LMFDB - Embedded newform 475.2.l.b.351.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(101,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("475.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.l (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 12 x^{16} - 8 x^{15} + 96 x^{14} - 75 x^{13} + 448 x^{12} - 405 x^{11} + 1521 x^{10} + \cdots + 361 $ x^18 + 12x^16 - 8x^15 + 96x^14 - 75x^13 + 448x^12 - 405x^11 + 1521x^10 - 1294x^9 + 3333x^8 - 2616x^7 + 5113x^6 - 3126x^5 + 4032x^4 - 1359x^3 + 1698x^2 - 513x + 361
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			351.3
Root			$0.731154 + 1.26640i$ of defining polynomial
Character	$\chi$	$=$	475.351
Dual form			475.2.l.b.226.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.253927 + 1.44009i) q^{2} +(-1.15700 + 0.970838i) q^{3} +(-0.130002 + 0.0473169i) q^{4} +(-1.69189 - 1.41966i) q^{6} +(2.03586 - 3.52622i) q^{7} +(1.36116 + 2.35759i) q^{8} +(-0.124823 + 0.707907i) q^{9} +O(q^{10})$	\(q+(0.253927 + 1.44009i) q^{2} +(-1.15700 + 0.970838i) q^{3} +(-0.130002 + 0.0473169i) q^{4} +(-1.69189 - 1.41966i) q^{6} +(2.03586 - 3.52622i) q^{7} +(1.36116 + 2.35759i) q^{8} +(-0.124823 + 0.707907i) q^{9} +(0.310503 + 0.537807i) q^{11} +(0.104475 - 0.180957i) q^{12} +(3.90168 + 3.27390i) q^{13} +(5.59504 + 2.03643i) q^{14} +(-3.26147 + 2.73670i) q^{16} +(0.0462744 + 0.262435i) q^{17} -1.05115 q^{18} +(0.399960 + 4.34051i) q^{19} +(1.06789 + 6.05632i) q^{21} +(-0.695646 + 0.583716i) q^{22} +(-5.48944 + 1.99799i) q^{23} +(-3.86370 - 1.40627i) q^{24} +(-3.72398 + 6.45012i) q^{26} +(-2.80837 - 4.86425i) q^{27} +(-0.0978169 + 0.554747i) q^{28} +(0.708058 - 4.01560i) q^{29} +(3.24496 - 5.62043i) q^{31} +(-0.598455 - 0.502163i) q^{32} +(-0.881374 - 0.320794i) q^{33} +(-0.366180 + 0.133279i) q^{34} +(-0.0172687 - 0.0979357i) q^{36} +8.83927 q^{37} +(-6.14918 + 1.67815i) q^{38} -7.69267 q^{39} +(-3.43252 + 2.88022i) q^{41} +(-8.45050 + 3.07573i) q^{42} +(-1.69213 - 0.615885i) q^{43} +(-0.0658134 - 0.0552240i) q^{44} +(-4.27121 - 7.39795i) q^{46} +(-2.00502 + 11.3711i) q^{47} +(1.11663 - 6.33272i) q^{48} +(-4.78947 - 8.29561i) q^{49} +(-0.308321 - 0.258712i) q^{51} +(-0.662139 - 0.240999i) q^{52} +(-2.37077 + 0.862891i) q^{53} +(6.29184 - 5.27948i) q^{54} +11.0845 q^{56} +(-4.67668 - 4.63367i) q^{57} +5.96263 q^{58} +(0.154624 + 0.876916i) q^{59} +(-2.03905 + 0.742153i) q^{61} +(8.91792 + 3.24586i) q^{62} +(2.24211 + 1.88135i) q^{63} +(-3.68635 + 6.38495i) q^{64} +(0.238168 - 1.35072i) q^{66} +(2.44476 - 13.8649i) q^{67} +(-0.0184334 - 0.0319276i) q^{68} +(4.41155 - 7.64103i) q^{69} +(1.54737 + 0.563198i) q^{71} +(-1.83886 + 0.669290i) q^{72} +(-1.37639 + 1.15493i) q^{73} +(2.24453 + 12.7294i) q^{74} +(-0.257375 - 0.545351i) q^{76} +2.52856 q^{77} +(-1.95338 - 11.0782i) q^{78} +(3.94242 - 3.30809i) q^{79} +(5.94525 + 2.16389i) q^{81} +(-5.01940 - 4.21177i) q^{82} +(6.89167 - 11.9367i) q^{83} +(-0.425395 - 0.736806i) q^{84} +(0.457253 - 2.59321i) q^{86} +(3.07927 + 5.33345i) q^{87} +(-0.845286 + 1.46408i) q^{88} +(-0.000572418 - 0.000480315i) q^{89} +(19.4878 - 7.09297i) q^{91} +(0.619100 - 0.519487i) q^{92} +(1.70211 + 9.65316i) q^{93} -16.8845 q^{94} +1.17993 q^{96} +(1.80985 + 10.2642i) q^{97} +(10.7303 - 9.00376i) q^{98} +(-0.419475 + 0.152676i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 12 q^{8} - 21 q^{9}+O(q^{10}) $ 18 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 12 * q^8 - 21 * q^9	$ 18 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 12 q^{8} - 21 q^{9} - 6 q^{12} + 3 q^{13} + 24 q^{14} + 21 q^{16} + 24 q^{17} + 12 q^{18} - 12 q^{19} + 3 q^{21} - 15 q^{22} - 21 q^{23} + 21 q^{24} - 21 q^{26} - 6 q^{27} + 24 q^{28} - 9 q^{29} + 30 q^{31} - 45 q^{32} + 3 q^{33} + 24 q^{34} - 21 q^{36} + 60 q^{37} + 15 q^{38} + 12 q^{39} - 6 q^{41} - 39 q^{42} + 6 q^{43} - 30 q^{44} + 21 q^{46} - 33 q^{47} + 63 q^{48} - 3 q^{49} + 27 q^{51} - 9 q^{52} - 24 q^{53} + 30 q^{54} - 72 q^{56} + 30 q^{57} - 36 q^{58} + 18 q^{59} + 6 q^{61} - 12 q^{62} - 24 q^{63} - 24 q^{64} - 33 q^{66} + 24 q^{67} + 3 q^{68} + 27 q^{69} + 24 q^{71} - 18 q^{72} - 6 q^{73} - 39 q^{74} + 27 q^{76} - 24 q^{77} - 72 q^{78} + 9 q^{79} + 15 q^{81} + 57 q^{82} - 12 q^{84} - 33 q^{86} + 45 q^{87} - 39 q^{88} - 6 q^{89} - 6 q^{91} + 66 q^{92} + 72 q^{93} - 66 q^{94} - 18 q^{96} + 87 q^{97} - 39 q^{98} + 3 q^{99}+O(q^{100}) $ 18 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 12 * q^8 - 21 * q^9 - 6 * q^12 + 3 * q^13 + 24 * q^14 + 21 * q^16 + 24 * q^17 + 12 * q^18 - 12 * q^19 + 3 * q^21 - 15 * q^22 - 21 * q^23 + 21 * q^24 - 21 * q^26 - 6 * q^27 + 24 * q^28 - 9 * q^29 + 30 * q^31 - 45 * q^32 + 3 * q^33 + 24 * q^34 - 21 * q^36 + 60 * q^37 + 15 * q^38 + 12 * q^39 - 6 * q^41 - 39 * q^42 + 6 * q^43 - 30 * q^44 + 21 * q^46 - 33 * q^47 + 63 * q^48 - 3 * q^49 + 27 * q^51 - 9 * q^52 - 24 * q^53 + 30 * q^54 - 72 * q^56 + 30 * q^57 - 36 * q^58 + 18 * q^59 + 6 * q^61 - 12 * q^62 - 24 * q^63 - 24 * q^64 - 33 * q^66 + 24 * q^67 + 3 * q^68 + 27 * q^69 + 24 * q^71 - 18 * q^72 - 6 * q^73 - 39 * q^74 + 27 * q^76 - 24 * q^77 - 72 * q^78 + 9 * q^79 + 15 * q^81 + 57 * q^82 - 12 * q^84 - 33 * q^86 + 45 * q^87 - 39 * q^88 - 6 * q^89 - 6 * q^91 + 66 * q^92 + 72 * q^93 - 66 * q^94 - 18 * q^96 + 87 * q^97 - 39 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	0.253927	+	1.44009i	0.179554	+	1.01830i	0.932755	+	0.360510i	$0.117397\pi$
$2$	0.253927	+	1.44009i	0.179554	+	1.01830i	−0.753202	+	0.657789i	$0.771492\pi$
$3$	−1.15700	+	0.970838i	−0.667994	+	0.560513i	−0.912471	−	0.409142i	$-0.865828\pi$
$3$	−1.15700	+	0.970838i	−0.667994	+	0.560513i	0.244477	+	0.969655i	$0.421384\pi$
$4$	−0.130002	+	0.0473169i	−0.0650011	+	0.0236585i
$5$		0			0
$5$		0			0
$6$	−1.69189	−	1.41966i	−0.690711	−	0.579575i
$7$	2.03586	−	3.52622i	0.769484	−	1.33278i	−0.168360	−	0.985726i	$-0.553847\pi$
$7$	2.03586	−	3.52622i	0.769484	−	1.33278i	0.937843	−	0.347059i	$-0.112820\pi$
$8$	1.36116	+	2.35759i	0.481241	+	0.833535i
$9$	−0.124823	+	0.707907i	−0.0416077	+	0.235969i
$10$		0			0
$11$	0.310503	+	0.537807i	0.0936201	+	0.162155i	0.909032	−	0.416727i	$-0.136823\pi$
$11$	0.310503	+	0.537807i	0.0936201	+	0.162155i	−0.815412	+	0.578881i	$0.803489\pi$
$12$	0.104475	−	0.180957i	0.0301595	−	0.0522377i
$13$	3.90168	+	3.27390i	1.08213	+	0.908017i	0.996096	−	0.0882750i	$-0.0281354\pi$
$13$	3.90168	+	3.27390i	1.08213	+	0.908017i	0.0860363	+	0.996292i	$0.472580\pi$
$14$	5.59504	+	2.03643i	1.49534	+	0.544258i
$15$		0			0
$16$	−3.26147	+	2.73670i	−0.815368	+	0.684175i
$17$	0.0462744	+	0.262435i	0.0112232	+	0.0636498i	0.989905	−	0.141733i	$-0.0452673\pi$
$17$	0.0462744	+	0.262435i	0.0112232	+	0.0636498i	−0.978682	+	0.205382i	$0.934156\pi$
$18$	−1.05115			−0.247758
$19$	0.399960	+	4.34051i	0.0917571	+	0.995781i
$19$	0.399960	+	4.34051i	0.0917571	+	0.995781i
$20$		0			0
$21$	1.06789	+	6.05632i	0.233033	+	1.32160i
$22$	−0.695646	+	0.583716i	−0.148312	+	0.124449i
$23$	−5.48944	+	1.99799i	−1.14463	+	0.416610i	−0.843582	−	0.537000i	$-0.819558\pi$
$23$	−5.48944	+	1.99799i	−1.14463	+	0.416610i	−0.301045	+	0.953610i	$0.597335\pi$
$24$	−3.86370	−	1.40627i	−0.788674	−	0.287054i
$25$		0			0
$26$	−3.72398	+	6.45012i	−0.730332	+	1.26497i
$27$	−2.80837	−	4.86425i	−0.540472	−	0.936125i
$28$	−0.0978169	+	0.554747i	−0.0184856	+	0.104837i
$29$	0.708058	−	4.01560i	0.131483	−	0.745678i	−0.845761	−	0.533561i	$-0.820853\pi$
$29$	0.708058	−	4.01560i	0.131483	−	0.745678i	0.977244	−	0.212116i	$-0.0680356\pi$
$30$		0			0
$31$	3.24496	−	5.62043i	0.582811	−	1.00946i	−0.412333	−	0.911033i	$-0.635286\pi$
$31$	3.24496	−	5.62043i	0.582811	−	1.00946i	0.995144	−	0.0984257i	$-0.0313807\pi$
$32$	−0.598455	−	0.502163i	−0.105793	−	0.0887708i
$33$	−0.881374	−	0.320794i	−0.153428	−	0.0558431i
$34$	−0.366180	+	0.133279i	−0.0627994	+	0.0228571i
$35$		0			0
$36$	−0.0172687	−	0.0979357i	−0.00287812	−	0.0163226i
$37$	8.83927			1.45317			0.726584	−	0.687078i	$-0.241107\pi$
$37$	8.83927			1.45317			0.726584	+	0.687078i	$0.241107\pi$
$38$	−6.14918	+	1.67815i	−0.997528	+	0.272232i
$39$	−7.69267			−1.23181
$40$		0			0
$41$	−3.43252	+	2.88022i	−0.536069	+	0.449815i	−0.870191	−	0.492714i	$-0.836005\pi$
$41$	−3.43252	+	2.88022i	−0.536069	+	0.449815i	0.334122	+	0.942530i	$0.391560\pi$
$42$	−8.45050	+	3.07573i	−1.30394	+	0.474595i
$43$	−1.69213	−	0.615885i	−0.258047	−	0.0939215i	0.209757	−	0.977753i	$-0.432733\pi$
$43$	−1.69213	−	0.615885i	−0.258047	−	0.0939215i	−0.467804	+	0.883832i	$0.654955\pi$
$44$	−0.0658134	−	0.0552240i	−0.00992175	−	0.00832533i
$45$		0			0
$46$	−4.27121	−	7.39795i	−0.629756	−	1.09077i
$47$	−2.00502	+	11.3711i	−0.292463	+	1.65864i	0.384877	+	0.922968i	$0.374244\pi$
$47$	−2.00502	+	11.3711i	−0.292463	+	1.65864i	−0.677339	+	0.735671i	$0.736867\pi$
$48$	1.11663	−	6.33272i	0.161172	−	0.914050i
$49$	−4.78947	−	8.29561i	−0.684210	−	1.18509i
$50$		0			0
$51$	−0.308321	−	0.258712i	−0.0431736	−	0.0362269i
$52$	−0.662139	−	0.240999i	−0.0918221	−	0.0334205i
$53$	−2.37077	+	0.862891i	−0.325651	+	0.118527i	−0.499672	−	0.866215i	$-0.666546\pi$
$53$	−2.37077	+	0.862891i	−0.325651	+	0.118527i	0.174021	+	0.984742i	$0.444324\pi$
$54$	6.29184	−	5.27948i	0.856212	−	0.718447i
$55$		0			0
$56$	11.0845			1.48123
$57$	−4.67668	−	4.63367i	−0.619442	−	0.613745i
$58$	5.96263			0.782931
$59$	0.154624	+	0.876916i	0.0201303	+	0.114165i	0.993217	−	0.116274i	$-0.0370950\pi$
$59$	0.154624	+	0.876916i	0.0201303	+	0.114165i	−0.973087	+	0.230439i	$0.925984\pi$
$60$		0			0
$61$	−2.03905	+	0.742153i	−0.261073	+	0.0950229i	−0.469241	−	0.883070i	$-0.655472\pi$
$61$	−2.03905	+	0.742153i	−0.261073	+	0.0950229i	0.208167	+	0.978093i	$0.433250\pi$
$62$	8.91792	+	3.24586i	1.13258	+	0.412224i
$63$	2.24211	+	1.88135i	0.282479	+	0.237028i
$64$	−3.68635	+	6.38495i	−0.460794	+	0.798119i
$65$		0			0
$66$	0.238168	−	1.35072i	0.0293165	−	0.166262i
$67$	2.44476	−	13.8649i	0.298674	−	1.69387i	−0.353206	−	0.935546i	$-0.614909\pi$
$67$	2.44476	−	13.8649i	0.298674	−	1.69387i	0.651881	−	0.758322i	$-0.273980\pi$
$68$	−0.0184334	−	0.0319276i	−0.00223538	−	0.00387179i
$69$	4.41155	−	7.64103i	0.531088	−	0.919872i
$70$		0			0
$71$	1.54737	+	0.563198i	0.183639	+	0.0668393i	0.432203	−	0.901776i	$-0.357736\pi$
$71$	1.54737	+	0.563198i	0.183639	+	0.0668393i	−0.248564	+	0.968616i	$0.579959\pi$
$72$	−1.83886	+	0.669290i	−0.216712	+	0.0788766i
$73$	−1.37639	+	1.15493i	−0.161095	+	0.135174i	−0.719772	−	0.694211i	$-0.755754\pi$
$73$	−1.37639	+	1.15493i	−0.161095	+	0.135174i	0.558677	+	0.829385i	$0.311309\pi$
$74$	2.24453	+	12.7294i	0.260922	+	1.47976i
$75$		0			0
$76$	−0.257375	−	0.545351i	−0.0295230	−	0.0625561i
$77$	2.52856			0.288157
$78$	−1.95338	−	11.0782i	−0.221177	−	1.25435i
$79$	3.94242	−	3.30809i	0.443557	−	0.372189i	−0.393481	−	0.919333i	$-0.628729\pi$
$79$	3.94242	−	3.30809i	0.443557	−	0.372189i	0.837039	+	0.547144i	$0.184285\pi$
$80$		0			0
$81$	5.94525	+	2.16389i	0.660584	+	0.240433i
$82$	−5.01940	−	4.21177i	−0.554300	−	0.465113i
$83$	6.89167	−	11.9367i	0.756459	−	1.31023i	−0.188187	−	0.982133i	$-0.560261\pi$
$83$	6.89167	−	11.9367i	0.756459	−	1.31023i	0.944646	−	0.328092i	$-0.106406\pi$
$84$	−0.425395	−	0.736806i	−0.0464144	−	0.0803921i
$85$		0			0
$86$	0.457253	−	2.59321i	0.0493069	−	0.279633i
$87$	3.07927	+	5.33345i	0.330132	+	0.571806i
$88$	−0.845286	+	1.46408i	−0.0901078	+	0.156071i
$89$	−0.000572418	0	0.000480315i	−6.06762e−5	0	5.09133e-5i	0.642757	−	0.766070i	$-0.277790\pi$
$89$	−0.000572418	0	0.000480315i	−6.06762e−5	0	5.09133e-5i	−0.642818	+	0.766019i	$0.722235\pi$
$90$		0			0
$91$	19.4878	−	7.09297i	2.04287	−	0.743545i
$92$	0.619100	−	0.519487i	0.0645457	−	0.0541603i
$93$	1.70211	+	9.65316i	0.176501	+	1.00099i
$94$	−16.8845			−1.74150
$95$		0			0
$96$	1.17993			0.120426
$97$	1.80985	+	10.2642i	0.183762	+	1.04217i	0.927535	+	0.373736i	$0.121923\pi$
$97$	1.80985	+	10.2642i	0.183762	+	1.04217i	−0.743773	+	0.668432i	$0.766966\pi$
$98$	10.7303	−	9.00376i	1.08392	−	0.909517i
$99$	−0.419475	+	0.152676i	−0.0421588	+	0.0153445i
$100$		0			0
$101$	−9.36086	−	7.85469i	−0.931440	−	0.781571i	0.0446350	−	0.999003i	$-0.485788\pi$
$101$	−9.36086	−	7.85469i	−0.931440	−	0.781571i	−0.976075	+	0.217432i	$0.930232\pi$
$102$	0.294278	−	0.509705i	0.0291379	−	0.0504683i
$103$	−3.90186	−	6.75822i	−0.384462	−	0.665908i	0.607232	−	0.794524i	$-0.292280\pi$
$103$	−3.90186	−	6.75822i	−0.384462	−	0.665908i	−0.991694	+	0.128617i	$0.958946\pi$
$104$	−2.40772	+	13.6549i	−0.236097	+	1.33897i
$105$		0			0
$106$	−1.84465	−	3.19502i	−0.179168	−	0.310328i
$107$	2.85207	−	4.93993i	0.275720	−	0.477561i	−0.694597	−	0.719399i	$-0.744417\pi$
$107$	2.85207	−	4.93993i	0.275720	−	0.477561i	0.970316	+	0.241839i	$0.0777505\pi$
$108$	0.595256	+	0.499479i	0.0572786	+	0.0480624i
$109$	6.32712	+	2.30288i	0.606029	+	0.220576i	0.626765	−	0.779209i	$-0.284379\pi$
$109$	6.32712	+	2.30288i	0.606029	+	0.220576i	−0.0207361	+	0.999785i	$0.506601\pi$
$110$		0			0
$111$	−10.2270	+	8.58150i	−0.970707	+	0.814520i
$112$	3.01029	+	17.0722i	0.284446	+	1.61317i
$113$	4.78878			0.450490			0.225245	−	0.974302i	$-0.427682\pi$
$113$	4.78878			0.450490			0.225245	+	0.974302i	$0.427682\pi$
$114$	5.48538	−	7.91147i	0.513753	−	0.740977i
$115$		0			0
$116$	0.0979567	+	0.555540i	0.00909505	+	0.0515806i
$117$	−2.80464	+	2.35337i	−0.259289	+	0.217569i
$118$	−1.22358	+	0.445346i	−0.112639	+	0.0409974i
$119$	1.01961	+	0.371108i	0.0934676	+	0.0340194i
$120$		0			0
$121$	5.30718	−	9.19230i	0.482471	−	0.835664i
$122$	−1.58654	−	2.74796i	−0.143638	−	0.248789i
$123$	1.17519	−	6.66483i	0.105963	−	0.600948i
$124$	−0.155910	+	0.884210i	−0.0140011	+	0.0794044i
$125$		0			0
$126$	−2.13999	+	3.70657i	−0.190646	+	0.330208i
$127$	−14.1693	−	11.8894i	−1.25732	−	1.05502i	−0.995962	−	0.0897732i	$-0.971386\pi$
$127$	−14.1693	−	11.8894i	−1.25732	−	1.05502i	−0.261356	−	0.965242i	$-0.584170\pi$
$128$	−11.5992	−	4.22177i	−1.02524	−	0.373155i
$129$	2.55572	−	0.930204i	0.225018	−	0.0818999i
$130$		0			0
$131$	−3.40080	−	19.2869i	−0.297129	−	1.68510i	−0.658420	−	0.752650i	$-0.728775\pi$
$131$	−3.40080	−	19.2869i	−0.297129	−	1.68510i	0.361291	−	0.932453i	$-0.382336\pi$
$132$	0.129760			0.0112941
$133$	16.1198	+	7.42634i	1.39777	+	0.643945i
$134$	20.5875			1.77849
$135$		0			0
$136$	−0.555728	+	0.466311i	−0.0476533	+	0.0399858i
$137$	−2.21454	+	0.806027i	−0.189201	+	0.0688635i	−0.434883	−	0.900487i	$-0.643210\pi$
$137$	−2.21454	+	0.806027i	−0.189201	+	0.0688635i	0.245682	+	0.969350i	$0.420988\pi$
$138$	12.1240	+	4.41278i	1.03206	+	0.375640i
$139$	2.93433	+	2.46220i	0.248887	+	0.208841i	0.758693	−	0.651448i	$-0.225838\pi$
$139$	2.93433	+	2.46220i	0.248887	+	0.208841i	−0.509806	+	0.860289i	$0.670283\pi$
$140$		0			0
$141$	−8.71964	−	15.1029i	−0.734326	−	1.27189i
$142$	−0.418137	+	2.37137i	−0.0350893	+	0.199001i
$143$	−0.549242	+	3.11491i	−0.0459299	+	0.260482i
$144$	−1.53022	−	2.65042i	−0.127519	−	0.220869i
$145$		0			0
$146$	−2.01271	−	1.68887i	−0.166573	−	0.139772i
$147$	13.5951	+	4.94821i	1.12130	+	0.408122i
$148$	−1.14913	+	0.418247i	−0.0944575	+	0.0343797i
$149$	13.9310	−	11.6895i	1.14127	−	0.957638i	0.141789	−	0.989897i	$-0.454714\pi$
$149$	13.9310	−	11.6895i	1.14127	−	0.957638i	0.999480	+	0.0322585i	$0.0102700\pi$
$150$		0			0
$151$	−2.29340			−0.186634			−0.0933170	−	0.995636i	$-0.529747\pi$
$151$	−2.29340			−0.186634			−0.0933170	+	0.995636i	$0.529747\pi$
$152$	−9.68875	+	6.85106i	−0.785861	+	0.555694i
$153$	−0.191556			−0.0154863
$154$	0.642071	+	3.64137i	0.0517396	+	0.293430i
$155$		0			0
$156$	1.00006	−	0.363994i	0.0800693	−	0.0291428i
$157$	−19.5874	−	7.12925i	−1.56325	−	0.568976i	−0.591771	−	0.806106i	$-0.701571\pi$
$157$	−19.5874	−	7.12925i	−1.56325	−	0.568976i	−0.971478	+	0.237130i	$0.923793\pi$
$158$	5.76504	+	4.83744i	0.458642	+	0.384846i
$159$	1.90526	−	3.30000i	0.151097	−	0.261707i
$160$		0			0
$161$	−4.13039	+	23.4246i	−0.325520	+	1.84612i
$162$	−1.60655	+	9.11119i	−0.126222	+	0.715842i
$163$	−3.95845	−	6.85624i	−0.310050	−	0.537022i	0.668323	−	0.743871i	$-0.267012\pi$
$163$	−3.95845	−	6.85624i	−0.310050	−	0.537022i	−0.978373	+	0.206849i	$0.933679\pi$
$164$	0.309952	−	0.536852i	0.0242031	−	0.0419211i
$165$		0			0
$166$	18.9400	+	6.89358i	1.47003	+	0.535046i
$167$	13.2435	−	4.82025i	1.02482	−	0.373002i	0.225711	−	0.974194i	$-0.427530\pi$
$167$	13.2435	−	4.82025i	1.02482	−	0.373002i	0.799105	+	0.601192i	$0.205307\pi$
$168$	−12.8248	+	10.7613i	−0.989452	+	0.830249i
$169$	2.24728	+	12.7450i	0.172868	+	0.980382i
$170$		0			0
$171$	−3.12260	−	0.258662i	−0.238791	−	0.0197803i
$172$	0.249122			0.0189954
$173$	1.82553	+	10.3531i	0.138792	+	0.787130i	0.972144	+	0.234386i	$0.0753081\pi$
$173$	1.82553	+	10.3531i	0.138792	+	0.787130i	−0.833351	+	0.552744i	$0.813581\pi$
$174$	−6.89876	+	5.78874i	−0.522993	+	0.438843i
$175$		0			0
$176$	−2.48451	−	0.904289i	−0.187277	−	0.0681633i
$177$	−1.03024	−	0.864477i	−0.0774378	−	0.0649780i
$178$	0.000546346	0	0.000946300i	4.09504e−5	0	7.09282e-5i
$179$	−2.50164	−	4.33298i	−0.186982	−	0.323862i	0.757261	−	0.653113i	$-0.226537\pi$
$179$	−2.50164	−	4.33298i	−0.186982	−	0.323862i	−0.944243	+	0.329251i	$0.893204\pi$
$180$		0			0
$181$	−4.60022	+	26.0891i	−0.341932	+	1.93919i	0.00146347	+	0.999999i	$0.499534\pi$
$181$	−4.60022	+	26.0891i	−0.341932	+	1.93919i	−0.343395	+	0.939191i	$0.611577\pi$
$182$	15.1630	+	26.2631i	1.12396	+	1.94675i
$183$	1.63867	−	2.83825i	0.121134	−	0.209810i
$184$	−12.1824	−	10.2223i	−0.898101	−	0.753596i
$185$		0			0
$186$	−13.4692	+	4.90240i	−0.987612	+	0.359461i
$187$	−0.126771	+	0.106373i	−0.00927041	+	0.00777879i
$188$	−0.277386	−	1.57313i	−0.0202305	−	0.114733i
$189$	−22.8699			−1.66354
$190$		0			0
$191$	−0.143815			−0.0104061			−0.00520303	−	0.999986i	$-0.501656\pi$
$191$	−0.143815			−0.0104061			−0.00520303	+	0.999986i	$0.501656\pi$
$192$	−1.93364	−	10.9662i	−0.139549	−	0.791420i
$193$	−1.57893	+	1.32488i	−0.113654	+	0.0953669i	−0.697843	−	0.716250i	$-0.745857\pi$
$193$	−1.57893	+	1.32488i	−0.113654	+	0.0953669i	0.584190	+	0.811617i	$0.301412\pi$
$194$	−14.3218	+	5.21270i	−1.02824	+	0.374250i
$195$		0			0
$196$	1.01516	+	0.851824i	0.0725118	+	0.0608446i
$197$	9.12413	−	15.8035i	0.650068	−	1.12595i	−0.333038	−	0.942913i	$-0.608074\pi$
$197$	9.12413	−	15.8035i	0.650068	−	1.12595i	0.983106	−	0.183037i	$-0.0585928\pi$
$198$	−0.326384	−	0.565314i	−0.0231951	−	0.0401751i
$199$	1.38971	−	7.88142i	0.0985137	−	0.558699i	−0.895100	−	0.445865i	$-0.852896\pi$
$199$	1.38971	−	7.88142i	0.0985137	−	0.558699i	0.993614	−	0.112834i	$-0.0359928\pi$
$200$		0			0
$201$	10.6320	+	18.4151i	0.749922	+	1.29890i
$202$	8.93451	−	15.4750i	0.628630	−	1.08882i
$203$	−12.7184	−	10.6720i	−0.892654	−	0.749026i
$204$	0.0523239	+	0.0190443i	0.00366341	+	0.00133337i
$205$		0			0
$206$	8.74168	−	7.33514i	0.609062	−	0.511063i
$207$	−0.729184	−	4.13541i	−0.0506818	−	0.287431i
$208$	−21.6849			−1.50358
$209$	−2.21017	+	1.56284i	−0.152880	+	0.108104i
$210$		0			0
$211$	−2.44545	−	13.8689i	−0.168352	−	0.954772i	−0.945541	−	0.325504i	$-0.894466\pi$
$211$	−2.44545	−	13.8689i	−0.168352	−	0.954772i	0.777189	−	0.629268i	$-0.216645\pi$
$212$	0.267377	−	0.224356i	0.0183635	−	0.0154088i
$213$	−2.33708	+	0.850628i	−0.160134	+	0.0582841i
$214$	7.83817	+	2.85286i	0.535806	+	0.195018i
$215$		0			0
$216$	7.64528	−	13.2420i	0.520195	−	0.901004i
$217$	−13.2126	−	22.8848i	−0.896928	−	1.55352i
$218$	−1.70974	+	9.69641i	−0.115798	+	0.656724i
$219$	0.471235	−	2.67251i	0.0318431	−	0.180591i
$220$		0			0
$221$	−0.678638	+	1.17544i	−0.0456501	+	0.0790684i
$222$	−14.9551	−	12.5488i	−1.00372	−	0.842220i
$223$	4.61022	+	1.67798i	0.308723	+	0.112366i	0.491736	−	0.870744i	$-0.336363\pi$
$223$	4.61022	+	1.67798i	0.308723	+	0.112366i	−0.183012	+	0.983111i	$0.558585\pi$
$224$	−2.98911	+	1.08795i	−0.199718	+	0.0726915i
$225$		0			0
$226$	1.21600	+	6.89629i	0.0808872	+	0.458734i
$227$	−2.65246			−0.176050			−0.0880250	−	0.996118i	$-0.528056\pi$
$227$	−2.65246			−0.176050			−0.0880250	+	0.996118i	$0.528056\pi$
$228$	0.827231	+	0.381101i	0.0547847	+	0.0252390i
$229$	−23.1372			−1.52895			−0.764473	−	0.644655i	$-0.777001\pi$
$229$	−23.1372			−1.52895			−0.764473	+	0.644655i	$0.777001\pi$
$230$		0			0
$231$	−2.92555	+	2.45482i	−0.192487	+	0.161516i
$232$	10.4309	−	3.79654i	0.684823	−	0.249255i
$233$	−27.1663	−	9.88772i	−1.77972	−	0.647766i	−0.999759	−	0.0219420i	$-0.993015\pi$
$233$	−27.1663	−	9.88772i	−1.77972	−	0.647766i	−0.779964	−	0.625824i	$-0.784763\pi$
$234$	−4.10124	−	3.44135i	−0.268107	−	0.224968i
$235$		0			0
$236$	−0.0615945	−	0.106685i	−0.00400946	−	0.00694458i
$237$	−1.34977	+	7.65490i	−0.0876767	+	0.497239i
$238$	−0.275523	+	1.56257i	−0.0178595	+	0.101286i
$239$	10.3736	+	17.9677i	0.671016	+	1.16223i	0.977616	+	0.210395i	$0.0674750\pi$
$239$	10.3736	+	17.9677i	0.671016	+	1.16223i	−0.306601	+	0.951838i	$0.599192\pi$
$240$		0			0
$241$	4.74748	+	3.98361i	0.305812	+	0.256607i	0.782759	−	0.622326i	$-0.213812\pi$
$241$	4.74748	+	3.98361i	0.305812	+	0.256607i	−0.476946	+	0.878932i	$0.658256\pi$
$242$	14.5854	+	5.30865i	0.937585	+	0.341253i
$243$	6.85461	−	2.49487i	0.439724	−	0.160046i
$244$	0.229964	−	0.192963i	0.0147220	−	0.0123532i
$245$		0			0
$246$	9.89639			0.630971
$247$	−12.6499	+	18.2447i	−0.804893	+	1.16088i
$248$	17.6676			1.12189
$249$	3.61496	+	20.5015i	0.229089	+	1.29923i
$250$		0			0
$251$	−7.32016	+	2.66432i	−0.462044	+	0.168170i	−0.562545	−	0.826767i	$-0.690178\pi$
$251$	−7.32016	+	2.66432i	−0.462044	+	0.168170i	0.100501	+	0.994937i	$0.467956\pi$
$252$	−0.380499	−	0.138490i	−0.0239692	−	0.00872408i
$253$	−2.77902	−	2.33187i	−0.174715	−	0.146604i
$254$	13.5239	−	23.4241i	0.848565	−	1.46976i
$255$		0			0
$256$	0.573868	−	3.25456i	0.0358667	−	0.203410i
$257$	−3.50026	+	19.8510i	−0.218340	+	1.23827i	0.656675	+	0.754174i	$0.271962\pi$
$257$	−3.50026	+	19.8510i	−0.218340	+	1.23827i	−0.875015	+	0.484096i	$0.839149\pi$
$258$	1.98855	+	3.44426i	0.123801	+	0.214430i
$259$	17.9955	−	31.1692i	1.11819	−	1.93676i
$260$		0			0
$261$	2.75429	+	1.00248i	0.170486	+	0.0620518i
$262$	26.9114	−	9.79493i	1.66259	−	0.605133i
$263$	−8.18579	+	6.86869i	−0.504758	+	0.423542i	−0.859280	−	0.511506i	$-0.829088\pi$
$263$	−8.18579	+	6.86869i	−0.504758	+	0.423542i	0.354522	+	0.935048i	$0.384643\pi$
$264$	−0.443387	−	2.51457i	−0.0272886	−	0.154761i
$265$		0			0
$266$	−6.60135	+	25.0998i	−0.404754	+	1.53897i
$267$	0.00112860			6.90689e−5
$268$	0.338221	+	1.91815i	0.0206601	+	0.117169i
$269$	−18.3284	+	15.3793i	−1.11750	+	0.937693i	−0.998475	−	0.0551980i	$-0.982421\pi$
$269$	−18.3284	+	15.3793i	−1.11750	+	0.937693i	−0.119024	+	0.992891i	$0.537977\pi$
$270$		0			0
$271$	−24.4040	−	8.88231i	−1.48243	−	0.539562i	−0.530989	−	0.847379i	$-0.678179\pi$
$271$	−24.4040	−	8.88231i	−1.48243	−	0.539562i	−0.951446	+	0.307817i	$0.900402\pi$
$272$	−0.869129	−	0.729285i	−0.0526987	−	0.0442194i
$273$	−15.6612	+	27.1260i	−0.947860	+	1.64174i
$274$	−1.72309	−	2.98447i	−0.104095	−	0.180299i
$275$		0			0
$276$	−0.211961	+	1.20209i	−0.0127586	+	0.0723574i
$277$	−0.916850	−	1.58803i	−0.0550882	−	0.0954156i	0.837166	−	0.546949i	$-0.184211\pi$
$277$	−0.916850	−	1.58803i	−0.0550882	−	0.0954156i	−0.892254	+	0.451533i	$0.850877\pi$
$278$	−2.80069	+	4.85093i	−0.167974	+	0.290940i
$279$	3.57369	+	2.99869i	0.213951	+	0.179527i
$280$		0			0
$281$	12.8592	−	4.68035i	0.767114	−	0.279207i	0.0713251	−	0.997453i	$-0.477277\pi$
$281$	12.8592	−	4.68035i	0.767114	−	0.279207i	0.695789	+	0.718247i	$0.255055\pi$
$282$	19.5354	−	16.3921i	1.16331	−	0.976136i
$283$	−1.82961	−	10.3762i	−0.108759	−	0.616803i	−0.989652	−	0.143488i	$-0.954168\pi$
$283$	−1.82961	−	10.3762i	−0.108759	−	0.616803i	0.880893	−	0.473315i	$-0.156943\pi$
$284$	−0.227811			−0.0135181
$285$		0			0
$286$	−4.62522			−0.273495
$287$	3.16816	+	17.9675i	0.187011	+	1.06059i
$288$	0.430186	−	0.360969i	0.0253489	−	0.0212703i
$289$	15.9080	−	5.79005i	0.935767	−	0.340591i
$290$		0			0
$291$	−12.0588	−	10.1186i	−0.706901	−	0.593161i
$292$	0.124286	−	0.215270i	0.00727331	−	0.0125977i
$293$	11.9521	+	20.7017i	0.698251	+	1.20941i	0.969072	+	0.246776i	$0.0793713\pi$
$293$	11.9521	+	20.7017i	0.698251	+	1.20941i	−0.270822	+	0.962630i	$0.587295\pi$
$294$	−3.67372	+	20.8347i	−0.214256	+	1.21510i
$295$		0			0
$296$	12.0316	+	20.8394i	0.699325	+	1.21127i
$297$	1.74402	−	3.02072i	0.101198	−	0.175280i
$298$	20.3714	+	17.0936i	1.18008	+	0.990206i
$299$	−27.9593	−	10.1763i	−1.61693	−	0.588513i
$300$		0			0
$301$	−5.61668	+	4.71296i	−0.323740	+	0.271650i
$302$	−0.582356	−	3.30271i	−0.0335108	−	0.190049i
$303$	18.4561			1.06028
$304$	−13.1831	−	13.0619i	−0.756105	−	0.749151i
$305$		0			0
$306$	−0.0486412	−	0.275858i	−0.00278063	−	0.0157697i
$307$	−12.0029	+	10.0716i	−0.685040	+	0.574817i	−0.917474	−	0.397795i	$-0.869775\pi$
$307$	−12.0029	+	10.0716i	−0.685040	+	0.574817i	0.232434	+	0.972612i	$0.425331\pi$
$308$	−0.328719	+	0.119644i	−0.0187305	+	0.00681734i
$309$	11.0756	+	4.03118i	0.630068	+	0.229326i
$310$		0			0
$311$	1.75605	−	3.04157i	0.0995764	−	0.172471i	−0.811933	−	0.583751i	$-0.801585\pi$
$311$	1.75605	−	3.04157i	0.0995764	−	0.172471i	0.911509	+	0.411279i	$0.134918\pi$
$312$	−10.4709	−	18.1362i	−0.592800	−	1.02676i
$313$	−0.203702	+	1.15525i	−0.0115139	+	0.0652987i	−0.990023	−	0.140903i	$-0.954999\pi$
$313$	−0.203702	+	1.15525i	−0.0115139	+	0.0652987i	0.978509	+	0.206202i	$0.0661104\pi$
$314$	5.29299	−	30.0180i	0.298701	−	1.69402i
$315$		0			0
$316$	−0.355995	+	0.616602i	−0.0200263	+	0.0346866i
$317$	1.00475	+	0.843086i	0.0564324	+	0.0473524i	0.670568	−	0.741848i	$-0.266051\pi$
$317$	1.00475	+	0.843086i	0.0564324	+	0.0473524i	−0.614135	+	0.789201i	$0.710495\pi$
$318$	5.23610	+	1.90579i	0.293626	+	0.106871i
$319$	2.37947	−	0.866056i	0.133225	−	0.0484898i
$320$		0			0
$321$	1.49603	+	8.48439i	0.0835000	+	0.473552i
$322$	−34.7824			−1.93835
$323$	−1.12059	+	0.305818i	−0.0623515	+	0.0170162i
$324$	−0.875285			−0.0486270
$325$		0			0
$326$	8.86847	−	7.44153i	0.491179	−	0.412148i
$327$	−9.55620	+	3.47817i	−0.528459	+	0.192343i
$328$	−11.4626	−	4.17204i	−0.632915	−	0.230362i
$329$	36.0148	+	30.2200i	1.98556	+	1.66609i
$330$		0			0
$331$	6.36245	+	11.0201i	0.349712	+	0.605718i	0.986198	−	0.165570i	$-0.0529462\pi$
$331$	6.36245	+	11.0201i	0.349712	+	0.605718i	−0.636487	+	0.771288i	$0.719613\pi$
$332$	−0.331123	+	1.87789i	−0.0181727	+	0.103063i
$333$	−1.10335	+	6.25738i	−0.0604629	+	0.342902i
$334$	10.3045	+	17.8479i	0.563837	+	0.976595i
$335$		0			0
$336$	−20.0572	−	16.8300i	−1.09421	−	0.918153i
$337$	14.3017	+	5.20541i	0.779066	+	0.283557i	0.700783	−	0.713374i	$-0.252834\pi$
$337$	14.3017	+	5.20541i	0.779066	+	0.283557i	0.0782827	+	0.996931i	$0.475056\pi$
$338$	−17.7833	+	6.47258i	−0.967283	+	0.352062i
$339$	−5.54061	+	4.64913i	−0.300925	+	0.252506i
$340$		0			0
$341$	4.03027			0.218251
$342$	−0.420417	−	4.56251i	−0.0227335	−	0.246713i
$343$	−10.5007			−0.566987
$344$	−0.851248	−	4.82766i	−0.0458962	−	0.260290i
$345$		0			0
$346$	−14.4458	+	5.25786i	−0.776613	+	0.282664i
$347$	18.8107	+	6.84652i	1.00981	+	0.367541i	0.793360	−	0.608753i	$-0.208330\pi$
$347$	18.8107	+	6.84652i	1.00981	+	0.367541i	0.216450	+	0.976294i	$0.430552\pi$
$348$	−0.652675	−	0.547659i	−0.0349870	−	0.0293576i
$349$	−11.1408	+	19.2964i	−0.596353	+	1.03291i	0.397002	+	0.917818i	$0.370051\pi$
$349$	−11.1408	+	19.2964i	−0.596353	+	1.03291i	−0.993354	+	0.115095i	$0.963283\pi$
$350$		0			0
$351$	4.96768	−	28.1731i	0.265155	−	1.50377i
$352$	0.0842448	−	0.477776i	0.00449026	−	0.0254655i
$353$	−13.1075	−	22.7029i	−0.697642	−	1.20835i	−0.969282	−	0.245952i	$-0.920899\pi$
$353$	−13.1075	−	22.7029i	−0.697642	−	1.20835i	0.271640	−	0.962399i	$-0.412434\pi$
$354$	0.983319	−	1.70316i	0.0522628	−	0.0905219i
$355$		0			0
$356$	9.71426e−5	0	3.53570e-5i	5.14855e−6	0	1.87392e-6i
$357$	−1.53997	+	0.560505i	−0.0815041	+	0.0296651i
$358$	5.60465	−	4.70286i	0.296215	−	0.248554i
$359$	4.91047	+	27.8486i	0.259164	+	1.46979i	0.785152	+	0.619303i	$0.212585\pi$
$359$	4.91047	+	27.8486i	0.259164	+	1.46979i	−0.525988	+	0.850492i	$0.676304\pi$
$360$		0			0
$361$	−18.6801	+	3.47206i	−0.983161	+	0.182740i
$362$	−38.7389			−2.03607
$363$	2.78383	+	15.7879i	0.146113	+	0.828649i
$364$	−2.19784	+	1.84420i	−0.115198	+	0.0966626i
$365$		0			0
$366$	4.50345	+	1.63912i	0.235399	+	0.0856783i
$367$	7.35010	+	6.16747i	0.383672	+	0.321939i	0.814142	−	0.580666i	$-0.197208\pi$
$367$	7.35010	+	6.16747i	0.383672	+	0.321939i	−0.430470	+	0.902605i	$0.641652\pi$
$368$	12.4358	−	21.5394i	0.648258	−	1.12282i
$369$	−1.61047	−	2.78942i	−0.0838378	−	0.145211i
$370$		0			0
$371$	−1.78383	+	10.1166i	−0.0926117	+	0.525227i
$372$	−0.678036	−	1.17439i	−0.0351545	−	0.0608895i
$373$	6.52003	−	11.2930i	0.337595	−	0.584731i	−0.646385	−	0.763011i	$-0.723720\pi$
$373$	6.52003	−	11.2930i	0.337595	−	0.584731i	0.983980	+	0.178280i	$0.0570534\pi$
$374$	−0.185378	−	0.155551i	−0.00958568	−	0.00804334i
$375$		0			0
$376$	−29.5375	+	10.7508i	−1.52328	+	0.554428i
$377$	15.9093	−	13.3495i	0.819370	−	0.687533i
$378$	−5.80728	−	32.9347i	−0.298694	−	1.69398i
$379$	9.93895			0.510530			0.255265	−	0.966871i	$-0.417837\pi$
$379$	9.93895			0.510530			0.255265	+	0.966871i	$0.417837\pi$
$380$		0			0
$381$	27.9365			1.43123
$382$	−0.0365184	−	0.207106i	−0.00186845	−	0.0105965i
$383$	13.8106	−	11.5885i	0.705689	−	0.592144i	−0.217697	−	0.976017i	$-0.569854\pi$
$383$	13.8106	−	11.5885i	0.705689	−	0.592144i	0.923386	+	0.383873i	$0.125410\pi$
$384$	17.5189	−	6.37637i	0.894009	−	0.325393i
$385$		0			0
$386$	−2.30888	−	1.93738i	−0.117519	−	0.0986102i
$387$	0.647205	−	1.12099i	0.0328993	−	0.0569833i
$388$	−0.720954	−	1.24873i	−0.0366009	−	0.0633946i
$389$	4.22852	−	23.9811i	0.214395	−	1.21589i	−0.667559	−	0.744557i	$-0.732661\pi$
$389$	4.22852	−	23.9811i	0.214395	−	1.21589i	0.881954	−	0.471336i	$-0.156228\pi$
$390$		0			0
$391$	−0.778363	−	1.34816i	−0.0393635	−	0.0681796i
$392$	13.0384	−	22.5832i	0.658541	−	1.14063i
$393$	22.6592	+	19.0133i	1.14300	+	0.959094i
$394$	25.0753	+	9.12667i	1.26328	+	0.459795i
$395$		0			0
$396$	0.0473085	−	0.0396965i	0.00237734	−	0.00199483i
$397$	3.46808	+	19.6684i	0.174058	+	0.987131i	0.939226	+	0.343300i	$0.111545\pi$
$397$	3.46808	+	19.6684i	0.174058	+	0.987131i	−0.765168	+	0.643831i	$0.777344\pi$
$398$	11.7029			0.586611
$399$	−25.8604	+	7.05749i	−1.29464	+	0.353316i
$400$		0			0
$401$	−2.84848	−	16.1545i	−0.142246	−	0.806718i	−0.969537	−	0.244944i	$-0.921230\pi$
$401$	−2.84848	−	16.1545i	−0.142246	−	0.806718i	0.827291	−	0.561774i	$-0.189881\pi$
$402$	−23.8198	+	19.9871i	−1.18802	+	0.996868i
$403$	31.0615	−	11.3055i	1.54728	−	0.563166i
$404$	1.58859	+	0.578201i	0.0790355	+	0.0287666i
$405$		0			0
$406$	12.1391	−	21.0255i	0.602453	−	1.04348i
$407$	2.74462	+	4.75382i	0.136046	+	0.235638i
$408$	0.190264	−	1.07904i	0.00941949	−	0.0534206i
$409$	1.44702	−	8.20643i	0.0715503	−	0.405782i	−0.927906	−	0.372814i	$-0.878393\pi$
$409$	1.44702	−	8.20643i	0.0715503	−	0.405782i	0.999456	−	0.0329680i	$-0.0104960\pi$
$410$		0			0
$411$	1.77970	−	3.08253i	0.0877862	−	0.152050i
$412$	0.827029	+	0.693960i	0.0407448	+	0.0341890i
$413$	3.40699	+	1.24004i	0.167647	+	0.0610185i
$414$	5.77021	−	2.10018i	0.283590	−	0.103218i
$415$		0			0
$416$	−0.690949	−	3.91856i	−0.0338765	−	0.192123i
$417$	−5.78542			−0.283313
$418$	−2.81186	−	2.78600i	−0.137532	−	0.136268i
$419$	−11.6553			−0.569397			−0.284698	−	0.958617i	$-0.591893\pi$
$419$	−11.6553			−0.569397			−0.284698	+	0.958617i	$0.591893\pi$
$420$		0			0
$421$	16.2337	−	13.6217i	0.791182	−	0.663881i	−0.154855	−	0.987937i	$-0.549491\pi$
$421$	16.2337	−	13.6217i	0.791182	−	0.663881i	0.946038	+	0.324056i	$0.105047\pi$
$422$	19.3515	−	7.04336i	0.942015	−	0.342866i
$423$	−7.79937	−	2.83874i	−0.379218	−	0.138024i
$424$	−5.26134	−	4.41479i	−0.255513	−	0.214401i
$425$		0			0
$426$	−1.81843	−	3.14962i	−0.0881033	−	0.152599i
$427$	−1.53423	+	8.70105i	−0.0742465	+	0.421073i
$428$	−0.137033	+	0.777153i	−0.00662374	+	0.0375651i
$429$	−2.38860	−	4.13717i	−0.115322	−	0.199744i
$430$		0			0
$431$	0.300492	+	0.252142i	0.0144742	+	0.0121453i	0.649996	−	0.759938i	$-0.274771\pi$
$431$	0.300492	+	0.252142i	0.0144742	+	0.0121453i	−0.635522	+	0.772083i	$0.719215\pi$
$432$	22.4714	+	8.17893i	1.08116	+	0.393509i
$433$	12.1889	−	4.43639i	0.585761	−	0.213199i	−0.0321031	−	0.999485i	$-0.510220\pi$
$433$	12.1889	−	4.43639i	0.585761	−	0.213199i	0.617864	+	0.786285i	$0.287998\pi$
$434$	29.6013	−	24.8384i	1.42091	−	1.19228i
$435$		0			0
$436$	−0.931506			−0.0446110
$437$	−10.8679	−	23.0278i	−0.519880	−	1.10157i
$438$	3.96832			0.189614
$439$	−0.946035	−	5.36523i	−0.0451518	−	0.256068i	0.953874	−	0.300209i	$-0.0970563\pi$
$439$	−0.946035	−	5.36523i	−0.0451518	−	0.256068i	−0.999025	+	0.0441401i	$0.985945\pi$
$440$		0			0
$441$	6.47035	−	2.35502i	0.308112	−	0.112144i
$442$	−1.86506	−	0.678827i	−0.0887119	−	0.0322885i
$443$	−18.9540	−	15.9043i	−0.900532	−	0.755636i	0.0697627	−	0.997564i	$-0.477776\pi$
$443$	−18.9540	−	15.9043i	−0.900532	−	0.755636i	−0.970294	+	0.241928i	$0.922220\pi$
$444$	0.923487	−	1.59953i	0.0438267	−	0.0759102i
$445$		0			0
$446$	−1.24579	+	7.06523i	−0.0589899	+	0.334549i
$447$	−4.76954	+	27.0494i	−0.225591	+	1.27939i
$448$	15.0098	+	25.9978i	0.709147	+	1.22828i
$449$	−17.2809	+	29.9315i	−0.815538	+	1.41255i	0.0934033	+	0.995628i	$0.470225\pi$
$449$	−17.2809	+	29.9315i	−0.815538	+	1.41255i	−0.908941	+	0.416925i	$0.863108\pi$
$450$		0			0
$451$	−2.61481	−	0.951713i	−0.123127	−	0.0448144i
$452$	−0.622552	+	0.226590i	−0.0292824	+	0.0106579i
$453$	2.65346	−	2.22652i	0.124670	−	0.104611i
$454$	−0.673532	−	3.81979i	−0.0316104	−	0.179272i
$455$		0			0
$456$	4.55861	−	17.3329i	0.213476	−	0.811686i
$457$	11.6425			0.544613			0.272307	−	0.962211i	$-0.412214\pi$
$457$	11.6425			0.544613			0.272307	+	0.962211i	$0.412214\pi$
$458$	−5.87515	−	33.3197i	−0.274528	−	1.55693i
$459$	1.14659	−	0.962106i	0.0535184	−	0.0449072i
$460$		0			0
$461$	−2.80943	−	1.02255i	−0.130848	−	0.0476248i	0.275766	−	0.961225i	$-0.411068\pi$
$461$	−2.80943	−	1.02255i	−0.130848	−	0.0476248i	−0.406614	+	0.913600i	$0.633291\pi$
$462$	−4.27805	−	3.58971i	−0.199033	−	0.167008i
$463$	−4.24358	+	7.35009i	−0.197216	+	0.341588i	−0.947625	−	0.319386i	$-0.896523\pi$
$463$	−4.24358	+	7.35009i	−0.197216	+	0.341588i	0.750409	+	0.660974i	$0.229857\pi$
$464$	8.68018	+	15.0345i	0.402967	+	0.697960i
$465$		0			0
$466$	7.34098	−	41.6327i	0.340064	−	1.92860i
$467$	8.96512	+	15.5280i	0.414856	+	0.718552i	0.995413	−	0.0956676i	$-0.0304986\pi$
$467$	8.96512	+	15.5280i	0.414856	+	0.718552i	−0.580557	+	0.814219i	$0.697165\pi$
$468$	0.253255	−	0.438650i	0.0117067	−	0.0202766i
$469$	−43.9135	−	36.8478i	−2.02774	−	1.70147i
$470$		0			0
$471$	29.5840	−	10.7677i	1.36316	−	0.496149i
$472$	−1.85694	+	1.55816i	−0.0854727	+	0.0717201i
$473$	−0.194184	−	1.10127i	−0.00892859	−	0.0506365i
$474$	−11.3665			−0.522081
$475$		0			0
$476$	−0.150111			−0.00688034
$477$	−0.314919	−	1.78599i	−0.0144192	−	0.0817751i
$478$	−23.2410	+	19.5015i	−1.06302	+	0.891978i
$479$	−3.18514	+	1.15929i	−0.145533	+	0.0529695i	−0.413759	−	0.910386i	$-0.635785\pi$
$479$	−3.18514	+	1.15929i	−0.145533	+	0.0529695i	0.268227	+	0.963356i	$0.413562\pi$
$480$		0			0
$481$	34.4881	+	28.9389i	1.57252	+	1.31950i
$482$	−4.53125	+	7.84836i	−0.206393	+	0.357483i
$483$	−17.9626	−	31.1122i	−0.817327	−	1.41565i
$484$	−0.254993	+	1.44614i	−0.0115906	+	0.0657336i
$485$		0			0
$486$	5.33342	+	9.23776i	0.241929	+	0.419033i
$487$	−5.58098	+	9.66655i	−0.252899	+	0.438033i	−0.964323	−	0.264730i	$-0.914717\pi$
$487$	−5.58098	+	9.66655i	−0.252899	+	0.438033i	0.711424	+	0.702763i	$0.248051\pi$
$488$	−4.52516	−	3.79706i	−0.204844	−	0.171885i
$489$	11.2362	+	4.08965i	0.508120	+	0.184940i
$490$		0			0
$491$	17.6060	−	14.7732i	0.794547	−	0.666704i	−0.152320	−	0.988331i	$-0.548674\pi$
$491$	17.6060	−	14.7732i	0.794547	−	0.666704i	0.946866	+	0.321627i	$0.104230\pi$
$492$	0.162582	+	0.922050i	0.00732977	+	0.0415692i
$493$	1.08660			0.0489379
$494$	−29.4862	−	13.5842i	−1.32665	−	0.611181i
$495$		0			0
$496$	4.79810	+	27.2114i	0.215441	+	1.22183i
$497$	5.13620	−	4.30978i	0.230390	−	0.193320i
$498$	−28.6061	+	10.4118i	−1.28187	+	0.466562i
$499$	−0.921587	−	0.335430i	−0.0412559	−	0.0150159i	0.321310	−	0.946974i	$-0.395877\pi$
$499$	−0.921587	−	0.335430i	−0.0412559	−	0.0150159i	−0.362566	+	0.931958i	$0.618099\pi$
$500$		0			0
$501$	−10.6431	+	18.4343i	−0.475498	+	0.823586i
$502$	−5.69566	−	9.86516i	−0.254210	−	0.440304i
$503$	−0.620262	+	3.51768i	−0.0276561	+	0.156846i	−0.995508	−	0.0946739i	$-0.969819\pi$
$503$	−0.620262	+	3.51768i	−0.0276561	+	0.156846i	0.967852	+	0.251520i	$0.0809303\pi$
$504$	−1.38360	+	7.84680i	−0.0616305	+	0.349524i
$505$		0			0
$506$	2.65245	−	4.59417i	0.117916	−	0.204236i
$507$	−14.9734	−	12.5642i	−0.664991	−	0.557994i
$508$	2.40461	+	0.875205i	0.106687	+	0.0388310i
$509$	12.2069	−	4.44293i	0.541059	−	0.196929i	−0.0570105	−	0.998374i	$-0.518157\pi$
$509$	12.2069	−	4.44293i	0.541059	−	0.196929i	0.598070	+	0.801444i	$0.295935\pi$
$510$		0			0
$511$	1.27039	+	7.20474i	0.0561988	+	0.318719i
$512$	−19.8547			−0.877460
$513$	19.9901	−	14.1353i	0.882584	−	0.624088i
$514$	−29.4761			−1.30013
$515$		0			0
$516$	−0.288234	+	0.241857i	−0.0126888	+	0.0106472i
$517$	−6.73799	+	2.45243i	−0.296337	+	0.107858i
$518$	49.4561	+	18.0005i	2.17298	+	0.790898i
$519$	−12.1633	−	10.2062i	−0.533909	−	0.448003i
$520$		0			0
$521$	−11.4598	−	19.8490i	−0.502064	−	0.869601i	−0.999997	−	0.00238537i	$-0.999241\pi$
$521$	−11.4598	−	19.8490i	−0.502064	−	0.869601i	0.497933	−	0.867216i	$-0.334093\pi$
$522$	−0.744273	+	4.22098i	−0.0325760	+	0.184747i
$523$	−0.342497	+	1.94240i	−0.0149764	+	0.0849352i	−0.991380	−	0.131019i	$-0.958175\pi$
$523$	−0.342497	+	1.94240i	−0.0149764	+	0.0849352i	0.976403	+	0.215954i	$0.0692862\pi$
$524$	1.35471	+	2.34642i	0.0591807	+	0.102504i
$525$		0			0
$526$	−11.9702	−	10.0441i	−0.521923	−	0.437946i
$527$	1.62515	+	0.591508i	0.0707929	+	0.0257665i
$528$	3.75250	−	1.36580i	0.163306	−	0.0594387i
$529$	8.52294	−	7.15159i	0.370563	−	0.310939i
$530$		0			0
$531$	−0.640075			−0.0277769
$532$	−2.44701	−	0.202699i	−0.106091	−	0.00878810i
$533$	−22.8222			−0.988538
$534$	0.000286581		0.00162528i	1.24016e−5		7.03328e-5i
$535$		0			0
$536$	36.0155	−	13.1086i	1.55563	−	0.566204i
$537$	7.10102	+	2.58456i	0.306431	+	0.111532i
$538$	−26.8017	−	22.4893i	−1.15550	−	0.969583i
$539$	2.97429	−	5.15162i	0.128112	−	0.221896i
$540$		0			0
$541$	−4.78002	+	27.1088i	−0.205509	+	1.16550i	0.691128	+	0.722733i	$0.257114\pi$
$541$	−4.78002	+	27.1088i	−0.205509	+	1.16550i	−0.896637	+	0.442767i	$0.853997\pi$
$542$	6.59452	−	37.3994i	0.283259	−	1.60644i
$543$	−20.0059	−	34.6512i	−0.858534	−	1.48702i
$544$	0.104092	−	0.180293i	0.00446291	−	0.00772999i
$545$		0			0
$546$	−43.0408	−	15.6656i	−1.84198	−	0.670425i
$547$	7.84310	−	2.85466i	0.335347	−	0.122056i	−0.168858	−	0.985640i	$-0.554008\pi$
$547$	7.84310	−	2.85466i	0.335347	−	0.122056i	0.504205	+	0.863584i	$0.331786\pi$
$548$	0.249757	−	0.209571i	0.0106691	−	0.00895241i
$549$	−0.270855	−	1.53609i	−0.0115598	−	0.0655589i
$550$		0			0
$551$	17.7129	+	1.46726i	0.754597	+	0.0625072i
$552$	24.0192			1.02233
$553$	−3.63880	−	20.6366i	−0.154737	−	0.877559i
$554$	2.05410	−	1.72359i	0.0872703	−	0.0732285i
$555$		0			0
$556$	−0.497974	−	0.181248i	−0.0211188	−	0.00768661i
$557$	−18.2574	−	15.3198i	−0.773591	−	0.649120i	0.168035	−	0.985781i	$-0.446258\pi$
$557$	−18.2574	−	15.3198i	−0.773591	−	0.649120i	−0.941626	+	0.336661i	$0.890702\pi$
$558$	−3.41093	+	5.90790i	−0.144396	+	0.250101i
$559$	−4.58581	−	7.94285i	−0.193959	−	0.335947i
$560$		0			0
$561$	0.0434025	−	0.246148i	0.00183246	−	0.0103924i
$562$	10.0054	+	17.3299i	0.422054	+	0.731019i
$563$	−9.81371	+	16.9979i	−0.413599	+	0.716374i	−0.995280	−	0.0970426i	$-0.969062\pi$
$563$	−9.81371	+	16.9979i	−0.413599	+	0.716374i	0.581681	+	0.813417i	$0.302395\pi$
$564$	1.84819	+	1.55082i	0.0778230	+	0.0653012i
$565$		0			0
$566$	14.4782	−	5.26962i	0.608562	−	0.221499i
$567$	19.7341	−	16.5589i	0.828753	−	0.695407i
$568$	0.778426	+	4.41467i	0.0326620	+	0.185236i
$569$	23.7705			0.996510			0.498255	−	0.867030i	$-0.333974\pi$
$569$	23.7705			0.996510			0.498255	+	0.867030i	$0.333974\pi$
$570$		0			0
$571$	−17.5361			−0.733865			−0.366933	−	0.930248i	$-0.619592\pi$
$571$	−17.5361			−0.733865			−0.366933	+	0.930248i	$0.619592\pi$
$572$	−0.0759852	−	0.430933i	−0.00317710	−	0.0180182i
$573$	0.166393	−	0.139621i	0.00695118	−	0.00583273i
$574$	−25.0704	+	9.12489i	−1.04642	+	0.380866i
$575$		0			0
$576$	−4.05981	−	3.40658i	−0.169159	−	0.141941i
$577$	−12.9640	+	22.4543i	−0.539699	+	0.934786i	0.459221	+	0.888322i	$0.348128\pi$
$577$	−12.9640	+	22.4543i	−0.539699	+	0.934786i	−0.998920	+	0.0464636i	$0.985205\pi$
$578$	12.3777	+	21.4388i	0.514844	+	0.891737i
$579$	0.540578	−	3.06577i	0.0224656	−	0.127409i
$580$		0			0
$581$	−28.0610	−	48.6030i	−1.16417	−	2.01639i
$582$	11.5096	−	19.9352i	0.477088	−	0.826341i
$583$	−1.20020	−	1.00709i	−0.0497072	−	0.0417093i
$584$	−4.59634	−	1.67293i	−0.190198	−	0.0692264i
$585$		0			0
$586$	−26.7774	+	22.4689i	−1.10616	+	0.928182i
$587$	0.701894	+	3.98064i	0.0289703	+	0.164299i	0.995861	−	0.0908937i	$-0.0289723\pi$
$587$	0.701894	+	3.98064i	0.0289703	+	0.164299i	−0.966890	+	0.255192i	$0.917861\pi$
$588$	−2.00153			−0.0825416
$589$	25.6934	+	11.8368i	1.05868	+	0.487728i
$590$		0			0
$591$	4.78598	+	27.1426i	0.196869	+	1.11650i
$592$	−28.8291	+	24.1905i	−1.18487	+	0.994221i
$593$	17.7190	−	6.44918i	0.727631	−	0.264836i	0.0484695	−	0.998825i	$-0.484566\pi$
$593$	17.7190	−	6.44918i	0.727631	−	0.264836i	0.679162	+	0.733988i	$0.262343\pi$
$594$	4.79298	+	1.74450i	0.196658	+	0.0715777i
$595$		0			0
$596$	−1.25795	+	2.17883i	−0.0515275	+	0.0892482i
$597$	6.04369	+	10.4680i	0.247352	+	0.428426i
$598$	7.55526	−	42.8480i	0.308958	−	1.75219i
$599$	−6.74122	+	38.2313i	−0.275439	+	1.56209i	0.462126	+	0.886814i	$0.347087\pi$
$599$	−6.74122	+	38.2313i	−0.275439	+	1.56209i	−0.737565	+	0.675276i	$0.764024\pi$
$600$		0			0
$601$	−0.179210	+	0.310400i	−0.00731011	+	0.0126615i	−0.869657	−	0.493656i	$-0.835660\pi$
$601$	−0.179210	+	0.310400i	−0.00731011	+	0.0126615i	0.862347	+	0.506317i	$0.168994\pi$
$602$	−8.21332	−	6.89180i	−0.334750	−	0.280889i
$603$	9.50989	+	3.46132i	0.387273	+	0.140956i
$604$	0.298147	−	0.108517i	0.0121314	−	0.00441548i
$605$		0			0
$606$	4.68652	+	26.5785i	0.190377	+	1.07968i
$607$	−4.56885			−0.185444			−0.0927219	−	0.995692i	$-0.529557\pi$
$607$	−4.56885			−0.185444			−0.0927219	+	0.995692i	$0.529557\pi$
$608$	1.94029	−	2.79844i	0.0786890	−	0.113492i
$609$	25.0759			1.01613
$610$		0			0
$611$	−45.0507	+	37.8020i	−1.82256	+	1.52931i
$612$	0.0249026	−	0.00906382i	0.00100663	−	0.000366383i
$613$	15.8739	+	5.77762i	0.641140	+	0.233356i	0.642073	−	0.766644i	$-0.278075\pi$
$613$	15.8739	+	5.77762i	0.641140	+	0.233356i	−0.000932984		1.00000i	$0.500297\pi$
$614$	−17.5519	−	14.7278i	−0.708337	−	0.594365i
$615$		0			0
$616$	3.44177	+	5.96132i	0.138673	+	0.240188i
$617$	−4.23101	+	23.9952i	−0.170334	+	0.966011i	0.773059	+	0.634334i	$0.218726\pi$
$617$	−4.23101	+	23.9952i	−0.170334	+	0.966011i	−0.943393	+	0.331677i	$0.892385\pi$
$618$	−2.99289	+	16.9735i	−0.120392	+	0.682774i
$619$	16.6616	+	28.8588i	0.669687	+	1.15993i	0.977992	+	0.208644i	$0.0669049\pi$
$619$	16.6616	+	28.8588i	0.669687	+	1.15993i	−0.308305	+	0.951288i	$0.599762\pi$
$620$		0			0
$621$	25.1351	+	21.0909i	1.00864	+	0.846348i
$622$	4.82605	+	1.75654i	0.193507	+	0.0704307i
$623$	−0.00285906	+	0.00104061i	−0.000114546	+	4.16913e-5i
$624$	25.0894	−	21.0525i	1.00438	−	0.842776i
$625$		0			0
$626$	−1.71540			−0.0685610
$627$	1.03990	−	3.95392i	0.0415294	−	0.157904i
$628$	2.88375			0.115074
$629$	0.409032	+	2.31973i	0.0163092	+	0.0924939i
$630$		0			0
$631$	−35.2681	+	12.8365i	−1.40400	+	0.511014i	−0.929363	−	0.369167i	$-0.879643\pi$
$631$	−35.2681	+	12.8365i	−1.40400	+	0.511014i	−0.474637	+	0.880181i	$0.657421\pi$
$632$	13.1654	+	4.79180i	0.523690	+	0.190608i
$633$	16.2938	+	13.6721i	0.647621	+	0.543418i
$634$	−0.958988	+	1.66102i	−0.0380863	+	0.0659674i
$635$		0			0
$636$	−0.0915416	+	0.519158i	−0.00362986	+	0.0205860i
$637$	8.47200	−	48.0471i	0.335673	−	1.90370i
$638$	1.85141	+	3.20674i	0.0732981	+	0.126956i
$639$	−0.591839	+	1.02510i	−0.0234128	+	0.0405522i
$640$		0			0
$641$	6.62106	+	2.40987i	0.261516	+	0.0951841i	0.469451	−	0.882959i	$-0.344452\pi$
$641$	6.62106	+	2.40987i	0.261516	+	0.0951841i	−0.207935	+	0.978143i	$0.566674\pi$
$642$	−11.8384	+	4.30883i	−0.467225	+	0.170056i
$643$	−11.7063	+	9.82279i	−0.461653	+	0.387373i	−0.843739	−	0.536754i	$-0.819650\pi$
$643$	−11.7063	+	9.82279i	−0.461653	+	0.387373i	0.382086	+	0.924127i	$0.375206\pi$
$644$	−0.571420	−	3.24069i	−0.0225171	−	0.127701i
$645$		0			0
$646$	−0.724955	−	1.53610i	−0.0285230	−	0.0604372i
$647$	−23.8972			−0.939495			−0.469748	−	0.882801i	$-0.655655\pi$
$647$	−23.8972			−0.939495			−0.469748	+	0.882801i	$0.655655\pi$
$648$	2.99084	+	16.9619i	0.117491	+	0.666326i
$649$	−0.423600	+	0.355443i	−0.0166278	+	0.0139523i
$650$		0			0
$651$	37.5044	+	13.6505i	1.46991	+	0.535005i
$652$	0.839024	+	0.704025i	0.0328587	+	0.0275718i
$653$	−13.5704	+	23.5046i	−0.531050	+	0.919805i	0.468294	+	0.883573i	$0.344869\pi$
$653$	−13.5704	+	23.5046i	−0.531050	+	0.919805i	−0.999343	+	0.0362323i	$0.988464\pi$
$654$	−7.43547	−	12.8786i	−0.290750	−	0.503594i
$655$		0			0
$656$	3.31275	−	18.7875i	0.129341	−	0.733530i
$657$	−0.645778	−	1.11852i	−0.0251942	−	0.0436376i
$658$	−34.3745	+	59.5384i	−1.34006	+	2.32105i
$659$	−35.1081	−	29.4592i	−1.36762	−	1.14757i	−0.973546	−	0.228490i	$-0.926621\pi$
$659$	−35.1081	−	29.4592i	−1.36762	−	1.14757i	−0.394073	−	0.919079i	$-0.628934\pi$
$660$		0			0
$661$	−17.2794	+	6.28920i	−0.672092	+	0.244622i	−0.655448	−	0.755240i	$-0.727520\pi$
$661$	−17.2794	+	6.28920i	−0.672092	+	0.244622i	−0.0166438	+	0.999861i	$0.505298\pi$
$662$	−14.2543	+	11.9608i	−0.554010	+	0.464870i
$663$	−0.355973	−	2.01883i	−0.0138249	−	0.0784047i
$664$	37.5226			1.45616
$665$		0			0
$666$	−9.29138			−0.360034
$667$	4.13629	+	23.4581i	0.160158	+	0.908300i
$668$	−1.49361	+	1.25329i	−0.0577895	+	0.0484911i
$669$	−6.96308	+	2.53435i	−0.269208	+	0.0979837i
$670$		0			0
$671$	−1.03226	−	0.866173i	−0.0398501	−	0.0334382i
$672$	2.40218	−	4.16069i	0.0926660	−	0.160502i
$673$	−2.90989	−	5.04007i	−0.112168	−	0.194280i	0.804476	−	0.593985i	$-0.202446\pi$
$673$	−2.90989	−	5.04007i	−0.112168	−	0.194280i	−0.916644	+	0.399704i	$0.869113\pi$
$674$	−3.86467	+	21.9176i	−0.148862	+	0.844236i
$675$		0			0
$676$	−0.895204	−	1.55054i	−0.0344309	−	0.0596361i
$677$	8.94182	−	15.4877i	0.343662	−	0.595240i	−0.641448	−	0.767167i	$-0.721666\pi$
$677$	8.94182	−	15.4877i	0.343662	−	0.595240i	0.985110	+	0.171926i	$0.0549992\pi$
$678$	−8.10209	−	6.79846i	−0.311159	−	0.261093i
$679$	39.8783	+	14.5145i	1.53039	+	0.557016i
$680$		0			0
$681$	3.06890	−	2.57511i	0.117600	−	0.0986784i
$682$	1.02340	+	5.80396i	0.0391878	+	0.222245i
$683$	13.4534			0.514779			0.257390	−	0.966308i	$-0.417138\pi$
$683$	13.4534			0.514779			0.257390	+	0.966308i	$0.417138\pi$
$684$	0.418184	−	0.114125i	0.0159897	−	0.00436369i
$685$		0			0
$686$	−2.66642	−	15.1220i	−0.101804	−	0.577362i
$687$	26.7697	−	22.4624i	1.02133	−	0.856995i
$688$	7.20433	−	2.62216i	0.274662	−	0.0999689i
$689$	−12.0750	−	4.39495i	−0.460022	−	0.167434i
$690$		0			0
$691$	−1.15757	+	2.00498i	−0.0440362	+	0.0762729i	−0.887203	−	0.461379i	$-0.847355\pi$
$691$	−1.15757	+	2.00498i	−0.0440362	+	0.0762729i	0.843167	+	0.537651i	$0.180688\pi$
$692$	−0.727199	−	1.25955i	−0.0276439	−	0.0478807i
$693$	−0.315623	+	1.78999i	−0.0119895	+	0.0679960i
$694$	−5.08309	+	28.8276i	−0.192951	+	1.09428i
$695$		0			0
$696$	−8.38274	+	14.5193i	−0.317747	+	0.550354i
$697$	−0.914709	−	0.767532i	−0.0346471	−	0.0290723i
$698$	−30.6176	−	11.1439i	−1.15889	−	0.421802i
$699$	41.0308	−	14.9340i	1.55193	−	0.564855i
$700$		0			0
$701$	0.542849	+	3.07865i	0.0205031	+	0.116279i	0.993342	−	0.115206i	$-0.0367528\pi$
$701$	0.542849	+	3.07865i	0.0205031	+	0.116279i	−0.972839	+	0.231485i	$0.925642\pi$
$702$	41.8333			1.57890
$703$	3.53535	+	38.3670i	0.133338	+	1.44704i
$704$	−4.57849			−0.172558
$705$		0			0
$706$	29.3659	−	24.6409i	1.10520	−	0.927372i
$707$	−46.7548	+	17.0173i	−1.75839	+	0.640003i
$708$	0.174838	+	0.0636359i	0.00657083	+	0.00239158i
$709$	−21.5824	−	18.1098i	−0.810544	−	0.680127i	0.140193	−	0.990124i	$-0.455228\pi$
$709$	−21.5824	−	18.1098i	−0.810544	−	0.680127i	−0.950738	+	0.309997i	$0.899672\pi$
$710$		0			0
$711$	1.84971	+	3.20379i	0.0693696	+	0.120152i
$712$	0.000353238	−	0.00200331i	1.32382e−5	−	7.50773e-5i
$713$	−6.58341	+	37.3364i	−0.246551	+	1.39826i
$714$	−1.19822	−	2.07538i	−0.0448423	−	0.0776691i
$715$		0			0
$716$	0.530243	+	0.444926i	0.0198161	+	0.0166277i
$717$	−29.4460	−	10.7175i	−1.09968	−	0.400251i
$718$	−38.8577	+	14.1431i	−1.45016	+	0.527814i
$719$	−0.929140	+	0.779641i	−0.0346511	+	0.0290757i	−0.659949	−	0.751311i	$-0.729422\pi$
$719$	−0.929140	+	0.779641i	−0.0346511	+	0.0290757i	0.625298	+	0.780386i	$0.284978\pi$
$720$		0			0
$721$	−31.7746			−1.18335
$722$	−9.74346	−	26.0194i	−0.362614	−	0.968341i
$723$	−9.36027			−0.348112
$724$	−0.636420	−	3.60931i	−0.0236523	−	0.134139i
$725$		0			0
$726$	−22.0291	+	8.01795i	−0.817578	+	0.297574i
$727$	33.6146	+	12.2347i	1.24670	+	0.453761i	0.879284	−	0.476297i	$-0.158021\pi$
$727$	33.6146	+	12.2347i	1.24670	+	0.453761i	0.367413	+	0.930058i	$0.380244\pi$
$728$	43.2482	+	36.2896i	1.60289	+	1.34498i
$729$	−14.9989	+	25.9788i	−0.555514	+	0.962178i
$730$		0			0
$731$	0.0833274	−	0.472573i	0.00308198	−	0.0174788i
$732$	−0.0787328	+	0.446516i	−0.00291005	+	0.0165037i
$733$	18.9235	+	32.7765i	0.698957	+	1.21063i	0.968828	+	0.247732i	$0.0796854\pi$
$733$	18.9235	+	32.7765i	0.698957	+	1.21063i	−0.269872	+	0.962896i	$0.586981\pi$
$734$	−7.01533	+	12.1509i	−0.258941	+	0.448498i
$735$		0			0
$736$	4.28850	+	1.56089i	0.158076	+	0.0575350i
$737$	8.21574	−	2.99028i	0.302631	−	0.110149i
$738$	3.60808	−	3.02754i	0.132815	−	0.111445i
$739$	1.31048	+	7.43210i	0.0482067	+	0.273394i	0.999378	−	0.0352702i	$-0.0112292\pi$
$739$	1.31048	+	7.43210i	0.0482067	+	0.273394i	−0.951171	+	0.308664i	$0.900118\pi$
$740$		0			0
$741$	−3.07676	−	33.3901i	−0.113028	−	1.22662i
$742$	−15.0218			−0.551467
$743$	1.59337	+	9.03644i	0.0584550	+	0.331515i	0.999985	−	0.00541343i	$-0.00172316\pi$
$743$	1.59337	+	9.03644i	0.0584550	+	0.331515i	−0.941530	+	0.336928i	$0.890612\pi$
$744$	−20.4414	+	17.1523i	−0.749417	+	0.628835i
$745$		0			0
$746$	17.9186	+	6.52185i	0.656047	+	0.238782i
$747$	7.58984	+	6.36864i	0.277698	+	0.233016i
$748$	0.0114472	−	0.0198272i	0.000418552	−	0.000724954i
$749$	−11.6128	−	20.1140i	−0.424324	−	0.734950i
$750$		0			0
$751$	1.81833	−	10.3123i	0.0663519	−	0.376300i	−0.933491	−	0.358600i	$-0.883254\pi$
$751$	1.81833	−	10.3123i	0.0663519	−	0.376300i	0.999843	−	0.0177006i	$-0.00563457\pi$
$752$	−24.5798	−	42.5735i	−0.896335	−	1.55250i
$753$	5.88280	−	10.1893i	0.214381	−	0.371319i
$754$	23.2643	+	19.5211i	0.847235	+	0.710915i
$755$		0			0
$756$	2.97313	−	1.08213i	0.108132	−	0.0393568i
$757$	40.6582	−	34.1163i	1.47775	−	1.23998i	0.569199	−	0.822199i	$-0.307253\pi$
$757$	40.6582	−	34.1163i	1.47775	−	1.23998i	0.908549	−	0.417779i	$-0.137191\pi$
$758$	2.52377	+	14.3130i	0.0916675	+	0.519872i
$759$	5.47919			0.198882
$760$		0			0
$761$	−16.6886			−0.604960			−0.302480	−	0.953156i	$-0.597815\pi$
$761$	−16.6886			−0.604960			−0.302480	+	0.953156i	$0.597815\pi$
$762$	7.09384	+	40.2312i	0.256983	+	1.45742i
$763$	21.0016	−	17.6225i	0.760310	−	0.637976i
$764$	0.0186962	−	0.00680487i	0.000676405	−	0.000246191i
$765$		0			0
$766$	20.1954	+	16.9459i	0.729689	+	0.612281i
$767$	−2.26764	+	3.92767i	−0.0818799	+	0.141820i
$768$	2.49569	+	4.32266i	0.0900554	+	0.155981i
$769$	−1.07276	+	6.08395i	−0.0386849	+	0.219393i	−0.998022	−	0.0628711i	$-0.979974\pi$
$769$	−1.07276	+	6.08395i	−0.0386849	+	0.219393i	0.959337	+	0.282264i	$0.0910854\pi$
$770$		0			0
$771$	−15.2223	−	26.3657i	−0.548217	−	0.949539i
$772$	0.142575	−	0.246947i	0.00513139	−	0.00888783i
$773$	−21.5686	−	18.0982i	−0.775769	−	0.650948i	0.166410	−	0.986057i	$-0.446782\pi$
$773$	−21.5686	−	18.0982i	−0.775769	−	0.650948i	−0.942179	+	0.335109i	$0.891227\pi$
$774$	1.77868	+	0.647385i	0.0639332	+	0.0232698i
$775$		0			0
$776$	−21.7352	+	18.2380i	−0.780249	+	0.654707i
$777$	9.43940	+	53.5335i	0.338637	+	1.92050i
$778$	35.6088			1.27664
$779$	−13.8745	−	13.7469i	−0.497106	−	0.492534i
$780$		0			0
$781$	0.177572	+	1.00706i	0.00635403	+	0.0360355i
$782$	1.74383	−	1.46325i	0.0623594	−	0.0523257i
$783$	−21.5214	+	7.83313i	−0.769111	+	0.279933i
$784$	38.3233	+	13.9486i	1.36869	+	0.498163i
$785$		0			0
$786$	−21.6271	+	37.4593i	−0.771414	+	1.33613i
$787$	2.73433	+	4.73601i	0.0974685	+	0.168820i	0.910636	−	0.413209i	$-0.135592\pi$
$787$	2.73433	+	4.73601i	0.0974685	+	0.168820i	−0.813168	+	0.582030i	$0.802259\pi$
$788$	−0.438386	+	2.48621i	−0.0156169	+	0.0885676i
$789$	2.80257	−	15.8941i	0.0997740	−	0.565847i
$790$		0			0
$791$	9.74930	−	16.8863i	0.346645	−	0.600407i
$792$	−0.930919	−	0.781134i	−0.0330788	−	0.0277564i
$793$	−10.3855	−	3.78000i	−0.368798	−	0.134232i
$794$	−27.4437	+	9.98870i	−0.973942	+	0.354486i
$795$		0			0
$796$	0.192260	+	1.09036i	0.00681447	+	0.0386468i
$797$	47.2273			1.67288			0.836439	−	0.548061i	$-0.184634\pi$
$797$	47.2273			1.67288			0.836439	+	0.548061i	$0.184634\pi$
$798$	−16.7301	−	35.4493i	−0.592239	−	1.25489i
$799$	−3.07694			−0.108854
$800$		0			0
$801$	0.000411469	0	0.000345264i	1.45386e−5	0	1.21993e-5i
$802$	22.5407	−	8.20414i	0.795939	−	0.289698i
$803$	−1.04850	−	0.381624i	−0.0370009	−	0.0134672i
$804$	−2.25353	−	1.89094i	−0.0794759	−	0.0666882i
$805$		0			0
$806$	24.1683	+	41.8607i	0.851292	+	1.47448i
$807$	6.27507	−	35.5877i	0.220893	−	1.25275i
$808$	5.77657	−	32.7606i	0.203219	−	1.15251i
$809$	3.06691	+	5.31204i	0.107827	+	0.186762i	0.914890	−	0.403704i	$-0.132277\pi$
$809$	3.06691	+	5.31204i	0.107827	+	0.186762i	−0.807063	+	0.590466i	$0.798944\pi$
$810$		0			0
$811$	20.6831	+	17.3552i	0.726281	+	0.609422i	0.929115	−	0.369791i	$-0.120571\pi$
$811$	20.6831	+	17.3552i	0.726281	+	0.609422i	−0.202834	+	0.979213i	$0.565015\pi$
$812$	2.15838	+	0.785586i	0.0757443	+	0.0275687i
$813$	36.8586	−	13.4154i	1.29269	−	0.470500i
$814$	−6.14901	+	5.15963i	−0.215523	+	0.180845i
$815$		0			0
$816$	1.71360			0.0599880
$817$	1.99647	−	7.59103i	0.0698476	−	0.265577i
$818$	12.1855			0.426055
$819$	2.58864	+	14.6809i	0.0904543	+	0.512992i
$820$		0			0
$821$	42.5186	−	15.4755i	1.48391	−	0.540099i	0.532072	−	0.846699i	$-0.321414\pi$
$821$	42.5186	−	15.4755i	1.48391	−	0.540099i	0.951838	+	0.306600i	$0.0991914\pi$
$822$	4.89105	+	1.78020i	0.170595	+	0.0620914i
$823$	−23.0915	−	19.3760i	−0.804918	−	0.675407i	0.144471	−	0.989509i	$-0.453852\pi$
$823$	−23.0915	−	19.3760i	−0.804918	−	0.675407i	−0.949389	+	0.314102i	$0.898296\pi$
$824$	10.6221	−	18.3980i	0.370038	−	0.640925i
$825$		0			0
$826$	−0.920649	+	5.22126i	−0.0320335	+	0.181671i
$827$	3.55475	−	20.1600i	0.123611	−	0.701032i	−0.858512	−	0.512793i	$-0.828611\pi$
$827$	3.55475	−	20.1600i	0.123611	−	0.701032i	0.982123	−	0.188239i	$-0.0602779\pi$
$828$	0.290470	+	0.503109i	0.0100945	+	0.0174843i
$829$	10.4604	−	18.1179i	0.363303	−	0.629259i	−0.625199	−	0.780465i	$-0.714982\pi$
$829$	10.4604	−	18.1179i	0.363303	−	0.629259i	0.988502	+	0.151206i	$0.0483156\pi$
$830$		0			0
$831$	2.60252	+	0.947238i	0.0902803	+	0.0328593i
$832$	−35.2867	+	12.8433i	−1.22335	+	0.445262i
$833$	1.95543	−	1.64080i	0.0677515	−	0.0568503i
$834$	−1.46907	−	8.33154i	−0.0508699	−	0.288498i
$835$		0			0
$836$	0.213378	−	0.307751i	0.00737982	−	0.0106438i
$837$	−36.4522			−1.25997
$838$	−2.95959	−	16.7847i	−0.102237	−	0.579816i
$839$	3.25369	−	2.73017i	0.112330	−	0.0942559i	−0.584893	−	0.811111i	$-0.698863\pi$
$839$	3.25369	−	2.73017i	0.112330	−	0.0942559i	0.697222	+	0.716855i	$0.254419\pi$
$840$		0			0
$841$	11.6274	+	4.23203i	0.400945	+	0.145932i
$842$	23.7387	+	19.9191i	0.818089	+	0.686458i
$843$	−10.3342	+	17.8993i	−0.355928	+	0.616486i
$844$	0.974147	+	1.68727i	0.0335315	+	0.0580783i
$845$		0			0
$846$	2.10757	−	11.9526i	0.0724599	−	0.410941i
$847$	−21.6094	−	37.4285i	−0.742506	−	1.28606i
$848$	5.37074	−	9.30239i	0.184432	−	0.319446i
$849$	12.1905	+	10.2290i	0.418377	+	0.351060i
$850$		0			0
$851$	−48.5226	+	17.6608i	−1.66334	+	0.605404i
$852$	0.263577	−	0.221167i	0.00902999	−	0.00757706i
$853$	0.289897	+	1.64409i	0.00992590	+	0.0562926i	0.989368	−	0.145431i	$-0.0464569\pi$
$853$	0.289897	+	1.64409i	0.00992590	+	0.0562926i	−0.979443	+	0.201724i	$0.935346\pi$
$854$	−12.9199			−0.442110
$855$		0			0
$856$	15.5284			0.530751
$857$	−0.148759	−	0.843653i	−0.00508150	−	0.0288186i	0.982162	−	0.188039i	$-0.0602131\pi$
$857$	−0.148759	−	0.843653i	−0.00508150	−	0.0288186i	−0.987243	+	0.159220i	$0.949102\pi$
$858$	5.35138	−	4.49034i	0.182693	−	0.153298i
$859$	49.8985	−	18.1616i	1.70251	−	0.619665i	0.706407	−	0.707806i	$-0.250315\pi$
$859$	49.8985	−	18.1616i	1.70251	−	0.619665i	0.996108	+	0.0881416i	$0.0280928\pi$
$860$		0			0
$861$	−21.1091	−	17.7127i	−0.719397	−	0.603646i
$862$	−0.286805	+	0.496761i	−0.00976863	+	0.0169198i
$863$	14.7804	+	25.6004i	0.503130	+	0.871447i	0.999993	+	0.00361786i	$0.00115160\pi$
$863$	14.7804	+	25.6004i	0.503130	+	0.871447i	−0.496864	+	0.867829i	$0.665515\pi$
$864$	−0.761961	+	4.32130i	−0.0259224	+	0.147013i
$865$		0			0
$866$	9.48391	+	16.4266i	0.322276	+	0.558199i
$867$	−12.7844	+	22.1432i	−0.434181	+	0.752023i
$868$	2.80050	+	2.34990i	0.0950553	+	0.0797609i
$869$	3.00324	+	1.09309i	0.101878	+	0.0370806i
$870$		0			0
$871$	54.9310	−	46.0926i	1.86127	−	1.56179i
$872$	3.18294	+	18.0514i	0.107788	+	0.611296i
$873$	−7.49198			−0.253565
$874$	30.4026	−	21.4981i	1.02838	−	0.727185i
$875$		0			0
$876$	0.0651933	+	0.369730i	0.00220268	+	0.0124920i
$877$	−6.73412	+	5.65060i	−0.227395	+	0.190807i	−0.749366	−	0.662156i	$-0.769641\pi$
$877$	−6.73412	+	5.65060i	−0.227395	+	0.190807i	0.521971	+	0.852963i	$0.325197\pi$
$878$	7.48620	−	2.72476i	0.252647	−	0.0919560i
$879$	−33.9266	−	12.3483i	−1.14432	−	0.416497i
$880$		0			0
$881$	−13.6335	+	23.6139i	−0.459324	+	0.795572i	−0.998925	−	0.0463485i	$-0.985242\pi$
$881$	−13.6335	+	23.6139i	−0.459324	+	0.795572i	0.539602	+	0.841920i	$0.318575\pi$
$882$	5.03444	+	8.71990i	0.169518	+	0.293614i
$883$	1.50219	−	8.51936i	0.0505528	−	0.286699i	−0.949042	−	0.315148i	$-0.897946\pi$
$883$	1.50219	−	8.51936i	0.0505528	−	0.286699i	0.999595	+	0.0284490i	$0.00905681\pi$
$884$	0.0326065	−	0.184920i	0.00109667	−	0.00621955i
$885$		0			0
$886$	18.0907	−	31.3340i	0.607769	−	1.05269i
$887$	−30.3733	−	25.4862i	−1.01984	−	0.855744i	−0.0302292	−	0.999543i	$-0.509624\pi$
$887$	−30.3733	−	25.4862i	−1.01984	−	0.855744i	−0.989607	+	0.143799i	$0.954068\pi$
$888$	−34.1523	−	12.4304i	−1.14607	−	0.417137i
$889$	−70.7713	+	25.7587i	−2.37359	+	0.863918i
$890$		0			0
$891$	0.682260	+	3.86929i	0.0228566	+	0.129626i
$892$	−0.678737			−0.0227258
$893$	−50.1581	−	4.15486i	−1.67848	−	0.139037i
$894$	−40.1648			−1.34331
$895$		0			0
$896$	−38.5013	+	32.3064i	−1.28624	+	1.07928i
$897$	42.2284	−	15.3699i	1.40997	−	0.513186i
$898$	−47.4922	−	17.2857i	−1.58483	−	0.576832i
$899$	−20.2718	−	17.0100i	−0.676101	−	0.567316i
$900$		0			0
$901$	−0.336159	−	0.582244i	−0.0111991	−	0.0193974i
$902$	0.706583	−	4.00723i	0.0235266	−	0.133426i
$903$	1.92298	−	10.9058i	0.0639929	−	0.362921i
$904$	6.51828	+	11.2900i	0.216795	+	0.375499i
$905$		0			0
$906$	3.88018	+	3.25585i	0.128910	+	0.108169i
$907$	−31.3645	−	11.4157i	−1.04144	−	0.379053i	−0.236014	−	0.971750i	$-0.575841\pi$
$907$	−31.3645	−	11.4157i	−1.04144	−	0.379053i	−0.805426	+	0.592696i	$0.798063\pi$
$908$	0.344826	−	0.125506i	0.0114435	−	0.00416508i
$909$	6.72884	−	5.64617i	0.223182	−	0.187272i
$910$		0			0
$911$	−46.3977			−1.53722			−0.768611	−	0.639716i	$-0.779052\pi$
$911$	−46.3977			−1.53722			−0.768611	+	0.639716i	$0.779052\pi$
$912$	27.9339	+	2.31391i	0.924982	+	0.0766212i
$913$	8.55953			0.283279
$914$	2.95635	+	16.7663i	0.0977873	+	0.554579i
$915$		0			0
$916$	3.00788	−	1.09478i	0.0993833	−	0.0361726i
$917$	−74.9333	−	27.2735i	−2.47452	−	0.900650i
$918$	1.67667	+	1.40689i	0.0553384	+	0.0464345i
$919$	−4.25997	+	7.37849i	−0.140524	+	0.243394i	−0.927694	−	0.373342i	$-0.878212\pi$
$919$	−4.25997	+	7.37849i	−0.140524	+	0.243394i	0.787170	+	0.616736i	$0.211545\pi$
$920$		0			0
$921$	4.10942	−	23.3057i	0.135410	−	0.767948i
$922$	0.759174	−	4.30549i	0.0250021	−	0.141794i
$923$	4.19351	+	7.26337i	0.138031	+	0.239077i
$924$	0.264173	−	0.457561i	0.00869065	−	0.0150526i
$925$		0			0
$926$	−11.6624	−	4.24475i	−0.383249	−	0.139491i
$927$	5.27123	−	1.91857i	0.173130	−	0.0630142i
$928$	−2.44023	+	2.04759i	−0.0801044	+	0.0672155i
$929$	−8.18896	−	46.4419i	−0.268671	−	1.52371i	−0.758373	−	0.651820i	$-0.774006\pi$
$929$	−8.18896	−	46.4419i	−0.268671	−	1.52371i	0.489702	−	0.871890i	$-0.337106\pi$
$930$		0			0
$931$	34.0916	−	24.1067i	1.11731	−	0.790064i
$932$	3.99954			0.131009
$933$	0.921119	+	5.22393i	0.0301561	+	0.171024i
$934$	−20.0853	+	16.8536i	−0.657212	+	0.551466i
$935$		0			0
$936$	−9.36584	−	3.40889i	−0.306132	−	0.111423i
$937$	22.5986	+	18.9625i	0.738264	+	0.619477i	0.932371	−	0.361504i	$-0.117736\pi$
$937$	22.5986	+	18.9625i	0.738264	+	0.619477i	−0.194107	+	0.980980i	$0.562181\pi$
$938$	41.9134	−	72.5961i	1.36852	−	2.37035i
$939$	−0.885879	−	1.53439i	−0.0289096	−	0.0500729i
$940$		0			0
$941$	−1.64948	+	9.35464i	−0.0537714	+	0.304953i	−0.999818	−	0.0190779i	$-0.993927\pi$
$941$	−1.64948	+	9.35464i	−0.0537714	+	0.304953i	0.946047	+	0.324031i	$0.105038\pi$
$942$	23.0187	+	39.8695i	0.749989	+	1.29902i
$943$	13.0879	−	22.6690i	0.426201	−	0.738203i
$944$	−2.90416	−	2.43688i	−0.0945223	−	0.0793137i
$945$		0			0
$946$	1.53662	−	0.559286i	0.0499600	−	0.0181839i
$947$	7.55292	−	6.33765i	0.245437	−	0.205946i	−0.511768	−	0.859124i	$-0.671009\pi$
$947$	7.55292	−	6.33765i	0.245437	−	0.205946i	0.757204	+	0.653178i	$0.226565\pi$
$948$	−0.186734	−	1.05902i	−0.00606484	−	0.0343954i
$949$	−9.15138			−0.297066
$950$		0			0
$951$	−1.98099			−0.0642381
$952$	0.512928	+	2.90896i	0.0166241	+	0.0942800i
$953$	−41.1172	+	34.5014i	−1.33192	+	1.11761i	−0.348290	+	0.937387i	$0.613237\pi$
$953$	−41.1172	+	34.5014i	−1.33192	+	1.11761i	−0.983626	+	0.180223i	$0.942318\pi$
$954$	2.49203	−	0.907025i	0.0806825	−	0.0293660i
$955$		0			0
$956$	−2.19877	−	1.84499i	−0.0711134	−	0.0596712i
$957$	−1.91224	+	3.31210i	−0.0618141	+	0.107065i
$958$	−2.47828	−	4.29251i	−0.0800697	−	0.138685i
$959$	−1.66627	+	9.44991i	−0.0538068	+	0.305154i
$960$		0			0
$961$	−5.55948	−	9.62930i	−0.179338	−	0.310623i
$962$	−32.9173	+	57.0144i	−1.06130	+	1.83822i
$963$	3.14100	+	2.63561i	0.101217	+	0.0849315i
$964$	−0.805675	−	0.293242i	−0.0259491	−	0.00944468i
$965$		0			0
$966$	40.2432	−	33.7681i	1.29480	−	1.08647i
$967$	−5.94528	−	33.7173i	−0.191187	−	1.08428i	−0.917745	−	0.397171i	$-0.869992\pi$
$967$	−5.94528	−	33.7173i	−0.191187	−	1.08428i	0.726557	−	0.687106i	$-0.241119\pi$
$968$	28.8956			0.928739
$969$	0.999627	−	1.44175i	0.0321126	−	0.0463155i
$970$		0			0
$971$	2.46056	+	13.9545i	0.0789630	+	0.447821i	0.998497	+	0.0548105i	$0.0174555\pi$
$971$	2.46056	+	13.9545i	0.0789630	+	0.447821i	−0.919534	+	0.393011i	$0.871433\pi$
$972$	−0.773065	+	0.648679i	−0.0247961	+	0.0208064i
$973$	14.6561	−	5.33440i	0.469855	−	0.171013i
$974$	−15.3379	−	5.58254i	−0.491458	−	0.178876i
$975$		0			0
$976$	4.61925	−	8.00078i	0.147859	−	0.256099i
$977$	22.8088	+	39.5060i	0.729717	+	1.26391i	0.957003	+	0.290079i	$0.0936817\pi$
$977$	22.8088	+	39.5060i	0.729717	+	1.26391i	−0.227285	+	0.973828i	$0.572985\pi$
$978$	−3.03629	+	17.2197i	−0.0970900	+	0.550625i
$979$	8.05795e−5	0	0.000456989i	2.57533e−6	0	1.46054e-5i
$980$		0			0
$981$	−2.42000	+	4.19156i	−0.0772646	+	0.133826i
$982$	25.7454	+	21.6029i	0.821568	+	0.689377i
$983$	18.9686	+	6.90400i	0.605004	+	0.220203i	0.626316	−	0.779569i	$-0.284562\pi$
$983$	18.9686	+	6.90400i	0.605004	+	0.220203i	−0.0213117	+	0.999773i	$0.506784\pi$
$984$	17.3126	−	6.30126i	0.551905	−	0.200877i
$985$		0			0
$986$	0.275917	+	1.56480i	0.00878698	+	0.0498334i
$987$	−71.0079			−2.26021
$988$	0.781229	−	2.97041i	0.0248542	−	0.0945013i
$989$	10.5194			0.334496
$990$		0			0
$991$	−8.46987	+	7.10707i	−0.269054	+	0.225763i	−0.767325	−	0.641258i	$-0.778413\pi$
$991$	−8.46987	+	7.10707i	−0.269054	+	0.225763i	0.498271	+	0.867021i	$0.333968\pi$
$992$	−4.76433	+	1.73408i	−0.151268	+	0.0550569i
$993$	−18.0601	−	6.57332i	−0.573118	−	0.208598i
$994$	7.51070	+	6.30223i	0.238225	+	0.199894i
$995$		0			0
$996$	−1.44002	−	2.49419i	−0.0456288	−	0.0790314i
$997$	−5.42251	+	30.7526i	−0.171733	+	0.973945i	0.770115	+	0.637905i	$0.220199\pi$
$997$	−5.42251	+	30.7526i	−0.171733	+	0.973945i	−0.941848	+	0.336040i	$0.890912\pi$
$998$	0.249035	−	1.41235i	0.00788305	−	0.0447070i
$999$	−24.8240	−	42.9964i	−0.785396	−	1.36035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.l.b.351.3		18
5.2	odd	4		475.2.u.c.199.2		36
5.3	odd	4		475.2.u.c.199.5		36
5.4	even	2		95.2.k.b.66.1	yes	18
15.14	odd	2		855.2.bs.b.541.3		18
19.6	even	9		9025.2.a.ce.1.7		9
19.13	odd	18		9025.2.a.cd.1.3		9
19.17	even	9	inner	475.2.l.b.226.3		18
95.17	odd	36		475.2.u.c.74.5		36
95.44	even	18		1805.2.a.t.1.3		9
95.74	even	18		95.2.k.b.36.1	✓	18
95.89	odd	18		1805.2.a.u.1.7		9
95.93	odd	36		475.2.u.c.74.2		36
285.74	odd	18		855.2.bs.b.226.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.36.1	✓	18	95.74	even	18
95.2.k.b.66.1	yes	18	5.4	even	2
475.2.l.b.226.3		18	19.17	even	9	inner
475.2.l.b.351.3		18	1.1	even	1	trivial
475.2.u.c.74.2		36	95.93	odd	36
475.2.u.c.74.5		36	95.17	odd	36
475.2.u.c.199.2		36	5.2	odd	4
475.2.u.c.199.5		36	5.3	odd	4
855.2.bs.b.226.3		18	285.74	odd	18
855.2.bs.b.541.3		18	15.14	odd	2
1805.2.a.t.1.3		9	95.44	even	18
1805.2.a.u.1.7		9	95.89	odd	18
9025.2.a.cd.1.3		9	19.13	odd	18
9025.2.a.ce.1.7		9	19.6	even	9

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.253927 + 1.44009i) q^{2} +(-1.15700 + 0.970838i) q^{3} +(-0.130002 + 0.0473169i) q^{4} +(-1.69189 - 1.41966i) q^{6} +(2.03586 - 3.52622i) q^{7} +(1.36116 + 2.35759i) q^{8} +(-0.124823 + 0.707907i) q^{9} +O(q^{10})\)	\(q+(0.253927 + 1.44009i) q^{2} +(-1.15700 + 0.970838i) q^{3} +(-0.130002 + 0.0473169i) q^{4} +(-1.69189 - 1.41966i) q^{6} +(2.03586 - 3.52622i) q^{7} +(1.36116 + 2.35759i) q^{8} +(-0.124823 + 0.707907i) q^{9} +(0.310503 + 0.537807i) q^{11} +(0.104475 - 0.180957i) q^{12} +(3.90168 + 3.27390i) q^{13} +(5.59504 + 2.03643i) q^{14} +(-3.26147 + 2.73670i) q^{16} +(0.0462744 + 0.262435i) q^{17} -1.05115 q^{18} +(0.399960 + 4.34051i) q^{19} +(1.06789 + 6.05632i) q^{21} +(-0.695646 + 0.583716i) q^{22} +(-5.48944 + 1.99799i) q^{23} +(-3.86370 - 1.40627i) q^{24} +(-3.72398 + 6.45012i) q^{26} +(-2.80837 - 4.86425i) q^{27} +(-0.0978169 + 0.554747i) q^{28} +(0.708058 - 4.01560i) q^{29} +(3.24496 - 5.62043i) q^{31} +(-0.598455 - 0.502163i) q^{32} +(-0.881374 - 0.320794i) q^{33} +(-0.366180 + 0.133279i) q^{34} +(-0.0172687 - 0.0979357i) q^{36} +8.83927 q^{37} +(-6.14918 + 1.67815i) q^{38} -7.69267 q^{39} +(-3.43252 + 2.88022i) q^{41} +(-8.45050 + 3.07573i) q^{42} +(-1.69213 - 0.615885i) q^{43} +(-0.0658134 - 0.0552240i) q^{44} +(-4.27121 - 7.39795i) q^{46} +(-2.00502 + 11.3711i) q^{47} +(1.11663 - 6.33272i) q^{48} +(-4.78947 - 8.29561i) q^{49} +(-0.308321 - 0.258712i) q^{51} +(-0.662139 - 0.240999i) q^{52} +(-2.37077 + 0.862891i) q^{53} +(6.29184 - 5.27948i) q^{54} +11.0845 q^{56} +(-4.67668 - 4.63367i) q^{57} +5.96263 q^{58} +(0.154624 + 0.876916i) q^{59} +(-2.03905 + 0.742153i) q^{61} +(8.91792 + 3.24586i) q^{62} +(2.24211 + 1.88135i) q^{63} +(-3.68635 + 6.38495i) q^{64} +(0.238168 - 1.35072i) q^{66} +(2.44476 - 13.8649i) q^{67} +(-0.0184334 - 0.0319276i) q^{68} +(4.41155 - 7.64103i) q^{69} +(1.54737 + 0.563198i) q^{71} +(-1.83886 + 0.669290i) q^{72} +(-1.37639 + 1.15493i) q^{73} +(2.24453 + 12.7294i) q^{74} +(-0.257375 - 0.545351i) q^{76} +2.52856 q^{77} +(-1.95338 - 11.0782i) q^{78} +(3.94242 - 3.30809i) q^{79} +(5.94525 + 2.16389i) q^{81} +(-5.01940 - 4.21177i) q^{82} +(6.89167 - 11.9367i) q^{83} +(-0.425395 - 0.736806i) q^{84} +(0.457253 - 2.59321i) q^{86} +(3.07927 + 5.33345i) q^{87} +(-0.845286 + 1.46408i) q^{88} +(-0.000572418 - 0.000480315i) q^{89} +(19.4878 - 7.09297i) q^{91} +(0.619100 - 0.519487i) q^{92} +(1.70211 + 9.65316i) q^{93} -16.8845 q^{94} +1.17993 q^{96} +(1.80985 + 10.2642i) q^{97} +(10.7303 - 9.00376i) q^{98} +(-0.419475 + 0.152676i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 12 q^{8} - 21 q^{9}+O(q^{10}) \) 18 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 12 * q^8 - 21 * q^9	\( 18 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 12 q^{8} - 21 q^{9} - 6 q^{12} + 3 q^{13} + 24 q^{14} + 21 q^{16} + 24 q^{17} + 12 q^{18} - 12 q^{19} + 3 q^{21} - 15 q^{22} - 21 q^{23} + 21 q^{24} - 21 q^{26} - 6 q^{27} + 24 q^{28} - 9 q^{29} + 30 q^{31} - 45 q^{32} + 3 q^{33} + 24 q^{34} - 21 q^{36} + 60 q^{37} + 15 q^{38} + 12 q^{39} - 6 q^{41} - 39 q^{42} + 6 q^{43} - 30 q^{44} + 21 q^{46} - 33 q^{47} + 63 q^{48} - 3 q^{49} + 27 q^{51} - 9 q^{52} - 24 q^{53} + 30 q^{54} - 72 q^{56} + 30 q^{57} - 36 q^{58} + 18 q^{59} + 6 q^{61} - 12 q^{62} - 24 q^{63} - 24 q^{64} - 33 q^{66} + 24 q^{67} + 3 q^{68} + 27 q^{69} + 24 q^{71} - 18 q^{72} - 6 q^{73} - 39 q^{74} + 27 q^{76} - 24 q^{77} - 72 q^{78} + 9 q^{79} + 15 q^{81} + 57 q^{82} - 12 q^{84} - 33 q^{86} + 45 q^{87} - 39 q^{88} - 6 q^{89} - 6 q^{91} + 66 q^{92} + 72 q^{93} - 66 q^{94} - 18 q^{96} + 87 q^{97} - 39 q^{98} + 3 q^{99}+O(q^{100}) \) 18 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 12 * q^8 - 21 * q^9 - 6 * q^12 + 3 * q^13 + 24 * q^14 + 21 * q^16 + 24 * q^17 + 12 * q^18 - 12 * q^19 + 3 * q^21 - 15 * q^22 - 21 * q^23 + 21 * q^24 - 21 * q^26 - 6 * q^27 + 24 * q^28 - 9 * q^29 + 30 * q^31 - 45 * q^32 + 3 * q^33 + 24 * q^34 - 21 * q^36 + 60 * q^37 + 15 * q^38 + 12 * q^39 - 6 * q^41 - 39 * q^42 + 6 * q^43 - 30 * q^44 + 21 * q^46 - 33 * q^47 + 63 * q^48 - 3 * q^49 + 27 * q^51 - 9 * q^52 - 24 * q^53 + 30 * q^54 - 72 * q^56 + 30 * q^57 - 36 * q^58 + 18 * q^59 + 6 * q^61 - 12 * q^62 - 24 * q^63 - 24 * q^64 - 33 * q^66 + 24 * q^67 + 3 * q^68 + 27 * q^69 + 24 * q^71 - 18 * q^72 - 6 * q^73 - 39 * q^74 + 27 * q^76 - 24 * q^77 - 72 * q^78 + 9 * q^79 + 15 * q^81 + 57 * q^82 - 12 * q^84 - 33 * q^86 + 45 * q^87 - 39 * q^88 - 6 * q^89 - 6 * q^91 + 66 * q^92 + 72 * q^93 - 66 * q^94 - 18 * q^96 + 87 * q^97 - 39 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

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