LMFDB - Embedded newform 775.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(1,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, 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("775.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.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:	$6.18840615665$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.8468.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 5x^{2} + 3x + 4 $ x^4 - x^3 - 5x^2 + 3x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 155)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.704624$ of defining polynomial
Character	$\chi$	$=$	775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.50350 q^{2} +0.704624 q^{3} +4.26753 q^{4} -1.76403 q^{6} +4.77104 q^{7} -5.67678 q^{8} -2.50350 q^{9} +O(q^{10})$	\(q-2.50350 q^{2} +0.704624 q^{3} +4.26753 q^{4} -1.76403 q^{6} +4.77104 q^{7} -5.67678 q^{8} -2.50350 q^{9} -1.76403 q^{11} +3.00701 q^{12} -5.17328 q^{13} -11.9443 q^{14} +5.67678 q^{16} -4.46865 q^{17} +6.26753 q^{18} -4.91275 q^{19} +3.36179 q^{21} +4.41626 q^{22} -4.77104 q^{23} -4.00000 q^{24} +12.9513 q^{26} -3.87790 q^{27} +20.3606 q^{28} -5.36179 q^{29} -1.00000 q^{31} -2.85829 q^{32} -1.24298 q^{33} +11.1873 q^{34} -10.6838 q^{36} +7.00372 q^{37} +12.2991 q^{38} -3.64522 q^{39} +1.33723 q^{41} -8.41626 q^{42} -7.87790 q^{43} -7.52806 q^{44} +11.9443 q^{46} -4.60477 q^{47} +4.00000 q^{48} +15.7628 q^{49} -3.14872 q^{51} -22.0771 q^{52} +1.52312 q^{53} +9.70835 q^{54} -27.0842 q^{56} -3.46165 q^{57} +13.4233 q^{58} +7.61409 q^{59} +7.40925 q^{61} +2.50350 q^{62} -11.9443 q^{63} -4.19784 q^{64} +3.11180 q^{66} +5.29209 q^{67} -19.0701 q^{68} -3.36179 q^{69} -7.50350 q^{71} +14.2119 q^{72} -0.358066 q^{73} -17.5339 q^{74} -20.9653 q^{76} -8.41626 q^{77} +9.12582 q^{78} -4.39402 q^{79} +4.77805 q^{81} -3.34777 q^{82} +4.39895 q^{83} +14.3466 q^{84} +19.7224 q^{86} -3.77805 q^{87} +10.0140 q^{88} -16.7851 q^{89} -24.6819 q^{91} -20.3606 q^{92} -0.704624 q^{93} +11.5281 q^{94} -2.01402 q^{96} -0.541639 q^{97} -39.4623 q^{98} +4.41626 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - q^{3} + 5 q^{4} - 4 q^{6} - 2 q^{7} - 3 q^{8} - q^{9}+O(q^{10}) $ 4 * q - q^2 - q^3 + 5 * q^4 - 4 * q^6 - 2 * q^7 - 3 * q^8 - q^9	$ 4 q - q^{2} - q^{3} + 5 q^{4} - 4 q^{6} - 2 q^{7} - 3 q^{8} - q^{9} - 4 q^{11} - 6 q^{12} - 10 q^{13} - 16 q^{14} + 3 q^{16} - 11 q^{17} + 13 q^{18} - 3 q^{19} - 8 q^{22} + 2 q^{23} - 16 q^{24} + 2 q^{26} - q^{27} + 24 q^{28} - 8 q^{29} - 4 q^{31} - 7 q^{32} + 10 q^{33} - 2 q^{34} - 5 q^{36} - 3 q^{37} + 22 q^{38} - 10 q^{39} - 11 q^{41} - 8 q^{42} - 17 q^{43} - 24 q^{44} + 16 q^{46} + 10 q^{47} + 16 q^{48} + 16 q^{49} + q^{51} - 22 q^{52} - 13 q^{53} + 4 q^{54} - 24 q^{56} - 25 q^{57} + 10 q^{58} - 3 q^{59} + 22 q^{61} + q^{62} - 16 q^{63} - 9 q^{64} + 32 q^{66} + 12 q^{67} - 28 q^{68} - 21 q^{71} + 13 q^{72} - 19 q^{73} - 2 q^{74} + 2 q^{76} - 8 q^{77} + 20 q^{78} - 2 q^{79} - 20 q^{81} - 36 q^{82} + 15 q^{83} + 36 q^{84} + 8 q^{86} + 24 q^{87} + 4 q^{88} - 10 q^{89} - 4 q^{91} - 24 q^{92} + q^{93} + 40 q^{94} + 28 q^{96} - 4 q^{97} - 37 q^{98} - 8 q^{99}+O(q^{100}) $ 4 * q - q^2 - q^3 + 5 * q^4 - 4 * q^6 - 2 * q^7 - 3 * q^8 - q^9 - 4 * q^11 - 6 * q^12 - 10 * q^13 - 16 * q^14 + 3 * q^16 - 11 * q^17 + 13 * q^18 - 3 * q^19 - 8 * q^22 + 2 * q^23 - 16 * q^24 + 2 * q^26 - q^27 + 24 * q^28 - 8 * q^29 - 4 * q^31 - 7 * q^32 + 10 * q^33 - 2 * q^34 - 5 * q^36 - 3 * q^37 + 22 * q^38 - 10 * q^39 - 11 * q^41 - 8 * q^42 - 17 * q^43 - 24 * q^44 + 16 * q^46 + 10 * q^47 + 16 * q^48 + 16 * q^49 + q^51 - 22 * q^52 - 13 * q^53 + 4 * q^54 - 24 * q^56 - 25 * q^57 + 10 * q^58 - 3 * q^59 + 22 * q^61 + q^62 - 16 * q^63 - 9 * q^64 + 32 * q^66 + 12 * q^67 - 28 * q^68 - 21 * q^71 + 13 * q^72 - 19 * q^73 - 2 * q^74 + 2 * q^76 - 8 * q^77 + 20 * q^78 - 2 * q^79 - 20 * q^81 - 36 * q^82 + 15 * q^83 + 36 * q^84 + 8 * q^86 + 24 * q^87 + 4 * q^88 - 10 * q^89 - 4 * q^91 - 24 * q^92 + q^93 + 40 * q^94 + 28 * q^96 - 4 * q^97 - 37 * q^98 - 8 * 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 $

$2$	−2.50350	−1.77025	−0.885123	−	0.465358i	$-0.845926\pi$
$2$	−2.50350	−1.77025	−0.885123	+	0.465358i	$0.845926\pi$
$3$	0.704624	0.406815	0.203408	−	0.979094i	$-0.434798\pi$
$3$	0.704624	0.406815	0.203408	+	0.979094i	$0.434798\pi$
$4$	4.26753	2.13377
$5$	0	0
$5$	0	0
$6$	−1.76403	−0.720162
$7$	4.77104	1.80328	0.901642	−	0.432484i	$-0.142363\pi$
$7$	4.77104	1.80328	0.901642	+	0.432484i	$0.142363\pi$
$8$	−5.67678	−2.00705
$9$	−2.50350	−0.834501
$10$	0	0
$11$	−1.76403	−0.531875	−0.265938	−	0.963990i	$-0.585682\pi$
$11$	−1.76403	−0.531875	−0.265938	+	0.963990i	$0.585682\pi$
$12$	3.00701	0.868049
$13$	−5.17328	−1.43481	−0.717405	−	0.696657i	$-0.754670\pi$
$13$	−5.17328	−1.43481	−0.717405	+	0.696657i	$0.754670\pi$
$14$	−11.9443	−3.19225
$15$	0	0
$16$	5.67678	1.41920
$17$	−4.46865	−1.08381	−0.541904	−	0.840440i	$-0.682296\pi$
$17$	−4.46865	−1.08381	−0.541904	+	0.840440i	$0.682296\pi$
$18$	6.26753	1.47727
$19$	−4.91275	−1.12706	−0.563531	−	0.826095i	$-0.690558\pi$
$19$	−4.91275	−1.12706	−0.563531	+	0.826095i	$0.690558\pi$
$20$	0	0
$21$	3.36179	0.733603
$22$	4.41626	0.941549
$23$	−4.77104	−0.994830	−0.497415	−	0.867513i	$-0.665717\pi$
$23$	−4.77104	−0.994830	−0.497415	+	0.867513i	$0.665717\pi$
$24$	−4.00000	−0.816497
$25$	0	0
$26$	12.9513	2.53996
$27$	−3.87790	−0.746303
$28$	20.3606	3.84779
$29$	−5.36179	−0.995660	−0.497830	−	0.867275i	$-0.665870\pi$
$29$	−5.36179	−0.995660	−0.497830	+	0.867275i	$0.665870\pi$
$30$	0	0
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−2.85829	−0.505278
$33$	−1.24298	−0.216375
$34$	11.1873	1.91861
$35$	0	0
$36$	−10.6838	−1.78063
$37$	7.00372	1.15141	0.575703	−	0.817659i	$-0.304729\pi$
$37$	7.00372	1.15141	0.575703	+	0.817659i	$0.304729\pi$
$38$	12.2991	1.99518
$39$	−3.64522	−0.583702
$40$	0	0
$41$	1.33723	0.208841	0.104420	−	0.994533i	$-0.466701\pi$
$41$	1.33723	0.208841	0.104420	+	0.994533i	$0.466701\pi$
$42$	−8.41626	−1.29866
$43$	−7.87790	−1.20137	−0.600685	−	0.799486i	$-0.705105\pi$
$43$	−7.87790	−1.20137	−0.600685	+	0.799486i	$0.705105\pi$
$44$	−7.52806	−1.13490
$45$	0	0
$46$	11.9443	1.76109
$47$	−4.60477	−0.671675	−0.335837	−	0.941920i	$-0.609019\pi$
$47$	−4.60477	−0.671675	−0.335837	+	0.941920i	$0.609019\pi$
$48$	4.00000	0.577350
$49$	15.7628	2.25183
$50$	0	0
$51$	−3.14872	−0.440909
$52$	−22.0771	−3.06155
$53$	1.52312	0.209217	0.104608	−	0.994513i	$-0.466641\pi$
$53$	1.52312	0.209217	0.104608	+	0.994513i	$0.466641\pi$
$54$	9.70835	1.32114
$55$	0	0
$56$	−27.0842	−3.61927
$57$	−3.46165	−0.458506
$58$	13.4233	1.76256
$59$	7.61409	0.991270	0.495635	−	0.868531i	$-0.334935\pi$
$59$	7.61409	0.991270	0.495635	+	0.868531i	$0.334935\pi$
$60$	0	0
$61$	7.40925	0.948657	0.474329	−	0.880348i	$-0.342691\pi$
$61$	7.40925	0.948657	0.474329	+	0.880348i	$0.342691\pi$
$62$	2.50350	0.317945
$63$	−11.9443	−1.50484
$64$	−4.19784	−0.524729
$65$	0	0
$66$	3.11180	0.383036
$67$	5.29209	0.646532	0.323266	−	0.946308i	$-0.395219\pi$
$67$	5.29209	0.646532	0.323266	+	0.946308i	$0.395219\pi$
$68$	−19.0701	−2.31259
$69$	−3.36179	−0.404712
$70$	0	0
$71$	−7.50350	−0.890502	−0.445251	−	0.895406i	$-0.646886\pi$
$71$	−7.50350	−0.890502	−0.445251	+	0.895406i	$0.646886\pi$
$72$	14.2119	1.67488
$73$	−0.358066	−0.0419085	−0.0209542	−	0.999780i	$-0.506670\pi$
$73$	−0.358066	−0.0419085	−0.0209542	+	0.999780i	$0.506670\pi$
$74$	−17.5339	−2.03827
$75$	0	0
$76$	−20.9653	−2.40489
$77$	−8.41626	−0.959122
$78$	9.12582	1.03330
$79$	−4.39402	−0.494365	−0.247183	−	0.968969i	$-0.579505\pi$
$79$	−4.39402	−0.494365	−0.247183	+	0.968969i	$0.579505\pi$
$80$	0	0
$81$	4.77805	0.530894
$82$	−3.34777	−0.369700
$83$	4.39895	0.482848	0.241424	−	0.970420i	$-0.422386\pi$
$83$	4.39895	0.482848	0.241424	+	0.970420i	$0.422386\pi$
$84$	14.3466	1.56534
$85$	0	0
$86$	19.7224	2.12672
$87$	−3.77805	−0.405049
$88$	10.0140	1.06750
$89$	−16.7851	−1.77921	−0.889606	−	0.456728i	$-0.849021\pi$
$89$	−16.7851	−1.77921	−0.889606	+	0.456728i	$0.849021\pi$
$90$	0	0
$91$	−24.6819	−2.58737
$92$	−20.3606	−2.12274
$93$	−0.704624	−0.0730661
$94$	11.5281	1.18903
$95$	0	0
$96$	−2.01402	−0.205555
$97$	−0.541639	−0.0549951	−0.0274976	−	0.999622i	$-0.508754\pi$
$97$	−0.541639	−0.0549951	−0.0274976	+	0.999622i	$0.508754\pi$
$98$	−39.4623	−3.98629
$99$	4.41626	0.443851
$100$	0	0
$101$	1.36411	0.135734	0.0678668	−	0.997694i	$-0.478381\pi$
$101$	1.36411	0.135734	0.0678668	+	0.997694i	$0.478381\pi$
$102$	7.88284	0.780518
$103$	−11.9443	−1.17691	−0.588454	−	0.808530i	$-0.700263\pi$
$103$	−11.9443	−1.17691	−0.588454	+	0.808530i	$0.700263\pi$
$104$	29.3676	2.87973
$105$	0	0
$106$	−3.81314	−0.370365
$107$	6.35313	0.614180	0.307090	−	0.951680i	$-0.400645\pi$
$107$	6.35313	0.614180	0.307090	+	0.951680i	$0.400645\pi$
$108$	−16.5491	−1.59244
$109$	3.76172	0.360307	0.180154	−	0.983639i	$-0.442341\pi$
$109$	3.76172	0.360307	0.180154	+	0.983639i	$0.442341\pi$
$110$	0	0
$111$	4.93499	0.468409
$112$	27.0842	2.55921
$113$	10.9039	1.02575	0.512875	−	0.858463i	$-0.328580\pi$
$113$	10.9039	1.02575	0.512875	+	0.858463i	$0.328580\pi$
$114$	8.66625	0.811668
$115$	0	0
$116$	−22.8816	−2.12451
$117$	12.9513	1.19735
$118$	−19.0619	−1.75479
$119$	−21.3201	−1.95441
$120$	0	0
$121$	−7.88820	−0.717109
$122$	−18.5491	−1.67936
$123$	0.942248	0.0849596
$124$	−4.26753	−0.383236
$125$	0	0
$126$	29.9027	2.66394
$127$	−12.2434	−1.08643	−0.543214	−	0.839594i	$-0.682793\pi$
$127$	−12.2434	−1.08643	−0.543214	+	0.839594i	$0.682793\pi$
$128$	16.2259	1.43418
$129$	−5.55096	−0.488735
$130$	0	0
$131$	1.85006	0.161641	0.0808204	−	0.996729i	$-0.474246\pi$
$131$	1.85006	0.161641	0.0808204	+	0.996729i	$0.474246\pi$
$132$	−5.30445	−0.461694
$133$	−23.4389	−2.03241
$134$	−13.2488	−1.14452
$135$	0	0
$136$	25.3676	2.17525
$137$	2.65551	0.226876	0.113438	−	0.993545i	$-0.463814\pi$
$137$	2.65551	0.226876	0.113438	+	0.993545i	$0.463814\pi$
$138$	8.41626	0.716439
$139$	1.71492	0.145457	0.0727287	−	0.997352i	$-0.476829\pi$
$139$	1.71492	0.145457	0.0727287	+	0.997352i	$0.476829\pi$
$140$	0	0
$141$	−3.24463	−0.273247
$142$	18.7851	1.57641
$143$	9.12582	0.763139
$144$	−14.2119	−1.18432
$145$	0	0
$146$	0.896421	0.0741883
$147$	11.1069	0.916079
$148$	29.8886	2.45683
$149$	−4.02290	−0.329569	−0.164784	−	0.986330i	$-0.552693\pi$
$149$	−4.02290	−0.329569	−0.164784	+	0.986330i	$0.552693\pi$
$150$	0	0
$151$	8.71536	0.709246	0.354623	−	0.935009i	$-0.384609\pi$
$151$	8.71536	0.709246	0.354623	+	0.935009i	$0.384609\pi$
$152$	27.8886	2.26207
$153$	11.1873	0.904439
$154$	21.0701	1.69788
$155$	0	0
$156$	−15.5561	−1.24548
$157$	−11.2364	−0.896763	−0.448382	−	0.893842i	$-0.647999\pi$
$157$	−11.2364	−0.896763	−0.448382	+	0.893842i	$0.647999\pi$
$158$	11.0004	0.875148
$159$	1.07323	0.0851126
$160$	0	0
$161$	−22.7628	−1.79396
$162$	−11.9619	−0.939813
$163$	22.3354	1.74944	0.874720	−	0.484628i	$-0.161045\pi$
$163$	22.3354	1.74944	0.874720	+	0.484628i	$0.161045\pi$
$164$	5.70669	0.445618
$165$	0	0
$166$	−11.0128	−0.854759
$167$	19.6782	1.52274	0.761372	−	0.648315i	$-0.224526\pi$
$167$	19.6782	1.52274	0.761372	+	0.648315i	$0.224526\pi$
$168$	−19.0842	−1.47237
$169$	13.7628	1.05868
$170$	0	0
$171$	12.2991	0.940536
$172$	−33.6192	−2.56344
$173$	16.0689	1.22170	0.610849	−	0.791747i	$-0.290828\pi$
$173$	16.0689	1.22170	0.610849	+	0.791747i	$0.290828\pi$
$174$	9.45836	0.717036
$175$	0	0
$176$	−10.0140	−0.754835
$177$	5.36508	0.403264
$178$	42.0215	3.14964
$179$	15.5830	1.16473	0.582363	−	0.812929i	$-0.302128\pi$
$179$	15.5830	1.16473	0.582363	+	0.812929i	$0.302128\pi$
$180$	0	0
$181$	18.3213	1.36181	0.680907	−	0.732370i	$-0.261586\pi$
$181$	18.3213	1.36181	0.680907	+	0.732370i	$0.261586\pi$
$182$	61.7913	4.58028
$183$	5.22074	0.385928
$184$	27.0842	1.99667
$185$	0	0
$186$	1.76403	0.129345
$187$	7.88284	0.576451
$188$	−19.6510	−1.43320
$189$	−18.5016	−1.34580
$190$	0	0
$191$	−9.50284	−0.687602	−0.343801	−	0.939043i	$-0.611715\pi$
$191$	−9.50284	−0.687602	−0.343801	+	0.939043i	$0.611715\pi$
$192$	−2.95790	−0.213468
$193$	−18.5982	−1.33873	−0.669364	−	0.742935i	$-0.733433\pi$
$193$	−18.5982	−1.33873	−0.669364	+	0.742935i	$0.733433\pi$
$194$	1.35600	0.0973548
$195$	0	0
$196$	67.2684	4.80488
$197$	−19.5643	−1.39390	−0.696950	−	0.717120i	$-0.745460\pi$
$197$	−19.5643	−1.39390	−0.696950	+	0.717120i	$0.745460\pi$
$198$	−11.0561	−0.785724
$199$	−9.70835	−0.688207	−0.344103	−	0.938932i	$-0.611817\pi$
$199$	−9.70835	−0.688207	−0.344103	+	0.938932i	$0.611817\pi$
$200$	0	0
$201$	3.72894	0.263019
$202$	−3.41504	−0.240282
$203$	−25.5813	−1.79546
$204$	−13.4373	−0.940798
$205$	0	0
$206$	29.9027	2.08342
$207$	11.9443	0.830188
$208$	−29.3676	−2.03628
$209$	8.66625	0.599457
$210$	0	0
$211$	−1.59776	−0.109994	−0.0549972	−	0.998487i	$-0.517515\pi$
$211$	−1.59776	−0.109994	−0.0549972	+	0.998487i	$0.517515\pi$
$212$	6.49998	0.446420
$213$	−5.28715	−0.362270
$214$	−15.9051	−1.08725
$215$	0	0
$216$	22.0140	1.49786
$217$	−4.77104	−0.323879
$218$	−9.41747	−0.637832
$219$	−0.252302	−0.0170490
$220$	0	0
$221$	23.1176	1.55506
$222$	−12.3548	−0.829199
$223$	−19.1448	−1.28203	−0.641015	−	0.767529i	$-0.721486\pi$
$223$	−19.1448	−1.28203	−0.641015	+	0.767529i	$0.721486\pi$
$224$	−13.6370	−0.911160
$225$	0	0
$226$	−27.2979	−1.81583
$227$	10.5573	0.700713	0.350357	−	0.936616i	$-0.386060\pi$
$227$	10.5573	0.700713	0.350357	+	0.936616i	$0.386060\pi$
$228$	−14.7727	−0.978346
$229$	4.62419	0.305575	0.152788	−	0.988259i	$-0.451175\pi$
$229$	4.62419	0.305575	0.152788	+	0.988259i	$0.451175\pi$
$230$	0	0
$231$	−5.93030	−0.390185
$232$	30.4377	1.99833
$233$	−10.5825	−0.693284	−0.346642	−	0.937997i	$-0.612678\pi$
$233$	−10.5825	−0.693284	−0.346642	+	0.937997i	$0.612678\pi$
$234$	−32.4237	−2.11960
$235$	0	0
$236$	32.4934	2.11514
$237$	−3.09613	−0.201115
$238$	53.3750	3.45979
$239$	−18.4237	−1.19173	−0.595865	−	0.803084i	$-0.703191\pi$
$239$	−18.4237	−1.19173	−0.595865	+	0.803084i	$0.703191\pi$
$240$	0	0
$241$	−23.4642	−1.51146	−0.755730	−	0.654884i	$-0.772718\pi$
$241$	−23.4642	−1.51146	−0.755730	+	0.654884i	$0.772718\pi$
$242$	19.7481	1.26946
$243$	15.0004	0.962279
$244$	31.6192	2.02421
$245$	0	0
$246$	−2.35892	−0.150399
$247$	25.4150	1.61712
$248$	5.67678	0.360476
$249$	3.09961	0.196430
$250$	0	0
$251$	−3.67209	−0.231780	−0.115890	−	0.993262i	$-0.536972\pi$
$251$	−3.67209	−0.231780	−0.115890	+	0.993262i	$0.536972\pi$
$252$	−50.9728	−3.21098
$253$	8.41626	0.529126
$254$	30.6515	1.92324
$255$	0	0
$256$	−32.2259	−2.01412
$257$	29.0619	1.81283	0.906416	−	0.422386i	$-0.138807\pi$
$257$	29.0619	1.81283	0.906416	+	0.422386i	$0.138807\pi$
$258$	13.8969	0.865181
$259$	33.4150	2.07631
$260$	0	0
$261$	13.4233	0.830879
$262$	−4.63164	−0.286144
$263$	−15.9493	−0.983473	−0.491737	−	0.870744i	$-0.663638\pi$
$263$	−15.9493	−0.983473	−0.491737	+	0.870744i	$0.663638\pi$
$264$	7.05612	0.434274
$265$	0	0
$266$	58.6795	3.59787
$267$	−11.8272	−0.723810
$268$	22.5842	1.37955
$269$	1.40103	0.0854220	0.0427110	−	0.999087i	$-0.486401\pi$
$269$	1.40103	0.0854220	0.0427110	+	0.999087i	$0.486401\pi$
$270$	0	0
$271$	12.8103	0.778169	0.389084	−	0.921202i	$-0.372791\pi$
$271$	12.8103	0.778169	0.389084	+	0.921202i	$0.372791\pi$
$272$	−25.3676	−1.53814
$273$	−17.3915	−1.05258
$274$	−6.64809	−0.401626
$275$	0	0
$276$	−14.3466	−0.863561
$277$	−25.7116	−1.54486	−0.772431	−	0.635098i	$-0.780959\pi$
$277$	−25.7116	−1.54486	−0.772431	+	0.635098i	$0.780959\pi$
$278$	−4.29331	−0.257495
$279$	2.50350	0.149881
$280$	0	0
$281$	−21.2102	−1.26529	−0.632647	−	0.774440i	$-0.718032\pi$
$281$	−21.2102	−1.26529	−0.632647	+	0.774440i	$0.718032\pi$
$282$	8.12295	0.483715
$283$	−5.40925	−0.321546	−0.160773	−	0.986991i	$-0.551399\pi$
$283$	−5.40925	−0.321546	−0.160773	+	0.986991i	$0.551399\pi$
$284$	−32.0215	−1.90012
$285$	0	0
$286$	−22.8465	−1.35094
$287$	6.38000	0.376599
$288$	7.15573	0.421656
$289$	2.96887	0.174640
$290$	0	0
$291$	−0.381652	−0.0223728
$292$	−1.52806	−0.0894230
$293$	3.99178	0.233202	0.116601	−	0.993179i	$-0.462800\pi$
$293$	3.99178	0.233202	0.116601	+	0.993179i	$0.462800\pi$
$294$	−27.8061	−1.62168
$295$	0	0
$296$	−39.7586	−2.31092
$297$	6.84074	0.396940
$298$	10.0714	0.583418
$299$	24.6819	1.42739
$300$	0	0
$301$	−37.5858	−2.16641
$302$	−21.8189	−1.25554
$303$	0.961182	0.0552184
$304$	−27.8886	−1.59952
$305$	0	0
$306$	−28.0074	−1.60108
$307$	−27.4782	−1.56826	−0.784131	−	0.620595i	$-0.786891\pi$
$307$	−27.4782	−1.56826	−0.784131	+	0.620595i	$0.786891\pi$
$308$	−35.9167	−2.04654
$309$	−8.41626	−0.478784
$310$	0	0
$311$	−11.6978	−0.663322	−0.331661	−	0.943399i	$-0.607609\pi$
$311$	−11.6978	−0.663322	−0.331661	+	0.943399i	$0.607609\pi$
$312$	20.6931	1.17152
$313$	23.0652	1.30372	0.651861	−	0.758338i	$-0.273989\pi$
$313$	23.0652	1.30372	0.651861	+	0.758338i	$0.273989\pi$
$314$	28.1304	1.58749
$315$	0	0
$316$	−18.7516	−1.05486
$317$	−21.0907	−1.18457	−0.592287	−	0.805727i	$-0.701775\pi$
$317$	−21.0907	−1.18457	−0.592287	+	0.805727i	$0.701775\pi$
$318$	−2.68683	−0.150670
$319$	9.45836	0.529567
$320$	0	0
$321$	4.47657	0.249858
$322$	56.9868	3.17575
$323$	21.9534	1.22152
$324$	20.3905	1.13280
$325$	0	0
$326$	−55.9167	−3.09694
$327$	2.65060	0.146578
$328$	−7.59119	−0.419153
$329$	−21.9695	−1.21122
$330$	0	0
$331$	16.8751	0.927537	0.463769	−	0.885956i	$-0.346497\pi$
$331$	16.8751	0.927537	0.463769	+	0.885956i	$0.346497\pi$
$332$	18.7727	1.03029
$333$	−17.5339	−0.960849
$334$	−49.2644	−2.69563
$335$	0	0
$336$	19.0842	1.04113
$337$	−31.9691	−1.74147	−0.870733	−	0.491756i	$-0.836355\pi$
$337$	−31.9691	−1.74147	−0.870733	+	0.491756i	$0.836355\pi$
$338$	−34.4553	−1.87412
$339$	7.68313	0.417290
$340$	0	0
$341$	1.76403	0.0955276
$342$	−30.7909	−1.66498
$343$	41.8077	2.25741
$344$	44.7212	2.41120
$345$	0	0
$346$	−40.2286	−2.16270
$347$	−25.6036	−1.37447	−0.687235	−	0.726435i	$-0.741176\pi$
$347$	−25.6036	−1.37447	−0.687235	+	0.726435i	$0.741176\pi$
$348$	−16.1230	−0.864281
$349$	8.24933	0.441576	0.220788	−	0.975322i	$-0.429137\pi$
$349$	8.24933	0.441576	0.220788	+	0.975322i	$0.429137\pi$
$350$	0	0
$351$	20.0615	1.07080
$352$	5.04210	0.268745
$353$	−14.4777	−0.770572	−0.385286	−	0.922797i	$-0.625897\pi$
$353$	−14.4777	−0.770572	−0.385286	+	0.922797i	$0.625897\pi$
$354$	−13.4315	−0.713876
$355$	0	0
$356$	−71.6308	−3.79643
$357$	−15.0227	−0.795085
$358$	−39.0120	−2.06185
$359$	23.9331	1.26314	0.631571	−	0.775318i	$-0.282410\pi$
$359$	23.9331	1.26314	0.631571	+	0.775318i	$0.282410\pi$
$360$	0	0
$361$	5.13514	0.270271
$362$	−45.8676	−2.41075
$363$	−5.55822	−0.291731
$364$	−105.331	−5.52084
$365$	0	0
$366$	−13.0701	−0.683187
$367$	−4.78255	−0.249647	−0.124823	−	0.992179i	$-0.539836\pi$
$367$	−4.78255	−0.249647	−0.124823	+	0.992179i	$0.539836\pi$
$368$	−27.0842	−1.41186
$369$	−3.34777	−0.174278
$370$	0	0
$371$	7.26687	0.377277
$372$	−3.00701	−0.155906
$373$	22.2434	1.15172	0.575860	−	0.817548i	$-0.304667\pi$
$373$	22.2434	1.15172	0.575860	+	0.817548i	$0.304667\pi$
$374$	−19.7347	−1.02046
$375$	0	0
$376$	26.1403	1.34808
$377$	27.7380	1.42858
$378$	46.3189	2.38239
$379$	−11.3419	−0.582592	−0.291296	−	0.956633i	$-0.594087\pi$
$379$	−11.3419	−0.582592	−0.291296	+	0.956633i	$0.594087\pi$
$380$	0	0
$381$	−8.62701	−0.441975
$382$	23.7904	1.21722
$383$	−24.5507	−1.25448	−0.627242	−	0.778825i	$-0.715816\pi$
$383$	−24.5507	−1.25448	−0.627242	+	0.778825i	$0.715816\pi$
$384$	11.4331	0.583445
$385$	0	0
$386$	46.5607	2.36988
$387$	19.7224	1.00254
$388$	−2.31146	−0.117347
$389$	24.5565	1.24507	0.622533	−	0.782594i	$-0.286104\pi$
$389$	24.5565	1.24507	0.622533	+	0.782594i	$0.286104\pi$
$390$	0	0
$391$	21.3201	1.07821
$392$	−89.4821	−4.51953
$393$	1.30360	0.0657579
$394$	48.9794	2.46754
$395$	0	0
$396$	18.8465	0.947074
$397$	−10.8490	−0.544494	−0.272247	−	0.962227i	$-0.587767\pi$
$397$	−10.8490	−0.544494	−0.272247	+	0.962227i	$0.587767\pi$
$398$	24.3049	1.21829
$399$	−16.5156	−0.826817
$400$	0	0
$401$	−4.00822	−0.200161	−0.100081	−	0.994979i	$-0.531910\pi$
$401$	−4.00822	−0.200161	−0.100081	+	0.994979i	$0.531910\pi$
$402$	−9.33541	−0.465608
$403$	5.17328	0.257699
$404$	5.82137	0.289624
$405$	0	0
$406$	64.0429	3.17840
$407$	−12.3548	−0.612404
$408$	17.8746	0.884925
$409$	−30.9319	−1.52948	−0.764742	−	0.644336i	$-0.777134\pi$
$409$	−30.9319	−1.52948	−0.764742	+	0.644336i	$0.777134\pi$
$410$	0	0
$411$	1.87114	0.0922965
$412$	−50.9728	−2.51125
$413$	36.3271	1.78754
$414$	−29.9027	−1.46964
$415$	0	0
$416$	14.7867	0.724978
$417$	1.20837	0.0591743
$418$	−21.6960	−1.06119
$419$	28.3302	1.38402	0.692011	−	0.721887i	$-0.256725\pi$
$419$	28.3302	1.38402	0.692011	+	0.721887i	$0.256725\pi$
$420$	0	0
$421$	−11.2511	−0.548344	−0.274172	−	0.961681i	$-0.588404\pi$
$421$	−11.2511	−0.548344	−0.274172	+	0.961681i	$0.588404\pi$
$422$	4.00000	0.194717
$423$	11.5281	0.560513
$424$	−8.64643	−0.419908
$425$	0	0
$426$	13.2364	0.641306
$427$	35.3498	1.71070
$428$	27.1122	1.31052
$429$	6.43028	0.310457
$430$	0	0
$431$	17.1293	0.825089	0.412545	−	0.910937i	$-0.364640\pi$
$431$	17.1293	0.825089	0.412545	+	0.910937i	$0.364640\pi$
$432$	−22.0140	−1.05915
$433$	20.8407	1.00154	0.500771	−	0.865580i	$-0.333050\pi$
$433$	20.8407	1.00154	0.500771	+	0.865580i	$0.333050\pi$
$434$	11.9443	0.573346
$435$	0	0
$436$	16.0533	0.768811
$437$	23.4389	1.12124
$438$	0.631640	0.0301809
$439$	27.8699	1.33016	0.665078	−	0.746774i	$-0.268398\pi$
$439$	27.8699	1.33016	0.665078	+	0.746774i	$0.268398\pi$
$440$	0	0
$441$	−39.4623	−1.87916
$442$	−57.8750	−2.75283
$443$	17.0603	0.810557	0.405279	−	0.914193i	$-0.367174\pi$
$443$	17.0603	0.810557	0.405279	+	0.914193i	$0.367174\pi$
$444$	21.0603	0.999476
$445$	0	0
$446$	47.9290	2.26951
$447$	−2.83463	−0.134074
$448$	−20.0280	−0.946236
$449$	11.0537	0.521656	0.260828	−	0.965385i	$-0.416004\pi$
$449$	11.0537	0.521656	0.260828	+	0.965385i	$0.416004\pi$
$450$	0	0
$451$	−2.35892	−0.111077
$452$	46.5326	2.18871
$453$	6.14105	0.288532
$454$	−26.4303	−1.24043
$455$	0	0
$456$	19.6510	0.920243
$457$	3.56432	0.166732	0.0833659	−	0.996519i	$-0.473433\pi$
$457$	3.56432	0.166732	0.0833659	+	0.996519i	$0.473433\pi$
$458$	−11.5767	−0.540943
$459$	17.3290	0.808849
$460$	0	0
$461$	−8.35235	−0.389008	−0.194504	−	0.980902i	$-0.562310\pi$
$461$	−8.35235	−0.389008	−0.194504	+	0.980902i	$0.562310\pi$
$462$	14.8465	0.690723
$463$	1.24298	0.0577661	0.0288831	−	0.999583i	$-0.490805\pi$
$463$	1.24298	0.0577661	0.0288831	+	0.999583i	$0.490805\pi$
$464$	−30.4377	−1.41304
$465$	0	0
$466$	26.4934	1.22728
$467$	3.71194	0.171768	0.0858841	−	0.996305i	$-0.472629\pi$
$467$	3.71194	0.171768	0.0858841	+	0.996305i	$0.472629\pi$
$468$	55.2702	2.55487
$469$	25.2488	1.16588
$470$	0	0
$471$	−7.91745	−0.364817
$472$	−43.2236	−1.98953
$473$	13.8969	0.638978
$474$	7.75118	0.356023
$475$	0	0
$476$	−90.9844	−4.17026
$477$	−3.81314	−0.174592
$478$	46.1238	2.10965
$479$	−21.8634	−0.998965	−0.499483	−	0.866324i	$-0.666477\pi$
$479$	−21.8634	−0.998965	−0.499483	+	0.866324i	$0.666477\pi$
$480$	0	0
$481$	−36.2322	−1.65205
$482$	58.7426	2.67565
$483$	−16.0392	−0.729810
$484$	−33.6632	−1.53014
$485$	0	0
$486$	−37.5537	−1.70347
$487$	33.3486	1.51117	0.755585	−	0.655050i	$-0.227353\pi$
$487$	33.3486	1.51117	0.755585	+	0.655050i	$0.227353\pi$
$488$	−42.0607	−1.90400
$489$	15.7380	0.711699
$490$	0	0
$491$	23.1955	1.04680	0.523400	−	0.852087i	$-0.324664\pi$
$491$	23.1955	1.04680	0.523400	+	0.852087i	$0.324664\pi$
$492$	4.02108	0.181284
$493$	23.9600	1.07910
$494$	−63.6267	−2.86270
$495$	0	0
$496$	−5.67678	−0.254895
$497$	−35.7995	−1.60583
$498$	−7.75989	−0.347729
$499$	−18.5474	−0.830297	−0.415149	−	0.909754i	$-0.636270\pi$
$499$	−18.5474	−0.830297	−0.415149	+	0.909754i	$0.636270\pi$
$500$	0	0
$501$	13.8657	0.619475
$502$	9.19309	0.410308
$503$	−26.0132	−1.15987	−0.579937	−	0.814662i	$-0.696923\pi$
$503$	−26.0132	−1.15987	−0.579937	+	0.814662i	$0.696923\pi$
$504$	67.8053	3.02029
$505$	0	0
$506$	−21.0701	−0.936682
$507$	9.69762	0.430686
$508$	−52.2492	−2.31818
$509$	14.5046	0.642905	0.321453	−	0.946926i	$-0.395829\pi$
$509$	14.5046	0.642905	0.321453	+	0.946926i	$0.395829\pi$
$510$	0	0
$511$	−1.70835	−0.0755729
$512$	48.2259	2.13130
$513$	19.0512	0.841130
$514$	−72.7566	−3.20916
$515$	0	0
$516$	−23.6889	−1.04285
$517$	8.12295	0.357247
$518$	−83.6547	−3.67558
$519$	11.3226	0.497005
$520$	0	0
$521$	20.0109	0.876695	0.438347	−	0.898806i	$-0.355564\pi$
$521$	20.0109	0.876695	0.438347	+	0.898806i	$0.355564\pi$
$522$	−33.6052	−1.47086
$523$	−2.56882	−0.112327	−0.0561633	−	0.998422i	$-0.517887\pi$
$523$	−2.56882	−0.112327	−0.0561633	+	0.998422i	$0.517887\pi$
$524$	7.89521	0.344904
$525$	0	0
$526$	39.9290	1.74099
$527$	4.46865	0.194658
$528$	−7.05612	−0.307078
$529$	−0.237184	−0.0103124
$530$	0	0
$531$	−19.0619	−0.827217
$532$	−100.026	−4.33670
$533$	−6.91789	−0.299647
$534$	29.6093	1.28132
$535$	0	0
$536$	−30.0421	−1.29762
$537$	10.9801	0.473828
$538$	−3.50747	−0.151218
$539$	−27.8061	−1.19769
$540$	0	0
$541$	8.03047	0.345257	0.172628	−	0.984987i	$-0.444774\pi$
$541$	8.03047	0.345257	0.172628	+	0.984987i	$0.444774\pi$
$542$	−32.0706	−1.37755
$543$	12.9097	0.554007
$544$	12.7727	0.547625
$545$	0	0
$546$	43.5396	1.86332
$547$	−14.1200	−0.603727	−0.301863	−	0.953351i	$-0.597609\pi$
$547$	−14.1200	−0.603727	−0.301863	+	0.953351i	$0.597609\pi$
$548$	11.3325	0.484100
$549$	−18.5491	−0.791656
$550$	0	0
$551$	26.3412	1.12217
$552$	19.0842	0.812276
$553$	−20.9640	−0.891481
$554$	64.3692	2.73478
$555$	0	0
$556$	7.31847	0.310372
$557$	5.65047	0.239418	0.119709	−	0.992809i	$-0.461804\pi$
$557$	5.65047	0.239418	0.119709	+	0.992809i	$0.461804\pi$
$558$	−6.26753	−0.265326
$559$	40.7546	1.72374
$560$	0	0
$561$	5.55444	0.234509
$562$	53.0998	2.23988
$563$	15.5961	0.657298	0.328649	−	0.944452i	$-0.393407\pi$
$563$	15.5961	0.657298	0.328649	+	0.944452i	$0.393407\pi$
$564$	−13.8466	−0.583046
$565$	0	0
$566$	13.5421	0.569216
$567$	22.7963	0.957353
$568$	42.5958	1.78728
$569$	−36.3235	−1.52276	−0.761381	−	0.648305i	$-0.775478\pi$
$569$	−36.3235	−1.52276	−0.761381	+	0.648305i	$0.775478\pi$
$570$	0	0
$571$	−21.3528	−0.893587	−0.446793	−	0.894637i	$-0.647434\pi$
$571$	−21.3528	−0.893587	−0.446793	+	0.894637i	$0.647434\pi$
$572$	38.9448	1.62836
$573$	−6.69594	−0.279727
$574$	−15.9724	−0.666673
$575$	0	0
$576$	10.5093	0.437887
$577$	−11.4642	−0.477259	−0.238630	−	0.971111i	$-0.576698\pi$
$577$	−11.4642	−0.477259	−0.238630	+	0.971111i	$0.576698\pi$
$578$	−7.43259	−0.309155
$579$	−13.1047	−0.544615
$580$	0	0
$581$	20.9876	0.870712
$582$	0.955468	0.0396054
$583$	−2.68683	−0.111277
$584$	2.03267	0.0841123
$585$	0	0
$586$	−9.99343	−0.412825
$587$	−0.549863	−0.0226953	−0.0113476	−	0.999936i	$-0.503612\pi$
$587$	−0.549863	−0.0226953	−0.0113476	+	0.999936i	$0.503612\pi$
$588$	47.3989	1.95470
$589$	4.91275	0.202426
$590$	0	0
$591$	−13.7855	−0.567060
$592$	39.7586	1.63407
$593$	14.1721	0.581977	0.290988	−	0.956727i	$-0.406016\pi$
$593$	14.1721	0.581977	0.290988	+	0.956727i	$0.406016\pi$
$594$	−17.1258	−0.702681
$595$	0	0
$596$	−17.1679	−0.703224
$597$	−6.84074	−0.279973
$598$	−61.7913	−2.52683
$599$	−27.8774	−1.13904	−0.569521	−	0.821977i	$-0.692871\pi$
$599$	−27.8774	−1.13904	−0.569521	+	0.821977i	$0.692871\pi$
$600$	0	0
$601$	37.2850	1.52089	0.760444	−	0.649403i	$-0.224981\pi$
$601$	37.2850	1.52089	0.760444	+	0.649403i	$0.224981\pi$
$602$	94.0962	3.83507
$603$	−13.2488	−0.539532
$604$	37.1931	1.51337
$605$	0	0
$606$	−2.40632	−0.0977502
$607$	−3.20594	−0.130125	−0.0650626	−	0.997881i	$-0.520725\pi$
$607$	−3.20594	−0.130125	−0.0650626	+	0.997881i	$0.520725\pi$
$608$	14.0421	0.569480
$609$	−18.0252	−0.730419
$610$	0	0
$611$	23.8218	0.963725
$612$	47.7422	1.92986
$613$	7.33164	0.296122	0.148061	−	0.988978i	$-0.452697\pi$
$613$	7.33164	0.296122	0.148061	+	0.988978i	$0.452697\pi$
$614$	68.7917	2.77621
$615$	0	0
$616$	47.7773	1.92500
$617$	2.44313	0.0983566	0.0491783	−	0.998790i	$-0.484340\pi$
$617$	2.44313	0.0983566	0.0491783	+	0.998790i	$0.484340\pi$
$618$	21.0701	0.847565
$619$	−18.8073	−0.755929	−0.377965	−	0.925820i	$-0.623376\pi$
$619$	−18.8073	−0.755929	−0.377965	+	0.925820i	$0.623376\pi$
$620$	0	0
$621$	18.5016	0.742445
$622$	29.2855	1.17424
$623$	−80.0822	−3.20842
$624$	−20.6931	−0.828388
$625$	0	0
$626$	−57.7438	−2.30791
$627$	6.10645	0.243868
$628$	−47.9518	−1.91348
$629$	−31.2972	−1.24790
$630$	0	0
$631$	−11.8069	−0.470024	−0.235012	−	0.971993i	$-0.575513\pi$
$631$	−11.8069	−0.470024	−0.235012	+	0.971993i	$0.575513\pi$
$632$	24.9439	0.992214
$633$	−1.12582	−0.0447474
$634$	52.8007	2.09698
$635$	0	0
$636$	4.58004	0.181610
$637$	−81.5454	−3.23095
$638$	−23.6790	−0.937463
$639$	18.7851	0.743125
$640$	0	0
$641$	−15.1604	−0.598801	−0.299400	−	0.954128i	$-0.596787\pi$
$641$	−15.1604	−0.598801	−0.299400	+	0.954128i	$0.596787\pi$
$642$	−11.2071	−0.442309
$643$	−30.3573	−1.19717	−0.598587	−	0.801058i	$-0.704271\pi$
$643$	−30.3573	−1.19717	−0.598587	+	0.801058i	$0.704271\pi$
$644$	−97.1411	−3.82790
$645$	0	0
$646$	−54.9604	−2.16239
$647$	−12.7595	−0.501629	−0.250814	−	0.968035i	$-0.580698\pi$
$647$	−12.7595	−0.501629	−0.250814	+	0.968035i	$0.580698\pi$
$648$	−27.1239	−1.06553
$649$	−13.4315	−0.527232
$650$	0	0
$651$	−3.36179	−0.131759
$652$	95.3169	3.73290
$653$	47.5210	1.85964	0.929820	−	0.368014i	$-0.119962\pi$
$653$	47.5210	1.85964	0.929820	+	0.368014i	$0.119962\pi$
$654$	−6.63578	−0.259480
$655$	0	0
$656$	7.59119	0.296386
$657$	0.896421	0.0349727
$658$	55.0008	2.14416
$659$	−25.2210	−0.982469	−0.491234	−	0.871027i	$-0.663454\pi$
$659$	−25.2210	−0.982469	−0.491234	+	0.871027i	$0.663454\pi$
$660$	0	0
$661$	30.3805	1.18166	0.590832	−	0.806794i	$-0.298799\pi$
$661$	30.3805	1.18166	0.590832	+	0.806794i	$0.298799\pi$
$662$	−42.2468	−1.64197
$663$	16.2892	0.632621
$664$	−24.9719	−0.969098
$665$	0	0
$666$	43.8961	1.70094
$667$	25.5813	0.990512
$668$	83.9774	3.24918
$669$	−13.4899	−0.521549
$670$	0	0
$671$	−13.0701	−0.504567
$672$	−9.60896	−0.370674
$673$	25.1506	0.969483	0.484742	−	0.874657i	$-0.338914\pi$
$673$	25.1506	0.969483	0.484742	+	0.874657i	$0.338914\pi$
$674$	80.0347	3.08282
$675$	0	0
$676$	58.7333	2.25897
$677$	−20.9897	−0.806700	−0.403350	−	0.915046i	$-0.632154\pi$
$677$	−20.9897	−0.806700	−0.403350	+	0.915046i	$0.632154\pi$
$678$	−19.2348	−0.738706
$679$	−2.58418	−0.0991718
$680$	0	0
$681$	7.43894	0.285061
$682$	−4.41626	−0.169107
$683$	26.0198	0.995620	0.497810	−	0.867286i	$-0.334138\pi$
$683$	26.0198	0.995620	0.497810	+	0.867286i	$0.334138\pi$
$684$	52.4868	2.00688
$685$	0	0
$686$	−104.666	−3.99616
$687$	3.25832	0.124313
$688$	−44.7212	−1.70498
$689$	−7.87953	−0.300186
$690$	0	0
$691$	−17.3282	−0.659197	−0.329599	−	0.944121i	$-0.606913\pi$
$691$	−17.3282	−0.659197	−0.329599	+	0.944121i	$0.606913\pi$
$692$	68.5747	2.60682
$693$	21.0701	0.800388
$694$	64.0986	2.43315
$695$	0	0
$696$	21.4472	0.812953
$697$	−5.97564	−0.226343
$698$	−20.6522	−0.781698
$699$	−7.45671	−0.282039
$700$	0	0
$701$	−18.3639	−0.693594	−0.346797	−	0.937940i	$-0.612731\pi$
$701$	−18.3639	−0.693594	−0.346797	+	0.937940i	$0.612731\pi$
$702$	−50.2240	−1.89558
$703$	−34.4076	−1.29771
$704$	7.40511	0.279091
$705$	0	0
$706$	36.2451	1.36410
$707$	6.50820	0.244766
$708$	22.8956	0.860471
$709$	−39.2637	−1.47458	−0.737289	−	0.675577i	$-0.763894\pi$
$709$	−39.2637	−1.47458	−0.737289	+	0.675577i	$0.763894\pi$
$710$	0	0
$711$	11.0004	0.412549
$712$	95.2851	3.57096
$713$	4.77104	0.178677
$714$	37.6093	1.40749
$715$	0	0
$716$	66.5009	2.48525
$717$	−12.9818	−0.484814
$718$	−59.9167	−2.23607
$719$	−1.79090	−0.0667893	−0.0333947	−	0.999442i	$-0.510632\pi$
$719$	−1.79090	−0.0667893	−0.0333947	+	0.999442i	$0.510632\pi$
$720$	0	0
$721$	−56.9868	−2.12230
$722$	−12.8559	−0.478445
$723$	−16.5334	−0.614884
$724$	78.1870	2.90580
$725$	0	0
$726$	13.9150	0.516435
$727$	−6.05325	−0.224503	−0.112251	−	0.993680i	$-0.535806\pi$
$727$	−6.05325	−0.224503	−0.112251	+	0.993680i	$0.535806\pi$
$728$	140.114	5.19297
$729$	−3.76447	−0.139425
$730$	0	0
$731$	35.2036	1.30205
$732$	22.2797	0.823481
$733$	−50.4213	−1.86235	−0.931176	−	0.364569i	$-0.881216\pi$
$733$	−50.4213	−1.86235	−0.931176	+	0.364569i	$0.881216\pi$
$734$	11.9731	0.441936
$735$	0	0
$736$	13.6370	0.502666
$737$	−9.33541	−0.343874
$738$	8.38116	0.308515
$739$	49.2291	1.81092	0.905460	−	0.424431i	$-0.139526\pi$
$739$	49.2291	1.81092	0.905460	+	0.424431i	$0.139526\pi$
$740$	0	0
$741$	17.9081	0.657869
$742$	−18.1927	−0.667873
$743$	2.05240	0.0752951	0.0376476	−	0.999291i	$-0.488014\pi$
$743$	2.05240	0.0752951	0.0376476	+	0.999291i	$0.488014\pi$
$744$	4.00000	0.146647
$745$	0	0
$746$	−55.6865	−2.03883
$747$	−11.0128	−0.402937
$748$	33.6403	1.23001
$749$	30.3110	1.10754
$750$	0	0
$751$	30.6907	1.11992	0.559960	−	0.828520i	$-0.310817\pi$
$751$	30.6907	1.11992	0.559960	+	0.828520i	$0.310817\pi$
$752$	−26.1403	−0.953238
$753$	−2.58744	−0.0942917
$754$	−69.4423	−2.52894
$755$	0	0
$756$	−78.9563	−2.87161
$757$	35.9782	1.30765	0.653824	−	0.756646i	$-0.273163\pi$
$757$	35.9782	1.30765	0.653824	+	0.756646i	$0.273163\pi$
$758$	28.3944	1.03133
$759$	5.93030	0.215256
$760$	0	0
$761$	16.8564	0.611044	0.305522	−	0.952185i	$-0.401169\pi$
$761$	16.8564	0.611044	0.305522	+	0.952185i	$0.401169\pi$
$762$	21.5978	0.782404
$763$	17.9473	0.649736
$764$	−40.5537	−1.46718
$765$	0	0
$766$	61.4628	2.22074
$767$	−39.3898	−1.42228
$768$	−22.7071	−0.819373
$769$	−38.8385	−1.40055	−0.700277	−	0.713872i	$-0.746940\pi$
$769$	−38.8385	−1.40055	−0.700277	+	0.713872i	$0.746940\pi$
$770$	0	0
$771$	20.4777	0.737488
$772$	−79.3685	−2.85653
$773$	8.75702	0.314968	0.157484	−	0.987522i	$-0.449662\pi$
$773$	8.75702	0.314968	0.157484	+	0.987522i	$0.449662\pi$
$774$	−49.3750	−1.77475
$775$	0	0
$776$	3.07477	0.110378
$777$	23.5451	0.844674
$778$	−61.4774	−2.20407
$779$	−6.56950	−0.235377
$780$	0	0
$781$	13.2364	0.473636
$782$	−53.3750	−1.90869
$783$	20.7925	0.743064
$784$	89.4821	3.19579
$785$	0	0
$786$	−3.26357	−0.116408
$787$	−6.67369	−0.237891	−0.118946	−	0.992901i	$-0.537951\pi$
$787$	−6.67369	−0.237891	−0.118946	+	0.992901i	$0.537951\pi$
$788$	−83.4914	−2.97426
$789$	−11.2382	−0.400092
$790$	0	0
$791$	52.0228	1.84972
$792$	−25.0701	−0.890829
$793$	−38.3301	−1.36114
$794$	27.1604	0.963887
$795$	0	0
$796$	−41.4307	−1.46847
$797$	−4.07880	−0.144479	−0.0722393	−	0.997387i	$-0.523015\pi$
$797$	−4.07880	−0.144479	−0.0722393	+	0.997387i	$0.523015\pi$
$798$	41.3470	1.46367
$799$	20.5771	0.727966
$800$	0	0
$801$	42.0215	1.48476
$802$	10.0346	0.354334
$803$	0.631640	0.0222901
$804$	15.9134	0.561221
$805$	0	0
$806$	−12.9513	−0.456191
$807$	0.987197	0.0347510
$808$	−7.74373	−0.272423
$809$	−49.5553	−1.74227	−0.871136	−	0.491042i	$-0.836616\pi$
$809$	−49.5553	−1.74227	−0.871136	+	0.491042i	$0.836616\pi$
$810$	0	0
$811$	−15.5472	−0.545936	−0.272968	−	0.962023i	$-0.588005\pi$
$811$	−15.5472	−0.545936	−0.272968	+	0.962023i	$0.588005\pi$
$812$	−109.169	−3.83109
$813$	9.02643	0.316571
$814$	30.9303	1.08410
$815$	0	0
$816$	−17.8746	−0.625737
$817$	38.7022	1.35402
$818$	77.4382	2.70756
$819$	61.7913	2.15916
$820$	0	0
$821$	−23.0367	−0.803986	−0.401993	−	0.915643i	$-0.631682\pi$
$821$	−23.0367	−0.803986	−0.401993	+	0.915643i	$0.631682\pi$
$822$	−4.68440	−0.163387
$823$	−2.49747	−0.0870562	−0.0435281	−	0.999052i	$-0.513860\pi$
$823$	−2.49747	−0.0870562	−0.0435281	+	0.999052i	$0.513860\pi$
$824$	67.8053	2.36211
$825$	0	0
$826$	−90.9451	−3.16439
$827$	−35.9839	−1.25128	−0.625641	−	0.780111i	$-0.715162\pi$
$827$	−35.9839	−1.25128	−0.625641	+	0.780111i	$0.715162\pi$
$828$	50.9728	1.77143
$829$	−4.75162	−0.165030	−0.0825152	−	0.996590i	$-0.526295\pi$
$829$	−4.75162	−0.165030	−0.0825152	+	0.996590i	$0.526295\pi$
$830$	0	0
$831$	−18.1170	−0.628473
$832$	21.7166	0.752887
$833$	−70.4386	−2.44055
$834$	−3.02517	−0.104753
$835$	0	0
$836$	36.9835	1.27910
$837$	3.87790	0.134040
$838$	−70.9248	−2.45006
$839$	37.2288	1.28528	0.642641	−	0.766167i	$-0.277839\pi$
$839$	37.2288	1.28528	0.642641	+	0.766167i	$0.277839\pi$
$840$	0	0
$841$	−0.251202	−0.00866215
$842$	28.1671	0.970704
$843$	−14.9452	−0.514741
$844$	−6.81850	−0.234702
$845$	0	0
$846$	−28.8606	−0.992246
$847$	−37.6349	−1.29315
$848$	8.64643	0.296920
$849$	−3.81149	−0.130810
$850$	0	0
$851$	−33.4150	−1.14545
$852$	−22.5631	−0.772999
$853$	−9.57717	−0.327916	−0.163958	−	0.986467i	$-0.552426\pi$
$853$	−9.57717	−0.327916	−0.163958	+	0.986467i	$0.552426\pi$
$854$	−88.4984	−3.02835
$855$	0	0
$856$	−36.0653	−1.23269
$857$	16.1952	0.553217	0.276608	−	0.960983i	$-0.410789\pi$
$857$	16.1952	0.553217	0.276608	+	0.960983i	$0.410789\pi$
$858$	−16.0982	−0.549584
$859$	−12.4712	−0.425511	−0.212755	−	0.977106i	$-0.568244\pi$
$859$	−12.4712	−0.425511	−0.212755	+	0.977106i	$0.568244\pi$
$860$	0	0
$861$	4.49550	0.153206
$862$	−42.8833	−1.46061
$863$	29.9921	1.02094	0.510471	−	0.859895i	$-0.329471\pi$
$863$	29.9921	1.02094	0.510471	+	0.859895i	$0.329471\pi$
$864$	11.0842	0.377091
$865$	0	0
$866$	−52.1749	−1.77297
$867$	2.09194	0.0710460
$868$	−20.3606	−0.691083
$869$	7.75118	0.262941
$870$	0	0
$871$	−27.3775	−0.927650
$872$	−21.3544	−0.723153
$873$	1.35600	0.0458935
$874$	−58.6795	−1.98486
$875$	0	0
$876$	−1.07671	−0.0363786
$877$	−52.1919	−1.76239	−0.881197	−	0.472749i	$-0.843262\pi$
$877$	−52.1919	−1.76239	−0.881197	+	0.472749i	$0.843262\pi$
$878$	−69.7724	−2.35470
$879$	2.81270	0.0948701
$880$	0	0
$881$	37.1391	1.25125	0.625623	−	0.780125i	$-0.284845\pi$
$881$	37.1391	1.25125	0.625623	+	0.780125i	$0.284845\pi$
$882$	98.7940	3.32657
$883$	37.9468	1.27701	0.638506	−	0.769617i	$-0.279553\pi$
$883$	37.9468	1.27701	0.638506	+	0.769617i	$0.279553\pi$
$884$	98.6552	3.31813
$885$	0	0
$886$	−42.7104	−1.43489
$887$	49.3429	1.65677	0.828386	−	0.560157i	$-0.189259\pi$
$887$	49.3429	1.65677	0.828386	+	0.560157i	$0.189259\pi$
$888$	−28.0149	−0.940118
$889$	−58.4138	−1.95914
$890$	0	0
$891$	−8.42862	−0.282369
$892$	−81.7010	−2.73555
$893$	22.6221	0.757020
$894$	7.09652	0.237343
$895$	0	0
$896$	77.4143	2.58623
$897$	17.3915	0.580685
$898$	−27.6730	−0.923459
$899$	5.36179	0.178826
$900$	0	0
$901$	−6.80631	−0.226751
$902$	5.90557	0.196634
$903$	−26.4839	−0.881328
$904$	−61.8989	−2.05873
$905$	0	0
$906$	−15.3742	−0.510772
$907$	−3.92787	−0.130423	−0.0652114	−	0.997871i	$-0.520772\pi$
$907$	−3.92787	−0.130423	−0.0652114	+	0.997871i	$0.520772\pi$
$908$	45.0537	1.49516
$909$	−3.41504	−0.113270
$910$	0	0
$911$	23.1779	0.767918	0.383959	−	0.923350i	$-0.374560\pi$
$911$	23.1779	0.767918	0.383959	+	0.923350i	$0.374560\pi$
$912$	−19.6510	−0.650710
$913$	−7.75989	−0.256815
$914$	−8.92329	−0.295156
$915$	0	0
$916$	19.7339	0.652026
$917$	8.82672	0.291484
$918$	−43.3833	−1.43186
$919$	−2.20231	−0.0726475	−0.0363238	−	0.999340i	$-0.511565\pi$
$919$	−2.20231	−0.0726475	−0.0363238	+	0.999340i	$0.511565\pi$
$920$	0	0
$921$	−19.3618	−0.637993
$922$	20.9102	0.688639
$923$	38.8177	1.27770
$924$	−25.3078	−0.832564
$925$	0	0
$926$	−3.11180	−0.102260
$927$	29.9027	0.982132
$928$	15.3255	0.503085
$929$	−16.6464	−0.546152	−0.273076	−	0.961992i	$-0.588041\pi$
$929$	−16.6464	−0.546152	−0.273076	+	0.961992i	$0.588041\pi$
$930$	0	0
$931$	−77.4388	−2.53795
$932$	−45.1613	−1.47931
$933$	−8.24256	−0.269849
$934$	−9.29287	−0.304072
$935$	0	0
$936$	−73.5219	−2.40314
$937$	14.5104	0.474034	0.237017	−	0.971505i	$-0.423830\pi$
$937$	14.5104	0.474034	0.237017	+	0.971505i	$0.423830\pi$
$938$	−63.2104	−2.06389
$939$	16.2523	0.530374
$940$	0	0
$941$	43.1654	1.40715	0.703577	−	0.710619i	$-0.251585\pi$
$941$	43.1654	1.40715	0.703577	+	0.710619i	$0.251585\pi$
$942$	19.8214	0.645815
$943$	−6.38000	−0.207761
$944$	43.2236	1.40681
$945$	0	0
$946$	−34.7909	−1.13115
$947$	43.1498	1.40218	0.701090	−	0.713073i	$-0.252697\pi$
$947$	43.1498	1.40218	0.701090	+	0.713073i	$0.252697\pi$
$948$	−13.2128	−0.429133
$949$	1.85238	0.0601307
$950$	0	0
$951$	−14.8610	−0.481902
$952$	121.030	3.92260
$953$	43.1147	1.39662	0.698311	−	0.715794i	$-0.253935\pi$
$953$	43.1147	1.39662	0.698311	+	0.715794i	$0.253935\pi$
$954$	9.54622	0.309070
$955$	0	0
$956$	−78.6238	−2.54288
$957$	6.66459	0.215436
$958$	54.7352	1.76841
$959$	12.6696	0.409121
$960$	0	0
$961$	1.00000	0.0322581
$962$	90.7075	2.92453
$963$	−15.9051	−0.512534
$964$	−100.134	−3.22510
$965$	0	0
$966$	40.1543	1.29194
$967$	−10.3688	−0.333438	−0.166719	−	0.986004i	$-0.553317\pi$
$967$	−10.3688	−0.333438	−0.166719	+	0.986004i	$0.553317\pi$
$968$	44.7796	1.43927
$969$	15.4689	0.496933
$970$	0	0
$971$	−2.53081	−0.0812177	−0.0406089	−	0.999175i	$-0.512930\pi$
$971$	−2.53081	−0.0812177	−0.0406089	+	0.999175i	$0.512930\pi$
$972$	64.0149	2.05328
$973$	8.18194	0.262301
$974$	−83.4884	−2.67514
$975$	0	0
$976$	42.0607	1.34633
$977$	−19.0825	−0.610503	−0.305252	−	0.952272i	$-0.598741\pi$
$977$	−19.0825	−0.610503	−0.305252	+	0.952272i	$0.598741\pi$
$978$	−39.4003	−1.25988
$979$	29.6093	0.946319
$980$	0	0
$981$	−9.41747	−0.300677
$982$	−58.0701	−1.85309
$983$	49.4642	1.57766	0.788831	−	0.614610i	$-0.210687\pi$
$983$	49.4642	1.57766	0.788831	+	0.614610i	$0.210687\pi$
$984$	−5.34894	−0.170518
$985$	0	0
$986$	−59.9839	−1.91028
$987$	−15.4803	−0.492742
$988$	108.460	3.45056
$989$	37.5858	1.19516
$990$	0	0
$991$	12.0437	0.382581	0.191290	−	0.981533i	$-0.438733\pi$
$991$	12.0437	0.382581	0.191290	+	0.981533i	$0.438733\pi$
$992$	2.85829	0.0907507
$993$	11.8906	0.377336
$994$	89.6242	2.84271
$995$	0	0
$996$	13.2277	0.419136
$997$	−10.0342	−0.317787	−0.158893	−	0.987296i	$-0.550793\pi$
$997$	−10.0342	−0.317787	−0.158893	+	0.987296i	$0.550793\pi$
$998$	46.4336	1.46983
$999$	−27.1598	−0.859297

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.a.e.1.1		4
3.2	odd	2		6975.2.a.bn.1.4		4
5.2	odd	4		775.2.b.f.249.1		8
5.3	odd	4		775.2.b.f.249.8		8
5.4	even	2		155.2.a.e.1.4	✓	4
15.14	odd	2		1395.2.a.l.1.1		4
20.19	odd	2		2480.2.a.x.1.3		4
35.34	odd	2		7595.2.a.s.1.4		4
40.19	odd	2		9920.2.a.cg.1.2		4
40.29	even	2		9920.2.a.cb.1.3		4
155.154	odd	2		4805.2.a.n.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.a.e.1.4	✓	4	5.4	even	2
775.2.a.e.1.1		4	1.1	even	1	trivial
775.2.b.f.249.1		8	5.2	odd	4
775.2.b.f.249.8		8	5.3	odd	4
1395.2.a.l.1.1		4	15.14	odd	2
2480.2.a.x.1.3		4	20.19	odd	2
4805.2.a.n.1.4		4	155.154	odd	2
6975.2.a.bn.1.4		4	3.2	odd	2
7595.2.a.s.1.4		4	35.34	odd	2
9920.2.a.cb.1.3		4	40.29	even	2
9920.2.a.cg.1.2		4	40.19	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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.a (trivial)

\(f(q)\)	\(=\)	\(q-2.50350 q^{2} +0.704624 q^{3} +4.26753 q^{4} -1.76403 q^{6} +4.77104 q^{7} -5.67678 q^{8} -2.50350 q^{9} +O(q^{10})\)	\(q-2.50350 q^{2} +0.704624 q^{3} +4.26753 q^{4} -1.76403 q^{6} +4.77104 q^{7} -5.67678 q^{8} -2.50350 q^{9} -1.76403 q^{11} +3.00701 q^{12} -5.17328 q^{13} -11.9443 q^{14} +5.67678 q^{16} -4.46865 q^{17} +6.26753 q^{18} -4.91275 q^{19} +3.36179 q^{21} +4.41626 q^{22} -4.77104 q^{23} -4.00000 q^{24} +12.9513 q^{26} -3.87790 q^{27} +20.3606 q^{28} -5.36179 q^{29} -1.00000 q^{31} -2.85829 q^{32} -1.24298 q^{33} +11.1873 q^{34} -10.6838 q^{36} +7.00372 q^{37} +12.2991 q^{38} -3.64522 q^{39} +1.33723 q^{41} -8.41626 q^{42} -7.87790 q^{43} -7.52806 q^{44} +11.9443 q^{46} -4.60477 q^{47} +4.00000 q^{48} +15.7628 q^{49} -3.14872 q^{51} -22.0771 q^{52} +1.52312 q^{53} +9.70835 q^{54} -27.0842 q^{56} -3.46165 q^{57} +13.4233 q^{58} +7.61409 q^{59} +7.40925 q^{61} +2.50350 q^{62} -11.9443 q^{63} -4.19784 q^{64} +3.11180 q^{66} +5.29209 q^{67} -19.0701 q^{68} -3.36179 q^{69} -7.50350 q^{71} +14.2119 q^{72} -0.358066 q^{73} -17.5339 q^{74} -20.9653 q^{76} -8.41626 q^{77} +9.12582 q^{78} -4.39402 q^{79} +4.77805 q^{81} -3.34777 q^{82} +4.39895 q^{83} +14.3466 q^{84} +19.7224 q^{86} -3.77805 q^{87} +10.0140 q^{88} -16.7851 q^{89} -24.6819 q^{91} -20.3606 q^{92} -0.704624 q^{93} +11.5281 q^{94} -2.01402 q^{96} -0.541639 q^{97} -39.4623 q^{98} +4.41626 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{3} + 5 q^{4} - 4 q^{6} - 2 q^{7} - 3 q^{8} - q^{9}+O(q^{10}) \) 4 * q - q^2 - q^3 + 5 * q^4 - 4 * q^6 - 2 * q^7 - 3 * q^8 - q^9	\( 4 q - q^{2} - q^{3} + 5 q^{4} - 4 q^{6} - 2 q^{7} - 3 q^{8} - q^{9} - 4 q^{11} - 6 q^{12} - 10 q^{13} - 16 q^{14} + 3 q^{16} - 11 q^{17} + 13 q^{18} - 3 q^{19} - 8 q^{22} + 2 q^{23} - 16 q^{24} + 2 q^{26} - q^{27} + 24 q^{28} - 8 q^{29} - 4 q^{31} - 7 q^{32} + 10 q^{33} - 2 q^{34} - 5 q^{36} - 3 q^{37} + 22 q^{38} - 10 q^{39} - 11 q^{41} - 8 q^{42} - 17 q^{43} - 24 q^{44} + 16 q^{46} + 10 q^{47} + 16 q^{48} + 16 q^{49} + q^{51} - 22 q^{52} - 13 q^{53} + 4 q^{54} - 24 q^{56} - 25 q^{57} + 10 q^{58} - 3 q^{59} + 22 q^{61} + q^{62} - 16 q^{63} - 9 q^{64} + 32 q^{66} + 12 q^{67} - 28 q^{68} - 21 q^{71} + 13 q^{72} - 19 q^{73} - 2 q^{74} + 2 q^{76} - 8 q^{77} + 20 q^{78} - 2 q^{79} - 20 q^{81} - 36 q^{82} + 15 q^{83} + 36 q^{84} + 8 q^{86} + 24 q^{87} + 4 q^{88} - 10 q^{89} - 4 q^{91} - 24 q^{92} + q^{93} + 40 q^{94} + 28 q^{96} - 4 q^{97} - 37 q^{98} - 8 q^{99}+O(q^{100}) \) 4 * q - q^2 - q^3 + 5 * q^4 - 4 * q^6 - 2 * q^7 - 3 * q^8 - q^9 - 4 * q^11 - 6 * q^12 - 10 * q^13 - 16 * q^14 + 3 * q^16 - 11 * q^17 + 13 * q^18 - 3 * q^19 - 8 * q^22 + 2 * q^23 - 16 * q^24 + 2 * q^26 - q^27 + 24 * q^28 - 8 * q^29 - 4 * q^31 - 7 * q^32 + 10 * q^33 - 2 * q^34 - 5 * q^36 - 3 * q^37 + 22 * q^38 - 10 * q^39 - 11 * q^41 - 8 * q^42 - 17 * q^43 - 24 * q^44 + 16 * q^46 + 10 * q^47 + 16 * q^48 + 16 * q^49 + q^51 - 22 * q^52 - 13 * q^53 + 4 * q^54 - 24 * q^56 - 25 * q^57 + 10 * q^58 - 3 * q^59 + 22 * q^61 + q^62 - 16 * q^63 - 9 * q^64 + 32 * q^66 + 12 * q^67 - 28 * q^68 - 21 * q^71 + 13 * q^72 - 19 * q^73 - 2 * q^74 + 2 * q^76 - 8 * q^77 + 20 * q^78 - 2 * q^79 - 20 * q^81 - 36 * q^82 + 15 * q^83 + 36 * q^84 + 8 * q^86 + 24 * q^87 + 4 * q^88 - 10 * q^89 - 4 * q^91 - 24 * q^92 + q^93 + 40 * q^94 + 28 * q^96 - 4 * q^97 - 37 * q^98 - 8 * q^99

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