LMFDB - Embedded newform 4025.2.a.q.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1397868136$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.255877.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 6x^{2} + 6x - 5 $ x^5 - x^4 - 6x^3 + 6x^2 + 6*x - 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.10917$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.10917 q^{2} +1.54702 q^{3} +2.44859 q^{4} +3.26292 q^{6} -1.00000 q^{7} +0.946160 q^{8} -0.606735 q^{9} +O(q^{10})$	\(q+2.10917 q^{2} +1.54702 q^{3} +2.44859 q^{4} +3.26292 q^{6} -1.00000 q^{7} +0.946160 q^{8} -0.606735 q^{9} -4.35017 q^{11} +3.78802 q^{12} -5.05094 q^{13} -2.10917 q^{14} -2.90158 q^{16} -0.962204 q^{17} -1.27971 q^{18} +1.01074 q^{19} -1.54702 q^{21} -9.17524 q^{22} -1.00000 q^{23} +1.46373 q^{24} -10.6533 q^{26} -5.57968 q^{27} -2.44859 q^{28} -1.27484 q^{29} -0.393265 q^{31} -8.01223 q^{32} -6.72979 q^{33} -2.02945 q^{34} -1.48565 q^{36} -7.66254 q^{37} +2.13183 q^{38} -7.81390 q^{39} +3.78951 q^{41} -3.26292 q^{42} +5.25853 q^{43} -10.6518 q^{44} -2.10917 q^{46} +8.91911 q^{47} -4.48879 q^{48} +1.00000 q^{49} -1.48855 q^{51} -12.3677 q^{52} +5.73104 q^{53} -11.7685 q^{54} -0.946160 q^{56} +1.56364 q^{57} -2.68885 q^{58} -0.768255 q^{59} -8.02679 q^{61} -0.829462 q^{62} +0.606735 q^{63} -11.0960 q^{64} -14.1943 q^{66} +5.74583 q^{67} -2.35605 q^{68} -1.54702 q^{69} -5.29045 q^{71} -0.574069 q^{72} +11.9246 q^{73} -16.1616 q^{74} +2.47490 q^{76} +4.35017 q^{77} -16.4808 q^{78} +6.83747 q^{79} -6.81167 q^{81} +7.99271 q^{82} +8.52263 q^{83} -3.78802 q^{84} +11.0911 q^{86} -1.97220 q^{87} -4.11596 q^{88} -5.18932 q^{89} +5.05094 q^{91} -2.44859 q^{92} -0.608387 q^{93} +18.8119 q^{94} -12.3951 q^{96} +3.18378 q^{97} +2.10917 q^{98} +2.63940 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} + 4 q^{3} + 3 q^{4} - 5 q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + q^2 + 4 * q^3 + 3 * q^4 - 5 * q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9	$ 5 q + q^{2} + 4 q^{3} + 3 q^{4} - 5 q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9} - 7 q^{11} + 10 q^{12} + 5 q^{13} - q^{14} - 9 q^{16} + 7 q^{17} - 11 q^{18} - 10 q^{19} - 4 q^{21} - 4 q^{22} - 5 q^{23} - 4 q^{24} - 2 q^{26} + 7 q^{27} - 3 q^{28} - 14 q^{29} - 10 q^{31} - 4 q^{33} - 10 q^{34} + 20 q^{36} + 3 q^{37} + 15 q^{38} - 13 q^{39} - 15 q^{41} + 5 q^{42} - 8 q^{43} - 27 q^{44} - q^{46} + 10 q^{47} + 2 q^{48} + 5 q^{49} - 18 q^{51} - 18 q^{52} + 9 q^{53} - 39 q^{54} + 3 q^{56} - 23 q^{57} + 31 q^{58} - 19 q^{59} - 21 q^{61} + 10 q^{62} - 5 q^{63} - 7 q^{64} + 25 q^{66} - 5 q^{67} + 15 q^{68} - 4 q^{69} - 16 q^{71} - 26 q^{72} - q^{73} - 16 q^{74} + 7 q^{77} - 28 q^{78} + 20 q^{79} - 3 q^{81} - 11 q^{82} + 31 q^{83} - 10 q^{84} + 10 q^{86} - 38 q^{87} + 3 q^{88} - 21 q^{89} - 5 q^{91} - 3 q^{92} - 23 q^{93} + 28 q^{94} + 24 q^{96} - 19 q^{97} + q^{98} - 26 q^{99}+O(q^{100}) $ 5 * q + q^2 + 4 * q^3 + 3 * q^4 - 5 * q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9 - 7 * q^11 + 10 * q^12 + 5 * q^13 - q^14 - 9 * q^16 + 7 * q^17 - 11 * q^18 - 10 * q^19 - 4 * q^21 - 4 * q^22 - 5 * q^23 - 4 * q^24 - 2 * q^26 + 7 * q^27 - 3 * q^28 - 14 * q^29 - 10 * q^31 - 4 * q^33 - 10 * q^34 + 20 * q^36 + 3 * q^37 + 15 * q^38 - 13 * q^39 - 15 * q^41 + 5 * q^42 - 8 * q^43 - 27 * q^44 - q^46 + 10 * q^47 + 2 * q^48 + 5 * q^49 - 18 * q^51 - 18 * q^52 + 9 * q^53 - 39 * q^54 + 3 * q^56 - 23 * q^57 + 31 * q^58 - 19 * q^59 - 21 * q^61 + 10 * q^62 - 5 * q^63 - 7 * q^64 + 25 * q^66 - 5 * q^67 + 15 * q^68 - 4 * q^69 - 16 * q^71 - 26 * q^72 - q^73 - 16 * q^74 + 7 * q^77 - 28 * q^78 + 20 * q^79 - 3 * q^81 - 11 * q^82 + 31 * q^83 - 10 * q^84 + 10 * q^86 - 38 * q^87 + 3 * q^88 - 21 * q^89 - 5 * q^91 - 3 * q^92 - 23 * q^93 + 28 * q^94 + 24 * q^96 - 19 * q^97 + q^98 - 26 * 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 $

$2$	2.10917	1.49141	0.745704	−	0.666278i	$-0.232113\pi$
$2$	2.10917	1.49141	0.745704	+	0.666278i	$0.232113\pi$
$3$	1.54702	0.893171	0.446586	−	0.894741i	$-0.352640\pi$
$3$	1.54702	0.893171	0.446586	+	0.894741i	$0.352640\pi$
$4$	2.44859	1.22430
$5$	0	0
$5$	0	0
$6$	3.26292	1.33208
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.946160	0.334518
$9$	−0.606735	−0.202245
$10$	0	0
$11$	−4.35017	−1.31163	−0.655813	−	0.754924i	$-0.727674\pi$
$11$	−4.35017	−1.31163	−0.655813	+	0.754924i	$0.727674\pi$
$12$	3.78802	1.09351
$13$	−5.05094	−1.40088	−0.700439	−	0.713712i	$-0.747013\pi$
$13$	−5.05094	−1.40088	−0.700439	+	0.713712i	$0.747013\pi$
$14$	−2.10917	−0.563699
$15$	0	0
$16$	−2.90158	−0.725394
$17$	−0.962204	−0.233369	−0.116684	−	0.993169i	$-0.537227\pi$
$17$	−0.962204	−0.233369	−0.116684	+	0.993169i	$0.537227\pi$
$18$	−1.27971	−0.301630
$19$	1.01074	0.231881	0.115940	−	0.993256i	$-0.463012\pi$
$19$	1.01074	0.231881	0.115940	+	0.993256i	$0.463012\pi$
$20$	0	0
$21$	−1.54702	−0.337587
$22$	−9.17524	−1.95617
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.46373	0.298782
$25$	0	0
$26$	−10.6533	−2.08928
$27$	−5.57968	−1.07381
$28$	−2.44859	−0.462741
$29$	−1.27484	−0.236732	−0.118366	−	0.992970i	$-0.537766\pi$
$29$	−1.27484	−0.236732	−0.118366	+	0.992970i	$0.537766\pi$
$30$	0	0
$31$	−0.393265	−0.0706324	−0.0353162	−	0.999376i	$-0.511244\pi$
$31$	−0.393265	−0.0706324	−0.0353162	+	0.999376i	$0.511244\pi$
$32$	−8.01223	−1.41638
$33$	−6.72979	−1.17151
$34$	−2.02945	−0.348048
$35$	0	0
$36$	−1.48565	−0.247608
$37$	−7.66254	−1.25971	−0.629857	−	0.776711i	$-0.716887\pi$
$37$	−7.66254	−1.25971	−0.629857	+	0.776711i	$0.716887\pi$
$38$	2.13183	0.345829
$39$	−7.81390	−1.25122
$40$	0	0
$41$	3.78951	0.591822	0.295911	−	0.955216i	$-0.404377\pi$
$41$	3.78951	0.591822	0.295911	+	0.955216i	$0.404377\pi$
$42$	−3.26292	−0.503480
$43$	5.25853	0.801919	0.400959	−	0.916096i	$-0.368677\pi$
$43$	5.25853	0.801919	0.400959	+	0.916096i	$0.368677\pi$
$44$	−10.6518	−1.60582
$45$	0	0
$46$	−2.10917	−0.310980
$47$	8.91911	1.30099	0.650493	−	0.759512i	$-0.274562\pi$
$47$	8.91911	1.30099	0.650493	+	0.759512i	$0.274562\pi$
$48$	−4.48879	−0.647901
$49$	1.00000	0.142857
$50$	0	0
$51$	−1.48855	−0.208438
$52$	−12.3677	−1.71509
$53$	5.73104	0.787219	0.393609	−	0.919278i	$-0.371226\pi$
$53$	5.73104	0.787219	0.393609	+	0.919278i	$0.371226\pi$
$54$	−11.7685	−1.60149
$55$	0	0
$56$	−0.946160	−0.126436
$57$	1.56364	0.207109
$58$	−2.68885	−0.353064
$59$	−0.768255	−0.100018	−0.0500091	−	0.998749i	$-0.515925\pi$
$59$	−0.768255	−0.100018	−0.0500091	+	0.998749i	$0.515925\pi$
$60$	0	0
$61$	−8.02679	−1.02773	−0.513863	−	0.857873i	$-0.671786\pi$
$61$	−8.02679	−1.02773	−0.513863	+	0.857873i	$0.671786\pi$
$62$	−0.829462	−0.105342
$63$	0.606735	0.0764415
$64$	−11.0960	−1.38700
$65$	0	0
$66$	−14.1943	−1.74719
$67$	5.74583	0.701965	0.350983	−	0.936382i	$-0.385848\pi$
$67$	5.74583	0.701965	0.350983	+	0.936382i	$0.385848\pi$
$68$	−2.35605	−0.285713
$69$	−1.54702	−0.186239
$70$	0	0
$71$	−5.29045	−0.627861	−0.313931	−	0.949446i	$-0.601646\pi$
$71$	−5.29045	−0.627861	−0.313931	+	0.949446i	$0.601646\pi$
$72$	−0.574069	−0.0676547
$73$	11.9246	1.39566	0.697832	−	0.716262i	$-0.254148\pi$
$73$	11.9246	1.39566	0.697832	+	0.716262i	$0.254148\pi$
$74$	−16.1616	−1.87875
$75$	0	0
$76$	2.47490	0.283891
$77$	4.35017	0.495748
$78$	−16.4808	−1.86609
$79$	6.83747	0.769276	0.384638	−	0.923068i	$-0.374326\pi$
$79$	6.83747	0.769276	0.384638	+	0.923068i	$0.374326\pi$
$80$	0	0
$81$	−6.81167	−0.756852
$82$	7.99271	0.882648
$83$	8.52263	0.935480	0.467740	−	0.883866i	$-0.345068\pi$
$83$	8.52263	0.935480	0.467740	+	0.883866i	$0.345068\pi$
$84$	−3.78802	−0.413307
$85$	0	0
$86$	11.0911	1.19599
$87$	−1.97220	−0.211442
$88$	−4.11596	−0.438763
$89$	−5.18932	−0.550067	−0.275033	−	0.961435i	$-0.588689\pi$
$89$	−5.18932	−0.550067	−0.275033	+	0.961435i	$0.588689\pi$
$90$	0	0
$91$	5.05094	0.529482
$92$	−2.44859	−0.255284
$93$	−0.608387	−0.0630868
$94$	18.8119	1.94030
$95$	0	0
$96$	−12.3951	−1.26507
$97$	3.18378	0.323264	0.161632	−	0.986851i	$-0.448324\pi$
$97$	3.18378	0.323264	0.161632	+	0.986851i	$0.448324\pi$
$98$	2.10917	0.213058
$99$	2.63940	0.265270
$100$	0	0
$101$	−12.5094	−1.24473	−0.622364	−	0.782728i	$-0.713828\pi$
$101$	−12.5094	−1.24473	−0.622364	+	0.782728i	$0.713828\pi$
$102$	−3.13960	−0.310866
$103$	8.84069	0.871099	0.435549	−	0.900165i	$-0.356554\pi$
$103$	8.84069	0.871099	0.435549	+	0.900165i	$0.356554\pi$
$104$	−4.77900	−0.468619
$105$	0	0
$106$	12.0877	1.17406
$107$	−5.09461	−0.492515	−0.246257	−	0.969204i	$-0.579201\pi$
$107$	−5.09461	−0.492515	−0.246257	+	0.969204i	$0.579201\pi$
$108$	−13.6624	−1.31466
$109$	−3.09847	−0.296780	−0.148390	−	0.988929i	$-0.547409\pi$
$109$	−3.09847	−0.296780	−0.148390	+	0.988929i	$0.547409\pi$
$110$	0	0
$111$	−11.8541	−1.12514
$112$	2.90158	0.274173
$113$	−1.40502	−0.132173	−0.0660866	−	0.997814i	$-0.521051\pi$
$113$	−1.40502	−0.132173	−0.0660866	+	0.997814i	$0.521051\pi$
$114$	3.29798	0.308884
$115$	0	0
$116$	−3.12157	−0.289830
$117$	3.06458	0.283321
$118$	−1.62038	−0.149168
$119$	0.962204	0.0882051
$120$	0	0
$121$	7.92398	0.720362
$122$	−16.9299	−1.53276
$123$	5.86244	0.528598
$124$	−0.962945	−0.0864750
$125$	0	0
$126$	1.27971	0.114005
$127$	−9.49906	−0.842905	−0.421452	−	0.906851i	$-0.638480\pi$
$127$	−9.49906	−0.842905	−0.421452	+	0.906851i	$0.638480\pi$
$128$	−7.37888	−0.652207
$129$	8.13505	0.716251
$130$	0	0
$131$	−21.1131	−1.84466	−0.922328	−	0.386407i	$-0.873716\pi$
$131$	−21.1131	−1.84466	−0.922328	+	0.386407i	$0.873716\pi$
$132$	−16.4785	−1.43427
$133$	−1.01074	−0.0876427
$134$	12.1189	1.04692
$135$	0	0
$136$	−0.910399	−0.0780661
$137$	−13.4795	−1.15163	−0.575817	−	0.817578i	$-0.695316\pi$
$137$	−13.4795	−1.15163	−0.575817	+	0.817578i	$0.695316\pi$
$138$	−3.26292	−0.277758
$139$	−15.0409	−1.27576	−0.637878	−	0.770137i	$-0.720188\pi$
$139$	−15.0409	−1.27576	−0.637878	+	0.770137i	$0.720188\pi$
$140$	0	0
$141$	13.7980	1.16200
$142$	−11.1585	−0.936397
$143$	21.9725	1.83743
$144$	1.76049	0.146707
$145$	0	0
$146$	25.1509	2.08150
$147$	1.54702	0.127596
$148$	−18.7625	−1.54226
$149$	10.2825	0.842374	0.421187	−	0.906974i	$-0.361614\pi$
$149$	10.2825	0.842374	0.421187	+	0.906974i	$0.361614\pi$
$150$	0	0
$151$	−14.7373	−1.19930	−0.599652	−	0.800261i	$-0.704694\pi$
$151$	−14.7373	−1.19930	−0.599652	+	0.800261i	$0.704694\pi$
$152$	0.956327	0.0775683
$153$	0.583803	0.0471977
$154$	9.17524	0.739362
$155$	0	0
$156$	−19.1331	−1.53187
$157$	−18.6621	−1.48940	−0.744699	−	0.667400i	$-0.767407\pi$
$157$	−18.6621	−1.48940	−0.744699	+	0.667400i	$0.767407\pi$
$158$	14.4214	1.14730
$159$	8.86602	0.703121
$160$	0	0
$161$	1.00000	0.0788110
$162$	−14.3670	−1.12877
$163$	17.5176	1.37209	0.686044	−	0.727560i	$-0.259346\pi$
$163$	17.5176	1.37209	0.686044	+	0.727560i	$0.259346\pi$
$164$	9.27897	0.724566
$165$	0	0
$166$	17.9757	1.39518
$167$	−9.77874	−0.756701	−0.378351	−	0.925662i	$-0.623509\pi$
$167$	−9.77874	−0.756701	−0.378351	+	0.925662i	$0.623509\pi$
$168$	−1.46373	−0.112929
$169$	12.5120	0.962462
$170$	0	0
$171$	−0.613255	−0.0468968
$172$	12.8760	0.981787
$173$	12.2425	0.930779	0.465390	−	0.885106i	$-0.345914\pi$
$173$	12.2425	0.930779	0.465390	+	0.885106i	$0.345914\pi$
$174$	−4.15970	−0.315346
$175$	0	0
$176$	12.6223	0.951445
$177$	−1.18850	−0.0893334
$178$	−10.9451	−0.820374
$179$	13.8376	1.03427	0.517134	−	0.855905i	$-0.326999\pi$
$179$	13.8376	1.03427	0.517134	+	0.855905i	$0.326999\pi$
$180$	0	0
$181$	−11.9035	−0.884780	−0.442390	−	0.896823i	$-0.645869\pi$
$181$	−11.9035	−0.884780	−0.442390	+	0.896823i	$0.645869\pi$
$182$	10.6533	0.789674
$183$	−12.4176	−0.917934
$184$	−0.946160	−0.0697519
$185$	0	0
$186$	−1.28319	−0.0940882
$187$	4.18575	0.306092
$188$	21.8393	1.59279
$189$	5.57968	0.405862
$190$	0	0
$191$	−5.23175	−0.378556	−0.189278	−	0.981924i	$-0.560615\pi$
$191$	−5.23175	−0.378556	−0.189278	+	0.981924i	$0.560615\pi$
$192$	−17.1657	−1.23883
$193$	−25.5759	−1.84100	−0.920498	−	0.390748i	$-0.872216\pi$
$193$	−25.5759	−1.84100	−0.920498	+	0.390748i	$0.872216\pi$
$194$	6.71514	0.482119
$195$	0	0
$196$	2.44859	0.174900
$197$	21.6624	1.54338	0.771692	−	0.635996i	$-0.219411\pi$
$197$	21.6624	1.54338	0.771692	+	0.635996i	$0.219411\pi$
$198$	5.56694	0.395626
$199$	15.7681	1.11777	0.558887	−	0.829244i	$-0.311229\pi$
$199$	15.7681	1.11777	0.558887	+	0.829244i	$0.311229\pi$
$200$	0	0
$201$	8.88891	0.626975
$202$	−26.3844	−1.85640
$203$	1.27484	0.0894762
$204$	−3.64485	−0.255190
$205$	0	0
$206$	18.6465	1.29916
$207$	0.606735	0.0421710
$208$	14.6557	1.01619
$209$	−4.39691	−0.304141
$210$	0	0
$211$	15.1776	1.04487	0.522436	−	0.852678i	$-0.325023\pi$
$211$	15.1776	1.04487	0.522436	+	0.852678i	$0.325023\pi$
$212$	14.0330	0.963789
$213$	−8.18442	−0.560788
$214$	−10.7454	−0.734541
$215$	0	0
$216$	−5.27928	−0.359209
$217$	0.393265	0.0266965
$218$	−6.53520	−0.442620
$219$	18.4475	1.24657
$220$	0	0
$221$	4.86004	0.326921
$222$	−25.0023	−1.67804
$223$	2.53911	0.170031	0.0850155	−	0.996380i	$-0.472906\pi$
$223$	2.53911	0.170031	0.0850155	+	0.996380i	$0.472906\pi$
$224$	8.01223	0.535340
$225$	0	0
$226$	−2.96342	−0.197124
$227$	0.0827126	0.00548983	0.00274491	−	0.999996i	$-0.499126\pi$
$227$	0.0827126	0.00548983	0.00274491	+	0.999996i	$0.499126\pi$
$228$	3.82872	0.253563
$229$	8.67859	0.573497	0.286749	−	0.958006i	$-0.407426\pi$
$229$	8.67859	0.573497	0.286749	+	0.958006i	$0.407426\pi$
$230$	0	0
$231$	6.72979	0.442788
$232$	−1.20620	−0.0791911
$233$	−16.6231	−1.08902	−0.544508	−	0.838756i	$-0.683283\pi$
$233$	−16.6231	−1.08902	−0.544508	+	0.838756i	$0.683283\pi$
$234$	6.46373	0.422547
$235$	0	0
$236$	−1.88114	−0.122452
$237$	10.5777	0.687095
$238$	2.02945	0.131550
$239$	−25.9541	−1.67883	−0.839415	−	0.543491i	$-0.817102\pi$
$239$	−25.9541	−1.67883	−0.839415	+	0.543491i	$0.817102\pi$
$240$	0	0
$241$	−0.700576	−0.0451280	−0.0225640	−	0.999745i	$-0.507183\pi$
$241$	−0.700576	−0.0451280	−0.0225640	+	0.999745i	$0.507183\pi$
$242$	16.7130	1.07435
$243$	6.20128	0.397813
$244$	−19.6543	−1.25824
$245$	0	0
$246$	12.3649	0.788355
$247$	−5.10521	−0.324837
$248$	−0.372091	−0.0236278
$249$	13.1847	0.835544
$250$	0	0
$251$	−1.86519	−0.117730	−0.0588649	−	0.998266i	$-0.518748\pi$
$251$	−1.86519	−0.117730	−0.0588649	+	0.998266i	$0.518748\pi$
$252$	1.48565	0.0935871
$253$	4.35017	0.273493
$254$	−20.0351	−1.25711
$255$	0	0
$256$	6.62870	0.414294
$257$	−8.06733	−0.503226	−0.251613	−	0.967828i	$-0.580961\pi$
$257$	−8.06733	−0.503226	−0.251613	+	0.967828i	$0.580961\pi$
$258$	17.1582	1.06822
$259$	7.66254	0.476127
$260$	0	0
$261$	0.773491	0.0478779
$262$	−44.5310	−2.75113
$263$	−1.61160	−0.0993757	−0.0496878	−	0.998765i	$-0.515823\pi$
$263$	−1.61160	−0.0993757	−0.0496878	+	0.998765i	$0.515823\pi$
$264$	−6.36746	−0.391890
$265$	0	0
$266$	−2.13183	−0.130711
$267$	−8.02797	−0.491304
$268$	14.0692	0.859414
$269$	−11.8571	−0.722942	−0.361471	−	0.932383i	$-0.617725\pi$
$269$	−11.8571	−0.722942	−0.361471	+	0.932383i	$0.617725\pi$
$270$	0	0
$271$	−20.3129	−1.23392	−0.616960	−	0.786995i	$-0.711636\pi$
$271$	−20.3129	−1.23392	−0.616960	+	0.786995i	$0.711636\pi$
$272$	2.79191	0.169284
$273$	7.81390	0.472919
$274$	−28.4306	−1.71756
$275$	0	0
$276$	−3.78802	−0.228012
$277$	18.4508	1.10860	0.554301	−	0.832316i	$-0.312986\pi$
$277$	18.4508	1.10860	0.554301	+	0.832316i	$0.312986\pi$
$278$	−31.7239	−1.90267
$279$	0.238608	0.0142851
$280$	0	0
$281$	17.7395	1.05825	0.529124	−	0.848545i	$-0.322521\pi$
$281$	17.7395	1.05825	0.529124	+	0.848545i	$0.322521\pi$
$282$	29.1024	1.73302
$283$	28.7057	1.70638	0.853188	−	0.521603i	$-0.174666\pi$
$283$	28.7057	1.70638	0.853188	+	0.521603i	$0.174666\pi$
$284$	−12.9542	−0.768689
$285$	0	0
$286$	46.3436	2.74036
$287$	−3.78951	−0.223688
$288$	4.86131	0.286455
$289$	−16.0742	−0.945539
$290$	0	0
$291$	4.92537	0.288730
$292$	29.1984	1.70871
$293$	6.04159	0.352953	0.176477	−	0.984305i	$-0.443530\pi$
$293$	6.04159	0.352953	0.176477	+	0.984305i	$0.443530\pi$
$294$	3.26292	0.190297
$295$	0	0
$296$	−7.24999	−0.421397
$297$	24.2726	1.40844
$298$	21.6875	1.25632
$299$	5.05094	0.292103
$300$	0	0
$301$	−5.25853	−0.303097
$302$	−31.0834	−1.78865
$303$	−19.3522	−1.11176
$304$	−2.93275	−0.168205
$305$	0	0
$306$	1.23134	0.0703910
$307$	−29.5291	−1.68532	−0.842658	−	0.538450i	$-0.819010\pi$
$307$	−29.5291	−1.68532	−0.842658	+	0.538450i	$0.819010\pi$
$308$	10.6518	0.606943
$309$	13.6767	0.778040
$310$	0	0
$311$	−30.2554	−1.71563	−0.857813	−	0.513962i	$-0.828177\pi$
$311$	−30.2554	−1.71563	−0.857813	+	0.513962i	$0.828177\pi$
$312$	−7.39320	−0.418557
$313$	−19.6884	−1.11285	−0.556426	−	0.830897i	$-0.687828\pi$
$313$	−19.6884	−1.11285	−0.556426	+	0.830897i	$0.687828\pi$
$314$	−39.3615	−2.22130
$315$	0	0
$316$	16.7422	0.941822
$317$	−8.33727	−0.468268	−0.234134	−	0.972204i	$-0.575225\pi$
$317$	−8.33727	−0.468268	−0.234134	+	0.972204i	$0.575225\pi$
$318$	18.6999	1.04864
$319$	5.54577	0.310504
$320$	0	0
$321$	−7.88146	−0.439900
$322$	2.10917	0.117539
$323$	−0.972543	−0.0541137
$324$	−16.6790	−0.926611
$325$	0	0
$326$	36.9477	2.04634
$327$	−4.79339	−0.265075
$328$	3.58548	0.197975
$329$	−8.91911	−0.491726
$330$	0	0
$331$	−25.6595	−1.41037	−0.705186	−	0.709022i	$-0.749137\pi$
$331$	−25.6595	−1.41037	−0.705186	+	0.709022i	$0.749137\pi$
$332$	20.8685	1.14531
$333$	4.64914	0.254771
$334$	−20.6250	−1.12855
$335$	0	0
$336$	4.48879	0.244884
$337$	25.0488	1.36449	0.682247	−	0.731121i	$-0.261003\pi$
$337$	25.0488	1.36449	0.682247	+	0.731121i	$0.261003\pi$
$338$	26.3899	1.43542
$339$	−2.17359	−0.118053
$340$	0	0
$341$	1.71077	0.0926433
$342$	−1.29346	−0.0699422
$343$	−1.00000	−0.0539949
$344$	4.97542	0.268256
$345$	0	0
$346$	25.8215	1.38817
$347$	12.5311	0.672707	0.336354	−	0.941736i	$-0.390806\pi$
$347$	12.5311	0.672707	0.336354	+	0.941736i	$0.390806\pi$
$348$	−4.82912	−0.258868
$349$	−32.3086	−1.72944	−0.864720	−	0.502254i	$-0.832504\pi$
$349$	−32.3086	−1.72944	−0.864720	+	0.502254i	$0.832504\pi$
$350$	0	0
$351$	28.1827	1.50428
$352$	34.8546	1.85776
$353$	−18.3804	−0.978289	−0.489145	−	0.872203i	$-0.662691\pi$
$353$	−18.3804	−0.978289	−0.489145	+	0.872203i	$0.662691\pi$
$354$	−2.50676	−0.133233
$355$	0	0
$356$	−12.7065	−0.673445
$357$	1.48855	0.0787823
$358$	29.1857	1.54251
$359$	−27.0782	−1.42913	−0.714567	−	0.699567i	$-0.753376\pi$
$359$	−27.0782	−1.42913	−0.714567	+	0.699567i	$0.753376\pi$
$360$	0	0
$361$	−17.9784	−0.946231
$362$	−25.1065	−1.31957
$363$	12.2585	0.643406
$364$	12.3677	0.648244
$365$	0	0
$366$	−26.1908	−1.36901
$367$	−20.3649	−1.06304	−0.531520	−	0.847046i	$-0.678379\pi$
$367$	−20.3649	−1.06304	−0.531520	+	0.847046i	$0.678379\pi$
$368$	2.90158	0.151255
$369$	−2.29923	−0.119693
$370$	0	0
$371$	−5.73104	−0.297541
$372$	−1.48969	−0.0772370
$373$	25.2625	1.30804	0.654021	−	0.756477i	$-0.273081\pi$
$373$	25.2625	1.30804	0.654021	+	0.756477i	$0.273081\pi$
$374$	8.82846	0.456509
$375$	0	0
$376$	8.43891	0.435203
$377$	6.43914	0.331633
$378$	11.7685	0.605306
$379$	10.3706	0.532701	0.266351	−	0.963876i	$-0.414182\pi$
$379$	10.3706	0.532701	0.266351	+	0.963876i	$0.414182\pi$
$380$	0	0
$381$	−14.6952	−0.752858
$382$	−11.0346	−0.564581
$383$	13.0631	0.667495	0.333747	−	0.942663i	$-0.391687\pi$
$383$	13.0631	0.667495	0.333747	+	0.942663i	$0.391687\pi$
$384$	−11.4153	−0.582533
$385$	0	0
$386$	−53.9439	−2.74567
$387$	−3.19054	−0.162184
$388$	7.79579	0.395771
$389$	−10.5930	−0.537086	−0.268543	−	0.963268i	$-0.586542\pi$
$389$	−10.5930	−0.537086	−0.268543	+	0.963268i	$0.586542\pi$
$390$	0	0
$391$	0.962204	0.0486608
$392$	0.946160	0.0477883
$393$	−32.6623	−1.64759
$394$	45.6897	2.30181
$395$	0	0
$396$	6.46282	0.324769
$397$	−22.7268	−1.14063	−0.570313	−	0.821428i	$-0.693178\pi$
$397$	−22.7268	−1.14063	−0.570313	+	0.821428i	$0.693178\pi$
$398$	33.2577	1.66706
$399$	−1.56364	−0.0782799
$400$	0	0
$401$	34.9364	1.74464	0.872321	−	0.488934i	$-0.162614\pi$
$401$	34.9364	1.74464	0.872321	+	0.488934i	$0.162614\pi$
$402$	18.7482	0.935076
$403$	1.98636	0.0989475
$404$	−30.6304	−1.52392
$405$	0	0
$406$	2.68885	0.133446
$407$	33.3334	1.65227
$408$	−1.40840	−0.0697264
$409$	21.4418	1.06023	0.530115	−	0.847926i	$-0.322149\pi$
$409$	21.4418	1.06023	0.530115	+	0.847926i	$0.322149\pi$
$410$	0	0
$411$	−20.8531	−1.02861
$412$	21.6472	1.06648
$413$	0.768255	0.0378033
$414$	1.27971	0.0628942
$415$	0	0
$416$	40.4693	1.98417
$417$	−23.2686	−1.13947
$418$	−9.27383	−0.453598
$419$	−21.5965	−1.05506	−0.527530	−	0.849536i	$-0.676882\pi$
$419$	−21.5965	−1.05506	−0.527530	+	0.849536i	$0.676882\pi$
$420$	0	0
$421$	−9.68701	−0.472116	−0.236058	−	0.971739i	$-0.575856\pi$
$421$	−9.68701	−0.472116	−0.236058	+	0.971739i	$0.575856\pi$
$422$	32.0122	1.55833
$423$	−5.41154	−0.263118
$424$	5.42248	0.263339
$425$	0	0
$426$	−17.2623	−0.836363
$427$	8.02679	0.388444
$428$	−12.4746	−0.602985
$429$	33.9918	1.64114
$430$	0	0
$431$	8.32657	0.401077	0.200538	−	0.979686i	$-0.435731\pi$
$431$	8.32657	0.401077	0.200538	+	0.979686i	$0.435731\pi$
$432$	16.1899	0.778936
$433$	−37.5013	−1.80220	−0.901100	−	0.433612i	$-0.857239\pi$
$433$	−37.5013	−1.80220	−0.901100	+	0.433612i	$0.857239\pi$
$434$	0.829462	0.0398154
$435$	0	0
$436$	−7.58690	−0.363347
$437$	−1.01074	−0.0483505
$438$	38.9089	1.85914
$439$	−7.20212	−0.343739	−0.171869	−	0.985120i	$-0.554981\pi$
$439$	−7.20212	−0.343739	−0.171869	+	0.985120i	$0.554981\pi$
$440$	0	0
$441$	−0.606735	−0.0288922
$442$	10.2506	0.487573
$443$	−25.9382	−1.23236	−0.616181	−	0.787604i	$-0.711321\pi$
$443$	−25.9382	−1.23236	−0.616181	+	0.787604i	$0.711321\pi$
$444$	−29.0259	−1.37751
$445$	0	0
$446$	5.35540	0.253586
$447$	15.9072	0.752385
$448$	11.0960	0.524237
$449$	6.82366	0.322028	0.161014	−	0.986952i	$-0.448524\pi$
$449$	6.82366	0.322028	0.161014	+	0.986952i	$0.448524\pi$
$450$	0	0
$451$	−16.4850	−0.776249
$452$	−3.44032	−0.161819
$453$	−22.7989	−1.07118
$454$	0.174455	0.00818757
$455$	0	0
$456$	1.47945	0.0692818
$457$	−20.7776	−0.971935	−0.485967	−	0.873977i	$-0.661533\pi$
$457$	−20.7776	−0.971935	−0.485967	+	0.873977i	$0.661533\pi$
$458$	18.3046	0.855318
$459$	5.36880	0.250594
$460$	0	0
$461$	−5.94781	−0.277017	−0.138509	−	0.990361i	$-0.544231\pi$
$461$	−5.94781	−0.277017	−0.138509	+	0.990361i	$0.544231\pi$
$462$	14.1943	0.660377
$463$	24.2250	1.12583	0.562915	−	0.826515i	$-0.309680\pi$
$463$	24.2250	1.12583	0.562915	+	0.826515i	$0.309680\pi$
$464$	3.69905	0.171724
$465$	0	0
$466$	−35.0609	−1.62417
$467$	2.78581	0.128912	0.0644559	−	0.997921i	$-0.479469\pi$
$467$	2.78581	0.128912	0.0644559	+	0.997921i	$0.479469\pi$
$468$	7.50392	0.346869
$469$	−5.74583	−0.265318
$470$	0	0
$471$	−28.8706	−1.33029
$472$	−0.726892	−0.0334579
$473$	−22.8755	−1.05182
$474$	22.3101	1.02474
$475$	0	0
$476$	2.35605	0.107989
$477$	−3.47722	−0.159211
$478$	−54.7416	−2.50382
$479$	29.0644	1.32799	0.663994	−	0.747738i	$-0.268860\pi$
$479$	29.0644	1.32799	0.663994	+	0.747738i	$0.268860\pi$
$480$	0	0
$481$	38.7031	1.76471
$482$	−1.47763	−0.0673043
$483$	1.54702	0.0703918
$484$	19.4026	0.881936
$485$	0	0
$486$	13.0796	0.593301
$487$	−4.89464	−0.221797	−0.110899	−	0.993832i	$-0.535373\pi$
$487$	−4.89464	−0.221797	−0.110899	+	0.993832i	$0.535373\pi$
$488$	−7.59463	−0.343793
$489$	27.1001	1.22551
$490$	0	0
$491$	40.9749	1.84917	0.924586	−	0.380974i	$-0.124411\pi$
$491$	40.9749	1.84917	0.924586	+	0.380974i	$0.124411\pi$
$492$	14.3547	0.647161
$493$	1.22666	0.0552458
$494$	−10.7678	−0.484464
$495$	0	0
$496$	1.14109	0.0512363
$497$	5.29045	0.237309
$498$	27.8087	1.24614
$499$	−3.51171	−0.157206	−0.0786030	−	0.996906i	$-0.525046\pi$
$499$	−3.51171	−0.157206	−0.0786030	+	0.996906i	$0.525046\pi$
$500$	0	0
$501$	−15.1279	−0.675864
$502$	−3.93400	−0.175583
$503$	−7.72289	−0.344347	−0.172173	−	0.985067i	$-0.555079\pi$
$503$	−7.72289	−0.344347	−0.172173	+	0.985067i	$0.555079\pi$
$504$	0.574069	0.0255711
$505$	0	0
$506$	9.17524	0.407889
$507$	19.3563	0.859643
$508$	−23.2593	−1.03197
$509$	15.7996	0.700303	0.350152	−	0.936693i	$-0.386130\pi$
$509$	15.7996	0.700303	0.350152	+	0.936693i	$0.386130\pi$
$510$	0	0
$511$	−11.9246	−0.527511
$512$	28.7388	1.27009
$513$	−5.63964	−0.248996
$514$	−17.0154	−0.750515
$515$	0	0
$516$	19.9194	0.876904
$517$	−38.7996	−1.70641
$518$	16.1616	0.710100
$519$	18.9394	0.831345
$520$	0	0
$521$	1.31031	0.0574059	0.0287029	−	0.999588i	$-0.490862\pi$
$521$	1.31031	0.0574059	0.0287029	+	0.999588i	$0.490862\pi$
$522$	1.63142	0.0714054
$523$	16.0884	0.703495	0.351747	−	0.936095i	$-0.385588\pi$
$523$	16.0884	0.703495	0.351747	+	0.936095i	$0.385588\pi$
$524$	−51.6973	−2.25841
$525$	0	0
$526$	−3.39914	−0.148210
$527$	0.378401	0.0164834
$528$	19.5270	0.849804
$529$	1.00000	0.0434783
$530$	0	0
$531$	0.466127	0.0202282
$532$	−2.47490	−0.107301
$533$	−19.1406	−0.829071
$534$	−16.9323	−0.732734
$535$	0	0
$536$	5.43648	0.234820
$537$	21.4069	0.923778
$538$	−25.0087	−1.07820
$539$	−4.35017	−0.187375
$540$	0	0
$541$	16.3654	0.703602	0.351801	−	0.936075i	$-0.385569\pi$
$541$	16.3654	0.703602	0.351801	+	0.936075i	$0.385569\pi$
$542$	−42.8433	−1.84028
$543$	−18.4149	−0.790260
$544$	7.70941	0.330538
$545$	0	0
$546$	16.4808	0.705314
$547$	43.1180	1.84359	0.921797	−	0.387672i	$-0.126721\pi$
$547$	43.1180	1.84359	0.921797	+	0.387672i	$0.126721\pi$
$548$	−33.0059	−1.40994
$549$	4.87014	0.207852
$550$	0	0
$551$	−1.28854	−0.0548936
$552$	−1.46373	−0.0623004
$553$	−6.83747	−0.290759
$554$	38.9159	1.65338
$555$	0	0
$556$	−36.8292	−1.56190
$557$	−23.9248	−1.01373	−0.506864	−	0.862026i	$-0.669195\pi$
$557$	−23.9248	−1.01373	−0.506864	+	0.862026i	$0.669195\pi$
$558$	0.503264	0.0213048
$559$	−26.5605	−1.12339
$560$	0	0
$561$	6.47543	0.273393
$562$	37.4155	1.57828
$563$	−6.27933	−0.264642	−0.132321	−	0.991207i	$-0.542243\pi$
$563$	−6.27933	−0.264642	−0.132321	+	0.991207i	$0.542243\pi$
$564$	33.7858	1.42264
$565$	0	0
$566$	60.5452	2.54490
$567$	6.81167	0.286063
$568$	−5.00562	−0.210031
$569$	25.6504	1.07532	0.537661	−	0.843161i	$-0.319308\pi$
$569$	25.6504	1.07532	0.537661	+	0.843161i	$0.319308\pi$
$570$	0	0
$571$	−11.4251	−0.478124	−0.239062	−	0.971004i	$-0.576840\pi$
$571$	−11.4251	−0.478124	−0.239062	+	0.971004i	$0.576840\pi$
$572$	53.8016	2.24956
$573$	−8.09360	−0.338115
$574$	−7.99271	−0.333609
$575$	0	0
$576$	6.73234	0.280514
$577$	41.1144	1.71161	0.855807	−	0.517296i	$-0.173061\pi$
$577$	41.1144	1.71161	0.855807	+	0.517296i	$0.173061\pi$
$578$	−33.9031	−1.41018
$579$	−39.5664	−1.64432
$580$	0	0
$581$	−8.52263	−0.353578
$582$	10.3884	0.430615
$583$	−24.9310	−1.03254
$584$	11.2825	0.466875
$585$	0	0
$586$	12.7427	0.526397
$587$	−8.34564	−0.344462	−0.172231	−	0.985057i	$-0.555097\pi$
$587$	−8.34564	−0.344462	−0.172231	+	0.985057i	$0.555097\pi$
$588$	3.78802	0.156215
$589$	−0.397490	−0.0163783
$590$	0	0
$591$	33.5122	1.37851
$592$	22.2335	0.913789
$593$	−21.6983	−0.891044	−0.445522	−	0.895271i	$-0.646982\pi$
$593$	−21.6983	−0.891044	−0.445522	+	0.895271i	$0.646982\pi$
$594$	51.1950	2.10055
$595$	0	0
$596$	25.1776	1.03132
$597$	24.3936	0.998363
$598$	10.6533	0.435645
$599$	16.1654	0.660502	0.330251	−	0.943893i	$-0.392867\pi$
$599$	16.1654	0.660502	0.330251	+	0.943893i	$0.392867\pi$
$600$	0	0
$601$	−44.3767	−1.81016	−0.905081	−	0.425238i	$-0.860190\pi$
$601$	−44.3767	−1.81016	−0.905081	+	0.425238i	$0.860190\pi$
$602$	−11.0911	−0.452041
$603$	−3.48620	−0.141969
$604$	−36.0856	−1.46830
$605$	0	0
$606$	−40.8171	−1.65808
$607$	−0.997193	−0.0404748	−0.0202374	−	0.999795i	$-0.506442\pi$
$607$	−0.997193	−0.0404748	−0.0202374	+	0.999795i	$0.506442\pi$
$608$	−8.09832	−0.328430
$609$	1.97220	0.0799176
$610$	0	0
$611$	−45.0499	−1.82252
$612$	1.42950	0.0577840
$613$	30.4672	1.23056	0.615279	−	0.788310i	$-0.289044\pi$
$613$	30.4672	1.23056	0.615279	+	0.788310i	$0.289044\pi$
$614$	−62.2819	−2.51349
$615$	0	0
$616$	4.11596	0.165837
$617$	44.0427	1.77309	0.886546	−	0.462640i	$-0.153098\pi$
$617$	44.0427	1.77309	0.886546	+	0.462640i	$0.153098\pi$
$618$	28.8465	1.16038
$619$	−34.5401	−1.38828	−0.694142	−	0.719838i	$-0.744216\pi$
$619$	−34.5401	−1.38828	−0.694142	+	0.719838i	$0.744216\pi$
$620$	0	0
$621$	5.57968	0.223905
$622$	−63.8137	−2.55870
$623$	5.18932	0.207906
$624$	22.6726	0.907631
$625$	0	0
$626$	−41.5261	−1.65972
$627$	−6.80210	−0.271650
$628$	−45.6959	−1.82347
$629$	7.37293	0.293978
$630$	0	0
$631$	−41.4837	−1.65144	−0.825720	−	0.564081i	$-0.809231\pi$
$631$	−41.4837	−1.65144	−0.825720	+	0.564081i	$0.809231\pi$
$632$	6.46934	0.257337
$633$	23.4801	0.933250
$634$	−17.5847	−0.698378
$635$	0	0
$636$	21.7093	0.860829
$637$	−5.05094	−0.200126
$638$	11.6970	0.463087
$639$	3.20990	0.126982
$640$	0	0
$641$	24.0075	0.948240	0.474120	−	0.880460i	$-0.342766\pi$
$641$	24.0075	0.948240	0.474120	+	0.880460i	$0.342766\pi$
$642$	−16.6233	−0.656071
$643$	35.8657	1.41440	0.707202	−	0.707011i	$-0.249957\pi$
$643$	35.8657	1.41440	0.707202	+	0.707011i	$0.249957\pi$
$644$	2.44859	0.0964881
$645$	0	0
$646$	−2.05126	−0.0807056
$647$	2.08756	0.0820703	0.0410352	−	0.999158i	$-0.486934\pi$
$647$	2.08756	0.0820703	0.0410352	+	0.999158i	$0.486934\pi$
$648$	−6.44493	−0.253181
$649$	3.34204	0.131186
$650$	0	0
$651$	0.608387	0.0238446
$652$	42.8936	1.67984
$653$	−18.7170	−0.732452	−0.366226	−	0.930526i	$-0.619350\pi$
$653$	−18.7170	−0.732452	−0.366226	+	0.930526i	$0.619350\pi$
$654$	−10.1101	−0.395335
$655$	0	0
$656$	−10.9955	−0.429304
$657$	−7.23505	−0.282266
$658$	−18.8119	−0.733365
$659$	0.511404	0.0199215	0.00996073	−	0.999950i	$-0.496829\pi$
$659$	0.511404	0.0199215	0.00996073	+	0.999950i	$0.496829\pi$
$660$	0	0
$661$	−13.5112	−0.525525	−0.262762	−	0.964861i	$-0.584633\pi$
$661$	−13.5112	−0.525525	−0.262762	+	0.964861i	$0.584633\pi$
$662$	−54.1202	−2.10344
$663$	7.51856	0.291997
$664$	8.06377	0.312935
$665$	0	0
$666$	9.80581	0.379968
$667$	1.27484	0.0493620
$668$	−23.9442	−0.926427
$669$	3.92804	0.151867
$670$	0	0
$671$	34.9179	1.34799
$672$	12.3951	0.478150
$673$	−5.39910	−0.208120	−0.104060	−	0.994571i	$-0.533183\pi$
$673$	−5.39910	−0.208120	−0.104060	+	0.994571i	$0.533183\pi$
$674$	52.8321	2.03502
$675$	0	0
$676$	30.6368	1.17834
$677$	33.8245	1.29998	0.649991	−	0.759942i	$-0.274773\pi$
$677$	33.8245	1.29998	0.649991	+	0.759942i	$0.274773\pi$
$678$	−4.58447	−0.176066
$679$	−3.18378	−0.122182
$680$	0	0
$681$	0.127958	0.00490336
$682$	3.60830	0.138169
$683$	3.41070	0.130507	0.0652534	−	0.997869i	$-0.479214\pi$
$683$	3.41070	0.130507	0.0652534	+	0.997869i	$0.479214\pi$
$684$	−1.50161	−0.0574156
$685$	0	0
$686$	−2.10917	−0.0805284
$687$	13.4259	0.512231
$688$	−15.2580	−0.581707
$689$	−28.9471	−1.10280
$690$	0	0
$691$	31.7159	1.20653	0.603265	−	0.797541i	$-0.293866\pi$
$691$	31.7159	1.20653	0.603265	+	0.797541i	$0.293866\pi$
$692$	29.9769	1.13955
$693$	−2.63940	−0.100263
$694$	26.4303	1.00328
$695$	0	0
$696$	−1.86602	−0.0707312
$697$	−3.64628	−0.138113
$698$	−68.1443	−2.57930
$699$	−25.7162	−0.972677
$700$	0	0
$701$	34.5591	1.30528	0.652639	−	0.757669i	$-0.273662\pi$
$701$	34.5591	1.30528	0.652639	+	0.757669i	$0.273662\pi$
$702$	59.4420	2.24349
$703$	−7.74488	−0.292104
$704$	48.2695	1.81923
$705$	0	0
$706$	−38.7673	−1.45903
$707$	12.5094	0.470463
$708$	−2.91016	−0.109371
$709$	49.3659	1.85397	0.926987	−	0.375092i	$-0.122389\pi$
$709$	49.3659	1.85397	0.926987	+	0.375092i	$0.122389\pi$
$710$	0	0
$711$	−4.14854	−0.155582
$712$	−4.90993	−0.184007
$713$	0.393265	0.0147279
$714$	3.13960	0.117496
$715$	0	0
$716$	33.8825	1.26625
$717$	−40.1514	−1.49948
$718$	−57.1126	−2.13142
$719$	5.42303	0.202245	0.101122	−	0.994874i	$-0.467757\pi$
$719$	5.42303	0.202245	0.101122	+	0.994874i	$0.467757\pi$
$720$	0	0
$721$	−8.84069	−0.329244
$722$	−37.9195	−1.41122
$723$	−1.08380	−0.0403071
$724$	−29.1468	−1.08323
$725$	0	0
$726$	25.8553	0.959581
$727$	−40.8718	−1.51585	−0.757925	−	0.652342i	$-0.773787\pi$
$727$	−40.8718	−1.51585	−0.757925	+	0.652342i	$0.773787\pi$
$728$	4.77900	0.177122
$729$	30.0285	1.11217
$730$	0	0
$731$	−5.05978	−0.187143
$732$	−30.4056	−1.12382
$733$	−8.68501	−0.320788	−0.160394	−	0.987053i	$-0.551277\pi$
$733$	−8.68501	−0.320788	−0.160394	+	0.987053i	$0.551277\pi$
$734$	−42.9530	−1.58543
$735$	0	0
$736$	8.01223	0.295335
$737$	−24.9954	−0.920716
$738$	−4.84946	−0.178511
$739$	50.8009	1.86874	0.934370	−	0.356303i	$-0.115963\pi$
$739$	50.8009	1.86874	0.934370	+	0.356303i	$0.115963\pi$
$740$	0	0
$741$	−7.89786	−0.290135
$742$	−12.0877	−0.443754
$743$	−47.0383	−1.72567	−0.862834	−	0.505488i	$-0.831313\pi$
$743$	−47.0383	−1.72567	−0.862834	+	0.505488i	$0.831313\pi$
$744$	−0.575632	−0.0211037
$745$	0	0
$746$	53.2828	1.95082
$747$	−5.17098	−0.189196
$748$	10.2492	0.374748
$749$	5.09461	0.186153
$750$	0	0
$751$	21.3490	0.779035	0.389518	−	0.921019i	$-0.372642\pi$
$751$	21.3490	0.779035	0.389518	+	0.921019i	$0.372642\pi$
$752$	−25.8795	−0.943727
$753$	−2.88548	−0.105153
$754$	13.5812	0.494600
$755$	0	0
$756$	13.6624	0.496896
$757$	40.1581	1.45957	0.729785	−	0.683676i	$-0.239620\pi$
$757$	40.1581	1.45957	0.729785	+	0.683676i	$0.239620\pi$
$758$	21.8733	0.794474
$759$	6.72979	0.244276
$760$	0	0
$761$	17.4920	0.634086	0.317043	−	0.948411i	$-0.397310\pi$
$761$	17.4920	0.634086	0.317043	+	0.948411i	$0.397310\pi$
$762$	−30.9947	−1.12282
$763$	3.09847	0.112172
$764$	−12.8104	−0.463465
$765$	0	0
$766$	27.5523	0.995507
$767$	3.88041	0.140113
$768$	10.2547	0.370035
$769$	−29.0922	−1.04909	−0.524545	−	0.851383i	$-0.675765\pi$
$769$	−29.0922	−1.04909	−0.524545	+	0.851383i	$0.675765\pi$
$770$	0	0
$771$	−12.4803	−0.449467
$772$	−62.6250	−2.25392
$773$	−11.8671	−0.426828	−0.213414	−	0.976962i	$-0.568458\pi$
$773$	−11.8671	−0.426828	−0.213414	+	0.976962i	$0.568458\pi$
$774$	−6.72939	−0.241883
$775$	0	0
$776$	3.01237	0.108138
$777$	11.8541	0.425263
$778$	−22.3424	−0.801015
$779$	3.83023	0.137232
$780$	0	0
$781$	23.0144	0.823519
$782$	2.02945	0.0725730
$783$	7.11321	0.254205
$784$	−2.90158	−0.103628
$785$	0	0
$786$	−68.8903	−2.45723
$787$	38.4524	1.37068	0.685339	−	0.728224i	$-0.259654\pi$
$787$	38.4524	1.37068	0.685339	+	0.728224i	$0.259654\pi$
$788$	53.0425	1.88956
$789$	−2.49318	−0.0887595
$790$	0	0
$791$	1.40502	0.0499568
$792$	2.49730	0.0887376
$793$	40.5428	1.43972
$794$	−47.9347	−1.70114
$795$	0	0
$796$	38.6098	1.36849
$797$	43.6690	1.54683	0.773417	−	0.633897i	$-0.218546\pi$
$797$	43.6690	1.54683	0.773417	+	0.633897i	$0.218546\pi$
$798$	−3.29798	−0.116747
$799$	−8.58200	−0.303610
$800$	0	0
$801$	3.14854	0.111248
$802$	73.6868	2.60197
$803$	−51.8738	−1.83059
$804$	21.7653	0.767604
$805$	0	0
$806$	4.18956	0.147571
$807$	−18.3432	−0.645711
$808$	−11.8359	−0.416384
$809$	−31.4556	−1.10592	−0.552959	−	0.833208i	$-0.686501\pi$
$809$	−31.4556	−1.10592	−0.552959	+	0.833208i	$0.686501\pi$
$810$	0	0
$811$	−22.8130	−0.801071	−0.400536	−	0.916281i	$-0.631176\pi$
$811$	−22.8130	−0.801071	−0.400536	+	0.916281i	$0.631176\pi$
$812$	3.12157	0.109545
$813$	−31.4244	−1.10210
$814$	70.3057	2.46421
$815$	0	0
$816$	4.31913	0.151200
$817$	5.31504	0.185950
$818$	45.2244	1.58123
$819$	−3.06458	−0.107085
$820$	0	0
$821$	57.1067	1.99304	0.996519	−	0.0833711i	$-0.0265687\pi$
$821$	57.1067	1.99304	0.996519	+	0.0833711i	$0.0265687\pi$
$822$	−43.9827	−1.53407
$823$	−33.3085	−1.16106	−0.580531	−	0.814238i	$-0.697155\pi$
$823$	−33.3085	−1.16106	−0.580531	+	0.814238i	$0.697155\pi$
$824$	8.36470	0.291398
$825$	0	0
$826$	1.62038	0.0563802
$827$	−5.35280	−0.186135	−0.0930676	−	0.995660i	$-0.529667\pi$
$827$	−5.35280	−0.186135	−0.0930676	+	0.995660i	$0.529667\pi$
$828$	1.48565	0.0516299
$829$	−12.3673	−0.429536	−0.214768	−	0.976665i	$-0.568899\pi$
$829$	−12.3673	−0.429536	−0.214768	+	0.976665i	$0.568899\pi$
$830$	0	0
$831$	28.5437	0.990171
$832$	56.0453	1.94302
$833$	−0.962204	−0.0333384
$834$	−49.0774	−1.69941
$835$	0	0
$836$	−10.7663	−0.372359
$837$	2.19429	0.0758458
$838$	−45.5508	−1.57352
$839$	10.6817	0.368774	0.184387	−	0.982854i	$-0.440970\pi$
$839$	10.6817	0.368774	0.184387	+	0.982854i	$0.440970\pi$
$840$	0	0
$841$	−27.3748	−0.943958
$842$	−20.4315	−0.704118
$843$	27.4433	0.945196
$844$	37.1639	1.27923
$845$	0	0
$846$	−11.4139	−0.392416
$847$	−7.92398	−0.272271
$848$	−16.6290	−0.571044
$849$	44.4082	1.52409
$850$	0	0
$851$	7.66254	0.262669
$852$	−20.0403	−0.686570
$853$	48.7430	1.66893	0.834465	−	0.551061i	$-0.185777\pi$
$853$	48.7430	1.66893	0.834465	+	0.551061i	$0.185777\pi$
$854$	16.9299	0.579328
$855$	0	0
$856$	−4.82032	−0.164755
$857$	10.3782	0.354511	0.177255	−	0.984165i	$-0.443278\pi$
$857$	10.3782	0.354511	0.177255	+	0.984165i	$0.443278\pi$
$858$	71.6944	2.44761
$859$	−7.87741	−0.268774	−0.134387	−	0.990929i	$-0.542906\pi$
$859$	−7.87741	−0.268774	−0.134387	+	0.990929i	$0.542906\pi$
$860$	0	0
$861$	−5.86244	−0.199791
$862$	17.5621	0.598169
$863$	39.8526	1.35660	0.678300	−	0.734785i	$-0.262717\pi$
$863$	39.8526	1.35660	0.678300	+	0.734785i	$0.262717\pi$
$864$	44.7057	1.52092
$865$	0	0
$866$	−79.0967	−2.68781
$867$	−24.8670	−0.844528
$868$	0.962945	0.0326845
$869$	−29.7442	−1.00900
$870$	0	0
$871$	−29.0219	−0.983369
$872$	−2.93165	−0.0992782
$873$	−1.93171	−0.0653786
$874$	−2.13183	−0.0721103
$875$	0	0
$876$	45.1704	1.52617
$877$	−54.1157	−1.82736	−0.913678	−	0.406438i	$-0.866771\pi$
$877$	−54.1157	−1.82736	−0.913678	+	0.406438i	$0.866771\pi$
$878$	−15.1905	−0.512654
$879$	9.34644	0.315248
$880$	0	0
$881$	−1.43974	−0.0485062	−0.0242531	−	0.999706i	$-0.507721\pi$
$881$	−1.43974	−0.0485062	−0.0242531	+	0.999706i	$0.507721\pi$
$882$	−1.27971	−0.0430900
$883$	26.9617	0.907333	0.453666	−	0.891172i	$-0.350116\pi$
$883$	26.9617	0.907333	0.453666	+	0.891172i	$0.350116\pi$
$884$	11.9003	0.400249
$885$	0	0
$886$	−54.7081	−1.83795
$887$	16.3978	0.550583	0.275291	−	0.961361i	$-0.411226\pi$
$887$	16.3978	0.550583	0.275291	+	0.961361i	$0.411226\pi$
$888$	−11.2159	−0.376380
$889$	9.49906	0.318588
$890$	0	0
$891$	29.6319	0.992706
$892$	6.21724	0.208169
$893$	9.01494	0.301674
$894$	33.5510	1.12211
$895$	0	0
$896$	7.37888	0.246511
$897$	7.81390	0.260898
$898$	14.3922	0.480275
$899$	0.501350	0.0167209
$900$	0	0
$901$	−5.51443	−0.183712
$902$	−34.7697	−1.15770
$903$	−8.13505	−0.270717
$904$	−1.32937	−0.0442143
$905$	0	0
$906$	−48.0866	−1.59757
$907$	48.9740	1.62615	0.813077	−	0.582156i	$-0.197791\pi$
$907$	48.9740	1.62615	0.813077	+	0.582156i	$0.197791\pi$
$908$	0.202530	0.00672118
$909$	7.58988	0.251740
$910$	0	0
$911$	−32.4549	−1.07528	−0.537640	−	0.843175i	$-0.680684\pi$
$911$	−32.4549	−1.07528	−0.537640	+	0.843175i	$0.680684\pi$
$912$	−4.53702	−0.150236
$913$	−37.0749	−1.22700
$914$	−43.8235	−1.44955
$915$	0	0
$916$	21.2503	0.702131
$917$	21.1131	0.697215
$918$	11.3237	0.373738
$919$	26.9145	0.887826	0.443913	−	0.896070i	$-0.353590\pi$
$919$	26.9145	0.887826	0.443913	+	0.896070i	$0.353590\pi$
$920$	0	0
$921$	−45.6821	−1.50528
$922$	−12.5449	−0.413146
$923$	26.7218	0.879558
$924$	16.4785	0.542104
$925$	0	0
$926$	51.0946	1.67907
$927$	−5.36396	−0.176175
$928$	10.2143	0.335301
$929$	−25.9261	−0.850608	−0.425304	−	0.905050i	$-0.639833\pi$
$929$	−25.9261	−0.850608	−0.425304	+	0.905050i	$0.639833\pi$
$930$	0	0
$931$	1.01074	0.0331258
$932$	−40.7032	−1.33328
$933$	−46.8056	−1.53235
$934$	5.87574	0.192260
$935$	0	0
$936$	2.89959	0.0947760
$937$	−54.4368	−1.77837	−0.889187	−	0.457545i	$-0.848729\pi$
$937$	−54.4368	−1.77837	−0.889187	+	0.457545i	$0.848729\pi$
$938$	−12.1189	−0.395697
$939$	−30.4583	−0.993968
$940$	0	0
$941$	17.1296	0.558409	0.279205	−	0.960232i	$-0.409929\pi$
$941$	17.1296	0.558409	0.279205	+	0.960232i	$0.409929\pi$
$942$	−60.8930	−1.98400
$943$	−3.78951	−0.123403
$944$	2.22915	0.0725526
$945$	0	0
$946$	−48.2483	−1.56869
$947$	−9.46776	−0.307661	−0.153830	−	0.988097i	$-0.549161\pi$
$947$	−9.46776	−0.307661	−0.153830	+	0.988097i	$0.549161\pi$
$948$	25.9005	0.841208
$949$	−60.2302	−1.95516
$950$	0	0
$951$	−12.8979	−0.418244
$952$	0.910399	0.0295062
$953$	50.1624	1.62492	0.812460	−	0.583017i	$-0.198128\pi$
$953$	50.1624	1.62492	0.812460	+	0.583017i	$0.198128\pi$
$954$	−7.33405	−0.237449
$955$	0	0
$956$	−63.5510	−2.05539
$957$	8.57941	0.277333
$958$	61.3018	1.98057
$959$	13.4795	0.435277
$960$	0	0
$961$	−30.8453	−0.995011
$962$	81.6313	2.63190
$963$	3.09108	0.0996088
$964$	−1.71543	−0.0552501
$965$	0	0
$966$	3.26292	0.104983
$967$	−39.5788	−1.27277	−0.636384	−	0.771372i	$-0.719571\pi$
$967$	−39.5788	−1.27277	−0.636384	+	0.771372i	$0.719571\pi$
$968$	7.49735	0.240974
$969$	−1.50454	−0.0483328
$970$	0	0
$971$	−19.8650	−0.637498	−0.318749	−	0.947839i	$-0.603263\pi$
$971$	−19.8650	−0.637498	−0.318749	+	0.947839i	$0.603263\pi$
$972$	15.1844	0.487041
$973$	15.0409	0.482191
$974$	−10.3236	−0.330790
$975$	0	0
$976$	23.2903	0.745506
$977$	2.08274	0.0666327	0.0333164	−	0.999445i	$-0.489393\pi$
$977$	2.08274	0.0666327	0.0333164	+	0.999445i	$0.489393\pi$
$978$	57.1587	1.82773
$979$	22.5744	0.721481
$980$	0	0
$981$	1.87995	0.0600223
$982$	86.4230	2.75787
$983$	54.2221	1.72942	0.864708	−	0.502275i	$-0.167504\pi$
$983$	54.2221	1.72942	0.864708	+	0.502275i	$0.167504\pi$
$984$	5.54680	0.176826
$985$	0	0
$986$	2.58723	0.0823941
$987$	−13.7980	−0.439196
$988$	−12.5006	−0.397697
$989$	−5.25853	−0.167212
$990$	0	0
$991$	−25.7712	−0.818649	−0.409324	−	0.912389i	$-0.634236\pi$
$991$	−25.7712	−0.818649	−0.409324	+	0.912389i	$0.634236\pi$
$992$	3.15093	0.100042
$993$	−39.6957	−1.25970
$994$	11.1585	0.353925
$995$	0	0
$996$	32.2839	1.02295
$997$	−18.6133	−0.589489	−0.294744	−	0.955576i	$-0.595234\pi$
$997$	−18.6133	−0.589489	−0.294744	+	0.955576i	$0.595234\pi$
$998$	−7.40680	−0.234458
$999$	42.7546	1.35269

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.q.1.5		5
5.4	even	2		805.2.a.l.1.1	✓	5
15.14	odd	2		7245.2.a.bh.1.5		5
35.34	odd	2		5635.2.a.y.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.l.1.1	✓	5	5.4	even	2
4025.2.a.q.1.5		5	1.1	even	1	trivial
5635.2.a.y.1.1		5	35.34	odd	2
7245.2.a.bh.1.5		5	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+2.10917 q^{2} +1.54702 q^{3} +2.44859 q^{4} +3.26292 q^{6} -1.00000 q^{7} +0.946160 q^{8} -0.606735 q^{9} +O(q^{10})\)	\(q+2.10917 q^{2} +1.54702 q^{3} +2.44859 q^{4} +3.26292 q^{6} -1.00000 q^{7} +0.946160 q^{8} -0.606735 q^{9} -4.35017 q^{11} +3.78802 q^{12} -5.05094 q^{13} -2.10917 q^{14} -2.90158 q^{16} -0.962204 q^{17} -1.27971 q^{18} +1.01074 q^{19} -1.54702 q^{21} -9.17524 q^{22} -1.00000 q^{23} +1.46373 q^{24} -10.6533 q^{26} -5.57968 q^{27} -2.44859 q^{28} -1.27484 q^{29} -0.393265 q^{31} -8.01223 q^{32} -6.72979 q^{33} -2.02945 q^{34} -1.48565 q^{36} -7.66254 q^{37} +2.13183 q^{38} -7.81390 q^{39} +3.78951 q^{41} -3.26292 q^{42} +5.25853 q^{43} -10.6518 q^{44} -2.10917 q^{46} +8.91911 q^{47} -4.48879 q^{48} +1.00000 q^{49} -1.48855 q^{51} -12.3677 q^{52} +5.73104 q^{53} -11.7685 q^{54} -0.946160 q^{56} +1.56364 q^{57} -2.68885 q^{58} -0.768255 q^{59} -8.02679 q^{61} -0.829462 q^{62} +0.606735 q^{63} -11.0960 q^{64} -14.1943 q^{66} +5.74583 q^{67} -2.35605 q^{68} -1.54702 q^{69} -5.29045 q^{71} -0.574069 q^{72} +11.9246 q^{73} -16.1616 q^{74} +2.47490 q^{76} +4.35017 q^{77} -16.4808 q^{78} +6.83747 q^{79} -6.81167 q^{81} +7.99271 q^{82} +8.52263 q^{83} -3.78802 q^{84} +11.0911 q^{86} -1.97220 q^{87} -4.11596 q^{88} -5.18932 q^{89} +5.05094 q^{91} -2.44859 q^{92} -0.608387 q^{93} +18.8119 q^{94} -12.3951 q^{96} +3.18378 q^{97} +2.10917 q^{98} +2.63940 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} + 4 q^{3} + 3 q^{4} - 5 q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + q^2 + 4 * q^3 + 3 * q^4 - 5 * q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9	\( 5 q + q^{2} + 4 q^{3} + 3 q^{4} - 5 q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9} - 7 q^{11} + 10 q^{12} + 5 q^{13} - q^{14} - 9 q^{16} + 7 q^{17} - 11 q^{18} - 10 q^{19} - 4 q^{21} - 4 q^{22} - 5 q^{23} - 4 q^{24} - 2 q^{26} + 7 q^{27} - 3 q^{28} - 14 q^{29} - 10 q^{31} - 4 q^{33} - 10 q^{34} + 20 q^{36} + 3 q^{37} + 15 q^{38} - 13 q^{39} - 15 q^{41} + 5 q^{42} - 8 q^{43} - 27 q^{44} - q^{46} + 10 q^{47} + 2 q^{48} + 5 q^{49} - 18 q^{51} - 18 q^{52} + 9 q^{53} - 39 q^{54} + 3 q^{56} - 23 q^{57} + 31 q^{58} - 19 q^{59} - 21 q^{61} + 10 q^{62} - 5 q^{63} - 7 q^{64} + 25 q^{66} - 5 q^{67} + 15 q^{68} - 4 q^{69} - 16 q^{71} - 26 q^{72} - q^{73} - 16 q^{74} + 7 q^{77} - 28 q^{78} + 20 q^{79} - 3 q^{81} - 11 q^{82} + 31 q^{83} - 10 q^{84} + 10 q^{86} - 38 q^{87} + 3 q^{88} - 21 q^{89} - 5 q^{91} - 3 q^{92} - 23 q^{93} + 28 q^{94} + 24 q^{96} - 19 q^{97} + q^{98} - 26 q^{99}+O(q^{100}) \) 5 * q + q^2 + 4 * q^3 + 3 * q^4 - 5 * q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9 - 7 * q^11 + 10 * q^12 + 5 * q^13 - q^14 - 9 * q^16 + 7 * q^17 - 11 * q^18 - 10 * q^19 - 4 * q^21 - 4 * q^22 - 5 * q^23 - 4 * q^24 - 2 * q^26 + 7 * q^27 - 3 * q^28 - 14 * q^29 - 10 * q^31 - 4 * q^33 - 10 * q^34 + 20 * q^36 + 3 * q^37 + 15 * q^38 - 13 * q^39 - 15 * q^41 + 5 * q^42 - 8 * q^43 - 27 * q^44 - q^46 + 10 * q^47 + 2 * q^48 + 5 * q^49 - 18 * q^51 - 18 * q^52 + 9 * q^53 - 39 * q^54 + 3 * q^56 - 23 * q^57 + 31 * q^58 - 19 * q^59 - 21 * q^61 + 10 * q^62 - 5 * q^63 - 7 * q^64 + 25 * q^66 - 5 * q^67 + 15 * q^68 - 4 * q^69 - 16 * q^71 - 26 * q^72 - q^73 - 16 * q^74 + 7 * q^77 - 28 * q^78 + 20 * q^79 - 3 * q^81 - 11 * q^82 + 31 * q^83 - 10 * q^84 + 10 * q^86 - 38 * q^87 + 3 * q^88 - 21 * q^89 - 5 * q^91 - 3 * q^92 - 23 * q^93 + 28 * q^94 + 24 * q^96 - 19 * q^97 + q^98 - 26 * q^99

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