LMFDB - Embedded newform 1512.2.s.o.865.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(865,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("1512.865");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.s (of order $3$, degree $2$, 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} + 28x^{5} + 14x^{4} - 52x^{3} + 306x^{2} + 1052x + 1051 $ x^8 - 3x^7 + 4x^6 + 28x^5 + 14x^4 - 52x^3 + 306x^2 + 1052*x + 1051
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			865.4
Root			$-1.30724 + 1.29485i$ of defining polynomial
Character	$\chi$	$=$	1512.865
Dual form			1512.2.s.o.1297.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.70873 + 2.95960i) q^{5} +(-2.27499 - 1.35071i) q^{7} +O(q^{10})$	$q+(1.70873 + 2.95960i) q^{5} +(-2.27499 - 1.35071i) q^{7} +(-3.01597 + 5.22381i) q^{11} +0.417453 q^{13} +(-1.27499 + 2.20835i) q^{17} +(-1.74274 - 3.01852i) q^{19} +(-4.54822 - 7.87774i) q^{23} +(-3.33949 + 5.78417i) q^{25} +1.67898 q^{29} +(-3.82321 + 6.62200i) q^{31} +(0.110210 - 9.04106i) q^{35} +(-4.69245 - 8.12755i) q^{37} +2.13253 q^{41} -6.03194 q^{43} +(3.94970 + 6.84108i) q^{47} +(3.35119 + 6.14569i) q^{49} +(-0.967751 + 1.67619i) q^{53} -20.6139 q^{55} +(3.91922 - 6.78829i) q^{59} +(-4.67648 - 8.09990i) q^{61} +(0.713312 + 1.23549i) q^{65} +(-0.516281 + 0.894224i) q^{67} +0.650582 q^{71} +(-0.642460 + 1.11277i) q^{73} +(13.9171 - 7.81045i) q^{77} +(8.20665 + 14.2143i) q^{79} -14.1645 q^{83} -8.71446 q^{85} +(6.70841 + 11.6193i) q^{89} +(-0.949702 - 0.563856i) q^{91} +(5.95574 - 10.3157i) q^{95} -2.26507 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{5} - 4 q^{7}+O(q^{10}) $ 8 * q + 2 * q^5 - 4 * q^7	$ 8 q + 2 q^{5} - 4 q^{7} + q^{11} - 20 q^{13} + 4 q^{17} + q^{19} - 12 q^{23} - 14 q^{25} - 12 q^{29} + 8 q^{31} - 9 q^{35} + 12 q^{41} + 2 q^{43} + 9 q^{47} + 6 q^{49} - 7 q^{53} - 36 q^{55} + 4 q^{59} - 25 q^{61} + 28 q^{65} - 30 q^{67} + 22 q^{71} + 4 q^{73} + 37 q^{77} + 7 q^{79} - 58 q^{83} + 14 q^{85} - 9 q^{89} + 15 q^{91} + 4 q^{95} - 8 q^{97}+O(q^{100}) $ 8 * q + 2 * q^5 - 4 * q^7 + q^11 - 20 * q^13 + 4 * q^17 + q^19 - 12 * q^23 - 14 * q^25 - 12 * q^29 + 8 * q^31 - 9 * q^35 + 12 * q^41 + 2 * q^43 + 9 * q^47 + 6 * q^49 - 7 * q^53 - 36 * q^55 + 4 * q^59 - 25 * q^61 + 28 * q^65 - 30 * q^67 + 22 * q^71 + 4 * q^73 + 37 * q^77 + 7 * q^79 - 58 * q^83 + 14 * q^85 - 9 * q^89 + 15 * q^91 + 4 * q^95 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.70873	+	2.95960i	0.764166	+	1.32357i	0.940687	+	0.339277i	$0.110182\pi$
$5$	1.70873	+	2.95960i	0.764166	+	1.32357i	−0.176521	+	0.984297i	$0.556484\pi$
$6$		0			0
$7$	−2.27499	−	1.35071i	−0.859867	−	0.510519i
$7$	−2.27499	−	1.35071i	−0.859867	−	0.510519i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.01597	+	5.22381i	−0.909349	+	1.57504i	−0.0943778	+	0.995536i	$0.530086\pi$
$11$	−3.01597	+	5.22381i	−0.909349	+	1.57504i	−0.814971	+	0.579502i	$0.803247\pi$
$12$		0			0
$13$	0.417453			0.115781			0.0578903	−	0.998323i	$-0.481563\pi$
$13$	0.417453			0.115781			0.0578903	+	0.998323i	$0.481563\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.27499	+	2.20835i	−0.309231	+	0.535604i	−0.978194	−	0.207691i	$-0.933405\pi$
$17$	−1.27499	+	2.20835i	−0.309231	+	0.535604i	0.668963	+	0.743296i	$0.266738\pi$
$18$		0			0
$19$	−1.74274	−	3.01852i	−0.399813	−	0.692496i	0.593890	−	0.804546i	$-0.297592\pi$
$19$	−1.74274	−	3.01852i	−0.399813	−	0.692496i	−0.993703	+	0.112050i	$0.964258\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.54822	−	7.87774i	−0.948369	−	1.64262i	−0.748861	−	0.662727i	$-0.769399\pi$
$23$	−4.54822	−	7.87774i	−0.948369	−	1.64262i	−0.199508	−	0.979896i	$-0.563934\pi$
$24$		0			0
$25$	−3.33949	+	5.78417i	−0.667898	+	1.15683i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.67898			0.311779			0.155890	−	0.987774i	$-0.450176\pi$
$29$	1.67898			0.311779			0.155890	+	0.987774i	$0.450176\pi$
$30$		0			0
$31$	−3.82321	+	6.62200i	−0.686669	+	1.18935i	0.286240	+	0.958158i	$0.407594\pi$
$31$	−3.82321	+	6.62200i	−0.686669	+	1.18935i	−0.972909	+	0.231188i	$0.925739\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.110210	−	9.04106i	0.0186290	−	1.52822i
$36$		0			0
$37$	−4.69245	−	8.12755i	−0.771433	−	1.33616i	−0.936777	−	0.349926i	$-0.886207\pi$
$37$	−4.69245	−	8.12755i	−0.771433	−	1.33616i	0.165344	−	0.986236i	$-0.447127\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.13253			0.333046			0.166523	−	0.986038i	$-0.446746\pi$
$41$	2.13253			0.333046			0.166523	+	0.986038i	$0.446746\pi$
$42$		0			0
$43$	−6.03194			−0.919862			−0.459931	−	0.887955i	$-0.652126\pi$
$43$	−6.03194			−0.919862			−0.459931	+	0.887955i	$0.652126\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.94970	+	6.84108i	0.576123	+	0.997875i	0.995919	+	0.0902560i	$0.0287685\pi$
$47$	3.94970	+	6.84108i	0.576123	+	0.997875i	−0.419795	+	0.907619i	$0.637898\pi$
$48$		0			0
$49$	3.35119	+	6.14569i	0.478741	+	0.877956i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.967751	+	1.67619i	−0.132931	+	0.230243i	−0.924805	−	0.380441i	$-0.875772\pi$
$53$	−0.967751	+	1.67619i	−0.132931	+	0.230243i	0.791874	+	0.610684i	$0.209105\pi$
$54$		0			0
$55$	−20.6139			−2.77957
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.91922	−	6.78829i	0.510239	−	0.883760i	−0.489691	−	0.871896i	$-0.662890\pi$
$59$	3.91922	−	6.78829i	0.510239	−	0.883760i	0.999930	−	0.0118637i	$-0.00377642\pi$
$60$		0			0
$61$	−4.67648	−	8.09990i	−0.598762	−	1.03709i	−0.993004	−	0.118079i	$-0.962326\pi$
$61$	−4.67648	−	8.09990i	−0.598762	−	1.03709i	0.394243	−	0.919006i	$-0.371007\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.713312	+	1.23549i	0.0884755	+	0.153244i
$66$		0			0
$67$	−0.516281	+	0.894224i	−0.0630737	+	0.109247i	−0.895838	−	0.444381i	$-0.853424\pi$
$67$	−0.516281	+	0.894224i	−0.0630737	+	0.109247i	0.832764	+	0.553628i	$0.186757\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.650582			0.0772099			0.0386049	−	0.999255i	$-0.487709\pi$
$71$	0.650582			0.0772099			0.0386049	+	0.999255i	$0.487709\pi$
$72$		0			0
$73$	−0.642460	+	1.11277i	−0.0751942	+	0.130240i	−0.901171	−	0.433464i	$-0.857291\pi$
$73$	−0.642460	+	1.11277i	−0.0751942	+	0.130240i	0.825976	+	0.563705i	$0.190624\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	13.9171	−	7.81045i	1.58601	−	0.890083i
$78$		0			0
$79$	8.20665	+	14.2143i	0.923320	+	1.59924i	0.794241	+	0.607603i	$0.207869\pi$
$79$	8.20665	+	14.2143i	0.923320	+	1.59924i	0.129079	+	0.991634i	$0.458798\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−14.1645			−1.55475			−0.777376	−	0.629036i	$-0.783450\pi$
$83$	−14.1645			−1.55475			−0.777376	+	0.629036i	$0.783450\pi$
$84$		0			0
$85$	−8.71446			−0.945216
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.70841	+	11.6193i	0.711090	+	1.23164i	0.964448	+	0.264272i	$0.0851317\pi$
$89$	6.70841	+	11.6193i	0.711090	+	1.23164i	−0.253358	+	0.967373i	$0.581535\pi$
$90$		0			0
$91$	−0.949702	−	0.563856i	−0.0995558	−	0.0591082i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	5.95574	−	10.3157i	0.611046	−	1.05836i
$96$		0			0
$97$	−2.26507			−0.229983			−0.114991	−	0.993366i	$-0.536684\pi$
$97$	−2.26507			−0.229983			−0.114991	+	0.993366i	$0.536684\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	0.576193	−	0.997996i	0.0573334	−	0.0993043i	−0.835934	−	0.548830i	$-0.815074\pi$
$101$	0.576193	−	0.997996i	0.0573334	−	0.0993043i	0.893268	+	0.449525i	$0.148407\pi$
$102$		0			0
$103$	−2.32352	−	4.02446i	−0.228944	−	0.396542i	0.728552	−	0.684991i	$-0.240194\pi$
$103$	−2.32352	−	4.02446i	−0.228944	−	0.396542i	−0.957495	+	0.288449i	$0.906860\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.50177	−	4.33319i	−0.241855	−	0.418905i	0.719388	−	0.694609i	$-0.244423\pi$
$107$	−2.50177	−	4.33319i	−0.241855	−	0.418905i	−0.961243	+	0.275704i	$0.911089\pi$
$108$		0			0
$109$	−6.54999	+	11.3449i	−0.627375	+	1.08665i	0.360702	+	0.932681i	$0.382537\pi$
$109$	−6.54999	+	11.3449i	−0.627375	+	1.08665i	−0.988076	+	0.153964i	$0.950796\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−16.3169			−1.53496			−0.767480	−	0.641072i	$-0.778490\pi$
$113$	−16.3169			−1.53496			−0.767480	+	0.641072i	$0.778490\pi$
$114$		0			0
$115$	15.5433	−	26.9218i	1.44942	−	2.51047i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	5.88344	−	3.30185i	0.539334	−	0.302680i
$120$		0			0
$121$	−12.6921	−	21.9834i	−1.15383	−	1.99849i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−5.73785			−0.513209
$126$		0			0
$127$	14.5373			1.28997			0.644987	−	0.764193i	$-0.276863\pi$
$127$	14.5373			1.28997			0.644987	+	0.764193i	$0.276863\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.536523	−	0.929286i	−0.0468763	−	0.0811921i	0.841635	−	0.540046i	$-0.181593\pi$
$131$	−0.536523	−	0.929286i	−0.0468763	−	0.0811921i	−0.888512	+	0.458854i	$0.848260\pi$
$132$		0			0
$133$	−0.112405	+	9.22105i	−0.00974671	+	0.799566i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.96744	+	12.0680i	−0.595268	+	1.03104i	0.398240	+	0.917281i	$0.369621\pi$
$137$	−6.96744	+	12.0680i	−0.595268	+	1.03104i	−0.993509	+	0.113754i	$0.963712\pi$
$138$		0			0
$139$	0.811516			0.0688319			0.0344160	−	0.999408i	$-0.489043\pi$
$139$	0.811516			0.0688319			0.0344160	+	0.999408i	$0.489043\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.25902	+	2.18069i	−0.105285	+	0.182359i
$144$		0			0
$145$	2.86892	+	4.96912i	0.238251	+	0.412663i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.33667	+	9.24339i	0.437197	+	0.757248i	0.997472	−	0.0710588i	$-0.0226378\pi$
$149$	5.33667	+	9.24339i	0.437197	+	0.757248i	−0.560275	+	0.828307i	$0.689304\pi$
$150$		0			0
$151$	−8.69245	+	15.0558i	−0.707381	+	1.22522i	0.258444	+	0.966026i	$0.416790\pi$
$151$	−8.69245	+	15.0558i	−0.707381	+	1.22522i	−0.965825	+	0.259194i	$0.916543\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−26.1313			−2.09892
$156$		0			0
$157$	−9.98164	+	17.2887i	−0.796622	+	1.37979i	0.125183	+	0.992134i	$0.460048\pi$
$157$	−9.98164	+	17.2887i	−0.796622	+	1.37979i	−0.921804	+	0.387655i	$0.873285\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.293354	+	24.0651i	−0.0231195	+	1.89660i
$162$		0			0
$163$	0.224695	+	0.389183i	0.0175995	+	0.0304832i	0.874691	−	0.484681i	$-0.161064\pi$
$163$	0.224695	+	0.389183i	0.0175995	+	0.0304832i	−0.857092	+	0.515164i	$0.827731\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.15946			0.167104			0.0835520	−	0.996503i	$-0.473374\pi$
$167$	2.15946			0.167104			0.0835520	+	0.996503i	$0.473374\pi$
$168$		0			0
$169$	−12.8257			−0.986595
$170$		0			0
$171$		0			0
$172$		0			0
$173$	7.80693	+	13.5220i	0.593550	+	1.02806i	0.993750	+	0.111631i	$0.0356074\pi$
$173$	7.80693	+	13.5220i	0.593550	+	1.02806i	−0.400200	+	0.916428i	$0.631059\pi$
$174$		0			0
$175$	15.4100	−	8.64827i	1.16489	−	0.653748i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−4.38771	+	7.59974i	−0.327953	+	0.568031i	−0.982105	−	0.188332i	$-0.939692\pi$
$179$	−4.38771	+	7.59974i	−0.327953	+	0.568031i	0.654153	+	0.756363i	$0.273025\pi$
$180$		0			0
$181$	14.7464			1.09609			0.548045	−	0.836449i	$-0.315372\pi$
$181$	14.7464			1.09609			0.548045	+	0.836449i	$0.315372\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	16.0362	−	27.7755i	1.17901	−	2.04210i
$186$		0			0
$187$	−7.69068	−	13.3206i	−0.562398	−	0.974102i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.01597	+	3.49176i	0.145870	+	0.252655i	0.929697	−	0.368324i	$-0.120068\pi$
$191$	2.01597	+	3.49176i	0.145870	+	0.252655i	−0.783827	+	0.620979i	$0.786735\pi$
$192$		0			0
$193$	−2.93373	+	5.08138i	−0.211175	+	0.365765i	−0.952082	−	0.305841i	$-0.901062\pi$
$193$	−2.93373	+	5.08138i	−0.211175	+	0.365765i	0.740908	+	0.671607i	$0.234396\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	0.711544			0.0506954			0.0253477	−	0.999679i	$-0.491931\pi$
$197$	0.711544			0.0506954			0.0253477	+	0.999679i	$0.491931\pi$
$198$		0			0
$199$	−5.11448	+	8.85855i	−0.362556	+	0.627966i	−0.988381	−	0.151998i	$-0.951429\pi$
$199$	−5.11448	+	8.85855i	−0.362556	+	0.627966i	0.625825	+	0.779964i	$0.284763\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.81967	−	2.26781i	−0.268089	−	0.159169i
$204$		0			0
$205$	3.64392	+	6.31145i	0.254502	+	0.440811i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	21.0242			1.45428
$210$		0			0
$211$	20.5500			1.41472			0.707360	−	0.706854i	$-0.249886\pi$
$211$	20.5500			1.41472			0.707360	+	0.706854i	$0.249886\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−10.3069	−	17.8521i	−0.702927	−	1.21750i
$216$		0			0
$217$	17.6421	−	9.90096i	1.19763	−	0.672121i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.532249	+	0.921883i	−0.0358030	+	0.0620125i
$222$		0			0
$223$	−17.8633			−1.19622			−0.598108	−	0.801416i	$-0.704081\pi$
$223$	−17.8633			−1.19622			−0.598108	+	0.801416i	$0.704081\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.63077	+	9.75277i	−0.373727	+	0.647314i	−0.990136	−	0.140112i	$-0.955254\pi$
$227$	−5.63077	+	9.75277i	−0.373727	+	0.647314i	0.616409	+	0.787426i	$0.288587\pi$
$228$		0			0
$229$	−10.5132	−	18.2093i	−0.694729	−	1.20331i	−0.970272	−	0.242017i	$-0.922191\pi$
$229$	−10.5132	−	18.2093i	−0.694729	−	1.20331i	0.275544	−	0.961289i	$-0.411142\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.80901	+	11.7936i	0.446073	+	0.772621i	0.998126	−	0.0611876i	$-0.0194888\pi$
$233$	6.80901	+	11.7936i	0.446073	+	0.772621i	−0.552053	+	0.833809i	$0.686155\pi$
$234$		0			0
$235$	−13.4979	+	23.3791i	−0.880507	+	1.52508i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	19.9384			1.28971			0.644854	−	0.764305i	$-0.276918\pi$
$239$	19.9384			1.28971			0.644854	+	0.764305i	$0.276918\pi$
$240$		0			0
$241$	6.39940	−	11.0841i	0.412222	−	0.713989i	−0.582911	−	0.812536i	$-0.698086\pi$
$241$	6.39940	−	11.0841i	0.412222	−	0.713989i	0.995132	+	0.0985472i	$0.0314195\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−12.4625	+	20.4195i	−0.796203	+	1.30455i
$246$		0			0
$247$	−0.727513	−	1.26009i	−0.0462906	−	0.0801776i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	5.03194			0.317613			0.158807	−	0.987310i	$-0.449235\pi$
$251$	5.03194			0.317613			0.158807	+	0.987310i	$0.449235\pi$
$252$		0			0
$253$	54.8691			3.44959
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−5.19037	−	8.98998i	−0.323766	−	0.560779i	0.657496	−	0.753458i	$-0.271616\pi$
$257$	−5.19037	−	8.98998i	−0.323766	−	0.560779i	−0.981262	+	0.192679i	$0.938282\pi$
$258$		0			0
$259$	−0.302656	+	24.8282i	−0.0188061	+	1.54275i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.64215	−	8.04044i	0.286247	−	0.495795i	−0.686664	−	0.726975i	$-0.740926\pi$
$263$	4.64215	−	8.04044i	0.286247	−	0.495795i	0.972911	+	0.231181i	$0.0742588\pi$
$264$		0			0
$265$	−6.61448			−0.406325
$266$		0			0
$267$		0			0
$268$		0			0
$269$	5.74243	−	9.94618i	0.350122	−	0.606430i	−0.636148	−	0.771567i	$-0.719473\pi$
$269$	5.74243	−	9.94618i	0.350122	−	0.606430i	0.986271	+	0.165137i	$0.0528067\pi$
$270$		0			0
$271$	0.142148	+	0.246207i	0.00863486	+	0.0149560i	0.870311	−	0.492503i	$-0.163918\pi$
$271$	0.142148	+	0.246207i	0.00863486	+	0.0149560i	−0.861676	+	0.507459i	$0.830585\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−20.1436	−	34.8897i	−1.21471	−	2.10393i
$276$		0			0
$277$	13.4973	−	23.3780i	0.810974	−	1.40465i	−0.101209	−	0.994865i	$-0.532271\pi$
$277$	13.4973	−	23.3780i	0.810974	−	1.40465i	0.912183	−	0.409783i	$-0.134396\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−15.6145			−0.931482			−0.465741	−	0.884921i	$-0.654212\pi$
$281$	−15.6145			−0.931482			−0.465741	+	0.884921i	$0.654212\pi$
$282$		0			0
$283$	16.0504	−	27.8001i	0.954098	−	1.65255i	0.217679	−	0.976020i	$-0.430151\pi$
$283$	16.0504	−	27.8001i	0.954098	−	1.65255i	0.736419	−	0.676526i	$-0.236515\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.85150	−	2.88043i	−0.286375	−	0.170026i
$288$		0			0
$289$	5.24879	+	9.09116i	0.308752	+	0.534774i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	16.2964			0.952045			0.476022	−	0.879433i	$-0.342078\pi$
$293$	16.2964			0.952045			0.476022	+	0.879433i	$0.342078\pi$
$294$		0			0
$295$	26.7875			1.55963
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.89867	−	3.28859i	−0.109803	−	0.190184i
$300$		0			0
$301$	13.7226	+	8.14737i	0.790958	+	0.469607i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	15.9816	−	27.6810i	0.915106	−	1.58501i
$306$		0			0
$307$	−0.673971			−0.0384656			−0.0192328	−	0.999815i	$-0.506122\pi$
$307$	−0.673971			−0.0384656			−0.0192328	+	0.999815i	$0.506122\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	11.7754	−	20.3956i	0.667723	−	1.15653i	−0.310817	−	0.950470i	$-0.600603\pi$
$311$	11.7754	−	20.3956i	0.667723	−	1.15653i	0.978539	−	0.206060i	$-0.0660642\pi$
$312$		0			0
$313$	−2.08255	−	3.60708i	−0.117713	−	0.203884i	0.801148	−	0.598466i	$-0.204223\pi$
$313$	−2.08255	−	3.60708i	−0.117713	−	0.203884i	−0.918861	+	0.394582i	$0.870889\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.82321	+	4.88994i	0.158567	+	0.274647i	0.934352	−	0.356351i	$-0.115979\pi$
$317$	2.82321	+	4.88994i	0.158567	+	0.274647i	−0.775785	+	0.630997i	$0.782646\pi$
$318$		0			0
$319$	−5.06376	+	8.77069i	−0.283516	+	0.491064i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	8.88794			0.494538
$324$		0			0
$325$	−1.39408	+	2.41462i	−0.0773296	+	0.133939i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.254750	−	20.8983i	0.0140448	−	1.15216i
$330$		0			0
$331$	4.20622	+	7.28539i	0.231195	+	0.400441i	0.958160	−	0.286233i	$-0.0924032\pi$
$331$	4.20622	+	7.28539i	0.231195	+	0.400441i	−0.726965	+	0.686674i	$0.759070\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−3.52873			−0.192795
$336$		0			0
$337$	11.0390			0.601333			0.300667	−	0.953729i	$-0.402791\pi$
$337$	11.0390			0.601333			0.300667	+	0.953729i	$0.402791\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−23.0614	−	39.9435i	−1.24884	−	2.16306i
$342$		0			0
$343$	0.677101	−	18.5079i	0.0365600	−	0.999331i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.75902	+	8.24287i	−0.255478	+	0.442501i	−0.965025	−	0.262157i	$-0.915566\pi$
$347$	−4.75902	+	8.24287i	−0.255478	+	0.442501i	0.709547	+	0.704658i	$0.248899\pi$
$348$		0			0
$349$	15.7053			0.840685			0.420342	−	0.907366i	$-0.361910\pi$
$349$	15.7053			0.840685			0.420342	+	0.907366i	$0.361910\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−12.5636	+	21.7607i	−0.668691	+	1.15821i	0.309579	+	0.950874i	$0.399812\pi$
$353$	−12.5636	+	21.7607i	−0.668691	+	1.15821i	−0.978270	+	0.207333i	$0.933522\pi$
$354$		0			0
$355$	1.11167	+	1.92546i	0.0590011	+	0.102193i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	11.8544	+	20.5324i	0.625652	+	1.08366i	0.988414	+	0.151779i	$0.0485003\pi$
$359$	11.8544	+	20.5324i	0.625652	+	1.08366i	−0.362763	+	0.931882i	$0.618166\pi$
$360$		0			0
$361$	3.42569	−	5.93347i	0.180299	−	0.312288i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−4.39115			−0.229843
$366$		0			0
$367$	14.2410	−	24.6661i	0.743373	−	1.28756i	−0.207578	−	0.978218i	$-0.566558\pi$
$367$	14.2410	−	24.6661i	0.743373	−	1.28756i	0.950951	−	0.309341i	$-0.100109\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	4.46567	−	2.50618i	0.231846	−	0.130114i
$372$		0			0
$373$	8.22897	+	14.2530i	0.426080	+	0.737992i	0.996521	−	0.0833468i	$-0.0265609\pi$
$373$	8.22897	+	14.2530i	0.426080	+	0.737992i	−0.570441	+	0.821339i	$0.693228\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.700896			0.0360980
$378$		0			0
$379$	−16.4934			−0.847210			−0.423605	−	0.905847i	$-0.639235\pi$
$379$	−16.4934			−0.847210			−0.423605	+	0.905847i	$0.639235\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	18.3892	+	31.8510i	0.939642	+	1.62751i	0.766139	+	0.642675i	$0.222176\pi$
$383$	18.3892	+	31.8510i	0.939642	+	1.62751i	0.173504	+	0.984833i	$0.444491\pi$
$384$		0			0
$385$	46.8964	+	27.8433i	2.39006	+	1.41902i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−9.95116	+	17.2359i	−0.504544	+	0.873895i	0.495442	+	0.868641i	$0.335006\pi$
$389$	−9.95116	+	17.2359i	−0.504544	+	0.873895i	−0.999986	+	0.00525463i	$0.998327\pi$
$390$		0			0
$391$	23.1958			1.17306
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−28.0458	+	48.5768i	−1.41114	+	2.44416i
$396$		0			0
$397$	−12.9781	−	22.4787i	−0.651352	−	1.12818i	−0.982795	−	0.184700i	$-0.940869\pi$
$397$	−12.9781	−	22.4787i	−0.651352	−	1.12818i	0.331443	−	0.943475i	$-0.392465\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	15.2506	+	26.4148i	0.761578	+	1.31909i	0.942037	+	0.335509i	$0.108908\pi$
$401$	15.2506	+	26.4148i	0.761578	+	1.31909i	−0.180459	+	0.983583i	$0.557758\pi$
$402$		0			0
$403$	−1.59601	+	2.76437i	−0.0795029	+	0.137703i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	56.6091			2.80601
$408$		0			0
$409$	3.69276	−	6.39604i	0.182595	−	0.316264i	−0.760168	−	0.649726i	$-0.774884\pi$
$409$	3.69276	−	6.39604i	0.182595	−	0.316264i	0.942764	+	0.333462i	$0.108217\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−18.0852	+	10.1496i	−0.889914	+	0.499429i
$414$		0			0
$415$	−24.2032	−	41.9212i	−1.18809	−	2.05783i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−22.0760			−1.07848			−0.539241	−	0.842152i	$-0.681289\pi$
$419$	−22.0760			−1.07848			−0.539241	+	0.842152i	$0.681289\pi$
$420$		0			0
$421$	−11.9952			−0.584611			−0.292306	−	0.956325i	$-0.594422\pi$
$421$	−11.9952			−0.584611			−0.292306	+	0.956325i	$0.594422\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−8.51566	−	14.7495i	−0.413070	−	0.715458i
$426$		0			0
$427$	−0.301626	+	24.7438i	−0.0145967	+	1.19743i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−2.17793	+	3.77229i	−0.104907	+	0.181705i	−0.913700	−	0.406389i	$-0.866788\pi$
$431$	−2.17793	+	3.77229i	−0.104907	+	0.181705i	0.808793	+	0.588093i	$0.200121\pi$
$432$		0			0
$433$	−10.6024			−0.509519			−0.254759	−	0.967004i	$-0.581996\pi$
$433$	−10.6024			−0.509519			−0.254759	+	0.967004i	$0.581996\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−15.8528	+	27.4578i	−0.758340	+	1.31348i
$438$		0			0
$439$	1.13504	+	1.96595i	0.0541725	+	0.0938295i	0.891840	−	0.452351i	$-0.149415\pi$
$439$	1.13504	+	1.96595i	0.0541725	+	0.0938295i	−0.837667	+	0.546181i	$0.816081\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	6.95932	+	12.0539i	0.330647	+	0.572698i	0.982639	−	0.185528i	$-0.0593997\pi$
$443$	6.95932	+	12.0539i	0.330647	+	0.572698i	−0.651992	+	0.758226i	$0.726066\pi$
$444$		0			0
$445$	−22.9257	+	39.7085i	−1.08678	+	1.88236i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	20.6657			0.975272			0.487636	−	0.873047i	$-0.337859\pi$
$449$	20.6657			0.975272			0.487636	+	0.873047i	$0.337859\pi$
$450$		0			0
$451$	−6.43165	+	11.1400i	−0.302855	+	0.524560i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.0460077	−	3.77421i	0.00215687	−	0.176938i
$456$		0			0
$457$	−6.17825	−	10.7010i	−0.289006	−	0.500573i	0.684567	−	0.728950i	$-0.259991\pi$
$457$	−6.17825	−	10.7010i	−0.289006	−	0.500573i	−0.973573	+	0.228377i	$0.926658\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−24.4304			−1.13784			−0.568918	−	0.822394i	$-0.692638\pi$
$461$	−24.4304			−1.13784			−0.568918	+	0.822394i	$0.692638\pi$
$462$		0			0
$463$	36.7458			1.70772			0.853860	−	0.520502i	$-0.174255\pi$
$463$	36.7458			1.70772			0.853860	+	0.520502i	$0.174255\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−6.61052	−	11.4498i	−0.305898	−	0.529832i	0.671562	−	0.740948i	$-0.265623\pi$
$467$	−6.61052	−	11.4498i	−0.305898	−	0.529832i	−0.977461	+	0.211116i	$0.932290\pi$
$468$		0			0
$469$	2.38237	−	1.33701i	0.110008	−	0.0617374i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	18.1921	−	31.5097i	0.836475	−	1.44882i
$474$		0			0
$475$	23.2795			1.06814
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−18.8140	+	32.5869i	−0.859635	+	1.48893i	0.0126417	+	0.999920i	$0.495976\pi$
$479$	−18.8140	+	32.5869i	−0.859635	+	1.48893i	−0.872277	+	0.489012i	$0.837357\pi$
$480$		0			0
$481$	−1.95887	−	3.39287i	−0.0893170	−	0.154702i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3.87038	−	6.70369i	−0.175745	−	0.304399i
$486$		0			0
$487$	−8.64497	+	14.9735i	−0.391741	+	0.678515i	−0.992679	−	0.120780i	$-0.961460\pi$
$487$	−8.64497	+	14.9735i	−0.391741	+	0.678515i	0.600938	+	0.799295i	$0.294794\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	10.1837			0.459584			0.229792	−	0.973240i	$-0.426195\pi$
$491$	10.1837			0.459584			0.229792	+	0.973240i	$0.426195\pi$
$492$		0			0
$493$	−2.14069	+	3.70779i	−0.0964119	+	0.166990i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.48007	−	0.878745i	−0.0663902	−	0.0394171i
$498$		0			0
$499$	12.5359	+	21.7128i	0.561184	+	0.971999i	0.997394	+	0.0721540i	$0.0229873\pi$
$499$	12.5359	+	21.7128i	0.561184	+	0.971999i	−0.436210	+	0.899845i	$0.643679\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	32.2887			1.43968			0.719841	−	0.694139i	$-0.244215\pi$
$503$	32.2887			1.43968			0.719841	+	0.694139i	$0.244215\pi$
$504$		0			0
$505$	3.93823			0.175249
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−12.9799	−	22.4818i	−0.575323	−	0.996488i	−0.996006	−	0.0892808i	$-0.971543\pi$
$509$	−12.9799	−	22.4818i	−0.575323	−	0.996488i	0.420684	−	0.907207i	$-0.361790\pi$
$510$		0			0
$511$	2.96462	−	1.66378i	0.131147	−	0.0736011i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	7.94053	−	13.7534i	0.349902	−	0.606047i
$516$		0			0
$517$	−47.6487			−2.09559
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−4.81894	+	8.34664i	−0.211121	+	0.365673i	−0.952066	−	0.305893i	$-0.901045\pi$
$521$	−4.81894	+	8.34664i	−0.211121	+	0.365673i	0.740944	+	0.671566i	$0.234378\pi$
$522$		0			0
$523$	−8.48372	−	14.6942i	−0.370967	−	0.642534i	0.618747	−	0.785590i	$-0.287640\pi$
$523$	−8.48372	−	14.6942i	−0.370967	−	0.642534i	−0.989715	+	0.143056i	$0.954307\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−9.74913	−	16.8860i	−0.424679	−	0.735566i
$528$		0			0
$529$	−29.8726	+	51.7408i	−1.29881	+	2.24960i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.890232			0.0385602
$534$		0			0
$535$	8.54967	−	14.8085i	0.369635	−	0.640226i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−42.2110	−	1.02926i	−1.81816	−	0.0443332i
$540$		0			0
$541$	3.01346	+	5.21947i	0.129559	+	0.224403i	0.923506	−	0.383585i	$-0.125311\pi$
$541$	3.01346	+	5.21947i	0.129559	+	0.224403i	−0.793947	+	0.607987i	$0.791977\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−44.7685			−1.91767
$546$		0			0
$547$	−12.6423			−0.540544			−0.270272	−	0.962784i	$-0.587114\pi$
$547$	−12.6423			−0.540544			−0.270272	+	0.962784i	$0.587114\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.92604	−	5.06805i	−0.124653	−	0.215906i
$552$		0			0
$553$	0.529317	−	43.4223i	0.0225089	−	1.84650i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	2.32883	−	4.03365i	0.0986756	−	0.170911i	−0.812461	−	0.583015i	$-0.801873\pi$
$557$	2.32883	−	4.03365i	0.0986756	−	0.170911i	0.911137	+	0.412104i	$0.135206\pi$
$558$		0			0
$559$	−2.51805			−0.106502
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−9.93770	+	17.2126i	−0.418824	+	0.725424i	−0.995821	−	0.0913216i	$-0.970891\pi$
$563$	−9.93770	+	17.2126i	−0.418824	+	0.725424i	0.576998	+	0.816746i	$0.304224\pi$
$564$		0			0
$565$	−27.8810	−	48.2914i	−1.17296	−	2.03163i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−17.4856	−	30.2860i	−0.733035	−	1.26965i	−0.955580	−	0.294731i	$-0.904770\pi$
$569$	−17.4856	−	30.2860i	−0.733035	−	1.26965i	0.222546	−	0.974922i	$-0.428563\pi$
$570$		0			0
$571$	−5.21049	+	9.02484i	−0.218052	+	0.377678i	−0.954212	−	0.299130i	$-0.903304\pi$
$571$	−5.21049	+	9.02484i	−0.218052	+	0.377678i	0.736160	+	0.676807i	$0.236637\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	60.7549			2.53366
$576$		0			0
$577$	18.4791	−	32.0068i	0.769296	−	1.33246i	−0.168649	−	0.985676i	$-0.553940\pi$
$577$	18.4791	−	32.0068i	0.769296	−	1.33246i	0.937945	−	0.346784i	$-0.112726\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	32.2241	+	19.1320i	1.33688	+	0.793731i
$582$		0			0
$583$	−5.83741	−	10.1107i	−0.241761	−	0.418742i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−26.6168			−1.09859			−0.549296	−	0.835628i	$-0.685104\pi$
$587$	−26.6168			−1.09859			−0.549296	+	0.835628i	$0.685104\pi$
$588$		0			0
$589$	26.6515			1.09816
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−2.49781	−	4.32633i	−0.102573	−	0.177661i	0.810171	−	0.586193i	$-0.199374\pi$
$593$	−2.49781	−	4.32633i	−0.102573	−	0.177661i	−0.912744	+	0.408532i	$0.866041\pi$
$594$		0			0
$595$	19.8253	+	11.7707i	0.812759	+	0.482550i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−15.7084	+	27.2078i	−0.641828	+	1.11168i	0.343196	+	0.939264i	$0.388491\pi$
$599$	−15.7084	+	27.2078i	−0.641828	+	1.11168i	−0.985024	+	0.172416i	$0.944843\pi$
$600$		0			0
$601$	−19.5402			−0.797061			−0.398530	−	0.917155i	$-0.630480\pi$
$601$	−19.5402			−0.797061			−0.398530	+	0.917155i	$0.630480\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	43.3748	−	75.1273i	1.76344	−	3.05436i
$606$		0			0
$607$	3.09852	+	5.36679i	0.125765	+	0.217831i	0.922032	−	0.387114i	$-0.126528\pi$
$607$	3.09852	+	5.36679i	0.125765	+	0.217831i	−0.796267	+	0.604946i	$0.793195\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.64881	+	2.85583i	0.0667039	+	0.115534i
$612$		0			0
$613$	6.83918	−	11.8458i	0.276232	−	0.478448i	−0.694213	−	0.719769i	$-0.744248\pi$
$613$	6.83918	−	11.8458i	0.276232	−	0.478448i	0.970445	+	0.241322i	$0.0775809\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−15.8071			−0.636371			−0.318186	−	0.948028i	$-0.603073\pi$
$617$	−15.8071			−0.636371			−0.318186	+	0.948028i	$0.603073\pi$
$618$		0			0
$619$	−17.6961	+	30.6505i	−0.711266	+	1.23195i	0.253116	+	0.967436i	$0.418545\pi$
$619$	−17.6961	+	30.6505i	−0.711266	+	1.23195i	−0.964382	+	0.264513i	$0.914789\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.432683	−	35.4950i	0.0173351	−	1.42208i
$624$		0			0
$625$	6.89305	+	11.9391i	0.275722	+	0.477565i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	23.9313			0.954205
$630$		0			0
$631$	14.9994			0.597116			0.298558	−	0.954392i	$-0.403494\pi$
$631$	14.9994			0.597116			0.298558	+	0.954392i	$0.403494\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	24.8402	+	43.0245i	0.985754	+	1.70738i
$636$		0			0
$637$	1.39896	+	2.56554i	0.0554289	+	0.101650i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	2.08327	−	3.60832i	0.0822840	−	0.142520i	−0.821947	−	0.569565i	$-0.807112\pi$
$641$	2.08327	−	3.60832i	0.0822840	−	0.142520i	0.904231	+	0.427044i	$0.140445\pi$
$642$		0			0
$643$	−35.1973			−1.38804			−0.694022	−	0.719954i	$-0.744163\pi$
$643$	−35.1973			−1.38804			−0.694022	+	0.719954i	$0.744163\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−5.50031	+	9.52682i	−0.216240	+	0.374538i	−0.953655	−	0.300901i	$-0.902713\pi$
$647$	−5.50031	+	9.52682i	−0.216240	+	0.374538i	0.737416	+	0.675439i	$0.236046\pi$
$648$		0			0
$649$	23.6405	+	40.9465i	0.927971	+	1.60729i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−6.65454	−	11.5260i	−0.260412	−	0.451048i	0.705939	−	0.708273i	$-0.250525\pi$
$653$	−6.65454	−	11.5260i	−0.260412	−	0.451048i	−0.966352	+	0.257225i	$0.917192\pi$
$654$		0			0
$655$	1.83354	−	3.17579i	0.0716425	−	0.124088i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	27.7265			1.08007			0.540036	−	0.841642i	$-0.318410\pi$
$659$	27.7265			1.08007			0.540036	+	0.841642i	$0.318410\pi$
$660$		0			0
$661$	7.65561	−	13.2599i	0.297769	−	0.515751i	−0.677856	−	0.735194i	$-0.737091\pi$
$661$	7.65561	−	13.2599i	0.297769	−	0.515751i	0.975625	+	0.219444i	$0.0704242\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−27.4827	+	15.4236i	−1.06573	+	0.598101i
$666$		0			0
$667$	−7.63638	−	13.2266i	−0.295682	−	0.512136i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	56.4164			2.17793
$672$		0			0
$673$	−28.8109			−1.11058			−0.555289	−	0.831657i	$-0.687392\pi$
$673$	−28.8109			−1.11058			−0.555289	+	0.831657i	$0.687392\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−2.08608	−	3.61320i	−0.0801747	−	0.138867i	0.823150	−	0.567824i	$-0.192214\pi$
$677$	−2.08608	−	3.61320i	−0.0801747	−	0.138867i	−0.903325	+	0.428957i	$0.858881\pi$
$678$		0			0
$679$	5.15301	+	3.05944i	0.197754	+	0.117410i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	11.4214	−	19.7825i	0.437028	−	0.756955i	−0.560430	−	0.828201i	$-0.689364\pi$
$683$	11.4214	−	19.7825i	0.437028	−	0.756955i	0.997459	+	0.0712463i	$0.0226976\pi$
$684$		0			0
$685$	−47.6218			−1.81953
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.403990	+	0.699732i	−0.0153908	+	0.0266576i
$690$		0			0
$691$	−11.6708	−	20.2145i	−0.443979	−	0.768994i	0.554001	−	0.832516i	$-0.313100\pi$
$691$	−11.6708	−	20.2145i	−0.443979	−	0.768994i	−0.997980	+	0.0635214i	$0.979767\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.38666	+	2.40176i	0.0525990	+	0.0911041i
$696$		0			0
$697$	−2.71896	+	4.70939i	−0.102988	+	0.178381i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−8.51536			−0.321621			−0.160810	−	0.986985i	$-0.551411\pi$
$701$	−8.51536			−0.321621			−0.160810	+	0.986985i	$0.551411\pi$
$702$		0			0
$703$	−16.3555	+	28.3285i	−0.616858	+	1.06843i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.65883	+	1.49217i	−0.0999958	+	0.0561187i
$708$		0			0
$709$	−11.8310	−	20.4919i	−0.444323	−	0.769591i	0.553681	−	0.832729i	$-0.313223\pi$
$709$	−11.8310	−	20.4919i	−0.444323	−	0.769591i	−0.998005	+	0.0631380i	$0.979889\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	69.5552			2.60486
$714$		0			0
$715$	−8.60531			−0.321820
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−4.93197	−	8.54241i	−0.183931	−	0.318578i	0.759285	−	0.650759i	$-0.225549\pi$
$719$	−4.93197	−	8.54241i	−0.183931	−	0.318578i	−0.943216	+	0.332180i	$0.892216\pi$
$720$		0			0
$721$	−0.149864	+	12.2940i	−0.00558123	+	0.457853i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−5.60695	+	9.71152i	−0.208237	+	0.360677i
$726$		0			0
$727$	6.37428			0.236409			0.118205	−	0.992989i	$-0.462286\pi$
$727$	6.37428			0.236409			0.118205	+	0.992989i	$0.462286\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	7.69068	−	13.3206i	0.284450	−	0.492682i
$732$		0			0
$733$	−8.09319	−	14.0178i	−0.298929	−	0.517760i	0.676962	−	0.736018i	$-0.263296\pi$
$733$	−8.09319	−	14.0178i	−0.298929	−	0.517760i	−0.975891	+	0.218258i	$0.929963\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.11417	−	5.39391i	−0.114712	−	0.198687i
$738$		0			0
$739$	−6.59036	+	11.4148i	−0.242430	+	0.419901i	−0.961406	−	0.275134i	$-0.911278\pi$
$739$	−6.59036	+	11.4148i	−0.242430	+	0.419901i	0.718976	+	0.695035i	$0.244611\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−30.9733			−1.13630			−0.568149	−	0.822925i	$-0.692340\pi$
$743$	−30.9733			−1.13630			−0.568149	+	0.822925i	$0.692340\pi$
$744$		0			0
$745$	−18.2378	+	31.5888i	−0.668182	+	1.15733i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.161361	+	13.2371i	−0.00589599	+	0.483674i
$750$		0			0
$751$	−25.0433	−	43.3763i	−0.913844	−	1.58282i	−0.808585	−	0.588379i	$-0.799766\pi$
$751$	−25.0433	−	43.3763i	−0.913844	−	1.58282i	−0.105258	−	0.994445i	$-0.533567\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−59.4120			−2.16223
$756$		0			0
$757$	19.8647			0.721996			0.360998	−	0.932567i	$-0.382436\pi$
$757$	19.8647			0.721996			0.360998	+	0.932567i	$0.382436\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.83627	+	3.18051i	0.0665646	+	0.115293i	0.897387	−	0.441244i	$-0.145463\pi$
$761$	1.83627	+	3.18051i	0.0665646	+	0.115293i	−0.830822	+	0.556538i	$0.812129\pi$
$762$		0			0
$763$	30.2248	−	16.9625i	1.09421	−	0.614083i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.63609	−	2.83379i	0.0590758	−	0.102322i
$768$		0			0
$769$	−16.4494			−0.593180			−0.296590	−	0.955005i	$-0.595850\pi$
$769$	−16.4494			−0.593180			−0.296590	+	0.955005i	$0.595850\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	2.93020	−	5.07525i	0.105392	−	0.182544i	−0.808506	−	0.588487i	$-0.799724\pi$
$773$	2.93020	−	5.07525i	0.105392	−	0.182544i	0.913898	+	0.405943i	$0.133057\pi$
$774$		0			0
$775$	−25.5352	−	44.2282i	−0.917250	−	1.58872i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−3.71646	−	6.43710i	−0.133156	−	0.230633i
$780$		0			0
$781$	−1.96213	+	3.39852i	−0.0702107	+	0.121608i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−68.2236			−2.43500
$786$		0			0
$787$	−7.09393	+	12.2870i	−0.252871	+	0.437986i	−0.964315	−	0.264757i	$-0.914708\pi$
$787$	−7.09393	+	12.2870i	−0.252871	+	0.437986i	0.711444	+	0.702743i	$0.248042\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	37.1207	+	22.0393i	1.31986	+	0.783627i
$792$		0			0
$793$	−1.95221	−	3.38132i	−0.0693249	−	0.120074i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	5.48696			0.194358			0.0971791	−	0.995267i	$-0.469018\pi$
$797$	5.48696			0.194358			0.0971791	+	0.995267i	$0.469018\pi$
$798$		0			0
$799$	−20.1434			−0.712621
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.87528	−	6.71218i	−0.136756	−	0.236868i
$804$		0			0
$805$	−71.7244	+	40.2525i	−2.52795	+	1.41871i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	5.95033	−	10.3063i	0.209202	−	0.362349i	−0.742261	−	0.670111i	$-0.766247\pi$
$809$	5.95033	−	10.3063i	0.209202	−	0.362349i	0.951463	+	0.307762i	$0.0995799\pi$
$810$		0			0
$811$	−14.3624			−0.504330			−0.252165	−	0.967684i	$-0.581143\pi$
$811$	−14.3624			−0.504330			−0.252165	+	0.967684i	$0.581143\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.767885	+	1.33002i	−0.0268978	+	0.0465884i
$816$		0			0
$817$	10.5121	+	18.2075i	0.367773	+	0.637001i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.490073	+	0.848832i	0.0171037	+	0.0296244i	0.874451	−	0.485115i	$-0.161222\pi$
$821$	0.490073	+	0.848832i	0.0171037	+	0.0296244i	−0.857347	+	0.514739i	$0.827889\pi$
$822$		0			0
$823$	−8.15458	+	14.1241i	−0.284251	+	0.492337i	−0.972427	−	0.233207i	$-0.925078\pi$
$823$	−8.15458	+	14.1241i	−0.284251	+	0.492337i	0.688176	+	0.725543i	$0.258412\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	34.8944			1.21340			0.606698	−	0.794932i	$-0.292494\pi$
$827$	34.8944			1.21340			0.606698	+	0.794932i	$0.292494\pi$
$828$		0			0
$829$	3.62014	−	6.27026i	0.125733	−	0.217775i	−0.796286	−	0.604920i	$-0.793205\pi$
$829$	3.62014	−	6.27026i	0.125733	−	0.217775i	0.922019	+	0.387145i	$0.126539\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−17.8446	−	0.435116i	−0.618279	−	0.0150759i
$834$		0			0
$835$	3.68992	+	6.39113i	0.127695	+	0.221174i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−14.8646			−0.513181			−0.256591	−	0.966520i	$-0.582599\pi$
$839$	−14.8646			−0.513181			−0.256591	+	0.966520i	$0.582599\pi$
$840$		0			0
$841$	−26.1810			−0.902794
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−21.9157	−	37.9591i	−0.753922	−	1.30583i
$846$		0			0
$847$	−0.818625	+	67.1555i	−0.0281283	+	2.30749i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−42.6845	+	73.9318i	−1.46321	+	2.53435i
$852$		0			0
$853$	47.2313			1.61717			0.808584	−	0.588381i	$-0.200235\pi$
$853$	47.2313			1.61717			0.808584	+	0.588381i	$0.200235\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	18.8218	−	32.6004i	0.642942	−	1.11361i	−0.341831	−	0.939762i	$-0.611047\pi$
$857$	18.8218	−	32.6004i	0.642942	−	1.11361i	0.984773	−	0.173847i	$-0.0556198\pi$
$858$		0			0
$859$	−21.1571	−	36.6451i	−0.721870	−	1.25032i	−0.960250	−	0.279143i	$-0.909950\pi$
$859$	−21.1571	−	36.6451i	−0.721870	−	1.25032i	0.238380	−	0.971172i	$-0.423384\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	8.30163	+	14.3788i	0.282591	+	0.489461i	0.972022	−	0.234890i	$-0.0754729\pi$
$863$	8.30163	+	14.3788i	0.282591	+	0.489461i	−0.689431	+	0.724351i	$0.742140\pi$
$864$		0			0
$865$	−26.6798	+	46.2108i	−0.907141	+	1.57121i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−99.0040			−3.35848
$870$		0			0
$871$	−0.215523	+	0.373296i	−0.00730271	+	0.0126487i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	13.0536	+	7.75014i	0.441291	+	0.262003i
$876$		0			0
$877$	7.96390	+	13.7939i	0.268922	+	0.465786i	0.968584	−	0.248688i	$-0.0799993\pi$
$877$	7.96390	+	13.7939i	0.268922	+	0.465786i	−0.699662	+	0.714474i	$0.746666\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−3.32330			−0.111965			−0.0559825	−	0.998432i	$-0.517829\pi$
$881$	−3.32330			−0.111965			−0.0559825	+	0.998432i	$0.517829\pi$
$882$		0			0
$883$	−34.0603			−1.14622			−0.573111	−	0.819478i	$-0.694264\pi$
$883$	−34.0603			−1.14622			−0.573111	+	0.819478i	$0.694264\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	27.4529	+	47.5499i	0.921779	+	1.59657i	0.796661	+	0.604426i	$0.206598\pi$
$887$	27.4529	+	47.5499i	0.921779	+	1.59657i	0.125118	+	0.992142i	$0.460069\pi$
$888$		0			0
$889$	−33.0722	−	19.6356i	−1.10921	−	0.658557i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	13.7666	−	23.8445i	0.460683	−	0.797926i
$894$		0			0
$895$	−29.9896			−1.00244
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−6.41911	+	11.1182i	−0.214089	+	0.370813i
$900$		0			0
$901$	−2.46775	−	4.27427i	−0.0822127	−	0.142397i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	25.1976	+	43.6434i	0.837595	+	1.45076i
$906$		0			0
$907$	−10.8314	+	18.7605i	−0.359650	+	0.622932i	−0.987902	−	0.155078i	$-0.950437\pi$
$907$	−10.8314	+	18.7605i	−0.359650	+	0.622932i	0.628253	+	0.778009i	$0.283770\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−20.5771			−0.681751			−0.340876	−	0.940108i	$-0.610723\pi$
$911$	−20.5771			−0.681751			−0.340876	+	0.940108i	$0.610723\pi$
$912$		0			0
$913$	42.7196	−	73.9925i	1.41381	−	2.44879i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.0346050	+	2.83880i	−0.00114276	+	0.0937456i
$918$		0			0
$919$	10.0458	+	17.3999i	0.331381	+	0.573969i	0.982783	−	0.184764i	$-0.0591520\pi$
$919$	10.0458	+	17.3999i	0.331381	+	0.573969i	−0.651402	+	0.758733i	$0.725819\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	0.271587			0.00893940
$924$		0			0
$925$	62.6815			2.06096
$926$		0			0
$927$		0			0
$928$		0			0
$929$	12.3664	+	21.4193i	0.405729	+	0.702743i	0.994406	−	0.105625i	$-0.0336844\pi$
$929$	12.3664	+	21.4193i	0.405729	+	0.702743i	−0.588677	+	0.808368i	$0.700351\pi$
$930$		0			0
$931$	12.7106	−	20.8260i	0.416575	−	0.682544i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	26.2825	−	45.5227i	0.859531	−	1.48875i
$936$		0			0
$937$	8.06826			0.263579			0.131789	−	0.991278i	$-0.457928\pi$
$937$	8.06826			0.263579			0.131789	+	0.991278i	$0.457928\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	23.5985	−	40.8738i	0.769290	−	1.33245i	−0.168659	−	0.985674i	$-0.553944\pi$
$941$	23.5985	−	40.8738i	0.769290	−	1.33245i	0.937949	−	0.346774i	$-0.112723\pi$
$942$		0			0
$943$	−9.69923	−	16.7996i	−0.315850	−	0.547069i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	12.8445	+	22.2474i	0.417391	+	0.722942i	0.995676	−	0.0928925i	$-0.0296113\pi$
$947$	12.8445	+	22.2474i	0.417391	+	0.722942i	−0.578285	+	0.815835i	$0.696278\pi$
$948$		0			0
$949$	−0.268197	+	0.464530i	−0.00870603	+	0.0150793i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−15.2971			−0.495521			−0.247760	−	0.968821i	$-0.579695\pi$
$953$	−15.2971			−0.495521			−0.247760	+	0.968821i	$0.579695\pi$
$954$		0			0
$955$	−6.88948	+	11.9329i	−0.222938	+	0.386140i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	32.1511	−	18.0436i	1.03821	−	0.582657i
$960$		0			0
$961$	−13.7339	−	23.7878i	−0.443028	−	0.767348i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−20.0518			−0.645490
$966$		0			0
$967$	−36.9754			−1.18905			−0.594524	−	0.804078i	$-0.702659\pi$
$967$	−36.9754			−1.18905			−0.594524	+	0.804078i	$0.702659\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−8.66624	−	15.0104i	−0.278113	−	0.481706i	0.692803	−	0.721127i	$-0.256376\pi$
$971$	−8.66624	−	15.0104i	−0.278113	−	0.481706i	−0.970916	+	0.239421i	$0.923042\pi$
$972$		0			0
$973$	−1.84619	−	1.09612i	−0.0591863	−	0.0351400i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−21.7004	+	37.5861i	−0.694256	+	1.20249i	0.276174	+	0.961108i	$0.410933\pi$
$977$	−21.7004	+	37.5861i	−0.694256	+	1.20249i	−0.970431	+	0.241380i	$0.922400\pi$
$978$		0			0
$979$	−80.9295			−2.58652
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−10.6538	+	18.4530i	−0.339805	+	0.588559i	−0.984396	−	0.175968i	$-0.943694\pi$
$983$	−10.6538	+	18.4530i	−0.339805	+	0.588559i	0.644591	+	0.764528i	$0.277028\pi$
$984$		0			0
$985$	1.21583	+	2.10589i	0.0387397	+	0.0670992i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	27.4346	+	47.5181i	0.872368	+	1.51099i
$990$		0			0
$991$	3.60875	−	6.25055i	0.114636	−	0.198555i	−0.802998	−	0.595981i	$-0.796763\pi$
$991$	3.60875	−	6.25055i	0.114636	−	0.198555i	0.917634	+	0.397426i	$0.130097\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−34.9570			−1.10821
$996$		0			0
$997$	−8.42738	+	14.5966i	−0.266898	+	0.462281i	−0.968059	−	0.250722i	$-0.919332\pi$
$997$	−8.42738	+	14.5966i	−0.266898	+	0.462281i	0.701161	+	0.713003i	$0.252665\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.s.o.865.4	yes	8
3.2	odd	2		1512.2.s.n.865.1	✓	8
7.2	even	3	inner	1512.2.s.o.1297.4	yes	8
21.2	odd	6		1512.2.s.n.1297.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.s.n.865.1	✓	8	3.2	odd	2
1512.2.s.n.1297.1	yes	8	21.2	odd	6
1512.2.s.o.865.4	yes	8	1.1	even	1	trivial
1512.2.s.o.1297.4	yes	8	7.2	even	3	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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.70873 + 2.95960i) q^{5} +(-2.27499 - 1.35071i) q^{7} +O(q^{10})\)	\(q+(1.70873 + 2.95960i) q^{5} +(-2.27499 - 1.35071i) q^{7} +(-3.01597 + 5.22381i) q^{11} +0.417453 q^{13} +(-1.27499 + 2.20835i) q^{17} +(-1.74274 - 3.01852i) q^{19} +(-4.54822 - 7.87774i) q^{23} +(-3.33949 + 5.78417i) q^{25} +1.67898 q^{29} +(-3.82321 + 6.62200i) q^{31} +(0.110210 - 9.04106i) q^{35} +(-4.69245 - 8.12755i) q^{37} +2.13253 q^{41} -6.03194 q^{43} +(3.94970 + 6.84108i) q^{47} +(3.35119 + 6.14569i) q^{49} +(-0.967751 + 1.67619i) q^{53} -20.6139 q^{55} +(3.91922 - 6.78829i) q^{59} +(-4.67648 - 8.09990i) q^{61} +(0.713312 + 1.23549i) q^{65} +(-0.516281 + 0.894224i) q^{67} +0.650582 q^{71} +(-0.642460 + 1.11277i) q^{73} +(13.9171 - 7.81045i) q^{77} +(8.20665 + 14.2143i) q^{79} -14.1645 q^{83} -8.71446 q^{85} +(6.70841 + 11.6193i) q^{89} +(-0.949702 - 0.563856i) q^{91} +(5.95574 - 10.3157i) q^{95} -2.26507 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{5} - 4 q^{7}+O(q^{10}) \) 8 * q + 2 * q^5 - 4 * q^7	\( 8 q + 2 q^{5} - 4 q^{7} + q^{11} - 20 q^{13} + 4 q^{17} + q^{19} - 12 q^{23} - 14 q^{25} - 12 q^{29} + 8 q^{31} - 9 q^{35} + 12 q^{41} + 2 q^{43} + 9 q^{47} + 6 q^{49} - 7 q^{53} - 36 q^{55} + 4 q^{59} - 25 q^{61} + 28 q^{65} - 30 q^{67} + 22 q^{71} + 4 q^{73} + 37 q^{77} + 7 q^{79} - 58 q^{83} + 14 q^{85} - 9 q^{89} + 15 q^{91} + 4 q^{95} - 8 q^{97}+O(q^{100}) \) 8 * q + 2 * q^5 - 4 * q^7 + q^11 - 20 * q^13 + 4 * q^17 + q^19 - 12 * q^23 - 14 * q^25 - 12 * q^29 + 8 * q^31 - 9 * q^35 + 12 * q^41 + 2 * q^43 + 9 * q^47 + 6 * q^49 - 7 * q^53 - 36 * q^55 + 4 * q^59 - 25 * q^61 + 28 * q^65 - 30 * q^67 + 22 * q^71 + 4 * q^73 + 37 * q^77 + 7 * q^79 - 58 * q^83 + 14 * q^85 - 9 * q^89 + 15 * q^91 + 4 * q^95 - 8 * q^97

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