LMFDB - Embedded newform 275.2.z.a.174.3

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			174.3
Root			$-0.280526 + 0.386111i$ of defining polynomial
Character	$\chi$	$=$	275.174
Dual form			275.2.z.a.49.3

$q$-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	0.465064	−	0.885277i	$-0.346031\pi$
$2$	0.453901	+	0.147481i	0.320957	+	0.104285i	−0.144108	+	0.989562i	$0.546031\pi$
$3$	0.189896	+	0.261370i	0.109637	+	0.150902i	0.860309	−	0.509772i	$-0.170270\pi$
$3$	0.189896	+	0.261370i	0.109637	+	0.150902i	−0.750673	+	0.660674i	$0.770270\pi$
$4$	−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	−0.398834	−	0.917023i	$-0.630585\pi$
$7$	1.57833	−	2.17239i	0.596554	−	0.821086i	0.995387	+	0.0959376i	$0.0305849\pi$
$8$	−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	0.851172	−	0.524886i	$-0.175892\pi$
$13$	4.43939	+	1.44244i	1.23126	+	0.400062i	0.380092	+	0.924949i	$0.375892\pi$
$14$	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	0.277762	−	0.960650i	$-0.410407\pi$
$17$	4.39990	−	1.42961i	1.06713	−	0.346732i	0.789370	+	0.613918i	$0.210407\pi$
$18$	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	$-0.906669\pi$
$23$		−	2.77222i		−	0.578048i	0.957322	−	0.289024i	$-0.0933308\pi$
$24$	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	$0.539035\pi$
$37$	−6.25574	+	8.61029i	−1.02844	+	1.41552i	−0.906114	+	0.423033i	$0.860965\pi$
$38$	−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	$0.181148\pi$
$43$			7.06719i			1.07774i	−0.842390	+	0.538868i	$0.818852\pi$
$44$	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	0.579983	−	0.814628i	$-0.303059\pi$
$47$	−2.56401	−	3.52905i	−0.373999	−	0.514765i	−0.953982	+	0.299863i	$0.903059\pi$
$48$	−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	0.691977	−	0.721920i	$-0.256740\pi$
$53$	6.02403	+	1.95733i	0.827464	+	0.268859i	0.135487	+	0.990779i	$0.456740\pi$
$54$	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	$0.147554\pi$
$67$			7.31984i			0.894260i	−0.894469	+	0.447130i	$0.852446\pi$
$68$	−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	−0.842714	−	0.538362i	$-0.819043\pi$
$73$	−0.600544	+	0.826577i	−0.0702883	+	0.0967436i	0.772425	+	0.635105i	$0.219043\pi$
$74$	−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	0.335351	−	0.942093i	$-0.391145\pi$
$83$	10.5718	−	3.43498i	1.16040	−	0.377038i	0.825053	+	0.565055i	$0.191145\pi$
$84$	−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	0.999511	−	0.0312615i	$-0.00995248\pi$
$97$	17.6271	+	5.72738i	1.78976	+	0.581528i	0.790247	+	0.612789i	$0.209952\pi$
$98$		−	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	−0.969320	−	0.245801i	$-0.920949\pi$
$103$	−4.42505	+	6.09056i	−0.436014	+	0.600121i	0.533307	+	0.845922i	$0.320949\pi$
$104$	−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	$-0.863164\pi$
$107$	−10.5973	−	14.5859i	−1.02448	−	1.41008i	−0.115465	−	0.993312i	$-0.536836\pi$
$108$	−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	0.748453	−	0.663188i	$-0.230797\pi$
$113$	−1.20718	−	1.66154i	−0.113562	−	0.156304i	−0.862014	+	0.506884i	$0.830797\pi$
$114$	−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	−0.305797	−	0.952097i	$-0.598923\pi$
$127$	0.0725340	−	0.0235677i	0.00643635	−	0.00209130i	0.312233	+	0.950005i	$0.398923\pi$
$128$	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	0.552447	−	0.833548i	$-0.313694\pi$
$137$	17.4322	−	5.66406i	1.48933	−	0.483914i	0.936886	+	0.349635i	$0.113694\pi$
$138$	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	0.997888	−	0.0649531i	$-0.0206898\pi$
$157$	7.86568	+	10.8262i	0.627750	+	0.864023i	−0.370139	+	0.928977i	$0.620690\pi$
$158$	−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	0.337629	−	0.941279i	$-0.390375\pi$
$163$	0.734206	+	0.238558i	0.0575075	+	0.0186853i	−0.280122	+	0.959964i	$0.590375\pi$
$164$	−3.91733			−0.305892
$165$		0			0
$166$	5.30514			0.411759
$167$	−8.06716	−	2.62118i	−0.624256	−	0.202833i	−0.0202268	−	0.999795i	$-0.506439\pi$
$167$	−8.06716	−	2.62118i	−0.624256	−	0.202833i	−0.604029	+	0.796962i	$0.706439\pi$
$168$	−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	0.907276	−	0.420535i	$-0.138158\pi$
$173$	2.98519	+	4.10876i	0.226960	+	0.312384i	−0.680316	+	0.732919i	$0.738158\pi$
$174$	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	−0.443768	−	0.896142i	$-0.646359\pi$
$193$	−3.83494	+	1.24605i	−0.276045	+	0.0896925i	0.167723	+	0.985834i	$0.446359\pi$
$194$	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	$0.133333\pi$
$197$			11.4176i			0.813469i	−0.913547	+	0.406734i	$0.866667\pi$
$198$	−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	0.964443	−	0.264290i	$-0.0851376\pi$
$223$	6.19816	+	8.53103i	0.415059	+	0.571280i	−0.549384	+	0.835570i	$0.685138\pi$
$224$	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	−0.804782	−	0.593570i	$-0.797718\pi$
$227$	0.126972	−	0.174762i	0.00842743	−	0.0115994i	0.813210	+	0.581970i	$0.197718\pi$
$228$	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	−0.202579	−	0.979266i	$-0.564932\pi$
$233$	−14.3800	−	4.67235i	−0.942067	−	0.306096i	−0.739488	+	0.673170i	$0.764932\pi$
$234$	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	−0.986194	−	0.165593i	$-0.947046\pi$
$257$	−8.39964	+	11.5611i	−0.523955	+	0.721163i	0.462239	+	0.886755i	$0.347046\pi$
$258$	−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	$-0.959345\pi$
$263$		−	4.13132i		−	0.254748i	0.991855	−	0.127374i	$-0.0406548\pi$
$264$	−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	0.209446	−	0.977820i	$-0.432834\pi$
$277$	−3.25969	−	1.05914i	−0.195856	−	0.0636375i	−0.405303	+	0.914183i	$0.632834\pi$
$278$	−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	$-0.867394\pi$
$283$	−17.1040	−	23.5416i	−1.01673	−	1.39941i	−0.102255	−	0.994758i	$-0.532606\pi$
$284$	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	$0.412727\pi$
$293$	−12.4690	+	17.1621i	−0.728448	+	1.00262i	−0.999201	+	0.0399740i	$0.987273\pi$
$294$	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	$-0.937142\pi$
$307$		−	6.87520i		−	0.392388i	0.980565	−	0.196194i	$-0.0628583\pi$
$308$	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	−0.603236	−	0.797563i	$-0.706122\pi$
$313$	−11.0126	+	3.57821i	−0.622469	+	0.202252i	−0.0192328	+	0.999815i	$0.506122\pi$
$314$	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	0.805149	−	0.593073i	$-0.202085\pi$
$317$	19.7261	+	6.40940i	1.10793	+	0.359988i	0.302780	+	0.953061i	$0.402085\pi$
$318$			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	−0.993275	−	0.115782i	$-0.963063\pi$
$337$	−10.5780	+	14.5594i	−0.576221	+	0.793100i	0.417054	+	0.908882i	$0.363063\pi$
$338$	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	−0.0962243	−	0.995360i	$-0.530677\pi$
$347$	7.65583	−	2.48753i	0.410986	−	0.133538i	0.507211	+	0.861822i	$0.330677\pi$
$348$	−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	$-0.870680\pi$
$353$		−	14.8497i		−	0.790371i	0.918601	−	0.395186i	$-0.129320\pi$
$354$	−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	−0.534905	−	0.844912i	$-0.679653\pi$
$367$	8.31327	−	11.4422i	0.433949	−	0.597280i	0.968854	+	0.247632i	$0.0796525\pi$
$368$	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	$-0.895451\pi$
$373$		−	12.4600i		−	0.645154i	0.946543	−	0.322577i	$-0.104549\pi$
$374$	−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	0.328696	−	0.944436i	$-0.393391\pi$
$383$	0.772874	+	0.251122i	0.0394920	+	0.0128317i	−0.289204	+	0.957267i	$0.593391\pi$
$384$	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	$-0.878022\pi$
$397$		−	14.8996i		−	0.747789i	0.927471	−	0.373894i	$-0.121978\pi$
$398$	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	$-0.584886\pi$
$433$	15.3015	−	21.0607i	0.735345	−	1.01212i	0.998873	−	0.0474634i	$-0.0151137\pi$
$434$	−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	0.804376	−	0.594121i	$-0.202500\pi$
$443$	−0.194326	−	0.267467i	−0.00923273	−	0.0127078i	−0.813608	+	0.581413i	$0.802500\pi$
$444$	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	−0.334232	−	0.942491i	$-0.608477\pi$
$457$	−1.08275	+	0.351807i	−0.0506490	+	0.0164569i	0.283583	+	0.958948i	$0.408477\pi$
$458$	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	$0.0363025\pi$
$463$			4.89739i			0.227601i	−0.993504	+	0.113801i	$0.963698\pi$
$464$	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	−0.917796	−	0.397053i	$-0.870033\pi$
$467$	−30.8361	+	10.0193i	−1.42693	+	0.463637i	−0.509131	+	0.860689i	$0.670033\pi$
$468$	−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	0.980699	−	0.195525i	$-0.0626411\pi$
$487$	10.8507	+	14.9347i	0.491691	+	0.676754i	−0.489008	+	0.872279i	$0.662641\pi$
$488$	−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	$0.275699\pi$
$503$	26.2885	+	36.1830i	1.17215	+	1.61332i	0.524371	+	0.851490i	$0.324301\pi$
$504$	−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	−0.410873	−	0.911693i	$-0.634776\pi$
$523$	−4.74299	+	1.54109i	−0.207396	+	0.0673872i	0.203476	+	0.979080i	$0.434776\pi$
$524$	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	0.998402	−	0.0565056i	$-0.0179959\pi$
$547$	14.8780	+	20.4779i	0.636139	+	0.875570i	−0.362263	+	0.932076i	$0.617996\pi$
$548$	−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	$0.505576\pi$
$557$	−22.7280	+	31.2824i	−0.963015	+	1.32548i	−0.945497	+	0.325630i	$0.894424\pi$
$558$	−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	0.0160940	−	0.999870i	$-0.494877\pi$
$563$	−13.2541	−	4.30653i	−0.558595	−	0.181498i	−0.574689	+	0.818372i	$0.694877\pi$
$564$	−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	−0.689232	−	0.724541i	$-0.742052\pi$
$577$	−19.7201	+	6.40744i	−0.820958	+	0.266745i	−0.131726	+	0.991286i	$0.542052\pi$
$578$	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	−0.583156	−	0.812360i	$-0.698182\pi$
$587$	8.95591	−	12.3267i	0.369650	−	0.508779i	0.952806	+	0.303581i	$0.0981823\pi$
$588$	−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	$-0.808686\pi$
$593$		−	27.5413i		−	1.13098i	0.824754	−	0.565492i	$-0.191314\pi$
$594$	−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	0.500864	−	0.865526i	$-0.333016\pi$
$607$	9.78909	+	3.18067i	0.397327	+	0.129099i	−0.103536	+	0.994626i	$0.533016\pi$
$608$	−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	0.999539	−	0.0303715i	$-0.00966905\pi$
$613$	16.3849	+	22.5519i	0.661779	+	0.910861i	−0.337759	+	0.941232i	$0.609669\pi$
$614$	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	$-0.803778\pi$
$617$		−	28.7216i		−	1.15629i	0.815935	−	0.578143i	$-0.196222\pi$
$618$	−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	−0.0881244	−	0.996109i	$-0.528087\pi$
$643$	10.8043	−	3.51053i	0.426080	−	0.138442i	0.514204	+	0.857668i	$0.328087\pi$
$644$	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	$-0.999198\pi$
$647$	−46.0520	−	14.9632i	−1.81049	−	0.588264i	−0.810495	−	0.585746i	$-0.800802\pi$
$648$			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	−0.999976	−	0.00688905i	$-0.997807\pi$
$653$	−17.4894	+	24.0722i	−0.684415	+	0.942016i	0.315562	+	0.948905i	$0.397807\pi$
$654$	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	0.0601327	−	0.998190i	$-0.480848\pi$
$673$	−12.3988	−	4.02863i	−0.477940	−	0.155292i	−0.538073	+	0.842898i	$0.680848\pi$
$674$	−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	0.461505	−	0.887138i	$-0.347310\pi$
$677$	35.2903	−	11.4665i	1.35632	−	0.440694i	0.894812	+	0.446444i	$0.147310\pi$
$678$	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	$0.216710\pi$
$683$			32.8992i			1.25885i	−0.777061	+	0.629426i	$0.783290\pi$
$684$	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	$0.0872760\pi$
$727$			14.6011i			0.541526i	−0.962646	+	0.270763i	$0.912724\pi$
$728$	−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	$0.481064\pi$
$733$	−24.5911	+	33.8468i	−0.908293	+	1.25016i	−0.967746	+	0.251927i	$0.918936\pi$
$734$	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	0.654740	−	0.755854i	$-0.272778\pi$
$743$	44.3956	−	14.4250i	1.62872	−	0.529202i	0.973976	+	0.226652i	$0.0727780\pi$
$744$	−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	0.0179624	−	0.999839i	$-0.494282\pi$
$757$	−15.2755	−	4.96330i	−0.555196	−	0.180394i	−0.573159	+	0.819444i	$0.694282\pi$
$758$		−	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	0.717877	−	0.696170i	$-0.245114\pi$
$773$	−4.61683	−	6.35452i	−0.166056	−	0.228556i	−0.883933	+	0.467613i	$0.845114\pi$
$774$	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	−0.108882	−	0.994055i	$-0.534727\pi$
$787$	10.8657	−	3.53048i	0.387321	−	0.125848i	0.496203	+	0.868206i	$0.334727\pi$
$788$	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	−0.235949	−	0.971766i	$-0.575820\pi$
$797$	4.07529	−	1.32414i	0.144354	−	0.0469035i	0.380303	+	0.924862i	$0.375820\pi$
$798$	−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	0.511195	−	0.859465i	$-0.329203\pi$
$823$	12.0369	+	3.91103i	0.419580	+	0.136330i	−0.0916150	+	0.995795i	$0.529203\pi$
$824$	13.5535			0.472159
$825$		0			0
$826$	15.0547			0.523820
$827$	28.7443	+	9.33959i	0.999538	+	0.324770i	0.762681	−	0.646775i	$-0.223883\pi$
$827$	28.7443	+	9.33959i	0.999538	+	0.324770i	0.236857	+	0.971545i	$0.423883\pi$
$828$	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	−0.590012	−	0.807395i	$-0.700877\pi$
$853$	−17.3124	+	5.62515i	−0.592767	+	0.192602i	−0.00275489	+	0.999996i	$0.500877\pi$
$854$	−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	$-0.833276\pi$
$857$		−	29.2837i		−	1.00031i	0.865935	−	0.500156i	$-0.166724\pi$
$858$	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	−0.604980	−	0.796241i	$-0.706819\pi$
$863$	−18.4017	+	5.97907i	−0.626400	+	0.203530i	−0.0214204	+	0.999771i	$0.506819\pi$
$864$	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	0.599028	−	0.800728i	$-0.295554\pi$
$877$	−10.2945	−	14.1691i	−0.347619	−	0.478456i	−0.946647	+	0.322271i	$0.895554\pi$
$878$	−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	0.987442	−	0.157981i	$-0.0504986\pi$
$883$	15.8102	+	21.7609i	0.532057	+	0.732313i	−0.455386	+	0.890294i	$0.650499\pi$
$884$	−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	−0.736561	−	0.676371i	$-0.763552\pi$
$887$	4.00028	−	5.50591i	0.134316	−	0.184870i	0.870877	+	0.491501i	$0.163552\pi$
$888$	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	0.0478248	−	0.998856i	$-0.484771\pi$
$907$	20.2873	−	6.59174i	0.673629	−	0.218875i	0.625804	+	0.779981i	$0.284771\pi$
$908$	−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	−0.359628	−	0.933096i	$-0.617096\pi$
$937$	−36.7029	−	11.9255i	−1.19903	−	0.389589i	−0.839405	+	0.543507i	$0.817096\pi$
$938$	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	$0.274696\pi$
$947$			46.7623i			1.51957i	−0.650174	+	0.759785i	$0.725304\pi$
$948$	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	−0.746419	−	0.665476i	$-0.768228\pi$
$953$	3.61628	−	4.97738i	0.117143	−	0.161233i	0.863562	+	0.504243i	$0.168228\pi$
$954$	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	$0.0173909\pi$
$967$			3.39625i			0.109216i	−0.998508	+	0.0546080i	$0.982609\pi$
$968$	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	0.0461210	−	0.998936i	$-0.485314\pi$
$977$	−15.7450	−	5.11585i	−0.503726	−	0.163671i	−0.549847	+	0.835265i	$0.685314\pi$
$978$			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	$0.500762\pi$
$983$	−29.8701	+	41.1126i	−0.952707	+	1.31129i	−0.950315	+	0.311291i	$0.899238\pi$
$984$	−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	−0.989028	−	0.147726i	$-0.952805\pi$
$997$	−17.1424	+	23.5945i	−0.542906	+	0.747246i	0.446122	+	0.894972i	$0.352805\pi$
$998$	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.174.3		16
5.2	odd	4		275.2.h.a.251.1		8
5.3	odd	4		55.2.g.b.31.2	yes	8
5.4	even	2	inner	275.2.z.a.174.2		16
11.5	even	5	inner	275.2.z.a.49.2		16
15.8	even	4		495.2.n.e.361.1		8
20.3	even	4		880.2.bo.h.801.1		8
55.3	odd	20		605.2.g.m.81.1		8
55.7	even	20		3025.2.a.w.1.3		4
55.8	even	20		605.2.g.e.81.2		8
55.13	even	20		605.2.g.e.366.2		8
55.18	even	20		605.2.a.k.1.2		4
55.27	odd	20		275.2.h.a.126.1		8
55.28	even	20		605.2.g.k.511.1		8
55.37	odd	20		3025.2.a.bd.1.2		4
55.38	odd	20		55.2.g.b.16.2	✓	8
55.43	even	4		605.2.g.k.251.1		8
55.48	odd	20		605.2.a.j.1.3		4
55.49	even	10	inner	275.2.z.a.49.3		16
55.53	odd	20		605.2.g.m.366.1		8
165.38	even	20		495.2.n.e.181.1		8
165.128	odd	20		5445.2.a.bi.1.3		4
165.158	even	20		5445.2.a.bp.1.2		4
220.103	even	20		9680.2.a.cn.1.3		4
220.183	odd	20		9680.2.a.cm.1.3		4
220.203	even	20		880.2.bo.h.401.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.16.2	✓	8	55.38	odd	20
55.2.g.b.31.2	yes	8	5.3	odd	4
275.2.h.a.126.1		8	55.27	odd	20
275.2.h.a.251.1		8	5.2	odd	4
275.2.z.a.49.2		16	11.5	even	5	inner
275.2.z.a.49.3		16	55.49	even	10	inner
275.2.z.a.174.2		16	5.4	even	2	inner
275.2.z.a.174.3		16	1.1	even	1	trivial
495.2.n.e.181.1		8	165.38	even	20
495.2.n.e.361.1		8	15.8	even	4
605.2.a.j.1.3		4	55.48	odd	20
605.2.a.k.1.2		4	55.18	even	20
605.2.g.e.81.2		8	55.8	even	20
605.2.g.e.366.2		8	55.13	even	20
605.2.g.k.251.1		8	55.43	even	4
605.2.g.k.511.1		8	55.28	even	20
605.2.g.m.81.1		8	55.3	odd	20
605.2.g.m.366.1		8	55.53	odd	20
880.2.bo.h.401.1		8	220.203	even	20
880.2.bo.h.801.1		8	20.3	even	4
3025.2.a.w.1.3		4	55.7	even	20
3025.2.a.bd.1.2		4	55.37	odd	20
5445.2.a.bi.1.3		4	165.128	odd	20
5445.2.a.bp.1.2		4	165.158	even	20
9680.2.a.cm.1.3		4	220.183	odd	20
9680.2.a.cn.1.3		4	220.103	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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