LMFDB - Embedded newform 354.2.e.a.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$2$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			127.1
Character	$\chi$	$=$	354.127
Dual form			354.2.e.a.223.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.647386 - 0.762162i) q^{2} +(0.796093 + 0.605174i) q^{3} +(-0.161782 - 0.986827i) q^{4} +(-0.659445 - 1.24384i) q^{5} +(0.976621 - 0.214970i) q^{6} +(1.04625 + 0.113786i) q^{7} +(-0.856857 - 0.515554i) q^{8} +(0.267528 + 0.963550i) q^{9} +O(q^{10})$	\(q+(0.647386 - 0.762162i) q^{2} +(0.796093 + 0.605174i) q^{3} +(-0.161782 - 0.986827i) q^{4} +(-0.659445 - 1.24384i) q^{5} +(0.976621 - 0.214970i) q^{6} +(1.04625 + 0.113786i) q^{7} +(-0.856857 - 0.515554i) q^{8} +(0.267528 + 0.963550i) q^{9} +(-1.37493 - 0.302644i) q^{10} +(4.13316 + 1.39262i) q^{11} +(0.468408 - 0.883512i) q^{12} +(1.87032 - 6.73628i) q^{13} +(0.764051 - 0.723748i) q^{14} +(0.227763 - 1.38929i) q^{15} +(-0.947653 + 0.319302i) q^{16} +(-0.401429 + 0.0436581i) q^{17} +(0.907575 + 0.419889i) q^{18} +(-0.0140881 + 0.259841i) q^{19} +(-1.12077 + 0.851989i) q^{20} +(0.764051 + 0.723748i) q^{21} +(3.73715 - 2.24857i) q^{22} +(-8.04980 + 3.72423i) q^{23} +(-0.370138 - 0.928977i) q^{24} +(1.69365 - 2.49795i) q^{25} +(-3.92332 - 5.78646i) q^{26} +(-0.370138 + 0.928977i) q^{27} +(-0.0569768 - 1.05088i) q^{28} +(2.38522 + 2.80809i) q^{29} +(-0.911417 - 1.07300i) q^{30} +(0.218536 + 4.03066i) q^{31} +(-0.370138 + 0.928977i) q^{32} +(2.44760 + 3.60994i) q^{33} +(-0.226605 + 0.334218i) q^{34} +(-0.548411 - 1.37641i) q^{35} +(0.907575 - 0.419889i) q^{36} +(-8.56513 + 5.15347i) q^{37} +(0.188920 + 0.178955i) q^{38} +(5.56557 - 4.23083i) q^{39} +(-0.0762190 + 1.40578i) q^{40} +(8.44149 + 3.90545i) q^{41} +(1.04625 - 0.113786i) q^{42} +(6.46206 - 2.17732i) q^{43} +(0.705607 - 4.30401i) q^{44} +(1.02209 - 0.968171i) q^{45} +(-2.37286 + 8.54627i) q^{46} +(-3.50327 + 6.60788i) q^{47} +(-0.947653 - 0.319302i) q^{48} +(-5.75465 - 1.26670i) q^{49} +(-0.807396 - 2.90798i) q^{50} +(-0.345996 - 0.208179i) q^{51} +(-6.95012 - 0.755871i) q^{52} +(-13.8581 + 3.05040i) q^{53} +(0.468408 + 0.883512i) q^{54} +(-0.993382 - 6.05936i) q^{55} +(-0.837823 - 0.636897i) q^{56} +(-0.168464 + 0.198331i) q^{57} +3.68438 q^{58} +(-2.82052 - 7.14455i) q^{59} -1.40784 q^{60} +(1.58472 - 1.86568i) q^{61} +(3.21349 + 2.44283i) q^{62} +(0.170262 + 1.03855i) q^{63} +(0.468408 + 0.883512i) q^{64} +(-9.61225 + 2.11582i) q^{65} +(4.33590 + 0.471557i) q^{66} +(11.2745 + 6.78367i) q^{67} +(0.108027 + 0.389078i) q^{68} +(-8.66220 - 1.90669i) q^{69} +(-1.40408 - 0.473089i) q^{70} +(-5.60729 + 10.5765i) q^{71} +(0.267528 - 0.963550i) q^{72} +(-2.68921 + 2.54736i) q^{73} +(-1.61717 + 9.86430i) q^{74} +(2.86000 - 0.963647i) q^{75} +(0.258697 - 0.0281350i) q^{76} +(4.16585 + 1.92733i) q^{77} +(0.378491 - 6.98085i) q^{78} +(5.37891 - 4.08894i) q^{79} +(1.02209 + 0.968171i) q^{80} +(-0.856857 + 0.515554i) q^{81} +(8.44149 - 3.90545i) q^{82} +(-2.31074 - 5.79951i) q^{83} +(0.590604 - 0.871075i) q^{84} +(0.319024 + 0.470526i) q^{85} +(2.52398 - 6.33471i) q^{86} +(0.199468 + 3.67897i) q^{87} +(-2.82355 - 3.32414i) q^{88} +(0.778995 + 0.917104i) q^{89} +(-0.0762190 - 1.40578i) q^{90} +(2.72332 - 6.83501i) q^{91} +(4.97749 + 7.34124i) q^{92} +(-2.26527 + 3.34103i) q^{93} +(2.76830 + 6.94791i) q^{94} +(0.332492 - 0.153827i) q^{95} +(-0.856857 + 0.515554i) q^{96} +(-0.228792 - 0.216724i) q^{97} +(-4.69091 + 3.56594i) q^{98} +(-0.236125 + 4.35507i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} - 18 q^{11} - 2 q^{12} + 13 q^{13} - 20 q^{14} + 4 q^{15} - 2 q^{16} + 21 q^{17} - 2 q^{18} + 20 q^{19} + 4 q^{20} - 20 q^{21} + 11 q^{22} + 34 q^{23} - 2 q^{24} - 28 q^{25} - 16 q^{26} - 2 q^{27} + 9 q^{28} + 38 q^{29} + 4 q^{30} + 34 q^{31} - 2 q^{32} + 11 q^{33} - 8 q^{34} - 19 q^{35} - 2 q^{36} - 29 q^{37} + 20 q^{38} + 13 q^{39} + 4 q^{40} + 43 q^{41} + 9 q^{42} - 65 q^{43} + 11 q^{44} + 4 q^{45} + 5 q^{46} - 60 q^{47} - 2 q^{48} - 13 q^{49} - 86 q^{50} + 21 q^{51} - 16 q^{52} - 15 q^{53} - 2 q^{54} - 15 q^{55} + 9 q^{56} + 20 q^{57} - 78 q^{58} - 2 q^{59} - 54 q^{60} + 4 q^{61} + 5 q^{62} + 9 q^{63} - 2 q^{64} - 57 q^{65} + 11 q^{66} - 56 q^{67} - 8 q^{68} - 53 q^{69} + 10 q^{70} + 23 q^{71} - 2 q^{72} - 21 q^{73} + 30 q^{75} - 9 q^{76} - 57 q^{77} + 13 q^{78} + 99 q^{79} + 4 q^{80} - 2 q^{81} + 43 q^{82} + 33 q^{83} + 9 q^{84} - 45 q^{85} - 7 q^{86} + 9 q^{87} - 18 q^{88} + 32 q^{89} + 4 q^{90} - 75 q^{91} + 34 q^{92} + 5 q^{93} + 27 q^{94} + 82 q^{95} - 2 q^{96} + 70 q^{97} + 45 q^{98} + 11 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 - 18 * q^11 - 2 * q^12 + 13 * q^13 - 20 * q^14 + 4 * q^15 - 2 * q^16 + 21 * q^17 - 2 * q^18 + 20 * q^19 + 4 * q^20 - 20 * q^21 + 11 * q^22 + 34 * q^23 - 2 * q^24 - 28 * q^25 - 16 * q^26 - 2 * q^27 + 9 * q^28 + 38 * q^29 + 4 * q^30 + 34 * q^31 - 2 * q^32 + 11 * q^33 - 8 * q^34 - 19 * q^35 - 2 * q^36 - 29 * q^37 + 20 * q^38 + 13 * q^39 + 4 * q^40 + 43 * q^41 + 9 * q^42 - 65 * q^43 + 11 * q^44 + 4 * q^45 + 5 * q^46 - 60 * q^47 - 2 * q^48 - 13 * q^49 - 86 * q^50 + 21 * q^51 - 16 * q^52 - 15 * q^53 - 2 * q^54 - 15 * q^55 + 9 * q^56 + 20 * q^57 - 78 * q^58 - 2 * q^59 - 54 * q^60 + 4 * q^61 + 5 * q^62 + 9 * q^63 - 2 * q^64 - 57 * q^65 + 11 * q^66 - 56 * q^67 - 8 * q^68 - 53 * q^69 + 10 * q^70 + 23 * q^71 - 2 * q^72 - 21 * q^73 + 30 * q^75 - 9 * q^76 - 57 * q^77 + 13 * q^78 + 99 * q^79 + 4 * q^80 - 2 * q^81 + 43 * q^82 + 33 * q^83 + 9 * q^84 - 45 * q^85 - 7 * q^86 + 9 * q^87 - 18 * q^88 + 32 * q^89 + 4 * q^90 - 75 * q^91 + 34 * q^92 + 5 * q^93 + 27 * q^94 + 82 * q^95 - 2 * q^96 + 70 * q^97 + 45 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{21}{29}\right)$	$1$

Coefficient data

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

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

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

$2$	0.647386	−	0.762162i	0.457771	−	0.538930i
$2$	0.647386	−	0.762162i	0.457771	−	0.538930i
$3$	0.796093	+	0.605174i	0.459625	+	0.349397i
$3$	0.796093	+	0.605174i	0.459625	+	0.349397i
$4$	−0.161782	−	0.986827i	−0.0808910	−	0.493413i
$5$	−0.659445	−	1.24384i	−0.294913	−	0.556264i	0.691135	−	0.722725i	$-0.257111\pi$
$5$	−0.659445	−	1.24384i	−0.294913	−	0.556264i	−0.986048	+	0.166461i	$0.946766\pi$
$6$	0.976621	−	0.214970i	0.398704	−	0.0877613i
$7$	1.04625	+	0.113786i	0.395445	+	0.0430072i	0.303682	−	0.952774i	$-0.401784\pi$
$7$	1.04625	+	0.113786i	0.395445	+	0.0430072i	0.0917635	+	0.995781i	$0.470750\pi$
$8$	−0.856857	−	0.515554i	−0.302945	−	0.182276i
$9$	0.267528	+	0.963550i	0.0891761	+	0.321183i
$10$	−1.37493	−	0.302644i	−0.434790	−	0.0957045i
$11$	4.13316	+	1.39262i	1.24619	+	0.419892i	0.863672	−	0.504055i	$-0.168159\pi$
$11$	4.13316	+	1.39262i	1.24619	+	0.419892i	0.382522	+	0.923946i	$0.375056\pi$
$12$	0.468408	−	0.883512i	0.135218	−	0.255048i
$13$	1.87032	−	6.73628i	0.518733	−	1.86831i	0.0231756	−	0.999731i	$-0.492622\pi$
$13$	1.87032	−	6.73628i	0.518733	−	1.86831i	0.495557	−	0.868575i	$-0.334964\pi$
$14$	0.764051	−	0.723748i	0.204201	−	0.193430i
$15$	0.227763	−	1.38929i	0.0588082	−	0.358714i
$16$	−0.947653	+	0.319302i	−0.236913	+	0.0798254i
$17$	−0.401429	+	0.0436581i	−0.0973609	+	0.0105886i	−0.156670	−	0.987651i	$-0.550076\pi$
$17$	−0.401429	+	0.0436581i	−0.0973609	+	0.0105886i	0.0593089	+	0.998240i	$0.481110\pi$
$18$	0.907575	+	0.419889i	0.213918	+	0.0989688i
$19$	−0.0140881	+	0.259841i	−0.00323204	+	0.0596115i	−0.999704	−	0.0243090i	$-0.992261\pi$
$19$	−0.0140881	+	0.259841i	−0.00323204	+	0.0596115i	0.996472	+	0.0839205i	$0.0267442\pi$
$20$	−1.12077	+	0.851989i	−0.250612	+	0.190511i
$21$	0.764051	+	0.723748i	0.166730	+	0.157935i
$22$	3.73715	−	2.24857i	0.796764	−	0.479397i
$23$	−8.04980	+	3.72423i	−1.67850	+	0.776556i	−0.679416	+	0.733754i	$0.737767\pi$
$23$	−8.04980	+	3.72423i	−1.67850	+	0.776556i	−0.999084	+	0.0428028i	$0.986371\pi$
$24$	−0.370138	−	0.928977i	−0.0755541	−	0.189627i
$25$	1.69365	−	2.49795i	0.338731	−	0.499590i
$26$	−3.92332	−	5.78646i	−0.769426	−	1.13482i
$27$	−0.370138	+	0.928977i	−0.0712331	+	0.178782i
$28$	−0.0569768	−	1.05088i	−0.0107676	−	0.198597i
$29$	2.38522	+	2.80809i	0.442923	+	0.521450i	0.937642	−	0.347604i	$-0.113005\pi$
$29$	2.38522	+	2.80809i	0.442923	+	0.521450i	−0.494718	+	0.869054i	$0.664729\pi$
$30$	−0.911417	−	1.07300i	−0.166401	−	0.195903i
$31$	0.218536	+	4.03066i	0.0392502	+	0.723927i	0.950244	+	0.311507i	$0.100834\pi$
$31$	0.218536	+	4.03066i	0.0392502	+	0.723927i	−0.910994	+	0.412420i	$0.864684\pi$
$32$	−0.370138	+	0.928977i	−0.0654318	+	0.164221i
$33$	2.44760	+	3.60994i	0.426072	+	0.628409i
$34$	−0.226605	+	0.334218i	−0.0388625	+	0.0573179i
$35$	−0.548411	−	1.37641i	−0.0926983	−	0.232655i
$36$	0.907575	−	0.419889i	0.151263	−	0.0699815i
$37$	−8.56513	+	5.15347i	−1.40810	+	0.847225i	−0.997900	−	0.0647718i	$-0.979368\pi$
$37$	−8.56513	+	5.15347i	−1.40810	+	0.847225i	−0.410198	+	0.911996i	$0.634540\pi$
$38$	0.188920	+	0.178955i	0.0306469	+	0.0290303i
$39$	5.56557	−	4.23083i	0.891204	−	0.677476i
$40$	−0.0762190	+	1.40578i	−0.0120513	+	0.222273i
$41$	8.44149	+	3.90545i	1.31834	+	0.609929i	0.947793	−	0.318885i	$-0.103308\pi$
$41$	8.44149	+	3.90545i	1.31834	+	0.609929i	0.370546	+	0.928814i	$0.379170\pi$
$42$	1.04625	−	0.113786i	0.161440	−	0.0175576i
$43$	6.46206	−	2.17732i	0.985455	−	0.332038i	0.219980	−	0.975504i	$-0.429401\pi$
$43$	6.46206	−	2.17732i	0.985455	−	0.332038i	0.765475	+	0.643466i	$0.222504\pi$
$44$	0.705607	−	4.30401i	0.106374	−	0.648854i
$45$	1.02209	−	0.968171i	0.152364	−	0.144326i
$46$	−2.37286	+	8.54627i	−0.349859	+	1.26008i
$47$	−3.50327	+	6.60788i	−0.511005	+	0.963858i	0.484996	+	0.874516i	$0.338821\pi$
$47$	−3.50327	+	6.60788i	−0.511005	+	0.963858i	−0.996001	+	0.0893414i	$0.971524\pi$
$48$	−0.947653	−	0.319302i	−0.136782	−	0.0460872i
$49$	−5.75465	−	1.26670i	−0.822093	−	0.180956i
$50$	−0.807396	−	2.90798i	−0.114183	−	0.411250i
$51$	−0.345996	−	0.208179i	−0.0484491	−	0.0291509i
$52$	−6.95012	−	0.755871i	−0.963808	−	0.104820i
$53$	−13.8581	+	3.05040i	−1.90356	+	0.419005i	−0.999956	−	0.00936302i	$-0.997020\pi$
$53$	−13.8581	+	3.05040i	−1.90356	+	0.419005i	−0.903604	+	0.428368i	$0.859089\pi$
$54$	0.468408	+	0.883512i	0.0637423	+	0.120231i
$55$	−0.993382	−	6.05936i	−0.133948	−	0.817044i
$56$	−0.837823	−	0.636897i	−0.111959	−	0.0851089i
$57$	−0.168464	+	0.198331i	−0.0223136	+	0.0262696i
$58$	3.68438			0.483783
$59$	−2.82052	−	7.14455i	−0.367201	−	0.930142i
$59$	−2.82052	−	7.14455i	−0.367201	−	0.930142i
$60$	−1.40784			−0.181751
$61$	1.58472	−	1.86568i	0.202903	−	0.238875i	−0.651294	−	0.758825i	$-0.725774\pi$
$61$	1.58472	−	1.86568i	0.202903	−	0.238875i	0.854197	+	0.519950i	$0.174049\pi$
$62$	3.21349	+	2.44283i	0.408114	+	0.310240i
$63$	0.170262	+	1.03855i	0.0214510	+	0.130846i
$64$	0.468408	+	0.883512i	0.0585511	+	0.110439i
$65$	−9.61225	+	2.11582i	−1.19225	+	0.262435i
$66$	4.33590	+	0.471557i	0.533712	+	0.0580447i
$67$	11.2745	+	6.78367i	1.37741	+	0.828757i	0.995437	−	0.0954183i	$-0.0304189\pi$
$67$	11.2745	+	6.78367i	1.37741	+	0.828757i	0.381968	+	0.924176i	$0.375246\pi$
$68$	0.108027	+	0.389078i	0.0131002	+	0.0471826i
$69$	−8.66220	−	1.90669i	−1.04281	−	0.229539i
$70$	−1.40408	−	0.473089i	−0.167820	−	0.0565450i
$71$	−5.60729	+	10.5765i	−0.665463	+	1.25520i	0.289132	+	0.957289i	$0.406633\pi$
$71$	−5.60729	+	10.5765i	−0.665463	+	1.25520i	−0.954595	+	0.297907i	$0.903712\pi$
$72$	0.267528	−	0.963550i	0.0315285	−	0.113555i
$73$	−2.68921	+	2.54736i	−0.314748	+	0.298146i	−0.828722	−	0.559660i	$-0.810932\pi$
$73$	−2.68921	+	2.54736i	−0.314748	+	0.298146i	0.513974	+	0.857806i	$0.328173\pi$
$74$	−1.61717	+	9.86430i	−0.187992	+	1.14670i
$75$	2.86000	−	0.963647i	0.330245	−	0.111272i
$76$	0.258697	−	0.0281350i	0.0296746	−	0.00322730i
$77$	4.16585	+	1.92733i	0.474743	+	0.219639i
$78$	0.378491	−	6.98085i	0.0428556	−	0.790425i
$79$	5.37891	−	4.08894i	0.605174	−	0.460041i	−0.257169	−	0.966367i	$-0.582790\pi$
$79$	5.37891	−	4.08894i	0.605174	−	0.460041i	0.862343	+	0.506325i	$0.168996\pi$
$80$	1.02209	+	0.968171i	0.114273	+	0.108245i
$81$	−0.856857	+	0.515554i	−0.0952064	+	0.0572838i
$82$	8.44149	−	3.90545i	0.932207	−	0.431285i
$83$	−2.31074	−	5.79951i	−0.253636	−	0.636579i	0.745930	−	0.666024i	$-0.232005\pi$
$83$	−2.31074	−	5.79951i	−0.253636	−	0.636579i	−0.999566	+	0.0294452i	$0.990626\pi$
$84$	0.590604	−	0.871075i	0.0644401	−	0.0950421i
$85$	0.319024	+	0.470526i	0.0346030	+	0.0510357i
$86$	2.52398	−	6.33471i	0.272167	−	0.683089i
$87$	0.199468	+	3.67897i	0.0213852	+	0.394427i
$88$	−2.82355	−	3.32414i	−0.300992	−	0.354355i
$89$	0.778995	+	0.917104i	0.0825733	+	0.0972128i	0.801897	−	0.597462i	$-0.203824\pi$
$89$	0.778995	+	0.917104i	0.0825733	+	0.0972128i	−0.719324	+	0.694675i	$0.755548\pi$
$90$	−0.0762190	−	1.40578i	−0.00803418	−	0.148182i
$91$	2.72332	−	6.83501i	0.285481	−	0.716503i
$92$	4.97749	+	7.34124i	0.518939	+	0.765377i
$93$	−2.26527	+	3.34103i	−0.234898	+	0.346449i
$94$	2.76830	+	6.94791i	0.285528	+	0.716622i
$95$	0.332492	−	0.153827i	0.0341129	−	0.0157823i
$96$	−0.856857	+	0.515554i	−0.0874526	+	0.0526185i
$97$	−0.228792	−	0.216724i	−0.0232303	−	0.0220050i	0.675996	−	0.736905i	$-0.263714\pi$
$97$	−0.228792	−	0.216724i	−0.0232303	−	0.0220050i	−0.699227	+	0.714900i	$0.746472\pi$
$98$	−4.69091	+	3.56594i	−0.473854	+	0.360214i
$99$	−0.236125	+	4.35507i	−0.0237315	+	0.437701i
$100$	−2.73905	−	1.26722i	−0.273905	−	0.126722i
$101$	0.603470	−	0.0656313i	0.0600475	−	0.00653056i	−0.0780459	−	0.996950i	$-0.524868\pi$
$101$	0.603470	−	0.0656313i	0.0600475	−	0.00653056i	0.138093	+	0.990419i	$0.455903\pi$
$102$	−0.382659	+	0.128933i	−0.0378889	+	0.0127662i
$103$	0.807591	−	4.92609i	0.0795743	−	0.485382i	−0.916731	−	0.399504i	$-0.869182\pi$
$103$	0.807591	−	4.92609i	0.0795743	−	0.485382i	0.996306	−	0.0858778i	$-0.0273695\pi$
$104$	−5.07551	+	4.80778i	−0.497695	+	0.471441i
$105$	0.396380	−	1.42763i	0.0386827	−	0.139323i
$106$	−6.64666	+	12.5369i	−0.645581	+	1.21769i
$107$	5.36601	+	1.80802i	0.518752	+	0.174788i	0.566485	−	0.824072i	$-0.308303\pi$
$107$	5.36601	+	1.80802i	0.518752	+	0.174788i	−0.0477328	+	0.998860i	$0.515200\pi$
$108$	0.976621	+	0.214970i	0.0939754	+	0.0206855i
$109$	2.57227	+	9.26447i	0.246378	+	0.887375i	0.978508	+	0.206210i	$0.0661128\pi$
$109$	2.57227	+	9.26447i	0.246378	+	0.887375i	−0.732129	+	0.681166i	$0.761473\pi$
$110$	−5.26132	−	3.16563i	−0.501647	−	0.301831i
$111$	−9.93738	−	1.08076i	−0.943215	−	0.102581i
$112$	−1.02781	+	0.226239i	−0.0971193	+	0.0213776i
$113$	−2.32827	−	4.39159i	−0.219025	−	0.413126i	0.749513	−	0.661990i	$-0.230288\pi$
$113$	−2.32827	−	4.39159i	−0.219025	−	0.413126i	−0.968538	+	0.248864i	$0.919943\pi$
$114$	0.0420993	+	0.256794i	0.00394296	+	0.0240510i
$115$	9.94076	+	7.55677i	0.926981	+	0.704673i
$116$	2.38522	−	2.80809i	0.221462	−	0.260725i
$117$	6.99110			0.646328
$118$	−7.27128	−	2.47559i	−0.669375	−	0.227896i
$119$	−0.424963			−0.0389563
$120$	−0.911417	+	1.07300i	−0.0832006	+	0.0979513i
$121$	6.38657	+	4.85494i	0.580597	+	0.441358i
$122$	−0.396022	−	2.41563i	−0.0358541	−	0.218701i
$123$	4.35674	+	8.21768i	0.392834	+	0.740963i
$124$	3.94220	−	0.867744i	0.354020	−	0.0779258i
$125$	−11.2219	−	1.22045i	−1.00371	−	0.109161i
$126$	0.901772	+	0.542578i	0.0803363	+	0.0483367i
$127$	−3.19695	−	11.5144i	−0.283684	−	1.02174i	−0.958813	−	0.284037i	$-0.908326\pi$
$127$	−3.19695	−	11.5144i	−0.283684	−	1.02174i	0.675130	−	0.737699i	$-0.264088\pi$
$128$	0.976621	+	0.214970i	0.0863219	+	0.0190009i
$129$	6.46206	+	2.17732i	0.568953	+	0.191702i
$130$	−4.61024	+	8.69584i	−0.404345	+	0.762676i
$131$	−2.51689	+	9.06501i	−0.219901	+	0.792013i	0.768461	+	0.639897i	$0.221023\pi$
$131$	−2.51689	+	9.06501i	−0.219901	+	0.792013i	−0.988363	+	0.152117i	$0.951391\pi$
$132$	3.16640	−	2.99938i	0.275600	−	0.261062i
$133$	−0.0443060	+	0.270255i	−0.00384182	+	0.0234341i
$134$	12.4692	−	4.20138i	1.07718	−	0.362944i
$135$	1.39959	−	0.152214i	0.120457	−	0.0131005i
$136$	0.366476	+	0.169550i	0.0314250	+	0.0145388i
$137$	0.275556	−	5.08233i	0.0235423	−	0.434213i	−0.962874	−	0.269950i	$-0.912993\pi$
$137$	0.275556	−	5.08233i	0.0235423	−	0.434213i	0.986417	−	0.164263i	$-0.0525244\pi$
$138$	−7.06100	+	5.36763i	−0.601072	+	0.456923i
$139$	5.27190	+	4.99381i	0.447157	+	0.423570i	0.877855	−	0.478926i	$-0.158974\pi$
$139$	5.27190	+	4.99381i	0.447157	+	0.423570i	−0.430698	+	0.902496i	$0.641733\pi$
$140$	−1.26955	+	0.763864i	−0.107297	+	0.0645583i
$141$	−6.78785	+	3.14039i	−0.571640	+	0.264469i
$142$	4.43090	+	11.1207i	0.371833	+	0.933230i
$143$	17.1114	−	25.2374i	1.43093	−	2.11046i
$144$	−0.561187	−	0.827689i	−0.0467656	−	0.0689741i
$145$	1.91991	−	4.81862i	0.159440	−	0.400165i
$146$	0.200540	+	3.69874i	0.0165968	+	0.306110i
$147$	−3.81467	−	4.49098i	−0.314629	−	0.370409i
$148$	6.47126	+	7.61856i	0.531934	+	0.626242i
$149$	−0.675142	−	12.4523i	−0.0553098	−	1.02013i	−0.886086	−	0.463522i	$-0.846586\pi$
$149$	−0.675142	−	12.4523i	−0.0553098	−	1.02013i	0.830776	−	0.556607i	$-0.187897\pi$
$150$	1.11707	−	2.80364i	0.0912085	−	0.228916i
$151$	−10.7320	−	15.8285i	−0.873356	−	1.28810i	−0.956549	−	0.291571i	$-0.905822\pi$
$151$	−10.7320	−	15.8285i	−0.873356	−	1.28810i	0.0831932	−	0.996533i	$-0.473488\pi$
$152$	0.146033	−	0.215383i	0.0118449	−	0.0174699i
$153$	−0.149460	−	0.375117i	−0.0120832	−	0.0303264i
$154$	4.16585	−	1.92733i	0.335694	−	0.155309i
$155$	4.86940	−	2.92982i	0.391119	−	0.235329i
$156$	−5.07551	−	4.80778i	−0.406366	−	0.384930i
$157$	−5.46583	+	4.15502i	−0.436221	+	0.331607i	−0.800129	−	0.599828i	$-0.795235\pi$
$157$	−5.46583	+	4.15502i	−0.436221	+	0.331607i	0.363908	+	0.931435i	$0.381442\pi$
$158$	0.365797	−	6.74672i	0.0291012	−	0.536740i
$159$	−12.8784	−	5.95818i	−1.02132	−	0.472514i
$160$	1.39959	−	0.152214i	0.110647	−	0.0120336i
$161$	−8.84586	+	2.98052i	−0.697152	+	0.234898i
$162$	−0.161782	+	0.986827i	−0.0127108	+	0.0775324i
$163$	2.73836	−	2.59391i	0.214485	−	0.203171i	−0.572913	−	0.819616i	$-0.694187\pi$
$163$	2.73836	−	2.59391i	0.214485	−	0.203171i	0.787397	+	0.616446i	$0.211428\pi$
$164$	2.48832	−	8.96212i	0.194305	−	0.699824i
$165$	2.87614	−	5.42498i	0.223908	−	0.422335i
$166$	−5.91611	−	1.99337i	−0.459179	−	0.154715i
$167$	13.7133	+	3.01852i	1.06117	+	0.233580i	0.711061	−	0.703130i	$-0.248215\pi$
$167$	13.7133	+	3.01852i	1.06117	+	0.233580i	0.350105	+	0.936710i	$0.386146\pi$
$168$	−0.281552	−	1.01406i	−0.0217222	−	0.0782363i
$169$	−30.7402	−	18.4958i	−2.36463	−	1.42275i
$170$	0.565149	+	0.0614636i	0.0433449	+	0.00471404i
$171$	−0.254138	+	0.0559401i	−0.0194344	+	0.00427784i
$172$	−3.19408	−	6.02468i	−0.243547	−	0.459378i
$173$	1.44529	+	8.81585i	0.109883	+	0.670257i	0.983120	+	0.182961i	$0.0585683\pi$
$173$	1.44529	+	8.81585i	0.109883	+	0.670257i	−0.873237	+	0.487296i	$0.837983\pi$
$174$	2.93311	+	2.22969i	0.222358	+	0.169032i
$175$	2.05622	−	2.42077i	0.155435	−	0.182993i
$176$	−4.36147			−0.328758
$177$	2.07830	−	7.39464i	0.156215	−	0.555815i
$178$	1.20329			0.0901906
$179$	5.82883	−	6.86223i	0.435668	−	0.512907i	−0.499887	−	0.866091i	$-0.666625\pi$
$179$	5.82883	−	6.86223i	0.435668	−	0.512907i	0.935554	+	0.353183i	$0.114901\pi$
$180$	−1.12077	−	0.851989i	−0.0835374	−	0.0635035i
$181$	0.112340	+	0.685242i	0.00835014	+	0.0509336i	0.990673	−	0.136261i	$-0.0435087\pi$
$181$	0.112340	+	0.685242i	0.00835014	+	0.0509336i	−0.982323	+	0.187195i	$0.940060\pi$
$182$	−3.44635	−	6.50050i	−0.255460	−	0.481849i
$183$	2.39064	−	0.526221i	0.176722	−	0.0388993i
$184$	8.81757	+	0.958969i	0.650040	+	0.0706961i
$185$	12.0583	+	7.25526i	0.886547	+	0.533417i
$186$	1.07990	+	3.88944i	0.0791820	+	0.285188i
$187$	−1.71997	−	0.378594i	−0.125777	−	0.0276855i
$188$	7.08759	+	2.38809i	0.516916	+	0.174169i
$189$	−0.492962	+	0.929825i	−0.0358577	+	0.0676348i
$190$	0.0980094	−	0.352998i	0.00711035	−	0.0256092i
$191$	1.12704	−	1.06759i	0.0815495	−	0.0772478i	−0.645839	−	0.763473i	$-0.723492\pi$
$191$	1.12704	−	1.06759i	0.0815495	−	0.0772478i	0.727389	+	0.686226i	$0.240734\pi$
$192$	−0.161782	+	0.986827i	−0.0116756	+	0.0712181i
$193$	−16.4848	+	5.55439i	−1.18660	+	0.399813i	−0.842281	−	0.539038i	$-0.818788\pi$
$193$	−16.4848	+	5.55439i	−1.18660	+	0.399813i	−0.344323	+	0.938851i	$0.611891\pi$
$194$	−0.313296	+	0.0340730i	−0.0224933	+	0.00244630i
$195$	−8.93268	−	4.13270i	−0.639683	−	0.295949i
$196$	−0.319009	+	5.88377i	−0.0227864	+	0.420270i
$197$	14.0855	−	10.7075i	1.00355	−	0.762879i	0.0319453	−	0.999490i	$-0.489830\pi$
$197$	14.0855	−	10.7075i	1.00355	−	0.762879i	0.971604	+	0.236611i	$0.0760367\pi$
$198$	3.16640	+	2.99938i	0.225027	+	0.213156i
$199$	21.5697	−	12.9781i	1.52904	−	0.919991i	0.531709	−	0.846927i	$-0.321550\pi$
$199$	21.5697	−	12.9781i	1.52904	−	0.919991i	0.997327	−	0.0730638i	$-0.0232777\pi$
$200$	−2.73905	+	1.26722i	−0.193680	+	0.0896059i
$201$	4.87029	+	12.2235i	0.343524	+	0.862179i
$202$	0.340657	−	0.502431i	0.0239685	−	0.0353509i
$203$	2.17601	+	3.20937i	0.152726	+	0.225254i
$204$	−0.149460	+	0.375117i	−0.0104643	+	0.0262635i
$205$	−0.708924	−	13.0753i	−0.0495134	−	0.913221i
$206$	−3.23165	−	3.80460i	−0.225160	−	0.265079i
$207$	−5.74203	−	6.76005i	−0.399099	−	0.469856i
$208$	0.378491	+	6.98085i	0.0262436	+	0.484035i
$209$	−0.420088	+	1.05434i	−0.0290581	+	0.0729304i
$210$	−0.831476	−	1.22634i	−0.0573773	−	0.0846252i
$211$	−8.53794	+	12.5925i	−0.587776	+	0.866904i	−0.999004	−	0.0446281i	$-0.985790\pi$
$211$	−8.53794	+	12.5925i	−0.587776	+	0.866904i	0.411228	+	0.911533i	$0.365100\pi$
$212$	5.25222	+	13.1821i	0.360724	+	0.905348i
$213$	−10.8645	+	5.02647i	−0.744425	+	0.344408i
$214$	4.85189	−	2.91928i	0.331668	−	0.199558i
$215$	−6.96962	−	6.60198i	−0.475324	−	0.450251i
$216$	0.796093	−	0.605174i	0.0541673	−	0.0411769i
$217$	−0.229991	+	4.24194i	−0.0156128	+	0.287961i
$218$	8.72628	+	4.03721i	0.591018	+	0.273434i
$219$	−3.68246	+	0.400491i	−0.248837	+	0.0270627i
$220$	−5.81883	+	1.96059i	−0.392305	+	0.132183i
$221$	−0.456708	+	2.78579i	−0.0307215	+	0.187393i
$222$	−7.25704	+	6.87423i	−0.487060	+	0.461368i
$223$	5.37339	−	19.3532i	0.359828	−	1.29599i	−0.533202	−	0.845988i	$-0.679011\pi$
$223$	5.37339	−	19.3532i	0.359828	−	1.29599i	0.893030	−	0.449997i	$-0.148575\pi$
$224$	−0.492962	+	0.929825i	−0.0329374	+	0.0621265i
$225$	2.86000	+	0.963647i	0.190667	+	0.0642431i
$226$	−4.85439	−	1.06853i	−0.322909	−	0.0710777i
$227$	−1.17893	−	4.24611i	−0.0782482	−	0.281824i	0.914067	−	0.405564i	$-0.132925\pi$
$227$	−1.17893	−	4.24611i	−0.0782482	−	0.281824i	−0.992315	+	0.123740i	$0.960511\pi$
$228$	0.222973	+	0.134159i	0.0147668	+	0.00888487i
$229$	26.9740	+	2.93360i	1.78249	+	0.193858i	0.939147	−	0.343516i	$-0.111618\pi$
$229$	26.9740	+	2.93360i	1.78249	+	0.193858i	0.843344	+	0.537374i	$0.180584\pi$
$230$	12.1950	−	2.68432i	0.804114	−	0.176999i
$231$	2.15004	+	4.05540i	0.141462	+	0.266826i
$232$	−0.596066	−	3.63584i	−0.0391337	−	0.238705i
$233$	−1.79893	−	1.36751i	−0.117852	−	0.0895885i	0.544588	−	0.838704i	$-0.316686\pi$
$233$	−1.79893	−	1.36751i	−0.117852	−	0.0895885i	−0.662440	+	0.749115i	$0.730479\pi$
$234$	4.52594	−	5.32835i	0.295870	−	0.348325i
$235$	10.5294			0.686861
$236$	−6.59412	+	3.93923i	−0.429241	+	0.256422i
$237$	6.75663			0.438890
$238$	−0.275115	+	0.323891i	−0.0178331	+	0.0209947i
$239$	−12.9720	−	9.86106i	−0.839089	−	0.637859i	0.0947702	−	0.995499i	$-0.469788\pi$
$239$	−12.9720	−	9.86106i	−0.839089	−	0.637859i	−0.933860	+	0.357640i	$0.883581\pi$
$240$	0.227763	+	1.38929i	0.0147021	+	0.0896786i
$241$	0.202291	+	0.381562i	0.0130307	+	0.0245786i	0.889942	−	0.456074i	$-0.150745\pi$
$241$	0.202291	+	0.381562i	0.0130307	+	0.0245786i	−0.876911	+	0.480652i	$0.840400\pi$
$242$	7.83483	−	1.72458i	0.503642	−	0.110860i
$243$	−0.994138	−	0.108119i	−0.0637740	−	0.00693584i
$244$	−2.09748	−	1.26201i	−0.134277	−	0.0807920i
$245$	2.21930	+	7.99321i	0.141786	+	0.510667i
$246$	9.08369	+	1.99947i	0.579155	+	0.127482i
$247$	1.72401	+	0.580886i	0.109696	+	0.0369609i
$248$	1.89077	−	3.56636i	0.120064	−	0.226464i
$249$	1.67015	−	6.01535i	0.105842	−	0.381207i
$250$	−8.19507	+	7.76278i	−0.518302	+	0.490961i
$251$	1.70989	−	10.4299i	0.107927	−	0.658328i	−0.876347	−	0.481681i	$-0.840027\pi$
$251$	1.70989	−	10.4299i	0.107927	−	0.658328i	0.984274	−	0.176647i	$-0.0565252\pi$
$252$	0.997328	−	0.336039i	0.0628257	−	0.0211685i
$253$	−38.4575	+	4.18251i	−2.41780	+	0.262952i
$254$	−10.8455	−	5.01766i	−0.680506	−	0.314836i
$255$	−0.0307769	+	0.567647i	−0.00192733	+	0.0355475i
$256$	0.796093	−	0.605174i	0.0497558	−	0.0378234i
$257$	14.0946	+	13.3511i	0.879194	+	0.832817i	0.986895	−	0.161367i	$-0.0515901\pi$
$257$	14.0946	+	13.3511i	0.879194	+	0.832817i	−0.107700	+	0.994183i	$0.534349\pi$
$258$	5.84292	−	3.51557i	0.363764	−	0.218870i
$259$	−9.54765	+	4.41721i	−0.593262	+	0.274472i
$260$	3.64303	+	9.14332i	0.225931	+	0.567045i
$261$	−2.06763	+	3.04952i	−0.127983	+	0.188760i
$262$	5.27961	+	7.78684i	0.326175	+	0.481072i
$263$	−1.11038	+	2.78685i	−0.0684690	+	0.171844i	−0.959229	−	0.282629i	$-0.908793\pi$
$263$	−1.11038	+	2.78685i	−0.0684690	+	0.171844i	0.890760	+	0.454474i	$0.150173\pi$
$264$	−0.236125	−	4.35507i	−0.0145325	−	0.268036i
$265$	12.9329	+	15.2258i	0.794461	+	0.935312i
$266$	0.177295	+	0.208728i	0.0108706	+	0.0127979i
$267$	0.0651449	+	1.20153i	0.00398681	+	0.0735323i
$268$	4.87029	−	12.2235i	0.297500	−	0.746669i
$269$	3.69472	+	5.44931i	0.225271	+	0.332250i	0.923482	−	0.383642i	$-0.125330\pi$
$269$	3.69472	+	5.44931i	0.225271	+	0.332250i	−0.698211	+	0.715893i	$0.746020\pi$
$270$	0.790062	−	1.16525i	0.0480816	−	0.0709151i
$271$	9.91268	+	24.8790i	0.602153	+	1.51129i	0.841446	+	0.540342i	$0.181705\pi$
$271$	9.91268	+	24.8790i	0.602153	+	1.51129i	−0.239293	+	0.970947i	$0.576916\pi$
$272$	0.366476	−	0.169550i	0.0222209	−	0.0102805i
$273$	6.30438	−	3.79322i	0.381559	−	0.229576i
$274$	−3.69517	−	3.50025i	−0.223233	−	0.211458i
$275$	10.4788	−	7.96581i	0.631898	−	0.480356i
$276$	−0.480189	+	8.85656i	−0.0289040	+	0.533102i
$277$	−19.8666	−	9.19129i	−1.19367	−	0.552251i	−0.280510	−	0.959851i	$-0.590504\pi$
$277$	−19.8666	−	9.19129i	−1.19367	−	0.552251i	−0.913161	+	0.407600i	$0.866366\pi$
$278$	7.21905	−	0.785119i	0.432970	−	0.0470883i
$279$	−3.82527	+	1.28888i	−0.229013	+	0.0771635i
$280$	−0.239702	+	1.46212i	−0.0143250	+	0.0873784i
$281$	11.4901	−	10.8840i	0.685440	−	0.649283i	−0.263529	−	0.964651i	$-0.584887\pi$
$281$	11.4901	−	10.8840i	0.685440	−	0.649283i	0.948969	+	0.315368i	$0.102128\pi$
$282$	−2.00087	+	7.20649i	−0.119150	+	0.429140i
$283$	−3.63133	+	6.84942i	−0.215860	+	0.407156i	−0.967668	−	0.252226i	$-0.918837\pi$
$283$	−3.63133	+	6.84942i	−0.215860	+	0.407156i	0.751808	+	0.659382i	$0.229182\pi$
$284$	11.3443	+	3.82234i	0.673160	+	0.226814i
$285$	0.357786	+	0.0787547i	0.0211934	+	0.00466503i
$286$	−8.15733	−	29.3800i	−0.482353	−	1.73728i
$287$	8.38752	+	5.04660i	0.495100	+	0.297892i
$288$	−0.994138	−	0.108119i	−0.0585801	−	0.00637097i
$289$	−16.4433	+	3.61945i	−0.967254	+	0.212909i
$290$	−2.42964	−	4.58279i	−0.142674	−	0.269111i
$291$	−0.0509845	−	0.310991i	−0.00298876	−	0.0182306i
$292$	2.94886	+	2.24167i	0.172569	+	0.131184i
$293$	5.98803	−	7.04965i	0.349824	−	0.411845i	−0.558905	−	0.829232i	$-0.688778\pi$
$293$	5.98803	−	7.04965i	0.349824	−	0.411845i	0.908729	+	0.417387i	$0.137054\pi$
$294$	−5.89242			−0.343653
$295$	−7.02673	+	8.21973i	−0.409112	+	0.478571i
$296$	9.99598			0.581005
$297$	−2.82355	+	3.32414i	−0.163839	+	0.192886i
$298$	−9.92772	−	7.54685i	−0.575097	−	0.437177i
$299$	10.0318	+	61.1912i	0.580153	+	3.53878i
$300$	−1.41365	−	2.66643i	−0.0816171	−	0.153946i
$301$	7.00868	−	1.54273i	0.403973	−	0.0889213i
$302$	−19.0116	−	2.06764i	−1.09400	−	0.118979i
$303$	0.520137	+	0.312956i	0.0298811	+	0.0179788i
$304$	−0.0696168	−	0.250737i	−0.00399280	−	0.0143808i
$305$	−3.36565	−	0.740835i	−0.192716	−	0.0424201i
$306$	−0.382659	−	0.128933i	−0.0218752	−	0.00737060i
$307$	−4.67719	+	8.82212i	−0.266941	+	0.503505i	−0.980356	−	0.197238i	$-0.936803\pi$
$307$	−4.67719	+	8.82212i	−0.266941	+	0.503505i	0.713414	+	0.700742i	$0.247148\pi$
$308$	1.22798	−	4.42278i	0.0699706	−	0.252011i
$309$	3.62406	−	3.43289i	0.206166	−	0.195290i
$310$	0.919384	−	5.60799i	0.0522175	−	0.318513i
$311$	16.0546	−	5.40943i	0.910374	−	0.306741i	0.175132	−	0.984545i	$-0.443965\pi$
$311$	16.0546	−	5.40943i	0.910374	−	0.306741i	0.735242	+	0.677804i	$0.237068\pi$
$312$	−6.95012	+	0.755871i	−0.393473	+	0.0427928i
$313$	−11.6246	−	5.37811i	−0.657060	−	0.303989i	0.0628834	−	0.998021i	$-0.479970\pi$
$313$	−11.6246	−	5.37811i	−0.657060	−	0.303989i	−0.719944	+	0.694032i	$0.755832\pi$
$314$	−0.371708	+	6.85575i	−0.0209767	+	0.386892i
$315$	1.17952	−	0.896649i	0.0664585	−	0.0505205i
$316$	−4.90528	−	4.64653i	−0.275944	−	0.261388i
$317$	8.92545	−	5.37027i	0.501303	−	0.301624i	−0.242351	−	0.970189i	$-0.577918\pi$
$317$	8.92545	−	5.37027i	0.501303	−	0.301624i	0.743654	+	0.668564i	$0.233091\pi$
$318$	−12.8784	+	5.95818i	−0.722184	+	0.334118i
$319$	5.94786	+	14.9280i	0.333016	+	0.835807i
$320$	0.790062	−	1.16525i	0.0441658	−	0.0651397i
$321$	3.17768	+	4.68672i	0.177361	+	0.261587i
$322$	−3.45505	+	8.67153i	−0.192543	+	0.483245i
$323$	−0.00568874	−	0.104923i	−0.000316530	−	0.00583805i
$324$	0.647386	+	0.762162i	0.0359659	+	0.0423423i
$325$	−13.6592	−	16.0809i	−0.757677	−	0.892007i
$326$	−0.204205	−	3.76633i	−0.0113098	−	0.208598i
$327$	−3.55885	+	8.93205i	−0.196805	+	0.493943i
$328$	−5.21968	−	7.69846i	−0.288209	−	0.425076i
$329$	−4.41718	+	6.51486i	−0.243527	+	0.359176i
$330$	−2.27274	−	5.70415i	−0.125110	−	0.314003i
$331$	0.106083	−	0.0490790i	0.00583083	−	0.00269763i	−0.416972	−	0.908920i	$-0.636909\pi$
$331$	0.106083	−	0.0490790i	0.00583083	−	0.00269763i	0.422802	+	0.906222i	$0.361046\pi$
$332$	−5.34928	+	3.21855i	−0.293580	+	0.176641i
$333$	−7.25704	−	6.87423i	−0.397683	−	0.376705i
$334$	11.1784	−	8.49760i	0.611655	−	0.464968i
$335$	1.00289	−	18.4972i	0.0547938	−	1.01061i
$336$	−0.955149	−	0.441899i	−0.0521077	−	0.0241076i
$337$	1.12216	−	0.122042i	0.0611278	−	0.00664805i	−0.0775040	−	0.996992i	$-0.524695\pi$
$337$	1.12216	−	0.122042i	0.0611278	−	0.00664805i	0.138632	+	0.990344i	$0.455730\pi$
$338$	−33.9975	+	11.4551i	−1.84922	+	0.623075i
$339$	0.804154	−	4.90512i	0.0436756	−	0.266410i
$340$	0.412715	−	0.390944i	0.0223826	−	0.0212019i
$341$	−4.70994	+	16.9637i	−0.255058	+	0.918634i
$342$	−0.121890	+	0.229909i	−0.00659107	+	0.0124321i
$343$	−12.8580	−	4.33235i	−0.694265	−	0.233925i
$344$	−6.65959	−	1.46589i	−0.359061	−	0.0790353i
$345$	3.34061	+	12.0318i	0.179852	+	0.647770i
$346$	7.65477	+	4.60572i	0.411523	+	0.247605i
$347$	−11.7644	−	1.27946i	−0.631548	−	0.0686850i	−0.213254	−	0.976997i	$-0.568406\pi$
$347$	−11.7644	−	1.27946i	−0.631548	−	0.0686850i	−0.418294	+	0.908312i	$0.637372\pi$
$348$	3.59824	−	0.792032i	0.192886	−	0.0424574i
$349$	−1.09583	−	2.06695i	−0.0586583	−	0.110641i	0.852449	−	0.522810i	$-0.175116\pi$
$349$	−1.09583	−	2.06695i	−0.0586583	−	0.110641i	−0.911108	+	0.412169i	$0.864771\pi$
$350$	−0.513849	−	3.13434i	−0.0274664	−	0.167538i
$351$	5.56557	+	4.23083i	0.297068	+	0.225825i
$352$	−2.82355	+	3.32414i	−0.150496	+	0.177177i
$353$	−23.2674			−1.23840			−0.619199	−	0.785234i	$-0.712543\pi$
$353$	−23.2674			−1.23840			−0.619199	+	0.785234i	$0.712543\pi$
$354$	−4.29045	−	6.37119i	−0.228035	−	0.338625i
$355$	16.8532			0.894474
$356$	0.778995	−	0.917104i	0.0412867	−	0.0486064i
$357$	−0.338310	−	0.257177i	−0.0179053	−	0.0136112i
$358$	−1.45663	−	8.88503i	−0.0769851	−	0.469589i
$359$	1.41565	+	2.67020i	0.0747151	+	0.140928i	0.918055	−	0.396453i	$-0.129759\pi$
$359$	1.41565	+	2.67020i	0.0747151	+	0.140928i	−0.843340	+	0.537380i	$0.819414\pi$
$360$	−1.37493	+	0.302644i	−0.0724650	+	0.0159507i
$361$	18.8213	+	2.04694i	0.990595	+	0.107734i
$362$	0.594992	+	0.357995i	0.0312721	+	0.0188158i
$363$	2.14622	+	7.72997i	0.112647	+	0.405718i
$364$	−7.18555	−	1.58166i	−0.376625	−	0.0829015i
$365$	4.94190	+	1.66512i	0.258671	+	0.0871564i
$366$	1.14661	−	2.16273i	0.0599340	−	0.113048i
$367$	−9.87462	+	35.5652i	−0.515451	+	1.85649i	0.000717517		1.00000i	$0.499772\pi$
$367$	−9.87462	+	35.5652i	−0.515451	+	1.85649i	−0.516169	+	0.856487i	$0.672642\pi$
$368$	6.43926	−	6.09960i	0.335670	−	0.317963i
$369$	−1.50476	+	9.17862i	−0.0783346	+	0.477820i
$370$	13.3361	−	4.49345i	0.693310	−	0.233603i
$371$	−14.8462	+	1.61462i	−0.770774	+	0.0838267i
$372$	3.66350	+	1.69491i	0.189943	+	0.0878772i
$373$	−1.16142	+	21.4211i	−0.0601359	+	1.10914i	0.800306	+	0.599592i	$0.204671\pi$
$373$	−1.16142	+	21.4211i	−0.0601359	+	1.10914i	−0.860442	+	0.509549i	$0.829812\pi$
$374$	−1.40203	+	1.06580i	−0.0724975	+	0.0551112i
$375$	−8.19507	−	7.76278i	−0.423192	−	0.400868i
$376$	6.40852	−	3.85588i	0.330494	−	0.198852i
$377$	23.3772	−	10.8154i	1.20399	−	0.557024i
$378$	0.389540	+	0.977672i	0.0200358	+	0.0502860i
$379$	−12.8772	+	18.9925i	−0.661459	+	0.975578i	0.337949	+	0.941164i	$0.390267\pi$
$379$	−12.8772	+	18.9925i	−0.661459	+	0.975578i	−0.999408	+	0.0344140i	$0.989044\pi$
$380$	−0.205592	−	0.303225i	−0.0105466	−	0.0155551i
$381$	4.42314	−	11.1012i	0.226604	−	0.568733i
$382$	−0.0840453	−	1.55012i	−0.00430013	−	0.0793113i
$383$	−14.5157	−	17.0892i	−0.741719	−	0.873219i	0.253851	−	0.967243i	$-0.418303\pi$
$383$	−14.5157	−	17.0892i	−0.741719	−	0.873219i	−0.995570	+	0.0940246i	$0.970027\pi$
$384$	0.647386	+	0.762162i	0.0330368	+	0.0388939i
$385$	−0.349852	−	6.45264i	−0.0178301	−	0.328857i
$386$	−6.43871	+	16.1599i	−0.327722	+	0.822520i
$387$	3.82674	+	5.64402i	0.194524	+	0.286902i
$388$	−0.176854	+	0.260840i	−0.00897841	+	0.0132422i
$389$	9.14310	+	22.9475i	0.463574	+	1.16348i	0.956062	+	0.293163i	$0.0947080\pi$
$389$	9.14310	+	22.9475i	0.463574	+	1.16348i	−0.492489	+	0.870319i	$0.663913\pi$
$390$	−8.93268	+	4.13270i	−0.452324	+	0.209267i
$391$	3.06883	−	1.84646i	0.155198	−	0.0933793i
$392$	4.27787	+	4.05221i	0.216065	+	0.204668i
$393$	−7.48958	+	5.69343i	−0.377800	+	0.287196i
$394$	0.957895	−	17.6673i	0.0482580	−	0.890067i
$395$	−8.63309	−	3.99409i	−0.434378	−	0.200965i
$396$	4.33590	−	0.471557i	0.217887	−	0.0236967i
$397$	−33.5264	+	11.2963i	−1.68264	+	0.566947i	−0.988276	−	0.152677i	$-0.951211\pi$
$397$	−33.5264	+	11.2963i	−1.68264	+	0.566947i	−0.694364	+	0.719624i	$0.744314\pi$
$398$	4.07255	−	24.8414i	0.204138	−	1.24519i
$399$	−0.198823	+	0.188335i	−0.00995360	+	0.00942855i
$400$	−0.807396	+	2.90798i	−0.0403698	+	0.145399i
$401$	4.04076	−	7.62167i	0.201786	−	0.380608i	−0.761880	−	0.647718i	$-0.775724\pi$
$401$	4.04076	−	7.62167i	0.201786	−	0.380608i	0.963666	+	0.267109i	$0.0860685\pi$
$402$	12.4692	+	4.20138i	0.621909	+	0.209546i
$403$	27.5603	+	6.06649i	1.37288	+	0.302193i
$404$	−0.162397	−	0.584902i	−0.00807957	−	0.0291000i
$405$	1.20632	+	0.725818i	0.0599425	+	0.0360662i
$406$	3.85478	+	0.419232i	0.191309	+	0.0208062i
$407$	−42.5779	+	9.37209i	−2.11051	+	0.464557i
$408$	0.189142	+	0.356759i	0.00936391	+	0.0176622i
$409$	−5.29573	−	32.3026i	−0.261857	−	1.59726i	−0.710599	−	0.703597i	$-0.751576\pi$
$409$	−5.29573	−	32.3026i	−0.261857	−	1.59726i	0.448742	−	0.893661i	$-0.351872\pi$
$410$	−10.4245	−	7.92448i	−0.514828	−	0.391362i
$411$	3.29506	−	3.87925i	0.162533	−	0.191349i
$412$	−4.99185			−0.245931
$413$	−2.13802	−	7.79592i	−0.105205	−	0.383612i
$414$	−8.86957			−0.435915
$415$	−5.68989	+	6.69865i	−0.279306	+	0.328824i
$416$	5.56557	+	4.23083i	0.272874	+	0.207434i
$417$	1.17480	+	7.16596i	0.0575302	+	0.350919i
$418$	0.531620	+	1.00274i	0.0260024	+	0.0490457i
$419$	−3.62807	+	0.798598i	−0.177243	+	0.0390141i	−0.302705	−	0.953084i	$-0.597890\pi$
$419$	−3.62807	+	0.798598i	−0.177243	+	0.0390141i	0.125462	+	0.992098i	$0.459959\pi$
$420$	−1.47295	−	0.160193i	−0.0718727	−	0.00781663i
$421$	6.19890	+	3.72975i	0.302116	+	0.181777i	0.658537	−	0.752548i	$-0.271176\pi$
$421$	6.19890	+	3.72975i	0.302116	+	0.181777i	−0.356421	+	0.934325i	$0.616003\pi$
$422$	4.07019	+	14.6595i	0.198134	+	0.713614i
$423$	−7.30424	−	1.60779i	−0.355144	−	0.0781732i
$424$	13.4471	+	4.53085i	0.653048	+	0.220038i
$425$	−0.570826	+	1.07669i	−0.0276891	+	0.0522273i
$426$	−3.20257	+	11.5346i	−0.155165	+	0.558853i
$427$	1.87030	−	1.77164i	0.0905102	−	0.0857358i
$428$	0.916078	−	5.58783i	0.0442803	−	0.270098i
$429$	28.8953	−	9.73597i	1.39508	−	0.470057i
$430$	−9.54381	+	1.03795i	−0.460243	+	0.0500545i
$431$	−35.6725	−	16.5038i	−1.71828	−	0.794962i	−0.994477	−	0.104958i	$-0.966529\pi$
$431$	−35.6725	−	16.5038i	−1.71828	−	0.794962i	−0.723806	−	0.690004i	$-0.757609\pi$
$432$	0.0541389	−	0.998533i	0.00260476	−	0.0480420i
$433$	24.3499	−	18.5103i	1.17018	−	0.889550i	0.174712	−	0.984620i	$-0.444101\pi$
$433$	24.3499	−	18.5103i	1.17018	−	0.889550i	0.995471	+	0.0950701i	$0.0303075\pi$
$434$	3.08415	+	2.92146i	0.148044	+	0.140235i
$435$	4.44453	−	2.67419i	0.213099	−	0.128217i
$436$	8.72628	−	4.03721i	0.417913	−	0.193347i
$437$	−0.854300	−	2.14413i	−0.0408667	−	0.102568i
$438$	−2.07873	+	3.06590i	−0.0993257	+	0.146494i
$439$	−4.10990	−	6.06165i	−0.196155	−	0.289307i	0.716873	−	0.697204i	$-0.245573\pi$
$439$	−4.10990	−	6.06165i	−0.196155	−	0.289307i	−0.913028	+	0.407897i	$0.866262\pi$
$440$	−2.27274	+	5.70415i	−0.108349	+	0.271935i
$441$	−0.319009	−	5.88377i	−0.0151909	−	0.280180i
$442$	1.82756	+	2.15157i	0.0869281	+	0.102340i
$443$	2.16932	+	2.55392i	0.103067	+	0.121340i	0.811277	−	0.584662i	$-0.198773\pi$
$443$	2.16932	+	2.55392i	0.103067	+	0.121340i	−0.708210	+	0.706002i	$0.750497\pi$
$444$	0.541171	+	9.98132i	0.0256829	+	0.473692i
$445$	0.627030	−	1.57373i	0.0297241	−	0.0746018i
$446$	−11.2716	−	16.6244i	−0.533726	−	0.787187i
$447$	6.99831	−	10.3217i	0.331009	−	0.488201i
$448$	0.389540	+	0.977672i	0.0184040	+	0.0461907i
$449$	−22.7206	+	10.5117i	−1.07225	+	0.496077i	−0.874924	−	0.484261i	$-0.839089\pi$
$449$	−22.7206	+	10.5117i	−1.07225	+	0.496077i	−0.197328	+	0.980337i	$0.563227\pi$
$450$	2.58598	−	1.55593i	0.121904	−	0.0733474i
$451$	29.4512	+	27.8977i	1.38680	+	1.31365i
$452$	−3.95706	+	3.00808i	−0.186125	+	0.141488i
$453$	1.03534	−	19.0957i	0.0486444	−	0.897193i
$454$	−3.99945	−	1.85034i	−0.187703	−	0.0868408i
$455$	−10.2976	+	1.11993i	−0.482757	+	0.0525030i
$456$	0.246600	−	0.0830893i	0.0115481	−	0.00389101i
$457$	2.57991	−	15.7368i	0.120683	−	0.736135i	−0.855275	−	0.518175i	$-0.826612\pi$
$457$	2.57991	−	15.7368i	0.120683	−	0.736135i	0.975958	−	0.217960i	$-0.0699402\pi$
$458$	19.6985	−	18.6594i	0.920449	−	0.871895i
$459$	0.108027	−	0.389078i	0.00504227	−	0.0181606i
$460$	5.84899	−	11.0324i	0.272710	−	0.514386i
$461$	24.9889	+	8.41976i	1.16385	+	0.392147i	0.833935	−	0.551863i	$-0.186083\pi$
$461$	24.9889	+	8.41976i	1.16385	+	0.392147i	0.329916	+	0.944010i	$0.392979\pi$
$462$	4.48277	+	0.986733i	0.208558	+	0.0459070i
$463$	6.22462	+	22.4190i	0.289283	+	1.04190i	0.955221	+	0.295894i	$0.0956177\pi$
$463$	6.22462	+	22.4190i	0.289283	+	1.04190i	−0.665938	+	0.746007i	$0.731969\pi$
$464$	−3.15699	−	1.89950i	−0.146559	−	0.0881819i
$465$	5.64954	+	0.614425i	0.261991	+	0.0284933i
$466$	−2.20687	+	0.485768i	−0.102231	+	0.0225028i
$467$	−6.93040	−	13.0721i	−0.320700	−	0.604905i	0.669780	−	0.742560i	$-0.266388\pi$
$467$	−6.93040	−	13.0721i	−0.320700	−	0.604905i	−0.990480	+	0.137654i	$0.956044\pi$
$468$	−1.13103	−	6.89900i	−0.0522821	−	0.318907i
$469$	11.0241	+	8.38030i	0.509046	+	0.386966i
$470$	6.81658	−	8.02510i	0.314425	−	0.370170i
$471$	−6.86582			−0.316360
$472$	−1.26662	+	7.57599i	−0.0583007	+	0.348713i
$473$	29.7409			1.36749
$474$	4.37415	−	5.14965i	0.200911	−	0.236531i
$475$	0.625209	+	0.475271i	0.0286865	+	0.0218069i
$476$	0.0687513	+	0.419365i	0.00315121	+	0.0192215i
$477$	−6.64666	−	12.5369i	−0.304330	−	0.574027i
$478$	−15.9136	+	3.50285i	−0.727872	+	0.160217i
$479$	25.9322	+	2.82029i	1.18487	+	0.128862i	0.679259	−	0.733899i	$-0.262301\pi$
$479$	25.9322	+	2.82029i	1.18487	+	0.128862i	0.505612	+	0.862761i	$0.331267\pi$
$480$	1.20632	+	0.725818i	0.0550607	+	0.0331289i
$481$	18.6957	+	67.3357i	0.852449	+	3.07024i
$482$	0.421773	+	0.0928392i	0.0192112	+	0.00422871i
$483$	−8.84586	−	2.98052i	−0.402501	−	0.135618i
$484$	3.75775	−	7.08787i	0.170807	−	0.322176i
$485$	−0.118695	+	0.427499i	−0.00538965	+	0.0194117i
$486$	−0.725995	+	0.687699i	−0.0329318	+	0.0311947i
$487$	3.02527	−	18.4534i	0.137088	−	0.836201i	−0.825334	−	0.564644i	$-0.809013\pi$
$487$	3.02527	−	18.4534i	0.137088	−	0.836201i	0.962422	−	0.271557i	$-0.0875384\pi$
$488$	−2.31974	+	0.781610i	−0.105010	+	0.0353818i
$489$	3.74975	−	0.407810i	0.169570	−	0.0184418i
$490$	7.52887	+	3.48322i	0.340120	+	0.157356i
$491$	−0.941243	+	17.3602i	−0.0424777	+	0.783455i	0.897248	+	0.441526i	$0.145563\pi$
$491$	−0.941243	+	17.3602i	−0.0424777	+	0.783455i	−0.939726	+	0.341929i	$0.888920\pi$
$492$	7.40458	−	5.62882i	0.333824	−	0.253767i
$493$	−1.08009	−	1.02312i	−0.0486449	−	0.0460789i
$494$	1.55883	−	0.937916i	0.0701350	−	0.0421988i
$495$	5.57274	−	2.57822i	0.250476	−	0.115883i
$496$	−1.49409	−	3.74988i	−0.0670867	−	0.168375i
$497$	−7.07008	+	10.4276i	−0.317136	+	0.467741i
$498$	−3.50344	−	5.16718i	−0.156993	−	0.231547i
$499$	9.77880	−	24.5429i	0.437759	−	1.09869i	−0.530264	−	0.847833i	$-0.677907\pi$
$499$	9.77880	−	24.5429i	0.437759	−	1.09869i	0.968023	−	0.250861i	$-0.0807135\pi$
$500$	0.611122	+	11.2715i	0.0273302	+	0.504076i
$501$	9.09032	+	10.7020i	0.406126	+	0.478128i
$502$	−6.84229	−	8.05537i	−0.305387	−	0.359529i
$503$	−0.902622	−	16.6479i	−0.0402459	−	0.742292i	−0.947118	−	0.320886i	$-0.896019\pi$
$503$	−0.902622	−	16.6479i	−0.0402459	−	0.742292i	0.906872	−	0.421406i	$-0.138463\pi$
$504$	0.389540	−	0.977672i	0.0173515	−	0.0435490i
$505$	−0.479590	−	0.707343i	−0.0213415	−	0.0314763i
$506$	−21.7091	+	32.0186i	−0.965089	+	1.42340i
$507$	−13.2789	−	33.3275i	−0.589736	−	1.48013i
$508$	−10.8455	+	5.01766i	−0.481191	+	0.222623i
$509$	−20.3620	+	12.2514i	−0.902530	+	0.543034i	−0.889528	−	0.456881i	$-0.848966\pi$
$509$	−20.3620	+	12.2514i	−0.902530	+	0.543034i	−0.0130020	+	0.999915i	$0.504139\pi$
$510$	0.412715	+	0.390944i	0.0182753	+	0.0173113i
$511$	−3.10344	+	2.35917i	−0.137288	+	0.104364i
$512$	0.0541389	−	0.998533i	0.00239262	−	0.0441294i
$513$	−0.236171	−	0.109264i	−0.0104272	−	0.00482414i
$514$	19.3003	−	2.09903i	0.851300	−	0.0925844i
$515$	−6.65985	+	2.24396i	−0.293468	+	0.0988809i
$516$	1.10319	−	6.72918i	0.0485654	−	0.296236i
$517$	−23.6819	+	22.4326i	−1.04153	+	0.986587i
$518$	−2.81439	+	10.1365i	−0.123657	+	0.445372i
$519$	−4.18454	+	7.89289i	−0.183681	+	0.346459i
$520$	9.32714	+	3.14268i	0.409022	+	0.137816i
$521$	2.95202	+	0.649789i	0.129330	+	0.0284678i	0.279164	−	0.960243i	$-0.409943\pi$
$521$	2.95202	+	0.649789i	0.129330	+	0.0284678i	−0.149834	+	0.988711i	$0.547874\pi$
$522$	0.985676	+	3.55008i	0.0431418	+	0.155383i
$523$	−3.74491	−	2.25324i	−0.163754	−	0.0985273i	0.431318	−	0.902200i	$-0.358049\pi$
$523$	−3.74491	−	2.25324i	−0.163754	−	0.0985273i	−0.595072	+	0.803673i	$0.702876\pi$
$524$	9.35278	+	1.01718i	0.408578	+	0.0444355i
$525$	3.10193	−	0.682785i	0.135379	−	0.0297992i
$526$	1.40518	+	2.65046i	0.0612689	+	0.115565i
$527$	−0.263697	−	1.60848i	−0.0114868	−	0.0700666i
$528$	−3.47213	−	2.63945i	−0.151105	−	0.114867i
$529$	36.0395	−	42.4289i	1.56693	−	1.84474i
$530$	19.9771			0.867749
$531$	6.12956	−	4.62909i	0.266000	−	0.200885i
$532$	0.273863			0.0118735
$533$	42.0965	−	49.5598i	1.82340	−	2.14667i
$534$	0.957933	+	0.728202i	0.0414538	+	0.0315124i
$535$	−1.28969	−	7.86677i	−0.0557582	−	0.340110i
$536$	−6.16333	−	11.6253i	−0.266215	−	0.502135i
$537$	8.79314	−	1.93552i	0.379452	−	0.0835237i
$538$	6.54517	+	0.711830i	0.282182	+	0.0306892i
$539$	−22.0209	−	13.2495i	−0.948506	−	0.570697i
$540$	−0.376637	−	1.35653i	−0.0162079	−	0.0583755i
$541$	18.6296	+	4.10068i	0.800947	+	0.176302i	0.596539	−	0.802584i	$-0.296542\pi$
$541$	18.6296	+	4.10068i	0.800947	+	0.176302i	0.204408	+	0.978886i	$0.434473\pi$
$542$	25.3791	+	8.55123i	1.09013	+	0.367307i
$543$	−0.325258	+	0.613501i	−0.0139581	+	0.0263279i
$544$	0.108027	−	0.389078i	0.00463162	−	0.0166816i
$545$	9.82729	−	9.30890i	0.420955	−	0.398750i
$546$	1.19032	−	7.26064i	0.0509411	−	0.310727i
$547$	6.16353	−	2.07673i	0.263533	−	0.0887947i	−0.184433	−	0.982845i	$-0.559045\pi$
$547$	6.16353	−	2.07673i	0.263533	−	0.0887947i	0.447967	+	0.894050i	$0.352148\pi$
$548$	−5.05996	+	0.550303i	−0.216151	+	0.0235078i
$549$	2.22163	+	1.02784i	0.0948169	+	0.0438670i
$550$	0.712622	−	13.1435i	0.0303863	−	0.560442i
$551$	−0.763260	+	0.580215i	−0.0325160	+	0.0247180i
$552$	6.43926	+	6.09960i	0.274073	+	0.259616i
$553$	6.09294	−	3.66600i	0.259098	−	0.155894i
$554$	−19.8666	+	9.19129i	−0.844053	+	0.390500i
$555$	5.20886	+	13.0733i	0.221104	+	0.554929i
$556$	4.07513	−	6.01036i	0.172824	−	0.254896i
$557$	−18.5241	−	27.3210i	−0.784890	−	1.15763i	−0.984091	−	0.177668i	$-0.943145\pi$
$557$	−18.5241	−	27.3210i	−0.784890	−	1.15763i	0.199200	−	0.979959i	$-0.436166\pi$
$558$	−1.49409	+	3.74988i	−0.0632499	+	0.158745i
$559$	−2.58093	−	47.6025i	−0.109162	−	2.01337i
$560$	0.959192	+	1.12925i	0.0405333	+	0.0477194i
$561$	−1.14014	−	1.34228i	−0.0481368	−	0.0566710i
$562$	−0.856837	−	15.8034i	−0.0361435	−	0.666627i
$563$	6.04600	−	15.1743i	0.254809	−	0.639521i	−0.744806	−	0.667281i	$-0.767458\pi$
$563$	6.04600	−	15.1743i	0.254809	−	0.639521i	0.999615	+	0.0277596i	$0.00883729\pi$
$564$	4.19717	+	6.19037i	0.176733	+	0.260662i
$565$	−3.92708	+	5.79202i	−0.165214	+	0.243672i
$566$	2.86949	+	7.20188i	0.120614	+	0.302718i
$567$	−0.955149	+	0.441899i	−0.0401125	+	0.0185580i
$568$	10.2574	−	6.17166i	0.430390	−	0.258957i
$569$	−14.1798	−	13.4318i	−0.594449	−	0.563092i	0.330201	−	0.943911i	$-0.392884\pi$
$569$	−14.1798	−	13.4318i	−0.594449	−	0.563092i	−0.924650	+	0.380819i	$0.875642\pi$
$570$	0.291650	−	0.221706i	0.0122159	−	0.00928626i
$571$	−0.103618	+	1.91112i	−0.00433627	+	0.0799779i	−0.999900	−	0.0141065i	$-0.995510\pi$
$571$	−0.103618	+	1.91112i	−0.00433627	+	0.0799779i	0.995564	+	0.0940844i	$0.0299924\pi$
$572$	−27.6733	−	12.8030i	−1.15708	−	0.535321i
$573$	1.54330	−	0.167844i	0.0644723	−	0.00701179i
$574$	9.27629	−	3.12555i	0.387185	−	0.130458i
$575$	−4.33061	+	26.4156i	−0.180599	+	1.10161i
$576$	−0.725995	+	0.687699i	−0.0302498	+	0.0286541i
$577$	4.65253	−	16.7569i	0.193687	−	0.697599i	−0.801359	−	0.598184i	$-0.795889\pi$
$577$	4.65253	−	16.7569i	0.193687	−	0.697599i	0.995046	−	0.0994147i	$-0.0316970\pi$
$578$	−7.88657	+	14.8756i	−0.328038	+	0.618745i
$579$	−16.4848	−	5.55439i	−0.685086	−	0.230832i
$580$	−5.06575	−	1.11506i	−0.210344	−	0.0463002i
$581$	−1.75770	−	6.33067i	−0.0729217	−	0.262640i
$582$	−0.270033	−	0.162473i	−0.0111932	−	0.00673473i
$583$	−61.5259	−	6.69134i	−2.54814	−	0.277127i
$584$	3.61757	−	0.796287i	0.149696	−	0.0329506i
$585$	−4.61024	−	8.69584i	−0.190610	−	0.359529i
$586$	−1.49641	−	9.12769i	−0.0618161	−	0.377062i
$587$	16.6630	+	12.6669i	0.687757	+	0.522820i	0.889682	−	0.456582i	$-0.150926\pi$
$587$	16.6630	+	12.6669i	0.687757	+	0.522820i	−0.201924	+	0.979401i	$0.564719\pi$
$588$	−3.81467	+	4.49098i	−0.157314	+	0.185205i
$589$	−1.05041			−0.0432812
$590$	1.71576	+	10.6768i	0.0706365	+	0.439559i
$591$	17.6933			0.727804
$592$	6.47126	−	7.61856i	0.265967	−	0.313121i
$593$	−34.3131	−	26.0841i	−1.40907	−	1.07115i	−0.986309	−	0.164907i	$-0.947268\pi$
$593$	−34.3131	−	26.0841i	−1.40907	−	1.07115i	−0.422761	−	0.906241i	$-0.638939\pi$
$594$	0.705607	+	4.30401i	0.0289514	+	0.176596i
$595$	0.280239	+	0.528588i	0.0114887	+	0.0216700i
$596$	−12.1790	+	2.68080i	−0.498871	+	0.109810i
$597$	25.0255	+	2.72169i	1.02423	+	0.111391i
$598$	53.1320	+	31.9685i	2.17273	+	1.30729i
$599$	−4.86332	−	17.5161i	−0.198710	−	0.715688i	−0.993992	−	0.109449i	$-0.965091\pi$
$599$	−4.86332	−	17.5161i	−0.198710	−	0.715688i	0.795283	−	0.606239i	$-0.207322\pi$
$600$	−2.94743	−	0.648777i	−0.120328	−	0.0264862i
$601$	12.3954	+	4.17649i	0.505618	+	0.170363i	0.560539	−	0.828128i	$-0.310594\pi$
$601$	12.3954	+	4.17649i	0.505618	+	0.170363i	−0.0549206	+	0.998491i	$0.517491\pi$
$602$	3.36151	−	6.34049i	0.137005	−	0.258419i
$603$	−3.52014	+	12.6784i	−0.143351	+	0.516305i
$604$	−13.8837	+	13.1514i	−0.564921	+	0.535122i
$605$	1.82721	−	11.1455i	0.0742864	−	0.453127i
$606$	0.575253	−	0.193825i	0.0233680	−	0.00787361i
$607$	22.2048	−	2.41492i	0.901265	−	0.0980184i	0.354259	−	0.935147i	$-0.384733\pi$
$607$	22.2048	−	2.41492i	0.901265	−	0.0980184i	0.547006	+	0.837129i	$0.315768\pi$
$608$	−0.236171	−	0.109264i	−0.00957801	−	0.00443126i
$609$	−0.209924	+	3.87182i	−0.00850655	+	0.156894i
$610$	−2.74351	+	2.08556i	−0.111081	+	0.0844419i
$611$	37.9602	+	35.9578i	1.53571	+	1.45470i
$612$	−0.345996	+	0.208179i	−0.0139861	+	0.00841513i
$613$	18.6203	−	8.61468i	0.752068	−	0.347943i	−0.00611895	−	0.999981i	$-0.501948\pi$
$613$	18.6203	−	8.61468i	0.752068	−	0.347943i	0.758186	+	0.652038i	$0.226086\pi$
$614$	3.69593	+	9.27610i	0.149156	+	0.374353i
$615$	7.34849	−	10.8382i	0.296320	−	0.437039i
$616$	−2.57590	−	3.79917i	−0.103786	−	0.153073i
$617$	−10.9603	+	27.5082i	−0.441244	+	1.10744i	0.525295	+	0.850920i	$0.323955\pi$
$617$	−10.9603	+	27.5082i	−0.441244	+	1.10744i	−0.966539	+	0.256519i	$0.917424\pi$
$618$	−0.270253	−	4.98453i	−0.0108712	−	0.200507i
$619$	7.15385	+	8.42217i	0.287538	+	0.338515i	0.886899	−	0.461963i	$-0.152855\pi$
$619$	7.15385	+	8.42217i	0.287538	+	0.338515i	−0.599362	+	0.800478i	$0.704579\pi$
$620$	−3.67900	−	4.33126i	−0.147752	−	0.173947i
$621$	−0.480189	−	8.85656i	−0.0192693	−	0.355401i
$622$	6.27068	−	15.7382i	0.251431	−	0.631045i
$623$	0.710669	+	1.04816i	0.0284724	+	0.0419936i
$624$	−3.92332	+	5.78646i	−0.157058	+	0.231644i
$625$	0.296796	+	0.744901i	0.0118718	+	0.0297961i
$626$	−11.6246	+	5.37811i	−0.464612	+	0.214952i
$627$	−0.972490	+	0.585128i	−0.0388375	+	0.0233678i
$628$	4.98456	+	4.72162i	0.198905	+	0.188413i
$629$	3.21330	−	2.44269i	0.128123	−	0.0973964i
$630$	0.0802143	−	1.47946i	0.00319581	−	0.0589433i
$631$	15.8952	+	7.35390i	0.632778	+	0.292754i	0.709938	−	0.704265i	$-0.248723\pi$
$631$	15.8952	+	7.35390i	0.632778	+	0.292754i	−0.0771600	+	0.997019i	$0.524585\pi$
$632$	−6.71702	+	0.730520i	−0.267189	+	0.0290585i
$633$	−14.4177	+	4.85787i	−0.573050	+	0.193083i
$634$	1.68520	−	10.2793i	0.0669279	−	0.408242i
$635$	−12.2139	+	11.5696i	−0.484693	+	0.459126i
$636$	−3.79620	+	13.6727i	−0.150529	+	0.542156i
$637$	−19.2958	+	36.3958i	−0.764529	+	1.44205i
$638$	15.2281	+	5.13095i	0.602887	+	0.203136i
$639$	−11.6911	−	2.57340i	−0.462491	−	0.101802i
$640$	−0.376637	−	1.35653i	−0.0148879	−	0.0536214i
$641$	−17.0917	−	10.2837i	−0.675080	−	0.406182i	0.136327	−	0.990664i	$-0.456470\pi$
$641$	−17.0917	−	10.2837i	−0.675080	−	0.406182i	−0.811407	+	0.584482i	$0.801298\pi$
$642$	5.62923	+	0.612215i	0.222168	+	0.0241622i
$643$	8.95938	−	1.97211i	0.353324	−	0.0777724i	−0.0347623	−	0.999396i	$-0.511067\pi$
$643$	8.95938	−	1.97211i	0.353324	−	0.0777724i	0.388086	+	0.921623i	$0.373136\pi$
$644$	4.37236	+	8.24714i	0.172295	+	0.324983i
$645$	−1.55312	−	9.47362i	−0.0611541	−	0.373023i
$646$	−0.0836509	−	0.0635898i	−0.00329120	−	0.00250191i
$647$	−5.88607	+	6.92962i	−0.231405	+	0.272431i	−0.865594	−	0.500747i	$-0.833059\pi$
$647$	−5.88607	+	6.92962i	−0.231405	+	0.272431i	0.634188	+	0.773179i	$0.281334\pi$
$648$	1.00000			0.0392837
$649$	−1.70800	−	33.4575i	−0.0670450	−	1.31332i
$650$	−21.0990			−0.827572
$651$	−2.75021	+	3.23779i	−0.107789	+	0.126899i
$652$	−3.00275	−	2.28263i	−0.117597	−	0.0893948i
$653$	−2.87164	−	17.5162i	−0.112376	−	0.685463i	−0.981586	−	0.191020i	$-0.938820\pi$
$653$	−2.87164	−	17.5162i	−0.112376	−	0.685463i	0.869210	−	0.494443i	$-0.164628\pi$
$654$	4.50372	+	8.49491i	0.176109	+	0.332177i
$655$	12.9352	−	2.84725i	0.505420	−	0.111251i
$656$	−9.24663	−	1.00563i	−0.361020	−	0.0392633i
$657$	−3.17395	−	1.90970i	−0.123827	−	0.0745045i
$658$	2.10575	+	7.58424i	0.0820909	+	0.295665i
$659$	−10.1268	−	2.22907i	−0.394483	−	0.0868322i	0.0132992	−	0.999912i	$-0.495767\pi$
$659$	−10.1268	−	2.22907i	−0.394483	−	0.0868322i	−0.407782	+	0.913079i	$0.633698\pi$
$660$	−5.81883	−	1.96059i	−0.226498	−	0.0763159i
$661$	−6.26957	+	11.8257i	−0.243858	+	0.459965i	−0.974983	−	0.222278i	$-0.928651\pi$
$661$	−6.26957	+	11.8257i	−0.243858	+	0.459965i	0.731125	+	0.682243i	$0.238996\pi$
$662$	0.0312702	−	0.112625i	0.00121535	−	0.00437730i
$663$	−2.04947	+	1.94136i	−0.0795949	+	0.0753963i
$664$	−1.00999	+	6.16066i	−0.0391952	+	0.239080i
$665$	0.365372	−	0.123108i	0.0141685	−	0.00477394i
$666$	−9.93738	+	1.08076i	−0.385066	+	0.0418784i
$667$	−29.6585	−	13.7215i	−1.14838	−	0.531298i
$668$	0.760196	−	14.0210i	0.0294129	−	0.542488i
$669$	15.9898	−	12.1551i	0.618200	−	0.469943i
$670$	−13.4486	−	12.7392i	−0.519566	−	0.492159i
$671$	9.14808	−	5.50422i	0.353158	−	0.212488i
$672$	−0.955149	+	0.441899i	−0.0368457	+	0.0170466i
$673$	−6.73942	−	16.9147i	−0.259786	−	0.652012i	0.740002	−	0.672604i	$-0.234824\pi$
$673$	−6.73942	−	16.9147i	−0.259786	−	0.652012i	−0.999788	+	0.0205917i	$0.993445\pi$
$674$	0.633454	−	0.934275i	0.0243997	−	0.0359869i
$675$	1.69365	+	2.49795i	0.0651888	+	0.0961462i
$676$	−13.2789	+	33.3275i	−0.510727	+	1.28183i
$677$	−1.12661	−	20.7791i	−0.0432991	−	0.798606i	−0.936869	−	0.349681i	$-0.886290\pi$
$677$	−1.12661	−	20.7791i	−0.0432991	−	0.798606i	0.893570	−	0.448924i	$-0.148193\pi$
$678$	−3.21790	−	3.78840i	−0.123583	−	0.145493i
$679$	−0.214714	−	0.252780i	−0.00823995	−	0.00970082i
$680$	−0.0307769	−	0.567647i	−0.00118024	−	0.0217683i
$681$	1.63110	−	4.09376i	0.0625040	−	0.156873i
$682$	9.87992	+	14.5718i	0.378322	+	0.557983i
$683$	−21.4834	+	31.6856i	−0.822039	+	1.21242i	0.152523	+	0.988300i	$0.451260\pi$
$683$	−21.4834	+	31.6856i	−0.822039	+	1.21242i	−0.974562	+	0.224117i	$0.928050\pi$
$684$	0.0963182	+	0.241740i	0.00368282	+	0.00924317i
$685$	−6.50334	+	3.00876i	−0.248480	+	0.114959i
$686$	−11.6260	+	6.99515i	−0.443884	+	0.267076i
$687$	19.6985	+	18.6594i	0.751543	+	0.711900i
$688$	−5.42857	+	4.12669i	−0.206962	+	0.157329i
$689$	−5.37074	+	99.0574i	−0.204609	+	3.77379i
$690$	11.3328	+	5.24313i	0.431434	+	0.199602i
$691$	−9.72497	+	1.05765i	−0.369955	+	0.0402350i	−0.291208	−	0.956660i	$-0.594057\pi$
$691$	−9.72497	+	1.05765i	−0.369955	+	0.0402350i	−0.0787467	+	0.996895i	$0.525092\pi$
$692$	8.46589	−	2.85249i	0.321825	−	0.108435i
$693$	−0.742594	+	4.52962i	−0.0282088	+	0.172066i
$694$	−8.59129	+	8.13810i	−0.326121	+	0.308918i
$695$	2.73500	−	9.85057i	0.103744	−	0.373653i
$696$	1.72579	−	3.25519i	0.0654160	−	0.123388i
$697$	−3.55917	−	1.19922i	−0.134813	−	0.0454238i
$698$	−2.28477	−	0.502917i	−0.0864800	−	0.0190357i
$699$	−0.604533	−	2.17733i	−0.0228655	−	0.0823542i
$700$	−2.72153	−	1.63749i	−0.102864	−	0.0618914i
$701$	−7.43698	−	0.808820i	−0.280891	−	0.0305487i	−0.0334108	−	0.999442i	$-0.510637\pi$
$701$	−7.43698	−	0.808820i	−0.280891	−	0.0305487i	−0.247480	+	0.968893i	$0.579602\pi$
$702$	6.82765	−	1.50288i	0.257693	−	0.0567226i
$703$	−1.21841	−	2.29817i	−0.0459533	−	0.0866771i
$704$	0.705607	+	4.30401i	0.0265936	+	0.162213i
$705$	8.38237	+	6.37211i	0.315698	+	0.239988i
$706$	−15.0630	+	17.7335i	−0.566903	+	0.667410i
$707$	0.638848			0.0240264
$708$	−7.63346	−	0.854602i	−0.286883	−	0.0321179i
$709$	−30.7323			−1.15418			−0.577088	−	0.816682i	$-0.695811\pi$
$709$	−30.7323			−1.15418			−0.577088	+	0.816682i	$0.695811\pi$
$710$	10.9105	−	12.8449i	0.409464	−	0.482059i
$711$	5.37891	+	4.08894i	0.201725	+	0.153347i
$712$	−0.194671	−	1.18744i	−0.00729561	−	0.0445012i
$713$	−16.7703	−	31.6321i	−0.628052	−	1.18463i
$714$	−0.415027	+	0.0913544i	−0.0155320	+	0.00341885i
$715$	−42.6755	−	4.64124i	−1.59597	−	0.173572i
$716$	−7.71483	−	4.64186i	−0.288317	−	0.173475i
$717$	−4.35926	−	15.7006i	−0.162800	−	0.586351i
$718$	2.95159	+	0.649695i	0.110152	+	0.0242464i
$719$	−12.8439	−	4.32762i	−0.478997	−	0.161393i	0.0694374	−	0.997586i	$-0.477880\pi$
$719$	−12.8439	−	4.32762i	−0.478997	−	0.161393i	−0.548435	+	0.836193i	$0.684776\pi$
$720$	−0.659445	+	1.24384i	−0.0245760	+	0.0463553i
$721$	1.40546	−	5.06202i	0.0523422	−	0.188520i
$722$	13.7448	−	13.0197i	0.511527	−	0.484544i
$723$	−0.0698687	+	0.426180i	−0.00259845	+	0.0158498i
$724$	0.658040	−	0.221720i	0.0244559	−	0.00824014i
$725$	11.0542	−	1.20222i	0.410543	−	0.0446493i
$726$	7.28092	+	3.36851i	0.270220	+	0.125017i
$727$	−0.0984386	+	1.81559i	−0.00365089	+	0.0673367i	−0.999791	−	0.0204398i	$-0.993493\pi$
$727$	−0.0984386	+	1.81559i	−0.00365089	+	0.0673367i	0.996140	+	0.0877765i	$0.0279761\pi$
$728$	−5.85731	+	4.45261i	−0.217086	+	0.165025i
$729$	−0.725995	−	0.687699i	−0.0268887	−	0.0254704i
$730$	4.46841	−	2.68855i	0.165383	−	0.0995078i
$731$	−2.49900	+	1.15616i	−0.0924290	+	0.0427622i
$732$	−0.906052	−	2.27402i	−0.0334886	−	0.0840501i
$733$	26.3270	−	38.8295i	0.972411	−	1.43420i	0.0728814	−	0.997341i	$-0.476781\pi$
$733$	26.3270	−	38.8295i	0.972411	−	1.43420i	0.899530	−	0.436859i	$-0.143909\pi$
$734$	20.7137	+	30.5505i	0.764558	+	1.12764i
$735$	−3.07051	+	7.70640i	−0.113258	+	0.284255i
$736$	−0.480189	−	8.85656i	−0.0177000	−	0.326457i
$737$	37.1524	+	43.7392i	1.36853	+	1.61115i
$738$	6.02144	+	7.08898i	0.221652	+	0.260949i
$739$	1.08145	+	19.9463i	0.0397819	+	0.733735i	0.948588	+	0.316515i	$0.102513\pi$
$739$	1.08145	+	19.9463i	0.0397819	+	0.733735i	−0.908806	+	0.417220i	$0.863004\pi$
$740$	5.20886	−	13.0733i	0.191482	−	0.480582i
$741$	1.02093	+	1.50576i	0.0375049	+	0.0553156i
$742$	−8.38060	+	12.3605i	−0.307661	+	0.453767i
$743$	2.81588	+	7.06732i	0.103305	+	0.259275i	0.971539	−	0.236879i	$-0.0761245\pi$
$743$	2.81588	+	7.06732i	0.103305	+	0.259275i	−0.868235	+	0.496154i	$0.834745\pi$
$744$	3.66350	−	1.69491i	0.134310	−	0.0621386i
$745$	−15.0435	+	9.05134i	−0.551149	+	0.331616i
$746$	15.5744	+	14.7529i	0.570221	+	0.540142i
$747$	4.96993	−	3.77804i	0.181840	−	0.138231i
$748$	−0.0953464	+	1.75856i	−0.00348621	+	0.0642994i
$749$	5.40846	+	2.50222i	0.197621	+	0.0914291i
$750$	−11.2219	+	1.22045i	−0.409765	+	0.0445646i
$751$	−40.6302	+	13.6899i	−1.48262	+	0.499552i	−0.940220	−	0.340569i	$-0.889380\pi$
$751$	−40.6302	+	13.6899i	−1.48262	+	0.499552i	−0.542399	+	0.840121i	$0.682484\pi$
$752$	1.20998	−	7.38058i	0.0441236	−	0.269142i
$753$	7.67312	−	7.26837i	0.279624	−	0.264874i
$754$	6.89096	−	24.8190i	0.250954	−	0.903854i
$755$	−12.6110	+	23.7869i	−0.458962	+	0.865695i
$756$	0.997328	+	0.336039i	0.0362725	+	0.0122216i
$757$	45.0682	+	9.92026i	1.63803	+	0.360558i	0.936113	−	0.351700i	$-0.114396\pi$
$757$	45.0682	+	9.92026i	1.63803	+	0.360558i	0.701918	+	0.712258i	$0.252327\pi$
$758$	6.13881	+	22.1100i	0.222972	+	0.803072i
$759$	−33.1469	−	19.9438i	−1.20316	−	0.723916i
$760$	−0.364204	−	0.0396096i	−0.0132111	−	0.00143679i
$761$	50.0356	−	11.0137i	1.81379	−	0.399245i	0.827124	−	0.562019i	$-0.189975\pi$
$761$	50.0356	−	11.0137i	1.81379	−	0.399245i	0.986663	+	0.162775i	$0.0520443\pi$
$762$	−5.59746	−	10.5579i	−0.202775	−	0.382474i
$763$	1.63706	+	9.98563i	0.0592656	+	0.361504i
$764$	−1.23586	−	0.939473i	−0.0447117	−	0.0339889i
$765$	−0.368027	+	0.433275i	−0.0133060	+	0.0156651i
$766$	−22.4220			−0.810141
$767$	−53.4030	+	5.63724i	−1.92827	+	0.203549i
$768$	1.00000			0.0360844
$769$	−17.7035	+	20.8422i	−0.638404	+	0.751588i	−0.982278	−	0.187428i	$-0.939985\pi$
$769$	−17.7035	+	20.8422i	−0.638404	+	0.751588i	0.343874	+	0.939016i	$0.388261\pi$
$770$	−5.14444	−	3.91070i	−0.185393	−	0.140932i
$771$	3.14085	+	19.1584i	0.113115	+	0.689971i
$772$	8.14816	+	15.3691i	0.293259	+	0.553145i
$773$	40.1962	−	8.84785i	1.44576	−	0.318235i	0.578331	−	0.815802i	$-0.303704\pi$
$773$	40.1962	−	8.84785i	1.44576	−	0.318235i	0.867426	+	0.497567i	$0.165773\pi$
$774$	6.77904	+	0.737265i	0.243668	+	0.0265004i
$775$	10.4385	+	6.28064i	0.374962	+	0.225607i
$776$	0.0843097	+	0.303656i	0.00302654	+	0.0109006i
$777$	−10.2740	−	2.26148i	−0.368578	−	0.0811301i
$778$	23.4088	+	7.88734i	0.839246	+	0.282775i
$779$	−1.13372	+	2.13842i	−0.0406197	+	0.0766169i
$780$	−2.63311	+	9.48360i	−0.0942805	+	0.339568i
$781$	−37.9048	+	35.9054i	−1.35634	+	1.28480i
$782$	0.579422	−	3.53432i	0.0207201	−	0.126387i
$783$	−3.49151	+	1.17643i	−0.124776	+	0.0420421i
$784$	5.85787	−	0.637082i	0.209210	−	0.0227529i
$785$	8.77261	+	4.05864i	0.313108	+	0.144859i
$786$	−0.509335	+	9.39413i	−0.0181674	+	0.335077i
$787$	−29.4657	+	22.3992i	−1.05034	+	0.798446i	−0.979984	−	0.199076i	$-0.936206\pi$
$787$	−29.4657	+	22.3992i	−1.05034	+	0.798446i	−0.0703534	+	0.997522i	$0.522413\pi$
$788$	−12.8452	−	12.1677i	−0.457593	−	0.433455i
$789$	−2.57049	+	1.54662i	−0.0915120	+	0.0550610i
$790$	−8.63309	+	3.99409i	−0.307152	+	0.142103i
$791$	−1.93625	−	4.85962i	−0.0688451	−	0.172788i
$792$	2.44760	−	3.60994i	0.0869716	−	0.128274i
$793$	−9.60378	−	14.1645i	−0.341040	−	0.502997i
$794$	−13.0949	+	32.8656i	−0.464719	+	1.16636i
$795$	1.08154	+	19.9478i	0.0383582	+	0.707475i
$796$	−16.2967	−	19.1859i	−0.577621	−	0.680028i
$797$	−28.3094	−	33.3284i	−1.00277	−	1.18055i	−0.983531	−	0.180737i	$-0.942152\pi$
$797$	−28.3094	−	33.3284i	−1.00277	−	1.18055i	−0.0192384	−	0.999815i	$-0.506124\pi$
$798$	0.0148266	+	0.273461i	0.000524857	+	0.00968041i
$799$	1.11783	−	2.80554i	0.0395460	−	0.0992529i
$800$	1.69365	+	2.49795i	0.0598797	+	0.0883159i
$801$	−0.675272	+	0.995952i	−0.0238596	+	0.0351902i
$802$	−3.19302	−	8.01388i	−0.112749	−	0.282980i
$803$	−14.6624	+	6.78357i	−0.517426	+	0.239387i
$804$	11.2745	−	6.78367i	0.397623	−	0.239242i
$805$	9.54066	+	9.03739i	0.336264	+	0.318526i
$806$	22.4658	−	17.0781i	0.791325	−	0.601550i
$807$	−0.356438	+	6.57411i	−0.0125472	+	0.231420i
$808$	−0.550924	−	0.254885i	−0.0193814	−	0.00896681i
$809$	−23.2953	+	2.53351i	−0.819018	+	0.0890735i	−0.508029	−	0.861340i	$-0.669626\pi$
$809$	−23.2953	+	2.53351i	−0.819018	+	0.0890735i	−0.310989	+	0.950414i	$0.600660\pi$
$810$	1.33414	−	0.449526i	0.0468771	−	0.0157947i
$811$	1.95404	−	11.9191i	0.0686158	−	0.418538i	−0.930074	−	0.367371i	$-0.880258\pi$
$811$	1.95404	−	11.9191i	0.0686158	−	0.418538i	0.998690	−	0.0511664i	$-0.0162939\pi$
$812$	2.81505	−	2.66656i	0.0987890	−	0.0935779i
$813$	−7.16469	+	25.8049i	−0.251277	+	0.905016i
$814$	−20.4213	+	38.5186i	−0.715765	+	1.35008i
$815$	−5.03221	−	1.69555i	−0.176271	−	0.0593925i
$816$	0.394356	+	0.0868043i	0.0138052	+	0.00303876i
$817$	0.474718	+	1.70978i	0.0166083	+	0.0598176i
$818$	−28.0482	−	16.8760i	−0.980681	−	0.590056i
$819$	7.31443	+	0.795493i	0.255587	+	0.0277968i
$820$	−12.7884	+	2.81494i	−0.446590	+	0.0983019i
$821$	1.37520	+	2.59390i	0.0479948	+	0.0905278i	0.906349	−	0.422529i	$-0.138858\pi$
$821$	1.37520	+	2.59390i	0.0479948	+	0.0905278i	−0.858354	+	0.513057i	$0.828513\pi$
$822$	−0.823437	−	5.02274i	−0.0287207	−	0.175188i
$823$	16.7246	+	12.7137i	0.582984	+	0.443173i	0.854640	−	0.519222i	$-0.173778\pi$
$823$	16.7246	+	12.7137i	0.582984	+	0.443173i	−0.271656	+	0.962394i	$0.587571\pi$
$824$	−3.23165	+	3.80460i	−0.112580	+	0.132539i
$825$	13.1628			0.458271
$826$	−7.32588	−	3.41746i	−0.254900	−	0.118909i
$827$	6.80815			0.236743			0.118371	−	0.992969i	$-0.462233\pi$
$827$	6.80815			0.236743			0.118371	+	0.992969i	$0.462233\pi$
$828$	−5.74203	+	6.76005i	−0.199550	+	0.234928i
$829$	−1.50645	−	1.14518i	−0.0523213	−	0.0397736i	0.578687	−	0.815550i	$-0.303565\pi$
$829$	−1.50645	−	1.14518i	−0.0523213	−	0.0397736i	−0.631008	+	0.775776i	$0.717359\pi$
$830$	1.42190	+	8.67323i	0.0493550	+	0.301052i
$831$	−10.2534	−	19.3399i	−0.355685	−	0.670894i
$832$	6.82765	−	1.50288i	0.236706	−	0.0521030i
$833$	2.36539	+	0.257251i	0.0819558	+	0.00891323i
$834$	6.22217	+	3.74376i	0.215456	+	0.129636i
$835$	−5.28858	−	19.0478i	−0.183019	−	0.659175i
$836$	1.10842	+	0.243981i	0.0383354	+	0.00843825i
$837$	−3.82527	−	1.28888i	−0.132221	−	0.0445504i
$838$	−1.74010	+	3.28218i	−0.0601107	+	0.113381i
$839$	12.6931	−	45.7166i	0.438216	−	1.57831i	−0.333759	−	0.942658i	$-0.608317\pi$
$839$	12.6931	−	45.7166i	0.438216	−	1.57831i	0.771975	−	0.635653i	$-0.219269\pi$
$840$	−1.07566	+	1.01892i	−0.0371139	+	0.0351561i
$841$	2.49555	−	15.2222i	0.0860533	−	0.524902i
$842$	6.85576	−	2.30997i	0.236265	−	0.0796070i
$843$	15.7339	−	1.71116i	0.541903	−	0.0589355i
$844$	13.8079	+	6.38822i	0.475288	+	0.219892i
$845$	−2.73439	+	50.4329i	−0.0940660	+	1.73495i
$846$	−5.95406	+	4.52616i	−0.204705	+	0.155613i
$847$	6.12951	+	5.80618i	0.210613	+	0.199503i
$848$	12.1587	−	7.31565i	0.417531	−	0.251220i
$849$	−7.03597	+	3.25519i	−0.241474	+	0.111718i
$850$	0.451069	+	1.13210i	0.0154715	+	0.0388307i
$851$	49.7548	−	73.3829i	1.70557	−	2.51553i
$852$	6.71794	+	9.90821i	0.230153	+	0.339450i
$853$	15.9327	−	39.9881i	0.545526	−	1.36917i	−0.355204	−	0.934789i	$-0.615589\pi$
$853$	15.9327	−	39.9881i	0.545526	−	1.36917i	0.900730	−	0.434378i	$-0.143032\pi$
$854$	−0.139472	−	2.57241i	−0.00477263	−	0.0880261i
$855$	0.237171	+	0.279219i	0.00811107	+	0.00954909i
$856$	−3.66577	−	4.31568i	−0.125294	−	0.147507i
$857$	−2.67604	−	49.3566i	−0.0914118	−	1.68599i	−0.580895	−	0.813978i	$-0.697298\pi$
$857$	−2.67604	−	49.3566i	−0.0914118	−	1.68599i	0.489484	−	0.872012i	$-0.337185\pi$
$858$	11.2860	−	28.3258i	0.385299	−	0.967029i
$859$	26.1096	+	38.5088i	0.890847	+	1.31390i	0.948896	+	0.315588i	$0.102202\pi$
$859$	26.1096	+	38.5088i	0.890847	+	1.31390i	−0.0580489	+	0.998314i	$0.518488\pi$
$860$	−5.38744	+	7.94589i	−0.183710	+	0.270952i
$861$	3.62317	+	9.09348i	0.123477	+	0.309905i
$862$	−35.6725	+	16.5038i	−1.21501	+	0.562123i
$863$	−7.29320	+	4.38817i	−0.248263	+	0.149375i	−0.634247	−	0.773131i	$-0.718690\pi$
$863$	−7.29320	+	4.38817i	−0.248263	+	0.149375i	0.385984	+	0.922506i	$0.373862\pi$
$864$	−0.725995	−	0.687699i	−0.0246989	−	0.0233960i
$865$	10.0125	−	7.61128i	0.340434	−	0.258791i
$866$	1.65593	−	30.5419i	0.0562709	−	1.03786i
$867$	−15.2808	−	7.06965i	−0.518963	−	0.240098i
$868$	4.22326	−	0.459308i	0.143347	−	0.0155899i
$869$	27.9262	−	9.40943i	0.947332	−	0.319193i
$870$	0.839166	−	5.11869i	0.0284504	−	0.173540i
$871$	66.7837	−	63.2608i	2.26288	−	2.14351i
$872$	2.57227	−	9.26447i	0.0871080	−	0.313734i
$873$	0.147616	−	0.278433i	0.00499603	−	0.00942352i
$874$	−2.18724	−	0.736966i	−0.0739844	−	0.0249283i
$875$	−11.6020	−	2.55379i	−0.392219	−	0.0863340i
$876$	0.990971	+	3.56915i	0.0334818	+	0.120591i
$877$	13.3005	+	8.00265i	0.449126	+	0.270230i	0.722097	−	0.691792i	$-0.243179\pi$
$877$	13.3005	+	8.00265i	0.449126	+	0.270230i	−0.272970	+	0.962022i	$0.588006\pi$
$878$	−7.28066	−	0.791819i	−0.245710	−	0.0267226i
$879$	9.03329	−	1.98838i	0.304685	−	0.0670663i
$880$	2.87614	+	5.42498i	0.0969548	+	0.182876i
$881$	−0.660633	−	4.02968i	−0.0222573	−	0.135763i	0.973360	−	0.229281i	$-0.0736373\pi$
$881$	−0.660633	−	4.02968i	−0.0222573	−	0.135763i	−0.995618	+	0.0935171i	$0.970189\pi$
$882$	−4.69091	−	3.56594i	−0.157951	−	0.120071i
$883$	−21.3026	+	25.0793i	−0.716888	+	0.843986i	−0.993120	−	0.117105i	$-0.962639\pi$
$883$	−21.3026	+	25.0793i	−0.716888	+	0.843986i	0.276231	+	0.961091i	$0.410914\pi$
$884$	2.82298			0.0949471
$885$	−10.5683	+	2.29127i	−0.355250	+	0.0770203i
$886$	3.35088			0.112575
$887$	2.51051	−	2.95560i	0.0842947	−	0.0992394i	−0.718398	−	0.695633i	$-0.755124\pi$
$887$	2.51051	−	2.95560i	0.0842947	−	0.0992394i	0.802692	+	0.596393i	$0.203400\pi$
$888$	7.95773	+	6.04931i	0.267044	+	0.203002i
$889$	−2.03463	−	12.4107i	−0.0682392	−	0.416241i
$890$	−0.793505	−	1.49671i	−0.0265983	−	0.0501698i
$891$	−4.25950	+	0.937586i	−0.142699	+	0.0314103i
$892$	−19.9676	−	2.17160i	−0.668563	−	0.0727106i
$893$	−1.66764	−	1.00339i	−0.0558054	−	0.0335770i
$894$	−3.33622	−	12.0160i	−0.111580	−	0.401875i
$895$	−12.3793	−	2.72490i	−0.413796	−	0.0910833i
$896$	0.997328	+	0.336039i	0.0333184	+	0.0112263i
$897$	−29.0451	+	54.7848i	−0.969787	+	1.82921i
$898$	−6.69741	+	24.1219i	−0.223496	+	0.804958i
$899$	−10.7972	+	10.2277i	−0.360107	+	0.341111i
$900$	0.488255	−	2.97823i	0.0162752	−	0.0992742i
$901$	5.42988	−	1.82954i	0.180896	−	0.0609508i
$902$	40.3288	−	4.38603i	1.34280	−	0.146039i
$903$	6.51318	+	3.01332i	0.216745	+	0.100277i
$904$	−0.269103	+	4.96331i	−0.00895023	+	0.165077i
$905$	0.778252	−	0.591612i	0.0258700	−	0.0196658i
$906$	−13.8837	−	13.1514i	−0.461256	−	0.436925i
$907$	32.3156	−	19.4437i	1.07302	−	0.645616i	0.134528	−	0.990910i	$-0.457048\pi$
$907$	32.3156	−	19.4437i	1.07302	−	0.645616i	0.938495	+	0.345293i	$0.112221\pi$
$908$	−3.99945	+	1.85034i	−0.132726	+	0.0614057i
$909$	0.224684	+	0.563915i	0.00745231	+	0.0187039i
$910$	−5.81293	+	8.57344i	−0.192697	+	0.284207i
$911$	3.36807	+	4.96753i	0.111589	+	0.164582i	0.879383	−	0.476116i	$-0.157956\pi$
$911$	3.36807	+	4.96753i	0.111589	+	0.164582i	−0.767793	+	0.640697i	$0.778645\pi$
$912$	0.0963182	−	0.241740i	0.00318941	−	0.00800482i
$913$	−1.47411	−	27.1883i	−0.0487858	−	0.899801i
$914$	−10.3238	−	12.1541i	−0.341480	−	0.402021i
$915$	−2.23103	−	2.62658i	−0.0737557	−	0.0868319i
$916$	−1.46895	−	27.0932i	−0.0485356	−	0.895186i
$917$	−3.66477	+	9.19787i	−0.121021	+	0.303740i
$918$	−0.226605	−	0.334218i	−0.00747909	−	0.0110308i
$919$	7.81437	−	11.5253i	0.257772	−	0.380186i	−0.676678	−	0.736279i	$-0.736581\pi$
$919$	7.81437	−	11.5253i	0.257772	−	0.380186i	0.934450	+	0.356093i	$0.115891\pi$
$920$	−4.62189	−	11.6001i	−0.152379	−	0.382443i
$921$	−9.06240	+	4.19271i	−0.298616	+	0.138155i
$922$	22.5947	−	13.5948i	0.744117	−	0.447721i
$923$	60.7586	+	57.5536i	1.99989	+	1.89440i
$924$	3.65414	−	2.77780i	0.120212	−	0.0913830i
$925$	−1.63325	+	30.1235i	−0.0537008	+	0.990453i
$926$	21.1167	+	9.76962i	0.693937	+	0.321050i
$927$	4.96259	−	0.539714i	0.162993	−	0.0177265i
$928$	−3.49151	+	1.17643i	−0.114615	+	0.0386181i
$929$	−2.82012	+	17.2020i	−0.0925252	+	0.564379i	0.899357	+	0.437216i	$0.144035\pi$
$929$	−2.82012	+	17.2020i	−0.0925252	+	0.564379i	−0.991882	+	0.127163i	$0.959413\pi$
$930$	4.12573	−	3.90810i	0.135288	−	0.128152i
$931$	0.410211	−	1.47745i	0.0134441	−	0.0484214i
$932$	−1.05846	+	1.99647i	−0.0346710	+	0.0653965i
$933$	16.0546	+	5.40943i	0.525605	+	0.177097i
$934$	−14.4497	−	3.18062i	−0.472809	−	0.104073i
$935$	0.663313	+	2.38904i	0.0216926	+	0.0781298i
$936$	−5.99038	−	3.60429i	−0.195802	−	0.117810i
$937$	−55.5972	−	6.04656i	−1.81628	−	0.197533i	−0.864153	−	0.503229i	$-0.832145\pi$
$937$	−55.5972	−	6.04656i	−1.81628	−	0.197533i	−0.952129	+	0.305696i	$0.901111\pi$
$938$	13.5240	−	2.97686i	0.441574	−	0.0971978i
$939$	−5.99956	−	11.3164i	−0.195788	−	0.369296i
$940$	−1.70346	−	10.3907i	−0.0555609	−	0.338906i
$941$	25.3623	+	19.2799i	0.826787	+	0.628507i	0.930579	−	0.366092i	$-0.119304\pi$
$941$	25.3623	+	19.2799i	0.826787	+	0.628507i	−0.103792	+	0.994599i	$0.533098\pi$
$942$	−4.44484	+	5.23287i	−0.144821	+	0.170496i
$943$	−82.4971			−2.68648
$944$	4.95415	+	5.86996i	0.161244	+	0.191051i
$945$	1.48164			0.0481977
$946$	19.2539	−	22.6674i	0.625997	−	0.736980i
$947$	23.8516	+	18.1315i	0.775073	+	0.589195i	0.916165	−	0.400801i	$-0.131268\pi$
$947$	23.8516	+	18.1315i	0.775073	+	0.589195i	−0.141092	+	0.989996i	$0.545061\pi$
$948$	−1.09310	−	6.66762i	−0.0355023	−	0.216554i
$949$	12.1300	+	22.8796i	0.393757	+	0.742704i
$950$	0.766985	−	0.168826i	0.0248843	−	0.00547745i
$951$	10.3554	+	1.12622i	0.335798	+	0.0365202i
$952$	0.364132	+	0.219091i	0.0118016	+	0.00710079i
$953$	−2.75122	−	9.90900i	−0.0891208	−	0.320984i	0.905530	−	0.424283i	$-0.139474\pi$
$953$	−2.75122	−	9.90900i	−0.0891208	−	0.320984i	−0.994650	+	0.103299i	$0.967060\pi$
$954$	−13.8581	−	3.05040i	−0.448673	−	0.0987605i
$955$	−2.07113	−	0.697844i	−0.0670201	−	0.0225817i
$956$	−7.63252	+	14.3965i	−0.246853	+	0.465615i
$957$	−4.29899	+	15.4836i	−0.138967	+	0.500513i
$958$	18.9376	−	17.9387i	0.611848	−	0.579573i
$959$	0.866600	−	5.28603i	0.0279840	−	0.170695i
$960$	1.33414	−	0.449526i	0.0430593	−	0.0145084i
$961$	14.6198	−	1.59000i	0.471608	−	0.0512905i
$962$	63.4240	+	29.3431i	2.04487	+	0.946059i
$963$	−0.306557	+	5.65412i	−0.00987867	+	0.182201i
$964$	0.343808	−	0.261356i	0.0110733	−	0.00841772i
$965$	17.7796	+	16.8418i	0.572346	+	0.542155i
$966$	−7.99833	+	4.81244i	−0.257342	+	0.154838i
$967$	19.0129	−	8.79629i	0.611413	−	0.282870i	−0.0896453	−	0.995974i	$-0.528573\pi$
$967$	19.0129	−	8.79629i	0.611413	−	0.282870i	0.701058	+	0.713104i	$0.252711\pi$
$968$	−2.96939	−	7.45261i	−0.0954398	−	0.239536i
$969$	0.0589677	−	0.0869709i	0.00189432	−	0.00279391i
$970$	0.248983	+	0.367222i	0.00799435	+	0.0117908i
$971$	2.74506	−	6.88958i	0.0880931	−	0.221097i	−0.878329	−	0.478057i	$-0.841341\pi$
$971$	2.74506	−	6.88958i	0.0880931	−	0.221097i	0.966422	+	0.256960i	$0.0827207\pi$
$972$	0.0541389	+	0.998533i	0.00173651	+	0.0320280i
$973$	4.94750	+	5.82464i	0.158609	+	0.186730i
$974$	−12.1059	−	14.2522i	−0.387899	−	0.456670i
$975$	−1.14228	−	21.0681i	−0.0365822	−	0.674719i
$976$	−0.906052	+	2.27402i	−0.0290020	+	0.0727896i
$977$	−13.1118	−	19.3385i	−0.419483	−	0.618692i	0.557965	−	0.829864i	$-0.311582\pi$
$977$	−13.1118	−	19.3385i	−0.419483	−	0.618692i	−0.977449	+	0.211172i	$0.932272\pi$
$978$	2.11672	−	3.12193i	0.0676853	−	0.0998283i
$979$	1.94253	+	4.87538i	0.0620835	+	0.155818i
$980$	7.52887	−	3.48322i	0.240501	−	0.111268i
$981$	−8.23862	+	4.95702i	−0.263039	+	0.158265i
$982$	12.6219	+	11.9561i	0.402782	+	0.381536i
$983$	18.1664	−	13.8097i	0.579417	−	0.440461i	−0.273971	−	0.961738i	$-0.588337\pi$
$983$	18.1664	−	13.8097i	0.579417	−	0.440461i	0.853388	+	0.521277i	$0.174544\pi$
$984$	0.503554	−	9.28751i	0.0160527	−	0.296075i
$985$	−22.6071	−	10.4591i	−0.720321	−	0.333256i
$986$	−1.47902	+	0.160853i	−0.0471015	+	0.00512260i
$987$	−7.45912	+	2.51327i	−0.237426	+	0.0799982i
$988$	0.294320	−	1.79527i	0.00936357	−	0.0571153i
$989$	−43.9094	+	41.5932i	−1.39624	+	1.32259i
$990$	1.64269	−	5.91644i	0.0522081	−	0.188037i
$991$	−24.4869	+	46.1872i	−0.777852	+	1.46718i	0.103452	+	0.994634i	$0.467011\pi$
$991$	−24.4869	+	46.1872i	−0.777852	+	1.46718i	−0.881304	+	0.472550i	$0.843333\pi$
$992$	−3.82527	−	1.28888i	−0.121453	−	0.0409221i
$993$	0.114153	+	0.0251270i	0.00362254	+	0.000797380i
$994$	3.37044	+	12.1392i	0.106904	+	0.385033i
$995$	−30.3667	−	18.2711i	−0.962690	−	0.579231i
$996$	−6.20631	−	0.674977i	−0.196654	−	0.0213874i
$997$	−1.13175	+	0.249116i	−0.0358428	+	0.00788959i	−0.232856	−	0.972511i	$-0.574807\pi$
$997$	−1.13175	+	0.249116i	−0.0358428	+	0.00788959i	0.197013	+	0.980401i	$0.436876\pi$
$998$	−12.3750	−	23.3418i	−0.391725	−	0.738872i
$999$	−1.61717	−	9.86430i	−0.0511650	−	0.312093i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.a.127.1	✓	56
59.46	even	29	inner	354.2.e.a.223.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.a.127.1	✓	56	1.1	even	1	trivial
354.2.e.a.223.1	yes	56	59.46	even	29	inner

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(0.647386 - 0.762162i) q^{2} +(0.796093 + 0.605174i) q^{3} +(-0.161782 - 0.986827i) q^{4} +(-0.659445 - 1.24384i) q^{5} +(0.976621 - 0.214970i) q^{6} +(1.04625 + 0.113786i) q^{7} +(-0.856857 - 0.515554i) q^{8} +(0.267528 + 0.963550i) q^{9} +O(q^{10})\)	\(q+(0.647386 - 0.762162i) q^{2} +(0.796093 + 0.605174i) q^{3} +(-0.161782 - 0.986827i) q^{4} +(-0.659445 - 1.24384i) q^{5} +(0.976621 - 0.214970i) q^{6} +(1.04625 + 0.113786i) q^{7} +(-0.856857 - 0.515554i) q^{8} +(0.267528 + 0.963550i) q^{9} +(-1.37493 - 0.302644i) q^{10} +(4.13316 + 1.39262i) q^{11} +(0.468408 - 0.883512i) q^{12} +(1.87032 - 6.73628i) q^{13} +(0.764051 - 0.723748i) q^{14} +(0.227763 - 1.38929i) q^{15} +(-0.947653 + 0.319302i) q^{16} +(-0.401429 + 0.0436581i) q^{17} +(0.907575 + 0.419889i) q^{18} +(-0.0140881 + 0.259841i) q^{19} +(-1.12077 + 0.851989i) q^{20} +(0.764051 + 0.723748i) q^{21} +(3.73715 - 2.24857i) q^{22} +(-8.04980 + 3.72423i) q^{23} +(-0.370138 - 0.928977i) q^{24} +(1.69365 - 2.49795i) q^{25} +(-3.92332 - 5.78646i) q^{26} +(-0.370138 + 0.928977i) q^{27} +(-0.0569768 - 1.05088i) q^{28} +(2.38522 + 2.80809i) q^{29} +(-0.911417 - 1.07300i) q^{30} +(0.218536 + 4.03066i) q^{31} +(-0.370138 + 0.928977i) q^{32} +(2.44760 + 3.60994i) q^{33} +(-0.226605 + 0.334218i) q^{34} +(-0.548411 - 1.37641i) q^{35} +(0.907575 - 0.419889i) q^{36} +(-8.56513 + 5.15347i) q^{37} +(0.188920 + 0.178955i) q^{38} +(5.56557 - 4.23083i) q^{39} +(-0.0762190 + 1.40578i) q^{40} +(8.44149 + 3.90545i) q^{41} +(1.04625 - 0.113786i) q^{42} +(6.46206 - 2.17732i) q^{43} +(0.705607 - 4.30401i) q^{44} +(1.02209 - 0.968171i) q^{45} +(-2.37286 + 8.54627i) q^{46} +(-3.50327 + 6.60788i) q^{47} +(-0.947653 - 0.319302i) q^{48} +(-5.75465 - 1.26670i) q^{49} +(-0.807396 - 2.90798i) q^{50} +(-0.345996 - 0.208179i) q^{51} +(-6.95012 - 0.755871i) q^{52} +(-13.8581 + 3.05040i) q^{53} +(0.468408 + 0.883512i) q^{54} +(-0.993382 - 6.05936i) q^{55} +(-0.837823 - 0.636897i) q^{56} +(-0.168464 + 0.198331i) q^{57} +3.68438 q^{58} +(-2.82052 - 7.14455i) q^{59} -1.40784 q^{60} +(1.58472 - 1.86568i) q^{61} +(3.21349 + 2.44283i) q^{62} +(0.170262 + 1.03855i) q^{63} +(0.468408 + 0.883512i) q^{64} +(-9.61225 + 2.11582i) q^{65} +(4.33590 + 0.471557i) q^{66} +(11.2745 + 6.78367i) q^{67} +(0.108027 + 0.389078i) q^{68} +(-8.66220 - 1.90669i) q^{69} +(-1.40408 - 0.473089i) q^{70} +(-5.60729 + 10.5765i) q^{71} +(0.267528 - 0.963550i) q^{72} +(-2.68921 + 2.54736i) q^{73} +(-1.61717 + 9.86430i) q^{74} +(2.86000 - 0.963647i) q^{75} +(0.258697 - 0.0281350i) q^{76} +(4.16585 + 1.92733i) q^{77} +(0.378491 - 6.98085i) q^{78} +(5.37891 - 4.08894i) q^{79} +(1.02209 + 0.968171i) q^{80} +(-0.856857 + 0.515554i) q^{81} +(8.44149 - 3.90545i) q^{82} +(-2.31074 - 5.79951i) q^{83} +(0.590604 - 0.871075i) q^{84} +(0.319024 + 0.470526i) q^{85} +(2.52398 - 6.33471i) q^{86} +(0.199468 + 3.67897i) q^{87} +(-2.82355 - 3.32414i) q^{88} +(0.778995 + 0.917104i) q^{89} +(-0.0762190 - 1.40578i) q^{90} +(2.72332 - 6.83501i) q^{91} +(4.97749 + 7.34124i) q^{92} +(-2.26527 + 3.34103i) q^{93} +(2.76830 + 6.94791i) q^{94} +(0.332492 - 0.153827i) q^{95} +(-0.856857 + 0.515554i) q^{96} +(-0.228792 - 0.216724i) q^{97} +(-4.69091 + 3.56594i) q^{98} +(-0.236125 + 4.35507i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} - 18 q^{11} - 2 q^{12} + 13 q^{13} - 20 q^{14} + 4 q^{15} - 2 q^{16} + 21 q^{17} - 2 q^{18} + 20 q^{19} + 4 q^{20} - 20 q^{21} + 11 q^{22} + 34 q^{23} - 2 q^{24} - 28 q^{25} - 16 q^{26} - 2 q^{27} + 9 q^{28} + 38 q^{29} + 4 q^{30} + 34 q^{31} - 2 q^{32} + 11 q^{33} - 8 q^{34} - 19 q^{35} - 2 q^{36} - 29 q^{37} + 20 q^{38} + 13 q^{39} + 4 q^{40} + 43 q^{41} + 9 q^{42} - 65 q^{43} + 11 q^{44} + 4 q^{45} + 5 q^{46} - 60 q^{47} - 2 q^{48} - 13 q^{49} - 86 q^{50} + 21 q^{51} - 16 q^{52} - 15 q^{53} - 2 q^{54} - 15 q^{55} + 9 q^{56} + 20 q^{57} - 78 q^{58} - 2 q^{59} - 54 q^{60} + 4 q^{61} + 5 q^{62} + 9 q^{63} - 2 q^{64} - 57 q^{65} + 11 q^{66} - 56 q^{67} - 8 q^{68} - 53 q^{69} + 10 q^{70} + 23 q^{71} - 2 q^{72} - 21 q^{73} + 30 q^{75} - 9 q^{76} - 57 q^{77} + 13 q^{78} + 99 q^{79} + 4 q^{80} - 2 q^{81} + 43 q^{82} + 33 q^{83} + 9 q^{84} - 45 q^{85} - 7 q^{86} + 9 q^{87} - 18 q^{88} + 32 q^{89} + 4 q^{90} - 75 q^{91} + 34 q^{92} + 5 q^{93} + 27 q^{94} + 82 q^{95} - 2 q^{96} + 70 q^{97} + 45 q^{98} + 11 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 - 18 * q^11 - 2 * q^12 + 13 * q^13 - 20 * q^14 + 4 * q^15 - 2 * q^16 + 21 * q^17 - 2 * q^18 + 20 * q^19 + 4 * q^20 - 20 * q^21 + 11 * q^22 + 34 * q^23 - 2 * q^24 - 28 * q^25 - 16 * q^26 - 2 * q^27 + 9 * q^28 + 38 * q^29 + 4 * q^30 + 34 * q^31 - 2 * q^32 + 11 * q^33 - 8 * q^34 - 19 * q^35 - 2 * q^36 - 29 * q^37 + 20 * q^38 + 13 * q^39 + 4 * q^40 + 43 * q^41 + 9 * q^42 - 65 * q^43 + 11 * q^44 + 4 * q^45 + 5 * q^46 - 60 * q^47 - 2 * q^48 - 13 * q^49 - 86 * q^50 + 21 * q^51 - 16 * q^52 - 15 * q^53 - 2 * q^54 - 15 * q^55 + 9 * q^56 + 20 * q^57 - 78 * q^58 - 2 * q^59 - 54 * q^60 + 4 * q^61 + 5 * q^62 + 9 * q^63 - 2 * q^64 - 57 * q^65 + 11 * q^66 - 56 * q^67 - 8 * q^68 - 53 * q^69 + 10 * q^70 + 23 * q^71 - 2 * q^72 - 21 * q^73 + 30 * q^75 - 9 * q^76 - 57 * q^77 + 13 * q^78 + 99 * q^79 + 4 * q^80 - 2 * q^81 + 43 * q^82 + 33 * q^83 + 9 * q^84 - 45 * q^85 - 7 * q^86 + 9 * q^87 - 18 * q^88 + 32 * q^89 + 4 * q^90 - 75 * q^91 + 34 * q^92 + 5 * q^93 + 27 * q^94 + 82 * q^95 - 2 * q^96 + 70 * q^97 + 45 * q^98 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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