LMFDB - Embedded newform 216.2.t.a.205.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(13,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 8]))

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

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

chi := DirichletCharacter("216.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, degree $6$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			205.27
Character	$\chi$	$=$	216.205
Dual form			216.2.t.a.157.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12116 - 0.861977i) q^{2} +(0.684682 - 1.59098i) q^{3} +(0.513991 - 1.93283i) q^{4} +(-1.15428 + 3.17134i) q^{5} +(-0.603749 - 2.37392i) q^{6} +(0.593321 - 3.36489i) q^{7} +(-1.08978 - 2.61005i) q^{8} +(-2.06242 - 2.17863i) q^{9} +O(q^{10})$	\(q+(1.12116 - 0.861977i) q^{2} +(0.684682 - 1.59098i) q^{3} +(0.513991 - 1.93283i) q^{4} +(-1.15428 + 3.17134i) q^{5} +(-0.603749 - 2.37392i) q^{6} +(0.593321 - 3.36489i) q^{7} +(-1.08978 - 2.61005i) q^{8} +(-2.06242 - 2.17863i) q^{9} +(1.43950 + 4.55054i) q^{10} +(-0.197048 - 0.541384i) q^{11} +(-2.72316 - 2.14112i) q^{12} +(4.30199 + 5.12691i) q^{13} +(-2.23525 - 4.28400i) q^{14} +(4.25523 + 4.00779i) q^{15} +(-3.47163 - 1.98691i) q^{16} +(1.15893 + 2.00733i) q^{17} +(-4.19023 - 0.664827i) q^{18} +(-0.353289 - 0.203971i) q^{19} +(5.53637 + 3.86106i) q^{20} +(-4.94723 - 3.24784i) q^{21} +(-0.687582 - 0.437127i) q^{22} +(1.15186 + 6.53250i) q^{23} +(-4.89869 - 0.0532318i) q^{24} +(-4.89486 - 4.10727i) q^{25} +(9.24249 + 2.03986i) q^{26} +(-4.87825 + 1.78960i) q^{27} +(-6.19878 - 2.87631i) q^{28} +(-2.24644 + 2.67721i) q^{29} +(8.22541 + 0.825457i) q^{30} +(-0.382945 - 2.17179i) q^{31} +(-5.60491 + 0.764819i) q^{32} +(-0.996245 - 0.0571774i) q^{33} +(3.02962 + 1.25156i) q^{34} +(9.98637 + 5.76564i) q^{35} +(-5.27097 + 2.86650i) q^{36} +(-1.05249 + 0.607656i) q^{37} +(-0.571912 + 0.0758426i) q^{38} +(11.1023 - 3.33407i) q^{39} +(9.53529 - 0.443366i) q^{40} +(5.09057 - 4.27150i) q^{41} +(-8.34619 + 0.623055i) q^{42} +(0.442145 + 1.21478i) q^{43} +(-1.14768 + 0.102592i) q^{44} +(9.28978 - 4.02591i) q^{45} +(6.92227 + 6.33109i) q^{46} +(-0.547022 + 3.10232i) q^{47} +(-5.53809 + 4.16288i) q^{48} +(-4.39261 - 1.59878i) q^{49} +(-9.02828 - 0.385648i) q^{50} +(3.98712 - 0.469453i) q^{51} +(12.1206 - 5.67980i) q^{52} -9.35460i q^{53} +(-3.92670 + 6.21136i) q^{54} +1.94436 q^{55} +(-9.42913 + 2.11841i) q^{56} +(-0.566405 + 0.422419i) q^{57} +(-0.210928 + 4.93796i) q^{58} +(-3.00302 + 8.25072i) q^{59} +(9.93351 - 6.16464i) q^{60} +(-4.67459 - 0.824257i) q^{61} +(-2.30137 - 2.10483i) q^{62} +(-8.55452 + 5.64720i) q^{63} +(-5.62474 + 5.68879i) q^{64} +(-21.2249 + 7.72523i) q^{65} +(-1.16623 + 0.794635i) q^{66} +(-9.67062 - 11.5250i) q^{67} +(4.47550 - 1.20826i) q^{68} +(11.1817 + 2.64011i) q^{69} +(16.1662 - 2.14383i) q^{70} +(-3.92323 - 6.79524i) q^{71} +(-3.43874 + 7.75726i) q^{72} +(0.641809 - 1.11165i) q^{73} +(-0.656224 + 1.58850i) q^{74} +(-9.88600 + 4.97543i) q^{75} +(-0.575829 + 0.578006i) q^{76} +(-1.93861 + 0.341829i) q^{77} +(9.57354 - 13.3079i) q^{78} +(3.84081 + 3.22282i) q^{79} +(10.3084 - 8.71628i) q^{80} +(-0.492839 + 8.98650i) q^{81} +(2.02541 - 9.17698i) q^{82} +(6.67152 - 7.95081i) q^{83} +(-8.82034 + 7.89277i) q^{84} +(-7.70366 + 1.35836i) q^{85} +(1.54283 + 0.980846i) q^{86} +(2.72128 + 5.40708i) q^{87} +(-1.19830 + 1.10430i) q^{88} +(-2.86501 + 4.96234i) q^{89} +(6.94507 - 12.5213i) q^{90} +(19.8040 - 11.4338i) q^{91} +(13.2182 + 1.13131i) q^{92} +(-3.71746 - 0.877728i) q^{93} +(2.06083 + 3.94971i) q^{94} +(1.05466 - 0.884962i) q^{95} +(-2.62077 + 9.44095i) q^{96} +(10.5548 - 3.84165i) q^{97} +(-6.30293 + 1.99385i) q^{98} +(-0.773079 + 1.54586i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	1.12116	−	0.861977i	0.792779	−	0.609510i
$2$	1.12116	−	0.861977i	0.792779	−	0.609510i
$3$	0.684682	−	1.59098i	0.395301	−	0.918551i
$3$	0.684682	−	1.59098i	0.395301	−	0.918551i
$4$	0.513991	−	1.93283i	0.256996	−	0.966413i
$5$	−1.15428	+	3.17134i	−0.516208	+	1.41827i	0.358460	+	0.933545i	$0.383302\pi$
$5$	−1.15428	+	3.17134i	−0.516208	+	1.41827i	−0.874667	+	0.484723i	$0.838920\pi$
$6$	−0.603749	−	2.37392i	−0.246480	−	0.969148i
$7$	0.593321	−	3.36489i	0.224254	−	1.27181i	−0.639851	−	0.768499i	$-0.721004\pi$
$7$	0.593321	−	3.36489i	0.224254	−	1.27181i	0.864106	−	0.503311i	$-0.167885\pi$
$8$	−1.08978	−	2.61005i	−0.385297	−	0.922793i
$9$	−2.06242	−	2.17863i	−0.687474	−	0.726209i
$10$	1.43950	+	4.55054i	0.455210	+	1.43901i
$11$	−0.197048	−	0.541384i	−0.0594121	−	0.163233i	0.906435	−	0.422344i	$-0.138793\pi$
$11$	−0.197048	−	0.541384i	−0.0594121	−	0.163233i	−0.965848	+	0.259111i	$0.916570\pi$
$12$	−2.72316	−	2.14112i	−0.786109	−	0.618088i
$13$	4.30199	+	5.12691i	1.19316	+	1.42195i	0.881779	+	0.471664i	$0.156346\pi$
$13$	4.30199	+	5.12691i	1.19316	+	1.42195i	0.311379	+	0.950286i	$0.399209\pi$
$14$	−2.23525	−	4.28400i	−0.597396	−	1.14495i
$15$	4.25523	+	4.00779i	1.09870	+	1.03481i
$16$	−3.47163	−	1.98691i	−0.867906	−	0.496728i
$17$	1.15893	+	2.00733i	0.281082	+	0.486849i	0.971652	−	0.236417i	$-0.0759732\pi$
$17$	1.15893	+	2.00733i	0.281082	+	0.486849i	−0.690569	+	0.723266i	$0.742640\pi$
$18$	−4.19023	−	0.664827i	−0.987646	−	0.156701i
$19$	−0.353289	−	0.203971i	−0.0810500	−	0.0467943i	0.458927	−	0.888474i	$-0.348234\pi$
$19$	−0.353289	−	0.203971i	−0.0810500	−	0.0467943i	−0.539977	+	0.841680i	$0.681567\pi$
$20$	5.53637	+	3.86106i	1.23797	+	0.863358i
$21$	−4.94723	−	3.24784i	−1.07957	−	0.708737i
$22$	−0.687582	−	0.437127i	−0.146593	−	0.0931957i
$23$	1.15186	+	6.53250i	0.240178	+	1.36212i	0.831429	+	0.555631i	$0.187523\pi$
$23$	1.15186	+	6.53250i	0.240178	+	1.36212i	−0.591250	+	0.806488i	$0.701365\pi$
$24$	−4.89869	−	0.0532318i	−0.999941	−	0.0108659i
$25$	−4.89486	−	4.10727i	−0.978971	−	0.821454i
$26$	9.24249	+	2.03986i	1.81260	+	0.400050i
$27$	−4.87825	+	1.78960i	−0.938820	+	0.344408i
$28$	−6.19878	−	2.87631i	−1.17146	−	0.543572i
$29$	−2.24644	+	2.67721i	−0.417154	+	0.497145i	−0.933171	−	0.359434i	$-0.882970\pi$
$29$	−2.24644	+	2.67721i	−0.417154	+	0.497145i	0.516016	+	0.856579i	$0.327414\pi$
$30$	8.22541	+	0.825457i	1.50175	+	0.150707i
$31$	−0.382945	−	2.17179i	−0.0687790	−	0.390065i	−0.999692	−	0.0248236i	$-0.992098\pi$
$31$	−0.382945	−	2.17179i	−0.0687790	−	0.390065i	0.930913	−	0.365241i	$-0.119014\pi$
$32$	−5.60491	+	0.764819i	−0.990818	+	0.135202i
$33$	−0.996245	−	0.0571774i	−0.173424	−	0.00995332i
$34$	3.02962	+	1.25156i	0.519575	+	0.214641i
$35$	9.98637	+	5.76564i	1.68801	+	0.974570i
$36$	−5.27097	+	2.86650i	−0.878496	+	0.477750i
$37$	−1.05249	+	0.607656i	−0.173028	+	0.0998980i	−0.584013	−	0.811744i	$-0.698518\pi$
$37$	−1.05249	+	0.607656i	−0.173028	+	0.0998980i	0.410985	+	0.911642i	$0.365185\pi$
$38$	−0.571912	+	0.0758426i	−0.0927763	+	0.0123033i
$39$	11.1023	−	3.33407i	1.77779	−	0.533878i
$40$	9.53529	−	0.443366i	1.50766	−	0.0701023i
$41$	5.09057	−	4.27150i	0.795014	−	0.667096i	−0.151967	−	0.988386i	$-0.548561\pi$
$41$	5.09057	−	4.27150i	0.795014	−	0.667096i	0.946981	+	0.321290i	$0.104116\pi$
$42$	−8.34619	+	0.623055i	−1.28785	+	0.0961395i
$43$	0.442145	+	1.21478i	0.0674265	+	0.185253i	0.968830	−	0.247728i	$-0.0796840\pi$
$43$	0.442145	+	1.21478i	0.0674265	+	0.185253i	−0.901403	+	0.432981i	$0.857462\pi$
$44$	−1.14768	+	0.102592i	−0.173020	+	0.0154663i
$45$	9.28978	−	4.02591i	1.38484	−	0.600148i
$46$	6.92227	+	6.33109i	1.02063	+	0.933468i
$47$	−0.547022	+	3.10232i	−0.0797914	+	0.452520i	0.918568	+	0.395263i	$0.129346\pi$
$47$	−0.547022	+	3.10232i	−0.0797914	+	0.452520i	−0.998359	+	0.0572567i	$0.981765\pi$
$48$	−5.53809	+	4.16288i	−0.799355	+	0.600860i
$49$	−4.39261	−	1.59878i	−0.627516	−	0.228397i
$50$	−9.02828	−	0.385648i	−1.27679	−	0.0545389i
$51$	3.98712	−	0.469453i	0.558308	−	0.0657366i
$52$	12.1206	−	5.67980i	1.68083	−	0.787647i
$53$		−	9.35460i		−	1.28495i	−0.766305	−	0.642477i	$-0.777907\pi$
$53$		−	9.35460i		−	1.28495i	0.766305	−	0.642477i	$-0.222093\pi$
$54$	−3.92670	+	6.21136i	−0.534356	+	0.845260i
$55$	1.94436			0.262178
$56$	−9.42913	+	2.11841i	−1.26002	+	0.283084i
$57$	−0.566405	+	0.422419i	−0.0750221	+	0.0559508i
$58$	−0.210928	+	4.93796i	−0.0276962	+	0.648385i
$59$	−3.00302	+	8.25072i	−0.390959	+	1.07415i	0.575605	+	0.817728i	$0.304767\pi$
$59$	−3.00302	+	8.25072i	−0.390959	+	1.07415i	−0.966564	+	0.256424i	$0.917456\pi$
$60$	9.93351	−	6.16464i	1.28241	−	0.795852i
$61$	−4.67459	−	0.824257i	−0.598520	−	0.105535i	−0.133824	−	0.991005i	$-0.542726\pi$
$61$	−4.67459	−	0.824257i	−0.598520	−	0.105535i	−0.464697	+	0.885470i	$0.653837\pi$
$62$	−2.30137	−	2.10483i	−0.292275	−	0.267314i
$63$	−8.55452	+	5.64720i	−1.07777	+	0.711480i
$64$	−5.62474	+	5.68879i	−0.703092	+	0.711099i
$65$	−21.2249	+	7.72523i	−2.63262	+	0.958196i
$66$	−1.16623	+	0.794635i	−0.143553	+	0.0978129i
$67$	−9.67062	−	11.5250i	−1.18145	−	1.40800i	−0.892731	−	0.450589i	$-0.851214\pi$
$67$	−9.67062	−	11.5250i	−1.18145	−	1.40800i	−0.288723	−	0.957413i	$-0.593231\pi$
$68$	4.47550	−	1.20826i	0.542734	−	0.146523i
$69$	11.1817	+	2.64011i	1.34612	+	0.317831i
$70$	16.1662	−	2.14383i	1.93222	−	0.256237i
$71$	−3.92323	−	6.79524i	−0.465602	−	0.806446i	0.533627	−	0.845720i	$-0.320829\pi$
$71$	−3.92323	−	6.79524i	−0.465602	−	0.806446i	−0.999228	+	0.0392740i	$0.987495\pi$
$72$	−3.43874	+	7.75726i	−0.405259	+	0.914202i
$73$	0.641809	−	1.11165i	0.0751180	−	0.130108i	−0.826020	−	0.563641i	$-0.809400\pi$
$73$	0.641809	−	1.11165i	0.0751180	−	0.130108i	0.901138	+	0.433533i	$0.142733\pi$
$74$	−0.656224	+	1.58850i	−0.0762844	+	0.184660i
$75$	−9.88600	+	4.97543i	−1.14154	+	0.574513i
$76$	−0.575829	+	0.578006i	−0.0660521	+	0.0663019i
$77$	−1.93861	+	0.341829i	−0.220925	+	0.0389551i
$78$	9.57354	−	13.3079i	1.08399	−	1.50683i
$79$	3.84081	+	3.22282i	0.432125	+	0.362596i	0.832753	−	0.553645i	$-0.186764\pi$
$79$	3.84081	+	3.22282i	0.432125	+	0.362596i	−0.400628	+	0.916241i	$0.631208\pi$
$80$	10.3084	−	8.71628i	1.15251	−	0.974510i
$81$	−0.492839	+	8.98650i	−0.0547599	+	0.998500i
$82$	2.02541	−	9.17698i	0.223669	−	1.01343i
$83$	6.67152	−	7.95081i	0.732295	−	0.872715i	−0.263468	−	0.964668i	$-0.584866\pi$
$83$	6.67152	−	7.95081i	0.732295	−	0.872715i	0.995763	+	0.0919529i	$0.0293109\pi$
$84$	−8.82034	+	7.89277i	−0.962378	+	0.861172i
$85$	−7.70366	+	1.35836i	−0.835580	+	0.147335i
$86$	1.54283	+	0.980846i	0.166368	+	0.105767i
$87$	2.72128	+	5.40708i	0.291752	+	0.579700i
$88$	−1.19830	+	1.10430i	−0.127739	+	0.117718i
$89$	−2.86501	+	4.96234i	−0.303690	+	0.526007i	−0.976969	−	0.213382i	$-0.931552\pi$
$89$	−2.86501	+	4.96234i	−0.303690	+	0.526007i	0.673278	+	0.739389i	$0.264886\pi$
$90$	6.94507	−	12.5213i	0.732075	−	1.31986i
$91$	19.8040	−	11.4338i	2.07602	−	1.19859i
$92$	13.2182	+	1.13131i	1.37809	+	0.117947i
$93$	−3.71746	−	0.877728i	−0.385483	−	0.0910161i
$94$	2.06083	+	3.94971i	0.212558	+	0.407381i
$95$	1.05466	−	0.884962i	0.108205	−	0.0907952i
$96$	−2.62077	+	9.44095i	−0.267481	+	0.963563i
$97$	10.5548	−	3.84165i	1.07168	−	0.390061i	0.254877	−	0.966974i	$-0.417965\pi$
$97$	10.5548	−	3.84165i	1.07168	−	0.390061i	0.816806	+	0.576913i	$0.195743\pi$
$98$	−6.30293	+	1.99385i	−0.636692	+	0.201409i
$99$	−0.773079	+	1.54586i	−0.0776974	+	0.155364i
$100$	−10.4546	+	7.34980i	−1.04546	+	0.734980i
$101$	−12.2411	−	2.15844i	−1.21804	−	0.214773i	−0.472557	−	0.881300i	$-0.656669\pi$
$101$	−12.2411	−	2.15844i	−1.21804	−	0.214773i	−0.745481	+	0.666527i	$0.767780\pi$
$102$	4.06553	−	3.96313i	0.402548	−	0.392409i
$103$	−14.8537	−	5.40632i	−1.46358	−	0.532701i	−0.517233	−	0.855844i	$-0.673038\pi$
$103$	−14.8537	−	5.40632i	−1.46358	−	0.532701i	−0.946350	+	0.323144i	$0.895260\pi$
$104$	8.69326	−	16.8156i	0.852444	−	1.64891i
$105$	16.0105	−	11.9405i	1.56246	−	1.16527i
$106$	−8.06345	−	10.4880i	−0.783192	−	1.01868i
$107$		−	2.44491i		−	0.236359i	−0.992992	−	0.118179i	$-0.962294\pi$
$107$		−	2.44491i		−	0.236359i	0.992992	−	0.118179i	$-0.0377058\pi$
$108$	0.951602	+	10.3486i	0.0915679	+	0.995799i
$109$			16.2522i			1.55668i	0.627843	+	0.778340i	$0.283938\pi$
$109$			16.2522i			1.55668i	−0.627843	+	0.778340i	$0.716062\pi$
$110$	2.17994	−	1.67600i	0.207849	−	0.159800i
$111$	0.246146	+	2.09054i	0.0233631	+	0.198425i
$112$	−8.74553	+	10.5028i	−0.826375	+	0.992418i
$113$	−11.4376	−	4.16294i	−1.07596	−	0.391617i	−0.257556	−	0.966263i	$-0.582917\pi$
$113$	−11.4376	−	4.16294i	−1.07596	−	0.391617i	−0.818402	+	0.574646i	$0.805140\pi$
$114$	−0.270914	+	0.961827i	−0.0253734	+	0.0900833i
$115$	−22.0464	−	3.88737i	−2.05583	−	0.362499i
$116$	4.01992	+	5.71804i	0.373240	+	0.530907i
$117$	2.29712	−	19.9463i	0.212369	−	1.84403i
$118$	3.74507	+	11.8389i	0.344762	+	1.08986i
$119$	7.44207	−	2.70869i	0.682213	−	0.248305i
$120$	5.82325	−	15.4740i	0.531588	−	1.41258i
$121$	8.17222	−	6.85731i	0.742929	−	0.623392i
$122$	−5.95145	+	3.10527i	−0.538819	+	0.281138i
$123$	−3.31044	−	11.0236i	−0.298492	−	0.993965i
$124$	−4.39452	−	0.376115i	−0.394639	−	0.0337762i
$125$	4.06195	−	2.34517i	0.363312	−	0.209758i
$126$	−4.72322	+	13.7052i	−0.420778	+	1.22096i
$127$	−4.79341	+	8.30243i	−0.425346	+	0.736722i	−0.996453	−	0.0841546i	$-0.973181\pi$
$127$	−4.79341	+	8.30243i	−0.425346	+	0.736722i	0.571106	+	0.820876i	$0.306514\pi$
$128$	−1.40262	+	11.2264i	−0.123975	+	0.992285i
$129$	2.23542	+	0.128297i	0.196818	+	0.0112960i
$130$	−17.1375	+	26.9566i	−1.50306	+	2.36425i
$131$	0.406480	−	0.0716734i	0.0355143	−	0.00626213i	−0.155863	−	0.987779i	$-0.549816\pi$
$131$	0.406480	−	0.0716734i	0.0355143	−	0.00626213i	0.191377	+	0.981517i	$0.438705\pi$
$132$	−0.622576	+	1.89618i	−0.0541882	+	0.165041i
$133$	−0.895956	+	1.06776i	−0.0776892	+	0.0925864i
$134$	−20.7766	−	4.58549i	−1.79482	−	0.396126i
$135$	−0.0445910	−	17.5363i	−0.00383778	−	1.50928i
$136$	3.97625	−	5.21243i	0.340960	−	0.446962i
$137$	12.0727	+	10.1302i	1.03144	+	0.865480i	0.991021	−	0.133703i	$-0.0426867\pi$
$137$	12.0727	+	10.1302i	1.03144	+	0.865480i	0.0404177	+	0.999183i	$0.487131\pi$
$138$	14.8122	−	6.67840i	1.26090	−	0.568503i
$139$	2.17442	−	0.383409i	0.184432	−	0.0325204i	−0.0806691	−	0.996741i	$-0.525706\pi$
$139$	2.17442	−	0.383409i	0.184432	−	0.0325204i	0.265101	+	0.964221i	$0.414595\pi$
$140$	16.2769	−	16.3384i	1.37565	−	1.38085i
$141$	4.56118	+	2.99440i	0.384121	+	0.252174i
$142$	−10.2559	−	4.23680i	−0.860656	−	0.355544i
$143$	1.92793	−	3.33928i	0.161222	−	0.279244i
$144$	2.83121	+	11.6612i	0.235934	+	0.971769i
$145$	−5.89733	−	10.2145i	−0.489747	−	0.848267i
$146$	−0.238644	−	1.79955i	−0.0197503	−	0.148932i
$147$	−5.55117	+	5.89389i	−0.457853	+	0.486120i
$148$	0.633521	+	2.34661i	0.0520751	+	0.192890i
$149$	−4.40044	−	5.24424i	−0.360498	−	0.429625i	0.555060	−	0.831810i	$-0.312695\pi$
$149$	−4.40044	−	5.24424i	−0.360498	−	0.429625i	−0.915558	+	0.402186i	$0.868251\pi$
$150$	−6.79506	+	14.0997i	−0.554814	+	1.15124i
$151$	11.0866	−	4.03519i	0.902213	−	0.328379i	0.151074	−	0.988522i	$-0.451727\pi$
$151$	11.0866	−	4.03519i	0.902213	−	0.328379i	0.751139	+	0.660144i	$0.229505\pi$
$152$	−0.147367	+	1.14439i	−0.0119531	+	0.0928221i
$153$	1.98302	−	6.66484i	0.160318	−	0.538821i
$154$	−1.87884	+	2.05428i	−0.151401	+	0.165539i
$155$	7.32952	+	1.29239i	0.588721	+	0.103807i
$156$	−0.737680	−	23.1725i	−0.0590617	−	1.85528i
$157$	4.12184	−	11.3247i	0.328959	−	0.903808i	−0.659417	−	0.751778i	$-0.729197\pi$
$157$	4.12184	−	11.3247i	0.328959	−	0.903808i	0.988376	−	0.152030i	$-0.0485810\pi$
$158$	7.08416	+	0.302604i	0.563585	+	0.0240739i
$159$	−14.8830	−	6.40493i	−1.18030	−	0.507944i
$160$	4.04411	−	18.6579i	0.319715	−	1.47504i
$161$	22.6646			1.78622
$162$	7.19360	+	10.5001i	0.565183	+	0.824966i
$163$			13.3972i			1.04935i	0.851303	+	0.524675i	$0.175813\pi$
$163$			13.3972i			1.04935i	−0.851303	+	0.524675i	$0.824187\pi$
$164$	−5.63955	−	12.0347i	−0.440375	−	0.939752i
$165$	1.33127	−	3.09344i	0.103639	−	0.240824i
$166$	0.626417	−	14.6648i	0.0486194	−	1.13821i
$167$	−6.36473	−	2.31657i	−0.492517	−	0.179262i	0.0838081	−	0.996482i	$-0.473292\pi$
$167$	−6.36473	−	2.31657i	−0.492517	−	0.179262i	−0.576325	+	0.817220i	$0.695514\pi$
$168$	−3.08562	+	16.4520i	−0.238060	+	1.26930i
$169$	−5.52068	+	31.3093i	−0.424668	+	2.40841i
$170$	−7.46615	+	8.16332i	−0.572627	+	0.626098i
$171$	0.284253	+	1.19036i	0.0217373	+	0.0910291i
$172$	2.57522	−	0.230201i	0.196359	−	0.0175526i
$173$	0.576454	+	1.58380i	0.0438270	+	0.120414i	0.959675	−	0.281111i	$-0.0907028\pi$
$173$	0.576454	+	1.58380i	0.0438270	+	0.120414i	−0.915848	+	0.401524i	$0.868481\pi$
$174$	7.71176	+	3.71651i	0.584627	+	0.281748i
$175$	−16.7247	+	14.0337i	−1.26427	+	1.06085i
$176$	−0.391606	+	2.27100i	−0.0295184	+	0.171183i
$177$	11.0706	+	10.4269i	0.832117	+	0.783730i
$178$	1.06530	+	8.03314i	0.0798473	+	0.602110i
$179$	10.3190	−	5.95768i	0.771279	−	0.445298i	−0.0620517	−	0.998073i	$-0.519764\pi$
$179$	10.3190	−	5.95768i	0.771279	−	0.445298i	0.833331	+	0.552775i	$0.186431\pi$
$180$	−3.00652	−	20.0248i	−0.224092	−	1.49256i
$181$	14.3027	+	8.25769i	1.06311	+	0.613789i	0.926292	−	0.376806i	$-0.122978\pi$
$181$	14.3027	+	8.25769i	1.06311	+	0.613789i	0.136822	+	0.990596i	$0.456311\pi$
$182$	12.3477	−	29.8897i	0.915271	−	2.21557i
$183$	−4.51198	+	6.87282i	−0.333536	+	0.508054i
$184$	15.7949	−	10.1254i	1.16441	−	0.746456i
$185$	−0.712223	−	4.03922i	−0.0523636	−	0.296969i
$186$	−4.92445	+	2.22030i	−0.361078	+	0.162800i
$187$	0.858372	−	1.02297i	0.0627703	−	0.0748068i
$188$	5.71507	+	2.65186i	0.416815	+	0.193407i
$189$	3.12744	+	17.4766i	0.227487	+	1.27123i
$190$	0.419620	−	1.90127i	0.0304424	−	0.137933i
$191$	−10.1267	−	8.49734i	−0.732745	−	0.614846i	0.198134	−	0.980175i	$-0.436512\pi$
$191$	−10.1267	−	8.49734i	−0.732745	−	0.614846i	−0.930878	+	0.365329i	$0.880956\pi$
$192$	5.19958	+	12.8438i	0.375247	+	0.926925i
$193$	−0.0307325	−	0.174293i	−0.00221218	−	0.0125459i	0.983682	−	0.179918i	$-0.0575831\pi$
$193$	−0.0307325	−	0.174293i	−0.00221218	−	0.0125459i	−0.985894	+	0.167372i	$0.946472\pi$
$194$	8.52224	−	13.4051i	0.611861	−	0.962433i
$195$	−2.24163	+	39.0576i	−0.160527	+	2.79698i
$196$	−5.34793	+	7.66839i	−0.381995	+	0.547742i
$197$	−0.841221	−	0.485679i	−0.0599345	−	0.0346032i	0.469733	−	0.882808i	$-0.344350\pi$
$197$	−0.841221	−	0.485679i	−0.0599345	−	0.0346032i	−0.529668	+	0.848205i	$0.677683\pi$
$198$	0.465748	+	2.39953i	0.0330993	+	0.170527i
$199$	2.04926	+	3.54942i	0.145268	+	0.251612i	0.929473	−	0.368890i	$-0.120262\pi$
$199$	2.04926	+	3.54942i	0.145268	+	0.251612i	−0.784205	+	0.620502i	$0.786929\pi$
$200$	−5.38585	+	17.2519i	−0.380837	+	1.21989i
$201$	−24.9573	+	7.49478i	−1.76035	+	0.528641i
$202$	−15.5848	+	8.13161i	−1.09654	+	0.572138i
$203$	7.67565	+	9.14748i	0.538725	+	0.642027i
$204$	1.14197	−	7.94770i	0.0799542	−	0.556450i
$205$	7.67047	+	21.0745i	0.535729	+	1.47190i
$206$	−21.3135	+	6.74225i	−1.48498	+	0.469755i
$207$	11.8563	−	15.9822i	0.824068	−	1.11084i
$208$	−4.74818	−	26.3464i	−0.329227	−	1.82679i
$209$	−0.0408121	+	0.231457i	−0.00282303	+	0.0160102i
$210$	7.65788	−	27.1878i	0.528444	−	1.87614i
$211$	1.28341	−	3.52613i	0.0883534	−	0.242749i	−0.887644	−	0.460530i	$-0.847660\pi$
$211$	1.28341	−	3.52613i	0.0883534	−	0.242749i	0.975998	+	0.217781i	$0.0698817\pi$
$212$	−18.0808	−	4.80819i	−1.24180	−	0.330228i
$213$	−13.4972	+	1.58920i	−0.924815	+	0.108890i
$214$	−2.10746	−	2.74114i	−0.144063	−	0.187380i
$215$	−4.36285			−0.297544
$216$	9.98719	+	10.7822i	0.679542	+	0.733636i
$217$	−7.53504			−0.511512
$218$	14.0090	+	18.2213i	0.948812	+	1.23410i
$219$	−1.32917	−	1.78223i	−0.0898169	−	0.120432i
$220$	0.999386	−	3.75811i	0.0673786	−	0.253372i
$221$	−5.30569	+	14.5773i	−0.356899	+	0.980572i
$222$	2.07797	+	2.13166i	0.139464	+	0.143067i
$223$	0.680991	−	3.86209i	0.0456025	−	0.258625i	−0.953480	−	0.301457i	$-0.902527\pi$
$223$	0.680991	−	3.86209i	0.0456025	−	0.258625i	0.999082	+	0.0428323i	$0.0136381\pi$
$224$	−0.751980	+	19.3137i	−0.0502437	+	1.29045i
$225$	1.14704	+	19.1350i	0.0764691	+	1.27567i
$226$	−16.4117	+	5.19162i	−1.09169	+	0.345342i
$227$	−4.04735	−	11.1200i	−0.268632	−	0.738061i	−0.998514	−	0.0544879i	$-0.982647\pi$
$227$	−4.04735	−	11.1200i	−0.268632	−	0.738061i	0.729882	−	0.683573i	$-0.239575\pi$
$228$	0.525335	+	1.31188i	0.0347912	+	0.0868815i
$229$	−6.81207	−	8.11831i	−0.450154	−	0.536473i	0.492470	−	0.870330i	$-0.336094\pi$
$229$	−6.81207	−	8.11831i	−0.450154	−	0.536473i	−0.942624	+	0.333857i	$0.891650\pi$
$230$	−28.0683	+	14.6451i	−1.85077	+	0.965669i
$231$	−0.783489	+	3.31833i	−0.0515498	+	0.218330i
$232$	9.43579	+	2.94575i	0.619490	+	0.193398i
$233$	−0.565006	−	0.978619i	−0.0370148	−	0.0641115i	0.846925	−	0.531713i	$-0.178452\pi$
$233$	−0.565006	−	0.978619i	−0.0370148	−	0.0641115i	−0.883939	+	0.467602i	$0.845118\pi$
$234$	−14.6178	−	24.3430i	−0.955596	−	1.59135i
$235$	−9.20711	−	5.31572i	−0.600605	−	0.346760i
$236$	14.4037	+	10.0451i	0.937599	+	0.653881i
$237$	7.75717	−	3.90404i	0.503883	−	0.253594i
$238$	6.00890	−	9.45176i	0.389499	−	0.612667i
$239$	1.00787	+	5.71591i	0.0651936	+	0.369731i	0.999898	+	0.0143045i	$0.00455341\pi$
$239$	1.00787	+	5.71591i	0.0651936	+	0.369731i	−0.934704	+	0.355427i	$0.884335\pi$
$240$	−6.80944	−	22.3683i	−0.439547	−	1.44387i
$241$	22.5974	+	18.9615i	1.45563	+	1.22142i	0.928342	+	0.371728i	$0.121235\pi$
$241$	22.5974	+	18.9615i	1.45563	+	1.22142i	0.527286	+	0.849688i	$0.323210\pi$
$242$	3.25151	−	14.7324i	0.209015	−	0.947034i
$243$	13.9599	+	6.93699i	0.895527	+	0.445008i
$244$	−3.99585	+	8.61151i	−0.255808	+	0.551295i
$245$	10.1406	−	12.0851i	0.647857	−	0.772086i
$246$	−13.2136	−	9.50569i	−0.842470	−	0.606061i
$247$	−0.474102	−	2.68876i	−0.0301664	−	0.171082i
$248$	−5.25115	+	3.36629i	−0.333449	+	0.213760i
$249$	−8.08169	−	16.0580i	−0.512157	−	1.01764i
$250$	2.53261	−	6.13061i	0.160176	−	0.387734i
$251$	−5.20730	−	3.00644i	−0.328682	−	0.189765i	0.326574	−	0.945172i	$-0.394106\pi$
$251$	−5.20730	−	3.00644i	−0.328682	−	0.189765i	−0.655256	+	0.755407i	$0.727439\pi$
$252$	6.51809	+	19.4370i	0.410601	+	1.22442i
$253$	3.30962	−	1.91081i	0.208074	−	0.120132i
$254$	1.78233	+	13.4401i	0.111833	+	0.843310i
$255$	−3.11343	+	13.1864i	−0.194971	+	0.825765i
$256$	8.10437	+	13.7956i	0.506523	+	0.862226i
$257$	19.8936	−	16.6927i	1.24093	−	1.04126i	0.243480	−	0.969906i	$-0.421711\pi$
$257$	19.8936	−	16.6927i	1.24093	−	1.04126i	0.997451	−	0.0713589i	$-0.0227336\pi$
$258$	2.61685	−	1.78304i	0.162918	−	0.111007i
$259$	1.42023	+	3.90205i	0.0882489	+	0.242462i
$260$	4.02210	+	44.9947i	0.249440	+	2.79045i
$261$	10.4658	−	0.627364i	0.647814	−	0.0388329i
$262$	0.393948	−	0.430734i	0.0243382	−	0.0266108i
$263$	−2.41565	+	13.6998i	−0.148956	+	0.844769i	0.815150	+	0.579250i	$0.196654\pi$
$263$	−2.41565	+	13.6998i	−0.148956	+	0.844769i	−0.964106	+	0.265519i	$0.914457\pi$
$264$	0.936457	+	2.66256i	0.0576349	+	0.163869i
$265$	29.6667	+	10.7978i	1.82241	+	0.663303i
$266$	−0.0841249	+	1.96942i	−0.00515803	+	0.120753i
$267$	5.93336	+	7.95579i	0.363115	+	0.486887i
$268$	−27.2464	+	12.7679i	−1.66434	+	0.779921i
$269$		−	3.89404i		−	0.237424i	−0.992929	−	0.118712i	$-0.962123\pi$
$269$		−	3.89404i		−	0.237424i	0.992929	−	0.118712i	$-0.0378765\pi$
$270$	−15.1659	−	19.6225i	−0.922966	−	1.19419i
$271$	27.1005			1.64624			0.823119	−	0.567869i	$-0.192232\pi$
$271$	27.1005			1.64624			0.823119	+	0.567869i	$0.192232\pi$
$272$	−0.0349931	−	9.27139i	−0.00212177	−	0.562161i
$273$	−4.63154	−	39.3362i	−0.280314	−	2.38073i
$274$	22.2674	+	0.951165i	1.34522	+	0.0574620i
$275$	−1.25909	+	3.45933i	−0.0759261	+	0.208605i
$276$	10.8502	−	20.2553i	0.653103	−	1.21923i
$277$	−7.05421	−	1.24385i	−0.423847	−	0.0747356i	−0.0423435	−	0.999103i	$-0.513482\pi$
$277$	−7.05421	−	1.24385i	−0.423847	−	0.0747356i	−0.381503	+	0.924368i	$0.624593\pi$
$278$	2.10738	−	2.30417i	0.126392	−	0.138195i
$279$	−3.94173	+	5.31344i	−0.235985	+	0.318107i
$280$	4.16561	−	32.3483i	0.248943	−	1.93318i
$281$	−0.728892	+	0.265295i	−0.0434820	+	0.0158262i	−0.363670	−	0.931528i	$-0.618476\pi$
$281$	−0.728892	+	0.265295i	−0.0434820	+	0.0158262i	0.320188	+	0.947354i	$0.396254\pi$
$282$	7.69491	−	0.574436i	0.458225	−	0.0342072i
$283$	0.982704	+	1.17114i	0.0584157	+	0.0696171i	0.794461	−	0.607315i	$-0.207753\pi$
$283$	0.982704	+	1.17114i	0.0584157	+	0.0696171i	−0.736045	+	0.676932i	$0.763309\pi$
$284$	−15.1505	+	4.09023i	−0.899017	+	0.242710i
$285$	−0.685850	−	2.28385i	−0.0406263	−	0.135284i
$286$	−0.716862	−	5.40569i	−0.0423889	−	0.319645i
$287$	−11.3528	−	19.6636i	−0.670134	−	1.16071i
$288$	13.2259	+	10.6336i	0.779346	+	0.626593i
$289$	5.81375	−	10.0697i	0.341985	−	0.592336i
$290$	−15.4165	−	6.36868i	−0.905288	−	0.373982i
$291$	1.11473	−	19.4228i	0.0653469	−	1.13859i
$292$	−1.81873	−	1.81188i	−0.106433	−	0.106032i
$293$	−15.6621	+	2.76164i	−0.914987	+	0.161337i	−0.611267	−	0.791424i	$-0.709340\pi$
$293$	−15.6621	+	2.76164i	−0.914987	+	0.161337i	−0.303720	+	0.952761i	$0.598229\pi$
$294$	−1.14334	+	11.3930i	−0.0666807	+	0.664451i
$295$	−22.6996	−	19.0472i	−1.32162	−	1.10897i
$296$	2.73300	+	2.08484i	0.158853	+	0.121179i
$297$	1.93011	+	2.28837i	0.111996	+	0.132785i
$298$	−9.45399	−	2.08654i	−0.547655	−	0.120870i
$299$	−28.5363	+	34.0082i	−1.65029	+	1.96674i
$300$	4.53532	+	21.6652i	0.261847	+	1.25084i
$301$	4.34995	−	0.767013i	0.250727	−	0.0442099i
$302$	8.95158	−	14.0805i	0.515105	−	0.810240i
$303$	−11.8153	+	17.9975i	−0.678772	+	1.03393i
$304$	0.821214	+	1.41007i	0.0470998	+	0.0808729i
$305$	8.00977	−	13.8733i	0.458638	−	0.794385i
$306$	−3.52166	−	9.18166i	−0.201320	−	0.524880i
$307$	0.370582	−	0.213955i	0.0211502	−	0.0122111i	−0.489388	−	0.872066i	$-0.662780\pi$
$307$	0.370582	−	0.213955i	0.0211502	−	0.0122111i	0.510538	+	0.859855i	$0.329446\pi$
$308$	−0.335733	+	3.92269i	−0.0191302	+	0.223516i
$309$	−18.7714	+	19.9304i	−1.06787	+	1.13380i
$310$	9.33156	−	4.86890i	0.529997	−	0.276535i
$311$	8.46179	−	7.10028i	0.479824	−	0.402620i	−0.370539	−	0.928817i	$-0.620827\pi$
$311$	8.46179	−	7.10028i	0.479824	−	0.402620i	0.850363	+	0.526197i	$0.176383\pi$
$312$	−20.8012	−	25.3442i	−1.17764	−	1.43483i
$313$	−26.1193	+	9.50664i	−1.47635	+	0.537347i	−0.949817	−	0.312807i	$-0.898731\pi$
$313$	−26.1193	+	9.50664i	−1.47635	+	0.537347i	−0.526533	+	0.850155i	$0.676508\pi$
$314$	−5.14037	−	16.2497i	−0.290088	−	0.917023i
$315$	−8.03493	−	33.6478i	−0.452717	−	1.89584i
$316$	8.20330	−	5.76711i	0.461472	−	0.324425i
$317$	−3.46040	−	0.610163i	−0.194356	−	0.0342701i	0.0756229	−	0.997136i	$-0.475905\pi$
$317$	−3.46040	−	0.610163i	−0.194356	−	0.0342701i	−0.269979	+	0.962866i	$0.587017\pi$
$318$	−22.2071	+	5.64784i	−1.24531	+	0.316715i
$319$	1.89205	+	0.688651i	0.105935	+	0.0385571i
$320$	−11.5486	−	24.4044i	−0.645587	−	1.36425i
$321$	−3.88980	−	1.67399i	−0.217108	−	0.0934329i
$322$	25.4106	−	19.5363i	1.41607	−	1.08872i
$323$		−	0.945557i		−	0.0526122i
$324$	17.1160	+	5.57155i	0.950889	+	0.309531i
$325$		−	42.7649i		−	2.37217i
$326$	11.5481	+	15.0204i	0.639589	+	0.831902i
$327$	25.8569	+	11.1276i	1.42989	+	0.615358i
$328$	−16.6965	−	8.63165i	−0.921908	−	0.476603i
$329$	10.1144	+	3.68134i	0.557625	+	0.202959i
$330$	−1.17391	−	4.61576i	−0.0646215	−	0.254089i
$331$	17.1533	+	3.02459i	0.942832	+	0.166247i	0.623876	−	0.781523i	$-0.285557\pi$
$331$	17.1533	+	3.02459i	0.942832	+	0.166247i	0.318956	+	0.947770i	$0.396668\pi$
$332$	−11.9384	−	16.9815i	−0.655206	−	0.931983i
$333$	3.49454	+	1.03974i	0.191499	+	0.0569776i
$334$	−9.13270	+	2.88901i	−0.499719	+	0.158079i
$335$	47.7123	−	17.3659i	2.60680	−	0.948798i
$336$	10.7218	+	21.1050i	0.584920	+	1.15137i
$337$	−2.18023	+	1.82943i	−0.118765	+	0.0996554i	−0.700236	−	0.713912i	$-0.746922\pi$
$337$	−2.18023	+	1.82943i	−0.118765	+	0.0996554i	0.581471	+	0.813567i	$0.302477\pi$
$338$	20.7984	+	39.8614i	1.13128	+	2.16818i
$339$	−14.4543	+	15.3467i	−0.785048	+	0.833516i
$340$	−1.33414	+	15.5880i	−0.0723538	+	0.845379i
$341$	−1.10031	+	0.635266i	−0.0595853	+	0.0344016i
$342$	1.34476	+	1.08956i	0.0727160	+	0.0589168i
$343$	3.97285	−	6.88117i	0.214514	−	0.371548i
$344$	2.68880	−	2.47787i	0.144971	−	0.133598i
$345$	−21.2795	+	32.4137i	−1.14565	+	1.74509i
$346$	2.01149	+	1.27879i	0.108138	+	0.0687484i
$347$	25.7859	−	4.54675i	1.38426	−	0.244082i	0.568599	−	0.822615i	$-0.307486\pi$
$347$	25.7859	−	4.54675i	1.38426	−	0.244082i	0.815659	+	0.578533i	$0.196374\pi$
$348$	11.8496	−	2.48056i	0.635208	−	0.132972i
$349$	−3.27963	+	3.90851i	−0.175555	+	0.209218i	−0.846646	−	0.532157i	$-0.821382\pi$
$349$	−3.27963	+	3.90851i	−0.175555	+	0.209218i	0.671091	+	0.741375i	$0.265826\pi$
$350$	−6.65433	+	30.1504i	−0.355689	+	1.61160i
$351$	−30.1613	−	17.3115i	−1.60989	−	0.924021i
$352$	1.51850	+	2.88371i	0.0809361	+	0.153702i
$353$	−11.4022	−	9.56754i	−0.606875	−	0.509229i	0.286772	−	0.957999i	$-0.407418\pi$
$353$	−11.4022	−	9.56754i	−0.606875	−	0.509229i	−0.893647	+	0.448770i	$0.851862\pi$
$354$	21.3996	+	2.14755i	1.13738	+	0.114141i
$355$	26.0785	−	4.59835i	1.38410	−	0.244055i
$356$	8.11875	+	8.08816i	0.430293	+	0.428672i
$357$	0.785982	−	13.6948i	0.0415986	−	0.724803i
$358$	6.43386	−	15.5743i	0.340040	−	0.823125i
$359$	−7.74329	+	13.4118i	−0.408675	+	0.707846i	−0.994742	−	0.102417i	$-0.967342\pi$
$359$	−7.74329	+	13.4118i	−0.408675	+	0.707846i	0.586066	+	0.810263i	$0.300676\pi$
$360$	−20.6317	−	19.8594i	−1.08739	−	1.04668i
$361$	−9.41679	−	16.3104i	−0.495621	−	0.858440i
$362$	23.1536	−	3.07045i	1.21693	−	0.161380i
$363$	−5.31445	−	17.6969i	−0.278936	−	0.928846i
$364$	−11.9205	−	44.1545i	−0.624805	−	2.31432i
$365$	2.78459	+	3.31854i	0.145752	+	0.173700i
$366$	0.865564	+	11.5947i	0.0452438	+	0.606067i
$367$	24.0744	−	8.76237i	1.25667	−	0.457392i	0.374023	−	0.927419i	$-0.377978\pi$
$367$	24.0744	−	8.76237i	1.25667	−	0.457392i	0.882652	+	0.470027i	$0.155756\pi$
$368$	8.98068	−	24.9670i	0.468150	−	1.30150i
$369$	−19.8049	−	2.28084i	−1.03100	−	0.118736i
$370$	−4.28022	−	3.91468i	−0.222518	−	0.203515i
$371$	−31.4772	−	5.55028i	−1.63422	−	0.288156i
$372$	−3.60724	+	6.73406i	−0.187027	+	0.349145i
$373$	4.86012	−	13.3531i	0.251648	−	0.691396i	−0.747970	−	0.663733i	$-0.768971\pi$
$373$	4.86012	−	13.3531i	0.251648	−	0.691396i	0.999617	−	0.0276634i	$-0.00880666\pi$
$374$	0.0805960	−	1.88680i	0.00416752	−	0.0975644i
$375$	−0.949965	−	8.06816i	−0.0490560	−	0.416638i
$376$	8.69335	−	1.95310i	0.448325	−	0.100724i
$377$	−23.3900			−1.20465
$378$	18.5708	+	16.8982i	0.955177	+	0.869152i
$379$			1.93137i			0.0992080i	0.998769	+	0.0496040i	$0.0157959\pi$
$379$			1.93137i			0.0992080i	−0.998769	+	0.0496040i	$0.984204\pi$
$380$	−1.16839	−	2.49333i	−0.0599373	−	0.127905i
$381$	9.92702	+	13.3107i	0.508577	+	0.681930i
$382$	−18.6782	−	0.797850i	−0.955659	−	0.0408216i
$383$	12.4377	+	4.52695i	0.635537	+	0.231317i	0.639639	−	0.768675i	$-0.279084\pi$
$383$	12.4377	+	4.52695i	0.635537	+	0.231317i	−0.00410258	+	0.999992i	$0.501306\pi$
$384$	16.9007	+	9.91806i	0.862458	+	0.506129i
$385$	1.15363	−	6.54257i	0.0587945	−	0.333440i
$386$	−0.184692	−	0.168919i	−0.00940060	−	0.00859776i
$387$	1.73467	−	3.46866i	0.0881783	−	0.176322i
$388$	−2.00014	−	22.3753i	−0.101542	−	1.13593i
$389$	−8.22522	−	22.5986i	−0.417035	−	1.14579i	−0.953374	−	0.301792i	$-0.902415\pi$
$389$	−8.22522	−	22.5986i	−0.417035	−	1.14579i	0.536339	−	0.844003i	$-0.319807\pi$
$390$	31.1536	+	45.7220i	1.57752	+	2.31523i
$391$	−11.7780	+	9.88288i	−0.595637	+	0.499799i
$392$	0.614104	+	13.2073i	0.0310169	+	0.667068i
$393$	0.164279	−	0.695774i	0.00828677	−	0.0350972i
$394$	−1.36179	+	0.180590i	−0.0686058	+	0.00909799i
$395$	−14.6540	+	8.46051i	−0.737325	+	0.425695i
$396$	2.59051	+	2.28878i	0.130178	+	0.115016i
$397$	28.6833	+	16.5603i	1.43957	+	0.831137i	0.997820	−	0.0659997i	$-0.0210236\pi$
$397$	28.6833	+	16.5603i	1.43957	+	0.831137i	0.441752	+	0.897137i	$0.354357\pi$
$398$	5.35707	+	2.21305i	0.268525	+	0.110930i
$399$	1.08534	+	2.15652i	0.0543347	+	0.107961i
$400$	8.83232	+	23.9846i	0.441616	+	1.19923i
$401$	1.94567	+	11.0344i	0.0971620	+	0.551033i	0.994063	+	0.108802i	$0.0347016\pi$
$401$	1.94567	+	11.0344i	0.0971620	+	0.551033i	−0.896901	+	0.442231i	$0.854187\pi$
$402$	−21.5208	+	29.9155i	−1.07336	+	1.49205i
$403$	9.48715	−	11.3063i	0.472588	−	0.563209i
$404$	−10.4637	+	22.5505i	−0.520590	+	1.12193i
$405$	−27.9304	−	11.9359i	−1.38787	−	0.593097i
$406$	16.4905	+	3.63954i	0.818412	+	0.180627i
$407$	0.536366	+	0.450065i	0.0265867	+	0.0223089i
$408$	−5.57040	−	9.89498i	−0.275776	−	0.489875i
$409$	1.95004	+	11.0592i	0.0964233	+	0.546844i	0.994302	+	0.106601i	$0.0339966\pi$
$409$	1.95004	+	11.0592i	0.0964233	+	0.546844i	−0.897879	+	0.440243i	$0.854892\pi$
$410$	26.7655	+	17.0160i	1.32185	+	0.840362i
$411$	24.3829	−	12.2714i	1.20272	−	0.605305i
$412$	−18.0842	+	25.9309i	−0.890943	+	1.27752i
$413$	25.9810	+	15.0001i	1.27844	+	0.738109i
$414$	−0.483555	−	28.1384i	−0.0237654	−	1.38293i
$415$	17.5140	+	30.3351i	0.859728	+	1.48909i
$416$	−28.0334	−	25.4457i	−1.37445	−	1.24758i
$417$	0.878792	−	3.72197i	0.0430347	−	0.182266i
$418$	0.153754	+	0.294679i	0.00752035	+	0.0144132i
$419$	−8.95678	−	10.6743i	−0.437567	−	0.521472i	0.501522	−	0.865145i	$-0.332774\pi$
$419$	−8.95678	−	10.6743i	−0.437567	−	0.521472i	−0.939090	+	0.343672i	$0.888329\pi$
$420$	−14.8496	−	37.0828i	−0.724586	−	1.80945i
$421$	4.06687	+	11.1736i	0.198207	+	0.544570i	0.998483	−	0.0550623i	$-0.0175358\pi$
$421$	4.06687	+	11.1736i	0.198207	+	0.544570i	−0.800276	+	0.599632i	$0.795314\pi$
$422$	−1.60054	−	5.05962i	−0.0779132	−	0.246298i
$423$	7.88699	−	5.20653i	0.383478	−	0.253150i
$424$	−24.4160	+	10.1945i	−1.18575	+	0.495089i
$425$	2.57184	−	14.5856i	0.124753	−	0.707507i
$426$	−13.7627	+	13.4161i	−0.666804	+	0.650010i
$427$	−5.54707	+	15.2404i	−0.268442	+	0.737537i
$428$	−4.72559	−	1.25666i	−0.228420	−	0.0607432i
$429$	−3.99269	−	5.35364i	−0.192769	−	0.258476i
$430$	−4.89145	+	3.76068i	−0.235887	+	0.181356i
$431$	−28.2506			−1.36079			−0.680393	−	0.732848i	$-0.738191\pi$
$431$	−28.2506			−1.36079			−0.680393	+	0.732848i	$0.738191\pi$
$432$	20.4912	+	3.47984i	0.985885	+	0.167424i
$433$	−27.8524			−1.33850			−0.669251	−	0.743036i	$-0.733385\pi$
$433$	−27.8524			−1.33850			−0.669251	+	0.743036i	$0.733385\pi$
$434$	−8.44798	+	6.49503i	−0.405516	+	0.311772i
$435$	−20.2888	+	2.38886i	−0.972774	+	0.114537i
$436$	31.4127	+	8.35350i	1.50440	+	0.400060i
$437$	0.925505	−	2.54280i	0.0442729	−	0.121639i
$438$	−3.02645	−	0.852446i	−0.144609	−	0.0407315i
$439$	−2.13242	+	12.0935i	−0.101775	+	0.577193i	0.890685	+	0.454621i	$0.150225\pi$
$439$	−2.13242	+	12.0935i	−0.101775	+	0.577193i	−0.992460	+	0.122572i	$0.960886\pi$
$440$	−2.11894	−	5.07489i	−0.101016	−	0.241936i
$441$	5.57627	+	12.8672i	0.265537	+	0.612725i
$442$	6.61674	+	20.9168i	0.314726	+	0.994910i
$443$	−7.22670	−	19.8552i	−0.343351	−	0.943348i	−0.984415	−	0.175861i	$-0.943729\pi$
$443$	−7.22670	−	19.8552i	−0.343351	−	0.943348i	0.641064	−	0.767487i	$-0.278493\pi$
$444$	4.16717	+	0.598764i	0.197765	+	0.0284161i
$445$	−12.4303	−	14.8138i	−0.589252	−	0.702243i
$446$	−2.56554	−	4.91701i	−0.121482	−	0.232827i
$447$	−11.3564	+	3.41036i	−0.537137	+	0.161305i
$448$	15.8049	+	22.3019i	0.746710	+	1.05367i
$449$	13.8708	+	24.0249i	0.654604	+	1.13381i	0.981993	+	0.188917i	$0.0604978\pi$
$449$	13.8708	+	24.0249i	0.654604	+	1.13381i	−0.327389	+	0.944890i	$0.606169\pi$
$450$	17.7799	+	20.4646i	0.838154	+	0.964712i
$451$	−3.31561	−	1.91427i	−0.156126	−	0.0901393i
$452$	−13.9251	+	19.9671i	−0.654980	+	0.939176i
$453$	1.17089	−	20.4013i	0.0550133	−	0.958538i
$454$	−14.1229	−	8.97856i	−0.662821	−	0.421385i
$455$	13.4014	+	76.0030i	0.628266	+	3.56307i
$456$	1.71980	+	1.01800i	0.0805368	+	0.0476722i
$457$	−26.0906	−	21.8926i	−1.22047	−	1.02409i	−0.998800	−	0.0489720i	$-0.984405\pi$
$457$	−26.0906	−	21.8926i	−1.22047	−	1.02409i	−0.221668	−	0.975122i	$-0.571150\pi$
$458$	−14.6352	−	3.23006i	−0.683858	−	0.150931i
$459$	−9.24588	−	7.71824i	−0.431561	−	0.360256i
$460$	−18.8452	+	40.6137i	−0.878664	+	1.89362i
$461$	−8.93591	+	10.6494i	−0.416187	+	0.495992i	−0.932884	−	0.360176i	$-0.882717\pi$
$461$	−8.93591	+	10.6494i	−0.416187	+	0.495992i	0.516698	+	0.856168i	$0.327161\pi$
$462$	1.98191	+	4.39572i	0.0922068	+	0.204508i
$463$	3.22751	+	18.3041i	0.149995	+	0.850665i	0.963220	+	0.268715i	$0.0865991\pi$
$463$	3.22751	+	18.3041i	0.149995	+	0.850665i	−0.813224	+	0.581950i	$0.802290\pi$
$464$	13.1182	−	4.83078i	0.608996	−	0.224263i
$465$	7.07455	−	10.7762i	0.328075	−	0.499735i
$466$	−1.47701	−	0.610165i	−0.0684211	−	0.0282653i
$467$	−8.34116	−	4.81577i	−0.385983	−	0.222847i	0.294435	−	0.955671i	$-0.404868\pi$
$467$	−8.34116	−	4.81577i	−0.385983	−	0.222847i	−0.680418	+	0.732824i	$0.738202\pi$
$468$	−37.3720	−	14.6921i	−1.72752	−	0.679145i
$469$	−44.5181	+	25.7026i	−2.05566	+	1.18683i
$470$	−14.9047	+	1.97654i	−0.687500	+	0.0911712i
$471$	−15.1952	−	14.3116i	−0.700156	−	0.659442i
$472$	24.8074	−	1.15348i	1.14186	−	0.0530933i
$473$	0.570541	−	0.478741i	0.0262335	−	0.0220125i
$474$	5.33183	−	11.0635i	0.244899	−	0.508166i
$475$	0.891532	+	2.44946i	0.0409063	+	0.112389i
$476$	−1.41027	−	15.7765i	−0.0646395	−	0.723113i
$477$	−20.3802	+	19.2931i	−0.933145	+	0.883372i
$478$	6.05696	+	5.53968i	0.277039	+	0.253379i
$479$	5.05443	−	28.6651i	0.230943	−	1.30974i	−0.620049	−	0.784563i	$-0.712887\pi$
$479$	5.05443	−	28.6651i	0.230943	−	1.30974i	0.850992	−	0.525179i	$-0.176002\pi$
$480$	−26.9154	−	19.2088i	−1.22852	−	0.876759i
$481$	−7.64321	−	2.78190i	−0.348500	−	0.126844i
$482$	41.6796	+	1.78037i	1.89846	+	0.0810937i
$483$	15.5180	−	36.0588i	0.706094	−	1.64073i
$484$	−9.05352	−	19.3201i	−0.411524	−	0.878185i
$485$			37.9074i			1.72129i
$486$	21.6308	−	4.25563i	0.981191	−	0.193039i
$487$	−13.1429			−0.595563			−0.297782	−	0.954634i	$-0.596247\pi$
$487$	−13.1429			−0.595563			−0.297782	+	0.954634i	$0.596247\pi$
$488$	2.94295	+	13.0992i	0.133221	+	0.592973i
$489$	21.3147	+	9.17282i	0.963882	+	0.414809i
$490$	0.952140	−	22.2902i	0.0430133	−	1.00697i
$491$	4.01945	−	11.0433i	0.181395	−	0.498379i	−0.815352	−	0.578965i	$-0.803457\pi$
$491$	4.01945	−	11.0433i	0.181395	−	0.498379i	0.996748	+	0.0805856i	$0.0256791\pi$
$492$	−23.0082	+	0.732451i	−1.03729	+	0.0330215i
$493$	−7.97752	−	1.40665i	−0.359289	−	0.0633524i
$494$	−2.84920	−	2.60587i	−0.128191	−	0.117243i
$495$	−4.01010	−	4.23604i	−0.180240	−	0.190396i
$496$	−2.98571	+	8.30052i	−0.134062	+	0.372704i
$497$	−25.1930	+	9.16949i	−1.13006	+	0.411308i
$498$	−22.9025	−	11.0374i	−1.02629	−	0.494596i
$499$	23.2598	+	27.7199i	1.04125	+	1.24091i	0.969911	+	0.243461i	$0.0782827\pi$
$499$	23.2598	+	27.7199i	1.04125	+	1.24091i	0.0713387	+	0.997452i	$0.477273\pi$
$500$	−2.44499	−	9.05643i	−0.109343	−	0.405016i
$501$	−8.04343	+	8.54003i	−0.359354	+	0.381540i
$502$	−8.42969	+	1.11788i	−0.376236	+	0.0498936i
$503$	1.18773	+	2.05720i	0.0529581	+	0.0917261i	0.891289	−	0.453435i	$-0.149802\pi$
$503$	1.18773	+	2.05720i	0.0529581	+	0.0917261i	−0.838331	+	0.545161i	$0.816468\pi$
$504$	24.0621	+	16.1735i	1.07181	+	0.720426i
$505$	20.9748	−	36.3294i	0.933366	−	1.61664i
$506$	2.06353	−	4.99514i	0.0917352	−	0.222061i
$507$	46.0326	+	30.2202i	2.04438	+	1.34213i
$508$	13.5834	+	13.5322i	0.602665	+	0.600394i
$509$	40.5051	−	7.14215i	1.79536	−	0.316570i	0.826269	−	0.563276i	$-0.190459\pi$
$509$	40.5051	−	7.14215i	1.79536	−	0.316570i	0.969090	+	0.246706i	$0.0793482\pi$
$510$	7.87573	+	17.4678i	0.348743	+	0.773485i
$511$	−3.35977	−	2.81918i	−0.148627	−	0.124713i
$512$	20.9778	+	8.48130i	0.927096	+	0.374824i
$513$	2.08846	+	0.362779i	0.0922077	+	0.0160171i
$514$	7.91515	−	35.8631i	0.349123	−	1.58185i
$515$	34.2906	−	40.8660i	1.51103	−	1.80077i
$516$	1.39696	−	4.25474i	0.0614979	−	0.187304i
$517$	1.78734	−	0.315155i	0.0786069	−	0.0138605i
$518$	4.95578	+	3.15061i	0.217745	+	0.138430i
$519$	2.91447	+	0.167270i	0.127931	+	0.00734234i
$520$	43.2938	+	46.9792i	1.89856	+	2.06017i
$521$	−5.21530	+	9.03316i	−0.228486	+	0.395750i	−0.957360	−	0.288899i	$-0.906711\pi$
$521$	−5.21530	+	9.03316i	−0.228486	+	0.395750i	0.728873	+	0.684649i	$0.240044\pi$
$522$	11.1930	−	9.72461i	0.489904	−	0.425635i
$523$	−14.6626	+	8.46543i	−0.641149	+	0.370167i	−0.785057	−	0.619424i	$-0.787366\pi$
$523$	−14.6626	+	8.46543i	−0.641149	+	0.370167i	0.143908	+	0.989591i	$0.454033\pi$
$524$	0.0703951	−	0.822494i	0.00307523	−	0.0359308i
$525$	10.8762	+	36.2173i	0.474677	+	1.58065i
$526$	9.10062	+	17.4419i	0.396806	+	0.760504i
$527$	3.91569	−	3.28565i	0.170570	−	0.143125i
$528$	3.34498	+	2.17795i	0.145572	+	0.0947831i
$529$	−19.7338	+	7.18252i	−0.857992	+	0.312283i
$530$	42.5685	−	13.4660i	1.84906	−	0.584924i
$531$	24.1687	−	10.4740i	1.04883	−	0.454533i
$532$	1.60328	+	2.28054i	0.0695109	+	0.0988741i
$533$	43.7992	+	7.72298i	1.89715	+	0.334519i
$534$	13.5099	+	3.80529i	0.584632	+	0.164671i
$535$	7.75366	+	2.82210i	0.335220	+	0.122010i
$536$	−19.5419	+	37.8006i	−0.844083	+	1.63274i
$537$	−2.41330	−	20.4964i	−0.104142	−	0.884486i
$538$	−3.35658	−	4.36584i	−0.144712	−	0.188225i
$539$			2.69313i			0.116001i
$540$	−33.9175	−	8.92733i	−1.45958	−	0.384171i
$541$		−	29.4745i		−	1.26721i	−0.773658	−	0.633603i	$-0.781575\pi$
$541$		−	29.4745i		−	1.26721i	0.773658	−	0.633603i	$-0.218425\pi$
$542$	30.3839	−	23.3600i	1.30510	−	1.00340i
$543$	22.9306	−	17.1015i	0.984048	−	0.733894i
$544$	−8.03096	−	10.3645i	−0.344325	−	0.444376i
$545$	−51.5414	−	18.7595i	−2.20779	−	0.803570i
$546$	−39.0996	−	40.1098i	−1.67331	−	1.71654i
$547$	−31.4846	−	5.55158i	−1.34618	−	0.237369i	−0.546333	−	0.837568i	$-0.683977\pi$
$547$	−31.4846	−	5.55158i	−1.34618	−	0.237369i	−0.799850	+	0.600199i	$0.795088\pi$
$548$	25.7851	−	18.1276i	1.10149	−	0.774371i
$549$	7.84523	+	11.8842i	0.334826	+	0.507204i
$550$	1.57022	+	4.96376i	0.0669543	+	0.211655i
$551$	1.33972	−	0.487617i	0.0570739	−	0.0207732i
$552$	−5.29485	−	32.0620i	−0.225364	−	1.36465i
$553$	13.1233	−	11.0117i	0.558059	−	0.468267i
$554$	−8.98106	+	4.68602i	−0.381569	+	0.199090i
$555$	−6.91395	−	1.63245i	−0.293481	−	0.0692935i
$556$	0.376572	−	4.39985i	0.0159702	−	0.186595i
$557$	7.19468	−	4.15385i	0.304849	−	0.176004i	−0.339770	−	0.940508i	$-0.610349\pi$
$557$	7.19468	−	4.15385i	0.304849	−	0.176004i	0.644619	+	0.764504i	$0.277016\pi$
$558$	0.160762	+	9.35488i	0.00680561	+	0.396024i
$559$	−4.32598	+	7.49282i	−0.182970	+	0.316913i
$560$	−23.2131	−	39.8582i	−0.980934	−	1.68432i
$561$	−1.03981	−	2.06606i	−0.0439007	−	0.0872290i
$562$	−0.588525	+	0.925725i	−0.0248254	+	0.0390494i
$563$	−6.57453	+	1.15927i	−0.277083	+	0.0488573i	−0.310463	−	0.950585i	$-0.600484\pi$
$563$	−6.57453	+	1.15927i	−0.277083	+	0.0488573i	0.0333796	+	0.999443i	$0.489373\pi$
$564$	8.13206	−	7.27687i	0.342422	−	0.306412i
$565$	26.4043	−	31.4674i	1.11084	−	1.32384i
$566$	2.11126	+	0.465966i	0.0887430	+	0.0195860i
$567$	29.9462	+	6.99023i	1.25762	+	0.293562i
$568$	−13.4604	+	17.6452i	−0.564787	+	0.740375i
$569$	−24.2709	−	20.3657i	−1.01749	−	0.853775i	−0.0281798	−	0.999603i	$-0.508971\pi$
$569$	−24.2709	−	20.3657i	−1.01749	−	0.853775i	−0.989310	+	0.145827i	$0.953416\pi$
$570$	−2.73758	−	1.96937i	−0.114664	−	0.0824880i
$571$	−32.6020	+	5.74861i	−1.36435	+	0.240572i	−0.807416	−	0.589983i	$-0.799134\pi$
$571$	−32.6020	+	5.74861i	−1.36435	+	0.240572i	−0.556936	+	0.830555i	$0.688023\pi$
$572$	−5.46329	−	5.44271i	−0.228432	−	0.227571i
$573$	−20.4527	+	10.2934i	−0.854423	+	0.430014i
$574$	−29.6778	−	12.2602i	−1.23873	−	0.511729i
$575$	21.1926	−	36.7066i	0.883791	−	1.53077i
$576$	23.9943	+	0.521532i	0.999764	+	0.0217305i
$577$	15.0611	+	26.0866i	0.627001	+	1.08600i	0.988150	+	0.153490i	$0.0490512\pi$
$577$	15.0611	+	26.0866i	0.627001	+	1.08600i	−0.361149	+	0.932508i	$0.617615\pi$
$578$	−2.16172	−	16.3011i	−0.0899159	−	0.678035i
$579$	−0.298338	−	0.0704404i	−0.0123985	−	0.00292740i
$580$	−22.7740	+	6.14836i	−0.945638	+	0.255297i
$581$	−22.7953	−	27.1663i	−0.945707	−	1.12705i
$582$	−15.4922	−	22.7370i	−0.642174	−	0.942477i
$583$	−5.06443	+	1.84330i	−0.209747	+	0.0763418i
$584$	−3.60089	−	0.463700i	−0.149006	−	0.0191880i
$585$	60.6050	+	30.3085i	2.50571	+	1.25310i
$586$	−15.1792	+	16.5966i	−0.627046	+	0.685598i
$587$	15.0318	+	2.65051i	0.620427	+	0.109398i	0.475022	−	0.879974i	$-0.342440\pi$
$587$	15.0318	+	2.65051i	0.620427	+	0.109398i	0.145406	+	0.989372i	$0.453551\pi$
$588$	8.53861	+	13.7588i	0.352126	+	0.567405i
$589$	−0.307693	+	0.845379i	−0.0126783	+	0.0348332i
$590$	−41.8681	−	1.78842i	−1.72368	−	0.0736281i
$591$	−1.34867	+	1.00583i	−0.0554770	+	0.0413743i
$592$	4.86121	−	0.0183477i	0.199795	−	0.000754087i
$593$	27.1813			1.11620			0.558101	−	0.829773i	$-0.311530\pi$
$593$	27.1813			1.11620			0.558101	+	0.829773i	$0.311530\pi$
$594$	4.13648	+	0.901917i	0.169722	+	0.0370061i
$595$			26.7279i			1.09574i
$596$	−12.3980	+	5.80978i	−0.507841	+	0.237978i
$597$	7.05014	−	0.830102i	0.288543	−	0.0339738i
$598$	−2.67939	+	62.7262i	−0.109568	+	2.56506i
$599$	−39.7660	−	14.4737i	−1.62480	−	0.591378i	−0.640509	−	0.767951i	$-0.721277\pi$
$599$	−39.7660	−	14.4737i	−1.62480	−	0.591378i	−0.984288	+	0.176573i	$0.943499\pi$
$600$	23.7597	+	20.3808i	0.969987	+	0.832043i
$601$	−0.648834	+	3.67972i	−0.0264665	+	0.150099i	−0.995177	−	0.0980937i	$-0.968726\pi$
$601$	−0.648834	+	3.67972i	−0.0264665	+	0.150099i	0.968711	+	0.248193i	$0.0798366\pi$
$602$	4.21583	−	4.60950i	0.171824	−	0.187869i
$603$	−5.16379	+	44.8381i	−0.210286	+	1.82595i
$604$	−2.10090	−	23.5025i	−0.0854844	−	0.956302i
$605$	12.3139	+	33.8321i	0.500631	+	1.37547i
$606$	2.26661	+	30.3626i	0.0920747	+	1.23340i
$607$	35.5497	−	29.8298i	1.44292	−	1.21075i	0.505370	−	0.862903i	$-0.331356\pi$
$607$	35.5497	−	29.8298i	1.44292	−	1.21075i	0.937550	−	0.347850i	$-0.113088\pi$
$608$	2.13616	+	0.873040i	0.0866325	+	0.0354065i
$609$	19.8088	−	5.94867i	0.802694	−	0.241052i
$610$	−2.97827	−	22.4584i	−0.120587	−	0.909315i
$611$	−18.2586	+	10.5416i	−0.738664	+	0.426468i
$612$	−11.8627	−	7.25850i	−0.479522	−	0.293407i
$613$	−21.9670	−	12.6827i	−0.887239	−	0.512248i	−0.0142005	−	0.999899i	$-0.504520\pi$
$613$	−21.9670	−	12.6827i	−0.887239	−	0.512248i	−0.873038	+	0.487652i	$0.837854\pi$
$614$	0.231056	−	0.559311i	0.00932466	−	0.0225719i
$615$	38.7808	+	2.22575i	1.56379	+	0.0897507i
$616$	3.00486	+	4.68735i	0.121069	+	0.188859i
$617$	1.23909	+	7.02722i	0.0498838	+	0.282905i	0.999538	−	0.0303950i	$-0.00967653\pi$
$617$	1.23909	+	7.02722i	0.0498838	+	0.282905i	−0.949654	+	0.313300i	$0.898565\pi$
$618$	−3.86622	+	38.5256i	−0.155522	+	1.54973i
$619$	−17.2889	+	20.6041i	−0.694900	+	0.828149i	−0.991939	−	0.126716i	$-0.959556\pi$
$619$	−17.2889	+	20.6041i	−0.694900	+	0.828149i	0.297039	+	0.954865i	$0.404001\pi$
$620$	6.26528	−	13.5024i	0.251620	−	0.542269i
$621$	−17.3096	−	29.8058i	−0.694610	−	1.19607i
$622$	3.36672	−	15.2544i	0.134993	−	0.611646i
$623$	14.9979	+	12.5847i	0.600877	+	0.504196i
$624$	−45.1675	−	10.4847i	−1.80815	−	0.419722i
$625$	−2.79914	−	15.8747i	−0.111966	−	0.634989i
$626$	−21.0893	+	33.1727i	−0.842900	+	1.32585i
$627$	0.340300	+	0.223406i	0.0135903	+	0.00892197i
$628$	−19.7700	−	13.7876i	−0.788910	−	0.550185i
$629$	−2.43953	−	1.40846i	−0.0972705	−	0.0561592i
$630$	−38.0120	−	30.7985i	−1.51444	−	1.22704i
$631$	−11.7466	−	20.3457i	−0.467624	−	0.809949i	0.531691	−	0.846938i	$-0.321557\pi$
$631$	−11.7466	−	20.3457i	−0.467624	−	0.809949i	−0.999316	+	0.0369893i	$0.988223\pi$
$632$	4.22608	−	13.5369i	0.168104	−	0.538469i
$633$	−4.73127	−	4.45615i	−0.188051	−	0.177116i
$634$	−4.40561	+	2.29870i	−0.174969	+	0.0912930i
$635$	−20.7970	−	24.7848i	−0.825302	−	0.983557i
$636$	−20.0293	+	25.4741i	−0.794214	+	1.01011i
$637$	−10.7002	−	29.3985i	−0.423956	−	1.16481i
$638$	2.71489	−	0.858820i	0.107484	−	0.0340010i
$639$	−6.71294	+	22.5619i	−0.265560	+	0.892535i
$640$	−33.9839	−	17.4066i	−1.34333	−	0.688055i
$641$	−7.57282	+	42.9476i	−0.299108	+	1.69633i	0.350911	+	0.936409i	$0.385872\pi$
$641$	−7.57282	+	42.9476i	−0.299108	+	1.69633i	−0.650019	+	0.759918i	$0.725239\pi$
$642$	−5.80402	+	1.47612i	−0.229067	+	0.0582576i
$643$	−0.120739	+	0.331727i	−0.00476148	+	0.0130820i	−0.942051	−	0.335471i	$-0.891105\pi$
$643$	−0.120739	+	0.331727i	−0.00476148	+	0.0130820i	0.937289	+	0.348553i	$0.113327\pi$
$644$	11.6494	−	43.8066i	0.459050	−	1.72622i
$645$	−2.98717	+	6.94120i	−0.117620	+	0.273310i
$646$	−0.815048	−	1.06012i	−0.0320676	−	0.0417098i
$647$	−26.0967			−1.02597			−0.512984	−	0.858398i	$-0.671460\pi$
$647$	−26.0967			−1.02597			−0.512984	+	0.858398i	$0.671460\pi$
$648$	23.9923	−	8.50701i	0.942507	−	0.334187i
$649$	5.05855			0.198565
$650$	−36.8624	−	47.9463i	−1.44586	−	1.88061i
$651$	−5.15911	+	11.9881i	−0.202201	+	0.469850i
$652$	25.8944	+	6.88605i	1.01410	+	0.269678i
$653$	0.281991	−	0.774764i	0.0110352	−	0.0303189i	−0.934053	−	0.357135i	$-0.883754\pi$
$653$	0.281991	−	0.774764i	0.0110352	−	0.0303189i	0.945088	+	0.326816i	$0.105976\pi$
$654$	38.5814	−	9.81226i	1.50865	−	0.383690i
$655$	−0.241889	+	1.37182i	−0.00945137	+	0.0536014i
$656$	−26.1597	+	4.71453i	−1.02136	+	0.184071i
$657$	−3.74554	+	0.894418i	−0.146127	+	0.0348946i
$658$	14.5131	−	4.59101i	0.565779	−	0.178976i
$659$	14.2971	+	39.2809i	0.556935	+	1.53017i	0.824058	+	0.566505i	$0.191705\pi$
$659$	14.2971	+	39.2809i	0.556935	+	1.53017i	−0.267123	+	0.963662i	$0.586073\pi$
$660$	−5.29481	−	4.16311i	−0.206100	−	0.162049i
$661$	1.06741	+	1.27208i	0.0415173	+	0.0494784i	0.786404	−	0.617713i	$-0.211941\pi$
$661$	1.06741	+	1.27208i	0.0415173	+	0.0494784i	−0.744886	+	0.667192i	$0.767496\pi$
$662$	21.8387	−	11.3947i	0.848786	−	0.442868i
$663$	19.5594	+	18.4220i	0.759624	+	0.715452i
$664$	−28.0226	−	8.74835i	−1.08749	−	0.339502i
$665$	−2.35205	−	4.07387i	−0.0912086	−	0.157978i
$666$	4.81416	−	1.84649i	0.186545	−	0.0715501i
$667$	−20.0764	−	11.5911i	−0.777362	−	0.448810i
$668$	−7.74894	+	11.1112i	−0.299816	+	0.429905i
$669$	−5.67824	−	3.72775i	−0.219533	−	0.144123i
$670$	38.5241	−	60.5968i	1.48831	−	2.34106i
$671$	0.474878	+	2.69317i	0.0183325	+	0.103969i
$672$	30.2128	+	14.4201i	1.16548	+	0.556269i
$673$	−4.23311	−	3.55200i	−0.163175	−	0.136920i	0.557544	−	0.830147i	$-0.311744\pi$
$673$	−4.23311	−	3.55200i	−0.163175	−	0.136920i	−0.720719	+	0.693227i	$0.756188\pi$
$674$	−0.867456	+	3.93039i	−0.0334132	+	0.151393i
$675$	31.2287	+	11.2765i	1.20199	+	0.434032i
$676$	57.6779	+	26.7632i	2.21838	+	1.02936i
$677$	−2.08429	+	2.48396i	−0.0801056	+	0.0954662i	−0.804609	−	0.593805i	$-0.797625\pi$
$677$	−2.08429	+	2.48396i	−0.0801056	+	0.0954662i	0.724503	+	0.689272i	$0.242069\pi$
$678$	−2.97705	+	29.6653i	−0.114333	+	1.13929i
$679$	−6.66432	−	37.7952i	−0.255753	−	1.45045i
$680$	11.9407	+	18.6266i	0.457906	+	0.714299i
$681$	−20.4628	−	1.17442i	−0.784137	−	0.0450040i
$682$	−0.686041	+	1.66068i	−0.0262699	+	0.0635907i
$683$	−22.4547	−	12.9642i	−0.859206	−	0.496063i	0.00454025	−	0.999990i	$-0.498555\pi$
$683$	−22.4547	−	12.9642i	−0.859206	−	0.496063i	−0.863746	+	0.503927i	$0.831888\pi$
$684$	2.44686	+	0.0624244i	0.0935581	+	0.00238686i
$685$	−46.0615	+	26.5936i	−1.75992	+	1.01609i
$686$	−1.47722	−	11.1394i	−0.0564006	−	0.425304i
$687$	−17.5801	+	5.27939i	−0.670724	+	0.201421i
$688$	0.878705	−	5.09578i	0.0335003	−	0.194275i
$689$	47.9602	−	40.2434i	1.82714	−	1.53315i
$690$	4.08218	+	54.6832i	0.155406	+	2.08176i
$691$	10.2247	+	28.0920i	0.388964	+	1.06867i	0.967469	+	0.252991i	$0.0814145\pi$
$691$	10.2247	+	28.0920i	0.388964	+	1.06867i	−0.578504	+	0.815679i	$0.696363\pi$
$692$	3.35749	−	0.300128i	0.127633	−	0.0114092i
$693$	4.74295	+	3.51852i	0.180170	+	0.133657i
$694$	24.9909	−	27.3245i	0.948640	−	1.03722i
$695$	−1.29396	+	7.33841i	−0.0490827	+	0.278362i
$696$	11.1471	−	12.9952i	0.422531	−	0.492583i
$697$	14.4739	+	5.26808i	0.548240	+	0.199543i
$698$	−0.307938	+	7.20902i	−0.0116556	+	0.272866i
$699$	−1.94381	+	0.228869i	−0.0735217	+	0.00865663i
$700$	18.5284	+	39.5392i	0.700306	+	1.49444i
$701$		−	24.6223i		−	0.929973i	−0.885318	−	0.464987i	$-0.846059\pi$
$701$		−	24.6223i		−	0.929973i	0.885318	−	0.464987i	$-0.153941\pi$
$702$	−48.7377	+	6.58939i	−1.83949	+	0.248700i
$703$	0.495778			0.0186986
$704$	4.18816	+	1.92418i	0.157847	+	0.0725203i
$705$	−14.7611	+	11.0087i	−0.555937	+	0.414612i
$706$	−21.0306	−	0.898336i	−0.791498	−	0.0338093i
$707$	−14.5258	+	39.9094i	−0.546300	+	1.50095i
$708$	25.8435	−	16.0382i	0.971257	−	0.602753i
$709$	26.4148	+	4.65765i	0.992030	+	0.174922i	0.646029	−	0.763313i	$-0.276428\pi$
$709$	26.4148	+	4.65765i	0.992030	+	0.174922i	0.346001	+	0.938234i	$0.387540\pi$
$710$	25.2745	−	27.6346i	0.948535	−	1.03711i
$711$	−0.900037	−	15.0145i	−0.0337540	−	0.563088i
$712$	16.0742	+	2.06994i	0.602407	+	0.0775742i
$713$	13.7461	−	5.00317i	0.514796	−	0.187370i
$714$	−10.9234	−	16.0315i	−0.408796	−	0.599963i
$715$	8.36463	+	9.96858i	0.312819	+	0.372804i
$716$	−6.21128	−	23.0070i	−0.232126	−	0.859813i
$717$	9.78395	+	2.31008i	0.365388	+	0.0862716i
$718$	2.87919	+	21.7113i	0.107450	+	0.810257i
$719$	9.26666	+	16.0503i	0.345588	+	0.598576i	0.985460	−	0.169905i	$-0.0543462\pi$
$719$	9.26666	+	16.0503i	0.345588	+	0.598576i	−0.639872	+	0.768481i	$0.721013\pi$
$720$	−40.2498	−	4.48151i	−1.50002	−	0.167016i
$721$	−27.0047	+	46.7736i	−1.00571	+	1.74194i
$722$	−24.6169	−	10.1694i	−0.916145	−	0.378467i
$723$	45.6393	−	22.9694i	1.69735	−	0.854241i
$724$	23.3122	−	23.4003i	0.866390	−	0.869666i
$725$	21.9920	−	3.87779i	0.816764	−	0.144017i
$726$	−21.2127	−	15.2601i	−0.787276	−	0.566355i
$727$	4.82234	+	4.04643i	0.178851	+	0.150074i	0.727818	−	0.685770i	$-0.240534\pi$
$727$	4.82234	+	4.04643i	0.178851	+	0.150074i	−0.548967	+	0.835844i	$0.684979\pi$
$728$	−51.4249	−	39.2290i	−1.90593	−	1.45392i
$729$	20.5947	−	17.4602i	0.762766	−	0.646675i
$730$	5.98247	+	1.32036i	0.221421	+	0.0488687i
$731$	−1.92605	+	2.29538i	−0.0712377	+	0.0848978i
$732$	10.9648	+	12.2534i	0.405272	+	0.452900i
$733$	22.4113	−	3.95172i	0.827781	−	0.145960i	0.256323	−	0.966591i	$-0.417489\pi$
$733$	22.4113	−	3.95172i	0.827781	−	0.145960i	0.571458	+	0.820631i	$0.306378\pi$
$734$	19.4383	−	30.5756i	0.717480	−	1.12857i
$735$	−12.2840	−	24.4078i	−0.453102	−	0.900297i
$736$	−11.4522	−	35.7331i	−0.422135	−	1.31714i
$737$	−4.33388	+	7.50649i	−0.159640	+	0.276505i
$738$	−24.1705	+	14.5142i	−0.889727	+	0.534275i
$739$	37.2940	−	21.5317i	1.37188	−	0.792056i	0.380717	−	0.924692i	$-0.375677\pi$
$739$	37.2940	−	21.5317i	1.37188	−	0.792056i	0.991165	+	0.132636i	$0.0423440\pi$
$740$	−8.17317	−	0.699520i	−0.300452	−	0.0257149i
$741$	−4.60237	−	1.08666i	−0.169072	−	0.0399196i
$742$	−40.0752	+	20.9099i	−1.47121	+	0.767626i
$743$	−27.0616	+	22.7074i	−0.992794	+	0.833053i	−0.985970	−	0.166924i	$-0.946617\pi$
$743$	−27.0616	+	22.7074i	−0.992794	+	0.833053i	−0.00682406	+	0.999977i	$0.502172\pi$
$744$	1.76032	+	10.6593i	0.0645365	+	0.390789i
$745$	21.7106	−	7.90201i	0.795415	−	0.289507i
$746$	−6.06108	−	19.1602i	−0.221912	−	0.701506i
$747$	−31.0814	+	1.86316i	−1.13721	+	0.0681693i
$748$	−1.53602	−	2.18488i	−0.0561625	−	0.0798871i
$749$	−8.22687	−	1.45062i	−0.300603	−	0.0530045i
$750$	−8.01963	−	8.22684i	−0.292835	−	0.300402i
$751$	−23.5008	−	8.55359i	−0.857557	−	0.312125i	−0.124439	−	0.992227i	$-0.539713\pi$
$751$	−23.5008	−	8.55359i	−0.857557	−	0.312125i	−0.733117	+	0.680102i	$0.761935\pi$
$752$	8.06309	−	9.68320i	0.294031	−	0.353110i
$753$	−8.34852	+	6.22625i	−0.304237	+	0.226897i
$754$	−26.2239	+	20.1616i	−0.955017	+	0.734243i
$755$			39.8171i			1.44909i
$756$	35.3867	+	2.93803i	1.28700	+	0.106855i
$757$		−	31.3025i		−	1.13771i	−0.822439	−	0.568853i	$-0.807387\pi$
$757$		−	31.3025i		−	1.13771i	0.822439	−	0.568853i	$-0.192613\pi$
$758$	1.66480	+	2.16538i	0.0604682	+	0.0786500i
$759$	−0.774019	−	6.57383i	−0.0280951	−	0.238615i
$760$	−3.45915	−	1.78829i	−0.125476	−	0.0648681i
$761$	−2.59308	−	0.943805i	−0.0939992	−	0.0342129i	0.294592	−	0.955623i	$-0.404816\pi$
$761$	−2.59308	−	0.943805i	−0.0939992	−	0.0342129i	−0.388592	+	0.921410i	$0.627038\pi$
$762$	22.6033	+	6.36658i	0.818831	+	0.230637i
$763$	54.6869	+	9.64278i	1.97980	+	0.349092i
$764$	−21.6289	+	15.2056i	−0.782507	+	0.550121i
$765$	18.8476	+	13.9819i	0.681435	+	0.505517i
$766$	17.8468	−	5.64558i	0.644830	−	0.203983i
$767$	−55.2197	+	20.0983i	−1.99387	+	0.725708i
$768$	27.4974	−	3.44825i	0.992229	−	0.124428i
$769$	3.61913	−	3.03681i	0.130509	−	0.109510i	−0.575197	−	0.818015i	$-0.695074\pi$
$769$	3.61913	−	3.03681i	0.130509	−	0.109510i	0.705706	+	0.708505i	$0.250630\pi$
$770$	−4.34614	−	8.32966i	−0.156624	−	0.300180i
$771$	−12.9370	−	43.0796i	−0.465914	−	1.55147i
$772$	−0.352674	−	0.0301844i	−0.0126930	−	0.00108636i
$773$	17.3435	−	10.0133i	0.623803	−	0.360153i	−0.154545	−	0.987986i	$-0.549391\pi$
$773$	17.3435	−	10.0133i	0.623803	−	0.360153i	0.778348	+	0.627833i	$0.216058\pi$
$774$	−1.04507	−	5.38417i	−0.0375642	−	0.193530i
$775$	−7.04567	+	12.2035i	−0.253088	+	0.438361i
$776$	−21.5294	−	23.3621i	−0.772861	−	0.838651i
$777$	7.18049	+	0.412109i	0.257599	+	0.0147843i
$778$	−28.7012	−	18.2467i	−1.02899	−	0.654175i
$779$	−2.66971	+	0.470742i	−0.0956522	+	0.0168661i
$780$	74.3394	+	24.4080i	2.66178	+	0.873946i
$781$	−2.90577	+	3.46296i	−0.103977	+	0.123914i
$782$	−4.68614	+	21.2326i	−0.167576	+	0.759276i
$783$	6.16759	−	17.0803i	0.220412	−	0.610401i
$784$	12.0729	+	14.2781i	0.431174	+	0.509932i
$785$	31.1567	+	26.1436i	1.11203	+	0.933105i
$786$	−0.415559	−	0.921677i	−0.0148225	−	0.0328751i
$787$	−41.5062	+	7.31867i	−1.47954	+	0.260882i	−0.854393	−	0.519627i	$-0.826071\pi$
$787$	−41.5062	+	7.31867i	−1.47954	+	0.260882i	−0.625144	+	0.780510i	$0.714960\pi$
$788$	−1.37111	+	1.37630i	−0.0488439	+	0.0490286i
$789$	20.1422	+	13.2233i	0.717081	+	0.470762i
$790$	−9.13673	+	22.1170i	−0.325070	+	0.786888i
$791$	−20.7940	+	36.0163i	−0.739350	+	1.28059i
$792$	4.87725	+	0.333126i	0.173306	+	0.0118371i
$793$	−15.8842	−	27.5122i	−0.564063	−	0.976986i
$794$	46.4331	−	6.15761i	1.64785	−	0.218525i
$795$	37.4913	−	39.8060i	1.32968	−	1.41177i
$796$	7.91372	−	2.13649i	0.280494	−	0.0757258i
$797$	32.1711	+	38.3400i	1.13956	+	1.35807i	0.924369	+	0.381500i	$0.124592\pi$
$797$	32.1711	+	38.3400i	1.13956	+	1.35807i	0.215189	+	0.976572i	$0.430963\pi$
$798$	3.07570	+	1.48227i	0.108879	+	0.0524717i
$799$	−6.86134	+	2.49732i	−0.242737	+	0.0883489i
$800$	30.5766	+	19.2772i	1.08104	+	0.681553i
$801$	16.7200	−	3.99265i	0.590771	−	0.141073i
$802$	11.6928	+	10.6942i	0.412888	+	0.377626i
$803$	−0.728294	−	0.128418i	−0.0257009	−	0.00453177i
$804$	1.65826	+	52.0904i	0.0584823	+	1.83709i
$805$	−26.1611	+	71.8771i	−0.922059	+	2.53334i
$806$	0.890787	−	20.8539i	0.0313766	−	0.734547i
$807$	−6.19534	−	2.66618i	−0.218086	−	0.0938541i
$808$	7.70655	+	34.3022i	0.271116	+	1.20675i
$809$	7.89082			0.277426			0.138713	−	0.990333i	$-0.455703\pi$
$809$	7.89082			0.277426			0.138713	+	0.990333i	$0.455703\pi$
$810$	−41.6028	+	10.6934i	−1.46177	+	0.375727i
$811$			16.9433i			0.594960i	0.954728	+	0.297480i	$0.0961461\pi$
$811$			16.9433i			0.594960i	−0.954728	+	0.297480i	$0.903854\pi$
$812$	21.6257	−	10.1340i	0.758913	−	0.355632i
$813$	18.5552	−	43.1163i	0.650760	−	1.51215i
$814$	0.989297	+	0.0422584i	0.0346748	+	0.00148116i
$815$	−42.4871	−	15.4641i	−1.48826	−	0.541682i
$816$	−14.7745	−	6.29228i	−0.517212	−	0.220274i
$817$	0.0915762	−	0.519355i	0.00320385	−	0.0181699i
$818$	11.7191	+	10.7183i	0.409749	+	0.374755i
$819$	−65.7541	−	19.5641i	−2.29764	−	0.683625i
$820$	44.6758	−	3.99359i	1.56015	−	0.139462i
$821$	16.2209	+	44.5665i	0.566112	+	1.55538i	0.810522	+	0.585708i	$0.199184\pi$
$821$	16.2209	+	44.5665i	0.566112	+	1.55538i	−0.244410	+	0.969672i	$0.578594\pi$
$822$	16.7594	−	34.7757i	0.584550	−	1.21294i
$823$	−3.65996	+	3.07107i	−0.127578	+	0.107051i	−0.704344	−	0.709858i	$-0.748759\pi$
$823$	−3.65996	+	3.07107i	−0.127578	+	0.107051i	0.576766	+	0.816909i	$0.304314\pi$
$824$	2.07661	+	44.6608i	0.0723422	+	1.55583i
$825$	4.64163	+	4.37172i	0.161601	+	0.152204i
$826$	42.0586	−	5.57750i	1.46341	−	0.194066i
$827$	25.0451	−	14.4598i	0.870903	−	0.502816i	0.00325451	−	0.999995i	$-0.498964\pi$
$827$	25.0451	−	14.4598i	0.870903	−	0.502816i	0.867648	+	0.497179i	$0.165631\pi$
$828$	−24.7968	−	31.1308i	−0.861749	−	1.08187i
$829$	17.1833	+	9.92077i	0.596800	+	0.344563i	0.767782	−	0.640711i	$-0.221361\pi$
$829$	17.1833	+	9.92077i	0.596800	+	0.344563i	−0.170982	+	0.985274i	$0.554694\pi$
$830$	45.7841	+	18.9138i	1.58919	+	0.656508i
$831$	−6.80883	+	10.3715i	−0.236196	+	0.359782i
$832$	−53.3635	−	4.36442i	−1.85005	−	0.151309i
$833$	−1.88146	−	10.6703i	−0.0651888	−	0.369704i
$834$	−2.22299	−	4.93042i	−0.0769758	−	0.170726i
$835$	14.6933	−	17.5108i	0.508482	−	0.605986i
$836$	0.426389	+	0.197850i	0.0147470	+	0.00684278i
$837$	5.75473	+	9.90922i	0.198913	+	0.342513i
$838$	−19.2429	−	4.24701i	−0.664737	−	0.146711i
$839$	26.2638	+	22.0379i	0.906725	+	0.760833i	0.971493	−	0.237067i	$-0.0761862\pi$
$839$	26.2638	+	22.0379i	0.906725	+	0.760833i	−0.0647677	+	0.997900i	$0.520631\pi$
$840$	−48.6132	−	28.7757i	−1.67732	−	0.992854i
$841$	2.91487	+	16.5310i	0.100513	+	0.570036i
$842$	14.1910	+	9.02187i	0.489055	+	0.310914i
$843$	−0.0769808	+	1.34129i	−0.00265136	+	0.0461966i
$844$	−6.15574	−	4.29300i	−0.211889	−	0.147771i
$845$	−92.9203	−	53.6476i	−3.19656	−	1.84553i
$846$	4.35465	−	12.6357i	0.149716	−	0.434426i
$847$	−18.2253	−	31.5672i	−0.626230	−	1.08466i
$848$	−18.5868	+	32.4757i	−0.638272	+	1.11522i
$849$	2.53610	−	0.761601i	0.0870387	−	0.0261381i
$850$	−9.68904	−	18.5697i	−0.332331	−	0.636935i
$851$	−5.18183	−	6.17546i	−0.177631	−	0.211692i
$852$	−3.86582	+	26.9046i	−0.132441	+	0.921738i
$853$	−11.5939	−	31.8539i	−0.396967	−	1.09066i	−0.963754	−	0.266793i	$-0.914036\pi$
$853$	−11.5939	−	31.8539i	−0.396967	−	1.09066i	0.566787	−	0.823865i	$-0.308186\pi$
$854$	6.91777	+	21.8684i	0.236721	+	0.748321i
$855$	−4.10315	−	0.472540i	−0.140325	−	0.0161605i
$856$	−6.38135	+	2.66443i	−0.218110	+	0.0910683i
$857$	0.670084	−	3.80024i	0.0228896	−	0.129814i	−0.971222	−	0.238177i	$-0.923450\pi$
$857$	0.670084	−	3.80024i	0.0228896	−	0.129814i	0.994111	+	0.108364i	$0.0345611\pi$
$858$	−9.09115	−	2.56067i	−0.310367	−	0.0874197i
$859$	7.37600	−	20.2654i	0.251666	−	0.691446i	−0.747951	−	0.663754i	$-0.768962\pi$
$859$	7.37600	−	20.2654i	0.251666	−	0.691446i	0.999617	−	0.0276917i	$-0.00881567\pi$
$860$	−2.24247	+	8.43263i	−0.0764676	+	0.287550i
$861$	−39.0574	+	4.59872i	−1.33107	+	0.156724i
$862$	−31.6734	+	24.3514i	−1.07880	+	0.829412i
$863$	30.2497			1.02971			0.514857	−	0.857276i	$-0.327845\pi$
$863$	30.2497			1.02971			0.514857	+	0.857276i	$0.327845\pi$
$864$	25.9735	−	13.7615i	0.883635	−	0.468177i
$865$	−5.68815			−0.193403
$866$	−31.2270	+	24.0082i	−1.06114	+	0.815830i
$867$	−12.0401	−	16.1441i	−0.408904	−	0.548282i
$868$	−3.87295	+	14.5639i	−0.131456	+	0.494332i
$869$	0.987962	−	2.71440i	0.0335143	−	0.0920799i
$870$	−20.6878	+	20.1668i	−0.701383	+	0.683718i
$871$	17.4847	−	99.1608i	0.592447	−	3.35994i
$872$	42.4191	−	17.7114i	1.43649	−	0.599784i
$873$	−30.1381	−	15.0720i	−1.02002	−	0.510109i
$874$	−1.15420	−	3.64865i	−0.0390414	−	0.123417i
$875$	−5.48119	−	15.0594i	−0.185298	−	0.509102i
$876$	−4.12791	+	1.65300i	−0.139469	+	0.0558497i
$877$	10.0265	+	11.9491i	0.338571	+	0.403493i	0.908286	−	0.418349i	$-0.137391\pi$
$877$	10.0265	+	11.9491i	0.338571	+	0.403493i	−0.569715	+	0.821842i	$0.692947\pi$
$878$	8.03357	+	15.3969i	0.271120	+	0.519619i
$879$	−6.32982	+	26.8088i	−0.213499	+	0.904239i
$880$	−6.75010	−	3.86328i	−0.227546	−	0.130231i
$881$	18.2832	+	31.6674i	0.615977	+	1.06690i	0.990212	+	0.139569i	$0.0445719\pi$
$881$	18.2832	+	31.6674i	0.615977	+	1.06690i	−0.374235	+	0.927334i	$0.622095\pi$
$882$	17.3431	+	9.61958i	0.583974	+	0.323908i
$883$	−26.1355	−	15.0893i	−0.879529	−	0.507796i	−0.00902592	−	0.999959i	$-0.502873\pi$
$883$	−26.1355	−	15.0893i	−0.879529	−	0.507796i	−0.870503	+	0.492163i	$0.836206\pi$
$884$	25.4482	+	17.7476i	0.855916	+	0.596915i
$885$	−45.8457	+	23.0732i	−1.54109	+	0.775598i
$886$	−25.2170	−	16.0316i	−0.847181	−	0.538591i
$887$	−7.16882	−	40.6564i	−0.240705	−	1.36511i	−0.830258	−	0.557379i	$-0.811807\pi$
$887$	−7.16882	−	40.6564i	−0.240705	−	1.36511i	0.589553	−	0.807730i	$-0.299304\pi$
$888$	5.18818	−	2.92069i	0.174104	−	0.0980120i
$889$	25.0927	+	21.0553i	0.841584	+	0.706172i
$890$	−26.7055	−	5.89404i	−0.895171	−	0.197569i
$891$	4.96226	−	1.50395i	0.166242	−	0.0503843i
$892$	−7.11472	−	3.30132i	−0.238219	−	0.110536i
$893$	0.826041	−	0.984438i	0.0276424	−	0.0329430i
$894$	−9.79262	+	13.6125i	−0.327514	+	0.455269i
$895$	6.98289	+	39.6019i	0.233412	+	1.32375i
$896$	36.9435	+	11.3805i	1.23420	+	0.380197i
$897$	34.5680	+	68.6854i	1.15419	+	2.29334i
$898$	36.2603	+	14.9794i	1.21002	+	0.499870i
$899$	6.67459	+	3.85358i	0.222610	+	0.128524i
$900$	37.5742	+	7.61820i	1.25247	+	0.253940i
$901$	18.7778	−	10.8414i	0.625578	−	0.361178i
$902$	−5.36737	+	0.711781i	−0.178714	+	0.0236997i
$903$	1.75803	−	7.44583i	0.0585036	−	0.247782i
$904$	1.59902	+	34.3894i	0.0531826	+	1.14378i
$905$	−42.6973	+	35.8273i	−1.41931	+	1.19094i
$906$	−16.2727	−	23.8824i	−0.540625	−	0.793440i
$907$	−13.9229	−	38.2529i	−0.462303	−	1.27017i	−0.923749	−	0.382999i	$-0.874891\pi$
$907$	−13.9229	−	38.2529i	−0.462303	−	1.27017i	0.461446	−	0.887168i	$-0.347331\pi$
$908$	−23.5733	+	2.10723i	−0.782308	+	0.0699310i
$909$	20.5439	+	31.1205i	0.681399	+	1.03220i
$910$	80.5379	+	73.6597i	2.66980	+	2.44179i
$911$	7.42318	−	42.0989i	0.245941	−	1.39480i	−0.572357	−	0.820005i	$-0.693971\pi$
$911$	7.42318	−	42.0989i	0.245941	−	1.39480i	0.818298	−	0.574795i	$-0.194918\pi$
$912$	2.80565	−	0.341086i	0.0929045	−	0.0112945i
$913$	−5.61905	−	2.04517i	−0.185963	−	0.0676852i
$914$	−48.1227	−	2.05559i	−1.59176	−	0.0679928i
$915$	−16.5880	−	22.2422i	−0.548383	−	0.735304i
$916$	−19.1926	+	8.99380i	−0.634142	+	0.297163i
$917$		−	1.41029i		−	0.0465717i
$918$	−17.0190	−	0.683629i	−0.561712	−	0.0225631i
$919$	−4.00742			−0.132193			−0.0660963	−	0.997813i	$-0.521054\pi$
$919$	−4.00742			−0.132193			−0.0660963	+	0.997813i	$0.521054\pi$
$920$	13.8796	+	61.7785i	0.457595	+	2.03678i
$921$	−0.0866677	−	0.736078i	−0.00285580	−	0.0242546i
$922$	−0.839029	+	19.6422i	−0.0276319	+	0.646882i
$923$	17.9609	−	49.3471i	0.591189	−	1.62428i
$924$	6.01105	+	3.21994i	0.197749	+	0.105928i
$925$	7.64760	+	1.34848i	0.251452	+	0.0443377i
$926$	19.3963	+	17.7398i	0.637402	+	0.582966i
$927$	18.8563	+	43.5109i	0.619323	+	1.42909i
$928$	10.5435	−	16.7236i	0.346109	−	0.548980i
$929$	46.5451	−	16.9410i	1.52710	−	0.555818i	0.564188	−	0.825646i	$-0.309189\pi$
$929$	46.5451	−	16.9410i	1.52710	−	0.555818i	0.962908	+	0.269829i	$0.0869671\pi$
$930$	−1.35716	−	18.1800i	−0.0445030	−	0.596144i
$931$	1.22576	+	1.46080i	0.0401725	+	0.0478758i
$932$	−2.18191	+	0.589056i	−0.0714708	+	0.0192952i
$933$	−5.50276	−	18.3239i	−0.180152	−	0.599899i
$934$	−13.5028	+	1.79065i	−0.441826	+	0.0585917i
$935$	2.25339	+	3.90298i	0.0736936	+	0.127641i
$936$	−54.5642	+	15.7416i	−1.78349	+	0.514529i
$937$	4.84280	−	8.38798i	0.158207	−	0.274023i	−0.776015	−	0.630715i	$-0.782762\pi$
$937$	4.84280	−	8.38798i	0.158207	−	0.274023i	0.934222	+	0.356691i	$0.116095\pi$
$938$	−27.7569	+	67.1902i	−0.906293	+	2.19384i
$939$	−2.75855	+	48.0642i	−0.0900218	+	1.56852i
$940$	−15.0067	+	15.0635i	−0.489466	+	0.491317i
$941$	5.10500	−	0.900150i	0.166418	−	0.0293440i	−0.0898181	−	0.995958i	$-0.528629\pi$
$941$	5.10500	−	0.900150i	0.166418	−	0.0293440i	0.256236	+	0.966614i	$0.417517\pi$
$942$	−29.3724	−	2.94766i	−0.957005	−	0.0960398i
$943$	33.7672	+	28.3340i	1.09961	+	0.922682i
$944$	26.8188	−	22.6767i	0.872877	−	0.738063i
$945$	−59.0342	−	10.2546i	−1.92038	−	0.333583i
$946$	0.227003	−	1.02854i	0.00738051	−	0.0334406i
$947$	−19.6357	+	23.4009i	−0.638075	+	0.760428i	−0.984065	−	0.177811i	$-0.943099\pi$
$947$	−19.6357	+	23.4009i	−0.638075	+	0.760428i	0.345990	+	0.938238i	$0.387543\pi$
$948$	−3.55870	−	16.9999i	−0.115581	−	0.552131i
$949$	8.46036	−	1.49179i	0.274635	−	0.0484256i
$950$	3.11093	+	1.97776i	0.100932	+	0.0641669i
$951$	−3.34003	+	5.08766i	−0.108308	+	0.164979i
$952$	−15.1801	−	16.4723i	−0.491989	−	0.533870i
$953$	8.71927	−	15.1022i	0.282445	−	0.489209i	−0.689542	−	0.724246i	$-0.742188\pi$
$953$	8.71927	−	15.1022i	0.282445	−	0.489209i	0.971986	+	0.235037i	$0.0755213\pi$
$954$	−6.21919	+	39.1979i	−0.201354	+	1.26908i
$955$	38.6370	−	22.3071i	1.25027	−	0.721841i
$956$	11.5659	+	0.989894i	0.374068	+	0.0320155i
$957$	2.39108	−	2.53871i	0.0772928	−	0.0820648i
$958$	−19.0418	−	36.4949i	−0.615214	−	1.17910i
$959$	41.2500	−	34.6128i	1.33203	−	1.11771i
$960$	−46.7340	+	1.66433i	−1.50833	+	0.0537161i
$961$	24.5605	−	8.93927i	0.792273	−	0.288364i
$962$	−10.9672	+	3.46932i	−0.353596	+	0.111855i
$963$	−5.32656	+	5.04244i	−0.171646	+	0.162490i
$964$	48.2641	−	33.9308i	1.55448	−	1.09284i
$965$	0.588217	+	0.103718i	0.0189354	+	0.00333882i
$966$	−13.6837	−	53.8038i	−0.440266	−	1.73111i
$967$	−46.2859	−	16.8467i	−1.48845	−	0.541752i	−0.535411	−	0.844592i	$-0.679843\pi$
$967$	−46.2859	−	16.8467i	−1.48845	−	0.541752i	−0.953042	+	0.302839i	$0.902065\pi$
$968$	−26.8039	−	13.8569i	−0.861510	−	0.445378i
$969$	−1.50436	−	0.647406i	−0.0483270	−	0.0207977i
$970$	32.6753	+	42.5002i	1.04914	+	1.36460i
$971$		−	13.2201i		−	0.424253i	−0.977242	−	0.212126i	$-0.931961\pi$
$971$		−	13.2201i		−	0.424253i	0.977242	−	0.212126i	$-0.0680388\pi$
$972$	20.5832	−	23.4164i	0.660208	−	0.751083i
$973$		−	7.54418i		−	0.241855i
$974$	−14.7353	+	11.3289i	−0.472150	+	0.363002i
$975$	−68.0381	−	29.2804i	−2.17896	−	0.937723i
$976$	14.5907	+	12.1495i	0.467037	+	0.388896i
$977$	−22.1311	−	8.05506i	−0.708037	−	0.257704i	−0.0371983	−	0.999308i	$-0.511843\pi$
$977$	−22.1311	−	8.05506i	−0.708037	−	0.257704i	−0.670838	+	0.741604i	$0.734066\pi$
$978$	31.8039	−	8.08855i	1.01698	−	0.258643i
$979$	3.25108	+	0.573253i	0.103905	+	0.0183212i
$980$	−18.1461	−	25.8116i	−0.579657	−	0.824520i
$981$	35.4075	−	33.5189i	1.13048	−	1.07018i
$982$	−5.01267	−	15.8460i	−0.159961	−	0.505667i
$983$	−44.1620	+	16.0737i	−1.40855	+	0.512670i	−0.930704	−	0.365773i	$-0.880805\pi$
$983$	−44.1620	+	16.0737i	−1.40855	+	0.512670i	−0.477846	+	0.878444i	$0.658582\pi$
$984$	−25.1645	+	20.6538i	−0.802216	+	0.658418i
$985$	2.51126	−	2.10719i	0.0800153	−	0.0671408i
$986$	−10.1566	+	5.29936i	−0.323451	+	0.168766i
$987$	12.7821	−	13.5712i	0.406858	−	0.431977i
$988$	−5.44060	−	0.465646i	−0.173088	−	0.0148142i
$989$	−7.42628	+	4.28756i	−0.236142	+	0.136337i
$990$	−8.14732	−	1.29267i	−0.258939	−	0.0410836i
$991$	−10.5119	+	18.2072i	−0.333922	+	0.578370i	−0.983277	−	0.182115i	$-0.941706\pi$
$991$	−10.5119	+	18.2072i	−0.333922	+	0.578370i	0.649355	+	0.760486i	$0.275039\pi$
$992$	3.80740	+	11.8798i	0.120885	+	0.377184i
$993$	16.5566	−	25.2197i	0.525409	−	0.800322i
$994$	−20.3414	+	31.9962i	−0.645190	+	1.01486i
$995$	−13.6219	+	2.40190i	−0.431842	+	0.0761454i
$996$	−35.1913	+	7.36681i	−1.11508	+	0.233426i
$997$	−1.15413	+	1.37543i	−0.0365515	+	0.0435604i	−0.784011	−	0.620748i	$-0.786829\pi$
$997$	−1.15413	+	1.37543i	−0.0365515	+	0.0435604i	0.747459	+	0.664308i	$0.231274\pi$
$998$	49.9718	+	11.0290i	1.58183	+	0.349117i
$999$	4.04686	−	4.84784i	0.128037	−	0.153379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.205.27	yes	204
3.2	odd	2		648.2.t.a.613.8		204
4.3	odd	2		864.2.bf.a.529.13		204
8.3	odd	2		864.2.bf.a.529.22		204
8.5	even	2	inner	216.2.t.a.205.12	yes	204
24.5	odd	2		648.2.t.a.613.23		204
27.5	odd	18		648.2.t.a.37.23		204
27.22	even	9	inner	216.2.t.a.157.12	✓	204
108.103	odd	18		864.2.bf.a.49.22		204
216.5	odd	18		648.2.t.a.37.8		204
216.157	even	18	inner	216.2.t.a.157.27	yes	204
216.211	odd	18		864.2.bf.a.49.13		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.12	✓	204	27.22	even	9	inner
216.2.t.a.157.27	yes	204	216.157	even	18	inner
216.2.t.a.205.12	yes	204	8.5	even	2	inner
216.2.t.a.205.27	yes	204	1.1	even	1	trivial
648.2.t.a.37.8		204	216.5	odd	18
648.2.t.a.37.23		204	27.5	odd	18
648.2.t.a.613.8		204	3.2	odd	2
648.2.t.a.613.23		204	24.5	odd	2
864.2.bf.a.49.13		204	216.211	odd	18
864.2.bf.a.49.22		204	108.103	odd	18
864.2.bf.a.529.13		204	4.3	odd	2
864.2.bf.a.529.22		204	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.12116 - 0.861977i) q^{2} +(0.684682 - 1.59098i) q^{3} +(0.513991 - 1.93283i) q^{4} +(-1.15428 + 3.17134i) q^{5} +(-0.603749 - 2.37392i) q^{6} +(0.593321 - 3.36489i) q^{7} +(-1.08978 - 2.61005i) q^{8} +(-2.06242 - 2.17863i) q^{9} +O(q^{10})\)	\(q+(1.12116 - 0.861977i) q^{2} +(0.684682 - 1.59098i) q^{3} +(0.513991 - 1.93283i) q^{4} +(-1.15428 + 3.17134i) q^{5} +(-0.603749 - 2.37392i) q^{6} +(0.593321 - 3.36489i) q^{7} +(-1.08978 - 2.61005i) q^{8} +(-2.06242 - 2.17863i) q^{9} +(1.43950 + 4.55054i) q^{10} +(-0.197048 - 0.541384i) q^{11} +(-2.72316 - 2.14112i) q^{12} +(4.30199 + 5.12691i) q^{13} +(-2.23525 - 4.28400i) q^{14} +(4.25523 + 4.00779i) q^{15} +(-3.47163 - 1.98691i) q^{16} +(1.15893 + 2.00733i) q^{17} +(-4.19023 - 0.664827i) q^{18} +(-0.353289 - 0.203971i) q^{19} +(5.53637 + 3.86106i) q^{20} +(-4.94723 - 3.24784i) q^{21} +(-0.687582 - 0.437127i) q^{22} +(1.15186 + 6.53250i) q^{23} +(-4.89869 - 0.0532318i) q^{24} +(-4.89486 - 4.10727i) q^{25} +(9.24249 + 2.03986i) q^{26} +(-4.87825 + 1.78960i) q^{27} +(-6.19878 - 2.87631i) q^{28} +(-2.24644 + 2.67721i) q^{29} +(8.22541 + 0.825457i) q^{30} +(-0.382945 - 2.17179i) q^{31} +(-5.60491 + 0.764819i) q^{32} +(-0.996245 - 0.0571774i) q^{33} +(3.02962 + 1.25156i) q^{34} +(9.98637 + 5.76564i) q^{35} +(-5.27097 + 2.86650i) q^{36} +(-1.05249 + 0.607656i) q^{37} +(-0.571912 + 0.0758426i) q^{38} +(11.1023 - 3.33407i) q^{39} +(9.53529 - 0.443366i) q^{40} +(5.09057 - 4.27150i) q^{41} +(-8.34619 + 0.623055i) q^{42} +(0.442145 + 1.21478i) q^{43} +(-1.14768 + 0.102592i) q^{44} +(9.28978 - 4.02591i) q^{45} +(6.92227 + 6.33109i) q^{46} +(-0.547022 + 3.10232i) q^{47} +(-5.53809 + 4.16288i) q^{48} +(-4.39261 - 1.59878i) q^{49} +(-9.02828 - 0.385648i) q^{50} +(3.98712 - 0.469453i) q^{51} +(12.1206 - 5.67980i) q^{52} -9.35460i q^{53} +(-3.92670 + 6.21136i) q^{54} +1.94436 q^{55} +(-9.42913 + 2.11841i) q^{56} +(-0.566405 + 0.422419i) q^{57} +(-0.210928 + 4.93796i) q^{58} +(-3.00302 + 8.25072i) q^{59} +(9.93351 - 6.16464i) q^{60} +(-4.67459 - 0.824257i) q^{61} +(-2.30137 - 2.10483i) q^{62} +(-8.55452 + 5.64720i) q^{63} +(-5.62474 + 5.68879i) q^{64} +(-21.2249 + 7.72523i) q^{65} +(-1.16623 + 0.794635i) q^{66} +(-9.67062 - 11.5250i) q^{67} +(4.47550 - 1.20826i) q^{68} +(11.1817 + 2.64011i) q^{69} +(16.1662 - 2.14383i) q^{70} +(-3.92323 - 6.79524i) q^{71} +(-3.43874 + 7.75726i) q^{72} +(0.641809 - 1.11165i) q^{73} +(-0.656224 + 1.58850i) q^{74} +(-9.88600 + 4.97543i) q^{75} +(-0.575829 + 0.578006i) q^{76} +(-1.93861 + 0.341829i) q^{77} +(9.57354 - 13.3079i) q^{78} +(3.84081 + 3.22282i) q^{79} +(10.3084 - 8.71628i) q^{80} +(-0.492839 + 8.98650i) q^{81} +(2.02541 - 9.17698i) q^{82} +(6.67152 - 7.95081i) q^{83} +(-8.82034 + 7.89277i) q^{84} +(-7.70366 + 1.35836i) q^{85} +(1.54283 + 0.980846i) q^{86} +(2.72128 + 5.40708i) q^{87} +(-1.19830 + 1.10430i) q^{88} +(-2.86501 + 4.96234i) q^{89} +(6.94507 - 12.5213i) q^{90} +(19.8040 - 11.4338i) q^{91} +(13.2182 + 1.13131i) q^{92} +(-3.71746 - 0.877728i) q^{93} +(2.06083 + 3.94971i) q^{94} +(1.05466 - 0.884962i) q^{95} +(-2.62077 + 9.44095i) q^{96} +(10.5548 - 3.84165i) q^{97} +(-6.30293 + 1.99385i) q^{98} +(-0.773079 + 1.54586i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more