LMFDB - Embedded newform 7175.2.a.n.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7175,2,Mod(1,7175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7175, 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("7175.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7175 = 5^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7175.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:	$57.2926634503$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.633117.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 4x^{2} + 6x - 3 $ x^5 - x^4 - 6x^3 + 4x^2 + 6*x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 287)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.08727$ of defining polynomial
Character	$\chi$	$=$	7175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.08727 q^{2} -2.08727 q^{3} -0.817843 q^{4} +2.26943 q^{6} -1.00000 q^{7} +3.06376 q^{8} +1.35670 q^{9} +O(q^{10})$	\(q-1.08727 q^{2} -2.08727 q^{3} -0.817843 q^{4} +2.26943 q^{6} -1.00000 q^{7} +3.06376 q^{8} +1.35670 q^{9} +6.03819 q^{11} +1.70706 q^{12} -3.67193 q^{13} +1.08727 q^{14} -1.69545 q^{16} +5.37138 q^{17} -1.47510 q^{18} -3.54285 q^{19} +2.08727 q^{21} -6.56515 q^{22} +1.30362 q^{23} -6.39489 q^{24} +3.99238 q^{26} +3.43002 q^{27} +0.817843 q^{28} -8.00307 q^{29} -0.384208 q^{31} -4.28411 q^{32} -12.6033 q^{33} -5.84014 q^{34} -1.10957 q^{36} +3.68876 q^{37} +3.85204 q^{38} +7.66432 q^{39} -1.00000 q^{41} -2.26943 q^{42} -0.824527 q^{43} -4.93829 q^{44} -1.41739 q^{46} -5.11625 q^{47} +3.53885 q^{48} +1.00000 q^{49} -11.2115 q^{51} +3.00307 q^{52} -1.53217 q^{53} -3.72936 q^{54} -3.06376 q^{56} +7.39489 q^{57} +8.70150 q^{58} +10.2669 q^{59} +9.36070 q^{61} +0.417738 q^{62} -1.35670 q^{63} +8.04887 q^{64} +13.7032 q^{66} -11.3638 q^{67} -4.39294 q^{68} -2.72101 q^{69} -14.9494 q^{71} +4.15659 q^{72} -7.77203 q^{73} -4.01068 q^{74} +2.89750 q^{76} -6.03819 q^{77} -8.33318 q^{78} -6.04703 q^{79} -11.2295 q^{81} +1.08727 q^{82} -14.1871 q^{83} -1.70706 q^{84} +0.896484 q^{86} +16.7046 q^{87} +18.4996 q^{88} +0.520905 q^{89} +3.67193 q^{91} -1.06616 q^{92} +0.801946 q^{93} +5.56275 q^{94} +8.94209 q^{96} +3.65270 q^{97} -1.08727 q^{98} +8.19200 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} - 4 q^{3} + 3 q^{4} + 12 q^{6} - 5 q^{7} + 3 q^{8} + q^{9}+O(q^{10}) $ 5 * q + q^2 - 4 * q^3 + 3 * q^4 + 12 * q^6 - 5 * q^7 + 3 * q^8 + q^9	$ 5 q + q^{2} - 4 q^{3} + 3 q^{4} + 12 q^{6} - 5 q^{7} + 3 q^{8} + q^{9} + 2 q^{11} + 2 q^{12} - 5 q^{13} - q^{14} - q^{16} - 13 q^{17} - 21 q^{18} + 4 q^{21} - q^{22} - 2 q^{23} + 2 q^{24} - 10 q^{27} - 3 q^{28} - 5 q^{29} + 17 q^{31} + 12 q^{32} - 3 q^{33} - 8 q^{34} + 15 q^{36} + 7 q^{37} + 3 q^{38} + 5 q^{39} - 5 q^{41} - 12 q^{42} - q^{43} - 47 q^{44} - 24 q^{46} - 9 q^{47} + 19 q^{48} + 5 q^{49} + 5 q^{51} - 20 q^{52} - 5 q^{53} + 2 q^{54} - 3 q^{56} + 3 q^{57} + 27 q^{58} + 7 q^{59} + 22 q^{61} + 28 q^{62} - q^{63} - 3 q^{64} - 42 q^{66} + 3 q^{67} - 17 q^{68} - 22 q^{69} - 24 q^{71} + 12 q^{72} - 40 q^{73} - 5 q^{74} - 19 q^{76} - 2 q^{77} - 30 q^{78} - 42 q^{79} + 9 q^{81} - q^{82} + 12 q^{83} - 2 q^{84} + 16 q^{86} + 32 q^{87} - 26 q^{88} + 8 q^{89} + 5 q^{91} - 12 q^{92} + 11 q^{93} - 23 q^{94} - 17 q^{96} - 16 q^{97} + q^{98} - 45 q^{99}+O(q^{100}) $ 5 * q + q^2 - 4 * q^3 + 3 * q^4 + 12 * q^6 - 5 * q^7 + 3 * q^8 + q^9 + 2 * q^11 + 2 * q^12 - 5 * q^13 - q^14 - q^16 - 13 * q^17 - 21 * q^18 + 4 * q^21 - q^22 - 2 * q^23 + 2 * q^24 - 10 * q^27 - 3 * q^28 - 5 * q^29 + 17 * q^31 + 12 * q^32 - 3 * q^33 - 8 * q^34 + 15 * q^36 + 7 * q^37 + 3 * q^38 + 5 * q^39 - 5 * q^41 - 12 * q^42 - q^43 - 47 * q^44 - 24 * q^46 - 9 * q^47 + 19 * q^48 + 5 * q^49 + 5 * q^51 - 20 * q^52 - 5 * q^53 + 2 * q^54 - 3 * q^56 + 3 * q^57 + 27 * q^58 + 7 * q^59 + 22 * q^61 + 28 * q^62 - q^63 - 3 * q^64 - 42 * q^66 + 3 * q^67 - 17 * q^68 - 22 * q^69 - 24 * q^71 + 12 * q^72 - 40 * q^73 - 5 * q^74 - 19 * q^76 - 2 * q^77 - 30 * q^78 - 42 * q^79 + 9 * q^81 - q^82 + 12 * q^83 - 2 * q^84 + 16 * q^86 + 32 * q^87 - 26 * q^88 + 8 * q^89 + 5 * q^91 - 12 * q^92 + 11 * q^93 - 23 * q^94 - 17 * q^96 - 16 * q^97 + q^98 - 45 * 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 $

$2$	−1.08727	−0.768816	−0.384408	−	0.923163i	$-0.625594\pi$
$2$	−1.08727	−0.768816	−0.384408	+	0.923163i	$0.625594\pi$
$3$	−2.08727	−1.20509	−0.602543	−	0.798086i	$-0.705846\pi$
$3$	−2.08727	−1.20509	−0.602543	+	0.798086i	$0.705846\pi$
$4$	−0.817843	−0.408922
$5$	0	0
$5$	0	0
$6$	2.26943	0.926490
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.06376	1.08320
$9$	1.35670	0.452232
$10$	0	0
$11$	6.03819	1.82058	0.910292	−	0.413967i	$-0.135857\pi$
$11$	6.03819	1.82058	0.910292	+	0.413967i	$0.135857\pi$
$12$	1.70706	0.492786
$13$	−3.67193	−1.01841	−0.509205	−	0.860645i	$-0.670061\pi$
$13$	−3.67193	−1.01841	−0.509205	+	0.860645i	$0.670061\pi$
$14$	1.08727	0.290585
$15$	0	0
$16$	−1.69545	−0.423862
$17$	5.37138	1.30275	0.651375	−	0.758756i	$-0.274192\pi$
$17$	5.37138	1.30275	0.651375	+	0.758756i	$0.274192\pi$
$18$	−1.47510	−0.347684
$19$	−3.54285	−0.812786	−0.406393	−	0.913698i	$-0.633214\pi$
$19$	−3.54285	−0.812786	−0.406393	+	0.913698i	$0.633214\pi$
$20$	0	0
$21$	2.08727	0.455480
$22$	−6.56515	−1.39969
$23$	1.30362	0.271824	0.135912	−	0.990721i	$-0.456604\pi$
$23$	1.30362	0.271824	0.135912	+	0.990721i	$0.456604\pi$
$24$	−6.39489	−1.30535
$25$	0	0
$26$	3.99238	0.782971
$27$	3.43002	0.660107
$28$	0.817843	0.154558
$29$	−8.00307	−1.48613	−0.743066	−	0.669218i	$-0.766629\pi$
$29$	−8.00307	−1.48613	−0.743066	+	0.669218i	$0.766629\pi$
$30$	0	0
$31$	−0.384208	−0.0690058	−0.0345029	−	0.999405i	$-0.510985\pi$
$31$	−0.384208	−0.0690058	−0.0345029	+	0.999405i	$0.510985\pi$
$32$	−4.28411	−0.757330
$33$	−12.6033	−2.19396
$34$	−5.84014	−1.00158
$35$	0	0
$36$	−1.10957	−0.184928
$37$	3.68876	0.606429	0.303214	−	0.952922i	$-0.401940\pi$
$37$	3.68876	0.606429	0.303214	+	0.952922i	$0.401940\pi$
$38$	3.85204	0.624883
$39$	7.66432	1.22727
$40$	0	0
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	−2.26943	−0.350180
$43$	−0.824527	−0.125739	−0.0628696	−	0.998022i	$-0.520025\pi$
$43$	−0.824527	−0.125739	−0.0628696	+	0.998022i	$0.520025\pi$
$44$	−4.93829	−0.744476
$45$	0	0
$46$	−1.41739	−0.208983
$47$	−5.11625	−0.746282	−0.373141	−	0.927775i	$-0.621719\pi$
$47$	−5.11625	−0.746282	−0.373141	+	0.927775i	$0.621719\pi$
$48$	3.53885	0.510790
$49$	1.00000	0.142857
$50$	0	0
$51$	−11.2115	−1.56993
$52$	3.00307	0.416450
$53$	−1.53217	−0.210460	−0.105230	−	0.994448i	$-0.533558\pi$
$53$	−1.53217	−0.210460	−0.105230	+	0.994448i	$0.533558\pi$
$54$	−3.72936	−0.507501
$55$	0	0
$56$	−3.06376	−0.409412
$57$	7.39489	0.979477
$58$	8.70150	1.14256
$59$	10.2669	1.33664	0.668320	−	0.743874i	$-0.267014\pi$
$59$	10.2669	1.33664	0.668320	+	0.743874i	$0.267014\pi$
$60$	0	0
$61$	9.36070	1.19851	0.599257	−	0.800557i	$-0.295463\pi$
$61$	9.36070	1.19851	0.599257	+	0.800557i	$0.295463\pi$
$62$	0.417738	0.0530528
$63$	−1.35670	−0.170928
$64$	8.04887	1.00611
$65$	0	0
$66$	13.7032	1.68675
$67$	−11.3638	−1.38830	−0.694152	−	0.719828i	$-0.744221\pi$
$67$	−11.3638	−1.38830	−0.694152	+	0.719828i	$0.744221\pi$
$68$	−4.39294	−0.532723
$69$	−2.72101	−0.327571
$70$	0	0
$71$	−14.9494	−1.77416	−0.887081	−	0.461614i	$-0.847271\pi$
$71$	−14.9494	−1.77416	−0.887081	+	0.461614i	$0.847271\pi$
$72$	4.15659	0.489859
$73$	−7.77203	−0.909648	−0.454824	−	0.890581i	$-0.650298\pi$
$73$	−7.77203	−0.909648	−0.454824	+	0.890581i	$0.650298\pi$
$74$	−4.01068	−0.466232
$75$	0	0
$76$	2.89750	0.332366
$77$	−6.03819	−0.688116
$78$	−8.33318	−0.943547
$79$	−6.04703	−0.680344	−0.340172	−	0.940363i	$-0.610485\pi$
$79$	−6.04703	−0.680344	−0.340172	+	0.940363i	$0.610485\pi$
$80$	0	0
$81$	−11.2295	−1.24772
$82$	1.08727	0.120069
$83$	−14.1871	−1.55723	−0.778617	−	0.627500i	$-0.784078\pi$
$83$	−14.1871	−1.55723	−0.778617	+	0.627500i	$0.784078\pi$
$84$	−1.70706	−0.186256
$85$	0	0
$86$	0.896484	0.0966703
$87$	16.7046	1.79092
$88$	18.4996	1.97206
$89$	0.520905	0.0552159	0.0276079	−	0.999619i	$-0.491211\pi$
$89$	0.520905	0.0552159	0.0276079	+	0.999619i	$0.491211\pi$
$90$	0	0
$91$	3.67193	0.384923
$92$	−1.06616	−0.111155
$93$	0.801946	0.0831580
$94$	5.56275	0.573754
$95$	0	0
$96$	8.94209	0.912648
$97$	3.65270	0.370876	0.185438	−	0.982656i	$-0.440630\pi$
$97$	3.65270	0.370876	0.185438	+	0.982656i	$0.440630\pi$
$98$	−1.08727	−0.109831
$99$	8.19200	0.823327
$100$	0	0
$101$	−2.45465	−0.244247	−0.122123	−	0.992515i	$-0.538970\pi$
$101$	−2.45465	−0.244247	−0.122123	+	0.992515i	$0.538970\pi$
$102$	12.1899	1.20698
$103$	10.2479	1.00975	0.504876	−	0.863192i	$-0.331538\pi$
$103$	10.2479	1.00975	0.504876	+	0.863192i	$0.331538\pi$
$104$	−11.2499	−1.10314
$105$	0	0
$106$	1.66588	0.161805
$107$	5.33318	0.515578	0.257789	−	0.966201i	$-0.417006\pi$
$107$	5.33318	0.515578	0.257789	+	0.966201i	$0.417006\pi$
$108$	−2.80522	−0.269932
$109$	8.82638	0.845413	0.422707	−	0.906267i	$-0.361080\pi$
$109$	8.82638	0.845413	0.422707	+	0.906267i	$0.361080\pi$
$110$	0	0
$111$	−7.69944	−0.730799
$112$	1.69545	0.160205
$113$	18.2045	1.71253	0.856267	−	0.516534i	$-0.172778\pi$
$113$	18.2045	1.71253	0.856267	+	0.516534i	$0.172778\pi$
$114$	−8.04024	−0.753038
$115$	0	0
$116$	6.54525	0.607711
$117$	−4.98170	−0.460559
$118$	−11.1629	−1.02763
$119$	−5.37138	−0.492393
$120$	0	0
$121$	25.4598	2.31452
$122$	−10.1776	−0.921437
$123$	2.08727	0.188203
$124$	0.314222	0.0282180
$125$	0	0
$126$	1.47510	0.131412
$127$	13.1751	1.16910	0.584551	−	0.811357i	$-0.301271\pi$
$127$	13.1751	1.16910	0.584551	+	0.811357i	$0.301271\pi$
$128$	−0.183089	−0.0161829
$129$	1.72101	0.151527
$130$	0	0
$131$	13.0506	1.14023	0.570117	−	0.821563i	$-0.306898\pi$
$131$	13.0506	1.14023	0.570117	+	0.821563i	$0.306898\pi$
$132$	10.3076	0.897158
$133$	3.54285	0.307204
$134$	12.3555	1.06735
$135$	0	0
$136$	16.4566	1.41114
$137$	−12.7699	−1.09100	−0.545502	−	0.838109i	$-0.683661\pi$
$137$	−12.7699	−1.09100	−0.545502	+	0.838109i	$0.683661\pi$
$138$	2.95847	0.251842
$139$	13.9759	1.18542	0.592712	−	0.805415i	$-0.298057\pi$
$139$	13.9759	1.18542	0.592712	+	0.805415i	$0.298057\pi$
$140$	0	0
$141$	10.6790	0.899334
$142$	16.2540	1.36400
$143$	−22.1718	−1.85410
$144$	−2.30021	−0.191684
$145$	0	0
$146$	8.45030	0.699352
$147$	−2.08727	−0.172155
$148$	−3.01683	−0.247982
$149$	−2.02136	−0.165597	−0.0827983	−	0.996566i	$-0.526386\pi$
$149$	−2.02136	−0.165597	−0.0827983	+	0.996566i	$0.526386\pi$
$150$	0	0
$151$	11.7648	0.957406	0.478703	−	0.877977i	$-0.341107\pi$
$151$	11.7648	0.957406	0.478703	+	0.877977i	$0.341107\pi$
$152$	−10.8544	−0.880411
$153$	7.28733	0.589146
$154$	6.56515	0.529035
$155$	0	0
$156$	−6.26821	−0.501858
$157$	−18.8859	−1.50726	−0.753631	−	0.657297i	$-0.771700\pi$
$157$	−18.8859	−1.50726	−0.753631	+	0.657297i	$0.771700\pi$
$158$	6.57475	0.523059
$159$	3.19805	0.253622
$160$	0	0
$161$	−1.30362	−0.102740
$162$	12.2095	0.959266
$163$	−16.3263	−1.27877	−0.639387	−	0.768885i	$-0.720812\pi$
$163$	−16.3263	−1.27877	−0.639387	+	0.768885i	$0.720812\pi$
$164$	0.817843	0.0638628
$165$	0	0
$166$	15.4252	1.19723
$167$	22.5846	1.74765	0.873824	−	0.486242i	$-0.161633\pi$
$167$	22.5846	1.74765	0.873824	+	0.486242i	$0.161633\pi$
$168$	6.39489	0.493376
$169$	0.483092	0.0371609
$170$	0	0
$171$	−4.80658	−0.367568
$172$	0.674334	0.0514175
$173$	22.2230	1.68958	0.844790	−	0.535097i	$-0.179725\pi$
$173$	22.2230	1.68958	0.844790	+	0.535097i	$0.179725\pi$
$174$	−18.1624	−1.37689
$175$	0	0
$176$	−10.2374	−0.771675
$177$	−21.4299	−1.61077
$178$	−0.566365	−0.0424508
$179$	−10.0095	−0.748142	−0.374071	−	0.927400i	$-0.622038\pi$
$179$	−10.0095	−0.748142	−0.374071	+	0.927400i	$0.622038\pi$
$180$	0	0
$181$	10.8101	0.803511	0.401755	−	0.915747i	$-0.368400\pi$
$181$	10.8101	0.803511	0.401755	+	0.915747i	$0.368400\pi$
$182$	−3.99238	−0.295935
$183$	−19.5383	−1.44431
$184$	3.99398	0.294440
$185$	0	0
$186$	−0.871932	−0.0639332
$187$	32.4334	2.37177
$188$	4.18429	0.305171
$189$	−3.43002	−0.249497
$190$	0	0
$191$	−19.7693	−1.43046	−0.715229	−	0.698890i	$-0.753678\pi$
$191$	−19.7693	−1.43046	−0.715229	+	0.698890i	$0.753678\pi$
$192$	−16.8002	−1.21245
$193$	−18.0955	−1.30254	−0.651270	−	0.758846i	$-0.725763\pi$
$193$	−18.0955	−1.30254	−0.651270	+	0.758846i	$0.725763\pi$
$194$	−3.97148	−0.285135
$195$	0	0
$196$	−0.817843	−0.0584174
$197$	−4.47538	−0.318858	−0.159429	−	0.987209i	$-0.550965\pi$
$197$	−4.47538	−0.318858	−0.159429	+	0.987209i	$0.550965\pi$
$198$	−8.90692	−0.632987
$199$	10.1956	0.722744	0.361372	−	0.932422i	$-0.382308\pi$
$199$	10.1956	0.722744	0.361372	+	0.932422i	$0.382308\pi$
$200$	0	0
$201$	23.7192	1.67303
$202$	2.66887	0.187781
$203$	8.00307	0.561705
$204$	9.16926	0.641977
$205$	0	0
$206$	−11.1422	−0.776313
$207$	1.76862	0.122928
$208$	6.22556	0.431665
$209$	−21.3924	−1.47974
$210$	0	0
$211$	−14.0477	−0.967081	−0.483540	−	0.875322i	$-0.660649\pi$
$211$	−14.0477	−0.967081	−0.483540	+	0.875322i	$0.660649\pi$
$212$	1.25308	0.0860616
$213$	31.2033	2.13802
$214$	−5.79861	−0.396385
$215$	0	0
$216$	10.5087	0.715029
$217$	0.384208	0.0260818
$218$	−9.59666	−0.649968
$219$	16.2223	1.09620
$220$	0	0
$221$	−19.7233	−1.32674
$222$	8.37138	0.561850
$223$	0.701496	0.0469756	0.0234878	−	0.999724i	$-0.492523\pi$
$223$	0.701496	0.0469756	0.0234878	+	0.999724i	$0.492523\pi$
$224$	4.28411	0.286244
$225$	0	0
$226$	−19.7932	−1.31662
$227$	−9.36869	−0.621822	−0.310911	−	0.950439i	$-0.600634\pi$
$227$	−9.36869	−0.621822	−0.310911	+	0.950439i	$0.600634\pi$
$228$	−6.04786	−0.400529
$229$	12.4012	0.819496	0.409748	−	0.912199i	$-0.365617\pi$
$229$	12.4012	0.819496	0.409748	+	0.912199i	$0.365617\pi$
$230$	0	0
$231$	12.6033	0.829239
$232$	−24.5195	−1.60978
$233$	−9.61739	−0.630056	−0.315028	−	0.949082i	$-0.602014\pi$
$233$	−9.61739	−0.630056	−0.315028	+	0.949082i	$0.602014\pi$
$234$	5.41646	0.354085
$235$	0	0
$236$	−8.39674	−0.546581
$237$	12.6218	0.819873
$238$	5.84014	0.378560
$239$	−16.5603	−1.07120	−0.535600	−	0.844472i	$-0.679914\pi$
$239$	−16.5603	−1.07120	−0.535600	+	0.844472i	$0.679914\pi$
$240$	0	0
$241$	9.29684	0.598862	0.299431	−	0.954118i	$-0.403203\pi$
$241$	9.29684	0.598862	0.299431	+	0.954118i	$0.403203\pi$
$242$	−27.6816	−1.77944
$243$	13.1489	0.843501
$244$	−7.65558	−0.490098
$245$	0	0
$246$	−2.26943	−0.144693
$247$	13.0091	0.827750
$248$	−1.17712	−0.0747472
$249$	29.6123	1.87660
$250$	0	0
$251$	2.89503	0.182733	0.0913664	−	0.995817i	$-0.470877\pi$
$251$	2.89503	0.182733	0.0913664	+	0.995817i	$0.470877\pi$
$252$	1.10957	0.0698961
$253$	7.87152	0.494878
$254$	−14.3249	−0.898824
$255$	0	0
$256$	−15.8987	−0.993668
$257$	−5.41470	−0.337760	−0.168880	−	0.985637i	$-0.554015\pi$
$257$	−5.41470	−0.337760	−0.168880	+	0.985637i	$0.554015\pi$
$258$	−1.87120	−0.116496
$259$	−3.68876	−0.229209
$260$	0	0
$261$	−10.8577	−0.672077
$262$	−14.1895	−0.876631
$263$	26.7339	1.64848	0.824242	−	0.566238i	$-0.191602\pi$
$263$	26.7339	1.64848	0.824242	+	0.566238i	$0.191602\pi$
$264$	−38.6136	−2.37650
$265$	0	0
$266$	−3.85204	−0.236184
$267$	−1.08727	−0.0665399
$268$	9.29377	0.567708
$269$	−14.6488	−0.893151	−0.446576	−	0.894746i	$-0.647357\pi$
$269$	−14.6488	−0.893151	−0.446576	+	0.894746i	$0.647357\pi$
$270$	0	0
$271$	22.8241	1.38646	0.693232	−	0.720714i	$-0.256186\pi$
$271$	22.8241	1.38646	0.693232	+	0.720714i	$0.256186\pi$
$272$	−9.10688	−0.552186
$273$	−7.66432	−0.463866
$274$	13.8843	0.838782
$275$	0	0
$276$	2.22536	0.133951
$277$	8.31190	0.499414	0.249707	−	0.968321i	$-0.419666\pi$
$277$	8.31190	0.499414	0.249707	+	0.968321i	$0.419666\pi$
$278$	−15.1956	−0.911373
$279$	−0.521254	−0.0312067
$280$	0	0
$281$	17.3137	1.03285	0.516423	−	0.856333i	$-0.327263\pi$
$281$	17.3137	1.03285	0.516423	+	0.856333i	$0.327263\pi$
$282$	−11.6110	−0.691422
$283$	14.7818	0.878686	0.439343	−	0.898319i	$-0.355211\pi$
$283$	14.7818	0.878686	0.439343	+	0.898319i	$0.355211\pi$
$284$	12.2262	0.725493
$285$	0	0
$286$	24.1068	1.42546
$287$	1.00000	0.0590281
$288$	−5.81224	−0.342489
$289$	11.8517	0.697158
$290$	0	0
$291$	−7.62418	−0.446937
$292$	6.35631	0.371975
$293$	−4.99638	−0.291892	−0.145946	−	0.989293i	$-0.546623\pi$
$293$	−4.99638	−0.291892	−0.145946	+	0.989293i	$0.546623\pi$
$294$	2.26943	0.132356
$295$	0	0
$296$	11.3015	0.656885
$297$	20.7111	1.20178
$298$	2.19777	0.127313
$299$	−4.78681	−0.276828
$300$	0	0
$301$	0.824527	0.0475250
$302$	−12.7915	−0.736069
$303$	5.12352	0.294338
$304$	6.00671	0.344509
$305$	0	0
$306$	−7.92330	−0.452945
$307$	7.85295	0.448192	0.224096	−	0.974567i	$-0.428057\pi$
$307$	7.85295	0.448192	0.224096	+	0.974567i	$0.428057\pi$
$308$	4.93829	0.281385
$309$	−21.3901	−1.21684
$310$	0	0
$311$	−27.0379	−1.53318	−0.766589	−	0.642138i	$-0.778048\pi$
$311$	−27.0379	−1.53318	−0.766589	+	0.642138i	$0.778048\pi$
$312$	23.4816	1.32938
$313$	0.168393	0.00951815	0.00475907	−	0.999989i	$-0.498485\pi$
$313$	0.168393	0.00951815	0.00475907	+	0.999989i	$0.498485\pi$
$314$	20.5341	1.15881
$315$	0	0
$316$	4.94552	0.278207
$317$	−5.33690	−0.299750	−0.149875	−	0.988705i	$-0.547887\pi$
$317$	−5.33690	−0.299750	−0.149875	+	0.988705i	$0.547887\pi$
$318$	−3.47715	−0.194989
$319$	−48.3240	−2.70563
$320$	0	0
$321$	−11.1318	−0.621316
$322$	1.41739	0.0789880
$323$	−19.0300	−1.05886
$324$	9.18394	0.510219
$325$	0	0
$326$	17.7511	0.983142
$327$	−18.4230	−1.01880
$328$	−3.06376	−0.169168
$329$	5.11625	0.282068
$330$	0	0
$331$	−8.09405	−0.444889	−0.222445	−	0.974945i	$-0.571404\pi$
$331$	−8.09405	−0.444889	−0.222445	+	0.974945i	$0.571404\pi$
$332$	11.6028	0.636786
$333$	5.00453	0.274247
$334$	−24.5556	−1.34362
$335$	0	0
$336$	−3.53885	−0.193060
$337$	−20.1540	−1.09786	−0.548929	−	0.835869i	$-0.684964\pi$
$337$	−20.1540	−1.09786	−0.548929	+	0.835869i	$0.684964\pi$
$338$	−0.525252	−0.0285699
$339$	−37.9977	−2.06375
$340$	0	0
$341$	−2.31992	−0.125631
$342$	5.22605	0.282592
$343$	−1.00000	−0.0539949
$344$	−2.52615	−0.136201
$345$	0	0
$346$	−24.1624	−1.29898
$347$	−18.2807	−0.981359	−0.490679	−	0.871340i	$-0.663251\pi$
$347$	−18.2807	−0.981359	−0.490679	+	0.871340i	$0.663251\pi$
$348$	−13.6617	−0.732345
$349$	9.74567	0.521674	0.260837	−	0.965383i	$-0.416001\pi$
$349$	9.74567	0.521674	0.260837	+	0.965383i	$0.416001\pi$
$350$	0	0
$351$	−12.5948	−0.672260
$352$	−25.8683	−1.37878
$353$	−26.2143	−1.39525	−0.697624	−	0.716464i	$-0.745759\pi$
$353$	−26.2143	−1.39525	−0.697624	+	0.716464i	$0.745759\pi$
$354$	23.3000	1.23838
$355$	0	0
$356$	−0.426019	−0.0225790
$357$	11.2115	0.593376
$358$	10.8830	0.575184
$359$	0.473108	0.0249697	0.0124849	−	0.999922i	$-0.496026\pi$
$359$	0.473108	0.0249697	0.0124849	+	0.999922i	$0.496026\pi$
$360$	0	0
$361$	−6.44820	−0.339379
$362$	−11.7535	−0.617752
$363$	−53.1414	−2.78920
$364$	−3.00307	−0.157403
$365$	0	0
$366$	21.2434	1.11041
$367$	−10.2670	−0.535932	−0.267966	−	0.963428i	$-0.586352\pi$
$367$	−10.2670	−0.535932	−0.267966	+	0.963428i	$0.586352\pi$
$368$	−2.21022	−0.115216
$369$	−1.35670	−0.0706268
$370$	0	0
$371$	1.53217	0.0795463
$372$	−0.655866	−0.0340051
$373$	−20.1653	−1.04412	−0.522061	−	0.852908i	$-0.674837\pi$
$373$	−20.1653	−1.04412	−0.522061	+	0.852908i	$0.674837\pi$
$374$	−35.2639	−1.82345
$375$	0	0
$376$	−15.6749	−0.808374
$377$	29.3867	1.51349
$378$	3.72936	0.191817
$379$	−26.8293	−1.37813	−0.689063	−	0.724701i	$-0.741978\pi$
$379$	−26.8293	−1.37813	−0.689063	+	0.724701i	$0.741978\pi$
$380$	0	0
$381$	−27.5000	−1.40887
$382$	21.4946	1.09976
$383$	24.1679	1.23492	0.617461	−	0.786602i	$-0.288161\pi$
$383$	24.1679	1.23492	0.617461	+	0.786602i	$0.288161\pi$
$384$	0.382156	0.0195018
$385$	0	0
$386$	19.6746	1.00141
$387$	−1.11863	−0.0568634
$388$	−2.98734	−0.151659
$389$	15.9595	0.809180	0.404590	−	0.914498i	$-0.367414\pi$
$389$	15.9595	0.809180	0.404590	+	0.914498i	$0.367414\pi$
$390$	0	0
$391$	7.00224	0.354119
$392$	3.06376	0.154743
$393$	−27.2401	−1.37408
$394$	4.86595	0.245143
$395$	0	0
$396$	−6.69977	−0.336676
$397$	8.73399	0.438346	0.219173	−	0.975686i	$-0.429664\pi$
$397$	8.73399	0.438346	0.219173	+	0.975686i	$0.429664\pi$
$398$	−11.0853	−0.555657
$399$	−7.39489	−0.370208
$400$	0	0
$401$	1.77238	0.0885086	0.0442543	−	0.999020i	$-0.485909\pi$
$401$	1.77238	0.0885086	0.0442543	+	0.999020i	$0.485909\pi$
$402$	−25.7892	−1.28625
$403$	1.41079	0.0702763
$404$	2.00752	0.0998778
$405$	0	0
$406$	−8.70150	−0.431848
$407$	22.2735	1.10405
$408$	−34.3494	−1.70055
$409$	−27.0895	−1.33949	−0.669746	−	0.742590i	$-0.733597\pi$
$409$	−27.0895	−1.33949	−0.669746	+	0.742590i	$0.733597\pi$
$410$	0	0
$411$	26.6542	1.31475
$412$	−8.38114	−0.412909
$413$	−10.2669	−0.505203
$414$	−1.92297	−0.0945087
$415$	0	0
$416$	15.7310	0.771273
$417$	−29.1716	−1.42854
$418$	23.2593	1.13765
$419$	−18.3386	−0.895898	−0.447949	−	0.894059i	$-0.647845\pi$
$419$	−18.3386	−0.895898	−0.447949	+	0.894059i	$0.647845\pi$
$420$	0	0
$421$	16.7202	0.814894	0.407447	−	0.913229i	$-0.366419\pi$
$421$	16.7202	0.814894	0.407447	+	0.913229i	$0.366419\pi$
$422$	15.2736	0.743507
$423$	−6.94120	−0.337493
$424$	−4.69420	−0.227970
$425$	0	0
$426$	−33.9265	−1.64374
$427$	−9.36070	−0.452996
$428$	−4.36171	−0.210831
$429$	46.2786	2.23435
$430$	0	0
$431$	0.204738	0.00986186	0.00493093	−	0.999988i	$-0.498430\pi$
$431$	0.204738	0.00986186	0.00493093	+	0.999988i	$0.498430\pi$
$432$	−5.81541	−0.279794
$433$	−31.9997	−1.53781	−0.768903	−	0.639366i	$-0.779197\pi$
$433$	−31.9997	−1.53781	−0.768903	+	0.639366i	$0.779197\pi$
$434$	−0.417738	−0.0200521
$435$	0	0
$436$	−7.21859	−0.345708
$437$	−4.61854	−0.220935
$438$	−17.6381	−0.842779
$439$	24.9052	1.18866	0.594330	−	0.804221i	$-0.297417\pi$
$439$	24.9052	1.18866	0.594330	+	0.804221i	$0.297417\pi$
$440$	0	0
$441$	1.35670	0.0646046
$442$	21.4446	1.02002
$443$	−19.0300	−0.904142	−0.452071	−	0.891982i	$-0.649315\pi$
$443$	−19.0300	−0.904142	−0.452071	+	0.891982i	$0.649315\pi$
$444$	6.29694	0.298839
$445$	0	0
$446$	−0.762716	−0.0361156
$447$	4.21913	0.199558
$448$	−8.04887	−0.380274
$449$	−5.95010	−0.280802	−0.140401	−	0.990095i	$-0.544839\pi$
$449$	−5.95010	−0.280802	−0.140401	+	0.990095i	$0.544839\pi$
$450$	0	0
$451$	−6.03819	−0.284327
$452$	−14.8884	−0.700292
$453$	−24.5563	−1.15376
$454$	10.1863	0.478067
$455$	0	0
$456$	22.6561	1.06097
$457$	31.8410	1.48946	0.744729	−	0.667367i	$-0.232579\pi$
$457$	31.8410	1.48946	0.744729	+	0.667367i	$0.232579\pi$
$458$	−13.4835	−0.630042
$459$	18.4239	0.859955
$460$	0	0
$461$	4.99638	0.232705	0.116352	−	0.993208i	$-0.462880\pi$
$461$	4.99638	0.232705	0.116352	+	0.993208i	$0.462880\pi$
$462$	−13.7032	−0.637532
$463$	−17.6038	−0.818119	−0.409060	−	0.912508i	$-0.634143\pi$
$463$	−17.6038	−0.818119	−0.409060	+	0.912508i	$0.634143\pi$
$464$	13.5688	0.629914
$465$	0	0
$466$	10.4567	0.484397
$467$	42.9444	1.98723	0.993614	−	0.112833i	$-0.0359925\pi$
$467$	42.9444	1.98723	0.993614	+	0.112833i	$0.0359925\pi$
$468$	4.07425	0.188332
$469$	11.3638	0.524730
$470$	0	0
$471$	39.4201	1.81638
$472$	31.4554	1.44785
$473$	−4.97865	−0.228919
$474$	−13.7233	−0.630331
$475$	0	0
$476$	4.39294	0.201350
$477$	−2.07869	−0.0951767
$478$	18.0056	0.823556
$479$	2.85249	0.130334	0.0651669	−	0.997874i	$-0.479242\pi$
$479$	2.85249	0.130334	0.0651669	+	0.997874i	$0.479242\pi$
$480$	0	0
$481$	−13.5449	−0.617594
$482$	−10.1082	−0.460415
$483$	2.72101	0.123810
$484$	−20.8221	−0.946459
$485$	0	0
$486$	−14.2964	−0.648497
$487$	6.23225	0.282410	0.141205	−	0.989980i	$-0.454902\pi$
$487$	6.23225	0.282410	0.141205	+	0.989980i	$0.454902\pi$
$488$	28.6789	1.29823
$489$	34.0774	1.54103
$490$	0	0
$491$	−2.13846	−0.0965071	−0.0482536	−	0.998835i	$-0.515366\pi$
$491$	−2.13846	−0.0965071	−0.0482536	+	0.998835i	$0.515366\pi$
$492$	−1.70706	−0.0769602
$493$	−42.9875	−1.93606
$494$	−14.1444	−0.636388
$495$	0	0
$496$	0.651404	0.0292489
$497$	14.9494	0.670570
$498$	−32.1965	−1.44276
$499$	25.1110	1.12412	0.562060	−	0.827096i	$-0.310009\pi$
$499$	25.1110	1.12412	0.562060	+	0.827096i	$0.310009\pi$
$500$	0	0
$501$	−47.1402	−2.10607
$502$	−3.14768	−0.140488
$503$	−37.1641	−1.65707	−0.828534	−	0.559939i	$-0.810824\pi$
$503$	−37.1641	−1.65707	−0.828534	+	0.559939i	$0.810824\pi$
$504$	−4.15659	−0.185149
$505$	0	0
$506$	−8.55847	−0.380470
$507$	−1.00834	−0.0447821
$508$	−10.7752	−0.478071
$509$	−2.36319	−0.104747	−0.0523734	−	0.998628i	$-0.516679\pi$
$509$	−2.36319	−0.104747	−0.0523734	+	0.998628i	$0.516679\pi$
$510$	0	0
$511$	7.77203	0.343815
$512$	17.6523	0.780131
$513$	−12.1520	−0.536526
$514$	5.88725	0.259675
$515$	0	0
$516$	−1.40752	−0.0619625
$517$	−30.8929	−1.35867
$518$	4.01068	0.176219
$519$	−46.3853	−2.03609
$520$	0	0
$521$	−2.27368	−0.0996116	−0.0498058	−	0.998759i	$-0.515860\pi$
$521$	−2.27368	−0.0996116	−0.0498058	+	0.998759i	$0.515860\pi$
$522$	11.8053	0.516704
$523$	35.7432	1.56294	0.781471	−	0.623941i	$-0.214469\pi$
$523$	35.7432	1.56294	0.781471	+	0.623941i	$0.214469\pi$
$524$	−10.6733	−0.466266
$525$	0	0
$526$	−29.0670	−1.26738
$527$	−2.06373	−0.0898974
$528$	21.3683	0.929935
$529$	−21.3006	−0.926112
$530$	0	0
$531$	13.9291	0.604472
$532$	−2.89750	−0.125622
$533$	3.67193	0.159049
$534$	1.18216	0.0511569
$535$	0	0
$536$	−34.8158	−1.50381
$537$	20.8925	0.901576
$538$	15.9272	0.686669
$539$	6.03819	0.260083
$540$	0	0
$541$	−22.5224	−0.968314	−0.484157	−	0.874981i	$-0.660874\pi$
$541$	−22.5224	−0.968314	−0.484157	+	0.874981i	$0.660874\pi$
$542$	−24.8159	−1.06594
$543$	−22.5637	−0.968299
$544$	−23.0116	−0.986612
$545$	0	0
$546$	8.33318	0.356627
$547$	−3.63915	−0.155599	−0.0777994	−	0.996969i	$-0.524789\pi$
$547$	−3.63915	−0.155599	−0.0777994	+	0.996969i	$0.524789\pi$
$548$	10.4438	0.446135
$549$	12.6996	0.542007
$550$	0	0
$551$	28.3537	1.20791
$552$	−8.33652	−0.354826
$553$	6.04703	0.257146
$554$	−9.03729	−0.383957
$555$	0	0
$556$	−11.4301	−0.484745
$557$	−4.80008	−0.203386	−0.101693	−	0.994816i	$-0.532426\pi$
$557$	−4.80008	−0.203386	−0.101693	+	0.994816i	$0.532426\pi$
$558$	0.566744	0.0239922
$559$	3.02761	0.128054
$560$	0	0
$561$	−67.6973	−2.85818
$562$	−18.8246	−0.794069
$563$	−31.7115	−1.33648	−0.668241	−	0.743945i	$-0.732952\pi$
$563$	−31.7115	−1.33648	−0.668241	+	0.743945i	$0.732952\pi$
$564$	−8.73374	−0.367757
$565$	0	0
$566$	−16.0718	−0.675548
$567$	11.2295	0.471593
$568$	−45.8012	−1.92178
$569$	−35.4970	−1.48811	−0.744055	−	0.668118i	$-0.767100\pi$
$569$	−35.4970	−1.48811	−0.744055	+	0.668118i	$0.767100\pi$
$570$	0	0
$571$	−38.7912	−1.62336	−0.811681	−	0.584100i	$-0.801447\pi$
$571$	−38.7912	−1.62336	−0.811681	+	0.584100i	$0.801447\pi$
$572$	18.1331	0.758182
$573$	41.2639	1.72383
$574$	−1.08727	−0.0453818
$575$	0	0
$576$	10.9199	0.454995
$577$	0.335828	0.0139807	0.00699035	−	0.999976i	$-0.497775\pi$
$577$	0.335828	0.0139807	0.00699035	+	0.999976i	$0.497775\pi$
$578$	−12.8860	−0.535987
$579$	37.7701	1.56967
$580$	0	0
$581$	14.1871	0.588579
$582$	8.28954	0.343613
$583$	−9.25154	−0.383160
$584$	−23.8116	−0.985332
$585$	0	0
$586$	5.43242	0.224411
$587$	−8.19386	−0.338197	−0.169098	−	0.985599i	$-0.554086\pi$
$587$	−8.19386	−0.338197	−0.169098	+	0.985599i	$0.554086\pi$
$588$	1.70706	0.0703980
$589$	1.36119	0.0560870
$590$	0	0
$591$	9.34132	0.384251
$592$	−6.25410	−0.257042
$593$	−30.1222	−1.23697	−0.618486	−	0.785796i	$-0.712254\pi$
$593$	−30.1222	−1.23697	−0.618486	+	0.785796i	$0.712254\pi$
$594$	−22.5186	−0.923948
$595$	0	0
$596$	1.65316	0.0677160
$597$	−21.2809	−0.870968
$598$	5.20456	0.212830
$599$	−39.6072	−1.61831	−0.809153	−	0.587599i	$-0.800073\pi$
$599$	−39.6072	−1.61831	−0.809153	+	0.587599i	$0.800073\pi$
$600$	0	0
$601$	−35.0329	−1.42902	−0.714511	−	0.699624i	$-0.753351\pi$
$601$	−35.0329	−1.42902	−0.714511	+	0.699624i	$0.753351\pi$
$602$	−0.896484	−0.0365380
$603$	−15.4172	−0.627836
$604$	−9.62176	−0.391504
$605$	0	0
$606$	−5.57065	−0.226292
$607$	−13.4657	−0.546555	−0.273278	−	0.961935i	$-0.588108\pi$
$607$	−13.4657	−0.546555	−0.273278	+	0.961935i	$0.588108\pi$
$608$	15.1780	0.615547
$609$	−16.7046	−0.676903
$610$	0	0
$611$	18.7865	0.760022
$612$	−5.95990	−0.240915
$613$	6.49820	0.262460	0.131230	−	0.991352i	$-0.458107\pi$
$613$	6.49820	0.262460	0.131230	+	0.991352i	$0.458107\pi$
$614$	−8.53828	−0.344577
$615$	0	0
$616$	−18.4996	−0.745368
$617$	−6.63045	−0.266932	−0.133466	−	0.991053i	$-0.542611\pi$
$617$	−6.63045	−0.266932	−0.133466	+	0.991053i	$0.542611\pi$
$618$	23.2568	0.935525
$619$	−4.50756	−0.181174	−0.0905871	−	0.995889i	$-0.528874\pi$
$619$	−4.50756	−0.181174	−0.0905871	+	0.995889i	$0.528874\pi$
$620$	0	0
$621$	4.47144	0.179433
$622$	29.3975	1.17873
$623$	−0.520905	−0.0208696
$624$	−12.9944	−0.520194
$625$	0	0
$626$	−0.183089	−0.00731771
$627$	44.6518	1.78322
$628$	15.4457	0.616352
$629$	19.8137	0.790025
$630$	0	0
$631$	−24.2677	−0.966081	−0.483040	−	0.875598i	$-0.660468\pi$
$631$	−24.2677	−0.966081	−0.483040	+	0.875598i	$0.660468\pi$
$632$	−18.5266	−0.736949
$633$	29.3213	1.16542
$634$	5.80265	0.230453
$635$	0	0
$636$	−2.61551	−0.103712
$637$	−3.67193	−0.145487
$638$	52.5413	2.08013
$639$	−20.2818	−0.802334
$640$	0	0
$641$	22.2964	0.880653	0.440327	−	0.897838i	$-0.354863\pi$
$641$	22.2964	0.880653	0.440327	+	0.897838i	$0.354863\pi$
$642$	12.1033	0.477678
$643$	16.2405	0.640464	0.320232	−	0.947339i	$-0.396239\pi$
$643$	16.2405	0.640464	0.320232	+	0.947339i	$0.396239\pi$
$644$	1.06616	0.0420125
$645$	0	0
$646$	20.6907	0.814067
$647$	−13.5814	−0.533939	−0.266969	−	0.963705i	$-0.586022\pi$
$647$	−13.5814	−0.533939	−0.266969	+	0.963705i	$0.586022\pi$
$648$	−34.4044	−1.35153
$649$	61.9937	2.43347
$650$	0	0
$651$	−0.801946	−0.0314308
$652$	13.3524	0.522918
$653$	47.1222	1.84403	0.922016	−	0.387151i	$-0.126541\pi$
$653$	47.1222	1.84403	0.922016	+	0.387151i	$0.126541\pi$
$654$	20.0308	0.783267
$655$	0	0
$656$	1.69545	0.0661960
$657$	−10.5443	−0.411372
$658$	−5.56275	−0.216858
$659$	5.27483	0.205478	0.102739	−	0.994708i	$-0.467239\pi$
$659$	5.27483	0.205478	0.102739	+	0.994708i	$0.467239\pi$
$660$	0	0
$661$	−47.8044	−1.85938	−0.929689	−	0.368346i	$-0.879924\pi$
$661$	−47.8044	−1.85938	−0.929689	+	0.368346i	$0.879924\pi$
$662$	8.80042	0.342038
$663$	41.1679	1.59883
$664$	−43.4657	−1.68680
$665$	0	0
$666$	−5.44128	−0.210845
$667$	−10.4330	−0.403966
$668$	−18.4707	−0.714651
$669$	−1.46421	−0.0566097
$670$	0	0
$671$	56.5217	2.18200
$672$	−8.94209	−0.344949
$673$	5.11960	0.197346	0.0986730	−	0.995120i	$-0.468540\pi$
$673$	5.11960	0.197346	0.0986730	+	0.995120i	$0.468540\pi$
$674$	21.9128	0.844051
$675$	0	0
$676$	−0.395094	−0.0151959
$677$	−30.7985	−1.18368	−0.591842	−	0.806054i	$-0.701599\pi$
$677$	−30.7985	−1.18368	−0.591842	+	0.806054i	$0.701599\pi$
$678$	41.3137	1.58664
$679$	−3.65270	−0.140178
$680$	0	0
$681$	19.5550	0.749349
$682$	2.52238	0.0965870
$683$	18.8534	0.721407	0.360703	−	0.932681i	$-0.382537\pi$
$683$	18.8534	0.721407	0.360703	+	0.932681i	$0.382537\pi$
$684$	3.93103	0.150307
$685$	0	0
$686$	1.08727	0.0415122
$687$	−25.8847	−0.987563
$688$	1.39794	0.0532960
$689$	5.62603	0.214335
$690$	0	0
$691$	−6.22638	−0.236863	−0.118431	−	0.992962i	$-0.537787\pi$
$691$	−6.22638	−0.236863	−0.118431	+	0.992962i	$0.537787\pi$
$692$	−18.1749	−0.690906
$693$	−8.19200	−0.311188
$694$	19.8761	0.754485
$695$	0	0
$696$	51.1787	1.93992
$697$	−5.37138	−0.203455
$698$	−10.5962	−0.401071
$699$	20.0741	0.759272
$700$	0	0
$701$	40.6743	1.53625	0.768124	−	0.640301i	$-0.221190\pi$
$701$	40.6743	1.53625	0.768124	+	0.640301i	$0.221190\pi$
$702$	13.6939	0.516845
$703$	−13.0687	−0.492897
$704$	48.6006	1.83171
$705$	0	0
$706$	28.5021	1.07269
$707$	2.45465	0.0923166
$708$	17.5263	0.658677
$709$	−47.5660	−1.78638	−0.893189	−	0.449681i	$-0.851538\pi$
$709$	−47.5660	−1.78638	−0.893189	+	0.449681i	$0.851538\pi$
$710$	0	0
$711$	−8.20398	−0.307673
$712$	1.59593	0.0598099
$713$	−0.500862	−0.0187574
$714$	−12.1899	−0.456197
$715$	0	0
$716$	8.18617	0.305932
$717$	34.5659	1.29089
$718$	−0.514397	−0.0191971
$719$	−0.700457	−0.0261226	−0.0130613	−	0.999915i	$-0.504158\pi$
$719$	−0.700457	−0.0261226	−0.0130613	+	0.999915i	$0.504158\pi$
$720$	0	0
$721$	−10.2479	−0.381650
$722$	7.01094	0.260920
$723$	−19.4050	−0.721680
$724$	−8.84099	−0.328573
$725$	0	0
$726$	57.7791	2.14438
$727$	−38.6447	−1.43325	−0.716625	−	0.697458i	$-0.754314\pi$
$727$	−38.6447	−1.43325	−0.716625	+	0.697458i	$0.754314\pi$
$728$	11.2499	0.416949
$729$	6.24313	0.231227
$730$	0	0
$731$	−4.42885	−0.163807
$732$	15.9793	0.590611
$733$	31.3572	1.15820	0.579101	−	0.815255i	$-0.303404\pi$
$733$	31.3572	1.15820	0.579101	+	0.815255i	$0.303404\pi$
$734$	11.1630	0.412033
$735$	0	0
$736$	−5.58485	−0.205860
$737$	−68.6166	−2.52752
$738$	1.47510	0.0542991
$739$	51.5448	1.89611	0.948054	−	0.318110i	$-0.103048\pi$
$739$	51.5448	1.89611	0.948054	+	0.318110i	$0.103048\pi$
$740$	0	0
$741$	−27.1535	−0.997510
$742$	−1.66588	−0.0611565
$743$	15.7347	0.577251	0.288626	−	0.957442i	$-0.406802\pi$
$743$	15.7347	0.577251	0.288626	+	0.957442i	$0.406802\pi$
$744$	2.45697	0.0900769
$745$	0	0
$746$	21.9252	0.802737
$747$	−19.2476	−0.704231
$748$	−26.5254	−0.969866
$749$	−5.33318	−0.194870
$750$	0	0
$751$	−12.1375	−0.442904	−0.221452	−	0.975171i	$-0.571080\pi$
$751$	−12.1375	−0.442904	−0.221452	+	0.975171i	$0.571080\pi$
$752$	8.67433	0.316320
$753$	−6.04271	−0.220209
$754$	−31.9513	−1.16360
$755$	0	0
$756$	2.80522	0.102025
$757$	17.9846	0.653660	0.326830	−	0.945083i	$-0.394019\pi$
$757$	17.9846	0.653660	0.326830	+	0.945083i	$0.394019\pi$
$758$	29.1707	1.05953
$759$	−16.4300	−0.596371
$760$	0	0
$761$	23.2298	0.842079	0.421039	−	0.907042i	$-0.361665\pi$
$761$	23.2298	0.842079	0.421039	+	0.907042i	$0.361665\pi$
$762$	29.8999	1.08316
$763$	−8.82638	−0.319536
$764$	16.1682	0.584945
$765$	0	0
$766$	−26.2770	−0.949428
$767$	−37.6995	−1.36125
$768$	33.1848	1.19745
$769$	−34.9703	−1.26106	−0.630530	−	0.776165i	$-0.717162\pi$
$769$	−34.9703	−1.26106	−0.630530	+	0.776165i	$0.717162\pi$
$770$	0	0
$771$	11.3019	0.407030
$772$	14.7992	0.532636
$773$	26.7805	0.963228	0.481614	−	0.876384i	$-0.340051\pi$
$773$	26.7805	0.963228	0.481614	+	0.876384i	$0.340051\pi$
$774$	1.21626	0.0437175
$775$	0	0
$776$	11.1910	0.401733
$777$	7.69944	0.276216
$778$	−17.3523	−0.622111
$779$	3.54285	0.126936
$780$	0	0
$781$	−90.2671	−3.23001
$782$	−7.61333	−0.272252
$783$	−27.4506	−0.981006
$784$	−1.69545	−0.0605516
$785$	0	0
$786$	29.6173	1.05642
$787$	−0.177103	−0.00631303	−0.00315652	−	0.999995i	$-0.501005\pi$
$787$	−0.177103	−0.00631303	−0.00315652	+	0.999995i	$0.501005\pi$
$788$	3.66016	0.130388
$789$	−55.8009	−1.98657
$790$	0	0
$791$	−18.2045	−0.647277
$792$	25.0983	0.891829
$793$	−34.3718	−1.22058
$794$	−9.49621	−0.337008
$795$	0	0
$796$	−8.33837	−0.295546
$797$	15.4863	0.548555	0.274277	−	0.961651i	$-0.411561\pi$
$797$	15.4863	0.548555	0.274277	+	0.961651i	$0.411561\pi$
$798$	8.04024	0.284622
$799$	−27.4813	−0.972219
$800$	0	0
$801$	0.706711	0.0249704
$802$	−1.92706	−0.0680469
$803$	−46.9290	−1.65609
$804$	−19.3986	−0.684137
$805$	0	0
$806$	−1.53391	−0.0540296
$807$	30.5759	1.07632
$808$	−7.52045	−0.264569
$809$	−12.8695	−0.452467	−0.226234	−	0.974073i	$-0.572641\pi$
$809$	−12.8695	−0.452467	−0.226234	+	0.974073i	$0.572641\pi$
$810$	0	0
$811$	24.8951	0.874185	0.437092	−	0.899417i	$-0.356008\pi$
$811$	24.8951	0.874185	0.437092	+	0.899417i	$0.356008\pi$
$812$	−6.54525	−0.229693
$813$	−47.6400	−1.67081
$814$	−24.2173	−0.848815
$815$	0	0
$816$	19.0085	0.665431
$817$	2.92118	0.102199
$818$	29.4537	1.02982
$819$	4.98170	0.174075
$820$	0	0
$821$	−21.8002	−0.760834	−0.380417	−	0.924815i	$-0.624220\pi$
$821$	−21.8002	−0.760834	−0.380417	+	0.924815i	$0.624220\pi$
$822$	−28.9803	−1.01080
$823$	1.76071	0.0613744	0.0306872	−	0.999529i	$-0.490230\pi$
$823$	1.76071	0.0613744	0.0306872	+	0.999529i	$0.490230\pi$
$824$	31.3970	1.09376
$825$	0	0
$826$	11.1629	0.388408
$827$	−9.93134	−0.345347	−0.172673	−	0.984979i	$-0.555240\pi$
$827$	−9.93134	−0.345347	−0.172673	+	0.984979i	$0.555240\pi$
$828$	−1.44645	−0.0502678
$829$	4.85768	0.168714	0.0843571	−	0.996436i	$-0.473116\pi$
$829$	4.85768	0.168714	0.0843571	+	0.996436i	$0.473116\pi$
$830$	0	0
$831$	−17.3492	−0.601837
$832$	−29.5549	−1.02463
$833$	5.37138	0.186107
$834$	31.7174	1.09828
$835$	0	0
$836$	17.4956	0.605100
$837$	−1.31784	−0.0455512
$838$	19.9390	0.688781
$839$	15.9065	0.549152	0.274576	−	0.961565i	$-0.411463\pi$
$839$	15.9065	0.549152	0.274576	+	0.961565i	$0.411463\pi$
$840$	0	0
$841$	35.0491	1.20859
$842$	−18.1794	−0.626504
$843$	−36.1383	−1.24467
$844$	11.4888	0.395460
$845$	0	0
$846$	7.54696	0.259470
$847$	−25.4598	−0.874808
$848$	2.59771	0.0892058
$849$	−30.8536	−1.05889
$850$	0	0
$851$	4.80875	0.164842
$852$	−25.5194	−0.874282
$853$	−1.08814	−0.0372572	−0.0186286	−	0.999826i	$-0.505930\pi$
$853$	−1.08814	−0.0372572	−0.0186286	+	0.999826i	$0.505930\pi$
$854$	10.1776	0.348271
$855$	0	0
$856$	16.3396	0.558475
$857$	1.53174	0.0523232	0.0261616	−	0.999658i	$-0.491672\pi$
$857$	1.53174	0.0523232	0.0261616	+	0.999658i	$0.491672\pi$
$858$	−50.3174	−1.71781
$859$	10.9042	0.372047	0.186024	−	0.982545i	$-0.440440\pi$
$859$	10.9042	0.372047	0.186024	+	0.982545i	$0.440440\pi$
$860$	0	0
$861$	−2.08727	−0.0711340
$862$	−0.222605	−0.00758196
$863$	54.7487	1.86367	0.931834	−	0.362884i	$-0.118208\pi$
$863$	54.7487	1.86367	0.931834	+	0.362884i	$0.118208\pi$
$864$	−14.6946	−0.499919
$865$	0	0
$866$	34.7923	1.18229
$867$	−24.7377	−0.840136
$868$	−0.314222	−0.0106654
$869$	−36.5131	−1.23862
$870$	0	0
$871$	41.7270	1.41386
$872$	27.0419	0.915753
$873$	4.95561	0.167722
$874$	5.02160	0.169858
$875$	0	0
$876$	−13.2673	−0.448261
$877$	0.0143469	0.000484459 0	0.000242229	−	1.00000i	$-0.499923\pi$
$877$	0.0143469	0.000484459 0	0.000242229		1.00000i	$0.499923\pi$
$878$	−27.0787	−0.913862
$879$	10.4288	0.351755
$880$	0	0
$881$	−56.3960	−1.90003	−0.950014	−	0.312206i	$-0.898932\pi$
$881$	−56.3960	−1.90003	−0.950014	+	0.312206i	$0.898932\pi$
$882$	−1.47510	−0.0496691
$883$	26.5606	0.893835	0.446917	−	0.894575i	$-0.352522\pi$
$883$	26.5606	0.893835	0.446917	+	0.894575i	$0.352522\pi$
$884$	16.1306	0.542531
$885$	0	0
$886$	20.6907	0.695119
$887$	29.3990	0.987121	0.493560	−	0.869712i	$-0.335695\pi$
$887$	29.3990	0.987121	0.493560	+	0.869712i	$0.335695\pi$
$888$	−23.5892	−0.791603
$889$	−13.1751	−0.441879
$890$	0	0
$891$	−67.8057	−2.27158
$892$	−0.573714	−0.0192094
$893$	18.1261	0.606567
$894$	−4.58734	−0.153423
$895$	0	0
$896$	0.183089	0.00611657
$897$	9.99137	0.333602
$898$	6.46936	0.215885
$899$	3.07484	0.102552
$900$	0	0
$901$	−8.22986	−0.274177
$902$	6.56515	0.218595
$903$	−1.72101	−0.0572717
$904$	55.7741	1.85502
$905$	0	0
$906$	26.6994	0.887027
$907$	12.9258	0.429196	0.214598	−	0.976702i	$-0.431156\pi$
$907$	12.9258	0.429196	0.214598	+	0.976702i	$0.431156\pi$
$908$	7.66212	0.254276
$909$	−3.33022	−0.110456
$910$	0	0
$911$	33.8152	1.12035	0.560174	−	0.828375i	$-0.310734\pi$
$911$	33.8152	1.12035	0.560174	+	0.828375i	$0.310734\pi$
$912$	−12.5376	−0.415163
$913$	−85.6643	−2.83507
$914$	−34.6198	−1.14512
$915$	0	0
$916$	−10.1423	−0.335110
$917$	−13.0506	−0.430968
$918$	−20.0318	−0.661147
$919$	−2.96555	−0.0978246	−0.0489123	−	0.998803i	$-0.515575\pi$
$919$	−2.96555	−0.0978246	−0.0489123	+	0.998803i	$0.515575\pi$
$920$	0	0
$921$	−16.3912	−0.540110
$922$	−5.43242	−0.178907
$923$	54.8930	1.80683
$924$	−10.3076	−0.339094
$925$	0	0
$926$	19.1401	0.628983
$927$	13.9032	0.456642
$928$	34.2860	1.12549
$929$	−24.4362	−0.801726	−0.400863	−	0.916138i	$-0.631290\pi$
$929$	−24.4362	−0.801726	−0.400863	+	0.916138i	$0.631290\pi$
$930$	0	0
$931$	−3.54285	−0.116112
$932$	7.86552	0.257644
$933$	56.4354	1.84761
$934$	−46.6921	−1.52781
$935$	0	0
$936$	−15.2627	−0.498878
$937$	−35.9240	−1.17359	−0.586793	−	0.809737i	$-0.699610\pi$
$937$	−35.9240	−1.17359	−0.586793	+	0.809737i	$0.699610\pi$
$938$	−12.3555	−0.403421
$939$	−0.351482	−0.0114702
$940$	0	0
$941$	−42.9108	−1.39885	−0.699426	−	0.714705i	$-0.746561\pi$
$941$	−42.9108	−1.39885	−0.699426	+	0.714705i	$0.746561\pi$
$942$	−42.8603	−1.39646
$943$	−1.30362	−0.0424518
$944$	−17.4070	−0.566550
$945$	0	0
$946$	5.41314	0.175996
$947$	−44.6039	−1.44943	−0.724716	−	0.689048i	$-0.758029\pi$
$947$	−44.6039	−1.44943	−0.724716	+	0.689048i	$0.758029\pi$
$948$	−10.3226	−0.335264
$949$	28.5384	0.926395
$950$	0	0
$951$	11.1395	0.361225
$952$	−16.4566	−0.533361
$953$	12.8800	0.417224	0.208612	−	0.977999i	$-0.433105\pi$
$953$	12.8800	0.417224	0.208612	+	0.977999i	$0.433105\pi$
$954$	2.26010	0.0731734
$955$	0	0
$956$	13.5438	0.438037
$957$	100.865	3.26051
$958$	−3.10143	−0.100203
$959$	12.7699	0.412361
$960$	0	0
$961$	−30.8524	−0.995238
$962$	14.7270	0.474816
$963$	7.23552	0.233161
$964$	−7.60336	−0.244888
$965$	0	0
$966$	−2.95847	−0.0951874
$967$	−49.0909	−1.57866	−0.789329	−	0.613970i	$-0.789571\pi$
$967$	−49.0909	−1.57866	−0.789329	+	0.613970i	$0.789571\pi$
$968$	78.0025	2.50710
$969$	39.7207	1.27601
$970$	0	0
$971$	−5.24060	−0.168179	−0.0840895	−	0.996458i	$-0.526798\pi$
$971$	−5.24060	−0.168179	−0.0840895	+	0.996458i	$0.526798\pi$
$972$	−10.7537	−0.344926
$973$	−13.9759	−0.448048
$974$	−6.77614	−0.217121
$975$	0	0
$976$	−15.8706	−0.508004
$977$	−44.0772	−1.41015	−0.705077	−	0.709130i	$-0.749088\pi$
$977$	−44.0772	−1.41015	−0.705077	+	0.709130i	$0.749088\pi$
$978$	−37.0513	−1.18477
$979$	3.14533	0.100525
$980$	0	0
$981$	11.9747	0.382323
$982$	2.32508	0.0741963
$983$	54.1938	1.72851	0.864256	−	0.503052i	$-0.167789\pi$
$983$	54.1938	1.72851	0.864256	+	0.503052i	$0.167789\pi$
$984$	6.39489	0.203862
$985$	0	0
$986$	46.7390	1.48847
$987$	−10.6790	−0.339916
$988$	−10.6394	−0.338485
$989$	−1.07487	−0.0341789
$990$	0	0
$991$	−0.908400	−0.0288563	−0.0144281	−	0.999896i	$-0.504593\pi$
$991$	−0.908400	−0.0288563	−0.0144281	+	0.999896i	$0.504593\pi$
$992$	1.64599	0.0522602
$993$	16.8945	0.536130
$994$	−16.2540	−0.515545
$995$	0	0
$996$	−24.2182	−0.767382
$997$	−36.8530	−1.16715	−0.583573	−	0.812061i	$-0.698346\pi$
$997$	−36.8530	−1.16715	−0.583573	+	0.812061i	$0.698346\pi$
$998$	−27.3024	−0.864242
$999$	12.6525	0.400308

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7175.2.a.n.1.2		5
5.4	even	2		287.2.a.e.1.4	✓	5
15.14	odd	2		2583.2.a.r.1.2		5
20.19	odd	2		4592.2.a.bb.1.2		5
35.34	odd	2		2009.2.a.n.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.a.e.1.4	✓	5	5.4	even	2
2009.2.a.n.1.4		5	35.34	odd	2
2583.2.a.r.1.2		5	15.14	odd	2
4592.2.a.bb.1.2		5	20.19	odd	2
7175.2.a.n.1.2		5	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 7175 = 5^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7175.a (trivial)

\(f(q)\)	\(=\)	\(q-1.08727 q^{2} -2.08727 q^{3} -0.817843 q^{4} +2.26943 q^{6} -1.00000 q^{7} +3.06376 q^{8} +1.35670 q^{9} +O(q^{10})\)	\(q-1.08727 q^{2} -2.08727 q^{3} -0.817843 q^{4} +2.26943 q^{6} -1.00000 q^{7} +3.06376 q^{8} +1.35670 q^{9} +6.03819 q^{11} +1.70706 q^{12} -3.67193 q^{13} +1.08727 q^{14} -1.69545 q^{16} +5.37138 q^{17} -1.47510 q^{18} -3.54285 q^{19} +2.08727 q^{21} -6.56515 q^{22} +1.30362 q^{23} -6.39489 q^{24} +3.99238 q^{26} +3.43002 q^{27} +0.817843 q^{28} -8.00307 q^{29} -0.384208 q^{31} -4.28411 q^{32} -12.6033 q^{33} -5.84014 q^{34} -1.10957 q^{36} +3.68876 q^{37} +3.85204 q^{38} +7.66432 q^{39} -1.00000 q^{41} -2.26943 q^{42} -0.824527 q^{43} -4.93829 q^{44} -1.41739 q^{46} -5.11625 q^{47} +3.53885 q^{48} +1.00000 q^{49} -11.2115 q^{51} +3.00307 q^{52} -1.53217 q^{53} -3.72936 q^{54} -3.06376 q^{56} +7.39489 q^{57} +8.70150 q^{58} +10.2669 q^{59} +9.36070 q^{61} +0.417738 q^{62} -1.35670 q^{63} +8.04887 q^{64} +13.7032 q^{66} -11.3638 q^{67} -4.39294 q^{68} -2.72101 q^{69} -14.9494 q^{71} +4.15659 q^{72} -7.77203 q^{73} -4.01068 q^{74} +2.89750 q^{76} -6.03819 q^{77} -8.33318 q^{78} -6.04703 q^{79} -11.2295 q^{81} +1.08727 q^{82} -14.1871 q^{83} -1.70706 q^{84} +0.896484 q^{86} +16.7046 q^{87} +18.4996 q^{88} +0.520905 q^{89} +3.67193 q^{91} -1.06616 q^{92} +0.801946 q^{93} +5.56275 q^{94} +8.94209 q^{96} +3.65270 q^{97} -1.08727 q^{98} +8.19200 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} - 4 q^{3} + 3 q^{4} + 12 q^{6} - 5 q^{7} + 3 q^{8} + q^{9}+O(q^{10}) \) 5 * q + q^2 - 4 * q^3 + 3 * q^4 + 12 * q^6 - 5 * q^7 + 3 * q^8 + q^9	\( 5 q + q^{2} - 4 q^{3} + 3 q^{4} + 12 q^{6} - 5 q^{7} + 3 q^{8} + q^{9} + 2 q^{11} + 2 q^{12} - 5 q^{13} - q^{14} - q^{16} - 13 q^{17} - 21 q^{18} + 4 q^{21} - q^{22} - 2 q^{23} + 2 q^{24} - 10 q^{27} - 3 q^{28} - 5 q^{29} + 17 q^{31} + 12 q^{32} - 3 q^{33} - 8 q^{34} + 15 q^{36} + 7 q^{37} + 3 q^{38} + 5 q^{39} - 5 q^{41} - 12 q^{42} - q^{43} - 47 q^{44} - 24 q^{46} - 9 q^{47} + 19 q^{48} + 5 q^{49} + 5 q^{51} - 20 q^{52} - 5 q^{53} + 2 q^{54} - 3 q^{56} + 3 q^{57} + 27 q^{58} + 7 q^{59} + 22 q^{61} + 28 q^{62} - q^{63} - 3 q^{64} - 42 q^{66} + 3 q^{67} - 17 q^{68} - 22 q^{69} - 24 q^{71} + 12 q^{72} - 40 q^{73} - 5 q^{74} - 19 q^{76} - 2 q^{77} - 30 q^{78} - 42 q^{79} + 9 q^{81} - q^{82} + 12 q^{83} - 2 q^{84} + 16 q^{86} + 32 q^{87} - 26 q^{88} + 8 q^{89} + 5 q^{91} - 12 q^{92} + 11 q^{93} - 23 q^{94} - 17 q^{96} - 16 q^{97} + q^{98} - 45 q^{99}+O(q^{100}) \) 5 * q + q^2 - 4 * q^3 + 3 * q^4 + 12 * q^6 - 5 * q^7 + 3 * q^8 + q^9 + 2 * q^11 + 2 * q^12 - 5 * q^13 - q^14 - q^16 - 13 * q^17 - 21 * q^18 + 4 * q^21 - q^22 - 2 * q^23 + 2 * q^24 - 10 * q^27 - 3 * q^28 - 5 * q^29 + 17 * q^31 + 12 * q^32 - 3 * q^33 - 8 * q^34 + 15 * q^36 + 7 * q^37 + 3 * q^38 + 5 * q^39 - 5 * q^41 - 12 * q^42 - q^43 - 47 * q^44 - 24 * q^46 - 9 * q^47 + 19 * q^48 + 5 * q^49 + 5 * q^51 - 20 * q^52 - 5 * q^53 + 2 * q^54 - 3 * q^56 + 3 * q^57 + 27 * q^58 + 7 * q^59 + 22 * q^61 + 28 * q^62 - q^63 - 3 * q^64 - 42 * q^66 + 3 * q^67 - 17 * q^68 - 22 * q^69 - 24 * q^71 + 12 * q^72 - 40 * q^73 - 5 * q^74 - 19 * q^76 - 2 * q^77 - 30 * q^78 - 42 * q^79 + 9 * q^81 - q^82 + 12 * q^83 - 2 * q^84 + 16 * q^86 + 32 * q^87 - 26 * q^88 + 8 * q^89 + 5 * q^91 - 12 * q^92 + 11 * q^93 - 23 * q^94 - 17 * q^96 - 16 * q^97 + q^98 - 45 * q^99

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