LMFDB - Embedded newform 275.2.h.a.126.1

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			126.1
Root			$-0.386111 - 0.280526i$ of defining polynomial
Character	$\chi$	$=$	275.126
Dual form			275.2.h.a.251.1

$q$-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 $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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	0.885277	−	0.465064i	$-0.153969\pi$
$2$	−0.147481	−	0.453901i	−0.104285	−	0.320957i	−0.989562	+	0.144108i	$0.953969\pi$
$3$	0.261370	+	0.189896i	0.150902	+	0.109637i	0.660674	−	0.750673i	$-0.270270\pi$
$3$	0.261370	+	0.189896i	0.150902	+	0.109637i	−0.509772	+	0.860309i	$0.670270\pi$
$4$	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	−0.0959376	−	0.995387i	$-0.530585\pi$
$7$	2.17239	−	1.57833i	0.821086	−	0.596554i	0.917023	+	0.398834i	$0.130585\pi$
$8$	−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	0.924949	+	0.380092i	$0.124108\pi$
$13$	1.44244	+	4.43939i	0.400062	+	1.23126i	−0.524886	+	0.851172i	$0.675892\pi$
$14$	−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	−0.613918	−	0.789370i	$-0.710407\pi$
$17$	1.42961	−	4.39990i	0.346732	−	1.06713i	0.960650	−	0.277762i	$-0.0895926\pi$
$18$	−1.11803	+	0.812299i	−0.263523	+	0.191461i
$19$	3.51149	+	2.55125i	0.805592	+	0.585297i	0.912549	−	0.408967i	$-0.134111\pi$
$19$	3.51149	+	2.55125i	0.805592	+	0.585297i	−0.106958	+	0.994264i	$0.534111\pi$
$20$		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	−0.337956	−	0.941162i	$-0.609736\pi$
$29$	2.43790	−	1.77124i	0.452707	−	0.328911i	0.790664	+	0.612251i	$0.209736\pi$
$30$		0			0
$31$	0.737407	+	2.26951i	0.132442	+	0.407615i	0.995183	−	0.0980305i	$-0.0312543\pi$
$31$	0.737407	+	2.26951i	0.132442	+	0.407615i	−0.862741	+	0.505646i	$0.831254\pi$
$32$	−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	−0.423033	+	0.906114i	$0.639035\pi$
$37$	−8.61029	+	6.25574i	−1.41552	+	1.02844i	−0.992490	+	0.122324i	$0.960965\pi$
$38$	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	0.718603	−	0.695421i	$-0.244782\pi$
$41$	1.78826	+	1.29924i	0.279279	+	0.202908i	−0.439324	+	0.898329i	$0.644782\pi$
$42$	−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	0.814628	−	0.579983i	$-0.196941\pi$
$47$	3.52905	+	2.56401i	0.514765	+	0.373999i	−0.299863	+	0.953982i	$0.596941\pi$
$48$	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	0.990779	+	0.135487i	$0.0432600\pi$
$53$	1.95733	+	6.02403i	0.268859	+	0.827464i	−0.721920	+	0.691977i	$0.756740\pi$
$54$	−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	−0.997414	−	0.0718667i	$-0.977104\pi$
$59$	−9.50375	+	6.90488i	−1.23728	+	0.898939i	−0.239869	+	0.970805i	$0.577104\pi$
$60$		0			0
$61$	−1.23070	+	3.78770i	−0.157575	+	0.484966i	−0.998413	−	0.0563214i	$-0.982063\pi$
$61$	−1.23070	+	3.78770i	−0.157575	+	0.484966i	0.840838	+	0.541287i	$0.182063\pi$
$62$	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	−0.926734	−	0.375718i	$-0.877396\pi$
$71$	0.369495	−	1.13719i	0.0438510	−	0.134960i	0.970585	+	0.240758i	$0.0773961\pi$
$72$	−1.61093	+	4.95794i	−0.189850	+	0.584299i
$73$	0.826577	−	0.600544i	0.0967436	−	0.0702883i	−0.538362	−	0.842714i	$-0.680957\pi$
$73$	0.826577	−	0.600544i	0.0967436	−	0.0702883i	0.635105	+	0.772425i	$0.280957\pi$
$74$	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	0.993297	−	0.115593i	$-0.0368767\pi$
$79$	1.08222	+	3.33073i	0.121759	+	0.374736i	−0.871538	+	0.490329i	$0.836877\pi$
$80$		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	0.565055	+	0.825053i	$0.308855\pi$
$83$	−3.43498	+	10.5718i	−0.377038	+	1.16040i	−0.942093	+	0.335351i	$0.891145\pi$
$84$	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	−0.612789	−	0.790247i	$-0.709952\pi$
$97$	−5.72738	−	17.6271i	−0.581528	−	1.78976i	0.0312615	−	0.999511i	$-0.490048\pi$
$98$	−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	−0.998865	−	0.0476270i	$-0.984834\pi$
$101$	−2.19852	−	6.76634i	−0.218761	−	0.673276i	0.780104	−	0.625649i	$-0.215166\pi$
$102$	−0.577094	−	0.419284i	−0.0571409	−	0.0415153i
$103$	6.09056	−	4.42505i	0.600121	−	0.436014i	−0.245801	−	0.969320i	$-0.579051\pi$
$103$	6.09056	−	4.42505i	0.600121	−	0.436014i	0.845922	+	0.533307i	$0.179051\pi$
$104$	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	0.993312	+	0.115465i	$0.0368358\pi$
$107$	14.5859	+	10.5973i	1.41008	+	1.02448i	0.416764	+	0.909015i	$0.363164\pi$
$108$	−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	0.506884	−	0.862014i	$-0.330797\pi$
$113$	−1.66154	−	1.20718i	−0.156304	−	0.113562i	−0.663188	+	0.748453i	$0.730797\pi$
$114$	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	−0.950005	−	0.312233i	$-0.898923\pi$
$127$	0.0235677	−	0.0725340i	0.00209130	−	0.00643635i	0.952097	+	0.305797i	$0.0989229\pi$
$128$	−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	−0.349635	−	0.936886i	$-0.613694\pi$
$137$	5.66406	−	17.4322i	0.483914	−	1.48933i	0.833548	−	0.552447i	$-0.186306\pi$
$138$	−0.132088	+	0.406525i	−0.0112441	+	0.0346057i
$139$	18.7590	−	13.6292i	1.59111	−	1.15601i	0.688785	−	0.724966i	$-0.258145\pi$
$139$	18.7590	−	13.6292i	1.59111	−	1.15601i	0.902330	−	0.431046i	$-0.141855\pi$
$140$		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	−0.574733	−	0.818341i	$-0.694894\pi$
$149$	4.53161	−	13.9469i	0.371244	−	1.14257i	0.945978	−	0.324232i	$-0.105106\pi$
$150$		0			0
$151$	6.08301	+	4.41957i	0.495028	+	0.359659i	0.807115	−	0.590394i	$-0.201028\pi$
$151$	6.08301	+	4.41957i	0.495028	+	0.359659i	−0.312086	+	0.950054i	$0.601028\pi$
$152$	−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	0.0649531	−	0.997888i	$-0.479310\pi$
$157$	−10.8262	−	7.86568i	−0.864023	−	0.627750i	−0.928977	+	0.370139i	$0.879310\pi$
$158$	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	0.959964	−	0.280122i	$-0.0903749\pi$
$163$	0.238558	+	0.734206i	0.0186853	+	0.0575075i	−0.941279	+	0.337629i	$0.890375\pi$
$164$	3.91733			0.305892
$165$		0			0
$166$	5.30514			0.411759
$167$	2.62118	+	8.06716i	0.202833	+	0.624256i	0.999795	+	0.0202268i	$0.00643884\pi$
$167$	2.62118	+	8.06716i	0.202833	+	0.624256i	−0.796962	+	0.604029i	$0.793561\pi$
$168$	−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	0.732919	−	0.680316i	$-0.238158\pi$
$173$	4.10876	+	2.98519i	0.312384	+	0.226960i	−0.420535	+	0.907276i	$0.638158\pi$
$174$	−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	0.874791	−	0.484501i	$-0.160999\pi$
$179$	9.15568	+	6.65199i	0.684328	+	0.497193i	−0.190463	+	0.981694i	$0.560999\pi$
$180$		0			0
$181$	2.28674	−	7.03787i	0.169972	−	0.523121i	−0.829396	−	0.558661i	$-0.811315\pi$
$181$	2.28674	−	7.03787i	0.169972	−	0.523121i	0.999368	+	0.0355402i	$0.0113152\pi$
$182$	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	−0.426554	−	0.904462i	$-0.640272\pi$
$191$	4.17135	−	3.03067i	0.301829	−	0.219291i	0.728382	+	0.685171i	$0.240272\pi$
$192$	0.303532	−	0.934176i	0.0219056	−	0.0674184i
$193$	1.24605	−	3.83494i	0.0896925	−	0.276045i	−0.896142	−	0.443768i	$-0.853641\pi$
$193$	1.24605	−	3.83494i	0.0896925	−	0.276045i	0.985834	+	0.167723i	$0.0536414\pi$
$194$	−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	0.981249	−	0.192746i	$-0.0617393\pi$
$211$	1.07649	+	3.31309i	0.0741086	+	0.228083i	−0.907140	+	0.420829i	$0.861739\pi$
$212$	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	0.835570	−	0.549384i	$-0.185138\pi$
$223$	8.53103	+	6.19816i	0.571280	+	0.415059i	−0.264290	+	0.964443i	$0.585138\pi$
$224$	−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	−0.581970	−	0.813210i	$-0.697718\pi$
$227$	0.174762	−	0.126972i	0.0115994	−	0.00842743i	0.593570	+	0.804782i	$0.297718\pi$
$228$	2.01052	+	1.46073i	0.133150	+	0.0967390i
$229$	−0.0233956	−	0.0720042i	−0.00154602	−	0.00475817i	0.950281	−	0.311395i	$-0.100796\pi$
$229$	−0.0233956	−	0.0720042i	−0.00154602	−	0.00475817i	−0.951827	+	0.306637i	$0.900796\pi$
$230$		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	−0.979266	−	0.202579i	$-0.935068\pi$
$233$	−4.67235	−	14.3800i	−0.306096	−	0.942067i	0.673170	−	0.739488i	$-0.264932\pi$
$234$	−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	0.995431	−	0.0954825i	$-0.0304394\pi$
$239$	18.7406	+	13.6158i	1.21223	+	0.880734i	0.216796	+	0.976217i	$0.430439\pi$
$240$		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	0.871863	−	0.489751i	$-0.162912\pi$
$251$	−1.92266	−	5.91734i	−0.121357	−	0.373499i	−0.993220	+	0.116251i	$0.962912\pi$
$252$	−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	−0.886755	−	0.462239i	$-0.847046\pi$
$257$	−11.5611	+	8.39964i	−0.721163	+	0.523955i	0.165593	+	0.986194i	$0.447046\pi$
$258$	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	−0.965666	−	0.259786i	$-0.916348\pi$
$269$	−0.520367	+	1.60152i	−0.0317273	+	0.0976466i	0.933939	+	0.357433i	$0.116348\pi$
$270$		0			0
$271$	14.9110	−	10.8335i	0.905778	−	0.658086i	−0.0341657	−	0.999416i	$-0.510877\pi$
$271$	14.9110	−	10.8335i	0.905778	−	0.658086i	0.939943	+	0.341330i	$0.110877\pi$
$272$	−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	0.977820	−	0.209446i	$-0.0671662\pi$
$277$	1.05914	+	3.25969i	0.0636375	+	0.195856i	−0.914183	+	0.405303i	$0.867166\pi$
$278$	−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	0.486342	+	0.873769i	$0.338331\pi$
$281$	−7.05230	+	21.7048i	−0.420705	+	1.29480i	−0.907047	+	0.421029i	$0.861669\pi$
$282$	0.544141	−	0.395341i	0.0324031	−	0.0235422i
$283$	−23.5416	−	17.1040i	−1.39941	−	1.01673i	−0.994758	−	0.102255i	$-0.967394\pi$
$283$	−23.5416	−	17.1040i	−1.39941	−	1.01673i	−0.404647	−	0.914473i	$-0.632606\pi$
$284$	−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	0.0399740	−	0.999201i	$-0.487273\pi$
$293$	17.1621	−	12.4690i	1.00262	−	0.728448i	0.962649	+	0.270753i	$0.0872725\pi$
$294$	−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	−0.165089	−	0.986279i	$-0.552791\pi$
$311$	−20.3530	−	14.7873i	−1.15411	−	0.838511i	−0.989022	+	0.147768i	$0.952791\pi$
$312$	2.19647	−	1.59583i	0.124350	−	0.0903459i
$313$	3.57821	−	11.0126i	0.202252	−	0.622469i	−0.797563	−	0.603236i	$-0.793878\pi$
$313$	3.57821	−	11.0126i	0.202252	−	0.622469i	0.999815	−	0.0192328i	$-0.00612237\pi$
$314$	−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	−0.953061	−	0.302780i	$-0.902085\pi$
$317$	−6.40940	−	19.7261i	−0.359988	−	1.10793i	0.593073	−	0.805149i	$-0.297915\pi$
$318$	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	−0.908882	−	0.417054i	$-0.863063\pi$
$337$	−14.5594	+	10.5780i	−0.793100	+	0.576221i	0.115782	+	0.993275i	$0.463063\pi$
$338$	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	−0.861822	−	0.507211i	$-0.830677\pi$
$347$	2.48753	−	7.65583i	0.133538	−	0.410986i	0.995360	+	0.0962243i	$0.0306766\pi$
$348$	1.39583	−	1.01413i	0.0748244	−	0.0543631i
$349$	−15.5569	−	11.3027i	−0.832741	−	0.605022i	0.0875926	−	0.996156i	$-0.472083\pi$
$349$	−15.5569	−	11.3027i	−0.832741	−	0.605022i	−0.920333	+	0.391135i	$0.872083\pi$
$350$		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	−0.784249	−	0.620446i	$-0.786952\pi$
$359$	−8.27079	+	6.00908i	−0.436516	+	0.317147i	0.347733	+	0.937594i	$0.386952\pi$
$360$		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	−0.247632	−	0.968854i	$-0.579653\pi$
$367$	11.4422	−	8.31327i	0.597280	−	0.433949i	0.844912	+	0.534905i	$0.179653\pi$
$368$	−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	−0.733629	−	0.679550i	$-0.762175\pi$
$379$	5.04840	−	15.5374i	0.259319	−	0.798102i	0.992948	−	0.118552i	$-0.0378251\pi$
$380$		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	0.957267	−	0.289204i	$-0.0933907\pi$
$383$	0.251122	+	0.772874i	0.0128317	+	0.0394920i	−0.944436	+	0.328696i	$0.893391\pi$
$384$	−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	0.248702	−	0.968580i	$-0.419996\pi$
$389$	24.5894	−	17.8652i	1.24673	−	0.905802i	0.998028	+	0.0627780i	$0.0199960\pi$
$390$		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	−0.812196	−	0.583385i	$-0.801728\pi$
$401$	3.76049	−	11.5736i	0.187790	−	0.577957i	0.999985	+	0.00542792i	$0.00172777\pi$
$402$	−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	0.949034	−	0.315174i	$-0.102063\pi$
$409$	−0.0809957	−	0.249279i	−0.00400498	−	0.0123261i	−0.953039	+	0.302847i	$0.902063\pi$
$410$		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	0.990971	−	0.134078i	$-0.0428071\pi$
$421$	23.9999	+	17.4369i	1.16968	+	0.849824i	0.178712	+	0.983902i	$0.442807\pi$
$422$	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	0.856817	+	0.515621i	$0.172439\pi$
$431$	9.68919	+	29.8203i	0.466712	+	1.43639i	−0.390105	+	0.920771i	$0.627561\pi$
$432$	−4.13776	−	3.00626i	−0.199078	−	0.144639i
$433$	−21.0607	+	15.3015i	−1.01212	+	0.735345i	−0.964652	−	0.263528i	$-0.915114\pi$
$433$	−21.0607	+	15.3015i	−1.01212	+	0.735345i	−0.0474634	+	0.998873i	$0.515114\pi$
$434$	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	0.581413	−	0.813608i	$-0.302500\pi$
$443$	−0.267467	−	0.194326i	−0.0127078	−	0.00923273i	−0.594121	+	0.804376i	$0.702500\pi$
$444$	−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	0.993732	−	0.111786i	$-0.0356571\pi$
$449$	2.62920	+	8.09185i	0.124080	+	0.381878i	−0.869653	+	0.493664i	$0.835657\pi$
$450$		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	−0.958948	−	0.283583i	$-0.908477\pi$
$457$	−0.351807	+	1.08275i	−0.0164569	+	0.0506490i	0.942491	+	0.334232i	$0.108477\pi$
$458$	−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	0.397053	+	0.917796i	$0.370033\pi$
$467$	−10.0193	+	30.8361i	−0.463637	+	1.42693i	−0.860689	+	0.509131i	$0.829967\pi$
$468$	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	−0.744287	−	0.667860i	$-0.767210\pi$
$479$	5.48054	−	16.8674i	0.250412	−	0.770690i	0.994699	−	0.102830i	$-0.0327897\pi$
$480$		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	0.195525	−	0.980699i	$-0.437359\pi$
$487$	−14.9347	−	10.8507i	−0.676754	−	0.491691i	−0.872279	+	0.489008i	$0.837359\pi$
$488$	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	−0.359158	−	0.933277i	$-0.616936\pi$
$491$	9.25018	−	6.72065i	0.417455	−	0.303299i	0.776613	+	0.629978i	$0.216936\pi$
$492$	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	−0.767130	−	0.641491i	$-0.778316\pi$
$499$	−8.80335	+	6.39601i	−0.394092	+	0.286325i	0.373038	+	0.927816i	$0.378316\pi$
$500$		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	0.851490	+	0.524371i	$0.175699\pi$
$503$	36.1830	+	26.2885i	1.61332	+	1.17215i	0.761831	+	0.647776i	$0.224301\pi$
$504$	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	0.807177	−	0.590310i	$-0.200994\pi$
$509$	11.1720	+	8.11693i	0.495190	+	0.359777i	−0.311987	+	0.950086i	$0.600994\pi$
$510$		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	−0.521224	−	0.853420i	$-0.674524\pi$
$521$	2.95269	−	2.14525i	0.129360	−	0.0939852i	0.650584	+	0.759435i	$0.274524\pi$
$522$	−1.28688	+	3.96061i	−0.0563253	+	0.173351i
$523$	1.54109	−	4.74299i	0.0673872	−	0.207396i	−0.911693	−	0.410873i	$-0.865224\pi$
$523$	1.54109	−	4.74299i	0.0673872	−	0.207396i	0.979080	+	0.203476i	$0.0652240\pi$
$524$	−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	0.952688	−	0.303951i	$-0.0983058\pi$
$541$	0.0765109	+	0.235476i	0.00328946	+	0.0101239i	−0.949398	+	0.314075i	$0.898306\pi$
$542$	−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	0.0565056	−	0.998402i	$-0.482004\pi$
$547$	−20.4779	−	14.8780i	−0.875570	−	0.636139i	−0.932076	+	0.362263i	$0.882004\pi$
$548$	−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	−0.325630	+	0.945497i	$0.605576\pi$
$557$	−31.2824	+	22.7280i	−1.32548	+	0.963015i	−0.999847	+	0.0175177i	$0.994424\pi$
$558$	−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	0.818372	−	0.574689i	$-0.194877\pi$
$563$	−4.30653	−	13.2541i	−0.181498	−	0.558595i	−0.999870	+	0.0160940i	$0.994877\pi$
$564$	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	0.00334520	−	0.999994i	$-0.498935\pi$
$569$	−22.5817	−	16.4065i	−0.946672	−	0.687798i	−0.950017	+	0.312197i	$0.898935\pi$
$570$		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	0.724541	+	0.689232i	$0.242052\pi$
$577$	−6.40744	+	19.7201i	−0.266745	+	0.820958i	−0.991286	+	0.131726i	$0.957948\pi$
$578$	−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	−0.303581	−	0.952806i	$-0.598182\pi$
$587$	12.3267	−	8.95591i	0.508779	−	0.369650i	0.812360	+	0.583156i	$0.198182\pi$
$588$	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	0.627926	+	0.778273i	$0.283904\pi$
$599$	−8.26097	+	25.4247i	−0.337534	+	1.03882i	−0.965460	+	0.260551i	$0.916096\pi$
$600$		0			0
$601$	−1.94714	+	1.41468i	−0.0794255	+	0.0577060i	−0.626789	−	0.779189i	$-0.715631\pi$
$601$	−1.94714	+	1.41468i	−0.0794255	+	0.0577060i	0.547364	+	0.836895i	$0.315631\pi$
$602$	−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	0.865526	−	0.500864i	$-0.166984\pi$
$607$	−3.18067	−	9.78909i	−0.129099	−	0.397327i	−0.994626	+	0.103536i	$0.966984\pi$
$608$	−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	0.941232	−	0.337759i	$-0.109669\pi$
$613$	22.5519	+	16.3849i	0.910861	+	0.661779i	−0.0303715	+	0.999539i	$0.509669\pi$
$614$	−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	0.154060	−	0.988061i	$-0.450765\pi$
$619$	−18.3621	−	13.3408i	−0.738035	−	0.536214i	−0.892095	+	0.451848i	$0.850765\pi$
$620$		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	−0.943289	−	0.331973i	$-0.892286\pi$
$631$	−23.0864	+	16.7733i	−0.919056	+	0.667733i	0.0242327	+	0.999706i	$0.492286\pi$
$632$	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	0.549213	−	0.835682i	$-0.314927\pi$
$641$	−1.92040	−	1.39526i	−0.0758514	−	0.0551093i	−0.625065	+	0.780573i	$0.714927\pi$
$642$	2.24899	−	1.63399i	0.0887605	−	0.0644883i
$643$	−3.51053	+	10.8043i	−0.138442	+	0.426080i	−0.996109	−	0.0881244i	$-0.971913\pi$
$643$	−3.51053	+	10.8043i	−0.138442	+	0.426080i	0.857668	+	0.514204i	$0.171913\pi$
$644$	−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	0.585746	+	0.810495i	$0.300802\pi$
$647$	14.9632	+	46.0520i	0.588264	+	1.81049i	0.00251822	+	0.999997i	$0.499198\pi$
$648$	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	−0.00688905	−	0.999976i	$-0.502193\pi$
$653$	24.0722	−	17.4894i	0.942016	−	0.684415i	0.948905	+	0.315562i	$0.102193\pi$
$654$	−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	0.842898	−	0.538073i	$-0.180848\pi$
$673$	−4.02863	−	12.3988i	−0.155292	−	0.477940i	−0.998190	+	0.0601327i	$0.980848\pi$
$674$	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	−0.446444	−	0.894812i	$-0.647310\pi$
$677$	11.4665	−	35.2903i	0.440694	−	1.35632i	0.887138	−	0.461505i	$-0.152690\pi$
$678$	−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	0.896704	+	0.442631i	$0.145955\pi$
$691$	11.3409	+	34.9036i	0.431427	+	1.32780i	−0.465277	+	0.885165i	$0.654045\pi$
$692$	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	0.982292	−	0.187356i	$-0.0599919\pi$
$701$	29.3266	+	21.3070i	1.10765	+	0.804755i	0.125359	+	0.992111i	$0.459992\pi$
$702$	−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	0.783216	+	0.621750i	$0.213578\pi$
$709$	−5.74811	+	17.6909i	−0.215875	+	0.664394i	−0.999090	+	0.0426440i	$0.986422\pi$
$710$		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	0.143664	−	0.989627i	$-0.454112\pi$
$719$	30.2799	−	21.9996i	1.12925	−	0.820447i	0.985585	+	0.169179i	$0.0541117\pi$
$720$		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	0.251927	−	0.967746i	$-0.418936\pi$
$733$	33.8468	−	24.5911i	1.25016	−	0.908293i	0.998231	+	0.0594528i	$0.0189356\pi$
$734$	−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	0.860073	−	0.510171i	$-0.170418\pi$
$739$	−3.68654	−	11.3460i	−0.135612	−	0.417370i	−0.995685	+	0.0928012i	$0.970418\pi$
$740$		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	0.226652	+	0.973976i	$0.427222\pi$
$743$	−14.4250	+	44.3956i	−0.529202	+	1.62872i	−0.755854	+	0.654740i	$0.772778\pi$
$744$	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	0.354512	−	0.935052i	$-0.384647\pi$
$751$	−11.6530	−	8.46642i	−0.425225	−	0.308944i	−0.779737	+	0.626108i	$0.784647\pi$
$752$	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	0.999839	−	0.0179624i	$-0.00571791\pi$
$757$	4.96330	+	15.2755i	0.180394	+	0.555196i	−0.819444	+	0.573159i	$0.805718\pi$
$758$	−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	−0.892498	−	0.451051i	$-0.851049\pi$
$761$	−12.0158	−	36.9809i	−0.435573	−	1.34056i	0.456925	−	0.889505i	$-0.348951\pi$
$762$	−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	0.467613	−	0.883933i	$-0.345114\pi$
$773$	−6.35452	−	4.61683i	−0.228556	−	0.166056i	−0.696170	+	0.717877i	$0.745114\pi$
$774$	−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	−0.868206	−	0.496203i	$-0.834727\pi$
$787$	3.53048	−	10.8657i	0.125848	−	0.387321i	0.994055	+	0.108882i	$0.0347271\pi$
$788$	−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	−0.924862	−	0.380303i	$-0.875820\pi$
$797$	1.32414	−	4.07529i	0.0469035	−	0.144354i	0.971766	+	0.235949i	$0.0758197\pi$
$798$	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	0.783465	+	0.621436i	$0.213450\pi$
$809$	−6.13350	+	18.8770i	−0.215642	+	0.663679i	−0.999107	+	0.0422430i	$0.986550\pi$
$810$		0			0
$811$	2.53899	+	1.84468i	0.0891559	+	0.0647756i	0.631470	−	0.775400i	$-0.282452\pi$
$811$	2.53899	+	1.84468i	0.0891559	+	0.0647756i	−0.542314	+	0.840176i	$0.682452\pi$
$812$	−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	−0.867849	−	0.496829i	$-0.834498\pi$
$821$	−19.0118	+	13.8129i	−0.663516	+	0.482073i	0.204332	+	0.978902i	$0.434498\pi$
$822$	−2.28642	−	1.66118i	−0.0797481	−	0.0579404i
$823$	3.91103	+	12.0369i	0.136330	+	0.419580i	0.995795	−	0.0916150i	$-0.0292029\pi$
$823$	3.91103	+	12.0369i	0.136330	+	0.419580i	−0.859465	+	0.511195i	$0.829203\pi$
$824$	−13.5535			−0.472159
$825$		0			0
$826$	15.0547			0.523820
$827$	−9.33959	−	28.7443i	−0.324770	−	0.999538i	−0.971545	−	0.236857i	$-0.923883\pi$
$827$	−9.33959	−	28.7443i	−0.324770	−	0.999538i	0.646775	−	0.762681i	$-0.276117\pi$
$828$	11.5092	+	8.36195i	0.399974	+	0.290598i
$829$	−1.61937	+	1.17654i	−0.0562432	+	0.0408630i	−0.615552	−	0.788097i	$-0.711067\pi$
$829$	−1.61937	+	1.17654i	−0.0562432	+	0.0408630i	0.559308	+	0.828960i	$0.311067\pi$
$830$		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	−0.0285326	−	0.999593i	$-0.509083\pi$
$839$	−28.6185	−	20.7925i	−0.988019	−	0.717838i	−0.959486	+	0.281755i	$0.909083\pi$
$840$		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	−0.807395	−	0.590012i	$-0.799123\pi$
$853$	5.62515	−	17.3124i	0.192602	−	0.592767i	0.999996	−	0.00275489i	$-0.000876911\pi$
$854$	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	−0.796241	−	0.604980i	$-0.793181\pi$
$863$	5.97907	−	18.4017i	0.203530	−	0.626400i	0.999771	−	0.0214204i	$-0.00681885\pi$
$864$	−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	0.800728	−	0.599028i	$-0.204446\pi$
$877$	14.1691	+	10.2945i	0.478456	+	0.347619i	−0.322271	+	0.946647i	$0.604446\pi$
$878$	−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	0.890294	−	0.455386i	$-0.150499\pi$
$883$	21.7609	+	15.8102i	0.732313	+	0.532057i	−0.157981	+	0.987442i	$0.550499\pi$
$884$	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	−0.491501	−	0.870877i	$-0.663552\pi$
$887$	5.50591	−	4.00028i	0.184870	−	0.134316i	0.676371	+	0.736561i	$0.263552\pi$
$888$	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	−0.779981	−	0.625804i	$-0.784771\pi$
$907$	6.59174	−	20.2873i	0.218875	−	0.673629i	0.998856	−	0.0478248i	$-0.0152289\pi$
$908$	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	−0.987149	−	0.159805i	$-0.948913\pi$
$911$	−8.52542	−	26.2385i	−0.282460	−	0.869322i	0.704689	−	0.709516i	$-0.251087\pi$
$912$	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	−0.977000	−	0.213239i	$-0.931599\pi$
$919$	−1.85685	+	5.71479i	−0.0612518	+	0.188514i	0.915748	+	0.401752i	$0.131599\pi$
$920$		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	−0.890544	−	0.454898i	$-0.849676\pi$
$929$	2.96576	−	9.12766i	0.0973034	−	0.299469i	0.987847	+	0.155429i	$0.0496759\pi$
$930$		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	0.933096	+	0.359628i	$0.117096\pi$
$937$	11.9255	+	36.7029i	0.389589	+	1.19903i	−0.543507	+	0.839405i	$0.682904\pi$
$938$	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	0.689561	+	0.724228i	$0.257804\pi$
$941$	−9.01854	+	27.7562i	−0.293996	+	0.904826i	−0.983557	+	0.180599i	$0.942196\pi$
$942$	−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	−0.665476	−	0.746419i	$-0.731772\pi$
$953$	−4.97738	+	3.61628i	−0.161233	+	0.117143i	0.504243	+	0.863562i	$0.331772\pi$
$954$	−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	0.703027	−	0.711163i	$-0.251831\pi$
$971$	7.60072	+	5.52224i	0.243919	+	0.177217i	−0.459109	+	0.888380i	$0.651831\pi$
$972$	−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	0.998936	−	0.0461210i	$-0.0146860\pi$
$977$	5.11585	+	15.7450i	0.163671	+	0.503726i	−0.835265	+	0.549847i	$0.814686\pi$
$978$	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	0.311291	−	0.950315i	$-0.399238\pi$
$983$	41.1126	−	29.8701i	1.31129	−	0.952707i	0.999997	−	0.00239240i	$-0.000761525\pi$
$984$	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	−0.894972	−	0.446122i	$-0.852805\pi$
$997$	−23.5945	+	17.1424i	−0.747246	+	0.542906i	0.147726	+	0.989028i	$0.452805\pi$
$998$	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.126.1		8
5.2	odd	4		275.2.z.a.49.3		16
5.3	odd	4		275.2.z.a.49.2		16
5.4	even	2		55.2.g.b.16.2	✓	8
11.3	even	5		3025.2.a.bd.1.2		4
11.8	odd	10		3025.2.a.w.1.3		4
11.9	even	5	inner	275.2.h.a.251.1		8
15.14	odd	2		495.2.n.e.181.1		8
20.19	odd	2		880.2.bo.h.401.1		8
55.4	even	10		605.2.g.m.366.1		8
55.9	even	10		55.2.g.b.31.2	yes	8
55.14	even	10		605.2.a.j.1.3		4
55.19	odd	10		605.2.a.k.1.2		4
55.24	odd	10		605.2.g.k.251.1		8
55.29	odd	10		605.2.g.e.366.2		8
55.39	odd	10		605.2.g.e.81.2		8
55.42	odd	20		275.2.z.a.174.2		16
55.49	even	10		605.2.g.m.81.1		8
55.53	odd	20		275.2.z.a.174.3		16
55.54	odd	2		605.2.g.k.511.1		8
165.14	odd	10		5445.2.a.bp.1.2		4
165.74	even	10		5445.2.a.bi.1.3		4
165.119	odd	10		495.2.n.e.361.1		8
220.19	even	10		9680.2.a.cm.1.3		4
220.119	odd	10		880.2.bo.h.801.1		8
220.179	odd	10		9680.2.a.cn.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.16.2	✓	8	5.4	even	2
55.2.g.b.31.2	yes	8	55.9	even	10
275.2.h.a.126.1		8	1.1	even	1	trivial
275.2.h.a.251.1		8	11.9	even	5	inner
275.2.z.a.49.2		16	5.3	odd	4
275.2.z.a.49.3		16	5.2	odd	4
275.2.z.a.174.2		16	55.42	odd	20
275.2.z.a.174.3		16	55.53	odd	20
495.2.n.e.181.1		8	15.14	odd	2
495.2.n.e.361.1		8	165.119	odd	10
605.2.a.j.1.3		4	55.14	even	10
605.2.a.k.1.2		4	55.19	odd	10
605.2.g.e.81.2		8	55.39	odd	10
605.2.g.e.366.2		8	55.29	odd	10
605.2.g.k.251.1		8	55.24	odd	10
605.2.g.k.511.1		8	55.54	odd	2
605.2.g.m.81.1		8	55.49	even	10
605.2.g.m.366.1		8	55.4	even	10
880.2.bo.h.401.1		8	20.19	odd	2
880.2.bo.h.801.1		8	220.119	odd	10
3025.2.a.w.1.3		4	11.8	odd	10
3025.2.a.bd.1.2		4	11.3	even	5
5445.2.a.bi.1.3		4	165.74	even	10
5445.2.a.bp.1.2		4	165.14	odd	10
9680.2.a.cm.1.3		4	220.19	even	10
9680.2.a.cn.1.3		4	220.179	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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