LMFDB - Embedded newform 522.2.x.a.101.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [522,2,Mod(11,522)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(522, base_ring=CyclotomicField(84)) chi = DirichletCharacter(H, H._module([14, 75])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("522.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 522 = 2 \cdot 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	522.x (of order $84$, degree $24$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.16819098551$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$30$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			101.24
Character	$\chi$	$=$	522.101
Dual form			522.2.x.a.491.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.399892 - 0.916562i) q^{2} +(0.301254 + 1.70565i) q^{3} +(-0.680173 - 0.733052i) q^{4} +(-1.96808 - 0.296641i) q^{5} +(1.68380 + 0.405959i) q^{6} +(0.334771 + 0.310622i) q^{7} +(-0.943883 + 0.330279i) q^{8} +(-2.81849 + 1.02767i) q^{9} +(-1.05891 + 1.68525i) q^{10} +(-1.29917 + 1.11803i) q^{11} +(1.04543 - 1.38097i) q^{12} +(-3.76635 + 5.52422i) q^{13} +(0.418577 - 0.182623i) q^{14} +(-0.0869264 - 3.44623i) q^{15} +(-0.0747301 + 0.997204i) q^{16} +(0.0272331 + 0.0272331i) q^{17} +(-0.185172 + 2.99428i) q^{18} +(2.18594 + 1.37352i) q^{19} +(1.12118 + 1.64448i) q^{20} +(-0.428962 + 0.664579i) q^{21} +(0.505214 + 1.63786i) q^{22} +(-5.18670 - 2.03563i) q^{23} +(-0.847689 - 1.51044i) q^{24} +(-0.992502 - 0.306146i) q^{25} +(3.55716 + 5.66119i) q^{26} +(-2.60192 - 4.49778i) q^{27} -0.456681i q^{28} +(5.25838 + 1.16166i) q^{29} +(-3.19345 - 1.29845i) q^{30} +(-0.974205 + 0.718996i) q^{31} +(0.884115 + 0.467269i) q^{32} +(-2.29835 - 1.87913i) q^{33} +(0.0358511 - 0.0140705i) q^{34} +(-0.566715 - 0.710638i) q^{35} +(2.67040 + 1.36711i) q^{36} +(3.61983 + 10.3449i) q^{37} +(2.13306 - 1.45429i) q^{38} +(-10.5570 - 4.75989i) q^{39} +(1.95562 - 0.370023i) q^{40} +(-1.67440 - 0.448654i) q^{41} +(0.437589 + 0.658930i) q^{42} +(-4.03870 + 5.47224i) q^{43} +(1.70324 + 0.191909i) q^{44} +(5.85188 - 1.18646i) q^{45} +(-3.93991 + 3.93991i) q^{46} +(1.56398 + 1.81738i) q^{47} +(-1.72339 + 0.172948i) q^{48} +(-0.507525 - 6.77245i) q^{49} +(-0.677496 + 0.787264i) q^{50} +(-0.0382461 + 0.0546542i) q^{51} +(6.61131 - 0.996494i) q^{52} +(-9.03075 - 7.20178i) q^{53} +(-5.16298 + 0.586199i) q^{54} +(2.88854 - 1.81499i) q^{55} +(-0.418577 - 0.182623i) q^{56} +(-1.68422 + 4.14224i) q^{57} +(3.16752 - 4.35509i) q^{58} +(-4.21675 + 2.43454i) q^{59} +(-2.46714 + 2.40775i) q^{60} +(11.6298 - 0.435156i) q^{61} +(0.269428 + 1.18044i) q^{62} +(-1.26277 - 0.531453i) q^{63} +(0.781831 - 0.623490i) q^{64} +(9.05121 - 9.75488i) q^{65} +(-2.64143 + 1.35513i) q^{66} +(10.3253 - 0.773774i) q^{67} +(0.00144006 - 0.0384865i) q^{68} +(1.90956 - 9.45995i) q^{69} +(-0.877969 + 0.235251i) q^{70} +(0.0664613 - 0.0320061i) q^{71} +(2.32091 - 1.90089i) q^{72} +(0.383626 - 3.40477i) q^{73} +(10.9293 + 0.819035i) q^{74} +(0.223184 - 1.78509i) q^{75} +(-0.479959 - 2.53664i) q^{76} +(-0.782211 - 0.0292683i) q^{77} +(-8.58440 + 7.77272i) q^{78} +(-2.10598 + 11.1304i) q^{79} +(0.442887 - 1.94041i) q^{80} +(6.88780 - 5.79294i) q^{81} +(-1.08080 + 1.35528i) q^{82} +(2.82530 - 9.15941i) q^{83} +(0.778939 - 0.137577i) q^{84} +(-0.0455186 - 0.0616755i) q^{85} +(3.40061 + 5.89002i) q^{86} +(-0.397283 + 9.31891i) q^{87} +(0.857007 - 1.48438i) q^{88} +(11.3604 - 1.28001i) q^{89} +(1.25266 - 5.83807i) q^{90} +(-2.97681 + 0.679438i) q^{91} +(2.03563 + 5.18670i) q^{92} +(-1.51984 - 1.44505i) q^{93} +(2.29117 - 0.706732i) q^{94} +(-3.89468 - 3.35165i) q^{95} +(-0.530654 + 1.64876i) q^{96} +(-3.21126 - 6.07601i) q^{97} +(-6.41033 - 2.24307i) q^{98} +(2.51275 - 4.48627i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q + 24 q^{11} - 12 q^{14} - 20 q^{15} - 60 q^{16} + 84 q^{21} + 20 q^{24} + 60 q^{25} - 144 q^{27} - 12 q^{29} + 72 q^{30} + 84 q^{33} - 40 q^{36} + 40 q^{39} - 12 q^{41} - 104 q^{45} + 24 q^{46} - 24 q^{47}+ \cdots - 84 q^{99}+O(q^{100}) $ 720 * q + 24 * q^11 - 12 * q^14 - 20 * q^15 - 60 * q^16 + 84 * q^21 + 20 * q^24 + 60 * q^25 - 144 * q^27 - 12 * q^29 + 72 * q^30 + 84 * q^33 - 40 * q^36 + 40 * q^39 - 12 * q^41 - 104 * q^45 + 24 * q^46 - 24 * q^47 + 60 * q^49 + 16 * q^54 - 144 * q^55 + 12 * q^56 + 12 * q^58 + 120 * q^59 - 16 * q^60 - 12 * q^61 + 36 * q^65 - 48 * q^66 - 36 * q^68 + 52 * q^69 - 180 * q^74 - 184 * q^75 - 132 * q^77 - 68 * q^78 + 12 * q^79 - 216 * q^81 + 96 * q^82 - 432 * q^83 - 80 * q^84 - 48 * q^85 - 200 * q^87 - 112 * q^90 - 252 * q^92 - 112 * q^93 + 192 * q^95 + 24 * q^97 - 84 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/522\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.399892	−	0.916562i	0.282766	−	0.648107i
$2$	0.399892	−	0.916562i	0.282766	−	0.648107i
$3$	0.301254	+	1.70565i	0.173929	+	0.984758i
$3$	0.301254	+	1.70565i	0.173929	+	0.984758i
$4$	−0.680173	−	0.733052i	−0.340086	−	0.366526i
$5$	−1.96808	−	0.296641i	−0.880154	−	0.132662i	−0.306609	−	0.951836i	$-0.599194\pi$
$5$	−1.96808	−	0.296641i	−0.880154	−	0.132662i	−0.573546	+	0.819174i	$0.694432\pi$
$6$	1.68380	+	0.405959i	0.687410	+	0.165732i
$7$	0.334771	+	0.310622i	0.126532	+	0.117404i	0.740901	−	0.671615i	$-0.234399\pi$
$7$	0.334771	+	0.310622i	0.126532	+	0.117404i	−0.614369	+	0.789019i	$0.710589\pi$
$8$	−0.943883	+	0.330279i	−0.333713	+	0.116771i
$9$	−2.81849	+	1.02767i	−0.939498	+	0.342556i
$10$	−1.05891	+	1.68525i	−0.334857	+	0.532922i
$11$	−1.29917	+	1.11803i	−0.391716	+	0.337098i	−0.825993	−	0.563681i	$-0.809385\pi$
$11$	−1.29917	+	1.11803i	−0.391716	+	0.337098i	0.434277	+	0.900779i	$0.357004\pi$
$12$	1.04543	−	1.38097i	0.301789	−	0.398652i
$13$	−3.76635	+	5.52422i	−1.04460	+	1.53214i	−0.212775	+	0.977101i	$0.568250\pi$
$13$	−3.76635	+	5.52422i	−1.04460	+	1.53214i	−0.831823	+	0.555042i	$0.812702\pi$
$14$	0.418577	−	0.182623i	0.111869	−	0.0488081i
$15$	−0.0869264	−	3.44623i	−0.0224443	−	0.889813i
$16$	−0.0747301	+	0.997204i	−0.0186825	+	0.249301i
$17$	0.0272331	+	0.0272331i	0.00660500	+	0.00660500i	0.710402	−	0.703797i	$-0.248513\pi$
$17$	0.0272331	+	0.0272331i	0.00660500	+	0.00660500i	−0.703797	+	0.710402i	$0.748513\pi$
$18$	−0.185172	+	2.99428i	−0.0436454	+	0.705759i
$19$	2.18594	+	1.37352i	0.501490	+	0.315107i	0.758913	−	0.651192i	$-0.225731\pi$
$19$	2.18594	+	1.37352i	0.501490	+	0.315107i	−0.257423	+	0.966299i	$0.582873\pi$
$20$	1.12118	+	1.64448i	0.250704	+	0.367716i
$21$	−0.428962	+	0.664579i	−0.0936072	+	0.145023i
$22$	0.505214	+	1.63786i	0.107712	+	0.349194i
$23$	−5.18670	−	2.03563i	−1.08150	−	0.424459i	−0.243375	−	0.969932i	$-0.578255\pi$
$23$	−5.18670	−	2.03563i	−1.08150	−	0.424459i	−0.838128	+	0.545474i	$0.816350\pi$
$24$	−0.847689	−	1.51044i	−0.173034	−	0.308317i
$25$	−0.992502	−	0.306146i	−0.198500	−	0.0612293i
$26$	3.55716	+	5.66119i	0.697616	+	1.11025i
$27$	−2.60192	−	4.49778i	−0.500740	−	0.865598i
$28$		−	0.456681i		−	0.0863047i
$29$	5.25838	+	1.16166i	0.976456	+	0.215715i
$29$	5.25838	+	1.16166i	0.976456	+	0.215715i
$30$	−3.19345	−	1.29845i	−0.583041	−	0.237063i
$31$	−0.974205	+	0.718996i	−0.174972	+	0.129136i	−0.677786	−	0.735260i	$-0.737060\pi$
$31$	−0.974205	+	0.718996i	−0.174972	+	0.129136i	0.502813	+	0.864395i	$0.332298\pi$
$32$	0.884115	+	0.467269i	0.156291	+	0.0826022i
$33$	−2.29835	−	1.87913i	−0.400091	−	0.327114i
$34$	0.0358511	−	0.0140705i	0.00614842	−	0.00241308i
$35$	−0.566715	−	0.710638i	−0.0957923	−	0.120120i
$36$	2.67040	+	1.36711i	0.445066	+	0.227852i
$37$	3.61983	+	10.3449i	0.595096	+	1.70069i	0.707222	+	0.706992i	$0.249948\pi$
$37$	3.61983	+	10.3449i	0.595096	+	1.70069i	−0.112126	+	0.993694i	$0.535766\pi$
$38$	2.13306	−	1.45429i	0.346028	−	0.235918i
$39$	−10.5570	−	4.75989i	−1.69048	−	0.762192i
$40$	1.95562	−	0.370023i	0.309210	−	0.0585057i
$41$	−1.67440	−	0.448654i	−0.261497	−	0.0700680i	0.125688	−	0.992070i	$-0.459886\pi$
$41$	−1.67440	−	0.448654i	−0.261497	−	0.0700680i	−0.387186	+	0.922002i	$0.626553\pi$
$42$	0.437589	+	0.658930i	0.0675215	+	0.101675i
$43$	−4.03870	+	5.47224i	−0.615895	+	0.834509i	−0.995899	−	0.0904765i	$-0.971161\pi$
$43$	−4.03870	+	5.47224i	−0.615895	+	0.834509i	0.380003	+	0.924985i	$0.375923\pi$
$44$	1.70324	+	0.191909i	0.256772	+	0.0289313i
$45$	5.85188	−	1.18646i	0.872347	−	0.176866i
$46$	−3.93991	+	3.93991i	−0.580907	+	0.580907i
$47$	1.56398	+	1.81738i	0.228130	+	0.265092i	0.860358	−	0.509691i	$-0.170240\pi$
$47$	1.56398	+	1.81738i	0.228130	+	0.265092i	−0.632227	+	0.774783i	$0.717859\pi$
$48$	−1.72339	+	0.172948i	−0.248751	+	0.0249629i
$49$	−0.507525	−	6.77245i	−0.0725036	−	0.967493i
$50$	−0.677496	+	0.787264i	−0.0958124	+	0.111336i
$51$	−0.0382461	+	0.0546542i	−0.00535552	+	0.00765312i
$52$	6.61131	−	0.996494i	0.916823	−	0.138189i
$53$	−9.03075	−	7.20178i	−1.24047	−	0.989241i	−0.999827	−	0.0186270i	$-0.994071\pi$
$53$	−9.03075	−	7.20178i	−1.24047	−	0.989241i	−0.240642	−	0.970614i	$-0.577358\pi$
$54$	−5.16298	+	0.586199i	−0.702593	+	0.0797716i
$55$	2.88854	−	1.81499i	0.389490	−	0.244733i
$56$	−0.418577	−	0.182623i	−0.0559347	−	0.0244041i
$57$	−1.68422	+	4.14224i	−0.223081	+	0.548653i
$58$	3.16752	−	4.35509i	0.415915	−	0.571852i
$59$	−4.21675	+	2.43454i	−0.548974	+	0.316950i	−0.748708	−	0.662900i	$-0.769326\pi$
$59$	−4.21675	+	2.43454i	−0.548974	+	0.316950i	0.199734	+	0.979850i	$0.435992\pi$
$60$	−2.46714	+	2.40775i	−0.318507	+	0.310840i
$61$	11.6298	−	0.435156i	1.48904	−	0.0557160i	0.719580	−	0.694409i	$-0.244334\pi$
$61$	11.6298	−	0.435156i	1.48904	−	0.0557160i	0.769461	+	0.638693i	$0.220525\pi$
$62$	0.269428	+	1.18044i	0.0342174	+	0.149916i
$63$	−1.26277	−	0.531453i	−0.159094	−	0.0669568i
$64$	0.781831	−	0.623490i	0.0977289	−	0.0779362i
$65$	9.05121	−	9.75488i	1.12266	−	1.20994i
$66$	−2.64143	+	1.35513i	−0.325137	+	0.166805i
$67$	10.3253	−	0.773774i	1.26144	−	0.0945316i	0.572834	−	0.819671i	$-0.305844\pi$
$67$	10.3253	−	0.773774i	1.26144	−	0.0945316i	0.688602	+	0.725140i	$0.258225\pi$
$68$	0.00144006	−	0.0384865i	0.000174633	−	0.00466717i
$69$	1.90956	−	9.45995i	0.229885	−	1.13884i
$70$	−0.877969	+	0.235251i	−0.104937	+	0.0281179i
$71$	0.0664613	−	0.0320061i	0.00788750	−	0.00379842i	−0.429936	−	0.902859i	$-0.641464\pi$
$71$	0.0664613	−	0.0320061i	0.00788750	−	0.00379842i	0.437823	+	0.899061i	$0.355750\pi$
$72$	2.32091	−	1.90089i	0.273522	−	0.224022i
$73$	0.383626	−	3.40477i	0.0449000	−	0.398499i	−0.951082	−	0.308940i	$-0.900026\pi$
$73$	0.383626	−	3.40477i	0.0449000	−	0.398499i	0.995982	−	0.0895587i	$-0.0285457\pi$
$74$	10.9293	+	0.819035i	1.27050	+	0.0952108i
$75$	0.223184	−	1.78509i	0.0257711	−	0.206124i
$76$	−0.479959	−	2.53664i	−0.0550550	−	0.290973i
$77$	−0.782211	−	0.0292683i	−0.0891412	−	0.00333543i
$78$	−8.58440	+	7.77272i	−0.971992	+	0.880088i
$79$	−2.10598	+	11.1304i	−0.236942	+	1.25227i	0.638757	+	0.769408i	$0.279449\pi$
$79$	−2.10598	+	11.1304i	−0.236942	+	1.25227i	−0.875699	+	0.482858i	$0.839599\pi$
$80$	0.442887	−	1.94041i	0.0495162	−	0.216945i
$81$	6.88780	−	5.79294i	0.765311	−	0.643660i
$82$	−1.08080	+	1.35528i	−0.119354	+	0.149666i
$83$	2.82530	−	9.15941i	0.310117	−	1.00538i	−0.657606	−	0.753362i	$-0.728431\pi$
$83$	2.82530	−	9.15941i	0.310117	−	1.00538i	0.967724	−	0.252014i	$-0.0810928\pi$
$84$	0.778939	−	0.137577i	0.0849893	−	0.0150109i
$85$	−0.0455186	−	0.0616755i	−0.00493718	−	0.00668965i
$86$	3.40061	+	5.89002i	0.366697	+	0.635137i
$87$	−0.397283	+	9.31891i	−0.0425932	+	0.999092i
$88$	0.857007	−	1.48438i	0.0913572	−	0.158235i
$89$	11.3604	−	1.28001i	1.20420	−	0.135681i	0.513029	−	0.858372i	$-0.328523\pi$
$89$	11.3604	−	1.28001i	1.20420	−	0.135681i	0.691171	+	0.722691i	$0.257095\pi$
$90$	1.25266	−	5.83807i	0.132042	−	0.615386i
$91$	−2.97681	+	0.679438i	−0.312055	+	0.0712244i
$92$	2.03563	+	5.18670i	0.212229	+	0.540751i
$93$	−1.51984	−	1.44505i	−0.157600	−	0.149845i
$94$	2.29117	−	0.706732i	0.236316	−	0.0728938i
$95$	−3.89468	−	3.35165i	−0.399586	−	0.343872i
$96$	−0.530654	+	1.64876i	−0.0541597	+	0.168276i
$97$	−3.21126	−	6.07601i	−0.326054	−	0.616925i	0.665532	−	0.746369i	$-0.268205\pi$
$97$	−3.21126	−	6.07601i	−0.326054	−	0.616925i	−0.991587	+	0.129444i	$0.958681\pi$
$98$	−6.41033	−	2.24307i	−0.647541	−	0.226584i
$99$	2.51275	−	4.48627i	0.252541	−	0.450888i
$100$	0.450652	+	0.935788i	0.0450652	+	0.0935788i
$101$	4.09774	+	3.02427i	0.407740	+	0.300926i	0.778312	−	0.627878i	$-0.216076\pi$
$101$	4.09774	+	3.02427i	0.407740	+	0.300926i	−0.370572	+	0.928804i	$0.620838\pi$
$102$	0.0347997	+	0.0569107i	0.00344568	+	0.00563500i
$103$	1.28494	+	0.876055i	0.126609	+	0.0863202i	0.624968	−	0.780650i	$-0.285112\pi$
$103$	1.28494	+	0.876055i	0.126609	+	0.0863202i	−0.498360	+	0.866970i	$0.666064\pi$
$104$	1.73046	−	6.45817i	0.169686	−	0.633275i
$105$	1.04138	−	1.18070i	0.101628	−	0.115225i
$106$	−10.2122	+	5.39731i	−0.991897	+	0.524233i
$107$	5.81783	−	12.0809i	0.562431	−	1.16790i	−0.404895	−	0.914363i	$-0.632692\pi$
$107$	5.81783	−	12.0809i	0.562431	−	1.16790i	0.967326	−	0.253537i	$-0.0815939\pi$
$108$	−1.52735	+	4.96661i	−0.146969	+	0.477912i
$109$	0.914848	+	0.208808i	0.0876265	+	0.0200002i	0.266109	−	0.963943i	$-0.414262\pi$
$109$	0.914848	+	0.208808i	0.0876265	+	0.0200002i	−0.178483	+	0.983943i	$0.557119\pi$
$110$	−0.508447	−	3.37332i	−0.0484785	−	0.321634i
$111$	−16.5543	+	9.29059i	−1.57126	+	0.881824i
$112$	−0.334771	+	0.310622i	−0.0316329	+	0.0293510i
$113$	−4.64678	+	8.79213i	−0.437132	+	0.827094i	0.562868	+	0.826547i	$0.309698\pi$
$113$	−4.64678	+	8.79213i	−0.437132	+	0.827094i	−1.00000		0.000547377i	$0.999826\pi$
$114$	3.12311	+	3.20014i	0.292506	+	0.299721i
$115$	9.60402	+	5.54489i	0.895580	+	0.517063i
$116$	−2.72505	−	4.64479i	−0.253014	−	0.431258i
$117$	4.93837	−	19.4405i	0.456552	−	1.79728i
$118$	0.545164	+	4.83847i	0.0501864	+	0.445417i
$119$	0.000657650		0.0175761i	6.02867e−5		0.00161119i
$120$	1.22027	+	3.22413i	0.111395	+	0.294321i
$121$	−1.20160	+	7.97211i	−0.109237	+	0.724737i
$122$	4.25181	−	10.8334i	0.384941	−	0.980813i
$123$	0.260829	−	2.99110i	0.0235181	−	0.269699i
$124$	1.18969	+	0.225101i	0.106837	+	0.0202147i
$125$	10.8286	+	5.21477i	0.968537	+	0.466423i
$126$	−0.992080	+	0.944880i	−0.0883815	+	0.0841766i
$127$	−4.65129	+	13.2926i	−0.412735	+	1.17953i	0.530581	+	0.847634i	$0.321974\pi$
$127$	−4.65129	+	13.2926i	−0.412735	+	1.17953i	−0.943316	+	0.331895i	$0.892312\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	−10.5504	−	5.24008i	−0.928911	−	0.461363i
$130$	−5.32145	−	12.1969i	−0.466722	−	1.06974i
$131$	1.87160	+	4.28975i	0.163522	+	0.374797i	0.978961	−	0.204046i	$-0.0654091\pi$
$131$	1.87160	+	4.28975i	0.163522	+	0.374797i	−0.815439	+	0.578843i	$0.803504\pi$
$132$	0.185777	+	2.96294i	0.0161698	+	0.257891i
$133$	0.305145	+	1.13882i	0.0264595	+	0.0987481i
$134$	3.41979	−	9.77321i	0.295425	−	0.844276i
$135$	3.78658	+	9.62384i	0.325897	+	0.828289i
$136$	−0.0346994	−	0.0167103i	−0.00297545	−	0.00143290i
$137$	−2.05676	−	0.389159i	−0.175721	−	0.0332481i	0.0973066	−	0.995254i	$-0.468977\pi$
$137$	−2.05676	−	0.389159i	−0.175721	−	0.0332481i	−0.273027	+	0.962006i	$0.588025\pi$
$138$	−7.90701	−	5.53319i	−0.673090	−	0.471017i
$139$	−4.43629	+	11.3035i	−0.376281	+	0.958748i	0.609811	+	0.792547i	$0.291245\pi$
$139$	−4.43629	+	11.3035i	−0.376281	+	0.958748i	−0.986092	+	0.166201i	$0.946850\pi$
$140$	−0.135470	+	0.898788i	−0.0114493	+	0.0759614i
$141$	−2.62866	+	3.21510i	−0.221373	+	0.270761i
$142$	−0.00275821	−	0.0737148i	−0.000231464	−	0.00618601i
$143$	−1.28310	−	11.3878i	−0.107298	−	0.952296i
$144$	−0.814167	−	2.88741i	−0.0678473	−	0.240617i
$145$	−10.0043	−	3.84610i	−0.830815	−	0.319401i
$146$	−2.96728	−	1.71316i	−0.245574	−	0.141782i
$147$	11.3985	−	2.90589i	0.940136	−	0.239673i
$148$	5.12122	−	9.68982i	0.420962	−	0.796498i
$149$	−8.96200	+	8.31552i	−0.734196	+	0.681234i	−0.955838	−	0.293894i	$-0.905049\pi$
$149$	−8.96200	+	8.31552i	−0.734196	+	0.681234i	0.221642	+	0.975128i	$0.428858\pi$
$150$	−1.54690	−	0.918405i	−0.126304	−	0.0749875i
$151$	1.32798	+	8.81055i	0.108069	+	0.716993i	0.975591	+	0.219594i	$0.0704733\pi$
$151$	1.32798	+	8.81055i	0.108069	+	0.716993i	−0.867522	+	0.497399i	$0.834289\pi$
$152$	−2.51692	−	0.574471i	−0.204149	−	0.0465958i
$153$	−0.104743	−	0.0487697i	−0.00846796	−	0.00394280i
$154$	−0.339626	+	0.705241i	−0.0273678	+	0.0568299i
$155$	2.13060	−	1.12606i	0.171134	−	0.0904470i
$156$	3.69135	+	10.9764i	0.295545	+	0.878814i
$157$	4.38547	−	16.3668i	0.349999	−	1.30621i	−0.536664	−	0.843796i	$-0.680316\pi$
$157$	4.38547	−	16.3668i	0.349999	−	1.30621i	0.886662	−	0.462417i	$-0.153018\pi$
$158$	9.35953	+	6.38122i	0.744604	+	0.507662i
$159$	9.56318	−	17.5729i	0.758410	−	1.39362i
$160$	−1.60140	−	1.18189i	−0.126602	−	0.0934366i
$161$	−1.10405	−	2.29258i	−0.0870111	−	0.180680i
$162$	−2.55522	−	8.62965i	−0.200757	−	0.678009i
$163$	−16.0096	−	5.60201i	−1.25397	−	0.438783i	−0.380101	−	0.924945i	$-0.624111\pi$
$163$	−16.0096	−	5.60201i	−1.25397	−	0.438783i	−0.873869	+	0.486162i	$0.838397\pi$
$164$	0.809995	+	1.53259i	0.0632500	+	0.119675i
$165$	3.96592	+	4.38007i	0.308746	+	0.340988i
$166$	−7.26535	−	6.25234i	−0.563901	−	0.485276i
$167$	−11.6245	+	3.58568i	−0.899529	+	0.277468i	−0.709829	−	0.704374i	$-0.751228\pi$
$167$	−11.6245	+	3.58568i	−0.899529	+	0.277468i	−0.189700	+	0.981842i	$0.560752\pi$
$168$	0.185394	−	0.768962i	0.0143034	−	0.0593267i
$169$	−11.5822	−	29.5109i	−0.890937	−	2.27007i
$170$	−0.0747319	+	0.0170571i	−0.00573168	+	0.00130822i
$171$	−7.57259	−	1.62483i	−0.579091	−	0.124254i
$172$	6.75845	−	0.761494i	0.515327	−	0.0580634i
$173$	2.24434	−	3.88732i	0.170634	−	0.295547i	−0.768007	−	0.640441i	$-0.778752\pi$
$173$	2.24434	−	3.88732i	0.170634	−	0.295547i	0.938642	+	0.344894i	$0.112085\pi$
$174$	8.38250	+	4.09069i	0.635475	+	0.310115i
$175$	−0.237165	−	0.410782i	−0.0179280	−	0.0310522i
$176$	−1.01782	−	1.37909i	−0.0767207	−	0.103953i
$177$	−5.42279	−	6.45889i	−0.407602	−	0.485480i
$178$	3.36972	−	10.9244i	0.252572	−	0.818817i
$179$	2.14690	−	2.69212i	0.160467	−	0.201219i	−0.695098	−	0.718915i	$-0.744639\pi$
$179$	2.14690	−	2.69212i	0.160467	−	0.201219i	0.855564	+	0.517696i	$0.173210\pi$
$180$	−4.85002	−	3.48274i	−0.361499	−	0.259588i
$181$	1.86255	−	8.16036i	0.138442	−	0.606555i	−0.857336	−	0.514758i	$-0.827882\pi$
$181$	1.86255	−	8.16036i	0.138442	−	0.606555i	0.995778	−	0.0917969i	$-0.0292611\pi$
$182$	−0.567656	+	3.00013i	−0.0420775	+	0.222385i
$183$	4.24574	+	19.7053i	0.313854	+	1.45666i
$184$	5.56797	+	0.208339i	0.410476	+	0.0153589i
$185$	−4.05541	−	21.4334i	−0.298160	−	1.57581i
$186$	−1.93225	+	0.815162i	−0.141680	+	0.0597706i
$187$	−0.0658279	−	0.00493312i	−0.00481381	−	0.000360745i
$188$	0.268456	−	2.38261i	0.0195792	−	0.173770i
$189$	0.526061	−	2.31394i	0.0382653	−	0.168314i
$190$	−4.62944	+	2.22942i	−0.335855	+	0.161739i
$191$	7.68059	−	2.05801i	0.555748	−	0.148912i	0.0299959	−	0.999550i	$-0.490451\pi$
$191$	7.68059	−	2.05801i	0.555748	−	0.148912i	0.525752	+	0.850638i	$0.323784\pi$
$192$	1.29899	+	1.14570i	0.0937462	+	0.0826840i
$193$	−0.489133	+	13.0723i	−0.0352085	+	0.940968i	0.864012	+	0.503472i	$0.167944\pi$
$193$	−0.489133	+	13.0723i	−0.0352085	+	0.940968i	−0.899220	+	0.437496i	$0.855865\pi$
$194$	−6.85320	+	0.513576i	−0.492031	+	0.0368726i
$195$	19.3651	+	12.4995i	1.38677	+	0.895108i
$196$	−4.61935	+	4.97848i	−0.329954	+	0.355606i
$197$	−18.1779	+	14.4964i	−1.29512	+	1.03282i	−0.298191	+	0.954506i	$0.596383\pi$
$197$	−18.1779	+	14.4964i	−1.29512	+	1.03282i	−0.996929	+	0.0783168i	$0.975045\pi$
$198$	−3.10712	−	4.09712i	−0.220814	−	0.291169i
$199$	4.04524	+	17.7233i	0.286759	+	1.25637i	0.888944	+	0.458017i	$0.151440\pi$
$199$	4.04524	+	17.7233i	0.286759	+	1.25637i	−0.602184	+	0.798357i	$0.705703\pi$
$200$	1.03792	−	0.0388362i	0.0733920	−	0.00274613i
$201$	4.43032	+	17.3783i	0.312491	+	1.22577i
$202$	4.41058	−	2.54645i	0.310327	−	0.179168i
$203$	1.39952	+	2.02226i	0.0982268	+	0.141935i
$204$	0.0660783	−	0.00913794i	0.00462641	−	0.000639784i
$205$	3.16227	+	1.37969i	0.220863	+	0.0963614i
$206$	1.31679	−	0.827397i	0.0917454	−	0.0576475i
$207$	16.7106	+	0.407207i	1.16147	+	0.0283028i
$208$	−5.22731	−	4.16864i	−0.362449	−	0.289043i
$209$	−4.37556	+	0.659509i	−0.302664	+	0.0456192i
$210$	−0.665747	−	1.42664i	−0.0459409	−	0.0984474i
$211$	−1.43505	+	1.66755i	−0.0987926	+	0.114799i	−0.805192	−	0.593015i	$-0.797938\pi$
$211$	−1.43505	+	1.66755i	−0.0987926	+	0.114799i	0.706399	+	0.707814i	$0.250318\pi$
$212$	0.863189	+	11.5185i	0.0592841	+	0.791091i
$213$	0.0746129	+	0.103718i	0.00511239	+	0.00710663i
$214$	−8.74635	−	10.1634i	−0.597888	−	0.694759i
$215$	9.57179	−	9.57179i	0.652791	−	0.652791i
$216$	3.94143	+	3.38602i	0.268181	+	0.230389i
$217$	−0.549472	−	0.0619106i	−0.0373006	−	0.00420277i
$218$	0.557226	−	0.755014i	0.0377401	−	0.0511360i
$219$	5.92293	−	0.371368i	0.400234	−	0.0250947i
$220$	−3.29518	−	0.882942i	−0.222161	−	0.0595279i
$221$	−0.253011	+	0.0478723i	−0.0170194	+	0.00322024i
$222$	1.89549	+	18.8882i	0.127217	+	1.26770i
$223$	−16.8290	+	11.4738i	−1.12695	+	0.768344i	−0.975474	−	0.220116i	$-0.929356\pi$
$223$	−16.8290	+	11.4738i	−1.12695	+	0.768344i	−0.151480	+	0.988460i	$0.548404\pi$
$224$	0.150832	+	0.431054i	0.0100779	+	0.0288010i
$225$	3.11198	−	0.157090i	0.207465	−	0.0104727i
$226$	6.20033	+	7.77497i	0.412440	+	0.517183i
$227$	−22.8349	+	8.96205i	−1.51561	+	0.594832i	−0.969978	−	0.243194i	$-0.921805\pi$
$227$	−22.8349	+	8.96205i	−1.51561	+	0.594832i	−0.545630	+	0.838026i	$0.683710\pi$
$228$	4.18204	−	1.58281i	0.276962	−	0.104824i
$229$	16.9617	+	8.96454i	1.12086	+	0.592394i	0.921828	−	0.387599i	$-0.126695\pi$
$229$	16.9617	+	8.96454i	1.12086	+	0.592394i	0.199035	+	0.979992i	$0.436219\pi$
$230$	8.92281	−	6.58533i	0.588352	−	0.434224i
$231$	−0.185722	−	1.34300i	−0.0122196	−	0.0883626i
$232$	−5.34697	+	0.640260i	−0.351046	+	0.0420351i
$233$			2.50671i			0.164220i	0.996623	+	0.0821100i	$0.0261659\pi$
$233$			2.50671i			0.164220i	−0.996623	+	0.0821100i	$0.973834\pi$
$234$	−15.8436	−	12.3004i	−1.03573	−	0.804104i
$235$	−2.53894	−	4.04070i	−0.165622	−	0.263586i
$236$	4.65276	+	1.43519i	0.302869	+	0.0934227i
$237$	−19.6190	−	0.239003i	−1.27439	−	0.0155249i
$238$	0.0163725	+	0.00642575i	0.00106127	+	0.000416519i
$239$	4.50645	+	14.6096i	0.291498	+	0.945014i	0.976325	+	0.216308i	$0.0694016\pi$
$239$	4.50645	+	14.6096i	0.291498	+	0.945014i	−0.684827	+	0.728706i	$0.740122\pi$
$240$	3.44309	+	0.170854i	0.222251	+	0.0110286i
$241$	−2.08302	−	3.05523i	−0.134179	−	0.196805i	0.753269	−	0.657713i	$-0.228476\pi$
$241$	−2.08302	−	3.05523i	−0.134179	−	0.196805i	−0.887448	+	0.460908i	$0.847524\pi$
$242$	6.82643	+	4.28933i	0.438819	+	0.275728i
$243$	11.9557	+	10.0030i	0.766960	+	0.641695i
$244$	−8.22926	−	8.22926i	−0.526824	−	0.526824i
$245$	−1.01013	+	13.4793i	−0.0645351	+	0.861162i
$246$	−2.63723	−	1.43518i	−0.168144	−	0.0915040i
$247$	−15.8207	+	6.90248i	−1.00664	+	0.439195i
$248$	0.682067	−	1.00041i	0.0433113	−	0.0635260i
$249$	16.4739	+	2.05968i	1.04399	+	0.130527i
$250$	9.10992	−	7.83972i	0.576162	−	0.495827i
$251$	−5.31337	+	8.45617i	−0.335377	+	0.533749i	−0.971255	−	0.238040i	$-0.923495\pi$
$251$	−5.31337	+	8.45617i	−0.335377	+	0.533749i	0.635879	+	0.771789i	$0.280638\pi$
$252$	0.469317	+	1.28715i	0.0295642	+	0.0810830i
$253$	9.01432	−	3.15425i	0.566726	−	0.198306i
$254$	10.3235	+	9.57881i	0.647754	+	0.601028i
$255$	0.0914842	−	0.0962188i	0.00572897	−	0.00602545i
$256$	−0.988831	−	0.149042i	−0.0618019	−	0.00931514i
$257$	11.0594	+	11.9192i	0.689868	+	0.743501i	0.976730	−	0.214471i	$-0.0688027\pi$
$257$	11.0594	+	11.9192i	0.689868	+	0.743501i	−0.286862	+	0.957972i	$0.592612\pi$
$258$	−9.02188	+	7.57464i	−0.561678	+	0.471576i
$259$	−2.00153	+	4.58756i	−0.124369	+	0.285057i
$260$	−13.3072			−0.825279
$261$	−16.0145	+	2.12973i	−0.991273	+	0.131827i
$262$	4.68026			0.289148
$263$	−11.9475	+	27.3840i	−0.736715	+	1.68857i	−0.0116081	+	0.999933i	$0.503695\pi$
$263$	−11.9475	+	27.3840i	−0.736715	+	1.68857i	−0.725107	+	0.688636i	$0.758210\pi$
$264$	2.79001	+	1.01458i	0.171713	+	0.0624431i
$265$	15.6369	+	16.8526i	0.960569	+	1.03525i
$266$	1.16582	+	0.175720i	0.0714812	+	0.0107741i
$267$	5.60561	+	18.9913i	0.343058	+	1.16225i
$268$	−7.59020	−	7.04268i	−0.463645	−	0.430200i
$269$	3.89830	−	1.36407i	0.237683	−	0.0831690i	−0.208809	−	0.977956i	$-0.566959\pi$
$269$	3.89830	−	1.36407i	0.237683	−	0.0831690i	0.446492	+	0.894787i	$0.352673\pi$
$270$	10.3351	+	0.377863i	0.628973	+	0.0229960i
$271$	12.1657	−	19.3616i	0.739012	−	1.17613i	−0.239691	−	0.970849i	$-0.577046\pi$
$271$	12.1657	−	19.3616i	0.739012	−	1.17613i	0.978703	−	0.205282i	$-0.0658111\pi$
$272$	−0.0291921	+	0.0251218i	−0.00177003	+	0.00152323i
$273$	−2.05566	−	4.87272i	−0.124414	−	0.294910i
$274$	−1.17917	+	1.72952i	−0.0712362	+	0.104484i
$275$	1.63171	−	0.711909i	0.0983960	−	0.0429297i
$276$	−8.23347	+	5.03459i	−0.495597	+	0.303047i
$277$	0.362342	−	4.83512i	0.0217710	−	0.290514i	−0.975682	−	0.219190i	$-0.929659\pi$
$277$	0.362342	−	4.83512i	0.0217710	−	0.290514i	0.997453	−	0.0713241i	$-0.0227224\pi$
$278$	8.58630	+	8.58630i	0.514972	+	0.514972i
$279$	2.00690	−	3.02764i	0.120150	−	0.181260i
$280$	0.769622	+	0.483585i	0.0459937	+	0.0288997i
$281$	5.14978	+	7.55334i	0.307210	+	0.450595i	0.948534	−	0.316676i	$-0.102567\pi$
$281$	5.14978	+	7.55334i	0.307210	+	0.450595i	−0.641324	+	0.767271i	$0.721614\pi$
$282$	1.89566	+	3.69503i	0.112885	+	0.220036i
$283$	3.88246	+	12.5866i	0.230788	+	0.748197i	0.994695	+	0.102870i	$0.0328027\pi$
$283$	3.88246	+	12.5866i	0.230788	+	0.748197i	−0.763906	+	0.645327i	$0.776721\pi$
$284$	−0.0686672	−	0.0269499i	−0.00407465	−	0.00159918i
$285$	4.54345	−	7.65267i	0.269131	−	0.453305i
$286$	−10.9507	−	3.37785i	−0.647531	−	0.199737i
$287$	−0.421179	−	0.670303i	−0.0248614	−	0.0395667i
$288$	−2.97207	−	0.408417i	−0.175131	−	0.0240662i
$289$		−	16.9985i		−	0.999913i
$290$	−7.52584	+	7.63158i	−0.441933	+	0.448142i
$291$	9.39614	−	7.30771i	0.550812	−	0.428386i
$292$	−2.75681	+	2.03462i	−0.161330	+	0.119067i
$293$	7.03903	+	3.72023i	0.411224	+	0.217338i	0.660069	−	0.751205i	$-0.270527\pi$
$293$	7.03903	+	3.72023i	0.411224	+	0.217338i	−0.248845	+	0.968543i	$0.580051\pi$
$294$	1.89476	−	11.6095i	0.110505	−	0.677081i
$295$	9.02111	−	3.54052i	0.525229	−	0.206137i
$296$	−6.83339	−	8.56880i	−0.397183	−	0.498051i
$297$	8.40899	+	2.93437i	0.487939	+	0.170269i
$298$	4.03786	+	11.5395i	0.233907	+	0.668468i
$299$	30.7802	−	20.9856i	1.78007	−	1.21363i
$300$	−1.46037	+	1.05056i	−0.0843143	+	0.0606543i
$301$	−3.05184	+	0.577439i	−0.175905	+	0.0332830i
$302$	8.60647	+	2.30610i	0.495247	+	0.132701i
$303$	−3.92389	+	7.90038i	−0.225421	+	0.453865i
$304$	−1.53304	+	2.07719i	−0.0879256	+	0.119135i
$305$	−23.0175	−	2.59345i	−1.31798	−	0.148500i
$306$	−0.0865863	+	0.0765007i	−0.00494981	+	0.00437325i
$307$	2.51771	−	2.51771i	0.143693	−	0.143693i	−0.631601	−	0.775294i	$-0.717602\pi$
$307$	2.51771	−	2.51771i	0.143693	−	0.143693i	0.775294	+	0.631601i	$0.217602\pi$
$308$	0.510583	+	0.593308i	0.0290932	+	0.0338069i
$309$	−1.10715	+	2.45557i	−0.0629837	+	0.139692i
$310$	−0.180090	−	2.40313i	−0.0102284	−	0.136489i
$311$	−12.5379	+	14.5694i	−0.710962	+	0.826152i	−0.991004	−	0.133835i	$-0.957271\pi$
$311$	−12.5379	+	14.5694i	−0.710962	+	0.826152i	0.280042	+	0.959988i	$0.409652\pi$
$312$	11.5367	+	1.00602i	0.653136	+	0.0569545i
$313$	9.49846	−	1.43166i	0.536885	−	0.0809223i	0.124997	−	0.992157i	$-0.460108\pi$
$313$	9.49846	−	1.43166i	0.536885	−	0.0809223i	0.411887	+	0.911235i	$0.364870\pi$
$314$	−13.2475	−	10.5645i	−0.747599	−	0.596190i
$315$	2.32758	+	1.42053i	0.131144	+	0.0800380i
$316$	9.59158	−	6.02679i	0.539569	−	0.339033i
$317$	8.75566	+	3.82006i	0.491767	+	0.214556i	0.631117	−	0.775687i	$-0.282597\pi$
$317$	8.75566	+	3.82006i	0.491767	+	0.214556i	−0.139350	+	0.990243i	$0.544501\pi$
$318$	−12.2824	−	15.7925i	−0.688762	−	0.885600i
$319$	−8.13032	+	4.36982i	−0.455210	+	0.244663i
$320$	−1.72366	+	0.995158i	−0.0963557	+	0.0556310i
$321$	22.3584	+	6.28379i	1.24792	+	0.350727i
$322$	−2.54279	+	0.0951445i	−0.141704	+	0.00530219i
$323$	0.0221248	+	0.0969352i	0.00123106	+	0.00539362i
$324$	−8.93142	−	1.10891i	−0.496190	−	0.0616062i
$325$	5.42933	−	4.32974i	0.301165	−	0.240171i
$326$	−11.5367	+	12.4336i	−0.638959	+	0.688634i
$327$	−0.0805525	+	1.62332i	−0.00445456	+	0.0897695i
$328$	1.72862	−	0.129542i	0.0954471	−	0.00715277i
$329$	−0.0409426	+	1.09422i	−0.00225724	+	0.0603260i
$330$	5.60054	−	1.88346i	0.308300	−	0.103681i
$331$	7.95514	−	2.13157i	0.437254	−	0.117162i	−0.0334752	−	0.999440i	$-0.510657\pi$
$331$	7.95514	−	2.13157i	0.437254	−	0.117162i	0.470729	+	0.882278i	$0.343991\pi$
$332$	−8.63601	+	4.15888i	−0.473963	+	0.228248i
$333$	−20.8335	−	25.4370i	−1.14167	−	1.39394i
$334$	−1.36204	+	12.0884i	−0.0745275	+	0.661450i
$335$	−20.5506	−	1.54005i	−1.12280	−	0.0841422i
$336$	−0.630664	−	0.477427i	−0.0344056	−	0.0260458i
$337$	−5.18404	−	27.3983i	−0.282393	−	1.49248i	−0.780385	−	0.625299i	$-0.784977\pi$
$337$	−5.18404	−	27.3983i	−0.282393	−	1.49248i	0.497992	−	0.867181i	$-0.334071\pi$
$338$	−31.6802	−	1.18539i	−1.72318	−	0.0644767i
$339$	−16.3962	−	5.27712i	−0.890518	−	0.286614i
$340$	−0.0142508	+	0.0753175i	−0.000772860	+	0.00408466i
$341$	0.461803	−	2.02329i	0.0250080	−	0.109567i
$342$	−4.51748	+	6.29099i	−0.244277	+	0.340178i
$343$	3.92692	−	4.92421i	0.212034	−	0.265882i
$344$	2.00469	−	6.49905i	0.108086	−	0.350405i
$345$	−6.56439	+	18.0515i	−0.353415	+	0.971862i
$346$	−2.66547	−	3.61159i	−0.143297	−	0.194160i
$347$	11.9244	+	20.6537i	0.640137	+	1.10875i	0.985402	+	0.170244i	$0.0544556\pi$
$347$	11.9244	+	20.6537i	0.640137	+	1.10875i	−0.345265	+	0.938505i	$0.612211\pi$
$348$	7.10147	−	6.04724i	0.380679	−	0.324166i
$349$	−6.25954	+	10.8418i	−0.335065	+	0.580350i	−0.983497	−	0.180922i	$-0.942092\pi$
$349$	−6.25954	+	10.8418i	−0.335065	+	0.580350i	0.648432	+	0.761273i	$0.275425\pi$
$350$	−0.471348	+	0.0531082i	−0.0251946	+	0.00283875i
$351$	34.6465	+	2.56661i	1.84929	+	0.136995i
$352$	−1.67104	+	0.381404i	−0.0890667	+	0.0203289i
$353$	−9.63130	−	24.5402i	−0.512623	−	1.30614i	−0.919655	−	0.392727i	$-0.871532\pi$
$353$	−9.63130	−	24.5402i	−0.512623	−	1.30614i	0.407032	−	0.913414i	$-0.366564\pi$
$354$	−8.08851	+	2.38747i	−0.429899	+	0.126892i
$355$	−0.140296	+	0.0432755i	−0.00744612	+	0.00229682i
$356$	−8.66535	−	7.45714i	−0.459263	−	0.395227i
$357$	−0.0297805	+	0.00641657i	−0.00157615	+	0.000339601i
$358$	−1.60897	−	3.04432i	−0.0850368	−	0.160898i
$359$	−28.4867	−	9.96794i	−1.50347	−	0.526088i	−0.552006	−	0.833840i	$-0.686137\pi$
$359$	−28.4867	−	9.96794i	−1.50347	−	0.526088i	−0.951466	+	0.307753i	$0.900423\pi$
$360$	−5.13163	+	3.05263i	−0.270461	+	0.160888i
$361$	−5.35199	−	11.1135i	−0.281684	−	0.584923i
$362$	−6.73466	−	4.97041i	−0.353966	−	0.261239i
$363$	−13.9596	+	0.352112i	−0.732691	+	0.0184811i
$364$	2.52281	+	1.72002i	0.132231	+	0.0901536i
$365$	−1.76500	+	6.58709i	−0.0923845	+	0.344784i
$366$	19.7589	+	3.98850i	1.03282	+	0.208482i
$367$	14.4261	−	7.62444i	0.753038	−	0.397992i	−0.0462580	−	0.998930i	$-0.514730\pi$
$367$	14.4261	−	7.62444i	0.753038	−	0.397992i	0.799296	+	0.600937i	$0.205206\pi$
$368$	2.41754	−	5.02008i	0.126023	−	0.261690i
$369$	5.18035	−	0.456198i	0.269678	−	0.0237487i
$370$	−21.2667	−	4.85400i	−1.10561	−	0.252347i
$371$	−0.786201	−	5.21610i	−0.0408175	−	0.270806i
$372$	−0.0255463	+	2.09701i	−0.00132451	+	0.108725i
$373$	−8.73394	+	8.10391i	−0.452226	+	0.419605i	−0.873120	−	0.487505i	$-0.837907\pi$
$373$	−8.73394	+	8.10391i	−0.452226	+	0.419605i	0.420894	+	0.907110i	$0.361717\pi$
$374$	−0.0308456	+	0.0583627i	−0.00159499	+	0.00301786i
$375$	−5.63243	+	20.0407i	−0.290857	+	1.03490i
$376$	−2.07646	−	1.19885i	−0.107085	−	0.0618257i
$377$	−26.2222	+	24.6732i	−1.35051	+	1.27074i
$378$	−1.91050	−	1.40749i	−0.0982657	−	0.0723937i
$379$	−3.26794	−	29.0038i	−0.167863	−	1.48982i	−0.741633	−	0.670806i	$-0.765948\pi$
$379$	−3.26794	−	29.0038i	−0.167863	−	1.48982i	0.573770	−	0.819017i	$-0.305480\pi$
$380$	0.192127	+	5.13470i	0.00985591	+	0.263405i
$381$	−24.0738	−	3.92903i	−1.23334	−	0.201290i
$382$	1.18511	−	7.86272i	0.0606357	−	0.402292i
$383$	−0.597705	+	1.52293i	−0.0305413	+	0.0778180i	−0.945331	−	0.326113i	$-0.894261\pi$
$383$	−0.597705	+	1.52293i	−0.0305413	+	0.0778180i	0.914790	+	0.403931i	$0.132356\pi$
$384$	1.56956	−	0.732444i	0.0800964	−	0.0373774i
$385$	1.53077	+	0.289638i	0.0780155	+	0.0147613i
$386$	11.7860	+	5.67585i	0.599892	+	0.288893i
$387$	5.75940	−	19.5739i	0.292767	−	0.994997i
$388$	−2.26981	+	6.48676i	−0.115232	+	0.329315i
$389$	5.81083	+	21.6863i	0.294621	+	1.09954i	0.941518	+	0.336963i	$0.109400\pi$
$389$	5.81083	+	21.6863i	0.294621	+	1.09954i	−0.646897	+	0.762577i	$0.723934\pi$
$390$	19.2005	−	12.7509i	0.972257	−	0.645667i
$391$	−0.0858135	−	0.196687i	−0.00433977	−	0.00994687i
$392$	2.71584	+	6.22478i	0.137171	+	0.314399i
$393$	−6.75299	+	4.48460i	−0.340643	+	0.226218i
$394$	6.01764	+	22.4581i	0.303164	+	1.13142i
$395$	7.44648	−	21.2808i	0.374673	−	1.07075i
$396$	−4.99778	+	1.20947i	−0.251148	+	0.0607780i
$397$	22.4098	+	10.7920i	1.12472	+	0.541635i	0.901346	−	0.433099i	$-0.142580\pi$
$397$	22.4098	+	10.7920i	1.12472	+	0.541635i	0.223370	+	0.974734i	$0.428294\pi$
$398$	17.8622	+	3.37971i	0.895351	+	0.169410i
$399$	−1.85050	+	0.863545i	−0.0926409	+	0.0432313i
$400$	0.379460	−	0.966848i	0.0189730	−	0.0483424i
$401$	−0.753602	+	4.99982i	−0.0376331	+	0.249679i	−0.999735	−	0.0230101i	$-0.992675\pi$
$401$	−0.753602	+	4.99982i	−0.0376331	+	0.249679i	0.962102	+	0.272689i	$0.0879131\pi$
$402$	17.6999	+	2.88876i	0.882791	+	0.144078i
$403$	−0.302696	−	8.08971i	−0.0150783	−	0.402977i
$404$	−0.570224	−	5.06088i	−0.0283697	−	0.251788i
$405$	−15.2742	+	9.35780i	−0.758981	+	0.464993i
$406$	2.41318	−	0.474058i	0.119764	−	0.0235271i
$407$	−16.2686	−	9.39271i	−0.806407	−	0.465579i
$408$	0.0180487	−	0.0642191i	0.000893544	−	0.00317932i
$409$	13.0610	−	24.7125i	0.645823	−	1.22196i	−0.316124	−	0.948718i	$-0.602382\pi$
$409$	13.0610	−	24.7125i	0.645823	−	1.22196i	0.961946	−	0.273238i	$-0.0880947\pi$
$410$	2.52914	−	2.34670i	0.124905	−	0.115895i
$411$	0.0441649	−	3.62535i	0.00217849	−	0.178825i
$412$	−0.231785	−	1.53779i	−0.0114192	−	0.0757617i
$413$	−2.16787	−	0.494802i	−0.106674	−	0.0243476i
$414$	7.05568	−	15.1535i	0.346768	−	0.744754i
$415$	−8.27749	+	17.1884i	−0.406326	+	0.843745i
$416$	−5.91118	+	3.12415i	−0.289820	+	0.153174i
$417$	−20.6162	−	4.16154i	−1.00958	−	0.203792i
$418$	−1.14527	+	4.27420i	−0.0560170	+	0.209058i
$419$	−24.4531	−	16.6719i	−1.19461	−	0.814474i	−0.208093	−	0.978109i	$-0.566726\pi$
$419$	−24.4531	−	16.6719i	−1.19461	−	0.814474i	−0.986521	+	0.163635i	$0.947678\pi$
$420$	−1.57383	+	0.0396977i	−0.0767950	+	0.00193705i
$421$	−14.4208	−	10.6430i	−0.702825	−	0.518708i	0.182777	−	0.983154i	$-0.441492\pi$
$421$	−14.4208	−	10.6430i	−0.702825	−	0.518708i	−0.885601	+	0.464446i	$0.846253\pi$
$422$	0.954553	+	1.98215i	0.0464669	+	0.0964896i
$423$	−6.27574	−	3.51502i	−0.305137	−	0.170906i
$424$	10.9026	+	3.81497i	0.529476	+	0.185272i
$425$	−0.0186916	−	0.0353662i	−0.000906675	−	0.00171551i
$426$	0.124901	−	0.0269114i	0.00605147	−	0.00130386i
$427$	4.02849	+	3.46679i	0.194952	+	0.167770i
$428$	−12.8130	+	3.95229i	−0.619341	+	0.191041i
$429$	19.0371	−	5.61914i	0.919119	−	0.271294i
$430$	−4.94546	−	12.6008i	−0.238491	−	0.607666i
$431$	34.6721	−	7.91367i	1.67009	−	0.381188i	0.720202	−	0.693765i	$-0.244049\pi$
$431$	34.6721	−	7.91367i	1.67009	−	0.381188i	0.949893	+	0.312577i	$0.101192\pi$
$432$	4.67964	−	2.25853i	0.225149	−	0.108663i
$433$	26.5836	−	2.99526i	1.27753	−	0.143943i	0.552996	−	0.833184i	$-0.313484\pi$
$433$	26.5836	−	2.99526i	1.27753	−	0.143943i	0.724532	+	0.689241i	$0.242056\pi$
$434$	−0.276474	+	0.478868i	−0.0132712	+	0.0229864i
$435$	3.54626	−	18.2226i	0.170030	−	0.873705i
$436$	−0.469187	−	0.812656i	−0.0224700	−	0.0389192i
$437$	−8.54187	−	11.5738i	−0.408613	−	0.553651i
$438$	2.02815	−	5.57724i	0.0969087	−	0.266491i
$439$	−4.12860	+	13.3846i	−0.197047	+	0.638811i	0.802087	+	0.597207i	$0.203723\pi$
$439$	−4.12860	+	13.3846i	−0.197047	+	0.638811i	−0.999134	+	0.0416042i	$0.986753\pi$
$440$	−2.12699	+	2.66716i	−0.101400	+	0.127152i
$441$	8.39028	+	18.5665i	0.399537	+	0.884121i
$442$	−0.0572992	+	0.251044i	−0.00272544	+	0.0119409i
$443$	−1.74785	+	9.23762i	−0.0830430	+	0.438893i	0.916226	+	0.400662i	$0.131220\pi$
$443$	−1.74785	+	9.23762i	−0.0830430	+	0.438893i	−0.999269	+	0.0382307i	$0.987828\pi$
$444$	18.0702	+	5.81592i	0.857575	+	0.276011i
$445$	−22.7379	−	0.850794i	−1.07788	−	0.0403315i
$446$	3.78669	+	20.0131i	0.179305	+	0.947649i
$447$	−16.8832	−	12.7810i	−0.798549	−	0.604519i
$448$	0.455405	+	0.0341279i	0.0215158	+	0.00161239i
$449$	1.75312	−	15.5593i	0.0827346	−	0.734290i	−0.882033	−	0.471187i	$-0.843826\pi$
$449$	1.75312	−	15.5593i	0.0827346	−	0.734290i	0.964768	−	0.263103i	$-0.0847458\pi$
$450$	1.10047	−	2.91514i	0.0518767	−	0.137421i
$451$	2.67695	−	1.28915i	0.126052	−	0.0607037i
$452$	9.60570	−	2.57384i	0.451814	−	0.121063i
$453$	−14.6277	+	4.91928i	−0.687268	+	0.231128i
$454$	−0.917230	+	24.5135i	−0.0430477	+	1.15048i
$455$	6.06017	−	0.454147i	0.284105	−	0.0212907i
$456$	0.221615	−	4.46605i	0.0103781	−	0.209142i
$457$	7.41772	−	7.99441i	0.346986	−	0.373963i	−0.535311	−	0.844655i	$-0.679805\pi$
$457$	7.41772	−	7.99441i	0.346986	−	0.373963i	0.882297	+	0.470693i	$0.155996\pi$
$458$	14.9994	−	11.9616i	0.700877	−	0.558931i
$459$	0.0516300	−	0.193347i	0.00240988	−	0.00902465i
$460$	−2.46771	−	10.8117i	−0.115057	−	0.504099i
$461$	11.0386	−	0.413037i	0.514121	−	0.0192370i	0.220928	−	0.975290i	$-0.429092\pi$
$461$	11.0386	−	0.413037i	0.514121	−	0.0192370i	0.293193	+	0.956053i	$0.405282\pi$
$462$	−1.30521	−	0.366827i	−0.0607238	−	0.0170663i
$463$	−9.67739	+	5.58724i	−0.449746	+	0.259661i	−0.707723	−	0.706490i	$-0.750278\pi$
$463$	−9.67739	+	5.58724i	−0.449746	+	0.259661i	0.257977	+	0.966151i	$0.416944\pi$
$464$	−1.55137	+	5.15686i	−0.0720206	+	0.239401i
$465$	2.56251	+	3.29484i	0.118834	+	0.152794i
$466$	2.29756	+	1.00241i	0.106432	+	0.0464359i
$467$	1.60394	−	1.00782i	0.0742214	−	0.0466364i	−0.494410	−	0.869229i	$-0.664616\pi$
$467$	1.60394	−	1.00782i	0.0742214	−	0.0466364i	0.568632	+	0.822592i	$0.307473\pi$
$468$	−17.6099	+	9.60284i	−0.814016	+	0.443891i
$469$	3.69696	+	2.94823i	0.170710	+	0.136137i
$470$	−4.71886	+	0.711254i	−0.217665	+	0.0328077i
$471$	29.2372	+	2.54953i	1.34718	+	0.117476i
$472$	3.17604	−	3.69063i	0.146189	−	0.169875i
$473$	−0.871156	−	11.6248i	−0.0400558	−	0.534507i
$474$	−8.06454	+	17.8865i	−0.370417	+	0.821552i
$475$	−1.74906	−	2.03244i	−0.0802522	−	0.0932548i
$476$	0.0124368	−	0.0124368i	0.000570042	−	0.000570042i
$477$	32.8541	+	11.0176i	1.50429	+	0.504460i
$478$	15.1927	+	1.71180i	0.694896	+	0.0782960i
$479$	−13.6035	+	18.4320i	−0.621558	+	0.842181i	−0.996388	−	0.0849124i	$-0.972939\pi$
$479$	−13.6035	+	18.4320i	−0.621558	+	0.842181i	0.374831	+	0.927093i	$0.377701\pi$
$480$	1.53346	−	3.08748i	0.0699927	−	0.140924i
$481$	−70.7809	−	18.9657i	−3.22733	−	0.864760i
$482$	−3.63329	+	0.687456i	−0.165492	+	0.0313128i
$483$	3.57774	−	2.57377i	0.162793	−	0.117110i
$484$	6.66127	−	4.54158i	0.302785	−	0.206435i
$485$	4.51765	+	12.9107i	0.205136	+	0.586244i
$486$	13.9494	−	6.95802i	0.632758	−	0.315622i
$487$	−15.3982	−	19.3087i	−0.697759	−	0.874962i	0.299095	−	0.954223i	$-0.403315\pi$
$487$	−15.3982	−	19.3087i	−0.697759	−	0.874962i	−0.996854	+	0.0792617i	$0.974744\pi$
$488$	−10.8334	+	4.25181i	−0.490407	+	0.192470i
$489$	4.73212	−	28.9944i	0.213994	−	1.31117i
$490$	11.9507	+	6.31612i	0.539877	+	0.285333i
$491$	−3.88265	+	2.86553i	−0.175222	+	0.129319i	−0.677900	−	0.735154i	$-0.737110\pi$
$491$	−3.88265	+	2.86553i	−0.175222	+	0.129319i	0.502679	+	0.864473i	$0.332348\pi$
$492$	−2.37004	+	1.84327i	−0.106850	+	0.0831008i
$493$	0.111566	+	0.174838i	0.00502469	+	0.00787429i
$494$			17.2609i			0.776603i
$495$	−6.27612	+	8.08399i	−0.282090	+	0.363348i
$496$	−0.644183	−	1.02521i	−0.0289247	−	0.0460334i
$497$	0.0321911	+	0.00992964i	0.00144397	+	0.000445405i
$498$	8.47560	−	14.2757i	0.379801	−	0.639709i
$499$	34.2432	+	13.4395i	1.53294	+	0.601633i	0.973793	−	0.227438i	$-0.0730348\pi$
$499$	34.2432	+	13.4395i	1.53294	+	0.601633i	0.559144	+	0.829071i	$0.311130\pi$
$500$	−3.54261	−	11.4848i	−0.158430	−	0.513618i
$501$	−9.61783	−	18.7471i	−0.429693	−	0.837559i
$502$	5.62584	+	8.25159i	0.251093	+	0.368286i
$503$	−31.7166	−	19.9289i	−1.41417	−	0.888585i	−0.414406	−	0.910092i	$-0.636011\pi$
$503$	−31.7166	−	19.9289i	−1.41417	−	0.888585i	−0.999769	+	0.0215077i	$0.993153\pi$
$504$	1.36743	+	0.0845645i	0.0609103	+	0.00376680i
$505$	−7.16757	−	7.16757i	−0.318953	−	0.318953i
$506$	0.713691	−	9.52355i	0.0317274	−	0.423373i
$507$	46.8462	−	28.6454i	2.08051	−	1.27219i
$508$	12.9079	−	5.63164i	0.572694	−	0.249864i
$509$	22.8771	−	33.5546i	1.01401	−	1.48728i	0.146909	−	0.989150i	$-0.453068\pi$
$509$	22.8771	−	33.5546i	1.01401	−	1.48728i	0.867102	−	0.498131i	$-0.165980\pi$
$510$	−0.0516067	−	0.122328i	−0.00228518	−	0.00541678i
$511$	1.18603	−	1.02066i	0.0524667	−	0.0451512i
$512$	−0.532032	+	0.846724i	−0.0235127	+	0.0374203i
$513$	0.490128	−	13.4057i	0.0216397	−	0.591876i
$514$	15.3473	−	5.37025i	0.676940	−	0.236872i
$515$	−2.26899	−	2.10532i	−0.0999836	−	0.0927713i
$516$	3.33485	+	11.2982i	0.146809	+	0.497373i
$517$	−4.06377	−	0.612515i	−0.178724	−	0.0269384i
$518$	3.40439	+	3.66906i	0.149580	+	0.161209i
$519$	7.30652	+	2.65700i	0.320721	+	0.116629i
$520$	−5.32145	+	12.1969i	−0.233361	+	0.534869i
$521$	7.98842			0.349979			0.174989	−	0.984570i	$-0.444011\pi$
$521$	7.98842			0.349979			0.174989	+	0.984570i	$0.444011\pi$
$522$	−4.45204	+	15.5299i	−0.194861	+	0.679727i
$523$	−19.6131			−0.857621			−0.428810	−	0.903395i	$-0.641067\pi$
$523$	−19.6131			−0.857621			−0.428810	+	0.903395i	$0.641067\pi$
$524$	1.87160	−	4.28975i	0.0817612	−	0.187399i
$525$	0.629204	−	0.528271i	0.0274607	−	0.0230556i
$526$	20.3214	+	21.9013i	0.886056	+	0.954941i
$527$	−0.0461111	−	0.00695013i	−0.00200863	−	0.000302752i
$528$	2.04563	−	2.15149i	0.0890245	−	0.0936318i
$529$	5.89792	+	5.47247i	0.256431	+	0.237933i
$530$	21.6996	−	7.59300i	0.942568	−	0.329819i
$531$	9.38298	−	11.1952i	0.407187	−	0.485828i
$532$	0.627261	−	0.998281i	0.0271952	−	0.0432810i
$533$	8.78484	−	7.55997i	0.380514	−	0.327459i
$534$	19.6483	+	2.45657i	0.850266	+	0.106306i
$535$	−15.0337	+	22.0503i	−0.649962	+	0.953319i
$536$	−9.49032	+	4.14058i	−0.409919	+	0.178846i
$537$	5.23859	+	2.85085i	0.226062	+	0.123023i
$538$	0.308640	−	4.11852i	0.0133064	−	0.177562i
$539$	8.23116	+	8.23116i	0.354541	+	0.354541i
$540$	4.47925	−	9.32164i	0.192756	−	0.401139i
$541$	19.8936	+	12.5000i	0.855292	+	0.537416i	0.886835	−	0.462087i	$-0.152899\pi$
$541$	19.8936	+	12.5000i	0.855292	+	0.537416i	−0.0315426	+	0.999502i	$0.510042\pi$
$542$	−12.8811	−	18.8931i	−0.553291	−	0.811529i
$543$	14.4798	+	0.718521i	0.621389	+	0.0308347i
$544$	0.0113520	+	0.0368024i	0.000486714	+	0.00157789i
$545$	−1.73856	−	0.682333i	−0.0744716	−	0.0292279i
$546$	−5.28819	−	0.0644221i	−0.226314	−	0.00275701i
$547$	38.9084	+	12.0017i	1.66360	+	0.513154i	0.976884	−	0.213769i	$-0.0685739\pi$
$547$	38.9084	+	12.0017i	1.66360	+	0.513154i	0.686720	+	0.726922i	$0.259050\pi$
$548$	1.11368	+	1.77241i	0.0475739	+	0.0757134i
$549$	−32.3313	+	13.1780i	−1.37987	+	0.562425i
$550$		−	1.78025i		−	0.0759102i
$551$	9.89896	+	9.76182i	0.421710	+	0.415867i
$552$	1.32202	+	9.55978i	0.0562688	+	0.406891i
$553$	−4.16237	+	3.07197i	−0.177002	+	0.130633i
$554$	−4.28679	−	2.26563i	−0.182128	−	0.0962576i
$555$	35.3361	−	13.3740i	1.49994	−	0.567695i
$556$	11.3035	−	4.43629i	0.479374	−	0.188140i
$557$	29.1864	+	36.5986i	1.23667	+	1.55073i	0.718670	+	0.695351i	$0.244751\pi$
$557$	29.1864	+	36.5986i	1.23667	+	1.55073i	0.517998	+	0.855382i	$0.326678\pi$
$558$	−1.97248	−	3.05018i	−0.0835017	−	0.129124i
$559$	−15.0187	−	42.9210i	−0.635224	−	1.81537i
$560$	0.751002	−	0.512024i	0.0317356	−	0.0216370i
$561$	−0.0114167	−	0.113766i	−0.000482014	−	0.00480319i
$562$	8.98246	−	1.69957i	0.378902	−	0.0716922i
$563$	20.2583	+	5.42819i	0.853785	+	0.228771i	0.659063	−	0.752087i	$-0.270953\pi$
$563$	20.2583	+	5.42819i	0.853785	+	0.228771i	0.194722	+	0.980859i	$0.437620\pi$
$564$	4.14478	−	0.259879i	0.174527	−	0.0109429i
$565$	11.7534	−	15.9252i	0.494468	−	0.669980i
$566$	13.0890	+	1.47478i	0.550171	+	0.0619894i
$567$	4.10526	+	0.200193i	0.172405	+	0.00840734i
$568$	−0.0521607	+	0.0521607i	−0.00218862	+	0.00218862i
$569$	9.46128	+	10.9942i	0.396638	+	0.460901i	0.920409	−	0.390958i	$-0.127856\pi$
$569$	9.46128	+	10.9942i	0.396638	+	0.460901i	−0.523771	+	0.851859i	$0.675475\pi$
$570$	−5.19725	−	7.22460i	−0.217689	−	0.302605i
$571$	−0.339775	−	4.53398i	−0.0142191	−	0.189741i	−0.999790	−	0.0204794i	$-0.993481\pi$
$571$	−0.339775	−	4.53398i	−0.0142191	−	0.189741i	0.985571	−	0.169262i	$-0.0541383\pi$
$572$	−7.47513	+	8.68625i	−0.312551	+	0.363191i
$573$	5.82405	+	12.4804i	0.243303	+	0.521377i
$574$	−0.782800	+	0.117988i	−0.0326735	+	0.00492473i
$575$	4.52461	+	3.60826i	0.188689	+	0.150475i
$576$	−1.56285	+	2.56076i	−0.0651186	+	0.106698i
$577$	3.89517	−	2.44750i	0.162158	−	0.101891i	−0.448508	−	0.893779i	$-0.648045\pi$
$577$	3.89517	−	2.44750i	0.162158	−	0.101891i	0.610666	+	0.791888i	$0.290902\pi$
$578$	−15.5802	−	6.79757i	−0.648051	−	0.282742i
$579$	−22.4442	+	3.10380i	−0.932750	+	0.128990i
$580$	3.98529	+	9.94971i	0.165480	+	0.413139i
$581$	3.79095	−	2.18870i	0.157275	−	0.0908027i
$582$	−2.94053	−	11.5344i	−0.121889	−	0.478118i
$583$	19.7843	−	0.740277i	0.819382	−	0.0306591i
$584$	0.762428	+	3.34041i	0.0315495	+	0.138227i
$585$	−15.4860	+	36.7957i	−0.640267	+	1.52131i
$586$	6.22468	−	4.96401i	0.257139	−	0.205062i
$587$	5.27417	−	5.68421i	0.217688	−	0.234612i	−0.614761	−	0.788714i	$-0.710747\pi$
$587$	5.27417	−	5.68421i	0.217688	−	0.234612i	0.832449	+	0.554101i	$0.186938\pi$
$588$	−9.88315	−	6.37922i	−0.407574	−	0.263075i
$589$	−3.11711	+	0.233595i	−0.128438	+	0.00962513i
$590$	0.362358	−	9.68423i	0.0149181	−	0.398694i
$591$	−30.2019	−	26.6380i	−1.24234	−	1.09574i
$592$	−10.5865	+	2.83663i	−0.435101	+	0.116585i
$593$	18.7166	−	9.01342i	0.768597	−	0.370137i	−0.00813610	−	0.999967i	$-0.502590\pi$
$593$	18.7166	−	9.01342i	0.768597	−	0.370137i	0.776733	+	0.629830i	$0.216876\pi$
$594$	6.05222	−	6.53394i	0.248326	−	0.268091i
$595$	0.00391947	−	0.0347863i	0.000160683	−	0.00142610i
$596$	12.1914	+	0.913621i	0.499380	+	0.0374234i
$597$	−29.0112	+	12.2390i	−1.18735	+	0.500908i
$598$	−6.92584	−	36.6040i	−0.283219	−	1.49685i
$599$	−33.1933	−	1.24200i	−1.35624	−	0.0507469i	−0.650656	−	0.759373i	$-0.725506\pi$
$599$	−33.1933	−	1.24200i	−1.35624	−	0.0507469i	−0.705584	+	0.708626i	$0.749315\pi$
$600$	0.378918	+	1.75863i	0.0154693	+	0.0717957i
$601$	−0.898591	+	4.74917i	−0.0366543	+	0.193723i	−0.996108	−	0.0881448i	$-0.971906\pi$
$601$	−0.898591	+	4.74917i	−0.0366543	+	0.193723i	0.959453	+	0.281867i	$0.0909538\pi$
$602$	−0.691147	+	3.02811i	−0.0281691	+	0.123417i
$603$	−28.3066	+	12.7918i	−1.15273	+	0.520924i
$604$	5.55534	−	6.96617i	0.226044	−	0.283450i
$605$	4.72971	−	15.3333i	0.192290	−	0.623389i
$606$	5.67206	+	6.75578i	0.230412	+	0.274435i
$607$	−19.1491	−	25.9462i	−0.777240	−	1.05312i	−0.996987	−	0.0775656i	$-0.975285\pi$
$607$	−19.1491	−	25.9462i	−0.777240	−	1.05312i	0.219748	−	0.975557i	$-0.429477\pi$
$608$	1.29082	+	2.23577i	0.0523499	+	0.0906726i
$609$	−3.02766	+	2.99630i	−0.122687	+	0.121416i
$610$	−11.5816	+	20.0599i	−0.468924	+	0.812200i
$611$	−15.9301	+	1.79489i	−0.644464	+	0.0726136i
$612$	0.0354925	+	0.109954i	0.00143470	+	0.00444462i
$613$	−21.0991	+	4.81574i	−0.852186	+	0.194506i	−0.626236	−	0.779633i	$-0.715406\pi$
$613$	−21.0991	+	4.81574i	−0.852186	+	0.194506i	−0.225949	+	0.974139i	$0.572548\pi$
$614$	−1.30083	−	3.31445i	−0.0524971	−	0.133760i
$615$	−1.40062	+	5.80937i	−0.0564783	+	0.234256i
$616$	0.747982	−	0.230722i	0.0301371	−	0.00929605i
$617$	9.68721	+	8.33652i	0.389992	+	0.335616i	0.825329	−	0.564652i	$-0.190990\pi$
$617$	9.68721	+	8.33652i	0.389992	+	0.335616i	−0.435337	+	0.900268i	$0.643371\pi$
$618$	1.80794	+	1.99674i	0.0727260	+	0.0803205i
$619$	−6.36317	−	12.0397i	−0.255757	−	0.483917i	0.722484	−	0.691388i	$-0.243000\pi$
$619$	−6.36317	−	12.0397i	−0.255757	−	0.483917i	−0.978241	+	0.207471i	$0.933477\pi$
$620$	−2.27463	−	0.795929i	−0.0913515	−	0.0319653i
$621$	4.33959	+	28.6252i	0.174142	+	1.14869i
$622$	8.33990	+	17.3180i	0.334399	+	0.694388i
$623$	4.20073	+	3.10028i	0.168299	+	0.124210i
$624$	5.53550	−	10.1718i	0.221598	−	0.407198i
$625$	−15.4738	−	10.5498i	−0.618951	−	0.421994i
$626$	2.48615	−	9.27844i	0.0993665	−	0.370841i
$627$	−2.44304	−	7.26450i	−0.0975658	−	0.290116i
$628$	−14.9806	+	7.91748i	−0.597791	+	0.315942i
$629$	−0.183144	+	0.380302i	−0.00730242	+	0.0151636i
$630$	2.23279	−	1.56531i	0.0889564	−	0.0623635i
$631$	−39.4383	−	9.00154i	−1.57001	−	0.358346i	−0.653050	−	0.757315i	$-0.726511\pi$
$631$	−39.4383	−	9.00154i	−1.57001	−	0.358346i	−0.916964	+	0.398969i	$0.869368\pi$
$632$	−1.68833	−	11.2013i	−0.0671582	−	0.445566i
$633$	−3.27658	−	1.94533i	−0.130232	−	0.0773200i
$634$	7.00264	−	6.49750i	0.278110	−	0.258049i
$635$	13.0973	−	24.7812i	0.519749	−	0.983414i
$636$	−19.3864	+	4.94228i	−0.768722	+	0.195974i
$637$	39.3240	+	22.7037i	1.55807	+	0.899555i
$638$	0.753965	+	9.19940i	0.0298498	+	0.364208i
$639$	−0.154429	+	0.158509i	−0.00610912	+	0.00627051i
$640$	0.222845	+	1.97780i	0.00880871	+	0.0781794i
$641$	0.688166	+	18.3916i	0.0271809	+	0.726425i	0.944546	+	0.328379i	$0.106502\pi$
$641$	0.688166	+	18.3916i	0.0271809	+	0.726425i	−0.917365	+	0.398047i	$0.869688\pi$
$642$	14.7004	−	17.9800i	0.580179	−	0.709614i
$643$	−4.38407	+	29.0864i	−0.172891	+	1.14706i	0.719068	+	0.694939i	$0.244569\pi$
$643$	−4.38407	+	29.0864i	−0.172891	+	1.14706i	−0.891959	+	0.452116i	$0.850669\pi$
$644$	−0.929635	+	2.36867i	−0.0366328	+	0.0933388i
$645$	19.2097	+	13.4426i	0.756380	+	0.529302i
$646$	0.0976947	+	0.0184848i	0.00384375	+	0.000727276i
$647$	−29.8398	−	14.3701i	−1.17312	−	0.564946i	−0.257222	−	0.966352i	$-0.582807\pi$
$647$	−29.8398	−	14.3701i	−1.17312	−	0.564946i	−0.915900	+	0.401407i	$0.868521\pi$
$648$	−4.58799	+	7.74276i	−0.180233	+	0.304164i
$649$	2.75640	−	7.87734i	0.108198	−	0.309213i
$650$	−1.79734	−	6.70775i	−0.0704973	−	0.263099i
$651$	−0.0599325	−	0.955858i	−0.00234894	−	0.0374630i
$652$	6.78274	+	15.5462i	0.265633	+	0.608837i
$653$	13.1912	+	30.2345i	0.516211	+	1.18317i	0.958187	+	0.286141i	$0.0923727\pi$
$653$	13.1912	+	30.2345i	0.516211	+	1.18317i	−0.441976	+	0.897027i	$0.645723\pi$
$654$	1.45566	+	0.722982i	0.0569207	+	0.0282708i
$655$	−2.41095	−	8.99779i	−0.0942036	−	0.351573i
$656$	0.572528	−	1.63619i	0.0223535	−	0.0638825i
$657$	2.41773	+	9.99057i	0.0943245	+	0.389769i
$658$	0.986544	+	0.475094i	0.0384595	+	0.0185211i
$659$	−10.7307	−	2.03035i	−0.418008	−	0.0790913i	−0.0273467	−	0.999626i	$-0.508706\pi$
$659$	−10.7307	−	2.03035i	−0.418008	−	0.0790913i	−0.390661	+	0.920535i	$0.627753\pi$
$660$	0.513305	−	5.88643i	0.0199804	−	0.229129i
$661$	12.6676	−	32.2766i	0.492713	−	1.25541i	−0.441038	−	0.897489i	$-0.645389\pi$
$661$	12.6676	−	32.2766i	0.492713	−	1.25541i	0.933751	−	0.357924i	$-0.116515\pi$
$662$	1.22748	−	8.14378i	0.0477073	−	0.316517i
$663$	−0.157874	−	0.417127i	−0.00613131	−	0.0161999i
$664$	0.358404	+	9.57855i	0.0139088	+	0.371720i
$665$	−0.262732	−	2.33181i	−0.0101883	−	0.0904237i
$666$	−31.6457	+	8.92319i	−1.22625	+	0.345767i
$667$	−24.9089	−	16.7293i	−0.964478	−	0.647762i
$668$	10.5351	+	6.08247i	0.407617	+	0.235338i
$669$	−24.6401	−	25.2479i	−0.952643	−	0.976140i
$670$	−9.62958	+	18.2200i	−0.372023	+	0.703902i
$671$	−14.6226	+	13.5678i	−0.564499	+	0.523778i
$672$	−0.689789	+	0.387124i	−0.0266092	+	0.0149336i
$673$	7.20711	+	47.8160i	0.277814	+	1.84317i	0.497327	+	0.867563i	$0.334315\pi$
$673$	7.20711	+	47.8160i	0.277814	+	1.84317i	−0.219514	+	0.975609i	$0.570447\pi$
$674$	−27.1853	−	6.20487i	−1.04714	−	0.239003i
$675$	1.20544	+	5.26062i	0.0463972	+	0.202481i
$676$	−13.7552	+	28.5629i	−0.529044	+	1.09857i
$677$	−3.90574	+	2.06425i	−0.150110	+	0.0793354i	−0.540637	−	0.841256i	$-0.681817\pi$
$677$	−3.90574	+	2.06425i	−0.150110	+	0.0793354i	0.390527	+	0.920592i	$0.372293\pi$
$678$	−11.3935	+	12.9178i	−0.437565	+	0.496106i
$679$	0.812305	−	3.03156i	0.0311734	−	0.116341i
$680$	0.0633344	+	0.0431806i	0.00242876	+	0.00165590i
$681$	−22.1652	−	36.2486i	−0.849374	−	1.38905i
$682$	−1.66980	−	1.23237i	−0.0639400	−	0.0471898i
$683$	12.6787	+	26.3276i	0.485137	+	1.00740i	0.989584	+	0.143955i	$0.0459820\pi$
$683$	12.6787	+	26.3276i	0.485137	+	1.00740i	−0.504447	+	0.863443i	$0.668304\pi$
$684$	3.95958	+	6.65627i	0.151398	+	0.254509i
$685$	3.93243	+	1.37602i	0.150250	+	0.0525749i
$686$	−2.94300	−	5.56842i	−0.112364	−	0.212603i
$687$	−10.1806	+	31.6314i	−0.388414	+	1.20681i
$688$	−5.15513	−	4.43634i	−0.196537	−	0.169134i
$689$	73.7972	−	22.7634i	2.81145	−	0.867217i
$690$	13.9203	+	13.2353i	0.529937	+	0.503861i
$691$	−10.6163	−	27.0499i	−0.403863	−	1.02903i	−0.977691	−	0.210050i	$-0.932637\pi$
$691$	−10.6163	−	27.0499i	−0.403863	−	1.02903i	0.573827	−	0.818976i	$-0.305458\pi$
$692$	−4.37615	+	0.998827i	−0.166356	+	0.0379697i
$693$	2.23473	−	0.721360i	0.0848905	−	0.0274022i
$694$	23.6989	−	2.67022i	0.899598	−	0.101360i
$695$	12.0841	−	20.9302i	0.458374	−	0.793928i
$696$	−2.70285	−	8.92718i	−0.102451	−	0.338384i
$697$	−0.0333809	−	0.0578174i	−0.00126439	−	0.00218999i
$698$	7.43408	+	10.0728i	0.281384	+	0.381262i
$699$	−4.27557	+	0.755155i	−0.161717	+	0.0285626i
$700$	−0.139811	+	0.453257i	−0.00528437	+	0.0171315i
$701$	10.6039	−	13.2968i	0.400503	−	0.502215i	−0.540157	−	0.841564i	$-0.681635\pi$
$701$	10.6039	−	13.2968i	0.400503	−	0.502215i	0.940661	+	0.339349i	$0.110207\pi$
$702$	16.2073	−	30.7293i	0.611705	−	1.15980i
$703$	−6.29615	+	27.5852i	−0.237464	+	1.04040i
$704$	−0.318655	+	1.68413i	−0.0120098	+	0.0634731i
$705$	6.12717	−	5.54783i	0.230762	−	0.208943i
$706$	−26.3441	−	0.985725i	−0.991472	−	0.0370983i
$707$	0.432399	+	2.28529i	0.0162621	+	0.0859470i
$708$	−1.04627	+	8.36835i	−0.0393211	+	0.314502i
$709$	−18.1581	−	1.36076i	−0.681943	−	0.0511045i	−0.270746	−	0.962651i	$-0.587270\pi$
$709$	−18.1581	−	1.36076i	−0.681943	−	0.0511045i	−0.411197	+	0.911546i	$0.634889\pi$
$710$	−0.0164384	+	0.145895i	−0.000616924	+	0.00547535i
$711$	−5.50264	−	33.5352i	−0.206365	−	1.25767i
$712$	−10.3001	+	4.96028i	−0.386014	+	0.185894i
$713$	6.51653	−	1.74610i	0.244046	−	0.0653919i
$714$	−0.00602780	+	0.0298616i	−0.000225585	+	0.00111754i
$715$	−0.852846	+	22.7928i	−0.0318946	+	0.852402i
$716$	−3.43373	+	0.257322i	−0.128324	+	0.00961659i
$717$	−23.5612	+	12.0876i	−0.879910	+	0.451420i
$718$	−20.5279	+	22.1238i	−0.766093	+	0.825652i
$719$	24.1042	−	19.2225i	0.898936	−	0.716877i	−0.0606902	−	0.998157i	$-0.519330\pi$
$719$	24.1042	−	19.2225i	0.898936	−	0.716877i	0.959626	+	0.281279i	$0.0907587\pi$
$720$	0.745826	+	5.92418i	0.0277953	+	0.220781i
$721$	0.158038	+	0.692408i	0.00588563	+	0.0257866i
$722$	−12.3265	+	0.461224i	−0.458743	+	0.0171650i
$723$	4.58364	−	4.47331i	0.170467	−	0.166364i
$724$	−7.24882	+	4.18511i	−0.269400	+	0.155538i
$725$	−4.86331	−	2.76278i	−0.180619	−	0.102607i
$726$	−5.25961	+	12.9357i	−0.195202	+	0.480088i
$727$	−9.66177	−	4.21539i	−0.358335	−	0.156340i	0.213010	−	0.977050i	$-0.431673\pi$
$727$	−9.66177	−	4.21539i	−0.358335	−	0.156340i	−0.571345	+	0.820710i	$0.693578\pi$
$728$	2.58536	−	1.62449i	0.0958198	−	0.0602075i
$729$	−13.4600	+	23.4057i	−0.498518	+	0.866879i
$730$	5.33166	+	4.25186i	0.197334	+	0.157368i
$731$	−0.259012	+	0.0390398i	−0.00957991	+	0.00144394i
$732$	11.5571	−	16.5153i	0.427164	−	0.610424i
$733$	6.74464	−	7.83741i	0.249119	−	0.289481i	−0.619464	−	0.785025i	$-0.712650\pi$
$733$	6.74464	−	7.83741i	0.249119	−	0.289481i	0.868583	+	0.495543i	$0.165031\pi$
$734$	−1.21937	−	16.2714i	−0.0450079	−	0.600589i
$735$	−23.2953	+	2.33775i	−0.859261	+	0.0862293i
$736$	−3.63446	−	4.22332i	−0.133968	−	0.155674i
$737$	−12.5493	+	12.5493i	−0.462258	+	0.462258i
$738$	1.65345	−	4.93055i	0.0608643	−	0.181496i
$739$	−4.88825	−	0.550774i	−0.179817	−	0.0202605i	0.0215966	−	0.999767i	$-0.493125\pi$
$739$	−4.88825	−	0.550774i	−0.179817	−	0.0202605i	−0.201414	+	0.979506i	$0.564554\pi$
$740$	−12.9534	+	17.5512i	−0.476176	+	0.645196i
$741$	−16.5393	−	24.9051i	−0.607585	−	0.914913i
$742$	−5.09528	−	1.36528i	−0.187054	−	0.0501208i
$743$	38.7163	−	7.32551i	1.42036	−	0.268747i	0.581702	−	0.813402i	$-0.302387\pi$
$743$	38.7163	−	7.32551i	1.42036	−	0.268747i	0.838660	+	0.544655i	$0.183339\pi$
$744$	1.91182	+	0.861991i	0.0700908	+	0.0316021i
$745$	20.1047	−	13.7072i	0.736580	−	0.502191i
$746$	3.93511	+	11.2459i	0.144075	+	0.411741i
$747$	1.44973	+	28.7192i	0.0530427	+	1.05078i
$748$	0.0411581	+	0.0516106i	0.00150489	+	0.00188707i
$749$	5.70023	−	2.23717i	0.208282	−	0.0817445i
$750$	16.1162	+	13.1766i	0.588481	+	0.481141i
$751$	0.0367502	+	0.0194231i	0.00134104	+	0.000708758i	0.467939	−	0.883761i	$-0.344997\pi$
$751$	0.0367502	+	0.0194231i	0.00134104	+	0.000708758i	−0.466598	+	0.884470i	$0.654520\pi$
$752$	−1.92918	+	1.42380i	−0.0703498	+	0.0519205i
$753$	−16.0240	−	6.51530i	−0.583945	−	0.237431i
$754$	12.1285	+	33.9009i	0.441694	+	1.23460i
$755$		−	17.7338i		−	0.645401i
$756$	−2.05405	+	1.18825i	−0.0747051	+	0.0432162i
$757$	2.96890	+	4.72498i	0.107907	+	0.171732i	0.896312	−	0.443423i	$-0.146236\pi$
$757$	2.96890	+	4.72498i	0.107907	+	0.171732i	−0.788406	+	0.615155i	$0.789093\pi$
$758$	−27.8906	−	8.60310i	−1.01303	−	0.312479i
$759$	8.09565	+	14.4251i	0.293853	+	0.523597i
$760$	4.78310	+	1.87723i	0.173501	+	0.0680943i
$761$	−0.695146	−	2.25361i	−0.0251990	−	0.0816932i	0.942100	−	0.335332i	$-0.108849\pi$
$761$	−0.695146	−	2.25361i	−0.0251990	−	0.0816932i	−0.967299	+	0.253639i	$0.918372\pi$
$762$	−13.2281	+	20.4939i	−0.479204	+	0.742417i
$763$	0.241404	+	0.354075i	0.00873942	+	0.0128184i
$764$	−6.73276	−	4.23047i	−0.243583	−	0.153053i
$765$	0.191676	+	0.127054i	0.00693005	+	0.00459365i
$766$	1.15684	+	1.15684i	0.0417984	+	0.0417984i
$767$	2.43281	−	32.4636i	0.0878437	−	1.17219i
$768$	−0.0436747	−	1.73150i	−0.00157597	−	0.0624801i
$769$	42.2056	−	18.4141i	1.52197	−	0.664030i	0.538097	−	0.842883i	$-0.319143\pi$
$769$	42.2056	−	18.4141i	1.52197	−	0.664030i	0.983876	+	0.178852i	$0.0572385\pi$
$770$	0.877616	−	1.28723i	0.0316271	−	0.0463884i
$771$	−16.9984	+	22.4542i	−0.612181	+	0.808670i
$772$	9.91540	−	8.53289i	0.356863	−	0.307106i
$773$	−12.7511	+	20.2932i	−0.458625	+	0.729897i	−0.993351	−	0.115129i	$-0.963272\pi$
$773$	−12.7511	+	20.2932i	−0.458625	+	0.729897i	0.534726	+	0.845026i	$0.320415\pi$
$774$	−15.6376	−	13.1063i	−0.562081	−	0.471096i
$775$	1.18702	−	0.415356i	0.0426390	−	0.0149200i
$776$	5.03784	+	4.67443i	0.180848	+	0.167802i
$777$	−8.42775	−	2.03190i	−0.302344	−	0.0728939i
$778$	22.2006	+	3.34620i	0.795929	+	0.119967i
$779$	−3.04391	−	3.28056i	−0.109059	−	0.117538i
$780$	−4.00885	−	22.6975i	−0.143540	−	0.812700i
$781$	−0.0505610	+	0.115887i	−0.00180921	+	0.00414676i
$782$	−0.214592			−0.00767378
$783$	−8.45700	−	26.6736i	−0.302229	−	0.953235i
$784$	6.79144			0.242552
$785$	−13.4861	+	30.9104i	−0.481338	+	1.10324i
$786$	1.40995	+	7.98289i	0.0502911	+	0.284740i
$787$	−1.64504	−	1.77293i	−0.0586394	−	0.0631983i	0.703051	−	0.711140i	$-0.251821\pi$
$787$	−1.64504	−	1.77293i	−0.0586394	−	0.0631983i	−0.761690	+	0.647941i	$0.775630\pi$
$788$	22.9907	+	3.46529i	0.819009	+	0.123446i
$789$	−50.3068	−	12.1288i	−1.79097	−	0.431795i
$790$	−16.5274	−	15.3352i	−0.588019	−	0.545602i
$791$	−4.28664	+	1.49996i	−0.152415	+	0.0533325i
$792$	−0.890019	+	5.06443i	−0.0316255	+	0.179957i
$793$	−41.3979	+	65.8844i	−1.47008	+	2.33963i
$794$	18.8530	−	16.2244i	0.669069	−	0.575781i
$795$	−24.0340	+	31.7481i	−0.852398	+	1.12599i
$796$	10.2407	−	15.0203i	0.362971	−	0.532380i
$797$	−34.2481	+	14.9423i	−1.21313	+	0.529284i	−0.906363	−	0.422501i	$-0.861152\pi$
$797$	−34.2481	+	14.9423i	−1.21313	+	0.529284i	−0.306768	+	0.951784i	$0.599248\pi$
$798$	0.0514921	+	2.04142i	0.00182280	+	0.0722656i
$799$	−0.00690082	+	0.0920850i	−0.000244133	+	0.00325773i
$800$	−0.734434	−	0.734434i	−0.0259661	−	0.0259661i
$801$	−30.7038	+	15.2824i	−1.08486	+	0.539977i
$802$	4.28129	+	2.69011i	0.151178	+	0.0949911i
$803$	3.30824	+	4.85230i	0.116745	+	0.171234i
$804$	9.72578	−	15.0679i	0.343002	−	0.531403i
$805$	1.49279	+	4.83949i	0.0526138	+	0.170570i
$806$	−7.53577	−	2.95757i	−0.265436	−	0.104176i
$807$	3.50101	+	6.23821i	0.123241	+	0.219595i
$808$	−4.86664	−	1.50116i	−0.171208	−	0.0528106i
$809$	−13.2641	−	21.1097i	−0.466341	−	0.742178i	0.527904	−	0.849304i	$-0.322978\pi$
$809$	−13.2641	−	21.1097i	−0.466341	−	0.742178i	−0.994245	+	0.107126i	$0.965835\pi$
$810$	2.46898	+	17.7419i	0.0867510	+	0.623386i
$811$		−	15.5910i		−	0.547474i	−0.961805	−	0.273737i	$-0.911740\pi$
$811$		−	15.5910i		−	0.547474i	0.961805	−	0.273737i	$-0.0882597\pi$
$812$	0.530509	−	2.40140i	0.0186172	−	0.0842728i
$813$	36.6890	+	14.9177i	1.28674	+	0.523185i
$814$	−15.1147	+	11.1552i	−0.529770	+	0.390988i
$815$	29.8465	+	15.7743i	1.04548	+	0.552551i
$816$	−0.0516433	−	0.0422235i	−0.00180788	−	0.00147812i
$817$	−16.3446	+	6.41478i	−0.571825	+	0.224425i
$818$	−17.4276	−	21.8535i	−0.609342	−	0.764090i
$819$	7.69188	−	4.97416i	0.268776	−	0.173811i
$820$	−1.13951	−	3.25654i	−0.0397935	−	0.113723i
$821$	36.3435	−	24.7786i	1.26840	−	0.864779i	0.273133	−	0.961976i	$-0.411940\pi$
$821$	36.3435	−	24.7786i	1.26840	−	0.864779i	0.995265	+	0.0971974i	$0.0309878\pi$
$822$	−3.30519	−	1.49023i	−0.115282	−	0.0519776i
$823$	−29.7927	+	5.63709i	−1.03851	+	0.196497i	−0.677085	−	0.735905i	$-0.736757\pi$
$823$	−29.7927	+	5.63709i	−1.03851	+	0.196497i	−0.361425	+	0.932401i	$0.617709\pi$
$824$	−1.50217	−	0.402506i	−0.0523307	−	0.0140220i
$825$	1.70583	+	2.56867i	0.0593893	+	0.0894295i
$826$	−1.32043	+	1.78912i	−0.0459437	+	0.0622514i
$827$	27.2207	+	3.06704i	0.946557	+	0.106651i	0.571729	−	0.820443i	$-0.306273\pi$
$827$	27.2207	+	3.06704i	0.946557	+	0.106651i	0.374829	+	0.927094i	$0.377702\pi$
$828$	−11.0676	−	12.5267i	−0.384626	−	0.435334i
$829$	10.4760	−	10.4760i	0.363845	−	0.363845i	−0.501381	−	0.865226i	$-0.667175\pi$
$829$	10.4760	−	10.4760i	0.363845	−	0.363845i	0.865226	+	0.501381i	$0.167175\pi$
$830$	12.4441	+	14.4603i	0.431942	+	0.501926i
$831$	8.35618	−	0.838568i	0.289873	−	0.0290896i
$832$	0.499644	+	6.66729i	0.0173220	+	0.231147i
$833$	0.170613	−	0.198256i	0.00591140	−	0.00686917i
$834$	−12.0586	+	17.2319i	−0.417554	+	0.596691i
$835$	23.9416	−	3.60862i	0.828534	−	0.124881i
$836$	3.45959	+	2.75893i	0.119652	+	0.0954196i
$837$	5.76869	+	2.51098i	0.199395	+	0.0867923i
$838$	−25.0594	+	15.7459i	−0.865663	+	0.543932i
$839$	32.8277	+	14.3226i	1.13334	+	0.494471i	0.880976	−	0.473161i	$-0.156887\pi$
$839$	32.8277	+	14.3226i	1.13334	+	0.494471i	0.252364	+	0.967632i	$0.418792\pi$
$840$	−0.592977	+	1.45839i	−0.0204596	+	0.0503192i
$841$	26.3011	+	12.2169i	0.906934	+	0.421273i
$842$	−15.5217	+	8.96147i	−0.534914	+	0.308833i
$843$	−11.3320	+	11.0592i	−0.390294	+	0.380899i
$844$	2.19848	−	0.0822614i	0.0756749	−	0.00283155i
$845$	14.0406	+	61.5158i	0.483010	+	2.11621i
$846$	−5.73136	+	4.34648i	−0.197048	+	0.149435i
$847$	−2.87858	+	2.29559i	−0.0989091	+	0.0788774i
$848$	7.85651	−	8.46731i	0.269794	−	0.290769i
$849$	−20.2988	+	10.4139i	−0.696653	+	0.357404i
$850$	−0.0398899	+	0.00298934i	−0.00136821	+	0.000102533i
$851$	2.28337	−	61.0244i	0.0782730	−	2.09189i
$852$	0.0252809	−	0.125241i	0.000866109	−	0.00429069i
$853$	28.6680	−	7.68157i	0.981573	−	0.263012i	0.267866	−	0.963456i	$-0.413681\pi$
$853$	28.6680	−	7.68157i	0.981573	−	0.263012i	0.713707	+	0.700444i	$0.247015\pi$
$854$	4.78849	−	2.30602i	0.163859	−	0.0789102i
$855$	14.4215	+	5.44415i	0.493205	+	0.186186i
$856$	−1.50130	+	13.3244i	−0.0513134	+	0.455419i
$857$	−23.8155	−	1.78472i	−0.813521	−	0.0609650i	−0.338530	−	0.940956i	$-0.609930\pi$
$857$	−23.8155	−	1.78472i	−0.813521	−	0.0609650i	−0.474991	+	0.879991i	$0.657549\pi$
$858$	2.46249	−	19.6957i	0.0840682	−	0.672401i
$859$	1.46541	+	7.74488i	0.0499991	+	0.264252i	0.998642	−	0.0520972i	$-0.0165906\pi$
$859$	1.46541	+	7.74488i	0.0499991	+	0.264252i	−0.948643	+	0.316349i	$0.897543\pi$
$860$	−13.5271	−	0.506148i	−0.461270	−	0.0172595i
$861$	1.01642	−	0.920316i	0.0346395	−	0.0313643i
$862$	6.61171	−	34.9437i	0.225196	−	1.19019i
$863$	−6.02180	+	26.3832i	−0.204985	+	0.898096i	0.762863	+	0.646560i	$0.223793\pi$
$863$	−6.02180	+	26.3832i	−0.204985	+	0.898096i	−0.967848	+	0.251536i	$0.919064\pi$
$864$	−0.198730	−	5.19235i	−0.00676092	−	0.176647i
$865$	−5.57020	+	6.98481i	−0.189392	+	0.237491i
$866$	7.88525	−	25.5633i	0.267952	−	0.868678i
$867$	28.9935	−	5.12086i	0.984672	−	0.173914i
$868$	0.328352	+	0.444901i	0.0111450	+	0.0151009i
$869$	−9.70806	−	16.8149i	−0.329323	−	0.570405i
$870$	−15.2840	−	10.5374i	−0.518176	−	0.357252i
$871$	−34.6142	+	59.9535i	−1.17286	+	2.03145i
$872$	−0.932474	+	0.105065i	−0.0315776	+	0.00355794i
$873$	15.2950	+	13.8251i	0.517658	+	0.467908i
$874$	−14.0240	+	3.20088i	−0.474367	+	0.108271i
$875$	2.00527	+	5.10935i	0.0677906	+	0.172728i
$876$	−4.30085	−	4.08922i	−0.145312	−	0.138162i
$877$	9.23369	−	2.84822i	0.311800	−	0.0961775i	−0.134906	−	0.990858i	$-0.543073\pi$
$877$	9.23369	−	2.84822i	0.311800	−	0.0961775i	0.446706	+	0.894681i	$0.352597\pi$
$878$	10.6168	+	9.13651i	0.358300	+	0.308342i
$879$	−4.22489	+	13.1269i	−0.142502	+	0.442758i
$880$	1.59405	+	3.01609i	0.0537355	+	0.101673i
$881$	−6.81195	−	2.38360i	−0.229500	−	0.0803057i	0.213079	−	0.977035i	$-0.431651\pi$
$881$	−6.81195	−	2.38360i	−0.229500	−	0.0803057i	−0.442579	+	0.896729i	$0.645937\pi$
$882$	20.3726	−	0.265605i	0.685981	−	0.00894338i
$883$	10.3982	+	21.5921i	0.349927	+	0.726632i	0.999431	−	0.0337268i	$-0.0107376\pi$
$883$	10.3982	+	21.5921i	0.349927	+	0.726632i	−0.649504	+	0.760358i	$0.725023\pi$
$884$	0.207184	+	0.152909i	0.00696835	+	0.00514288i
$885$	8.75654	+	14.3203i	0.294348	+	0.481370i
$886$	7.76790	+	5.29607i	0.260968	+	0.177925i
$887$	13.6794	−	51.0522i	0.459309	−	1.71416i	−0.215792	−	0.976439i	$-0.569233\pi$
$887$	13.6794	−	51.0522i	0.459309	−	1.71416i	0.675101	−	0.737725i	$-0.264100\pi$
$888$	12.5568	−	14.2368i	0.421379	−	0.477754i
$889$	−5.68610	+	3.00519i	−0.190706	+	0.100791i
$890$	−9.87252	+	20.5005i	−0.330928	+	0.687179i
$891$	−2.47177	+	15.2268i	−0.0828073	+	0.510117i
$892$	19.8575	+	4.53236i	0.664880	+	0.151754i
$893$	0.922571	+	6.12086i	0.0308727	+	0.204827i
$894$	−18.4660	+	10.3635i	−0.617596	+	0.346608i
$895$	−5.02387	+	4.66147i	−0.167929	+	0.155816i
$896$	0.213393	−	0.403759i	0.00712896	−	0.0134886i
$897$	45.0668	+	46.1783i	1.50474	+	1.54185i
$898$	−13.5600	−	7.82889i	−0.452504	−	0.261253i
$899$	−5.95797	+	2.64906i	−0.198709	+	0.0883510i
$900$	−2.23184	−	2.17439i	−0.0743945	−	0.0724797i
$901$	−0.0498084	−	0.442062i	−0.00165936	−	0.0147272i
$902$	−0.111096	−	2.96911i	−0.00369910	−	0.0988605i
$903$	−1.90429	−	5.03142i	−0.0633707	−	0.167435i
$904$	1.48216	−	9.83348i	0.0492959	−	0.327057i
$905$	−6.08635	+	15.5078i	−0.202317	+	0.515496i
$906$	−1.34067	+	15.3744i	−0.0445407	+	0.510779i
$907$	22.5241	+	4.26179i	0.747901	+	0.141511i	0.545872	−	0.837869i	$-0.316199\pi$
$907$	22.5241	+	4.26179i	0.747901	+	0.141511i	0.202030	+	0.979379i	$0.435246\pi$
$908$	22.1014	+	10.6434i	0.733459	+	0.353215i
$909$	−14.6574	−	4.31276i	−0.486154	−	0.143045i
$910$	2.00716	−	5.73613i	0.0665367	−	0.190151i
$911$	−3.93731	−	14.6942i	−0.130449	−	0.486842i	0.869526	−	0.493887i	$-0.164424\pi$
$911$	−3.93731	−	14.6942i	−0.130449	−	0.486842i	−0.999975	+	0.00704480i	$0.997758\pi$
$912$	−4.00479	−	1.98906i	−0.132612	−	0.0658645i
$913$	6.56992	+	15.0584i	0.217433	+	0.498361i
$914$	−4.36108	−	9.99570i	−0.144252	−	0.330629i
$915$	−2.51058	−	40.0411i	−0.0829973	−	1.32372i
$916$	−4.96544	−	18.5313i	−0.164063	−	0.612291i
$917$	−0.705935	+	2.01745i	−0.0233120	+	0.0666219i
$918$	−0.156568	−	0.124640i	−0.00516751	−	0.00411373i
$919$	45.5314	+	21.9267i	1.50194	+	0.723297i	0.990690	−	0.136135i	$-0.0434681\pi$
$919$	45.5314	+	21.9267i	1.50194	+	0.723297i	0.511251	+	0.859432i	$0.329182\pi$
$920$	−10.8964	−	2.06172i	−0.359245	−	0.0679728i
$921$	5.05281	+	3.53587i	0.166496	+	0.116511i
$922$	4.03569	−	10.2828i	0.132908	−	0.338645i
$923$	−0.0735078	+	0.487693i	−0.00241954	+	0.0160526i
$924$	−0.858162	+	1.04961i	−0.0282315	+	0.0345297i
$925$	−0.425641	−	11.3755i	−0.0139950	−	0.374024i
$926$	1.25115	+	11.1042i	0.0411152	+	0.364907i
$927$	−4.52188	−	1.14867i	−0.148518	−	0.0377272i
$928$	4.10621	+	3.48412i	0.134793	+	0.114372i
$929$	14.8877	+	8.59544i	0.488451	+	0.282007i	0.723931	−	0.689872i	$-0.242333\pi$
$929$	14.8877	+	8.59544i	0.488451	+	0.282007i	−0.235481	+	0.971879i	$0.575666\pi$
$930$	4.04465	−	1.03112i	0.132629	−	0.0338118i
$931$	8.19268	−	15.5013i	0.268504	−	0.508035i
$932$	1.83755	−	1.70500i	0.0601909	−	0.0558490i
$933$	−28.6273	−	16.9963i	−0.937217	−	0.556434i
$934$	−0.282329	−	1.87313i	−0.00923808	−	0.0612906i
$935$	0.128092	+	0.0292361i	0.00418904	+	0.000956121i
$936$	1.75955	+	19.9806i	0.0575129	+	0.653087i
$937$	−21.5852	+	44.8221i	−0.705157	+	1.46427i	0.172513	+	0.985007i	$0.444811\pi$
$937$	−21.5852	+	44.8221i	−0.705157	+	1.46427i	−0.877670	+	0.479266i	$0.840903\pi$
$938$	4.18062	−	2.20952i	0.136502	−	0.0721435i
$939$	5.30336	+	15.7698i	0.173069	+	0.514627i
$940$	−1.23513	+	4.60955i	−0.0402854	+	0.150347i
$941$	−20.3344	−	13.8637i	−0.662882	−	0.451945i	0.184569	−	0.982820i	$-0.440911\pi$
$941$	−20.3344	−	13.8637i	−0.662882	−	0.451945i	−0.847450	+	0.530874i	$0.821864\pi$
$942$	14.0285	−	25.7782i	0.457074	−	0.839899i
$943$	7.77133	+	5.73550i	0.253069	+	0.186774i
$944$	−2.11262	−	4.38689i	−0.0687598	−	0.142781i
$945$	−1.72174	+	4.39798i	−0.0560083	+	0.143066i
$946$	−11.0032	−	3.85018i	−0.357745	−	0.125180i
$947$	−25.2641	−	47.8020i	−0.820973	−	1.55336i	−0.832898	−	0.553427i	$-0.813320\pi$
$947$	−25.2641	−	47.8020i	−0.820973	−	1.55336i	0.0119249	−	0.999929i	$-0.496204\pi$
$948$	13.1691	+	14.5443i	0.427713	+	0.472377i
$949$	17.3639	+	14.9428i	0.563655	+	0.485064i
$950$	−2.56229	+	0.790362i	−0.0831317	+	0.0256427i
$951$	−3.87801	+	16.0849i	−0.125753	+	0.521589i
$952$	−0.00642575	−	0.0163725i	−0.000208260	−	0.000530637i
$953$	29.8848	−	6.82100i	0.968062	−	0.220954i	0.290872	−	0.956762i	$-0.406055\pi$
$953$	29.8848	−	6.82100i	0.968062	−	0.220954i	0.677190	+	0.735808i	$0.263197\pi$
$954$	23.2364	−	25.7070i	0.752306	−	0.832296i
$955$	−15.7265	+	1.77196i	−0.508899	+	0.0573391i
$956$	7.64440	−	13.2405i	0.247238	−	0.428228i
$957$	−9.90268	−	12.5511i	−0.320108	−	0.405718i
$958$	11.4542	+	19.8392i	0.370068	+	0.640977i
$959$	−0.567661	−	0.769154i	−0.0183307	−	0.0248373i
$960$	−2.21665	−	2.64017i	−0.0715421	−	0.0852112i
$961$	−8.70529	+	28.2219i	−0.280816	+	0.910383i
$962$	−45.6879	+	57.2908i	−1.47304	+	1.84713i
$963$	−3.98242	+	40.0286i	−0.128332	+	1.28990i
$964$	−0.822828	+	3.60505i	−0.0265015	+	0.116111i
$965$	4.84045	−	25.5824i	0.155820	−	0.823526i
$966$	−0.928308	−	4.30845i	−0.0298678	−	0.138622i
$967$	−16.4471	−	0.615406i	−0.528902	−	0.0197901i	−0.228393	−	0.973569i	$-0.573347\pi$
$967$	−16.4471	−	0.615406i	−0.528902	−	0.0197901i	−0.300509	+	0.953779i	$0.597157\pi$
$968$	−1.49885	−	7.92161i	−0.0481748	−	0.254610i
$969$	−0.158673	+	0.0669393i	−0.00509730	+	0.00215040i
$970$	13.6400	+	1.02218i	0.437955	+	0.0328202i
$971$	−4.02493	+	35.7222i	−0.129166	+	1.14638i	0.747154	+	0.664651i	$0.231420\pi$
$971$	−4.02493	+	35.7222i	−0.129166	+	1.14638i	−0.876320	+	0.481730i	$0.840009\pi$
$972$	−0.799205	−	15.5680i	−0.0256345	−	0.499342i
$973$	−4.99625	+	2.40607i	−0.160172	+	0.0771350i
$974$	−23.8553	+	6.39200i	−0.764372	+	0.204813i
$975$	9.02064	+	7.95619i	0.288892	+	0.254802i
$976$	−0.435156	+	11.6298i	−0.0139290	+	0.372260i
$977$	−38.3086	+	2.87083i	−1.22560	+	0.0918460i	−0.671754	−	0.740774i	$-0.734459\pi$
$977$	−38.3086	+	2.87083i	−1.22560	+	0.0918460i	−0.553845	+	0.832620i	$0.686840\pi$
$978$	−24.6829	−	15.9319i	−0.789271	−	0.509447i
$979$	−13.3280	+	14.3642i	−0.425966	+	0.459082i
$980$	10.5681	−	8.42778i	0.337586	−	0.269216i
$981$	−2.79308	+	0.351635i	−0.0891761	+	0.0112268i
$982$	1.07379	+	4.70459i	0.0342661	+	0.150130i
$983$	−36.0320	+	1.34822i	−1.14924	+	0.0430017i	−0.605213	−	0.796064i	$-0.706912\pi$
$983$	−36.0320	+	1.34822i	−1.14924	+	0.0430017i	−0.544031	+	0.839065i	$0.683102\pi$
$984$	0.741707	+	2.90940i	0.0236447	+	0.0927482i
$985$	40.0758	−	23.1378i	1.27692	−	0.737231i
$986$	0.204864	−	0.0323413i	0.00652420	−	0.00102996i
$987$	−1.87868	+	0.259802i	−0.0597992	+	0.00826960i
$988$	15.8207	+	6.90248i	0.503322	+	0.219597i
$989$	32.0870	−	20.1616i	1.02031	−	0.641101i
$990$	4.89971	+	8.98517i	0.155723	+	0.285568i
$991$	−5.65665	−	4.51103i	−0.179690	−	0.143298i	0.529515	−	0.848301i	$-0.322374\pi$
$991$	−5.65665	−	4.51103i	−0.179690	−	0.143298i	−0.709204	+	0.705003i	$0.750946\pi$
$992$	−1.19727	+	0.180460i	−0.0380135	+	0.00572961i
$993$	6.03224	+	12.9266i	0.191427	+	0.410212i
$994$	0.0219741	−	0.0255344i	0.000696976	−	0.000809901i
$995$	−2.70390	−	36.0810i	−0.0857193	−	1.14384i
$996$	−9.69524	−	13.4771i	−0.307205	−	0.427040i
$997$	−36.9229	−	42.9052i	−1.16936	−	1.35882i	−0.920720	−	0.390224i	$-0.872397\pi$
$997$	−36.9229	−	42.9052i	−1.16936	−	1.35882i	−0.248640	−	0.968596i	$-0.579984\pi$
$998$	26.0117	−	26.0117i	0.823386	−	0.823386i
$999$	37.1104	−	43.1977i	1.17412	−	1.36672i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	522.2.x.a.101.24	✓	720
9.5	odd	6	inner	522.2.x.a.275.13	yes	720
29.27	odd	28	inner	522.2.x.a.317.13	yes	720
261.230	even	84	inner	522.2.x.a.491.24	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
522.2.x.a.101.24	✓	720	1.1	even	1	trivial
522.2.x.a.275.13	yes	720	9.5	odd	6	inner
522.2.x.a.317.13	yes	720	29.27	odd	28	inner
522.2.x.a.491.24	yes	720	261.230	even	84	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 522 = 2 \cdot 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	522.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.399892 - 0.916562i) q^{2} +(0.301254 + 1.70565i) q^{3} +(-0.680173 - 0.733052i) q^{4} +(-1.96808 - 0.296641i) q^{5} +(1.68380 + 0.405959i) q^{6} +(0.334771 + 0.310622i) q^{7} +(-0.943883 + 0.330279i) q^{8} +(-2.81849 + 1.02767i) q^{9} +(-1.05891 + 1.68525i) q^{10} +(-1.29917 + 1.11803i) q^{11} +(1.04543 - 1.38097i) q^{12} +(-3.76635 + 5.52422i) q^{13} +(0.418577 - 0.182623i) q^{14} +(-0.0869264 - 3.44623i) q^{15} +(-0.0747301 + 0.997204i) q^{16} +(0.0272331 + 0.0272331i) q^{17} +(-0.185172 + 2.99428i) q^{18} +(2.18594 + 1.37352i) q^{19} +(1.12118 + 1.64448i) q^{20} +(-0.428962 + 0.664579i) q^{21} +(0.505214 + 1.63786i) q^{22} +(-5.18670 - 2.03563i) q^{23} +(-0.847689 - 1.51044i) q^{24} +(-0.992502 - 0.306146i) q^{25} +(3.55716 + 5.66119i) q^{26} +(-2.60192 - 4.49778i) q^{27} -0.456681i q^{28} +(5.25838 + 1.16166i) q^{29} +(-3.19345 - 1.29845i) q^{30} +(-0.974205 + 0.718996i) q^{31} +(0.884115 + 0.467269i) q^{32} +(-2.29835 - 1.87913i) q^{33} +(0.0358511 - 0.0140705i) q^{34} +(-0.566715 - 0.710638i) q^{35} +(2.67040 + 1.36711i) q^{36} +(3.61983 + 10.3449i) q^{37} +(2.13306 - 1.45429i) q^{38} +(-10.5570 - 4.75989i) q^{39} +(1.95562 - 0.370023i) q^{40} +(-1.67440 - 0.448654i) q^{41} +(0.437589 + 0.658930i) q^{42} +(-4.03870 + 5.47224i) q^{43} +(1.70324 + 0.191909i) q^{44} +(5.85188 - 1.18646i) q^{45} +(-3.93991 + 3.93991i) q^{46} +(1.56398 + 1.81738i) q^{47} +(-1.72339 + 0.172948i) q^{48} +(-0.507525 - 6.77245i) q^{49} +(-0.677496 + 0.787264i) q^{50} +(-0.0382461 + 0.0546542i) q^{51} +(6.61131 - 0.996494i) q^{52} +(-9.03075 - 7.20178i) q^{53} +(-5.16298 + 0.586199i) q^{54} +(2.88854 - 1.81499i) q^{55} +(-0.418577 - 0.182623i) q^{56} +(-1.68422 + 4.14224i) q^{57} +(3.16752 - 4.35509i) q^{58} +(-4.21675 + 2.43454i) q^{59} +(-2.46714 + 2.40775i) q^{60} +(11.6298 - 0.435156i) q^{61} +(0.269428 + 1.18044i) q^{62} +(-1.26277 - 0.531453i) q^{63} +(0.781831 - 0.623490i) q^{64} +(9.05121 - 9.75488i) q^{65} +(-2.64143 + 1.35513i) q^{66} +(10.3253 - 0.773774i) q^{67} +(0.00144006 - 0.0384865i) q^{68} +(1.90956 - 9.45995i) q^{69} +(-0.877969 + 0.235251i) q^{70} +(0.0664613 - 0.0320061i) q^{71} +(2.32091 - 1.90089i) q^{72} +(0.383626 - 3.40477i) q^{73} +(10.9293 + 0.819035i) q^{74} +(0.223184 - 1.78509i) q^{75} +(-0.479959 - 2.53664i) q^{76} +(-0.782211 - 0.0292683i) q^{77} +(-8.58440 + 7.77272i) q^{78} +(-2.10598 + 11.1304i) q^{79} +(0.442887 - 1.94041i) q^{80} +(6.88780 - 5.79294i) q^{81} +(-1.08080 + 1.35528i) q^{82} +(2.82530 - 9.15941i) q^{83} +(0.778939 - 0.137577i) q^{84} +(-0.0455186 - 0.0616755i) q^{85} +(3.40061 + 5.89002i) q^{86} +(-0.397283 + 9.31891i) q^{87} +(0.857007 - 1.48438i) q^{88} +(11.3604 - 1.28001i) q^{89} +(1.25266 - 5.83807i) q^{90} +(-2.97681 + 0.679438i) q^{91} +(2.03563 + 5.18670i) q^{92} +(-1.51984 - 1.44505i) q^{93} +(2.29117 - 0.706732i) q^{94} +(-3.89468 - 3.35165i) q^{95} +(-0.530654 + 1.64876i) q^{96} +(-3.21126 - 6.07601i) q^{97} +(-6.41033 - 2.24307i) q^{98} +(2.51275 - 4.48627i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q + 24 q^{11} - 12 q^{14} - 20 q^{15} - 60 q^{16} + 84 q^{21} + 20 q^{24} + 60 q^{25} - 144 q^{27} - 12 q^{29} + 72 q^{30} + 84 q^{33} - 40 q^{36} + 40 q^{39} - 12 q^{41} - 104 q^{45} + 24 q^{46} - 24 q^{47}+ \cdots - 84 q^{99}+O(q^{100}) \) 720 * q + 24 * q^11 - 12 * q^14 - 20 * q^15 - 60 * q^16 + 84 * q^21 + 20 * q^24 + 60 * q^25 - 144 * q^27 - 12 * q^29 + 72 * q^30 + 84 * q^33 - 40 * q^36 + 40 * q^39 - 12 * q^41 - 104 * q^45 + 24 * q^46 - 24 * q^47 + 60 * q^49 + 16 * q^54 - 144 * q^55 + 12 * q^56 + 12 * q^58 + 120 * q^59 - 16 * q^60 - 12 * q^61 + 36 * q^65 - 48 * q^66 - 36 * q^68 + 52 * q^69 - 180 * q^74 - 184 * q^75 - 132 * q^77 - 68 * q^78 + 12 * q^79 - 216 * q^81 + 96 * q^82 - 432 * q^83 - 80 * q^84 - 48 * q^85 - 200 * q^87 - 112 * q^90 - 252 * q^92 - 112 * q^93 + 192 * q^95 + 24 * q^97 - 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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