LMFDB - Embedded newform 819.2.gh.d.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(19,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("819.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.gh (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	819.19
Dual form			819.2.gh.d.388.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.18205 - 0.584679i) q^{2} +(2.68745 + 1.55160i) q^{4} +(-2.27456 + 0.609466i) q^{5} +(-2.33957 + 1.23548i) q^{7} +(-1.76223 - 1.76223i) q^{8} +O(q^{10})$	\(q+(-2.18205 - 0.584679i) q^{2} +(2.68745 + 1.55160i) q^{4} +(-2.27456 + 0.609466i) q^{5} +(-2.33957 + 1.23548i) q^{7} +(-1.76223 - 1.76223i) q^{8} +5.31955 q^{10} +(3.57017 + 3.57017i) q^{11} +(1.62322 - 3.21950i) q^{13} +(5.82743 - 1.32798i) q^{14} +(-0.288264 - 0.499288i) q^{16} +(2.64387 - 4.57931i) q^{17} +(2.98754 + 2.98754i) q^{19} +(-7.05842 - 1.89130i) q^{20} +(-5.70290 - 9.87771i) q^{22} +(-3.44956 + 1.99161i) q^{23} +(0.472034 - 0.272529i) q^{25} +(-5.42433 + 6.07604i) q^{26} +(-8.20446 - 0.309797i) q^{28} +(-0.565030 + 0.978660i) q^{29} +(-1.40198 + 5.23228i) q^{31} +(1.62713 + 6.07252i) q^{32} +(-8.44649 + 8.44649i) q^{34} +(4.56851 - 4.23605i) q^{35} +(1.37587 - 5.13480i) q^{37} +(-4.77222 - 8.26572i) q^{38} +(5.08231 + 2.93428i) q^{40} +(-5.61474 + 1.50446i) q^{41} +(-9.65143 + 5.57225i) q^{43} +(4.05519 + 15.1342i) q^{44} +(8.69158 - 2.32890i) q^{46} +(-1.95174 - 7.28399i) q^{47} +(3.94719 - 5.78098i) q^{49} +(-1.18935 + 0.318684i) q^{50} +(9.35771 - 6.13365i) q^{52} +(0.538076 + 0.931975i) q^{53} +(-10.2965 - 5.94466i) q^{55} +(6.30006 + 1.94567i) q^{56} +(1.80513 - 1.80513i) q^{58} +(2.18873 + 8.16845i) q^{59} -3.15666i q^{61} +(6.11841 - 10.5974i) q^{62} -13.0488i q^{64} +(-1.72994 + 8.31222i) q^{65} +(-3.75730 + 3.75730i) q^{67} +(14.2105 - 8.20446i) q^{68} +(-12.4455 + 6.57218i) q^{70} +(-12.9802 - 3.47804i) q^{71} +(1.56120 + 0.418321i) q^{73} +(-6.00443 + 10.4000i) q^{74} +(3.39340 + 12.6644i) q^{76} +(-12.7635 - 3.94181i) q^{77} +(-6.31940 + 10.9455i) q^{79} +(0.959971 + 0.959971i) q^{80} +13.1313 q^{82} +(7.21679 + 7.21679i) q^{83} +(-3.22269 + 12.0273i) q^{85} +(24.3179 - 6.51596i) q^{86} -12.5829i q^{88} +(-8.63520 - 2.31379i) q^{89} +(0.179969 + 9.53769i) q^{91} -12.3607 q^{92} +17.0352i q^{94} +(-8.61613 - 4.97453i) q^{95} +(-4.32019 + 16.1232i) q^{97} +(-11.9930 + 10.3066i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7}+O(q^{10}) $ 40 * q - 8 * q^7	$ 40 q - 8 q^{7} - 4 q^{11} + 18 q^{14} + 32 q^{16} - 4 q^{17} + 14 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} + 24 q^{25} + 32 q^{26} + 16 q^{28} - 8 q^{29} + 14 q^{31} + 26 q^{32} - 24 q^{34} - 26 q^{35} + 36 q^{37} + 8 q^{38} - 30 q^{40} + 2 q^{41} - 66 q^{43} + 32 q^{44} - 26 q^{46} + 4 q^{47} - 14 q^{49} + 20 q^{50} + 2 q^{52} + 8 q^{53} - 42 q^{55} - 46 q^{56} + 24 q^{58} - 14 q^{59} - 24 q^{62} - 28 q^{65} - 44 q^{67} + 18 q^{68} - 4 q^{70} + 6 q^{71} + 14 q^{73} + 20 q^{74} - 64 q^{76} - 24 q^{77} - 20 q^{80} + 48 q^{82} + 12 q^{83} + 2 q^{85} + 60 q^{86} + 2 q^{89} - 14 q^{91} - 236 q^{92} - 24 q^{95} - 62 q^{97} + 88 q^{98}+O(q^{100}) $ 40 * q - 8 * q^7 - 4 * q^11 + 18 * q^14 + 32 * q^16 - 4 * q^17 + 14 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 + 24 * q^25 + 32 * q^26 + 16 * q^28 - 8 * q^29 + 14 * q^31 + 26 * q^32 - 24 * q^34 - 26 * q^35 + 36 * q^37 + 8 * q^38 - 30 * q^40 + 2 * q^41 - 66 * q^43 + 32 * q^44 - 26 * q^46 + 4 * q^47 - 14 * q^49 + 20 * q^50 + 2 * q^52 + 8 * q^53 - 42 * q^55 - 46 * q^56 + 24 * q^58 - 14 * q^59 - 24 * q^62 - 28 * q^65 - 44 * q^67 + 18 * q^68 - 4 * q^70 + 6 * q^71 + 14 * q^73 + 20 * q^74 - 64 * q^76 - 24 * q^77 - 20 * q^80 + 48 * q^82 + 12 * q^83 + 2 * q^85 + 60 * q^86 + 2 * q^89 - 14 * q^91 - 236 * q^92 - 24 * q^95 - 62 * q^97 + 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.18205	−	0.584679i	−1.54294	−	0.413431i	−0.615729	−	0.787958i	$-0.711138\pi$
$2$	−2.18205	−	0.584679i	−1.54294	−	0.413431i	−0.927216	+	0.374528i	$0.877805\pi$
$3$		0			0
$3$		0			0
$4$	2.68745	+	1.55160i	1.34373	+	0.775801i
$5$	−2.27456	+	0.609466i	−1.01721	+	0.272561i	−0.728640	−	0.684897i	$-0.759847\pi$
$5$	−2.27456	+	0.609466i	−1.01721	+	0.272561i	−0.288573	+	0.957458i	$0.593181\pi$
$6$		0			0
$7$	−2.33957	+	1.23548i	−0.884275	+	0.466967i
$7$	−2.33957	+	1.23548i	−0.884275	+	0.466967i
$8$	−1.76223	−	1.76223i	−0.623043	−	0.623043i
$9$		0			0
$10$	5.31955			1.68219
$11$	3.57017	+	3.57017i	1.07645	+	1.07645i	0.996825	+	0.0796226i	$0.0253715\pi$
$11$	3.57017	+	3.57017i	1.07645	+	1.07645i	0.0796226	+	0.996825i	$0.474628\pi$
$12$		0			0
$13$	1.62322	−	3.21950i	0.450201	−	0.892927i
$13$	1.62322	−	3.21950i	0.450201	−	0.892927i
$14$	5.82743	−	1.32798i	1.55745	−	0.354917i
$15$		0			0
$16$	−0.288264	−	0.499288i	−0.0720660	−	0.124822i
$17$	2.64387	−	4.57931i	0.641232	−	1.11065i	−0.343926	−	0.938997i	$-0.611757\pi$
$17$	2.64387	−	4.57931i	0.641232	−	1.11065i	0.985158	−	0.171650i	$-0.0549097\pi$
$18$		0			0
$19$	2.98754	+	2.98754i	0.685389	+	0.685389i	0.961209	−	0.275820i	$-0.0889495\pi$
$19$	2.98754	+	2.98754i	0.685389	+	0.685389i	−0.275820	+	0.961209i	$0.588950\pi$
$20$	−7.05842	−	1.89130i	−1.57831	−	0.422907i
$21$		0			0
$22$	−5.70290	−	9.87771i	−1.21586	−	2.10594i
$23$	−3.44956	+	1.99161i	−0.719283	+	0.415278i	−0.814489	−	0.580179i	$-0.802983\pi$
$23$	−3.44956	+	1.99161i	−0.719283	+	0.415278i	0.0952055	+	0.995458i	$0.469649\pi$
$24$		0			0
$25$	0.472034	−	0.272529i	0.0944069	−	0.0545058i
$26$	−5.42433	+	6.07604i	−1.06380	+	1.19161i
$27$		0			0
$28$	−8.20446	−	0.309797i	−1.55050	−	0.0585460i
$29$	−0.565030	+	0.978660i	−0.104923	+	0.181733i	−0.913707	−	0.406374i	$-0.866793\pi$
$29$	−0.565030	+	0.978660i	−0.104923	+	0.181733i	0.808784	+	0.588106i	$0.200126\pi$
$30$		0			0
$31$	−1.40198	+	5.23228i	−0.251804	+	0.939745i	0.718037	+	0.696005i	$0.245041\pi$
$31$	−1.40198	+	5.23228i	−0.251804	+	0.939745i	−0.969841	+	0.243740i	$0.921626\pi$
$32$	1.62713	+	6.07252i	0.287638	+	1.07348i
$33$		0			0
$34$	−8.44649	+	8.44649i	−1.44856	+	1.44856i
$35$	4.56851	−	4.23605i	0.772219	−	0.716024i
$36$		0			0
$37$	1.37587	−	5.13480i	0.226191	−	0.844156i	−0.755733	−	0.654880i	$-0.772719\pi$
$37$	1.37587	−	5.13480i	0.226191	−	0.844156i	0.981924	−	0.189276i	$-0.0606142\pi$
$38$	−4.77222	−	8.26572i	−0.774156	−	1.34088i
$39$		0			0
$40$	5.08231	+	2.93428i	0.803584	+	0.463950i
$41$	−5.61474	+	1.50446i	−0.876875	+	0.234958i	−0.669058	−	0.743210i	$-0.733302\pi$
$41$	−5.61474	+	1.50446i	−0.876875	+	0.234958i	−0.207817	+	0.978168i	$0.566636\pi$
$42$		0			0
$43$	−9.65143	+	5.57225i	−1.47183	+	0.849761i	−0.999499	−	0.0316610i	$-0.989920\pi$
$43$	−9.65143	+	5.57225i	−1.47183	+	0.849761i	−0.472330	+	0.881422i	$0.656587\pi$
$44$	4.05519	+	15.1342i	0.611343	+	2.28156i
$45$		0			0
$46$	8.69158	−	2.32890i	1.28150	−	0.343378i
$47$	−1.95174	−	7.28399i	−0.284691	−	1.06248i	−0.949065	−	0.315080i	$-0.897969\pi$
$47$	−1.95174	−	7.28399i	−0.284691	−	1.06248i	0.664375	−	0.747400i	$-0.268698\pi$
$48$		0			0
$49$	3.94719	−	5.78098i	0.563885	−	0.825854i
$50$	−1.18935	+	0.318684i	−0.168199	+	0.0450688i
$51$		0			0
$52$	9.35771	−	6.13365i	1.29768	−	0.850584i
$53$	0.538076	+	0.931975i	0.0739104	+	0.128017i	0.900612	−	0.434624i	$-0.143119\pi$
$53$	0.538076	+	0.931975i	0.0739104	+	0.128017i	−0.826702	+	0.562641i	$0.809785\pi$
$54$		0			0
$55$	−10.2965	−	5.94466i	−1.38837	−	0.801578i
$56$	6.30006	+	1.94567i	0.841881	+	0.260001i
$57$		0			0
$58$	1.80513	−	1.80513i	0.237025	−	0.237025i
$59$	2.18873	+	8.16845i	0.284948	+	1.06344i	0.948877	+	0.315645i	$0.102221\pi$
$59$	2.18873	+	8.16845i	0.284948	+	1.06344i	−0.663929	+	0.747796i	$0.731112\pi$
$60$		0			0
$61$		−	3.15666i		−	0.404169i	−0.979368	−	0.202085i	$-0.935228\pi$
$61$		−	3.15666i		−	0.404169i	0.979368	−	0.202085i	$-0.0647716\pi$
$62$	6.11841	−	10.5974i	0.777039	−	1.34587i
$63$		0			0
$64$		−	13.0488i		−	1.63111i
$65$	−1.72994	+	8.31222i	−0.214573	+	1.03100i
$66$		0			0
$67$	−3.75730	+	3.75730i	−0.459027	+	0.459027i	−0.898336	−	0.439309i	$-0.855223\pi$
$67$	−3.75730	+	3.75730i	−0.459027	+	0.459027i	0.439309	+	0.898336i	$0.355223\pi$
$68$	14.2105	−	8.20446i	1.72328	−	0.994937i
$69$		0			0
$70$	−12.4455	+	6.57218i	−1.48752	+	0.785526i
$71$	−12.9802	−	3.47804i	−1.54047	−	0.412767i	−0.614052	−	0.789266i	$-0.710461\pi$
$71$	−12.9802	−	3.47804i	−1.54047	−	0.412767i	−0.926417	+	0.376498i	$0.877128\pi$
$72$		0			0
$73$	1.56120	+	0.418321i	0.182724	+	0.0489608i	0.349021	−	0.937115i	$-0.386514\pi$
$73$	1.56120	+	0.418321i	0.182724	+	0.0489608i	−0.166297	+	0.986076i	$0.553181\pi$
$74$	−6.00443	+	10.4000i	−0.698000	+	1.20897i
$75$		0			0
$76$	3.39340	+	12.6644i	0.389250	+	1.45270i
$77$	−12.7635	−	3.94181i	−1.45454	−	0.449211i
$78$		0			0
$79$	−6.31940	+	10.9455i	−0.710988	+	1.23147i	0.253498	+	0.967336i	$0.418419\pi$
$79$	−6.31940	+	10.9455i	−0.710988	+	1.23147i	−0.964486	+	0.264132i	$0.914914\pi$
$80$	0.959971	+	0.959971i	0.107328	+	0.107328i
$81$		0			0
$82$	13.1313			1.45011
$83$	7.21679	+	7.21679i	0.792145	+	0.792145i	0.981843	−	0.189697i	$-0.0607507\pi$
$83$	7.21679	+	7.21679i	0.792145	+	0.792145i	−0.189697	+	0.981843i	$0.560751\pi$
$84$		0			0
$85$	−3.22269	+	12.0273i	−0.349550	+	1.30454i
$86$	24.3179	−	6.51596i	2.62227	−	0.702634i
$87$		0			0
$88$		−	12.5829i		−	1.34135i
$89$	−8.63520	−	2.31379i	−0.915329	−	0.245262i	−0.229741	−	0.973252i	$-0.573788\pi$
$89$	−8.63520	−	2.31379i	−0.915329	−	0.245262i	−0.685588	+	0.727990i	$0.740455\pi$
$90$		0			0
$91$	0.179969	+	9.53769i	0.0188658	+	0.999822i
$92$	−12.3607			−1.28869
$93$		0			0
$94$			17.0352i			1.75705i
$95$	−8.61613	−	4.97453i	−0.883997	−	0.510376i
$96$		0			0
$97$	−4.32019	+	16.1232i	−0.438649	+	1.63706i	0.293531	+	0.955950i	$0.405170\pi$
$97$	−4.32019	+	16.1232i	−0.438649	+	1.63706i	−0.732180	+	0.681111i	$0.761497\pi$
$98$	−11.9930	+	10.3066i	−1.21148	+	1.04112i
$99$		0			0
$100$	1.69143			0.169143
$101$	−0.765232			−0.0761434			−0.0380717	−	0.999275i	$-0.512122\pi$
$101$	−0.765232			−0.0761434			−0.0380717	+	0.999275i	$0.512122\pi$
$102$		0			0
$103$	2.76861	−	4.79537i	0.272799	−	0.472502i	−0.696778	−	0.717287i	$-0.745384\pi$
$103$	2.76861	−	4.79537i	0.272799	−	0.472502i	0.969578	+	0.244784i	$0.0787172\pi$
$104$	−8.53399	+	2.81300i	−0.836826	+	0.275838i
$105$		0			0
$106$	−0.629204	−	2.34822i	−0.0611137	−	0.228079i
$107$	−3.87296	−	6.70816i	−0.374413	−	0.648502i	0.615826	−	0.787882i	$-0.288822\pi$
$107$	−3.87296	−	6.70816i	−0.374413	−	0.648502i	−0.990239	+	0.139380i	$0.955489\pi$
$108$		0			0
$109$	−10.8053	−	2.89526i	−1.03496	−	0.277316i	−0.298935	−	0.954273i	$-0.596631\pi$
$109$	−10.8053	−	2.89526i	−1.03496	−	0.277316i	−0.736022	+	0.676958i	$0.763298\pi$
$110$	18.9917	+	18.9917i	1.81079	+	1.81079i
$111$		0			0
$112$	1.29127	+	0.811976i	0.122014	+	0.0767245i
$113$	−4.62961	−	8.01871i	−0.435517	−	0.754337i	0.561821	−	0.827259i	$-0.310101\pi$
$113$	−4.62961	−	8.01871i	−0.435517	−	0.754337i	−0.997338	+	0.0729218i	$0.976768\pi$
$114$		0			0
$115$	6.63241	−	6.63241i	0.618475	−	0.618475i
$116$	−3.03698	+	1.75340i	−0.281977	+	0.162799i
$117$		0			0
$118$		−	19.1037i		−	1.75864i
$119$	−0.527881	+	13.9801i	−0.0483907	+	1.28155i
$120$		0			0
$121$			14.4923i			1.31748i
$122$	−1.84564	+	6.88801i	−0.167096	+	0.623611i
$123$		0			0
$124$	−11.8862	+	11.8862i	−1.06741	+	1.06741i
$125$	7.41788	−	7.41788i	0.663476	−	0.663476i
$126$		0			0
$127$	−0.963214	−	0.556112i	−0.0854714	−	0.0493470i	0.456655	−	0.889644i	$-0.349047\pi$
$127$	−0.963214	−	0.556112i	−0.0854714	−	0.0493470i	−0.542127	+	0.840297i	$0.682381\pi$
$128$	−4.37514	+	16.3282i	−0.386711	+	1.44323i
$129$		0			0
$130$	8.63481	−	17.1263i	0.757323	−	1.50207i
$131$	1.01316	+	0.584948i	0.0885201	+	0.0511071i	0.543607	−	0.839340i	$-0.317058\pi$
$131$	1.01316	+	0.584948i	0.0885201	+	0.0511071i	−0.455087	+	0.890447i	$0.650392\pi$
$132$		0			0
$133$	−10.6806	−	3.29853i	−0.926126	−	0.286019i
$134$	10.3954	−	6.00180i	0.898028	−	0.518477i
$135$		0			0
$136$	−12.7289	+	3.41070i	−1.09150	+	0.292465i
$137$	−11.8263	+	3.16885i	−1.01039	+	0.270733i	−0.725792	−	0.687914i	$-0.758527\pi$
$137$	−11.8263	+	3.16885i	−1.01039	+	0.270733i	−0.284597	+	0.958647i	$0.591860\pi$
$138$		0			0
$139$	−17.4448	+	10.0718i	−1.47965	+	0.854276i	−0.999735	−	0.0230384i	$-0.992666\pi$
$139$	−17.4448	+	10.0718i	−1.47965	+	0.854276i	−0.479915	+	0.877315i	$0.659333\pi$
$140$	18.8503	−	4.29569i	1.59314	−	0.363052i
$141$		0			0
$142$	26.2900	+	15.1785i	2.20621	+	1.27375i
$143$	17.2893	−	5.69897i	1.44581	−	0.476572i
$144$		0			0
$145$	0.688733	−	2.57039i	0.0571961	−	0.213459i
$146$	−3.16203	−	1.82560i	−0.261691	−	0.151088i
$147$		0			0
$148$	11.6648	−	11.6648i	0.958837	−	0.958837i
$149$	−11.1605	+	11.1605i	−0.914302	+	0.914302i	−0.996607	−	0.0823053i	$-0.973772\pi$
$149$	−11.1605	+	11.1605i	−0.914302	+	0.914302i	0.0823053	+	0.996607i	$0.473772\pi$
$150$		0			0
$151$	4.18906	−	15.6338i	0.340901	−	1.27226i	−0.556428	−	0.830896i	$-0.687828\pi$
$151$	4.18906	−	15.6338i	0.340901	−	1.27226i	0.897329	−	0.441363i	$-0.145505\pi$
$152$		−	10.5295i		−	0.854053i
$153$		0			0
$154$	25.5460	+	16.0638i	2.05856	+	1.29446i
$155$		−	12.7556i		−	1.02455i
$156$		0			0
$157$	7.65145	−	4.41757i	0.610652	−	0.352560i	−0.162568	−	0.986697i	$-0.551978\pi$
$157$	7.65145	−	4.41757i	0.610652	−	0.352560i	0.773221	+	0.634137i	$0.218645\pi$
$158$	20.1889	−	20.1889i	1.60614	−	1.60614i
$159$		0			0
$160$	−7.40198	−	12.8206i	−0.585178	−	1.01356i
$161$	5.60991	−	8.92136i	0.442123	−	0.703102i
$162$		0			0
$163$	−5.61466	−	5.61466i	−0.439774	−	0.439774i	0.452162	−	0.891936i	$-0.350653\pi$
$163$	−5.61466	−	5.61466i	−0.439774	−	0.439774i	−0.891936	+	0.452162i	$0.850653\pi$
$164$	−17.4237	−	4.66866i	−1.36056	−	0.364561i
$165$		0			0
$166$	−11.5279	−	19.9669i	−0.894739	−	1.54973i
$167$	−2.54898	−	9.51291i	−0.197246	−	0.736131i	−0.991674	−	0.128773i	$-0.958896\pi$
$167$	−2.54898	−	9.51291i	−0.197246	−	0.736131i	0.794428	−	0.607358i	$-0.207771\pi$
$168$		0			0
$169$	−7.73030	−	10.4519i	−0.594638	−	0.803993i
$170$	14.0642	−	24.3599i	1.07867	−	1.86832i
$171$		0			0
$172$	−34.5837			−2.63698
$173$	−3.39025			−0.257756			−0.128878	−	0.991660i	$-0.541138\pi$
$173$	−3.39025			−0.257756			−0.128878	+	0.991660i	$0.541138\pi$
$174$		0			0
$175$	−0.767655	+	1.22079i	−0.0580292	+	0.0922830i
$176$	0.753391	−	2.81170i	0.0567890	−	0.211939i
$177$		0			0
$178$	17.4896	+	10.0976i	1.31090	+	0.756850i
$179$			6.78191i			0.506904i	0.967348	+	0.253452i	$0.0815659\pi$
$179$			6.78191i			0.506904i	−0.967348	+	0.253452i	$0.918434\pi$
$180$		0			0
$181$	10.9124			0.811109			0.405554	−	0.914071i	$-0.367078\pi$
$181$	10.9124			0.811109			0.405554	+	0.914071i	$0.367078\pi$
$182$	5.18379	−	20.9170i	0.384248	−	1.55047i
$183$		0			0
$184$	9.58859	+	2.56926i	0.706880	+	0.189408i
$185$			12.5179i			0.920338i
$186$		0			0
$187$	25.7880	−	6.90987i	1.88581	−	0.505300i
$188$	6.05665	−	22.6037i	0.441727	−	1.64855i
$189$		0			0
$190$	15.8924	+	15.8924i	1.15295	+	1.15295i
$191$	1.04515			0.0756246			0.0378123	−	0.999285i	$-0.487961\pi$
$191$	1.04515			0.0756246			0.0378123	+	0.999285i	$0.487961\pi$
$192$		0			0
$193$	6.96641	+	6.96641i	0.501453	+	0.501453i	0.911889	−	0.410436i	$-0.134624\pi$
$193$	6.96641	+	6.96641i	0.501453	+	0.501453i	−0.410436	+	0.911889i	$0.634624\pi$
$194$	18.8538	−	32.6557i	1.35362	−	2.34454i
$195$		0			0
$196$	19.5777	−	9.41164i	1.39841	−	0.672260i
$197$	1.53092	+	5.71348i	0.109074	+	0.407069i	0.998775	−	0.0494737i	$-0.0157544\pi$
$197$	1.53092	+	5.71348i	0.109074	+	0.407069i	−0.889702	+	0.456542i	$0.849088\pi$
$198$		0			0
$199$	2.65808	−	4.60393i	0.188426	−	0.326364i	−0.756299	−	0.654226i	$-0.772995\pi$
$199$	2.65808	−	4.60393i	0.188426	−	0.326364i	0.944726	+	0.327862i	$0.106328\pi$
$200$	−1.31209	−	0.351574i	−0.0927790	−	0.0248601i
$201$		0			0
$202$	1.66978	+	0.447415i	0.117485	+	0.0314800i
$203$	0.112815	−	2.98773i	0.00791807	−	0.209697i
$204$		0			0
$205$	11.8541	−	6.84398i	0.827928	−	0.478004i
$206$	−8.84501	+	8.84501i	−0.616261	+	0.616261i
$207$		0			0
$208$	−2.07537	+	0.117609i	−0.143901	+	0.00815474i
$209$			21.3321i			1.47557i
$210$		0			0
$211$	8.76315	−	15.1782i	0.603280	−	1.04491i	−0.389041	−	0.921221i	$-0.627193\pi$
$211$	8.76315	−	15.1782i	0.603280	−	1.04491i	0.992321	−	0.123691i	$-0.0394732\pi$
$212$			3.33952i			0.229359i
$213$		0			0
$214$	4.52888	+	16.9020i	0.309588	+	1.15540i
$215$	18.5566	−	18.5566i	1.26555	−	1.26555i
$216$		0			0
$217$	−3.18432	−	13.9734i	−0.216166	−	0.948577i
$218$	21.8849	+	12.6352i	1.48223	+	0.855766i
$219$		0			0
$220$	−18.4475	−	31.9520i	−1.24373	−	2.15421i
$221$	−10.4515	−	15.9452i	−0.703043	−	1.07259i
$222$		0			0
$223$	−12.8318	+	3.43827i	−0.859282	+	0.230244i	−0.661447	−	0.749992i	$-0.730057\pi$
$223$	−12.8318	+	3.43827i	−0.859282	+	0.230244i	−0.197834	+	0.980235i	$0.563391\pi$
$224$	−11.3092	−	12.1968i	−0.755630	−	0.814934i
$225$		0			0
$226$	5.41367	+	20.2041i	0.360112	+	1.34396i
$227$	−19.2938	+	5.16977i	−1.28058	+	0.343130i	−0.834074	−	0.551652i	$-0.813997\pi$
$227$	−19.2938	+	5.16977i	−1.28058	+	0.343130i	−0.446503	+	0.894782i	$0.647331\pi$
$228$		0			0
$229$	−0.350071	−	1.30648i	−0.0231333	−	0.0863347i	0.953394	−	0.301728i	$-0.0975634\pi$
$229$	−0.350071	−	1.30648i	−0.0231333	−	0.0863347i	−0.976527	+	0.215393i	$0.930897\pi$
$230$	−18.3501	+	10.5944i	−1.20997	+	0.698576i
$231$		0			0
$232$	2.72034	−	0.728913i	0.178599	−	0.0478555i
$233$	18.9116	+	10.9186i	1.23894	+	0.715301i	0.968877	−	0.247542i	$-0.0796229\pi$
$233$	18.9116	+	10.9186i	1.23894	+	0.715301i	0.270061	+	0.962843i	$0.412956\pi$
$234$		0			0
$235$	8.87869	+	15.3783i	0.579182	+	1.00317i
$236$	−6.79207	+	25.3484i	−0.442126	+	1.65004i
$237$		0			0
$238$	9.32572	−	30.1966i	0.604497	−	1.95736i
$239$	−2.43660	+	2.43660i	−0.157611	+	0.157611i	−0.781507	−	0.623896i	$-0.785549\pi$
$239$	−2.43660	+	2.43660i	−0.157611	+	0.157611i	0.623896	+	0.781507i	$0.285549\pi$
$240$		0			0
$241$	1.24212	+	4.63565i	0.0800120	+	0.298609i	0.994323	−	0.106404i	$-0.0339337\pi$
$241$	1.24212	+	4.63565i	0.0800120	+	0.298609i	−0.914311	+	0.405013i	$0.867267\pi$
$242$	8.47333	−	31.6229i	0.544686	−	2.03280i
$243$		0			0
$244$	4.89789	−	8.48339i	0.313555	−	0.543094i
$245$	−5.45481	+	15.5548i	−0.348495	+	0.993762i
$246$		0			0
$247$	14.4678	−	4.76893i	0.920565	−	0.303440i
$248$	11.6911	−	6.74986i	0.742386	−	0.428617i
$249$		0			0
$250$	−20.5233	+	11.8491i	−1.29801	+	0.749405i
$251$	8.94953	+	15.5010i	0.564890	+	0.978417i	0.997060	+	0.0766255i	$0.0244146\pi$
$251$	8.94953	+	15.5010i	0.564890	+	0.978417i	−0.432170	+	0.901792i	$0.642252\pi$
$252$		0			0
$253$	−19.4259	−	5.20516i	−1.22130	−	0.327245i
$254$	1.77664	+	1.77664i	0.111476	+	0.111476i
$255$		0			0
$256$	6.04472	−	10.4698i	0.377795	−	0.654361i
$257$	3.20380	+	5.54914i	0.199847	+	0.346146i	0.948479	−	0.316841i	$-0.102622\pi$
$257$	3.20380	+	5.54914i	0.199847	+	0.346146i	−0.748631	+	0.662986i	$0.769289\pi$
$258$		0			0
$259$	3.12499	+	13.7131i	0.194178	+	0.852090i
$260$	−17.5464	+	19.6545i	−1.08818	+	1.21892i
$261$		0			0
$262$	−1.86876	−	1.86876i	−0.115452	−	0.115452i
$263$	−2.42997			−0.149838			−0.0749191	−	0.997190i	$-0.523870\pi$
$263$	−2.42997			−0.149838			−0.0749191	+	0.997190i	$0.523870\pi$
$264$		0			0
$265$	−1.79189	−	1.79189i	−0.110075	−	0.110075i
$266$	21.3771	+	13.4423i	1.31071	+	0.824200i
$267$		0			0
$268$	−15.9274	+	4.26773i	−0.972920	+	0.260693i
$269$	13.7556	+	7.94178i	0.838691	+	0.484219i	0.856819	−	0.515617i	$-0.172437\pi$
$269$	13.7556	+	7.94178i	0.838691	+	0.484219i	−0.0181279	+	0.999836i	$0.505771\pi$
$270$		0			0
$271$	−8.61532	−	2.30847i	−0.523344	−	0.140230i	−0.0125308	−	0.999921i	$-0.503989\pi$
$271$	−8.61532	−	2.30847i	−0.523344	−	0.140230i	−0.510813	+	0.859692i	$0.670655\pi$
$272$	−3.04853			−0.184844
$273$		0			0
$274$	27.6584			1.67090
$275$	2.65822	+	0.712268i	0.160297	+	0.0429514i
$276$		0			0
$277$	−19.5494	−	11.2868i	−1.17461	−	0.678160i	−0.219846	−	0.975535i	$-0.570555\pi$
$277$	−19.5494	−	11.2868i	−1.17461	−	0.678160i	−0.954761	+	0.297375i	$0.903889\pi$
$278$	43.9543	−	11.7775i	2.63620	−	0.706368i
$279$		0			0
$280$	−15.5157	−	0.585864i	−0.927239	−	0.0350121i
$281$	2.03059	+	2.03059i	0.121135	+	0.121135i	0.765075	−	0.643941i	$-0.222702\pi$
$281$	2.03059	+	2.03059i	0.121135	+	0.121135i	−0.643941	+	0.765075i	$0.722702\pi$
$282$		0			0
$283$	−7.12281			−0.423407			−0.211704	−	0.977334i	$-0.567901\pi$
$283$	−7.12281			−0.423407			−0.211704	+	0.977334i	$0.567901\pi$
$284$	−29.4872	−	29.4872i	−1.74974	−	1.74974i
$285$		0			0
$286$	−41.0583	+	2.32674i	−2.42783	+	0.137583i
$287$	11.2774	−	10.4567i	0.665681	−	0.617239i
$288$		0			0
$289$	−5.48007	−	9.49176i	−0.322357	−	0.558339i
$290$	−3.00570	+	5.20603i	−0.176501	+	0.305709i
$291$		0			0
$292$	3.54657	+	3.54657i	0.207548	+	0.207548i
$293$	−8.65417	−	2.31888i	−0.505582	−	0.135470i	−0.00299266	−	0.999996i	$-0.500953\pi$
$293$	−8.65417	−	2.31888i	−0.505582	−	0.135470i	−0.502589	+	0.864525i	$0.667619\pi$
$294$		0			0
$295$	−9.95678	−	17.2456i	−0.579706	−	1.00408i
$296$	−11.4733	+	6.62411i	−0.666872	+	0.385019i
$297$		0			0
$298$	30.8781	−	17.8275i	1.78872	−	1.03272i
$299$	0.812559	+	14.3387i	0.0469915	+	0.829226i
$300$		0			0
$301$	15.6958	−	24.9608i	0.904692	−	1.43872i
$302$	−18.2815	+	31.6645i	−1.05198	+	1.82209i
$303$		0			0
$304$	0.630442	−	2.35284i	0.0361583	−	0.134945i
$305$	1.92388	+	7.18001i	0.110161	+	0.411126i
$306$		0			0
$307$	16.8943	−	16.8943i	0.964206	−	0.964206i	−0.0351747	−	0.999381i	$-0.511199\pi$
$307$	16.8943	−	16.8943i	0.964206	−	0.964206i	0.999381	+	0.0351747i	$0.0111988\pi$
$308$	−28.1853	−	30.3974i	−1.60601	−	1.73205i
$309$		0			0
$310$	−7.45792	+	27.8333i	−0.423582	+	1.58083i
$311$	8.73808	+	15.1348i	0.495491	+	0.858215i	0.999986	−	0.00519889i	$-0.00165487\pi$
$311$	8.73808	+	15.1348i	0.495491	+	0.858215i	−0.504496	+	0.863414i	$0.668322\pi$
$312$		0			0
$313$	−5.69274	−	3.28670i	−0.321773	−	0.185775i	0.330410	−	0.943838i	$-0.392813\pi$
$313$	−5.69274	−	3.28670i	−0.321773	−	0.185775i	−0.652182	+	0.758062i	$0.726146\pi$
$314$	−19.2787	+	5.16572i	−1.08796	+	0.291518i
$315$		0			0
$316$	−33.9662	+	19.6104i	−1.91075	+	1.10317i
$317$	−8.34364	−	31.1389i	−0.468626	−	1.74894i	−0.644580	−	0.764537i	$-0.722968\pi$
$317$	−8.34364	−	31.1389i	−0.468626	−	1.74894i	0.175954	−	0.984398i	$-0.443699\pi$
$318$		0			0
$319$	−5.51124	+	1.47673i	−0.308570	+	0.0826812i
$320$	7.95283	+	29.6804i	0.444577	+	1.65918i
$321$		0			0
$322$	−17.4573	+	16.1869i	−0.972855	+	0.902059i
$323$	21.5795	−	5.78222i	1.20072	−	0.321731i
$324$		0			0
$325$	−0.111190	−	1.96209i	−0.00616770	−	0.108837i
$326$	8.96870	+	15.5343i	0.496731	+	0.860363i
$327$		0			0
$328$	12.5457	+	7.24325i	0.692719	+	0.399942i
$329$	13.5654	+	14.6301i	0.747887	+	0.806583i
$330$		0			0
$331$	19.1496	−	19.1496i	1.05256	−	1.05256i	0.0540185	−	0.998540i	$-0.482797\pi$
$331$	19.1496	−	19.1496i	1.05256	−	1.05256i	0.998540	−	0.0540185i	$-0.0172030\pi$
$332$	8.19720	+	30.5924i	0.449880	+	1.67897i
$333$		0			0
$334$			22.2480i			1.21736i
$335$	6.25624	−	10.8361i	0.341815	−	0.592041i
$336$		0			0
$337$		−	9.62356i		−	0.524229i	−0.965037	−	0.262114i	$-0.915580\pi$
$337$		−	9.62356i		−	0.524229i	0.965037	−	0.262114i	$-0.0844197\pi$
$338$	10.7569	+	27.3264i	0.585099	+	1.48636i
$339$		0			0
$340$	−27.3224	+	27.3224i	−1.48176	+	1.48176i
$341$	−23.6855	+	13.6748i	−1.28264	+	0.740533i
$342$		0			0
$343$	−2.09247	+	18.4017i	−0.112983	+	0.993597i
$344$	26.8276	+	7.18844i	1.44645	+	0.387575i
$345$		0			0
$346$	7.39771	+	1.98221i	0.397703	+	0.106564i
$347$	−1.14751	+	1.98755i	−0.0616016	+	0.106697i	−0.895181	−	0.445702i	$-0.852954\pi$
$347$	−1.14751	+	1.98755i	−0.0616016	+	0.106697i	0.833580	+	0.552399i	$0.186287\pi$
$348$		0			0
$349$	5.06133	+	18.8891i	0.270927	+	1.01111i	0.958522	+	0.285019i	$0.0919998\pi$
$349$	5.06133	+	18.8891i	0.270927	+	1.01111i	−0.687595	+	0.726094i	$0.741334\pi$
$350$	2.38883	−	2.21499i	0.127689	−	0.118396i
$351$		0			0
$352$	−15.8708	+	27.4891i	−0.845918	+	1.46517i
$353$	−11.7665	−	11.7665i	−0.626267	−	0.626267i	0.320860	−	0.947127i	$-0.396028\pi$
$353$	−11.7665	−	11.7665i	−0.626267	−	0.626267i	−0.947127	+	0.320860i	$0.896028\pi$
$354$		0			0
$355$	31.6440			1.67949
$356$	−19.6166	−	19.6166i	−1.03968	−	1.03968i
$357$		0			0
$358$	3.96524	−	14.7985i	0.209570	−	0.782124i
$359$	−22.5333	+	6.03777i	−1.18926	+	0.318661i	−0.798594	−	0.601870i	$-0.794422\pi$
$359$	−22.5333	+	6.03777i	−1.18926	+	0.318661i	−0.390667	+	0.920532i	$0.627756\pi$
$360$		0			0
$361$		−	1.14920i		−	0.0604845i
$362$	−23.8113	−	6.38023i	−1.25150	−	0.335337i
$363$		0			0
$364$	−14.3151	+	25.9114i	−0.750313	+	1.35812i
$365$	−3.80598			−0.199214
$366$		0			0
$367$			23.9471i			1.25003i	0.780613	+	0.625014i	$0.214907\pi$
$367$			23.9471i			1.25003i	−0.780613	+	0.625014i	$0.785093\pi$
$368$	1.98877	+	1.14822i	0.103672	+	0.0598549i
$369$		0			0
$370$	7.31898	−	27.3148i	0.380496	−	1.42003i
$371$	−2.41030	−	1.51564i	−0.125137	−	0.0786882i
$372$		0			0
$373$	−19.5555			−1.01254			−0.506272	−	0.862374i	$-0.668977\pi$
$373$	−19.5555			−1.01254			−0.506272	+	0.862374i	$0.668977\pi$
$374$	−60.3108			−3.11860
$375$		0			0
$376$	−9.39666	+	16.2755i	−0.484596	+	0.839345i
$377$	2.23362	+	3.40769i	0.115037	+	0.175505i
$378$		0			0
$379$	9.94478	+	37.1144i	0.510829	+	1.90644i	0.411572	+	0.911377i	$0.364980\pi$
$379$	9.94478	+	37.1144i	0.510829	+	1.90644i	0.0992573	+	0.995062i	$0.468353\pi$
$380$	−15.4370	−	26.7376i	−0.791900	−	1.37161i
$381$		0			0
$382$	−2.28058	−	0.611079i	−0.116684	−	0.0312655i
$383$	−4.26748	−	4.26748i	−0.218058	−	0.218058i	0.589622	−	0.807680i	$-0.299277\pi$
$383$	−4.26748	−	4.26748i	−0.218058	−	0.218058i	−0.807680	+	0.589622i	$0.799277\pi$
$384$		0			0
$385$	31.4338	+	1.18693i	1.60202	+	0.0604913i
$386$	−11.1280	−	19.2742i	−0.566398	−	0.981031i
$387$		0			0
$388$	−36.6271	+	36.6271i	−1.85946	+	1.85946i
$389$	19.6532	−	11.3468i	0.996456	−	0.575304i	0.0892580	−	0.996009i	$-0.471550\pi$
$389$	19.6532	−	11.3468i	0.996456	−	0.575304i	0.907198	+	0.420705i	$0.138217\pi$
$390$		0			0
$391$			21.0622i			1.06516i
$392$	−17.1433	+	3.23155i	−0.865866	+	0.163218i
$393$		0			0
$394$		−	13.3622i		−	0.673179i
$395$	7.70292	−	28.7477i	0.387576	−	1.44645i
$396$		0			0
$397$	−21.6586	+	21.6586i	−1.08702	+	1.08702i	−0.0911808	+	0.995834i	$0.529064\pi$
$397$	−21.6586	+	21.6586i	−1.08702	+	1.08702i	−0.995834	+	0.0911808i	$0.970936\pi$
$398$	−8.49190	+	8.49190i	−0.425660	+	0.425660i
$399$		0			0
$400$	−0.272141	−	0.157121i	−0.0136070	−	0.00785603i
$401$	−3.78423	+	14.1230i	−0.188976	+	0.705267i	0.804769	+	0.593588i	$0.202289\pi$
$401$	−3.78423	+	14.1230i	−0.188976	+	0.705267i	−0.993744	+	0.111678i	$0.964377\pi$
$402$		0			0
$403$	14.5696	+	13.0068i	0.725762	+	0.647916i
$404$	−2.05653	−	1.18734i	−0.102316	−	0.0590721i
$405$		0			0
$406$	−1.99303	+	6.45342i	−0.0989125	+	0.320278i
$407$	23.2442	−	13.4201i	1.15217	−	0.665207i
$408$		0			0
$409$	0.688306	−	0.184431i	0.0340346	−	0.00911953i	−0.241762	−	0.970336i	$-0.577725\pi$
$409$	0.688306	−	0.184431i	0.0340346	−	0.00911953i	0.275796	+	0.961216i	$0.411059\pi$
$410$	−29.8679	+	8.00307i	−1.47507	+	0.395243i
$411$		0			0
$412$	14.8810	−	8.59157i	0.733136	−	0.423276i
$413$	−15.2126	−	16.4065i	−0.748564	−	0.807313i
$414$		0			0
$415$	−20.8134	−	12.0166i	−1.02169	−	0.589872i
$416$	22.1916	+	4.61852i	1.08803	+	0.226442i
$417$		0			0
$418$	12.4724	−	46.5477i	0.610046	−	2.27672i
$419$	30.2738	+	17.4786i	1.47897	+	0.853886i	0.999717	−	0.0237891i	$-0.00757303\pi$
$419$	30.2738	+	17.4786i	1.47897	+	0.853886i	0.479257	+	0.877675i	$0.340906\pi$
$420$		0			0
$421$	9.56456	−	9.56456i	0.466148	−	0.466148i	−0.434516	−	0.900664i	$-0.643081\pi$
$421$	9.56456	−	9.56456i	0.466148	−	0.466148i	0.900664	+	0.434516i	$0.143081\pi$
$422$	−27.9960	+	27.9960i	−1.36283	+	1.36283i
$423$		0			0
$424$	0.694141	−	2.59057i	0.0337105	−	0.125809i
$425$		−	2.88212i		−	0.139804i
$426$		0			0
$427$	3.89999	+	7.38524i	0.188734	+	0.357397i
$428$		−	24.0372i		−	1.16188i
$429$		0			0
$430$	−51.3412	+	29.6419i	−2.47589	+	1.42946i
$431$	6.95507	−	6.95507i	0.335014	−	0.335014i	−0.519473	−	0.854487i	$-0.673872\pi$
$431$	6.95507	−	6.95507i	0.335014	−	0.335014i	0.854487	+	0.519473i	$0.173872\pi$
$432$		0			0
$433$	6.68014	+	11.5703i	0.321027	+	0.556035i	0.980700	−	0.195517i	$-0.0626386\pi$
$433$	6.68014	+	11.5703i	0.321027	+	0.556035i	−0.659673	+	0.751553i	$0.729305\pi$
$434$	−1.22162	+	32.3525i	−0.0586394	+	1.55297i
$435$		0			0
$436$	−24.5464	−	24.5464i	−1.17556	−	1.17556i
$437$	−16.2557	−	4.35570i	−0.777616	−	0.208362i
$438$		0			0
$439$	0.272532	+	0.472039i	0.0130072	+	0.0225292i	0.872456	−	0.488693i	$-0.162526\pi$
$439$	0.272532	+	0.472039i	0.0130072	+	0.0225292i	−0.859449	+	0.511222i	$0.829193\pi$
$440$	7.66887	+	28.6206i	0.365599	+	1.36443i
$441$		0			0
$442$	13.4829	+	40.9040i	0.641316	+	1.94560i
$443$	−20.9929	+	36.3608i	−0.997402	+	1.72755i	−0.436319	+	0.899792i	$0.643718\pi$
$443$	−20.9929	+	36.3608i	−0.997402	+	1.72755i	−0.561083	+	0.827760i	$0.689615\pi$
$444$		0			0
$445$	21.0514			0.997933
$446$	30.0100			1.42101
$447$		0			0
$448$	16.1216	+	30.5287i	0.761672	+	1.44235i
$449$	−9.43152	+	35.1989i	−0.445101	+	1.66114i	0.270570	+	0.962700i	$0.412788\pi$
$449$	−9.43152	+	35.1989i	−0.445101	+	1.66114i	−0.715670	+	0.698438i	$0.753879\pi$
$450$		0			0
$451$	−25.4168	−	14.6744i	−1.19683	−	0.690990i
$452$		−	28.7332i		−	1.35150i
$453$		0			0
$454$	45.1228			2.11772
$455$	−6.22225	−	21.5843i	−0.291703	−	1.01189i
$456$		0			0
$457$	0.735237	+	0.197006i	0.0343930	+	0.00921556i	0.275975	−	0.961165i	$-0.410999\pi$
$457$	0.735237	+	0.197006i	0.0343930	+	0.00921556i	−0.241582	+	0.970381i	$0.577666\pi$
$458$			3.05549i			0.142774i
$459$		0			0
$460$	28.1152	−	7.53344i	1.31088	−	0.351248i
$461$	8.56724	−	31.9734i	0.399016	−	1.48915i	−0.415814	−	0.909450i	$-0.636503\pi$
$461$	8.56724	−	31.9734i	0.399016	−	1.48915i	0.814830	−	0.579700i	$-0.196830\pi$
$462$		0			0
$463$	−5.33423	−	5.33423i	−0.247902	−	0.247902i	0.572207	−	0.820109i	$-0.306087\pi$
$463$	−5.33423	−	5.33423i	−0.247902	−	0.247902i	−0.820109	+	0.572207i	$0.806087\pi$
$464$	0.651511			0.0302456
$465$		0			0
$466$	−34.8822	−	34.8822i	−1.61588	−	1.61588i
$467$	−5.83331	+	10.1036i	−0.269933	+	0.467538i	−0.968844	−	0.247670i	$-0.920335\pi$
$467$	−5.83331	+	10.1036i	−0.269933	+	0.467538i	0.698911	+	0.715209i	$0.253668\pi$
$468$		0			0
$469$	4.14841	−	13.4325i	0.191556	−	0.620256i
$470$	−10.3824	−	38.7475i	−0.478903	−	1.78729i
$471$		0			0
$472$	10.5376	−	18.2517i	0.485034	−	0.840104i
$473$	−54.3512	−	14.5634i	−2.49907	−	0.669624i
$474$		0			0
$475$	2.22441	+	0.596030i	0.102063	+	0.0273477i
$476$	−23.1102	+	36.7517i	−1.05925	+	1.68451i
$477$		0			0
$478$	6.74143	−	3.89217i	0.308346	−	0.178024i
$479$	6.06425	−	6.06425i	0.277083	−	0.277083i	−0.554861	−	0.831943i	$-0.687228\pi$
$479$	6.06425	−	6.06425i	0.277083	−	0.277083i	0.831943	+	0.554861i	$0.187228\pi$
$480$		0			0
$481$	−14.2981	−	12.7645i	−0.651939	−	0.582012i
$482$		−	10.8415i		−	0.493816i
$483$		0			0
$484$	−22.4862	+	38.9473i	−1.02210	+	1.77033i
$485$		−	39.3061i		−	1.78480i
$486$		0			0
$487$	10.9821	+	40.9858i	0.497647	+	1.85724i	0.514672	+	0.857387i	$0.327914\pi$
$487$	10.9821	+	40.9858i	0.497647	+	1.85724i	−0.0170255	+	0.999855i	$0.505420\pi$
$488$	−5.56277	+	5.56277i	−0.251815	+	0.251815i
$489$		0			0
$490$	20.9973	−	30.7522i	0.948560	−	1.38924i
$491$	−20.0110	−	11.5533i	−0.903082	−	0.521394i	−0.0248830	−	0.999690i	$-0.507921\pi$
$491$	−20.0110	−	11.5533i	−0.903082	−	0.521394i	−0.878199	+	0.478296i	$0.841255\pi$
$492$		0			0
$493$	2.98773	+	5.17490i	0.134560	+	0.233066i
$494$	−34.3578	+	1.94703i	−1.54583	+	0.0876009i
$495$		0			0
$496$	3.01655	−	0.808283i	0.135447	−	0.0362930i
$497$	34.6652	−	7.89965i	1.55495	−	0.354348i
$498$		0			0
$499$	−8.91242	−	33.2616i	−0.398975	−	1.48899i	−0.814904	−	0.579596i	$-0.803210\pi$
$499$	−8.91242	−	33.2616i	−0.398975	−	1.48899i	0.415929	−	0.909397i	$-0.363456\pi$
$500$	31.4448	−	8.42562i	1.40626	−	0.376805i
$501$		0			0
$502$	−10.4652	−	39.0567i	−0.467085	−	1.74319i
$503$	1.49019	−	0.860359i	0.0664441	−	0.0383615i	−0.466410	−	0.884569i	$-0.654453\pi$
$503$	1.49019	−	0.860359i	0.0664441	−	0.0383615i	0.532854	+	0.846207i	$0.321119\pi$
$504$		0			0
$505$	1.74056	−	0.466382i	0.0774540	−	0.0207537i
$506$	39.3450	+	22.7159i	1.74910	+	1.00984i
$507$		0			0
$508$	−1.72573	−	2.98905i	−0.0765669	−	0.132618i
$509$	−4.08516	+	15.2460i	−0.181071	+	0.675768i	0.814366	+	0.580352i	$0.197085\pi$
$509$	−4.08516	+	15.2460i	−0.181071	+	0.675768i	−0.995437	+	0.0954162i	$0.969582\pi$
$510$		0			0
$511$	−4.16935	+	0.950129i	−0.184441	+	0.0420312i
$512$	4.59484	−	4.59484i	0.203065	−	0.203065i
$513$		0			0
$514$	−3.74639	−	13.9817i	−0.165246	−	0.616707i
$515$	−3.37475	+	12.5947i	−0.148709	+	0.554990i
$516$		0			0
$517$	19.0371	−	32.9732i	0.837249	−	1.45016i
$518$	1.19886	−	31.7498i	0.0526748	−	1.39501i
$519$		0			0
$520$	17.6966	−	11.5995i	0.776048	−	0.508672i
$521$	23.8356	−	13.7615i	1.04426	−	0.602902i	0.123221	−	0.992379i	$-0.460677\pi$
$521$	23.8356	−	13.7615i	1.04426	−	0.602902i	0.921036	+	0.389477i	$0.127344\pi$
$522$		0			0
$523$	24.8550	−	14.3500i	1.08683	−	0.627484i	0.154102	−	0.988055i	$-0.450752\pi$
$523$	24.8550	−	14.3500i	1.08683	−	0.627484i	0.932732	+	0.360571i	$0.117418\pi$
$524$	1.81521	+	3.14404i	0.0792979	+	0.137348i
$525$		0			0
$526$	5.30232	+	1.42075i	0.231192	+	0.0619477i
$527$	20.2536	+	20.2536i	0.882260	+	0.882260i
$528$		0			0
$529$	−3.56702	+	6.17825i	−0.155088	+	0.268620i
$530$	2.86232	+	4.95768i	0.124331	+	0.215348i
$531$		0			0
$532$	−23.5856	−	25.4367i	−1.02257	−	1.10282i
$533$	−4.27035	+	20.5187i	−0.184969	+	0.888764i
$534$		0			0
$535$	12.8977	+	12.8977i	0.557614	+	0.557614i
$536$	13.2424			0.571986
$537$		0			0
$538$	−25.3720	−	25.3720i	−1.09386	−	1.09386i
$539$	34.7312	−	6.54693i	1.49598	−	0.281996i
$540$		0			0
$541$	−12.5009	+	3.34960i	−0.537454	+	0.144010i	−0.517328	−	0.855787i	$-0.673073\pi$
$541$	−12.5009	+	3.34960i	−0.537454	+	0.144010i	−0.0201258	+	0.999797i	$0.506407\pi$
$542$	17.4494	+	10.0744i	0.749515	+	0.432733i
$543$		0			0
$544$	32.1099	+	8.60381i	1.37670	+	0.368885i
$545$	26.3418			1.12836
$546$		0			0
$547$	9.86784			0.421918			0.210959	−	0.977495i	$-0.432341\pi$
$547$	9.86784			0.421918			0.210959	+	0.977495i	$0.432341\pi$
$548$	−36.6994	−	9.83359i	−1.56772	−	0.420070i
$549$		0			0
$550$	−5.38393	−	3.10841i	−0.229572	−	0.132543i
$551$	−4.61184	+	1.23574i	−0.196471	+	0.0526442i
$552$		0			0
$553$	1.26175	−	33.4153i	0.0536549	−	1.42096i
$554$	36.0586	+	36.0586i	1.53198	+	1.53198i
$555$		0			0
$556$	−62.5095			−2.65099
$557$	23.4101	+	23.4101i	0.991919	+	0.991919i	0.999968	−	0.00804826i	$-0.00256187\pi$
$557$	23.4101	+	23.4101i	0.991919	+	0.991919i	−0.00804826	+	0.999968i	$0.502562\pi$
$558$		0			0
$559$	2.27343	+	40.1177i	0.0961560	+	1.69680i
$560$	−3.43194	−	1.05990i	−0.145026	−	0.0447889i
$561$		0			0
$562$	−3.24361	−	5.61810i	−0.136823	−	0.236985i
$563$	19.0236	−	32.9499i	0.801750	−	1.38867i	−0.116714	−	0.993166i	$-0.537236\pi$
$563$	19.0236	−	32.9499i	0.801750	−	1.38867i	0.918464	−	0.395505i	$-0.129431\pi$
$564$		0			0
$565$	15.4174	+	15.4174i	0.648616	+	0.648616i
$566$	15.5424	+	4.16456i	0.653294	+	0.175050i
$567$		0			0
$568$	16.7450	+	29.0033i	0.702606	+	1.21695i
$569$	15.4440	−	8.91660i	0.647446	−	0.373803i	−0.140031	−	0.990147i	$-0.544720\pi$
$569$	15.4440	−	8.91660i	0.647446	−	0.373803i	0.787477	+	0.616344i	$0.211387\pi$
$570$		0			0
$571$	−35.0123	+	20.2143i	−1.46522	+	0.845944i	−0.999245	−	0.0388557i	$-0.987629\pi$
$571$	−35.0123	+	20.2143i	−1.46522	+	0.845944i	−0.465972	+	0.884799i	$0.654295\pi$
$572$	55.3069	+	11.5105i	2.31250	+	0.481276i
$573$		0			0
$574$	−30.7216	+	16.2234i	−1.28229	+	0.677152i
$575$	−1.08554	+	1.88021i	−0.0452702	+	0.0784103i
$576$		0			0
$577$	−0.274766	+	1.02544i	−0.0114387	+	0.0426897i	−0.971409	−	0.237411i	$-0.923701\pi$
$577$	−0.274766	+	1.02544i	−0.0114387	+	0.0426897i	0.959971	+	0.280101i	$0.0903679\pi$
$578$	6.40816	+	23.9156i	0.266545	+	0.994758i
$579$		0			0
$580$	5.83915	−	5.83915i	0.242458	−	0.242458i
$581$	−25.8004	−	7.96801i	−1.07038	−	0.330569i
$582$		0			0
$583$	−1.40629	+	5.24834i	−0.0582425	+	0.217364i
$584$	−2.01401	−	3.48837i	−0.0833403	−	0.144350i
$585$		0			0
$586$	17.5281	+	10.1198i	0.724078	+	0.418046i
$587$	−24.5244	+	6.57129i	−1.01223	+	0.271226i	−0.726561	−	0.687102i	$-0.758882\pi$
$587$	−24.5244	+	6.57129i	−1.01223	+	0.271226i	−0.285669	+	0.958328i	$0.592216\pi$
$588$		0			0
$589$	−19.8201	+	11.4432i	−0.816674	+	0.471507i
$590$	11.6430	+	43.4524i	0.479336	+	1.78891i
$591$		0			0
$592$	−2.96036	+	0.793225i	−0.121670	+	0.0326013i
$593$	−3.58927	−	13.3953i	−0.147394	−	0.550081i	−0.999637	−	0.0269353i	$-0.991425\pi$
$593$	−3.58927	−	13.3953i	−0.147394	−	0.550081i	0.852244	−	0.523145i	$-0.175241\pi$
$594$		0			0
$595$	−7.31968	−	32.1202i	−0.300078	−	1.31680i
$596$	−47.3099	+	12.6766i	−1.93789	+	0.519256i
$597$		0			0
$598$	6.61047	−	31.7628i	0.270322	−	1.29888i
$599$	15.3267	+	26.5466i	0.626232	+	1.08467i	0.988301	+	0.152515i	$0.0487371\pi$
$599$	15.3267	+	26.5466i	0.626232	+	1.08467i	−0.362069	+	0.932151i	$0.617930\pi$
$600$		0			0
$601$	8.40143	+	4.85057i	0.342701	+	0.197859i	0.661466	−	0.749975i	$-0.269935\pi$
$601$	8.40143	+	4.85057i	0.342701	+	0.197859i	−0.318765	+	0.947834i	$0.603268\pi$
$602$	−48.8432	+	45.2888i	−1.99070	+	1.84583i
$603$		0			0
$604$	35.5153	−	35.5153i	1.44510	−	1.44510i
$605$	−8.83254	−	32.9635i	−0.359094	−	1.34016i
$606$		0			0
$607$			14.6956i			0.596475i	0.954492	+	0.298238i	$0.0963988\pi$
$607$			14.6956i			0.596475i	−0.954492	+	0.298238i	$0.903601\pi$
$608$	−13.2808	+	23.0030i	−0.538607	+	0.932895i
$609$		0			0
$610$		−	16.7920i		−	0.679889i
$611$	−26.6189	−	5.53992i	−1.07689	−	0.224121i
$612$		0			0
$613$	−25.7393	+	25.7393i	−1.03960	+	1.03960i	−0.0404173	+	0.999183i	$0.512869\pi$
$613$	−25.7393	+	25.7393i	−1.03960	+	1.03960i	−0.999183	+	0.0404173i	$0.987131\pi$
$614$	−46.7419	+	26.9864i	−1.88635	+	1.08908i
$615$		0			0
$616$	15.5459	+	29.4387i	0.626364	+	1.18612i
$617$	−11.0647	−	2.96476i	−0.445446	−	0.119357i	0.0291217	−	0.999576i	$-0.490729\pi$
$617$	−11.0647	−	2.96476i	−0.445446	−	0.119357i	−0.474568	+	0.880219i	$0.657396\pi$
$618$		0			0
$619$	42.1253	+	11.2874i	1.69316	+	0.453681i	0.971202	−	0.238257i	$-0.0765761\pi$
$619$	42.1253	+	11.2874i	1.69316	+	0.453681i	0.721957	+	0.691938i	$0.243243\pi$
$620$	19.7916	−	34.2800i	0.794849	−	1.37672i
$621$		0			0
$622$	−10.2179	−	38.1339i	−0.409702	−	1.52903i
$623$	23.0613	−	5.25530i	0.923932	−	0.210549i
$624$		0			0
$625$	−13.7141	+	23.7535i	−0.548564	+	0.950141i
$626$	10.5002	+	10.5002i	0.419672	+	0.419672i
$627$		0			0
$628$	27.4172			1.09407
$629$	−19.8763	−	19.8763i	−0.792518	−	0.792518i
$630$		0			0
$631$	−0.0773405	+	0.288639i	−0.00307888	+	0.0114905i	−0.967448	−	0.253069i	$-0.918560\pi$
$631$	−0.0773405	+	0.288639i	−0.00307888	+	0.0114905i	0.964369	+	0.264560i	$0.0852266\pi$
$632$	30.4248	−	8.15230i	1.21023	−	0.324281i
$633$		0			0
$634$			72.8251i			2.89225i
$635$	2.52982	+	0.677862i	0.100393	+	0.0269001i
$636$		0			0
$637$	−12.2047	−	22.0918i	−0.483566	−	0.875308i
$638$	12.8892			0.510290
$639$		0			0
$640$		−	39.8060i		−	1.57347i
$641$	−4.23982	−	2.44786i	−0.167463	−	0.0966847i	0.413926	−	0.910310i	$-0.364157\pi$
$641$	−4.23982	−	2.44786i	−0.167463	−	0.0966847i	−0.581389	+	0.813626i	$0.697491\pi$
$642$		0			0
$643$	11.4094	−	42.5806i	0.449944	−	1.67921i	−0.252598	−	0.967571i	$-0.581285\pi$
$643$	11.4094	−	42.5806i	0.449944	−	1.67921i	0.702542	−	0.711643i	$-0.252048\pi$
$644$	28.9188	−	15.2714i	1.13956	−	0.601777i
$645$		0			0
$646$	−50.4684			−1.98565
$647$	2.94231			0.115674			0.0578370	−	0.998326i	$-0.481580\pi$
$647$	2.94231			0.115674			0.0578370	+	0.998326i	$0.481580\pi$
$648$		0			0
$649$	−21.3486	+	36.9769i	−0.838007	+	1.45147i
$650$	−0.904570	+	4.34639i	−0.0354802	+	0.170479i
$651$		0			0
$652$	−6.37742	−	23.8009i	−0.249759	−	0.932113i
$653$	3.97706	+	6.88846i	0.155634	+	0.269566i	0.933290	−	0.359124i	$-0.116925\pi$
$653$	3.97706	+	6.88846i	0.155634	+	0.269566i	−0.777656	+	0.628691i	$0.783591\pi$
$654$		0			0
$655$	−2.66099	−	0.713011i	−0.103974	−	0.0278596i
$656$	2.36969	+	2.36969i	0.0925207	+	0.0925207i
$657$		0			0
$658$	−21.0466	−	39.8551i	−0.820482	−	1.55371i
$659$	−1.30483	−	2.26004i	−0.0508291	−	0.0880385i	0.839491	−	0.543373i	$-0.182853\pi$
$659$	−1.30483	−	2.26004i	−0.0508291	−	0.0880385i	−0.890320	+	0.455334i	$0.849520\pi$
$660$		0			0
$661$	20.7944	−	20.7944i	0.808808	−	0.808808i	−0.175646	−	0.984453i	$-0.556201\pi$
$661$	20.7944	−	20.7944i	0.808808	−	0.808808i	0.984453	+	0.175646i	$0.0562013\pi$
$662$	−52.9819	+	30.5891i	−2.05920	+	1.18888i
$663$		0			0
$664$		−	25.4353i		−	0.987081i
$665$	26.3040	+	0.993226i	1.02002	+	0.0385156i
$666$		0			0
$667$		−	4.50127i		−	0.174290i
$668$	7.91000	−	29.5205i	0.306047	−	1.14218i
$669$		0			0
$670$	−19.9871	+	19.9871i	−0.772169	+	0.772169i
$671$	11.2698	−	11.2698i	0.435067	−	0.435067i
$672$		0			0
$673$	16.3940	+	9.46510i	0.631943	+	0.364853i	0.781504	−	0.623900i	$-0.214453\pi$
$673$	16.3940	+	9.46510i	0.631943	+	0.364853i	−0.149561	+	0.988753i	$0.547786\pi$
$674$	−5.62669	+	20.9991i	−0.216732	+	0.808855i
$675$		0			0
$676$	−4.55761	−	40.0834i	−0.175293	−	1.54167i
$677$	−42.4727	−	24.5216i	−1.63236	−	0.942443i	−0.983363	−	0.181650i	$-0.941856\pi$
$677$	−42.4727	−	24.5216i	−1.63236	−	0.942443i	−0.648995	−	0.760793i	$-0.724810\pi$
$678$		0			0
$679$	−9.81242	−	43.0588i	−0.376566	−	1.65245i
$680$	26.8739	−	15.5157i	1.03057	−	0.594999i
$681$		0			0
$682$	59.6783	−	15.9908i	2.28520	−	0.612318i
$683$	−31.9962	+	8.57335i	−1.22430	+	0.328050i	−0.812357	−	0.583160i	$-0.801816\pi$
$683$	−31.9962	+	8.57335i	−1.22430	+	0.328050i	−0.411942	+	0.911210i	$0.635149\pi$
$684$		0			0
$685$	24.9683	−	14.4155i	0.953990	−	0.550786i
$686$	15.3250	−	38.9300i	0.585110	−	1.48635i
$687$		0			0
$688$	5.56431	+	3.21256i	0.212138	+	0.122478i
$689$	3.87391	−	0.219531i	0.147584	−	0.00836345i
$690$		0			0
$691$	−1.36491	+	5.09390i	−0.0519235	+	0.193781i	−0.987016	−	0.160623i	$-0.948650\pi$
$691$	−1.36491	+	5.09390i	−0.0519235	+	0.193781i	0.935092	+	0.354404i	$0.115316\pi$
$692$	−9.11115	−	5.26032i	−0.346354	−	0.199968i
$693$		0			0
$694$	3.66600	−	3.66600i	0.139160	−	0.139160i
$695$	33.5408	−	33.5408i	1.27228	−	1.27228i
$696$		0			0
$697$	−7.95521	+	29.6892i	−0.301325	+	1.12456i
$698$		−	44.1764i		−	1.67210i
$699$		0			0
$700$	−3.95722	+	2.08972i	−0.149569	+	0.0789840i
$701$			16.2025i			0.611960i	0.952038	+	0.305980i	$0.0989841\pi$
$701$			16.2025i			0.611960i	−0.952038	+	0.305980i	$0.901016\pi$
$702$		0			0
$703$	19.4509	−	11.2300i	0.733604	−	0.423546i
$704$	46.5867	−	46.5867i	1.75580	−	1.75580i
$705$		0			0
$706$	18.7955	+	32.5547i	0.707377	+	1.22521i
$707$	1.79031	−	0.945426i	0.0673317	−	0.0355564i
$708$		0			0
$709$	18.4817	+	18.4817i	0.694096	+	0.694096i	0.963131	−	0.269034i	$-0.0867045\pi$
$709$	18.4817	+	18.4817i	0.694096	+	0.694096i	−0.269034	+	0.963131i	$0.586704\pi$
$710$	−69.0489	−	18.5016i	−2.59136	−	0.694353i
$711$		0			0
$712$	11.1398	+	19.2947i	0.417481	+	0.723098i
$713$	−5.58440	−	20.8413i	−0.209137	−	0.780512i
$714$		0			0
$715$	−35.8523	+	23.4999i	−1.34080	+	0.878846i
$716$	−10.5228	+	18.2261i	−0.393256	+	0.681140i
$717$		0			0
$718$	52.6990			1.96671
$719$	−12.7257			−0.474588			−0.237294	−	0.971438i	$-0.576260\pi$
$719$	−12.7257			−0.474588			−0.237294	+	0.971438i	$0.576260\pi$
$720$		0			0
$721$	−0.552787	+	14.6397i	−0.0205869	+	0.545210i
$722$	−0.671916	+	2.50763i	−0.0250061	+	0.0933242i
$723$		0			0
$724$	29.3265	+	16.9316i	1.08991	+	0.629259i
$725$			0.615948i			0.0228758i
$726$		0			0
$727$	43.5266			1.61431			0.807157	−	0.590337i	$-0.201005\pi$
$727$	43.5266			1.61431			0.807157	+	0.590337i	$0.201005\pi$
$728$	16.4905	−	17.1248i	0.611178	−	0.634686i
$729$		0			0
$730$	8.30485	+	2.22528i	0.307376	+	0.0823612i
$731$			58.9292i			2.17958i
$732$		0			0
$733$	−33.2097	+	8.89851i	−1.22663	+	0.328674i	−0.813265	−	0.581893i	$-0.802312\pi$
$733$	−33.2097	+	8.89851i	−1.22663	+	0.328674i	−0.413362	+	0.910567i	$0.635646\pi$
$734$	14.0014	−	52.2538i	0.516800	−	1.92872i
$735$		0			0
$736$	−17.7069	−	17.7069i	−0.652686	−	0.652686i
$737$	−26.8284			−0.988236
$738$		0			0
$739$	−11.8263	−	11.8263i	−0.435038	−	0.435038i	0.455300	−	0.890338i	$-0.349532\pi$
$739$	−11.8263	−	11.8263i	−0.435038	−	0.435038i	−0.890338	+	0.455300i	$0.849532\pi$
$740$	−19.4229	+	33.6414i	−0.713999	+	1.23668i
$741$		0			0
$742$	4.37324	+	4.71646i	0.160547	+	0.173147i
$743$	5.21828	+	19.4749i	0.191440	+	0.714465i	0.993160	+	0.116764i	$0.0372521\pi$
$743$	5.21828	+	19.4749i	0.191440	+	0.714465i	−0.801719	+	0.597700i	$0.796081\pi$
$744$		0			0
$745$	18.5832	−	32.1871i	0.680836	−	1.17924i
$746$	42.6711	+	11.4337i	1.56230	+	0.418617i
$747$		0			0
$748$	80.0255	+	21.4428i	2.92602	+	0.784025i
$749$	17.3488	+	10.9093i	0.633913	+	0.398616i
$750$		0			0
$751$	16.8568	−	9.73227i	0.615113	−	0.355136i	−0.159851	−	0.987141i	$-0.551101\pi$
$751$	16.8568	−	9.73227i	0.615113	−	0.355136i	0.774964	+	0.632006i	$0.217768\pi$
$752$	−3.07419	+	3.07419i	−0.112104	+	0.112104i
$753$		0			0
$754$	−2.88148	−	8.74172i	−0.104937	−	0.318355i
$755$			38.1130i			1.38707i
$756$		0			0
$757$	6.53791	−	11.3240i	0.237624	−	0.411577i	−0.722408	−	0.691467i	$-0.756965\pi$
$757$	6.53791	−	11.3240i	0.237624	−	0.411577i	0.960032	+	0.279890i	$0.0902980\pi$
$758$		−	86.8001i		−	3.15272i
$759$		0			0
$760$	6.41735	+	23.9499i	0.232782	+	0.868754i
$761$	31.1657	−	31.1657i	1.12975	−	1.12975i	0.139537	−	0.990217i	$-0.455438\pi$
$761$	31.1657	−	31.1657i	1.12975	−	1.12975i	0.990217	−	0.139537i	$-0.0445616\pi$
$762$		0			0
$763$	28.8567	−	6.57599i	1.04468	−	0.238067i
$764$	2.80880	+	1.62166i	0.101619	+	0.0586696i
$765$		0			0
$766$	6.81676	+	11.8070i	0.246299	+	0.426603i
$767$	29.8511	+	6.21260i	1.07786	+	0.224324i
$768$		0			0
$769$	−12.8186	+	3.43473i	−0.462250	+	0.123860i	−0.482426	−	0.875937i	$-0.660244\pi$
$769$	−12.8186	+	3.43473i	−0.462250	+	0.123860i	0.0201755	+	0.999796i	$0.493578\pi$
$770$	−67.8963	−	20.9686i	−2.44681	−	0.755657i
$771$		0			0
$772$	7.91281	+	29.5310i	0.284788	+	1.06284i
$773$	16.4501	−	4.40779i	0.591669	−	0.158537i	0.0494533	−	0.998776i	$-0.484252\pi$
$773$	16.4501	−	4.40779i	0.591669	−	0.158537i	0.542216	+	0.840239i	$0.317585\pi$
$774$		0			0
$775$	0.764163	+	2.85190i	0.0274496	+	0.102443i
$776$	36.0259	−	20.7996i	1.29326	−	0.746662i
$777$		0			0
$778$	−49.5185	+	13.2684i	−1.77532	+	0.475697i
$779$	−21.2689	−	12.2796i	−0.762038	−	0.439963i
$780$		0			0
$781$	−33.9244	−	58.7589i	−1.21391	−	2.10256i
$782$	12.3146	−	45.9588i	0.440370	−	1.64348i
$783$		0			0
$784$	−4.02420	−	0.304338i	−0.143722	−	0.0108692i
$785$	−14.7113	+	14.7113i	−0.525069	+	0.525069i
$786$		0			0
$787$	4.78972	+	17.8755i	0.170735	+	0.637192i	0.997239	+	0.0742610i	$0.0236598\pi$
$787$	4.78972	+	17.8755i	0.170735	+	0.637192i	−0.826504	+	0.562931i	$0.809674\pi$
$788$	−4.75077	+	17.7301i	−0.169239	+	0.631609i
$789$		0			0
$790$	−33.6164	+	58.2252i	−1.19602	+	2.07156i
$791$	20.7382	+	13.0406i	0.737367	+	0.463670i
$792$		0			0
$793$	−10.1629	−	5.12397i	−0.360894	−	0.181957i
$794$	59.9236	−	34.5969i	2.12661	−	1.22780i
$795$		0			0
$796$	14.2869	−	8.24857i	0.506387	−	0.292363i
$797$	0.826191	+	1.43100i	0.0292652	+	0.0506888i	0.880287	−	0.474441i	$-0.157350\pi$
$797$	0.826191	+	1.43100i	0.0292652	+	0.0506888i	−0.851022	+	0.525130i	$0.824017\pi$
$798$		0			0
$799$	−38.5158	−	10.3203i	−1.36259	−	0.365105i
$800$	2.42300	+	2.42300i	0.0856659	+	0.0856659i
$801$		0			0
$802$	16.5148	−	28.6045i	0.583158	−	1.01006i
$803$	4.08026	+	7.06722i	0.143989	+	0.249397i
$804$		0			0
$805$	−7.32281	+	23.7112i	−0.258095	+	0.835710i
$806$	−24.1867	−	36.9001i	−0.851941	−	1.29975i
$807$		0			0
$808$	1.34851	+	1.34851i	0.0474406	+	0.0474406i
$809$	39.0959			1.37454			0.687270	−	0.726402i	$-0.258809\pi$
$809$	39.0959			1.37454			0.687270	+	0.726402i	$0.258809\pi$
$810$		0			0
$811$	−13.7840	−	13.7840i	−0.484023	−	0.484023i	0.422391	−	0.906414i	$-0.361191\pi$
$811$	−13.7840	−	13.7840i	−0.484023	−	0.484023i	−0.906414	+	0.422391i	$0.861191\pi$
$812$	4.93895	−	7.85434i	0.173323	−	0.275633i
$813$		0			0
$814$	−58.5665	+	15.6929i	−2.05276	+	0.550034i
$815$	16.1928	+	9.34892i	0.567209	+	0.327478i
$816$		0			0
$817$	−45.4814	−	12.1867i	−1.59119	−	0.426358i
$818$	−1.60975			−0.0562837
$819$		0			0
$820$	42.4766			1.48335
$821$	8.58998	+	2.30168i	0.299792	+	0.0803291i	0.405580	−	0.914060i	$-0.367070\pi$
$821$	8.58998	+	2.30168i	0.299792	+	0.0803291i	−0.105787	+	0.994389i	$0.533736\pi$
$822$		0			0
$823$	33.8210	+	19.5266i	1.17893	+	0.680654i	0.955766	−	0.294128i	$-0.0950292\pi$
$823$	33.8210	+	19.5266i	1.17893	+	0.680654i	0.223161	+	0.974782i	$0.428362\pi$
$824$	−13.3295	+	3.57163i	−0.464355	+	0.124423i
$825$		0			0
$826$	23.6022	+	44.6944i	0.821224	+	1.55512i
$827$	23.1975	+	23.1975i	0.806658	+	0.806658i	0.984126	−	0.177469i	$-0.0567908\pi$
$827$	23.1975	+	23.1975i	0.806658	+	0.806658i	−0.177469	+	0.984126i	$0.556791\pi$
$828$		0			0
$829$	−22.8221			−0.792644			−0.396322	−	0.918112i	$-0.629714\pi$
$829$	−22.8221			−0.792644			−0.396322	+	0.918112i	$0.629714\pi$
$830$	38.3900	+	38.3900i	1.33254	+	1.33254i
$831$		0			0
$832$	−42.0107	−	21.1812i	−1.45646	−	0.734325i
$833$	−16.0370	−	33.3596i	−0.555651	−	1.15584i
$834$		0			0
$835$	11.5956	+	20.0841i	0.401282	+	0.695041i
$836$	−33.0989	+	57.3290i	−1.14475	+	1.98276i
$837$		0			0
$838$	−55.8397	−	55.8397i	−1.92895	−	1.92895i
$839$	−5.67692	−	1.52113i	−0.195989	−	0.0525151i	0.159489	−	0.987200i	$-0.449015\pi$
$839$	−5.67692	−	1.52113i	−0.195989	−	0.0525151i	−0.355478	+	0.934685i	$0.615682\pi$
$840$		0			0
$841$	13.8615	+	24.0088i	0.477982	+	0.827889i
$842$	−26.4626	+	15.2782i	−0.911960	+	0.526520i
$843$		0			0
$844$	47.1011	−	27.1939i	1.62129	−	0.936051i
$845$	23.9531	+	19.0621i	0.824011	+	0.655757i
$846$		0			0
$847$	−17.9049	−	33.9057i	−0.615219	−	1.16501i
$848$	0.310216	−	0.537309i	0.0106529	−	0.0184513i
$849$		0			0
$850$	−1.68512	+	6.28895i	−0.0577991	+	0.215709i
$851$	5.48036	+	20.4530i	0.187864	+	0.701120i
$852$		0			0
$853$	−19.3964	+	19.3964i	−0.664121	+	0.664121i	−0.956349	−	0.292228i	$-0.905603\pi$
$853$	−19.3964	+	19.3964i	−0.664121	+	0.664121i	0.292228	+	0.956349i	$0.405603\pi$
$854$	−4.19198	−	18.3952i	−0.143447	−	0.629472i
$855$		0			0
$856$	−4.99628	+	18.6464i	−0.170769	+	0.637320i
$857$	−2.06684	−	3.57986i	−0.0706017	−	0.122286i	0.828563	−	0.559895i	$-0.189159\pi$
$857$	−2.06684	−	3.57986i	−0.0706017	−	0.122286i	−0.899165	+	0.437609i	$0.855825\pi$
$858$		0			0
$859$	−36.1933	−	20.8962i	−1.23490	−	0.712969i	−0.266851	−	0.963738i	$-0.585983\pi$
$859$	−36.1933	−	20.8962i	−1.23490	−	0.712969i	−0.968047	+	0.250769i	$0.919317\pi$
$860$	78.6626	−	21.0776i	2.68237	−	0.718739i
$861$		0			0
$862$	−19.2428	+	11.1099i	−0.655413	+	0.378403i
$863$	0.399033	+	1.48921i	0.0135832	+	0.0506933i	0.972385	−	0.233383i	$-0.0749797\pi$
$863$	0.399033	+	1.48921i	0.0135832	+	0.0506933i	−0.958802	+	0.284077i	$0.908313\pi$
$864$		0			0
$865$	7.71132	−	2.06624i	0.262193	−	0.0702544i
$866$	−7.81148	−	29.1529i	−0.265445	−	0.990654i
$867$		0			0
$868$	13.1235	−	42.4937i	0.445440	−	1.44233i
$869$	−61.6388	+	16.5161i	−2.09095	+	0.560269i
$870$		0			0
$871$	5.99767	+	18.1955i	0.203223	+	0.616532i
$872$	13.9393	+	24.1435i	0.472043	+	0.817602i
$873$		0			0
$874$	32.9241	+	19.0088i	1.11368	+	0.642981i
$875$	−8.19005	+	26.5193i	−0.276874	+	0.896516i
$876$		0			0
$877$	−37.8335	+	37.8335i	−1.27755	+	1.27755i	−0.335511	+	0.942036i	$0.608909\pi$
$877$	−37.8335	+	37.8335i	−1.27755	+	1.27755i	−0.942036	+	0.335511i	$0.891091\pi$
$878$	−0.318687	−	1.18936i	−0.0107552	−	0.0401389i
$879$		0			0
$880$			6.85453i			0.231066i
$881$	−10.7817	+	18.6745i	−0.363246	+	0.629160i	−0.988493	−	0.151266i	$-0.951665\pi$
$881$	−10.7817	+	18.6745i	−0.363246	+	0.629160i	0.625247	+	0.780427i	$0.284998\pi$
$882$		0			0
$883$		−	28.6771i		−	0.965061i	−0.875879	−	0.482530i	$-0.839718\pi$
$883$		−	28.6771i		−	0.965061i	0.875879	−	0.482530i	$-0.160282\pi$
$884$	−3.34735	−	59.0685i	−0.112584	−	1.98669i
$885$		0			0
$886$	67.0670	−	67.0670i	2.25316	−	2.25316i
$887$	21.9875	−	12.6945i	0.738269	−	0.426240i	−0.0831704	−	0.996535i	$-0.526505\pi$
$887$	21.9875	−	12.6945i	0.738269	−	0.426240i	0.821440	+	0.570295i	$0.193171\pi$
$888$		0			0
$889$	2.94057	+	0.111035i	0.0986236	+	0.00372398i
$890$	−45.9353	−	12.3083i	−1.53976	−	0.412576i
$891$		0			0
$892$	−39.8197	−	10.6697i	−1.33326	−	0.357247i
$893$	15.9303	−	27.5921i	0.533088	−	0.923335i
$894$		0			0
$895$	−4.13334	−	15.4258i	−0.138162	−	0.515629i
$896$	−9.93722	−	43.6065i	−0.331979	−	1.45679i
$897$		0			0
$898$	41.1601	−	71.2914i	1.37353	−	2.37903i
$899$	−4.32846	−	4.32846i	−0.144362	−	0.144362i
$900$		0			0
$901$	5.69041			0.189575
$902$	46.8810	+	46.8810i	1.56097	+	1.56097i
$903$		0			0
$904$	−5.97239	+	22.2893i	−0.198639	+	0.741330i
$905$	−24.8208	+	6.65070i	−0.825070	+	0.221077i
$906$		0			0
$907$			19.4640i			0.646293i	0.946349	+	0.323146i	$0.104741\pi$
$907$			19.4640i			0.646293i	−0.946349	+	0.323146i	$0.895259\pi$
$908$	−59.8727	−	16.0429i	−1.98695	−	0.532401i
$909$		0			0
$910$	0.957351	+	50.7362i	0.0317359	+	1.68189i
$911$	50.4080			1.67009			0.835046	−	0.550180i	$-0.185441\pi$
$911$	50.4080			1.67009			0.835046	+	0.550180i	$0.185441\pi$
$912$		0			0
$913$			51.5304i			1.70541i
$914$	−1.48914	−	0.859756i	−0.0492564	−	0.0284382i
$915$		0			0
$916$	1.08634	−	4.05428i	0.0358937	−	0.133957i
$917$	−3.09305	−	0.116792i	−0.102141	−	0.00385681i
$918$		0			0
$919$	−56.5934			−1.86684			−0.933422	−	0.358781i	$-0.883193\pi$
$919$	−56.5934			−1.86684			−0.933422	+	0.358781i	$0.883193\pi$
$920$	−23.3757			−0.770673
$921$		0			0
$922$	−37.3884	+	64.7585i	−1.23132	+	2.13271i
$923$	−32.2673	+	36.1441i	−1.06209	+	1.18970i
$924$		0			0
$925$	−0.749927	−	2.79877i	−0.0246575	−	0.0920229i
$926$	8.52075	+	14.7584i	0.280009	+	0.484990i
$927$		0			0
$928$	−6.86231	−	1.83875i	−0.225266	−	0.0603599i
$929$	2.62133	+	2.62133i	0.0860029	+	0.0860029i	0.748799	−	0.662797i	$-0.230631\pi$
$929$	2.62133	+	2.62133i	0.0860029	+	0.0860029i	−0.662797	+	0.748799i	$0.730631\pi$
$930$		0			0
$931$	29.0633	−	5.47850i	0.952511	−	0.179551i
$932$	33.8826	+	58.6865i	1.10986	+	1.92234i
$933$		0			0
$934$	18.6359	−	18.6359i	0.609787	−	0.609787i
$935$	−54.4449	+	31.4338i	−1.78054	+	1.02800i
$936$		0			0
$937$			24.1869i			0.790151i	0.918649	+	0.395076i	$0.129282\pi$
$937$			24.1869i			0.790151i	−0.918649	+	0.395076i	$0.870718\pi$
$938$	−16.9058	+	26.8850i	−0.551993	+	0.877825i
$939$		0			0
$940$			55.1048i			1.79732i
$941$	5.44880	−	20.3352i	0.177626	−	0.662909i	−0.818464	−	0.574558i	$-0.805174\pi$
$941$	5.44880	−	20.3352i	0.177626	−	0.662909i	0.996089	−	0.0883504i	$-0.0281595\pi$
$942$		0			0
$943$	16.3721	−	16.3721i	0.533149	−	0.533149i
$944$	3.44747	−	3.44747i	0.112206	−	0.112206i
$945$		0			0
$946$	110.082	+	63.5560i	3.57908	+	2.06638i
$947$	8.82979	−	32.9532i	0.286930	−	1.07084i	−0.660488	−	0.750836i	$-0.729651\pi$
$947$	8.82979	−	32.9532i	0.286930	−	1.07084i	0.947418	−	0.319999i	$-0.103683\pi$
$948$		0			0
$949$	3.88095	−	4.34723i	0.125981	−	0.141117i
$950$	−4.50530	−	2.60114i	−0.146171	−	0.0843920i
$951$		0			0
$952$	25.5664	−	23.7059i	0.828610	−	0.768311i
$953$	−42.0367	+	24.2699i	−1.36170	+	0.786180i	−0.989851	−	0.142111i	$-0.954611\pi$
$953$	−42.0367	+	24.2699i	−1.36170	+	0.786180i	−0.371853	+	0.928292i	$0.621278\pi$
$954$		0			0
$955$	−2.37726	+	0.636984i	−0.0769263	+	0.0206123i
$956$	−10.3289	+	2.76762i	−0.334061	+	0.0895113i
$957$		0			0
$958$	−16.7782	+	9.68687i	−0.542078	+	0.312969i
$959$	23.7534	−	22.0249i	0.767039	−	0.711220i
$960$		0			0
$961$	1.43561	+	0.828853i	0.0463102	+	0.0267372i
$962$	23.7361	+	36.2127i	0.765284	+	1.16754i
$963$		0			0
$964$	−3.85455	+	14.3854i	−0.124147	+	0.463322i
$965$	−20.0913	−	11.5997i	−0.646761	−	0.373408i
$966$		0			0
$967$	5.80997	−	5.80997i	0.186836	−	0.186836i	−0.607491	−	0.794327i	$-0.707824\pi$
$967$	5.80997	−	5.80997i	0.186836	−	0.186836i	0.794327	+	0.607491i	$0.207824\pi$
$968$	25.5387	−	25.5387i	0.820846	−	0.820846i
$969$		0			0
$970$	−22.9815	+	85.7680i	−0.737890	+	2.75384i
$971$		−	13.1439i		−	0.421806i	−0.977507	−	0.210903i	$-0.932360\pi$
$971$		−	13.1439i		−	0.421806i	0.977507	−	0.210903i	$-0.0676405\pi$
$972$		0			0
$973$	28.3700	−	45.1163i	0.909499	−	1.44636i
$974$		−	95.8541i		−	3.07136i
$975$		0			0
$976$	−1.57608	+	0.909952i	−0.0504492	+	0.0291269i
$977$	6.93033	−	6.93033i	0.221721	−	0.221721i	−0.587502	−	0.809223i	$-0.699889\pi$
$977$	6.93033	−	6.93033i	0.221721	−	0.221721i	0.809223	+	0.587502i	$0.199889\pi$
$978$		0			0
$979$	−22.5685	−	39.0898i	−0.721292	−	1.24932i
$980$	−38.7945	+	33.3392i	−1.23924	+	1.06498i
$981$		0			0
$982$	36.9100	+	36.9100i	1.17784	+	1.17784i
$983$	52.1268	+	13.9673i	1.66259	+	0.445489i	0.963097	−	0.269154i	$-0.0867440\pi$
$983$	52.1268	+	13.9673i	1.66259	+	0.445489i	0.699490	+	0.714643i	$0.253411\pi$
$984$		0			0
$985$	−6.96434	−	12.0626i	−0.221902	−	0.384346i
$986$	−3.49373	−	13.0388i	−0.111263	−	0.415239i
$987$		0			0
$988$	46.2811	+	9.63201i	1.47240	+	0.306435i
$989$	22.1955	−	38.4437i	0.705775	−	1.22244i
$990$		0			0
$991$	−45.8226			−1.45560			−0.727801	−	0.685789i	$-0.759457\pi$
$991$	−45.8226			−1.45560			−0.727801	+	0.685789i	$0.759457\pi$
$992$	−34.0543			−1.08123
$993$		0			0
$994$	−80.2601	−	3.03058i	−2.54569	−	0.0961242i
$995$	−3.24002	+	12.0919i	−0.102716	+	0.383339i
$996$		0			0
$997$	−14.5145	−	8.37997i	−0.459680	−	0.265396i	0.252230	−	0.967667i	$-0.418836\pi$
$997$	−14.5145	−	8.37997i	−0.459680	−	0.265396i	−0.711910	+	0.702271i	$0.752170\pi$
$998$			77.7895i			2.46238i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.gh.d.19.2		40
3.2	odd	2		273.2.cg.b.19.9	yes	40
7.3	odd	6		819.2.et.d.136.9		40
13.11	odd	12		819.2.et.d.271.9		40
21.17	even	6		273.2.bt.b.136.2	✓	40
39.11	even	12		273.2.bt.b.271.2	yes	40
91.24	even	12	inner	819.2.gh.d.388.2		40
273.206	odd	12		273.2.cg.b.115.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.136.2	✓	40	21.17	even	6
273.2.bt.b.271.2	yes	40	39.11	even	12
273.2.cg.b.19.9	yes	40	3.2	odd	2
273.2.cg.b.115.9	yes	40	273.206	odd	12
819.2.et.d.136.9		40	7.3	odd	6
819.2.et.d.271.9		40	13.11	odd	12
819.2.gh.d.19.2		40	1.1	even	1	trivial
819.2.gh.d.388.2		40	91.24	even	12	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.gh (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.18205 - 0.584679i) q^{2} +(2.68745 + 1.55160i) q^{4} +(-2.27456 + 0.609466i) q^{5} +(-2.33957 + 1.23548i) q^{7} +(-1.76223 - 1.76223i) q^{8} +O(q^{10})\)	\(q+(-2.18205 - 0.584679i) q^{2} +(2.68745 + 1.55160i) q^{4} +(-2.27456 + 0.609466i) q^{5} +(-2.33957 + 1.23548i) q^{7} +(-1.76223 - 1.76223i) q^{8} +5.31955 q^{10} +(3.57017 + 3.57017i) q^{11} +(1.62322 - 3.21950i) q^{13} +(5.82743 - 1.32798i) q^{14} +(-0.288264 - 0.499288i) q^{16} +(2.64387 - 4.57931i) q^{17} +(2.98754 + 2.98754i) q^{19} +(-7.05842 - 1.89130i) q^{20} +(-5.70290 - 9.87771i) q^{22} +(-3.44956 + 1.99161i) q^{23} +(0.472034 - 0.272529i) q^{25} +(-5.42433 + 6.07604i) q^{26} +(-8.20446 - 0.309797i) q^{28} +(-0.565030 + 0.978660i) q^{29} +(-1.40198 + 5.23228i) q^{31} +(1.62713 + 6.07252i) q^{32} +(-8.44649 + 8.44649i) q^{34} +(4.56851 - 4.23605i) q^{35} +(1.37587 - 5.13480i) q^{37} +(-4.77222 - 8.26572i) q^{38} +(5.08231 + 2.93428i) q^{40} +(-5.61474 + 1.50446i) q^{41} +(-9.65143 + 5.57225i) q^{43} +(4.05519 + 15.1342i) q^{44} +(8.69158 - 2.32890i) q^{46} +(-1.95174 - 7.28399i) q^{47} +(3.94719 - 5.78098i) q^{49} +(-1.18935 + 0.318684i) q^{50} +(9.35771 - 6.13365i) q^{52} +(0.538076 + 0.931975i) q^{53} +(-10.2965 - 5.94466i) q^{55} +(6.30006 + 1.94567i) q^{56} +(1.80513 - 1.80513i) q^{58} +(2.18873 + 8.16845i) q^{59} -3.15666i q^{61} +(6.11841 - 10.5974i) q^{62} -13.0488i q^{64} +(-1.72994 + 8.31222i) q^{65} +(-3.75730 + 3.75730i) q^{67} +(14.2105 - 8.20446i) q^{68} +(-12.4455 + 6.57218i) q^{70} +(-12.9802 - 3.47804i) q^{71} +(1.56120 + 0.418321i) q^{73} +(-6.00443 + 10.4000i) q^{74} +(3.39340 + 12.6644i) q^{76} +(-12.7635 - 3.94181i) q^{77} +(-6.31940 + 10.9455i) q^{79} +(0.959971 + 0.959971i) q^{80} +13.1313 q^{82} +(7.21679 + 7.21679i) q^{83} +(-3.22269 + 12.0273i) q^{85} +(24.3179 - 6.51596i) q^{86} -12.5829i q^{88} +(-8.63520 - 2.31379i) q^{89} +(0.179969 + 9.53769i) q^{91} -12.3607 q^{92} +17.0352i q^{94} +(-8.61613 - 4.97453i) q^{95} +(-4.32019 + 16.1232i) q^{97} +(-11.9930 + 10.3066i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7}+O(q^{10}) \) 40 * q - 8 * q^7	\( 40 q - 8 q^{7} - 4 q^{11} + 18 q^{14} + 32 q^{16} - 4 q^{17} + 14 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} + 24 q^{25} + 32 q^{26} + 16 q^{28} - 8 q^{29} + 14 q^{31} + 26 q^{32} - 24 q^{34} - 26 q^{35} + 36 q^{37} + 8 q^{38} - 30 q^{40} + 2 q^{41} - 66 q^{43} + 32 q^{44} - 26 q^{46} + 4 q^{47} - 14 q^{49} + 20 q^{50} + 2 q^{52} + 8 q^{53} - 42 q^{55} - 46 q^{56} + 24 q^{58} - 14 q^{59} - 24 q^{62} - 28 q^{65} - 44 q^{67} + 18 q^{68} - 4 q^{70} + 6 q^{71} + 14 q^{73} + 20 q^{74} - 64 q^{76} - 24 q^{77} - 20 q^{80} + 48 q^{82} + 12 q^{83} + 2 q^{85} + 60 q^{86} + 2 q^{89} - 14 q^{91} - 236 q^{92} - 24 q^{95} - 62 q^{97} + 88 q^{98}+O(q^{100}) \) 40 * q - 8 * q^7 - 4 * q^11 + 18 * q^14 + 32 * q^16 - 4 * q^17 + 14 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 + 24 * q^25 + 32 * q^26 + 16 * q^28 - 8 * q^29 + 14 * q^31 + 26 * q^32 - 24 * q^34 - 26 * q^35 + 36 * q^37 + 8 * q^38 - 30 * q^40 + 2 * q^41 - 66 * q^43 + 32 * q^44 - 26 * q^46 + 4 * q^47 - 14 * q^49 + 20 * q^50 + 2 * q^52 + 8 * q^53 - 42 * q^55 - 46 * q^56 + 24 * q^58 - 14 * q^59 - 24 * q^62 - 28 * q^65 - 44 * q^67 + 18 * q^68 - 4 * q^70 + 6 * q^71 + 14 * q^73 + 20 * q^74 - 64 * q^76 - 24 * q^77 - 20 * q^80 + 48 * q^82 + 12 * q^83 + 2 * q^85 + 60 * q^86 + 2 * q^89 - 14 * q^91 - 236 * q^92 - 24 * q^95 - 62 * q^97 + 88 * q^98

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