LMFDB - Embedded newform 415.2.l.a.102.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [415,2,Mod(2,415)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("415.2"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(415, base_ring=CyclotomicField(164)) chi = DirichletCharacter(H, H._module([41, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 415 = 5 \cdot 83 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	415.l (of order $164$, degree $80$, 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:	$3.31379168388$
Analytic rank:	$0$
Dimension:	$3200$
Relative dimension:	$40$ over $\Q(\zeta_{164})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{164}]$

Embedding invariants

Embedding label			102.11
Character	$\chi$	$=$	415.102
Dual form			415.2.l.a.118.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.25922 + 0.781639i) q^{2} +(0.676722 + 0.0389329i) q^{3} +(0.0872318 - 0.176179i) q^{4} +(1.18255 - 1.89778i) q^{5} +(-0.882573 + 0.479928i) q^{6} +(-1.49333 + 0.849508i) q^{7} +(-0.255612 - 2.66056i) q^{8} +(-2.52377 - 0.291357i) q^{9} +(-0.00571634 + 3.31405i) q^{10} +(2.70035 - 2.59882i) q^{11} +(0.0658908 - 0.115828i) q^{12} +(3.28050 - 1.24966i) q^{13} +(1.21642 - 2.23696i) q^{14} +(0.874147 - 1.23823i) q^{15} +(2.63983 + 3.46313i) q^{16} +(-2.81899 - 5.42933i) q^{17} +(3.40571 - 1.60580i) q^{18} +(0.00502328 + 0.0259014i) q^{19} +(-0.231192 - 0.373888i) q^{20} +(-1.04364 + 0.516741i) q^{21} +(-1.36898 + 5.38318i) q^{22} +(-1.49181 - 0.703388i) q^{23} +(-0.0693947 - 1.81041i) q^{24} +(-2.20313 - 4.48845i) q^{25} +(-3.15408 + 4.13776i) q^{26} +(-3.69992 - 0.644280i) q^{27} +(0.0193995 + 0.337198i) q^{28} +(1.24056 + 3.07804i) q^{29} +(-0.132894 + 2.24247i) q^{30} +(2.38284 - 1.96511i) q^{31} +(-1.03559 - 0.394495i) q^{32} +(1.92856 - 1.65355i) q^{33} +(7.79350 + 4.63328i) q^{34} +(-0.153768 + 3.83860i) q^{35} +(-0.271484 + 0.419219i) q^{36} +(5.46535 - 6.89194i) q^{37} +(-0.0265709 - 0.0286891i) q^{38} +(2.26864 - 0.717954i) q^{39} +(-5.35143 - 2.66117i) q^{40} +(11.5382 - 2.70005i) q^{41} +(0.910271 - 1.46644i) q^{42} +(0.549324 + 3.15462i) q^{43} +(-0.222302 - 0.702444i) q^{44} +(-3.53743 + 4.44501i) q^{45} +(2.42831 - 0.280336i) q^{46} +(-0.0937262 - 0.438194i) q^{47} +(1.65160 + 2.44635i) q^{48} +(-2.06875 + 3.47979i) q^{49} +(6.28257 + 3.92989i) q^{50} +(-1.69629 - 3.78390i) q^{51} +(0.0659996 - 0.686965i) q^{52} +(0.709103 - 3.31524i) q^{53} +(5.16261 - 2.08072i) q^{54} +(-1.73868 - 8.19791i) q^{55} +(2.64188 + 3.75596i) q^{56} +(0.00239095 + 0.0177236i) q^{57} +(-3.96806 - 2.90626i) q^{58} +(13.8287 - 0.530065i) q^{59} +(-0.141897 - 0.262019i) q^{60} +(-12.4490 + 7.40097i) q^{61} +(-1.46450 + 4.33702i) q^{62} +(4.01633 - 1.70887i) q^{63} +(-6.93738 + 1.34542i) q^{64} +(1.50779 - 7.70345i) q^{65} +(-1.13600 + 3.58962i) q^{66} +(-7.97978 - 1.07649i) q^{67} +(-1.20244 + 0.0230368i) q^{68} +(-0.982154 - 0.534079i) q^{69} +(-2.80678 - 4.95383i) q^{70} +(-2.61316 + 0.718108i) q^{71} +(-0.130069 + 6.78912i) q^{72} +(-5.43977 - 7.42720i) q^{73} +(-1.49506 + 12.9504i) q^{74} +(-1.31616 - 3.12321i) q^{75} +(0.00500147 + 0.00137443i) q^{76} +(-1.82479 + 6.17487i) q^{77} +(-2.29553 + 2.67732i) q^{78} +(8.81890 + 4.36651i) q^{79} +(9.69400 - 0.914471i) q^{80} +(4.94237 + 1.15656i) q^{81} +(-12.4187 + 12.4187i) q^{82} +(-8.76045 + 2.50089i) q^{83} +0.228945i q^{84} +(-13.6373 - 1.07066i) q^{85} +(-3.15749 - 3.54298i) q^{86} +(0.719680 + 2.13128i) q^{87} +(-7.60457 - 6.52015i) q^{88} +(1.28420 + 2.36161i) q^{89} +(0.979998 - 8.36223i) q^{90} +(-3.83727 + 4.65297i) q^{91} +(-0.254055 + 0.201467i) q^{92} +(1.68903 - 1.23706i) q^{93} +(0.460532 + 0.478523i) q^{94} +(0.0550954 + 0.0210967i) q^{95} +(-0.685450 - 0.307282i) q^{96} +(-3.72367 - 12.6004i) q^{97} +(-0.114928 - 5.99884i) q^{98} +(-7.57223 + 5.77206i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3200 q - 82 q^{2} - 78 q^{3} - 82 q^{5} - 164 q^{6} - 74 q^{7} - 82 q^{8} - 102 q^{10} - 164 q^{11} - 114 q^{12} - 82 q^{13} - 82 q^{15} - 96 q^{16} - 82 q^{17} - 82 q^{18} - 82 q^{20} - 148 q^{21} - 82 q^{22}+ \cdots + 246 q^{98}+O(q^{100}) $ 3200 * q - 82 * q^2 - 78 * q^3 - 82 * q^5 - 164 * q^6 - 74 * q^7 - 82 * q^8 - 102 * q^10 - 164 * q^11 - 114 * q^12 - 82 * q^13 - 82 * q^15 - 96 * q^16 - 82 * q^17 - 82 * q^18 - 82 * q^20 - 148 * q^21 - 82 * q^22 - 86 * q^23 - 74 * q^25 - 140 * q^26 - 90 * q^27 - 78 * q^28 - 114 * q^30 - 148 * q^31 - 82 * q^32 - 42 * q^33 - 82 * q^35 - 104 * q^36 - 66 * q^37 - 26 * q^38 - 130 * q^40 - 156 * q^41 - 82 * q^42 - 82 * q^43 - 82 * q^45 - 164 * q^46 - 82 * q^47 - 102 * q^48 - 82 * q^50 - 164 * q^51 - 82 * q^52 - 82 * q^53 - 82 * q^55 - 164 * q^56 - 82 * q^57 - 82 * q^58 - 82 * q^60 - 100 * q^61 - 82 * q^62 - 38 * q^63 - 134 * q^65 - 164 * q^66 - 82 * q^67 + 182 * q^68 - 138 * q^70 - 164 * q^71 - 82 * q^72 + 164 * q^73 - 138 * q^75 - 164 * q^76 - 106 * q^77 + 606 * q^78 - 82 * q^80 - 188 * q^81 + 192 * q^83 - 82 * q^85 - 84 * q^86 - 54 * q^87 + 738 * q^88 - 198 * q^90 - 164 * q^91 - 82 * q^92 + 576 * q^93 - 50 * q^95 - 164 * q^96 - 82 * q^97 + 246 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/415\mathbb{Z}\right)^\times$.

$n$	$167$	$251$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{47}{82}\right)$

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 $

$2$	−1.25922	+	0.781639i	−0.890402	+	0.552703i	−0.894389	−	0.447289i	$-0.852389\pi$
$2$	−1.25922	+	0.781639i	−0.890402	+	0.552703i	0.00398717	+	0.999992i	$0.498731\pi$
$3$	0.676722	+	0.0389329i	0.390706	+	0.0224779i	0.251679	−	0.967811i	$-0.419017\pi$
$3$	0.676722	+	0.0389329i	0.390706	+	0.0224779i	0.139027	+	0.990289i	$0.455603\pi$
$4$	0.0872318	−	0.176179i	0.0436159	−	0.0880895i
$5$	1.18255	−	1.89778i	0.528855	−	0.848712i
$5$	1.18255	−	1.89778i	0.528855	−	0.848712i
$6$	−0.882573	+	0.479928i	−0.360309	+	0.195930i
$7$	−1.49333	+	0.849508i	−0.564426	+	0.321084i	−0.749885	−	0.661568i	$-0.769891\pi$
$7$	−1.49333	+	0.849508i	−0.564426	+	0.321084i	0.185459	+	0.982652i	$0.440623\pi$
$8$	−0.255612	−	2.66056i	−0.0903723	−	0.940651i
$9$	−2.52377	−	0.291357i	−0.841256	−	0.0971189i
$10$	−0.00571634	+	3.31405i	−0.00180766	+	1.04799i
$11$	2.70035	−	2.59882i	0.814185	−	0.783575i	−0.165054	−	0.986285i	$-0.552780\pi$
$11$	2.70035	−	2.59882i	0.814185	−	0.783575i	0.979239	+	0.202710i	$0.0649749\pi$
$12$	0.0658908	−	0.115828i	0.0190210	−	0.0334367i
$13$	3.28050	−	1.24966i	0.909846	−	0.346594i	0.143970	−	0.989582i	$-0.454013\pi$
$13$	3.28050	−	1.24966i	0.909846	−	0.346594i	0.765876	+	0.642988i	$0.222306\pi$
$14$	1.21642	−	2.23696i	0.325103	−	0.597854i
$15$	0.874147	−	1.23823i	0.225704	−	0.319709i
$16$	2.63983	+	3.46313i	0.659958	+	0.865783i
$17$	−2.81899	−	5.42933i	−0.683705	−	1.31680i	−0.936971	−	0.349408i	$-0.886383\pi$
$17$	−2.81899	−	5.42933i	−0.683705	−	1.31680i	0.253266	−	0.967397i	$-0.418495\pi$
$18$	3.40571	−	1.60580i	0.802734	−	0.378490i
$19$	0.00502328	+	0.0259014i	0.00115242	+	0.00594218i	0.982280	−	0.187419i	$-0.0600123\pi$
$19$	0.00502328	+	0.0259014i	0.00115242	+	0.00594218i	−0.981128	+	0.193361i	$0.938061\pi$
$20$	−0.231192	−	0.373888i	−0.0516962	−	0.0836039i
$21$	−1.04364	+	0.516741i	−0.227742	+	0.112762i
$22$	−1.36898	+	5.38318i	−0.291868	+	1.14770i
$23$	−1.49181	−	0.703388i	−0.311063	−	0.146666i	0.264589	−	0.964361i	$-0.414764\pi$
$23$	−1.49181	−	0.703388i	−0.311063	−	0.146666i	−0.575652	+	0.817695i	$0.695252\pi$
$24$	−0.0693947	−	1.81041i	−0.0141651	−	0.369549i
$25$	−2.20313	−	4.48845i	−0.440626	−	0.897691i
$26$	−3.15408	+	4.13776i	−0.618566	+	0.811482i
$27$	−3.69992	−	0.644280i	−0.712051	−	0.123992i
$28$	0.0193995	+	0.337198i	0.00366616	+	0.0637244i
$29$	1.24056	+	3.07804i	0.230367	+	0.571578i	0.997558	−	0.0698399i	$-0.0222488\pi$
$29$	1.24056	+	3.07804i	0.230367	+	0.571578i	−0.767191	+	0.641418i	$0.778346\pi$
$30$	−0.132894	+	2.24247i	−0.0242630	+	0.409417i
$31$	2.38284	−	1.96511i	0.427970	−	0.352944i	−0.397294	−	0.917691i	$-0.630051\pi$
$31$	2.38284	−	1.96511i	0.427970	−	0.352944i	0.825264	+	0.564747i	$0.191026\pi$
$32$	−1.03559	−	0.394495i	−0.183069	−	0.0697376i
$33$	1.92856	−	1.65355i	0.335720	−	0.287846i
$34$	7.79350	+	4.63328i	1.33657	+	0.794600i
$35$	−0.153768	+	3.83860i	−0.0259916	+	0.648842i
$36$	−0.271484	+	0.419219i	−0.0452473	+	0.0698699i
$37$	5.46535	−	6.89194i	0.898498	−	1.13303i	−0.0920353	−	0.995756i	$-0.529337\pi$
$37$	5.46535	−	6.89194i	0.898498	−	1.13303i	0.990533	−	0.137272i	$-0.0438335\pi$
$38$	−0.0265709	−	0.0286891i	−0.00431038	−	0.00465399i
$39$	2.26864	−	0.717954i	0.363273	−	0.114965i
$40$	−5.35143	−	2.66117i	−0.846136	−	0.420768i
$41$	11.5382	−	2.70005i	1.80197	−	0.421677i	0.814588	−	0.580040i	$-0.196963\pi$
$41$	11.5382	−	2.70005i	1.80197	−	0.421677i	0.987381	+	0.158363i	$0.0506215\pi$
$42$	0.910271	−	1.46644i	0.140458	−	0.226277i
$43$	0.549324	+	3.15462i	0.0837711	+	0.481075i	0.997245	+	0.0741777i	$0.0236332\pi$
$43$	0.549324	+	3.15462i	0.0837711	+	0.481075i	−0.913474	+	0.406897i	$0.866611\pi$
$44$	−0.222302	−	0.702444i	−0.0335133	−	0.105897i
$45$	−3.53743	+	4.44501i	−0.527328	+	0.662623i
$46$	2.42831	−	0.280336i	0.358034	−	0.0413333i
$47$	−0.0937262	−	0.438194i	−0.0136714	−	0.0639172i	0.970523	−	0.241008i	$-0.0774779\pi$
$47$	−0.0937262	−	0.438194i	−0.0136714	−	0.0639172i	−0.984195	+	0.177090i	$0.943332\pi$
$48$	1.65160	+	2.44635i	0.238388	+	0.353101i
$49$	−2.06875	+	3.47979i	−0.295536	+	0.497113i
$50$	6.28257	+	3.92989i	0.888490	+	0.555771i
$51$	−1.69629	−	3.78390i	−0.237529	−	0.529852i
$52$	0.0659996	−	0.686965i	0.00915250	−	0.0952649i
$53$	0.709103	−	3.31524i	0.0974027	−	0.455383i	−0.902302	−	0.431104i	$-0.858124\pi$
$53$	0.709103	−	3.31524i	0.0974027	−	0.455383i	0.999705	−	0.0242799i	$-0.00772929\pi$
$54$	5.16261	−	2.08072i	0.702542	−	0.283150i
$55$	−1.73868	−	8.19791i	−0.234444	−	1.10541i
$56$	2.64188	+	3.75596i	0.353036	+	0.501911i
$57$	0.00239095	+	0.0177236i	0.000316689	+	0.00234755i
$58$	−3.96806	−	2.90626i	−0.521032	−	0.381610i
$59$	13.8287	−	0.530065i	1.80034	−	0.0690086i	0.883541	−	0.468354i	$-0.155153\pi$
$59$	13.8287	−	0.530065i	1.80034	−	0.0690086i	0.916800	+	0.399346i	$0.130763\pi$
$60$	−0.141897	−	0.262019i	−0.0183188	−	0.0338265i
$61$	−12.4490	+	7.40097i	−1.59392	+	0.947597i	−0.605507	+	0.795840i	$0.707030\pi$
$61$	−12.4490	+	7.40097i	−1.59392	+	0.947597i	−0.988418	+	0.151757i	$0.951507\pi$
$62$	−1.46450	+	4.33702i	−0.185992	+	0.550802i
$63$	4.01633	−	1.70887i	0.506011	−	0.215297i
$64$	−6.93738	+	1.34542i	−0.867172	+	0.168178i
$65$	1.50779	−	7.70345i	0.187018	−	0.955495i
$66$	−1.13600	+	3.58962i	−0.139833	+	0.441852i
$67$	−7.97978	−	1.07649i	−0.974885	−	0.131514i	−0.371041	−	0.928616i	$-0.620999\pi$
$67$	−7.97978	−	1.07649i	−0.974885	−	0.131514i	−0.603844	+	0.797103i	$0.706365\pi$
$68$	−1.20244	+	0.0230368i	−0.145817	+	0.00279362i
$69$	−0.982154	−	0.534079i	−0.118237	−	0.0642955i
$70$	−2.80678	−	4.95383i	−0.335474	−	0.592096i
$71$	−2.61316	+	0.718108i	−0.310125	+	0.0852238i	−0.416595	−	0.909092i	$-0.636777\pi$
$71$	−2.61316	+	0.718108i	−0.310125	+	0.0852238i	0.106470	+	0.994316i	$0.466045\pi$
$72$	−0.130069	+	6.78912i	−0.0153287	+	0.800106i
$73$	−5.43977	−	7.42720i	−0.636677	−	0.869287i	0.361327	−	0.932439i	$-0.382324\pi$
$73$	−5.43977	−	7.42720i	−0.636677	−	0.869287i	−0.998004	+	0.0631517i	$0.979885\pi$
$74$	−1.49506	+	12.9504i	−0.173797	+	1.50545i
$75$	−1.31616	−	3.12321i	−0.151977	−	0.360637i
$76$	0.00500147	+	0.00137443i	0.000573708	+	0.000157658i
$77$	−1.82479	+	6.17487i	−0.207954	+	0.703692i
$78$	−2.29553	+	2.67732i	−0.259918	+	0.303147i
$79$	8.81890	+	4.36651i	0.992203	+	0.491271i	0.865629	−	0.500686i	$-0.166919\pi$
$79$	8.81890	+	4.36651i	0.992203	+	0.491271i	0.126574	+	0.991957i	$0.459602\pi$
$80$	9.69400	−	0.914471i	1.08382	−	0.102241i
$81$	4.94237	+	1.15656i	0.549153	+	0.128507i
$82$	−12.4187	+	12.4187i	−1.37142	+	1.37142i
$83$	−8.76045	+	2.50089i	−0.961585	+	0.274509i
$83$	−8.76045	+	2.50089i	−0.961585	+	0.274509i
$84$			0.228945i			0.0249799i
$85$	−13.6373	−	1.07066i	−1.47917	−	0.116129i
$86$	−3.15749	−	3.54298i	−0.340481	−	0.382050i
$87$	0.719680	+	2.13128i	0.0771578	+	0.228497i
$88$	−7.60457	−	6.52015i	−0.810650	−	0.695051i
$89$	1.28420	+	2.36161i	0.136125	+	0.250330i	0.937613	−	0.347681i	$-0.113031\pi$
$89$	1.28420	+	2.36161i	0.136125	+	0.250330i	−0.801488	+	0.598011i	$0.795958\pi$
$90$	0.979998	−	8.36223i	0.103301	−	0.881457i
$91$	−3.83727	+	4.65297i	−0.402256	+	0.487763i
$92$	−0.254055	+	0.201467i	−0.0264871	+	0.0210044i
$93$	1.68903	−	1.23706i	0.175144	−	0.128278i
$94$	0.460532	+	0.478523i	0.0475002	+	0.0493558i
$95$	0.0550954	+	0.0210967i	0.00565267	+	0.00216448i
$96$	−0.685450	−	0.307282i	−0.0699585	−	0.0313619i
$97$	−3.72367	−	12.6004i	−0.378081	−	1.27938i	−0.903519	−	0.428548i	$-0.859025\pi$
$97$	−3.72367	−	12.6004i	−0.378081	−	1.27938i	0.525438	−	0.850832i	$-0.323902\pi$
$98$	−0.114928	−	5.99884i	−0.0116095	−	0.605974i
$99$	−7.57223	+	5.77206i	−0.761038	+	0.580114i
$100$	−0.982954	−	0.00339097i	−0.0982954	−	0.000339097i
$101$	−9.69166	−	3.48083i	−0.964356	−	0.346355i	−0.191894	−	0.981416i	$-0.561463\pi$
$101$	−9.69166	−	3.48083i	−0.964356	−	0.346355i	−0.772462	+	0.635061i	$0.780975\pi$
$102$	5.09365	+	3.43886i	0.504346	+	0.340498i
$103$	5.90874	+	13.8872i	0.582205	+	1.36835i	0.906425	+	0.422368i	$0.138801\pi$
$103$	5.90874	+	13.8872i	0.582205	+	1.36835i	−0.324219	+	0.945982i	$0.605102\pi$
$104$	−4.16333	−	8.40854i	−0.408249	−	0.824525i
$105$	−0.253506	+	2.59168i	−0.0247397	+	0.252922i
$106$	1.69841	+	4.72888i	0.164964	+	0.459309i
$107$	3.10572	+	2.87642i	0.300241	+	0.278074i	0.815248	−	0.579112i	$-0.196601\pi$
$107$	3.10572	+	2.87642i	0.300241	+	0.278074i	−0.515006	+	0.857186i	$0.672210\pi$
$108$	−0.436260	+	0.595647i	−0.0419791	+	0.0573162i
$109$	0.831606	+	0.633906i	0.0796534	+	0.0607172i	0.645292	−	0.763936i	$-0.276736\pi$
$109$	0.831606	+	0.633906i	0.0796534	+	0.0607172i	−0.565638	+	0.824654i	$0.691370\pi$
$110$	8.59719	+	8.96394i	0.819710	+	0.854678i
$111$	3.96685	−	4.45115i	0.376517	−	0.422484i
$112$	−6.88410	−	2.92905i	−0.650486	−	0.276769i
$113$	−9.05352	−	1.93647i	−0.851684	−	0.182168i	−0.237555	−	0.971374i	$-0.576346\pi$
$113$	−9.05352	−	1.93647i	−0.851684	−	0.182168i	−0.614129	+	0.789206i	$0.710492\pi$
$114$	−0.0168642	−	0.0204490i	−0.00157948	−	0.00191523i
$115$	−3.09902	+	1.99933i	−0.288985	+	0.186438i
$116$	0.650503	+	0.0499421i	0.0603977	+	0.00463700i
$117$	−8.64331	+	2.19806i	−0.799075	+	0.203211i
$118$	−16.9990	+	11.4765i	−1.56489	+	1.05650i
$119$	8.82194	+	5.71303i	0.808706	+	0.523713i
$120$	−3.51783	−	2.00922i	−0.321132	−	0.183416i
$121$	0.116661	−	3.04351i	0.0106055	−	0.276683i
$122$	9.89106	−	19.0500i	0.895495	−	1.72471i
$123$	7.91330	−	1.37797i	0.713518	−	0.124247i
$124$	−0.138352	−	0.591226i	−0.0124244	−	0.0530936i
$125$	−11.1234	−	1.12679i	−0.994908	−	0.100783i
$126$	−3.72172	+	5.29117i	−0.331557	+	0.471375i
$127$	−6.76457	−	3.51227i	−0.600259	−	0.311663i	0.133526	−	0.991045i	$-0.457370\pi$
$127$	−6.76457	−	3.51227i	−0.600259	−	0.311663i	−0.733785	+	0.679382i	$0.762248\pi$
$128$	9.31013	−	8.62275i	0.822907	−	0.762150i
$129$	0.248921	+	2.15619i	0.0219163	+	0.189842i
$130$	4.12269	+	10.8789i	0.361583	+	0.954140i
$131$	−1.85855	+	9.58318i	−0.162382	+	0.837287i	0.806778	+	0.590855i	$0.201209\pi$
$131$	−1.85855	+	9.58318i	−0.162382	+	0.837287i	−0.969160	+	0.246432i	$0.920742\pi$
$132$	−0.123089	−	0.484014i	−0.0107135	−	0.0421281i
$133$	−0.0295048	−	0.0344120i	−0.00255839	−	0.00298390i
$134$	10.8897	−	4.88178i	0.940727	−	0.421721i
$135$	−5.59806	+	6.25974i	−0.481805	+	0.538753i
$136$	−13.7245	+	8.88789i	−1.17687	+	0.762131i
$137$	−2.12678	+	4.99855i	−0.181703	+	0.427055i	−0.985906	−	0.167300i	$-0.946495\pi$
$137$	−2.12678	+	4.99855i	−0.181703	+	0.427055i	0.804203	+	0.594355i	$0.202593\pi$
$138$	1.65420	−	0.0951688i	0.140815	−	0.00810131i
$139$	2.74349	−	1.92973i	0.232700	−	0.163677i	−0.453118	−	0.891450i	$-0.649689\pi$
$139$	2.74349	−	1.92973i	0.232700	−	0.163677i	0.685818	+	0.727773i	$0.259445\pi$
$140$	0.662868	+	0.361939i	0.0560225	+	0.0305894i
$141$	−0.0463664	−	0.300185i	−0.00390476	−	0.0252801i
$142$	2.72924	−	2.94680i	0.229032	−	0.247290i
$143$	5.61083	−	11.8999i	0.469201	−	0.995124i
$144$	−5.65331	−	9.50928i	−0.471110	−	0.792440i
$145$	7.30848	+	1.28564i	0.606936	+	0.106767i
$146$	12.6552	+	5.10052i	1.04736	+	0.422122i
$147$	−1.53545	+	2.27431i	−0.126642	+	0.187582i
$148$	−0.737463	−	1.56408i	−0.0606191	−	0.128566i
$149$	2.01044	+	0.636241i	0.164701	+	0.0521229i	0.382944	−	0.923772i	$-0.374910\pi$
$149$	2.01044	+	0.636241i	0.164701	+	0.0521229i	−0.218242	+	0.975895i	$0.570032\pi$
$150$	4.09856	+	2.90405i	0.334646	+	0.237114i
$151$	−7.23969	−	6.96751i	−0.589158	−	0.567008i	0.338251	−	0.941056i	$-0.390165\pi$
$151$	−7.23969	−	6.96751i	−0.589158	−	0.567008i	−0.927409	+	0.374048i	$0.877969\pi$
$152$	0.0676282	−	0.0199854i	0.00548537	−	0.00162103i
$153$	5.53260	+	14.5237i	0.447285	+	1.17417i
$154$	−2.52871	−	9.20184i	−0.203769	−	0.741506i
$155$	−0.911511	−	6.84595i	−0.0732143	−	0.549880i
$156$	0.0714089	−	0.462315i	0.00571729	−	0.0370148i
$157$	10.7977	+	13.6162i	0.861754	+	1.08669i	0.995414	+	0.0956652i	$0.0304978\pi$
$157$	10.7977	+	13.6162i	0.861754	+	1.08669i	−0.133660	+	0.991027i	$0.542673\pi$
$158$	−14.5180	+	1.39480i	−1.15499	+	0.110964i
$159$	0.608937	−	2.21589i	0.0482919	−	0.175732i
$160$	−1.97331	+	1.49882i	−0.156004	+	0.118492i
$161$	2.82530	−	0.216911i	0.222665	−	0.0170950i
$162$	−7.12754	+	2.40679i	−0.559993	+	0.189095i
$163$	−0.0770638	+	1.33951i	−0.00603610	+	0.104918i	−0.999988	−	0.00489810i	$-0.998441\pi$
$163$	−0.0770638	+	1.33951i	−0.00603610	+	0.104918i	0.993952	+	0.109816i	$0.0350262\pi$
$164$	0.530808	−	2.26832i	0.0414492	−	0.177126i
$165$	−0.857438	−	5.61540i	−0.0667514	−	0.437158i
$166$	9.07653	−	9.99669i	0.704475	−	0.775894i
$167$	15.8669	+	15.8669i	1.22782	+	1.22782i	0.964787	+	0.263032i	$0.0847224\pi$
$167$	15.8669	+	15.8669i	1.22782	+	1.22782i	0.263032	+	0.964787i	$0.415278\pi$
$168$	1.64159	+	2.64460i	0.126651	+	0.204035i
$169$	−0.505183	+	0.450217i	−0.0388602	+	0.0346321i
$170$	18.0092	−	9.31123i	1.38124	−	0.714139i
$171$	−0.00513104	−	0.0668326i	−0.000392381	−	0.00511082i
$172$	0.603696	+	0.178404i	0.0460314	+	0.0136032i
$173$	1.44158	+	2.53412i	0.109601	+	0.192666i	0.918646	−	0.395081i	$-0.129284\pi$
$173$	1.44158	+	2.53412i	0.109601	+	0.192666i	−0.809045	+	0.587747i	$0.800015\pi$
$174$	−2.57213	−	2.12122i	−0.194992	−	0.160809i
$175$	7.10298	+	4.83118i	0.536935	+	0.365203i
$176$	16.1285	+	2.49120i	1.21573	+	0.187781i
$177$	9.37881	+	0.179683i	0.704955	+	0.0135058i
$178$	−3.46302	−	1.97000i	−0.259564	−	0.147658i
$179$	4.31288	−	9.62068i	0.322360	−	0.719084i	−0.677505	−	0.735518i	$-0.736939\pi$
$179$	4.31288	−	9.62068i	0.322360	−	0.719084i	0.999865	+	0.0164345i	$0.00523149\pi$
$180$	0.474541	+	1.01097i	0.0353702	+	0.0753530i
$181$	3.24218	−	3.36883i	0.240989	−	0.250403i	−0.589066	−	0.808085i	$-0.700504\pi$
$181$	3.24218	−	3.36883i	0.240989	−	0.250403i	0.830055	+	0.557682i	$0.188309\pi$
$182$	1.19502	−	8.85847i	0.0885811	−	0.656633i
$183$	−8.71262	+	4.52373i	−0.644056	+	0.334403i
$184$	−1.49008	+	4.14884i	−0.109850	+	0.305857i
$185$	−6.61630	−	18.5221i	−0.486440	−	1.36177i
$186$	−1.15992	+	2.87794i	−0.0850491	+	0.211021i
$187$	−21.7221	−	7.33501i	−1.58848	−	0.536389i
$188$	−0.0853766	−	0.0217119i	−0.00622672	−	0.00158350i
$189$	6.07254	−	2.18099i	0.441712	−	0.158644i
$190$	−0.0858672	+	0.0164993i	−0.00622946	+	0.00119699i
$191$	12.6937	−	1.96066i	0.918483	−	0.141868i	0.324074	−	0.946032i	$-0.394947\pi$
$191$	12.6937	−	1.96066i	0.918483	−	0.141868i	0.594408	+	0.804163i	$0.297386\pi$
$192$	−4.74706	+	0.640387i	−0.342589	+	0.0462160i
$193$	−0.565661	+	3.24844i	−0.0407172	+	0.233828i	−0.998572	−	0.0534255i	$-0.982986\pi$
$193$	−0.565661	+	3.24844i	−0.0407172	+	0.233828i	0.957855	+	0.287253i	$0.0927421\pi$
$194$	14.5379	+	12.9561i	1.04376	+	0.930197i
$195$	1.32027	−	5.15439i	0.0945466	−	0.369114i
$196$	0.432605	+	0.668020i	0.0309004	+	0.0477157i
$197$	−3.22073	−	0.309429i	−0.229467	−	0.0220459i	−0.0197371	−	0.999805i	$-0.506283\pi$
$197$	−3.22073	−	0.309429i	−0.229467	−	0.0220459i	−0.209730	+	0.977759i	$0.567259\pi$
$198$	5.02343	−	13.1870i	0.356999	−	0.937163i
$199$	2.10179	−	27.3762i	0.148992	−	1.94065i	−0.154881	−	0.987933i	$-0.549500\pi$
$199$	2.10179	−	27.3762i	0.148992	−	1.94065i	0.303873	−	0.952712i	$-0.401720\pi$
$200$	−11.3787	+	7.00886i	−0.804594	+	0.495601i
$201$	−5.35818	−	1.03916i	−0.377937	−	0.0732966i
$202$	14.9247	−	3.19226i	1.05010	−	0.224607i
$203$	−4.46739	−	3.54267i	−0.313550	−	0.248647i
$204$	−0.814614	−	0.0312248i	−0.0570344	−	0.00218618i
$205$	8.52049	−	25.0900i	0.595097	−	1.75236i
$206$	−18.2952	−	12.8686i	−1.27469	−	0.896595i
$207$	3.56004	+	2.20984i	0.247440	+	0.153594i
$208$	12.9877	+	8.06190i	0.900535	+	0.558992i
$209$	0.0808777	+	0.0568881i	0.00559442	+	0.00393503i
$210$	−1.70654	−	3.46164i	−0.117763	−	0.238876i
$211$	1.99935	+	0.0766367i	0.137641	+	0.00527589i	0.107032	−	0.994256i	$-0.465865\pi$
$211$	1.99935	+	0.0766367i	0.137641	+	0.00527589i	0.0306086	+	0.999531i	$0.490255\pi$
$212$	−0.522220	−	0.414123i	−0.0358662	−	0.0284421i
$213$	−1.79634	+	0.384222i	−0.123083	+	0.0263265i
$214$	−6.15910	−	1.19449i	−0.421028	−	0.0816535i
$215$	6.63637	+	2.68801i	0.452597	+	0.183321i
$216$	−0.768403	+	10.0086i	−0.0522832	+	0.680997i
$217$	−1.88899	+	4.95880i	−0.128233	+	0.336625i
$218$	−1.54266	−	0.148210i	−0.104482	−	0.0100380i
$219$	−3.39205	−	5.23793i	−0.229214	−	0.353947i
$220$	−1.59597	−	0.408799i	−0.107600	−	0.0275612i
$221$	−16.0325	−	14.2881i	−1.07846	−	0.961122i
$222$	−1.51594	+	8.70561i	−0.101743	+	0.584282i
$223$	22.8931	−	3.08832i	1.53304	−	0.206809i	0.681779	−	0.731559i	$-0.261207\pi$
$223$	22.8931	−	3.08832i	1.53304	−	0.206809i	0.851257	+	0.524749i	$0.175841\pi$
$224$	1.88161	−	0.290633i	0.125720	−	0.0194187i
$225$	4.25244	+	11.9697i	0.283496	+	0.797981i
$226$	12.9140	−	4.63815i	0.859026	−	0.308525i
$227$	27.9418	+	7.10580i	1.85456	+	0.471628i	0.998942	−	0.0459811i	$-0.0146414\pi$
$227$	27.9418	+	7.10580i	1.85456	+	0.471628i	0.855617	+	0.517610i	$0.173178\pi$
$228$	0.00333109	+	0.00112483i	0.000220607	+	7.44935e-5i
$229$	−4.67085	+	11.5892i	−0.308659	+	0.765833i	0.690440	+	0.723389i	$0.257417\pi$
$229$	−4.67085	+	11.5892i	−0.308659	+	0.765833i	−0.999099	+	0.0424440i	$0.986486\pi$
$230$	2.33959	−	4.93990i	0.154268	−	0.325728i
$231$	−1.47528	+	4.10763i	−0.0970665	+	0.270262i
$232$	7.87223	−	4.08738i	0.516837	−	0.268350i
$233$	0.625308	−	4.63528i	0.0409653	−	0.303667i	−0.958840	−	0.283946i	$-0.908356\pi$
$233$	0.625308	−	4.63528i	0.0409653	−	0.303667i	0.999806	−	0.0197212i	$-0.00627787\pi$
$234$	9.16573	−	9.52379i	0.599183	−	0.622590i
$235$	−0.942432	−	0.340317i	−0.0614775	−	0.0221999i
$236$	1.11291	−	2.48256i	0.0724445	−	0.161601i
$237$	5.79794	+	3.29826i	0.376617	+	0.214245i
$238$	−15.5743	−	0.298378i	−1.00953	−	0.0193410i
$239$	7.60498	+	1.17466i	0.491925	+	0.0759825i	0.393809	−	0.919192i	$-0.371157\pi$
$239$	7.60498	+	1.17466i	0.491925	+	0.0759825i	0.0981165	+	0.995175i	$0.468718\pi$
$240$	6.59575	−	0.241428i	0.425754	−	0.0155841i
$241$	21.8140	+	17.9898i	1.40516	+	1.15883i	0.965419	+	0.260704i	$0.0839545\pi$
$241$	21.8140	+	17.9898i	1.40516	+	1.15883i	0.439742	+	0.898124i	$0.355070\pi$
$242$	2.23203	+	3.92364i	0.143480	+	0.252221i
$243$	14.1045	+	4.16814i	0.904802	+	0.267386i
$244$	0.217951	+	2.83884i	0.0139529	+	0.181738i
$245$	4.15746	+	8.04108i	0.265610	+	0.513726i
$246$	−8.88750	+	7.92051i	−0.566646	+	0.504993i
$247$	0.0488468	+	0.0786920i	0.00310805	+	0.00500705i
$248$	−5.83738	−	5.83738i	−0.370674	−	0.370674i
$249$	−6.02576	+	1.35134i	−0.381867	+	0.0856378i
$250$	14.8876	−	7.27562i	0.941572	−	0.460151i
$251$	−5.33318	+	22.7905i	−0.336627	+	1.43852i	0.487999	+	0.872844i	$0.337727\pi$
$251$	−5.33318	+	22.7905i	−0.336627	+	1.43852i	−0.824626	+	0.565678i	$0.808615\pi$
$252$	0.0492850	−	0.856661i	0.00310466	−	0.0539646i
$253$	−5.85638	+	1.97755i	−0.368187	+	0.124328i
$254$	11.2634	−	0.864743i	0.706729	−	0.0542588i
$255$	−9.18696	−	1.25548i	−0.575310	−	0.0786210i
$256$	−1.23855	+	4.50703i	−0.0774096	+	0.281689i
$257$	3.77010	−	0.362210i	0.235173	−	0.0225940i	0.0226220	−	0.999744i	$-0.492799\pi$
$257$	3.77010	−	0.362210i	0.235173	−	0.0225940i	0.212551	+	0.977150i	$0.431823\pi$
$258$	−1.99881	−	2.52055i	−0.124440	−	0.156922i
$259$	−2.30682	+	14.9348i	−0.143339	+	0.928004i
$260$	−1.22566	−	0.937626i	−0.0760121	−	0.0581491i
$261$	−2.23409	−	8.12972i	−0.138286	−	0.503217i
$262$	−5.15028	−	13.5200i	−0.318185	−	0.835271i
$263$	13.8215	−	4.08453i	0.852273	−	0.251863i	0.172250	−	0.985053i	$-0.444896\pi$
$263$	13.8215	−	4.08453i	0.852273	−	0.251863i	0.680023	+	0.733190i	$0.261970\pi$
$264$	−4.89233	−	4.70840i	−0.301102	−	0.289782i
$265$	−5.45304	−	5.26617i	−0.334978	−	0.323499i
$266$	0.0640509	+	0.0202701i	0.00392721	+	0.00124284i
$267$	0.777104	+	1.64815i	0.0475580	+	0.100865i
$268$	−0.885744	+	1.31196i	−0.0541054	+	0.0801410i
$269$	−22.4439	−	9.04570i	−1.36843	−	0.551526i	−0.431837	−	0.901952i	$-0.642134\pi$
$269$	−22.4439	−	9.04570i	−1.36843	−	0.551526i	−0.936591	+	0.350426i	$0.886037\pi$
$270$	2.15632	−	12.2581i	0.131230	−	0.746001i
$271$	2.05952	+	3.46426i	0.125107	+	0.210439i	0.915659	−	0.401956i	$-0.131670\pi$
$271$	2.05952	+	3.46426i	0.125107	+	0.210439i	−0.790552	+	0.612395i	$0.790206\pi$
$272$	11.3608	−	24.0950i	0.688851	−	1.46098i
$273$	−2.77792	+	2.99937i	−0.168127	+	0.181530i
$274$	−1.22898	−	7.95665i	−0.0742454	−	0.480679i
$275$	−17.6139	−	6.39484i	−1.06216	−	0.385624i
$276$	−0.179768	+	0.126446i	−0.0108208	+	0.00761117i
$277$	13.7602	−	0.791643i	0.826769	−	0.0475652i	0.361103	−	0.932526i	$-0.382400\pi$
$277$	13.7602	−	0.791643i	0.826769	−	0.0475652i	0.465666	+	0.884961i	$0.345815\pi$
$278$	−1.94630	+	4.57436i	−0.116731	+	0.274352i
$279$	−6.58628	+	4.26523i	−0.394310	+	0.255353i
$280$	10.2522	−	0.572081i	0.612683	−	0.0341884i
$281$	−4.34507	+	1.94786i	−0.259205	+	0.116200i	−0.534524	−	0.845153i	$-0.679509\pi$
$281$	−4.34507	+	1.94786i	−0.259205	+	0.116200i	0.275319	+	0.961353i	$0.411217\pi$
$282$	0.293022	+	0.341757i	0.0174492	+	0.0203513i
$283$	4.80540	+	18.8960i	0.285651	+	1.12325i	0.932657	+	0.360765i	$0.117485\pi$
$283$	4.80540	+	18.8960i	0.285651	+	1.12325i	−0.647005	+	0.762485i	$0.723979\pi$
$284$	−0.101435	+	0.523025i	−0.00601905	+	0.0310358i
$285$	0.0364629	+	0.0164216i	0.00215988	+	0.000972734i
$286$	2.23620	+	19.3703i	0.132230	+	1.14539i
$287$	−14.9367	+	13.8339i	−0.881685	+	0.816589i
$288$	2.49866	+	1.29734i	0.147235	+	0.0764466i
$289$	−11.7505	+	16.7056i	−0.691204	+	0.982683i
$290$	−10.2079	+	4.09369i	−0.599427	+	0.240390i
$291$	−2.02932	−	8.67197i	−0.118961	−	0.508360i
$292$	−1.78304	+	0.310486i	−0.104344	+	0.0181698i
$293$	2.64731	−	5.09867i	0.154657	−	0.297868i	−0.797587	−	0.603203i	$-0.793891\pi$
$293$	2.64731	−	5.09867i	0.154657	−	0.297868i	0.952245	+	0.305336i	$0.0987688\pi$
$294$	0.155778	−	4.06402i	0.00908513	−	0.237019i
$295$	15.3472	−	26.8706i	0.893550	−	1.56447i
$296$	−19.7334	−	12.7793i	−1.14698	−	0.742779i
$297$	−11.6654	+	7.87567i	−0.676898	+	0.456993i
$298$	−3.02889	+	0.770270i	−0.175459	+	0.0446205i
$299$	−5.77286	−	0.443209i	−0.333853	−	0.0256314i
$300$	−0.665055	−	0.0405640i	−0.0383970	−	0.00234196i
$301$	−3.50020	−	4.24424i	−0.201748	−	0.244634i
$302$	14.5624	+	3.11478i	0.837974	+	0.179236i
$303$	−6.42304	−	2.73288i	−0.368994	−	0.157000i
$304$	−0.0764393	+	0.0857715i	−0.00438409	+	0.00491933i
$305$	−0.676169	+	32.3774i	−0.0387173	+	1.85392i
$306$	−18.3191	−	13.9640i	−1.04723	−	0.798269i
$307$	−15.1976	+	20.7501i	−0.867375	+	1.18427i	0.114250	+	0.993452i	$0.463554\pi$
$307$	−15.1976	+	20.7501i	−0.867375	+	1.18427i	−0.981625	+	0.190819i	$0.938886\pi$
$308$	0.928703	+	0.860135i	0.0529177	+	0.0490107i
$309$	3.45791	+	9.62784i	0.196713	+	0.547709i
$310$	6.49885	+	7.90807i	0.369110	+	0.449148i
$311$	−12.7176	−	25.6853i	−0.721150	−	1.45648i	−0.882857	−	0.469642i	$-0.844383\pi$
$311$	−12.7176	−	25.6853i	−0.721150	−	1.45648i	0.161707	−	0.986839i	$-0.448300\pi$
$312$	−2.49005	−	5.85234i	−0.140971	−	0.331323i
$313$	6.66405	+	4.49909i	0.376674	+	0.254304i	0.733244	−	0.679965i	$-0.238005\pi$
$313$	6.66405	+	4.49909i	0.376674	+	0.254304i	−0.356570	+	0.934269i	$0.616054\pi$
$314$	−24.2397	−	8.70585i	−1.36793	−	0.491300i
$315$	1.50648	−	9.64295i	0.0848805	−	0.543318i
$316$	1.53858	−	1.17281i	0.0865517	−	0.0659755i
$317$	−0.392247	−	20.4739i	−0.0220308	−	1.14993i	−0.828969	−	0.559294i	$-0.811072\pi$
$317$	−0.392247	−	20.4739i	−0.0220308	−	1.14993i	0.806939	−	0.590635i	$-0.201123\pi$
$318$	0.965242	+	3.26626i	0.0541281	+	0.183163i
$319$	11.3492	+	5.08778i	0.635435	+	0.284861i
$320$	−5.65051	+	14.7566i	−0.315873	+	0.824921i
$321$	1.98972	+	2.06745i	0.111056	+	0.115394i
$322$	−3.38812	+	2.48150i	−0.188813	+	0.138289i
$323$	0.126466	−	0.100289i	0.00703678	−	0.00558021i
$324$	0.634893	−	0.769853i	0.0352719	−	0.0427696i
$325$	−12.8364	−	11.9712i	−0.712035	−	0.664043i
$326$	−0.949970	−	1.74697i	−0.0526140	−	0.0967555i
$327$	0.538087	+	0.461355i	0.0297563	+	0.0255130i
$328$	−10.1330	−	30.0080i	−0.559499	−	1.65692i
$329$	0.512214	+	0.574749i	0.0282393	+	0.0316869i
$330$	5.46892	+	6.40081i	0.301054	+	0.352353i
$331$			8.29184i			0.455761i	0.973689	+	0.227880i	$0.0731795\pi$
$331$			8.29184i			0.455761i	−0.973689	+	0.227880i	$0.926820\pi$
$332$	−0.323585	+	1.76157i	−0.0177590	+	0.0966784i
$333$	−15.8013	+	15.8013i	−0.865906	+	0.865906i
$334$	−32.3821	−	7.57771i	−1.77187	−	0.414634i
$335$	−11.4795	+	13.8708i	−0.627190	+	0.757845i
$336$	−4.54459	−	2.25017i	−0.247928	−	0.122757i
$337$	−17.5918	+	20.5176i	−0.958284	+	1.11766i	0.0346977	+	0.999398i	$0.488953\pi$
$337$	−17.5918	+	20.5176i	−0.958284	+	1.11766i	−0.992982	+	0.118266i	$0.962266\pi$
$338$	0.284228	−	0.961793i	0.0154600	−	0.0523146i
$339$	−6.05133	−	1.66293i	−0.328663	−	0.0903182i
$340$	−1.37823	+	2.30920i	−0.0747451	+	0.125234i
$341$	1.32751	−	11.4990i	0.0718886	−	0.622708i
$342$	0.0587001	+	0.0801463i	0.00317414	+	0.00433382i
$343$	0.363589	−	18.9781i	0.0196320	−	1.02472i
$344$	8.25265	−	2.26787i	0.444953	−	0.122275i
$345$	−2.17501	+	1.23233i	−0.117099	+	0.0663466i
$346$	−3.79603	−	2.06422i	−0.204076	−	0.110973i
$347$	15.1356	−	0.289975i	0.812524	−	0.0155666i	0.388760	−	0.921339i	$-0.372904\pi$
$347$	15.1356	−	0.289975i	0.812524	−	0.0155666i	0.423764	+	0.905773i	$0.360709\pi$
$348$	0.438266	+	0.0591228i	0.0234935	+	0.00316932i
$349$	−5.87074	+	18.5507i	−0.314253	+	0.992999i	0.656786	+	0.754077i	$0.271916\pi$
$349$	−5.87074	+	18.5507i	−0.314253	+	0.992999i	−0.971039	+	0.238921i	$0.923206\pi$
$350$	−12.7204	−	0.531538i	−0.679936	−	0.0284119i
$351$	−12.9427	+	2.51009i	−0.690831	+	0.133979i
$352$	−3.82168	+	1.62605i	−0.203696	+	0.0866688i
$353$	−3.57419	+	10.5847i	−0.190235	+	0.563367i	−0.999717	−	0.0237771i	$-0.992431\pi$
$353$	−3.57419	+	10.5847i	−0.190235	+	0.563367i	0.809482	+	0.587144i	$0.199748\pi$
$354$	−11.9504	+	7.10459i	−0.635158	+	0.377605i
$355$	−1.72739	+	5.80840i	−0.0916804	+	0.308278i
$356$	0.528089	−	0.0202421i	0.0279887	−	0.00107283i
$357$	5.74758	+	4.20960i	0.304194	+	0.222796i
$358$	2.08905	+	15.4857i	0.110409	+	0.818443i
$359$	8.13975	+	11.5723i	0.429600	+	0.610761i	0.973583	−	0.228335i	$-0.0733282\pi$
$359$	8.13975	+	11.5723i	0.429600	+	0.610761i	−0.543983	+	0.839096i	$0.683084\pi$
$360$	12.7304	+	8.27535i	0.670953	+	0.436149i
$361$	17.6219	−	7.10226i	0.927468	−	0.373803i
$362$	−1.44940	+	6.77631i	−0.0761786	+	0.356155i
$363$	0.197440	−	2.05507i	0.0103629	−	0.107863i
$364$	0.485023	+	1.08193i	0.0254221	+	0.0567087i
$365$	−20.5280	+	1.54042i	−1.07448	+	0.0806290i
$366$	7.43518	−	12.5065i	0.388643	−	0.653725i
$367$	−2.41467	−	3.57661i	−0.126045	−	0.186698i	0.760503	−	0.649334i	$-0.224952\pi$
$367$	−2.41467	−	3.57661i	−0.126045	−	0.186698i	−0.886548	+	0.462637i	$0.846904\pi$
$368$	−1.50219	−	7.02315i	−0.0783072	−	0.366107i
$369$	−29.9065	+	3.45256i	−1.55687	+	0.179733i
$370$	22.8090	+	18.1518i	1.18578	+	0.943669i
$371$	1.75740	+	5.55314i	0.0912396	+	0.288305i
$372$	−0.0706079	−	0.405482i	−0.00366085	−	0.0210233i
$373$	−4.74766	+	7.64847i	−0.245825	+	0.396023i	−0.949140	−	0.314856i	$-0.898044\pi$
$373$	−4.74766	+	7.64847i	−0.245825	+	0.396023i	0.703315	+	0.710878i	$0.251702\pi$
$374$	33.0862	−	7.74247i	1.71085	−	0.400354i
$375$	−7.48359	−	1.19559i	−0.386451	−	0.0617401i
$376$	−1.14189	+	0.361372i	−0.0588883	+	0.0186363i
$377$	7.91617	+	8.54723i	0.407704	+	0.440205i
$378$	−5.94190	+	7.49288i	−0.305618	+	0.385392i
$379$	13.5919	−	20.9883i	0.698169	−	1.07810i	−0.294313	−	0.955709i	$-0.595091\pi$
$379$	13.5919	−	20.9883i	0.698169	−	1.07810i	0.992482	−	0.122389i	$-0.0390556\pi$
$380$	0.00852287	−	0.00786634i	0.000437214	−	0.000403535i
$381$	−4.44099	−	2.64019i	−0.227519	−	0.135261i
$382$	−14.4516	+	12.3908i	−0.739408	+	0.633968i
$383$	3.29838	+	1.25647i	0.168540	+	0.0642029i	0.438802	−	0.898584i	$-0.355403\pi$
$383$	3.29838	+	1.25647i	0.168540	+	0.0642029i	−0.270262	+	0.962787i	$0.587110\pi$
$384$	6.63608	−	5.47273i	0.338646	−	0.279279i
$385$	9.56062	+	10.7652i	0.487254	+	0.548644i
$386$	−1.82682	−	4.53264i	−0.0929826	−	0.230705i
$387$	−0.467247	−	8.12158i	−0.0237515	−	0.412843i
$388$	−2.54475	−	0.443126i	−0.129190	−	0.0224963i
$389$	15.3112	−	20.0864i	0.776307	−	1.01842i	−0.222744	−	0.974877i	$-0.571501\pi$
$389$	15.3112	−	20.0864i	0.776307	−	1.01842i	0.999052	−	0.0435424i	$-0.0138644\pi$
$390$	2.36637	+	7.52249i	0.119826	+	0.380916i
$391$	0.386465	+	10.0823i	0.0195444	+	0.509886i
$392$	9.78700	+	4.61458i	0.494318	+	0.233071i
$393$	−1.63082	+	6.41280i	−0.0822641	+	0.323483i
$394$	4.29746	−	2.12781i	0.216503	−	0.107197i
$395$	18.7155	−	11.5727i	0.941679	−	0.582284i
$396$	0.356377	+	1.83758i	0.0179086	+	0.0923417i
$397$	13.2063	−	6.22677i	0.662805	−	0.312513i	−0.0654132	−	0.997858i	$-0.520837\pi$
$397$	13.2063	−	6.22677i	0.662805	−	0.312513i	0.728218	+	0.685345i	$0.240349\pi$
$398$	18.7517	+	36.1154i	0.939937	+	1.81030i
$399$	−0.0186268	−	0.0244361i	−0.000932508	−	0.00122333i
$400$	9.72822	−	19.4785i	0.486411	−	0.973924i
$401$	6.05724	−	11.1391i	0.302484	−	0.556260i	−0.682081	−	0.731277i	$-0.738925\pi$
$401$	6.05724	−	11.1391i	0.302484	−	0.556260i	0.984565	+	0.175017i	$0.0559981\pi$
$402$	7.55937	−	2.87964i	0.377027	−	0.143623i
$403$	5.36117	−	9.42428i	0.267059	−	0.469457i
$404$	−1.45867	+	1.40383i	−0.0725715	+	0.0698431i
$405$	8.03952	−	8.01183i	0.399487	−	0.398111i
$406$	8.39452	+	0.969106i	0.416613	+	0.0480959i
$407$	−3.15259	−	32.8141i	−0.156268	−	1.62653i
$408$	−9.63370	+	5.48030i	−0.476939	+	0.271315i
$409$	−20.5248	+	11.1610i	−1.01489	+	0.551877i	−0.897410	−	0.441198i	$-0.854554\pi$
$409$	−20.5248	+	11.1610i	−1.01489	+	0.551877i	−0.117476	+	0.993076i	$0.537480\pi$
$410$	8.88215	+	38.2537i	0.438658	+	1.88922i
$411$	−1.63385	+	3.29983i	−0.0805919	+	0.162769i
$412$	2.96207	+	0.170412i	0.145931	+	0.00839561i
$413$	−20.2005	+	12.5391i	−0.994002	+	0.617011i
$414$	−6.21016			−0.305213
$415$	−5.61357	+	19.5828i	−0.275559	+	0.961284i
$416$	−3.89025			−0.190735
$417$	1.93171	−	1.19908i	0.0945962	−	0.0587190i
$418$	−0.146309	−	0.00841736i	−0.00715619	−	0.000411706i
$419$	−5.04773	+	10.1947i	−0.246598	+	0.498045i	−0.984171	−	0.177222i	$-0.943289\pi$
$419$	−5.04773	+	10.1947i	−0.246598	+	0.498045i	0.737573	+	0.675267i	$0.235972\pi$
$420$	0.434486	+	0.270739i	0.0212007	+	0.0132107i
$421$	33.7762	−	18.3669i	1.64615	−	0.895149i	0.656064	−	0.754706i	$-0.272220\pi$
$421$	33.7762	−	18.3669i	1.64615	−	0.895149i	0.990089	−	0.140444i	$-0.0448529\pi$
$422$	−2.57752	+	1.46627i	−0.125472	+	0.0713768i
$423$	0.108872	+	1.13321i	0.00529355	+	0.0550985i
$424$	−9.00166	−	1.03920i	−0.437159	−	0.0504679i
$425$	−18.1587	+	24.6144i	−0.880826	+	1.19397i
$426$	1.96166	−	1.88791i	0.0950428	−	0.0914696i
$427$	12.3032	−	21.6276i	0.595395	−	1.04663i
$428$	0.777682	−	0.296247i	0.0375907	−	0.0143197i
$429$	4.26027	−	7.83451i	0.205688	−	0.378254i
$430$	−10.4577	+	1.80245i	−0.504315	+	0.0869220i
$431$	−3.12280	−	4.09673i	−0.150420	−	0.197332i	0.713939	−	0.700208i	$-0.246909\pi$
$431$	−3.12280	−	4.09673i	−0.150420	−	0.197332i	−0.864359	+	0.502876i	$0.832275\pi$
$432$	−7.53595	−	14.5141i	−0.362573	−	0.698311i
$433$	16.6974	−	7.87284i	0.802426	−	0.378344i	0.0189924	−	0.999820i	$-0.493954\pi$
$433$	16.6974	−	7.87284i	0.802426	−	0.378344i	0.783434	+	0.621475i	$0.213466\pi$
$434$	−1.49735	−	7.72072i	−0.0718749	−	0.370607i
$435$	4.89576	+	1.15456i	0.234734	+	0.0553570i
$436$	0.184223	−	0.0912148i	0.00882270	−	0.00436840i
$437$	0.0107250	−	0.0421732i	0.000513044	−	0.00201742i
$438$	8.36551	+	3.94434i	0.399720	+	0.188468i
$439$	0.827150	+	21.5792i	0.0394777	+	1.02992i	0.876097	+	0.482135i	$0.160139\pi$
$439$	0.827150	+	21.5792i	0.0394777	+	1.02992i	−0.836619	+	0.547785i	$0.815471\pi$
$440$	−21.3666	+	6.72136i	−1.01861	+	0.320428i
$441$	6.23492	−	8.17945i	0.296901	−	0.389497i
$442$	31.3566	+	5.46022i	1.49148	+	0.259716i
$443$	0.0710440	+	1.23487i	0.00337540	+	0.0586705i	0.999606	−	0.0280765i	$-0.00893819\pi$
$443$	0.0710440	+	1.23487i	0.00337540	+	0.0586705i	−0.996230	+	0.0867470i	$0.972353\pi$
$444$	−0.438163	−	1.08716i	−0.0207943	−	0.0515942i
$445$	6.00045	+	0.355600i	0.284449	+	0.0168571i
$446$	−26.4135	+	21.7830i	−1.25071	+	1.03146i
$447$	1.33574	+	0.508831i	0.0631782	+	0.0240669i
$448$	9.21685	−	7.90252i	0.435455	−	0.373359i
$449$	−26.9335	−	16.0121i	−1.27107	−	0.755659i	−0.291465	−	0.956582i	$-0.594143\pi$
$449$	−26.9335	−	16.0121i	−1.27107	−	0.755659i	−0.979607	+	0.200923i	$0.935606\pi$
$450$	−14.7108	−	11.7486i	−0.693472	−	0.553835i
$451$	24.1403	−	37.2769i	1.13672	−	1.75530i
$452$	−1.13092	+	1.42612i	−0.0531940	+	0.0670790i
$453$	−4.62800	−	4.99693i	−0.217442	−	0.234776i
$454$	−40.7390	+	12.8926i	−1.91197	+	0.605081i
$455$	4.29252	+	12.7847i	0.201236	+	0.599355i
$456$	0.0465436	−	0.0108916i	0.00217960	−	0.000510047i
$457$	7.66247	−	12.3442i	0.358435	−	0.577438i	−0.619845	−	0.784724i	$-0.712805\pi$
$457$	7.66247	−	12.3442i	0.358435	−	0.577438i	0.978280	+	0.207286i	$0.0664632\pi$
$458$	−3.17692	−	18.2442i	−0.148448	−	0.852496i
$459$	6.93204	+	21.9043i	0.323560	+	1.02241i
$460$	0.0819062	+	0.720387i	0.00381890	+	0.0335882i
$461$	−11.1165	+	1.28334i	−0.517746	+	0.0597712i	−0.369594	−	0.929193i	$-0.620503\pi$
$461$	−11.1165	+	1.28334i	−0.517746	+	0.0597712i	−0.148152	+	0.988965i	$0.547332\pi$
$462$	−1.35298	−	6.32554i	−0.0629464	−	0.294291i
$463$	14.8423	+	21.9844i	0.689778	+	1.02170i	0.997531	+	0.0702331i	$0.0223743\pi$
$463$	14.8423	+	21.9844i	0.689778	+	1.02170i	−0.307753	+	0.951466i	$0.599577\pi$
$464$	−7.38479	+	12.4217i	−0.342830	+	0.576665i
$465$	−0.350307	−	4.66829i	−0.0162451	−	0.216487i
$466$	2.83572	+	6.32560i	0.131362	+	0.293028i
$467$	2.29733	−	23.9121i	0.106308	−	1.10652i	−0.774347	−	0.632761i	$-0.781922\pi$
$467$	2.29733	−	23.9121i	0.106308	−	1.10652i	0.880655	−	0.473758i	$-0.157103\pi$
$468$	−0.366720	+	1.71451i	−0.0169516	+	0.0792533i
$469$	12.8309	−	5.17133i	0.592478	−	0.238790i
$470$	1.45273	−	0.308108i	0.0670096	−	0.0142120i
$471$	6.77696	+	9.63479i	0.312266	+	0.443947i
$472$	−4.94504	−	36.6566i	−0.227614	−	1.68726i
$473$	9.68166	+	7.09097i	0.445163	+	0.326043i
$474$	−9.87893	+	0.378668i	−0.453754	+	0.0173928i
$475$	0.105190	−	0.0796108i	0.00482646	−	0.00365279i
$476$	1.77607	−	1.05588i	0.0814060	−	0.0483963i
$477$	−2.75553	+	8.16030i	−0.126167	+	0.373635i
$478$	−10.4945	+	4.46520i	−0.480007	+	0.204233i
$479$	7.45273	−	1.44537i	0.340524	−	0.0660407i	−0.0172438	−	0.999851i	$-0.505489\pi$
$479$	7.45273	−	1.44537i	0.340524	−	0.0660407i	0.357768	+	0.933811i	$0.383538\pi$
$480$	−1.39374	+	0.937455i	−0.0636151	+	0.0427888i
$481$	9.31648	−	29.4388i	0.424795	−	1.34229i
$482$	−41.5301	−	5.60249i	−1.89165	−	0.255187i
$483$	1.92039	−	0.0367915i	0.0873806	−	0.00167407i
$484$	−0.526027	−	0.286044i	−0.0239103	−	0.0130020i
$485$	−28.3163	−	7.83401i	−1.28578	−	0.355724i
$486$	−21.0186	+	5.77601i	−0.953422	+	0.262005i
$487$	−0.0759857	+	3.96618i	−0.00344324	+	0.179725i	0.994048	+	0.108940i	$0.0347456\pi$
$487$	−0.0759857	+	3.96618i	−0.00344324	+	0.179725i	−0.997492	+	0.0707851i	$0.977450\pi$
$488$	22.8728	+	31.2294i	1.03540	+	1.41369i
$489$	−0.104302	+	0.903473i	−0.00471668	+	0.0408565i
$490$	−11.5204	−	6.87585i	−0.520438	−	0.310619i
$491$	38.1334	+	10.4792i	1.72094	+	0.472922i	0.980057	−	0.198715i	$-0.0636769\pi$
$491$	38.1334	+	10.4792i	1.72094	+	0.472922i	0.740880	+	0.671637i	$0.234409\pi$
$492$	0.447522	−	1.51436i	0.0201759	−	0.0682726i
$493$	13.2146	−	15.4124i	0.595154	−	0.694139i
$494$	−0.123018	−	0.0609099i	−0.00553482	−	0.00274046i
$495$	1.99952	+	21.1962i	0.0898716	+	0.952699i
$496$	13.0957	+	3.06452i	0.588015	+	0.137601i
$497$	3.29227	−	3.29227i	0.147679	−	0.147679i
$498$	6.53149	−	6.41161i	0.292683	−	0.287311i
$499$			36.1297i			1.61739i	0.588230	+	0.808694i	$0.299825\pi$
$499$			36.1297i			1.61739i	−0.588230	+	0.808694i	$0.700175\pi$
$500$	−1.16883	+	1.86142i	−0.0522718	+	0.0832452i
$501$	10.1198	+	11.3552i	0.452117	+	0.507315i
$502$	−11.0983	−	32.8668i	−0.495341	−	1.46692i
$503$	−14.4105	−	12.3556i	−0.642533	−	0.550907i	0.268480	−	0.963285i	$-0.413479\pi$
$503$	−14.4105	−	12.3556i	−0.642533	−	0.550907i	−0.911013	+	0.412378i	$0.864698\pi$
$504$	−5.57318	−	10.2489i	−0.248249	−	0.456522i
$505$	−18.0668	+	14.2764i	−0.803960	+	0.635290i
$506$	5.82873	−	7.06774i	0.259118	−	0.314200i
$507$	−0.359397	+	0.285004i	−0.0159614	+	0.0126575i
$508$	−1.20887	+	0.885394i	−0.0536351	+	0.0392830i
$509$	7.39674	+	7.68569i	0.327855	+	0.340662i	0.864026	−	0.503447i	$-0.167935\pi$
$509$	7.39674	+	7.68569i	0.327855	+	0.340662i	−0.536172	+	0.844109i	$0.680130\pi$
$510$	12.5497	−	5.59997i	0.555711	−	0.247971i
$511$	14.4328	+	6.47014i	0.638471	+	0.286222i
$512$	5.22938	+	17.6956i	0.231108	+	0.782041i
$513$	−0.00189801	−	0.0990695i	−8.37993e−5	−	0.00437403i
$514$	−4.46427	+	3.40296i	−0.196910	+	0.150098i
$515$	33.3423	+	5.20893i	1.46924	+	0.229533i
$516$	0.401589	+	0.144233i	0.0176790	+	0.00634952i
$517$	−1.39188	−	0.939699i	−0.0612149	−	0.0413279i
$518$	−8.76884	−	20.6093i	−0.385281	−	0.905521i
$519$	0.876888	+	1.77102i	0.0384911	+	0.0777391i
$520$	−20.8809	−	2.04247i	−0.915689	−	0.0895684i
$521$	0.501061	+	1.39510i	0.0219519	+	0.0611206i	0.951620	−	0.307278i	$-0.0994182\pi$
$521$	0.501061	+	1.39510i	0.0219519	+	0.0611206i	−0.929668	+	0.368399i	$0.879906\pi$
$522$	9.16771	+	8.49084i	0.401260	+	0.371634i
$523$	−20.6057	+	28.1340i	−0.901025	+	1.23022i	0.0715058	+	0.997440i	$0.477220\pi$
$523$	−20.6057	+	28.1340i	−0.901025	+	1.23022i	−0.972531	+	0.232775i	$0.925219\pi$
$524$	1.52623	+	1.16340i	0.0666737	+	0.0508232i
$525$	4.61865	+	3.54590i	0.201575	+	0.154756i
$526$	−14.2117	+	15.9468i	−0.619660	+	0.695313i
$527$	−17.3864	−	7.39757i	−0.757364	−	0.322243i
$528$	10.8175	+	2.31378i	0.470773	+	0.100694i
$529$	−12.9028	−	15.6456i	−0.560993	−	0.680244i
$530$	10.9828	+	2.36895i	0.477063	+	0.102901i
$531$	−35.0548	−	2.69132i	−1.52125	−	0.116793i
$532$	−0.00863644	+	0.00219631i	−0.000374437	+	9.52222e-5i
$533$	34.4770	−	23.2764i	1.49336	−	1.00821i
$534$	−2.26680	−	1.46797i	−0.0980942	−	0.0635252i
$535$	9.13149	−	2.49245i	0.394789	−	0.107758i
$536$	−0.824338	+	21.5059i	−0.0356060	+	0.928912i
$537$	3.29318	−	6.34262i	0.142111	−	0.273704i
$538$	35.3322	−	6.15251i	1.52328	−	0.265254i
$539$	3.45701	+	14.7730i	0.148904	+	0.636317i
$540$	0.614506	+	1.53231i	0.0264441	+	0.0659401i
$541$	17.4805	−	24.8520i	0.751546	−	1.06847i	−0.243582	−	0.969880i	$-0.578322\pi$
$541$	17.4805	−	24.8520i	0.751546	−	1.06847i	0.995128	−	0.0985916i	$-0.0314337\pi$
$542$	−5.30119	−	2.75246i	−0.227706	−	0.118228i
$543$	2.32521	−	2.15354i	0.0997844	−	0.0924171i
$544$	0.777483	+	6.73465i	0.0333343	+	0.288746i
$545$	2.18643	−	0.828576i	0.0936565	−	0.0354923i
$546$	1.15358	−	5.94820i	0.0493689	−	0.254559i
$547$	9.96672	+	39.1916i	0.426146	+	1.67571i	0.700160	+	0.713986i	$0.253112\pi$
$547$	9.96672	+	39.1916i	0.426146	+	1.67571i	−0.274014	+	0.961726i	$0.588352\pi$
$548$	0.695117	+	0.810727i	0.0296939	+	0.0346326i
$549$	33.5746	−	15.0512i	1.43293	−	0.642371i
$550$	27.1782	−	5.71522i	1.15888	−	0.243698i
$551$	−0.0734939	+	0.0475941i	−0.00313094	+	0.00202758i
$552$	−1.16990	+	2.74960i	−0.0497942	+	0.117031i
$553$	−16.8789	+	0.971070i	−0.717765	+	0.0412941i
$554$	−16.7083	+	11.7523i	−0.709867	+	0.499309i
$555$	−3.75628	−	12.7919i	−0.159445	−	0.542987i
$556$	−0.100658	−	0.651678i	−0.00426884	−	0.0276373i
$557$	6.66837	−	7.19996i	0.282548	−	0.305072i	−0.576366	−	0.817192i	$-0.695530\pi$
$557$	6.66837	−	7.19996i	0.282548	−	0.305072i	0.858914	+	0.512120i	$0.171140\pi$
$558$	4.95969	−	10.5190i	0.209960	−	0.445303i
$559$	5.74426	+	9.66225i	0.242956	+	0.408670i
$560$	−13.6995	+	9.60074i	−0.578910	+	0.405705i
$561$	−14.4143	−	5.80947i	−0.608570	−	0.245276i
$562$	3.94887	−	5.84907i	0.166573	−	0.246728i
$563$	−9.79195	−	20.7676i	−0.412681	−	0.875251i	−0.997925	−	0.0643934i	$-0.979489\pi$
$563$	−9.79195	−	20.7676i	−0.412681	−	0.875251i	0.585243	−	0.810858i	$-0.300999\pi$
$564$	−0.0569309	−	0.0180169i	−0.00239722	−	0.000758647i
$565$	−14.3813	+	14.8916i	−0.605025	+	0.626494i
$566$	−20.8209	−	20.0381i	−0.875168	−	0.842265i
$567$	−8.36311	+	2.47146i	−0.351218	+	0.103791i
$568$	2.57853	+	6.76892i	0.108193	+	0.284017i
$569$	−1.64967	−	6.00305i	−0.0691577	−	0.251661i	0.921429	−	0.388546i	$-0.127023\pi$
$569$	−1.64967	−	6.00305i	−0.0691577	−	0.251661i	−0.990587	+	0.136885i	$0.956291\pi$
$570$	−0.0587506	+	0.00782241i	−0.00246079	+	0.000327645i
$571$	2.70316	−	17.5008i	0.113124	−	0.732385i	−0.861371	−	0.507976i	$-0.830394\pi$
$571$	2.70316	−	17.5008i	0.113124	−	0.732385i	0.974495	−	0.224409i	$-0.0720451\pi$
$572$	−1.60708	−	2.02656i	−0.0671953	−	0.0847349i
$573$	8.66643	−	0.832621i	0.362045	−	0.0347832i
$574$	7.99545	−	29.0950i	0.333724	−	1.21440i
$575$	0.129518	+	8.24556i	0.00540127	+	0.343864i
$576$	17.9003	−	1.37429i	0.745847	−	0.0572621i
$577$	−36.5712	+	12.3492i	−1.52248	+	0.514103i	−0.951707	−	0.307007i	$-0.900673\pi$
$577$	−36.5712	+	12.3492i	−1.52248	+	0.514103i	−0.570771	+	0.821109i	$0.693356\pi$
$578$	1.73864	−	30.2206i	0.0723179	−	1.25701i
$579$	−0.509266	+	2.17627i	−0.0211644	+	0.0904426i
$580$	0.864035	−	1.17545i	0.0358771	−	0.0488080i
$581$	10.9577	−	11.1767i	0.454603	−	0.463689i
$582$	9.33371	+	9.33371i	0.386895	+	0.386895i
$583$	−6.70090	−	10.7951i	−0.277523	−	0.447089i
$584$	−18.3701	+	16.3713i	−0.760158	+	0.677450i
$585$	−6.04976	+	19.0024i	−0.250127	+	0.785654i
$586$	0.651784	+	8.48958i	0.0269249	+	0.350701i
$587$	−10.4288	−	3.08190i	−0.430442	−	0.127204i	0.0609532	−	0.998141i	$-0.480586\pi$
$587$	−10.4288	−	3.08190i	−0.430442	−	0.127204i	−0.491395	+	0.870937i	$0.663513\pi$
$588$	0.266746	+	0.468906i	0.0110004	+	0.0193374i
$589$	0.0628687	+	0.0518474i	0.00259046	+	0.00213634i
$590$	1.67761	+	45.8320i	0.0690663	+	1.88687i
$591$	−2.16749	−	0.334789i	−0.0891586	−	0.0137714i
$592$	38.2953	+	0.733676i	1.57393	+	0.0301539i
$593$	−16.4808	−	9.37540i	−0.676786	−	0.385002i	0.117056	−	0.993125i	$-0.462654\pi$
$593$	−16.4808	−	9.37540i	−0.676786	−	0.385002i	−0.793842	+	0.608124i	$0.791922\pi$
$594$	8.53341	−	19.0354i	0.350130	−	0.781030i
$595$	21.2745	−	9.98612i	0.872169	−	0.409391i
$596$	0.287466	−	0.298696i	0.0117751	−	0.0122351i
$597$	2.48816	−	18.4442i	0.101834	−	0.754872i
$598$	7.61573	−	3.95420i	0.311430	−	0.161699i
$599$	12.9493	−	36.0547i	0.529094	−	1.47316i	−0.321284	−	0.946983i	$-0.604114\pi$
$599$	12.9493	−	36.0547i	0.529094	−	1.47316i	0.850378	−	0.526172i	$-0.176373\pi$
$600$	−7.97308	+	4.30005i	−0.325499	+	0.175549i
$601$	2.80474	−	6.95904i	0.114408	−	0.283865i	−0.859374	−	0.511347i	$-0.829147\pi$
$601$	2.80474	−	6.95904i	0.114408	−	0.283865i	0.973782	+	0.227482i	$0.0730492\pi$
$602$	7.72498	+	2.60853i	0.314847	+	0.106316i
$603$	19.8255	+	5.04177i	0.807356	+	0.205317i
$604$	−1.85906	+	0.667694i	−0.0756441	+	0.0271681i
$605$	−5.63796	−	3.82052i	−0.229216	−	0.155326i
$606$	10.2241	−	1.57922i	0.415327	−	0.0641512i
$607$	−41.4013	+	5.58512i	−1.68043	+	0.226693i	−0.911107	−	0.412170i	$-0.864771\pi$
$607$	−41.4013	+	5.58512i	−1.68043	+	0.226693i	−0.769321	+	0.638863i	$0.779405\pi$
$608$	0.00501590	−	0.0288050i	0.000203422	−	0.00116820i
$609$	−2.88526	−	2.57133i	−0.116917	−	0.104196i
$610$	−24.4560	−	41.2988i	−0.990195	−	1.67214i
$611$	−0.855063	−	1.32037i	−0.0345921	−	0.0534164i
$612$	3.04139	+	0.292199i	0.122941	+	0.0118114i
$613$	−11.2803	+	29.6119i	−0.455606	+	1.19602i	0.490294	+	0.871557i	$0.336889\pi$
$613$	−11.2803	+	29.6119i	−0.455606	+	1.19602i	−0.945900	+	0.324458i	$0.894818\pi$
$614$	2.91805	−	38.0080i	0.117763	−	1.53388i
$615$	6.74283	−	16.6472i	0.271897	−	0.671281i
$616$	16.8951	+	3.27661i	0.680722	+	0.132018i
$617$	−39.0768	+	8.35820i	−1.57317	+	0.336488i	−0.910852	−	0.412733i	$-0.864574\pi$
$617$	−39.0768	+	8.35820i	−1.57317	+	0.336488i	−0.662320	+	0.749221i	$0.730428\pi$
$618$	−11.8798	−	9.42073i	−0.477874	−	0.378957i
$619$	−32.3118	−	1.23854i	−1.29872	−	0.0497811i	−0.620247	−	0.784407i	$-0.712968\pi$
$619$	−32.3118	−	1.23854i	−1.29872	−	0.0497811i	−0.678473	+	0.734625i	$0.737358\pi$
$620$	−1.28562	−	0.436595i	−0.0516319	−	0.0175341i
$621$	5.06640	+	3.56362i	0.203307	+	0.143003i
$622$	36.0909	+	22.4028i	1.44711	+	0.898272i
$623$	−3.92395	−	2.43573i	−0.157210	−	0.0975853i
$624$	8.47519	+	5.96132i	0.339279	+	0.238644i
$625$	−15.2925	+	19.7773i	−0.611698	+	0.791091i
$626$	−11.9082	−	0.456450i	−0.475946	−	0.0182434i
$627$	0.0525169	+	0.0416462i	0.00209732	+	0.00166319i
$628$	3.34080	−	0.714569i	0.133312	−	0.0285144i
$629$	−52.8253	−	10.2449i	−2.10628	−	0.408490i
$630$	5.64032	+	13.3201i	0.224716	+	0.530686i
$631$	−0.108430	+	1.41232i	−0.00431654	+	0.0562236i	−0.998828	−	0.0484070i	$-0.984586\pi$
$631$	−0.108430	+	1.41232i	−0.00431654	+	0.0562236i	0.994511	+	0.104631i	$0.0333660\pi$
$632$	9.36317	−	24.5794i	0.372447	−	0.977715i
$633$	1.35002	+	0.129702i	0.0536585	+	0.00515520i
$634$	16.4971	+	25.4745i	0.655185	+	1.01172i
$635$	−14.6650	+	8.68421i	−0.581962	+	0.344622i
$636$	−0.337275	−	0.300578i	−0.0133738	−	0.0119187i
$637$	−2.43798	+	14.0007i	−0.0965965	+	0.554728i
$638$	−18.2680	+	2.46439i	−0.723236	+	0.0975660i
$639$	6.80423	−	1.05098i	0.269171	−	0.0415761i
$640$	−5.35433	−	27.8654i	−0.211648	−	1.10148i
$641$	−0.715005	+	0.256799i	−0.0282410	+	0.0101430i	−0.352099	−	0.935963i	$-0.614532\pi$
$641$	−0.715005	+	0.256799i	−0.0282410	+	0.0101430i	0.323858	+	0.946106i	$0.395020\pi$
$642$	−4.12150	−	1.04813i	−0.162663	−	0.0413663i
$643$	6.63921	+	2.24189i	0.261825	+	0.0884116i	0.447771	−	0.894148i	$-0.352218\pi$
$643$	6.63921	+	2.24189i	0.261825	+	0.0884116i	−0.185946	+	0.982560i	$0.559535\pi$
$644$	0.208241	−	0.516679i	0.00820583	−	0.0203600i
$645$	4.38633	+	2.07741i	0.172712	+	0.0817980i
$646$	−0.0808593	+	0.225137i	−0.00318137	+	0.00885788i
$647$	23.3886	−	12.1437i	0.919500	−	0.477418i	0.0655946	−	0.997846i	$-0.479106\pi$
$647$	23.3886	−	12.1437i	0.919500	−	0.477418i	0.853906	+	0.520428i	$0.174228\pi$
$648$	1.81377	−	13.4451i	0.0712517	−	0.528174i
$649$	35.9647	−	37.3697i	1.41174	−	1.46689i
$650$	25.5210	+	5.04092i	1.00102	+	0.197721i
$651$	−1.47138	+	3.28219i	−0.0576679	+	0.128639i
$652$	0.229270	+	0.130424i	0.00897892	+	0.00510782i
$653$	−18.0012	−	0.344874i	−0.704440	−	0.0134959i	−0.334293	−	0.942469i	$-0.608498\pi$
$653$	−18.0012	−	0.344874i	−0.704440	−	0.0134959i	−0.370147	+	0.928973i	$0.620693\pi$
$654$	−1.03818	−	0.160357i	−0.0405961	−	0.00627046i
$655$	15.9889	+	14.8598i	0.624739	+	0.580619i
$656$	39.8096	+	32.8307i	1.55430	+	1.28183i
$657$	11.5648	+	20.3294i	0.451184	+	0.793127i
$658$	−1.09424	−	0.323367i	−0.0426577	−	0.0126062i
$659$	3.43322	+	44.7183i	0.133739	+	1.74198i	0.552174	+	0.833729i	$0.313798\pi$
$659$	3.43322	+	44.7183i	0.133739	+	1.74198i	−0.418434	+	0.908247i	$0.637421\pi$
$660$	−1.06411	−	0.338779i	−0.0414205	−	0.0131869i
$661$	−4.02152	+	3.58397i	−0.156419	+	0.139400i	−0.739874	−	0.672745i	$-0.765115\pi$
$661$	−4.02152	+	3.58397i	−0.156419	+	0.139400i	0.583455	+	0.812145i	$0.301700\pi$
$662$	−6.48123	−	10.4412i	−0.251900	−	0.405810i
$663$	−10.2933	−	10.2933i	−0.399758	−	0.399758i
$664$	8.89306	+	22.6685i	0.345118	+	0.879708i
$665$	−0.100198	+	0.0152996i	−0.00388549	+	0.000593291i
$666$	7.54637	−	32.2482i	0.292416	−	1.24959i
$667$	0.314378	−	5.46444i	0.0121728	−	0.211584i
$668$	4.17952	−	1.41132i	0.161710	−	0.0546055i
$669$	15.6125	−	1.19864i	0.603614	−	0.0463422i
$670$	3.61315	−	26.4392i	0.139588	−	1.02144i
$671$	−14.3827	+	52.3378i	−0.555237	+	2.02048i
$672$	1.28464	−	0.123421i	0.0495562	−	0.00476108i
$673$	9.71836	+	12.2551i	0.374615	+	0.472399i	0.934393	−	0.356244i	$-0.115943\pi$
$673$	9.71836	+	12.2551i	0.374615	+	0.472399i	−0.559778	+	0.828643i	$0.689114\pi$
$674$	6.11452	−	39.5865i	0.235522	−	1.52482i
$675$	5.25959	+	18.0264i	0.202442	+	0.693835i
$676$	0.0352508	+	0.128276i	0.00135580	+	0.00493369i
$677$	1.13439	+	2.97789i	0.0435981	+	0.114450i	0.954538	−	0.298089i	$-0.0963493\pi$
$677$	1.13439	+	2.97789i	0.0435981	+	0.114450i	−0.910940	+	0.412539i	$0.864642\pi$
$678$	8.91976	−	2.63596i	0.342561	−	0.101233i
$679$	16.2648	+	15.6533i	0.624188	+	0.600720i
$680$	0.637287	+	36.5565i	0.0244388	+	1.40188i
$681$	18.6322	+	5.89650i	0.713986	+	0.225955i
$682$	7.31649	+	15.5175i	0.280163	+	0.594194i
$683$	17.2732	−	25.5851i	0.660941	−	0.978986i	−0.338338	−	0.941025i	$-0.609865\pi$
$683$	17.2732	−	25.5851i	0.660941	−	0.978986i	0.999279	−	0.0379614i	$-0.0120864\pi$
$684$	−0.0122221	−	0.00492595i	−0.000467324	−	0.000188348i
$685$	6.97111	+	9.94723i	0.266352	+	0.380064i
$686$	14.3762	+	24.1817i	0.548885	+	0.923263i
$687$	−3.61207	+	7.66080i	−0.137809	+	0.292278i
$688$	−9.47474	+	10.2300i	−0.361221	+	0.390017i
$689$	−1.81672	−	11.7618i	−0.0692114	−	0.448088i
$690$	1.77558	−	3.25186i	0.0675951	−	0.123796i
$691$	−14.2270	+	10.0070i	−0.541221	+	0.380686i	−0.813529	−	0.581524i	$-0.802457\pi$
$691$	−14.2270	+	10.0070i	−0.541221	+	0.380686i	0.272309	+	0.962210i	$0.412213\pi$
$692$	0.572210	−	0.0329201i	0.0217522	−	0.00125143i
$693$	6.40444	−	15.0523i	0.243285	−	0.571789i
$694$	−18.8324	+	12.1958i	−0.714869	+	0.462944i
$695$	−0.417869	−	7.48854i	−0.0158507	−	0.284056i
$696$	5.48644	−	2.45953i	0.207963	−	0.0932283i
$697$	−47.1856	−	55.0334i	−1.78728	−	2.08454i
$698$	−7.10745	−	27.9482i	−0.269021	−	1.05786i
$699$	0.603625	−	3.11245i	0.0228312	−	0.117724i
$700$	1.47076	−	0.829964i	0.0555894	−	0.0313697i
$701$	3.16826	+	27.4439i	0.119664	+	1.03654i	0.907324	+	0.420432i	$0.138121\pi$
$701$	3.16826	+	27.4439i	0.119664	+	1.03654i	−0.787660	+	0.616110i	$0.788708\pi$
$702$	14.3357	−	13.2773i	0.541067	−	0.501119i
$703$	0.205965	+	0.106940i	0.00776810	+	0.00403332i
$704$	−15.2368	+	21.6621i	−0.574258	+	0.816422i
$705$	−0.624516	−	0.266992i	−0.0235206	−	0.0100555i
$706$	−3.77274	−	16.1222i	−0.141989	−	0.606767i
$707$	17.4299	−	3.03512i	0.655517	−	0.114147i
$708$	0.849787	−	1.63668i	0.0319370	−	0.0615101i
$709$	1.68993	−	44.0879i	0.0634665	−	1.65575i	−0.527866	−	0.849327i	$-0.677008\pi$
$709$	1.68993	−	44.0879i	0.0634665	−	1.65575i	0.591333	−	0.806428i	$-0.298602\pi$
$710$	−2.36491	−	8.66424i	−0.0887535	−	0.325163i
$711$	−20.9846	−	13.5895i	−0.786986	−	0.509647i
$712$	5.95495	−	4.02036i	0.223171	−	0.150669i
$713$	−4.93697	+	1.25551i	−0.184891	+	0.0470191i
$714$	−10.5278	−	0.808271i	−0.393995	−	0.0302488i
$715$	−15.9484	−	24.7205i	−0.596435	−	0.924493i
$716$	−1.31874	−	1.59907i	−0.0492837	−	0.0597600i
$717$	5.10073	+	1.09100i	0.190490	+	0.0407443i
$718$	−19.2951	−	8.20967i	−0.720086	−	0.306382i
$719$	15.0838	−	16.9254i	0.562533	−	0.631210i	−0.395295	−	0.918554i	$-0.629358\pi$
$719$	15.0838	−	16.9254i	0.562533	−	0.631210i	0.957827	+	0.287344i	$0.0927722\pi$
$720$	−24.7319	−	0.516499i	−0.921702	−	0.0192488i
$721$	−20.6210	−	15.7187i	−0.767967	−	0.585396i
$722$	−16.6384	+	22.7173i	−0.619218	+	0.845450i
$723$	14.0616	+	13.0234i	0.522957	+	0.484346i
$724$	−0.310697	−	0.865073i	−0.0115470	−	0.0321502i
$725$	11.0825	−	12.3495i	0.411595	−	0.458650i
$726$	1.35771	+	2.74211i	0.0503892	+	0.101769i
$727$	−12.1056	−	28.4517i	−0.448973	−	1.05522i	−0.978374	−	0.206844i	$-0.933681\pi$
$727$	−12.1056	−	28.4517i	−0.448973	−	1.05522i	0.529400	−	0.848372i	$-0.322417\pi$
$728$	13.3604	+	9.01996i	0.495168	+	0.334302i
$729$	−4.94885	−	1.77741i	−0.183291	−	0.0658301i
$730$	24.6452	−	17.9852i	0.912159	−	0.665663i
$731$	15.5789	−	11.8753i	0.576207	−	0.439224i
$732$	0.0369679	+	1.92959i	0.00136637	+	0.0713198i
$733$	−6.24629	−	21.1367i	−0.230712	−	0.780701i	−0.991318	−	0.131487i	$-0.958025\pi$
$733$	−6.24629	−	21.1367i	−0.230712	−	0.780701i	0.760606	−	0.649214i	$-0.224902\pi$
$734$	5.83622	+	2.61633i	0.215419	+	0.0965706i
$735$	2.50038	+	5.60344i	0.0922280	+	0.206686i
$736$	1.26742	+	1.31693i	0.0467178	+	0.0485429i
$737$	−24.3458	+	17.8311i	−0.896787	+	0.656818i
$738$	34.9602	−	27.7236i	1.28690	−	1.02052i
$739$	6.00135	−	7.27706i	0.220763	−	0.267691i	−0.649408	−	0.760440i	$-0.724983\pi$
$739$	6.00135	−	7.27706i	0.220763	−	0.267691i	0.870172	+	0.492749i	$0.164008\pi$
$740$	−3.84036	−	0.450065i	−0.141174	−	0.0165447i
$741$	0.0299920	+	0.0551544i	0.00110178	+	0.00202615i
$742$	−6.55351	−	5.61897i	−0.240587	−	0.206279i
$743$	10.2782	+	30.4382i	0.377071	+	1.11667i	0.953983	+	0.299862i	$0.0969406\pi$
$743$	10.2782	+	30.4382i	0.377071	+	1.11667i	−0.576912	+	0.816806i	$0.695742\pi$
$744$	−3.72302	−	4.17755i	−0.136493	−	0.153156i
$745$	3.58490	−	3.06297i	0.131340	−	0.112219i
$746$		−	13.3421i		−	0.488487i
$747$	22.8380	−	3.75926i	0.835599	−	0.137544i
$748$	−3.18713	+	3.18713i	−0.116533	+	0.116533i
$749$	−7.08141	−	1.65711i	−0.258749	−	0.0605496i
$750$	10.3580	−	4.34396i	0.378221	−	0.158619i
$751$	9.13389	+	4.52247i	0.333300	+	0.165027i	0.602630	−	0.798020i	$-0.294119\pi$
$751$	9.13389	+	4.52247i	0.333300	+	0.165027i	−0.269330	+	0.963048i	$0.586802\pi$
$752$	1.27010	−	1.48134i	0.0463159	−	0.0540191i
$753$	−4.49638	+	15.2152i	−0.163857	+	0.554472i
$754$	−16.6490	−	4.57524i	−0.606322	−	0.166620i
$755$	−21.7841	+	5.49988i	−0.792805	+	0.200161i
$756$	0.145473	−	1.26011i	0.00529080	−	0.0458296i
$757$	12.2241	+	16.6902i	0.444292	+	0.606615i	0.969719	−	0.244224i	$-0.0785333\pi$
$757$	12.2241	+	16.6902i	0.444292	+	0.606615i	−0.525427	+	0.850839i	$0.676094\pi$
$758$	−0.709874	+	37.0529i	−0.0257838	+	1.34582i
$759$	−4.04013	+	1.11025i	−0.146647	+	0.0402994i
$760$	0.0420462	−	0.151977i	0.00152517	−	0.00551280i
$761$	−17.7368	−	9.64494i	−0.642957	−	0.349629i	0.123107	−	0.992393i	$-0.460714\pi$
$761$	−17.7368	−	9.64494i	−0.642957	−	0.349629i	−0.766064	+	0.642765i	$0.777787\pi$
$762$	7.65586	−	0.146674i	0.277343	−	0.00531344i
$763$	−1.78037	−	0.240176i	−0.0644538	−	0.00869494i
$764$	0.761865	−	2.40739i	0.0275633	−	0.0870964i
$765$	34.1054	+	6.67541i	1.23308	+	0.241350i
$766$	−5.13550	+	0.995971i	−0.185553	+	0.0359859i
$767$	44.7026	−	19.0200i	1.61412	−	0.686774i
$768$	−1.01363	+	3.00179i	−0.0365762	+	0.108318i
$769$	−3.32685	+	1.97783i	−0.119969	+	0.0713224i	−0.569758	−	0.821813i	$-0.692963\pi$
$769$	−3.32685	+	1.97783i	−0.119969	+	0.0713224i	0.449788	+	0.893135i	$0.351499\pi$
$770$	−20.4534	−	6.08275i	−0.737089	−	0.219207i
$771$	2.56542	−	0.0983346i	0.0923912	−	0.00354143i
$772$	0.522963	+	0.383025i	0.0188219	+	0.0137854i
$773$	2.86467	+	21.2352i	0.103035	+	0.763778i	0.966005	+	0.258523i	$0.0832357\pi$
$773$	2.86467	+	21.2352i	0.103035	+	0.763778i	−0.862970	+	0.505255i	$0.831398\pi$
$774$	6.93651	+	9.86163i	0.249328	+	0.354469i
$775$	−14.0700	−	6.36586i	−0.505409	−	0.228669i
$776$	−32.5724	+	13.1279i	−1.16928	+	0.471263i
$777$	−2.14253	+	10.0169i	−0.0768630	+	0.359355i
$778$	−3.57982	+	37.2609i	−0.128343	+	1.33587i
$779$	0.127895	+	0.285293i	0.00458230	+	0.0102217i
$780$	−0.792926	−	0.682231i	−0.0283913	−	0.0244278i
$781$	−5.19020	+	8.73028i	−0.185720	+	0.312394i
$782$	−8.36741	−	12.3938i	−0.299218	−	0.443202i
$783$	−2.60687	−	12.1878i	−0.0931619	−	0.435556i
$784$	−17.5121	+	2.02169i	−0.625434	+	0.0722032i
$785$	38.6095	−	4.38981i	1.37803	−	0.156679i
$786$	−2.95893	−	9.34983i	−0.105542	−	0.333497i
$787$	0.967034	+	5.55342i	0.0344710	+	0.197958i	0.997426	−	0.0717047i	$-0.0228439\pi$
$787$	0.967034	+	5.55342i	0.0344710	+	0.197958i	−0.962955	+	0.269663i	$0.913088\pi$
$788$	−0.335464	+	0.540432i	−0.0119504	+	0.0192521i
$789$	9.51237	−	2.22598i	0.338649	−	0.0792470i
$790$	−14.5213	+	29.2013i	−0.516643	+	1.03894i
$791$	15.1650	−	4.79924i	0.539204	−	0.170641i
$792$	17.2925	+	18.6710i	0.614462	+	0.663445i
$793$	−31.5900	+	39.8358i	−1.12180	+	1.41461i
$794$	−11.7625	+	18.1634i	−0.417436	+	0.644596i
$795$	−3.48517	−	3.77604i	−0.123606	−	0.133922i
$796$	−4.63976	−	2.75836i	−0.164452	−	0.0977676i
$797$	37.4187	−	32.0828i	1.32544	−	1.13643i	0.345220	−	0.938522i	$-0.387804\pi$
$797$	37.4187	−	32.0828i	1.32544	−	1.13643i	0.980220	−	0.197909i	$-0.0634151\pi$
$798$	0.0425555	+	0.0162109i	0.00150645	+	0.000573861i
$799$	−2.11489	+	1.74413i	−0.0748193	+	0.0617031i
$800$	0.510871	+	5.51734i	0.0180620	+	0.195067i
$801$	−2.55296	−	6.33432i	−0.0902044	−	0.223812i
$802$	1.07936	+	18.7611i	0.0381134	+	0.662479i
$803$	−33.9912	−	5.91900i	−1.19952	−	0.208877i
$804$	−0.650481	+	0.853351i	−0.0229407	+	0.0300954i
$805$	2.92942	−	5.61830i	0.103248	−	0.198019i
$806$	0.615506	+	16.0577i	0.0216803	+	0.565609i
$807$	−14.8361	−	6.99523i	−0.522255	−	0.246244i
$808$	−6.78366	+	26.6750i	−0.238648	+	0.938424i
$809$	−32.1308	+	15.9090i	−1.12966	+	0.559330i	−0.909322	−	0.416093i	$-0.863399\pi$
$809$	−32.1308	+	15.9090i	−1.12966	+	0.559330i	−0.220338	+	0.975424i	$0.570716\pi$
$810$	−3.86115	+	16.3727i	−0.135667	+	0.575277i
$811$	4.69694	+	24.2187i	0.164932	+	0.850433i	0.967306	+	0.253612i	$0.0816186\pi$
$811$	4.69694	+	24.2187i	0.164932	+	0.850433i	−0.802374	+	0.596821i	$0.796430\pi$
$812$	−1.01384	+	0.478028i	−0.0355789	+	0.0167755i
$813$	1.25885	+	2.42452i	0.0441498	+	0.0850318i
$814$	29.6186	+	38.8559i	1.03813	+	1.36190i
$815$	2.45095	+	1.73029i	0.0858531	+	0.0606094i
$816$	8.62621	−	15.8633i	0.301978	−	0.555328i
$817$	−0.0789496	+	0.0300748i	−0.00276210	+	0.00105218i
$818$	17.1213	−	30.0972i	0.598632	−	1.05232i
$819$	11.0401	−	10.6250i	0.385771	−	0.371267i
$820$	−3.67707	−	3.68977i	−0.128409	−	0.128853i
$821$	−20.3253	−	2.34646i	−0.709358	−	0.0818919i	−0.247554	−	0.968874i	$-0.579627\pi$
$821$	−20.3253	−	2.34646i	−0.709358	−	0.0818919i	−0.461804	+	0.886982i	$0.652798\pi$
$822$	−0.521903	−	5.43229i	−0.0182035	−	0.189473i
$823$	−30.6004	+	17.4076i	−1.06666	+	0.606789i	−0.923770	−	0.382949i	$-0.874909\pi$
$823$	−30.6004	+	17.4076i	−1.06666	+	0.606789i	−0.142892	+	0.989738i	$0.545640\pi$
$824$	35.4375	−	19.2703i	1.23452	−	0.671313i
$825$	−11.6708	−	5.01329i	−0.406324	−	0.174540i
$826$	15.6358	−	31.5790i	0.544038	−	1.09878i
$827$	−54.1774	−	3.11691i	−1.88393	−	0.108385i	−0.922937	−	0.384952i	$-0.874218\pi$
$827$	−54.1774	−	3.11691i	−1.88393	−	0.108385i	−0.960995	+	0.276566i	$0.910803\pi$
$828$	0.699875	−	0.434436i	0.0243223	−	0.0150977i
$829$	23.1876			0.805337			0.402669	−	0.915346i	$-0.368083\pi$
$829$	23.1876			0.805337			0.402669	+	0.915346i	$0.368083\pi$
$830$	−8.23801	−	29.0469i	−0.285946	−	1.00823i
$831$	9.34264			0.324092
$832$	−21.0767	+	13.0830i	−0.730704	+	0.453572i
$833$	24.7247	+	1.42245i	0.856661	+	0.0492850i
$834$	−1.49520	+	3.01980i	−0.0517745	+	0.104567i
$835$	48.8754	−	11.3484i	1.69140	−	0.392728i
$836$	0.0170776	−	0.00928650i	0.000590641	−	0.000321180i
$837$	−10.0824	+	5.73555i	−0.348499	+	0.198250i
$838$	−1.61240	−	16.7829i	−0.0556996	−	0.579756i
$839$	8.19725	+	0.946332i	0.283000	+	0.0326710i	0.255014	−	0.966937i	$-0.417920\pi$
$839$	8.19725	+	0.946332i	0.283000	+	0.0326710i	0.0279862	+	0.999608i	$0.491091\pi$
$840$	6.96013	+	0.0120054i	0.240147	+	0.000414225i
$841$	12.9598	−	12.4725i	0.446889	−	0.430087i
$842$	−28.1753	+	49.5288i	−0.970986	+	1.70688i
$843$	−3.01624	+	1.14900i	−0.103885	+	0.0395736i
$844$	0.187908	−	0.345558i	0.00646808	−	0.0118946i
$845$	0.257006	+	1.49113i	0.00884129	+	0.0512965i
$846$	−1.02286	−	1.34186i	−0.0351665	−	0.0461341i
$847$	2.41128	+	4.64408i	0.0828525	+	0.159573i
$848$	13.3530	−	6.29596i	0.458545	−	0.216204i
$849$	2.51624	+	12.9744i	0.0863572	+	0.445281i
$850$	3.62617	−	45.1885i	0.124377	−	1.54995i
$851$	−13.0010	+	6.43718i	−0.445667	+	0.220664i
$852$	−0.0890061	+	0.349994i	−0.00304930	+	0.0119906i
$853$	−10.9474	−	5.16170i	−0.374832	−	0.176733i	0.229801	−	0.973238i	$-0.426192\pi$
$853$	−10.9474	−	5.16170i	−0.374832	−	0.176733i	−0.604633	+	0.796504i	$0.706680\pi$
$854$	1.41251	+	36.8506i	0.0483352	+	1.26100i
$855$	−0.132901	−	0.0692957i	−0.00454513	−	0.00236986i
$856$	6.85904	−	8.99821i	0.234437	−	0.307553i
$857$	21.9922	+	3.82958i	0.751241	+	0.130816i	0.534213	−	0.845350i	$-0.320608\pi$
$857$	21.9922	+	3.82958i	0.751241	+	0.130816i	0.217027	+	0.976166i	$0.430364\pi$
$858$	0.759149	+	13.1954i	0.0259169	+	0.450482i
$859$	−10.2773	−	25.4997i	−0.350657	−	0.870040i	−0.994486	−	0.104870i	$-0.966557\pi$
$859$	−10.2773	−	25.4997i	−0.350657	−	0.870040i	0.643829	−	0.765170i	$-0.277345\pi$
$860$	1.05247	−	0.934709i	0.0358891	−	0.0318733i
$861$	−10.6466	+	8.78018i	−0.362835	+	0.299228i
$862$	7.13445	+	2.71777i	0.243000	+	0.0925677i
$863$	4.83574	−	4.14616i	0.164611	−	0.141137i	−0.564762	−	0.825254i	$-0.691032\pi$
$863$	4.83574	−	4.14616i	0.164611	−	0.141137i	0.729372	+	0.684117i	$0.239812\pi$
$864$	3.57745	+	2.12681i	0.121707	+	0.0723557i
$865$	6.51394	+	0.260938i	0.221481	+	0.00887216i
$866$	−14.8720	+	22.9650i	−0.505370	+	0.780382i
$867$	−8.60220	+	10.8476i	−0.292146	+	0.368403i
$868$	0.708857	+	0.765365i	0.0240602	+	0.0259782i
$869$	35.1619	−	11.1277i	1.19278	−	0.377480i
$870$	−7.06728	+	2.37287i	−0.239603	+	0.0804479i
$871$	−27.5229	+	6.44060i	−0.932577	+	0.218231i
$872$	1.47398	−	2.37457i	0.0499152	−	0.0804133i
$873$	5.72646	+	32.8855i	0.193811	+	1.11301i
$874$	0.0194591	+	0.0614883i	0.000658215	+	0.00207987i
$875$	17.5682	−	7.76675i	0.593912	−	0.262564i
$876$	−1.21871	+	0.140694i	−0.0411763	+	0.00475361i
$877$	−4.08023	−	19.0762i	−0.137780	−	0.644156i	−0.992209	−	0.124588i	$-0.960239\pi$
$877$	−4.08023	−	19.0762i	−0.137780	−	0.644156i	0.854429	−	0.519568i	$-0.173907\pi$
$878$	−17.9087	−	26.5264i	−0.604390	−	0.895223i
$879$	1.99000	−	3.34732i	0.0671209	−	0.112902i
$880$	23.8006	−	27.6624i	0.802318	−	0.932499i
$881$	3.64653	+	8.13426i	0.122855	+	0.274050i	0.963584	−	0.267405i	$-0.0861662\pi$
$881$	3.64653	+	8.13426i	0.122855	+	0.274050i	−0.840729	+	0.541455i	$0.817874\pi$
$882$	−1.45775	+	15.1732i	−0.0490850	+	0.510907i
$883$	−6.74222	+	31.5217i	−0.226894	+	1.06079i	0.708097	+	0.706115i	$0.249554\pi$
$883$	−6.74222	+	31.5217i	−0.226894	+	1.06079i	−0.934991	+	0.354673i	$0.884592\pi$
$884$	−3.91581	+	1.57821i	−0.131703	+	0.0530810i
$885$	11.4320	−	17.5864i	0.384281	−	0.591161i
$886$	−1.05468	−	1.49944i	−0.0354328	−	0.0503748i
$887$	1.18958	+	8.81814i	0.0399423	+	0.296084i	0.999874	+	0.0158512i	$0.00504582\pi$
$887$	1.18958	+	8.81814i	0.0399423	+	0.296084i	−0.959932	+	0.280233i	$0.909588\pi$
$888$	−12.8565	−	9.41628i	−0.431437	−	0.315990i
$889$	13.0855	−	0.501577i	0.438872	−	0.0168223i
$890$	−7.83383	+	4.24241i	−0.262591	+	0.142206i
$891$	16.3518	−	9.72124i	0.547806	−	0.325674i
$892$	1.45291	−	4.30268i	0.0486470	−	0.144064i
$893$	0.0108790	−	0.00462881i	0.000364053	−	0.000154897i
$894$	−2.07971	+	0.403335i	−0.0695558	+	0.0134896i
$895$	−13.1577	−	19.5619i	−0.439814	−	0.653882i
$896$	−6.57802	+	20.7857i	−0.219756	+	0.694400i
$897$	−3.88937	−	0.524683i	−0.129862	−	0.0175187i
$898$	46.4309	−	0.889542i	1.54942	−	0.0296844i
$899$	9.00475	+	4.89663i	0.300325	+	0.163312i
$900$	2.47976	+	0.294948i	0.0826587	+	0.00983161i
$901$	−19.9985	+	5.49568i	−0.666246	+	0.183088i
$902$	−1.26079	+	65.8088i	−0.0419797	+	2.19119i
$903$	−2.20342	−	3.00844i	−0.0733253	−	0.100115i
$904$	−2.83792	+	24.5825i	−0.0943880	+	0.817600i
$905$	−2.55925	−	10.1368i	−0.0850723	−	0.336957i
$906$	9.73346	+	2.67480i	0.323373	+	0.0888643i
$907$	5.71504	−	19.3390i	0.189765	−	0.642140i	−0.808775	−	0.588118i	$-0.799869\pi$
$907$	5.71504	−	19.3390i	0.189765	−	0.642140i	0.998540	−	0.0540221i	$-0.0172041\pi$
$908$	3.68930	−	4.30290i	0.122434	−	0.142797i
$909$	23.4453	+	11.6085i	0.777633	+	0.385031i
$910$	−15.3982	−	12.7435i	−0.510446	−	0.422443i
$911$	−35.3169	−	8.26448i	−1.17010	−	0.273814i	−0.402915	−	0.915238i	$-0.632003\pi$
$911$	−35.3169	−	8.26448i	−1.17010	−	0.273814i	−0.767187	+	0.641423i	$0.778344\pi$
$912$	−0.0550675	+	0.0550675i	−0.00182347	+	0.00182347i
$913$	−17.1569	+	29.5201i	−0.567810	+	0.976974i
$914$			21.5333i			0.712260i
$915$	−1.71812	+	21.8842i	−0.0567994	+	0.723469i
$916$	1.63432	+	1.83385i	0.0539995	+	0.0605921i
$917$	−5.36556	−	15.8897i	−0.177186	−	0.524725i
$918$	−25.8502	−	22.1640i	−0.853185	−	0.731520i
$919$	−0.405579	−	0.745847i	−0.0133788	−	0.0246032i	0.871737	−	0.489975i	$-0.162994\pi$
$919$	−0.405579	−	0.745847i	−0.0133788	−	0.0246032i	−0.885116	+	0.465371i	$0.845921\pi$
$920$	6.11148	+	7.73408i	0.201489	+	0.254985i
$921$	−11.0924	+	13.4504i	−0.365508	+	0.443205i
$922$	12.9950	−	10.3051i	0.427966	−	0.339380i
$923$	−7.67507	+	5.62131i	−0.252628	+	0.185028i
$924$	0.594986	+	0.618230i	0.0195736	+	0.0203383i
$925$	−42.9750	−	9.34715i	−1.41301	−	0.307332i
$926$	−35.8735	−	16.0818i	−1.17888	−	0.528481i
$927$	−10.8662	−	36.7697i	−0.356891	−	1.20768i
$928$	−0.0704454	−	3.67700i	−0.00231248	−	0.120703i
$929$	18.1703	−	13.8506i	0.596149	−	0.454425i	−0.263961	−	0.964533i	$-0.585029\pi$
$929$	18.1703	−	13.8506i	0.596149	−	0.454425i	0.860110	+	0.510109i	$0.170395\pi$
$930$	4.09004	+	5.60459i	0.134118	+	0.183782i
$931$	−0.100523	−	0.0361036i	−0.00329452	−	0.00118325i
$932$	−0.762093	−	0.514510i	−0.0249632	−	0.0168533i
$933$	−7.60629	−	17.8770i	−0.249019	−	0.585265i
$934$	15.7978	+	31.9062i	0.516919	+	1.04400i
$935$	−39.6078	+	32.5497i	−1.29531	+	1.06449i
$936$	8.05741	+	22.4342i	0.263365	+	0.733286i
$937$	16.5078	+	15.2890i	0.539287	+	0.499471i	0.901591	−	0.432589i	$-0.142400\pi$
$937$	16.5078	+	15.2890i	0.539287	+	0.499471i	−0.362304	+	0.932060i	$0.618010\pi$
$938$	−12.1148	+	16.5410i	−0.395564	+	0.540083i
$939$	4.33455	+	3.30408i	0.141453	+	0.107825i
$940$	−0.142167	+	0.136350i	−0.00463697	+	0.00444726i
$941$	17.8134	−	19.9882i	0.580700	−	0.651596i	−0.381363	−	0.924426i	$-0.624545\pi$
$941$	17.8134	−	19.9882i	0.580700	−	0.651596i	0.962062	+	0.272830i	$0.0879597\pi$
$942$	−16.0646	−	6.83516i	−0.523413	−	0.222702i
$943$	−19.1120	−	4.08790i	−0.622372	−	0.133120i
$944$	38.3411	+	46.4913i	1.24790	+	1.51316i
$945$	3.04206	−	14.1035i	0.0989584	−	0.458786i
$946$	−17.7339	−	1.36151i	−0.576579	−	0.0442666i
$947$	−24.1710	+	6.14686i	−0.785451	+	0.199746i	−0.618046	−	0.786142i	$-0.712075\pi$
$947$	−24.1710	+	6.14686i	−0.785451	+	0.199746i	−0.167405	+	0.985888i	$0.553539\pi$
$948$	1.08685	−	0.733763i	0.0352992	−	0.0238315i
$949$	−27.1266	−	17.5670i	−0.880568	−	0.570250i
$950$	−0.0702306	+	0.182468i	−0.00227858	+	0.00592005i
$951$	0.531665	−	13.8704i	0.0172404	−	0.449779i
$952$	12.9449	−	24.9316i	0.419546	−	0.808039i
$953$	−26.0018	+	4.52778i	−0.842282	+	0.146669i	−0.576228	−	0.817289i	$-0.695476\pi$
$953$	−26.0018	+	4.52778i	−0.842282	+	0.146669i	−0.266054	+	0.963958i	$0.585720\pi$
$954$	−2.90860	−	12.4294i	−0.0941694	−	0.402418i
$955$	11.2901	−	26.4084i	0.365338	−	0.854555i
$956$	0.870346	−	1.23737i	0.0281490	−	0.0400194i
$957$	7.48220	+	3.88487i	0.241865	+	0.125580i
$958$	−8.25486	+	7.64539i	−0.266702	+	0.247011i
$959$	−1.07032	−	9.27122i	−0.0345623	−	0.299383i
$960$	−4.39834	+	9.76616i	−0.141956	+	0.315201i
$961$	−4.08588	+	21.0679i	−0.131802	+	0.679609i
$962$	11.2791	+	44.3520i	0.363651	+	1.42997i
$963$	−7.00006	−	8.16429i	−0.225574	−	0.263091i
$964$	5.07230	−	2.27388i	0.163368	−	0.0732366i
$965$	5.49589	+	4.91496i	0.176919	+	0.158218i
$966$	−2.38943	+	1.54738i	−0.0768786	+	0.0497861i
$967$	−4.08785	+	9.60761i	−0.131456	+	0.308960i	−0.972840	−	0.231478i	$-0.925644\pi$
$967$	−4.08785	+	9.60761i	−0.131456	+	0.308960i	0.841384	+	0.540438i	$0.181741\pi$
$968$	−8.12728	+	0.467575i	−0.261221	+	0.0150284i
$969$	0.0894872	−	0.0629439i	0.00287474	−	0.00202205i
$970$	41.7798	−	12.2684i	1.34147	−	0.393915i
$971$	4.13219	+	26.7526i	0.132608	+	0.858532i	0.956489	+	0.291768i	$0.0942436\pi$
$971$	4.13219	+	26.7526i	0.132608	+	0.858532i	−0.823881	+	0.566763i	$0.808195\pi$
$972$	1.96470	−	2.12132i	0.0630176	−	0.0680412i
$973$	−2.45762	+	5.21234i	−0.0787876	+	0.167100i
$974$	−3.00444	−	5.05369i	−0.0962686	−	0.161931i
$975$	−8.22061	−	8.60094i	−0.263270	−	0.275450i
$976$	−58.4936	−	23.5751i	−1.87234	−	0.754619i
$977$	−11.9199	+	17.6558i	−0.381352	+	0.564859i	−0.969869	−	0.243626i	$-0.921663\pi$
$977$	−11.9199	+	17.6558i	−0.381352	+	0.564859i	0.588517	+	0.808485i	$0.299712\pi$
$978$	−0.574852	−	1.21920i	−0.0183817	−	0.0389856i
$979$	9.60519	+	3.03975i	0.306983	+	0.0971508i
$980$	1.77933	−	0.0310190i	0.0568387	−	0.000990866i
$981$	−1.91409	−	1.84213i	−0.0611122	−	0.0588146i
$982$	−56.2093	+	16.6109i	−1.79371	+	0.530076i
$983$	−7.84833	−	20.6027i	−0.250323	−	0.657125i	0.749666	−	0.661816i	$-0.230214\pi$
$983$	−7.84833	−	20.6027i	−0.250323	−	0.657125i	−0.999989	+	0.00469105i	$0.998507\pi$
$984$	−5.68890	−	20.7016i	−0.181356	−	0.659943i
$985$	−4.39591	+	5.74631i	−0.140065	+	0.183093i
$986$	−4.59310	+	29.7366i	−0.146274	+	0.947006i
$987$	0.324250	+	0.408887i	0.0103210	+	0.0130150i
$988$	0.0181249	−	0.00174133i	0.000576629	−	5.53992e-5i
$989$	1.39944	−	5.09247i	0.0444995	−	0.161931i
$990$	−19.0856	−	25.1278i	−0.606581	−	0.798613i
$991$	37.7590	−	2.89893i	1.19945	−	0.0920874i	0.538573	−	0.842579i	$-0.318964\pi$
$991$	37.7590	−	2.89893i	1.19945	−	0.0920874i	0.660880	+	0.750491i	$0.270183\pi$
$992$	−3.24288	+	1.09504i	−0.102961	+	0.0347675i
$993$	−0.322825	+	5.61127i	−0.0102445	+	0.178068i
$994$	−1.57232	+	6.71906i	−0.0498710	+	0.213116i
$995$	−49.4684	−	36.3626i	−1.56825	−	1.15277i
$996$	−0.287560	+	1.17949i	−0.00911168	+	0.0373736i
$997$	33.2947	+	33.2947i	1.05445	+	1.05445i	0.998429	+	0.0560232i	$0.0178421\pi$
$997$	33.2947	+	33.2947i	1.05445	+	1.05445i	0.0560232	+	0.998429i	$0.482158\pi$
$998$	−28.2404	−	45.4952i	−0.893934	−	1.44013i
$999$	−24.6617	+	21.9784i	−0.780262	+	0.695367i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	415.2.l.a.102.11	✓	3200
5.3	odd	4	inner	415.2.l.a.268.30	yes	3200
83.35	odd	82	inner	415.2.l.a.367.30	yes	3200
415.118	even	164	inner	415.2.l.a.118.11	yes	3200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
415.2.l.a.102.11	✓	3200	1.1	even	1	trivial
415.2.l.a.118.11	yes	3200	415.118	even	164	inner
415.2.l.a.268.30	yes	3200	5.3	odd	4	inner
415.2.l.a.367.30	yes	3200	83.35	odd	82	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:	\( N \)	\(=\)	\( 415 = 5 \cdot 83 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	415.l (of order \(164\), degree \(80\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25922 + 0.781639i) q^{2} +(0.676722 + 0.0389329i) q^{3} +(0.0872318 - 0.176179i) q^{4} +(1.18255 - 1.89778i) q^{5} +(-0.882573 + 0.479928i) q^{6} +(-1.49333 + 0.849508i) q^{7} +(-0.255612 - 2.66056i) q^{8} +(-2.52377 - 0.291357i) q^{9} +(-0.00571634 + 3.31405i) q^{10} +(2.70035 - 2.59882i) q^{11} +(0.0658908 - 0.115828i) q^{12} +(3.28050 - 1.24966i) q^{13} +(1.21642 - 2.23696i) q^{14} +(0.874147 - 1.23823i) q^{15} +(2.63983 + 3.46313i) q^{16} +(-2.81899 - 5.42933i) q^{17} +(3.40571 - 1.60580i) q^{18} +(0.00502328 + 0.0259014i) q^{19} +(-0.231192 - 0.373888i) q^{20} +(-1.04364 + 0.516741i) q^{21} +(-1.36898 + 5.38318i) q^{22} +(-1.49181 - 0.703388i) q^{23} +(-0.0693947 - 1.81041i) q^{24} +(-2.20313 - 4.48845i) q^{25} +(-3.15408 + 4.13776i) q^{26} +(-3.69992 - 0.644280i) q^{27} +(0.0193995 + 0.337198i) q^{28} +(1.24056 + 3.07804i) q^{29} +(-0.132894 + 2.24247i) q^{30} +(2.38284 - 1.96511i) q^{31} +(-1.03559 - 0.394495i) q^{32} +(1.92856 - 1.65355i) q^{33} +(7.79350 + 4.63328i) q^{34} +(-0.153768 + 3.83860i) q^{35} +(-0.271484 + 0.419219i) q^{36} +(5.46535 - 6.89194i) q^{37} +(-0.0265709 - 0.0286891i) q^{38} +(2.26864 - 0.717954i) q^{39} +(-5.35143 - 2.66117i) q^{40} +(11.5382 - 2.70005i) q^{41} +(0.910271 - 1.46644i) q^{42} +(0.549324 + 3.15462i) q^{43} +(-0.222302 - 0.702444i) q^{44} +(-3.53743 + 4.44501i) q^{45} +(2.42831 - 0.280336i) q^{46} +(-0.0937262 - 0.438194i) q^{47} +(1.65160 + 2.44635i) q^{48} +(-2.06875 + 3.47979i) q^{49} +(6.28257 + 3.92989i) q^{50} +(-1.69629 - 3.78390i) q^{51} +(0.0659996 - 0.686965i) q^{52} +(0.709103 - 3.31524i) q^{53} +(5.16261 - 2.08072i) q^{54} +(-1.73868 - 8.19791i) q^{55} +(2.64188 + 3.75596i) q^{56} +(0.00239095 + 0.0177236i) q^{57} +(-3.96806 - 2.90626i) q^{58} +(13.8287 - 0.530065i) q^{59} +(-0.141897 - 0.262019i) q^{60} +(-12.4490 + 7.40097i) q^{61} +(-1.46450 + 4.33702i) q^{62} +(4.01633 - 1.70887i) q^{63} +(-6.93738 + 1.34542i) q^{64} +(1.50779 - 7.70345i) q^{65} +(-1.13600 + 3.58962i) q^{66} +(-7.97978 - 1.07649i) q^{67} +(-1.20244 + 0.0230368i) q^{68} +(-0.982154 - 0.534079i) q^{69} +(-2.80678 - 4.95383i) q^{70} +(-2.61316 + 0.718108i) q^{71} +(-0.130069 + 6.78912i) q^{72} +(-5.43977 - 7.42720i) q^{73} +(-1.49506 + 12.9504i) q^{74} +(-1.31616 - 3.12321i) q^{75} +(0.00500147 + 0.00137443i) q^{76} +(-1.82479 + 6.17487i) q^{77} +(-2.29553 + 2.67732i) q^{78} +(8.81890 + 4.36651i) q^{79} +(9.69400 - 0.914471i) q^{80} +(4.94237 + 1.15656i) q^{81} +(-12.4187 + 12.4187i) q^{82} +(-8.76045 + 2.50089i) q^{83} +0.228945i q^{84} +(-13.6373 - 1.07066i) q^{85} +(-3.15749 - 3.54298i) q^{86} +(0.719680 + 2.13128i) q^{87} +(-7.60457 - 6.52015i) q^{88} +(1.28420 + 2.36161i) q^{89} +(0.979998 - 8.36223i) q^{90} +(-3.83727 + 4.65297i) q^{91} +(-0.254055 + 0.201467i) q^{92} +(1.68903 - 1.23706i) q^{93} +(0.460532 + 0.478523i) q^{94} +(0.0550954 + 0.0210967i) q^{95} +(-0.685450 - 0.307282i) q^{96} +(-3.72367 - 12.6004i) q^{97} +(-0.114928 - 5.99884i) q^{98} +(-7.57223 + 5.77206i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3200 q - 82 q^{2} - 78 q^{3} - 82 q^{5} - 164 q^{6} - 74 q^{7} - 82 q^{8} - 102 q^{10} - 164 q^{11} - 114 q^{12} - 82 q^{13} - 82 q^{15} - 96 q^{16} - 82 q^{17} - 82 q^{18} - 82 q^{20} - 148 q^{21} - 82 q^{22}+ \cdots + 246 q^{98}+O(q^{100}) \) 3200 * q - 82 * q^2 - 78 * q^3 - 82 * q^5 - 164 * q^6 - 74 * q^7 - 82 * q^8 - 102 * q^10 - 164 * q^11 - 114 * q^12 - 82 * q^13 - 82 * q^15 - 96 * q^16 - 82 * q^17 - 82 * q^18 - 82 * q^20 - 148 * q^21 - 82 * q^22 - 86 * q^23 - 74 * q^25 - 140 * q^26 - 90 * q^27 - 78 * q^28 - 114 * q^30 - 148 * q^31 - 82 * q^32 - 42 * q^33 - 82 * q^35 - 104 * q^36 - 66 * q^37 - 26 * q^38 - 130 * q^40 - 156 * q^41 - 82 * q^42 - 82 * q^43 - 82 * q^45 - 164 * q^46 - 82 * q^47 - 102 * q^48 - 82 * q^50 - 164 * q^51 - 82 * q^52 - 82 * q^53 - 82 * q^55 - 164 * q^56 - 82 * q^57 - 82 * q^58 - 82 * q^60 - 100 * q^61 - 82 * q^62 - 38 * q^63 - 134 * q^65 - 164 * q^66 - 82 * q^67 + 182 * q^68 - 138 * q^70 - 164 * q^71 - 82 * q^72 + 164 * q^73 - 138 * q^75 - 164 * q^76 - 106 * q^77 + 606 * q^78 - 82 * q^80 - 188 * q^81 + 192 * q^83 - 82 * q^85 - 84 * q^86 - 54 * q^87 + 738 * q^88 - 198 * q^90 - 164 * q^91 - 82 * q^92 + 576 * q^93 - 50 * q^95 - 164 * q^96 - 82 * q^97 + 246 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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