LMFDB - Embedded newform 4025.2.a.t.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, 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("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 11x^{6} + 9x^{5} + 36x^{4} - 23x^{3} - 30x^{2} + 17x - 2 $ x^8 - x^7 - 11x^6 + 9x^5 + 36x^4 - 23x^3 - 30x^2 + 17x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.322285$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.322285 q^{2} +1.07802 q^{3} -1.89613 q^{4} -0.347431 q^{6} -1.00000 q^{7} +1.25566 q^{8} -1.83786 q^{9} +O(q^{10})$	\(q-0.322285 q^{2} +1.07802 q^{3} -1.89613 q^{4} -0.347431 q^{6} -1.00000 q^{7} +1.25566 q^{8} -1.83786 q^{9} +1.93810 q^{11} -2.04408 q^{12} -1.66972 q^{13} +0.322285 q^{14} +3.38758 q^{16} +2.35426 q^{17} +0.592316 q^{18} -1.86218 q^{19} -1.07802 q^{21} -0.624622 q^{22} -1.00000 q^{23} +1.35364 q^{24} +0.538124 q^{26} -5.21533 q^{27} +1.89613 q^{28} +6.67460 q^{29} +3.84044 q^{31} -3.60309 q^{32} +2.08932 q^{33} -0.758742 q^{34} +3.48483 q^{36} -0.829816 q^{37} +0.600154 q^{38} -1.79999 q^{39} +12.2075 q^{41} +0.347431 q^{42} -6.41319 q^{43} -3.67490 q^{44} +0.322285 q^{46} -10.1975 q^{47} +3.65190 q^{48} +1.00000 q^{49} +2.53795 q^{51} +3.16600 q^{52} -0.466953 q^{53} +1.68082 q^{54} -1.25566 q^{56} -2.00748 q^{57} -2.15112 q^{58} -14.9372 q^{59} +1.48613 q^{61} -1.23772 q^{62} +1.83786 q^{63} -5.61394 q^{64} -0.673357 q^{66} +3.24275 q^{67} -4.46399 q^{68} -1.07802 q^{69} -12.3379 q^{71} -2.30774 q^{72} -0.0689507 q^{73} +0.267437 q^{74} +3.53095 q^{76} -1.93810 q^{77} +0.580110 q^{78} +15.8987 q^{79} -0.108662 q^{81} -3.93428 q^{82} -11.3227 q^{83} +2.04408 q^{84} +2.06687 q^{86} +7.19538 q^{87} +2.43361 q^{88} -8.54395 q^{89} +1.66972 q^{91} +1.89613 q^{92} +4.14009 q^{93} +3.28650 q^{94} -3.88422 q^{96} +1.35135 q^{97} -0.322285 q^{98} -3.56197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 7 q^{3} + 7 q^{4} + q^{6} - 8 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) $ 8 * q - q^2 - 7 * q^3 + 7 * q^4 + q^6 - 8 * q^7 - 3 * q^8 + 9 * q^9	$ 8 q - q^{2} - 7 q^{3} + 7 q^{4} + q^{6} - 8 q^{7} - 3 q^{8} + 9 q^{9} + 6 q^{11} - 8 q^{12} - 8 q^{13} + q^{14} + q^{16} - 4 q^{17} + 11 q^{18} + 7 q^{21} + 8 q^{22} - 8 q^{23} - 8 q^{24} + 2 q^{26} - 28 q^{27} - 7 q^{28} - 3 q^{29} - 16 q^{31} - 12 q^{32} - 5 q^{33} - 4 q^{34} - 14 q^{36} + 7 q^{37} - 11 q^{38} + 16 q^{39} + 7 q^{41} - q^{42} + 10 q^{43} + 7 q^{44} + q^{46} - 19 q^{47} + 6 q^{48} + 8 q^{49} + 7 q^{51} - 18 q^{52} + q^{53} - 25 q^{54} + 3 q^{56} + 25 q^{57} + 9 q^{58} + 21 q^{59} - 7 q^{61} - 18 q^{62} - 9 q^{63} - 37 q^{64} - 43 q^{66} - 11 q^{67} + 17 q^{68} + 7 q^{69} + 8 q^{71} - 4 q^{72} + 3 q^{73} + 12 q^{74} + 8 q^{76} - 6 q^{77} + 50 q^{78} - 15 q^{79} + 28 q^{81} - 41 q^{82} - 25 q^{83} + 8 q^{84} - 12 q^{86} - 21 q^{87} + 29 q^{88} + q^{89} + 8 q^{91} - 7 q^{92} + 5 q^{93} - 36 q^{94} + 30 q^{96} - 10 q^{97} - q^{98} - 18 q^{99}+O(q^{100}) $ 8 * q - q^2 - 7 * q^3 + 7 * q^4 + q^6 - 8 * q^7 - 3 * q^8 + 9 * q^9 + 6 * q^11 - 8 * q^12 - 8 * q^13 + q^14 + q^16 - 4 * q^17 + 11 * q^18 + 7 * q^21 + 8 * q^22 - 8 * q^23 - 8 * q^24 + 2 * q^26 - 28 * q^27 - 7 * q^28 - 3 * q^29 - 16 * q^31 - 12 * q^32 - 5 * q^33 - 4 * q^34 - 14 * q^36 + 7 * q^37 - 11 * q^38 + 16 * q^39 + 7 * q^41 - q^42 + 10 * q^43 + 7 * q^44 + q^46 - 19 * q^47 + 6 * q^48 + 8 * q^49 + 7 * q^51 - 18 * q^52 + q^53 - 25 * q^54 + 3 * q^56 + 25 * q^57 + 9 * q^58 + 21 * q^59 - 7 * q^61 - 18 * q^62 - 9 * q^63 - 37 * q^64 - 43 * q^66 - 11 * q^67 + 17 * q^68 + 7 * q^69 + 8 * q^71 - 4 * q^72 + 3 * q^73 + 12 * q^74 + 8 * q^76 - 6 * q^77 + 50 * q^78 - 15 * q^79 + 28 * q^81 - 41 * q^82 - 25 * q^83 + 8 * q^84 - 12 * q^86 - 21 * q^87 + 29 * q^88 + q^89 + 8 * q^91 - 7 * q^92 + 5 * q^93 - 36 * q^94 + 30 * q^96 - 10 * q^97 - q^98 - 18 * q^99

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 $

$2$	−0.322285	−0.227890	−0.113945	−	0.993487i	$-0.536349\pi$
$2$	−0.322285	−0.227890	−0.113945	+	0.993487i	$0.536349\pi$
$3$	1.07802	0.622397	0.311199	−	0.950345i	$-0.399270\pi$
$3$	1.07802	0.622397	0.311199	+	0.950345i	$0.399270\pi$
$4$	−1.89613	−0.948066
$5$	0	0
$5$	0	0
$6$	−0.347431	−0.141838
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.25566	0.443944
$9$	−1.83786	−0.612621
$10$	0	0
$11$	1.93810	0.584361	0.292180	−	0.956363i	$-0.405619\pi$
$11$	1.93810	0.584361	0.292180	+	0.956363i	$0.405619\pi$
$12$	−2.04408	−0.590074
$13$	−1.66972	−0.463096	−0.231548	−	0.972824i	$-0.574379\pi$
$13$	−1.66972	−0.463096	−0.231548	+	0.972824i	$0.574379\pi$
$14$	0.322285	0.0861342
$15$	0	0
$16$	3.38758	0.846896
$17$	2.35426	0.570992	0.285496	−	0.958380i	$-0.407842\pi$
$17$	2.35426	0.570992	0.285496	+	0.958380i	$0.407842\pi$
$18$	0.592316	0.139610
$19$	−1.86218	−0.427215	−0.213607	−	0.976920i	$-0.568521\pi$
$19$	−1.86218	−0.427215	−0.213607	+	0.976920i	$0.568521\pi$
$20$	0	0
$21$	−1.07802	−0.235244
$22$	−0.624622	−0.133170
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.35364	0.276310
$25$	0	0
$26$	0.538124	0.105535
$27$	−5.21533	−1.00369
$28$	1.89613	0.358335
$29$	6.67460	1.23944	0.619721	−	0.784822i	$-0.287246\pi$
$29$	6.67460	1.23944	0.619721	+	0.784822i	$0.287246\pi$
$30$	0	0
$31$	3.84044	0.689764	0.344882	−	0.938646i	$-0.387919\pi$
$31$	3.84044	0.689764	0.344882	+	0.938646i	$0.387919\pi$
$32$	−3.60309	−0.636943
$33$	2.08932	0.363704
$34$	−0.758742	−0.130123
$35$	0	0
$36$	3.48483	0.580806
$37$	−0.829816	−0.136421	−0.0682105	−	0.997671i	$-0.521729\pi$
$37$	−0.829816	−0.136421	−0.0682105	+	0.997671i	$0.521729\pi$
$38$	0.600154	0.0973578
$39$	−1.79999	−0.288230
$40$	0	0
$41$	12.2075	1.90648	0.953242	−	0.302209i	$-0.0977239\pi$
$41$	12.2075	1.90648	0.953242	+	0.302209i	$0.0977239\pi$
$42$	0.347431	0.0536097
$43$	−6.41319	−0.978003	−0.489001	−	0.872283i	$-0.662639\pi$
$43$	−6.41319	−0.978003	−0.489001	+	0.872283i	$0.662639\pi$
$44$	−3.67490	−0.554013
$45$	0	0
$46$	0.322285	0.0475183
$47$	−10.1975	−1.48746	−0.743729	−	0.668481i	$-0.766945\pi$
$47$	−10.1975	−1.48746	−0.743729	+	0.668481i	$0.766945\pi$
$48$	3.65190	0.527106
$49$	1.00000	0.142857
$50$	0	0
$51$	2.53795	0.355384
$52$	3.16600	0.439045
$53$	−0.466953	−0.0641409	−0.0320705	−	0.999486i	$-0.510210\pi$
$53$	−0.466953	−0.0641409	−0.0320705	+	0.999486i	$0.510210\pi$
$54$	1.68082	0.228731
$55$	0	0
$56$	−1.25566	−0.167795
$57$	−2.00748	−0.265897
$58$	−2.15112	−0.282456
$59$	−14.9372	−1.94466	−0.972329	−	0.233617i	$-0.924944\pi$
$59$	−14.9372	−1.94466	−0.972329	+	0.233617i	$0.924944\pi$
$60$	0	0
$61$	1.48613	0.190280	0.0951398	−	0.995464i	$-0.469670\pi$
$61$	1.48613	0.190280	0.0951398	+	0.995464i	$0.469670\pi$
$62$	−1.23772	−0.157190
$63$	1.83786	0.231549
$64$	−5.61394	−0.701743
$65$	0	0
$66$	−0.673357	−0.0828845
$67$	3.24275	0.396165	0.198082	−	0.980185i	$-0.436529\pi$
$67$	3.24275	0.396165	0.198082	+	0.980185i	$0.436529\pi$
$68$	−4.46399	−0.541338
$69$	−1.07802	−0.129779
$70$	0	0
$71$	−12.3379	−1.46424	−0.732120	−	0.681176i	$-0.761469\pi$
$71$	−12.3379	−1.46424	−0.732120	+	0.681176i	$0.761469\pi$
$72$	−2.30774	−0.271970
$73$	−0.0689507	−0.00807007	−0.00403504	−	0.999992i	$-0.501284\pi$
$73$	−0.0689507	−0.00807007	−0.00403504	+	0.999992i	$0.501284\pi$
$74$	0.267437	0.0310889
$75$	0	0
$76$	3.53095	0.405028
$77$	−1.93810	−0.220868
$78$	0.580110	0.0656846
$79$	15.8987	1.78875	0.894373	−	0.447322i	$-0.147622\pi$
$79$	15.8987	1.78875	0.894373	+	0.447322i	$0.147622\pi$
$80$	0	0
$81$	−0.108662	−0.0120735
$82$	−3.93428	−0.434468
$83$	−11.3227	−1.24283	−0.621414	−	0.783483i	$-0.713441\pi$
$83$	−11.3227	−1.24283	−0.621414	+	0.783483i	$0.713441\pi$
$84$	2.04408	0.223027
$85$	0	0
$86$	2.06687	0.222877
$87$	7.19538	0.771425
$88$	2.43361	0.259424
$89$	−8.54395	−0.905657	−0.452829	−	0.891598i	$-0.649585\pi$
$89$	−8.54395	−0.905657	−0.452829	+	0.891598i	$0.649585\pi$
$90$	0	0
$91$	1.66972	0.175034
$92$	1.89613	0.197685
$93$	4.14009	0.429307
$94$	3.28650	0.338977
$95$	0	0
$96$	−3.88422	−0.396432
$97$	1.35135	0.137209	0.0686046	−	0.997644i	$-0.478145\pi$
$97$	1.35135	0.137209	0.0686046	+	0.997644i	$0.478145\pi$
$98$	−0.322285	−0.0325557
$99$	−3.56197	−0.357992
$100$	0	0
$101$	6.56946	0.653685	0.326843	−	0.945079i	$-0.394015\pi$
$101$	6.56946	0.653685	0.326843	+	0.945079i	$0.394015\pi$
$102$	−0.817942	−0.0809884
$103$	−16.8696	−1.66222	−0.831108	−	0.556112i	$-0.812293\pi$
$103$	−16.8696	−1.66222	−0.831108	+	0.556112i	$0.812293\pi$
$104$	−2.09660	−0.205589
$105$	0	0
$106$	0.150492	0.0146171
$107$	−9.81304	−0.948662	−0.474331	−	0.880347i	$-0.657310\pi$
$107$	−9.81304	−0.948662	−0.474331	+	0.880347i	$0.657310\pi$
$108$	9.88896	0.951566
$109$	−12.7345	−1.21974	−0.609870	−	0.792501i	$-0.708779\pi$
$109$	−12.7345	−1.21974	−0.609870	+	0.792501i	$0.708779\pi$
$110$	0	0
$111$	−0.894562	−0.0849080
$112$	−3.38758	−0.320097
$113$	20.3192	1.91147	0.955736	−	0.294225i	$-0.0950615\pi$
$113$	20.3192	1.91147	0.955736	+	0.294225i	$0.0950615\pi$
$114$	0.646980	0.0605952
$115$	0	0
$116$	−12.6559	−1.17507
$117$	3.06871	0.283702
$118$	4.81403	0.443167
$119$	−2.35426	−0.215815
$120$	0	0
$121$	−7.24375	−0.658523
$122$	−0.478957	−0.0433628
$123$	13.1599	1.18659
$124$	−7.28199	−0.653942
$125$	0	0
$126$	−0.592316	−0.0527677
$127$	−3.70741	−0.328979	−0.164490	−	0.986379i	$-0.552598\pi$
$127$	−3.70741	−0.328979	−0.164490	+	0.986379i	$0.552598\pi$
$128$	9.01548	0.796863
$129$	−6.91357	−0.608706
$130$	0	0
$131$	−11.7094	−1.02306	−0.511529	−	0.859266i	$-0.670921\pi$
$131$	−11.7094	−1.02306	−0.511529	+	0.859266i	$0.670921\pi$
$132$	−3.96163	−0.344816
$133$	1.86218	0.161472
$134$	−1.04509	−0.0902819
$135$	0	0
$136$	2.95616	0.253489
$137$	−8.21249	−0.701640	−0.350820	−	0.936443i	$-0.614097\pi$
$137$	−8.21249	−0.701640	−0.350820	+	0.936443i	$0.614097\pi$
$138$	0.347431	0.0295753
$139$	11.3830	0.965497	0.482749	−	0.875759i	$-0.339639\pi$
$139$	11.3830	0.965497	0.482749	+	0.875759i	$0.339639\pi$
$140$	0	0
$141$	−10.9932	−0.925790
$142$	3.97632	0.333685
$143$	−3.23608	−0.270615
$144$	−6.22592	−0.518827
$145$	0	0
$146$	0.0222218	0.00183909
$147$	1.07802	0.0889139
$148$	1.57344	0.129336
$149$	−12.3777	−1.01402	−0.507009	−	0.861941i	$-0.669249\pi$
$149$	−12.3777	−1.01402	−0.507009	+	0.861941i	$0.669249\pi$
$150$	0	0
$151$	−21.8547	−1.77851	−0.889254	−	0.457414i	$-0.848776\pi$
$151$	−21.8547	−1.77851	−0.889254	+	0.457414i	$0.848776\pi$
$152$	−2.33828	−0.189659
$153$	−4.32681	−0.349802
$154$	0.624622	0.0503334
$155$	0	0
$156$	3.41303	0.273261
$157$	6.90754	0.551281	0.275641	−	0.961261i	$-0.411110\pi$
$157$	6.90754	0.551281	0.275641	+	0.961261i	$0.411110\pi$
$158$	−5.12392	−0.407637
$159$	−0.503386	−0.0399211
$160$	0	0
$161$	1.00000	0.0788110
$162$	0.0350201	0.00275144
$163$	16.6945	1.30761	0.653806	−	0.756662i	$-0.273171\pi$
$163$	16.6945	1.30761	0.653806	+	0.756662i	$0.273171\pi$
$164$	−23.1469	−1.80747
$165$	0	0
$166$	3.64913	0.283228
$167$	−18.5662	−1.43670	−0.718348	−	0.695684i	$-0.755101\pi$
$167$	−18.5662	−1.43670	−0.718348	+	0.695684i	$0.755101\pi$
$168$	−1.35364	−0.104435
$169$	−10.2121	−0.785542
$170$	0	0
$171$	3.42244	0.261721
$172$	12.1603	0.927211
$173$	−18.2080	−1.38433	−0.692166	−	0.721738i	$-0.743343\pi$
$173$	−18.2080	−1.38433	−0.692166	+	0.721738i	$0.743343\pi$
$174$	−2.31896	−0.175800
$175$	0	0
$176$	6.56549	0.494893
$177$	−16.1027	−1.21035
$178$	2.75359	0.206390
$179$	13.8751	1.03707	0.518537	−	0.855055i	$-0.326477\pi$
$179$	13.8751	1.03707	0.518537	+	0.855055i	$0.326477\pi$
$180$	0	0
$181$	1.58706	0.117965	0.0589826	−	0.998259i	$-0.481214\pi$
$181$	1.58706	0.117965	0.0589826	+	0.998259i	$0.481214\pi$
$182$	−0.538124	−0.0398884
$183$	1.60209	0.118430
$184$	−1.25566	−0.0925688
$185$	0	0
$186$	−1.33429	−0.0978347
$187$	4.56280	0.333665
$188$	19.3358	1.41021
$189$	5.21533	0.379360
$190$	0	0
$191$	6.18007	0.447174	0.223587	−	0.974684i	$-0.428223\pi$
$191$	6.18007	0.447174	0.223587	+	0.974684i	$0.428223\pi$
$192$	−6.05197	−0.436763
$193$	5.51515	0.396989	0.198495	−	0.980102i	$-0.436395\pi$
$193$	5.51515	0.396989	0.198495	+	0.980102i	$0.436395\pi$
$194$	−0.435521	−0.0312686
$195$	0	0
$196$	−1.89613	−0.135438
$197$	3.44232	0.245255	0.122628	−	0.992453i	$-0.460868\pi$
$197$	3.44232	0.245255	0.122628	+	0.992453i	$0.460868\pi$
$198$	1.14797	0.0815827
$199$	4.90529	0.347726	0.173863	−	0.984770i	$-0.444375\pi$
$199$	4.90529	0.347726	0.173863	+	0.984770i	$0.444375\pi$
$200$	0	0
$201$	3.49576	0.246572
$202$	−2.11724	−0.148968
$203$	−6.67460	−0.468465
$204$	−4.81229	−0.336928
$205$	0	0
$206$	5.43683	0.378802
$207$	1.83786	0.127740
$208$	−5.65630	−0.392194
$209$	−3.60911	−0.249647
$210$	0	0
$211$	−4.94491	−0.340422	−0.170211	−	0.985408i	$-0.554445\pi$
$211$	−4.94491	−0.340422	−0.170211	+	0.985408i	$0.554445\pi$
$212$	0.885404	0.0608098
$213$	−13.3006	−0.911339
$214$	3.16259	0.216190
$215$	0	0
$216$	−6.54871	−0.445583
$217$	−3.84044	−0.260706
$218$	4.10412	0.277966
$219$	−0.0743305	−0.00502279
$220$	0	0
$221$	−3.93094	−0.264424
$222$	0.288304	0.0193497
$223$	−23.6215	−1.58181	−0.790905	−	0.611938i	$-0.790390\pi$
$223$	−23.6215	−1.58181	−0.790905	+	0.611938i	$0.790390\pi$
$224$	3.60309	0.240742
$225$	0	0
$226$	−6.54858	−0.435605
$227$	−11.9182	−0.791036	−0.395518	−	0.918458i	$-0.629435\pi$
$227$	−11.9182	−0.791036	−0.395518	+	0.918458i	$0.629435\pi$
$228$	3.80645	0.252088
$229$	−13.0846	−0.864652	−0.432326	−	0.901717i	$-0.642307\pi$
$229$	−13.0846	−0.864652	−0.432326	+	0.901717i	$0.642307\pi$
$230$	0	0
$231$	−2.08932	−0.137467
$232$	8.38105	0.550243
$233$	−8.78907	−0.575791	−0.287895	−	0.957662i	$-0.592956\pi$
$233$	−8.78907	−0.575791	−0.287895	+	0.957662i	$0.592956\pi$
$234$	−0.988999	−0.0646529
$235$	0	0
$236$	28.3229	1.84366
$237$	17.1392	1.11331
$238$	0.758742	0.0491820
$239$	1.65745	0.107211	0.0536057	−	0.998562i	$-0.482929\pi$
$239$	1.65745	0.107211	0.0536057	+	0.998562i	$0.482929\pi$
$240$	0	0
$241$	−14.3772	−0.926120	−0.463060	−	0.886327i	$-0.653248\pi$
$241$	−14.3772	−0.926120	−0.463060	+	0.886327i	$0.653248\pi$
$242$	2.33455	0.150071
$243$	15.5289	0.996177
$244$	−2.81790	−0.180398
$245$	0	0
$246$	−4.24124	−0.270412
$247$	3.10932	0.197841
$248$	4.82231	0.306217
$249$	−12.2061	−0.773533
$250$	0	0
$251$	1.63504	0.103203	0.0516015	−	0.998668i	$-0.483567\pi$
$251$	1.63504	0.103203	0.0516015	+	0.998668i	$0.483567\pi$
$252$	−3.48483	−0.219524
$253$	−1.93810	−0.121848
$254$	1.19484	0.0749710
$255$	0	0
$256$	8.32234	0.520146
$257$	0.760324	0.0474277	0.0237138	−	0.999719i	$-0.492451\pi$
$257$	0.760324	0.0474277	0.0237138	+	0.999719i	$0.492451\pi$
$258$	2.22814	0.138718
$259$	0.829816	0.0515623
$260$	0	0
$261$	−12.2670	−0.759309
$262$	3.77377	0.233144
$263$	−19.9781	−1.23190	−0.615952	−	0.787784i	$-0.711228\pi$
$263$	−19.9781	−1.23190	−0.615952	+	0.787784i	$0.711228\pi$
$264$	2.62349	0.161465
$265$	0	0
$266$	−0.600154	−0.0367978
$267$	−9.21059	−0.563679
$268$	−6.14868	−0.375590
$269$	15.8523	0.966534	0.483267	−	0.875473i	$-0.339450\pi$
$269$	15.8523	0.966534	0.483267	+	0.875473i	$0.339450\pi$
$270$	0	0
$271$	9.56754	0.581187	0.290593	−	0.956847i	$-0.406147\pi$
$271$	9.56754	0.581187	0.290593	+	0.956847i	$0.406147\pi$
$272$	7.97525	0.483571
$273$	1.79999	0.108941
$274$	2.64676	0.159897
$275$	0	0
$276$	2.04408	0.123039
$277$	7.78388	0.467688	0.233844	−	0.972274i	$-0.424870\pi$
$277$	7.78388	0.467688	0.233844	+	0.972274i	$0.424870\pi$
$278$	−3.66858	−0.220027
$279$	−7.05821	−0.422564
$280$	0	0
$281$	−25.8913	−1.54454	−0.772271	−	0.635293i	$-0.780879\pi$
$281$	−25.8913	−1.54454	−0.772271	+	0.635293i	$0.780879\pi$
$282$	3.54293	0.210978
$283$	28.5376	1.69639	0.848193	−	0.529687i	$-0.177691\pi$
$283$	28.5376	1.69639	0.848193	+	0.529687i	$0.177691\pi$
$284$	23.3943	1.38820
$285$	0	0
$286$	1.04294	0.0616704
$287$	−12.2075	−0.720583
$288$	6.62200	0.390205
$289$	−11.4575	−0.673968
$290$	0	0
$291$	1.45679	0.0853987
$292$	0.130740	0.00765096
$293$	13.9467	0.814773	0.407387	−	0.913256i	$-0.366440\pi$
$293$	13.9467	0.814773	0.407387	+	0.913256i	$0.366440\pi$
$294$	−0.347431	−0.0202626
$295$	0	0
$296$	−1.04197	−0.0605633
$297$	−10.1079	−0.586518
$298$	3.98913	0.231084
$299$	1.66972	0.0965621
$300$	0	0
$301$	6.41319	0.369650
$302$	7.04343	0.405304
$303$	7.08203	0.406852
$304$	−6.30831	−0.361806
$305$	0	0
$306$	1.39447	0.0797163
$307$	−24.5408	−1.40062	−0.700310	−	0.713839i	$-0.746955\pi$
$307$	−24.5408	−1.40062	−0.700310	+	0.713839i	$0.746955\pi$
$308$	3.67490	0.209397
$309$	−18.1859	−1.03456
$310$	0	0
$311$	22.8172	1.29385	0.646923	−	0.762555i	$-0.276055\pi$
$311$	22.8172	1.29385	0.646923	+	0.762555i	$0.276055\pi$
$312$	−2.26019	−0.127958
$313$	−4.72574	−0.267115	−0.133557	−	0.991041i	$-0.542640\pi$
$313$	−4.72574	−0.267115	−0.133557	+	0.991041i	$0.542640\pi$
$314$	−2.22619	−0.125631
$315$	0	0
$316$	−30.1461	−1.69585
$317$	−5.57464	−0.313103	−0.156551	−	0.987670i	$-0.550038\pi$
$317$	−5.57464	−0.313103	−0.156551	+	0.987670i	$0.550038\pi$
$318$	0.162234	0.00909762
$319$	12.9361	0.724281
$320$	0	0
$321$	−10.5787	−0.590445
$322$	−0.322285	−0.0179602
$323$	−4.38407	−0.243936
$324$	0.206037	0.0114465
$325$	0	0
$326$	−5.38037	−0.297991
$327$	−13.7281	−0.759164
$328$	15.3285	0.846373
$329$	10.1975	0.562207
$330$	0	0
$331$	5.82002	0.319897	0.159949	−	0.987125i	$-0.448867\pi$
$331$	5.82002	0.319897	0.159949	+	0.987125i	$0.448867\pi$
$332$	21.4693	1.17828
$333$	1.52509	0.0835744
$334$	5.98361	0.327408
$335$	0	0
$336$	−3.65190	−0.199227
$337$	−24.2863	−1.32296	−0.661480	−	0.749962i	$-0.730072\pi$
$337$	−24.2863	−1.32296	−0.661480	+	0.749962i	$0.730072\pi$
$338$	3.29119	0.179017
$339$	21.9046	1.18970
$340$	0	0
$341$	7.44318	0.403071
$342$	−1.10300	−0.0596435
$343$	−1.00000	−0.0539949
$344$	−8.05282	−0.434179
$345$	0	0
$346$	5.86818	0.315475
$347$	−18.3155	−0.983227	−0.491614	−	0.870813i	$-0.663593\pi$
$347$	−18.3155	−0.983227	−0.491614	+	0.870813i	$0.663593\pi$
$348$	−13.6434	−0.731362
$349$	−8.88536	−0.475622	−0.237811	−	0.971311i	$-0.576430\pi$
$349$	−8.88536	−0.475622	−0.237811	+	0.971311i	$0.576430\pi$
$350$	0	0
$351$	8.70812	0.464805
$352$	−6.98317	−0.372204
$353$	12.8074	0.681670	0.340835	−	0.940123i	$-0.389290\pi$
$353$	12.8074	0.681670	0.340835	+	0.940123i	$0.389290\pi$
$354$	5.18964	0.275826
$355$	0	0
$356$	16.2005	0.858623
$357$	−2.53795	−0.134323
$358$	−4.47174	−0.236339
$359$	8.50566	0.448911	0.224456	−	0.974484i	$-0.427940\pi$
$359$	8.50566	0.448911	0.224456	+	0.974484i	$0.427940\pi$
$360$	0	0
$361$	−15.5323	−0.817488
$362$	−0.511485	−0.0268831
$363$	−7.80894	−0.409863
$364$	−3.16600	−0.165944
$365$	0	0
$366$	−0.516328	−0.0269889
$367$	20.7741	1.08440	0.542198	−	0.840250i	$-0.317592\pi$
$367$	20.7741	1.08440	0.542198	+	0.840250i	$0.317592\pi$
$368$	−3.38758	−0.176590
$369$	−22.4356	−1.16795
$370$	0	0
$371$	0.466953	0.0242430
$372$	−7.85016	−0.407012
$373$	−26.8305	−1.38923	−0.694616	−	0.719381i	$-0.744426\pi$
$373$	−26.8305	−1.38923	−0.694616	+	0.719381i	$0.744426\pi$
$374$	−1.47052	−0.0760389
$375$	0	0
$376$	−12.8046	−0.660349
$377$	−11.1447	−0.573980
$378$	−1.68082	−0.0864522
$379$	−25.7156	−1.32092	−0.660460	−	0.750861i	$-0.729639\pi$
$379$	−25.7156	−1.32092	−0.660460	+	0.750861i	$0.729639\pi$
$380$	0	0
$381$	−3.99668	−0.204756
$382$	−1.99174	−0.101906
$383$	−20.6242	−1.05385	−0.526923	−	0.849913i	$-0.676654\pi$
$383$	−20.6242	−1.05385	−0.526923	+	0.849913i	$0.676654\pi$
$384$	9.71890	0.495966
$385$	0	0
$386$	−1.77745	−0.0904697
$387$	11.7866	0.599145
$388$	−2.56235	−0.130083
$389$	39.3769	1.99649	0.998245	−	0.0592224i	$-0.0188621\pi$
$389$	39.3769	1.99649	0.998245	+	0.0592224i	$0.0188621\pi$
$390$	0	0
$391$	−2.35426	−0.119060
$392$	1.25566	0.0634206
$393$	−12.6231	−0.636749
$394$	−1.10941	−0.0558912
$395$	0	0
$396$	6.75397	0.339400
$397$	11.3217	0.568218	0.284109	−	0.958792i	$-0.408302\pi$
$397$	11.3217	0.568218	0.284109	+	0.958792i	$0.408302\pi$
$398$	−1.58090	−0.0792433
$399$	2.00748	0.100500
$400$	0	0
$401$	−10.4209	−0.520397	−0.260199	−	0.965555i	$-0.583788\pi$
$401$	−10.4209	−0.520397	−0.260199	+	0.965555i	$0.583788\pi$
$402$	−1.12663	−0.0561912
$403$	−6.41245	−0.319427
$404$	−12.4566	−0.619737
$405$	0	0
$406$	2.15112	0.106758
$407$	−1.60827	−0.0797190
$408$	3.18681	0.157771
$409$	17.7500	0.877682	0.438841	−	0.898565i	$-0.355389\pi$
$409$	17.7500	0.877682	0.438841	+	0.898565i	$0.355389\pi$
$410$	0	0
$411$	−8.85326	−0.436699
$412$	31.9871	1.57589
$413$	14.9372	0.735011
$414$	−0.592316	−0.0291107
$415$	0	0
$416$	6.01614	0.294966
$417$	12.2712	0.600923
$418$	1.16316	0.0568921
$419$	14.8346	0.724715	0.362358	−	0.932039i	$-0.381972\pi$
$419$	14.8346	0.724715	0.362358	+	0.932039i	$0.381972\pi$
$420$	0	0
$421$	14.0325	0.683904	0.341952	−	0.939717i	$-0.388912\pi$
$421$	14.0325	0.683904	0.341952	+	0.939717i	$0.388912\pi$
$422$	1.59367	0.0775786
$423$	18.7416	0.911249
$424$	−0.586336	−0.0284750
$425$	0	0
$426$	4.28656	0.207685
$427$	−1.48613	−0.0719189
$428$	18.6068	0.899395
$429$	−3.48858	−0.168430
$430$	0	0
$431$	−29.3500	−1.41374	−0.706869	−	0.707344i	$-0.749893\pi$
$431$	−29.3500	−1.41374	−0.706869	+	0.707344i	$0.749893\pi$
$432$	−17.6674	−0.850022
$433$	−7.84982	−0.377238	−0.188619	−	0.982050i	$-0.560401\pi$
$433$	−7.84982	−0.377238	−0.188619	+	0.982050i	$0.560401\pi$
$434$	1.23772	0.0594123
$435$	0	0
$436$	24.1462	1.15640
$437$	1.86218	0.0890804
$438$	0.0239556	0.00114464
$439$	−1.28403	−0.0612835	−0.0306418	−	0.999530i	$-0.509755\pi$
$439$	−1.28403	−0.0612835	−0.0306418	+	0.999530i	$0.509755\pi$
$440$	0	0
$441$	−1.83786	−0.0875173
$442$	1.26688	0.0602595
$443$	−2.09197	−0.0993926	−0.0496963	−	0.998764i	$-0.515825\pi$
$443$	−2.09197	−0.0993926	−0.0496963	+	0.998764i	$0.515825\pi$
$444$	1.69621	0.0804984
$445$	0	0
$446$	7.61284	0.360478
$447$	−13.3434	−0.631122
$448$	5.61394	0.265234
$449$	−13.1010	−0.618276	−0.309138	−	0.951017i	$-0.600040\pi$
$449$	−13.1010	−0.618276	−0.309138	+	0.951017i	$0.600040\pi$
$450$	0	0
$451$	23.6593	1.11407
$452$	−38.5280	−1.81220
$453$	−23.5599	−1.10694
$454$	3.84104	0.180269
$455$	0	0
$456$	−2.52072	−0.118044
$457$	39.5344	1.84934	0.924670	−	0.380770i	$-0.124341\pi$
$457$	39.5344	1.84934	0.924670	+	0.380770i	$0.124341\pi$
$458$	4.21695	0.197045
$459$	−12.2783	−0.573100
$460$	0	0
$461$	−15.6500	−0.728893	−0.364446	−	0.931224i	$-0.618742\pi$
$461$	−15.6500	−0.728893	−0.364446	+	0.931224i	$0.618742\pi$
$462$	0.673357	0.0313274
$463$	19.0936	0.887357	0.443678	−	0.896186i	$-0.353673\pi$
$463$	19.0936	0.887357	0.443678	+	0.896186i	$0.353673\pi$
$464$	22.6108	1.04968
$465$	0	0
$466$	2.83258	0.131217
$467$	−20.5371	−0.950343	−0.475171	−	0.879893i	$-0.657614\pi$
$467$	−20.5371	−0.950343	−0.475171	+	0.879893i	$0.657614\pi$
$468$	−5.81868	−0.268969
$469$	−3.24275	−0.149736
$470$	0	0
$471$	7.44649	0.343116
$472$	−18.7561	−0.863320
$473$	−12.4294	−0.571506
$474$	−5.52371	−0.253712
$475$	0	0
$476$	4.46399	0.204607
$477$	0.858196	0.0392941
$478$	−0.534170	−0.0244324
$479$	13.7859	0.629896	0.314948	−	0.949109i	$-0.398013\pi$
$479$	13.7859	0.629896	0.314948	+	0.949109i	$0.398013\pi$
$480$	0	0
$481$	1.38556	0.0631759
$482$	4.63357	0.211053
$483$	1.07802	0.0490518
$484$	13.7351	0.624323
$485$	0	0
$486$	−5.00472	−0.227018
$487$	37.3346	1.69179	0.845897	−	0.533347i	$-0.179066\pi$
$487$	37.3346	1.69179	0.845897	+	0.533347i	$0.179066\pi$
$488$	1.86608	0.0844736
$489$	17.9970	0.813854
$490$	0	0
$491$	11.6002	0.523512	0.261756	−	0.965134i	$-0.415698\pi$
$491$	11.6002	0.523512	0.261756	+	0.965134i	$0.415698\pi$
$492$	−24.9530	−1.12497
$493$	15.7137	0.707711
$494$	−1.00209	−0.0450860
$495$	0	0
$496$	13.0098	0.584158
$497$	12.3379	0.553430
$498$	3.93385	0.176280
$499$	24.2272	1.08456	0.542279	−	0.840199i	$-0.317562\pi$
$499$	24.2272	1.08456	0.542279	+	0.840199i	$0.317562\pi$
$500$	0	0
$501$	−20.0148	−0.894196
$502$	−0.526950	−0.0235189
$503$	−1.52677	−0.0680751	−0.0340375	−	0.999421i	$-0.510837\pi$
$503$	−1.52677	−0.0680751	−0.0340375	+	0.999421i	$0.510837\pi$
$504$	2.30774	0.102795
$505$	0	0
$506$	0.624622	0.0277678
$507$	−11.0088	−0.488920
$508$	7.02974	0.311894
$509$	−0.123657	−0.00548099	−0.00274050	−	0.999996i	$-0.500872\pi$
$509$	−0.123657	−0.00548099	−0.00274050	+	0.999996i	$0.500872\pi$
$510$	0	0
$511$	0.0689507	0.00305020
$512$	−20.7131	−0.915399
$513$	9.71192	0.428792
$514$	−0.245041	−0.0108083
$515$	0	0
$516$	13.1091	0.577094
$517$	−19.7638	−0.869212
$518$	−0.267437	−0.0117505
$519$	−19.6287	−0.861605
$520$	0	0
$521$	10.1493	0.444650	0.222325	−	0.974973i	$-0.428635\pi$
$521$	10.1493	0.444650	0.222325	+	0.974973i	$0.428635\pi$
$522$	3.95347	0.173039
$523$	18.6647	0.816151	0.408076	−	0.912948i	$-0.366200\pi$
$523$	18.6647	0.816151	0.408076	+	0.912948i	$0.366200\pi$
$524$	22.2026	0.969927
$525$	0	0
$526$	6.43865	0.280738
$527$	9.04140	0.393850
$528$	7.07776	0.308020
$529$	1.00000	0.0434783
$530$	0	0
$531$	27.4525	1.19134
$532$	−3.53095	−0.153086
$533$	−20.3830	−0.882884
$534$	2.96843	0.128457
$535$	0	0
$536$	4.07180	0.175875
$537$	14.9577	0.645472
$538$	−5.10897	−0.220263
$539$	1.93810	0.0834801
$540$	0	0
$541$	5.99190	0.257612	0.128806	−	0.991670i	$-0.458886\pi$
$541$	5.99190	0.257612	0.128806	+	0.991670i	$0.458886\pi$
$542$	−3.08347	−0.132446
$543$	1.71089	0.0734213
$544$	−8.48262	−0.363689
$545$	0	0
$546$	−0.580110	−0.0248264
$547$	3.79598	0.162304	0.0811521	−	0.996702i	$-0.474140\pi$
$547$	3.79598	0.162304	0.0811521	+	0.996702i	$0.474140\pi$
$548$	15.5720	0.665201
$549$	−2.73131	−0.116569
$550$	0	0
$551$	−12.4293	−0.529508
$552$	−1.35364	−0.0576146
$553$	−15.8987	−0.676083
$554$	−2.50863	−0.106581
$555$	0	0
$556$	−21.5838	−0.915355
$557$	−21.4749	−0.909921	−0.454961	−	0.890512i	$-0.650347\pi$
$557$	−21.4749	−0.909921	−0.454961	+	0.890512i	$0.650347\pi$
$558$	2.27475	0.0962980
$559$	10.7082	0.452909
$560$	0	0
$561$	4.91881	0.207672
$562$	8.34436	0.351985
$563$	−11.5489	−0.486727	−0.243364	−	0.969935i	$-0.578251\pi$
$563$	−11.5489	−0.486727	−0.243364	+	0.969935i	$0.578251\pi$
$564$	20.8445	0.877711
$565$	0	0
$566$	−9.19724	−0.386589
$567$	0.108662	0.00456337
$568$	−15.4923	−0.650041
$569$	−24.3393	−1.02036	−0.510178	−	0.860069i	$-0.670421\pi$
$569$	−24.3393	−1.02036	−0.510178	+	0.860069i	$0.670421\pi$
$570$	0	0
$571$	−6.10527	−0.255497	−0.127749	−	0.991807i	$-0.540775\pi$
$571$	−6.10527	−0.255497	−0.127749	+	0.991807i	$0.540775\pi$
$572$	6.13604	0.256561
$573$	6.66227	0.278320
$574$	3.93428	0.164213
$575$	0	0
$576$	10.3177	0.429903
$577$	35.2404	1.46708	0.733539	−	0.679648i	$-0.237867\pi$
$577$	35.2404	1.46708	0.733539	+	0.679648i	$0.237867\pi$
$578$	3.69256	0.153590
$579$	5.94546	0.247085
$580$	0	0
$581$	11.3227	0.469745
$582$	−0.469502	−0.0194615
$583$	−0.905003	−0.0374814
$584$	−0.0865789	−0.00358266
$585$	0	0
$586$	−4.49480	−0.185678
$587$	−11.3626	−0.468986	−0.234493	−	0.972118i	$-0.575343\pi$
$587$	−11.3626	−0.468986	−0.234493	+	0.972118i	$0.575343\pi$
$588$	−2.04408	−0.0842963
$589$	−7.15161	−0.294677
$590$	0	0
$591$	3.71091	0.152646
$592$	−2.81107	−0.115534
$593$	−5.81980	−0.238991	−0.119495	−	0.992835i	$-0.538128\pi$
$593$	−5.81980	−0.238991	−0.119495	+	0.992835i	$0.538128\pi$
$594$	3.25761	0.133661
$595$	0	0
$596$	23.4697	0.961356
$597$	5.28802	0.216424
$598$	−0.538124	−0.0220055
$599$	−21.2671	−0.868950	−0.434475	−	0.900684i	$-0.643066\pi$
$599$	−21.2671	−0.868950	−0.434475	+	0.900684i	$0.643066\pi$
$600$	0	0
$601$	−33.1147	−1.35078	−0.675389	−	0.737461i	$-0.736024\pi$
$601$	−33.1147	−1.35078	−0.675389	+	0.737461i	$0.736024\pi$
$602$	−2.06687	−0.0842395
$603$	−5.95973	−0.242699
$604$	41.4393	1.68614
$605$	0	0
$606$	−2.28243	−0.0927174
$607$	20.1072	0.816125	0.408063	−	0.912954i	$-0.366204\pi$
$607$	20.1072	0.816125	0.408063	+	0.912954i	$0.366204\pi$
$608$	6.70963	0.272111
$609$	−7.19538	−0.291571
$610$	0	0
$611$	17.0269	0.688836
$612$	8.20421	0.331635
$613$	−19.1553	−0.773674	−0.386837	−	0.922148i	$-0.626432\pi$
$613$	−19.1553	−0.773674	−0.386837	+	0.922148i	$0.626432\pi$
$614$	7.90914	0.319187
$615$	0	0
$616$	−2.43361	−0.0980529
$617$	24.5384	0.987880	0.493940	−	0.869496i	$-0.335556\pi$
$617$	24.5384	0.987880	0.493940	+	0.869496i	$0.335556\pi$
$618$	5.86103	0.235765
$619$	−42.3106	−1.70061	−0.850303	−	0.526293i	$-0.823582\pi$
$619$	−42.3106	−1.70061	−0.850303	+	0.526293i	$0.823582\pi$
$620$	0	0
$621$	5.21533	0.209284
$622$	−7.35365	−0.294854
$623$	8.54395	0.342306
$624$	−6.09763	−0.244100
$625$	0	0
$626$	1.52303	0.0608727
$627$	−3.89071	−0.155380
$628$	−13.0976	−0.522651
$629$	−1.95360	−0.0778953
$630$	0	0
$631$	−26.3687	−1.04972	−0.524861	−	0.851188i	$-0.675883\pi$
$631$	−26.3687	−1.04972	−0.524861	+	0.851188i	$0.675883\pi$
$632$	19.9635	0.794104
$633$	−5.33073	−0.211878
$634$	1.79662	0.0713529
$635$	0	0
$636$	0.954487	0.0378479
$637$	−1.66972	−0.0661565
$638$	−4.16910	−0.165056
$639$	22.6754	0.897024
$640$	0	0
$641$	28.4791	1.12486	0.562428	−	0.826846i	$-0.309867\pi$
$641$	28.4791	1.12486	0.562428	+	0.826846i	$0.309867\pi$
$642$	3.40935	0.134556
$643$	11.2351	0.443069	0.221534	−	0.975153i	$-0.428894\pi$
$643$	11.2351	0.443069	0.221534	+	0.975153i	$0.428894\pi$
$644$	−1.89613	−0.0747181
$645$	0	0
$646$	1.41292	0.0555905
$647$	0.149677	0.00588442	0.00294221	−	0.999996i	$-0.499063\pi$
$647$	0.149677	0.00588442	0.00294221	+	0.999996i	$0.499063\pi$
$648$	−0.136443	−0.00535998
$649$	−28.9499	−1.13638
$650$	0	0
$651$	−4.14009	−0.162263
$652$	−31.6549	−1.23970
$653$	10.4370	0.408433	0.204216	−	0.978926i	$-0.434535\pi$
$653$	10.4370	0.408433	0.204216	+	0.978926i	$0.434535\pi$
$654$	4.42435	0.173006
$655$	0	0
$656$	41.3538	1.61459
$657$	0.126722	0.00494390
$658$	−3.28650	−0.128121
$659$	0.722400	0.0281407	0.0140704	−	0.999901i	$-0.495521\pi$
$659$	0.722400	0.0281407	0.0140704	+	0.999901i	$0.495521\pi$
$660$	0	0
$661$	−36.1530	−1.40619	−0.703095	−	0.711096i	$-0.748199\pi$
$661$	−36.1530	−1.40619	−0.703095	+	0.711096i	$0.748199\pi$
$662$	−1.87570	−0.0729012
$663$	−4.23765	−0.164577
$664$	−14.2175	−0.551746
$665$	0	0
$666$	−0.491513	−0.0190457
$667$	−6.67460	−0.258442
$668$	35.2040	1.36208
$669$	−25.4645	−0.984515
$670$	0	0
$671$	2.88028	0.111192
$672$	3.88422	0.149837
$673$	−3.09327	−0.119237	−0.0596184	−	0.998221i	$-0.518988\pi$
$673$	−3.09327	−0.119237	−0.0596184	+	0.998221i	$0.518988\pi$
$674$	7.82711	0.301489
$675$	0	0
$676$	19.3634	0.744746
$677$	8.90591	0.342282	0.171141	−	0.985247i	$-0.445255\pi$
$677$	8.90591	0.342282	0.171141	+	0.985247i	$0.445255\pi$
$678$	−7.05952	−0.271119
$679$	−1.35135	−0.0518602
$680$	0	0
$681$	−12.8481	−0.492339
$682$	−2.39882	−0.0918557
$683$	38.8509	1.48659	0.743295	−	0.668964i	$-0.233262\pi$
$683$	38.8509	1.48659	0.743295	+	0.668964i	$0.233262\pi$
$684$	−6.48941	−0.248129
$685$	0	0
$686$	0.322285	0.0123049
$687$	−14.1055	−0.538157
$688$	−21.7252	−0.828266
$689$	0.779678	0.0297034
$690$	0	0
$691$	−29.3840	−1.11782	−0.558910	−	0.829228i	$-0.688780\pi$
$691$	−29.3840	−1.11782	−0.558910	+	0.829228i	$0.688780\pi$
$692$	34.5249	1.31244
$693$	3.56197	0.135308
$694$	5.90281	0.224067
$695$	0	0
$696$	9.03498	0.342470
$697$	28.7395	1.08859
$698$	2.86362	0.108389
$699$	−9.47482	−0.358371
$700$	0	0
$701$	37.0819	1.40057	0.700283	−	0.713866i	$-0.253057\pi$
$701$	37.0819	1.40057	0.700283	+	0.713866i	$0.253057\pi$
$702$	−2.80650	−0.105924
$703$	1.54527	0.0582810
$704$	−10.8804	−0.410071
$705$	0	0
$706$	−4.12763	−0.155346
$707$	−6.56946	−0.247070
$708$	30.5328	1.14749
$709$	−7.78161	−0.292244	−0.146122	−	0.989267i	$-0.546679\pi$
$709$	−7.78161	−0.292244	−0.146122	+	0.989267i	$0.546679\pi$
$710$	0	0
$711$	−29.2197	−1.09582
$712$	−10.7283	−0.402061
$713$	−3.84044	−0.143826
$714$	0.817942	0.0306107
$715$	0	0
$716$	−26.3090	−0.983215
$717$	1.78677	0.0667281
$718$	−2.74124	−0.102302
$719$	−23.5593	−0.878612	−0.439306	−	0.898337i	$-0.644776\pi$
$719$	−23.5593	−0.878612	−0.439306	+	0.898337i	$0.644776\pi$
$720$	0	0
$721$	16.8696	0.628258
$722$	5.00581	0.186297
$723$	−15.4990	−0.576414
$724$	−3.00928	−0.111839
$725$	0	0
$726$	2.51670	0.0934035
$727$	11.9919	0.444755	0.222377	−	0.974961i	$-0.428618\pi$
$727$	11.9919	0.444755	0.222377	+	0.974961i	$0.428618\pi$
$728$	2.09660	0.0777052
$729$	17.0665	0.632091
$730$	0	0
$731$	−15.0983	−0.558432
$732$	−3.03777	−0.112279
$733$	−54.0711	−1.99716	−0.998580	−	0.0532715i	$-0.983035\pi$
$733$	−54.0711	−1.99716	−0.998580	+	0.0532715i	$0.983035\pi$
$734$	−6.69516	−0.247123
$735$	0	0
$736$	3.60309	0.132812
$737$	6.28479	0.231503
$738$	7.23066	0.266164
$739$	40.5578	1.49194	0.745972	−	0.665977i	$-0.231985\pi$
$739$	40.5578	1.49194	0.745972	+	0.665977i	$0.231985\pi$
$740$	0	0
$741$	3.35192	0.123136
$742$	−0.150492	−0.00552473
$743$	−35.3209	−1.29580	−0.647900	−	0.761726i	$-0.724352\pi$
$743$	−35.3209	−1.29580	−0.647900	+	0.761726i	$0.724352\pi$
$744$	5.19856	0.190589
$745$	0	0
$746$	8.64707	0.316592
$747$	20.8096	0.761383
$748$	−8.65168	−0.316337
$749$	9.81304	0.358561
$750$	0	0
$751$	−42.8065	−1.56203	−0.781015	−	0.624513i	$-0.785298\pi$
$751$	−42.8065	−1.56203	−0.781015	+	0.624513i	$0.785298\pi$
$752$	−34.5449	−1.25972
$753$	1.76262	0.0642333
$754$	3.59176	0.130804
$755$	0	0
$756$	−9.88896	−0.359658
$757$	14.6128	0.531111	0.265555	−	0.964096i	$-0.414445\pi$
$757$	14.6128	0.531111	0.265555	+	0.964096i	$0.414445\pi$
$758$	8.28774	0.301024
$759$	−2.08932	−0.0758376
$760$	0	0
$761$	14.7592	0.535022	0.267511	−	0.963555i	$-0.413799\pi$
$761$	14.7592	0.535022	0.267511	+	0.963555i	$0.413799\pi$
$762$	1.28807	0.0466618
$763$	12.7345	0.461019
$764$	−11.7182	−0.423951
$765$	0	0
$766$	6.64685	0.240161
$767$	24.9409	0.900563
$768$	8.97168	0.323738
$769$	25.6445	0.924765	0.462382	−	0.886681i	$-0.346995\pi$
$769$	25.6445	0.924765	0.462382	+	0.886681i	$0.346995\pi$
$770$	0	0
$771$	0.819647	0.0295189
$772$	−10.4575	−0.376372
$773$	10.1920	0.366582	0.183291	−	0.983059i	$-0.441325\pi$
$773$	10.1920	0.366582	0.183291	+	0.983059i	$0.441325\pi$
$774$	−3.79863	−0.136539
$775$	0	0
$776$	1.69685	0.0609133
$777$	0.894562	0.0320922
$778$	−12.6906	−0.454979
$779$	−22.7325	−0.814477
$780$	0	0
$781$	−23.9121	−0.855644
$782$	0.758742	0.0271326
$783$	−34.8103	−1.24402
$784$	3.38758	0.120985
$785$	0	0
$786$	4.06822	0.145108
$787$	−11.7453	−0.418675	−0.209338	−	0.977843i	$-0.567131\pi$
$787$	−11.7453	−0.418675	−0.209338	+	0.977843i	$0.567131\pi$
$788$	−6.52710	−0.232518
$789$	−21.5369	−0.766734
$790$	0	0
$791$	−20.3192	−0.722469
$792$	−4.47264	−0.158928
$793$	−2.48142	−0.0881177
$794$	−3.64880	−0.129491
$795$	0	0
$796$	−9.30107	−0.329668
$797$	25.3838	0.899139	0.449570	−	0.893245i	$-0.351577\pi$
$797$	25.3838	0.899139	0.449570	+	0.893245i	$0.351577\pi$
$798$	−0.646980	−0.0229029
$799$	−24.0076	−0.849327
$800$	0	0
$801$	15.7026	0.554825
$802$	3.35851	0.118593
$803$	−0.133634	−0.00471583
$804$	−6.62842	−0.233767
$805$	0	0
$806$	2.06663	0.0727941
$807$	17.0892	0.601568
$808$	8.24903	0.290200
$809$	33.4240	1.17512	0.587562	−	0.809179i	$-0.300088\pi$
$809$	33.4240	1.17512	0.587562	+	0.809179i	$0.300088\pi$
$810$	0	0
$811$	10.1344	0.355868	0.177934	−	0.984042i	$-0.443059\pi$
$811$	10.1344	0.355868	0.177934	+	0.984042i	$0.443059\pi$
$812$	12.6559	0.444136
$813$	10.3140	0.361729
$814$	0.518321	0.0181671
$815$	0	0
$816$	8.59751	0.300973
$817$	11.9425	0.417817
$818$	−5.72056	−0.200015
$819$	−3.06871	−0.107229
$820$	0	0
$821$	−3.38242	−0.118047	−0.0590236	−	0.998257i	$-0.518799\pi$
$821$	−3.38242	−0.118047	−0.0590236	+	0.998257i	$0.518799\pi$
$822$	2.85327	0.0995192
$823$	−36.5963	−1.27567	−0.637833	−	0.770174i	$-0.720169\pi$
$823$	−36.5963	−1.27567	−0.637833	+	0.770174i	$0.720169\pi$
$824$	−21.1826	−0.737931
$825$	0	0
$826$	−4.81403	−0.167502
$827$	42.5426	1.47935	0.739675	−	0.672964i	$-0.234979\pi$
$827$	42.5426	1.47935	0.739675	+	0.672964i	$0.234979\pi$
$828$	−3.48483	−0.121106
$829$	41.1978	1.43086	0.715429	−	0.698686i	$-0.246231\pi$
$829$	41.1978	1.43086	0.715429	+	0.698686i	$0.246231\pi$
$830$	0	0
$831$	8.39121	0.291088
$832$	9.37369	0.324974
$833$	2.35426	0.0815703
$834$	−3.95482	−0.136944
$835$	0	0
$836$	6.84335	0.236682
$837$	−20.0292	−0.692310
$838$	−4.78095	−0.165155
$839$	−25.0273	−0.864038	−0.432019	−	0.901864i	$-0.642199\pi$
$839$	−25.0273	−0.864038	−0.432019	+	0.901864i	$0.642199\pi$
$840$	0	0
$841$	15.5503	0.536216
$842$	−4.52248	−0.155855
$843$	−27.9114	−0.961320
$844$	9.37620	0.322742
$845$	0	0
$846$	−6.04014	−0.207664
$847$	7.24375	0.248898
$848$	−1.58184	−0.0543207
$849$	30.7643	1.05583
$850$	0	0
$851$	0.829816	0.0284457
$852$	25.2196	0.864010
$853$	−30.7105	−1.05151	−0.525754	−	0.850637i	$-0.676217\pi$
$853$	−30.7105	−1.05151	−0.525754	+	0.850637i	$0.676217\pi$
$854$	0.478957	0.0163896
$855$	0	0
$856$	−12.3219	−0.421153
$857$	45.8495	1.56619	0.783095	−	0.621902i	$-0.213640\pi$
$857$	45.8495	1.56619	0.783095	+	0.621902i	$0.213640\pi$
$858$	1.12431	0.0383835
$859$	−33.8930	−1.15642	−0.578208	−	0.815890i	$-0.696248\pi$
$859$	−33.8930	−1.15642	−0.578208	+	0.815890i	$0.696248\pi$
$860$	0	0
$861$	−13.1599	−0.448489
$862$	9.45905	0.322177
$863$	48.6010	1.65440	0.827198	−	0.561911i	$-0.189934\pi$
$863$	48.6010	1.65440	0.827198	+	0.561911i	$0.189934\pi$
$864$	18.7913	0.639294
$865$	0	0
$866$	2.52988	0.0859688
$867$	−12.3514	−0.419476
$868$	7.28199	0.247167
$869$	30.8134	1.04527
$870$	0	0
$871$	−5.41447	−0.183462
$872$	−15.9902	−0.541497
$873$	−2.48361	−0.0840573
$874$	−0.600154	−0.0203005
$875$	0	0
$876$	0.140941	0.00476194
$877$	11.4174	0.385538	0.192769	−	0.981244i	$-0.438253\pi$
$877$	11.4174	0.385538	0.192769	+	0.981244i	$0.438253\pi$
$878$	0.413824	0.0139659
$879$	15.0348	0.507113
$880$	0	0
$881$	11.5321	0.388525	0.194262	−	0.980950i	$-0.437769\pi$
$881$	11.5321	0.388525	0.194262	+	0.980950i	$0.437769\pi$
$882$	0.592316	0.0199443
$883$	−40.1358	−1.35068	−0.675339	−	0.737507i	$-0.736003\pi$
$883$	−40.1358	−1.35068	−0.675339	+	0.737507i	$0.736003\pi$
$884$	7.45359	0.250691
$885$	0	0
$886$	0.674211	0.0226506
$887$	−37.9521	−1.27431	−0.637153	−	0.770737i	$-0.719888\pi$
$887$	−37.9521	−1.27431	−0.637153	+	0.770737i	$0.719888\pi$
$888$	−1.12327	−0.0376944
$889$	3.70741	0.124343
$890$	0	0
$891$	−0.210598	−0.00705530
$892$	44.7894	1.49966
$893$	18.9896	0.635464
$894$	4.30038	0.143826
$895$	0	0
$896$	−9.01548	−0.301186
$897$	1.79999	0.0601000
$898$	4.22226	0.140899
$899$	25.6334	0.854922
$900$	0	0
$901$	−1.09933	−0.0366239
$902$	−7.62504	−0.253886
$903$	6.91357	0.230069
$904$	25.5141	0.848587
$905$	0	0
$906$	7.59298	0.252260
$907$	46.8795	1.55661	0.778305	−	0.627887i	$-0.216080\pi$
$907$	46.8795	1.55661	0.778305	+	0.627887i	$0.216080\pi$
$908$	22.5984	0.749954
$909$	−12.0738	−0.400462
$910$	0	0
$911$	31.4652	1.04249	0.521245	−	0.853407i	$-0.325468\pi$
$911$	31.4652	1.04249	0.521245	+	0.853407i	$0.325468\pi$
$912$	−6.80051	−0.225187
$913$	−21.9446	−0.726259
$914$	−12.7413	−0.421446
$915$	0	0
$916$	24.8101	0.819748
$917$	11.7094	0.386680
$918$	3.95709	0.130604
$919$	−16.2947	−0.537512	−0.268756	−	0.963208i	$-0.586612\pi$
$919$	−16.2947	−0.537512	−0.268756	+	0.963208i	$0.586612\pi$
$920$	0	0
$921$	−26.4556	−0.871742
$922$	5.04375	0.166107
$923$	20.6008	0.678083
$924$	3.96163	0.130328
$925$	0	0
$926$	−6.15359	−0.202220
$927$	31.0041	1.01831
$928$	−24.0492	−0.789454
$929$	2.70477	0.0887407	0.0443703	−	0.999015i	$-0.485872\pi$
$929$	2.70477	0.0887407	0.0443703	+	0.999015i	$0.485872\pi$
$930$	0	0
$931$	−1.86218	−0.0610306
$932$	16.6652	0.545888
$933$	24.5975	0.805287
$934$	6.61879	0.216573
$935$	0	0
$936$	3.85327	0.125948
$937$	54.5112	1.78080	0.890402	−	0.455175i	$-0.150423\pi$
$937$	54.5112	1.78080	0.890402	+	0.455175i	$0.150423\pi$
$938$	1.04509	0.0341233
$939$	−5.09446	−0.166251
$940$	0	0
$941$	−50.6969	−1.65267	−0.826336	−	0.563178i	$-0.809579\pi$
$941$	−50.6969	−1.65267	−0.826336	+	0.563178i	$0.809579\pi$
$942$	−2.39989	−0.0781926
$943$	−12.2075	−0.397529
$944$	−50.6010	−1.64692
$945$	0	0
$946$	4.00582	0.130240
$947$	−11.7521	−0.381891	−0.190946	−	0.981601i	$-0.561155\pi$
$947$	−11.7521	−0.381891	−0.190946	+	0.981601i	$0.561155\pi$
$948$	−32.4982	−1.05549
$949$	0.115128	0.00373722
$950$	0	0
$951$	−6.00960	−0.194874
$952$	−2.95616	−0.0958097
$953$	−4.10711	−0.133042	−0.0665211	−	0.997785i	$-0.521190\pi$
$953$	−4.10711	−0.133042	−0.0665211	+	0.997785i	$0.521190\pi$
$954$	−0.276583	−0.00895472
$955$	0	0
$956$	−3.14274	−0.101643
$957$	13.9454	0.450791
$958$	−4.44300	−0.143547
$959$	8.21249	0.265195
$960$	0	0
$961$	−16.2510	−0.524226
$962$	−0.446544	−0.0143972
$963$	18.0350	0.581171
$964$	27.2612	0.878023
$965$	0	0
$966$	−0.347431	−0.0111784
$967$	26.6098	0.855714	0.427857	−	0.903846i	$-0.359269\pi$
$967$	26.6098	0.855714	0.427857	+	0.903846i	$0.359269\pi$
$968$	−9.09572	−0.292347
$969$	−4.72613	−0.151825
$970$	0	0
$971$	56.1456	1.80180	0.900899	−	0.434028i	$-0.142908\pi$
$971$	56.1456	1.80180	0.900899	+	0.434028i	$0.142908\pi$
$972$	−29.4448	−0.944442
$973$	−11.3830	−0.364924
$974$	−12.0324	−0.385542
$975$	0	0
$976$	5.03439	0.161147
$977$	56.8610	1.81914	0.909572	−	0.415547i	$-0.136410\pi$
$977$	56.8610	1.81914	0.909572	+	0.415547i	$0.136410\pi$
$978$	−5.80017	−0.185469
$979$	−16.5591	−0.529230
$980$	0	0
$981$	23.4042	0.747239
$982$	−3.73858	−0.119303
$983$	−10.7319	−0.342295	−0.171147	−	0.985245i	$-0.554747\pi$
$983$	−10.7319	−0.342295	−0.171147	+	0.985245i	$0.554747\pi$
$984$	16.5244	0.526780
$985$	0	0
$986$	−5.06430	−0.161280
$987$	10.9932	0.349916
$988$	−5.89568	−0.187567
$989$	6.41319	0.203928
$990$	0	0
$991$	−26.6503	−0.846574	−0.423287	−	0.905996i	$-0.639124\pi$
$991$	−26.6503	−0.846574	−0.423287	+	0.905996i	$0.639124\pi$
$992$	−13.8375	−0.439340
$993$	6.27412	0.199103
$994$	−3.97632	−0.126121
$995$	0	0
$996$	23.1445	0.733360
$997$	1.74881	0.0553853	0.0276927	−	0.999616i	$-0.491184\pi$
$997$	1.74881	0.0553853	0.0276927	+	0.999616i	$0.491184\pi$
$998$	−7.80805	−0.247160
$999$	4.32777	0.136925

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.t.1.4		8
5.4	even	2		805.2.a.m.1.5	✓	8
15.14	odd	2		7245.2.a.bp.1.4		8
35.34	odd	2		5635.2.a.bb.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.m.1.5	✓	8	5.4	even	2
4025.2.a.t.1.4		8	1.1	even	1	trivial
5635.2.a.bb.1.5		8	35.34	odd	2
7245.2.a.bp.1.4		8	15.14	odd	2

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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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q-0.322285 q^{2} +1.07802 q^{3} -1.89613 q^{4} -0.347431 q^{6} -1.00000 q^{7} +1.25566 q^{8} -1.83786 q^{9} +O(q^{10})\)	\(q-0.322285 q^{2} +1.07802 q^{3} -1.89613 q^{4} -0.347431 q^{6} -1.00000 q^{7} +1.25566 q^{8} -1.83786 q^{9} +1.93810 q^{11} -2.04408 q^{12} -1.66972 q^{13} +0.322285 q^{14} +3.38758 q^{16} +2.35426 q^{17} +0.592316 q^{18} -1.86218 q^{19} -1.07802 q^{21} -0.624622 q^{22} -1.00000 q^{23} +1.35364 q^{24} +0.538124 q^{26} -5.21533 q^{27} +1.89613 q^{28} +6.67460 q^{29} +3.84044 q^{31} -3.60309 q^{32} +2.08932 q^{33} -0.758742 q^{34} +3.48483 q^{36} -0.829816 q^{37} +0.600154 q^{38} -1.79999 q^{39} +12.2075 q^{41} +0.347431 q^{42} -6.41319 q^{43} -3.67490 q^{44} +0.322285 q^{46} -10.1975 q^{47} +3.65190 q^{48} +1.00000 q^{49} +2.53795 q^{51} +3.16600 q^{52} -0.466953 q^{53} +1.68082 q^{54} -1.25566 q^{56} -2.00748 q^{57} -2.15112 q^{58} -14.9372 q^{59} +1.48613 q^{61} -1.23772 q^{62} +1.83786 q^{63} -5.61394 q^{64} -0.673357 q^{66} +3.24275 q^{67} -4.46399 q^{68} -1.07802 q^{69} -12.3379 q^{71} -2.30774 q^{72} -0.0689507 q^{73} +0.267437 q^{74} +3.53095 q^{76} -1.93810 q^{77} +0.580110 q^{78} +15.8987 q^{79} -0.108662 q^{81} -3.93428 q^{82} -11.3227 q^{83} +2.04408 q^{84} +2.06687 q^{86} +7.19538 q^{87} +2.43361 q^{88} -8.54395 q^{89} +1.66972 q^{91} +1.89613 q^{92} +4.14009 q^{93} +3.28650 q^{94} -3.88422 q^{96} +1.35135 q^{97} -0.322285 q^{98} -3.56197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 7 q^{3} + 7 q^{4} + q^{6} - 8 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) \) 8 * q - q^2 - 7 * q^3 + 7 * q^4 + q^6 - 8 * q^7 - 3 * q^8 + 9 * q^9	\( 8 q - q^{2} - 7 q^{3} + 7 q^{4} + q^{6} - 8 q^{7} - 3 q^{8} + 9 q^{9} + 6 q^{11} - 8 q^{12} - 8 q^{13} + q^{14} + q^{16} - 4 q^{17} + 11 q^{18} + 7 q^{21} + 8 q^{22} - 8 q^{23} - 8 q^{24} + 2 q^{26} - 28 q^{27} - 7 q^{28} - 3 q^{29} - 16 q^{31} - 12 q^{32} - 5 q^{33} - 4 q^{34} - 14 q^{36} + 7 q^{37} - 11 q^{38} + 16 q^{39} + 7 q^{41} - q^{42} + 10 q^{43} + 7 q^{44} + q^{46} - 19 q^{47} + 6 q^{48} + 8 q^{49} + 7 q^{51} - 18 q^{52} + q^{53} - 25 q^{54} + 3 q^{56} + 25 q^{57} + 9 q^{58} + 21 q^{59} - 7 q^{61} - 18 q^{62} - 9 q^{63} - 37 q^{64} - 43 q^{66} - 11 q^{67} + 17 q^{68} + 7 q^{69} + 8 q^{71} - 4 q^{72} + 3 q^{73} + 12 q^{74} + 8 q^{76} - 6 q^{77} + 50 q^{78} - 15 q^{79} + 28 q^{81} - 41 q^{82} - 25 q^{83} + 8 q^{84} - 12 q^{86} - 21 q^{87} + 29 q^{88} + q^{89} + 8 q^{91} - 7 q^{92} + 5 q^{93} - 36 q^{94} + 30 q^{96} - 10 q^{97} - q^{98} - 18 q^{99}+O(q^{100}) \) 8 * q - q^2 - 7 * q^3 + 7 * q^4 + q^6 - 8 * q^7 - 3 * q^8 + 9 * q^9 + 6 * q^11 - 8 * q^12 - 8 * q^13 + q^14 + q^16 - 4 * q^17 + 11 * q^18 + 7 * q^21 + 8 * q^22 - 8 * q^23 - 8 * q^24 + 2 * q^26 - 28 * q^27 - 7 * q^28 - 3 * q^29 - 16 * q^31 - 12 * q^32 - 5 * q^33 - 4 * q^34 - 14 * q^36 + 7 * q^37 - 11 * q^38 + 16 * q^39 + 7 * q^41 - q^42 + 10 * q^43 + 7 * q^44 + q^46 - 19 * q^47 + 6 * q^48 + 8 * q^49 + 7 * q^51 - 18 * q^52 + q^53 - 25 * q^54 + 3 * q^56 + 25 * q^57 + 9 * q^58 + 21 * q^59 - 7 * q^61 - 18 * q^62 - 9 * q^63 - 37 * q^64 - 43 * q^66 - 11 * q^67 + 17 * q^68 + 7 * q^69 + 8 * q^71 - 4 * q^72 + 3 * q^73 + 12 * q^74 + 8 * q^76 - 6 * q^77 + 50 * q^78 - 15 * q^79 + 28 * q^81 - 41 * q^82 - 25 * q^83 + 8 * q^84 - 12 * q^86 - 21 * q^87 + 29 * q^88 + q^89 + 8 * q^91 - 7 * q^92 + 5 * q^93 - 36 * q^94 + 30 * q^96 - 10 * q^97 - q^98 - 18 * q^99

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