LMFDB - Embedded newform 378.2.v.b.79.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(67,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8, 12]))

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

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

chi := DirichletCharacter("378.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.v (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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			79.7
Character	$\chi$	$=$	378.79
Dual form			378.2.v.b.67.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(0.586306 - 1.62980i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.483736 + 2.74340i) q^{5} +(1.49675 - 0.871628i) q^{6} +(0.286196 + 2.63023i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.31249 - 1.91112i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(0.586306 - 1.62980i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.483736 + 2.74340i) q^{5} +(1.49675 - 0.871628i) q^{6} +(0.286196 + 2.63023i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.31249 - 1.91112i) q^{9} +(-1.39286 + 2.41251i) q^{10} +(-0.275449 + 1.56215i) q^{11} +(1.70685 + 0.294387i) q^{12} +(0.943280 + 5.34960i) q^{13} +(-1.47144 + 2.19883i) q^{14} +(4.75482 + 0.820082i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(3.17470 - 5.49875i) q^{17} +(-0.543024 - 2.95044i) q^{18} +(-3.31733 - 5.74579i) q^{19} +(-2.61773 + 0.952774i) q^{20} +(4.45454 + 1.07568i) q^{21} +(-1.21514 + 1.01962i) q^{22} +(6.11761 - 5.13328i) q^{23} +(1.11829 + 1.32266i) q^{24} +(-2.59380 + 0.944067i) q^{25} +(-2.71607 + 4.70436i) q^{26} +(-4.47057 + 2.64839i) q^{27} +(-2.54057 + 0.738582i) q^{28} +(-0.0620252 + 0.351762i) q^{29} +(3.11526 + 3.68456i) q^{30} +(-0.432843 - 2.45477i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(2.38449 + 1.36482i) q^{33} +(5.96649 - 2.17162i) q^{34} +(-7.07733 + 2.05749i) q^{35} +(1.48053 - 2.60922i) q^{36} -3.96417 q^{37} +(1.15210 - 6.53387i) q^{38} +(9.27183 + 1.59915i) q^{39} +(-2.61773 - 0.952774i) q^{40} +(-0.0866442 - 0.491383i) q^{41} +(2.72094 + 3.68734i) q^{42} +(9.13494 + 7.66513i) q^{43} -1.58625 q^{44} +(4.12435 - 7.26857i) q^{45} +7.98597 q^{46} +(1.92737 - 10.9307i) q^{47} +(0.00647654 + 1.73204i) q^{48} +(-6.83618 + 1.50552i) q^{49} +(-2.59380 - 0.944067i) q^{50} +(-7.10050 - 8.39808i) q^{51} +(-5.10453 + 1.85790i) q^{52} +(3.02977 + 5.24771i) q^{53} +(-5.12701 - 0.844843i) q^{54} -4.41885 q^{55} +(-2.42094 - 1.06726i) q^{56} +(-11.3094 + 2.03779i) q^{57} +(-0.273622 + 0.229596i) q^{58} +(-8.96243 - 3.26206i) q^{59} +(0.0180419 + 4.82499i) q^{60} +(-0.975123 + 5.53019i) q^{61} +(1.24632 - 2.15869i) q^{62} +(4.36486 - 6.62933i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-14.2198 + 5.17559i) q^{65} +(0.949335 + 2.57824i) q^{66} +(1.75315 - 1.47107i) q^{67} +(5.96649 + 2.17162i) q^{68} +(-4.77943 - 12.9802i) q^{69} +(-6.74408 - 2.97310i) q^{70} +(0.0982486 + 0.170172i) q^{71} +(2.81133 - 1.04711i) q^{72} -6.65444 q^{73} +(-3.03673 - 2.54812i) q^{74} +(0.0178770 + 4.78089i) q^{75} +(5.08245 - 4.26468i) q^{76} +(-4.18764 - 0.277413i) q^{77} +(6.07472 + 7.18484i) q^{78} +(1.98128 + 1.66249i) q^{79} +(-1.39286 - 2.41251i) q^{80} +(1.69522 + 8.83890i) q^{81} +(0.249482 - 0.432115i) q^{82} +(3.07726 - 17.4520i) q^{83} +(-0.285812 + 4.57365i) q^{84} +(16.6210 + 6.04955i) q^{85} +(2.07072 + 11.7437i) q^{86} +(0.536936 + 0.307329i) q^{87} +(-1.21514 - 1.01962i) q^{88} +(0.662790 + 1.14799i) q^{89} +(7.83158 - 2.91697i) q^{90} +(-13.8007 + 4.01207i) q^{91} +(6.11761 + 5.13328i) q^{92} +(-4.25457 - 0.733802i) q^{93} +(8.50255 - 7.13449i) q^{94} +(14.1583 - 11.8802i) q^{95} +(-1.10837 + 1.33098i) q^{96} +(-6.75544 - 5.66849i) q^{97} +(-6.20455 - 3.24092i) q^{98} +(3.62243 - 3.08604i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9}+O(q^{10}) $ 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9	$ 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9} - 6 q^{10} + 12 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} - 18 q^{19} - 30 q^{21} - 6 q^{22} + 30 q^{23} + 6 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} - 18 q^{35} + 9 q^{36} - 24 q^{39} - 6 q^{41} + 12 q^{42} + 24 q^{43} + 51 q^{45} + 45 q^{47} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 51 q^{51} + 6 q^{52} - 15 q^{53} + 27 q^{54} + 72 q^{55} - 3 q^{56} - 63 q^{57} + 3 q^{58} - 30 q^{59} - 3 q^{60} + 9 q^{61} - 24 q^{62} - 39 q^{63} - 36 q^{64} + 9 q^{65} - 6 q^{67} + 9 q^{68} - 21 q^{69} - 33 q^{70} + 12 q^{71} - 12 q^{72} + 132 q^{73} - 18 q^{74} - 30 q^{75} - 33 q^{77} + 30 q^{78} - 9 q^{79} - 6 q^{80} + 36 q^{81} - 33 q^{82} - 18 q^{83} + 15 q^{84} + 21 q^{85} - 12 q^{86} - 39 q^{87} - 6 q^{88} - 36 q^{89} + 69 q^{90} + 39 q^{91} + 30 q^{92} - 66 q^{93} - 9 q^{94} - 33 q^{95} - 48 q^{97} - 12 q^{98} - 54 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9 - 6 * q^10 + 12 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 - 18 * q^19 - 30 * q^21 - 6 * q^22 + 30 * q^23 + 6 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 - 18 * q^35 + 9 * q^36 - 24 * q^39 - 6 * q^41 + 12 * q^42 + 24 * q^43 + 51 * q^45 + 45 * q^47 - 6 * q^48 - 12 * q^49 + 6 * q^50 - 51 * q^51 + 6 * q^52 - 15 * q^53 + 27 * q^54 + 72 * q^55 - 3 * q^56 - 63 * q^57 + 3 * q^58 - 30 * q^59 - 3 * q^60 + 9 * q^61 - 24 * q^62 - 39 * q^63 - 36 * q^64 + 9 * q^65 - 6 * q^67 + 9 * q^68 - 21 * q^69 - 33 * q^70 + 12 * q^71 - 12 * q^72 + 132 * q^73 - 18 * q^74 - 30 * q^75 - 33 * q^77 + 30 * q^78 - 9 * q^79 - 6 * q^80 + 36 * q^81 - 33 * q^82 - 18 * q^83 + 15 * q^84 + 21 * q^85 - 12 * q^86 - 39 * q^87 - 6 * q^88 - 36 * q^89 + 69 * q^90 + 39 * q^91 + 30 * q^92 - 66 * q^93 - 9 * q^94 - 33 * q^95 - 48 * q^97 - 12 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	0.586306	−	1.62980i	0.338504	−	0.940965i
$3$	0.586306	−	1.62980i	0.338504	−	0.940965i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	0.483736	+	2.74340i	0.216333	+	1.22689i	0.878578	+	0.477600i	$0.158493\pi$
$5$	0.483736	+	2.74340i	0.216333	+	1.22689i	−0.662244	+	0.749288i	$0.730396\pi$
$6$	1.49675	−	0.871628i	0.611046	−	0.355841i
$7$	0.286196	+	2.63023i	0.108172	+	0.994132i
$7$	0.286196	+	2.63023i	0.108172	+	0.994132i
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−2.31249	−	1.91112i	−0.770830	−	0.637041i
$10$	−1.39286	+	2.41251i	−0.440462	+	0.762902i
$11$	−0.275449	+	1.56215i	−0.0830510	+	0.471006i	0.914709	+	0.404113i	$0.132420\pi$
$11$	−0.275449	+	1.56215i	−0.0830510	+	0.471006i	−0.997760	+	0.0668929i	$0.978691\pi$
$12$	1.70685	+	0.294387i	0.492725	+	0.0849823i
$13$	0.943280	+	5.34960i	0.261619	+	1.48371i	0.778494	+	0.627652i	$0.215984\pi$
$13$	0.943280	+	5.34960i	0.261619	+	1.48371i	−0.516875	+	0.856061i	$0.672905\pi$
$14$	−1.47144	+	2.19883i	−0.393259	+	0.587663i
$15$	4.75482	+	0.820082i	1.22769	+	0.211744i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	3.17470	−	5.49875i	0.769979	−	1.33364i	−0.167595	−	0.985856i	$-0.553600\pi$
$17$	3.17470	−	5.49875i	0.769979	−	1.33364i	0.937574	−	0.347786i	$-0.113066\pi$
$18$	−0.543024	−	2.95044i	−0.127992	−	0.695427i
$19$	−3.31733	−	5.74579i	−0.761048	−	1.31817i	−0.942311	−	0.334739i	$-0.891352\pi$
$19$	−3.31733	−	5.74579i	−0.761048	−	1.31817i	0.181263	−	0.983435i	$-0.441981\pi$
$20$	−2.61773	+	0.952774i	−0.585341	+	0.213047i
$21$	4.45454	+	1.07568i	0.972060	+	0.234732i
$22$	−1.21514	+	1.01962i	−0.259068	+	0.217384i
$23$	6.11761	−	5.13328i	1.27561	−	1.07036i	0.281777	−	0.959480i	$-0.409076\pi$
$23$	6.11761	−	5.13328i	1.27561	−	1.07036i	0.993833	−	0.110884i	$-0.0353682\pi$
$24$	1.11829	+	1.32266i	0.228271	+	0.269986i
$25$	−2.59380	+	0.944067i	−0.518761	+	0.188813i
$26$	−2.71607	+	4.70436i	−0.532664	+	0.922601i
$27$	−4.47057	+	2.64839i	−0.860362	+	0.509683i
$28$	−2.54057	+	0.738582i	−0.480123	+	0.139579i
$29$	−0.0620252	+	0.351762i	−0.0115178	+	0.0653206i	−0.990025	−	0.140892i	$-0.955003\pi$
$29$	−0.0620252	+	0.351762i	−0.0115178	+	0.0653206i	0.978507	+	0.206213i	$0.0661140\pi$
$30$	3.11526	+	3.68456i	0.568766	+	0.672705i
$31$	−0.432843	−	2.45477i	−0.0777409	−	0.440891i	−0.998688	−	0.0512035i	$-0.983694\pi$
$31$	−0.432843	−	2.45477i	−0.0777409	−	0.440891i	0.920947	−	0.389687i	$-0.127417\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	2.38449	+	1.36482i	0.415087	+	0.237585i
$34$	5.96649	−	2.17162i	1.02324	−	0.372431i
$35$	−7.07733	+	2.05749i	−1.19629	+	0.347779i
$36$	1.48053	−	2.60922i	0.246755	−	0.434870i
$37$	−3.96417			−0.651705			−0.325853	−	0.945421i	$-0.605651\pi$
$37$	−3.96417			−0.651705			−0.325853	+	0.945421i	$0.605651\pi$
$38$	1.15210	−	6.53387i	0.186895	−	1.05993i
$39$	9.27183	+	1.59915i	1.48468	+	0.256069i
$40$	−2.61773	−	0.952774i	−0.413899	−	0.150647i
$41$	−0.0866442	−	0.491383i	−0.0135315	−	0.0767412i	0.977294	−	0.211887i	$-0.0679609\pi$
$41$	−0.0866442	−	0.491383i	−0.0135315	−	0.0767412i	−0.990826	+	0.135146i	$0.956850\pi$
$42$	2.72094	+	3.68734i	0.419851	+	0.568969i
$43$	9.13494	+	7.66513i	1.39307	+	1.16892i	0.964081	+	0.265609i	$0.0855732\pi$
$43$	9.13494	+	7.66513i	1.39307	+	1.16892i	0.428985	+	0.903312i	$0.358871\pi$
$44$	−1.58625			−0.239136
$45$	4.12435	−	7.26857i	0.614821	−	1.08354i
$46$	7.98597			1.17747
$47$	1.92737	−	10.9307i	0.281136	−	1.59440i	−0.437633	−	0.899154i	$-0.644183\pi$
$47$	1.92737	−	10.9307i	0.281136	−	1.59440i	0.718769	−	0.695249i	$-0.244706\pi$
$48$	0.00647654	+	1.73204i	0.000934808	+	0.249998i
$49$	−6.83618	+	1.50552i	−0.976598	+	0.215074i
$50$	−2.59380	−	0.944067i	−0.366819	−	0.133511i
$51$	−7.10050	−	8.39808i	−0.994270	−	1.17597i
$52$	−5.10453	+	1.85790i	−0.707871	+	0.257644i
$53$	3.02977	+	5.24771i	0.416171	+	0.720829i	0.995551	−	0.0942287i	$-0.0300385\pi$
$53$	3.02977	+	5.24771i	0.416171	+	0.720829i	−0.579380	+	0.815058i	$0.696705\pi$
$54$	−5.12701	−	0.844843i	−0.697698	−	0.114969i
$55$	−4.41885			−0.595838
$56$	−2.42094	−	1.06726i	−0.323512	−	0.142619i
$57$	−11.3094	+	2.03779i	−1.49797	+	0.269912i
$58$	−0.273622	+	0.229596i	−0.0359284	+	0.0301475i
$59$	−8.96243	−	3.26206i	−1.16681	−	0.424684i	−0.315283	−	0.948998i	$-0.602100\pi$
$59$	−8.96243	−	3.26206i	−1.16681	−	0.424684i	−0.851525	+	0.524314i	$0.824322\pi$
$60$	0.0180419	+	4.82499i	0.00232919	+	0.622903i
$61$	−0.975123	+	5.53019i	−0.124852	+	0.708069i	0.856544	+	0.516074i	$0.172607\pi$
$61$	−0.975123	+	5.53019i	−0.124852	+	0.708069i	−0.981396	+	0.191995i	$0.938504\pi$
$62$	1.24632	−	2.15869i	0.158283	−	0.274154i
$63$	4.36486	−	6.62933i	0.549921	−	0.835217i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−14.2198	+	5.17559i	−1.76375	+	0.641953i
$66$	0.949335	+	2.57824i	0.116855	+	0.317359i
$67$	1.75315	−	1.47107i	0.214181	−	0.179719i	−0.529385	−	0.848382i	$-0.677577\pi$
$67$	1.75315	−	1.47107i	0.214181	−	0.179719i	0.743566	+	0.668662i	$0.233133\pi$
$68$	5.96649	+	2.17162i	0.723543	+	0.263348i
$69$	−4.77943	−	12.9802i	−0.575376	−	1.56263i
$70$	−6.74408	−	2.97310i	−0.806071	−	0.355353i
$71$	0.0982486	+	0.170172i	0.0116600	+	0.0201956i	0.871797	−	0.489868i	$-0.162955\pi$
$71$	0.0982486	+	0.170172i	0.0116600	+	0.0201956i	−0.860137	+	0.510064i	$0.829622\pi$
$72$	2.81133	−	1.04711i	0.331318	−	0.123404i
$73$	−6.65444			−0.778843			−0.389421	−	0.921060i	$-0.627325\pi$
$73$	−6.65444			−0.778843			−0.389421	+	0.921060i	$0.627325\pi$
$74$	−3.03673	−	2.54812i	−0.353013	−	0.296213i
$75$	0.0178770	+	4.78089i	0.00206426	+	0.552050i
$76$	5.08245	−	4.26468i	0.582996	−	0.489192i
$77$	−4.18764	−	0.277413i	−0.477226	−	0.0316142i
$78$	6.07472	+	7.18484i	0.687827	+	0.813523i
$79$	1.98128	+	1.66249i	0.222911	+	0.187045i	0.747403	−	0.664371i	$-0.231300\pi$
$79$	1.98128	+	1.66249i	0.222911	+	0.187045i	−0.524492	+	0.851415i	$0.675745\pi$
$80$	−1.39286	−	2.41251i	−0.155727	−	0.269727i
$81$	1.69522	+	8.83890i	0.188358	+	0.982100i
$82$	0.249482	−	0.432115i	0.0275507	−	0.0477192i
$83$	3.07726	−	17.4520i	0.337773	−	1.91561i	−0.0601547	−	0.998189i	$-0.519159\pi$
$83$	3.07726	−	17.4520i	0.337773	−	1.91561i	0.397928	−	0.917417i	$-0.369729\pi$
$84$	−0.285812	+	4.57365i	−0.0311847	+	0.499027i
$85$	16.6210	+	6.04955i	1.80280	+	0.656166i
$86$	2.07072	+	11.7437i	0.223292	+	1.26635i
$87$	0.536936	+	0.307329i	0.0575656	+	0.0329491i
$88$	−1.21514	−	1.01962i	−0.129534	−	0.108692i
$89$	0.662790	+	1.14799i	0.0702556	+	0.121686i	0.899013	−	0.437921i	$-0.144285\pi$
$89$	0.662790	+	1.14799i	0.0702556	+	0.121686i	−0.828758	+	0.559608i	$0.810952\pi$
$90$	7.83158	−	2.91697i	0.825521	−	0.307476i
$91$	−13.8007	+	4.01207i	−1.44671	+	0.420579i
$92$	6.11761	+	5.13328i	0.637805	+	0.535182i
$93$	−4.25457	−	0.733802i	−0.441178	−	0.0760918i
$94$	8.50255	−	7.13449i	0.876971	−	0.735866i
$95$	14.1583	−	11.8802i	1.45261	−	1.21889i
$96$	−1.10837	+	1.33098i	−0.113123	+	0.135843i
$97$	−6.75544	−	5.66849i	−0.685911	−	0.575548i	0.231816	−	0.972760i	$-0.425533\pi$
$97$	−6.75544	−	5.66849i	−0.685911	−	0.575548i	−0.917727	+	0.397212i	$0.869978\pi$
$98$	−6.20455	−	3.24092i	−0.626754	−	0.327382i
$99$	3.62243	−	3.08604i	0.364068	−	0.310159i
$100$	−1.38013	−	2.39046i	−0.138013	−	0.239046i
$101$	−6.28632	−	5.27485i	−0.625512	−	0.524867i	0.274019	−	0.961724i	$-0.411647\pi$
$101$	−6.28632	−	5.27485i	−0.625512	−	0.524867i	−0.899531	+	0.436857i	$0.856091\pi$
$102$	−0.0411222	−	10.9974i	−0.00407170	−	1.08891i
$103$	1.40680	+	7.97834i	0.138616	+	0.786129i	0.972273	+	0.233847i	$0.0751316\pi$
$103$	1.40680	+	7.97834i	0.138616	+	0.786129i	−0.833657	+	0.552282i	$0.813757\pi$
$104$	−5.10453	−	1.85790i	−0.500541	−	0.182182i
$105$	−0.796195	+	12.7409i	−0.0777006	+	1.24339i
$106$	−1.05223	+	5.96748i	−0.102201	+	0.579613i
$107$	0.811790	−	1.40606i	0.0784787	−	0.135929i	−0.824115	−	0.566422i	$-0.808327\pi$
$107$	0.811790	−	1.40606i	0.0784787	−	0.135929i	0.902594	+	0.430493i	$0.141660\pi$
$108$	−3.38446	−	3.94277i	−0.325670	−	0.379393i
$109$	−4.63410	−	8.02650i	−0.443866	−	0.768799i	0.554106	−	0.832446i	$-0.313060\pi$
$109$	−4.63410	−	8.02650i	−0.443866	−	0.768799i	−0.997972	+	0.0636468i	$0.979727\pi$
$110$	−3.38504	−	2.84038i	−0.322751	−	0.270820i
$111$	−2.32422	+	6.46080i	−0.220605	+	0.613232i
$112$	−1.16853	−	2.37372i	−0.110415	−	0.224295i
$113$	1.67323	−	1.40401i	0.157404	−	0.132078i	−0.560684	−	0.828030i	$-0.689462\pi$
$113$	1.67323	−	1.40401i	0.157404	−	0.132078i	0.718088	+	0.695952i	$0.245017\pi$
$114$	−9.97341	−	5.70853i	−0.934095	−	0.534653i
$115$	17.0420	+	14.2999i	1.58917	+	1.33347i
$116$	−0.357189			−0.0331641
$117$	8.04242	−	14.1736i	0.743522	−	1.31035i
$118$	−4.76881	−	8.25982i	−0.439004	−	0.760378i
$119$	15.3715	+	6.77647i	1.40911	+	0.621198i
$120$	−3.08762	+	3.70775i	−0.281860	+	0.338470i
$121$	7.97218	+	2.90164i	0.724744	+	0.263785i
$122$	−4.30173	+	3.60958i	−0.389460	+	0.326796i
$123$	−0.851656	−	0.146889i	−0.0767913	−	0.0132445i
$124$	2.34232	−	0.852534i	0.210346	−	0.0765598i
$125$	3.11964	+	5.40337i	0.279029	+	0.483292i
$126$	7.60493	−	2.27268i	0.677501	−	0.202467i
$127$	−6.62007	+	11.4663i	−0.587436	+	1.01747i	0.407131	+	0.913370i	$0.366529\pi$
$127$	−6.62007	+	11.4663i	−0.587436	+	1.01747i	−0.994567	+	0.104100i	$0.966804\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	17.8485	−	10.3940i	1.57147	−	0.915142i
$130$	−14.2198	−	5.17559i	−1.24716	−	0.453930i
$131$	1.41329	−	1.18589i	0.123480	−	0.103612i	−0.578957	−	0.815358i	$-0.696540\pi$
$131$	1.41329	−	1.18589i	0.123480	−	0.103612i	0.702436	+	0.711747i	$0.252096\pi$
$132$	−0.930027	+	2.58527i	−0.0809485	+	0.225019i
$133$	14.1633	−	10.3697i	1.22811	−	0.899171i
$134$	2.28857			0.197703
$135$	−9.42819	−	10.9835i	−0.811449	−	0.945306i
$136$	3.17470	+	5.49875i	0.272229	+	0.471514i
$137$	−5.42356	+	1.97402i	−0.463366	+	0.168652i	−0.563145	−	0.826358i	$-0.690409\pi$
$137$	−5.42356	+	1.97402i	−0.463366	+	0.168652i	0.0997787	+	0.995010i	$0.468187\pi$
$138$	4.68223	−	13.0155i	0.398578	−	1.10796i
$139$	17.9535	+	6.53454i	1.52280	+	0.554252i	0.961845	−	0.273597i	$-0.0882133\pi$
$139$	17.9535	+	6.53454i	1.52280	+	0.554252i	0.560951	+	0.827849i	$0.310436\pi$
$140$	−3.25519	−	6.61253i	−0.275114	−	0.558861i
$141$	−16.6848	−	9.54995i	−1.40511	−	0.804251i
$142$	−0.0341214	+	0.193512i	−0.00286340	+	0.0162392i
$143$	−8.61671			−0.720565
$144$	2.82667	+	1.00495i	0.235556	+	0.0837458i
$145$	−0.995030			−0.0826327
$146$	−5.09759	−	4.27739i	−0.421880	−	0.353999i
$147$	−1.55440	+	12.0243i	−0.128205	+	0.991748i
$148$	−0.688371	−	3.90394i	−0.0565837	−	0.320902i
$149$	5.77529	+	2.10203i	0.473130	+	0.172205i	0.567570	−	0.823325i	$-0.307884\pi$
$149$	5.77529	+	2.10203i	0.473130	+	0.172205i	−0.0944398	+	0.995531i	$0.530106\pi$
$150$	−3.05940	+	3.67387i	−0.249799	+	0.299970i
$151$	0.581997	−	3.30067i	0.0473623	−	0.268605i	−0.951926	−	0.306328i	$-0.900899\pi$
$151$	0.581997	−	3.30067i	0.0473623	−	0.268605i	0.999288	+	0.0377235i	$0.0120106\pi$
$152$	6.63466			0.538142
$153$	−17.8502	+	6.64855i	−1.44311	+	0.537504i
$154$	−3.02960	−	2.90427i	−0.244132	−	0.234033i
$155$	6.52506	−	2.37493i	0.524105	−	0.190759i
$156$	0.0351814	+	9.40866i	0.00281677	+	0.753296i
$157$	−7.01902	−	2.55471i	−0.560178	−	0.203888i	0.0463846	−	0.998924i	$-0.485230\pi$
$157$	−7.01902	−	2.55471i	−0.560178	−	0.203888i	−0.606563	+	0.795035i	$0.707452\pi$
$158$	0.449119	+	2.54708i	0.0357300	+	0.202635i
$159$	10.3291	−	1.86115i	0.819150	−	0.147599i
$160$	0.483736	−	2.74340i	0.0382427	−	0.216885i
$161$	15.2525	+	14.6216i	1.20207	+	1.15234i
$162$	−4.38292	+	7.86066i	−0.344355	+	0.617592i
$163$	0.283776	−	0.491514i	0.0222271	−	0.0384984i	−0.854698	−	0.519126i	$-0.826258\pi$
$163$	0.283776	−	0.491514i	0.0222271	−	0.0384984i	0.876925	+	0.480627i	$0.159591\pi$
$164$	0.468873	−	0.170656i	0.0366128	−	0.0133260i
$165$	−2.59080	+	7.20184i	−0.201694	+	0.560663i
$166$	13.5752	−	11.3910i	1.05364	−	0.884112i
$167$	−8.03215	+	6.73978i	−0.621547	+	0.521540i	−0.898289	−	0.439404i	$-0.855190\pi$
$167$	−8.03215	+	6.73978i	−0.621547	+	0.521540i	0.276743	+	0.960944i	$0.410745\pi$
$168$	−3.15883	+	3.31991i	−0.243709	+	0.256136i
$169$	−15.5125	+	5.64608i	−1.19327	+	0.434314i
$170$	8.84385	+	15.3180i	0.678292	+	1.17484i
$171$	−3.30961	+	19.6269i	−0.253092	+	1.50091i
$172$	−5.96241	+	10.3272i	−0.454630	+	0.787442i
$173$	−1.30516	+	0.475039i	−0.0992294	+	0.0361165i	−0.391158	−	0.920324i	$-0.627925\pi$
$173$	−1.30516	+	0.475039i	−0.0992294	+	0.0361165i	0.291928	+	0.956440i	$0.405703\pi$
$174$	0.213770	+	0.580563i	0.0162058	+	0.0440124i
$175$	−3.22545	−	6.55210i	−0.243821	−	0.495293i
$176$	−0.275449	−	1.56215i	−0.0207628	−	0.117751i
$177$	−10.5712	+	12.6944i	−0.794582	+	0.954169i
$178$	−0.230185	+	1.30544i	−0.0172531	+	0.0978470i
$179$	−3.70163	+	6.41141i	−0.276673	+	0.479211i	−0.970556	−	0.240877i	$-0.922565\pi$
$179$	−3.70163	+	6.41141i	−0.276673	+	0.479211i	0.693883	+	0.720088i	$0.255898\pi$
$180$	7.87433	+	2.79951i	0.586918	+	0.208663i
$181$	−6.70877	+	11.6199i	−0.498659	+	0.863702i	−0.999999	−	0.00154822i	$-0.999507\pi$
$181$	−6.70877	+	11.6199i	−0.498659	+	0.863702i	0.501340	+	0.865250i	$0.332841\pi$
$182$	−13.1509	−	5.79750i	−0.974807	−	0.429739i
$183$	8.44139	+	4.83164i	0.624005	+	0.357165i
$184$	1.38675	+	7.86465i	0.102233	+	0.579790i
$185$	−1.91761	−	10.8753i	−0.140986	−	0.799569i
$186$	−2.78751	−	3.29691i	−0.204390	−	0.241741i
$187$	7.71540	+	6.47399i	0.564206	+	0.473425i
$188$	11.0993			0.809499
$189$	−8.24533	−	11.0007i	−0.599759	−	0.800180i
$190$	18.4823			1.34085
$191$	−3.29563	−	2.76537i	−0.238464	−	0.200095i	0.515722	−	0.856756i	$-0.327524\pi$
$191$	−3.29563	−	2.76537i	−0.238464	−	0.200095i	−0.754186	+	0.656661i	$0.771968\pi$
$192$	−1.70460	+	0.307144i	−0.123019	+	0.0221662i
$193$	−3.34878	−	18.9919i	−0.241050	−	1.36706i	−0.829490	−	0.558522i	$-0.811369\pi$
$193$	−3.34878	−	18.9919i	−0.241050	−	1.36706i	0.588439	−	0.808541i	$-0.299743\pi$
$194$	−1.53133	−	8.68462i	−0.109943	−	0.623520i
$195$	0.0980057	+	26.2099i	0.00701834	+	1.87693i
$196$	−2.66974	−	6.47090i	−0.190696	−	0.462207i
$197$	−6.79535	+	11.7699i	−0.484149	+	0.838570i	−0.999834	−	0.0182080i	$-0.994204\pi$
$197$	−6.79535	+	11.7699i	−0.484149	+	0.838570i	0.515686	+	0.856778i	$0.327537\pi$
$198$	4.75861	−	0.0355878i	0.338180	−	0.00252912i
$199$	4.28539	−	7.42251i	0.303783	−	0.526168i	−0.673207	−	0.739454i	$-0.735084\pi$
$199$	4.28539	−	7.42251i	0.303783	−	0.526168i	0.976990	+	0.213287i	$0.0684169\pi$
$200$	0.479316	−	2.71833i	0.0338927	−	0.192215i
$201$	−1.36966	−	3.71978i	−0.0966084	−	0.262373i
$202$	−1.42499	−	8.08154i	−0.100262	−	0.568615i
$203$	−0.942966	−	0.0624675i	−0.0661832	−	0.00438436i
$204$	7.03750	−	8.45094i	0.492724	−	0.591684i
$205$	1.30615	−	0.475400i	0.0912255	−	0.0332034i
$206$	−4.05071	+	7.01603i	−0.282226	+	0.488830i
$207$	−23.9573	+	0.179167i	−1.66514	+	0.0124530i
$208$	−2.71607	−	4.70436i	−0.188325	−	0.326189i
$209$	9.88953	−	3.59950i	0.684073	−	0.248982i
$210$	−8.79964	+	9.24835i	−0.607233	+	0.638197i
$211$	0.423929	−	0.355718i	0.0291844	−	0.0244887i	−0.628079	−	0.778150i	$-0.716158\pi$
$211$	0.423929	−	0.355718i	0.0291844	−	0.0244887i	0.657263	+	0.753661i	$0.271714\pi$
$212$	−4.64188	+	3.89500i	−0.318805	+	0.267509i
$213$	0.334949	−	0.0603528i	0.0229503	−	0.00413531i
$214$	1.52567	−	0.555297i	0.104292	−	0.0379593i
$215$	−16.6096	+	28.7687i	−1.13277	+	1.96201i
$216$	−0.0582878	−	5.19583i	−0.00396598	−	0.353531i
$217$	6.33274	−	1.84102i	0.429894	−	0.124977i
$218$	1.60941	−	9.12740i	0.109003	−	0.618185i
$219$	−3.90154	+	10.8454i	−0.263641	+	0.732864i
$220$	−0.767326	−	4.35172i	−0.0517331	−	0.293393i
$221$	32.4107	+	11.7965i	2.18018	+	0.793522i
$222$	−5.93337	+	3.45528i	−0.398222	+	0.231903i
$223$	−12.9524	+	4.71428i	−0.867355	+	0.315691i	−0.737096	−	0.675789i	$-0.763803\pi$
$223$	−12.9524	+	4.71428i	−0.867355	+	0.315691i	−0.130259	+	0.991480i	$0.541581\pi$
$224$	0.630655	−	2.56949i	0.0421374	−	0.171681i
$225$	7.80237	+	2.77393i	0.520158	+	0.184929i
$226$	2.18425			0.145294
$227$	−2.49048	+	14.1242i	−0.165299	+	0.937457i	0.783457	+	0.621446i	$0.213455\pi$
$227$	−2.49048	+	14.1242i	−0.165299	+	0.937457i	−0.948756	+	0.316010i	$0.897657\pi$
$228$	−3.97070	−	10.7838i	−0.262966	−	0.714173i
$229$	−15.6032	−	5.67911i	−1.03109	−	0.375286i	−0.229594	−	0.973286i	$-0.573740\pi$
$229$	−15.6032	−	5.67911i	−1.03109	−	0.375286i	−0.801496	+	0.598001i	$0.795962\pi$
$230$	3.86310	+	21.9088i	0.254726	+	1.44462i
$231$	−2.90737	+	6.66236i	−0.191291	+	0.438351i
$232$	−0.273622	−	0.229596i	−0.0179642	−	0.0150737i
$233$	−10.9925			−0.720144			−0.360072	−	0.932924i	$-0.617248\pi$
$233$	−10.9925			−0.720144			−0.360072	+	0.932924i	$0.617248\pi$
$234$	15.2715	−	5.68806i	0.998328	−	0.371840i
$235$	30.9196			2.01697
$236$	1.65619	−	9.39272i	0.107809	−	0.611414i
$237$	3.87116	−	2.25436i	0.251459	−	0.146436i
$238$	7.41945	+	15.0717i	0.480931	+	0.976954i
$239$	7.37903	+	2.68575i	0.477310	+	0.173727i	0.569461	−	0.822019i	$-0.307152\pi$
$239$	7.37903	+	2.68575i	0.477310	+	0.173727i	−0.0921511	+	0.995745i	$0.529374\pi$
$240$	−4.74855	+	0.855618i	−0.306518	+	0.0552299i
$241$	6.78791	−	2.47060i	0.437248	−	0.159145i	−0.114011	−	0.993479i	$-0.536370\pi$
$241$	6.78791	−	2.47060i	0.437248	−	0.159145i	0.551259	+	0.834334i	$0.314148\pi$
$242$	4.24191	+	7.34720i	0.272680	+	0.472296i
$243$	15.3996	+	2.41943i	0.987882	+	0.155207i
$244$	−5.61551			−0.359496
$245$	−7.43716	−	18.0261i	−0.475142	−	1.15165i
$246$	−0.557988	−	0.659957i	−0.0355760	−	0.0420773i
$247$	27.6085	−	23.1663i	1.75669	−	1.47404i
$248$	2.34232	+	0.852534i	0.148737	+	0.0541360i
$249$	−26.6390	−	15.2475i	−1.68818	−	0.966273i
$250$	−1.08344	+	6.14449i	−0.0685227	+	0.388612i
$251$	13.8030	−	23.9075i	0.871237	−	1.50903i	0.0105180	−	0.999945i	$-0.496652\pi$
$251$	13.8030	−	23.9075i	0.871237	−	1.50903i	0.860718	−	0.509081i	$-0.170015\pi$
$252$	7.28656	+	3.14738i	0.459010	+	0.198266i
$253$	6.33387	+	10.9706i	0.398207	+	0.689715i
$254$	−12.4417	+	4.52840i	−0.780659	+	0.284137i
$255$	19.6046	−	23.5420i	1.22768	−	1.47426i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	8.46330	+	3.08039i	0.527926	+	0.192149i	0.592212	−	0.805782i	$-0.298255\pi$
$257$	8.46330	+	3.08039i	0.527926	+	0.192149i	−0.0642860	+	0.997932i	$0.520477\pi$
$258$	20.3539	+	3.51052i	1.26718	+	0.218555i
$259$	−1.13453	−	10.4267i	−0.0704961	−	0.647881i
$260$	−7.56621	−	13.1051i	−0.469237	−	0.812742i
$261$	0.815693	−	0.694909i	0.0504901	−	0.0430138i
$262$	1.84492			0.113979
$263$	−0.816348	−	0.684998i	−0.0503382	−	0.0422388i	0.617271	−	0.786750i	$-0.288238\pi$
$263$	−0.816348	−	0.684998i	−0.0503382	−	0.0422388i	−0.667610	+	0.744511i	$0.732682\pi$
$264$	−2.37422	+	1.38262i	−0.146123	+	0.0850943i
$265$	−12.9310	+	10.8504i	−0.794345	+	0.666534i
$266$	17.5153	+	1.16031i	1.07393	+	0.0711433i
$267$	2.25958	−	0.407143i	0.138284	−	0.0249168i
$268$	1.75315	+	1.47107i	0.107091	+	0.0898597i
$269$	−5.72064	−	9.90845i	−0.348794	−	0.604129i	0.637242	−	0.770664i	$-0.280075\pi$
$269$	−5.72064	−	9.90845i	−0.348794	−	0.604129i	−0.986035	+	0.166535i	$0.946742\pi$
$270$	−0.162374	−	14.4741i	−0.00988175	−	0.880868i
$271$	0.632743	−	1.09594i	0.0384364	−	0.0665738i	−0.846167	−	0.532917i	$-0.821096\pi$
$271$	0.632743	−	1.09594i	0.0384364	−	0.0665738i	0.884604	+	0.466344i	$0.154429\pi$
$272$	−1.10256	+	6.25294i	−0.0668527	+	0.379140i
$273$	−1.55257	+	24.8447i	−0.0939658	+	1.50367i
$274$	−5.42356	−	1.97402i	−0.327649	−	0.119255i
$275$	−0.760314	−	4.31195i	−0.0458486	−	0.260021i
$276$	11.9530	−	6.96080i	0.719487	−	0.418991i
$277$	−2.03688	−	1.70914i	−0.122384	−	0.102692i	0.579542	−	0.814943i	$-0.303232\pi$
$277$	−2.03688	−	1.70914i	−0.122384	−	0.102692i	−0.701926	+	0.712250i	$0.747676\pi$
$278$	9.55286	+	16.5460i	0.572942	+	0.992365i
$279$	−3.69043	+	6.50386i	−0.220940	+	0.389376i
$280$	1.75683	−	7.15789i	0.104991	−	0.427766i
$281$	15.1420	+	12.7057i	0.903297	+	0.757956i	0.970832	−	0.239761i	$-0.0770691\pi$
$281$	15.1420	+	12.7057i	0.903297	+	0.757956i	−0.0675354	+	0.997717i	$0.521514\pi$
$282$	−6.64268	−	18.0404i	−0.395566	−	1.07429i
$283$	−9.77769	+	8.20445i	−0.581223	+	0.487704i	−0.885349	−	0.464928i	$-0.846080\pi$
$283$	−9.77769	+	8.20445i	−0.581223	+	0.487704i	0.304125	+	0.952632i	$0.401636\pi$
$284$	−0.150526	+	0.126306i	−0.00893205	+	0.00749488i
$285$	−11.0613	−	30.0406i	−0.655214	−	1.77945i
$286$	−6.60078	−	5.53871i	−0.390312	−	0.327511i
$287$	1.26765	−	0.368526i	0.0748272	−	0.0217534i
$288$	1.51939	+	2.58679i	0.0895308	+	0.152428i
$289$	−11.6575	−	20.1913i	−0.685734	−	1.18773i
$290$	−0.762237	−	0.639593i	−0.0447601	−	0.0375582i
$291$	−13.1992	+	7.68654i	−0.773754	+	0.450593i
$292$	−1.15553	−	6.55334i	−0.0676223	−	0.383505i
$293$	20.1819	+	7.34561i	1.17904	+	0.429135i	0.855863	−	0.517203i	$-0.173027\pi$
$293$	20.1819	+	7.34561i	1.17904	+	0.429135i	0.323177	+	0.946339i	$0.395249\pi$
$294$	−8.91982	+	8.21200i	−0.520214	+	0.478933i
$295$	4.61369	−	26.1655i	0.268619	−	1.52342i
$296$	1.98208	−	3.43307i	0.115206	−	0.199543i
$297$	−2.90577	−	7.71320i	−0.168610	−	0.447565i
$298$	3.07297	+	5.32253i	0.178012	+	0.308326i
$299$	33.2317	+	27.8847i	1.92184	+	1.61261i
$300$	−4.70516	+	0.847799i	−0.271652	+	0.0489477i
$301$	−17.5466	+	26.2207i	−1.01137	+	1.51134i
$302$	2.56747	−	2.15436i	0.147741	−	0.123969i
$303$	−12.2826	+	7.15276i	−0.705620	+	0.410915i
$304$	5.08245	+	4.26468i	0.291498	+	0.244596i
$305$	−15.6433			−0.895731
$306$	−17.9477	−	6.38083i	−1.02600	−	0.364768i
$307$	−17.0932	−	29.6062i	−0.975558	−	1.68972i	−0.678081	−	0.734987i	$-0.737188\pi$
$307$	−17.0932	−	29.6062i	−0.975558	−	1.68972i	−0.297477	−	0.954729i	$-0.596145\pi$
$308$	−0.453977	−	4.17219i	−0.0258678	−	0.237733i
$309$	13.8279	+	2.38495i	0.786642	+	0.135675i
$310$	6.52506	+	2.37493i	0.370598	+	0.134887i
$311$	6.66513	−	5.59271i	0.377945	−	0.317133i	−0.433950	−	0.900937i	$-0.642881\pi$
$311$	6.66513	−	5.59271i	0.377945	−	0.317133i	0.811895	+	0.583804i	$0.198436\pi$
$312$	−6.02082	+	7.23007i	−0.340862	+	0.409322i
$313$	−11.8442	+	4.31095i	−0.669476	+	0.243669i	−0.654322	−	0.756216i	$-0.727046\pi$
$313$	−11.8442	+	4.31095i	−0.669476	+	0.243669i	−0.0151536	+	0.999885i	$0.504824\pi$
$314$	−3.73474	−	6.46876i	−0.210764	−	0.365053i
$315$	20.2984	+	8.76773i	1.14368	+	0.494006i
$316$	−1.29319	+	2.23987i	−0.0727474	+	0.126002i
$317$	−3.15383	+	17.8863i	−0.177137	+	1.00459i	0.758512	+	0.651659i	$0.225927\pi$
$317$	−3.15383	+	17.8863i	−0.177137	+	1.00459i	−0.935649	+	0.352933i	$0.885184\pi$
$318$	9.10887	+	5.21369i	0.510800	+	0.292369i
$319$	−0.532420	−	0.193785i	−0.0298098	−	0.0108499i
$320$	2.13399	−	1.79063i	0.119294	−	0.100099i
$321$	−1.81564	−	2.14744i	−0.101339	−	0.119858i
$322$	2.28555	+	21.0049i	0.127369	+	1.17056i
$323$	−42.1262			−2.34396
$324$	−8.41025	+	3.20433i	−0.467236	+	0.178018i
$325$	−7.49707	−	12.9853i	−0.415863	−	0.720295i
$326$	0.533324	−	0.194114i	0.0295381	−	0.0107510i
$327$	−15.7986	+	2.84667i	−0.873664	+	0.157421i
$328$	0.468873	+	0.170656i	0.0258892	+	0.00942288i
$329$	29.3017	+	1.94112i	1.61546	+	0.107017i
$330$	−6.61392	+	3.85160i	−0.364085	+	0.212023i
$331$	3.97953	−	22.5690i	0.218735	−	1.24051i	−0.655573	−	0.755132i	$-0.727573\pi$
$331$	3.97953	−	22.5690i	0.218735	−	1.24051i	0.874307	−	0.485373i	$-0.161316\pi$
$332$	17.7212			0.972579
$333$	9.16710	+	7.57601i	0.502354	+	0.415163i
$334$	−10.4852			−0.573726
$335$	4.88379	+	4.09799i	0.266830	+	0.223897i
$336$	−4.55380	+	0.512737i	−0.248430	+	0.0279721i
$337$	−5.11480	−	29.0075i	−0.278621	−	1.58014i	−0.727220	−	0.686404i	$-0.759188\pi$
$337$	−5.11480	−	29.0075i	−0.278621	−	1.58014i	0.448599	−	0.893733i	$-0.351923\pi$
$338$	−15.5125	−	5.64608i	−0.843768	−	0.307106i
$339$	−1.30722	−	3.55021i	−0.0709987	−	0.192821i
$340$	−3.07144	+	17.4190i	−0.166572	+	0.944677i
$341$	3.95395			0.214118
$342$	−15.1512	+	12.9077i	−0.819285	+	0.697969i
$343$	−5.91634	−	17.5498i	−0.319452	−	0.947602i
$344$	−11.2057	+	4.07853i	−0.604169	+	0.219900i
$345$	33.2978	−	19.3909i	1.79269	−	1.04397i
$346$	−1.30516	−	0.475039i	−0.0701658	−	0.0255383i
$347$	0.103428	+	0.586568i	0.00555230	+	0.0314886i	0.987458	−	0.157882i	$-0.0504665\pi$
$347$	0.103428	+	0.586568i	0.00555230	+	0.0314886i	−0.981906	+	0.189370i	$0.939355\pi$
$348$	−0.209422	+	0.582146i	−0.0112262	+	0.0312063i
$349$	−2.79952	+	15.8769i	−0.149855	+	0.849870i	0.813485	+	0.581586i	$0.197568\pi$
$349$	−2.79952	+	15.8769i	−0.149855	+	0.849870i	−0.963340	+	0.268284i	$0.913544\pi$
$350$	1.74078	−	7.09248i	0.0930484	−	0.379109i
$351$	−18.3848	−	21.4176i	−0.981310	−	1.14319i
$352$	0.793124	−	1.37373i	0.0422737	−	0.0732201i
$353$	−8.94675	+	3.25635i	−0.476187	+	0.173318i	−0.568953	−	0.822370i	$-0.692651\pi$
$353$	−8.94675	+	3.25635i	−0.476187	+	0.173318i	0.0927658	+	0.995688i	$0.470429\pi$
$354$	−16.2578	+	2.92942i	−0.864094	+	0.155697i
$355$	−0.419323	+	0.351854i	−0.0222553	+	0.0186745i
$356$	−1.01545	+	0.852066i	−0.0538189	+	0.0451594i
$357$	20.0567	−	21.0794i	1.06151	−	1.11564i
$358$	−6.95678	+	2.53206i	−0.367677	+	0.133824i
$359$	−2.99162	−	5.18165i	−0.157892	−	0.273477i	0.776216	−	0.630467i	$-0.217136\pi$
$359$	−2.99162	−	5.18165i	−0.157892	−	0.273477i	−0.934108	+	0.356990i	$0.883803\pi$
$360$	4.23260	+	7.20608i	0.223077	+	0.379794i
$361$	−12.5094	+	21.6669i	−0.658388	+	1.14036i
$362$	−12.6084	+	4.58907i	−0.662680	+	0.241196i
$363$	9.40322	−	11.2918i	0.493541	−	0.592666i
$364$	−6.34759	−	12.8944i	−0.332704	−	0.675848i
$365$	−3.21899	−	18.2558i	−0.168490	−	0.955553i
$366$	3.36076	+	9.12727i	0.175670	+	0.477090i
$367$	−2.10734	+	11.9513i	−0.110002	+	0.623854i	0.879102	+	0.476634i	$0.158143\pi$
$367$	−2.10734	+	11.9513i	−0.110002	+	0.623854i	−0.989104	+	0.147219i	$0.952968\pi$
$368$	−3.99299	+	6.91606i	−0.208149	+	0.360524i
$369$	−0.738730	+	1.30191i	−0.0384568	+	0.0677746i
$370$	5.52154	−	9.56359i	0.287051	−	0.497187i
$371$	−12.9356	+	9.47085i	−0.671581	+	0.491702i
$372$	−0.0161437	−	4.31735i	−0.000837012	−	0.223844i
$373$	5.54424	+	31.4430i	0.287070	+	1.62805i	0.697797	+	0.716296i	$0.254164\pi$
$373$	5.54424	+	31.4430i	0.287070	+	1.62805i	−0.410727	+	0.911758i	$0.634725\pi$
$374$	1.74894	+	9.91872i	0.0904354	+	0.512885i
$375$	10.6355	−	1.91635i	0.549214	−	0.0989601i
$376$	8.50255	+	7.13449i	0.438486	+	0.367933i
$377$	−1.94030			−0.0999303
$378$	0.754802	−	13.7270i	0.0388228	−	0.706040i
$379$	−9.11400			−0.468154			−0.234077	−	0.972218i	$-0.575207\pi$
$379$	−9.11400			−0.468154			−0.234077	+	0.972218i	$0.575207\pi$
$380$	14.1583	+	11.8802i	0.726305	+	0.609443i
$381$	14.8064	+	17.5121i	0.758554	+	0.897174i
$382$	−0.747060	−	4.23679i	−0.0382229	−	0.216773i
$383$	−0.959928	−	5.44402i	−0.0490500	−	0.278176i	0.950411	−	0.310996i	$-0.100663\pi$
$383$	−0.959928	−	5.44402i	−0.0490500	−	0.278176i	−0.999461	+	0.0328193i	$0.989551\pi$
$384$	−1.50323	−	0.860411i	−0.0767113	−	0.0439076i
$385$	−1.26466	−	11.6226i	−0.0644528	−	0.592342i
$386$	9.64242	−	16.7012i	0.490786	−	0.850066i
$387$	−6.47547	−	35.1835i	−0.329167	−	1.78848i
$388$	4.40930	−	7.63713i	0.223848	−	0.387717i
$389$	1.91558	−	10.8638i	0.0971238	−	0.550817i	−0.896952	−	0.442128i	$-0.854224\pi$
$389$	1.91558	−	10.8638i	0.0971238	−	0.550817i	0.994076	−	0.108689i	$-0.0346652\pi$
$390$	−16.7724	+	20.1410i	−0.849301	+	1.01988i
$391$	−8.80504	−	49.9358i	−0.445290	−	2.52536i
$392$	2.11428	−	6.67307i	0.106787	−	0.337041i
$393$	−1.10414	−	2.99867i	−0.0556967	−	0.151263i
$394$	−12.7711	+	4.64829i	−0.643398	+	0.234178i
$395$	−3.60246	+	6.23965i	−0.181260	+	0.313951i
$396$	3.66818	+	3.03151i	0.184333	+	0.152339i
$397$	−5.81627	−	10.0741i	−0.291910	−	0.505603i	0.682351	−	0.731024i	$-0.260957\pi$
$397$	−5.81627	−	10.0741i	−0.291910	−	0.505603i	−0.974261	+	0.225421i	$0.927624\pi$
$398$	8.05389	−	2.93138i	0.403705	−	0.146937i
$399$	−8.59657	−	29.1632i	−0.430367	−	1.45999i
$400$	2.11449	−	1.77427i	0.105724	−	0.0887133i
$401$	−6.56881	+	5.51189i	−0.328031	+	0.275251i	−0.791897	−	0.610655i	$-0.790906\pi$
$401$	−6.56881	+	5.51189i	−0.328031	+	0.275251i	0.463866	+	0.885905i	$0.346462\pi$
$402$	1.34180	−	3.72992i	0.0669231	−	0.186031i
$403$	12.7238	−	4.63108i	0.633817	−	0.230690i
$404$	4.10310	−	7.10678i	0.204137	−	0.353576i
$405$	−23.4286	+	8.92638i	−1.16418	+	0.443555i
$406$	−0.682200	−	0.653979i	−0.0338570	−	0.0324565i
$407$	1.09193	−	6.19262i	0.0541248	−	0.306957i
$408$	10.8232	−	1.95018i	0.535828	−	0.0965482i
$409$	5.60050	+	31.7620i	0.276927	+	1.57053i	0.732774	+	0.680472i	$0.238225\pi$
$409$	5.60050	+	31.7620i	0.276927	+	1.57053i	−0.455847	+	0.890058i	$0.650664\pi$
$410$	1.30615	+	0.475400i	0.0645062	+	0.0234783i
$411$	0.0373802	+	9.99670i	0.00184383	+	0.493101i
$412$	−7.61284	+	2.77085i	−0.375058	+	0.136510i
$413$	6.01494	−	24.5068i	0.295976	−	1.20590i
$414$	−18.4675	−	15.2622i	−0.907627	−	0.750095i
$415$	49.3665			2.42330
$416$	0.943280	−	5.34960i	0.0462481	−	0.262286i
$417$	21.1762	−	25.4294i	1.03700	−	1.24528i
$418$	9.88953	+	3.59950i	0.483713	+	0.176057i
$419$	2.99828	+	17.0041i	0.146475	+	0.830703i	0.966171	+	0.257903i	$0.0830316\pi$
$419$	2.99828	+	17.0041i	0.146475	+	0.830703i	−0.819695	+	0.572800i	$0.805857\pi$
$420$	−12.6856	+	1.42834i	−0.618996	+	0.0696960i
$421$	25.5691	+	21.4550i	1.24616	+	1.04565i	0.997016	+	0.0771891i	$0.0245945\pi$
$421$	25.5691	+	21.4550i	1.24616	+	1.04565i	0.249147	+	0.968466i	$0.419850\pi$
$422$	0.553399			0.0269391
$423$	−25.3469	+	21.5936i	−1.23241	+	1.04992i
$424$	−6.05954			−0.294277
$425$	−3.04337	+	17.2598i	−0.147625	+	0.837224i
$426$	0.295380	+	0.169068i	0.0143112	+	0.00819138i
$427$	−14.8247	−	0.982076i	−0.717420	−	0.0475260i
$428$	1.52567	+	0.555297i	0.0737459	+	0.0268413i
$429$	−5.05203	+	14.0435i	−0.243914	+	0.678027i
$430$	−31.2159	+	11.3617i	−1.50537	+	0.547908i
$431$	−11.4752	−	19.8756i	−0.552741	−	0.957375i	−0.998075	−	0.0620112i	$-0.980249\pi$
$431$	−11.4752	−	19.8756i	−0.552741	−	0.957375i	0.445334	−	0.895364i	$-0.353085\pi$
$432$	3.29516	−	4.01770i	0.158539	−	0.193302i
$433$	−15.4656			−0.743231			−0.371615	−	0.928387i	$-0.621196\pi$
$433$	−15.4656			−0.743231			−0.371615	+	0.928387i	$0.621196\pi$
$434$	6.03454	+	2.66030i	0.289667	+	0.127698i
$435$	−0.583392	+	1.62170i	−0.0279715	+	0.0777545i
$436$	7.09986	−	5.95749i	0.340021	−	0.285312i
$437$	−49.7889	−	18.1217i	−2.38173	−	0.866877i
$438$	−9.96004	+	5.80019i	−0.475909	+	0.277144i
$439$	−2.71277	+	15.3849i	−0.129473	+	0.734280i	0.849077	+	0.528270i	$0.177159\pi$
$439$	−2.71277	+	15.3849i	−0.129473	+	0.734280i	−0.978550	+	0.206010i	$0.933952\pi$
$440$	2.20943	−	3.82684i	0.105330	−	0.182437i
$441$	18.6858	+	9.58329i	0.889802	+	0.456347i
$442$	17.2454	+	29.8699i	0.820280	+	1.42077i
$443$	−10.0422	+	3.65505i	−0.477118	+	0.173657i	−0.569374	−	0.822079i	$-0.692814\pi$
$443$	−10.0422	+	3.65505i	−0.477118	+	0.173657i	0.0922563	+	0.995735i	$0.470592\pi$
$444$	−6.76624	−	1.16700i	−0.321111	−	0.0553834i
$445$	−2.82877	+	2.37362i	−0.134097	+	0.112521i
$446$	−12.9524	−	4.71428i	−0.613313	−	0.223228i
$447$	6.81198	−	8.18012i	0.322195	−	0.386906i
$448$	2.13475	−	1.56297i	0.100857	−	0.0738432i
$449$	6.55973	+	11.3618i	0.309573	+	0.536196i	0.978269	−	0.207340i	$-0.0664807\pi$
$449$	6.55973	+	11.3618i	0.309573	+	0.536196i	−0.668696	+	0.743536i	$0.733147\pi$
$450$	4.19392	+	7.14022i	0.197703	+	0.336593i
$451$	0.791481			0.0372694
$452$	1.67323	+	1.40401i	0.0787021	+	0.0660389i
$453$	−5.03820	−	2.88374i	−0.236715	−	0.135490i
$454$	−10.9867	+	9.21892i	−0.515631	+	0.432665i
$455$	−17.6826	−	35.9201i	−0.828975	−	1.68396i
$456$	3.88994	−	10.8132i	0.182163	−	0.506373i
$457$	−1.58081	−	1.32645i	−0.0739470	−	0.0620489i	0.605065	−	0.796176i	$-0.293147\pi$
$457$	−1.58081	−	1.32645i	−0.0739470	−	0.0620489i	−0.679012	+	0.734127i	$0.737592\pi$
$458$	−8.30230	−	14.3800i	−0.387941	−	0.671933i
$459$	0.370093	+	32.9904i	0.0172744	+	1.53986i
$460$	−11.1234	+	19.2662i	−0.518630	+	0.898293i
$461$	−0.665461	+	3.77402i	−0.0309936	+	0.175774i	−0.996375	−	0.0850685i	$-0.972889\pi$
$461$	−0.665461	+	3.77402i	−0.0309936	+	0.175774i	0.965381	+	0.260842i	$0.0840002\pi$
$462$	−6.50966	+	3.23485i	−0.302857	+	0.150499i
$463$	13.3257	+	4.85018i	0.619300	+	0.225407i	0.632568	−	0.774505i	$-0.282001\pi$
$463$	13.3257	+	4.85018i	0.619300	+	0.225407i	−0.0132675	+	0.999912i	$0.504223\pi$
$464$	−0.0620252	−	0.351762i	−0.00287945	−	0.0163301i
$465$	−0.0449719	−	12.0270i	−0.00208552	−	0.557737i
$466$	−8.42076	−	7.06586i	−0.390084	−	0.327320i
$467$	−2.09984	−	3.63703i	−0.0971690	−	0.168302i	0.813343	−	0.581785i	$-0.197645\pi$
$467$	−2.09984	−	3.63703i	−0.0971690	−	0.168302i	−0.910512	+	0.413483i	$0.864312\pi$
$468$	15.3549	+	5.45902i	0.709778	+	0.252343i
$469$	4.37098	+	4.19017i	0.201833	+	0.193484i
$470$	23.6858	+	19.8747i	1.09254	+	0.916753i
$471$	−8.27896	+	9.94174i	−0.381474	+	0.458091i
$472$	7.30624	−	6.13066i	0.336297	−	0.282187i
$473$	−14.4903	+	12.1588i	−0.666264	+	0.559062i
$474$	4.41455	+	0.761395i	0.202767	+	0.0349720i
$475$	14.0289	+	11.7717i	0.643691	+	0.540121i
$476$	−4.00428	+	16.3147i	−0.183536	+	0.747784i
$477$	3.02271	−	17.9255i	0.138401	−	0.820755i
$478$	3.92630	+	6.80055i	0.179585	+	0.311050i
$479$	−33.3768	−	28.0065i	−1.52503	−	1.27965i	−0.824159	−	0.566358i	$-0.808352\pi$
$479$	−33.3768	−	28.0065i	−1.52503	−	1.27965i	−0.700868	−	0.713291i	$-0.747204\pi$
$480$	−4.18758	−	2.39687i	−0.191136	−	0.109402i
$481$	−3.73932	−	21.2067i	−0.170498	−	0.966944i
$482$	6.78791	+	2.47060i	0.309181	+	0.112533i
$483$	32.7729	−	16.2858i	1.49122	−	0.741032i
$484$	−1.47320	+	8.35493i	−0.0669636	+	0.379769i
$485$	12.2831	−	21.2750i	0.557747	−	0.966046i
$486$	10.2416	+	11.7520i	0.464567	+	0.533083i
$487$	7.51091	+	13.0093i	0.340352	+	0.589507i	0.984498	−	0.175396i	$-0.0561205\pi$
$487$	7.51091	+	13.0093i	0.340352	+	0.589507i	−0.644146	+	0.764902i	$0.722787\pi$
$488$	−4.30173	−	3.60958i	−0.194730	−	0.163398i
$489$	−0.634690	−	0.750676i	−0.0287017	−	0.0339467i
$490$	5.88979	−	18.5893i	0.266074	−	0.839781i
$491$	−21.7701	+	18.2672i	−0.982469	+	0.824389i	−0.984460	−	0.175609i	$-0.943811\pi$
$491$	−21.7701	+	18.2672i	−0.982469	+	0.824389i	0.00199135	+	0.999998i	$0.499366\pi$
$492$	−0.00323156	−	0.864225i	−0.000145690	−	0.0389623i
$493$	1.73734	+	1.45780i	0.0782458	+	0.0656561i
$494$	36.0403			1.62153
$495$	10.2186	+	8.44497i	0.459290	+	0.379573i
$496$	1.24632	+	2.15869i	0.0559615	+	0.0969282i
$497$	−0.419471	+	0.307118i	−0.0188159	+	0.0137761i
$498$	−10.6058	−	28.8035i	−0.475256	−	1.29072i
$499$	16.5113	+	6.00961i	0.739145	+	0.269027i	0.684031	−	0.729453i	$-0.260225\pi$
$499$	16.5113	+	6.00961i	0.739145	+	0.269027i	0.0551145	+	0.998480i	$0.482448\pi$
$500$	−4.77956	+	4.01053i	−0.213749	+	0.179356i
$501$	6.27518	+	17.0424i	0.280354	+	0.761397i
$502$	25.9411	−	9.44180i	1.15781	−	0.421408i
$503$	−12.3330	−	21.3614i	−0.549902	−	0.952457i	−0.998281	−	0.0586140i	$-0.981332\pi$
$503$	−12.3330	−	21.3614i	−0.549902	−	0.952457i	0.448379	−	0.893843i	$-0.352001\pi$
$504$	3.55874	+	7.09474i	0.158519	+	0.316025i
$505$	11.4301	−	19.7975i	0.508634	−	0.880979i
$506$	−2.19973	+	12.4753i	−0.0977899	+	0.554594i
$507$	0.106915	+	28.5926i	0.00474826	+	1.26984i
$508$	−12.4417	−	4.52840i	−0.552010	−	0.200915i
$509$	−18.4789	+	15.5057i	−0.819065	+	0.687277i	−0.952753	−	0.303747i	$-0.901762\pi$
$509$	−18.4789	+	15.5057i	−0.819065	+	0.687277i	0.133688	+	0.991023i	$0.457318\pi$
$510$	30.1505	−	5.43266i	1.33509	−	0.240562i
$511$	−1.90447	−	17.5027i	−0.0842488	−	0.774273i
$512$	1.00000			0.0441942
$513$	30.0475	+	16.9014i	1.32663	+	0.746213i
$514$	4.50323	+	7.79982i	0.198629	+	0.344035i
$515$	−21.2073	+	7.71882i	−0.934505	+	0.340132i
$516$	13.3355	+	15.7724i	0.587061	+	0.694343i
$517$	16.5445	+	6.02169i	0.727624	+	0.264834i
$518$	5.83303	−	8.71654i	0.256289	−	0.382983i
$519$	0.00899540	+	2.40566i	0.000394854	+	0.105597i
$520$	2.62772	−	14.9025i	0.115233	−	0.653519i
$521$	7.52398			0.329632			0.164816	−	0.986324i	$-0.447297\pi$
$521$	7.52398			0.329632			0.164816	+	0.986324i	$0.447297\pi$
$522$	1.07154	−	0.00801361i	0.0468999	−	0.000350746i
$523$	24.6061			1.07595			0.537975	−	0.842961i	$-0.319189\pi$
$523$	24.6061			1.07595			0.537975	+	0.842961i	$0.319189\pi$
$524$	1.41329	+	1.18589i	0.0617399	+	0.0518059i
$525$	−12.5697	+	1.41529i	−0.548587	+	0.0617683i
$526$	−0.185051	−	1.04948i	−0.00806861	−	0.0457594i
$527$	−14.8723	−	5.41309i	−0.647849	−	0.235798i
$528$	−2.70749	−	0.466971i	−0.117828	−	0.0203223i
$529$	7.08064	−	40.1563i	0.307854	−	1.74593i
$530$	−16.8802			−0.733230
$531$	14.4913	+	24.6718i	0.628870	+	1.07066i
$532$	12.6716	+	12.1475i	0.549385	+	0.526659i
$533$	2.54698	−	0.927024i	0.110322	−	0.0401539i
$534$	1.99265	+	1.14054i	0.0862303	+	0.0493561i
$535$	4.25009	+	1.54691i	0.183747	+	0.0668786i
$536$	0.397407	+	2.25381i	0.0171654	+	0.0973496i
$537$	8.27902	+	9.79195i	0.357266	+	0.422554i
$538$	1.98676	−	11.2675i	0.0856552	−	0.485775i
$539$	−0.468824	−	11.0938i	−0.0201937	−	0.477845i
$540$	9.17942	−	11.1922i	0.395019	−	0.481636i
$541$	19.9879	−	34.6201i	0.859347	−	1.48843i	−0.0132052	−	0.999913i	$-0.504203\pi$
$541$	19.9879	−	34.6201i	0.859347	−	1.48843i	0.872552	−	0.488520i	$-0.162463\pi$
$542$	1.18917	−	0.432822i	0.0510792	−	0.0185913i
$543$	15.0047	+	17.7468i	0.643915	+	0.761587i
$544$	−4.86393	+	4.08132i	−0.208539	+	0.174985i
$545$	19.7783	−	16.5959i	0.847207	−	0.710891i
$546$	−17.1592	+	18.0342i	−0.734346	+	0.771791i
$547$	−6.60822	+	2.40520i	−0.282547	+	0.102839i	−0.479406	−	0.877593i	$-0.659148\pi$
$547$	−6.60822	+	2.40520i	−0.282547	+	0.102839i	0.196859	+	0.980432i	$0.436926\pi$
$548$	−2.88582	−	4.99838i	−0.123276	−	0.213520i
$549$	12.8238	−	10.9249i	0.547308	−	0.466265i
$550$	2.18924	−	3.79187i	0.0933493	−	0.161686i
$551$	2.22691	−	0.810528i	0.0948695	−	0.0345297i
$552$	13.6309	+	2.35097i	0.580168	+	0.100064i
$553$	−3.80569	+	5.68700i	−0.161834	+	0.241836i
$554$	−0.461722	−	2.61856i	−0.0196167	−	0.111252i
$555$	−18.8489	−	3.25094i	−0.800091	−	0.137995i
$556$	−3.31767	+	18.8155i	−0.140701	+	0.797953i
$557$	5.05497	−	8.75547i	0.214186	−	0.370981i	−0.738834	−	0.673887i	$-0.764623\pi$
$557$	5.05497	−	8.75547i	0.214186	−	0.370981i	0.953020	+	0.302906i	$0.0979568\pi$
$558$	−7.00763	+	2.61008i	−0.296657	+	0.110494i
$559$	−32.3886	+	56.0987i	−1.36989	+	2.37272i
$560$	5.94682	−	4.35399i	0.251299	−	0.183990i
$561$	15.0749	−	8.77881i	0.636462	−	0.370642i
$562$	3.43241	+	19.4662i	0.144788	+	0.821132i
$563$	1.84251	+	10.4494i	0.0776527	+	0.440390i	0.998702	+	0.0509433i	$0.0162228\pi$
$563$	1.84251	+	10.4494i	0.0776527	+	0.440390i	−0.921049	+	0.389447i	$0.872666\pi$
$564$	6.50759	−	18.0896i	0.274019	−	0.761710i
$565$	4.66116	+	3.91118i	0.196097	+	0.164545i
$566$	−12.7639			−0.536505
$567$	−22.7632	+	6.98847i	−0.955963	+	0.293488i
$568$	−0.196497			−0.00824484
$569$	13.9329	+	11.6911i	0.584096	+	0.490115i	0.886289	−	0.463132i	$-0.153274\pi$
$569$	13.9329	+	11.6911i	0.584096	+	0.490115i	−0.302193	+	0.953247i	$0.597719\pi$
$570$	10.8363	−	30.1225i	0.453883	−	1.26169i
$571$	7.93900	+	45.0243i	0.332237	+	1.88421i	0.452972	+	0.891525i	$0.350364\pi$
$571$	7.93900	+	45.0243i	0.332237	+	1.88421i	−0.120735	+	0.992685i	$0.538525\pi$
$572$	−1.49628	−	8.48580i	−0.0625624	−	0.354809i
$573$	−6.43924	+	3.74987i	−0.269003	+	0.156653i
$574$	1.20796	+	0.532524i	0.0504194	+	0.0222271i
$575$	−11.0217	+	19.0902i	−0.459637	+	0.796115i
$576$	−0.498836	+	2.95824i	−0.0207848	+	0.123260i
$577$	−9.55290	+	16.5461i	−0.397693	+	0.688824i	−0.993441	−	0.114348i	$-0.963522\pi$
$577$	−9.55290	+	16.5461i	−0.397693	+	0.688824i	0.595748	+	0.803171i	$0.296856\pi$
$578$	4.04860	−	22.9607i	0.168400	−	0.955041i
$579$	−32.9163	−	5.67721i	−1.36796	−	0.235937i
$580$	−0.172785	−	0.979913i	−0.00717451	−	0.0406887i
$581$	46.7834	+	3.09920i	1.94090	+	0.128577i
$582$	−15.0520	−	2.59608i	−0.623926	−	0.107611i
$583$	−9.03226	+	3.28747i	−0.374078	+	0.136153i
$584$	3.32722	−	5.76291i	0.137681	−	0.238471i
$585$	42.7744	+	15.2073i	1.76850	+	0.628745i
$586$	10.7386	+	18.5997i	0.443606	+	0.768348i
$587$	29.0244	−	10.5640i	1.19797	−	0.436024i	0.335453	−	0.942057i	$-0.391111\pi$
$587$	29.0244	−	10.5640i	1.19797	−	0.436024i	0.862514	+	0.506033i	$0.168889\pi$
$588$	−12.1115	+	0.557208i	−0.499472	+	0.0229789i
$589$	−12.6687	+	10.6303i	−0.522006	+	0.438015i
$590$	20.3532	−	17.0783i	0.837927	−	0.703104i
$591$	15.1984	+	17.9758i	0.625179	+	0.739426i
$592$	3.72510	−	1.35583i	0.153101	−	0.0557241i
$593$	9.09010	−	15.7445i	0.373286	−	0.646550i	−0.616783	−	0.787133i	$-0.711564\pi$
$593$	9.09010	−	15.7445i	0.373286	−	0.646550i	0.990069	+	0.140583i	$0.0448978\pi$
$594$	2.73200	−	7.77645i	0.112095	−	0.319071i
$595$	−11.1548	+	45.4484i	−0.457304	+	1.86320i
$596$	−1.06723	+	6.05256i	−0.0437154	+	0.247923i
$597$	−9.58465	−	11.3362i	−0.392274	−	0.463959i
$598$	7.53301	+	42.7218i	0.308047	+	1.74702i
$599$	−5.32970	−	1.93985i	−0.217765	−	0.0792601i	0.230834	−	0.972993i	$-0.425855\pi$
$599$	−5.32970	−	1.93985i	−0.217765	−	0.0792601i	−0.448599	+	0.893733i	$0.648077\pi$
$600$	−4.14931	−	2.37496i	−0.169395	−	0.0969575i
$601$	35.0446	−	12.7552i	1.42950	−	0.520295i	0.492711	−	0.870193i	$-0.336006\pi$
$601$	35.0446	−	12.7552i	1.42950	−	0.520295i	0.936788	+	0.349898i	$0.113784\pi$
$602$	−30.2958	+	8.80745i	−1.23477	+	0.358965i
$603$	−6.86553	+	0.0513447i	−0.279586	+	0.00209092i
$604$	3.35159			0.136374
$605$	−4.10393	+	23.2745i	−0.166848	+	0.946245i
$606$	−14.0068	−	2.41580i	−0.568986	−	0.0981353i
$607$	−24.3953	−	8.87916i	−0.990174	−	0.360394i	−0.204386	−	0.978890i	$-0.565520\pi$
$607$	−24.3953	−	8.87916i	−0.990174	−	0.360394i	−0.785788	+	0.618496i	$0.787742\pi$
$608$	1.15210	+	6.53387i	0.0467237	+	0.264983i
$609$	−0.654676	+	1.50022i	−0.0265288	+	0.0607920i
$610$	−11.9834	−	10.0553i	−0.485195	−	0.407127i
$611$	60.2928			2.43919
$612$	−9.64721	−	16.4246i	−0.389965	−	0.663923i
$613$	3.91973			0.158317			0.0791583	−	0.996862i	$-0.474777\pi$
$613$	3.91973			0.158317			0.0791583	+	0.996862i	$0.474777\pi$
$614$	5.93639	−	33.6669i	0.239573	−	1.35869i
$615$	−0.00900224	−	2.40749i	−0.000363005	−	0.0970795i
$616$	2.33407	−	3.48790i	0.0940422	−	0.140531i
$617$	−34.4264	−	12.5302i	−1.38595	−	0.504446i	−0.461976	−	0.886892i	$-0.652859\pi$
$617$	−34.4264	−	12.5302i	−1.38595	−	0.504446i	−0.923978	+	0.382446i	$0.875082\pi$
$618$	9.05977	+	10.7154i	0.364437	+	0.431036i
$619$	−46.4200	+	16.8955i	−1.86578	+	0.679087i	−0.891803	+	0.452425i	$0.850559\pi$
$619$	−46.4200	+	16.8955i	−1.86578	+	0.679087i	−0.973973	+	0.226662i	$0.927219\pi$
$620$	3.47191	+	6.01353i	0.139435	+	0.241509i
$621$	−13.7543	+	39.1506i	−0.551940	+	1.57106i
$622$	8.70071			0.348867
$623$	−2.82978	+	2.07184i	−0.113373	+	0.0830064i
$624$	−9.25961	+	1.66844i	−0.370681	+	0.0667912i
$625$	−23.8870	+	20.0436i	−0.955480	+	0.801743i
$626$	−11.8442	−	4.31095i	−0.473391	−	0.172300i
$627$	−0.0681605	−	18.2284i	−0.00272207	−	0.727970i
$628$	1.29706	−	7.35600i	0.0517584	−	0.293536i
$629$	−12.5851	+	21.7980i	−0.501799	+	0.869141i
$630$	9.91366	+	19.7640i	0.394970	+	0.787417i
$631$	−10.3646	−	17.9519i	−0.412606	−	0.714655i	0.582568	−	0.812782i	$-0.302048\pi$
$631$	−10.3646	−	17.9519i	−0.412606	−	0.714655i	−0.995174	+	0.0981271i	$0.968715\pi$
$632$	−2.43040	+	0.884592i	−0.0966760	+	0.0351872i
$633$	−0.331197	−	0.899478i	−0.0131639	−	0.0357511i
$634$	−13.9130	+	11.6744i	−0.552557	+	0.463651i
$635$	−34.6591	−	12.6149i	−1.37540	−	0.500606i
$636$	3.62650	+	9.84899i	0.143800	+	0.390538i
$637$	−14.5024	−	35.1508i	−0.574604	−	1.39272i
$638$	−0.283295	−	0.490681i	−0.0112158	−	0.0194263i
$639$	0.0980198	−	0.581285i	0.00387760	−	0.0229953i
$640$	2.78573			0.110115
$641$	17.6880	+	14.8420i	0.698634	+	0.586223i	0.921385	−	0.388652i	$-0.127059\pi$
$641$	17.6880	+	14.8420i	0.698634	+	0.586223i	−0.222751	+	0.974875i	$0.571504\pi$
$642$	−0.0105152	−	2.81210i	−0.000415001	−	0.110985i
$643$	8.83350	−	7.41219i	0.348359	−	0.292308i	−0.451772	−	0.892134i	$-0.649208\pi$
$643$	8.83350	−	7.41219i	0.348359	−	0.292308i	0.800131	+	0.599826i	$0.204763\pi$
$644$	−11.7509	+	17.5598i	−0.463049	+	0.691954i
$645$	37.1489	+	43.9377i	1.46274	+	1.73004i
$646$	−32.2705	−	27.0782i	−1.26967	−	1.06538i
$647$	9.88562	+	17.1224i	0.388644	+	0.673151i	0.992267	−	0.124119i	$-0.0396103\pi$
$647$	9.88562	+	17.1224i	0.388644	+	0.673151i	−0.603624	+	0.797269i	$0.706277\pi$
$648$	−8.50233	−	2.95135i	−0.334003	−	0.115940i
$649$	7.56451	−	13.1021i	0.296933	−	0.514303i
$650$	2.60370	−	14.7663i	0.102126	−	0.579184i
$651$	0.712428	−	11.4005i	0.0279223	−	0.446820i
$652$	0.533324	+	0.194114i	0.0208866	+	0.00760210i
$653$	−1.10737	−	6.28022i	−0.0433348	−	0.245764i	0.955444	−	0.295173i	$-0.0953773\pi$
$653$	−1.10737	−	6.28022i	−0.0433348	−	0.245764i	−0.998779	+	0.0494091i	$0.984266\pi$
$654$	−13.9322	−	7.97446i	−0.544793	−	0.311826i
$655$	3.93704	+	3.30357i	0.153833	+	0.129081i
$656$	0.249482	+	0.432115i	0.00974063	+	0.0168713i
$657$	15.3883	+	12.7174i	0.600355	+	0.496155i
$658$	21.1987	+	20.3218i	0.826412	+	0.792226i
$659$	−16.9418	−	14.2158i	−0.659958	−	0.553770i	0.250116	−	0.968216i	$-0.419531\pi$
$659$	−16.9418	−	14.2158i	−0.659958	−	0.553770i	−0.910074	+	0.414445i	$0.863976\pi$
$660$	−7.54232	−	1.30085i	−0.293584	−	0.0506357i
$661$	−18.1265	+	15.2099i	−0.705038	+	0.591597i	−0.923202	−	0.384315i	$-0.874438\pi$
$661$	−18.1265	+	15.2099i	−0.705038	+	0.591597i	0.218164	+	0.975912i	$0.429993\pi$
$662$	17.5556	−	14.7309i	0.682317	−	0.572532i
$663$	38.2286	−	45.9066i	1.48468	−	1.78287i
$664$	13.5752	+	11.3910i	0.526822	+	0.442056i
$665$	35.2997	+	33.8395i	1.36886	+	1.31224i
$666$	2.15264	+	11.6961i	0.0834131	+	0.453213i
$667$	1.42625	+	2.47034i	0.0552246	+	0.0956518i
$668$	−8.03215	−	6.73978i	−0.310773	−	0.260770i
$669$	0.0892702	+	23.8738i	0.00345139	+	0.923013i
$670$	1.10707	+	6.27848i	0.0427697	+	0.242559i
$671$	−8.37039	−	3.04657i	−0.323136	−	0.117612i
$672$	−3.81799	−	2.53435i	−0.147282	−	0.0977646i
$673$	−1.50081	+	8.51150i	−0.0578518	+	0.328094i	−0.999974	−	0.00717497i	$-0.997716\pi$
$673$	−1.50081	+	8.51150i	−0.0578518	+	0.328094i	0.942122	+	0.335269i	$0.108827\pi$
$674$	14.7275	−	25.5087i	0.567281	−	0.982560i
$675$	9.09553	−	11.0899i	0.350087	−	0.426852i
$676$	−8.25402	−	14.2964i	−0.317462	−	0.549861i
$677$	−0.903327	−	0.757982i	−0.0347177	−	0.0291316i	0.625264	−	0.780414i	$-0.284991\pi$
$677$	−0.903327	−	0.757982i	−0.0347177	−	0.0291316i	−0.659981	+	0.751282i	$0.729436\pi$
$678$	1.28064	−	3.55988i	0.0491826	−	0.136717i
$679$	12.9760	−	19.3906i	0.497974	−	0.744144i
$680$	−13.5496	+	11.3694i	−0.519602	+	0.435998i
$681$	21.5594	+	12.3401i	0.826160	+	0.472873i
$682$	3.02890	+	2.54155i	0.115983	+	0.0973210i
$683$	−36.7444			−1.40598			−0.702992	−	0.711197i	$-0.748153\pi$
$683$	−36.7444			−1.40598			−0.702992	+	0.711197i	$0.748153\pi$
$684$	−19.9034	+	0.148850i	−0.761027	+	0.00569143i
$685$	−8.03910	−	13.9241i	−0.307158	−	0.532014i
$686$	6.74864	−	17.2469i	0.257664	−	0.658490i
$687$	−18.4041	+	22.1004i	−0.702159	+	0.843183i
$688$	−11.2057	−	4.07853i	−0.427212	−	0.155492i
$689$	−25.2153	+	21.1581i	−0.960625	+	0.806060i
$690$	37.9718	+	6.54915i	1.44556	+	0.249322i
$691$	−32.5887	+	11.8613i	−1.23973	+	0.451226i	−0.876920	−	0.480636i	$-0.840406\pi$
$691$	−32.5887	+	11.8613i	−1.23973	+	0.451226i	−0.362813	+	0.931862i	$0.618184\pi$
$692$	−0.694460	−	1.20284i	−0.0263994	−	0.0457251i
$693$	9.15370	+	8.64461i	0.347720	+	0.328382i
$694$	−0.297809	+	0.515819i	−0.0113047	+	0.0195802i
$695$	−9.24213	+	52.4147i	−0.350574	+	1.98820i
$696$	−0.534623	+	0.311336i	−0.0202648	+	0.0118011i
$697$	−2.97706	−	1.08356i	−0.112764	−	0.0410428i
$698$	−12.3500	+	10.3629i	−0.467455	+	0.392241i
$699$	−6.44499	+	17.9156i	−0.243772	+	0.677631i
$700$	5.89247	−	4.31421i	0.222714	−	0.163062i
$701$	−14.0402			−0.530292			−0.265146	−	0.964208i	$-0.585420\pi$
$701$	−14.0402			−0.530292			−0.265146	+	0.964208i	$0.585420\pi$
$702$	−0.316627	−	28.2244i	−0.0119503	−	1.06526i
$703$	13.1505	+	22.7773i	0.495979	+	0.859061i
$704$	1.49059	−	0.542529i	0.0561786	−	0.0204473i
$705$	18.1283	−	50.3927i	0.682753	−	1.89790i
$706$	−8.94675	−	3.25635i	−0.336715	−	0.122554i
$707$	12.0749	−	18.0441i	0.454124	−	0.678617i
$708$	−14.3372	−	8.20626i	−0.538825	−	0.308410i
$709$	−5.41002	+	30.6818i	−0.203178	+	1.15228i	0.697104	+	0.716970i	$0.254472\pi$
$709$	−5.41002	+	30.6818i	−0.203178	+	1.15228i	−0.900282	+	0.435308i	$0.856639\pi$
$710$	−0.547387			−0.0205431
$711$	−1.40446	−	7.63095i	−0.0526715	−	0.286183i
$712$	−1.32558			−0.0496782
$713$	−15.2490	−	12.7954i	−0.571080	−	0.479193i
$714$	28.9139	−	3.25557i	1.08208	−	0.121837i
$715$	−4.16821	−	23.6391i	−0.155882	−	0.884053i
$716$	−6.95678	−	2.53206i	−0.259987	−	0.0946276i
$717$	8.70360	−	10.4517i	0.325042	−	0.390325i
$718$	1.03898	−	5.89235i	0.0387744	−	0.219901i
$719$	−14.3269			−0.534303			−0.267152	−	0.963655i	$-0.586082\pi$
$719$	−14.3269			−0.534303			−0.267152	+	0.963655i	$0.586082\pi$
$720$	−1.38962	+	8.24084i	−0.0517880	+	0.307118i
$721$	−20.5822	+	5.98356i	−0.766522	+	0.222839i
$722$	−23.5099	+	8.55691i	−0.874949	+	0.318455i
$723$	−0.0467836	−	12.5115i	−0.00173990	−	0.465306i
$724$	−12.6084	−	4.58907i	−0.468586	−	0.170551i
$725$	−0.171206	−	0.970958i	−0.00635844	−	0.0360605i
$726$	14.4615	−	2.60575i	0.536717	−	0.0967084i
$727$	−0.936272	+	5.30986i	−0.0347244	+	0.196932i	−0.997235	−	0.0743121i	$-0.976324\pi$
$727$	−0.936272	+	5.30986i	−0.0347244	+	0.196932i	0.962511	+	0.271244i	$0.0874350\pi$
$728$	3.42580	−	13.9578i	0.126969	−	0.517310i
$729$	12.9720	−	23.6797i	0.480446	−	0.877024i
$730$	9.26872	−	16.0539i	0.343051	−	0.594181i
$731$	71.1493	−	25.8962i	2.63155	−	0.957807i
$732$	−3.29241	+	9.15215i	−0.121691	+	0.338273i
$733$	13.6687	−	11.4694i	0.504864	−	0.423631i	−0.354453	−	0.935074i	$-0.615333\pi$
$733$	13.6687	−	11.4694i	0.504864	−	0.423631i	0.859318	+	0.511442i	$0.170889\pi$
$734$	−9.29648	+	7.80067i	−0.343139	+	0.287928i
$735$	−33.7394	+	1.55223i	−1.24450	+	0.0572549i
$736$	−7.50436	+	2.73136i	−0.276614	+	0.100679i
$737$	1.81512	+	3.14389i	0.0668609	+	0.115807i
$738$	−1.40275	+	0.522472i	−0.0516359	+	0.0192325i
$739$	20.3205	−	35.1961i	0.747501	−	1.29471i	−0.201516	−	0.979485i	$-0.564587\pi$
$739$	20.3205	−	35.1961i	0.747501	−	1.29471i	0.949017	−	0.315225i	$-0.102080\pi$
$740$	10.3771	−	3.77696i	0.381470	−	0.138844i
$741$	−21.5694	−	58.5789i	−0.792370	−	2.15195i
$742$	−15.9970	−	1.05973i	−0.587267	−	0.0389040i
$743$	−5.13821	−	29.1402i	−0.188502	−	1.06905i	−0.921372	−	0.388682i	$-0.872931\pi$
$743$	−5.13821	−	29.1402i	−0.188502	−	1.06905i	0.732870	−	0.680369i	$-0.238180\pi$
$744$	2.76278	−	3.31766i	0.101288	−	0.121631i
$745$	−2.97301	+	16.8608i	−0.108923	+	0.617731i
$746$	−15.9640	+	27.6505i	−0.584484	+	1.01236i
$747$	−40.4690	+	34.4766i	−1.48068	+	1.26143i
$748$	−5.03587	+	8.72238i	−0.184130	+	0.318922i
$749$	3.93059	+	1.73278i	0.143621	+	0.0633145i
$750$	9.37906	+	5.36834i	0.342475	+	0.196024i
$751$	3.20254	+	18.1625i	0.116862	+	0.662759i	0.985811	+	0.167857i	$0.0536848\pi$
$751$	3.20254	+	18.1625i	0.116862	+	0.662759i	−0.868949	+	0.494902i	$0.835204\pi$
$752$	1.92737	+	10.9307i	0.0702840	+	0.398601i
$753$	−30.8716	−	36.5132i	−1.12502	−	1.33061i
$754$	−1.48635	−	1.24720i	−0.0541298	−	0.0454203i
$755$	9.33661			0.339794
$756$	9.40175	−	10.0303i	0.341938	−	0.364799i
$757$	−27.3164			−0.992830			−0.496415	−	0.868085i	$-0.665351\pi$
$757$	−27.3164			−0.992830			−0.496415	+	0.868085i	$0.665351\pi$
$758$	−6.98173	−	5.85836i	−0.253588	−	0.212785i
$759$	21.5934	−	3.89081i	0.783792	−	0.141228i
$760$	3.20943	+	18.2016i	0.116418	+	0.660240i
$761$	7.29600	+	41.3777i	0.264480	+	1.49994i	0.770512	+	0.637425i	$0.220000\pi$
$761$	7.29600	+	41.3777i	0.264480	+	1.49994i	−0.506033	+	0.862514i	$0.668888\pi$
$762$	0.0857503	+	22.9324i	0.00310641	+	0.830755i
$763$	19.7853	−	14.4859i	0.716274	−	0.524424i
$764$	2.15107	−	3.72577i	0.0778231	−	0.134794i
$765$	−26.8745	−	45.7543i	−0.971649	−	1.65425i
$766$	2.76400	−	4.78739i	0.0998674	−	0.172975i
$767$	8.99664	−	51.0225i	0.324850	−	1.84231i
$768$	−0.598478	−	1.62537i	−0.0215957	−	0.0586504i
$769$	3.36957	+	19.1098i	0.121510	+	0.689116i	0.983320	+	0.181885i	$0.0582198\pi$
$769$	3.36957	+	19.1098i	0.121510	+	0.689116i	−0.861810	+	0.507231i	$0.830669\pi$
$770$	6.50207	−	9.71632i	0.234318	−	0.350152i
$771$	9.98250	−	11.9874i	0.359511	−	0.431717i
$772$	18.1218	−	6.59580i	0.652218	−	0.237388i
$773$	16.4618	−	28.5126i	0.592088	−	1.02553i	−0.401863	−	0.915700i	$-0.631637\pi$
$773$	16.4618	−	28.5126i	0.592088	−	1.02553i	0.993951	−	0.109827i	$-0.0350296\pi$
$774$	17.6550	−	31.1145i	0.634597	−	1.11839i
$775$	3.44018	+	5.95857i	0.123575	+	0.214038i
$776$	8.28677	−	3.01614i	0.297478	−	0.108273i
$777$	−17.6585	−	4.26416i	−0.633497	−	0.152976i
$778$	8.45054	−	7.09084i	0.302966	−	0.254219i
$779$	−2.53596	+	2.12792i	−0.0908601	+	0.0762407i
$780$	−25.7947	+	4.64783i	−0.923600	+	0.166419i
$781$	−0.292896	+	0.106605i	−0.0104806	+	0.00381464i
$782$	25.3531	−	43.9128i	0.906625	−	1.57032i
$783$	−0.654316	−	1.73685i	−0.0233833	−	0.0620698i
$784$	5.90899	−	3.75284i	0.211036	−	0.134030i
$785$	3.61326	−	20.4918i	0.128963	−	0.731384i
$786$	1.08169	−	3.00685i	0.0385825	−	0.107251i
$787$	−5.52931	−	31.3583i	−0.197099	−	1.11780i	−0.909398	−	0.415926i	$-0.863458\pi$
$787$	−5.52931	−	31.3583i	−0.197099	−	1.11780i	0.712300	−	0.701875i	$-0.247654\pi$
$788$	−12.7711	−	4.64829i	−0.454951	−	0.165589i
$789$	−1.59504	+	0.928866i	−0.0567849	+	0.0330685i
$790$	−6.77042	+	2.46423i	−0.240881	+	0.0876734i
$791$	4.17173	+	3.99915i	0.148330	+	0.142194i
$792$	0.861371	+	4.68014i	0.0306075	+	0.166301i
$793$	−30.5042			−1.08323
$794$	2.01997	−	11.4558i	0.0716860	−	0.406552i
$795$	10.1024	+	27.4366i	0.358297	+	0.973075i
$796$	8.05389	+	2.93138i	0.285463	+	0.103900i
$797$	−0.723329	−	4.10221i	−0.0256216	−	0.145308i	0.969313	−	0.245829i	$-0.0790601\pi$
$797$	−0.723329	−	4.10221i	−0.0256216	−	0.145308i	−0.994935	+	0.100521i	$0.967949\pi$
$798$	12.1604	−	27.8661i	0.430473	−	0.986448i
$799$	−53.9862	−	45.2998i	−1.90989	−	1.60259i
$800$	2.76027			0.0975902
$801$	0.661246	−	3.92138i	0.0233640	−	0.138555i
$802$	−8.57498			−0.302793
$803$	1.83296	−	10.3952i	0.0646837	−	0.366840i
$804$	3.42543	−	1.99479i	0.120805	−	0.0703507i
$805$	−32.7347	+	48.9169i	−1.15375	+	1.72409i
$806$	12.7238	+	4.63108i	0.448176	+	0.163123i
$807$	−19.5028	+	3.51412i	−0.686532	+	0.123703i
$808$	7.71131	−	2.80669i	0.271283	−	0.0987389i
$809$	10.2560	+	17.7639i	0.360582	+	0.624547i	0.988057	−	0.154090i	$-0.0492447\pi$
$809$	10.2560	+	17.7639i	0.360582	+	0.624547i	−0.627475	+	0.778637i	$0.715911\pi$
$810$	−23.6851	−	8.22164i	−0.832211	−	0.288879i
$811$	43.6906			1.53418			0.767092	−	0.641538i	$-0.221703\pi$
$811$	43.6906			1.53418			0.767092	+	0.641538i	$0.221703\pi$
$812$	−0.102226	−	0.939487i	−0.00358742	−	0.0329695i
$813$	−1.41519	−	1.67380i	−0.0496328	−	0.0587028i
$814$	4.81701	−	4.04195i	0.168836	−	0.141670i
$815$	1.48570	+	0.540749i	0.0520417	+	0.0189416i
$816$	9.54460	+	5.46310i	0.334128	+	0.191247i
$817$	13.7386	−	77.9152i	0.480651	−	2.72591i
$818$	−16.1260	+	27.9310i	−0.563832	+	0.976586i
$819$	39.5816	+	17.0970i	1.38309	+	0.597416i
$820$	0.694988	+	1.20375i	0.0242700	+	0.0420369i
$821$	−12.5386	+	4.56367i	−0.437599	+	0.159273i	−0.551419	−	0.834228i	$-0.685913\pi$
$821$	−12.5386	+	4.56367i	−0.437599	+	0.159273i	0.113820	+	0.993501i	$0.463691\pi$
$822$	−6.39712	+	7.68194i	−0.223125	+	0.267938i
$823$	7.66255	−	6.42964i	0.267100	−	0.224123i	−0.499394	−	0.866375i	$-0.666444\pi$
$823$	7.66255	−	6.42964i	0.267100	−	0.224123i	0.766494	+	0.642252i	$0.222000\pi$
$824$	−7.61284	−	2.77085i	−0.265206	−	0.0965271i
$825$	−7.47339	−	1.28897i	−0.260190	−	0.0448760i
$826$	20.3604	−	14.9070i	0.708428	−	0.518680i
$827$	0.709907	+	1.22959i	0.0246859	+	0.0427572i	0.878104	−	0.478469i	$-0.158808\pi$
$827$	0.709907	+	1.22959i	0.0246859	+	0.0427572i	−0.853419	+	0.521226i	$0.825475\pi$
$828$	−4.33658	−	23.5622i	−0.150707	−	0.818842i
$829$	44.8628			1.55815			0.779075	−	0.626931i	$-0.215689\pi$
$829$	44.8628			1.55815			0.779075	+	0.626931i	$0.215689\pi$
$830$	37.8169	+	31.7322i	1.31264	+	1.10144i
$831$	−3.97979	+	2.31762i	−0.138057	+	0.0803973i
$832$	4.16125	−	3.49171i	0.144265	−	0.121053i
$833$	−13.4244	+	42.3700i	−0.465128	+	1.46803i
$834$	32.5676	−	5.86820i	1.12772	−	0.203199i
$835$	−22.3754	−	18.7752i	−0.774332	−	0.649742i
$836$	5.26211	+	9.11424i	0.181994	+	0.315223i
$837$	8.43626	+	9.82791i	0.291600	+	0.339702i
$838$	−8.63319	+	14.9531i	−0.298229	+	0.516547i
$839$	−7.61327	+	43.1770i	−0.262839	+	1.49064i	0.512279	+	0.858819i	$0.328801\pi$
$839$	−7.61327	+	43.1770i	−0.262839	+	1.49064i	−0.775118	+	0.631816i	$0.782310\pi$
$840$	−10.6359	−	7.06000i	−0.366973	−	0.243593i
$841$	27.1312	+	9.87495i	0.935558	+	0.340515i
$842$	5.79605	+	32.8710i	0.199745	+	1.13281i
$843$	29.5855	−	17.2290i	1.01898	−	0.593399i
$844$	0.423929	+	0.355718i	0.0145922	+	0.0122443i
$845$	−22.9934	−	39.8258i	−0.790998	−	1.37005i
$846$	−33.2970	+	0.249015i	−1.14477	+	0.00856132i
$847$	−5.35036	+	21.7991i	−0.183840	+	0.749025i
$848$	−4.64188	−	3.89500i	−0.159403	−	0.133755i
$849$	7.63889	+	20.7460i	0.262166	+	0.712000i
$850$	−13.4257	+	11.2655i	−0.460499	+	0.386405i
$851$	−24.2512	+	20.3492i	−0.831322	+	0.697562i
$852$	0.117599	+	0.319380i	0.00402888	+	0.0109418i
$853$	42.6198	+	35.7623i	1.45927	+	1.22448i	0.925443	+	0.378886i	$0.123693\pi$
$853$	42.6198	+	35.7623i	1.45927	+	1.22448i	0.533832	+	0.845591i	$0.320752\pi$
$854$	−10.7251	−	10.2815i	−0.367007	−	0.351825i
$855$	−55.4455	+	0.414656i	−1.89620	+	0.0141809i
$856$	0.811790	+	1.40606i	0.0277464	+	0.0480582i
$857$	27.3508	+	22.9500i	0.934284	+	0.783957i	0.976582	−	0.215148i	$-0.0690233\pi$
$857$	27.3508	+	22.9500i	0.934284	+	0.783957i	−0.0422974	+	0.999105i	$0.513468\pi$
$858$	−12.8971	+	7.51056i	−0.440299	+	0.256406i
$859$	2.91700	+	16.5431i	0.0995267	+	0.564444i	0.993266	+	0.115857i	$0.0369614\pi$
$859$	2.91700	+	16.5431i	0.0995267	+	0.564444i	−0.893739	+	0.448587i	$0.851927\pi$
$860$	−31.2159	−	11.3617i	−1.06445	−	0.387430i
$861$	0.142610	−	2.28209i	0.00486014	−	0.0777733i
$862$	3.98530	−	22.6017i	0.135740	−	0.769818i
$863$	−4.78225	+	8.28309i	−0.162790	+	0.281960i	−0.935868	−	0.352351i	$-0.885382\pi$
$863$	−4.78225	+	8.28309i	−0.162790	+	0.281960i	0.773079	+	0.634310i	$0.218716\pi$
$864$	5.10677	−	0.959648i	0.173736	−	0.0326479i
$865$	−1.93458	−	3.35078i	−0.0657776	−	0.113930i
$866$	−11.8474	−	9.94112i	−0.402590	−	0.337813i
$867$	−39.7427	+	7.16104i	−1.34973	+	0.243202i
$868$	2.91272	+	5.91684i	0.0988641	+	0.200831i
$869$	−3.14280	+	2.63712i	−0.106612	+	0.0894582i
$870$	−1.48931	+	0.867296i	−0.0504924	+	0.0294041i
$871$	9.52333	+	7.99103i	0.322686	+	0.270766i
$872$	9.26820			0.313861
$873$	4.78871	+	26.0188i	0.162073	+	0.880603i
$874$	−26.4921	−	45.8857i	−0.896109	−	1.55211i
$875$	−13.3193	+	9.75178i	−0.450273	+	0.329670i
$876$	−11.3581	−	1.95898i	−0.383755	−	0.0661878i
$877$	−17.6124	−	6.41040i	−0.594729	−	0.216464i	0.0270789	−	0.999633i	$-0.491379\pi$
$877$	−17.6124	−	6.41040i	−0.594729	−	0.216464i	−0.621808	+	0.783170i	$0.713602\pi$
$878$	−11.9673	+	10.0418i	−0.403877	+	0.338893i
$879$	23.8046	−	28.5857i	0.802911	−	0.964171i
$880$	4.15236	−	1.51134i	0.139976	−	0.0509471i
$881$	−18.6948	−	32.3803i	−0.629843	−	1.09092i	−0.987583	−	0.157099i	$-0.949786\pi$
$881$	−18.6948	−	32.3803i	−0.629843	−	1.09092i	0.357740	−	0.933821i	$-0.383548\pi$
$882$	8.15416	+	19.3523i	0.274565	+	0.651624i
$883$	−11.5451	+	19.9968i	−0.388525	+	0.672945i	−0.992251	−	0.124247i	$-0.960349\pi$
$883$	−11.5451	+	19.9968i	−0.388525	+	0.672945i	0.603726	+	0.797192i	$0.293682\pi$
$884$	−5.98926	+	33.9668i	−0.201441	+	1.14243i
$885$	−39.9395	−	22.8604i	−1.34255	−	0.768444i
$886$	−10.0422	−	3.65505i	−0.337373	−	0.122794i
$887$	42.1587	−	35.3753i	1.41555	−	1.18779i	0.461876	−	0.886944i	$-0.347176\pi$
$887$	42.1587	−	35.3753i	1.41555	−	1.18779i	0.953674	−	0.300843i	$-0.0972680\pi$
$888$	−4.43311	−	5.24323i	−0.148765	−	0.175951i
$889$	−32.0536	−	14.1307i	−1.07504	−	0.473928i
$890$	−3.69270			−0.123780
$891$	−14.2746	+	0.213521i	−0.478218	+	0.00715323i
$892$	−6.89181	−	11.9370i	−0.230755	−	0.399679i
$893$	−69.1990	+	25.1864i	−2.31566	+	0.842830i
$894$	10.4764	−	1.88768i	0.350382	−	0.0631335i
$895$	−19.3797	−	7.05363i	−0.647792	−	0.235777i
$896$	2.63996	+	0.174886i	0.0881950	+	0.00584255i
$897$	64.9303	−	37.8120i	2.16796	−	1.26250i
$898$	−2.27817	+	12.9201i	−0.0760235	+	0.431151i
$899$	0.890344			0.0296946
$900$	−1.37692	+	8.16553i	−0.0458973	+	0.272184i
$901$	38.4745			1.28177
$902$	0.606309	+	0.508754i	0.0201879	+	0.0169397i
$903$	32.4468	+	43.9709i	1.07976	+	1.46326i
$904$	0.379291	+	2.15106i	0.0126150	+	0.0715433i
$905$	−35.1234	−	12.7839i	−1.16754	−	0.424951i
$906$	−2.00585	−	5.44757i	−0.0666400	−	0.180983i
$907$	3.64041	−	20.6458i	0.120878	−	0.685532i	−0.862793	−	0.505557i	$-0.831287\pi$
$907$	3.64041	−	20.6458i	0.120878	−	0.685532i	0.983671	−	0.179975i	$-0.0576017\pi$
$908$	−14.3421			−0.475959
$909$	4.45617	+	24.2120i	0.147802	+	0.803060i
$910$	9.54333	−	38.8826i	0.316358	−	1.28895i
$911$	−21.7296	+	7.90894i	−0.719935	+	0.262035i	−0.675898	−	0.736995i	$-0.736244\pi$
$911$	−21.7296	+	7.90894i	−0.719935	+	0.262035i	−0.0440369	+	0.999030i	$0.514022\pi$
$912$	9.93044	−	5.78296i	0.328830	−	0.191493i
$913$	26.4150	+	9.61428i	0.874209	+	0.318186i
$914$	−0.358340	−	2.03225i	−0.0118528	−	0.0672207i
$915$	−9.17174	+	25.4954i	−0.303208	+	0.842851i
$916$	2.88336	−	16.3523i	0.0952688	−	0.540296i
$917$	3.52364	+	3.37788i	0.116361	+	0.111547i
$918$	−20.9223	+	25.5100i	−0.690539	+	0.841956i
$919$	4.97400	−	8.61521i	0.164077	−	0.284190i	−0.772250	−	0.635319i	$-0.780869\pi$
$919$	4.97400	−	8.61521i	0.164077	−	0.284190i	0.936327	+	0.351129i	$0.114202\pi$
$920$	−20.9051	+	7.60883i	−0.689220	+	0.250856i
$921$	−58.2740	+	10.5001i	−1.92019	+	0.345990i
$922$	−2.93566	+	2.46332i	−0.0966810	+	0.0811250i
$923$	−0.817674	+	0.686110i	−0.0269141	+	0.0225836i
$924$	−7.06601	−	1.70629i	−0.232455	−	0.0561328i
$925$	10.2823	−	3.74244i	0.338079	−	0.123051i
$926$	7.09048	+	12.2811i	0.233008	+	0.403581i
$927$	11.9944	−	21.1384i	0.393947	−	0.694276i
$928$	0.178594	−	0.309334i	0.00586265	−	0.0101544i
$929$	−3.77757	+	1.37492i	−0.123938	+	0.0451098i	−0.403245	−	0.915092i	$-0.632118\pi$
$929$	−3.77757	+	1.37492i	−0.123938	+	0.0451098i	0.279307	+	0.960202i	$0.409895\pi$
$930$	7.69633	−	9.24210i	0.252373	−	0.303060i
$931$	31.3283	+	34.2849i	1.02674	+	1.12364i
$932$	−1.90883	−	10.8255i	−0.0625259	−	0.354602i
$933$	−5.20718	−	14.1419i	−0.170475	−	0.462984i
$934$	0.729266	−	4.13588i	0.0238623	−	0.135330i
$935$	−14.0285	+	24.2982i	−0.458782	+	0.794635i
$936$	8.25351	+	14.0518i	0.269774	+	0.459296i
$937$	19.0888	−	33.0627i	0.623602	−	1.08011i	−0.365207	−	0.930926i	$-0.619002\pi$
$937$	19.0888	−	33.0627i	0.623602	−	1.08011i	0.988809	−	0.149185i	$-0.0476649\pi$
$938$	0.654980	+	6.01947i	0.0213858	+	0.196543i
$939$	0.0816327	+	21.8313i	0.00266398	+	0.712436i
$940$	5.36913	+	30.4499i	0.175122	+	0.993165i
$941$	2.48530	+	14.0948i	0.0810184	+	0.459478i	0.998145	+	0.0608821i	$0.0193914\pi$
$941$	2.48530	+	14.0948i	0.0810184	+	0.459478i	−0.917127	+	0.398596i	$0.869498\pi$
$942$	−12.7325	+	2.29420i	−0.414847	+	0.0747492i
$943$	−3.05247	−	2.56132i	−0.0994020	−	0.0834082i
$944$	9.53761			0.310423
$945$	26.1907	−	27.9417i	0.851984	−	0.908943i
$946$	−18.9157			−0.615003
$947$	23.4216	+	19.6531i	0.761101	+	0.638640i	0.938413	−	0.345515i	$-0.112296\pi$
$947$	23.4216	+	19.6531i	0.761101	+	0.638640i	−0.177312	+	0.984155i	$0.556740\pi$
$948$	2.89233	+	3.42088i	0.0939384	+	0.111105i
$949$	−6.27699	−	35.5986i	−0.203760	−	1.15558i
$950$	3.18010	+	18.0352i	0.103176	+	0.585140i
$951$	27.3019	+	15.6269i	0.885324	+	0.506738i
$952$	−13.5544	+	9.92391i	−0.439299	+	0.321636i
$953$	10.4786	−	18.1494i	0.339434	−	0.587918i	−0.644892	−	0.764274i	$-0.723098\pi$
$953$	10.4786	−	18.1494i	0.339434	−	0.587918i	0.984326	+	0.176356i	$0.0564310\pi$
$954$	13.8379	−	11.7888i	0.448017	−	0.381677i
$955$	5.99230	−	10.3790i	0.193906	−	0.335855i
$956$	−1.36359	+	7.73330i	−0.0441016	+	0.250113i
$957$	−0.627992	+	0.754121i	−0.0203001	+	0.0243773i
$958$	−7.56592	−	42.9084i	−0.244444	−	1.38631i
$959$	−6.74431	−	13.7002i	−0.217785	−	0.442404i
$960$	−1.66720	−	4.52783i	−0.0538085	−	0.146135i
$961$	23.2919	−	8.47756i	0.751352	−	0.273470i
$962$	10.7669	−	18.6489i	0.347140	−	0.601264i
$963$	−4.56441	+	1.70007i	−0.147086	+	0.0547841i
$964$	3.61177	+	6.25578i	0.116327	+	0.201485i
$965$	50.4824	−	18.3741i	1.62509	−	0.591483i
$966$	35.5738	+	8.59033i	1.14457	+	0.276389i
$967$	−8.66337	+	7.26943i	−0.278595	+	0.233769i	−0.771369	−	0.636388i	$-0.780428\pi$
$967$	−8.66337	+	7.26943i	−0.278595	+	0.233769i	0.492774	+	0.870158i	$0.335983\pi$
$968$	−6.49898	+	5.45329i	−0.208885	+	0.175275i
$969$	−24.6988	+	68.6572i	−0.793441	+	2.20559i
$970$	23.0847	−	8.40213i	0.741204	−	0.269776i
$971$	−25.1116	+	43.4947i	−0.805871	+	1.39581i	0.109830	+	0.993950i	$0.464969\pi$
$971$	−25.1116	+	43.4947i	−0.805871	+	1.39581i	−0.915701	+	0.401859i	$0.868364\pi$
$972$	0.291428	+	15.5857i	0.00934756	+	0.499913i
$973$	−12.0491	+	49.0919i	−0.386277	+	1.57381i
$974$	−2.60851	+	14.7936i	−0.0835821	+	0.474018i
$975$	−25.5590	+	4.60535i	−0.818544	+	0.147489i
$976$	−0.975123	−	5.53019i	−0.0312129	−	0.177017i
$977$	14.8212	+	5.39448i	0.474172	+	0.172585i	0.568042	−	0.823000i	$-0.307701\pi$
$977$	14.8212	+	5.39448i	0.474172	+	0.172585i	−0.0938691	+	0.995585i	$0.529924\pi$
$978$	−0.00367577	−	0.983022i	−0.000117538	−	0.0314336i
$979$	−1.97589	+	0.719165i	−0.0631497	+	0.0229846i
$980$	16.4608	−	10.4544i	0.525822	−	0.333953i
$981$	−4.62331	+	27.4175i	−0.147611	+	0.875375i
$982$	−28.4188			−0.906880
$983$	1.68501	−	9.55614i	0.0537434	−	0.304794i	−0.946073	−	0.323953i	$-0.894988\pi$
$983$	1.68501	−	9.55614i	0.0537434	−	0.304794i	0.999816	+	0.0191596i	$0.00609905\pi$
$984$	0.553037	−	0.664112i	0.0176302	−	0.0211711i
$985$	−35.5767	−	12.9489i	−1.13357	−	0.412585i
$986$	0.393823	+	2.23348i	0.0125419	+	0.0711285i
$987$	20.3434	−	46.6179i	0.647538	−	1.48386i
$988$	27.6085	+	23.1663i	0.878344	+	0.737018i
$989$	95.2313			3.02818
$990$	2.39954	+	13.0376i	0.0762625	+	0.414362i
$991$	9.12606			0.289899			0.144949	−	0.989439i	$-0.453698\pi$
$991$	9.12606			0.289899			0.144949	+	0.989439i	$0.453698\pi$
$992$	−0.432843	+	2.45477i	−0.0137428	+	0.0779392i
$993$	−34.4497	−	19.7182i	−1.09323	−	0.625738i
$994$	−0.518746	−	0.0343647i	−0.0164536	−	0.00108998i
$995$	22.4359	+	8.16601i	0.711267	+	0.258880i
$996$	10.3901	−	28.8820i	0.329222	−	0.915162i
$997$	45.9868	−	16.7378i	1.45642	−	0.530092i	0.512041	−	0.858961i	$-0.328890\pi$
$997$	45.9868	−	16.7378i	1.45642	−	0.530092i	0.944376	+	0.328869i	$0.106667\pi$
$998$	8.78546	+	15.2169i	0.278099	+	0.481681i
$999$	17.7221	−	10.4987i	0.560702	−	0.332163i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.v.b.79.7	yes	72
7.4	even	3		378.2.w.a.25.1	yes	72
27.13	even	9		378.2.w.a.121.1	yes	72
189.67	even	9	inner	378.2.v.b.67.7	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.b.67.7	✓	72	189.67	even	9	inner
378.2.v.b.79.7	yes	72	1.1	even	1	trivial
378.2.w.a.25.1	yes	72	7.4	even	3
378.2.w.a.121.1	yes	72	27.13	even	9

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.586306 - 1.62980i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.483736 + 2.74340i) q^{5} +(1.49675 - 0.871628i) q^{6} +(0.286196 + 2.63023i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.31249 - 1.91112i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.586306 - 1.62980i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.483736 + 2.74340i) q^{5} +(1.49675 - 0.871628i) q^{6} +(0.286196 + 2.63023i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.31249 - 1.91112i) q^{9} +(-1.39286 + 2.41251i) q^{10} +(-0.275449 + 1.56215i) q^{11} +(1.70685 + 0.294387i) q^{12} +(0.943280 + 5.34960i) q^{13} +(-1.47144 + 2.19883i) q^{14} +(4.75482 + 0.820082i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(3.17470 - 5.49875i) q^{17} +(-0.543024 - 2.95044i) q^{18} +(-3.31733 - 5.74579i) q^{19} +(-2.61773 + 0.952774i) q^{20} +(4.45454 + 1.07568i) q^{21} +(-1.21514 + 1.01962i) q^{22} +(6.11761 - 5.13328i) q^{23} +(1.11829 + 1.32266i) q^{24} +(-2.59380 + 0.944067i) q^{25} +(-2.71607 + 4.70436i) q^{26} +(-4.47057 + 2.64839i) q^{27} +(-2.54057 + 0.738582i) q^{28} +(-0.0620252 + 0.351762i) q^{29} +(3.11526 + 3.68456i) q^{30} +(-0.432843 - 2.45477i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(2.38449 + 1.36482i) q^{33} +(5.96649 - 2.17162i) q^{34} +(-7.07733 + 2.05749i) q^{35} +(1.48053 - 2.60922i) q^{36} -3.96417 q^{37} +(1.15210 - 6.53387i) q^{38} +(9.27183 + 1.59915i) q^{39} +(-2.61773 - 0.952774i) q^{40} +(-0.0866442 - 0.491383i) q^{41} +(2.72094 + 3.68734i) q^{42} +(9.13494 + 7.66513i) q^{43} -1.58625 q^{44} +(4.12435 - 7.26857i) q^{45} +7.98597 q^{46} +(1.92737 - 10.9307i) q^{47} +(0.00647654 + 1.73204i) q^{48} +(-6.83618 + 1.50552i) q^{49} +(-2.59380 - 0.944067i) q^{50} +(-7.10050 - 8.39808i) q^{51} +(-5.10453 + 1.85790i) q^{52} +(3.02977 + 5.24771i) q^{53} +(-5.12701 - 0.844843i) q^{54} -4.41885 q^{55} +(-2.42094 - 1.06726i) q^{56} +(-11.3094 + 2.03779i) q^{57} +(-0.273622 + 0.229596i) q^{58} +(-8.96243 - 3.26206i) q^{59} +(0.0180419 + 4.82499i) q^{60} +(-0.975123 + 5.53019i) q^{61} +(1.24632 - 2.15869i) q^{62} +(4.36486 - 6.62933i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-14.2198 + 5.17559i) q^{65} +(0.949335 + 2.57824i) q^{66} +(1.75315 - 1.47107i) q^{67} +(5.96649 + 2.17162i) q^{68} +(-4.77943 - 12.9802i) q^{69} +(-6.74408 - 2.97310i) q^{70} +(0.0982486 + 0.170172i) q^{71} +(2.81133 - 1.04711i) q^{72} -6.65444 q^{73} +(-3.03673 - 2.54812i) q^{74} +(0.0178770 + 4.78089i) q^{75} +(5.08245 - 4.26468i) q^{76} +(-4.18764 - 0.277413i) q^{77} +(6.07472 + 7.18484i) q^{78} +(1.98128 + 1.66249i) q^{79} +(-1.39286 - 2.41251i) q^{80} +(1.69522 + 8.83890i) q^{81} +(0.249482 - 0.432115i) q^{82} +(3.07726 - 17.4520i) q^{83} +(-0.285812 + 4.57365i) q^{84} +(16.6210 + 6.04955i) q^{85} +(2.07072 + 11.7437i) q^{86} +(0.536936 + 0.307329i) q^{87} +(-1.21514 - 1.01962i) q^{88} +(0.662790 + 1.14799i) q^{89} +(7.83158 - 2.91697i) q^{90} +(-13.8007 + 4.01207i) q^{91} +(6.11761 + 5.13328i) q^{92} +(-4.25457 - 0.733802i) q^{93} +(8.50255 - 7.13449i) q^{94} +(14.1583 - 11.8802i) q^{95} +(-1.10837 + 1.33098i) q^{96} +(-6.75544 - 5.66849i) q^{97} +(-6.20455 - 3.24092i) q^{98} +(3.62243 - 3.08604i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9}+O(q^{10}) \) 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9	\( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9} - 6 q^{10} + 12 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} - 18 q^{19} - 30 q^{21} - 6 q^{22} + 30 q^{23} + 6 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} - 18 q^{35} + 9 q^{36} - 24 q^{39} - 6 q^{41} + 12 q^{42} + 24 q^{43} + 51 q^{45} + 45 q^{47} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 51 q^{51} + 6 q^{52} - 15 q^{53} + 27 q^{54} + 72 q^{55} - 3 q^{56} - 63 q^{57} + 3 q^{58} - 30 q^{59} - 3 q^{60} + 9 q^{61} - 24 q^{62} - 39 q^{63} - 36 q^{64} + 9 q^{65} - 6 q^{67} + 9 q^{68} - 21 q^{69} - 33 q^{70} + 12 q^{71} - 12 q^{72} + 132 q^{73} - 18 q^{74} - 30 q^{75} - 33 q^{77} + 30 q^{78} - 9 q^{79} - 6 q^{80} + 36 q^{81} - 33 q^{82} - 18 q^{83} + 15 q^{84} + 21 q^{85} - 12 q^{86} - 39 q^{87} - 6 q^{88} - 36 q^{89} + 69 q^{90} + 39 q^{91} + 30 q^{92} - 66 q^{93} - 9 q^{94} - 33 q^{95} - 48 q^{97} - 12 q^{98} - 54 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9 - 6 * q^10 + 12 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 - 18 * q^19 - 30 * q^21 - 6 * q^22 + 30 * q^23 + 6 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 - 18 * q^35 + 9 * q^36 - 24 * q^39 - 6 * q^41 + 12 * q^42 + 24 * q^43 + 51 * q^45 + 45 * q^47 - 6 * q^48 - 12 * q^49 + 6 * q^50 - 51 * q^51 + 6 * q^52 - 15 * q^53 + 27 * q^54 + 72 * q^55 - 3 * q^56 - 63 * q^57 + 3 * q^58 - 30 * q^59 - 3 * q^60 + 9 * q^61 - 24 * q^62 - 39 * q^63 - 36 * q^64 + 9 * q^65 - 6 * q^67 + 9 * q^68 - 21 * q^69 - 33 * q^70 + 12 * q^71 - 12 * q^72 + 132 * q^73 - 18 * q^74 - 30 * q^75 - 33 * q^77 + 30 * q^78 - 9 * q^79 - 6 * q^80 + 36 * q^81 - 33 * q^82 - 18 * q^83 + 15 * q^84 + 21 * q^85 - 12 * q^86 - 39 * q^87 - 6 * q^88 - 36 * q^89 + 69 * q^90 + 39 * q^91 + 30 * q^92 - 66 * q^93 - 9 * q^94 - 33 * q^95 - 48 * q^97 - 12 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more