LMFDB - Embedded newform 693.2.m.j.379.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 12 x^{18} - 3 x^{17} + 94 x^{16} - 10 x^{15} + 662 x^{14} - 153 x^{13} + 4638 x^{12} + \cdots + 121 $ x^20 + 12x^18 - 3x^17 + 94x^16 - 10x^15 + 662x^14 - 153x^13 + 4638x^12 - 1174x^11 + 15808x^10 - 3393x^9 + 26062x^8 - 15494x^7 + 11660x^6 - 33295x^5 + 67756x^4 - 43696x^3 + 13084x^2 - 1155x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			379.5
Root			$0.739775 - 2.27679i$ of defining polynomial
Character	$\chi$	$=$	693.379
Dual form			693.2.m.j.64.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.739775 + 2.27679i) q^{2} +(-3.01849 + 2.19306i) q^{4} +(1.21700 - 3.74554i) q^{5} +(0.809017 - 0.587785i) q^{7} +(-3.35264 - 2.43583i) q^{8} +O(q^{10})$	\(q+(0.739775 + 2.27679i) q^{2} +(-3.01849 + 2.19306i) q^{4} +(1.21700 - 3.74554i) q^{5} +(0.809017 - 0.587785i) q^{7} +(-3.35264 - 2.43583i) q^{8} +9.42812 q^{10} +(-2.04163 - 2.61376i) q^{11} +(-0.926710 - 2.85212i) q^{13} +(1.93676 + 1.40714i) q^{14} +(0.759773 - 2.33834i) q^{16} +(2.04092 - 6.28132i) q^{17} +(4.77571 + 3.46976i) q^{19} +(4.54069 + 13.9748i) q^{20} +(4.44064 - 6.58197i) q^{22} +6.02551 q^{23} +(-8.50288 - 6.17770i) q^{25} +(5.80813 - 4.21986i) q^{26} +(-1.15296 + 3.54845i) q^{28} +(-1.23031 + 0.893876i) q^{29} +(2.61707 + 8.05452i) q^{31} -2.40219 q^{32} +15.8111 q^{34} +(-1.21700 - 3.74554i) q^{35} +(0.491753 - 0.357279i) q^{37} +(-4.36697 + 13.4401i) q^{38} +(-13.2037 + 9.59302i) q^{40} +(-1.37802 - 1.00119i) q^{41} -3.23364 q^{43} +(11.8948 + 3.41217i) q^{44} +(4.45752 + 13.7188i) q^{46} +(-3.88520 - 2.82276i) q^{47} +(0.309017 - 0.951057i) q^{49} +(7.77514 - 23.9294i) q^{50} +(9.05214 + 6.57676i) q^{52} +(1.89376 + 5.82840i) q^{53} +(-12.2746 + 4.46608i) q^{55} -4.14409 q^{56} +(-2.94533 - 2.13990i) q^{58} +(5.04732 - 3.66709i) q^{59} +(-0.645533 + 1.98674i) q^{61} +(-16.4024 + 11.9171i) q^{62} +(-3.29663 - 10.1460i) q^{64} -11.8105 q^{65} -0.599719 q^{67} +(7.61481 + 23.4360i) q^{68} +(7.62751 - 5.54171i) q^{70} +(-0.435614 + 1.34068i) q^{71} +(-5.73473 + 4.16652i) q^{73} +(1.17724 + 0.855314i) q^{74} -22.0248 q^{76} +(-3.18805 - 0.914531i) q^{77} +(-0.316207 - 0.973184i) q^{79} +(-7.83370 - 5.69152i) q^{80} +(1.26008 - 3.87812i) q^{82} +(-0.954026 + 2.93619i) q^{83} +(-21.0431 - 15.2887i) q^{85} +(-2.39216 - 7.36232i) q^{86} +(0.478184 + 13.7361i) q^{88} +2.48531 q^{89} +(-2.42616 - 1.76271i) q^{91} +(-18.1879 + 13.2143i) q^{92} +(3.55268 - 10.9340i) q^{94} +(18.8081 - 13.6649i) q^{95} +(0.788908 + 2.42801i) q^{97} +2.39396 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8}+O(q^{10}) $ 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8	$ 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8} + 12 q^{10} + q^{11} + 13 q^{13} - 24 q^{16} + q^{17} + 10 q^{19} + 46 q^{20} + 26 q^{22} - 8 q^{25} + 53 q^{26} + 4 q^{28} - 3 q^{29} - 13 q^{31} - 82 q^{32} + 42 q^{34} - 5 q^{35} - 32 q^{37} - 16 q^{38} + 20 q^{40} + 3 q^{41} + 12 q^{43} - 25 q^{44} - 13 q^{46} - 20 q^{47} - 5 q^{49} + 83 q^{50} - 80 q^{52} - 3 q^{53} - 28 q^{55} + 6 q^{56} + 2 q^{58} + 9 q^{59} - 15 q^{61} + 37 q^{62} - 49 q^{64} - 58 q^{65} + 76 q^{67} - 51 q^{68} + 3 q^{70} - 37 q^{71} + 27 q^{73} + 32 q^{74} + 4 q^{76} - 6 q^{77} + 5 q^{79} - 137 q^{80} - 55 q^{82} + 42 q^{83} - 48 q^{85} - 3 q^{86} + 151 q^{88} + 18 q^{89} + 7 q^{91} - 39 q^{92} - 35 q^{94} + 96 q^{95} - 27 q^{97}+O(q^{100}) $ 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8 + 12 * q^10 + q^11 + 13 * q^13 - 24 * q^16 + q^17 + 10 * q^19 + 46 * q^20 + 26 * q^22 - 8 * q^25 + 53 * q^26 + 4 * q^28 - 3 * q^29 - 13 * q^31 - 82 * q^32 + 42 * q^34 - 5 * q^35 - 32 * q^37 - 16 * q^38 + 20 * q^40 + 3 * q^41 + 12 * q^43 - 25 * q^44 - 13 * q^46 - 20 * q^47 - 5 * q^49 + 83 * q^50 - 80 * q^52 - 3 * q^53 - 28 * q^55 + 6 * q^56 + 2 * q^58 + 9 * q^59 - 15 * q^61 + 37 * q^62 - 49 * q^64 - 58 * q^65 + 76 * q^67 - 51 * q^68 + 3 * q^70 - 37 * q^71 + 27 * q^73 + 32 * q^74 + 4 * q^76 - 6 * q^77 + 5 * q^79 - 137 * q^80 - 55 * q^82 + 42 * q^83 - 48 * q^85 - 3 * q^86 + 151 * q^88 + 18 * q^89 + 7 * q^91 - 39 * q^92 - 35 * q^94 + 96 * q^95 - 27 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.739775	+	2.27679i	0.523100	+	1.60994i	0.768043	+	0.640399i	$0.221231\pi$
$2$	0.739775	+	2.27679i	0.523100	+	1.60994i	−0.244942	+	0.969538i	$0.578769\pi$
$3$		0			0
$3$		0			0
$4$	−3.01849	+	2.19306i	−1.50924	+	1.09653i
$5$	1.21700	−	3.74554i	0.544258	−	1.67506i	−0.178488	−	0.983942i	$-0.557121\pi$
$5$	1.21700	−	3.74554i	0.544258	−	1.67506i	0.722747	−	0.691113i	$-0.242879\pi$
$6$		0			0
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$8$	−3.35264	−	2.43583i	−1.18534	−	0.861197i
$9$		0			0
$10$	9.42812			2.98143
$11$	−2.04163	−	2.61376i	−0.615576	−	0.788077i
$11$	−2.04163	−	2.61376i	−0.615576	−	0.788077i
$12$		0			0
$13$	−0.926710	−	2.85212i	−0.257023	−	0.791036i	−0.993424	−	0.114491i	$-0.963476\pi$
$13$	−0.926710	−	2.85212i	−0.257023	−	0.791036i	0.736401	−	0.676545i	$-0.236524\pi$
$14$	1.93676	+	1.40714i	0.517620	+	0.376073i
$15$		0			0
$16$	0.759773	−	2.33834i	0.189943	−	0.584585i
$17$	2.04092	−	6.28132i	0.494997	−	1.52344i	−0.321965	−	0.946752i	$-0.604343\pi$
$17$	2.04092	−	6.28132i	0.494997	−	1.52344i	0.816961	−	0.576692i	$-0.195657\pi$
$18$		0			0
$19$	4.77571	+	3.46976i	1.09562	+	0.796017i	0.980340	−	0.197316i	$-0.0632225\pi$
$19$	4.77571	+	3.46976i	1.09562	+	0.796017i	0.115283	+	0.993333i	$0.463222\pi$
$20$	4.54069	+	13.9748i	1.01533	+	3.12486i
$21$		0			0
$22$	4.44064	−	6.58197i	0.946747	−	1.40328i
$23$	6.02551			1.25641			0.628203	−	0.778049i	$-0.283791\pi$
$23$	6.02551			1.25641			0.628203	+	0.778049i	$0.283791\pi$
$24$		0			0
$25$	−8.50288	−	6.17770i	−1.70058	−	1.23554i
$26$	5.80813	−	4.21986i	1.13907	−	0.827582i
$27$		0			0
$28$	−1.15296	+	3.54845i	−0.217889	+	0.670593i
$29$	−1.23031	+	0.893876i	−0.228464	+	0.165989i	−0.696128	−	0.717917i	$-0.745096\pi$
$29$	−1.23031	+	0.893876i	−0.228464	+	0.165989i	0.467665	+	0.883906i	$0.345096\pi$
$30$		0			0
$31$	2.61707	+	8.05452i	0.470040	+	1.44663i	0.852532	+	0.522675i	$0.175066\pi$
$31$	2.61707	+	8.05452i	0.470040	+	1.44663i	−0.382492	+	0.923959i	$0.624934\pi$
$32$	−2.40219			−0.424652
$33$		0			0
$34$	15.8111			2.71158
$35$	−1.21700	−	3.74554i	−0.205710	−	0.633111i
$36$		0			0
$37$	0.491753	−	0.357279i	0.0808437	−	0.0587364i	−0.546629	−	0.837375i	$-0.684089\pi$
$37$	0.491753	−	0.357279i	0.0808437	−	0.0587364i	0.627473	+	0.778638i	$0.284089\pi$
$38$	−4.36697	+	13.4401i	−0.708416	+	2.18028i
$39$		0			0
$40$	−13.2037	+	9.59302i	−2.08768	+	1.51679i
$41$	−1.37802	−	1.00119i	−0.215211	−	0.156360i	0.474958	−	0.880009i	$-0.342463\pi$
$41$	−1.37802	−	1.00119i	−0.215211	−	0.156360i	−0.690168	+	0.723649i	$0.742463\pi$
$42$		0			0
$43$	−3.23364			−0.493125			−0.246562	−	0.969127i	$-0.579301\pi$
$43$	−3.23364			−0.493125			−0.246562	+	0.969127i	$0.579301\pi$
$44$	11.8948	+	3.41217i	1.79321	+	0.514404i
$45$		0			0
$46$	4.45752	+	13.7188i	0.657226	+	2.02273i
$47$	−3.88520	−	2.82276i	−0.566715	−	0.411742i	0.267196	−	0.963642i	$-0.413903\pi$
$47$	−3.88520	−	2.82276i	−0.566715	−	0.411742i	−0.833910	+	0.551900i	$0.813903\pi$
$48$		0			0
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	7.77514	−	23.9294i	1.09957	−	3.38413i
$51$		0			0
$52$	9.05214	+	6.57676i	1.25531	+	0.912033i
$53$	1.89376	+	5.82840i	0.260128	+	0.800593i	0.992776	+	0.119984i	$0.0382844\pi$
$53$	1.89376	+	5.82840i	0.260128	+	0.800593i	−0.732647	+	0.680608i	$0.761716\pi$
$54$		0			0
$55$	−12.2746	+	4.46608i	−1.65511	+	0.602206i
$56$	−4.14409			−0.553777
$57$		0			0
$58$	−2.94533	−	2.13990i	−0.386740	−	0.280983i
$59$	5.04732	−	3.66709i	0.657105	−	0.477415i	−0.208579	−	0.978006i	$-0.566884\pi$
$59$	5.04732	−	3.66709i	0.657105	−	0.477415i	0.865684	+	0.500591i	$0.166884\pi$
$60$		0			0
$61$	−0.645533	+	1.98674i	−0.0826520	+	0.254377i	−0.983839	−	0.179053i	$-0.942697\pi$
$61$	−0.645533	+	1.98674i	−0.0826520	+	0.254377i	0.901187	+	0.433429i	$0.142697\pi$
$62$	−16.4024	+	11.9171i	−2.08311	+	1.51347i
$63$		0			0
$64$	−3.29663	−	10.1460i	−0.412079	−	1.26825i
$65$	−11.8105			−1.46492
$66$		0			0
$67$	−0.599719			−0.0732673			−0.0366337	−	0.999329i	$-0.511663\pi$
$67$	−0.599719			−0.0732673			−0.0366337	+	0.999329i	$0.511663\pi$
$68$	7.61481	+	23.4360i	0.923431	+	2.84203i
$69$		0			0
$70$	7.62751	−	5.54171i	0.911662	−	0.662361i
$71$	−0.435614	+	1.34068i	−0.0516978	+	0.159110i	−0.973572	−	0.228379i	$-0.926657\pi$
$71$	−0.435614	+	1.34068i	−0.0516978	+	0.159110i	0.921874	+	0.387489i	$0.126657\pi$
$72$		0			0
$73$	−5.73473	+	4.16652i	−0.671199	+	0.487655i	−0.870426	−	0.492299i	$-0.836157\pi$
$73$	−5.73473	+	4.16652i	−0.671199	+	0.487655i	0.199227	+	0.979953i	$0.436157\pi$
$74$	1.17724	+	0.855314i	0.136851	+	0.0994282i
$75$		0			0
$76$	−22.0248			−2.52642
$77$	−3.18805	−	0.914531i	−0.363311	−	0.104220i
$78$		0			0
$79$	−0.316207	−	0.973184i	−0.0355760	−	0.109492i	0.931692	−	0.363250i	$-0.118333\pi$
$79$	−0.316207	−	0.973184i	−0.0355760	−	0.109492i	−0.967268	+	0.253759i	$0.918333\pi$
$80$	−7.83370	−	5.69152i	−0.875834	−	0.636331i
$81$		0			0
$82$	1.26008	−	3.87812i	0.139152	−	0.428267i
$83$	−0.954026	+	2.93619i	−0.104718	+	0.322289i	−0.989664	−	0.143405i	$-0.954195\pi$
$83$	−0.954026	+	2.93619i	−0.104718	+	0.322289i	0.884946	+	0.465693i	$0.154195\pi$
$84$		0			0
$85$	−21.0431	−	15.2887i	−2.28245	−	1.65829i
$86$	−2.39216	−	7.36232i	−0.257954	−	0.793900i
$87$		0			0
$88$	0.478184	+	13.7361i	0.0509746	+	1.46427i
$89$	2.48531			0.263442			0.131721	−	0.991287i	$-0.457950\pi$
$89$	2.48531			0.263442			0.131721	+	0.991287i	$0.457950\pi$
$90$		0			0
$91$	−2.42616	−	1.76271i	−0.254331	−	0.184782i
$92$	−18.1879	+	13.2143i	−1.89622	+	1.37769i
$93$		0			0
$94$	3.55268	−	10.9340i	0.366430	−	1.12776i
$95$	18.8081	−	13.6649i	1.92967	−	1.40199i
$96$		0			0
$97$	0.788908	+	2.42801i	0.0801015	+	0.246527i	0.983086	−	0.183147i	$-0.0586284\pi$
$97$	0.788908	+	2.42801i	0.0801015	+	0.246527i	−0.902984	+	0.429674i	$0.858628\pi$
$98$	2.39396			0.241827
$99$		0			0
$100$	39.2139			3.92139
$101$	4.68387	+	14.4155i	0.466063	+	1.43439i	0.857641	+	0.514249i	$0.171929\pi$
$101$	4.68387	+	14.4155i	0.466063	+	1.43439i	−0.391578	+	0.920145i	$0.628071\pi$
$102$		0			0
$103$	11.1939	−	8.13282i	1.10296	−	0.801351i	0.121423	−	0.992601i	$-0.461254\pi$
$103$	11.1939	−	8.13282i	1.10296	−	0.801351i	0.981541	+	0.191250i	$0.0612542\pi$
$104$	−3.84037	+	11.8194i	−0.376579	+	1.15899i
$105$		0			0
$106$	−11.8691	+	8.62341i	−1.15283	+	0.837580i
$107$	0.360539	+	0.261947i	0.0348546	+	0.0253234i	0.605076	−	0.796168i	$-0.293143\pi$
$107$	0.360539	+	0.261947i	0.0348546	+	0.0253234i	−0.570222	+	0.821491i	$0.693143\pi$
$108$		0			0
$109$	11.0988			1.06307			0.531536	−	0.847036i	$-0.321615\pi$
$109$	11.0988			1.06307			0.531536	+	0.847036i	$0.321615\pi$
$110$	−19.2488	−	24.6428i	−1.83530	−	2.34960i
$111$		0			0
$112$	−0.759773	−	2.33834i	−0.0717918	−	0.220952i
$113$	−6.54445	−	4.75482i	−0.615650	−	0.447296i	0.235750	−	0.971814i	$-0.424245\pi$
$113$	−6.54445	−	4.75482i	−0.615650	−	0.447296i	−0.851399	+	0.524518i	$0.824245\pi$
$114$		0			0
$115$	7.33304	−	22.5688i	0.683810	−	2.10455i
$116$	1.75337	−	5.39631i	0.162796	−	0.501035i
$117$		0			0
$118$	12.0831	+	8.77889i	1.11234	+	0.808162i
$119$	−2.04092	−	6.28132i	−0.187091	−	0.575808i
$120$		0			0
$121$	−2.66345	+	10.6727i	−0.242132	+	0.970243i
$122$	−5.00096			−0.452765
$123$		0			0
$124$	−25.5637	−	18.5731i	−2.29568	−	1.66791i
$125$	−17.5561	+	12.7552i	−1.57026	+	1.14086i
$126$		0			0
$127$	0.0555178	−	0.170866i	0.00492640	−	0.0151619i	−0.948563	−	0.316588i	$-0.897463\pi$
$127$	0.0555178	−	0.170866i	0.00492640	−	0.0151619i	0.953490	+	0.301426i	$0.0974627\pi$
$128$	16.7747	−	12.1875i	1.48269	−	1.07724i
$129$		0			0
$130$	−8.73714	−	26.8901i	−0.766298	−	2.35842i
$131$	−9.38232			−0.819737			−0.409868	−	0.912145i	$-0.634425\pi$
$131$	−9.38232			−0.819737			−0.409868	+	0.912145i	$0.634425\pi$
$132$		0			0
$133$	5.90310			0.511864
$134$	−0.443657	−	1.36544i	−0.0383261	−	0.117956i
$135$		0			0
$136$	−22.1427	+	16.0876i	−1.89872	+	1.37950i
$137$	−0.276143	+	0.849880i	−0.0235925	+	0.0726102i	−0.962160	−	0.272487i	$-0.912154\pi$
$137$	−0.276143	+	0.849880i	−0.0235925	+	0.0726102i	0.938567	+	0.345097i	$0.112154\pi$
$138$		0			0
$139$	−1.71739	+	1.24775i	−0.145667	+	0.105833i	−0.658232	−	0.752815i	$-0.728695\pi$
$139$	−1.71739	+	1.24775i	−0.145667	+	0.105833i	0.512565	+	0.858648i	$0.328695\pi$
$140$	11.8877	+	8.63691i	1.00469	+	0.729952i
$141$		0			0
$142$	−3.37471			−0.283199
$143$	−5.56275	+	8.24518i	−0.465180	+	0.689497i
$144$		0			0
$145$	1.85075	+	5.69603i	0.153697	+	0.473030i
$146$	−13.7287	−	9.97450i	−1.13620	−	0.825496i
$147$		0			0
$148$	−0.700815	+	2.15689i	−0.0576067	+	0.177295i
$149$	−4.42575	+	13.6211i	−0.362572	+	1.11588i	0.588916	+	0.808194i	$0.299555\pi$
$149$	−4.42575	+	13.6211i	−0.362572	+	1.11588i	−0.951488	+	0.307687i	$0.900445\pi$
$150$		0			0
$151$	11.1512	+	8.10184i	0.907474	+	0.659318i	0.940375	−	0.340140i	$-0.110475\pi$
$151$	11.1512	+	8.10184i	0.907474	+	0.659318i	−0.0329007	+	0.999459i	$0.510475\pi$
$152$	−7.55948	−	23.2657i	−0.613154	−	1.88710i
$153$		0			0
$154$	−0.276238	−	7.93507i	−0.0222599	−	0.639426i
$155$	33.3535			2.67902
$156$		0			0
$157$	9.27195	+	6.73647i	0.739982	+	0.537628i	0.892706	−	0.450641i	$-0.148804\pi$
$157$	9.27195	+	6.73647i	0.739982	+	0.537628i	−0.152723	+	0.988269i	$0.548804\pi$
$158$	1.98182	−	1.43987i	0.157665	−	0.114550i
$159$		0			0
$160$	−2.92347	+	8.99751i	−0.231120	+	0.711316i
$161$	4.87474	−	3.54171i	0.384183	−	0.279126i
$162$		0			0
$163$	1.52735	+	4.70071i	0.119632	+	0.368188i	0.992885	−	0.119079i	$-0.0379940\pi$
$163$	1.52735	+	4.70071i	0.119632	+	0.368188i	−0.873253	+	0.487266i	$0.837994\pi$
$164$	6.35521			0.496258
$165$		0			0
$166$	−7.39086			−0.573642
$167$	−2.63722	−	8.11651i	−0.204074	−	0.628075i	−0.999750	−	0.0223527i	$-0.992884\pi$
$167$	−2.63722	−	8.11651i	−0.204074	−	0.628075i	0.795676	−	0.605722i	$-0.207116\pi$
$168$		0			0
$169$	3.24142	−	2.35503i	0.249340	−	0.181156i
$170$	19.2421	−	59.2211i	1.47580	−	4.54205i
$171$		0			0
$172$	9.76069	−	7.09156i	0.744246	−	0.540726i
$173$	10.5881	+	7.69269i	0.804997	+	0.584864i	0.912376	−	0.409354i	$-0.134246\pi$
$173$	10.5881	+	7.69269i	0.804997	+	0.584864i	−0.107379	+	0.994218i	$0.534246\pi$
$174$		0			0
$175$	−10.5101			−0.794492
$176$	−7.66303	+	2.78818i	−0.577623	+	0.210167i
$177$		0			0
$178$	1.83857	+	5.65853i	0.137807	+	0.424125i
$179$	20.9229	+	15.2014i	1.56385	+	1.13621i	0.932759	+	0.360499i	$0.117394\pi$
$179$	20.9229	+	15.2014i	1.56385	+	1.13621i	0.631094	+	0.775707i	$0.282606\pi$
$180$		0			0
$181$	6.61922	−	20.3719i	0.492003	−	1.51423i	−0.329574	−	0.944130i	$-0.606905\pi$
$181$	6.61922	−	20.3719i	0.492003	−	1.51423i	0.821576	−	0.570099i	$-0.193095\pi$
$182$	2.21851	−	6.82787i	0.164447	−	0.506115i
$183$		0			0
$184$	−20.2014	−	14.6771i	−1.48926	−	1.08201i
$185$	−0.739741	−	2.27669i	−0.0543868	−	0.167385i
$186$		0			0
$187$	−20.5847	+	7.48968i	−1.50530	+	0.547700i
$188$	17.9179			1.30680
$189$		0			0
$190$	45.0260	+	32.7133i	3.26653	+	2.37327i
$191$	−3.02562	+	2.19825i	−0.218927	+	0.159059i	−0.691843	−	0.722048i	$-0.743201\pi$
$191$	−3.02562	+	2.19825i	−0.218927	+	0.159059i	0.472917	+	0.881107i	$0.343201\pi$
$192$		0			0
$193$	1.87861	−	5.78178i	0.135225	−	0.416181i	−0.860400	−	0.509620i	$-0.829786\pi$
$193$	1.87861	−	5.78178i	0.135225	−	0.416181i	0.995625	+	0.0934388i	$0.0297860\pi$
$194$	−4.94446	+	3.59236i	−0.354992	+	0.257917i
$195$		0			0
$196$	1.15296	+	3.54845i	0.0823543	+	0.253460i
$197$	−21.5458			−1.53508			−0.767538	−	0.641003i	$-0.778518\pi$
$197$	−21.5458			−1.53508			−0.767538	+	0.641003i	$0.778518\pi$
$198$		0			0
$199$	−14.8965			−1.05598			−0.527992	−	0.849249i	$-0.677055\pi$
$199$	−14.8965			−1.05598			−0.527992	+	0.849249i	$0.677055\pi$
$200$	13.4592	+	41.4232i	0.951710	+	2.92906i
$201$		0			0
$202$	−29.3561	+	21.3284i	−2.06549	+	1.50066i
$203$	−0.469938	+	1.44632i	−0.0329832	+	0.101512i
$204$		0			0
$205$	−5.42704	+	3.94298i	−0.379041	+	0.275389i
$206$	26.7977	+	19.4697i	1.86708	+	1.35652i
$207$		0			0
$208$	−7.37332			−0.511248
$209$	−0.681155	−	19.5665i	−0.0471165	−	1.35344i
$210$		0			0
$211$	5.24074	+	16.1293i	0.360787	+	1.11039i	0.952577	+	0.304296i	$0.0984214\pi$
$211$	5.24074	+	16.1293i	0.360787	+	1.11039i	−0.591790	+	0.806092i	$0.701579\pi$
$212$	−18.4983	−	13.4398i	−1.27047	−	0.923051i
$213$		0			0
$214$	−0.329681	+	1.01465i	−0.0225365	+	0.0693604i
$215$	−3.93533	+	12.1117i	−0.268387	+	0.826011i
$216$		0			0
$217$	6.85158	+	4.97797i	0.465116	+	0.337926i
$218$	8.21061	+	25.2697i	0.556093	+	1.71148i
$219$		0			0
$220$	27.2563	−	40.3997i	1.83762	−	2.72375i
$221$	−19.8064			−1.33232
$222$		0			0
$223$	11.1746	+	8.11879i	0.748304	+	0.543675i	0.895301	−	0.445462i	$-0.146961\pi$
$223$	11.1746	+	8.11879i	0.748304	+	0.543675i	−0.146997	+	0.989137i	$0.546961\pi$
$224$	−1.94342	+	1.41197i	−0.129850	+	0.0943415i
$225$		0			0
$226$	5.98432	−	18.4179i	0.398071	−	1.22514i
$227$	−5.86816	+	4.26347i	−0.389484	+	0.282976i	−0.765244	−	0.643740i	$-0.777382\pi$
$227$	−5.86816	+	4.26347i	−0.389484	+	0.282976i	0.375760	+	0.926717i	$0.377382\pi$
$228$		0			0
$229$	−0.101091	−	0.311125i	−0.00668026	−	0.0205597i	0.947661	−	0.319279i	$-0.103441\pi$
$229$	−0.101091	−	0.311125i	−0.00668026	−	0.0205597i	−0.954341	+	0.298719i	$0.903441\pi$
$230$	56.8093			3.74589
$231$		0			0
$232$	6.30213			0.413755
$233$	−5.02003	−	15.4501i	−0.328873	−	1.01217i	−0.969662	−	0.244450i	$-0.921393\pi$
$233$	−5.02003	−	15.4501i	−0.328873	−	1.01217i	0.640789	−	0.767717i	$-0.278607\pi$
$234$		0			0
$235$	−15.3010	+	11.1169i	−0.998130	+	0.725184i
$236$	−7.19313	+	22.1382i	−0.468233	+	1.44107i
$237$		0			0
$238$	12.7914	−	9.29353i	0.829146	−	0.602410i
$239$	−23.4622	−	17.0463i	−1.51764	−	1.10263i	−0.962640	−	0.270785i	$-0.912717\pi$
$239$	−23.4622	−	17.0463i	−1.51764	−	1.10263i	−0.555004	−	0.831848i	$-0.687283\pi$
$240$		0			0
$241$	−29.3358			−1.88968			−0.944841	−	0.327530i	$-0.893784\pi$
$241$	−29.3358			−1.88968			−0.944841	+	0.327530i	$0.893784\pi$
$242$	−26.2698	+	1.83125i	−1.68869	+	0.117717i
$243$		0			0
$244$	−2.40852	−	7.41266i	−0.154190	−	0.474547i
$245$	−3.18614	−	2.31487i	−0.203555	−	0.147892i
$246$		0			0
$247$	5.47046	−	16.8364i	0.348077	−	1.07127i
$248$	10.8454	−	33.3786i	0.688682	−	2.11955i
$249$		0			0
$250$	−42.0286	−	30.5356i	−2.65812	−	1.93124i
$251$	−3.96519	−	12.2036i	−0.250281	−	0.770285i	−0.994723	−	0.102598i	$-0.967285\pi$
$251$	−3.96519	−	12.2036i	−0.250281	−	0.770285i	0.744442	−	0.667687i	$-0.232715\pi$
$252$		0			0
$253$	−12.3019	−	15.7492i	−0.773413	−	0.990145i
$254$	0.430097			0.0269867
$255$		0			0
$256$	22.8967	+	16.6354i	1.43104	+	1.03971i
$257$	15.7928	−	11.4742i	0.985131	−	0.715739i	0.0262812	−	0.999655i	$-0.491633\pi$
$257$	15.7928	−	11.4742i	0.985131	−	0.715739i	0.958849	+	0.283915i	$0.0916335\pi$
$258$		0			0
$259$	0.187833	−	0.578090i	0.0116714	−	0.0359208i
$260$	35.6500	−	25.9012i	2.21092	−	1.60632i
$261$		0			0
$262$	−6.94081	−	21.3616i	−0.428804	−	1.31972i
$263$	−23.9606			−1.47747			−0.738736	−	0.673995i	$-0.764577\pi$
$263$	−23.9606			−1.47747			−0.738736	+	0.673995i	$0.764577\pi$
$264$		0			0
$265$	24.1352			1.48261
$266$	4.36697	+	13.4401i	0.267756	+	0.824068i
$267$		0			0
$268$	1.81024	−	1.31522i	0.110578	−	0.0803398i
$269$	−3.49993	+	10.7717i	−0.213394	+	0.656760i	0.785869	+	0.618393i	$0.212216\pi$
$269$	−3.49993	+	10.7717i	−0.213394	+	0.656760i	−0.999264	+	0.0383676i	$0.987784\pi$
$270$		0			0
$271$	−4.95343	+	3.59888i	−0.300900	+	0.218616i	−0.727982	−	0.685596i	$-0.759541\pi$
$271$	−4.95343	+	3.59888i	−0.300900	+	0.218616i	0.427082	+	0.904213i	$0.359541\pi$
$272$	−13.1372	−	9.54476i	−0.796561	−	0.578736i
$273$		0			0
$274$	−2.13929			−0.129239
$275$	1.21276	+	34.8371i	0.0731321	+	2.10075i
$276$		0			0
$277$	0.185461	+	0.570791i	0.0111433	+	0.0342955i	0.956474	−	0.291819i	$-0.0942605\pi$
$277$	0.185461	+	0.570791i	0.0111433	+	0.0342955i	−0.945330	+	0.326115i	$0.894260\pi$
$278$	−4.11136	−	2.98708i	−0.246583	−	0.179153i
$279$		0			0
$280$	−5.04335	+	15.5218i	−0.301398	+	0.927607i
$281$	−7.35528	+	22.6372i	−0.438779	+	1.35042i	0.450385	+	0.892835i	$0.351287\pi$
$281$	−7.35528	+	22.6372i	−0.438779	+	1.35042i	−0.889164	+	0.457589i	$0.848713\pi$
$282$		0			0
$283$	14.0284	+	10.1922i	0.833901	+	0.605864i	0.920660	−	0.390365i	$-0.127651\pi$
$283$	14.0284	+	10.1922i	0.833901	+	0.605864i	−0.0867595	+	0.996229i	$0.527651\pi$
$284$	−1.62530	−	5.00216i	−0.0964438	−	0.296824i
$285$		0			0
$286$	−22.8878	−	6.56565i	−1.35338	−	0.388235i
$287$	−1.70333			−0.100544
$288$		0			0
$289$	−21.5363	−	15.6471i	−1.26684	−	0.920415i
$290$	−11.5996	+	8.42757i	−0.681149	+	0.494884i
$291$		0			0
$292$	8.17278	−	25.1532i	0.478276	−	1.47198i
$293$	−12.0642	+	8.76516i	−0.704799	+	0.512066i	−0.881491	−	0.472200i	$-0.843460\pi$
$293$	−12.0642	+	8.76516i	−0.704799	+	0.512066i	0.176693	+	0.984266i	$0.443460\pi$
$294$		0			0
$295$	−7.59265	−	23.3678i	−0.442061	−	1.36052i
$296$	−2.51894			−0.146411
$297$		0			0
$298$	−34.2864			−1.98616
$299$	−5.58390	−	17.1855i	−0.322925	−	0.993862i
$300$		0			0
$301$	−2.61607	+	1.90068i	−0.150788	+	0.109554i
$302$	−10.1968	+	31.3826i	−0.586761	+	1.80587i
$303$		0			0
$304$	11.7419	−	8.53101i	0.673446	−	0.489287i
$305$	6.65581	+	4.83573i	0.381111	+	0.276893i
$306$		0			0
$307$	29.0453			1.65771			0.828853	−	0.559467i	$-0.188994\pi$
$307$	29.0453			1.65771			0.828853	+	0.559467i	$0.188994\pi$
$308$	11.6287	−	4.23107i	0.662607	−	0.241088i
$309$		0			0
$310$	24.6741	+	75.9390i	1.40139	+	4.31304i
$311$	−16.4757	−	11.9703i	−0.934251	−	0.678773i	0.0127790	−	0.999918i	$-0.495932\pi$
$311$	−16.4757	−	11.9703i	−0.934251	−	0.678773i	−0.947030	+	0.321145i	$0.895932\pi$
$312$		0			0
$313$	−9.11004	+	28.0378i	−0.514930	+	1.58479i	0.268479	+	0.963286i	$0.413479\pi$
$313$	−9.11004	+	28.0378i	−0.514930	+	1.58479i	−0.783409	+	0.621506i	$0.786521\pi$
$314$	−8.47839	+	26.0938i	−0.478463	+	1.47256i
$315$		0			0
$316$	3.08872	+	2.24408i	0.173754	+	0.126240i
$317$	−2.35635	−	7.25210i	−0.132346	−	0.407318i	0.862822	−	0.505508i	$-0.168695\pi$
$317$	−2.35635	−	7.25210i	−0.132346	−	0.407318i	−0.995168	+	0.0981896i	$0.968695\pi$
$318$		0			0
$319$	4.84823	+	1.39077i	0.271449	+	0.0778684i
$320$	−42.0142			−2.34866
$321$		0			0
$322$	11.6699	+	8.47871i	0.650341	+	0.472500i
$323$	31.5415	−	22.9163i	1.75502	−	1.27509i
$324$		0			0
$325$	−9.73985	+	29.9762i	−0.540270	+	1.66278i
$326$	−9.57265	+	6.95494i	−0.530180	+	0.385198i
$327$		0			0
$328$	2.18127	+	6.71325i	0.120440	+	0.370677i
$329$	−4.80237			−0.264763
$330$		0			0
$331$	20.6731			1.13630			0.568148	−	0.822926i	$-0.307660\pi$
$331$	20.6731			1.13630			0.568148	+	0.822926i	$0.307660\pi$
$332$	−3.55953	−	10.9551i	−0.195354	−	0.601239i
$333$		0			0
$334$	16.5287	−	12.0088i	0.904409	−	0.657092i
$335$	−0.729857	+	2.24627i	−0.0398764	+	0.122727i
$336$		0			0
$337$	4.41929	−	3.21080i	0.240734	−	0.174904i	−0.460876	−	0.887464i	$-0.652465\pi$
$337$	4.41929	−	3.21080i	0.240734	−	0.174904i	0.701610	+	0.712561i	$0.252465\pi$
$338$	7.75984	+	5.63785i	0.422080	+	0.306659i
$339$		0			0
$340$	97.0475			5.26314
$341$	15.7095	−	23.2848i	0.850714	−	1.26094i
$342$		0			0
$343$	−0.309017	−	0.951057i	−0.0166853	−	0.0513522i
$344$	10.8412	+	7.87660i	0.584519	+	0.424678i
$345$		0			0
$346$	−9.68187	+	29.7977i	−0.520501	+	1.60194i
$347$	−2.96072	+	9.11217i	−0.158940	+	0.489167i	−0.998539	−	0.0540400i	$-0.982790\pi$
$347$	−2.96072	+	9.11217i	−0.158940	+	0.489167i	0.839599	+	0.543207i	$0.182790\pi$
$348$		0			0
$349$	−7.57277	−	5.50194i	−0.405361	−	0.294512i	0.366360	−	0.930473i	$-0.380604\pi$
$349$	−7.57277	−	5.50194i	−0.405361	−	0.294512i	−0.771721	+	0.635961i	$0.780604\pi$
$350$	−7.77514	−	23.9294i	−0.415599	−	1.27908i
$351$		0			0
$352$	4.90440	+	6.27875i	0.261406	+	0.334659i
$353$	27.6629			1.47235			0.736173	−	0.676794i	$-0.236631\pi$
$353$	27.6629			1.47235			0.736173	+	0.676794i	$0.236631\pi$
$354$		0			0
$355$	4.49143	+	3.26322i	0.238380	+	0.173193i
$356$	−7.50187	+	5.45043i	−0.397598	+	0.288872i
$357$		0			0
$358$	−19.1322	+	58.8828i	−1.01117	+	3.11205i
$359$	−2.10554	+	1.52976i	−0.111126	+	0.0807377i	−0.641960	−	0.766738i	$-0.721879\pi$
$359$	−2.10554	+	1.52976i	−0.111126	+	0.0807377i	0.530834	+	0.847476i	$0.321879\pi$
$360$		0			0
$361$	4.89687	+	15.0710i	0.257730	+	0.793212i
$362$	51.2793			2.69518
$363$		0			0
$364$	11.1891			0.586466
$365$	8.62671	+	26.5503i	0.451543	+	1.38971i
$366$		0			0
$367$	8.36472	−	6.07732i	0.436635	−	0.317234i	−0.347662	−	0.937620i	$-0.613024\pi$
$367$	8.36472	−	6.07732i	0.436635	−	0.317234i	0.784296	+	0.620386i	$0.213024\pi$
$368$	4.57802	−	14.0897i	0.238646	−	0.734476i
$369$		0			0
$370$	4.63631	−	3.36847i	0.241030	−	0.175119i
$371$	4.95793	+	3.60215i	0.257403	+	0.187014i
$372$		0			0
$373$	−5.15587			−0.266961			−0.133480	−	0.991051i	$-0.542615\pi$
$373$	−5.15587			−0.266961			−0.133480	+	0.991051i	$0.542615\pi$
$374$	−32.2805	−	41.3264i	−1.66918	−	2.13694i
$375$		0			0
$376$	6.14989	+	18.9274i	0.317156	+	0.976106i
$377$	3.68959	+	2.68064i	0.190023	+	0.138060i
$378$		0			0
$379$	−10.9461	+	33.6886i	−0.562263	+	1.73047i	0.113683	+	0.993517i	$0.463735\pi$
$379$	−10.9461	+	33.6886i	−0.562263	+	1.73047i	−0.675946	+	0.736951i	$0.736265\pi$
$380$	−26.8042	+	82.4948i	−1.37503	+	4.23189i
$381$		0			0
$382$	−7.24323	−	5.26252i	−0.370596	−	0.269254i
$383$	9.70549	+	29.8704i	0.495927	+	1.52631i	0.815506	+	0.578748i	$0.196459\pi$
$383$	9.70549	+	29.8704i	0.495927	+	1.52631i	−0.319579	+	0.947560i	$0.603541\pi$
$384$		0			0
$385$	−7.30526	+	10.8280i	−0.372310	+	0.551844i
$386$	14.5537			0.740762
$387$		0			0
$388$	−7.70608	−	5.59880i	−0.391217	−	0.284236i
$389$	16.2441	−	11.8021i	0.823611	−	0.598388i	−0.0941336	−	0.995560i	$-0.530008\pi$
$389$	16.2441	−	11.8021i	0.823611	−	0.598388i	0.917745	+	0.397171i	$0.130008\pi$
$390$		0			0
$391$	12.2976	−	37.8482i	0.621917	−	1.91406i
$392$	−3.35264	+	2.43583i	−0.169334	+	0.123028i
$393$		0			0
$394$	−15.9391	−	49.0554i	−0.802998	−	2.47137i
$395$	−4.02992			−0.202767
$396$		0			0
$397$	3.63351			0.182361			0.0911804	−	0.995834i	$-0.470936\pi$
$397$	3.63351			0.182361			0.0911804	+	0.995834i	$0.470936\pi$
$398$	−11.0201	−	33.9162i	−0.552385	−	1.70007i
$399$		0			0
$400$	−20.9058	+	15.1890i	−1.04529	+	0.759449i
$401$	−11.6286	+	35.7891i	−0.580704	+	1.78722i	0.0351753	+	0.999381i	$0.488801\pi$
$401$	−11.6286	+	35.7891i	−0.580704	+	1.78722i	−0.615879	+	0.787841i	$0.711199\pi$
$402$		0			0
$403$	20.5472	−	14.9284i	1.02353	−	0.743637i
$404$	−45.7523	−	33.2410i	−2.27626	−	1.65380i
$405$		0			0
$406$	−3.64062			−0.180681
$407$	−1.93782	−	0.555889i	−0.0960542	−	0.0275544i
$408$		0			0
$409$	4.97700	+	15.3176i	0.246097	+	0.757409i	0.995454	+	0.0952425i	$0.0303627\pi$
$409$	4.97700	+	15.3176i	0.246097	+	0.757409i	−0.749357	+	0.662166i	$0.769637\pi$
$410$	−12.9921	−	9.43934i	−0.641636	−	0.466176i
$411$		0			0
$412$	−15.9528	+	49.0977i	−0.785938	+	2.41887i
$413$	1.92791	−	5.93348i	0.0948660	−	0.291968i
$414$		0			0
$415$	9.83656	+	7.14668i	0.482858	+	0.350817i
$416$	2.22614	+	6.85135i	0.109145	+	0.335915i
$417$		0			0
$418$	44.0450	−	16.0257i	2.15431	−	0.783842i
$419$	17.7128			0.865325			0.432662	−	0.901556i	$-0.357574\pi$
$419$	17.7128			0.865325			0.432662	+	0.901556i	$0.357574\pi$
$420$		0			0
$421$	−24.4906	−	17.7935i	−1.19360	−	0.867202i	−0.199961	−	0.979804i	$-0.564081\pi$
$421$	−24.4906	−	17.7935i	−1.19360	−	0.867202i	−0.993640	+	0.112602i	$0.964081\pi$
$422$	−32.8462	+	23.8641i	−1.59893	+	1.16169i
$423$		0			0
$424$	7.84792	−	24.1534i	0.381129	−	1.17299i
$425$	−56.1579	+	40.8011i	−2.72406	+	1.97914i
$426$		0			0
$427$	0.645533	+	1.98674i	0.0312395	+	0.0961453i
$428$	−1.66275			−0.0803720
$429$		0			0
$430$	−30.4871			−1.47022
$431$	−5.93060	−	18.2525i	−0.285667	−	0.879193i	−0.986198	−	0.165571i	$-0.947053\pi$
$431$	−5.93060	−	18.2525i	−0.285667	−	0.879193i	0.700531	−	0.713622i	$-0.252947\pi$
$432$		0			0
$433$	−17.5992	+	12.7866i	−0.845765	+	0.614484i	−0.923975	−	0.382453i	$-0.875079\pi$
$433$	−17.5992	+	12.7866i	−0.845765	+	0.614484i	0.0782102	+	0.996937i	$0.475079\pi$
$434$	−6.26517	+	19.2822i	−0.300738	+	0.925576i
$435$		0			0
$436$	−33.5016	+	24.3403i	−1.60443	+	1.16569i
$437$	28.7761	+	20.9071i	1.37655	+	1.00012i
$438$		0			0
$439$	2.70519			0.129112			0.0645558	−	0.997914i	$-0.479437\pi$
$439$	2.70519			0.129112			0.0645558	+	0.997914i	$0.479437\pi$
$440$	52.0309	+	14.9257i	2.48048	+	0.711556i
$441$		0			0
$442$	−14.6523	−	45.0952i	−0.696939	−	2.14496i
$443$	30.9266	+	22.4695i	1.46937	+	1.06756i	0.980797	+	0.195032i	$0.0624812\pi$
$443$	30.9266	+	22.4695i	1.46937	+	1.06756i	0.488570	+	0.872525i	$0.337519\pi$
$444$		0			0
$445$	3.02462	−	9.30881i	0.143381	−	0.441280i
$446$	−10.2182	+	31.4482i	−0.483844	+	1.48912i
$447$		0			0
$448$	−8.63069	−	6.27056i	−0.407762	−	0.296256i
$449$	−7.01814	−	21.5996i	−0.331207	−	1.01935i	−0.968561	−	0.248778i	$-0.919971\pi$
$449$	−7.01814	−	21.5996i	−0.331207	−	1.01935i	0.637354	−	0.770571i	$-0.280029\pi$
$450$		0			0
$451$	0.196546	+	5.64587i	0.00925498	+	0.265854i
$452$	30.1819			1.41964
$453$		0			0
$454$	−14.0482	−	10.2066i	−0.659313	−	0.479019i
$455$	−9.55492	+	6.94205i	−0.447942	+	0.325449i
$456$		0			0
$457$	−0.485722	+	1.49490i	−0.0227211	+	0.0699285i	−0.961774	−	0.273844i	$-0.911705\pi$
$457$	−0.485722	+	1.49490i	−0.0227211	+	0.0699285i	0.939053	+	0.343772i	$0.111705\pi$
$458$	0.633583	−	0.460325i	0.0296054	−	0.0215096i
$459$		0			0
$460$	27.3600	+	84.2054i	1.27567	+	3.92610i
$461$	28.1276			1.31003			0.655017	−	0.755614i	$-0.272661\pi$
$461$	28.1276			1.31003			0.655017	+	0.755614i	$0.272661\pi$
$462$		0			0
$463$	−4.69202			−0.218057			−0.109028	−	0.994039i	$-0.534774\pi$
$463$	−4.69202			−0.218057			−0.109028	+	0.994039i	$0.534774\pi$
$464$	1.15543	+	3.55604i	0.0536393	+	0.165085i
$465$		0			0
$466$	31.4629	−	22.8591i	1.45749	−	1.05893i
$467$	5.44286	−	16.7514i	0.251866	−	0.775163i	−0.742565	−	0.669773i	$-0.766391\pi$
$467$	5.44286	−	16.7514i	0.251866	−	0.775163i	0.994431	−	0.105389i	$-0.0336088\pi$
$468$		0			0
$469$	−0.485183	+	0.352506i	−0.0224037	+	0.0162772i
$470$	−36.6301	−	26.6134i	−1.68962	−	1.22758i
$471$		0			0
$472$	−25.8543			−1.19004
$473$	6.60190	+	8.45194i	0.303556	+	0.388621i
$474$		0			0
$475$	−19.1722	−	59.0058i	−0.879679	−	2.70737i
$476$	19.9358	+	14.4842i	0.913757	+	0.663883i
$477$		0			0
$478$	21.4541	−	66.0290i	0.981289	−	3.02010i
$479$	3.30865	−	10.1830i	0.151176	−	0.465271i	−0.846578	−	0.532265i	$-0.821341\pi$
$479$	3.30865	−	10.1830i	0.151176	−	0.465271i	0.997753	+	0.0669940i	$0.0213408\pi$
$480$		0			0
$481$	−1.47472	−	1.07144i	−0.0672413	−	0.0488536i
$482$	−21.7019	−	66.7915i	−0.988493	−	3.04227i
$483$		0			0
$484$	−15.3662	−	38.0565i	−0.698465	−	1.72984i
$485$	10.0543			0.456542
$486$		0			0
$487$	−31.3577	−	22.7827i	−1.42095	−	1.03238i	−0.991613	−	0.129239i	$-0.958746\pi$
$487$	−31.3577	−	22.7827i	−1.42095	−	1.03238i	−0.429339	−	0.903143i	$-0.641254\pi$
$488$	7.00362	−	5.08843i	0.317039	−	0.230342i
$489$		0			0
$490$	2.91345	−	8.96668i	0.131616	−	0.405073i
$491$	−4.85460	+	3.52707i	−0.219085	+	0.159174i	−0.691915	−	0.721979i	$-0.743233\pi$
$491$	−4.85460	+	3.52707i	−0.219085	+	0.159174i	0.472830	+	0.881154i	$0.343233\pi$
$492$		0			0
$493$	3.10374	+	9.55233i	0.139785	+	0.430215i
$494$	42.3798			1.90676
$495$		0			0
$496$	20.8226			0.934962
$497$	0.435614	+	1.34068i	0.0195399	+	0.0601378i
$498$		0			0
$499$	23.4434	−	17.0326i	1.04947	−	0.762484i	0.0773578	−	0.997003i	$-0.475352\pi$
$499$	23.4434	−	17.0326i	1.04947	−	0.762484i	0.972111	+	0.234519i	$0.0753516\pi$
$500$	25.0198	−	77.0031i	1.11892	−	3.44369i
$501$		0			0
$502$	24.8517	−	18.0559i	1.10919	−	0.805872i
$503$	−10.4086	−	7.56227i	−0.464095	−	0.337185i	0.331040	−	0.943617i	$-0.392600\pi$
$503$	−10.4086	−	7.56227i	−0.464095	−	0.337185i	−0.795136	+	0.606432i	$0.792600\pi$
$504$		0			0
$505$	59.6940			2.65635
$506$	26.7571	−	39.6598i	1.18950	−	1.76309i
$507$		0			0
$508$	0.207140	+	0.637511i	0.00919035	+	0.0282850i
$509$	15.9668	+	11.6006i	0.707718	+	0.514187i	0.882437	−	0.470431i	$-0.155902\pi$
$509$	15.9668	+	11.6006i	0.707718	+	0.514187i	−0.174719	+	0.984618i	$0.555902\pi$
$510$		0			0
$511$	−2.19047	+	6.74158i	−0.0969008	+	0.298230i
$512$	−8.12226	+	24.9977i	−0.358956	+	1.10475i
$513$		0			0
$514$	37.8075	+	27.4687i	1.66762	+	1.21159i
$515$	−16.8389	−	51.8247i	−0.742009	−	2.28367i
$516$		0			0
$517$	0.554143	+	15.9180i	0.0243712	+	0.700074i
$518$	1.45515			0.0639355
$519$		0			0
$520$	39.5964	+	28.7685i	1.73642	+	1.26158i
$521$	−18.9250	+	13.7498i	−0.829118	+	0.602390i	−0.919310	−	0.393535i	$-0.871252\pi$
$521$	−18.9250	+	13.7498i	−0.829118	+	0.602390i	0.0901914	+	0.995924i	$0.471252\pi$
$522$		0			0
$523$	−3.33109	+	10.2520i	−0.145659	+	0.448291i	−0.997095	−	0.0761668i	$-0.975732\pi$
$523$	−3.33109	+	10.2520i	−0.145659	+	0.448291i	0.851437	+	0.524458i	$0.175732\pi$
$524$	28.3204	−	20.5760i	1.23718	−	0.898866i
$525$		0			0
$526$	−17.7254	−	54.5533i	−0.772866	−	2.37864i
$527$	55.9343			2.43653
$528$		0			0
$529$	13.3068			0.578556
$530$	17.8546	+	54.9509i	0.775555	+	2.38691i
$531$		0			0
$532$	−17.8185	+	12.9459i	−0.772528	+	0.561274i
$533$	−1.57849	+	4.85809i	−0.0683720	+	0.210427i
$534$		0			0
$535$	1.41991	−	1.03162i	0.0613879	−	0.0446010i
$536$	2.01064	+	1.46082i	0.0868464	+	0.0630976i
$537$		0			0
$538$	−27.1140			−1.16897
$539$	−3.11673	+	1.13401i	−0.134247	+	0.0488455i
$540$		0			0
$541$	−1.98437	−	6.10725i	−0.0853146	−	0.262571i	0.899294	−	0.437344i	$-0.144081\pi$
$541$	−1.98437	−	6.10725i	−0.0853146	−	0.262571i	−0.984609	+	0.174773i	$0.944081\pi$
$542$	−11.8583	−	8.61558i	−0.509359	−	0.370071i
$543$		0			0
$544$	−4.90270	+	15.0890i	−0.210201	+	0.646934i
$545$	13.5072	−	41.5709i	0.578585	−	1.78070i
$546$		0			0
$547$	22.6953	+	16.4891i	0.970380	+	0.705022i	0.955538	−	0.294868i	$-0.0952756\pi$
$547$	22.6953	+	16.4891i	0.970380	+	0.705022i	0.0148415	+	0.999890i	$0.495276\pi$
$548$	−1.03030	−	3.17095i	−0.0440124	−	0.135456i
$549$		0			0
$550$	−78.4197	+	28.5328i	−3.34383	+	1.21664i
$551$	−8.97715			−0.382440
$552$		0			0
$553$	−0.827839	−	0.601461i	−0.0352033	−	0.0255767i
$554$	−1.16237	+	0.844514i	−0.0493846	+	0.0358800i
$555$		0			0
$556$	2.44751	−	7.53267i	0.103798	−	0.319456i
$557$	18.6966	−	13.5838i	0.792198	−	0.575566i	−0.116417	−	0.993200i	$-0.537141\pi$
$557$	18.6966	−	13.5838i	0.792198	−	0.575566i	0.908615	+	0.417635i	$0.137141\pi$
$558$		0			0
$559$	2.99664	+	9.22272i	0.126744	+	0.390079i
$560$	−9.68299			−0.409181
$561$		0			0
$562$	−56.9815			−2.40362
$563$	8.91315	+	27.4319i	0.375644	+	1.15611i	0.943043	+	0.332671i	$0.107950\pi$
$563$	8.91315	+	27.4319i	0.375644	+	1.15611i	−0.567398	+	0.823443i	$0.692050\pi$
$564$		0			0
$565$	−25.7739	+	18.7259i	−1.08432	+	0.787803i
$566$	−12.8277	+	39.4797i	−0.539189	+	1.65945i
$567$		0			0
$568$	4.72613	−	3.43374i	0.198304	−	0.144076i
$569$	−14.3811	−	10.4485i	−0.602886	−	0.438022i	0.244016	−	0.969771i	$-0.421535\pi$
$569$	−14.3811	−	10.4485i	−0.602886	−	0.438022i	−0.846902	+	0.531749i	$0.821535\pi$
$570$		0			0
$571$	17.8981			0.749012			0.374506	−	0.927225i	$-0.377812\pi$
$571$	17.8981			0.749012			0.374506	+	0.927225i	$0.377812\pi$
$572$	−1.29110	−	37.0874i	−0.0539835	−	1.55070i
$573$		0			0
$574$	−1.26008	−	3.87812i	−0.0525947	−	0.161870i
$575$	−51.2342	−	37.2238i	−2.13661	−	1.55234i
$576$		0			0
$577$	6.51311	−	20.0453i	0.271144	−	0.834496i	−0.719070	−	0.694938i	$-0.755432\pi$
$577$	6.51311	−	20.0453i	0.271144	−	0.834496i	0.990214	−	0.139558i	$-0.0445682\pi$
$578$	19.6931	−	60.6091i	0.819124	−	2.52101i
$579$		0			0
$580$	−18.0782	−	13.1346i	−0.750657	−	0.545385i
$581$	0.954026	+	2.93619i	0.0395797	+	0.121814i
$582$		0			0
$583$	11.3677	−	16.8493i	0.470800	−	0.697827i
$584$	29.3754			1.21556
$585$		0			0
$586$	−28.8813	−	20.9835i	−1.19307	−	0.866819i
$587$	14.0070	−	10.1767i	0.578131	−	0.420037i	−0.259919	−	0.965630i	$-0.583696\pi$
$587$	14.0070	−	10.1767i	0.578131	−	0.420037i	0.838050	+	0.545594i	$0.183696\pi$
$588$		0			0
$589$	−15.4488	+	47.5466i	−0.636558	+	1.95913i
$590$	47.5868	−	34.5738i	1.95912	−	1.42338i
$591$		0			0
$592$	−0.461820	−	1.42134i	−0.0189807	−	0.0584166i
$593$	26.3881			1.08363			0.541814	−	0.840498i	$-0.317738\pi$
$593$	26.3881			1.08363			0.541814	+	0.840498i	$0.317738\pi$
$594$		0			0
$595$	−26.0107			−1.06634
$596$	−16.5127	−	50.8210i	−0.676388	−	2.08171i
$597$		0			0
$598$	34.9970	−	25.4268i	1.43113	−	1.03978i
$599$	8.73262	−	26.8762i	0.356805	−	1.09813i	−0.598150	−	0.801384i	$-0.704097\pi$
$599$	8.73262	−	26.8762i	0.356805	−	1.09813i	0.954955	−	0.296749i	$-0.0959026\pi$
$600$		0			0
$601$	0.356702	−	0.259159i	0.0145502	−	0.0105713i	−0.580486	−	0.814270i	$-0.697138\pi$
$601$	0.356702	−	0.259159i	0.0145502	−	0.0105713i	0.595037	+	0.803699i	$0.297138\pi$
$602$	−6.26276	−	4.55016i	−0.255251	−	0.185451i
$603$		0			0
$604$	−51.4277			−2.09256
$605$	36.7335	+	22.9647i	1.49343	+	0.933648i
$606$		0			0
$607$	0.172767	+	0.531721i	0.00701238	+	0.0215819i	0.954501	−	0.298206i	$-0.0963883\pi$
$607$	0.172767	+	0.531721i	0.00701238	+	0.0215819i	−0.947489	+	0.319788i	$0.896388\pi$
$608$	−11.4722	−	8.33503i	−0.465259	−	0.338030i
$609$		0			0
$610$	−6.08616	+	18.7313i	−0.246421	+	0.758407i
$611$	−4.45041	+	13.6969i	−0.180044	+	0.554119i
$612$		0			0
$613$	−24.5796	−	17.8581i	−0.992759	−	0.721282i	−0.0322356	−	0.999480i	$-0.510263\pi$
$613$	−24.5796	−	17.8581i	−0.992759	−	0.721282i	−0.960524	+	0.278199i	$0.910263\pi$
$614$	21.4870	+	66.1303i	0.867146	+	2.66880i
$615$		0			0
$616$	8.46072	+	10.8316i	0.340892	+	0.436419i
$617$	−2.35080			−0.0946395			−0.0473198	−	0.998880i	$-0.515068\pi$
$617$	−2.35080			−0.0946395			−0.0473198	+	0.998880i	$0.515068\pi$
$618$		0			0
$619$	−4.94340	−	3.59159i	−0.198692	−	0.144358i	0.483991	−	0.875073i	$-0.339187\pi$
$619$	−4.94340	−	3.59159i	−0.198692	−	0.144358i	−0.682683	+	0.730715i	$0.739187\pi$
$620$	−100.677	+	73.1462i	−4.04329	+	2.93762i
$621$		0			0
$622$	15.0656	−	46.3671i	0.604075	−	1.85915i
$623$	2.01066	−	1.46083i	0.0805552	−	0.0585268i
$624$		0			0
$625$	10.1705	+	31.3014i	0.406818	+	1.25206i
$626$	−70.5757			−2.82077
$627$		0			0
$628$	−42.7608			−1.70634
$629$	−1.24056	−	3.81804i	−0.0494642	−	0.152235i
$630$		0			0
$631$	23.3662	−	16.9765i	0.930193	−	0.675824i	−0.0158474	−	0.999874i	$-0.505045\pi$
$631$	23.3662	−	16.9765i	0.930193	−	0.675824i	0.946040	+	0.324050i	$0.105045\pi$
$632$	−1.31039	+	4.03296i	−0.0521244	+	0.160422i
$633$		0			0
$634$	14.7684	−	10.7298i	0.586526	−	0.426136i
$635$	−0.572420	−	0.415888i	−0.0227158	−	0.0165040i
$636$		0			0
$637$	−2.99890			−0.118821
$638$	0.420089	+	12.0673i	0.0166315	+	0.477748i
$639$		0			0
$640$	−25.2341	−	77.6626i	−0.997465	−	3.06988i
$641$	−32.2196	−	23.4089i	−1.27260	−	0.924596i	−0.273295	−	0.961930i	$-0.588113\pi$
$641$	−32.2196	−	23.4089i	−1.27260	−	0.924596i	−0.999303	+	0.0373342i	$0.988113\pi$
$642$		0			0
$643$	1.80999	−	5.57056i	0.0713788	−	0.219681i	−0.909003	−	0.416790i	$-0.863155\pi$
$643$	1.80999	−	5.57056i	0.0713788	−	0.219681i	0.980382	+	0.197108i	$0.0631551\pi$
$644$	−6.94718	+	21.3812i	−0.273757	+	0.842538i
$645$		0			0
$646$	75.5092	+	54.8607i	2.97087	+	2.15846i
$647$	−6.97929	−	21.4801i	−0.274384	−	0.844468i	−0.989382	−	0.145341i	$-0.953572\pi$
$647$	−6.97929	−	21.4801i	−0.274384	−	0.844468i	0.714997	−	0.699127i	$-0.246428\pi$
$648$		0			0
$649$	−19.8897	−	5.70561i	−0.780738	−	0.223965i
$650$	−75.4549			−2.95958
$651$		0			0
$652$	−14.9192	−	10.8395i	−0.584282	−	0.424506i
$653$	−33.0377	+	24.0033i	−1.29287	+	0.939323i	−0.999859	−	0.0167876i	$-0.994656\pi$
$653$	−33.0377	+	24.0033i	−1.29287	+	0.939323i	−0.293007	+	0.956110i	$0.594656\pi$
$654$		0			0
$655$	−11.4183	+	35.1418i	−0.446149	+	1.37310i
$656$	−3.38811	+	2.46160i	−0.132283	+	0.0961094i
$657$		0			0
$658$	−3.55268	−	10.9340i	−0.138498	−	0.426252i
$659$	−32.5869			−1.26941			−0.634703	−	0.772756i	$-0.718878\pi$
$659$	−32.5869			−1.26941			−0.634703	+	0.772756i	$0.718878\pi$
$660$		0			0
$661$	43.6393			1.69737			0.848686	−	0.528898i	$-0.177395\pi$
$661$	43.6393			1.69737			0.848686	+	0.528898i	$0.177395\pi$
$662$	15.2934	+	47.0684i	0.594397	+	1.82936i
$663$		0			0
$664$	10.3506	−	7.52013i	0.401680	−	0.291838i
$665$	7.18407	−	22.1103i	0.278586	−	0.857400i
$666$		0			0
$667$	−7.41327	+	5.38606i	−0.287043	+	0.208549i
$668$	25.7604	+	18.7160i	0.996700	+	0.724145i
$669$		0			0
$670$	−5.65422			−0.218442
$671$	6.51081	−	2.36894i	0.251347	−	0.0914520i
$672$		0			0
$673$	−7.37679	−	22.7034i	−0.284354	−	0.875153i	−0.986591	−	0.163210i	$-0.947815\pi$
$673$	−7.37679	−	22.7034i	−0.284354	−	0.875153i	0.702237	−	0.711943i	$-0.252185\pi$
$674$	10.5796	+	7.68655i	0.407512	+	0.296075i
$675$		0			0
$676$	−4.61947	+	14.2173i	−0.177672	+	0.546818i
$677$	1.31843	−	4.05770i	0.0506712	−	0.155950i	−0.922519	−	0.385952i	$-0.873873\pi$
$677$	1.31843	−	4.05770i	0.0506712	−	0.155950i	0.973190	+	0.230002i	$0.0738732\pi$
$678$		0			0
$679$	2.06539	+	1.50059i	0.0792623	+	0.0575875i
$680$	33.3092	+	102.515i	1.27735	+	3.93127i
$681$		0			0
$682$	64.6361	+	18.5417i	2.47504	+	0.709998i
$683$	−5.88217			−0.225075			−0.112537	−	0.993647i	$-0.535898\pi$
$683$	−5.88217			−0.225075			−0.112537	+	0.993647i	$0.535898\pi$
$684$		0			0
$685$	2.84719	+	2.06861i	0.108786	+	0.0790374i
$686$	1.93676	−	1.40714i	0.0739457	−	0.0537247i
$687$		0			0
$688$	−2.45683	+	7.56134i	−0.0936657	+	0.288273i
$689$	14.8683	−	10.8025i	0.566438	−	0.411542i
$690$		0			0
$691$	−0.0734097	−	0.225932i	−0.00279264	−	0.00859485i	0.949650	−	0.313311i	$-0.101438\pi$
$691$	−0.0734097	−	0.225932i	−0.00279264	−	0.00859485i	−0.952443	+	0.304716i	$0.901438\pi$
$692$	−48.8305			−1.85626
$693$		0			0
$694$	−22.9368			−0.870669
$695$	2.58345	+	7.95105i	0.0979960	+	0.301601i
$696$		0			0
$697$	−9.10123	+	6.61243i	−0.344734	+	0.250464i
$698$	6.92463	−	21.3118i	0.262101	−	0.806664i
$699$		0			0
$700$	31.7247	−	23.0494i	1.19908	−	0.871184i
$701$	−8.57852	−	6.23266i	−0.324006	−	0.235404i	0.413877	−	0.910333i	$-0.364174\pi$
$701$	−8.57852	−	6.23266i	−0.324006	−	0.235404i	−0.737883	+	0.674929i	$0.764174\pi$
$702$		0			0
$703$	3.58814			0.135329
$704$	−19.7886	+	29.3310i	−0.745812	+	1.10545i
$705$		0			0
$706$	20.4643	+	62.9826i	0.770184	+	2.37038i
$707$	12.2625	+	8.90926i	0.461180	+	0.335067i
$708$		0			0
$709$	−14.9328	+	45.9585i	−0.560813	+	1.72601i	0.119261	+	0.992863i	$0.461947\pi$
$709$	−14.9328	+	45.9585i	−0.560813	+	1.72601i	−0.680074	+	0.733143i	$0.738053\pi$
$710$	−4.10702	+	12.6401i	−0.154134	+	0.474375i
$711$		0			0
$712$	−8.33233	−	6.05379i	−0.312267	−	0.226876i
$713$	15.7692	+	48.5326i	0.590561	+	1.81756i
$714$		0			0
$715$	24.1128	+	30.8699i	0.901767	+	1.15447i
$716$	−96.4932			−3.60612
$717$		0			0
$718$	−5.04057	−	3.66219i	−0.188113	−	0.136672i
$719$	−29.3379	+	21.3152i	−1.09412	+	0.794925i	−0.980090	−	0.198553i	$-0.936376\pi$
$719$	−29.3379	+	21.3152i	−1.09412	+	0.794925i	−0.114030	+	0.993477i	$0.536376\pi$
$720$		0			0
$721$	4.27568	−	13.1592i	0.159235	−	0.490073i
$722$	−30.6910	+	22.2983i	−1.14220	+	0.829859i
$723$		0			0
$724$	24.6967	+	76.0086i	0.917845	+	2.82484i
$725$	15.9833			0.593605
$726$		0			0
$727$	1.15184			0.0427195			0.0213597	−	0.999772i	$-0.493200\pi$
$727$	1.15184			0.0427195			0.0213597	+	0.999772i	$0.493200\pi$
$728$	3.84037	+	11.8194i	0.142334	+	0.438058i
$729$		0			0
$730$	−54.0677	+	39.2825i	−2.00114	+	1.45391i
$731$	−6.59961	+	20.3115i	−0.244095	+	0.751248i
$732$		0			0
$733$	21.9277	−	15.9314i	0.809919	−	0.588441i	−0.103888	−	0.994589i	$-0.533128\pi$
$733$	21.9277	−	15.9314i	0.809919	−	0.588441i	0.913807	+	0.406148i	$0.133128\pi$
$734$	20.0248	+	14.5489i	0.739130	+	0.537009i
$735$		0			0
$736$	−14.4745			−0.533535
$737$	1.22441	+	1.56752i	0.0451016	+	0.0577403i
$738$		0			0
$739$	−7.35516	−	22.6369i	−0.270564	−	0.832710i	−0.990359	−	0.138524i	$-0.955764\pi$
$739$	−7.35516	−	22.6369i	−0.270564	−	0.832710i	0.719795	−	0.694186i	$-0.244236\pi$
$740$	7.22581	+	5.24986i	0.265626	+	0.192989i
$741$		0			0
$742$	−4.53360	+	13.9530i	−0.166434	+	0.512230i
$743$	−4.65554	+	14.3283i	−0.170795	+	0.525653i	−0.999417	−	0.0341562i	$-0.989126\pi$
$743$	−4.65554	+	14.3283i	−0.170795	+	0.525653i	0.828621	+	0.559809i	$0.189126\pi$
$744$		0			0
$745$	45.6321	+	33.1536i	1.67183	+	1.21466i
$746$	−3.81418	−	11.7389i	−0.139647	−	0.429790i
$747$		0			0
$748$	45.7093	−	67.7510i	1.67130	−	2.47722i
$749$	0.445651			0.0162837
$750$		0			0
$751$	−8.58427	−	6.23684i	−0.313244	−	0.227585i	0.420043	−	0.907504i	$-0.362015\pi$
$751$	−8.58427	−	6.23684i	−0.313244	−	0.227585i	−0.733287	+	0.679919i	$0.762015\pi$
$752$	−9.55245	+	6.94026i	−0.348342	+	0.253085i
$753$		0			0
$754$	−3.37380	+	10.3835i	−0.122867	+	0.378145i
$755$	43.9168	−	31.9074i	1.59830	−	1.16123i
$756$		0			0
$757$	−10.8422	−	33.3690i	−0.394068	−	1.21282i	−0.929685	−	0.368355i	$-0.879921\pi$
$757$	−10.8422	−	33.3690i	−0.394068	−	1.21282i	0.535618	−	0.844461i	$-0.320079\pi$
$758$	−84.7997			−3.08006
$759$		0			0
$760$	−96.3423			−3.49470
$761$	−11.5231	−	35.4644i	−0.417712	−	1.28558i	−0.909803	−	0.415040i	$-0.863767\pi$
$761$	−11.5231	−	35.4644i	−0.417712	−	1.28558i	0.492091	−	0.870544i	$-0.336233\pi$
$762$		0			0
$763$	8.97911	−	6.52370i	0.325066	−	0.236174i
$764$	4.31193	−	13.2708i	0.156000	−	0.480119i
$765$		0			0
$766$	−60.8289	+	44.1948i	−2.19784	+	1.59682i
$767$	−15.1364	−	10.9972i	−0.546544	−	0.397087i
$768$		0			0
$769$	21.8827			0.789110			0.394555	−	0.918872i	$-0.370899\pi$
$769$	21.8827			0.789110			0.394555	+	0.918872i	$0.370899\pi$
$770$	−30.0573	−	8.62231i	−1.08319	−	0.310727i
$771$		0			0
$772$	7.00921	+	21.5721i	0.252267	+	0.776398i
$773$	−27.8902	−	20.2634i	−1.00314	−	0.728824i	−0.0403807	−	0.999184i	$-0.512857\pi$
$773$	−27.8902	−	20.2634i	−1.00314	−	0.728824i	−0.962759	+	0.270361i	$0.912857\pi$
$774$		0			0
$775$	27.5058	−	84.6541i	0.988037	−	3.04086i
$776$	3.26931	−	10.0619i	0.117361	−	0.361201i
$777$		0			0
$778$	38.8879	+	28.2537i	1.39420	+	1.01294i
$779$	−3.10714	−	9.56279i	−0.111325	−	0.342622i
$780$		0			0
$781$	4.39358	−	1.59859i	0.157215	−	0.0572022i
$782$	95.2699			3.40685
$783$		0			0
$784$	−1.98911	−	1.44517i	−0.0710397	−	0.0516134i
$785$	36.5156	−	26.5302i	1.30330	−	0.946902i
$786$		0			0
$787$	3.60525	−	11.0958i	0.128513	−	0.395524i	−0.866011	−	0.500024i	$-0.833324\pi$
$787$	3.60525	−	11.0958i	0.128513	−	0.395524i	0.994525	+	0.104501i	$0.0333244\pi$
$788$	65.0358	−	47.2513i	2.31681	−	1.68326i
$789$		0			0
$790$	−2.98123	−	9.17529i	−0.106068	−	0.326442i
$791$	−8.08938			−0.287625
$792$		0			0
$793$	6.26466			0.222464
$794$	2.68798	+	8.27276i	0.0953929	+	0.293589i
$795$		0			0
$796$	44.9649	−	32.6689i	1.59374	−	1.15792i
$797$	10.8564	−	33.4127i	0.384555	−	1.18354i	−0.552248	−	0.833680i	$-0.686230\pi$
$797$	10.8564	−	33.4127i	0.384555	−	1.18354i	0.936803	−	0.349858i	$-0.113770\pi$
$798$		0			0
$799$	−25.6601	+	18.6431i	−0.907788	+	0.659547i
$800$	20.4256	+	14.8400i	0.722153	+	0.524675i
$801$		0			0
$802$	−90.0869			−3.18108
$803$	22.5985	+	6.48267i	0.797484	+	0.228768i
$804$		0			0
$805$	−7.33304	−	22.5688i	−0.258456	−	0.795445i
$806$	49.1892	+	35.7381i	1.73262	+	1.25882i
$807$		0			0
$808$	19.4104	−	59.7390i	0.682855	−	2.10161i
$809$	4.48802	−	13.8127i	0.157790	−	0.485629i	−0.840643	−	0.541590i	$-0.817822\pi$
$809$	4.48802	−	13.8127i	0.157790	−	0.485629i	0.998433	+	0.0559616i	$0.0178225\pi$
$810$		0			0
$811$	−1.42724	−	1.03695i	−0.0501172	−	0.0364123i	0.562445	−	0.826835i	$-0.309861\pi$
$811$	−1.42724	−	1.03695i	−0.0501172	−	0.0364123i	−0.612562	+	0.790423i	$0.709861\pi$
$812$	−1.75337	−	5.39631i	−0.0615311	−	0.189373i
$813$		0			0
$814$	−0.167908	−	4.82325i	−0.00588519	−	0.169055i
$815$	19.4655			0.681846
$816$		0			0
$817$	−15.4429	−	11.2199i	−0.540279	−	0.392536i
$818$	−31.1932	+	22.6632i	−1.09065	+	0.792401i
$819$		0			0
$820$	7.73428	−	23.8037i	0.270093	−	0.831260i
$821$	−7.89660	+	5.73722i	−0.275593	+	0.200230i	−0.716993	−	0.697080i	$-0.754482\pi$
$821$	−7.89660	+	5.73722i	−0.275593	+	0.200230i	0.441400	+	0.897311i	$0.354482\pi$
$822$		0			0
$823$	−14.1011	−	43.3988i	−0.491534	−	1.51279i	−0.822289	−	0.569070i	$-0.807303\pi$
$823$	−14.1011	−	43.3988i	−0.491534	−	1.51279i	0.330755	−	0.943717i	$-0.392697\pi$
$824$	−57.3392			−1.99750
$825$		0			0
$826$	14.9355			0.519674
$827$	−6.41263	−	19.7361i	−0.222989	−	0.686290i	−0.998490	−	0.0549428i	$-0.982502\pi$
$827$	−6.41263	−	19.7361i	−0.222989	−	0.686290i	0.775500	−	0.631347i	$-0.217498\pi$
$828$		0			0
$829$	−13.2572	+	9.63191i	−0.460441	+	0.334530i	−0.793704	−	0.608304i	$-0.791850\pi$
$829$	−13.2572	+	9.63191i	−0.460441	+	0.334530i	0.333263	+	0.942834i	$0.391850\pi$
$830$	−8.99467	+	27.6828i	−0.312210	+	0.960883i
$831$		0			0
$832$	−25.8825	+	18.8048i	−0.897316	+	0.651938i
$833$	−5.34321	−	3.88207i	−0.185131	−	0.134506i
$834$		0			0
$835$	−33.6102			−1.16313
$836$	44.9666	+	57.5675i	1.55520	+	1.99101i
$837$		0			0
$838$	13.1035	+	40.3283i	0.452651	+	1.39312i
$839$	28.3913	+	20.6275i	0.980176	+	0.712139i	0.957748	−	0.287609i	$-0.0928604\pi$
$839$	28.3913	+	20.6275i	0.980176	+	0.712139i	0.0224277	+	0.999748i	$0.492860\pi$
$840$		0			0
$841$	−8.24683	+	25.3811i	−0.284374	+	0.875212i
$842$	22.3945	−	68.9233i	0.771767	−	2.37525i
$843$		0			0
$844$	−51.1917	−	37.1929i	−1.76209	−	1.28023i
$845$	−4.87605	−	15.0069i	−0.167741	−	0.516254i
$846$		0			0
$847$	4.11846	+	10.1999i	0.141512	+	0.350473i
$848$	15.0676			0.517424
$849$		0			0
$850$	−134.440	−	97.6763i	−4.61125	−	3.35027i
$851$	2.96306	−	2.15279i	0.101572	−	0.0737967i
$852$		0			0
$853$	−3.49282	+	10.7498i	−0.119592	+	0.368066i	−0.992877	−	0.119144i	$-0.961985\pi$
$853$	−3.49282	+	10.7498i	−0.119592	+	0.368066i	0.873285	+	0.487209i	$0.161985\pi$
$854$	−4.04586	+	2.93949i	−0.138446	+	0.100587i
$855$		0			0
$856$	−0.570697	−	1.75643i	−0.0195060	−	0.0600334i
$857$	−13.8531			−0.473214			−0.236607	−	0.971605i	$-0.576035\pi$
$857$	−13.8531			−0.473214			−0.236607	+	0.971605i	$0.576035\pi$
$858$		0			0
$859$	−5.23831			−0.178729			−0.0893645	−	0.995999i	$-0.528484\pi$
$859$	−5.23831			−0.178729			−0.0893645	+	0.995999i	$0.528484\pi$
$860$	−14.6829	−	45.1895i	−0.500684	−	1.54095i
$861$		0			0
$862$	37.1699	−	27.0055i	1.26601	−	0.919812i
$863$	12.7095	−	39.1159i	0.432637	−	1.33152i	−0.462851	−	0.886436i	$-0.653174\pi$
$863$	12.7095	−	39.1159i	0.432637	−	1.33152i	0.895489	−	0.445085i	$-0.146826\pi$
$864$		0			0
$865$	41.6989	−	30.2960i	1.41781	−	1.03010i
$866$	−42.1319	−	30.6106i	−1.43170	−	1.04019i
$867$		0			0
$868$	−31.5984			−1.07252
$869$	−1.89809	+	2.81337i	−0.0643882	+	0.0954371i
$870$		0			0
$871$	0.555765	+	1.71047i	0.0188314	+	0.0579571i
$872$	−37.2102	−	27.0348i	−1.26010	−	0.915514i
$873$		0			0
$874$	−26.3132	+	80.9838i	−0.890058	+	2.73932i
$875$	−6.70583	+	20.6384i	−0.226698	+	0.697706i
$876$		0			0
$877$	4.38073	+	3.18279i	0.147927	+	0.107475i	0.659287	−	0.751891i	$-0.270858\pi$
$877$	4.38073	+	3.18279i	0.147927	+	0.107475i	−0.511360	+	0.859366i	$0.670858\pi$
$878$	2.00123	+	6.15915i	0.0675382	+	0.207861i
$879$		0			0
$880$	1.11731	+	32.0954i	0.0376646	+	1.08194i
$881$	−11.0961			−0.373837			−0.186918	−	0.982375i	$-0.559850\pi$
$881$	−11.0961			−0.373837			−0.186918	+	0.982375i	$0.559850\pi$
$882$		0			0
$883$	41.6317	+	30.2472i	1.40102	+	1.01790i	0.994553	+	0.104234i	$0.0332391\pi$
$883$	41.6317	+	30.2472i	1.40102	+	1.01790i	0.406466	+	0.913666i	$0.366761\pi$
$884$	59.7855	−	43.4367i	2.01080	−	1.46093i
$885$		0			0
$886$	−28.2797	+	87.0358i	−0.950074	+	2.92403i
$887$	−16.1753	+	11.7520i	−0.543113	+	0.394595i	−0.825240	−	0.564782i	$-0.808960\pi$
$887$	−16.1753	+	11.7520i	−0.543113	+	0.394595i	0.282127	+	0.959377i	$0.408960\pi$
$888$		0			0
$889$	−0.0555178	−	0.170866i	−0.00186201	−	0.00573066i
$890$	23.4318			0.785435
$891$		0			0
$892$	−51.5353			−1.72553
$893$	−8.76029	−	26.9614i	−0.293152	−	0.902229i
$894$		0			0
$895$	82.4006	−	59.8675i	2.75435	−	2.00115i
$896$	6.40737	−	19.7199i	0.214055	−	0.658794i
$897$		0			0
$898$	43.9860	−	31.9577i	1.46783	−	1.06644i
$899$	−10.4196	−	7.57025i	−0.347512	−	0.252482i
$900$		0			0
$901$	40.4751			1.34842
$902$	−12.7091	+	4.62417i	−0.423166	+	0.153968i
$903$		0			0
$904$	10.3592	+	31.8824i	0.344542	+	1.06039i
$905$	−68.2480	−	49.5851i	−2.26864	−	1.64826i
$906$		0			0
$907$	−1.61880	+	4.98215i	−0.0537514	+	0.165430i	−0.974328	−	0.225131i	$-0.927719\pi$
$907$	−1.61880	+	4.98215i	−0.0537514	+	0.165430i	0.920577	+	0.390561i	$0.127719\pi$
$908$	8.36294	−	25.7385i	0.277534	−	0.854161i
$909$		0			0
$910$	−22.8741	−	16.6190i	−0.758270	−	0.550915i
$911$	3.40325	+	10.4741i	0.112755	+	0.347023i	0.991472	−	0.130319i	$-0.0416002\pi$
$911$	3.40325	+	10.4741i	0.112755	+	0.347023i	−0.878717	+	0.477342i	$0.841600\pi$
$912$		0			0
$913$	9.62226	−	3.50104i	0.318450	−	0.115867i
$914$	−3.76290			−0.124466
$915$		0			0
$916$	0.987457	+	0.717430i	0.0326265	+	0.0237045i
$917$	−7.59045	+	5.51479i	−0.250659	+	0.182114i
$918$		0			0
$919$	−8.91382	+	27.4339i	−0.294040	+	0.904962i	0.689502	+	0.724283i	$0.257829\pi$
$919$	−8.91382	+	27.4339i	−0.294040	+	0.904962i	−0.983542	+	0.180678i	$0.942171\pi$
$920$	−79.5588	+	57.8029i	−2.62298	+	1.90570i
$921$		0			0
$922$	20.8081	+	64.0408i	0.685279	+	2.10907i
$923$	4.22747			0.139149
$924$		0			0
$925$	−6.38848			−0.210052
$926$	−3.47104	−	10.6828i	−0.114065	−	0.351057i
$927$		0			0
$928$	2.95545	−	2.14726i	0.0970175	−	0.0704874i
$929$	−5.01250	+	15.4269i	−0.164455	+	0.506139i	−0.998996	−	0.0448064i	$-0.985733\pi$
$929$	−5.01250	+	15.4269i	−0.164455	+	0.506139i	0.834541	+	0.550946i	$0.185733\pi$
$930$		0			0
$931$	4.77571	−	3.46976i	0.156518	−	0.113717i
$932$	49.0358	+	35.6266i	1.60622	+	1.16699i
$933$		0			0
$934$	42.1660			1.37971
$935$	3.00136	+	86.2156i	0.0981550	+	2.81955i
$936$		0			0
$937$	−8.48784	−	26.1229i	−0.277286	−	0.853397i	−0.988606	−	0.150529i	$-0.951902\pi$
$937$	−8.48784	−	26.1229i	−0.277286	−	0.853397i	0.711320	−	0.702868i	$-0.248098\pi$
$938$	−1.16151	−	0.843886i	−0.0379246	−	0.0275539i
$939$		0			0
$940$	21.8061	−	67.1123i	0.711236	−	2.18896i
$941$	−15.0560	+	46.3376i	−0.490812	+	1.51056i	0.332572	+	0.943078i	$0.392084\pi$
$941$	−15.0560	+	46.3376i	−0.490812	+	1.51056i	−0.823384	+	0.567485i	$0.807916\pi$
$942$		0			0
$943$	−8.30327	−	6.03268i	−0.270392	−	0.196451i
$944$	−4.74010	−	14.5885i	−0.154277	−	0.474816i
$945$		0			0
$946$	−14.3594	+	21.2837i	−0.466864	+	0.691993i
$947$	−21.1998			−0.688902			−0.344451	−	0.938804i	$-0.611935\pi$
$947$	−21.1998			−0.688902			−0.344451	+	0.938804i	$0.611935\pi$
$948$		0			0
$949$	17.1979	+	12.4950i	0.558266	+	0.405604i
$950$	120.161	−	87.3021i	3.89854	−	2.83245i
$951$		0			0
$952$	−8.45777	+	26.0303i	−0.274118	+	0.843648i
$953$	27.6059	−	20.0569i	0.894244	−	0.649707i	−0.0427369	−	0.999086i	$-0.513608\pi$
$953$	27.6059	−	20.0569i	0.894244	−	0.649707i	0.936981	+	0.349380i	$0.113608\pi$
$954$		0			0
$955$	4.55143	+	14.0079i	0.147281	+	0.453283i
$956$	108.204			3.49957
$957$		0			0
$958$	25.6322			0.828138
$959$	0.276143	+	0.849880i	0.00891712	+	0.0274441i
$960$		0			0
$961$	−32.9467	+	23.9372i	−1.06280	+	0.772166i
$962$	1.34850	−	4.15025i	0.0434773	−	0.133810i
$963$		0			0
$964$	88.5496	−	64.3351i	2.85199	−	2.07209i
$965$	−19.3696	−	14.0728i	−0.623529	−	0.453020i
$966$		0			0
$967$	−18.8881			−0.607400			−0.303700	−	0.952768i	$-0.598222\pi$
$967$	−18.8881			−0.607400			−0.303700	+	0.952768i	$0.598222\pi$
$968$	34.9265	−	29.2939i	1.12258	−	0.941541i
$969$		0			0
$970$	7.43792	+	22.8916i	0.238817	+	0.735004i
$971$	10.1003	+	7.33830i	0.324134	+	0.235497i	0.737937	−	0.674869i	$-0.235800\pi$
$971$	10.1003	+	7.33830i	0.324134	+	0.235497i	−0.413803	+	0.910366i	$0.635800\pi$
$972$		0			0
$973$	−0.655983	+	2.01891i	−0.0210299	+	0.0647233i
$974$	28.6739	−	88.2491i	0.918770	−	2.82768i
$975$		0			0
$976$	4.15523	+	3.01895i	0.133006	+	0.0966342i
$977$	4.28751	+	13.1956i	0.137170	+	0.422165i	0.995921	−	0.0902274i	$-0.0287594\pi$
$977$	4.28751	+	13.1956i	0.137170	+	0.422165i	−0.858752	+	0.512392i	$0.828759\pi$
$978$		0			0
$979$	−5.07409	−	6.49599i	−0.162169	−	0.207613i
$980$	14.6940			0.469382
$981$		0			0
$982$	−11.6217	−	8.44367i	−0.370864	−	0.269448i
$983$	35.4613	−	25.7641i	1.13104	−	0.821749i	0.145194	−	0.989403i	$-0.453619\pi$
$983$	35.4613	−	25.7641i	1.13104	−	0.821749i	0.985846	+	0.167655i	$0.0536193\pi$
$984$		0			0
$985$	−26.2212	+	80.7007i	−0.835478	+	2.57134i
$986$	−19.4526	+	14.1332i	−0.619498	+	0.450091i
$987$		0			0
$988$	20.4106	+	62.8174i	0.649348	+	1.99849i
$989$	−19.4843			−0.619565
$990$		0			0
$991$	42.8926			1.36253			0.681264	−	0.732037i	$-0.261430\pi$
$991$	42.8926			1.36253			0.681264	+	0.732037i	$0.261430\pi$
$992$	−6.28672	−	19.3485i	−0.199603	−	0.614316i
$993$		0			0
$994$	−2.73020	+	1.98361i	−0.0865967	+	0.0629162i
$995$	−18.1290	+	55.7954i	−0.574728	+	1.76883i
$996$		0			0
$997$	22.8940	−	16.6335i	0.725060	−	0.526787i	−0.162937	−	0.986637i	$-0.552097\pi$
$997$	22.8940	−	16.6335i	0.725060	−	0.526787i	0.887997	+	0.459849i	$0.152097\pi$
$998$	56.1225	+	40.7754i	1.77653	+	1.29072i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.j.379.5		20
3.2	odd	2		231.2.j.g.148.1	yes	20
11.3	even	5		7623.2.a.cx.1.9		10
11.8	odd	10		7623.2.a.cy.1.2		10
11.9	even	5	inner	693.2.m.j.64.5		20
33.8	even	10		2541.2.a.br.1.9		10
33.14	odd	10		2541.2.a.bq.1.2		10
33.20	odd	10		231.2.j.g.64.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.g.64.1	✓	20	33.20	odd	10
231.2.j.g.148.1	yes	20	3.2	odd	2
693.2.m.j.64.5		20	11.9	even	5	inner
693.2.m.j.379.5		20	1.1	even	1	trivial
2541.2.a.bq.1.2		10	33.14	odd	10
2541.2.a.br.1.9		10	33.8	even	10
7623.2.a.cx.1.9		10	11.3	even	5
7623.2.a.cy.1.2		10	11.8	odd	10

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.739775 + 2.27679i) q^{2} +(-3.01849 + 2.19306i) q^{4} +(1.21700 - 3.74554i) q^{5} +(0.809017 - 0.587785i) q^{7} +(-3.35264 - 2.43583i) q^{8} +O(q^{10})\)	\(q+(0.739775 + 2.27679i) q^{2} +(-3.01849 + 2.19306i) q^{4} +(1.21700 - 3.74554i) q^{5} +(0.809017 - 0.587785i) q^{7} +(-3.35264 - 2.43583i) q^{8} +9.42812 q^{10} +(-2.04163 - 2.61376i) q^{11} +(-0.926710 - 2.85212i) q^{13} +(1.93676 + 1.40714i) q^{14} +(0.759773 - 2.33834i) q^{16} +(2.04092 - 6.28132i) q^{17} +(4.77571 + 3.46976i) q^{19} +(4.54069 + 13.9748i) q^{20} +(4.44064 - 6.58197i) q^{22} +6.02551 q^{23} +(-8.50288 - 6.17770i) q^{25} +(5.80813 - 4.21986i) q^{26} +(-1.15296 + 3.54845i) q^{28} +(-1.23031 + 0.893876i) q^{29} +(2.61707 + 8.05452i) q^{31} -2.40219 q^{32} +15.8111 q^{34} +(-1.21700 - 3.74554i) q^{35} +(0.491753 - 0.357279i) q^{37} +(-4.36697 + 13.4401i) q^{38} +(-13.2037 + 9.59302i) q^{40} +(-1.37802 - 1.00119i) q^{41} -3.23364 q^{43} +(11.8948 + 3.41217i) q^{44} +(4.45752 + 13.7188i) q^{46} +(-3.88520 - 2.82276i) q^{47} +(0.309017 - 0.951057i) q^{49} +(7.77514 - 23.9294i) q^{50} +(9.05214 + 6.57676i) q^{52} +(1.89376 + 5.82840i) q^{53} +(-12.2746 + 4.46608i) q^{55} -4.14409 q^{56} +(-2.94533 - 2.13990i) q^{58} +(5.04732 - 3.66709i) q^{59} +(-0.645533 + 1.98674i) q^{61} +(-16.4024 + 11.9171i) q^{62} +(-3.29663 - 10.1460i) q^{64} -11.8105 q^{65} -0.599719 q^{67} +(7.61481 + 23.4360i) q^{68} +(7.62751 - 5.54171i) q^{70} +(-0.435614 + 1.34068i) q^{71} +(-5.73473 + 4.16652i) q^{73} +(1.17724 + 0.855314i) q^{74} -22.0248 q^{76} +(-3.18805 - 0.914531i) q^{77} +(-0.316207 - 0.973184i) q^{79} +(-7.83370 - 5.69152i) q^{80} +(1.26008 - 3.87812i) q^{82} +(-0.954026 + 2.93619i) q^{83} +(-21.0431 - 15.2887i) q^{85} +(-2.39216 - 7.36232i) q^{86} +(0.478184 + 13.7361i) q^{88} +2.48531 q^{89} +(-2.42616 - 1.76271i) q^{91} +(-18.1879 + 13.2143i) q^{92} +(3.55268 - 10.9340i) q^{94} +(18.8081 - 13.6649i) q^{95} +(0.788908 + 2.42801i) q^{97} +2.39396 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8}+O(q^{10}) \) 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8	\( 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8} + 12 q^{10} + q^{11} + 13 q^{13} - 24 q^{16} + q^{17} + 10 q^{19} + 46 q^{20} + 26 q^{22} - 8 q^{25} + 53 q^{26} + 4 q^{28} - 3 q^{29} - 13 q^{31} - 82 q^{32} + 42 q^{34} - 5 q^{35} - 32 q^{37} - 16 q^{38} + 20 q^{40} + 3 q^{41} + 12 q^{43} - 25 q^{44} - 13 q^{46} - 20 q^{47} - 5 q^{49} + 83 q^{50} - 80 q^{52} - 3 q^{53} - 28 q^{55} + 6 q^{56} + 2 q^{58} + 9 q^{59} - 15 q^{61} + 37 q^{62} - 49 q^{64} - 58 q^{65} + 76 q^{67} - 51 q^{68} + 3 q^{70} - 37 q^{71} + 27 q^{73} + 32 q^{74} + 4 q^{76} - 6 q^{77} + 5 q^{79} - 137 q^{80} - 55 q^{82} + 42 q^{83} - 48 q^{85} - 3 q^{86} + 151 q^{88} + 18 q^{89} + 7 q^{91} - 39 q^{92} - 35 q^{94} + 96 q^{95} - 27 q^{97}+O(q^{100}) \) 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8 + 12 * q^10 + q^11 + 13 * q^13 - 24 * q^16 + q^17 + 10 * q^19 + 46 * q^20 + 26 * q^22 - 8 * q^25 + 53 * q^26 + 4 * q^28 - 3 * q^29 - 13 * q^31 - 82 * q^32 + 42 * q^34 - 5 * q^35 - 32 * q^37 - 16 * q^38 + 20 * q^40 + 3 * q^41 + 12 * q^43 - 25 * q^44 - 13 * q^46 - 20 * q^47 - 5 * q^49 + 83 * q^50 - 80 * q^52 - 3 * q^53 - 28 * q^55 + 6 * q^56 + 2 * q^58 + 9 * q^59 - 15 * q^61 + 37 * q^62 - 49 * q^64 - 58 * q^65 + 76 * q^67 - 51 * q^68 + 3 * q^70 - 37 * q^71 + 27 * q^73 + 32 * q^74 + 4 * q^76 - 6 * q^77 + 5 * q^79 - 137 * q^80 - 55 * q^82 + 42 * q^83 - 48 * q^85 - 3 * q^86 + 151 * q^88 + 18 * q^89 + 7 * q^91 - 39 * q^92 - 35 * q^94 + 96 * q^95 - 27 * q^97

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