LMFDB - Embedded newform 275.2.h.a.251.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(26,275)]

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([0, 2]))

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

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

chi := DirichletCharacter("275.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.h (of order $5$, degree $4$, 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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 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:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			251.1
Root			$-0.386111 + 0.280526i$ of defining polynomial
Character	$\chi$	$=$	275.251
Dual form			275.2.h.a.126.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.147481 + 0.453901i) q^{2} +(0.261370 - 0.189896i) q^{3} +(1.43376 + 1.04169i) q^{4} +(0.0476470 + 0.146642i) q^{6} +(2.17239 + 1.57833i) q^{7} +(-1.45650 + 1.05821i) q^{8} +(-0.894797 + 2.75390i) q^{9} +O(q^{10})$	\(q+(-0.147481 + 0.453901i) q^{2} +(0.261370 - 0.189896i) q^{3} +(1.43376 + 1.04169i) q^{4} +(0.0476470 + 0.146642i) q^{6} +(2.17239 + 1.57833i) q^{7} +(-1.45650 + 1.05821i) q^{8} +(-0.894797 + 2.75390i) q^{9} +(-2.79042 - 1.79264i) q^{11} +0.572554 q^{12} +(1.44244 - 4.43939i) q^{13} +(-1.03679 + 0.753275i) q^{14} +(0.829779 + 2.55380i) q^{16} +(1.42961 + 4.39990i) q^{17} +(-1.11803 - 0.812299i) q^{18} +(3.51149 - 2.55125i) q^{19} +0.867517 q^{21} +(1.22522 - 1.00220i) q^{22} -2.77222 q^{23} +(-0.179735 + 0.553168i) q^{24} +(1.80231 + 1.30945i) q^{26} +(0.588587 + 1.81148i) q^{27} +(1.47055 + 4.52590i) q^{28} +(2.43790 + 1.77124i) q^{29} +(0.737407 - 2.26951i) q^{31} -4.88221 q^{32} +(-1.06975 + 0.0613500i) q^{33} -2.20796 q^{34} +(-4.15163 + 3.01633i) q^{36} +(-8.61029 - 6.25574i) q^{37} +(0.640135 + 1.97013i) q^{38} +(-0.466012 - 1.43424i) q^{39} +(1.78826 - 1.29924i) q^{41} +(-0.127943 + 0.393767i) q^{42} +7.06719 q^{43} +(-2.13343 - 5.47695i) q^{44} +(0.408851 - 1.25832i) q^{46} +(3.52905 - 2.56401i) q^{47} +(0.701836 + 0.509914i) q^{48} +(0.0650188 + 0.200107i) q^{49} +(1.20918 + 0.878523i) q^{51} +(6.69257 - 4.86243i) q^{52} +(1.95733 - 6.02403i) q^{53} -0.909040 q^{54} -4.83428 q^{56} +(0.433326 - 1.33364i) q^{57} +(-1.16351 + 0.845342i) q^{58} +(-9.50375 - 6.90488i) q^{59} +(-1.23070 - 3.78770i) q^{61} +(0.921378 + 0.669420i) q^{62} +(-6.29042 + 4.57026i) q^{63} +(-0.939522 + 2.89155i) q^{64} +(0.129921 - 0.494608i) q^{66} -7.31984 q^{67} +(-2.53359 + 7.79760i) q^{68} +(-0.724576 + 0.526435i) q^{69} +(0.369495 + 1.13719i) q^{71} +(-1.61093 - 4.95794i) q^{72} +(0.826577 + 0.600544i) q^{73} +(4.10935 - 2.98562i) q^{74} +7.69223 q^{76} +(-3.23251 - 8.29852i) q^{77} +0.719730 q^{78} +(1.08222 - 3.33073i) q^{79} +(-6.53000 - 4.74432i) q^{81} +(0.325994 + 1.00331i) q^{82} +(-3.43498 - 10.5718i) q^{83} +(1.24381 + 0.903681i) q^{84} +(-1.04228 + 3.20780i) q^{86} +0.973547 q^{87} +(5.96123 - 0.341876i) q^{88} +2.76978 q^{89} +(10.1404 - 7.36742i) q^{91} +(-3.97470 - 2.88779i) q^{92} +(-0.238235 - 0.733212i) q^{93} +(0.643336 + 1.97998i) q^{94} +(-1.27606 + 0.927114i) q^{96} +(-5.72738 + 17.6271i) q^{97} -0.100418 q^{98} +(7.43361 - 6.08051i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 5 q^{3} - 2 q^{4} - 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 5 * q^3 - 2 * q^4 - 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9	$ 8 q + 2 q^{2} + 5 q^{3} - 2 q^{4} - 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9} + 3 q^{11} - 16 q^{12} + 2 q^{13} - 16 q^{14} + 4 q^{16} + 13 q^{17} + 15 q^{19} - 20 q^{21} + 7 q^{22} - 10 q^{23} + 13 q^{24} + 10 q^{26} - 10 q^{27} + 6 q^{28} - 9 q^{29} - 10 q^{31} - 16 q^{32} - 5 q^{33} + 4 q^{34} - 15 q^{36} - 24 q^{37} + 21 q^{39} + 8 q^{41} - 9 q^{42} + 38 q^{43} - 12 q^{44} + 3 q^{46} - 5 q^{48} + q^{49} + q^{51} + 28 q^{52} - 13 q^{53} + 16 q^{54} + 22 q^{56} + 45 q^{57} - 12 q^{58} - 27 q^{59} + 6 q^{61} + 30 q^{62} - 25 q^{63} - 26 q^{64} + 13 q^{66} + 38 q^{67} - 11 q^{68} - q^{69} - 20 q^{71} + 30 q^{72} - 13 q^{73} + 20 q^{74} - 34 q^{77} + 16 q^{78} + 37 q^{79} + 8 q^{81} - 28 q^{82} - 27 q^{83} + 28 q^{84} - 3 q^{86} - 38 q^{87} + 36 q^{88} - 16 q^{89} + 44 q^{91} - 11 q^{92} + 35 q^{93} + 17 q^{94} - 17 q^{96} - 24 q^{97} - 16 q^{98} - 20 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 + 5 * q^3 - 2 * q^4 - 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9 + 3 * q^11 - 16 * q^12 + 2 * q^13 - 16 * q^14 + 4 * q^16 + 13 * q^17 + 15 * q^19 - 20 * q^21 + 7 * q^22 - 10 * q^23 + 13 * q^24 + 10 * q^26 - 10 * q^27 + 6 * q^28 - 9 * q^29 - 10 * q^31 - 16 * q^32 - 5 * q^33 + 4 * q^34 - 15 * q^36 - 24 * q^37 + 21 * q^39 + 8 * q^41 - 9 * q^42 + 38 * q^43 - 12 * q^44 + 3 * q^46 - 5 * q^48 + q^49 + q^51 + 28 * q^52 - 13 * q^53 + 16 * q^54 + 22 * q^56 + 45 * q^57 - 12 * q^58 - 27 * q^59 + 6 * q^61 + 30 * q^62 - 25 * q^63 - 26 * q^64 + 13 * q^66 + 38 * q^67 - 11 * q^68 - q^69 - 20 * q^71 + 30 * q^72 - 13 * q^73 + 20 * q^74 - 34 * q^77 + 16 * q^78 + 37 * q^79 + 8 * q^81 - 28 * q^82 - 27 * q^83 + 28 * q^84 - 3 * q^86 - 38 * q^87 + 36 * q^88 - 16 * q^89 + 44 * q^91 - 11 * q^92 + 35 * q^93 + 17 * q^94 - 17 * q^96 - 24 * q^97 - 16 * q^98 - 20 * 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 $

$2$	−0.147481	+	0.453901i	−0.104285	+	0.320957i	−0.989562	−	0.144108i	$-0.953969\pi$
$2$	−0.147481	+	0.453901i	−0.104285	+	0.320957i	0.885277	+	0.465064i	$0.153969\pi$
$3$	0.261370	−	0.189896i	0.150902	−	0.109637i	−0.509772	−	0.860309i	$-0.670270\pi$
$3$	0.261370	−	0.189896i	0.150902	−	0.109637i	0.660674	+	0.750673i	$0.270270\pi$
$4$	1.43376	+	1.04169i	0.716879	+	0.520843i
$5$		0			0
$5$		0			0
$6$	0.0476470	+	0.146642i	0.0194518	+	0.0598665i
$7$	2.17239	+	1.57833i	0.821086	+	0.596554i	0.917023	−	0.398834i	$-0.130585\pi$
$7$	2.17239	+	1.57833i	0.821086	+	0.596554i	−0.0959376	+	0.995387i	$0.530585\pi$
$8$	−1.45650	+	1.05821i	−0.514950	+	0.374133i
$9$	−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
$12$	0.572554			0.165282
$13$	1.44244	−	4.43939i	0.400062	−	1.23126i	−0.524886	−	0.851172i	$-0.675892\pi$
$13$	1.44244	−	4.43939i	0.400062	−	1.23126i	0.924949	−	0.380092i	$-0.124108\pi$
$14$	−1.03679	+	0.753275i	−0.277095	+	0.201321i
$15$		0			0
$16$	0.829779	+	2.55380i	0.207445	+	0.638449i
$17$	1.42961	+	4.39990i	0.346732	+	1.06713i	0.960650	+	0.277762i	$0.0895926\pi$
$17$	1.42961	+	4.39990i	0.346732	+	1.06713i	−0.613918	+	0.789370i	$0.710407\pi$
$18$	−1.11803	−	0.812299i	−0.263523	−	0.191461i
$19$	3.51149	−	2.55125i	0.805592	−	0.585297i	−0.106958	−	0.994264i	$-0.534111\pi$
$19$	3.51149	−	2.55125i	0.805592	−	0.585297i	0.912549	+	0.408967i	$0.134111\pi$
$20$		0			0
$21$	0.867517			0.189308
$22$	1.22522	−	1.00220i	0.261217	−	0.213669i
$23$	−2.77222			−0.578048			−0.289024	−	0.957322i	$-0.593331\pi$
$23$	−2.77222			−0.578048			−0.289024	+	0.957322i	$0.593331\pi$
$24$	−0.179735	+	0.553168i	−0.0366883	+	0.112915i
$25$		0			0
$26$	1.80231	+	1.30945i	0.353462	+	0.256805i
$27$	0.588587	+	1.81148i	0.113274	+	0.348620i
$28$	1.47055	+	4.52590i	0.277908	+	0.855314i
$29$	2.43790	+	1.77124i	0.452707	+	0.328911i	0.790664	−	0.612251i	$-0.209736\pi$
$29$	2.43790	+	1.77124i	0.452707	+	0.328911i	−0.337956	+	0.941162i	$0.609736\pi$
$30$		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	$0.0312543\pi$
$32$	−4.88221			−0.863061
$33$	−1.06975	+	0.0613500i	−0.186219	+	0.0106797i
$34$	−2.20796			−0.378662
$35$		0			0
$36$	−4.15163	+	3.01633i	−0.691938	+	0.502722i
$37$	−8.61029	−	6.25574i	−1.41552	−	1.02844i	−0.992490	−	0.122324i	$-0.960965\pi$
$37$	−8.61029	−	6.25574i	−1.41552	−	1.02844i	−0.423033	−	0.906114i	$-0.639035\pi$
$38$	0.640135	+	1.97013i	0.103844	+	0.319598i
$39$	−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	$0.244782\pi$
$42$	−0.127943	+	0.393767i	−0.0197420	+	0.0607596i
$43$	7.06719			1.07774			0.538868	−	0.842390i	$-0.318852\pi$
$43$	7.06719			1.07774			0.538868	+	0.842390i	$0.318852\pi$
$44$	−2.13343	−	5.47695i	−0.321626	−	0.825682i
$45$		0			0
$46$	0.408851	−	1.25832i	0.0602819	−	0.185528i
$47$	3.52905	−	2.56401i	0.514765	−	0.373999i	−0.299863	−	0.953982i	$-0.596941\pi$
$47$	3.52905	−	2.56401i	0.514765	−	0.373999i	0.814628	+	0.579983i	$0.196941\pi$
$48$	0.701836	+	0.509914i	0.101301	+	0.0735997i
$49$	0.0650188	+	0.200107i	0.00928840	+	0.0285868i
$50$		0			0
$51$	1.20918	+	0.878523i	0.169319	+	0.123018i
$52$	6.69257	−	4.86243i	0.928092	−	0.674298i
$53$	1.95733	−	6.02403i	0.268859	−	0.827464i	−0.721920	−	0.691977i	$-0.756740\pi$
$53$	1.95733	−	6.02403i	0.268859	−	0.827464i	0.990779	−	0.135487i	$-0.0432600\pi$
$54$	−0.909040			−0.123705
$55$		0			0
$56$	−4.83428			−0.646008
$57$	0.433326	−	1.33364i	0.0573954	−	0.176645i
$58$	−1.16351	+	0.845342i	−0.152777	+	0.110999i
$59$	−9.50375	−	6.90488i	−1.23728	−	0.898939i	−0.239869	−	0.970805i	$-0.577104\pi$
$59$	−9.50375	−	6.90488i	−1.23728	−	0.898939i	−0.997414	+	0.0718667i	$0.977104\pi$
$60$		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	$0.982063\pi$
$62$	0.921378	+	0.669420i	0.117015	+	0.0850164i
$63$	−6.29042	+	4.57026i	−0.792519	+	0.575799i
$64$	−0.939522	+	2.89155i	−0.117440	+	0.361444i
$65$		0			0
$66$	0.129921	−	0.494608i	0.0159922	−	0.0608820i
$67$	−7.31984			−0.894260			−0.447130	−	0.894469i	$-0.647554\pi$
$67$	−7.31984			−0.894260			−0.447130	+	0.894469i	$0.647554\pi$
$68$	−2.53359	+	7.79760i	−0.307243	+	0.945598i
$69$	−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	$0.877396\pi$
$72$	−1.61093	−	4.95794i	−0.189850	−	0.584299i
$73$	0.826577	+	0.600544i	0.0967436	+	0.0702883i	0.635105	−	0.772425i	$-0.280957\pi$
$73$	0.826577	+	0.600544i	0.0967436	+	0.0702883i	−0.538362	+	0.842714i	$0.680957\pi$
$74$	4.10935	−	2.98562i	0.477702	−	0.347071i
$75$		0			0
$76$	7.69223			0.882360
$77$	−3.23251	−	8.29852i	−0.368378	−	0.945704i
$78$	0.719730			0.0814934
$79$	1.08222	−	3.33073i	0.121759	−	0.374736i	−0.871538	−	0.490329i	$-0.836877\pi$
$79$	1.08222	−	3.33073i	0.121759	−	0.374736i	0.993297	+	0.115593i	$0.0368767\pi$
$80$		0			0
$81$	−6.53000	−	4.74432i	−0.725555	−	0.527147i
$82$	0.325994	+	1.00331i	0.0360000	+	0.110797i
$83$	−3.43498	−	10.5718i	−0.377038	−	1.16040i	−0.942093	−	0.335351i	$-0.891145\pi$
$83$	−3.43498	−	10.5718i	−0.377038	−	1.16040i	0.565055	−	0.825053i	$-0.308855\pi$
$84$	1.24381	+	0.903681i	0.135711	+	0.0985996i
$85$		0			0
$86$	−1.04228	+	3.20780i	−0.112392	+	0.345906i
$87$	0.973547			0.104375
$88$	5.96123	−	0.341876i	0.635469	−	0.0364442i
$89$	2.76978			0.293596			0.146798	−	0.989167i	$-0.453103\pi$
$89$	2.76978			0.293596			0.146798	+	0.989167i	$0.453103\pi$
$90$		0			0
$91$	10.1404	−	7.36742i	1.06300	−	0.772315i
$92$	−3.97470	−	2.88779i	−0.414391	−	0.301073i
$93$	−0.238235	−	0.733212i	−0.0247038	−	0.0760305i
$94$	0.643336	+	1.97998i	0.0663550	+	0.204220i
$95$		0			0
$96$	−1.27606	+	0.927114i	−0.130238	+	0.0946232i
$97$	−5.72738	+	17.6271i	−0.581528	+	1.78976i	0.0312615	+	0.999511i	$0.490048\pi$
$97$	−5.72738	+	17.6271i	−0.581528	+	1.78976i	−0.612789	+	0.790247i	$0.709952\pi$
$98$	−0.100418			−0.0101438
$99$	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	$0.984834\pi$
$102$	−0.577094	+	0.419284i	−0.0571409	+	0.0415153i
$103$	6.09056	+	4.42505i	0.600121	+	0.436014i	0.845922	−	0.533307i	$-0.179051\pi$
$103$	6.09056	+	4.42505i	0.600121	+	0.436014i	−0.245801	+	0.969320i	$0.579051\pi$
$104$	2.59688	+	7.99237i	0.254645	+	0.783716i
$105$		0			0
$106$	2.44565	+	1.77687i	0.237542	+	0.172584i
$107$	14.5859	−	10.5973i	1.41008	−	1.02448i	0.416764	−	0.909015i	$-0.363164\pi$
$107$	14.5859	−	10.5973i	1.41008	−	1.02448i	0.993312	−	0.115465i	$-0.0368358\pi$
$108$	−1.04311	+	3.21035i	−0.100373	+	0.308916i
$109$	−16.3653			−1.56751			−0.783756	−	0.621068i	$-0.786699\pi$
$109$	−16.3653			−1.56751			−0.783756	+	0.621068i	$0.786699\pi$
$110$		0			0
$111$	−3.43842			−0.326360
$112$	−2.22814	+	6.85750i	−0.210539	+	0.647973i
$113$	−1.66154	+	1.20718i	−0.156304	+	0.113562i	−0.663188	−	0.748453i	$-0.730797\pi$
$113$	−1.66154	+	1.20718i	−0.156304	+	0.113562i	0.506884	+	0.862014i	$0.330797\pi$
$114$	0.541433	+	0.393374i	0.0507099	+	0.0368429i
$115$		0			0
$116$	1.65029	+	5.07906i	0.153225	+	0.471579i
$117$	10.9349	+	7.94470i	1.01094	+	0.734488i
$118$	4.53576	−	3.29542i	0.417551	−	0.303368i
$119$	−3.83883	+	11.8147i	−0.351905	+	1.08305i
$120$		0			0
$121$	4.57291	+	10.0044i	0.415720	+	0.909493i
$122$	1.90075			0.172086
$123$	0.220675	−	0.679167i	0.0198976	−	0.0612384i
$124$	3.42138	−	2.48578i	0.307249	−	0.223229i
$125$		0			0
$126$	−1.14673	−	3.52926i	−0.102158	−	0.314411i
$127$	0.0235677	+	0.0725340i	0.00209130	+	0.00643635i	0.952097	−	0.305797i	$-0.0989229\pi$
$127$	0.0235677	+	0.0725340i	0.00209130	+	0.00643635i	−0.950005	+	0.312233i	$0.898923\pi$
$128$	−9.07350	−	6.59228i	−0.801992	−	0.582681i
$129$	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	$0.667270\pi$
$132$	−1.59767	−	1.02638i	−0.139059	−	0.0893350i
$133$	11.6550			1.01062
$134$	1.07954	−	3.32248i	0.0932580	−	0.287019i
$135$		0			0
$136$	−6.73823	−	4.89561i	−0.577799	−	0.419795i
$137$	5.66406	+	17.4322i	0.483914	+	1.48933i	0.833548	+	0.552447i	$0.186306\pi$
$137$	5.66406	+	17.4322i	0.483914	+	1.48933i	−0.349635	+	0.936886i	$0.613694\pi$
$138$	−0.132088	−	0.406525i	−0.0112441	−	0.0346057i
$139$	18.7590	+	13.6292i	1.59111	+	1.15601i	0.902330	+	0.431046i	$0.141855\pi$
$139$	18.7590	+	13.6292i	1.59111	+	1.15601i	0.688785	+	0.724966i	$0.258145\pi$
$140$		0			0
$141$	0.435493	−	1.34031i	0.0366751	−	0.112874i
$142$	−0.570666			−0.0478892
$143$	−11.9832	+	9.80199i	−1.00209	+	0.819683i
$144$	−7.77539			−0.647949
$145$		0			0
$146$	−0.394492	+	0.286615i	−0.0326484	+	0.0237205i
$147$	0.0549936	+	0.0399552i	0.00453580	+	0.00329545i
$148$	−5.82856	−	17.9385i	−0.479104	−	1.47453i
$149$	4.53161	+	13.9469i	0.371244	+	1.14257i	0.945978	+	0.324232i	$0.105106\pi$
$149$	4.53161	+	13.9469i	0.371244	+	1.14257i	−0.574733	+	0.818341i	$0.694894\pi$
$150$		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	$0.201028\pi$
$152$	−2.41473	+	7.43178i	−0.195861	+	0.602797i
$153$	−13.3961			−1.08301
$154$	4.24344	−	0.243361i	0.341946	−	0.0196106i
$155$		0			0
$156$	0.825877	−	2.54179i	0.0661231	−	0.203506i
$157$	−10.8262	+	7.86568i	−0.864023	+	0.627750i	−0.928977	−	0.370139i	$-0.879310\pi$
$157$	−10.8262	+	7.86568i	−0.864023	+	0.627750i	0.0649531	+	0.997888i	$0.479310\pi$
$158$	1.35221	+	0.982441i	0.107576	+	0.0781588i
$159$	−0.632355	−	1.94619i	−0.0501491	−	0.154343i
$160$		0			0
$161$	−6.02234	−	4.37549i	−0.474627	−	0.344837i
$162$	3.11651	−	2.26427i	0.244856	−	0.177898i
$163$	0.238558	−	0.734206i	0.0186853	−	0.0575075i	−0.941279	−	0.337629i	$-0.890375\pi$
$163$	0.238558	−	0.734206i	0.0186853	−	0.0575075i	0.959964	+	0.280122i	$0.0903749\pi$
$164$	3.91733			0.305892
$165$		0			0
$166$	5.30514			0.411759
$167$	2.62118	−	8.06716i	0.202833	−	0.624256i	−0.796962	−	0.604029i	$-0.793561\pi$
$167$	2.62118	−	8.06716i	0.202833	−	0.624256i	0.999795	−	0.0202268i	$-0.00643884\pi$
$168$	−1.26354	+	0.918013i	−0.0974840	+	0.0708263i
$169$	−7.11029	−	5.16593i	−0.546946	−	0.397379i
$170$		0			0
$171$	3.88382	+	11.9532i	0.297003	+	0.914081i
$172$	10.1326	+	7.36179i	0.772606	+	0.561331i
$173$	4.10876	−	2.98519i	0.312384	−	0.226960i	−0.420535	−	0.907276i	$-0.638158\pi$
$173$	4.10876	−	2.98519i	0.312384	−	0.226960i	0.732919	+	0.680316i	$0.238158\pi$
$174$	−0.143580	+	0.441894i	−0.0108848	+	0.0334999i
$175$		0			0
$176$	2.26259	−	8.61366i	0.170549	−	0.649279i
$177$	−3.79521			−0.285265
$178$	−0.408491	+	1.25721i	−0.0306177	+	0.0942315i
$179$	9.15568	−	6.65199i	0.684328	−	0.497193i	−0.190463	−	0.981694i	$-0.560999\pi$
$179$	9.15568	−	6.65199i	0.684328	−	0.497193i	0.874791	+	0.484501i	$0.160999\pi$
$180$		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	$0.811315\pi$
$182$	1.84856	+	5.68929i	0.137025	+	0.421718i
$183$	−1.04094	−	0.756287i	−0.0769485	−	0.0559063i
$184$	4.03774	−	2.93359i	0.297666	−	0.216267i
$185$		0			0
$186$	0.367941			0.0269787
$187$	3.89819	−	14.8403i	0.285064	−	1.08523i
$188$	7.73070			0.563819
$189$	−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	$0.640272\pi$
$192$	0.303532	+	0.934176i	0.0219056	+	0.0674184i
$193$	1.24605	+	3.83494i	0.0896925	+	0.276045i	0.985834	−	0.167723i	$-0.0536414\pi$
$193$	1.24605	+	3.83494i	0.0896925	+	0.276045i	−0.896142	+	0.443768i	$0.853641\pi$
$194$	−7.15627	−	5.19933i	−0.513790	−	0.373290i
$195$		0			0
$196$	−0.115228	+	0.354635i	−0.00823056	+	0.0253311i
$197$	−11.4176			−0.813469			−0.406734	−	0.913547i	$-0.633333\pi$
$197$	−11.4176			−0.813469			−0.406734	+	0.913547i	$0.633333\pi$
$198$	1.66363	+	4.27089i	0.118229	+	0.303519i
$199$	−7.16644			−0.508015			−0.254008	−	0.967202i	$-0.581749\pi$
$199$	−7.16644			−0.508015			−0.254008	+	0.967202i	$0.581749\pi$
$200$		0			0
$201$	−1.91319	+	1.39001i	−0.134946	+	0.0980438i
$202$	−2.74701	−	1.99582i	−0.193279	−	0.140425i
$203$	2.50047	+	7.69565i	0.175498	+	0.540128i
$204$	0.818531	+	2.51918i	0.0573086	+	0.176378i
$205$		0			0
$206$	−2.90678	+	2.11190i	−0.202525	+	0.147143i
$207$	2.48058	−	7.63443i	0.172412	−	0.530630i
$208$	12.5342			0.869090
$209$	−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	$0.0617393\pi$
$212$	9.08148	−	6.59808i	0.623719	−	0.453158i
$213$	0.312523	+	0.227061i	0.0214137	+	0.0155580i
$214$	2.65897	+	8.18348i	0.181764	+	0.559411i
$215$		0			0
$216$	−2.77420	−	2.01558i	−0.188760	−	0.137143i
$217$	5.18397	−	3.76638i	0.351911	−	0.255678i
$218$	2.41358	−	7.42824i	0.163468	−	0.503104i
$219$	0.330084			0.0223050
$220$		0			0
$221$	21.5950			1.45264
$222$	0.507102	−	1.56070i	0.0340345	−	0.104747i
$223$	8.53103	−	6.19816i	0.571280	−	0.415059i	−0.264290	−	0.964443i	$-0.585138\pi$
$223$	8.53103	−	6.19816i	0.571280	−	0.415059i	0.835570	+	0.549384i	$0.185138\pi$
$224$	−10.6061	−	7.70575i	−0.708647	−	0.514862i
$225$		0			0
$226$	−0.302893	−	0.932209i	−0.0201481	−	0.0620096i
$227$	0.174762	+	0.126972i	0.0115994	+	0.00842743i	0.593570	−	0.804782i	$-0.297718\pi$
$227$	0.174762	+	0.126972i	0.0115994	+	0.00842743i	−0.581970	+	0.813210i	$0.697718\pi$
$228$	2.01052	−	1.46073i	0.133150	−	0.0967390i
$229$	−0.0233956	+	0.0720042i	−0.00154602	+	0.00475817i	−0.951827	−	0.306637i	$-0.900796\pi$
$229$	−0.0233956	+	0.0720042i	−0.00154602	+	0.00475817i	0.950281	+	0.311395i	$0.100796\pi$
$230$		0			0
$231$	−2.42074	−	1.55514i	−0.159273	−	0.102321i
$232$	−5.42514			−0.356178
$233$	−4.67235	+	14.3800i	−0.306096	+	0.942067i	0.673170	+	0.739488i	$0.264932\pi$
$233$	−4.67235	+	14.3800i	−0.306096	+	0.942067i	−0.979266	+	0.202579i	$0.935068\pi$
$234$	−5.21881	+	3.79169i	−0.341164	+	0.247870i
$235$		0			0
$236$	−6.43336	−	19.7999i	−0.418776	−	1.28886i
$237$	−0.349634	−	1.07606i	−0.0227111	−	0.0698977i
$238$	−4.79655	−	3.48489i	−0.310914	−	0.225892i
$239$	18.7406	−	13.6158i	1.21223	−	0.880734i	0.216796	−	0.976217i	$-0.430439\pi$
$239$	18.7406	−	13.6158i	1.21223	−	0.880734i	0.995431	+	0.0954825i	$0.0304394\pi$
$240$		0			0
$241$	−21.3349			−1.37430			−0.687151	−	0.726515i	$-0.741139\pi$
$241$	−21.3349			−1.37430			−0.687151	+	0.726515i	$0.741139\pi$
$242$	−5.21544	+	0.600185i	−0.335261	+	0.0385814i
$243$	−8.32179			−0.533843
$244$	2.18107	−	6.71266i	0.139629	−	0.429734i
$245$		0			0
$246$	0.275729	+	0.200329i	0.0175798	+	0.0127725i
$247$	−6.26085	−	19.2689i	−0.398368	−	1.22605i
$248$	1.32758	+	4.08586i	0.0843012	+	0.259453i
$249$	−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	$0.162912\pi$
$252$	−13.7797			−0.868041
$253$	7.73567	+	4.96959i	0.486338	+	0.312435i
$254$	−0.0363991			−0.00228388
$255$		0			0
$256$	−0.588982	+	0.427920i	−0.0368113	+	0.0267450i
$257$	−11.5611	−	8.39964i	−0.721163	−	0.523955i	0.165593	−	0.986194i	$-0.447046\pi$
$257$	−11.5611	−	8.39964i	−0.721163	−	0.523955i	−0.886755	+	0.462239i	$0.847046\pi$
$258$	0.336730	+	1.03635i	0.0209639	+	0.0645203i
$259$	−8.83126	−	27.1798i	−0.548748	−	1.68887i
$260$		0			0
$261$	−7.05926	+	5.12885i	−0.436957	+	0.317468i
$262$	1.69355	−	5.21220i	0.104628	−	0.322011i
$263$	−4.13132			−0.254748			−0.127374	−	0.991855i	$-0.540655\pi$
$263$	−4.13132			−0.254748			−0.127374	+	0.991855i	$0.540655\pi$
$264$	1.49316	−	1.22137i	0.0918979	−	0.0751703i
$265$		0			0
$266$	−1.71890	+	5.29024i	−0.105393	+	0.324365i
$267$	0.723937	−	0.525971i	0.0443042	−	0.0321889i
$268$	−10.4949	−	7.62497i	−0.641077	−	0.465769i
$269$	−0.520367	−	1.60152i	−0.0317273	−	0.0976466i	0.933939	−	0.357433i	$-0.116348\pi$
$269$	−0.520367	−	1.60152i	−0.0317273	−	0.0976466i	−0.965666	+	0.259786i	$0.916348\pi$
$270$		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	$0.510877\pi$
$272$	−10.0502	+	7.30188i	−0.609381	+	0.442741i
$273$	1.25134	−	3.85124i	0.0757348	−	0.233088i
$274$	−8.74784			−0.528476
$275$		0			0
$276$	−1.58725			−0.0955411
$277$	1.05914	−	3.25969i	0.0636375	−	0.195856i	−0.914183	−	0.405303i	$-0.867166\pi$
$277$	1.05914	−	3.25969i	0.0636375	−	0.195856i	0.977820	+	0.209446i	$0.0671662\pi$
$278$	−8.95290	+	6.50466i	−0.536959	+	0.390124i
$279$	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	$-0.338331\pi$
$282$	0.544141	+	0.395341i	0.0324031	+	0.0235422i
$283$	−23.5416	+	17.1040i	−1.39941	+	1.01673i	−0.404647	+	0.914473i	$0.632606\pi$
$283$	−23.5416	+	17.1040i	−1.39941	+	1.01673i	−0.994758	+	0.102255i	$0.967394\pi$
$284$	−0.654828	+	2.01535i	−0.0388569	+	0.119589i
$285$		0			0
$286$	−2.68183	−	6.88482i	−0.158580	−	0.407108i
$287$	5.93542			0.350357
$288$	4.36859	−	13.4451i	0.257422	−	0.792262i
$289$	−3.56201	+	2.58795i	−0.209530	+	0.152232i
$290$		0			0
$291$	1.85035	+	5.69480i	0.108470	+	0.333835i
$292$	0.559534	+	1.72207i	0.0327443	+	0.100776i
$293$	17.1621	+	12.4690i	1.00262	+	0.728448i	0.962649	−	0.270753i	$-0.0872725\pi$
$293$	17.1621	+	12.4690i	1.00262	+	0.728448i	0.0399740	+	0.999201i	$0.487273\pi$
$294$	−0.0262463	+	0.0190690i	−0.00153071	+	0.00111213i
$295$		0			0
$296$	19.1608			1.11370
$297$	1.60492	−	6.10992i	0.0931271	−	0.354534i
$298$	−6.99883			−0.405432
$299$	−3.99878	+	12.3070i	−0.231255	+	0.711731i
$300$		0			0
$301$	15.3527	+	11.1544i	0.884913	+	0.642927i
$302$	1.10892	+	3.41289i	0.0638109	+	0.196390i
$303$	0.710278	+	2.18601i	0.0408044	+	0.125583i
$304$	9.42913	+	6.85066i	0.540798	+	0.392912i
$305$		0			0
$306$	1.97568	−	6.08051i	0.112942	−	0.347599i
$307$	6.87520			0.392388			0.196194	−	0.980565i	$-0.437142\pi$
$307$	6.87520			0.392388			0.196194	+	0.980565i	$0.437142\pi$
$308$	4.00982	−	15.2653i	0.228481	−	0.869823i
$309$	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	$0.552791\pi$
$312$	2.19647	+	1.59583i	0.124350	+	0.0903459i
$313$	3.57821	+	11.0126i	0.202252	+	0.622469i	0.999815	+	0.0192328i	$0.00612237\pi$
$313$	3.57821	+	11.0126i	0.202252	+	0.622469i	−0.797563	+	0.603236i	$0.793878\pi$
$314$	−1.97358	−	6.07406i	−0.111376	−	0.342779i
$315$		0			0
$316$	5.02121	−	3.64812i	0.282465	−	0.205223i
$317$	−6.40940	+	19.7261i	−0.359988	+	1.10793i	0.593073	+	0.805149i	$0.297915\pi$
$317$	−6.40940	+	19.7261i	−0.359988	+	1.10793i	−0.953061	+	0.302780i	$0.902085\pi$
$318$	0.976639			0.0547672
$319$	−3.62759	−	9.31278i	−0.203106	−	0.521416i
$320$		0			0
$321$	1.79994	−	5.53963i	0.100463	−	0.309192i
$322$	2.87422	−	2.08825i	0.160174	−	0.116373i
$323$	16.2453	+	11.8029i	0.903913	+	0.656731i
$324$	−4.42034	−	13.6044i	−0.245575	−	0.755801i
$325$		0			0
$326$	0.298074	+	0.216564i	0.0165088	+	0.0119943i
$327$	−4.27740	+	3.10771i	−0.236541	+	0.171857i
$328$	−1.22972	+	3.78469i	−0.0679000	+	0.208975i
$329$	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	$0.844702\pi$
$332$	6.08755	−	18.7356i	0.334098	−	1.02825i
$333$	24.9322	−	18.1143i	1.36627	−	0.992657i
$334$	3.27512	+	2.37951i	0.179207	+	0.130201i
$335$		0			0
$336$	0.719847	+	2.21546i	0.0392709	+	0.120863i
$337$	−14.5594	−	10.5780i	−0.793100	−	0.576221i	0.115782	−	0.993275i	$-0.463063\pi$
$337$	−14.5594	−	10.5780i	−0.793100	−	0.576221i	−0.908882	+	0.417054i	$0.863063\pi$
$338$	3.39346	−	2.46549i	0.184580	−	0.134105i
$339$	−0.205037	+	0.631039i	−0.0111361	+	0.0342734i
$340$		0			0
$341$	−6.12608	+	5.01098i	−0.331746	+	0.271360i
$342$	−5.99834			−0.324353
$343$	5.63386	−	17.3392i	0.304200	−	0.936231i
$344$	−10.2933	+	7.47855i	−0.554980	+	0.403217i
$345$		0			0
$346$	0.749016	+	2.30523i	0.0402673	+	0.123930i
$347$	2.48753	+	7.65583i	0.133538	+	0.410986i	0.995360	−	0.0962243i	$-0.0306766\pi$
$347$	2.48753	+	7.65583i	0.133538	+	0.410986i	−0.861822	+	0.507211i	$0.830677\pi$
$348$	1.39583	+	1.01413i	0.0748244	+	0.0543631i
$349$	−15.5569	+	11.3027i	−0.832741	+	0.605022i	−0.920333	−	0.391135i	$-0.872083\pi$
$349$	−15.5569	+	11.3027i	−0.832741	+	0.605022i	0.0875926	+	0.996156i	$0.472083\pi$
$350$		0			0
$351$	8.89088			0.474560
$352$	13.6234	+	8.75202i	0.726131	+	0.466484i
$353$	−14.8497			−0.790371			−0.395186	−	0.918601i	$-0.629320\pi$
$353$	−14.8497			−0.790371			−0.395186	+	0.918601i	$0.629320\pi$
$354$	0.559723	−	1.72265i	0.0297489	−	0.0915578i
$355$		0			0
$356$	3.97119	+	2.88524i	0.210473	+	0.152917i
$357$	1.24021	+	3.81698i	0.0656391	+	0.202016i
$358$	1.66905	+	5.13682i	0.0882123	+	0.271489i
$359$	−8.27079	−	6.00908i	−0.436516	−	0.317147i	0.347733	−	0.937594i	$-0.386952\pi$
$359$	−8.27079	−	6.00908i	−0.436516	−	0.317147i	−0.784249	+	0.620446i	$0.786952\pi$
$360$		0			0
$361$	−0.0496143	+	0.152697i	−0.00261128	+	0.00803670i
$362$	−3.53175			−0.185625
$363$	3.09503	+	1.74648i	0.162447	+	0.0916662i
$364$	22.2134			1.16430
$365$		0			0
$366$	0.496799	−	0.360945i	0.0259681	−	0.0188669i
$367$	11.4422	+	8.31327i	0.597280	+	0.433949i	0.844912	−	0.534905i	$-0.179653\pi$
$367$	11.4422	+	8.31327i	0.597280	+	0.433949i	−0.247632	+	0.968854i	$0.579653\pi$
$368$	−2.30033	−	7.07969i	−0.119913	−	0.369054i
$369$	1.97786	+	6.08724i	0.102964	+	0.316889i
$370$		0			0
$371$	13.7600	−	9.99722i	0.714383	−	0.519030i
$372$	0.422205	−	1.29941i	0.0218903	−	0.0673715i
$373$	−12.4600			−0.645154			−0.322577	−	0.946543i	$-0.604549\pi$
$373$	−12.4600			−0.645154			−0.322577	+	0.946543i	$0.604549\pi$
$374$	6.16114	+	3.95807i	0.318585	+	0.204667i
$375$		0			0
$376$	−2.42681	+	7.46894i	−0.125153	+	0.385181i
$377$	11.3798	−	8.26788i	0.586088	−	0.425818i
$378$	−1.97479	−	1.43477i	−0.101572	−	0.0737965i
$379$	5.04840	+	15.5374i	0.259319	+	0.798102i	0.992948	+	0.118552i	$0.0378251\pi$
$379$	5.04840	+	15.5374i	0.259319	+	0.798102i	−0.733629	+	0.679550i	$0.762175\pi$
$380$		0			0
$381$	0.0199338	+	0.0144828i	0.00102124	+	0.000741975i
$382$	−1.99082	+	1.44642i	−0.101859	+	0.0740051i
$383$	0.251122	−	0.772874i	0.0128317	−	0.0394920i	−0.944436	−	0.328696i	$-0.893391\pi$
$383$	0.251122	−	0.772874i	0.0128317	−	0.0394920i	0.957267	+	0.289204i	$0.0933907\pi$
$384$	−3.62339			−0.184905
$385$		0			0
$386$	−1.92445			−0.0979522
$387$	−6.32370	+	19.4623i	−0.321452	+	0.989327i
$388$	−26.5736	+	19.3068i	−1.34907	+	0.980155i
$389$	24.5894	+	17.8652i	1.24673	+	0.905802i	0.998028	−	0.0627780i	$-0.0199960\pi$
$389$	24.5894	+	17.8652i	1.24673	+	0.905802i	0.248702	+	0.968580i	$0.419996\pi$
$390$		0			0
$391$	−3.96321	−	12.1975i	−0.200428	−	0.616854i
$392$	−0.306455	−	0.222653i	−0.0154783	−	0.0112457i
$393$	−3.00134	+	2.18060i	−0.151398	+	0.109997i
$394$	1.68388	−	5.18245i	0.0848327	−	0.261088i
$395$		0			0
$396$	16.9920	−	0.974490i	0.853879	−	0.0489700i
$397$	14.8996			0.747789			0.373894	−	0.927471i	$-0.378022\pi$
$397$	14.8996			0.747789			0.373894	+	0.927471i	$0.378022\pi$
$398$	1.05692	−	3.25285i	0.0529784	−	0.163051i
$399$	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	$0.801728\pi$
$402$	−0.348768	−	1.07340i	−0.0173950	−	0.0535362i
$403$	−9.01155	−	6.54727i	−0.448897	−	0.326143i
$404$	−10.2006	+	7.41114i	−0.507496	+	0.368718i
$405$		0			0
$406$	−3.86184			−0.191660
$407$	12.8121	+	32.8913i	0.635071	+	1.63036i
$408$	−2.69083			−0.133216
$409$	−0.0809957	+	0.249279i	−0.00400498	+	0.0123261i	−0.953039	−	0.302847i	$-0.902063\pi$
$409$	−0.0809957	+	0.249279i	−0.00400498	+	0.0123261i	0.949034	+	0.315174i	$0.102063\pi$
$410$		0			0
$411$	4.79073	+	3.48067i	0.236309	+	0.171689i
$412$	4.12288	+	12.6889i	0.203120	+	0.625138i
$413$	−9.74764	−	30.0002i	−0.479650	−	1.47621i
$414$	3.09944	+	2.25187i	0.152329	+	0.110674i
$415$		0			0
$416$	−7.04232	+	21.6740i	−0.345278	+	1.06266i
$417$	7.49116			0.366844
$418$	1.74548	−	6.64503i	0.0853744	−	0.325019i
$419$	−1.26916			−0.0620023			−0.0310012	−	0.999519i	$-0.509870\pi$
$419$	−1.26916			−0.0620023			−0.0310012	+	0.999519i	$0.509870\pi$
$420$		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	$0.0428071\pi$
$422$	1.34506	+	0.977240i	0.0654763	+	0.0475713i
$423$	3.90324	+	12.0129i	0.189782	+	0.584089i
$424$	3.52384	+	10.8452i	0.171133	+	0.526692i
$425$		0			0
$426$	−0.149155	+	0.108367i	−0.00722658	+	0.00525041i
$427$	3.30470	−	10.1708i	0.159926	−	0.492200i
$428$	31.9518			1.54445
$429$	−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	$-0.172439\pi$
$432$	−4.13776	+	3.00626i	−0.199078	+	0.144639i
$433$	−21.0607	−	15.3015i	−1.01212	−	0.735345i	−0.0474634	−	0.998873i	$-0.515114\pi$
$433$	−21.0607	−	15.3015i	−1.01212	−	0.735345i	−0.964652	+	0.263528i	$0.915114\pi$
$434$	0.945023	+	2.90848i	0.0453625	+	0.139612i
$435$		0			0
$436$	−23.4639	−	17.0475i	−1.12372	−	0.816429i
$437$	−9.73464	+	7.07263i	−0.465671	+	0.338330i
$438$	−0.0486812	+	0.149825i	−0.00232608	+	0.00715893i
$439$	14.4191			0.688185			0.344093	−	0.938936i	$-0.388187\pi$
$439$	14.4191			0.688185			0.344093	+	0.938936i	$0.388187\pi$
$440$		0			0
$441$	−0.609255			−0.0290121
$442$	−3.18486	+	9.80199i	−0.151488	+	0.466233i
$443$	−0.267467	+	0.194326i	−0.0127078	+	0.00923273i	−0.594121	−	0.804376i	$-0.702500\pi$
$443$	−0.267467	+	0.194326i	−0.0127078	+	0.00923273i	0.581413	+	0.813608i	$0.302500\pi$
$444$	−4.92986	−	3.58175i	−0.233961	−	0.169982i
$445$		0			0
$446$	1.55518	+	4.78636i	0.0736400	+	0.226641i
$447$	3.83289	+	2.78476i	0.181289	+	0.131715i
$448$	−6.60483	+	4.79869i	−0.312049	+	0.226717i
$449$	2.62920	−	8.09185i	0.124080	−	0.381878i	−0.869653	−	0.493664i	$-0.835657\pi$
$449$	2.62920	−	8.09185i	0.124080	−	0.381878i	0.993732	+	0.111786i	$0.0356571\pi$
$450$		0			0
$451$	−7.31906	+	0.419748i	−0.344641	+	0.0197652i
$452$	−3.63974			−0.171199
$453$	0.750657	−	2.31028i	0.0352689	−	0.108547i
$454$	−0.0834069	+	0.0605986i	−0.00391448	+	0.00284404i
$455$		0			0
$456$	0.780130	+	2.40099i	0.0365329	+	0.112437i
$457$	−0.351807	−	1.08275i	−0.0164569	−	0.0506490i	0.942491	−	0.334232i	$-0.108477\pi$
$457$	−0.351807	−	1.08275i	−0.0164569	−	0.0506490i	−0.958948	+	0.283583i	$0.908477\pi$
$458$	−0.0292324	−	0.0212386i	−0.00136594	−	0.000992413i
$459$	−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	$0.390305\pi$
$462$	1.06289	−	0.869422i	0.0494503	−	0.0404492i
$463$	4.89739			0.227601			0.113801	−	0.993504i	$-0.463698\pi$
$463$	4.89739			0.227601			0.113801	+	0.993504i	$0.463698\pi$
$464$	−2.50047	+	7.69565i	−0.116081	+	0.357261i
$465$		0			0
$466$	−5.83803	−	4.24157i	−0.270441	−	0.196487i
$467$	−10.0193	−	30.8361i	−0.463637	−	1.42693i	−0.860689	−	0.509131i	$-0.829967\pi$
$467$	−10.0193	−	30.8361i	−0.463637	−	1.42693i	0.397053	−	0.917796i	$-0.370033\pi$
$468$	7.40218	+	22.7816i	0.342166	+	1.05308i
$469$	−15.9015	−	11.5531i	−0.734264	−	0.533474i
$470$		0			0
$471$	−1.33597	+	4.11171i	−0.0615585	+	0.189457i
$472$	21.1490			0.973461
$473$	−19.7204	−	12.6689i	−0.906747	−	0.582516i
$474$	0.539990			0.0248026
$475$		0			0
$476$	−17.8111	+	12.9406i	−0.816373	+	0.593129i
$477$	14.8382	+	10.7806i	0.679394	+	0.493609i
$478$	3.41635	+	10.5145i	0.156260	+	0.480920i
$479$	5.48054	+	16.8674i	0.250412	+	0.770690i	0.994699	+	0.102830i	$0.0327897\pi$
$479$	5.48054	+	16.8674i	0.250412	+	0.770690i	−0.744287	+	0.667860i	$0.767210\pi$
$480$		0			0
$481$	−40.1915	+	29.2009i	−1.83258	+	1.33144i
$482$	3.14650	−	9.68394i	0.143319	−	0.441091i
$483$	−2.40495			−0.109429
$484$	−3.86502	+	19.1075i	−0.175683	+	0.868521i
$485$		0			0
$486$	1.22731	−	3.77727i	0.0556719	−	0.171341i
$487$	−14.9347	+	10.8507i	−0.676754	+	0.491691i	−0.872279	−	0.489008i	$-0.837359\pi$
$487$	−14.9347	+	10.8507i	−0.676754	+	0.491691i	0.195525	+	0.980699i	$0.437359\pi$
$488$	5.80069	+	4.21445i	0.262585	+	0.190779i
$489$	−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	$0.616936\pi$
$492$	1.02387	−	0.743887i	0.0461597	−	0.0335370i
$493$	−4.30802	+	13.2587i	−0.194023	+	0.597142i
$494$	9.66954			0.435053
$495$		0			0
$496$	6.40774			0.287716
$497$	−0.992176	+	3.05360i	−0.0445052	+	0.136973i
$498$	1.38661	−	1.00743i	0.0621353	−	0.0451439i
$499$	−8.80335	−	6.39601i	−0.394092	−	0.286325i	0.373038	−	0.927816i	$-0.378316\pi$
$499$	−8.80335	−	6.39601i	−0.394092	−	0.286325i	−0.767130	+	0.641491i	$0.778316\pi$
$500$		0			0
$501$	−0.846827	−	2.60627i	−0.0378335	−	0.116439i
$502$	−2.40233	−	1.74540i	−0.107221	−	0.0779009i
$503$	36.1830	−	26.2885i	1.61332	−	1.17215i	0.761831	−	0.647776i	$-0.224301\pi$
$503$	36.1830	−	26.2885i	1.61332	−	1.17215i	0.851490	−	0.524371i	$-0.175699\pi$
$504$	4.32571	−	13.3132i	0.192682	−	0.593015i
$505$		0			0
$506$	−3.39657	+	2.77831i	−0.150996	+	0.123511i
$507$	−2.83941			−0.126103
$508$	−0.0417673	+	0.128546i	−0.00185312	+	0.00570332i
$509$	11.1720	−	8.11693i	0.495190	−	0.359777i	−0.311987	−	0.950086i	$-0.600994\pi$
$509$	11.1720	−	8.11693i	0.495190	−	0.359777i	0.807177	+	0.590310i	$0.200994\pi$
$510$		0			0
$511$	0.847790	+	2.60923i	0.0375040	+	0.115425i
$512$	−7.03891	−	21.6635i	−0.311079	−	0.957402i
$513$	6.68836	+	4.85938i	0.295298	+	0.214547i
$514$	5.51766	−	4.00881i	0.243374	−	0.176821i
$515$		0			0
$516$	4.04635			0.178130
$517$	−14.4439	+	0.828356i	−0.635241	+	0.0364311i
$518$	13.6394			0.599281
$519$	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	$0.674524\pi$
$522$	−1.28688	−	3.96061i	−0.0563253	−	0.173351i
$523$	1.54109	+	4.74299i	0.0673872	+	0.207396i	0.979080	−	0.203476i	$-0.0652240\pi$
$523$	1.54109	+	4.74299i	0.0673872	+	0.207396i	−0.911693	+	0.410873i	$0.865224\pi$
$524$	−16.4640	−	11.9618i	−0.719233	−	0.522553i
$525$		0			0
$526$	0.609292	−	1.87521i	0.0265664	−	0.0817630i
$527$	11.0398			0.480901
$528$	−1.04433	−	2.68101i	−0.0454486	−	0.116676i
$529$	−15.3148			−0.665860
$530$		0			0
$531$	27.5193	−	19.9939i	1.19424	−	0.867663i
$532$	16.7105	+	12.1409i	0.724493	+	0.526375i
$533$	−3.18839	−	9.81284i	−0.138104	−	0.425041i
$534$	0.131972	+	0.406167i	0.00571097	+	0.0175766i
$535$		0			0
$536$	10.6613	−	7.74591i	0.460499	−	0.334572i
$537$	1.12983	−	3.47726i	0.0487558	−	0.150055i
$538$	0.803678			0.0346490
$539$	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	$0.0983058\pi$
$542$	−7.11642	+	5.17038i	−0.305676	+	0.222087i
$543$	1.93415	+	1.40524i	0.0830025	+	0.0603048i
$544$	−6.97967	−	21.4812i	−0.299251	−	0.921000i
$545$		0			0
$546$	1.56353	+	1.13597i	0.0669131	+	0.0486152i
$547$	−20.4779	+	14.8780i	−0.875570	+	0.636139i	−0.932076	−	0.362263i	$-0.882004\pi$
$547$	−20.4779	+	14.8780i	−0.875570	+	0.636139i	0.0565056	+	0.998402i	$0.482004\pi$
$548$	−10.0380	+	30.8937i	−0.428801	+	1.31971i
$549$	11.5322			0.492182
$550$		0			0
$551$	13.0796			0.557208
$552$	0.498266	−	1.53350i	0.0212076	−	0.0652703i
$553$	7.60799	−	5.52753i	0.323525	−	0.235054i
$554$	1.32338	+	0.961489i	0.0562249	+	0.0408498i
$555$		0			0
$556$	12.6985	+	39.0819i	0.538536	+	1.65744i
$557$	−31.2824	−	22.7280i	−1.32548	−	0.963015i	−0.999847	−	0.0175177i	$-0.994424\pi$
$557$	−31.2824	−	22.7280i	−1.32548	−	0.963015i	−0.325630	−	0.945497i	$-0.605576\pi$
$558$	−2.66796	+	1.93839i	−0.112944	+	0.0820586i
$559$	10.1940	−	31.3740i	0.431161	−	1.32698i
$560$		0			0
$561$	−1.79926	−	4.61907i	−0.0759648	−	0.195017i
$562$	10.8919			0.459447
$563$	−4.30653	+	13.2541i	−0.181498	+	0.558595i	−0.999870	−	0.0160940i	$-0.994877\pi$
$563$	−4.30653	+	13.2541i	−0.181498	+	0.558595i	0.818372	+	0.574689i	$0.194877\pi$
$564$	2.02057	−	1.46803i	0.0850815	−	0.0618153i
$565$		0			0
$566$	−4.29157	−	13.2081i	−0.180388	−	0.555178i
$567$	−6.69757	−	20.6130i	−0.281272	−	0.865665i
$568$	−1.74155	−	1.26531i	−0.0730739	−	0.0530913i
$569$	−22.5817	+	16.4065i	−0.946672	+	0.687798i	−0.950017	−	0.312197i	$-0.898935\pi$
$569$	−22.5817	+	16.4065i	−0.946672	+	0.687798i	0.00334520	+	0.999994i	$0.498935\pi$
$570$		0			0
$571$	−31.4113			−1.31452			−0.657261	−	0.753663i	$-0.728285\pi$
$571$	−31.4113			−1.31452			−0.657261	+	0.753663i	$0.728285\pi$
$572$	−27.3917	+	1.57091i	−1.14530	+	0.0656831i
$573$	1.66578			0.0695889
$574$	−0.875365	+	2.69410i	−0.0365370	+	0.112449i
$575$		0			0
$576$	−7.12237	−	5.17470i	−0.296765	−	0.215613i
$577$	−6.40744	−	19.7201i	−0.266745	−	0.820958i	−0.991286	−	0.131726i	$-0.957948\pi$
$577$	−6.40744	−	19.7201i	−0.266745	−	0.820958i	0.724541	−	0.689232i	$-0.242052\pi$
$578$	−0.649343	−	1.99847i	−0.0270091	−	0.0831255i
$579$	1.05392	+	0.765719i	0.0437995	+	0.0318222i
$580$		0			0
$581$	9.22368	−	28.3876i	0.382663	−	1.17771i
$582$	−2.85777			−0.118458
$583$	−16.2607	+	13.3008i	−0.673448	+	0.550864i
$584$	−1.83941			−0.0761153
$585$		0			0
$586$	−8.19080	+	5.95097i	−0.338359	+	0.245832i
$587$	12.3267	+	8.95591i	0.508779	+	0.369650i	0.812360	−	0.583156i	$-0.198182\pi$
$587$	12.3267	+	8.95591i	0.508779	+	0.369650i	−0.303581	+	0.952806i	$0.598182\pi$
$588$	0.0372268	+	0.114572i	0.00153521	+	0.00472488i
$589$	−3.20067	−	9.85066i	−0.131881	−	0.405889i
$590$		0			0
$591$	−2.98421	+	2.16816i	−0.122754	+	0.0891860i
$592$	8.83126	−	27.1798i	0.362962	−	1.11708i
$593$	−27.5413			−1.13098			−0.565492	−	0.824754i	$-0.691314\pi$
$593$	−27.5413			−1.13098			−0.565492	+	0.824754i	$0.691314\pi$
$594$	2.53661	+	1.62958i	0.104078	+	0.0668624i
$595$		0			0
$596$	−8.03103	+	24.7170i	−0.328964	+	1.01245i
$597$	−1.87309	+	1.36088i	−0.0766605	+	0.0556971i
$598$	−4.99640	−	3.63010i	−0.204318	−	0.148446i
$599$	−8.26097	−	25.4247i	−0.337534	−	1.03882i	−0.965460	−	0.260551i	$-0.916096\pi$
$599$	−8.26097	−	25.4247i	−0.337534	−	1.03882i	0.627926	−	0.778273i	$-0.283904\pi$
$600$		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	$0.715631\pi$
$602$	−7.32722	+	5.32353i	−0.298635	+	0.216971i
$603$	6.54977	−	20.1581i	0.266727	−	0.820902i
$604$	13.3254			0.542202
$605$		0			0
$606$	−1.09699			−0.0445620
$607$	−3.18067	+	9.78909i	−0.129099	+	0.397327i	−0.994626	−	0.103536i	$-0.966984\pi$
$607$	−3.18067	+	9.78909i	−0.129099	+	0.397327i	0.865526	+	0.500864i	$0.166984\pi$
$608$	−17.1438	+	12.4557i	−0.695275	+	0.505147i
$609$	2.11492	+	1.53658i	0.0857010	+	0.0622654i
$610$		0			0
$611$	−6.29216	−	19.3653i	−0.254553	−	0.783435i
$612$	−19.2068	−	13.9545i	−0.776388	−	0.564079i
$613$	22.5519	−	16.3849i	0.910861	−	0.661779i	−0.0303715	−	0.999539i	$-0.509669\pi$
$613$	22.5519	−	16.3849i	0.910861	−	0.661779i	0.941232	+	0.337759i	$0.109669\pi$
$614$	−1.01396	+	3.12066i	−0.0409203	+	0.125940i
$615$		0			0
$616$	13.4897	+	8.66611i	0.543515	+	0.349168i
$617$	28.7216			1.15629			0.578143	−	0.815935i	$-0.303778\pi$
$617$	28.7216			1.15629			0.578143	+	0.815935i	$0.303778\pi$
$618$	−0.358703	+	1.10398i	−0.0144292	+	0.0444084i
$619$	−18.3621	+	13.3408i	−0.738035	+	0.536214i	−0.892095	−	0.451848i	$-0.850765\pi$
$619$	−18.3621	+	13.3408i	−0.738035	+	0.536214i	0.154060	+	0.988061i	$0.450765\pi$
$620$		0			0
$621$	−1.63169	−	5.02183i	−0.0654776	−	0.201519i
$622$	−3.71029	−	11.4191i	−0.148769	−	0.457864i
$623$	6.01703	+	4.37163i	0.241067	+	0.175146i
$624$	3.27606	−	2.38020i	0.131147	−	0.0952842i
$625$		0			0
$626$	−5.52635			−0.220877
$627$	−3.59989	+	2.94462i	−0.143766	+	0.117597i
$628$	−23.7157			−0.946360
$629$	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	$0.892286\pi$
$632$	1.94835	+	5.99641i	0.0775013	+	0.238524i
$633$	−0.347783	−	1.07037i	−0.0138231	−	0.0425432i
$634$	−8.00844	−	5.81847i	−0.318056	−	0.231081i
$635$		0			0
$636$	1.12067	−	3.44908i	0.0444376	−	0.136765i
$637$	0.982140			0.0389138
$638$	4.76209	−	0.273106i	0.188533	−	0.0108124i
$639$	−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	$0.314927\pi$
$642$	2.24899	+	1.63399i	0.0887605	+	0.0644883i
$643$	−3.51053	−	10.8043i	−0.138442	−	0.426080i	0.857668	−	0.514204i	$-0.171913\pi$
$643$	−3.51053	−	10.8043i	−0.138442	−	0.426080i	−0.996109	+	0.0881244i	$0.971913\pi$
$644$	−4.07670	−	12.5468i	−0.160644	−	0.494413i
$645$		0			0
$646$	−7.75323	+	5.63305i	−0.305047	+	0.221630i
$647$	14.9632	−	46.0520i	0.588264	−	1.81049i	0.00251822	−	0.999997i	$-0.499198\pi$
$647$	14.9632	−	46.0520i	0.588264	−	1.81049i	0.585746	−	0.810495i	$-0.300802\pi$
$648$	14.5314			0.570848
$649$	14.1415	+	36.3043i	0.555104	+	1.42507i
$650$		0			0
$651$	0.639713	−	1.96883i	0.0250723	−	0.0771647i
$652$	1.10685	−	0.804171i	0.0433475	−	0.0314938i
$653$	24.0722	+	17.4894i	0.942016	+	0.684415i	0.948905	−	0.315562i	$-0.102193\pi$
$653$	24.0722	+	17.4894i	0.942016	+	0.684415i	−0.00688905	+	0.999976i	$0.502193\pi$
$654$	−0.779758	−	2.39985i	−0.0304910	−	0.0938415i
$655$		0			0
$656$	4.80186	+	3.48875i	0.187481	+	0.136213i
$657$	−2.39346	+	1.73895i	−0.0933777	+	0.0678429i
$658$	−1.72750	+	5.31669i	−0.0673449	+	0.207266i
$659$	−28.4931			−1.10993			−0.554966	−	0.831873i	$-0.687269\pi$
$659$	−28.4931			−1.10993			−0.554966	+	0.831873i	$0.687269\pi$
$660$		0			0
$661$	−1.02875			−0.0400139			−0.0200070	−	0.999800i	$-0.506369\pi$
$661$	−1.02875			−0.0400139			−0.0200070	+	0.999800i	$0.506369\pi$
$662$	4.74027	−	14.5890i	0.184236	−	0.567019i
$663$	5.64428	−	4.10081i	0.219206	−	0.159262i
$664$	16.1902	+	11.7629i	0.628301	+	0.456488i
$665$		0			0
$666$	4.54506	+	13.9883i	0.176118	+	0.542034i
$667$	−6.75841	−	4.91027i	−0.261687	−	0.190127i
$668$	12.1616	−	8.83591i	0.470546	−	0.341872i
$669$	1.05275	−	3.24002i	0.0407016	−	0.125267i
$670$		0			0
$671$	−3.35580	+	12.7755i	−0.129549	+	0.493192i
$672$	−4.23540			−0.163384
$673$	−4.02863	+	12.3988i	−0.155292	+	0.477940i	−0.998190	−	0.0601327i	$-0.980848\pi$
$673$	−4.02863	+	12.3988i	−0.155292	+	0.477940i	0.842898	+	0.538073i	$0.180848\pi$
$674$	6.94861	−	5.04846i	0.267651	−	0.194459i
$675$		0			0
$676$	−4.81316	−	14.8134i	−0.185122	−	0.569746i
$677$	11.4665	+	35.2903i	0.440694	+	1.35632i	0.887138	+	0.461505i	$0.152690\pi$
$677$	11.4665	+	35.2903i	0.440694	+	1.35632i	−0.446444	+	0.894812i	$0.647310\pi$
$678$	−0.256190	−	0.186133i	−0.00983893	−	0.00714840i
$679$	−40.2635	+	29.2531i	−1.54517	+	1.12263i
$680$		0			0
$681$	0.0697890			0.00267432
$682$	−1.37101	−	3.51966i	−0.0524986	−	0.134775i
$683$	32.8992			1.25885			0.629426	−	0.777061i	$-0.283290\pi$
$683$	32.8992			1.25885			0.629426	+	0.777061i	$0.283290\pi$
$684$	−6.88299	+	21.1837i	−0.263178	+	0.809978i
$685$		0			0
$686$	7.03941	+	5.11443i	0.268766	+	0.195270i
$687$	0.00755844	+	0.0232625i	0.000288372	+	0.000887519i
$688$	5.86420	+	18.0481i	0.223570	+	0.688079i
$689$	−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	$-0.145955\pi$
$692$	9.00061			0.342152
$693$	25.7457	−	1.47652i	0.978000	−	0.0560883i
$694$	−3.84185			−0.145835
$695$		0			0
$696$	−1.41797	+	1.03022i	−0.0537480	+	0.0390502i
$697$	8.27305	+	6.01072i	0.313364	+	0.227672i
$698$	−2.83597	−	8.72823i	−0.107343	−	0.330368i
$699$	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	$0.0599919\pi$
$702$	−1.31124	+	4.03558i	−0.0494895	+	0.152313i
$703$	−46.1949			−1.74227
$704$	7.80516	−	6.38443i	0.294168	−	0.240622i
$705$		0			0
$706$	2.19006	−	6.74031i	0.0824240	−	0.253675i
$707$	−15.4556	+	11.2291i	−0.581267	+	0.422315i
$708$	−5.44141	−	3.95342i	−0.204501	−	0.148578i
$709$	−5.74811	−	17.6909i	−0.215875	−	0.664394i	−0.999090	−	0.0426440i	$-0.986422\pi$
$709$	−5.74811	−	17.6909i	−0.215875	−	0.664394i	0.783216	−	0.621750i	$-0.213578\pi$
$710$		0			0
$711$	8.20413	+	5.96065i	0.307679	+	0.223542i
$712$	−4.03418	+	2.93100i	−0.151187	+	0.109844i
$713$	−2.04426	+	6.29158i	−0.0765580	+	0.235621i
$714$	−1.91544			−0.0716836
$715$		0			0
$716$	20.0563			0.749540
$717$	2.31263	−	7.11754i	0.0863667	−	0.265809i
$718$	3.94732	−	2.86790i	0.147313	−	0.107029i
$719$	30.2799	+	21.9996i	1.12925	+	0.820447i	0.985585	−	0.169179i	$-0.0541117\pi$
$719$	30.2799	+	21.9996i	1.12925	+	0.820447i	0.143664	+	0.989627i	$0.454112\pi$
$720$		0			0
$721$	6.24687	+	19.2259i	0.232645	+	0.716009i
$722$	−0.0619923	−	0.0450400i	−0.00230711	−	0.00167622i
$723$	−5.57630	+	4.05142i	−0.207385	+	0.150674i
$724$	−4.05262	+	12.4727i	−0.150614	+	0.463544i
$725$		0			0
$726$	−1.24919	+	1.14726i	−0.0463617	+	0.0425789i
$727$	−14.6011			−0.541526			−0.270763	−	0.962646i	$-0.587276\pi$
$727$	−14.6011			−0.541526			−0.270763	+	0.962646i	$0.587276\pi$
$728$	−6.97319	+	21.4613i	−0.258443	+	0.795407i
$729$	17.4149	−	12.6527i	0.644997	−	0.468618i
$730$		0			0
$731$	10.1033	+	31.0949i	0.373686	+	1.15009i
$732$	−0.704642	−	2.16867i	−0.0260443	−	0.0801562i
$733$	33.8468	+	24.5911i	1.25016	+	0.908293i	0.998231	−	0.0594528i	$-0.0189356\pi$
$733$	33.8468	+	24.5911i	1.25016	+	0.908293i	0.251927	+	0.967746i	$0.418936\pi$
$734$	−5.46092	+	3.96759i	−0.201566	+	0.146447i
$735$		0			0
$736$	13.5346			0.498891
$737$	20.4254	+	13.1218i	0.752381	+	0.483348i
$738$	−3.05470			−0.112445
$739$	−3.68654	+	11.3460i	−0.135612	+	0.417370i	−0.995685	−	0.0928012i	$-0.970418\pi$
$739$	−3.68654	+	11.3460i	−0.135612	+	0.417370i	0.860073	+	0.510171i	$0.170418\pi$
$740$		0			0
$741$	−5.29549	−	3.84740i	−0.194535	−	0.141338i
$742$	2.50841	+	7.72008i	0.0920865	+	0.283413i
$743$	−14.4250	−	44.3956i	−0.529202	−	1.62872i	−0.755854	−	0.654740i	$-0.772778\pi$
$743$	−14.4250	−	44.3956i	−0.529202	−	1.62872i	0.226652	−	0.973976i	$-0.427222\pi$
$744$	1.12288	+	0.815820i	0.0411668	+	0.0299094i
$745$		0			0
$746$	1.83762	−	5.65561i	0.0672800	−	0.207067i
$747$	32.1873			1.17767
$748$	21.0480	−	17.2168i	0.769593	−	0.629508i
$749$	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	$0.384647\pi$
$752$	9.47628	+	6.88492i	0.345564	+	0.251067i
$753$	0.621156	+	1.91172i	0.0226362	+	0.0696670i
$754$	2.07450	+	6.38465i	0.0755488	+	0.232515i
$755$		0			0
$756$	−7.33304	+	5.32776i	−0.266700	+	0.193769i
$757$	4.96330	−	15.2755i	0.180394	−	0.555196i	−0.819444	−	0.573159i	$-0.805718\pi$
$757$	4.96330	−	15.2755i	0.180394	−	0.555196i	0.999839	+	0.0179624i	$0.00571791\pi$
$758$	−7.79698			−0.283199
$759$	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	$0.851049\pi$
$762$	−0.00951362	+	0.00691205i	−0.000344642	+	0.000250397i
$763$	−35.5518	−	25.8299i	−1.28706	−	0.935106i
$764$	2.82371	+	8.69049i	0.102158	+	0.314411i
$765$		0			0
$766$	0.313773	+	0.227969i	0.0113371	+	0.00823686i
$767$	−44.3621	+	32.2309i	−1.60182	+	1.16379i
$768$	−0.0726816	+	0.223691i	−0.00262267	+	0.00807175i
$769$	43.0017			1.55068			0.775341	−	0.631543i	$-0.217578\pi$
$769$	43.0017			1.55068			0.775341	+	0.631543i	$0.217578\pi$
$770$		0			0
$771$	−4.61679			−0.166270
$772$	−2.20828	+	6.79637i	−0.0794776	+	0.244607i
$773$	−6.35452	+	4.61683i	−0.228556	+	0.166056i	−0.696170	−	0.717877i	$-0.745114\pi$
$773$	−6.35452	+	4.61683i	−0.228556	+	0.166056i	0.467613	+	0.883933i	$0.345114\pi$
$774$	−7.90135	−	5.74067i	−0.284008	−	0.206344i
$775$		0			0
$776$	−10.3112	−	31.7346i	−0.370150	−	1.13920i
$777$	−7.46957	−	5.42696i	−0.267969	−	0.194691i
$778$	−11.7355	+	8.52635i	−0.420739	+	0.305684i
$779$	2.96475	−	9.12457i	0.106223	−	0.326922i
$780$		0			0
$781$	1.00752	−	3.83561i	0.0360519	−	0.137249i
$782$	6.12096			0.218885
$783$	−1.77366	+	5.45875i	−0.0633853	+	0.195080i
$784$	−0.457082	+	0.332090i	−0.0163244	+	0.0118603i
$785$		0			0
$786$	−0.547135	−	1.68391i	−0.0195157	−	0.0600631i
$787$	3.53048	+	10.8657i	0.125848	+	0.387321i	0.994055	−	0.108882i	$-0.0347271\pi$
$787$	3.53048	+	10.8657i	0.125848	+	0.387321i	−0.868206	+	0.496203i	$0.834727\pi$
$788$	−16.3700	−	11.8935i	−0.583159	−	0.423690i
$789$	−1.07980	+	0.784522i	−0.0384420	+	0.0279297i
$790$		0			0
$791$	−5.51483			−0.196085
$792$	−4.39260	+	16.7226i	−0.156084	+	0.594210i
$793$	−18.5903			−0.660161
$794$	−2.19741	+	6.76294i	−0.0779832	+	0.240008i
$795$		0			0
$796$	−10.2749	−	7.46518i	−0.364186	−	0.264596i
$797$	1.32414	+	4.07529i	0.0469035	+	0.144354i	0.971766	−	0.235949i	$-0.0758197\pi$
$797$	1.32414	+	4.07529i	0.0469035	+	0.144354i	−0.924862	+	0.380303i	$0.875820\pi$
$798$	0.555328	+	1.70912i	0.0196584	+	0.0605023i
$799$	16.3265	+	11.8619i	0.577592	+	0.419645i
$800$		0			0
$801$	−2.47839	+	7.62770i	−0.0875696	+	0.269511i
$802$	−5.80787			−0.205083
$803$	−1.22994	−	3.15752i	−0.0434038	−	0.111427i
$804$	−4.19100			−0.147805
$805$		0			0
$806$	4.30085	−	3.12475i	0.151491	−	0.110065i
$807$	−0.440132	−	0.319774i	−0.0154934	−	0.0112566i
$808$	−3.95806	−	12.1817i	−0.139244	−	0.428549i
$809$	−6.13350	−	18.8770i	−0.215642	−	0.663679i	−0.999107	−	0.0422430i	$-0.986550\pi$
$809$	−6.13350	−	18.8770i	−0.215642	−	0.663679i	0.783465	−	0.621436i	$-0.213450\pi$
$810$		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	$0.282452\pi$
$812$	−4.43138	+	13.6384i	−0.155511	+	0.478614i
$813$	5.95452			0.208834
$814$	−16.8189	+	0.964566i	−0.589504	+	0.0338080i
$815$		0			0
$816$	−1.24021	+	3.81698i	−0.0434162	+	0.133621i
$817$	24.8164	−	18.0301i	0.868215	−	0.630795i
$818$	−0.101203	−	0.0735281i	−0.00353847	−	0.00257085i
$819$	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	$0.834498\pi$
$822$	−2.28642	+	1.66118i	−0.0797481	+	0.0579404i
$823$	3.91103	−	12.0369i	0.136330	−	0.419580i	−0.859465	−	0.511195i	$-0.829203\pi$
$823$	3.91103	−	12.0369i	0.136330	−	0.419580i	0.995795	+	0.0916150i	$0.0292029\pi$
$824$	−13.5535			−0.472159
$825$		0			0
$826$	15.0547			0.523820
$827$	−9.33959	+	28.7443i	−0.324770	+	0.999538i	0.646775	+	0.762681i	$0.276117\pi$
$827$	−9.33959	+	28.7443i	−0.324770	+	0.999538i	−0.971545	+	0.236857i	$0.923883\pi$
$828$	11.5092	−	8.36195i	0.399974	−	0.290598i
$829$	−1.61937	−	1.17654i	−0.0562432	−	0.0408630i	0.559308	−	0.828960i	$-0.311067\pi$
$829$	−1.61937	−	1.17654i	−0.0562432	−	0.0408630i	−0.615552	+	0.788097i	$0.711067\pi$
$830$		0			0
$831$	−0.342177	−	1.05311i	−0.0118700	−	0.0365321i
$832$	11.4815	+	8.34180i	0.398050	+	0.289200i
$833$	−0.787500	+	0.572152i	−0.0272852	+	0.0198239i
$834$	−1.10481	+	3.40025i	−0.0382564	+	0.117741i
$835$		0			0
$836$	−21.4646	−	13.7894i	−0.742368	−	0.476915i
$837$	4.54520			0.157105
$838$	0.187177	−	0.576072i	0.00646592	−	0.0199001i
$839$	−28.6185	+	20.7925i	−0.988019	+	0.717838i	−0.959486	−	0.281755i	$-0.909083\pi$
$839$	−28.6185	+	20.7925i	−0.988019	+	0.717838i	−0.0285326	+	0.999593i	$0.509083\pi$
$840$		0			0
$841$	−6.15541	−	18.9444i	−0.212256	−	0.653255i
$842$	4.37511	+	13.4652i	0.150776	+	0.464041i
$843$	−5.96492	−	4.33377i	−0.205443	−	0.149263i
$844$	4.99463	−	3.62881i	0.171922	−	0.124909i
$845$		0			0
$846$	−6.02834			−0.207259
$847$	−5.85616	+	28.9511i	−0.201220	+	0.994771i
$848$	17.0083			0.584067
$849$	−2.90509	+	8.94095i	−0.0997024	+	0.306853i
$850$		0			0
$851$	23.8696	+	17.3423i	0.818241	+	0.594487i
$852$	0.211556	+	0.651102i	0.00724779	+	0.0223064i
$853$	5.62515	+	17.3124i	0.192602	+	0.592767i	0.999996	+	0.00275489i	$0.000876911\pi$
$853$	5.62515	+	17.3124i	0.192602	+	0.592767i	−0.807395	+	0.590012i	$0.799123\pi$
$854$	4.12917	+	3.00001i	0.141297	+	0.102658i
$855$		0			0
$856$	−10.0302	+	30.8699i	−0.342827	+	1.05511i
$857$	29.2837			1.00031			0.500156	−	0.865935i	$-0.333276\pi$
$857$	29.2837			1.00031			0.500156	+	0.865935i	$0.333276\pi$
$858$	−2.00835	−	1.29021i	−0.0685640	−	0.0440472i
$859$	8.44030			0.287979			0.143990	−	0.989579i	$-0.454007\pi$
$859$	8.44030			0.287979			0.143990	+	0.989579i	$0.454007\pi$
$860$		0			0
$861$	1.55134	−	1.12712i	0.0528696	−	0.0384120i
$862$	12.1065	+	8.79587i	0.412348	+	0.299589i
$863$	5.97907	+	18.4017i	0.203530	+	0.626400i	0.999771	+	0.0214204i	$0.00681885\pi$
$863$	5.97907	+	18.4017i	0.203530	+	0.626400i	−0.796241	+	0.604980i	$0.793181\pi$
$864$	−2.87360	−	8.84404i	−0.0977620	−	0.300880i
$865$		0			0
$866$	10.0515	−	7.30281i	0.341562	−	0.248160i
$867$	−0.439559	+	1.35282i	−0.0149282	+	0.0459443i
$868$	11.3559			0.385446
$869$	−8.99063	+	7.35411i	−0.304986	+	0.249471i
$870$		0			0
$871$	−10.5585	+	32.4956i	−0.357760	+	1.10107i
$872$	23.8361	−	17.3179i	0.807191	−	0.586458i
$873$	−43.4184	−	31.5453i	−1.46949	−	1.06765i
$874$	−1.77460	−	5.46165i	−0.0600266	−	0.184743i
$875$		0			0
$876$	0.473260	+	0.343844i	0.0159900	+	0.0116174i
$877$	14.1691	−	10.2945i	0.478456	−	0.347619i	−0.322271	−	0.946647i	$-0.604446\pi$
$877$	14.1691	−	10.2945i	0.478456	−	0.347619i	0.800728	+	0.599028i	$0.204446\pi$
$878$	−2.12655	+	6.54484i	−0.0717675	+	0.220878i
$879$	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	$0.609709\pi$
$882$	0.0898538	−	0.276542i	0.00302553	−	0.00931164i
$883$	21.7609	−	15.8102i	0.732313	−	0.532057i	−0.157981	−	0.987442i	$-0.550499\pi$
$883$	21.7609	−	15.8102i	0.732313	−	0.532057i	0.890294	+	0.455386i	$0.150499\pi$
$884$	30.9620	+	22.4952i	1.04136	+	0.756595i
$885$		0			0
$886$	−0.0487585	−	0.150063i	−0.00163807	−	0.00504148i
$887$	5.50591	+	4.00028i	0.184870	+	0.134316i	0.676371	−	0.736561i	$-0.263552\pi$
$887$	5.50591	+	4.00028i	0.184870	+	0.134316i	−0.491501	+	0.870877i	$0.663552\pi$
$888$	5.00805	−	3.63856i	0.168059	−	0.122102i
$889$	−0.0632845	+	0.194770i	−0.00212249	+	0.00653237i
$890$		0			0
$891$	9.71661	+	24.9446i	0.325519	+	0.835674i
$892$	18.6880			0.625720
$893$	5.85082	−	18.0070i	0.195790	−	0.602581i
$894$	−1.82928	+	1.32905i	−0.0611804	+	0.0444502i
$895$		0			0
$896$	−9.30635	−	28.6420i	−0.310903	−	0.956862i
$897$	1.29189	+	3.97603i	0.0431349	+	0.132756i
$898$	3.28514	+	2.38680i	0.109627	+	0.0796484i
$899$	5.81757	−	4.22671i	0.194027	−	0.140969i
$900$		0			0
$901$	29.3033			0.976235
$902$	0.888901	−	3.38403i	0.0295972	−	0.112676i
$903$	6.13090			0.204024
$904$	1.14258	−	3.51650i	0.0380017	−	0.116957i
$905$		0			0
$906$	0.937933	+	0.681448i	0.0311607	+	0.0226396i
$907$	6.59174	+	20.2873i	0.218875	+	0.673629i	0.998856	+	0.0478248i	$0.0152289\pi$
$907$	6.59174	+	20.2873i	0.218875	+	0.673629i	−0.779981	+	0.625804i	$0.784771\pi$
$908$	0.118301	+	0.364094i	0.00392597	+	0.0120829i
$909$	−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	$0.948913\pi$
$912$	3.76541			0.124685
$913$	−9.36631	+	35.6574i	−0.309980	+	1.18009i
$914$	0.543347			0.0179723
$915$		0			0
$916$	−0.108549	+	0.0788658i	−0.00358657	+	0.00260580i
$917$	−24.9458	−	18.1242i	−0.823782	−	0.598512i
$918$	−1.29958	−	3.99968i	−0.0428924	−	0.132009i
$919$	−1.85685	−	5.71479i	−0.0612518	−	0.188514i	0.915748	−	0.401752i	$-0.131599\pi$
$919$	−1.85685	−	5.71479i	−0.0612518	−	0.188514i	−0.977000	+	0.213239i	$0.931599\pi$
$920$		0			0
$921$	1.79697	−	1.30558i	0.0592122	−	0.0430202i
$922$	−2.13955	+	6.58486i	−0.0704624	+	0.216861i
$923$	5.58140			0.183714
$924$	−1.85078	−	4.75135i	−0.0608863	−	0.156308i
$925$		0			0
$926$	−0.722274	+	2.22293i	−0.0237354	+	0.0730501i
$927$	−17.6360	+	12.8133i	−0.579242	+	0.420844i
$928$	−11.9024	−	8.64757i	−0.390714	−	0.283870i
$929$	2.96576	+	9.12766i	0.0973034	+	0.299469i	0.987847	−	0.155429i	$-0.0496759\pi$
$929$	2.96576	+	9.12766i	0.0973034	+	0.299469i	−0.890544	+	0.454898i	$0.849676\pi$
$930$		0			0
$931$	0.738836	+	0.536796i	0.0242144	+	0.0175928i
$932$	−21.6785	+	15.7504i	−0.710103	+	0.515920i
$933$	−2.51160	+	7.72992i	−0.0822261	+	0.253066i
$934$	15.4742			0.506332
$935$		0			0
$936$	−24.3339			−0.795378
$937$	11.9255	−	36.7029i	0.389589	−	1.19903i	−0.543507	−	0.839405i	$-0.682904\pi$
$937$	11.9255	−	36.7029i	0.389589	−	1.19903i	0.933096	−	0.359628i	$-0.117096\pi$
$938$	7.58916	−	5.51385i	0.247795	−	0.180034i
$939$	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	$-0.257804\pi$
$942$	−1.66928	−	1.21280i	−0.0543880	−	0.0395152i
$943$	−4.95744	+	3.60179i	−0.161437	+	0.117291i
$944$	9.74764	−	30.0002i	0.317259	−	0.976422i
$945$		0			0
$946$	8.65882	−	7.08270i	0.281523	−	0.230279i
$947$	−46.7623			−1.51957			−0.759785	−	0.650174i	$-0.774696\pi$
$947$	−46.7623			−1.51957			−0.759785	+	0.650174i	$0.774696\pi$
$948$	0.619629	−	1.90702i	0.0201246	−	0.0619371i
$949$	3.85834	−	2.80325i	0.125247	−	0.0909972i
$950$		0			0
$951$	2.07069	+	6.37293i	0.0671468	+	0.206657i
$952$	−6.91116	−	21.2704i	−0.223992	−	0.689376i
$953$	−4.97738	−	3.61628i	−0.161233	−	0.117143i	0.504243	−	0.863562i	$-0.331772\pi$
$953$	−4.97738	−	3.61628i	−0.161233	−	0.117143i	−0.665476	+	0.746419i	$0.731772\pi$
$954$	−7.08167	+	5.14514i	−0.229278	+	0.166580i
$955$		0			0
$956$	41.0529			1.32774
$957$	−2.71661	−	1.74522i	−0.0878155	−	0.0564148i
$958$	−8.46440			−0.273472
$959$	−15.2093	+	46.8093i	−0.491132	+	1.51155i
$960$		0			0
$961$	20.4726	+	14.8742i	0.660408	+	0.479814i
$962$	−7.32680	−	22.5496i	−0.236226	−	0.727027i
$963$	16.1325	+	49.6507i	0.519862	+	1.59997i
$964$	−30.5891	−	22.2243i	−0.985209	−	0.715796i
$965$		0			0
$966$	0.354686	−	1.09161i	0.0114118	−	0.0351220i
$967$	−3.39625			−0.109216			−0.0546080	−	0.998508i	$-0.517391\pi$
$967$	−3.39625			−0.109216			−0.0546080	+	0.998508i	$0.517391\pi$
$968$	−17.2472	−	9.73233i	−0.554346	−	0.312809i
$969$	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	$0.251831\pi$
$972$	−11.9314	−	8.66870i	−0.382701	−	0.278049i
$973$	19.2404	+	59.2158i	0.616818	+	1.89837i
$974$	−2.72255	−	8.37914i	−0.0872360	−	0.268485i
$975$		0			0
$976$	8.65182	−	6.28591i	0.276938	−	0.201207i
$977$	5.11585	−	15.7450i	0.163671	−	0.503726i	−0.835265	−	0.549847i	$-0.814686\pi$
$977$	5.11585	−	15.7450i	0.163671	−	0.503726i	0.998936	+	0.0461210i	$0.0146860\pi$
$978$	0.119032			0.00380623
$979$	−7.72885	−	4.96520i	−0.247015	−	0.158689i
$980$		0			0
$981$	14.6436	−	45.0685i	0.467535	−	1.43893i
$982$	−4.41474	+	3.20750i	−0.140880	+	0.102355i
$983$	41.1126	+	29.8701i	1.31129	+	0.952707i	0.999997	+	0.00239240i	$0.000761525\pi$
$983$	41.1126	+	29.8701i	1.31129	+	0.952707i	0.311291	+	0.950315i	$0.399238\pi$
$984$	0.397287	+	1.22272i	0.0126651	+	0.0389790i
$985$		0			0
$986$	−5.38279	−	3.91083i	−0.171423	−	0.124546i
$987$	3.06151	−	2.22432i	0.0974490	−	0.0708009i
$988$	11.0956	−	34.1488i	0.352999	−	1.08642i
$989$	−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	$0.442229\pi$
$992$	−3.60018	+	11.0802i	−0.114306	+	0.351797i
$993$	−8.40081	+	6.10355i	−0.266592	+	0.193690i
$994$	−1.23971	−	0.900700i	−0.0393211	−	0.0285685i
$995$		0			0
$996$	−1.96671	−	6.05292i	−0.0623177	−	0.191794i
$997$	−23.5945	−	17.1424i	−0.747246	−	0.542906i	0.147726	−	0.989028i	$-0.452805\pi$
$997$	−23.5945	−	17.1424i	−0.747246	−	0.542906i	−0.894972	+	0.446122i	$0.852805\pi$
$998$	4.20149	−	3.05256i	0.132996	−	0.0966271i
$999$	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.h.a.251.1		8
5.2	odd	4		275.2.z.a.174.2		16
5.3	odd	4		275.2.z.a.174.3		16
5.4	even	2		55.2.g.b.31.2	yes	8
11.4	even	5		3025.2.a.bd.1.2		4
11.5	even	5	inner	275.2.h.a.126.1		8
11.7	odd	10		3025.2.a.w.1.3		4
15.14	odd	2		495.2.n.e.361.1		8
20.19	odd	2		880.2.bo.h.801.1		8
55.4	even	10		605.2.a.j.1.3		4
55.9	even	10		605.2.g.m.366.1		8
55.14	even	10		605.2.g.m.81.1		8
55.19	odd	10		605.2.g.e.81.2		8
55.24	odd	10		605.2.g.e.366.2		8
55.27	odd	20		275.2.z.a.49.3		16
55.29	odd	10		605.2.a.k.1.2		4
55.38	odd	20		275.2.z.a.49.2		16
55.39	odd	10		605.2.g.k.511.1		8
55.49	even	10		55.2.g.b.16.2	✓	8
55.54	odd	2		605.2.g.k.251.1		8
165.29	even	10		5445.2.a.bi.1.3		4
165.59	odd	10		5445.2.a.bp.1.2		4
165.104	odd	10		495.2.n.e.181.1		8
220.59	odd	10		9680.2.a.cn.1.3		4
220.139	even	10		9680.2.a.cm.1.3		4
220.159	odd	10		880.2.bo.h.401.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.16.2	✓	8	55.49	even	10
55.2.g.b.31.2	yes	8	5.4	even	2
275.2.h.a.126.1		8	11.5	even	5	inner
275.2.h.a.251.1		8	1.1	even	1	trivial
275.2.z.a.49.2		16	55.38	odd	20
275.2.z.a.49.3		16	55.27	odd	20
275.2.z.a.174.2		16	5.2	odd	4
275.2.z.a.174.3		16	5.3	odd	4
495.2.n.e.181.1		8	165.104	odd	10
495.2.n.e.361.1		8	15.14	odd	2
605.2.a.j.1.3		4	55.4	even	10
605.2.a.k.1.2		4	55.29	odd	10
605.2.g.e.81.2		8	55.19	odd	10
605.2.g.e.366.2		8	55.24	odd	10
605.2.g.k.251.1		8	55.54	odd	2
605.2.g.k.511.1		8	55.39	odd	10
605.2.g.m.81.1		8	55.14	even	10
605.2.g.m.366.1		8	55.9	even	10
880.2.bo.h.401.1		8	220.159	odd	10
880.2.bo.h.801.1		8	20.19	odd	2
3025.2.a.w.1.3		4	11.7	odd	10
3025.2.a.bd.1.2		4	11.4	even	5
5445.2.a.bi.1.3		4	165.29	even	10
5445.2.a.bp.1.2		4	165.59	odd	10
9680.2.a.cm.1.3		4	220.139	even	10
9680.2.a.cn.1.3		4	220.59	odd	10

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.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.147481 + 0.453901i) q^{2} +(0.261370 - 0.189896i) q^{3} +(1.43376 + 1.04169i) q^{4} +(0.0476470 + 0.146642i) q^{6} +(2.17239 + 1.57833i) q^{7} +(-1.45650 + 1.05821i) q^{8} +(-0.894797 + 2.75390i) q^{9} +O(q^{10})\)	\(q+(-0.147481 + 0.453901i) q^{2} +(0.261370 - 0.189896i) q^{3} +(1.43376 + 1.04169i) q^{4} +(0.0476470 + 0.146642i) q^{6} +(2.17239 + 1.57833i) q^{7} +(-1.45650 + 1.05821i) q^{8} +(-0.894797 + 2.75390i) q^{9} +(-2.79042 - 1.79264i) q^{11} +0.572554 q^{12} +(1.44244 - 4.43939i) q^{13} +(-1.03679 + 0.753275i) q^{14} +(0.829779 + 2.55380i) q^{16} +(1.42961 + 4.39990i) q^{17} +(-1.11803 - 0.812299i) q^{18} +(3.51149 - 2.55125i) q^{19} +0.867517 q^{21} +(1.22522 - 1.00220i) q^{22} -2.77222 q^{23} +(-0.179735 + 0.553168i) q^{24} +(1.80231 + 1.30945i) q^{26} +(0.588587 + 1.81148i) q^{27} +(1.47055 + 4.52590i) q^{28} +(2.43790 + 1.77124i) q^{29} +(0.737407 - 2.26951i) q^{31} -4.88221 q^{32} +(-1.06975 + 0.0613500i) q^{33} -2.20796 q^{34} +(-4.15163 + 3.01633i) q^{36} +(-8.61029 - 6.25574i) q^{37} +(0.640135 + 1.97013i) q^{38} +(-0.466012 - 1.43424i) q^{39} +(1.78826 - 1.29924i) q^{41} +(-0.127943 + 0.393767i) q^{42} +7.06719 q^{43} +(-2.13343 - 5.47695i) q^{44} +(0.408851 - 1.25832i) q^{46} +(3.52905 - 2.56401i) q^{47} +(0.701836 + 0.509914i) q^{48} +(0.0650188 + 0.200107i) q^{49} +(1.20918 + 0.878523i) q^{51} +(6.69257 - 4.86243i) q^{52} +(1.95733 - 6.02403i) q^{53} -0.909040 q^{54} -4.83428 q^{56} +(0.433326 - 1.33364i) q^{57} +(-1.16351 + 0.845342i) q^{58} +(-9.50375 - 6.90488i) q^{59} +(-1.23070 - 3.78770i) q^{61} +(0.921378 + 0.669420i) q^{62} +(-6.29042 + 4.57026i) q^{63} +(-0.939522 + 2.89155i) q^{64} +(0.129921 - 0.494608i) q^{66} -7.31984 q^{67} +(-2.53359 + 7.79760i) q^{68} +(-0.724576 + 0.526435i) q^{69} +(0.369495 + 1.13719i) q^{71} +(-1.61093 - 4.95794i) q^{72} +(0.826577 + 0.600544i) q^{73} +(4.10935 - 2.98562i) q^{74} +7.69223 q^{76} +(-3.23251 - 8.29852i) q^{77} +0.719730 q^{78} +(1.08222 - 3.33073i) q^{79} +(-6.53000 - 4.74432i) q^{81} +(0.325994 + 1.00331i) q^{82} +(-3.43498 - 10.5718i) q^{83} +(1.24381 + 0.903681i) q^{84} +(-1.04228 + 3.20780i) q^{86} +0.973547 q^{87} +(5.96123 - 0.341876i) q^{88} +2.76978 q^{89} +(10.1404 - 7.36742i) q^{91} +(-3.97470 - 2.88779i) q^{92} +(-0.238235 - 0.733212i) q^{93} +(0.643336 + 1.97998i) q^{94} +(-1.27606 + 0.927114i) q^{96} +(-5.72738 + 17.6271i) q^{97} -0.100418 q^{98} +(7.43361 - 6.08051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 5 q^{3} - 2 q^{4} - 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 5 * q^3 - 2 * q^4 - 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9	\( 8 q + 2 q^{2} + 5 q^{3} - 2 q^{4} - 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9} + 3 q^{11} - 16 q^{12} + 2 q^{13} - 16 q^{14} + 4 q^{16} + 13 q^{17} + 15 q^{19} - 20 q^{21} + 7 q^{22} - 10 q^{23} + 13 q^{24} + 10 q^{26} - 10 q^{27} + 6 q^{28} - 9 q^{29} - 10 q^{31} - 16 q^{32} - 5 q^{33} + 4 q^{34} - 15 q^{36} - 24 q^{37} + 21 q^{39} + 8 q^{41} - 9 q^{42} + 38 q^{43} - 12 q^{44} + 3 q^{46} - 5 q^{48} + q^{49} + q^{51} + 28 q^{52} - 13 q^{53} + 16 q^{54} + 22 q^{56} + 45 q^{57} - 12 q^{58} - 27 q^{59} + 6 q^{61} + 30 q^{62} - 25 q^{63} - 26 q^{64} + 13 q^{66} + 38 q^{67} - 11 q^{68} - q^{69} - 20 q^{71} + 30 q^{72} - 13 q^{73} + 20 q^{74} - 34 q^{77} + 16 q^{78} + 37 q^{79} + 8 q^{81} - 28 q^{82} - 27 q^{83} + 28 q^{84} - 3 q^{86} - 38 q^{87} + 36 q^{88} - 16 q^{89} + 44 q^{91} - 11 q^{92} + 35 q^{93} + 17 q^{94} - 17 q^{96} - 24 q^{97} - 16 q^{98} - 20 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 5 * q^3 - 2 * q^4 - 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9 + 3 * q^11 - 16 * q^12 + 2 * q^13 - 16 * q^14 + 4 * q^16 + 13 * q^17 + 15 * q^19 - 20 * q^21 + 7 * q^22 - 10 * q^23 + 13 * q^24 + 10 * q^26 - 10 * q^27 + 6 * q^28 - 9 * q^29 - 10 * q^31 - 16 * q^32 - 5 * q^33 + 4 * q^34 - 15 * q^36 - 24 * q^37 + 21 * q^39 + 8 * q^41 - 9 * q^42 + 38 * q^43 - 12 * q^44 + 3 * q^46 - 5 * q^48 + q^49 + q^51 + 28 * q^52 - 13 * q^53 + 16 * q^54 + 22 * q^56 + 45 * q^57 - 12 * q^58 - 27 * q^59 + 6 * q^61 + 30 * q^62 - 25 * q^63 - 26 * q^64 + 13 * q^66 + 38 * q^67 - 11 * q^68 - q^69 - 20 * q^71 + 30 * q^72 - 13 * q^73 + 20 * q^74 - 34 * q^77 + 16 * q^78 + 37 * q^79 + 8 * q^81 - 28 * q^82 - 27 * q^83 + 28 * q^84 - 3 * q^86 - 38 * q^87 + 36 * q^88 - 16 * q^89 + 44 * q^91 - 11 * q^92 + 35 * q^93 + 17 * q^94 - 17 * q^96 - 24 * q^97 - 16 * q^98 - 20 * q^99

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