LMFDB - Embedded newform 3525.2.a.z.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.a (trivial)

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:	yes
Analytic conductor:	$28.1472667125$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 9x^{5} + 10x^{4} + 16x^{3} - 15x^{2} - 6x + 5 $ x^7 - x^6 - 9x^5 + 10x^4 + 16x^3 - 15x^2 - 6*x + 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.21680$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.21680 q^{2} +1.00000 q^{3} -0.519390 q^{4} +1.21680 q^{6} +4.53738 q^{7} -3.06560 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.21680 q^{2} +1.00000 q^{3} -0.519390 q^{4} +1.21680 q^{6} +4.53738 q^{7} -3.06560 q^{8} +1.00000 q^{9} -3.28509 q^{11} -0.519390 q^{12} -1.39156 q^{13} +5.52110 q^{14} -2.69145 q^{16} +4.08481 q^{17} +1.21680 q^{18} +0.420377 q^{19} +4.53738 q^{21} -3.99731 q^{22} -2.30430 q^{23} -3.06560 q^{24} -1.69325 q^{26} +1.00000 q^{27} -2.35667 q^{28} +8.22544 q^{29} +8.24059 q^{31} +2.85623 q^{32} -3.28509 q^{33} +4.97041 q^{34} -0.519390 q^{36} -4.59805 q^{37} +0.511516 q^{38} -1.39156 q^{39} +2.52605 q^{41} +5.52110 q^{42} +10.2312 q^{43} +1.70624 q^{44} -2.80388 q^{46} +1.00000 q^{47} -2.69145 q^{48} +13.5878 q^{49} +4.08481 q^{51} +0.722760 q^{52} +11.0093 q^{53} +1.21680 q^{54} -13.9098 q^{56} +0.420377 q^{57} +10.0087 q^{58} +8.49265 q^{59} -9.77918 q^{61} +10.0272 q^{62} +4.53738 q^{63} +8.85838 q^{64} -3.99731 q^{66} -11.8522 q^{67} -2.12161 q^{68} -2.30430 q^{69} -1.30371 q^{71} -3.06560 q^{72} -9.42994 q^{73} -5.59493 q^{74} -0.218340 q^{76} -14.9057 q^{77} -1.69325 q^{78} -6.44218 q^{79} +1.00000 q^{81} +3.07371 q^{82} +4.45292 q^{83} -2.35667 q^{84} +12.4493 q^{86} +8.22544 q^{87} +10.0708 q^{88} +12.5554 q^{89} -6.31402 q^{91} +1.19683 q^{92} +8.24059 q^{93} +1.21680 q^{94} +2.85623 q^{96} -5.04406 q^{97} +16.5337 q^{98} -3.28509 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} + 7 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 + 7 * q^7 + 6 * q^8 + 7 * q^9	$ 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} + 7 q^{7} + 6 q^{8} + 7 q^{9} + 5 q^{12} + 5 q^{13} + 7 q^{14} + 9 q^{16} + 2 q^{17} - q^{18} - 13 q^{19} + 7 q^{21} - 14 q^{22} + 6 q^{23} + 6 q^{24} + 7 q^{27} + 30 q^{28} + 9 q^{29} + 5 q^{31} + 26 q^{32} - 8 q^{34} + 5 q^{36} - 5 q^{37} - 2 q^{38} + 5 q^{39} + 18 q^{41} + 7 q^{42} + 14 q^{43} + 17 q^{44} - 27 q^{46} + 7 q^{47} + 9 q^{48} + 14 q^{49} + 2 q^{51} - 3 q^{52} + 20 q^{53} - q^{54} + 17 q^{56} - 13 q^{57} + 37 q^{58} + 10 q^{59} - 8 q^{61} - 6 q^{62} + 7 q^{63} + 18 q^{64} - 14 q^{66} + 4 q^{67} + 10 q^{68} + 6 q^{69} + 12 q^{71} + 6 q^{72} + 4 q^{73} - 25 q^{74} - 66 q^{76} + 6 q^{77} - 5 q^{79} + 7 q^{81} - 29 q^{82} + 52 q^{83} + 30 q^{84} - 17 q^{86} + 9 q^{87} + 26 q^{88} + 32 q^{89} - 26 q^{91} - 17 q^{92} + 5 q^{93} - q^{94} + 26 q^{96} - 12 q^{97} + 40 q^{98}+O(q^{100}) $ 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 + 7 * q^7 + 6 * q^8 + 7 * q^9 + 5 * q^12 + 5 * q^13 + 7 * q^14 + 9 * q^16 + 2 * q^17 - q^18 - 13 * q^19 + 7 * q^21 - 14 * q^22 + 6 * q^23 + 6 * q^24 + 7 * q^27 + 30 * q^28 + 9 * q^29 + 5 * q^31 + 26 * q^32 - 8 * q^34 + 5 * q^36 - 5 * q^37 - 2 * q^38 + 5 * q^39 + 18 * q^41 + 7 * q^42 + 14 * q^43 + 17 * q^44 - 27 * q^46 + 7 * q^47 + 9 * q^48 + 14 * q^49 + 2 * q^51 - 3 * q^52 + 20 * q^53 - q^54 + 17 * q^56 - 13 * q^57 + 37 * q^58 + 10 * q^59 - 8 * q^61 - 6 * q^62 + 7 * q^63 + 18 * q^64 - 14 * q^66 + 4 * q^67 + 10 * q^68 + 6 * q^69 + 12 * q^71 + 6 * q^72 + 4 * q^73 - 25 * q^74 - 66 * q^76 + 6 * q^77 - 5 * q^79 + 7 * q^81 - 29 * q^82 + 52 * q^83 + 30 * q^84 - 17 * q^86 + 9 * q^87 + 26 * q^88 + 32 * q^89 - 26 * q^91 - 17 * q^92 + 5 * q^93 - q^94 + 26 * q^96 - 12 * q^97 + 40 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	1.21680	0.860410	0.430205	−	0.902731i	$-0.358441\pi$
$2$	1.21680	0.860410	0.430205	+	0.902731i	$0.358441\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.519390	−0.259695
$5$	0	0
$5$	0	0
$6$	1.21680	0.496758
$7$	4.53738	1.71497	0.857484	−	0.514510i	$-0.172026\pi$
$7$	4.53738	1.71497	0.857484	+	0.514510i	$0.172026\pi$
$8$	−3.06560	−1.08385
$9$	1.00000	0.333333
$10$	0	0
$11$	−3.28509	−0.990493	−0.495246	−	0.868753i	$-0.664922\pi$
$11$	−3.28509	−0.990493	−0.495246	+	0.868753i	$0.664922\pi$
$12$	−0.519390	−0.149935
$13$	−1.39156	−0.385948	−0.192974	−	0.981204i	$-0.561813\pi$
$13$	−1.39156	−0.385948	−0.192974	+	0.981204i	$0.561813\pi$
$14$	5.52110	1.47558
$15$	0	0
$16$	−2.69145	−0.672864
$17$	4.08481	0.990711	0.495355	−	0.868690i	$-0.335038\pi$
$17$	4.08481	0.990711	0.495355	+	0.868690i	$0.335038\pi$
$18$	1.21680	0.286803
$19$	0.420377	0.0964412	0.0482206	−	0.998837i	$-0.484645\pi$
$19$	0.420377	0.0964412	0.0482206	+	0.998837i	$0.484645\pi$
$20$	0	0
$21$	4.53738	0.990138
$22$	−3.99731	−0.852230
$23$	−2.30430	−0.480479	−0.240240	−	0.970714i	$-0.577226\pi$
$23$	−2.30430	−0.480479	−0.240240	+	0.970714i	$0.577226\pi$
$24$	−3.06560	−0.625763
$25$	0	0
$26$	−1.69325	−0.332074
$27$	1.00000	0.192450
$28$	−2.35667	−0.445369
$29$	8.22544	1.52743	0.763713	−	0.645556i	$-0.223374\pi$
$29$	8.22544	1.52743	0.763713	+	0.645556i	$0.223374\pi$
$30$	0	0
$31$	8.24059	1.48005	0.740027	−	0.672577i	$-0.234813\pi$
$31$	8.24059	1.48005	0.740027	+	0.672577i	$0.234813\pi$
$32$	2.85623	0.504915
$33$	−3.28509	−0.571861
$34$	4.97041	0.852417
$35$	0	0
$36$	−0.519390	−0.0865650
$37$	−4.59805	−0.755915	−0.377958	−	0.925823i	$-0.623374\pi$
$37$	−4.59805	−0.755915	−0.377958	+	0.925823i	$0.623374\pi$
$38$	0.511516	0.0829789
$39$	−1.39156	−0.222827
$40$	0	0
$41$	2.52605	0.394503	0.197252	−	0.980353i	$-0.436798\pi$
$41$	2.52605	0.394503	0.197252	+	0.980353i	$0.436798\pi$
$42$	5.52110	0.851924
$43$	10.2312	1.56024	0.780120	−	0.625630i	$-0.215158\pi$
$43$	10.2312	1.56024	0.780120	+	0.625630i	$0.215158\pi$
$44$	1.70624	0.257226
$45$	0	0
$46$	−2.80388	−0.413409
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	−2.69145	−0.388478
$49$	13.5878	1.94112
$50$	0	0
$51$	4.08481	0.571987
$52$	0.722760	0.100229
$53$	11.0093	1.51225	0.756125	−	0.654427i	$-0.227090\pi$
$53$	11.0093	1.51225	0.756125	+	0.654427i	$0.227090\pi$
$54$	1.21680	0.165586
$55$	0	0
$56$	−13.9098	−1.85878
$57$	0.420377	0.0556803
$58$	10.0087	1.31421
$59$	8.49265	1.10565	0.552824	−	0.833298i	$-0.313550\pi$
$59$	8.49265	1.10565	0.552824	+	0.833298i	$0.313550\pi$
$60$	0	0
$61$	−9.77918	−1.25210	−0.626048	−	0.779784i	$-0.715329\pi$
$61$	−9.77918	−1.25210	−0.626048	+	0.779784i	$0.715329\pi$
$62$	10.0272	1.27345
$63$	4.53738	0.571656
$64$	8.85838	1.10730
$65$	0	0
$66$	−3.99731	−0.492035
$67$	−11.8522	−1.44798	−0.723991	−	0.689810i	$-0.757694\pi$
$67$	−11.8522	−1.44798	−0.723991	+	0.689810i	$0.757694\pi$
$68$	−2.12161	−0.257283
$69$	−2.30430	−0.277405
$70$	0	0
$71$	−1.30371	−0.154722	−0.0773612	−	0.997003i	$-0.524649\pi$
$71$	−1.30371	−0.154722	−0.0773612	+	0.997003i	$0.524649\pi$
$72$	−3.06560	−0.361285
$73$	−9.42994	−1.10369	−0.551846	−	0.833946i	$-0.686076\pi$
$73$	−9.42994	−1.10369	−0.551846	+	0.833946i	$0.686076\pi$
$74$	−5.59493	−0.650397
$75$	0	0
$76$	−0.218340	−0.0250453
$77$	−14.9057	−1.69866
$78$	−1.69325	−0.191723
$79$	−6.44218	−0.724802	−0.362401	−	0.932022i	$-0.618043\pi$
$79$	−6.44218	−0.724802	−0.362401	+	0.932022i	$0.618043\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	3.07371	0.339435
$83$	4.45292	0.488772	0.244386	−	0.969678i	$-0.421414\pi$
$83$	4.45292	0.488772	0.244386	+	0.969678i	$0.421414\pi$
$84$	−2.35667	−0.257134
$85$	0	0
$86$	12.4493	1.34245
$87$	8.22544	0.881860
$88$	10.0708	1.07355
$89$	12.5554	1.33087	0.665434	−	0.746457i	$-0.268247\pi$
$89$	12.5554	1.33087	0.665434	+	0.746457i	$0.268247\pi$
$90$	0	0
$91$	−6.31402	−0.661889
$92$	1.19683	0.124778
$93$	8.24059	0.854509
$94$	1.21680	0.125504
$95$	0	0
$96$	2.85623	0.291513
$97$	−5.04406	−0.512146	−0.256073	−	0.966657i	$-0.582429\pi$
$97$	−5.04406	−0.512146	−0.256073	+	0.966657i	$0.582429\pi$
$98$	16.5337	1.67016
$99$	−3.28509	−0.330164
$100$	0	0
$101$	13.0371	1.29724	0.648622	−	0.761111i	$-0.275346\pi$
$101$	13.0371	1.29724	0.648622	+	0.761111i	$0.275346\pi$
$102$	4.97041	0.492143
$103$	−14.4516	−1.42396	−0.711978	−	0.702201i	$-0.752201\pi$
$103$	−14.4516	−1.42396	−0.711978	+	0.702201i	$0.752201\pi$
$104$	4.26596	0.418311
$105$	0	0
$106$	13.3962	1.30115
$107$	12.9917	1.25595	0.627977	−	0.778232i	$-0.283883\pi$
$107$	12.9917	1.25595	0.627977	+	0.778232i	$0.283883\pi$
$108$	−0.519390	−0.0499783
$109$	−3.47284	−0.332638	−0.166319	−	0.986072i	$-0.553188\pi$
$109$	−3.47284	−0.332638	−0.166319	+	0.986072i	$0.553188\pi$
$110$	0	0
$111$	−4.59805	−0.436428
$112$	−12.2122	−1.15394
$113$	−5.81310	−0.546850	−0.273425	−	0.961893i	$-0.588157\pi$
$113$	−5.81310	−0.546850	−0.273425	+	0.961893i	$0.588157\pi$
$114$	0.511516	0.0479079
$115$	0	0
$116$	−4.27221	−0.396665
$117$	−1.39156	−0.128649
$118$	10.3339	0.951311
$119$	18.5343	1.69904
$120$	0	0
$121$	−0.208164	−0.0189240
$122$	−11.8993	−1.07732
$123$	2.52605	0.227767
$124$	−4.28008	−0.384362
$125$	0	0
$126$	5.52110	0.491859
$127$	6.07694	0.539241	0.269621	−	0.962967i	$-0.413102\pi$
$127$	6.07694	0.539241	0.269621	+	0.962967i	$0.413102\pi$
$128$	5.06644	0.447815
$129$	10.2312	0.900805
$130$	0	0
$131$	6.45627	0.564086	0.282043	−	0.959402i	$-0.408988\pi$
$131$	6.45627	0.564086	0.282043	+	0.959402i	$0.408988\pi$
$132$	1.70624	0.148509
$133$	1.90741	0.165394
$134$	−14.4218	−1.24586
$135$	0	0
$136$	−12.5224	−1.07379
$137$	−0.742677	−0.0634512	−0.0317256	−	0.999497i	$-0.510100\pi$
$137$	−0.742677	−0.0634512	−0.0317256	+	0.999497i	$0.510100\pi$
$138$	−2.80388	−0.238682
$139$	−7.70607	−0.653620	−0.326810	−	0.945090i	$-0.605974\pi$
$139$	−7.70607	−0.653620	−0.326810	+	0.945090i	$0.605974\pi$
$140$	0	0
$141$	1.00000	0.0842152
$142$	−1.58636	−0.133125
$143$	4.57139	0.382279
$144$	−2.69145	−0.224288
$145$	0	0
$146$	−11.4744	−0.949627
$147$	13.5878	1.12071
$148$	2.38818	0.196307
$149$	−13.9733	−1.14474	−0.572370	−	0.819996i	$-0.693976\pi$
$149$	−13.9733	−1.14474	−0.572370	+	0.819996i	$0.693976\pi$
$150$	0	0
$151$	−15.3707	−1.25085	−0.625426	−	0.780283i	$-0.715075\pi$
$151$	−15.3707	−1.25085	−0.625426	+	0.780283i	$0.715075\pi$
$152$	−1.28871	−0.104528
$153$	4.08481	0.330237
$154$	−18.1373	−1.46155
$155$	0	0
$156$	0.722760	0.0578671
$157$	20.1294	1.60650	0.803250	−	0.595643i	$-0.203103\pi$
$157$	20.1294	1.60650	0.803250	+	0.595643i	$0.203103\pi$
$158$	−7.83887	−0.623627
$159$	11.0093	0.873098
$160$	0	0
$161$	−10.4555	−0.824007
$162$	1.21680	0.0956011
$163$	5.59796	0.438466	0.219233	−	0.975673i	$-0.429645\pi$
$163$	5.59796	0.438466	0.219233	+	0.975673i	$0.429645\pi$
$164$	−1.31201	−0.102451
$165$	0	0
$166$	5.41833	0.420544
$167$	16.9149	1.30891	0.654457	−	0.756099i	$-0.272897\pi$
$167$	16.9149	1.30891	0.654457	+	0.756099i	$0.272897\pi$
$168$	−13.9098	−1.07316
$169$	−11.0636	−0.851044
$170$	0	0
$171$	0.420377	0.0321471
$172$	−5.31397	−0.405186
$173$	−19.9579	−1.51737	−0.758686	−	0.651457i	$-0.774158\pi$
$173$	−19.9579	−1.51737	−0.758686	+	0.651457i	$0.774158\pi$
$174$	10.0087	0.758761
$175$	0	0
$176$	8.84168	0.666467
$177$	8.49265	0.638347
$178$	15.2774	1.14509
$179$	16.2458	1.21426	0.607132	−	0.794601i	$-0.292320\pi$
$179$	16.2458	1.21426	0.607132	+	0.794601i	$0.292320\pi$
$180$	0	0
$181$	18.0843	1.34420	0.672099	−	0.740461i	$-0.265393\pi$
$181$	18.0843	1.34420	0.672099	+	0.740461i	$0.265393\pi$
$182$	−7.68292	−0.569496
$183$	−9.77918	−0.722898
$184$	7.06406	0.520769
$185$	0	0
$186$	10.0272	0.735228
$187$	−13.4190	−0.981292
$188$	−0.519390	−0.0378804
$189$	4.53738	0.330046
$190$	0	0
$191$	−1.54758	−0.111979	−0.0559895	−	0.998431i	$-0.517831\pi$
$191$	−1.54758	−0.111979	−0.0559895	+	0.998431i	$0.517831\pi$
$192$	8.85838	0.639299
$193$	11.1141	0.800010	0.400005	−	0.916513i	$-0.369008\pi$
$193$	11.1141	0.800010	0.400005	+	0.916513i	$0.369008\pi$
$194$	−6.13763	−0.440656
$195$	0	0
$196$	−7.05738	−0.504099
$197$	5.69750	0.405930	0.202965	−	0.979186i	$-0.434942\pi$
$197$	5.69750	0.405930	0.202965	+	0.979186i	$0.434942\pi$
$198$	−3.99731	−0.284077
$199$	−15.9456	−1.13036	−0.565178	−	0.824969i	$-0.691192\pi$
$199$	−15.9456	−1.13036	−0.565178	+	0.824969i	$0.691192\pi$
$200$	0	0
$201$	−11.8522	−0.835992
$202$	15.8636	1.11616
$203$	37.3220	2.61949
$204$	−2.12161	−0.148542
$205$	0	0
$206$	−17.5847	−1.22519
$207$	−2.30430	−0.160160
$208$	3.74531	0.259691
$209$	−1.38098	−0.0955243
$210$	0	0
$211$	−10.1813	−0.700909	−0.350454	−	0.936580i	$-0.613973\pi$
$211$	−10.1813	−0.700909	−0.350454	+	0.936580i	$0.613973\pi$
$212$	−5.71814	−0.392724
$213$	−1.30371	−0.0893290
$214$	15.8083	1.08064
$215$	0	0
$216$	−3.06560	−0.208588
$217$	37.3907	2.53825
$218$	−4.22576	−0.286205
$219$	−9.42994	−0.637216
$220$	0	0
$221$	−5.68424	−0.382363
$222$	−5.59493	−0.375507
$223$	−13.3592	−0.894596	−0.447298	−	0.894385i	$-0.647614\pi$
$223$	−13.3592	−0.894596	−0.447298	+	0.894385i	$0.647614\pi$
$224$	12.9598	0.865914
$225$	0	0
$226$	−7.07340	−0.470515
$227$	−6.45688	−0.428558	−0.214279	−	0.976772i	$-0.568740\pi$
$227$	−6.45688	−0.428558	−0.214279	+	0.976772i	$0.568740\pi$
$228$	−0.218340	−0.0144599
$229$	0.0244753	0.00161737	0.000808687	−	1.00000i	$-0.499743\pi$
$229$	0.0244753	0.00161737	0.000808687		1.00000i	$0.499743\pi$
$230$	0	0
$231$	−14.9057	−0.980724
$232$	−25.2159	−1.65551
$233$	−25.2026	−1.65108	−0.825538	−	0.564346i	$-0.809128\pi$
$233$	−25.2026	−1.65108	−0.825538	+	0.564346i	$0.809128\pi$
$234$	−1.69325	−0.110691
$235$	0	0
$236$	−4.41100	−0.287131
$237$	−6.44218	−0.418465
$238$	22.5526	1.46187
$239$	20.4604	1.32347	0.661737	−	0.749736i	$-0.269820\pi$
$239$	20.4604	1.32347	0.661737	+	0.749736i	$0.269820\pi$
$240$	0	0
$241$	−16.0936	−1.03668	−0.518340	−	0.855174i	$-0.673450\pi$
$241$	−16.0936	−1.03668	−0.518340	+	0.855174i	$0.673450\pi$
$242$	−0.253294	−0.0162824
$243$	1.00000	0.0641500
$244$	5.07921	0.325163
$245$	0	0
$246$	3.07371	0.195973
$247$	−0.584979	−0.0372213
$248$	−25.2624	−1.60416
$249$	4.45292	0.282193
$250$	0	0
$251$	−29.2674	−1.84734	−0.923671	−	0.383186i	$-0.874827\pi$
$251$	−29.2674	−1.84734	−0.923671	+	0.383186i	$0.874827\pi$
$252$	−2.35667	−0.148456
$253$	7.56983	0.475911
$254$	7.39444	0.463968
$255$	0	0
$256$	−11.5519	−0.721994
$257$	−17.5663	−1.09576	−0.547879	−	0.836558i	$-0.684565\pi$
$257$	−17.5663	−1.09576	−0.547879	+	0.836558i	$0.684565\pi$
$258$	12.4493	0.775061
$259$	−20.8631	−1.29637
$260$	0	0
$261$	8.22544	0.509142
$262$	7.85600	0.485346
$263$	12.4928	0.770340	0.385170	−	0.922846i	$-0.374143\pi$
$263$	12.4928	0.770340	0.385170	+	0.922846i	$0.374143\pi$
$264$	10.0708	0.619814
$265$	0	0
$266$	2.32095	0.142306
$267$	12.5554	0.768377
$268$	6.15593	0.376033
$269$	14.7905	0.901795	0.450897	−	0.892576i	$-0.351104\pi$
$269$	14.7905	0.901795	0.450897	+	0.892576i	$0.351104\pi$
$270$	0	0
$271$	−0.892777	−0.0542323	−0.0271162	−	0.999632i	$-0.508632\pi$
$271$	−0.892777	−0.0542323	−0.0271162	+	0.999632i	$0.508632\pi$
$272$	−10.9941	−0.666613
$273$	−6.31402	−0.382142
$274$	−0.903692	−0.0545940
$275$	0	0
$276$	1.19683	0.0720406
$277$	23.7459	1.42675	0.713377	−	0.700780i	$-0.247165\pi$
$277$	23.7459	1.42675	0.713377	+	0.700780i	$0.247165\pi$
$278$	−9.37677	−0.562381
$279$	8.24059	0.493351
$280$	0	0
$281$	1.77855	0.106099	0.0530496	−	0.998592i	$-0.483106\pi$
$281$	1.77855	0.106099	0.0530496	+	0.998592i	$0.483106\pi$
$282$	1.21680	0.0724596
$283$	32.6718	1.94213	0.971067	−	0.238806i	$-0.0767561\pi$
$283$	32.6718	1.94213	0.971067	+	0.238806i	$0.0767561\pi$
$284$	0.677136	0.0401806
$285$	0	0
$286$	5.56248	0.328917
$287$	11.4617	0.676561
$288$	2.85623	0.168305
$289$	−0.314361	−0.0184918
$290$	0	0
$291$	−5.04406	−0.295688
$292$	4.89782	0.286623
$293$	−12.4826	−0.729243	−0.364621	−	0.931156i	$-0.618802\pi$
$293$	−12.4826	−0.729243	−0.364621	+	0.931156i	$0.618802\pi$
$294$	16.5337	0.964266
$295$	0	0
$296$	14.0958	0.819302
$297$	−3.28509	−0.190620
$298$	−17.0028	−0.984945
$299$	3.20656	0.185440
$300$	0	0
$301$	46.4227	2.67576
$302$	−18.7032	−1.07625
$303$	13.0371	0.748964
$304$	−1.13143	−0.0648918
$305$	0	0
$306$	4.97041	0.284139
$307$	26.6908	1.52332	0.761662	−	0.647974i	$-0.224384\pi$
$307$	26.6908	1.52332	0.761662	+	0.647974i	$0.224384\pi$
$308$	7.74188	0.441135
$309$	−14.4516	−0.822122
$310$	0	0
$311$	−28.6855	−1.62661	−0.813304	−	0.581839i	$-0.802333\pi$
$311$	−28.6855	−1.62661	−0.813304	+	0.581839i	$0.802333\pi$
$312$	4.26596	0.241512
$313$	−8.01895	−0.453258	−0.226629	−	0.973981i	$-0.572770\pi$
$313$	−8.01895	−0.453258	−0.226629	+	0.973981i	$0.572770\pi$
$314$	24.4935	1.38225
$315$	0	0
$316$	3.34601	0.188228
$317$	−2.89460	−0.162577	−0.0812883	−	0.996691i	$-0.525903\pi$
$317$	−2.89460	−0.162577	−0.0812883	+	0.996691i	$0.525903\pi$
$318$	13.3962	0.751222
$319$	−27.0213	−1.51290
$320$	0	0
$321$	12.9917	0.725126
$322$	−12.7223	−0.708984
$323$	1.71716	0.0955453
$324$	−0.519390	−0.0288550
$325$	0	0
$326$	6.81161	0.377260
$327$	−3.47284	−0.192048
$328$	−7.74387	−0.427584
$329$	4.53738	0.250154
$330$	0	0
$331$	0.276954	0.0152228	0.00761140	−	0.999971i	$-0.497577\pi$
$331$	0.276954	0.0152228	0.00761140	+	0.999971i	$0.497577\pi$
$332$	−2.31280	−0.126932
$333$	−4.59805	−0.251972
$334$	20.5821	1.12620
$335$	0	0
$336$	−12.2122	−0.666228
$337$	28.5186	1.55351	0.776753	−	0.629806i	$-0.216865\pi$
$337$	28.5186	1.55351	0.776753	+	0.629806i	$0.216865\pi$
$338$	−13.4622	−0.732247
$339$	−5.81310	−0.315724
$340$	0	0
$341$	−27.0711	−1.46598
$342$	0.511516	0.0276596
$343$	29.8915	1.61399
$344$	−31.3647	−1.69107
$345$	0	0
$346$	−24.2848	−1.30556
$347$	5.37779	0.288695	0.144347	−	0.989527i	$-0.453892\pi$
$347$	5.37779	0.288695	0.144347	+	0.989527i	$0.453892\pi$
$348$	−4.27221	−0.229015
$349$	−19.9855	−1.06980	−0.534899	−	0.844916i	$-0.679650\pi$
$349$	−19.9855	−1.06980	−0.534899	+	0.844916i	$0.679650\pi$
$350$	0	0
$351$	−1.39156	−0.0742758
$352$	−9.38299	−0.500115
$353$	3.17104	0.168777	0.0843886	−	0.996433i	$-0.473106\pi$
$353$	3.17104	0.168777	0.0843886	+	0.996433i	$0.473106\pi$
$354$	10.3339	0.549240
$355$	0	0
$356$	−6.52114	−0.345620
$357$	18.5343	0.980940
$358$	19.7679	1.04477
$359$	−5.61963	−0.296593	−0.148296	−	0.988943i	$-0.547379\pi$
$359$	−5.61963	−0.296593	−0.148296	+	0.988943i	$0.547379\pi$
$360$	0	0
$361$	−18.8233	−0.990699
$362$	22.0051	1.15656
$363$	−0.208164	−0.0109258
$364$	3.27944	0.171889
$365$	0	0
$366$	−11.8993	−0.621989
$367$	−3.81477	−0.199130	−0.0995648	−	0.995031i	$-0.531745\pi$
$367$	−3.81477	−0.199130	−0.0995648	+	0.995031i	$0.531745\pi$
$368$	6.20191	0.323297
$369$	2.52605	0.131501
$370$	0	0
$371$	49.9536	2.59346
$372$	−4.28008	−0.221912
$373$	−16.1014	−0.833696	−0.416848	−	0.908976i	$-0.636865\pi$
$373$	−16.1014	−0.833696	−0.416848	+	0.908976i	$0.636865\pi$
$374$	−16.3282	−0.844313
$375$	0	0
$376$	−3.06560	−0.158096
$377$	−11.4462	−0.589507
$378$	5.52110	0.283975
$379$	3.52863	0.181254	0.0906268	−	0.995885i	$-0.471113\pi$
$379$	3.52863	0.181254	0.0906268	+	0.995885i	$0.471113\pi$
$380$	0	0
$381$	6.07694	0.311331
$382$	−1.88310	−0.0963479
$383$	8.10798	0.414299	0.207149	−	0.978309i	$-0.433581\pi$
$383$	8.10798	0.414299	0.207149	+	0.978309i	$0.433581\pi$
$384$	5.06644	0.258546
$385$	0	0
$386$	13.5237	0.688336
$387$	10.2312	0.520080
$388$	2.61983	0.133002
$389$	−18.2015	−0.922854	−0.461427	−	0.887178i	$-0.652662\pi$
$389$	−18.2015	−0.922854	−0.461427	+	0.887178i	$0.652662\pi$
$390$	0	0
$391$	−9.41261	−0.476016
$392$	−41.6549	−2.10389
$393$	6.45627	0.325675
$394$	6.93274	0.349267
$395$	0	0
$396$	1.70624	0.0857420
$397$	−12.5382	−0.629272	−0.314636	−	0.949212i	$-0.601883\pi$
$397$	−12.5382	−0.629272	−0.314636	+	0.949212i	$0.601883\pi$
$398$	−19.4027	−0.972569
$399$	1.90741	0.0954900
$400$	0	0
$401$	7.92662	0.395836	0.197918	−	0.980219i	$-0.436582\pi$
$401$	7.92662	0.395836	0.197918	+	0.980219i	$0.436582\pi$
$402$	−14.4218	−0.719296
$403$	−11.4672	−0.571224
$404$	−6.77136	−0.336888
$405$	0	0
$406$	45.4135	2.25383
$407$	15.1050	0.748729
$408$	−12.5224	−0.619951
$409$	−33.4393	−1.65347	−0.826733	−	0.562594i	$-0.809803\pi$
$409$	−33.4393	−1.65347	−0.826733	+	0.562594i	$0.809803\pi$
$410$	0	0
$411$	−0.742677	−0.0366335
$412$	7.50601	0.369794
$413$	38.5344	1.89615
$414$	−2.80388	−0.137803
$415$	0	0
$416$	−3.97461	−0.194871
$417$	−7.70607	−0.377368
$418$	−1.68038	−0.0821900
$419$	−30.0288	−1.46701	−0.733503	−	0.679687i	$-0.762116\pi$
$419$	−30.0288	−1.46701	−0.733503	+	0.679687i	$0.762116\pi$
$420$	0	0
$421$	21.9845	1.07146	0.535730	−	0.844389i	$-0.320037\pi$
$421$	21.9845	1.07146	0.535730	+	0.844389i	$0.320037\pi$
$422$	−12.3886	−0.603069
$423$	1.00000	0.0486217
$424$	−33.7503	−1.63906
$425$	0	0
$426$	−1.58636	−0.0768596
$427$	−44.3719	−2.14731
$428$	−6.74775	−0.326165
$429$	4.57139	0.220709
$430$	0	0
$431$	−17.5585	−0.845764	−0.422882	−	0.906185i	$-0.638981\pi$
$431$	−17.5585	−0.845764	−0.422882	+	0.906185i	$0.638981\pi$
$432$	−2.69145	−0.129493
$433$	22.5672	1.08451	0.542254	−	0.840215i	$-0.317571\pi$
$433$	22.5672	1.08451	0.542254	+	0.840215i	$0.317571\pi$
$434$	45.4971	2.18393
$435$	0	0
$436$	1.80376	0.0863843
$437$	−0.968674	−0.0463380
$438$	−11.4744	−0.548267
$439$	−26.6267	−1.27082	−0.635412	−	0.772173i	$-0.719170\pi$
$439$	−26.6267	−1.27082	−0.635412	+	0.772173i	$0.719170\pi$
$440$	0	0
$441$	13.5878	0.647040
$442$	−6.91660	−0.328989
$443$	−32.0263	−1.52162	−0.760809	−	0.648976i	$-0.775197\pi$
$443$	−32.0263	−1.52162	−0.760809	+	0.648976i	$0.775197\pi$
$444$	2.38818	0.113338
$445$	0	0
$446$	−16.2555	−0.769719
$447$	−13.9733	−0.660915
$448$	40.1939	1.89898
$449$	27.5424	1.29981	0.649904	−	0.760017i	$-0.274809\pi$
$449$	27.5424	1.29981	0.649904	+	0.760017i	$0.274809\pi$
$450$	0	0
$451$	−8.29832	−0.390753
$452$	3.01926	0.142014
$453$	−15.3707	−0.722180
$454$	−7.85676	−0.368736
$455$	0	0
$456$	−1.28871	−0.0603493
$457$	−33.4278	−1.56369	−0.781843	−	0.623476i	$-0.785720\pi$
$457$	−33.4278	−1.56369	−0.781843	+	0.623476i	$0.785720\pi$
$458$	0.0297817	0.00139161
$459$	4.08481	0.190662
$460$	0	0
$461$	−16.4232	−0.764903	−0.382452	−	0.923976i	$-0.624920\pi$
$461$	−16.4232	−0.764903	−0.382452	+	0.923976i	$0.624920\pi$
$462$	−18.1373	−0.843825
$463$	−21.0123	−0.976525	−0.488262	−	0.872697i	$-0.662369\pi$
$463$	−21.0123	−0.976525	−0.488262	+	0.872697i	$0.662369\pi$
$464$	−22.1384	−1.02775
$465$	0	0
$466$	−30.6666	−1.42060
$467$	−20.9392	−0.968950	−0.484475	−	0.874805i	$-0.660989\pi$
$467$	−20.9392	−0.968950	−0.484475	+	0.874805i	$0.660989\pi$
$468$	0.722760	0.0334096
$469$	−53.7781	−2.48324
$470$	0	0
$471$	20.1294	0.927513
$472$	−26.0351	−1.19836
$473$	−33.6104	−1.54541
$474$	−7.83887	−0.360051
$475$	0	0
$476$	−9.62654	−0.441232
$477$	11.0093	0.504083
$478$	24.8963	1.13873
$479$	11.5084	0.525832	0.262916	−	0.964819i	$-0.415316\pi$
$479$	11.5084	0.525832	0.262916	+	0.964819i	$0.415316\pi$
$480$	0	0
$481$	6.39845	0.291744
$482$	−19.5828	−0.891970
$483$	−10.4555	−0.475741
$484$	0.108118	0.00491446
$485$	0	0
$486$	1.21680	0.0551953
$487$	18.7989	0.851859	0.425930	−	0.904756i	$-0.359947\pi$
$487$	18.7989	0.851859	0.425930	+	0.904756i	$0.359947\pi$
$488$	29.9791	1.35709
$489$	5.59796	0.253148
$490$	0	0
$491$	−5.72474	−0.258354	−0.129177	−	0.991622i	$-0.541233\pi$
$491$	−5.72474	−0.258354	−0.129177	+	0.991622i	$0.541233\pi$
$492$	−1.31201	−0.0591498
$493$	33.5993	1.51324
$494$	−0.711804	−0.0320256
$495$	0	0
$496$	−22.1792	−0.995874
$497$	−5.91545	−0.265344
$498$	5.41833	0.242801
$499$	2.94138	0.131674	0.0658372	−	0.997830i	$-0.479028\pi$
$499$	2.94138	0.131674	0.0658372	+	0.997830i	$0.479028\pi$
$500$	0	0
$501$	16.9149	0.755702
$502$	−35.6127	−1.58947
$503$	0.508294	0.0226637	0.0113319	−	0.999936i	$-0.496393\pi$
$503$	0.508294	0.0226637	0.0113319	+	0.999936i	$0.496393\pi$
$504$	−13.9098	−0.619592
$505$	0	0
$506$	9.21099	0.409479
$507$	−11.0636	−0.491350
$508$	−3.15630	−0.140038
$509$	0.366001	0.0162227	0.00811136	−	0.999967i	$-0.497418\pi$
$509$	0.366001	0.0162227	0.00811136	+	0.999967i	$0.497418\pi$
$510$	0	0
$511$	−42.7872	−1.89280
$512$	−24.1893	−1.06903
$513$	0.420377	0.0185601
$514$	−21.3748	−0.942801
$515$	0	0
$516$	−5.31397	−0.233934
$517$	−3.28509	−0.144478
$518$	−25.3863	−1.11541
$519$	−19.9579	−0.876055
$520$	0	0
$521$	−12.2508	−0.536715	−0.268358	−	0.963319i	$-0.586481\pi$
$521$	−12.2508	−0.536715	−0.268358	+	0.963319i	$0.586481\pi$
$522$	10.0087	0.438071
$523$	10.6546	0.465895	0.232947	−	0.972489i	$-0.425163\pi$
$523$	10.6546	0.465895	0.232947	+	0.972489i	$0.425163\pi$
$524$	−3.35332	−0.146490
$525$	0	0
$526$	15.2013	0.662808
$527$	33.6612	1.46631
$528$	8.84168	0.384785
$529$	−17.6902	−0.769140
$530$	0	0
$531$	8.49265	0.368550
$532$	−0.990690	−0.0429519
$533$	−3.51515	−0.152258
$534$	15.2774	0.661119
$535$	0	0
$536$	36.3342	1.56940
$537$	16.2458	0.701056
$538$	17.9972	0.775913
$539$	−44.6373	−1.92266
$540$	0	0
$541$	24.5089	1.05372	0.526861	−	0.849952i	$-0.323369\pi$
$541$	24.5089	1.05372	0.526861	+	0.849952i	$0.323369\pi$
$542$	−1.08633	−0.0466620
$543$	18.0843	0.776073
$544$	11.6672	0.500225
$545$	0	0
$546$	−7.68292	−0.328799
$547$	−5.90832	−0.252622	−0.126311	−	0.991991i	$-0.540314\pi$
$547$	−5.90832	−0.252622	−0.126311	+	0.991991i	$0.540314\pi$
$548$	0.385739	0.0164779
$549$	−9.77918	−0.417365
$550$	0	0
$551$	3.45779	0.147307
$552$	7.06406	0.300666
$553$	−29.2306	−1.24301
$554$	28.8941	1.22759
$555$	0	0
$556$	4.00245	0.169742
$557$	26.6451	1.12899	0.564494	−	0.825437i	$-0.309071\pi$
$557$	26.6451	1.12899	0.564494	+	0.825437i	$0.309071\pi$
$558$	10.0272	0.424484
$559$	−14.2373	−0.602172
$560$	0	0
$561$	−13.4190	−0.566549
$562$	2.16414	0.0912888
$563$	−39.5577	−1.66716	−0.833579	−	0.552401i	$-0.813712\pi$
$563$	−39.5577	−1.66716	−0.833579	+	0.552401i	$0.813712\pi$
$564$	−0.519390	−0.0218703
$565$	0	0
$566$	39.7551	1.67103
$567$	4.53738	0.190552
$568$	3.99667	0.167697
$569$	24.6602	1.03381	0.516905	−	0.856042i	$-0.327084\pi$
$569$	24.6602	1.03381	0.516905	+	0.856042i	$0.327084\pi$
$570$	0	0
$571$	−14.7836	−0.618676	−0.309338	−	0.950952i	$-0.600107\pi$
$571$	−14.7836	−0.618676	−0.309338	+	0.950952i	$0.600107\pi$
$572$	−2.37433	−0.0992759
$573$	−1.54758	−0.0646511
$574$	13.9466	0.582120
$575$	0	0
$576$	8.85838	0.369099
$577$	−3.82148	−0.159090	−0.0795452	−	0.996831i	$-0.525347\pi$
$577$	−3.82148	−0.159090	−0.0795452	+	0.996831i	$0.525347\pi$
$578$	−0.382515	−0.0159105
$579$	11.1141	0.461886
$580$	0	0
$581$	20.2046	0.838228
$582$	−6.13763	−0.254413
$583$	−36.1667	−1.49787
$584$	28.9084	1.19624
$585$	0	0
$586$	−15.1889	−0.627448
$587$	8.39335	0.346431	0.173215	−	0.984884i	$-0.444584\pi$
$587$	8.39335	0.346431	0.173215	+	0.984884i	$0.444584\pi$
$588$	−7.05738	−0.291041
$589$	3.46416	0.142738
$590$	0	0
$591$	5.69750	0.234364
$592$	12.3755	0.508628
$593$	−17.1392	−0.703821	−0.351911	−	0.936034i	$-0.614468\pi$
$593$	−17.1392	−0.703821	−0.351911	+	0.936034i	$0.614468\pi$
$594$	−3.99731	−0.164012
$595$	0	0
$596$	7.25760	0.297283
$597$	−15.9456	−0.652611
$598$	3.90175	0.159554
$599$	−38.6697	−1.58000	−0.790001	−	0.613105i	$-0.789920\pi$
$599$	−38.6697	−1.58000	−0.790001	+	0.613105i	$0.789920\pi$
$600$	0	0
$601$	10.9414	0.446309	0.223155	−	0.974783i	$-0.428364\pi$
$601$	10.9414	0.446309	0.223155	+	0.974783i	$0.428364\pi$
$602$	56.4874	2.30225
$603$	−11.8522	−0.482660
$604$	7.98340	0.324840
$605$	0	0
$606$	15.8636	0.644416
$607$	−27.5639	−1.11879	−0.559393	−	0.828903i	$-0.688966\pi$
$607$	−27.5639	−1.11879	−0.559393	+	0.828903i	$0.688966\pi$
$608$	1.20070	0.0486946
$609$	37.3220	1.51236
$610$	0	0
$611$	−1.39156	−0.0562963
$612$	−2.12161	−0.0857609
$613$	−21.4502	−0.866365	−0.433182	−	0.901306i	$-0.642609\pi$
$613$	−21.4502	−0.866365	−0.433182	+	0.901306i	$0.642609\pi$
$614$	32.4775	1.31068
$615$	0	0
$616$	45.6950	1.84110
$617$	27.1945	1.09481	0.547405	−	0.836868i	$-0.315616\pi$
$617$	27.1945	1.09481	0.547405	+	0.836868i	$0.315616\pi$
$618$	−17.5847	−0.707362
$619$	21.3451	0.857932	0.428966	−	0.903321i	$-0.358878\pi$
$619$	21.3451	0.857932	0.428966	+	0.903321i	$0.358878\pi$
$620$	0	0
$621$	−2.30430	−0.0924683
$622$	−34.9047	−1.39955
$623$	56.9686	2.28240
$624$	3.74531	0.149932
$625$	0	0
$626$	−9.75749	−0.389988
$627$	−1.38098	−0.0551510
$628$	−10.4550	−0.417200
$629$	−18.7822	−0.748894
$630$	0	0
$631$	−28.7846	−1.14590	−0.572948	−	0.819591i	$-0.694200\pi$
$631$	−28.7846	−1.14590	−0.572948	+	0.819591i	$0.694200\pi$
$632$	19.7492	0.785580
$633$	−10.1813	−0.404670
$634$	−3.52215	−0.139883
$635$	0	0
$636$	−5.71814	−0.226739
$637$	−18.9082	−0.749171
$638$	−32.8797	−1.30172
$639$	−1.30371	−0.0515741
$640$	0	0
$641$	36.1126	1.42636	0.713181	−	0.700980i	$-0.247254\pi$
$641$	36.1126	1.42636	0.713181	+	0.700980i	$0.247254\pi$
$642$	15.8083	0.623905
$643$	−48.2977	−1.90467	−0.952337	−	0.305047i	$-0.901328\pi$
$643$	−48.2977	−1.90467	−0.952337	+	0.305047i	$0.901328\pi$
$644$	5.43047	0.213990
$645$	0	0
$646$	2.08945	0.0822081
$647$	−24.6297	−0.968293	−0.484147	−	0.874987i	$-0.660870\pi$
$647$	−24.6297	−0.968293	−0.484147	+	0.874987i	$0.660870\pi$
$648$	−3.06560	−0.120428
$649$	−27.8991	−1.09514
$650$	0	0
$651$	37.3907	1.46546
$652$	−2.90752	−0.113867
$653$	16.6932	0.653254	0.326627	−	0.945153i	$-0.394088\pi$
$653$	16.6932	0.653254	0.326627	+	0.945153i	$0.394088\pi$
$654$	−4.22576	−0.165240
$655$	0	0
$656$	−6.79876	−0.265447
$657$	−9.42994	−0.367897
$658$	5.52110	0.215235
$659$	9.45140	0.368174	0.184087	−	0.982910i	$-0.441067\pi$
$659$	9.45140	0.368174	0.184087	+	0.982910i	$0.441067\pi$
$660$	0	0
$661$	24.6888	0.960283	0.480141	−	0.877191i	$-0.340585\pi$
$661$	24.6888	0.960283	0.480141	+	0.877191i	$0.340585\pi$
$662$	0.336999	0.0130978
$663$	−5.68424	−0.220757
$664$	−13.6509	−0.529757
$665$	0	0
$666$	−5.59493	−0.216799
$667$	−18.9539	−0.733897
$668$	−8.78542	−0.339918
$669$	−13.3592	−0.516495
$670$	0	0
$671$	32.1255	1.24019
$672$	12.9598	0.499936
$673$	−43.9136	−1.69275	−0.846373	−	0.532591i	$-0.821218\pi$
$673$	−43.9136	−1.69275	−0.846373	+	0.532591i	$0.821218\pi$
$674$	34.7015	1.33665
$675$	0	0
$676$	5.74631	0.221012
$677$	−18.5210	−0.711819	−0.355910	−	0.934520i	$-0.615829\pi$
$677$	−18.5210	−0.711819	−0.355910	+	0.934520i	$0.615829\pi$
$678$	−7.07340	−0.271652
$679$	−22.8868	−0.878315
$680$	0	0
$681$	−6.45688	−0.247428
$682$	−32.9402	−1.26135
$683$	32.7847	1.25447	0.627236	−	0.778829i	$-0.284186\pi$
$683$	32.7847	1.25447	0.627236	+	0.778829i	$0.284186\pi$
$684$	−0.218340	−0.00834843
$685$	0	0
$686$	36.3721	1.38869
$687$	0.0244753	0.000933792 0
$688$	−27.5367	−1.04983
$689$	−15.3201	−0.583650
$690$	0	0
$691$	−27.9501	−1.06327	−0.531636	−	0.846973i	$-0.678423\pi$
$691$	−27.9501	−1.06327	−0.531636	+	0.846973i	$0.678423\pi$
$692$	10.3659	0.394054
$693$	−14.9057	−0.566221
$694$	6.54371	0.248396
$695$	0	0
$696$	−25.2159	−0.955807
$697$	10.3184	0.390839
$698$	−24.3184	−0.920465
$699$	−25.2026	−0.953249
$700$	0	0
$701$	−0.00146894	−5.54810e−5 0	−2.77405e−5	−	1.00000i	$-0.500009\pi$
$701$	−0.00146894	−5.54810e−5 0	−2.77405e−5		1.00000i	$0.500009\pi$
$702$	−1.69325	−0.0639076
$703$	−1.93292	−0.0729014
$704$	−29.1006	−1.09677
$705$	0	0
$706$	3.85853	0.145218
$707$	59.1545	2.22473
$708$	−4.41100	−0.165775
$709$	52.8005	1.98296	0.991482	−	0.130246i	$-0.0415768\pi$
$709$	52.8005	1.98296	0.991482	+	0.130246i	$0.0415768\pi$
$710$	0	0
$711$	−6.44218	−0.241601
$712$	−38.4898	−1.44247
$713$	−18.9888	−0.711135
$714$	22.5526	0.844011
$715$	0	0
$716$	−8.43788	−0.315338
$717$	20.4604	0.764108
$718$	−6.83798	−0.255191
$719$	−18.3694	−0.685061	−0.342531	−	0.939507i	$-0.611284\pi$
$719$	−18.3694	−0.685061	−0.342531	+	0.939507i	$0.611284\pi$
$720$	0	0
$721$	−65.5724	−2.44204
$722$	−22.9042	−0.852407
$723$	−16.0936	−0.598528
$724$	−9.39282	−0.349082
$725$	0	0
$726$	−0.253294	−0.00940062
$727$	24.2720	0.900198	0.450099	−	0.892979i	$-0.351389\pi$
$727$	24.2720	0.900198	0.450099	+	0.892979i	$0.351389\pi$
$728$	19.3563	0.717391
$729$	1.00000	0.0370370
$730$	0	0
$731$	41.7924	1.54575
$732$	5.07921	0.187733
$733$	20.3235	0.750666	0.375333	−	0.926890i	$-0.377528\pi$
$733$	20.3235	0.750666	0.375333	+	0.926890i	$0.377528\pi$
$734$	−4.64183	−0.171333
$735$	0	0
$736$	−6.58161	−0.242601
$737$	38.9357	1.43421
$738$	3.07371	0.113145
$739$	19.3772	0.712803	0.356401	−	0.934333i	$-0.384004\pi$
$739$	19.3772	0.712803	0.356401	+	0.934333i	$0.384004\pi$
$740$	0	0
$741$	−0.584979	−0.0214897
$742$	60.7837	2.23144
$743$	5.32143	0.195224	0.0976122	−	0.995225i	$-0.468880\pi$
$743$	5.32143	0.195224	0.0976122	+	0.995225i	$0.468880\pi$
$744$	−25.2624	−0.926163
$745$	0	0
$746$	−19.5922	−0.717321
$747$	4.45292	0.162924
$748$	6.96968	0.254837
$749$	58.9483	2.15392
$750$	0	0
$751$	31.1352	1.13614	0.568069	−	0.822981i	$-0.307690\pi$
$751$	31.1352	1.13614	0.568069	+	0.822981i	$0.307690\pi$
$752$	−2.69145	−0.0981472
$753$	−29.2674	−1.06656
$754$	−13.9277	−0.507218
$755$	0	0
$756$	−2.35667	−0.0857113
$757$	48.2526	1.75377	0.876884	−	0.480701i	$-0.159618\pi$
$757$	48.2526	1.75377	0.876884	+	0.480701i	$0.159618\pi$
$758$	4.29365	0.155952
$759$	7.56983	0.274767
$760$	0	0
$761$	9.72785	0.352634	0.176317	−	0.984333i	$-0.443582\pi$
$761$	9.72785	0.352634	0.176317	+	0.984333i	$0.443582\pi$
$762$	7.39444	0.267872
$763$	−15.7576	−0.570463
$764$	0.803798	0.0290804
$765$	0	0
$766$	9.86582	0.356467
$767$	−11.8180	−0.426723
$768$	−11.5519	−0.416843
$769$	3.95939	0.142779	0.0713896	−	0.997449i	$-0.477257\pi$
$769$	3.95939	0.142779	0.0713896	+	0.997449i	$0.477257\pi$
$770$	0	0
$771$	−17.5663	−0.632636
$772$	−5.77255	−0.207759
$773$	45.8561	1.64933	0.824665	−	0.565621i	$-0.191363\pi$
$773$	45.8561	1.64933	0.824665	+	0.565621i	$0.191363\pi$
$774$	12.4493	0.447482
$775$	0	0
$776$	15.4631	0.555092
$777$	−20.8631	−0.748460
$778$	−22.1477	−0.794033
$779$	1.06190	0.0380464
$780$	0	0
$781$	4.28282	0.153251
$782$	−11.4533	−0.409569
$783$	8.22544	0.293953
$784$	−36.5710	−1.30611
$785$	0	0
$786$	7.85600	0.280214
$787$	30.0780	1.07216	0.536082	−	0.844166i	$-0.319904\pi$
$787$	30.0780	1.07216	0.536082	+	0.844166i	$0.319904\pi$
$788$	−2.95923	−0.105418
$789$	12.4928	0.444756
$790$	0	0
$791$	−26.3762	−0.937831
$792$	10.0708	0.357850
$793$	13.6083	0.483244
$794$	−15.2565	−0.541432
$795$	0	0
$796$	8.28200	0.293548
$797$	−36.4652	−1.29166	−0.645832	−	0.763480i	$-0.723489\pi$
$797$	−36.4652	−1.29166	−0.645832	+	0.763480i	$0.723489\pi$
$798$	2.32095	0.0821606
$799$	4.08481	0.144510
$800$	0	0
$801$	12.5554	0.443623
$802$	9.64513	0.340582
$803$	30.9782	1.09320
$804$	6.15593	0.217103
$805$	0	0
$806$	−13.9534	−0.491487
$807$	14.7905	0.520651
$808$	−39.9667	−1.40602
$809$	−3.72681	−0.131028	−0.0655138	−	0.997852i	$-0.520869\pi$
$809$	−3.72681	−0.131028	−0.0655138	+	0.997852i	$0.520869\pi$
$810$	0	0
$811$	−19.0252	−0.668066	−0.334033	−	0.942561i	$-0.608410\pi$
$811$	−19.0252	−0.668066	−0.334033	+	0.942561i	$0.608410\pi$
$812$	−19.3847	−0.680268
$813$	−0.892777	−0.0313111
$814$	18.3799	0.644214
$815$	0	0
$816$	−10.9941	−0.384869
$817$	4.30095	0.150471
$818$	−40.6890	−1.42266
$819$	−6.31402	−0.220630
$820$	0	0
$821$	−11.1054	−0.387581	−0.193791	−	0.981043i	$-0.562078\pi$
$821$	−11.1054	−0.387581	−0.193791	+	0.981043i	$0.562078\pi$
$822$	−0.903692	−0.0315199
$823$	2.44235	0.0851350	0.0425675	−	0.999094i	$-0.486446\pi$
$823$	2.44235	0.0851350	0.0425675	+	0.999094i	$0.486446\pi$
$824$	44.3028	1.54336
$825$	0	0
$826$	46.8888	1.63147
$827$	11.8394	0.411698	0.205849	−	0.978584i	$-0.434004\pi$
$827$	11.8394	0.411698	0.205849	+	0.978584i	$0.434004\pi$
$828$	1.19683	0.0415927
$829$	−19.5019	−0.677329	−0.338664	−	0.940907i	$-0.609975\pi$
$829$	−19.5019	−0.677329	−0.338664	+	0.940907i	$0.609975\pi$
$830$	0	0
$831$	23.7459	0.823737
$832$	−12.3269	−0.427360
$833$	55.5036	1.92309
$834$	−9.37677	−0.324691
$835$	0	0
$836$	0.717266	0.0248072
$837$	8.24059	0.284836
$838$	−36.5392	−1.26223
$839$	−25.8602	−0.892792	−0.446396	−	0.894835i	$-0.647293\pi$
$839$	−25.8602	−0.892792	−0.446396	+	0.894835i	$0.647293\pi$
$840$	0	0
$841$	38.6579	1.33303
$842$	26.7508	0.921894
$843$	1.77855	0.0612564
$844$	5.28806	0.182022
$845$	0	0
$846$	1.21680	0.0418346
$847$	−0.944517	−0.0324540
$848$	−29.6312	−1.01754
$849$	32.6718	1.12129
$850$	0	0
$851$	10.5953	0.363202
$852$	0.677136	0.0231983
$853$	−15.0064	−0.513810	−0.256905	−	0.966437i	$-0.582703\pi$
$853$	−15.0064	−0.513810	−0.256905	+	0.966437i	$0.582703\pi$
$854$	−53.9919	−1.84756
$855$	0	0
$856$	−39.8274	−1.36127
$857$	−21.2990	−0.727558	−0.363779	−	0.931485i	$-0.618514\pi$
$857$	−21.2990	−0.727558	−0.363779	+	0.931485i	$0.618514\pi$
$858$	5.56248	0.189900
$859$	34.6759	1.18313	0.591563	−	0.806259i	$-0.298511\pi$
$859$	34.6759	1.18313	0.591563	+	0.806259i	$0.298511\pi$
$860$	0	0
$861$	11.4617	0.390613
$862$	−21.3653	−0.727704
$863$	36.8717	1.25513	0.627563	−	0.778565i	$-0.284052\pi$
$863$	36.8717	1.25513	0.627563	+	0.778565i	$0.284052\pi$
$864$	2.85623	0.0971710
$865$	0	0
$866$	27.4598	0.933122
$867$	−0.314361	−0.0106762
$868$	−19.4203	−0.659170
$869$	21.1632	0.717912
$870$	0	0
$871$	16.4931	0.558846
$872$	10.6463	0.360531
$873$	−5.04406	−0.170715
$874$	−1.17869	−0.0398696
$875$	0	0
$876$	4.89782	0.165482
$877$	−39.1958	−1.32355	−0.661773	−	0.749704i	$-0.730196\pi$
$877$	−39.1958	−1.32355	−0.661773	+	0.749704i	$0.730196\pi$
$878$	−32.3995	−1.09343
$879$	−12.4826	−0.421028
$880$	0	0
$881$	−7.61293	−0.256486	−0.128243	−	0.991743i	$-0.540934\pi$
$881$	−7.61293	−0.256486	−0.128243	+	0.991743i	$0.540934\pi$
$882$	16.5337	0.556719
$883$	−10.6256	−0.357581	−0.178790	−	0.983887i	$-0.557218\pi$
$883$	−10.6256	−0.357581	−0.178790	+	0.983887i	$0.557218\pi$
$884$	2.95233	0.0992978
$885$	0	0
$886$	−38.9697	−1.30921
$887$	25.2841	0.848956	0.424478	−	0.905438i	$-0.360458\pi$
$887$	25.2841	0.848956	0.424478	+	0.905438i	$0.360458\pi$
$888$	14.0958	0.473024
$889$	27.5734	0.924782
$890$	0	0
$891$	−3.28509	−0.110055
$892$	6.93861	0.232322
$893$	0.420377	0.0140674
$894$	−17.0028	−0.568658
$895$	0	0
$896$	22.9884	0.767988
$897$	3.20656	0.107064
$898$	33.5137	1.11837
$899$	67.7825	2.26067
$900$	0	0
$901$	44.9710	1.49820
$902$	−10.0974	−0.336207
$903$	46.4227	1.54485
$904$	17.8206	0.592706
$905$	0	0
$906$	−18.7032	−0.621371
$907$	−6.73495	−0.223630	−0.111815	−	0.993729i	$-0.535666\pi$
$907$	−6.73495	−0.223630	−0.111815	+	0.993729i	$0.535666\pi$
$908$	3.35364	0.111294
$909$	13.0371	0.432414
$910$	0	0
$911$	−3.85056	−0.127575	−0.0637874	−	0.997964i	$-0.520318\pi$
$911$	−3.85056	−0.127575	−0.0637874	+	0.997964i	$0.520318\pi$
$912$	−1.13143	−0.0374653
$913$	−14.6283	−0.484125
$914$	−40.6750	−1.34541
$915$	0	0
$916$	−0.0127122	−0.000420024 0
$917$	29.2945	0.967391
$918$	4.97041	0.164048
$919$	58.5612	1.93176	0.965879	−	0.258995i	$-0.0833914\pi$
$919$	58.5612	1.93176	0.965879	+	0.258995i	$0.0833914\pi$
$920$	0	0
$921$	26.6908	0.879492
$922$	−19.9838	−0.658130
$923$	1.81419	0.0597148
$924$	7.74188	0.254689
$925$	0	0
$926$	−25.5679	−0.840212
$927$	−14.4516	−0.474652
$928$	23.4938	0.771221
$929$	−13.9853	−0.458843	−0.229422	−	0.973327i	$-0.573683\pi$
$929$	−13.9853	−0.458843	−0.229422	+	0.973327i	$0.573683\pi$
$930$	0	0
$931$	5.71202	0.187204
$932$	13.0900	0.428776
$933$	−28.6855	−0.939122
$934$	−25.4789	−0.833694
$935$	0	0
$936$	4.26596	0.139437
$937$	−6.33437	−0.206935	−0.103467	−	0.994633i	$-0.532994\pi$
$937$	−6.33437	−0.206935	−0.103467	+	0.994633i	$0.532994\pi$
$938$	−65.4374	−2.13661
$939$	−8.01895	−0.261689
$940$	0	0
$941$	10.1005	0.329266	0.164633	−	0.986355i	$-0.447356\pi$
$941$	10.1005	0.329266	0.164633	+	0.986355i	$0.447356\pi$
$942$	24.4935	0.798041
$943$	−5.82078	−0.189551
$944$	−22.8576	−0.743951
$945$	0	0
$946$	−40.8972	−1.32968
$947$	−0.0670193	−0.00217783	−0.00108892	−	0.999999i	$-0.500347\pi$
$947$	−0.0670193	−0.00217783	−0.00108892	+	0.999999i	$0.500347\pi$
$948$	3.34601	0.108673
$949$	13.1223	0.425968
$950$	0	0
$951$	−2.89460	−0.0938637
$952$	−56.8189	−1.84151
$953$	−34.7911	−1.12699	−0.563497	−	0.826118i	$-0.690544\pi$
$953$	−34.7911	−1.12699	−0.563497	+	0.826118i	$0.690544\pi$
$954$	13.3962	0.433718
$955$	0	0
$956$	−10.6269	−0.343700
$957$	−27.0213	−0.873476
$958$	14.0034	0.452431
$959$	−3.36981	−0.108817
$960$	0	0
$961$	36.9073	1.19056
$962$	7.78565	0.251020
$963$	12.9917	0.418651
$964$	8.35886	0.269221
$965$	0	0
$966$	−12.7223	−0.409332
$967$	−31.6550	−1.01796	−0.508978	−	0.860779i	$-0.669977\pi$
$967$	−31.6550	−1.01796	−0.508978	+	0.860779i	$0.669977\pi$
$968$	0.638147	0.0205108
$969$	1.71716	0.0551631
$970$	0	0
$971$	11.6040	0.372391	0.186195	−	0.982513i	$-0.440384\pi$
$971$	11.6040	0.372391	0.186195	+	0.982513i	$0.440384\pi$
$972$	−0.519390	−0.0166594
$973$	−34.9654	−1.12094
$974$	22.8746	0.732948
$975$	0	0
$976$	26.3202	0.842490
$977$	−1.43176	−0.0458060	−0.0229030	−	0.999738i	$-0.507291\pi$
$977$	−1.43176	−0.0458060	−0.0229030	+	0.999738i	$0.507291\pi$
$978$	6.81161	0.217811
$979$	−41.2456	−1.31821
$980$	0	0
$981$	−3.47284	−0.110879
$982$	−6.96588	−0.222290
$983$	−2.10999	−0.0672981	−0.0336491	−	0.999434i	$-0.510713\pi$
$983$	−2.10999	−0.0672981	−0.0336491	+	0.999434i	$0.510713\pi$
$984$	−7.74387	−0.246866
$985$	0	0
$986$	40.8838	1.30200
$987$	4.53738	0.144426
$988$	0.303832	0.00966618
$989$	−23.5757	−0.749663
$990$	0	0
$991$	−24.0461	−0.763851	−0.381925	−	0.924193i	$-0.624739\pi$
$991$	−24.0461	−0.763851	−0.381925	+	0.924193i	$0.624739\pi$
$992$	23.5370	0.747302
$993$	0.276954	0.00878888
$994$	−7.19794	−0.228305
$995$	0	0
$996$	−2.31280	−0.0732840
$997$	33.9068	1.07384	0.536920	−	0.843633i	$-0.319588\pi$
$997$	33.9068	1.07384	0.536920	+	0.843633i	$0.319588\pi$
$998$	3.57908	0.113294
$999$	−4.59805	−0.145476

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.z.1.6	✓	7
5.4	even	2		3525.2.a.ba.1.2	yes	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.2.a.z.1.6	✓	7	1.1	even	1	trivial
3525.2.a.ba.1.2	yes	7	5.4	even	2

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:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q+1.21680 q^{2} +1.00000 q^{3} -0.519390 q^{4} +1.21680 q^{6} +4.53738 q^{7} -3.06560 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.21680 q^{2} +1.00000 q^{3} -0.519390 q^{4} +1.21680 q^{6} +4.53738 q^{7} -3.06560 q^{8} +1.00000 q^{9} -3.28509 q^{11} -0.519390 q^{12} -1.39156 q^{13} +5.52110 q^{14} -2.69145 q^{16} +4.08481 q^{17} +1.21680 q^{18} +0.420377 q^{19} +4.53738 q^{21} -3.99731 q^{22} -2.30430 q^{23} -3.06560 q^{24} -1.69325 q^{26} +1.00000 q^{27} -2.35667 q^{28} +8.22544 q^{29} +8.24059 q^{31} +2.85623 q^{32} -3.28509 q^{33} +4.97041 q^{34} -0.519390 q^{36} -4.59805 q^{37} +0.511516 q^{38} -1.39156 q^{39} +2.52605 q^{41} +5.52110 q^{42} +10.2312 q^{43} +1.70624 q^{44} -2.80388 q^{46} +1.00000 q^{47} -2.69145 q^{48} +13.5878 q^{49} +4.08481 q^{51} +0.722760 q^{52} +11.0093 q^{53} +1.21680 q^{54} -13.9098 q^{56} +0.420377 q^{57} +10.0087 q^{58} +8.49265 q^{59} -9.77918 q^{61} +10.0272 q^{62} +4.53738 q^{63} +8.85838 q^{64} -3.99731 q^{66} -11.8522 q^{67} -2.12161 q^{68} -2.30430 q^{69} -1.30371 q^{71} -3.06560 q^{72} -9.42994 q^{73} -5.59493 q^{74} -0.218340 q^{76} -14.9057 q^{77} -1.69325 q^{78} -6.44218 q^{79} +1.00000 q^{81} +3.07371 q^{82} +4.45292 q^{83} -2.35667 q^{84} +12.4493 q^{86} +8.22544 q^{87} +10.0708 q^{88} +12.5554 q^{89} -6.31402 q^{91} +1.19683 q^{92} +8.24059 q^{93} +1.21680 q^{94} +2.85623 q^{96} -5.04406 q^{97} +16.5337 q^{98} -3.28509 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} + 7 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 + 7 * q^7 + 6 * q^8 + 7 * q^9	\( 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} + 7 q^{7} + 6 q^{8} + 7 q^{9} + 5 q^{12} + 5 q^{13} + 7 q^{14} + 9 q^{16} + 2 q^{17} - q^{18} - 13 q^{19} + 7 q^{21} - 14 q^{22} + 6 q^{23} + 6 q^{24} + 7 q^{27} + 30 q^{28} + 9 q^{29} + 5 q^{31} + 26 q^{32} - 8 q^{34} + 5 q^{36} - 5 q^{37} - 2 q^{38} + 5 q^{39} + 18 q^{41} + 7 q^{42} + 14 q^{43} + 17 q^{44} - 27 q^{46} + 7 q^{47} + 9 q^{48} + 14 q^{49} + 2 q^{51} - 3 q^{52} + 20 q^{53} - q^{54} + 17 q^{56} - 13 q^{57} + 37 q^{58} + 10 q^{59} - 8 q^{61} - 6 q^{62} + 7 q^{63} + 18 q^{64} - 14 q^{66} + 4 q^{67} + 10 q^{68} + 6 q^{69} + 12 q^{71} + 6 q^{72} + 4 q^{73} - 25 q^{74} - 66 q^{76} + 6 q^{77} - 5 q^{79} + 7 q^{81} - 29 q^{82} + 52 q^{83} + 30 q^{84} - 17 q^{86} + 9 q^{87} + 26 q^{88} + 32 q^{89} - 26 q^{91} - 17 q^{92} + 5 q^{93} - q^{94} + 26 q^{96} - 12 q^{97} + 40 q^{98}+O(q^{100}) \) 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 + 7 * q^7 + 6 * q^8 + 7 * q^9 + 5 * q^12 + 5 * q^13 + 7 * q^14 + 9 * q^16 + 2 * q^17 - q^18 - 13 * q^19 + 7 * q^21 - 14 * q^22 + 6 * q^23 + 6 * q^24 + 7 * q^27 + 30 * q^28 + 9 * q^29 + 5 * q^31 + 26 * q^32 - 8 * q^34 + 5 * q^36 - 5 * q^37 - 2 * q^38 + 5 * q^39 + 18 * q^41 + 7 * q^42 + 14 * q^43 + 17 * q^44 - 27 * q^46 + 7 * q^47 + 9 * q^48 + 14 * q^49 + 2 * q^51 - 3 * q^52 + 20 * q^53 - q^54 + 17 * q^56 - 13 * q^57 + 37 * q^58 + 10 * q^59 - 8 * q^61 - 6 * q^62 + 7 * q^63 + 18 * q^64 - 14 * q^66 + 4 * q^67 + 10 * q^68 + 6 * q^69 + 12 * q^71 + 6 * q^72 + 4 * q^73 - 25 * q^74 - 66 * q^76 + 6 * q^77 - 5 * q^79 + 7 * q^81 - 29 * q^82 + 52 * q^83 + 30 * q^84 - 17 * q^86 + 9 * q^87 + 26 * q^88 + 32 * q^89 - 26 * q^91 - 17 * q^92 + 5 * q^93 - q^94 + 26 * q^96 - 12 * q^97 + 40 * q^98

Introduction

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