LMFDB - Embedded newform 950.2.l.d.701.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			701.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	950.701
Dual form			950.2.l.d.351.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(-0.266044 - 0.223238i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.266044 - 0.223238i) q^{6} +(-0.879385 - 1.52314i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.500000 - 2.83564i) q^{9} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.266044 - 0.223238i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.266044 - 0.223238i) q^{6} +(-0.879385 - 1.52314i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.500000 - 2.83564i) q^{9} +(-2.11334 + 3.66041i) q^{11} +(0.173648 + 0.300767i) q^{12} +(-0.815207 + 0.684040i) q^{13} +(1.65270 - 0.601535i) q^{14} +(0.766044 + 0.642788i) q^{16} +(-1.23783 + 7.02006i) q^{17} +2.87939 q^{18} +(3.93969 - 1.86516i) q^{19} +(-0.106067 + 0.601535i) q^{21} +(-3.23783 - 2.71686i) q^{22} +(3.53209 + 1.28558i) q^{23} +(-0.326352 + 0.118782i) q^{24} +(-0.532089 - 0.921605i) q^{26} +(-1.02094 + 1.76833i) q^{27} +(0.305407 + 1.73205i) q^{28} +(1.10607 + 6.27282i) q^{29} +(4.41147 + 7.64090i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(1.37939 - 0.502055i) q^{33} +(-6.69846 - 2.43804i) q^{34} +(-0.500000 + 2.83564i) q^{36} +6.45336 q^{37} +(1.15270 + 4.20372i) q^{38} +0.369585 q^{39} +(1.43969 + 1.20805i) q^{41} +(-0.573978 - 0.208911i) q^{42} +(3.47178 - 1.26363i) q^{43} +(3.23783 - 2.71686i) q^{44} +(-1.87939 + 3.25519i) q^{46} +(0.638156 + 3.61916i) q^{47} +(-0.0603074 - 0.342020i) q^{48} +(1.95336 - 3.38332i) q^{49} +(1.89646 - 1.59132i) q^{51} +(1.00000 - 0.363970i) q^{52} +(-9.29086 - 3.38160i) q^{53} +(-1.56418 - 1.31250i) q^{54} -1.75877 q^{56} +(-1.46451 - 0.383273i) q^{57} -6.36959 q^{58} +(-1.26604 + 7.18009i) q^{59} +(-4.98545 - 1.81456i) q^{61} +(-8.29086 + 3.01763i) q^{62} +(-3.87939 + 3.25519i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.254900 + 1.44561i) q^{66} +(2.02094 + 11.4613i) q^{67} +(3.56418 - 6.17334i) q^{68} +(-0.652704 - 1.13052i) q^{69} +(-2.65270 + 0.965505i) q^{71} +(-2.70574 - 0.984808i) q^{72} +(-0.607411 - 0.509678i) q^{73} +(-1.12061 + 6.35532i) q^{74} +(-4.34002 + 0.405223i) q^{76} +7.43376 q^{77} +(-0.0641778 + 0.363970i) q^{78} +(-5.12836 - 4.30320i) q^{79} +(-7.45084 + 2.71188i) q^{81} +(-1.43969 + 1.20805i) q^{82} +(0.754900 + 1.30753i) q^{83} +(0.305407 - 0.528981i) q^{84} +(0.641559 + 3.63846i) q^{86} +(1.10607 - 1.91576i) q^{87} +(2.11334 + 3.66041i) q^{88} +(9.12108 - 7.65350i) q^{89} +(1.75877 + 0.640140i) q^{91} +(-2.87939 - 2.41609i) q^{92} +(0.532089 - 3.01763i) q^{93} -3.67499 q^{94} +0.347296 q^{96} +(-0.326352 + 1.85083i) q^{97} +(2.99273 + 2.51120i) q^{98} +(11.4363 + 4.16247i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 3 q^{6} + 6 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 - 3 * q^6 + 6 * q^7 + 3 * q^8 - 3 * q^9	$ 6 q + 3 q^{3} - 3 q^{6} + 6 q^{7} + 3 q^{8} - 3 q^{9} - 6 q^{11} - 12 q^{13} + 12 q^{14} + 12 q^{17} + 6 q^{18} + 18 q^{19} + 24 q^{21} + 12 q^{23} - 3 q^{24} + 6 q^{26} - 3 q^{27} + 6 q^{28} - 18 q^{29} + 6 q^{31} - 3 q^{33} - 12 q^{34} - 3 q^{36} + 12 q^{37} + 9 q^{38} - 12 q^{39} + 3 q^{41} + 12 q^{42} + 6 q^{43} - 30 q^{47} - 6 q^{48} - 15 q^{49} + 21 q^{51} + 6 q^{52} - 24 q^{53} + 9 q^{54} + 12 q^{56} + 24 q^{57} - 24 q^{58} - 3 q^{59} + 6 q^{61} - 18 q^{62} - 12 q^{63} - 3 q^{64} + 3 q^{66} + 9 q^{67} + 3 q^{68} - 6 q^{69} - 18 q^{71} - 6 q^{72} + 30 q^{73} - 18 q^{74} - 6 q^{76} + 12 q^{77} + 18 q^{78} + 6 q^{79} - 33 q^{81} - 3 q^{82} + 6 q^{83} + 6 q^{84} + 12 q^{86} - 18 q^{87} + 6 q^{88} - 12 q^{91} - 6 q^{92} - 6 q^{93} - 12 q^{94} - 3 q^{97} + 21 q^{99}+O(q^{100}) $ 6 * q + 3 * q^3 - 3 * q^6 + 6 * q^7 + 3 * q^8 - 3 * q^9 - 6 * q^11 - 12 * q^13 + 12 * q^14 + 12 * q^17 + 6 * q^18 + 18 * q^19 + 24 * q^21 + 12 * q^23 - 3 * q^24 + 6 * q^26 - 3 * q^27 + 6 * q^28 - 18 * q^29 + 6 * q^31 - 3 * q^33 - 12 * q^34 - 3 * q^36 + 12 * q^37 + 9 * q^38 - 12 * q^39 + 3 * q^41 + 12 * q^42 + 6 * q^43 - 30 * q^47 - 6 * q^48 - 15 * q^49 + 21 * q^51 + 6 * q^52 - 24 * q^53 + 9 * q^54 + 12 * q^56 + 24 * q^57 - 24 * q^58 - 3 * q^59 + 6 * q^61 - 18 * q^62 - 12 * q^63 - 3 * q^64 + 3 * q^66 + 9 * q^67 + 3 * q^68 - 6 * q^69 - 18 * q^71 - 6 * q^72 + 30 * q^73 - 18 * q^74 - 6 * q^76 + 12 * q^77 + 18 * q^78 + 6 * q^79 - 33 * q^81 - 3 * q^82 + 6 * q^83 + 6 * q^84 + 12 * q^86 - 18 * q^87 + 6 * q^88 - 12 * q^91 - 6 * q^92 - 6 * q^93 - 12 * q^94 - 3 * q^97 + 21 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$	−0.266044	−	0.223238i	−0.153601	−	0.128886i	0.562749	−	0.826628i	$-0.309744\pi$
$3$	−0.266044	−	0.223238i	−0.153601	−	0.128886i	−0.716349	+	0.697742i	$0.754188\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$		0			0
$5$		0			0
$6$	0.266044	−	0.223238i	0.108612	−	0.0911364i
$7$	−0.879385	−	1.52314i	−0.332376	−	0.575693i	0.650601	−	0.759420i	$-0.274517\pi$
$7$	−0.879385	−	1.52314i	−0.332376	−	0.575693i	−0.982977	+	0.183727i	$0.941184\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−0.500000	−	2.83564i	−0.166667	−	0.945214i
$10$		0			0
$11$	−2.11334	+	3.66041i	−0.637196	+	1.10366i	0.348849	+	0.937179i	$0.386573\pi$
$11$	−2.11334	+	3.66041i	−0.637196	+	1.10366i	−0.986045	+	0.166477i	$0.946761\pi$
$12$	0.173648	+	0.300767i	0.0501279	+	0.0868241i
$13$	−0.815207	+	0.684040i	−0.226098	+	0.189719i	−0.748799	−	0.662798i	$-0.769369\pi$
$13$	−0.815207	+	0.684040i	−0.226098	+	0.189719i	0.522701	+	0.852516i	$0.324925\pi$
$14$	1.65270	−	0.601535i	0.441704	−	0.160767i
$15$		0			0
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−1.23783	+	7.02006i	−0.300217	+	1.70261i	0.344990	+	0.938606i	$0.387882\pi$
$17$	−1.23783	+	7.02006i	−0.300217	+	1.70261i	−0.645207	+	0.764008i	$0.723229\pi$
$18$	2.87939			0.678678
$19$	3.93969	−	1.86516i	0.903827	−	0.427897i
$19$	3.93969	−	1.86516i	0.903827	−	0.427897i
$20$		0			0
$21$	−0.106067	+	0.601535i	−0.0231457	+	0.131266i
$22$	−3.23783	−	2.71686i	−0.690307	−	0.579236i
$23$	3.53209	+	1.28558i	0.736491	+	0.268061i	0.682910	−	0.730503i	$-0.260714\pi$
$23$	3.53209	+	1.28558i	0.736491	+	0.268061i	0.0535814	+	0.998563i	$0.482936\pi$
$24$	−0.326352	+	0.118782i	−0.0666163	+	0.0242463i
$25$		0			0
$26$	−0.532089	−	0.921605i	−0.104351	−	0.180742i
$27$	−1.02094	+	1.76833i	−0.196481	+	0.340315i
$28$	0.305407	+	1.73205i	0.0577166	+	0.327327i
$29$	1.10607	+	6.27282i	0.205391	+	1.16483i	0.896823	+	0.442390i	$0.145869\pi$
$29$	1.10607	+	6.27282i	0.205391	+	1.16483i	−0.691431	+	0.722442i	$0.743019\pi$
$30$		0			0
$31$	4.41147	+	7.64090i	0.792324	+	1.37235i	0.924524	+	0.381123i	$0.124462\pi$
$31$	4.41147	+	7.64090i	0.792324	+	1.37235i	−0.132200	+	0.991223i	$0.542204\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	1.37939	−	0.502055i	0.240120	−	0.0873966i
$34$	−6.69846	−	2.43804i	−1.14878	−	0.418121i
$35$		0			0
$36$	−0.500000	+	2.83564i	−0.0833333	+	0.472607i
$37$	6.45336			1.06093			0.530463	−	0.847708i	$-0.322018\pi$
$37$	6.45336			1.06093			0.530463	+	0.847708i	$0.322018\pi$
$38$	1.15270	+	4.20372i	0.186993	+	0.681934i
$39$	0.369585			0.0591810
$40$		0			0
$41$	1.43969	+	1.20805i	0.224842	+	0.188665i	0.748249	−	0.663418i	$-0.230895\pi$
$41$	1.43969	+	1.20805i	0.224842	+	0.188665i	−0.523407	+	0.852083i	$0.675339\pi$
$42$	−0.573978	−	0.208911i	−0.0885667	−	0.0322357i
$43$	3.47178	−	1.26363i	0.529442	−	0.192701i	−0.0634473	−	0.997985i	$-0.520209\pi$
$43$	3.47178	−	1.26363i	0.529442	−	0.192701i	0.592889	+	0.805284i	$0.297987\pi$
$44$	3.23783	−	2.71686i	0.488121	−	0.409582i
$45$		0			0
$46$	−1.87939	+	3.25519i	−0.277100	+	0.479952i
$47$	0.638156	+	3.61916i	0.0930846	+	0.527909i	0.995317	+	0.0966598i	$0.0308159\pi$
$47$	0.638156	+	3.61916i	0.0930846	+	0.527909i	−0.902233	+	0.431249i	$0.858073\pi$
$48$	−0.0603074	−	0.342020i	−0.00870462	−	0.0493664i
$49$	1.95336	−	3.38332i	0.279052	−	0.483332i
$50$		0			0
$51$	1.89646	−	1.59132i	0.265557	−	0.222829i
$52$	1.00000	−	0.363970i	0.138675	−	0.0504736i
$53$	−9.29086	−	3.38160i	−1.27620	−	0.464498i	−0.387025	−	0.922069i	$-0.626497\pi$
$53$	−9.29086	−	3.38160i	−1.27620	−	0.464498i	−0.889173	+	0.457571i	$0.848719\pi$
$54$	−1.56418	−	1.31250i	−0.212858	−	0.178609i
$55$		0			0
$56$	−1.75877			−0.235026
$57$	−1.46451	−	0.383273i	−0.193979	−	0.0507657i
$58$	−6.36959			−0.836367
$59$	−1.26604	+	7.18009i	−0.164825	+	0.934769i	0.784420	+	0.620230i	$0.212961\pi$
$59$	−1.26604	+	7.18009i	−0.164825	+	0.934769i	−0.949245	+	0.314538i	$0.898150\pi$
$60$		0			0
$61$	−4.98545	−	1.81456i	−0.638322	−	0.232330i	0.00252758	−	0.999997i	$-0.499195\pi$
$61$	−4.98545	−	1.81456i	−0.638322	−	0.232330i	−0.640849	+	0.767667i	$0.721418\pi$
$62$	−8.29086	+	3.01763i	−1.05294	+	0.383239i
$63$	−3.87939	+	3.25519i	−0.488757	+	0.410115i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$		0			0
$66$	0.254900	+	1.44561i	0.0313760	+	0.177942i
$67$	2.02094	+	11.4613i	0.246898	+	1.40023i	0.816044	+	0.577990i	$0.196163\pi$
$67$	2.02094	+	11.4613i	0.246898	+	1.40023i	−0.569146	+	0.822236i	$0.692726\pi$
$68$	3.56418	−	6.17334i	0.432220	−	0.748627i
$69$	−0.652704	−	1.13052i	−0.0785763	−	0.136098i
$70$		0			0
$71$	−2.65270	+	0.965505i	−0.314818	+	0.114584i	−0.494596	−	0.869123i	$-0.664684\pi$
$71$	−2.65270	+	0.965505i	−0.314818	+	0.114584i	0.179778	+	0.983707i	$0.442462\pi$
$72$	−2.70574	−	0.984808i	−0.318874	−	0.116061i
$73$	−0.607411	−	0.509678i	−0.0710921	−	0.0596533i	0.606549	−	0.795046i	$-0.292553\pi$
$73$	−0.607411	−	0.509678i	−0.0710921	−	0.0596533i	−0.677641	+	0.735393i	$0.736998\pi$
$74$	−1.12061	+	6.35532i	−0.130269	+	0.738791i
$75$		0			0
$76$	−4.34002	+	0.405223i	−0.497835	+	0.0464823i
$77$	7.43376			0.847156
$78$	−0.0641778	+	0.363970i	−0.00726670	+	0.0412115i
$79$	−5.12836	−	4.30320i	−0.576985	−	0.484148i	0.306970	−	0.951719i	$-0.400685\pi$
$79$	−5.12836	−	4.30320i	−0.576985	−	0.484148i	−0.883955	+	0.467571i	$0.845129\pi$
$80$		0			0
$81$	−7.45084	+	2.71188i	−0.827871	+	0.301320i
$82$	−1.43969	+	1.20805i	−0.158987	+	0.133406i
$83$	0.754900	+	1.30753i	0.0828610	+	0.143520i	0.904478	−	0.426521i	$-0.140261\pi$
$83$	0.754900	+	1.30753i	0.0828610	+	0.143520i	−0.821617	+	0.570040i	$0.806928\pi$
$84$	0.305407	−	0.528981i	0.0333227	−	0.0577166i
$85$		0			0
$86$	0.641559	+	3.63846i	0.0691811	+	0.392346i
$87$	1.10607	−	1.91576i	0.118583	−	0.205391i
$88$	2.11334	+	3.66041i	0.225283	+	0.390201i
$89$	9.12108	−	7.65350i	0.966833	−	0.811269i	−0.0152184	−	0.999884i	$-0.504844\pi$
$89$	9.12108	−	7.65350i	0.966833	−	0.811269i	0.982051	+	0.188615i	$0.0603999\pi$
$90$		0			0
$91$	1.75877	+	0.640140i	0.184369	+	0.0671049i
$92$	−2.87939	−	2.41609i	−0.300197	−	0.251895i
$93$	0.532089	−	3.01763i	0.0551750	−	0.312913i
$94$	−3.67499			−0.379047
$95$		0			0
$96$	0.347296			0.0354458
$97$	−0.326352	+	1.85083i	−0.0331360	+	0.187924i	−0.996883	−	0.0788942i	$-0.974861\pi$
$97$	−0.326352	+	1.85083i	−0.0331360	+	0.187924i	0.963747	+	0.266818i	$0.0859722\pi$
$98$	2.99273	+	2.51120i	0.302311	+	0.253669i
$99$	11.4363	+	4.16247i	1.14939	+	0.418344i
$100$		0			0
$101$	−1.87939	+	1.57699i	−0.187006	+	0.156917i	−0.731484	−	0.681858i	$-0.761172\pi$
$101$	−1.87939	+	1.57699i	−0.187006	+	0.156917i	0.544478	+	0.838775i	$0.316728\pi$
$102$	1.23783	+	2.14398i	0.122563	+	0.212285i
$103$	−3.71688	+	6.43783i	−0.366235	+	0.634338i	−0.988974	−	0.148092i	$-0.952687\pi$
$103$	−3.71688	+	6.43783i	−0.366235	+	0.634338i	0.622738	+	0.782430i	$0.286020\pi$
$104$	0.184793	+	1.04801i	0.0181204	+	0.102766i
$105$		0			0
$106$	4.94356	−	8.56250i	0.480161	−	0.831664i
$107$	−0.0885259	−	0.153331i	−0.00855812	−	0.0148231i	0.861715	−	0.507393i	$-0.169391\pi$
$107$	−0.0885259	−	0.153331i	−0.00855812	−	0.0148231i	−0.870273	+	0.492570i	$0.836058\pi$
$108$	1.56418	−	1.31250i	0.150513	−	0.126295i
$109$	−3.98545	+	1.45059i	−0.381737	+	0.138941i	−0.525759	−	0.850634i	$-0.676219\pi$
$109$	−3.98545	+	1.45059i	−0.381737	+	0.138941i	0.144022	+	0.989574i	$0.453996\pi$
$110$		0			0
$111$	−1.71688	−	1.44063i	−0.162959	−	0.136739i
$112$	0.305407	−	1.73205i	0.0288583	−	0.163663i
$113$	−10.4388			−0.982001			−0.491001	−	0.871159i	$-0.663369\pi$
$113$	−10.4388			−0.982001			−0.491001	+	0.871159i	$0.663369\pi$
$114$	0.631759	−	1.37570i	0.0591697	−	0.128846i
$115$		0			0
$116$	1.10607	−	6.27282i	0.102696	−	0.582416i
$117$	2.34730	+	1.96962i	0.217008	+	0.182091i
$118$	−6.85117	−	2.49362i	−0.630701	−	0.229556i
$119$	11.7811	−	4.28795i	1.07997	−	0.393076i
$120$		0			0
$121$	−3.43242	−	5.94512i	−0.312038	−	0.540466i
$122$	2.65270	−	4.59462i	0.240165	−	0.415977i
$123$	−0.113341	−	0.642788i	−0.0102196	−	0.0579582i
$124$	−1.53209	−	8.68891i	−0.137586	−	0.780287i
$125$		0			0
$126$	−2.53209	−	4.38571i	−0.225576	−	0.390710i
$127$	16.8648	−	14.1513i	1.49651	−	1.25572i	0.610539	−	0.791986i	$-0.290953\pi$
$127$	16.8648	−	14.1513i	1.49651	−	1.25572i	0.885973	−	0.463737i	$-0.153492\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	−1.20574	−	0.438852i	−0.106159	−	0.0386388i
$130$		0			0
$131$	−1.32888	+	7.53644i	−0.116105	+	0.658462i	0.870093	+	0.492888i	$0.164059\pi$
$131$	−1.32888	+	7.53644i	−0.116105	+	0.658462i	−0.986197	+	0.165574i	$0.947052\pi$
$132$	−1.46791			−0.127765
$133$	−6.30541	−	4.36051i	−0.546748	−	0.378104i
$134$	−11.6382			−1.00538
$135$		0			0
$136$	5.46064	+	4.58202i	0.468246	+	0.392905i
$137$	−5.39053	−	1.96199i	−0.460544	−	0.167624i	0.101320	−	0.994854i	$-0.467693\pi$
$137$	−5.39053	−	1.96199i	−0.460544	−	0.167624i	−0.561864	+	0.827230i	$0.689916\pi$
$138$	1.22668	−	0.446476i	0.104422	−	0.0380065i
$139$	−14.8589	+	12.4681i	−1.26032	+	1.05753i	−0.264668	+	0.964340i	$0.585262\pi$
$139$	−14.8589	+	12.4681i	−1.26032	+	1.05753i	−0.995648	+	0.0931911i	$0.970293\pi$
$140$		0			0
$141$	0.638156	−	1.10532i	0.0537424	−	0.0930846i
$142$	−0.490200	−	2.78006i	−0.0411367	−	0.233298i
$143$	−0.781059	−	4.42961i	−0.0653155	−	0.370422i
$144$	1.43969	−	2.49362i	0.119974	−	0.207802i
$145$		0			0
$146$	0.607411	−	0.509678i	0.0502697	−	0.0421813i
$147$	−1.27497	+	0.464050i	−0.105158	+	0.0382742i
$148$	−6.06418	−	2.20718i	−0.498472	−	0.181429i
$149$	−3.96585	−	3.32774i	−0.324895	−	0.272619i	0.465721	−	0.884932i	$-0.345795\pi$
$149$	−3.96585	−	3.32774i	−0.324895	−	0.272619i	−0.790616	+	0.612312i	$0.790240\pi$
$150$		0			0
$151$	22.1830			1.80523			0.902615	−	0.430449i	$-0.141645\pi$
$151$	22.1830			1.80523			0.902615	+	0.430449i	$0.141645\pi$
$152$	0.354570	−	4.34445i	0.0287595	−	0.352382i
$153$	20.5253			1.65937
$154$	−1.29086	+	7.32083i	−0.104020	+	0.589929i
$155$		0			0
$156$	−0.347296	−	0.126406i	−0.0278060	−	0.0101205i
$157$	−2.65270	+	0.965505i	−0.211709	+	0.0770557i	−0.445698	−	0.895184i	$-0.647044\pi$
$157$	−2.65270	+	0.965505i	−0.211709	+	0.0770557i	0.233989	+	0.972239i	$0.424822\pi$
$158$	5.12836	−	4.30320i	0.407990	−	0.342344i
$159$	1.71688	+	2.97373i	0.136158	+	0.235832i
$160$		0			0
$161$	−1.14796	−	6.51038i	−0.0904716	−	0.513090i
$162$	−1.37686	−	7.80856i	−0.108176	−	0.613498i
$163$	1.10947	−	1.92166i	0.0869004	−	0.150516i	−0.819299	−	0.573366i	$-0.805637\pi$
$163$	1.10947	−	1.92166i	0.0869004	−	0.150516i	0.906199	+	0.422851i	$0.138970\pi$
$164$	−0.939693	−	1.62760i	−0.0733777	−	0.127094i
$165$		0			0
$166$	−1.41875	+	0.516382i	−0.110116	+	0.0400790i
$167$	3.68004	+	1.33943i	0.284770	+	0.103648i	0.480456	−	0.877019i	$-0.340471\pi$
$167$	3.68004	+	1.33943i	0.284770	+	0.103648i	−0.195686	+	0.980667i	$0.562693\pi$
$168$	0.467911	+	0.392624i	0.0361001	+	0.0302916i
$169$	−2.06077	+	11.6872i	−0.158521	+	0.899018i
$170$		0			0
$171$	−7.25877	−	10.2390i	−0.555092	−	0.782994i
$172$	−3.69459			−0.281710
$173$	−1.31046	+	7.43199i	−0.0996324	+	0.565043i	0.893597	+	0.448871i	$0.148174\pi$
$173$	−1.31046	+	7.43199i	−0.0996324	+	0.565043i	−0.993229	+	0.116173i	$0.962937\pi$
$174$	1.69459	+	1.42193i	0.128467	+	0.107796i
$175$		0			0
$176$	−3.97178	+	1.44561i	−0.299384	+	0.108967i
$177$	1.93969	−	1.62760i	0.145796	−	0.122338i
$178$	5.95336	+	10.3115i	0.446223	+	0.772882i
$179$	5.49407	−	9.51601i	0.410646	−	0.711260i	−0.584314	−	0.811527i	$-0.698637\pi$
$179$	5.49407	−	9.51601i	0.410646	−	0.711260i	0.994961	+	0.100267i	$0.0319698\pi$
$180$		0			0
$181$	−2.61081	−	14.8067i	−0.194060	−	1.10057i	−0.913751	−	0.406276i	$-0.866827\pi$
$181$	−2.61081	−	14.8067i	−0.194060	−	1.10057i	0.719690	−	0.694295i	$-0.244284\pi$
$182$	−0.935822	+	1.62089i	−0.0693678	+	0.120148i
$183$	0.921274	+	1.59569i	0.0681026	+	0.117957i
$184$	2.87939	−	2.41609i	0.212271	−	0.178117i
$185$		0			0
$186$	2.87939	+	1.04801i	0.211127	+	0.0768439i
$187$	−23.0804	−	19.3667i	−1.68780	−	1.41624i
$188$	0.638156	−	3.61916i	0.0465423	−	0.263954i
$189$	3.59121			0.261222
$190$		0			0
$191$	4.53714			0.328296			0.164148	−	0.986436i	$-0.447513\pi$
$191$	4.53714			0.328296			0.164148	+	0.986436i	$0.447513\pi$
$192$	−0.0603074	+	0.342020i	−0.00435231	+	0.0246832i
$193$	−16.8498	−	14.1387i	−1.21288	−	1.01772i	−0.999166	−	0.0408274i	$-0.987001\pi$
$193$	−16.8498	−	14.1387i	−1.21288	−	1.01772i	−0.213711	−	0.976897i	$-0.568555\pi$
$194$	−1.76604	−	0.642788i	−0.126795	−	0.0461495i
$195$		0			0
$196$	−2.99273	+	2.51120i	−0.213766	+	0.179371i
$197$	7.96585	+	13.7973i	0.567543	+	0.983014i	0.996808	+	0.0798353i	$0.0254394\pi$
$197$	7.96585	+	13.7973i	0.567543	+	0.983014i	−0.429265	+	0.903179i	$0.641227\pi$
$198$	−6.08512	+	10.5397i	−0.432451	+	0.749027i
$199$	−0.568926	−	3.22654i	−0.0403301	−	0.228723i	0.957980	−	0.286835i	$-0.0926031\pi$
$199$	−0.568926	−	3.22654i	−0.0403301	−	0.228723i	−0.998310	+	0.0581118i	$0.981492\pi$
$200$		0			0
$201$	2.02094	−	3.50038i	0.142546	−	0.246898i
$202$	−1.22668	−	2.12467i	−0.0863090	−	0.149492i
$203$	8.58172	−	7.20092i	0.602319	−	0.505405i
$204$	−2.32635	+	0.846723i	−0.162877	+	0.0592825i
$205$		0			0
$206$	−5.69459	−	4.77833i	−0.396761	−	0.332922i
$207$	1.87939	−	10.6585i	0.130626	−	0.740819i
$208$	−1.06418			−0.0737875
$209$	−1.49866	+	18.3626i	−0.103664	+	1.27017i
$210$		0			0
$211$	1.99154	−	11.2946i	0.137104	−	0.777553i	−0.836268	−	0.548321i	$-0.815267\pi$
$211$	1.99154	−	11.2946i	0.137104	−	0.777553i	0.973372	−	0.229232i	$-0.0736215\pi$
$212$	7.57398	+	6.35532i	0.520183	+	0.436485i
$213$	0.921274	+	0.335316i	0.0631247	+	0.0229755i
$214$	0.166374	−	0.0605553i	0.0113731	−	0.00413947i
$215$		0			0
$216$	1.02094	+	1.76833i	0.0694665	+	0.120319i
$217$	7.75877	−	13.4386i	0.526700	−	0.912271i
$218$	−0.736482	−	4.17680i	−0.0498808	−	0.282888i
$219$	0.0478189	+	0.271194i	0.00323130	+	0.0183256i
$220$		0			0
$221$	−3.79292	−	6.56953i	−0.255139	−	0.441914i
$222$	1.71688	−	1.44063i	0.115230	−	0.0966891i
$223$	10.5175	−	3.82807i	0.704307	−	0.256347i	0.0350581	−	0.999385i	$-0.488838\pi$
$223$	10.5175	−	3.82807i	0.704307	−	0.256347i	0.669249	+	0.743039i	$0.266616\pi$
$224$	1.65270	+	0.601535i	0.110426	+	0.0401917i
$225$		0			0
$226$	1.81268	−	10.2802i	0.120578	−	0.683830i
$227$	3.39693			0.225462			0.112731	−	0.993626i	$-0.464040\pi$
$227$	3.39693			0.225462			0.112731	+	0.993626i	$0.464040\pi$
$228$	1.24510	+	0.861050i	0.0824588	+	0.0570244i
$229$	4.25671			0.281291			0.140646	−	0.990060i	$-0.455082\pi$
$229$	4.25671			0.281291			0.140646	+	0.990060i	$0.455082\pi$
$230$		0			0
$231$	−1.97771	−	1.65950i	−0.130124	−	0.109187i
$232$	5.98545	+	2.17853i	0.392964	+	0.143027i
$233$	6.24257	−	2.27211i	0.408965	−	0.148851i	−0.129342	−	0.991600i	$-0.541286\pi$
$233$	6.24257	−	2.27211i	0.408965	−	0.148851i	0.538307	+	0.842749i	$0.319064\pi$
$234$	−2.34730	+	1.96962i	−0.153448	+	0.128758i
$235$		0			0
$236$	3.64543	−	6.31407i	0.237297	−	0.411011i
$237$	0.403733	+	2.28969i	0.0262253	+	0.148731i
$238$	2.17705	+	12.3467i	0.141117	+	0.800316i
$239$	−8.00774	+	13.8698i	−0.517978	+	0.897164i	0.481804	+	0.876279i	$0.339982\pi$
$239$	−8.00774	+	13.8698i	−0.517978	+	0.897164i	−0.999782	+	0.0208848i	$0.993352\pi$
$240$		0			0
$241$	−6.59105	+	5.53055i	−0.424567	+	0.356254i	−0.829897	−	0.557916i	$-0.811601\pi$
$241$	−6.59105	+	5.53055i	−0.424567	+	0.356254i	0.405330	+	0.914170i	$0.367157\pi$
$242$	6.45084	−	2.34791i	0.414676	−	0.150930i
$243$	8.34389	+	3.03693i	0.535261	+	0.194819i
$244$	4.06418	+	3.41025i	0.260182	+	0.218319i
$245$		0			0
$246$	0.652704			0.0416149
$247$	−1.93582	+	4.21540i	−0.123173	+	0.268220i
$248$	8.82295			0.560258
$249$	0.0910521	−	0.516382i	0.00577019	−	0.0327244i
$250$		0			0
$251$	18.7087	+	6.80942i	1.18088	+	0.429807i	0.856514	−	0.516123i	$-0.172625\pi$
$251$	18.7087	+	6.80942i	1.18088	+	0.429807i	0.324370	+	0.945930i	$0.394848\pi$
$252$	4.75877	−	1.73205i	0.299774	−	0.109109i
$253$	−12.1702	+	10.2120i	−0.765137	+	0.642026i
$254$	11.0077	+	19.0660i	0.690687	+	1.19631i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−4.58734	−	26.0161i	−0.286151	−	1.62284i	−0.701146	−	0.713018i	$-0.747328\pi$
$257$	−4.58734	−	26.0161i	−0.286151	−	1.62284i	0.414996	−	0.909823i	$-0.363783\pi$
$258$	0.641559	−	1.11121i	0.0399417	−	0.0691811i
$259$	−5.67499	−	9.82938i	−0.352627	−	0.610768i
$260$		0			0
$261$	17.2344	−	6.27282i	1.06678	−	0.388278i
$262$	−7.19119	−	2.61738i	−0.444273	−	0.161702i
$263$	21.4047	+	17.9606i	1.31987	+	1.10750i	0.986333	+	0.164763i	$0.0526860\pi$
$263$	21.4047	+	17.9606i	1.31987	+	1.10750i	0.333535	+	0.942738i	$0.391758\pi$
$264$	0.254900	−	1.44561i	0.0156880	−	0.0889712i
$265$		0			0
$266$	5.38919	−	5.45242i	0.330432	−	0.334309i
$267$	−4.13516			−0.253068
$268$	2.02094	−	11.4613i	0.123449	−	0.700113i
$269$	11.1702	+	9.37295i	0.681062	+	0.571479i	0.916316	−	0.400455i	$-0.131148\pi$
$269$	11.1702	+	9.37295i	0.681062	+	0.571479i	−0.235255	+	0.971934i	$0.575592\pi$
$270$		0			0
$271$	17.1284	−	6.23421i	1.04047	−	0.378701i	0.235414	−	0.971895i	$-0.424355\pi$
$271$	17.1284	−	6.23421i	1.04047	−	0.378701i	0.805060	+	0.593194i	$0.202133\pi$
$272$	−5.46064	+	4.58202i	−0.331100	+	0.277826i
$273$	−0.325008	−	0.562930i	−0.0196704	−	0.0340701i
$274$	2.86824	−	4.96794i	0.173277	−	0.300124i
$275$		0			0
$276$	0.226682	+	1.28558i	0.0136446	+	0.0773825i
$277$	−8.23442	+	14.2624i	−0.494758	+	0.856947i	−0.999982	−	0.00604184i	$-0.998077\pi$
$277$	−8.23442	+	14.2624i	−0.494758	+	0.856947i	0.505223	+	0.862989i	$0.331410\pi$
$278$	−9.69846	−	16.7982i	−0.581675	−	1.00749i
$279$	19.4611	−	16.3298i	1.16511	−	0.977640i
$280$		0			0
$281$	6.73783	+	2.45237i	0.401945	+	0.146296i	0.535079	−	0.844802i	$-0.320282\pi$
$281$	6.73783	+	2.45237i	0.401945	+	0.146296i	−0.133134	+	0.991098i	$0.542504\pi$
$282$	0.977711	+	0.820397i	0.0582219	+	0.0488539i
$283$	−3.63563	+	20.6187i	−0.216116	+	1.22565i	0.662844	+	0.748757i	$0.269349\pi$
$283$	−3.63563	+	20.6187i	−0.216116	+	1.22565i	−0.878960	+	0.476896i	$0.841762\pi$
$284$	2.82295			0.167511
$285$		0			0
$286$	4.49794			0.265969
$287$	0.573978	−	3.25519i	0.0338808	−	0.192148i
$288$	2.20574	+	1.85083i	0.129974	+	0.109061i
$289$	−31.7743	−	11.5649i	−1.86907	−	0.680287i
$290$		0			0
$291$	0.500000	−	0.419550i	0.0293105	−	0.0245944i
$292$	0.396459	+	0.686688i	0.0232010	+	0.0401854i
$293$	4.73917	−	8.20848i	0.276865	−	0.479545i	−0.693739	−	0.720227i	$-0.744038\pi$
$293$	4.73917	−	8.20848i	0.276865	−	0.479545i	0.970604	+	0.240682i	$0.0773711\pi$
$294$	−0.235604	−	1.33618i	−0.0137407	−	0.0779275i
$295$		0			0
$296$	3.22668	−	5.58878i	0.187547	−	0.324841i
$297$	−4.31521	−	7.47416i	−0.250394	−	0.433695i
$298$	3.96585	−	3.32774i	0.229736	−	0.192771i
$299$	−3.75877	+	1.36808i	−0.217375	+	0.0791181i
$300$		0			0
$301$	−4.97771	−	4.17680i	−0.286911	−	0.240747i
$302$	−3.85204	+	21.8460i	−0.221660	+	1.25710i
$303$	0.852044			0.0489487
$304$	4.21688	+	1.10359i	0.241855	+	0.0632952i
$305$		0			0
$306$	−3.56418	+	20.2135i	−0.203750	+	1.15553i
$307$	−1.01889	−	0.854946i	−0.0581508	−	0.0487944i	0.613249	−	0.789890i	$-0.289862\pi$
$307$	−1.01889	−	0.854946i	−0.0581508	−	0.0487944i	−0.671400	+	0.741095i	$0.734307\pi$
$308$	−6.98545	−	2.54250i	−0.398033	−	0.144872i
$309$	2.42602	−	0.883000i	0.138012	−	0.0502321i
$310$		0			0
$311$	−3.73917	−	6.47643i	−0.212029	−	0.367245i	0.740320	−	0.672254i	$-0.234674\pi$
$311$	−3.73917	−	6.47643i	−0.212029	−	0.367245i	−0.952349	+	0.305009i	$0.901340\pi$
$312$	0.184793	−	0.320070i	0.0104618	−	0.0181204i
$313$	−5.08765	−	28.8535i	−0.287571	−	1.63090i	−0.695955	−	0.718085i	$-0.745019\pi$
$313$	−5.08765	−	28.8535i	−0.287571	−	1.63090i	0.408384	−	0.912810i	$-0.366092\pi$
$314$	−0.490200	−	2.78006i	−0.0276636	−	0.156888i
$315$		0			0
$316$	3.34730	+	5.79769i	0.188300	+	0.326145i
$317$	−4.29086	+	3.60046i	−0.240999	+	0.202222i	−0.755285	−	0.655397i	$-0.772501\pi$
$317$	−4.29086	+	3.60046i	−0.240999	+	0.202222i	0.514286	+	0.857619i	$0.328057\pi$
$318$	−3.22668	+	1.17442i	−0.180943	+	0.0658580i
$319$	−25.2986	−	9.20794i	−1.41645	−	0.515546i
$320$		0			0
$321$	−0.0106775	+	0.0605553i	−0.000595961	+	0.00337987i
$322$	6.61081			0.368406
$323$	8.21688	+	29.9656i	0.457200	+	1.66733i
$324$	7.92902			0.440501
$325$		0			0
$326$	1.69981	+	1.42631i	0.0941436	+	0.0789959i
$327$	1.38413	+	0.503783i	0.0765427	+	0.0278593i
$328$	1.76604	−	0.642788i	0.0975135	−	0.0354920i
$329$	4.95130	−	4.15464i	0.272974	−	0.229053i
$330$		0			0
$331$	−11.4880	+	19.8978i	−0.631436	+	1.09368i	0.355822	+	0.934554i	$0.384201\pi$
$331$	−11.4880	+	19.8978i	−0.631436	+	1.09368i	−0.987258	+	0.159126i	$0.949132\pi$
$332$	−0.262174	−	1.48686i	−0.0143887	−	0.0816022i
$333$	−3.22668	−	18.2994i	−0.176821	−	1.00280i
$334$	−1.95811	+	3.39155i	−0.107143	+	0.185577i
$335$		0			0
$336$	−0.467911	+	0.392624i	−0.0255266	+	0.0214194i
$337$	1.23308	−	0.448804i	0.0671701	−	0.0244479i	−0.308217	−	0.951316i	$-0.599732\pi$
$337$	1.23308	−	0.448804i	0.0671701	−	0.0244479i	0.375387	+	0.926868i	$0.377510\pi$
$338$	−11.1518	−	4.05893i	−0.606579	−	0.220777i
$339$	2.77719	+	2.33034i	0.150836	+	0.126567i
$340$		0			0
$341$	−37.2918			−2.01946
$342$	11.3439	−	5.37051i	0.613407	−	0.290404i
$343$	−19.1824			−1.03575
$344$	0.641559	−	3.63846i	0.0345906	−	0.196173i
$345$		0			0
$346$	−7.09152	−	2.58110i	−0.381242	−	0.138761i
$347$	2.27079	−	0.826501i	0.121903	−	0.0443689i	−0.280349	−	0.959898i	$-0.590450\pi$
$347$	2.27079	−	0.826501i	0.121903	−	0.0443689i	0.402251	+	0.915529i	$0.368228\pi$
$348$	−1.69459	+	1.42193i	−0.0908397	+	0.0762236i
$349$	4.24897	+	7.35943i	0.227442	+	0.393941i	0.957049	−	0.289925i	$-0.0936304\pi$
$349$	4.24897	+	7.35943i	0.227442	+	0.393941i	−0.729607	+	0.683866i	$0.760297\pi$
$350$		0			0
$351$	−0.377326	−	2.13992i	−0.0201402	−	0.114221i
$352$	−0.733956	−	4.16247i	−0.0391200	−	0.221860i
$353$	−1.92009	+	3.32570i	−0.102196	+	0.177009i	−0.912589	−	0.408878i	$-0.865920\pi$
$353$	−1.92009	+	3.32570i	−0.102196	+	0.177009i	0.810393	+	0.585887i	$0.199254\pi$
$354$	1.26604	+	2.19285i	0.0672895	+	0.116549i
$355$		0			0
$356$	−11.1887	+	4.07234i	−0.592998	+	0.215834i
$357$	−4.09152	−	1.48919i	−0.216546	−	0.0788164i
$358$	8.41740	+	7.06304i	0.444874	+	0.373293i
$359$	−4.15476	+	23.5628i	−0.219280	+	1.24360i	0.654043	+	0.756457i	$0.273071\pi$
$359$	−4.15476	+	23.5628i	−0.219280	+	1.24360i	−0.873323	+	0.487141i	$0.838040\pi$
$360$		0			0
$361$	12.0424	−	14.6963i	0.633808	−	0.773490i
$362$	15.0351			0.790226
$363$	−0.414000	+	2.34791i	−0.0217294	+	0.123233i
$364$	−1.43376	−	1.20307i	−0.0751496	−	0.0630580i
$365$		0			0
$366$	−1.73143	+	0.630189i	−0.0905033	+	0.0329405i
$367$	−13.1061	+	10.9973i	−0.684131	+	0.574054i	−0.917210	−	0.398404i	$-0.869564\pi$
$367$	−13.1061	+	10.9973i	−0.684131	+	0.574054i	0.233079	+	0.972458i	$0.425120\pi$
$368$	1.87939	+	3.25519i	0.0979697	+	0.169689i
$369$	2.70574	−	4.68647i	0.140855	−	0.243968i
$370$		0			0
$371$	3.01960	+	17.1250i	0.156770	+	0.889086i
$372$	−1.53209	+	2.65366i	−0.0794351	+	0.137586i
$373$	−1.98040	−	3.43015i	−0.102541	−	0.177607i	0.810190	−	0.586168i	$-0.199364\pi$
$373$	−1.98040	−	3.43015i	−0.102541	−	0.177607i	−0.912731	+	0.408561i	$0.866031\pi$
$374$	23.0804	−	19.3667i	1.19346	−	1.00143i
$375$		0			0
$376$	3.45336	+	1.25692i	0.178094	+	0.0648208i
$377$	−5.19253	−	4.35705i	−0.267429	−	0.224400i
$378$	−0.623608	+	3.53666i	−0.0320749	+	0.181906i
$379$	−27.2918			−1.40189			−0.700943	−	0.713218i	$-0.747237\pi$
$379$	−27.2918			−1.40189			−0.700943	+	0.713218i	$0.747237\pi$
$380$		0			0
$381$	−7.64590			−0.391711
$382$	−0.787866	+	4.46821i	−0.0403107	+	0.228614i
$383$	−4.90941	−	4.11949i	−0.250859	−	0.210496i	0.508683	−	0.860954i	$-0.330133\pi$
$383$	−4.90941	−	4.11949i	−0.250859	−	0.210496i	−0.759542	+	0.650458i	$0.774577\pi$
$384$	−0.326352	−	0.118782i	−0.0166541	−	0.00606159i
$385$		0			0
$386$	16.8498	−	14.1387i	0.857633	−	0.719640i
$387$	−5.31908	−	9.21291i	−0.270384	−	0.468319i
$388$	0.939693	−	1.62760i	0.0477057	−	0.0826286i
$389$	−4.41653	−	25.0474i	−0.223927	−	1.26995i	−0.864726	−	0.502244i	$-0.832508\pi$
$389$	−4.41653	−	25.0474i	−0.223927	−	1.26995i	0.640799	−	0.767708i	$-0.278603\pi$
$390$		0			0
$391$	−13.3969	+	23.2042i	−0.677512	+	1.17348i
$392$	−1.95336	−	3.38332i	−0.0986597	−	0.170884i
$393$	2.03596	−	1.70837i	0.102701	−	0.0861760i
$394$	−14.9709	+	5.44896i	−0.754223	+	0.274515i
$395$		0			0
$396$	−9.32295	−	7.82288i	−0.468496	−	0.393115i
$397$	−3.92127	+	22.2387i	−0.196803	+	1.11613i	0.713024	+	0.701139i	$0.247325\pi$
$397$	−3.92127	+	22.2387i	−0.196803	+	1.11613i	−0.909827	+	0.414987i	$0.863786\pi$
$398$	3.27631			0.164227
$399$	0.704088	+	2.56769i	0.0352485	+	0.128546i
$400$		0			0
$401$	0.132636	−	0.752219i	0.00662355	−	0.0375640i	−0.981317	−	0.192399i	$-0.938373\pi$
$401$	0.132636	−	0.752219i	0.00662355	−	0.0375640i	0.987940	+	0.154835i	$0.0494845\pi$
$402$	3.09627	+	2.59808i	0.154428	+	0.129580i
$403$	−8.82295	−	3.21129i	−0.439502	−	0.159966i
$404$	2.30541	−	0.839100i	0.114698	−	0.0417468i
$405$		0			0
$406$	5.60132	+	9.70177i	0.277989	+	0.481491i
$407$	−13.6382	+	23.6220i	−0.676018	+	1.17090i
$408$	−0.429892	−	2.43804i	−0.0212828	−	0.120701i
$409$	−2.92144	−	16.5683i	−0.144456	−	0.819249i	−0.967803	−	0.251711i	$-0.919007\pi$
$409$	−2.92144	−	16.5683i	−0.144456	−	0.819249i	0.823347	−	0.567539i	$-0.192104\pi$
$410$		0			0
$411$	0.996130	+	1.72535i	0.0491354	+	0.0851051i
$412$	5.69459	−	4.77833i	0.280552	−	0.235411i
$413$	12.0496	−	4.38571i	0.592924	−	0.215807i
$414$	10.1702	+	3.70167i	0.499840	+	0.181927i
$415$		0			0
$416$	0.184793	−	1.04801i	0.00906020	−	0.0513829i
$417$	6.73648			0.329887
$418$	−17.8234	−	4.66452i	−0.871772	−	0.228149i
$419$	35.8931			1.75349			0.876747	−	0.480953i	$-0.159709\pi$
$419$	35.8931			1.75349			0.876747	+	0.480953i	$0.159709\pi$
$420$		0			0
$421$	15.8648	+	13.3122i	0.773205	+	0.648796i	0.941528	−	0.336936i	$-0.109391\pi$
$421$	15.8648	+	13.3122i	0.773205	+	0.648796i	−0.168323	+	0.985732i	$0.553835\pi$
$422$	10.7772	+	3.92258i	0.524625	+	0.190948i
$423$	9.94356	−	3.61916i	0.483473	−	0.175970i
$424$	−7.57398	+	6.35532i	−0.367825	+	0.308642i
$425$		0			0
$426$	−0.490200	+	0.849051i	−0.0237503	+	0.0411367i
$427$	1.62031	+	9.18923i	0.0784123	+	0.444698i
$428$	0.0307447	+	0.174362i	0.00148610	+	0.00842810i
$429$	−0.781059	+	1.35283i	−0.0377099	+	0.0653155i
$430$		0			0
$431$	−14.0378	+	11.7791i	−0.676176	+	0.567379i	−0.914886	−	0.403712i	$-0.867720\pi$
$431$	−14.0378	+	11.7791i	−0.676176	+	0.567379i	0.238710	+	0.971091i	$0.423275\pi$
$432$	−1.91875	+	0.698367i	−0.0923158	+	0.0336002i
$433$	4.78611	+	1.74200i	0.230006	+	0.0837153i	0.454452	−	0.890771i	$-0.349835\pi$
$433$	4.78611	+	1.74200i	0.230006	+	0.0837153i	−0.224446	+	0.974486i	$0.572057\pi$
$434$	11.8871	+	9.97448i	0.570600	+	0.478791i
$435$		0			0
$436$	4.24123			0.203118
$437$	16.3131	−	1.52314i	0.780364	−	0.0728617i
$438$	−0.275378			−0.0131581
$439$	−1.79055	+	10.1547i	−0.0854585	+	0.484659i	0.911798	+	0.410639i	$0.134694\pi$
$439$	−1.79055	+	10.1547i	−0.0854585	+	0.484659i	−0.997257	+	0.0740207i	$0.976417\pi$
$440$		0			0
$441$	−10.5706	−	3.84737i	−0.503361	−	0.183208i
$442$	7.12836	−	2.59451i	0.339061	−	0.123408i
$443$	6.75356	−	5.66691i	0.320871	−	0.269243i	−0.468097	−	0.883677i	$-0.655060\pi$
$443$	6.75356	−	5.66691i	0.320871	−	0.269243i	0.788968	+	0.614434i	$0.210616\pi$
$444$	1.12061	+	1.94096i	0.0531820	+	0.0921140i
$445$		0			0
$446$	1.94356	+	11.0225i	0.0920304	+	0.521930i
$447$	0.312214	+	1.77066i	0.0147672	+	0.0837492i
$448$	−0.879385	+	1.52314i	−0.0415470	+	0.0719616i
$449$	−6.03849	−	10.4590i	−0.284974	−	0.493589i	0.687629	−	0.726062i	$-0.258652\pi$
$449$	−6.03849	−	10.4590i	−0.284974	−	0.493589i	−0.972603	+	0.232473i	$0.925318\pi$
$450$		0			0
$451$	−7.46451	+	2.71686i	−0.351490	+	0.127932i
$452$	9.80928	+	3.57029i	0.461390	+	0.167932i
$453$	−5.90167	−	4.95209i	−0.277285	−	0.232670i
$454$	−0.589870	+	3.34532i	−0.0276840	+	0.157004i
$455$		0			0
$456$	−1.06418	+	1.07666i	−0.0498347	+	0.0504194i
$457$	0.731429			0.0342148			0.0171074	−	0.999854i	$-0.494554\pi$
$457$	0.731429			0.0342148			0.0171074	+	0.999854i	$0.494554\pi$
$458$	−0.739170	+	4.19204i	−0.0345392	+	0.195881i
$459$	−11.1500	−	9.35597i	−0.520438	−	0.436699i
$460$		0			0
$461$	−21.6878	+	7.89371i	−1.01010	+	0.367647i	−0.793472	−	0.608607i	$-0.791729\pi$
$461$	−21.6878	+	7.89371i	−1.01010	+	0.367647i	−0.216629	+	0.976254i	$0.569506\pi$
$462$	1.97771	−	1.65950i	0.0920115	−	0.0772068i
$463$	9.02229	+	15.6271i	0.419301	+	0.726251i	0.995869	−	0.0907980i	$-0.0289418\pi$
$463$	9.02229	+	15.6271i	0.419301	+	0.726251i	−0.576568	+	0.817049i	$0.695608\pi$
$464$	−3.18479	+	5.51622i	−0.147850	+	0.256084i
$465$		0			0
$466$	1.15358	+	6.54228i	0.0534386	+	0.303065i
$467$	5.48633	−	9.50260i	0.253877	−	0.439728i	−0.710713	−	0.703482i	$-0.751627\pi$
$467$	5.48633	−	9.50260i	0.253877	−	0.439728i	0.964590	+	0.263754i	$0.0849608\pi$
$468$	−1.53209	−	2.65366i	−0.0708208	−	0.122665i
$469$	15.6800	−	13.1571i	0.724037	−	0.607539i
$470$		0			0
$471$	0.921274	+	0.335316i	0.0424501	+	0.0154506i
$472$	5.58512	+	4.68647i	0.257076	+	0.215712i
$473$	−2.71167	+	15.3786i	−0.124683	+	0.707110i
$474$	−2.32501			−0.106791
$475$		0			0
$476$	−12.5371			−0.574639
$477$	−4.94356	+	28.0363i	−0.226350	+	1.28370i
$478$	−12.2686	−	10.2946i	−0.561151	−	0.470862i
$479$	−21.0351	−	7.65614i	−0.961117	−	0.349818i	−0.186646	−	0.982427i	$-0.559762\pi$
$479$	−21.0351	−	7.65614i	−0.961117	−	0.349818i	−0.774471	+	0.632609i	$0.781984\pi$
$480$		0			0
$481$	−5.26083	+	4.41436i	−0.239873	+	0.201278i
$482$	−4.30200	−	7.45129i	−0.195951	−	0.339397i
$483$	−1.14796	+	1.98832i	−0.0522338	+	0.0904716i
$484$	1.19207	+	6.76055i	0.0541848	+	0.307298i
$485$		0			0
$486$	−4.43969	+	7.68977i	−0.201389	+	0.348815i
$487$	−18.8803	−	32.7017i	−0.855549	−	1.48185i	−0.876135	−	0.482066i	$-0.839887\pi$
$487$	−18.8803	−	32.7017i	−0.855549	−	1.48185i	0.0205859	−	0.999788i	$-0.493447\pi$
$488$	−4.06418	+	3.41025i	−0.183977	+	0.154375i
$489$	−0.724155	+	0.263571i	−0.0327474	+	0.0119191i
$490$		0			0
$491$	−0.958578	−	0.804342i	−0.0432600	−	0.0362995i	0.620901	−	0.783889i	$-0.286767\pi$
$491$	−0.958578	−	0.804342i	−0.0432600	−	0.0362995i	−0.664161	+	0.747589i	$0.731211\pi$
$492$	−0.113341	+	0.642788i	−0.00510980	+	0.0289791i
$493$	−45.4047			−2.04492
$494$	−3.81521	−	2.63841i	−0.171654	−	0.118708i
$495$		0			0
$496$	−1.53209	+	8.68891i	−0.0687928	+	0.390143i
$497$	3.80335	+	3.19139i	0.170603	+	0.143153i
$498$	0.492726	+	0.179338i	0.0220796	+	0.00803631i
$499$	8.76739	−	3.19107i	0.392482	−	0.142852i	−0.138238	−	0.990399i	$-0.544144\pi$
$499$	8.76739	−	3.19107i	0.392482	−	0.142852i	0.530720	+	0.847547i	$0.321922\pi$
$500$		0			0
$501$	−0.680045	−	1.17787i	−0.0303822	−	0.0526234i
$502$	−9.95471	+	17.2421i	−0.444300	+	0.769551i
$503$	1.68273	+	9.54325i	0.0750294	+	0.425513i	0.999066	+	0.0432089i	$0.0137581\pi$
$503$	1.68273	+	9.54325i	0.0750294	+	0.425513i	−0.924037	+	0.382304i	$0.875131\pi$
$504$	0.879385	+	4.98724i	0.0391709	+	0.222149i
$505$		0			0
$506$	−7.94356	−	13.7587i	−0.353134	−	0.611647i
$507$	3.15729	−	2.64928i	0.140220	−	0.117659i
$508$	−20.6878	+	7.52974i	−0.917872	+	0.334078i
$509$	−27.2053	−	9.90193i	−1.20585	−	0.438895i	−0.340591	−	0.940212i	$-0.610627\pi$
$509$	−27.2053	−	9.90193i	−1.20585	−	0.438895i	−0.865264	+	0.501316i	$0.832849\pi$
$510$		0			0
$511$	−0.242163	+	1.37338i	−0.0107127	+	0.0607546i
$512$	−1.00000			−0.0441942
$513$	−0.723993	+	8.87089i	−0.0319651	+	0.391659i
$514$	26.4175			1.16522
$515$		0			0
$516$	0.982926	+	0.824773i	0.0432709	+	0.0363086i
$517$	−14.5963	−	5.31261i	−0.641943	−	0.233648i
$518$	10.6655	−	3.88192i	0.468615	−	0.170562i
$519$	2.00774	−	1.68469i	0.0881300	−	0.0739499i
$520$		0			0
$521$	1.08037	−	1.87126i	0.0473321	−	0.0819815i	−0.841389	−	0.540430i	$-0.818261\pi$
$521$	1.08037	−	1.87126i	0.0473321	−	0.0819815i	0.888721	+	0.458449i	$0.151595\pi$
$522$	3.18479	+	18.0619i	0.139395	+	0.790546i
$523$	−2.49794	−	14.1665i	−0.109227	−	0.619459i	−0.989447	−	0.144893i	$-0.953716\pi$
$523$	−2.49794	−	14.1665i	−0.109227	−	0.619459i	0.880220	−	0.474566i	$-0.157395\pi$
$524$	3.82635	−	6.62744i	0.167155	−	0.289521i
$525$		0			0
$526$	−21.4047	+	17.9606i	−0.933288	+	0.783121i
$527$	−59.1002	+	21.5107i	−2.57444	+	0.937021i
$528$	1.37939	+	0.502055i	0.0600300	+	0.0218491i
$529$	−6.79607	−	5.70258i	−0.295481	−	0.247938i
$530$		0			0
$531$	20.9932			0.911027
$532$	4.43376	+	6.25411i	0.192228	+	0.271150i
$533$	−2.00000			−0.0866296
$534$	0.718063	−	4.07234i	0.0310736	−	0.176227i
$535$		0			0
$536$	10.9363	+	3.98048i	0.472376	+	0.171931i
$537$	−3.58600	+	1.30520i	−0.154747	+	0.0563234i
$538$	−11.1702	+	9.37295i	−0.481583	+	0.404096i
$539$	8.25624	+	14.3002i	0.355622	+	0.615955i
$540$		0			0
$541$	2.24897	+	12.7545i	0.0966908	+	0.548361i	0.994216	+	0.107398i	$0.0342518\pi$
$541$	2.24897	+	12.7545i	0.0966908	+	0.548361i	−0.897525	+	0.440963i	$0.854637\pi$
$542$	3.16519	+	17.9507i	0.135957	+	0.771048i
$543$	−2.61081	+	4.52206i	−0.112041	+	0.194060i
$544$	−3.56418	−	6.17334i	−0.152813	−	0.264680i
$545$		0			0
$546$	0.610815	−	0.222318i	0.0261405	−	0.00951435i
$547$	1.31433	+	0.478377i	0.0561967	+	0.0204539i	0.369966	−	0.929045i	$-0.379369\pi$
$547$	1.31433	+	0.478377i	0.0561967	+	0.0204539i	−0.313769	+	0.949499i	$0.601592\pi$
$548$	4.39440	+	3.68734i	0.187719	+	0.157515i
$549$	−2.65270	+	15.0442i	−0.113215	+	0.642072i
$550$		0			0
$551$	16.0574	+	22.6500i	0.684067	+	0.964922i
$552$	−1.30541			−0.0555618
$553$	−2.04458	+	11.5954i	−0.0869443	+	0.493085i
$554$	−12.6159	−	10.5860i	−0.535997	−	0.449755i
$555$		0			0
$556$	18.2271	−	6.63414i	0.773003	−	0.281350i
$557$	22.7178	−	19.0625i	0.962585	−	0.807704i	−0.0187869	−	0.999824i	$-0.505980\pi$
$557$	22.7178	−	19.0625i	0.962585	−	0.807704i	0.981372	+	0.192119i	$0.0615360\pi$
$558$	12.7023	+	22.0011i	0.537733	+	0.931380i
$559$	−1.96585	+	3.40496i	−0.0831467	+	0.144014i
$560$		0			0
$561$	1.81702	+	10.3048i	0.0767146	+	0.435070i
$562$	−3.58512	+	6.20961i	−0.151229	+	0.261937i
$563$	21.0646	+	36.4850i	0.887769	+	1.53766i	0.842507	+	0.538686i	$0.181079\pi$
$563$	21.0646	+	36.4850i	0.887769	+	1.53766i	0.0452621	+	0.998975i	$0.485588\pi$
$564$	−0.977711	+	0.820397i	−0.0411691	+	0.0345450i
$565$		0			0
$566$	−19.6741	−	7.16079i	−0.826965	−	0.300991i
$567$	10.6827	+	8.96388i	0.448633	+	0.376447i
$568$	−0.490200	+	2.78006i	−0.0205683	+	0.116649i
$569$	5.08915			0.213348			0.106674	−	0.994294i	$-0.465980\pi$
$569$	5.08915			0.213348			0.106674	+	0.994294i	$0.465980\pi$
$570$		0			0
$571$	−12.6486			−0.529327			−0.264663	−	0.964341i	$-0.585261\pi$
$571$	−12.6486			−0.529327			−0.264663	+	0.964341i	$0.585261\pi$
$572$	−0.781059	+	4.42961i	−0.0326577	+	0.185211i
$573$	−1.20708	−	1.01286i	−0.0504265	−	0.0423129i
$574$	3.10607	+	1.13052i	0.129645	+	0.0471868i
$575$		0			0
$576$	−2.20574	+	1.85083i	−0.0919057	+	0.0771180i
$577$	5.00727	+	8.67285i	0.208456	+	0.361056i	0.951228	−	0.308488i	$-0.0998230\pi$
$577$	5.00727	+	8.67285i	0.208456	+	0.361056i	−0.742773	+	0.669544i	$0.766490\pi$
$578$	16.9067	−	29.2833i	0.703227	−	1.21803i
$579$	1.32651	+	7.52303i	0.0551280	+	0.312647i
$580$		0			0
$581$	1.32770	−	2.29964i	0.0550821	−	0.0954050i
$582$	0.326352	+	0.565258i	0.0135277	+	0.0234307i
$583$	32.0128	−	26.8619i	1.32583	−	1.11251i
$584$	−0.745100	+	0.271194i	−0.0308325	+	0.0112221i
$585$		0			0
$586$	7.26083	+	6.09256i	0.299942	+	0.251681i
$587$	−0.769915	+	4.36640i	−0.0317778	+	0.180221i	−0.996565	−	0.0828093i	$-0.973611\pi$
$587$	−0.769915	+	4.36640i	−0.0317778	+	0.180221i	0.964788	+	0.263030i	$0.0847219\pi$
$588$	1.35679			0.0559532
$589$	31.6313	+	21.8747i	1.30335	+	0.901331i
$590$		0			0
$591$	0.960799	−	5.44896i	0.0395220	−	0.224140i
$592$	4.94356	+	4.14814i	0.203179	+	0.170488i
$593$	−22.5758	−	8.21692i	−0.927077	−	0.337428i	−0.166026	−	0.986121i	$-0.553094\pi$
$593$	−22.5758	−	8.21692i	−0.927077	−	0.337428i	−0.761050	+	0.648693i	$0.775316\pi$
$594$	8.10994	−	2.95178i	0.332755	−	0.121113i
$595$		0			0
$596$	2.58853	+	4.48346i	0.106030	+	0.183650i
$597$	−0.568926	+	0.985408i	−0.0232846	+	0.0403301i
$598$	−0.694593	−	3.93923i	−0.0284040	−	0.161087i
$599$	−5.89992	−	33.4601i	−0.241064	−	1.36714i	−0.829458	−	0.558569i	$-0.811351\pi$
$599$	−5.89992	−	33.4601i	−0.241064	−	1.36714i	0.588394	−	0.808574i	$-0.299760\pi$
$600$		0			0
$601$	−8.07145	−	13.9802i	−0.329241	−	0.570263i	0.653120	−	0.757254i	$-0.273460\pi$
$601$	−8.07145	−	13.9802i	−0.329241	−	0.570263i	−0.982362	+	0.186991i	$0.940126\pi$
$602$	4.97771	−	4.17680i	0.202876	−	0.170233i
$603$	31.4898	−	11.4613i	1.28236	−	0.466742i
$604$	−20.8452	−	7.58705i	−0.848181	−	0.308713i
$605$		0			0
$606$	−0.147956	+	0.839100i	−0.00601030	+	0.0340861i
$607$	−8.92221			−0.362141			−0.181071	−	0.983470i	$-0.557956\pi$
$607$	−8.92221			−0.362141			−0.181071	+	0.983470i	$0.557956\pi$
$608$	−1.81908	+	3.96118i	−0.0737733	+	0.160647i
$609$	−3.89064			−0.157657
$610$		0			0
$611$	−2.99588	−	2.51384i	−0.121200	−	0.101699i
$612$	−19.2875	−	7.02006i	−0.779649	−	0.283769i
$613$	24.2713	−	8.83402i	0.980307	−	0.356803i	0.198347	−	0.980132i	$-0.436443\pi$
$613$	24.2713	−	8.83402i	0.980307	−	0.356803i	0.781960	+	0.623329i	$0.214220\pi$
$614$	1.01889	−	0.854946i	0.0411189	−	0.0345028i
$615$		0			0
$616$	3.71688	−	6.43783i	0.149757	−	0.259387i
$617$	−3.21735	−	18.2465i	−0.129526	−	0.734576i	−0.978516	−	0.206169i	$-0.933900\pi$
$617$	−3.21735	−	18.2465i	−0.129526	−	0.734576i	0.848991	−	0.528407i	$-0.177211\pi$
$618$	0.448311	+	2.54250i	0.0180337	+	0.102274i
$619$	17.6061	−	30.4946i	0.707648	−	1.22568i	−0.258080	−	0.966124i	$-0.583090\pi$
$619$	17.6061	−	30.4946i	0.707648	−	1.22568i	0.965728	−	0.259558i	$-0.0835769\pi$
$620$		0			0
$621$	−5.87939	+	4.93339i	−0.235932	+	0.197970i
$622$	7.02734	−	2.55774i	0.281771	−	0.102556i
$623$	−19.6783	−	7.16231i	−0.788394	−	0.286952i
$624$	0.283119	+	0.237565i	0.0113338	+	0.00951020i
$625$		0			0
$626$	29.2986			1.17101
$627$	4.49794	−	4.55072i	0.179630	−	0.181738i
$628$	2.82295			0.112648
$629$	−7.98814	+	45.3030i	−0.318508	+	1.80635i
$630$		0			0
$631$	1.73143	+	0.630189i	0.0689271	+	0.0250874i	0.376254	−	0.926517i	$-0.377212\pi$
$631$	1.73143	+	0.630189i	0.0689271	+	0.0250874i	−0.307326	+	0.951604i	$0.599434\pi$
$632$	−6.29086	+	2.28969i	−0.250237	+	0.0910788i
$633$	−3.05122	+	2.56028i	−0.121275	+	0.101762i
$634$	−2.80066	−	4.85088i	−0.111228	−	0.192653i
$635$		0			0
$636$	−0.596267	−	3.38160i	−0.0236435	−	0.134089i
$637$	0.721934	+	4.09429i	0.0286041	+	0.162222i
$638$	13.4611	−	23.3153i	0.532930	−	0.923062i
$639$	4.06418	+	7.03936i	0.160776	+	0.278473i
$640$		0			0
$641$	4.89945	−	1.78325i	0.193517	−	0.0704343i	−0.243444	−	0.969915i	$-0.578277\pi$
$641$	4.89945	−	1.78325i	0.193517	−	0.0704343i	0.436961	+	0.899481i	$0.356055\pi$
$642$	−0.0577812	−	0.0210306i	−0.00228044	−	0.000830012i
$643$	−4.52276	−	3.79504i	−0.178360	−	0.149662i	0.549237	−	0.835667i	$-0.314918\pi$
$643$	−4.52276	−	3.79504i	−0.178360	−	0.149662i	−0.727597	+	0.686005i	$0.759363\pi$
$644$	−1.14796	+	6.51038i	−0.0452358	+	0.256545i
$645$		0			0
$646$	−30.9372	+	2.88857i	−1.21721	+	0.113649i
$647$	42.6810			1.67796			0.838981	−	0.544160i	$-0.183152\pi$
$647$	42.6810			1.67796			0.838981	+	0.544160i	$0.183152\pi$
$648$	−1.37686	+	7.80856i	−0.0540881	+	0.306749i
$649$	−23.6065	−	19.8082i	−0.926638	−	0.777541i
$650$		0			0
$651$	−5.06418	+	1.84321i	−0.198481	+	0.0722411i
$652$	−1.69981	+	1.42631i	−0.0665696	+	0.0558585i
$653$	3.87939	+	6.71929i	0.151812	+	0.262946i	0.931894	−	0.362732i	$-0.118156\pi$
$653$	3.87939	+	6.71929i	0.151812	+	0.262946i	−0.780082	+	0.625678i	$0.784822\pi$
$654$	−0.736482	+	1.27562i	−0.0287987	+	0.0498808i
$655$		0			0
$656$	0.326352	+	1.85083i	0.0127419	+	0.0722629i
$657$	−1.14156	+	1.97724i	−0.0445365	+	0.0771394i
$658$	3.23173	+	5.59753i	0.125986	+	0.218214i
$659$	22.2049	−	18.6321i	0.864979	−	0.725803i	−0.0980561	−	0.995181i	$-0.531262\pi$
$659$	22.2049	−	18.6321i	0.864979	−	0.725803i	0.963035	+	0.269378i	$0.0868180\pi$
$660$		0			0
$661$	30.7374	+	11.1875i	1.19555	+	0.435143i	0.861668	−	0.507472i	$-0.169420\pi$
$661$	30.7374	+	11.1875i	1.19555	+	0.435143i	0.333879	+	0.942616i	$0.391642\pi$
$662$	−17.6006	−	14.7687i	−0.684067	−	0.574000i
$663$	−0.457482	+	2.59451i	−0.0177671	+	0.100762i
$664$	1.50980			0.0585916
$665$		0			0
$666$	18.5817			0.720027
$667$	−4.15745	+	23.5781i	−0.160977	+	0.912947i
$668$	−3.00000	−	2.51730i	−0.116073	−	0.0973972i
$669$	−3.65270	−	1.32948i	−0.141222	−	0.0514005i
$670$		0			0
$671$	17.1780	−	14.4140i	0.663149	−	0.556448i
$672$	−0.305407	−	0.528981i	−0.0117813	−	0.0204059i
$673$	−16.4222	+	28.4441i	−0.633030	+	1.09644i	0.353899	+	0.935284i	$0.384856\pi$
$673$	−16.4222	+	28.4441i	−0.633030	+	1.09644i	−0.986929	+	0.161156i	$0.948478\pi$
$674$	0.227864	+	1.29228i	0.00877698	+	0.0497767i
$675$		0			0
$676$	5.93376	−	10.2776i	0.228222	−	0.395291i
$677$	12.3209	+	21.3404i	0.473530	+	0.820178i	0.999541	−	0.0302996i	$-0.00964613\pi$
$677$	12.3209	+	21.3404i	0.473530	+	0.820178i	−0.526011	+	0.850478i	$0.676313\pi$
$678$	−2.77719	+	2.33034i	−0.106657	+	0.0894961i
$679$	3.10607	−	1.13052i	0.119200	−	0.0433852i
$680$		0			0
$681$	−0.903733	−	0.758322i	−0.0346311	−	0.0290590i
$682$	6.47565	−	36.7252i	0.247966	−	1.40628i
$683$	−29.9905			−1.14755			−0.573777	−	0.819011i	$-0.694523\pi$
$683$	−29.9905			−1.14755			−0.573777	+	0.819011i	$0.694523\pi$
$684$	3.31908	+	12.1041i	0.126908	+	0.462813i
$685$		0			0
$686$	3.33099	−	18.8910i	0.127178	−	0.721262i
$687$	−1.13247	−	0.950259i	−0.0432066	−	0.0362546i
$688$	3.47178	+	1.26363i	0.132360	+	0.0481753i
$689$	9.88713	−	3.59862i	0.376670	−	0.137096i
$690$		0			0
$691$	−11.2365	−	19.4622i	−0.427456	−	0.740375i	0.569190	−	0.822206i	$-0.307257\pi$
$691$	−11.2365	−	19.4622i	−0.427456	−	0.740375i	−0.996646	+	0.0818304i	$0.973923\pi$
$692$	3.77332	−	6.53558i	0.143440	−	0.248445i
$693$	−3.71688	−	21.0795i	−0.141193	−	0.800743i
$694$	0.419625	+	2.37981i	0.0159288	+	0.0903365i
$695$		0			0
$696$	−1.10607	−	1.91576i	−0.0419254	−	0.0726168i
$697$	−10.2626	+	8.61138i	−0.388725	+	0.326179i
$698$	−7.98545	+	2.90647i	−0.302254	+	0.110011i
$699$	−2.16802	−	0.789096i	−0.0820022	−	0.0298463i
$700$		0			0
$701$	−0.837496	+	4.74968i	−0.0316318	+	0.179393i	−0.996530	−	0.0832300i	$-0.973476\pi$
$701$	−0.837496	+	4.74968i	−0.0316318	+	0.179393i	0.964899	+	0.262623i	$0.0845875\pi$
$702$	2.17293			0.0820121
$703$	25.4243	−	12.0366i	0.958894	−	0.453967i
$704$	4.22668			0.159299
$705$		0			0
$706$	−2.94175	−	2.46842i	−0.110714	−	0.0929003i
$707$	4.05468	+	1.47578i	0.152492	+	0.0555026i
$708$	−2.37939	+	0.866025i	−0.0894228	+	0.0325472i
$709$	−31.6955	+	26.5957i	−1.19035	+	0.998823i	−0.190497	+	0.981688i	$0.561010\pi$
$709$	−31.6955	+	26.5957i	−1.19035	+	0.998823i	−0.999853	+	0.0171349i	$0.994546\pi$
$710$		0			0
$711$	−9.63816	+	16.6938i	−0.361459	+	0.626065i
$712$	−2.06758	−	11.7258i	−0.0774859	−	0.439444i
$713$	5.75877	+	32.6596i	0.215668	+	1.22311i
$714$	2.17705	−	3.77076i	0.0814741	−	0.141117i
$715$		0			0
$716$	−8.41740	+	7.06304i	−0.314573	+	0.263958i
$717$	5.22668	−	1.90236i	0.195194	−	0.0710448i
$718$	−22.4834	−	8.18329i	−0.839073	−	0.305398i
$719$	17.4730	+	14.6616i	0.651632	+	0.546784i	0.907566	−	0.419910i	$-0.137939\pi$
$719$	17.4730	+	14.6616i	0.651632	+	0.546784i	−0.255934	+	0.966694i	$0.582383\pi$
$720$		0			0
$721$	13.0743			0.486912
$722$	12.3819	+	14.4114i	0.460807	+	0.536337i
$723$	2.98814			0.111130
$724$	−2.61081	+	14.8067i	−0.0970302	+	0.550285i
$725$		0			0
$726$	−2.24035	−	0.815422i	−0.0831473	−	0.0302631i
$727$	8.48070	−	3.08672i	0.314532	−	0.114480i	−0.179930	−	0.983679i	$-0.557587\pi$
$727$	8.48070	−	3.08672i	0.314532	−	0.114480i	0.494462	+	0.869199i	$0.335365\pi$
$728$	1.43376	−	1.20307i	0.0531388	−	0.0445887i
$729$	10.3516	+	17.9296i	0.383394	+	0.664058i
$730$		0			0
$731$	4.57326	+	25.9363i	0.169148	+	0.959287i
$732$	−0.319955	−	1.81456i	−0.0118259	−	0.0670679i
$733$	14.4561	−	25.0386i	0.533946	−	0.924822i	−0.465267	−	0.885170i	$-0.654042\pi$
$733$	14.4561	−	25.0386i	0.533946	−	0.924822i	0.999214	−	0.0396520i	$-0.0126249\pi$
$734$	−8.55438	−	14.8166i	−0.315748	−	0.546891i
$735$		0			0
$736$	−3.53209	+	1.28558i	−0.130195	+	0.0473869i
$737$	−46.2242	−	16.8242i	−1.70269	−	0.619729i
$738$	4.14543	+	3.47843i	0.152595	+	0.128043i
$739$	−1.05685	+	5.99368i	−0.0388768	+	0.220481i	−0.998056	−	0.0623162i	$-0.980151\pi$
$739$	−1.05685	+	5.99368i	−0.0388768	+	0.220481i	0.959180	+	0.282797i	$0.0912624\pi$
$740$		0			0
$741$	1.45605	−	0.689335i	0.0534894	−	0.0253234i
$742$	−17.3892			−0.638377
$743$	5.10513	−	28.9526i	0.187289	−	1.06217i	−0.735690	−	0.677319i	$-0.763142\pi$
$743$	5.10513	−	28.9526i	0.187289	−	1.06217i	0.922979	−	0.384851i	$-0.125747\pi$
$744$	−2.34730	−	1.96962i	−0.0860561	−	0.0722096i
$745$		0			0
$746$	3.72193	−	1.35467i	0.136270	−	0.0495981i
$747$	3.33022	−	2.79439i	0.121846	−	0.102241i
$748$	15.0646	+	26.0927i	0.550818	+	0.954045i
$749$	−0.155697	+	0.269675i	−0.00568903	+	0.00985369i
$750$		0			0
$751$	−6.67736	−	37.8692i	−0.243660	−	1.38187i	−0.823584	−	0.567195i	$-0.808029\pi$
$751$	−6.67736	−	37.8692i	−0.243660	−	1.38187i	0.579924	−	0.814671i	$-0.303082\pi$
$752$	−1.83750	+	3.18264i	−0.0670066	+	0.116059i
$753$	−3.45723	−	5.98810i	−0.125989	−	0.218219i
$754$	5.19253	−	4.35705i	0.189101	−	0.158675i
$755$		0			0
$756$	−3.37464	−	1.22827i	−0.122734	−	0.0446717i
$757$	5.82295	+	4.88603i	0.211639	+	0.177586i	0.742445	−	0.669907i	$-0.233666\pi$
$757$	5.82295	+	4.88603i	0.211639	+	0.177586i	−0.530806	+	0.847493i	$0.678111\pi$
$758$	4.73917	−	26.8772i	0.172134	−	0.976223i
$759$	5.51754			0.200274
$760$		0			0
$761$	−2.89992			−0.105122			−0.0525610	−	0.998618i	$-0.516738\pi$
$761$	−2.89992			−0.105122			−0.0525610	+	0.998618i	$0.516738\pi$
$762$	1.32770	−	7.52974i	0.0480974	−	0.272774i
$763$	5.71419	+	4.79478i	0.206868	+	0.173583i
$764$	−4.26352	−	1.55179i	−0.154249	−	0.0561419i
$765$		0			0
$766$	4.90941	−	4.11949i	0.177384	−	0.148843i
$767$	−3.87939	−	6.71929i	−0.140076	−	0.242620i
$768$	0.173648	−	0.300767i	0.00626599	−	0.0108530i
$769$	−2.94521	−	16.7031i	−0.106207	−	0.602330i	−0.990731	−	0.135836i	$-0.956628\pi$
$769$	−2.94521	−	16.7031i	−0.106207	−	0.602330i	0.884524	−	0.466494i	$-0.154483\pi$
$770$		0			0
$771$	−4.58734	+	7.94551i	−0.165209	+	0.286151i
$772$	10.9979	+	19.0490i	0.395825	+	0.685588i
$773$	36.7597	−	30.8451i	1.32215	−	1.10942i	0.336311	−	0.941751i	$-0.390821\pi$
$773$	36.7597	−	30.8451i	1.32215	−	1.10942i	0.985843	−	0.167669i	$-0.0536239\pi$
$774$	9.99660	−	3.63846i	0.359320	−	0.130782i
$775$		0			0
$776$	1.43969	+	1.20805i	0.0516820	+	0.0433663i
$777$	−0.684488	+	3.88192i	−0.0245559	+	0.139263i
$778$	25.4338			0.911845
$779$	7.92514	+	2.07407i	0.283948	+	0.0743113i
$780$		0			0
$781$	2.07192	−	11.7504i	0.0741391	−	0.420464i
$782$	−20.5253	−	17.2228i	−0.733983	−	0.615885i
$783$	−12.2216	−	4.44831i	−0.436765	−	0.158970i
$784$	3.67112	−	1.33618i	0.131111	−	0.0477207i
$785$		0			0
$786$	1.32888	+	2.30168i	0.0473995	+	0.0820984i
$787$	25.2913	−	43.8059i	0.901538	−	1.56151i	0.0760408	−	0.997105i	$-0.475772\pi$
$787$	25.2913	−	43.8059i	0.901538	−	1.56151i	0.825498	−	0.564406i	$-0.190895\pi$
$788$	−2.76651	−	15.6897i	−0.0985529	−	0.558921i
$789$	−1.68510	−	9.55666i	−0.0599910	−	0.340226i
$790$		0			0
$791$	9.17974	+	15.8998i	0.326394	+	0.565331i
$792$	9.32295	−	7.82288i	0.331277	−	0.277974i
$793$	5.30541	−	1.93101i	0.188401	−	0.0685722i
$794$	−21.2199	−	7.72340i	−0.753065	−	0.274093i
$795$		0			0
$796$	−0.568926	+	3.22654i	−0.0201650	+	0.114362i
$797$	3.87702			0.137331			0.0686656	−	0.997640i	$-0.478126\pi$
$797$	3.87702			0.137331			0.0686656	+	0.997640i	$0.478126\pi$
$798$	−2.65095	+	0.247516i	−0.0938426	+	0.00876197i
$799$	−26.1967			−0.926771
$800$		0			0
$801$	−26.2631	−	22.0374i	−0.927961	−	0.778652i
$802$	0.717759	+	0.261243i	0.0253449	+	0.00922480i
$803$	3.14930	−	1.14625i	0.111136	−	0.0404503i
$804$	−3.09627	+	2.59808i	−0.109197	+	0.0916271i
$805$		0			0
$806$	4.69459	−	8.13127i	0.165360	−	0.286412i
$807$	−0.879385	−	4.98724i	−0.0309558	−	0.175559i
$808$	0.426022	+	2.41609i	0.0149874	+	0.0849978i
$809$	8.65317	−	14.9877i	0.304229	−	0.526941i	−0.672860	−	0.739770i	$-0.734934\pi$
$809$	8.65317	−	14.9877i	0.304229	−	0.526941i	0.977089	+	0.212829i	$0.0682678\pi$
$810$		0			0
$811$	37.5330	−	31.4939i	1.31796	−	1.10590i	0.331230	−	0.943550i	$-0.392536\pi$
$811$	37.5330	−	31.4939i	1.31796	−	1.10590i	0.986733	−	0.162352i	$-0.0519080\pi$
$812$	−10.5270	+	3.83153i	−0.369427	+	0.134460i
$813$	−5.94862	−	2.16512i	−0.208627	−	0.0759340i
$814$	−20.8949	−	17.5329i	−0.732365	−	0.614527i
$815$		0			0
$816$	2.47565			0.0866652
$817$	11.3209	−	11.4537i	0.396068	−	0.400715i
$818$	16.8239			0.588233
$819$	0.935822	−	5.30731i	0.0327003	−	0.185452i
$820$		0			0
$821$	26.8307	+	9.76557i	0.936398	+	0.340821i	0.764742	−	0.644336i	$-0.222866\pi$
$821$	26.8307	+	9.76557i	0.936398	+	0.340821i	0.171655	+	0.985157i	$0.445088\pi$
$822$	−1.87211	+	0.681393i	−0.0652974	+	0.0237663i
$823$	−36.0547	+	30.2535i	−1.25679	+	1.05457i	−0.260771	+	0.965401i	$0.583977\pi$
$823$	−36.0547	+	30.2535i	−1.25679	+	1.05457i	−0.996017	+	0.0891689i	$0.971579\pi$
$824$	3.71688	+	6.43783i	0.129484	+	0.224272i
$825$		0			0
$826$	2.22668	+	12.6281i	0.0774762	+	0.439389i
$827$	−4.30113	−	24.3929i	−0.149565	−	0.848224i	−0.963588	−	0.267392i	$-0.913838\pi$
$827$	−4.30113	−	24.3929i	−0.149565	−	0.848224i	0.814023	−	0.580833i	$-0.197273\pi$
$828$	−5.41147	+	9.37295i	−0.188062	+	0.325732i
$829$	17.2959	+	29.9574i	0.600712	+	1.04046i	0.992713	+	0.120499i	$0.0384494\pi$
$829$	17.2959	+	29.9574i	0.600712	+	1.04046i	−0.392002	+	0.919965i	$0.628217\pi$
$830$		0			0
$831$	5.37464	−	1.95621i	0.186444	−	0.0678601i
$832$	1.00000	+	0.363970i	0.0346688	+	0.0126184i
$833$	21.3332	+	17.9007i	0.739152	+	0.620222i
$834$	−1.16978	+	6.63414i	−0.0405061	+	0.229721i
$835$		0			0
$836$	7.68866	−	16.7427i	0.265918	−	0.579057i
$837$	−18.0155			−0.622706
$838$	−6.23277	+	35.3478i	−0.215308	+	1.22107i
$839$	5.15207	+	4.32310i	0.177869	+	0.149250i	0.727376	−	0.686239i	$-0.240740\pi$
$839$	5.15207	+	4.32310i	0.177869	+	0.149250i	−0.549506	+	0.835490i	$0.685184\pi$
$840$		0			0
$841$	−10.8738	+	3.95773i	−0.374957	+	0.136473i
$842$	−15.8648	+	13.3122i	−0.546738	+	0.458768i
$843$	−1.24510	−	2.15658i	−0.0428835	−	0.0742764i
$844$	−5.73442	+	9.93231i	−0.197387	+	0.341884i
$845$		0			0
$846$	1.83750	+	10.4210i	0.0631744	+	0.358280i
$847$	−6.03684	+	10.4561i	−0.207428	+	0.359276i
$848$	−4.94356	−	8.56250i	−0.169763	−	0.294038i
$849$	5.57011	−	4.67388i	0.191166	−	0.160407i
$850$		0			0
$851$	22.7939	+	8.29628i	0.781363	+	0.284393i
$852$	−0.751030	−	0.630189i	−0.0257299	−	0.0215899i
$853$	−3.76053	+	21.3270i	−0.128758	+	0.730223i	0.850247	+	0.526384i	$0.176453\pi$
$853$	−3.76053	+	21.3270i	−0.128758	+	0.730223i	−0.979005	+	0.203838i	$0.934658\pi$
$854$	−9.33099			−0.319300
$855$		0			0
$856$	−0.177052			−0.00605150
$857$	6.68123	−	37.8911i	0.228226	−	1.29434i	−0.628194	−	0.778057i	$-0.716206\pi$
$857$	6.68123	−	37.8911i	0.228226	−	1.29434i	0.856420	−	0.516279i	$-0.172683\pi$
$858$	−1.19665	−	1.00411i	−0.0408530	−	0.0342798i
$859$	15.5731	+	5.66815i	0.531347	+	0.193395i	0.593740	−	0.804657i	$-0.297651\pi$
$859$	15.5731	+	5.66815i	0.531347	+	0.193395i	−0.0623925	+	0.998052i	$0.519873\pi$
$860$		0			0
$861$	−0.879385	+	0.737892i	−0.0299694	+	0.0251473i
$862$	−9.16250	−	15.8699i	−0.312076	−	0.540532i
$863$	−12.9290	+	22.3937i	−0.440109	+	0.762291i	−0.997697	−	0.0678268i	$-0.978393\pi$
$863$	−12.9290	+	22.3937i	−0.440109	+	0.762291i	0.557588	+	0.830118i	$0.311727\pi$
$864$	−0.354570	−	2.01087i	−0.0120627	−	0.0684111i
$865$		0			0
$866$	−2.54664	+	4.41090i	−0.0865382	+	0.149889i
$867$	5.87164	+	10.1700i	0.199412	+	0.345391i
$868$	−11.8871	+	9.97448i	−0.403475	+	0.338556i
$869$	26.5895	−	9.67777i	0.901986	−	0.328296i
$870$		0			0
$871$	−9.48751	−	7.96097i	−0.321472	−	0.269747i
$872$	−0.736482	+	4.17680i	−0.0249404	+	0.141444i
$873$	5.41147			0.183151
$874$	−1.33275	+	16.3298i	−0.0450809	+	0.552364i
$875$		0			0
$876$	0.0478189	−	0.271194i	0.00161565	−	0.00916280i
$877$	38.7793	+	32.5397i	1.30948	+	1.09879i	0.988422	+	0.151729i	$0.0484842\pi$
$877$	38.7793	+	32.5397i	1.30948	+	1.09879i	0.321062	+	0.947058i	$0.395960\pi$
$878$	−9.68954	−	3.52670i	−0.327006	−	0.119021i
$879$	−3.09327	+	1.12586i	−0.104334	+	0.0379743i
$880$		0			0
$881$	−25.4846	−	44.1406i	−0.858597	−	1.48713i	−0.873267	−	0.487241i	$-0.838003\pi$
$881$	−25.4846	−	44.1406i	−0.858597	−	1.48713i	0.0146701	−	0.999892i	$-0.495330\pi$
$882$	5.62449	−	9.74189i	0.189386	−	0.328027i
$883$	−6.61897	−	37.5380i	−0.222746	−	1.26325i	−0.866948	−	0.498399i	$-0.833921\pi$
$883$	−6.61897	−	37.5380i	−0.222746	−	1.26325i	0.644202	−	0.764856i	$-0.277190\pi$
$884$	1.31727	+	7.47059i	0.0443045	+	0.251263i
$885$		0			0
$886$	4.40807	+	7.63500i	0.148092	+	0.256503i
$887$	24.1215	−	20.2404i	0.809922	−	0.679606i	−0.140667	−	0.990057i	$-0.544925\pi$
$887$	24.1215	−	20.2404i	0.809922	−	0.679606i	0.950589	+	0.310451i	$0.100480\pi$
$888$	−2.10607	+	0.766546i	−0.0706750	+	0.0257236i
$889$	−36.3851	−	13.2431i	−1.22032	−	0.444159i
$890$		0			0
$891$	5.81954	−	33.0043i	0.194962	−	1.10568i
$892$	−11.1925			−0.374754
$893$	9.26445	+	13.0681i	0.310023	+	0.437308i
$894$	−1.79797			−0.0601332
$895$		0			0
$896$	−1.34730	−	1.13052i	−0.0450100	−	0.0377679i
$897$	1.30541	+	0.475129i	0.0435863	+	0.0158641i
$898$	11.3486	−	4.13057i	0.378709	−	0.137839i
$899$	−43.0506	+	36.1237i	−1.43582	+	1.20479i
$900$		0			0
$901$	35.2395	−	61.0366i	1.17400	−	2.03342i
$902$	−1.37939	−	7.82288i	−0.0459285	−	0.260473i
$903$	0.391874	+	2.22243i	0.0130407	+	0.0739577i
$904$	−5.21941	+	9.04028i	−0.173595	+	0.300675i
$905$		0			0
$906$	5.90167	−	4.95209i	0.196070	−	0.164522i
$907$	8.36871	−	3.04596i	0.277878	−	0.101139i	−0.199322	−	0.979934i	$-0.563874\pi$
$907$	8.36871	−	3.04596i	0.277878	−	0.101139i	0.477200	+	0.878795i	$0.341652\pi$
$908$	−3.19207	−	1.16182i	−0.105932	−	0.0385563i
$909$	5.41147	+	4.54077i	0.179487	+	0.150608i
$910$		0			0
$911$	−44.2959			−1.46759			−0.733795	−	0.679371i	$-0.762253\pi$
$911$	−44.2959			−1.46759			−0.733795	+	0.679371i	$0.762253\pi$
$912$	−0.875515	−	1.23497i	−0.0289912	−	0.0408940i
$913$	−6.38144			−0.211195
$914$	−0.127011	+	0.720317i	−0.00420116	+	0.0238260i
$915$		0			0
$916$	−4.00000	−	1.45588i	−0.132164	−	0.0481037i
$917$	12.6477	−	4.60337i	0.417662	−	0.152017i
$918$	11.1500	−	9.35597i	0.368005	−	0.308793i
$919$	27.3969	+	47.4529i	0.903741	+	1.56533i	0.822598	+	0.568623i	$0.192524\pi$
$919$	27.3969	+	47.4529i	0.903741	+	1.56533i	0.0811431	+	0.996702i	$0.474143\pi$
$920$		0			0
$921$	0.0802124	+	0.454907i	0.00264309	+	0.0149897i
$922$	−4.00774	−	22.7290i	−0.131988	−	0.748541i
$923$	1.50206	−	2.60164i	0.0494409	−	0.0856341i
$924$	1.29086	+	2.23583i	0.0424662	+	0.0735535i
$925$		0			0
$926$	−16.9564	+	6.17161i	−0.557220	+	0.202812i
$927$	20.1138	+	7.32083i	0.660624	+	0.240448i
$928$	−4.87939	−	4.09429i	−0.160174	−	0.134402i
$929$	5.28059	−	29.9477i	0.173251	−	0.982553i	−0.766893	−	0.641775i	$-0.778198\pi$
$929$	5.28059	−	29.9477i	0.173251	−	0.982553i	0.940144	−	0.340778i	$-0.110691\pi$
$930$		0			0
$931$	1.38521	−	16.9726i	0.0453984	−	0.556254i
$932$	−6.64321			−0.217606
$933$	−0.450999	+	2.55774i	−0.0147650	+	0.0837367i
$934$	8.40554	+	7.05309i	0.275038	+	0.230784i
$935$		0			0
$936$	2.87939	−	1.04801i	0.0941157	−	0.0342553i
$937$	−22.6065	+	18.9691i	−0.738523	+	0.619695i	−0.932441	−	0.361323i	$-0.882325\pi$
$937$	−22.6065	+	18.9691i	−0.738523	+	0.619695i	0.193917	+	0.981018i	$0.437881\pi$
$938$	10.2344	+	17.7265i	0.334166	+	0.578792i
$939$	−5.08765	+	8.81207i	−0.166029	+	0.287571i
$940$		0			0
$941$	−2.34905	−	13.3221i	−0.0765769	−	0.434289i	−0.998858	−	0.0477701i	$-0.984789\pi$
$941$	−2.34905	−	13.3221i	−0.0765769	−	0.434289i	0.922281	−	0.386519i	$-0.126323\pi$
$942$	−0.490200	+	0.849051i	−0.0159716	+	0.0276636i
$943$	3.53209	+	6.11776i	0.115021	+	0.199222i
$944$	−5.58512	+	4.68647i	−0.181780	+	0.152532i
$945$		0			0
$946$	−14.6741	−	5.34094i	−0.477097	−	0.173649i
$947$	6.65002	+	5.58003i	0.216096	+	0.181326i	0.744410	−	0.667723i	$-0.232731\pi$
$947$	6.65002	+	5.58003i	0.216096	+	0.181326i	−0.528313	+	0.849049i	$0.677175\pi$
$948$	0.403733	−	2.28969i	0.0131126	−	0.0743655i
$949$	0.843807			0.0273911
$950$		0			0
$951$	1.94532			0.0630812
$952$	2.17705	−	12.3467i	0.0705587	−	0.400158i
$953$	−32.0498	−	26.8930i	−1.03820	−	0.871150i	−0.0463930	−	0.998923i	$-0.514773\pi$
$953$	−32.0498	−	26.8930i	−1.03820	−	0.871150i	−0.991803	+	0.127773i	$0.959217\pi$
$954$	−26.7520	−	9.73692i	−0.866127	−	0.315244i
$955$		0			0
$956$	12.2686	−	10.2946i	0.396794	−	0.332950i
$957$	4.67499	+	8.09732i	0.151121	+	0.261749i
$958$	11.1925	−	19.3860i	0.361614	−	0.626334i
$959$	1.75196	+	9.93588i	0.0565738	+	0.320846i
$960$		0			0
$961$	−23.4222	+	40.5685i	−0.755555	+	1.30866i
$962$	−3.43376	−	5.94745i	−0.110709	−	0.191754i
$963$	−0.390530	+	0.327693i	−0.0125846	+	0.0105598i
$964$	8.08512	−	2.94274i	0.260404	−	0.0947794i
$965$		0			0
$966$	−1.75877	−	1.47578i	−0.0565875	−	0.0474826i
$967$	2.44326	−	13.8564i	0.0785699	−	0.445592i	−0.919990	−	0.391942i	$-0.871803\pi$
$967$	2.44326	−	13.8564i	0.0785699	−	0.445592i	0.998560	−	0.0536500i	$-0.0170855\pi$
$968$	−6.86484			−0.220644
$969$	4.50340	−	9.80651i	0.144670	−	0.315030i
$970$		0			0
$971$	6.49819	−	36.8531i	0.208537	−	1.18267i	−0.683239	−	0.730194i	$-0.739429\pi$
$971$	6.49819	−	36.8531i	0.208537	−	1.18267i	0.891776	−	0.452477i	$-0.149459\pi$
$972$	−6.80200	−	5.70756i	−0.218174	−	0.183070i
$973$	32.0574	+	11.6679i	1.02771	+	0.374057i
$974$	35.4834	−	12.9149i	1.13696	−	0.413820i
$975$		0			0
$976$	−2.65270	−	4.59462i	−0.0849110	−	0.147070i
$977$	24.8769	−	43.0881i	0.795883	−	1.37851i	−0.126394	−	0.991980i	$-0.540340\pi$
$977$	24.8769	−	43.0881i	0.795883	−	1.37851i	0.922277	−	0.386530i	$-0.126326\pi$
$978$	−0.133819	−	0.758922i	−0.00427904	−	0.0242677i
$979$	8.73901	+	49.5614i	0.279300	+	1.58399i
$980$		0			0
$981$	6.10607	+	10.5760i	0.194952	+	0.337666i
$982$	0.958578	−	0.804342i	0.0305894	−	0.0256676i
$983$	−21.0300	+	7.65430i	−0.670754	+	0.244134i	−0.654872	−	0.755739i	$-0.727278\pi$
$983$	−21.0300	+	7.65430i	−0.670754	+	0.244134i	−0.0158814	+	0.999874i	$0.505055\pi$
$984$	−0.613341	−	0.223238i	−0.0195526	−	0.00711656i
$985$		0			0
$986$	7.88444	−	44.7149i	0.251092	−	1.42401i
$987$	−2.24474			−0.0714508
$988$	3.26083	−	3.29909i	0.103741	−	0.104958i
$989$	13.8871			0.441585
$990$		0			0
$991$	36.8803	+	30.9463i	1.17154	+	0.983040i	0.999998	−	0.00213601i	$-0.000679914\pi$
$991$	36.8803	+	30.9463i	1.17154	+	0.983040i	0.171544	+	0.985176i	$0.445124\pi$
$992$	−8.29086	−	3.01763i	−0.263235	−	0.0958097i
$993$	7.49825	−	2.72914i	0.237950	−	0.0866066i
$994$	−3.80335	+	3.19139i	−0.120635	+	0.101225i
$995$		0			0
$996$	−0.262174	+	0.454099i	−0.00830730	+	0.0143887i
$997$	7.40642	+	42.0039i	0.234564	+	1.33028i	0.843530	+	0.537081i	$0.180473\pi$
$997$	7.40642	+	42.0039i	0.234564	+	1.33028i	−0.608967	+	0.793196i	$0.708416\pi$
$998$	1.62015	+	9.18832i	0.0512849	+	0.290851i
$999$	−6.58853	+	11.4117i	−0.208452	+	0.361049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.d.701.1		6
5.2	odd	4		950.2.u.b.549.1		12
5.3	odd	4		950.2.u.b.549.2		12
5.4	even	2		38.2.e.a.17.1	yes	6
15.14	odd	2		342.2.u.c.55.1		6
19.9	even	9	inner	950.2.l.d.351.1		6
20.19	odd	2		304.2.u.c.17.1		6
95.4	even	18		722.2.e.b.595.1		6
95.9	even	18		38.2.e.a.9.1	✓	6
95.14	odd	18		722.2.c.l.653.2		6
95.24	even	18		722.2.c.k.653.2		6
95.28	odd	36		950.2.u.b.199.1		12
95.29	odd	18		722.2.e.k.389.1		6
95.34	odd	18		722.2.e.l.595.1		6
95.44	even	18		722.2.e.m.99.1		6
95.47	odd	36		950.2.u.b.199.2		12
95.49	even	6		722.2.e.m.423.1		6
95.54	even	18		722.2.a.l.1.2		3
95.59	odd	18		722.2.c.l.429.2		6
95.64	even	6		722.2.e.b.415.1		6
95.69	odd	6		722.2.e.l.415.1		6
95.74	even	18		722.2.c.k.429.2		6
95.79	odd	18		722.2.a.k.1.2		3
95.84	odd	6		722.2.e.a.423.1		6
95.89	odd	18		722.2.e.a.99.1		6
95.94	odd	2		722.2.e.k.245.1		6
285.104	odd	18		342.2.u.c.199.1		6
285.149	odd	18		6498.2.a.bl.1.1		3
285.269	even	18		6498.2.a.bq.1.1		3
380.79	even	18		5776.2.a.bo.1.2		3
380.199	odd	18		304.2.u.c.161.1		6
380.339	odd	18		5776.2.a.bn.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.e.a.9.1	✓	6	95.9	even	18
38.2.e.a.17.1	yes	6	5.4	even	2
304.2.u.c.17.1		6	20.19	odd	2
304.2.u.c.161.1		6	380.199	odd	18
342.2.u.c.55.1		6	15.14	odd	2
342.2.u.c.199.1		6	285.104	odd	18
722.2.a.k.1.2		3	95.79	odd	18
722.2.a.l.1.2		3	95.54	even	18
722.2.c.k.429.2		6	95.74	even	18
722.2.c.k.653.2		6	95.24	even	18
722.2.c.l.429.2		6	95.59	odd	18
722.2.c.l.653.2		6	95.14	odd	18
722.2.e.a.99.1		6	95.89	odd	18
722.2.e.a.423.1		6	95.84	odd	6
722.2.e.b.415.1		6	95.64	even	6
722.2.e.b.595.1		6	95.4	even	18
722.2.e.k.245.1		6	95.94	odd	2
722.2.e.k.389.1		6	95.29	odd	18
722.2.e.l.415.1		6	95.69	odd	6
722.2.e.l.595.1		6	95.34	odd	18
722.2.e.m.99.1		6	95.44	even	18
722.2.e.m.423.1		6	95.49	even	6
950.2.l.d.351.1		6	19.9	even	9	inner
950.2.l.d.701.1		6	1.1	even	1	trivial
950.2.u.b.199.1		12	95.28	odd	36
950.2.u.b.199.2		12	95.47	odd	36
950.2.u.b.549.1		12	5.2	odd	4
950.2.u.b.549.2		12	5.3	odd	4
5776.2.a.bn.1.2		3	380.339	odd	18
5776.2.a.bo.1.2		3	380.79	even	18
6498.2.a.bl.1.1		3	285.149	odd	18
6498.2.a.bq.1.1		3	285.269	even	18

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.266044 - 0.223238i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.266044 - 0.223238i) q^{6} +(-0.879385 - 1.52314i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.500000 - 2.83564i) q^{9} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.266044 - 0.223238i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.266044 - 0.223238i) q^{6} +(-0.879385 - 1.52314i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.500000 - 2.83564i) q^{9} +(-2.11334 + 3.66041i) q^{11} +(0.173648 + 0.300767i) q^{12} +(-0.815207 + 0.684040i) q^{13} +(1.65270 - 0.601535i) q^{14} +(0.766044 + 0.642788i) q^{16} +(-1.23783 + 7.02006i) q^{17} +2.87939 q^{18} +(3.93969 - 1.86516i) q^{19} +(-0.106067 + 0.601535i) q^{21} +(-3.23783 - 2.71686i) q^{22} +(3.53209 + 1.28558i) q^{23} +(-0.326352 + 0.118782i) q^{24} +(-0.532089 - 0.921605i) q^{26} +(-1.02094 + 1.76833i) q^{27} +(0.305407 + 1.73205i) q^{28} +(1.10607 + 6.27282i) q^{29} +(4.41147 + 7.64090i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(1.37939 - 0.502055i) q^{33} +(-6.69846 - 2.43804i) q^{34} +(-0.500000 + 2.83564i) q^{36} +6.45336 q^{37} +(1.15270 + 4.20372i) q^{38} +0.369585 q^{39} +(1.43969 + 1.20805i) q^{41} +(-0.573978 - 0.208911i) q^{42} +(3.47178 - 1.26363i) q^{43} +(3.23783 - 2.71686i) q^{44} +(-1.87939 + 3.25519i) q^{46} +(0.638156 + 3.61916i) q^{47} +(-0.0603074 - 0.342020i) q^{48} +(1.95336 - 3.38332i) q^{49} +(1.89646 - 1.59132i) q^{51} +(1.00000 - 0.363970i) q^{52} +(-9.29086 - 3.38160i) q^{53} +(-1.56418 - 1.31250i) q^{54} -1.75877 q^{56} +(-1.46451 - 0.383273i) q^{57} -6.36959 q^{58} +(-1.26604 + 7.18009i) q^{59} +(-4.98545 - 1.81456i) q^{61} +(-8.29086 + 3.01763i) q^{62} +(-3.87939 + 3.25519i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.254900 + 1.44561i) q^{66} +(2.02094 + 11.4613i) q^{67} +(3.56418 - 6.17334i) q^{68} +(-0.652704 - 1.13052i) q^{69} +(-2.65270 + 0.965505i) q^{71} +(-2.70574 - 0.984808i) q^{72} +(-0.607411 - 0.509678i) q^{73} +(-1.12061 + 6.35532i) q^{74} +(-4.34002 + 0.405223i) q^{76} +7.43376 q^{77} +(-0.0641778 + 0.363970i) q^{78} +(-5.12836 - 4.30320i) q^{79} +(-7.45084 + 2.71188i) q^{81} +(-1.43969 + 1.20805i) q^{82} +(0.754900 + 1.30753i) q^{83} +(0.305407 - 0.528981i) q^{84} +(0.641559 + 3.63846i) q^{86} +(1.10607 - 1.91576i) q^{87} +(2.11334 + 3.66041i) q^{88} +(9.12108 - 7.65350i) q^{89} +(1.75877 + 0.640140i) q^{91} +(-2.87939 - 2.41609i) q^{92} +(0.532089 - 3.01763i) q^{93} -3.67499 q^{94} +0.347296 q^{96} +(-0.326352 + 1.85083i) q^{97} +(2.99273 + 2.51120i) q^{98} +(11.4363 + 4.16247i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 3 q^{6} + 6 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 - 3 * q^6 + 6 * q^7 + 3 * q^8 - 3 * q^9	\( 6 q + 3 q^{3} - 3 q^{6} + 6 q^{7} + 3 q^{8} - 3 q^{9} - 6 q^{11} - 12 q^{13} + 12 q^{14} + 12 q^{17} + 6 q^{18} + 18 q^{19} + 24 q^{21} + 12 q^{23} - 3 q^{24} + 6 q^{26} - 3 q^{27} + 6 q^{28} - 18 q^{29} + 6 q^{31} - 3 q^{33} - 12 q^{34} - 3 q^{36} + 12 q^{37} + 9 q^{38} - 12 q^{39} + 3 q^{41} + 12 q^{42} + 6 q^{43} - 30 q^{47} - 6 q^{48} - 15 q^{49} + 21 q^{51} + 6 q^{52} - 24 q^{53} + 9 q^{54} + 12 q^{56} + 24 q^{57} - 24 q^{58} - 3 q^{59} + 6 q^{61} - 18 q^{62} - 12 q^{63} - 3 q^{64} + 3 q^{66} + 9 q^{67} + 3 q^{68} - 6 q^{69} - 18 q^{71} - 6 q^{72} + 30 q^{73} - 18 q^{74} - 6 q^{76} + 12 q^{77} + 18 q^{78} + 6 q^{79} - 33 q^{81} - 3 q^{82} + 6 q^{83} + 6 q^{84} + 12 q^{86} - 18 q^{87} + 6 q^{88} - 12 q^{91} - 6 q^{92} - 6 q^{93} - 12 q^{94} - 3 q^{97} + 21 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 - 3 * q^6 + 6 * q^7 + 3 * q^8 - 3 * q^9 - 6 * q^11 - 12 * q^13 + 12 * q^14 + 12 * q^17 + 6 * q^18 + 18 * q^19 + 24 * q^21 + 12 * q^23 - 3 * q^24 + 6 * q^26 - 3 * q^27 + 6 * q^28 - 18 * q^29 + 6 * q^31 - 3 * q^33 - 12 * q^34 - 3 * q^36 + 12 * q^37 + 9 * q^38 - 12 * q^39 + 3 * q^41 + 12 * q^42 + 6 * q^43 - 30 * q^47 - 6 * q^48 - 15 * q^49 + 21 * q^51 + 6 * q^52 - 24 * q^53 + 9 * q^54 + 12 * q^56 + 24 * q^57 - 24 * q^58 - 3 * q^59 + 6 * q^61 - 18 * q^62 - 12 * q^63 - 3 * q^64 + 3 * q^66 + 9 * q^67 + 3 * q^68 - 6 * q^69 - 18 * q^71 - 6 * q^72 + 30 * q^73 - 18 * q^74 - 6 * q^76 + 12 * q^77 + 18 * q^78 + 6 * q^79 - 33 * q^81 - 3 * q^82 + 6 * q^83 + 6 * q^84 + 12 * q^86 - 18 * q^87 + 6 * q^88 - 12 * q^91 - 6 * q^92 - 6 * q^93 - 12 * q^94 - 3 * q^97 + 21 * q^99

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