LMFDB - Embedded newform 315.2.be.c.236.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(236,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0, 5]))

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

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

chi := DirichletCharacter("315.236");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.be (of order $6$, degree $2$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			236.3
Character	$\chi$	$=$	315.236
Dual form			315.2.be.c.311.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.91788 + 1.10729i) q^{2} +(0.302150 - 1.70549i) q^{3} +(1.45217 - 2.51523i) q^{4} -1.00000 q^{5} +(1.30898 + 3.60549i) q^{6} +(2.53521 - 0.756781i) q^{7} +2.00271i q^{8} +(-2.81741 - 1.03063i) q^{9} +O(q^{10})$	\(q+(-1.91788 + 1.10729i) q^{2} +(0.302150 - 1.70549i) q^{3} +(1.45217 - 2.51523i) q^{4} -1.00000 q^{5} +(1.30898 + 3.60549i) q^{6} +(2.53521 - 0.756781i) q^{7} +2.00271i q^{8} +(-2.81741 - 1.03063i) q^{9} +(1.91788 - 1.10729i) q^{10} +1.58936i q^{11} +(-3.85093 - 3.23664i) q^{12} +(1.44269 - 0.832938i) q^{13} +(-4.02424 + 4.25861i) q^{14} +(-0.302150 + 1.70549i) q^{15} +(0.686756 + 1.18950i) q^{16} +(-1.59537 - 2.76327i) q^{17} +(6.54465 - 1.14306i) q^{18} +(-5.82047 - 3.36045i) q^{19} +(-1.45217 + 2.51523i) q^{20} +(-0.524670 - 4.55244i) q^{21} +(-1.75987 - 3.04819i) q^{22} -8.51380i q^{23} +(3.41561 + 0.605120i) q^{24} +1.00000 q^{25} +(-1.84460 + 3.19495i) q^{26} +(-2.60901 + 4.49367i) q^{27} +(1.77807 - 7.47560i) q^{28} +(3.79591 + 2.19157i) q^{29} +(-1.30898 - 3.60549i) q^{30} +(-4.71121 - 2.72002i) q^{31} +(-6.10303 - 3.52358i) q^{32} +(2.71063 + 0.480224i) q^{33} +(6.11945 + 3.53307i) q^{34} +(-2.53521 + 0.756781i) q^{35} +(-6.68362 + 5.58978i) q^{36} +(5.21460 - 9.03195i) q^{37} +14.8839 q^{38} +(-0.984661 - 2.71217i) q^{39} -2.00271i q^{40} +(0.207028 + 0.358583i) q^{41} +(6.04711 + 8.15006i) q^{42} +(2.14880 - 3.72183i) q^{43} +(3.99759 + 2.30801i) q^{44} +(2.81741 + 1.03063i) q^{45} +(9.42721 + 16.3284i) q^{46} +(1.73001 + 2.99646i) q^{47} +(2.23618 - 0.811851i) q^{48} +(5.85457 - 3.83719i) q^{49} +(-1.91788 + 1.10729i) q^{50} +(-5.19477 + 1.88598i) q^{51} -4.83826i q^{52} +(-0.301628 + 0.174145i) q^{53} +(0.0279834 - 11.5072i) q^{54} -1.58936i q^{55} +(1.51562 + 5.07730i) q^{56} +(-7.48987 + 8.91140i) q^{57} -9.70678 q^{58} +(1.25895 - 2.18056i) q^{59} +(3.85093 + 3.23664i) q^{60} +(-9.88538 + 5.70733i) q^{61} +12.0474 q^{62} +(-7.92268 - 0.480699i) q^{63} +12.8594 q^{64} +(-1.44269 + 0.832938i) q^{65} +(-5.73041 + 2.08044i) q^{66} +(-5.42062 + 9.38878i) q^{67} -9.26699 q^{68} +(-14.5202 - 2.57244i) q^{69} +(4.02424 - 4.25861i) q^{70} -8.45822i q^{71} +(2.06406 - 5.64247i) q^{72} +(-9.85355 + 5.68895i) q^{73} +23.0962i q^{74} +(0.302150 - 1.70549i) q^{75} +(-16.9046 + 9.75986i) q^{76} +(1.20279 + 4.02935i) q^{77} +(4.89161 + 4.11131i) q^{78} +(3.52228 + 6.10077i) q^{79} +(-0.686756 - 1.18950i) q^{80} +(6.87561 + 5.80741i) q^{81} +(-0.794108 - 0.458479i) q^{82} +(4.33787 - 7.51342i) q^{83} +(-12.2123 - 5.29124i) q^{84} +(1.59537 + 2.76327i) q^{85} +9.51735i q^{86} +(4.88464 - 5.81171i) q^{87} -3.18302 q^{88} +(0.218561 - 0.378558i) q^{89} +(-6.54465 + 1.14306i) q^{90} +(3.02717 - 3.20347i) q^{91} +(-21.4141 - 12.3635i) q^{92} +(-6.06246 + 7.21308i) q^{93} +(-6.63589 - 3.83123i) q^{94} +(5.82047 + 3.36045i) q^{95} +(-7.85348 + 9.34402i) q^{96} +(3.10554 + 1.79298i) q^{97} +(-6.97946 + 13.8419i) q^{98} +(1.63804 - 4.47787i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9}+O(q^{10}) $ 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9	$ 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9} + 15 q^{12} - 6 q^{13} - 6 q^{14} - q^{15} - 16 q^{16} + 3 q^{17} + 41 q^{18} - 16 q^{20} - 17 q^{21} - 21 q^{22} - 26 q^{24} + 32 q^{25} - 12 q^{26} - 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 24 q^{31} - 19 q^{33} + 30 q^{34} - q^{35} + 18 q^{36} - q^{37} - 60 q^{38} - 36 q^{39} - 6 q^{41} + 44 q^{42} - 19 q^{43} - 21 q^{44} - 7 q^{45} + 6 q^{46} - 15 q^{47} + 35 q^{48} + 23 q^{49} - 9 q^{51} + 24 q^{53} - 58 q^{54} + 33 q^{56} + 27 q^{57} + 15 q^{59} - 15 q^{60} - 9 q^{61} - 11 q^{63} + 76 q^{64} + 6 q^{65} + 22 q^{66} + 25 q^{67} - 6 q^{68} + 50 q^{69} + 6 q^{70} + 61 q^{72} + 12 q^{73} + q^{75} - 54 q^{76} - 27 q^{77} - 42 q^{78} - 2 q^{79} + 16 q^{80} + 43 q^{81} - 24 q^{82} + 42 q^{83} - 36 q^{84} - 3 q^{85} - 55 q^{87} - 84 q^{88} - 30 q^{89} - 41 q^{90} - 57 q^{91} + 6 q^{92} - 48 q^{93} + 24 q^{94} - 9 q^{96} + 42 q^{97} - 6 q^{98} - q^{99}+O(q^{100}) $ 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9 + 15 * q^12 - 6 * q^13 - 6 * q^14 - q^15 - 16 * q^16 + 3 * q^17 + 41 * q^18 - 16 * q^20 - 17 * q^21 - 21 * q^22 - 26 * q^24 + 32 * q^25 - 12 * q^26 - 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 24 * q^31 - 19 * q^33 + 30 * q^34 - q^35 + 18 * q^36 - q^37 - 60 * q^38 - 36 * q^39 - 6 * q^41 + 44 * q^42 - 19 * q^43 - 21 * q^44 - 7 * q^45 + 6 * q^46 - 15 * q^47 + 35 * q^48 + 23 * q^49 - 9 * q^51 + 24 * q^53 - 58 * q^54 + 33 * q^56 + 27 * q^57 + 15 * q^59 - 15 * q^60 - 9 * q^61 - 11 * q^63 + 76 * q^64 + 6 * q^65 + 22 * q^66 + 25 * q^67 - 6 * q^68 + 50 * q^69 + 6 * q^70 + 61 * q^72 + 12 * q^73 + q^75 - 54 * q^76 - 27 * q^77 - 42 * q^78 - 2 * q^79 + 16 * q^80 + 43 * q^81 - 24 * q^82 + 42 * q^83 - 36 * q^84 - 3 * q^85 - 55 * q^87 - 84 * q^88 - 30 * q^89 - 41 * q^90 - 57 * q^91 + 6 * q^92 - 48 * q^93 + 24 * q^94 - 9 * q^96 + 42 * q^97 - 6 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.91788	+	1.10729i	−1.35614	+	0.782970i	−0.989102	−	0.147235i	$-0.952963\pi$
$2$	−1.91788	+	1.10729i	−1.35614	+	0.782970i	−0.367042	+	0.930204i	$0.619629\pi$
$3$	0.302150	−	1.70549i	0.174446	−	0.984667i
$3$	0.302150	−	1.70549i	0.174446	−	0.984667i
$4$	1.45217	−	2.51523i	0.726084	−	1.25761i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	1.30898	+	3.60549i	0.534390	+	1.47194i
$7$	2.53521	−	0.756781i	0.958219	−	0.286036i
$7$	2.53521	−	0.756781i	0.958219	−	0.286036i
$8$			2.00271i			0.708066i
$9$	−2.81741	−	1.03063i	−0.939137	−	0.343543i
$10$	1.91788	−	1.10729i	0.606486	−	0.350155i
$11$			1.58936i			0.479209i	0.970871	+	0.239604i	$0.0770177\pi$
$11$			1.58936i			0.479209i	−0.970871	+	0.239604i	$0.922982\pi$
$12$	−3.85093	−	3.23664i	−1.11167	−	0.934336i
$13$	1.44269	−	0.832938i	0.400131	−	0.231016i	−0.286410	−	0.958107i	$-0.592462\pi$
$13$	1.44269	−	0.832938i	0.400131	−	0.231016i	0.686540	+	0.727092i	$0.259129\pi$
$14$	−4.02424	+	4.25861i	−1.07552	+	1.13816i
$15$	−0.302150	+	1.70549i	−0.0780148	+	0.440356i
$16$	0.686756	+	1.18950i	0.171689	+	0.297374i
$17$	−1.59537	−	2.76327i	−0.386935	−	0.670190i	0.605101	−	0.796149i	$-0.293133\pi$
$17$	−1.59537	−	2.76327i	−0.386935	−	0.670190i	−0.992036	+	0.125958i	$0.959799\pi$
$18$	6.54465	−	1.14306i	1.54259	−	0.269422i
$19$	−5.82047	−	3.36045i	−1.33531	−	0.770940i	−0.349199	−	0.937048i	$-0.613546\pi$
$19$	−5.82047	−	3.36045i	−1.33531	−	0.770940i	−0.986107	+	0.166109i	$0.946880\pi$
$20$	−1.45217	+	2.51523i	−0.324714	+	0.562422i
$21$	−0.524670	−	4.55244i	−0.114492	−	0.993424i
$22$	−1.75987	−	3.04819i	−0.375206	−	0.649876i
$23$		−	8.51380i		−	1.77525i	−0.460567	−	0.887625i	$-0.652354\pi$
$23$		−	8.51380i		−	1.77525i	0.460567	−	0.887625i	$-0.347646\pi$
$24$	3.41561	+	0.605120i	0.697209	+	0.123520i
$25$	1.00000			0.200000
$26$	−1.84460	+	3.19495i	−0.361756	+	0.626580i
$27$	−2.60901	+	4.49367i	−0.502105	+	0.864807i
$28$	1.77807	−	7.47560i	0.336024	−	1.41276i
$29$	3.79591	+	2.19157i	0.704883	+	0.406964i	0.809163	−	0.587584i	$-0.199921\pi$
$29$	3.79591	+	2.19157i	0.704883	+	0.406964i	−0.104281	+	0.994548i	$0.533254\pi$
$30$	−1.30898	−	3.60549i	−0.238986	−	0.658270i
$31$	−4.71121	−	2.72002i	−0.846158	−	0.488530i	0.0131944	−	0.999913i	$-0.495800\pi$
$31$	−4.71121	−	2.72002i	−0.846158	−	0.488530i	−0.859353	+	0.511383i	$0.829133\pi$
$32$	−6.10303	−	3.52358i	−1.07887	−	0.622888i
$33$	2.71063	+	0.480224i	0.471861	+	0.0835962i
$34$	6.11945	+	3.53307i	1.04948	+	0.605916i
$35$	−2.53521	+	0.756781i	−0.428528	+	0.127919i
$36$	−6.68362	+	5.58978i	−1.11394	+	0.931630i
$37$	5.21460	−	9.03195i	0.857275	−	1.48484i	−0.0172439	−	0.999851i	$-0.505489\pi$
$37$	5.21460	−	9.03195i	0.857275	−	1.48484i	0.874519	−	0.484992i	$-0.161178\pi$
$38$	14.8839			2.41449
$39$	−0.984661	−	2.71217i	−0.157672	−	0.434295i
$40$		−	2.00271i		−	0.316657i
$41$	0.207028	+	0.358583i	0.0323323	+	0.0560013i	0.881739	−	0.471738i	$-0.156373\pi$
$41$	0.207028	+	0.358583i	0.0323323	+	0.0560013i	−0.849406	+	0.527739i	$0.823040\pi$
$42$	6.04711	+	8.15006i	0.933089	+	1.25758i
$43$	2.14880	−	3.72183i	0.327689	−	0.567574i	−0.654364	−	0.756180i	$-0.727063\pi$
$43$	2.14880	−	3.72183i	0.327689	−	0.567574i	0.982053	+	0.188606i	$0.0603968\pi$
$44$	3.99759	+	2.30801i	0.602659	+	0.347946i
$45$	2.81741	+	1.03063i	0.419995	+	0.153637i
$46$	9.42721	+	16.3284i	1.38997	+	2.40749i
$47$	1.73001	+	2.99646i	0.252348	+	0.437079i	0.964172	−	0.265279i	$-0.0854640\pi$
$47$	1.73001	+	2.99646i	0.252348	+	0.437079i	−0.711824	+	0.702358i	$0.752131\pi$
$48$	2.23618	−	0.811851i	0.322765	−	0.117181i
$49$	5.85457	−	3.83719i	0.836367	−	0.548171i
$50$	−1.91788	+	1.10729i	−0.271229	+	0.156594i
$51$	−5.19477	+	1.88598i	−0.727414	+	0.264089i
$52$		−	4.83826i		−	0.670946i
$53$	−0.301628	+	0.174145i	−0.0414318	+	0.0239206i	−0.520573	−	0.853817i	$-0.674282\pi$
$53$	−0.301628	+	0.174145i	−0.0414318	+	0.0239206i	0.479141	+	0.877738i	$0.340948\pi$
$54$	0.0279834	−	11.5072i	0.00380805	−	1.56594i
$55$		−	1.58936i		−	0.214309i
$56$	1.51562	+	5.07730i	0.202533	+	0.678483i
$57$	−7.48987	+	8.91140i	−0.992058	+	1.18034i
$58$	−9.70678			−1.27456
$59$	1.25895	−	2.18056i	0.163901	−	0.283885i	−0.772363	−	0.635181i	$-0.780926\pi$
$59$	1.25895	−	2.18056i	0.163901	−	0.283885i	0.936264	+	0.351296i	$0.114259\pi$
$60$	3.85093	+	3.23664i	0.497153	+	0.417848i
$61$	−9.88538	+	5.70733i	−1.26569	+	0.730748i	−0.974170	−	0.225815i	$-0.927495\pi$
$61$	−9.88538	+	5.70733i	−1.26569	+	0.730748i	−0.291523	+	0.956564i	$0.594162\pi$
$62$	12.0474			1.53002
$63$	−7.92268	−	0.480699i	−0.998164	−	0.0605623i
$64$	12.8594			1.60743
$65$	−1.44269	+	0.832938i	−0.178944	+	0.103313i
$66$	−5.73041	+	2.08044i	−0.705364	+	0.256084i
$67$	−5.42062	+	9.38878i	−0.662234	+	1.14702i	0.317794	+	0.948160i	$0.397058\pi$
$67$	−5.42062	+	9.38878i	−0.662234	+	1.14702i	−0.980027	+	0.198862i	$0.936275\pi$
$68$	−9.26699			−1.12379
$69$	−14.5202	−	2.57244i	−1.74803	−	0.309686i
$70$	4.02424	−	4.25861i	0.480989	−	0.509002i
$71$		−	8.45822i		−	1.00381i	−0.864924	−	0.501903i	$-0.832633\pi$
$71$		−	8.45822i		−	1.00381i	0.864924	−	0.501903i	$-0.167367\pi$
$72$	2.06406	−	5.64247i	0.243251	−	0.664971i
$73$	−9.85355	+	5.68895i	−1.15327	+	0.665842i	−0.949682	−	0.313215i	$-0.898594\pi$
$73$	−9.85355	+	5.68895i	−1.15327	+	0.665842i	−0.203589	+	0.979056i	$0.565261\pi$
$74$			23.0962i			2.68488i
$75$	0.302150	−	1.70549i	0.0348893	−	0.196933i
$76$	−16.9046	+	9.75986i	−1.93909	+	1.11953i
$77$	1.20279	+	4.02935i	0.137071	+	0.459187i
$78$	4.89161	+	4.11131i	0.553866	+	0.465514i
$79$	3.52228	+	6.10077i	0.396287	+	0.686390i	0.993265	−	0.115868i	$-0.0369651\pi$
$79$	3.52228	+	6.10077i	0.396287	+	0.686390i	−0.596977	+	0.802258i	$0.703632\pi$
$80$	−0.686756	−	1.18950i	−0.0767816	−	0.132990i
$81$	6.87561	+	5.80741i	0.763956	+	0.645268i
$82$	−0.794108	−	0.458479i	−0.0876946	−	0.0506305i
$83$	4.33787	−	7.51342i	0.476143	−	0.824704i	−0.523483	−	0.852036i	$-0.675368\pi$
$83$	4.33787	−	7.51342i	0.476143	−	0.824704i	0.999626	+	0.0273316i	$0.00870101\pi$
$84$	−12.2123	−	5.29124i	−1.33247	−	0.577322i
$85$	1.59537	+	2.76327i	0.173042	+	0.299718i
$86$			9.51735i			1.02628i
$87$	4.88464	−	5.81171i	0.523688	−	0.623081i
$88$	−3.18302			−0.339312
$89$	0.218561	−	0.378558i	0.0231674	−	0.0401271i	−0.854209	−	0.519929i	$-0.825958\pi$
$89$	0.218561	−	0.378558i	0.0231674	−	0.0401271i	0.877377	+	0.479802i	$0.159292\pi$
$90$	−6.54465	+	1.14306i	−0.689866	+	0.120489i
$91$	3.02717	−	3.20347i	0.317334	−	0.335815i
$92$	−21.4141	−	12.3635i	−2.23258	−	1.28898i
$93$	−6.06246	+	7.21308i	−0.628648	+	0.747962i
$94$	−6.63589	−	3.83123i	−0.684440	−	0.395161i
$95$	5.82047	+	3.36045i	0.597167	+	0.344775i
$96$	−7.85348	+	9.34402i	−0.801542	+	0.953670i
$97$	3.10554	+	1.79298i	0.315320	+	0.182050i	0.649304	−	0.760529i	$-0.275060\pi$
$97$	3.10554	+	1.79298i	0.315320	+	0.182050i	−0.333985	+	0.942578i	$0.608393\pi$
$98$	−6.97946	+	13.8419i	−0.705032	+	1.39825i
$99$	1.63804	−	4.47787i	0.164629	−	0.450043i
$100$	1.45217	−	2.51523i	0.145217	−	0.251523i
$101$	8.28504			0.824392			0.412196	−	0.911095i	$-0.364762\pi$
$101$	8.28504			0.824392			0.412196	+	0.911095i	$0.364762\pi$
$102$	7.87462	−	9.36917i	0.779703	−	0.927686i
$103$			1.75039i			0.172471i	0.996275	+	0.0862357i	$0.0274838\pi$
$103$			1.75039i			0.172471i	−0.996275	+	0.0862357i	$0.972516\pi$
$104$	1.66814	+	2.88930i	0.163574	+	0.283319i
$105$	0.524670	+	4.55244i	0.0512026	+	0.444273i
$106$	0.385657	−	0.667977i	0.0374583	−	0.0648797i
$107$	10.8669	+	6.27401i	1.05054	+	0.606531i	0.922801	−	0.385276i	$-0.125894\pi$
$107$	10.8669	+	6.27401i	1.05054	+	0.606531i	0.127742	+	0.991807i	$0.459227\pi$
$108$	7.51388	+	13.0878i	0.723023	+	1.25938i
$109$	5.51885	+	9.55892i	0.528610	+	0.915579i	0.999444	+	0.0333567i	$0.0106197\pi$
$109$	5.51885	+	9.55892i	0.528610	+	0.915579i	−0.470834	+	0.882222i	$0.656047\pi$
$110$	1.75987	+	3.04819i	0.167797	+	0.290633i
$111$	−13.8283	−	11.6225i	−1.31253	−	1.10316i
$112$	2.64126	+	2.49590i	0.249575	+	0.235840i
$113$	−3.40337	+	1.96494i	−0.320163	+	0.184846i	−0.651465	−	0.758679i	$-0.725845\pi$
$113$	−3.40337	+	1.96494i	−0.320163	+	0.184846i	0.331302	+	0.943525i	$0.392512\pi$
$114$	4.49718	−	25.3844i	0.421199	−	2.37747i
$115$			8.51380i			0.793916i
$116$	11.0246	−	6.36505i	1.02361	−	0.590980i
$117$	−4.92311	+	0.859849i	−0.455141	+	0.0794931i
$118$			5.57607i			0.513318i
$119$	−6.13579	−	5.79811i	−0.562467	−	0.531512i
$120$	−3.41561	−	0.605120i	−0.311802	−	0.0552397i
$121$	8.47395			0.770359
$122$	12.6393	−	21.8919i	1.14431	−	1.98200i
$123$	0.674114	−	0.244739i	0.0607828	−	0.0220674i
$124$	−13.6829	+	7.89984i	−1.22876	+	0.709427i
$125$	−1.00000			−0.0894427
$126$	15.7270	−	7.85076i	1.40107	−	0.699401i
$127$	13.4434			1.19291			0.596456	−	0.802646i	$-0.296575\pi$
$127$	13.4434			1.19291			0.596456	+	0.802646i	$0.296575\pi$
$128$	−12.4568	+	7.19193i	−1.10103	+	0.635682i
$129$	−5.69830	−	4.78932i	−0.501707	−	0.421676i
$130$	1.84460	−	3.19495i	0.161782	−	0.280215i
$131$	8.68421			0.758743			0.379371	−	0.925245i	$-0.376140\pi$
$131$	8.68421			0.758743			0.379371	+	0.925245i	$0.376140\pi$
$132$	5.14417	−	6.12050i	0.447742	−	0.532721i
$133$	−17.2992	−	4.11462i	−1.50003	−	0.356783i
$134$		−	24.0087i		−	2.07404i
$135$	2.60901	−	4.49367i	0.224548	−	0.386753i
$136$	5.53403	−	3.19507i	0.474539	−	0.273975i
$137$		−	3.50456i		−	0.299415i	−0.988730	−	0.149707i	$-0.952167\pi$
$137$		−	3.50456i		−	0.299415i	0.988730	−	0.149707i	$-0.0478332\pi$
$138$	30.6964	−	11.1444i	2.61305	−	0.948675i
$139$	19.8175	−	11.4416i	1.68090	−	0.970467i	0.719831	−	0.694149i	$-0.244219\pi$
$139$	19.8175	−	11.4416i	1.68090	−	0.970467i	0.961066	−	0.276317i	$-0.0891141\pi$
$140$	−1.77807	+	7.47560i	−0.150274	+	0.631803i
$141$	5.63317	−	2.04514i	0.474399	−	0.172232i
$142$	9.36568	+	16.2218i	0.785950	+	1.36131i
$143$	1.32384	+	2.29295i	0.110705	+	0.191746i
$144$	−0.708944	−	4.05909i	−0.0590786	−	0.338257i
$145$	−3.79591	−	2.19157i	−0.315233	−	0.182000i
$146$	12.5986	−	21.8214i	1.04267	−	1.80595i
$147$	−4.77535	−	11.1443i	−0.393864	−	0.919169i
$148$	−15.1449	−	26.2318i	−1.24491	−	2.15624i
$149$			18.9788i			1.55480i	0.629004	+	0.777402i	$0.283463\pi$
$149$			18.9788i			1.55480i	−0.629004	+	0.777402i	$0.716537\pi$
$150$	1.30898	+	3.60549i	0.106878	+	0.294387i
$151$	−1.08223			−0.0880705			−0.0440353	−	0.999030i	$-0.514021\pi$
$151$	−1.08223			−0.0880705			−0.0440353	+	0.999030i	$0.514021\pi$
$152$	6.73002	−	11.6567i	0.545876	−	0.945486i
$153$	1.64692	+	9.42949i	0.133145	+	0.762329i
$154$	−6.76845	−	6.39596i	−0.545417	−	0.515401i
$155$	4.71121	+	2.72002i	0.378414	+	0.218477i
$156$	−8.25162	−	1.46188i	−0.660658	−	0.117044i
$157$	−2.04915	−	1.18308i	−0.163540	−	0.0944199i	0.415996	−	0.909366i	$-0.363433\pi$
$157$	−2.04915	−	1.18308i	−0.163540	−	0.0944199i	−0.579536	+	0.814946i	$0.696766\pi$
$158$	−13.5106	−	7.80034i	−1.07484	−	0.620562i
$159$	0.205866	+	0.567042i	0.0163262	+	0.0449694i
$160$	6.10303	+	3.52358i	0.482487	+	0.278564i
$161$	−6.44308	−	21.5843i	−0.507786	−	1.70108i
$162$	−19.6170	−	3.52463i	−1.54126	−	0.276921i
$163$	−6.69131	+	11.5897i	−0.524104	+	0.907774i	0.475503	+	0.879714i	$0.342266\pi$
$163$	−6.69131	+	11.5897i	−0.524104	+	0.907774i	−0.999606	+	0.0280599i	$0.991067\pi$
$164$	1.20256			0.0939039
$165$	−2.71063	−	0.480224i	−0.211023	−	0.0373854i
$166$			19.2131i			1.49122i
$167$	−4.11383	−	7.12536i	−0.318338	−	0.551377i	0.661804	−	0.749677i	$-0.269791\pi$
$167$	−4.11383	−	7.12536i	−0.318338	−	0.551377i	−0.980141	+	0.198300i	$0.936458\pi$
$168$	9.11724	−	1.05076i	0.703410	−	0.0810683i
$169$	−5.11243	+	8.85498i	−0.393264	+	0.681153i
$170$	−6.11945	−	3.53307i	−0.469341	−	0.270974i
$171$	12.9353	+	15.4665i	0.989185	+	1.18275i
$172$	−6.24084	−	10.8094i	−0.475859	−	0.824212i
$173$	−5.50218	−	9.53006i	−0.418323	−	0.724557i	0.577448	−	0.816428i	$-0.304049\pi$
$173$	−5.50218	−	9.53006i	−0.418323	−	0.724557i	−0.995771	+	0.0918707i	$0.970715\pi$
$174$	−2.93291	+	16.5548i	−0.222343	+	1.25502i
$175$	2.53521	−	0.756781i	0.191644	−	0.0572072i
$176$	−1.89053	+	1.09150i	−0.142504	+	0.0822748i
$177$	−3.33854	−	2.80598i	−0.250940	−	0.210911i
$178$			0.968037i			0.0725574i
$179$	5.12290	−	2.95771i	0.382903	−	0.221069i	−0.296177	−	0.955133i	$-0.595712\pi$
$179$	5.12290	−	2.95771i	0.382903	−	0.221069i	0.679081	+	0.734064i	$0.262379\pi$
$180$	6.68362	−	5.58978i	0.498167	−	0.416638i
$181$			4.08392i			0.303556i	0.988415	+	0.151778i	$0.0484998\pi$
$181$			4.08392i			0.303556i	−0.988415	+	0.151778i	$0.951500\pi$
$182$	−2.25858	+	9.49581i	−0.167417	+	0.703877i
$183$	6.74694	+	18.5839i	0.498748	+	1.37376i
$184$	17.0507			1.25699
$185$	−5.21460	+	9.03195i	−0.383385	+	0.664042i
$186$	3.64011	−	20.5467i	0.266906	−	1.50656i
$187$	4.39181	−	2.53561i	0.321161	−	0.185422i
$188$	10.0491			0.732902
$189$	−3.21367	+	13.3668i	−0.233760	+	0.972294i
$190$	−14.8839			−1.07979
$191$	3.69785	−	2.13496i	0.267567	−	0.154480i	−0.360214	−	0.932870i	$-0.617296\pi$
$191$	3.69785	−	2.13496i	0.267567	−	0.154480i	0.627782	+	0.778390i	$0.283963\pi$
$192$	3.88548	−	21.9317i	0.280411	−	1.58278i
$193$	10.4800	−	18.1518i	0.754364	−	1.30660i	−0.191326	−	0.981527i	$-0.561279\pi$
$193$	10.4800	−	18.1518i	0.754364	−	1.30660i	0.945690	−	0.325070i	$-0.105388\pi$
$194$	−7.94139			−0.570158
$195$	0.984661	+	2.71217i	0.0705130	+	0.194223i
$196$	−1.14961	−	20.2978i	−0.0821147	−	1.44984i
$197$			20.8279i			1.48393i	0.670439	+	0.741964i	$0.266106\pi$
$197$			20.8279i			1.48393i	−0.670439	+	0.741964i	$0.733894\pi$
$198$	1.81673	+	10.4018i	0.129109	+	0.739222i
$199$	10.3452	−	5.97279i	0.733351	−	0.423400i	−0.0862961	−	0.996270i	$-0.527503\pi$
$199$	10.3452	−	5.97279i	0.733351	−	0.423400i	0.819647	+	0.572869i	$0.194170\pi$
$200$			2.00271i			0.141613i
$201$	14.3747	+	12.0816i	1.01391	+	0.852173i
$202$	−15.8897	+	9.17391i	−1.11799	+	0.645474i
$203$	11.2820	+	2.68342i	0.791839	+	0.188339i
$204$	−2.80002	+	15.8048i	−0.196041	+	1.10656i
$205$	−0.207028	−	0.358583i	−0.0144595	−	0.0250445i
$206$	−1.93819	−	3.35704i	−0.135040	−	0.233896i
$207$	−8.77457	+	23.9869i	−0.609875	+	1.66720i
$208$	1.98155	+	1.14405i	0.137396	+	0.0793256i
$209$	5.34095	−	9.25079i	0.369441	−	0.639891i
$210$	−6.04711	−	8.15006i	−0.417290	−	0.562408i
$211$	−0.551620	−	0.955434i	−0.0379751	−	0.0657748i	0.846413	−	0.532527i	$-0.178757\pi$
$211$	−0.551620	−	0.955434i	−0.0379751	−	0.0657748i	−0.884388	+	0.466752i	$0.845424\pi$
$212$			1.01155i			0.0694736i
$213$	−14.4254	−	2.55565i	−0.988415	−	0.175110i
$214$	−27.7885			−1.89958
$215$	−2.14880	+	3.72183i	−0.146547	+	0.253827i
$216$	−8.99953	−	5.22510i	−0.612341	−	0.355523i
$217$	−14.0024	−	3.33046i	−0.950542	−	0.226086i
$218$	−21.1689	−	12.2219i	−1.43374	−	0.827771i
$219$	6.72521	+	18.5241i	0.454448	+	1.25174i
$220$	−3.99759	−	2.30801i	−0.269517	−	0.155606i
$221$	−4.60326	−	2.65769i	−0.309649	−	0.178776i
$222$	39.3904	+	6.97852i	2.64371	+	0.468368i
$223$	−11.3029	−	6.52571i	−0.756895	−	0.436994i	0.0712847	−	0.997456i	$-0.477290\pi$
$223$	−11.3029	−	6.52571i	−0.756895	−	0.436994i	−0.828180	+	0.560462i	$0.810623\pi$
$224$	−18.1390	−	4.31437i	−1.21196	−	0.288266i
$225$	−2.81741	−	1.03063i	−0.187827	−	0.0687086i
$226$	4.35150	−	7.53702i	0.289458	−	0.501355i
$227$	24.3345			1.61514			0.807570	−	0.589772i	$-0.200782\pi$
$227$	24.3345			1.61514			0.807570	+	0.589772i	$0.200782\pi$
$228$	11.5377	+	31.7796i	0.764100	+	2.10465i
$229$		−	10.2460i		−	0.677074i	−0.940953	−	0.338537i	$-0.890068\pi$
$229$		−	10.2460i		−	0.677074i	0.940953	−	0.338537i	$-0.109932\pi$
$230$	−9.42721	−	16.3284i	−0.621612	−	1.07666i
$231$	7.23545	−	0.833888i	0.476058	−	0.0548658i
$232$	−4.38909	+	7.60212i	−0.288158	+	0.499104i
$233$	−18.9788	−	10.9574i	−1.24334	−	0.717843i	−0.273568	−	0.961853i	$-0.588204\pi$
$233$	−18.9788	−	10.9574i	−1.24334	−	0.717843i	−0.969773	+	0.244010i	$0.921537\pi$
$234$	8.48981	−	7.10037i	0.554996	−	0.464166i
$235$	−1.73001	−	2.99646i	−0.112853	−	0.195468i
$236$	−3.65641	−	6.33308i	−0.238012	−	0.412248i
$237$	11.4691	−	4.16387i	0.744996	−	0.270473i
$238$	18.1879	+	4.32598i	1.17894	+	0.280412i
$239$	13.5602	−	7.82901i	0.877139	−	0.506416i	0.00742475	−	0.999972i	$-0.497637\pi$
$239$	13.5602	−	7.82901i	0.877139	−	0.506416i	0.869714	+	0.493556i	$0.164303\pi$
$240$	−2.23618	+	0.811851i	−0.144345	+	0.0524047i
$241$			17.7663i			1.14443i	0.820103	+	0.572215i	$0.193916\pi$
$241$			17.7663i			1.14443i	−0.820103	+	0.572215i	$0.806084\pi$
$242$	−16.2520	+	9.38309i	−1.04472	+	0.603168i
$243$	11.9820	−	9.97159i	0.768643	−	0.639678i
$244$			33.1520i			2.12234i
$245$	−5.85457	+	3.83719i	−0.374035	+	0.245149i
$246$	−1.02187	+	1.21582i	−0.0651522	+	0.0775176i
$247$	−11.1962			−0.712396
$248$	5.44742	−	9.43521i	0.345911	−	0.599136i
$249$	−11.5034	−	9.66839i	−0.728997	−	0.612709i
$250$	1.91788	−	1.10729i	0.121297	−	0.0700310i
$251$	−22.3868			−1.41304			−0.706521	−	0.707692i	$-0.749736\pi$
$251$	−22.3868			−1.41304			−0.706521	+	0.707692i	$0.749736\pi$
$252$	−12.7141	+	19.2293i	−0.800915	+	1.21133i
$253$	13.5315			0.850715
$254$	−25.7828	+	14.8857i	−1.61776	+	0.934014i
$255$	5.19477	−	1.88598i	0.325309	−	0.118104i
$256$	3.06760	−	5.31323i	0.191725	−	0.332077i
$257$	20.2218			1.26140			0.630699	−	0.776027i	$-0.282768\pi$
$257$	20.2218			1.26140			0.630699	+	0.776027i	$0.282768\pi$
$258$	16.2318	+	2.87567i	1.01055	+	0.179031i
$259$	6.38489	−	26.8442i	0.396738	−	1.66802i
$260$			4.83826i			0.300056i
$261$	−8.43594	−	10.0867i	−0.522172	−	0.624353i
$262$	−16.6552	+	9.61591i	−1.02896	+	0.594073i
$263$			11.2808i			0.695603i	0.937568	+	0.347802i	$0.113072\pi$
$263$			11.2808i			0.695603i	−0.937568	+	0.347802i	$0.886928\pi$
$264$	−0.961751	+	5.42863i	−0.0591917	+	0.334109i
$265$	0.301628	−	0.174145i	0.0185289	−	0.0106976i
$266$	37.7338	−	11.2639i	2.31361	−	0.690632i
$267$	−0.579590	−	0.487135i	−0.0354703	−	0.0298122i
$268$	15.7433	+	27.2682i	0.961674	+	1.66567i
$269$	7.11002	+	12.3149i	0.433506	+	0.750854i	0.997172	−	0.0751484i	$-0.0239431\pi$
$269$	7.11002	+	12.3149i	0.433506	+	0.750854i	−0.563667	+	0.826002i	$0.690610\pi$
$270$	−0.0279834	+	11.5072i	−0.00170301	+	0.700307i
$271$	−19.5526	−	11.2887i	−1.18774	−	0.685740i	−0.229945	−	0.973204i	$-0.573855\pi$
$271$	−19.5526	−	11.2887i	−1.18774	−	0.685740i	−0.957792	+	0.287464i	$0.907188\pi$
$272$	2.19126	−	3.79538i	0.132865	−	0.230129i
$273$	−4.54884	−	6.13075i	−0.275308	−	0.371050i
$274$	3.88055	+	6.72132i	0.234433	+	0.406050i
$275$			1.58936i			0.0958417i
$276$	−27.5561	+	32.7860i	−1.65868	+	1.97349i
$277$	−19.1691			−1.15176			−0.575878	−	0.817535i	$-0.695340\pi$
$277$	−19.1691			−1.15176			−0.575878	+	0.817535i	$0.695340\pi$
$278$	−25.3383	+	43.8873i	−1.51969	+	2.63218i
$279$	10.4701	+	12.5189i	0.626827	+	0.749488i
$280$	−1.51562	−	5.07730i	−0.0905753	−	0.303427i
$281$	−18.9766	−	10.9562i	−1.13205	−	0.653590i	−0.187602	−	0.982245i	$-0.560071\pi$
$281$	−18.9766	−	10.9562i	−1.13205	−	0.653590i	−0.944450	+	0.328655i	$0.893405\pi$
$282$	−8.53917	+	10.1599i	−0.508500	+	0.605011i
$283$	−15.0955	−	8.71539i	−0.897334	−	0.518076i	−0.0209998	−	0.999779i	$-0.506685\pi$
$283$	−15.0955	−	8.71539i	−0.897334	−	0.518076i	−0.876334	+	0.481703i	$0.840018\pi$
$284$	−21.2743	−	12.2828i	−1.26240	−	0.728847i
$285$	7.48987	−	8.91140i	0.443662	−	0.527866i
$286$	−5.07791	−	2.93173i	−0.300263	−	0.173357i
$287$	0.796228	+	0.752408i	0.0469998	+	0.0444132i
$288$	13.5632	+	16.2173i	0.799221	+	0.955616i
$289$	3.40957	−	5.90556i	0.200563	−	0.347386i
$290$	9.70678			0.570002
$291$	3.99626	−	4.75472i	0.234265	−	0.278727i
$292$			33.0452i			1.93383i
$293$	9.83508	+	17.0349i	0.574572	+	0.995187i	0.996088	+	0.0883664i	$0.0281646\pi$
$293$	9.83508	+	17.0349i	0.574572	+	0.995187i	−0.421516	+	0.906821i	$0.638502\pi$
$294$	21.4985	+	16.0858i	1.25382	+	0.938141i
$295$	−1.25895	+	2.18056i	−0.0732988	+	0.126957i
$296$	18.0884	+	10.4434i	1.05137	+	0.607007i
$297$	−7.14204	−	4.14665i	−0.414423	−	0.240613i
$298$	−21.0150	−	36.3990i	−1.21736	−	2.10854i
$299$	−7.09147	−	12.2828i	−0.410110	−	0.710332i
$300$	−3.85093	−	3.23664i	−0.222334	−	0.186867i
$301$	2.63105	−	11.0618i	0.151651	−	0.637591i
$302$	2.07558	−	1.19834i	0.119436	−	0.0689566i
$303$	2.50332	−	14.1301i	0.143812	−	0.811751i
$304$		−	9.23123i		−	0.529447i
$305$	9.88538	−	5.70733i	0.566035	−	0.326801i
$306$	−13.5997	−	16.2610i	−0.777445	−	0.929579i
$307$		−	7.80959i		−	0.445717i	−0.974851	−	0.222858i	$-0.928461\pi$
$307$		−	7.80959i		−	0.445717i	0.974851	−	0.222858i	$-0.0715387\pi$
$308$	11.8814	+	2.82599i	0.677005	+	0.161026i
$309$	2.98528	+	0.528882i	0.169827	+	0.0300870i
$310$	−12.0474			−0.684244
$311$	−13.4558	+	23.3061i	−0.763006	+	1.32157i	0.178288	+	0.983978i	$0.442944\pi$
$311$	−13.4558	+	23.3061i	−0.763006	+	1.32157i	−0.941294	+	0.337587i	$0.890389\pi$
$312$	5.43171	−	1.97199i	0.307510	−	0.111642i
$313$	11.7067	−	6.75886i	0.661701	−	0.382033i	−0.131224	−	0.991353i	$-0.541891\pi$
$313$	11.7067	−	6.75886i	0.661701	−	0.382033i	0.792925	+	0.609319i	$0.208557\pi$
$314$	5.24002			0.295712
$315$	7.92268	+	0.480699i	0.446393	+	0.0270843i
$316$	20.4597			1.15095
$317$	−19.4471	+	11.2278i	−1.09226	+	0.630614i	−0.934176	−	0.356812i	$-0.883864\pi$
$317$	−19.4471	+	11.2278i	−1.09226	+	0.630614i	−0.158080	+	0.987426i	$0.550530\pi$
$318$	−1.02270	−	0.859564i	−0.0573504	−	0.0482020i
$319$	−3.48318	+	6.03305i	−0.195021	+	0.337786i
$320$	−12.8594			−0.718865
$321$	13.9837	−	16.6377i	0.780495	−	0.928628i
$322$	36.2570	+	34.2616i	2.02052	+	1.90932i
$323$			21.4447i			1.19321i
$324$	24.5915	−	8.86038i	1.36619	−	0.492243i
$325$	1.44269	−	0.832938i	0.0800261	−	0.0462031i
$326$		−	29.6368i		−	1.64143i
$327$	17.9702	−	6.52412i	0.993754	−	0.360785i
$328$	−0.718139	+	0.414618i	−0.0396526	+	0.0228934i
$329$	6.65360	+	6.28743i	0.366825	+	0.346637i
$330$	5.73041	−	2.08044i	0.315449	−	0.114524i
$331$	4.82516	+	8.35742i	0.265215	+	0.459366i	0.967620	−	0.252412i	$-0.0812238\pi$
$331$	4.82516	+	8.35742i	0.265215	+	0.459366i	−0.702405	+	0.711777i	$0.747890\pi$
$332$	−12.5986	−	21.8215i	−0.691440	−	1.19761i
$333$	−24.0003	+	20.0724i	−1.31521	+	1.09996i
$334$	15.7796	+	9.11037i	0.863423	+	0.498497i
$335$	5.42062	−	9.38878i	0.296160	−	0.512964i
$336$	5.05479	−	3.75051i	0.275761	−	0.204607i
$337$	−5.77089	−	9.99547i	−0.314360	−	0.544488i	0.664941	−	0.746896i	$-0.268457\pi$
$337$	−5.77089	−	9.99547i	−0.314360	−	0.544488i	−0.979301	+	0.202408i	$0.935123\pi$
$338$		−	22.6437i		−	1.23165i
$339$	2.32286	+	6.39814i	0.126160	+	0.347499i
$340$	9.26699			0.502573
$341$	4.32308	−	7.48779i	0.234108	−	0.405486i
$342$	−41.9341	−	15.3398i	−2.26754	−	0.829481i
$343$	11.9386	−	14.1587i	0.644626	−	0.764498i
$344$	7.45377	+	4.30343i	0.401880	+	0.232026i
$345$	14.5202	+	2.57244i	0.781742	+	0.138496i
$346$	21.1050	+	12.1850i	1.13461	+	0.655069i
$347$	21.8175	+	12.5964i	1.17123	+	0.676208i	0.953969	−	0.299906i	$-0.0969555\pi$
$347$	21.8175	+	12.5964i	1.17123	+	0.676208i	0.217258	+	0.976114i	$0.430289\pi$
$348$	−7.52447	−	20.7256i	−0.403354	−	1.11101i
$349$	29.0757	+	16.7869i	1.55639	+	0.898580i	0.997598	+	0.0692689i	$0.0220666\pi$
$349$	29.0757	+	16.7869i	1.55639	+	0.898580i	0.558788	+	0.829311i	$0.311267\pi$
$350$	−4.02424	+	4.25861i	−0.215105	+	0.227633i
$351$	−0.0210500	+	8.65612i	−0.00112357	+	0.462030i
$352$	5.60023	−	9.69988i	0.298493	−	0.517005i
$353$	−22.4770			−1.19633			−0.598165	−	0.801373i	$-0.704103\pi$
$353$	−22.4770			−1.19633			−0.598165	+	0.801373i	$0.704103\pi$
$354$	9.50994	+	1.68481i	0.505448	+	0.0895466i
$355$			8.45822i			0.448916i
$356$	−0.634773	−	1.09946i	−0.0336429	−	0.0582712i
$357$	−11.7426	+	8.71264i	−0.621482	+	0.461122i
$358$	−6.55006	+	11.3450i	−0.346181	+	0.599604i
$359$	−4.64044	−	2.67916i	−0.244913	−	0.141401i	0.372520	−	0.928024i	$-0.378494\pi$
$359$	−4.64044	−	2.67916i	−0.244913	−	0.141401i	−0.617433	+	0.786624i	$0.711827\pi$
$360$	−2.06406	+	5.64247i	−0.108785	+	0.297384i
$361$	13.0852	+	22.6643i	0.688696	+	1.19286i
$362$	−4.52207	−	7.83246i	−0.237675	−	0.411665i
$363$	2.56040	−	14.4523i	0.134386	−	0.758547i
$364$	−3.66150	−	12.2660i	−0.191915	−	0.642913i
$365$	9.85355	−	5.68895i	0.515759	−	0.297773i
$366$	−33.5175	−	28.1709i	−1.75199	−	1.47251i
$367$		−	17.8941i		−	0.934065i	−0.884240	−	0.467033i	$-0.845323\pi$
$367$		−	17.8941i		−	0.934065i	0.884240	−	0.467033i	$-0.154677\pi$
$368$	10.1271	−	5.84690i	0.527913	−	0.304791i
$369$	−0.213717	−	1.22364i	−0.0111256	−	0.0637004i
$370$		−	23.0962i		−	1.20072i
$371$	−0.632900	+	0.669760i	−0.0328585	+	0.0347722i
$372$	9.33883	+	25.7231i	0.484196	+	1.33368i
$373$	33.4568			1.73233			0.866164	−	0.499760i	$-0.166579\pi$
$373$	33.4568			1.73233			0.866164	+	0.499760i	$0.166579\pi$
$374$	−5.61530	+	9.72599i	−0.290360	+	0.502919i
$375$	−0.302150	+	1.70549i	−0.0156030	+	0.0880713i
$376$	−6.00106	+	3.46471i	−0.309481	+	0.178679i
$377$	7.30177			0.376060
$378$	−8.63750	−	29.1944i	−0.444265	−	1.50160i
$379$	10.4032			0.534377			0.267188	−	0.963644i	$-0.413905\pi$
$379$	10.4032			0.534377			0.267188	+	0.963644i	$0.413905\pi$
$380$	16.9046	−	9.75986i	0.867187	−	0.500670i
$381$	4.06193	−	22.9277i	0.208099	−	1.17462i
$382$	−4.72802	+	8.18917i	−0.241906	+	0.418994i
$383$	−8.53923			−0.436334			−0.218167	−	0.975911i	$-0.570008\pi$
$383$	−8.53923			−0.436334			−0.218167	+	0.975911i	$0.570008\pi$
$384$	8.50196	+	23.4180i	0.433864	+	1.19504i
$385$	−1.20279	−	4.02935i	−0.0613000	−	0.205355i
$386$			46.4173i			2.36258i
$387$	−9.88988	+	8.27131i	−0.502731	+	0.420454i
$388$	9.01952	−	5.20742i	0.457897	−	0.264367i
$389$			9.41815i			0.477519i	0.971079	+	0.238760i	$0.0767408\pi$
$389$			9.41815i			0.477519i	−0.971079	+	0.238760i	$0.923259\pi$
$390$	−4.89161	−	4.11131i	−0.247696	−	0.208184i
$391$	−23.5259	+	13.5827i	−1.18976	+	0.686906i
$392$	7.68480	+	11.7250i	0.388141	+	0.592203i
$393$	2.62393	−	14.8109i	0.132360	−	0.747109i
$394$	−23.0625	−	39.9454i	−1.16187	−	2.01242i
$395$	−3.52228	−	6.10077i	−0.177225	−	0.306963i
$396$	−8.88415	−	10.6226i	−0.446445	−	0.533808i
$397$	0.580178	+	0.334966i	0.0291183	+	0.0168114i	0.514488	−	0.857497i	$-0.327982\pi$
$397$	0.580178	+	0.334966i	0.0291183	+	0.0168114i	−0.485370	+	0.874309i	$0.661315\pi$
$398$	−13.2272	+	22.9102i	−0.663019	+	1.14838i
$399$	−12.2444	+	28.2605i	−0.612988	+	1.41479i
$400$	0.686756	+	1.18950i	0.0343378	+	0.0594748i
$401$			2.90268i			0.144953i	0.997370	+	0.0724765i	$0.0230902\pi$
$401$			2.90268i			0.144953i	−0.997370	+	0.0724765i	$0.976910\pi$
$402$	−40.9467	−	7.25423i	−2.04223	−	0.361808i
$403$	−9.06243			−0.451432
$404$	12.0313	−	20.8387i	0.598577	−	1.03677i
$405$	−6.87561	−	5.80741i	−0.341652	−	0.288573i
$406$	−24.6087	+	7.34591i	−1.22131	+	0.364571i
$407$	14.3550	+	8.28785i	0.711550	+	0.410814i
$408$	−3.77707	−	10.4036i	−0.186993	−	0.515057i
$409$	−18.3364	−	10.5865i	−0.906674	−	0.523469i	−0.0273148	−	0.999627i	$-0.508696\pi$
$409$	−18.3364	−	10.5865i	−0.906674	−	0.523469i	−0.879360	+	0.476158i	$0.842029\pi$
$410$	0.794108	+	0.458479i	0.0392182	+	0.0226426i
$411$	−5.97701	−	1.05890i	−0.294824	−	0.0522319i
$412$	4.40264	+	2.54186i	0.216902	+	0.125229i
$413$	1.54149	−	6.48093i	0.0758517	−	0.318906i
$414$	−9.73179	−	55.7198i	−0.478291	−	2.73848i
$415$	−4.33787	+	7.51342i	−0.212938	+	0.368819i
$416$	−11.7397			−0.575587
$417$	−13.5258	−	37.2557i	−0.662360	−	1.82442i
$418$			23.6558i			1.15704i
$419$	−9.60594	−	16.6380i	−0.469281	−	0.812818i	0.530103	−	0.847934i	$-0.322153\pi$
$419$	−9.60594	−	16.6380i	−0.469281	−	0.812818i	−0.999383	+	0.0351155i	$0.988820\pi$
$420$	12.2123	+	5.29124i	0.595901	+	0.258186i
$421$	−3.20298	+	5.54773i	−0.156104	+	0.270380i	−0.933460	−	0.358680i	$-0.883227\pi$
$421$	−3.20298	+	5.54773i	−0.156104	+	0.270380i	0.777357	+	0.629060i	$0.216560\pi$
$422$	2.11588	+	1.22160i	0.102999	+	0.0594667i
$423$	−1.78590	−	10.2253i	−0.0868336	−	0.497170i
$424$	−0.348763	−	0.604074i	−0.0169374	−	0.0293364i
$425$	−1.59537	−	2.76327i	−0.0773869	−	0.134038i
$426$	30.4960	−	11.0717i	1.47754	−	0.536424i
$427$	−20.7423	+	21.9503i	−1.00379	+	1.06225i
$428$	31.5611	−	18.2218i	1.52556	−	0.880785i
$429$	4.31061	−	1.56498i	0.208118	−	0.0755578i
$430$		−	9.51735i		−	0.458968i
$431$	28.4828	−	16.4445i	1.37197	−	0.792106i	0.380792	−	0.924661i	$-0.375651\pi$
$431$	28.4828	−	16.4445i	1.37197	−	0.792106i	0.991176	+	0.132555i	$0.0423180\pi$
$432$	−7.13695	−	0.0173557i	−0.343377	−	0.000835026i
$433$		−	3.26720i		−	0.157011i	−0.996914	−	0.0785057i	$-0.974985\pi$
$433$		−	3.26720i		−	0.157011i	0.996914	−	0.0785057i	$-0.0250149\pi$
$434$	30.5426	−	9.11721i	1.46609	−	0.437640i
$435$	−4.88464	+	5.81171i	−0.234201	+	0.278650i
$436$	32.0571			1.53526
$437$	−28.6102	+	49.5543i	−1.36861	+	2.37050i
$438$	−33.4096	−	28.0802i	−1.59637	−	1.34172i
$439$	−17.8610	+	10.3121i	−0.852459	+	0.492167i	−0.861480	−	0.507792i	$-0.830462\pi$
$439$	−17.8610	+	10.3121i	−0.852459	+	0.492167i	0.00902076	+	0.999959i	$0.497129\pi$
$440$	3.18302			0.151745
$441$	−20.4494	+	4.77706i	−0.973783	+	0.227479i
$442$	11.7713			0.559904
$443$	28.2156	−	16.2903i	1.34057	−	0.773976i	0.353675	−	0.935368i	$-0.384932\pi$
$443$	28.2156	−	16.2903i	1.34057	−	0.773976i	0.986890	+	0.161392i	$0.0515985\pi$
$444$	−49.3142	+	17.9036i	−2.34035	+	0.849669i
$445$	−0.218561	+	0.378558i	−0.0103608	+	0.0179454i
$446$	28.9033			1.36861
$447$	32.3682	+	5.73444i	1.53096	+	0.271230i
$448$	32.6014	−	9.73178i	1.54027	−	0.459784i
$449$			14.0530i			0.663201i	0.943420	+	0.331601i	$0.107589\pi$
$449$			14.0530i			0.663201i	−0.943420	+	0.331601i	$0.892411\pi$
$450$	6.54465	−	1.14306i	0.308518	−	0.0538844i
$451$	−0.569916	+	0.329041i	−0.0268363	+	0.0154939i
$452$			11.4137i			0.536854i
$453$	−0.326995	+	1.84573i	−0.0153636	+	0.0867201i
$454$	−46.6706	+	26.9453i	−2.19036	+	1.26461i
$455$	−3.02717	+	3.20347i	−0.141916	+	0.150181i
$456$	−17.8470	−	15.0001i	−0.835762	−	0.702443i
$457$	−4.07151	−	7.05206i	−0.190457	−	0.329881i	0.754945	−	0.655788i	$-0.227664\pi$
$457$	−4.07151	−	7.05206i	−0.190457	−	0.329881i	−0.945402	+	0.325907i	$0.894330\pi$
$458$	11.3452	+	19.6505i	0.530129	+	0.918210i
$459$	16.5795	+	0.0403183i	0.773867	+	0.00188190i
$460$	21.4141	+	12.3635i	0.998439	+	0.576449i
$461$	−17.6844	+	30.6304i	−0.823647	+	1.42660i	0.0793025	+	0.996851i	$0.474731\pi$
$461$	−17.6844	+	30.6304i	−0.823647	+	1.42660i	−0.902949	+	0.429747i	$0.858603\pi$
$462$	−12.9533	+	9.61101i	−0.602644	+	0.447145i
$463$	−15.5085	−	26.8615i	−0.720741	−	1.24836i	−0.960703	−	0.277578i	$-0.910468\pi$
$463$	−15.5085	−	26.8615i	−0.720741	−	1.24836i	0.239962	−	0.970782i	$-0.422865\pi$
$464$			6.02029i			0.279485i
$465$	6.06246	−	7.21308i	0.281140	−	0.334499i
$466$	48.5319			2.24820
$467$	0.569520	−	0.986438i	0.0263542	−	0.0456469i	−0.852547	−	0.522650i	$-0.824944\pi$
$467$	0.569520	−	0.986438i	0.0263542	−	0.0456469i	0.878902	+	0.477003i	$0.158277\pi$
$468$	−4.98646	+	13.6314i	−0.230499	+	0.630110i
$469$	−6.63714	+	27.9047i	−0.306475	+	1.28852i
$470$	6.63589	+	3.83123i	0.306091	+	0.176722i
$471$	−2.63688	+	3.13734i	−0.121501	+	0.144561i
$472$	4.36704	+	2.52131i	0.201009	+	0.116053i
$473$	5.91532	+	3.41521i	0.271986	+	0.157031i
$474$	−17.3857	+	20.6853i	−0.798550	+	0.950109i
$475$	−5.82047	−	3.36045i	−0.267061	−	0.154188i
$476$	−23.4938	+	7.01308i	−1.07683	+	0.321444i
$477$	1.02929	−	0.179771i	0.0471279	−	0.00823116i
$478$	−17.3379	+	30.0301i	−0.793017	+	1.37355i
$479$	36.5307			1.66913			0.834565	−	0.550909i	$-0.185719\pi$
$479$	36.5307			1.66913			0.834565	+	0.550909i	$0.185719\pi$
$480$	7.85348	−	9.34402i	0.358461	−	0.426494i
$481$		−	17.3738i		−	0.792175i
$482$	−19.6724	−	34.0736i	−0.896055	−	1.55201i
$483$	−38.7586	+	4.46694i	−1.76358	+	0.203253i
$484$	12.3056	−	21.3139i	0.559345	−	0.968814i
$485$	−3.10554	−	1.79298i	−0.141015	−	0.0814152i
$486$	−11.9385	+	32.3917i	−0.541543	+	1.46932i
$487$	3.75435	+	6.50272i	0.170126	+	0.294667i	0.938464	−	0.345378i	$-0.112249\pi$
$487$	3.75435	+	6.50272i	0.170126	+	0.294667i	−0.768338	+	0.640044i	$0.778916\pi$
$488$	−11.4301	−	19.7976i	−0.517418	−	0.896195i
$489$	17.7443	+	14.9138i	0.802427	+	0.674425i
$490$	6.97946	−	13.8419i	0.315300	−	0.625315i
$491$	5.15612	−	2.97689i	0.232692	−	0.134345i	−0.379121	−	0.925347i	$-0.623774\pi$
$491$	5.15612	−	2.97689i	0.232692	−	0.134345i	0.611814	+	0.791002i	$0.290440\pi$
$492$	0.363353	−	2.05095i	0.0163812	−	0.0924641i
$493$		−	13.9855i		−	0.629874i
$494$	21.4729	−	12.3974i	0.966111	−	0.557785i
$495$	−1.63804	+	4.47787i	−0.0736243	+	0.201265i
$496$		−	7.47195i		−	0.335501i
$497$	−6.40102	−	21.4434i	−0.287125	−	0.961866i
$498$	32.7678	+	5.80523i	1.46836	+	0.260139i
$499$	−13.4879			−0.603799			−0.301900	−	0.953340i	$-0.597621\pi$
$499$	−13.4879			−0.603799			−0.301900	+	0.953340i	$0.597621\pi$
$500$	−1.45217	+	2.51523i	−0.0649429	+	0.112484i
$501$	−13.3952	+	4.86318i	−0.598455	+	0.217271i
$502$	42.9351	−	24.7886i	1.91629	−	1.10637i
$503$	−15.4403			−0.688450			−0.344225	−	0.938887i	$-0.611858\pi$
$503$	−15.4403			−0.688450			−0.344225	+	0.938887i	$0.611858\pi$
$504$	0.962702	−	15.8669i	0.0428822	−	0.706767i
$505$	−8.28504			−0.368679
$506$	−25.9517	+	14.9832i	−1.15369	+	0.666084i
$507$	13.5574	+	11.3947i	0.602105	+	0.506058i
$508$	19.5221	−	33.8133i	0.866154	−	1.50022i
$509$	−22.5894			−1.00126			−0.500628	−	0.865663i	$-0.666898\pi$
$509$	−22.5894			−1.00126			−0.500628	+	0.865663i	$0.666898\pi$
$510$	−7.87462	+	9.36917i	−0.348694	+	0.414874i
$511$	−20.6755	+	21.8797i	−0.914632	+	0.967899i
$512$		−	15.1809i		−	0.670906i
$513$	30.2864	−	17.3878i	1.33718	−	0.767690i
$514$	−38.7828	+	22.3913i	−1.71064	+	0.987637i
$515$		−	1.75039i		−	0.0771316i
$516$	−20.3211	+	7.37763i	−0.894586	+	0.324782i
$517$	−4.76245	+	2.74960i	−0.209452	+	0.120927i
$518$	17.4788	+	58.5537i	0.767973	+	2.57270i
$519$	−17.9159	+	6.50442i	−0.786422	+	0.285512i
$520$	−1.66814	−	2.88930i	−0.0731527	−	0.126704i
$521$	−3.34102	−	5.78682i	−0.146373	−	0.253525i	0.783511	−	0.621377i	$-0.213427\pi$
$521$	−3.34102	−	5.78682i	−0.146373	−	0.253525i	−0.929884	+	0.367852i	$0.880093\pi$
$522$	27.3480	+	10.0041i	1.19699	+	0.437867i
$523$	25.5193	+	14.7336i	1.11588	+	0.644254i	0.940346	−	0.340219i	$-0.110501\pi$
$523$	25.5193	+	14.7336i	1.11588	+	0.644254i	0.175535	+	0.984473i	$0.443835\pi$
$524$	12.6109	−	21.8428i	0.550911	−	0.954205i
$525$	−0.524670	−	4.55244i	−0.0228985	−	0.198685i
$526$	−12.4911	−	21.6352i	−0.544636	−	0.943338i
$527$			17.3578i			0.756116i
$528$	1.29032	+	3.55408i	0.0561539	+	0.154672i
$529$	−49.4847			−2.15151
$530$	−0.385657	+	0.667977i	−0.0167519	+	0.0290151i
$531$	−5.79433	+	4.84603i	−0.251452	+	0.210300i
$532$	−35.4706	+	37.5364i	−1.53784	+	1.62741i
$533$	0.597355	+	0.344883i	0.0258743	+	0.0149385i
$534$	1.65098	+	0.292492i	0.0714449	+	0.0126574i
$535$	−10.8669	−	6.27401i	−0.469817	−	0.271249i
$536$	−18.8030	−	10.8559i	−0.812168	−	0.468905i
$537$	−3.49646	−	9.63074i	−0.150884	−	0.415597i
$538$	−27.2723	−	15.7457i	−1.17579	−	0.678844i
$539$	6.09867	+	9.30499i	0.262688	+	0.400794i
$540$	−7.51388	−	13.0878i	−0.323346	−	0.563210i
$541$	3.50264	−	6.06674i	0.150590	−	0.260830i	−0.780854	−	0.624713i	$-0.785216\pi$
$541$	3.50264	−	6.06674i	0.150590	−	0.260830i	0.931445	+	0.363883i	$0.118549\pi$
$542$	49.9993			2.14765
$543$	6.96510	+	1.23396i	0.298901	+	0.0529542i
$544$			22.4857i			0.964067i
$545$	−5.51885	−	9.55892i	−0.236401	−	0.409459i
$546$	15.5126	+	6.72115i	0.663879	+	0.287639i
$547$	19.2012	−	33.2575i	0.820985	−	1.42199i	−0.0839652	−	0.996469i	$-0.526758\pi$
$547$	19.2012	−	33.2575i	0.820985	−	1.42199i	0.904950	−	0.425518i	$-0.139908\pi$
$548$	−8.81477	−	5.08921i	−0.376548	−	0.217400i
$549$	33.7333	−	5.89172i	1.43970	−	0.251453i
$550$	−1.75987	−	3.04819i	−0.0750412	−	0.129975i
$551$	−14.7293	−	25.5119i	−0.627490	−	1.08684i
$552$	5.15187	−	29.0798i	0.219278	−	1.23772i
$553$	13.5467	+	12.8011i	0.576062	+	0.544359i
$554$	36.7639	−	21.2256i	1.56195	−	0.901791i
$555$	13.8283	+	11.6225i	0.586980	+	0.493346i
$556$		−	66.4607i		−	2.81856i
$557$	−13.7112	+	7.91618i	−0.580964	+	0.335420i	−0.761516	−	0.648146i	$-0.775545\pi$
$557$	−13.7112	+	7.91618i	−0.580964	+	0.335420i	0.180553	+	0.983565i	$0.442211\pi$
$558$	−33.9424	−	12.4164i	−1.43689	−	0.525627i
$559$		−	7.15928i		−	0.302805i
$560$	−2.64126	−	2.49590i	−0.111613	−	0.105471i
$561$	−2.99748	−	8.25634i	−0.126554	−	0.348583i
$562$	48.5265			2.04697
$563$	11.5665	−	20.0338i	0.487470	−	0.844324i	−0.512426	−	0.858732i	$-0.671253\pi$
$563$	11.5665	−	20.0338i	0.487470	−	0.844324i	0.999896	+	0.0144080i	$0.00458636\pi$
$564$	3.03632	−	17.1386i	0.127852	−	0.721665i
$565$	3.40337	−	1.96494i	0.143181	−	0.0826656i
$566$	38.6017			1.62255
$567$	21.8260	+	9.51968i	0.916607	+	0.399789i
$568$	16.9394			0.710761
$569$	20.1468	−	11.6318i	0.844597	−	0.487628i	−0.0142270	−	0.999899i	$-0.504529\pi$
$569$	20.1468	−	11.6318i	0.844597	−	0.487628i	0.858824	+	0.512270i	$0.171195\pi$
$570$	−4.49718	+	25.3844i	−0.188366	+	1.06324i
$571$	−4.73996	+	8.20985i	−0.198361	+	0.343572i	−0.947997	−	0.318279i	$-0.896895\pi$
$571$	−4.73996	+	8.20985i	−0.198361	+	0.343572i	0.749636	+	0.661850i	$0.230229\pi$
$572$	7.68972			0.321523
$573$	−2.52385	−	6.95174i	−0.105435	−	0.290413i
$574$	−2.36020	−	0.561373i	−0.0985128	−	0.0234313i
$575$		−	8.51380i		−	0.355050i
$576$	−36.2304	−	13.2533i	−1.50960	−	0.552222i
$577$	21.7369	−	12.5498i	0.904920	−	0.522456i	0.0261271	−	0.999659i	$-0.491683\pi$
$577$	21.7369	−	12.5498i	0.904920	−	0.522456i	0.878793	+	0.477203i	$0.158349\pi$
$578$			15.1015i			0.628140i
$579$	−27.7913	−	23.3581i	−1.15497	−	0.970728i
$580$	−11.0246	+	6.36505i	−0.457771	+	0.264294i
$581$	5.31140	−	22.3309i	0.220354	−	0.926442i
$582$	−2.39949	+	13.5440i	−0.0994621	+	0.561416i
$583$	−0.276778	−	0.479394i	−0.0114630	−	0.0198545i
$584$	−11.3933	−	19.7339i	−0.471460	−	0.816593i
$585$	4.92311	−	0.859849i	0.203545	−	0.0355504i
$586$	−37.7249	−	21.7805i	−1.55840	−	0.899744i
$587$	−14.9770	+	25.9410i	−0.618168	+	1.07070i	0.371652	+	0.928372i	$0.378792\pi$
$587$	−14.9770	+	25.9410i	−0.618168	+	1.07070i	−0.989820	+	0.142326i	$0.954542\pi$
$588$	−34.9651	−	4.17234i	−1.44194	−	0.172064i
$589$	18.2810	+	31.6636i	0.753254	+	1.30467i
$590$		−	5.57607i		−	0.229563i
$591$	35.5219	+	6.29316i	1.46117	+	0.258866i
$592$	14.3246			0.588738
$593$	−17.6119	+	30.5047i	−0.723233	+	1.25268i	0.236464	+	0.971640i	$0.424012\pi$
$593$	−17.6119	+	30.5047i	−0.723233	+	1.25268i	−0.959697	+	0.281037i	$0.909322\pi$
$594$	18.2891	+	0.0444755i	0.750410	+	0.00182485i
$595$	6.13579	+	5.79811i	0.251543	+	0.237699i
$596$	47.7360	+	27.5604i	1.95534	+	1.12892i
$597$	−7.06076	−	19.4483i	−0.288978	−	0.795966i
$598$	27.2011	+	15.7046i	1.11234	+	0.642208i
$599$	−41.5600	−	23.9947i	−1.69810	−	0.980396i	−0.947566	−	0.319559i	$-0.896465\pi$
$599$	−41.5600	−	23.9947i	−1.69810	−	0.980396i	−0.750529	−	0.660837i	$-0.770201\pi$
$600$	3.41561	+	0.605120i	0.139442	+	0.0247039i
$601$	16.8639	+	9.73639i	0.687894	+	0.397156i	0.802823	−	0.596218i	$-0.203331\pi$
$601$	16.8639	+	9.73639i	0.687894	+	0.397156i	−0.114929	+	0.993374i	$0.536664\pi$
$602$	7.20255	+	24.1285i	0.293554	+	0.983403i
$603$	24.9485	−	20.8654i	1.01598	−	0.849705i
$604$	−1.57158	+	2.72205i	−0.0639466	+	0.110759i
$605$	−8.47395			−0.344515
$606$	10.8450	+	29.8716i	0.440547	+	1.21345i
$607$		−	21.7305i		−	0.882014i	−0.897504	−	0.441007i	$-0.854621\pi$
$607$		−	21.7305i		−	0.882014i	0.897504	−	0.441007i	$-0.145379\pi$
$608$	23.6816	+	41.0178i	0.960418	+	1.66349i
$609$	7.98539	−	18.4305i	0.323584	−	0.746842i
$610$	−12.6393	+	21.8919i	−0.511750	+	0.886377i
$611$	4.99174	+	2.88198i	0.201944	+	0.116593i
$612$	26.1089	+	9.55083i	1.05539	+	0.386069i
$613$	8.06608	+	13.9709i	0.325786	+	0.564278i	0.981671	−	0.190583i	$-0.0610378\pi$
$613$	8.06608	+	13.9709i	0.325786	+	0.564278i	−0.655885	+	0.754861i	$0.727704\pi$
$614$	8.64745	+	14.9778i	0.348983	+	0.604456i
$615$	−0.674114	+	0.244739i	−0.0271829	+	0.00986882i
$616$	−8.06963	+	2.40885i	−0.325135	+	0.0970554i
$617$	−19.7440	+	11.3992i	−0.794863	+	0.458914i	−0.841672	−	0.539990i	$-0.818428\pi$
$617$	−19.7440	+	11.3992i	−0.794863	+	0.458914i	0.0468091	+	0.998904i	$0.485095\pi$
$618$	−6.31103	+	2.29124i	−0.253867	+	0.0921670i
$619$			15.1578i			0.609244i	0.952473	+	0.304622i	$0.0985302\pi$
$619$			15.1578i			0.609244i	−0.952473	+	0.304622i	$0.901470\pi$
$620$	13.6829	−	7.89984i	0.549520	−	0.317265i
$621$	38.2582	+	22.2126i	1.53525	+	0.891361i
$622$		−	59.5975i		−	2.38964i
$623$	0.267611	−	1.12513i	0.0107216	−	0.0450772i
$624$	2.54990	−	3.03385i	0.102078	−	0.121451i
$625$	1.00000			0.0400000
$626$	−14.9680	+	25.9253i	−0.598241	+	1.03618i
$627$	−14.1634	−	11.9041i	−0.565631	−	0.475403i
$628$	−5.95142	+	3.43605i	−0.237487	+	0.137113i
$629$	−33.2769			−1.32684
$630$	−15.7270	+	7.85076i	−0.626579	+	0.312782i
$631$	4.92621			0.196109			0.0980547	−	0.995181i	$-0.468738\pi$
$631$	4.92621			0.196109			0.0980547	+	0.995181i	$0.468738\pi$
$632$	−12.2181	+	7.05412i	−0.486009	+	0.280598i
$633$	−1.79616	+	0.652099i	−0.0713908	+	0.0259186i
$634$	24.8647	−	43.0669i	0.987504	−	1.71041i
$635$	−13.4434			−0.533486
$636$	1.72519	+	0.305640i	0.0684083	+	0.0121194i
$637$	5.25019	−	10.4124i	0.208020	−	0.412554i
$638$		−	15.4275i		−	0.610782i
$639$	−8.71729	+	23.8303i	−0.344851	+	0.942711i
$640$	12.4568	−	7.19193i	0.492398	−	0.284286i
$641$			15.5270i			0.613279i	0.951826	+	0.306639i	$0.0992046\pi$
$641$			15.5270i			0.613279i	−0.951826	+	0.306639i	$0.900795\pi$
$642$	−8.39630	+	47.3931i	−0.331375	+	1.87046i
$643$	35.0512	−	20.2368i	1.38229	−	0.798063i	0.389856	−	0.920876i	$-0.372525\pi$
$643$	35.0512	−	20.2368i	1.38229	−	0.798063i	0.992430	+	0.122812i	$0.0391914\pi$
$644$	−63.6457	−	15.1381i	−2.50799	−	0.596526i
$645$	5.69830	+	4.78932i	0.224370	+	0.188579i
$646$	−23.7454	−	41.1282i	−0.934250	−	1.61817i
$647$	−14.0234	−	24.2892i	−0.551315	−	0.954906i	−0.998180	−	0.0603048i	$-0.980793\pi$
$647$	−14.0234	−	24.2892i	−0.551315	−	0.954906i	0.446865	−	0.894602i	$-0.352541\pi$
$648$	−11.6306	+	13.7699i	−0.456893	+	0.540932i
$649$	3.46569	+	2.00092i	0.136040	+	0.0785428i
$650$	−1.84460	+	3.19495i	−0.0723513	+	0.125316i
$651$	−9.91089	+	22.8746i	−0.388438	+	0.896527i
$652$	19.4338	+	33.6603i	0.761086	+	1.31824i
$653$		−	22.6931i		−	0.888048i	−0.896015	−	0.444024i	$-0.853550\pi$
$653$		−	22.6931i		−	0.888048i	0.896015	−	0.444024i	$-0.146450\pi$
$654$	−27.2405	+	32.4106i	−1.06519	+	1.26736i
$655$	−8.68421			−0.339320
$656$	−0.284355	+	0.492518i	−0.0111022	+	0.0192296i
$657$	33.6247	−	5.87275i	1.31182	−	0.229118i
$658$	−19.7228	−	4.69106i	−0.768874	−	0.182877i
$659$	32.0200	+	18.4868i	1.24732	+	0.720142i	0.970575	−	0.240800i	$-0.0774098\pi$
$659$	32.0200	+	18.4868i	1.24732	+	0.720142i	0.276748	+	0.960942i	$0.410743\pi$
$660$	−5.14417	+	6.12050i	−0.200236	+	0.238240i
$661$	16.7605	+	9.67668i	0.651908	+	0.376379i	0.789187	−	0.614153i	$-0.210502\pi$
$661$	16.7605	+	9.67668i	0.651908	+	0.376379i	−0.137279	+	0.990532i	$0.543836\pi$
$662$	−18.5081	−	10.6857i	−0.719339	−	0.415310i
$663$	−5.92355	+	7.04781i	−0.230052	+	0.273714i
$664$	15.0472	+	8.68752i	0.583945	+	0.337141i
$665$	17.2992	+	4.11462i	0.670835	+	0.159558i
$666$	23.8036	−	65.0715i	0.922372	−	2.52147i
$667$	18.6586	−	32.3176i	0.722463	−	1.25134i
$668$	−23.8959			−0.924559
$669$	−14.5447	+	17.3052i	−0.562331	+	0.669058i
$670$			24.0087i			0.927537i
$671$	−9.07097	−	15.7114i	−0.350181	−	0.606531i
$672$	−12.8388	+	29.6324i	−0.495269	+	1.14309i
$673$	0.294484	−	0.510061i	0.0113515	−	0.0196614i	−0.860294	−	0.509798i	$-0.829720\pi$
$673$	0.294484	−	0.510061i	0.0113515	−	0.0196614i	0.871645	+	0.490137i	$0.163053\pi$
$674$	22.1357	+	12.7800i	0.852635	+	0.492269i
$675$	−2.60901	+	4.49367i	−0.100421	+	0.172961i
$676$	14.8482	+	25.7178i	0.571085	+	0.989147i
$677$	−9.89463	−	17.1380i	−0.380281	−	0.658667i	0.610821	−	0.791769i	$-0.290840\pi$
$677$	−9.89463	−	17.1380i	−0.380281	−	0.658667i	−0.991102	+	0.133102i	$0.957506\pi$
$678$	−11.5395	−	9.69877i	−0.443173	−	0.372479i
$679$	9.23008	+	2.19538i	0.354218	+	0.0842508i
$680$	−5.53403	+	3.19507i	−0.212220	+	0.122526i
$681$	7.35268	−	41.5024i	0.281755	−	1.59037i
$682$			19.1475i			0.733197i
$683$	21.7627	−	12.5647i	0.832725	−	0.480774i	−0.0220596	−	0.999757i	$-0.507022\pi$
$683$	21.7627	−	12.5647i	0.832725	−	0.480774i	0.854785	+	0.518983i	$0.173689\pi$
$684$	57.6859	−	10.0752i	2.20568	−	0.385234i
$685$			3.50456i			0.133902i
$686$	−7.21908	+	40.3741i	−0.275626	+	1.54149i
$687$	−17.4745	−	3.09583i	−0.666692	−	0.118113i
$688$	5.90281			0.225042
$689$	−0.290104	+	0.502475i	−0.0110521	+	0.0191428i
$690$	−30.6964	+	11.1444i	−1.16859	+	0.424261i
$691$	9.30073	−	5.36978i	0.353817	−	0.204276i	−0.312548	−	0.949902i	$-0.601183\pi$
$691$	9.30073	−	5.36978i	0.353817	−	0.204276i	0.666365	+	0.745626i	$0.267849\pi$
$692$	−31.9603			−1.21495
$693$	0.764001	−	12.5920i	0.0290220	−	0.478329i
$694$	−55.7911			−2.11780
$695$	−19.8175	+	11.4416i	−0.751720	+	0.434006i
$696$	11.6392	+	9.78254i	0.441183	+	0.370806i
$697$	0.660573	−	1.14415i	0.0250210	−	0.0433376i
$698$	−74.3514			−2.81424
$699$	−24.4222	+	29.0574i	−0.923732	+	1.09905i
$700$	1.77807	−	7.47560i	0.0672048	−	0.282551i
$701$			30.8677i			1.16586i	0.812524	+	0.582928i	$0.198093\pi$
$701$			30.8677i			1.16586i	−0.812524	+	0.582928i	$0.801907\pi$
$702$	−9.54444	−	16.6247i	−0.360232	−	0.627458i
$703$	−60.7028	+	35.0468i	−2.28945	+	1.32181i
$704$			20.4382i			0.770295i
$705$	−5.63317	+	2.04514i	−0.212157	+	0.0770243i
$706$	43.1081	−	24.8885i	1.62240	−	0.936691i
$707$	21.0043	−	6.26995i	0.789948	−	0.235806i
$708$	−11.9058	+	4.32243i	−0.447448	+	0.162447i
$709$	−1.34423	−	2.32827i	−0.0504836	−	0.0874402i	0.839679	−	0.543083i	$-0.182743\pi$
$709$	−1.34423	−	2.32827i	−0.0504836	−	0.0874402i	−0.890163	+	0.455642i	$0.849410\pi$
$710$	−9.36568	−	16.2218i	−0.351488	−	0.608794i
$711$	−3.63608	−	20.8185i	−0.136364	−	0.780756i
$712$	0.758143	+	0.437714i	0.0284126	+	0.0164040i
$713$	−23.1577	+	40.1103i	−0.867262	+	1.50214i
$714$	12.8734	−	29.7122i	0.481775	−	1.11195i
$715$	−1.32384	−	2.29295i	−0.0495086	−	0.0857515i
$716$		−	17.1803i		−	0.642060i
$717$	−9.25509	−	25.4924i	−0.345638	−	0.952032i
$718$	11.8664			0.442849
$719$	−5.84456	+	10.1231i	−0.217965	+	0.377527i	−0.954186	−	0.299215i	$-0.903275\pi$
$719$	−5.84456	+	10.1231i	−0.217965	+	0.377527i	0.736220	+	0.676742i	$0.236609\pi$
$720$	0.708944	+	4.05909i	0.0264208	+	0.151273i
$721$	1.32466	+	4.43761i	0.0493331	+	0.165265i
$722$	−50.1917	−	28.9782i	−1.86794	−	1.07846i
$723$	30.3004	+	5.36810i	1.12688	+	0.199642i
$724$	10.2720	+	5.93054i	0.381756	+	0.220407i
$725$	3.79591	+	2.19157i	0.140977	+	0.0813929i
$726$	11.0923	+	30.5527i	0.411672	+	1.13392i
$727$	−26.2586	−	15.1604i	−0.973877	−	0.562268i	−0.0734608	−	0.997298i	$-0.523404\pi$
$727$	−26.2586	−	15.1604i	−0.973877	−	0.562268i	−0.900416	+	0.435030i	$0.856738\pi$
$728$	6.41564	+	6.06256i	0.237780	+	0.224693i
$729$	−13.3861	−	23.4481i	−0.495782	−	0.868447i
$730$	−12.5986	+	21.8214i	−0.466295	+	0.807647i
$731$	−13.7126			−0.507177
$732$	56.5405	+	10.0169i	2.08980	+	0.370234i
$733$			33.2108i			1.22667i	0.789824	+	0.613334i	$0.210172\pi$
$733$			33.2108i			1.22667i	−0.789824	+	0.613334i	$0.789828\pi$
$734$	19.8139	+	34.3187i	0.731345	+	1.26673i
$735$	4.77535	+	11.1443i	0.176141	+	0.411065i
$736$	−29.9991	+	51.9599i	−1.10578	+	1.91527i
$737$	−14.9221	−	8.61529i	−0.549663	−	0.317348i
$738$	1.76481	+	2.11015i	0.0649635	+	0.0776758i
$739$	13.7722	+	23.8541i	0.506617	+	0.877486i	0.999971	+	0.00765762i	$0.00243752\pi$
$739$	13.7722	+	23.8541i	0.506617	+	0.877486i	−0.493354	+	0.869829i	$0.664229\pi$
$740$	15.1449	+	26.2318i	0.556739	+	0.964300i
$741$	−3.38293	+	19.0950i	−0.124275	+	0.701473i
$742$	0.472208	−	1.98532i	0.0173353	−	0.0728833i
$743$	1.21017	−	0.698692i	0.0443968	−	0.0256325i	−0.477637	−	0.878557i	$-0.658507\pi$
$743$	1.21017	−	0.698692i	0.0443968	−	0.0256325i	0.522034	+	0.852925i	$0.325173\pi$
$744$	−14.4457	−	12.1414i	−0.529607	−	0.445125i
$745$		−	18.9788i		−	0.695329i
$746$	−64.1660	+	37.0463i	−2.34929	+	1.35636i
$747$	−19.9651	+	16.6976i	−0.730485	+	0.610935i
$748$		−	14.7285i		−	0.538529i
$749$	32.2979	+	7.68206i	1.18014	+	0.280696i
$750$	−1.30898	−	3.60549i	−0.0477973	−	0.131654i
$751$	33.1229			1.20867			0.604336	−	0.796730i	$-0.293439\pi$
$751$	33.1229			1.20867			0.604336	+	0.796730i	$0.293439\pi$
$752$	−2.37619	+	4.11568i	−0.0866507	+	0.150083i
$753$	−6.76417	+	38.1805i	−0.246500	+	1.39138i
$754$	−14.0039	+	8.08515i	−0.509992	+	0.294444i
$755$	1.08223			0.0393863
$756$	28.9539	+	27.4940i	1.05304	+	0.999947i
$757$	−41.6223			−1.51279			−0.756394	−	0.654116i	$-0.773041\pi$
$757$	−41.6223			−1.51279			−0.756394	+	0.654116i	$0.773041\pi$
$758$	−19.9521	+	11.5193i	−0.724692	+	0.418401i
$759$	4.08853	−	23.0778i	0.148404	−	0.837671i
$760$	−6.73002	+	11.6567i	−0.244123	+	0.422834i
$761$	30.6372			1.11060			0.555298	−	0.831651i	$-0.312604\pi$
$761$	30.6372			1.11060			0.555298	+	0.831651i	$0.312604\pi$
$762$	17.5972	+	48.4702i	0.637480	+	1.75589i
$763$	21.2254	+	20.0573i	0.768412	+	0.726123i
$764$		−	12.4013i		−	0.448662i
$765$	−1.64692	−	9.42949i	−0.0595444	−	0.340924i
$766$	16.3772	−	9.45538i	0.591732	−	0.341637i
$767$		−	4.19451i		−	0.151455i
$768$	−8.13481	−	6.83716i	−0.293540	−	0.246715i
$769$	30.4889	−	17.6028i	1.09946	−	0.634772i	0.163379	−	0.986563i	$-0.447761\pi$
$769$	30.4889	−	17.6028i	1.09946	−	0.634772i	0.936078	+	0.351791i	$0.114427\pi$
$770$	6.76845	+	6.39596i	0.243918	+	0.230494i
$771$	6.11000	−	34.4881i	0.220046	−	1.24206i
$772$	−30.4373	−	52.7190i	−1.09546	−	1.89740i
$773$	−6.96012	−	12.0553i	−0.250338	−	0.433598i	0.713281	−	0.700878i	$-0.247208\pi$
$773$	−6.96012	−	12.0553i	−0.250338	−	0.433598i	−0.963619	+	0.267280i	$0.913875\pi$
$774$	9.80886	−	26.8143i	0.352572	−	0.963820i
$775$	−4.71121	−	2.72002i	−0.169232	−	0.0977060i
$776$	−3.59083	+	6.21951i	−0.128903	+	0.223267i
$777$	−43.8534	−	19.0004i	−1.57323	−	0.681634i
$778$	−10.4286	−	18.0629i	−0.373883	−	0.647585i
$779$		−	2.78283i		−	0.0997051i
$780$	8.25162	+	1.46188i	0.295455	+	0.0523437i
$781$	13.4431			0.481033
$782$	30.0798	−	52.0998i	1.07565	−	1.86308i
$783$	−19.7518	+	11.3397i	−0.705870	+	0.405249i
$784$	8.58498	+	4.32877i	0.306607	+	0.154599i
$785$	2.04915	+	1.18308i	0.0731373	+	0.0422258i
$786$	11.3675	+	31.3108i	0.405464	+	1.11682i
$787$	−27.8132	−	16.0579i	−0.991432	−	0.572404i	−0.0857303	−	0.996318i	$-0.527322\pi$
$787$	−27.8132	−	16.0579i	−0.991432	−	0.572404i	−0.905702	+	0.423915i	$0.860656\pi$
$788$	52.3870	+	30.2456i	1.86621	+	1.07746i
$789$	19.2393	+	3.40849i	0.684937	+	0.121345i
$790$	13.5106	+	7.80034i	0.480685	+	0.277524i
$791$	−7.14124	+	7.55714i	−0.253913	+	0.268701i
$792$	8.96789	+	3.28052i	0.318660	+	0.116568i
$793$	−9.50771	+	16.4678i	−0.337629	+	0.584790i
$794$	−1.48361			−0.0526514
$795$	−0.205866	−	0.567042i	−0.00730132	−	0.0201109i
$796$		−	34.6940i		−	1.22970i
$797$	−9.97847	−	17.2832i	−0.353455	−	0.612203i	0.633397	−	0.773827i	$-0.281660\pi$
$797$	−9.97847	−	17.2832i	−0.353455	−	0.612203i	−0.986852	+	0.161624i	$0.948327\pi$
$798$	−7.80915	−	67.7582i	−0.276441	−	2.39861i
$799$	5.52002	−	9.56095i	0.195284	−	0.338242i
$800$	−6.10303	−	3.52358i	−0.215775	−	0.124578i
$801$	−1.00593	+	0.841298i	−0.0355427	+	0.0297258i
$802$	−3.21410	−	5.56698i	−0.113494	−	0.196577i
$803$	−9.04177	−	15.6608i	−0.319077	−	0.552658i
$804$	51.2625	−	18.6110i	1.80789	−	0.656358i
$805$	6.44308	+	21.5843i	0.227089	+	0.760745i
$806$	17.3806	−	10.0347i	0.612206	−	0.353458i
$807$	23.1513	−	8.40514i	0.814964	−	0.295875i
$808$			16.5926i			0.583724i
$809$	37.1900	−	21.4716i	1.30753	−	0.754902i	0.325846	−	0.945423i	$-0.394351\pi$
$809$	37.1900	−	21.4716i	1.30753	−	0.754902i	0.981683	+	0.190520i	$0.0610176\pi$
$810$	19.6170	+	3.52463i	0.689272	+	0.123843i
$811$		−	5.06788i		−	0.177957i	−0.996034	−	0.0889787i	$-0.971640\pi$
$811$		−	5.06788i		−	0.177957i	0.996034	−	0.0889787i	$-0.0283603\pi$
$812$	23.1327	−	24.4799i	0.811798	−	0.859077i
$813$	−25.1606	+	29.9360i	−0.882422	+	1.04990i
$814$	−36.7081			−1.28662
$815$	6.69131	−	11.5897i	0.234386	−	0.405969i
$816$	−5.81090	−	4.88396i	−0.203422	−	0.170973i
$817$	−25.0140	+	14.4419i	−0.875131	+	0.505257i
$818$	46.8892			1.63944
$819$	−11.8304	+	5.90561i	−0.413387	+	0.206359i
$820$	−1.20256			−0.0419951
$821$	0.450967	−	0.260366i	0.0157389	−	0.00908684i	−0.492110	−	0.870533i	$-0.663774\pi$
$821$	0.450967	−	0.260366i	0.0157389	−	0.00908684i	0.507849	+	0.861446i	$0.330441\pi$
$822$	12.6357	−	4.58741i	0.440720	−	0.160004i
$823$	−26.6982	+	46.2426i	−0.930640	+	1.61192i	−0.148410	+	0.988926i	$0.547416\pi$
$823$	−26.6982	+	46.2426i	−0.930640	+	1.61192i	−0.782230	+	0.622990i	$0.785918\pi$
$824$	−3.50554			−0.122121
$825$	2.71063	+	0.480224i	0.0943722	+	0.0167192i
$826$	4.21986	+	14.1365i	0.146828	+	0.491871i
$827$			10.8604i			0.377653i	0.982010	+	0.188826i	$0.0604684\pi$
$827$			10.8604i			0.377653i	−0.982010	+	0.188826i	$0.939532\pi$
$828$	47.5903	+	56.9030i	1.65388	+	1.97751i
$829$	2.18268	−	1.26017i	0.0758076	−	0.0437675i	−0.461617	−	0.887079i	$-0.652731\pi$
$829$	2.18268	−	1.26017i	0.0758076	−	0.0437675i	0.537425	+	0.843312i	$0.319397\pi$
$830$		−	19.2131i		−	0.666895i
$831$	−5.79193	+	32.6927i	−0.200920	+	1.13410i
$832$	18.5522	−	10.7111i	0.643183	−	0.371342i
$833$	−19.9434	−	10.0560i	−0.690998	−	0.348419i
$834$	67.1935	+	56.4749i	2.32672	+	1.95557i
$835$	4.11383	+	7.12536i	0.142365	+	0.246583i
$836$	−15.5119	−	26.8674i	−0.536490	−	0.929228i
$837$	24.5145	−	14.0741i	0.847344	−	0.486471i
$838$	36.8460	+	21.2730i	1.27282	+	0.734865i
$839$	−3.64848	+	6.31936i	−0.125960	+	0.218168i	−0.922108	−	0.386933i	$-0.873534\pi$
$839$	−3.64848	+	6.31936i	−0.125960	+	0.218168i	0.796148	+	0.605102i	$0.206868\pi$
$840$	−9.11724	+	1.05076i	−0.314575	+	0.0362548i
$841$	−4.89404	−	8.47673i	−0.168760	−	0.292301i
$842$		−	14.1865i		−	0.488898i
$843$	−24.4195	+	29.0541i	−0.841051	+	1.00068i
$844$	−3.20418			−0.110292
$845$	5.11243	−	8.85498i	0.175873	−	0.304621i
$846$	14.7474	+	17.6333i	0.507028	+	0.606245i
$847$	21.4832	−	6.41292i	0.738172	−	0.220351i
$848$	−0.414289	−	0.239190i	−0.0142268	−	0.00821382i
$849$	−19.4251	+	23.1119i	−0.666669	+	0.793199i
$850$	6.11945	+	3.53307i	0.209896	+	0.121183i
$851$	−76.8962	−	44.3960i	−2.63597	−	1.52188i
$852$	−27.3762	+	32.5720i	−0.937893	+	1.11590i
$853$	7.92955	+	4.57813i	0.271502	+	0.156752i	0.629570	−	0.776944i	$-0.283231\pi$
$853$	7.92955	+	4.57813i	0.271502	+	0.156752i	−0.358068	+	0.933696i	$0.616564\pi$
$854$	15.4759	−	65.0657i	0.529574	−	2.22650i
$855$	−12.9353	−	15.4665i	−0.442377	−	0.528943i
$856$	−12.5650	+	21.7633i	−0.429464	+	0.743854i
$857$	32.9291			1.12484			0.562418	−	0.826853i	$-0.309871\pi$
$857$	32.9291			1.12484			0.562418	+	0.826853i	$0.309871\pi$
$858$	−6.53433	+	7.77451i	−0.223078	+	0.265417i
$859$		−	47.9676i		−	1.63663i	−0.574769	−	0.818316i	$-0.694908\pi$
$859$		−	47.9676i		−	1.63663i	0.574769	−	0.818316i	$-0.305092\pi$
$860$	6.24084	+	10.8094i	0.212811	+	0.368599i
$861$	1.52381	−	1.13062i	0.0519312	−	0.0385314i
$862$	−36.4177	+	63.0772i	−1.24039	+	2.14842i
$863$	1.29502	+	0.747678i	0.0440829	+	0.0254513i	0.521879	−	0.853019i	$-0.325231\pi$
$863$	1.29502	+	0.747678i	0.0440829	+	0.0254513i	−0.477797	+	0.878470i	$0.658564\pi$
$864$	31.7567	−	18.2319i	1.08038	−	0.620262i
$865$	5.50218	+	9.53006i	0.187080	+	0.324032i
$866$	3.61772	+	6.26608i	0.122935	+	0.212930i
$867$	−9.04168	−	7.59937i	−0.307071	−	0.258088i
$868$	−28.7106	+	30.3827i	−0.974502	+	1.03126i
$869$	−9.69628	+	5.59815i	−0.328924	+	0.189904i
$870$	2.93291	−	16.5548i	0.0994348	−	0.561262i
$871$			18.0602i			0.611945i
$872$	−19.1438	+	11.0527i	−0.648290	+	0.374291i
$873$	−6.90168	−	8.25223i	−0.233586	−	0.279296i
$874$		−	126.719i		−	4.28632i
$875$	−2.53521	+	0.756781i	−0.0857057	+	0.0255839i
$876$	56.3584	+	9.98462i	1.90417	+	0.337349i
$877$	16.0945			0.543471			0.271736	−	0.962372i	$-0.412402\pi$
$877$	16.0945			0.543471			0.271736	+	0.962372i	$0.412402\pi$
$878$	22.8368	−	39.5545i	0.770705	−	1.33490i
$879$	32.0245	−	11.6266i	1.08016	−	0.392155i
$880$	1.89053	−	1.09150i	0.0637298	−	0.0367944i
$881$	−5.06470			−0.170634			−0.0853171	−	0.996354i	$-0.527190\pi$
$881$	−5.06470			−0.170634			−0.0853171	+	0.996354i	$0.527190\pi$
$882$	33.9299	−	31.8052i	1.14248	−	1.07094i
$883$	−36.8978			−1.24171			−0.620855	−	0.783926i	$-0.713214\pi$
$883$	−36.8978			−1.24171			−0.620855	+	0.783926i	$0.713214\pi$
$884$	−13.3694	+	7.71883i	−0.449662	+	0.259612i
$885$	3.33854	+	2.80598i	0.112224	+	0.0943221i
$886$	−36.0761	+	62.4856i	−1.21200	+	2.09924i
$887$	17.0655			0.573003			0.286502	−	0.958080i	$-0.407508\pi$
$887$	17.0655			0.573003			0.286502	+	0.958080i	$0.407508\pi$
$888$	23.2765	−	27.6942i	0.781107	−	0.929356i
$889$	34.0819	−	10.1737i	1.14307	−	0.341216i
$890$		−	0.968037i		−	0.0324487i
$891$	−9.23004	+	10.9278i	−0.309218	+	0.366095i
$892$	−32.8273	+	18.9528i	−1.09914	+	0.634588i
$893$		−	23.2544i		−	0.778180i
$894$	−68.4279	+	24.8429i	−2.28857	+	0.830871i
$895$	−5.12290	+	2.95771i	−0.171240	+	0.0988653i
$896$	−26.1378	+	27.6601i	−0.873204	+	0.924059i
$897$	−23.0909	+	8.38320i	−0.770982	+	0.279907i
$898$	−15.5607	−	26.9519i	−0.519267	−	0.899396i
$899$	−11.9222	−	20.6499i	−0.397628	−	0.688713i
$900$	−6.68362	+	5.58978i	−0.222787	+	0.186326i
$901$	0.962418	+	0.555652i	0.0320628	+	0.0185115i
$902$	0.728686	−	1.26212i	0.0242626	−	0.0420240i
$903$	−18.0708	−	7.82955i	−0.601360	−	0.260551i
$904$	−3.93521	−	6.81599i	−0.130883	−	0.226696i
$905$		−	4.08392i		−	0.135754i
$906$	−1.41662	−	3.90197i	−0.0470640	−	0.129634i
$907$	7.68131			0.255054			0.127527	−	0.991835i	$-0.459296\pi$
$907$	7.68131			0.255054			0.127527	+	0.991835i	$0.459296\pi$
$908$	35.3378	−	61.2069i	1.17273	−	2.03122i
$909$	−23.3423	−	8.53880i	−0.774217	−	0.283214i
$910$	2.25858	−	9.49581i	0.0748712	−	0.314783i
$911$	−4.00011	−	2.30946i	−0.132529	−	0.0765159i	0.432269	−	0.901744i	$-0.357713\pi$
$911$	−4.00011	−	2.30946i	−0.132529	−	0.0765159i	−0.564799	+	0.825229i	$0.691046\pi$
$912$	−15.7438	−	2.78922i	−0.521329	−	0.0923602i
$913$	11.9415	+	6.89442i	0.395206	+	0.228172i
$914$	15.6173	+	9.01665i	0.516574	+	0.298244i
$915$	−6.74694	−	18.5839i	−0.223047	−	0.614365i
$916$	−25.7710	−	14.8789i	−0.851498	−	0.491612i
$917$	22.0163	−	6.57204i	0.727042	−	0.217028i
$918$	−31.8422	+	18.2810i	−1.05095	+	0.603362i
$919$	−12.1207	+	20.9937i	−0.399826	+	0.692520i	−0.993704	−	0.112036i	$-0.964263\pi$
$919$	−12.1207	+	20.9937i	−0.399826	+	0.692520i	0.593878	+	0.804555i	$0.297596\pi$
$920$	−17.0507			−0.562145
$921$	−13.3192	−	2.35967i	−0.438882	−	0.0777537i
$922$		−	78.3270i		−	2.57956i
$923$	−7.04518	−	12.2026i	−0.231895	−	0.401654i
$924$	8.40966	−	19.4097i	0.276658	−	0.638534i
$925$	5.21460	−	9.03195i	0.171455	−	0.296969i
$926$	59.4868	+	34.3447i	1.95486	+	1.12864i
$927$	1.80401	−	4.93158i	0.0592514	−	0.161974i
$928$	−15.4444	−	26.7504i	−0.506986	−	0.878126i
$929$	−12.5888	−	21.8044i	−0.413025	−	0.715380i	0.582194	−	0.813050i	$-0.302194\pi$
$929$	−12.5888	−	21.8044i	−0.413025	−	0.715380i	−0.995219	+	0.0976699i	$0.968861\pi$
$930$	−3.64011	+	20.5467i	−0.119364	+	0.673752i
$931$	−46.9710	+	2.66029i	−1.53941	+	0.0871876i
$932$	−55.1207	+	31.8239i	−1.80554	+	1.04243i
$933$	35.6827	+	29.9906i	1.16820	+	0.981849i
$934$			2.52249i			0.0825383i
$935$	−4.39181	+	2.53561i	−0.143628	+	0.0829234i
$936$	−1.72203	−	9.85957i	−0.0562864	−	0.322270i
$937$			31.5241i			1.02985i	0.857236	+	0.514924i	$0.172180\pi$
$937$			31.5241i			1.02985i	−0.857236	+	0.514924i	$0.827820\pi$
$938$	−18.1693	−	60.8671i	−0.593249	−	1.98738i
$939$	−7.99001	−	22.0079i	−0.260744	−	0.718199i
$940$	−10.0491			−0.327764
$941$	24.1680	−	41.8601i	0.787853	−	1.36460i	−0.139427	−	0.990232i	$-0.544526\pi$
$941$	24.1680	−	41.8601i	0.787853	−	1.36460i	0.927280	−	0.374369i	$-0.122141\pi$
$942$	1.58327	−	8.93682i	0.0515858	−	0.291177i
$943$	3.05290	−	1.76259i	0.0994162	−	0.0573980i
$944$	3.45836			0.112560
$945$	3.21367	−	13.3668i	0.104541	−	0.434823i
$946$	−15.1265			−0.491804
$947$	0.242153	−	0.139807i	0.00786890	−	0.00454311i	−0.496060	−	0.868288i	$-0.665221\pi$
$947$	0.242153	−	0.139807i	0.00786890	−	0.00454311i	0.503929	+	0.863745i	$0.331887\pi$
$948$	6.18191	−	34.8939i	0.200779	−	1.13330i
$949$	−9.47709	+	16.4148i	−0.307639	+	0.532847i
$950$	14.8839			0.482898
$951$	13.2729	+	36.5593i	0.430405	+	1.18552i
$952$	11.6120	−	12.2882i	0.376346	−	0.398264i
$953$		−	16.8414i		−	0.545547i	−0.962078	−	0.272773i	$-0.912059\pi$
$953$		−	16.8414i		−	0.545547i	0.962078	−	0.272773i	$-0.0879409\pi$
$954$	−1.77499	+	1.48450i	−0.0574674	+	0.0480623i
$955$	−3.69785	+	2.13496i	−0.119660	+	0.0690856i
$956$		−	45.4761i		−	1.47080i
$957$	9.23688	+	7.76343i	0.298586	+	0.250956i
$958$	−70.0614	+	40.4500i	−2.26358	+	1.30688i
$959$	−2.65218	−	8.88480i	−0.0856435	−	0.286905i
$960$	−3.88548	+	21.9317i	−0.125403	+	0.707843i
$961$	−0.702998	−	1.21763i	−0.0226774	−	0.0392783i
$962$	19.2377	+	33.3207i	0.620249	+	1.07430i
$963$	−24.1503	−	28.8762i	−0.778234	−	0.930523i
$964$	44.6864	+	25.7997i	1.43925	+	0.830952i
$965$	−10.4800	+	18.1518i	−0.337362	+	0.584328i
$966$	69.3880	−	51.4839i	2.23252	−	1.65647i
$967$	−11.0577	−	19.1526i	−0.355593	−	0.615905i	0.631626	−	0.775273i	$-0.282388\pi$
$967$	−11.0577	−	19.1526i	−0.355593	−	0.615905i	−0.987219	+	0.159368i	$0.949054\pi$
$968$			16.9709i			0.545465i
$969$	36.5737	+	6.47951i	1.17492	+	0.208152i
$970$	7.94139			0.254983
$971$	9.39430	−	16.2714i	0.301477	−	0.522174i	−0.674993	−	0.737824i	$-0.735854\pi$
$971$	9.39430	−	16.2714i	0.301477	−	0.522174i	0.976471	+	0.215650i	$0.0691869\pi$
$972$	−7.68099	−	44.6178i	−0.246368	−	1.43112i
$973$	41.5827	−	44.0044i	1.33308	−	1.41072i
$974$	−14.4008	−	8.31428i	−0.461430	−	0.266407i
$975$	−0.984661	−	2.71217i	−0.0315344	−	0.0868590i
$976$	−13.5777	−	7.83908i	−0.434611	−	0.250923i
$977$	15.7636	+	9.10110i	0.504321	+	0.291170i	0.730496	−	0.682917i	$-0.239289\pi$
$977$	15.7636	+	9.10110i	0.504321	+	0.291170i	−0.226175	+	0.974087i	$0.572622\pi$
$978$	−50.5453	−	8.95476i	−1.61626	−	0.286342i
$979$	0.601663	+	0.347370i	0.0192292	+	0.0111020i
$980$	1.14961	+	20.2978i	0.0367228	+	0.648390i
$981$	−5.69715	−	32.6193i	−0.181896	−	1.04145i
$982$	−6.59253	+	11.4186i	−0.210376	+	0.364382i
$983$	10.6315			0.339094			0.169547	−	0.985522i	$-0.445770\pi$
$983$	10.6315			0.339094			0.169547	+	0.985522i	$0.445770\pi$
$984$	0.490142	+	1.35006i	0.0156252	+	0.0430383i
$985$		−	20.8279i		−	0.663633i
$986$	15.4859	+	26.8224i	0.493173	+	0.854200i
$987$	12.7335	−	9.44792i	0.405313	−	0.300731i
$988$	−16.2587	+	28.1609i	−0.517259	+	0.895919i
$989$	−31.6869	−	18.2945i	−1.00759	−	0.581730i
$990$	−1.81673	−	10.4018i	−0.0577395	−	0.330590i
$991$	1.91660	+	3.31964i	0.0608827	+	0.105452i	0.894860	−	0.446347i	$-0.147275\pi$
$991$	1.91660	+	3.31964i	0.0608827	+	0.105452i	−0.833978	+	0.551798i	$0.813942\pi$
$992$	19.1684	+	33.2007i	0.608598	+	1.05412i
$993$	15.7114	−	5.70408i	0.498588	−	0.181014i
$994$	36.0203	+	34.0380i	1.14249	+	1.07962i
$995$	−10.3452	+	5.97279i	−0.327964	+	0.189350i
$996$	−41.0230	+	14.8935i	−1.29986	+	0.471919i
$997$			29.4824i			0.933719i	0.884332	+	0.466859i	$0.154615\pi$
$997$			29.4824i			0.933719i	−0.884332	+	0.466859i	$0.845385\pi$
$998$	25.8680	−	14.9349i	0.818839	−	0.472757i
$999$	26.9816	+	46.9971i	0.853661	+	1.48692i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.be.c.236.3	yes	32
3.2	odd	2		945.2.be.c.656.14		32
7.3	odd	6		315.2.t.c.101.3	✓	32
9.4	even	3		945.2.t.c.341.3		32
9.5	odd	6		315.2.t.c.131.14	yes	32
21.17	even	6		945.2.t.c.521.14		32
63.31	odd	6		945.2.be.c.206.14		32
63.59	even	6	inner	315.2.be.c.311.3	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.c.101.3	✓	32	7.3	odd	6
315.2.t.c.131.14	yes	32	9.5	odd	6
315.2.be.c.236.3	yes	32	1.1	even	1	trivial
315.2.be.c.311.3	yes	32	63.59	even	6	inner
945.2.t.c.341.3		32	9.4	even	3
945.2.t.c.521.14		32	21.17	even	6
945.2.be.c.206.14		32	63.31	odd	6
945.2.be.c.656.14		32	3.2	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.91788 + 1.10729i) q^{2} +(0.302150 - 1.70549i) q^{3} +(1.45217 - 2.51523i) q^{4} -1.00000 q^{5} +(1.30898 + 3.60549i) q^{6} +(2.53521 - 0.756781i) q^{7} +2.00271i q^{8} +(-2.81741 - 1.03063i) q^{9} +O(q^{10})\)	\(q+(-1.91788 + 1.10729i) q^{2} +(0.302150 - 1.70549i) q^{3} +(1.45217 - 2.51523i) q^{4} -1.00000 q^{5} +(1.30898 + 3.60549i) q^{6} +(2.53521 - 0.756781i) q^{7} +2.00271i q^{8} +(-2.81741 - 1.03063i) q^{9} +(1.91788 - 1.10729i) q^{10} +1.58936i q^{11} +(-3.85093 - 3.23664i) q^{12} +(1.44269 - 0.832938i) q^{13} +(-4.02424 + 4.25861i) q^{14} +(-0.302150 + 1.70549i) q^{15} +(0.686756 + 1.18950i) q^{16} +(-1.59537 - 2.76327i) q^{17} +(6.54465 - 1.14306i) q^{18} +(-5.82047 - 3.36045i) q^{19} +(-1.45217 + 2.51523i) q^{20} +(-0.524670 - 4.55244i) q^{21} +(-1.75987 - 3.04819i) q^{22} -8.51380i q^{23} +(3.41561 + 0.605120i) q^{24} +1.00000 q^{25} +(-1.84460 + 3.19495i) q^{26} +(-2.60901 + 4.49367i) q^{27} +(1.77807 - 7.47560i) q^{28} +(3.79591 + 2.19157i) q^{29} +(-1.30898 - 3.60549i) q^{30} +(-4.71121 - 2.72002i) q^{31} +(-6.10303 - 3.52358i) q^{32} +(2.71063 + 0.480224i) q^{33} +(6.11945 + 3.53307i) q^{34} +(-2.53521 + 0.756781i) q^{35} +(-6.68362 + 5.58978i) q^{36} +(5.21460 - 9.03195i) q^{37} +14.8839 q^{38} +(-0.984661 - 2.71217i) q^{39} -2.00271i q^{40} +(0.207028 + 0.358583i) q^{41} +(6.04711 + 8.15006i) q^{42} +(2.14880 - 3.72183i) q^{43} +(3.99759 + 2.30801i) q^{44} +(2.81741 + 1.03063i) q^{45} +(9.42721 + 16.3284i) q^{46} +(1.73001 + 2.99646i) q^{47} +(2.23618 - 0.811851i) q^{48} +(5.85457 - 3.83719i) q^{49} +(-1.91788 + 1.10729i) q^{50} +(-5.19477 + 1.88598i) q^{51} -4.83826i q^{52} +(-0.301628 + 0.174145i) q^{53} +(0.0279834 - 11.5072i) q^{54} -1.58936i q^{55} +(1.51562 + 5.07730i) q^{56} +(-7.48987 + 8.91140i) q^{57} -9.70678 q^{58} +(1.25895 - 2.18056i) q^{59} +(3.85093 + 3.23664i) q^{60} +(-9.88538 + 5.70733i) q^{61} +12.0474 q^{62} +(-7.92268 - 0.480699i) q^{63} +12.8594 q^{64} +(-1.44269 + 0.832938i) q^{65} +(-5.73041 + 2.08044i) q^{66} +(-5.42062 + 9.38878i) q^{67} -9.26699 q^{68} +(-14.5202 - 2.57244i) q^{69} +(4.02424 - 4.25861i) q^{70} -8.45822i q^{71} +(2.06406 - 5.64247i) q^{72} +(-9.85355 + 5.68895i) q^{73} +23.0962i q^{74} +(0.302150 - 1.70549i) q^{75} +(-16.9046 + 9.75986i) q^{76} +(1.20279 + 4.02935i) q^{77} +(4.89161 + 4.11131i) q^{78} +(3.52228 + 6.10077i) q^{79} +(-0.686756 - 1.18950i) q^{80} +(6.87561 + 5.80741i) q^{81} +(-0.794108 - 0.458479i) q^{82} +(4.33787 - 7.51342i) q^{83} +(-12.2123 - 5.29124i) q^{84} +(1.59537 + 2.76327i) q^{85} +9.51735i q^{86} +(4.88464 - 5.81171i) q^{87} -3.18302 q^{88} +(0.218561 - 0.378558i) q^{89} +(-6.54465 + 1.14306i) q^{90} +(3.02717 - 3.20347i) q^{91} +(-21.4141 - 12.3635i) q^{92} +(-6.06246 + 7.21308i) q^{93} +(-6.63589 - 3.83123i) q^{94} +(5.82047 + 3.36045i) q^{95} +(-7.85348 + 9.34402i) q^{96} +(3.10554 + 1.79298i) q^{97} +(-6.97946 + 13.8419i) q^{98} +(1.63804 - 4.47787i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9}+O(q^{10}) \) 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9	\( 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9} + 15 q^{12} - 6 q^{13} - 6 q^{14} - q^{15} - 16 q^{16} + 3 q^{17} + 41 q^{18} - 16 q^{20} - 17 q^{21} - 21 q^{22} - 26 q^{24} + 32 q^{25} - 12 q^{26} - 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 24 q^{31} - 19 q^{33} + 30 q^{34} - q^{35} + 18 q^{36} - q^{37} - 60 q^{38} - 36 q^{39} - 6 q^{41} + 44 q^{42} - 19 q^{43} - 21 q^{44} - 7 q^{45} + 6 q^{46} - 15 q^{47} + 35 q^{48} + 23 q^{49} - 9 q^{51} + 24 q^{53} - 58 q^{54} + 33 q^{56} + 27 q^{57} + 15 q^{59} - 15 q^{60} - 9 q^{61} - 11 q^{63} + 76 q^{64} + 6 q^{65} + 22 q^{66} + 25 q^{67} - 6 q^{68} + 50 q^{69} + 6 q^{70} + 61 q^{72} + 12 q^{73} + q^{75} - 54 q^{76} - 27 q^{77} - 42 q^{78} - 2 q^{79} + 16 q^{80} + 43 q^{81} - 24 q^{82} + 42 q^{83} - 36 q^{84} - 3 q^{85} - 55 q^{87} - 84 q^{88} - 30 q^{89} - 41 q^{90} - 57 q^{91} + 6 q^{92} - 48 q^{93} + 24 q^{94} - 9 q^{96} + 42 q^{97} - 6 q^{98} - q^{99}+O(q^{100}) \) 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9 + 15 * q^12 - 6 * q^13 - 6 * q^14 - q^15 - 16 * q^16 + 3 * q^17 + 41 * q^18 - 16 * q^20 - 17 * q^21 - 21 * q^22 - 26 * q^24 + 32 * q^25 - 12 * q^26 - 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 24 * q^31 - 19 * q^33 + 30 * q^34 - q^35 + 18 * q^36 - q^37 - 60 * q^38 - 36 * q^39 - 6 * q^41 + 44 * q^42 - 19 * q^43 - 21 * q^44 - 7 * q^45 + 6 * q^46 - 15 * q^47 + 35 * q^48 + 23 * q^49 - 9 * q^51 + 24 * q^53 - 58 * q^54 + 33 * q^56 + 27 * q^57 + 15 * q^59 - 15 * q^60 - 9 * q^61 - 11 * q^63 + 76 * q^64 + 6 * q^65 + 22 * q^66 + 25 * q^67 - 6 * q^68 + 50 * q^69 + 6 * q^70 + 61 * q^72 + 12 * q^73 + q^75 - 54 * q^76 - 27 * q^77 - 42 * q^78 - 2 * q^79 + 16 * q^80 + 43 * q^81 - 24 * q^82 + 42 * q^83 - 36 * q^84 - 3 * q^85 - 55 * q^87 - 84 * q^88 - 30 * q^89 - 41 * q^90 - 57 * q^91 + 6 * q^92 - 48 * q^93 + 24 * q^94 - 9 * q^96 + 42 * q^97 - 6 * q^98 - q^99

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