LMFDB - Embedded newform 1075.2.a.r.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,2,Mod(1,1075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1075.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1075.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:	$8.58391821729$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.282109865.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 11x^{4} + 8x^{3} + 34x^{2} - 12x - 27 $ x^6 - x^5 - 11x^4 + 8x^3 + 34x^2 - 12x - 27
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.22887$ of defining polynomial
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.22887 q^{2} +0.651450 q^{3} -0.489869 q^{4} +0.800550 q^{6} +3.71874 q^{7} -3.05974 q^{8} -2.57561 q^{9} +O(q^{10})$	\(q+1.22887 q^{2} +0.651450 q^{3} -0.489869 q^{4} +0.800550 q^{6} +3.71874 q^{7} -3.05974 q^{8} -2.57561 q^{9} +0.806297 q^{11} -0.319126 q^{12} +1.77687 q^{13} +4.56987 q^{14} -2.78029 q^{16} +6.55716 q^{17} -3.16510 q^{18} +4.55716 q^{19} +2.42258 q^{21} +0.990837 q^{22} +4.91064 q^{23} -1.99327 q^{24} +2.18355 q^{26} -3.63223 q^{27} -1.82170 q^{28} -0.0967167 q^{29} +1.58317 q^{31} +2.70285 q^{32} +0.525263 q^{33} +8.05792 q^{34} +1.26171 q^{36} +1.74242 q^{37} +5.60018 q^{38} +1.15754 q^{39} +0.954351 q^{41} +2.97704 q^{42} -1.00000 q^{43} -0.394980 q^{44} +6.03455 q^{46} -4.00844 q^{47} -1.81122 q^{48} +6.82905 q^{49} +4.27167 q^{51} -0.870436 q^{52} -10.3162 q^{53} -4.46356 q^{54} -11.3784 q^{56} +2.96877 q^{57} -0.118853 q^{58} -1.94006 q^{59} -8.31058 q^{61} +1.94552 q^{62} -9.57804 q^{63} +8.88203 q^{64} +0.645481 q^{66} +1.31984 q^{67} -3.21215 q^{68} +3.19904 q^{69} +15.9131 q^{71} +7.88069 q^{72} -15.9988 q^{73} +2.14121 q^{74} -2.23241 q^{76} +2.99841 q^{77} +1.42248 q^{78} -9.54396 q^{79} +5.36062 q^{81} +1.17278 q^{82} +14.0925 q^{83} -1.18675 q^{84} -1.22887 q^{86} -0.0630061 q^{87} -2.46706 q^{88} +1.06591 q^{89} +6.60773 q^{91} -2.40557 q^{92} +1.03136 q^{93} -4.92587 q^{94} +1.76077 q^{96} -14.4667 q^{97} +8.39204 q^{98} -2.07671 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} + 2 q^{3} + 11 q^{4} + 11 q^{6} + 2 q^{7} + 6 q^{8} + 12 q^{9}+O(q^{10}) $ 6 * q + q^2 + 2 * q^3 + 11 * q^4 + 11 * q^6 + 2 * q^7 + 6 * q^8 + 12 * q^9	$ 6 q + q^{2} + 2 q^{3} + 11 q^{4} + 11 q^{6} + 2 q^{7} + 6 q^{8} + 12 q^{9} - 6 q^{11} - 4 q^{12} + 17 q^{14} + 5 q^{16} + 7 q^{17} - 15 q^{18} - 5 q^{19} + 19 q^{21} + 34 q^{22} - 3 q^{23} + 9 q^{24} + 14 q^{26} + 5 q^{27} - 21 q^{28} + 18 q^{29} - 12 q^{31} + 3 q^{32} - 10 q^{33} + q^{34} - 10 q^{36} + 7 q^{37} - q^{38} - 3 q^{39} - 9 q^{42} - 6 q^{43} + 9 q^{44} - 14 q^{46} - 6 q^{47} + 2 q^{48} - q^{51} + 3 q^{52} - 8 q^{53} + 12 q^{54} + 20 q^{56} - 5 q^{57} - 24 q^{58} + 21 q^{59} - 8 q^{61} + 47 q^{62} + 19 q^{63} + 6 q^{64} + q^{66} - 35 q^{68} + 37 q^{69} + 14 q^{71} + 44 q^{72} - q^{73} + 2 q^{74} - 57 q^{76} + 13 q^{77} - 49 q^{78} - 31 q^{79} + 62 q^{81} + 32 q^{82} - 13 q^{83} + 21 q^{84} - q^{86} + 22 q^{87} + 39 q^{88} + 40 q^{89} + 11 q^{91} - 32 q^{92} - 15 q^{93} + 35 q^{94} - 50 q^{96} + 11 q^{97} - 44 q^{98} - 53 q^{99}+O(q^{100}) $ 6 * q + q^2 + 2 * q^3 + 11 * q^4 + 11 * q^6 + 2 * q^7 + 6 * q^8 + 12 * q^9 - 6 * q^11 - 4 * q^12 + 17 * q^14 + 5 * q^16 + 7 * q^17 - 15 * q^18 - 5 * q^19 + 19 * q^21 + 34 * q^22 - 3 * q^23 + 9 * q^24 + 14 * q^26 + 5 * q^27 - 21 * q^28 + 18 * q^29 - 12 * q^31 + 3 * q^32 - 10 * q^33 + q^34 - 10 * q^36 + 7 * q^37 - q^38 - 3 * q^39 - 9 * q^42 - 6 * q^43 + 9 * q^44 - 14 * q^46 - 6 * q^47 + 2 * q^48 - q^51 + 3 * q^52 - 8 * q^53 + 12 * q^54 + 20 * q^56 - 5 * q^57 - 24 * q^58 + 21 * q^59 - 8 * q^61 + 47 * q^62 + 19 * q^63 + 6 * q^64 + q^66 - 35 * q^68 + 37 * q^69 + 14 * q^71 + 44 * q^72 - q^73 + 2 * q^74 - 57 * q^76 + 13 * q^77 - 49 * q^78 - 31 * q^79 + 62 * q^81 + 32 * q^82 - 13 * q^83 + 21 * q^84 - q^86 + 22 * q^87 + 39 * q^88 + 40 * q^89 + 11 * q^91 - 32 * q^92 - 15 * q^93 + 35 * q^94 - 50 * q^96 + 11 * q^97 - 44 * q^98 - 53 * 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 $

$2$	1.22887	0.868945	0.434472	−	0.900685i	$-0.356935\pi$
$2$	1.22887	0.868945	0.434472	+	0.900685i	$0.356935\pi$
$3$	0.651450	0.376115	0.188058	−	0.982158i	$-0.439781\pi$
$3$	0.651450	0.376115	0.188058	+	0.982158i	$0.439781\pi$
$4$	−0.489869	−0.244935
$5$	0	0
$5$	0	0
$6$	0.800550	0.326823
$7$	3.71874	1.40555	0.702776	−	0.711411i	$-0.251943\pi$
$7$	3.71874	1.40555	0.702776	+	0.711411i	$0.251943\pi$
$8$	−3.05974	−1.08178
$9$	−2.57561	−0.858537
$10$	0	0
$11$	0.806297	0.243108	0.121554	−	0.992585i	$-0.461212\pi$
$11$	0.806297	0.243108	0.121554	+	0.992585i	$0.461212\pi$
$12$	−0.319126	−0.0921236
$13$	1.77687	0.492816	0.246408	−	0.969166i	$-0.420750\pi$
$13$	1.77687	0.492816	0.246408	+	0.969166i	$0.420750\pi$
$14$	4.56987	1.22135
$15$	0	0
$16$	−2.78029	−0.695072
$17$	6.55716	1.59035	0.795173	−	0.606383i	$-0.207380\pi$
$17$	6.55716	1.59035	0.795173	+	0.606383i	$0.207380\pi$
$18$	−3.16510	−0.746022
$19$	4.55716	1.04548	0.522742	−	0.852491i	$-0.324909\pi$
$19$	4.55716	1.04548	0.522742	+	0.852491i	$0.324909\pi$
$20$	0	0
$21$	2.42258	0.528650
$22$	0.990837	0.211247
$23$	4.91064	1.02394	0.511969	−	0.859004i	$-0.328916\pi$
$23$	4.91064	1.02394	0.511969	+	0.859004i	$0.328916\pi$
$24$	−1.99327	−0.406874
$25$	0	0
$26$	2.18355	0.428230
$27$	−3.63223	−0.699024
$28$	−1.82170	−0.344269
$29$	−0.0967167	−0.0179598	−0.00897992	−	0.999960i	$-0.502858\pi$
$29$	−0.0967167	−0.0179598	−0.00897992	+	0.999960i	$0.502858\pi$
$30$	0	0
$31$	1.58317	0.284346	0.142173	−	0.989842i	$-0.454591\pi$
$31$	1.58317	0.284346	0.142173	+	0.989842i	$0.454591\pi$
$32$	2.70285	0.477800
$33$	0.525263	0.0914365
$34$	8.05792	1.38192
$35$	0	0
$36$	1.26171	0.210286
$37$	1.74242	0.286452	0.143226	−	0.989690i	$-0.454252\pi$
$37$	1.74242	0.286452	0.143226	+	0.989690i	$0.454252\pi$
$38$	5.60018	0.908469
$39$	1.15754	0.185355
$40$	0	0
$41$	0.954351	0.149045	0.0745223	−	0.997219i	$-0.476257\pi$
$41$	0.954351	0.149045	0.0745223	+	0.997219i	$0.476257\pi$
$42$	2.97704	0.459367
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−0.394980	−0.0595455
$45$	0	0
$46$	6.03455	0.889746
$47$	−4.00844	−0.584692	−0.292346	−	0.956313i	$-0.594436\pi$
$47$	−4.00844	−0.584692	−0.292346	+	0.956313i	$0.594436\pi$
$48$	−1.81122	−0.261427
$49$	6.82905	0.975579
$50$	0	0
$51$	4.27167	0.598153
$52$	−0.870436	−0.120708
$53$	−10.3162	−1.41704	−0.708521	−	0.705690i	$-0.750637\pi$
$53$	−10.3162	−1.41704	−0.708521	+	0.705690i	$0.750637\pi$
$54$	−4.46356	−0.607413
$55$	0	0
$56$	−11.3784	−1.52050
$57$	2.96877	0.393223
$58$	−0.118853	−0.0156061
$59$	−1.94006	−0.252574	−0.126287	−	0.991994i	$-0.540306\pi$
$59$	−1.94006	−0.252574	−0.126287	+	0.991994i	$0.540306\pi$
$60$	0	0
$61$	−8.31058	−1.06406	−0.532030	−	0.846725i	$-0.678571\pi$
$61$	−8.31058	−1.06406	−0.532030	+	0.846725i	$0.678571\pi$
$62$	1.94552	0.247081
$63$	−9.57804	−1.20672
$64$	8.88203	1.11025
$65$	0	0
$66$	0.645481	0.0794533
$67$	1.31984	0.161245	0.0806223	−	0.996745i	$-0.474309\pi$
$67$	1.31984	0.161245	0.0806223	+	0.996745i	$0.474309\pi$
$68$	−3.21215	−0.389531
$69$	3.19904	0.385119
$70$	0	0
$71$	15.9131	1.88853	0.944267	−	0.329182i	$-0.106773\pi$
$71$	15.9131	1.88853	0.944267	+	0.329182i	$0.106773\pi$
$72$	7.88069	0.928748
$73$	−15.9988	−1.87252	−0.936259	−	0.351310i	$-0.885736\pi$
$73$	−15.9988	−1.87252	−0.936259	+	0.351310i	$0.885736\pi$
$74$	2.14121	0.248911
$75$	0	0
$76$	−2.23241	−0.256075
$77$	2.99841	0.341701
$78$	1.42248	0.161064
$79$	−9.54396	−1.07378	−0.536890	−	0.843652i	$-0.680401\pi$
$79$	−9.54396	−1.07378	−0.536890	+	0.843652i	$0.680401\pi$
$80$	0	0
$81$	5.36062	0.595624
$82$	1.17278	0.129512
$83$	14.0925	1.54685	0.773425	−	0.633888i	$-0.218542\pi$
$83$	14.0925	1.54685	0.773425	+	0.633888i	$0.218542\pi$
$84$	−1.18675	−0.129485
$85$	0	0
$86$	−1.22887	−0.132513
$87$	−0.0630061	−0.00675497
$88$	−2.46706	−0.262989
$89$	1.06591	0.112986	0.0564931	−	0.998403i	$-0.482008\pi$
$89$	1.06591	0.112986	0.0564931	+	0.998403i	$0.482008\pi$
$90$	0	0
$91$	6.60773	0.692679
$92$	−2.40557	−0.250798
$93$	1.03136	0.106947
$94$	−4.92587	−0.508065
$95$	0	0
$96$	1.76077	0.179708
$97$	−14.4667	−1.46887	−0.734436	−	0.678678i	$-0.762553\pi$
$97$	−14.4667	−1.46887	−0.734436	+	0.678678i	$0.762553\pi$
$98$	8.39204	0.847724
$99$	−2.07671	−0.208717
$100$	0	0
$101$	13.8603	1.37915	0.689575	−	0.724214i	$-0.257797\pi$
$101$	13.8603	1.37915	0.689575	+	0.724214i	$0.257797\pi$
$102$	5.24934	0.519762
$103$	−9.46127	−0.932247	−0.466123	−	0.884720i	$-0.654350\pi$
$103$	−9.46127	−0.932247	−0.466123	+	0.884720i	$0.654350\pi$
$104$	−5.43676	−0.533118
$105$	0	0
$106$	−12.6773	−1.23133
$107$	2.30803	0.223125	0.111563	−	0.993757i	$-0.464414\pi$
$107$	2.30803	0.223125	0.111563	+	0.993757i	$0.464414\pi$
$108$	1.77932	0.171215
$109$	12.0223	1.15152	0.575762	−	0.817617i	$-0.304706\pi$
$109$	12.0223	1.15152	0.575762	+	0.817617i	$0.304706\pi$
$110$	0	0
$111$	1.13510	0.107739
$112$	−10.3392	−0.976961
$113$	−3.57291	−0.336112	−0.168056	−	0.985777i	$-0.553749\pi$
$113$	−3.57291	−0.336112	−0.168056	+	0.985777i	$0.553749\pi$
$114$	3.64824	0.341689
$115$	0	0
$116$	0.0473786	0.00439899
$117$	−4.57654	−0.423101
$118$	−2.38409	−0.219473
$119$	24.3844	2.23531
$120$	0	0
$121$	−10.3499	−0.940899
$122$	−10.2127	−0.924610
$123$	0.621712	0.0560579
$124$	−0.775547	−0.0696461
$125$	0	0
$126$	−11.7702	−1.04857
$127$	−0.902396	−0.0800747	−0.0400374	−	0.999198i	$-0.512748\pi$
$127$	−0.902396	−0.0800747	−0.0400374	+	0.999198i	$0.512748\pi$
$128$	5.50921	0.486950
$129$	−0.651450	−0.0573570
$130$	0	0
$131$	−5.69092	−0.497218	−0.248609	−	0.968604i	$-0.579973\pi$
$131$	−5.69092	−0.497218	−0.248609	+	0.968604i	$0.579973\pi$
$132$	−0.257310	−0.0223960
$133$	16.9469	1.46948
$134$	1.62192	0.140113
$135$	0	0
$136$	−20.0632	−1.72040
$137$	−20.6876	−1.76746	−0.883731	−	0.467996i	$-0.844976\pi$
$137$	−20.6876	−1.76746	−0.883731	+	0.467996i	$0.844976\pi$
$138$	3.93121	0.334647
$139$	−7.93514	−0.673049	−0.336525	−	0.941675i	$-0.609252\pi$
$139$	−7.93514	−0.673049	−0.336525	+	0.941675i	$0.609252\pi$
$140$	0	0
$141$	−2.61130	−0.219911
$142$	19.5551	1.64103
$143$	1.43269	0.119807
$144$	7.16095	0.596746
$145$	0	0
$146$	−19.6605	−1.62712
$147$	4.44879	0.366930
$148$	−0.853558	−0.0701621
$149$	7.20552	0.590299	0.295149	−	0.955451i	$-0.404631\pi$
$149$	7.20552	0.590299	0.295149	+	0.955451i	$0.404631\pi$
$150$	0	0
$151$	3.55063	0.288946	0.144473	−	0.989509i	$-0.453851\pi$
$151$	3.55063	0.288946	0.144473	+	0.989509i	$0.453851\pi$
$152$	−13.9437	−1.13098
$153$	−16.8887	−1.36537
$154$	3.68467	0.296919
$155$	0	0
$156$	−0.567046	−0.0454000
$157$	−8.06377	−0.643559	−0.321780	−	0.946815i	$-0.604281\pi$
$157$	−8.06377	−0.643559	−0.321780	+	0.946815i	$0.604281\pi$
$158$	−11.7283	−0.933055
$159$	−6.72051	−0.532971
$160$	0	0
$161$	18.2614	1.43920
$162$	6.58752	0.517564
$163$	18.7857	1.47141	0.735704	−	0.677303i	$-0.236851\pi$
$163$	18.7857	1.47141	0.735704	+	0.677303i	$0.236851\pi$
$164$	−0.467507	−0.0365062
$165$	0	0
$166$	17.3179	1.34413
$167$	−16.0351	−1.24084	−0.620418	−	0.784271i	$-0.713037\pi$
$167$	−16.0351	−1.24084	−0.620418	+	0.784271i	$0.713037\pi$
$168$	−7.41244	−0.571882
$169$	−9.84272	−0.757132
$170$	0	0
$171$	−11.7375	−0.897588
$172$	0.489869	0.0373522
$173$	1.31229	0.0997713	0.0498856	−	0.998755i	$-0.484114\pi$
$173$	1.31229	0.0997713	0.0498856	+	0.998755i	$0.484114\pi$
$174$	−0.0774266	−0.00586969
$175$	0	0
$176$	−2.24174	−0.168977
$177$	−1.26385	−0.0949970
$178$	1.30987	0.0981788
$179$	−16.2692	−1.21602	−0.608008	−	0.793931i	$-0.708031\pi$
$179$	−16.2692	−1.21602	−0.608008	+	0.793931i	$0.708031\pi$
$180$	0	0
$181$	−20.1612	−1.49857	−0.749284	−	0.662249i	$-0.769602\pi$
$181$	−20.1612	−1.49857	−0.749284	+	0.662249i	$0.769602\pi$
$182$	8.12007	0.601900
$183$	−5.41393	−0.400209
$184$	−15.0252	−1.10768
$185$	0	0
$186$	1.26741	0.0929308
$187$	5.28702	0.386625
$188$	1.96361	0.143211
$189$	−13.5073	−0.982515
$190$	0	0
$191$	9.16401	0.663084	0.331542	−	0.943440i	$-0.392431\pi$
$191$	9.16401	0.663084	0.331542	+	0.943440i	$0.392431\pi$
$192$	5.78620	0.417583
$193$	9.14194	0.658051	0.329026	−	0.944321i	$-0.393280\pi$
$193$	9.14194	0.658051	0.329026	+	0.944321i	$0.393280\pi$
$194$	−17.7778	−1.27637
$195$	0	0
$196$	−3.34534	−0.238953
$197$	−17.4582	−1.24384	−0.621921	−	0.783080i	$-0.713648\pi$
$197$	−17.4582	−1.24384	−0.621921	+	0.783080i	$0.713648\pi$
$198$	−2.55201	−0.181364
$199$	−21.6376	−1.53385	−0.766925	−	0.641737i	$-0.778214\pi$
$199$	−21.6376	−1.53385	−0.766925	+	0.641737i	$0.778214\pi$
$200$	0	0
$201$	0.859813	0.0606465
$202$	17.0325	1.19841
$203$	−0.359665	−0.0252435
$204$	−2.09256	−0.146508
$205$	0	0
$206$	−11.6267	−0.810071
$207$	−12.6479	−0.879089
$208$	−4.94022	−0.342543
$209$	3.67443	0.254165
$210$	0	0
$211$	8.69308	0.598456	0.299228	−	0.954182i	$-0.403271\pi$
$211$	8.69308	0.598456	0.299228	+	0.954182i	$0.403271\pi$
$212$	5.05360	0.347083
$213$	10.3666	0.710306
$214$	2.83627	0.193884
$215$	0	0
$216$	11.1137	0.756190
$217$	5.88740	0.399663
$218$	14.7738	1.00061
$219$	−10.4224	−0.704282
$220$	0	0
$221$	11.6512	0.783748
$222$	1.39490	0.0936192
$223$	18.7778	1.25745	0.628726	−	0.777627i	$-0.283577\pi$
$223$	18.7778	1.25745	0.628726	+	0.777627i	$0.283577\pi$
$224$	10.0512	0.671573
$225$	0	0
$226$	−4.39066	−0.292062
$227$	5.83924	0.387564	0.193782	−	0.981045i	$-0.437925\pi$
$227$	5.83924	0.387564	0.193782	+	0.981045i	$0.437925\pi$
$228$	−1.45431	−0.0963138
$229$	11.3962	0.753082	0.376541	−	0.926400i	$-0.377113\pi$
$229$	11.3962	0.753082	0.376541	+	0.926400i	$0.377113\pi$
$230$	0	0
$231$	1.95332	0.128519
$232$	0.295927	0.0194286
$233$	−2.19467	−0.143778	−0.0718888	−	0.997413i	$-0.522903\pi$
$233$	−2.19467	−0.143778	−0.0718888	+	0.997413i	$0.522903\pi$
$234$	−5.62398	−0.367651
$235$	0	0
$236$	0.950376	0.0618642
$237$	−6.21742	−0.403865
$238$	29.9653	1.94237
$239$	−18.8884	−1.22179	−0.610895	−	0.791712i	$-0.709190\pi$
$239$	−18.8884	−1.22179	−0.610895	+	0.791712i	$0.709190\pi$
$240$	0	0
$241$	4.25490	0.274082	0.137041	−	0.990565i	$-0.456241\pi$
$241$	4.25490	0.274082	0.137041	+	0.990565i	$0.456241\pi$
$242$	−12.7187	−0.817589
$243$	14.3889	0.923047
$244$	4.07110	0.260625
$245$	0	0
$246$	0.764006	0.0487113
$247$	8.09750	0.515231
$248$	−4.84408	−0.307599
$249$	9.18055	0.581794
$250$	0	0
$251$	14.9020	0.940605	0.470302	−	0.882505i	$-0.344145\pi$
$251$	14.9020	0.940605	0.470302	+	0.882505i	$0.344145\pi$
$252$	4.69199	0.295568
$253$	3.95943	0.248927
$254$	−1.10893	−0.0695805
$255$	0	0
$256$	−10.9939	−0.687122
$257$	19.4472	1.21308	0.606541	−	0.795052i	$-0.292557\pi$
$257$	19.4472	1.21308	0.606541	+	0.795052i	$0.292557\pi$
$258$	−0.800550	−0.0498401
$259$	6.47961	0.402624
$260$	0	0
$261$	0.249105	0.0154192
$262$	−6.99343	−0.432055
$263$	−6.24660	−0.385182	−0.192591	−	0.981279i	$-0.561689\pi$
$263$	−6.24660	−0.385182	−0.192591	+	0.981279i	$0.561689\pi$
$264$	−1.60716	−0.0989141
$265$	0	0
$266$	20.8256	1.27690
$267$	0.694387	0.0424958
$268$	−0.646551	−0.0394944
$269$	−11.3402	−0.691424	−0.345712	−	0.938341i	$-0.612363\pi$
$269$	−11.3402	−0.691424	−0.345712	+	0.938341i	$0.612363\pi$
$270$	0	0
$271$	−20.2696	−1.23129	−0.615645	−	0.788024i	$-0.711104\pi$
$271$	−20.2696	−1.23129	−0.615645	+	0.788024i	$0.711104\pi$
$272$	−18.2308	−1.10541
$273$	4.30461	0.260527
$274$	−25.4225	−1.53583
$275$	0	0
$276$	−1.56711	−0.0943289
$277$	14.8280	0.890930	0.445465	−	0.895299i	$-0.353038\pi$
$277$	14.8280	0.890930	0.445465	+	0.895299i	$0.353038\pi$
$278$	−9.75128	−0.584843
$279$	−4.07763	−0.244121
$280$	0	0
$281$	30.9067	1.84374	0.921869	−	0.387502i	$-0.126662\pi$
$281$	30.9067	1.84374	0.921869	+	0.387502i	$0.126662\pi$
$282$	−3.20896	−0.191091
$283$	16.4380	0.977138	0.488569	−	0.872525i	$-0.337519\pi$
$283$	16.4380	0.977138	0.488569	+	0.872525i	$0.337519\pi$
$284$	−7.79532	−0.462567
$285$	0	0
$286$	1.76059	0.104106
$287$	3.54899	0.209490
$288$	−6.96148	−0.410209
$289$	25.9964	1.52920
$290$	0	0
$291$	−9.42434	−0.552465
$292$	7.83733	0.458645
$293$	−11.5771	−0.676341	−0.338171	−	0.941085i	$-0.609808\pi$
$293$	−11.5771	−0.676341	−0.338171	+	0.941085i	$0.609808\pi$
$294$	5.46700	0.318842
$295$	0	0
$296$	−5.33134	−0.309878
$297$	−2.92866	−0.169938
$298$	8.85467	0.512937
$299$	8.72558	0.504613
$300$	0	0
$301$	−3.71874	−0.214345
$302$	4.36328	0.251079
$303$	9.02929	0.518719
$304$	−12.6702	−0.726687
$305$	0	0
$306$	−20.7541	−1.18643
$307$	−14.4820	−0.826530	−0.413265	−	0.910611i	$-0.635612\pi$
$307$	−14.4820	−0.826530	−0.413265	+	0.910611i	$0.635612\pi$
$308$	−1.46883	−0.0836944
$309$	−6.16355	−0.350632
$310$	0	0
$311$	3.46324	0.196383	0.0981913	−	0.995168i	$-0.468694\pi$
$311$	3.46324	0.196383	0.0981913	+	0.995168i	$0.468694\pi$
$312$	−3.54178	−0.200514
$313$	−20.3380	−1.14957	−0.574785	−	0.818304i	$-0.694914\pi$
$313$	−20.3380	−1.14957	−0.574785	+	0.818304i	$0.694914\pi$
$314$	−9.90936	−0.559217
$315$	0	0
$316$	4.67530	0.263006
$317$	−28.9658	−1.62688	−0.813440	−	0.581649i	$-0.802408\pi$
$317$	−28.9658	−1.62688	−0.813440	+	0.581649i	$0.802408\pi$
$318$	−8.25865	−0.463122
$319$	−0.0779824	−0.00436618
$320$	0	0
$321$	1.50357	0.0839208
$322$	22.4409	1.25058
$323$	29.8821	1.66268
$324$	−2.62600	−0.145889
$325$	0	0
$326$	23.0852	1.27857
$327$	7.83191	0.433105
$328$	−2.92006	−0.161233
$329$	−14.9064	−0.821815
$330$	0	0
$331$	−34.9294	−1.91989	−0.959946	−	0.280184i	$-0.909604\pi$
$331$	−34.9294	−1.91989	−0.959946	+	0.280184i	$0.909604\pi$
$332$	−6.90347	−0.378877
$333$	−4.48780	−0.245930
$334$	−19.7052	−1.07822
$335$	0	0
$336$	−6.73546	−0.367450
$337$	31.2069	1.69995	0.849973	−	0.526826i	$-0.176618\pi$
$337$	31.2069	1.69995	0.849973	+	0.526826i	$0.176618\pi$
$338$	−12.0955	−0.657906
$339$	−2.32758	−0.126417
$340$	0	0
$341$	1.27651	0.0691266
$342$	−14.4239	−0.779954
$343$	−0.635718	−0.0343255
$344$	3.05974	0.164970
$345$	0	0
$346$	1.61263	0.0866957
$347$	7.82706	0.420179	0.210089	−	0.977682i	$-0.432625\pi$
$347$	7.82706	0.420179	0.210089	+	0.977682i	$0.432625\pi$
$348$	0.0308648	0.00165453
$349$	18.4898	0.989734	0.494867	−	0.868969i	$-0.335217\pi$
$349$	18.4898	0.989734	0.494867	+	0.868969i	$0.335217\pi$
$350$	0	0
$351$	−6.45402	−0.344490
$352$	2.17930	0.116157
$353$	20.8637	1.11046	0.555230	−	0.831697i	$-0.312630\pi$
$353$	20.8637	1.11046	0.555230	+	0.831697i	$0.312630\pi$
$354$	−1.55311	−0.0825471
$355$	0	0
$356$	−0.522157	−0.0276742
$357$	15.8852	0.840735
$358$	−19.9928	−1.05665
$359$	−5.19769	−0.274324	−0.137162	−	0.990549i	$-0.543798\pi$
$359$	−5.19769	−0.274324	−0.137162	+	0.990549i	$0.543798\pi$
$360$	0	0
$361$	1.76773	0.0930383
$362$	−24.7755	−1.30217
$363$	−6.74244	−0.353886
$364$	−3.23693	−0.169661
$365$	0	0
$366$	−6.65304	−0.347760
$367$	−24.0847	−1.25721	−0.628604	−	0.777725i	$-0.716373\pi$
$367$	−24.0847	−1.25721	−0.628604	+	0.777725i	$0.716373\pi$
$368$	−13.6530	−0.711711
$369$	−2.45804	−0.127960
$370$	0	0
$371$	−38.3634	−1.99173
$372$	−0.505230	−0.0261950
$373$	12.3501	0.639464	0.319732	−	0.947508i	$-0.396407\pi$
$373$	12.3501	0.639464	0.319732	+	0.947508i	$0.396407\pi$
$374$	6.49708	0.335956
$375$	0	0
$376$	12.2648	0.632508
$377$	−0.171853	−0.00885089
$378$	−16.5988	−0.853751
$379$	28.5640	1.46723	0.733616	−	0.679564i	$-0.237831\pi$
$379$	28.5640	1.46723	0.733616	+	0.679564i	$0.237831\pi$
$380$	0	0
$381$	−0.587866	−0.0301173
$382$	11.2614	0.576184
$383$	7.29063	0.372534	0.186267	−	0.982499i	$-0.440361\pi$
$383$	7.29063	0.372534	0.186267	+	0.982499i	$0.440361\pi$
$384$	3.58897	0.183149
$385$	0	0
$386$	11.2343	0.571810
$387$	2.57561	0.130926
$388$	7.08680	0.359778
$389$	−10.1627	−0.515271	−0.257636	−	0.966242i	$-0.582943\pi$
$389$	−10.1627	−0.515271	−0.257636	+	0.966242i	$0.582943\pi$
$390$	0	0
$391$	32.1998	1.62842
$392$	−20.8951	−1.05536
$393$	−3.70735	−0.187011
$394$	−21.4539	−1.08083
$395$	0	0
$396$	1.01732	0.0511221
$397$	−17.3406	−0.870301	−0.435150	−	0.900358i	$-0.643305\pi$
$397$	−17.3406	−0.870301	−0.435150	+	0.900358i	$0.643305\pi$
$398$	−26.5899	−1.33283
$399$	11.0401	0.552695
$400$	0	0
$401$	17.3636	0.867096	0.433548	−	0.901130i	$-0.357261\pi$
$401$	17.3636	0.867096	0.433548	+	0.901130i	$0.357261\pi$
$402$	1.05660	0.0526985
$403$	2.81309	0.140130
$404$	−6.78973	−0.337802
$405$	0	0
$406$	−0.441982	−0.0219352
$407$	1.40491	0.0696387
$408$	−13.0702	−0.647070
$409$	28.3427	1.40146	0.700729	−	0.713428i	$-0.252858\pi$
$409$	28.3427	1.40146	0.700729	+	0.713428i	$0.252858\pi$
$410$	0	0
$411$	−13.4769	−0.664769
$412$	4.63479	0.228340
$413$	−7.21458	−0.355006
$414$	−15.5427	−0.763880
$415$	0	0
$416$	4.80261	0.235468
$417$	−5.16935	−0.253144
$418$	4.51541	0.220856
$419$	28.5947	1.39694	0.698472	−	0.715637i	$-0.253863\pi$
$419$	28.5947	1.39694	0.698472	+	0.715637i	$0.253863\pi$
$420$	0	0
$421$	−9.27620	−0.452094	−0.226047	−	0.974116i	$-0.572580\pi$
$421$	−9.27620	−0.452094	−0.226047	+	0.974116i	$0.572580\pi$
$422$	10.6827	0.520026
$423$	10.3242	0.501980
$424$	31.5649	1.53293
$425$	0	0
$426$	12.7392	0.617217
$427$	−30.9049	−1.49559
$428$	−1.13063	−0.0546512
$429$	0.933325	0.0450613
$430$	0	0
$431$	16.5064	0.795085	0.397542	−	0.917584i	$-0.369863\pi$
$431$	16.5064	0.795085	0.397542	+	0.917584i	$0.369863\pi$
$432$	10.0987	0.485872
$433$	−8.85795	−0.425686	−0.212843	−	0.977086i	$-0.568272\pi$
$433$	−8.85795	−0.425686	−0.212843	+	0.977086i	$0.568272\pi$
$434$	7.23487	0.347285
$435$	0	0
$436$	−5.88934	−0.282048
$437$	22.3786	1.07051
$438$	−12.8078	−0.611983
$439$	−27.7752	−1.32564	−0.662818	−	0.748780i	$-0.730640\pi$
$439$	−27.7752	−1.32564	−0.662818	+	0.748780i	$0.730640\pi$
$440$	0	0
$441$	−17.5890	−0.837571
$442$	14.3179	0.681033
$443$	−15.6972	−0.745797	−0.372898	−	0.927872i	$-0.621636\pi$
$443$	−15.6972	−0.745797	−0.372898	+	0.927872i	$0.621636\pi$
$444$	−0.556051	−0.0263890
$445$	0	0
$446$	23.0755	1.09266
$447$	4.69404	0.222020
$448$	33.0300	1.56052
$449$	−16.2408	−0.766452	−0.383226	−	0.923655i	$-0.625187\pi$
$449$	−16.2408	−0.766452	−0.383226	+	0.923655i	$0.625187\pi$
$450$	0	0
$451$	0.769491	0.0362339
$452$	1.75026	0.0823254
$453$	2.31306	0.108677
$454$	7.17569	0.336772
$455$	0	0
$456$	−9.08363	−0.425380
$457$	15.3474	0.717923	0.358962	−	0.933352i	$-0.383131\pi$
$457$	15.3474	0.717923	0.358962	+	0.933352i	$0.383131\pi$
$458$	14.0045	0.654387
$459$	−23.8172	−1.11169
$460$	0	0
$461$	35.3435	1.64611	0.823055	−	0.567961i	$-0.192268\pi$
$461$	35.3435	1.64611	0.823055	+	0.567961i	$0.192268\pi$
$462$	2.40038	0.111676
$463$	−36.4946	−1.69605	−0.848024	−	0.529957i	$-0.822208\pi$
$463$	−36.4946	−1.69605	−0.848024	+	0.529957i	$0.822208\pi$
$464$	0.268900	0.0124834
$465$	0	0
$466$	−2.69697	−0.124935
$467$	−14.7637	−0.683184	−0.341592	−	0.939848i	$-0.610966\pi$
$467$	−14.7637	−0.683184	−0.341592	+	0.939848i	$0.610966\pi$
$468$	2.24191	0.103632
$469$	4.90816	0.226638
$470$	0	0
$471$	−5.25315	−0.242052
$472$	5.93607	0.273230
$473$	−0.806297	−0.0370736
$474$	−7.64042	−0.350936
$475$	0	0
$476$	−11.9452	−0.547506
$477$	26.5706	1.21658
$478$	−23.2115	−1.06167
$479$	35.4722	1.62077	0.810384	−	0.585900i	$-0.199259\pi$
$479$	35.4722	1.62077	0.810384	+	0.585900i	$0.199259\pi$
$480$	0	0
$481$	3.09606	0.141168
$482$	5.22873	0.238162
$483$	11.8964	0.541305
$484$	5.07009	0.230459
$485$	0	0
$486$	17.6821	0.802077
$487$	−11.7276	−0.531430	−0.265715	−	0.964052i	$-0.585608\pi$
$487$	−11.7276	−0.531430	−0.265715	+	0.964052i	$0.585608\pi$
$488$	25.4282	1.15108
$489$	12.2379	0.553419
$490$	0	0
$491$	−11.5155	−0.519686	−0.259843	−	0.965651i	$-0.583671\pi$
$491$	−11.5155	−0.519686	−0.259843	+	0.965651i	$0.583671\pi$
$492$	−0.304558	−0.0137305
$493$	−0.634187	−0.0285623
$494$	9.95080	0.447708
$495$	0	0
$496$	−4.40167	−0.197641
$497$	59.1766	2.65443
$498$	11.2817	0.505547
$499$	−11.9126	−0.533279	−0.266640	−	0.963796i	$-0.585913\pi$
$499$	−11.9126	−0.533279	−0.266640	+	0.963796i	$0.585913\pi$
$500$	0	0
$501$	−10.4461	−0.466697
$502$	18.3127	0.817334
$503$	14.4442	0.644036	0.322018	−	0.946734i	$-0.395639\pi$
$503$	14.4442	0.644036	0.322018	+	0.946734i	$0.395639\pi$
$504$	29.3063	1.30540
$505$	0	0
$506$	4.86564	0.216304
$507$	−6.41205	−0.284769
$508$	0.442056	0.0196131
$509$	28.6387	1.26939	0.634695	−	0.772763i	$-0.281126\pi$
$509$	28.6387	1.26939	0.634695	+	0.772763i	$0.281126\pi$
$510$	0	0
$511$	−59.4955	−2.63192
$512$	−24.5286	−1.08402
$513$	−16.5527	−0.730819
$514$	23.8981	1.05410
$515$	0	0
$516$	0.319126	0.0140487
$517$	−3.23200	−0.142143
$518$	7.96263	0.349858
$519$	0.854889	0.0375255
$520$	0	0
$521$	−19.4521	−0.852212	−0.426106	−	0.904673i	$-0.640115\pi$
$521$	−19.4521	−0.852212	−0.426106	+	0.904673i	$0.640115\pi$
$522$	0.306118	0.0133984
$523$	−6.62136	−0.289532	−0.144766	−	0.989466i	$-0.546243\pi$
$523$	−6.62136	−0.289532	−0.144766	+	0.989466i	$0.546243\pi$
$524$	2.78781	0.121786
$525$	0	0
$526$	−7.67628	−0.334702
$527$	10.3811	0.452208
$528$	−1.46038	−0.0635550
$529$	1.11434	0.0484495
$530$	0	0
$531$	4.99684	0.216844
$532$	−8.30178	−0.359928
$533$	1.69576	0.0734516
$534$	0.853314	0.0369265
$535$	0	0
$536$	−4.03837	−0.174431
$537$	−10.5986	−0.457362
$538$	−13.9357	−0.600809
$539$	5.50624	0.237171
$540$	0	0
$541$	39.8975	1.71533	0.857664	−	0.514210i	$-0.171915\pi$
$541$	39.8975	1.71533	0.857664	+	0.514210i	$0.171915\pi$
$542$	−24.9088	−1.06992
$543$	−13.1340	−0.563634
$544$	17.7230	0.759867
$545$	0	0
$546$	5.28982	0.226384
$547$	−45.3641	−1.93963	−0.969814	−	0.243845i	$-0.921591\pi$
$547$	−45.3641	−1.93963	−0.969814	+	0.243845i	$0.921591\pi$
$548$	10.1342	0.432913
$549$	21.4048	0.913536
$550$	0	0
$551$	−0.440754	−0.0187767
$552$	−9.78820	−0.416613
$553$	−35.4915	−1.50925
$554$	18.2218	0.774170
$555$	0	0
$556$	3.88718	0.164853
$557$	−15.5718	−0.659797	−0.329899	−	0.944016i	$-0.607015\pi$
$557$	−15.5718	−0.659797	−0.329899	+	0.944016i	$0.607015\pi$
$558$	−5.01090	−0.212128
$559$	−1.77687	−0.0751537
$560$	0	0
$561$	3.44423	0.145416
$562$	37.9804	1.60211
$563$	22.2360	0.937135	0.468567	−	0.883428i	$-0.344770\pi$
$563$	22.2360	0.937135	0.468567	+	0.883428i	$0.344770\pi$
$564$	1.27920	0.0538639
$565$	0	0
$566$	20.2002	0.849079
$567$	19.9348	0.837181
$568$	−48.6898	−2.04298
$569$	22.9440	0.961864	0.480932	−	0.876758i	$-0.340298\pi$
$569$	22.9440	0.961864	0.480932	+	0.876758i	$0.340298\pi$
$570$	0	0
$571$	−13.3842	−0.560113	−0.280056	−	0.959984i	$-0.590353\pi$
$571$	−13.3842	−0.560113	−0.280056	+	0.959984i	$0.590353\pi$
$572$	−0.701830	−0.0293450
$573$	5.96990	0.249396
$574$	4.36126	0.182035
$575$	0	0
$576$	−22.8767	−0.953195
$577$	−18.0620	−0.751932	−0.375966	−	0.926633i	$-0.622689\pi$
$577$	−18.0620	−0.751932	−0.375966	+	0.926633i	$0.622689\pi$
$578$	31.9463	1.32879
$579$	5.95552	0.247503
$580$	0	0
$581$	52.4063	2.17418
$582$	−11.5813	−0.480061
$583$	−8.31794	−0.344494
$584$	48.9521	2.02565
$585$	0	0
$586$	−14.2268	−0.587703
$587$	−21.1662	−0.873621	−0.436810	−	0.899554i	$-0.643892\pi$
$587$	−21.1662	−0.873621	−0.436810	+	0.899554i	$0.643892\pi$
$588$	−2.17933	−0.0898738
$589$	7.21476	0.297279
$590$	0	0
$591$	−11.3731	−0.467828
$592$	−4.84443	−0.199105
$593$	−30.5340	−1.25388	−0.626941	−	0.779067i	$-0.715693\pi$
$593$	−30.5340	−1.25388	−0.626941	+	0.779067i	$0.715693\pi$
$594$	−3.59895	−0.147667
$595$	0	0
$596$	−3.52976	−0.144585
$597$	−14.0958	−0.576904
$598$	10.7226	0.438481
$599$	−0.469155	−0.0191692	−0.00958458	−	0.999954i	$-0.503051\pi$
$599$	−0.469155	−0.0191692	−0.00958458	+	0.999954i	$0.503051\pi$
$600$	0	0
$601$	−6.16313	−0.251399	−0.125700	−	0.992068i	$-0.540118\pi$
$601$	−6.16313	−0.251399	−0.125700	+	0.992068i	$0.540118\pi$
$602$	−4.56987	−0.186254
$603$	−3.39941	−0.138435
$604$	−1.73935	−0.0707730
$605$	0	0
$606$	11.0959	0.450738
$607$	1.75897	0.0713945	0.0356973	−	0.999363i	$-0.488635\pi$
$607$	1.75897	0.0713945	0.0356973	+	0.999363i	$0.488635\pi$
$608$	12.3173	0.499533
$609$	−0.234304	−0.00949446
$610$	0	0
$611$	−7.12250	−0.288145
$612$	8.27326	0.334427
$613$	15.1937	0.613669	0.306834	−	0.951763i	$-0.400730\pi$
$613$	15.1937	0.613669	0.306834	+	0.951763i	$0.400730\pi$
$614$	−17.7965	−0.718209
$615$	0	0
$616$	−9.17434	−0.369645
$617$	36.8100	1.48192	0.740958	−	0.671551i	$-0.234372\pi$
$617$	36.8100	1.48192	0.740958	+	0.671551i	$0.234372\pi$
$618$	−7.57422	−0.304680
$619$	43.4547	1.74659	0.873297	−	0.487188i	$-0.161977\pi$
$619$	43.4547	1.74659	0.873297	+	0.487188i	$0.161977\pi$
$620$	0	0
$621$	−17.8366	−0.715757
$622$	4.25589	0.170646
$623$	3.96385	0.158808
$624$	−3.21831	−0.128835
$625$	0	0
$626$	−24.9928	−0.998913
$627$	2.39371	0.0955954
$628$	3.95020	0.157630
$629$	11.4253	0.455558
$630$	0	0
$631$	30.8030	1.22625	0.613124	−	0.789987i	$-0.289913\pi$
$631$	30.8030	1.22625	0.613124	+	0.789987i	$0.289913\pi$
$632$	29.2020	1.16159
$633$	5.66311	0.225088
$634$	−35.5953	−1.41367
$635$	0	0
$636$	3.29217	0.130543
$637$	12.1344	0.480781
$638$	−0.0958305	−0.00379397
$639$	−40.9859	−1.62138
$640$	0	0
$641$	−30.0976	−1.18878	−0.594391	−	0.804176i	$-0.702607\pi$
$641$	−30.0976	−1.18878	−0.594391	+	0.804176i	$0.702607\pi$
$642$	1.84769	0.0729226
$643$	−46.5705	−1.83656	−0.918281	−	0.395929i	$-0.870423\pi$
$643$	−46.5705	−1.83656	−0.918281	+	0.395929i	$0.870423\pi$
$644$	−8.94570	−0.352510
$645$	0	0
$646$	36.7213	1.44478
$647$	−26.3051	−1.03416	−0.517081	−	0.855936i	$-0.672981\pi$
$647$	−26.3051	−1.03416	−0.517081	+	0.855936i	$0.672981\pi$
$648$	−16.4021	−0.644334
$649$	−1.56426	−0.0614027
$650$	0	0
$651$	3.83535	0.150319
$652$	−9.20253	−0.360399
$653$	−2.12418	−0.0831257	−0.0415628	−	0.999136i	$-0.513234\pi$
$653$	−2.12418	−0.0831257	−0.0415628	+	0.999136i	$0.513234\pi$
$654$	9.62442	0.376345
$655$	0	0
$656$	−2.65337	−0.103597
$657$	41.2067	1.60763
$658$	−18.3181	−0.714112
$659$	3.68332	0.143482	0.0717409	−	0.997423i	$-0.477145\pi$
$659$	3.68332	0.143482	0.0717409	+	0.997423i	$0.477145\pi$
$660$	0	0
$661$	−4.20554	−0.163577	−0.0817883	−	0.996650i	$-0.526063\pi$
$661$	−4.20554	−0.163577	−0.0817883	+	0.996650i	$0.526063\pi$
$662$	−42.9238	−1.66828
$663$	7.59021	0.294779
$664$	−43.1192	−1.67335
$665$	0	0
$666$	−5.51494	−0.213700
$667$	−0.474940	−0.0183898
$668$	7.85512	0.303924
$669$	12.2328	0.472947
$670$	0	0
$671$	−6.70080	−0.258681
$672$	6.54785	0.252589
$673$	15.1953	0.585734	0.292867	−	0.956153i	$-0.405391\pi$
$673$	15.1953	0.585734	0.292867	+	0.956153i	$0.405391\pi$
$674$	38.3493	1.47716
$675$	0	0
$676$	4.82165	0.185448
$677$	35.0004	1.34517	0.672587	−	0.740018i	$-0.265183\pi$
$677$	35.0004	1.34517	0.672587	+	0.740018i	$0.265183\pi$
$678$	−2.86030	−0.109849
$679$	−53.7980	−2.06458
$680$	0	0
$681$	3.80398	0.145769
$682$	1.56866	0.0600672
$683$	−38.7302	−1.48197	−0.740985	−	0.671521i	$-0.765641\pi$
$683$	−38.7302	−1.48197	−0.740985	+	0.671521i	$0.765641\pi$
$684$	5.74983	0.219850
$685$	0	0
$686$	−0.781217	−0.0298270
$687$	7.42406	0.283246
$688$	2.78029	0.105998
$689$	−18.3306	−0.698341
$690$	0	0
$691$	13.3997	0.509747	0.254874	−	0.966974i	$-0.417966\pi$
$691$	13.3997	0.509747	0.254874	+	0.966974i	$0.417966\pi$
$692$	−0.642849	−0.0244374
$693$	−7.72275	−0.293363
$694$	9.61847	0.365112
$695$	0	0
$696$	0.192782	0.00730739
$697$	6.25784	0.237032
$698$	22.7216	0.860024
$699$	−1.42972	−0.0540770
$700$	0	0
$701$	37.4227	1.41344	0.706718	−	0.707495i	$-0.250175\pi$
$701$	37.4227	1.41344	0.706718	+	0.707495i	$0.250175\pi$
$702$	−7.93118	−0.299343
$703$	7.94049	0.299481
$704$	7.16156	0.269911
$705$	0	0
$706$	25.6388	0.964929
$707$	51.5428	1.93847
$708$	0.619123	0.0232681
$709$	−48.6880	−1.82852	−0.914258	−	0.405131i	$-0.867226\pi$
$709$	−48.6880	−1.82852	−0.914258	+	0.405131i	$0.867226\pi$
$710$	0	0
$711$	24.5815	0.921880
$712$	−3.26140	−0.122226
$713$	7.77437	0.291152
$714$	19.5209	0.730553
$715$	0	0
$716$	7.96978	0.297845
$717$	−12.3049	−0.459534
$718$	−6.38731	−0.238372
$719$	17.8892	0.667155	0.333577	−	0.942723i	$-0.391744\pi$
$719$	17.8892	0.667155	0.333577	+	0.942723i	$0.391744\pi$
$720$	0	0
$721$	−35.1840	−1.31032
$722$	2.17231	0.0808451
$723$	2.77186	0.103086
$724$	9.87634	0.367051
$725$	0	0
$726$	−8.28560	−0.307508
$727$	1.64119	0.0608685	0.0304343	−	0.999537i	$-0.490311\pi$
$727$	1.64119	0.0608685	0.0304343	+	0.999537i	$0.490311\pi$
$728$	−20.2179	−0.749326
$729$	−6.70821	−0.248452
$730$	0	0
$731$	−6.55716	−0.242525
$732$	2.65212	0.0980251
$733$	17.8120	0.657903	0.328952	−	0.944347i	$-0.393305\pi$
$733$	17.8120	0.657903	0.328952	+	0.944347i	$0.393305\pi$
$734$	−29.5970	−1.09244
$735$	0	0
$736$	13.2727	0.489238
$737$	1.06419	0.0391998
$738$	−3.02062	−0.111191
$739$	−7.17554	−0.263956	−0.131978	−	0.991253i	$-0.542133\pi$
$739$	−7.17554	−0.263956	−0.131978	+	0.991253i	$0.542133\pi$
$740$	0	0
$741$	5.27512	0.193786
$742$	−47.1437	−1.73070
$743$	3.86346	0.141737	0.0708683	−	0.997486i	$-0.477423\pi$
$743$	3.86346	0.141737	0.0708683	+	0.997486i	$0.477423\pi$
$744$	−3.15568	−0.115693
$745$	0	0
$746$	15.1767	0.555659
$747$	−36.2968	−1.32803
$748$	−2.58995	−0.0946979
$749$	8.58296	0.313615
$750$	0	0
$751$	11.7242	0.427824	0.213912	−	0.976853i	$-0.431379\pi$
$751$	11.7242	0.427824	0.213912	+	0.976853i	$0.431379\pi$
$752$	11.1446	0.406403
$753$	9.70790	0.353776
$754$	−0.211186	−0.00769094
$755$	0	0
$756$	6.61684	0.240652
$757$	22.0492	0.801393	0.400696	−	0.916211i	$-0.368768\pi$
$757$	22.0492	0.801393	0.400696	+	0.916211i	$0.368768\pi$
$758$	35.1015	1.27494
$759$	2.57937	0.0936253
$760$	0	0
$761$	−28.0384	−1.01639	−0.508196	−	0.861241i	$-0.669688\pi$
$761$	−28.0384	−1.01639	−0.508196	+	0.861241i	$0.669688\pi$
$762$	−0.722414	−0.0261703
$763$	44.7077	1.61853
$764$	−4.48917	−0.162412
$765$	0	0
$766$	8.95926	0.323711
$767$	−3.44724	−0.124473
$768$	−7.16201	−0.258437
$769$	2.03767	0.0734802	0.0367401	−	0.999325i	$-0.488303\pi$
$769$	2.03767	0.0734802	0.0367401	+	0.999325i	$0.488303\pi$
$770$	0	0
$771$	12.6689	0.456258
$772$	−4.47836	−0.161180
$773$	−13.2762	−0.477511	−0.238755	−	0.971080i	$-0.576739\pi$
$773$	−13.2762	−0.477511	−0.238755	+	0.971080i	$0.576739\pi$
$774$	3.16510	0.113767
$775$	0	0
$776$	44.2643	1.58900
$777$	4.22115	0.151433
$778$	−12.4887	−0.447743
$779$	4.34913	0.155824
$780$	0	0
$781$	12.8307	0.459117
$782$	39.5695	1.41500
$783$	0.351298	0.0125544
$784$	−18.9867	−0.678098
$785$	0	0
$786$	−4.55587	−0.162503
$787$	49.3601	1.75950	0.879748	−	0.475440i	$-0.157711\pi$
$787$	49.3601	1.75950	0.879748	+	0.475440i	$0.157711\pi$
$788$	8.55222	0.304660
$789$	−4.06935	−0.144873
$790$	0	0
$791$	−13.2868	−0.472422
$792$	6.35418	0.225786
$793$	−14.7668	−0.524386
$794$	−21.3094	−0.756244
$795$	0	0
$796$	10.5996	0.375693
$797$	0.995941	0.0352780	0.0176390	−	0.999844i	$-0.494385\pi$
$797$	0.995941	0.0352780	0.0176390	+	0.999844i	$0.494385\pi$
$798$	13.5669	0.480262
$799$	−26.2840	−0.929862
$800$	0	0
$801$	−2.74537	−0.0970029
$802$	21.3377	0.753459
$803$	−12.8998	−0.455224
$804$	−0.421196	−0.0148544
$805$	0	0
$806$	3.45693	0.121765
$807$	−7.38757	−0.260055
$808$	−42.4088	−1.49194
$809$	21.6666	0.761759	0.380879	−	0.924625i	$-0.375621\pi$
$809$	21.6666	0.761759	0.380879	+	0.924625i	$0.375621\pi$
$810$	0	0
$811$	−32.7522	−1.15008	−0.575042	−	0.818124i	$-0.695014\pi$
$811$	−32.7522	−1.15008	−0.575042	+	0.818124i	$0.695014\pi$
$812$	0.176189	0.00618301
$813$	−13.2046	−0.463107
$814$	1.72645	0.0605122
$815$	0	0
$816$	−11.8765	−0.415759
$817$	−4.55716	−0.159435
$818$	34.8296	1.21779
$819$	−17.0190	−0.594691
$820$	0	0
$821$	20.6922	0.722162	0.361081	−	0.932534i	$-0.382408\pi$
$821$	20.6922	0.722162	0.361081	+	0.932534i	$0.382408\pi$
$822$	−16.5615	−0.577648
$823$	15.4198	0.537502	0.268751	−	0.963210i	$-0.413389\pi$
$823$	15.4198	0.537502	0.268751	+	0.963210i	$0.413389\pi$
$824$	28.9490	1.00849
$825$	0	0
$826$	−8.86581	−0.308481
$827$	17.9257	0.623336	0.311668	−	0.950191i	$-0.399112\pi$
$827$	17.9257	0.623336	0.311668	+	0.950191i	$0.399112\pi$
$828$	6.19582	0.215319
$829$	30.7806	1.06905	0.534527	−	0.845151i	$-0.320490\pi$
$829$	30.7806	1.06905	0.534527	+	0.845151i	$0.320490\pi$
$830$	0	0
$831$	9.65973	0.335092
$832$	15.7822	0.547151
$833$	44.7792	1.55151
$834$	−6.35248	−0.219968
$835$	0	0
$836$	−1.79999	−0.0622539
$837$	−5.75045	−0.198764
$838$	35.1393	1.21387
$839$	−40.9399	−1.41340	−0.706702	−	0.707512i	$-0.749818\pi$
$839$	−40.9399	−1.41340	−0.706702	+	0.707512i	$0.749818\pi$
$840$	0	0
$841$	−28.9906	−0.999677
$842$	−11.3993	−0.392845
$843$	20.1342	0.693458
$844$	−4.25847	−0.146583
$845$	0	0
$846$	12.6871	0.436193
$847$	−38.4886	−1.32248
$848$	28.6821	0.984947
$849$	10.7085	0.367516
$850$	0	0
$851$	8.55639	0.293309
$852$	−5.07827	−0.173979
$853$	10.8343	0.370960	0.185480	−	0.982648i	$-0.440616\pi$
$853$	10.8343	0.370960	0.185480	+	0.982648i	$0.440616\pi$
$854$	−37.9782	−1.29959
$855$	0	0
$856$	−7.06195	−0.241373
$857$	11.1418	0.380596	0.190298	−	0.981726i	$-0.439055\pi$
$857$	11.1418	0.380596	0.190298	+	0.981726i	$0.439055\pi$
$858$	1.14694	0.0391558
$859$	−54.7020	−1.86641	−0.933204	−	0.359347i	$-0.883000\pi$
$859$	−54.7020	−1.86641	−0.933204	+	0.359347i	$0.883000\pi$
$860$	0	0
$861$	2.31199	0.0787924
$862$	20.2843	0.690885
$863$	−4.57480	−0.155728	−0.0778639	−	0.996964i	$-0.524810\pi$
$863$	−4.57480	−0.155728	−0.0778639	+	0.996964i	$0.524810\pi$
$864$	−9.81737	−0.333994
$865$	0	0
$866$	−10.8853	−0.369898
$867$	16.9353	0.575155
$868$	−2.88406	−0.0978913
$869$	−7.69527	−0.261044
$870$	0	0
$871$	2.34519	0.0794639
$872$	−36.7849	−1.24570
$873$	37.2606	1.26108
$874$	27.5004	0.930216
$875$	0	0
$876$	5.10563	0.172503
$877$	31.9166	1.07775	0.538873	−	0.842387i	$-0.318850\pi$
$877$	31.9166	1.07775	0.538873	+	0.842387i	$0.318850\pi$
$878$	−34.1322	−1.15191
$879$	−7.54190	−0.254382
$880$	0	0
$881$	11.5663	0.389679	0.194839	−	0.980835i	$-0.437581\pi$
$881$	11.5663	0.389679	0.194839	+	0.980835i	$0.437581\pi$
$882$	−21.6146	−0.727803
$883$	−54.5713	−1.83647	−0.918236	−	0.396035i	$-0.870386\pi$
$883$	−54.5713	−1.83647	−0.918236	+	0.396035i	$0.870386\pi$
$884$	−5.70759	−0.191967
$885$	0	0
$886$	−19.2899	−0.648056
$887$	25.3921	0.852583	0.426291	−	0.904586i	$-0.359820\pi$
$887$	25.3921	0.852583	0.426291	+	0.904586i	$0.359820\pi$
$888$	−3.47311	−0.116550
$889$	−3.35578	−0.112549
$890$	0	0
$891$	4.32225	0.144801
$892$	−9.19865	−0.307994
$893$	−18.2671	−0.611286
$894$	5.76838	0.192923
$895$	0	0
$896$	20.4873	0.684433
$897$	5.68428	0.189793
$898$	−19.9579	−0.666005
$899$	−0.153119	−0.00510680
$900$	0	0
$901$	−67.6451	−2.25359
$902$	0.945607	0.0314853
$903$	−2.42258	−0.0806183
$904$	10.9322	0.363599
$905$	0	0
$906$	2.84246	0.0944344
$907$	−7.18299	−0.238507	−0.119254	−	0.992864i	$-0.538050\pi$
$907$	−7.18299	−0.238507	−0.119254	+	0.992864i	$0.538050\pi$
$908$	−2.86047	−0.0949279
$909$	−35.6987	−1.18405
$910$	0	0
$911$	−44.9483	−1.48920	−0.744602	−	0.667509i	$-0.767361\pi$
$911$	−44.9483	−1.48920	−0.744602	+	0.667509i	$0.767361\pi$
$912$	−8.25403	−0.273318
$913$	11.3627	0.376051
$914$	18.8601	0.623836
$915$	0	0
$916$	−5.58265	−0.184456
$917$	−21.1631	−0.698867
$918$	−29.2683	−0.965997
$919$	7.18922	0.237150	0.118575	−	0.992945i	$-0.462167\pi$
$919$	7.18922	0.237150	0.118575	+	0.992945i	$0.462167\pi$
$920$	0	0
$921$	−9.43429	−0.310871
$922$	43.4327	1.43038
$923$	28.2755	0.930699
$924$	−0.956870	−0.0314787
$925$	0	0
$926$	−44.8473	−1.47377
$927$	24.3686	0.800369
$928$	−0.261410	−0.00858121
$929$	20.6974	0.679060	0.339530	−	0.940595i	$-0.389732\pi$
$929$	20.6974	0.679060	0.339530	+	0.940595i	$0.389732\pi$
$930$	0	0
$931$	31.1211	1.01995
$932$	1.07510	0.0352161
$933$	2.25613	0.0738624
$934$	−18.1428	−0.593650
$935$	0	0
$936$	14.0030	0.457702
$937$	−47.6988	−1.55825	−0.779127	−	0.626867i	$-0.784337\pi$
$937$	−47.6988	−1.55825	−0.779127	+	0.626867i	$0.784337\pi$
$938$	6.03151	0.196936
$939$	−13.2492	−0.432371
$940$	0	0
$941$	−18.2628	−0.595349	−0.297675	−	0.954667i	$-0.596211\pi$
$941$	−18.2628	−0.595349	−0.297675	+	0.954667i	$0.596211\pi$
$942$	−6.45545	−0.210330
$943$	4.68647	0.152612
$944$	5.39393	0.175557
$945$	0	0
$946$	−0.990837	−0.0322149
$947$	30.9602	1.00607	0.503035	−	0.864266i	$-0.332217\pi$
$947$	30.9602	1.00607	0.503035	+	0.864266i	$0.332217\pi$
$948$	3.04572	0.0989205
$949$	−28.4278	−0.922807
$950$	0	0
$951$	−18.8698	−0.611894
$952$	−74.6098	−2.41812
$953$	−60.8519	−1.97119	−0.985594	−	0.169131i	$-0.945904\pi$
$953$	−60.8519	−1.97119	−0.985594	+	0.169131i	$0.945904\pi$
$954$	32.6519	1.05714
$955$	0	0
$956$	9.25286	0.299259
$957$	−0.0508017	−0.00164218
$958$	43.5909	1.40836
$959$	−76.9319	−2.48426
$960$	0	0
$961$	−28.4936	−0.919148
$962$	3.80467	0.122667
$963$	−5.94458	−0.191562
$964$	−2.08434	−0.0671322
$965$	0	0
$966$	14.6192	0.470364
$967$	−13.9090	−0.447284	−0.223642	−	0.974671i	$-0.571795\pi$
$967$	−13.9090	−0.447284	−0.223642	+	0.974671i	$0.571795\pi$
$968$	31.6679	1.01785
$969$	19.4667	0.625360
$970$	0	0
$971$	−52.0154	−1.66925	−0.834626	−	0.550817i	$-0.814316\pi$
$971$	−52.0154	−1.66925	−0.834626	+	0.550817i	$0.814316\pi$
$972$	−7.04867	−0.226086
$973$	−29.5087	−0.946006
$974$	−14.4118	−0.461783
$975$	0	0
$976$	23.1058	0.739599
$977$	−43.2564	−1.38390	−0.691948	−	0.721947i	$-0.743247\pi$
$977$	−43.2564	−1.38390	−0.691948	+	0.721947i	$0.743247\pi$
$978$	15.0389	0.480891
$979$	0.859440	0.0274678
$980$	0	0
$981$	−30.9647	−0.988626
$982$	−14.1511	−0.451579
$983$	35.4973	1.13219	0.566094	−	0.824341i	$-0.308454\pi$
$983$	35.4973	1.13219	0.566094	+	0.824341i	$0.308454\pi$
$984$	−1.90228	−0.0606423
$985$	0	0
$986$	−0.779336	−0.0248191
$987$	−9.71076	−0.309097
$988$	−3.96672	−0.126198
$989$	−4.91064	−0.156149
$990$	0	0
$991$	58.1709	1.84786	0.923930	−	0.382561i	$-0.124958\pi$
$991$	58.1709	1.84786	0.923930	+	0.382561i	$0.124958\pi$
$992$	4.27906	0.135860
$993$	−22.7548	−0.722100
$994$	72.7206	2.30656
$995$	0	0
$996$	−4.49727	−0.142501
$997$	16.0644	0.508765	0.254382	−	0.967104i	$-0.418128\pi$
$997$	16.0644	0.508765	0.254382	+	0.967104i	$0.418128\pi$
$998$	−14.6390	−0.463390
$999$	−6.32888	−0.200237

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.2.a.r.1.4	yes	6
3.2	odd	2		9675.2.a.cj.1.3		6
5.2	odd	4		1075.2.b.j.474.8		12
5.3	odd	4		1075.2.b.j.474.5		12
5.4	even	2		1075.2.a.q.1.3	✓	6
15.14	odd	2		9675.2.a.ck.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1075.2.a.q.1.3	✓	6	5.4	even	2
1075.2.a.r.1.4	yes	6	1.1	even	1	trivial
1075.2.b.j.474.5		12	5.3	odd	4
1075.2.b.j.474.8		12	5.2	odd	4
9675.2.a.cj.1.3		6	3.2	odd	2
9675.2.a.ck.1.4		6	15.14	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:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q+1.22887 q^{2} +0.651450 q^{3} -0.489869 q^{4} +0.800550 q^{6} +3.71874 q^{7} -3.05974 q^{8} -2.57561 q^{9} +O(q^{10})\)	\(q+1.22887 q^{2} +0.651450 q^{3} -0.489869 q^{4} +0.800550 q^{6} +3.71874 q^{7} -3.05974 q^{8} -2.57561 q^{9} +0.806297 q^{11} -0.319126 q^{12} +1.77687 q^{13} +4.56987 q^{14} -2.78029 q^{16} +6.55716 q^{17} -3.16510 q^{18} +4.55716 q^{19} +2.42258 q^{21} +0.990837 q^{22} +4.91064 q^{23} -1.99327 q^{24} +2.18355 q^{26} -3.63223 q^{27} -1.82170 q^{28} -0.0967167 q^{29} +1.58317 q^{31} +2.70285 q^{32} +0.525263 q^{33} +8.05792 q^{34} +1.26171 q^{36} +1.74242 q^{37} +5.60018 q^{38} +1.15754 q^{39} +0.954351 q^{41} +2.97704 q^{42} -1.00000 q^{43} -0.394980 q^{44} +6.03455 q^{46} -4.00844 q^{47} -1.81122 q^{48} +6.82905 q^{49} +4.27167 q^{51} -0.870436 q^{52} -10.3162 q^{53} -4.46356 q^{54} -11.3784 q^{56} +2.96877 q^{57} -0.118853 q^{58} -1.94006 q^{59} -8.31058 q^{61} +1.94552 q^{62} -9.57804 q^{63} +8.88203 q^{64} +0.645481 q^{66} +1.31984 q^{67} -3.21215 q^{68} +3.19904 q^{69} +15.9131 q^{71} +7.88069 q^{72} -15.9988 q^{73} +2.14121 q^{74} -2.23241 q^{76} +2.99841 q^{77} +1.42248 q^{78} -9.54396 q^{79} +5.36062 q^{81} +1.17278 q^{82} +14.0925 q^{83} -1.18675 q^{84} -1.22887 q^{86} -0.0630061 q^{87} -2.46706 q^{88} +1.06591 q^{89} +6.60773 q^{91} -2.40557 q^{92} +1.03136 q^{93} -4.92587 q^{94} +1.76077 q^{96} -14.4667 q^{97} +8.39204 q^{98} -2.07671 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} + 2 q^{3} + 11 q^{4} + 11 q^{6} + 2 q^{7} + 6 q^{8} + 12 q^{9}+O(q^{10}) \) 6 * q + q^2 + 2 * q^3 + 11 * q^4 + 11 * q^6 + 2 * q^7 + 6 * q^8 + 12 * q^9	\( 6 q + q^{2} + 2 q^{3} + 11 q^{4} + 11 q^{6} + 2 q^{7} + 6 q^{8} + 12 q^{9} - 6 q^{11} - 4 q^{12} + 17 q^{14} + 5 q^{16} + 7 q^{17} - 15 q^{18} - 5 q^{19} + 19 q^{21} + 34 q^{22} - 3 q^{23} + 9 q^{24} + 14 q^{26} + 5 q^{27} - 21 q^{28} + 18 q^{29} - 12 q^{31} + 3 q^{32} - 10 q^{33} + q^{34} - 10 q^{36} + 7 q^{37} - q^{38} - 3 q^{39} - 9 q^{42} - 6 q^{43} + 9 q^{44} - 14 q^{46} - 6 q^{47} + 2 q^{48} - q^{51} + 3 q^{52} - 8 q^{53} + 12 q^{54} + 20 q^{56} - 5 q^{57} - 24 q^{58} + 21 q^{59} - 8 q^{61} + 47 q^{62} + 19 q^{63} + 6 q^{64} + q^{66} - 35 q^{68} + 37 q^{69} + 14 q^{71} + 44 q^{72} - q^{73} + 2 q^{74} - 57 q^{76} + 13 q^{77} - 49 q^{78} - 31 q^{79} + 62 q^{81} + 32 q^{82} - 13 q^{83} + 21 q^{84} - q^{86} + 22 q^{87} + 39 q^{88} + 40 q^{89} + 11 q^{91} - 32 q^{92} - 15 q^{93} + 35 q^{94} - 50 q^{96} + 11 q^{97} - 44 q^{98} - 53 q^{99}+O(q^{100}) \) 6 * q + q^2 + 2 * q^3 + 11 * q^4 + 11 * q^6 + 2 * q^7 + 6 * q^8 + 12 * q^9 - 6 * q^11 - 4 * q^12 + 17 * q^14 + 5 * q^16 + 7 * q^17 - 15 * q^18 - 5 * q^19 + 19 * q^21 + 34 * q^22 - 3 * q^23 + 9 * q^24 + 14 * q^26 + 5 * q^27 - 21 * q^28 + 18 * q^29 - 12 * q^31 + 3 * q^32 - 10 * q^33 + q^34 - 10 * q^36 + 7 * q^37 - q^38 - 3 * q^39 - 9 * q^42 - 6 * q^43 + 9 * q^44 - 14 * q^46 - 6 * q^47 + 2 * q^48 - q^51 + 3 * q^52 - 8 * q^53 + 12 * q^54 + 20 * q^56 - 5 * q^57 - 24 * q^58 + 21 * q^59 - 8 * q^61 + 47 * q^62 + 19 * q^63 + 6 * q^64 + q^66 - 35 * q^68 + 37 * q^69 + 14 * q^71 + 44 * q^72 - q^73 + 2 * q^74 - 57 * q^76 + 13 * q^77 - 49 * q^78 - 31 * q^79 + 62 * q^81 + 32 * q^82 - 13 * q^83 + 21 * q^84 - q^86 + 22 * q^87 + 39 * q^88 + 40 * q^89 + 11 * q^91 - 32 * q^92 - 15 * q^93 + 35 * q^94 - 50 * q^96 + 11 * q^97 - 44 * q^98 - 53 * q^99

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