LMFDB - Embedded newform 324.2.l.a.179.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(35,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("324.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.l (of order $18$, degree $6$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			179.6
Character	$\chi$	$=$	324.179
Dual form			324.2.l.a.143.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654159 - 1.25382i) q^{2} +(-1.14415 + 1.64040i) q^{4} +(-0.137245 - 0.0242000i) q^{5} +(-2.98823 - 3.56123i) q^{7} +(2.80523 + 0.361485i) q^{8} +O(q^{10})$	\(q+(-0.654159 - 1.25382i) q^{2} +(-1.14415 + 1.64040i) q^{4} +(-0.137245 - 0.0242000i) q^{5} +(-2.98823 - 3.56123i) q^{7} +(2.80523 + 0.361485i) q^{8} +(0.0594376 + 0.187912i) q^{10} +(0.182573 + 1.03542i) q^{11} +(-1.46220 + 0.532196i) q^{13} +(-2.51039 + 6.07633i) q^{14} +(-1.38183 - 3.75374i) q^{16} +(-5.25631 - 3.03473i) q^{17} +(-3.80088 + 2.19444i) q^{19} +(0.196727 - 0.197449i) q^{20} +(1.17880 - 0.906244i) q^{22} +(-1.94128 - 1.62893i) q^{23} +(-4.68021 - 1.70346i) q^{25} +(1.62379 + 1.48520i) q^{26} +(9.26084 - 0.827297i) q^{28} +(-0.210458 + 0.578229i) q^{29} +(3.18818 - 3.79952i) q^{31} +(-3.80260 + 4.18811i) q^{32} +(-0.366562 + 8.57569i) q^{34} +(0.323938 + 0.561078i) q^{35} +(-1.43991 + 2.49400i) q^{37} +(5.23782 + 3.33012i) q^{38} +(-0.376257 - 0.117499i) q^{40} +(2.25297 + 6.18999i) q^{41} +(2.15530 - 0.380038i) q^{43} +(-1.90740 - 0.885188i) q^{44} +(-0.772484 + 3.49960i) q^{46} +(8.46639 - 7.10414i) q^{47} +(-2.53733 + 14.3899i) q^{49} +(0.925763 + 6.98250i) q^{50} +(0.799963 - 3.00750i) q^{52} -8.73360i q^{53} -0.146525i q^{55} +(-7.09534 - 11.0703i) q^{56} +(0.862670 - 0.114376i) q^{58} +(1.42477 - 8.08025i) q^{59} +(8.56477 - 7.18670i) q^{61} +(-6.84951 - 1.51193i) q^{62} +(7.73866 + 2.02810i) q^{64} +(0.213559 - 0.0376562i) q^{65} +(1.93034 + 5.30357i) q^{67} +(10.9922 - 5.15026i) q^{68} +(0.491586 - 0.773196i) q^{70} +(-2.33277 + 4.04048i) q^{71} +(-5.64518 - 9.77774i) q^{73} +(4.06898 + 0.173925i) q^{74} +(0.749029 - 8.74574i) q^{76} +(3.14181 - 3.74426i) q^{77} +(0.572755 - 1.57363i) q^{79} +(0.0988087 + 0.548623i) q^{80} +(6.28736 - 6.87406i) q^{82} +(-2.20553 - 0.802749i) q^{83} +(0.647964 + 0.543706i) q^{85} +(-1.88641 - 2.45377i) q^{86} +(0.137869 + 2.97059i) q^{88} +(-7.63741 + 4.40946i) q^{89} +(6.26466 + 3.61690i) q^{91} +(4.89321 - 1.32073i) q^{92} +(-14.4457 - 5.96813i) q^{94} +(0.574758 - 0.209195i) q^{95} +(-0.978443 - 5.54902i) q^{97} +(19.7022 - 6.23192i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.654159	−	1.25382i	−0.462560	−	0.886588i
$2$	−0.654159	−	1.25382i	−0.462560	−	0.886588i
$3$		0			0
$3$		0			0
$4$	−1.14415	+	1.64040i	−0.572077	+	0.820200i
$5$	−0.137245	−	0.0242000i	−0.0613780	−	0.0108226i	0.142875	−	0.989741i	$-0.454365\pi$
$5$	−0.137245	−	0.0242000i	−0.0613780	−	0.0108226i	−0.204253	+	0.978918i	$0.565476\pi$
$6$		0			0
$7$	−2.98823	−	3.56123i	−1.12944	−	1.34602i	−0.930621	−	0.365984i	$-0.880732\pi$
$7$	−2.98823	−	3.56123i	−1.12944	−	1.34602i	−0.198824	−	0.980035i	$-0.563712\pi$
$8$	2.80523	+	0.361485i	0.991799	+	0.127804i
$9$		0			0
$10$	0.0594376	+	0.187912i	0.0187958	+	0.0594231i
$11$	0.182573	+	1.03542i	0.0550477	+	0.312191i	0.999882	−	0.0153574i	$-0.00488861\pi$
$11$	0.182573	+	1.03542i	0.0550477	+	0.312191i	−0.944834	+	0.327549i	$0.893777\pi$
$12$		0			0
$13$	−1.46220	+	0.532196i	−0.405541	+	0.147605i	−0.536733	−	0.843752i	$-0.680342\pi$
$13$	−1.46220	+	0.532196i	−0.405541	+	0.147605i	0.131192	+	0.991357i	$0.458119\pi$
$14$	−2.51039	+	6.07633i	−0.670929	+	1.62397i
$15$		0			0
$16$	−1.38183	−	3.75374i	−0.345457	−	0.938435i
$17$	−5.25631	−	3.03473i	−1.27484	−	0.736031i	−0.298948	−	0.954269i	$-0.596636\pi$
$17$	−5.25631	−	3.03473i	−1.27484	−	0.736031i	−0.975895	+	0.218238i	$0.929969\pi$
$18$		0			0
$19$	−3.80088	+	2.19444i	−0.871981	+	0.503439i	−0.868006	−	0.496553i	$-0.834599\pi$
$19$	−3.80088	+	2.19444i	−0.871981	+	0.503439i	−0.00397518	+	0.999992i	$0.501265\pi$
$20$	0.196727	−	0.197449i	0.0439896	−	0.0441509i
$21$		0			0
$22$	1.17880	−	0.906244i	0.251322	−	0.193212i
$23$	−1.94128	−	1.62893i	−0.404785	−	0.339655i	0.417555	−	0.908652i	$-0.362887\pi$
$23$	−1.94128	−	1.62893i	−0.404785	−	0.339655i	−0.822340	+	0.568997i	$0.807332\pi$
$24$		0			0
$25$	−4.68021	−	1.70346i	−0.936042	−	0.340692i
$26$	1.62379	+	1.48520i	0.318451	+	0.291271i
$27$		0			0
$28$	9.26084	−	0.827297i	1.75013	−	0.156345i
$29$	−0.210458	+	0.578229i	−0.0390811	+	0.107374i	−0.957698	−	0.287774i	$-0.907085\pi$
$29$	−0.210458	+	0.578229i	−0.0390811	+	0.107374i	0.918617	+	0.395149i	$0.129307\pi$
$30$		0			0
$31$	3.18818	−	3.79952i	0.572613	−	0.682414i	−0.399552	−	0.916711i	$-0.630834\pi$
$31$	3.18818	−	3.79952i	0.572613	−	0.682414i	0.972165	+	0.234297i	$0.0752787\pi$
$32$	−3.80260	+	4.18811i	−0.672210	+	0.740360i
$33$		0			0
$34$	−0.366562	+	8.57569i	−0.0628648	+	1.47072i
$35$	0.323938	+	0.561078i	0.0547556	+	0.0948394i
$36$		0			0
$37$	−1.43991	+	2.49400i	−0.236720	+	0.410012i	−0.959771	−	0.280783i	$-0.909406\pi$
$37$	−1.43991	+	2.49400i	−0.236720	+	0.410012i	0.723051	+	0.690795i	$0.242739\pi$
$38$	5.23782	+	3.33012i	0.849686	+	0.540218i
$39$		0			0
$40$	−0.376257	−	0.117499i	−0.0594914	−	0.0185782i
$41$	2.25297	+	6.18999i	0.351855	+	0.966713i	0.981774	+	0.190053i	$0.0608658\pi$
$41$	2.25297	+	6.18999i	0.351855	+	0.966713i	−0.629919	+	0.776661i	$0.716912\pi$
$42$		0			0
$43$	2.15530	−	0.380038i	0.328681	−	0.0579553i	−0.00687300	−	0.999976i	$-0.502188\pi$
$43$	2.15530	−	0.380038i	0.328681	−	0.0579553i	0.335554	+	0.942021i	$0.391077\pi$
$44$	−1.90740	−	0.885188i	−0.287551	−	0.133447i
$45$		0			0
$46$	−0.772484	+	3.49960i	−0.113897	+	0.515988i
$47$	8.46639	−	7.10414i	1.23495	−	1.03625i	0.237048	−	0.971498i	$-0.423820\pi$
$47$	8.46639	−	7.10414i	1.23495	−	1.03625i	0.997902	−	0.0647475i	$-0.0206242\pi$
$48$		0			0
$49$	−2.53733	+	14.3899i	−0.362476	+	2.05570i
$50$	0.925763	+	6.98250i	0.130923	+	0.987474i
$51$		0			0
$52$	0.799963	−	3.00750i	0.110935	−	0.417066i
$53$		−	8.73360i		−	1.19965i	−0.800130	−	0.599826i	$-0.795236\pi$
$53$		−	8.73360i		−	1.19965i	0.800130	−	0.599826i	$-0.204764\pi$
$54$		0			0
$55$		−	0.146525i		−	0.0197574i
$56$	−7.09534	−	11.0703i	−0.948155	−	1.47933i
$57$		0			0
$58$	0.862670	−	0.114376i	0.113274	−	0.0150183i
$59$	1.42477	−	8.08025i	0.185489	−	1.05196i	−0.739837	−	0.672786i	$-0.765097\pi$
$59$	1.42477	−	8.08025i	0.185489	−	1.05196i	0.925326	−	0.379173i	$-0.123792\pi$
$60$		0			0
$61$	8.56477	−	7.18670i	1.09661	−	0.920162i	0.0994142	−	0.995046i	$-0.468303\pi$
$61$	8.56477	−	7.18670i	1.09661	−	0.920162i	0.997192	+	0.0748840i	$0.0238587\pi$
$62$	−6.84951	−	1.51193i	−0.869888	−	0.192015i
$63$		0			0
$64$	7.73866	+	2.02810i	0.967332	+	0.253513i
$65$	0.213559	−	0.0376562i	0.0264887	−	0.00467068i
$66$		0			0
$67$	1.93034	+	5.30357i	0.235829	+	0.647934i	0.999996	+	0.00291580i	$0.000928130\pi$
$67$	1.93034	+	5.30357i	0.235829	+	0.647934i	−0.764167	+	0.645019i	$0.776850\pi$
$68$	10.9922	−	5.15026i	1.33300	−	0.624561i
$69$		0			0
$70$	0.491586	−	0.773196i	0.0587558	−	0.0924146i
$71$	−2.33277	+	4.04048i	−0.276849	+	0.479517i	−0.970600	−	0.240698i	$-0.922624\pi$
$71$	−2.33277	+	4.04048i	−0.276849	+	0.479517i	0.693751	+	0.720215i	$0.255957\pi$
$72$		0			0
$73$	−5.64518	−	9.77774i	−0.660718	−	1.14440i	−0.980427	−	0.196882i	$-0.936918\pi$
$73$	−5.64518	−	9.77774i	−0.660718	−	1.14440i	0.319709	−	0.947516i	$-0.396415\pi$
$74$	4.06898	+	0.173925i	0.473009	+	0.0202184i
$75$		0			0
$76$	0.749029	−	8.74574i	0.0859195	−	1.00320i
$77$	3.14181	−	3.74426i	0.358042	−	0.426698i
$78$		0			0
$79$	0.572755	−	1.57363i	0.0644400	−	0.177047i	−0.903294	−	0.429023i	$-0.858858\pi$
$79$	0.572755	−	1.57363i	0.0644400	−	0.177047i	0.967734	+	0.251975i	$0.0810802\pi$
$80$	0.0988087	+	0.548623i	0.0110471	+	0.0613379i
$81$		0			0
$82$	6.28736	−	6.87406i	0.694322	−	0.759113i
$83$	−2.20553	−	0.802749i	−0.242089	−	0.0881131i	0.218126	−	0.975921i	$-0.430006\pi$
$83$	−2.20553	−	0.802749i	−0.242089	−	0.0881131i	−0.460215	+	0.887807i	$0.652228\pi$
$84$		0			0
$85$	0.647964	+	0.543706i	0.0702815	+	0.0589732i
$86$	−1.88641	−	2.45377i	−0.203417	−	0.264596i
$87$		0			0
$88$	0.137869	+	2.97059i	0.0146969	+	0.316666i
$89$	−7.63741	+	4.40946i	−0.809564	+	0.467402i	−0.846804	−	0.531905i	$-0.821476\pi$
$89$	−7.63741	+	4.40946i	−0.809564	+	0.467402i	0.0372408	+	0.999306i	$0.488143\pi$
$90$		0			0
$91$	6.26466	+	3.61690i	0.656715	+	0.379154i
$92$	4.89321	−	1.32073i	0.510153	−	0.137696i
$93$		0			0
$94$	−14.4457	−	5.96813i	−1.48996	−	0.615566i
$95$	0.574758	−	0.209195i	0.0589689	−	0.0214629i
$96$		0			0
$97$	−0.978443	−	5.54902i	−0.0993458	−	0.563418i	−0.993329	−	0.115317i	$-0.963212\pi$
$97$	−0.978443	−	5.54902i	−0.0993458	−	0.563418i	0.893983	−	0.448101i	$-0.147899\pi$
$98$	19.7022	−	6.23192i	1.99023	−	0.629519i
$99$		0			0
$100$	8.14923	−	5.72841i	0.814923	−	0.572841i
$101$	6.72190	+	8.01085i	0.668854	+	0.797109i	0.988628	−	0.150385i	$-0.0480512\pi$
$101$	6.72190	+	8.01085i	0.668854	+	0.797109i	−0.319773	+	0.947494i	$0.603607\pi$
$102$		0			0
$103$	−1.52148	−	0.268277i	−0.149915	−	0.0264341i	0.0981867	−	0.995168i	$-0.468696\pi$
$103$	−1.52148	−	0.268277i	−0.149915	−	0.0264341i	−0.248102	+	0.968734i	$0.579807\pi$
$104$	−4.29419	+	0.964372i	−0.421080	+	0.0945644i
$105$		0			0
$106$	−10.9504	+	5.71316i	−1.06360	+	0.554911i
$107$	−7.89051			−0.762805			−0.381402	−	0.924409i	$-0.624559\pi$
$107$	−7.89051			−0.762805			−0.381402	+	0.924409i	$0.624559\pi$
$108$		0			0
$109$	1.78550			0.171020			0.0855098	−	0.996337i	$-0.472748\pi$
$109$	1.78550			0.171020			0.0855098	+	0.996337i	$0.472748\pi$
$110$	−0.183717	+	0.0958505i	−0.0175167	+	0.00913899i
$111$		0			0
$112$	−9.23872	+	16.1380i	−0.872977	+	1.52490i
$113$	10.4607	+	1.84450i	0.984057	+	0.173516i	0.642451	−	0.766327i	$-0.277918\pi$
$113$	10.4607	+	1.84450i	0.984057	+	0.173516i	0.341607	+	0.939843i	$0.389029\pi$
$114$		0			0
$115$	0.227011	+	0.270542i	0.0211689	+	0.0252281i
$116$	−0.707730	−	1.00682i	−0.0657111	−	0.0934807i
$117$		0			0
$118$	−11.0632	+	3.49936i	−1.01845	+	0.322142i
$119$	4.89968	+	27.7874i	0.449152	+	2.54727i
$120$		0			0
$121$	9.29786	−	3.38414i	0.845260	−	0.307649i
$122$	−14.6136	−	6.03748i	−1.32305	−	0.546608i
$123$		0			0
$124$	2.58497	+	9.57712i	0.232138	+	0.860051i
$125$	1.20457	+	0.695459i	0.107740	+	0.0622038i
$126$		0			0
$127$	−2.89596	+	1.67198i	−0.256975	+	0.148364i	−0.622954	−	0.782259i	$-0.714067\pi$
$127$	−2.89596	+	1.67198i	−0.256975	+	0.148364i	0.365979	+	0.930623i	$0.380734\pi$
$128$	−2.51943	−	11.0296i	−0.222688	−	0.974890i
$129$		0			0
$130$	−0.186916	−	0.243132i	−0.0163936	−	0.0213241i
$131$	−2.00847	−	1.68531i	−0.175481	−	0.147246i	0.550817	−	0.834626i	$-0.314316\pi$
$131$	−2.00847	−	1.68531i	−0.175481	−	0.147246i	−0.726298	+	0.687380i	$0.758761\pi$
$132$		0			0
$133$	19.1728	+	6.97833i	1.66249	+	0.605098i
$134$	5.38700	−	5.88969i	0.465366	−	0.508791i
$135$		0			0
$136$	−13.6482	−	10.4132i	−1.17032	−	0.892926i
$137$	−3.04906	+	8.37723i	−0.260499	+	0.715715i	0.738635	+	0.674106i	$0.235471\pi$
$137$	−3.04906	+	8.37723i	−0.260499	+	0.715715i	−0.999134	+	0.0416094i	$0.986752\pi$
$138$		0			0
$139$	9.64531	−	11.4948i	0.818105	−	0.974979i	−0.181860	−	0.983324i	$-0.558212\pi$
$139$	9.64531	−	11.4948i	0.818105	−	0.974979i	0.999965	+	0.00834505i	$0.00265634\pi$
$140$	−1.29103	−	0.110570i	−0.109112	−	0.00934488i
$141$		0			0
$142$	6.59206	+	0.281773i	0.553193	+	0.0236458i
$143$	−0.818005	−	1.41683i	−0.0684050	−	0.118481i
$144$		0			0
$145$	0.0428775	−	0.0742661i	0.00356079	−	0.00616746i
$146$	−8.56673	+	13.4743i	−0.708987	+	1.11514i
$147$		0			0
$148$	−2.44368	−	5.21556i	−0.200870	−	0.428716i
$149$	−6.19266	−	17.0142i	−0.507323	−	1.39386i	−0.883989	−	0.467509i	$-0.845152\pi$
$149$	−6.19266	−	17.0142i	−0.507323	−	1.39386i	0.376666	−	0.926349i	$-0.377071\pi$
$150$		0			0
$151$	−14.3804	+	2.53565i	−1.17026	+	0.206348i	−0.724803	−	0.688956i	$-0.758069\pi$
$151$	−14.3804	+	2.53565i	−1.17026	+	0.206348i	−0.445456	+	0.895304i	$0.646958\pi$
$152$	−11.4556	+	4.78195i	−0.929172	+	0.387867i
$153$		0			0
$154$	−6.74988	−	1.48994i	−0.543921	−	0.120062i
$155$	−0.529511	+	0.444312i	−0.0425313	+	0.0356880i
$156$		0			0
$157$	0.0237965	−	0.134957i	0.00189917	−	0.0107707i	−0.983843	−	0.179031i	$-0.942704\pi$
$157$	0.0237965	−	0.134957i	0.00189917	−	0.0107707i	0.985743	+	0.168260i	$0.0538149\pi$
$158$	−2.34773	+	0.311270i	−0.186776	+	0.0247633i
$159$		0			0
$160$	0.623241	−	0.482775i	0.0492715	−	0.0381667i
$161$			11.7810i			0.928469i
$162$		0			0
$163$			12.0210i			0.941554i	0.882252	+	0.470777i	$0.156026\pi$
$163$			12.0210i			0.941554i	−0.882252	+	0.470777i	$0.843974\pi$
$164$	−12.7318	−	3.38652i	−0.994186	−	0.264443i
$165$		0			0
$166$	0.436263	+	3.29048i	0.0338606	+	0.255391i
$167$	−1.95387	+	11.0810i	−0.151195	+	0.857471i	0.810987	+	0.585064i	$0.198931\pi$
$167$	−1.95387	+	11.0810i	−0.151195	+	0.857471i	−0.962182	+	0.272407i	$0.912180\pi$
$168$		0			0
$169$	−8.10379	+	6.79989i	−0.623368	+	0.523068i
$170$	0.257841	−	1.16810i	0.0197755	−	0.0895894i
$171$		0			0
$172$	−1.84258	+	3.97038i	−0.140496	+	0.302739i
$173$	−5.61630	+	0.990305i	−0.426999	+	0.0752915i	−0.383018	−	0.923741i	$-0.625115\pi$
$173$	−5.61630	+	0.990305i	−0.426999	+	0.0752915i	−0.0439813	+	0.999032i	$0.514004\pi$
$174$		0			0
$175$	7.91914	+	21.7577i	0.598631	+	1.64472i
$176$	3.63442	−	2.11610i	0.273954	−	0.159507i
$177$		0			0
$178$	10.5248	+	6.69148i	0.788864	+	0.501548i
$179$	−6.20187	+	10.7419i	−0.463549	+	0.802891i	−0.999135	−	0.0415901i	$-0.986758\pi$
$179$	−6.20187	+	10.7419i	−0.463549	+	0.802891i	0.535585	+	0.844481i	$0.320091\pi$
$180$		0			0
$181$	0.582122	+	1.00827i	0.0432688	+	0.0749437i	0.886849	−	0.462060i	$-0.152889\pi$
$181$	0.582122	+	1.00827i	0.0432688	+	0.0749437i	−0.843580	+	0.537004i	$0.819556\pi$
$182$	0.436881	−	10.2208i	0.0323838	−	0.757617i
$183$		0			0
$184$	−4.85691	−	5.27126i	−0.358056	−	0.388603i
$185$	0.257976	−	0.307444i	0.0189668	−	0.0226037i
$186$		0			0
$187$	2.18257	−	5.99656i	0.159605	−	0.438512i
$188$	1.96680	+	22.0165i	0.143443	+	1.60572i
$189$		0			0
$190$	−0.638277	−	0.583799i	−0.0463055	−	0.0423533i
$191$	−13.5161	−	4.91947i	−0.977993	−	0.355960i	−0.196934	−	0.980417i	$-0.563098\pi$
$191$	−13.5161	−	4.91947i	−0.977993	−	0.355960i	−0.781060	+	0.624456i	$0.785321\pi$
$192$		0			0
$193$	−14.0915	−	11.8242i	−1.01433	−	0.851125i	−0.0254271	−	0.999677i	$-0.508095\pi$
$193$	−14.0915	−	11.8242i	−1.01433	−	0.851125i	−0.988905	+	0.148551i	$0.952539\pi$
$194$	−6.31745	+	4.85674i	−0.453566	+	0.348693i
$195$		0			0
$196$	−20.7021	−	20.6265i	−1.47872	−	1.47332i
$197$	18.3471	−	10.5927i	1.30718	−	0.754699i	0.325553	−	0.945524i	$-0.394450\pi$
$197$	18.3471	−	10.5927i	1.30718	−	0.754699i	0.981624	+	0.190825i	$0.0611163\pi$
$198$		0			0
$199$	−5.80763	−	3.35304i	−0.411692	−	0.237691i	0.279824	−	0.960051i	$-0.409724\pi$
$199$	−5.80763	−	3.35304i	−0.411692	−	0.237691i	−0.691517	+	0.722361i	$0.743057\pi$
$200$	−12.5133	−	6.47042i	−0.884825	−	0.457528i
$201$		0			0
$202$	5.64701	−	13.6685i	0.397322	−	0.961709i
$203$	2.68810	−	0.978390i	0.188668	−	0.0686695i
$204$		0			0
$205$	−0.159412	−	0.904068i	−0.0111338	−	0.0631429i
$206$	0.658914	+	2.08316i	0.0459087	+	0.145141i
$207$		0			0
$208$	4.01823	+	4.75330i	0.278614	+	0.329582i
$209$	−2.96610	−	3.53486i	−0.205170	−	0.244512i
$210$		0			0
$211$	−17.3303	−	3.05581i	−1.19307	−	0.210370i	−0.458369	−	0.888762i	$-0.651566\pi$
$211$	−17.3303	−	3.05581i	−1.19307	−	0.210370i	−0.734701	+	0.678391i	$0.762677\pi$
$212$	14.3266	+	9.99257i	0.983955	+	0.686293i
$213$		0			0
$214$	5.16165	+	9.89332i	0.352843	+	0.676293i
$215$	−0.305002			−0.0208010
$216$		0			0
$217$	−23.0580			−1.56528
$218$	−1.16800	−	2.23870i	−0.0791069	−	0.151624i
$219$		0			0
$220$	0.240360	+	0.167647i	0.0162050	+	0.0113028i
$221$	9.30084	+	1.63999i	0.625643	+	0.110318i
$222$		0			0
$223$	5.95915	+	7.10184i	0.399054	+	0.475574i	0.927731	−	0.373249i	$-0.121756\pi$
$223$	5.95915	+	7.10184i	0.399054	+	0.475574i	−0.528677	+	0.848823i	$0.677312\pi$
$224$	26.2779	+	1.02690i	1.75576	+	0.0686123i
$225$		0			0
$226$	−4.53026	−	14.3224i	−0.301348	−	0.952715i
$227$	−3.87558	−	21.9795i	−0.257231	−	1.45883i	−0.790280	−	0.612746i	$-0.790065\pi$
$227$	−3.87558	−	21.9795i	−0.257231	−	1.45883i	0.533049	−	0.846085i	$-0.321046\pi$
$228$		0			0
$229$	24.7476	−	9.00740i	1.63537	−	0.595226i	0.649149	−	0.760661i	$-0.275125\pi$
$229$	24.7476	−	9.00740i	1.63537	−	0.595226i	0.986221	+	0.165435i	$0.0529028\pi$
$230$	0.190710	−	0.461609i	0.0125751	−	0.0304376i
$231$		0			0
$232$	−0.799405	+	1.54599i	−0.0524835	+	0.101499i
$233$	6.49629	+	3.75063i	0.425586	+	0.245712i	0.697464	−	0.716619i	$-0.254312\pi$
$233$	6.49629	+	3.75063i	0.425586	+	0.245712i	−0.271878	+	0.962332i	$0.587645\pi$
$234$		0			0
$235$	−1.33389	+	0.770123i	−0.0870135	+	0.0502373i
$236$	11.6247	+	11.5822i	0.756704	+	0.753939i
$237$		0			0
$238$	31.6354	−	24.3207i	2.05062	−	1.57648i
$239$	−2.63068	−	2.20740i	−0.170165	−	0.142785i	0.553728	−	0.832697i	$-0.313205\pi$
$239$	−2.63068	−	2.20740i	−0.170165	−	0.142785i	−0.723893	+	0.689912i	$0.757649\pi$
$240$		0			0
$241$	1.59962	+	0.582213i	0.103040	+	0.0375036i	0.393026	−	0.919527i	$-0.371428\pi$
$241$	1.59962	+	0.582213i	0.103040	+	0.0375036i	−0.289986	+	0.957031i	$0.593650\pi$
$242$	−10.3254	−	9.44411i	−0.663741	−	0.607091i
$243$		0			0
$244$	1.98965	+	22.2723i	0.127374	+	1.42584i
$245$	0.696473	−	1.91354i	0.0444960	−	0.122252i
$246$		0			0
$247$	4.38976	−	5.23152i	0.279314	−	0.332873i
$248$	10.3170	−	9.50606i	0.655133	−	0.603635i
$249$		0			0
$250$	0.0840037	−	1.96526i	0.00531286	−	0.124294i
$251$	7.79783	+	13.5062i	0.492195	+	0.852506i	0.999960	−	0.00898943i	$-0.00286146\pi$
$251$	7.79783	+	13.5062i	0.492195	+	0.852506i	−0.507765	+	0.861496i	$0.669528\pi$
$252$		0			0
$253$	1.33220	−	2.30744i	0.0837547	−	0.145067i
$254$	3.99079	+	2.53728i	0.250404	+	0.159203i
$255$		0			0
$256$	−12.1811	+	10.3740i	−0.761319	+	0.648377i
$257$	3.39598	+	9.33039i	0.211836	+	0.582014i	0.999415	−	0.0341995i	$-0.0108882\pi$
$257$	3.39598	+	9.33039i	0.211836	+	0.582014i	−0.787579	+	0.616213i	$0.788666\pi$
$258$		0			0
$259$	13.1845	−	2.32479i	0.819246	−	0.144455i
$260$	−0.182573	+	0.393407i	−0.0113227	+	0.0243980i
$261$		0			0
$262$	−0.799223	+	3.62074i	−0.0493761	+	0.223690i
$263$	20.0312	−	16.8082i	1.23518	−	1.03644i	0.237292	−	0.971438i	$-0.423740\pi$
$263$	20.0312	−	16.8082i	1.23518	−	1.03644i	0.997885	−	0.0649985i	$-0.0207043\pi$
$264$		0			0
$265$	−0.211354	+	1.19865i	−0.0129833	+	0.0736322i
$266$	−3.79245	−	28.6043i	−0.232530	−	1.75384i
$267$		0			0
$268$	−10.9086	−	2.90156i	−0.666348	−	0.177241i
$269$			0.465194i			0.0283634i	0.999899	+	0.0141817i	$0.00451432\pi$
$269$			0.465194i			0.0283634i	−0.999899	+	0.0141817i	$0.995486\pi$
$270$		0			0
$271$		−	15.6578i		−	0.951143i	−0.879677	−	0.475571i	$-0.842241\pi$
$271$		−	15.6578i		−	0.951143i	0.879677	−	0.475571i	$-0.157759\pi$
$272$	−4.12828	+	23.9243i	−0.250314	+	1.45062i
$273$		0			0
$274$	12.4981	−	1.65705i	0.755041	−	0.100106i
$275$	0.909317	−	5.15699i	0.0548339	−	0.310978i
$276$		0			0
$277$	−7.55460	+	6.33906i	−0.453912	+	0.380877i	−0.840885	−	0.541214i	$-0.817965\pi$
$277$	−7.55460	+	6.33906i	−0.453912	+	0.380877i	0.386973	+	0.922091i	$0.373521\pi$
$278$	−20.7221	−	4.57409i	−1.24283	−	0.274335i
$279$		0			0
$280$	0.705901	+	1.69105i	0.0421857	+	0.101060i
$281$	−16.8051	+	2.96320i	−1.00251	+	0.176770i	−0.650727	−	0.759312i	$-0.725536\pi$
$281$	−16.8051	+	2.96320i	−1.00251	+	0.176770i	−0.351783	+	0.936081i	$0.614425\pi$
$282$		0			0
$283$	−3.24599	−	8.91828i	−0.192954	−	0.530137i	0.805056	−	0.593199i	$-0.202135\pi$
$283$	−3.24599	−	8.91828i	−0.192954	−	0.530137i	−0.998010	+	0.0630625i	$0.979913\pi$
$284$	−3.95896	−	8.44961i	−0.234921	−	0.501392i
$285$		0			0
$286$	−1.24135	+	1.95246i	−0.0734023	+	0.115452i
$287$	15.3116	−	26.5204i	0.903814	−	1.56545i
$288$		0			0
$289$	9.91922	+	17.1806i	0.583484	+	1.01062i
$290$	−0.121165	−	0.00517913i	−0.00711507	−	0.000304129i
$291$		0			0
$292$	22.4984	+	1.92687i	1.31662	+	0.112762i
$293$	−1.45797	+	1.73754i	−0.0851753	+	0.101508i	−0.806949	−	0.590621i	$-0.798883\pi$
$293$	−1.45797	+	1.73754i	−0.0851753	+	0.101508i	0.721774	+	0.692129i	$0.243327\pi$
$294$		0			0
$295$	−0.391085	+	1.07450i	−0.0227699	+	0.0625597i
$296$	−4.94084	+	6.47575i	−0.287180	+	0.376395i
$297$		0			0
$298$	−17.2818	+	18.8945i	−1.00111	+	1.09453i
$299$	3.70544	+	1.34867i	0.214291	+	0.0779957i
$300$		0			0
$301$	−7.79394	−	6.53989i	−0.449235	−	0.376953i
$302$	12.5863	+	16.3718i	0.724261	+	0.942089i
$303$		0			0
$304$	13.4895	+	11.2352i	0.773676	+	0.644381i
$305$	−1.34939	+	0.779072i	−0.0772660	+	0.0446095i
$306$		0			0
$307$	−10.5153	−	6.07100i	−0.600138	−	0.346490i	0.168958	−	0.985623i	$-0.445960\pi$
$307$	−10.5153	−	6.07100i	−0.600138	−	0.346490i	−0.769096	+	0.639133i	$0.779293\pi$
$308$	2.54738	+	9.43783i	0.145150	+	0.537770i
$309$		0			0
$310$	0.903474	+	0.373263i	0.0513139	+	0.0211999i
$311$	−16.3253	+	5.94192i	−0.925723	+	0.336936i	−0.760513	−	0.649323i	$-0.775052\pi$
$311$	−16.3253	+	5.94192i	−0.925723	+	0.336936i	−0.165210	+	0.986258i	$0.552830\pi$
$312$		0			0
$313$	2.82602	+	16.0272i	0.159736	+	0.905909i	0.954327	+	0.298764i	$0.0965743\pi$
$313$	2.82602	+	16.0272i	0.159736	+	0.905909i	−0.794591	+	0.607145i	$0.792315\pi$
$314$	−0.184779	+	0.0584465i	−0.0104277	+	0.00329832i
$315$		0			0
$316$	1.92607	+	2.74002i	0.108350	+	0.154138i
$317$	−18.7298	−	22.3213i	−1.05197	−	1.25369i	−0.966314	−	0.257366i	$-0.917145\pi$
$317$	−18.7298	−	22.3213i	−1.05197	−	1.25369i	−0.0856578	−	0.996325i	$-0.527299\pi$
$318$		0			0
$319$	−0.637134	−	0.112344i	−0.0356727	−	0.00629005i
$320$	−1.01301	−	0.465623i	−0.0566292	−	0.0260291i
$321$		0			0
$322$	14.7713	−	7.70661i	0.823170	−	0.429473i
$323$	26.6381			1.48219
$324$		0			0
$325$	7.74997			0.429891
$326$	15.0722	−	7.86361i	0.834770	−	0.435525i
$327$		0			0
$328$	4.08252	+	18.1788i	0.225419	+	1.00375i
$329$	−50.5990	−	8.92197i	−2.78961	−	0.491884i
$330$		0			0
$331$	−1.75836	−	2.09553i	−0.0966481	−	0.115181i	0.715553	−	0.698559i	$-0.246175\pi$
$331$	−1.75836	−	2.09553i	−0.0966481	−	0.115181i	−0.812201	+	0.583378i	$0.801731\pi$
$332$	3.84030	−	2.69949i	0.210764	−	0.148154i
$333$		0			0
$334$	15.1717	−	4.79889i	0.830160	−	0.262584i
$335$	−0.136584	−	0.774604i	−0.00746236	−	0.0423212i
$336$		0			0
$337$	−6.48096	+	2.35888i	−0.353040	+	0.128496i	−0.512452	−	0.858716i	$-0.671263\pi$
$337$	−6.48096	+	2.35888i	−0.353040	+	0.128496i	0.159411	+	0.987212i	$0.449040\pi$
$338$	13.8270	+	5.71253i	0.752091	+	0.310720i
$339$		0			0
$340$	−1.63326	+	0.440837i	−0.0885762	+	0.0239077i
$341$	4.51618	+	2.60742i	0.244565	+	0.141199i
$342$		0			0
$343$	30.6457	−	17.6933i	1.65471	−	0.955349i
$344$	6.18350	−	0.286985i	0.333392	−	0.0154732i
$345$		0			0
$346$	4.91562	+	6.39404i	0.264265	+	0.343746i
$347$	17.5469	+	14.7236i	0.941964	+	0.790402i	0.977926	−	0.208951i	$-0.0670050\pi$
$347$	17.5469	+	14.7236i	0.941964	+	0.790402i	−0.0359618	+	0.999353i	$0.511449\pi$
$348$		0			0
$349$	−25.4917	−	9.27824i	−1.36454	−	0.496653i	−0.447086	−	0.894491i	$-0.647538\pi$
$349$	−25.4917	−	9.27824i	−1.36454	−	0.496653i	−0.917456	+	0.397838i	$0.869760\pi$
$350$	22.0999	−	24.1622i	1.18129	−	1.29152i
$351$		0			0
$352$	−5.03071	−	3.17265i	−0.268138	−	0.169103i
$353$	2.30370	−	6.32935i	0.122613	−	0.336877i	−0.863166	−	0.504919i	$-0.831522\pi$
$353$	2.30370	−	6.32935i	0.122613	−	0.336877i	0.985780	+	0.168042i	$0.0537444\pi$
$354$		0			0
$355$	0.417942	−	0.498084i	0.0221820	−	0.0264355i
$356$	1.50508	−	17.5735i	0.0797693	−	0.931394i
$357$		0			0
$358$	17.5255	+	0.749116i	0.926253	+	0.0395920i
$359$	−14.3604	−	24.8729i	−0.757913	−	1.31274i	−0.943913	−	0.330194i	$-0.892886\pi$
$359$	−14.3604	−	24.8729i	−0.757913	−	1.31274i	0.186000	−	0.982550i	$-0.440448\pi$
$360$		0			0
$361$	0.131118	−	0.227104i	0.00690097	−	0.0119528i
$362$	0.883387	−	1.38944i	0.0464298	−	0.0730276i
$363$		0			0
$364$	−13.1009	+	6.13826i	−0.686674	+	0.321732i
$365$	0.538153	+	1.47856i	0.0281682	+	0.0773915i
$366$		0			0
$367$	−3.84637	+	0.678219i	−0.200779	+	0.0354027i	−0.273133	−	0.961976i	$-0.588060\pi$
$367$	−3.84637	+	0.678219i	−0.200779	+	0.0354027i	0.0723541	+	0.997379i	$0.476949\pi$
$368$	−3.43205	+	9.53795i	−0.178908	+	0.497200i
$369$		0			0
$370$	−0.554239	−	0.122340i	−0.0288135	−	0.00636014i
$371$	−31.1024	+	26.0980i	−1.61476	+	1.35494i
$372$		0			0
$373$	−1.89369	+	10.7397i	−0.0980518	+	0.556079i	0.895718	+	0.444623i	$0.146662\pi$
$373$	−1.89369	+	10.7397i	−0.0980518	+	0.556079i	−0.993769	+	0.111456i	$0.964449\pi$
$374$	−8.94638	+	1.18614i	−0.462606	+	0.0613339i
$375$		0			0
$376$	26.3182	−	16.8683i	1.35726	−	0.869916i
$377$		−	0.957490i		−	0.0493132i
$378$		0			0
$379$			5.95264i			0.305766i	0.988244	+	0.152883i	$0.0488558\pi$
$379$			5.95264i			0.305766i	−0.988244	+	0.152883i	$0.951144\pi$
$380$	−0.314448	+	1.18218i	−0.0161308	+	0.0606448i
$381$		0			0
$382$	2.67354	+	20.1650i	0.136790	+	1.03173i
$383$	1.15926	−	6.57451i	0.0592356	−	0.335942i	−0.940759	−	0.339075i	$-0.889886\pi$
$383$	1.15926	−	6.57451i	0.0592356	−	0.335942i	0.999995	+	0.00313275i	$0.000997186\pi$
$384$		0			0
$385$	−0.521809	+	0.437850i	−0.0265939	+	0.0223149i
$386$	−5.60738	+	25.4032i	−0.285408	+	1.29299i
$387$		0			0
$388$	10.2221	+	4.74389i	0.518949	+	0.240835i
$389$	30.0164	−	5.29270i	1.52189	−	0.268351i	0.650716	−	0.759321i	$-0.274469\pi$
$389$	30.0164	−	5.29270i	1.52189	−	0.268351i	0.871176	+	0.490970i	$0.163358\pi$
$390$		0			0
$391$	5.26061	+	14.4534i	0.266041	+	0.730941i
$392$	−12.3195	+	39.4498i	−0.622231	+	1.99252i
$393$		0			0
$394$	−25.2833	−	16.0747i	−1.27375	−	0.809834i
$395$	−0.116690	+	0.202113i	−0.00587131	+	0.0101694i
$396$		0			0
$397$	7.87633	+	13.6422i	0.395302	+	0.684683i	0.993140	−	0.116934i	$-0.0373067\pi$
$397$	7.87633	+	13.6422i	0.395302	+	0.684683i	−0.597838	+	0.801617i	$0.703973\pi$
$398$	−0.405009	+	9.47517i	−0.0203013	+	0.474947i
$399$		0			0
$400$	0.0729116	+	19.9222i	0.00364558	+	0.996109i
$401$	1.99200	−	2.37398i	0.0994758	−	0.118551i	−0.714010	−	0.700136i	$-0.753123\pi$
$401$	1.99200	−	2.37398i	0.0994758	−	0.118551i	0.813486	+	0.581585i	$0.197567\pi$
$402$		0			0
$403$	−2.63965	+	7.25239i	−0.131490	+	0.361267i
$404$	−20.8319	+	1.86097i	−1.03643	+	0.0925868i
$405$		0			0
$406$	−2.98518	−	2.73039i	−0.148152	−	0.135507i
$407$	−2.84523	−	1.03558i	−0.141033	−	0.0513318i
$408$		0			0
$409$	−20.1116	−	16.8756i	−0.994454	−	0.834446i	−0.00824757	−	0.999966i	$-0.502625\pi$
$409$	−20.1116	−	16.8756i	−0.994454	−	0.834446i	−0.986206	+	0.165520i	$0.947070\pi$
$410$	−1.02926	+	0.791278i	−0.0508317	+	0.0390784i
$411$		0			0
$412$	2.18088	−	2.18888i	0.107444	−	0.107838i
$413$	−33.0332	+	19.0717i	−1.62546	+	0.938458i
$414$		0			0
$415$	0.283273	+	0.163547i	0.0139053	+	0.00802823i
$416$	3.33125	−	8.14757i	0.163328	−	0.399468i
$417$		0			0
$418$	−2.49180	+	6.03134i	−0.121878	+	0.295002i
$419$	33.9869	−	12.3702i	1.66037	−	0.604325i	0.669949	−	0.742407i	$-0.266316\pi$
$419$	33.9869	−	12.3702i	1.66037	−	0.604325i	0.990421	+	0.138082i	$0.0440939\pi$
$420$		0			0
$421$	2.20155	+	12.4856i	0.107297	+	0.608511i	0.990278	+	0.139103i	$0.0444218\pi$
$421$	2.20155	+	12.4856i	0.107297	+	0.608511i	−0.882981	+	0.469409i	$0.844467\pi$
$422$	7.50535	+	23.7282i	0.365355	+	1.15507i
$423$		0			0
$424$	3.15707	−	24.4998i	0.153321	−	1.18981i
$425$	19.4311	+	23.1571i	0.942548	+	1.12328i
$426$		0			0
$427$	−51.1870	−	9.02565i	−2.47711	−	0.436782i
$428$	9.02795	−	12.9436i	0.436383	−	0.625652i
$429$		0			0
$430$	0.199520	+	0.382419i	0.00962169	+	0.0184419i
$431$	−11.3033			−0.544463			−0.272231	−	0.962232i	$-0.587762\pi$
$431$	−11.3033			−0.544463			−0.272231	+	0.962232i	$0.587762\pi$
$432$		0			0
$433$	18.1058			0.870111			0.435056	−	0.900404i	$-0.356729\pi$
$433$	18.1058			0.870111			0.435056	+	0.900404i	$0.356729\pi$
$434$	15.0836	+	28.9107i	0.724035	+	1.38776i
$435$		0			0
$436$	−2.04288	+	2.92893i	−0.0978363	+	0.140270i
$437$	10.9531	+	1.93133i	0.523960	+	0.0923883i
$438$		0			0
$439$	−8.79038	−	10.4760i	−0.419542	−	0.499991i	0.514333	−	0.857591i	$-0.328040\pi$
$439$	−8.79038	−	10.4760i	−0.419542	−	0.499991i	−0.933875	+	0.357600i	$0.883595\pi$
$440$	0.0529666	−	0.411036i	0.00252508	−	0.0195954i
$441$		0			0
$442$	−4.02797	−	12.7344i	−0.191591	−	0.605716i
$443$	−1.88953	−	10.7160i	−0.0897742	−	0.509135i	−0.996224	−	0.0868210i	$-0.972329\pi$
$443$	−1.88953	−	10.7160i	−0.0897742	−	0.509135i	0.906450	−	0.422314i	$-0.138782\pi$
$444$		0			0
$445$	1.15491	−	0.420352i	0.0547479	−	0.0199266i
$446$	5.00623	−	12.1175i	0.237052	−	0.573778i
$447$		0			0
$448$	−15.9023	−	33.6196i	−0.751315	−	1.58838i
$449$	6.10203	+	3.52301i	0.287973	+	0.166261i	0.637027	−	0.770841i	$-0.280164\pi$
$449$	6.10203	+	3.52301i	0.287973	+	0.166261i	−0.349055	+	0.937102i	$0.613497\pi$
$450$		0			0
$451$	−5.99791	+	3.46289i	−0.282431	+	0.163061i
$452$	−14.9943	+	15.0493i	−0.705274	+	0.707860i
$453$		0			0
$454$	−25.0232	+	19.2374i	−1.17440	+	0.902855i
$455$	−0.772266	−	0.648008i	−0.0362044	−	0.0303791i
$456$		0			0
$457$	−23.9184	−	8.70557i	−1.11885	−	0.407229i	−0.284620	−	0.958641i	$-0.591867\pi$
$457$	−23.9184	−	8.70557i	−1.11885	−	0.407229i	−0.834234	+	0.551411i	$0.814090\pi$
$458$	−27.4826	−	25.1369i	−1.28418	−	1.17457i
$459$		0			0
$460$	−0.703532	+	0.0628485i	−0.0328024	+	0.00293033i
$461$	13.4094	−	36.8420i	0.624538	−	1.71590i	−0.0710586	−	0.997472i	$-0.522638\pi$
$461$	13.4094	−	36.8420i	0.624538	−	1.71590i	0.695597	−	0.718432i	$-0.255140\pi$
$462$		0			0
$463$	4.80801	−	5.72997i	0.223447	−	0.266294i	−0.642661	−	0.766151i	$-0.722170\pi$
$463$	4.80801	−	5.72997i	0.223447	−	0.266294i	0.866108	+	0.499857i	$0.166614\pi$
$464$	2.46134	−	0.00900805i	0.114265	−	0.000418188i
$465$		0			0
$466$	0.453034	−	10.5987i	0.0209864	−	0.490976i
$467$	−0.689932	−	1.19500i	−0.0319262	−	0.0552979i	0.849621	−	0.527394i	$-0.176831\pi$
$467$	−0.689932	−	1.19500i	−0.0319262	−	0.0552979i	−0.881547	+	0.472096i	$0.843498\pi$
$468$		0			0
$469$	13.1189	−	22.7227i	0.605777	−	1.04924i
$470$	1.83818	+	1.16868i	0.0847887	+	0.0539074i
$471$		0			0
$472$	6.91769	−	22.1520i	0.318413	−	1.01963i
$473$	0.786999	+	2.16226i	0.0361862	+	0.0994209i
$474$		0			0
$475$	21.5271	−	3.79580i	0.987729	−	0.174163i
$476$	−51.1885	−	23.7557i	−2.34622	−	1.08884i
$477$		0			0
$478$	−1.04681	+	4.74241i	−0.0478802	+	0.216913i
$479$	−9.74905	+	8.18042i	−0.445445	+	0.373773i	−0.837742	−	0.546066i	$-0.816125\pi$
$479$	−9.74905	+	8.18042i	−0.445445	+	0.373773i	0.392297	+	0.919839i	$0.371681\pi$
$480$		0			0
$481$	0.778139	−	4.41304i	0.0354801	−	0.201217i
$482$	−0.316410	−	2.38650i	−0.0144121	−	0.108702i
$483$		0			0
$484$	−5.08682	+	19.1242i	−0.231219	+	0.869281i
$485$			0.785256i			0.0356566i
$486$		0			0
$487$		−	12.3932i		−	0.561588i	−0.959768	−	0.280794i	$-0.909402\pi$
$487$		−	12.3932i		−	0.561588i	0.959768	−	0.280794i	$-0.0905979\pi$
$488$	26.6241	−	17.0643i	1.20521	−	0.772465i
$489$		0			0
$490$	−2.85485	+	0.378506i	−0.128969	+	0.0170992i
$491$	−4.61221	+	26.1572i	−0.208146	+	1.18046i	0.684265	+	0.729233i	$0.260123\pi$
$491$	−4.61221	+	26.1572i	−0.208146	+	1.18046i	−0.892411	+	0.451223i	$0.850988\pi$
$492$		0			0
$493$	2.86100	−	2.40067i	0.128853	−	0.108121i
$494$	−9.43101	−	2.08175i	−0.424321	−	0.0936625i
$495$		0			0
$496$	−18.6679	−	6.71730i	−0.838214	−	0.301616i
$497$	21.3599	−	3.76634i	0.958125	−	0.168943i
$498$		0			0
$499$	−3.29755	−	9.05994i	−0.147619	−	0.405579i	0.843741	−	0.536750i	$-0.180348\pi$
$499$	−3.29755	−	9.05994i	−0.147619	−	0.405579i	−0.991360	+	0.131172i	$0.958126\pi$
$500$	−2.51904	+	1.18027i	−0.112655	+	0.0527831i
$501$		0			0
$502$	11.8334	−	18.6123i	0.528152	−	0.830709i
$503$	4.28642	−	7.42429i	0.191122	−	0.331033i	−0.754500	−	0.656300i	$-0.772121\pi$
$503$	4.28642	−	7.42429i	0.191122	−	0.331033i	0.945622	+	0.325267i	$0.105454\pi$
$504$		0			0
$505$	−0.728686	−	1.26212i	−0.0324261	−	0.0561637i
$506$	−3.76459	−	0.160915i	−0.167357	−	0.00715354i
$507$		0			0
$508$	0.570698	−	6.66353i	0.0253206	−	0.295646i
$509$	−19.9295	+	23.7511i	−0.883360	+	1.05275i	0.114876	+	0.993380i	$0.463353\pi$
$509$	−19.9295	+	23.7511i	−0.883360	+	1.05275i	−0.998236	+	0.0593674i	$0.981092\pi$
$510$		0			0
$511$	−17.9517	+	49.3219i	−0.794137	+	2.18187i
$512$	20.9756	+	8.48670i	0.926999	+	0.375063i
$513$		0			0
$514$	9.47716	−	10.3615i	0.418020	−	0.457027i
$515$	0.202323	+	0.0736396i	0.00891542	+	0.00324495i
$516$		0			0
$517$	8.90151	+	7.46925i	0.391488	+	0.328497i
$518$	−11.5396	−	15.0103i	−0.507023	−	0.659515i
$519$		0			0
$520$	0.612695	−	0.0284360i	0.0268684	−	0.00124700i
$521$	25.2374	−	14.5708i	1.10567	−	0.638359i	0.167966	−	0.985793i	$-0.446280\pi$
$521$	25.2374	−	14.5708i	1.10567	−	0.638359i	0.937705	+	0.347433i	$0.112947\pi$
$522$		0			0
$523$	−4.50959	−	2.60361i	−0.197190	−	0.113848i	0.398154	−	0.917319i	$-0.369651\pi$
$523$	−4.50959	−	2.60361i	−0.197190	−	0.113848i	−0.595344	+	0.803471i	$0.702984\pi$
$524$	5.06259	−	1.36645i	0.221160	−	0.0596936i
$525$		0			0
$526$	−34.1781	−	14.1204i	−1.49024	−	0.615679i
$527$	−28.2886	+	10.2962i	−1.23227	+	0.448510i
$528$		0			0
$529$	−2.87875	−	16.3262i	−0.125163	−	0.709834i
$530$	1.64115	−	0.519104i	0.0712870	−	0.0225484i
$531$		0			0
$532$	−33.3839	+	23.4668i	−1.44737	+	1.01741i
$533$	−6.58858	−	7.85196i	−0.285383	−	0.340106i
$534$		0			0
$535$	1.08294	+	0.190951i	0.0468194	+	0.00825552i
$536$	3.49790	+	15.5755i	0.151086	+	0.672761i
$537$		0			0
$538$	0.583272	−	0.304311i	0.0251466	−	0.0131198i
$539$	−15.3629			−0.661725
$540$		0			0
$541$	24.3664			1.04759			0.523797	−	0.851843i	$-0.324515\pi$
$541$	24.3664			1.04759			0.523797	+	0.851843i	$0.324515\pi$
$542$	−19.6321	+	10.2427i	−0.843272	+	0.439961i
$543$		0			0
$544$	32.6974	−	10.4742i	1.40189	−	0.449076i
$545$	−0.245051	−	0.0432091i	−0.0104968	−	0.00185088i
$546$		0			0
$547$	22.9927	+	27.4016i	0.983097	+	1.17161i	0.985165	+	0.171611i	$0.0548974\pi$
$547$	22.9927	+	27.4016i	0.983097	+	1.17161i	−0.00206780	+	0.999998i	$0.500658\pi$
$548$	−10.2534	−	14.5865i	−0.438004	−	0.623105i
$549$		0			0
$550$	−7.06081	+	2.23337i	−0.301074	+	0.0952311i
$551$	−0.468962	−	2.65961i	−0.0199784	−	0.113303i
$552$		0			0
$553$	−7.31560	+	2.66266i	−0.311091	+	0.113228i
$554$	12.8900	+	5.32539i	0.547643	+	0.226254i
$555$		0			0
$556$	7.82042	+	28.9740i	0.331660	+	1.22877i
$557$	−10.4040	−	6.00674i	−0.440831	−	0.254514i	0.263119	−	0.964763i	$-0.415249\pi$
$557$	−10.4040	−	6.00674i	−0.440831	−	0.254514i	−0.703950	+	0.710250i	$0.748582\pi$
$558$		0			0
$559$	−2.94922	+	1.70274i	−0.124739	+	0.0720180i
$560$	1.65851	−	1.99129i	0.0700849	−	0.0841475i
$561$		0			0
$562$	14.7086	+	19.1323i	0.620443	+	0.807047i
$563$	−3.65854	−	3.06988i	−0.154189	−	0.129380i	0.562430	−	0.826845i	$-0.309867\pi$
$563$	−3.65854	−	3.06988i	−0.154189	−	0.129380i	−0.716619	+	0.697465i	$0.754311\pi$
$564$		0			0
$565$	−1.39104	−	0.506297i	−0.0585215	−	0.0213001i
$566$	−9.05857	+	9.90387i	−0.380760	+	0.416291i
$567$		0			0
$568$	−8.00454	+	10.4912i	−0.335863	+	0.440202i
$569$	−2.71384	+	7.45620i	−0.113770	+	0.312580i	−0.983489	−	0.180966i	$-0.942078\pi$
$569$	−2.71384	+	7.45620i	−0.113770	+	0.312580i	0.869719	+	0.493547i	$0.164300\pi$
$570$		0			0
$571$	−10.4105	+	12.4067i	−0.435666	+	0.519206i	−0.938548	−	0.345149i	$-0.887828\pi$
$571$	−10.4105	+	12.4067i	−0.435666	+	0.519206i	0.502882	+	0.864355i	$0.332273\pi$
$572$	3.26008	+	0.279210i	0.136311	+	0.0116744i
$573$		0			0
$574$	−43.2682	−	1.84947i	−1.80598	−	0.0771953i
$575$	6.31079	+	10.9306i	0.263178	+	0.455838i
$576$		0			0
$577$	−8.09164	+	14.0151i	−0.336859	+	0.583458i	−0.983840	−	0.179049i	$-0.942698\pi$
$577$	−8.09164	+	14.0151i	−0.336859	+	0.583458i	0.646981	+	0.762506i	$0.276031\pi$
$578$	15.0527	−	23.6758i	0.626110	−	0.984783i
$579$		0			0
$580$	0.0727676	+	0.155308i	0.00302151	+	0.00644882i
$581$	3.73187	+	10.2532i	0.154824	+	0.425375i
$582$		0			0
$583$	9.04295	−	1.59452i	0.374521	−	0.0660381i
$584$	−12.3015	−	29.4695i	−0.509041	−	1.21946i
$585$		0			0
$586$	3.13231	+	0.691410i	0.129394	+	0.0285619i
$587$	−19.9180	+	16.7132i	−0.822103	+	0.689826i	−0.953464	−	0.301508i	$-0.902510\pi$
$587$	−19.9180	+	16.7132i	−0.822103	+	0.689826i	0.131361	+	0.991335i	$0.458065\pi$
$588$		0			0
$589$	−3.78006	+	21.4378i	−0.155755	+	0.883328i
$590$	1.60306	−	0.212540i	0.0659971	−	0.00875012i
$591$		0			0
$592$	11.3515	+	1.95878i	0.466546	+	0.0805052i
$593$			7.68968i			0.315778i	0.987457	+	0.157889i	$0.0504687\pi$
$593$			7.68968i			0.315778i	−0.987457	+	0.157889i	$0.949531\pi$
$594$		0			0
$595$		−	3.93227i		−	0.161207i
$596$	34.9955	+	9.30840i	1.43347	+	0.381287i
$597$		0			0
$598$	−0.732950	−	5.52822i	−0.0299726	−	0.226066i
$599$	−5.26567	+	29.8631i	−0.215150	+	1.22017i	0.665497	+	0.746400i	$0.268220\pi$
$599$	−5.26567	+	29.8631i	−0.215150	+	1.22017i	−0.880647	+	0.473773i	$0.842892\pi$
$600$		0			0
$601$	14.0780	−	11.8129i	0.574254	−	0.481857i	−0.308800	−	0.951127i	$-0.599927\pi$
$601$	14.0780	−	11.8129i	0.574254	−	0.481857i	0.883055	+	0.469270i	$0.155483\pi$
$602$	−3.10141	+	14.0504i	−0.126404	+	0.572650i
$603$		0			0
$604$	12.2939	−	26.4908i	0.500231	−	1.07789i
$605$	−1.35798	+	0.239449i	−0.0552099	+	0.00973499i
$606$		0			0
$607$	1.94501	+	5.34387i	0.0789455	+	0.216901i	0.972886	−	0.231284i	$-0.0742927\pi$
$607$	1.94501	+	5.34387i	0.0789455	+	0.216901i	−0.893941	+	0.448185i	$0.852070\pi$
$608$	5.26265	−	24.2631i	0.213429	−	0.983997i
$609$		0			0
$610$	1.85954	+	1.18227i	0.0752904	+	0.0478685i
$611$	−8.59873	+	14.8934i	−0.347867	+	0.602524i
$612$		0			0
$613$	−4.98728	−	8.63823i	−0.201434	−	0.348895i	0.747556	−	0.664198i	$-0.231227\pi$
$613$	−4.98728	−	8.63823i	−0.201434	−	0.348895i	−0.948991	+	0.315304i	$0.897894\pi$
$614$	−0.733308	+	17.1557i	−0.0295939	+	0.692348i
$615$		0			0
$616$	10.1670	−	9.36780i	0.409640	−	0.377439i
$617$	−12.6243	+	15.0451i	−0.508236	+	0.605692i	−0.957757	−	0.287577i	$-0.907150\pi$
$617$	−12.6243	+	15.0451i	−0.508236	+	0.605692i	0.449521	+	0.893270i	$0.351595\pi$
$618$		0			0
$619$	11.9916	−	32.9466i	0.481983	−	1.32424i	−0.425808	−	0.904814i	$-0.640010\pi$
$619$	11.9916	−	32.9466i	0.481983	−	1.32424i	0.907791	−	0.419423i	$-0.137768\pi$
$620$	−0.123009	−	1.37697i	−0.00494015	−	0.0553005i
$621$		0			0
$622$	18.1295	+	16.5821i	0.726926	+	0.664882i
$623$	38.5254	+	14.0221i	1.54349	+	0.561784i
$624$		0			0
$625$	18.9282	+	15.8827i	0.757129	+	0.635307i
$626$	18.2466	−	14.0276i	0.729280	−	0.560657i
$627$		0			0
$628$	0.194156	+	0.193447i	0.00774768	+	0.00771938i
$629$	15.1373	−	8.73951i	0.603563	−	0.348467i
$630$		0			0
$631$	20.6478	+	11.9210i	0.821976	+	0.474568i	0.851097	−	0.525008i	$-0.175938\pi$
$631$	20.6478	+	11.9210i	0.821976	+	0.474568i	−0.0291214	+	0.999576i	$0.509271\pi$
$632$	2.17556	−	4.20736i	0.0865390	−	0.167360i
$633$		0			0
$634$	−15.7348	+	38.0856i	−0.624907	+	1.51257i
$635$	0.437918	−	0.159389i	0.0173783	−	0.00632517i
$636$		0			0
$637$	−3.94818	−	22.3913i	−0.156433	−	0.887174i
$638$	0.275927	+	0.872345i	0.0109241	+	0.0345365i
$639$		0			0
$640$	0.0788622	+	1.57473i	0.00311730	+	0.0622468i
$641$	−11.9138	−	14.1983i	−0.470568	−	0.560801i	0.477598	−	0.878579i	$-0.341508\pi$
$641$	−11.9138	−	14.1983i	−0.470568	−	0.560801i	−0.948165	+	0.317778i	$0.897063\pi$
$642$		0			0
$643$	35.2470	+	6.21500i	1.39001	+	0.245096i	0.818031	−	0.575175i	$-0.195066\pi$
$643$	35.2470	+	6.21500i	1.39001	+	0.245096i	0.571976	+	0.820270i	$0.306177\pi$
$644$	−19.3255	−	13.4792i	−0.761531	−	0.531155i
$645$		0			0
$646$	−17.4256	−	33.3996i	−0.685600	−	1.31409i
$647$	31.4863			1.23785			0.618926	−	0.785449i	$-0.287568\pi$
$647$	31.4863			1.23785			0.618926	+	0.785449i	$0.287568\pi$
$648$		0			0
$649$	8.62659			0.338623
$650$	−5.06971	−	9.71711i	−0.198850	−	0.381136i
$651$		0			0
$652$	−19.7192	−	13.7538i	−0.772263	−	0.538641i
$653$	26.5025	+	4.67310i	1.03712	+	0.182873i	0.666186	−	0.745786i	$-0.267926\pi$
$653$	26.5025	+	4.67310i	1.03712	+	0.182873i	0.370936	+	0.928658i	$0.379037\pi$
$654$		0			0
$655$	0.234869	+	0.279906i	0.00917709	+	0.0109368i
$656$	20.1224	−	17.0106i	0.785647	−	0.664151i
$657$		0			0
$658$	21.9132	+	69.2787i	0.854265	+	2.70076i
$659$	−7.78431	−	44.1470i	−0.303234	−	1.71972i	−0.631705	−	0.775209i	$-0.717645\pi$
$659$	−7.78431	−	44.1470i	−0.303234	−	1.71972i	0.328471	−	0.944514i	$-0.393467\pi$
$660$		0			0
$661$	19.0048	−	6.91718i	0.739201	−	0.269047i	0.0551465	−	0.998478i	$-0.482437\pi$
$661$	19.0048	−	6.91718i	0.739201	−	0.269047i	0.684054	+	0.729431i	$0.260215\pi$
$662$	−1.47718	+	3.57548i	−0.0574123	+	0.138965i
$663$		0			0
$664$	−5.89685	−	3.04916i	−0.228842	−	0.118331i
$665$	−2.46250	−	1.42173i	−0.0954917	−	0.0551322i
$666$		0			0
$667$	1.35045	−	0.779683i	0.0522896	−	0.0301894i
$668$	−15.9417	−	15.8835i	−0.616803	−	0.614549i
$669$		0			0
$670$	−0.881871	+	0.677966i	−0.0340696	+	0.0261921i
$671$	9.00495	+	7.55605i	0.347632	+	0.291698i
$672$		0			0
$673$	40.4201	+	14.7117i	1.55808	+	0.567094i	0.970295	−	0.241924i	$-0.0777784\pi$
$673$	40.4201	+	14.7117i	1.55808	+	0.567094i	0.587784	+	0.809018i	$0.300001\pi$
$674$	7.19720	+	6.58291i	0.277226	+	0.253564i
$675$		0			0
$676$	−1.88256	−	21.0736i	−0.0724062	−	0.810522i
$677$	−6.79083	+	18.6577i	−0.260993	+	0.717072i	0.738108	+	0.674682i	$0.235719\pi$
$677$	−6.79083	+	18.6577i	−0.260993	+	0.717072i	−0.999101	+	0.0423898i	$0.986503\pi$
$678$		0			0
$679$	−16.8376	+	20.0662i	−0.646166	+	0.770071i
$680$	1.62115	+	1.75945i	0.0621681	+	0.0674719i
$681$		0			0
$682$	0.314947	−	7.36816i	0.0120599	−	0.282141i
$683$	16.6637	+	28.8624i	0.637618	+	1.10439i	0.985954	+	0.167017i	$0.0534136\pi$
$683$	16.6637	+	28.8624i	0.637618	+	1.10439i	−0.348336	+	0.937370i	$0.613253\pi$
$684$		0			0
$685$	0.621199	−	1.07595i	0.0237348	−	0.0411098i
$686$	−42.2315	−	26.8501i	−1.61241	−	1.02514i
$687$		0			0
$688$	−4.40482	−	7.56529i	−0.167932	−	0.288424i
$689$	4.64799	+	12.7703i	0.177074	+	0.486508i
$690$		0			0
$691$	−1.92394	+	0.339243i	−0.0731902	+	0.0129054i	−0.210123	−	0.977675i	$-0.567387\pi$
$691$	−1.92394	+	0.339243i	−0.0731902	+	0.0129054i	0.136933	+	0.990580i	$0.456275\pi$
$692$	4.80141	−	10.3460i	0.182522	−	0.393297i
$693$		0			0
$694$	6.98234	−	31.6322i	0.265046	−	1.20074i
$695$	−1.60195	+	1.34420i	−0.0607654	+	0.0509882i
$696$		0			0
$697$	6.94264	−	39.3737i	0.262971	−	1.49138i
$698$	5.04236	+	38.0316i	0.190856	+	1.43952i
$699$		0			0
$700$	−44.7520	−	11.9035i	−1.69147	−	0.449911i
$701$			15.9132i			0.601032i	0.953777	+	0.300516i	$0.0971588\pi$
$701$			15.9132i			0.601032i	−0.953777	+	0.300516i	$0.902841\pi$
$702$		0			0
$703$		−	12.6392i		−	0.476697i
$704$	−0.687070	+	8.38304i	−0.0258949	+	0.315948i
$705$		0			0
$706$	−9.44288	+	1.25197i	−0.355388	+	0.0471185i
$707$	8.44192	−	47.8765i	0.317491	−	1.80058i
$708$		0			0
$709$	−25.2965	+	21.2262i	−0.950028	+	0.797169i	−0.979302	−	0.202403i	$-0.935125\pi$
$709$	−25.2965	+	21.2262i	−0.950028	+	0.797169i	0.0292739	+	0.999571i	$0.490681\pi$
$710$	−0.897910	−	0.198200i	−0.0336980	−	0.00743832i
$711$		0			0
$712$	−23.0187	+	9.60875i	−0.862661	+	0.360103i
$713$	−12.3783	+	2.18262i	−0.463570	+	0.0817399i
$714$		0			0
$715$	0.0779800	+	0.214248i	0.00291629	+	0.00801244i
$716$	−10.5252	−	22.4640i	−0.393346	−	0.839518i
$717$		0			0
$718$	−21.7923	+	34.2763i	−0.813283	+	1.27918i
$719$	−4.06158	+	7.03487i	−0.151471	+	0.262356i	−0.931769	−	0.363053i	$-0.881734\pi$
$719$	−4.06158	+	7.03487i	−0.151471	+	0.262356i	0.780297	+	0.625409i	$0.215068\pi$
$720$		0			0
$721$	3.59112	+	6.22000i	0.133740	+	0.231645i
$722$	−0.370521	−	0.0158376i	−0.0137893	−	0.000589416i
$723$		0			0
$724$	−2.32000	−	0.198696i	−0.0862219	−	0.00738448i
$725$	1.96998	−	2.34773i	0.0731631	−	0.0871924i
$726$		0			0
$727$	12.8952	−	35.4294i	0.478258	−	1.31400i	−0.432713	−	0.901532i	$-0.642444\pi$
$727$	12.8952	−	35.4294i	0.478258	−	1.31400i	0.910971	−	0.412470i	$-0.135334\pi$
$728$	16.2664	+	12.4108i	0.602872	+	0.459976i
$729$		0			0
$730$	1.50182	−	1.64196i	0.0555849	−	0.0607718i
$731$	−12.4823	−	4.54317i	−0.461673	−	0.168035i
$732$		0			0
$733$	−22.3955	−	18.7921i	−0.827198	−	0.694101i	0.127448	−	0.991845i	$-0.459321\pi$
$733$	−22.3955	−	18.7921i	−0.827198	−	0.694101i	−0.954646	+	0.297744i	$0.903766\pi$
$734$	3.36650	+	4.37901i	0.124260	+	0.161632i
$735$		0			0
$736$	14.2040	−	1.93614i	0.523567	−	0.0713671i
$737$	−5.13900	+	2.96700i	−0.189298	+	0.109291i
$738$		0			0
$739$	34.0829	+	19.6778i	1.25376	+	0.723858i	0.971854	−	0.235584i	$-0.0757002\pi$
$739$	34.0829	+	19.6778i	1.25376	+	0.723858i	0.281905	+	0.959442i	$0.409034\pi$
$740$	0.209167	+	0.774948i	0.00768914	+	0.0284876i
$741$		0			0
$742$	53.0682	+	21.9247i	1.94820	+	0.804881i
$743$	−10.4717	+	3.81140i	−0.384171	+	0.139827i	−0.526884	−	0.849937i	$-0.676640\pi$
$743$	−10.4717	+	3.81140i	−0.384171	+	0.139827i	0.142713	+	0.989764i	$0.454417\pi$
$744$		0			0
$745$	0.438169	+	2.48498i	0.0160533	+	0.0910427i
$746$	14.7044	−	4.65109i	0.538368	−	0.170288i
$747$		0			0
$748$	7.33956	+	10.4413i	0.268361	+	0.381770i
$749$	23.5787	+	28.0999i	0.861545	+	1.02675i
$750$		0			0
$751$	28.7902	+	5.07650i	1.05057	+	0.185244i	0.672169	−	0.740397i	$-0.265363\pi$
$751$	28.7902	+	5.07650i	1.05057	+	0.185244i	0.378402	+	0.925641i	$0.376474\pi$
$752$	−38.3662	−	21.9639i	−1.39907	−	0.800941i
$753$		0			0
$754$	−1.20052	+	0.626350i	−0.0437205	+	0.0228103i
$755$	2.03500			0.0740613
$756$		0			0
$757$	−8.57552			−0.311682			−0.155841	−	0.987782i	$-0.549809\pi$
$757$	−8.57552			−0.311682			−0.155841	+	0.987782i	$0.549809\pi$
$758$	7.46356	−	3.89397i	0.271089	−	0.141435i
$759$		0			0
$760$	1.68795	−	0.379074i	0.0612284	−	0.0137504i
$761$	5.54033	+	0.976910i	0.200837	+	0.0354130i	0.273161	−	0.961968i	$-0.411931\pi$
$761$	5.54033	+	0.976910i	0.200837	+	0.0354130i	−0.0723247	+	0.997381i	$0.523042\pi$
$762$		0			0
$763$	−5.33548	−	6.35857i	−0.193157	−	0.230196i
$764$	23.5344	−	16.5432i	0.851446	−	0.598514i
$765$		0			0
$766$	−9.00163	+	2.84726i	−0.325242	+	0.102876i
$767$	2.21699	+	12.5732i	0.0800509	+	0.453991i
$768$		0			0
$769$	−2.35854	+	0.858439i	−0.0850512	+	0.0309561i	−0.384195	−	0.923252i	$-0.625521\pi$
$769$	−2.35854	+	0.858439i	−0.0850512	+	0.0309561i	0.299144	+	0.954208i	$0.403299\pi$
$770$	0.890333	+	0.367834i	0.0320854	+	0.0132558i
$771$		0			0
$772$	35.5193	−	9.58707i	1.27837	−	0.345046i
$773$	−0.0355587	−	0.0205298i	−0.00127896	−	0.000738407i	0.499360	−	0.866394i	$-0.333568\pi$
$773$	−0.0355587	−	0.0205298i	−0.00127896	−	0.000738407i	−0.500639	+	0.865656i	$0.666902\pi$
$774$		0			0
$775$	−21.3937	+	12.3516i	−0.768483	+	0.443684i
$776$	−0.738869	−	15.9200i	−0.0265238	−	0.571494i
$777$		0			0
$778$	−26.2716	−	34.1731i	−0.941883	−	1.22516i
$779$	−22.1468	−	18.5834i	−0.793492	−	0.665819i
$780$		0			0
$781$	−4.60950	−	1.67772i	−0.164941	−	0.0600335i
$782$	14.6808	−	16.0507i	0.524983	−	0.573972i
$783$		0			0
$784$	57.5221	−	10.3599i	2.05436	−	0.369997i
$785$	−0.00653192	+	0.0179463i	−0.000233134	+	0.000640531i
$786$		0			0
$787$	27.9726	−	33.3365i	0.997116	−	1.18832i	0.0150289	−	0.999887i	$-0.495216\pi$
$787$	27.9726	−	33.3365i	0.997116	−	1.18832i	0.982087	−	0.188429i	$-0.0603396\pi$
$788$	−3.61561	+	42.2163i	−0.128801	+	1.50389i
$789$		0			0
$790$	0.329748	+	0.0140948i	0.0117319	+	0.000501472i
$791$	−24.6902	−	42.7647i	−0.877882	−	1.52054i
$792$		0			0
$793$	−8.69865	+	15.0665i	−0.308898	+	0.535028i
$794$	11.9526	−	18.7997i	0.424181	−	0.667177i
$795$		0			0
$796$	12.1451	−	5.69045i	0.430473	−	0.201693i
$797$	−15.3705	−	42.2300i	−0.544450	−	1.49586i	−0.841102	−	0.540877i	$-0.818092\pi$
$797$	−15.3705	−	42.2300i	−0.544450	−	1.49586i	0.296652	−	0.954986i	$-0.404130\pi$
$798$		0			0
$799$	−66.0612	+	11.6484i	−2.33708	+	0.412090i
$800$	24.9312	−	13.1237i	0.881452	−	0.463992i
$801$		0			0
$802$	−4.27963	−	0.944665i	−0.151119	−	0.0333573i
$803$	9.09342	−	7.63028i	0.320900	−	0.269267i
$804$		0			0
$805$	0.285100	−	1.61688i	0.0100484	−	0.0569875i
$806$	10.8200	−	1.43455i	0.381117	−	0.0505298i
$807$		0			0
$808$	15.9607	+	24.9022i	0.561495	+	0.876055i
$809$		−	39.4534i		−	1.38711i	−0.720405	−	0.693553i	$-0.756044\pi$
$809$		−	39.4534i		−	1.38711i	0.720405	−	0.693553i	$-0.243956\pi$
$810$		0			0
$811$			49.4348i			1.73589i	0.496659	+	0.867946i	$0.334560\pi$
$811$			49.4348i			1.73589i	−0.496659	+	0.867946i	$0.665440\pi$
$812$	−1.47065	+	5.52900i	−0.0516097	+	0.194030i
$813$		0			0
$814$	0.562798	+	4.24486i	0.0197260	+	0.148782i
$815$	0.290908	−	1.64982i	0.0101900	−	0.0577906i
$816$		0			0
$817$	−7.35807	+	6.17416i	−0.257426	+	0.216006i
$818$	−8.00291	+	36.2557i	−0.279815	+	1.26765i
$819$		0			0
$820$	1.66543	+	0.772894i	0.0581592	+	0.0269906i
$821$	−21.7656	+	3.83786i	−0.759624	+	0.133942i	−0.540026	−	0.841648i	$-0.681586\pi$
$821$	−21.7656	+	3.83786i	−0.759624	+	0.133942i	−0.219598	+	0.975590i	$0.570475\pi$
$822$		0			0
$823$	6.69131	+	18.3842i	0.233244	+	0.640833i	0.999999	−	0.00110635i	$-0.000352162\pi$
$823$	6.69131	+	18.3842i	0.233244	+	0.640833i	−0.766755	+	0.641940i	$0.778130\pi$
$824$	−4.17112	−	1.30257i	−0.145308	−	0.0453772i
$825$		0			0
$826$	45.5216	+	28.9419i	1.58390	+	1.00702i
$827$	8.39197	−	14.5353i	0.291817	−	0.505442i	−0.682422	−	0.730958i	$-0.739073\pi$
$827$	8.39197	−	14.5353i	0.291817	−	0.505442i	0.974239	+	0.225516i	$0.0724068\pi$
$828$		0			0
$829$	−18.8116	−	32.5827i	−0.653355	−	1.13164i	−0.982304	−	0.187296i	$-0.940028\pi$
$829$	−18.8116	−	32.5827i	−0.653355	−	1.13164i	0.328949	−	0.944348i	$-0.393306\pi$
$830$	0.0197547	−	0.462160i	0.000685696	−	0.0160418i
$831$		0			0
$832$	−12.3948	+	1.15300i	−0.429712	+	0.0399732i
$833$	57.0065	−	67.9377i	1.97516	−	2.35390i
$834$		0			0
$835$	0.536320	−	1.47353i	0.0185601	−	0.0509935i
$836$	9.19227	−	0.821172i	0.317921	−	0.0284008i
$837$		0			0
$838$	−37.7429	−	34.5215i	−1.30381	−	1.19253i
$839$	51.7302	+	18.8283i	1.78592	+	0.650024i	0.999476	+	0.0323683i	$0.0103049\pi$
$839$	51.7302	+	18.8283i	1.78592	+	0.650024i	0.786449	+	0.617655i	$0.211917\pi$
$840$		0			0
$841$	21.9252	+	18.3975i	0.756043	+	0.634395i
$842$	14.2146	−	10.9279i	0.489868	−	0.376601i
$843$		0			0
$844$	24.8413	−	24.9324i	0.855073	−	0.858209i
$845$	1.27676	−	0.737140i	0.0439220	−	0.0253584i
$846$		0			0
$847$	−39.8358	−	22.9992i	−1.36878	−	0.790263i
$848$	−32.7836	+	12.0683i	−1.12580	+	0.414428i
$849$		0			0
$850$	16.3239	−	39.5116i	0.559906	−	1.35524i
$851$	6.85782	−	2.49604i	0.235083	−	0.0855633i
$852$		0			0
$853$	1.97889	+	11.2229i	0.0677560	+	0.384263i	0.999762	+	0.0218204i	$0.00694619\pi$
$853$	1.97889	+	11.2229i	0.0677560	+	0.384263i	−0.932006	+	0.362443i	$0.881943\pi$
$854$	22.1678	+	70.0837i	0.758568	+	2.39822i
$855$		0			0
$856$	−22.1347	−	2.85230i	−0.756549	−	0.0974897i
$857$	−17.0466	−	20.3153i	−0.582300	−	0.693958i	0.391807	−	0.920048i	$-0.371850\pi$
$857$	−17.0466	−	20.3153i	−0.582300	−	0.693958i	−0.974106	+	0.226090i	$0.927406\pi$
$858$		0			0
$859$	7.71712	+	1.36074i	0.263305	+	0.0464277i	0.303742	−	0.952754i	$-0.401764\pi$
$859$	7.71712	+	1.36074i	0.263305	+	0.0464277i	−0.0404372	+	0.999182i	$0.512875\pi$
$860$	0.348969	−	0.500326i	0.0118997	−	0.0170610i
$861$		0			0
$862$	7.39417	+	14.1724i	0.251847	+	0.482714i
$863$	−32.9090			−1.12023			−0.560117	−	0.828413i	$-0.689244\pi$
$863$	−32.9090			−1.12023			−0.560117	+	0.828413i	$0.689244\pi$
$864$		0			0
$865$	0.794776			0.0270232
$866$	−11.8441	−	22.7016i	−0.402479	−	0.771430i
$867$		0			0
$868$	26.3819	−	37.8243i	0.895459	−	1.28384i
$869$	1.73394	+	0.305741i	0.0588199	+	0.0103715i
$870$		0			0
$871$	−5.64508	−	6.72755i	−0.191276	−	0.227954i
$872$	5.00874	+	0.645431i	0.169617	+	0.0218571i
$873$		0			0
$874$	−4.74354	−	14.9967i	−0.160453	−	0.507272i
$875$	−1.12284	−	6.36795i	−0.0379590	−	0.215276i
$876$		0			0
$877$	−37.2032	+	13.5408i	−1.25626	+	0.457242i	−0.882513	−	0.470288i	$-0.844150\pi$
$877$	−37.2032	+	13.5408i	−1.25626	+	0.457242i	−0.373748	+	0.927530i	$0.621928\pi$
$878$	−7.38472	+	17.8745i	−0.249222	+	0.603237i
$879$		0			0
$880$	−0.550016	+	0.202472i	−0.0185410	+	0.00682534i
$881$	20.1797	+	11.6507i	0.679870	+	0.392523i	0.799806	−	0.600259i	$-0.204936\pi$
$881$	20.1797	+	11.6507i	0.679870	+	0.392523i	−0.119936	+	0.992782i	$0.538269\pi$
$882$		0			0
$883$	−44.2753	+	25.5624i	−1.48998	+	0.860242i	−0.999934	−	0.0114524i	$-0.996355\pi$
$883$	−44.2753	+	25.5624i	−1.48998	+	0.860242i	−0.490049	+	0.871695i	$0.663021\pi$
$884$	−13.3318	+	13.3807i	−0.448398	+	0.450042i
$885$		0			0
$886$	−12.2000	+	9.37913i	−0.409867	+	0.315098i
$887$	5.23482	+	4.39254i	0.175768	+	0.147487i	0.726428	−	0.687243i	$-0.241179\pi$
$887$	5.23482	+	4.39254i	0.175768	+	0.147487i	−0.550659	+	0.834730i	$0.685624\pi$
$888$		0			0
$889$	14.6081	+	5.31691i	0.489940	+	0.178324i
$890$	−1.28254	−	1.17307i	−0.0429908	−	0.0393215i
$891$		0			0
$892$	−18.4680	+	1.64980i	−0.618356	+	0.0552395i
$893$	−16.5901	+	45.5809i	−0.555167	+	1.52531i
$894$		0			0
$895$	1.11113	−	1.32420i	0.0371411	−	0.0442630i
$896$	−31.7504	+	41.9313i	−1.06071	+	1.40083i
$897$		0			0
$898$	0.425540	−	9.95549i	0.0142005	−	0.332219i
$899$	1.52601	+	2.64313i	0.0508954	+	0.0881535i
$900$		0			0
$901$	−26.5042	+	45.9065i	−0.882981	+	1.52937i
$902$	8.26545	+	5.25505i	0.275209	+	0.174974i
$903$		0			0
$904$	28.6779	+	8.95563i	0.953811	+	0.297860i
$905$	−0.0554934	−	0.152467i	−0.00184466	−	0.00506817i
$906$		0			0
$907$	7.37773	−	1.30089i	0.244974	−	0.0431955i	−0.0498130	−	0.998759i	$-0.515863\pi$
$907$	7.37773	−	1.30089i	0.244974	−	0.0431955i	0.294787	+	0.955563i	$0.404751\pi$
$908$	40.4894	+	18.7904i	1.34369	+	0.623582i
$909$		0			0
$910$	−0.307304	+	1.39219i	−0.0101870	+	0.0461505i
$911$	−19.8453	+	16.6521i	−0.657503	+	0.551710i	−0.909337	−	0.416060i	$-0.863411\pi$
$911$	−19.8453	+	16.6521i	−0.657503	+	0.551710i	0.251835	+	0.967770i	$0.418966\pi$
$912$		0			0
$913$	0.428513	−	2.43022i	0.0141817	−	0.0804284i
$914$	4.73114	+	35.6842i	0.156492	+	1.18033i
$915$		0			0
$916$	−13.5393	+	50.9019i	−0.447352	+	1.68185i
$917$			12.1887i			0.402508i
$918$		0			0
$919$		−	37.4197i		−	1.23436i	−0.786821	−	0.617182i	$-0.788274\pi$
$919$		−	37.4197i		−	1.23436i	0.786821	−	0.617182i	$-0.211726\pi$
$920$	0.539023	+	0.840993i	0.0177710	+	0.0277267i
$921$		0			0
$922$	−54.9653	+	7.28749i	−1.81019	+	0.240001i
$923$	1.26065	−	7.14947i	0.0414946	−	0.235328i
$924$		0			0
$925$	10.9875	−	9.21963i	0.361268	−	0.303140i
$926$	−10.3296	−	2.28010i	−0.339451	−	0.0749287i
$927$		0			0
$928$	−1.62140	−	3.08019i	−0.0532250	−	0.101112i
$929$	12.0979	−	2.13318i	0.396919	−	0.0699875i	0.0283738	−	0.999597i	$-0.490967\pi$
$929$	12.0979	−	2.13318i	0.396919	−	0.0699875i	0.368545	+	0.929610i	$0.379856\pi$
$930$		0			0
$931$	−21.9337	−	60.2623i	−0.718848	−	1.97502i
$932$	−13.5853	+	6.36521i	−0.445001	+	0.208500i
$933$		0			0
$934$	−1.04699	+	1.64677i	−0.0342586	+	0.0538840i
$935$	−0.444664	+	0.770181i	−0.0145421	+	0.0251876i
$936$		0			0
$937$	−20.8028	−	36.0316i	−0.679599	−	1.17710i	−0.975102	−	0.221758i	$-0.928821\pi$
$937$	−20.8028	−	36.0316i	−0.679599	−	1.17710i	0.295503	−	0.955342i	$-0.404513\pi$
$938$	−37.0721	−	1.58462i	−1.21045	−	0.0517397i
$939$		0			0
$940$	0.262867	−	3.06926i	0.00857376	−	0.100108i
$941$	−33.5803	+	40.0194i	−1.09469	+	1.30460i	−0.145682	+	0.989331i	$0.546538\pi$
$941$	−33.5803	+	40.0194i	−1.09469	+	1.30460i	−0.949004	+	0.315265i	$0.897907\pi$
$942$		0			0
$943$	5.70939	−	15.6864i	0.185923	−	0.510820i
$944$	−32.2999	+	5.81732i	−1.05127	+	0.189338i
$945$		0			0
$946$	2.19627	−	2.40122i	0.0714070	−	0.0780704i
$947$	−16.5986	−	6.04138i	−0.539380	−	0.196318i	0.0579415	−	0.998320i	$-0.481546\pi$
$947$	−16.5986	−	6.04138i	−0.539380	−	0.196318i	−0.597322	+	0.802002i	$0.703769\pi$
$948$		0			0
$949$	13.4580	+	11.2926i	0.436867	+	0.366575i
$950$	−18.8414	−	24.5081i	−0.611295	−	0.795148i
$951$		0			0
$952$	3.69998	+	79.7214i	0.119917	+	2.58378i
$953$	−47.6750	+	27.5252i	−1.54435	+	0.891628i	−0.545788	+	0.837923i	$0.683770\pi$
$953$	−47.6750	+	27.5252i	−1.54435	+	0.891628i	−0.998557	+	0.0537052i	$0.982897\pi$
$954$		0			0
$955$	1.73597	+	1.00227i	0.0561748	+	0.0324325i
$956$	6.63093	−	1.78976i	0.214460	−	0.0578851i
$957$		0			0
$958$	16.6342	+	6.87230i	0.537428	+	0.222034i
$959$	38.9446	−	14.1747i	1.25759	−	0.457724i
$960$		0			0
$961$	1.11121	+	6.30196i	0.0358453	+	0.203289i
$962$	−6.04221	+	1.91118i	−0.194809	+	0.0616189i
$963$		0			0
$964$	−2.78527	+	1.95787i	−0.0897075	+	0.0630588i
$965$	1.64785	+	1.96383i	0.0530462	+	0.0632180i
$966$		0			0
$967$	16.5590	+	2.91980i	0.532502	+	0.0938945i	0.433433	−	0.901186i	$-0.357302\pi$
$967$	16.5590	+	2.91980i	0.532502	+	0.0938945i	0.0990696	+	0.995081i	$0.468413\pi$
$968$	27.3060	−	6.13227i	0.877647	−	0.197099i
$969$		0			0
$970$	0.984573	−	0.513682i	0.0316127	−	0.0164933i
$971$	−22.4986			−0.722013			−0.361007	−	0.932563i	$-0.617567\pi$
$971$	−22.4986			−0.722013			−0.361007	+	0.932563i	$0.617567\pi$
$972$		0			0
$973$	−69.7582			−2.23635
$974$	−15.5389	+	8.10710i	−0.497898	+	0.259768i
$975$		0			0
$976$	−38.8120	−	22.2191i	−1.24234	−	0.711217i
$977$	−8.62912	−	1.52155i	−0.276070	−	0.0486786i	0.0338989	−	0.999425i	$-0.489208\pi$
$977$	−8.62912	−	1.52155i	−0.276070	−	0.0486786i	−0.309969	+	0.950747i	$0.600319\pi$
$978$		0			0
$979$	−5.96003	−	7.10288i	−0.190483	−	0.227009i
$980$	2.34211	+	3.33188i	0.0748158	+	0.106433i
$981$		0			0
$982$	35.8136	−	11.3280i	1.14286	−	0.361492i
$983$	−1.90169	−	10.7850i	−0.0606544	−	0.343988i	−0.999999	−	0.00101465i	$-0.999677\pi$
$983$	−1.90169	−	10.7850i	−0.0606544	−	0.343988i	0.939345	−	0.342973i	$-0.111434\pi$
$984$		0			0
$985$	−2.77440	+	1.00980i	−0.0883996	+	0.0321748i
$986$	−4.88157	−	2.01678i	−0.155461	−	0.0642274i
$987$		0			0
$988$	3.55922	+	13.1866i	0.113234	+	0.419522i
$989$	−4.80310	−	2.77307i	−0.152730	−	0.0881785i
$990$		0			0
$991$	31.9842	−	18.4661i	1.01601	−	0.586594i	0.103065	−	0.994675i	$-0.467135\pi$
$991$	31.9842	−	18.4661i	1.01601	−	0.586594i	0.912946	+	0.408081i	$0.133802\pi$
$992$	3.78947	+	27.8005i	0.120316	+	0.882666i
$993$		0			0
$994$	−18.6951	−	24.3179i	−0.592973	−	0.771315i
$995$	0.715926	+	0.600734i	0.0226964	+	0.0190445i
$996$		0			0
$997$	35.4190	+	12.8915i	1.12173	+	0.408276i	0.835283	−	0.549820i	$-0.185304\pi$
$997$	35.4190	+	12.8915i	1.12173	+	0.408276i	0.286447	+	0.958096i	$0.407526\pi$
$998$	−9.20246	+	10.0612i	−0.291299	+	0.318481i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.l.a.179.6		96
3.2	odd	2		108.2.l.a.23.11	yes	96
4.3	odd	2	inner	324.2.l.a.179.14		96
9.2	odd	6		972.2.l.c.215.11		96
9.4	even	3		972.2.l.a.863.16		96
9.5	odd	6		972.2.l.d.863.1		96
9.7	even	3		972.2.l.b.215.6		96
12.11	even	2		108.2.l.a.23.3	✓	96
27.2	odd	18		972.2.l.a.107.8		96
27.7	even	9		108.2.l.a.47.3	yes	96
27.11	odd	18		972.2.l.b.755.4		96
27.16	even	9		972.2.l.c.755.13		96
27.20	odd	18	inner	324.2.l.a.143.14		96
27.25	even	9		972.2.l.d.107.9		96
36.7	odd	6		972.2.l.b.215.4		96
36.11	even	6		972.2.l.c.215.13		96
36.23	even	6		972.2.l.d.863.9		96
36.31	odd	6		972.2.l.a.863.8		96
108.7	odd	18		108.2.l.a.47.11	yes	96
108.11	even	18		972.2.l.b.755.6		96
108.43	odd	18		972.2.l.c.755.11		96
108.47	even	18	inner	324.2.l.a.143.6		96
108.79	odd	18		972.2.l.d.107.1		96
108.83	even	18		972.2.l.a.107.16		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.3	✓	96	12.11	even	2
108.2.l.a.23.11	yes	96	3.2	odd	2
108.2.l.a.47.3	yes	96	27.7	even	9
108.2.l.a.47.11	yes	96	108.7	odd	18
324.2.l.a.143.6		96	108.47	even	18	inner
324.2.l.a.143.14		96	27.20	odd	18	inner
324.2.l.a.179.6		96	1.1	even	1	trivial
324.2.l.a.179.14		96	4.3	odd	2	inner
972.2.l.a.107.8		96	27.2	odd	18
972.2.l.a.107.16		96	108.83	even	18
972.2.l.a.863.8		96	36.31	odd	6
972.2.l.a.863.16		96	9.4	even	3
972.2.l.b.215.4		96	36.7	odd	6
972.2.l.b.215.6		96	9.7	even	3
972.2.l.b.755.4		96	27.11	odd	18
972.2.l.b.755.6		96	108.11	even	18
972.2.l.c.215.11		96	9.2	odd	6
972.2.l.c.215.13		96	36.11	even	6
972.2.l.c.755.11		96	108.43	odd	18
972.2.l.c.755.13		96	27.16	even	9
972.2.l.d.107.1		96	108.79	odd	18
972.2.l.d.107.9		96	27.25	even	9
972.2.l.d.863.1		96	9.5	odd	6
972.2.l.d.863.9		96	36.23	even	6

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.654159 - 1.25382i) q^{2} +(-1.14415 + 1.64040i) q^{4} +(-0.137245 - 0.0242000i) q^{5} +(-2.98823 - 3.56123i) q^{7} +(2.80523 + 0.361485i) q^{8} +O(q^{10})\)	\(q+(-0.654159 - 1.25382i) q^{2} +(-1.14415 + 1.64040i) q^{4} +(-0.137245 - 0.0242000i) q^{5} +(-2.98823 - 3.56123i) q^{7} +(2.80523 + 0.361485i) q^{8} +(0.0594376 + 0.187912i) q^{10} +(0.182573 + 1.03542i) q^{11} +(-1.46220 + 0.532196i) q^{13} +(-2.51039 + 6.07633i) q^{14} +(-1.38183 - 3.75374i) q^{16} +(-5.25631 - 3.03473i) q^{17} +(-3.80088 + 2.19444i) q^{19} +(0.196727 - 0.197449i) q^{20} +(1.17880 - 0.906244i) q^{22} +(-1.94128 - 1.62893i) q^{23} +(-4.68021 - 1.70346i) q^{25} +(1.62379 + 1.48520i) q^{26} +(9.26084 - 0.827297i) q^{28} +(-0.210458 + 0.578229i) q^{29} +(3.18818 - 3.79952i) q^{31} +(-3.80260 + 4.18811i) q^{32} +(-0.366562 + 8.57569i) q^{34} +(0.323938 + 0.561078i) q^{35} +(-1.43991 + 2.49400i) q^{37} +(5.23782 + 3.33012i) q^{38} +(-0.376257 - 0.117499i) q^{40} +(2.25297 + 6.18999i) q^{41} +(2.15530 - 0.380038i) q^{43} +(-1.90740 - 0.885188i) q^{44} +(-0.772484 + 3.49960i) q^{46} +(8.46639 - 7.10414i) q^{47} +(-2.53733 + 14.3899i) q^{49} +(0.925763 + 6.98250i) q^{50} +(0.799963 - 3.00750i) q^{52} -8.73360i q^{53} -0.146525i q^{55} +(-7.09534 - 11.0703i) q^{56} +(0.862670 - 0.114376i) q^{58} +(1.42477 - 8.08025i) q^{59} +(8.56477 - 7.18670i) q^{61} +(-6.84951 - 1.51193i) q^{62} +(7.73866 + 2.02810i) q^{64} +(0.213559 - 0.0376562i) q^{65} +(1.93034 + 5.30357i) q^{67} +(10.9922 - 5.15026i) q^{68} +(0.491586 - 0.773196i) q^{70} +(-2.33277 + 4.04048i) q^{71} +(-5.64518 - 9.77774i) q^{73} +(4.06898 + 0.173925i) q^{74} +(0.749029 - 8.74574i) q^{76} +(3.14181 - 3.74426i) q^{77} +(0.572755 - 1.57363i) q^{79} +(0.0988087 + 0.548623i) q^{80} +(6.28736 - 6.87406i) q^{82} +(-2.20553 - 0.802749i) q^{83} +(0.647964 + 0.543706i) q^{85} +(-1.88641 - 2.45377i) q^{86} +(0.137869 + 2.97059i) q^{88} +(-7.63741 + 4.40946i) q^{89} +(6.26466 + 3.61690i) q^{91} +(4.89321 - 1.32073i) q^{92} +(-14.4457 - 5.96813i) q^{94} +(0.574758 - 0.209195i) q^{95} +(-0.978443 - 5.54902i) q^{97} +(19.7022 - 6.23192i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Introduction

L-functions

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