LMFDB - Embedded newform 3780.2.q.d.2881.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3780,2,Mod(2881,3780)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3780, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 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("3780.2881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3780 = 2^{2} \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3780.q (of order $3$, degree $2$, not 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:	$30.1834519640$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 1260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2881.8
Character	$\chi$	$=$	3780.2881
Dual form			3780.2.q.d.3061.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{5} +(0.00201961 + 2.64575i) q^{7} +O(q^{10})$	$q+(0.500000 - 0.866025i) q^{5} +(0.00201961 + 2.64575i) q^{7} +(1.44197 + 2.49756i) q^{11} +(0.0827654 + 0.143354i) q^{13} +(0.347478 - 0.601849i) q^{17} +(2.26911 + 3.93021i) q^{19} +(2.15543 - 3.73332i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-3.34476 + 5.79329i) q^{29} -4.57479 q^{31} +(2.29230 + 1.32113i) q^{35} +(0.244258 + 0.423067i) q^{37} +(1.99120 + 3.44886i) q^{41} +(-0.488017 + 0.845269i) q^{43} +6.71021 q^{47} +(-6.99999 + 0.0106868i) q^{49} +(0.0191298 - 0.0331338i) q^{53} +2.88394 q^{55} +1.44083 q^{59} -6.57738 q^{61} +0.165531 q^{65} -5.56263 q^{67} +8.73689 q^{71} +(-3.12050 + 5.40487i) q^{73} +(-6.60502 + 3.82013i) q^{77} -9.89693 q^{79} +(4.42924 - 7.67166i) q^{83} +(-0.347478 - 0.601849i) q^{85} +(1.93095 + 3.34450i) q^{89} +(-0.379111 + 0.219266i) q^{91} +4.53822 q^{95} +(-7.94934 + 13.7687i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 13 q^{5} - 6 q^{7}+O(q^{10}) $ 26 * q + 13 * q^5 - 6 * q^7	$ 26 q + 13 q^{5} - 6 q^{7} - q^{11} + 7 q^{13} - 8 q^{17} - 9 q^{19} + 3 q^{23} - 13 q^{25} + 7 q^{29} + 2 q^{31} - 3 q^{35} + 10 q^{37} - 13 q^{41} - 8 q^{43} + 12 q^{47} - 28 q^{49} - 17 q^{53} - 2 q^{55} - 16 q^{59} - 20 q^{61} + 14 q^{65} - 48 q^{67} - 4 q^{71} - 17 q^{73} - 19 q^{77} - 38 q^{79} - 9 q^{83} + 8 q^{85} - q^{89} - 2 q^{91} - 18 q^{95} + 9 q^{97}+O(q^{100}) $ 26 * q + 13 * q^5 - 6 * q^7 - q^11 + 7 * q^13 - 8 * q^17 - 9 * q^19 + 3 * q^23 - 13 * q^25 + 7 * q^29 + 2 * q^31 - 3 * q^35 + 10 * q^37 - 13 * q^41 - 8 * q^43 + 12 * q^47 - 28 * q^49 - 17 * q^53 - 2 * q^55 - 16 * q^59 - 20 * q^61 + 14 * q^65 - 48 * q^67 - 4 * q^71 - 17 * q^73 - 19 * q^77 - 38 * q^79 - 9 * q^83 + 8 * q^85 - q^89 - 2 * q^91 - 18 * q^95 + 9 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3780\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$	$1891$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	0.00201961	+	2.64575i	0.000763342	+	1.00000i
$7$	0.00201961	+	2.64575i	0.000763342	+	1.00000i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.44197	+	2.49756i	0.434770	+	0.753043i	0.997277	−	0.0737491i	$-0.0234964\pi$
$11$	1.44197	+	2.49756i	0.434770	+	0.753043i	−0.562507	+	0.826793i	$0.690163\pi$
$12$		0			0
$13$	0.0827654	+	0.143354i	0.0229550	+	0.0397592i	0.877275	−	0.479989i	$-0.159359\pi$
$13$	0.0827654	+	0.143354i	0.0229550	+	0.0397592i	−0.854320	+	0.519748i	$0.826026\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.347478	−	0.601849i	0.0842757	−	0.145970i	−0.820807	−	0.571206i	$-0.806476\pi$
$17$	0.347478	−	0.601849i	0.0842757	−	0.145970i	0.905082	+	0.425236i	$0.139809\pi$
$18$		0			0
$19$	2.26911	+	3.93021i	0.520570	+	0.901653i	0.999714	+	0.0239169i	$0.00761372\pi$
$19$	2.26911	+	3.93021i	0.520570	+	0.901653i	−0.479144	+	0.877736i	$0.659053\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.15543	−	3.73332i	0.449439	−	0.778450i	−0.548911	−	0.835881i	$-0.684957\pi$
$23$	2.15543	−	3.73332i	0.449439	−	0.778450i	0.998350	+	0.0574305i	$0.0182908\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.34476	+	5.79329i	−0.621106	+	1.07579i	0.368174	+	0.929757i	$0.379983\pi$
$29$	−3.34476	+	5.79329i	−0.621106	+	1.07579i	−0.989280	+	0.146031i	$0.953350\pi$
$30$		0			0
$31$	−4.57479			−0.821657			−0.410829	−	0.911713i	$-0.634761\pi$
$31$	−4.57479			−0.821657			−0.410829	+	0.911713i	$0.634761\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.29230	+	1.32113i	0.387469	+	0.223311i
$36$		0			0
$37$	0.244258	+	0.423067i	0.0401557	+	0.0695518i	0.885405	−	0.464821i	$-0.153881\pi$
$37$	0.244258	+	0.423067i	0.0401557	+	0.0695518i	−0.845249	+	0.534373i	$0.820548\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.99120	+	3.44886i	0.310974	+	0.538622i	0.978573	−	0.205898i	$-0.0660116\pi$
$41$	1.99120	+	3.44886i	0.310974	+	0.538622i	−0.667600	+	0.744520i	$0.732678\pi$
$42$		0			0
$43$	−0.488017	+	0.845269i	−0.0744218	+	0.128902i	−0.900835	−	0.434162i	$-0.857044\pi$
$43$	−0.488017	+	0.845269i	−0.0744218	+	0.128902i	0.826413	+	0.563065i	$0.190378\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.71021			0.978785			0.489392	−	0.872064i	$-0.337219\pi$
$47$	6.71021			0.978785			0.489392	+	0.872064i	$0.337219\pi$
$48$		0			0
$49$	−6.99999	+	0.0106868i	−0.999999	+	0.00152668i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.0191298	−	0.0331338i	0.00262768	−	0.00455127i	−0.864709	−	0.502274i	$-0.832497\pi$
$53$	0.0191298	−	0.0331338i	0.00262768	−	0.00455127i	0.867336	+	0.497723i	$0.165830\pi$
$54$		0			0
$55$	2.88394			0.388870
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.44083			0.187580			0.0937898	−	0.995592i	$-0.470102\pi$
$59$	1.44083			0.187580			0.0937898	+	0.995592i	$0.470102\pi$
$60$		0			0
$61$	−6.57738			−0.842147			−0.421074	−	0.907026i	$-0.638347\pi$
$61$	−6.57738			−0.842147			−0.421074	+	0.907026i	$0.638347\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.165531			0.0205316
$66$		0			0
$67$	−5.56263			−0.679584			−0.339792	−	0.940501i	$-0.610357\pi$
$67$	−5.56263			−0.679584			−0.339792	+	0.940501i	$0.610357\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	8.73689			1.03688			0.518439	−	0.855115i	$-0.326513\pi$
$71$	8.73689			1.03688			0.518439	+	0.855115i	$0.326513\pi$
$72$		0			0
$73$	−3.12050	+	5.40487i	−0.365227	+	0.632592i	−0.988813	−	0.149163i	$-0.952342\pi$
$73$	−3.12050	+	5.40487i	−0.365227	+	0.632592i	0.623586	+	0.781755i	$0.285675\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−6.60502	+	3.82013i	−0.752711	+	0.435345i
$78$		0			0
$79$	−9.89693			−1.11349			−0.556746	−	0.830683i	$-0.687950\pi$
$79$	−9.89693			−1.11349			−0.556746	+	0.830683i	$0.687950\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.42924	−	7.67166i	0.486172	−	0.842074i	−0.513702	−	0.857969i	$-0.671726\pi$
$83$	4.42924	−	7.67166i	0.486172	−	0.842074i	0.999874	+	0.0158946i	$0.00505962\pi$
$84$		0			0
$85$	−0.347478	−	0.601849i	−0.0376892	−	0.0652797i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.93095	+	3.34450i	0.204680	+	0.354516i	0.950031	−	0.312156i	$-0.101051\pi$
$89$	1.93095	+	3.34450i	0.204680	+	0.354516i	−0.745351	+	0.666673i	$0.767718\pi$
$90$		0			0
$91$	−0.379111	+	0.219266i	−0.0397417	+	0.0229853i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	4.53822			0.465612
$96$		0			0
$97$	−7.94934	+	13.7687i	−0.807133	+	1.39800i	0.107708	+	0.994183i	$0.465649\pi$
$97$	−7.94934	+	13.7687i	−0.807133	+	1.39800i	−0.914841	+	0.403813i	$0.867685\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.47817	−	12.9526i	−0.744106	−	1.28883i	−0.950611	−	0.310384i	$-0.899542\pi$
$101$	−7.47817	−	12.9526i	−0.744106	−	1.28883i	0.206505	−	0.978446i	$-0.433791\pi$
$102$		0			0
$103$	−9.89472	+	17.1382i	−0.974955	+	1.68867i	−0.294873	+	0.955536i	$0.595277\pi$
$103$	−9.89472	+	17.1382i	−0.974955	+	1.68867i	−0.680082	+	0.733136i	$0.738056\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.70336	+	11.6106i	0.648038	+	1.12244i	0.983591	+	0.180414i	$0.0577437\pi$
$107$	6.70336	+	11.6106i	0.648038	+	1.12244i	−0.335552	+	0.942022i	$0.608923\pi$
$108$		0			0
$109$	−2.49944	+	4.32916i	−0.239403	+	0.414659i	−0.960543	−	0.278131i	$-0.910285\pi$
$109$	−2.49944	+	4.32916i	−0.239403	+	0.414659i	0.721140	+	0.692789i	$0.243618\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.49094	+	4.31444i	0.234328	+	0.405868i	0.959077	−	0.283145i	$-0.0913777\pi$
$113$	2.49094	+	4.31444i	0.234328	+	0.405868i	−0.724749	+	0.689013i	$0.758044\pi$
$114$		0			0
$115$	−2.15543	−	3.73332i	−0.200995	−	0.348134i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.59304	+	0.918124i	0.146034	+	0.0841643i
$120$		0			0
$121$	1.34145	−	2.32347i	0.121950	−	0.211224i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	20.5850			1.82663			0.913314	−	0.407257i	$-0.133514\pi$
$127$	20.5850			1.82663			0.913314	+	0.407257i	$0.133514\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−4.20673	+	7.28627i	−0.367544	+	0.636604i	−0.989181	−	0.146701i	$-0.953134\pi$
$131$	−4.20673	+	7.28627i	−0.367544	+	0.636604i	0.621637	+	0.783305i	$0.286468\pi$
$132$		0			0
$133$	−10.3938	+	6.01144i	−0.901255	+	0.521258i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.45388	+	9.44640i	0.465957	+	0.807060i	0.999244	−	0.0388736i	$-0.0123770\pi$
$137$	5.45388	+	9.44640i	0.465957	+	0.807060i	−0.533288	+	0.845934i	$0.679044\pi$
$138$		0			0
$139$	−6.94693	−	12.0324i	−0.589231	−	1.02058i	−0.994333	−	0.106307i	$-0.966097\pi$
$139$	−6.94693	−	12.0324i	−0.589231	−	1.02058i	0.405102	−	0.914271i	$-0.367236\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.238690	+	0.413423i	−0.0199603	+	0.0345722i
$144$		0			0
$145$	3.34476	+	5.79329i	0.277767	+	0.481107i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−10.5183	+	18.2182i	−0.861692	+	1.49250i	0.00860180	+	0.999963i	$0.497262\pi$
$149$	−10.5183	+	18.2182i	−0.861692	+	1.49250i	−0.870294	+	0.492532i	$0.836071\pi$
$150$		0			0
$151$	−6.07087	−	10.5151i	−0.494041	−	0.855703i	0.505936	−	0.862571i	$-0.331147\pi$
$151$	−6.07087	−	10.5151i	−0.494041	−	0.855703i	−0.999976	+	0.00686769i	$0.997814\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.28740	+	3.96189i	−0.183728	+	0.318226i
$156$		0			0
$157$	13.1153			1.04671			0.523356	−	0.852114i	$-0.324680\pi$
$157$	13.1153			1.04671			0.523356	+	0.852114i	$0.324680\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	9.88178	+	5.69519i	0.778793	+	0.448844i
$162$		0			0
$163$	3.34865	+	5.80003i	0.262287	+	0.454294i	0.966849	−	0.255348i	$-0.0821901\pi$
$163$	3.34865	+	5.80003i	0.262287	+	0.454294i	−0.704563	+	0.709642i	$0.748857\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.0544085	−	0.0942383i	−0.00421026	−	0.00729238i	0.863913	−	0.503642i	$-0.168007\pi$
$167$	−0.0544085	−	0.0942383i	−0.00421026	−	0.00729238i	−0.868123	+	0.496349i	$0.834674\pi$
$168$		0			0
$169$	6.48630	−	11.2346i	0.498946	−	0.864200i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.67343			0.431343			0.215672	−	0.976466i	$-0.430806\pi$
$173$	5.67343			0.431343			0.215672	+	0.976466i	$0.430806\pi$
$174$		0			0
$175$	2.29028	−	1.32462i	0.173129	−	0.100132i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.646477	+	1.11973i	−0.0483199	+	0.0836926i	−0.889174	−	0.457570i	$-0.848720\pi$
$179$	−0.646477	+	1.11973i	−0.0483199	+	0.0836926i	0.840854	+	0.541262i	$0.182053\pi$
$180$		0			0
$181$	4.96075			0.368730			0.184365	−	0.982858i	$-0.440977\pi$
$181$	4.96075			0.368730			0.184365	+	0.982858i	$0.440977\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.488515			0.0359164
$186$		0			0
$187$	2.00421			0.146562
$188$		0			0
$189$		0			0
$190$		0			0
$191$	22.1668			1.60393			0.801966	−	0.597370i	$-0.203788\pi$
$191$	22.1668			1.60393			0.801966	+	0.597370i	$0.203788\pi$
$192$		0			0
$193$	−9.41474			−0.677688			−0.338844	−	0.940843i	$-0.610036\pi$
$193$	−9.41474			−0.677688			−0.338844	+	0.940843i	$0.610036\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−14.4486			−1.02942			−0.514710	−	0.857364i	$-0.672100\pi$
$197$	−14.4486			−1.02942			−0.514710	+	0.857364i	$0.672100\pi$
$198$		0			0
$199$	6.58651	−	11.4082i	0.466905	−	0.808704i	−0.532380	−	0.846506i	$-0.678702\pi$
$199$	6.58651	−	11.4082i	0.466905	−	0.808704i	0.999285	+	0.0378018i	$0.0120355\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−15.3344	−	8.83770i	−1.07626	−	0.620285i
$204$		0			0
$205$	3.98240			0.278143
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−6.54397	+	11.3345i	−0.452656	+	0.784023i
$210$		0			0
$211$	5.09767	+	8.82942i	0.350938	+	0.607842i	0.986414	−	0.164278i	$-0.0525294\pi$
$211$	5.09767	+	8.82942i	0.350938	+	0.607842i	−0.635476	+	0.772121i	$0.719196\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.488017	+	0.845269i	0.0332825	+	0.0576469i
$216$		0			0
$217$	−0.00923931	−	12.1038i	−0.000627205	−	0.821657i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.115036			0.00773819
$222$		0			0
$223$	−11.3620	+	19.6795i	−0.760855	+	1.31784i	0.181555	+	0.983381i	$0.441887\pi$
$223$	−11.3620	+	19.6795i	−0.760855	+	1.31784i	−0.942410	+	0.334459i	$0.891446\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.19323	+	10.7270i	0.411059	+	0.711975i	0.995006	−	0.0998167i	$-0.0318256\pi$
$227$	6.19323	+	10.7270i	0.411059	+	0.711975i	−0.583947	+	0.811792i	$0.698492\pi$
$228$		0			0
$229$	−5.05512	+	8.75572i	−0.334052	+	0.578594i	−0.983302	−	0.181980i	$-0.941749\pi$
$229$	−5.05512	+	8.75572i	−0.334052	+	0.578594i	0.649251	+	0.760575i	$0.275083\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	11.6322	+	20.1476i	0.762051	+	1.31991i	0.941792	+	0.336197i	$0.109141\pi$
$233$	11.6322	+	20.1476i	0.762051	+	1.31991i	−0.179741	+	0.983714i	$0.557526\pi$
$234$		0			0
$235$	3.35510	−	5.81121i	0.218863	−	0.379082i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−8.25795	−	14.3032i	−0.534163	−	0.925197i	−0.999203	−	0.0399074i	$-0.987294\pi$
$239$	−8.25795	−	14.3032i	−0.534163	−	0.925197i	0.465041	−	0.885289i	$-0.346040\pi$
$240$		0			0
$241$	6.37240	+	11.0373i	0.410483	+	0.710977i	0.994943	−	0.100446i	$-0.0320269\pi$
$241$	6.37240	+	11.0373i	0.410483	+	0.710977i	−0.584460	+	0.811423i	$0.698694\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.49074	+	6.06751i	−0.223015	+	0.387639i
$246$		0			0
$247$	−0.375608	+	0.650571i	−0.0238993	+	0.0413949i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	1.88421			0.118930			0.0594652	−	0.998230i	$-0.481060\pi$
$251$	1.88421			0.118930			0.0594652	+	0.998230i	$0.481060\pi$
$252$		0			0
$253$	12.4323			0.781609
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.36431	+	12.7554i	−0.459373	+	0.795658i	−0.998928	−	0.0462929i	$-0.985259\pi$
$257$	−7.36431	+	12.7554i	−0.459373	+	0.795658i	0.539555	+	0.841950i	$0.318593\pi$
$258$		0			0
$259$	−1.11884	+	0.647099i	−0.0695211	+	0.0402088i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−14.0652	−	24.3617i	−0.867300	−	1.50221i	−0.864746	−	0.502210i	$-0.832520\pi$
$263$	−14.0652	−	24.3617i	−0.867300	−	1.50221i	−0.00255386	−	0.999997i	$-0.500813\pi$
$264$		0			0
$265$	−0.0191298	−	0.0331338i	−0.00117513	−	0.00203539i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	8.71758	−	15.0993i	0.531520	−	0.920620i	−0.467803	−	0.883833i	$-0.654954\pi$
$269$	8.71758	−	15.0993i	0.531520	−	0.920620i	0.999323	−	0.0367875i	$-0.0117125\pi$
$270$		0			0
$271$	3.00147	+	5.19869i	0.182326	+	0.315798i	0.942672	−	0.333720i	$-0.108304\pi$
$271$	3.00147	+	5.19869i	0.182326	+	0.315798i	−0.760346	+	0.649518i	$0.774971\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.44197	−	2.49756i	0.0869540	−	0.150609i
$276$		0			0
$277$	15.3749	+	26.6302i	0.923791	+	1.60005i	0.793494	+	0.608578i	$0.208260\pi$
$277$	15.3749	+	26.6302i	0.923791	+	1.60005i	0.130296	+	0.991475i	$0.458407\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.70731	−	2.95714i	0.101849	−	0.176408i	−0.810597	−	0.585604i	$-0.800857\pi$
$281$	1.70731	−	2.95714i	0.101849	−	0.176408i	0.912447	+	0.409196i	$0.134191\pi$
$282$		0			0
$283$	10.6453			0.632800			0.316400	−	0.948626i	$-0.397526\pi$
$283$	10.6453			0.632800			0.316400	+	0.948626i	$0.397526\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−9.12081	+	5.27519i	−0.538384	+	0.311385i
$288$		0			0
$289$	8.25852	+	14.3042i	0.485795	+	0.841422i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	5.81360	+	10.0694i	0.339634	+	0.588263i	0.984364	−	0.176147i	$-0.0563634\pi$
$293$	5.81360	+	10.0694i	0.339634	+	0.588263i	−0.644730	+	0.764411i	$0.723030\pi$
$294$		0			0
$295$	0.720413	−	1.24779i	0.0419441	−	0.0726493i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.713580			0.0412674
$300$		0			0
$301$	−2.23736	−	1.28946i	−0.128959	−	0.0743234i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−3.28869	+	5.69618i	−0.188310	+	0.326162i
$306$		0			0
$307$	−12.6798			−0.723674			−0.361837	−	0.932241i	$-0.617850\pi$
$307$	−12.6798			−0.723674			−0.361837	+	0.932241i	$0.617850\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−19.5976			−1.11128			−0.555639	−	0.831423i	$-0.687526\pi$
$311$	−19.5976			−1.11128			−0.555639	+	0.831423i	$0.687526\pi$
$312$		0			0
$313$	−4.69075			−0.265137			−0.132568	−	0.991174i	$-0.542322\pi$
$313$	−4.69075			−0.265137			−0.132568	+	0.991174i	$0.542322\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	26.6638			1.49759			0.748794	−	0.662803i	$-0.230633\pi$
$317$	26.6638			1.49759			0.748794	+	0.662803i	$0.230633\pi$
$318$		0			0
$319$	−19.2922			−1.08015
$320$		0			0
$321$		0			0
$322$		0			0
$323$	3.15386			0.175485
$324$		0			0
$325$	0.0827654	−	0.143354i	0.00459100	−	0.00795184i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.0135520	+	17.7535i	0.000747147	+	0.978784i
$330$		0			0
$331$	−9.90029			−0.544169			−0.272085	−	0.962273i	$-0.587713\pi$
$331$	−9.90029			−0.544169			−0.272085	+	0.962273i	$0.587713\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2.78132	+	4.81738i	−0.151960	+	0.263202i
$336$		0			0
$337$	5.76153	+	9.97926i	0.313850	+	0.543605i	0.979192	−	0.202934i	$-0.0650476\pi$
$337$	5.76153	+	9.97926i	0.313850	+	0.543605i	−0.665342	+	0.746539i	$0.731714\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−6.59671	−	11.4258i	−0.357232	−	0.618744i
$342$		0			0
$343$	−0.0424118	−	18.5202i	−0.00229002	−	0.999997i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.17679			0.438953			0.219477	−	0.975618i	$-0.429565\pi$
$347$	8.17679			0.438953			0.219477	+	0.975618i	$0.429565\pi$
$348$		0			0
$349$	7.11114	−	12.3169i	0.380651	−	0.659306i	−0.610505	−	0.792013i	$-0.709033\pi$
$349$	7.11114	−	12.3169i	0.380651	−	0.659306i	0.991155	+	0.132706i	$0.0423667\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−14.9193	−	25.8409i	−0.794072	−	1.37537i	−0.923427	−	0.383775i	$-0.874624\pi$
$353$	−14.9193	−	25.8409i	−0.794072	−	1.37537i	0.129354	−	0.991598i	$-0.458710\pi$
$354$		0			0
$355$	4.36844	−	7.56637i	0.231853	−	0.401581i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	2.24605	+	3.89027i	0.118542	+	0.205320i	0.919190	−	0.393814i	$-0.128845\pi$
$359$	2.24605	+	3.89027i	0.118542	+	0.205320i	−0.800648	+	0.599135i	$0.795511\pi$
$360$		0			0
$361$	−0.797724	+	1.38170i	−0.0419855	+	0.0727210i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	3.12050	+	5.40487i	0.163334	+	0.282904i
$366$		0			0
$367$	4.69690	+	8.13527i	0.245176	+	0.424658i	0.962181	−	0.272410i	$-0.0878208\pi$
$367$	4.69690	+	8.13527i	0.245176	+	0.424658i	−0.717005	+	0.697068i	$0.754487\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.0877023	+	0.0505458i	0.00455328	+	0.00262420i
$372$		0			0
$373$	4.37904	−	7.58472i	0.226738	−	0.392722i	−0.730101	−	0.683339i	$-0.760527\pi$
$373$	4.37904	−	7.58472i	0.226738	−	0.392722i	0.956840	+	0.290617i	$0.0938605\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.10732			−0.0570300
$378$		0			0
$379$	22.1660			1.13859			0.569295	−	0.822134i	$-0.307216\pi$
$379$	22.1660			1.13859			0.569295	+	0.822134i	$0.307216\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	7.57854	−	13.1264i	0.387245	−	0.670729i	−0.604833	−	0.796353i	$-0.706760\pi$
$383$	7.57854	−	13.1264i	0.387245	−	0.670729i	0.992078	+	0.125624i	$0.0400933\pi$
$384$		0			0
$385$	0.00582443	+	7.63018i	0.000296841	+	0.388870i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−10.1815	−	17.6349i	−0.516223	−	0.894125i	−0.999823	−	0.0188353i	$-0.994004\pi$
$389$	−10.1815	−	17.6349i	−0.516223	−	0.894125i	0.483599	−	0.875289i	$-0.339329\pi$
$390$		0			0
$391$	−1.49793	−	2.59449i	−0.0757535	−	0.131209i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−4.94847	+	8.57100i	−0.248984	+	0.431254i
$396$		0			0
$397$	−3.21832	−	5.57429i	−0.161523	−	0.279766i	0.773892	−	0.633317i	$-0.218307\pi$
$397$	−3.21832	−	5.57429i	−0.161523	−	0.279766i	−0.935415	+	0.353552i	$0.884974\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	11.4681	−	19.8633i	0.572688	−	0.991924i	−0.423601	−	0.905849i	$-0.639234\pi$
$401$	11.4681	−	19.8633i	0.572688	−	0.991924i	0.996289	−	0.0860754i	$-0.0274326\pi$
$402$		0			0
$403$	−0.378635	−	0.655814i	−0.0188611	−	0.0326684i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.704424	+	1.22010i	−0.0349170	+	0.0604780i
$408$		0			0
$409$	−29.8653			−1.47674			−0.738371	−	0.674394i	$-0.764405\pi$
$409$	−29.8653			−1.47674			−0.738371	+	0.674394i	$0.764405\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.00290991	+	3.81207i	0.000143187	+	0.187580i
$414$		0			0
$415$	−4.42924	−	7.67166i	−0.217423	−	0.376587i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	2.26868	+	3.92946i	0.110832	+	0.191967i	0.916106	−	0.400936i	$-0.131315\pi$
$419$	2.26868	+	3.92946i	0.110832	+	0.191967i	−0.805274	+	0.592903i	$0.797982\pi$
$420$		0			0
$421$	−14.5625	+	25.2231i	−0.709735	+	1.22930i	0.255221	+	0.966883i	$0.417852\pi$
$421$	−14.5625	+	25.2231i	−0.709735	+	1.22930i	−0.964955	+	0.262414i	$0.915481\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.694955			−0.0337103
$426$		0			0
$427$	−0.0132838	−	17.4021i	−0.000642846	−	0.842147i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−16.6581	+	28.8527i	−0.802394	+	1.38979i	0.115643	+	0.993291i	$0.463107\pi$
$431$	−16.6581	+	28.8527i	−0.802394	+	1.38979i	−0.918036	+	0.396496i	$0.870226\pi$
$432$		0			0
$433$	−12.0462			−0.578906			−0.289453	−	0.957192i	$-0.593473\pi$
$433$	−12.0462			−0.578906			−0.289453	+	0.957192i	$0.593473\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	19.5636			0.935856
$438$		0			0
$439$	1.84528			0.0880705			0.0440352	−	0.999030i	$-0.485979\pi$
$439$	1.84528			0.0880705			0.0440352	+	0.999030i	$0.485979\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	9.52596			0.452592			0.226296	−	0.974059i	$-0.427338\pi$
$443$	9.52596			0.452592			0.226296	+	0.974059i	$0.427338\pi$
$444$		0			0
$445$	3.86190			0.183071
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−11.5363			−0.544433			−0.272216	−	0.962236i	$-0.587757\pi$
$449$	−11.5363			−0.544433			−0.272216	+	0.962236i	$0.587757\pi$
$450$		0			0
$451$	−5.74250	+	9.94630i	−0.270404	+	0.468353i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.000334308		0.437953i	1.56726e−5		0.0205316i
$456$		0			0
$457$	−11.0284			−0.515886			−0.257943	−	0.966160i	$-0.583045\pi$
$457$	−11.0284			−0.515886			−0.257943	+	0.966160i	$0.583045\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−13.0348	+	22.5769i	−0.607091	+	1.05151i	0.384626	+	0.923072i	$0.374330\pi$
$461$	−13.0348	+	22.5769i	−0.607091	+	1.05151i	−0.991717	+	0.128440i	$0.959003\pi$
$462$		0			0
$463$	−5.01294	−	8.68267i	−0.232971	−	0.403518i	0.725710	−	0.688001i	$-0.241511\pi$
$463$	−5.01294	−	8.68267i	−0.232971	−	0.403518i	−0.958681	+	0.284483i	$0.908178\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.28156	−	3.95178i	−0.105578	−	0.182867i	0.808396	−	0.588639i	$-0.200336\pi$
$467$	−2.28156	−	3.95178i	−0.105578	−	0.182867i	−0.913974	+	0.405772i	$0.867003\pi$
$468$		0			0
$469$	−0.0112344	−	14.7173i	−0.000518755	−	0.679584i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.81482			−0.129425
$474$		0			0
$475$	2.26911	−	3.93021i	0.104114	−	0.180331i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−17.3679	−	30.0820i	−0.793558	−	1.37448i	−0.923751	−	0.382994i	$-0.874893\pi$
$479$	−17.3679	−	30.0820i	−0.793558	−	1.37448i	0.130193	−	0.991489i	$-0.458440\pi$
$480$		0			0
$481$	−0.0404322	+	0.0700306i	−0.00184355	+	0.00319312i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	7.94934	+	13.7687i	0.360961	+	0.625203i
$486$		0			0
$487$	2.36151	−	4.09026i	0.107010	−	0.185348i	−0.807547	−	0.589803i	$-0.799206\pi$
$487$	2.36151	−	4.09026i	0.107010	−	0.185348i	0.914558	+	0.404455i	$0.132539\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−18.0436	−	31.2523i	−0.814294	−	1.41040i	−0.909834	−	0.414973i	$-0.863791\pi$
$491$	−18.0436	−	31.2523i	−0.814294	−	1.41040i	0.0955396	−	0.995426i	$-0.469542\pi$
$492$		0			0
$493$	2.32446	+	4.02608i	0.104688	+	0.181326i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.0176451	+	23.1156i	0.000791492	+	1.03688i
$498$		0			0
$499$	−2.41475	+	4.18247i	−0.108099	+	0.187233i	−0.915000	−	0.403453i	$-0.867810\pi$
$499$	−2.41475	+	4.18247i	−0.108099	+	0.187233i	0.806901	+	0.590687i	$0.201143\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	10.3981			0.463630			0.231815	−	0.972760i	$-0.425534\pi$
$503$	10.3981			0.463630			0.231815	+	0.972760i	$0.425534\pi$
$504$		0			0
$505$	−14.9563			−0.665549
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.85088	+	3.20583i	−0.0820390	+	0.142096i	−0.904126	−	0.427267i	$-0.859477\pi$
$509$	−1.85088	+	3.20583i	−0.0820390	+	0.142096i	0.822087	+	0.569362i	$0.192810\pi$
$510$		0			0
$511$	−14.3062	−	8.24515i	−0.632870	−	0.364744i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	9.89472	+	17.1382i	0.436013	+	0.755197i
$516$		0			0
$517$	9.67591	+	16.7592i	0.425546	+	0.737067i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	22.1805	−	38.4177i	0.971744	−	1.68311i	0.281458	−	0.959574i	$-0.409182\pi$
$521$	22.1805	−	38.4177i	0.971744	−	1.68311i	0.690286	−	0.723536i	$-0.257485\pi$
$522$		0			0
$523$	7.72373	+	13.3779i	0.337735	+	0.584974i	0.984006	−	0.178133i	$-0.0570059\pi$
$523$	7.72373	+	13.3779i	0.337735	+	0.584974i	−0.646271	+	0.763108i	$0.723673\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.58964	+	2.75333i	−0.0692457	+	0.119937i
$528$		0			0
$529$	2.20823	+	3.82477i	0.0960101	+	0.166294i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−0.329605	+	0.570893i	−0.0142768	+	0.0247281i
$534$		0			0
$535$	13.4067			0.579623
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−10.1205	−	17.4675i	−0.435919	−	0.752379i
$540$		0			0
$541$	13.1549	+	22.7850i	0.565573	+	0.979602i	0.996996	+	0.0774520i	$0.0246784\pi$
$541$	13.1549	+	22.7850i	0.565573	+	0.979602i	−0.431423	+	0.902150i	$0.641988\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	2.49944	+	4.32916i	0.107064	+	0.185441i
$546$		0			0
$547$	1.95548	−	3.38700i	0.0836104	−	0.144818i	−0.821188	−	0.570658i	$-0.806688\pi$
$547$	1.95548	−	3.38700i	0.0836104	−	0.144818i	0.904798	+	0.425840i	$0.140022\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−30.3585			−1.29332
$552$		0			0
$553$	−0.0199880	−	26.1848i	−0.000849975	−	1.11349i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−2.07374	+	3.59182i	−0.0878672	+	0.152190i	−0.906609	−	0.421971i	$-0.861338\pi$
$557$	−2.07374	+	3.59182i	−0.0878672	+	0.152190i	0.818742	+	0.574161i	$0.194672\pi$
$558$		0			0
$559$	−0.161563			−0.00683341
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−16.4345			−0.692630			−0.346315	−	0.938118i	$-0.612567\pi$
$563$	−16.4345			−0.692630			−0.346315	+	0.938118i	$0.612567\pi$
$564$		0			0
$565$	4.98188			0.209589
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.38319			0.0579864			0.0289932	−	0.999580i	$-0.490770\pi$
$569$	1.38319			0.0579864			0.0289932	+	0.999580i	$0.490770\pi$
$570$		0			0
$571$	2.32789			0.0974192			0.0487096	−	0.998813i	$-0.484489\pi$
$571$	2.32789			0.0974192			0.0487096	+	0.998813i	$0.484489\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−4.31086			−0.179775
$576$		0			0
$577$	20.1634	−	34.9241i	0.839414	−	1.45391i	−0.0509707	−	0.998700i	$-0.516232\pi$
$577$	20.1634	−	34.9241i	0.839414	−	1.45391i	0.890385	−	0.455208i	$-0.150435\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	20.3062	+	11.7032i	0.842445	+	0.485529i
$582$		0			0
$583$	0.110338			0.00456974
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−10.1883	+	17.6466i	−0.420516	+	0.728354i	−0.995990	−	0.0894655i	$-0.971484\pi$
$587$	−10.1883	+	17.6466i	−0.420516	+	0.728354i	0.575474	+	0.817820i	$0.304817\pi$
$588$		0			0
$589$	−10.3807	−	17.9799i	−0.427730	−	0.740850i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−2.96318	−	5.13239i	−0.121683	−	0.210762i	0.798748	−	0.601665i	$-0.205496\pi$
$593$	−2.96318	−	5.13239i	−0.121683	−	0.210762i	−0.920432	+	0.390904i	$0.872163\pi$
$594$		0			0
$595$	1.59164	−	0.920555i	0.0652509	−	0.0377391i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	29.4187			1.20202			0.601009	−	0.799243i	$-0.294766\pi$
$599$	29.4187			1.20202			0.601009	+	0.799243i	$0.294766\pi$
$600$		0			0
$601$	−12.4991	+	21.6490i	−0.509847	+	0.883082i	0.490087	+	0.871673i	$0.336965\pi$
$601$	−12.4991	+	21.6490i	−0.509847	+	0.883082i	−0.999935	+	0.0114084i	$0.996369\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.34145	−	2.32347i	−0.0545379	−	0.0944623i
$606$		0			0
$607$	24.3132	−	42.1117i	0.986843	−	1.70926i	0.353398	−	0.935473i	$-0.385026\pi$
$607$	24.3132	−	42.1117i	0.986843	−	1.70926i	0.633444	−	0.773788i	$-0.281641\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.555373	+	0.961934i	0.0224680	+	0.0389157i
$612$		0			0
$613$	−2.04753	+	3.54643i	−0.0826990	+	0.143239i	−0.904408	−	0.426668i	$-0.859687\pi$
$613$	−2.04753	+	3.54643i	−0.0826990	+	0.143239i	0.821709	+	0.569907i	$0.193021\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	7.63565	+	13.2253i	0.307400	+	0.532432i	0.977793	−	0.209574i	$-0.0672079\pi$
$617$	7.63565	+	13.2253i	0.307400	+	0.532432i	−0.670393	+	0.742006i	$0.733875\pi$
$618$		0			0
$619$	−20.3552	−	35.2562i	−0.818144	−	1.41707i	−0.907048	−	0.421026i	$-0.861670\pi$
$619$	−20.3552	−	35.2562i	−0.818144	−	1.41707i	0.0889048	−	0.996040i	$-0.471663\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−8.84482	+	5.11556i	−0.354360	+	0.204951i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	0.339496			0.0135366
$630$		0			0
$631$	40.9878			1.63170			0.815849	−	0.578265i	$-0.196270\pi$
$631$	40.9878			1.63170			0.815849	+	0.578265i	$0.196270\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	10.2925	−	17.8272i	0.408446	−	0.707450i
$636$		0			0
$637$	−0.580889	−	1.00259i	−0.0230157	−	0.0397241i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−3.44510	−	5.96709i	−0.136073	−	0.235686i	0.789934	−	0.613192i	$-0.210115\pi$
$641$	−3.44510	−	5.96709i	−0.136073	−	0.235686i	−0.926007	+	0.377507i	$0.876782\pi$
$642$		0			0
$643$	−17.9934	−	31.1654i	−0.709590	−	1.22905i	−0.965010	−	0.262215i	$-0.915547\pi$
$643$	−17.9934	−	31.1654i	−0.709590	−	1.22905i	0.255420	−	0.966830i	$-0.417786\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	10.4158	−	18.0407i	0.409488	−	0.709253i	−0.585345	−	0.810785i	$-0.699041\pi$
$647$	10.4158	−	18.0407i	0.409488	−	0.709253i	0.994832	+	0.101531i	$0.0323742\pi$
$648$		0			0
$649$	2.07763	+	3.59855i	0.0815540	+	0.141256i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	15.7828	−	27.3366i	0.617629	−	1.06976i	−0.372288	−	0.928117i	$-0.621427\pi$
$653$	15.7828	−	27.3366i	0.617629	−	1.06976i	0.989917	−	0.141647i	$-0.0452400\pi$
$654$		0			0
$655$	4.20673	+	7.28627i	0.164370	+	0.284698i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	12.5849	−	21.7977i	0.490238	−	0.849117i	−0.509699	−	0.860353i	$-0.670243\pi$
$659$	12.5849	−	21.7977i	0.490238	−	0.849117i	0.999937	+	0.0112359i	$0.00357657\pi$
$660$		0			0
$661$	−26.0260			−1.01229			−0.506147	−	0.862447i	$-0.668931\pi$
$661$	−26.0260			−1.01229			−0.506147	+	0.862447i	$0.668931\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.00916545	+	12.0070i	0.000355421	+	0.465611i
$666$		0			0
$667$	14.4188	+	24.9741i	0.558298	+	0.967001i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−9.48437	−	16.4274i	−0.366140	−	0.634173i
$672$		0			0
$673$	2.20080	−	3.81189i	0.0848345	−	0.146938i	−0.820486	−	0.571666i	$-0.806297\pi$
$673$	2.20080	−	3.81189i	0.0848345	−	0.146938i	0.905321	+	0.424729i	$0.139631\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	47.5279			1.82665			0.913323	−	0.407237i	$-0.133508\pi$
$677$	47.5279			1.82665			0.913323	+	0.407237i	$0.133508\pi$
$678$		0			0
$679$	−36.4445	−	21.0042i	−1.39861	−	0.806066i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	5.43047	−	9.40586i	0.207791	−	0.359905i	−0.743227	−	0.669039i	$-0.766706\pi$
$683$	5.43047	−	9.40586i	0.207791	−	0.359905i	0.951018	+	0.309134i	$0.100039\pi$
$684$		0			0
$685$	10.9078			0.416764
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.00633314			0.000241273
$690$		0			0
$691$	51.4216			1.95617			0.978085	−	0.208205i	$-0.0667621\pi$
$691$	51.4216			1.95617			0.978085	+	0.208205i	$0.0667621\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−13.8939			−0.527024
$696$		0			0
$697$	2.76759			0.104830
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−9.99979			−0.377687			−0.188843	−	0.982007i	$-0.560474\pi$
$701$	−9.99979			−0.377687			−0.188843	+	0.982007i	$0.560474\pi$
$702$		0			0
$703$	−1.10850	+	1.91997i	−0.0418077	+	0.0724131i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	34.2542	−	19.8115i	1.28826	−	0.745090i
$708$		0			0
$709$	−14.2825			−0.536392			−0.268196	−	0.963364i	$-0.586427\pi$
$709$	−14.2825			−0.536392			−0.268196	+	0.963364i	$0.586427\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−9.86065	+	17.0792i	−0.369284	+	0.639619i
$714$		0			0
$715$	0.238690	+	0.413423i	0.00892651	+	0.0154612i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−24.0553	−	41.6650i	−0.897112	−	1.55384i	−0.831169	−	0.556020i	$-0.812328\pi$
$719$	−24.0553	−	41.6650i	−0.897112	−	1.55384i	−0.0659425	−	0.997823i	$-0.521005\pi$
$720$		0			0
$721$	−45.3633	−	26.1443i	−1.68942	−	0.973666i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	6.68952			0.248443
$726$		0			0
$727$	11.4883	−	19.8983i	0.426077	−	0.737988i	−0.570443	−	0.821337i	$-0.693228\pi$
$727$	11.4883	−	19.8983i	0.426077	−	0.737988i	0.996520	+	0.0833496i	$0.0265618\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.339150	+	0.587424i	0.0125439	+	0.0217267i
$732$		0			0
$733$	−12.8774	+	22.3043i	−0.475637	+	0.823828i	−0.999611	−	0.0279069i	$-0.991116\pi$
$733$	−12.8774	+	22.3043i	−0.475637	+	0.823828i	0.523973	+	0.851735i	$0.324449\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−8.02114	−	13.8930i	−0.295463	−	0.511756i
$738$		0			0
$739$	−23.5796	+	40.8411i	−0.867391	+	1.50237i	−0.00273810	+	0.999996i	$0.500872\pi$
$739$	−23.5796	+	40.8411i	−0.867391	+	1.50237i	−0.864653	+	0.502369i	$0.832462\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	5.01809	+	8.69159i	0.184096	+	0.318864i	0.943272	−	0.332022i	$-0.107731\pi$
$743$	5.01809	+	8.69159i	0.184096	+	0.318864i	−0.759176	+	0.650886i	$0.774398\pi$
$744$		0			0
$745$	10.5183	+	18.2182i	0.385361	+	0.667464i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−30.7051	+	17.7589i	−1.12194	+	0.648895i
$750$		0			0
$751$	11.1888	−	19.3796i	0.408287	−	0.707173i	−0.586411	−	0.810013i	$-0.699460\pi$
$751$	11.1888	−	19.3796i	0.408287	−	0.707173i	0.994698	+	0.102840i	$0.0327931\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−12.1417			−0.441883
$756$		0			0
$757$	41.3903			1.50436			0.752178	−	0.658960i	$-0.229003\pi$
$757$	41.3903			1.50436			0.752178	+	0.658960i	$0.229003\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	6.95237	−	12.0419i	0.252023	−	0.436517i	−0.712059	−	0.702119i	$-0.752237\pi$
$761$	6.95237	−	12.0419i	0.252023	−	0.436517i	0.964083	+	0.265602i	$0.0855707\pi$
$762$		0			0
$763$	−11.4589	−	6.60416i	−0.414841	−	0.239087i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.119251	+	0.206548i	0.00430589	+	0.00745802i
$768$		0			0
$769$	−11.8746	−	20.5674i	−0.428208	−	0.741678i	0.568506	−	0.822679i	$-0.307522\pi$
$769$	−11.8746	−	20.5674i	−0.428208	−	0.741678i	−0.996714	+	0.0810010i	$0.974188\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	11.2082	−	19.4132i	0.403132	−	0.698244i	−0.590970	−	0.806693i	$-0.701255\pi$
$773$	11.2082	−	19.4132i	0.403132	−	0.698244i	0.994102	+	0.108449i	$0.0345884\pi$
$774$		0			0
$775$	2.28740	+	3.96189i	0.0821657	+	0.142315i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−9.03651	+	15.6517i	−0.323767	+	0.560780i
$780$		0			0
$781$	12.5983	+	21.8209i	0.450803	+	0.780814i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	6.55764	−	11.3582i	0.234052	−	0.405390i
$786$		0			0
$787$	28.1346			1.00289			0.501444	−	0.865190i	$-0.332802\pi$
$787$	28.1346			1.00289			0.501444	+	0.865190i	$0.332802\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−11.4099	+	6.59912i	−0.405689	+	0.234638i
$792$		0			0
$793$	−0.544379	−	0.942893i	−0.0193315	−	0.0334831i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	0.447494	+	0.775082i	0.0158510	+	0.0274548i	0.873842	−	0.486210i	$-0.161621\pi$
$797$	0.447494	+	0.775082i	0.0158510	+	0.0274548i	−0.857991	+	0.513665i	$0.828288\pi$
$798$		0			0
$799$	2.33165	−	4.03853i	0.0824878	−	0.142873i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−17.9987			−0.635159
$804$		0			0
$805$	9.87307	−	5.71027i	0.347980	−	0.201261i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	16.2881	−	28.2118i	0.572659	−	0.991874i	−0.423633	−	0.905834i	$-0.639245\pi$
$809$	16.2881	−	28.2118i	0.572659	−	0.991874i	0.996292	−	0.0860398i	$-0.0274212\pi$
$810$		0			0
$811$	−24.9893			−0.877492			−0.438746	−	0.898611i	$-0.644577\pi$
$811$	−24.9893			−0.877492			−0.438746	+	0.898611i	$0.644577\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	6.69730			0.234596
$816$		0			0
$817$	−4.42945			−0.154967
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−18.0264			−0.629127			−0.314564	−	0.949236i	$-0.601858\pi$
$821$	−18.0264			−0.629127			−0.314564	+	0.949236i	$0.601858\pi$
$822$		0			0
$823$	−51.7586			−1.80419			−0.902095	−	0.431537i	$-0.857971\pi$
$823$	−51.7586			−1.80419			−0.902095	+	0.431537i	$0.857971\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−30.0446			−1.04475			−0.522376	−	0.852715i	$-0.674954\pi$
$827$	−30.0446			−1.04475			−0.522376	+	0.852715i	$0.674954\pi$
$828$		0			0
$829$	17.9543	−	31.0977i	0.623577	−	1.08007i	−0.365237	−	0.930914i	$-0.619012\pi$
$829$	17.9543	−	31.0977i	0.623577	−	1.08007i	0.988814	−	0.149152i	$-0.0476545\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−2.42591	+	4.21665i	−0.0840528	+	0.146098i
$834$		0			0
$835$	−0.108817			−0.00376577
$836$		0			0
$837$		0			0
$838$		0			0
$839$	23.9113	−	41.4157i	0.825511	−	1.42983i	−0.0760170	−	0.997107i	$-0.524220\pi$
$839$	23.9113	−	41.4157i	0.825511	−	1.42983i	0.901528	−	0.432721i	$-0.142446\pi$
$840$		0			0
$841$	−7.87484	−	13.6396i	−0.271546	−	0.470332i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−6.48630	−	11.2346i	−0.223135	−	0.386482i
$846$		0			0
$847$	6.15002	+	3.54446i	0.211317	+	0.121789i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	2.10592			0.0721901
$852$		0			0
$853$	−1.82607	+	3.16285i	−0.0625236	+	0.108294i	−0.895593	−	0.444875i	$-0.853248\pi$
$853$	−1.82607	+	3.16285i	−0.0625236	+	0.108294i	0.833069	+	0.553169i	$0.186582\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	10.5907	+	18.3436i	0.361770	+	0.626604i	0.988252	−	0.152832i	$-0.0488392\pi$
$857$	10.5907	+	18.3436i	0.361770	+	0.626604i	−0.626482	+	0.779436i	$0.715506\pi$
$858$		0			0
$859$	19.7367	−	34.1850i	0.673408	−	1.16638i	−0.303523	−	0.952824i	$-0.598163\pi$
$859$	19.7367	−	34.1850i	0.673408	−	1.16638i	0.976931	−	0.213553i	$-0.0685036\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−13.1256	−	22.7342i	−0.446800	−	0.773880i	0.551376	−	0.834257i	$-0.314103\pi$
$863$	−13.1256	−	22.7342i	−0.446800	−	0.773880i	−0.998176	+	0.0603773i	$0.980770\pi$
$864$		0			0
$865$	2.83672	−	4.91334i	0.0964512	−	0.167058i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−14.2711	−	24.7182i	−0.484113	−	0.838508i
$870$		0			0
$871$	−0.460393	−	0.797425i	−0.0155998	−	0.0270197i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.00201961	−	2.64575i	−6.82754e−5	−	0.0894427i
$876$		0			0
$877$	28.8607	−	49.9883i	0.974558	−	1.68798i	0.293172	−	0.956060i	$-0.405289\pi$
$877$	28.8607	−	49.9883i	0.974558	−	1.68798i	0.681386	−	0.731924i	$-0.261377\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	2.06626			0.0696142			0.0348071	−	0.999394i	$-0.488918\pi$
$881$	2.06626			0.0696142			0.0348071	+	0.999394i	$0.488918\pi$
$882$		0			0
$883$	15.8908			0.534768			0.267384	−	0.963590i	$-0.413841\pi$
$883$	15.8908			0.534768			0.267384	+	0.963590i	$0.413841\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−9.23782	+	16.0004i	−0.310176	+	0.537240i	−0.978400	−	0.206720i	$-0.933721\pi$
$887$	−9.23782	+	16.0004i	−0.310176	+	0.537240i	0.668224	+	0.743960i	$0.267055\pi$
$888$		0			0
$889$	0.0415738	+	54.4629i	0.00139434	+	1.82663i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	15.2262	+	26.3726i	0.509526	+	0.882524i
$894$		0			0
$895$	0.646477	+	1.11973i	0.0216093	+	0.0374285i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	15.3016	−	26.5031i	0.510337	−	0.883929i
$900$		0			0
$901$	−0.0132944	−	0.0230265i	−0.000442899	−	0.000767124i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.48038	−	4.29614i	0.0824505	−	0.142808i
$906$		0			0
$907$	27.4315	+	47.5128i	0.910848	+	1.57764i	0.812869	+	0.582447i	$0.197905\pi$
$907$	27.4315	+	47.5128i	0.910848	+	1.57764i	0.0979791	+	0.995188i	$0.468762\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	7.68535	−	13.3114i	0.254627	−	0.441027i	−0.710167	−	0.704033i	$-0.751381\pi$
$911$	7.68535	−	13.3114i	0.254627	−	0.441027i	0.964794	+	0.263006i	$0.0847140\pi$
$912$		0			0
$913$	25.5473			0.845491
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−19.2861	−	11.1152i	−0.636884	−	0.367057i
$918$		0			0
$919$	13.3607	+	23.1413i	0.440728	+	0.763363i	0.997744	−	0.0671392i	$-0.0213872\pi$
$919$	13.3607	+	23.1413i	0.440728	+	0.763363i	−0.557016	+	0.830502i	$0.688054\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	0.723112	+	1.25247i	0.0238015	+	0.0412254i
$924$		0			0
$925$	0.244258	−	0.423067i	0.00803114	−	0.0139104i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.956024			−0.0313661			−0.0156831	−	0.999877i	$-0.504992\pi$
$929$	−0.956024			−0.0313661			−0.0156831	+	0.999877i	$0.504992\pi$
$930$		0			0
$931$	−15.9258	−	27.4872i	−0.521946	−	0.900857i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.00210	−	1.73569i	0.0327723	−	0.0567633i
$936$		0			0
$937$	−47.2009			−1.54199			−0.770993	−	0.636844i	$-0.780239\pi$
$937$	−47.2009			−1.54199			−0.770993	+	0.636844i	$0.780239\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	38.0114			1.23914			0.619568	−	0.784943i	$-0.287308\pi$
$941$	38.0114			1.23914			0.619568	+	0.784943i	$0.287308\pi$
$942$		0			0
$943$	17.1676			0.559054
$944$		0			0
$945$		0			0
$946$		0			0
$947$	59.6964			1.93987			0.969936	−	0.243359i	$-0.0782493\pi$
$947$	59.6964			1.93987			0.969936	+	0.243359i	$0.0782493\pi$
$948$		0			0
$949$	−1.03308			−0.0335351
$950$		0			0
$951$		0			0
$952$		0			0
$953$	31.6658			1.02576			0.512879	−	0.858461i	$-0.328579\pi$
$953$	31.6658			1.02576			0.512879	+	0.858461i	$0.328579\pi$
$954$		0			0
$955$	11.0834	−	19.1970i	0.358650	−	0.621200i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−24.9818	+	14.4487i	−0.806705	+	0.466572i
$960$		0			0
$961$	−10.0713			−0.324879
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−4.70737	+	8.15340i	−0.151536	+	0.262467i
$966$		0			0
$967$	16.5585	+	28.6801i	0.532484	+	0.922290i	0.999281	+	0.0379247i	$0.0120747\pi$
$967$	16.5585	+	28.6801i	0.532484	+	0.922290i	−0.466797	+	0.884365i	$0.654592\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	27.2744	+	47.2406i	0.875276	+	1.51602i	0.856469	+	0.516199i	$0.172653\pi$
$971$	27.2744	+	47.2406i	0.875276	+	1.51602i	0.0188069	+	0.999823i	$0.494013\pi$
$972$		0			0
$973$	31.8208	−	18.4041i	1.02013	−	0.590010i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−3.74344			−0.119763			−0.0598817	−	0.998205i	$-0.519072\pi$
$977$	−3.74344			−0.119763			−0.0598817	+	0.998205i	$0.519072\pi$
$978$		0			0
$979$	−5.56873	+	9.64533i	−0.177978	+	0.308266i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−26.8131	−	46.4417i	−0.855205	−	1.48126i	−0.876455	−	0.481484i	$-0.840098\pi$
$983$	−26.8131	−	46.4417i	−0.855205	−	1.48126i	0.0212495	−	0.999774i	$-0.493236\pi$
$984$		0			0
$985$	−7.22430	+	12.5129i	−0.230185	+	0.398693i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.10377	+	3.64384i	0.0668961	+	0.115867i
$990$		0			0
$991$	28.7394	−	49.7781i	0.912938	−	1.58125i	0.103045	−	0.994677i	$-0.467142\pi$
$991$	28.7394	−	49.7781i	0.912938	−	1.58125i	0.809893	−	0.586578i	$-0.199525\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−6.58651	−	11.4082i	−0.208806	−	0.361663i
$996$		0			0
$997$	−0.977818	−	1.69363i	−0.0309678	−	0.0536378i	0.850126	−	0.526579i	$-0.176526\pi$
$997$	−0.977818	−	1.69363i	−0.0309678	−	0.0536378i	−0.881094	+	0.472941i	$0.843192\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3780.2.q.d.2881.8		26
3.2	odd	2		1260.2.q.d.781.2	yes	26
7.2	even	3		3780.2.t.d.1801.2		26
9.4	even	3		3780.2.t.d.361.2		26
9.5	odd	6		1260.2.t.d.1201.10	yes	26
21.2	odd	6		1260.2.t.d.961.10	yes	26
63.23	odd	6		1260.2.q.d.121.2	✓	26
63.58	even	3	inner	3780.2.q.d.3061.8		26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.2.q.d.121.2	✓	26	63.23	odd	6
1260.2.q.d.781.2	yes	26	3.2	odd	2
1260.2.t.d.961.10	yes	26	21.2	odd	6
1260.2.t.d.1201.10	yes	26	9.5	odd	6
3780.2.q.d.2881.8		26	1.1	even	1	trivial
3780.2.q.d.3061.8		26	63.58	even	3	inner
3780.2.t.d.361.2		26	9.4	even	3
3780.2.t.d.1801.2		26	7.2	even	3

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:	\( N \)	\(=\)	\( 3780 = 2^{2} \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3780.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{5} +(0.00201961 + 2.64575i) q^{7} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{5} +(0.00201961 + 2.64575i) q^{7} +(1.44197 + 2.49756i) q^{11} +(0.0827654 + 0.143354i) q^{13} +(0.347478 - 0.601849i) q^{17} +(2.26911 + 3.93021i) q^{19} +(2.15543 - 3.73332i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-3.34476 + 5.79329i) q^{29} -4.57479 q^{31} +(2.29230 + 1.32113i) q^{35} +(0.244258 + 0.423067i) q^{37} +(1.99120 + 3.44886i) q^{41} +(-0.488017 + 0.845269i) q^{43} +6.71021 q^{47} +(-6.99999 + 0.0106868i) q^{49} +(0.0191298 - 0.0331338i) q^{53} +2.88394 q^{55} +1.44083 q^{59} -6.57738 q^{61} +0.165531 q^{65} -5.56263 q^{67} +8.73689 q^{71} +(-3.12050 + 5.40487i) q^{73} +(-6.60502 + 3.82013i) q^{77} -9.89693 q^{79} +(4.42924 - 7.67166i) q^{83} +(-0.347478 - 0.601849i) q^{85} +(1.93095 + 3.34450i) q^{89} +(-0.379111 + 0.219266i) q^{91} +4.53822 q^{95} +(-7.94934 + 13.7687i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 13 q^{5} - 6 q^{7}+O(q^{10}) \) 26 * q + 13 * q^5 - 6 * q^7	\( 26 q + 13 q^{5} - 6 q^{7} - q^{11} + 7 q^{13} - 8 q^{17} - 9 q^{19} + 3 q^{23} - 13 q^{25} + 7 q^{29} + 2 q^{31} - 3 q^{35} + 10 q^{37} - 13 q^{41} - 8 q^{43} + 12 q^{47} - 28 q^{49} - 17 q^{53} - 2 q^{55} - 16 q^{59} - 20 q^{61} + 14 q^{65} - 48 q^{67} - 4 q^{71} - 17 q^{73} - 19 q^{77} - 38 q^{79} - 9 q^{83} + 8 q^{85} - q^{89} - 2 q^{91} - 18 q^{95} + 9 q^{97}+O(q^{100}) \) 26 * q + 13 * q^5 - 6 * q^7 - q^11 + 7 * q^13 - 8 * q^17 - 9 * q^19 + 3 * q^23 - 13 * q^25 + 7 * q^29 + 2 * q^31 - 3 * q^35 + 10 * q^37 - 13 * q^41 - 8 * q^43 + 12 * q^47 - 28 * q^49 - 17 * q^53 - 2 * q^55 - 16 * q^59 - 20 * q^61 + 14 * q^65 - 48 * q^67 - 4 * q^71 - 17 * q^73 - 19 * q^77 - 38 * q^79 - 9 * q^83 + 8 * q^85 - q^89 - 2 * q^91 - 18 * q^95 + 9 * q^97

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