LMFDB - Embedded newform 275.2.z.a.174.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(49,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 4]))

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

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

chi := DirichletCharacter("275.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.z (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{14} + 15x^{12} - 59x^{10} + 104x^{8} - 59x^{6} + 15x^{4} - x^{2} + 1 $ x^16 - x^14 + 15x^12 - 59x^10 + 104x^8 - 59x^6 + 15*x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			174.2
Root			$0.280526 - 0.386111i$ of defining polynomial
Character	$\chi$	$=$	275.174
Dual form			275.2.z.a.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453901 - 0.147481i) q^{2} +(-0.189896 - 0.261370i) q^{3} +(-1.43376 - 1.04169i) q^{4} +(0.0476470 + 0.146642i) q^{6} +(-1.57833 + 2.17239i) q^{7} +(1.05821 + 1.45650i) q^{8} +(0.894797 - 2.75390i) q^{9} +O(q^{10})$	\(q+(-0.453901 - 0.147481i) q^{2} +(-0.189896 - 0.261370i) q^{3} +(-1.43376 - 1.04169i) q^{4} +(0.0476470 + 0.146642i) q^{6} +(-1.57833 + 2.17239i) q^{7} +(1.05821 + 1.45650i) q^{8} +(0.894797 - 2.75390i) q^{9} +(-2.79042 - 1.79264i) q^{11} +0.572554i q^{12} +(-4.43939 - 1.44244i) q^{13} +(1.03679 - 0.753275i) q^{14} +(0.829779 + 2.55380i) q^{16} +(-4.39990 + 1.42961i) q^{17} +(-0.812299 + 1.11803i) q^{18} +(-3.51149 + 2.55125i) q^{19} +0.867517 q^{21} +(1.00220 + 1.22522i) q^{22} +2.77222i q^{23} +(0.179735 - 0.553168i) q^{24} +(1.80231 + 1.30945i) q^{26} +(-1.81148 + 0.588587i) q^{27} +(4.52590 - 1.47055i) q^{28} +(-2.43790 - 1.77124i) q^{29} +(0.737407 - 2.26951i) q^{31} -4.88221i q^{32} +(0.0613500 + 1.06975i) q^{33} +2.20796 q^{34} +(-4.15163 + 3.01633i) q^{36} +(6.25574 - 8.61029i) q^{37} +(1.97013 - 0.640135i) q^{38} +(0.466012 + 1.43424i) q^{39} +(1.78826 - 1.29924i) q^{41} +(-0.393767 - 0.127943i) q^{42} -7.06719i q^{43} +(2.13343 + 5.47695i) q^{44} +(0.408851 - 1.25832i) q^{46} +(2.56401 + 3.52905i) q^{47} +(0.509914 - 0.701836i) q^{48} +(-0.0650188 - 0.200107i) q^{49} +(1.20918 + 0.878523i) q^{51} +(4.86243 + 6.69257i) q^{52} +(-6.02403 - 1.95733i) q^{53} +0.909040 q^{54} -4.83428 q^{56} +(1.33364 + 0.433326i) q^{57} +(0.845342 + 1.16351i) q^{58} +(9.50375 + 6.90488i) q^{59} +(-1.23070 - 3.78770i) q^{61} +(-0.669420 + 0.921378i) q^{62} +(4.57026 + 6.29042i) q^{63} +(0.939522 - 2.89155i) q^{64} +(0.129921 - 0.494608i) q^{66} -7.31984i q^{67} +(7.79760 + 2.53359i) q^{68} +(0.724576 - 0.526435i) q^{69} +(0.369495 + 1.13719i) q^{71} +(4.95794 - 1.61093i) q^{72} +(0.600544 - 0.826577i) q^{73} +(-4.10935 + 2.98562i) q^{74} +7.69223 q^{76} +(8.29852 - 3.23251i) q^{77} -0.719730i q^{78} +(-1.08222 + 3.33073i) q^{79} +(-6.53000 - 4.74432i) q^{81} +(-1.00331 + 0.325994i) q^{82} +(-10.5718 + 3.43498i) q^{83} +(-1.24381 - 0.903681i) q^{84} +(-1.04228 + 3.20780i) q^{86} +0.973547i q^{87} +(-0.341876 - 5.96123i) q^{88} -2.76978 q^{89} +(10.1404 - 7.36742i) q^{91} +(2.88779 - 3.97470i) q^{92} +(-0.733212 + 0.238235i) q^{93} +(-0.643336 - 1.97998i) q^{94} +(-1.27606 + 0.927114i) q^{96} +(-17.6271 - 5.72738i) q^{97} +0.100418i q^{98} +(-7.43361 + 6.08051i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 14 q^{6} + 10 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 - 14 * q^6 + 10 * q^9	$ 16 q + 4 q^{4} - 14 q^{6} + 10 q^{9} + 6 q^{11} + 32 q^{14} + 8 q^{16} - 30 q^{19} - 40 q^{21} - 26 q^{24} + 20 q^{26} + 18 q^{29} - 20 q^{31} - 8 q^{34} - 30 q^{36} - 42 q^{39} + 16 q^{41} + 24 q^{44} + 6 q^{46} - 2 q^{49} + 2 q^{51} - 32 q^{54} + 44 q^{56} + 54 q^{59} + 12 q^{61} + 52 q^{64} + 26 q^{66} + 2 q^{69} - 40 q^{71} - 40 q^{74} - 74 q^{79} + 16 q^{81} - 56 q^{84} - 6 q^{86} + 32 q^{89} + 88 q^{91} - 34 q^{94} - 34 q^{96} + 40 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 - 14 * q^6 + 10 * q^9 + 6 * q^11 + 32 * q^14 + 8 * q^16 - 30 * q^19 - 40 * q^21 - 26 * q^24 + 20 * q^26 + 18 * q^29 - 20 * q^31 - 8 * q^34 - 30 * q^36 - 42 * q^39 + 16 * q^41 + 24 * q^44 + 6 * q^46 - 2 * q^49 + 2 * q^51 - 32 * q^54 + 44 * q^56 + 54 * q^59 + 12 * q^61 + 52 * q^64 + 26 * q^66 + 2 * q^69 - 40 * q^71 - 40 * q^74 - 74 * q^79 + 16 * q^81 - 56 * q^84 - 6 * q^86 + 32 * q^89 + 88 * q^91 - 34 * q^94 - 34 * q^96 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.453901	−	0.147481i	−0.320957	−	0.104285i	0.144108	−	0.989562i	$-0.453969\pi$
$2$	−0.453901	−	0.147481i	−0.320957	−	0.104285i	−0.465064	+	0.885277i	$0.653969\pi$
$3$	−0.189896	−	0.261370i	−0.109637	−	0.150902i	0.750673	−	0.660674i	$-0.229730\pi$
$3$	−0.189896	−	0.261370i	−0.109637	−	0.150902i	−0.860309	+	0.509772i	$0.829730\pi$
$4$	−1.43376	−	1.04169i	−0.716879	−	0.520843i
$5$		0			0
$5$		0			0
$6$	0.0476470	+	0.146642i	0.0194518	+	0.0598665i
$7$	−1.57833	+	2.17239i	−0.596554	+	0.821086i	−0.995387	−	0.0959376i	$-0.969415\pi$
$7$	−1.57833	+	2.17239i	−0.596554	+	0.821086i	0.398834	+	0.917023i	$0.369415\pi$
$8$	1.05821	+	1.45650i	0.374133	+	0.514950i
$9$	0.894797	−	2.75390i	0.298266	−	0.917968i
$10$		0			0
$11$	−2.79042	−	1.79264i	−0.841344	−	0.540500i
$11$	−2.79042	−	1.79264i	−0.841344	−	0.540500i
$12$			0.572554i			0.165282i
$13$	−4.43939	−	1.44244i	−1.23126	−	0.400062i	−0.380092	−	0.924949i	$-0.624108\pi$
$13$	−4.43939	−	1.44244i	−1.23126	−	0.400062i	−0.851172	+	0.524886i	$0.824108\pi$
$14$	1.03679	−	0.753275i	0.277095	−	0.201321i
$15$		0			0
$16$	0.829779	+	2.55380i	0.207445	+	0.638449i
$17$	−4.39990	+	1.42961i	−1.06713	+	0.346732i	−0.789370	−	0.613918i	$-0.789593\pi$
$17$	−4.39990	+	1.42961i	−1.06713	+	0.346732i	−0.277762	+	0.960650i	$0.589593\pi$
$18$	−0.812299	+	1.11803i	−0.191461	+	0.263523i
$19$	−3.51149	+	2.55125i	−0.805592	+	0.585297i	−0.912549	−	0.408967i	$-0.865889\pi$
$19$	−3.51149	+	2.55125i	−0.805592	+	0.585297i	0.106958	+	0.994264i	$0.465889\pi$
$20$		0			0
$21$	0.867517			0.189308
$22$	1.00220	+	1.22522i	0.213669	+	0.261217i
$23$			2.77222i			0.578048i	0.957322	+	0.289024i	$0.0933308\pi$
$23$			2.77222i			0.578048i	−0.957322	+	0.289024i	$0.906669\pi$
$24$	0.179735	−	0.553168i	0.0366883	−	0.112915i
$25$		0			0
$26$	1.80231	+	1.30945i	0.353462	+	0.256805i
$27$	−1.81148	+	0.588587i	−0.348620	+	0.113274i
$28$	4.52590	−	1.47055i	0.855314	−	0.277908i
$29$	−2.43790	−	1.77124i	−0.452707	−	0.328911i	0.337956	−	0.941162i	$-0.390264\pi$
$29$	−2.43790	−	1.77124i	−0.452707	−	0.328911i	−0.790664	+	0.612251i	$0.790264\pi$
$30$		0			0
$31$	0.737407	−	2.26951i	0.132442	−	0.407615i	−0.862741	−	0.505646i	$-0.831254\pi$
$31$	0.737407	−	2.26951i	0.132442	−	0.407615i	0.995183	+	0.0980305i	$0.0312543\pi$
$32$		−	4.88221i		−	0.863061i
$33$	0.0613500	+	1.06975i	0.0106797	+	0.186219i
$34$	2.20796			0.378662
$35$		0			0
$36$	−4.15163	+	3.01633i	−0.691938	+	0.502722i
$37$	6.25574	−	8.61029i	1.02844	−	1.41552i	0.122324	−	0.992490i	$-0.460965\pi$
$37$	6.25574	−	8.61029i	1.02844	−	1.41552i	0.906114	−	0.423033i	$-0.139035\pi$
$38$	1.97013	−	0.640135i	0.319598	−	0.103844i
$39$	0.466012	+	1.43424i	0.0746217	+	0.229662i
$40$		0			0
$41$	1.78826	−	1.29924i	0.279279	−	0.202908i	−0.439324	−	0.898329i	$-0.644782\pi$
$41$	1.78826	−	1.29924i	0.279279	−	0.202908i	0.718603	+	0.695421i	$0.244782\pi$
$42$	−0.393767	−	0.127943i	−0.0607596	−	0.0197420i
$43$		−	7.06719i		−	1.07774i	−0.842390	−	0.538868i	$-0.818852\pi$
$43$		−	7.06719i		−	1.07774i	0.842390	−	0.538868i	$-0.181148\pi$
$44$	2.13343	+	5.47695i	0.321626	+	0.825682i
$45$		0			0
$46$	0.408851	−	1.25832i	0.0602819	−	0.185528i
$47$	2.56401	+	3.52905i	0.373999	+	0.514765i	0.953982	−	0.299863i	$-0.0969410\pi$
$47$	2.56401	+	3.52905i	0.373999	+	0.514765i	−0.579983	+	0.814628i	$0.696941\pi$
$48$	0.509914	−	0.701836i	0.0735997	−	0.101301i
$49$	−0.0650188	−	0.200107i	−0.00928840	−	0.0285868i
$50$		0			0
$51$	1.20918	+	0.878523i	0.169319	+	0.123018i
$52$	4.86243	+	6.69257i	0.674298	+	0.928092i
$53$	−6.02403	−	1.95733i	−0.827464	−	0.268859i	−0.135487	−	0.990779i	$-0.543260\pi$
$53$	−6.02403	−	1.95733i	−0.827464	−	0.268859i	−0.691977	+	0.721920i	$0.743260\pi$
$54$	0.909040			0.123705
$55$		0			0
$56$	−4.83428			−0.646008
$57$	1.33364	+	0.433326i	0.176645	+	0.0573954i
$58$	0.845342	+	1.16351i	0.110999	+	0.152777i
$59$	9.50375	+	6.90488i	1.23728	+	0.898939i	0.997414	−	0.0718667i	$-0.0228956\pi$
$59$	9.50375	+	6.90488i	1.23728	+	0.898939i	0.239869	+	0.970805i	$0.422896\pi$
$60$		0			0
$61$	−1.23070	−	3.78770i	−0.157575	−	0.484966i	0.840838	−	0.541287i	$-0.182063\pi$
$61$	−1.23070	−	3.78770i	−0.157575	−	0.484966i	−0.998413	+	0.0563214i	$0.982063\pi$
$62$	−0.669420	+	0.921378i	−0.0850164	+	0.117015i
$63$	4.57026	+	6.29042i	0.575799	+	0.792519i
$64$	0.939522	−	2.89155i	0.117440	−	0.361444i
$65$		0			0
$66$	0.129921	−	0.494608i	0.0159922	−	0.0608820i
$67$		−	7.31984i		−	0.894260i	−0.894469	−	0.447130i	$-0.852446\pi$
$67$		−	7.31984i		−	0.894260i	0.894469	−	0.447130i	$-0.147554\pi$
$68$	7.79760	+	2.53359i	0.945598	+	0.307243i
$69$	0.724576	−	0.526435i	0.0872287	−	0.0633754i
$70$		0			0
$71$	0.369495	+	1.13719i	0.0438510	+	0.134960i	0.970585	−	0.240758i	$-0.0773961\pi$
$71$	0.369495	+	1.13719i	0.0438510	+	0.134960i	−0.926734	+	0.375718i	$0.877396\pi$
$72$	4.95794	−	1.61093i	0.584299	−	0.189850i
$73$	0.600544	−	0.826577i	0.0702883	−	0.0967436i	−0.772425	−	0.635105i	$-0.780957\pi$
$73$	0.600544	−	0.826577i	0.0702883	−	0.0967436i	0.842714	+	0.538362i	$0.180957\pi$
$74$	−4.10935	+	2.98562i	−0.477702	+	0.347071i
$75$		0			0
$76$	7.69223			0.882360
$77$	8.29852	−	3.23251i	0.945704	−	0.368378i
$78$		−	0.719730i		−	0.0814934i
$79$	−1.08222	+	3.33073i	−0.121759	+	0.374736i	−0.993297	−	0.115593i	$-0.963123\pi$
$79$	−1.08222	+	3.33073i	−0.121759	+	0.374736i	0.871538	+	0.490329i	$0.163123\pi$
$80$		0			0
$81$	−6.53000	−	4.74432i	−0.725555	−	0.527147i
$82$	−1.00331	+	0.325994i	−0.110797	+	0.0360000i
$83$	−10.5718	+	3.43498i	−1.16040	+	0.377038i	−0.825053	−	0.565055i	$-0.808855\pi$
$83$	−10.5718	+	3.43498i	−1.16040	+	0.377038i	−0.335351	+	0.942093i	$0.608855\pi$
$84$	−1.24381	−	0.903681i	−0.135711	−	0.0985996i
$85$		0			0
$86$	−1.04228	+	3.20780i	−0.112392	+	0.345906i
$87$			0.973547i			0.104375i
$88$	−0.341876	−	5.96123i	−0.0364442	−	0.635469i
$89$	−2.76978			−0.293596			−0.146798	−	0.989167i	$-0.546897\pi$
$89$	−2.76978			−0.293596			−0.146798	+	0.989167i	$0.546897\pi$
$90$		0			0
$91$	10.1404	−	7.36742i	1.06300	−	0.772315i
$92$	2.88779	−	3.97470i	0.301073	−	0.414391i
$93$	−0.733212	+	0.238235i	−0.0760305	+	0.0247038i
$94$	−0.643336	−	1.97998i	−0.0663550	−	0.204220i
$95$		0			0
$96$	−1.27606	+	0.927114i	−0.130238	+	0.0946232i
$97$	−17.6271	−	5.72738i	−1.78976	−	0.581528i	−0.790247	−	0.612789i	$-0.790048\pi$
$97$	−17.6271	−	5.72738i	−1.78976	−	0.581528i	−0.999511	+	0.0312615i	$0.990048\pi$
$98$			0.100418i			0.0101438i
$99$	−7.43361	+	6.08051i	−0.747106	+	0.611114i
$100$		0			0
$101$	−2.19852	+	6.76634i	−0.218761	+	0.673276i	0.780104	+	0.625649i	$0.215166\pi$
$101$	−2.19852	+	6.76634i	−0.218761	+	0.673276i	−0.998865	+	0.0476270i	$0.984834\pi$
$102$	−0.419284	−	0.577094i	−0.0415153	−	0.0571409i
$103$	4.42505	−	6.09056i	0.436014	−	0.600121i	−0.533307	−	0.845922i	$-0.679051\pi$
$103$	4.42505	−	6.09056i	0.436014	−	0.600121i	0.969320	+	0.245801i	$0.0790509\pi$
$104$	−2.59688	−	7.99237i	−0.254645	−	0.783716i
$105$		0			0
$106$	2.44565	+	1.77687i	0.237542	+	0.172584i
$107$	10.5973	+	14.5859i	1.02448	+	1.41008i	0.909015	+	0.416764i	$0.136836\pi$
$107$	10.5973	+	14.5859i	1.02448	+	1.41008i	0.115465	+	0.993312i	$0.463164\pi$
$108$	3.21035	+	1.04311i	0.308916	+	0.100373i
$109$	16.3653			1.56751			0.783756	−	0.621068i	$-0.213301\pi$
$109$	16.3653			1.56751			0.783756	+	0.621068i	$0.213301\pi$
$110$		0			0
$111$	−3.43842			−0.326360
$112$	−6.85750	−	2.22814i	−0.647973	−	0.210539i
$113$	1.20718	+	1.66154i	0.113562	+	0.156304i	0.862014	−	0.506884i	$-0.169203\pi$
$113$	1.20718	+	1.66154i	0.113562	+	0.156304i	−0.748453	+	0.663188i	$0.769203\pi$
$114$	−0.541433	−	0.393374i	−0.0507099	−	0.0368429i
$115$		0			0
$116$	1.65029	+	5.07906i	0.153225	+	0.471579i
$117$	−7.94470	+	10.9349i	−0.734488	+	1.01094i
$118$	−3.29542	−	4.53576i	−0.303368	−	0.417551i
$119$	3.83883	−	11.8147i	0.351905	−	1.08305i
$120$		0			0
$121$	4.57291	+	10.0044i	0.415720	+	0.909493i
$122$			1.90075i			0.172086i
$123$	−0.679167	−	0.220675i	−0.0612384	−	0.0198976i
$124$	−3.42138	+	2.48578i	−0.307249	+	0.223229i
$125$		0			0
$126$	−1.14673	−	3.52926i	−0.102158	−	0.314411i
$127$	−0.0725340	+	0.0235677i	−0.00643635	+	0.00209130i	−0.312233	−	0.950005i	$-0.601077\pi$
$127$	−0.0725340	+	0.0235677i	−0.00643635	+	0.00209130i	0.305797	+	0.952097i	$0.401077\pi$
$128$	−6.59228	+	9.07350i	−0.582681	+	0.801992i
$129$	−1.84715	+	1.34203i	−0.162633	+	0.118159i
$130$		0			0
$131$	−11.4831			−1.00328			−0.501642	−	0.865075i	$-0.667270\pi$
$131$	−11.4831			−1.00328			−0.501642	+	0.865075i	$0.667270\pi$
$132$	1.02638	−	1.59767i	0.0893350	−	0.139059i
$133$		−	11.6550i		−	1.01062i
$134$	−1.07954	+	3.32248i	−0.0932580	+	0.287019i
$135$		0			0
$136$	−6.73823	−	4.89561i	−0.577799	−	0.419795i
$137$	−17.4322	+	5.66406i	−1.48933	+	0.483914i	−0.936886	−	0.349635i	$-0.886306\pi$
$137$	−17.4322	+	5.66406i	−1.48933	+	0.483914i	−0.552447	+	0.833548i	$0.686306\pi$
$138$	−0.406525	+	0.132088i	−0.0346057	+	0.0112441i
$139$	−18.7590	−	13.6292i	−1.59111	−	1.15601i	−0.902330	−	0.431046i	$-0.858145\pi$
$139$	−18.7590	−	13.6292i	−1.59111	−	1.15601i	−0.688785	−	0.724966i	$-0.741855\pi$
$140$		0			0
$141$	0.435493	−	1.34031i	0.0366751	−	0.112874i
$142$		−	0.570666i		−	0.0478892i
$143$	9.80199	+	11.9832i	0.819683	+	1.00209i
$144$	7.77539			0.647949
$145$		0			0
$146$	−0.394492	+	0.286615i	−0.0326484	+	0.0237205i
$147$	−0.0399552	+	0.0549936i	−0.00329545	+	0.00453580i
$148$	−17.9385	+	5.82856i	−1.47453	+	0.479104i
$149$	−4.53161	−	13.9469i	−0.371244	−	1.14257i	−0.945978	−	0.324232i	$-0.894894\pi$
$149$	−4.53161	−	13.9469i	−0.371244	−	1.14257i	0.574733	−	0.818341i	$-0.305106\pi$
$150$		0			0
$151$	6.08301	−	4.41957i	0.495028	−	0.359659i	−0.312086	−	0.950054i	$-0.601028\pi$
$151$	6.08301	−	4.41957i	0.495028	−	0.359659i	0.807115	+	0.590394i	$0.201028\pi$
$152$	−7.43178	−	2.41473i	−0.602797	−	0.195861i
$153$			13.3961i			1.08301i
$154$	−4.24344	+	0.243361i	−0.341946	+	0.0196106i
$155$		0			0
$156$	0.825877	−	2.54179i	0.0661231	−	0.203506i
$157$	−7.86568	−	10.8262i	−0.627750	−	0.864023i	0.370139	−	0.928977i	$-0.379310\pi$
$157$	−7.86568	−	10.8262i	−0.627750	−	0.864023i	−0.997888	+	0.0649531i	$0.979310\pi$
$158$	0.982441	−	1.35221i	0.0781588	−	0.107576i
$159$	0.632355	+	1.94619i	0.0501491	+	0.154343i
$160$		0			0
$161$	−6.02234	−	4.37549i	−0.474627	−	0.344837i
$162$	2.26427	+	3.11651i	0.177898	+	0.244856i
$163$	−0.734206	−	0.238558i	−0.0575075	−	0.0186853i	0.280122	−	0.959964i	$-0.409625\pi$
$163$	−0.734206	−	0.238558i	−0.0575075	−	0.0186853i	−0.337629	+	0.941279i	$0.609625\pi$
$164$	−3.91733			−0.305892
$165$		0			0
$166$	5.30514			0.411759
$167$	8.06716	+	2.62118i	0.624256	+	0.202833i	0.604029	−	0.796962i	$-0.293561\pi$
$167$	8.06716	+	2.62118i	0.624256	+	0.202833i	0.0202268	+	0.999795i	$0.493561\pi$
$168$	0.918013	+	1.26354i	0.0708263	+	0.0974840i
$169$	7.11029	+	5.16593i	0.546946	+	0.397379i
$170$		0			0
$171$	3.88382	+	11.9532i	0.297003	+	0.914081i
$172$	−7.36179	+	10.1326i	−0.561331	+	0.772606i
$173$	−2.98519	−	4.10876i	−0.226960	−	0.312384i	0.680316	−	0.732919i	$-0.261842\pi$
$173$	−2.98519	−	4.10876i	−0.226960	−	0.312384i	−0.907276	+	0.420535i	$0.861842\pi$
$174$	0.143580	−	0.441894i	0.0108848	−	0.0334999i
$175$		0			0
$176$	2.26259	−	8.61366i	0.170549	−	0.649279i
$177$		−	3.79521i		−	0.285265i
$178$	1.25721	+	0.408491i	0.0942315	+	0.0306177i
$179$	−9.15568	+	6.65199i	−0.684328	+	0.497193i	−0.874791	−	0.484501i	$-0.839001\pi$
$179$	−9.15568	+	6.65199i	−0.684328	+	0.497193i	0.190463	+	0.981694i	$0.439001\pi$
$180$		0			0
$181$	2.28674	+	7.03787i	0.169972	+	0.523121i	0.999368	−	0.0355402i	$-0.0113152\pi$
$181$	2.28674	+	7.03787i	0.169972	+	0.523121i	−0.829396	+	0.558661i	$0.811315\pi$
$182$	−5.68929	+	1.84856i	−0.421718	+	0.137025i
$183$	−0.756287	+	1.04094i	−0.0559063	+	0.0769485i
$184$	−4.03774	+	2.93359i	−0.297666	+	0.216267i
$185$		0			0
$186$	0.367941			0.0269787
$187$	14.8403	+	3.89819i	1.08523	+	0.285064i
$188$		−	7.73070i		−	0.563819i
$189$	1.58048	−	4.86423i	0.114963	−	0.353821i
$190$		0			0
$191$	4.17135	+	3.03067i	0.301829	+	0.219291i	0.728382	−	0.685171i	$-0.240272\pi$
$191$	4.17135	+	3.03067i	0.301829	+	0.219291i	−0.426554	+	0.904462i	$0.640272\pi$
$192$	−0.934176	+	0.303532i	−0.0674184	+	0.0219056i
$193$	3.83494	−	1.24605i	0.276045	−	0.0896925i	−0.167723	−	0.985834i	$-0.553641\pi$
$193$	3.83494	−	1.24605i	0.276045	−	0.0896925i	0.443768	+	0.896142i	$0.353641\pi$
$194$	7.15627	+	5.19933i	0.513790	+	0.373290i
$195$		0			0
$196$	−0.115228	+	0.354635i	−0.00823056	+	0.0253311i
$197$		−	11.4176i		−	0.813469i	−0.913547	−	0.406734i	$-0.866667\pi$
$197$		−	11.4176i		−	0.813469i	0.913547	−	0.406734i	$-0.133333\pi$
$198$	4.27089	−	1.66363i	0.303519	−	0.118229i
$199$	7.16644			0.508015			0.254008	−	0.967202i	$-0.418251\pi$
$199$	7.16644			0.508015			0.254008	+	0.967202i	$0.418251\pi$
$200$		0			0
$201$	−1.91319	+	1.39001i	−0.134946	+	0.0980438i
$202$	1.99582	−	2.74701i	0.140425	−	0.193279i
$203$	7.69565	−	2.50047i	0.540128	−	0.175498i
$204$	−0.818531	−	2.51918i	−0.0573086	−	0.176378i
$205$		0			0
$206$	−2.90678	+	2.11190i	−0.202525	+	0.147143i
$207$	7.63443	+	2.48058i	0.530630	+	0.172412i
$208$		−	12.5342i		−	0.869090i
$209$	14.3720	−	0.824235i	0.994132	−	0.0570135i
$210$		0			0
$211$	1.07649	−	3.31309i	0.0741086	−	0.228083i	−0.907140	−	0.420829i	$-0.861739\pi$
$211$	1.07649	−	3.31309i	0.0741086	−	0.228083i	0.981249	+	0.192746i	$0.0617393\pi$
$212$	6.59808	+	9.08148i	0.453158	+	0.623719i
$213$	0.227061	−	0.312523i	0.0155580	−	0.0214137i
$214$	−2.65897	−	8.18348i	−0.181764	−	0.559411i
$215$		0			0
$216$	−2.77420	−	2.01558i	−0.188760	−	0.137143i
$217$	3.76638	+	5.18397i	0.255678	+	0.351911i
$218$	−7.42824	−	2.41358i	−0.503104	−	0.163468i
$219$	−0.330084			−0.0223050
$220$		0			0
$221$	21.5950			1.45264
$222$	1.56070	+	0.507102i	0.104747	+	0.0340345i
$223$	−6.19816	−	8.53103i	−0.415059	−	0.571280i	0.549384	−	0.835570i	$-0.314862\pi$
$223$	−6.19816	−	8.53103i	−0.415059	−	0.571280i	−0.964443	+	0.264290i	$0.914862\pi$
$224$	10.6061	+	7.70575i	0.708647	+	0.514862i
$225$		0			0
$226$	−0.302893	−	0.932209i	−0.0201481	−	0.0620096i
$227$	−0.126972	+	0.174762i	−0.00842743	+	0.0115994i	−0.813210	−	0.581970i	$-0.802282\pi$
$227$	−0.126972	+	0.174762i	−0.00842743	+	0.0115994i	0.804782	+	0.593570i	$0.202282\pi$
$228$	−1.46073	−	2.01052i	−0.0967390	−	0.133150i
$229$	0.0233956	−	0.0720042i	0.00154602	−	0.00475817i	−0.950281	−	0.311395i	$-0.899204\pi$
$229$	0.0233956	−	0.0720042i	0.00154602	−	0.00475817i	0.951827	+	0.306637i	$0.0992037\pi$
$230$		0			0
$231$	−2.42074	−	1.55514i	−0.159273	−	0.102321i
$232$		−	5.42514i		−	0.356178i
$233$	14.3800	+	4.67235i	0.942067	+	0.306096i	0.739488	−	0.673170i	$-0.235068\pi$
$233$	14.3800	+	4.67235i	0.942067	+	0.306096i	0.202579	+	0.979266i	$0.435068\pi$
$234$	5.21881	−	3.79169i	0.341164	−	0.247870i
$235$		0			0
$236$	−6.43336	−	19.7999i	−0.418776	−	1.28886i
$237$	1.07606	−	0.349634i	0.0698977	−	0.0227111i
$238$	−3.48489	+	4.79655i	−0.225892	+	0.310914i
$239$	−18.7406	+	13.6158i	−1.21223	+	0.880734i	−0.995431	−	0.0954825i	$-0.969561\pi$
$239$	−18.7406	+	13.6158i	−1.21223	+	0.880734i	−0.216796	+	0.976217i	$0.569561\pi$
$240$		0			0
$241$	−21.3349			−1.37430			−0.687151	−	0.726515i	$-0.741139\pi$
$241$	−21.3349			−1.37430			−0.687151	+	0.726515i	$0.741139\pi$
$242$	−0.600185	−	5.21544i	−0.0385814	−	0.335261i
$243$			8.32179i			0.533843i
$244$	−2.18107	+	6.71266i	−0.139629	+	0.429734i
$245$		0			0
$246$	0.275729	+	0.200329i	0.0175798	+	0.0127725i
$247$	19.2689	−	6.26085i	1.22605	−	0.398368i
$248$	4.08586	−	1.32758i	0.259453	−	0.0843012i
$249$	2.90535	+	2.11086i	0.184119	+	0.133770i
$250$		0			0
$251$	−1.92266	+	5.91734i	−0.121357	+	0.373499i	−0.993220	−	0.116251i	$-0.962912\pi$
$251$	−1.92266	+	5.91734i	−0.121357	+	0.373499i	0.871863	+	0.489751i	$0.162912\pi$
$252$		−	13.7797i		−	0.868041i
$253$	4.96959	−	7.73567i	0.312435	−	0.486338i
$254$	0.0363991			0.00228388
$255$		0			0
$256$	−0.588982	+	0.427920i	−0.0368113	+	0.0267450i
$257$	8.39964	−	11.5611i	0.523955	−	0.721163i	−0.462239	−	0.886755i	$-0.652954\pi$
$257$	8.39964	−	11.5611i	0.523955	−	0.721163i	0.986194	+	0.165593i	$0.0529537\pi$
$258$	1.03635	−	0.336730i	0.0645203	−	0.0209639i
$259$	8.83126	+	27.1798i	0.548748	+	1.68887i
$260$		0			0
$261$	−7.05926	+	5.12885i	−0.436957	+	0.317468i
$262$	5.21220	+	1.69355i	0.322011	+	0.104628i
$263$			4.13132i			0.254748i	0.991855	+	0.127374i	$0.0406548\pi$
$263$			4.13132i			0.254748i	−0.991855	+	0.127374i	$0.959345\pi$
$264$	−1.49316	+	1.22137i	−0.0918979	+	0.0751703i
$265$		0			0
$266$	−1.71890	+	5.29024i	−0.105393	+	0.324365i
$267$	0.525971	+	0.723937i	0.0321889	+	0.0443042i
$268$	−7.62497	+	10.4949i	−0.465769	+	0.641077i
$269$	0.520367	+	1.60152i	0.0317273	+	0.0976466i	0.965666	−	0.259786i	$-0.0836521\pi$
$269$	0.520367	+	1.60152i	0.0317273	+	0.0976466i	−0.933939	+	0.357433i	$0.883652\pi$
$270$		0			0
$271$	14.9110	+	10.8335i	0.905778	+	0.658086i	0.939943	−	0.341330i	$-0.110877\pi$
$271$	14.9110	+	10.8335i	0.905778	+	0.658086i	−0.0341657	+	0.999416i	$0.510877\pi$
$272$	−7.30188	−	10.0502i	−0.442741	−	0.609381i
$273$	−3.85124	−	1.25134i	−0.233088	−	0.0757348i
$274$	8.74784			0.528476
$275$		0			0
$276$	−1.58725			−0.0955411
$277$	3.25969	+	1.05914i	0.195856	+	0.0636375i	0.405303	−	0.914183i	$-0.367166\pi$
$277$	3.25969	+	1.05914i	0.195856	+	0.0636375i	−0.209446	+	0.977820i	$0.567166\pi$
$278$	6.50466	+	8.95290i	0.390124	+	0.536959i
$279$	−5.59017	−	4.06150i	−0.334675	−	0.243155i
$280$		0			0
$281$	−7.05230	−	21.7048i	−0.420705	−	1.29480i	−0.907047	−	0.421029i	$-0.861669\pi$
$281$	−7.05230	−	21.7048i	−0.420705	−	1.29480i	0.486342	−	0.873769i	$-0.338331\pi$
$282$	−0.395341	+	0.544141i	−0.0235422	+	0.0324031i
$283$	17.1040	+	23.5416i	1.01673	+	1.39941i	0.914473	+	0.404647i	$0.132606\pi$
$283$	17.1040	+	23.5416i	1.01673	+	1.39941i	0.102255	+	0.994758i	$0.467394\pi$
$284$	0.654828	−	2.01535i	0.0388569	−	0.119589i
$285$		0			0
$286$	−2.68183	−	6.88482i	−0.158580	−	0.407108i
$287$			5.93542i			0.350357i
$288$	−13.4451	−	4.36859i	−0.792262	−	0.257422i
$289$	3.56201	−	2.58795i	0.209530	−	0.152232i
$290$		0			0
$291$	1.85035	+	5.69480i	0.108470	+	0.333835i
$292$	−1.72207	+	0.559534i	−0.100776	+	0.0327443i
$293$	12.4690	−	17.1621i	0.728448	−	1.00262i	−0.270753	−	0.962649i	$-0.587273\pi$
$293$	12.4690	−	17.1621i	0.728448	−	1.00262i	0.999201	−	0.0399740i	$-0.0127275\pi$
$294$	0.0262463	−	0.0190690i	0.00153071	−	0.00111213i
$295$		0			0
$296$	19.1608			1.11370
$297$	6.10992	+	1.60492i	0.354534	+	0.0931271i
$298$			6.99883i			0.405432i
$299$	3.99878	−	12.3070i	0.231255	−	0.711731i
$300$		0			0
$301$	15.3527	+	11.1544i	0.884913	+	0.642927i
$302$	−3.41289	+	1.10892i	−0.196390	+	0.0638109i
$303$	2.18601	−	0.710278i	0.125583	−	0.0408044i
$304$	−9.42913	−	6.85066i	−0.540798	−	0.392912i
$305$		0			0
$306$	1.97568	−	6.08051i	0.112942	−	0.347599i
$307$			6.87520i			0.392388i	0.980565	+	0.196194i	$0.0628583\pi$
$307$			6.87520i			0.392388i	−0.980565	+	0.196194i	$0.937142\pi$
$308$	−15.2653	−	4.00982i	−0.869823	−	0.228481i
$309$	−2.43219			−0.138363
$310$		0			0
$311$	−20.3530	+	14.7873i	−1.15411	+	0.838511i	−0.989022	−	0.147768i	$-0.952791\pi$
$311$	−20.3530	+	14.7873i	−1.15411	+	0.838511i	−0.165089	+	0.986279i	$0.552791\pi$
$312$	−1.59583	+	2.19647i	−0.0903459	+	0.124350i
$313$	11.0126	−	3.57821i	0.622469	−	0.202252i	0.0192328	−	0.999815i	$-0.493878\pi$
$313$	11.0126	−	3.57821i	0.622469	−	0.202252i	0.603236	+	0.797563i	$0.293878\pi$
$314$	1.97358	+	6.07406i	0.111376	+	0.342779i
$315$		0			0
$316$	5.02121	−	3.64812i	0.282465	−	0.205223i
$317$	−19.7261	−	6.40940i	−1.10793	−	0.359988i	−0.302780	−	0.953061i	$-0.597915\pi$
$317$	−19.7261	−	6.40940i	−1.10793	−	0.359988i	−0.805149	+	0.593073i	$0.797915\pi$
$318$		−	0.976639i		−	0.0547672i
$319$	3.62759	+	9.31278i	0.203106	+	0.521416i
$320$		0			0
$321$	1.79994	−	5.53963i	0.100463	−	0.309192i
$322$	2.08825	+	2.87422i	0.116373	+	0.160174i
$323$	11.8029	−	16.2453i	0.656731	−	0.903913i
$324$	4.42034	+	13.6044i	0.245575	+	0.755801i
$325$		0			0
$326$	0.298074	+	0.216564i	0.0165088	+	0.0119943i
$327$	−3.10771	−	4.27740i	−0.171857	−	0.236541i
$328$	3.78469	+	1.22972i	0.208975	+	0.0679000i
$329$	−11.7133			−0.645777
$330$		0			0
$331$	−32.1415			−1.76665			−0.883327	−	0.468757i	$-0.844702\pi$
$331$	−32.1415			−1.76665			−0.883327	+	0.468757i	$0.844702\pi$
$332$	18.7356	+	6.08755i	1.02825	+	0.334098i
$333$	−18.1143	−	24.9322i	−0.992657	−	1.36627i
$334$	−3.27512	−	2.37951i	−0.179207	−	0.130201i
$335$		0			0
$336$	0.719847	+	2.21546i	0.0392709	+	0.120863i
$337$	10.5780	−	14.5594i	0.576221	−	0.793100i	−0.417054	−	0.908882i	$-0.636937\pi$
$337$	10.5780	−	14.5594i	0.576221	−	0.793100i	0.993275	+	0.115782i	$0.0369373\pi$
$338$	−2.46549	−	3.39346i	−0.134105	−	0.184580i
$339$	0.205037	−	0.631039i	0.0111361	−	0.0342734i
$340$		0			0
$341$	−6.12608	+	5.01098i	−0.331746	+	0.271360i
$342$		−	5.99834i		−	0.324353i
$343$	−17.3392	−	5.63386i	−0.936231	−	0.304200i
$344$	10.2933	−	7.47855i	0.554980	−	0.403217i
$345$		0			0
$346$	0.749016	+	2.30523i	0.0402673	+	0.123930i
$347$	−7.65583	+	2.48753i	−0.410986	+	0.133538i	−0.507211	−	0.861822i	$-0.669323\pi$
$347$	−7.65583	+	2.48753i	−0.410986	+	0.133538i	0.0962243	+	0.995360i	$0.469323\pi$
$348$	1.01413	−	1.39583i	0.0543631	−	0.0748244i
$349$	15.5569	−	11.3027i	0.832741	−	0.605022i	−0.0875926	−	0.996156i	$-0.527917\pi$
$349$	15.5569	−	11.3027i	0.832741	−	0.605022i	0.920333	+	0.391135i	$0.127917\pi$
$350$		0			0
$351$	8.89088			0.474560
$352$	−8.75202	+	13.6234i	−0.466484	+	0.726131i
$353$			14.8497i			0.790371i	0.918601	+	0.395186i	$0.129320\pi$
$353$			14.8497i			0.790371i	−0.918601	+	0.395186i	$0.870680\pi$
$354$	−0.559723	+	1.72265i	−0.0297489	+	0.0915578i
$355$		0			0
$356$	3.97119	+	2.88524i	0.210473	+	0.152917i
$357$	−3.81698	+	1.24021i	−0.202016	+	0.0656391i
$358$	5.13682	−	1.66905i	0.271489	−	0.0882123i
$359$	8.27079	+	6.00908i	0.436516	+	0.317147i	0.784249	−	0.620446i	$-0.213048\pi$
$359$	8.27079	+	6.00908i	0.436516	+	0.317147i	−0.347733	+	0.937594i	$0.613048\pi$
$360$		0			0
$361$	−0.0496143	+	0.152697i	−0.00261128	+	0.00803670i
$362$		−	3.53175i		−	0.185625i
$363$	1.74648	−	3.09503i	0.0916662	−	0.162447i
$364$	−22.2134			−1.16430
$365$		0			0
$366$	0.496799	−	0.360945i	0.0259681	−	0.0188669i
$367$	−8.31327	+	11.4422i	−0.433949	+	0.597280i	−0.968854	−	0.247632i	$-0.920347\pi$
$367$	−8.31327	+	11.4422i	−0.433949	+	0.597280i	0.534905	+	0.844912i	$0.320347\pi$
$368$	−7.07969	+	2.30033i	−0.369054	+	0.119913i
$369$	−1.97786	−	6.08724i	−0.102964	−	0.316889i
$370$		0			0
$371$	13.7600	−	9.99722i	0.714383	−	0.519030i
$372$	1.29941	+	0.422205i	0.0673715	+	0.0218903i
$373$			12.4600i			0.645154i	0.946543	+	0.322577i	$0.104549\pi$
$373$			12.4600i			0.645154i	−0.946543	+	0.322577i	$0.895451\pi$
$374$	−6.16114	−	3.95807i	−0.318585	−	0.204667i
$375$		0			0
$376$	−2.42681	+	7.46894i	−0.125153	+	0.385181i
$377$	8.26788	+	11.3798i	0.425818	+	0.586088i
$378$	−1.43477	+	1.97479i	−0.0737965	+	0.101572i
$379$	−5.04840	−	15.5374i	−0.259319	−	0.798102i	−0.992948	−	0.118552i	$-0.962175\pi$
$379$	−5.04840	−	15.5374i	−0.259319	−	0.798102i	0.733629	−	0.679550i	$-0.237825\pi$
$380$		0			0
$381$	0.0199338	+	0.0144828i	0.00102124	+	0.000741975i
$382$	−1.44642	−	1.99082i	−0.0740051	−	0.101859i
$383$	−0.772874	−	0.251122i	−0.0394920	−	0.0128317i	0.289204	−	0.957267i	$-0.406609\pi$
$383$	−0.772874	−	0.251122i	−0.0394920	−	0.0128317i	−0.328696	+	0.944436i	$0.606609\pi$
$384$	3.62339			0.184905
$385$		0			0
$386$	−1.92445			−0.0979522
$387$	−19.4623	−	6.32370i	−0.989327	−	0.321452i
$388$	19.3068	+	26.5736i	0.980155	+	1.34907i
$389$	−24.5894	−	17.8652i	−1.24673	−	0.905802i	−0.248702	−	0.968580i	$-0.580004\pi$
$389$	−24.5894	−	17.8652i	−1.24673	−	0.905802i	−0.998028	+	0.0627780i	$0.980004\pi$
$390$		0			0
$391$	−3.96321	−	12.1975i	−0.200428	−	0.616854i
$392$	0.222653	−	0.306455i	0.0112457	−	0.0154783i
$393$	2.18060	+	3.00134i	0.109997	+	0.151398i
$394$	−1.68388	+	5.18245i	−0.0848327	+	0.261088i
$395$		0			0
$396$	16.9920	−	0.974490i	0.853879	−	0.0489700i
$397$			14.8996i			0.747789i	0.927471	+	0.373894i	$0.121978\pi$
$397$			14.8996i			0.747789i	−0.927471	+	0.373894i	$0.878022\pi$
$398$	−3.25285	−	1.05692i	−0.163051	−	0.0529784i
$399$	−3.04628	+	2.21325i	−0.152505	+	0.110801i
$400$		0			0
$401$	3.76049	+	11.5736i	0.187790	+	0.577957i	0.999985	−	0.00542792i	$-0.00172777\pi$
$401$	3.76049	+	11.5736i	0.187790	+	0.577957i	−0.812196	+	0.583385i	$0.801728\pi$
$402$	1.07340	−	0.348768i	0.0535362	−	0.0173950i
$403$	−6.54727	+	9.01155i	−0.326143	+	0.448897i
$404$	10.2006	−	7.41114i	0.507496	−	0.368718i
$405$		0			0
$406$	−3.86184			−0.191660
$407$	−32.8913	+	12.8121i	−1.63036	+	0.635071i
$408$			2.69083i			0.133216i
$409$	0.0809957	−	0.249279i	0.00400498	−	0.0123261i	−0.949034	−	0.315174i	$-0.897937\pi$
$409$	0.0809957	−	0.249279i	0.00400498	−	0.0123261i	0.953039	+	0.302847i	$0.0979373\pi$
$410$		0			0
$411$	4.79073	+	3.48067i	0.236309	+	0.171689i
$412$	−12.6889	+	4.12288i	−0.625138	+	0.203120i
$413$	−30.0002	+	9.74764i	−1.47621	+	0.479650i
$414$	−3.09944	−	2.25187i	−0.152329	−	0.110674i
$415$		0			0
$416$	−7.04232	+	21.6740i	−0.345278	+	1.06266i
$417$			7.49116i			0.366844i
$418$	−6.64503	−	1.74548i	−0.325019	−	0.0853744i
$419$	1.26916			0.0620023			0.0310012	−	0.999519i	$-0.490130\pi$
$419$	1.26916			0.0620023			0.0310012	+	0.999519i	$0.490130\pi$
$420$		0			0
$421$	23.9999	−	17.4369i	1.16968	−	0.849824i	0.178712	−	0.983902i	$-0.442807\pi$
$421$	23.9999	−	17.4369i	1.16968	−	0.849824i	0.990971	+	0.134078i	$0.0428071\pi$
$422$	−0.977240	+	1.34506i	−0.0475713	+	0.0654763i
$423$	12.0129	−	3.90324i	0.584089	−	0.189782i
$424$	−3.52384	−	10.8452i	−0.171133	−	0.526692i
$425$		0			0
$426$	−0.149155	+	0.108367i	−0.00722658	+	0.00525041i
$427$	10.1708	+	3.30470i	0.492200	+	0.159926i
$428$		−	31.9518i		−	1.54445i
$429$	1.27070	−	4.83752i	0.0613497	−	0.233558i
$430$		0			0
$431$	9.68919	−	29.8203i	0.466712	−	1.43639i	−0.390105	−	0.920771i	$-0.627561\pi$
$431$	9.68919	−	29.8203i	0.466712	−	1.43639i	0.856817	−	0.515621i	$-0.172439\pi$
$432$	−3.00626	−	4.13776i	−0.144639	−	0.199078i
$433$	−15.3015	+	21.0607i	−0.735345	+	1.01212i	0.263528	+	0.964652i	$0.415114\pi$
$433$	−15.3015	+	21.0607i	−0.735345	+	1.01212i	−0.998873	+	0.0474634i	$0.984886\pi$
$434$	−0.945023	−	2.90848i	−0.0453625	−	0.139612i
$435$		0			0
$436$	−23.4639	−	17.0475i	−1.12372	−	0.816429i
$437$	−7.07263	−	9.73464i	−0.338330	−	0.465671i
$438$	0.149825	+	0.0486812i	0.00715893	+	0.00232608i
$439$	−14.4191			−0.688185			−0.344093	−	0.938936i	$-0.611813\pi$
$439$	−14.4191			−0.688185			−0.344093	+	0.938936i	$0.611813\pi$
$440$		0			0
$441$	−0.609255			−0.0290121
$442$	−9.80199	−	3.18486i	−0.466233	−	0.151488i
$443$	0.194326	+	0.267467i	0.00923273	+	0.0127078i	0.813608	−	0.581413i	$-0.197500\pi$
$443$	0.194326	+	0.267467i	0.00923273	+	0.0127078i	−0.804376	+	0.594121i	$0.797500\pi$
$444$	4.92986	+	3.58175i	0.233961	+	0.169982i
$445$		0			0
$446$	1.55518	+	4.78636i	0.0736400	+	0.226641i
$447$	−2.78476	+	3.83289i	−0.131715	+	0.181289i
$448$	4.79869	+	6.60483i	0.226717	+	0.312049i
$449$	−2.62920	+	8.09185i	−0.124080	+	0.381878i	−0.993732	−	0.111786i	$-0.964343\pi$
$449$	−2.62920	+	8.09185i	−0.124080	+	0.381878i	0.869653	+	0.493664i	$0.164343\pi$
$450$		0			0
$451$	−7.31906	+	0.419748i	−0.344641	+	0.0197652i
$452$		−	3.63974i		−	0.171199i
$453$	−2.31028	−	0.750657i	−0.108547	−	0.0352689i
$454$	0.0834069	−	0.0605986i	0.00391448	−	0.00284404i
$455$		0			0
$456$	0.780130	+	2.40099i	0.0365329	+	0.112437i
$457$	1.08275	−	0.351807i	0.0506490	−	0.0164569i	−0.283583	−	0.958948i	$-0.591523\pi$
$457$	1.08275	−	0.351807i	0.0506490	−	0.0164569i	0.334232	+	0.942491i	$0.391523\pi$
$458$	−0.0212386	+	0.0292324i	−0.000992413	+	0.00136594i
$459$	7.12889	−	5.17944i	0.332748	−	0.241756i
$460$		0			0
$461$	14.5073			0.675670			0.337835	−	0.941205i	$-0.390305\pi$
$461$	14.5073			0.675670			0.337835	+	0.941205i	$0.390305\pi$
$462$	0.869422	+	1.06289i	0.0404492	+	0.0494503i
$463$		−	4.89739i		−	0.227601i	−0.993504	−	0.113801i	$-0.963698\pi$
$463$		−	4.89739i		−	0.227601i	0.993504	−	0.113801i	$-0.0363025\pi$
$464$	2.50047	−	7.69565i	0.116081	−	0.357261i
$465$		0			0
$466$	−5.83803	−	4.24157i	−0.270441	−	0.196487i
$467$	30.8361	−	10.0193i	1.42693	−	0.463637i	0.509131	−	0.860689i	$-0.329967\pi$
$467$	30.8361	−	10.0193i	1.42693	−	0.463637i	0.917796	+	0.397053i	$0.129967\pi$
$468$	22.7816	−	7.40218i	1.05308	−	0.342166i
$469$	15.9015	+	11.5531i	0.734264	+	0.533474i
$470$		0			0
$471$	−1.33597	+	4.11171i	−0.0615585	+	0.189457i
$472$			21.1490i			0.973461i
$473$	−12.6689	+	19.7204i	−0.582516	+	0.906747i
$474$	−0.539990			−0.0248026
$475$		0			0
$476$	−17.8111	+	12.9406i	−0.816373	+	0.593129i
$477$	−10.7806	+	14.8382i	−0.493609	+	0.679394i
$478$	10.5145	−	3.41635i	0.480920	−	0.156260i
$479$	−5.48054	−	16.8674i	−0.250412	−	0.770690i	−0.994699	−	0.102830i	$-0.967210\pi$
$479$	−5.48054	−	16.8674i	−0.250412	−	0.770690i	0.744287	−	0.667860i	$-0.232790\pi$
$480$		0			0
$481$	−40.1915	+	29.2009i	−1.83258	+	1.33144i
$482$	9.68394	+	3.14650i	0.441091	+	0.143319i
$483$			2.40495i			0.109429i
$484$	3.86502	−	19.1075i	0.175683	−	0.868521i
$485$		0			0
$486$	1.22731	−	3.77727i	0.0556719	−	0.171341i
$487$	−10.8507	−	14.9347i	−0.491691	−	0.676754i	0.489008	−	0.872279i	$-0.337359\pi$
$487$	−10.8507	−	14.9347i	−0.491691	−	0.676754i	−0.980699	+	0.195525i	$0.937359\pi$
$488$	4.21445	−	5.80069i	0.190779	−	0.262585i
$489$	0.0770712	+	0.237201i	0.00348528	+	0.0107266i
$490$		0			0
$491$	9.25018	+	6.72065i	0.417455	+	0.303299i	0.776613	−	0.629978i	$-0.216936\pi$
$491$	9.25018	+	6.72065i	0.417455	+	0.303299i	−0.359158	+	0.933277i	$0.616936\pi$
$492$	0.743887	+	1.02387i	0.0335370	+	0.0461597i
$493$	13.2587	+	4.30802i	0.597142	+	0.194023i
$494$	−9.66954			−0.435053
$495$		0			0
$496$	6.40774			0.287716
$497$	−3.05360	−	0.992176i	−0.136973	−	0.0445052i
$498$	−1.00743	−	1.38661i	−0.0451439	−	0.0621353i
$499$	8.80335	+	6.39601i	0.394092	+	0.286325i	0.767130	−	0.641491i	$-0.221684\pi$
$499$	8.80335	+	6.39601i	0.394092	+	0.286325i	−0.373038	+	0.927816i	$0.621684\pi$
$500$		0			0
$501$	−0.846827	−	2.60627i	−0.0378335	−	0.116439i
$502$	1.74540	−	2.40233i	0.0779009	−	0.107221i
$503$	−26.2885	−	36.1830i	−1.17215	−	1.61332i	−0.647776	−	0.761831i	$-0.724301\pi$
$503$	−26.2885	−	36.1830i	−1.17215	−	1.61332i	−0.524371	−	0.851490i	$-0.675699\pi$
$504$	−4.32571	+	13.3132i	−0.192682	+	0.593015i
$505$		0			0
$506$	−3.39657	+	2.77831i	−0.150996	+	0.123511i
$507$		−	2.83941i		−	0.126103i
$508$	0.128546	+	0.0417673i	0.00570332	+	0.00185312i
$509$	−11.1720	+	8.11693i	−0.495190	+	0.359777i	−0.807177	−	0.590310i	$-0.799006\pi$
$509$	−11.1720	+	8.11693i	−0.495190	+	0.359777i	0.311987	+	0.950086i	$0.399006\pi$
$510$		0			0
$511$	0.847790	+	2.60923i	0.0375040	+	0.115425i
$512$	21.6635	−	7.03891i	0.957402	−	0.311079i
$513$	4.85938	−	6.68836i	0.214547	−	0.295298i
$514$	−5.51766	+	4.00881i	−0.243374	+	0.176821i
$515$		0			0
$516$	4.04635			0.178130
$517$	−0.828356	−	14.4439i	−0.0364311	−	0.635241i
$518$		−	13.6394i		−	0.599281i
$519$	−0.507030	+	1.56048i	−0.0222562	+	0.0684974i
$520$		0			0
$521$	2.95269	+	2.14525i	0.129360	+	0.0939852i	0.650584	−	0.759435i	$-0.274524\pi$
$521$	2.95269	+	2.14525i	0.129360	+	0.0939852i	−0.521224	+	0.853420i	$0.674524\pi$
$522$	3.96061	−	1.28688i	0.173351	−	0.0563253i
$523$	4.74299	−	1.54109i	0.207396	−	0.0673872i	−0.203476	−	0.979080i	$-0.565224\pi$
$523$	4.74299	−	1.54109i	0.207396	−	0.0673872i	0.410873	+	0.911693i	$0.365224\pi$
$524$	16.4640	+	11.9618i	0.719233	+	0.522553i
$525$		0			0
$526$	0.609292	−	1.87521i	0.0265664	−	0.0817630i
$527$			11.0398i			0.480901i
$528$	−2.68101	+	1.04433i	−0.116676	+	0.0454486i
$529$	15.3148			0.665860
$530$		0			0
$531$	27.5193	−	19.9939i	1.19424	−	0.867663i
$532$	−12.1409	+	16.7105i	−0.526375	+	0.724493i
$533$	−9.81284	+	3.18839i	−0.425041	+	0.138104i
$534$	−0.131972	−	0.406167i	−0.00571097	−	0.0175766i
$535$		0			0
$536$	10.6613	−	7.74591i	0.460499	−	0.334572i
$537$	3.47726	+	1.12983i	0.150055	+	0.0487558i
$538$		−	0.803678i		−	0.0346490i
$539$	−0.177290	+	0.674939i	−0.00763640	+	0.0290717i
$540$		0			0
$541$	0.0765109	−	0.235476i	0.00328946	−	0.0101239i	−0.949398	−	0.314075i	$-0.898306\pi$
$541$	0.0765109	−	0.235476i	0.00328946	−	0.0101239i	0.952688	+	0.303951i	$0.0983058\pi$
$542$	−5.17038	−	7.11642i	−0.222087	−	0.305676i
$543$	1.40524	−	1.93415i	0.0603048	−	0.0830025i
$544$	6.97967	+	21.4812i	0.299251	+	0.921000i
$545$		0			0
$546$	1.56353	+	1.13597i	0.0669131	+	0.0486152i
$547$	−14.8780	−	20.4779i	−0.636139	−	0.875570i	0.362263	−	0.932076i	$-0.382004\pi$
$547$	−14.8780	−	20.4779i	−0.636139	−	0.875570i	−0.998402	+	0.0565056i	$0.982004\pi$
$548$	30.8937	+	10.0380i	1.31971	+	0.428801i
$549$	−11.5322			−0.492182
$550$		0			0
$551$	13.0796			0.557208
$552$	1.53350	+	0.498266i	0.0652703	+	0.0212076i
$553$	−5.52753	−	7.60799i	−0.235054	−	0.323525i
$554$	−1.32338	−	0.961489i	−0.0562249	−	0.0408498i
$555$		0			0
$556$	12.6985	+	39.0819i	0.538536	+	1.65744i
$557$	22.7280	−	31.2824i	0.963015	−	1.32548i	0.0175177	−	0.999847i	$-0.494424\pi$
$557$	22.7280	−	31.2824i	0.963015	−	1.32548i	0.945497	−	0.325630i	$-0.105576\pi$
$558$	1.93839	+	2.66796i	0.0820586	+	0.112944i
$559$	−10.1940	+	31.3740i	−0.431161	+	1.32698i
$560$		0			0
$561$	−1.79926	−	4.61907i	−0.0759648	−	0.195017i
$562$			10.8919i			0.459447i
$563$	13.2541	+	4.30653i	0.558595	+	0.181498i	0.574689	−	0.818372i	$-0.305123\pi$
$563$	13.2541	+	4.30653i	0.558595	+	0.181498i	−0.0160940	+	0.999870i	$0.505123\pi$
$564$	−2.02057	+	1.46803i	−0.0850815	+	0.0618153i
$565$		0			0
$566$	−4.29157	−	13.2081i	−0.180388	−	0.555178i
$567$	20.6130	−	6.69757i	0.865665	−	0.281272i
$568$	−1.26531	+	1.74155i	−0.0530913	+	0.0730739i
$569$	22.5817	−	16.4065i	0.946672	−	0.687798i	−0.00334520	−	0.999994i	$-0.501065\pi$
$569$	22.5817	−	16.4065i	0.946672	−	0.687798i	0.950017	+	0.312197i	$0.101065\pi$
$570$		0			0
$571$	−31.4113			−1.31452			−0.657261	−	0.753663i	$-0.728285\pi$
$571$	−31.4113			−1.31452			−0.657261	+	0.753663i	$0.728285\pi$
$572$	−1.57091	−	27.3917i	−0.0656831	−	1.14530i
$573$		−	1.66578i		−	0.0695889i
$574$	0.875365	−	2.69410i	0.0365370	−	0.112449i
$575$		0			0
$576$	−7.12237	−	5.17470i	−0.296765	−	0.215613i
$577$	19.7201	−	6.40744i	0.820958	−	0.266745i	0.131726	−	0.991286i	$-0.457948\pi$
$577$	19.7201	−	6.40744i	0.820958	−	0.266745i	0.689232	+	0.724541i	$0.257948\pi$
$578$	−1.99847	+	0.649343i	−0.0831255	+	0.0270091i
$579$	−1.05392	−	0.765719i	−0.0437995	−	0.0318222i
$580$		0			0
$581$	9.22368	−	28.3876i	0.382663	−	1.17771i
$582$		−	2.85777i		−	0.118458i
$583$	13.3008	+	16.2607i	0.550864	+	0.673448i
$584$	1.83941			0.0761153
$585$		0			0
$586$	−8.19080	+	5.95097i	−0.338359	+	0.245832i
$587$	−8.95591	+	12.3267i	−0.369650	+	0.508779i	−0.952806	−	0.303581i	$-0.901818\pi$
$587$	−8.95591	+	12.3267i	−0.369650	+	0.508779i	0.583156	+	0.812360i	$0.301818\pi$
$588$	0.114572	−	0.0372268i	0.00472488	−	0.00153521i
$589$	3.20067	+	9.85066i	0.131881	+	0.405889i
$590$		0			0
$591$	−2.98421	+	2.16816i	−0.122754	+	0.0891860i
$592$	27.1798	+	8.83126i	1.11708	+	0.362962i
$593$			27.5413i			1.13098i	0.824754	+	0.565492i	$0.191314\pi$
$593$			27.5413i			1.13098i	−0.824754	+	0.565492i	$0.808686\pi$
$594$	−2.53661	−	1.62958i	−0.104078	−	0.0668624i
$595$		0			0
$596$	−8.03103	+	24.7170i	−0.328964	+	1.01245i
$597$	−1.36088	−	1.87309i	−0.0556971	−	0.0766605i
$598$	−3.63010	+	4.99640i	−0.148446	+	0.204318i
$599$	8.26097	+	25.4247i	0.337534	+	1.03882i	0.965460	+	0.260551i	$0.0839041\pi$
$599$	8.26097	+	25.4247i	0.337534	+	1.03882i	−0.627926	+	0.778273i	$0.716096\pi$
$600$		0			0
$601$	−1.94714	−	1.41468i	−0.0794255	−	0.0577060i	0.547364	−	0.836895i	$-0.315631\pi$
$601$	−1.94714	−	1.41468i	−0.0794255	−	0.0577060i	−0.626789	+	0.779189i	$0.715631\pi$
$602$	−5.32353	−	7.32722i	−0.216971	−	0.298635i
$603$	−20.1581	−	6.54977i	−0.820902	−	0.266727i
$604$	−13.3254			−0.542202
$605$		0			0
$606$	−1.09699			−0.0445620
$607$	−9.78909	−	3.18067i	−0.397327	−	0.129099i	0.103536	−	0.994626i	$-0.466984\pi$
$607$	−9.78909	−	3.18067i	−0.397327	−	0.129099i	−0.500864	+	0.865526i	$0.666984\pi$
$608$	12.4557	+	17.1438i	0.505147	+	0.695275i
$609$	−2.11492	−	1.53658i	−0.0857010	−	0.0622654i
$610$		0			0
$611$	−6.29216	−	19.3653i	−0.254553	−	0.783435i
$612$	13.9545	−	19.2068i	0.564079	−	0.776388i
$613$	−16.3849	−	22.5519i	−0.661779	−	0.910861i	0.337759	−	0.941232i	$-0.390331\pi$
$613$	−16.3849	−	22.5519i	−0.661779	−	0.910861i	−0.999539	+	0.0303715i	$0.990331\pi$
$614$	1.01396	−	3.12066i	0.0409203	−	0.125940i
$615$		0			0
$616$	13.4897	+	8.66611i	0.543515	+	0.349168i
$617$			28.7216i			1.15629i	0.815935	+	0.578143i	$0.196222\pi$
$617$			28.7216i			1.15629i	−0.815935	+	0.578143i	$0.803778\pi$
$618$	1.10398	+	0.358703i	0.0444084	+	0.0144292i
$619$	18.3621	−	13.3408i	0.738035	−	0.536214i	−0.154060	−	0.988061i	$-0.549235\pi$
$619$	18.3621	−	13.3408i	0.738035	−	0.536214i	0.892095	+	0.451848i	$0.149235\pi$
$620$		0			0
$621$	−1.63169	−	5.02183i	−0.0654776	−	0.201519i
$622$	11.4191	−	3.71029i	0.457864	−	0.148769i
$623$	4.37163	−	6.01703i	0.175146	−	0.241067i
$624$	−3.27606	+	2.38020i	−0.131147	+	0.0952842i
$625$		0			0
$626$	−5.52635			−0.220877
$627$	−2.94462	−	3.59989i	−0.117597	−	0.143766i
$628$			23.7157i			0.946360i
$629$	−15.2152	+	46.8277i	−0.606671	+	1.86714i
$630$		0			0
$631$	−23.0864	−	16.7733i	−0.919056	−	0.667733i	0.0242327	−	0.999706i	$-0.492286\pi$
$631$	−23.0864	−	16.7733i	−0.919056	−	0.667733i	−0.943289	+	0.331973i	$0.892286\pi$
$632$	−5.99641	+	1.94835i	−0.238524	+	0.0775013i
$633$	−1.07037	+	0.347783i	−0.0425432	+	0.0138231i
$634$	8.00844	+	5.81847i	0.318056	+	0.231081i
$635$		0			0
$636$	1.12067	−	3.44908i	0.0444376	−	0.136765i
$637$			0.982140i			0.0389138i
$638$	−0.273106	−	4.76209i	−0.0108124	−	0.188533i
$639$	3.46233			0.136968
$640$		0			0
$641$	−1.92040	+	1.39526i	−0.0758514	+	0.0551093i	−0.625065	−	0.780573i	$-0.714927\pi$
$641$	−1.92040	+	1.39526i	−0.0758514	+	0.0551093i	0.549213	+	0.835682i	$0.314927\pi$
$642$	−1.63399	+	2.24899i	−0.0644883	+	0.0887605i
$643$	−10.8043	+	3.51053i	−0.426080	+	0.138442i	−0.514204	−	0.857668i	$-0.671913\pi$
$643$	−10.8043	+	3.51053i	−0.426080	+	0.138442i	0.0881244	+	0.996109i	$0.471913\pi$
$644$	4.07670	+	12.5468i	0.160644	+	0.494413i
$645$		0			0
$646$	−7.75323	+	5.63305i	−0.305047	+	0.221630i
$647$	46.0520	+	14.9632i	1.81049	+	0.588264i	0.999997	+	0.00251822i	$0.000801574\pi$
$647$	46.0520	+	14.9632i	1.81049	+	0.588264i	0.810495	+	0.585746i	$0.199198\pi$
$648$		−	14.5314i		−	0.570848i
$649$	−14.1415	−	36.3043i	−0.555104	−	1.42507i
$650$		0			0
$651$	0.639713	−	1.96883i	0.0250723	−	0.0771647i
$652$	0.804171	+	1.10685i	0.0314938	+	0.0433475i
$653$	17.4894	−	24.0722i	0.684415	−	0.942016i	−0.315562	−	0.948905i	$-0.602193\pi$
$653$	17.4894	−	24.0722i	0.684415	−	0.942016i	0.999976	+	0.00688905i	$0.00219287\pi$
$654$	0.779758	+	2.39985i	0.0304910	+	0.0938415i
$655$		0			0
$656$	4.80186	+	3.48875i	0.187481	+	0.136213i
$657$	−1.73895	−	2.39346i	−0.0678429	−	0.0933777i
$658$	5.31669	+	1.72750i	0.207266	+	0.0673449i
$659$	28.4931			1.10993			0.554966	−	0.831873i	$-0.312731\pi$
$659$	28.4931			1.10993			0.554966	+	0.831873i	$0.312731\pi$
$660$		0			0
$661$	−1.02875			−0.0400139			−0.0200070	−	0.999800i	$-0.506369\pi$
$661$	−1.02875			−0.0400139			−0.0200070	+	0.999800i	$0.506369\pi$
$662$	14.5890	+	4.74027i	0.567019	+	0.184236i
$663$	−4.10081	−	5.64428i	−0.159262	−	0.219206i
$664$	−16.1902	−	11.7629i	−0.628301	−	0.456488i
$665$		0			0
$666$	4.54506	+	13.9883i	0.176118	+	0.542034i
$667$	4.91027	−	6.75841i	0.190127	−	0.261687i
$668$	−8.83591	−	12.1616i	−0.341872	−	0.470546i
$669$	−1.05275	+	3.24002i	−0.0407016	+	0.125267i
$670$		0			0
$671$	−3.35580	+	12.7755i	−0.129549	+	0.493192i
$672$		−	4.23540i		−	0.163384i
$673$	12.3988	+	4.02863i	0.477940	+	0.155292i	0.538073	−	0.842898i	$-0.319152\pi$
$673$	12.3988	+	4.02863i	0.477940	+	0.155292i	−0.0601327	+	0.998190i	$0.519152\pi$
$674$	−6.94861	+	5.04846i	−0.267651	+	0.194459i
$675$		0			0
$676$	−4.81316	−	14.8134i	−0.185122	−	0.569746i
$677$	−35.2903	+	11.4665i	−1.35632	+	0.440694i	−0.894812	−	0.446444i	$-0.852690\pi$
$677$	−35.2903	+	11.4665i	−1.35632	+	0.440694i	−0.461505	+	0.887138i	$0.652690\pi$
$678$	−0.186133	+	0.256190i	−0.00714840	+	0.00983893i
$679$	40.2635	−	29.2531i	1.54517	−	1.12263i
$680$		0			0
$681$	0.0697890			0.00267432
$682$	3.51966	−	1.37101i	0.134775	−	0.0524986i
$683$		−	32.8992i		−	1.25885i	−0.777061	−	0.629426i	$-0.783290\pi$
$683$		−	32.8992i		−	1.25885i	0.777061	−	0.629426i	$-0.216710\pi$
$684$	6.88299	−	21.1837i	0.263178	−	0.809978i
$685$		0			0
$686$	7.03941	+	5.11443i	0.268766	+	0.195270i
$687$	−0.0232625	+	0.00755844i	−0.000887519	+	0.000288372i
$688$	18.0481	−	5.86420i	0.688079	−	0.223570i
$689$	23.9197	+	17.3787i	0.911267	+	0.662074i
$690$		0			0
$691$	11.3409	−	34.9036i	0.431427	−	1.32780i	−0.465277	−	0.885165i	$-0.654045\pi$
$691$	11.3409	−	34.9036i	0.431427	−	1.32780i	0.896704	−	0.442631i	$-0.145955\pi$
$692$			9.00061i			0.342152i
$693$	−1.47652	−	25.7457i	−0.0560883	−	0.978000i
$694$	3.84185			0.145835
$695$		0			0
$696$	−1.41797	+	1.03022i	−0.0537480	+	0.0390502i
$697$	−6.01072	+	8.27305i	−0.227672	+	0.313364i
$698$	−8.72823	+	2.83597i	−0.330368	+	0.107343i
$699$	−1.50950	−	4.64577i	−0.0570946	−	0.175719i
$700$		0			0
$701$	29.3266	−	21.3070i	1.10765	−	0.804755i	0.125359	−	0.992111i	$-0.459992\pi$
$701$	29.3266	−	21.3070i	1.10765	−	0.804755i	0.982292	+	0.187356i	$0.0599919\pi$
$702$	−4.03558	−	1.31124i	−0.152313	−	0.0494895i
$703$			46.1949i			1.74227i
$704$	−7.80516	+	6.38443i	−0.294168	+	0.240622i
$705$		0			0
$706$	2.19006	−	6.74031i	0.0824240	−	0.253675i
$707$	−11.2291	−	15.4556i	−0.422315	−	0.581267i
$708$	−3.95342	+	5.44141i	−0.148578	+	0.204501i
$709$	5.74811	+	17.6909i	0.215875	+	0.664394i	0.999090	+	0.0426440i	$0.0135781\pi$
$709$	5.74811	+	17.6909i	0.215875	+	0.664394i	−0.783216	+	0.621750i	$0.786422\pi$
$710$		0			0
$711$	8.20413	+	5.96065i	0.307679	+	0.223542i
$712$	−2.93100	−	4.03418i	−0.109844	−	0.151187i
$713$	6.29158	+	2.04426i	0.235621	+	0.0765580i
$714$	1.91544			0.0716836
$715$		0			0
$716$	20.0563			0.749540
$717$	7.11754	+	2.31263i	0.265809	+	0.0863667i
$718$	−2.86790	−	3.94732i	−0.107029	−	0.147313i
$719$	−30.2799	−	21.9996i	−1.12925	−	0.820447i	−0.143664	−	0.989627i	$-0.545888\pi$
$719$	−30.2799	−	21.9996i	−1.12925	−	0.820447i	−0.985585	+	0.169179i	$0.945888\pi$
$720$		0			0
$721$	6.24687	+	19.2259i	0.232645	+	0.716009i
$722$	0.0450400	−	0.0619923i	0.00167622	−	0.00230711i
$723$	4.05142	+	5.57630i	0.150674	+	0.207385i
$724$	4.05262	−	12.4727i	0.150614	−	0.463544i
$725$		0			0
$726$	−1.24919	+	1.14726i	−0.0463617	+	0.0425789i
$727$		−	14.6011i		−	0.541526i	−0.962646	−	0.270763i	$-0.912724\pi$
$727$		−	14.6011i		−	0.541526i	0.962646	−	0.270763i	$-0.0872760\pi$
$728$	21.4613	+	6.97319i	0.795407	+	0.258443i
$729$	−17.4149	+	12.6527i	−0.644997	+	0.468618i
$730$		0			0
$731$	10.1033	+	31.0949i	0.373686	+	1.15009i
$732$	2.16867	−	0.704642i	0.0801562	−	0.0260443i
$733$	24.5911	−	33.8468i	0.908293	−	1.25016i	−0.0594528	−	0.998231i	$-0.518936\pi$
$733$	24.5911	−	33.8468i	0.908293	−	1.25016i	0.967746	−	0.251927i	$-0.0810644\pi$
$734$	5.46092	−	3.96759i	0.201566	−	0.146447i
$735$		0			0
$736$	13.5346			0.498891
$737$	−13.1218	+	20.4254i	−0.483348	+	0.752381i
$738$			3.05470i			0.112445i
$739$	3.68654	−	11.3460i	0.135612	−	0.417370i	−0.860073	−	0.510171i	$-0.829582\pi$
$739$	3.68654	−	11.3460i	0.135612	−	0.417370i	0.995685	+	0.0928012i	$0.0295821\pi$
$740$		0			0
$741$	−5.29549	−	3.84740i	−0.194535	−	0.141338i
$742$	−7.72008	+	2.50841i	−0.283413	+	0.0920865i
$743$	−44.3956	+	14.4250i	−1.62872	+	0.529202i	−0.973976	−	0.226652i	$-0.927222\pi$
$743$	−44.3956	+	14.4250i	−1.62872	+	0.529202i	−0.654740	+	0.755854i	$0.727222\pi$
$744$	−1.12288	−	0.815820i	−0.0411668	−	0.0299094i
$745$		0			0
$746$	1.83762	−	5.65561i	0.0672800	−	0.207067i
$747$			32.1873i			1.17767i
$748$	−17.2168	−	21.0480i	−0.629508	−	0.769593i
$749$	−48.4124			−1.76895
$750$		0			0
$751$	−11.6530	+	8.46642i	−0.425225	+	0.308944i	−0.779737	−	0.626108i	$-0.784647\pi$
$751$	−11.6530	+	8.46642i	−0.425225	+	0.308944i	0.354512	+	0.935052i	$0.384647\pi$
$752$	−6.88492	+	9.47628i	−0.251067	+	0.345564i
$753$	1.91172	−	0.621156i	0.0696670	−	0.0226362i
$754$	−2.07450	−	6.38465i	−0.0755488	−	0.232515i
$755$		0			0
$756$	−7.33304	+	5.32776i	−0.266700	+	0.193769i
$757$	15.2755	+	4.96330i	0.555196	+	0.180394i	0.573159	−	0.819444i	$-0.305718\pi$
$757$	15.2755	+	4.96330i	0.555196	+	0.180394i	−0.0179624	+	0.999839i	$0.505718\pi$
$758$			7.79698i			0.283199i
$759$	−2.96558	+	0.170076i	−0.107644	+	0.00617337i
$760$		0			0
$761$	−12.0158	+	36.9809i	−0.435573	+	1.34056i	0.456925	+	0.889505i	$0.348951\pi$
$761$	−12.0158	+	36.9809i	−0.435573	+	1.34056i	−0.892498	+	0.451051i	$0.851049\pi$
$762$	−0.00691205	−	0.00951362i	−0.000250397	−	0.000344642i
$763$	−25.8299	+	35.5518i	−0.935106	+	1.28706i
$764$	−2.82371	−	8.69049i	−0.102158	−	0.314411i
$765$		0			0
$766$	0.313773	+	0.227969i	0.0113371	+	0.00823686i
$767$	−32.2309	−	44.3621i	−1.16379	−	1.60182i
$768$	0.223691	+	0.0726816i	0.00807175	+	0.00262267i
$769$	−43.0017			−1.55068			−0.775341	−	0.631543i	$-0.782422\pi$
$769$	−43.0017			−1.55068			−0.775341	+	0.631543i	$0.782422\pi$
$770$		0			0
$771$	−4.61679			−0.166270
$772$	−6.79637	−	2.20828i	−0.244607	−	0.0794776i
$773$	4.61683	+	6.35452i	0.166056	+	0.228556i	0.883933	−	0.467613i	$-0.154886\pi$
$773$	4.61683	+	6.35452i	0.166056	+	0.228556i	−0.717877	+	0.696170i	$0.754886\pi$
$774$	7.90135	+	5.74067i	0.284008	+	0.206344i
$775$		0			0
$776$	−10.3112	−	31.7346i	−0.370150	−	1.13920i
$777$	5.42696	−	7.46957i	0.194691	−	0.267969i
$778$	8.52635	+	11.7355i	0.305684	+	0.420739i
$779$	−2.96475	+	9.12457i	−0.106223	+	0.326922i
$780$		0			0
$781$	1.00752	−	3.83561i	0.0360519	−	0.137249i
$782$			6.12096i			0.218885i
$783$	5.45875	+	1.77366i	0.195080	+	0.0633853i
$784$	0.457082	−	0.332090i	0.0163244	−	0.0118603i
$785$		0			0
$786$	−0.547135	−	1.68391i	−0.0195157	−	0.0600631i
$787$	−10.8657	+	3.53048i	−0.387321	+	0.125848i	−0.496203	−	0.868206i	$-0.665273\pi$
$787$	−10.8657	+	3.53048i	−0.387321	+	0.125848i	0.108882	+	0.994055i	$0.465273\pi$
$788$	−11.8935	+	16.3700i	−0.423690	+	0.583159i
$789$	1.07980	−	0.784522i	0.0384420	−	0.0279297i
$790$		0			0
$791$	−5.51483			−0.196085
$792$	−16.7226	−	4.39260i	−0.594210	−	0.156084i
$793$			18.5903i			0.660161i
$794$	2.19741	−	6.76294i	0.0779832	−	0.240008i
$795$		0			0
$796$	−10.2749	−	7.46518i	−0.364186	−	0.264596i
$797$	−4.07529	+	1.32414i	−0.144354	+	0.0469035i	−0.380303	−	0.924862i	$-0.624180\pi$
$797$	−4.07529	+	1.32414i	−0.144354	+	0.0469035i	0.235949	+	0.971766i	$0.424180\pi$
$798$	1.70912	−	0.555328i	0.0605023	−	0.0196584i
$799$	−16.3265	−	11.8619i	−0.577592	−	0.419645i
$800$		0			0
$801$	−2.47839	+	7.62770i	−0.0875696	+	0.269511i
$802$		−	5.80787i		−	0.205083i
$803$	−3.15752	+	1.22994i	−0.111427	+	0.0434038i
$804$	4.19100			0.147805
$805$		0			0
$806$	4.30085	−	3.12475i	0.151491	−	0.110065i
$807$	0.319774	−	0.440132i	0.0112566	−	0.0154934i
$808$	−12.1817	+	3.95806i	−0.428549	+	0.139244i
$809$	6.13350	+	18.8770i	0.215642	+	0.663679i	0.999107	+	0.0422430i	$0.0134504\pi$
$809$	6.13350	+	18.8770i	0.215642	+	0.663679i	−0.783465	+	0.621436i	$0.786550\pi$
$810$		0			0
$811$	2.53899	−	1.84468i	0.0891559	−	0.0647756i	−0.542314	−	0.840176i	$-0.682452\pi$
$811$	2.53899	−	1.84468i	0.0891559	−	0.0647756i	0.631470	+	0.775400i	$0.282452\pi$
$812$	−13.6384	−	4.43138i	−0.478614	−	0.155511i
$813$		−	5.95452i		−	0.208834i
$814$	16.8189	−	0.964566i	0.589504	−	0.0338080i
$815$		0			0
$816$	−1.24021	+	3.81698i	−0.0434162	+	0.133621i
$817$	18.0301	+	24.8164i	0.630795	+	0.868215i
$818$	−0.0735281	+	0.101203i	−0.00257085	+	0.00353847i
$819$	−11.2156	−	34.5180i	−0.391904	−	1.20616i
$820$		0			0
$821$	−19.0118	−	13.8129i	−0.663516	−	0.482073i	0.204332	−	0.978902i	$-0.434498\pi$
$821$	−19.0118	−	13.8129i	−0.663516	−	0.482073i	−0.867849	+	0.496829i	$0.834498\pi$
$822$	−1.66118	−	2.28642i	−0.0579404	−	0.0797481i
$823$	−12.0369	−	3.91103i	−0.419580	−	0.136330i	0.0916150	−	0.995795i	$-0.470797\pi$
$823$	−12.0369	−	3.91103i	−0.419580	−	0.136330i	−0.511195	+	0.859465i	$0.670797\pi$
$824$	13.5535			0.472159
$825$		0			0
$826$	15.0547			0.523820
$827$	−28.7443	−	9.33959i	−0.999538	−	0.324770i	−0.236857	−	0.971545i	$-0.576117\pi$
$827$	−28.7443	−	9.33959i	−0.999538	−	0.324770i	−0.762681	+	0.646775i	$0.776117\pi$
$828$	−8.36195	−	11.5092i	−0.290598	−	0.399974i
$829$	1.61937	+	1.17654i	0.0562432	+	0.0408630i	0.615552	−	0.788097i	$-0.288933\pi$
$829$	1.61937	+	1.17654i	0.0562432	+	0.0408630i	−0.559308	+	0.828960i	$0.688933\pi$
$830$		0			0
$831$	−0.342177	−	1.05311i	−0.0118700	−	0.0365321i
$832$	−8.34180	+	11.4815i	−0.289200	+	0.398050i
$833$	0.572152	+	0.787500i	0.0198239	+	0.0272852i
$834$	1.10481	−	3.40025i	0.0382564	−	0.117741i
$835$		0			0
$836$	−21.4646	−	13.7894i	−0.742368	−	0.476915i
$837$			4.54520i			0.157105i
$838$	−0.576072	−	0.187177i	−0.0199001	−	0.00646592i
$839$	28.6185	−	20.7925i	0.988019	−	0.717838i	0.0285326	−	0.999593i	$-0.490917\pi$
$839$	28.6185	−	20.7925i	0.988019	−	0.717838i	0.959486	+	0.281755i	$0.0909166\pi$
$840$		0			0
$841$	−6.15541	−	18.9444i	−0.212256	−	0.653255i
$842$	−13.4652	+	4.37511i	−0.464041	+	0.150776i
$843$	−4.33377	+	5.96492i	−0.149263	+	0.205443i
$844$	−4.99463	+	3.62881i	−0.171922	+	0.124909i
$845$		0			0
$846$	−6.02834			−0.207259
$847$	−28.9511	−	5.85616i	−0.994771	−	0.201220i
$848$		−	17.0083i		−	0.584067i
$849$	2.90509	−	8.94095i	0.0997024	−	0.306853i
$850$		0			0
$851$	23.8696	+	17.3423i	0.818241	+	0.594487i
$852$	−0.651102	+	0.211556i	−0.0223064	+	0.00724779i
$853$	17.3124	−	5.62515i	0.592767	−	0.192602i	0.00275489	−	0.999996i	$-0.499123\pi$
$853$	17.3124	−	5.62515i	0.592767	−	0.192602i	0.590012	+	0.807395i	$0.299123\pi$
$854$	−4.12917	−	3.00001i	−0.141297	−	0.102658i
$855$		0			0
$856$	−10.0302	+	30.8699i	−0.342827	+	1.05511i
$857$			29.2837i			1.00031i	0.865935	+	0.500156i	$0.166724\pi$
$857$			29.2837i			1.00031i	−0.865935	+	0.500156i	$0.833276\pi$
$858$	−1.29021	+	2.00835i	−0.0440472	+	0.0685640i
$859$	−8.44030			−0.287979			−0.143990	−	0.989579i	$-0.545993\pi$
$859$	−8.44030			−0.287979			−0.143990	+	0.989579i	$0.545993\pi$
$860$		0			0
$861$	1.55134	−	1.12712i	0.0528696	−	0.0384120i
$862$	−8.79587	+	12.1065i	−0.299589	+	0.412348i
$863$	18.4017	−	5.97907i	0.626400	−	0.203530i	0.0214204	−	0.999771i	$-0.493181\pi$
$863$	18.4017	−	5.97907i	0.626400	−	0.203530i	0.604980	+	0.796241i	$0.293181\pi$
$864$	2.87360	+	8.84404i	0.0977620	+	0.300880i
$865$		0			0
$866$	10.0515	−	7.30281i	0.341562	−	0.248160i
$867$	−1.35282	−	0.439559i	−0.0459443	−	0.0149282i
$868$		−	11.3559i		−	0.385446i
$869$	8.99063	−	7.35411i	0.304986	−	0.249471i
$870$		0			0
$871$	−10.5585	+	32.4956i	−0.357760	+	1.10107i
$872$	17.3179	+	23.8361i	0.586458	+	0.807191i
$873$	−31.5453	+	43.4184i	−1.06765	+	1.46949i
$874$	1.77460	+	5.46165i	0.0600266	+	0.184743i
$875$		0			0
$876$	0.473260	+	0.343844i	0.0159900	+	0.0116174i
$877$	10.2945	+	14.1691i	0.347619	+	0.478456i	0.946647	−	0.322271i	$-0.104446\pi$
$877$	10.2945	+	14.1691i	0.347619	+	0.478456i	−0.599028	+	0.800728i	$0.704446\pi$
$878$	6.54484	+	2.12655i	0.220878	+	0.0717675i
$879$	−6.85349			−0.231163
$880$		0			0
$881$	−20.0575			−0.675754			−0.337877	−	0.941190i	$-0.609709\pi$
$881$	−20.0575			−0.675754			−0.337877	+	0.941190i	$0.609709\pi$
$882$	0.276542	+	0.0898538i	0.00931164	+	0.00302553i
$883$	−15.8102	−	21.7609i	−0.532057	−	0.732313i	0.455386	−	0.890294i	$-0.349501\pi$
$883$	−15.8102	−	21.7609i	−0.532057	−	0.732313i	−0.987442	+	0.157981i	$0.949501\pi$
$884$	−30.9620	−	22.4952i	−1.04136	−	0.756595i
$885$		0			0
$886$	−0.0487585	−	0.150063i	−0.00163807	−	0.00504148i
$887$	−4.00028	+	5.50591i	−0.134316	+	0.184870i	−0.870877	−	0.491501i	$-0.836448\pi$
$887$	−4.00028	+	5.50591i	−0.134316	+	0.184870i	0.736561	+	0.676371i	$0.236448\pi$
$888$	−3.63856	−	5.00805i	−0.122102	−	0.168059i
$889$	0.0632845	−	0.194770i	0.00212249	−	0.00653237i
$890$		0			0
$891$	9.71661	+	24.9446i	0.325519	+	0.835674i
$892$			18.6880i			0.625720i
$893$	−18.0070	−	5.85082i	−0.602581	−	0.195790i
$894$	1.82928	−	1.32905i	0.0611804	−	0.0444502i
$895$		0			0
$896$	−9.30635	−	28.6420i	−0.310903	−	0.956862i
$897$	−3.97603	+	1.29189i	−0.132756	+	0.0431349i
$898$	2.38680	−	3.28514i	0.0796484	−	0.109627i
$899$	−5.81757	+	4.22671i	−0.194027	+	0.140969i
$900$		0			0
$901$	29.3033			0.976235
$902$	3.38403	+	0.888901i	0.112676	+	0.0295972i
$903$		−	6.13090i		−	0.204024i
$904$	−1.14258	+	3.51650i	−0.0380017	+	0.116957i
$905$		0			0
$906$	0.937933	+	0.681448i	0.0311607	+	0.0226396i
$907$	−20.2873	+	6.59174i	−0.673629	+	0.218875i	−0.625804	−	0.779981i	$-0.715229\pi$
$907$	−20.2873	+	6.59174i	−0.673629	+	0.218875i	−0.0478248	+	0.998856i	$0.515229\pi$
$908$	0.364094	−	0.118301i	0.0120829	−	0.00392597i
$909$	16.6666	+	12.1090i	0.552797	+	0.401631i
$910$		0			0
$911$	−8.52542	+	26.2385i	−0.282460	+	0.869322i	0.704689	+	0.709516i	$0.251087\pi$
$911$	−8.52542	+	26.2385i	−0.282460	+	0.869322i	−0.987149	+	0.159805i	$0.948913\pi$
$912$			3.76541i			0.124685i
$913$	35.6574	+	9.36631i	1.18009	+	0.309980i
$914$	−0.543347			−0.0179723
$915$		0			0
$916$	−0.108549	+	0.0788658i	−0.00358657	+	0.00260580i
$917$	18.1242	−	24.9458i	0.598512	−	0.823782i
$918$	−3.99968	+	1.29958i	−0.132009	+	0.0428924i
$919$	1.85685	+	5.71479i	0.0612518	+	0.188514i	0.977000	−	0.213239i	$-0.0684012\pi$
$919$	1.85685	+	5.71479i	0.0612518	+	0.188514i	−0.915748	+	0.401752i	$0.868401\pi$
$920$		0			0
$921$	1.79697	−	1.30558i	0.0592122	−	0.0430202i
$922$	−6.58486	−	2.13955i	−0.216861	−	0.0704624i
$923$		−	5.58140i		−	0.183714i
$924$	1.85078	+	4.75135i	0.0608863	+	0.156308i
$925$		0			0
$926$	−0.722274	+	2.22293i	−0.0237354	+	0.0730501i
$927$	−12.8133	−	17.6360i	−0.420844	−	0.579242i
$928$	−8.64757	+	11.9024i	−0.283870	+	0.390714i
$929$	−2.96576	−	9.12766i	−0.0973034	−	0.299469i	0.890544	−	0.454898i	$-0.150324\pi$
$929$	−2.96576	−	9.12766i	−0.0973034	−	0.299469i	−0.987847	+	0.155429i	$0.950324\pi$
$930$		0			0
$931$	0.738836	+	0.536796i	0.0242144	+	0.0175928i
$932$	−15.7504	−	21.6785i	−0.515920	−	0.710103i
$933$	7.72992	+	2.51160i	0.253066	+	0.0822261i
$934$	−15.4742			−0.506332
$935$		0			0
$936$	−24.3339			−0.795378
$937$	36.7029	+	11.9255i	1.19903	+	0.389589i	0.839405	−	0.543507i	$-0.182904\pi$
$937$	36.7029	+	11.9255i	1.19903	+	0.389589i	0.359628	+	0.933096i	$0.382904\pi$
$938$	−5.51385	−	7.58916i	−0.180034	−	0.247795i
$939$	−3.02649	−	2.19887i	−0.0987658	−	0.0717575i
$940$		0			0
$941$	−9.01854	−	27.7562i	−0.293996	−	0.904826i	−0.983557	−	0.180599i	$-0.942196\pi$
$941$	−9.01854	−	27.7562i	−0.293996	−	0.904826i	0.689561	−	0.724228i	$-0.257804\pi$
$942$	1.21280	−	1.66928i	0.0395152	−	0.0543880i
$943$	3.60179	+	4.95744i	0.117291	+	0.161437i
$944$	−9.74764	+	30.0002i	−0.317259	+	0.976422i
$945$		0			0
$946$	8.65882	−	7.08270i	0.281523	−	0.230279i
$947$		−	46.7623i		−	1.51957i	−0.650174	−	0.759785i	$-0.725304\pi$
$947$		−	46.7623i		−	1.51957i	0.650174	−	0.759785i	$-0.274696\pi$
$948$	−1.90702	−	0.619629i	−0.0619371	−	0.0201246i
$949$	−3.85834	+	2.80325i	−0.125247	+	0.0909972i
$950$		0			0
$951$	2.07069	+	6.37293i	0.0671468	+	0.206657i
$952$	21.2704	−	6.91116i	0.689376	−	0.223992i
$953$	−3.61628	+	4.97738i	−0.117143	+	0.161233i	−0.863562	−	0.504243i	$-0.831772\pi$
$953$	−3.61628	+	4.97738i	−0.117143	+	0.161233i	0.746419	+	0.665476i	$0.231772\pi$
$954$	7.08167	−	5.14514i	0.229278	−	0.166580i
$955$		0			0
$956$	41.0529			1.32774
$957$	1.74522	−	2.71661i	0.0564148	−	0.0878155i
$958$			8.46440i			0.273472i
$959$	15.2093	−	46.8093i	0.491132	−	1.51155i
$960$		0			0
$961$	20.4726	+	14.8742i	0.660408	+	0.479814i
$962$	22.5496	−	7.32680i	0.727027	−	0.236226i
$963$	49.6507	−	16.1325i	1.59997	−	0.519862i
$964$	30.5891	+	22.2243i	0.985209	+	0.715796i
$965$		0			0
$966$	0.354686	−	1.09161i	0.0114118	−	0.0351220i
$967$		−	3.39625i		−	0.109216i	−0.998508	−	0.0546080i	$-0.982609\pi$
$967$		−	3.39625i		−	0.109216i	0.998508	−	0.0546080i	$-0.0173909\pi$
$968$	−9.73233	+	17.2472i	−0.312809	+	0.554346i
$969$	−6.48736			−0.208404
$970$		0			0
$971$	7.60072	−	5.52224i	0.243919	−	0.177217i	−0.459109	−	0.888380i	$-0.651831\pi$
$971$	7.60072	−	5.52224i	0.243919	−	0.177217i	0.703027	+	0.711163i	$0.251831\pi$
$972$	8.66870	−	11.9314i	0.278049	−	0.382701i
$973$	59.2158	−	19.2404i	1.89837	−	0.616818i
$974$	2.72255	+	8.37914i	0.0872360	+	0.268485i
$975$		0			0
$976$	8.65182	−	6.28591i	0.276938	−	0.201207i
$977$	15.7450	+	5.11585i	0.503726	+	0.163671i	0.549847	−	0.835265i	$-0.314686\pi$
$977$	15.7450	+	5.11585i	0.503726	+	0.163671i	−0.0461210	+	0.998936i	$0.514686\pi$
$978$		−	0.119032i		−	0.00380623i
$979$	7.72885	+	4.96520i	0.247015	+	0.158689i
$980$		0			0
$981$	14.6436	−	45.0685i	0.467535	−	1.43893i
$982$	−3.20750	−	4.41474i	−0.102355	−	0.140880i
$983$	29.8701	−	41.1126i	0.952707	−	1.31129i	0.00239240	−	0.999997i	$-0.499238\pi$
$983$	29.8701	−	41.1126i	0.952707	−	1.31129i	0.950315	−	0.311291i	$-0.100762\pi$
$984$	−0.397287	−	1.22272i	−0.0126651	−	0.0389790i
$985$		0			0
$986$	−5.38279	−	3.91083i	−0.171423	−	0.124546i
$987$	2.22432	+	3.06151i	0.0708009	+	0.0974490i
$988$	−34.1488	−	11.0956i	−1.08642	−	0.352999i
$989$	19.5918			0.622983
$990$		0			0
$991$	11.3642			0.360996			0.180498	−	0.983575i	$-0.442229\pi$
$991$	11.3642			0.360996			0.180498	+	0.983575i	$0.442229\pi$
$992$	−11.0802	−	3.60018i	−0.351797	−	0.114306i
$993$	6.10355	+	8.40081i	0.193690	+	0.266592i
$994$	1.23971	+	0.900700i	0.0393211	+	0.0285685i
$995$		0			0
$996$	−1.96671	−	6.05292i	−0.0623177	−	0.191794i
$997$	17.1424	−	23.5945i	0.542906	−	0.747246i	−0.446122	−	0.894972i	$-0.647195\pi$
$997$	17.1424	−	23.5945i	0.542906	−	0.747246i	0.989028	+	0.147726i	$0.0471953\pi$
$998$	−3.05256	−	4.20149i	−0.0966271	−	0.132996i
$999$	−6.26427	+	19.2794i	−0.198193	+	0.609975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.z.a.174.2		16
5.2	odd	4		55.2.g.b.31.2	yes	8
5.3	odd	4		275.2.h.a.251.1		8
5.4	even	2	inner	275.2.z.a.174.3		16
11.5	even	5	inner	275.2.z.a.49.3		16
15.2	even	4		495.2.n.e.361.1		8
20.7	even	4		880.2.bo.h.801.1		8
55.2	even	20		605.2.g.e.366.2		8
55.7	even	20		605.2.a.k.1.2		4
55.17	even	20		605.2.g.k.511.1		8
55.18	even	20		3025.2.a.w.1.3		4
55.27	odd	20		55.2.g.b.16.2	✓	8
55.32	even	4		605.2.g.k.251.1		8
55.37	odd	20		605.2.a.j.1.3		4
55.38	odd	20		275.2.h.a.126.1		8
55.42	odd	20		605.2.g.m.366.1		8
55.47	odd	20		605.2.g.m.81.1		8
55.48	odd	20		3025.2.a.bd.1.2		4
55.49	even	10	inner	275.2.z.a.49.2		16
55.52	even	20		605.2.g.e.81.2		8
165.62	odd	20		5445.2.a.bi.1.3		4
165.92	even	20		5445.2.a.bp.1.2		4
165.137	even	20		495.2.n.e.181.1		8
220.7	odd	20		9680.2.a.cm.1.3		4
220.27	even	20		880.2.bo.h.401.1		8
220.147	even	20		9680.2.a.cn.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.16.2	✓	8	55.27	odd	20
55.2.g.b.31.2	yes	8	5.2	odd	4
275.2.h.a.126.1		8	55.38	odd	20
275.2.h.a.251.1		8	5.3	odd	4
275.2.z.a.49.2		16	55.49	even	10	inner
275.2.z.a.49.3		16	11.5	even	5	inner
275.2.z.a.174.2		16	1.1	even	1	trivial
275.2.z.a.174.3		16	5.4	even	2	inner
495.2.n.e.181.1		8	165.137	even	20
495.2.n.e.361.1		8	15.2	even	4
605.2.a.j.1.3		4	55.37	odd	20
605.2.a.k.1.2		4	55.7	even	20
605.2.g.e.81.2		8	55.52	even	20
605.2.g.e.366.2		8	55.2	even	20
605.2.g.k.251.1		8	55.32	even	4
605.2.g.k.511.1		8	55.17	even	20
605.2.g.m.81.1		8	55.47	odd	20
605.2.g.m.366.1		8	55.42	odd	20
880.2.bo.h.401.1		8	220.27	even	20
880.2.bo.h.801.1		8	20.7	even	4
3025.2.a.w.1.3		4	55.18	even	20
3025.2.a.bd.1.2		4	55.48	odd	20
5445.2.a.bi.1.3		4	165.62	odd	20
5445.2.a.bp.1.2		4	165.92	even	20
9680.2.a.cm.1.3		4	220.7	odd	20
9680.2.a.cn.1.3		4	220.147	even	20

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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.z (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.453901 - 0.147481i) q^{2} +(-0.189896 - 0.261370i) q^{3} +(-1.43376 - 1.04169i) q^{4} +(0.0476470 + 0.146642i) q^{6} +(-1.57833 + 2.17239i) q^{7} +(1.05821 + 1.45650i) q^{8} +(0.894797 - 2.75390i) q^{9} +O(q^{10})\)	\(q+(-0.453901 - 0.147481i) q^{2} +(-0.189896 - 0.261370i) q^{3} +(-1.43376 - 1.04169i) q^{4} +(0.0476470 + 0.146642i) q^{6} +(-1.57833 + 2.17239i) q^{7} +(1.05821 + 1.45650i) q^{8} +(0.894797 - 2.75390i) q^{9} +(-2.79042 - 1.79264i) q^{11} +0.572554i q^{12} +(-4.43939 - 1.44244i) q^{13} +(1.03679 - 0.753275i) q^{14} +(0.829779 + 2.55380i) q^{16} +(-4.39990 + 1.42961i) q^{17} +(-0.812299 + 1.11803i) q^{18} +(-3.51149 + 2.55125i) q^{19} +0.867517 q^{21} +(1.00220 + 1.22522i) q^{22} +2.77222i q^{23} +(0.179735 - 0.553168i) q^{24} +(1.80231 + 1.30945i) q^{26} +(-1.81148 + 0.588587i) q^{27} +(4.52590 - 1.47055i) q^{28} +(-2.43790 - 1.77124i) q^{29} +(0.737407 - 2.26951i) q^{31} -4.88221i q^{32} +(0.0613500 + 1.06975i) q^{33} +2.20796 q^{34} +(-4.15163 + 3.01633i) q^{36} +(6.25574 - 8.61029i) q^{37} +(1.97013 - 0.640135i) q^{38} +(0.466012 + 1.43424i) q^{39} +(1.78826 - 1.29924i) q^{41} +(-0.393767 - 0.127943i) q^{42} -7.06719i q^{43} +(2.13343 + 5.47695i) q^{44} +(0.408851 - 1.25832i) q^{46} +(2.56401 + 3.52905i) q^{47} +(0.509914 - 0.701836i) q^{48} +(-0.0650188 - 0.200107i) q^{49} +(1.20918 + 0.878523i) q^{51} +(4.86243 + 6.69257i) q^{52} +(-6.02403 - 1.95733i) q^{53} +0.909040 q^{54} -4.83428 q^{56} +(1.33364 + 0.433326i) q^{57} +(0.845342 + 1.16351i) q^{58} +(9.50375 + 6.90488i) q^{59} +(-1.23070 - 3.78770i) q^{61} +(-0.669420 + 0.921378i) q^{62} +(4.57026 + 6.29042i) q^{63} +(0.939522 - 2.89155i) q^{64} +(0.129921 - 0.494608i) q^{66} -7.31984i q^{67} +(7.79760 + 2.53359i) q^{68} +(0.724576 - 0.526435i) q^{69} +(0.369495 + 1.13719i) q^{71} +(4.95794 - 1.61093i) q^{72} +(0.600544 - 0.826577i) q^{73} +(-4.10935 + 2.98562i) q^{74} +7.69223 q^{76} +(8.29852 - 3.23251i) q^{77} -0.719730i q^{78} +(-1.08222 + 3.33073i) q^{79} +(-6.53000 - 4.74432i) q^{81} +(-1.00331 + 0.325994i) q^{82} +(-10.5718 + 3.43498i) q^{83} +(-1.24381 - 0.903681i) q^{84} +(-1.04228 + 3.20780i) q^{86} +0.973547i q^{87} +(-0.341876 - 5.96123i) q^{88} -2.76978 q^{89} +(10.1404 - 7.36742i) q^{91} +(2.88779 - 3.97470i) q^{92} +(-0.733212 + 0.238235i) q^{93} +(-0.643336 - 1.97998i) q^{94} +(-1.27606 + 0.927114i) q^{96} +(-17.6271 - 5.72738i) q^{97} +0.100418i q^{98} +(-7.43361 + 6.08051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 14 q^{6} + 10 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 - 14 * q^6 + 10 * q^9	\( 16 q + 4 q^{4} - 14 q^{6} + 10 q^{9} + 6 q^{11} + 32 q^{14} + 8 q^{16} - 30 q^{19} - 40 q^{21} - 26 q^{24} + 20 q^{26} + 18 q^{29} - 20 q^{31} - 8 q^{34} - 30 q^{36} - 42 q^{39} + 16 q^{41} + 24 q^{44} + 6 q^{46} - 2 q^{49} + 2 q^{51} - 32 q^{54} + 44 q^{56} + 54 q^{59} + 12 q^{61} + 52 q^{64} + 26 q^{66} + 2 q^{69} - 40 q^{71} - 40 q^{74} - 74 q^{79} + 16 q^{81} - 56 q^{84} - 6 q^{86} + 32 q^{89} + 88 q^{91} - 34 q^{94} - 34 q^{96} + 40 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 - 14 * q^6 + 10 * q^9 + 6 * q^11 + 32 * q^14 + 8 * q^16 - 30 * q^19 - 40 * q^21 - 26 * q^24 + 20 * q^26 + 18 * q^29 - 20 * q^31 - 8 * q^34 - 30 * q^36 - 42 * q^39 + 16 * q^41 + 24 * q^44 + 6 * q^46 - 2 * q^49 + 2 * q^51 - 32 * q^54 + 44 * q^56 + 54 * q^59 + 12 * q^61 + 52 * q^64 + 26 * q^66 + 2 * q^69 - 40 * q^71 - 40 * q^74 - 74 * q^79 + 16 * q^81 - 56 * q^84 - 6 * q^86 + 32 * q^89 + 88 * q^91 - 34 * q^94 - 34 * q^96 + 40 * q^99

Introduction

L-functions

Modular forms

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