LMFDB - Embedded newform 430.2.q.b.181.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			181.1
Character	$\chi$	$=$	430.181
Dual form			430.2.q.b.411.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.623490 + 0.781831i) q^{2} +(-2.67211 - 0.402755i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(-0.826239 - 0.563320i) q^{5} +(-1.35114 - 2.34025i) q^{6} +(0.0929644 - 0.161019i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(4.11122 + 1.26814i) q^{9} +O(q^{10})$	\(q+(0.623490 + 0.781831i) q^{2} +(-2.67211 - 0.402755i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(-0.826239 - 0.563320i) q^{5} +(-1.35114 - 2.34025i) q^{6} +(0.0929644 - 0.161019i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(4.11122 + 1.26814i) q^{9} +(-0.0747301 - 0.997204i) q^{10} +(0.172860 + 0.757349i) q^{11} +(0.987257 - 2.51549i) q^{12} +(0.208956 - 2.78832i) q^{13} +(0.183852 - 0.0277113i) q^{14} +(1.98092 + 1.83802i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(6.12155 - 4.17361i) q^{17} +(1.57183 + 4.00496i) q^{18} +(4.98696 - 1.53827i) q^{19} +(0.733052 - 0.680173i) q^{20} +(-0.313262 + 0.392818i) q^{21} +(-0.484343 + 0.607347i) q^{22} +(-1.06258 + 0.985934i) q^{23} +(2.58223 - 0.796514i) q^{24} +(0.365341 + 0.930874i) q^{25} +(2.31028 - 1.57512i) q^{26} +(-3.17084 - 1.52700i) q^{27} +(0.136295 + 0.126464i) q^{28} +(6.33179 - 0.954364i) q^{29} +(-0.201942 + 2.69473i) q^{30} +(0.593178 - 1.51139i) q^{31} +(-0.222521 - 0.974928i) q^{32} +(-0.156874 - 2.09334i) q^{33} +(7.07978 + 2.18382i) q^{34} +(-0.167516 + 0.0806715i) q^{35} +(-2.15118 + 3.72596i) q^{36} +(-4.26831 - 7.39293i) q^{37} +(4.31199 + 2.93986i) q^{38} +(-1.68136 + 7.36653i) q^{39} +(0.988831 + 0.149042i) q^{40} +(4.26798 + 5.35188i) q^{41} -0.502433 q^{42} +(-6.55140 - 0.281368i) q^{43} -0.776826 q^{44} +(-2.68248 - 3.36373i) q^{45} +(-1.43334 - 0.216042i) q^{46} +(-0.415749 + 1.82152i) q^{47} +(2.23274 + 1.52225i) q^{48} +(3.48272 + 6.03224i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-18.0384 + 8.68683i) q^{51} +(2.67191 + 0.824176i) q^{52} +(-0.719147 - 9.59634i) q^{53} +(-0.783133 - 3.43113i) q^{54} +(0.283806 - 0.723127i) q^{55} +(-0.0138945 + 0.185409i) q^{56} +(-13.9452 + 2.10191i) q^{57} +(4.69396 + 4.35536i) q^{58} +(0.477843 + 0.230117i) q^{59} +(-2.23274 + 1.52225i) q^{60} +(-3.63330 - 9.25751i) q^{61} +(1.55150 - 0.478573i) q^{62} +(0.586393 - 0.544093i) q^{63} +(0.623490 - 0.781831i) q^{64} +(-1.74336 + 2.18611i) q^{65} +(1.53883 - 1.42782i) q^{66} +(-0.0950454 + 0.0293176i) q^{67} +(2.70679 + 6.89679i) q^{68} +(3.23643 - 2.20656i) q^{69} +(-0.167516 - 0.0806715i) q^{70} +(-5.60833 - 5.20377i) q^{71} +(-4.25431 + 0.641234i) q^{72} +(0.693015 - 9.24764i) q^{73} +(3.11878 - 7.94652i) q^{74} +(-0.601316 - 2.63454i) q^{75} +(0.390003 + 5.20422i) q^{76} +(0.138018 + 0.0425728i) q^{77} +(-6.80770 + 3.27841i) q^{78} +(-1.83828 + 3.18399i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-2.80652 - 1.91346i) q^{81} +(-1.52322 + 6.67368i) q^{82} +(7.62612 + 1.14945i) q^{83} +(-0.313262 - 0.392818i) q^{84} -7.40894 q^{85} +(-3.86475 - 5.29752i) q^{86} -17.3036 q^{87} +(-0.484343 - 0.607347i) q^{88} +(4.10219 + 0.618306i) q^{89} +(0.957366 - 4.19450i) q^{90} +(-0.429547 - 0.292860i) q^{91} +(-0.724767 - 1.25533i) q^{92} +(-2.19376 + 3.79970i) q^{93} +(-1.68333 + 0.810650i) q^{94} +(-4.98696 - 1.53827i) q^{95} +(0.201942 + 2.69473i) q^{96} +(2.27805 + 9.98077i) q^{97} +(-2.54476 + 6.48394i) q^{98} +(-0.249762 + 3.33284i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9}+O(q^{10}) $ 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9} - 4 q^{10} - 9 q^{11} - q^{12} - 11 q^{13} + 7 q^{14} - 6 q^{15} - 8 q^{16} - 11 q^{17} - 15 q^{18} + 31 q^{19} - 4 q^{20} + 4 q^{21} + 12 q^{22} + 4 q^{23} + 6 q^{24} + 4 q^{25} + 31 q^{26} + 44 q^{27} + 13 q^{29} + q^{30} - q^{31} - 8 q^{32} - 30 q^{33} - 25 q^{34} + 14 q^{35} - 36 q^{36} - 27 q^{37} - 4 q^{38} + 4 q^{39} - 4 q^{40} + 16 q^{41} + 4 q^{42} - 7 q^{43} - 30 q^{44} + 12 q^{45} - 52 q^{46} - 43 q^{47} - q^{48} - 23 q^{49} - 24 q^{50} - 7 q^{51} - 25 q^{52} + 73 q^{53} - 61 q^{54} + 27 q^{55} + 7 q^{56} + 136 q^{57} - 36 q^{58} + 58 q^{59} + q^{60} - 61 q^{61} + 27 q^{62} + 32 q^{63} - 8 q^{64} - q^{65} + 12 q^{66} + 39 q^{67} + 17 q^{68} - 34 q^{69} + 14 q^{70} + 60 q^{71} + 27 q^{72} + 3 q^{73} + 29 q^{74} - 12 q^{75} + 17 q^{76} - 27 q^{77} - 17 q^{78} - 2 q^{79} + 24 q^{80} - 165 q^{81} + 2 q^{82} + 74 q^{83} + 4 q^{84} - 8 q^{85} + 14 q^{86} + 88 q^{87} + 12 q^{88} + 23 q^{89} - 2 q^{90} - 39 q^{91} + 4 q^{92} - 46 q^{93} + 55 q^{94} - 31 q^{95} - q^{96} - 85 q^{97} + 33 q^{98} - 168 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9 - 4 * q^10 - 9 * q^11 - q^12 - 11 * q^13 + 7 * q^14 - 6 * q^15 - 8 * q^16 - 11 * q^17 - 15 * q^18 + 31 * q^19 - 4 * q^20 + 4 * q^21 + 12 * q^22 + 4 * q^23 + 6 * q^24 + 4 * q^25 + 31 * q^26 + 44 * q^27 + 13 * q^29 + q^30 - q^31 - 8 * q^32 - 30 * q^33 - 25 * q^34 + 14 * q^35 - 36 * q^36 - 27 * q^37 - 4 * q^38 + 4 * q^39 - 4 * q^40 + 16 * q^41 + 4 * q^42 - 7 * q^43 - 30 * q^44 + 12 * q^45 - 52 * q^46 - 43 * q^47 - q^48 - 23 * q^49 - 24 * q^50 - 7 * q^51 - 25 * q^52 + 73 * q^53 - 61 * q^54 + 27 * q^55 + 7 * q^56 + 136 * q^57 - 36 * q^58 + 58 * q^59 + q^60 - 61 * q^61 + 27 * q^62 + 32 * q^63 - 8 * q^64 - q^65 + 12 * q^66 + 39 * q^67 + 17 * q^68 - 34 * q^69 + 14 * q^70 + 60 * q^71 + 27 * q^72 + 3 * q^73 + 29 * q^74 - 12 * q^75 + 17 * q^76 - 27 * q^77 - 17 * q^78 - 2 * q^79 + 24 * q^80 - 165 * q^81 + 2 * q^82 + 74 * q^83 + 4 * q^84 - 8 * q^85 + 14 * q^86 + 88 * q^87 + 12 * q^88 + 23 * q^89 - 2 * q^90 - 39 * q^91 + 4 * q^92 - 46 * q^93 + 55 * q^94 - 31 * q^95 - q^96 - 85 * q^97 + 33 * q^98 - 168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{1}{21}\right)$

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 $

$2$	0.623490	+	0.781831i	0.440874	+	0.552838i
$2$	0.623490	+	0.781831i	0.440874	+	0.552838i
$3$	−2.67211	−	0.402755i	−1.54274	−	0.232531i	−0.678119	−	0.734952i	$-0.737204\pi$
$3$	−2.67211	−	0.402755i	−1.54274	−	0.232531i	−0.864623	+	0.502422i	$0.832443\pi$
$4$	−0.222521	+	0.974928i	−0.111260	+	0.487464i
$5$	−0.826239	−	0.563320i	−0.369505	−	0.251924i
$5$	−0.826239	−	0.563320i	−0.369505	−	0.251924i
$6$	−1.35114	−	2.34025i	−0.551602	−	0.955403i
$7$	0.0929644	−	0.161019i	0.0351372	−	0.0608595i	−0.847922	−	0.530121i	$-0.822146\pi$
$7$	0.0929644	−	0.161019i	0.0351372	−	0.0608595i	0.883059	+	0.469261i	$0.155480\pi$
$8$	−0.900969	+	0.433884i	−0.318541	+	0.153401i
$9$	4.11122	+	1.26814i	1.37041	+	0.422715i
$10$	−0.0747301	−	0.997204i	−0.0236317	−	0.315344i
$11$	0.172860	+	0.757349i	0.0521193	+	0.228349i	0.994279	−	0.106815i	$-0.0340653\pi$
$11$	0.172860	+	0.757349i	0.0521193	+	0.228349i	−0.942160	+	0.335164i	$0.891208\pi$
$12$	0.987257	−	2.51549i	0.284997	−	0.726159i
$13$	0.208956	−	2.78832i	0.0579539	−	0.773341i	−0.890208	−	0.455554i	$-0.849441\pi$
$13$	0.208956	−	2.78832i	0.0579539	−	0.773341i	0.948162	−	0.317787i	$-0.102940\pi$
$14$	0.183852	−	0.0277113i	0.0491366	−	0.00740614i
$15$	1.98092	+	1.83802i	0.511471	+	0.474576i
$16$	−0.900969	−	0.433884i	−0.225242	−	0.108471i
$17$	6.12155	−	4.17361i	1.48470	−	1.01225i	0.495026	−	0.868878i	$-0.335159\pi$
$17$	6.12155	−	4.17361i	1.48470	−	1.01225i	0.989669	−	0.143370i	$-0.0457938\pi$
$18$	1.57183	+	4.00496i	0.370484	+	0.943978i
$19$	4.98696	−	1.53827i	1.14409	−	0.352904i	0.335939	−	0.941884i	$-0.390946\pi$
$19$	4.98696	−	1.53827i	1.14409	−	0.352904i	0.808148	+	0.588980i	$0.200470\pi$
$20$	0.733052	−	0.680173i	0.163915	−	0.152091i
$21$	−0.313262	+	0.392818i	−0.0683594	+	0.0857200i
$22$	−0.484343	+	0.607347i	−0.103262	+	0.129487i
$23$	−1.06258	+	0.985934i	−0.221564	+	0.205581i	−0.783143	−	0.621842i	$-0.786385\pi$
$23$	−1.06258	+	0.985934i	−0.221564	+	0.205581i	0.561579	+	0.827423i	$0.310194\pi$
$24$	2.58223	−	0.796514i	0.527096	−	0.162588i
$25$	0.365341	+	0.930874i	0.0730682	+	0.186175i
$26$	2.31028	−	1.57512i	0.453083	−	0.308907i
$27$	−3.17084	−	1.52700i	−0.610229	−	0.293871i
$28$	0.136295	+	0.126464i	0.0257574	+	0.0238994i
$29$	6.33179	−	0.954364i	1.17578	−	0.177221i	0.468051	−	0.883701i	$-0.344956\pi$
$29$	6.33179	−	0.954364i	1.17578	−	0.177221i	0.707733	+	0.706480i	$0.249718\pi$
$30$	−0.201942	+	2.69473i	−0.0368695	+	0.491989i
$31$	0.593178	−	1.51139i	0.106538	−	0.271454i	−0.867657	−	0.497164i	$-0.834375\pi$
$31$	0.593178	−	1.51139i	0.106538	−	0.271454i	0.974195	+	0.225710i	$0.0724700\pi$
$32$	−0.222521	−	0.974928i	−0.0393365	−	0.172345i
$33$	−0.156874	−	2.09334i	−0.0273083	−	0.364404i
$34$	7.07978	+	2.18382i	1.21417	+	0.374523i
$35$	−0.167516	+	0.0806715i	−0.0283154	+	0.0136360i
$36$	−2.15118	+	3.72596i	−0.358530	+	0.620993i
$37$	−4.26831	−	7.39293i	−0.701706	−	1.21539i	−0.967867	−	0.251462i	$-0.919089\pi$
$37$	−4.26831	−	7.39293i	−0.701706	−	1.21539i	0.266161	−	0.963929i	$-0.414245\pi$
$38$	4.31199	+	2.93986i	0.699497	+	0.476909i
$39$	−1.68136	+	7.36653i	−0.269234	+	1.17959i
$40$	0.988831	+	0.149042i	0.156348	+	0.0235657i
$41$	4.26798	+	5.35188i	0.666547	+	0.835823i	0.994038	−	0.109031i	$-0.0347748\pi$
$41$	4.26798	+	5.35188i	0.666547	+	0.835823i	−0.327492	+	0.944854i	$0.606203\pi$
$42$	−0.502433			−0.0775272
$43$	−6.55140	−	0.281368i	−0.999079	−	0.0429083i
$43$	−6.55140	−	0.281368i	−0.999079	−	0.0429083i
$44$	−0.776826			−0.117111
$45$	−2.68248	−	3.36373i	−0.399881	−	0.501435i
$46$	−1.43334	−	0.216042i	−0.211335	−	0.0318536i
$47$	−0.415749	+	1.82152i	−0.0606432	+	0.265695i	−0.996156	−	0.0875977i	$-0.972081\pi$
$47$	−0.415749	+	1.82152i	−0.0606432	+	0.265695i	0.935513	+	0.353293i	$0.114938\pi$
$48$	2.23274	+	1.52225i	0.322268	+	0.219718i
$49$	3.48272	+	6.03224i	0.497531	+	0.861749i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−18.0384	+	8.68683i	−2.52588	+	1.21640i
$52$	2.67191	+	0.824176i	0.370528	+	0.114293i
$53$	−0.719147	−	9.59634i	−0.0987824	−	1.31816i	−0.797742	−	0.602998i	$-0.793973\pi$
$53$	−0.719147	−	9.59634i	−0.0987824	−	1.31816i	0.698960	−	0.715161i	$-0.253647\pi$
$54$	−0.783133	−	3.43113i	−0.106571	−	0.466918i
$55$	0.283806	−	0.723127i	0.0382685	−	0.0975064i
$56$	−0.0138945	+	0.185409i	−0.00185673	+	0.0247763i
$57$	−13.9452	+	2.10191i	−1.84709	+	0.278404i
$58$	4.69396	+	4.35536i	0.616347	+	0.571886i
$59$	0.477843	+	0.230117i	0.0622099	+	0.0299587i	0.464730	−	0.885452i	$-0.346151\pi$
$59$	0.477843	+	0.230117i	0.0622099	+	0.0299587i	−0.402520	+	0.915411i	$0.631866\pi$
$60$	−2.23274	+	1.52225i	−0.288245	+	0.196522i
$61$	−3.63330	−	9.25751i	−0.465197	−	1.18530i	−0.950436	−	0.310921i	$-0.899363\pi$
$61$	−3.63330	−	9.25751i	−0.465197	−	1.18530i	0.485239	−	0.874382i	$-0.338733\pi$
$62$	1.55150	−	0.478573i	0.197040	−	0.0607788i
$63$	0.586393	−	0.544093i	0.0738786	−	0.0685493i
$64$	0.623490	−	0.781831i	0.0779362	−	0.0977289i
$65$	−1.74336	+	2.18611i	−0.216238	+	0.271154i
$66$	1.53883	−	1.42782i	0.189417	−	0.175753i
$67$	−0.0950454	+	0.0293176i	−0.0116116	+	0.00358172i	−0.300556	−	0.953764i	$-0.597172\pi$
$67$	−0.0950454	+	0.0293176i	−0.0116116	+	0.00358172i	0.288944	+	0.957346i	$0.406696\pi$
$68$	2.70679	+	6.89679i	0.328247	+	0.836359i
$69$	3.23643	−	2.20656i	0.389620	−	0.265638i
$70$	−0.167516	−	0.0806715i	−0.0200220	−	0.00964209i
$71$	−5.60833	−	5.20377i	−0.665587	−	0.617574i	0.273247	−	0.961944i	$-0.411902\pi$
$71$	−5.60833	−	5.20377i	−0.665587	−	0.617574i	−0.938834	+	0.344369i	$0.888093\pi$
$72$	−4.25431	+	0.641234i	−0.501375	+	0.0755702i
$73$	0.693015	−	9.24764i	0.0811113	−	1.08235i	−0.797026	−	0.603945i	$-0.793594\pi$
$73$	0.693015	−	9.24764i	0.0811113	−	1.08235i	0.878137	−	0.478409i	$-0.158786\pi$
$74$	3.11878	−	7.94652i	0.362551	−	0.923764i
$75$	−0.601316	−	2.63454i	−0.0694340	−	0.304210i
$76$	0.390003	+	5.20422i	0.0447364	+	0.596965i
$77$	0.138018	+	0.0425728i	0.0157286	+	0.00485162i
$78$	−6.80770	+	3.27841i	−0.770820	+	0.371207i
$79$	−1.83828	+	3.18399i	−0.206822	+	0.358227i	−0.950712	−	0.310076i	$-0.899646\pi$
$79$	−1.83828	+	3.18399i	−0.206822	+	0.358227i	0.743890	+	0.668303i	$0.232979\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−2.80652	−	1.91346i	−0.311836	−	0.212606i
$82$	−1.52322	+	6.67368i	−0.168212	+	0.736985i
$83$	7.62612	+	1.14945i	0.837075	+	0.126169i	0.553571	−	0.832802i	$-0.313265\pi$
$83$	7.62612	+	1.14945i	0.837075	+	0.126169i	0.283504	+	0.958971i	$0.408503\pi$
$84$	−0.313262	−	0.392818i	−0.0341797	−	0.0428600i
$85$	−7.40894			−0.803613
$86$	−3.86475	−	5.29752i	−0.416746	−	0.571246i
$87$	−17.3036			−1.85514
$88$	−0.484343	−	0.607347i	−0.0516312	−	0.0647434i
$89$	4.10219	+	0.618306i	0.434831	+	0.0655403i	0.362811	−	0.931863i	$-0.381817\pi$
$89$	4.10219	+	0.618306i	0.434831	+	0.0655403i	0.0720207	+	0.997403i	$0.477055\pi$
$90$	0.957366	−	4.19450i	0.100915	−	0.442139i
$91$	−0.429547	−	0.292860i	−0.0450288	−	0.0307001i
$92$	−0.724767	−	1.25533i	−0.0755622	−	0.130878i
$93$	−2.19376	+	3.79970i	−0.227482	+	0.394010i
$94$	−1.68333	+	0.810650i	−0.173623	+	0.0836122i
$95$	−4.98696	−	1.53827i	−0.511651	−	0.157824i
$96$	0.201942	+	2.69473i	0.0206107	+	0.275030i
$97$	2.27805	+	9.98077i	0.231301	+	1.01339i	0.948562	+	0.316590i	$0.102538\pi$
$97$	2.27805	+	9.98077i	0.231301	+	1.01339i	−0.717262	+	0.696804i	$0.754605\pi$
$98$	−2.54476	+	6.48394i	−0.257059	+	0.654976i
$99$	−0.249762	+	3.33284i	−0.0251020	+	0.334964i
$100$	−0.988831	+	0.149042i	−0.0988831	+	0.0149042i
$101$	7.22545	+	6.70424i	0.718959	+	0.667097i	0.952253	−	0.305310i	$-0.0987600\pi$
$101$	7.22545	+	6.70424i	0.718959	+	0.667097i	−0.233294	+	0.972406i	$0.574950\pi$
$102$	−18.0384	−	8.68683i	−1.78607	−	0.860124i
$103$	−3.08226	+	2.10145i	−0.303704	+	0.207062i	−0.705577	−	0.708634i	$-0.749312\pi$
$103$	−3.08226	+	2.10145i	−0.303704	+	0.207062i	0.401872	+	0.915696i	$0.368360\pi$
$104$	1.02154	+	2.60285i	0.100171	+	0.255231i
$105$	0.480112	−	0.148095i	0.0468541	−	0.0144526i
$106$	7.05434	−	6.54547i	0.685178	−	0.635753i
$107$	−0.410130	+	0.514287i	−0.0396488	+	0.0497180i	−0.801261	−	0.598316i	$-0.795837\pi$
$107$	−0.410130	+	0.514287i	−0.0396488	+	0.0497180i	0.761612	+	0.648034i	$0.224408\pi$
$108$	2.19429	−	2.75155i	0.211146	−	0.264768i
$109$	−2.63433	+	2.44430i	−0.252323	+	0.234121i	−0.796185	−	0.605053i	$-0.793152\pi$
$109$	−2.63433	+	2.44430i	−0.252323	+	0.234121i	0.543862	+	0.839174i	$0.316961\pi$
$110$	0.742314	−	0.228974i	0.0707769	−	0.0218318i
$111$	8.42784	+	21.4738i	0.799935	+	2.03820i
$112$	−0.153622	+	0.104737i	−0.0145159	+	0.00989676i
$113$	9.93838	+	4.78607i	0.934925	+	0.450236i	0.838376	−	0.545092i	$-0.183505\pi$
$113$	9.93838	+	4.78607i	0.934925	+	0.450236i	0.0965485	+	0.995328i	$0.469220\pi$
$114$	−10.3380	−	9.59231i	−0.968247	−	0.898402i
$115$	1.43334	−	0.216042i	0.133660	−	0.0201460i
$116$	−0.478520	+	6.38541i	−0.0444295	+	0.592870i
$117$	4.39506	−	11.1984i	0.406323	−	1.03529i
$118$	0.118018	+	0.517069i	0.0108644	+	0.0476000i
$119$	−0.102943	−	1.37368i	−0.00943680	−	0.125925i
$120$	−2.58223	−	0.796514i	−0.235725	−	0.0727114i
$121$	9.36696	−	4.51089i	0.851542	−	0.410081i
$122$	4.97248	−	8.61259i	0.450187	−	0.779748i
$123$	−9.24900	−	16.0197i	−0.833954	−	1.44445i
$124$	1.34151	+	0.914623i	0.120471	+	0.0821355i
$125$	0.222521	−	0.974928i	0.0199029	−	0.0872002i
$126$	0.790999	+	0.119224i	0.0704678	+	0.0106213i
$127$	8.48284	+	10.6371i	0.752730	+	0.943894i	0.999684	−	0.0251334i	$-0.00800106\pi$
$127$	8.48284	+	10.6371i	0.752730	+	0.943894i	−0.246954	+	0.969027i	$0.579430\pi$
$128$	1.00000			0.0883883
$129$	17.3927	+	3.39046i	1.53134	+	0.298513i
$130$	−2.79614			−0.245238
$131$	0.0226958	+	0.0284596i	0.00198294	+	0.00248652i	0.782822	−	0.622246i	$-0.213780\pi$
$131$	0.0226958	+	0.0284596i	0.00198294	+	0.00248652i	−0.780839	+	0.624732i	$0.785208\pi$
$132$	2.07576	+	0.312871i	0.180672	+	0.0272319i
$133$	0.215918	−	0.946000i	0.0187225	−	0.0820286i
$134$	−0.0821813	−	0.0560302i	−0.00709938	−	0.00484028i
$135$	1.75968	+	3.04786i	0.151450	+	0.262318i
$136$	−3.70447	+	6.41633i	−0.317656	+	0.550196i
$137$	−5.92238	+	2.85207i	−0.505983	+	0.243669i	−0.669419	−	0.742885i	$-0.733457\pi$
$137$	−5.92238	+	2.85207i	−0.505983	+	0.243669i	0.163436	+	0.986554i	$0.447742\pi$
$138$	3.74304	+	1.15457i	0.318628	+	0.0982838i
$139$	−1.27406	−	17.0011i	−0.108064	−	1.44202i	−0.742916	−	0.669385i	$-0.766558\pi$
$139$	−1.27406	−	17.0011i	−0.108064	−	1.44202i	0.634852	−	0.772634i	$-0.281061\pi$
$140$	−0.0413731	−	0.181267i	−0.00349666	−	0.0153199i
$141$	1.84455	−	4.69984i	0.155339	−	0.395798i
$142$	0.571735	−	7.62927i	0.0479789	−	0.640234i
$143$	2.14785	−	0.323737i	0.179612	−	0.0270722i
$144$	−3.15386	−	2.92635i	−0.262821	−	0.243863i
$145$	−5.76918	−	2.77829i	−0.479105	−	0.230725i
$146$	7.66219	−	5.22399i	0.634127	−	0.432341i
$147$	−6.87667	−	17.5215i	−0.567178	−	1.44515i
$148$	8.15736	−	2.51621i	0.670531	−	0.206831i
$149$	−9.09969	+	8.44328i	−0.745476	+	0.691700i	−0.958419	−	0.285364i	$-0.907885\pi$
$149$	−9.09969	+	8.44328i	−0.745476	+	0.691700i	0.212943	+	0.977065i	$0.431695\pi$
$150$	1.68485	−	2.11273i	0.137567	−	0.172504i
$151$	10.4347	−	13.0847i	0.849163	−	1.06482i	−0.147959	−	0.988994i	$-0.547270\pi$
$151$	10.4347	−	13.0847i	0.849163	−	1.06482i	0.997121	−	0.0758228i	$-0.0241583\pi$
$152$	−3.82566	+	3.54970i	−0.310302	+	0.287918i
$153$	30.4598	−	9.39561i	2.46253	−	0.759590i
$154$	0.0527678	+	0.134450i	0.00425215	+	0.0108343i
$155$	−1.34151	+	0.914623i	−0.107752	+	0.0734643i
$156$	−6.80770	−	3.27841i	−0.545052	−	0.262483i
$157$	−1.37588	−	1.27663i	−0.109807	−	0.101886i	0.623359	−	0.781936i	$-0.285768\pi$
$157$	−1.37588	−	1.27663i	−0.109807	−	0.101886i	−0.733166	+	0.680050i	$0.761958\pi$
$158$	−3.63549	+	0.547962i	−0.289224	+	0.0435935i
$159$	−1.94334	+	25.9321i	−0.154117	+	2.05655i
$160$	−0.365341	+	0.930874i	−0.0288827	+	0.0735920i
$161$	0.0599717	+	0.262753i	0.00472643	+	0.0207078i
$162$	−0.253839	−	3.38725i	−0.0199435	−	0.266127i
$163$	−20.9447	−	6.46059i	−1.64052	−	0.506032i	−0.669051	−	0.743216i	$-0.733299\pi$
$163$	−20.9447	−	6.46059i	−1.64052	−	0.506032i	−0.971465	+	0.237184i	$0.923776\pi$
$164$	−6.16741	+	2.97007i	−0.481594	+	0.231923i
$165$	−1.04960	+	1.81797i	−0.0817116	+	0.141529i
$166$	3.85613	+	6.67901i	0.299294	+	0.518392i
$167$	15.4159	+	10.5104i	1.19292	+	0.813319i	0.986277	−	0.165098i	$-0.0527939\pi$
$167$	15.4159	+	10.5104i	1.19292	+	0.813319i	0.206642	+	0.978417i	$0.433746\pi$
$168$	0.111802	−	0.489836i	0.00862571	−	0.0377917i
$169$	5.12373	+	0.772278i	0.394133	+	0.0594060i
$170$	−4.61940	−	5.79254i	−0.354292	−	0.444268i
$171$	22.4533			1.71704
$172$	1.73214	−	6.32453i	0.132074	−	0.482241i
$173$	11.8421			0.900337			0.450168	−	0.892944i	$-0.351364\pi$
$173$	11.8421			0.900337			0.450168	+	0.892944i	$0.351364\pi$
$174$	−10.7886	−	13.5285i	−0.817883	−	1.02559i
$175$	0.183852	+	0.0277113i	0.0138979	+	0.00209477i
$176$	0.172860	−	0.757349i	0.0130298	−	0.0570874i
$177$	−1.18417	−	0.807352i	−0.0890075	−	0.0606843i
$178$	2.07426	+	3.59273i	0.155473	+	0.269286i
$179$	−10.3760	+	17.9718i	−0.775542	+	1.34328i	0.158948	+	0.987287i	$0.449190\pi$
$179$	−10.3760	+	17.9718i	−0.775542	+	1.34328i	−0.934489	+	0.355991i	$0.884143\pi$
$180$	3.87630	−	1.86673i	0.288922	−	0.139138i
$181$	−15.7825	−	4.86827i	−1.17311	−	0.361856i	−0.353862	−	0.935298i	$-0.615132\pi$
$181$	−15.7825	−	4.86827i	−1.17311	−	0.361856i	−0.819246	+	0.573442i	$0.805608\pi$
$182$	−0.0388509	−	0.518429i	−0.00287982	−	0.0384285i
$183$	5.98007	+	26.2004i	0.442059	+	1.93679i
$184$	0.529574	−	1.34933i	0.0390407	−	0.0994742i
$185$	−0.637943	+	8.51275i	−0.0469025	+	0.625870i
$186$	−4.33851	+	0.653925i	−0.318115	+	0.0479481i
$187$	4.21905	+	3.91471i	0.308528	+	0.286272i
$188$	−1.68333	−	0.810650i	−0.122770	−	0.0591228i
$189$	−0.540651	+	0.368610i	−0.0393266	+	0.0268124i
$190$	−1.90665	−	4.85806i	−0.138323	−	0.352441i
$191$	15.3605	−	4.73807i	1.11144	−	0.342835i	0.315937	−	0.948780i	$-0.397681\pi$
$191$	15.3605	−	4.73807i	1.11144	−	0.342835i	0.795506	+	0.605945i	$0.207205\pi$
$192$	−1.98092	+	1.83802i	−0.142960	+	0.132648i
$193$	4.44030	−	5.56796i	0.319620	−	0.400791i	−0.595903	−	0.803056i	$-0.703206\pi$
$193$	4.44030	−	5.56796i	0.319620	−	0.400791i	0.915523	+	0.402266i	$0.131777\pi$
$194$	−6.38294	+	8.00396i	−0.458269	+	0.574651i
$195$	5.53892	−	5.13937i	0.396650	−	0.368038i
$196$	−6.65598	+	2.05310i	−0.475427	+	0.146650i
$197$	2.31859	+	5.90768i	0.165193	+	0.420905i	0.989369	−	0.145429i	$-0.0464564\pi$
$197$	2.31859	+	5.90768i	0.165193	+	0.420905i	−0.824176	+	0.566334i	$0.808361\pi$
$198$	−2.76145	+	1.88272i	−0.196248	+	0.133799i
$199$	−22.0237	−	10.6060i	−1.56122	−	0.751842i	−0.563955	−	0.825805i	$-0.690721\pi$
$199$	−22.0237	−	10.6060i	−1.56122	−	0.751842i	−0.997261	+	0.0739631i	$0.976435\pi$
$200$	−0.733052	−	0.680173i	−0.0518346	−	0.0480955i
$201$	0.265779	−	0.0400598i	0.0187466	−	0.00282560i
$202$	−0.736590	+	9.82911i	−0.0518263	+	0.691574i
$203$	0.434960	−	1.10826i	0.0305282	−	0.0777847i
$204$	−4.45511	−	19.5191i	−0.311920	−	1.36661i
$205$	−0.511551	−	6.82617i	−0.0357282	−	0.476760i
$206$	−3.56474	−	1.09958i	−0.248367	−	0.0766111i
$207$	−5.61883	+	2.70588i	−0.390535	+	0.188072i
$208$	−1.39807	+	2.42153i	−0.0969387	+	0.167903i
$209$	2.02706	+	3.51097i	0.140214	+	0.242859i
$210$	0.415130	+	0.283031i	0.0286467	+	0.0195310i
$211$	−4.27286	+	18.7206i	−0.294156	+	1.28878i	0.584527	+	0.811374i	$0.301280\pi$
$211$	−4.27286	+	18.7206i	−0.294156	+	1.28878i	−0.878683	+	0.477406i	$0.841577\pi$
$212$	9.51577	+	1.43427i	0.653546	+	0.0985062i
$213$	12.8902	+	16.1638i	0.883223	+	1.10753i
$214$	−0.657798			−0.0449661
$215$	5.25452	+	3.92301i	0.358355	+	0.267547i
$216$	3.51937			0.239463
$217$	−0.188219	−	0.236019i	−0.0127771	−	0.0160220i
$218$	−3.55350	−	0.535605i	−0.240674	−	0.0362757i
$219$	−5.57635	+	24.4316i	−0.376815	+	1.65093i
$220$	0.641844	+	0.437602i	0.0432731	+	0.0295031i
$221$	−10.3582	−	17.9410i	−0.696769	−	1.20684i
$222$	−11.5342	+	19.9778i	−0.774125	+	1.34082i
$223$	−16.8198	+	8.09999i	−1.12634	+	0.542416i	−0.901845	−	0.432060i	$-0.857787\pi$
$223$	−16.8198	+	8.09999i	−1.12634	+	0.542416i	−0.224493	+	0.974476i	$0.572073\pi$
$224$	−0.177669	−	0.0548035i	−0.0118710	−	0.00366171i
$225$	0.321516	+	4.29034i	0.0214344	+	0.286022i
$226$	2.45458	+	10.7542i	0.163276	+	0.715359i
$227$	8.11278	−	20.6710i	0.538464	−	1.37198i	−0.360006	−	0.932950i	$-0.617225\pi$
$227$	8.11278	−	20.6710i	0.538464	−	1.37198i	0.898470	−	0.439035i	$-0.144679\pi$
$228$	1.05390	−	14.0633i	0.0697962	−	0.931366i
$229$	14.1866	−	2.13829i	0.937479	−	0.141302i	0.337507	−	0.941323i	$-0.390416\pi$
$229$	14.1866	−	2.13829i	0.937479	−	0.141302i	0.599972	+	0.800021i	$0.295178\pi$
$230$	1.06258	+	0.985934i	0.0700647	+	0.0650105i
$231$	−0.351651	−	0.169346i	−0.0231370	−	0.0111422i
$232$	−5.29066	+	3.60711i	−0.347349	+	0.236819i
$233$	2.40222	+	6.12075i	0.157374	+	0.400984i	0.987714	−	0.156275i	$-0.0499485\pi$
$233$	2.40222	+	6.12075i	0.157374	+	0.400984i	−0.830339	+	0.557258i	$0.811853\pi$
$234$	11.4956	−	3.54591i	0.751488	−	0.231803i
$235$	1.36960	−	1.27081i	0.0893431	−	0.0828983i
$236$	−0.330678	+	0.414657i	−0.0215253	+	0.0269919i
$237$	6.19444	−	7.76758i	0.402372	−	0.504558i
$238$	1.00981	−	0.936962i	0.0654560	−	0.0607342i
$239$	15.3240	−	4.72683i	0.991228	−	0.305753i	0.243604	−	0.969875i	$-0.421670\pi$
$239$	15.3240	−	4.72683i	0.991228	−	0.305753i	0.747625	+	0.664121i	$0.231194\pi$
$240$	−0.987257	−	2.51549i	−0.0637272	−	0.162374i
$241$	−11.6368	+	7.93384i	−0.749592	+	0.511063i	−0.876825	−	0.480809i	$-0.840343\pi$
$241$	−11.6368	+	7.93384i	−0.749592	+	0.511063i	0.127233	+	0.991873i	$0.459391\pi$
$242$	9.36696	+	4.51089i	0.602131	+	0.289971i
$243$	14.4683	+	13.4246i	0.928143	+	0.861191i
$244$	9.83389	−	1.48222i	0.629550	−	0.0948894i
$245$	0.520527	−	6.94595i	0.0332553	−	0.443761i
$246$	6.75808	−	17.2193i	0.430879	−	1.09786i
$247$	−3.24715	−	14.2267i	−0.206611	−	0.905221i
$248$	0.121334	+	1.61909i	0.00770471	+	0.102812i
$249$	−19.9149	−	6.14292i	−1.26205	−	0.389292i
$250$	0.900969	−	0.433884i	0.0569823	−	0.0274412i
$251$	4.04089	−	6.99902i	0.255059	−	0.441774i	−0.709853	−	0.704350i	$-0.751239\pi$
$251$	4.04089	−	6.99902i	0.255059	−	0.441774i	0.964911	+	0.262576i	$0.0845719\pi$
$252$	0.399967	+	0.692763i	0.0251955	+	0.0436400i
$253$	−0.930375	−	0.634319i	−0.0584921	−	0.0398793i
$254$	−3.02749	+	13.2643i	−0.189962	+	0.832276i
$255$	19.7975	+	2.98399i	1.23977	+	0.186865i
$256$	0.623490	+	0.781831i	0.0389681	+	0.0488645i
$257$	−22.6962			−1.41575			−0.707874	−	0.706339i	$-0.750345\pi$
$257$	−22.6962			−1.41575			−0.707874	+	0.706339i	$0.750345\pi$
$258$	8.19341	+	15.7121i	0.510100	+	0.978192i
$259$	−1.58720			−0.0986241
$260$	−1.74336	−	2.18611i	−0.108119	−	0.135577i
$261$	27.2417	+	4.10602i	1.68622	+	0.254156i
$262$	−0.00810002	+	0.0354885i	−0.000500421	+	0.00219249i
$263$	12.9090	+	8.80119i	0.796001	+	0.542704i	0.891658	−	0.452710i	$-0.149543\pi$
$263$	12.9090	+	8.80119i	0.796001	+	0.542704i	−0.0956566	+	0.995414i	$0.530495\pi$
$264$	1.04960	+	1.81797i	0.0645987	+	0.111888i
$265$	−4.81163	+	8.33398i	−0.295576	+	0.511952i
$266$	0.874236	−	0.421010i	0.0536028	−	0.0258138i
$267$	−10.7125	−	3.30436i	−0.655592	−	0.202223i
$268$	−0.00743298	−	0.0991862i	−0.000454041	−	0.00605876i
$269$	0.164508	+	0.720757i	0.0100302	+	0.0439453i	0.979695	−	0.200492i	$-0.0642540\pi$
$269$	0.164508	+	0.720757i	0.0100302	+	0.0439453i	−0.969665	+	0.244437i	$0.921397\pi$
$270$	−1.28577	+	3.27609i	−0.0782495	+	0.199376i
$271$	1.27944	−	17.0729i	0.0777202	−	1.03710i	−0.812914	−	0.582383i	$-0.802120\pi$
$271$	1.27944	−	17.0729i	0.0777202	−	1.03710i	0.890634	−	0.454720i	$-0.150261\pi$
$272$	−7.32619	+	1.10425i	−0.444215	+	0.0669547i
$273$	1.02985	+	0.955557i	0.0623291	+	0.0578329i
$274$	−5.92238	−	2.85207i	−0.357784	−	0.172300i
$275$	−0.641844	+	0.437602i	−0.0387046	+	0.0263884i
$276$	1.43106	+	3.64629i	0.0861399	+	0.219481i
$277$	−19.5327	+	6.02505i	−1.17361	+	0.362010i	−0.819437	−	0.573170i	$-0.805714\pi$
$277$	−19.5327	+	6.02505i	−1.17361	+	0.362010i	−0.354172	+	0.935180i	$0.615237\pi$
$278$	12.4977	−	11.5961i	0.749560	−	0.695490i
$279$	4.35535	−	5.46144i	0.260748	−	0.326968i
$280$	0.115925	−	0.145365i	0.00692783	−	0.00868722i
$281$	−10.1970	+	9.46147i	−0.608304	+	0.564424i	−0.923015	−	0.384764i	$-0.874283\pi$
$281$	−10.1970	+	9.46147i	−0.608304	+	0.564424i	0.314711	+	0.949188i	$0.398092\pi$
$282$	4.82454	−	1.48817i	0.287297	−	0.0886194i
$283$	−9.59677	−	24.4522i	−0.570469	−	1.45353i	−0.866903	−	0.498477i	$-0.833893\pi$
$283$	−9.59677	−	24.4522i	−0.570469	−	1.45353i	0.296434	−	0.955053i	$-0.404202\pi$
$284$	6.32128	−	4.30977i	0.375099	−	0.255738i
$285$	12.7061	+	6.11895i	0.752647	+	0.362456i
$286$	1.59227	+	1.47741i	0.0941530	+	0.0873612i
$287$	1.25852	−	0.189692i	0.0742884	−	0.0111972i
$288$	0.321516	−	4.29034i	0.0189455	−	0.252810i
$289$	13.8437	−	35.2731i	0.814332	−	2.07489i
$290$	−1.42487	−	6.24277i	−0.0836713	−	0.366588i
$291$	−2.06737	−	27.5872i	−0.121192	−	1.61719i
$292$	8.86157	+	2.73343i	0.518584	+	0.159962i
$293$	−23.3087	+	11.2249i	−1.36171	+	0.655765i	−0.965017	−	0.262186i	$-0.915557\pi$
$293$	−23.3087	+	11.2249i	−1.36171	+	0.655765i	−0.396693	+	0.917951i	$0.629842\pi$
$294$	9.41130	−	16.3009i	0.548878	−	0.950685i
$295$	−0.265183	−	0.459310i	−0.0154396	−	0.0267421i
$296$	7.05329	+	4.80885i	0.409964	+	0.279509i
$297$	0.608358	−	2.66539i	0.0353005	−	0.154662i
$298$	−12.2748	−	1.85013i	−0.711059	−	0.107175i
$299$	2.52707	+	3.16884i	0.146144	+	0.183259i
$300$	2.70229			0.156017
$301$	−0.654353	+	1.02874i	−0.0377163	+	0.0592958i
$302$	16.7359			0.963045
$303$	−16.6070	−	20.8245i	−0.954048	−	1.19634i
$304$	−5.16053	−	0.777824i	−0.295977	−	0.0446113i
$305$	−2.21296	+	9.69563i	−0.126714	+	0.555170i
$306$	26.3372	+	17.9564i	1.50560	+	1.02650i
$307$	13.1885	+	22.8431i	0.752706	+	1.30372i	0.946507	+	0.322684i	$0.104585\pi$
$307$	13.1885	+	22.8431i	0.752706	+	1.30372i	−0.193801	+	0.981041i	$0.562082\pi$
$308$	−0.0722172	+	0.125084i	−0.00411496	+	0.00712731i
$309$	9.08250	−	4.37390i	0.516686	−	0.248823i
$310$	−1.55150	−	0.478573i	−0.0881190	−	0.0271811i
$311$	−1.55060	−	20.6913i	−0.0879265	−	1.17330i	−0.850349	−	0.526219i	$-0.823609\pi$
$311$	−1.55060	−	20.6913i	−0.0879265	−	1.17330i	0.762423	−	0.647079i	$-0.224010\pi$
$312$	−1.68136	−	7.36653i	−0.0951884	−	0.417048i
$313$	−7.63813	+	19.4616i	−0.431733	+	1.10004i	0.535137	+	0.844765i	$0.320260\pi$
$313$	−7.63813	+	19.4616i	−0.431733	+	1.10004i	−0.966869	+	0.255272i	$0.917835\pi$
$314$	0.140262	−	1.87167i	0.00791545	−	0.105624i
$315$	−0.790999	+	0.119224i	−0.0445678	+	0.00671751i
$316$	−2.69510	−	2.50069i	−0.151611	−	0.140675i
$317$	14.7651	+	7.11049i	0.829290	+	0.399365i	0.799849	−	0.600202i	$-0.204913\pi$
$317$	14.7651	+	7.11049i	0.829290	+	0.399365i	0.0294411	+	0.999567i	$0.490627\pi$
$318$	−21.4862	+	14.6490i	−1.20489	+	0.821477i
$319$	1.81730	+	4.63041i	0.101749	+	0.259253i
$320$	−0.955573	+	0.294755i	−0.0534181	+	0.0164773i
$321$	1.30304	−	1.20905i	0.0727288	−	0.0674825i
$322$	−0.168037	+	0.210712i	−0.00936433	+	0.0117425i
$323$	24.1078	−	30.2302i	1.34139	−	1.68205i
$324$	2.48999	−	2.31037i	0.138333	−	0.128354i
$325$	2.67191	−	0.824176i	0.148211	−	0.0457171i
$326$	−8.00772	−	20.4033i	−0.443507	−	1.13004i
$327$	8.02365	−	5.47043i	0.443709	−	0.302516i
$328$	−6.16741	−	2.97007i	−0.340538	−	0.163995i
$329$	0.254649	+	0.236280i	0.0140392	+	0.0130265i
$330$	−2.07576	+	0.312871i	−0.114267	+	0.0172230i
$331$	0.0217345	−	0.290027i	0.00119464	−	0.0159413i	−0.996575	−	0.0826984i	$-0.973646\pi$
$331$	0.0217345	−	0.290027i	0.00119464	−	0.0159413i	0.997769	+	0.0667570i	$0.0212652\pi$
$332$	−2.81760	+	7.17914i	−0.154636	+	0.394006i
$333$	−8.17268	−	35.8068i	−0.447860	−	1.96220i
$334$	1.39431	+	18.6058i	0.0762933	+	1.01806i
$335$	0.0950454	+	0.0293176i	0.00519288	+	0.00160179i
$336$	0.452677	−	0.217998i	0.0246955	−	0.0118927i
$337$	2.61208	−	4.52425i	0.142289	−	0.246452i	−0.786069	−	0.618138i	$-0.787887\pi$
$337$	2.61208	−	4.52425i	0.142289	−	0.246452i	0.928358	+	0.371687i	$0.121220\pi$
$338$	2.59080	+	4.48740i	0.140921	+	0.244083i
$339$	−24.6288	−	16.7916i	−1.33765	−	0.911996i
$340$	1.64864	−	7.22318i	0.0894103	−	0.391732i
$341$	1.24719	+	0.187984i	0.0675391	+	0.0101799i
$342$	13.9994	+	17.5547i	0.757000	+	0.949248i
$343$	2.59658			0.140202
$344$	6.02469	−	2.58904i	0.324829	−	0.139592i
$345$	−3.91706			−0.210887
$346$	7.38342	+	9.25851i	0.396935	+	0.497741i
$347$	14.4773	+	2.18210i	0.777182	+	0.117141i	0.525642	−	0.850706i	$-0.323825\pi$
$347$	14.4773	+	2.18210i	0.777182	+	0.117141i	0.251539	+	0.967847i	$0.419063\pi$
$348$	3.85041	−	16.8698i	0.206404	−	0.904314i
$349$	27.9977	+	19.0885i	1.49868	+	1.02178i	0.986657	+	0.162811i	$0.0520561\pi$
$349$	27.9977	+	19.0885i	1.49868	+	1.02178i	0.512023	+	0.858972i	$0.328896\pi$
$350$	0.0929644	+	0.161019i	0.00496916	+	0.00860683i
$351$	−4.92032	+	8.52225i	−0.262627	+	0.454884i
$352$	0.699896	−	0.337052i	0.0373046	−	0.0179649i
$353$	0.593618	+	0.183107i	0.0315951	+	0.00974580i	0.310512	−	0.950569i	$-0.399499\pi$
$353$	0.593618	+	0.183107i	0.0315951	+	0.00974580i	−0.278917	+	0.960315i	$0.589976\pi$
$354$	−0.107103	−	1.42919i	−0.00569248	−	0.0759609i
$355$	1.70243	+	7.45885i	0.0903558	+	0.395874i
$356$	−1.51563	+	3.86176i	−0.0803281	+	0.204673i
$357$	−0.278183	+	3.71209i	−0.0147230	+	0.196465i
$358$	−20.5203	+	3.09294i	−1.08453	+	0.163467i
$359$	14.0702	+	13.0552i	0.742597	+	0.689029i	0.957766	−	0.287548i	$-0.0928399\pi$
$359$	14.0702	+	13.0552i	0.742597	+	0.689029i	−0.215170	+	0.976577i	$0.569030\pi$
$360$	3.87630	+	1.86673i	0.204299	+	0.0983851i
$361$	6.80495	−	4.63953i	0.358155	−	0.244186i
$362$	−6.03409	−	15.3746i	−0.317145	−	0.808072i
$363$	−26.8463	+	8.28099i	−1.40907	+	0.434639i
$364$	0.381101	−	0.353610i	0.0199751	−	0.0185342i
$365$	−5.78198	+	7.25037i	−0.302643	+	0.379502i
$366$	−16.7558	+	21.0111i	−0.875838	+	1.09827i
$367$	−8.35366	+	7.75106i	−0.436057	+	0.404602i	−0.867420	−	0.497576i	$-0.834223\pi$
$367$	−8.35366	+	7.75106i	−0.436057	+	0.404602i	0.431363	+	0.902179i	$0.358033\pi$
$368$	1.38514	−	0.427258i	0.0722052	−	0.0222723i
$369$	10.7597	+	27.4152i	0.560126	+	1.42718i
$370$	−7.05329	+	4.80885i	−0.366683	+	0.250000i
$371$	−1.61205	−	0.776322i	−0.0836934	−	0.0403046i
$372$	−3.21628	−	2.98427i	−0.166756	−	0.154727i
$373$	−23.5868	+	3.55514i	−1.22128	+	0.184078i	−0.727867	−	0.685718i	$-0.759488\pi$
$373$	−23.5868	+	3.55514i	−1.22128	+	0.184078i	−0.493411	+	0.869796i	$0.664250\pi$
$374$	−0.430106	+	5.73937i	−0.0222403	+	0.296776i
$375$	−0.987257	+	2.51549i	−0.0509817	+	0.129899i
$376$	−0.415749	−	1.82152i	−0.0214406	−	0.0939375i
$377$	−1.33801	−	17.8545i	−0.0689109	−	0.919553i
$378$	−0.625281	−	0.192874i	−0.0321610	−	0.00992035i
$379$	−15.8832	+	7.64894i	−0.815865	+	0.392900i	−0.794795	−	0.606878i	$-0.792422\pi$
$379$	−15.8832	+	7.64894i	−0.815865	+	0.392900i	−0.0210700	+	0.999778i	$0.506707\pi$
$380$	2.60941	−	4.51963i	0.133860	−	0.231852i
$381$	−18.3829	−	31.8401i	−0.941784	−	1.63122i
$382$	13.2815	+	9.05515i	0.679539	+	0.463302i
$383$	−4.14519	+	18.1612i	−0.211809	+	0.927996i	0.751528	+	0.659702i	$0.229317\pi$
$383$	−4.14519	+	18.1612i	−0.211809	+	0.927996i	−0.963337	+	0.268295i	$0.913540\pi$
$384$	−2.67211	−	0.402755i	−0.136360	−	0.0205530i
$385$	−0.0900534	−	0.112923i	−0.00458954	−	0.00575511i
$386$	7.12169			0.362485
$387$	−26.5775	−	9.46489i	−1.35101	−	0.481127i
$388$	−10.2374			−0.519728
$389$	−9.12078	−	11.4371i	−0.462442	−	0.579884i	0.494860	−	0.868972i	$-0.335219\pi$
$389$	−9.12078	−	11.4371i	−0.462442	−	0.579884i	−0.957302	+	0.289089i	$0.906648\pi$
$390$	7.47158	+	1.12616i	0.378338	+	0.0570253i
$391$	−2.38977	+	10.4703i	−0.120856	+	0.529503i
$392$	−5.75511	−	3.92377i	−0.290677	−	0.198180i
$393$	−0.0491832	−	0.0851879i	−0.00248097	−	0.00429716i
$394$	−3.17319	+	5.49613i	−0.159863	+	0.276891i
$395$	3.31246	−	1.59520i	0.166668	−	0.0802630i
$396$	−3.19371	−	0.985128i	−0.160490	−	0.0495045i
$397$	1.67391	+	22.3367i	0.0840109	+	1.12105i	0.866765	+	0.498717i	$0.166195\pi$
$397$	1.67391	+	22.3367i	0.0840109	+	1.12105i	−0.782754	+	0.622331i	$0.786186\pi$
$398$	−5.43940	−	23.8316i	−0.272652	−	1.19457i
$399$	−0.957964	+	2.44085i	−0.0479582	+	0.122195i
$400$	0.0747301	−	0.997204i	0.00373650	−	0.0498602i
$401$	−37.8160	+	5.69985i	−1.88844	+	0.284637i	−0.988483	−	0.151334i	$-0.951643\pi$
$401$	−37.8160	+	5.69985i	−1.88844	+	0.284637i	−0.899961	+	0.435971i	$0.856405\pi$
$402$	0.197031	+	0.182818i	0.00982700	+	0.00911812i
$403$	−4.09030	−	1.96979i	−0.203752	−	0.0981220i
$404$	−8.14396	+	5.55246i	−0.405177	+	0.276245i
$405$	1.24097	+	3.16194i	0.0616643	+	0.157118i
$406$	1.13767	−	0.350924i	0.0564615	−	0.0174161i
$407$	4.86121	−	4.51055i	0.240961	−	0.223579i
$408$	12.4830	−	15.6531i	0.617998	−	0.774945i
$409$	9.19244	−	11.5270i	0.454537	−	0.569971i	−0.500773	−	0.865579i	$-0.666951\pi$
$409$	9.19244	−	11.5270i	0.454537	−	0.569971i	0.955309	+	0.295608i	$0.0955221\pi$
$410$	5.01797	−	4.65599i	0.247820	−	0.229943i
$411$	16.9739	−	5.23576i	0.837261	−	0.258261i
$412$	−1.36290	−	3.47260i	−0.0671450	−	0.171083i
$413$	0.0814757	−	0.0555492i	0.00400916	−	0.00273340i
$414$	−5.61883	−	2.70588i	−0.276150	−	0.132987i
$415$	−5.65349	−	5.24567i	−0.277519	−	0.257500i
$416$	−2.76491	+	0.416743i	−0.135561	+	0.0204325i
$417$	−3.44288	+	45.9420i	−0.168598	+	2.24979i
$418$	−1.48113	+	3.77387i	−0.0724446	+	0.184586i
$419$	−6.52852	−	28.6033i	−0.318939	−	1.39736i	−0.839417	−	0.543488i	$-0.817103\pi$
$419$	−6.52852	−	28.6033i	−0.318939	−	1.39736i	0.520478	−	0.853875i	$-0.325754\pi$
$420$	0.0375469	+	0.501029i	0.00183210	+	0.0244477i
$421$	−31.1400	−	9.60540i	−1.51767	−	0.468139i	−0.579691	−	0.814836i	$-0.696827\pi$
$421$	−31.1400	−	9.60540i	−1.51767	−	0.468139i	−0.937977	+	0.346697i	$0.887303\pi$
$422$	−17.3004	+	8.33146i	−0.842173	+	0.405569i
$423$	−4.01918	+	6.96143i	−0.195419	+	0.338476i
$424$	4.81163	+	8.33398i	0.233673	+	0.404734i
$425$	6.12155	+	4.17361i	0.296939	+	0.202450i
$426$	−4.60047	+	20.1560i	−0.222893	+	0.976559i
$427$	−1.82840	−	0.275587i	−0.0884826	−	0.0133366i
$428$	−0.410130	−	0.514287i	−0.0198244	−	0.0248590i
$429$	−5.86968			−0.283391
$430$	0.209005	+	6.55411i	0.0100791	+	0.316067i
$431$	−21.3121			−1.02657			−0.513285	−	0.858218i	$-0.671572\pi$
$431$	−21.3121			−1.02657			−0.513285	+	0.858218i	$0.671572\pi$
$432$	2.19429	+	2.75155i	0.105573	+	0.132384i
$433$	−29.2671	−	4.41130i	−1.40649	−	0.211994i	−0.598466	−	0.801148i	$-0.704223\pi$
$433$	−29.2671	−	4.41130i	−1.40649	−	0.211994i	−0.808020	+	0.589155i	$0.799461\pi$
$434$	0.0671745	−	0.294311i	0.00322448	−	0.0141274i
$435$	14.2969	+	9.74746i	0.685484	+	0.467355i
$436$	−1.79682	−	3.11219i	−0.0860521	−	0.149047i
$437$	−3.78243	+	6.55136i	−0.180938	+	0.313394i
$438$	−22.5782	+	10.8731i	−1.07883	+	0.519536i
$439$	−20.3956	−	6.29122i	−0.973431	−	0.300264i	−0.233060	−	0.972462i	$-0.574874\pi$
$439$	−20.3956	−	6.29122i	−0.973431	−	0.300264i	−0.740371	+	0.672199i	$0.765350\pi$
$440$	0.0580523	+	0.774654i	0.00276753	+	0.0369302i
$441$	6.66847	+	29.2165i	0.317546	+	1.39126i
$442$	7.56856	−	19.2844i	0.360000	−	0.917264i
$443$	−0.667095	+	8.90177i	−0.0316947	+	0.422936i	0.958677	+	0.284498i	$0.0918270\pi$
$443$	−0.667095	+	8.90177i	−0.0316947	+	0.422936i	−0.990371	+	0.138437i	$0.955792\pi$
$444$	−22.8108	+	3.43817i	−1.08255	+	0.163168i
$445$	−3.04109	−	2.82172i	−0.144161	−	0.133762i
$446$	−16.8198	−	8.09999i	−0.796441	−	0.383546i
$447$	27.7159	−	18.8964i	1.31092	−	0.893769i
$448$	−0.0679274	−	0.173076i	−0.00320927	−	0.00817709i
$449$	−25.1876	+	7.76934i	−1.18868	+	0.366658i	−0.825143	−	0.564923i	$-0.808906\pi$
$449$	−25.1876	+	7.76934i	−1.18868	+	0.366658i	−0.363533	+	0.931581i	$0.618430\pi$
$450$	−3.15386	+	2.92635i	−0.148674	+	0.137950i
$451$	−3.31548	+	4.15748i	−0.156120	+	0.195768i
$452$	−6.87758	+	8.62421i	−0.323494	+	0.405649i
$453$	−33.1525	+	30.7610i	−1.55764	+	1.44528i
$454$	21.2195	−	6.54535i	0.995881	−	0.307189i
$455$	0.189935	+	0.483945i	0.00890427	+	0.0226877i
$456$	11.6522	−	7.94436i	0.545666	−	0.372029i
$457$	29.7519	+	14.3278i	1.39173	+	0.670224i	0.971467	−	0.237176i	$-0.0762218\pi$
$457$	29.7519	+	14.3278i	1.39173	+	0.670224i	0.420268	+	0.907400i	$0.361936\pi$
$458$	10.5170	+	9.75835i	0.491427	+	0.455978i
$459$	−25.7836	+	3.88625i	−1.20347	+	0.181394i
$460$	−0.108324	+	1.44548i	−0.00505062	+	0.0673959i
$461$	−1.33486	+	3.40118i	−0.0621708	+	0.158409i	−0.958583	−	0.284812i	$-0.908069\pi$
$461$	−1.33486	+	3.40118i	−0.0621708	+	0.158409i	0.896413	+	0.443220i	$0.146164\pi$
$462$	−0.0868507	−	0.380518i	−0.00404066	−	0.0177033i
$463$	−0.865829	−	11.5537i	−0.0402385	−	0.536945i	−0.980503	−	0.196502i	$-0.937042\pi$
$463$	−0.865829	−	11.5537i	−0.0402385	−	0.536945i	0.940265	−	0.340443i	$-0.110577\pi$
$464$	−6.11883	−	1.88741i	−0.284060	−	0.0876208i
$465$	3.95301	−	1.90367i	0.183317	−	0.0882806i
$466$	−3.28764	+	5.69435i	−0.152297	+	0.263786i
$467$	13.7926	+	23.8895i	0.638245	+	1.10547i	0.985818	+	0.167819i	$0.0536725\pi$
$467$	13.7926	+	23.8895i	0.638245	+	1.10547i	−0.347573	+	0.937653i	$0.612994\pi$
$468$	9.93966	+	6.77675i	0.459461	+	0.313255i
$469$	−0.00411514	+	0.0180296i	−0.000190020	+	0.000832530i
$470$	1.84749	+	0.278464i	0.0852184	+	0.0128446i
$471$	3.16232	+	3.96542i	0.145712	+	0.182717i
$472$	−0.530366			−0.0244121
$473$	−0.919381	−	5.01034i	−0.0422732	−	0.230376i
$474$	9.93511			0.456335
$475$	3.25388	+	4.08024i	0.149298	+	0.187214i
$476$	1.36215	+	0.205311i	0.0624340	+	0.00941042i
$477$	9.21298	−	40.3647i	0.421833	−	1.84817i
$478$	13.2500	+	9.03367i	0.606039	+	0.413190i
$479$	−6.31794	−	10.9430i	−0.288674	−	0.499998i	0.684819	−	0.728713i	$-0.259881\pi$
$479$	−6.31794	−	10.9430i	−0.288674	−	0.499998i	−0.973493	+	0.228715i	$0.926548\pi$
$480$	1.35114	−	2.34025i	0.0616710	−	0.106817i
$481$	−21.5057	+	10.3566i	−0.980578	+	0.472221i
$482$	−13.4584	−	4.15135i	−0.613011	−	0.189089i
$483$	−0.0544255	−	0.726258i	−0.00247645	−	0.0330459i
$484$	2.31345	+	10.1359i	0.105157	+	0.460722i
$485$	3.74016	−	9.52977i	0.169832	−	0.432725i
$486$	−1.47495	+	19.6819i	−0.0669053	+	0.892789i
$487$	8.40832	−	1.26735i	0.381017	−	0.0574291i	0.0442586	−	0.999020i	$-0.485907\pi$
$487$	8.40832	−	1.26735i	0.381017	−	0.0574291i	0.336759	+	0.941591i	$0.390669\pi$
$488$	7.29018	+	6.76429i	0.330011	+	0.306205i
$489$	53.3645	+	25.6990i	2.41322	+	1.16215i
$490$	5.75511	−	3.92377i	0.259989	−	0.177258i
$491$	7.20895	+	18.3681i	0.325336	+	0.828941i	0.996178	+	0.0873419i	$0.0278373\pi$
$491$	7.20895	+	18.3681i	0.325336	+	0.828941i	−0.670843	+	0.741600i	$0.734067\pi$
$492$	17.6762	−	5.45238i	0.796904	−	0.245812i
$493$	34.7773	−	32.2686i	1.56629	−	1.45330i
$494$	9.09830	−	11.4089i	0.409352	−	0.513311i
$495$	2.08382	−	2.61303i	0.0936608	−	0.117447i
$496$	−1.19020	+	1.10435i	−0.0534417	+	0.0495867i
$497$	−1.35928	+	0.419283i	−0.0609722	+	0.0188074i
$498$	−7.61398	−	19.4001i	−0.341191	−	0.869340i
$499$	−8.68537	+	5.92159i	−0.388811	+	0.265087i	−0.741910	−	0.670499i	$-0.766080\pi$
$499$	−8.68537	+	5.92159i	−0.388811	+	0.265087i	0.353100	+	0.935586i	$0.385128\pi$
$500$	0.900969	+	0.433884i	0.0402926	+	0.0194039i
$501$	−36.9599	−	34.2937i	−1.65124	−	1.53213i
$502$	7.99151	−	1.20453i	0.356679	−	0.0537606i
$503$	−1.46751	+	19.5825i	−0.0654329	+	0.873142i	0.863844	+	0.503759i	$0.168050\pi$
$503$	−1.46751	+	19.5825i	−0.0654329	+	0.873142i	−0.929277	+	0.369383i	$0.879569\pi$
$504$	−0.292249	+	0.744637i	−0.0130178	+	0.0331688i
$505$	−2.19332	−	9.60954i	−0.0976013	−	0.427619i
$506$	−0.0841488	−	1.12289i	−0.00374087	−	0.0499184i
$507$	−13.3801	−	4.12722i	−0.594232	−	0.183296i
$508$	−12.2581	+	5.90317i	−0.543863	+	0.261911i
$509$	14.7133	−	25.4842i	0.652156	−	1.12957i	−0.330443	−	0.943826i	$-0.607198\pi$
$509$	14.7133	−	25.4842i	0.652156	−	1.12957i	0.982599	−	0.185741i	$-0.0594687\pi$
$510$	10.0106	+	17.3388i	0.443275	+	0.767774i
$511$	−1.42462	−	0.971290i	−0.0630215	−	0.0429674i
$512$	−0.222521	+	0.974928i	−0.00983413	+	0.0430861i
$513$	−18.1618	−	2.73745i	−0.801863	−	0.120861i
$514$	−14.1508	−	17.7446i	−0.624166	−	0.782679i
$515$	3.73047			0.164384
$516$	−7.17569	+	16.2022i	−0.315892	+	0.713262i
$517$	−1.45139			−0.0638321
$518$	−0.989606	−	1.24093i	−0.0434808	−	0.0545232i
$519$	−31.6433	−	4.76946i	−1.38899	−	0.209356i
$520$	0.622199	−	2.72603i	0.0272853	−	0.119544i
$521$	8.58681	+	5.85439i	0.376195	+	0.256485i	0.736626	−	0.676301i	$-0.236418\pi$
$521$	8.58681	+	5.85439i	0.376195	+	0.256485i	−0.360431	+	0.932786i	$0.617370\pi$
$522$	13.7747	+	23.8585i	0.602902	+	1.04426i
$523$	19.7624	−	34.2294i	0.864147	−	1.49675i	−0.00374369	−	0.999993i	$-0.501192\pi$
$523$	19.7624	−	34.2294i	0.864147	−	1.49675i	0.867891	−	0.496754i	$-0.165475\pi$
$524$	−0.0327963	+	0.0157939i	−0.00143271	+	0.000689959i
$525$	−0.480112	−	0.148095i	−0.0209538	−	0.00646339i
$526$	1.16757	+	15.5801i	0.0509083	+	0.679324i
$527$	−2.67679	−	11.7278i	−0.116603	−	0.510870i
$528$	−0.766927	+	1.95410i	−0.0333762	+	0.0850412i
$529$	−1.56177	+	20.8404i	−0.0679032	+	0.906105i
$530$	−9.51577	+	1.43427i	−0.413339	+	0.0623008i
$531$	1.67270	+	1.55204i	0.0725890	+	0.0673527i
$532$	0.874236	+	0.421010i	0.0379029	+	0.0182531i
$533$	15.8146	−	10.7822i	0.685005	−	0.467029i
$534$	−4.09566	−	10.4356i	−0.177237	−	0.451592i
$535$	0.628574	−	0.193889i	0.0271756	−	0.00838257i
$536$	0.0729125	−	0.0676529i	0.00314934	−	0.00292216i
$537$	34.9641	−	43.8436i	1.50881	−	1.89199i
$538$	−0.460941	+	0.578002i	−0.0198726	+	0.0249194i
$539$	−3.96649	+	3.68037i	−0.170849	+	0.158525i
$540$	−3.36301	+	1.03735i	−0.144721	+	0.0446405i
$541$	6.39622	+	16.2973i	0.274995	+	0.700675i	0.999930	+	0.0118579i	$0.00377459\pi$
$541$	6.39622	+	16.2973i	0.274995	+	0.700675i	−0.724935	+	0.688817i	$0.758130\pi$
$542$	14.1458	−	9.64446i	0.607615	−	0.414265i
$543$	40.2119	+	19.3650i	1.72566	+	0.831034i
$544$	−5.43114	−	5.03936i	−0.232858	−	0.216061i
$545$	3.55350	−	0.535605i	0.152215	−	0.0229428i
$546$	−0.104986	+	1.40095i	−0.00449300	+	0.0599549i
$547$	−9.12237	+	23.2434i	−0.390044	+	0.993817i	0.592130	+	0.805843i	$0.298287\pi$
$547$	−9.12237	+	23.2434i	−0.390044	+	0.993817i	−0.982174	+	0.187974i	$0.939808\pi$
$548$	−1.46271	−	6.40854i	−0.0624837	−	0.273759i
$549$	−3.19747	−	42.6672i	−0.136465	−	1.82099i
$550$	−0.742314	−	0.228974i	−0.0316524	−	0.00976346i
$551$	30.1083	−	14.4994i	1.28266	−	0.617695i
$552$	−1.95853	+	3.39227i	−0.0833606	+	0.144385i
$553$	0.341789	+	0.591995i	0.0145343	+	0.0251742i
$554$	−16.8890	−	11.5148i	−0.717547	−	0.489215i
$555$	5.13321	−	22.4900i	0.217892	−	0.954649i
$556$	16.8584	+	2.54099i	0.714955	+	0.107762i
$557$	20.3955	+	25.5752i	0.864187	+	1.08366i	0.995727	+	0.0923453i	$0.0294363\pi$
$557$	20.3955	+	25.5752i	0.864187	+	1.08366i	−0.131540	+	0.991311i	$0.541992\pi$
$558$	6.98545			0.295717
$559$	−2.15350	+	18.2086i	−0.0910833	+	0.770142i
$560$	0.185929			0.00785693
$561$	−9.69708	−	12.1598i	−0.409411	−	0.513385i
$562$	−13.7550	−	2.07324i	−0.580221	−	0.0874542i
$563$	−1.50772	+	6.60575i	−0.0635428	+	0.278399i	−0.996711	−	0.0810416i	$-0.974175\pi$
$563$	−1.50772	+	6.60575i	−0.0635428	+	0.278399i	0.933168	+	0.359441i	$0.117032\pi$
$564$	4.17155	+	2.84412i	0.175654	+	0.119759i
$565$	−5.51539	−	9.55293i	−0.232034	−	0.401895i
$566$	13.1340	−	22.7487i	0.552063	−	0.956200i
$567$	−0.569010	+	0.274021i	−0.0238962	+	0.0115078i
$568$	7.31077	+	2.25507i	0.306753	+	0.0946208i
$569$	0.136823	+	1.82577i	0.00573590	+	0.0765403i	0.999337	−	0.0364049i	$-0.0115906\pi$
$569$	0.136823	+	1.82577i	0.00573590	+	0.0765403i	−0.993601	+	0.112945i	$0.963972\pi$
$570$	3.13816	+	13.7492i	0.131443	+	0.575889i
$571$	−10.2950	+	26.2314i	−0.430834	+	1.09775i	0.536423	+	0.843949i	$0.319775\pi$
$571$	−10.2950	+	26.2314i	−0.430834	+	1.09775i	−0.967257	+	0.253799i	$0.918320\pi$
$572$	−0.162322	+	2.16604i	−0.00678704	+	0.0905667i
$573$	−42.9531	+	6.47413i	−1.79439	+	0.270461i
$574$	0.932985	+	0.865683i	0.0389420	+	0.0361329i
$575$	−1.30599	−	0.628929i	−0.0544633	−	0.0262282i
$576$	3.55478	−	2.42361i	0.148116	−	0.100984i
$577$	−12.9244	−	32.9307i	−0.538048	−	1.37092i	−0.898839	−	0.438278i	$-0.855588\pi$
$577$	−12.9244	−	32.9307i	−0.538048	−	1.37092i	0.360791	−	0.932647i	$-0.382507\pi$
$578$	36.2090	−	11.1690i	1.50609	−	0.464569i
$579$	−14.1075	+	13.0898i	−0.586287	+	0.543995i
$580$	3.99240	−	5.00631i	0.165775	−	0.207876i
$581$	0.894042	−	1.12109i	0.0370911	−	0.0465108i
$582$	20.2795	−	18.8167i	0.840614	−	0.779976i
$583$	7.14347	−	2.20347i	0.295852	−	0.0912584i
$584$	3.38802	+	8.63253i	0.140197	+	0.357216i
$585$	−9.93966	+	6.77675i	−0.410954	+	0.280184i
$586$	−23.3087	−	11.2249i	−0.962875	−	0.463696i
$587$	25.9867	+	24.1121i	1.07259	+	0.995214i	0.999998	−	0.00214769i	$-0.000683632\pi$
$587$	25.9867	+	24.1121i	1.07259	+	0.995214i	0.0725882	+	0.997362i	$0.476874\pi$
$588$	18.6124	−	2.80536i	0.767561	−	0.115691i
$589$	0.633220	−	8.44973i	0.0260914	−	0.348165i
$590$	0.193764	−	0.493704i	0.00797716	−	0.0203255i
$591$	−3.81618	−	16.7198i	−0.156977	−	0.687760i
$592$	0.637943	+	8.51275i	0.0262193	+	0.349872i
$593$	31.3217	+	9.66148i	1.28623	+	0.396749i	0.861124	−	0.508395i	$-0.169761\pi$
$593$	31.3217	+	9.66148i	1.28623	+	0.396749i	0.425105	+	0.905144i	$0.360237\pi$
$594$	2.46319	−	1.18621i	0.101066	−	0.0486708i
$595$	−0.688768	+	1.19298i	−0.0282367	+	0.0489075i
$596$	−6.20672	−	10.7503i	−0.254237	−	0.440351i
$597$	54.5780	+	37.2106i	2.23373	+	1.52293i
$598$	−0.901899	+	3.95148i	−0.0368814	+	0.161588i
$599$	−38.0787	−	5.73945i	−1.55585	−	0.234507i	−0.685921	−	0.727676i	$-0.740600\pi$
$599$	−38.0787	−	5.73945i	−1.55585	−	0.234507i	−0.869934	+	0.493169i	$0.835839\pi$
$600$	1.68485	+	2.11273i	0.0687837	+	0.0862520i
$601$	33.4658			1.36510			0.682549	−	0.730840i	$-0.260872\pi$
$601$	33.4658			1.36510			0.682549	+	0.730840i	$0.260872\pi$
$602$	−1.21229	+	0.129817i	−0.0494091	+	0.00529096i
$603$	−0.427932			−0.0174267
$604$	10.4347	+	13.0847i	0.424581	+	0.532408i
$605$	−10.2804	−	1.54952i	−0.417959	−	0.0629971i
$606$	5.92697	−	25.9678i	0.240767	−	1.05487i
$607$	14.8128	+	10.0992i	0.601234	+	0.409914i	0.825328	−	0.564653i	$-0.190990\pi$
$607$	14.8128	+	10.0992i	0.601234	+	0.409914i	−0.224095	+	0.974567i	$0.571942\pi$
$608$	−2.60941	−	4.51963i	−0.105825	−	0.183295i
$609$	−1.60862	+	2.78621i	−0.0651845	+	0.112903i
$610$	−8.96010	+	4.31496i	−0.362784	+	0.174708i
$611$	4.99209	+	1.53986i	0.201959	+	0.0622960i
$612$	2.38209	+	31.7868i	0.0962905	+	1.28491i
$613$	−1.27042	−	5.56607i	−0.0513117	−	0.224811i	0.942770	−	0.333443i	$-0.108210\pi$
$613$	−1.27042	−	5.56607i	−0.0513117	−	0.224811i	−0.994082	+	0.108631i	$0.965353\pi$
$614$	−9.63658	+	24.5536i	−0.388901	+	0.990903i
$615$	−1.38236	+	18.4463i	−0.0557420	+	0.743826i
$616$	−0.142821	+	0.0215268i	−0.00575443	+	0.000867341i
$617$	4.30056	+	3.99034i	0.173134	+	0.160645i	0.761980	−	0.647600i	$-0.224227\pi$
$617$	4.30056	+	3.99034i	0.173134	+	0.160645i	−0.588846	+	0.808245i	$0.700418\pi$
$618$	9.08250	+	4.37390i	0.365352	+	0.175944i
$619$	12.1251	−	8.26677i	0.487350	−	0.332270i	−0.294590	−	0.955624i	$-0.595183\pi$
$619$	12.1251	−	8.26677i	0.487350	−	0.332270i	0.781940	+	0.623354i	$0.214231\pi$
$620$	−0.593178	−	1.51139i	−0.0238226	−	0.0606990i
$621$	4.87480	−	1.50368i	0.195619	−	0.0603405i
$622$	15.2104	−	14.1131i	0.609880	−	0.565886i
$623$	0.480917	−	0.603051i	0.0192675	−	0.0241607i
$624$	4.71107	−	5.90750i	0.188594	−	0.236489i
$625$	−0.733052	+	0.680173i	−0.0293221	+	0.0272069i
$626$	−19.9780	+	6.16240i	−0.798482	+	0.246299i
$627$	−4.00245	−	10.1981i	−0.159843	−	0.407272i
$628$	1.55078	−	1.05730i	0.0618829	−	0.0421910i
$629$	−56.9839	−	27.4420i	−2.27210	−	1.09418i
$630$	−0.586393	−	0.544093i	−0.0233625	−	0.0216772i
$631$	24.0920	−	3.63128i	0.959086	−	0.144559i	0.349200	−	0.937048i	$-0.386453\pi$
$631$	24.0920	−	3.63128i	0.959086	−	0.144559i	0.609886	+	0.792489i	$0.291215\pi$
$632$	0.274749	−	3.66627i	0.0109289	−	0.145836i
$633$	18.9574	−	48.3026i	0.753487	−	1.91985i
$634$	3.64668	+	15.9771i	0.144828	+	0.634533i
$635$	−1.01673	−	13.5674i	−0.0403479	−	0.538405i
$636$	−24.8495	−	7.66505i	−0.985346	−	0.303939i
$637$	17.5476	−	8.45045i	0.695259	−	0.334819i
$638$	−2.48713	+	4.30783i	−0.0984664	+	0.170549i
$639$	−16.4580	−	28.5061i	−0.651068	−	1.12768i
$640$	−0.826239	−	0.563320i	−0.0326600	−	0.0222672i
$641$	−2.83919	+	12.4393i	−0.112141	+	0.491323i	0.887399	+	0.461002i	$0.152510\pi$
$641$	−2.83919	+	12.4393i	−0.112141	+	0.491323i	−0.999540	+	0.0303205i	$0.990347\pi$
$642$	1.75771	+	0.264932i	0.0693711	+	0.0104560i
$643$	2.08537	+	2.61497i	0.0822391	+	0.103125i	0.821249	−	0.570570i	$-0.193278\pi$
$643$	2.08537	+	2.61497i	0.0822391	+	0.103125i	−0.739010	+	0.673695i	$0.764706\pi$
$644$	−0.269510			−0.0106202
$645$	−12.4606	−	12.5990i	−0.490637	−	0.496085i
$646$	38.6659			1.52129
$647$	−18.5750	−	23.2923i	−0.730258	−	0.915715i	0.268611	−	0.963249i	$-0.413435\pi$
$647$	−18.5750	−	23.2923i	−0.730258	−	0.915715i	−0.998870	+	0.0475336i	$0.984864\pi$
$648$	3.35881	+	0.506259i	0.131946	+	0.0198877i
$649$	−0.0916791	+	0.401672i	−0.00359872	+	0.0157670i
$650$	2.31028	+	1.57512i	0.0906166	+	0.0617813i
$651$	0.407883	+	0.706474i	0.0159862	+	0.0276889i
$652$	10.9592	−	18.9820i	0.429197	−	0.743391i
$653$	17.4236	−	8.39077i	0.681839	−	0.328356i	−0.0607030	−	0.998156i	$-0.519334\pi$
$653$	17.4236	−	8.39077i	0.681839	−	0.328356i	0.742542	+	0.669800i	$0.233620\pi$
$654$	9.27962	+	2.86239i	0.362862	+	0.111928i
$655$	−0.00272026	−	0.0362994i	−0.000106289	−	0.00141833i
$656$	−1.52322	−	6.67368i	−0.0594719	−	0.260564i
$657$	14.5765	−	37.1403i	0.568683	−	1.44898i
$658$	−0.0259599	+	0.346410i	−0.00101202	+	0.0135045i
$659$	34.2147	−	5.15704i	1.33282	−	0.200890i	0.556297	−	0.830983i	$-0.312222\pi$
$659$	34.2147	−	5.15704i	1.33282	−	0.200890i	0.776519	+	0.630094i	$0.216983\pi$
$660$	−1.53883	−	1.42782i	−0.0598988	−	0.0555780i
$661$	22.1207	+	10.6528i	0.860395	+	0.414344i	0.811425	−	0.584456i	$-0.198692\pi$
$661$	22.1207	+	10.6528i	0.860395	+	0.414344i	0.0489694	+	0.998800i	$0.484406\pi$
$662$	0.240304	−	0.163836i	0.00933966	−	0.00636767i
$663$	20.4524	+	52.1120i	0.794307	+	2.02386i
$664$	−7.36962	+	2.27323i	−0.285997	+	0.0882184i
$665$	−0.711301	+	0.659991i	−0.0275831	+	0.0255934i
$666$	22.8993	−	28.7148i	0.887331	−	1.11268i
$667$	−5.78712	+	7.25682i	−0.224078	+	0.280985i
$668$	−13.6772	+	12.6906i	−0.529188	+	0.491015i
$669$	48.2066	−	14.8698i	1.86378	−	0.574899i
$670$	0.0363384	+	0.0925887i	0.00140387	+	0.00357701i
$671$	6.38312	−	4.35193i	0.246417	−	0.168005i
$672$	0.452677	+	0.217998i	0.0174624	+	0.00840944i
$673$	0.354785	+	0.329192i	0.0136760	+	0.0126894i	0.686981	−	0.726675i	$-0.258935\pi$
$673$	0.354785	+	0.329192i	0.0136760	+	0.0126894i	−0.673305	+	0.739365i	$0.735126\pi$
$674$	5.16580	−	0.778620i	0.198979	−	0.0299913i
$675$	0.263003	−	3.50953i	0.0101230	−	0.135082i
$676$	−1.89305	+	4.82342i	−0.0728098	+	0.185516i
$677$	−3.33039	−	14.5914i	−0.127997	−	0.560792i	−0.997734	−	0.0672771i	$-0.978569\pi$
$677$	−3.33039	−	14.5914i	−0.127997	−	0.560792i	0.869737	−	0.493515i	$-0.164288\pi$
$678$	−2.22758	−	29.7250i	−0.0855497	−	1.14158i
$679$	1.81887	+	0.561048i	0.0698019	+	0.0215310i
$680$	6.67523	−	3.21462i	0.255983	−	0.123275i
$681$	−30.0036	+	51.9677i	−1.14974	+	1.99141i
$682$	0.630639	+	1.09230i	0.0241484	+	0.0418263i
$683$	−25.5419	−	17.4141i	−0.977332	−	0.666334i	−0.0344313	−	0.999407i	$-0.510962\pi$
$683$	−25.5419	−	17.4141i	−0.977332	−	0.666334i	−0.942901	+	0.333073i	$0.891914\pi$
$684$	−4.99632	+	21.8903i	−0.191039	+	0.836997i
$685$	6.49992	+	0.979706i	0.248349	+	0.0374326i
$686$	1.61894	+	2.03009i	0.0618114	+	0.0775090i
$687$	−38.7694			−1.47914
$688$	5.78053	+	3.09605i	0.220380	+	0.118036i
$689$	−26.9080			−1.02511
$690$	−2.44225	−	3.06248i	−0.0929748	−	0.116587i
$691$	20.8923	+	3.14901i	0.794782	+	0.119794i	0.533868	−	0.845568i	$-0.320738\pi$
$691$	20.8923	+	3.14901i	0.794782	+	0.119794i	0.260914	+	0.965362i	$0.415976\pi$
$692$	−2.63511	+	11.5452i	−0.100172	+	0.438882i
$693$	0.513433	+	0.350052i	0.0195037	+	0.0132974i
$694$	7.32041	+	12.6793i	0.277879	+	0.481300i
$695$	−8.52441	+	14.7647i	−0.323349	+	0.560057i
$696$	15.5900	−	7.50775i	0.590937	−	0.284580i
$697$	48.4633	+	14.9489i	1.83568	+	0.566232i
$698$	2.53228	+	33.7909i	0.0958482	+	1.27901i
$699$	−3.95382	−	17.3228i	−0.149547	−	0.655208i
$700$	−0.0679274	+	0.173076i	−0.00256742	+	0.00654167i
$701$	−1.90696	+	25.4466i	−0.0720247	+	0.961103i	0.837764	+	0.546032i	$0.183862\pi$
$701$	−1.90696	+	25.4466i	−0.0720247	+	0.961103i	−0.909789	+	0.415071i	$0.863757\pi$
$702$	−9.73073	+	1.46667i	−0.367263	+	0.0553560i
$703$	−32.6582	−	30.3024i	−1.23173	−	1.14288i
$704$	0.699896	+	0.337052i	0.0263783	+	0.0127031i
$705$	−4.17155	+	2.84412i	−0.157110	+	0.107116i
$706$	0.226956	+	0.578275i	0.00854161	+	0.0217637i
$707$	1.75122	−	0.540180i	0.0658614	−	0.0203156i
$708$	1.05061	−	0.974825i	0.0394844	−	0.0366362i
$709$	−20.4126	+	25.5967i	−0.766613	+	0.961302i	−0.999938	−	0.0110963i	$-0.996468\pi$
$709$	−20.4126	+	25.5967i	−0.766613	+	0.961302i	0.233325	+	0.972399i	$0.425039\pi$
$710$	−4.77011	+	5.98153i	−0.179019	+	0.224483i
$711$	−11.5953	+	10.7589i	−0.434859	+	0.403490i
$712$	−3.96422	+	1.22280i	−0.148565	+	0.0458264i
$713$	0.859832	+	2.19082i	0.0322010	+	0.0820467i
$714$	−3.07567	+	2.09696i	−0.115104	+	0.0784767i
$715$	−1.95701	−	0.942445i	−0.0731879	−	0.0352454i
$716$	−15.2124	−	14.1150i	−0.568512	−	0.527502i
$717$	−42.8512	+	6.45877i	−1.60031	+	0.241207i
$718$	−1.43437	+	19.1403i	−0.0535302	+	0.714311i
$719$	9.62535	−	24.5250i	0.358965	−	0.914628i	−0.631313	−	0.775528i	$-0.717484\pi$
$719$	9.62535	−	24.5250i	0.358965	−	0.914628i	0.990278	−	0.139100i	$-0.0444209\pi$
$720$	0.957366	+	4.19450i	0.0356789	+	0.156320i
$721$	0.0518330	+	0.691663i	0.00193036	+	0.0257589i
$722$	7.87015	+	2.42762i	0.292897	+	0.0903466i
$723$	34.2902	−	16.5133i	1.27527	−	0.614135i
$724$	8.25816	−	14.3036i	0.306912	−	0.531587i
$725$	3.20166	+	5.54543i	0.118906	+	0.205952i
$726$	−23.2127	−	15.8262i	−0.861505	−	0.587364i
$727$	0.160889	−	0.704901i	0.00596704	−	0.0261433i	−0.971857	−	0.235573i	$-0.924303\pi$
$727$	0.160889	−	0.704901i	0.00596704	−	0.0261433i	0.977824	+	0.209429i	$0.0671606\pi$
$728$	0.514076	+	0.0774845i	0.0190529	+	0.00287177i
$729$	−26.9005	−	33.7322i	−0.996316	−	1.24934i
$730$	−9.27357			−0.343230
$731$	−41.2791	+	25.6205i	−1.52676	+	0.947610i
$732$	−26.8742			−0.993298
$733$	17.5441	+	21.9997i	0.648008	+	0.812576i	0.991979	−	0.126404i	$-0.0403436\pi$
$733$	17.5441	+	21.9997i	0.648008	+	0.812576i	−0.343971	+	0.938980i	$0.611772\pi$
$734$	−11.2684	−	1.69845i	−0.415926	−	0.0626908i
$735$	−4.18842	+	18.3507i	−0.154492	+	0.676875i
$736$	1.19766	+	0.816552i	0.0441464	+	0.0300985i
$737$	−0.0386332	−	0.0669147i	−0.00142307	−	0.00246484i
$738$	−14.7255	+	25.5053i	−0.542054	+	0.938864i
$739$	8.10913	−	3.90515i	0.298299	−	0.143653i	−0.278748	−	0.960364i	$-0.589919\pi$
$739$	8.10913	−	3.90515i	0.298299	−	0.143653i	0.577047	+	0.816711i	$0.304205\pi$
$740$	−8.15736	−	2.51621i	−0.299871	−	0.0924978i
$741$	2.94685	+	39.3230i	0.108255	+	1.44457i
$742$	−0.398143	−	1.74438i	−0.0146163	−	0.0640382i
$743$	−5.21877	+	13.2972i	−0.191458	+	0.487827i	−0.994079	−	0.108663i	$-0.965343\pi$
$743$	−5.21877	+	13.2972i	−0.191458	+	0.487827i	0.802621	+	0.596490i	$0.203438\pi$
$744$	0.327879	−	4.37525i	0.0120206	−	0.160404i
$745$	12.2748	−	1.85013i	0.449713	−	0.0677834i
$746$	−17.4857	−	16.2243i	−0.640195	−	0.594015i
$747$	29.8950	+	14.3967i	1.09380	+	0.526747i
$748$	−4.75538	+	3.24217i	−0.173874	+	0.118545i
$749$	0.0446825	+	0.113849i	0.00163266	+	0.00415996i
$750$	−2.58223	+	0.796514i	−0.0942898	+	0.0290846i
$751$	27.9457	−	25.9298i	1.01975	−	0.946191i	0.0211882	−	0.999776i	$-0.493255\pi$
$751$	27.9457	−	25.9298i	1.01975	−	0.946191i	0.998563	+	0.0535844i	$0.0170646\pi$
$752$	1.16490	−	1.46074i	0.0424796	−	0.0532678i
$753$	−13.6166	+	17.0746i	−0.496216	+	0.622235i
$754$	13.1250	−	12.1782i	0.477983	−	0.443503i
$755$	−15.9924	+	4.93300i	−0.582023	+	0.179530i
$756$	−0.239062	−	0.609119i	−0.00869459	−	0.0221535i
$757$	−43.6194	+	29.7392i	−1.58537	+	1.08089i	−0.633787	+	0.773508i	$0.718500\pi$
$757$	−43.6194	+	29.7392i	−1.58537	+	1.08089i	−0.951586	+	0.307382i	$0.900547\pi$
$758$	−15.8832	−	7.64894i	−0.576904	−	0.277822i
$759$	2.23058	+	2.06968i	0.0809651	+	0.0751246i
$760$	5.16053	−	0.777824i	0.187192	−	0.0282147i
$761$	0.726248	−	9.69110i	0.0263265	−	0.351302i	−0.968449	−	0.249213i	$-0.919828\pi$
$761$	0.726248	−	9.69110i	0.0263265	−	0.351302i	0.994775	−	0.102089i	$-0.0325528\pi$
$762$	13.4320	−	34.2243i	0.486592	−	1.23982i
$763$	0.148680	+	0.651410i	0.00538258	+	0.0235826i
$764$	1.20126	+	16.0297i	0.0434599	+	0.579933i
$765$	−30.4598	−	9.39561i	−1.10128	−	0.339699i
$766$	−16.7835	+	8.08252i	−0.606413	+	0.292033i
$767$	0.741489	−	1.28430i	0.0267736	−	0.0463732i
$768$	−1.35114	−	2.34025i	−0.0487552	−	0.0844465i
$769$	14.4708	+	9.86604i	0.521831	+	0.355778i	0.795411	−	0.606071i	$-0.207255\pi$
$769$	14.4708	+	9.86604i	0.521831	+	0.355778i	−0.273579	+	0.961849i	$0.588208\pi$
$770$	0.0321397	−	0.140813i	0.00115823	−	0.00507455i
$771$	60.6465	+	9.14100i	2.18413	+	0.329205i
$772$	4.44030	+	5.56796i	0.159810	+	0.200395i
$773$	17.6029			0.633131			0.316566	−	0.948571i	$-0.397470\pi$
$773$	17.6029			0.633131			0.316566	+	0.948571i	$0.397470\pi$
$774$	−9.17082	−	26.6804i	−0.329638	−	0.959005i
$775$	1.62363			0.0583225
$776$	−6.38294	−	8.00396i	−0.229134	−	0.287325i
$777$	4.24118	+	0.639255i	0.152151	+	0.0229331i
$778$	3.25517	−	14.2618i	0.116703	−	0.511311i
$779$	29.5169	+	20.1243i	1.05755	+	0.721027i
$780$	3.77799	+	6.54367i	0.135274	+	0.234301i
$781$	2.97162	−	5.14699i	0.106333	−	0.184174i
$782$	−9.67597	+	4.65970i	−0.346012	+	0.166631i
$783$	−21.5344	−	6.64249i	−0.769577	−	0.237383i
$784$	−0.520527	−	6.94595i	−0.0185903	−	0.248070i
$785$	0.417653	+	1.82986i	0.0149067	+	0.0653104i
$786$	0.0359373	−	0.0915668i	0.00128184	−	0.00326608i
$787$	−0.0233183	+	0.311161i	−0.000831208	+	0.0110917i	−0.997604	−	0.0691831i	$-0.977961\pi$
$787$	−0.0233183	+	0.311161i	−0.000831208	+	0.0110917i	0.996773	+	0.0802748i	$0.0255798\pi$
$788$	−6.27550	+	0.945879i	−0.223555	+	0.0336956i
$789$	−30.9494	−	28.7169i	−1.10183	−	1.02235i
$790$	3.31246	+	1.59520i	0.117852	+	0.0567545i
$791$	1.69457	−	1.15534i	0.0602518	−	0.0410790i
$792$	−1.22104	−	3.11116i	−0.0433877	−	0.110550i
$793$	−26.5721	+	8.19641i	−0.943603	+	0.291063i
$794$	−16.4199	+	15.2354i	−0.582720	+	0.540685i
$795$	16.2137	−	20.3314i	0.575042	−	0.721080i
$796$	15.2409	−	19.1114i	0.540198	−	0.677386i
$797$	−36.7345	+	34.0846i	−1.30120	+	1.20734i	−0.337204	+	0.941432i	$0.609481\pi$
$797$	−36.7345	+	34.0846i	−1.30120	+	1.20734i	−0.963998	+	0.265908i	$0.914328\pi$
$798$	−2.50562	+	0.772880i	−0.0886978	+	0.0273597i
$799$	5.05726	+	12.8857i	0.178913	+	0.455862i
$800$	0.826239	−	0.563320i	0.0292120	−	0.0199164i
$801$	16.0809	+	7.74417i	0.568192	+	0.273627i
$802$	−28.0342	−	26.0120i	−0.989923	−	0.918515i
$803$	7.12349	−	1.07369i	0.251383	−	0.0378898i
$804$	−0.0200861	+	0.268030i	−0.000708380	+	0.00945268i
$805$	0.0984631	−	0.250880i	0.00347037	−	0.00884236i
$806$	−1.01022	−	4.42607i	−0.0355835	−	0.155902i
$807$	−0.149294	−	1.99220i	−0.00525541	−	0.0701286i
$808$	−9.41877	−	2.90530i	−0.331351	−	0.102208i
$809$	−30.7016	+	14.7851i	−1.07941	+	0.519816i	−0.887128	−	0.461524i	$-0.847303\pi$
$809$	−30.7016	+	14.7851i	−1.07941	+	0.519816i	−0.192281	+	0.981340i	$0.561589\pi$
$810$	−1.69837	+	2.94167i	−0.0596747	+	0.103360i
$811$	17.0707	+	29.5672i	0.599432	+	1.03825i	0.992905	+	0.118910i	$0.0379400\pi$
$811$	17.0707	+	29.5672i	0.599432	+	1.03825i	−0.393473	+	0.919336i	$0.628727\pi$
$812$	0.983687	+	0.670666i	0.0345206	+	0.0235358i
$813$	−10.2950	+	45.1053i	−0.361061	+	1.58191i
$814$	6.55740	+	0.988369i	0.229837	+	0.0346423i
$815$	13.6659	+	17.1366i	0.478697	+	0.600267i
$816$	20.0211			0.700879
$817$	−33.1044	+	8.67467i	−1.15818	+	0.303488i
$818$	14.7435			0.515495
$819$	−1.39458	−	1.74874i	−0.0487304	−	0.0611060i
$820$	6.76885	+	1.02024i	0.236379	+	0.0356283i
$821$	0.763848	−	3.34663i	0.0266585	−	0.116798i	−0.959848	−	0.280521i	$-0.909493\pi$
$821$	0.763848	−	3.34663i	0.0266585	−	0.116798i	0.986506	+	0.163722i	$0.0523501\pi$
$822$	14.6765	+	10.0063i	0.511903	+	0.349010i
$823$	−2.83567	−	4.91152i	−0.0988452	−	0.171205i	0.812362	−	0.583154i	$-0.198182\pi$
$823$	−2.83567	−	4.91152i	−0.0988452	−	0.171205i	−0.911207	+	0.411949i	$0.864848\pi$
$824$	1.86524	−	3.23069i	0.0649786	−	0.112546i
$825$	1.89132	−	0.910813i	0.0658474	−	0.0317104i
$826$	0.0942294	+	0.0290659i	0.00327866	+	0.00101133i
$827$	−4.01779	−	53.6136i	−0.139712	−	1.86433i	−0.424096	−	0.905617i	$-0.639408\pi$
$827$	−4.01779	−	53.6136i	−0.139712	−	1.86433i	0.284383	−	0.958711i	$-0.408211\pi$
$828$	−1.38774	−	6.08007i	−0.0482271	−	0.211297i
$829$	12.4258	−	31.6605i	0.431567	−	1.09962i	−0.535374	−	0.844615i	$-0.679829\pi$
$829$	12.4258	−	31.6605i	0.431567	−	1.09962i	0.966941	−	0.255000i	$-0.0820755\pi$
$830$	0.576338	−	7.69069i	0.0200050	−	0.266948i
$831$	54.6202	−	8.23267i	1.89475	−	0.285588i
$832$	−2.04971	−	1.90186i	−0.0710611	−	0.0659350i
$833$	46.4958	+	22.3912i	1.61098	+	0.775809i
$834$	−38.0655	+	25.9526i	−1.31810	+	0.898666i
$835$	−6.81651	−	17.3682i	−0.235895	−	0.601051i
$836$	−3.87400	+	1.19497i	−0.133985	+	0.0413289i
$837$	−4.18877	+	3.88661i	−0.144785	+	0.134341i
$838$	18.2925	−	22.9381i	0.631904	−	0.792382i
$839$	15.2770	−	19.1567i	0.527419	−	0.661363i	−0.444746	−	0.895656i	$-0.646706\pi$
$839$	15.2770	−	19.1567i	0.527419	−	0.661363i	0.972166	+	0.234293i	$0.0752777\pi$
$840$	−0.368310	+	0.341742i	−0.0127079	+	0.0117912i
$841$	11.4692	−	3.53777i	0.395488	−	0.121992i
$842$	−11.9056	−	30.3351i	−0.410295	−	1.04542i
$843$	31.0582	−	21.1751i	1.06970	−	0.729311i
$844$	−17.3004	−	8.33146i	−0.595506	−	0.286781i
$845$	−3.79839	−	3.52439i	−0.130668	−	0.121243i
$846$	−7.94858	+	1.19806i	−0.273278	+	0.0411900i
$847$	0.144455	−	1.92761i	0.00496352	−	0.0662335i
$848$	−3.51577	+	8.95803i	−0.120732	+	0.307620i
$849$	15.7953	+	69.2039i	0.542095	+	2.37507i
$850$	0.553671	+	7.38822i	0.0189908	+	0.253414i
$851$	11.8244	+	3.64734i	0.405334	+	0.125029i
$852$	−18.6269	+	8.97025i	−0.638147	+	0.307316i
$853$	27.0277	−	46.8134i	0.925411	−	1.60286i	0.134512	−	0.990912i	$-0.457053\pi$
$853$	27.0277	−	46.8134i	0.925411	−	1.60286i	0.790899	−	0.611947i	$-0.209613\pi$
$854$	−0.924528	−	1.60133i	−0.0316367	−	0.0547964i
$855$	−18.5518	−	12.6484i	−0.634457	−	0.432565i
$856$	0.146374	−	0.641306i	0.00500295	−	0.0219194i
$857$	35.9237	+	5.41462i	1.22713	+	0.184960i	0.730445	−	0.682971i	$-0.239313\pi$
$857$	35.9237	+	5.41462i	1.22713	+	0.184960i	0.496684	+	0.867931i	$0.334551\pi$
$858$	−3.65969	−	4.58910i	−0.124940	−	0.156669i
$859$	44.3052			1.51167			0.755836	−	0.654761i	$-0.227231\pi$
$859$	44.3052			1.51167			0.755836	+	0.654761i	$0.227231\pi$
$860$	−4.99389	+	4.24983i	−0.170290	+	0.144918i
$861$	−3.43931			−0.117211
$862$	−13.2879	−	16.6625i	−0.452588	−	0.567527i
$863$	1.79047	+	0.269871i	0.0609485	+	0.00918650i	0.179446	−	0.983768i	$-0.442570\pi$
$863$	1.79047	+	0.269871i	0.0609485	+	0.00918650i	−0.118497	+	0.992954i	$0.537808\pi$
$864$	−0.783133	+	3.43113i	−0.0266427	+	0.116729i
$865$	−9.78438	−	6.67088i	−0.332679	−	0.226817i
$866$	−14.7988	−	25.6323i	−0.502885	−	0.871022i
$867$	−51.1981	+	88.6778i	−1.73878	+	3.01165i
$868$	0.271984	−	0.130981i	0.00923174	−	0.00444577i
$869$	−2.72916	−	0.841833i	−0.0925803	−	0.0285572i
$870$	1.29310	+	17.2552i	0.0438402	+	0.585006i
$871$	0.0618866	+	0.271143i	0.00209695	+	0.00918733i
$872$	1.31290	−	3.34523i	0.0444606	−	0.113284i
$873$	−3.29150	+	43.9221i	−0.111401	+	1.48654i
$874$	−7.48036	+	1.12748i	−0.253027	+	0.0381377i
$875$	−0.136295	−	0.126464i	−0.00460763	−	0.00427525i
$876$	−22.5782	−	10.8731i	−0.762846	−	0.367367i
$877$	37.9090	−	25.8459i	1.28010	−	0.872755i	0.283812	−	0.958880i	$-0.408401\pi$
$877$	37.9090	−	25.8459i	1.28010	−	0.872755i	0.996284	+	0.0861251i	$0.0274485\pi$
$878$	−7.79780	−	19.8685i	−0.263163	−	0.670529i
$879$	66.8043	−	20.6064i	2.25325	−	0.695037i
$880$	−0.569454	+	0.528376i	−0.0191963	+	0.0178115i
$881$	−13.0795	+	16.4012i	−0.440660	+	0.552570i	−0.951717	−	0.306977i	$-0.900683\pi$
$881$	−13.0795	+	16.4012i	−0.440660	+	0.552570i	0.511057	+	0.859547i	$0.329254\pi$
$882$	−18.6846	+	23.4298i	−0.629144	+	0.788922i
$883$	−6.84480	+	6.35104i	−0.230346	+	0.213730i	−0.786898	−	0.617083i	$-0.788314\pi$
$883$	−6.84480	+	6.35104i	−0.230346	+	0.213730i	0.556552	+	0.830813i	$0.312124\pi$
$884$	19.7961	−	6.10627i	0.665813	−	0.205376i
$885$	0.523608	+	1.33413i	0.0176009	+	0.0448463i
$886$	−7.37561	+	5.02861i	−0.247788	+	0.168939i
$887$	−20.6069	−	9.92377i	−0.691912	−	0.333207i	0.0546662	−	0.998505i	$-0.482591\pi$
$887$	−20.6069	−	9.92377i	−0.691912	−	0.333207i	−0.746579	+	0.665297i	$0.768305\pi$
$888$	−16.9103	−	15.6905i	−0.567474	−	0.526539i
$889$	2.50139	−	0.377023i	0.0838938	−	0.0126450i
$890$	0.310020	−	4.13693i	0.0103919	−	0.138670i
$891$	0.964018	−	2.45628i	0.0322958	−	0.0822884i
$892$	−4.15415	−	18.2005i	−0.139091	−	0.609398i
$893$	0.728665	+	9.72336i	0.0243838	+	0.325380i
$894$	32.0544	+	9.88747i	1.07206	+	0.330686i
$895$	18.6970	−	9.00399i	0.624971	−	0.300970i
$896$	0.0929644	−	0.161019i	0.00310572	−	0.00537927i
$897$	−5.47632	−	9.48527i	−0.182849	−	0.316704i
$898$	−21.7785	−	14.8483i	−0.726759	−	0.495496i
$899$	2.31346	−	10.1359i	0.0771583	−	0.338052i
$900$	−4.25431	−	0.641234i	−0.141810	−	0.0213745i
$901$	−44.4536	−	55.7431i	−1.48097	−	1.85707i
$902$	−5.31762			−0.177057
$903$	2.16283	−	2.48537i	0.0719745	−	0.0827078i
$904$	−11.0308			−0.366878
$905$	10.2978	+	12.9130i	0.342309	+	0.429242i
$906$	−44.7202	−	6.74049i	−1.48573	−	0.223938i
$907$	−7.58345	+	33.2253i	−0.251804	+	1.10323i	0.677968	+	0.735092i	$0.262861\pi$
$907$	−7.58345	+	33.2253i	−0.251804	+	1.10323i	−0.929772	+	0.368136i	$0.879996\pi$
$908$	18.3475	+	12.5091i	0.608883	+	0.415130i
$909$	21.2035	+	36.7255i	0.703276	+	1.21811i
$910$	−0.259941	+	0.450232i	−0.00861697	+	0.0149250i
$911$	−15.0024	+	7.22479i	−0.497053	+	0.239368i	−0.665577	−	0.746330i	$-0.731814\pi$
$911$	−15.0024	+	7.22479i	−0.497053	+	0.239368i	0.168524	+	0.985698i	$0.446100\pi$
$912$	13.4762	+	4.15686i	0.446242	+	0.137647i
$913$	0.447714	+	5.97433i	0.0148172	+	0.197722i
$914$	7.34811	+	32.1942i	0.243054	+	1.06489i
$915$	9.81824	−	25.0165i	0.324581	−	0.827019i
$916$	−1.07214	+	14.3068i	−0.0354246	+	0.472708i
$917$	0.00669243	−	0.00100872i	0.000221004	−	3.33109e-5i
$918$	−19.1142	−	17.7354i	−0.630862	−	0.585354i
$919$	8.42768	+	4.05856i	0.278003	+	0.133879i	0.567691	−	0.823242i	$-0.307837\pi$
$919$	8.42768	+	4.05856i	0.278003	+	0.133879i	−0.289687	+	0.957121i	$0.593551\pi$
$920$	−1.19766	+	0.816552i	−0.0394857	+	0.0269209i
$921$	−26.0408	−	66.3509i	−0.858074	−	2.18634i
$922$	−3.49142	+	1.07696i	−0.114984	+	0.0354678i
$923$	−15.6817	+	14.5505i	−0.516169	+	0.478935i
$924$	0.243350	−	0.305152i	0.00800563	−	0.0100387i
$925$	5.32250	−	6.67420i	0.175003	−	0.219446i
$926$	8.49320	−	7.88053i	0.279104	−	0.258970i
$927$	−15.3368	+	4.73078i	−0.503727	+	0.155379i
$928$	−2.33939	−	5.96067i	−0.0767943	−	0.195669i
$929$	−30.8217	+	21.0139i	−1.01123	+	0.689442i	−0.951143	−	0.308751i	$-0.900089\pi$
$929$	−30.8217	+	21.0139i	−1.01123	+	0.689442i	−0.0600835	+	0.998193i	$0.519137\pi$
$930$	3.95301	+	1.90367i	0.129624	+	0.0624238i
$931$	26.6474	+	24.7252i	0.873333	+	0.810335i
$932$	−6.50183	+	0.979994i	−0.212975	+	0.0321008i
$933$	−4.19017	+	55.9140i	−0.137180	+	1.83054i
$934$	−10.0780	+	25.6783i	−0.329762	+	0.840220i
$935$	−1.28071	−	5.61116i	−0.0418837	−	0.183504i
$936$	0.899004	+	11.9964i	0.0293849	+	0.392114i
$937$	31.2683	+	9.64500i	1.02149	+	0.315088i	0.759865	−	0.650081i	$-0.225265\pi$
$937$	31.2683	+	9.64500i	1.02149	+	0.315088i	0.261626	+	0.965169i	$0.415741\pi$
$938$	−0.0166619	+	0.00802394i	−0.000544029	+	0.000261991i
$939$	28.2482	−	48.9273i	0.921845	−	1.59668i
$940$	0.934179	+	1.61805i	0.0304696	+	0.0527748i
$941$	−22.0326	−	15.0215i	−0.718241	−	0.489688i	0.148207	−	0.988956i	$-0.452650\pi$
$941$	−22.0326	−	15.0215i	−0.718241	−	0.489688i	−0.866448	+	0.499268i	$0.833602\pi$
$942$	−1.12862	+	4.94480i	−0.0367724	+	0.161110i
$943$	−9.81168	−	1.47887i	−0.319512	−	0.0481587i
$944$	−0.330678	−	0.414657i	−0.0107626	−	0.0134959i
$945$	0.654352			0.0212861
$946$	3.34401	−	3.84269i	0.108723	−	0.124937i
$947$	−45.6457			−1.48329			−0.741644	−	0.670794i	$-0.765953\pi$
$947$	−45.6457			−1.48329			−0.741644	+	0.670794i	$0.765953\pi$
$948$	6.19444	+	7.76758i	0.201186	+	0.252279i
$949$	−25.6406	−	3.86470i	−0.832329	−	0.125453i
$950$	−1.16130	+	5.08797i	−0.0376774	+	0.165076i
$951$	−36.5901	−	24.9467i	−1.18652	−	0.808952i
$952$	0.688768	+	1.19298i	0.0223231	+	0.0386647i
$953$	12.2927	−	21.2916i	0.398200	−	0.689702i	−0.595304	−	0.803501i	$-0.702968\pi$
$953$	12.2927	−	21.2916i	0.398200	−	0.689702i	0.993504	+	0.113798i	$0.0363017\pi$
$954$	37.3026	−	17.9640i	1.20772	−	0.581605i
$955$	−15.3605	−	4.73807i	−0.497053	−	0.153320i
$956$	1.19841	+	15.9916i	0.0387593	+	0.517206i
$957$	−2.99110	−	13.1049i	−0.0966886	−	0.423620i
$958$	4.61640	−	11.7624i	0.149149	−	0.380026i
$959$	−0.0913332	+	1.21876i	−0.00294930	+	0.0393557i
$960$	2.67211	−	0.402755i	0.0862419	−	0.0129989i
$961$	20.7922	+	19.2923i	0.670715	+	0.622332i
$962$	−21.5057	−	10.3566i	−0.693373	−	0.333911i
$963$	−2.33833	+	1.59424i	−0.0753516	+	0.0513738i
$964$	−5.14549	−	13.1105i	−0.165725	−	0.422260i
$965$	−6.80530	+	2.09916i	−0.219070	+	0.0675742i
$966$	0.533878	−	0.495366i	0.0171772	−	0.0159381i
$967$	−1.36020	+	1.70564i	−0.0437412	+	0.0548497i	−0.803221	−	0.595681i	$-0.796882\pi$
$967$	−1.36020	+	1.70564i	−0.0437412	+	0.0548497i	0.759480	+	0.650531i	$0.225454\pi$
$968$	−6.48214	+	8.12834i	−0.208344	+	0.261255i
$969$	−76.5940	+	71.0688i	−2.46055	+	2.28306i
$970$	9.78262	−	3.01754i	0.314101	−	0.0968874i
$971$	0.565902	+	1.44190i	0.0181607	+	0.0462726i	0.939667	−	0.342092i	$-0.111135\pi$
$971$	0.565902	+	1.44190i	0.0181607	+	0.0462726i	−0.921506	+	0.388364i	$0.873040\pi$
$972$	−16.3076	+	11.1183i	−0.523065	+	0.356620i
$973$	−2.85595	−	1.37535i	−0.0915576	−	0.0440918i
$974$	6.23336	+	5.78371i	0.199730	+	0.185322i
$975$	−7.47158	+	1.12616i	−0.239282	+	0.0360660i
$976$	−0.743188	+	9.91716i	−0.0237889	+	0.317440i
$977$	−21.1129	+	53.7948i	−0.675461	+	1.72105i	0.0172686	+	0.999851i	$0.494503\pi$
$977$	−21.1129	+	53.7948i	−0.675461	+	1.72105i	−0.692730	+	0.721197i	$0.743592\pi$
$978$	13.1799	+	57.7451i	0.421448	+	1.84648i
$979$	0.240831	+	3.21367i	0.00769701	+	0.102709i
$980$	6.65598	+	2.05310i	0.212617	+	0.0655838i
$981$	−13.9300	+	6.70835i	−0.444752	+	0.214181i
$982$	−9.86606	+	17.0885i	−0.314839	+	0.545317i
$983$	−4.19641	−	7.26839i	−0.133845	−	0.231826i	0.791311	−	0.611414i	$-0.209399\pi$
$983$	−4.19641	−	7.26839i	−0.133845	−	0.231826i	−0.925156	+	0.379588i	$0.876066\pi$
$984$	15.2838	+	10.4203i	0.487229	+	0.332187i
$985$	1.41220	−	6.18727i	0.0449965	−	0.197143i
$986$	46.9119	+	7.07083i	1.49398	+	0.225181i
$987$	−0.585286	−	0.733925i	−0.0186299	−	0.0233611i
$988$	14.5925			0.464250
$989$	7.23882	−	6.16027i	0.230181	−	0.195885i
$990$	3.34219			0.106222
$991$	−27.6096	−	34.6214i	−0.877048	−	1.09978i	−0.994293	−	0.106681i	$-0.965978\pi$
$991$	−27.6096	−	34.6214i	−0.877048	−	1.09978i	0.117245	−	0.993103i	$-0.462594\pi$
$992$	−1.60549	−	0.241989i	−0.0509745	−	0.00768317i
$993$	−0.174887	+	0.766229i	−0.00554987	+	0.0243156i
$994$	−1.17531	−	0.801311i	−0.0372785	−	0.0254160i
$995$	12.2222	+	21.1695i	0.387470	+	0.671118i
$996$	10.4204	−	18.0486i	0.330182	−	0.571892i
$997$	49.9193	−	24.0398i	1.58096	−	0.761350i	0.582292	−	0.812979i	$-0.302156\pi$
$997$	49.9193	−	24.0398i	1.58096	−	0.761350i	0.998666	+	0.0516299i	$0.0164416\pi$
$998$	−10.0449	−	3.09845i	−0.317967	−	0.0980797i
$999$	2.24516	+	29.9595i	0.0710336	+	0.947877i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.b.181.1	✓	48
43.24	even	21	inner	430.2.q.b.411.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.b.181.1	✓	48	1.1	even	1	trivial
430.2.q.b.411.1	yes	48	43.24	even	21	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.623490 + 0.781831i) q^{2} +(-2.67211 - 0.402755i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(-0.826239 - 0.563320i) q^{5} +(-1.35114 - 2.34025i) q^{6} +(0.0929644 - 0.161019i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(4.11122 + 1.26814i) q^{9} +O(q^{10})\)	\(q+(0.623490 + 0.781831i) q^{2} +(-2.67211 - 0.402755i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(-0.826239 - 0.563320i) q^{5} +(-1.35114 - 2.34025i) q^{6} +(0.0929644 - 0.161019i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(4.11122 + 1.26814i) q^{9} +(-0.0747301 - 0.997204i) q^{10} +(0.172860 + 0.757349i) q^{11} +(0.987257 - 2.51549i) q^{12} +(0.208956 - 2.78832i) q^{13} +(0.183852 - 0.0277113i) q^{14} +(1.98092 + 1.83802i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(6.12155 - 4.17361i) q^{17} +(1.57183 + 4.00496i) q^{18} +(4.98696 - 1.53827i) q^{19} +(0.733052 - 0.680173i) q^{20} +(-0.313262 + 0.392818i) q^{21} +(-0.484343 + 0.607347i) q^{22} +(-1.06258 + 0.985934i) q^{23} +(2.58223 - 0.796514i) q^{24} +(0.365341 + 0.930874i) q^{25} +(2.31028 - 1.57512i) q^{26} +(-3.17084 - 1.52700i) q^{27} +(0.136295 + 0.126464i) q^{28} +(6.33179 - 0.954364i) q^{29} +(-0.201942 + 2.69473i) q^{30} +(0.593178 - 1.51139i) q^{31} +(-0.222521 - 0.974928i) q^{32} +(-0.156874 - 2.09334i) q^{33} +(7.07978 + 2.18382i) q^{34} +(-0.167516 + 0.0806715i) q^{35} +(-2.15118 + 3.72596i) q^{36} +(-4.26831 - 7.39293i) q^{37} +(4.31199 + 2.93986i) q^{38} +(-1.68136 + 7.36653i) q^{39} +(0.988831 + 0.149042i) q^{40} +(4.26798 + 5.35188i) q^{41} -0.502433 q^{42} +(-6.55140 - 0.281368i) q^{43} -0.776826 q^{44} +(-2.68248 - 3.36373i) q^{45} +(-1.43334 - 0.216042i) q^{46} +(-0.415749 + 1.82152i) q^{47} +(2.23274 + 1.52225i) q^{48} +(3.48272 + 6.03224i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-18.0384 + 8.68683i) q^{51} +(2.67191 + 0.824176i) q^{52} +(-0.719147 - 9.59634i) q^{53} +(-0.783133 - 3.43113i) q^{54} +(0.283806 - 0.723127i) q^{55} +(-0.0138945 + 0.185409i) q^{56} +(-13.9452 + 2.10191i) q^{57} +(4.69396 + 4.35536i) q^{58} +(0.477843 + 0.230117i) q^{59} +(-2.23274 + 1.52225i) q^{60} +(-3.63330 - 9.25751i) q^{61} +(1.55150 - 0.478573i) q^{62} +(0.586393 - 0.544093i) q^{63} +(0.623490 - 0.781831i) q^{64} +(-1.74336 + 2.18611i) q^{65} +(1.53883 - 1.42782i) q^{66} +(-0.0950454 + 0.0293176i) q^{67} +(2.70679 + 6.89679i) q^{68} +(3.23643 - 2.20656i) q^{69} +(-0.167516 - 0.0806715i) q^{70} +(-5.60833 - 5.20377i) q^{71} +(-4.25431 + 0.641234i) q^{72} +(0.693015 - 9.24764i) q^{73} +(3.11878 - 7.94652i) q^{74} +(-0.601316 - 2.63454i) q^{75} +(0.390003 + 5.20422i) q^{76} +(0.138018 + 0.0425728i) q^{77} +(-6.80770 + 3.27841i) q^{78} +(-1.83828 + 3.18399i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-2.80652 - 1.91346i) q^{81} +(-1.52322 + 6.67368i) q^{82} +(7.62612 + 1.14945i) q^{83} +(-0.313262 - 0.392818i) q^{84} -7.40894 q^{85} +(-3.86475 - 5.29752i) q^{86} -17.3036 q^{87} +(-0.484343 - 0.607347i) q^{88} +(4.10219 + 0.618306i) q^{89} +(0.957366 - 4.19450i) q^{90} +(-0.429547 - 0.292860i) q^{91} +(-0.724767 - 1.25533i) q^{92} +(-2.19376 + 3.79970i) q^{93} +(-1.68333 + 0.810650i) q^{94} +(-4.98696 - 1.53827i) q^{95} +(0.201942 + 2.69473i) q^{96} +(2.27805 + 9.98077i) q^{97} +(-2.54476 + 6.48394i) q^{98} +(-0.249762 + 3.33284i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9}+O(q^{10}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9} - 4 q^{10} - 9 q^{11} - q^{12} - 11 q^{13} + 7 q^{14} - 6 q^{15} - 8 q^{16} - 11 q^{17} - 15 q^{18} + 31 q^{19} - 4 q^{20} + 4 q^{21} + 12 q^{22} + 4 q^{23} + 6 q^{24} + 4 q^{25} + 31 q^{26} + 44 q^{27} + 13 q^{29} + q^{30} - q^{31} - 8 q^{32} - 30 q^{33} - 25 q^{34} + 14 q^{35} - 36 q^{36} - 27 q^{37} - 4 q^{38} + 4 q^{39} - 4 q^{40} + 16 q^{41} + 4 q^{42} - 7 q^{43} - 30 q^{44} + 12 q^{45} - 52 q^{46} - 43 q^{47} - q^{48} - 23 q^{49} - 24 q^{50} - 7 q^{51} - 25 q^{52} + 73 q^{53} - 61 q^{54} + 27 q^{55} + 7 q^{56} + 136 q^{57} - 36 q^{58} + 58 q^{59} + q^{60} - 61 q^{61} + 27 q^{62} + 32 q^{63} - 8 q^{64} - q^{65} + 12 q^{66} + 39 q^{67} + 17 q^{68} - 34 q^{69} + 14 q^{70} + 60 q^{71} + 27 q^{72} + 3 q^{73} + 29 q^{74} - 12 q^{75} + 17 q^{76} - 27 q^{77} - 17 q^{78} - 2 q^{79} + 24 q^{80} - 165 q^{81} + 2 q^{82} + 74 q^{83} + 4 q^{84} - 8 q^{85} + 14 q^{86} + 88 q^{87} + 12 q^{88} + 23 q^{89} - 2 q^{90} - 39 q^{91} + 4 q^{92} - 46 q^{93} + 55 q^{94} - 31 q^{95} - q^{96} - 85 q^{97} + 33 q^{98} - 168 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9 - 4 * q^10 - 9 * q^11 - q^12 - 11 * q^13 + 7 * q^14 - 6 * q^15 - 8 * q^16 - 11 * q^17 - 15 * q^18 + 31 * q^19 - 4 * q^20 + 4 * q^21 + 12 * q^22 + 4 * q^23 + 6 * q^24 + 4 * q^25 + 31 * q^26 + 44 * q^27 + 13 * q^29 + q^30 - q^31 - 8 * q^32 - 30 * q^33 - 25 * q^34 + 14 * q^35 - 36 * q^36 - 27 * q^37 - 4 * q^38 + 4 * q^39 - 4 * q^40 + 16 * q^41 + 4 * q^42 - 7 * q^43 - 30 * q^44 + 12 * q^45 - 52 * q^46 - 43 * q^47 - q^48 - 23 * q^49 - 24 * q^50 - 7 * q^51 - 25 * q^52 + 73 * q^53 - 61 * q^54 + 27 * q^55 + 7 * q^56 + 136 * q^57 - 36 * q^58 + 58 * q^59 + q^60 - 61 * q^61 + 27 * q^62 + 32 * q^63 - 8 * q^64 - q^65 + 12 * q^66 + 39 * q^67 + 17 * q^68 - 34 * q^69 + 14 * q^70 + 60 * q^71 + 27 * q^72 + 3 * q^73 + 29 * q^74 - 12 * q^75 + 17 * q^76 - 27 * q^77 - 17 * q^78 - 2 * q^79 + 24 * q^80 - 165 * q^81 + 2 * q^82 + 74 * q^83 + 4 * q^84 - 8 * q^85 + 14 * q^86 + 88 * q^87 + 12 * q^88 + 23 * q^89 - 2 * q^90 - 39 * q^91 + 4 * q^92 - 46 * q^93 + 55 * q^94 - 31 * q^95 - q^96 - 85 * q^97 + 33 * q^98 - 168 * q^99

Introduction

L-functions

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