LMFDB - Embedded newform 1450.2.b.g.349.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1450,2,Mod(349,1450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1450, 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("1450.349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1450.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:	$11.5783082931$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 9 $ x^4 + 7*x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 290)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.4
Root			$2.30278i$ of defining polynomial
Character	$\chi$	$=$	1450.349
Dual form			1450.2.b.g.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +2.30278i q^{3} -1.00000 q^{4} -2.30278 q^{6} -0.697224i q^{7} -1.00000i q^{8} -2.30278 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +2.30278i q^{3} -1.00000 q^{4} -2.30278 q^{6} -0.697224i q^{7} -1.00000i q^{8} -2.30278 q^{9} +2.60555 q^{11} -2.30278i q^{12} +6.30278i q^{13} +0.697224 q^{14} +1.00000 q^{16} +3.90833i q^{17} -2.30278i q^{18} +0.605551 q^{19} +1.60555 q^{21} +2.60555i q^{22} +1.69722i q^{23} +2.30278 q^{24} -6.30278 q^{26} +1.60555i q^{27} +0.697224i q^{28} -1.00000 q^{29} -7.90833 q^{31} +1.00000i q^{32} +6.00000i q^{33} -3.90833 q^{34} +2.30278 q^{36} -9.81665i q^{37} +0.605551i q^{38} -14.5139 q^{39} -8.60555 q^{41} +1.60555i q^{42} +3.30278i q^{43} -2.60555 q^{44} -1.69722 q^{46} +2.30278i q^{48} +6.51388 q^{49} -9.00000 q^{51} -6.30278i q^{52} -3.90833i q^{53} -1.60555 q^{54} -0.697224 q^{56} +1.39445i q^{57} -1.00000i q^{58} +0.908327 q^{59} -3.09167 q^{61} -7.90833i q^{62} +1.60555i q^{63} -1.00000 q^{64} -6.00000 q^{66} +9.21110i q^{67} -3.90833i q^{68} -3.90833 q^{69} +2.30278i q^{72} +2.51388i q^{73} +9.81665 q^{74} -0.605551 q^{76} -1.81665i q^{77} -14.5139i q^{78} +4.90833 q^{79} -10.6056 q^{81} -8.60555i q^{82} -8.60555i q^{83} -1.60555 q^{84} -3.30278 q^{86} -2.30278i q^{87} -2.60555i q^{88} +14.6056 q^{89} +4.39445 q^{91} -1.69722i q^{92} -18.2111i q^{93} -2.30278 q^{96} -1.09167i q^{97} +6.51388i q^{98} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 - 2 * q^6 - 2 * q^9	$ 4 q - 4 q^{4} - 2 q^{6} - 2 q^{9} - 4 q^{11} + 10 q^{14} + 4 q^{16} - 12 q^{19} - 8 q^{21} + 2 q^{24} - 18 q^{26} - 4 q^{29} - 10 q^{31} + 6 q^{34} + 2 q^{36} - 22 q^{39} - 20 q^{41} + 4 q^{44} - 14 q^{46} - 10 q^{49} - 36 q^{51} + 8 q^{54} - 10 q^{56} - 18 q^{59} - 34 q^{61} - 4 q^{64} - 24 q^{66} + 6 q^{69} - 4 q^{74} + 12 q^{76} - 2 q^{79} - 28 q^{81} + 8 q^{84} - 6 q^{86} + 44 q^{89} + 32 q^{91} - 2 q^{96} - 24 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 - 2 * q^6 - 2 * q^9 - 4 * q^11 + 10 * q^14 + 4 * q^16 - 12 * q^19 - 8 * q^21 + 2 * q^24 - 18 * q^26 - 4 * q^29 - 10 * q^31 + 6 * q^34 + 2 * q^36 - 22 * q^39 - 20 * q^41 + 4 * q^44 - 14 * q^46 - 10 * q^49 - 36 * q^51 + 8 * q^54 - 10 * q^56 - 18 * q^59 - 34 * q^61 - 4 * q^64 - 24 * q^66 + 6 * q^69 - 4 * q^74 + 12 * q^76 - 2 * q^79 - 28 * q^81 + 8 * q^84 - 6 * q^86 + 44 * q^89 + 32 * q^91 - 2 * q^96 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1450\mathbb{Z}\right)^\times$.

$n$	$901$	$1277$
$\chi(n)$	$1$	$-1$

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
$3$	2.30278i	1.32951i	0.747062	+	0.664754i	$0.231464\pi$
$3$	2.30278i	1.32951i	−0.747062	+	0.664754i	$0.768536\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−2.30278	−0.940104
$7$	− 0.697224i	− 0.263526i	−0.991281	−	0.131763i	$-0.957936\pi$
$7$	− 0.697224i	− 0.263526i	0.991281	−	0.131763i	$-0.0420638\pi$
$8$	− 1.00000i	− 0.353553i
$9$	−2.30278	−0.767592
$10$	0	0
$11$	2.60555	0.785603	0.392802	−	0.919623i	$-0.371506\pi$
$11$	2.60555	0.785603	0.392802	+	0.919623i	$0.371506\pi$
$12$	− 2.30278i	− 0.664754i
$13$	6.30278i	1.74808i	0.485858	+	0.874038i	$0.338507\pi$
$13$	6.30278i	1.74808i	−0.485858	+	0.874038i	$0.661493\pi$
$14$	0.697224	0.186341
$15$	0	0
$16$	1.00000	0.250000
$17$	3.90833i	0.947909i	0.880549	+	0.473954i	$0.157174\pi$
$17$	3.90833i	0.947909i	−0.880549	+	0.473954i	$0.842826\pi$
$18$	− 2.30278i	− 0.542769i
$19$	0.605551	0.138923	0.0694615	−	0.997585i	$-0.477872\pi$
$19$	0.605551	0.138923	0.0694615	+	0.997585i	$0.477872\pi$
$20$	0	0
$21$	1.60555	0.350360
$22$	2.60555i	0.555505i
$23$	1.69722i	0.353896i	0.984220	+	0.176948i	$0.0566224\pi$
$23$	1.69722i	0.353896i	−0.984220	+	0.176948i	$0.943378\pi$
$24$	2.30278	0.470052
$25$	0	0
$26$	−6.30278	−1.23608
$27$	1.60555i	0.308988i
$28$	0.697224i	0.131763i
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0	0
$31$	−7.90833	−1.42038	−0.710189	−	0.704011i	$-0.751390\pi$
$31$	−7.90833	−1.42038	−0.710189	+	0.704011i	$0.751390\pi$
$32$	1.00000i	0.176777i
$33$	6.00000i	1.04447i
$34$	−3.90833	−0.670273
$35$	0	0
$36$	2.30278	0.383796
$37$	− 9.81665i	− 1.61385i	−0.590655	−	0.806924i	$-0.701131\pi$
$37$	− 9.81665i	− 1.61385i	0.590655	−	0.806924i	$-0.298869\pi$
$38$	0.605551i	0.0982334i
$39$	−14.5139	−2.32408
$40$	0	0
$41$	−8.60555	−1.34396	−0.671981	−	0.740569i	$-0.734556\pi$
$41$	−8.60555	−1.34396	−0.671981	+	0.740569i	$0.734556\pi$
$42$	1.60555i	0.247742i
$43$	3.30278i	0.503669i	0.967770	+	0.251834i	$0.0810338\pi$
$43$	3.30278i	0.503669i	−0.967770	+	0.251834i	$0.918966\pi$
$44$	−2.60555	−0.392802
$45$	0	0
$46$	−1.69722	−0.250242
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	2.30278i	0.332377i
$49$	6.51388	0.930554
$50$	0	0
$51$	−9.00000	−1.26025
$52$	− 6.30278i	− 0.874038i
$53$	− 3.90833i	− 0.536850i	−0.963301	−	0.268425i	$-0.913497\pi$
$53$	− 3.90833i	− 0.536850i	0.963301	−	0.268425i	$-0.0865031\pi$
$54$	−1.60555	−0.218488
$55$	0	0
$56$	−0.697224	−0.0931705
$57$	1.39445i	0.184699i
$58$	− 1.00000i	− 0.131306i
$59$	0.908327	0.118254	0.0591270	−	0.998250i	$-0.481168\pi$
$59$	0.908327	0.118254	0.0591270	+	0.998250i	$0.481168\pi$
$60$	0	0
$61$	−3.09167	−0.395848	−0.197924	−	0.980217i	$-0.563420\pi$
$61$	−3.09167	−0.395848	−0.197924	+	0.980217i	$0.563420\pi$
$62$	− 7.90833i	− 1.00436i
$63$	1.60555i	0.202280i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−6.00000	−0.738549
$67$	9.21110i	1.12532i	0.826690	+	0.562658i	$0.190221\pi$
$67$	9.21110i	1.12532i	−0.826690	+	0.562658i	$0.809779\pi$
$68$	− 3.90833i	− 0.473954i
$69$	−3.90833	−0.470507
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	2.30278i	0.271385i
$73$	2.51388i	0.294227i	0.989120	+	0.147114i	$0.0469983\pi$
$73$	2.51388i	0.294227i	−0.989120	+	0.147114i	$0.953002\pi$
$74$	9.81665	1.14116
$75$	0	0
$76$	−0.605551	−0.0694615
$77$	− 1.81665i	− 0.207027i
$78$	− 14.5139i	− 1.64337i
$79$	4.90833	0.552230	0.276115	−	0.961125i	$-0.410953\pi$
$79$	4.90833	0.552230	0.276115	+	0.961125i	$0.410953\pi$
$80$	0	0
$81$	−10.6056	−1.17839
$82$	− 8.60555i	− 0.950324i
$83$	− 8.60555i	− 0.944582i	−0.881443	−	0.472291i	$-0.843427\pi$
$83$	− 8.60555i	− 0.944582i	0.881443	−	0.472291i	$-0.156573\pi$
$84$	−1.60555	−0.175180
$85$	0	0
$86$	−3.30278	−0.356147
$87$	− 2.30278i	− 0.246883i
$88$	− 2.60555i	− 0.277753i
$89$	14.6056	1.54819	0.774093	−	0.633072i	$-0.218206\pi$
$89$	14.6056	1.54819	0.774093	+	0.633072i	$0.218206\pi$
$90$	0	0
$91$	4.39445	0.460663
$92$	− 1.69722i	− 0.176948i
$93$	− 18.2111i	− 1.88840i
$94$	0	0
$95$	0	0
$96$	−2.30278	−0.235026
$97$	− 1.09167i	− 0.110843i	−0.998463	−	0.0554213i	$-0.982350\pi$
$97$	− 1.09167i	− 0.110843i	0.998463	−	0.0554213i	$-0.0176502\pi$
$98$	6.51388i	0.658001i
$99$	−6.00000	−0.603023
$100$	0	0
$101$	−12.9083	−1.28443	−0.642213	−	0.766526i	$-0.721984\pi$
$101$	−12.9083	−1.28443	−0.642213	+	0.766526i	$0.721984\pi$
$102$	− 9.00000i	− 0.891133i
$103$	18.4222i	1.81519i	0.419843	+	0.907597i	$0.362085\pi$
$103$	18.4222i	1.81519i	−0.419843	+	0.907597i	$0.637915\pi$
$104$	6.30278	0.618038
$105$	0	0
$106$	3.90833	0.379610
$107$	− 8.60555i	− 0.831930i	−0.909381	−	0.415965i	$-0.863444\pi$
$107$	− 8.60555i	− 0.831930i	0.909381	−	0.415965i	$-0.136556\pi$
$108$	− 1.60555i	− 0.154494i
$109$	7.39445	0.708260	0.354130	−	0.935196i	$-0.384777\pi$
$109$	7.39445	0.708260	0.354130	+	0.935196i	$0.384777\pi$
$110$	0	0
$111$	22.6056	2.14562
$112$	− 0.697224i	− 0.0658815i
$113$	10.3028i	0.969204i	0.874735	+	0.484602i	$0.161035\pi$
$113$	10.3028i	0.969204i	−0.874735	+	0.484602i	$0.838965\pi$
$114$	−1.39445	−0.130602
$115$	0	0
$116$	1.00000	0.0928477
$117$	− 14.5139i	− 1.34181i
$118$	0.908327i	0.0836183i
$119$	2.72498	0.249799
$120$	0	0
$121$	−4.21110	−0.382828
$122$	− 3.09167i	− 0.279907i
$123$	− 19.8167i	− 1.78681i
$124$	7.90833	0.710189
$125$	0	0
$126$	−1.60555	−0.143034
$127$	− 20.0000i	− 1.77471i	−0.461084	−	0.887357i	$-0.652539\pi$
$127$	− 20.0000i	− 1.77471i	0.461084	−	0.887357i	$-0.347461\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−7.60555	−0.669631
$130$	0	0
$131$	21.6333	1.89011	0.945055	−	0.326910i	$-0.106007\pi$
$131$	21.6333	1.89011	0.945055	+	0.326910i	$0.106007\pi$
$132$	− 6.00000i	− 0.522233i
$133$	− 0.422205i	− 0.0366098i
$134$	−9.21110	−0.795718
$135$	0	0
$136$	3.90833	0.335136
$137$	18.9083i	1.61545i	0.589561	+	0.807724i	$0.299301\pi$
$137$	18.9083i	1.61545i	−0.589561	+	0.807724i	$0.700699\pi$
$138$	− 3.90833i	− 0.332699i
$139$	−6.69722	−0.568051	−0.284026	−	0.958817i	$-0.591670\pi$
$139$	−6.69722	−0.568051	−0.284026	+	0.958817i	$0.591670\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	16.4222i	1.37329i
$144$	−2.30278	−0.191898
$145$	0	0
$146$	−2.51388	−0.208050
$147$	15.0000i	1.23718i
$148$	9.81665i	0.806924i
$149$	−19.8167	−1.62344	−0.811722	−	0.584044i	$-0.801469\pi$
$149$	−19.8167	−1.62344	−0.811722	+	0.584044i	$0.801469\pi$
$150$	0	0
$151$	4.60555	0.374794	0.187397	−	0.982284i	$-0.439995\pi$
$151$	4.60555	0.374794	0.187397	+	0.982284i	$0.439995\pi$
$152$	− 0.605551i	− 0.0491167i
$153$	− 9.00000i	− 0.727607i
$154$	1.81665	0.146390
$155$	0	0
$156$	14.5139	1.16204
$157$	8.42221i	0.672165i	0.941833	+	0.336083i	$0.109102\pi$
$157$	8.42221i	0.672165i	−0.941833	+	0.336083i	$0.890898\pi$
$158$	4.90833i	0.390486i
$159$	9.00000	0.713746
$160$	0	0
$161$	1.18335	0.0932607
$162$	− 10.6056i	− 0.833251i
$163$	− 21.2111i	− 1.66138i	−0.556734	−	0.830691i	$-0.687946\pi$
$163$	− 21.2111i	− 1.66138i	0.556734	−	0.830691i	$-0.312054\pi$
$164$	8.60555	0.671981
$165$	0	0
$166$	8.60555	0.667920
$167$	7.30278i	0.565106i	0.959252	+	0.282553i	$0.0911813\pi$
$167$	7.30278i	0.565106i	−0.959252	+	0.282553i	$0.908819\pi$
$168$	− 1.60555i	− 0.123871i
$169$	−26.7250	−2.05577
$170$	0	0
$171$	−1.39445	−0.106636
$172$	− 3.30278i	− 0.251834i
$173$	18.9083i	1.43757i	0.695231	+	0.718787i	$0.255302\pi$
$173$	18.9083i	1.43757i	−0.695231	+	0.718787i	$0.744698\pi$
$174$	2.30278	0.174573
$175$	0	0
$176$	2.60555	0.196401
$177$	2.09167i	0.157220i
$178$	14.6056i	1.09473i
$179$	−0.908327	−0.0678915	−0.0339458	−	0.999424i	$-0.510807\pi$
$179$	−0.908327	−0.0678915	−0.0339458	+	0.999424i	$0.510807\pi$
$180$	0	0
$181$	−12.6056	−0.936963	−0.468482	−	0.883473i	$-0.655199\pi$
$181$	−12.6056	−0.936963	−0.468482	+	0.883473i	$0.655199\pi$
$182$	4.39445i	0.325738i
$183$	− 7.11943i	− 0.526283i
$184$	1.69722	0.125121
$185$	0	0
$186$	18.2111	1.33530
$187$	10.1833i	0.744680i
$188$	0	0
$189$	1.11943	0.0814265
$190$	0	0
$191$	15.9083	1.15109	0.575543	−	0.817771i	$-0.304791\pi$
$191$	15.9083	1.15109	0.575543	+	0.817771i	$0.304791\pi$
$192$	− 2.30278i	− 0.166189i
$193$	− 24.7250i	− 1.77974i	−0.456211	−	0.889872i	$-0.650794\pi$
$193$	− 24.7250i	− 1.77974i	0.456211	−	0.889872i	$-0.349206\pi$
$194$	1.09167	0.0783776
$195$	0	0
$196$	−6.51388	−0.465277
$197$	3.90833i	0.278457i	0.990260	+	0.139228i	$0.0444622\pi$
$197$	3.90833i	0.278457i	−0.990260	+	0.139228i	$0.955538\pi$
$198$	− 6.00000i	− 0.426401i
$199$	−3.81665	−0.270555	−0.135278	−	0.990808i	$-0.543193\pi$
$199$	−3.81665	−0.270555	−0.135278	+	0.990808i	$0.543193\pi$
$200$	0	0
$201$	−21.2111	−1.49612
$202$	− 12.9083i	− 0.908227i
$203$	0.697224i	0.0489356i
$204$	9.00000	0.630126
$205$	0	0
$206$	−18.4222	−1.28354
$207$	− 3.90833i	− 0.271647i
$208$	6.30278i	0.437019i
$209$	1.57779	0.109138
$210$	0	0
$211$	27.8167	1.91498	0.957489	−	0.288471i	$-0.0931468\pi$
$211$	27.8167	1.91498	0.957489	+	0.288471i	$0.0931468\pi$
$212$	3.90833i	0.268425i
$213$	0	0
$214$	8.60555	0.588263
$215$	0	0
$216$	1.60555	0.109244
$217$	5.51388i	0.374306i
$218$	7.39445i	0.500815i
$219$	−5.78890	−0.391177
$220$	0	0
$221$	−24.6333	−1.65702
$222$	22.6056i	1.51719i
$223$	− 7.51388i	− 0.503166i	−0.967836	−	0.251583i	$-0.919049\pi$
$223$	− 7.51388i	− 0.503166i	0.967836	−	0.251583i	$-0.0809512\pi$
$224$	0.697224	0.0465853
$225$	0	0
$226$	−10.3028	−0.685330
$227$	− 0.788897i	− 0.0523610i	−0.999657	−	0.0261805i	$-0.991666\pi$
$227$	− 0.788897i	− 0.0523610i	0.999657	−	0.0261805i	$-0.00833446\pi$
$228$	− 1.39445i	− 0.0923496i
$229$	−5.90833	−0.390433	−0.195217	−	0.980760i	$-0.562541\pi$
$229$	−5.90833	−0.390433	−0.195217	+	0.980760i	$0.562541\pi$
$230$	0	0
$231$	4.18335	0.275244
$232$	1.00000i	0.0656532i
$233$	23.2111i	1.52061i	0.649566	+	0.760305i	$0.274950\pi$
$233$	23.2111i	1.52061i	−0.649566	+	0.760305i	$0.725050\pi$
$234$	14.5139	0.948802
$235$	0	0
$236$	−0.908327	−0.0591270
$237$	11.3028i	0.734194i
$238$	2.72498i	0.176634i
$239$	−6.00000	−0.388108	−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000	−0.388108	−0.194054	+	0.980991i	$0.562164\pi$
$240$	0	0
$241$	0.302776	0.0195035	0.00975175	−	0.999952i	$-0.496896\pi$
$241$	0.302776	0.0195035	0.00975175	+	0.999952i	$0.496896\pi$
$242$	− 4.21110i	− 0.270700i
$243$	− 19.6056i	− 1.25770i
$244$	3.09167	0.197924
$245$	0	0
$246$	19.8167	1.26346
$247$	3.81665i	0.242848i
$248$	7.90833i	0.502179i
$249$	19.8167	1.25583
$250$	0	0
$251$	−8.60555	−0.543178	−0.271589	−	0.962413i	$-0.587549\pi$
$251$	−8.60555	−0.543178	−0.271589	+	0.962413i	$0.587549\pi$
$252$	− 1.60555i	− 0.101140i
$253$	4.42221i	0.278022i
$254$	20.0000	1.25491
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 7.02776i	− 0.438379i	−0.975682	−	0.219190i	$-0.929659\pi$
$257$	− 7.02776i	− 0.438379i	0.975682	−	0.219190i	$-0.0703414\pi$
$258$	− 7.60555i	− 0.473501i
$259$	−6.84441	−0.425291
$260$	0	0
$261$	2.30278	0.142538
$262$	21.6333i	1.33651i
$263$	5.21110i	0.321330i	0.987009	+	0.160665i	$0.0513639\pi$
$263$	5.21110i	0.321330i	−0.987009	+	0.160665i	$0.948636\pi$
$264$	6.00000	0.369274
$265$	0	0
$266$	0.422205	0.0258871
$267$	33.6333i	2.05833i
$268$	− 9.21110i	− 0.562658i
$269$	12.5139	0.762985	0.381492	−	0.924372i	$-0.375410\pi$
$269$	12.5139	0.762985	0.381492	+	0.924372i	$0.375410\pi$
$270$	0	0
$271$	13.2111	0.802517	0.401259	−	0.915965i	$-0.368573\pi$
$271$	13.2111	0.802517	0.401259	+	0.915965i	$0.368573\pi$
$272$	3.90833i	0.236977i
$273$	10.1194i	0.612456i
$274$	−18.9083	−1.14229
$275$	0	0
$276$	3.90833	0.235254
$277$	− 14.0000i	− 0.841178i	−0.907251	−	0.420589i	$-0.861823\pi$
$277$	− 14.0000i	− 0.841178i	0.907251	−	0.420589i	$-0.138177\pi$
$278$	− 6.69722i	− 0.401673i
$279$	18.2111	1.09027
$280$	0	0
$281$	15.1194	0.901950	0.450975	−	0.892537i	$-0.351076\pi$
$281$	15.1194	0.901950	0.450975	+	0.892537i	$0.351076\pi$
$282$	0	0
$283$	15.0278i	0.893307i	0.894707	+	0.446654i	$0.147384\pi$
$283$	15.0278i	0.893307i	−0.894707	+	0.446654i	$0.852616\pi$
$284$	0	0
$285$	0	0
$286$	−16.4222	−0.971065
$287$	6.00000i	0.354169i
$288$	− 2.30278i	− 0.135692i
$289$	1.72498	0.101469
$290$	0	0
$291$	2.51388	0.147366
$292$	− 2.51388i	− 0.147114i
$293$	25.8167i	1.50823i	0.656745	+	0.754113i	$0.271933\pi$
$293$	25.8167i	1.50823i	−0.656745	+	0.754113i	$0.728067\pi$
$294$	−15.0000	−0.874818
$295$	0	0
$296$	−9.81665	−0.570581
$297$	4.18335i	0.242742i
$298$	− 19.8167i	− 1.14795i
$299$	−10.6972	−0.618636
$300$	0	0
$301$	2.30278	0.132730
$302$	4.60555i	0.265020i
$303$	− 29.7250i	− 1.70766i
$304$	0.605551	0.0347307
$305$	0	0
$306$	9.00000	0.514496
$307$	− 1.21110i	− 0.0691213i	−0.999403	−	0.0345606i	$-0.988997\pi$
$307$	− 1.21110i	− 0.0691213i	0.999403	−	0.0345606i	$-0.0110032\pi$
$308$	1.81665i	0.103513i
$309$	−42.4222	−2.41331
$310$	0	0
$311$	24.9083	1.41242	0.706211	−	0.708002i	$-0.250403\pi$
$311$	24.9083	1.41242	0.706211	+	0.708002i	$0.250403\pi$
$312$	14.5139i	0.821687i
$313$	0.422205i	0.0238644i	0.999929	+	0.0119322i	$0.00379823\pi$
$313$	0.422205i	0.0238644i	−0.999929	+	0.0119322i	$0.996202\pi$
$314$	−8.42221	−0.475293
$315$	0	0
$316$	−4.90833	−0.276115
$317$	25.0278i	1.40570i	0.711339	+	0.702849i	$0.248089\pi$
$317$	25.0278i	1.40570i	−0.711339	+	0.702849i	$0.751911\pi$
$318$	9.00000i	0.504695i
$319$	−2.60555	−0.145883
$320$	0	0
$321$	19.8167	1.10606
$322$	1.18335i	0.0659453i
$323$	2.36669i	0.131686i
$324$	10.6056	0.589197
$325$	0	0
$326$	21.2111	1.17477
$327$	17.0278i	0.941637i
$328$	8.60555i	0.475162i
$329$	0	0
$330$	0	0
$331$	22.6056	1.24251	0.621257	−	0.783607i	$-0.286622\pi$
$331$	22.6056	1.24251	0.621257	+	0.783607i	$0.286622\pi$
$332$	8.60555i	0.472291i
$333$	22.6056i	1.23878i
$334$	−7.30278	−0.399590
$335$	0	0
$336$	1.60555	0.0875900
$337$	5.30278i	0.288861i	0.989515	+	0.144430i	$0.0461349\pi$
$337$	5.30278i	0.288861i	−0.989515	+	0.144430i	$0.953865\pi$
$338$	− 26.7250i	− 1.45365i
$339$	−23.7250	−1.28856
$340$	0	0
$341$	−20.6056	−1.11585
$342$	− 1.39445i	− 0.0754032i
$343$	− 9.42221i	− 0.508751i
$344$	3.30278	0.178074
$345$	0	0
$346$	−18.9083	−1.01652
$347$	− 13.8167i	− 0.741717i	−0.928689	−	0.370858i	$-0.879064\pi$
$347$	− 13.8167i	− 0.741717i	0.928689	−	0.370858i	$-0.120936\pi$
$348$	2.30278i	0.123442i
$349$	−8.00000	−0.428230	−0.214115	−	0.976808i	$-0.568687\pi$
$349$	−8.00000	−0.428230	−0.214115	+	0.976808i	$0.568687\pi$
$350$	0	0
$351$	−10.1194	−0.540135
$352$	2.60555i	0.138876i
$353$	17.2111i	0.916055i	0.888938	+	0.458027i	$0.151444\pi$
$353$	17.2111i	0.916055i	−0.888938	+	0.458027i	$0.848556\pi$
$354$	−2.09167	−0.111171
$355$	0	0
$356$	−14.6056	−0.774093
$357$	6.27502i	0.332109i
$358$	− 0.908327i	− 0.0480066i
$359$	33.5139	1.76879	0.884397	−	0.466735i	$-0.154570\pi$
$359$	33.5139	1.76879	0.884397	+	0.466735i	$0.154570\pi$
$360$	0	0
$361$	−18.6333	−0.980700
$362$	− 12.6056i	− 0.662533i
$363$	− 9.69722i	− 0.508972i
$364$	−4.39445	−0.230332
$365$	0	0
$366$	7.11943	0.372139
$367$	24.6056i	1.28440i	0.766537	+	0.642200i	$0.221978\pi$
$367$	24.6056i	1.28440i	−0.766537	+	0.642200i	$0.778022\pi$
$368$	1.69722i	0.0884739i
$369$	19.8167	1.03161
$370$	0	0
$371$	−2.72498	−0.141474
$372$	18.2111i	0.944202i
$373$	− 31.9083i	− 1.65215i	−0.563560	−	0.826075i	$-0.690569\pi$
$373$	− 31.9083i	− 1.65215i	0.563560	−	0.826075i	$-0.309431\pi$
$374$	−10.1833	−0.526568
$375$	0	0
$376$	0	0
$377$	− 6.30278i	− 0.324609i
$378$	1.11943i	0.0575772i
$379$	30.6056	1.57210	0.786051	−	0.618162i	$-0.212122\pi$
$379$	30.6056	1.57210	0.786051	+	0.618162i	$0.212122\pi$
$380$	0	0
$381$	46.0555	2.35950
$382$	15.9083i	0.813941i
$383$	4.69722i	0.240017i	0.992773	+	0.120008i	$0.0382922\pi$
$383$	4.69722i	0.240017i	−0.992773	+	0.120008i	$0.961708\pi$
$384$	2.30278	0.117513
$385$	0	0
$386$	24.7250	1.25847
$387$	− 7.60555i	− 0.386612i
$388$	1.09167i	0.0554213i
$389$	18.0000	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$390$	0	0
$391$	−6.63331	−0.335461
$392$	− 6.51388i	− 0.329001i
$393$	49.8167i	2.51292i
$394$	−3.90833	−0.196899
$395$	0	0
$396$	6.00000	0.301511
$397$	− 11.9083i	− 0.597662i	−0.954306	−	0.298831i	$-0.903403\pi$
$397$	− 11.9083i	− 0.597662i	0.954306	−	0.298831i	$-0.0965967\pi$
$398$	− 3.81665i	− 0.191312i
$399$	0.972244	0.0486731
$400$	0	0
$401$	28.3028	1.41337	0.706687	−	0.707527i	$-0.250189\pi$
$401$	28.3028	1.41337	0.706687	+	0.707527i	$0.250189\pi$
$402$	− 21.2111i	− 1.05791i
$403$	− 49.8444i	− 2.48293i
$404$	12.9083	0.642213
$405$	0	0
$406$	−0.697224	−0.0346027
$407$	− 25.5778i	− 1.26784i
$408$	9.00000i	0.445566i
$409$	9.21110	0.455460	0.227730	−	0.973724i	$-0.426870\pi$
$409$	9.21110	0.455460	0.227730	+	0.973724i	$0.426870\pi$
$410$	0	0
$411$	−43.5416	−2.14775
$412$	− 18.4222i	− 0.907597i
$413$	− 0.633308i	− 0.0311630i
$414$	3.90833	0.192084
$415$	0	0
$416$	−6.30278	−0.309019
$417$	− 15.4222i	− 0.755229i
$418$	1.57779i	0.0771725i
$419$	9.11943	0.445513	0.222757	−	0.974874i	$-0.428494\pi$
$419$	9.11943	0.445513	0.222757	+	0.974874i	$0.428494\pi$
$420$	0	0
$421$	−25.6333	−1.24929	−0.624645	−	0.780908i	$-0.714757\pi$
$421$	−25.6333	−1.24929	−0.624645	+	0.780908i	$0.714757\pi$
$422$	27.8167i	1.35409i
$423$	0	0
$424$	−3.90833	−0.189805
$425$	0	0
$426$	0	0
$427$	2.15559i	0.104316i
$428$	8.60555i	0.415965i
$429$	−37.8167	−1.82581
$430$	0	0
$431$	12.2389	0.589525	0.294763	−	0.955571i	$-0.404759\pi$
$431$	12.2389	0.589525	0.294763	+	0.955571i	$0.404759\pi$
$432$	1.60555i	0.0772471i
$433$	− 15.2111i	− 0.730999i	−0.930812	−	0.365499i	$-0.880898\pi$
$433$	− 15.2111i	− 0.730999i	0.930812	−	0.365499i	$-0.119102\pi$
$434$	−5.51388	−0.264675
$435$	0	0
$436$	−7.39445	−0.354130
$437$	1.02776i	0.0491643i
$438$	− 5.78890i	− 0.276604i
$439$	37.6333	1.79614	0.898070	−	0.439853i	$-0.144969\pi$
$439$	37.6333	1.79614	0.898070	+	0.439853i	$0.144969\pi$
$440$	0	0
$441$	−15.0000	−0.714286
$442$	− 24.6333i	− 1.17169i
$443$	27.7527i	1.31857i	0.751892	+	0.659286i	$0.229141\pi$
$443$	27.7527i	1.31857i	−0.751892	+	0.659286i	$0.770859\pi$
$444$	−22.6056	−1.07281
$445$	0	0
$446$	7.51388	0.355792
$447$	− 45.6333i	− 2.15838i
$448$	0.697224i	0.0329408i
$449$	15.3944	0.726509	0.363254	−	0.931690i	$-0.381666\pi$
$449$	15.3944	0.726509	0.363254	+	0.931690i	$0.381666\pi$
$450$	0	0
$451$	−22.4222	−1.05582
$452$	− 10.3028i	− 0.484602i
$453$	10.6056i	0.498292i
$454$	0.788897	0.0370248
$455$	0	0
$456$	1.39445	0.0653010
$457$	10.0000i	0.467780i	0.972263	+	0.233890i	$0.0751456\pi$
$457$	10.0000i	0.467780i	−0.972263	+	0.233890i	$0.924854\pi$
$458$	− 5.90833i	− 0.276078i
$459$	−6.27502	−0.292893
$460$	0	0
$461$	25.5416	1.18959	0.594796	−	0.803876i	$-0.297233\pi$
$461$	25.5416	1.18959	0.594796	+	0.803876i	$0.297233\pi$
$462$	4.18335i	0.194627i
$463$	40.8444i	1.89820i	0.314974	+	0.949100i	$0.398004\pi$
$463$	40.8444i	1.89820i	−0.314974	+	0.949100i	$0.601996\pi$
$464$	−1.00000	−0.0464238
$465$	0	0
$466$	−23.2111	−1.07523
$467$	37.5416i	1.73722i	0.495497	+	0.868610i	$0.334986\pi$
$467$	37.5416i	1.73722i	−0.495497	+	0.868610i	$0.665014\pi$
$468$	14.5139i	0.670904i
$469$	6.42221	0.296550
$470$	0	0
$471$	−19.3944	−0.893649
$472$	− 0.908327i	− 0.0418091i
$473$	8.60555i	0.395684i
$474$	−11.3028	−0.519154
$475$	0	0
$476$	−2.72498	−0.124899
$477$	9.00000i	0.412082i
$478$	− 6.00000i	− 0.274434i
$479$	11.7250	0.535728	0.267864	−	0.963457i	$-0.413682\pi$
$479$	11.7250	0.535728	0.267864	+	0.963457i	$0.413682\pi$
$480$	0	0
$481$	61.8722	2.82113
$482$	0.302776i	0.0137911i
$483$	2.72498i	0.123991i
$484$	4.21110	0.191414
$485$	0	0
$486$	19.6056	0.889326
$487$	− 33.9361i	− 1.53779i	−0.639375	−	0.768895i	$-0.720807\pi$
$487$	− 33.9361i	− 1.53779i	0.639375	−	0.768895i	$-0.279193\pi$
$488$	3.09167i	0.139953i
$489$	48.8444	2.20882
$490$	0	0
$491$	−3.63331	−0.163969	−0.0819844	−	0.996634i	$-0.526126\pi$
$491$	−3.63331	−0.163969	−0.0819844	+	0.996634i	$0.526126\pi$
$492$	19.8167i	0.893404i
$493$	− 3.90833i	− 0.176022i
$494$	−3.81665	−0.171719
$495$	0	0
$496$	−7.90833	−0.355094
$497$	0	0
$498$	19.8167i	0.888005i
$499$	18.7250	0.838245	0.419123	−	0.907930i	$-0.362338\pi$
$499$	18.7250	0.838245	0.419123	+	0.907930i	$0.362338\pi$
$500$	0	0
$501$	−16.8167	−0.751313
$502$	− 8.60555i	− 0.384085i
$503$	− 12.0000i	− 0.535054i	−0.963550	−	0.267527i	$-0.913794\pi$
$503$	− 12.0000i	− 0.535054i	0.963550	−	0.267527i	$-0.0862064\pi$
$504$	1.60555	0.0715169
$505$	0	0
$506$	−4.42221	−0.196591
$507$	− 61.5416i	− 2.73316i
$508$	20.0000i	0.887357i
$509$	−1.81665	−0.0805218	−0.0402609	−	0.999189i	$-0.512819\pi$
$509$	−1.81665	−0.0805218	−0.0402609	+	0.999189i	$0.512819\pi$
$510$	0	0
$511$	1.75274	0.0775365
$512$	1.00000i	0.0441942i
$513$	0.972244i	0.0429256i
$514$	7.02776	0.309981
$515$	0	0
$516$	7.60555	0.334816
$517$	0	0
$518$	− 6.84441i	− 0.300726i
$519$	−43.5416	−1.91127
$520$	0	0
$521$	4.69722	0.205789	0.102895	−	0.994692i	$-0.467190\pi$
$521$	4.69722	0.205789	0.102895	+	0.994692i	$0.467190\pi$
$522$	2.30278i	0.100790i
$523$	− 14.1833i	− 0.620194i	−0.950705	−	0.310097i	$-0.899638\pi$
$523$	− 14.1833i	− 0.620194i	0.950705	−	0.310097i	$-0.100362\pi$
$524$	−21.6333	−0.945055
$525$	0	0
$526$	−5.21110	−0.227215
$527$	− 30.9083i	− 1.34639i
$528$	6.00000i	0.261116i
$529$	20.1194	0.874758
$530$	0	0
$531$	−2.09167	−0.0907709
$532$	0.422205i	0.0183049i
$533$	− 54.2389i	− 2.34935i
$534$	−33.6333	−1.45546
$535$	0	0
$536$	9.21110	0.397859
$537$	− 2.09167i	− 0.0902624i
$538$	12.5139i	0.539512i
$539$	16.9722	0.731046
$540$	0	0
$541$	−0.880571	−0.0378587	−0.0189293	−	0.999821i	$-0.506026\pi$
$541$	−0.880571	−0.0378587	−0.0189293	+	0.999821i	$0.506026\pi$
$542$	13.2111i	0.567465i
$543$	− 29.0278i	− 1.24570i
$544$	−3.90833	−0.167568
$545$	0	0
$546$	−10.1194	−0.433072
$547$	40.2389i	1.72049i	0.509881	+	0.860245i	$0.329689\pi$
$547$	40.2389i	1.72049i	−0.509881	+	0.860245i	$0.670311\pi$
$548$	− 18.9083i	− 0.807724i
$549$	7.11943	0.303850
$550$	0	0
$551$	−0.605551	−0.0257974
$552$	3.90833i	0.166349i
$553$	− 3.42221i	− 0.145527i
$554$	14.0000	0.594803
$555$	0	0
$556$	6.69722	0.284026
$557$	− 22.5416i	− 0.955120i	−0.878599	−	0.477560i	$-0.841521\pi$
$557$	− 22.5416i	− 0.955120i	0.878599	−	0.477560i	$-0.158479\pi$
$558$	18.2111i	0.770937i
$559$	−20.8167	−0.880451
$560$	0	0
$561$	−23.4500	−0.990058
$562$	15.1194i	0.637775i
$563$	17.0917i	0.720328i	0.932889	+	0.360164i	$0.117279\pi$
$563$	17.0917i	0.720328i	−0.932889	+	0.360164i	$0.882721\pi$
$564$	0	0
$565$	0	0
$566$	−15.0278	−0.631664
$567$	7.39445i	0.310538i
$568$	0	0
$569$	−39.6333	−1.66151	−0.830757	−	0.556635i	$-0.812092\pi$
$569$	−39.6333	−1.66151	−0.830757	+	0.556635i	$0.812092\pi$
$570$	0	0
$571$	26.1194	1.09306	0.546532	−	0.837438i	$-0.315948\pi$
$571$	26.1194	1.09306	0.546532	+	0.837438i	$0.315948\pi$
$572$	− 16.4222i	− 0.686647i
$573$	36.6333i	1.53038i
$574$	−6.00000	−0.250435
$575$	0	0
$576$	2.30278	0.0959490
$577$	− 38.5139i	− 1.60335i	−0.597758	−	0.801677i	$-0.703941\pi$
$577$	− 38.5139i	− 1.60335i	0.597758	−	0.801677i	$-0.296059\pi$
$578$	1.72498i	0.0717497i
$579$	56.9361	2.36618
$580$	0	0
$581$	−6.00000	−0.248922
$582$	2.51388i	0.104204i
$583$	− 10.1833i	− 0.421751i
$584$	2.51388	0.104025
$585$	0	0
$586$	−25.8167	−1.06648
$587$	0.788897i	0.0325613i	0.999867	+	0.0162806i	$0.00518252\pi$
$587$	0.788897i	0.0325613i	−0.999867	+	0.0162806i	$0.994817\pi$
$588$	− 15.0000i	− 0.618590i
$589$	−4.78890	−0.197323
$590$	0	0
$591$	−9.00000	−0.370211
$592$	− 9.81665i	− 0.403462i
$593$	19.8167i	0.813772i	0.913479	+	0.406886i	$0.133385\pi$
$593$	19.8167i	0.813772i	−0.913479	+	0.406886i	$0.866615\pi$
$594$	−4.18335	−0.171645
$595$	0	0
$596$	19.8167	0.811722
$597$	− 8.78890i	− 0.359706i
$598$	− 10.6972i	− 0.437442i
$599$	−20.0917	−0.820924	−0.410462	−	0.911878i	$-0.634632\pi$
$599$	−20.0917	−0.820924	−0.410462	+	0.911878i	$0.634632\pi$
$600$	0	0
$601$	−37.3944	−1.52535	−0.762676	−	0.646781i	$-0.776115\pi$
$601$	−37.3944	−1.52535	−0.762676	+	0.646781i	$0.776115\pi$
$602$	2.30278i	0.0938541i
$603$	− 21.2111i	− 0.863783i
$604$	−4.60555	−0.187397
$605$	0	0
$606$	29.7250	1.20749
$607$	19.6333i	0.796891i	0.917192	+	0.398446i	$0.130450\pi$
$607$	19.6333i	0.796891i	−0.917192	+	0.398446i	$0.869550\pi$
$608$	0.605551i	0.0245583i
$609$	−1.60555	−0.0650602
$610$	0	0
$611$	0	0
$612$	9.00000i	0.363803i
$613$	− 42.3305i	− 1.70971i	−0.518864	−	0.854857i	$-0.673645\pi$
$613$	− 42.3305i	− 1.70971i	0.518864	−	0.854857i	$-0.326355\pi$
$614$	1.21110	0.0488761
$615$	0	0
$616$	−1.81665	−0.0731951
$617$	− 3.90833i	− 0.157343i	−0.996901	−	0.0786717i	$-0.974932\pi$
$617$	− 3.90833i	− 0.157343i	0.996901	−	0.0786717i	$-0.0250679\pi$
$618$	− 42.4222i	− 1.70647i
$619$	3.21110	0.129065	0.0645326	−	0.997916i	$-0.479444\pi$
$619$	3.21110	0.129065	0.0645326	+	0.997916i	$0.479444\pi$
$620$	0	0
$621$	−2.72498	−0.109350
$622$	24.9083i	0.998733i
$623$	− 10.1833i	− 0.407987i
$624$	−14.5139	−0.581020
$625$	0	0
$626$	−0.422205	−0.0168747
$627$	3.63331i	0.145100i
$628$	− 8.42221i	− 0.336083i
$629$	38.3667	1.52978
$630$	0	0
$631$	−18.8444	−0.750184	−0.375092	−	0.926988i	$-0.622389\pi$
$631$	−18.8444	−0.750184	−0.375092	+	0.926988i	$0.622389\pi$
$632$	− 4.90833i	− 0.195243i
$633$	64.0555i	2.54598i
$634$	−25.0278	−0.993979
$635$	0	0
$636$	−9.00000	−0.356873
$637$	41.0555i	1.62668i
$638$	− 2.60555i	− 0.103155i
$639$	0	0
$640$	0	0
$641$	1.81665	0.0717535	0.0358768	−	0.999356i	$-0.488578\pi$
$641$	1.81665	0.0717535	0.0358768	+	0.999356i	$0.488578\pi$
$642$	19.8167i	0.782101i
$643$	− 18.6056i	− 0.733731i	−0.930274	−	0.366866i	$-0.880431\pi$
$643$	− 18.6056i	− 0.733731i	0.930274	−	0.366866i	$-0.119569\pi$
$644$	−1.18335	−0.0466304
$645$	0	0
$646$	−2.36669	−0.0931163
$647$	− 27.6333i	− 1.08638i	−0.839611	−	0.543189i	$-0.817217\pi$
$647$	− 27.6333i	− 1.08638i	0.839611	−	0.543189i	$-0.182783\pi$
$648$	10.6056i	0.416625i
$649$	2.36669	0.0929008
$650$	0	0
$651$	−12.6972	−0.497643
$652$	21.2111i	0.830691i
$653$	− 31.8167i	− 1.24508i	−0.782587	−	0.622541i	$-0.786100\pi$
$653$	− 31.8167i	− 1.24508i	0.782587	−	0.622541i	$-0.213900\pi$
$654$	−17.0278	−0.665838
$655$	0	0
$656$	−8.60555	−0.335990
$657$	− 5.78890i	− 0.225846i
$658$	0	0
$659$	16.1833	0.630414	0.315207	−	0.949023i	$-0.397926\pi$
$659$	16.1833	0.630414	0.315207	+	0.949023i	$0.397926\pi$
$660$	0	0
$661$	−11.8167	−0.459615	−0.229807	−	0.973236i	$-0.573810\pi$
$661$	−11.8167	−0.459615	−0.229807	+	0.973236i	$0.573810\pi$
$662$	22.6056i	0.878590i
$663$	− 56.7250i	− 2.20302i
$664$	−8.60555	−0.333960
$665$	0	0
$666$	−22.6056	−0.875947
$667$	− 1.69722i	− 0.0657168i
$668$	− 7.30278i	− 0.282553i
$669$	17.3028	0.668964
$670$	0	0
$671$	−8.05551	−0.310980
$672$	1.60555i	0.0619355i
$673$	49.4500i	1.90616i	0.302725	+	0.953078i	$0.402104\pi$
$673$	49.4500i	1.90616i	−0.302725	+	0.953078i	$0.597896\pi$
$674$	−5.30278	−0.204255
$675$	0	0
$676$	26.7250	1.02788
$677$	8.84441i	0.339918i	0.985451	+	0.169959i	$0.0543636\pi$
$677$	8.84441i	0.339918i	−0.985451	+	0.169959i	$0.945636\pi$
$678$	− 23.7250i	− 0.911152i
$679$	−0.761141	−0.0292099
$680$	0	0
$681$	1.81665	0.0696143
$682$	− 20.6056i	− 0.789027i
$683$	41.4500i	1.58604i	0.609196	+	0.793019i	$0.291492\pi$
$683$	41.4500i	1.58604i	−0.609196	+	0.793019i	$0.708508\pi$
$684$	1.39445	0.0533181
$685$	0	0
$686$	9.42221	0.359741
$687$	− 13.6056i	− 0.519084i
$688$	3.30278i	0.125917i
$689$	24.6333	0.938454
$690$	0	0
$691$	−24.0917	−0.916490	−0.458245	−	0.888826i	$-0.651522\pi$
$691$	−24.0917	−0.916490	−0.458245	+	0.888826i	$0.651522\pi$
$692$	− 18.9083i	− 0.718787i
$693$	4.18335i	0.158912i
$694$	13.8167	0.524473
$695$	0	0
$696$	−2.30278	−0.0872865
$697$	− 33.6333i	− 1.27395i
$698$	− 8.00000i	− 0.302804i
$699$	−53.4500	−2.02166
$700$	0	0
$701$	−9.39445	−0.354823	−0.177412	−	0.984137i	$-0.556772\pi$
$701$	−9.39445	−0.354823	−0.177412	+	0.984137i	$0.556772\pi$
$702$	− 10.1194i	− 0.381933i
$703$	− 5.94449i	− 0.224201i
$704$	−2.60555	−0.0982004
$705$	0	0
$706$	−17.2111	−0.647748
$707$	9.00000i	0.338480i
$708$	− 2.09167i	− 0.0786099i
$709$	−21.0278	−0.789714	−0.394857	−	0.918743i	$-0.629206\pi$
$709$	−21.0278	−0.789714	−0.394857	+	0.918743i	$0.629206\pi$
$710$	0	0
$711$	−11.3028	−0.423887
$712$	− 14.6056i	− 0.547366i
$713$	− 13.4222i	− 0.502666i
$714$	−6.27502	−0.234837
$715$	0	0
$716$	0.908327	0.0339458
$717$	− 13.8167i	− 0.515992i
$718$	33.5139i	1.25073i
$719$	−36.2389	−1.35148	−0.675741	−	0.737139i	$-0.736176\pi$
$719$	−36.2389	−1.35148	−0.675741	+	0.737139i	$0.736176\pi$
$720$	0	0
$721$	12.8444	0.478351
$722$	− 18.6333i	− 0.693460i
$723$	0.697224i	0.0259301i
$724$	12.6056	0.468482
$725$	0	0
$726$	9.69722	0.359898
$727$	− 34.6056i	− 1.28345i	−0.766935	−	0.641724i	$-0.778219\pi$
$727$	− 34.6056i	− 1.28345i	0.766935	−	0.641724i	$-0.221781\pi$
$728$	− 4.39445i	− 0.162869i
$729$	13.3305	0.493723
$730$	0	0
$731$	−12.9083	−0.477432
$732$	7.11943i	0.263142i
$733$	− 12.8444i	− 0.474419i	−0.971459	−	0.237210i	$-0.923767\pi$
$733$	− 12.8444i	− 0.474419i	0.971459	−	0.237210i	$-0.0762328\pi$
$734$	−24.6056	−0.908207
$735$	0	0
$736$	−1.69722	−0.0625605
$737$	24.0000i	0.884051i
$738$	19.8167i	0.729461i
$739$	−13.2111	−0.485978	−0.242989	−	0.970029i	$-0.578128\pi$
$739$	−13.2111	−0.485978	−0.242989	+	0.970029i	$0.578128\pi$
$740$	0	0
$741$	−8.78890	−0.322868
$742$	− 2.72498i	− 0.100037i
$743$	41.2111i	1.51189i	0.654636	+	0.755944i	$0.272822\pi$
$743$	41.2111i	1.51189i	−0.654636	+	0.755944i	$0.727178\pi$
$744$	−18.2111	−0.667651
$745$	0	0
$746$	31.9083	1.16825
$747$	19.8167i	0.725053i
$748$	− 10.1833i	− 0.372340i
$749$	−6.00000	−0.219235
$750$	0	0
$751$	40.8444	1.49043	0.745217	−	0.666822i	$-0.232346\pi$
$751$	40.8444	1.49043	0.745217	+	0.666822i	$0.232346\pi$
$752$	0	0
$753$	− 19.8167i	− 0.722159i
$754$	6.30278	0.229534
$755$	0	0
$756$	−1.11943	−0.0407133
$757$	21.4500i	0.779612i	0.920897	+	0.389806i	$0.127458\pi$
$757$	21.4500i	0.779612i	−0.920897	+	0.389806i	$0.872542\pi$
$758$	30.6056i	1.11164i
$759$	−10.1833	−0.369632
$760$	0	0
$761$	33.3583	1.20924	0.604619	−	0.796515i	$-0.293326\pi$
$761$	33.3583	1.20924	0.604619	+	0.796515i	$0.293326\pi$
$762$	46.0555i	1.66842i
$763$	− 5.15559i	− 0.186645i
$764$	−15.9083	−0.575543
$765$	0	0
$766$	−4.69722	−0.169718
$767$	5.72498i	0.206717i
$768$	2.30278i	0.0830943i
$769$	−45.0278	−1.62374	−0.811871	−	0.583837i	$-0.801551\pi$
$769$	−45.0278	−1.62374	−0.811871	+	0.583837i	$0.801551\pi$
$770$	0	0
$771$	16.1833	0.582829
$772$	24.7250i	0.889872i
$773$	− 40.4222i	− 1.45389i	−0.686698	−	0.726943i	$-0.740941\pi$
$773$	− 40.4222i	− 1.45389i	0.686698	−	0.726943i	$-0.259059\pi$
$774$	7.60555	0.273376
$775$	0	0
$776$	−1.09167	−0.0391888
$777$	− 15.7611i	− 0.565428i
$778$	18.0000i	0.645331i
$779$	−5.21110	−0.186707
$780$	0	0
$781$	0	0
$782$	− 6.63331i	− 0.237207i
$783$	− 1.60555i	− 0.0573777i
$784$	6.51388	0.232639
$785$	0	0
$786$	−49.8167	−1.77690
$787$	− 27.0278i	− 0.963435i	−0.876326	−	0.481718i	$-0.840013\pi$
$787$	− 27.0278i	− 0.963435i	0.876326	−	0.481718i	$-0.159987\pi$
$788$	− 3.90833i	− 0.139228i
$789$	−12.0000	−0.427211
$790$	0	0
$791$	7.18335	0.255410
$792$	6.00000i	0.213201i
$793$	− 19.4861i	− 0.691972i
$794$	11.9083	0.422611
$795$	0	0
$796$	3.81665	0.135278
$797$	31.2666i	1.10752i	0.832676	+	0.553760i	$0.186808\pi$
$797$	31.2666i	1.10752i	−0.832676	+	0.553760i	$0.813192\pi$
$798$	0.972244i	0.0344171i
$799$	0	0
$800$	0	0
$801$	−33.6333	−1.18837
$802$	28.3028i	0.999406i
$803$	6.55004i	0.231146i
$804$	21.2111	0.748058
$805$	0	0
$806$	49.8444	1.75569
$807$	28.8167i	1.01439i
$808$	12.9083i	0.454113i
$809$	26.0555	0.916063	0.458032	−	0.888936i	$-0.348555\pi$
$809$	26.0555	0.916063	0.458032	+	0.888936i	$0.348555\pi$
$810$	0	0
$811$	24.9361	0.875624	0.437812	−	0.899066i	$-0.355753\pi$
$811$	24.9361	0.875624	0.437812	+	0.899066i	$0.355753\pi$
$812$	− 0.697224i	− 0.0244678i
$813$	30.4222i	1.06695i
$814$	25.5778	0.896501
$815$	0	0
$816$	−9.00000	−0.315063
$817$	2.00000i	0.0699711i
$818$	9.21110i	0.322059i
$819$	−10.1194	−0.353601
$820$	0	0
$821$	−54.2389	−1.89295	−0.946475	−	0.322778i	$-0.895383\pi$
$821$	−54.2389	−1.89295	−0.946475	+	0.322778i	$0.895383\pi$
$822$	− 43.5416i	− 1.51869i
$823$	− 37.6333i	− 1.31181i	−0.754841	−	0.655907i	$-0.772286\pi$
$823$	− 37.6333i	− 1.31181i	0.754841	−	0.655907i	$-0.227714\pi$
$824$	18.4222	0.641768
$825$	0	0
$826$	0.633308	0.0220356
$827$	8.88057i	0.308808i	0.988008	+	0.154404i	$0.0493457\pi$
$827$	8.88057i	0.308808i	−0.988008	+	0.154404i	$0.950654\pi$
$828$	3.90833i	0.135824i
$829$	−50.7527	−1.76272	−0.881358	−	0.472450i	$-0.843370\pi$
$829$	−50.7527	−1.76272	−0.881358	+	0.472450i	$0.843370\pi$
$830$	0	0
$831$	32.2389	1.11835
$832$	− 6.30278i	− 0.218509i
$833$	25.4584i	0.882080i
$834$	15.4222	0.534027
$835$	0	0
$836$	−1.57779	−0.0545692
$837$	− 12.6972i	− 0.438880i
$838$	9.11943i	0.315025i
$839$	29.2111	1.00848	0.504240	−	0.863564i	$-0.331773\pi$
$839$	29.2111	1.00848	0.504240	+	0.863564i	$0.331773\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	− 25.6333i	− 0.883382i
$843$	34.8167i	1.19915i
$844$	−27.8167	−0.957489
$845$	0	0
$846$	0	0
$847$	2.93608i	0.100885i
$848$	− 3.90833i	− 0.134212i
$849$	−34.6056	−1.18766
$850$	0	0
$851$	16.6611	0.571134
$852$	0	0
$853$	− 28.2389i	− 0.966880i	−0.875377	−	0.483440i	$-0.839387\pi$
$853$	− 28.2389i	− 0.966880i	0.875377	−	0.483440i	$-0.160613\pi$
$854$	−2.15559	−0.0737628
$855$	0	0
$856$	−8.60555	−0.294132
$857$	30.2389i	1.03294i	0.856305	+	0.516470i	$0.172754\pi$
$857$	30.2389i	1.03294i	−0.856305	+	0.516470i	$0.827246\pi$
$858$	− 37.8167i	− 1.29104i
$859$	−28.6056	−0.976009	−0.488004	−	0.872841i	$-0.662275\pi$
$859$	−28.6056	−0.976009	−0.488004	+	0.872841i	$0.662275\pi$
$860$	0	0
$861$	−13.8167	−0.470870
$862$	12.2389i	0.416857i
$863$	5.09167i	0.173323i	0.996238	+	0.0866613i	$0.0276198\pi$
$863$	5.09167i	0.173323i	−0.996238	+	0.0866613i	$0.972380\pi$
$864$	−1.60555	−0.0546220
$865$	0	0
$866$	15.2111	0.516894
$867$	3.97224i	0.134904i
$868$	− 5.51388i	− 0.187153i
$869$	12.7889	0.433834
$870$	0	0
$871$	−58.0555	−1.96714
$872$	− 7.39445i	− 0.250408i
$873$	2.51388i	0.0850819i
$874$	−1.02776	−0.0347644
$875$	0	0
$876$	5.78890	0.195589
$877$	− 33.6972i	− 1.13787i	−0.822381	−	0.568937i	$-0.807355\pi$
$877$	− 33.6972i	− 1.13787i	0.822381	−	0.568937i	$-0.192645\pi$
$878$	37.6333i	1.27006i
$879$	−59.4500	−2.00520
$880$	0	0
$881$	−31.0278	−1.04535	−0.522676	−	0.852532i	$-0.675066\pi$
$881$	−31.0278	−1.04535	−0.522676	+	0.852532i	$0.675066\pi$
$882$	− 15.0000i	− 0.505076i
$883$	11.3944i	0.383454i	0.981448	+	0.191727i	$0.0614088\pi$
$883$	11.3944i	0.383454i	−0.981448	+	0.191727i	$0.938591\pi$
$884$	24.6333	0.828508
$885$	0	0
$886$	−27.7527	−0.932371
$887$	− 51.6333i	− 1.73368i	−0.498589	−	0.866838i	$-0.666148\pi$
$887$	− 51.6333i	− 1.73368i	0.498589	−	0.866838i	$-0.333852\pi$
$888$	− 22.6056i	− 0.758593i
$889$	−13.9445	−0.467683
$890$	0	0
$891$	−27.6333	−0.925751
$892$	7.51388i	0.251583i
$893$	0	0
$894$	45.6333	1.52621
$895$	0	0
$896$	−0.697224	−0.0232926
$897$	− 24.6333i	− 0.822482i
$898$	15.3944i	0.513719i
$899$	7.90833	0.263757
$900$	0	0
$901$	15.2750	0.508885
$902$	− 22.4222i	− 0.746578i
$903$	5.30278i	0.176465i
$904$	10.3028	0.342665
$905$	0	0
$906$	−10.6056	−0.352346
$907$	− 36.6972i	− 1.21851i	−0.792974	−	0.609256i	$-0.791468\pi$
$907$	− 36.6972i	− 1.21851i	0.792974	−	0.609256i	$-0.208532\pi$
$908$	0.788897i	0.0261805i
$909$	29.7250	0.985915
$910$	0	0
$911$	57.7527	1.91343	0.956717	−	0.291021i	$-0.0939948\pi$
$911$	57.7527	1.91343	0.956717	+	0.291021i	$0.0939948\pi$
$912$	1.39445i	0.0461748i
$913$	− 22.4222i	− 0.742067i
$914$	−10.0000	−0.330771
$915$	0	0
$916$	5.90833	0.195217
$917$	− 15.0833i	− 0.498093i
$918$	− 6.27502i	− 0.207106i
$919$	−35.6333	−1.17543	−0.587717	−	0.809066i	$-0.699973\pi$
$919$	−35.6333	−1.17543	−0.587717	+	0.809066i	$0.699973\pi$
$920$	0	0
$921$	2.78890	0.0918973
$922$	25.5416i	0.841169i
$923$	0	0
$924$	−4.18335	−0.137622
$925$	0	0
$926$	−40.8444	−1.34223
$927$	− 42.4222i	− 1.39333i
$928$	− 1.00000i	− 0.0328266i
$929$	16.6972	0.547818	0.273909	−	0.961756i	$-0.411683\pi$
$929$	16.6972	0.547818	0.273909	+	0.961756i	$0.411683\pi$
$930$	0	0
$931$	3.94449	0.129275
$932$	− 23.2111i	− 0.760305i
$933$	57.3583i	1.87783i
$934$	−37.5416	−1.22840
$935$	0	0
$936$	−14.5139	−0.474401
$937$	14.1833i	0.463350i	0.972793	+	0.231675i	$0.0744205\pi$
$937$	14.1833i	0.463350i	−0.972793	+	0.231675i	$0.925579\pi$
$938$	6.42221i	0.209692i
$939$	−0.972244	−0.0317280
$940$	0	0
$941$	8.36669	0.272746	0.136373	−	0.990658i	$-0.456455\pi$
$941$	8.36669	0.272746	0.136373	+	0.990658i	$0.456455\pi$
$942$	− 19.3944i	− 0.631905i
$943$	− 14.6056i	− 0.475622i
$944$	0.908327	0.0295635
$945$	0	0
$946$	−8.60555	−0.279791
$947$	− 43.1472i	− 1.40210i	−0.713115	−	0.701048i	$-0.752716\pi$
$947$	− 43.1472i	− 1.40210i	0.713115	−	0.701048i	$-0.247284\pi$
$948$	− 11.3028i	− 0.367097i
$949$	−15.8444	−0.514331
$950$	0	0
$951$	−57.6333	−1.86889
$952$	− 2.72498i	− 0.0883171i
$953$	− 28.4222i	− 0.920686i	−0.887741	−	0.460343i	$-0.847727\pi$
$953$	− 28.4222i	− 0.920686i	0.887741	−	0.460343i	$-0.152273\pi$
$954$	−9.00000	−0.291386
$955$	0	0
$956$	6.00000	0.194054
$957$	− 6.00000i	− 0.193952i
$958$	11.7250i	0.378817i
$959$	13.1833	0.425712
$960$	0	0
$961$	31.5416	1.01747
$962$	61.8722i	1.99484i
$963$	19.8167i	0.638583i
$964$	−0.302776	−0.00975175
$965$	0	0
$966$	−2.72498	−0.0876748
$967$	− 48.6611i	− 1.56483i	−0.622755	−	0.782417i	$-0.713987\pi$
$967$	− 48.6611i	− 1.56483i	0.622755	−	0.782417i	$-0.286013\pi$
$968$	4.21110i	0.135350i
$969$	−5.44996	−0.175078
$970$	0	0
$971$	−25.8167	−0.828496	−0.414248	−	0.910164i	$-0.635955\pi$
$971$	−25.8167	−0.828496	−0.414248	+	0.910164i	$0.635955\pi$
$972$	19.6056i	0.628848i
$973$	4.66947i	0.149696i
$974$	33.9361	1.08738
$975$	0	0
$976$	−3.09167	−0.0989620
$977$	31.8167i	1.01790i	0.860795	+	0.508952i	$0.169967\pi$
$977$	31.8167i	1.01790i	−0.860795	+	0.508952i	$0.830033\pi$
$978$	48.8444i	1.56187i
$979$	38.0555	1.21626
$980$	0	0
$981$	−17.0278	−0.543654
$982$	− 3.63331i	− 0.115944i
$983$	− 56.0555i	− 1.78789i	−0.448173	−	0.893947i	$-0.647925\pi$
$983$	− 56.0555i	− 1.78789i	0.448173	−	0.893947i	$-0.352075\pi$
$984$	−19.8167	−0.631732
$985$	0	0
$986$	3.90833	0.124466
$987$	0	0
$988$	− 3.81665i	− 0.121424i
$989$	−5.60555	−0.178246
$990$	0	0
$991$	34.6056	1.09928	0.549641	−	0.835401i	$-0.314765\pi$
$991$	34.6056	1.09928	0.549641	+	0.835401i	$0.314765\pi$
$992$	− 7.90833i	− 0.251090i
$993$	52.0555i	1.65193i
$994$	0	0
$995$	0	0
$996$	−19.8167	−0.627915
$997$	− 60.6611i	− 1.92116i	−0.278012	−	0.960578i	$-0.589676\pi$
$997$	− 60.6611i	− 1.92116i	0.278012	−	0.960578i	$-0.410324\pi$
$998$	18.7250i	0.592729i
$999$	15.7611	0.498660

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.b.g.349.4		4
5.2	odd	4		290.2.a.b.1.2	✓	2
5.3	odd	4		1450.2.a.m.1.1		2
5.4	even	2	inner	1450.2.b.g.349.1		4
15.2	even	4		2610.2.a.v.1.1		2
20.7	even	4		2320.2.a.i.1.1		2
40.27	even	4		9280.2.a.bc.1.2		2
40.37	odd	4		9280.2.a.z.1.1		2
145.57	odd	4		8410.2.a.r.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.a.b.1.2	✓	2	5.2	odd	4
1450.2.a.m.1.1		2	5.3	odd	4
1450.2.b.g.349.1		4	5.4	even	2	inner
1450.2.b.g.349.4		4	1.1	even	1	trivial
2320.2.a.i.1.1		2	20.7	even	4
2610.2.a.v.1.1		2	15.2	even	4
8410.2.a.r.1.1		2	145.57	odd	4
9280.2.a.z.1.1		2	40.37	odd	4
9280.2.a.bc.1.2		2	40.27	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:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +2.30278i q^{3} -1.00000 q^{4} -2.30278 q^{6} -0.697224i q^{7} -1.00000i q^{8} -2.30278 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +2.30278i q^{3} -1.00000 q^{4} -2.30278 q^{6} -0.697224i q^{7} -1.00000i q^{8} -2.30278 q^{9} +2.60555 q^{11} -2.30278i q^{12} +6.30278i q^{13} +0.697224 q^{14} +1.00000 q^{16} +3.90833i q^{17} -2.30278i q^{18} +0.605551 q^{19} +1.60555 q^{21} +2.60555i q^{22} +1.69722i q^{23} +2.30278 q^{24} -6.30278 q^{26} +1.60555i q^{27} +0.697224i q^{28} -1.00000 q^{29} -7.90833 q^{31} +1.00000i q^{32} +6.00000i q^{33} -3.90833 q^{34} +2.30278 q^{36} -9.81665i q^{37} +0.605551i q^{38} -14.5139 q^{39} -8.60555 q^{41} +1.60555i q^{42} +3.30278i q^{43} -2.60555 q^{44} -1.69722 q^{46} +2.30278i q^{48} +6.51388 q^{49} -9.00000 q^{51} -6.30278i q^{52} -3.90833i q^{53} -1.60555 q^{54} -0.697224 q^{56} +1.39445i q^{57} -1.00000i q^{58} +0.908327 q^{59} -3.09167 q^{61} -7.90833i q^{62} +1.60555i q^{63} -1.00000 q^{64} -6.00000 q^{66} +9.21110i q^{67} -3.90833i q^{68} -3.90833 q^{69} +2.30278i q^{72} +2.51388i q^{73} +9.81665 q^{74} -0.605551 q^{76} -1.81665i q^{77} -14.5139i q^{78} +4.90833 q^{79} -10.6056 q^{81} -8.60555i q^{82} -8.60555i q^{83} -1.60555 q^{84} -3.30278 q^{86} -2.30278i q^{87} -2.60555i q^{88} +14.6056 q^{89} +4.39445 q^{91} -1.69722i q^{92} -18.2111i q^{93} -2.30278 q^{96} -1.09167i q^{97} +6.51388i q^{98} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 - 2 * q^6 - 2 * q^9	\( 4 q - 4 q^{4} - 2 q^{6} - 2 q^{9} - 4 q^{11} + 10 q^{14} + 4 q^{16} - 12 q^{19} - 8 q^{21} + 2 q^{24} - 18 q^{26} - 4 q^{29} - 10 q^{31} + 6 q^{34} + 2 q^{36} - 22 q^{39} - 20 q^{41} + 4 q^{44} - 14 q^{46} - 10 q^{49} - 36 q^{51} + 8 q^{54} - 10 q^{56} - 18 q^{59} - 34 q^{61} - 4 q^{64} - 24 q^{66} + 6 q^{69} - 4 q^{74} + 12 q^{76} - 2 q^{79} - 28 q^{81} + 8 q^{84} - 6 q^{86} + 44 q^{89} + 32 q^{91} - 2 q^{96} - 24 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 - 2 * q^6 - 2 * q^9 - 4 * q^11 + 10 * q^14 + 4 * q^16 - 12 * q^19 - 8 * q^21 + 2 * q^24 - 18 * q^26 - 4 * q^29 - 10 * q^31 + 6 * q^34 + 2 * q^36 - 22 * q^39 - 20 * q^41 + 4 * q^44 - 14 * q^46 - 10 * q^49 - 36 * q^51 + 8 * q^54 - 10 * q^56 - 18 * q^59 - 34 * q^61 - 4 * q^64 - 24 * q^66 + 6 * q^69 - 4 * q^74 + 12 * q^76 - 2 * q^79 - 28 * q^81 + 8 * q^84 - 6 * q^86 + 44 * q^89 + 32 * q^91 - 2 * q^96 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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