LMFDB - Embedded newform 750.2.g.f.451.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(151,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("750.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.g (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 24 x^{14} + 94 x^{13} + 262 x^{12} - 936 x^{11} - 1584 x^{10} + 4642 x^{9} + \cdots + 11105 $ x^16 - 4x^15 - 24x^14 + 94x^13 + 262x^12 - 936x^11 - 1584x^10 + 4642x^9 + 6259x^8 - 11958x^7 - 15752x^6 + 14670x^5 + 18271x^4 - 10440x^3 + 1135x^2 + 21080*x + 11105
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 5^{6} $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			451.3
Root			$-1.16141 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	750.451
Dual form			750.2.g.f.301.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.309017 - 0.951057i) q^{6} +2.70913 q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.309017 - 0.951057i) q^{6} +2.70913 q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-4.54704 - 3.30361i) q^{11} +(-0.809017 + 0.587785i) q^{12} +(3.91630 - 2.84536i) q^{13} +(-2.19173 - 1.59239i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(0.323132 - 0.994499i) q^{17} +1.00000 q^{18} +(2.59109 - 7.97455i) q^{19} +(0.837167 + 2.57654i) q^{21} +(1.73681 + 5.34536i) q^{22} +(4.28357 + 3.11219i) q^{23} +1.00000 q^{24} -4.84082 q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.837167 + 2.57654i) q^{28} +(1.29490 + 3.98530i) q^{29} +(-1.72444 + 5.30729i) q^{31} +1.00000 q^{32} +(1.73681 - 5.34536i) q^{33} +(-0.845972 + 0.614634i) q^{34} +(-0.809017 - 0.587785i) q^{36} +(2.42041 - 1.75853i) q^{37} +(-6.78356 + 4.92854i) q^{38} +(3.91630 + 2.84536i) q^{39} +(1.27617 - 0.927190i) q^{41} +(0.837167 - 2.57654i) q^{42} +3.29669 q^{43} +(1.73681 - 5.34536i) q^{44} +(-1.63618 - 5.03563i) q^{46} +(-0.949838 - 2.92330i) q^{47} +(-0.809017 - 0.587785i) q^{48} +0.339383 q^{49} +1.04568 q^{51} +(3.91630 + 2.84536i) q^{52} +(1.90883 + 5.87478i) q^{53} +(0.309017 + 0.951057i) q^{54} +(0.837167 - 2.57654i) q^{56} +8.38494 q^{57} +(1.29490 - 3.98530i) q^{58} +(11.4780 - 8.33925i) q^{59} +(-0.218911 - 0.159048i) q^{61} +(4.51465 - 3.28009i) q^{62} +(-2.19173 + 1.59239i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-4.54704 + 3.30361i) q^{66} +(1.94984 - 6.00099i) q^{67} +1.04568 q^{68} +(-1.63618 + 5.03563i) q^{69} +(-1.40070 - 4.31091i) q^{71} +(0.309017 + 0.951057i) q^{72} +(6.60237 + 4.79691i) q^{73} -2.99179 q^{74} +8.38494 q^{76} +(-12.3185 - 8.94992i) q^{77} +(-1.49589 - 4.60389i) q^{78} +(3.85697 + 11.8705i) q^{79} +(0.309017 - 0.951057i) q^{81} -1.57743 q^{82} +(-0.0415695 + 0.127938i) q^{83} +(-2.19173 + 1.59239i) q^{84} +(-2.66708 - 1.93775i) q^{86} +(-3.39010 + 2.46305i) q^{87} +(-4.54704 + 3.30361i) q^{88} +(-9.53844 - 6.93008i) q^{89} +(10.6098 - 7.70845i) q^{91} +(-1.63618 + 5.03563i) q^{92} -5.58042 q^{93} +(-0.949838 + 2.92330i) q^{94} +(0.309017 + 0.951057i) q^{96} +(-0.815900 - 2.51108i) q^{97} +(-0.274567 - 0.199485i) q^{98} +5.62045 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^7 - 4 * q^8 - 4 * q^9	$ 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9} + 2 q^{11} - 4 q^{12} + 4 q^{13} - 2 q^{14} - 4 q^{16} - 2 q^{17} + 16 q^{18} - 2 q^{21} - 8 q^{22} - 6 q^{23} + 16 q^{24} + 4 q^{26} - 4 q^{27} - 2 q^{28} + 10 q^{29} - 18 q^{31} + 16 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 2 q^{37} - 10 q^{38} + 4 q^{39} + 22 q^{41} - 2 q^{42} + 4 q^{43} - 8 q^{44} - 6 q^{46} - 2 q^{47} - 4 q^{48} + 52 q^{49} + 28 q^{51} + 4 q^{52} - 16 q^{53} - 4 q^{54} - 2 q^{56} + 20 q^{57} + 10 q^{58} - 20 q^{59} + 12 q^{61} + 2 q^{62} - 2 q^{63} - 4 q^{64} + 2 q^{66} + 18 q^{67} + 28 q^{68} - 6 q^{69} - 28 q^{71} - 4 q^{72} + 24 q^{73} - 12 q^{74} + 20 q^{76} - 14 q^{77} - 6 q^{78} + 20 q^{79} - 4 q^{81} + 12 q^{82} - 36 q^{83} - 2 q^{84} - 6 q^{86} - 20 q^{87} + 2 q^{88} - 70 q^{89} + 12 q^{91} - 6 q^{92} + 32 q^{93} - 2 q^{94} - 4 q^{96} + 28 q^{97} - 38 q^{98} + 12 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^7 - 4 * q^8 - 4 * q^9 + 2 * q^11 - 4 * q^12 + 4 * q^13 - 2 * q^14 - 4 * q^16 - 2 * q^17 + 16 * q^18 - 2 * q^21 - 8 * q^22 - 6 * q^23 + 16 * q^24 + 4 * q^26 - 4 * q^27 - 2 * q^28 + 10 * q^29 - 18 * q^31 + 16 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 2 * q^37 - 10 * q^38 + 4 * q^39 + 22 * q^41 - 2 * q^42 + 4 * q^43 - 8 * q^44 - 6 * q^46 - 2 * q^47 - 4 * q^48 + 52 * q^49 + 28 * q^51 + 4 * q^52 - 16 * q^53 - 4 * q^54 - 2 * q^56 + 20 * q^57 + 10 * q^58 - 20 * q^59 + 12 * q^61 + 2 * q^62 - 2 * q^63 - 4 * q^64 + 2 * q^66 + 18 * q^67 + 28 * q^68 - 6 * q^69 - 28 * q^71 - 4 * q^72 + 24 * q^73 - 12 * q^74 + 20 * q^76 - 14 * q^77 - 6 * q^78 + 20 * q^79 - 4 * q^81 + 12 * q^82 - 36 * q^83 - 2 * q^84 - 6 * q^86 - 20 * q^87 + 2 * q^88 - 70 * q^89 + 12 * q^91 - 6 * q^92 + 32 * q^93 - 2 * q^94 - 4 * q^96 + 28 * q^97 - 38 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$		0			0
$5$		0			0
$6$	0.309017	−	0.951057i	0.126156	−	0.388267i
$7$	2.70913			1.02395			0.511977	−	0.858999i	$-0.328913\pi$
$7$	2.70913			1.02395			0.511977	+	0.858999i	$0.328913\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	−4.54704	−	3.30361i	−1.37098	−	0.996077i	−0.997660	−	0.0683760i	$-0.978218\pi$
$11$	−4.54704	−	3.30361i	−1.37098	−	0.996077i	−0.373323	−	0.927701i	$-0.621782\pi$
$12$	−0.809017	+	0.587785i	−0.233543	+	0.169679i
$13$	3.91630	−	2.84536i	1.08619	−	0.789161i	0.107436	−	0.994212i	$-0.465736\pi$
$13$	3.91630	−	2.84536i	1.08619	−	0.789161i	0.978751	+	0.205051i	$0.0657360\pi$
$14$	−2.19173	−	1.59239i	−0.585765	−	0.425583i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.323132	−	0.994499i	0.0783711	−	0.241202i	−0.904193	−	0.427123i	$-0.859527\pi$
$17$	0.323132	−	0.994499i	0.0783711	−	0.241202i	0.982565	+	0.185922i	$0.0595271\pi$
$18$	1.00000			0.235702
$19$	2.59109	−	7.97455i	0.594437	−	1.82949i	0.0369263	−	0.999318i	$-0.488243\pi$
$19$	2.59109	−	7.97455i	0.594437	−	1.82949i	0.557510	−	0.830170i	$-0.311757\pi$
$20$		0			0
$21$	0.837167	+	2.57654i	0.182685	+	0.562246i
$22$	1.73681	+	5.34536i	0.370290	+	1.13963i
$23$	4.28357	+	3.11219i	0.893185	+	0.648937i	0.936707	−	0.350115i	$-0.113858\pi$
$23$	4.28357	+	3.11219i	0.893185	+	0.648937i	−0.0435212	+	0.999053i	$0.513858\pi$
$24$	1.00000			0.204124
$25$		0			0
$26$	−4.84082			−0.949362
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	0.837167	+	2.57654i	0.158210	+	0.486919i
$29$	1.29490	+	3.98530i	0.240457	+	0.740051i	0.996350	+	0.0853563i	$0.0272028\pi$
$29$	1.29490	+	3.98530i	0.240457	+	0.740051i	−0.755893	+	0.654695i	$0.772797\pi$
$30$		0			0
$31$	−1.72444	+	5.30729i	−0.309719	+	0.953218i	0.668155	+	0.744022i	$0.267084\pi$
$31$	−1.72444	+	5.30729i	−0.309719	+	0.953218i	−0.977874	+	0.209195i	$0.932916\pi$
$32$	1.00000			0.176777
$33$	1.73681	−	5.34536i	0.302340	−	0.930508i
$34$	−0.845972	+	0.614634i	−0.145083	+	0.105409i
$35$		0			0
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	2.42041	−	1.75853i	0.397913	−	0.289101i	−0.370778	−	0.928722i	$-0.620909\pi$
$37$	2.42041	−	1.75853i	0.397913	−	0.289101i	0.768690	+	0.639621i	$0.220909\pi$
$38$	−6.78356	+	4.92854i	−1.10044	+	0.799516i
$39$	3.91630	+	2.84536i	0.627110	+	0.455622i
$40$		0			0
$41$	1.27617	−	0.927190i	0.199304	−	0.144803i	−0.483657	−	0.875258i	$-0.660692\pi$
$41$	1.27617	−	0.927190i	0.199304	−	0.144803i	0.682961	+	0.730455i	$0.260692\pi$
$42$	0.837167	−	2.57654i	0.129178	−	0.397568i
$43$	3.29669			0.502741			0.251370	−	0.967891i	$-0.419119\pi$
$43$	3.29669			0.502741			0.251370	+	0.967891i	$0.419119\pi$
$44$	1.73681	−	5.34536i	0.261834	−	0.805843i
$45$		0			0
$46$	−1.63618	−	5.03563i	−0.241241	−	0.742464i
$47$	−0.949838	−	2.92330i	−0.138548	−	0.426407i	0.857577	−	0.514356i	$-0.171969\pi$
$47$	−0.949838	−	2.92330i	−0.138548	−	0.426407i	−0.996125	+	0.0879484i	$0.971969\pi$
$48$	−0.809017	−	0.587785i	−0.116772	−	0.0848395i
$49$	0.339383			0.0484833
$50$		0			0
$51$	1.04568			0.146424
$52$	3.91630	+	2.84536i	0.543094	+	0.394581i
$53$	1.90883	+	5.87478i	0.262198	+	0.806962i	0.992326	+	0.123652i	$0.0394606\pi$
$53$	1.90883	+	5.87478i	0.262198	+	0.806962i	−0.730128	+	0.683311i	$0.760539\pi$
$54$	0.309017	+	0.951057i	0.0420519	+	0.129422i
$55$		0			0
$56$	0.837167	−	2.57654i	0.111871	−	0.344304i
$57$	8.38494			1.11061
$58$	1.29490	−	3.98530i	0.170029	−	0.523295i
$59$	11.4780	−	8.33925i	1.49431	−	1.08568i	0.521726	−	0.853113i	$-0.325288\pi$
$59$	11.4780	−	8.33925i	1.49431	−	1.08568i	0.972581	−	0.232565i	$-0.0747118\pi$
$60$		0			0
$61$	−0.218911	−	0.159048i	−0.0280286	−	0.0203640i	0.573683	−	0.819078i	$-0.305514\pi$
$61$	−0.218911	−	0.159048i	−0.0280286	−	0.0203640i	−0.601711	+	0.798714i	$0.705514\pi$
$62$	4.51465	−	3.28009i	0.573361	−	0.416571i
$63$	−2.19173	+	1.59239i	−0.276132	+	0.200622i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$		0			0
$66$	−4.54704	+	3.30361i	−0.559701	+	0.406647i
$67$	1.94984	−	6.00099i	0.238211	−	0.733137i	−0.758469	−	0.651710i	$-0.774052\pi$
$67$	1.94984	−	6.00099i	0.238211	−	0.733137i	0.996679	−	0.0814275i	$-0.0259479\pi$
$68$	1.04568			0.126807
$69$	−1.63618	+	5.03563i	−0.196973	+	0.606219i
$70$		0			0
$71$	−1.40070	−	4.31091i	−0.166233	−	0.511611i	0.832892	−	0.553435i	$-0.186683\pi$
$71$	−1.40070	−	4.31091i	−0.166233	−	0.511611i	−0.999125	+	0.0418237i	$0.986683\pi$
$72$	0.309017	+	0.951057i	0.0364180	+	0.112083i
$73$	6.60237	+	4.79691i	0.772749	+	0.561435i	0.902794	−	0.430073i	$-0.141512\pi$
$73$	6.60237	+	4.79691i	0.772749	+	0.561435i	−0.130045	+	0.991508i	$0.541512\pi$
$74$	−2.99179			−0.347788
$75$		0			0
$76$	8.38494			0.961819
$77$	−12.3185	−	8.94992i	−1.40382	−	1.01994i
$78$	−1.49589	−	4.60389i	−0.169377	−	0.521288i
$79$	3.85697	+	11.8705i	0.433943	+	1.33554i	0.894166	+	0.447736i	$0.147770\pi$
$79$	3.85697	+	11.8705i	0.433943	+	1.33554i	−0.460223	+	0.887804i	$0.652230\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−1.57743			−0.174198
$83$	−0.0415695	+	0.127938i	−0.00456285	+	0.0140430i	−0.953312	−	0.301987i	$-0.902350\pi$
$83$	−0.0415695	+	0.127938i	−0.00456285	+	0.0140430i	0.948749	+	0.316030i	$0.102350\pi$
$84$	−2.19173	+	1.59239i	−0.239138	+	0.173744i
$85$		0			0
$86$	−2.66708	−	1.93775i	−0.287599	−	0.208953i
$87$	−3.39010	+	2.46305i	−0.363456	+	0.264067i
$88$	−4.54704	+	3.30361i	−0.484716	+	0.352167i
$89$	−9.53844	−	6.93008i	−1.01107	−	0.734587i	−0.0466385	−	0.998912i	$-0.514851\pi$
$89$	−9.53844	−	6.93008i	−1.01107	−	0.734587i	−0.964434	+	0.264325i	$0.914851\pi$
$90$		0			0
$91$	10.6098	−	7.70845i	1.11221	−	0.808065i
$92$	−1.63618	+	5.03563i	−0.170583	+	0.525001i
$93$	−5.58042			−0.578662
$94$	−0.949838	+	2.92330i	−0.0979683	+	0.301516i
$95$		0			0
$96$	0.309017	+	0.951057i	0.0315389	+	0.0970668i
$97$	−0.815900	−	2.51108i	−0.0828421	−	0.254962i	0.901053	−	0.433709i	$-0.142795\pi$
$97$	−0.815900	−	2.51108i	−0.0828421	−	0.254962i	−0.983895	+	0.178748i	$0.942795\pi$
$98$	−0.274567	−	0.199485i	−0.0277354	−	0.0201510i
$99$	5.62045			0.564876
$100$		0			0
$101$	−3.82844			−0.380944			−0.190472	−	0.981693i	$-0.561002\pi$
$101$	−3.82844			−0.380944			−0.190472	+	0.981693i	$0.561002\pi$
$102$	−0.845972	−	0.614634i	−0.0837637	−	0.0608579i
$103$	−1.82111	−	5.60479i	−0.179439	−	0.552256i	0.820369	−	0.571834i	$-0.193768\pi$
$103$	−1.82111	−	5.60479i	−0.179439	−	0.552256i	−0.999808	+	0.0195778i	$0.993768\pi$
$104$	−1.49589	−	4.60389i	−0.146685	−	0.451449i
$105$		0			0
$106$	1.90883	−	5.87478i	0.185402	−	0.570609i
$107$	−5.90758			−0.571108			−0.285554	−	0.958363i	$-0.592178\pi$
$107$	−5.90758			−0.571108			−0.285554	+	0.958363i	$0.592178\pi$
$108$	0.309017	−	0.951057i	0.0297352	−	0.0915155i
$109$	−4.56128	+	3.31397i	−0.436892	+	0.317420i	−0.784399	−	0.620257i	$-0.787028\pi$
$109$	−4.56128	+	3.31397i	−0.436892	+	0.317420i	0.347507	+	0.937677i	$0.387028\pi$
$110$		0			0
$111$	2.42041	+	1.75853i	0.229735	+	0.166912i
$112$	−2.19173	+	1.59239i	−0.207099	+	0.150466i
$113$	−4.09923	+	2.97826i	−0.385623	+	0.280171i	−0.763659	−	0.645619i	$-0.776599\pi$
$113$	−4.09923	+	2.97826i	−0.385623	+	0.280171i	0.378037	+	0.925791i	$0.376599\pi$
$114$	−6.78356	−	4.92854i	−0.635339	−	0.461601i
$115$		0			0
$116$	−3.39010	+	2.46305i	−0.314763	+	0.228688i
$117$	−1.49589	+	4.60389i	−0.138296	+	0.425630i
$118$	−14.1876			−1.30607
$119$	0.875408	−	2.69423i	0.0802485	−	0.246979i
$120$		0			0
$121$	6.36248	+	19.5817i	0.578407	+	1.78015i
$122$	0.0836164	+	0.257345i	0.00757027	+	0.0232989i
$123$	1.27617	+	0.927190i	0.115068	+	0.0836019i
$124$	−5.58042			−0.501136
$125$		0			0
$126$	2.70913			0.241348
$127$	7.70919	+	5.60106i	0.684080	+	0.497013i	0.874709	−	0.484649i	$-0.161053\pi$
$127$	7.70919	+	5.60106i	0.684080	+	0.497013i	−0.190628	+	0.981662i	$0.561053\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	1.01873	+	3.13534i	0.0896945	+	0.276051i
$130$		0			0
$131$	0.0460083	−	0.141599i	0.00401976	−	0.0123716i	−0.949027	−	0.315196i	$-0.897930\pi$
$131$	0.0460083	−	0.141599i	0.00401976	−	0.0123716i	0.953046	+	0.302825i	$0.0979297\pi$
$132$	5.62045			0.489197
$133$	7.01960	−	21.6041i	0.608676	−	1.87331i
$134$	−5.10474	+	3.70881i	−0.440983	+	0.320393i
$135$		0			0
$136$	−0.845972	−	0.614634i	−0.0725415	−	0.0527045i
$137$	−7.30072	+	5.30429i	−0.623743	+	0.453176i	−0.854227	−	0.519900i	$-0.825969\pi$
$137$	−7.30072	+	5.30429i	−0.623743	+	0.453176i	0.230484	+	0.973076i	$0.425969\pi$
$138$	4.28357	−	3.11219i	0.364641	−	0.264927i
$139$	−5.75420	−	4.18067i	−0.488065	−	0.354600i	0.316375	−	0.948634i	$-0.397534\pi$
$139$	−5.75420	−	4.18067i	−0.488065	−	0.354600i	−0.804440	+	0.594034i	$0.797534\pi$
$140$		0			0
$141$	2.48671	−	1.80670i	0.209419	−	0.152152i
$142$	−1.40070	+	4.31091i	−0.117544	+	0.361764i
$143$	−27.2075			−2.27521
$144$	0.309017	−	0.951057i	0.0257514	−	0.0792547i
$145$		0			0
$146$	−2.52188	−	7.76156i	−0.208712	−	0.642351i
$147$	0.104875	+	0.322773i	0.00864996	+	0.0266218i
$148$	2.42041	+	1.75853i	0.198956	+	0.144550i
$149$	15.4351			1.26449			0.632246	−	0.774768i	$-0.282133\pi$
$149$	15.4351			1.26449			0.632246	+	0.774768i	$0.282133\pi$
$150$		0			0
$151$	−7.99801			−0.650868			−0.325434	−	0.945565i	$-0.605510\pi$
$151$	−7.99801			−0.650868			−0.325434	+	0.945565i	$0.605510\pi$
$152$	−6.78356	−	4.92854i	−0.550219	−	0.399758i
$153$	0.323132	+	0.994499i	0.0261237	+	0.0804005i
$154$	4.70525	+	14.4813i	0.379160	+	1.16693i
$155$		0			0
$156$	−1.49589	+	4.60389i	−0.119767	+	0.368606i
$157$	−15.6147			−1.24619			−0.623095	−	0.782146i	$-0.714125\pi$
$157$	−15.6147			−1.24619			−0.623095	+	0.782146i	$0.714125\pi$
$158$	3.85697	−	11.8705i	0.306844	−	0.944369i
$159$	−4.99738	+	3.63081i	−0.396318	+	0.287942i
$160$		0			0
$161$	11.6047	+	8.43133i	0.914581	+	0.664482i
$162$	−0.809017	+	0.587785i	−0.0635624	+	0.0461808i
$163$	−2.95881	+	2.14970i	−0.231752	+	0.168378i	−0.697601	−	0.716487i	$-0.745749\pi$
$163$	−2.95881	+	2.14970i	−0.231752	+	0.168378i	0.465849	+	0.884864i	$0.345749\pi$
$164$	1.27617	+	0.927190i	0.0996519	+	0.0724014i
$165$		0			0
$166$	0.108830	−	0.0790699i	0.00844688	−	0.00613702i
$167$	1.94776	−	5.99458i	0.150722	−	0.463874i	−0.846980	−	0.531624i	$-0.821582\pi$
$167$	1.94776	−	5.99458i	0.150722	−	0.463874i	0.997702	+	0.0677496i	$0.0215819\pi$
$168$	2.70913			0.209014
$169$	3.22413	−	9.92286i	0.248010	−	0.763297i
$170$		0			0
$171$	2.59109	+	7.97455i	0.198146	+	0.609829i
$172$	1.01873	+	3.13534i	0.0776777	+	0.239068i
$173$	8.61237	+	6.25725i	0.654786	+	0.475730i	0.864898	−	0.501947i	$-0.167383\pi$
$173$	8.61237	+	6.25725i	0.654786	+	0.475730i	−0.210112	+	0.977677i	$0.567383\pi$
$174$	4.19039			0.317673
$175$		0			0
$176$	5.62045			0.423657
$177$	11.4780	+	8.33925i	0.862739	+	0.626816i
$178$	3.64336	+	11.2131i	0.273081	+	0.840458i
$179$	−0.246999	−	0.760184i	−0.0184615	−	0.0568188i	0.941401	−	0.337288i	$-0.109510\pi$
$179$	−0.246999	−	0.760184i	−0.0184615	−	0.0568188i	−0.959863	+	0.280470i	$0.909510\pi$
$180$		0			0
$181$	−5.04439	+	15.5250i	−0.374946	+	1.15397i	0.568568	+	0.822636i	$0.307497\pi$
$181$	−5.04439	+	15.5250i	−0.374946	+	1.15397i	−0.943515	+	0.331330i	$0.892503\pi$
$182$	−13.1144			−0.972104
$183$	0.0836164	−	0.257345i	0.00618110	−	0.0190235i
$184$	4.28357	−	3.11219i	0.315789	−	0.229434i
$185$		0			0
$186$	4.51465	+	3.28009i	0.331030	+	0.240508i
$187$	−4.75474	+	3.45452i	−0.347701	+	0.252619i
$188$	2.48671	−	1.80670i	0.181362	−	0.131767i
$189$	−2.19173	−	1.59239i	−0.159425	−	0.115829i
$190$		0			0
$191$	12.5641	−	9.12835i	0.909106	−	0.660504i	−0.0316826	−	0.999498i	$-0.510087\pi$
$191$	12.5641	−	9.12835i	0.909106	−	0.660504i	0.940789	+	0.338994i	$0.110087\pi$
$192$	0.309017	−	0.951057i	0.0223014	−	0.0686366i
$193$	−21.0202			−1.51307			−0.756533	−	0.653956i	$-0.773108\pi$
$193$	−21.0202			−1.51307			−0.756533	+	0.653956i	$0.773108\pi$
$194$	−0.815900	+	2.51108i	−0.0585782	+	0.180285i
$195$		0			0
$196$	0.104875	+	0.322773i	0.00749109	+	0.0230552i
$197$	7.46505	+	22.9751i	0.531863	+	1.63691i	0.750331	+	0.661062i	$0.229894\pi$
$197$	7.46505	+	22.9751i	0.531863	+	1.63691i	−0.218468	+	0.975844i	$0.570106\pi$
$198$	−4.54704	−	3.30361i	−0.323144	−	0.234778i
$199$	−25.4930			−1.80715			−0.903574	−	0.428432i	$-0.859066\pi$
$199$	−25.4930			−1.80715			−0.903574	+	0.428432i	$0.859066\pi$
$200$		0			0
$201$	6.30981			0.445060
$202$	3.09727	+	2.25030i	0.217923	+	0.158331i
$203$	3.50806	+	10.7967i	0.246217	+	0.757779i
$204$	0.323132	+	0.994499i	0.0226238	+	0.0696289i
$205$		0			0
$206$	−1.82111	+	5.60479i	−0.126882	+	0.390504i
$207$	−5.29478			−0.368013
$208$	−1.49589	+	4.60389i	−0.103722	+	0.319222i
$209$	−38.1266	+	27.7006i	−2.63727	+	1.91609i
$210$		0			0
$211$	−4.24669	−	3.08540i	−0.292354	−	0.212408i	0.431934	−	0.901905i	$-0.357831\pi$
$211$	−4.24669	−	3.08540i	−0.292354	−	0.212408i	−0.724288	+	0.689498i	$0.757831\pi$
$212$	−4.99738	+	3.63081i	−0.343222	+	0.249365i
$213$	3.66708	−	2.66429i	0.251264	−	0.182554i
$214$	4.77934	+	3.47239i	0.326709	+	0.237368i
$215$		0			0
$216$	−0.809017	+	0.587785i	−0.0550466	+	0.0399937i
$217$	−4.67174	+	14.3781i	−0.317139	+	0.976052i
$218$	5.63805			0.381857
$219$	−2.52188	+	7.76156i	−0.170413	+	0.524477i
$220$		0			0
$221$	−1.56423	−	4.81419i	−0.105221	−	0.323837i
$222$	−0.924514	−	2.84536i	−0.0620493	−	0.190968i
$223$	11.9710	+	8.69743i	0.801637	+	0.582423i	0.911394	−	0.411535i	$-0.135007\pi$
$223$	11.9710	+	8.69743i	0.801637	+	0.582423i	−0.109757	+	0.993958i	$0.535007\pi$
$224$	2.70913			0.181011
$225$		0			0
$226$	5.06692			0.337047
$227$	−9.60986	−	6.98197i	−0.637829	−	0.463410i	0.221275	−	0.975211i	$-0.428978\pi$
$227$	−9.60986	−	6.98197i	−0.637829	−	0.463410i	−0.859104	+	0.511802i	$0.828978\pi$
$228$	2.59109	+	7.97455i	0.171599	+	0.528128i
$229$	5.64177	+	17.3636i	0.372819	+	1.14742i	0.944938	+	0.327248i	$0.106121\pi$
$229$	5.64177	+	17.3636i	0.372819	+	1.14742i	−0.572119	+	0.820170i	$0.693879\pi$
$230$		0			0
$231$	4.70525	−	14.4813i	0.309583	−	0.952798i
$232$	4.19039			0.275113
$233$	−0.883301	+	2.71852i	−0.0578669	+	0.178096i	−0.975812	−	0.218611i	$-0.929847\pi$
$233$	−0.883301	+	2.71852i	−0.0578669	+	0.178096i	0.917945	+	0.396708i	$0.129847\pi$
$234$	3.91630	−	2.84536i	0.256017	−	0.186007i
$235$		0			0
$236$	11.4780	+	8.33925i	0.747154	+	0.542839i
$237$	−10.0977	+	7.33640i	−0.655915	+	0.476550i
$238$	−2.29185	+	1.66512i	−0.148558	+	0.107934i
$239$	−13.2548	−	9.63014i	−0.857379	−	0.622922i	0.0697919	−	0.997562i	$-0.477766\pi$
$239$	−13.2548	−	9.63014i	−0.857379	−	0.622922i	−0.927171	+	0.374640i	$0.877766\pi$
$240$		0			0
$241$	−21.2995	+	15.4750i	−1.37202	+	0.996831i	−0.374443	+	0.927250i	$0.622166\pi$
$241$	−21.2995	+	15.4750i	−1.37202	+	0.996831i	−0.997576	+	0.0695808i	$0.977834\pi$
$242$	6.36248	−	19.5817i	0.408995	−	1.25876i
$243$	1.00000			0.0641500
$244$	0.0836164	−	0.257345i	0.00535299	−	0.0164748i
$245$		0			0
$246$	−0.487453	−	1.50022i	−0.0310788	−	0.0956508i
$247$	−12.5430	−	38.6034i	−0.798091	−	2.45627i
$248$	4.51465	+	3.28009i	0.286681	+	0.208286i
$249$	−0.134522			−0.00852497
$250$		0			0
$251$	−13.8356			−0.873295			−0.436647	−	0.899633i	$-0.643834\pi$
$251$	−13.8356			−0.873295			−0.436647	+	0.899633i	$0.643834\pi$
$252$	−2.19173	−	1.59239i	−0.138066	−	0.100311i
$253$	−9.19604	−	28.3025i	−0.578150	−	1.77936i
$254$	−2.94465	−	9.06270i	−0.184764	−	0.568644i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	28.6204			1.78529			0.892647	−	0.450756i	$-0.148846\pi$
$257$	28.6204			1.78529			0.892647	+	0.450756i	$0.148846\pi$
$258$	1.01873	−	3.13534i	0.0634236	−	0.195198i
$259$	6.55720	−	4.76409i	0.407445	−	0.296026i
$260$		0			0
$261$	−3.39010	−	2.46305i	−0.209842	−	0.152459i
$262$	−0.120451	+	0.0875130i	−0.00744150	+	0.00540657i
$263$	−2.52661	+	1.83569i	−0.155798	+	0.113194i	−0.662953	−	0.748661i	$-0.730697\pi$
$263$	−2.52661	+	1.83569i	−0.155798	+	0.113194i	0.507155	+	0.861855i	$0.330697\pi$
$264$	−4.54704	−	3.30361i	−0.279851	−	0.203323i
$265$		0			0
$266$	−18.3775	+	13.3521i	−1.12680	+	0.818668i
$267$	3.64336	−	11.2131i	0.222970	−	0.686231i
$268$	6.30981			0.385433
$269$	2.85284	−	8.78015i	0.173941	−	0.535335i	−0.825643	−	0.564194i	$-0.809187\pi$
$269$	2.85284	−	8.78015i	0.173941	−	0.535335i	0.999584	+	0.0288583i	$0.00918715\pi$
$270$		0			0
$271$	−6.70088	−	20.6232i	−0.407050	−	1.25277i	−0.919172	−	0.393857i	$-0.871140\pi$
$271$	−6.70088	−	20.6232i	−0.407050	−	1.25277i	0.512122	−	0.858913i	$-0.328860\pi$
$272$	0.323132	+	0.994499i	0.0195928	+	0.0603004i
$273$	10.6098	+	7.70845i	0.642133	+	0.466537i
$274$	9.02419			0.545171
$275$		0			0
$276$	−5.29478			−0.318708
$277$	8.32889	+	6.05129i	0.500434	+	0.363587i	0.809183	−	0.587557i	$-0.199910\pi$
$277$	8.32889	+	6.05129i	0.500434	+	0.363587i	−0.308749	+	0.951144i	$0.599910\pi$
$278$	2.19791	+	6.76447i	0.131822	+	0.405706i
$279$	−1.72444	−	5.30729i	−0.103240	−	0.317739i
$280$		0			0
$281$	−0.246763	+	0.759459i	−0.0147207	+	0.0453055i	−0.958147	−	0.286277i	$-0.907582\pi$
$281$	−0.246763	+	0.759459i	−0.0147207	+	0.0453055i	0.943426	+	0.331582i	$0.107582\pi$
$282$	−3.07374			−0.183039
$283$	0.225781	−	0.694882i	0.0134213	−	0.0413064i	−0.944122	−	0.329597i	$-0.893087\pi$
$283$	0.225781	−	0.694882i	0.0134213	−	0.0413064i	0.957543	+	0.288291i	$0.0930870\pi$
$284$	3.66708	−	2.66429i	0.217601	−	0.158097i
$285$		0			0
$286$	22.0114	+	15.9922i	1.30156	+	0.945638i
$287$	3.45730	−	2.51188i	0.204078	−	0.148271i
$288$	−0.809017	+	0.587785i	−0.0476718	+	0.0346356i
$289$	12.8687	+	9.34964i	0.756981	+	0.549979i
$290$		0			0
$291$	2.13605	−	1.55193i	0.125218	−	0.0909759i
$292$	−2.52188	+	7.76156i	−0.147582	+	0.454211i
$293$	18.4842			1.07986			0.539929	−	0.841711i	$-0.318451\pi$
$293$	18.4842			1.07986			0.539929	+	0.841711i	$0.318451\pi$
$294$	0.104875	−	0.322773i	0.00611645	−	0.0188245i
$295$		0			0
$296$	−0.924514	−	2.84536i	−0.0537363	−	0.165383i
$297$	1.73681	+	5.34536i	0.100780	+	0.310169i
$298$	−12.4872	−	9.07251i	−0.723367	−	0.525557i
$299$	25.6311			1.48228
$300$		0			0
$301$	8.93117			0.514784
$302$	6.47052	+	4.70111i	0.372337	+	0.270518i
$303$	−1.18305	−	3.64106i	−0.0679646	−	0.209173i
$304$	2.59109	+	7.97455i	0.148609	+	0.457372i
$305$		0			0
$306$	0.323132	−	0.994499i	0.0184723	−	0.0568518i
$307$	14.1923			0.809998			0.404999	−	0.914317i	$-0.367272\pi$
$307$	14.1923			0.809998			0.404999	+	0.914317i	$0.367272\pi$
$308$	4.70525	−	14.4813i	0.268107	−	0.825147i
$309$	4.76772	−	3.46395i	0.271226	−	0.197057i
$310$		0			0
$311$	−8.18254	−	5.94496i	−0.463989	−	0.337108i	0.331105	−	0.943594i	$-0.392579\pi$
$311$	−8.18254	−	5.94496i	−0.463989	−	0.337108i	−0.795094	+	0.606486i	$0.792579\pi$
$312$	3.91630	−	2.84536i	0.221717	−	0.161087i
$313$	−5.66348	+	4.11476i	−0.320119	+	0.232580i	−0.736226	−	0.676735i	$-0.763394\pi$
$313$	−5.66348	+	4.11476i	−0.320119	+	0.232580i	0.416107	+	0.909316i	$0.363394\pi$
$314$	12.6326	+	9.17810i	0.712898	+	0.517950i
$315$		0			0
$316$	−10.0977	+	7.33640i	−0.568039	+	0.412704i
$317$	−4.73987	+	14.5878i	−0.266218	+	0.819333i	0.725193	+	0.688546i	$0.241751\pi$
$317$	−4.73987	+	14.5878i	−0.266218	+	0.819333i	−0.991410	+	0.130788i	$0.958249\pi$
$318$	6.17710			0.346395
$319$	7.27792	−	22.3991i	0.407485	−	1.25411i
$320$		0			0
$321$	−1.82554	−	5.61845i	−0.101892	−	0.313591i
$322$	−4.43261	−	13.6422i	−0.247020	−	0.760249i
$323$	−7.09342	−	5.15367i	−0.394689	−	0.286758i
$324$	1.00000			0.0555556
$325$		0			0
$326$	3.65730			0.202559
$327$	−4.56128	−	3.31397i	−0.252239	−	0.183263i
$328$	−0.487453	−	1.50022i	−0.0269151	−	0.0828361i
$329$	−2.57324	−	7.91960i	−0.141867	−	0.436622i
$330$		0			0
$331$	7.30737	−	22.4898i	0.401650	−	1.23615i	−0.522011	−	0.852939i	$-0.674818\pi$
$331$	7.30737	−	22.4898i	0.401650	−	1.23615i	0.923661	−	0.383212i	$-0.125182\pi$
$332$	−0.134522			−0.00738284
$333$	−0.924514	+	2.84536i	−0.0506630	+	0.155925i
$334$	−5.09929	+	3.70485i	−0.279021	+	0.202721i
$335$		0			0
$336$	−2.19173	−	1.59239i	−0.119569	−	0.0868718i
$337$	22.4196	−	16.2888i	1.22127	−	0.887306i	0.225067	−	0.974343i	$-0.427740\pi$
$337$	22.4196	−	16.2888i	1.22127	−	0.887306i	0.996205	+	0.0870374i	$0.0277400\pi$
$338$	−8.44089	+	6.13266i	−0.459124	+	0.333573i
$339$	−4.09923	−	2.97826i	−0.222639	−	0.161757i
$340$		0			0
$341$	25.3744	−	18.4355i	1.37410	−	0.998341i
$342$	2.59109	−	7.97455i	0.140110	−	0.431214i
$343$	−18.0445			−0.974310
$344$	1.01873	−	3.13534i	0.0549265	−	0.169046i
$345$		0			0
$346$	−3.28963	−	10.1244i	−0.176852	−	0.544294i
$347$	8.24643	+	25.3799i	0.442692	+	1.36246i	0.884996	+	0.465600i	$0.154161\pi$
$347$	8.24643	+	25.3799i	0.442692	+	1.36246i	−0.442304	+	0.896865i	$0.645839\pi$
$348$	−3.39010	−	2.46305i	−0.181728	−	0.132033i
$349$	−5.73576			−0.307028			−0.153514	−	0.988146i	$-0.549059\pi$
$349$	−5.73576			−0.307028			−0.153514	+	0.988146i	$0.549059\pi$
$350$		0			0
$351$	−4.84082			−0.258384
$352$	−4.54704	−	3.30361i	−0.242358	−	0.176083i
$353$	−8.99327	−	27.6785i	−0.478664	−	1.47318i	−0.840952	−	0.541109i	$-0.818004\pi$
$353$	−8.99327	−	27.6785i	−0.478664	−	1.47318i	0.362288	−	0.932066i	$-0.381996\pi$
$354$	−4.38420	−	13.4932i	−0.233018	−	0.717155i
$355$		0			0
$356$	3.64336	−	11.2131i	0.193098	−	0.594293i
$357$	2.83288			0.149932
$358$	−0.246999	+	0.760184i	−0.0130543	+	0.0401770i
$359$	10.5088	−	7.63506i	0.554631	−	0.402963i	−0.274859	−	0.961485i	$-0.588631\pi$
$359$	10.5088	−	7.63506i	0.554631	−	0.402963i	0.829490	+	0.558521i	$0.188631\pi$
$360$		0			0
$361$	−41.5084	−	30.1576i	−2.18465	−	1.58724i
$362$	13.2064	−	9.59500i	0.694112	−	0.504302i
$363$	−16.6572	+	12.1021i	−0.874275	+	0.635198i
$364$	10.6098	+	7.70845i	0.556103	+	0.404033i
$365$		0			0
$366$	−0.218911	+	0.159048i	−0.0114426	+	0.00831356i
$367$	−1.13968	+	3.50756i	−0.0594906	+	0.183093i	−0.976386	−	0.216035i	$-0.930687\pi$
$367$	−1.13968	+	3.50756i	−0.0594906	+	0.183093i	0.916895	+	0.399129i	$0.130687\pi$
$368$	−5.29478			−0.276009
$369$	−0.487453	+	1.50022i	−0.0253758	+	0.0780986i
$370$		0			0
$371$	5.17127	+	15.9155i	0.268479	+	0.826293i
$372$	−1.72444	−	5.30729i	−0.0894083	−	0.275170i
$373$	21.0383	+	15.2853i	1.08932	+	0.791440i	0.979285	−	0.202487i	$-0.0649024\pi$
$373$	21.0383	+	15.2853i	1.08932	+	0.791440i	0.110039	+	0.993927i	$0.464902\pi$
$374$	5.87718			0.303902
$375$		0			0
$376$	−3.07374			−0.158516
$377$	16.4108	+	11.9232i	0.845201	+	0.614074i
$378$	0.837167	+	2.57654i	0.0430592	+	0.132523i
$379$	−9.32153	−	28.6887i	−0.478815	−	1.47364i	−0.840743	−	0.541434i	$-0.817882\pi$
$379$	−9.32153	−	28.6887i	−0.478815	−	1.47364i	0.361929	−	0.932206i	$-0.382118\pi$
$380$		0			0
$381$	−2.94465	+	9.06270i	−0.150859	+	0.464296i
$382$	−15.5301			−0.794588
$383$	−4.13001	+	12.7109i	−0.211034	+	0.649495i	0.788378	+	0.615191i	$0.210921\pi$
$383$	−4.13001	+	12.7109i	−0.211034	+	0.649495i	−0.999411	+	0.0343033i	$0.989079\pi$
$384$	−0.809017	+	0.587785i	−0.0412850	+	0.0299953i
$385$		0			0
$386$	17.0057	+	12.3554i	0.865567	+	0.628871i
$387$	−2.66708	+	1.93775i	−0.135575	+	0.0985012i
$388$	2.13605	−	1.55193i	0.108442	−	0.0787875i
$389$	7.84772	+	5.70170i	0.397895	+	0.289088i	0.768683	−	0.639630i	$-0.220912\pi$
$389$	7.84772	+	5.70170i	0.397895	+	0.289088i	−0.370788	+	0.928718i	$0.620912\pi$
$390$		0			0
$391$	4.47923	−	3.25435i	0.226525	−	0.164580i
$392$	0.104875	−	0.322773i	0.00529700	−	0.0163025i
$393$	0.148886			0.00751030
$394$	7.46505	−	22.9751i	0.376084	−	1.15747i
$395$		0			0
$396$	1.73681	+	5.34536i	0.0872781	+	0.268614i
$397$	−2.44508	−	7.52519i	−0.122715	−	0.377679i	0.870763	−	0.491704i	$-0.163626\pi$
$397$	−2.44508	−	7.52519i	−0.122715	−	0.377679i	−0.993478	+	0.114025i	$0.963626\pi$
$398$	20.6242	+	14.9844i	1.03380	+	0.751100i
$399$	22.7159			1.13722
$400$		0			0
$401$	−20.1362			−1.00555			−0.502777	−	0.864416i	$-0.667688\pi$
$401$	−20.1362			−1.00555			−0.502777	+	0.864416i	$0.667688\pi$
$402$	−5.10474	−	3.70881i	−0.254601	−	0.184979i
$403$	8.34772	+	25.6916i	0.415829	+	1.27979i
$404$	−1.18305	−	3.64106i	−0.0588591	−	0.181150i
$405$		0			0
$406$	3.50806	−	10.7967i	0.174102	−	0.535831i
$407$	−16.8152			−0.833498
$408$	0.323132	−	0.994499i	0.0159974	−	0.0492351i
$409$	2.27125	−	1.65016i	0.112306	−	0.0815951i	−0.530215	−	0.847863i	$-0.677889\pi$
$409$	2.27125	−	1.65016i	0.112306	−	0.0815951i	0.642521	+	0.766268i	$0.277889\pi$
$410$		0			0
$411$	−7.30072	−	5.30429i	−0.360118	−	0.261641i
$412$	4.76772	−	3.46395i	0.234889	−	0.170657i
$413$	31.0954	−	22.5921i	1.53010	−	1.11168i
$414$	4.28357	+	3.11219i	0.210526	+	0.152956i
$415$		0			0
$416$	3.91630	−	2.84536i	0.192013	−	0.139505i
$417$	2.19791	−	6.76447i	0.107632	−	0.331258i
$418$	47.1271			2.30506
$419$	−10.2582	+	31.5714i	−0.501144	+	1.54236i	0.306013	+	0.952027i	$0.401005\pi$
$419$	−10.2582	+	31.5714i	−0.501144	+	1.54236i	−0.807157	+	0.590337i	$0.798995\pi$
$420$		0			0
$421$	5.91384	+	18.2009i	0.288223	+	0.887059i	0.985414	+	0.170174i	$0.0544329\pi$
$421$	5.91384	+	18.2009i	0.288223	+	0.887059i	−0.697191	+	0.716885i	$0.745567\pi$
$422$	1.62209	+	4.99228i	0.0789622	+	0.243021i
$423$	2.48671	+	1.80670i	0.120908	+	0.0878447i
$424$	6.17710			0.299987
$425$		0			0
$426$	−4.53276			−0.219613
$427$	−0.593057	−	0.430881i	−0.0287000	−	0.0208518i
$428$	−1.82554	−	5.61845i	−0.0882410	−	0.271578i
$429$	−8.40759	−	25.8759i	−0.405922	−	1.24930i
$430$		0			0
$431$	−6.19003	+	19.0510i	−0.298163	+	0.917652i	0.683977	+	0.729503i	$0.260249\pi$
$431$	−6.19003	+	19.0510i	−0.298163	+	0.917652i	−0.982141	+	0.188149i	$0.939751\pi$
$432$	1.00000			0.0481125
$433$	−10.0003	+	30.7778i	−0.480585	+	1.47909i	0.357691	+	0.933840i	$0.383564\pi$
$433$	−10.0003	+	30.7778i	−0.480585	+	1.47909i	−0.838275	+	0.545247i	$0.816436\pi$
$434$	12.2308	−	8.88618i	0.587096	−	0.426550i
$435$		0			0
$436$	−4.56128	−	3.31397i	−0.218446	−	0.158710i
$437$	35.9175	−	26.0956i	1.71816	−	1.24832i
$438$	6.60237	−	4.79691i	0.315474	−	0.229205i
$439$	−14.0178	−	10.1846i	−0.669035	−	0.486083i	0.200667	−	0.979660i	$-0.435689\pi$
$439$	−14.0178	−	10.1846i	−0.669035	−	0.486083i	−0.869702	+	0.493577i	$0.835689\pi$
$440$		0			0
$441$	−0.274567	+	0.199485i	−0.0130746	+	0.00949926i
$442$	−1.56423	+	4.81419i	−0.0744026	+	0.228988i
$443$	−16.5326			−0.785489			−0.392745	−	0.919648i	$-0.628474\pi$
$443$	−16.5326			−0.785489			−0.392745	+	0.919648i	$0.628474\pi$
$444$	−0.924514	+	2.84536i	−0.0438755	+	0.135035i
$445$		0			0
$446$	−4.57251	−	14.0727i	−0.216515	−	0.666364i
$447$	4.76970	+	14.6796i	0.225599	+	0.694323i
$448$	−2.19173	−	1.59239i	−0.103550	−	0.0752332i
$449$	2.51289			0.118591			0.0592954	−	0.998240i	$-0.481115\pi$
$449$	2.51289			0.118591			0.0592954	+	0.998240i	$0.481115\pi$
$450$		0			0
$451$	−8.86586			−0.417477
$452$	−4.09923	−	2.97826i	−0.192811	−	0.140086i
$453$	−2.47152	−	7.60655i	−0.116122	−	0.357387i
$454$	3.67064	+	11.2971i	0.172272	+	0.530198i
$455$		0			0
$456$	2.59109	−	7.97455i	0.121339	−	0.373443i
$457$	−36.7686			−1.71996			−0.859982	−	0.510324i	$-0.829525\pi$
$457$	−36.7686			−1.71996			−0.859982	+	0.510324i	$0.829525\pi$
$458$	5.64177	−	17.3636i	0.263623	−	0.811347i
$459$	−0.845972	+	0.614634i	−0.0394866	+	0.0286887i
$460$		0			0
$461$	−4.91129	−	3.56826i	−0.228741	−	0.166190i	0.467511	−	0.883987i	$-0.345151\pi$
$461$	−4.91129	−	3.56826i	−0.228741	−	0.166190i	−0.696253	+	0.717797i	$0.745151\pi$
$462$	−12.3185	+	8.94992i	−0.573109	+	0.416388i
$463$	26.9502	−	19.5805i	1.25248	−	0.909982i	0.254120	−	0.967173i	$-0.418214\pi$
$463$	26.9502	−	19.5805i	1.25248	−	0.909982i	0.998363	+	0.0571903i	$0.0182142\pi$
$464$	−3.39010	−	2.46305i	−0.157381	−	0.114344i
$465$		0			0
$466$	2.31251	−	1.68014i	0.107125	−	0.0778309i
$467$	2.82334	−	8.68934i	0.130648	−	0.402094i	−0.864239	−	0.503081i	$-0.832200\pi$
$467$	2.82334	−	8.68934i	0.130648	−	0.402094i	0.994888	+	0.100986i	$0.0321998\pi$
$468$	−4.84082			−0.223767
$469$	5.28236	−	16.2574i	0.243917	−	0.750699i
$470$		0			0
$471$	−4.82522	−	14.8505i	−0.222334	−	0.684274i
$472$	−4.38420	−	13.4932i	−0.201799	−	0.621074i
$473$	−14.9902	−	10.8910i	−0.689249	−	0.500769i
$474$	12.4814			0.573291
$475$		0			0
$476$	2.83288			0.129845
$477$	−4.99738	−	3.63081i	−0.228814	−	0.166243i
$478$	5.06286	+	15.5819i	0.231570	+	0.712699i
$479$	6.44637	+	19.8399i	0.294542	+	0.906507i	0.983375	+	0.181587i	$0.0581233\pi$
$479$	6.44637	+	19.8399i	0.294542	+	0.906507i	−0.688833	+	0.724920i	$0.741877\pi$
$480$		0			0
$481$	4.47540	−	13.7739i	0.204061	−	0.628034i
$482$	26.3276			1.19919
$483$	−4.43261	+	13.6422i	−0.201691	+	0.620741i
$484$	−16.6572	+	12.1021i	−0.757144	+	0.550098i
$485$		0			0
$486$	−0.809017	−	0.587785i	−0.0366978	−	0.0266625i
$487$	−1.02981	+	0.748202i	−0.0466652	+	0.0339043i	−0.610873	−	0.791728i	$-0.709182\pi$
$487$	−1.02981	+	0.748202i	−0.0466652	+	0.0339043i	0.564208	+	0.825633i	$0.309182\pi$
$488$	−0.218911	+	0.159048i	−0.00990961	+	0.00719976i
$489$	−2.95881	−	2.14970i	−0.133802	−	0.0972130i
$490$		0			0
$491$	−8.65507	+	6.28827i	−0.390598	+	0.283786i	−0.765700	−	0.643197i	$-0.777607\pi$
$491$	−8.65507	+	6.28827i	−0.390598	+	0.283786i	0.375103	+	0.926983i	$0.377607\pi$
$492$	−0.487453	+	1.50022i	−0.0219761	+	0.0676354i
$493$	4.38180			0.197346
$494$	−12.5430	+	38.6034i	−0.564336	+	1.73685i
$495$		0			0
$496$	−1.72444	−	5.30729i	−0.0774298	−	0.238304i
$497$	−3.79468	−	11.6788i	−0.170215	−	0.523867i
$498$	0.108830	+	0.0790699i	0.00487681	+	0.00354321i
$499$	−7.08035			−0.316960			−0.158480	−	0.987362i	$-0.550659\pi$
$499$	−7.08035			−0.316960			−0.158480	+	0.987362i	$0.550659\pi$
$500$		0			0
$501$	6.30307			0.281601
$502$	11.1932	+	8.13236i	0.499578	+	0.362965i
$503$	1.70912	+	5.26012i	0.0762058	+	0.234537i	0.981902	−	0.189390i	$-0.0606511\pi$
$503$	1.70912	+	5.26012i	0.0762058	+	0.234537i	−0.905696	+	0.423928i	$0.860651\pi$
$504$	0.837167	+	2.57654i	0.0372904	+	0.114768i
$505$		0			0
$506$	−9.19604	+	28.3025i	−0.408814	+	1.25820i
$507$	10.4335			0.463368
$508$	−2.94465	+	9.06270i	−0.130648	+	0.402092i
$509$	−7.79724	+	5.66503i	−0.345607	+	0.251098i	−0.747024	−	0.664798i	$-0.768518\pi$
$509$	−7.79724	+	5.66503i	−0.345607	+	0.251098i	0.401417	+	0.915895i	$0.368518\pi$
$510$		0			0
$511$	17.8867	+	12.9954i	0.791260	+	0.574884i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−6.78356	+	4.92854i	−0.299501	+	0.217601i
$514$	−23.1544	−	16.8227i	−1.02130	−	0.742016i
$515$		0			0
$516$	−2.66708	+	1.93775i	−0.117412	+	0.0853046i
$517$	−5.33851	+	16.4303i	−0.234788	+	0.722602i
$518$	−8.10515			−0.356120
$519$	−3.28963	+	10.1244i	−0.144399	+	0.444414i
$520$		0			0
$521$	6.26109	+	19.2697i	0.274304	+	0.844219i	0.989403	+	0.145197i	$0.0463814\pi$
$521$	6.26109	+	19.2697i	0.274304	+	0.844219i	−0.715099	+	0.699023i	$0.753619\pi$
$522$	1.29490	+	3.98530i	0.0566763	+	0.174432i
$523$	−20.7659	−	15.0873i	−0.908030	−	0.659722i	0.0324859	−	0.999472i	$-0.489658\pi$
$523$	−20.7659	−	15.0873i	−0.908030	−	0.659722i	−0.940516	+	0.339750i	$0.889658\pi$
$524$	0.148886			0.00650411
$525$		0			0
$526$	3.12306			0.136172
$527$	4.72088	+	3.42992i	0.205645	+	0.149410i
$528$	1.73681	+	5.34536i	0.0755851	+	0.232627i
$529$	1.55580	+	4.78827i	0.0676436	+	0.208186i
$530$		0			0
$531$	−4.38420	+	13.4932i	−0.190258	+	0.585554i
$532$	22.7159			0.984859
$533$	2.35967	−	7.26231i	0.102209	−	0.314566i
$534$	−9.53844	+	6.93008i	−0.412769	+	0.299894i
$535$		0			0
$536$	−5.10474	−	3.70881i	−0.220491	−	0.160196i
$537$	0.646651	−	0.469819i	0.0279050	−	0.0202742i
$538$	−7.46884	+	5.42643i	−0.322005	+	0.233950i
$539$	−1.54319	−	1.12119i	−0.0664698	−	0.0482932i
$540$		0			0
$541$	3.20447	−	2.32818i	0.137771	−	0.100096i	−0.516765	−	0.856127i	$-0.672864\pi$
$541$	3.20447	−	2.32818i	0.137771	−	0.100096i	0.654536	+	0.756031i	$0.272864\pi$
$542$	−6.70088	+	20.6232i	−0.287828	+	0.885842i
$543$	−16.3240			−0.700529
$544$	0.323132	−	0.994499i	0.0138542	−	0.0426388i
$545$		0			0
$546$	−4.05257	−	12.4725i	−0.173434	−	0.533775i
$547$	3.07502	+	9.46392i	0.131478	+	0.404648i	0.995026	−	0.0996194i	$-0.0317625\pi$
$547$	3.07502	+	9.46392i	0.131478	+	0.404648i	−0.863547	+	0.504268i	$0.831763\pi$
$548$	−7.30072	−	5.30429i	−0.311871	−	0.226588i
$549$	0.270588			0.0115484
$550$		0			0
$551$	35.1362			1.49685
$552$	4.28357	+	3.11219i	0.182321	+	0.132464i
$553$	10.4490	+	32.1588i	0.444338	+	1.36753i
$554$	−3.18135	−	9.79119i	−0.135163	−	0.415988i
$555$		0			0
$556$	2.19791	−	6.76447i	0.0932122	−	0.286878i
$557$	−18.7017			−0.792415			−0.396207	−	0.918161i	$-0.629674\pi$
$557$	−18.7017			−0.792415			−0.396207	+	0.918161i	$0.629674\pi$
$558$	−1.72444	+	5.30729i	−0.0730015	+	0.224676i
$559$	12.9108	−	9.38028i	0.546071	−	0.396744i
$560$		0			0
$561$	−4.75474	−	3.45452i	−0.200745	−	0.145850i
$562$	0.646034	−	0.469371i	0.0272513	−	0.0197992i
$563$	31.0553	−	22.5630i	1.30882	−	0.950917i	0.308825	−	0.951119i	$-0.400064\pi$
$563$	31.0553	−	22.5630i	1.30882	−	0.950917i	1.00000		0.000202039i	$6.43111e-5\pi$
$564$	2.48671	+	1.80670i	0.104709	+	0.0760758i
$565$		0			0
$566$	−0.591102	+	0.429461i	−0.0248459	+	0.0180516i
$567$	0.837167	−	2.57654i	0.0351577	−	0.108204i
$568$	−4.53276			−0.190190
$569$	−4.90344	+	15.0913i	−0.205563	+	0.632658i	0.794127	+	0.607752i	$0.207929\pi$
$569$	−4.90344	+	15.0913i	−0.205563	+	0.632658i	−0.999690	+	0.0249059i	$0.992071\pi$
$570$		0			0
$571$	9.96877	+	30.6807i	0.417180	+	1.28395i	0.910286	+	0.413979i	$0.135861\pi$
$571$	9.96877	+	30.6807i	0.417180	+	1.28395i	−0.493106	+	0.869969i	$0.664139\pi$
$572$	−8.40759	−	25.8759i	−0.351539	−	1.08193i
$573$	12.5641	+	9.12835i	0.524873	+	0.381342i
$574$	−4.27346			−0.178371
$575$		0			0
$576$	1.00000			0.0416667
$577$	22.6848	+	16.4815i	0.944379	+	0.686132i	0.949471	−	0.313855i	$-0.101621\pi$
$577$	22.6848	+	16.4815i	0.944379	+	0.686132i	−0.00509145	+	0.999987i	$0.501621\pi$
$578$	−4.91540	−	15.1280i	−0.204454	−	0.629243i
$579$	−6.49559	−	19.9914i	−0.269948	−	0.830813i
$580$		0			0
$581$	−0.112617	+	0.346600i	−0.00467215	+	0.0143794i
$582$	−2.64031			−0.109444
$583$	10.7285	−	33.0189i	0.444328	−	1.36750i
$584$	6.60237	−	4.79691i	0.273208	−	0.198497i
$585$		0			0
$586$	−14.9540	−	10.8647i	−0.617745	−	0.448818i
$587$	−9.21228	+	6.69311i	−0.380231	+	0.276254i	−0.761441	−	0.648234i	$-0.775508\pi$
$587$	−9.21228	+	6.69311i	−0.380231	+	0.276254i	0.381209	+	0.924489i	$0.375508\pi$
$588$	−0.274567	+	0.199485i	−0.0113229	+	0.00822660i
$589$	37.8551	+	27.5033i	1.55979	+	1.13326i
$590$		0			0
$591$	−19.5438	+	14.1994i	−0.803923	+	0.584084i
$592$	−0.924514	+	2.84536i	−0.0379973	+	0.116944i
$593$	34.9063			1.43343			0.716715	−	0.697366i	$-0.245645\pi$
$593$	34.9063			1.43343			0.716715	+	0.697366i	$0.245645\pi$
$594$	1.73681	−	5.34536i	0.0712623	−	0.219323i
$595$		0			0
$596$	4.76970	+	14.6796i	0.195375	+	0.601301i
$597$	−7.87776	−	24.2453i	−0.322415	−	0.992292i
$598$	−20.7360	−	15.0656i	−0.847957	−	0.616076i
$599$	21.2325			0.867535			0.433768	−	0.901025i	$-0.357184\pi$
$599$	21.2325			0.867535			0.433768	+	0.901025i	$0.357184\pi$
$600$		0			0
$601$	−22.6617			−0.924389			−0.462195	−	0.886779i	$-0.652938\pi$
$601$	−22.6617			−0.924389			−0.462195	+	0.886779i	$0.652938\pi$
$602$	−7.22547	−	5.24961i	−0.294488	−	0.213958i
$603$	1.94984	+	6.00099i	0.0794036	+	0.244379i
$604$	−2.47152	−	7.60655i	−0.100565	−	0.309506i
$605$		0			0
$606$	−1.18305	+	3.64106i	−0.0480582	+	0.147908i
$607$	21.3752			0.867591			0.433796	−	0.901011i	$-0.357174\pi$
$607$	21.3752			0.867591			0.433796	+	0.901011i	$0.357174\pi$
$608$	2.59109	−	7.97455i	0.105083	−	0.323411i
$609$	−9.18421	+	6.67272i	−0.372163	+	0.270392i
$610$		0			0
$611$	−12.0377	−	8.74590i	−0.486993	−	0.353821i
$612$	−0.845972	+	0.614634i	−0.0341964	+	0.0248451i
$613$	−27.5136	+	19.9898i	−1.11126	+	0.807380i	−0.982862	−	0.184342i	$-0.940985\pi$
$613$	−27.5136	+	19.9898i	−1.11126	+	0.807380i	−0.128401	+	0.991722i	$0.540985\pi$
$614$	−11.4818	−	8.34203i	−0.463368	−	0.336657i
$615$		0			0
$616$	−12.3185	+	8.94992i	−0.496327	+	0.360603i
$617$	−7.53787	+	23.1992i	−0.303463	+	0.933963i	0.676783	+	0.736182i	$0.263373\pi$
$617$	−7.53787	+	23.1992i	−0.303463	+	0.933963i	−0.980246	+	0.197781i	$0.936627\pi$
$618$	−5.89322			−0.237060
$619$	−7.50529	+	23.0989i	−0.301663	+	0.928423i	0.679239	+	0.733918i	$0.262310\pi$
$619$	−7.50529	+	23.0989i	−0.301663	+	0.928423i	−0.980901	+	0.194505i	$0.937690\pi$
$620$		0			0
$621$	−1.63618	−	5.03563i	−0.0656575	−	0.202073i
$622$	3.12545	+	9.61915i	0.125319	+	0.385693i
$623$	−25.8409	−	18.7745i	−1.03529	−	0.752184i
$624$	−4.84082			−0.193788
$625$		0			0
$626$	7.00045			0.279794
$627$	−38.1266	−	27.7006i	−1.52263	−	1.10626i
$628$	−4.82522	−	14.8505i	−0.192547	−	0.592599i
$629$	−0.966744	−	2.97533i	−0.0385466	−	0.118634i
$630$		0			0
$631$	0.319506	−	0.983337i	0.0127193	−	0.0391460i	−0.944495	−	0.328525i	$-0.893449\pi$
$631$	0.319506	−	0.983337i	0.0127193	−	0.0391460i	0.957215	+	0.289379i	$0.0934486\pi$
$632$	12.4814			0.496484
$633$	1.62209	−	4.99228i	0.0644723	−	0.198425i
$634$	12.4091	−	9.01577i	0.492830	−	0.358062i
$635$		0			0
$636$	−4.99738	−	3.63081i	−0.198159	−	0.143971i
$637$	1.32913	−	0.965668i	0.0526620	−	0.0382612i
$638$	−19.0538	+	13.8434i	−0.754349	+	0.548067i
$639$	3.66708	+	2.66429i	0.145067	+	0.105398i
$640$		0			0
$641$	−3.99638	+	2.90354i	−0.157847	+	0.114683i	−0.663905	−	0.747817i	$-0.731102\pi$
$641$	−3.99638	+	2.90354i	−0.157847	+	0.114683i	0.506058	+	0.862499i	$0.331102\pi$
$642$	−1.82554	+	5.61845i	−0.0720485	+	0.221742i
$643$	36.3220			1.43240			0.716199	−	0.697896i	$-0.245880\pi$
$643$	36.3220			1.43240			0.716199	+	0.697896i	$0.245880\pi$
$644$	−4.43261	+	13.6422i	−0.174669	+	0.537577i
$645$		0			0
$646$	2.70945	+	8.33882i	0.106602	+	0.328086i
$647$	4.41077	+	13.5750i	0.173405	+	0.533687i	0.999557	−	0.0297610i	$-0.00947462\pi$
$647$	4.41077	+	13.5750i	0.173405	+	0.533687i	−0.826152	+	0.563448i	$0.809475\pi$
$648$	−0.809017	−	0.587785i	−0.0317812	−	0.0230904i
$649$	−79.7405			−3.13009
$650$		0			0
$651$	−15.1181			−0.592524
$652$	−2.95881	−	2.14970i	−0.115876	−	0.0841889i
$653$	1.78195	+	5.48428i	0.0697331	+	0.214616i	0.979850	−	0.199736i	$-0.0640083\pi$
$653$	1.78195	+	5.48428i	0.0697331	+	0.214616i	−0.910117	+	0.414352i	$0.864008\pi$
$654$	1.74225	+	5.36211i	0.0681275	+	0.209675i
$655$		0			0
$656$	−0.487453	+	1.50022i	−0.0190318	+	0.0585739i
$657$	−8.16098			−0.318390
$658$	−2.57324	+	7.91960i	−0.100315	+	0.308738i
$659$	−8.14688	+	5.91906i	−0.317357	+	0.230574i	−0.735047	−	0.678016i	$-0.762840\pi$
$659$	−8.14688	+	5.91906i	−0.317357	+	0.230574i	0.417690	+	0.908590i	$0.362840\pi$
$660$		0			0
$661$	29.8762	+	21.7064i	1.16205	+	0.844279i	0.990036	−	0.140815i	$-0.0449723\pi$
$661$	29.8762	+	21.7064i	1.16205	+	0.844279i	0.172015	+	0.985094i	$0.444972\pi$
$662$	−19.1310	+	13.8995i	−0.743546	+	0.540218i
$663$	4.09519	−	2.97533i	0.159044	−	0.115552i
$664$	0.108830	+	0.0790699i	0.00422344	+	0.00306851i
$665$		0			0
$666$	2.42041	−	1.75853i	0.0937889	−	0.0681416i
$667$	−6.85622	+	21.1013i	−0.265474	+	0.817044i
$668$	6.30307			0.243873
$669$	−4.57251	+	14.0727i	−0.176783	+	0.544084i
$670$		0			0
$671$	0.469961	+	1.44639i	0.0181427	+	0.0558373i
$672$	0.837167	+	2.57654i	0.0322944	+	0.0993920i
$673$	−21.8708	−	15.8901i	−0.843059	−	0.612518i	0.0801645	−	0.996782i	$-0.474455\pi$
$673$	−21.8708	−	15.8901i	−0.843059	−	0.612518i	−0.923223	+	0.384263i	$0.874455\pi$
$674$	−27.7121			−1.06743
$675$		0			0
$676$	10.4335			0.401289
$677$	6.99862	+	5.08479i	0.268979	+	0.195425i	0.714096	−	0.700048i	$-0.246838\pi$
$677$	6.99862	+	5.08479i	0.268979	+	0.195425i	−0.445117	+	0.895472i	$0.646838\pi$
$678$	1.56576	+	4.81893i	0.0601328	+	0.185070i
$679$	−2.21038	−	6.80284i	−0.0848265	−	0.261069i
$680$		0			0
$681$	3.67064	−	11.2971i	0.140659	−	0.432904i
$682$	−31.3644			−1.20101
$683$	−14.3605	+	44.1971i	−0.549489	+	1.69115i	0.160580	+	0.987023i	$0.448664\pi$
$683$	−14.3605	+	44.1971i	−0.549489	+	1.69115i	−0.710069	+	0.704132i	$0.751336\pi$
$684$	−6.78356	+	4.92854i	−0.259376	+	0.188448i
$685$		0			0
$686$	14.5983	+	10.6063i	0.557365	+	0.404949i
$687$	−14.7704	+	10.7313i	−0.563524	+	0.409424i
$688$	−2.66708	+	1.93775i	−0.101681	+	0.0738759i
$689$	24.1914	+	17.5761i	0.921619	+	0.669596i
$690$		0			0
$691$	38.2570	−	27.7954i	1.45537	−	1.05739i	0.470826	−	0.882226i	$-0.343956\pi$
$691$	38.2570	−	27.7954i	1.45537	−	1.05739i	0.984540	−	0.175159i	$-0.0560440\pi$
$692$	−3.28963	+	10.1244i	−0.125053	+	0.384874i
$693$	15.2265			0.578407
$694$	8.24643	−	25.3799i	0.313030	−	0.963408i
$695$		0			0
$696$	1.29490	+	3.98530i	0.0490831	+	0.151062i
$697$	−0.509719	−	1.56875i	−0.0193070	−	0.0594208i
$698$	4.64032	+	3.37139i	0.175639	+	0.127609i
$699$	−2.85842			−0.108115
$700$		0			0
$701$	30.1858			1.14010			0.570052	−	0.821609i	$-0.306923\pi$
$701$	30.1858			1.14010			0.570052	+	0.821609i	$0.306923\pi$
$702$	3.91630	+	2.84536i	0.147811	+	0.107391i
$703$	−7.75199	−	23.8582i	−0.292372	−	0.899828i
$704$	1.73681	+	5.34536i	0.0654586	+	0.201461i
$705$		0			0
$706$	−8.99327	+	27.6785i	−0.338466	+	1.04169i
$707$	−10.3717			−0.390069
$708$	−4.38420	+	13.4932i	−0.164768	+	0.507105i
$709$	14.0202	−	10.1862i	0.526538	−	0.382553i	−0.292523	−	0.956259i	$-0.594495\pi$
$709$	14.0202	−	10.1862i	0.526538	−	0.382553i	0.819061	+	0.573706i	$0.194495\pi$
$710$		0			0
$711$	−10.0977	−	7.33640i	−0.378693	−	0.275136i
$712$	−9.53844	+	6.93008i	−0.357468	+	0.259716i
$713$	−23.9041	+	17.3673i	−0.895215	+	0.650412i
$714$	−2.29185	−	1.66512i	−0.0857702	−	0.0623157i
$715$		0			0
$716$	0.646651	−	0.469819i	0.0241665	−	0.0175580i
$717$	5.06286	−	15.5819i	0.189076	−	0.581917i
$718$	−12.9895			−0.484765
$719$	−5.82077	+	17.9145i	−0.217078	+	0.668098i	0.781921	+	0.623377i	$0.214240\pi$
$719$	−5.82077	+	17.9145i	−0.217078	+	0.668098i	−0.999000	+	0.0447207i	$0.985760\pi$
$720$		0			0
$721$	−4.93361	−	15.1841i	−0.183737	−	0.565485i
$722$	15.8548	+	48.7961i	0.590055	+	1.81600i
$723$	−21.2995	−	15.4750i	−0.792136	−	0.575520i
$724$	−16.3240			−0.606676
$725$		0			0
$726$	20.5894			0.764144
$727$	−17.2593	−	12.5396i	−0.640111	−	0.465068i	0.219777	−	0.975550i	$-0.429467\pi$
$727$	−17.2593	−	12.5396i	−0.640111	−	0.465068i	−0.859888	+	0.510482i	$0.829467\pi$
$728$	−4.05257	−	12.4725i	−0.150198	−	0.462263i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	1.06527	−	3.27856i	0.0394004	−	0.121262i
$732$	0.270588			0.0100012
$733$	−6.44956	+	19.8497i	−0.238220	+	0.733165i	0.758458	+	0.651722i	$0.225953\pi$
$733$	−6.44956	+	19.8497i	−0.238220	+	0.733165i	−0.996678	+	0.0814434i	$0.974047\pi$
$734$	2.98371	−	2.16779i	0.110131	−	0.0800147i
$735$		0			0
$736$	4.28357	+	3.11219i	0.157894	+	0.114717i
$737$	−28.6909	+	20.8452i	−1.05684	+	0.767842i
$738$	1.27617	−	0.927190i	0.0469764	−	0.0341303i
$739$	13.1129	+	9.52707i	0.482365	+	0.350459i	0.802241	−	0.597001i	$-0.203641\pi$
$739$	13.1129	+	9.52707i	0.482365	+	0.350459i	−0.319875	+	0.947460i	$0.603641\pi$
$740$		0			0
$741$	32.8380	−	23.8582i	1.20633	−	0.876452i
$742$	5.17127	−	15.9155i	0.189843	−	0.584277i
$743$	34.7758			1.27580			0.637900	−	0.770120i	$-0.279803\pi$
$743$	34.7758			1.27580			0.637900	+	0.770120i	$0.279803\pi$
$744$	−1.72444	+	5.30729i	−0.0632212	+	0.194575i
$745$		0			0
$746$	−8.03593	−	24.7321i	−0.294216	−	0.905505i
$747$	−0.0415695	−	0.127938i	−0.00152095	−	0.00468100i
$748$	−4.75474	−	3.45452i	−0.173850	−	0.126310i
$749$	−16.0044			−0.584788
$750$		0			0
$751$	21.2393			0.775034			0.387517	−	0.921863i	$-0.373333\pi$
$751$	21.2393			0.775034			0.387517	+	0.921863i	$0.373333\pi$
$752$	2.48671	+	1.80670i	0.0906809	+	0.0658836i
$753$	−4.27543	−	13.1584i	−0.155805	−	0.479520i
$754$	−6.26838	−	19.2921i	−0.228281	−	0.702577i
$755$		0			0
$756$	0.837167	−	2.57654i	0.0304475	−	0.0937077i
$757$	−53.9563			−1.96107			−0.980537	−	0.196335i	$-0.937096\pi$
$757$	−53.9563			−1.96107			−0.980537	+	0.196335i	$0.937096\pi$
$758$	−9.32153	+	28.6887i	−0.338573	+	1.04202i
$759$	24.0755	−	17.4919i	0.873887	−	0.634916i
$760$		0			0
$761$	34.2990	+	24.9197i	1.24334	+	0.903339i	0.997816	−	0.0660520i	$-0.0210403\pi$
$761$	34.2990	+	24.9197i	1.24334	+	0.903339i	0.245523	+	0.969391i	$0.421040\pi$
$762$	7.70919	−	5.60106i	0.279275	−	0.202905i
$763$	−12.3571	+	8.97796i	−0.447357	+	0.325024i
$764$	12.5641	+	9.12835i	0.454553	+	0.330252i
$765$		0			0
$766$	10.8125	−	7.85574i	0.390672	−	0.283840i
$767$	21.2231	−	65.3181i	0.766323	−	2.35850i
$768$	1.00000			0.0360844
$769$	1.55943	−	4.79943i	0.0562345	−	0.173072i	−0.918994	−	0.394271i	$-0.870997\pi$
$769$	1.55943	−	4.79943i	0.0562345	−	0.173072i	0.975229	+	0.221199i	$0.0709971\pi$
$770$		0			0
$771$	8.84420	+	27.2197i	0.318516	+	0.980292i
$772$	−6.49559	−	19.9914i	−0.233782	−	0.719506i
$773$	−28.1938	−	20.4840i	−1.01406	−	0.736758i	−0.0490036	−	0.998799i	$-0.515605\pi$
$773$	−28.1938	−	20.4840i	−1.01406	−	0.736758i	−0.965057	+	0.262041i	$0.915605\pi$
$774$	3.29669			0.118497
$775$		0			0
$776$	−2.64031			−0.0947815
$777$	6.55720	+	4.76409i	0.235238	+	0.170911i
$778$	−2.99756	−	9.22554i	−0.107468	−	0.330752i
$779$	−4.08726	−	12.5793i	−0.146441	−	0.450700i
$780$		0			0
$781$	−7.87256	+	24.2292i	−0.281702	+	0.866990i
$782$	−5.53664			−0.197990
$783$	1.29490	−	3.98530i	0.0462760	−	0.142423i
$784$	−0.274567	+	0.199485i	−0.00980596	+	0.00712445i
$785$		0			0
$786$	−0.120451	−	0.0875130i	−0.00429635	−	0.00312148i
$787$	12.9790	−	9.42980i	0.462652	−	0.336136i	−0.331919	−	0.943308i	$-0.607696\pi$
$787$	12.9790	−	9.42980i	0.462652	−	0.336136i	0.794571	+	0.607172i	$0.207696\pi$
$788$	−19.5438	+	14.1994i	−0.696218	+	0.505832i
$789$	−2.52661	−	1.83569i	−0.0899497	−	0.0653523i
$790$		0			0
$791$	−11.1053	+	8.06850i	−0.394860	+	0.286883i
$792$	1.73681	−	5.34536i	0.0617150	−	0.189939i
$793$	−1.30987			−0.0465148
$794$	−2.44508	+	7.52519i	−0.0867728	+	0.267059i
$795$		0			0
$796$	−7.87776	−	24.2453i	−0.279220	−	0.859350i
$797$	−11.5093	−	35.4218i	−0.407679	−	1.25471i	−0.918638	−	0.395101i	$-0.870710\pi$
$797$	−11.5093	−	35.4218i	−0.407679	−	1.25471i	0.510959	−	0.859605i	$-0.329290\pi$
$798$	−18.3775	−	13.3521i	−0.650558	−	0.472658i
$799$	−3.21415			−0.113708
$800$		0			0
$801$	11.7902			0.416585
$802$	16.2905	+	11.8358i	0.575239	+	0.417935i
$803$	−14.1741	−	43.6234i	−0.500193	−	1.53944i
$804$	1.94984	+	6.00099i	0.0687655	+	0.211638i
$805$		0			0
$806$	8.34772	−	25.6916i	0.294036	−	0.904949i
$807$	9.23200			0.324982
$808$	−1.18305	+	3.64106i	−0.0416196	+	0.128092i
$809$	6.97671	−	5.06888i	0.245288	−	0.178212i	−0.458348	−	0.888773i	$-0.651559\pi$
$809$	6.97671	−	5.06888i	0.245288	−	0.178212i	0.703636	+	0.710561i	$0.251559\pi$
$810$		0			0
$811$	−0.148704	−	0.108040i	−0.00522171	−	0.00379379i	0.585171	−	0.810910i	$-0.301027\pi$
$811$	−0.148704	−	0.108040i	−0.00522171	−	0.00379379i	−0.590393	+	0.807116i	$0.701027\pi$
$812$	−9.18421	+	6.67272i	−0.322303	+	0.234167i
$813$	17.5431	−	12.7458i	0.615265	−	0.447016i
$814$	13.6038	+	9.88372i	0.476812	+	0.346424i
$815$		0			0
$816$	−0.845972	+	0.614634i	−0.0296149	+	0.0215165i
$817$	8.54203	−	26.2897i	0.298848	−	0.919758i
$818$	−2.80742			−0.0981591
$819$	−4.05257	+	12.4725i	−0.141608	+	0.435826i
$820$		0			0
$821$	8.46892	+	26.0647i	0.295567	+	0.909663i	0.983030	+	0.183443i	$0.0587244\pi$
$821$	8.46892	+	26.0647i	0.295567	+	0.909663i	−0.687463	+	0.726220i	$0.741276\pi$
$822$	2.78863	+	8.58252i	0.0972646	+	0.299350i
$823$	26.3728	+	19.1609i	0.919296	+	0.667908i	0.943349	−	0.331803i	$-0.107657\pi$
$823$	26.3728	+	19.1609i	0.919296	+	0.667908i	−0.0240525	+	0.999711i	$0.507657\pi$
$824$	−5.89322			−0.205300
$825$		0			0
$826$	−38.4360			−1.33736
$827$	−31.2347	−	22.6934i	−1.08614	−	0.789125i	−0.107395	−	0.994216i	$-0.534251\pi$
$827$	−31.2347	−	22.6934i	−1.08614	−	0.789125i	−0.978743	+	0.205091i	$0.934251\pi$
$828$	−1.63618	−	5.03563i	−0.0568611	−	0.175000i
$829$	11.1557	+	34.3338i	0.387455	+	1.19246i	0.934684	+	0.355480i	$0.115683\pi$
$829$	11.1557	+	34.3338i	0.387455	+	1.19246i	−0.547229	+	0.836983i	$0.684317\pi$
$830$		0			0
$831$	−3.18135	+	9.79119i	−0.110360	+	0.339653i
$832$	−4.84082			−0.167825
$833$	0.109666	−	0.337517i	0.00379969	−	0.0116943i
$834$	−5.75420	+	4.18067i	−0.199252	+	0.144765i
$835$		0			0
$836$	−38.1266	−	27.7006i	−1.31864	−	0.958046i
$837$	4.51465	−	3.28009i	0.156049	−	0.113376i
$838$	26.8562	−	19.5122i	0.927733	−	0.674038i
$839$	−26.7665	−	19.4470i	−0.924081	−	0.671384i	0.0204558	−	0.999791i	$-0.493488\pi$
$839$	−26.7665	−	19.4470i	−0.924081	−	0.671384i	−0.944536	+	0.328407i	$0.893488\pi$
$840$		0			0
$841$	9.25567	−	6.72464i	0.319161	−	0.231884i
$842$	5.91384	−	18.2009i	0.203804	−	0.627246i
$843$	−0.798542			−0.0275033
$844$	1.62209	−	4.99228i	0.0558347	−	0.171841i
$845$		0			0
$846$	−0.949838	−	2.92330i	−0.0326561	−	0.100505i
$847$	17.2368	+	53.0493i	0.592262	+	1.82280i
$848$	−4.99738	−	3.63081i	−0.171611	−	0.124683i
$849$	0.730642			0.0250756
$850$		0			0
$851$	15.8409			0.543018
$852$	3.66708	+	2.66429i	0.125632	+	0.0912771i
$853$	−6.22591	−	19.1614i	−0.213171	−	0.656073i	−0.999278	−	0.0379832i	$-0.987907\pi$
$853$	−6.22591	−	19.1614i	−0.213171	−	0.656073i	0.786107	−	0.618090i	$-0.212093\pi$
$854$	0.226528	+	0.697180i	0.00775162	+	0.0238570i
$855$		0			0
$856$	−1.82554	+	5.61845i	−0.0623958	+	0.192035i
$857$	55.8400			1.90746			0.953729	−	0.300668i	$-0.0972098\pi$
$857$	55.8400			1.90746			0.953729	+	0.300668i	$0.0972098\pi$
$858$	−8.40759	+	25.8759i	−0.287031	+	0.883389i
$859$	41.2044	−	29.9368i	1.40588	−	1.02143i	0.411971	−	0.911197i	$-0.364841\pi$
$859$	41.2044	−	29.9368i	1.40588	−	1.02143i	0.993906	−	0.110232i	$-0.0351595\pi$
$860$		0			0
$861$	3.45730	+	2.51188i	0.117825	+	0.0856046i
$862$	16.2057	−	11.7741i	0.551969	−	0.401029i
$863$	22.3882	−	16.2660i	0.762104	−	0.553701i	−0.137451	−	0.990509i	$-0.543891\pi$
$863$	22.3882	−	16.2660i	0.762104	−	0.553701i	0.899555	+	0.436808i	$0.143891\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$		0			0
$866$	26.1812	−	19.0217i	0.889672	−	0.646385i
$867$	−4.91540	+	15.1280i	−0.166936	+	0.513775i
$868$	−15.1181			−0.513141
$869$	21.6779	−	66.7177i	0.735372	−	2.26324i
$870$		0			0
$871$	−9.43881	−	29.0497i	−0.319822	−	0.984311i
$872$	1.74225	+	5.36211i	0.0590002	+	0.181584i
$873$	2.13605	+	1.55193i	0.0722944	+	0.0525250i
$874$	−44.3964			−1.50173
$875$		0			0
$876$	−8.16098			−0.275734
$877$	−27.1845	−	19.7507i	−0.917956	−	0.666934i	0.0250581	−	0.999686i	$-0.492023\pi$
$877$	−27.1845	−	19.7507i	−0.917956	−	0.666934i	−0.943015	+	0.332752i	$0.892023\pi$
$878$	5.35434	+	16.4790i	0.180700	+	0.556138i
$879$	5.71193	+	17.5795i	0.192659	+	0.592942i
$880$		0			0
$881$	0.801894	−	2.46798i	0.0270165	−	0.0831482i	−0.936639	−	0.350296i	$-0.886081\pi$
$881$	0.801894	−	2.46798i	0.0270165	−	0.0831482i	0.963656	+	0.267147i	$0.0860811\pi$
$882$	0.339383			0.0114276
$883$	−12.3541	+	38.0222i	−0.415750	+	1.27955i	0.495828	+	0.868421i	$0.334865\pi$
$883$	−12.3541	+	38.0222i	−0.415750	+	1.27955i	−0.911578	+	0.411127i	$0.865135\pi$
$884$	4.09519	−	2.97533i	0.137736	−	0.100071i
$885$		0			0
$886$	13.3752	+	9.71764i	0.449348	+	0.326470i
$887$	−17.7050	+	12.8634i	−0.594475	+	0.431911i	−0.843913	−	0.536480i	$-0.819754\pi$
$887$	−17.7050	+	12.8634i	−0.594475	+	0.431911i	0.249439	+	0.968391i	$0.419754\pi$
$888$	2.42041	−	1.75853i	0.0812236	−	0.0590124i
$889$	20.8852	+	15.1740i	0.700467	+	0.508919i
$890$		0			0
$891$	−4.54704	+	3.30361i	−0.152331	+	0.110675i
$892$	−4.57251	+	14.0727i	−0.153099	+	0.471190i
$893$	−25.7731			−0.862465
$894$	4.76970	−	14.6796i	0.159523	−	0.490961i
$895$		0			0
$896$	0.837167	+	2.57654i	0.0279678	+	0.0860760i
$897$	7.92043	+	24.3766i	0.264456	+	0.813910i
$898$	−2.03297	−	1.47704i	−0.0678412	−	0.0492895i
$899$	−23.3841			−0.779904
$900$		0			0
$901$	6.45927			0.215189
$902$	7.17263	+	5.21122i	0.238822	+	0.173515i
$903$	2.75988	+	8.49405i	0.0918431	+	0.282664i
$904$	1.56576	+	4.81893i	0.0520766	+	0.160275i
$905$		0			0
$906$	−2.47152	+	7.60655i	−0.0821107	+	0.252711i
$907$	22.6784			0.753025			0.376512	−	0.926412i	$-0.377123\pi$
$907$	22.6784			0.753025			0.376512	+	0.926412i	$0.377123\pi$
$908$	3.67064	−	11.2971i	0.121814	−	0.374906i
$909$	3.09727	−	2.25030i	0.102730	−	0.0746377i
$910$		0			0
$911$	−39.1006	−	28.4082i	−1.29546	−	0.941207i	−0.295560	−	0.955324i	$-0.595506\pi$
$911$	−39.1006	−	28.4082i	−1.29546	−	0.941207i	−0.999900	+	0.0141173i	$0.995506\pi$
$912$	−6.78356	+	4.92854i	−0.224626	+	0.163200i
$913$	0.611676	−	0.444408i	0.0202435	−	0.0147078i
$914$	29.7465	+	21.6121i	0.983925	+	0.714863i
$915$		0			0
$916$	−14.7704	+	10.7313i	−0.488026	+	0.354572i
$917$	0.124642	−	0.383610i	0.00411606	−	0.0126679i
$918$	1.04568			0.0345125
$919$	−13.3112	+	40.9678i	−0.439097	+	1.35140i	0.449732	+	0.893164i	$0.351519\pi$
$919$	−13.3112	+	40.9678i	−0.439097	+	1.35140i	−0.888829	+	0.458239i	$0.848481\pi$
$920$		0			0
$921$	4.38566	+	13.4977i	0.144513	+	0.444764i
$922$	1.87594	+	5.77356i	0.0617809	+	0.190142i
$923$	−17.7517	−	12.8973i	−0.584303	−	0.424521i
$924$	15.2265			0.500916
$925$		0			0
$926$	−33.3123			−1.09471
$927$	4.76772	+	3.46395i	0.156592	+	0.113771i
$928$	1.29490	+	3.98530i	0.0425072	+	0.130824i
$929$	−11.7192	−	36.0680i	−0.384495	−	1.18335i	−0.936846	−	0.349742i	$-0.886269\pi$
$929$	−11.7192	−	36.0680i	−0.384495	−	1.18335i	0.552351	−	0.833612i	$-0.313731\pi$
$930$		0			0
$931$	0.879373	−	2.70643i	0.0288203	−	0.0886997i
$932$	−2.85842			−0.0936307
$933$	3.12545	−	9.61915i	0.102323	−	0.314917i
$934$	−7.39159	+	5.37030i	−0.241860	+	0.175722i
$935$		0			0
$936$	3.91630	+	2.84536i	0.128008	+	0.0930035i
$937$	−13.4115	+	9.74401i	−0.438134	+	0.318323i	−0.784893	−	0.619631i	$-0.787282\pi$
$937$	−13.4115	+	9.74401i	−0.438134	+	0.318323i	0.346759	+	0.937954i	$0.387282\pi$
$938$	−13.8294	+	10.0477i	−0.451546	+	0.328068i
$939$	−5.66348	−	4.11476i	−0.184821	−	0.134280i
$940$		0			0
$941$	−20.7160	+	15.0510i	−0.675321	+	0.490650i	−0.871802	−	0.489858i	$-0.837049\pi$
$941$	−20.7160	+	15.0510i	−0.675321	+	0.490650i	0.196481	+	0.980508i	$0.437049\pi$
$942$	−4.82522	+	14.8505i	−0.157214	+	0.483855i
$943$	8.35214			0.271983
$944$	−4.38420	+	13.4932i	−0.142694	+	0.439166i
$945$		0			0
$946$	5.72574	+	17.6220i	0.186160	+	0.572941i
$947$	−6.16914	−	18.9867i	−0.200470	−	0.616984i	−0.999869	−	0.0161830i	$-0.994849\pi$
$947$	−6.16914	−	18.9867i	−0.200470	−	0.616984i	0.799399	−	0.600801i	$-0.205151\pi$
$948$	−10.0977	−	7.33640i	−0.327957	−	0.238275i
$949$	39.5058			1.28241
$950$		0			0
$951$	−15.3385			−0.497386
$952$	−2.29185	−	1.66512i	−0.0742792	−	0.0539670i
$953$	13.9470	+	42.9246i	0.451789	+	1.39046i	0.874864	+	0.484368i	$0.160951\pi$
$953$	13.9470	+	42.9246i	0.451789	+	1.39046i	−0.423075	+	0.906094i	$0.639049\pi$
$954$	1.90883	+	5.87478i	0.0618007	+	0.190203i
$955$		0			0
$956$	5.06286	−	15.5819i	0.163745	−	0.503955i
$957$	23.5519			0.761323
$958$	6.44637	−	19.8399i	0.208273	−	0.640997i
$959$	−19.7786	+	14.3700i	−0.638685	+	0.464031i
$960$		0			0
$961$	−0.114121	−	0.0829138i	−0.00368132	−	0.00267464i
$962$	−11.7168	+	8.51272i	−0.377763	+	0.274461i
$963$	4.77934	−	3.47239i	0.154012	−	0.111896i
$964$	−21.2995	−	15.4750i	−0.686010	−	0.498415i
$965$		0			0
$966$	11.6047	−	8.43133i	0.373376	−	0.271274i
$967$	2.42552	−	7.46499i	0.0779995	−	0.240058i	−0.904452	−	0.426575i	$-0.859720\pi$
$967$	2.42552	−	7.46499i	0.0779995	−	0.240058i	0.982452	+	0.186517i	$0.0597200\pi$
$968$	20.5894			0.661768
$969$	2.70945	−	8.33882i	0.0870400	−	0.267881i
$970$		0			0
$971$	1.32948	+	4.09171i	0.0426649	+	0.131309i	0.970120	−	0.242625i	$-0.0780085\pi$
$971$	1.32948	+	4.09171i	0.0426649	+	0.131309i	−0.927455	+	0.373934i	$0.878009\pi$
$972$	0.309017	+	0.951057i	0.00991172	+	0.0305052i
$973$	−15.5889	−	11.3260i	−0.499757	−	0.363095i
$974$	1.27292			0.0407869
$975$		0			0
$976$	0.270588			0.00866132
$977$	−0.344912	−	0.250593i	−0.0110347	−	0.00801720i	0.582254	−	0.813007i	$-0.302171\pi$
$977$	−0.344912	−	0.250593i	−0.0110347	−	0.00801720i	−0.593289	+	0.804990i	$0.702171\pi$
$978$	1.13017	+	3.47829i	0.0361387	+	0.111224i
$979$	20.4773	+	63.0226i	0.654457	+	2.01421i
$980$		0			0
$981$	1.74225	−	5.36211i	0.0556259	−	0.171199i
$982$	10.6983			0.341395
$983$	−18.4146	+	56.6743i	−0.587335	+	1.80763i	0.00234965	+	0.999997i	$0.499252\pi$
$983$	−18.4146	+	56.6743i	−0.587335	+	1.80763i	−0.589685	+	0.807634i	$0.700748\pi$
$984$	1.27617	−	0.927190i	0.0406827	−	0.0295577i
$985$		0			0
$986$	−3.54495	−	2.57556i	−0.112894	−	0.0820225i
$987$	6.73682	−	4.89458i	0.214435	−	0.155796i
$988$	32.8380	−	23.8582i	1.04472	−	0.759030i
$989$	14.1216	+	10.2599i	0.449041	+	0.326247i
$990$		0			0
$991$	−17.7809	+	12.9186i	−0.564830	+	0.410373i	−0.833224	−	0.552936i	$-0.813507\pi$
$991$	−17.7809	+	12.9186i	−0.564830	+	0.410373i	0.268393	+	0.963309i	$0.413507\pi$
$992$	−1.72444	+	5.30729i	−0.0547511	+	0.168507i
$993$	23.6472			0.750420
$994$	−3.79468	+	11.6788i	−0.120360	+	0.370430i
$995$		0			0
$996$	−0.0415695	−	0.127938i	−0.00131718	−	0.00405387i
$997$	−13.8580	−	42.6506i	−0.438887	−	1.35076i	−0.889050	−	0.457810i	$-0.848634\pi$
$997$	−13.8580	−	42.6506i	−0.438887	−	1.35076i	0.450163	−	0.892947i	$-0.351366\pi$
$998$	5.72812	+	4.16172i	0.181320	+	0.131737i
$999$	−2.99179			−0.0946560

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.g.f.451.3		16
5.2	odd	4		150.2.h.b.109.4	✓	16
5.3	odd	4		750.2.h.d.49.1		16
5.4	even	2		750.2.g.g.451.2		16
15.2	even	4		450.2.l.c.109.1		16
25.2	odd	20		750.2.h.d.199.2		16
25.6	even	5		3750.2.a.v.1.6		8
25.8	odd	20		3750.2.c.k.1249.3		16
25.11	even	5	inner	750.2.g.f.301.3		16
25.14	even	10		750.2.g.g.301.2		16
25.17	odd	20		3750.2.c.k.1249.14		16
25.19	even	10		3750.2.a.u.1.3		8
25.23	odd	20		150.2.h.b.139.4	yes	16
75.23	even	20		450.2.l.c.289.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.109.4	✓	16	5.2	odd	4
150.2.h.b.139.4	yes	16	25.23	odd	20
450.2.l.c.109.1		16	15.2	even	4
450.2.l.c.289.1		16	75.23	even	20
750.2.g.f.301.3		16	25.11	even	5	inner
750.2.g.f.451.3		16	1.1	even	1	trivial
750.2.g.g.301.2		16	25.14	even	10
750.2.g.g.451.2		16	5.4	even	2
750.2.h.d.49.1		16	5.3	odd	4
750.2.h.d.199.2		16	25.2	odd	20
3750.2.a.u.1.3		8	25.19	even	10
3750.2.a.v.1.6		8	25.6	even	5
3750.2.c.k.1249.3		16	25.8	odd	20
3750.2.c.k.1249.14		16	25.17	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.309017 - 0.951057i) q^{6} +2.70913 q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.309017 - 0.951057i) q^{6} +2.70913 q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-4.54704 - 3.30361i) q^{11} +(-0.809017 + 0.587785i) q^{12} +(3.91630 - 2.84536i) q^{13} +(-2.19173 - 1.59239i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(0.323132 - 0.994499i) q^{17} +1.00000 q^{18} +(2.59109 - 7.97455i) q^{19} +(0.837167 + 2.57654i) q^{21} +(1.73681 + 5.34536i) q^{22} +(4.28357 + 3.11219i) q^{23} +1.00000 q^{24} -4.84082 q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.837167 + 2.57654i) q^{28} +(1.29490 + 3.98530i) q^{29} +(-1.72444 + 5.30729i) q^{31} +1.00000 q^{32} +(1.73681 - 5.34536i) q^{33} +(-0.845972 + 0.614634i) q^{34} +(-0.809017 - 0.587785i) q^{36} +(2.42041 - 1.75853i) q^{37} +(-6.78356 + 4.92854i) q^{38} +(3.91630 + 2.84536i) q^{39} +(1.27617 - 0.927190i) q^{41} +(0.837167 - 2.57654i) q^{42} +3.29669 q^{43} +(1.73681 - 5.34536i) q^{44} +(-1.63618 - 5.03563i) q^{46} +(-0.949838 - 2.92330i) q^{47} +(-0.809017 - 0.587785i) q^{48} +0.339383 q^{49} +1.04568 q^{51} +(3.91630 + 2.84536i) q^{52} +(1.90883 + 5.87478i) q^{53} +(0.309017 + 0.951057i) q^{54} +(0.837167 - 2.57654i) q^{56} +8.38494 q^{57} +(1.29490 - 3.98530i) q^{58} +(11.4780 - 8.33925i) q^{59} +(-0.218911 - 0.159048i) q^{61} +(4.51465 - 3.28009i) q^{62} +(-2.19173 + 1.59239i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-4.54704 + 3.30361i) q^{66} +(1.94984 - 6.00099i) q^{67} +1.04568 q^{68} +(-1.63618 + 5.03563i) q^{69} +(-1.40070 - 4.31091i) q^{71} +(0.309017 + 0.951057i) q^{72} +(6.60237 + 4.79691i) q^{73} -2.99179 q^{74} +8.38494 q^{76} +(-12.3185 - 8.94992i) q^{77} +(-1.49589 - 4.60389i) q^{78} +(3.85697 + 11.8705i) q^{79} +(0.309017 - 0.951057i) q^{81} -1.57743 q^{82} +(-0.0415695 + 0.127938i) q^{83} +(-2.19173 + 1.59239i) q^{84} +(-2.66708 - 1.93775i) q^{86} +(-3.39010 + 2.46305i) q^{87} +(-4.54704 + 3.30361i) q^{88} +(-9.53844 - 6.93008i) q^{89} +(10.6098 - 7.70845i) q^{91} +(-1.63618 + 5.03563i) q^{92} -5.58042 q^{93} +(-0.949838 + 2.92330i) q^{94} +(0.309017 + 0.951057i) q^{96} +(-0.815900 - 2.51108i) q^{97} +(-0.274567 - 0.199485i) q^{98} +5.62045 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^7 - 4 * q^8 - 4 * q^9	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9} + 2 q^{11} - 4 q^{12} + 4 q^{13} - 2 q^{14} - 4 q^{16} - 2 q^{17} + 16 q^{18} - 2 q^{21} - 8 q^{22} - 6 q^{23} + 16 q^{24} + 4 q^{26} - 4 q^{27} - 2 q^{28} + 10 q^{29} - 18 q^{31} + 16 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 2 q^{37} - 10 q^{38} + 4 q^{39} + 22 q^{41} - 2 q^{42} + 4 q^{43} - 8 q^{44} - 6 q^{46} - 2 q^{47} - 4 q^{48} + 52 q^{49} + 28 q^{51} + 4 q^{52} - 16 q^{53} - 4 q^{54} - 2 q^{56} + 20 q^{57} + 10 q^{58} - 20 q^{59} + 12 q^{61} + 2 q^{62} - 2 q^{63} - 4 q^{64} + 2 q^{66} + 18 q^{67} + 28 q^{68} - 6 q^{69} - 28 q^{71} - 4 q^{72} + 24 q^{73} - 12 q^{74} + 20 q^{76} - 14 q^{77} - 6 q^{78} + 20 q^{79} - 4 q^{81} + 12 q^{82} - 36 q^{83} - 2 q^{84} - 6 q^{86} - 20 q^{87} + 2 q^{88} - 70 q^{89} + 12 q^{91} - 6 q^{92} + 32 q^{93} - 2 q^{94} - 4 q^{96} + 28 q^{97} - 38 q^{98} + 12 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^7 - 4 * q^8 - 4 * q^9 + 2 * q^11 - 4 * q^12 + 4 * q^13 - 2 * q^14 - 4 * q^16 - 2 * q^17 + 16 * q^18 - 2 * q^21 - 8 * q^22 - 6 * q^23 + 16 * q^24 + 4 * q^26 - 4 * q^27 - 2 * q^28 + 10 * q^29 - 18 * q^31 + 16 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 2 * q^37 - 10 * q^38 + 4 * q^39 + 22 * q^41 - 2 * q^42 + 4 * q^43 - 8 * q^44 - 6 * q^46 - 2 * q^47 - 4 * q^48 + 52 * q^49 + 28 * q^51 + 4 * q^52 - 16 * q^53 - 4 * q^54 - 2 * q^56 + 20 * q^57 + 10 * q^58 - 20 * q^59 + 12 * q^61 + 2 * q^62 - 2 * q^63 - 4 * q^64 + 2 * q^66 + 18 * q^67 + 28 * q^68 - 6 * q^69 - 28 * q^71 - 4 * q^72 + 24 * q^73 - 12 * q^74 + 20 * q^76 - 14 * q^77 - 6 * q^78 + 20 * q^79 - 4 * q^81 + 12 * q^82 - 36 * q^83 - 2 * q^84 - 6 * q^86 - 20 * q^87 + 2 * q^88 - 70 * q^89 + 12 * q^91 - 6 * q^92 + 32 * q^93 - 2 * q^94 - 4 * q^96 + 28 * q^97 - 38 * q^98 + 12 * q^99

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