LMFDB - Embedded newform 38.2.e.a.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,2,Mod(5,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	38.e (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:	$0.303431527681$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			9.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	38.9
Dual form			38.2.e.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(0.266044 - 0.223238i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.87939 - 0.684040i) q^{5} +(0.266044 + 0.223238i) q^{6} +(0.879385 - 1.52314i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.500000 + 2.83564i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(0.266044 - 0.223238i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.87939 - 0.684040i) q^{5} +(0.266044 + 0.223238i) q^{6} +(0.879385 - 1.52314i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.500000 + 2.83564i) q^{9} +(0.347296 - 1.96962i) q^{10} +(-2.11334 - 3.66041i) q^{11} +(-0.173648 + 0.300767i) q^{12} +(0.815207 + 0.684040i) q^{13} +(1.65270 + 0.601535i) q^{14} +(-0.652704 + 0.237565i) q^{15} +(0.766044 - 0.642788i) q^{16} +(1.23783 + 7.02006i) q^{17} -2.87939 q^{18} +(3.93969 + 1.86516i) q^{19} +2.00000 q^{20} +(-0.106067 - 0.601535i) q^{21} +(3.23783 - 2.71686i) q^{22} +(-3.53209 + 1.28558i) q^{23} +(-0.326352 - 0.118782i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(-0.532089 + 0.921605i) q^{26} +(1.02094 + 1.76833i) q^{27} +(-0.305407 + 1.73205i) q^{28} +(1.10607 - 6.27282i) q^{29} +(-0.347296 - 0.601535i) q^{30} +(4.41147 - 7.64090i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-1.37939 - 0.502055i) q^{33} +(-6.69846 + 2.43804i) q^{34} +(-2.69459 + 2.26103i) q^{35} +(-0.500000 - 2.83564i) q^{36} -6.45336 q^{37} +(-1.15270 + 4.20372i) q^{38} +0.369585 q^{39} +(0.347296 + 1.96962i) q^{40} +(1.43969 - 1.20805i) q^{41} +(0.573978 - 0.208911i) q^{42} +(-3.47178 - 1.26363i) q^{43} +(3.23783 + 2.71686i) q^{44} +(2.87939 - 4.98724i) q^{45} +(-1.87939 - 3.25519i) q^{46} +(-0.638156 + 3.61916i) q^{47} +(0.0603074 - 0.342020i) q^{48} +(1.95336 + 3.38332i) q^{49} +(0.500000 - 0.866025i) q^{50} +(1.89646 + 1.59132i) q^{51} +(-1.00000 - 0.363970i) q^{52} +(9.29086 - 3.38160i) q^{53} +(-1.56418 + 1.31250i) q^{54} +(1.46791 + 8.32494i) q^{55} -1.75877 q^{56} +(1.46451 - 0.383273i) q^{57} +6.36959 q^{58} +(-1.26604 - 7.18009i) q^{59} +(0.532089 - 0.446476i) q^{60} +(-4.98545 + 1.81456i) q^{61} +(8.29086 + 3.01763i) q^{62} +(3.87939 + 3.25519i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.06418 - 1.84321i) q^{65} +(0.254900 - 1.44561i) q^{66} +(-2.02094 + 11.4613i) q^{67} +(-3.56418 - 6.17334i) q^{68} +(-0.652704 + 1.13052i) q^{69} +(-2.69459 - 2.26103i) q^{70} +(-2.65270 - 0.965505i) q^{71} +(2.70574 - 0.984808i) q^{72} +(0.607411 - 0.509678i) q^{73} +(-1.12061 - 6.35532i) q^{74} -0.347296 q^{75} +(-4.34002 - 0.405223i) q^{76} -7.43376 q^{77} +(0.0641778 + 0.363970i) q^{78} +(-5.12836 + 4.30320i) q^{79} +(-1.87939 + 0.684040i) q^{80} +(-7.45084 - 2.71188i) q^{81} +(1.43969 + 1.20805i) q^{82} +(-0.754900 + 1.30753i) q^{83} +(0.305407 + 0.528981i) q^{84} +(2.47565 - 14.0401i) q^{85} +(0.641559 - 3.63846i) q^{86} +(-1.10607 - 1.91576i) q^{87} +(-2.11334 + 3.66041i) q^{88} +(9.12108 + 7.65350i) q^{89} +(5.41147 + 1.96962i) q^{90} +(1.75877 - 0.640140i) q^{91} +(2.87939 - 2.41609i) q^{92} +(-0.532089 - 3.01763i) q^{93} -3.67499 q^{94} +(-6.12836 - 6.20026i) q^{95} +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} - 6 q^{15} - 12 q^{17} - 6 q^{18} + 18 q^{19} + 12 q^{20} + 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} - 12 q^{35} - 3 q^{36} - 12 q^{37} - 9 q^{38} - 12 q^{39} + 3 q^{41} - 12 q^{42} - 6 q^{43} + 6 q^{45} + 30 q^{47} + 6 q^{48} - 15 q^{49} + 3 q^{50} + 21 q^{51} - 6 q^{52} + 24 q^{53} + 9 q^{54} + 18 q^{55} + 12 q^{56} - 24 q^{57} + 24 q^{58} - 3 q^{59} - 6 q^{60} + 6 q^{61} + 18 q^{62} + 12 q^{63} - 3 q^{64} + 12 q^{65} + 3 q^{66} - 9 q^{67} - 3 q^{68} - 6 q^{69} - 12 q^{70} - 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} - 24 q^{85} + 12 q^{86} + 18 q^{87} - 6 q^{88} + 12 q^{90} - 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 - 6 * q^15 - 12 * q^17 - 6 * q^18 + 18 * q^19 + 12 * q^20 + 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 - 12 * q^35 - 3 * q^36 - 12 * q^37 - 9 * q^38 - 12 * q^39 + 3 * q^41 - 12 * q^42 - 6 * q^43 + 6 * q^45 + 30 * q^47 + 6 * q^48 - 15 * q^49 + 3 * q^50 + 21 * q^51 - 6 * q^52 + 24 * q^53 + 9 * q^54 + 18 * q^55 + 12 * q^56 - 24 * q^57 + 24 * q^58 - 3 * q^59 - 6 * q^60 + 6 * q^61 + 18 * q^62 + 12 * q^63 - 3 * q^64 + 12 * q^65 + 3 * q^66 - 9 * q^67 - 3 * q^68 - 6 * q^69 - 12 * q^70 - 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 - 24 * q^85 + 12 * q^86 + 18 * q^87 - 6 * q^88 + 12 * q^90 - 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 $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	0.173648	+	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	$-0.690256\pi$
$3$	0.266044	−	0.223238i	0.153601	−	0.128886i	0.716349	+	0.697742i	$0.245812\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−1.87939	−	0.684040i	−0.840487	−	0.305912i	−0.114331	−	0.993443i	$-0.536473\pi$
$5$	−1.87939	−	0.684040i	−0.840487	−	0.305912i	−0.726155	+	0.687531i	$0.758695\pi$
$6$	0.266044	+	0.223238i	0.108612	+	0.0911364i
$7$	0.879385	−	1.52314i	0.332376	−	0.575693i	−0.650601	−	0.759420i	$-0.725483\pi$
$7$	0.879385	−	1.52314i	0.332376	−	0.575693i	0.982977	+	0.183727i	$0.0588162\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−0.500000	+	2.83564i	−0.166667	+	0.945214i
$10$	0.347296	−	1.96962i	0.109825	−	0.622847i
$11$	−2.11334	−	3.66041i	−0.637196	−	1.10366i	−0.986045	−	0.166477i	$-0.946761\pi$
$11$	−2.11334	−	3.66041i	−0.637196	−	1.10366i	0.348849	−	0.937179i	$-0.386573\pi$
$12$	−0.173648	+	0.300767i	−0.0501279	+	0.0868241i
$13$	0.815207	+	0.684040i	0.226098	+	0.189719i	0.748799	−	0.662798i	$-0.230631\pi$
$13$	0.815207	+	0.684040i	0.226098	+	0.189719i	−0.522701	+	0.852516i	$0.675075\pi$
$14$	1.65270	+	0.601535i	0.441704	+	0.160767i
$15$	−0.652704	+	0.237565i	−0.168527	+	0.0613389i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	1.23783	+	7.02006i	0.300217	+	1.70261i	0.645207	+	0.764008i	$0.276771\pi$
$17$	1.23783	+	7.02006i	0.300217	+	1.70261i	−0.344990	+	0.938606i	$0.612118\pi$
$18$	−2.87939			−0.678678
$19$	3.93969	+	1.86516i	0.903827	+	0.427897i
$19$	3.93969	+	1.86516i	0.903827	+	0.427897i
$20$	2.00000			0.447214
$21$	−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	$-0.739286\pi$
$23$	−3.53209	+	1.28558i	−0.736491	+	0.268061i	−0.0535814	+	0.998563i	$0.517064\pi$
$24$	−0.326352	−	0.118782i	−0.0666163	−	0.0242463i
$25$	−0.766044	−	0.642788i	−0.153209	−	0.128558i
$26$	−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	−0.691431	−	0.722442i	$-0.743019\pi$
$29$	1.10607	−	6.27282i	0.205391	−	1.16483i	0.896823	−	0.442390i	$-0.145869\pi$
$30$	−0.347296	−	0.601535i	−0.0634073	−	0.109825i
$31$	4.41147	−	7.64090i	0.792324	−	1.37235i	−0.132200	−	0.991223i	$-0.542204\pi$
$31$	4.41147	−	7.64090i	0.792324	−	1.37235i	0.924524	−	0.381123i	$-0.124462\pi$
$32$	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
$35$	−2.69459	+	2.26103i	−0.455469	+	0.382184i
$36$	−0.500000	−	2.83564i	−0.0833333	−	0.472607i
$37$	−6.45336			−1.06093			−0.530463	−	0.847708i	$-0.677982\pi$
$37$	−6.45336			−1.06093			−0.530463	+	0.847708i	$0.677982\pi$
$38$	−1.15270	+	4.20372i	−0.186993	+	0.681934i
$39$	0.369585			0.0591810
$40$	0.347296	+	1.96962i	0.0549124	+	0.311424i
$41$	1.43969	−	1.20805i	0.224842	−	0.188665i	−0.523407	−	0.852083i	$-0.675339\pi$
$41$	1.43969	−	1.20805i	0.224842	−	0.188665i	0.748249	+	0.663418i	$0.230895\pi$
$42$	0.573978	−	0.208911i	0.0885667	−	0.0322357i
$43$	−3.47178	−	1.26363i	−0.529442	−	0.192701i	0.0634473	−	0.997985i	$-0.479791\pi$
$43$	−3.47178	−	1.26363i	−0.529442	−	0.192701i	−0.592889	+	0.805284i	$0.702013\pi$
$44$	3.23783	+	2.71686i	0.488121	+	0.409582i
$45$	2.87939	−	4.98724i	0.429233	−	0.743454i
$46$	−1.87939	−	3.25519i	−0.277100	−	0.479952i
$47$	−0.638156	+	3.61916i	−0.0930846	+	0.527909i	0.902233	+	0.431249i	$0.141927\pi$
$47$	−0.638156	+	3.61916i	−0.0930846	+	0.527909i	−0.995317	+	0.0966598i	$0.969184\pi$
$48$	0.0603074	−	0.342020i	0.00870462	−	0.0493664i
$49$	1.95336	+	3.38332i	0.279052	+	0.483332i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	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	$-0.373503\pi$
$53$	9.29086	−	3.38160i	1.27620	−	0.464498i	0.889173	+	0.457571i	$0.151281\pi$
$54$	−1.56418	+	1.31250i	−0.212858	+	0.178609i
$55$	1.46791	+	8.32494i	0.197933	+	1.12253i
$56$	−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	−0.949245	−	0.314538i	$-0.898150\pi$
$59$	−1.26604	−	7.18009i	−0.164825	−	0.934769i	0.784420	−	0.620230i	$-0.212961\pi$
$60$	0.532089	−	0.446476i	0.0686924	−	0.0576398i
$61$	−4.98545	+	1.81456i	−0.638322	+	0.232330i	−0.640849	−	0.767667i	$-0.721418\pi$
$61$	−4.98545	+	1.81456i	−0.638322	+	0.232330i	0.00252758	+	0.999997i	$0.499195\pi$
$62$	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
$65$	−1.06418	−	1.84321i	−0.131995	−	0.228622i
$66$	0.254900	−	1.44561i	0.0313760	−	0.177942i
$67$	−2.02094	+	11.4613i	−0.246898	+	1.40023i	0.569146	+	0.822236i	$0.307274\pi$
$67$	−2.02094	+	11.4613i	−0.246898	+	1.40023i	−0.816044	+	0.577990i	$0.803837\pi$
$68$	−3.56418	−	6.17334i	−0.432220	−	0.748627i
$69$	−0.652704	+	1.13052i	−0.0785763	+	0.136098i
$70$	−2.69459	−	2.26103i	−0.322065	−	0.270245i
$71$	−2.65270	−	0.965505i	−0.314818	−	0.114584i	0.179778	−	0.983707i	$-0.442462\pi$
$71$	−2.65270	−	0.965505i	−0.314818	−	0.114584i	−0.494596	+	0.869123i	$0.664684\pi$
$72$	2.70574	−	0.984808i	0.318874	−	0.116061i
$73$	0.607411	−	0.509678i	0.0710921	−	0.0596533i	−0.606549	−	0.795046i	$-0.707447\pi$
$73$	0.607411	−	0.509678i	0.0710921	−	0.0596533i	0.677641	+	0.735393i	$0.263002\pi$
$74$	−1.12061	−	6.35532i	−0.130269	−	0.738791i
$75$	−0.347296			−0.0401023
$76$	−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	−0.883955	−	0.467571i	$-0.845129\pi$
$79$	−5.12836	+	4.30320i	−0.576985	+	0.484148i	0.306970	+	0.951719i	$0.400685\pi$
$80$	−1.87939	+	0.684040i	−0.210122	+	0.0764780i
$81$	−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	$-0.859739\pi$
$83$	−0.754900	+	1.30753i	−0.0828610	+	0.143520i	0.821617	+	0.570040i	$0.193072\pi$
$84$	0.305407	+	0.528981i	0.0333227	+	0.0577166i
$85$	2.47565	−	14.0401i	0.268522	−	1.52286i
$86$	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	0.982051	−	0.188615i	$-0.0603999\pi$
$89$	9.12108	+	7.65350i	0.966833	+	0.811269i	−0.0152184	+	0.999884i	$0.504844\pi$
$90$	5.41147	+	1.96962i	0.570419	+	0.207616i
$91$	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
$95$	−6.12836	−	6.20026i	−0.628756	−	0.636134i
$96$	0.347296			0.0354458
$97$	0.326352	+	1.85083i	0.0331360	+	0.187924i	0.996883	−	0.0788942i	$-0.0251389\pi$
$97$	0.326352	+	1.85083i	0.0331360	+	0.187924i	−0.963747	+	0.266818i	$0.914028\pi$
$98$	−2.99273	+	2.51120i	−0.302311	+	0.253669i
$99$	11.4363	−	4.16247i	1.14939	−	0.418344i
$100$	0.939693	+	0.342020i	0.0939693	+	0.0342020i
$101$	−1.87939	−	1.57699i	−0.187006	−	0.156917i	0.544478	−	0.838775i	$-0.316728\pi$
$101$	−1.87939	−	1.57699i	−0.187006	−	0.156917i	−0.731484	+	0.681858i	$0.761172\pi$
$102$	−1.23783	+	2.14398i	−0.122563	+	0.212285i
$103$	3.71688	+	6.43783i	0.366235	+	0.634338i	0.988974	−	0.148092i	$-0.0473132\pi$
$103$	3.71688	+	6.43783i	0.366235	+	0.634338i	−0.622738	+	0.782430i	$0.713980\pi$
$104$	0.184793	−	1.04801i	0.0181204	−	0.102766i
$105$	−0.212134	+	1.20307i	−0.0207021	+	0.117408i
$106$	4.94356	+	8.56250i	0.480161	+	0.831664i
$107$	0.0885259	−	0.153331i	0.00855812	−	0.0148231i	−0.861715	−	0.507393i	$-0.830609\pi$
$107$	0.0885259	−	0.153331i	0.00855812	−	0.0148231i	0.870273	+	0.492570i	$0.163942\pi$
$108$	−1.56418	−	1.31250i	−0.150513	−	0.126295i
$109$	−3.98545	−	1.45059i	−0.381737	−	0.138941i	0.144022	−	0.989574i	$-0.453996\pi$
$109$	−3.98545	−	1.45059i	−0.381737	−	0.138941i	−0.525759	+	0.850634i	$0.676219\pi$
$110$	−7.94356	+	2.89122i	−0.757389	+	0.275667i
$111$	−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	$-0.336631\pi$
$113$	10.4388			0.982001			0.491001	+	0.871159i	$0.336631\pi$
$114$	0.631759	+	1.37570i	0.0591697	+	0.128846i
$115$	7.51754			0.701014
$116$	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
$120$	0.532089	+	0.446476i	0.0485728	+	0.0407575i
$121$	−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
$125$	6.00000	+	10.3923i	0.536656	+	0.929516i
$126$	−2.53209	+	4.38571i	−0.225576	+	0.390710i
$127$	−16.8648	−	14.1513i	−1.49651	−	1.25572i	−0.885973	−	0.463737i	$-0.846508\pi$
$127$	−16.8648	−	14.1513i	−1.49651	−	1.25572i	−0.610539	−	0.791986i	$-0.709047\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	−1.20574	+	0.438852i	−0.106159	+	0.0386388i
$130$	1.63041	−	1.36808i	0.142997	−	0.119989i
$131$	−1.32888	−	7.53644i	−0.116105	−	0.658462i	−0.986197	−	0.165574i	$-0.947052\pi$
$131$	−1.32888	−	7.53644i	−0.116105	−	0.658462i	0.870093	−	0.492888i	$-0.164059\pi$
$132$	1.46791			0.127765
$133$	6.30541	−	4.36051i	0.546748	−	0.378104i
$134$	−11.6382			−1.00538
$135$	−0.709141	−	4.02174i	−0.0610331	−	0.346136i
$136$	5.46064	−	4.58202i	0.468246	−	0.392905i
$137$	5.39053	−	1.96199i	0.460544	−	0.167624i	−0.101320	−	0.994854i	$-0.532307\pi$
$137$	5.39053	−	1.96199i	0.460544	−	0.167624i	0.561864	+	0.827230i	$0.310084\pi$
$138$	−1.22668	−	0.446476i	−0.104422	−	0.0380065i
$139$	−14.8589	−	12.4681i	−1.26032	−	1.05753i	−0.995648	−	0.0931911i	$-0.970293\pi$
$139$	−14.8589	−	12.4681i	−1.26032	−	1.05753i	−0.264668	−	0.964340i	$-0.585262\pi$
$140$	1.75877	−	3.04628i	0.148643	−	0.257458i
$141$	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
$145$	−6.36959	+	11.0324i	−0.528965	+	0.916195i
$146$	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	−0.790616	−	0.612312i	$-0.790240\pi$
$149$	−3.96585	+	3.32774i	−0.324895	+	0.272619i	0.465721	+	0.884932i	$0.345795\pi$
$150$	−0.0603074	−	0.342020i	−0.00492408	−	0.0279258i
$151$	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
$155$	−13.5175	+	11.3426i	−1.08576	+	0.911057i
$156$	−0.347296	+	0.126406i	−0.0278060	+	0.0101205i
$157$	2.65270	+	0.965505i	0.211709	+	0.0770557i	0.445698	−	0.895184i	$-0.352956\pi$
$157$	2.65270	+	0.965505i	0.211709	+	0.0770557i	−0.233989	+	0.972239i	$0.575178\pi$
$158$	−5.12836	−	4.30320i	−0.407990	−	0.342344i
$159$	1.71688	−	2.97373i	0.136158	−	0.235832i
$160$	−1.00000	−	1.73205i	−0.0790569	−	0.136931i
$161$	−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	$-0.194363\pi$
$163$	−1.10947	−	1.92166i	−0.0869004	−	0.150516i	−0.906199	+	0.422851i	$0.861030\pi$
$164$	−0.939693	+	1.62760i	−0.0733777	+	0.127094i
$165$	2.24897	+	1.88711i	0.175082	+	0.146911i
$166$	−1.41875	−	0.516382i	−0.110116	−	0.0400790i
$167$	−3.68004	+	1.33943i	−0.284770	+	0.103648i	−0.480456	−	0.877019i	$-0.659529\pi$
$167$	−3.68004	+	1.33943i	−0.284770	+	0.103648i	0.195686	+	0.980667i	$0.437307\pi$
$168$	−0.467911	+	0.392624i	−0.0361001	+	0.0302916i
$169$	−2.06077	−	11.6872i	−0.158521	−	0.899018i
$170$	14.2567			1.09344
$171$	−7.25877	+	10.2390i	−0.555092	+	0.782994i
$172$	3.69459			0.281710
$173$	1.31046	+	7.43199i	0.0996324	+	0.565043i	0.993229	+	0.116173i	$0.0370626\pi$
$173$	1.31046	+	7.43199i	0.0996324	+	0.565043i	−0.893597	+	0.448871i	$0.851826\pi$
$174$	1.69459	−	1.42193i	0.128467	−	0.107796i
$175$	−1.65270	+	0.601535i	−0.124933	+	0.0454718i
$176$	−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	0.994961	−	0.100267i	$-0.0319698\pi$
$179$	5.49407	+	9.51601i	0.410646	+	0.711260i	−0.584314	+	0.811527i	$0.698637\pi$
$180$	−1.00000	+	5.67128i	−0.0745356	+	0.422712i
$181$	−2.61081	+	14.8067i	−0.194060	+	1.10057i	0.719690	+	0.694295i	$0.244284\pi$
$181$	−2.61081	+	14.8067i	−0.194060	+	1.10057i	−0.913751	+	0.406276i	$0.866827\pi$
$182$	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
$185$	12.1284	+	4.41436i	0.891694	+	0.324550i
$186$	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
$190$	5.04189	−	7.11192i	0.365777	−	0.515953i
$191$	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	0.213711	−	0.976897i	$-0.431445\pi$
$193$	16.8498	−	14.1387i	1.21288	−	1.01772i	0.999166	−	0.0408274i	$-0.0129994\pi$
$194$	−1.76604	+	0.642788i	−0.126795	+	0.0461495i
$195$	−0.694593	−	0.252811i	−0.0497408	−	0.0181042i
$196$	−2.99273	−	2.51120i	−0.213766	−	0.179371i
$197$	−7.96585	+	13.7973i	−0.567543	+	0.983014i	0.429265	+	0.903179i	$0.358773\pi$
$197$	−7.96585	+	13.7973i	−0.567543	+	0.983014i	−0.996808	+	0.0798353i	$0.974561\pi$
$198$	6.08512	+	10.5397i	0.432451	+	0.749027i
$199$	−0.568926	+	3.22654i	−0.0403301	+	0.228723i	−0.998310	−	0.0581118i	$-0.981492\pi$
$199$	−0.568926	+	3.22654i	−0.0403301	+	0.228723i	0.957980	+	0.286835i	$0.0926031\pi$
$200$	−0.173648	+	0.984808i	−0.0122788	+	0.0696364i
$201$	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
$205$	−3.53209	+	1.28558i	−0.246692	+	0.0897885i
$206$	−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
$210$	−1.22163			−0.0843004
$211$	1.99154	+	11.2946i	0.137104	+	0.777553i	0.973372	+	0.229232i	$0.0736215\pi$
$211$	1.99154	+	11.2946i	0.137104	+	0.777553i	−0.836268	+	0.548321i	$0.815267\pi$
$212$	−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
$215$	5.66044	+	4.74968i	0.386039	+	0.323925i
$216$	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
$220$	−4.22668	−	7.32083i	−0.284963	−	0.493570i
$221$	−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	$-0.511162\pi$
$223$	−10.5175	−	3.82807i	−0.704307	−	0.256347i	−0.669249	+	0.743039i	$0.733384\pi$
$224$	1.65270	−	0.601535i	0.110426	−	0.0401917i
$225$	2.20574	−	1.85083i	0.147049	−	0.123389i
$226$	1.81268	+	10.2802i	0.120578	+	0.683830i
$227$	−3.39693			−0.225462			−0.112731	−	0.993626i	$-0.535960\pi$
$227$	−3.39693			−0.225462			−0.112731	+	0.993626i	$0.535960\pi$
$228$	−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	$0.455082\pi$
$230$	1.30541	+	7.40333i	0.0860760	+	0.488161i
$231$	−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	$-0.458714\pi$
$233$	−6.24257	−	2.27211i	−0.408965	−	0.148851i	−0.538307	+	0.842749i	$0.680936\pi$
$234$	−2.34730	−	1.96962i	−0.153448	−	0.128758i
$235$	3.67499	−	6.36527i	0.239730	−	0.415225i
$236$	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	−0.999782	−	0.0208848i	$-0.993352\pi$
$239$	−8.00774	−	13.8698i	−0.517978	−	0.897164i	0.481804	−	0.876279i	$-0.339982\pi$
$240$	−0.347296	+	0.601535i	−0.0224179	+	0.0388289i
$241$	−6.59105	−	5.53055i	−0.424567	−	0.356254i	0.405330	−	0.914170i	$-0.367157\pi$
$241$	−6.59105	−	5.53055i	−0.424567	−	0.356254i	−0.829897	+	0.557916i	$0.811601\pi$
$242$	−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
$245$	−1.35679	−	7.69475i	−0.0866823	−	0.491599i
$246$	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
$250$	−9.19253	+	7.71345i	−0.581387	+	0.487841i
$251$	18.7087	−	6.80942i	1.18088	−	0.429807i	0.324370	−	0.945930i	$-0.394848\pi$
$251$	18.7087	−	6.80942i	1.18088	−	0.429807i	0.856514	+	0.516123i	$0.172625\pi$
$252$	−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
$255$	−2.47565	−	4.28795i	−0.155031	−	0.268522i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	4.58734	−	26.0161i	0.286151	−	1.62284i	−0.414996	−	0.909823i	$-0.636217\pi$
$257$	4.58734	−	26.0161i	0.286151	−	1.62284i	0.701146	−	0.713018i	$-0.252672\pi$
$258$	−0.641559	−	1.11121i	−0.0399417	−	0.0691811i
$259$	−5.67499	+	9.82938i	−0.352627	+	0.610768i
$260$	1.63041	+	1.36808i	0.101114	+	0.0848448i
$261$	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	−0.333535	+	0.942738i	$0.608242\pi$
$263$	−21.4047	+	17.9606i	−1.31987	+	1.10750i	−0.986333	+	0.164763i	$0.947314\pi$
$264$	0.254900	+	1.44561i	0.0156880	+	0.0889712i
$265$	−19.7743			−1.21472
$266$	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	−0.235255	−	0.971934i	$-0.575592\pi$
$269$	11.1702	−	9.37295i	0.681062	−	0.571479i	0.916316	+	0.400455i	$0.131148\pi$
$270$	3.83750	−	1.39673i	0.233543	−	0.0850025i
$271$	17.1284	+	6.23421i	1.04047	+	0.378701i	0.805060	−	0.593194i	$-0.202133\pi$
$271$	17.1284	+	6.23421i	1.04047	+	0.378701i	0.235414	+	0.971895i	$0.424355\pi$
$272$	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
$275$	−0.733956	+	4.16247i	−0.0442592	+	0.251006i
$276$	0.226682	−	1.28558i	0.0136446	−	0.0773825i
$277$	8.23442	+	14.2624i	0.494758	+	0.856947i	0.999982	−	0.00604184i	$-0.00192319\pi$
$277$	8.23442	+	14.2624i	0.494758	+	0.856947i	−0.505223	+	0.862989i	$0.668590\pi$
$278$	9.69846	−	16.7982i	0.581675	−	1.00749i
$279$	19.4611	+	16.3298i	1.16511	+	0.977640i
$280$	3.30541	+	1.20307i	0.197536	+	0.0718972i
$281$	6.73783	−	2.45237i	0.401945	−	0.146296i	−0.133134	−	0.991098i	$-0.542504\pi$
$281$	6.73783	−	2.45237i	0.401945	−	0.146296i	0.535079	+	0.844802i	$0.320282\pi$
$282$	−0.977711	+	0.820397i	−0.0582219	+	0.0488539i
$283$	3.63563	+	20.6187i	0.216116	+	1.22565i	0.878960	+	0.476896i	$0.158238\pi$
$283$	3.63563	+	20.6187i	0.216116	+	1.22565i	−0.662844	+	0.748757i	$0.730651\pi$
$284$	2.82295			0.167511
$285$	−3.01455	−	0.281465i	−0.178566	−	0.0166725i
$286$	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
$290$	−11.9709	−	4.35705i	−0.702956	−	0.255855i
$291$	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	$-0.255962\pi$
$293$	−4.73917	−	8.20848i	−0.276865	−	0.479545i	−0.970604	+	0.240682i	$0.922629\pi$
$294$	−0.235604	+	1.33618i	−0.0137407	+	0.0779275i
$295$	−2.53209	+	14.3602i	−0.147424	+	0.836083i
$296$	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
$300$	0.326352	−	0.118782i	0.0188419	−	0.00685790i
$301$	−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
$305$	10.6108			0.607573
$306$	−3.56418	−	20.2135i	−0.203750	−	1.15553i
$307$	1.01889	−	0.854946i	0.0581508	−	0.0487944i	−0.613249	−	0.789890i	$-0.710138\pi$
$307$	1.01889	−	0.854946i	0.0581508	−	0.0487944i	0.671400	+	0.741095i	$0.265693\pi$
$308$	6.98545	−	2.54250i	0.398033	−	0.144872i
$309$	2.42602	+	0.883000i	0.138012	+	0.0502321i
$310$	−13.5175	−	11.3426i	−0.767745	−	0.644214i
$311$	−3.73917	+	6.47643i	−0.212029	+	0.367245i	−0.952349	−	0.305009i	$-0.901340\pi$
$311$	−3.73917	+	6.47643i	−0.212029	+	0.367245i	0.740320	+	0.672254i	$0.234674\pi$
$312$	−0.184793	−	0.320070i	−0.0104618	−	0.0181204i
$313$	5.08765	−	28.8535i	0.287571	−	1.63090i	−0.408384	−	0.912810i	$-0.633908\pi$
$313$	5.08765	−	28.8535i	0.287571	−	1.63090i	0.695955	−	0.718085i	$-0.254981\pi$
$314$	−0.490200	+	2.78006i	−0.0276636	+	0.156888i
$315$	−5.06418	−	8.77141i	−0.285334	−	0.494213i
$316$	3.34730	−	5.79769i	0.188300	−	0.326145i
$317$	4.29086	+	3.60046i	0.240999	+	0.202222i	0.755285	−	0.655397i	$-0.227499\pi$
$317$	4.29086	+	3.60046i	0.240999	+	0.202222i	−0.514286	+	0.857619i	$0.671943\pi$
$318$	3.22668	+	1.17442i	0.180943	+	0.0658580i
$319$	−25.2986	+	9.20794i	−1.41645	+	0.515546i
$320$	1.53209	−	1.28558i	0.0856464	−	0.0718658i
$321$	−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
$325$	−0.184793	−	1.04801i	−0.0102504	−	0.0581332i
$326$	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
$330$	−1.46791	+	2.54250i	−0.0808058	+	0.139960i
$331$	−11.4880	−	19.8978i	−0.631436	−	1.09368i	−0.987258	−	0.159126i	$-0.949132\pi$
$331$	−11.4880	−	19.8978i	−0.631436	−	1.09368i	0.355822	−	0.934554i	$-0.384201\pi$
$332$	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
$335$	11.6382	−	20.1579i	0.635860	−	1.10134i
$336$	−0.467911	−	0.392624i	−0.0255266	−	0.0214194i
$337$	−1.23308	−	0.448804i	−0.0671701	−	0.0244479i	0.308217	−	0.951316i	$-0.400268\pi$
$337$	−1.23308	−	0.448804i	−0.0671701	−	0.0244479i	−0.375387	+	0.926868i	$0.622490\pi$
$338$	11.1518	−	4.05893i	0.606579	−	0.220777i
$339$	2.77719	−	2.33034i	0.150836	−	0.126567i
$340$	2.47565	+	14.0401i	0.134261	+	0.761432i
$341$	−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
$345$	2.00000	−	1.67820i	0.107676	−	0.0903512i
$346$	−7.09152	+	2.58110i	−0.381242	+	0.138761i
$347$	−2.27079	−	0.826501i	−0.121903	−	0.0443689i	0.280349	−	0.959898i	$-0.409550\pi$
$347$	−2.27079	−	0.826501i	−0.121903	−	0.0443689i	−0.402251	+	0.915529i	$0.631772\pi$
$348$	1.69459	+	1.42193i	0.0908397	+	0.0762236i
$349$	4.24897	−	7.35943i	0.227442	−	0.393941i	−0.729607	−	0.683866i	$-0.760297\pi$
$349$	4.24897	−	7.35943i	0.227442	−	0.393941i	0.957049	+	0.289925i	$0.0936304\pi$
$350$	−0.879385	−	1.52314i	−0.0470051	−	0.0814153i
$351$	−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	$-0.134080\pi$
$353$	1.92009	+	3.32570i	0.102196	+	0.177009i	−0.810393	+	0.585887i	$0.800746\pi$
$354$	1.26604	−	2.19285i	0.0672895	−	0.116549i
$355$	4.32501	+	3.62911i	0.229548	+	0.192613i
$356$	−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	−0.873323	−	0.487141i	$-0.838040\pi$
$359$	−4.15476	−	23.5628i	−0.219280	−	1.24360i	0.654043	−	0.756457i	$-0.273071\pi$
$360$	−5.75877			−0.303514
$361$	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
$365$	−1.49020	+	0.542388i	−0.0780006	+	0.0283899i
$366$	−1.73143	−	0.630189i	−0.0905033	−	0.0329405i
$367$	13.1061	+	10.9973i	0.684131	+	0.574054i	0.917210	−	0.398404i	$-0.130436\pi$
$367$	13.1061	+	10.9973i	0.684131	+	0.574054i	−0.233079	+	0.972458i	$0.574880\pi$
$368$	−1.87939	+	3.25519i	−0.0979697	+	0.169689i
$369$	2.70574	+	4.68647i	0.140855	+	0.243968i
$370$	−2.24123	+	12.7106i	−0.116516	+	0.660795i
$371$	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	$-0.800636\pi$
$373$	1.98040	−	3.43015i	0.102541	−	0.177607i	0.912731	+	0.408561i	$0.133969\pi$
$374$	23.0804	+	19.3667i	1.19346	+	1.00143i
$375$	3.91622	+	1.42539i	0.202233	+	0.0736067i
$376$	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	$0.747237\pi$
$380$	7.87939	+	3.73032i	0.404204	+	0.191361i
$381$	−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	$-0.669867\pi$
$383$	4.90941	−	4.11949i	0.250859	−	0.210496i	0.759542	+	0.650458i	$0.225423\pi$
$384$	−0.326352	+	0.118782i	−0.0166541	+	0.00606159i
$385$	13.9709	+	5.08499i	0.712023	+	0.259155i
$386$	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	0.640799	+	0.767708i	$0.278603\pi$
$389$	−4.41653	+	25.0474i	−0.223927	+	1.26995i	−0.864726	+	0.502244i	$0.832508\pi$
$390$	0.128356	−	0.727940i	0.00649954	−	0.0368607i
$391$	−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
$395$	12.5817	−	4.57937i	0.633055	−	0.230413i
$396$	−9.32295	+	7.82288i	−0.468496	+	0.393115i
$397$	3.92127	+	22.2387i	0.196803	+	1.11613i	0.909827	+	0.414987i	$0.136214\pi$
$397$	3.92127	+	22.2387i	0.196803	+	1.11613i	−0.713024	+	0.701139i	$0.752675\pi$
$398$	−3.27631			−0.164227
$399$	0.704088	−	2.56769i	0.0352485	−	0.128546i
$400$	−1.00000			−0.0500000
$401$	0.132636	+	0.752219i	0.00662355	+	0.0375640i	0.987940	−	0.154835i	$-0.0494845\pi$
$401$	0.132636	+	0.752219i	0.00662355	+	0.0375640i	−0.981317	+	0.192399i	$0.938373\pi$
$402$	−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
$405$	12.1480	+	10.1933i	0.603637	+	0.506511i
$406$	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	0.823347	+	0.567539i	$0.192104\pi$
$409$	−2.92144	+	16.5683i	−0.144456	+	0.819249i	−0.967803	+	0.251711i	$0.919007\pi$
$410$	−1.87939	−	3.25519i	−0.0928162	−	0.160762i
$411$	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
$415$	2.31315	−	1.94096i	0.113548	−	0.0952781i
$416$	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	$0.159709\pi$
$420$	−0.212134	−	1.20307i	−0.0103511	−	0.0587038i
$421$	15.8648	−	13.3122i	0.773205	−	0.648796i	−0.168323	−	0.985732i	$-0.553835\pi$
$421$	15.8648	−	13.3122i	0.773205	−	0.648796i	0.941528	+	0.336936i	$0.109391\pi$
$422$	−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
$425$	3.56418	−	6.17334i	0.172888	−	0.299451i
$426$	−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
$430$	−3.69459	+	6.39922i	−0.178169	+	0.308598i
$431$	−14.0378	−	11.7791i	−0.676176	−	0.567379i	0.238710	−	0.971091i	$-0.423275\pi$
$431$	−14.0378	−	11.7791i	−0.676176	−	0.567379i	−0.914886	+	0.403712i	$0.867720\pi$
$432$	1.91875	+	0.698367i	0.0923158	+	0.0336002i
$433$	−4.78611	+	1.74200i	−0.230006	+	0.0837153i	−0.454452	−	0.890771i	$-0.650165\pi$
$433$	−4.78611	+	1.74200i	−0.230006	+	0.0837153i	0.224446	+	0.974486i	$0.427943\pi$
$434$	11.8871	−	9.97448i	0.570600	−	0.478791i
$435$	0.768266	+	4.35705i	0.0368355	+	0.208905i
$436$	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	−0.997257	−	0.0740207i	$-0.976417\pi$
$439$	−1.79055	−	10.1547i	−0.0854585	−	0.484659i	0.911798	−	0.410639i	$-0.134694\pi$
$440$	6.47565	−	5.43372i	0.308715	−	0.259042i
$441$	−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	$-0.344940\pi$
$443$	−6.75356	−	5.66691i	−0.320871	−	0.269243i	−0.788968	+	0.614434i	$0.789384\pi$
$444$	1.12061	−	1.94096i	0.0531820	−	0.0921140i
$445$	−11.9067	−	20.6231i	−0.564433	−	0.977627i
$446$	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	−0.972603	−	0.232473i	$-0.925318\pi$
$449$	−6.03849	+	10.4590i	−0.284974	+	0.493589i	0.687629	+	0.726062i	$0.258652\pi$
$450$	2.20574	+	1.85083i	0.103979	+	0.0872491i
$451$	−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
$455$	−3.74329			−0.175488
$456$	−1.06418	−	1.07666i	−0.0498347	−	0.0504194i
$457$	−0.731429			−0.0342148			−0.0171074	−	0.999854i	$-0.505446\pi$
$457$	−0.731429			−0.0342148			−0.0171074	+	0.999854i	$0.505446\pi$
$458$	0.739170	+	4.19204i	0.0345392	+	0.195881i
$459$	−11.1500	+	9.35597i	−0.520438	+	0.436699i
$460$	−7.06418	+	2.57115i	−0.329369	+	0.119881i
$461$	−21.6878	−	7.89371i	−1.01010	−	0.367647i	−0.216629	−	0.976254i	$-0.569506\pi$
$461$	−21.6878	−	7.89371i	−1.01010	−	0.367647i	−0.793472	+	0.608607i	$0.791729\pi$
$462$	−1.97771	−	1.65950i	−0.0920115	−	0.0772068i
$463$	−9.02229	+	15.6271i	−0.419301	+	0.726251i	−0.995869	−	0.0907980i	$-0.971058\pi$
$463$	−9.02229	+	15.6271i	−0.419301	+	0.726251i	0.576568	+	0.817049i	$0.304392\pi$
$464$	−3.18479	−	5.51622i	−0.147850	−	0.256084i
$465$	−1.06418	+	6.03525i	−0.0493501	+	0.279878i
$466$	1.15358	−	6.54228i	0.0534386	−	0.303065i
$467$	−5.48633	−	9.50260i	−0.253877	−	0.439728i	0.710713	−	0.703482i	$-0.248373\pi$
$467$	−5.48633	−	9.50260i	−0.253877	−	0.439728i	−0.964590	+	0.263754i	$0.915039\pi$
$468$	1.53209	−	2.65366i	0.0708208	−	0.122665i
$469$	15.6800	+	13.1571i	0.724037	+	0.607539i
$470$	6.90673	+	2.51384i	0.318584	+	0.115955i
$471$	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
$475$	−1.81908	−	3.96118i	−0.0834650	−	0.181751i
$476$	−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	−0.774471	−	0.632609i	$-0.781984\pi$
$479$	−21.0351	+	7.65614i	−0.961117	+	0.349818i	−0.186646	+	0.982427i	$0.559762\pi$
$480$	−0.652704	−	0.237565i	−0.0297917	−	0.0108433i
$481$	−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
$485$	0.652704	−	3.70167i	0.0296377	−	0.168084i
$486$	−4.43969	−	7.68977i	−0.201389	−	0.348815i
$487$	18.8803	−	32.7017i	0.855549	−	1.48185i	−0.0205859	−	0.999788i	$-0.506553\pi$
$487$	18.8803	−	32.7017i	0.855549	−	1.48185i	0.876135	−	0.482066i	$-0.160113\pi$
$488$	4.06418	+	3.41025i	0.183977	+	0.154375i
$489$	−0.724155	−	0.263571i	−0.0327474	−	0.0119191i
$490$	7.34224	−	2.67236i	0.331689	−	0.120725i
$491$	−0.958578	+	0.804342i	−0.0432600	+	0.0362995i	−0.664161	−	0.747589i	$-0.731211\pi$
$491$	−0.958578	+	0.804342i	−0.0432600	+	0.0362995i	0.620901	+	0.783889i	$0.286767\pi$
$492$	0.113341	+	0.642788i	0.00510980	+	0.0289791i
$493$	45.4047			2.04492
$494$	−3.81521	+	2.63841i	−0.171654	+	0.118708i
$495$	−24.3405			−1.09402
$496$	−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	0.530720	−	0.847547i	$-0.321922\pi$
$499$	8.76739	+	3.19107i	0.392482	+	0.142852i	−0.138238	+	0.990399i	$0.544144\pi$
$500$	−9.19253	−	7.71345i	−0.411103	−	0.344956i
$501$	−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	0.924037	+	0.382304i	$0.124869\pi$
$503$	−1.68273	+	9.54325i	−0.0750294	+	0.425513i	−0.999066	+	0.0432089i	$0.986242\pi$
$504$	0.879385	−	4.98724i	0.0391709	−	0.222149i
$505$	2.45336	+	4.24935i	0.109173	+	0.189094i
$506$	−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	−0.865264	−	0.501316i	$-0.832849\pi$
$509$	−27.2053	+	9.90193i	−1.20585	+	0.438895i	−0.340591	+	0.940212i	$0.610627\pi$
$510$	3.79292	−	3.18264i	0.167953	−	0.140930i
$511$	−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
$515$	−2.58172	−	14.6417i	−0.113764	−	0.645188i
$516$	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
$520$	−1.06418	+	1.84321i	−0.0466673	+	0.0808301i
$521$	1.08037	+	1.87126i	0.0473321	+	0.0819815i	0.888721	−	0.458449i	$-0.151595\pi$
$521$	1.08037	+	1.87126i	0.0473321	+	0.0819815i	−0.841389	+	0.540430i	$0.818261\pi$
$522$	−3.18479	+	18.0619i	−0.139395	+	0.790546i
$523$	2.49794	−	14.1665i	0.109227	−	0.619459i	−0.880220	−	0.474566i	$-0.842605\pi$
$523$	2.49794	−	14.1665i	0.109227	−	0.619459i	0.989447	−	0.144893i	$-0.0462838\pi$
$524$	3.82635	+	6.62744i	0.167155	+	0.289521i
$525$	−0.305407	+	0.528981i	−0.0133291	+	0.0230866i
$526$	−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
$530$	−3.43376	−	19.4738i	−0.149153	−	0.845889i
$531$	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
$535$	−0.271259	+	0.227613i	−0.0117275	+	0.00984058i
$536$	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
$540$	2.04189	+	3.53666i	0.0878689	+	0.152193i
$541$	2.24897	−	12.7545i	0.0966908	−	0.548361i	−0.897525	−	0.440963i	$-0.854637\pi$
$541$	2.24897	−	12.7545i	0.0966908	−	0.548361i	0.994216	−	0.107398i	$-0.0342518\pi$
$542$	−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
$545$	6.49794	+	5.45242i	0.278341	+	0.233556i
$546$	0.610815	+	0.222318i	0.0261405	+	0.00951435i
$547$	−1.31433	+	0.478377i	−0.0561967	+	0.0204539i	−0.369966	−	0.929045i	$-0.620631\pi$
$547$	−1.31433	+	0.478377i	−0.0561967	+	0.0204539i	0.313769	+	0.949499i	$0.398408\pi$
$548$	−4.39440	+	3.68734i	−0.187719	+	0.157515i
$549$	−2.65270	−	15.0442i	−0.113215	−	0.642072i
$550$	−4.22668			−0.180226
$551$	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
$555$	4.21213	−	1.53309i	0.178795	−	0.0650761i
$556$	18.2271	+	6.63414i	0.773003	+	0.281350i
$557$	−22.7178	−	19.0625i	−0.962585	−	0.807704i	0.0187869	−	0.999824i	$-0.494020\pi$
$557$	−22.7178	−	19.0625i	−0.962585	−	0.807704i	−0.981372	+	0.192119i	$0.938464\pi$
$558$	−12.7023	+	22.0011i	−0.537733	+	0.931380i
$559$	−1.96585	−	3.40496i	−0.0831467	−	0.144014i
$560$	−0.610815	+	3.46410i	−0.0258116	+	0.146385i
$561$	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	−0.0452621	+	0.998975i	$0.514412\pi$
$563$	−21.0646	+	36.4850i	−0.887769	+	1.53766i	−0.842507	+	0.538686i	$0.818921\pi$
$564$	−0.977711	−	0.820397i	−0.0411691	−	0.0345450i
$565$	−19.6186	−	7.14057i	−0.825359	−	0.300406i
$566$	−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	$0.465980\pi$
$570$	−0.246282	−	3.01763i	−0.0103156	−	0.126394i
$571$	−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
$575$	3.53209	+	1.28558i	0.147298	+	0.0536122i
$576$	−2.20574	−	1.85083i	−0.0919057	−	0.0771180i
$577$	−5.00727	+	8.67285i	−0.208456	+	0.361056i	−0.951228	−	0.308488i	$-0.900177\pi$
$577$	−5.00727	+	8.67285i	−0.208456	+	0.361056i	0.742773	+	0.669544i	$0.233510\pi$
$578$	−16.9067	−	29.2833i	−0.703227	−	1.21803i
$579$	1.32651	−	7.52303i	0.0551280	−	0.312647i
$580$	2.21213	−	12.5456i	0.0918539	−	0.520929i
$581$	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
$585$	5.75877	−	2.09602i	0.238096	−	0.0866598i
$586$	7.26083	−	6.09256i	0.299942	−	0.251681i
$587$	0.769915	+	4.36640i	0.0317778	+	0.180221i	0.996565	−	0.0828093i	$-0.0263893\pi$
$587$	0.769915	+	4.36640i	0.0317778	+	0.180221i	−0.964788	+	0.263030i	$0.915278\pi$
$588$	−1.35679			−0.0559532
$589$	31.6313	−	21.8747i	1.30335	−	0.901331i
$590$	−14.5817			−0.600320
$591$	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	$-0.446906\pi$
$593$	22.5758	−	8.21692i	0.927077	−	0.337428i	0.761050	+	0.648693i	$0.224684\pi$
$594$	8.10994	+	2.95178i	0.332755	+	0.121113i
$595$	−19.2080	−	16.1174i	−0.787452	−	0.660751i
$596$	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	0.588394	+	0.808574i	$0.299760\pi$
$599$	−5.89992	+	33.4601i	−0.241064	+	1.36714i	−0.829458	+	0.558569i	$0.811351\pi$
$600$	0.173648	+	0.300767i	0.00708916	+	0.0122788i
$601$	−8.07145	+	13.9802i	−0.329241	+	0.570263i	−0.982362	−	0.186991i	$-0.940126\pi$
$601$	−8.07145	+	13.9802i	−0.329241	+	0.570263i	0.653120	+	0.757254i	$0.273460\pi$
$602$	−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
$605$	10.5175	−	8.82526i	0.427599	−	0.358798i
$606$	−0.147956	−	0.839100i	−0.00601030	−	0.0340861i
$607$	8.92221			0.362141			0.181071	−	0.983470i	$-0.442044\pi$
$607$	8.92221			0.362141			0.181071	+	0.983470i	$0.442044\pi$
$608$	1.81908	+	3.96118i	0.0737733	+	0.160647i
$609$	−3.89064			−0.157657
$610$	1.84255	+	10.4496i	0.0746026	+	0.423092i
$611$	−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	$-0.563557\pi$
$613$	−24.2713	−	8.83402i	−0.980307	−	0.356803i	−0.781960	+	0.623329i	$0.785780\pi$
$614$	1.01889	+	0.854946i	0.0411189	+	0.0345028i
$615$	−0.652704	+	1.13052i	−0.0263196	+	0.0455868i
$616$	3.71688	+	6.43783i	0.149757	+	0.259387i
$617$	3.21735	−	18.2465i	0.129526	−	0.734576i	−0.848991	−	0.528407i	$-0.822789\pi$
$617$	3.21735	−	18.2465i	0.129526	−	0.734576i	0.978516	−	0.206169i	$-0.0660995\pi$
$618$	−0.448311	+	2.54250i	−0.0180337	+	0.102274i
$619$	17.6061	+	30.4946i	0.707648	+	1.22568i	0.965728	+	0.259558i	$0.0835769\pi$
$619$	17.6061	+	30.4946i	0.707648	+	1.22568i	−0.258080	+	0.966124i	$0.583090\pi$
$620$	8.82295	−	15.2818i	0.354338	−	0.613732i
$621$	−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
$625$	−3.29932	−	18.7113i	−0.131973	−	0.748454i
$626$	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
$630$	7.75877	−	6.51038i	0.309117	−	0.259380i
$631$	1.73143	−	0.630189i	0.0689271	−	0.0250874i	−0.307326	−	0.951604i	$-0.599434\pi$
$631$	1.73143	−	0.630189i	0.0689271	−	0.0250874i	0.376254	+	0.926517i	$0.377212\pi$
$632$	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
$635$	22.0155	+	38.1319i	0.873658	+	1.51322i
$636$	−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
$640$	1.53209	+	1.28558i	0.0605611	+	0.0508168i
$641$	4.89945	+	1.78325i	0.193517	+	0.0704343i	0.436961	−	0.899481i	$-0.356055\pi$
$641$	4.89945	+	1.78325i	0.193517	+	0.0704343i	−0.243444	+	0.969915i	$0.578277\pi$
$642$	0.0577812	−	0.0210306i	0.00228044	−	0.000830012i
$643$	4.52276	−	3.79504i	0.178360	−	0.149662i	−0.549237	−	0.835667i	$-0.685082\pi$
$643$	4.52276	−	3.79504i	0.178360	−	0.149662i	0.727597	+	0.686005i	$0.240637\pi$
$644$	−1.14796	−	6.51038i	−0.0452358	−	0.256545i
$645$	2.56624			0.101045
$646$	−30.9372	−	2.88857i	−1.21721	−	0.113649i
$647$	−42.6810			−1.67796			−0.838981	−	0.544160i	$-0.816848\pi$
$647$	−42.6810			−1.67796			−0.838981	+	0.544160i	$0.816848\pi$
$648$	1.37686	+	7.80856i	0.0540881	+	0.306749i
$649$	−23.6065	+	19.8082i	−0.926638	+	0.777541i
$650$	1.00000	−	0.363970i	0.0392232	−	0.0142761i
$651$	−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	$-0.881844\pi$
$653$	−3.87939	+	6.71929i	−0.151812	+	0.262946i	0.780082	+	0.625678i	$0.215178\pi$
$654$	−0.736482	−	1.27562i	−0.0287987	−	0.0498808i
$655$	−2.65776	+	15.0729i	−0.103847	+	0.588946i
$656$	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	0.963035	−	0.269378i	$-0.0868180\pi$
$659$	22.2049	+	18.6321i	0.864979	+	0.725803i	−0.0980561	+	0.995181i	$0.531262\pi$
$660$	−2.75877	−	1.00411i	−0.107385	−	0.0390849i
$661$	30.7374	−	11.1875i	1.19555	−	0.435143i	0.333879	−	0.942616i	$-0.391642\pi$
$661$	30.7374	−	11.1875i	1.19555	−	0.435143i	0.861668	+	0.507472i	$0.169420\pi$
$662$	17.6006	−	14.7687i	0.684067	−	0.574000i
$663$	0.457482	+	2.59451i	0.0177671	+	0.100762i
$664$	1.50980			0.0585916
$665$	−14.8331	+	3.88192i	−0.575201	+	0.150535i
$666$	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
$670$	21.8726	+	7.96097i	0.845011	+	0.307559i
$671$	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	0.986929	+	0.161156i	$0.0515222\pi$
$673$	16.4222	+	28.4441i	0.633030	+	1.09644i	−0.353899	+	0.935284i	$0.615144\pi$
$674$	0.227864	−	1.29228i	0.00877698	−	0.0497767i
$675$	0.354570	−	2.01087i	0.0136474	−	0.0773984i
$676$	5.93376	+	10.2776i	0.228222	+	0.395291i
$677$	−12.3209	+	21.3404i	−0.473530	+	0.820178i	−0.999541	−	0.0302996i	$-0.990354\pi$
$677$	−12.3209	+	21.3404i	−0.473530	+	0.820178i	0.526011	+	0.850478i	$0.323687\pi$
$678$	2.77719	+	2.33034i	0.106657	+	0.0894961i
$679$	3.10607	+	1.13052i	0.119200	+	0.0433852i
$680$	−13.3969	+	4.87608i	−0.513749	+	0.186989i
$681$	−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	$-0.305477\pi$
$683$	29.9905			1.14755			0.573777	+	0.819011i	$0.305477\pi$
$684$	3.31908	−	12.1041i	0.126908	−	0.462813i
$685$	−11.4730			−0.438359
$686$	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
$690$	2.00000	+	1.67820i	0.0761387	+	0.0638880i
$691$	−11.2365	+	19.4622i	−0.427456	+	0.740375i	−0.996646	−	0.0818304i	$-0.973923\pi$
$691$	−11.2365	+	19.4622i	−0.427456	+	0.740375i	0.569190	+	0.822206i	$0.307257\pi$
$692$	−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
$695$	19.3969	+	33.5965i	0.735767	+	1.27439i
$696$	−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
$700$	1.34730	−	1.13052i	0.0509230	−	0.0427295i
$701$	−0.837496	−	4.74968i	−0.0316318	−	0.179393i	0.964899	−	0.262623i	$-0.0845875\pi$
$701$	−0.837496	−	4.74968i	−0.0316318	−	0.179393i	−0.996530	+	0.0832300i	$0.973476\pi$
$702$	−2.17293			−0.0820121
$703$	−25.4243	−	12.0366i	−0.958894	−	0.453967i
$704$	4.22668			0.159299
$705$	−0.443258	−	2.51384i	−0.0166941	−	0.0946768i
$706$	−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	−0.999853	−	0.0171349i	$-0.994546\pi$
$709$	−31.6955	−	26.5957i	−1.19035	−	0.998823i	−0.190497	−	0.981688i	$-0.561010\pi$
$710$	−2.82295	+	4.88949i	−0.105943	+	0.183499i
$711$	−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
$715$	−4.49794	+	7.79066i	−0.168213	+	0.291354i
$716$	−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	−0.255934	−	0.966694i	$-0.582383\pi$
$719$	17.4730	−	14.6616i	0.651632	−	0.546784i	0.907566	+	0.419910i	$0.137939\pi$
$720$	−1.00000	−	5.67128i	−0.0372678	−	0.211356i
$721$	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
$725$	−4.87939	+	4.09429i	−0.181216	+	0.152058i
$726$	−2.24035	+	0.815422i	−0.0831473	+	0.0302631i
$727$	−8.48070	−	3.08672i	−0.314532	−	0.114480i	0.179930	−	0.983679i	$-0.442413\pi$
$727$	−8.48070	−	3.08672i	−0.314532	−	0.114480i	−0.494462	+	0.869199i	$0.664635\pi$
$728$	−1.43376	−	1.20307i	−0.0531388	−	0.0445887i
$729$	10.3516	−	17.9296i	0.383394	−	0.664058i
$730$	−0.792919	−	1.37338i	−0.0293472	−	0.0508309i
$731$	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	−0.999214	−	0.0396520i	$-0.987375\pi$
$733$	−14.4561	−	25.0386i	−0.533946	−	0.924822i	0.465267	−	0.885170i	$-0.345958\pi$
$734$	−8.55438	+	14.8166i	−0.315748	+	0.546891i
$735$	−2.07873	−	1.74426i	−0.0766750	−	0.0643379i
$736$	−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	0.959180	−	0.282797i	$-0.0912624\pi$
$739$	−1.05685	−	5.99368i	−0.0388768	−	0.220481i	−0.998056	+	0.0623162i	$0.980151\pi$
$740$	−12.9067			−0.474461
$741$	1.45605	+	0.689335i	0.0534894	+	0.0253234i
$742$	17.3892			0.638377
$743$	−5.10513	−	28.9526i	−0.187289	−	1.06217i	−0.922979	−	0.384851i	$-0.874253\pi$
$743$	−5.10513	−	28.9526i	−0.187289	−	1.06217i	0.735690	−	0.677319i	$-0.236858\pi$
$744$	−2.34730	+	1.96962i	−0.0860561	+	0.0722096i
$745$	9.72967	−	3.54131i	0.356468	−	0.129744i
$746$	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
$750$	−0.723689	+	4.10424i	−0.0264254	+	0.149866i
$751$	−6.67736	+	37.8692i	−0.243660	+	1.38187i	0.579924	+	0.814671i	$0.303082\pi$
$751$	−6.67736	+	37.8692i	−0.243660	+	1.38187i	−0.823584	+	0.567195i	$0.808029\pi$
$752$	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
$755$	−41.6905	−	15.1741i	−1.51727	−	0.552242i
$756$	−3.37464	+	1.22827i	−0.122734	+	0.0446717i
$757$	−5.82295	+	4.88603i	−0.211639	+	0.177586i	−0.742445	−	0.669907i	$-0.766334\pi$
$757$	−5.82295	+	4.88603i	−0.211639	+	0.177586i	0.530806	+	0.847493i	$0.321889\pi$
$758$	−4.73917	−	26.8772i	−0.172134	−	0.976223i
$759$	5.51754			0.200274
$760$	−2.30541	+	8.40744i	−0.0836259	+	0.304970i
$761$	−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
$765$	38.5749	+	14.0401i	1.39468	+	0.507622i
$766$	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	0.884524	+	0.466494i	$0.154483\pi$
$769$	−2.94521	+	16.7031i	−0.106207	+	0.602330i	−0.990731	+	0.135836i	$0.956628\pi$
$770$	−2.58172	+	14.6417i	−0.0930387	+	0.527649i
$771$	−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	−0.985843	−	0.167669i	$-0.946376\pi$
$773$	−36.7597	−	30.8451i	−1.32215	−	1.10942i	−0.336311	−	0.941751i	$-0.609179\pi$
$774$	9.99660	+	3.63846i	0.359320	+	0.130782i
$775$	−8.29086	+	3.01763i	−0.297816	+	0.108396i
$776$	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
$780$	0.739170			0.0264665
$781$	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
$785$	−4.32501	−	3.62911i	−0.154366	−	0.129529i
$786$	1.32888	−	2.30168i	0.0473995	−	0.0820984i
$787$	−25.2913	−	43.8059i	−0.901538	−	1.56151i	−0.825498	−	0.564406i	$-0.809105\pi$
$787$	−25.2913	−	43.8059i	−0.901538	−	1.56151i	−0.0760408	−	0.997105i	$-0.524228\pi$
$788$	2.76651	−	15.6897i	0.0985529	−	0.558921i
$789$	−1.68510	+	9.55666i	−0.0599910	+	0.340226i
$790$	6.69459	+	11.5954i	0.238183	+	0.412545i
$791$	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
$795$	−5.26083	+	4.41436i	−0.186582	+	0.156561i
$796$	−0.568926	−	3.22654i	−0.0201650	−	0.114362i
$797$	−3.87702			−0.137331			−0.0686656	−	0.997640i	$-0.521874\pi$
$797$	−3.87702			−0.137331			−0.0686656	+	0.997640i	$0.521874\pi$
$798$	2.65095	+	0.247516i	0.0938426	+	0.00876197i
$799$	−26.1967			−0.926771
$800$	−0.173648	−	0.984808i	−0.00613939	−	0.0348182i
$801$	−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
$805$	6.61081	−	11.4503i	0.233001	−	0.403569i
$806$	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	0.977089	−	0.212829i	$-0.0682678\pi$
$809$	8.65317	+	14.9877i	0.304229	+	0.526941i	−0.672860	+	0.739770i	$0.734934\pi$
$810$	−7.92902	+	13.7335i	−0.278597	+	0.482544i
$811$	37.5330	+	31.4939i	1.31796	+	1.10590i	0.986733	+	0.162352i	$0.0519080\pi$
$811$	37.5330	+	31.4939i	1.31796	+	1.10590i	0.331230	+	0.943550i	$0.392536\pi$
$812$	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
$815$	0.770630	+	4.37046i	0.0269940	+	0.153091i
$816$	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
$820$	2.87939	−	2.41609i	0.100552	−	0.0843736i
$821$	26.8307	−	9.76557i	0.936398	−	0.340821i	0.171655	−	0.985157i	$-0.445088\pi$
$821$	26.8307	−	9.76557i	0.936398	−	0.340821i	0.764742	+	0.644336i	$0.222866\pi$
$822$	1.87211	+	0.681393i	0.0652974	+	0.0237663i
$823$	36.0547	+	30.2535i	1.25679	+	1.05457i	0.996017	+	0.0891689i	$0.0284211\pi$
$823$	36.0547	+	30.2535i	1.25679	+	1.05457i	0.260771	+	0.965401i	$0.416023\pi$
$824$	3.71688	−	6.43783i	0.129484	−	0.224272i
$825$	0.733956	+	1.27125i	0.0255531	+	0.0442592i
$826$	2.22668	−	12.6281i	0.0774762	−	0.439389i
$827$	4.30113	−	24.3929i	0.149565	−	0.848224i	−0.814023	−	0.580833i	$-0.802727\pi$
$827$	4.30113	−	24.3929i	0.149565	−	0.848224i	0.963588	−	0.267392i	$-0.0861618\pi$
$828$	5.41147	+	9.37295i	0.188062	+	0.325732i
$829$	17.2959	−	29.9574i	0.600712	−	1.04046i	−0.392002	−	0.919965i	$-0.628217\pi$
$829$	17.2959	−	29.9574i	0.600712	−	1.04046i	0.992713	−	0.120499i	$-0.0384494\pi$
$830$	2.31315	+	1.94096i	0.0802905	+	0.0673718i
$831$	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
$835$	7.83244			0.271053
$836$	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	−0.549506	−	0.835490i	$-0.685184\pi$
$839$	5.15207	−	4.32310i	0.177869	−	0.149250i	0.727376	+	0.686239i	$0.240740\pi$
$840$	1.14796	−	0.417822i	0.0396082	−	0.0144162i
$841$	−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
$845$	−4.12155	+	23.3745i	−0.141786	+	0.804106i
$846$	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
$850$	6.69846	+	2.43804i	0.229755	+	0.0836241i
$851$	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	0.979005	+	0.203838i	$0.0653416\pi$
$853$	3.76053	+	21.3270i	0.128758	+	0.730223i	−0.850247	+	0.526384i	$0.823547\pi$
$854$	−9.33099			−0.319300
$855$	20.6459	−	14.2777i	0.706075	−	0.488287i
$856$	−0.177052			−0.00605150
$857$	−6.68123	−	37.8911i	−0.228226	−	1.29434i	−0.856420	−	0.516279i	$-0.827317\pi$
$857$	−6.68123	−	37.8911i	−0.228226	−	1.29434i	0.628194	−	0.778057i	$-0.283794\pi$
$858$	1.19665	−	1.00411i	0.0408530	−	0.0342798i
$859$	15.5731	−	5.66815i	0.531347	−	0.193395i	−0.0623925	−	0.998052i	$-0.519873\pi$
$859$	15.5731	−	5.66815i	0.531347	−	0.193395i	0.593740	+	0.804657i	$0.297651\pi$
$860$	−6.94356	−	2.52725i	−0.236774	−	0.0861785i
$861$	−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	$-0.0216065\pi$
$863$	12.9290	+	22.3937i	0.440109	+	0.762291i	−0.557588	+	0.830118i	$0.688273\pi$
$864$	−0.354570	+	2.01087i	−0.0120627	+	0.0684111i
$865$	2.62092	−	14.8640i	0.0891139	−	0.505390i
$866$	−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
$870$	−4.15745	+	1.51319i	−0.140951	+	0.0513019i
$871$	−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
$875$	21.1052			0.713488
$876$	0.0478189	+	0.271194i	0.00161565	+	0.00916280i
$877$	−38.7793	+	32.5397i	−1.30948	+	1.09879i	−0.321062	+	0.947058i	$0.604040\pi$
$877$	−38.7793	+	32.5397i	−1.30948	+	1.09879i	−0.988422	+	0.151729i	$0.951516\pi$
$878$	9.68954	−	3.52670i	0.327006	−	0.119021i
$879$	−3.09327	−	1.12586i	−0.104334	−	0.0379743i
$880$	6.47565	+	5.43372i	0.218294	+	0.183171i
$881$	−25.4846	+	44.1406i	−0.858597	+	1.48713i	0.0146701	+	0.999892i	$0.495330\pi$
$881$	−25.4846	+	44.1406i	−0.858597	+	1.48713i	−0.873267	+	0.487241i	$0.838003\pi$
$882$	−5.62449	−	9.74189i	−0.189386	−	0.328027i
$883$	6.61897	−	37.5380i	0.222746	−	1.26325i	−0.644202	−	0.764856i	$-0.722810\pi$
$883$	6.61897	−	37.5380i	0.222746	−	1.26325i	0.866948	−	0.498399i	$-0.166079\pi$
$884$	1.31727	−	7.47059i	0.0443045	−	0.251263i
$885$	2.53209	+	4.38571i	0.0851152	+	0.147424i
$886$	4.40807	−	7.63500i	0.148092	−	0.256503i
$887$	−24.1215	−	20.2404i	−0.809922	−	0.679606i	0.140667	−	0.990057i	$-0.455075\pi$
$887$	−24.1215	−	20.2404i	−0.809922	−	0.679606i	−0.950589	+	0.310451i	$0.899520\pi$
$888$	2.10607	+	0.766546i	0.0706750	+	0.0257236i
$889$	−36.3851	+	13.2431i	−1.22032	+	0.444159i
$890$	18.2422	−	15.3070i	0.611479	−	0.513092i
$891$	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
$895$	−3.81614	−	21.6424i	−0.127560	−	0.723426i
$896$	−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
$900$	−1.43969	+	2.49362i	−0.0479898	+	0.0831207i
$901$	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
$905$	15.0351	−	26.0415i	0.499783	−	0.865650i
$906$	5.90167	+	4.95209i	0.196070	+	0.164522i
$907$	−8.36871	−	3.04596i	−0.277878	−	0.101139i	0.199322	−	0.979934i	$-0.436126\pi$
$907$	−8.36871	−	3.04596i	−0.277878	−	0.101139i	−0.477200	+	0.878795i	$0.658348\pi$
$908$	3.19207	−	1.16182i	0.105932	−	0.0385563i
$909$	5.41147	−	4.54077i	0.179487	−	0.150608i
$910$	−0.650015	−	3.68642i	−0.0215478	−	0.122204i
$911$	−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
$915$	2.82295	−	2.36873i	0.0933238	−	0.0783080i
$916$	−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	0.0811431	−	0.996702i	$-0.474143\pi$
$919$	27.3969	−	47.4529i	0.903741	−	1.56533i	0.822598	−	0.568623i	$-0.192524\pi$
$920$	−3.75877	−	6.51038i	−0.123923	−	0.214641i
$921$	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
$925$	4.94356	+	4.14814i	0.162543	+	0.136390i
$926$	−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	0.940144	+	0.340778i	$0.110691\pi$
$929$	5.28059	+	29.9477i	0.173251	+	0.982553i	−0.766893	+	0.641775i	$0.778198\pi$
$930$	−6.12836			−0.200957
$931$	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
$935$	−56.6245	+	20.6096i	−1.85182	+	0.674008i
$936$	2.87939	+	1.04801i	0.0941157	+	0.0342553i
$937$	22.6065	+	18.9691i	0.738523	+	0.619695i	0.932441	−	0.361323i	$-0.117675\pi$
$937$	22.6065	+	18.9691i	0.738523	+	0.619695i	−0.193917	+	0.981018i	$0.562119\pi$
$938$	−10.2344	+	17.7265i	−0.334166	+	0.578792i
$939$	−5.08765	−	8.81207i	−0.166029	−	0.287571i
$940$	−1.27631	+	7.23832i	−0.0416287	+	0.236088i
$941$	−2.34905	+	13.3221i	−0.0765769	+	0.434289i	0.922281	+	0.386519i	$0.126323\pi$
$941$	−2.34905	+	13.3221i	−0.0765769	+	0.434289i	−0.998858	+	0.0477701i	$0.984789\pi$
$942$	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
$945$	−6.74928	−	2.45654i	−0.219554	−	0.0799111i
$946$	−14.6741	+	5.34094i	−0.477097	+	0.173649i
$947$	−6.65002	+	5.58003i	−0.216096	+	0.181326i	−0.744410	−	0.667723i	$-0.767269\pi$
$947$	−6.65002	+	5.58003i	−0.216096	+	0.181326i	0.528313	+	0.849049i	$0.322825\pi$
$948$	−0.403733	−	2.28969i	−0.0131126	−	0.0743655i
$949$	0.843807			0.0273911
$950$	3.58512	−	2.47929i	0.116317	−	0.0804389i
$951$	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	$-0.485227\pi$
$953$	32.0498	−	26.8930i	1.03820	−	0.871150i	0.991803	+	0.127773i	$0.0407829\pi$
$954$	−26.7520	+	9.73692i	−0.866127	+	0.315244i
$955$	−8.52704	−	3.10359i	−0.275928	−	0.100430i
$956$	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
$960$	0.120615	−	0.684040i	0.00389282	−	0.0220773i
$961$	−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
$965$	−41.3387	+	15.0461i	−1.33074	+	0.484350i
$966$	−1.75877	+	1.47578i	−0.0565875	+	0.0474826i
$967$	−2.44326	−	13.8564i	−0.0785699	−	0.445592i	−0.998560	−	0.0536500i	$-0.982914\pi$
$967$	−2.44326	−	13.8564i	−0.0785699	−	0.445592i	0.919990	−	0.391942i	$-0.128197\pi$
$968$	6.86484			0.220644
$969$	4.50340	+	9.80651i	0.144670	+	0.315030i
$970$	3.75877			0.120687
$971$	6.49819	+	36.8531i	0.208537	+	1.18267i	0.891776	+	0.452477i	$0.149459\pi$
$971$	6.49819	+	36.8531i	0.208537	+	1.18267i	−0.683239	+	0.730194i	$0.739429\pi$
$972$	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
$975$	−0.283119	−	0.237565i	−0.00906705	−	0.00760816i
$976$	−2.65270	+	4.59462i	−0.0849110	+	0.147070i
$977$	−24.8769	−	43.0881i	−0.795883	−	1.37851i	−0.922277	−	0.386530i	$-0.873674\pi$
$977$	−24.8769	−	43.0881i	−0.795883	−	1.37851i	0.126394	−	0.991980i	$-0.459660\pi$
$978$	0.133819	−	0.758922i	0.00427904	−	0.0242677i
$979$	8.73901	−	49.5614i	0.279300	−	1.58399i
$980$	3.90673	+	6.76665i	0.124796	+	0.216153i
$981$	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	$-0.272722\pi$
$983$	21.0300	+	7.65430i	0.670754	+	0.244134i	0.0158814	+	0.999874i	$0.494945\pi$
$984$	−0.613341	+	0.223238i	−0.0195526	+	0.00711656i
$985$	24.4088	−	20.4814i	0.777729	−	0.652592i
$986$	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
$990$	−4.22668	−	23.9707i	−0.134333	−	0.761839i
$991$	36.8803	−	30.9463i	1.17154	−	0.983040i	0.171544	−	0.985176i	$-0.445124\pi$
$991$	36.8803	−	30.9463i	1.17154	−	0.983040i	0.999998	+	0.00213601i	$0.000679914\pi$
$992$	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
$995$	3.27631	−	5.67474i	0.103866	−	0.179901i
$996$	−0.262174	−	0.454099i	−0.00830730	−	0.0143887i
$997$	−7.40642	+	42.0039i	−0.234564	+	1.33028i	0.608967	+	0.793196i	$0.291584\pi$
$997$	−7.40642	+	42.0039i	−0.234564	+	1.33028i	−0.843530	+	0.537081i	$0.819527\pi$
$998$	−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	38.2.e.a.9.1	✓	6
3.2	odd	2		342.2.u.c.199.1		6
4.3	odd	2		304.2.u.c.161.1		6
5.2	odd	4		950.2.u.b.199.1		12
5.3	odd	4		950.2.u.b.199.2		12
5.4	even	2		950.2.l.d.351.1		6
19.2	odd	18		722.2.e.k.245.1		6
19.3	odd	18		722.2.e.a.423.1		6
19.4	even	9		722.2.c.k.429.2		6
19.5	even	9		722.2.e.b.415.1		6
19.6	even	9		722.2.a.l.1.2		3
19.7	even	3		722.2.e.m.99.1		6
19.8	odd	6		722.2.e.l.595.1		6
19.9	even	9		722.2.c.k.653.2		6
19.10	odd	18		722.2.c.l.653.2		6
19.11	even	3		722.2.e.b.595.1		6
19.12	odd	6		722.2.e.a.99.1		6
19.13	odd	18		722.2.a.k.1.2		3
19.14	odd	18		722.2.e.l.415.1		6
19.15	odd	18		722.2.c.l.429.2		6
19.16	even	9		722.2.e.m.423.1		6
19.17	even	9	inner	38.2.e.a.17.1	yes	6
19.18	odd	2		722.2.e.k.389.1		6
57.17	odd	18		342.2.u.c.55.1		6
57.32	even	18		6498.2.a.bq.1.1		3
57.44	odd	18		6498.2.a.bl.1.1		3
76.51	even	18		5776.2.a.bo.1.2		3
76.55	odd	18		304.2.u.c.17.1		6
76.63	odd	18		5776.2.a.bn.1.2		3
95.17	odd	36		950.2.u.b.549.2		12
95.74	even	18		950.2.l.d.701.1		6
95.93	odd	36		950.2.u.b.549.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.e.a.9.1	✓	6	1.1	even	1	trivial
38.2.e.a.17.1	yes	6	19.17	even	9	inner
304.2.u.c.17.1		6	76.55	odd	18
304.2.u.c.161.1		6	4.3	odd	2
342.2.u.c.55.1		6	57.17	odd	18
342.2.u.c.199.1		6	3.2	odd	2
722.2.a.k.1.2		3	19.13	odd	18
722.2.a.l.1.2		3	19.6	even	9
722.2.c.k.429.2		6	19.4	even	9
722.2.c.k.653.2		6	19.9	even	9
722.2.c.l.429.2		6	19.15	odd	18
722.2.c.l.653.2		6	19.10	odd	18
722.2.e.a.99.1		6	19.12	odd	6
722.2.e.a.423.1		6	19.3	odd	18
722.2.e.b.415.1		6	19.5	even	9
722.2.e.b.595.1		6	19.11	even	3
722.2.e.k.245.1		6	19.2	odd	18
722.2.e.k.389.1		6	19.18	odd	2
722.2.e.l.415.1		6	19.14	odd	18
722.2.e.l.595.1		6	19.8	odd	6
722.2.e.m.99.1		6	19.7	even	3
722.2.e.m.423.1		6	19.16	even	9
950.2.l.d.351.1		6	5.4	even	2
950.2.l.d.701.1		6	95.74	even	18
950.2.u.b.199.1		12	5.2	odd	4
950.2.u.b.199.2		12	5.3	odd	4
950.2.u.b.549.1		12	95.93	odd	36
950.2.u.b.549.2		12	95.17	odd	36
5776.2.a.bn.1.2		3	76.63	odd	18
5776.2.a.bo.1.2		3	76.51	even	18
6498.2.a.bl.1.1		3	57.44	odd	18
6498.2.a.bq.1.1		3	57.32	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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(0.266044 - 0.223238i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.87939 - 0.684040i) q^{5} +(0.266044 + 0.223238i) q^{6} +(0.879385 - 1.52314i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.500000 + 2.83564i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(0.266044 - 0.223238i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.87939 - 0.684040i) q^{5} +(0.266044 + 0.223238i) q^{6} +(0.879385 - 1.52314i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.500000 + 2.83564i) q^{9} +(0.347296 - 1.96962i) q^{10} +(-2.11334 - 3.66041i) q^{11} +(-0.173648 + 0.300767i) q^{12} +(0.815207 + 0.684040i) q^{13} +(1.65270 + 0.601535i) q^{14} +(-0.652704 + 0.237565i) q^{15} +(0.766044 - 0.642788i) q^{16} +(1.23783 + 7.02006i) q^{17} -2.87939 q^{18} +(3.93969 + 1.86516i) q^{19} +2.00000 q^{20} +(-0.106067 - 0.601535i) q^{21} +(3.23783 - 2.71686i) q^{22} +(-3.53209 + 1.28558i) q^{23} +(-0.326352 - 0.118782i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(-0.532089 + 0.921605i) q^{26} +(1.02094 + 1.76833i) q^{27} +(-0.305407 + 1.73205i) q^{28} +(1.10607 - 6.27282i) q^{29} +(-0.347296 - 0.601535i) q^{30} +(4.41147 - 7.64090i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-1.37939 - 0.502055i) q^{33} +(-6.69846 + 2.43804i) q^{34} +(-2.69459 + 2.26103i) q^{35} +(-0.500000 - 2.83564i) q^{36} -6.45336 q^{37} +(-1.15270 + 4.20372i) q^{38} +0.369585 q^{39} +(0.347296 + 1.96962i) q^{40} +(1.43969 - 1.20805i) q^{41} +(0.573978 - 0.208911i) q^{42} +(-3.47178 - 1.26363i) q^{43} +(3.23783 + 2.71686i) q^{44} +(2.87939 - 4.98724i) q^{45} +(-1.87939 - 3.25519i) q^{46} +(-0.638156 + 3.61916i) q^{47} +(0.0603074 - 0.342020i) q^{48} +(1.95336 + 3.38332i) q^{49} +(0.500000 - 0.866025i) q^{50} +(1.89646 + 1.59132i) q^{51} +(-1.00000 - 0.363970i) q^{52} +(9.29086 - 3.38160i) q^{53} +(-1.56418 + 1.31250i) q^{54} +(1.46791 + 8.32494i) q^{55} -1.75877 q^{56} +(1.46451 - 0.383273i) q^{57} +6.36959 q^{58} +(-1.26604 - 7.18009i) q^{59} +(0.532089 - 0.446476i) q^{60} +(-4.98545 + 1.81456i) q^{61} +(8.29086 + 3.01763i) q^{62} +(3.87939 + 3.25519i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.06418 - 1.84321i) q^{65} +(0.254900 - 1.44561i) q^{66} +(-2.02094 + 11.4613i) q^{67} +(-3.56418 - 6.17334i) q^{68} +(-0.652704 + 1.13052i) q^{69} +(-2.69459 - 2.26103i) q^{70} +(-2.65270 - 0.965505i) q^{71} +(2.70574 - 0.984808i) q^{72} +(0.607411 - 0.509678i) q^{73} +(-1.12061 - 6.35532i) q^{74} -0.347296 q^{75} +(-4.34002 - 0.405223i) q^{76} -7.43376 q^{77} +(0.0641778 + 0.363970i) q^{78} +(-5.12836 + 4.30320i) q^{79} +(-1.87939 + 0.684040i) q^{80} +(-7.45084 - 2.71188i) q^{81} +(1.43969 + 1.20805i) q^{82} +(-0.754900 + 1.30753i) q^{83} +(0.305407 + 0.528981i) q^{84} +(2.47565 - 14.0401i) q^{85} +(0.641559 - 3.63846i) q^{86} +(-1.10607 - 1.91576i) q^{87} +(-2.11334 + 3.66041i) q^{88} +(9.12108 + 7.65350i) q^{89} +(5.41147 + 1.96962i) q^{90} +(1.75877 - 0.640140i) q^{91} +(2.87939 - 2.41609i) q^{92} +(-0.532089 - 3.01763i) q^{93} -3.67499 q^{94} +(-6.12836 - 6.20026i) q^{95} +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	\( 6 q - 3 q^{3} - 3 q^{6} - 6 q^{7} - 3 q^{8} - 3 q^{9} - 6 q^{11} + 12 q^{13} + 12 q^{14} - 6 q^{15} - 12 q^{17} - 6 q^{18} + 18 q^{19} + 12 q^{20} + 24 q^{21} - 12 q^{23} - 3 q^{24} + 6 q^{26} + 3 q^{27} - 6 q^{28} - 18 q^{29} + 6 q^{31} + 3 q^{33} - 12 q^{34} - 12 q^{35} - 3 q^{36} - 12 q^{37} - 9 q^{38} - 12 q^{39} + 3 q^{41} - 12 q^{42} - 6 q^{43} + 6 q^{45} + 30 q^{47} + 6 q^{48} - 15 q^{49} + 3 q^{50} + 21 q^{51} - 6 q^{52} + 24 q^{53} + 9 q^{54} + 18 q^{55} + 12 q^{56} - 24 q^{57} + 24 q^{58} - 3 q^{59} - 6 q^{60} + 6 q^{61} + 18 q^{62} + 12 q^{63} - 3 q^{64} + 12 q^{65} + 3 q^{66} - 9 q^{67} - 3 q^{68} - 6 q^{69} - 12 q^{70} - 18 q^{71} + 6 q^{72} - 30 q^{73} - 18 q^{74} - 6 q^{76} - 12 q^{77} - 18 q^{78} + 6 q^{79} - 33 q^{81} + 3 q^{82} - 6 q^{83} + 6 q^{84} - 24 q^{85} + 12 q^{86} + 18 q^{87} - 6 q^{88} + 12 q^{90} - 12 q^{91} + 6 q^{92} + 6 q^{93} - 12 q^{94} + 3 q^{97} + 21 q^{99}+O(q^{100}) \) 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 - 6 * q^15 - 12 * q^17 - 6 * q^18 + 18 * q^19 + 12 * q^20 + 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 - 12 * q^35 - 3 * q^36 - 12 * q^37 - 9 * q^38 - 12 * q^39 + 3 * q^41 - 12 * q^42 - 6 * q^43 + 6 * q^45 + 30 * q^47 + 6 * q^48 - 15 * q^49 + 3 * q^50 + 21 * q^51 - 6 * q^52 + 24 * q^53 + 9 * q^54 + 18 * q^55 + 12 * q^56 - 24 * q^57 + 24 * q^58 - 3 * q^59 - 6 * q^60 + 6 * q^61 + 18 * q^62 + 12 * q^63 - 3 * q^64 + 12 * q^65 + 3 * q^66 - 9 * q^67 - 3 * q^68 - 6 * q^69 - 12 * q^70 - 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 - 24 * q^85 + 12 * q^86 + 18 * q^87 - 6 * q^88 + 12 * q^90 - 12 * q^91 + 6 * q^92 + 6 * q^93 - 12 * q^94 + 3 * q^97 + 21 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more