LMFDB - Embedded newform 819.2.gh.d.262.3

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			262.3
Character	$\chi$	$=$	819.262
Dual form			819.2.gh.d.397.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.323834 - 1.20856i) q^{2} +(0.376291 - 0.217252i) q^{4} +(-0.986163 + 3.68041i) q^{5} +(-1.80936 + 1.93034i) q^{7} +(-2.15388 - 2.15388i) q^{8} +O(q^{10})$	\(q+(-0.323834 - 1.20856i) q^{2} +(0.376291 - 0.217252i) q^{4} +(-0.986163 + 3.68041i) q^{5} +(-1.80936 + 1.93034i) q^{7} +(-2.15388 - 2.15388i) q^{8} +4.76737 q^{10} +(-3.16350 - 3.16350i) q^{11} +(3.57886 - 0.437877i) q^{13} +(2.91888 + 1.56161i) q^{14} +(-1.47110 + 2.54802i) q^{16} +(-0.601776 - 1.04231i) q^{17} +(-3.79295 - 3.79295i) q^{19} +(0.428491 + 1.59915i) q^{20} +(-2.79885 + 4.84774i) q^{22} +(-2.92841 - 1.69072i) q^{23} +(-8.24277 - 4.75896i) q^{25} +(-1.68816 - 4.18349i) q^{26} +(-0.261474 + 1.11946i) q^{28} +(3.96435 + 6.86645i) q^{29} +(-5.16347 + 1.38355i) q^{31} +(-2.32867 - 0.623965i) q^{32} +(-1.06482 + 1.06482i) q^{34} +(-5.32014 - 8.56280i) q^{35} +(-6.75142 + 1.80904i) q^{37} +(-3.35574 + 5.81231i) q^{38} +(10.0512 - 5.80308i) q^{40} +(-0.914977 + 3.41474i) q^{41} +(-8.74306 - 5.04781i) q^{43} +(-1.87767 - 0.503121i) q^{44} +(-1.09502 + 4.08668i) q^{46} +(-4.98837 - 1.33663i) q^{47} +(-0.452462 - 6.98536i) q^{49} +(-3.08223 + 11.5030i) q^{50} +(1.25156 - 0.942283i) q^{52} +(1.14727 - 1.98713i) q^{53} +(14.7627 - 8.52325i) q^{55} +(8.05487 - 0.260595i) q^{56} +(7.01476 - 7.01476i) q^{58} +(5.88602 + 1.57716i) q^{59} -5.40651i q^{61} +(3.34421 + 5.79234i) q^{62} +8.90081i q^{64} +(-1.91777 + 13.6035i) q^{65} +(-3.83925 + 3.83925i) q^{67} +(-0.452886 - 0.261474i) q^{68} +(-8.62586 + 9.20266i) q^{70} +(-3.05313 - 11.3945i) q^{71} +(1.92074 + 7.16831i) q^{73} +(4.37268 + 7.57370i) q^{74} +(-2.25128 - 0.603228i) q^{76} +(11.8305 - 0.382748i) q^{77} +(5.76343 + 9.98255i) q^{79} +(-7.92701 - 7.92701i) q^{80} +4.42323 q^{82} +(5.00708 + 5.00708i) q^{83} +(4.42956 - 1.18690i) q^{85} +(-3.26930 + 12.2012i) q^{86} +13.6276i q^{88} +(-1.36380 - 5.08976i) q^{89} +(-5.63018 + 7.70072i) q^{91} -1.46924 q^{92} +6.46162i q^{94} +(17.7001 - 10.2191i) q^{95} +(2.69756 - 0.722808i) q^{97} +(-8.29574 + 2.80893i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.323834	−	1.20856i	−0.228985	−	0.854584i	−0.980769	−	0.195174i	$-0.937473\pi$
$2$	−0.323834	−	1.20856i	−0.228985	−	0.854584i	0.751783	−	0.659410i	$-0.229194\pi$
$3$		0			0
$3$		0			0
$4$	0.376291	−	0.217252i	0.188145	−	0.108626i
$5$	−0.986163	+	3.68041i	−0.441025	+	1.64593i	0.285197	+	0.958469i	$0.407941\pi$
$5$	−0.986163	+	3.68041i	−0.441025	+	1.64593i	−0.726222	+	0.687460i	$0.758726\pi$
$6$		0			0
$7$	−1.80936	+	1.93034i	−0.683872	+	0.729602i
$7$	−1.80936	+	1.93034i	−0.683872	+	0.729602i
$8$	−2.15388	−	2.15388i	−0.761511	−	0.761511i
$9$		0			0
$10$	4.76737			1.50757
$11$	−3.16350	−	3.16350i	−0.953831	−	0.953831i	0.0451488	−	0.998980i	$-0.485624\pi$
$11$	−3.16350	−	3.16350i	−0.953831	−	0.953831i	−0.998980	+	0.0451488i	$0.985624\pi$
$12$		0			0
$13$	3.57886	−	0.437877i	0.992598	−	0.121445i
$13$	3.57886	−	0.437877i	0.992598	−	0.121445i
$14$	2.91888	+	1.56161i	0.780103	+	0.417358i
$15$		0			0
$16$	−1.47110	+	2.54802i	−0.367775	+	0.637005i
$17$	−0.601776	−	1.04231i	−0.145952	−	0.252796i	0.783776	−	0.621044i	$-0.213291\pi$
$17$	−0.601776	−	1.04231i	−0.145952	−	0.252796i	−0.929728	+	0.368248i	$0.879958\pi$
$18$		0			0
$19$	−3.79295	−	3.79295i	−0.870163	−	0.870163i	0.122327	−	0.992490i	$-0.460964\pi$
$19$	−3.79295	−	3.79295i	−0.870163	−	0.870163i	−0.992490	+	0.122327i	$0.960964\pi$
$20$	0.428491	+	1.59915i	0.0958135	+	0.357581i
$21$		0			0
$22$	−2.79885	+	4.84774i	−0.596716	+	1.03354i
$23$	−2.92841	−	1.69072i	−0.610615	−	0.352539i	0.162591	−	0.986693i	$-0.448015\pi$
$23$	−2.92841	−	1.69072i	−0.610615	−	0.352539i	−0.773206	+	0.634155i	$0.781348\pi$
$24$		0			0
$25$	−8.24277	−	4.75896i	−1.64855	−	0.951793i
$26$	−1.68816	−	4.18349i	−0.331075	−	0.820449i
$27$		0			0
$28$	−0.261474	+	1.11946i	−0.0494139	+	0.211557i
$29$	3.96435	+	6.86645i	0.736161	+	1.27507i	0.954212	+	0.299131i	$0.0966967\pi$
$29$	3.96435	+	6.86645i	0.736161	+	1.27507i	−0.218051	+	0.975937i	$0.569970\pi$
$30$		0			0
$31$	−5.16347	+	1.38355i	−0.927386	+	0.248492i	−0.690740	−	0.723104i	$-0.742715\pi$
$31$	−5.16347	+	1.38355i	−0.927386	+	0.248492i	−0.236646	+	0.971596i	$0.576048\pi$
$32$	−2.32867	−	0.623965i	−0.411655	−	0.110303i
$33$		0			0
$34$	−1.06482	+	1.06482i	−0.182615	+	0.182615i
$35$	−5.32014	−	8.56280i	−0.899268	−	1.44738i
$36$		0			0
$37$	−6.75142	+	1.80904i	−1.10993	+	0.297404i	−0.766801	−	0.641885i	$-0.778153\pi$
$37$	−6.75142	+	1.80904i	−1.10993	+	0.297404i	−0.343126	+	0.939289i	$0.611486\pi$
$38$	−3.35574	+	5.81231i	−0.544373	+	0.942882i
$39$		0			0
$40$	10.0512	−	5.80308i	1.58924	−	0.917548i
$41$	−0.914977	+	3.41474i	−0.142895	+	0.533293i	0.856945	+	0.515408i	$0.172360\pi$
$41$	−0.914977	+	3.41474i	−0.142895	+	0.533293i	−0.999840	+	0.0178844i	$0.994307\pi$
$42$		0			0
$43$	−8.74306	−	5.04781i	−1.33330	−	0.769784i	−0.347500	−	0.937680i	$-0.612969\pi$
$43$	−8.74306	−	5.04781i	−1.33330	−	0.769784i	−0.985805	+	0.167896i	$0.946303\pi$
$44$	−1.87767	−	0.503121i	−0.283070	−	0.0758483i
$45$		0			0
$46$	−1.09502	+	4.08668i	−0.161452	+	0.602548i
$47$	−4.98837	−	1.33663i	−0.727629	−	0.194968i	−0.124056	−	0.992275i	$-0.539590\pi$
$47$	−4.98837	−	1.33663i	−0.727629	−	0.194968i	−0.603573	+	0.797308i	$0.706257\pi$
$48$		0			0
$49$	−0.452462	−	6.98536i	−0.0646374	−	0.997909i
$50$	−3.08223	+	11.5030i	−0.435893	+	1.62677i
$51$		0			0
$52$	1.25156	−	0.942283i	0.173561	−	0.130671i
$53$	1.14727	−	1.98713i	0.157590	−	0.272953i	−0.776409	−	0.630229i	$-0.782961\pi$
$53$	1.14727	−	1.98713i	0.157590	−	0.272953i	0.933999	+	0.357276i	$0.116294\pi$
$54$		0			0
$55$	14.7627	−	8.52325i	1.99060	−	1.14928i
$56$	8.05487	−	0.260595i	1.07638	−	0.0348235i
$57$		0			0
$58$	7.01476	−	7.01476i	0.921083	−	0.921083i
$59$	5.88602	+	1.57716i	0.766295	+	0.205328i	0.620734	−	0.784021i	$-0.286835\pi$
$59$	5.88602	+	1.57716i	0.766295	+	0.205328i	0.145561	+	0.989349i	$0.453501\pi$
$60$		0			0
$61$		−	5.40651i		−	0.692233i	−0.938192	−	0.346116i	$-0.887500\pi$
$61$		−	5.40651i		−	0.692233i	0.938192	−	0.346116i	$-0.112500\pi$
$62$	3.34421	+	5.79234i	0.424715	+	0.735628i
$63$		0			0
$64$			8.90081i			1.11260i
$65$	−1.91777	+	13.6035i	−0.237871	+	1.68731i
$66$		0			0
$67$	−3.83925	+	3.83925i	−0.469039	+	0.469039i	−0.901603	−	0.432564i	$-0.857609\pi$
$67$	−3.83925	+	3.83925i	−0.469039	+	0.469039i	0.432564	+	0.901603i	$0.357609\pi$
$68$	−0.452886	−	0.261474i	−0.0549205	−	0.0317083i
$69$		0			0
$70$	−8.62586	+	9.20266i	−1.03099	+	1.09993i
$71$	−3.05313	−	11.3945i	−0.362340	−	1.35227i	−0.870991	−	0.491299i	$-0.836522\pi$
$71$	−3.05313	−	11.3945i	−0.362340	−	1.35227i	0.508650	−	0.860973i	$-0.330145\pi$
$72$		0			0
$73$	1.92074	+	7.16831i	0.224806	+	0.838987i	0.982482	+	0.186357i	$0.0596680\pi$
$73$	1.92074	+	7.16831i	0.224806	+	0.838987i	−0.757676	+	0.652631i	$0.773665\pi$
$74$	4.37268	+	7.57370i	0.508313	+	0.880425i
$75$		0			0
$76$	−2.25128	−	0.603228i	−0.258239	−	0.0691950i
$77$	11.8305	−	0.382748i	1.34822	−	0.0436182i
$78$		0			0
$79$	5.76343	+	9.98255i	0.648436	+	1.12312i	0.983496	+	0.180928i	$0.0579101\pi$
$79$	5.76343	+	9.98255i	0.648436	+	1.12312i	−0.335060	+	0.942197i	$0.608757\pi$
$80$	−7.92701	−	7.92701i	−0.886267	−	0.886267i
$81$		0			0
$82$	4.42323			0.488464
$83$	5.00708	+	5.00708i	0.549598	+	0.549598i	0.926325	−	0.376727i	$-0.122950\pi$
$83$	5.00708	+	5.00708i	0.549598	+	0.549598i	−0.376727	+	0.926325i	$0.622950\pi$
$84$		0			0
$85$	4.42956	−	1.18690i	0.480454	−	0.128737i
$86$	−3.26930	+	12.2012i	−0.352538	+	1.31569i
$87$		0			0
$88$			13.6276i			1.45271i
$89$	−1.36380	−	5.08976i	−0.144562	−	0.539514i	−0.999774	−	0.0212358i	$-0.993240\pi$
$89$	−1.36380	−	5.08976i	−0.144562	−	0.539514i	0.855212	−	0.518278i	$-0.173427\pi$
$90$		0			0
$91$	−5.63018	+	7.70072i	−0.590204	+	0.807254i
$92$	−1.46924			−0.153179
$93$		0			0
$94$			6.46162i			0.666465i
$95$	17.7001	−	10.2191i	1.81599	−	1.04846i
$96$		0			0
$97$	2.69756	−	0.722808i	0.273895	−	0.0733901i	−0.119257	−	0.992863i	$-0.538051\pi$
$97$	2.69756	−	0.722808i	0.273895	−	0.0733901i	0.393152	+	0.919473i	$0.371385\pi$
$98$	−8.29574	+	2.80893i	−0.837996	+	0.283744i
$99$		0			0
$100$	−4.13557			−0.413557
$101$	6.67768			0.664454			0.332227	−	0.943199i	$-0.392200\pi$
$101$	6.67768			0.664454			0.332227	+	0.943199i	$0.392200\pi$
$102$		0			0
$103$	−1.06760	−	1.84913i	−0.105193	−	0.182200i	0.808624	−	0.588326i	$-0.200213\pi$
$103$	−1.06760	−	1.84913i	−0.105193	−	0.182200i	−0.913817	+	0.406126i	$0.866880\pi$
$104$	−8.65158	−	6.76531i	−0.848357	−	0.663393i
$105$		0			0
$106$	−2.77310	−	0.743050i	−0.269347	−	0.0721714i
$107$	−8.96843	+	15.5338i	−0.867011	+	1.50171i	−0.00197496	+	0.999998i	$0.500629\pi$
$107$	−8.96843	+	15.5338i	−0.867011	+	1.50171i	−0.865036	+	0.501709i	$0.832705\pi$
$108$		0			0
$109$	0.0524960	+	0.195918i	0.00502820	+	0.0187655i	0.968394	−	0.249424i	$-0.0802413\pi$
$109$	0.0524960	+	0.195918i	0.00502820	+	0.0187655i	−0.963366	+	0.268190i	$0.913575\pi$
$110$	−15.0816	−	15.0816i	−1.43797	−	1.43797i
$111$		0			0
$112$	−2.25681	−	7.45001i	−0.213249	−	0.703959i
$113$	−2.98143	+	5.16398i	−0.280469	+	0.485787i	−0.971500	−	0.237038i	$-0.923823\pi$
$113$	−2.98143	+	5.16398i	−0.280469	+	0.485787i	0.691031	+	0.722825i	$0.257157\pi$
$114$		0			0
$115$	9.11041	−	9.11041i	0.849550	−	0.849550i
$116$	2.98350	+	1.72252i	0.277011	+	0.159932i
$117$		0			0
$118$		−	7.62437i		−	0.701881i
$119$	3.10084	+	0.724268i	0.284253	+	0.0663936i
$120$		0			0
$121$			9.01548i			0.819589i
$122$	−6.53412	+	1.75081i	−0.591571	+	0.158511i
$123$		0			0
$124$	−1.64239	+	1.64239i	−0.147491	+	0.147491i
$125$	12.1724	−	12.1724i	1.08873	−	1.08873i
$126$		0			0
$127$	11.1060	−	6.41205i	0.985497	−	0.568977i	0.0815719	−	0.996667i	$-0.474006\pi$
$127$	11.1060	−	6.41205i	0.985497	−	0.568977i	0.903925	+	0.427690i	$0.140673\pi$
$128$	6.09986	−	1.63445i	0.539157	−	0.144467i
$129$		0			0
$130$	17.0617	−	2.08752i	1.49641	−	0.183088i
$131$	−4.86044	+	2.80617i	−0.424658	+	0.245177i	−0.697068	−	0.717005i	$-0.745513\pi$
$131$	−4.86044	+	2.80617i	−0.424658	+	0.245177i	0.272410	+	0.962181i	$0.412179\pi$
$132$		0			0
$133$	14.1845	−	0.458905i	1.22995	−	0.0397921i
$134$	5.88326	+	3.39670i	0.508236	+	0.293430i
$135$		0			0
$136$	−0.948850	+	3.54116i	−0.0813632	+	0.303652i
$137$	2.52492	−	9.42312i	0.215718	−	0.805072i	−0.770194	−	0.637810i	$-0.779841\pi$
$137$	2.52492	−	9.42312i	0.215718	−	0.805072i	0.985912	−	0.167262i	$-0.0534926\pi$
$138$		0			0
$139$	−12.9533	−	7.47860i	−1.09869	−	0.634327i	−0.162810	−	0.986657i	$-0.552056\pi$
$139$	−12.9533	−	7.47860i	−1.09869	−	0.634327i	−0.935875	+	0.352331i	$0.885389\pi$
$140$	−3.86220	−	2.06630i	−0.326416	−	0.174634i
$141$		0			0
$142$	−12.7822	+	7.37982i	−1.07266	+	0.619301i
$143$	−12.7070	−	9.93651i	−1.06261	−	0.830933i
$144$		0			0
$145$	−29.1808	+	7.81898i	−2.42334	+	0.649331i
$146$	8.04137	−	4.64268i	0.665508	−	0.384231i
$147$		0			0
$148$	−2.14748	+	2.14748i	−0.176522	+	0.176522i
$149$	11.9474	−	11.9474i	0.978769	−	0.978769i	−0.0210106	−	0.999779i	$-0.506688\pi$
$149$	11.9474	−	11.9474i	0.978769	−	0.978769i	0.999779	+	0.0210106i	$0.00668836\pi$
$150$		0			0
$151$	−8.51059	+	2.28041i	−0.692582	+	0.185577i	−0.587906	−	0.808929i	$-0.700047\pi$
$151$	−8.51059	+	2.28041i	−0.692582	+	0.185577i	−0.104677	+	0.994506i	$0.533381\pi$
$152$			16.3391i			1.32528i
$153$		0			0
$154$	−4.29371	−	14.1740i	−0.345997	−	1.14218i
$155$		−	20.3681i		−	1.63600i
$156$		0			0
$157$	11.2840	+	6.51483i	0.900562	+	0.519940i	0.877383	−	0.479791i	$-0.159288\pi$
$157$	11.2840	+	6.51483i	0.900562	+	0.519940i	0.0231797	+	0.999731i	$0.492621\pi$
$158$	10.1982	−	10.1982i	0.811322	−	0.811322i
$159$		0			0
$160$	4.59290	−	7.95513i	0.363100	−	0.628908i
$161$	8.56219	−	2.59373i	0.674795	−	0.204414i
$162$		0			0
$163$	1.98678	+	1.98678i	0.155617	+	0.155617i	0.780621	−	0.625004i	$-0.214903\pi$
$163$	1.98678	+	1.98678i	0.155617	+	0.155617i	−0.625004	+	0.780621i	$0.714903\pi$
$164$	0.397560	+	1.48372i	0.0310443	+	0.115859i
$165$		0			0
$166$	4.42991	−	7.67284i	0.343828	−	0.595528i
$167$	6.46991	+	1.73361i	0.500657	+	0.134151i	0.500305	−	0.865849i	$-0.333221\pi$
$167$	6.46991	+	1.73361i	0.500657	+	0.134151i	0.000351905		1.00000i	$0.499888\pi$
$168$		0			0
$169$	12.6165	−	3.13421i	0.970502	−	0.241093i
$170$	−2.86889	−	4.96906i	−0.220033	−	0.381109i
$171$		0			0
$172$	−4.38658			−0.334474
$173$	−9.78650			−0.744054			−0.372027	−	0.928222i	$-0.621337\pi$
$173$	−9.78650			−0.744054			−0.372027	+	0.928222i	$0.621337\pi$
$174$		0			0
$175$	24.1005	−	7.30072i	1.82183	−	0.551883i
$176$	12.7145	−	3.40684i	0.958391	−	0.256800i
$177$		0			0
$178$	−5.70966	+	3.29648i	−0.427957	+	0.247081i
$179$			11.5463i			0.863013i	0.902110	+	0.431507i	$0.142018\pi$
$179$			11.5463i			0.863013i	−0.902110	+	0.431507i	$0.857982\pi$
$180$		0			0
$181$	16.9576			1.26045			0.630226	−	0.776412i	$-0.282962\pi$
$181$	16.9576			1.26045			0.630226	+	0.776412i	$0.282962\pi$
$182$	11.1301	+	4.31069i	0.825015	+	0.319529i
$183$		0			0
$184$	2.66583	+	9.94903i	0.196528	+	0.733452i
$185$		−	26.6320i		−	1.95802i
$186$		0			0
$187$	−1.39362	+	5.20106i	−0.101911	+	0.380339i
$188$	−2.16746	+	0.580770i	−0.158079	+	0.0423570i
$189$		0			0
$190$	−18.0824	−	18.0824i	−1.31183	−	1.31183i
$191$	1.97758			0.143093			0.0715463	−	0.997437i	$-0.477207\pi$
$191$	1.97758			0.143093			0.0715463	+	0.997437i	$0.477207\pi$
$192$		0			0
$193$	2.27776	+	2.27776i	0.163957	+	0.163957i	0.784317	−	0.620360i	$-0.213014\pi$
$193$	2.27776	+	2.27776i	0.163957	+	0.163957i	−0.620360	+	0.784317i	$0.713014\pi$
$194$	−1.74712	−	3.02610i	−0.125436	−	0.217261i
$195$		0			0
$196$	−1.68784	−	2.53023i	−0.120560	−	0.180731i
$197$	−5.66631	−	1.51828i	−0.403708	−	0.108173i	0.0512506	−	0.998686i	$-0.483679\pi$
$197$	−5.66631	−	1.51828i	−0.403708	−	0.108173i	−0.454959	+	0.890513i	$0.650346\pi$
$198$		0			0
$199$	−0.945648	−	1.63791i	−0.0670352	−	0.116108i	0.830560	−	0.556930i	$-0.188021\pi$
$199$	−0.945648	−	1.63791i	−0.0670352	−	0.116108i	−0.897595	+	0.440821i	$0.854687\pi$
$200$	7.50369	+	28.0042i	0.530591	+	1.98019i
$201$		0			0
$202$	−2.16246	−	8.07041i	−0.152150	−	0.567832i
$203$	−20.4275	−	4.77130i	−1.43373	−	0.334879i
$204$		0			0
$205$	−11.6653	−	6.73498i	−0.814742	−	0.470391i
$206$	−1.88907	+	1.88907i	−0.131618	+	0.131618i
$207$		0			0
$208$	−4.14915	+	9.76318i	−0.287691	+	0.676955i
$209$			23.9980i			1.65998i
$210$		0			0
$211$	0.967437	+	1.67565i	0.0666011	+	0.115357i	0.897403	−	0.441212i	$-0.145451\pi$
$211$	0.967437	+	1.67565i	0.0666011	+	0.115357i	−0.830802	+	0.556568i	$0.812118\pi$
$212$		−	0.996985i		−	0.0684732i
$213$		0			0
$214$	21.6779	+	5.80857i	1.48187	+	0.397065i
$215$	27.2001	−	27.2001i	1.85503	−	1.85503i
$216$		0			0
$217$	6.67183	−	12.4706i	0.452913	−	0.846559i
$218$	0.219779	−	0.126890i	0.0148853	−	0.00859405i
$219$		0			0
$220$	3.70338	−	6.41445i	0.249682	−	0.432462i
$221$	−2.61008	−	3.46677i	−0.175573	−	0.233200i
$222$		0			0
$223$	−3.88477	+	14.4982i	−0.260144	+	0.970869i	0.705013	+	0.709195i	$0.250941\pi$
$223$	−3.88477	+	14.4982i	−0.260144	+	0.970869i	−0.965156	+	0.261674i	$0.915725\pi$
$224$	5.41786	−	3.36616i	0.361996	−	0.224911i
$225$		0			0
$226$	7.20649	+	1.93097i	0.479369	+	0.128446i
$227$	−6.31931	+	23.5840i	−0.419428	+	1.56533i	0.356371	+	0.934345i	$0.384014\pi$
$227$	−6.31931	+	23.5840i	−0.419428	+	1.56533i	−0.775799	+	0.630981i	$0.782653\pi$
$228$		0			0
$229$	−4.48718	−	1.20234i	−0.296521	−	0.0794526i	0.107491	−	0.994206i	$-0.465718\pi$
$229$	−4.48718	−	1.20234i	−0.296521	−	0.0794526i	−0.404013	+	0.914753i	$0.632385\pi$
$230$	−13.9608	−	8.06026i	−0.920546	−	0.531478i
$231$		0			0
$232$	6.25078	−	23.3282i	0.410384	−	1.53157i
$233$	−15.1770	+	8.76243i	−0.994277	+	0.574046i	−0.906550	−	0.422098i	$-0.861294\pi$
$233$	−15.1770	+	8.76243i	−0.994277	+	0.574046i	−0.0877270	+	0.996145i	$0.527960\pi$
$234$		0			0
$235$	9.83869	−	17.0411i	0.641806	−	1.11164i
$236$	2.55750	−	0.685279i	0.166479	−	0.0446079i
$237$		0			0
$238$	−0.128831	−	3.98210i	−0.00835088	−	0.258122i
$239$	−1.79773	+	1.79773i	−0.116285	+	0.116285i	−0.762855	−	0.646570i	$-0.776203\pi$
$239$	−1.79773	+	1.79773i	−0.116285	+	0.116285i	0.646570	+	0.762855i	$0.276203\pi$
$240$		0			0
$241$	−4.21647	−	1.12980i	−0.271607	−	0.0727768i	0.120445	−	0.992720i	$-0.461568\pi$
$241$	−4.21647	−	1.12980i	−0.271607	−	0.0727768i	−0.392052	+	0.919943i	$0.628235\pi$
$242$	10.8958	−	2.91952i	0.700408	−	0.187674i
$243$		0			0
$244$	−1.17457	−	2.03442i	−0.0751944	−	0.130240i
$245$	26.1552	+	5.22346i	1.67099	+	0.333715i
$246$		0			0
$247$	−15.2353	−	11.9136i	−0.969399	−	0.758045i
$248$	14.1015	+	8.14149i	0.895445	+	0.516985i
$249$		0			0
$250$	−18.6530	−	10.7693i	−1.17972	−	0.681111i
$251$	10.4875	−	18.1649i	0.661964	−	1.14656i	−0.318135	−	0.948046i	$-0.603056\pi$
$251$	10.4875	−	18.1649i	0.661964	−	1.14656i	0.980099	−	0.198510i	$-0.0636103\pi$
$252$		0			0
$253$	3.91543	+	14.6126i	0.246161	+	0.918686i
$254$	−11.3459	−	11.3459i	−0.711903	−	0.711903i
$255$		0			0
$256$	4.95013	+	8.57387i	0.309383	+	0.535867i
$257$	−3.70449	+	6.41636i	−0.231080	+	0.400242i	−0.958126	−	0.286347i	$-0.907559\pi$
$257$	−3.70449	+	6.41636i	−0.231080	+	0.400242i	0.727047	+	0.686588i	$0.240892\pi$
$258$		0			0
$259$	8.72366	−	16.3058i	0.542062	−	1.01319i
$260$	2.23374	+	5.53551i	0.138531	+	0.343298i
$261$		0			0
$262$	4.96542	+	4.96542i	0.306764	+	0.306764i
$263$	−22.7469			−1.40263			−0.701317	−	0.712850i	$-0.747404\pi$
$263$	−22.7469			−1.40263			−0.701317	+	0.712850i	$0.747404\pi$
$264$		0			0
$265$	6.18206	+	6.18206i	0.379761	+	0.379761i
$266$	−5.14804	−	16.9943i	−0.315647	−	1.04199i
$267$		0			0
$268$	−0.610591	+	2.27876i	−0.0372978	+	0.139197i
$269$	4.45808	−	2.57388i	0.271814	−	0.156932i	−0.357898	−	0.933761i	$-0.616506\pi$
$269$	4.45808	−	2.57388i	0.271814	−	0.156932i	0.629712	+	0.776829i	$0.283173\pi$
$270$		0			0
$271$	4.15851	+	15.5198i	0.252612	+	0.942759i	0.969404	+	0.245472i	$0.0789430\pi$
$271$	4.15851	+	15.5198i	0.252612	+	0.942759i	−0.716792	+	0.697287i	$0.754390\pi$
$272$	3.54109			0.214710
$273$		0			0
$274$	−12.2061			−0.737398
$275$	11.0210	+	41.1310i	0.664592	+	2.48029i
$276$		0			0
$277$	−6.82673	+	3.94142i	−0.410179	+	0.236817i	−0.690867	−	0.722982i	$-0.742771\pi$
$277$	−6.82673	+	3.94142i	−0.410179	+	0.236817i	0.280688	+	0.959799i	$0.409437\pi$
$278$	−4.84365	+	18.0767i	−0.290503	+	1.08417i
$279$		0			0
$280$	−6.98431	+	29.9022i	−0.417392	+	1.78700i
$281$	−12.0099	−	12.0099i	−0.716448	−	0.716448i	0.251428	−	0.967876i	$-0.419100\pi$
$281$	−12.0099	−	12.0099i	−0.716448	−	0.716448i	−0.967876	+	0.251428i	$0.919100\pi$
$282$		0			0
$283$	−12.3954			−0.736831			−0.368416	−	0.929661i	$-0.620100\pi$
$283$	−12.3954			−0.736831			−0.368416	+	0.929661i	$0.620100\pi$
$284$	−3.62433	−	3.62433i	−0.215064	−	0.215064i
$285$		0			0
$286$	−7.89397	+	18.5750i	−0.466780	+	1.09836i
$287$	−4.93611	−	7.94470i	−0.291369	−	0.468961i
$288$		0			0
$289$	7.77573	−	13.4680i	0.457396	−	0.792233i
$290$	18.8995	+	32.7349i	1.10982	+	1.92226i
$291$		0			0
$292$	2.28009	+	2.28009i	0.133432	+	0.133432i
$293$	−2.23957	−	8.35820i	−0.130837	−	0.488291i	0.869143	−	0.494561i	$-0.164671\pi$
$293$	−2.23957	−	8.35820i	−0.130837	−	0.488291i	−0.999980	+	0.00626941i	$0.998004\pi$
$294$		0			0
$295$	−11.6092	+	20.1076i	−0.675911	+	1.17071i
$296$	18.4382	+	10.6453i	1.07170	+	0.618745i
$297$		0			0
$298$	−18.3082	−	10.5702i	−1.06056	−	0.612317i
$299$	−11.2207	−	4.76856i	−0.648909	−	0.275773i
$300$		0			0
$301$	25.5633	−	7.74384i	1.47345	−	0.446348i
$302$	5.51204	+	9.54713i	0.317182	+	0.549375i
$303$		0			0
$304$	15.2443	−	4.08471i	0.874322	−	0.234274i
$305$	19.8982	+	5.33170i	1.13937	+	0.305292i
$306$		0			0
$307$	7.24945	−	7.24945i	0.413748	−	0.413748i	−0.469294	−	0.883042i	$-0.655492\pi$
$307$	7.24945	−	7.24945i	0.413748	−	0.413748i	0.883042	+	0.469294i	$0.155492\pi$
$308$	4.36858	−	2.71423i	0.248923	−	0.154658i
$309$		0			0
$310$	−24.6161	+	6.59587i	−1.39810	+	0.374620i
$311$	0.447316	−	0.774775i	0.0253650	−	0.0439334i	−0.853064	−	0.521806i	$-0.825259\pi$
$311$	0.447316	−	0.774775i	0.0253650	−	0.0439334i	0.878429	+	0.477872i	$0.158592\pi$
$312$		0			0
$313$	−28.3762	+	16.3830i	−1.60392	+	0.926022i	−0.613224	+	0.789909i	$0.710128\pi$
$313$	−28.3762	+	16.3830i	−1.60392	+	0.926022i	−0.990693	+	0.136113i	$0.956539\pi$
$314$	4.21944	−	15.7472i	0.238117	−	0.888665i
$315$		0			0
$316$	4.33745	+	2.50423i	0.244001	+	0.140874i
$317$	−22.1717	−	5.94088i	−1.24529	−	0.333673i	−0.424772	−	0.905300i	$-0.639646\pi$
$317$	−22.1717	−	5.94088i	−1.24529	−	0.333673i	−0.820514	+	0.571627i	$0.806312\pi$
$318$		0			0
$319$	9.18081	−	34.2632i	0.514027	−	1.91837i
$320$	−32.7586	−	8.77765i	−1.83126	−	0.490685i
$321$		0			0
$322$	−5.90741	−	9.50802i	−0.329207	−	0.529861i
$323$	−1.67091	+	6.23592i	−0.0929720	+	0.346976i
$324$		0			0
$325$	−31.5836	−	13.4224i	−1.75194	−	0.744539i
$326$	1.75777	−	3.04455i	0.0973538	−	0.168622i
$327$		0			0
$328$	9.32569	−	5.38419i	0.514925	−	0.297292i
$329$	11.6059	−	7.21084i	0.639854	−	0.397546i
$330$		0			0
$331$	11.8814	−	11.8814i	0.653059	−	0.653059i	−0.300670	−	0.953728i	$-0.597210\pi$
$331$	11.8814	−	11.8814i	0.653059	−	0.653059i	0.953728	+	0.300670i	$0.0972102\pi$
$332$	2.97191	+	0.796322i	0.163105	+	0.0437038i
$333$		0			0
$334$		−	8.38070i		−	0.458572i
$335$	−10.3439	−	17.9161i	−0.565147	−	0.978863i
$336$		0			0
$337$		−	26.5544i		−	1.44651i	−0.690582	−	0.723254i	$-0.742645\pi$
$337$		−	26.5544i		−	1.44651i	0.690582	−	0.723254i	$-0.257355\pi$
$338$	−7.87355	−	14.2329i	−0.428265	−	0.774169i
$339$		0			0
$340$	1.40895	−	1.40895i	0.0764110	−	0.0764110i
$341$	20.7115	+	11.9578i	1.12159	+	0.647550i
$342$		0			0
$343$	14.3028	+	11.7656i	0.772280	+	0.635283i
$344$	7.95913	+	29.7039i	0.429128	+	1.60153i
$345$		0			0
$346$	3.16920	+	11.8276i	0.170377	+	0.635856i
$347$	−9.40270	−	16.2860i	−0.504763	−	0.874276i	−0.999985	−	0.00550914i	$-0.998246\pi$
$347$	−9.40270	−	16.2860i	−0.504763	−	0.874276i	0.495221	−	0.868767i	$-0.335087\pi$
$348$		0			0
$349$	−28.4085	−	7.61204i	−1.52067	−	0.407463i	−0.600709	−	0.799468i	$-0.705115\pi$
$349$	−28.4085	−	7.61204i	−1.52067	−	0.407463i	−0.919963	+	0.392005i	$0.871782\pi$
$350$	−16.6280	−	26.7628i	−0.888802	−	1.43053i
$351$		0			0
$352$	5.39284	+	9.34067i	0.287439	+	0.497859i
$353$	5.59741	+	5.59741i	0.297920	+	0.297920i	0.840199	−	0.542279i	$-0.182438\pi$
$353$	5.59741	+	5.59741i	0.297920	+	0.297920i	−0.542279	+	0.840199i	$0.682438\pi$
$354$		0			0
$355$	44.9471			2.38555
$356$	−1.61894	−	1.61894i	−0.0858039	−	0.0858039i
$357$		0			0
$358$	13.9545	−	3.73909i	0.737517	−	0.197617i
$359$	−6.59681	+	24.6196i	−0.348166	+	1.29937i	0.540703	+	0.841213i	$0.318158\pi$
$359$	−6.59681	+	24.6196i	−0.348166	+	1.29937i	−0.888870	+	0.458160i	$0.848509\pi$
$360$		0			0
$361$			9.77296i			0.514366i
$362$	−5.49146	−	20.4944i	−0.288625	−	1.07716i
$363$		0			0
$364$	−0.445594	+	4.12088i	−0.0233555	+	0.215993i
$365$	−28.2765			−1.48006
$366$		0			0
$367$			33.4625i			1.74673i	0.487068	+	0.873364i	$0.338066\pi$
$367$			33.4625i			1.74673i	−0.487068	+	0.873364i	$0.661934\pi$
$368$	8.61595	−	4.97442i	0.449138	−	0.259310i
$369$		0			0
$370$	−32.1865	+	8.62434i	−1.67330	+	0.448358i
$371$	1.76003	+	5.81005i	0.0913760	+	0.301643i
$372$		0			0
$373$	1.88815			0.0977649			0.0488825	−	0.998805i	$-0.484434\pi$
$373$	1.88815			0.0977649			0.0488825	+	0.998805i	$0.484434\pi$
$374$	6.73711			0.348368
$375$		0			0
$376$	7.86541	+	13.6233i	0.405628	+	0.702568i
$377$	17.1945	+	22.8382i	0.885563	+	1.17623i
$378$		0			0
$379$	−1.67371	−	0.448469i	−0.0859726	−	0.0230363i	0.215576	−	0.976487i	$-0.430837\pi$
$379$	−1.67371	−	0.448469i	−0.0859726	−	0.0230363i	−0.301549	+	0.953451i	$0.597504\pi$
$380$	4.44025	−	7.69074i	0.227780	−	0.394527i
$381$		0			0
$382$	−0.640407	−	2.39003i	−0.0327661	−	0.122285i
$383$	−3.76832	−	3.76832i	−0.192552	−	0.192552i	0.604246	−	0.796798i	$-0.293474\pi$
$383$	−3.76832	−	3.76832i	−0.192552	−	0.192552i	−0.796798	+	0.604246i	$0.793474\pi$
$384$		0			0
$385$	−10.2582	+	43.9187i	−0.522805	+	2.23830i
$386$	2.01520	−	3.49043i	0.102571	−	0.177658i
$387$		0			0
$388$	0.858035	−	0.858035i	0.0435601	−	0.0435601i
$389$	−13.5597	−	7.82869i	−0.687503	−	0.396930i	0.115173	−	0.993345i	$-0.463258\pi$
$389$	−13.5597	−	7.82869i	−0.687503	−	0.396930i	−0.802676	+	0.596415i	$0.796591\pi$
$390$		0			0
$391$			4.06973i			0.205815i
$392$	−14.0711	+	16.0202i	−0.710697	+	0.809141i
$393$		0			0
$394$			7.33978i			0.369773i
$395$	−42.4235	+	11.3674i	−2.13456	+	0.571954i
$396$		0			0
$397$	14.9475	−	14.9475i	0.750192	−	0.750192i	−0.224323	−	0.974515i	$-0.572017\pi$
$397$	14.9475	−	14.9475i	0.750192	−	0.750192i	0.974515	+	0.224323i	$0.0720170\pi$
$398$	−1.67329	+	1.67329i	−0.0838743	+	0.0838743i
$399$		0			0
$400$	24.2519	−	14.0018i	1.21259	−	0.700091i
$401$	−8.10958	+	2.17296i	−0.404973	+	0.108512i	−0.455555	−	0.890208i	$-0.650559\pi$
$401$	−8.10958	+	2.17296i	−0.404973	+	0.108512i	0.0505817	+	0.998720i	$0.483892\pi$
$402$		0			0
$403$	−17.8735	+	7.21249i	−0.890343	+	0.359280i
$404$	2.51275	−	1.45074i	0.125014	−	0.0721769i
$405$		0			0
$406$	0.848707	+	26.2331i	0.0421206	+	1.30193i
$407$	27.0810	+	15.6352i	1.34236	+	0.775010i
$408$		0			0
$409$	−3.52993	+	13.1739i	−0.174544	+	0.651407i	0.822085	+	0.569365i	$0.192811\pi$
$409$	−3.52993	+	13.1739i	−0.174544	+	0.651407i	−0.996629	+	0.0820418i	$0.973856\pi$
$410$	−4.36203	+	16.2793i	−0.215425	+	0.803978i
$411$		0			0
$412$	−0.803454	−	0.463874i	−0.0395833	−	0.0228535i
$413$	−13.6944	+	8.50842i	−0.673856	+	0.418672i
$414$		0			0
$415$	−23.3659	+	13.4903i	−1.14699	+	0.662213i
$416$	−8.60721	−	1.21341i	−0.422003	−	0.0594925i
$417$		0			0
$418$	29.0031	−	7.77137i	1.41859	−	0.380110i
$419$	14.4313	−	8.33192i	0.705015	−	0.407041i	−0.104197	−	0.994557i	$-0.533227\pi$
$419$	14.4313	−	8.33192i	0.705015	−	0.407041i	0.809213	+	0.587516i	$0.199894\pi$
$420$		0			0
$421$	−23.8562	+	23.8562i	−1.16268	+	1.16268i	−0.178794	+	0.983887i	$0.557220\pi$
$421$	−23.8562	+	23.8562i	−1.16268	+	1.16268i	−0.983887	+	0.178794i	$0.942780\pi$
$422$	1.71184	−	1.71184i	0.0833312	−	0.0833312i
$423$		0			0
$424$	−6.75112	+	1.80896i	−0.327863	+	0.0878507i
$425$			11.4553i			0.555665i
$426$		0			0
$427$	10.4364	+	9.78230i	0.505054	+	0.473399i
$428$			7.79363i			0.376719i
$429$		0			0
$430$	−41.6814	−	24.0648i	−2.01005	−	1.16051i
$431$	−6.36851	+	6.36851i	−0.306760	+	0.306760i	−0.843652	−	0.536891i	$-0.819599\pi$
$431$	−6.36851	+	6.36851i	−0.306760	+	0.306760i	0.536891	+	0.843652i	$0.319599\pi$
$432$		0			0
$433$	−7.92993	+	13.7350i	−0.381088	+	0.660064i	−0.991218	−	0.132238i	$-0.957784\pi$
$433$	−7.92993	+	13.7350i	−0.381088	+	0.660064i	0.610130	+	0.792301i	$0.291117\pi$
$434$	−17.2321	−	4.02493i	−0.827166	−	0.193203i
$435$		0			0
$436$	0.0623172	+	0.0623172i	0.00298445	+	0.00298445i
$437$	4.69450	+	17.5201i	0.224568	+	0.838100i
$438$		0			0
$439$	9.64300	−	16.7022i	0.460235	−	0.797151i	−0.538737	−	0.842474i	$-0.681098\pi$
$439$	9.64300	−	16.7022i	0.460235	−	0.797151i	0.998972	+	0.0453228i	$0.0144316\pi$
$440$	−50.1552	−	13.4390i	−2.39105	−	0.640681i
$441$		0			0
$442$	−3.34458	+	4.27710i	−0.159086	+	0.203441i
$443$	−14.7573	−	25.5603i	−0.701139	−	1.21441i	−0.968067	−	0.250692i	$-0.919342\pi$
$443$	−14.7573	−	25.5603i	−0.701139	−	1.21441i	0.266928	−	0.963716i	$-0.413991\pi$
$444$		0			0
$445$	20.0773			0.951757
$446$	18.7800			0.889258
$447$		0			0
$448$	−17.1816	−	16.1047i	−0.811756	−	0.760877i
$449$	14.6691	−	3.93057i	0.692276	−	0.185495i	0.104508	−	0.994524i	$-0.466673\pi$
$449$	14.6691	−	3.93057i	0.692276	−	0.185495i	0.587768	+	0.809029i	$0.300007\pi$
$450$		0			0
$451$	13.6971	−	7.90800i	0.644970	−	0.372373i
$452$			2.59088i			0.121865i
$453$		0			0
$454$	30.5492			1.43374
$455$	−22.7895	−	28.3155i	−1.06839	−	1.32745i
$456$		0			0
$457$	7.98659	+	29.8063i	0.373597	+	1.39428i	0.855384	+	0.517994i	$0.173321\pi$
$457$	7.98659	+	29.8063i	0.373597	+	1.39428i	−0.481788	+	0.876288i	$0.660012\pi$
$458$			5.81240i			0.271596i
$459$		0			0
$460$	1.44891	−	5.40742i	0.0675559	−	0.252122i
$461$	−25.0349	+	6.70809i	−1.16599	+	0.312427i	−0.789357	−	0.613934i	$-0.789586\pi$
$461$	−25.0349	+	6.70809i	−1.16599	+	0.312427i	−0.376636	+	0.926361i	$0.622919\pi$
$462$		0			0
$463$	12.0612	+	12.0612i	0.560529	+	0.560529i	0.929458	−	0.368928i	$-0.120275\pi$
$463$	12.0612	+	12.0612i	0.560529	+	0.560529i	−0.368928	+	0.929458i	$0.620275\pi$
$464$	−23.3278			−1.08297
$465$		0			0
$466$	15.5048	+	15.5048i	0.718245	+	0.718245i
$467$	−11.5656	−	20.0323i	−0.535193	−	0.926982i	−0.999154	−	0.0411263i	$-0.986905\pi$
$467$	−11.5656	−	20.0323i	−0.535193	−	0.926982i	0.463961	−	0.885856i	$-0.346428\pi$
$468$		0			0
$469$	−0.464506	−	14.3576i	−0.0214489	−	0.662974i
$470$	−23.7814	−	6.37220i	−1.09695	−	0.293928i
$471$		0			0
$472$	−9.28078	−	16.0748i	−0.427183	−	0.739902i
$473$	11.6899	+	43.6274i	0.537504	+	2.00599i
$474$		0			0
$475$	13.2139	+	49.3149i	0.606295	+	2.26272i
$476$	1.32417	−	0.401127i	0.0606930	−	0.0183856i
$477$		0			0
$478$	2.75483	+	1.59050i	0.126003	+	0.0727479i
$479$	20.3154	−	20.3154i	0.928236	−	0.928236i	−0.0693556	−	0.997592i	$-0.522094\pi$
$479$	20.3154	−	20.3154i	0.928236	−	0.928236i	0.997592	+	0.0693556i	$0.0220943\pi$
$480$		0			0
$481$	−23.3703	+	9.43059i	−1.06559	+	0.429998i
$482$			5.46174i			0.248776i
$483$		0			0
$484$	1.95863	+	3.39244i	0.0890285	+	0.154202i
$485$			10.6409i			0.483179i
$486$		0			0
$487$	16.7161	+	4.47906i	0.757478	+	0.202966i	0.616833	−	0.787094i	$-0.288415\pi$
$487$	16.7161	+	4.47906i	0.757478	+	0.202966i	0.140646	+	0.990060i	$0.455082\pi$
$488$	−11.6450	+	11.6450i	−0.527143	+	0.527143i
$489$		0			0
$490$	−2.15705	−	33.3018i	−0.0974456	−	1.50442i
$491$	30.2502	−	17.4649i	1.36517	−	0.788182i	0.374865	−	0.927080i	$-0.377689\pi$
$491$	30.2502	−	17.4649i	1.36517	−	0.788182i	0.990307	+	0.138898i	$0.0443559\pi$
$492$		0			0
$493$	4.77130	−	8.26413i	0.214888	−	0.372198i
$494$	−9.46466	+	22.2709i	−0.425835	+	1.00201i
$495$		0			0
$496$	4.07067	−	15.1919i	0.182778	−	0.682139i
$497$	27.5194	+	14.7230i	1.23441	+	0.660418i
$498$		0			0
$499$	23.0606	+	6.17906i	1.03233	+	0.276613i	0.734933	−	0.678140i	$-0.237214\pi$
$499$	23.0606	+	6.17906i	1.03233	+	0.276613i	0.297400	+	0.954753i	$0.403880\pi$
$500$	1.93589	−	7.22485i	0.0865757	−	0.323105i
$501$		0			0
$502$	−25.3496	−	6.79241i	−1.13141	−	0.303160i
$503$	23.7508	+	13.7125i	1.05900	+	0.611412i	0.925155	−	0.379591i	$-0.123935\pi$
$503$	23.7508	+	13.7125i	1.05900	+	0.611412i	0.133842	+	0.991003i	$0.457268\pi$
$504$		0			0
$505$	−6.58528	+	24.5766i	−0.293041	+	1.09364i
$506$	16.3923	−	9.46411i	0.728727	−	0.420731i
$507$		0			0
$508$	2.78606	−	4.82559i	0.123611	−	0.214101i
$509$	1.60605	−	0.430339i	0.0711868	−	0.0190744i	−0.223050	−	0.974807i	$-0.571601\pi$
$509$	1.60605	−	0.430339i	0.0711868	−	0.0190744i	0.294237	+	0.955733i	$0.404935\pi$
$510$		0			0
$511$	−17.3126	−	9.26233i	−0.765865	−	0.409741i
$512$	17.6899	−	17.6899i	0.781789	−	0.781789i
$513$		0			0
$514$	8.95422	+	2.39928i	0.394954	+	0.105828i
$515$	7.85839	−	2.10565i	0.346282	−	0.0927860i
$516$		0			0
$517$	11.5523	+	20.0092i	0.508069	+	0.880001i
$518$	−22.5316	−	5.26274i	−0.989981	−	0.231232i
$519$		0			0
$520$	33.4310	−	25.1697i	1.46604	−	1.10376i
$521$	31.3898	+	18.1229i	1.37521	+	0.793979i	0.991579	−	0.129507i	$-0.0413394\pi$
$521$	31.3898	+	18.1229i	1.37521	+	0.793979i	0.383633	+	0.923486i	$0.374673\pi$
$522$		0			0
$523$	−33.5801	−	19.3875i	−1.46835	−	0.847754i	−0.468982	−	0.883208i	$-0.655379\pi$
$523$	−33.5801	−	19.3875i	−1.46835	−	0.847754i	−0.999371	+	0.0354536i	$0.988712\pi$
$524$	−1.21929	+	2.11188i	−0.0532650	+	0.0922577i
$525$		0			0
$526$	7.36622	+	27.4911i	0.321182	+	1.19867i
$527$	4.54933	+	4.54933i	0.198172	+	0.198172i
$528$		0			0
$529$	−5.78296	−	10.0164i	−0.251433	−	0.435495i
$530$	5.46945	−	9.47337i	0.237578	−	0.411497i
$531$		0			0
$532$	5.23780	−	3.25429i	0.227088	−	0.141091i
$533$	−1.77934	+	12.6215i	−0.0770718	+	0.546699i
$534$		0			0
$535$	−48.3263	−	48.3263i	−2.08933	−	2.08933i
$536$	16.5386			0.714357
$537$		0			0
$538$	−4.55437	−	4.55437i	−0.196353	−	0.196353i
$539$	−20.6668	+	23.5296i	−0.890184	+	1.01349i
$540$		0			0
$541$	6.82499	−	25.4712i	0.293429	−	1.09509i	−0.649028	−	0.760765i	$-0.724824\pi$
$541$	6.82499	−	25.4712i	0.293429	−	1.09509i	0.942457	−	0.334328i	$-0.108509\pi$
$542$	17.4100	−	10.0517i	0.747823	−	0.431756i
$543$		0			0
$544$	0.750975	+	2.80268i	0.0321978	+	0.120164i
$545$	−0.772827			−0.0331043
$546$		0			0
$547$	−1.40037			−0.0598755			−0.0299378	−	0.999552i	$-0.509531\pi$
$547$	−1.40037			−0.0598755			−0.0299378	+	0.999552i	$0.509531\pi$
$548$	−1.09709	−	4.09438i	−0.0468652	−	0.174903i
$549$		0			0
$550$	46.1405	−	26.6392i	1.96744	−	1.13590i
$551$	11.0075	−	41.0807i	0.468937	−	1.75010i
$552$		0			0
$553$	−29.6979	−	6.93658i	−1.26288	−	0.294974i
$554$	6.97419	+	6.97419i	0.296305	+	0.296305i
$555$		0			0
$556$	−6.49895			−0.275617
$557$	15.9249	+	15.9249i	0.674760	+	0.674760i	0.958810	−	0.284049i	$-0.0916779\pi$
$557$	15.9249	+	15.9249i	0.674760	+	0.674760i	−0.284049	+	0.958810i	$0.591678\pi$
$558$		0			0
$559$	−33.5006	−	14.2370i	−1.41692	−	0.602162i
$560$	29.6447	−	0.959079i	1.25272	−	0.0405285i
$561$		0			0
$562$	−10.6255	+	18.4039i	−0.448209	+	0.776321i
$563$	−4.63798	−	8.03322i	−0.195468	−	0.338560i	0.751586	−	0.659635i	$-0.229289\pi$
$563$	−4.63798	−	8.03322i	−0.195468	−	0.338560i	−0.947054	+	0.321075i	$0.895956\pi$
$564$		0			0
$565$	−16.0654	−	16.0654i	−0.675876	−	0.675876i
$566$	4.01406	+	14.9807i	0.168723	+	0.629684i
$567$		0			0
$568$	−17.9662	+	31.1184i	−0.753845	+	1.30570i
$569$	−19.3383	−	11.1650i	−0.810705	−	0.468061i	0.0364957	−	0.999334i	$-0.488380\pi$
$569$	−19.3383	−	11.1650i	−0.810705	−	0.468061i	−0.847201	+	0.531273i	$0.821714\pi$
$570$		0			0
$571$	−9.81204	−	5.66499i	−0.410621	−	0.237072i	0.280435	−	0.959873i	$-0.409521\pi$
$571$	−9.81204	−	5.66499i	−0.410621	−	0.237072i	−0.691057	+	0.722801i	$0.742855\pi$
$572$	−6.94024	−	0.978411i	−0.290186	−	0.0409094i
$573$		0			0
$574$	−8.00320	+	8.53837i	−0.334047	+	0.356385i
$575$	16.0921	+	27.8724i	0.671087	+	1.16236i
$576$		0			0
$577$	29.0695	−	7.78915i	1.21018	−	0.324267i	0.403347	−	0.915047i	$-0.367847\pi$
$577$	29.0695	−	7.78915i	1.21018	−	0.324267i	0.806832	+	0.590781i	$0.201180\pi$
$578$	−18.7949	−	5.03609i	−0.781767	−	0.209474i
$579$		0			0
$580$	−9.28180	+	9.28180i	−0.385406	+	0.385406i
$581$	−18.7250	+	0.605800i	−0.776842	+	0.0251328i
$582$		0			0
$583$	−9.91568	+	2.65690i	−0.410665	+	0.110037i
$584$	11.3026	−	19.5767i	0.467706	−	0.810091i
$585$		0			0
$586$	−9.37618	+	5.41334i	−0.387326	+	0.223623i
$587$	8.03018	−	29.9690i	0.331441	−	1.23695i	−0.576235	−	0.817284i	$-0.695479\pi$
$587$	8.03018	−	29.9690i	0.331441	−	1.23695i	0.907676	−	0.419671i	$-0.137855\pi$
$588$		0			0
$589$	24.8325	+	14.3370i	1.02321	+	0.590748i
$590$	28.0608	+	7.51887i	1.15525	+	0.309547i
$591$		0			0
$592$	5.32255	−	19.8640i	0.218756	−	0.816407i
$593$	−3.81290	−	1.02166i	−0.156577	−	0.0419547i	0.179679	−	0.983725i	$-0.442494\pi$
$593$	−3.81290	−	1.02166i	−0.156577	−	0.0419547i	−0.336256	+	0.941771i	$0.609161\pi$
$594$		0			0
$595$	−5.72353	+	10.6981i	−0.234642	+	0.438580i
$596$	1.90010	−	7.09129i	0.0778313	−	0.290470i
$597$		0			0
$598$	−2.12947	+	15.1051i	−0.0870805	+	0.617695i
$599$	9.50796	−	16.4683i	0.388485	−	0.672876i	−0.603761	−	0.797165i	$-0.706332\pi$
$599$	9.50796	−	16.4683i	0.388485	−	0.672876i	0.992246	+	0.124290i	$0.0396652\pi$
$600$		0			0
$601$	17.8089	−	10.2820i	0.726440	−	0.419410i	−0.0906786	−	0.995880i	$-0.528904\pi$
$601$	17.8089	−	10.2820i	0.726440	−	0.419410i	0.817118	+	0.576470i	$0.195570\pi$
$602$	−17.6372	−	28.3872i	−0.718839	−	1.15698i
$603$		0			0
$604$	−2.70704	+	2.70704i	−0.110148	+	0.110148i
$605$	−33.1806	−	8.89073i	−1.34899	−	0.361459i
$606$		0			0
$607$		−	27.5412i		−	1.11786i	−0.829214	−	0.558931i	$-0.811212\pi$
$607$		−	27.5412i		−	1.11786i	0.829214	−	0.558931i	$-0.188788\pi$
$608$	6.46586	+	11.1992i	0.262225	+	0.454188i
$609$		0			0
$610$		−	25.7748i		−	1.04359i
$611$	−18.4380	−	2.59932i	−0.745921	−	0.105157i
$612$		0			0
$613$	−6.76040	+	6.76040i	−0.273050	+	0.273050i	−0.830327	−	0.557277i	$-0.811846\pi$
$613$	−6.76040	+	6.76040i	−0.273050	+	0.273050i	0.557277	+	0.830327i	$0.311846\pi$
$614$	−11.1090	−	6.41381i	−0.448325	−	0.258840i
$615$		0			0
$616$	−26.3060	−	24.6572i	−1.05990	−	0.993466i
$617$	0.316773	+	1.18221i	0.0127528	+	0.0475941i	0.972009	−	0.234943i	$-0.0754905\pi$
$617$	0.316773	+	1.18221i	0.0127528	+	0.0475941i	−0.959256	+	0.282538i	$0.908824\pi$
$618$		0			0
$619$	−5.25875	−	19.6259i	−0.211367	−	0.788832i	−0.987414	−	0.158157i	$-0.949445\pi$
$619$	−5.25875	−	19.6259i	−0.211367	−	0.788832i	0.776047	−	0.630675i	$-0.217222\pi$
$620$	−4.42500	−	7.66432i	−0.177712	−	0.307806i
$621$		0			0
$622$	−1.08122	−	0.289712i	−0.0433530	−	0.0116164i
$623$	12.2926	+	6.57659i	0.492492	+	0.263486i
$624$		0			0
$625$	9.00066	+	15.5896i	0.360027	+	0.623584i
$626$	28.9891	+	28.9891i	1.15864	+	1.15864i
$627$		0			0
$628$	5.66143			0.225916
$629$	5.94841	+	5.94841i	0.237179	+	0.237179i
$630$		0			0
$631$	0.282038	−	0.0755720i	0.0112278	−	0.00300847i	−0.253201	−	0.967414i	$-0.581483\pi$
$631$	0.282038	−	0.0755720i	0.0112278	−	0.00300847i	0.264429	+	0.964405i	$0.414817\pi$
$632$	9.08748	−	33.9149i	0.361481	−	1.34906i
$633$		0			0
$634$			28.7198i			1.14061i
$635$	12.6466	+	47.1979i	0.501867	+	1.87299i
$636$		0			0
$637$	−4.67803	−	24.8015i	−0.185350	−	0.982673i
$638$	−44.3824			−1.75712
$639$		0			0
$640$			24.0618i			0.951127i
$641$	−33.4427	+	19.3082i	−1.32091	+	0.762626i	−0.983873	−	0.178866i	$-0.942757\pi$
$641$	−33.4427	+	19.3082i	−1.32091	+	0.762626i	−0.337034	+	0.941493i	$0.609424\pi$
$642$		0			0
$643$	−20.7961	+	5.57229i	−0.820116	+	0.219749i	−0.644397	−	0.764691i	$-0.722892\pi$
$643$	−20.7961	+	5.57229i	−0.820116	+	0.219749i	−0.175719	+	0.984440i	$0.556225\pi$
$644$	2.65838	−	2.83615i	0.104755	−	0.111760i
$645$		0			0
$646$	8.07761			0.317809
$647$	7.27173			0.285881			0.142941	−	0.989731i	$-0.454344\pi$
$647$	7.27173			0.285881			0.142941	+	0.989731i	$0.454344\pi$
$648$		0			0
$649$	−13.6311	−	23.6098i	−0.535068	−	0.926765i
$650$	−5.99396	+	42.5174i	−0.235102	+	1.66767i
$651$		0			0
$652$	1.17924	+	0.315977i	0.0461827	+	0.0123746i
$653$	−9.18591	+	15.9105i	−0.359473	+	0.622625i	−0.987873	−	0.155265i	$-0.950377\pi$
$653$	−9.18591	+	15.9105i	−0.359473	+	0.622625i	0.628400	+	0.777890i	$0.283710\pi$
$654$		0			0
$655$	−5.53469	−	20.6557i	−0.216258	−	0.807086i
$656$	−7.35480	−	7.35480i	−0.287157	−	0.287157i
$657$		0			0
$658$	−12.4731	−	11.6914i	−0.486254	−	0.455777i
$659$	−7.69490	+	13.3280i	−0.299751	+	0.519183i	−0.976079	−	0.217417i	$-0.930237\pi$
$659$	−7.69490	+	13.3280i	−0.299751	+	0.519183i	0.676328	+	0.736600i	$0.263570\pi$
$660$		0			0
$661$	22.9763	−	22.9763i	0.893676	−	0.893676i	−0.101191	−	0.994867i	$-0.532265\pi$
$661$	22.9763	−	22.9763i	0.893676	−	0.893676i	0.994867	+	0.101191i	$0.0322654\pi$
$662$	−18.2070	−	10.5118i	−0.707634	−	0.408553i
$663$		0			0
$664$		−	21.5693i		−	0.837050i
$665$	−12.2993	+	52.6573i	−0.476945	+	2.04196i
$666$		0			0
$667$		−	26.8103i		−	1.03810i
$668$	2.81120	−	0.753258i	0.108768	−	0.0291444i
$669$		0			0
$670$	−18.3031	+	18.3031i	−0.707111	+	0.707111i
$671$	−17.1035	+	17.1035i	−0.660273	+	0.660273i
$672$		0			0
$673$	−31.0836	+	17.9461i	−1.19818	+	0.691772i	−0.960150	−	0.279485i	$-0.909836\pi$
$673$	−31.0836	+	17.9461i	−1.19818	+	0.691772i	−0.238034	+	0.971257i	$0.576503\pi$
$674$	−32.0927	+	8.59921i	−1.23616	+	0.331229i
$675$		0			0
$676$	4.06657	−	3.92034i	0.156407	−	0.150782i
$677$	5.45989	−	3.15227i	0.209840	−	0.121151i	−0.391397	−	0.920222i	$-0.628008\pi$
$677$	5.45989	−	3.15227i	0.209840	−	0.121151i	0.601237	+	0.799071i	$0.294675\pi$
$678$		0			0
$679$	−3.48557	+	6.51503i	−0.133764	+	0.250024i
$680$	−12.0972	−	6.98431i	−0.463906	−	0.267836i
$681$		0			0
$682$	7.74467	−	28.9035i	0.296559	−	1.10677i
$683$	0.964556	−	3.59977i	0.0369077	−	0.137741i	−0.945014	−	0.327031i	$-0.893952\pi$
$683$	0.964556	−	3.59977i	0.0369077	−	0.137741i	0.981921	+	0.189290i	$0.0606185\pi$
$684$		0			0
$685$	32.1910	+	18.5855i	1.22995	+	0.710114i
$686$	9.58775	−	21.0960i	0.366062	−	0.805448i
$687$		0			0
$688$	25.7238	−	14.8517i	0.980712	−	0.566215i
$689$	3.23580	−	7.61403i	0.123274	−	0.290071i
$690$		0			0
$691$	39.3550	−	10.5451i	1.49713	−	0.401156i	0.584994	−	0.811037i	$-0.301097\pi$
$691$	39.3550	−	10.5451i	1.49713	−	0.401156i	0.912139	+	0.409882i	$0.134430\pi$
$692$	−3.68257	+	2.12613i	−0.139990	+	0.0808235i
$693$		0			0
$694$	−16.6377	+	16.6377i	−0.631559	+	0.631559i
$695$	40.2984	−	40.2984i	1.52860	−	1.52860i
$696$		0			0
$697$	4.10982	−	1.10122i	0.155670	−	0.0417118i
$698$			36.7985i			1.39285i
$699$		0			0
$700$	7.48272	−	7.98308i	0.282820	−	0.301732i
$701$		−	26.1623i		−	0.988136i	−0.869423	−	0.494068i	$-0.835509\pi$
$701$		−	26.1623i		−	0.988136i	0.869423	−	0.494068i	$-0.164491\pi$
$702$		0			0
$703$	32.4694	+	18.7462i	1.22461	+	0.707027i
$704$	28.1577	−	28.1577i	1.06123	−	1.06123i
$705$		0			0
$706$	4.95220	−	8.57746i	0.186378	−	0.322817i
$707$	−12.0823	+	12.8902i	−0.454402	+	0.484787i
$708$		0			0
$709$	−33.1997	−	33.1997i	−1.24684	−	1.24684i	−0.957108	−	0.289731i	$-0.906434\pi$
$709$	−33.1997	−	33.1997i	−1.24684	−	1.24684i	−0.289731	−	0.957108i	$-0.593566\pi$
$710$	−14.5554	−	54.3215i	−0.546255	−	2.03865i
$711$		0			0
$712$	−8.02528	+	13.9002i	−0.300760	+	0.520932i
$713$	17.4599	+	4.67837i	0.653878	+	0.175206i
$714$		0			0
$715$	49.1016	−	36.9678i	1.83629	−	1.38252i
$716$	2.50846	+	4.34478i	0.0937455	+	0.162372i
$717$		0			0
$718$	31.8907			1.19015
$719$	10.5889			0.394898			0.197449	−	0.980313i	$-0.436734\pi$
$719$	10.5889			0.394898			0.197449	+	0.980313i	$0.436734\pi$
$720$		0			0
$721$	5.50113	+	1.28491i	0.204873	+	0.0478525i
$722$	11.8113	−	3.16482i	0.439569	−	0.117782i
$723$		0			0
$724$	6.38101	−	3.68408i	0.237148	−	0.136918i
$725$		−	75.4648i		−	2.80269i
$726$		0			0
$727$	−23.3269			−0.865148			−0.432574	−	0.901598i	$-0.642395\pi$
$727$	−23.3269			−0.865148			−0.432574	+	0.901598i	$0.642395\pi$
$728$	28.7132	−	4.45968i	1.06418	−	0.165287i
$729$		0			0
$730$	9.15688	+	34.1740i	0.338911	+	1.26483i
$731$			12.1506i			0.449406i
$732$		0			0
$733$	−10.7328	+	40.0554i	−0.396426	+	1.47948i	0.422912	+	0.906171i	$0.361008\pi$
$733$	−10.7328	+	40.0554i	−0.396426	+	1.47948i	−0.819338	+	0.573311i	$0.805659\pi$
$734$	40.4416	−	10.8363i	1.49273	−	0.399975i
$735$		0			0
$736$	5.76434	+	5.76434i	0.212476	+	0.212476i
$737$	24.2909			0.894768
$738$		0			0
$739$	3.17436	+	3.17436i	0.116771	+	0.116771i	0.763078	−	0.646307i	$-0.223687\pi$
$739$	3.17436	+	3.17436i	0.116771	+	0.116771i	−0.646307	+	0.763078i	$0.723687\pi$
$740$	−5.78585	−	10.0214i	−0.212692	−	0.368393i
$741$		0			0
$742$	6.45187	−	4.00860i	0.236855	−	0.147160i
$743$	11.0839	+	2.96992i	0.406629	+	0.108956i	0.456335	−	0.889808i	$-0.349162\pi$
$743$	11.0839	+	2.96992i	0.406629	+	0.108956i	−0.0497063	+	0.998764i	$0.515829\pi$
$744$		0			0
$745$	32.1892	+	55.7534i	1.17932	+	2.04265i
$746$	−0.611448	−	2.28196i	−0.0223867	−	0.0835484i
$747$		0			0
$748$	0.605532	+	2.25988i	0.0221404	+	0.0826293i
$749$	−13.7585	−	45.4183i	−0.502723	−	1.65955i
$750$		0			0
$751$	−13.4143	−	7.74474i	−0.489494	−	0.282609i	0.234871	−	0.972027i	$-0.424533\pi$
$751$	−13.4143	−	7.74474i	−0.489494	−	0.282609i	−0.724365	+	0.689417i	$0.757867\pi$
$752$	10.7442	−	10.7442i	0.391799	−	0.391799i
$753$		0			0
$754$	22.0333	−	28.1765i	0.802404	−	1.02613i
$755$		−	33.5713i		−	1.22179i
$756$		0			0
$757$	−20.6838	−	35.8253i	−0.751765	−	1.30209i	−0.946967	−	0.321331i	$-0.895870\pi$
$757$	−20.6838	−	35.8253i	−0.751765	−	1.30209i	0.195202	−	0.980763i	$-0.437464\pi$
$758$			2.16801i			0.0787458i
$759$		0			0
$760$	−60.1347	−	16.1130i	−2.18131	−	0.584481i
$761$	−15.5732	+	15.5732i	−0.564529	+	0.564529i	−0.930591	−	0.366062i	$-0.880706\pi$
$761$	−15.5732	+	15.5732i	−0.564529	+	0.564529i	0.366062	+	0.930591i	$0.380706\pi$
$762$		0			0
$763$	−0.473173	−	0.253150i	−0.0171300	−	0.00916463i
$764$	0.744145	−	0.429632i	0.0269222	−	0.0155436i
$765$		0			0
$766$	−3.33395	+	5.77456i	−0.120460	+	0.208643i
$767$	21.7559	+	3.06707i	0.785559	+	0.110745i
$768$		0			0
$769$	8.12503	−	30.3230i	0.292996	−	1.09348i	−0.649799	−	0.760106i	$-0.725147\pi$
$769$	8.12503	−	30.3230i	0.292996	−	1.09348i	0.942796	−	0.333371i	$-0.108186\pi$
$770$	56.4005	−	1.82470i	2.03253	−	0.0657576i
$771$		0			0
$772$	1.35195	+	0.362253i	0.0486576	+	0.0130378i
$773$	4.35215	−	16.2425i	0.156536	−	0.584201i	−0.842433	−	0.538801i	$-0.818877\pi$
$773$	4.35215	−	16.2425i	0.156536	−	0.584201i	0.998969	−	0.0453993i	$-0.0144560\pi$
$774$		0			0
$775$	49.1455	+	13.1685i	1.76536	+	0.473026i
$776$	−7.36706	−	4.25337i	−0.264462	−	0.152687i
$777$		0			0
$778$	−5.07039	+	18.9229i	−0.181782	+	0.678421i
$779$	16.4224	−	9.48148i	0.588394	−	0.339709i
$780$		0			0
$781$	−26.3878	+	45.7049i	−0.944228	+	1.63545i
$782$	4.91853	−	1.31792i	0.175886	−	0.0471286i
$783$		0			0
$784$	18.4645	+	9.12328i	0.659445	+	0.325832i
$785$	−35.1051	+	35.1051i	−1.25295	+	1.25295i
$786$		0			0
$787$	10.6185	+	2.84522i	0.378508	+	0.101421i	0.443057	−	0.896494i	$-0.353894\pi$
$787$	10.6185	+	2.84522i	0.378508	+	0.101421i	−0.0645484	+	0.997915i	$0.520561\pi$
$788$	−2.46203	+	0.659699i	−0.0877063	+	0.0235008i
$789$		0			0
$790$	27.4764	+	47.5905i	0.977565	+	1.69319i
$791$	−4.57380	−	15.0987i	−0.162626	−	0.536847i
$792$		0			0
$793$	−2.36739	−	19.3492i	−0.0840684	−	0.687109i
$794$	−22.9055	−	13.2245i	−0.812885	−	0.469319i
$795$		0			0
$796$	−0.711678	−	0.410887i	−0.0252247	−	0.0145635i
$797$	2.77166	−	4.80066i	0.0981772	−	0.170048i	−0.812753	−	0.582608i	$-0.802032\pi$
$797$	2.77166	−	4.80066i	0.0981772	−	0.170048i	0.910930	+	0.412560i	$0.135365\pi$
$798$		0			0
$799$	1.60870	+	6.00376i	0.0569118	+	0.212398i
$800$	16.2253	+	16.2253i	0.573650	+	0.573650i
$801$		0			0
$802$	5.25232	+	9.09728i	0.185466	+	0.321236i
$803$	16.6007	−	28.7532i	0.585826	−	1.01468i
$804$		0			0
$805$	1.10226	+	34.0702i	0.0388495	+	1.20082i
$806$	14.5048	+	19.2656i	0.510910	+	0.678603i
$807$		0			0
$808$	−14.3829	−	14.3829i	−0.505989	−	0.505989i
$809$	−47.6802			−1.67635			−0.838174	−	0.545403i	$-0.816377\pi$
$809$	−47.6802			−1.67635			−0.838174	+	0.545403i	$0.816377\pi$
$810$		0			0
$811$	−3.30449	−	3.30449i	−0.116036	−	0.116036i	0.646704	−	0.762741i	$-0.276147\pi$
$811$	−3.30449	−	3.30449i	−0.116036	−	0.116036i	−0.762741	+	0.646704i	$0.776147\pi$
$812$	−8.72327	+	2.64252i	−0.306127	+	0.0927343i
$813$		0			0
$814$	10.1264	−	37.7924i	0.354931	−	1.32462i
$815$	−9.27147	+	5.35289i	−0.324766	+	0.187503i
$816$		0			0
$817$	14.0159	+	52.3081i	0.490355	+	1.83003i
$818$	17.0646			0.596650
$819$		0			0
$820$	−5.85274			−0.204387
$821$	−11.0324	−	41.1736i	−0.385035	−	1.43697i	−0.838112	−	0.545498i	$-0.816340\pi$
$821$	−11.0324	−	41.1736i	−0.385035	−	1.43697i	0.453077	−	0.891471i	$-0.350326\pi$
$822$		0			0
$823$	−27.8995	+	16.1078i	−0.972517	+	0.561483i	−0.900003	−	0.435885i	$-0.856436\pi$
$823$	−27.8995	+	16.1078i	−0.972517	+	0.561483i	−0.0725142	+	0.997367i	$0.523102\pi$
$824$	−1.68333	+	6.28228i	−0.0586417	+	0.218854i
$825$		0			0
$826$	14.7177	+	13.7952i	0.512093	+	0.479997i
$827$	16.5275	+	16.5275i	0.574718	+	0.574718i	0.933443	−	0.358725i	$-0.116789\pi$
$827$	16.5275	+	16.5275i	0.574718	+	0.574718i	−0.358725	+	0.933443i	$0.616789\pi$
$828$		0			0
$829$	24.3425			0.845451			0.422725	−	0.906258i	$-0.361073\pi$
$829$	24.3425			0.845451			0.422725	+	0.906258i	$0.361073\pi$
$830$	23.8706	+	23.8706i	0.828559	+	0.828559i
$831$		0			0
$832$	3.89746	+	31.8548i	0.135120	+	1.10437i
$833$	−7.00861	+	4.67523i	−0.242834	+	0.161987i
$834$		0			0
$835$	−12.7608	+	22.1023i	−0.441605	+	0.764882i
$836$	5.21361	+	9.03023i	0.180316	+	0.312317i
$837$		0			0
$838$	−14.7430	−	14.7430i	−0.509289	−	0.509289i
$839$	7.84399	+	29.2742i	0.270805	+	1.01066i	0.958601	+	0.284753i	$0.0919115\pi$
$839$	7.84399	+	29.2742i	0.270805	+	1.01066i	−0.687797	+	0.725904i	$0.741422\pi$
$840$		0			0
$841$	−16.9321	+	29.3273i	−0.583866	+	1.01129i
$842$	36.5572	+	21.1063i	1.25985	+	0.727372i
$843$		0			0
$844$	0.728076	+	0.420355i	0.0250614	+	0.0144692i
$845$	−0.906785	+	49.5248i	−0.0311943	+	1.70371i
$846$		0			0
$847$	−17.4030	−	16.3122i	−0.597973	−	0.560494i
$848$	3.37550	+	5.84653i	0.115915	+	0.200771i
$849$		0			0
$850$	13.8445	−	3.70962i	0.474862	−	0.127239i
$851$	22.8295	+	6.11714i	0.782584	+	0.209693i
$852$		0			0
$853$	29.1952	−	29.1952i	0.999624	−	0.999624i	−0.000375643	−	1.00000i	$-0.500120\pi$
$853$	29.1952	−	29.1952i	0.999624	−	0.999624i	1.00000		0.000375643i	$0.000119571\pi$
$854$	8.44287	−	15.7809i	0.288909	−	0.540013i
$855$		0			0
$856$	52.7748	−	14.1410i	1.80381	−	0.483328i
$857$	−19.8885	+	34.4479i	−0.679379	+	1.17672i	0.295790	+	0.955253i	$0.404417\pi$
$857$	−19.8885	+	34.4479i	−0.679379	+	1.17672i	−0.975168	+	0.221465i	$0.928916\pi$
$858$		0			0
$859$	2.87941	−	1.66243i	0.0982443	−	0.0567214i	−0.450073	−	0.892992i	$-0.648602\pi$
$859$	2.87941	−	1.66243i	0.0982443	−	0.0567214i	0.548317	+	0.836270i	$0.315269\pi$
$860$	4.32588	−	16.1444i	0.147511	−	0.550520i
$861$		0			0
$862$	9.75910	+	5.63442i	0.332396	+	0.191909i
$863$	29.0179	+	7.77531i	0.987779	+	0.264675i	0.716317	−	0.697775i	$-0.245826\pi$
$863$	29.0179	+	7.77531i	0.987779	+	0.264675i	0.271462	+	0.962449i	$0.412493\pi$
$864$		0			0
$865$	9.65108	−	36.0183i	0.328147	−	1.22466i
$866$	19.1677	+	5.13596i	0.651343	+	0.174527i
$867$		0			0
$868$	−0.198710	−	6.14204i	−0.00674467	−	0.208474i
$869$	13.3472	−	49.8124i	0.452773	−	1.68977i
$870$		0			0
$871$	−12.0590	+	15.4213i	−0.408605	+	0.522530i
$872$	0.308913	−	0.535053i	0.0104611	−	0.0181192i
$873$		0			0
$874$	19.6539	−	11.3472i	0.664804	−	0.383825i
$875$	1.47273	+	45.5212i	0.0497872	+	1.53890i
$876$		0			0
$877$	−6.09999	+	6.09999i	−0.205982	+	0.205982i	−0.802557	−	0.596575i	$-0.796528\pi$
$877$	−6.09999	+	6.09999i	−0.205982	+	0.205982i	0.596575	+	0.802557i	$0.296528\pi$
$878$	−23.3084	−	6.24546i	−0.786620	−	0.210774i
$879$		0			0
$880$			50.1542i			1.69070i
$881$	1.81740	+	3.14783i	0.0612299	+	0.106053i	0.895015	−	0.446035i	$-0.147164\pi$
$881$	1.81740	+	3.14783i	0.0612299	+	0.106053i	−0.833786	+	0.552088i	$0.813831\pi$
$882$		0			0
$883$			9.84592i			0.331342i	0.986181	+	0.165671i	$0.0529789\pi$
$883$			9.84592i			0.331342i	−0.986181	+	0.165671i	$0.947021\pi$
$884$	−1.73531	−	0.737470i	−0.0583648	−	0.0248038i
$885$		0			0
$886$	−26.1124	+	26.1124i	−0.877264	+	0.877264i
$887$	−35.4119	−	20.4450i	−1.18901	−	0.686478i	−0.230932	−	0.972970i	$-0.574177\pi$
$887$	−35.4119	−	20.4450i	−1.18901	−	0.686478i	−0.958083	+	0.286492i	$0.907511\pi$
$888$		0			0
$889$	−7.71723	+	33.0401i	−0.258828	+	1.10813i
$890$	−6.50172	−	24.2648i	−0.217938	−	0.813356i
$891$		0			0
$892$	1.68795	+	6.29950i	0.0565166	+	0.210923i
$893$	13.8509	+	23.9904i	0.463502	+	0.802809i
$894$		0			0
$895$	−42.4952	−	11.3866i	−1.42046	−	0.380611i
$896$	−7.88176	+	14.7321i	−0.263311	+	0.492166i
$897$		0			0
$898$	−9.50068	−	16.4557i	−0.317042	−	0.549133i
$899$	−29.9698	−	29.9698i	−0.999550	−	0.999550i
$900$		0			0
$901$	−2.76160			−0.0920022
$902$	−13.9929	−	13.9929i	−0.465913	−	0.465913i
$903$		0			0
$904$	17.5442	−	4.70096i	0.583512	−	0.156352i
$905$	−16.7230	+	62.4110i	−0.555891	+	2.07461i
$906$		0			0
$907$		−	19.1425i		−	0.635618i	−0.948155	−	0.317809i	$-0.897053\pi$
$907$		−	19.1425i		−	0.635618i	0.948155	−	0.317809i	$-0.102947\pi$
$908$	2.74576	+	10.2473i	0.0911214	+	0.340070i
$909$		0			0
$910$	−26.8411	+	36.7121i	−0.889775	+	1.21700i
$911$	−2.12009			−0.0702418			−0.0351209	−	0.999383i	$-0.511182\pi$
$911$	−2.12009			−0.0702418			−0.0351209	+	0.999383i	$0.511182\pi$
$912$		0			0
$913$		−	31.6798i		−	1.04845i
$914$	33.4366	−	19.3046i	1.10598	−	0.638540i
$915$		0			0
$916$	−1.94970	+	0.522419i	−0.0644197	+	0.0172612i
$917$	3.37738	−	14.4597i	0.111531	−	0.477501i
$918$		0			0
$919$	7.19783			0.237435			0.118717	−	0.992928i	$-0.462122\pi$
$919$	7.19783			0.237435			0.118717	+	0.992928i	$0.462122\pi$
$920$	−39.2454			−1.29388
$921$		0			0
$922$	16.2143	+	28.0840i	0.533990	+	0.924898i
$923$	−15.9161	−	39.4423i	−0.523886	−	1.29826i
$924$		0			0
$925$	64.2595	+	17.2183i	2.11284	+	0.566134i
$926$	10.6709	−	18.4825i	0.350667	−	0.607372i
$927$		0			0
$928$	−4.94723	−	18.4633i	−0.162401	−	0.606088i
$929$	19.6636	+	19.6636i	0.645141	+	0.645141i	0.951815	−	0.306674i	$-0.0992162\pi$
$929$	19.6636	+	19.6636i	0.645141	+	0.645141i	−0.306674	+	0.951815i	$0.599216\pi$
$930$		0			0
$931$	−24.7790	+	28.2113i	−0.812098	+	0.924588i
$932$	−3.80731	+	6.59445i	−0.124712	+	0.216008i
$933$		0			0
$934$	−20.4649	+	20.4649i	−0.669633	+	0.669633i
$935$	−17.7677	−	10.2582i	−0.581065	−	0.335478i
$936$		0			0
$937$			47.3785i			1.54779i	0.633315	+	0.773894i	$0.281694\pi$
$937$			47.3785i			1.54779i	−0.633315	+	0.773894i	$0.718306\pi$
$938$	−17.2017	+	5.21088i	−0.561656	+	0.170141i
$939$		0			0
$940$		−	8.54989i		−	0.278867i
$941$	−29.0378	+	7.78065i	−0.946604	+	0.253642i	−0.698921	−	0.715199i	$-0.746336\pi$
$941$	−29.0378	+	7.78065i	−0.946604	+	0.253642i	−0.247683	+	0.968841i	$0.579669\pi$
$942$		0			0
$943$	8.45278	−	8.45278i	0.275260	−	0.275260i
$944$	−12.6776	+	12.6776i	−0.412619	+	0.412619i
$945$		0			0
$946$	48.9410	−	28.2561i	1.59121	−	0.918685i
$947$	−1.50945	+	0.404457i	−0.0490506	+	0.0131431i	−0.283261	−	0.959043i	$-0.591416\pi$
$947$	−1.50945	+	0.404457i	−0.0490506	+	0.0131431i	0.234210	+	0.972186i	$0.424750\pi$
$948$		0			0
$949$	10.0129	+	24.8134i	0.325033	+	0.805476i
$950$	55.3212	−	31.9397i	1.79486	−	1.03626i
$951$		0			0
$952$	−5.11884	−	8.23882i	−0.165903	−	0.267022i
$953$	−20.1615	−	11.6403i	−0.653096	−	0.377065i	0.136545	−	0.990634i	$-0.456400\pi$
$953$	−20.1615	−	11.6403i	−0.653096	−	0.377065i	−0.789641	+	0.613569i	$0.789733\pi$
$954$		0			0
$955$	−1.95021	+	7.27830i	−0.0631075	+	0.235520i
$956$	−0.285909	+	1.06703i	−0.00924696	+	0.0345101i
$957$		0			0
$958$	−31.1314	−	17.9737i	−1.00581	−	0.580704i
$959$	13.6214	+	21.9237i	0.439858	+	0.707955i
$960$		0			0
$961$	−2.09961	+	1.21221i	−0.0677295	+	0.0391037i
$962$	18.9656	+	25.1905i	0.611475	+	0.812176i
$963$		0			0
$964$	−1.83207	+	0.490902i	−0.0590070	+	0.0158109i
$965$	−10.6293	+	6.13684i	−0.342170	+	0.197552i
$966$		0			0
$967$	−5.77720	+	5.77720i	−0.185782	+	0.185782i	−0.793870	−	0.608088i	$-0.791937\pi$
$967$	−5.77720	+	5.77720i	−0.185782	+	0.185782i	0.608088	+	0.793870i	$0.291937\pi$
$968$	19.4183	−	19.4183i	0.624126	−	0.624126i
$969$		0			0
$970$	12.8602	−	3.44589i	0.412917	−	0.110641i
$971$			15.5472i			0.498934i	0.968383	+	0.249467i	$0.0802554\pi$
$971$			15.5472i			0.498934i	−0.968383	+	0.249467i	$0.919745\pi$
$972$		0			0
$973$	37.8734	−	11.4729i	1.21417	−	0.367805i
$974$		−	21.6529i		−	0.693805i
$975$		0			0
$976$	13.7759	+	7.95352i	0.440956	+	0.254586i
$977$	−21.0735	+	21.0735i	−0.674200	+	0.674200i	−0.958682	−	0.284481i	$-0.908179\pi$
$977$	−21.0735	+	21.0735i	−0.674200	+	0.674200i	0.284481	+	0.958682i	$0.408179\pi$
$978$		0			0
$979$	−11.7871	+	20.4158i	−0.376717	+	0.652493i
$980$	10.9768	−	3.71672i	0.350640	−	0.118726i
$981$		0			0
$982$	−30.9035	−	30.9035i	−0.986172	−	0.986172i
$983$	−13.2861	−	49.5845i	−0.423762	−	1.58150i	−0.766612	−	0.642111i	$-0.778059\pi$
$983$	−13.2861	−	49.5845i	−0.423762	−	1.58150i	0.342850	−	0.939390i	$-0.388608\pi$
$984$		0			0
$985$	11.1758	−	19.3571i	0.356091	−	0.616768i
$986$	−11.5328	−	3.09022i	−0.367281	−	0.0984125i
$987$		0			0
$988$	−8.32116	−	1.17309i	−0.264731	−	0.0373209i
$989$	17.0688	+	29.5641i	0.542757	+	0.940083i
$990$		0			0
$991$	−20.0235			−0.636069			−0.318034	−	0.948079i	$-0.603023\pi$
$991$	−20.0235			−0.636069			−0.318034	+	0.948079i	$0.603023\pi$
$992$	12.8873			0.409172
$993$		0			0
$994$	8.88199	−	38.0268i	0.281720	−	1.20614i
$995$	6.96074	−	1.86513i	0.220670	−	0.0591285i
$996$		0			0
$997$	−10.6118	+	6.12675i	−0.336080	+	0.194036i	−0.658537	−	0.752548i	$-0.728825\pi$
$997$	−10.6118	+	6.12675i	−0.336080	+	0.194036i	0.322457	+	0.946584i	$0.395491\pi$
$998$		−	29.8712i		−	0.945555i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.gh.d.262.3		40
3.2	odd	2		273.2.cg.b.262.8	yes	40
7.5	odd	6		819.2.et.d.145.3		40
13.7	odd	12		819.2.et.d.514.3		40
21.5	even	6		273.2.bt.b.145.8	✓	40
39.20	even	12		273.2.bt.b.241.8	yes	40
91.33	even	12	inner	819.2.gh.d.397.3		40
273.215	odd	12		273.2.cg.b.124.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.145.8	✓	40	21.5	even	6
273.2.bt.b.241.8	yes	40	39.20	even	12
273.2.cg.b.124.8	yes	40	273.215	odd	12
273.2.cg.b.262.8	yes	40	3.2	odd	2
819.2.et.d.145.3		40	7.5	odd	6
819.2.et.d.514.3		40	13.7	odd	12
819.2.gh.d.262.3		40	1.1	even	1	trivial
819.2.gh.d.397.3		40	91.33	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)

\(f(q)\)	\(=\)	\(q+(-0.323834 - 1.20856i) q^{2} +(0.376291 - 0.217252i) q^{4} +(-0.986163 + 3.68041i) q^{5} +(-1.80936 + 1.93034i) q^{7} +(-2.15388 - 2.15388i) q^{8} +O(q^{10})\)	\(q+(-0.323834 - 1.20856i) q^{2} +(0.376291 - 0.217252i) q^{4} +(-0.986163 + 3.68041i) q^{5} +(-1.80936 + 1.93034i) q^{7} +(-2.15388 - 2.15388i) q^{8} +4.76737 q^{10} +(-3.16350 - 3.16350i) q^{11} +(3.57886 - 0.437877i) q^{13} +(2.91888 + 1.56161i) q^{14} +(-1.47110 + 2.54802i) q^{16} +(-0.601776 - 1.04231i) q^{17} +(-3.79295 - 3.79295i) q^{19} +(0.428491 + 1.59915i) q^{20} +(-2.79885 + 4.84774i) q^{22} +(-2.92841 - 1.69072i) q^{23} +(-8.24277 - 4.75896i) q^{25} +(-1.68816 - 4.18349i) q^{26} +(-0.261474 + 1.11946i) q^{28} +(3.96435 + 6.86645i) q^{29} +(-5.16347 + 1.38355i) q^{31} +(-2.32867 - 0.623965i) q^{32} +(-1.06482 + 1.06482i) q^{34} +(-5.32014 - 8.56280i) q^{35} +(-6.75142 + 1.80904i) q^{37} +(-3.35574 + 5.81231i) q^{38} +(10.0512 - 5.80308i) q^{40} +(-0.914977 + 3.41474i) q^{41} +(-8.74306 - 5.04781i) q^{43} +(-1.87767 - 0.503121i) q^{44} +(-1.09502 + 4.08668i) q^{46} +(-4.98837 - 1.33663i) q^{47} +(-0.452462 - 6.98536i) q^{49} +(-3.08223 + 11.5030i) q^{50} +(1.25156 - 0.942283i) q^{52} +(1.14727 - 1.98713i) q^{53} +(14.7627 - 8.52325i) q^{55} +(8.05487 - 0.260595i) q^{56} +(7.01476 - 7.01476i) q^{58} +(5.88602 + 1.57716i) q^{59} -5.40651i q^{61} +(3.34421 + 5.79234i) q^{62} +8.90081i q^{64} +(-1.91777 + 13.6035i) q^{65} +(-3.83925 + 3.83925i) q^{67} +(-0.452886 - 0.261474i) q^{68} +(-8.62586 + 9.20266i) q^{70} +(-3.05313 - 11.3945i) q^{71} +(1.92074 + 7.16831i) q^{73} +(4.37268 + 7.57370i) q^{74} +(-2.25128 - 0.603228i) q^{76} +(11.8305 - 0.382748i) q^{77} +(5.76343 + 9.98255i) q^{79} +(-7.92701 - 7.92701i) q^{80} +4.42323 q^{82} +(5.00708 + 5.00708i) q^{83} +(4.42956 - 1.18690i) q^{85} +(-3.26930 + 12.2012i) q^{86} +13.6276i q^{88} +(-1.36380 - 5.08976i) q^{89} +(-5.63018 + 7.70072i) q^{91} -1.46924 q^{92} +6.46162i q^{94} +(17.7001 - 10.2191i) q^{95} +(2.69756 - 0.722808i) q^{97} +(-8.29574 + 2.80893i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7}+O(q^{10}) \) 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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