LMFDB - Embedded newform 775.2.a.e.1.2

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			1.2
Root			$1.31743$ 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)

$f(q)$	$=$	$q-1.26438 q^{2} -1.31743 q^{3} -0.401352 q^{4} +1.66573 q^{6} -1.13698 q^{7} +3.03621 q^{8} -1.26438 q^{9} +O(q^{10})$	\(q-1.26438 q^{2} -1.31743 q^{3} -0.401352 q^{4} +1.66573 q^{6} -1.13698 q^{7} +3.03621 q^{8} -1.26438 q^{9} +1.66573 q^{11} +0.528753 q^{12} +2.30059 q^{13} +1.43756 q^{14} -3.03621 q^{16} +0.983159 q^{17} +1.59865 q^{18} +0.370485 q^{19} +1.49789 q^{21} -2.10611 q^{22} +1.13698 q^{23} -4.00000 q^{24} -2.90881 q^{26} +5.61802 q^{27} +0.456327 q^{28} -3.49789 q^{29} -1.00000 q^{31} -2.23351 q^{32} -2.19448 q^{33} -1.24308 q^{34} +0.507460 q^{36} -7.78586 q^{37} -0.468432 q^{38} -3.03087 q^{39} +5.09372 q^{41} -1.89389 q^{42} +1.61802 q^{43} -0.668543 q^{44} -1.43756 q^{46} -3.69237 q^{47} +4.00000 q^{48} -5.70729 q^{49} -1.29524 q^{51} -0.923346 q^{52} -8.58715 q^{53} -7.10329 q^{54} -3.45210 q^{56} -0.488088 q^{57} +4.42265 q^{58} -12.0025 q^{59} +3.36514 q^{61} +1.26438 q^{62} +1.43756 q^{63} +8.89642 q^{64} +2.77465 q^{66} -4.99719 q^{67} -0.394593 q^{68} -1.49789 q^{69} -6.26438 q^{71} -3.83892 q^{72} -13.2837 q^{73} +9.84426 q^{74} -0.148695 q^{76} -1.89389 q^{77} +3.83216 q^{78} +12.7339 q^{79} -3.60822 q^{81} -6.44038 q^{82} -9.47823 q^{83} -0.601179 q^{84} -2.04579 q^{86} +4.60822 q^{87} +5.05751 q^{88} -5.92053 q^{89} -2.61571 q^{91} -0.456327 q^{92} +1.31743 q^{93} +4.66854 q^{94} +2.94249 q^{96} -15.8265 q^{97} +7.21616 q^{98} -2.10611 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.26438	−0.894049	−0.447025	−	0.894522i	$-0.647516\pi$
$2$	−1.26438	−0.894049	−0.447025	+	0.894522i	$0.647516\pi$
$3$	−1.31743	−0.760619	−0.380309	−	0.924859i	$-0.624183\pi$
$3$	−1.31743	−0.760619	−0.380309	+	0.924859i	$0.624183\pi$
$4$	−0.401352	−0.200676
$5$	0	0
$5$	0	0
$6$	1.66573	0.680031
$7$	−1.13698	−0.429736	−0.214868	−	0.976643i	$-0.568932\pi$
$7$	−1.13698	−0.429736	−0.214868	+	0.976643i	$0.568932\pi$
$8$	3.03621	1.07346
$9$	−1.26438	−0.421459
$10$	0	0
$11$	1.66573	0.502236	0.251118	−	0.967956i	$-0.419202\pi$
$11$	1.66573	0.502236	0.251118	+	0.967956i	$0.419202\pi$
$12$	0.528753	0.152638
$13$	2.30059	0.638069	0.319034	−	0.947743i	$-0.396641\pi$
$13$	2.30059	0.638069	0.319034	+	0.947743i	$0.396641\pi$
$14$	1.43756	0.384205
$15$	0	0
$16$	−3.03621	−0.759053
$17$	0.983159	0.238451	0.119226	−	0.992867i	$-0.461959\pi$
$17$	0.983159	0.238451	0.119226	+	0.992867i	$0.461959\pi$
$18$	1.59865	0.376805
$19$	0.370485	0.0849950	0.0424975	−	0.999097i	$-0.486469\pi$
$19$	0.370485	0.0849950	0.0424975	+	0.999097i	$0.486469\pi$
$20$	0	0
$21$	1.49789	0.326866
$22$	−2.10611	−0.449024
$23$	1.13698	0.237076	0.118538	−	0.992950i	$-0.462179\pi$
$23$	1.13698	0.237076	0.118538	+	0.992950i	$0.462179\pi$
$24$	−4.00000	−0.816497
$25$	0	0
$26$	−2.90881	−0.570465
$27$	5.61802	1.08119
$28$	0.456327	0.0862377
$29$	−3.49789	−0.649541	−0.324771	−	0.945793i	$-0.605287\pi$
$29$	−3.49789	−0.649541	−0.324771	+	0.945793i	$0.605287\pi$
$30$	0	0
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−2.23351	−0.394832
$33$	−2.19448	−0.382010
$34$	−1.24308	−0.213187
$35$	0	0
$36$	0.507460	0.0845766
$37$	−7.78586	−1.27999	−0.639994	−	0.768380i	$-0.721063\pi$
$37$	−7.78586	−1.27999	−0.639994	+	0.768380i	$0.721063\pi$
$38$	−0.468432	−0.0759897
$39$	−3.03087	−0.485327
$40$	0	0
$41$	5.09372	0.795505	0.397753	−	0.917493i	$-0.369790\pi$
$41$	5.09372	0.795505	0.397753	+	0.917493i	$0.369790\pi$
$42$	−1.89389	−0.292234
$43$	1.61802	0.246746	0.123373	−	0.992360i	$-0.460629\pi$
$43$	1.61802	0.246746	0.123373	+	0.992360i	$0.460629\pi$
$44$	−0.668543	−0.100787
$45$	0	0
$46$	−1.43756	−0.211957
$47$	−3.69237	−0.538587	−0.269294	−	0.963058i	$-0.586790\pi$
$47$	−3.69237	−0.538587	−0.269294	+	0.963058i	$0.586790\pi$
$48$	4.00000	0.577350
$49$	−5.70729	−0.815327
$50$	0	0
$51$	−1.29524	−0.181370
$52$	−0.923346	−0.128045
$53$	−8.58715	−1.17954	−0.589768	−	0.807573i	$-0.700781\pi$
$53$	−8.58715	−1.17954	−0.589768	+	0.807573i	$0.700781\pi$
$54$	−7.10329	−0.966636
$55$	0	0
$56$	−3.45210	−0.461306
$57$	−0.488088	−0.0646488
$58$	4.42265	0.580722
$59$	−12.0025	−1.56260	−0.781298	−	0.624158i	$-0.785442\pi$
$59$	−12.0025	−1.56260	−0.781298	+	0.624158i	$0.785442\pi$
$60$	0	0
$61$	3.36514	0.430862	0.215431	−	0.976519i	$-0.430884\pi$
$61$	3.36514	0.430862	0.215431	+	0.976519i	$0.430884\pi$
$62$	1.26438	0.160576
$63$	1.43756	0.181116
$64$	8.89642	1.11205
$65$	0	0
$66$	2.77465	0.341536
$67$	−4.99719	−0.610503	−0.305252	−	0.952272i	$-0.598741\pi$
$67$	−4.99719	−0.610503	−0.305252	+	0.952272i	$0.598741\pi$
$68$	−0.394593	−0.0478514
$69$	−1.49789	−0.180324
$70$	0	0
$71$	−6.26438	−0.743445	−0.371722	−	0.928344i	$-0.621233\pi$
$71$	−6.26438	−0.743445	−0.371722	+	0.928344i	$0.621233\pi$
$72$	−3.83892	−0.452421
$73$	−13.2837	−1.55475	−0.777373	−	0.629040i	$-0.783448\pi$
$73$	−13.2837	−1.55475	−0.777373	+	0.629040i	$0.783448\pi$
$74$	9.84426	1.14437
$75$	0	0
$76$	−0.148695	−0.0170564
$77$	−1.89389	−0.215829
$78$	3.83216	0.433906
$79$	12.7339	1.43268	0.716339	−	0.697752i	$-0.245816\pi$
$79$	12.7339	1.43268	0.716339	+	0.697752i	$0.245816\pi$
$80$	0	0
$81$	−3.60822	−0.400914
$82$	−6.44038	−0.711221
$83$	−9.47823	−1.04037	−0.520185	−	0.854053i	$-0.674137\pi$
$83$	−9.47823	−1.04037	−0.520185	+	0.854053i	$0.674137\pi$
$84$	−0.601179	−0.0655940
$85$	0	0
$86$	−2.04579	−0.220603
$87$	4.60822	0.494053
$88$	5.05751	0.539132
$89$	−5.92053	−0.627575	−0.313788	−	0.949493i	$-0.601598\pi$
$89$	−5.92053	−0.627575	−0.313788	+	0.949493i	$0.601598\pi$
$90$	0	0
$91$	−2.61571	−0.274201
$92$	−0.456327	−0.0475754
$93$	1.31743	0.136611
$94$	4.66854	0.481523
$95$	0	0
$96$	2.94249	0.300317
$97$	−15.8265	−1.60694	−0.803470	−	0.595345i	$-0.797015\pi$
$97$	−15.8265	−1.60694	−0.803470	+	0.595345i	$0.797015\pi$
$98$	7.21616	0.728942
$99$	−2.10611	−0.211672
$100$	0	0
$101$	−16.7258	−1.66428	−0.832138	−	0.554569i	$-0.812883\pi$
$101$	−16.7258	−1.66428	−0.832138	+	0.554569i	$0.812883\pi$
$102$	1.63768	0.162154
$103$	1.43756	0.141647	0.0708237	−	0.997489i	$-0.477437\pi$
$103$	1.43756	0.141647	0.0708237	+	0.997489i	$0.477437\pi$
$104$	6.98508	0.684943
$105$	0	0
$106$	10.8574	1.05456
$107$	16.0281	1.54949	0.774745	−	0.632274i	$-0.217878\pi$
$107$	16.0281	1.54949	0.774745	+	0.632274i	$0.217878\pi$
$108$	−2.25480	−0.216968
$109$	16.5579	1.58596	0.792981	−	0.609247i	$-0.208528\pi$
$109$	16.5579	1.58596	0.792981	+	0.609247i	$0.208528\pi$
$110$	0	0
$111$	10.2573	0.973583
$112$	3.45210	0.326193
$113$	−2.77606	−0.261150	−0.130575	−	0.991438i	$-0.541682\pi$
$113$	−2.77606	−0.261150	−0.130575	+	0.991438i	$0.541682\pi$
$114$	0.617127	0.0577992
$115$	0	0
$116$	1.40388	0.130347
$117$	−2.90881	−0.268920
$118$	15.1757	1.39704
$119$	−1.11783	−0.102471
$120$	0	0
$121$	−8.22535	−0.747759
$122$	−4.25480	−0.385212
$123$	−6.71062	−0.605076
$124$	0.401352	0.0360425
$125$	0	0
$126$	−1.81762	−0.161927
$127$	13.9060	1.23396	0.616979	−	0.786980i	$-0.288356\pi$
$127$	13.9060	1.23396	0.616979	+	0.786980i	$0.288356\pi$
$128$	−6.78141	−0.599398
$129$	−2.13163	−0.187680
$130$	0	0
$131$	−14.3368	−1.25261	−0.626306	−	0.779577i	$-0.715434\pi$
$131$	−14.3368	−1.25261	−0.626306	+	0.779577i	$0.715434\pi$
$132$	0.880759	0.0766602
$133$	−0.421232	−0.0365254
$134$	6.31832	0.545820
$135$	0	0
$136$	2.98508	0.255969
$137$	11.8742	1.01448	0.507242	−	0.861804i	$-0.330665\pi$
$137$	11.8742	1.01448	0.507242	+	0.861804i	$0.330665\pi$
$138$	1.89389	0.161219
$139$	9.52594	0.807980	0.403990	−	0.914763i	$-0.367623\pi$
$139$	9.52594	0.807980	0.403990	+	0.914763i	$0.367623\pi$
$140$	0	0
$141$	4.86444	0.409660
$142$	7.92053	0.664676
$143$	3.83216	0.320461
$144$	3.83892	0.319910
$145$	0	0
$146$	16.7957	1.39002
$147$	7.51895	0.620153
$148$	3.12487	0.256863
$149$	−7.46309	−0.611400	−0.305700	−	0.952128i	$-0.598890\pi$
$149$	−7.46309	−0.611400	−0.305700	+	0.952128i	$0.598890\pi$
$150$	0	0
$151$	−10.5745	−0.860544	−0.430272	−	0.902699i	$-0.641582\pi$
$151$	−10.5745	−0.860544	−0.430272	+	0.902699i	$0.641582\pi$
$152$	1.12487	0.0912390
$153$	−1.24308	−0.100497
$154$	2.39459	0.192962
$155$	0	0
$156$	1.21644	0.0973935
$157$	12.4348	0.992401	0.496201	−	0.868208i	$-0.334728\pi$
$157$	12.4348	0.992401	0.496201	+	0.868208i	$0.334728\pi$
$158$	−16.1005	−1.28089
$159$	11.3130	0.897178
$160$	0	0
$161$	−1.29271	−0.101880
$162$	4.56215	0.358436
$163$	15.2169	1.19188	0.595940	−	0.803029i	$-0.296780\pi$
$163$	15.2169	1.19188	0.595940	+	0.803029i	$0.296780\pi$
$164$	−2.04437	−0.159639
$165$	0	0
$166$	11.9841	0.930143
$167$	12.4016	0.959663	0.479831	−	0.877361i	$-0.340698\pi$
$167$	12.4016	0.959663	0.479831	+	0.877361i	$0.340698\pi$
$168$	4.54790	0.350878
$169$	−7.70729	−0.592868
$170$	0	0
$171$	−0.468432	−0.0358219
$172$	−0.649395	−0.0495159
$173$	−20.6470	−1.56976	−0.784880	−	0.619648i	$-0.787275\pi$
$173$	−20.6470	−1.56976	−0.784880	+	0.619648i	$0.787275\pi$
$174$	−5.82653	−0.441708
$175$	0	0
$176$	−5.05751	−0.381224
$177$	15.8125	1.18854
$178$	7.48578	0.561083
$179$	−23.0359	−1.72179	−0.860893	−	0.508786i	$-0.830094\pi$
$179$	−23.0359	−1.72179	−0.860893	+	0.508786i	$0.830094\pi$
$180$	0	0
$181$	16.1594	1.20112	0.600559	−	0.799581i	$-0.294945\pi$
$181$	16.1594	1.20112	0.600559	+	0.799581i	$0.294945\pi$
$182$	3.30725	0.245149
$183$	−4.43334	−0.327722
$184$	3.45210	0.254492
$185$	0	0
$186$	−1.66573	−0.122137
$187$	1.63768	0.119759
$188$	1.48194	0.108081
$189$	−6.38755	−0.464626
$190$	0	0
$191$	−15.4291	−1.11641	−0.558206	−	0.829703i	$-0.688510\pi$
$191$	−15.4291	−1.11641	−0.558206	+	0.829703i	$0.688510\pi$
$192$	−11.7204	−0.845848
$193$	6.93686	0.499326	0.249663	−	0.968333i	$-0.419680\pi$
$193$	6.93686	0.499326	0.249663	+	0.968333i	$0.419680\pi$
$194$	20.0107	1.43668
$195$	0	0
$196$	2.29063	0.163616
$197$	−18.3539	−1.30766	−0.653829	−	0.756642i	$-0.726839\pi$
$197$	−18.3539	−1.30766	−0.653829	+	0.756642i	$0.726839\pi$
$198$	2.66291	0.189245
$199$	7.10329	0.503539	0.251770	−	0.967787i	$-0.418987\pi$
$199$	7.10329	0.503539	0.251770	+	0.967787i	$0.418987\pi$
$200$	0	0
$201$	6.58344	0.464360
$202$	21.1477	1.48794
$203$	3.97701	0.279131
$204$	0.519848	0.0363967
$205$	0	0
$206$	−1.81762	−0.126640
$207$	−1.43756	−0.0999177
$208$	−6.98508	−0.484328
$209$	0.617127	0.0426876
$210$	0	0
$211$	−3.16361	−0.217792	−0.108896	−	0.994053i	$-0.534732\pi$
$211$	−3.16361	−0.217792	−0.108896	+	0.994053i	$0.534732\pi$
$212$	3.44647	0.236705
$213$	8.25288	0.565478
$214$	−20.2655	−1.38532
$215$	0	0
$216$	17.0575	1.16062
$217$	1.13698	0.0771829
$218$	−20.9355	−1.41793
$219$	17.5004	1.18257
$220$	0	0
$221$	2.26185	0.152148
$222$	−12.9691	−0.870431
$223$	−12.1454	−0.813313	−0.406657	−	0.913581i	$-0.633305\pi$
$223$	−12.1454	−0.813313	−0.406657	+	0.913581i	$0.633305\pi$
$224$	2.53944	0.169674
$225$	0	0
$226$	3.50999	0.233481
$227$	11.8251	0.784860	0.392430	−	0.919782i	$-0.371634\pi$
$227$	11.8251	0.784860	0.392430	+	0.919782i	$0.371634\pi$
$228$	0.195895	0.0129735
$229$	11.4446	0.756281	0.378140	−	0.925748i	$-0.376564\pi$
$229$	11.4446	0.756281	0.378140	+	0.925748i	$0.376564\pi$
$230$	0	0
$231$	2.49507	0.164164
$232$	−10.6203	−0.697259
$233$	0.935451	0.0612834	0.0306417	−	0.999530i	$-0.490245\pi$
$233$	0.935451	0.0612834	0.0306417	+	0.999530i	$0.490245\pi$
$234$	3.67783	0.240427
$235$	0	0
$236$	4.81724	0.313575
$237$	−16.7761	−1.08972
$238$	1.41335	0.0916142
$239$	17.6778	1.14348	0.571742	−	0.820433i	$-0.306268\pi$
$239$	17.6778	1.14348	0.571742	+	0.820433i	$0.306268\pi$
$240$	0	0
$241$	12.3393	0.794846	0.397423	−	0.917635i	$-0.369905\pi$
$241$	12.3393	0.794846	0.397423	+	0.917635i	$0.369905\pi$
$242$	10.3999	0.668533
$243$	−12.1005	−0.776246
$244$	−1.35060	−0.0864636
$245$	0	0
$246$	8.48475	0.540968
$247$	0.852333	0.0542327
$248$	−3.03621	−0.192800
$249$	12.4869	0.791326
$250$	0	0
$251$	18.7886	1.18593	0.592964	−	0.805229i	$-0.297958\pi$
$251$	18.7886	1.18593	0.592964	+	0.805229i	$0.297958\pi$
$252$	−0.576969	−0.0363456
$253$	1.89389	0.119068
$254$	−17.5824	−1.10322
$255$	0	0
$256$	−9.21859	−0.576162
$257$	−5.17572	−0.322853	−0.161426	−	0.986885i	$-0.551609\pi$
$257$	−5.17572	−0.322853	−0.161426	+	0.986885i	$0.551609\pi$
$258$	2.69518	0.167795
$259$	8.85233	0.550057
$260$	0	0
$261$	4.42265	0.273755
$262$	18.1271	1.11990
$263$	−5.81813	−0.358761	−0.179381	−	0.983780i	$-0.557409\pi$
$263$	−5.81813	−0.358761	−0.179381	+	0.983780i	$0.557409\pi$
$264$	−6.66291	−0.410074
$265$	0	0
$266$	0.532596	0.0326555
$267$	7.79989	0.477345
$268$	2.00563	0.122513
$269$	−18.2052	−1.10999	−0.554995	−	0.831854i	$-0.687280\pi$
$269$	−18.2052	−1.10999	−0.554995	+	0.831854i	$0.687280\pi$
$270$	0	0
$271$	−10.8400	−0.658485	−0.329243	−	0.944245i	$-0.606793\pi$
$271$	−10.8400	−0.658485	−0.329243	+	0.944245i	$0.606793\pi$
$272$	−2.98508	−0.180997
$273$	3.44602	0.208563
$274$	−15.0135	−0.906999
$275$	0	0
$276$	0.601179	0.0361867
$277$	−21.2113	−1.27446	−0.637232	−	0.770672i	$-0.719921\pi$
$277$	−21.2113	−1.27446	−0.637232	+	0.770672i	$0.719921\pi$
$278$	−12.0444	−0.722374
$279$	1.26438	0.0756962
$280$	0	0
$281$	−12.2200	−0.728984	−0.364492	−	0.931206i	$-0.618757\pi$
$281$	−12.2200	−0.728984	−0.364492	+	0.931206i	$0.618757\pi$
$282$	−6.15048	−0.366256
$283$	−1.36514	−0.0811491	−0.0405745	−	0.999177i	$-0.512919\pi$
$283$	−1.36514	−0.0811491	−0.0405745	+	0.999177i	$0.512919\pi$
$284$	2.51422	0.149191
$285$	0	0
$286$	−4.84529	−0.286508
$287$	−5.79143	−0.341857
$288$	2.82400	0.166406
$289$	−16.0334	−0.943141
$290$	0	0
$291$	20.8504	1.22227
$292$	5.33146	0.312000
$293$	−11.5703	−0.675945	−0.337972	−	0.941156i	$-0.609741\pi$
$293$	−11.5703	−0.675945	−0.337972	+	0.941156i	$0.609741\pi$
$294$	−9.50679	−0.554447
$295$	0	0
$296$	−23.6395	−1.37402
$297$	9.35810	0.543012
$298$	9.43615	0.546622
$299$	2.61571	0.151271
$300$	0	0
$301$	−1.83965	−0.106036
$302$	13.3702	0.769369
$303$	22.0350	1.26588
$304$	−1.12487	−0.0645157
$305$	0	0
$306$	1.57173	0.0898496
$307$	13.2818	0.758034	0.379017	−	0.925390i	$-0.376262\pi$
$307$	13.2818	0.758034	0.379017	+	0.925390i	$0.376262\pi$
$308$	0.760117	0.0433117
$309$	−1.89389	−0.107740
$310$	0	0
$311$	4.44995	0.252334	0.126167	−	0.992009i	$-0.459733\pi$
$311$	4.44995	0.252334	0.126167	+	0.992009i	$0.459733\pi$
$312$	−9.20236	−0.520981
$313$	1.13890	0.0643742	0.0321871	−	0.999482i	$-0.489753\pi$
$313$	1.13890	0.0643742	0.0321871	+	0.999482i	$0.489753\pi$
$314$	−15.7222	−0.887255
$315$	0	0
$316$	−5.11078	−0.287504
$317$	−22.0813	−1.24021	−0.620106	−	0.784518i	$-0.712910\pi$
$317$	−22.0813	−1.24021	−0.620106	+	0.784518i	$0.712910\pi$
$318$	−14.3039	−0.802121
$319$	−5.82653	−0.326223
$320$	0	0
$321$	−21.1158	−1.17857
$322$	1.63448	0.0910858
$323$	0.364245	0.0202672
$324$	1.44817	0.0804537
$325$	0	0
$326$	−19.2399	−1.06560
$327$	−21.8139	−1.20631
$328$	15.4656	0.853946
$329$	4.19813	0.231450
$330$	0	0
$331$	−32.0331	−1.76070	−0.880350	−	0.474325i	$-0.842692\pi$
$331$	−32.0331	−1.76070	−0.880350	+	0.474325i	$0.842692\pi$
$332$	3.80411	0.208777
$333$	9.84426	0.539462
$334$	−15.6803	−0.857986
$335$	0	0
$336$	−4.54790	−0.248108
$337$	3.63717	0.198129	0.0990646	−	0.995081i	$-0.468415\pi$
$337$	3.63717	0.198129	0.0990646	+	0.995081i	$0.468415\pi$
$338$	9.74491	0.530053
$339$	3.65727	0.198636
$340$	0	0
$341$	−1.66573	−0.0902043
$342$	0.592275	0.0320265
$343$	14.4479	0.780112
$344$	4.91265	0.264873
$345$	0	0
$346$	26.1055	1.40344
$347$	−6.65081	−0.357034	−0.178517	−	0.983937i	$-0.557130\pi$
$347$	−6.65081	−0.357034	−0.178517	+	0.983937i	$0.557130\pi$
$348$	−1.84952	−0.0991446
$349$	13.8880	0.743406	0.371703	−	0.928352i	$-0.378774\pi$
$349$	13.8880	0.743406	0.371703	+	0.928352i	$0.378774\pi$
$350$	0	0
$351$	12.9248	0.689873
$352$	−3.72042	−0.198299
$353$	−0.818651	−0.0435724	−0.0217862	−	0.999763i	$-0.506935\pi$
$353$	−0.818651	−0.0435724	−0.0217862	+	0.999763i	$0.506935\pi$
$354$	−19.9930	−1.06261
$355$	0	0
$356$	2.37622	0.125939
$357$	1.47266	0.0779414
$358$	29.1261	1.53936
$359$	18.3805	0.970086	0.485043	−	0.874490i	$-0.338804\pi$
$359$	18.3805	0.970086	0.485043	+	0.874490i	$0.338804\pi$
$360$	0	0
$361$	−18.8627	−0.992776
$362$	−20.4315	−1.07386
$363$	10.8363	0.568760
$364$	1.04982	0.0550256
$365$	0	0
$366$	5.60541	0.292999
$367$	−26.7480	−1.39623	−0.698116	−	0.715985i	$-0.745978\pi$
$367$	−26.7480	−1.39623	−0.698116	+	0.715985i	$0.745978\pi$
$368$	−3.45210	−0.179953
$369$	−6.44038	−0.335273
$370$	0	0
$371$	9.76338	0.506889
$372$	−0.528753	−0.0274146
$373$	−3.90600	−0.202245	−0.101122	−	0.994874i	$-0.532243\pi$
$373$	−3.90600	−0.202245	−0.101122	+	0.994874i	$0.532243\pi$
$374$	−2.07064	−0.107070
$375$	0	0
$376$	−11.2108	−0.578154
$377$	−8.04720	−0.414452
$378$	8.07627	0.415398
$379$	17.3536	0.891394	0.445697	−	0.895184i	$-0.352956\pi$
$379$	17.3536	0.891394	0.445697	+	0.895184i	$0.352956\pi$
$380$	0	0
$381$	−18.3202	−0.938572
$382$	19.5082	0.998127
$383$	−31.6283	−1.61613	−0.808066	−	0.589092i	$-0.799486\pi$
$383$	−31.6283	−1.61613	−0.808066	+	0.589092i	$0.799486\pi$
$384$	8.93404	0.455913
$385$	0	0
$386$	−8.77081	−0.446422
$387$	−2.04579	−0.103993
$388$	6.35201	0.322474
$389$	−19.3169	−0.979407	−0.489703	−	0.871889i	$-0.662895\pi$
$389$	−19.3169	−0.979407	−0.489703	+	0.871889i	$0.662895\pi$
$390$	0	0
$391$	1.11783	0.0565310
$392$	−17.3285	−0.875223
$393$	18.8877	0.952761
$394$	23.2062	1.16911
$395$	0	0
$396$	0.845290	0.0424774
$397$	−28.9284	−1.45188	−0.725938	−	0.687761i	$-0.758594\pi$
$397$	−28.9284	−1.45188	−0.725938	+	0.687761i	$0.758594\pi$
$398$	−8.98124	−0.450189
$399$	0.554944	0.0277819
$400$	0	0
$401$	−19.5703	−0.977295	−0.488647	−	0.872481i	$-0.662510\pi$
$401$	−19.5703	−0.977295	−0.488647	+	0.872481i	$0.662510\pi$
$402$	−8.32395	−0.415161
$403$	−2.30059	−0.114601
$404$	6.71292	0.333980
$405$	0	0
$406$	−5.02844	−0.249557
$407$	−12.9691	−0.642856
$408$	−3.93264	−0.194694
$409$	−7.33895	−0.362888	−0.181444	−	0.983401i	$-0.558077\pi$
$409$	−7.33895	−0.362888	−0.181444	+	0.983401i	$0.558077\pi$
$410$	0	0
$411$	−15.6435	−0.771636
$412$	−0.576969	−0.0284252
$413$	13.6466	0.671504
$414$	1.81762	0.0893313
$415$	0	0
$416$	−5.13839	−0.251930
$417$	−12.5498	−0.614565
$418$	−0.780281	−0.0381648
$419$	34.5650	1.68861	0.844305	−	0.535864i	$-0.180014\pi$
$419$	34.5650	1.68861	0.844305	+	0.535864i	$0.180014\pi$
$420$	0	0
$421$	24.5420	1.19610	0.598051	−	0.801458i	$-0.295942\pi$
$421$	24.5420	1.19610	0.598051	+	0.801458i	$0.295942\pi$
$422$	4.00000	0.194717
$423$	4.66854	0.226992
$424$	−26.0724	−1.26619
$425$	0	0
$426$	−10.4348	−0.505565
$427$	−3.82608	−0.185157
$428$	−6.43289	−0.310945
$429$	−5.04860	−0.243749
$430$	0	0
$431$	7.54300	0.363334	0.181667	−	0.983360i	$-0.441851\pi$
$431$	7.54300	0.363334	0.181667	+	0.983360i	$0.441851\pi$
$432$	−17.0575	−0.820680
$433$	23.3581	1.12252	0.561259	−	0.827640i	$-0.310317\pi$
$433$	23.3581	1.12252	0.561259	+	0.827640i	$0.310317\pi$
$434$	−1.43756	−0.0690053
$435$	0	0
$436$	−6.64555	−0.318264
$437$	0.421232	0.0201503
$438$	−22.1271	−1.05727
$439$	−13.7921	−0.658261	−0.329131	−	0.944284i	$-0.606756\pi$
$439$	−13.7921	−0.658261	−0.329131	+	0.944284i	$0.606756\pi$
$440$	0	0
$441$	7.21616	0.343627
$442$	−2.85982	−0.136028
$443$	−8.11680	−0.385641	−0.192820	−	0.981234i	$-0.561763\pi$
$443$	−8.11680	−0.385641	−0.192820	+	0.981234i	$0.561763\pi$
$444$	−4.11680	−0.195375
$445$	0	0
$446$	15.3563	0.727142
$447$	9.83210	0.465042
$448$	−10.1150	−0.477889
$449$	−38.7460	−1.82854	−0.914269	−	0.405107i	$-0.867234\pi$
$449$	−38.7460	−1.82854	−0.914269	+	0.405107i	$0.867234\pi$
$450$	0	0
$451$	8.48475	0.399531
$452$	1.11418	0.0524066
$453$	13.9312	0.654546
$454$	−14.9514	−0.701704
$455$	0	0
$456$	−1.48194	−0.0693981
$457$	2.35387	0.110109	0.0550546	−	0.998483i	$-0.482467\pi$
$457$	2.35387	0.110109	0.0550546	+	0.998483i	$0.482467\pi$
$458$	−14.4703	−0.676152
$459$	5.52341	0.257811
$460$	0	0
$461$	27.1140	1.26282	0.631412	−	0.775447i	$-0.282476\pi$
$461$	27.1140	1.26282	0.631412	+	0.775447i	$0.282476\pi$
$462$	−3.15471	−0.146770
$463$	2.19448	0.101986	0.0509931	−	0.998699i	$-0.483761\pi$
$463$	2.19448	0.101986	0.0509931	+	0.998699i	$0.483761\pi$
$464$	10.6203	0.493036
$465$	0	0
$466$	−1.18276	−0.0547904
$467$	34.9143	1.61564	0.807821	−	0.589428i	$-0.200647\pi$
$467$	34.9143	1.61564	0.807821	+	0.589428i	$0.200647\pi$
$468$	1.16746	0.0539657
$469$	5.68168	0.262355
$470$	0	0
$471$	−16.3819	−0.754839
$472$	−36.4422	−1.67739
$473$	2.69518	0.123925
$474$	21.2113	0.974266
$475$	0	0
$476$	0.448642	0.0205635
$477$	10.8574	0.497126
$478$	−22.3514	−1.02233
$479$	−7.88544	−0.360295	−0.180147	−	0.983640i	$-0.557657\pi$
$479$	−7.88544	−0.360295	−0.180147	+	0.983640i	$0.557657\pi$
$480$	0	0
$481$	−17.9121	−0.816720
$482$	−15.6016	−0.710632
$483$	1.70306	0.0774919
$484$	3.30126	0.150057
$485$	0	0
$486$	15.2996	0.694002
$487$	12.6719	0.574218	0.287109	−	0.957898i	$-0.407306\pi$
$487$	12.6719	0.574218	0.287109	+	0.957898i	$0.407306\pi$
$488$	10.2173	0.462514
$489$	−20.0472	−0.906566
$490$	0	0
$491$	26.3272	1.18813	0.594066	−	0.804417i	$-0.297522\pi$
$491$	26.3272	1.18813	0.594066	+	0.804417i	$0.297522\pi$
$492$	2.69332	0.121424
$493$	−3.43898	−0.154884
$494$	−1.07767	−0.0484867
$495$	0	0
$496$	3.03621	0.136330
$497$	7.12244	0.319485
$498$	−15.7882	−0.707484
$499$	−13.3137	−0.596004	−0.298002	−	0.954565i	$-0.596320\pi$
$499$	−13.3137	−0.596004	−0.298002	+	0.954565i	$0.596320\pi$
$500$	0	0
$501$	−16.3382	−0.729938
$502$	−23.7559	−1.06028
$503$	24.0845	1.07388	0.536938	−	0.843622i	$-0.319581\pi$
$503$	24.0845	1.07388	0.536938	+	0.843622i	$0.319581\pi$
$504$	4.36475	0.194422
$505$	0	0
$506$	−2.39459	−0.106453
$507$	10.1538	0.450947
$508$	−5.58120	−0.247626
$509$	−21.0008	−0.930846	−0.465423	−	0.885088i	$-0.654098\pi$
$509$	−21.0008	−0.930846	−0.465423	+	0.885088i	$0.654098\pi$
$510$	0	0
$511$	15.1033	0.668130
$512$	25.2186	1.11451
$513$	2.08139	0.0918956
$514$	6.54406	0.288646
$515$	0	0
$516$	0.855533	0.0376628
$517$	−6.15048	−0.270498
$518$	−11.1927	−0.491778
$519$	27.2009	1.19399
$520$	0	0
$521$	−13.8609	−0.607256	−0.303628	−	0.952791i	$-0.598198\pi$
$521$	−13.8609	−0.607256	−0.303628	+	0.952791i	$0.598198\pi$
$522$	−5.59189	−0.244750
$523$	−31.7100	−1.38658	−0.693292	−	0.720657i	$-0.743840\pi$
$523$	−31.7100	−1.38658	−0.693292	+	0.720657i	$0.743840\pi$
$524$	5.75410	0.251369
$525$	0	0
$526$	7.35631	0.320750
$527$	−0.983159	−0.0428271
$528$	6.66291	0.289966
$529$	−21.7073	−0.943795
$530$	0	0
$531$	15.1757	0.658570
$532$	0.169062	0.00732977
$533$	11.7186	0.507587
$534$	−9.86200	−0.426770
$535$	0	0
$536$	−15.1725	−0.655353
$537$	30.3482	1.30962
$538$	23.0182	0.992385
$539$	−9.50679	−0.409486
$540$	0	0
$541$	34.1981	1.47029	0.735146	−	0.677909i	$-0.237113\pi$
$541$	34.1981	1.47029	0.735146	+	0.677909i	$0.237113\pi$
$542$	13.7059	0.588718
$543$	−21.2889	−0.913593
$544$	−2.19589	−0.0941482
$545$	0	0
$546$	−4.35707	−0.186465
$547$	−23.2379	−0.993581	−0.496790	−	0.867871i	$-0.665488\pi$
$547$	−23.2379	−0.993581	−0.496790	+	0.867871i	$0.665488\pi$
$548$	−4.76575	−0.203583
$549$	−4.25480	−0.181591
$550$	0	0
$551$	−1.29591	−0.0552077
$552$	−4.54790	−0.193572
$553$	−14.4782	−0.615674
$554$	26.8191	1.13943
$555$	0	0
$556$	−3.82325	−0.162142
$557$	43.9896	1.86390	0.931949	−	0.362590i	$-0.118107\pi$
$557$	43.9896	1.86390	0.931949	+	0.362590i	$0.118107\pi$
$558$	−1.59865	−0.0676762
$559$	3.72240	0.157441
$560$	0	0
$561$	−2.15752	−0.0910908
$562$	15.4507	0.651748
$563$	26.2225	1.10515	0.552574	−	0.833464i	$-0.313646\pi$
$563$	26.2225	1.10515	0.552574	+	0.833464i	$0.313646\pi$
$564$	−1.95235	−0.0822088
$565$	0	0
$566$	1.72605	0.0725513
$567$	4.10246	0.172287
$568$	−19.0200	−0.798061
$569$	34.3710	1.44091	0.720454	−	0.693502i	$-0.243933\pi$
$569$	34.3710	1.44091	0.720454	+	0.693502i	$0.243933\pi$
$570$	0	0
$571$	41.2145	1.72477	0.862386	−	0.506252i	$-0.168969\pi$
$571$	41.2145	1.72477	0.862386	+	0.506252i	$0.168969\pi$
$572$	−1.53804	−0.0643088
$573$	20.3268	0.849163
$574$	7.32255	0.305637
$575$	0	0
$576$	−11.2484	−0.468685
$577$	24.3393	1.01326	0.506630	−	0.862164i	$-0.330891\pi$
$577$	24.3393	1.01326	0.506630	+	0.862164i	$0.330891\pi$
$578$	20.2723	0.843215
$579$	−9.13884	−0.379797
$580$	0	0
$581$	10.7765	0.447085
$582$	−26.3627	−1.09277
$583$	−14.3039	−0.592406
$584$	−40.3323	−1.66896
$585$	0	0
$586$	14.6292	0.604328
$587$	−31.3968	−1.29589	−0.647943	−	0.761689i	$-0.724371\pi$
$587$	−31.3968	−1.29589	−0.647943	+	0.761689i	$0.724371\pi$
$588$	−3.01775	−0.124450
$589$	−0.370485	−0.0152656
$590$	0	0
$591$	24.1799	0.994630
$592$	23.6395	0.971579
$593$	−11.3421	−0.465766	−0.232883	−	0.972505i	$-0.574816\pi$
$593$	−11.3421	−0.465766	−0.232883	+	0.972505i	$0.574816\pi$
$594$	−11.8322	−0.485479
$595$	0	0
$596$	2.99532	0.122693
$597$	−9.35810	−0.383001
$598$	−3.30725	−0.135243
$599$	−8.94294	−0.365399	−0.182699	−	0.983169i	$-0.558483\pi$
$599$	−8.94294	−0.365399	−0.182699	+	0.983169i	$0.558483\pi$
$600$	0	0
$601$	23.3670	0.953160	0.476580	−	0.879131i	$-0.341876\pi$
$601$	23.3670	0.953160	0.476580	+	0.879131i	$0.341876\pi$
$602$	2.32601	0.0948011
$603$	6.31832	0.257302
$604$	4.24411	0.172690
$605$	0	0
$606$	−27.8606	−1.13176
$607$	46.6329	1.89277	0.946385	−	0.323041i	$-0.104705\pi$
$607$	46.6329	1.89277	0.946385	+	0.323041i	$0.104705\pi$
$608$	−0.827481	−0.0335588
$609$	−5.23943	−0.212313
$610$	0	0
$611$	−8.49462	−0.343656
$612$	0.498914	0.0201674
$613$	15.0028	0.605956	0.302978	−	0.952998i	$-0.402019\pi$
$613$	15.0028	0.605956	0.302978	+	0.952998i	$0.402019\pi$
$614$	−16.7932	−0.677720
$615$	0	0
$616$	−5.75026	−0.231685
$617$	−25.9256	−1.04373	−0.521863	−	0.853030i	$-0.674763\pi$
$617$	−25.9256	−1.04373	−0.521863	+	0.853030i	$0.674763\pi$
$618$	2.39459	0.0963246
$619$	−18.5483	−0.745521	−0.372761	−	0.927928i	$-0.621589\pi$
$619$	−18.5483	−0.745521	−0.372761	+	0.927928i	$0.621589\pi$
$620$	0	0
$621$	6.38755	0.256324
$622$	−5.62642	−0.225599
$623$	6.73150	0.269692
$624$	9.20236	0.368389
$625$	0	0
$626$	−1.43999	−0.0575537
$627$	−0.813022	−0.0324690
$628$	−4.99071	−0.199151
$629$	−7.65474	−0.305215
$630$	0	0
$631$	−38.6488	−1.53859	−0.769293	−	0.638896i	$-0.779391\pi$
$631$	−38.6488	−1.53859	−0.769293	+	0.638896i	$0.779391\pi$
$632$	38.6629	1.53793
$633$	4.16784	0.165657
$634$	27.9191	1.10881
$635$	0	0
$636$	−4.54048	−0.180042
$637$	−13.1301	−0.520235
$638$	7.36693	0.291659
$639$	7.92053	0.313331
$640$	0	0
$641$	−24.5764	−0.970710	−0.485355	−	0.874317i	$-0.661310\pi$
$641$	−24.5764	−0.970710	−0.485355	+	0.874317i	$0.661310\pi$
$642$	26.6984	1.05370
$643$	1.85829	0.0732838	0.0366419	−	0.999328i	$-0.488334\pi$
$643$	1.85829	0.0732838	0.0366419	+	0.999328i	$0.488334\pi$
$644$	0.518833	0.0204449
$645$	0	0
$646$	−0.460543	−0.0181198
$647$	21.0219	0.826456	0.413228	−	0.910628i	$-0.364401\pi$
$647$	21.0219	0.826456	0.413228	+	0.910628i	$0.364401\pi$
$648$	−10.9553	−0.430366
$649$	−19.9930	−0.784792
$650$	0	0
$651$	−1.49789	−0.0587068
$652$	−6.10733	−0.239181
$653$	37.0327	1.44920	0.724601	−	0.689168i	$-0.242024\pi$
$653$	37.0327	1.44920	0.724601	+	0.689168i	$0.242024\pi$
$654$	27.5810	1.07850
$655$	0	0
$656$	−15.4656	−0.603831
$657$	16.7957	0.655261
$658$	−5.30802	−0.206928
$659$	31.4696	1.22588	0.612940	−	0.790129i	$-0.289987\pi$
$659$	31.4696	1.22588	0.612940	+	0.790129i	$0.289987\pi$
$660$	0	0
$661$	37.3078	1.45111	0.725553	−	0.688167i	$-0.241584\pi$
$661$	37.3078	1.45111	0.725553	+	0.688167i	$0.241584\pi$
$662$	40.5019	1.57415
$663$	−2.97982	−0.115727
$664$	−28.7779	−1.11680
$665$	0	0
$666$	−12.4469	−0.482306
$667$	−3.97701	−0.153990
$668$	−4.97740	−0.192581
$669$	16.0007	0.618622
$670$	0	0
$671$	5.60541	0.216394
$672$	−3.34554	−0.129057
$673$	−2.36745	−0.0912583	−0.0456292	−	0.998958i	$-0.514529\pi$
$673$	−2.36745	−0.0912583	−0.0456292	+	0.998958i	$0.514529\pi$
$674$	−4.59875	−0.177137
$675$	0	0
$676$	3.09333	0.118974
$677$	−11.1566	−0.428784	−0.214392	−	0.976748i	$-0.568777\pi$
$677$	−11.1566	−0.428784	−0.214392	+	0.976748i	$0.568777\pi$
$678$	−4.62417	−0.177590
$679$	17.9944	0.690561
$680$	0	0
$681$	−15.5788	−0.596980
$682$	2.10611	0.0806470
$683$	0.544701	0.0208424	0.0104212	−	0.999946i	$-0.496683\pi$
$683$	0.544701	0.0208424	0.0104212	+	0.999946i	$0.496683\pi$
$684$	0.188006	0.00718859
$685$	0	0
$686$	−18.2675	−0.697458
$687$	−15.0775	−0.575242
$688$	−4.91265	−0.187293
$689$	−19.7555	−0.752625
$690$	0	0
$691$	39.6186	1.50716	0.753582	−	0.657354i	$-0.228324\pi$
$691$	39.6186	1.50716	0.753582	+	0.657354i	$0.228324\pi$
$692$	8.28670	0.315013
$693$	2.39459	0.0909631
$694$	8.40913	0.319206
$695$	0	0
$696$	13.9915	0.530348
$697$	5.00794	0.189689
$698$	−17.5596	−0.664641
$699$	−1.23239	−0.0466133
$700$	0	0
$701$	19.6615	0.742605	0.371303	−	0.928512i	$-0.378911\pi$
$701$	19.6615	0.742605	0.371303	+	0.928512i	$0.378911\pi$
$702$	−16.3418	−0.616780
$703$	−2.88454	−0.108793
$704$	14.8190	0.558513
$705$	0	0
$706$	1.03508	0.0389559
$707$	19.0168	0.715200
$708$	−6.34638	−0.238511
$709$	39.4618	1.48202	0.741009	−	0.671495i	$-0.234348\pi$
$709$	39.4618	1.48202	0.741009	+	0.671495i	$0.234348\pi$
$710$	0	0
$711$	−16.1005	−0.603815
$712$	−17.9760	−0.673679
$713$	−1.13698	−0.0425801
$714$	−1.86200	−0.0696835
$715$	0	0
$716$	9.24551	0.345521
$717$	−23.2893	−0.869756
$718$	−23.2399	−0.867305
$719$	23.4852	0.875851	0.437925	−	0.899011i	$-0.355713\pi$
$719$	23.4852	0.875851	0.437925	+	0.899011i	$0.355713\pi$
$720$	0	0
$721$	−1.63448	−0.0608711
$722$	23.8496	0.887591
$723$	−16.2562	−0.604575
$724$	−6.48560	−0.241035
$725$	0	0
$726$	−13.7012	−0.508499
$727$	16.6456	0.617349	0.308675	−	0.951168i	$-0.400115\pi$
$727$	16.6456	0.617349	0.308675	+	0.951168i	$0.400115\pi$
$728$	−7.94186	−0.294345
$729$	26.7662	0.991341
$730$	0	0
$731$	1.59077	0.0588368
$732$	1.77933	0.0657658
$733$	21.7610	0.803759	0.401880	−	0.915693i	$-0.368357\pi$
$733$	21.7610	0.803759	0.401880	+	0.915693i	$0.368357\pi$
$734$	33.8195	1.24830
$735$	0	0
$736$	−2.53944	−0.0936052
$737$	−8.32395	−0.306617
$738$	8.14307	0.299750
$739$	−44.2060	−1.62614	−0.813072	−	0.582163i	$-0.802207\pi$
$739$	−44.2060	−1.62614	−0.813072	+	0.582163i	$0.802207\pi$
$740$	0	0
$741$	−1.12289	−0.0412504
$742$	−12.3446	−0.453184
$743$	3.12295	0.114570	0.0572849	−	0.998358i	$-0.481756\pi$
$743$	3.12295	0.114570	0.0572849	+	0.998358i	$0.481756\pi$
$744$	4.00000	0.146647
$745$	0	0
$746$	4.93865	0.180817
$747$	11.9841	0.438474
$748$	−0.657284	−0.0240327
$749$	−18.2235	−0.665872
$750$	0	0
$751$	−35.2855	−1.28759	−0.643793	−	0.765200i	$-0.722640\pi$
$751$	−35.2855	−1.28759	−0.643793	+	0.765200i	$0.722640\pi$
$752$	11.2108	0.408816
$753$	−24.7527	−0.902039
$754$	10.1747	0.370540
$755$	0	0
$756$	2.56365	0.0932392
$757$	−38.2678	−1.39087	−0.695434	−	0.718590i	$-0.744788\pi$
$757$	−38.2678	−1.39087	−0.695434	+	0.718590i	$0.744788\pi$
$758$	−21.9415	−0.796950
$759$	−2.49507	−0.0905653
$760$	0	0
$761$	5.35668	0.194180	0.0970898	−	0.995276i	$-0.469047\pi$
$761$	5.35668	0.194180	0.0970898	+	0.995276i	$0.469047\pi$
$762$	23.1636	0.839129
$763$	−18.8259	−0.681545
$764$	6.19250	0.224037
$765$	0	0
$766$	39.9901	1.44490
$767$	−27.6129	−0.997044
$768$	12.1449	0.438240
$769$	41.7612	1.50595	0.752975	−	0.658050i	$-0.228618\pi$
$769$	41.7612	1.50595	0.752975	+	0.658050i	$0.228618\pi$
$770$	0	0
$771$	6.81865	0.245568
$772$	−2.78412	−0.100203
$773$	7.80552	0.280745	0.140372	−	0.990099i	$-0.455170\pi$
$773$	7.80552	0.280745	0.140372	+	0.990099i	$0.455170\pi$
$774$	2.58665	0.0929750
$775$	0	0
$776$	−48.0527	−1.72499
$777$	−11.6623	−0.418384
$778$	24.4239	0.875638
$779$	1.88714	0.0676140
$780$	0	0
$781$	−10.4348	−0.373385
$782$	−1.41335	−0.0505415
$783$	−19.6512	−0.702276
$784$	17.3285	0.618876
$785$	0	0
$786$	−23.8812	−0.851815
$787$	30.9546	1.10341	0.551706	−	0.834039i	$-0.313977\pi$
$787$	30.9546	1.10341	0.551706	+	0.834039i	$0.313977\pi$
$788$	7.36636	0.262416
$789$	7.66498	0.272881
$790$	0	0
$791$	3.15632	0.112226
$792$	−6.39459	−0.227222
$793$	7.74180	0.274920
$794$	36.5764	1.29805
$795$	0	0
$796$	−2.85092	−0.101048
$797$	26.1356	0.925770	0.462885	−	0.886418i	$-0.346814\pi$
$797$	26.1356	0.925770	0.462885	+	0.886418i	$0.346814\pi$
$798$	−0.701658	−0.0248384
$799$	−3.63018	−0.128427
$800$	0	0
$801$	7.48578	0.264497
$802$	24.7442	0.873750
$803$	−22.1271	−0.780849
$804$	−2.64228	−0.0931859
$805$	0	0
$806$	2.90881	0.102459
$807$	23.9841	0.844279
$808$	−50.7830	−1.78654
$809$	12.3585	0.434501	0.217251	−	0.976116i	$-0.430291\pi$
$809$	12.3585	0.434501	0.217251	+	0.976116i	$0.430291\pi$
$810$	0	0
$811$	9.62202	0.337875	0.168937	−	0.985627i	$-0.445966\pi$
$811$	9.62202	0.337875	0.168937	+	0.985627i	$0.445966\pi$
$812$	−1.59618	−0.0560149
$813$	14.2810	0.500856
$814$	16.3979	0.574745
$815$	0	0
$816$	3.93264	0.137670
$817$	0.599452	0.0209722
$818$	9.27919	0.324439
$819$	3.30725	0.115565
$820$	0	0
$821$	−1.58485	−0.0553115	−0.0276558	−	0.999618i	$-0.508804\pi$
$821$	−1.58485	−0.0553115	−0.0276558	+	0.999618i	$0.508804\pi$
$822$	19.7793	0.689881
$823$	−32.2739	−1.12500	−0.562499	−	0.826798i	$-0.690160\pi$
$823$	−32.2739	−1.12500	−0.562499	+	0.826798i	$0.690160\pi$
$824$	4.36475	0.152053
$825$	0	0
$826$	−17.2544	−0.600358
$827$	−40.5624	−1.41049	−0.705246	−	0.708963i	$-0.749163\pi$
$827$	−40.5624	−1.41049	−0.705246	+	0.708963i	$0.749163\pi$
$828$	0.576969	0.0200511
$829$	8.88922	0.308735	0.154368	−	0.988013i	$-0.450666\pi$
$829$	8.88922	0.308735	0.154368	+	0.988013i	$0.450666\pi$
$830$	0	0
$831$	27.9444	0.969382
$832$	20.4670	0.709566
$833$	−5.61117	−0.194416
$834$	15.8676	0.549451
$835$	0	0
$836$	−0.247685	−0.00856636
$837$	−5.61802	−0.194187
$838$	−43.7031	−1.50970
$839$	−9.16979	−0.316576	−0.158288	−	0.987393i	$-0.550598\pi$
$839$	−9.16979	−0.316576	−0.158288	+	0.987393i	$0.550598\pi$
$840$	0	0
$841$	−16.7648	−0.578096
$842$	−31.0303	−1.06937
$843$	16.0990	0.554479
$844$	1.26972	0.0437056
$845$	0	0
$846$	−5.90280	−0.202942
$847$	9.35202	0.321339
$848$	26.0724	0.895331
$849$	1.79848	0.0617235
$850$	0	0
$851$	−8.85233	−0.303454
$852$	−3.31231	−0.113478
$853$	8.52312	0.291826	0.145913	−	0.989297i	$-0.453388\pi$
$853$	8.52312	0.291826	0.145913	+	0.989297i	$0.453388\pi$
$854$	4.83761	0.165539
$855$	0	0
$856$	48.6646	1.66332
$857$	−52.9153	−1.80755	−0.903776	−	0.428006i	$-0.859216\pi$
$857$	−52.9153	−1.80755	−0.903776	+	0.428006i	$0.859216\pi$
$858$	6.38333	0.217923
$859$	25.8106	0.880646	0.440323	−	0.897840i	$-0.354864\pi$
$859$	25.8106	0.880646	0.440323	+	0.897840i	$0.354864\pi$
$860$	0	0
$861$	7.62981	0.260023
$862$	−9.53720	−0.324838
$863$	50.1327	1.70654	0.853268	−	0.521472i	$-0.174617\pi$
$863$	50.1327	1.70654	0.853268	+	0.521472i	$0.174617\pi$
$864$	−12.5479	−0.426888
$865$	0	0
$866$	−29.5334	−1.00359
$867$	21.1229	0.717371
$868$	−0.456327	−0.0154888
$869$	21.2113	0.719543
$870$	0	0
$871$	−11.4965	−0.389543
$872$	50.2734	1.70247
$873$	20.0107	0.677259
$874$	−0.532596	−0.0180153
$875$	0	0
$876$	−7.02382	−0.237313
$877$	−1.20255	−0.0406073	−0.0203037	−	0.999794i	$-0.506463\pi$
$877$	−1.20255	−0.0406073	−0.0203037	+	0.999794i	$0.506463\pi$
$878$	17.4384	0.588518
$879$	15.2431	0.514136
$880$	0	0
$881$	−18.2524	−0.614938	−0.307469	−	0.951558i	$-0.599482\pi$
$881$	−18.2524	−0.614938	−0.307469	+	0.951558i	$0.599482\pi$
$882$	−9.12394	−0.307219
$883$	−8.26499	−0.278139	−0.139069	−	0.990283i	$-0.544411\pi$
$883$	−8.26499	−0.278139	−0.139069	+	0.990283i	$0.544411\pi$
$884$	−0.907796	−0.0305325
$885$	0	0
$886$	10.2627	0.344782
$887$	−19.7259	−0.662329	−0.331165	−	0.943573i	$-0.607442\pi$
$887$	−19.7259	−0.662329	−0.331165	+	0.943573i	$0.607442\pi$
$888$	31.1435	1.04511
$889$	−15.8108	−0.530276
$890$	0	0
$891$	−6.01032	−0.201353
$892$	4.87456	0.163212
$893$	−1.36797	−0.0457772
$894$	−12.4315	−0.415771
$895$	0	0
$896$	7.71030	0.257583
$897$	−3.44602	−0.115059
$898$	48.9896	1.63480
$899$	3.49789	0.116661
$900$	0	0
$901$	−8.44254	−0.281262
$902$	−10.7279	−0.357201
$903$	2.42361	0.0806527
$904$	−8.42872	−0.280335
$905$	0	0
$906$	−17.6143	−0.585196
$907$	40.5782	1.34738	0.673688	−	0.739016i	$-0.264709\pi$
$907$	40.5782	1.34738	0.673688	+	0.739016i	$0.264709\pi$
$908$	−4.74603	−0.157503
$909$	21.1477	0.701424
$910$	0	0
$911$	−16.7479	−0.554882	−0.277441	−	0.960743i	$-0.589486\pi$
$911$	−16.7479	−0.554882	−0.277441	+	0.960743i	$0.589486\pi$
$912$	1.48194	0.0490719
$913$	−15.7882	−0.522512
$914$	−2.97618	−0.0984431
$915$	0	0
$916$	−4.59331	−0.151767
$917$	16.3006	0.538293
$918$	−6.98367	−0.230495
$919$	−49.8922	−1.64579	−0.822896	−	0.568192i	$-0.807643\pi$
$919$	−49.8922	−1.64579	−0.822896	+	0.568192i	$0.807643\pi$
$920$	0	0
$921$	−17.4979	−0.576575
$922$	−34.2823	−1.12903
$923$	−14.4118	−0.474369
$924$	−1.00140	−0.0329437
$925$	0	0
$926$	−2.77465	−0.0911807
$927$	−1.81762	−0.0596986
$928$	7.81256	0.256460
$929$	−34.0724	−1.11788	−0.558940	−	0.829208i	$-0.688792\pi$
$929$	−34.0724	−1.11788	−0.558940	+	0.829208i	$0.688792\pi$
$930$	0	0
$931$	−2.11446	−0.0692987
$932$	−0.375445	−0.0122981
$933$	−5.86250	−0.191930
$934$	−44.1449	−1.44446
$935$	0	0
$936$	−8.83177	−0.288675
$937$	−41.5136	−1.35619	−0.678096	−	0.734974i	$-0.737195\pi$
$937$	−41.5136	−1.35619	−0.678096	+	0.734974i	$0.737195\pi$
$938$	−7.18378	−0.234559
$939$	−1.50042	−0.0489643
$940$	0	0
$941$	−13.0784	−0.426345	−0.213172	−	0.977015i	$-0.568380\pi$
$941$	−13.0784	−0.426345	−0.213172	+	0.977015i	$0.568380\pi$
$942$	20.7129	0.674863
$943$	5.79143	0.188595
$944$	36.4422	1.18609
$945$	0	0
$946$	−3.40773	−0.110795
$947$	−29.5095	−0.958929	−0.479465	−	0.877561i	$-0.659169\pi$
$947$	−29.5095	−0.958929	−0.479465	+	0.877561i	$0.659169\pi$
$948$	6.73310	0.218681
$949$	−30.5605	−0.992034
$950$	0	0
$951$	29.0906	0.943328
$952$	−3.39396	−0.109999
$953$	−23.2603	−0.753475	−0.376738	−	0.926320i	$-0.622954\pi$
$953$	−23.2603	−0.753475	−0.376738	+	0.926320i	$0.622954\pi$
$954$	−13.7278	−0.444455
$955$	0	0
$956$	−7.09503	−0.229470
$957$	7.67605	0.248131
$958$	9.97016	0.322121
$959$	−13.5007	−0.435961
$960$	0	0
$961$	1.00000	0.0322581
$962$	22.6476	0.730188
$963$	−20.2655	−0.653046
$964$	−4.95241	−0.159507
$965$	0	0
$966$	−2.15331	−0.0692816
$967$	−6.02664	−0.193804	−0.0969018	−	0.995294i	$-0.530893\pi$
$967$	−6.02664	−0.193804	−0.0969018	+	0.995294i	$0.530893\pi$
$968$	−24.9739	−0.802692
$969$	−0.479868	−0.0154156
$970$	0	0
$971$	47.6556	1.52934	0.764670	−	0.644422i	$-0.222902\pi$
$971$	47.6556	1.52934	0.764670	+	0.644422i	$0.222902\pi$
$972$	4.85655	0.155774
$973$	−10.8308	−0.347218
$974$	−16.0220	−0.513379
$975$	0	0
$976$	−10.2173	−0.327047
$977$	−4.51102	−0.144320	−0.0721601	−	0.997393i	$-0.522989\pi$
$977$	−4.51102	−0.144320	−0.0721601	+	0.997393i	$0.522989\pi$
$978$	25.3472	0.810514
$979$	−9.86200	−0.315191
$980$	0	0
$981$	−20.9355	−0.668418
$982$	−33.2875	−1.06225
$983$	13.6607	0.435708	0.217854	−	0.975981i	$-0.430094\pi$
$983$	13.6607	0.435708	0.217854	+	0.975981i	$0.430094\pi$
$984$	−20.3749	−0.649527
$985$	0	0
$986$	4.34816	0.138474
$987$	−5.53075	−0.176046
$988$	−0.342085	−0.0108832
$989$	1.83965	0.0584974
$990$	0	0
$991$	−11.8864	−0.377584	−0.188792	−	0.982017i	$-0.560457\pi$
$991$	−11.8864	−0.377584	−0.188792	+	0.982017i	$0.560457\pi$
$992$	2.23351	0.0709140
$993$	42.2014	1.33922
$994$	−9.00545	−0.285635
$995$	0	0
$996$	−5.01164	−0.158800
$997$	−57.9518	−1.83535	−0.917676	−	0.397330i	$-0.869937\pi$
$997$	−57.9518	−1.83535	−0.917676	+	0.397330i	$0.869937\pi$
$998$	16.8336	0.532857
$999$	−43.7411	−1.38391

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.a.e.1.2		4
3.2	odd	2		6975.2.a.bn.1.3		4
5.2	odd	4		775.2.b.f.249.3		8
5.3	odd	4		775.2.b.f.249.6		8
5.4	even	2		155.2.a.e.1.3	✓	4
15.14	odd	2		1395.2.a.l.1.2		4
20.19	odd	2		2480.2.a.x.1.2		4
35.34	odd	2		7595.2.a.s.1.3		4
40.19	odd	2		9920.2.a.cg.1.3		4
40.29	even	2		9920.2.a.cb.1.2		4
155.154	odd	2		4805.2.a.n.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.a.e.1.3	✓	4	5.4	even	2
775.2.a.e.1.2		4	1.1	even	1	trivial
775.2.b.f.249.3		8	5.2	odd	4
775.2.b.f.249.6		8	5.3	odd	4
1395.2.a.l.1.2		4	15.14	odd	2
2480.2.a.x.1.2		4	20.19	odd	2
4805.2.a.n.1.3		4	155.154	odd	2
6975.2.a.bn.1.3		4	3.2	odd	2
7595.2.a.s.1.3		4	35.34	odd	2
9920.2.a.cb.1.2		4	40.29	even	2
9920.2.a.cg.1.3		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)

\(f(q)\)	\(=\)	\(q-1.26438 q^{2} -1.31743 q^{3} -0.401352 q^{4} +1.66573 q^{6} -1.13698 q^{7} +3.03621 q^{8} -1.26438 q^{9} +O(q^{10})\)	\(q-1.26438 q^{2} -1.31743 q^{3} -0.401352 q^{4} +1.66573 q^{6} -1.13698 q^{7} +3.03621 q^{8} -1.26438 q^{9} +1.66573 q^{11} +0.528753 q^{12} +2.30059 q^{13} +1.43756 q^{14} -3.03621 q^{16} +0.983159 q^{17} +1.59865 q^{18} +0.370485 q^{19} +1.49789 q^{21} -2.10611 q^{22} +1.13698 q^{23} -4.00000 q^{24} -2.90881 q^{26} +5.61802 q^{27} +0.456327 q^{28} -3.49789 q^{29} -1.00000 q^{31} -2.23351 q^{32} -2.19448 q^{33} -1.24308 q^{34} +0.507460 q^{36} -7.78586 q^{37} -0.468432 q^{38} -3.03087 q^{39} +5.09372 q^{41} -1.89389 q^{42} +1.61802 q^{43} -0.668543 q^{44} -1.43756 q^{46} -3.69237 q^{47} +4.00000 q^{48} -5.70729 q^{49} -1.29524 q^{51} -0.923346 q^{52} -8.58715 q^{53} -7.10329 q^{54} -3.45210 q^{56} -0.488088 q^{57} +4.42265 q^{58} -12.0025 q^{59} +3.36514 q^{61} +1.26438 q^{62} +1.43756 q^{63} +8.89642 q^{64} +2.77465 q^{66} -4.99719 q^{67} -0.394593 q^{68} -1.49789 q^{69} -6.26438 q^{71} -3.83892 q^{72} -13.2837 q^{73} +9.84426 q^{74} -0.148695 q^{76} -1.89389 q^{77} +3.83216 q^{78} +12.7339 q^{79} -3.60822 q^{81} -6.44038 q^{82} -9.47823 q^{83} -0.601179 q^{84} -2.04579 q^{86} +4.60822 q^{87} +5.05751 q^{88} -5.92053 q^{89} -2.61571 q^{91} -0.456327 q^{92} +1.31743 q^{93} +4.66854 q^{94} +2.94249 q^{96} -15.8265 q^{97} +7.21616 q^{98} -2.10611 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{3} + 5 q^{4} - 4 q^{6} - 2 q^{7} - 3 q^{8} - q^{9}+O(q^{10}) \) 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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