LMFDB - Embedded newform 575.2.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(1,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("575.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.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:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 12x^{5} + 9x^{4} + 43x^{3} - 14x^{2} - 49x - 9 $ x^7 - x^6 - 12x^5 + 9x^4 + 43x^3 - 14x^2 - 49*x - 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.53289$ of defining polynomial
Character	$\chi$	$=$	575.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53289 q^{2} +0.345624 q^{3} +4.41555 q^{4} -0.875428 q^{6} -5.12894 q^{7} -6.11832 q^{8} -2.88054 q^{9} +O(q^{10})$	\(q-2.53289 q^{2} +0.345624 q^{3} +4.41555 q^{4} -0.875428 q^{6} -5.12894 q^{7} -6.11832 q^{8} -2.88054 q^{9} -2.30402 q^{11} +1.52612 q^{12} +3.81740 q^{13} +12.9910 q^{14} +6.66597 q^{16} +4.36717 q^{17} +7.29611 q^{18} +4.76177 q^{19} -1.77268 q^{21} +5.83583 q^{22} -1.00000 q^{23} -2.11464 q^{24} -9.66905 q^{26} -2.03246 q^{27} -22.6471 q^{28} -1.35932 q^{29} +6.46086 q^{31} -4.64753 q^{32} -0.796323 q^{33} -11.0616 q^{34} -12.7192 q^{36} +10.0020 q^{37} -12.0611 q^{38} +1.31938 q^{39} -1.21247 q^{41} +4.49001 q^{42} +6.05487 q^{43} -10.1735 q^{44} +2.53289 q^{46} -6.80648 q^{47} +2.30392 q^{48} +19.3060 q^{49} +1.50940 q^{51} +16.8559 q^{52} +2.60186 q^{53} +5.14799 q^{54} +31.3805 q^{56} +1.64578 q^{57} +3.44302 q^{58} -3.53871 q^{59} +1.62546 q^{61} -16.3647 q^{62} +14.7741 q^{63} -1.56023 q^{64} +2.01700 q^{66} -4.92999 q^{67} +19.2834 q^{68} -0.345624 q^{69} -6.80648 q^{71} +17.6241 q^{72} +8.89855 q^{73} -25.3339 q^{74} +21.0258 q^{76} +11.8172 q^{77} -3.34185 q^{78} +5.45919 q^{79} +7.93917 q^{81} +3.07105 q^{82} +8.89424 q^{83} -7.82736 q^{84} -15.3363 q^{86} -0.469814 q^{87} +14.0967 q^{88} -9.61914 q^{89} -19.5792 q^{91} -4.41555 q^{92} +2.23303 q^{93} +17.2401 q^{94} -1.60630 q^{96} -10.3199 q^{97} -48.9000 q^{98} +6.63682 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 11 q^{4} + 5 q^{6} + 3 q^{7} - 6 q^{8} + 15 q^{9}+O(q^{10}) $ 7 * q - q^2 + 11 * q^4 + 5 * q^6 + 3 * q^7 - 6 * q^8 + 15 * q^9	$ 7 q - q^{2} + 11 q^{4} + 5 q^{6} + 3 q^{7} - 6 q^{8} + 15 q^{9} - q^{11} + 6 q^{12} - 3 q^{13} + 7 q^{14} + 7 q^{16} + 10 q^{17} - 24 q^{18} + 15 q^{19} + 2 q^{21} + 21 q^{22} - 7 q^{23} + 18 q^{24} - 20 q^{26} - 11 q^{28} + 3 q^{29} + 14 q^{31} + 17 q^{32} + 6 q^{33} + 20 q^{34} - 10 q^{37} - 31 q^{38} - 8 q^{39} + 19 q^{41} + 44 q^{42} + 5 q^{43} - 3 q^{44} + q^{46} - 14 q^{47} - 27 q^{48} + 40 q^{49} + 2 q^{51} + 16 q^{52} + 4 q^{53} - q^{54} - 9 q^{56} - 4 q^{57} - 13 q^{58} - 16 q^{59} + 40 q^{61} - 12 q^{62} + 53 q^{63} - 4 q^{64} - 54 q^{66} - 4 q^{67} + 20 q^{68} - 14 q^{71} - 6 q^{72} - 3 q^{73} - 18 q^{74} + 35 q^{76} - 17 q^{77} + 23 q^{78} - q^{79} + 47 q^{81} - 22 q^{82} + 17 q^{83} - 60 q^{84} - 35 q^{86} - 56 q^{87} + 57 q^{88} + 16 q^{89} + 25 q^{91} - 11 q^{92} + 14 q^{93} + 7 q^{94} - 19 q^{96} - 24 q^{97} - 46 q^{98} - 53 q^{99}+O(q^{100}) $ 7 * q - q^2 + 11 * q^4 + 5 * q^6 + 3 * q^7 - 6 * q^8 + 15 * q^9 - q^11 + 6 * q^12 - 3 * q^13 + 7 * q^14 + 7 * q^16 + 10 * q^17 - 24 * q^18 + 15 * q^19 + 2 * q^21 + 21 * q^22 - 7 * q^23 + 18 * q^24 - 20 * q^26 - 11 * q^28 + 3 * q^29 + 14 * q^31 + 17 * q^32 + 6 * q^33 + 20 * q^34 - 10 * q^37 - 31 * q^38 - 8 * q^39 + 19 * q^41 + 44 * q^42 + 5 * q^43 - 3 * q^44 + q^46 - 14 * q^47 - 27 * q^48 + 40 * q^49 + 2 * q^51 + 16 * q^52 + 4 * q^53 - q^54 - 9 * q^56 - 4 * q^57 - 13 * q^58 - 16 * q^59 + 40 * q^61 - 12 * q^62 + 53 * q^63 - 4 * q^64 - 54 * q^66 - 4 * q^67 + 20 * q^68 - 14 * q^71 - 6 * q^72 - 3 * q^73 - 18 * q^74 + 35 * q^76 - 17 * q^77 + 23 * q^78 - q^79 + 47 * q^81 - 22 * q^82 + 17 * q^83 - 60 * q^84 - 35 * q^86 - 56 * q^87 + 57 * q^88 + 16 * q^89 + 25 * q^91 - 11 * q^92 + 14 * q^93 + 7 * q^94 - 19 * q^96 - 24 * q^97 - 46 * q^98 - 53 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.53289	−1.79103	−0.895513	−	0.445035i	$-0.853191\pi$
$2$	−2.53289	−1.79103	−0.895513	+	0.445035i	$0.853191\pi$
$3$	0.345624	0.199546	0.0997730	−	0.995010i	$-0.468188\pi$
$3$	0.345624	0.199546	0.0997730	+	0.995010i	$0.468188\pi$
$4$	4.41555	2.20777
$5$	0	0
$5$	0	0
$6$	−0.875428	−0.357392
$7$	−5.12894	−1.93856	−0.969278	−	0.245969i	$-0.920894\pi$
$7$	−5.12894	−1.93856	−0.969278	+	0.245969i	$0.920894\pi$
$8$	−6.11832	−2.16315
$9$	−2.88054	−0.960181
$10$	0	0
$11$	−2.30402	−0.694687	−0.347344	−	0.937738i	$-0.612916\pi$
$11$	−2.30402	−0.694687	−0.347344	+	0.937738i	$0.612916\pi$
$12$	1.52612	0.440552
$13$	3.81740	1.05876	0.529378	−	0.848386i	$-0.322426\pi$
$13$	3.81740	1.05876	0.529378	+	0.848386i	$0.322426\pi$
$14$	12.9910	3.47200
$15$	0	0
$16$	6.66597	1.66649
$17$	4.36717	1.05919	0.529597	−	0.848250i	$-0.322343\pi$
$17$	4.36717	1.05919	0.529597	+	0.848250i	$0.322343\pi$
$18$	7.29611	1.71971
$19$	4.76177	1.09242	0.546212	−	0.837647i	$-0.316069\pi$
$19$	4.76177	1.09242	0.546212	+	0.837647i	$0.316069\pi$
$20$	0	0
$21$	−1.77268	−0.386831
$22$	5.83583	1.24420
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−2.11464	−0.431649
$25$	0	0
$26$	−9.66905	−1.89626
$27$	−2.03246	−0.391146
$28$	−22.6471	−4.27989
$29$	−1.35932	−0.252420	−0.126210	−	0.992004i	$-0.540281\pi$
$29$	−1.35932	−0.252420	−0.126210	+	0.992004i	$0.540281\pi$
$30$	0	0
$31$	6.46086	1.16040	0.580202	−	0.814472i	$-0.302974\pi$
$31$	6.46086	1.16040	0.580202	+	0.814472i	$0.302974\pi$
$32$	−4.64753	−0.821575
$33$	−0.796323	−0.138622
$34$	−11.0616	−1.89704
$35$	0	0
$36$	−12.7192	−2.11986
$37$	10.0020	1.64431	0.822156	−	0.569263i	$-0.192771\pi$
$37$	10.0020	1.64431	0.822156	+	0.569263i	$0.192771\pi$
$38$	−12.0611	−1.95656
$39$	1.31938	0.211270
$40$	0	0
$41$	−1.21247	−0.189356	−0.0946779	−	0.995508i	$-0.530182\pi$
$41$	−1.21247	−0.189356	−0.0946779	+	0.995508i	$0.530182\pi$
$42$	4.49001	0.692824
$43$	6.05487	0.923360	0.461680	−	0.887047i	$-0.347247\pi$
$43$	6.05487	0.923360	0.461680	+	0.887047i	$0.347247\pi$
$44$	−10.1735	−1.53371
$45$	0	0
$46$	2.53289	0.373455
$47$	−6.80648	−0.992828	−0.496414	−	0.868086i	$-0.665350\pi$
$47$	−6.80648	−0.992828	−0.496414	+	0.868086i	$0.665350\pi$
$48$	2.30392	0.332542
$49$	19.3060	2.75800
$50$	0	0
$51$	1.50940	0.211358
$52$	16.8559	2.33749
$53$	2.60186	0.357393	0.178696	−	0.983904i	$-0.442812\pi$
$53$	2.60186	0.357393	0.178696	+	0.983904i	$0.442812\pi$
$54$	5.14799	0.700553
$55$	0	0
$56$	31.3805	4.19339
$57$	1.64578	0.217989
$58$	3.44302	0.452091
$59$	−3.53871	−0.460701	−0.230350	−	0.973108i	$-0.573987\pi$
$59$	−3.53871	−0.460701	−0.230350	+	0.973108i	$0.573987\pi$
$60$	0	0
$61$	1.62546	0.208119	0.104059	−	0.994571i	$-0.466817\pi$
$61$	1.62546	0.208119	0.104059	+	0.994571i	$0.466817\pi$
$62$	−16.3647	−2.07831
$63$	14.7741	1.86136
$64$	−1.56023	−0.195029
$65$	0	0
$66$	2.01700	0.248276
$67$	−4.92999	−0.602295	−0.301147	−	0.953578i	$-0.597370\pi$
$67$	−4.92999	−0.602295	−0.301147	+	0.953578i	$0.597370\pi$
$68$	19.2834	2.33846
$69$	−0.345624	−0.0416082
$70$	0	0
$71$	−6.80648	−0.807781	−0.403890	−	0.914807i	$-0.632342\pi$
$71$	−6.80648	−0.807781	−0.403890	+	0.914807i	$0.632342\pi$
$72$	17.6241	2.07702
$73$	8.89855	1.04150	0.520748	−	0.853710i	$-0.325653\pi$
$73$	8.89855	1.04150	0.520748	+	0.853710i	$0.325653\pi$
$74$	−25.3339	−2.94500
$75$	0	0
$76$	21.0258	2.41183
$77$	11.8172	1.34669
$78$	−3.34185	−0.378391
$79$	5.45919	0.614207	0.307104	−	0.951676i	$-0.400640\pi$
$79$	5.45919	0.614207	0.307104	+	0.951676i	$0.400640\pi$
$80$	0	0
$81$	7.93917	0.882130
$82$	3.07105	0.339141
$83$	8.89424	0.976270	0.488135	−	0.872768i	$-0.337677\pi$
$83$	8.89424	0.976270	0.488135	+	0.872768i	$0.337677\pi$
$84$	−7.82736	−0.854035
$85$	0	0
$86$	−15.3363	−1.65376
$87$	−0.469814	−0.0503694
$88$	14.0967	1.50272
$89$	−9.61914	−1.01963	−0.509814	−	0.860285i	$-0.670286\pi$
$89$	−9.61914	−1.01963	−0.509814	+	0.860285i	$0.670286\pi$
$90$	0	0
$91$	−19.5792	−2.05246
$92$	−4.41555	−0.460353
$93$	2.23303	0.231554
$94$	17.2401	1.77818
$95$	0	0
$96$	−1.60630	−0.163942
$97$	−10.3199	−1.04782	−0.523912	−	0.851773i	$-0.675528\pi$
$97$	−10.3199	−1.04782	−0.523912	+	0.851773i	$0.675528\pi$
$98$	−48.9000	−4.93964
$99$	6.63682	0.667026
$100$	0	0
$101$	18.8295	1.87361	0.936803	−	0.349857i	$-0.113770\pi$
$101$	18.8295	1.87361	0.936803	+	0.349857i	$0.113770\pi$
$102$	−3.82314	−0.378547
$103$	−5.96003	−0.587259	−0.293630	−	0.955919i	$-0.594863\pi$
$103$	−5.96003	−0.587259	−0.293630	+	0.955919i	$0.594863\pi$
$104$	−23.3561	−2.29025
$105$	0	0
$106$	−6.59023	−0.640099
$107$	17.7590	1.71683	0.858413	−	0.512959i	$-0.171451\pi$
$107$	17.7590	1.71683	0.858413	+	0.512959i	$0.171451\pi$
$108$	−8.97440	−0.863562
$109$	2.96899	0.284377	0.142189	−	0.989840i	$-0.454586\pi$
$109$	2.96899	0.284377	0.142189	+	0.989840i	$0.454586\pi$
$110$	0	0
$111$	3.45691	0.328116
$112$	−34.1893	−3.23059
$113$	12.0102	1.12983	0.564914	−	0.825150i	$-0.308909\pi$
$113$	12.0102	1.12983	0.564914	+	0.825150i	$0.308909\pi$
$114$	−4.16859	−0.390424
$115$	0	0
$116$	−6.00216	−0.557286
$117$	−10.9962	−1.01660
$118$	8.96317	0.825127
$119$	−22.3989	−2.05330
$120$	0	0
$121$	−5.69150	−0.517409
$122$	−4.11712	−0.372746
$123$	−0.419058	−0.0377852
$124$	28.5282	2.56191
$125$	0	0
$126$	−37.4213	−3.33375
$127$	−20.7311	−1.83959	−0.919793	−	0.392404i	$-0.871644\pi$
$127$	−20.7311	−1.83959	−0.919793	+	0.392404i	$0.871644\pi$
$128$	13.2470	1.17088
$129$	2.09271	0.184253
$130$	0	0
$131$	10.6035	0.926432	0.463216	−	0.886246i	$-0.346695\pi$
$131$	10.6035	0.926432	0.463216	+	0.886246i	$0.346695\pi$
$132$	−3.51620	−0.306046
$133$	−24.4228	−2.11773
$134$	12.4871	1.07873
$135$	0	0
$136$	−26.7197	−2.29120
$137$	−8.11994	−0.693733	−0.346867	−	0.937914i	$-0.612754\pi$
$137$	−8.11994	−0.693733	−0.346867	+	0.937914i	$0.612754\pi$
$138$	0.875428	0.0745214
$139$	10.0320	0.850905	0.425453	−	0.904981i	$-0.360115\pi$
$139$	10.0320	0.850905	0.425453	+	0.904981i	$0.360115\pi$
$140$	0	0
$141$	−2.35248	−0.198115
$142$	17.2401	1.44676
$143$	−8.79535	−0.735504
$144$	−19.2016	−1.60013
$145$	0	0
$146$	−22.5391	−1.86535
$147$	6.67260	0.550347
$148$	44.1641	3.63027
$149$	4.70148	0.385160	0.192580	−	0.981281i	$-0.438314\pi$
$149$	4.70148	0.385160	0.192580	+	0.981281i	$0.438314\pi$
$150$	0	0
$151$	3.77973	0.307590	0.153795	−	0.988103i	$-0.450850\pi$
$151$	3.77973	0.307590	0.153795	+	0.988103i	$0.450850\pi$
$152$	−29.1340	−2.36308
$153$	−12.5798	−1.01702
$154$	−29.9316	−2.41196
$155$	0	0
$156$	5.82580	0.466437
$157$	14.7089	1.17389	0.586947	−	0.809625i	$-0.300330\pi$
$157$	14.7089	1.17389	0.586947	+	0.809625i	$0.300330\pi$
$158$	−13.8276	−1.10006
$159$	0.899264	0.0713162
$160$	0	0
$161$	5.12894	0.404217
$162$	−20.1091	−1.57992
$163$	6.27347	0.491376	0.245688	−	0.969349i	$-0.420986\pi$
$163$	6.27347	0.491376	0.245688	+	0.969349i	$0.420986\pi$
$164$	−5.35371	−0.418055
$165$	0	0
$166$	−22.5282	−1.74853
$167$	−10.4518	−0.808786	−0.404393	−	0.914585i	$-0.632517\pi$
$167$	−10.4518	−0.808786	−0.404393	+	0.914585i	$0.632517\pi$
$168$	10.8458	0.836775
$169$	1.57251	0.120962
$170$	0	0
$171$	−13.7165	−1.04893
$172$	26.7356	2.03857
$173$	−23.7784	−1.80784	−0.903918	−	0.427705i	$-0.859322\pi$
$173$	−23.7784	−1.80784	−0.903918	+	0.427705i	$0.859322\pi$
$174$	1.18999	0.0902129
$175$	0	0
$176$	−15.3585	−1.15769
$177$	−1.22306	−0.0919309
$178$	24.3643	1.82618
$179$	4.39269	0.328325	0.164163	−	0.986433i	$-0.447508\pi$
$179$	4.39269	0.328325	0.164163	+	0.986433i	$0.447508\pi$
$180$	0	0
$181$	5.31493	0.395056	0.197528	−	0.980297i	$-0.436709\pi$
$181$	5.31493	0.395056	0.197528	+	0.980297i	$0.436709\pi$
$182$	49.5920	3.67600
$183$	0.561798	0.0415293
$184$	6.11832	0.451049
$185$	0	0
$186$	−5.65602	−0.414719
$187$	−10.0620	−0.735808
$188$	−30.0543	−2.19194
$189$	10.4243	0.758259
$190$	0	0
$191$	20.5754	1.48879	0.744393	−	0.667742i	$-0.232739\pi$
$191$	20.5754	1.48879	0.744393	+	0.667742i	$0.232739\pi$
$192$	−0.539253	−0.0389173
$193$	7.79422	0.561041	0.280520	−	0.959848i	$-0.409493\pi$
$193$	7.79422	0.561041	0.280520	+	0.959848i	$0.409493\pi$
$194$	26.1391	1.87668
$195$	0	0
$196$	85.2465	6.08903
$197$	−12.7696	−0.909798	−0.454899	−	0.890543i	$-0.650325\pi$
$197$	−12.7696	−0.909798	−0.454899	+	0.890543i	$0.650325\pi$
$198$	−16.8104	−1.19466
$199$	−4.30927	−0.305476	−0.152738	−	0.988267i	$-0.548809\pi$
$199$	−4.30927	−0.305476	−0.152738	+	0.988267i	$0.548809\pi$
$200$	0	0
$201$	−1.70392	−0.120185
$202$	−47.6931	−3.35568
$203$	6.97188	0.489330
$204$	6.66481	0.466630
$205$	0	0
$206$	15.0961	1.05180
$207$	2.88054	0.200212
$208$	25.4466	1.76441
$209$	−10.9712	−0.758894
$210$	0	0
$211$	16.7812	1.15526	0.577632	−	0.816297i	$-0.303977\pi$
$211$	16.7812	1.15526	0.577632	+	0.816297i	$0.303977\pi$
$212$	11.4886	0.789042
$213$	−2.35248	−0.161189
$214$	−44.9816	−3.07488
$215$	0	0
$216$	12.4352	0.846110
$217$	−33.1373	−2.24951
$218$	−7.52012	−0.509327
$219$	3.07555	0.207826
$220$	0	0
$221$	16.6712	1.12143
$222$	−8.75599	−0.587664
$223$	−21.3201	−1.42770	−0.713850	−	0.700298i	$-0.753050\pi$
$223$	−21.3201	−1.42770	−0.713850	+	0.700298i	$0.753050\pi$
$224$	23.8369	1.59267
$225$	0	0
$226$	−30.4206	−2.02355
$227$	6.73343	0.446913	0.223457	−	0.974714i	$-0.428266\pi$
$227$	6.73343	0.446913	0.223457	+	0.974714i	$0.428266\pi$
$228$	7.26702	0.481270
$229$	4.49466	0.297015	0.148508	−	0.988911i	$-0.452553\pi$
$229$	4.49466	0.297015	0.148508	+	0.988911i	$0.452553\pi$
$230$	0	0
$231$	4.08429	0.268727
$232$	8.31678	0.546024
$233$	3.95605	0.259169	0.129585	−	0.991568i	$-0.458636\pi$
$233$	3.95605	0.259169	0.129585	+	0.991568i	$0.458636\pi$
$234$	27.8521	1.82075
$235$	0	0
$236$	−15.6253	−1.01712
$237$	1.88683	0.122563
$238$	56.7341	3.67752
$239$	−20.4985	−1.32593	−0.662967	−	0.748648i	$-0.730703\pi$
$239$	−20.4985	−1.32593	−0.662967	+	0.748648i	$0.730703\pi$
$240$	0	0
$241$	3.53050	0.227419	0.113710	−	0.993514i	$-0.463727\pi$
$241$	3.53050	0.227419	0.113710	+	0.993514i	$0.463727\pi$
$242$	14.4160	0.926694
$243$	8.84133	0.567172
$244$	7.17730	0.459480
$245$	0	0
$246$	1.06143	0.0676742
$247$	18.1776	1.15661
$248$	−39.5296	−2.51013
$249$	3.07406	0.194811
$250$	0	0
$251$	−14.7691	−0.932218	−0.466109	−	0.884727i	$-0.654344\pi$
$251$	−14.7691	−0.932218	−0.466109	+	0.884727i	$0.654344\pi$
$252$	65.2359	4.10947
$253$	2.30402	0.144852
$254$	52.5096	3.29475
$255$	0	0
$256$	−30.4327	−1.90204
$257$	4.21813	0.263120	0.131560	−	0.991308i	$-0.458001\pi$
$257$	4.21813	0.263120	0.131560	+	0.991308i	$0.458001\pi$
$258$	−5.30061	−0.330001
$259$	−51.2994	−3.18759
$260$	0	0
$261$	3.91559	0.242369
$262$	−26.8575	−1.65926
$263$	15.6004	0.961964	0.480982	−	0.876731i	$-0.340280\pi$
$263$	15.6004	0.961964	0.480982	+	0.876731i	$0.340280\pi$
$264$	4.87216	0.299861
$265$	0	0
$266$	61.8603	3.79290
$267$	−3.32460	−0.203462
$268$	−21.7686	−1.32973
$269$	12.6725	0.772653	0.386327	−	0.922362i	$-0.373744\pi$
$269$	12.6725	0.772653	0.386327	+	0.922362i	$0.373744\pi$
$270$	0	0
$271$	−0.313168	−0.0190236	−0.00951181	−	0.999955i	$-0.503028\pi$
$271$	−0.313168	−0.0190236	−0.00951181	+	0.999955i	$0.503028\pi$
$272$	29.1114	1.76514
$273$	−6.76703	−0.409559
$274$	20.5669	1.24249
$275$	0	0
$276$	−1.52612	−0.0918615
$277$	11.2030	0.673123	0.336561	−	0.941662i	$-0.390736\pi$
$277$	11.2030	0.673123	0.336561	+	0.941662i	$0.390736\pi$
$278$	−25.4100	−1.52399
$279$	−18.6108	−1.11420
$280$	0	0
$281$	7.92236	0.472608	0.236304	−	0.971679i	$-0.424064\pi$
$281$	7.92236	0.472608	0.236304	+	0.971679i	$0.424064\pi$
$282$	5.95858	0.354829
$283$	0.234691	0.0139509	0.00697546	−	0.999976i	$-0.497780\pi$
$283$	0.234691	0.0139509	0.00697546	+	0.999976i	$0.497780\pi$
$284$	−30.0543	−1.78340
$285$	0	0
$286$	22.2777	1.31731
$287$	6.21867	0.367076
$288$	13.3874	0.788861
$289$	2.07214	0.121891
$290$	0	0
$291$	−3.56679	−0.209089
$292$	39.2920	2.29939
$293$	−4.63451	−0.270751	−0.135375	−	0.990794i	$-0.543224\pi$
$293$	−4.63451	−0.270751	−0.135375	+	0.990794i	$0.543224\pi$
$294$	−16.9010	−0.985686
$295$	0	0
$296$	−61.1952	−3.55690
$297$	4.68281	0.271724
$298$	−11.9083	−0.689832
$299$	−3.81740	−0.220766
$300$	0	0
$301$	−31.0551	−1.78998
$302$	−9.57364	−0.550901
$303$	6.50793	0.373871
$304$	31.7418	1.82052
$305$	0	0
$306$	31.8633	1.82151
$307$	3.33709	0.190458	0.0952290	−	0.995455i	$-0.469642\pi$
$307$	3.33709	0.190458	0.0952290	+	0.995455i	$0.469642\pi$
$308$	52.1792	2.97319
$309$	−2.05993	−0.117185
$310$	0	0
$311$	−2.80345	−0.158969	−0.0794845	−	0.996836i	$-0.525327\pi$
$311$	−2.80345	−0.158969	−0.0794845	+	0.996836i	$0.525327\pi$
$312$	−8.07241	−0.457010
$313$	−1.92506	−0.108811	−0.0544055	−	0.998519i	$-0.517326\pi$
$313$	−1.92506	−0.108811	−0.0544055	+	0.998519i	$0.517326\pi$
$314$	−37.2560	−2.10247
$315$	0	0
$316$	24.1053	1.35603
$317$	19.1282	1.07434	0.537172	−	0.843473i	$-0.319493\pi$
$317$	19.1282	1.07434	0.537172	+	0.843473i	$0.319493\pi$
$318$	−2.27774	−0.127729
$319$	3.13191	0.175353
$320$	0	0
$321$	6.13793	0.342586
$322$	−12.9910	−0.723963
$323$	20.7954	1.15709
$324$	35.0558	1.94754
$325$	0	0
$326$	−15.8900	−0.880068
$327$	1.02615	0.0567463
$328$	7.41827	0.409606
$329$	34.9100	1.92465
$330$	0	0
$331$	−3.47836	−0.191188	−0.0955939	−	0.995420i	$-0.530475\pi$
$331$	−3.47836	−0.191188	−0.0955939	+	0.995420i	$0.530475\pi$
$332$	39.2730	2.15538
$333$	−28.8111	−1.57884
$334$	26.4733	1.44856
$335$	0	0
$336$	−11.8166	−0.644650
$337$	26.7136	1.45518	0.727590	−	0.686012i	$-0.240640\pi$
$337$	26.7136	1.45518	0.727590	+	0.686012i	$0.240640\pi$
$338$	−3.98300	−0.216646
$339$	4.15102	0.225453
$340$	0	0
$341$	−14.8859	−0.806118
$342$	34.7424	1.87865
$343$	−63.1165	−3.40797
$344$	−37.0457	−1.99737
$345$	0	0
$346$	60.2281	3.23788
$347$	−13.4205	−0.720451	−0.360226	−	0.932865i	$-0.617300\pi$
$347$	−13.4205	−0.720451	−0.360226	+	0.932865i	$0.617300\pi$
$348$	−2.07449	−0.111204
$349$	−21.2695	−1.13853	−0.569265	−	0.822154i	$-0.692772\pi$
$349$	−21.2695	−1.13853	−0.569265	+	0.822154i	$0.692772\pi$
$350$	0	0
$351$	−7.75869	−0.414128
$352$	10.7080	0.570738
$353$	−26.7914	−1.42596	−0.712982	−	0.701182i	$-0.752656\pi$
$353$	−26.7914	−1.42596	−0.712982	+	0.701182i	$0.752656\pi$
$354$	3.09788	0.164651
$355$	0	0
$356$	−42.4738	−2.25111
$357$	−7.74160	−0.409729
$358$	−11.1262	−0.588039
$359$	−4.42048	−0.233304	−0.116652	−	0.993173i	$-0.537216\pi$
$359$	−4.42048	−0.233304	−0.116652	+	0.993173i	$0.537216\pi$
$360$	0	0
$361$	3.67444	0.193392
$362$	−13.4622	−0.707555
$363$	−1.96712	−0.103247
$364$	−86.4528	−4.53136
$365$	0	0
$366$	−1.42297	−0.0743800
$367$	10.9009	0.569020	0.284510	−	0.958673i	$-0.408169\pi$
$367$	10.9009	0.569020	0.284510	+	0.958673i	$0.408169\pi$
$368$	−6.66597	−0.347487
$369$	3.49257	0.181816
$370$	0	0
$371$	−13.3448	−0.692825
$372$	9.86003	0.511219
$373$	12.5001	0.647228	0.323614	−	0.946189i	$-0.395102\pi$
$373$	12.5001	0.647228	0.323614	+	0.946189i	$0.395102\pi$
$374$	25.4860	1.31785
$375$	0	0
$376$	41.6443	2.14764
$377$	−5.18908	−0.267251
$378$	−26.4037	−1.35806
$379$	21.5615	1.10754	0.553770	−	0.832670i	$-0.313189\pi$
$379$	21.5615	1.10754	0.553770	+	0.832670i	$0.313189\pi$
$380$	0	0
$381$	−7.16515	−0.367082
$382$	−52.1154	−2.66646
$383$	2.90388	0.148381	0.0741907	−	0.997244i	$-0.476363\pi$
$383$	2.90388	0.148381	0.0741907	+	0.997244i	$0.476363\pi$
$384$	4.57846	0.233644
$385$	0	0
$386$	−19.7419	−1.00484
$387$	−17.4413	−0.886593
$388$	−45.5678	−2.31336
$389$	26.8153	1.35959	0.679796	−	0.733401i	$-0.262068\pi$
$389$	26.8153	1.35959	0.679796	+	0.733401i	$0.262068\pi$
$390$	0	0
$391$	−4.36717	−0.220857
$392$	−118.120	−5.96597
$393$	3.66482	0.184866
$394$	32.3441	1.62947
$395$	0	0
$396$	29.3052	1.47264
$397$	0.317656	0.0159427	0.00797134	−	0.999968i	$-0.497463\pi$
$397$	0.317656	0.0159427	0.00797134	+	0.999968i	$0.497463\pi$
$398$	10.9149	0.547115
$399$	−8.44110	−0.422584
$400$	0	0
$401$	32.7432	1.63512	0.817559	−	0.575846i	$-0.195327\pi$
$401$	32.7432	1.63512	0.817559	+	0.575846i	$0.195327\pi$
$402$	4.31585	0.215255
$403$	24.6637	1.22858
$404$	83.1426	4.13650
$405$	0	0
$406$	−17.6590	−0.876403
$407$	−23.0447	−1.14228
$408$	−9.23498	−0.457199
$409$	24.7142	1.22204	0.611019	−	0.791616i	$-0.290760\pi$
$409$	24.7142	1.22204	0.611019	+	0.791616i	$0.290760\pi$
$410$	0	0
$411$	−2.80644	−0.138432
$412$	−26.3168	−1.29654
$413$	18.1498	0.893094
$414$	−7.29611	−0.358584
$415$	0	0
$416$	−17.7415	−0.869847
$417$	3.46730	0.169795
$418$	27.7889	1.35920
$419$	−23.0040	−1.12382	−0.561909	−	0.827199i	$-0.689933\pi$
$419$	−23.0040	−1.12382	−0.561909	+	0.827199i	$0.689933\pi$
$420$	0	0
$421$	−22.7425	−1.10840	−0.554200	−	0.832384i	$-0.686976\pi$
$421$	−22.7425	−1.10840	−0.554200	+	0.832384i	$0.686976\pi$
$422$	−42.5050	−2.06911
$423$	19.6064	0.953295
$424$	−15.9190	−0.773095
$425$	0	0
$426$	5.95858	0.288694
$427$	−8.33688	−0.403450
$428$	78.4157	3.79036
$429$	−3.03988	−0.146767
$430$	0	0
$431$	21.9158	1.05565	0.527824	−	0.849353i	$-0.323008\pi$
$431$	21.9158	1.05565	0.527824	+	0.849353i	$0.323008\pi$
$432$	−13.5483	−0.651842
$433$	−1.91465	−0.0920123	−0.0460062	−	0.998941i	$-0.514649\pi$
$433$	−1.91465	−0.0920123	−0.0460062	+	0.998941i	$0.514649\pi$
$434$	83.9333	4.02893
$435$	0	0
$436$	13.1097	0.627841
$437$	−4.76177	−0.227786
$438$	−7.79004	−0.372222
$439$	−29.9828	−1.43100	−0.715501	−	0.698612i	$-0.753802\pi$
$439$	−29.9828	−1.43100	−0.715501	+	0.698612i	$0.753802\pi$
$440$	0	0
$441$	−55.6117	−2.64818
$442$	−42.2264	−2.00850
$443$	29.6355	1.40803	0.704013	−	0.710187i	$-0.251390\pi$
$443$	29.6355	1.40803	0.704013	+	0.710187i	$0.251390\pi$
$444$	15.2642	0.724405
$445$	0	0
$446$	54.0016	2.55705
$447$	1.62494	0.0768572
$448$	8.00233	0.378075
$449$	−12.7074	−0.599700	−0.299850	−	0.953986i	$-0.596937\pi$
$449$	−12.7074	−0.599700	−0.299850	+	0.953986i	$0.596937\pi$
$450$	0	0
$451$	2.79355	0.131543
$452$	53.0318	2.49440
$453$	1.30636	0.0613783
$454$	−17.0551	−0.800434
$455$	0	0
$456$	−10.0694	−0.471544
$457$	−13.6307	−0.637620	−0.318810	−	0.947819i	$-0.603283\pi$
$457$	−13.6307	−0.637620	−0.318810	+	0.947819i	$0.603283\pi$
$458$	−11.3845	−0.531962
$459$	−8.87607	−0.414300
$460$	0	0
$461$	−4.48211	−0.208753	−0.104376	−	0.994538i	$-0.533285\pi$
$461$	−4.48211	−0.208753	−0.104376	+	0.994538i	$0.533285\pi$
$462$	−10.3451	−0.481296
$463$	−8.96365	−0.416576	−0.208288	−	0.978068i	$-0.566789\pi$
$463$	−8.96365	−0.416576	−0.208288	+	0.978068i	$0.566789\pi$
$464$	−9.06120	−0.420656
$465$	0	0
$466$	−10.0202	−0.464179
$467$	40.5083	1.87450	0.937249	−	0.348660i	$-0.113363\pi$
$467$	40.5083	1.87450	0.937249	+	0.348660i	$0.113363\pi$
$468$	−48.5541	−2.24442
$469$	25.2856	1.16758
$470$	0	0
$471$	5.08373	0.234246
$472$	21.6510	0.996566
$473$	−13.9505	−0.641446
$474$	−4.77913	−0.219513
$475$	0	0
$476$	−98.9035	−4.53323
$477$	−7.49477	−0.343162
$478$	51.9204	2.37478
$479$	−2.81021	−0.128402	−0.0642009	−	0.997937i	$-0.520450\pi$
$479$	−2.81021	−0.128402	−0.0642009	+	0.997937i	$0.520450\pi$
$480$	0	0
$481$	38.1814	1.74092
$482$	−8.94237	−0.407314
$483$	1.77268	0.0806598
$484$	−25.1311	−1.14232
$485$	0	0
$486$	−22.3941	−1.01582
$487$	−39.8243	−1.80461	−0.902305	−	0.431098i	$-0.858126\pi$
$487$	−39.8243	−1.80461	−0.902305	+	0.431098i	$0.858126\pi$
$488$	−9.94510	−0.450193
$489$	2.16826	0.0980522
$490$	0	0
$491$	−1.33456	−0.0602278	−0.0301139	−	0.999546i	$-0.509587\pi$
$491$	−1.33456	−0.0602278	−0.0301139	+	0.999546i	$0.509587\pi$
$492$	−1.85037	−0.0834211
$493$	−5.93639	−0.267362
$494$	−46.0418	−2.07152
$495$	0	0
$496$	43.0679	1.93380
$497$	34.9100	1.56593
$498$	−7.78627	−0.348911
$499$	9.67137	0.432950	0.216475	−	0.976288i	$-0.430544\pi$
$499$	9.67137	0.432950	0.216475	+	0.976288i	$0.430544\pi$
$500$	0	0
$501$	−3.61240	−0.161390
$502$	37.4086	1.66963
$503$	−10.0501	−0.448110	−0.224055	−	0.974576i	$-0.571930\pi$
$503$	−10.0501	−0.448110	−0.224055	+	0.974576i	$0.571930\pi$
$504$	−90.3929	−4.02642
$505$	0	0
$506$	−5.83583	−0.259434
$507$	0.543496	0.0241375
$508$	−91.5391	−4.06139
$509$	−22.6023	−1.00183	−0.500915	−	0.865497i	$-0.667003\pi$
$509$	−22.6023	−1.00183	−0.500915	+	0.865497i	$0.667003\pi$
$510$	0	0
$511$	−45.6401	−2.01900
$512$	50.5888	2.23573
$513$	−9.67808	−0.427298
$514$	−10.6841	−0.471254
$515$	0	0
$516$	9.24045	0.406788
$517$	15.6823	0.689705
$518$	129.936	5.70905
$519$	−8.21837	−0.360746
$520$	0	0
$521$	3.13143	0.137190	0.0685952	−	0.997645i	$-0.478148\pi$
$521$	3.13143	0.137190	0.0685952	+	0.997645i	$0.478148\pi$
$522$	−9.91778	−0.434089
$523$	−4.29661	−0.187878	−0.0939388	−	0.995578i	$-0.529946\pi$
$523$	−4.29661	−0.187878	−0.0939388	+	0.995578i	$0.529946\pi$
$524$	46.8202	2.04535
$525$	0	0
$526$	−39.5142	−1.72290
$527$	28.2156	1.22909
$528$	−5.30826	−0.231012
$529$	1.00000	0.0434783
$530$	0	0
$531$	10.1934	0.442356
$532$	−107.840	−4.67546
$533$	−4.62847	−0.200481
$534$	8.42087	0.364407
$535$	0	0
$536$	30.1633	1.30286
$537$	1.51822	0.0655159
$538$	−32.0980	−1.38384
$539$	−44.4813	−1.91595
$540$	0	0
$541$	10.5572	0.453891	0.226945	−	0.973908i	$-0.427126\pi$
$541$	10.5572	0.453891	0.226945	+	0.973908i	$0.427126\pi$
$542$	0.793222	0.0340718
$543$	1.83697	0.0788318
$544$	−20.2965	−0.870207
$545$	0	0
$546$	17.1402	0.733531
$547$	12.2585	0.524137	0.262068	−	0.965049i	$-0.415595\pi$
$547$	12.2585	0.524137	0.262068	+	0.965049i	$0.415595\pi$
$548$	−35.8540	−1.53161
$549$	−4.68221	−0.199832
$550$	0	0
$551$	−6.47278	−0.275750
$552$	2.11464	0.0900050
$553$	−27.9999	−1.19067
$554$	−28.3760	−1.20558
$555$	0	0
$556$	44.2969	1.87861
$557$	20.0748	0.850595	0.425297	−	0.905054i	$-0.360169\pi$
$557$	20.0748	0.850595	0.425297	+	0.905054i	$0.360169\pi$
$558$	47.1391	1.99556
$559$	23.1138	0.977612
$560$	0	0
$561$	−3.47768	−0.146828
$562$	−20.0665	−0.846454
$563$	−30.0124	−1.26487	−0.632436	−	0.774613i	$-0.717945\pi$
$563$	−30.0124	−1.26487	−0.632436	+	0.774613i	$0.717945\pi$
$564$	−10.3875	−0.437392
$565$	0	0
$566$	−0.594447	−0.0249865
$567$	−40.7195	−1.71006
$568$	41.6443	1.74735
$569$	−19.6988	−0.825817	−0.412908	−	0.910773i	$-0.635487\pi$
$569$	−19.6988	−0.825817	−0.412908	+	0.910773i	$0.635487\pi$
$570$	0	0
$571$	−28.7974	−1.20513	−0.602566	−	0.798069i	$-0.705855\pi$
$571$	−28.7974	−1.20513	−0.602566	+	0.798069i	$0.705855\pi$
$572$	−38.8363	−1.62383
$573$	7.11136	0.297081
$574$	−15.7512	−0.657444
$575$	0	0
$576$	4.49432	0.187263
$577$	16.5121	0.687409	0.343705	−	0.939078i	$-0.388318\pi$
$577$	16.5121	0.687409	0.343705	+	0.939078i	$0.388318\pi$
$578$	−5.24851	−0.218309
$579$	2.69387	0.111953
$580$	0	0
$581$	−45.6180	−1.89255
$582$	9.03429	0.374484
$583$	−5.99472	−0.248276
$584$	−54.4442	−2.25292
$585$	0	0
$586$	11.7387	0.484922
$587$	22.1968	0.916159	0.458080	−	0.888911i	$-0.348537\pi$
$587$	22.1968	0.916159	0.458080	+	0.888911i	$0.348537\pi$
$588$	29.4632	1.21504
$589$	30.7651	1.26765
$590$	0	0
$591$	−4.41348	−0.181546
$592$	66.6727	2.74023
$593$	43.3570	1.78046	0.890229	−	0.455514i	$-0.150545\pi$
$593$	43.3570	1.78046	0.890229	+	0.455514i	$0.150545\pi$
$594$	−11.8611	−0.486665
$595$	0	0
$596$	20.7596	0.850347
$597$	−1.48938	−0.0609565
$598$	9.66905	0.395397
$599$	26.6942	1.09069	0.545347	−	0.838210i	$-0.316398\pi$
$599$	26.6942	1.09069	0.545347	+	0.838210i	$0.316398\pi$
$600$	0	0
$601$	43.9222	1.79163	0.895813	−	0.444432i	$-0.146595\pi$
$601$	43.9222	1.79163	0.895813	+	0.444432i	$0.146595\pi$
$602$	78.6591	3.20591
$603$	14.2011	0.578312
$604$	16.6896	0.679089
$605$	0	0
$606$	−16.4839	−0.669612
$607$	−14.6468	−0.594495	−0.297248	−	0.954800i	$-0.596069\pi$
$607$	−14.6468	−0.594495	−0.297248	+	0.954800i	$0.596069\pi$
$608$	−22.1305	−0.897509
$609$	2.40965	0.0976439
$610$	0	0
$611$	−25.9830	−1.05116
$612$	−55.5468	−2.24535
$613$	9.34091	0.377276	0.188638	−	0.982047i	$-0.439593\pi$
$613$	9.34091	0.377276	0.188638	+	0.982047i	$0.439593\pi$
$614$	−8.45250	−0.341115
$615$	0	0
$616$	−72.3012	−2.91310
$617$	23.1312	0.931226	0.465613	−	0.884988i	$-0.345834\pi$
$617$	23.1312	0.931226	0.465613	+	0.884988i	$0.345834\pi$
$618$	5.21758	0.209882
$619$	2.25036	0.0904498	0.0452249	−	0.998977i	$-0.485600\pi$
$619$	2.25036	0.0904498	0.0452249	+	0.998977i	$0.485600\pi$
$620$	0	0
$621$	2.03246	0.0815596
$622$	7.10083	0.284718
$623$	49.3360	1.97660
$624$	8.79496	0.352080
$625$	0	0
$626$	4.87598	0.194883
$627$	−3.79191	−0.151434
$628$	64.9476	2.59169
$629$	43.6802	1.74164
$630$	0	0
$631$	15.8712	0.631823	0.315912	−	0.948789i	$-0.397690\pi$
$631$	15.8712	0.631823	0.315912	+	0.948789i	$0.397690\pi$
$632$	−33.4011	−1.32863
$633$	5.79998	0.230528
$634$	−48.4496	−1.92418
$635$	0	0
$636$	3.97074	0.157450
$637$	73.6985	2.92004
$638$	−7.93278	−0.314062
$639$	19.6064	0.775616
$640$	0	0
$641$	−5.95018	−0.235018	−0.117509	−	0.993072i	$-0.537491\pi$
$641$	−5.95018	−0.235018	−0.117509	+	0.993072i	$0.537491\pi$
$642$	−15.5467	−0.613580
$643$	−24.5574	−0.968449	−0.484225	−	0.874944i	$-0.660898\pi$
$643$	−24.5574	−0.968449	−0.484225	+	0.874944i	$0.660898\pi$
$644$	22.6471	0.892419
$645$	0	0
$646$	−52.6726	−2.07238
$647$	46.0798	1.81158	0.905791	−	0.423725i	$-0.139278\pi$
$647$	46.0798	1.81158	0.905791	+	0.423725i	$0.139278\pi$
$648$	−48.5744	−1.90818
$649$	8.15325	0.320043
$650$	0	0
$651$	−11.4530	−0.448880
$652$	27.7008	1.08485
$653$	−6.10566	−0.238933	−0.119467	−	0.992838i	$-0.538118\pi$
$653$	−6.10566	−0.238933	−0.119467	+	0.992838i	$0.538118\pi$
$654$	−2.59913	−0.101634
$655$	0	0
$656$	−8.08227	−0.315560
$657$	−25.6327	−1.00003
$658$	−88.4233	−3.44710
$659$	19.0282	0.741235	0.370618	−	0.928786i	$-0.379146\pi$
$659$	19.0282	0.741235	0.370618	+	0.928786i	$0.379146\pi$
$660$	0	0
$661$	−29.4700	−1.14625	−0.573125	−	0.819468i	$-0.694269\pi$
$661$	−29.4700	−1.14625	−0.573125	+	0.819468i	$0.694269\pi$
$662$	8.81031	0.342422
$663$	5.76196	0.223776
$664$	−54.4179	−2.11182
$665$	0	0
$666$	72.9754	2.82774
$667$	1.35932	0.0526332
$668$	−46.1505	−1.78562
$669$	−7.36874	−0.284892
$670$	0	0
$671$	−3.74509	−0.144578
$672$	8.23859	0.317811
$673$	15.4821	0.596789	0.298395	−	0.954443i	$-0.403549\pi$
$673$	15.4821	0.596789	0.298395	+	0.954443i	$0.403549\pi$
$674$	−67.6626	−2.60627
$675$	0	0
$676$	6.94348	0.267057
$677$	23.1585	0.890055	0.445027	−	0.895517i	$-0.353194\pi$
$677$	23.1585	0.890055	0.445027	+	0.895517i	$0.353194\pi$
$678$	−10.5141	−0.403791
$679$	52.9299	2.03126
$680$	0	0
$681$	2.32723	0.0891798
$682$	37.7045	1.44378
$683$	31.7569	1.21514	0.607572	−	0.794265i	$-0.292144\pi$
$683$	31.7569	1.21514	0.607572	+	0.794265i	$0.292144\pi$
$684$	−60.5658	−2.31579
$685$	0	0
$686$	159.867	6.10377
$687$	1.55346	0.0592682
$688$	40.3616	1.53877
$689$	9.93232	0.378391
$690$	0	0
$691$	10.8507	0.412781	0.206391	−	0.978470i	$-0.433828\pi$
$691$	10.8507	0.412781	0.206391	+	0.978470i	$0.433828\pi$
$692$	−104.995	−3.99129
$693$	−34.0398	−1.29307
$694$	33.9927	1.29035
$695$	0	0
$696$	2.87448	0.108957
$697$	−5.29505	−0.200564
$698$	53.8734	2.03914
$699$	1.36730	0.0517162
$700$	0	0
$701$	−34.4464	−1.30102	−0.650512	−	0.759496i	$-0.725446\pi$
$701$	−34.4464	−1.30102	−0.650512	+	0.759496i	$0.725446\pi$
$702$	19.6519	0.741714
$703$	47.6270	1.79629
$704$	3.59480	0.135484
$705$	0	0
$706$	67.8599	2.55394
$707$	−96.5753	−3.63209
$708$	−5.40049	−0.202963
$709$	7.23289	0.271637	0.135818	−	0.990734i	$-0.456634\pi$
$709$	7.23289	0.271637	0.135818	+	0.990734i	$0.456634\pi$
$710$	0	0
$711$	−15.7254	−0.589750
$712$	58.8530	2.20561
$713$	−6.46086	−0.241961
$714$	19.6086	0.733835
$715$	0	0
$716$	19.3961	0.724868
$717$	−7.08475	−0.264585
$718$	11.1966	0.417854
$719$	13.9067	0.518632	0.259316	−	0.965793i	$-0.416503\pi$
$719$	13.9067	0.518632	0.259316	+	0.965793i	$0.416503\pi$
$720$	0	0
$721$	30.5686	1.13843
$722$	−9.30697	−0.346369
$723$	1.22022	0.0453806
$724$	23.4683	0.872194
$725$	0	0
$726$	4.98250	0.184918
$727$	−25.2181	−0.935287	−0.467644	−	0.883917i	$-0.654897\pi$
$727$	−25.2181	−0.935287	−0.467644	+	0.883917i	$0.654897\pi$
$728$	119.792	4.43978
$729$	−20.7617	−0.768953
$730$	0	0
$731$	26.4426	0.978016
$732$	2.48065	0.0916873
$733$	42.3600	1.56460	0.782301	−	0.622900i	$-0.214046\pi$
$733$	42.3600	1.56460	0.782301	+	0.622900i	$0.214046\pi$
$734$	−27.6107	−1.01913
$735$	0	0
$736$	4.64753	0.171310
$737$	11.3588	0.418406
$738$	−8.84630	−0.325637
$739$	−28.6553	−1.05410	−0.527052	−	0.849833i	$-0.676703\pi$
$739$	−28.6553	−1.05410	−0.527052	+	0.849833i	$0.676703\pi$
$740$	0	0
$741$	6.28259	0.230797
$742$	33.8008	1.24087
$743$	25.3041	0.928319	0.464159	−	0.885752i	$-0.346357\pi$
$743$	25.3041	0.928319	0.464159	+	0.885752i	$0.346357\pi$
$744$	−13.6624	−0.500887
$745$	0	0
$746$	−31.6613	−1.15920
$747$	−25.6203	−0.937396
$748$	−44.4294	−1.62450
$749$	−91.0847	−3.32816
$750$	0	0
$751$	−35.4277	−1.29277	−0.646387	−	0.763009i	$-0.723721\pi$
$751$	−35.4277	−1.29277	−0.646387	+	0.763009i	$0.723721\pi$
$752$	−45.3718	−1.65454
$753$	−5.10455	−0.186020
$754$	13.1434	0.478653
$755$	0	0
$756$	46.0291	1.67406
$757$	11.6369	0.422952	0.211476	−	0.977383i	$-0.432173\pi$
$757$	11.6369	0.422952	0.211476	+	0.977383i	$0.432173\pi$
$758$	−54.6130	−1.98363
$759$	0.796323	0.0289047
$760$	0	0
$761$	26.2934	0.953135	0.476567	−	0.879138i	$-0.341881\pi$
$761$	26.2934	0.953135	0.476567	+	0.879138i	$0.341881\pi$
$762$	18.1486	0.657453
$763$	−15.2277	−0.551281
$764$	90.8518	3.28690
$765$	0	0
$766$	−7.35522	−0.265755
$767$	−13.5086	−0.487769
$768$	−10.5183	−0.379545
$769$	5.53910	0.199745	0.0998725	−	0.995000i	$-0.468157\pi$
$769$	5.53910	0.199745	0.0998725	+	0.995000i	$0.468157\pi$
$770$	0	0
$771$	1.45789	0.0525045
$772$	34.4158	1.23865
$773$	−49.3615	−1.77541	−0.887704	−	0.460415i	$-0.847701\pi$
$773$	−49.3615	−1.77541	−0.887704	+	0.460415i	$0.847701\pi$
$774$	44.1770	1.58791
$775$	0	0
$776$	63.1403	2.26660
$777$	−17.7303	−0.636070
$778$	−67.9204	−2.43506
$779$	−5.77349	−0.206857
$780$	0	0
$781$	15.6823	0.561155
$782$	11.0616	0.395561
$783$	2.76276	0.0987332
$784$	128.693	4.59618
$785$	0	0
$786$	−9.28259	−0.331099
$787$	32.5598	1.16063	0.580315	−	0.814392i	$-0.302929\pi$
$787$	32.5598	1.16063	0.580315	+	0.814392i	$0.302929\pi$
$788$	−56.3849	−2.00863
$789$	5.39188	0.191956
$790$	0	0
$791$	−61.5997	−2.19023
$792$	−40.6062	−1.44288
$793$	6.20503	0.220347
$794$	−0.804588	−0.0285537
$795$	0	0
$796$	−19.0278	−0.674422
$797$	−22.1958	−0.786215	−0.393107	−	0.919493i	$-0.628600\pi$
$797$	−22.1958	−0.786215	−0.393107	+	0.919493i	$0.628600\pi$
$798$	21.3804	0.756858
$799$	−29.7250	−1.05160
$800$	0	0
$801$	27.7084	0.979027
$802$	−82.9350	−2.92854
$803$	−20.5024	−0.723514
$804$	−7.52375	−0.265342
$805$	0	0
$806$	−62.4704	−2.20043
$807$	4.37990	0.154180
$808$	−115.205	−4.05290
$809$	−50.2889	−1.76806	−0.884032	−	0.467427i	$-0.845181\pi$
$809$	−50.2889	−1.76806	−0.884032	+	0.467427i	$0.845181\pi$
$810$	0	0
$811$	44.8502	1.57490	0.787451	−	0.616377i	$-0.211400\pi$
$811$	44.8502	1.57490	0.787451	+	0.616377i	$0.211400\pi$
$812$	30.7847	1.08033
$813$	−0.108238	−0.00379608
$814$	58.3697	2.04586
$815$	0	0
$816$	10.0616	0.352226
$817$	28.8319	1.00870
$818$	−62.5984	−2.18870
$819$	56.3987	1.97073
$820$	0	0
$821$	−53.8480	−1.87931	−0.939654	−	0.342126i	$-0.888853\pi$
$821$	−53.8480	−1.87931	−0.939654	+	0.342126i	$0.888853\pi$
$822$	7.10842	0.247935
$823$	−30.7304	−1.07120	−0.535598	−	0.844473i	$-0.679914\pi$
$823$	−30.7304	−1.07120	−0.535598	+	0.844473i	$0.679914\pi$
$824$	36.4654	1.27033
$825$	0	0
$826$	−45.9715	−1.59955
$827$	−16.5165	−0.574334	−0.287167	−	0.957881i	$-0.592713\pi$
$827$	−16.5165	−0.574334	−0.287167	+	0.957881i	$0.592713\pi$
$828$	12.7192	0.442022
$829$	4.13937	0.143766	0.0718831	−	0.997413i	$-0.477099\pi$
$829$	4.13937	0.143766	0.0718831	+	0.997413i	$0.477099\pi$
$830$	0	0
$831$	3.87202	0.134319
$832$	−5.95602	−0.206488
$833$	84.3124	2.92125
$834$	−8.78231	−0.304107
$835$	0	0
$836$	−48.4439	−1.67547
$837$	−13.1314	−0.453888
$838$	58.2667	2.01279
$839$	−26.4649	−0.913669	−0.456835	−	0.889552i	$-0.651017\pi$
$839$	−26.4649	−0.913669	−0.456835	+	0.889552i	$0.651017\pi$
$840$	0	0
$841$	−27.1522	−0.936284
$842$	57.6042	1.98517
$843$	2.73816	0.0943071
$844$	74.0981	2.55056
$845$	0	0
$846$	−49.6609	−1.70738
$847$	29.1913	1.00303
$848$	17.3439	0.595592
$849$	0.0811148	0.00278385
$850$	0	0
$851$	−10.0020	−0.342863
$852$	−10.3875	−0.355870
$853$	25.5390	0.874438	0.437219	−	0.899355i	$-0.355963\pi$
$853$	25.5390	0.874438	0.437219	+	0.899355i	$0.355963\pi$
$854$	21.1164	0.722590
$855$	0	0
$856$	−108.655	−3.71376
$857$	9.24798	0.315905	0.157952	−	0.987447i	$-0.449511\pi$
$857$	9.24798	0.315905	0.157952	+	0.987447i	$0.449511\pi$
$858$	7.69969	0.262863
$859$	−5.45768	−0.186214	−0.0931068	−	0.995656i	$-0.529680\pi$
$859$	−5.45768	−0.186214	−0.0931068	+	0.995656i	$0.529680\pi$
$860$	0	0
$861$	2.14932	0.0732486
$862$	−55.5105	−1.89069
$863$	−18.5611	−0.631825	−0.315913	−	0.948788i	$-0.602311\pi$
$863$	−18.5611	−0.631825	−0.315913	+	0.948788i	$0.602311\pi$
$864$	9.44590	0.321356
$865$	0	0
$866$	4.84961	0.164796
$867$	0.716181	0.0243228
$868$	−146.319	−4.96641
$869$	−12.5781	−0.426682
$870$	0	0
$871$	−18.8197	−0.637682
$872$	−18.1652	−0.615152
$873$	29.7268	1.00610
$874$	12.0611	0.407971
$875$	0	0
$876$	13.5802	0.458834
$877$	−2.33728	−0.0789242	−0.0394621	−	0.999221i	$-0.512564\pi$
$877$	−2.33728	−0.0789242	−0.0394621	+	0.999221i	$0.512564\pi$
$878$	75.9433	2.56296
$879$	−1.60180	−0.0540272
$880$	0	0
$881$	21.8340	0.735606	0.367803	−	0.929904i	$-0.380110\pi$
$881$	21.8340	0.735606	0.367803	+	0.929904i	$0.380110\pi$
$882$	140.859	4.74295
$883$	−48.0512	−1.61705	−0.808526	−	0.588461i	$-0.799734\pi$
$883$	−48.0512	−1.61705	−0.808526	+	0.588461i	$0.799734\pi$
$884$	73.6125	2.47586
$885$	0	0
$886$	−75.0636	−2.52181
$887$	7.92260	0.266015	0.133007	−	0.991115i	$-0.457537\pi$
$887$	7.92260	0.266015	0.133007	+	0.991115i	$0.457537\pi$
$888$	−21.1505	−0.709765
$889$	106.328	3.56614
$890$	0	0
$891$	−18.2920	−0.612804
$892$	−94.1400	−3.15204
$893$	−32.4109	−1.08459
$894$	−4.11581	−0.137653
$895$	0	0
$896$	−67.9428	−2.26981
$897$	−1.31938	−0.0440529
$898$	32.1865	1.07408
$899$	−8.78240	−0.292909
$900$	0	0
$901$	11.3627	0.378548
$902$	−7.07576	−0.235597
$903$	−10.7334	−0.357184
$904$	−73.4825	−2.44399
$905$	0	0
$906$	−3.30888	−0.109930
$907$	−21.4157	−0.711098	−0.355549	−	0.934658i	$-0.615706\pi$
$907$	−21.4157	−0.711098	−0.355549	+	0.934658i	$0.615706\pi$
$908$	29.7318	0.986684
$909$	−54.2392	−1.79900
$910$	0	0
$911$	13.7968	0.457109	0.228555	−	0.973531i	$-0.426600\pi$
$911$	13.7968	0.457109	0.228555	+	0.973531i	$0.426600\pi$
$912$	10.9707	0.363277
$913$	−20.4925	−0.678203
$914$	34.5252	1.14199
$915$	0	0
$916$	19.8464	0.655743
$917$	−54.3846	−1.79594
$918$	22.4821	0.742021
$919$	−55.8236	−1.84145	−0.920725	−	0.390213i	$-0.872401\pi$
$919$	−55.8236	−1.84145	−0.920725	+	0.390213i	$0.872401\pi$
$920$	0	0
$921$	1.15338	0.0380051
$922$	11.3527	0.373881
$923$	−25.9830	−0.855242
$924$	18.0344	0.593287
$925$	0	0
$926$	22.7040	0.746098
$927$	17.1681	0.563875
$928$	6.31750	0.207382
$929$	0.153368	0.00503183	0.00251591	−	0.999997i	$-0.499199\pi$
$929$	0.153368	0.00503183	0.00251591	+	0.999997i	$0.499199\pi$
$930$	0	0
$931$	91.9306	3.01290
$932$	17.4681	0.572187
$933$	−0.968938	−0.0317216
$934$	−102.603	−3.35728
$935$	0	0
$936$	67.2782	2.19906
$937$	−32.1591	−1.05059	−0.525297	−	0.850919i	$-0.676046\pi$
$937$	−32.1591	−1.05059	−0.525297	+	0.850919i	$0.676046\pi$
$938$	−64.0458	−2.09117
$939$	−0.665347	−0.0217128
$940$	0	0
$941$	35.8054	1.16722	0.583612	−	0.812033i	$-0.301639\pi$
$941$	35.8054	1.16722	0.583612	+	0.812033i	$0.301639\pi$
$942$	−12.8765	−0.419540
$943$	1.21247	0.0394834
$944$	−23.5889	−0.767754
$945$	0	0
$946$	35.3352	1.14885
$947$	−44.4662	−1.44496	−0.722479	−	0.691393i	$-0.756997\pi$
$947$	−44.4662	−1.44496	−0.722479	+	0.691393i	$0.756997\pi$
$948$	8.33137	0.270590
$949$	33.9693	1.10269
$950$	0	0
$951$	6.61114	0.214381
$952$	137.044	4.44162
$953$	−0.0798149	−0.00258546	−0.00129273	−	0.999999i	$-0.500411\pi$
$953$	−0.0798149	−0.00258546	−0.00129273	+	0.999999i	$0.500411\pi$
$954$	18.9834	0.614612
$955$	0	0
$956$	−90.5119	−2.92736
$957$	1.08246	0.0349910
$958$	7.11796	0.229971
$959$	41.6467	1.34484
$960$	0	0
$961$	10.7427	0.346539
$962$	−96.7095	−3.11804
$963$	−51.1556	−1.64846
$964$	15.5891	0.502090
$965$	0	0
$966$	−4.49001	−0.144464
$967$	19.1074	0.614451	0.307226	−	0.951637i	$-0.400599\pi$
$967$	19.1074	0.614451	0.307226	+	0.951637i	$0.400599\pi$
$968$	34.8225	1.11924
$969$	7.18740	0.230892
$970$	0	0
$971$	−45.3791	−1.45629	−0.728143	−	0.685425i	$-0.759616\pi$
$971$	−45.3791	−1.45629	−0.728143	+	0.685425i	$0.759616\pi$
$972$	39.0393	1.25219
$973$	−51.4536	−1.64953
$974$	100.871	3.23210
$975$	0	0
$976$	10.8353	0.346828
$977$	41.0121	1.31209	0.656047	−	0.754720i	$-0.272227\pi$
$977$	41.0121	1.31209	0.656047	+	0.754720i	$0.272227\pi$
$978$	−5.49197	−0.175614
$979$	22.1627	0.708322
$980$	0	0
$981$	−8.55230	−0.273054
$982$	3.38030	0.107870
$983$	23.6442	0.754133	0.377067	−	0.926186i	$-0.376933\pi$
$983$	23.6442	0.754133	0.377067	+	0.926186i	$0.376933\pi$
$984$	2.56393	0.0817351
$985$	0	0
$986$	15.0362	0.478852
$987$	12.0657	0.384056
$988$	80.2639	2.55353
$989$	−6.05487	−0.192534
$990$	0	0
$991$	−11.0599	−0.351330	−0.175665	−	0.984450i	$-0.556208\pi$
$991$	−11.0599	−0.351330	−0.175665	+	0.984450i	$0.556208\pi$
$992$	−30.0270	−0.953360
$993$	−1.20220	−0.0381508
$994$	−88.4233	−2.80462
$995$	0	0
$996$	13.5737	0.430098
$997$	−24.5440	−0.777316	−0.388658	−	0.921382i	$-0.627061\pi$
$997$	−24.5440	−0.777316	−0.388658	+	0.921382i	$0.627061\pi$
$998$	−24.4965	−0.775424
$999$	−20.3285	−0.643166

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.a.k.1.1	✓	7
3.2	odd	2		5175.2.a.cg.1.7		7
4.3	odd	2		9200.2.a.da.1.4		7
5.2	odd	4		575.2.b.f.24.2		14
5.3	odd	4		575.2.b.f.24.13		14
5.4	even	2		575.2.a.l.1.7	yes	7
15.14	odd	2		5175.2.a.cb.1.1		7
20.19	odd	2		9200.2.a.db.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
575.2.a.k.1.1	✓	7	1.1	even	1	trivial
575.2.a.l.1.7	yes	7	5.4	even	2
575.2.b.f.24.2		14	5.2	odd	4
575.2.b.f.24.13		14	5.3	odd	4
5175.2.a.cb.1.1		7	15.14	odd	2
5175.2.a.cg.1.7		7	3.2	odd	2
9200.2.a.da.1.4		7	4.3	odd	2
9200.2.a.db.1.4		7	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53289 q^{2} +0.345624 q^{3} +4.41555 q^{4} -0.875428 q^{6} -5.12894 q^{7} -6.11832 q^{8} -2.88054 q^{9} +O(q^{10})\)	\(q-2.53289 q^{2} +0.345624 q^{3} +4.41555 q^{4} -0.875428 q^{6} -5.12894 q^{7} -6.11832 q^{8} -2.88054 q^{9} -2.30402 q^{11} +1.52612 q^{12} +3.81740 q^{13} +12.9910 q^{14} +6.66597 q^{16} +4.36717 q^{17} +7.29611 q^{18} +4.76177 q^{19} -1.77268 q^{21} +5.83583 q^{22} -1.00000 q^{23} -2.11464 q^{24} -9.66905 q^{26} -2.03246 q^{27} -22.6471 q^{28} -1.35932 q^{29} +6.46086 q^{31} -4.64753 q^{32} -0.796323 q^{33} -11.0616 q^{34} -12.7192 q^{36} +10.0020 q^{37} -12.0611 q^{38} +1.31938 q^{39} -1.21247 q^{41} +4.49001 q^{42} +6.05487 q^{43} -10.1735 q^{44} +2.53289 q^{46} -6.80648 q^{47} +2.30392 q^{48} +19.3060 q^{49} +1.50940 q^{51} +16.8559 q^{52} +2.60186 q^{53} +5.14799 q^{54} +31.3805 q^{56} +1.64578 q^{57} +3.44302 q^{58} -3.53871 q^{59} +1.62546 q^{61} -16.3647 q^{62} +14.7741 q^{63} -1.56023 q^{64} +2.01700 q^{66} -4.92999 q^{67} +19.2834 q^{68} -0.345624 q^{69} -6.80648 q^{71} +17.6241 q^{72} +8.89855 q^{73} -25.3339 q^{74} +21.0258 q^{76} +11.8172 q^{77} -3.34185 q^{78} +5.45919 q^{79} +7.93917 q^{81} +3.07105 q^{82} +8.89424 q^{83} -7.82736 q^{84} -15.3363 q^{86} -0.469814 q^{87} +14.0967 q^{88} -9.61914 q^{89} -19.5792 q^{91} -4.41555 q^{92} +2.23303 q^{93} +17.2401 q^{94} -1.60630 q^{96} -10.3199 q^{97} -48.9000 q^{98} +6.63682 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 11 q^{4} + 5 q^{6} + 3 q^{7} - 6 q^{8} + 15 q^{9}+O(q^{10}) \) 7 * q - q^2 + 11 * q^4 + 5 * q^6 + 3 * q^7 - 6 * q^8 + 15 * q^9	\( 7 q - q^{2} + 11 q^{4} + 5 q^{6} + 3 q^{7} - 6 q^{8} + 15 q^{9} - q^{11} + 6 q^{12} - 3 q^{13} + 7 q^{14} + 7 q^{16} + 10 q^{17} - 24 q^{18} + 15 q^{19} + 2 q^{21} + 21 q^{22} - 7 q^{23} + 18 q^{24} - 20 q^{26} - 11 q^{28} + 3 q^{29} + 14 q^{31} + 17 q^{32} + 6 q^{33} + 20 q^{34} - 10 q^{37} - 31 q^{38} - 8 q^{39} + 19 q^{41} + 44 q^{42} + 5 q^{43} - 3 q^{44} + q^{46} - 14 q^{47} - 27 q^{48} + 40 q^{49} + 2 q^{51} + 16 q^{52} + 4 q^{53} - q^{54} - 9 q^{56} - 4 q^{57} - 13 q^{58} - 16 q^{59} + 40 q^{61} - 12 q^{62} + 53 q^{63} - 4 q^{64} - 54 q^{66} - 4 q^{67} + 20 q^{68} - 14 q^{71} - 6 q^{72} - 3 q^{73} - 18 q^{74} + 35 q^{76} - 17 q^{77} + 23 q^{78} - q^{79} + 47 q^{81} - 22 q^{82} + 17 q^{83} - 60 q^{84} - 35 q^{86} - 56 q^{87} + 57 q^{88} + 16 q^{89} + 25 q^{91} - 11 q^{92} + 14 q^{93} + 7 q^{94} - 19 q^{96} - 24 q^{97} - 46 q^{98} - 53 q^{99}+O(q^{100}) \) 7 * q - q^2 + 11 * q^4 + 5 * q^6 + 3 * q^7 - 6 * q^8 + 15 * q^9 - q^11 + 6 * q^12 - 3 * q^13 + 7 * q^14 + 7 * q^16 + 10 * q^17 - 24 * q^18 + 15 * q^19 + 2 * q^21 + 21 * q^22 - 7 * q^23 + 18 * q^24 - 20 * q^26 - 11 * q^28 + 3 * q^29 + 14 * q^31 + 17 * q^32 + 6 * q^33 + 20 * q^34 - 10 * q^37 - 31 * q^38 - 8 * q^39 + 19 * q^41 + 44 * q^42 + 5 * q^43 - 3 * q^44 + q^46 - 14 * q^47 - 27 * q^48 + 40 * q^49 + 2 * q^51 + 16 * q^52 + 4 * q^53 - q^54 - 9 * q^56 - 4 * q^57 - 13 * q^58 - 16 * q^59 + 40 * q^61 - 12 * q^62 + 53 * q^63 - 4 * q^64 - 54 * q^66 - 4 * q^67 + 20 * q^68 - 14 * q^71 - 6 * q^72 - 3 * q^73 - 18 * q^74 + 35 * q^76 - 17 * q^77 + 23 * q^78 - q^79 + 47 * q^81 - 22 * q^82 + 17 * q^83 - 60 * q^84 - 35 * q^86 - 56 * q^87 + 57 * q^88 + 16 * q^89 + 25 * q^91 - 11 * q^92 + 14 * q^93 + 7 * q^94 - 19 * q^96 - 24 * q^97 - 46 * q^98 - 53 * q^99

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