LMFDB - Embedded newform 1150.2.b.g.599.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,2,Mod(599,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("1150.599");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1150.b (of order $2$, degree $1$, 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:	$9.18279623245$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{21})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 11x^{2} + 25 $ x^4 + 11*x^2 + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			599.2
Root			$2.79129i$ of defining polynomial
Character	$\chi$	$=$	1150.599
Dual form			1150.2.b.g.599.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +2.79129i q^{3} -1.00000 q^{4} +2.79129 q^{6} -1.79129i q^{7} +1.00000i q^{8} -4.79129 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +2.79129i q^{3} -1.00000 q^{4} +2.79129 q^{6} -1.79129i q^{7} +1.00000i q^{8} -4.79129 q^{9} -0.791288 q^{11} -2.79129i q^{12} -5.79129i q^{13} -1.79129 q^{14} +1.00000 q^{16} +0.791288i q^{17} +4.79129i q^{18} -5.79129 q^{19} +5.00000 q^{21} +0.791288i q^{22} -1.00000i q^{23} -2.79129 q^{24} -5.79129 q^{26} -5.00000i q^{27} +1.79129i q^{28} -7.58258 q^{29} -3.37386 q^{31} -1.00000i q^{32} -2.20871i q^{33} +0.791288 q^{34} +4.79129 q^{36} -4.00000i q^{37} +5.79129i q^{38} +16.1652 q^{39} -6.79129 q^{41} -5.00000i q^{42} -11.1652i q^{43} +0.791288 q^{44} -1.00000 q^{46} -4.41742i q^{47} +2.79129i q^{48} +3.79129 q^{49} -2.20871 q^{51} +5.79129i q^{52} -6.00000i q^{53} -5.00000 q^{54} +1.79129 q^{56} -16.1652i q^{57} +7.58258i q^{58} +13.5826 q^{59} +10.3739 q^{61} +3.37386i q^{62} +8.58258i q^{63} -1.00000 q^{64} -2.20871 q^{66} +11.1652i q^{67} -0.791288i q^{68} +2.79129 q^{69} +8.37386 q^{71} -4.79129i q^{72} -12.7477i q^{73} -4.00000 q^{74} +5.79129 q^{76} +1.41742i q^{77} -16.1652i q^{78} -8.00000 q^{79} -0.417424 q^{81} +6.79129i q^{82} +6.00000i q^{83} -5.00000 q^{84} -11.1652 q^{86} -21.1652i q^{87} -0.791288i q^{88} -15.1652 q^{89} -10.3739 q^{91} +1.00000i q^{92} -9.41742i q^{93} -4.41742 q^{94} +2.79129 q^{96} -7.95644i q^{97} -3.79129i q^{98} +3.79129 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 2 q^{6} - 10 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 2 * q^6 - 10 * q^9	$ 4 q - 4 q^{4} + 2 q^{6} - 10 q^{9} + 6 q^{11} + 2 q^{14} + 4 q^{16} - 14 q^{19} + 20 q^{21} - 2 q^{24} - 14 q^{26} - 12 q^{29} + 14 q^{31} - 6 q^{34} + 10 q^{36} + 28 q^{39} - 18 q^{41} - 6 q^{44} - 4 q^{46} + 6 q^{49} - 18 q^{51} - 20 q^{54} - 2 q^{56} + 36 q^{59} + 14 q^{61} - 4 q^{64} - 18 q^{66} + 2 q^{69} + 6 q^{71} - 16 q^{74} + 14 q^{76} - 32 q^{79} - 20 q^{81} - 20 q^{84} - 8 q^{86} - 24 q^{89} - 14 q^{91} - 36 q^{94} + 2 q^{96} + 6 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 2 * q^6 - 10 * q^9 + 6 * q^11 + 2 * q^14 + 4 * q^16 - 14 * q^19 + 20 * q^21 - 2 * q^24 - 14 * q^26 - 12 * q^29 + 14 * q^31 - 6 * q^34 + 10 * q^36 + 28 * q^39 - 18 * q^41 - 6 * q^44 - 4 * q^46 + 6 * q^49 - 18 * q^51 - 20 * q^54 - 2 * q^56 + 36 * q^59 + 14 * q^61 - 4 * q^64 - 18 * q^66 + 2 * q^69 + 6 * q^71 - 16 * q^74 + 14 * q^76 - 32 * q^79 - 20 * q^81 - 20 * q^84 - 8 * q^86 - 24 * q^89 - 14 * q^91 - 36 * q^94 + 2 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 1.00000i	− 0.707107i
$2$	− 1.00000i	− 0.707107i
$3$	2.79129i	1.61155i	0.592221	+	0.805775i	$0.298251\pi$
$3$	2.79129i	1.61155i	−0.592221	+	0.805775i	$0.701749\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	2.79129	1.13954
$7$	− 1.79129i	− 0.677043i	−0.940959	−	0.338522i	$-0.890073\pi$
$7$	− 1.79129i	− 0.677043i	0.940959	−	0.338522i	$-0.109927\pi$
$8$	1.00000i	0.353553i
$9$	−4.79129	−1.59710
$10$	0	0
$11$	−0.791288	−0.238582	−0.119291	−	0.992859i	$-0.538062\pi$
$11$	−0.791288	−0.238582	−0.119291	+	0.992859i	$0.538062\pi$
$12$	− 2.79129i	− 0.805775i
$13$	− 5.79129i	− 1.60621i	−0.595835	−	0.803107i	$-0.703179\pi$
$13$	− 5.79129i	− 1.60621i	0.595835	−	0.803107i	$-0.296821\pi$
$14$	−1.79129	−0.478742
$15$	0	0
$16$	1.00000	0.250000
$17$	0.791288i	0.191915i	0.995385	+	0.0959577i	$0.0305914\pi$
$17$	0.791288i	0.191915i	−0.995385	+	0.0959577i	$0.969409\pi$
$18$	4.79129i	1.12932i
$19$	−5.79129	−1.32861	−0.664306	−	0.747460i	$-0.731273\pi$
$19$	−5.79129	−1.32861	−0.664306	+	0.747460i	$0.731273\pi$
$20$	0	0
$21$	5.00000	1.09109
$22$	0.791288i	0.168703i
$23$	− 1.00000i	− 0.208514i
$23$	− 1.00000i	− 0.208514i
$24$	−2.79129	−0.569769
$25$	0	0
$26$	−5.79129	−1.13576
$27$	− 5.00000i	− 0.962250i
$28$	1.79129i	0.338522i
$29$	−7.58258	−1.40805	−0.704024	−	0.710176i	$-0.748615\pi$
$29$	−7.58258	−1.40805	−0.704024	+	0.710176i	$0.748615\pi$
$30$	0	0
$31$	−3.37386	−0.605964	−0.302982	−	0.952996i	$-0.597982\pi$
$31$	−3.37386	−0.605964	−0.302982	+	0.952996i	$0.597982\pi$
$32$	− 1.00000i	− 0.176777i
$33$	− 2.20871i	− 0.384487i
$34$	0.791288	0.135705
$35$	0	0
$36$	4.79129	0.798548
$37$	− 4.00000i	− 0.657596i	−0.944400	−	0.328798i	$-0.893356\pi$
$37$	− 4.00000i	− 0.657596i	0.944400	−	0.328798i	$-0.106644\pi$
$38$	5.79129i	0.939471i
$39$	16.1652	2.58850
$40$	0	0
$41$	−6.79129	−1.06062	−0.530310	−	0.847804i	$-0.677925\pi$
$41$	−6.79129	−1.06062	−0.530310	+	0.847804i	$0.677925\pi$
$42$	− 5.00000i	− 0.771517i
$43$	− 11.1652i	− 1.70267i	−0.524623	−	0.851335i	$-0.675794\pi$
$43$	− 11.1652i	− 1.70267i	0.524623	−	0.851335i	$-0.324206\pi$
$44$	0.791288	0.119291
$45$	0	0
$46$	−1.00000	−0.147442
$47$	− 4.41742i	− 0.644348i	−0.946681	−	0.322174i	$-0.895586\pi$
$47$	− 4.41742i	− 0.644348i	0.946681	−	0.322174i	$-0.104414\pi$
$48$	2.79129i	0.402888i
$49$	3.79129	0.541613
$50$	0	0
$51$	−2.20871	−0.309282
$52$	5.79129i	0.803107i
$53$	− 6.00000i	− 0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$	− 6.00000i	− 0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$	−5.00000	−0.680414
$55$	0	0
$56$	1.79129	0.239371
$57$	− 16.1652i	− 2.14113i
$58$	7.58258i	0.995641i
$59$	13.5826	1.76830	0.884150	−	0.467202i	$-0.154738\pi$
$59$	13.5826	1.76830	0.884150	+	0.467202i	$0.154738\pi$
$60$	0	0
$61$	10.3739	1.32824	0.664119	−	0.747627i	$-0.268807\pi$
$61$	10.3739	1.32824	0.664119	+	0.747627i	$0.268807\pi$
$62$	3.37386i	0.428481i
$63$	8.58258i	1.08130i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−2.20871	−0.271874
$67$	11.1652i	1.36404i	0.731333	+	0.682020i	$0.238898\pi$
$67$	11.1652i	1.36404i	−0.731333	+	0.682020i	$0.761102\pi$
$68$	− 0.791288i	− 0.0959577i
$69$	2.79129	0.336032
$70$	0	0
$71$	8.37386	0.993795	0.496897	−	0.867809i	$-0.334473\pi$
$71$	8.37386	0.993795	0.496897	+	0.867809i	$0.334473\pi$
$72$	− 4.79129i	− 0.564659i
$73$	− 12.7477i	− 1.49201i	−0.665941	−	0.746004i	$-0.731970\pi$
$73$	− 12.7477i	− 1.49201i	0.665941	−	0.746004i	$-0.268030\pi$
$74$	−4.00000	−0.464991
$75$	0	0
$76$	5.79129	0.664306
$77$	1.41742i	0.161530i
$78$	− 16.1652i	− 1.83034i
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	0	0
$81$	−0.417424	−0.0463805
$82$	6.79129i	0.749972i
$83$	6.00000i	0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$	6.00000i	0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$	−5.00000	−0.545545
$85$	0	0
$86$	−11.1652	−1.20397
$87$	− 21.1652i	− 2.26914i
$88$	− 0.791288i	− 0.0843516i
$89$	−15.1652	−1.60750	−0.803751	−	0.594965i	$-0.797166\pi$
$89$	−15.1652	−1.60750	−0.803751	+	0.594965i	$0.797166\pi$
$90$	0	0
$91$	−10.3739	−1.08748
$92$	1.00000i	0.104257i
$93$	− 9.41742i	− 0.976541i
$94$	−4.41742	−0.455623
$95$	0	0
$96$	2.79129	0.284885
$97$	− 7.95644i	− 0.807854i	−0.914791	−	0.403927i	$-0.867645\pi$
$97$	− 7.95644i	− 0.807854i	0.914791	−	0.403927i	$-0.132355\pi$
$98$	− 3.79129i	− 0.382978i
$99$	3.79129	0.381039
$100$	0	0
$101$	4.41742	0.439550	0.219775	−	0.975551i	$-0.429468\pi$
$101$	4.41742	0.439550	0.219775	+	0.975551i	$0.429468\pi$
$102$	2.20871i	0.218695i
$103$	6.37386i	0.628035i	0.949417	+	0.314018i	$0.101675\pi$
$103$	6.37386i	0.628035i	−0.949417	+	0.314018i	$0.898325\pi$
$104$	5.79129	0.567882
$105$	0	0
$106$	−6.00000	−0.582772
$107$	4.41742i	0.427049i	0.976938	+	0.213524i	$0.0684942\pi$
$107$	4.41742i	0.427049i	−0.976938	+	0.213524i	$0.931506\pi$
$108$	5.00000i	0.481125i
$109$	3.37386	0.323158	0.161579	−	0.986860i	$-0.448341\pi$
$109$	3.37386	0.323158	0.161579	+	0.986860i	$0.448341\pi$
$110$	0	0
$111$	11.1652	1.05975
$112$	− 1.79129i	− 0.169261i
$113$	− 6.00000i	− 0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$	− 6.00000i	− 0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$	−16.1652	−1.51401
$115$	0	0
$116$	7.58258	0.704024
$117$	27.7477i	2.56528i
$118$	− 13.5826i	− 1.25038i
$119$	1.41742	0.129935
$120$	0	0
$121$	−10.3739	−0.943079
$122$	− 10.3739i	− 0.939205i
$123$	− 18.9564i	− 1.70924i
$124$	3.37386	0.302982
$125$	0	0
$126$	8.58258	0.764597
$127$	12.7477i	1.13118i	0.824687	+	0.565589i	$0.191351\pi$
$127$	12.7477i	1.13118i	−0.824687	+	0.565589i	$0.808649\pi$
$128$	1.00000i	0.0883883i
$129$	31.1652	2.74394
$130$	0	0
$131$	−9.16515	−0.800763	−0.400381	−	0.916349i	$-0.631122\pi$
$131$	−9.16515	−0.800763	−0.400381	+	0.916349i	$0.631122\pi$
$132$	2.20871i	0.192244i
$133$	10.3739i	0.899528i
$134$	11.1652	0.964522
$135$	0	0
$136$	−0.791288	−0.0678524
$137$	3.79129i	0.323912i	0.986798	+	0.161956i	$0.0517802\pi$
$137$	3.79129i	0.323912i	−0.986798	+	0.161956i	$0.948220\pi$
$138$	− 2.79129i	− 0.237610i
$139$	−12.7477	−1.08125	−0.540624	−	0.841264i	$-0.681812\pi$
$139$	−12.7477	−1.08125	−0.540624	+	0.841264i	$0.681812\pi$
$140$	0	0
$141$	12.3303	1.03840
$142$	− 8.37386i	− 0.702719i
$143$	4.58258i	0.383214i
$144$	−4.79129	−0.399274
$145$	0	0
$146$	−12.7477	−1.05501
$147$	10.5826i	0.872836i
$148$	4.00000i	0.328798i
$149$	−8.20871	−0.672484	−0.336242	−	0.941776i	$-0.609156\pi$
$149$	−8.20871	−0.672484	−0.336242	+	0.941776i	$0.609156\pi$
$150$	0	0
$151$	−10.7913	−0.878183	−0.439091	−	0.898442i	$-0.644700\pi$
$151$	−10.7913	−0.878183	−0.439091	+	0.898442i	$0.644700\pi$
$152$	− 5.79129i	− 0.469735i
$153$	− 3.79129i	− 0.306507i
$154$	1.41742	0.114219
$155$	0	0
$156$	−16.1652	−1.29425
$157$	− 14.7477i	− 1.17700i	−0.808498	−	0.588498i	$-0.799719\pi$
$157$	− 14.7477i	− 1.17700i	0.808498	−	0.588498i	$-0.200281\pi$
$158$	8.00000i	0.636446i
$159$	16.7477	1.32818
$160$	0	0
$161$	−1.79129	−0.141173
$162$	0.417424i	0.0327960i
$163$	− 8.62614i	− 0.675651i	−0.941209	−	0.337826i	$-0.890309\pi$
$163$	− 8.62614i	− 0.675651i	0.941209	−	0.337826i	$-0.109691\pi$
$164$	6.79129	0.530310
$165$	0	0
$166$	6.00000	0.465690
$167$	18.3303i	1.41844i	0.704987	+	0.709221i	$0.250953\pi$
$167$	18.3303i	1.41844i	−0.704987	+	0.709221i	$0.749047\pi$
$168$	5.00000i	0.385758i
$169$	−20.5390	−1.57992
$170$	0	0
$171$	27.7477	2.12192
$172$	11.1652i	0.851335i
$173$	18.7913i	1.42868i	0.699801	+	0.714338i	$0.253272\pi$
$173$	18.7913i	1.42868i	−0.699801	+	0.714338i	$0.746728\pi$
$174$	−21.1652	−1.60453
$175$	0	0
$176$	−0.791288	−0.0596456
$177$	37.9129i	2.84971i
$178$	15.1652i	1.13668i
$179$	−10.7477	−0.803323	−0.401661	−	0.915788i	$-0.631567\pi$
$179$	−10.7477	−0.803323	−0.401661	+	0.915788i	$0.631567\pi$
$180$	0	0
$181$	−18.5390	−1.37799	−0.688997	−	0.724764i	$-0.741949\pi$
$181$	−18.5390	−1.37799	−0.688997	+	0.724764i	$0.741949\pi$
$182$	10.3739i	0.768962i
$183$	28.9564i	2.14052i
$184$	1.00000	0.0737210
$185$	0	0
$186$	−9.41742	−0.690519
$187$	− 0.626136i	− 0.0457876i
$188$	4.41742i	0.322174i
$189$	−8.95644	−0.651485
$190$	0	0
$191$	25.5826	1.85109	0.925545	−	0.378637i	$-0.123607\pi$
$191$	25.5826	1.85109	0.925545	+	0.378637i	$0.123607\pi$
$192$	− 2.79129i	− 0.201444i
$193$	20.7477i	1.49345i	0.665131	+	0.746727i	$0.268376\pi$
$193$	20.7477i	1.49345i	−0.665131	+	0.746727i	$0.731624\pi$
$194$	−7.95644	−0.571239
$195$	0	0
$196$	−3.79129	−0.270806
$197$	− 11.5390i	− 0.822121i	−0.911608	−	0.411060i	$-0.865159\pi$
$197$	− 11.5390i	− 0.822121i	0.911608	−	0.411060i	$-0.134841\pi$
$198$	− 3.79129i	− 0.269435i
$199$	16.3303	1.15762	0.578812	−	0.815461i	$-0.303516\pi$
$199$	16.3303	1.15762	0.578812	+	0.815461i	$0.303516\pi$
$200$	0	0
$201$	−31.1652	−2.19822
$202$	− 4.41742i	− 0.310809i
$203$	13.5826i	0.953310i
$204$	2.20871	0.154641
$205$	0	0
$206$	6.37386	0.444088
$207$	4.79129i	0.333018i
$208$	− 5.79129i	− 0.401554i
$209$	4.58258	0.316983
$210$	0	0
$211$	−10.0000	−0.688428	−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000	−0.688428	−0.344214	+	0.938891i	$0.611855\pi$
$212$	6.00000i	0.412082i
$213$	23.3739i	1.60155i
$214$	4.41742	0.301969
$215$	0	0
$216$	5.00000	0.340207
$217$	6.04356i	0.410264i
$218$	− 3.37386i	− 0.228507i
$219$	35.5826	2.40445
$220$	0	0
$221$	4.58258	0.308257
$222$	− 11.1652i	− 0.749356i
$223$	7.16515i	0.479814i	0.970796	+	0.239907i	$0.0771170\pi$
$223$	7.16515i	0.479814i	−0.970796	+	0.239907i	$0.922883\pi$
$224$	−1.79129	−0.119685
$225$	0	0
$226$	−6.00000	−0.399114
$227$	− 22.7477i	− 1.50982i	−0.655829	−	0.754910i	$-0.727681\pi$
$227$	− 22.7477i	− 1.50982i	0.655829	−	0.754910i	$-0.272319\pi$
$228$	16.1652i	1.07056i
$229$	−20.3303	−1.34346	−0.671732	−	0.740794i	$-0.734449\pi$
$229$	−20.3303	−1.34346	−0.671732	+	0.740794i	$0.734449\pi$
$230$	0	0
$231$	−3.95644	−0.260315
$232$	− 7.58258i	− 0.497820i
$233$	1.58258i	0.103678i	0.998655	+	0.0518390i	$0.0165083\pi$
$233$	1.58258i	0.103678i	−0.998655	+	0.0518390i	$0.983492\pi$
$234$	27.7477	1.81393
$235$	0	0
$236$	−13.5826	−0.884150
$237$	− 22.3303i	− 1.45051i
$238$	− 1.41742i	− 0.0918780i
$239$	15.1652	0.980952	0.490476	−	0.871455i	$-0.336823\pi$
$239$	15.1652	0.980952	0.490476	+	0.871455i	$0.336823\pi$
$240$	0	0
$241$	−28.0000	−1.80364	−0.901819	−	0.432113i	$-0.857768\pi$
$241$	−28.0000	−1.80364	−0.901819	+	0.432113i	$0.857768\pi$
$242$	10.3739i	0.666857i
$243$	− 16.1652i	− 1.03699i
$244$	−10.3739	−0.664119
$245$	0	0
$246$	−18.9564	−1.20862
$247$	33.5390i	2.13404i
$248$	− 3.37386i	− 0.214241i
$249$	−16.7477	−1.06134
$250$	0	0
$251$	26.2087	1.65428	0.827140	−	0.561996i	$-0.189967\pi$
$251$	26.2087	1.65428	0.827140	+	0.561996i	$0.189967\pi$
$252$	− 8.58258i	− 0.540651i
$253$	0.791288i	0.0497478i
$254$	12.7477	0.799864
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 4.74773i	− 0.296155i	−0.988976	−	0.148078i	$-0.952691\pi$
$257$	− 4.74773i	− 0.296155i	0.988976	−	0.148078i	$-0.0473085\pi$
$258$	− 31.1652i	− 1.94026i
$259$	−7.16515	−0.445221
$260$	0	0
$261$	36.3303	2.24879
$262$	9.16515i	0.566225i
$263$	− 11.2087i	− 0.691159i	−0.938390	−	0.345579i	$-0.887682\pi$
$263$	− 11.2087i	− 0.691159i	0.938390	−	0.345579i	$-0.112318\pi$
$264$	2.20871	0.135937
$265$	0	0
$266$	10.3739	0.636062
$267$	− 42.3303i	− 2.59057i
$268$	− 11.1652i	− 0.682020i
$269$	10.7477	0.655300	0.327650	−	0.944799i	$-0.393743\pi$
$269$	10.7477	0.655300	0.327650	+	0.944799i	$0.393743\pi$
$270$	0	0
$271$	18.1216	1.10081	0.550404	−	0.834898i	$-0.314474\pi$
$271$	18.1216	1.10081	0.550404	+	0.834898i	$0.314474\pi$
$272$	0.791288i	0.0479789i
$273$	− 28.9564i	− 1.75252i
$274$	3.79129	0.229040
$275$	0	0
$276$	−2.79129	−0.168016
$277$	17.1652i	1.03135i	0.856783	+	0.515677i	$0.172460\pi$
$277$	17.1652i	1.03135i	−0.856783	+	0.515677i	$0.827540\pi$
$278$	12.7477i	0.764558i
$279$	16.1652	0.967782
$280$	0	0
$281$	10.7477	0.641156	0.320578	−	0.947222i	$-0.396123\pi$
$281$	10.7477	0.641156	0.320578	+	0.947222i	$0.396123\pi$
$282$	− 12.3303i	− 0.734259i
$283$	− 8.33030i	− 0.495185i	−0.968864	−	0.247593i	$-0.920361\pi$
$283$	− 8.33030i	− 0.495185i	0.968864	−	0.247593i	$-0.0796394\pi$
$284$	−8.37386	−0.496897
$285$	0	0
$286$	4.58258	0.270973
$287$	12.1652i	0.718086i
$288$	4.79129i	0.282329i
$289$	16.3739	0.963168
$290$	0	0
$291$	22.2087	1.30190
$292$	12.7477i	0.746004i
$293$	− 27.4955i	− 1.60630i	−0.595776	−	0.803151i	$-0.703155\pi$
$293$	− 27.4955i	− 1.60630i	0.595776	−	0.803151i	$-0.296845\pi$
$294$	10.5826	0.617188
$295$	0	0
$296$	4.00000	0.232495
$297$	3.95644i	0.229576i
$298$	8.20871i	0.475518i
$299$	−5.79129	−0.334919
$300$	0	0
$301$	−20.0000	−1.15278
$302$	10.7913i	0.620969i
$303$	12.3303i	0.708357i
$304$	−5.79129	−0.332153
$305$	0	0
$306$	−3.79129	−0.216734
$307$	− 15.5390i	− 0.886858i	−0.896309	−	0.443429i	$-0.853762\pi$
$307$	− 15.5390i	− 0.886858i	0.896309	−	0.443429i	$-0.146238\pi$
$308$	− 1.41742i	− 0.0807652i
$309$	−17.7913	−1.01211
$310$	0	0
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	16.1652i	0.915171i
$313$	4.62614i	0.261485i	0.991416	+	0.130742i	$0.0417361\pi$
$313$	4.62614i	0.261485i	−0.991416	+	0.130742i	$0.958264\pi$
$314$	−14.7477	−0.832262
$315$	0	0
$316$	8.00000	0.450035
$317$	9.79129i	0.549934i	0.961454	+	0.274967i	$0.0886669\pi$
$317$	9.79129i	0.549934i	−0.961454	+	0.274967i	$0.911333\pi$
$318$	− 16.7477i	− 0.939166i
$319$	6.00000	0.335936
$320$	0	0
$321$	−12.3303	−0.688210
$322$	1.79129i	0.0998246i
$323$	− 4.58258i	− 0.254981i
$324$	0.417424	0.0231902
$325$	0	0
$326$	−8.62614	−0.477758
$327$	9.41742i	0.520785i
$328$	− 6.79129i	− 0.374986i
$329$	−7.91288	−0.436251
$330$	0	0
$331$	−20.7477	−1.14040	−0.570199	−	0.821507i	$-0.693134\pi$
$331$	−20.7477	−1.14040	−0.570199	+	0.821507i	$0.693134\pi$
$332$	− 6.00000i	− 0.329293i
$333$	19.1652i	1.05024i
$334$	18.3303	1.00299
$335$	0	0
$336$	5.00000	0.272772
$337$	− 12.2087i	− 0.665051i	−0.943094	−	0.332525i	$-0.892099\pi$
$337$	− 12.2087i	− 0.665051i	0.943094	−	0.332525i	$-0.107901\pi$
$338$	20.5390i	1.11718i
$339$	16.7477	0.909612
$340$	0	0
$341$	2.66970	0.144572
$342$	− 27.7477i	− 1.50043i
$343$	− 19.3303i	− 1.04374i
$344$	11.1652	0.601985
$345$	0	0
$346$	18.7913	1.01023
$347$	5.20871i	0.279618i	0.990178	+	0.139809i	$0.0446489\pi$
$347$	5.20871i	0.279618i	−0.990178	+	0.139809i	$0.955351\pi$
$348$	21.1652i	1.13457i
$349$	−26.0000	−1.39175	−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000	−1.39175	−0.695874	+	0.718164i	$0.744983\pi$
$350$	0	0
$351$	−28.9564	−1.54558
$352$	0.791288i	0.0421758i
$353$	− 3.16515i	− 0.168464i	−0.996446	−	0.0842320i	$-0.973156\pi$
$353$	− 3.16515i	− 0.168464i	0.996446	−	0.0842320i	$-0.0268437\pi$
$354$	37.9129	2.01505
$355$	0	0
$356$	15.1652	0.803751
$357$	3.95644i	0.209397i
$358$	10.7477i	0.568035i
$359$	−9.16515	−0.483718	−0.241859	−	0.970311i	$-0.577757\pi$
$359$	−9.16515	−0.483718	−0.241859	+	0.970311i	$0.577757\pi$
$360$	0	0
$361$	14.5390	0.765211
$362$	18.5390i	0.974389i
$363$	− 28.9564i	− 1.51982i
$364$	10.3739	0.543738
$365$	0	0
$366$	28.9564	1.51358
$367$	− 19.1652i	− 1.00041i	−0.865906	−	0.500206i	$-0.833257\pi$
$367$	− 19.1652i	− 1.00041i	0.865906	−	0.500206i	$-0.166743\pi$
$368$	− 1.00000i	− 0.0521286i
$369$	32.5390	1.69391
$370$	0	0
$371$	−10.7477	−0.557994
$372$	9.41742i	0.488271i
$373$	− 12.7477i	− 0.660052i	−0.943972	−	0.330026i	$-0.892942\pi$
$373$	− 12.7477i	− 0.660052i	0.943972	−	0.330026i	$-0.107058\pi$
$374$	−0.626136	−0.0323767
$375$	0	0
$376$	4.41742	0.227811
$377$	43.9129i	2.26163i
$378$	8.95644i	0.460670i
$379$	6.37386	0.327403	0.163702	−	0.986510i	$-0.447657\pi$
$379$	6.37386	0.327403	0.163702	+	0.986510i	$0.447657\pi$
$380$	0	0
$381$	−35.5826	−1.82295
$382$	− 25.5826i	− 1.30892i
$383$	24.0000i	1.22634i	0.789950	+	0.613171i	$0.210106\pi$
$383$	24.0000i	1.22634i	−0.789950	+	0.613171i	$0.789894\pi$
$384$	−2.79129	−0.142442
$385$	0	0
$386$	20.7477	1.05603
$387$	53.4955i	2.71933i
$388$	7.95644i	0.403927i
$389$	20.7042	1.04974	0.524871	−	0.851182i	$-0.324113\pi$
$389$	20.7042	1.04974	0.524871	+	0.851182i	$0.324113\pi$
$390$	0	0
$391$	0.791288	0.0400171
$392$	3.79129i	0.191489i
$393$	− 25.5826i	− 1.29047i
$394$	−11.5390	−0.581327
$395$	0	0
$396$	−3.79129	−0.190519
$397$	− 15.5390i	− 0.779881i	−0.920840	−	0.389940i	$-0.872496\pi$
$397$	− 15.5390i	− 0.779881i	0.920840	−	0.389940i	$-0.127504\pi$
$398$	− 16.3303i	− 0.818564i
$399$	−28.9564	−1.44964
$400$	0	0
$401$	−4.74773	−0.237090	−0.118545	−	0.992949i	$-0.537823\pi$
$401$	−4.74773	−0.237090	−0.118545	+	0.992949i	$0.537823\pi$
$402$	31.1652i	1.55438i
$403$	19.5390i	0.973308i
$404$	−4.41742	−0.219775
$405$	0	0
$406$	13.5826	0.674092
$407$	3.16515i	0.156891i
$408$	− 2.20871i	− 0.109348i
$409$	18.2087	0.900363	0.450181	−	0.892937i	$-0.351359\pi$
$409$	18.2087	0.900363	0.450181	+	0.892937i	$0.351359\pi$
$410$	0	0
$411$	−10.5826	−0.522000
$412$	− 6.37386i	− 0.314018i
$413$	− 24.3303i	− 1.19722i
$414$	4.79129	0.235479
$415$	0	0
$416$	−5.79129	−0.283941
$417$	− 35.5826i	− 1.74249i
$418$	− 4.58258i	− 0.224141i
$419$	−20.8348	−1.01785	−0.508924	−	0.860811i	$-0.669957\pi$
$419$	−20.8348	−1.01785	−0.508924	+	0.860811i	$0.669957\pi$
$420$	0	0
$421$	18.1216	0.883192	0.441596	−	0.897214i	$-0.354412\pi$
$421$	18.1216	0.883192	0.441596	+	0.897214i	$0.354412\pi$
$422$	10.0000i	0.486792i
$423$	21.1652i	1.02908i
$424$	6.00000	0.291386
$425$	0	0
$426$	23.3739	1.13247
$427$	− 18.5826i	− 0.899274i
$428$	− 4.41742i	− 0.213524i
$429$	−12.7913	−0.617569
$430$	0	0
$431$	25.9129	1.24818	0.624090	−	0.781353i	$-0.285470\pi$
$431$	25.9129	1.24818	0.624090	+	0.781353i	$0.285470\pi$
$432$	− 5.00000i	− 0.240563i
$433$	30.5390i	1.46761i	0.679359	+	0.733806i	$0.262258\pi$
$433$	30.5390i	1.46761i	−0.679359	+	0.733806i	$0.737742\pi$
$434$	6.04356	0.290100
$435$	0	0
$436$	−3.37386	−0.161579
$437$	5.79129i	0.277035i
$438$	− 35.5826i	− 1.70020i
$439$	6.53901	0.312090	0.156045	−	0.987750i	$-0.450125\pi$
$439$	6.53901	0.312090	0.156045	+	0.987750i	$0.450125\pi$
$440$	0	0
$441$	−18.1652	−0.865007
$442$	− 4.58258i	− 0.217971i
$443$	39.7913i	1.89054i	0.326288	+	0.945271i	$0.394202\pi$
$443$	39.7913i	1.89054i	−0.326288	+	0.945271i	$0.605798\pi$
$444$	−11.1652	−0.529875
$445$	0	0
$446$	7.16515	0.339280
$447$	− 22.9129i	− 1.08374i
$448$	1.79129i	0.0846304i
$449$	16.1216	0.760825	0.380412	−	0.924817i	$-0.375782\pi$
$449$	16.1216	0.760825	0.380412	+	0.924817i	$0.375782\pi$
$450$	0	0
$451$	5.37386	0.253045
$452$	6.00000i	0.282216i
$453$	− 30.1216i	− 1.41524i
$454$	−22.7477	−1.06760
$455$	0	0
$456$	16.1652	0.757003
$457$	− 10.0000i	− 0.467780i	−0.972263	−	0.233890i	$-0.924854\pi$
$457$	− 10.0000i	− 0.467780i	0.972263	−	0.233890i	$-0.0751456\pi$
$458$	20.3303i	0.949973i
$459$	3.95644	0.184671
$460$	0	0
$461$	−28.7477	−1.33892	−0.669458	−	0.742850i	$-0.733473\pi$
$461$	−28.7477	−1.33892	−0.669458	+	0.742850i	$0.733473\pi$
$462$	3.95644i	0.184070i
$463$	10.0000i	0.464739i	0.972628	+	0.232370i	$0.0746479\pi$
$463$	10.0000i	0.464739i	−0.972628	+	0.232370i	$0.925352\pi$
$464$	−7.58258	−0.352012
$465$	0	0
$466$	1.58258	0.0733114
$467$	− 19.9129i	− 0.921458i	−0.887541	−	0.460729i	$-0.847588\pi$
$467$	− 19.9129i	− 0.921458i	0.887541	−	0.460729i	$-0.152412\pi$
$468$	− 27.7477i	− 1.28264i
$469$	20.0000	0.923514
$470$	0	0
$471$	41.1652	1.89679
$472$	13.5826i	0.625189i
$473$	8.83485i	0.406227i
$474$	−22.3303	−1.02566
$475$	0	0
$476$	−1.41742	−0.0649675
$477$	28.7477i	1.31627i
$478$	− 15.1652i	− 0.693638i
$479$	−15.4955	−0.708005	−0.354003	−	0.935244i	$-0.615180\pi$
$479$	−15.4955	−0.708005	−0.354003	+	0.935244i	$0.615180\pi$
$480$	0	0
$481$	−23.1652	−1.05624
$482$	28.0000i	1.27537i
$483$	− 5.00000i	− 0.227508i
$484$	10.3739	0.471539
$485$	0	0
$486$	−16.1652	−0.733266
$487$	6.41742i	0.290801i	0.989373	+	0.145401i	$0.0464471\pi$
$487$	6.41742i	0.290801i	−0.989373	+	0.145401i	$0.953553\pi$
$488$	10.3739i	0.469603i
$489$	24.0780	1.08885
$490$	0	0
$491$	10.7477	0.485038	0.242519	−	0.970147i	$-0.422026\pi$
$491$	10.7477	0.485038	0.242519	+	0.970147i	$0.422026\pi$
$492$	18.9564i	0.854622i
$493$	− 6.00000i	− 0.270226i
$494$	33.5390	1.50899
$495$	0	0
$496$	−3.37386	−0.151491
$497$	− 15.0000i	− 0.672842i
$498$	16.7477i	0.750484i
$499$	−4.83485	−0.216438	−0.108219	−	0.994127i	$-0.534515\pi$
$499$	−4.83485	−0.216438	−0.108219	+	0.994127i	$0.534515\pi$
$500$	0	0
$501$	−51.1652	−2.28589
$502$	− 26.2087i	− 1.16975i
$503$	− 14.2087i	− 0.633535i	−0.948503	−	0.316768i	$-0.897402\pi$
$503$	− 14.2087i	− 0.633535i	0.948503	−	0.316768i	$-0.102598\pi$
$504$	−8.58258	−0.382298
$505$	0	0
$506$	0.791288	0.0351770
$507$	− 57.3303i	− 2.54613i
$508$	− 12.7477i	− 0.565589i
$509$	−34.7477	−1.54017	−0.770083	−	0.637944i	$-0.779785\pi$
$509$	−34.7477	−1.54017	−0.770083	+	0.637944i	$0.779785\pi$
$510$	0	0
$511$	−22.8348	−1.01015
$512$	− 1.00000i	− 0.0441942i
$513$	28.9564i	1.27846i
$514$	−4.74773	−0.209413
$515$	0	0
$516$	−31.1652	−1.37197
$517$	3.49545i	0.153730i
$518$	7.16515i	0.314819i
$519$	−52.4519	−2.30238
$520$	0	0
$521$	18.0000	0.788594	0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000	0.788594	0.394297	+	0.918983i	$0.370988\pi$
$522$	− 36.3303i	− 1.59013i
$523$	− 17.1652i	− 0.750580i	−0.926908	−	0.375290i	$-0.877543\pi$
$523$	− 17.1652i	− 0.750580i	0.926908	−	0.375290i	$-0.122457\pi$
$524$	9.16515	0.400381
$525$	0	0
$526$	−11.2087	−0.488723
$527$	− 2.66970i	− 0.116294i
$528$	− 2.20871i	− 0.0961219i
$529$	−1.00000	−0.0434783
$530$	0	0
$531$	−65.0780	−2.82415
$532$	− 10.3739i	− 0.449764i
$533$	39.3303i	1.70358i
$534$	−42.3303	−1.83181
$535$	0	0
$536$	−11.1652	−0.482261
$537$	− 30.0000i	− 1.29460i
$538$	− 10.7477i	− 0.463367i
$539$	−3.00000	−0.129219
$540$	0	0
$541$	1.66970	0.0717859	0.0358929	−	0.999356i	$-0.488572\pi$
$541$	1.66970	0.0717859	0.0358929	+	0.999356i	$0.488572\pi$
$542$	− 18.1216i	− 0.778389i
$543$	− 51.7477i	− 2.22071i
$544$	0.791288	0.0339262
$545$	0	0
$546$	−28.9564	−1.23922
$547$	− 26.1216i	− 1.11688i	−0.829545	−	0.558439i	$-0.811400\pi$
$547$	− 26.1216i	− 1.11688i	0.829545	−	0.558439i	$-0.188600\pi$
$548$	− 3.79129i	− 0.161956i
$549$	−49.7042	−2.12132
$550$	0	0
$551$	43.9129	1.87075
$552$	2.79129i	0.118805i
$553$	14.3303i	0.609386i
$554$	17.1652	0.729277
$555$	0	0
$556$	12.7477	0.540624
$557$	− 6.33030i	− 0.268224i	−0.990966	−	0.134112i	$-0.957182\pi$
$557$	− 6.33030i	− 0.268224i	0.990966	−	0.134112i	$-0.0428181\pi$
$558$	− 16.1652i	− 0.684325i
$559$	−64.6606	−2.73485
$560$	0	0
$561$	1.74773	0.0737891
$562$	− 10.7477i	− 0.453366i
$563$	15.1652i	0.639135i	0.947564	+	0.319567i	$0.103538\pi$
$563$	15.1652i	0.639135i	−0.947564	+	0.319567i	$0.896462\pi$
$564$	−12.3303	−0.519199
$565$	0	0
$566$	−8.33030	−0.350149
$567$	0.747727i	0.0314016i
$568$	8.37386i	0.351360i
$569$	39.4955	1.65574	0.827868	−	0.560923i	$-0.189554\pi$
$569$	39.4955	1.65574	0.827868	+	0.560923i	$0.189554\pi$
$570$	0	0
$571$	−11.1216	−0.465424	−0.232712	−	0.972546i	$-0.574760\pi$
$571$	−11.1216	−0.465424	−0.232712	+	0.972546i	$0.574760\pi$
$572$	− 4.58258i	− 0.191607i
$573$	71.4083i	2.98313i
$574$	12.1652	0.507764
$575$	0	0
$576$	4.79129	0.199637
$577$	41.1652i	1.71373i	0.515543	+	0.856864i	$0.327590\pi$
$577$	41.1652i	1.71373i	−0.515543	+	0.856864i	$0.672410\pi$
$578$	− 16.3739i	− 0.681063i
$579$	−57.9129	−2.40678
$580$	0	0
$581$	10.7477	0.445891
$582$	− 22.2087i	− 0.920581i
$583$	4.74773i	0.196631i
$584$	12.7477	0.527505
$585$	0	0
$586$	−27.4955	−1.13583
$587$	− 30.7913i	− 1.27089i	−0.772145	−	0.635446i	$-0.780816\pi$
$587$	− 30.7913i	− 1.27089i	0.772145	−	0.635446i	$-0.219184\pi$
$588$	− 10.5826i	− 0.436418i
$589$	19.5390	0.805091
$590$	0	0
$591$	32.2087	1.32489
$592$	− 4.00000i	− 0.164399i
$593$	31.9129i	1.31050i	0.755410	+	0.655252i	$0.227438\pi$
$593$	31.9129i	1.31050i	−0.755410	+	0.655252i	$0.772562\pi$
$594$	3.95644	0.162335
$595$	0	0
$596$	8.20871	0.336242
$597$	45.5826i	1.86557i
$598$	5.79129i	0.236823i
$599$	−1.12159	−0.0458270	−0.0229135	−	0.999737i	$-0.507294\pi$
$599$	−1.12159	−0.0458270	−0.0229135	+	0.999737i	$0.507294\pi$
$600$	0	0
$601$	−18.2087	−0.742749	−0.371374	−	0.928483i	$-0.621113\pi$
$601$	−18.2087	−0.742749	−0.371374	+	0.928483i	$0.621113\pi$
$602$	20.0000i	0.815139i
$603$	− 53.4955i	− 2.17850i
$604$	10.7913	0.439091
$605$	0	0
$606$	12.3303	0.500884
$607$	− 28.0000i	− 1.13648i	−0.822861	−	0.568242i	$-0.807624\pi$
$607$	− 28.0000i	− 1.13648i	0.822861	−	0.568242i	$-0.192376\pi$
$608$	5.79129i	0.234868i
$609$	−37.9129	−1.53631
$610$	0	0
$611$	−25.5826	−1.03496
$612$	3.79129i	0.153254i
$613$	− 14.0000i	− 0.565455i	−0.959200	−	0.282727i	$-0.908761\pi$
$613$	− 14.0000i	− 0.565455i	0.959200	−	0.282727i	$-0.0912392\pi$
$614$	−15.5390	−0.627104
$615$	0	0
$616$	−1.41742	−0.0571097
$617$	− 23.8693i	− 0.960943i	−0.877010	−	0.480471i	$-0.840466\pi$
$617$	− 23.8693i	− 0.960943i	0.877010	−	0.480471i	$-0.159534\pi$
$618$	17.7913i	0.715671i
$619$	1.79129	0.0719979	0.0359990	−	0.999352i	$-0.488539\pi$
$619$	1.79129	0.0719979	0.0359990	+	0.999352i	$0.488539\pi$
$620$	0	0
$621$	−5.00000	−0.200643
$622$	− 12.0000i	− 0.481156i
$623$	27.1652i	1.08835i
$624$	16.1652	0.647124
$625$	0	0
$626$	4.62614	0.184898
$627$	12.7913i	0.510835i
$628$	14.7477i	0.588498i
$629$	3.16515	0.126203
$630$	0	0
$631$	27.9129	1.11119	0.555597	−	0.831452i	$-0.312490\pi$
$631$	27.9129	1.11119	0.555597	+	0.831452i	$0.312490\pi$
$632$	− 8.00000i	− 0.318223i
$633$	− 27.9129i	− 1.10944i
$634$	9.79129	0.388862
$635$	0	0
$636$	−16.7477	−0.664091
$637$	− 21.9564i	− 0.869946i
$638$	− 6.00000i	− 0.237542i
$639$	−40.1216	−1.58719
$640$	0	0
$641$	15.1652	0.598987	0.299494	−	0.954098i	$-0.403182\pi$
$641$	15.1652	0.598987	0.299494	+	0.954098i	$0.403182\pi$
$642$	12.3303i	0.486638i
$643$	− 6.74773i	− 0.266104i	−0.991109	−	0.133052i	$-0.957522\pi$
$643$	− 6.74773i	− 0.266104i	0.991109	−	0.133052i	$-0.0424778\pi$
$644$	1.79129	0.0705866
$645$	0	0
$646$	−4.58258	−0.180299
$647$	21.1652i	0.832088i	0.909344	+	0.416044i	$0.136584\pi$
$647$	21.1652i	0.832088i	−0.909344	+	0.416044i	$0.863416\pi$
$648$	− 0.417424i	− 0.0163980i
$649$	−10.7477	−0.421885
$650$	0	0
$651$	−16.8693	−0.661161
$652$	8.62614i	0.337826i
$653$	− 3.46099i	− 0.135439i	−0.997704	−	0.0677194i	$-0.978428\pi$
$653$	− 3.46099i	− 0.135439i	0.997704	−	0.0677194i	$-0.0215723\pi$
$654$	9.41742	0.368250
$655$	0	0
$656$	−6.79129	−0.265155
$657$	61.0780i	2.38288i
$658$	7.91288i	0.308476i
$659$	8.83485	0.344157	0.172078	−	0.985083i	$-0.444952\pi$
$659$	8.83485	0.344157	0.172078	+	0.985083i	$0.444952\pi$
$660$	0	0
$661$	−25.6261	−0.996741	−0.498371	−	0.866964i	$-0.666068\pi$
$661$	−25.6261	−0.996741	−0.498371	+	0.866964i	$0.666068\pi$
$662$	20.7477i	0.806383i
$663$	12.7913i	0.496772i
$664$	−6.00000	−0.232845
$665$	0	0
$666$	19.1652	0.742635
$667$	7.58258i	0.293599i
$668$	− 18.3303i	− 0.709221i
$669$	−20.0000	−0.773245
$670$	0	0
$671$	−8.20871	−0.316894
$672$	− 5.00000i	− 0.192879i
$673$	− 38.0000i	− 1.46479i	−0.680879	−	0.732396i	$-0.738402\pi$
$673$	− 38.0000i	− 1.46479i	0.680879	−	0.732396i	$-0.261598\pi$
$674$	−12.2087	−0.470262
$675$	0	0
$676$	20.5390	0.789962
$677$	42.6606i	1.63958i	0.572664	+	0.819790i	$0.305910\pi$
$677$	42.6606i	1.63958i	−0.572664	+	0.819790i	$0.694090\pi$
$678$	− 16.7477i	− 0.643193i
$679$	−14.2523	−0.546952
$680$	0	0
$681$	63.4955	2.43315
$682$	− 2.66970i	− 0.102228i
$683$	11.3739i	0.435209i	0.976037	+	0.217604i	$0.0698243\pi$
$683$	11.3739i	0.435209i	−0.976037	+	0.217604i	$0.930176\pi$
$684$	−27.7477	−1.06096
$685$	0	0
$686$	−19.3303	−0.738034
$687$	− 56.7477i	− 2.16506i
$688$	− 11.1652i	− 0.425667i
$689$	−34.7477	−1.32378
$690$	0	0
$691$	42.7477	1.62620	0.813100	−	0.582124i	$-0.197778\pi$
$691$	42.7477	1.62620	0.813100	+	0.582124i	$0.197778\pi$
$692$	− 18.7913i	− 0.714338i
$693$	− 6.79129i	− 0.257980i
$694$	5.20871	0.197720
$695$	0	0
$696$	21.1652	0.802263
$697$	− 5.37386i	− 0.203550i
$698$	26.0000i	0.984115i
$699$	−4.41742	−0.167082
$700$	0	0
$701$	23.3739	0.882819	0.441409	−	0.897306i	$-0.354479\pi$
$701$	23.3739	0.882819	0.441409	+	0.897306i	$0.354479\pi$
$702$	28.9564i	1.09289i
$703$	23.1652i	0.873690i
$704$	0.791288	0.0298228
$705$	0	0
$706$	−3.16515	−0.119122
$707$	− 7.91288i	− 0.297594i
$708$	− 37.9129i	− 1.42485i
$709$	−2.46099	−0.0924242	−0.0462121	−	0.998932i	$-0.514715\pi$
$709$	−2.46099	−0.0924242	−0.0462121	+	0.998932i	$0.514715\pi$
$710$	0	0
$711$	38.3303	1.43750
$712$	− 15.1652i	− 0.568338i
$713$	3.37386i	0.126352i
$714$	3.95644	0.148066
$715$	0	0
$716$	10.7477	0.401661
$717$	42.3303i	1.58085i
$718$	9.16515i	0.342040i
$719$	−2.53901	−0.0946893	−0.0473446	−	0.998879i	$-0.515076\pi$
$719$	−2.53901	−0.0946893	−0.0473446	+	0.998879i	$0.515076\pi$
$720$	0	0
$721$	11.4174	0.425207
$722$	− 14.5390i	− 0.541086i
$723$	− 78.1561i	− 2.90666i
$724$	18.5390	0.688997
$725$	0	0
$726$	−28.9564	−1.07467
$727$	39.1216i	1.45094i	0.688254	+	0.725470i	$0.258377\pi$
$727$	39.1216i	1.45094i	−0.688254	+	0.725470i	$0.741623\pi$
$728$	− 10.3739i	− 0.384481i
$729$	43.8693	1.62479
$730$	0	0
$731$	8.83485	0.326769
$732$	− 28.9564i	− 1.07026i
$733$	− 26.0000i	− 0.960332i	−0.877178	−	0.480166i	$-0.840576\pi$
$733$	− 26.0000i	− 0.960332i	0.877178	−	0.480166i	$-0.159424\pi$
$734$	−19.1652	−0.707399
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	− 8.83485i	− 0.325436i
$738$	− 32.5390i	− 1.19778i
$739$	−8.00000	−0.294285	−0.147142	−	0.989115i	$-0.547008\pi$
$739$	−8.00000	−0.294285	−0.147142	+	0.989115i	$0.547008\pi$
$740$	0	0
$741$	−93.6170	−3.43911
$742$	10.7477i	0.394561i
$743$	12.9564i	0.475326i	0.971348	+	0.237663i	$0.0763813\pi$
$743$	12.9564i	0.475326i	−0.971348	+	0.237663i	$0.923619\pi$
$744$	9.41742	0.345260
$745$	0	0
$746$	−12.7477	−0.466727
$747$	− 28.7477i	− 1.05182i
$748$	0.626136i	0.0228938i
$749$	7.91288	0.289130
$750$	0	0
$751$	−8.74773	−0.319209	−0.159605	−	0.987181i	$-0.551022\pi$
$751$	−8.74773	−0.319209	−0.159605	+	0.987181i	$0.551022\pi$
$752$	− 4.41742i	− 0.161087i
$753$	73.1561i	2.66596i
$754$	43.9129	1.59921
$755$	0	0
$756$	8.95644	0.325743
$757$	− 10.3303i	− 0.375461i	−0.982221	−	0.187731i	$-0.939887\pi$
$757$	− 10.3303i	− 0.375461i	0.982221	−	0.187731i	$-0.0601132\pi$
$758$	− 6.37386i	− 0.231509i
$759$	−2.20871	−0.0801712
$760$	0	0
$761$	−11.0436	−0.400329	−0.200164	−	0.979762i	$-0.564148\pi$
$761$	−11.0436	−0.400329	−0.200164	+	0.979762i	$0.564148\pi$
$762$	35.5826i	1.28902i
$763$	− 6.04356i	− 0.218792i
$764$	−25.5826	−0.925545
$765$	0	0
$766$	24.0000	0.867155
$767$	− 78.6606i	− 2.84027i
$768$	2.79129i	0.100722i
$769$	40.3303	1.45435	0.727174	−	0.686453i	$-0.240833\pi$
$769$	40.3303	1.45435	0.727174	+	0.686453i	$0.240833\pi$
$770$	0	0
$771$	13.2523	0.477269
$772$	− 20.7477i	− 0.746727i
$773$	− 33.4955i	− 1.20475i	−0.798214	−	0.602374i	$-0.794222\pi$
$773$	− 33.4955i	− 1.20475i	0.798214	−	0.602374i	$-0.205778\pi$
$774$	53.4955	1.92285
$775$	0	0
$776$	7.95644	0.285620
$777$	− 20.0000i	− 0.717496i
$778$	− 20.7042i	− 0.742280i
$779$	39.3303	1.40915
$780$	0	0
$781$	−6.62614	−0.237102
$782$	− 0.791288i	− 0.0282964i
$783$	37.9129i	1.35490i
$784$	3.79129	0.135403
$785$	0	0
$786$	−25.5826	−0.912500
$787$	− 17.5826i	− 0.626751i	−0.949629	−	0.313376i	$-0.898540\pi$
$787$	− 17.5826i	− 0.626751i	0.949629	−	0.313376i	$-0.101460\pi$
$788$	11.5390i	0.411060i
$789$	31.2867	1.11384
$790$	0	0
$791$	−10.7477	−0.382145
$792$	3.79129i	0.134718i
$793$	− 60.0780i	− 2.13343i
$794$	−15.5390	−0.551459
$795$	0	0
$796$	−16.3303	−0.578812
$797$	− 4.08712i	− 0.144773i	−0.997377	−	0.0723866i	$-0.976938\pi$
$797$	− 4.08712i	− 0.144773i	0.997377	−	0.0723866i	$-0.0230616\pi$
$798$	28.9564i	1.02505i
$799$	3.49545	0.123660
$800$	0	0
$801$	72.6606	2.56734
$802$	4.74773i	0.167648i
$803$	10.0871i	0.355967i
$804$	31.1652	1.09911
$805$	0	0
$806$	19.5390	0.688232
$807$	30.0000i	1.05605i
$808$	4.41742i	0.155404i
$809$	−33.9564	−1.19384	−0.596922	−	0.802299i	$-0.703610\pi$
$809$	−33.9564	−1.19384	−0.596922	+	0.802299i	$0.703610\pi$
$810$	0	0
$811$	−2.08712	−0.0732887	−0.0366444	−	0.999328i	$-0.511667\pi$
$811$	−2.08712	−0.0732887	−0.0366444	+	0.999328i	$0.511667\pi$
$812$	− 13.5826i	− 0.476655i
$813$	50.5826i	1.77401i
$814$	3.16515	0.110938
$815$	0	0
$816$	−2.20871	−0.0773204
$817$	64.6606i	2.26219i
$818$	− 18.2087i	− 0.636653i
$819$	49.7042	1.73680
$820$	0	0
$821$	21.1652	0.738669	0.369334	−	0.929297i	$-0.379586\pi$
$821$	21.1652	0.738669	0.369334	+	0.929297i	$0.379586\pi$
$822$	10.5826i	0.369110i
$823$	− 22.8348i	− 0.795973i	−0.917391	−	0.397986i	$-0.869709\pi$
$823$	− 22.8348i	− 0.795973i	0.917391	−	0.397986i	$-0.130291\pi$
$824$	−6.37386	−0.222044
$825$	0	0
$826$	−24.3303	−0.846560
$827$	− 23.0780i	− 0.802502i	−0.915968	−	0.401251i	$-0.868576\pi$
$827$	− 23.0780i	− 0.802502i	0.915968	−	0.401251i	$-0.131424\pi$
$828$	− 4.79129i	− 0.166509i
$829$	−23.4955	−0.816031	−0.408015	−	0.912975i	$-0.633779\pi$
$829$	−23.4955	−0.816031	−0.408015	+	0.912975i	$0.633779\pi$
$830$	0	0
$831$	−47.9129	−1.66208
$832$	5.79129i	0.200777i
$833$	3.00000i	0.103944i
$834$	−35.5826	−1.23212
$835$	0	0
$836$	−4.58258	−0.158492
$837$	16.8693i	0.583089i
$838$	20.8348i	0.719728i
$839$	31.5826	1.09035	0.545176	−	0.838322i	$-0.316463\pi$
$839$	31.5826	1.09035	0.545176	+	0.838322i	$0.316463\pi$
$840$	0	0
$841$	28.4955	0.982602
$842$	− 18.1216i	− 0.624511i
$843$	30.0000i	1.03325i
$844$	10.0000	0.344214
$845$	0	0
$846$	21.1652	0.727673
$847$	18.5826i	0.638505i
$848$	− 6.00000i	− 0.206041i
$849$	23.2523	0.798016
$850$	0	0
$851$	−4.00000	−0.137118
$852$	− 23.3739i	− 0.800775i
$853$	− 40.5390i	− 1.38803i	−0.719961	−	0.694015i	$-0.755840\pi$
$853$	− 40.5390i	− 1.38803i	0.719961	−	0.694015i	$-0.244160\pi$
$854$	−18.5826	−0.635883
$855$	0	0
$856$	−4.41742	−0.150984
$857$	− 9.16515i	− 0.313076i	−0.987672	−	0.156538i	$-0.949967\pi$
$857$	− 9.16515i	− 0.313076i	0.987672	−	0.156538i	$-0.0500333\pi$
$858$	12.7913i	0.436687i
$859$	26.7477	0.912621	0.456310	−	0.889821i	$-0.349171\pi$
$859$	26.7477	0.912621	0.456310	+	0.889821i	$0.349171\pi$
$860$	0	0
$861$	−33.9564	−1.15723
$862$	− 25.9129i	− 0.882596i
$863$	22.4174i	0.763098i	0.924349	+	0.381549i	$0.124609\pi$
$863$	22.4174i	0.763098i	−0.924349	+	0.381549i	$0.875391\pi$
$864$	−5.00000	−0.170103
$865$	0	0
$866$	30.5390	1.03776
$867$	45.7042i	1.55219i
$868$	− 6.04356i	− 0.205132i
$869$	6.33030	0.214741
$870$	0	0
$871$	64.6606	2.19094
$872$	3.37386i	0.114253i
$873$	38.1216i	1.29022i
$874$	5.79129	0.195893
$875$	0	0
$876$	−35.5826	−1.20222
$877$	− 42.7042i	− 1.44202i	−0.692926	−	0.721009i	$-0.743679\pi$
$877$	− 42.7042i	− 1.44202i	0.692926	−	0.721009i	$-0.256321\pi$
$878$	− 6.53901i	− 0.220681i
$879$	76.7477	2.58864
$880$	0	0
$881$	30.3303	1.02185	0.510927	−	0.859624i	$-0.329302\pi$
$881$	30.3303	1.02185	0.510927	+	0.859624i	$0.329302\pi$
$882$	18.1652i	0.611652i
$883$	34.9564i	1.17638i	0.808724	+	0.588189i	$0.200159\pi$
$883$	34.9564i	1.17638i	−0.808724	+	0.588189i	$0.799841\pi$
$884$	−4.58258	−0.154129
$885$	0	0
$886$	39.7913	1.33681
$887$	15.1652i	0.509196i	0.967047	+	0.254598i	$0.0819431\pi$
$887$	15.1652i	0.509196i	−0.967047	+	0.254598i	$0.918057\pi$
$888$	11.1652i	0.374678i
$889$	22.8348	0.765856
$890$	0	0
$891$	0.330303	0.0110656
$892$	− 7.16515i	− 0.239907i
$893$	25.5826i	0.856088i
$894$	−22.9129	−0.766321
$895$	0	0
$896$	1.79129	0.0598427
$897$	− 16.1652i	− 0.539739i
$898$	− 16.1216i	− 0.537984i
$899$	25.5826	0.853227
$900$	0	0
$901$	4.74773	0.158170
$902$	− 5.37386i	− 0.178930i
$903$	− 55.8258i	− 1.85776i
$904$	6.00000	0.199557
$905$	0	0
$906$	−30.1216	−1.00072
$907$	6.74773i	0.224055i	0.993705	+	0.112027i	$0.0357344\pi$
$907$	6.74773i	0.224055i	−0.993705	+	0.112027i	$0.964266\pi$
$908$	22.7477i	0.754910i
$909$	−21.1652	−0.702004
$910$	0	0
$911$	4.41742	0.146356	0.0731779	−	0.997319i	$-0.476686\pi$
$911$	4.41742	0.146356	0.0731779	+	0.997319i	$0.476686\pi$
$912$	− 16.1652i	− 0.535282i
$913$	− 4.74773i	− 0.157127i
$914$	−10.0000	−0.330771
$915$	0	0
$916$	20.3303	0.671732
$917$	16.4174i	0.542151i
$918$	− 3.95644i	− 0.130582i
$919$	55.1652	1.81973	0.909865	−	0.414904i	$-0.136185\pi$
$919$	55.1652	1.81973	0.909865	+	0.414904i	$0.136185\pi$
$920$	0	0
$921$	43.3739	1.42922
$922$	28.7477i	0.946756i
$923$	− 48.4955i	− 1.59625i
$924$	3.95644	0.130157
$925$	0	0
$926$	10.0000	0.328620
$927$	− 30.5390i	− 1.00303i
$928$	7.58258i	0.248910i
$929$	−15.4955	−0.508389	−0.254195	−	0.967153i	$-0.581810\pi$
$929$	−15.4955	−0.508389	−0.254195	+	0.967153i	$0.581810\pi$
$930$	0	0
$931$	−21.9564	−0.719593
$932$	− 1.58258i	− 0.0518390i
$933$	33.4955i	1.09659i
$934$	−19.9129	−0.651569
$935$	0	0
$936$	−27.7477	−0.906963
$937$	44.6261i	1.45787i	0.684582	+	0.728936i	$0.259985\pi$
$937$	44.6261i	1.45787i	−0.684582	+	0.728936i	$0.740015\pi$
$938$	− 20.0000i	− 0.653023i
$939$	−12.9129	−0.421396
$940$	0	0
$941$	32.0436	1.04459	0.522295	−	0.852765i	$-0.325076\pi$
$941$	32.0436	1.04459	0.522295	+	0.852765i	$0.325076\pi$
$942$	− 41.1652i	− 1.34123i
$943$	6.79129i	0.221155i
$944$	13.5826	0.442075
$945$	0	0
$946$	8.83485	0.287246
$947$	2.53901i	0.0825069i	0.999149	+	0.0412534i	$0.0131351\pi$
$947$	2.53901i	0.0825069i	−0.999149	+	0.0412534i	$0.986865\pi$
$948$	22.3303i	0.725255i
$949$	−73.8258	−2.39649
$950$	0	0
$951$	−27.3303	−0.886246
$952$	1.41742i	0.0459390i
$953$	− 5.53901i	− 0.179426i	−0.995968	−	0.0897131i	$-0.971405\pi$
$953$	− 5.53901i	− 0.179426i	0.995968	−	0.0897131i	$-0.0285950\pi$
$954$	28.7477	0.930742
$955$	0	0
$956$	−15.1652	−0.490476
$957$	16.7477i	0.541377i
$958$	15.4955i	0.500635i
$959$	6.79129	0.219302
$960$	0	0
$961$	−19.6170	−0.632808
$962$	23.1652i	0.746874i
$963$	− 21.1652i	− 0.682037i
$964$	28.0000	0.901819
$965$	0	0
$966$	−5.00000	−0.160872
$967$	− 32.7477i	− 1.05310i	−0.850145	−	0.526548i	$-0.823486\pi$
$967$	− 32.7477i	− 1.05310i	0.850145	−	0.526548i	$-0.176514\pi$
$968$	− 10.3739i	− 0.333429i
$969$	12.7913	0.410915
$970$	0	0
$971$	15.9564	0.512067	0.256033	−	0.966668i	$-0.417584\pi$
$971$	15.9564	0.512067	0.256033	+	0.966668i	$0.417584\pi$
$972$	16.1652i	0.518497i
$973$	22.8348i	0.732052i
$974$	6.41742	0.205628
$975$	0	0
$976$	10.3739	0.332059
$977$	− 34.1216i	− 1.09165i	−0.837900	−	0.545823i	$-0.816217\pi$
$977$	− 34.1216i	− 1.09165i	0.837900	−	0.545823i	$-0.183783\pi$
$978$	− 24.0780i	− 0.769930i
$979$	12.0000	0.383522
$980$	0	0
$981$	−16.1652	−0.516114
$982$	− 10.7477i	− 0.342974i
$983$	14.3739i	0.458455i	0.973373	+	0.229228i	$0.0736200\pi$
$983$	14.3739i	0.458455i	−0.973373	+	0.229228i	$0.926380\pi$
$984$	18.9564	0.604309
$985$	0	0
$986$	−6.00000	−0.191079
$987$	− 22.0871i	− 0.703041i
$988$	− 33.5390i	− 1.06702i
$989$	−11.1652	−0.355031
$990$	0	0
$991$	−33.2087	−1.05491	−0.527455	−	0.849583i	$-0.676854\pi$
$991$	−33.2087	−1.05491	−0.527455	+	0.849583i	$0.676854\pi$
$992$	3.37386i	0.107120i
$993$	− 57.9129i	− 1.83781i
$994$	−15.0000	−0.475771
$995$	0	0
$996$	16.7477	0.530672
$997$	− 43.4955i	− 1.37751i	−0.724992	−	0.688757i	$-0.758157\pi$
$997$	− 43.4955i	− 1.37751i	0.724992	−	0.688757i	$-0.241843\pi$
$998$	4.83485i	0.153044i
$999$	−20.0000	−0.632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.b.g.599.2		4
5.2	odd	4		1150.2.a.o.1.2		2
5.3	odd	4		230.2.a.a.1.1	✓	2
5.4	even	2	inner	1150.2.b.g.599.3		4
15.8	even	4		2070.2.a.x.1.1		2
20.3	even	4		1840.2.a.n.1.2		2
20.7	even	4		9200.2.a.bs.1.1		2
40.3	even	4		7360.2.a.bk.1.1		2
40.13	odd	4		7360.2.a.bq.1.2		2
115.68	even	4		5290.2.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.a.a.1.1	✓	2	5.3	odd	4
1150.2.a.o.1.2		2	5.2	odd	4
1150.2.b.g.599.2		4	1.1	even	1	trivial
1150.2.b.g.599.3		4	5.4	even	2	inner
1840.2.a.n.1.2		2	20.3	even	4
2070.2.a.x.1.1		2	15.8	even	4
5290.2.a.e.1.1		2	115.68	even	4
7360.2.a.bk.1.1		2	40.3	even	4
7360.2.a.bq.1.2		2	40.13	odd	4
9200.2.a.bs.1.1		2	20.7	even	4

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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +2.79129i q^{3} -1.00000 q^{4} +2.79129 q^{6} -1.79129i q^{7} +1.00000i q^{8} -4.79129 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +2.79129i q^{3} -1.00000 q^{4} +2.79129 q^{6} -1.79129i q^{7} +1.00000i q^{8} -4.79129 q^{9} -0.791288 q^{11} -2.79129i q^{12} -5.79129i q^{13} -1.79129 q^{14} +1.00000 q^{16} +0.791288i q^{17} +4.79129i q^{18} -5.79129 q^{19} +5.00000 q^{21} +0.791288i q^{22} -1.00000i q^{23} -2.79129 q^{24} -5.79129 q^{26} -5.00000i q^{27} +1.79129i q^{28} -7.58258 q^{29} -3.37386 q^{31} -1.00000i q^{32} -2.20871i q^{33} +0.791288 q^{34} +4.79129 q^{36} -4.00000i q^{37} +5.79129i q^{38} +16.1652 q^{39} -6.79129 q^{41} -5.00000i q^{42} -11.1652i q^{43} +0.791288 q^{44} -1.00000 q^{46} -4.41742i q^{47} +2.79129i q^{48} +3.79129 q^{49} -2.20871 q^{51} +5.79129i q^{52} -6.00000i q^{53} -5.00000 q^{54} +1.79129 q^{56} -16.1652i q^{57} +7.58258i q^{58} +13.5826 q^{59} +10.3739 q^{61} +3.37386i q^{62} +8.58258i q^{63} -1.00000 q^{64} -2.20871 q^{66} +11.1652i q^{67} -0.791288i q^{68} +2.79129 q^{69} +8.37386 q^{71} -4.79129i q^{72} -12.7477i q^{73} -4.00000 q^{74} +5.79129 q^{76} +1.41742i q^{77} -16.1652i q^{78} -8.00000 q^{79} -0.417424 q^{81} +6.79129i q^{82} +6.00000i q^{83} -5.00000 q^{84} -11.1652 q^{86} -21.1652i q^{87} -0.791288i q^{88} -15.1652 q^{89} -10.3739 q^{91} +1.00000i q^{92} -9.41742i q^{93} -4.41742 q^{94} +2.79129 q^{96} -7.95644i q^{97} -3.79129i q^{98} +3.79129 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 2 q^{6} - 10 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 2 * q^6 - 10 * q^9	\( 4 q - 4 q^{4} + 2 q^{6} - 10 q^{9} + 6 q^{11} + 2 q^{14} + 4 q^{16} - 14 q^{19} + 20 q^{21} - 2 q^{24} - 14 q^{26} - 12 q^{29} + 14 q^{31} - 6 q^{34} + 10 q^{36} + 28 q^{39} - 18 q^{41} - 6 q^{44} - 4 q^{46} + 6 q^{49} - 18 q^{51} - 20 q^{54} - 2 q^{56} + 36 q^{59} + 14 q^{61} - 4 q^{64} - 18 q^{66} + 2 q^{69} + 6 q^{71} - 16 q^{74} + 14 q^{76} - 32 q^{79} - 20 q^{81} - 20 q^{84} - 8 q^{86} - 24 q^{89} - 14 q^{91} - 36 q^{94} + 2 q^{96} + 6 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 2 * q^6 - 10 * q^9 + 6 * q^11 + 2 * q^14 + 4 * q^16 - 14 * q^19 + 20 * q^21 - 2 * q^24 - 14 * q^26 - 12 * q^29 + 14 * q^31 - 6 * q^34 + 10 * q^36 + 28 * q^39 - 18 * q^41 - 6 * q^44 - 4 * q^46 + 6 * q^49 - 18 * q^51 - 20 * q^54 - 2 * q^56 + 36 * q^59 + 14 * q^61 - 4 * q^64 - 18 * q^66 + 2 * q^69 + 6 * q^71 - 16 * q^74 + 14 * q^76 - 32 * q^79 - 20 * q^81 - 20 * q^84 - 8 * q^86 - 24 * q^89 - 14 * q^91 - 36 * q^94 + 2 * q^96 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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