LMFDB - Embedded newform 3780.2.t.d.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3780,2,Mod(361,3780)]

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, 2, 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("3780.361");

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.t (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			361.2
Character	$\chi$	$=$	3780.361
Dual form			3780.2.t.d.1801.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{5} +(-2.29230 - 1.32113i) q^{7} +O(q^{10})$	$q-1.00000 q^{5} +(-2.29230 - 1.32113i) q^{7} -2.88394 q^{11} +(0.0827654 - 0.143354i) q^{13} +(0.347478 - 0.601849i) q^{17} +(2.26911 + 3.93021i) q^{19} -4.31086 q^{23} +1.00000 q^{25} +(-3.34476 - 5.79329i) q^{29} +(2.28740 + 3.96189i) q^{31} +(2.29230 + 1.32113i) q^{35} +(0.244258 + 0.423067i) q^{37} +(1.99120 - 3.44886i) q^{41} +(-0.488017 - 0.845269i) q^{43} +(-3.35510 + 5.81121i) q^{47} +(3.50925 + 6.05683i) q^{49} +(0.0191298 - 0.0331338i) q^{53} +2.88394 q^{55} +(-0.720413 - 1.24779i) q^{59} +(3.28869 - 5.69618i) q^{61} +(-0.0827654 + 0.143354i) q^{65} +(2.78132 + 4.81738i) q^{67} +8.73689 q^{71} +(-3.12050 + 5.40487i) q^{73} +(6.61084 + 3.81004i) q^{77} +(4.94847 - 8.57100i) q^{79} +(4.42924 + 7.67166i) q^{83} +(-0.347478 + 0.601849i) q^{85} +(1.93095 + 3.34450i) q^{89} +(-0.379111 + 0.219266i) q^{91} +(-2.26911 - 3.93021i) q^{95} +(-7.94934 - 13.7687i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 26 q^{5} + 3 q^{7}+O(q^{10}) $ 26 * q - 26 * q^5 + 3 * q^7	$ 26 q - 26 q^{5} + 3 q^{7} + 2 q^{11} + 7 q^{13} - 8 q^{17} - 9 q^{19} - 6 q^{23} + 26 q^{25} + 7 q^{29} - q^{31} - 3 q^{35} + 10 q^{37} - 13 q^{41} - 8 q^{43} - 6 q^{47} + 11 q^{49} - 17 q^{53} - 2 q^{55} + 8 q^{59} + 10 q^{61} - 7 q^{65} + 24 q^{67} - 4 q^{71} - 17 q^{73} + 11 q^{77} + 19 q^{79} - 9 q^{83} + 8 q^{85} - q^{89} - 2 q^{91} + 9 q^{95} + 9 q^{97}+O(q^{100}) $ 26 * q - 26 * q^5 + 3 * q^7 + 2 * q^11 + 7 * q^13 - 8 * q^17 - 9 * q^19 - 6 * q^23 + 26 * q^25 + 7 * q^29 - q^31 - 3 * q^35 + 10 * q^37 - 13 * q^41 - 8 * q^43 - 6 * q^47 + 11 * q^49 - 17 * q^53 - 2 * q^55 + 8 * q^59 + 10 * q^61 - 7 * q^65 + 24 * q^67 - 4 * q^71 - 17 * q^73 + 11 * q^77 + 19 * q^79 - 9 * q^83 + 8 * q^85 - q^89 - 2 * q^91 + 9 * q^95 + 9 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−2.29230	−	1.32113i	−0.866407	−	0.499339i
$7$	−2.29230	−	1.32113i	−0.866407	−	0.499339i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.88394			−0.869540			−0.434770	−	0.900542i	$-0.643170\pi$
$11$	−2.88394			−0.869540			−0.434770	+	0.900542i	$0.643170\pi$
$12$		0			0
$13$	0.0827654	−	0.143354i	0.0229550	−	0.0397592i	−0.854320	−	0.519748i	$-0.826026\pi$
$13$	0.0827654	−	0.143354i	0.0229550	−	0.0397592i	0.877275	+	0.479989i	$0.159359\pi$
$14$		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
$23$	−4.31086			−0.898877			−0.449439	−	0.893311i	$-0.648376\pi$
$23$	−4.31086			−0.898877			−0.449439	+	0.893311i	$0.648376\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.34476	−	5.79329i	−0.621106	−	1.07579i	−0.989280	−	0.146031i	$-0.953350\pi$
$29$	−3.34476	−	5.79329i	−0.621106	−	1.07579i	0.368174	−	0.929757i	$-0.379983\pi$
$30$		0			0
$31$	2.28740	+	3.96189i	0.410829	+	0.711576i	0.994981	−	0.100068i	$-0.0319061\pi$
$31$	2.28740	+	3.96189i	0.410829	+	0.711576i	−0.584152	+	0.811644i	$0.698573\pi$
$32$		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	−0.667600	−	0.744520i	$-0.732678\pi$
$41$	1.99120	−	3.44886i	0.310974	−	0.538622i	0.978573	+	0.205898i	$0.0660116\pi$
$42$		0			0
$43$	−0.488017	−	0.845269i	−0.0744218	−	0.128902i	0.826413	−	0.563065i	$-0.190378\pi$
$43$	−0.488017	−	0.845269i	−0.0744218	−	0.128902i	−0.900835	+	0.434162i	$0.857044\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.35510	+	5.81121i	−0.489392	+	0.847652i	−0.999926	−	0.0122057i	$-0.996115\pi$
$47$	−3.35510	+	5.81121i	−0.489392	+	0.847652i	0.510533	+	0.859858i	$0.329448\pi$
$48$		0			0
$49$	3.50925	+	6.05683i	0.501322	+	0.865261i
$50$		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
$59$	−0.720413	−	1.24779i	−0.0937898	−	0.162449i	0.815313	−	0.579020i	$-0.196565\pi$
$59$	−0.720413	−	1.24779i	−0.0937898	−	0.162449i	−0.909103	+	0.416572i	$0.863232\pi$
$60$		0			0
$61$	3.28869	−	5.69618i	0.421074	−	0.729321i	−0.574971	−	0.818174i	$-0.694987\pi$
$61$	3.28869	−	5.69618i	0.421074	−	0.729321i	0.996045	+	0.0888528i	$0.0283201\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.0827654	+	0.143354i	−0.0102658	+	0.0177809i
$66$		0			0
$67$	2.78132	+	4.81738i	0.339792	+	0.588537i	0.984393	−	0.175982i	$-0.0563100\pi$
$67$	2.78132	+	4.81738i	0.339792	+	0.588537i	−0.644602	+	0.764519i	$0.722977\pi$
$68$		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
$77$	6.61084	+	3.81004i	0.753375	+	0.434195i
$78$		0			0
$79$	4.94847	−	8.57100i	0.556746	−	0.964312i	−0.441019	−	0.897498i	$-0.645383\pi$
$79$	4.94847	−	8.57100i	0.556746	−	0.964312i	0.997765	−	0.0668147i	$-0.0212836\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.42924	+	7.67166i	0.486172	+	0.842074i	0.999874	−	0.0158946i	$-0.00505962\pi$
$83$	4.42924	+	7.67166i	0.486172	+	0.842074i	−0.513702	+	0.857969i	$0.671726\pi$
$84$		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
$95$	−2.26911	−	3.93021i	−0.232806	−	0.403231i
$96$		0			0
$97$	−7.94934	−	13.7687i	−0.807133	−	1.39800i	−0.914841	−	0.403813i	$-0.867685\pi$
$97$	−7.94934	−	13.7687i	−0.807133	−	1.39800i	0.107708	−	0.994183i	$-0.465649\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	14.9563			1.48821			0.744106	−	0.668061i	$-0.232876\pi$
$101$	14.9563			1.48821			0.744106	+	0.668061i	$0.232876\pi$
$102$		0			0
$103$	19.7894			1.94991			0.974955	−	0.222401i	$-0.0713893\pi$
$103$	19.7894			1.94991			0.974955	+	0.222401i	$0.0713893\pi$
$104$		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	−0.724749	−	0.689013i	$-0.758044\pi$
$113$	2.49094	−	4.31444i	0.234328	−	0.405868i	0.959077	+	0.283145i	$0.0913777\pi$
$114$		0			0
$115$	4.31086			0.401990
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.59164	+	0.920555i	−0.145905	+	0.0843871i
$120$		0			0
$121$	−2.68291			−0.243901
$122$		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
$131$	8.41346			0.735087			0.367544	−	0.930006i	$-0.380199\pi$
$131$	8.41346			0.735087			0.367544	+	0.930006i	$0.380199\pi$
$132$		0			0
$133$	−0.00916545	−	12.0070i	−0.000794745	−	1.04114i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−10.9078			−0.931913			−0.465957	−	0.884808i	$-0.654290\pi$
$137$	−10.9078			−0.931913			−0.465957	+	0.884808i	$0.654290\pi$
$138$		0			0
$139$	−6.94693	+	12.0324i	−0.589231	+	1.02058i	0.405102	+	0.914271i	$0.367236\pi$
$139$	−6.94693	+	12.0324i	−0.589231	+	1.02058i	−0.994333	+	0.106307i	$0.966097\pi$
$140$		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
$149$	21.0366			1.72338			0.861692	−	0.507431i	$-0.169405\pi$
$149$	21.0366			1.72338			0.861692	+	0.507431i	$0.169405\pi$
$150$		0			0
$151$	12.1417			0.988081			0.494041	−	0.869439i	$-0.335519\pi$
$151$	12.1417			0.988081			0.494041	+	0.869439i	$0.335519\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.28740	−	3.96189i	−0.183728	−	0.318226i
$156$		0			0
$157$	−6.55764	−	11.3582i	−0.523356	−	0.906480i	−0.999630	−	0.0271828i	$-0.991346\pi$
$157$	−6.55764	−	11.3582i	−0.523356	−	0.906480i	0.476274	−	0.879297i	$-0.341987\pi$
$158$		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	−0.868123	−	0.496349i	$-0.834674\pi$
$167$	−0.0544085	+	0.0942383i	−0.00421026	+	0.00729238i	0.863913	+	0.503642i	$0.168007\pi$
$168$		0			0
$169$	6.48630	+	11.2346i	0.498946	+	0.864200i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2.83672	+	4.91334i	−0.215672	+	0.373554i	−0.953480	−	0.301456i	$-0.902527\pi$
$173$	−2.83672	+	4.91334i	−0.215672	+	0.373554i	0.737809	+	0.675010i	$0.235861\pi$
$174$		0			0
$175$	−2.29230	−	1.32113i	−0.173281	−	0.0998678i
$176$		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
$185$	−0.244258	−	0.423067i	−0.0179582	−	0.0311045i
$186$		0			0
$187$	−1.00210	+	1.73569i	−0.0732811	+	0.126927i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−11.0834	+	19.1970i	−0.801966	+	1.38905i	0.116354	+	0.993208i	$0.462879\pi$
$191$	−11.0834	+	19.1970i	−0.801966	+	1.38905i	−0.918320	+	0.395838i	$0.870454\pi$
$192$		0			0
$193$	4.70737	+	8.15340i	0.338844	+	0.586895i	0.984216	−	0.176974i	$-0.0566308\pi$
$193$	4.70737	+	8.15340i	0.338844	+	0.586895i	−0.645372	+	0.763869i	$0.723297\pi$
$194$		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
$203$	0.0135102	+	17.6988i	0.000948233	+	1.24221i
$204$		0			0
$205$	−1.99120	+	3.44886i	−0.139072	+	0.240879i
$206$		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	−0.635476	−	0.772121i	$-0.719196\pi$
$211$	5.09767	−	8.82942i	0.350938	−	0.607842i	0.986414	+	0.164278i	$0.0525294\pi$
$212$		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
$221$	−0.0575182	−	0.0996245i	−0.00386910	−	0.00670147i
$222$		0			0
$223$	−11.3620	−	19.6795i	−0.760855	−	1.31784i	−0.942410	−	0.334459i	$-0.891446\pi$
$223$	−11.3620	−	19.6795i	−0.760855	−	1.31784i	0.181555	−	0.983381i	$-0.441887\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−12.3865			−0.822118			−0.411059	−	0.911609i	$-0.634841\pi$
$227$	−12.3865			−0.822118			−0.411059	+	0.911609i	$0.634841\pi$
$228$		0			0
$229$	10.1102			0.668103			0.334052	−	0.942555i	$-0.391584\pi$
$229$	10.1102			0.668103			0.334052	+	0.942555i	$0.391584\pi$
$230$		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	0.465041	+	0.885289i	$0.346040\pi$
$239$	−8.25795	+	14.3032i	−0.534163	+	0.925197i	−0.999203	+	0.0399074i	$0.987294\pi$
$240$		0			0
$241$	−12.7448			−0.820965			−0.410483	−	0.911868i	$-0.634640\pi$
$241$	−12.7448			−0.820965			−0.410483	+	0.911868i	$0.634640\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.50925	−	6.05683i	−0.224198	−	0.386957i
$246$		0			0
$247$	0.751215			0.0477987
$248$		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
$257$	14.7286			0.918746			0.459373	−	0.888243i	$-0.348074\pi$
$257$	14.7286			0.918746			0.459373	+	0.888243i	$0.348074\pi$
$258$		0			0
$259$	−0.000986612	−	1.29249i	−6.13051e−5	−	0.0803114i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	28.1305			1.73460			0.867300	−	0.497787i	$-0.165854\pi$
$263$	28.1305			1.73460			0.867300	+	0.497787i	$0.165854\pi$
$264$		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
$275$	−2.88394			−0.173908
$276$		0			0
$277$	−30.7499			−1.84758			−0.923791	−	0.382898i	$-0.874926\pi$
$277$	−30.7499			−1.84758			−0.923791	+	0.382898i	$0.874926\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.70731	+	2.95714i	0.101849	+	0.176408i	0.912447	−	0.409196i	$-0.134191\pi$
$281$	1.70731	+	2.95714i	0.101849	+	0.176408i	−0.810597	+	0.585604i	$0.800857\pi$
$282$		0			0
$283$	−5.32267	−	9.21914i	−0.316400	−	0.548021i	0.663334	−	0.748323i	$-0.269141\pi$
$283$	−5.32267	−	9.21914i	−0.316400	−	0.548021i	−0.979734	+	0.200302i	$0.935808\pi$
$284$		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	−0.644730	−	0.764411i	$-0.723030\pi$
$293$	5.81360	−	10.0694i	0.339634	−	0.588263i	0.984364	+	0.176147i	$0.0563634\pi$
$294$		0			0
$295$	0.720413	+	1.24779i	0.0419441	+	0.0726493i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.356790	+	0.617979i	−0.0206337	+	0.0357386i
$300$		0			0
$301$	0.00197121	+	2.58234i	0.000113619	+	0.148844i
$302$		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
$311$	9.79881	+	16.9720i	0.555639	+	0.962396i	0.997853	+	0.0654861i	$0.0208598\pi$
$311$	9.79881	+	16.9720i	0.555639	+	0.962396i	−0.442214	+	0.896910i	$0.645807\pi$
$312$		0			0
$313$	2.34537	−	4.06231i	0.132568	−	0.229615i	−0.792098	−	0.610394i	$-0.791011\pi$
$313$	2.34537	−	4.06231i	0.132568	−	0.229615i	0.924666	+	0.380779i	$0.124344\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−13.3319	+	23.0915i	−0.748794	+	1.29695i	0.199607	+	0.979876i	$0.436033\pi$
$317$	−13.3319	+	23.0915i	−0.748794	+	1.29695i	−0.948401	+	0.317073i	$0.897300\pi$
$318$		0			0
$319$	9.64608	+	16.7075i	0.540077	+	0.935440i
$320$		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
$329$	15.3682	−	8.88851i	0.847279	−	0.490039i
$330$		0			0
$331$	4.95015	−	8.57391i	0.272085	−	0.471265i	−0.697311	−	0.716769i	$-0.745620\pi$
$331$	4.95015	−	8.57391i	0.272085	−	0.471265i	0.969395	+	0.245504i	$0.0789536\pi$
$332$		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	−0.665342	−	0.746539i	$-0.731714\pi$
$337$	5.76153	−	9.97926i	0.313850	−	0.543605i	0.979192	+	0.202934i	$0.0650476\pi$
$338$		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
$347$	−4.08840	−	7.08131i	−0.219477	−	0.380145i	0.735171	−	0.677881i	$-0.237102\pi$
$347$	−4.08840	−	7.08131i	−0.219477	−	0.380145i	−0.954648	+	0.297737i	$0.903768\pi$
$348$		0			0
$349$	7.11114	+	12.3169i	0.380651	+	0.659306i	0.991155	−	0.132706i	$-0.0423667\pi$
$349$	7.11114	+	12.3169i	0.380651	+	0.659306i	−0.610505	+	0.792013i	$0.709033\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	29.8385			1.58814			0.794072	−	0.607823i	$-0.207957\pi$
$353$	29.8385			1.58814			0.794072	+	0.607823i	$0.207957\pi$
$354$		0			0
$355$	−8.73689			−0.463706
$356$		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
$367$	−9.39381			−0.490353			−0.245176	−	0.969478i	$-0.578846\pi$
$367$	−9.39381			−0.490353			−0.245176	+	0.969478i	$0.578846\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.0876251	+	0.0506796i	−0.00454927	+	0.00263115i
$372$		0			0
$373$	−8.75808			−0.453476			−0.226738	−	0.973956i	$-0.572806\pi$
$373$	−8.75808			−0.453476			−0.226738	+	0.973956i	$0.572806\pi$
$374$		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
$383$	−15.1571			−0.774491			−0.387245	−	0.921977i	$-0.626573\pi$
$383$	−15.1571			−0.774491			−0.387245	+	0.921977i	$0.626573\pi$
$384$		0			0
$385$	−6.61084	−	3.81004i	−0.336920	−	0.194178i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	20.3630			1.03245			0.516223	−	0.856454i	$-0.327338\pi$
$389$	20.3630			1.03245			0.516223	+	0.856454i	$0.327338\pi$
$390$		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
$401$	−22.9361			−1.14538			−0.572688	−	0.819774i	$-0.694099\pi$
$401$	−22.9361			−1.14538			−0.572688	+	0.819774i	$0.694099\pi$
$402$		0			0
$403$	0.757269			0.0377223
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.704424	−	1.22010i	−0.0349170	−	0.0604780i
$408$		0			0
$409$	14.9326	+	25.8641i	0.738371	+	1.27890i	0.953228	+	0.302251i	$0.0977381\pi$
$409$	14.9326	+	25.8641i	0.738371	+	1.27890i	−0.214857	+	0.976645i	$0.568929\pi$
$410$		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	−0.805274	−	0.592903i	$-0.797982\pi$
$419$	2.26868	−	3.92946i	0.110832	−	0.191967i	0.916106	+	0.400936i	$0.131315\pi$
$420$		0			0
$421$	−14.5625	−	25.2231i	−0.709735	−	1.22930i	−0.964955	−	0.262414i	$-0.915481\pi$
$421$	−14.5625	−	25.2231i	−0.709735	−	1.22930i	0.255221	−	0.966883i	$-0.417852\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.347478	−	0.601849i	0.0168551	−	0.0291940i
$426$		0			0
$427$	−15.0640	+	8.71256i	−0.728999	+	0.421630i
$428$		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
$437$	−9.78182	−	16.9426i	−0.467928	−	0.810475i
$438$		0			0
$439$	−0.922641	+	1.59806i	−0.0440352	+	0.0762713i	−0.887203	−	0.461379i	$-0.847355\pi$
$439$	−0.922641	+	1.59806i	−0.0440352	+	0.0762713i	0.843168	+	0.537651i	$0.180688\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4.76298	+	8.24972i	−0.226296	+	0.391956i	−0.956707	−	0.291051i	$-0.905995\pi$
$443$	−4.76298	+	8.24972i	−0.226296	+	0.391956i	0.730412	+	0.683007i	$0.239328\pi$
$444$		0			0
$445$	−1.93095	−	3.34450i	−0.0915357	−	0.158545i
$446$		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
$455$	0.379111	−	0.219266i	0.0177730	−	0.0102794i
$456$		0			0
$457$	5.51419	−	9.55086i	0.257943	−	0.446770i	−0.707748	−	0.706465i	$-0.750289\pi$
$457$	5.51419	−	9.55086i	0.257943	−	0.446770i	0.965691	+	0.259695i	$0.0836220\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−13.0348	−	22.5769i	−0.607091	−	1.05151i	−0.991717	−	0.128440i	$-0.959003\pi$
$461$	−13.0348	−	22.5769i	−0.607091	−	1.05151i	0.384626	−	0.923072i	$-0.374330\pi$
$462$		0			0
$463$	−5.01294	+	8.68267i	−0.232971	+	0.403518i	−0.958681	−	0.284483i	$-0.908178\pi$
$463$	−5.01294	+	8.68267i	−0.232971	+	0.403518i	0.725710	+	0.688001i	$0.241511\pi$
$464$		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
$473$	1.40741	+	2.43770i	0.0647127	+	0.112086i
$474$		0			0
$475$	2.26911	+	3.93021i	0.104114	+	0.180331i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	34.7357			1.58712			0.793558	−	0.608495i	$-0.208226\pi$
$479$	34.7357			1.58712			0.793558	+	0.608495i	$0.208226\pi$
$480$		0			0
$481$	0.0808643			0.00368710
$482$		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	0.0955396	+	0.995426i	$0.469542\pi$
$491$	−18.0436	+	31.2523i	−0.814294	+	1.41040i	−0.909834	+	0.414973i	$0.863791\pi$
$492$		0			0
$493$	−4.64892			−0.209377
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−20.0275	−	11.5425i	−0.898358	−	0.517753i
$498$		0			0
$499$	4.82950			0.216198			0.108099	−	0.994140i	$-0.465524\pi$
$499$	4.82950			0.216198			0.108099	+	0.994140i	$0.465524\pi$
$500$		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
$509$	3.70177			0.164078			0.0820390	−	0.996629i	$-0.473857\pi$
$509$	3.70177			0.164078			0.0820390	+	0.996629i	$0.473857\pi$
$510$		0			0
$511$	14.2936	−	8.26698i	0.632313	−	0.365710i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−19.7894			−0.872027
$516$		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
$527$	3.17928			0.138491
$528$		0			0
$529$	−4.41646			−0.192020
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−0.329605	−	0.570893i	−0.0142768	−	0.0247281i
$534$		0			0
$535$	−6.70336	−	11.6106i	−0.289812	−	0.501968i
$536$		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	0.904798	−	0.425840i	$-0.140022\pi$
$547$	1.95548	+	3.38700i	0.0836104	+	0.144818i	−0.821188	+	0.570658i	$0.806688\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	15.1793	−	26.2912i	0.646658	−	1.12004i
$552$		0			0
$553$	−22.6667	+	13.1097i	−0.963887	+	0.557482i
$554$		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
$563$	8.21723	+	14.2327i	0.346315	+	0.599835i	0.985592	−	0.169142i	$-0.0540996\pi$
$563$	8.21723	+	14.2327i	0.346315	+	0.599835i	−0.639277	+	0.768977i	$0.720766\pi$
$564$		0			0
$565$	−2.49094	+	4.31444i	−0.104795	+	0.181510i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−0.691596	+	1.19788i	−0.0289932	+	0.0502177i	−0.880158	−	0.474681i	$-0.842563\pi$
$569$	−0.691596	+	1.19788i	−0.0289932	+	0.0502177i	0.851165	+	0.524899i	$0.175897\pi$
$570$		0			0
$571$	−1.16395	−	2.01601i	−0.0487096	−	0.0843675i	0.840643	−	0.541590i	$-0.182178\pi$
$571$	−1.16395	−	2.01601i	−0.0487096	−	0.0843675i	−0.889352	+	0.457223i	$0.848844\pi$
$572$		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
$581$	−0.0178907	−	23.4373i	−0.000742230	−	0.972343i
$582$		0			0
$583$	−0.0551691	+	0.0955557i	−0.00228487	+	0.00395751i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−10.1883	−	17.6466i	−0.420516	−	0.728354i	0.575474	−	0.817820i	$-0.304817\pi$
$587$	−10.1883	−	17.6466i	−0.420516	−	0.728354i	−0.995990	+	0.0894655i	$0.971484\pi$
$588$		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
$599$	−14.7094	−	25.4774i	−0.601009	−	1.04098i	−0.992669	−	0.120867i	$-0.961432\pi$
$599$	−14.7094	−	25.4774i	−0.601009	−	1.04098i	0.391660	−	0.920110i	$-0.371901\pi$
$600$		0			0
$601$	−12.4991	−	21.6490i	−0.509847	−	0.883082i	−0.999935	−	0.0114084i	$-0.996369\pi$
$601$	−12.4991	−	21.6490i	−0.509847	−	0.883082i	0.490087	−	0.871673i	$-0.336965\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.68291			0.109076
$606$		0			0
$607$	−48.6264			−1.97369			−0.986843	−	0.161684i	$-0.948307\pi$
$607$	−48.6264			−1.97369			−0.986843	+	0.161684i	$0.948307\pi$
$608$		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	−0.670393	−	0.742006i	$-0.733875\pi$
$617$	7.63565	−	13.2253i	0.307400	−	0.532432i	0.977793	+	0.209574i	$0.0672079\pi$
$618$		0			0
$619$	40.7104			1.63629			0.818144	−	0.575014i	$-0.195003\pi$
$619$	40.7104			1.63629			0.818144	+	0.575014i	$0.195003\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−0.00779953	−	10.2176i	−0.000312482	−	0.409360i
$624$		0			0
$625$	1.00000			0.0400000
$626$		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
$635$	−20.5850			−0.816893
$636$		0			0
$637$	1.15871	−	0.00176899i	0.0459099	−	7.00900e-5i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	6.89020			0.272146			0.136073	−	0.990699i	$-0.456552\pi$
$641$	6.89020			0.272146			0.136073	+	0.990699i	$0.456552\pi$
$642$		0			0
$643$	−17.9934	+	31.1654i	−0.709590	+	1.22905i	0.255420	+	0.966830i	$0.417786\pi$
$643$	−17.9934	+	31.1654i	−0.709590	+	1.22905i	−0.965010	+	0.262215i	$0.915547\pi$
$644$		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
$653$	−31.5656			−1.23526			−0.617629	−	0.786470i	$-0.711907\pi$
$653$	−31.5656			−1.23526			−0.617629	+	0.786470i	$0.711907\pi$
$654$		0			0
$655$	−8.41346			−0.328741
$656$		0			0
$657$		0			0
$658$		0			0
$659$	12.5849	+	21.7977i	0.490238	+	0.849117i	0.999937	−	0.0112359i	$-0.00357657\pi$
$659$	12.5849	+	21.7977i	0.490238	+	0.849117i	−0.509699	+	0.860353i	$0.670243\pi$
$660$		0			0
$661$	13.0130	+	22.5392i	0.506147	+	0.876672i	0.999975	+	0.00711213i	$0.00226388\pi$
$661$	13.0130	+	22.5392i	0.506147	+	0.876672i	−0.493828	+	0.869560i	$0.664403\pi$
$662$		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	0.905321	−	0.424729i	$-0.139631\pi$
$673$	2.20080	+	3.81189i	0.0848345	+	0.146938i	−0.820486	+	0.571666i	$0.806297\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−23.7639	+	41.1604i	−0.913323	+	1.58192i	−0.103984	+	0.994579i	$0.533159\pi$
$677$	−23.7639	+	41.1604i	−0.913323	+	1.58192i	−0.809339	+	0.587342i	$0.800174\pi$
$678$		0			0
$679$	0.0321092	+	42.0639i	0.00123224	+	1.61427i
$680$		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
$689$	−0.00316657	−	0.00548466i	−0.000120637	−	0.000208949i
$690$		0			0
$691$	−25.7108	+	44.5324i	−0.978085	+	1.69409i	−0.308732	+	0.951149i	$0.599905\pi$
$691$	−25.7108	+	44.5324i	−0.978085	+	1.69409i	−0.669353	+	0.742944i	$0.733429\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	6.94693	−	12.0324i	0.263512	−	0.456416i
$696$		0			0
$697$	−1.38380	−	2.39681i	−0.0524150	−	0.0907855i
$698$		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
$707$	−34.2844	−	19.7592i	−1.28940	−	0.743122i
$708$		0			0
$709$	7.14126	−	12.3690i	0.268196	−	0.464529i	−0.700200	−	0.713947i	$-0.746906\pi$
$709$	7.14126	−	12.3690i	0.268196	−	0.464529i	0.968396	+	0.249418i	$0.0802393\pi$
$710$		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
$725$	−3.34476	−	5.79329i	−0.124221	−	0.215158i
$726$		0			0
$727$	11.4883	+	19.8983i	0.426077	+	0.737988i	0.996520	−	0.0833496i	$-0.0265618\pi$
$727$	11.4883	+	19.8983i	0.426077	+	0.737988i	−0.570443	+	0.821337i	$0.693228\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.678299			−0.0250878
$732$		0			0
$733$	25.7548			0.951274			0.475637	−	0.879642i	$-0.342218\pi$
$733$	25.7548			0.951274			0.475637	+	0.879642i	$0.342218\pi$
$734$		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	−0.759176	−	0.650886i	$-0.774398\pi$
$743$	5.01809	−	8.69159i	0.184096	−	0.318864i	0.943272	+	0.332022i	$0.107731\pi$
$744$		0			0
$745$	−21.0366			−0.770721
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.0270764	−	35.4708i	−0.000989349	−	1.29608i
$750$		0			0
$751$	−22.3777			−0.816573			−0.408287	−	0.912854i	$-0.633874\pi$
$751$	−22.3777			−0.816573			−0.408287	+	0.912854i	$0.633874\pi$
$752$		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
$761$	−13.9047			−0.504047			−0.252023	−	0.967721i	$-0.581096\pi$
$761$	−13.9047			−0.504047			−0.252023	+	0.967721i	$0.581096\pi$
$762$		0			0
$763$	11.4488	−	6.62165i	0.414476	−	0.239720i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.238501			−0.00861178
$768$		0			0
$769$	−11.8746	+	20.5674i	−0.428208	+	0.741678i	−0.996714	−	0.0810010i	$-0.974188\pi$
$769$	−11.8746	+	20.5674i	−0.428208	+	0.741678i	0.568506	+	0.822679i	$0.307522\pi$
$770$		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
$779$	18.0730			0.647533
$780$		0			0
$781$	−25.1966			−0.901606
$782$		0			0
$783$		0			0
$784$		0			0
$785$	6.55764	+	11.3582i	0.234052	+	0.405390i
$786$		0			0
$787$	−14.0673	−	24.3652i	−0.501444	−	0.868527i	−0.999999	−	0.00166851i	$-0.999469\pi$
$787$	−14.0673	−	24.3652i	−0.501444	−	0.868527i	0.498554	−	0.866858i	$-0.333864\pi$
$788$		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	−0.857991	−	0.513665i	$-0.828288\pi$
$797$	0.447494	−	0.775082i	0.0158510	−	0.0274548i	0.873842	+	0.486210i	$0.161621\pi$
$798$		0			0
$799$	2.33165	+	4.03853i	0.0824878	+	0.142873i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	8.99933	−	15.5873i	0.317579	−	0.550064i
$804$		0			0
$805$	−9.88178	−	5.69519i	−0.348287	−	0.200729i
$806$		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
$815$	−3.34865	−	5.80003i	−0.117298	−	0.203166i
$816$		0			0
$817$	2.21473	−	3.83602i	0.0774835	−	0.134205i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	9.01322	−	15.6114i	0.314564	−	0.544840i	−0.664781	−	0.747038i	$-0.731475\pi$
$821$	9.01322	−	15.6114i	0.314564	−	0.544840i	0.979345	+	0.202198i	$0.0648085\pi$
$822$		0			0
$823$	25.8793	+	44.8242i	0.902095	+	1.56247i	0.824770	+	0.565469i	$0.191305\pi$
$823$	25.8793	+	44.8242i	0.902095	+	1.56247i	0.0773252	+	0.997006i	$0.475362\pi$
$824$		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
$833$	4.86468	−	0.00742683i	0.168551	−	0.000257325i
$834$		0			0
$835$	0.0544085	−	0.0942383i	0.00188288	−	0.00326125i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	23.9113	+	41.4157i	0.825511	+	1.42983i	0.901528	+	0.432721i	$0.142446\pi$
$839$	23.9113	+	41.4157i	0.825511	+	1.42983i	−0.0760170	+	0.997107i	$0.524220\pi$
$840$		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
$851$	−1.05296	−	1.82378i	−0.0360951	−	0.0625185i
$852$		0			0
$853$	−1.82607	−	3.16285i	−0.0625236	−	0.108294i	0.833069	−	0.553169i	$-0.186582\pi$
$853$	−1.82607	−	3.16285i	−0.0625236	−	0.108294i	−0.895593	+	0.444875i	$0.853248\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−21.1813			−0.723540			−0.361770	−	0.932267i	$-0.617827\pi$
$857$	−21.1813			−0.723540			−0.361770	+	0.932267i	$0.617827\pi$
$858$		0			0
$859$	−39.4734			−1.34682			−0.673408	−	0.739271i	$-0.735170\pi$
$859$	−39.4734			−1.34682			−0.673408	+	0.739271i	$0.735170\pi$
$860$		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
$871$	0.920787			0.0311997
$872$		0			0
$873$		0			0
$874$		0			0
$875$	2.29230	+	1.32113i	0.0774938	+	0.0446622i
$876$		0			0
$877$	−57.7215			−1.94912			−0.974558	−	0.224136i	$-0.928044\pi$
$877$	−57.7215			−1.94912			−0.974558	+	0.224136i	$0.928044\pi$
$878$		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
$887$	18.4756			0.620352			0.310176	−	0.950679i	$-0.399612\pi$
$887$	18.4756			0.620352			0.310176	+	0.950679i	$0.399612\pi$
$888$		0			0
$889$	−47.1870	−	27.1954i	−1.58260	−	0.912106i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−30.4524			−1.01905
$894$		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
$905$	−4.96075			−0.164901
$906$		0			0
$907$	−54.8630			−1.82170			−0.910848	−	0.412742i	$-0.864571\pi$
$907$	−54.8630			−1.82170			−0.910848	+	0.412742i	$0.864571\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	7.68535	+	13.3114i	0.254627	+	0.441027i	0.964794	−	0.263006i	$-0.0847140\pi$
$911$	7.68535	+	13.3114i	0.254627	+	0.441027i	−0.710167	+	0.704033i	$0.751381\pi$
$912$		0			0
$913$	−12.7736	−	22.1246i	−0.422746	−	0.732217i
$914$		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
$929$	0.478012	−	0.827941i	0.0156831	−	0.0271639i	−0.858077	−	0.513520i	$-0.828341\pi$
$929$	0.478012	−	0.827941i	0.0156831	−	0.0271639i	0.873760	+	0.486357i	$0.161674\pi$
$930$		0			0
$931$	−15.8418	+	27.5357i	−0.519192	+	0.902447i
$932$		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
$941$	−19.0057	−	32.9188i	−0.619568	−	1.07312i	−0.989565	−	0.144090i	$-0.953975\pi$
$941$	−19.0057	−	32.9188i	−0.619568	−	1.07312i	0.369997	−	0.929033i	$-0.379359\pi$
$942$		0			0
$943$	−8.58380	+	14.8676i	−0.279527	+	0.484155i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−29.8482	+	51.6986i	−0.969936	+	1.67998i	−0.274213	+	0.961669i	$0.588417\pi$
$947$	−29.8482	+	51.6986i	−0.969936	+	1.67998i	−0.695723	+	0.718310i	$0.744916\pi$
$948$		0			0
$949$	0.516539	+	0.894671i	0.0167676	+	0.0290423i
$950$		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
$959$	25.0038	+	14.4105i	0.807416	+	0.465340i
$960$		0			0
$961$	5.03563	−	8.72197i	0.162440	−	0.281354i
$962$		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	−0.466797	−	0.884365i	$-0.654592\pi$
$967$	16.5585	−	28.6801i	0.532484	−	0.922290i	0.999281	−	0.0379247i	$-0.0120747\pi$
$968$		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
$977$	1.87172	+	3.24192i	0.0598817	+	0.103718i	0.894412	−	0.447244i	$-0.147594\pi$
$977$	1.87172	+	3.24192i	0.0598817	+	0.103718i	−0.834530	+	0.550962i	$0.814261\pi$
$978$		0			0
$979$	−5.56873	−	9.64533i	−0.177978	−	0.308266i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	53.6262			1.71041			0.855205	−	0.518290i	$-0.173431\pi$
$983$	53.6262			1.71041			0.855205	+	0.518290i	$0.173431\pi$
$984$		0			0
$985$	14.4486			0.460371
$986$		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
$997$	1.95564			0.0619356			0.0309678	−	0.999520i	$-0.490141\pi$
$997$	1.95564			0.0619356			0.0309678	+	0.999520i	$0.490141\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.2.q.d.121.2	✓	26	21.2	odd	6
1260.2.q.d.781.2	yes	26	9.2	odd	6
1260.2.t.d.961.10	yes	26	63.2	odd	6
1260.2.t.d.1201.10	yes	26	3.2	odd	2
3780.2.q.d.2881.8		26	9.7	even	3
3780.2.q.d.3061.8		26	7.2	even	3
3780.2.t.d.361.2		26	1.1	even	1	trivial
3780.2.t.d.1801.2		26	63.16	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:	\( N \)	\(=\)	\( 3780 = 2^{2} \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3780.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{5} +(-2.29230 - 1.32113i) q^{7} +O(q^{10})\)	\(q-1.00000 q^{5} +(-2.29230 - 1.32113i) q^{7} -2.88394 q^{11} +(0.0827654 - 0.143354i) q^{13} +(0.347478 - 0.601849i) q^{17} +(2.26911 + 3.93021i) q^{19} -4.31086 q^{23} +1.00000 q^{25} +(-3.34476 - 5.79329i) q^{29} +(2.28740 + 3.96189i) q^{31} +(2.29230 + 1.32113i) q^{35} +(0.244258 + 0.423067i) q^{37} +(1.99120 - 3.44886i) q^{41} +(-0.488017 - 0.845269i) q^{43} +(-3.35510 + 5.81121i) q^{47} +(3.50925 + 6.05683i) q^{49} +(0.0191298 - 0.0331338i) q^{53} +2.88394 q^{55} +(-0.720413 - 1.24779i) q^{59} +(3.28869 - 5.69618i) q^{61} +(-0.0827654 + 0.143354i) q^{65} +(2.78132 + 4.81738i) q^{67} +8.73689 q^{71} +(-3.12050 + 5.40487i) q^{73} +(6.61084 + 3.81004i) q^{77} +(4.94847 - 8.57100i) q^{79} +(4.42924 + 7.67166i) q^{83} +(-0.347478 + 0.601849i) q^{85} +(1.93095 + 3.34450i) q^{89} +(-0.379111 + 0.219266i) q^{91} +(-2.26911 - 3.93021i) q^{95} +(-7.94934 - 13.7687i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 26 q^{5} + 3 q^{7}+O(q^{10}) \) 26 * q - 26 * q^5 + 3 * q^7	\( 26 q - 26 q^{5} + 3 q^{7} + 2 q^{11} + 7 q^{13} - 8 q^{17} - 9 q^{19} - 6 q^{23} + 26 q^{25} + 7 q^{29} - q^{31} - 3 q^{35} + 10 q^{37} - 13 q^{41} - 8 q^{43} - 6 q^{47} + 11 q^{49} - 17 q^{53} - 2 q^{55} + 8 q^{59} + 10 q^{61} - 7 q^{65} + 24 q^{67} - 4 q^{71} - 17 q^{73} + 11 q^{77} + 19 q^{79} - 9 q^{83} + 8 q^{85} - q^{89} - 2 q^{91} + 9 q^{95} + 9 q^{97}+O(q^{100}) \) 26 * q - 26 * q^5 + 3 * q^7 + 2 * q^11 + 7 * q^13 - 8 * q^17 - 9 * q^19 - 6 * q^23 + 26 * q^25 + 7 * q^29 - q^31 - 3 * q^35 + 10 * q^37 - 13 * q^41 - 8 * q^43 - 6 * q^47 + 11 * q^49 - 17 * q^53 - 2 * q^55 + 8 * q^59 + 10 * q^61 - 7 * q^65 + 24 * q^67 - 4 * q^71 - 17 * q^73 + 11 * q^77 + 19 * q^79 - 9 * q^83 + 8 * q^85 - q^89 - 2 * q^91 + 9 * q^95 + 9 * q^97

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