LMFDB - Embedded newform 7007.2.a.bh.1.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7007,2,Mod(1,7007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7007, 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("7007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7007 = 7^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7007.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:	$55.9511766963$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 1001)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.23
Character	$\chi$	$=$	7007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.55937 q^{2} -2.66135 q^{3} +4.55036 q^{4} -2.47506 q^{5} -6.81138 q^{6} +6.52730 q^{8} +4.08281 q^{9} +O(q^{10})$	\(q+2.55937 q^{2} -2.66135 q^{3} +4.55036 q^{4} -2.47506 q^{5} -6.81138 q^{6} +6.52730 q^{8} +4.08281 q^{9} -6.33458 q^{10} +1.00000 q^{11} -12.1101 q^{12} -1.00000 q^{13} +6.58701 q^{15} +7.60504 q^{16} +6.90669 q^{17} +10.4494 q^{18} -3.30020 q^{19} -11.2624 q^{20} +2.55937 q^{22} -4.48329 q^{23} -17.3715 q^{24} +1.12592 q^{25} -2.55937 q^{26} -2.88174 q^{27} -4.82099 q^{29} +16.8586 q^{30} +9.52596 q^{31} +6.40948 q^{32} -2.66135 q^{33} +17.6767 q^{34} +18.5782 q^{36} +0.601369 q^{37} -8.44643 q^{38} +2.66135 q^{39} -16.1555 q^{40} -2.83361 q^{41} +6.51660 q^{43} +4.55036 q^{44} -10.1052 q^{45} -11.4744 q^{46} -5.04089 q^{47} -20.2397 q^{48} +2.88163 q^{50} -18.3811 q^{51} -4.55036 q^{52} -9.00445 q^{53} -7.37543 q^{54} -2.47506 q^{55} +8.78301 q^{57} -12.3387 q^{58} -2.60906 q^{59} +29.9733 q^{60} -2.77835 q^{61} +24.3804 q^{62} +1.19414 q^{64} +2.47506 q^{65} -6.81138 q^{66} +16.2775 q^{67} +31.4279 q^{68} +11.9316 q^{69} +5.66827 q^{71} +26.6497 q^{72} +6.68989 q^{73} +1.53912 q^{74} -2.99646 q^{75} -15.0171 q^{76} +6.81138 q^{78} +16.4478 q^{79} -18.8229 q^{80} -4.57909 q^{81} -7.25226 q^{82} -5.26198 q^{83} -17.0945 q^{85} +16.6784 q^{86} +12.8304 q^{87} +6.52730 q^{88} +12.6501 q^{89} -25.8629 q^{90} -20.4006 q^{92} -25.3520 q^{93} -12.9015 q^{94} +8.16819 q^{95} -17.0579 q^{96} +4.67310 q^{97} +4.08281 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} - 2 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 21 q^{8} + 37 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 - 2 * q^3 + 30 * q^4 - q^5 + 2 * q^6 + 21 * q^8 + 37 * q^9	$ 25 q + 6 q^{2} - 2 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 21 q^{8} + 37 q^{9} - 3 q^{10} + 25 q^{11} + 9 q^{12} - 25 q^{13} + 32 q^{16} - q^{17} + 44 q^{18} + 5 q^{19} + 4 q^{20} + 6 q^{22} + 15 q^{23} - 4 q^{24} + 50 q^{25} - 6 q^{26} - 17 q^{27} + 24 q^{29} + q^{30} - 12 q^{31} + 48 q^{32} - 2 q^{33} - 8 q^{34} + 30 q^{36} + 33 q^{37} + 16 q^{38} + 2 q^{39} - 21 q^{40} + 12 q^{41} + 38 q^{43} + 30 q^{44} - 22 q^{45} + 39 q^{46} + 4 q^{47} + 82 q^{48} + 16 q^{50} + 51 q^{51} - 30 q^{52} + 2 q^{53} + 10 q^{54} - q^{55} + 38 q^{57} + 17 q^{58} - 4 q^{59} - 33 q^{60} - 22 q^{61} + 42 q^{62} + 41 q^{64} + q^{65} + 2 q^{66} + 24 q^{67} + 14 q^{68} - 30 q^{69} + 9 q^{71} + 102 q^{72} + 11 q^{73} + 39 q^{74} - 16 q^{75} + 58 q^{76} - 2 q^{78} + 19 q^{79} - 33 q^{80} + 73 q^{81} - 32 q^{82} + 16 q^{83} + 14 q^{85} + 27 q^{86} - 11 q^{87} + 21 q^{88} + 13 q^{89} + 40 q^{90} + 17 q^{93} - 56 q^{94} + 15 q^{95} + 55 q^{96} + 34 q^{97} + 37 q^{99}+O(q^{100}) $ 25 * q + 6 * q^2 - 2 * q^3 + 30 * q^4 - q^5 + 2 * q^6 + 21 * q^8 + 37 * q^9 - 3 * q^10 + 25 * q^11 + 9 * q^12 - 25 * q^13 + 32 * q^16 - q^17 + 44 * q^18 + 5 * q^19 + 4 * q^20 + 6 * q^22 + 15 * q^23 - 4 * q^24 + 50 * q^25 - 6 * q^26 - 17 * q^27 + 24 * q^29 + q^30 - 12 * q^31 + 48 * q^32 - 2 * q^33 - 8 * q^34 + 30 * q^36 + 33 * q^37 + 16 * q^38 + 2 * q^39 - 21 * q^40 + 12 * q^41 + 38 * q^43 + 30 * q^44 - 22 * q^45 + 39 * q^46 + 4 * q^47 + 82 * q^48 + 16 * q^50 + 51 * q^51 - 30 * q^52 + 2 * q^53 + 10 * q^54 - q^55 + 38 * q^57 + 17 * q^58 - 4 * q^59 - 33 * q^60 - 22 * q^61 + 42 * q^62 + 41 * q^64 + q^65 + 2 * q^66 + 24 * q^67 + 14 * q^68 - 30 * q^69 + 9 * q^71 + 102 * q^72 + 11 * q^73 + 39 * q^74 - 16 * q^75 + 58 * q^76 - 2 * q^78 + 19 * q^79 - 33 * q^80 + 73 * q^81 - 32 * q^82 + 16 * q^83 + 14 * q^85 + 27 * q^86 - 11 * q^87 + 21 * q^88 + 13 * q^89 + 40 * q^90 + 17 * q^93 - 56 * q^94 + 15 * q^95 + 55 * q^96 + 34 * q^97 + 37 * 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 $

$2$	2.55937	1.80975	0.904873	−	0.425682i	$-0.139966\pi$
$2$	2.55937	1.80975	0.904873	+	0.425682i	$0.139966\pi$
$3$	−2.66135	−1.53653	−0.768267	−	0.640130i	$-0.778881\pi$
$3$	−2.66135	−1.53653	−0.768267	+	0.640130i	$0.778881\pi$
$4$	4.55036	2.27518
$5$	−2.47506	−1.10688	−0.553440	−	0.832889i	$-0.686685\pi$
$5$	−2.47506	−1.10688	−0.553440	+	0.832889i	$0.686685\pi$
$6$	−6.81138	−2.78074
$7$	0	0
$7$	0	0
$8$	6.52730	2.30775
$9$	4.08281	1.36094
$10$	−6.33458	−2.00317
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−12.1101	−3.49589
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	6.58701	1.70076
$16$	7.60504	1.90126
$17$	6.90669	1.67512	0.837559	−	0.546347i	$-0.183982\pi$
$17$	6.90669	1.67512	0.837559	+	0.546347i	$0.183982\pi$
$18$	10.4494	2.46295
$19$	−3.30020	−0.757118	−0.378559	−	0.925577i	$-0.623580\pi$
$19$	−3.30020	−0.757118	−0.378559	+	0.925577i	$0.623580\pi$
$20$	−11.2624	−2.51835
$21$	0	0
$22$	2.55937	0.545659
$23$	−4.48329	−0.934831	−0.467415	−	0.884038i	$-0.654815\pi$
$23$	−4.48329	−0.934831	−0.467415	+	0.884038i	$0.654815\pi$
$24$	−17.3715	−3.54593
$25$	1.12592	0.225183
$26$	−2.55937	−0.501933
$27$	−2.88174	−0.554591
$28$	0	0
$29$	−4.82099	−0.895235	−0.447617	−	0.894225i	$-0.647727\pi$
$29$	−4.82099	−0.895235	−0.447617	+	0.894225i	$0.647727\pi$
$30$	16.8586	3.07794
$31$	9.52596	1.71091	0.855456	−	0.517875i	$-0.173277\pi$
$31$	9.52596	1.71091	0.855456	+	0.517875i	$0.173277\pi$
$32$	6.40948	1.13305
$33$	−2.66135	−0.463282
$34$	17.6767	3.03154
$35$	0	0
$36$	18.5782	3.09637
$37$	0.601369	0.0988645	0.0494322	−	0.998777i	$-0.484259\pi$
$37$	0.601369	0.0988645	0.0494322	+	0.998777i	$0.484259\pi$
$38$	−8.44643	−1.37019
$39$	2.66135	0.426158
$40$	−16.1555	−2.55440
$41$	−2.83361	−0.442536	−0.221268	−	0.975213i	$-0.571020\pi$
$41$	−2.83361	−0.442536	−0.221268	+	0.975213i	$0.571020\pi$
$42$	0	0
$43$	6.51660	0.993772	0.496886	−	0.867816i	$-0.334477\pi$
$43$	6.51660	0.993772	0.496886	+	0.867816i	$0.334477\pi$
$44$	4.55036	0.685992
$45$	−10.1052	−1.50639
$46$	−11.4744	−1.69181
$47$	−5.04089	−0.735289	−0.367645	−	0.929966i	$-0.619836\pi$
$47$	−5.04089	−0.735289	−0.367645	+	0.929966i	$0.619836\pi$
$48$	−20.2397	−2.92135
$49$	0	0
$50$	2.88163	0.407525
$51$	−18.3811	−2.57388
$52$	−4.55036	−0.631021
$53$	−9.00445	−1.23686	−0.618428	−	0.785841i	$-0.712230\pi$
$53$	−9.00445	−1.23686	−0.618428	+	0.785841i	$0.712230\pi$
$54$	−7.37543	−1.00367
$55$	−2.47506	−0.333737
$56$	0	0
$57$	8.78301	1.16334
$58$	−12.3387	−1.62015
$59$	−2.60906	−0.339671	−0.169836	−	0.985472i	$-0.554324\pi$
$59$	−2.60906	−0.339671	−0.169836	+	0.985472i	$0.554324\pi$
$60$	29.9733	3.86953
$61$	−2.77835	−0.355731	−0.177865	−	0.984055i	$-0.556919\pi$
$61$	−2.77835	−0.355731	−0.177865	+	0.984055i	$0.556919\pi$
$62$	24.3804	3.09632
$63$	0	0
$64$	1.19414	0.149267
$65$	2.47506	0.306993
$66$	−6.81138	−0.838423
$67$	16.2775	1.98862	0.994309	−	0.106536i	$-0.0339760\pi$
$67$	16.2775	1.98862	0.994309	+	0.106536i	$0.0339760\pi$
$68$	31.4279	3.81119
$69$	11.9316	1.43640
$70$	0	0
$71$	5.66827	0.672700	0.336350	−	0.941737i	$-0.390808\pi$
$71$	5.66827	0.672700	0.336350	+	0.941737i	$0.390808\pi$
$72$	26.6497	3.14070
$73$	6.68989	0.782993	0.391496	−	0.920180i	$-0.371958\pi$
$73$	6.68989	0.782993	0.391496	+	0.920180i	$0.371958\pi$
$74$	1.53912	0.178920
$75$	−2.99646	−0.346002
$76$	−15.0171	−1.72258
$77$	0	0
$78$	6.81138	0.771237
$79$	16.4478	1.85052	0.925262	−	0.379328i	$-0.123845\pi$
$79$	16.4478	1.85052	0.925262	+	0.379328i	$0.123845\pi$
$80$	−18.8229	−2.10447
$81$	−4.57909	−0.508788
$82$	−7.25226	−0.800878
$83$	−5.26198	−0.577578	−0.288789	−	0.957393i	$-0.593253\pi$
$83$	−5.26198	−0.577578	−0.288789	+	0.957393i	$0.593253\pi$
$84$	0	0
$85$	−17.0945	−1.85415
$86$	16.6784	1.79847
$87$	12.8304	1.37556
$88$	6.52730	0.695812
$89$	12.6501	1.34091	0.670456	−	0.741949i	$-0.266098\pi$
$89$	12.6501	1.34091	0.670456	+	0.741949i	$0.266098\pi$
$90$	−25.8629	−2.72619
$91$	0	0
$92$	−20.4006	−2.12691
$93$	−25.3520	−2.62888
$94$	−12.9015	−1.33069
$95$	8.16819	0.838039
$96$	−17.0579	−1.74096
$97$	4.67310	0.474481	0.237241	−	0.971451i	$-0.423757\pi$
$97$	4.67310	0.474481	0.237241	+	0.971451i	$0.423757\pi$
$98$	0	0
$99$	4.08281	0.410338
$100$	5.12332	0.512332
$101$	10.2708	1.02198	0.510989	−	0.859587i	$-0.329279\pi$
$101$	10.2708	1.02198	0.510989	+	0.859587i	$0.329279\pi$
$102$	−47.0441	−4.65806
$103$	−0.639210	−0.0629832	−0.0314916	−	0.999504i	$-0.510026\pi$
$103$	−0.639210	−0.0629832	−0.0314916	+	0.999504i	$0.510026\pi$
$104$	−6.52730	−0.640054
$105$	0	0
$106$	−23.0457	−2.23840
$107$	−8.51911	−0.823574	−0.411787	−	0.911280i	$-0.635095\pi$
$107$	−8.51911	−0.823574	−0.411787	+	0.911280i	$0.635095\pi$
$108$	−13.1130	−1.26179
$109$	1.23028	0.117840	0.0589198	−	0.998263i	$-0.481234\pi$
$109$	1.23028	0.117840	0.0589198	+	0.998263i	$0.481234\pi$
$110$	−6.33458	−0.603979
$111$	−1.60046	−0.151909
$112$	0	0
$113$	3.17268	0.298461	0.149230	−	0.988802i	$-0.452320\pi$
$113$	3.17268	0.298461	0.149230	+	0.988802i	$0.452320\pi$
$114$	22.4789	2.10535
$115$	11.0964	1.03475
$116$	−21.9372	−2.03682
$117$	−4.08281	−0.377456
$118$	−6.67755	−0.614718
$119$	0	0
$120$	42.9954	3.92492
$121$	1.00000	0.0909091
$122$	−7.11081	−0.643782
$123$	7.54125	0.679972
$124$	43.3465	3.89263
$125$	9.58858	0.857629
$126$	0	0
$127$	2.53846	0.225252	0.112626	−	0.993637i	$-0.464074\pi$
$127$	2.53846	0.225252	0.112626	+	0.993637i	$0.464074\pi$
$128$	−9.76273	−0.862912
$129$	−17.3430	−1.52696
$130$	6.33458	0.555580
$131$	18.9097	1.65215	0.826076	−	0.563559i	$-0.190568\pi$
$131$	18.9097	1.65215	0.826076	+	0.563559i	$0.190568\pi$
$132$	−12.1101	−1.05405
$133$	0	0
$134$	41.6602	3.59889
$135$	7.13248	0.613866
$136$	45.0820	3.86575
$137$	18.3053	1.56393	0.781964	−	0.623323i	$-0.214218\pi$
$137$	18.3053	1.56393	0.781964	+	0.623323i	$0.214218\pi$
$138$	30.5374	2.59952
$139$	−13.9288	−1.18142	−0.590712	−	0.806882i	$-0.701153\pi$
$139$	−13.9288	−1.18142	−0.590712	+	0.806882i	$0.701153\pi$
$140$	0	0
$141$	13.4156	1.12980
$142$	14.5072	1.21742
$143$	−1.00000	−0.0836242
$144$	31.0499	2.58749
$145$	11.9322	0.990917
$146$	17.1219	1.41702
$147$	0	0
$148$	2.73645	0.224934
$149$	−12.5651	−1.02937	−0.514685	−	0.857379i	$-0.672091\pi$
$149$	−12.5651	−1.02937	−0.514685	+	0.857379i	$0.672091\pi$
$150$	−7.66905	−0.626175
$151$	14.5693	1.18563	0.592816	−	0.805338i	$-0.298016\pi$
$151$	14.5693	1.18563	0.592816	+	0.805338i	$0.298016\pi$
$152$	−21.5414	−1.74724
$153$	28.1987	2.27973
$154$	0	0
$155$	−23.5773	−1.89378
$156$	12.1101	0.969585
$157$	16.1391	1.28804	0.644022	−	0.765007i	$-0.277264\pi$
$157$	16.1391	1.28804	0.644022	+	0.765007i	$0.277264\pi$
$158$	42.0960	3.34898
$159$	23.9640	1.90047
$160$	−15.8638	−1.25415
$161$	0	0
$162$	−11.7196	−0.920777
$163$	−3.86758	−0.302932	−0.151466	−	0.988462i	$-0.548399\pi$
$163$	−3.86758	−0.302932	−0.151466	+	0.988462i	$0.548399\pi$
$164$	−12.8940	−1.00685
$165$	6.58701	0.512798
$166$	−13.4673	−1.04527
$167$	4.93658	0.382004	0.191002	−	0.981590i	$-0.438826\pi$
$167$	4.93658	0.382004	0.191002	+	0.981590i	$0.438826\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−43.7510	−3.35555
$171$	−13.4741	−1.03039
$172$	29.6528	2.26101
$173$	8.40734	0.639198	0.319599	−	0.947553i	$-0.396452\pi$
$173$	8.40734	0.639198	0.319599	+	0.947553i	$0.396452\pi$
$174$	32.8376	2.48941
$175$	0	0
$176$	7.60504	0.573251
$177$	6.94364	0.521916
$178$	32.3764	2.42671
$179$	−13.3960	−1.00126	−0.500632	−	0.865660i	$-0.666899\pi$
$179$	−13.3960	−1.00126	−0.500632	+	0.865660i	$0.666899\pi$
$180$	−45.9822	−3.42731
$181$	20.6995	1.53858	0.769291	−	0.638899i	$-0.220610\pi$
$181$	20.6995	1.53858	0.769291	+	0.638899i	$0.220610\pi$
$182$	0	0
$183$	7.39417	0.546593
$184$	−29.2638	−2.15735
$185$	−1.48842	−0.109431
$186$	−64.8850	−4.75760
$187$	6.90669	0.505067
$188$	−22.9378	−1.67291
$189$	0	0
$190$	20.9054	1.51664
$191$	0.00563513	0.000407744 0	0.000203872	−	1.00000i	$-0.499935\pi$
$191$	0.00563513	0.000407744 0	0.000203872		1.00000i	$0.499935\pi$
$192$	−3.17802	−0.229354
$193$	4.09411	0.294701	0.147350	−	0.989084i	$-0.452926\pi$
$193$	4.09411	0.294701	0.147350	+	0.989084i	$0.452926\pi$
$194$	11.9602	0.858690
$195$	−6.58701	−0.471706
$196$	0	0
$197$	19.4971	1.38911	0.694554	−	0.719441i	$-0.255602\pi$
$197$	19.4971	1.38911	0.694554	+	0.719441i	$0.255602\pi$
$198$	10.4494	0.742607
$199$	21.1017	1.49586	0.747930	−	0.663777i	$-0.231048\pi$
$199$	21.1017	1.49586	0.747930	+	0.663777i	$0.231048\pi$
$200$	7.34920	0.519667
$201$	−43.3203	−3.05558
$202$	26.2866	1.84952
$203$	0	0
$204$	−83.6408	−5.85603
$205$	7.01336	0.489835
$206$	−1.63597	−0.113984
$207$	−18.3044	−1.27225
$208$	−7.60504	−0.527315
$209$	−3.30020	−0.228280
$210$	0	0
$211$	15.6068	1.07442	0.537209	−	0.843449i	$-0.319479\pi$
$211$	15.6068	1.07442	0.537209	+	0.843449i	$0.319479\pi$
$212$	−40.9735	−2.81407
$213$	−15.0853	−1.03363
$214$	−21.8035	−1.49046
$215$	−16.1290	−1.09999
$216$	−18.8100	−1.27986
$217$	0	0
$218$	3.14874	0.213260
$219$	−17.8042	−1.20310
$220$	−11.2624	−0.759311
$221$	−6.90669	−0.464594
$222$	−4.09616	−0.274916
$223$	−23.1059	−1.54728	−0.773642	−	0.633623i	$-0.781567\pi$
$223$	−23.1059	−1.54728	−0.773642	+	0.633623i	$0.781567\pi$
$224$	0	0
$225$	4.59690	0.306460
$226$	8.12005	0.540138
$227$	−18.1938	−1.20757	−0.603783	−	0.797148i	$-0.706341\pi$
$227$	−18.1938	−1.20757	−0.603783	+	0.797148i	$0.706341\pi$
$228$	39.9658	2.64680
$229$	−12.3232	−0.814340	−0.407170	−	0.913352i	$-0.633484\pi$
$229$	−12.3232	−0.814340	−0.407170	+	0.913352i	$0.633484\pi$
$230$	28.3998	1.87263
$231$	0	0
$232$	−31.4680	−2.06598
$233$	23.5564	1.54323	0.771615	−	0.636089i	$-0.219449\pi$
$233$	23.5564	1.54323	0.771615	+	0.636089i	$0.219449\pi$
$234$	−10.4494	−0.683099
$235$	12.4765	0.813877
$236$	−11.8722	−0.772812
$237$	−43.7735	−2.84339
$238$	0	0
$239$	−2.13263	−0.137948	−0.0689741	−	0.997618i	$-0.521973\pi$
$239$	−2.13263	−0.137948	−0.0689741	+	0.997618i	$0.521973\pi$
$240$	50.0945	3.23358
$241$	−1.51749	−0.0977501	−0.0488750	−	0.998805i	$-0.515564\pi$
$241$	−1.51749	−0.0977501	−0.0488750	+	0.998805i	$0.515564\pi$
$242$	2.55937	0.164522
$243$	20.8318	1.33636
$244$	−12.6425	−0.809351
$245$	0	0
$246$	19.3008	1.23058
$247$	3.30020	0.209987
$248$	62.1788	3.94836
$249$	14.0040	0.887468
$250$	24.5407	1.55209
$251$	−16.0503	−1.01309	−0.506544	−	0.862214i	$-0.669077\pi$
$251$	−16.0503	−1.01309	−0.506544	+	0.862214i	$0.669077\pi$
$252$	0	0
$253$	−4.48329	−0.281862
$254$	6.49686	0.407649
$255$	45.4944	2.84897
$256$	−27.3747	−1.71092
$257$	1.78142	0.111122	0.0555609	−	0.998455i	$-0.482305\pi$
$257$	1.78142	0.111122	0.0555609	+	0.998455i	$0.482305\pi$
$258$	−44.3870	−2.76342
$259$	0	0
$260$	11.2624	0.698465
$261$	−19.6832	−1.21836
$262$	48.3969	2.98997
$263$	16.9614	1.04589	0.522943	−	0.852368i	$-0.324834\pi$
$263$	16.9614	1.04589	0.522943	+	0.852368i	$0.324834\pi$
$264$	−17.3715	−1.06914
$265$	22.2866	1.36905
$266$	0	0
$267$	−33.6665	−2.06036
$268$	74.0686	4.52446
$269$	−28.6201	−1.74500	−0.872499	−	0.488615i	$-0.837502\pi$
$269$	−28.6201	−1.74500	−0.872499	+	0.488615i	$0.837502\pi$
$270$	18.2546	1.11094
$271$	−20.2246	−1.22856	−0.614278	−	0.789089i	$-0.710553\pi$
$271$	−20.2246	−1.22856	−0.614278	+	0.789089i	$0.710553\pi$
$272$	52.5256	3.18483
$273$	0	0
$274$	46.8500	2.83031
$275$	1.12592	0.0678953
$276$	54.2932	3.26806
$277$	−2.68320	−0.161218	−0.0806088	−	0.996746i	$-0.525686\pi$
$277$	−2.68320	−0.161218	−0.0806088	+	0.996746i	$0.525686\pi$
$278$	−35.6489	−2.13808
$279$	38.8927	2.32844
$280$	0	0
$281$	8.64838	0.515919	0.257959	−	0.966156i	$-0.416950\pi$
$281$	8.64838	0.515919	0.257959	+	0.966156i	$0.416950\pi$
$282$	34.3354	2.04464
$283$	8.14492	0.484165	0.242083	−	0.970256i	$-0.422169\pi$
$283$	8.14492	0.484165	0.242083	+	0.970256i	$0.422169\pi$
$284$	25.7926	1.53051
$285$	−21.7385	−1.28768
$286$	−2.55937	−0.151339
$287$	0	0
$288$	26.1687	1.54200
$289$	30.7023	1.80602
$290$	30.5389	1.79331
$291$	−12.4368	−0.729057
$292$	30.4414	1.78145
$293$	31.6783	1.85067	0.925333	−	0.379154i	$-0.123785\pi$
$293$	31.6783	1.85067	0.925333	+	0.379154i	$0.123785\pi$
$294$	0	0
$295$	6.45758	0.375975
$296$	3.92532	0.228154
$297$	−2.88174	−0.167216
$298$	−32.1586	−1.86290
$299$	4.48329	0.259275
$300$	−13.6350	−0.787216
$301$	0	0
$302$	37.2882	2.14569
$303$	−27.3341	−1.57030
$304$	−25.0982	−1.43948
$305$	6.87657	0.393751
$306$	72.1708	4.12573
$307$	−15.5414	−0.886995	−0.443498	−	0.896276i	$-0.646263\pi$
$307$	−15.5414	−0.886995	−0.443498	+	0.896276i	$0.646263\pi$
$308$	0	0
$309$	1.70116	0.0967759
$310$	−60.3430	−3.42725
$311$	11.8596	0.672496	0.336248	−	0.941773i	$-0.390842\pi$
$311$	11.8596	0.672496	0.336248	+	0.941773i	$0.390842\pi$
$312$	17.3715	0.983465
$313$	−23.0154	−1.30091	−0.650453	−	0.759547i	$-0.725421\pi$
$313$	−23.0154	−1.30091	−0.650453	+	0.759547i	$0.725421\pi$
$314$	41.3060	2.33103
$315$	0	0
$316$	74.8435	4.21027
$317$	10.6054	0.595660	0.297830	−	0.954619i	$-0.403737\pi$
$317$	10.6054	0.595660	0.297830	+	0.954619i	$0.403737\pi$
$318$	61.3328	3.43937
$319$	−4.82099	−0.269923
$320$	−2.95556	−0.165221
$321$	22.6724	1.26545
$322$	0	0
$323$	−22.7935	−1.26826
$324$	−20.8365	−1.15758
$325$	−1.12592	−0.0624546
$326$	−9.89855	−0.548230
$327$	−3.27421	−0.181064
$328$	−18.4959	−1.02126
$329$	0	0
$330$	16.8586	0.928034
$331$	27.6812	1.52150	0.760748	−	0.649047i	$-0.224832\pi$
$331$	27.6812	1.52150	0.760748	+	0.649047i	$0.224832\pi$
$332$	−23.9439	−1.31409
$333$	2.45528	0.134548
$334$	12.6345	0.691330
$335$	−40.2879	−2.20116
$336$	0	0
$337$	17.2822	0.941423	0.470712	−	0.882287i	$-0.343997\pi$
$337$	17.2822	0.941423	0.470712	+	0.882287i	$0.343997\pi$
$338$	2.55937	0.139211
$339$	−8.44363	−0.458595
$340$	−77.7859	−4.21853
$341$	9.52596	0.515860
$342$	−34.4851	−1.86474
$343$	0	0
$344$	42.5358	2.29338
$345$	−29.5315	−1.58992
$346$	21.5175	1.15679
$347$	−26.1212	−1.40226	−0.701130	−	0.713034i	$-0.747321\pi$
$347$	−26.1212	−1.40226	−0.701130	+	0.713034i	$0.747321\pi$
$348$	58.3827	3.12964
$349$	5.72089	0.306232	0.153116	−	0.988208i	$-0.451069\pi$
$349$	5.72089	0.306232	0.153116	+	0.988208i	$0.451069\pi$
$350$	0	0
$351$	2.88174	0.153816
$352$	6.40948	0.341626
$353$	7.84655	0.417630	0.208815	−	0.977955i	$-0.433039\pi$
$353$	7.84655	0.417630	0.208815	+	0.977955i	$0.433039\pi$
$354$	17.7713	0.944535
$355$	−14.0293	−0.744598
$356$	57.5627	3.05082
$357$	0	0
$358$	−34.2852	−1.81203
$359$	−24.4573	−1.29081	−0.645403	−	0.763843i	$-0.723310\pi$
$359$	−24.4573	−1.29081	−0.645403	+	0.763843i	$0.723310\pi$
$360$	−65.9596	−3.47638
$361$	−8.10867	−0.426772
$362$	52.9776	2.78444
$363$	−2.66135	−0.139685
$364$	0	0
$365$	−16.5579	−0.866679
$366$	18.9244	0.989193
$367$	18.1500	0.947422	0.473711	−	0.880680i	$-0.342914\pi$
$367$	18.1500	0.947422	0.473711	+	0.880680i	$0.342914\pi$
$368$	−34.0956	−1.77736
$369$	−11.5691	−0.602264
$370$	−3.80942	−0.198043
$371$	0	0
$372$	−115.360	−5.98116
$373$	−4.24372	−0.219731	−0.109866	−	0.993946i	$-0.535042\pi$
$373$	−4.24372	−0.219731	−0.109866	+	0.993946i	$0.535042\pi$
$374$	17.6767	0.914043
$375$	−25.5186	−1.31778
$376$	−32.9034	−1.69686
$377$	4.82099	0.248293
$378$	0	0
$379$	13.5471	0.695869	0.347935	−	0.937519i	$-0.386883\pi$
$379$	13.5471	0.695869	0.347935	+	0.937519i	$0.386883\pi$
$380$	37.1682	1.90669
$381$	−6.75575	−0.346108
$382$	0.0144224	0.000737913 0
$383$	−29.9337	−1.52954	−0.764770	−	0.644304i	$-0.777147\pi$
$383$	−29.9337	−1.52954	−0.764770	+	0.644304i	$0.777147\pi$
$384$	25.9821	1.32589
$385$	0	0
$386$	10.4783	0.533333
$387$	26.6060	1.35246
$388$	21.2643	1.07953
$389$	1.43839	0.0729293	0.0364647	−	0.999335i	$-0.488390\pi$
$389$	1.43839	0.0729293	0.0364647	+	0.999335i	$0.488390\pi$
$390$	−16.8586	−0.853667
$391$	−30.9647	−1.56595
$392$	0	0
$393$	−50.3255	−2.53859
$394$	49.9001	2.51393
$395$	−40.7093	−2.04831
$396$	18.5782	0.933592
$397$	−4.57304	−0.229514	−0.114757	−	0.993394i	$-0.536609\pi$
$397$	−4.57304	−0.229514	−0.114757	+	0.993394i	$0.536609\pi$
$398$	54.0070	2.70713
$399$	0	0
$400$	8.56264	0.428132
$401$	27.9255	1.39454	0.697268	−	0.716811i	$-0.254399\pi$
$401$	27.9255	1.39454	0.697268	+	0.716811i	$0.254399\pi$
$402$	−110.873	−5.52982
$403$	−9.52596	−0.474522
$404$	46.7356	2.32518
$405$	11.3335	0.563167
$406$	0	0
$407$	0.601369	0.0298088
$408$	−119.979	−5.93986
$409$	−28.2963	−1.39916	−0.699580	−	0.714554i	$-0.746629\pi$
$409$	−28.2963	−1.39916	−0.699580	+	0.714554i	$0.746629\pi$
$410$	17.9498	0.886476
$411$	−48.7169	−2.40303
$412$	−2.90863	−0.143298
$413$	0	0
$414$	−46.8477	−2.30244
$415$	13.0237	0.639309
$416$	−6.40948	−0.314251
$417$	37.0694	1.81530
$418$	−8.44643	−0.413128
$419$	27.8573	1.36092	0.680460	−	0.732785i	$-0.261780\pi$
$419$	27.8573	1.36092	0.680460	+	0.732785i	$0.261780\pi$
$420$	0	0
$421$	21.3945	1.04270	0.521351	−	0.853342i	$-0.325428\pi$
$421$	21.3945	1.04270	0.521351	+	0.853342i	$0.325428\pi$
$422$	39.9436	1.94442
$423$	−20.5810	−1.00068
$424$	−58.7748	−2.85435
$425$	7.77635	0.377209
$426$	−38.6087	−1.87060
$427$	0	0
$428$	−38.7650	−1.87378
$429$	2.66135	0.128491
$430$	−41.2799	−1.99069
$431$	21.0826	1.01551	0.507756	−	0.861501i	$-0.330475\pi$
$431$	21.0826	1.01551	0.507756	+	0.861501i	$0.330475\pi$
$432$	−21.9158	−1.05442
$433$	10.0562	0.483268	0.241634	−	0.970367i	$-0.422317\pi$
$433$	10.0562	0.483268	0.241634	+	0.970367i	$0.422317\pi$
$434$	0	0
$435$	−31.7559	−1.52258
$436$	5.59822	0.268106
$437$	14.7958	0.707777
$438$	−45.5674	−2.17730
$439$	−32.0460	−1.52947	−0.764735	−	0.644345i	$-0.777130\pi$
$439$	−32.0460	−1.52947	−0.764735	+	0.644345i	$0.777130\pi$
$440$	−16.1555	−0.770181
$441$	0	0
$442$	−17.6767	−0.840797
$443$	−15.7369	−0.747682	−0.373841	−	0.927493i	$-0.621959\pi$
$443$	−15.7369	−0.747682	−0.373841	+	0.927493i	$0.621959\pi$
$444$	−7.28265	−0.345619
$445$	−31.3099	−1.48423
$446$	−59.1364	−2.80019
$447$	33.4401	1.58166
$448$	0	0
$449$	−31.1907	−1.47198	−0.735989	−	0.676994i	$-0.763282\pi$
$449$	−31.1907	−1.47198	−0.735989	+	0.676994i	$0.763282\pi$
$450$	11.7652	0.554615
$451$	−2.83361	−0.133430
$452$	14.4368	0.679051
$453$	−38.7741	−1.82176
$454$	−46.5647	−2.18539
$455$	0	0
$456$	57.3293	2.68469
$457$	11.2385	0.525714	0.262857	−	0.964835i	$-0.415335\pi$
$457$	11.2385	0.525714	0.262857	+	0.964835i	$0.415335\pi$
$458$	−31.5396	−1.47375
$459$	−19.9033	−0.929006
$460$	50.4926	2.35423
$461$	−8.75503	−0.407763	−0.203881	−	0.978996i	$-0.565356\pi$
$461$	−8.75503	−0.407763	−0.203881	+	0.978996i	$0.565356\pi$
$462$	0	0
$463$	−33.0084	−1.53403	−0.767016	−	0.641628i	$-0.778259\pi$
$463$	−33.0084	−1.53403	−0.767016	+	0.641628i	$0.778259\pi$
$464$	−36.6638	−1.70207
$465$	62.7476	2.90985
$466$	60.2894	2.79285
$467$	17.1506	0.793637	0.396818	−	0.917897i	$-0.370114\pi$
$467$	17.1506	0.793637	0.396818	+	0.917897i	$0.370114\pi$
$468$	−18.5782	−0.858780
$469$	0	0
$470$	31.9319	1.47291
$471$	−42.9520	−1.97912
$472$	−17.0301	−0.783876
$473$	6.51660	0.299633
$474$	−112.032	−5.14582
$475$	−3.71575	−0.170490
$476$	0	0
$477$	−36.7635	−1.68328
$478$	−5.45818	−0.249651
$479$	−29.6392	−1.35425	−0.677125	−	0.735868i	$-0.736774\pi$
$479$	−29.6392	−1.35425	−0.677125	+	0.735868i	$0.736774\pi$
$480$	42.2193	1.92704
$481$	−0.601369	−0.0274201
$482$	−3.88381	−0.176903
$483$	0	0
$484$	4.55036	0.206834
$485$	−11.5662	−0.525194
$486$	53.3163	2.41847
$487$	31.4802	1.42651	0.713253	−	0.700907i	$-0.247221\pi$
$487$	31.4802	1.42651	0.713253	+	0.700907i	$0.247221\pi$
$488$	−18.1351	−0.820937
$489$	10.2930	0.465466
$490$	0	0
$491$	0.603228	0.0272233	0.0136117	−	0.999907i	$-0.495667\pi$
$491$	0.603228	0.0272233	0.0136117	+	0.999907i	$0.495667\pi$
$492$	34.3154	1.54706
$493$	−33.2970	−1.49962
$494$	8.44643	0.380023
$495$	−10.1052	−0.454195
$496$	72.4453	3.25289
$497$	0	0
$498$	35.8414	1.60609
$499$	−12.8369	−0.574659	−0.287329	−	0.957832i	$-0.592767\pi$
$499$	−12.8369	−0.574659	−0.287329	+	0.957832i	$0.592767\pi$
$500$	43.6315	1.95126
$501$	−13.1380	−0.586962
$502$	−41.0787	−1.83343
$503$	32.7945	1.46224	0.731118	−	0.682251i	$-0.238999\pi$
$503$	32.7945	1.46224	0.731118	+	0.682251i	$0.238999\pi$
$504$	0	0
$505$	−25.4207	−1.13121
$506$	−11.4744	−0.510099
$507$	−2.66135	−0.118195
$508$	11.5509	0.512489
$509$	32.9946	1.46246	0.731230	−	0.682131i	$-0.238947\pi$
$509$	32.9946	1.46246	0.731230	+	0.682131i	$0.238947\pi$
$510$	116.437	5.15591
$511$	0	0
$512$	−50.5364	−2.23341
$513$	9.51033	0.419891
$514$	4.55930	0.201102
$515$	1.58208	0.0697149
$516$	−78.9167	−3.47412
$517$	−5.04089	−0.221698
$518$	0	0
$519$	−22.3749	−0.982149
$520$	16.1555	0.708463
$521$	−5.71009	−0.250164	−0.125082	−	0.992146i	$-0.539919\pi$
$521$	−5.71009	−0.250164	−0.125082	+	0.992146i	$0.539919\pi$
$522$	−50.3764	−2.20492
$523$	6.78835	0.296834	0.148417	−	0.988925i	$-0.452582\pi$
$523$	6.78835	0.296834	0.148417	+	0.988925i	$0.452582\pi$
$524$	86.0461	3.75894
$525$	0	0
$526$	43.4105	1.89279
$527$	65.7928	2.86598
$528$	−20.2397	−0.880820
$529$	−2.90010	−0.126091
$530$	57.0395	2.47764
$531$	−10.6523	−0.462271
$532$	0	0
$533$	2.83361	0.122737
$534$	−86.1650	−3.72872
$535$	21.0853	0.911597
$536$	106.248	4.58923
$537$	35.6515	1.53848
$538$	−73.2493	−3.15800
$539$	0	0
$540$	32.4553	1.39666
$541$	−5.74577	−0.247030	−0.123515	−	0.992343i	$-0.539417\pi$
$541$	−5.74577	−0.247030	−0.123515	+	0.992343i	$0.539417\pi$
$542$	−51.7622	−2.22338
$543$	−55.0887	−2.36408
$544$	44.2683	1.89799
$545$	−3.04502	−0.130434
$546$	0	0
$547$	3.00514	0.128490	0.0642452	−	0.997934i	$-0.479536\pi$
$547$	3.00514	0.128490	0.0642452	+	0.997934i	$0.479536\pi$
$548$	83.2957	3.55822
$549$	−11.3435	−0.484127
$550$	2.88163	0.122873
$551$	15.9102	0.677798
$552$	77.8813	3.31485
$553$	0	0
$554$	−6.86728	−0.291763
$555$	3.96123	0.168145
$556$	−63.3810	−2.68795
$557$	−43.5107	−1.84361	−0.921805	−	0.387655i	$-0.873285\pi$
$557$	−43.5107	−1.84361	−0.921805	+	0.387655i	$0.873285\pi$
$558$	99.5406	4.21389
$559$	−6.51660	−0.275623
$560$	0	0
$561$	−18.3811	−0.776053
$562$	22.1344	0.933682
$563$	13.5570	0.571361	0.285680	−	0.958325i	$-0.407780\pi$
$563$	13.5570	0.571361	0.285680	+	0.958325i	$0.407780\pi$
$564$	61.0457	2.57049
$565$	−7.85257	−0.330360
$566$	20.8458	0.876216
$567$	0	0
$568$	36.9985	1.55242
$569$	30.2342	1.26749	0.633743	−	0.773544i	$-0.281518\pi$
$569$	30.2342	1.26749	0.633743	+	0.773544i	$0.281518\pi$
$570$	−55.6367	−2.33036
$571$	24.4922	1.02497	0.512483	−	0.858697i	$-0.328726\pi$
$571$	24.4922	1.02497	0.512483	+	0.858697i	$0.328726\pi$
$572$	−4.55036	−0.190260
$573$	−0.0149971	−0.000626512 0
$574$	0	0
$575$	−5.04781	−0.210508
$576$	4.87543	0.203143
$577$	18.5297	0.771401	0.385701	−	0.922624i	$-0.373960\pi$
$577$	18.5297	0.771401	0.385701	+	0.922624i	$0.373960\pi$
$578$	78.5785	3.26843
$579$	−10.8959	−0.452817
$580$	54.2959	2.25451
$581$	0	0
$582$	−31.8303	−1.31941
$583$	−9.00445	−0.372926
$584$	43.6669	1.80695
$585$	10.1052	0.417798
$586$	81.0764	3.34924
$587$	5.23101	0.215907	0.107953	−	0.994156i	$-0.465570\pi$
$587$	5.23101	0.215907	0.107953	+	0.994156i	$0.465570\pi$
$588$	0	0
$589$	−31.4376	−1.29536
$590$	16.5273	0.680419
$591$	−51.8886	−2.13441
$592$	4.57344	0.187967
$593$	−25.3289	−1.04013	−0.520066	−	0.854126i	$-0.674093\pi$
$593$	−25.3289	−1.04013	−0.520066	+	0.854126i	$0.674093\pi$
$594$	−7.37543	−0.302618
$595$	0	0
$596$	−57.1756	−2.34200
$597$	−56.1591	−2.29844
$598$	11.4744	0.469222
$599$	−31.6122	−1.29164	−0.645820	−	0.763490i	$-0.723484\pi$
$599$	−31.6122	−1.29164	−0.645820	+	0.763490i	$0.723484\pi$
$600$	−19.5588	−0.798485
$601$	4.36846	0.178193	0.0890966	−	0.996023i	$-0.471602\pi$
$601$	4.36846	0.178193	0.0890966	+	0.996023i	$0.471602\pi$
$602$	0	0
$603$	66.4581	2.70638
$604$	66.2955	2.69753
$605$	−2.47506	−0.100625
$606$	−69.9580	−2.84185
$607$	−25.3038	−1.02705	−0.513524	−	0.858075i	$-0.671660\pi$
$607$	−25.3038	−1.02705	−0.513524	+	0.858075i	$0.671660\pi$
$608$	−21.1526	−0.857850
$609$	0	0
$610$	17.5997	0.712590
$611$	5.04089	0.203932
$612$	128.314	5.18679
$613$	6.93551	0.280122	0.140061	−	0.990143i	$-0.455270\pi$
$613$	6.93551	0.280122	0.140061	+	0.990143i	$0.455270\pi$
$614$	−39.7762	−1.60524
$615$	−18.6651	−0.752647
$616$	0	0
$617$	−4.98006	−0.200490	−0.100245	−	0.994963i	$-0.531963\pi$
$617$	−4.98006	−0.200490	−0.100245	+	0.994963i	$0.531963\pi$
$618$	4.35390	0.175140
$619$	−0.630667	−0.0253486	−0.0126743	−	0.999920i	$-0.504034\pi$
$619$	−0.630667	−0.0253486	−0.0126743	+	0.999920i	$0.504034\pi$
$620$	−107.285	−4.30868
$621$	12.9197	0.518449
$622$	30.3531	1.21705
$623$	0	0
$624$	20.2397	0.810237
$625$	−29.3619	−1.17448
$626$	−58.9048	−2.35431
$627$	8.78301	0.350760
$628$	73.4389	2.93053
$629$	4.15347	0.165610
$630$	0	0
$631$	−33.0103	−1.31412	−0.657059	−	0.753839i	$-0.728200\pi$
$631$	−33.0103	−1.31412	−0.657059	+	0.753839i	$0.728200\pi$
$632$	107.360	4.27055
$633$	−41.5353	−1.65088
$634$	27.1432	1.07799
$635$	−6.28285	−0.249327
$636$	109.045	4.32391
$637$	0	0
$638$	−12.3387	−0.488493
$639$	23.1425	0.915502
$640$	24.1633	0.955140
$641$	−23.2350	−0.917728	−0.458864	−	0.888506i	$-0.651744\pi$
$641$	−23.2350	−0.917728	−0.458864	+	0.888506i	$0.651744\pi$
$642$	58.0270	2.29014
$643$	−26.4692	−1.04384	−0.521921	−	0.852994i	$-0.674784\pi$
$643$	−26.4692	−1.04384	−0.521921	+	0.852994i	$0.674784\pi$
$644$	0	0
$645$	42.9249	1.69017
$646$	−58.3368	−2.29523
$647$	42.5172	1.67152	0.835762	−	0.549092i	$-0.185027\pi$
$647$	42.5172	1.67152	0.835762	+	0.549092i	$0.185027\pi$
$648$	−29.8891	−1.17416
$649$	−2.60906	−0.102415
$650$	−2.88163	−0.113027
$651$	0	0
$652$	−17.5989	−0.689225
$653$	6.23700	0.244073	0.122036	−	0.992526i	$-0.461058\pi$
$653$	6.23700	0.244073	0.122036	+	0.992526i	$0.461058\pi$
$654$	−8.37991	−0.327681
$655$	−46.8027	−1.82873
$656$	−21.5497	−0.841376
$657$	27.3136	1.06560
$658$	0	0
$659$	0.895886	0.0348988	0.0174494	−	0.999848i	$-0.494445\pi$
$659$	0.895886	0.0348988	0.0174494	+	0.999848i	$0.494445\pi$
$660$	29.9733	1.16671
$661$	−15.3875	−0.598504	−0.299252	−	0.954174i	$-0.596737\pi$
$661$	−15.3875	−0.598504	−0.299252	+	0.954174i	$0.596737\pi$
$662$	70.8464	2.75352
$663$	18.3811	0.713865
$664$	−34.3466	−1.33290
$665$	0	0
$666$	6.28395	0.243498
$667$	21.6139	0.836893
$668$	22.4632	0.869128
$669$	61.4929	2.37745
$670$	−103.111	−3.98354
$671$	−2.77835	−0.107257
$672$	0	0
$673$	−12.5318	−0.483067	−0.241534	−	0.970392i	$-0.577650\pi$
$673$	−12.5318	−0.483067	−0.241534	+	0.970392i	$0.577650\pi$
$674$	44.2316	1.70374
$675$	−3.24460	−0.124885
$676$	4.55036	0.175014
$677$	−8.11185	−0.311764	−0.155882	−	0.987776i	$-0.549822\pi$
$677$	−8.11185	−0.311764	−0.155882	+	0.987776i	$0.549822\pi$
$678$	−21.6103	−0.829940
$679$	0	0
$680$	−111.581	−4.27892
$681$	48.4202	1.85547
$682$	24.3804	0.933575
$683$	−36.4218	−1.39364	−0.696820	−	0.717246i	$-0.745402\pi$
$683$	−36.4218	−1.39364	−0.696820	+	0.717246i	$0.745402\pi$
$684$	−61.3119	−2.34432
$685$	−45.3067	−1.73108
$686$	0	0
$687$	32.7964	1.25126
$688$	49.5590	1.88942
$689$	9.00445	0.343042
$690$	−75.5819	−2.87735
$691$	0.0422776	0.00160832	0.000804159	−	1.00000i	$-0.499744\pi$
$691$	0.0422776	0.00160832	0.000804159		1.00000i	$0.499744\pi$
$692$	38.2564	1.45429
$693$	0	0
$694$	−66.8537	−2.53773
$695$	34.4746	1.30769
$696$	83.7476	3.17444
$697$	−19.5709	−0.741300
$698$	14.6418	0.554202
$699$	−62.6919	−2.37123
$700$	0	0
$701$	2.17156	0.0820188	0.0410094	−	0.999159i	$-0.486943\pi$
$701$	2.17156	0.0820188	0.0410094	+	0.999159i	$0.486943\pi$
$702$	7.37543	0.278368
$703$	−1.98464	−0.0748521
$704$	1.19414	0.0450057
$705$	−33.2044	−1.25055
$706$	20.0822	0.755803
$707$	0	0
$708$	31.5961	1.18745
$709$	−26.5461	−0.996961	−0.498480	−	0.866901i	$-0.666108\pi$
$709$	−26.5461	−0.996961	−0.498480	+	0.866901i	$0.666108\pi$
$710$	−35.9061	−1.34753
$711$	67.1533	2.51845
$712$	82.5713	3.09449
$713$	−42.7076	−1.59941
$714$	0	0
$715$	2.47506	0.0925620
$716$	−60.9565	−2.27805
$717$	5.67568	0.211962
$718$	−62.5951	−2.33603
$719$	−18.4118	−0.686645	−0.343322	−	0.939218i	$-0.611552\pi$
$719$	−18.4118	−0.686645	−0.343322	+	0.939218i	$0.611552\pi$
$720$	−76.8504	−2.86404
$721$	0	0
$722$	−20.7531	−0.772349
$723$	4.03858	0.150196
$724$	94.1901	3.50055
$725$	−5.42803	−0.201592
$726$	−6.81138	−0.252794
$727$	34.3421	1.27368	0.636839	−	0.770997i	$-0.280242\pi$
$727$	34.3421	1.27368	0.636839	+	0.770997i	$0.280242\pi$
$728$	0	0
$729$	−41.7036	−1.54458
$730$	−42.3777	−1.56847
$731$	45.0081	1.66468
$732$	33.6461	1.24360
$733$	−17.6275	−0.651085	−0.325542	−	0.945527i	$-0.605547\pi$
$733$	−17.6275	−0.651085	−0.325542	+	0.945527i	$0.605547\pi$
$734$	46.4525	1.71459
$735$	0	0
$736$	−28.7356	−1.05921
$737$	16.2775	0.599591
$738$	−29.6096	−1.08994
$739$	−34.8790	−1.28304	−0.641522	−	0.767104i	$-0.721697\pi$
$739$	−34.8790	−1.28304	−0.641522	+	0.767104i	$0.721697\pi$
$740$	−6.77286	−0.248975
$741$	−8.78301	−0.322652
$742$	0	0
$743$	−31.8697	−1.16919	−0.584593	−	0.811326i	$-0.698746\pi$
$743$	−31.8697	−1.16919	−0.584593	+	0.811326i	$0.698746\pi$
$744$	−165.480	−6.06678
$745$	31.0993	1.13939
$746$	−10.8612	−0.397658
$747$	−21.4837	−0.786047
$748$	31.4279	1.14912
$749$	0	0
$750$	−65.3115	−2.38484
$751$	8.96907	0.327286	0.163643	−	0.986520i	$-0.447676\pi$
$751$	8.96907	0.327286	0.163643	+	0.986520i	$0.447676\pi$
$752$	−38.3361	−1.39798
$753$	42.7156	1.55664
$754$	12.3387	0.449348
$755$	−36.0599	−1.31235
$756$	0	0
$757$	−15.4668	−0.562150	−0.281075	−	0.959686i	$-0.590691\pi$
$757$	−15.4668	−0.562150	−0.281075	+	0.959686i	$0.590691\pi$
$758$	34.6721	1.25935
$759$	11.9316	0.433091
$760$	53.3162	1.93398
$761$	42.6448	1.54587	0.772936	−	0.634484i	$-0.218787\pi$
$761$	42.6448	1.54587	0.772936	+	0.634484i	$0.218787\pi$
$762$	−17.2904	−0.626367
$763$	0	0
$764$	0.0256419	0.000927690 0
$765$	−69.7934	−2.52339
$766$	−76.6113	−2.76808
$767$	2.60906	0.0942078
$768$	72.8537	2.62888
$769$	12.4040	0.447301	0.223651	−	0.974669i	$-0.428203\pi$
$769$	12.4040	0.447301	0.223651	+	0.974669i	$0.428203\pi$
$770$	0	0
$771$	−4.74098	−0.170742
$772$	18.6297	0.670496
$773$	−21.6888	−0.780093	−0.390046	−	0.920795i	$-0.627541\pi$
$773$	−21.6888	−0.780093	−0.390046	+	0.920795i	$0.627541\pi$
$774$	68.0946	2.44761
$775$	10.7254	0.385269
$776$	30.5027	1.09498
$777$	0	0
$778$	3.68137	0.131984
$779$	9.35150	0.335052
$780$	−29.9733	−1.07321
$781$	5.66827	0.202827
$782$	−79.2500	−2.83397
$783$	13.8928	0.496489
$784$	0	0
$785$	−39.9453	−1.42571
$786$	−128.801	−4.59420
$787$	13.6948	0.488166	0.244083	−	0.969754i	$-0.421513\pi$
$787$	13.6948	0.488166	0.244083	+	0.969754i	$0.421513\pi$
$788$	88.7186	3.16047
$789$	−45.1404	−1.60704
$790$	−104.190	−3.70692
$791$	0	0
$792$	26.6497	0.946957
$793$	2.77835	0.0986620
$794$	−11.7041	−0.415363
$795$	−59.3124	−2.10359
$796$	96.0203	3.40335
$797$	11.9000	0.421520	0.210760	−	0.977538i	$-0.432406\pi$
$797$	11.9000	0.421520	0.210760	+	0.977538i	$0.432406\pi$
$798$	0	0
$799$	−34.8158	−1.23170
$800$	7.21654	0.255143
$801$	51.6481	1.82490
$802$	71.4717	2.52375
$803$	6.68989	0.236081
$804$	−197.123	−6.95199
$805$	0	0
$806$	−24.3804	−0.858764
$807$	76.1682	2.68125
$808$	67.0403	2.35847
$809$	47.3836	1.66592	0.832960	−	0.553333i	$-0.186644\pi$
$809$	47.3836	1.66592	0.832960	+	0.553333i	$0.186644\pi$
$810$	29.0066	1.01919
$811$	−21.2885	−0.747542	−0.373771	−	0.927521i	$-0.621935\pi$
$811$	−21.2885	−0.747542	−0.373771	+	0.927521i	$0.621935\pi$
$812$	0	0
$813$	53.8248	1.88772
$814$	1.53912	0.0539463
$815$	9.57248	0.335310
$816$	−139.789	−4.89360
$817$	−21.5061	−0.752402
$818$	−72.4205	−2.53212
$819$	0	0
$820$	31.9133	1.11446
$821$	−1.85772	−0.0648347	−0.0324174	−	0.999474i	$-0.510321\pi$
$821$	−1.85772	−0.0648347	−0.0324174	+	0.999474i	$0.510321\pi$
$822$	−124.685	−4.34887
$823$	−46.9369	−1.63612	−0.818059	−	0.575134i	$-0.804950\pi$
$823$	−46.9369	−1.63612	−0.818059	+	0.575134i	$0.804950\pi$
$824$	−4.17232	−0.145349
$825$	−2.99646	−0.104323
$826$	0	0
$827$	1.05019	0.0365186	0.0182593	−	0.999833i	$-0.494188\pi$
$827$	1.05019	0.0365186	0.0182593	+	0.999833i	$0.494188\pi$
$828$	−83.2917	−2.89459
$829$	34.1944	1.18762	0.593811	−	0.804605i	$-0.297623\pi$
$829$	34.1944	1.18762	0.593811	+	0.804605i	$0.297623\pi$
$830$	33.3325	1.15699
$831$	7.14093	0.247716
$832$	−1.19414	−0.0413992
$833$	0	0
$834$	94.8743	3.28523
$835$	−12.2183	−0.422833
$836$	−15.0171	−0.519377
$837$	−27.4513	−0.948857
$838$	71.2972	2.46292
$839$	−52.8541	−1.82473	−0.912364	−	0.409381i	$-0.865745\pi$
$839$	−52.8541	−1.82473	−0.912364	+	0.409381i	$0.865745\pi$
$840$	0	0
$841$	−5.75810	−0.198555
$842$	54.7562	1.88702
$843$	−23.0164	−0.792727
$844$	71.0166	2.44449
$845$	−2.47506	−0.0851446
$846$	−52.6743	−1.81098
$847$	0	0
$848$	−68.4792	−2.35159
$849$	−21.6765	−0.743936
$850$	19.9025	0.682652
$851$	−2.69611	−0.0924216
$852$	−68.6434	−2.35168
$853$	33.7922	1.15702	0.578511	−	0.815674i	$-0.303634\pi$
$853$	33.7922	1.15702	0.578511	+	0.815674i	$0.303634\pi$
$854$	0	0
$855$	33.3492	1.14052
$856$	−55.6068	−1.90060
$857$	20.9646	0.716137	0.358068	−	0.933695i	$-0.383435\pi$
$857$	20.9646	0.716137	0.358068	+	0.933695i	$0.383435\pi$
$858$	6.81138	0.232537
$859$	10.7522	0.366861	0.183430	−	0.983033i	$-0.441280\pi$
$859$	10.7522	0.366861	0.183430	+	0.983033i	$0.441280\pi$
$860$	−73.3925	−2.50266
$861$	0	0
$862$	53.9580	1.83782
$863$	12.9496	0.440811	0.220405	−	0.975408i	$-0.429262\pi$
$863$	12.9496	0.440811	0.220405	+	0.975408i	$0.429262\pi$
$864$	−18.4705	−0.628378
$865$	−20.8086	−0.707515
$866$	25.7374	0.874592
$867$	−81.7098	−2.77501
$868$	0	0
$869$	16.4478	0.557954
$870$	−81.2749	−2.75548
$871$	−16.2775	−0.551543
$872$	8.03041	0.271944
$873$	19.0794	0.645739
$874$	37.8678	1.28090
$875$	0	0
$876$	−81.0154	−2.73726
$877$	13.7249	0.463457	0.231729	−	0.972780i	$-0.425562\pi$
$877$	13.7249	0.463457	0.231729	+	0.972780i	$0.425562\pi$
$878$	−82.0174	−2.76795
$879$	−84.3072	−2.84361
$880$	−18.8229	−0.634520
$881$	−9.62643	−0.324323	−0.162161	−	0.986764i	$-0.551847\pi$
$881$	−9.62643	−0.324323	−0.162161	+	0.986764i	$0.551847\pi$
$882$	0	0
$883$	−6.00751	−0.202169	−0.101084	−	0.994878i	$-0.532231\pi$
$883$	−6.00751	−0.202169	−0.101084	+	0.994878i	$0.532231\pi$
$884$	−31.4279	−1.05703
$885$	−17.1859	−0.577699
$886$	−40.2764	−1.35311
$887$	35.4451	1.19013	0.595065	−	0.803678i	$-0.297126\pi$
$887$	35.4451	1.19013	0.595065	+	0.803678i	$0.297126\pi$
$888$	−10.4467	−0.350567
$889$	0	0
$890$	−80.1334	−2.68608
$891$	−4.57909	−0.153405
$892$	−105.140	−3.52035
$893$	16.6359	0.556701
$894$	85.5855	2.86241
$895$	33.1559	1.10828
$896$	0	0
$897$	−11.9316	−0.398385
$898$	−79.8283	−2.66391
$899$	−45.9245	−1.53167
$900$	20.9176	0.697252
$901$	−62.1909	−2.07188
$902$	−7.25226	−0.241474
$903$	0	0
$904$	20.7090	0.688772
$905$	−51.2325	−1.70303
$906$	−99.2371	−3.29693
$907$	12.7625	0.423772	0.211886	−	0.977294i	$-0.432039\pi$
$907$	12.7625	0.423772	0.211886	+	0.977294i	$0.432039\pi$
$908$	−82.7884	−2.74743
$909$	41.9335	1.39085
$910$	0	0
$911$	37.8413	1.25374	0.626868	−	0.779125i	$-0.284336\pi$
$911$	37.8413	1.25374	0.626868	+	0.779125i	$0.284336\pi$
$912$	66.7951	2.21181
$913$	−5.26198	−0.174146
$914$	28.7634	0.951409
$915$	−18.3010	−0.605012
$916$	−56.0750	−1.85277
$917$	0	0
$918$	−50.9398	−1.68126
$919$	−42.7304	−1.40955	−0.704773	−	0.709433i	$-0.748951\pi$
$919$	−42.7304	−1.40955	−0.704773	+	0.709433i	$0.748951\pi$
$920$	72.4296	2.38793
$921$	41.3612	1.36290
$922$	−22.4073	−0.737946
$923$	−5.66827	−0.186573
$924$	0	0
$925$	0.677092	0.0222626
$926$	−84.4807	−2.77621
$927$	−2.60977	−0.0857162
$928$	−30.9000	−1.01434
$929$	52.6386	1.72701	0.863507	−	0.504336i	$-0.168263\pi$
$929$	52.6386	1.72701	0.863507	+	0.504336i	$0.168263\pi$
$930$	160.594	5.26609
$931$	0	0
$932$	107.190	3.51113
$933$	−31.5626	−1.03331
$934$	43.8948	1.43628
$935$	−17.0945	−0.559049
$936$	−26.6497	−0.871073
$937$	19.1160	0.624494	0.312247	−	0.950001i	$-0.398918\pi$
$937$	19.1160	0.624494	0.312247	+	0.950001i	$0.398918\pi$
$938$	0	0
$939$	61.2521	1.99889
$940$	56.7725	1.85172
$941$	−2.37817	−0.0775260	−0.0387630	−	0.999248i	$-0.512342\pi$
$941$	−2.37817	−0.0775260	−0.0387630	+	0.999248i	$0.512342\pi$
$942$	−109.930	−3.58171
$943$	12.7039	0.413697
$944$	−19.8420	−0.645803
$945$	0	0
$946$	16.6784	0.542260
$947$	2.32468	0.0755419	0.0377710	−	0.999286i	$-0.487974\pi$
$947$	2.32468	0.0755419	0.0377710	+	0.999286i	$0.487974\pi$
$948$	−199.185	−6.46923
$949$	−6.68989	−0.217163
$950$	−9.50997	−0.308544
$951$	−28.2248	−0.915252
$952$	0	0
$953$	33.1381	1.07345	0.536724	−	0.843758i	$-0.319662\pi$
$953$	33.1381	1.07345	0.536724	+	0.843758i	$0.319662\pi$
$954$	−94.0912	−3.04632
$955$	−0.0139473	−0.000451324 0
$956$	−9.70422	−0.313857
$957$	12.8304	0.414746
$958$	−75.8576	−2.45085
$959$	0	0
$960$	7.86578	0.253867
$961$	59.7439	1.92722
$962$	−1.53912	−0.0496234
$963$	−34.7819	−1.12083
$964$	−6.90512	−0.222399
$965$	−10.1332	−0.326198
$966$	0	0
$967$	56.0127	1.80125	0.900624	−	0.434599i	$-0.143110\pi$
$967$	56.0127	1.80125	0.900624	+	0.434599i	$0.143110\pi$
$968$	6.52730	0.209795
$969$	60.6615	1.94873
$970$	−29.6021	−0.950467
$971$	−49.4138	−1.58576	−0.792882	−	0.609375i	$-0.791420\pi$
$971$	−49.4138	−1.58576	−0.792882	+	0.609375i	$0.791420\pi$
$972$	94.7922	3.04046
$973$	0	0
$974$	80.5695	2.58161
$975$	2.99646	0.0959637
$976$	−21.1294	−0.676337
$977$	−29.9413	−0.957907	−0.478954	−	0.877840i	$-0.658984\pi$
$977$	−29.9413	−0.957907	−0.478954	+	0.877840i	$0.658984\pi$
$978$	26.3436	0.842374
$979$	12.6501	0.404300
$980$	0	0
$981$	5.02300	0.160372
$982$	1.54388	0.0492672
$983$	−31.7156	−1.01157	−0.505785	−	0.862660i	$-0.668797\pi$
$983$	−31.7156	−1.01157	−0.505785	+	0.862660i	$0.668797\pi$
$984$	49.2240	1.56920
$985$	−48.2564	−1.53758
$986$	−85.2193	−2.71394
$987$	0	0
$988$	15.0171	0.477757
$989$	−29.2158	−0.929008
$990$	−25.8629	−0.821977
$991$	−44.1244	−1.40166	−0.700829	−	0.713330i	$-0.747186\pi$
$991$	−44.1244	−1.40166	−0.700829	+	0.713330i	$0.747186\pi$
$992$	61.0565	1.93854
$993$	−73.6695	−2.33783
$994$	0	0
$995$	−52.2280	−1.65574
$996$	63.7232	2.01915
$997$	−11.9463	−0.378342	−0.189171	−	0.981944i	$-0.560580\pi$
$997$	−11.9463	−0.378342	−0.189171	+	0.981944i	$0.560580\pi$
$998$	−32.8543	−1.03999
$999$	−1.73299	−0.0548294

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7007.2.a.bh.1.23		25
7.2	even	3		1001.2.i.d.144.3	✓	50
7.4	even	3		1001.2.i.d.716.3	yes	50
7.6	odd	2		7007.2.a.bi.1.23		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1001.2.i.d.144.3	✓	50	7.2	even	3
1001.2.i.d.716.3	yes	50	7.4	even	3
7007.2.a.bh.1.23		25	1.1	even	1	trivial
7007.2.a.bi.1.23		25	7.6	odd	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:	\( N \)	\(=\)	\( 7007 = 7^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7007.a (trivial)

\(f(q)\)	\(=\)	\(q+2.55937 q^{2} -2.66135 q^{3} +4.55036 q^{4} -2.47506 q^{5} -6.81138 q^{6} +6.52730 q^{8} +4.08281 q^{9} +O(q^{10})\)	\(q+2.55937 q^{2} -2.66135 q^{3} +4.55036 q^{4} -2.47506 q^{5} -6.81138 q^{6} +6.52730 q^{8} +4.08281 q^{9} -6.33458 q^{10} +1.00000 q^{11} -12.1101 q^{12} -1.00000 q^{13} +6.58701 q^{15} +7.60504 q^{16} +6.90669 q^{17} +10.4494 q^{18} -3.30020 q^{19} -11.2624 q^{20} +2.55937 q^{22} -4.48329 q^{23} -17.3715 q^{24} +1.12592 q^{25} -2.55937 q^{26} -2.88174 q^{27} -4.82099 q^{29} +16.8586 q^{30} +9.52596 q^{31} +6.40948 q^{32} -2.66135 q^{33} +17.6767 q^{34} +18.5782 q^{36} +0.601369 q^{37} -8.44643 q^{38} +2.66135 q^{39} -16.1555 q^{40} -2.83361 q^{41} +6.51660 q^{43} +4.55036 q^{44} -10.1052 q^{45} -11.4744 q^{46} -5.04089 q^{47} -20.2397 q^{48} +2.88163 q^{50} -18.3811 q^{51} -4.55036 q^{52} -9.00445 q^{53} -7.37543 q^{54} -2.47506 q^{55} +8.78301 q^{57} -12.3387 q^{58} -2.60906 q^{59} +29.9733 q^{60} -2.77835 q^{61} +24.3804 q^{62} +1.19414 q^{64} +2.47506 q^{65} -6.81138 q^{66} +16.2775 q^{67} +31.4279 q^{68} +11.9316 q^{69} +5.66827 q^{71} +26.6497 q^{72} +6.68989 q^{73} +1.53912 q^{74} -2.99646 q^{75} -15.0171 q^{76} +6.81138 q^{78} +16.4478 q^{79} -18.8229 q^{80} -4.57909 q^{81} -7.25226 q^{82} -5.26198 q^{83} -17.0945 q^{85} +16.6784 q^{86} +12.8304 q^{87} +6.52730 q^{88} +12.6501 q^{89} -25.8629 q^{90} -20.4006 q^{92} -25.3520 q^{93} -12.9015 q^{94} +8.16819 q^{95} -17.0579 q^{96} +4.67310 q^{97} +4.08281 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} - 2 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 21 q^{8} + 37 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 - 2 * q^3 + 30 * q^4 - q^5 + 2 * q^6 + 21 * q^8 + 37 * q^9	\( 25 q + 6 q^{2} - 2 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 21 q^{8} + 37 q^{9} - 3 q^{10} + 25 q^{11} + 9 q^{12} - 25 q^{13} + 32 q^{16} - q^{17} + 44 q^{18} + 5 q^{19} + 4 q^{20} + 6 q^{22} + 15 q^{23} - 4 q^{24} + 50 q^{25} - 6 q^{26} - 17 q^{27} + 24 q^{29} + q^{30} - 12 q^{31} + 48 q^{32} - 2 q^{33} - 8 q^{34} + 30 q^{36} + 33 q^{37} + 16 q^{38} + 2 q^{39} - 21 q^{40} + 12 q^{41} + 38 q^{43} + 30 q^{44} - 22 q^{45} + 39 q^{46} + 4 q^{47} + 82 q^{48} + 16 q^{50} + 51 q^{51} - 30 q^{52} + 2 q^{53} + 10 q^{54} - q^{55} + 38 q^{57} + 17 q^{58} - 4 q^{59} - 33 q^{60} - 22 q^{61} + 42 q^{62} + 41 q^{64} + q^{65} + 2 q^{66} + 24 q^{67} + 14 q^{68} - 30 q^{69} + 9 q^{71} + 102 q^{72} + 11 q^{73} + 39 q^{74} - 16 q^{75} + 58 q^{76} - 2 q^{78} + 19 q^{79} - 33 q^{80} + 73 q^{81} - 32 q^{82} + 16 q^{83} + 14 q^{85} + 27 q^{86} - 11 q^{87} + 21 q^{88} + 13 q^{89} + 40 q^{90} + 17 q^{93} - 56 q^{94} + 15 q^{95} + 55 q^{96} + 34 q^{97} + 37 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 2 * q^3 + 30 * q^4 - q^5 + 2 * q^6 + 21 * q^8 + 37 * q^9 - 3 * q^10 + 25 * q^11 + 9 * q^12 - 25 * q^13 + 32 * q^16 - q^17 + 44 * q^18 + 5 * q^19 + 4 * q^20 + 6 * q^22 + 15 * q^23 - 4 * q^24 + 50 * q^25 - 6 * q^26 - 17 * q^27 + 24 * q^29 + q^30 - 12 * q^31 + 48 * q^32 - 2 * q^33 - 8 * q^34 + 30 * q^36 + 33 * q^37 + 16 * q^38 + 2 * q^39 - 21 * q^40 + 12 * q^41 + 38 * q^43 + 30 * q^44 - 22 * q^45 + 39 * q^46 + 4 * q^47 + 82 * q^48 + 16 * q^50 + 51 * q^51 - 30 * q^52 + 2 * q^53 + 10 * q^54 - q^55 + 38 * q^57 + 17 * q^58 - 4 * q^59 - 33 * q^60 - 22 * q^61 + 42 * q^62 + 41 * q^64 + q^65 + 2 * q^66 + 24 * q^67 + 14 * q^68 - 30 * q^69 + 9 * q^71 + 102 * q^72 + 11 * q^73 + 39 * q^74 - 16 * q^75 + 58 * q^76 - 2 * q^78 + 19 * q^79 - 33 * q^80 + 73 * q^81 - 32 * q^82 + 16 * q^83 + 14 * q^85 + 27 * q^86 - 11 * q^87 + 21 * q^88 + 13 * q^89 + 40 * q^90 + 17 * q^93 - 56 * q^94 + 15 * q^95 + 55 * q^96 + 34 * q^97 + 37 * q^99

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