.412719	−	0.110588i
$668$	19.9845	−	13.9933i	0.773224	−	0.541417i
$669$		0			0
$670$	12.0191	−	2.61065i	0.464340	−	0.100858i
$671$	6.44526	−	1.13647i	0.248816	−	0.0438730i
$672$		0			0
$673$	−1.83430	+	0.160481i	−0.0707073	+	0.00618608i	−0.122454	−	0.992474i	$-0.539077\pi$
$673$	−1.83430	+	0.160481i	−0.0707073	+	0.00618608i	0.0517472	+	0.998660i	$0.483521\pi$
$674$	−2.80899			−0.108198
$675$		0			0
$676$	6.31265			0.242794
$677$	−11.1662	+	0.976915i	−0.429151	+	0.0375459i	−0.299686	−	0.954038i	$-0.596882\pi$
$677$	−11.1662	+	0.976915i	−0.429151	+	0.0375459i	−0.129466	+	0.991584i	$0.541326\pi$
$678$		0			0
$679$	−15.1669	+	2.67433i	−0.582052	+	0.102631i
$680$	−1.36782	+	0.297102i	−0.0524536	+	0.0113933i
$681$		0			0
$682$	7.35191	−	5.14787i	0.281519	−	0.197122i
$683$	−31.7505	+	8.50752i	−1.21490	+	0.325531i	−0.808682	−	0.588246i	$-0.799819\pi$
$683$	−31.7505	+	8.50752i	−1.21490	+	0.325531i	−0.406216	+	0.913777i	$0.633152\pi$
$684$		0			0
$685$	−36.6963	+	11.3978i	−1.40209	+	0.435489i
$686$	1.66791	+	4.58253i	0.0636809	+	0.174962i
$687$		0			0
$688$	−1.74469	+	19.9419i	−0.0665155	+	0.760276i
$689$	6.19628	−	5.19930i	0.236060	−	0.198078i
$690$		0			0
$691$	35.2185	−	12.8185i	1.33977	−	0.487638i	0.430033	−	0.902813i	$-0.358502\pi$
$691$	35.2185	−	12.8185i	1.33977	−	0.487638i	0.909742	+	0.415175i	$0.136280\pi$
$692$	−15.0677	−	4.03739i	−0.572790	−	0.153479i
$693$		0			0
$694$	−9.37669	−	5.41364i	−0.355934	−	0.205499i
$695$	−7.33982	+	3.00351i	−0.278415	+	0.113930i
$696$		0			0
$697$	−0.471178	−	1.01044i	−0.0178471	−	0.0382733i
$698$	−2.99905	+	4.28308i	−0.113516	+	0.162117i
$699$		0			0
$700$	−9.88815	+	26.4604i	−0.373737	+	1.00011i
$701$			8.75525i			0.330681i	0.986237	+	0.165341i	$0.0528724\pi$
$701$			8.75525i			0.330681i	−0.986237	+	0.165341i	$0.947128\pi$
$702$		0			0
$703$	−17.3398	+	17.3398i	−0.653981	+	0.653981i
$704$	3.61744	+	3.03539i	0.136337	+	0.114401i
$705$		0			0
$706$	3.46283	+	19.6387i	0.130325	+	0.739112i
$707$	27.0074	−	12.5938i	1.01572	−	0.473638i
$708$		0			0
$709$	7.84342	+	1.38301i	0.294566	+	0.0519399i	0.318978	−	0.947762i	$-0.396660\pi$
$709$	7.84342	+	1.38301i	0.294566	+	0.0519399i	−0.0244124	+	0.999702i	$0.507771\pi$
$710$	0.739144	−	0.799734i	0.0277396	−	0.0300135i
$711$		0			0
$712$	−6.80890	+	25.4112i	−0.255174	+	0.952323i
$713$	−4.67685	−	2.18085i	−0.175149	−	0.0816735i
$714$		0			0
$715$	37.0887	−	19.1058i	1.38704	−	0.714517i
$716$	21.6823	+	25.8400i	0.810307	+	0.965687i
$717$		0			0
$718$	−1.19059	+	2.55323i	−0.0444324	+	0.0952856i
$719$	4.35425	+	7.54179i	0.162386	+	0.281261i	0.935724	−	0.352733i	$-0.114748\pi$
$719$	4.35425	+	7.54179i	0.162386	+	0.281261i	−0.773338	+	0.633994i	$0.781414\pi$
$720$		0			0
$721$	−5.22089	+	9.04285i	−0.194436	+	0.336773i
$722$	1.73436	+	2.47693i	0.0645463	+	0.0921816i
$723$		0			0
$724$	−6.50941	+	17.8845i	−0.241920	+	0.664671i
$725$	−35.0691	−	9.71927i	−1.30243	−	0.360965i
$726$		0			0
$727$	−3.05305	−	34.8965i	−0.113231	−	1.29424i	−0.814005	−	0.580857i	$-0.802717\pi$
$727$	−3.05305	−	34.8965i	−0.113231	−	1.29424i	0.700774	−	0.713383i	$-0.252838\pi$
$728$	20.8724	+	20.8724i	0.773581	+	0.773581i
$729$		0			0
$730$	−0.443465	−	0.702720i	−0.0164134	−	0.0260088i
$731$	1.80722	−	2.15377i	0.0668426	−	0.0796599i
$732$		0			0
$733$	15.4172	+	10.7952i	0.569447	+	0.398731i	0.822537	−	0.568711i	$-0.192558\pi$
$733$	15.4172	+	10.7952i	0.569447	+	0.398731i	−0.253090	+	0.967443i	$0.581447\pi$
$734$	9.69703	+	3.52943i	0.357924	+	0.130274i
$735$		0			0
$736$	−1.43777	+	8.15398i	−0.0529968	+	0.300560i
$737$	11.1919	+	41.7689i	0.412261	+	1.53858i
$738$		0			0
$739$	9.05915	−	5.23030i	0.333246	−	0.192400i	−0.324035	−	0.946045i	$-0.605040\pi$
$739$	9.05915	−	5.23030i	0.333246	−	0.192400i	0.657281	+	0.753645i	$0.271706\pi$
$740$	−2.34201	−	18.3975i	−0.0860940	−	0.676307i
$741$		0			0
$742$	3.86521	+	0.338162i	0.141896	+	0.0124143i
$743$	−26.5503	−	2.32285i	−0.974035	−	0.0852170i	−0.410987	−	0.911641i	$-0.634816\pi$
$743$	−26.5503	−	2.32285i	−0.974035	−	0.0852170i	−0.563048	+	0.826424i	$0.690371\pi$
$744$		0			0
$745$	−4.90570	+	6.33689i	−0.179731	+	0.232166i
$746$	0.804373	−	0.464405i	0.0294502	−	0.0170031i
$747$		0			0
$748$	−0.578551	−	2.15918i	−0.0211539	−	0.0789475i
$749$	0.700190	−	3.97098i	0.0255844	−	0.145096i
$750$		0			0
$751$	−33.4699	−	12.1820i	−1.22133	−	0.444529i	−0.350712	−	0.936483i	$-0.614061\pi$
$751$	−33.4699	−	12.1820i	−1.22133	−	0.444529i	−0.870621	+	0.491954i	$0.836283\pi$
$752$	−3.29628	−	2.30808i	−0.120203	−	0.0841670i
$753$		0			0
$754$	−11.1031	+	13.2322i	−0.404352	+	0.481888i
$755$	−37.0689	+	23.3930i	−1.34908	+	0.851360i
$756$		0			0
$757$	−23.2266	−	23.2266i	−0.844185	−	0.844185i	0.145215	−	0.989400i	$-0.453613\pi$
$757$	−23.2266	−	23.2266i	−0.844185	−	0.844185i	−0.989400	+	0.145215i	$0.953613\pi$
$758$	0.820445	+	9.37772i	0.0297999	+	0.340614i
$759$		0			0
$760$	−23.3294	−	1.11866i	−0.846247	−	0.0405780i
$761$	11.0481	−	30.3545i	0.400494	−	1.10035i	−0.561547	−	0.827445i	$-0.689794\pi$
$761$	11.0481	−	30.3545i	0.400494	−	1.10035i	0.962041	−	0.272904i	$-0.0879842\pi$
$762$		0			0
$763$	29.8633	+	42.6492i	1.08112	+	1.54400i
$764$	−4.38086	+	7.58787i	−0.158494	+	0.274519i
$765$		0			0
$766$	9.63504	+	16.6884i	0.348128	+	0.602976i
$767$	17.2251	−	36.9393i	0.621961	−	1.33380i
$768$		0			0
$769$	−24.2180	−	28.8618i	−0.873322	−	1.04078i	−0.998814	−	0.0486900i	$-0.984495\pi$
$769$	−24.2180	−	28.8618i	−0.873322	−	1.04078i	0.125492	−	0.992095i	$-0.459949\pi$
$770$	19.0603	+	6.09952i	0.686887	+	0.219812i
$771$		0			0
$772$	−16.4133	−	7.65364i	−0.590727	−	0.275461i
$773$	−1.80797	+	6.74744i	−0.0650282	+	0.242689i	−0.990788	−	0.135424i	$-0.956760\pi$
$773$	−1.80797	+	6.74744i	−0.0650282	+	0.242689i	0.925759	+	0.378113i	$0.123427\pi$
$774$		0			0
$775$	9.64119	+	14.0231i	0.346322	+	0.503723i
$776$	9.48439	+	1.67235i	0.340470	+	0.0600340i
$777$		0			0
$778$	−6.20507	+	2.89347i	−0.222463	+	0.103736i
$779$	−3.23050	−	18.3211i	−0.115745	−	0.656421i
$780$		0			0
$781$	2.93295	+	2.46104i	0.104949	+	0.0880630i
$782$	0.183133	−	0.183133i	0.00654881	−	0.00654881i
$783$		0			0
$784$		−	9.48986i		−	0.338924i
$785$	−0.766105	−	1.00731i	−0.0273435	−	0.0359523i
$786$		0			0
$787$	−8.41019	+	12.0110i	−0.299791	+	0.428146i	−0.940581	−	0.339571i	$-0.889718\pi$
$787$	−8.41019	+	12.0110i	−0.299791	+	0.428146i	0.640790	+	0.767717i	$0.278607\pi$
$788$	6.57055	+	14.0906i	0.234066	+	0.501956i
$789$		0			0
$790$	−7.44954	+	17.7693i	−0.265043	+	0.632202i
$791$	−10.9516	−	6.32294i	−0.389396	−	0.224818i
$792$		0			0
$793$	5.68957	+	1.52451i	0.202042	+	0.0541371i
$794$	7.03121	−	2.55915i	0.249528	−	0.0908209i
$795$		0			0
$796$	−14.9193	+	12.5188i	−0.528801	+	0.443717i
$797$	−4.08425	+	46.6832i	−0.144672	+	1.65360i	0.483364	+	0.875420i	$0.339415\pi$
$797$	−4.08425	+	46.6832i	−0.144672	+	1.65360i	−0.628035	+	0.778185i	$0.716141\pi$
$798$		0			0
$799$	0.193301	+	0.531090i	0.00683850	+	0.0187886i
$800$	17.7296	−	20.7657i	0.626836	−	0.734177i
$801$		0			0
$802$	4.54372	−	1.21749i	0.160444	−	0.0429909i
$803$	2.39312	−	1.67568i	0.0844515	−	0.0591335i
$804$		0			0
$805$	−2.44235	−	11.2443i	−0.0860816	−	0.396310i
$806$	7.95488	−	1.40266i	0.280199	−	0.0494066i
$807$		0			0
$808$	−18.5637	+	1.62411i	−0.653069	+	0.0571362i
$809$	48.2320			1.69575			0.847874	−	0.530198i	$-0.177882\pi$
$809$	48.2320			1.69575			0.847874	+	0.530198i	$0.177882\pi$
$810$		0			0
$811$	−25.8197			−0.906653			−0.453326	−	0.891345i	$-0.649763\pi$
$811$	−25.8197			−0.906653			−0.453326	+	0.891345i	$0.649763\pi$
$812$	40.9619	−	3.58370i	1.43748	−	0.125763i
$813$		0			0
$814$	−12.9396	+	2.28160i	−0.453533	+	0.0799702i
$815$	−5.96956	+	9.28241i	−0.209105	+	0.325149i
$816$		0			0
$817$	38.4301	−	26.9091i	1.34450	−	0.941429i
$818$	11.9561	−	3.20364i	0.418036	−	0.112013i
$819$		0			0
$820$	12.4523	+	6.55013i	0.434852	+	0.228741i
$821$	16.5087	+	45.3573i	0.576158	+	1.58298i	0.794601	+	0.607132i	$0.207680\pi$
$821$	16.5087	+	45.3573i	0.576158	+	1.58298i	−0.218443	+	0.975850i	$0.570098\pi$
$822$		0			0
$823$	−1.90579	+	21.7833i	−0.0664316	+	0.759316i	0.887796	+	0.460236i	$0.152235\pi$
$823$	−1.90579	+	21.7833i	−0.0664316	+	0.759316i	−0.954228	+	0.299080i	$0.903320\pi$
$824$	5.00198	−	4.19716i	0.174252	−	0.146215i
$825$		0			0
$826$	18.3717	−	6.68676i	0.639234	−	0.232662i
$827$	11.9876	+	3.21205i	0.416848	+	0.111694i	0.461146	−	0.887324i	$-0.347438\pi$
$827$	11.9876	+	3.21205i	0.416848	+	0.111694i	−0.0442980	+	0.999018i	$0.514105\pi$
$828$		0			0
$829$	36.4705	+	21.0563i	1.26667	+	0.731314i	0.974357	−	0.225008i	$-0.0722408\pi$
$829$	36.4705	+	21.0563i	1.26667	+	0.731314i	0.292316	+	0.956322i	$0.405574\pi$
$830$	4.67306	+	11.4198i	0.162204	+	0.396387i
$831$		0			0
$832$	1.79615	+	3.85185i	0.0622702	+	0.133539i
$833$	−0.764495	+	1.09181i	−0.0264882	+	0.0378290i
$834$		0			0
$835$	26.0854	−	19.8392i	0.902723	−	0.686564i
$836$		−	37.2999i		−	1.29005i
$837$		0			0
$838$	1.15054	−	1.15054i	0.0397447	−	0.0397447i
$839$	12.1068	+	10.1589i	0.417975	+	0.350723i	0.827392	−	0.561625i	$-0.189824\pi$
$839$	12.1068	+	10.1589i	0.417975	+	0.350723i	−0.409417	+	0.912347i	$0.634268\pi$
$840$		0			0
$841$	4.16273	+	23.6080i	0.143542	+	0.814069i
$842$	−2.72543	+	1.27089i	−0.0939244	+	0.0437976i
$843$		0			0
$844$	23.9157	+	4.21699i	0.823213	+	0.145155i
$845$	8.47339	−	0.333623i	0.291494	−	0.0114770i
$846$		0			0
$847$	−8.54789	+	31.9012i	−0.293709	+	1.09614i
$848$	3.75671	+	1.75178i	0.129006	+	0.0601564i
$849$		0			0
$850$	−0.826846	+	0.213983i	−0.0283606	+	0.00733955i
$851$	4.85600	+	5.78716i	0.166462	+	0.198381i
$852$		0			0
$853$	−1.32236	+	2.83580i	−0.0452766	+	0.0970960i	−0.927645	−	0.373463i	$-0.878170\pi$
$853$	−1.32236	+	2.83580i	−0.0452766	+	0.0970960i	0.882368	+	0.470560i	$0.155948\pi$
$854$	1.41272	+	2.44691i	0.0483424	+	0.0837314i
$855$		0			0
$856$	−1.26075	+	2.18368i	−0.0430915	+	0.0746367i
$857$	−9.61006	−	13.7246i	−0.328273	−	0.468823i	0.620759	−	0.784001i	$-0.286825\pi$
$857$	−9.61006	−	13.7246i	−0.328273	−	0.468823i	−0.949032	+	0.315178i	$0.897936\pi$
$858$		0			0
$859$	12.0888	−	33.2138i	0.412465	−	1.13324i	−0.543410	−	0.839467i	$-0.682867\pi$
$859$	12.0888	−	33.2138i	0.412465	−	1.13324i	0.955875	−	0.293772i	$-0.0949107\pi$
$860$	−1.69939	+	35.4406i	−0.0579489	+	1.20851i
$861$		0			0
$862$	−0.619907	−	7.08557i	−0.0211141	−	0.241336i
$863$	−18.3310	−	18.3310i	−0.623993	−	0.623993i	0.322557	−	0.946550i	$-0.395458\pi$
$863$	−18.3310	−	18.3310i	−0.623993	−	0.623993i	−0.946550	+	0.322557i	$0.895458\pi$
$864$		0			0
$865$	−20.4386	−	4.62301i	−0.694934	−	0.157187i
$866$	5.54478	−	6.60801i	0.188419	−	0.224549i
$867$		0			0
$868$	−15.7509	−	11.0289i	−0.534620	−	0.374345i
$869$	−63.6561	−	23.1689i	−2.15939	−	0.785952i
$870$		0			0
$871$	−6.75812	+	38.3272i	−0.228990	+	1.29867i
$872$	−8.42666	−	31.4487i	−0.285363	−	1.06499i
$873$		0			0
$874$	3.74260	−	2.16079i	0.126595	−	0.0730899i
$875$	−11.8743	+	36.0401i	−0.401425	+	1.21838i
$876$		0			0
$877$	0.651619	+	0.0570093i	0.0220036	+	0.00192507i	0.0981522	−	0.995171i	$-0.468707\pi$
$877$	0.651619	+	0.0570093i	0.0220036	+	0.00192507i	−0.0761486	+	0.997096i	$0.524262\pi$
$878$	−0.344433	−	0.0301339i	−0.0116240	−	0.00101697i
$879$		0			0
$880$	16.9059	+	13.0877i	0.569897	+	0.441186i
$881$	−47.1502	+	27.2222i	−1.58853	+	0.917139i	−0.594981	+	0.803740i	$0.702840\pi$
$881$	−47.1502	+	27.2222i	−1.58853	+	0.917139i	−0.993550	+	0.113399i	$0.963826\pi$
$882$		0			0
$883$	6.18571	+	23.0854i	0.208166	+	0.776885i	0.988461	+	0.151474i	$0.0484020\pi$
$883$	6.18571	+	23.0854i	0.208166	+	0.776885i	−0.780296	+	0.625411i	$0.784931\pi$
$884$	0.349351	−	1.98127i	0.0117500	−	0.0666373i
$885$		0			0
$886$	−12.0831	−	4.39790i	−0.405940	−	0.147750i
$887$	−3.61660	−	2.53237i	−0.121433	−	0.0850286i	0.511282	−	0.859413i	$-0.329171\pi$
$887$	−3.61660	−	2.53237i	−0.121433	−	0.0850286i	−0.632715	+	0.774384i	$0.718060\pi$
$888$		0			0
$889$	−38.5206	+	45.9070i	−1.29194	+	1.53967i
$890$	−3.54145	+	15.6570i	−0.118710	+	0.524822i
$891$		0			0
$892$	24.3473	+	24.3473i	0.815208	+	0.815208i
$893$	0.821942	+	9.39484i	0.0275052	+	0.314386i
$894$		0			0
$895$	30.4696	+	33.5388i	1.01849	+	1.12108i
$896$	−13.3755	+	36.7489i	−0.446845	+	1.22770i
$897$		0			0
$898$	1.91101	+	2.72921i	0.0637713	+	0.0910748i
$899$	12.3857	−	21.4527i	0.413088	−	0.715489i
$900$		0			0
$901$	−0.291088	−	0.504180i	−0.00969756	−	0.0167967i
$902$	4.21269	−	9.03415i	0.140267	−	0.300804i
$903$		0			0
$904$	5.08311	+	6.05781i	0.169062	+	0.201480i
$905$	−7.79231	+	24.3501i	−0.259025	+	0.809425i
$906$		0			0
$907$	−41.6059	−	19.4012i	−1.38150	−	0.644205i	−0.417152	−	0.908837i	$-0.636972\pi$
$907$	−41.6059	−	19.4012i	−1.38150	−	0.644205i	−0.964350	+	0.264632i	$0.914750\pi$
$908$	−4.25498	+	15.8798i	−0.141206	+	0.526989i
$909$		0			0
$910$	13.2272	+	12.2251i	0.438478	+	0.405257i
$911$	48.2873	+	8.51435i	1.59983	+	0.282093i	0.901204	−	0.433395i	$-0.142685\pi$
$911$	48.2873	+	8.51435i	1.59983	+	0.282093i	0.698625	+	0.715488i	$0.253796\pi$
$912$		0			0
$913$	−39.3169	+	18.3338i	−1.30120	+	0.606759i
$914$	2.65181	+	15.0391i	0.0877139	+	0.497451i
$915$		0			0
$916$	−34.3876	−	28.8547i	−1.13620	−	0.953385i
$917$	10.6419	−	10.6419i	0.351426	−	0.351426i
$918$		0			0
$919$		−	45.6321i		−	1.50526i	−0.658442	−	0.752632i	$-0.728784\pi$
$919$		−	45.6321i		−	1.50526i	0.658442	−	0.752632i	$-0.271216\pi$
$920$	−0.969719	+	7.12978i	−0.0319707	+	0.235062i
$921$		0			0
$922$	11.2673	−	16.0914i	0.371069	−	0.529941i
$923$	1.45628	+	3.12301i	0.0479342	+	0.102795i
$924$		0			0
$925$	−4.11596	−	24.5710i	−0.135332	−	0.807890i
$926$	−8.80472	−	5.08341i	−0.289341	−	0.167051i
$927$		0			0
$928$	−38.3916	−	10.2870i	−1.26027	−	0.337687i
$929$	37.4112	−	13.6166i	1.22742	−	0.446745i	0.354707	−	0.934977i	$-0.384581\pi$
$929$	37.4112	−	13.6166i	1.22742	−	0.446745i	0.872713	+	0.488233i	$0.162358\pi$
$930$		0			0
$931$	−17.0373	+	14.2960i	−0.558374	+	0.468531i
$932$	−0.936701	+	10.7065i	−0.0306827	+	0.350704i
$933$		0			0
$934$	−1.49337	−	4.10300i	−0.0488646	−	0.134254i
$935$	−0.890694	−	2.86767i	−0.0291288	−	0.0937827i
$936$		0			0
$937$	1.08557	−	0.290876i	0.0354639	−	0.00950252i	−0.241043	−	0.970514i	$-0.577490\pi$
$937$	1.08557	−	0.290876i	0.0354639	−	0.00950252i	0.276507	+	0.961012i	$0.410823\pi$
$938$	−15.2923	+	10.7078i	−0.499310	+	0.349621i
$939$		0			0
$940$	−5.99897	−	3.85797i	−0.195665	−	0.125833i
$941$	52.2436	−	9.21195i	1.70309	−	0.300301i	0.764319	−	0.644839i	$-0.223075\pi$
$941$	52.2436	−	9.21195i	1.70309	−	0.300301i	0.938773	+	0.344538i	$0.111964\pi$
$942$		0			0
$943$	−5.70949	+	0.499516i	−0.185927	+	0.0162665i
$944$	20.8866			0.679799
$945$		0			0
$946$	25.1373			0.817285
$947$	−55.3718	+	4.84441i	−1.79934	+	0.157422i	−0.937097	−	0.349068i	$-0.886498\pi$
$947$	−55.3718	+	4.84441i	−1.79934	+	0.157422i	−0.862246	+	0.506490i	$0.830943\pi$
$948$		0			0
$949$	2.58940	−	0.456580i	0.0840553	−	0.0148212i
$950$	−14.2511	−	0.122009i	−0.462366	−	0.00395849i
$951$		0			0
$952$	1.74032	−	1.21858i	0.0564040	−	0.0394945i
$953$	59.1867	−	15.8590i	1.91725	−	0.513724i	0.926856	−	0.375417i	$-0.122501\pi$
$953$	59.1867	−	15.8590i	1.91725	−	0.513724i	0.990389	−	0.138307i	$-0.0441661\pi$
$954$		0			0
$955$	−5.47935	+	10.4166i	−0.177308	+	0.337074i
$956$	−9.66022	−	26.5412i	−0.312434	−	0.858405i
$957$		0			0
$958$	−0.688466	+	7.86920i	−0.0222433	+	0.254242i
$959$	44.6785	−	37.4897i	1.44274	−	1.21061i
$960$		0			0
$961$	18.2451	−	6.64068i	0.588552	−	0.214216i
$962$	−11.4225	−	3.06064i	−0.368275	−	0.0986791i
$963$		0			0
$964$	7.30675	+	4.21855i	0.235335	+	0.135870i
$965$	−22.4359	−	9.40595i	−0.722236	−	0.302788i
$966$		0			0
$967$	−2.27975	−	4.88895i	−0.0733120	−	0.157218i	0.866236	−	0.499635i	$-0.166532\pi$
$967$	−2.27975	−	4.88895i	−0.0733120	−	0.157218i	−0.939548	+	0.342417i	$0.888755\pi$
$968$	11.8459	−	16.9177i	0.380741	−	0.543754i
$969$		0			0
$970$	5.82290	+	0.791971i	0.186962	+	0.0254287i
$971$			49.9614i			1.60334i	0.597769	+	0.801668i	$0.296054\pi$
$971$			49.9614i			1.60334i	−0.597769	+	0.801668i	$0.703946\pi$
$972$		0			0
$973$	8.51164	−	8.51164i	0.272871	−	0.272871i
$974$	10.7682	+	9.03556i	0.345034	+	0.289518i
$975$		0			0
$976$	0.524155	+	2.97263i	0.0167778	+	0.0951516i
$977$	30.2308	−	14.0969i	0.967169	−	0.450998i	0.126155	−	0.992011i	$-0.459736\pi$
$977$	30.2308	−	14.0969i	0.967169	−	0.450998i	0.841015	+	0.541012i	$0.181959\pi$
$978$		0			0
$979$	−55.5801	−	9.80028i	−1.77635	−	0.313218i
$980$	−0.661759	−	16.8075i	−0.0211391	−	0.536894i
$981$		0			0
$982$	−5.31550	+	19.8377i	−0.169625	+	0.633047i
$983$	−16.4610	−	7.67588i	−0.525024	−	0.244823i	0.141990	−	0.989868i	$-0.454650\pi$
$983$	−16.4610	−	7.67588i	−0.525024	−	0.244823i	−0.667014	+	0.745045i	$0.732428\pi$
$984$		0			0
$985$	9.56425	+	18.5664i	0.304742	+	0.591574i
$986$	0.799140	+	0.952378i	0.0254498	+	0.0303299i
$987$		0			0
$988$	14.1874	−	30.4250i	0.451361	−	0.967947i
$989$	−7.22655	−	12.5167i	−0.229791	−	0.398009i
$990$		0			0
$991$	3.17299	−	5.49579i	0.100793	−	0.174579i	−0.811218	−	0.584743i	$-0.801195\pi$
$991$	3.17299	−	5.49579i	0.100793	−	0.174579i	0.912012	+	0.410164i	$0.134529\pi$
$992$	10.6608	+	15.2251i	0.338480	+	0.483399i
$993$		0			0
$994$	−0.565329	+	1.55323i	−0.0179311	+	0.0492654i
$995$	−19.3644	+	17.5923i	−0.613893	+	0.557714i
$996$		0			0
$997$	1.87448	+	21.4254i	0.0593654	+	0.678549i	0.966324	+	0.257329i	$0.0828425\pi$
$997$	1.87448	+	21.4254i	0.0593654	+	0.678549i	−0.906958	+	0.421220i	$0.861602\pi$
$998$	−16.4520	−	16.4520i	−0.520779	−	0.520779i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.197.9		192
3.2	odd	2		135.2.q.a.92.8	yes	192
5.3	odd	4	inner	405.2.r.a.278.8		192
15.2	even	4		675.2.ba.b.443.8		192
15.8	even	4		135.2.q.a.38.9	yes	192
15.14	odd	2		675.2.ba.b.632.9		192
27.5	odd	18	inner	405.2.r.a.287.8		192
27.22	even	9		135.2.q.a.32.9	✓	192
135.22	odd	36		675.2.ba.b.518.9		192
135.49	even	18		675.2.ba.b.32.8		192
135.103	odd	36		135.2.q.a.113.8	yes	192
135.113	even	36	inner	405.2.r.a.368.9		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.9	✓	192	27.22	even	9
135.2.q.a.38.9	yes	192	15.8	even	4
135.2.q.a.92.8	yes	192	3.2	odd	2
135.2.q.a.113.8	yes	192	135.103	odd	36
405.2.r.a.197.9		192	1.1	even	1	trivial
405.2.r.a.278.8		192	5.3	odd	4	inner
405.2.r.a.287.8		192	27.5	odd	18	inner
405.2.r.a.368.9		192	135.113	even	36	inner
675.2.ba.b.32.8		192	135.49	even	18
675.2.ba.b.443.8		192	15.2	even	4
675.2.ba.b.518.9		192	135.22	odd	36
675.2.ba.b.632.9		192	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.576956 - 0.0504771i) q^{2} +(-1.63929 + 0.289050i) q^{4} +(-2.18512 + 0.474625i) q^{5} +(2.78018 - 1.94671i) q^{7} +(-2.05006 + 0.549311i) q^{8} +O(q^{10})\)	\(q+(0.576956 - 0.0504771i) q^{2} +(-1.63929 + 0.289050i) q^{4} +(-2.18512 + 0.474625i) q^{5} +(2.78018 - 1.94671i) q^{7} +(-2.05006 + 0.549311i) q^{8} +(-1.23676 + 0.384136i) q^{10} +(-1.55726 - 4.27854i) q^{11} +(0.357151 - 4.08225i) q^{13} +(1.50578 - 1.26350i) q^{14} +(1.97331 - 0.718227i) q^{16} +(-0.284890 - 0.0763360i) q^{17} +(-4.26213 - 2.46074i) q^{19} +(3.44484 - 1.40965i) q^{20} +(-1.11444 - 2.38992i) q^{22} +(-0.869642 + 1.24198i) q^{23} +(4.54946 - 2.07422i) q^{25} -2.37331i q^{26} +(-3.99482 + 3.99482i) q^{28} +(-5.57542 - 4.67834i) q^{29} +(0.591015 + 3.35181i) q^{31} +(4.94931 - 2.30790i) q^{32} +(-0.168222 - 0.0296621i) q^{34} +(-5.15107 + 5.57332i) q^{35} +(1.28961 - 4.81289i) q^{37} +(-2.58327 - 1.20460i) q^{38} +(4.21889 - 2.17331i) q^{40} +(2.42980 + 2.89573i) q^{41} +(-4.02865 + 8.63947i) q^{43} +(3.78950 + 6.56361i) q^{44} +(-0.439054 + 0.760463i) q^{46} +(-1.09911 - 1.56969i) q^{47} +(1.54562 - 4.24655i) q^{49} +(2.52014 - 1.42638i) q^{50} +(0.594504 + 6.79521i) q^{52} +(1.39575 + 1.39575i) q^{53} +(5.43349 + 8.60998i) q^{55} +(-4.63018 + 5.51804i) q^{56} +(-3.45292 - 2.41776i) q^{58} +(9.34637 + 3.40180i) q^{59} +(-0.249603 + 1.41557i) q^{61} +(0.510179 + 1.90402i) q^{62} +(-0.898191 + 0.518571i) q^{64} +(1.15712 + 9.08971i) q^{65} +(-9.46116 - 0.827744i) q^{67} +(0.489081 + 0.0427890i) q^{68} +(-2.69061 + 3.47557i) q^{70} +(-0.728237 + 0.420448i) q^{71} +(0.166069 + 0.619776i) q^{73} +(0.501107 - 2.84192i) q^{74} +(7.69812 + 2.80189i) q^{76} +(-12.6585 - 8.86359i) q^{77} +(9.56341 - 11.3972i) q^{79} +(-3.97103 + 2.50599i) q^{80} +(1.54806 + 1.54806i) q^{82} +(-0.830405 - 9.49158i) q^{83} +(0.658748 + 0.0315873i) q^{85} +(-1.88826 + 5.18795i) q^{86} +(5.54271 + 7.91582i) q^{88} +(6.19767 - 10.7347i) q^{89} +(-6.95400 - 12.0447i) q^{91} +(1.06660 - 2.28733i) q^{92} +(-0.713371 - 0.850162i) q^{94} +(10.4812 + 3.35409i) q^{95} +(-4.11255 - 1.91772i) q^{97} +(0.677399 - 2.52809i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

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