LMFDB - Embedded newform 650.2.b.c.599.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(599,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, 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("650.599");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			599.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	650.599
Dual form			650.2.b.c.599.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +4.00000i q^{7} +1.00000i q^{8} +2.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +4.00000i q^{7} +1.00000i q^{8} +2.00000 q^{9} +1.00000 q^{11} +1.00000i q^{12} -1.00000i q^{13} +4.00000 q^{14} +1.00000 q^{16} +7.00000i q^{17} -2.00000i q^{18} +3.00000 q^{19} +4.00000 q^{21} -1.00000i q^{22} +1.00000 q^{24} -1.00000 q^{26} -5.00000i q^{27} -4.00000i q^{28} +4.00000 q^{29} +6.00000 q^{31} -1.00000i q^{32} -1.00000i q^{33} +7.00000 q^{34} -2.00000 q^{36} +8.00000i q^{37} -3.00000i q^{38} -1.00000 q^{39} -5.00000 q^{41} -4.00000i q^{42} -4.00000i q^{43} -1.00000 q^{44} -12.0000i q^{47} -1.00000i q^{48} -9.00000 q^{49} +7.00000 q^{51} +1.00000i q^{52} -10.0000i q^{53} -5.00000 q^{54} -4.00000 q^{56} -3.00000i q^{57} -4.00000i q^{58} -4.00000 q^{59} +8.00000 q^{61} -6.00000i q^{62} +8.00000i q^{63} -1.00000 q^{64} -1.00000 q^{66} +9.00000i q^{67} -7.00000i q^{68} -8.00000 q^{71} +2.00000i q^{72} +13.0000i q^{73} +8.00000 q^{74} -3.00000 q^{76} +4.00000i q^{77} +1.00000i q^{78} -8.00000 q^{79} +1.00000 q^{81} +5.00000i q^{82} +3.00000i q^{83} -4.00000 q^{84} -4.00000 q^{86} -4.00000i q^{87} +1.00000i q^{88} +11.0000 q^{89} +4.00000 q^{91} -6.00000i q^{93} -12.0000 q^{94} -1.00000 q^{96} +10.0000i q^{97} +9.00000i q^{98} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} - 2 q^{6} + 4 q^{9}+O(q^{10}) $ 2 * q - 2 * q^4 - 2 * q^6 + 4 * q^9	$ 2 q - 2 q^{4} - 2 q^{6} + 4 q^{9} + 2 q^{11} + 8 q^{14} + 2 q^{16} + 6 q^{19} + 8 q^{21} + 2 q^{24} - 2 q^{26} + 8 q^{29} + 12 q^{31} + 14 q^{34} - 4 q^{36} - 2 q^{39} - 10 q^{41} - 2 q^{44} - 18 q^{49} + 14 q^{51} - 10 q^{54} - 8 q^{56} - 8 q^{59} + 16 q^{61} - 2 q^{64} - 2 q^{66} - 16 q^{71} + 16 q^{74} - 6 q^{76} - 16 q^{79} + 2 q^{81} - 8 q^{84} - 8 q^{86} + 22 q^{89} + 8 q^{91} - 24 q^{94} - 2 q^{96} + 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 - 2 * q^6 + 4 * q^9 + 2 * q^11 + 8 * q^14 + 2 * q^16 + 6 * q^19 + 8 * q^21 + 2 * q^24 - 2 * q^26 + 8 * q^29 + 12 * q^31 + 14 * q^34 - 4 * q^36 - 2 * q^39 - 10 * q^41 - 2 * q^44 - 18 * q^49 + 14 * q^51 - 10 * q^54 - 8 * q^56 - 8 * q^59 + 16 * q^61 - 2 * q^64 - 2 * q^66 - 16 * q^71 + 16 * q^74 - 6 * q^76 - 16 * q^79 + 2 * q^81 - 8 * q^84 - 8 * q^86 + 22 * q^89 + 8 * q^91 - 24 * q^94 - 2 * q^96 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$1$

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
$3$	− 1.00000i	− 0.577350i	−0.957427	−	0.288675i	$-0.906785\pi$
$3$	− 1.00000i	− 0.577350i	0.957427	−	0.288675i	$-0.0932147\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	4.00000i	1.51186i	0.654654	+	0.755929i	$0.272814\pi$
$7$	4.00000i	1.51186i	−0.654654	+	0.755929i	$0.727186\pi$
$8$	1.00000i	0.353553i
$9$	2.00000	0.666667
$10$	0	0
$11$	1.00000	0.301511	0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000	0.301511	0.150756	+	0.988571i	$0.451829\pi$
$12$	1.00000i	0.288675i
$13$	− 1.00000i	− 0.277350i
$13$	− 1.00000i	− 0.277350i
$14$	4.00000	1.06904
$15$	0	0
$16$	1.00000	0.250000
$17$	7.00000i	1.69775i	0.528594	+	0.848875i	$0.322719\pi$
$17$	7.00000i	1.69775i	−0.528594	+	0.848875i	$0.677281\pi$
$18$	− 2.00000i	− 0.471405i
$19$	3.00000	0.688247	0.344124	−	0.938924i	$-0.388176\pi$
$19$	3.00000	0.688247	0.344124	+	0.938924i	$0.388176\pi$
$20$	0	0
$21$	4.00000	0.872872
$22$	− 1.00000i	− 0.213201i
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	−1.00000	−0.196116
$27$	− 5.00000i	− 0.962250i
$28$	− 4.00000i	− 0.755929i
$29$	4.00000	0.742781	0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000	0.742781	0.371391	+	0.928477i	$0.378881\pi$
$30$	0	0
$31$	6.00000	1.07763	0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000	1.07763	0.538816	+	0.842424i	$0.318872\pi$
$32$	− 1.00000i	− 0.176777i
$33$	− 1.00000i	− 0.174078i
$34$	7.00000	1.20049
$35$	0	0
$36$	−2.00000	−0.333333
$37$	8.00000i	1.31519i	0.753371	+	0.657596i	$0.228427\pi$
$37$	8.00000i	1.31519i	−0.753371	+	0.657596i	$0.771573\pi$
$38$	− 3.00000i	− 0.486664i
$39$	−1.00000	−0.160128
$40$	0	0
$41$	−5.00000	−0.780869	−0.390434	−	0.920631i	$-0.627675\pi$
$41$	−5.00000	−0.780869	−0.390434	+	0.920631i	$0.627675\pi$
$42$	− 4.00000i	− 0.617213i
$43$	− 4.00000i	− 0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$	− 4.00000i	− 0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	0	0
$47$	− 12.0000i	− 1.75038i	−0.483779	−	0.875190i	$-0.660736\pi$
$47$	− 12.0000i	− 1.75038i	0.483779	−	0.875190i	$-0.339264\pi$
$48$	− 1.00000i	− 0.144338i
$49$	−9.00000	−1.28571
$50$	0	0
$51$	7.00000	0.980196
$52$	1.00000i	0.138675i
$53$	− 10.0000i	− 1.37361i	−0.726844	−	0.686803i	$-0.759014\pi$
$53$	− 10.0000i	− 1.37361i	0.726844	−	0.686803i	$-0.240986\pi$
$54$	−5.00000	−0.680414
$55$	0	0
$56$	−4.00000	−0.534522
$57$	− 3.00000i	− 0.397360i
$58$	− 4.00000i	− 0.525226i
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	0	0
$61$	8.00000	1.02430	0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000	1.02430	0.512148	+	0.858898i	$0.328850\pi$
$62$	− 6.00000i	− 0.762001i
$63$	8.00000i	1.00791i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−1.00000	−0.123091
$67$	9.00000i	1.09952i	0.835321	+	0.549762i	$0.185282\pi$
$67$	9.00000i	1.09952i	−0.835321	+	0.549762i	$0.814718\pi$
$68$	− 7.00000i	− 0.848875i
$69$	0	0
$70$	0	0
$71$	−8.00000	−0.949425	−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000	−0.949425	−0.474713	+	0.880141i	$0.657448\pi$
$72$	2.00000i	0.235702i
$73$	13.0000i	1.52153i	0.649025	+	0.760767i	$0.275177\pi$
$73$	13.0000i	1.52153i	−0.649025	+	0.760767i	$0.724823\pi$
$74$	8.00000	0.929981
$75$	0	0
$76$	−3.00000	−0.344124
$77$	4.00000i	0.455842i
$78$	1.00000i	0.113228i
$79$	−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
$81$	1.00000	0.111111
$82$	5.00000i	0.552158i
$83$	3.00000i	0.329293i	0.986353	+	0.164646i	$0.0526483\pi$
$83$	3.00000i	0.329293i	−0.986353	+	0.164646i	$0.947352\pi$
$84$	−4.00000	−0.436436
$85$	0	0
$86$	−4.00000	−0.431331
$87$	− 4.00000i	− 0.428845i
$88$	1.00000i	0.106600i
$89$	11.0000	1.16600	0.582999	−	0.812473i	$-0.301879\pi$
$89$	11.0000	1.16600	0.582999	+	0.812473i	$0.301879\pi$
$90$	0	0
$91$	4.00000	0.419314
$92$	0	0
$93$	− 6.00000i	− 0.622171i
$94$	−12.0000	−1.23771
$95$	0	0
$96$	−1.00000	−0.102062
$97$	10.0000i	1.01535i	0.861550	+	0.507673i	$0.169494\pi$
$97$	10.0000i	1.01535i	−0.861550	+	0.507673i	$0.830506\pi$
$98$	9.00000i	0.909137i
$99$	2.00000	0.201008
$100$	0	0
$101$	8.00000	0.796030	0.398015	−	0.917379i	$-0.369699\pi$
$101$	8.00000	0.796030	0.398015	+	0.917379i	$0.369699\pi$
$102$	− 7.00000i	− 0.693103i
$103$	− 6.00000i	− 0.591198i	−0.955312	−	0.295599i	$-0.904481\pi$
$103$	− 6.00000i	− 0.591198i	0.955312	−	0.295599i	$-0.0955191\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	−10.0000	−0.971286
$107$	− 3.00000i	− 0.290021i	−0.989430	−	0.145010i	$-0.953678\pi$
$107$	− 3.00000i	− 0.290021i	0.989430	−	0.145010i	$-0.0463216\pi$
$108$	5.00000i	0.481125i
$109$	12.0000	1.14939	0.574696	−	0.818367i	$-0.305120\pi$
$109$	12.0000	1.14939	0.574696	+	0.818367i	$0.305120\pi$
$110$	0	0
$111$	8.00000	0.759326
$112$	4.00000i	0.377964i
$113$	11.0000i	1.03479i	0.855746	+	0.517396i	$0.173099\pi$
$113$	11.0000i	1.03479i	−0.855746	+	0.517396i	$0.826901\pi$
$114$	−3.00000	−0.280976
$115$	0	0
$116$	−4.00000	−0.371391
$117$	− 2.00000i	− 0.184900i
$118$	4.00000i	0.368230i
$119$	−28.0000	−2.56676
$120$	0	0
$121$	−10.0000	−0.909091
$122$	− 8.00000i	− 0.724286i
$123$	5.00000i	0.450835i
$124$	−6.00000	−0.538816
$125$	0	0
$126$	8.00000	0.712697
$127$	− 10.0000i	− 0.887357i	−0.896186	−	0.443678i	$-0.853673\pi$
$127$	− 10.0000i	− 0.887357i	0.896186	−	0.443678i	$-0.146327\pi$
$128$	1.00000i	0.0883883i
$129$	−4.00000	−0.352180
$130$	0	0
$131$	4.00000	0.349482	0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000	0.349482	0.174741	+	0.984614i	$0.444091\pi$
$132$	1.00000i	0.0870388i
$133$	12.0000i	1.04053i
$134$	9.00000	0.777482
$135$	0	0
$136$	−7.00000	−0.600245
$137$	− 15.0000i	− 1.28154i	−0.767734	−	0.640768i	$-0.778616\pi$
$137$	− 15.0000i	− 1.28154i	0.767734	−	0.640768i	$-0.221384\pi$
$138$	0	0
$139$	−7.00000	−0.593732	−0.296866	−	0.954919i	$-0.595942\pi$
$139$	−7.00000	−0.593732	−0.296866	+	0.954919i	$0.595942\pi$
$140$	0	0
$141$	−12.0000	−1.01058
$142$	8.00000i	0.671345i
$143$	− 1.00000i	− 0.0836242i
$144$	2.00000	0.166667
$145$	0	0
$146$	13.0000	1.07589
$147$	9.00000i	0.742307i
$148$	− 8.00000i	− 0.657596i
$149$	16.0000	1.31077	0.655386	−	0.755295i	$-0.272506\pi$
$149$	16.0000	1.31077	0.655386	+	0.755295i	$0.272506\pi$
$150$	0	0
$151$	−18.0000	−1.46482	−0.732410	−	0.680864i	$-0.761604\pi$
$151$	−18.0000	−1.46482	−0.732410	+	0.680864i	$0.761604\pi$
$152$	3.00000i	0.243332i
$153$	14.0000i	1.13183i
$154$	4.00000	0.322329
$155$	0	0
$156$	1.00000	0.0800641
$157$	− 16.0000i	− 1.27694i	−0.769647	−	0.638470i	$-0.779568\pi$
$157$	− 16.0000i	− 1.27694i	0.769647	−	0.638470i	$-0.220432\pi$
$158$	8.00000i	0.636446i
$159$	−10.0000	−0.793052
$160$	0	0
$161$	0	0
$162$	− 1.00000i	− 0.0785674i
$163$	11.0000i	0.861586i	0.902451	+	0.430793i	$0.141766\pi$
$163$	11.0000i	0.861586i	−0.902451	+	0.430793i	$0.858234\pi$
$164$	5.00000	0.390434
$165$	0	0
$166$	3.00000	0.232845
$167$	10.0000i	0.773823i	0.922117	+	0.386912i	$0.126458\pi$
$167$	10.0000i	0.773823i	−0.922117	+	0.386912i	$0.873542\pi$
$168$	4.00000i	0.308607i
$169$	−1.00000	−0.0769231
$170$	0	0
$171$	6.00000	0.458831
$172$	4.00000i	0.304997i
$173$	10.0000i	0.760286i	0.924928	+	0.380143i	$0.124125\pi$
$173$	10.0000i	0.760286i	−0.924928	+	0.380143i	$0.875875\pi$
$174$	−4.00000	−0.303239
$175$	0	0
$176$	1.00000	0.0753778
$177$	4.00000i	0.300658i
$178$	− 11.0000i	− 0.824485i
$179$	−23.0000	−1.71910	−0.859550	−	0.511051i	$-0.829256\pi$
$179$	−23.0000	−1.71910	−0.859550	+	0.511051i	$0.829256\pi$
$180$	0	0
$181$	−20.0000	−1.48659	−0.743294	−	0.668965i	$-0.766738\pi$
$181$	−20.0000	−1.48659	−0.743294	+	0.668965i	$0.766738\pi$
$182$	− 4.00000i	− 0.296500i
$183$	− 8.00000i	− 0.591377i
$184$	0	0
$185$	0	0
$186$	−6.00000	−0.439941
$187$	7.00000i	0.511891i
$188$	12.0000i	0.875190i
$189$	20.0000	1.45479
$190$	0	0
$191$	−18.0000	−1.30243	−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000	−1.30243	−0.651217	+	0.758891i	$0.725741\pi$
$192$	1.00000i	0.0721688i
$193$	− 1.00000i	− 0.0719816i	−0.999352	−	0.0359908i	$-0.988541\pi$
$193$	− 1.00000i	− 0.0719816i	0.999352	−	0.0359908i	$-0.0114587\pi$
$194$	10.0000	0.717958
$195$	0	0
$196$	9.00000	0.642857
$197$	− 12.0000i	− 0.854965i	−0.904024	−	0.427482i	$-0.859401\pi$
$197$	− 12.0000i	− 0.854965i	0.904024	−	0.427482i	$-0.140599\pi$
$198$	− 2.00000i	− 0.142134i
$199$	18.0000	1.27599	0.637993	−	0.770042i	$-0.279765\pi$
$199$	18.0000	1.27599	0.637993	+	0.770042i	$0.279765\pi$
$200$	0	0
$201$	9.00000	0.634811
$202$	− 8.00000i	− 0.562878i
$203$	16.0000i	1.12298i
$204$	−7.00000	−0.490098
$205$	0	0
$206$	−6.00000	−0.418040
$207$	0	0
$208$	− 1.00000i	− 0.0693375i
$209$	3.00000	0.207514
$210$	0	0
$211$	−23.0000	−1.58339	−0.791693	−	0.610920i	$-0.790800\pi$
$211$	−23.0000	−1.58339	−0.791693	+	0.610920i	$0.790800\pi$
$212$	10.0000i	0.686803i
$213$	8.00000i	0.548151i
$214$	−3.00000	−0.205076
$215$	0	0
$216$	5.00000	0.340207
$217$	24.0000i	1.62923i
$218$	− 12.0000i	− 0.812743i
$219$	13.0000	0.878459
$220$	0	0
$221$	7.00000	0.470871
$222$	− 8.00000i	− 0.536925i
$223$	− 26.0000i	− 1.74109i	−0.492090	−	0.870544i	$-0.663767\pi$
$223$	− 26.0000i	− 1.74109i	0.492090	−	0.870544i	$-0.336233\pi$
$224$	4.00000	0.267261
$225$	0	0
$226$	11.0000	0.731709
$227$	− 20.0000i	− 1.32745i	−0.747978	−	0.663723i	$-0.768975\pi$
$227$	− 20.0000i	− 1.32745i	0.747978	−	0.663723i	$-0.231025\pi$
$228$	3.00000i	0.198680i
$229$	8.00000	0.528655	0.264327	−	0.964433i	$-0.414850\pi$
$229$	8.00000	0.528655	0.264327	+	0.964433i	$0.414850\pi$
$230$	0	0
$231$	4.00000	0.263181
$232$	4.00000i	0.262613i
$233$	− 18.0000i	− 1.17922i	−0.807688	−	0.589610i	$-0.799282\pi$
$233$	− 18.0000i	− 1.17922i	0.807688	−	0.589610i	$-0.200718\pi$
$234$	−2.00000	−0.130744
$235$	0	0
$236$	4.00000	0.260378
$237$	8.00000i	0.519656i
$238$	28.0000i	1.81497i
$239$	20.0000	1.29369	0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000	1.29369	0.646846	+	0.762620i	$0.276088\pi$
$240$	0	0
$241$	−25.0000	−1.61039	−0.805196	−	0.593009i	$-0.797940\pi$
$241$	−25.0000	−1.61039	−0.805196	+	0.593009i	$0.797940\pi$
$242$	10.0000i	0.642824i
$243$	− 16.0000i	− 1.02640i
$244$	−8.00000	−0.512148
$245$	0	0
$246$	5.00000	0.318788
$247$	− 3.00000i	− 0.190885i
$248$	6.00000i	0.381000i
$249$	3.00000	0.190117
$250$	0	0
$251$	9.00000	0.568075	0.284037	−	0.958813i	$-0.408326\pi$
$251$	9.00000	0.568075	0.284037	+	0.958813i	$0.408326\pi$
$252$	− 8.00000i	− 0.503953i
$253$	0	0
$254$	−10.0000	−0.627456
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 6.00000i	− 0.374270i	−0.982334	−	0.187135i	$-0.940080\pi$
$257$	− 6.00000i	− 0.374270i	0.982334	−	0.187135i	$-0.0599201\pi$
$258$	4.00000i	0.249029i
$259$	−32.0000	−1.98838
$260$	0	0
$261$	8.00000	0.495188
$262$	− 4.00000i	− 0.247121i
$263$	− 28.0000i	− 1.72655i	−0.504730	−	0.863277i	$-0.668408\pi$
$263$	− 28.0000i	− 1.72655i	0.504730	−	0.863277i	$-0.331592\pi$
$264$	1.00000	0.0615457
$265$	0	0
$266$	12.0000	0.735767
$267$	− 11.0000i	− 0.673189i
$268$	− 9.00000i	− 0.549762i
$269$	−24.0000	−1.46331	−0.731653	−	0.681677i	$-0.761251\pi$
$269$	−24.0000	−1.46331	−0.731653	+	0.681677i	$0.761251\pi$
$270$	0	0
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	7.00000i	0.424437i
$273$	− 4.00000i	− 0.242091i
$274$	−15.0000	−0.906183
$275$	0	0
$276$	0	0
$277$	22.0000i	1.32185i	0.750451	+	0.660926i	$0.229836\pi$
$277$	22.0000i	1.32185i	−0.750451	+	0.660926i	$0.770164\pi$
$278$	7.00000i	0.419832i
$279$	12.0000	0.718421
$280$	0	0
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	12.0000i	0.714590i
$283$	− 31.0000i	− 1.84276i	−0.388664	−	0.921379i	$-0.627063\pi$
$283$	− 31.0000i	− 1.84276i	0.388664	−	0.921379i	$-0.372937\pi$
$284$	8.00000	0.474713
$285$	0	0
$286$	−1.00000	−0.0591312
$287$	− 20.0000i	− 1.18056i
$288$	− 2.00000i	− 0.117851i
$289$	−32.0000	−1.88235
$290$	0	0
$291$	10.0000	0.586210
$292$	− 13.0000i	− 0.760767i
$293$	− 26.0000i	− 1.51894i	−0.650545	−	0.759468i	$-0.725459\pi$
$293$	− 26.0000i	− 1.51894i	0.650545	−	0.759468i	$-0.274541\pi$
$294$	9.00000	0.524891
$295$	0	0
$296$	−8.00000	−0.464991
$297$	− 5.00000i	− 0.290129i
$298$	− 16.0000i	− 0.926855i
$299$	0	0
$300$	0	0
$301$	16.0000	0.922225
$302$	18.0000i	1.03578i
$303$	− 8.00000i	− 0.459588i
$304$	3.00000	0.172062
$305$	0	0
$306$	14.0000	0.800327
$307$	27.0000i	1.54097i	0.637457	+	0.770486i	$0.279986\pi$
$307$	27.0000i	1.54097i	−0.637457	+	0.770486i	$0.720014\pi$
$308$	− 4.00000i	− 0.227921i
$309$	−6.00000	−0.341328
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	− 1.00000i	− 0.0566139i
$313$	6.00000i	0.339140i	0.985518	+	0.169570i	$0.0542379\pi$
$313$	6.00000i	0.339140i	−0.985518	+	0.169570i	$0.945762\pi$
$314$	−16.0000	−0.902932
$315$	0	0
$316$	8.00000	0.450035
$317$	− 6.00000i	− 0.336994i	−0.985702	−	0.168497i	$-0.946109\pi$
$317$	− 6.00000i	− 0.336994i	0.985702	−	0.168497i	$-0.0538913\pi$
$318$	10.0000i	0.560772i
$319$	4.00000	0.223957
$320$	0	0
$321$	−3.00000	−0.167444
$322$	0	0
$323$	21.0000i	1.16847i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	11.0000	0.609234
$327$	− 12.0000i	− 0.663602i
$328$	− 5.00000i	− 0.276079i
$329$	48.0000	2.64633
$330$	0	0
$331$	13.0000	0.714545	0.357272	−	0.934000i	$-0.383707\pi$
$331$	13.0000	0.714545	0.357272	+	0.934000i	$0.383707\pi$
$332$	− 3.00000i	− 0.164646i
$333$	16.0000i	0.876795i
$334$	10.0000	0.547176
$335$	0	0
$336$	4.00000	0.218218
$337$	13.0000i	0.708155i	0.935216	+	0.354078i	$0.115205\pi$
$337$	13.0000i	0.708155i	−0.935216	+	0.354078i	$0.884795\pi$
$338$	1.00000i	0.0543928i
$339$	11.0000	0.597438
$340$	0	0
$341$	6.00000	0.324918
$342$	− 6.00000i	− 0.324443i
$343$	− 8.00000i	− 0.431959i
$344$	4.00000	0.215666
$345$	0	0
$346$	10.0000	0.537603
$347$	− 27.0000i	− 1.44944i	−0.689046	−	0.724718i	$-0.741970\pi$
$347$	− 27.0000i	− 1.44944i	0.689046	−	0.724718i	$-0.258030\pi$
$348$	4.00000i	0.214423i
$349$	34.0000	1.81998	0.909989	−	0.414632i	$-0.136090\pi$
$349$	34.0000	1.81998	0.909989	+	0.414632i	$0.136090\pi$
$350$	0	0
$351$	−5.00000	−0.266880
$352$	− 1.00000i	− 0.0533002i
$353$	− 14.0000i	− 0.745145i	−0.928003	−	0.372572i	$-0.878476\pi$
$353$	− 14.0000i	− 0.745145i	0.928003	−	0.372572i	$-0.121524\pi$
$354$	4.00000	0.212598
$355$	0	0
$356$	−11.0000	−0.582999
$357$	28.0000i	1.48192i
$358$	23.0000i	1.21559i
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	−10.0000	−0.526316
$362$	20.0000i	1.05118i
$363$	10.0000i	0.524864i
$364$	−4.00000	−0.209657
$365$	0	0
$366$	−8.00000	−0.418167
$367$	− 24.0000i	− 1.25279i	−0.779506	−	0.626395i	$-0.784530\pi$
$367$	− 24.0000i	− 1.25279i	0.779506	−	0.626395i	$-0.215470\pi$
$368$	0	0
$369$	−10.0000	−0.520579
$370$	0	0
$371$	40.0000	2.07670
$372$	6.00000i	0.311086i
$373$	4.00000i	0.207112i	0.994624	+	0.103556i	$0.0330221\pi$
$373$	4.00000i	0.207112i	−0.994624	+	0.103556i	$0.966978\pi$
$374$	7.00000	0.361961
$375$	0	0
$376$	12.0000	0.618853
$377$	− 4.00000i	− 0.206010i
$378$	− 20.0000i	− 1.02869i
$379$	−15.0000	−0.770498	−0.385249	−	0.922813i	$-0.625884\pi$
$379$	−15.0000	−0.770498	−0.385249	+	0.922813i	$0.625884\pi$
$380$	0	0
$381$	−10.0000	−0.512316
$382$	18.0000i	0.920960i
$383$	− 6.00000i	− 0.306586i	−0.988181	−	0.153293i	$-0.951012\pi$
$383$	− 6.00000i	− 0.306586i	0.988181	−	0.153293i	$-0.0489878\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−1.00000	−0.0508987
$387$	− 8.00000i	− 0.406663i
$388$	− 10.0000i	− 0.507673i
$389$	16.0000	0.811232	0.405616	−	0.914044i	$-0.367057\pi$
$389$	16.0000	0.811232	0.405616	+	0.914044i	$0.367057\pi$
$390$	0	0
$391$	0	0
$392$	− 9.00000i	− 0.454569i
$393$	− 4.00000i	− 0.201773i
$394$	−12.0000	−0.604551
$395$	0	0
$396$	−2.00000	−0.100504
$397$	− 14.0000i	− 0.702640i	−0.936255	−	0.351320i	$-0.885733\pi$
$397$	− 14.0000i	− 0.702640i	0.936255	−	0.351320i	$-0.114267\pi$
$398$	− 18.0000i	− 0.902258i
$399$	12.0000	0.600751
$400$	0	0
$401$	−9.00000	−0.449439	−0.224719	−	0.974424i	$-0.572147\pi$
$401$	−9.00000	−0.449439	−0.224719	+	0.974424i	$0.572147\pi$
$402$	− 9.00000i	− 0.448879i
$403$	− 6.00000i	− 0.298881i
$404$	−8.00000	−0.398015
$405$	0	0
$406$	16.0000	0.794067
$407$	8.00000i	0.396545i
$408$	7.00000i	0.346552i
$409$	−7.00000	−0.346128	−0.173064	−	0.984911i	$-0.555367\pi$
$409$	−7.00000	−0.346128	−0.173064	+	0.984911i	$0.555367\pi$
$410$	0	0
$411$	−15.0000	−0.739895
$412$	6.00000i	0.295599i
$413$	− 16.0000i	− 0.787309i
$414$	0	0
$415$	0	0
$416$	−1.00000	−0.0490290
$417$	7.00000i	0.342791i
$418$	− 3.00000i	− 0.146735i
$419$	−19.0000	−0.928211	−0.464105	−	0.885780i	$-0.653624\pi$
$419$	−19.0000	−0.928211	−0.464105	+	0.885780i	$0.653624\pi$
$420$	0	0
$421$	−8.00000	−0.389896	−0.194948	−	0.980814i	$-0.562454\pi$
$421$	−8.00000	−0.389896	−0.194948	+	0.980814i	$0.562454\pi$
$422$	23.0000i	1.11962i
$423$	− 24.0000i	− 1.16692i
$424$	10.0000	0.485643
$425$	0	0
$426$	8.00000	0.387601
$427$	32.0000i	1.54859i
$428$	3.00000i	0.145010i
$429$	−1.00000	−0.0482805
$430$	0	0
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	− 5.00000i	− 0.240563i
$433$	25.0000i	1.20142i	0.799466	+	0.600712i	$0.205116\pi$
$433$	25.0000i	1.20142i	−0.799466	+	0.600712i	$0.794884\pi$
$434$	24.0000	1.15204
$435$	0	0
$436$	−12.0000	−0.574696
$437$	0	0
$438$	− 13.0000i	− 0.621164i
$439$	14.0000	0.668184	0.334092	−	0.942541i	$-0.391570\pi$
$439$	14.0000	0.668184	0.334092	+	0.942541i	$0.391570\pi$
$440$	0	0
$441$	−18.0000	−0.857143
$442$	− 7.00000i	− 0.332956i
$443$	− 11.0000i	− 0.522626i	−0.965254	−	0.261313i	$-0.915845\pi$
$443$	− 11.0000i	− 0.522626i	0.965254	−	0.261313i	$-0.0841554\pi$
$444$	−8.00000	−0.379663
$445$	0	0
$446$	−26.0000	−1.23114
$447$	− 16.0000i	− 0.756774i
$448$	− 4.00000i	− 0.188982i
$449$	9.00000	0.424736	0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000	0.424736	0.212368	+	0.977190i	$0.431882\pi$
$450$	0	0
$451$	−5.00000	−0.235441
$452$	− 11.0000i	− 0.517396i
$453$	18.0000i	0.845714i
$454$	−20.0000	−0.938647
$455$	0	0
$456$	3.00000	0.140488
$457$	25.0000i	1.16945i	0.811231	+	0.584725i	$0.198798\pi$
$457$	25.0000i	1.16945i	−0.811231	+	0.584725i	$0.801202\pi$
$458$	− 8.00000i	− 0.373815i
$459$	35.0000	1.63366
$460$	0	0
$461$	−6.00000	−0.279448	−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	− 4.00000i	− 0.186097i
$463$	10.0000i	0.464739i	0.972628	+	0.232370i	$0.0746479\pi$
$463$	10.0000i	0.464739i	−0.972628	+	0.232370i	$0.925352\pi$
$464$	4.00000	0.185695
$465$	0	0
$466$	−18.0000	−0.833834
$467$	− 4.00000i	− 0.185098i	−0.995708	−	0.0925490i	$-0.970499\pi$
$467$	− 4.00000i	− 0.185098i	0.995708	−	0.0925490i	$-0.0295015\pi$
$468$	2.00000i	0.0924500i
$469$	−36.0000	−1.66233
$470$	0	0
$471$	−16.0000	−0.737241
$472$	− 4.00000i	− 0.184115i
$473$	− 4.00000i	− 0.183920i
$474$	8.00000	0.367452
$475$	0	0
$476$	28.0000	1.28338
$477$	− 20.0000i	− 0.915737i
$478$	− 20.0000i	− 0.914779i
$479$	−14.0000	−0.639676	−0.319838	−	0.947472i	$-0.603629\pi$
$479$	−14.0000	−0.639676	−0.319838	+	0.947472i	$0.603629\pi$
$480$	0	0
$481$	8.00000	0.364769
$482$	25.0000i	1.13872i
$483$	0	0
$484$	10.0000	0.454545
$485$	0	0
$486$	−16.0000	−0.725775
$487$	4.00000i	0.181257i	0.995885	+	0.0906287i	$0.0288876\pi$
$487$	4.00000i	0.181257i	−0.995885	+	0.0906287i	$0.971112\pi$
$488$	8.00000i	0.362143i
$489$	11.0000	0.497437
$490$	0	0
$491$	36.0000	1.62466	0.812329	−	0.583200i	$-0.198200\pi$
$491$	36.0000	1.62466	0.812329	+	0.583200i	$0.198200\pi$
$492$	− 5.00000i	− 0.225417i
$493$	28.0000i	1.26106i
$494$	−3.00000	−0.134976
$495$	0	0
$496$	6.00000	0.269408
$497$	− 32.0000i	− 1.43540i
$498$	− 3.00000i	− 0.134433i
$499$	−20.0000	−0.895323	−0.447661	−	0.894203i	$-0.647743\pi$
$499$	−20.0000	−0.895323	−0.447661	+	0.894203i	$0.647743\pi$
$500$	0	0
$501$	10.0000	0.446767
$502$	− 9.00000i	− 0.401690i
$503$	40.0000i	1.78351i	0.452517	+	0.891756i	$0.350526\pi$
$503$	40.0000i	1.78351i	−0.452517	+	0.891756i	$0.649474\pi$
$504$	−8.00000	−0.356348
$505$	0	0
$506$	0	0
$507$	1.00000i	0.0444116i
$508$	10.0000i	0.443678i
$509$	−12.0000	−0.531891	−0.265945	−	0.963988i	$-0.585684\pi$
$509$	−12.0000	−0.531891	−0.265945	+	0.963988i	$0.585684\pi$
$510$	0	0
$511$	−52.0000	−2.30034
$512$	− 1.00000i	− 0.0441942i
$513$	− 15.0000i	− 0.662266i
$514$	−6.00000	−0.264649
$515$	0	0
$516$	4.00000	0.176090
$517$	− 12.0000i	− 0.527759i
$518$	32.0000i	1.40600i
$519$	10.0000	0.438951
$520$	0	0
$521$	1.00000	0.0438108	0.0219054	−	0.999760i	$-0.493027\pi$
$521$	1.00000	0.0438108	0.0219054	+	0.999760i	$0.493027\pi$
$522$	− 8.00000i	− 0.350150i
$523$	15.0000i	0.655904i	0.944694	+	0.327952i	$0.106358\pi$
$523$	15.0000i	0.655904i	−0.944694	+	0.327952i	$0.893642\pi$
$524$	−4.00000	−0.174741
$525$	0	0
$526$	−28.0000	−1.22086
$527$	42.0000i	1.82955i
$528$	− 1.00000i	− 0.0435194i
$529$	23.0000	1.00000
$530$	0	0
$531$	−8.00000	−0.347170
$532$	− 12.0000i	− 0.520266i
$533$	5.00000i	0.216574i
$534$	−11.0000	−0.476017
$535$	0	0
$536$	−9.00000	−0.388741
$537$	23.0000i	0.992523i
$538$	24.0000i	1.03471i
$539$	−9.00000	−0.387657
$540$	0	0
$541$	−14.0000	−0.601907	−0.300954	−	0.953639i	$-0.597305\pi$
$541$	−14.0000	−0.601907	−0.300954	+	0.953639i	$0.597305\pi$
$542$	− 16.0000i	− 0.687259i
$543$	20.0000i	0.858282i
$544$	7.00000	0.300123
$545$	0	0
$546$	−4.00000	−0.171184
$547$	17.0000i	0.726868i	0.931620	+	0.363434i	$0.118396\pi$
$547$	17.0000i	0.726868i	−0.931620	+	0.363434i	$0.881604\pi$
$548$	15.0000i	0.640768i
$549$	16.0000	0.682863
$550$	0	0
$551$	12.0000	0.511217
$552$	0	0
$553$	− 32.0000i	− 1.36078i
$554$	22.0000	0.934690
$555$	0	0
$556$	7.00000	0.296866
$557$	− 2.00000i	− 0.0847427i	−0.999102	−	0.0423714i	$-0.986509\pi$
$557$	− 2.00000i	− 0.0847427i	0.999102	−	0.0423714i	$-0.0134913\pi$
$558$	− 12.0000i	− 0.508001i
$559$	−4.00000	−0.169182
$560$	0	0
$561$	7.00000	0.295540
$562$	6.00000i	0.253095i
$563$	− 24.0000i	− 1.01148i	−0.862686	−	0.505740i	$-0.831220\pi$
$563$	− 24.0000i	− 1.01148i	0.862686	−	0.505740i	$-0.168780\pi$
$564$	12.0000	0.505291
$565$	0	0
$566$	−31.0000	−1.30303
$567$	4.00000i	0.167984i
$568$	− 8.00000i	− 0.335673i
$569$	−45.0000	−1.88650	−0.943249	−	0.332086i	$-0.892248\pi$
$569$	−45.0000	−1.88650	−0.943249	+	0.332086i	$0.892248\pi$
$570$	0	0
$571$	40.0000	1.67395	0.836974	−	0.547243i	$-0.184323\pi$
$571$	40.0000	1.67395	0.836974	+	0.547243i	$0.184323\pi$
$572$	1.00000i	0.0418121i
$573$	18.0000i	0.751961i
$574$	−20.0000	−0.834784
$575$	0	0
$576$	−2.00000	−0.0833333
$577$	3.00000i	0.124892i	0.998048	+	0.0624458i	$0.0198901\pi$
$577$	3.00000i	0.124892i	−0.998048	+	0.0624458i	$0.980110\pi$
$578$	32.0000i	1.33102i
$579$	−1.00000	−0.0415586
$580$	0	0
$581$	−12.0000	−0.497844
$582$	− 10.0000i	− 0.414513i
$583$	− 10.0000i	− 0.414158i
$584$	−13.0000	−0.537944
$585$	0	0
$586$	−26.0000	−1.07405
$587$	9.00000i	0.371470i	0.982600	+	0.185735i	$0.0594666\pi$
$587$	9.00000i	0.371470i	−0.982600	+	0.185735i	$0.940533\pi$
$588$	− 9.00000i	− 0.371154i
$589$	18.0000	0.741677
$590$	0	0
$591$	−12.0000	−0.493614
$592$	8.00000i	0.328798i
$593$	37.0000i	1.51941i	0.650269	+	0.759704i	$0.274656\pi$
$593$	37.0000i	1.51941i	−0.650269	+	0.759704i	$0.725344\pi$
$594$	−5.00000	−0.205152
$595$	0	0
$596$	−16.0000	−0.655386
$597$	− 18.0000i	− 0.736691i
$598$	0	0
$599$	−6.00000	−0.245153	−0.122577	−	0.992459i	$-0.539116\pi$
$599$	−6.00000	−0.245153	−0.122577	+	0.992459i	$0.539116\pi$
$600$	0	0
$601$	31.0000	1.26452	0.632258	−	0.774758i	$-0.282128\pi$
$601$	31.0000	1.26452	0.632258	+	0.774758i	$0.282128\pi$
$602$	− 16.0000i	− 0.652111i
$603$	18.0000i	0.733017i
$604$	18.0000	0.732410
$605$	0	0
$606$	−8.00000	−0.324978
$607$	− 26.0000i	− 1.05531i	−0.849460	−	0.527654i	$-0.823072\pi$
$607$	− 26.0000i	− 1.05531i	0.849460	−	0.527654i	$-0.176928\pi$
$608$	− 3.00000i	− 0.121666i
$609$	16.0000	0.648353
$610$	0	0
$611$	−12.0000	−0.485468
$612$	− 14.0000i	− 0.565916i
$613$	2.00000i	0.0807792i	0.999184	+	0.0403896i	$0.0128599\pi$
$613$	2.00000i	0.0807792i	−0.999184	+	0.0403896i	$0.987140\pi$
$614$	27.0000	1.08963
$615$	0	0
$616$	−4.00000	−0.161165
$617$	6.00000i	0.241551i	0.992680	+	0.120775i	$0.0385381\pi$
$617$	6.00000i	0.241551i	−0.992680	+	0.120775i	$0.961462\pi$
$618$	6.00000i	0.241355i
$619$	28.0000	1.12542	0.562708	−	0.826656i	$-0.309760\pi$
$619$	28.0000	1.12542	0.562708	+	0.826656i	$0.309760\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	44.0000i	1.76282i
$624$	−1.00000	−0.0400320
$625$	0	0
$626$	6.00000	0.239808
$627$	− 3.00000i	− 0.119808i
$628$	16.0000i	0.638470i
$629$	−56.0000	−2.23287
$630$	0	0
$631$	−36.0000	−1.43314	−0.716569	−	0.697517i	$-0.754288\pi$
$631$	−36.0000	−1.43314	−0.716569	+	0.697517i	$0.754288\pi$
$632$	− 8.00000i	− 0.318223i
$633$	23.0000i	0.914168i
$634$	−6.00000	−0.238290
$635$	0	0
$636$	10.0000	0.396526
$637$	9.00000i	0.356593i
$638$	− 4.00000i	− 0.158362i
$639$	−16.0000	−0.632950
$640$	0	0
$641$	42.0000	1.65890	0.829450	−	0.558581i	$-0.188654\pi$
$641$	42.0000	1.65890	0.829450	+	0.558581i	$0.188654\pi$
$642$	3.00000i	0.118401i
$643$	− 4.00000i	− 0.157745i	−0.996885	−	0.0788723i	$-0.974868\pi$
$643$	− 4.00000i	− 0.157745i	0.996885	−	0.0788723i	$-0.0251319\pi$
$644$	0	0
$645$	0	0
$646$	21.0000	0.826234
$647$	− 6.00000i	− 0.235884i	−0.993020	−	0.117942i	$-0.962370\pi$
$647$	− 6.00000i	− 0.235884i	0.993020	−	0.117942i	$-0.0376297\pi$
$648$	1.00000i	0.0392837i
$649$	−4.00000	−0.157014
$650$	0	0
$651$	24.0000	0.940634
$652$	− 11.0000i	− 0.430793i
$653$	30.0000i	1.17399i	0.809590	+	0.586995i	$0.199689\pi$
$653$	30.0000i	1.17399i	−0.809590	+	0.586995i	$0.800311\pi$
$654$	−12.0000	−0.469237
$655$	0	0
$656$	−5.00000	−0.195217
$657$	26.0000i	1.01436i
$658$	− 48.0000i	− 1.87123i
$659$	−29.0000	−1.12968	−0.564840	−	0.825201i	$-0.691062\pi$
$659$	−29.0000	−1.12968	−0.564840	+	0.825201i	$0.691062\pi$
$660$	0	0
$661$	18.0000	0.700119	0.350059	−	0.936727i	$-0.386161\pi$
$661$	18.0000	0.700119	0.350059	+	0.936727i	$0.386161\pi$
$662$	− 13.0000i	− 0.505259i
$663$	− 7.00000i	− 0.271857i
$664$	−3.00000	−0.116423
$665$	0	0
$666$	16.0000	0.619987
$667$	0	0
$668$	− 10.0000i	− 0.386912i
$669$	−26.0000	−1.00522
$670$	0	0
$671$	8.00000	0.308837
$672$	− 4.00000i	− 0.154303i
$673$	− 46.0000i	− 1.77317i	−0.462566	−	0.886585i	$-0.653071\pi$
$673$	− 46.0000i	− 1.77317i	0.462566	−	0.886585i	$-0.346929\pi$
$674$	13.0000	0.500741
$675$	0	0
$676$	1.00000	0.0384615
$677$	− 12.0000i	− 0.461197i	−0.973049	−	0.230599i	$-0.925932\pi$
$677$	− 12.0000i	− 0.461197i	0.973049	−	0.230599i	$-0.0740685\pi$
$678$	− 11.0000i	− 0.422452i
$679$	−40.0000	−1.53506
$680$	0	0
$681$	−20.0000	−0.766402
$682$	− 6.00000i	− 0.229752i
$683$	1.00000i	0.0382639i	0.999817	+	0.0191320i	$0.00609027\pi$
$683$	1.00000i	0.0382639i	−0.999817	+	0.0191320i	$0.993910\pi$
$684$	−6.00000	−0.229416
$685$	0	0
$686$	−8.00000	−0.305441
$687$	− 8.00000i	− 0.305219i
$688$	− 4.00000i	− 0.152499i
$689$	−10.0000	−0.380970
$690$	0	0
$691$	13.0000	0.494543	0.247272	−	0.968946i	$-0.420466\pi$
$691$	13.0000	0.494543	0.247272	+	0.968946i	$0.420466\pi$
$692$	− 10.0000i	− 0.380143i
$693$	8.00000i	0.303895i
$694$	−27.0000	−1.02491
$695$	0	0
$696$	4.00000	0.151620
$697$	− 35.0000i	− 1.32572i
$698$	− 34.0000i	− 1.28692i
$699$	−18.0000	−0.680823
$700$	0	0
$701$	−40.0000	−1.51078	−0.755390	−	0.655276i	$-0.772552\pi$
$701$	−40.0000	−1.51078	−0.755390	+	0.655276i	$0.772552\pi$
$702$	5.00000i	0.188713i
$703$	24.0000i	0.905177i
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	−14.0000	−0.526897
$707$	32.0000i	1.20348i
$708$	− 4.00000i	− 0.150329i
$709$	−26.0000	−0.976450	−0.488225	−	0.872718i	$-0.662356\pi$
$709$	−26.0000	−0.976450	−0.488225	+	0.872718i	$0.662356\pi$
$710$	0	0
$711$	−16.0000	−0.600047
$712$	11.0000i	0.412242i
$713$	0	0
$714$	28.0000	1.04787
$715$	0	0
$716$	23.0000	0.859550
$717$	− 20.0000i	− 0.746914i
$718$	0	0
$719$	−6.00000	−0.223762	−0.111881	−	0.993722i	$-0.535688\pi$
$719$	−6.00000	−0.223762	−0.111881	+	0.993722i	$0.535688\pi$
$720$	0	0
$721$	24.0000	0.893807
$722$	10.0000i	0.372161i
$723$	25.0000i	0.929760i
$724$	20.0000	0.743294
$725$	0	0
$726$	10.0000	0.371135
$727$	− 10.0000i	− 0.370879i	−0.982656	−	0.185440i	$-0.940629\pi$
$727$	− 10.0000i	− 0.370879i	0.982656	−	0.185440i	$-0.0593710\pi$
$728$	4.00000i	0.148250i
$729$	−13.0000	−0.481481
$730$	0	0
$731$	28.0000	1.03562
$732$	8.00000i	0.295689i
$733$	2.00000i	0.0738717i	0.999318	+	0.0369358i	$0.0117597\pi$
$733$	2.00000i	0.0738717i	−0.999318	+	0.0369358i	$0.988240\pi$
$734$	−24.0000	−0.885856
$735$	0	0
$736$	0	0
$737$	9.00000i	0.331519i
$738$	10.0000i	0.368105i
$739$	0	0		−	1.00000i	$-0.5\pi$
$739$	0	0			1.00000i	$0.5\pi$
$740$	0	0
$741$	−3.00000	−0.110208
$742$	− 40.0000i	− 1.46845i
$743$	− 36.0000i	− 1.32071i	−0.750953	−	0.660356i	$-0.770405\pi$
$743$	− 36.0000i	− 1.32071i	0.750953	−	0.660356i	$-0.229595\pi$
$744$	6.00000	0.219971
$745$	0	0
$746$	4.00000	0.146450
$747$	6.00000i	0.219529i
$748$	− 7.00000i	− 0.255945i
$749$	12.0000	0.438470
$750$	0	0
$751$	−10.0000	−0.364905	−0.182453	−	0.983215i	$-0.558404\pi$
$751$	−10.0000	−0.364905	−0.182453	+	0.983215i	$0.558404\pi$
$752$	− 12.0000i	− 0.437595i
$753$	− 9.00000i	− 0.327978i
$754$	−4.00000	−0.145671
$755$	0	0
$756$	−20.0000	−0.727393
$757$	− 36.0000i	− 1.30844i	−0.756303	−	0.654221i	$-0.772997\pi$
$757$	− 36.0000i	− 1.30844i	0.756303	−	0.654221i	$-0.227003\pi$
$758$	15.0000i	0.544825i
$759$	0	0
$760$	0	0
$761$	19.0000	0.688749	0.344375	−	0.938832i	$-0.388091\pi$
$761$	19.0000	0.688749	0.344375	+	0.938832i	$0.388091\pi$
$762$	10.0000i	0.362262i
$763$	48.0000i	1.73772i
$764$	18.0000	0.651217
$765$	0	0
$766$	−6.00000	−0.216789
$767$	4.00000i	0.144432i
$768$	− 1.00000i	− 0.0360844i
$769$	53.0000	1.91123	0.955614	−	0.294620i	$-0.0951931\pi$
$769$	53.0000	1.91123	0.955614	+	0.294620i	$0.0951931\pi$
$770$	0	0
$771$	−6.00000	−0.216085
$772$	1.00000i	0.0359908i
$773$	14.0000i	0.503545i	0.967786	+	0.251773i	$0.0810135\pi$
$773$	14.0000i	0.503545i	−0.967786	+	0.251773i	$0.918987\pi$
$774$	−8.00000	−0.287554
$775$	0	0
$776$	−10.0000	−0.358979
$777$	32.0000i	1.14799i
$778$	− 16.0000i	− 0.573628i
$779$	−15.0000	−0.537431
$780$	0	0
$781$	−8.00000	−0.286263
$782$	0	0
$783$	− 20.0000i	− 0.714742i
$784$	−9.00000	−0.321429
$785$	0	0
$786$	−4.00000	−0.142675
$787$	20.0000i	0.712923i	0.934310	+	0.356462i	$0.116017\pi$
$787$	20.0000i	0.712923i	−0.934310	+	0.356462i	$0.883983\pi$
$788$	12.0000i	0.427482i
$789$	−28.0000	−0.996826
$790$	0	0
$791$	−44.0000	−1.56446
$792$	2.00000i	0.0710669i
$793$	− 8.00000i	− 0.284088i
$794$	−14.0000	−0.496841
$795$	0	0
$796$	−18.0000	−0.637993
$797$	28.0000i	0.991811i	0.868377	+	0.495905i	$0.165164\pi$
$797$	28.0000i	0.991811i	−0.868377	+	0.495905i	$0.834836\pi$
$798$	− 12.0000i	− 0.424795i
$799$	84.0000	2.97171
$800$	0	0
$801$	22.0000	0.777332
$802$	9.00000i	0.317801i
$803$	13.0000i	0.458760i
$804$	−9.00000	−0.317406
$805$	0	0
$806$	−6.00000	−0.211341
$807$	24.0000i	0.844840i
$808$	8.00000i	0.281439i
$809$	−2.00000	−0.0703163	−0.0351581	−	0.999382i	$-0.511193\pi$
$809$	−2.00000	−0.0703163	−0.0351581	+	0.999382i	$0.511193\pi$
$810$	0	0
$811$	−20.0000	−0.702295	−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000	−0.702295	−0.351147	+	0.936320i	$0.614208\pi$
$812$	− 16.0000i	− 0.561490i
$813$	− 16.0000i	− 0.561144i
$814$	8.00000	0.280400
$815$	0	0
$816$	7.00000	0.245049
$817$	− 12.0000i	− 0.419827i
$818$	7.00000i	0.244749i
$819$	8.00000	0.279543
$820$	0	0
$821$	32.0000	1.11681	0.558404	−	0.829569i	$-0.311414\pi$
$821$	32.0000	1.11681	0.558404	+	0.829569i	$0.311414\pi$
$822$	15.0000i	0.523185i
$823$	− 4.00000i	− 0.139431i	−0.997567	−	0.0697156i	$-0.977791\pi$
$823$	− 4.00000i	− 0.139431i	0.997567	−	0.0697156i	$-0.0222092\pi$
$824$	6.00000	0.209020
$825$	0	0
$826$	−16.0000	−0.556711
$827$	33.0000i	1.14752i	0.819023	+	0.573761i	$0.194516\pi$
$827$	33.0000i	1.14752i	−0.819023	+	0.573761i	$0.805484\pi$
$828$	0	0
$829$	22.0000	0.764092	0.382046	−	0.924143i	$-0.375220\pi$
$829$	22.0000	0.764092	0.382046	+	0.924143i	$0.375220\pi$
$830$	0	0
$831$	22.0000	0.763172
$832$	1.00000i	0.0346688i
$833$	− 63.0000i	− 2.18282i
$834$	7.00000	0.242390
$835$	0	0
$836$	−3.00000	−0.103757
$837$	− 30.0000i	− 1.03695i
$838$	19.0000i	0.656344i
$839$	10.0000	0.345238	0.172619	−	0.984989i	$-0.444777\pi$
$839$	10.0000	0.345238	0.172619	+	0.984989i	$0.444777\pi$
$840$	0	0
$841$	−13.0000	−0.448276
$842$	8.00000i	0.275698i
$843$	6.00000i	0.206651i
$844$	23.0000	0.791693
$845$	0	0
$846$	−24.0000	−0.825137
$847$	− 40.0000i	− 1.37442i
$848$	− 10.0000i	− 0.343401i
$849$	−31.0000	−1.06392
$850$	0	0
$851$	0	0
$852$	− 8.00000i	− 0.274075i
$853$	− 8.00000i	− 0.273915i	−0.990577	−	0.136957i	$-0.956268\pi$
$853$	− 8.00000i	− 0.273915i	0.990577	−	0.136957i	$-0.0437323\pi$
$854$	32.0000	1.09502
$855$	0	0
$856$	3.00000	0.102538
$857$	− 37.0000i	− 1.26390i	−0.775011	−	0.631948i	$-0.782256\pi$
$857$	− 37.0000i	− 1.26390i	0.775011	−	0.631948i	$-0.217744\pi$
$858$	1.00000i	0.0341394i
$859$	9.00000	0.307076	0.153538	−	0.988143i	$-0.450933\pi$
$859$	9.00000	0.307076	0.153538	+	0.988143i	$0.450933\pi$
$860$	0	0
$861$	−20.0000	−0.681598
$862$	− 12.0000i	− 0.408722i
$863$	− 30.0000i	− 1.02121i	−0.859815	−	0.510606i	$-0.829421\pi$
$863$	− 30.0000i	− 1.02121i	0.859815	−	0.510606i	$-0.170579\pi$
$864$	−5.00000	−0.170103
$865$	0	0
$866$	25.0000	0.849535
$867$	32.0000i	1.08678i
$868$	− 24.0000i	− 0.814613i
$869$	−8.00000	−0.271381
$870$	0	0
$871$	9.00000	0.304953
$872$	12.0000i	0.406371i
$873$	20.0000i	0.676897i
$874$	0	0
$875$	0	0
$876$	−13.0000	−0.439229
$877$	32.0000i	1.08056i	0.841484	+	0.540282i	$0.181682\pi$
$877$	32.0000i	1.08056i	−0.841484	+	0.540282i	$0.818318\pi$
$878$	− 14.0000i	− 0.472477i
$879$	−26.0000	−0.876958
$880$	0	0
$881$	6.00000	0.202145	0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000	0.202145	0.101073	+	0.994879i	$0.467773\pi$
$882$	18.0000i	0.606092i
$883$	11.0000i	0.370179i	0.982722	+	0.185090i	$0.0592576\pi$
$883$	11.0000i	0.370179i	−0.982722	+	0.185090i	$0.940742\pi$
$884$	−7.00000	−0.235435
$885$	0	0
$886$	−11.0000	−0.369552
$887$	20.0000i	0.671534i	0.941945	+	0.335767i	$0.108996\pi$
$887$	20.0000i	0.671534i	−0.941945	+	0.335767i	$0.891004\pi$
$888$	8.00000i	0.268462i
$889$	40.0000	1.34156
$890$	0	0
$891$	1.00000	0.0335013
$892$	26.0000i	0.870544i
$893$	− 36.0000i	− 1.20469i
$894$	−16.0000	−0.535120
$895$	0	0
$896$	−4.00000	−0.133631
$897$	0	0
$898$	− 9.00000i	− 0.300334i
$899$	24.0000	0.800445
$900$	0	0
$901$	70.0000	2.33204
$902$	5.00000i	0.166482i
$903$	− 16.0000i	− 0.532447i
$904$	−11.0000	−0.365855
$905$	0	0
$906$	18.0000	0.598010
$907$	− 52.0000i	− 1.72663i	−0.504664	−	0.863316i	$-0.668384\pi$
$907$	− 52.0000i	− 1.72663i	0.504664	−	0.863316i	$-0.331616\pi$
$908$	20.0000i	0.663723i
$909$	16.0000	0.530687
$910$	0	0
$911$	−50.0000	−1.65657	−0.828287	−	0.560304i	$-0.810684\pi$
$911$	−50.0000	−1.65657	−0.828287	+	0.560304i	$0.810684\pi$
$912$	− 3.00000i	− 0.0993399i
$913$	3.00000i	0.0992855i
$914$	25.0000	0.826927
$915$	0	0
$916$	−8.00000	−0.264327
$917$	16.0000i	0.528367i
$918$	− 35.0000i	− 1.15517i
$919$	−4.00000	−0.131948	−0.0659739	−	0.997821i	$-0.521015\pi$
$919$	−4.00000	−0.131948	−0.0659739	+	0.997821i	$0.521015\pi$
$920$	0	0
$921$	27.0000	0.889680
$922$	6.00000i	0.197599i
$923$	8.00000i	0.263323i
$924$	−4.00000	−0.131590
$925$	0	0
$926$	10.0000	0.328620
$927$	− 12.0000i	− 0.394132i
$928$	− 4.00000i	− 0.131306i
$929$	−6.00000	−0.196854	−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000	−0.196854	−0.0984268	+	0.995144i	$0.531381\pi$
$930$	0	0
$931$	−27.0000	−0.884889
$932$	18.0000i	0.589610i
$933$	0	0
$934$	−4.00000	−0.130884
$935$	0	0
$936$	2.00000	0.0653720
$937$	21.0000i	0.686040i	0.939328	+	0.343020i	$0.111450\pi$
$937$	21.0000i	0.686040i	−0.939328	+	0.343020i	$0.888550\pi$
$938$	36.0000i	1.17544i
$939$	6.00000	0.195803
$940$	0	0
$941$	14.0000	0.456387	0.228193	−	0.973616i	$-0.426718\pi$
$941$	14.0000	0.456387	0.228193	+	0.973616i	$0.426718\pi$
$942$	16.0000i	0.521308i
$943$	0	0
$944$	−4.00000	−0.130189
$945$	0	0
$946$	−4.00000	−0.130051
$947$	56.0000i	1.81976i	0.414876	+	0.909878i	$0.363825\pi$
$947$	56.0000i	1.81976i	−0.414876	+	0.909878i	$0.636175\pi$
$948$	− 8.00000i	− 0.259828i
$949$	13.0000	0.421998
$950$	0	0
$951$	−6.00000	−0.194563
$952$	− 28.0000i	− 0.907485i
$953$	− 15.0000i	− 0.485898i	−0.970039	−	0.242949i	$-0.921885\pi$
$953$	− 15.0000i	− 0.485898i	0.970039	−	0.242949i	$-0.0781147\pi$
$954$	−20.0000	−0.647524
$955$	0	0
$956$	−20.0000	−0.646846
$957$	− 4.00000i	− 0.129302i
$958$	14.0000i	0.452319i
$959$	60.0000	1.93750
$960$	0	0
$961$	5.00000	0.161290
$962$	− 8.00000i	− 0.257930i
$963$	− 6.00000i	− 0.193347i
$964$	25.0000	0.805196
$965$	0	0
$966$	0	0
$967$	44.0000i	1.41494i	0.706741	+	0.707472i	$0.250165\pi$
$967$	44.0000i	1.41494i	−0.706741	+	0.707472i	$0.749835\pi$
$968$	− 10.0000i	− 0.321412i
$969$	21.0000	0.674617
$970$	0	0
$971$	47.0000	1.50830	0.754151	−	0.656701i	$-0.228049\pi$
$971$	47.0000	1.50830	0.754151	+	0.656701i	$0.228049\pi$
$972$	16.0000i	0.513200i
$973$	− 28.0000i	− 0.897639i
$974$	4.00000	0.128168
$975$	0	0
$976$	8.00000	0.256074
$977$	− 39.0000i	− 1.24772i	−0.781536	−	0.623860i	$-0.785563\pi$
$977$	− 39.0000i	− 1.24772i	0.781536	−	0.623860i	$-0.214437\pi$
$978$	− 11.0000i	− 0.351741i
$979$	11.0000	0.351562
$980$	0	0
$981$	24.0000	0.766261
$982$	− 36.0000i	− 1.14881i
$983$	− 4.00000i	− 0.127580i	−0.997963	−	0.0637901i	$-0.979681\pi$
$983$	− 4.00000i	− 0.127580i	0.997963	−	0.0637901i	$-0.0203188\pi$
$984$	−5.00000	−0.159394
$985$	0	0
$986$	28.0000	0.891702
$987$	− 48.0000i	− 1.52786i
$988$	3.00000i	0.0954427i
$989$	0	0
$990$	0	0
$991$	−18.0000	−0.571789	−0.285894	−	0.958261i	$-0.592291\pi$
$991$	−18.0000	−0.571789	−0.285894	+	0.958261i	$0.592291\pi$
$992$	− 6.00000i	− 0.190500i
$993$	− 13.0000i	− 0.412543i
$994$	−32.0000	−1.01498
$995$	0	0
$996$	−3.00000	−0.0950586
$997$	− 16.0000i	− 0.506725i	−0.967371	−	0.253363i	$-0.918463\pi$
$997$	− 16.0000i	− 0.506725i	0.967371	−	0.253363i	$-0.0815366\pi$
$998$	20.0000i	0.633089i
$999$	40.0000	1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.b.c.599.1		2
3.2	odd	2		5850.2.e.l.5149.2		2
5.2	odd	4		650.2.a.i.1.1	yes	1
5.3	odd	4		650.2.a.e.1.1	✓	1
5.4	even	2	inner	650.2.b.c.599.2		2
15.2	even	4		5850.2.a.b.1.1		1
15.8	even	4		5850.2.a.bz.1.1		1
15.14	odd	2		5850.2.e.l.5149.1		2
20.3	even	4		5200.2.a.j.1.1		1
20.7	even	4		5200.2.a.ba.1.1		1
65.12	odd	4		8450.2.a.e.1.1		1
65.38	odd	4		8450.2.a.t.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.a.e.1.1	✓	1	5.3	odd	4
650.2.a.i.1.1	yes	1	5.2	odd	4
650.2.b.c.599.1		2	1.1	even	1	trivial
650.2.b.c.599.2		2	5.4	even	2	inner
5200.2.a.j.1.1		1	20.3	even	4
5200.2.a.ba.1.1		1	20.7	even	4
5850.2.a.b.1.1		1	15.2	even	4
5850.2.a.bz.1.1		1	15.8	even	4
5850.2.e.l.5149.1		2	15.14	odd	2
5850.2.e.l.5149.2		2	3.2	odd	2
8450.2.a.e.1.1		1	65.12	odd	4
8450.2.a.t.1.1		1	65.38	odd	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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +4.00000i q^{7} +1.00000i q^{8} +2.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +4.00000i q^{7} +1.00000i q^{8} +2.00000 q^{9} +1.00000 q^{11} +1.00000i q^{12} -1.00000i q^{13} +4.00000 q^{14} +1.00000 q^{16} +7.00000i q^{17} -2.00000i q^{18} +3.00000 q^{19} +4.00000 q^{21} -1.00000i q^{22} +1.00000 q^{24} -1.00000 q^{26} -5.00000i q^{27} -4.00000i q^{28} +4.00000 q^{29} +6.00000 q^{31} -1.00000i q^{32} -1.00000i q^{33} +7.00000 q^{34} -2.00000 q^{36} +8.00000i q^{37} -3.00000i q^{38} -1.00000 q^{39} -5.00000 q^{41} -4.00000i q^{42} -4.00000i q^{43} -1.00000 q^{44} -12.0000i q^{47} -1.00000i q^{48} -9.00000 q^{49} +7.00000 q^{51} +1.00000i q^{52} -10.0000i q^{53} -5.00000 q^{54} -4.00000 q^{56} -3.00000i q^{57} -4.00000i q^{58} -4.00000 q^{59} +8.00000 q^{61} -6.00000i q^{62} +8.00000i q^{63} -1.00000 q^{64} -1.00000 q^{66} +9.00000i q^{67} -7.00000i q^{68} -8.00000 q^{71} +2.00000i q^{72} +13.0000i q^{73} +8.00000 q^{74} -3.00000 q^{76} +4.00000i q^{77} +1.00000i q^{78} -8.00000 q^{79} +1.00000 q^{81} +5.00000i q^{82} +3.00000i q^{83} -4.00000 q^{84} -4.00000 q^{86} -4.00000i q^{87} +1.00000i q^{88} +11.0000 q^{89} +4.00000 q^{91} -6.00000i q^{93} -12.0000 q^{94} -1.00000 q^{96} +10.0000i q^{97} +9.00000i q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} - 2 q^{6} + 4 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 - 2 * q^6 + 4 * q^9	\( 2 q - 2 q^{4} - 2 q^{6} + 4 q^{9} + 2 q^{11} + 8 q^{14} + 2 q^{16} + 6 q^{19} + 8 q^{21} + 2 q^{24} - 2 q^{26} + 8 q^{29} + 12 q^{31} + 14 q^{34} - 4 q^{36} - 2 q^{39} - 10 q^{41} - 2 q^{44} - 18 q^{49} + 14 q^{51} - 10 q^{54} - 8 q^{56} - 8 q^{59} + 16 q^{61} - 2 q^{64} - 2 q^{66} - 16 q^{71} + 16 q^{74} - 6 q^{76} - 16 q^{79} + 2 q^{81} - 8 q^{84} - 8 q^{86} + 22 q^{89} + 8 q^{91} - 24 q^{94} - 2 q^{96} + 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 - 2 * q^6 + 4 * q^9 + 2 * q^11 + 8 * q^14 + 2 * q^16 + 6 * q^19 + 8 * q^21 + 2 * q^24 - 2 * q^26 + 8 * q^29 + 12 * q^31 + 14 * q^34 - 4 * q^36 - 2 * q^39 - 10 * q^41 - 2 * q^44 - 18 * q^49 + 14 * q^51 - 10 * q^54 - 8 * q^56 - 8 * q^59 + 16 * q^61 - 2 * q^64 - 2 * q^66 - 16 * q^71 + 16 * q^74 - 6 * q^76 - 16 * q^79 + 2 * q^81 - 8 * q^84 - 8 * q^86 + 22 * q^89 + 8 * q^91 - 24 * q^94 - 2 * q^96 + 4 * q^99

Introduction

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