LMFDB - Embedded newform 475.2.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(1,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, 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("475.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.11344.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 4x + 3 $ x^4 - 2x^3 - 4x^2 + 4*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.51658$ of defining polynomial
Character	$\chi$	$=$	475.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.816594 q^{2} -1.53844 q^{3} -1.33317 q^{4} +1.25628 q^{6} -5.03316 q^{7} +2.72185 q^{8} -0.633188 q^{9} +O(q^{10})$	\(q-0.816594 q^{2} -1.53844 q^{3} -1.33317 q^{4} +1.25628 q^{6} -5.03316 q^{7} +2.72185 q^{8} -0.633188 q^{9} -3.03316 q^{11} +2.05101 q^{12} +4.57160 q^{13} +4.11005 q^{14} +0.443701 q^{16} +1.07689 q^{17} +0.517058 q^{18} +1.00000 q^{19} +7.74324 q^{21} +2.47686 q^{22} -4.11005 q^{23} -4.18742 q^{24} -3.73315 q^{26} +5.58946 q^{27} +6.71008 q^{28} -1.07689 q^{29} +5.58946 q^{31} -5.80602 q^{32} +4.66635 q^{33} -0.879381 q^{34} +0.844150 q^{36} -0.0947438 q^{37} -0.816594 q^{38} -7.03316 q^{39} +10.6663 q^{41} -6.32308 q^{42} -5.03316 q^{43} +4.04373 q^{44} +3.35624 q^{46} +12.2995 q^{47} -0.682609 q^{48} +18.3327 q^{49} -1.65673 q^{51} -6.09474 q^{52} +4.09474 q^{53} -4.56432 q^{54} -13.6995 q^{56} -1.53844 q^{57} +0.879381 q^{58} -1.39997 q^{59} -5.69951 q^{61} -4.56432 q^{62} +3.18694 q^{63} +3.85376 q^{64} -3.81051 q^{66} -5.28168 q^{67} -1.43568 q^{68} +6.32308 q^{69} -5.67692 q^{71} -1.72344 q^{72} -9.07689 q^{73} +0.0773672 q^{74} -1.33317 q^{76} +15.2664 q^{77} +5.74324 q^{78} -5.39997 q^{79} -6.69951 q^{81} -8.71008 q^{82} -1.95627 q^{83} -10.3231 q^{84} +4.11005 q^{86} +1.65673 q^{87} -8.25581 q^{88} -2.18949 q^{89} -23.0096 q^{91} +5.47941 q^{92} -8.59907 q^{93} -10.0437 q^{94} +8.93225 q^{96} +2.16106 q^{97} -14.9704 q^{98} +1.92056 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} + 8 q^{4} - 4 q^{7} + 12 q^{8} + 8 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^3 + 8 * q^4 - 4 * q^7 + 12 * q^8 + 8 * q^9	$ 4 q + 2 q^{2} - 2 q^{3} + 8 q^{4} - 4 q^{7} + 12 q^{8} + 8 q^{9} + 4 q^{11} - 6 q^{12} - 2 q^{13} - 8 q^{14} + 4 q^{16} - 4 q^{17} + 34 q^{18} + 4 q^{19} - 4 q^{21} - 4 q^{22} + 8 q^{23} - 24 q^{24} + 4 q^{26} + 4 q^{27} + 8 q^{28} + 4 q^{29} + 4 q^{31} + 6 q^{32} - 8 q^{33} - 4 q^{34} + 40 q^{36} + 6 q^{37} + 2 q^{38} - 12 q^{39} + 16 q^{41} - 28 q^{42} - 4 q^{43} + 24 q^{44} + 12 q^{47} - 38 q^{48} + 20 q^{49} - 36 q^{51} - 18 q^{52} + 10 q^{53} - 20 q^{54} - 12 q^{56} - 2 q^{57} + 4 q^{58} + 20 q^{61} - 20 q^{62} - 20 q^{63} - 4 q^{64} - 28 q^{66} + 18 q^{67} - 4 q^{68} + 28 q^{69} - 20 q^{71} + 52 q^{72} - 28 q^{73} + 32 q^{74} + 8 q^{76} + 40 q^{77} - 12 q^{78} - 16 q^{79} + 16 q^{81} - 16 q^{82} - 44 q^{84} - 8 q^{86} + 36 q^{87} + 12 q^{88} + 4 q^{89} - 36 q^{91} + 28 q^{92} + 40 q^{93} - 48 q^{94} - 52 q^{96} - 30 q^{97} - 38 q^{98} - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^3 + 8 * q^4 - 4 * q^7 + 12 * q^8 + 8 * q^9 + 4 * q^11 - 6 * q^12 - 2 * q^13 - 8 * q^14 + 4 * q^16 - 4 * q^17 + 34 * q^18 + 4 * q^19 - 4 * q^21 - 4 * q^22 + 8 * q^23 - 24 * q^24 + 4 * q^26 + 4 * q^27 + 8 * q^28 + 4 * q^29 + 4 * q^31 + 6 * q^32 - 8 * q^33 - 4 * q^34 + 40 * q^36 + 6 * q^37 + 2 * q^38 - 12 * q^39 + 16 * q^41 - 28 * q^42 - 4 * q^43 + 24 * q^44 + 12 * q^47 - 38 * q^48 + 20 * q^49 - 36 * q^51 - 18 * q^52 + 10 * q^53 - 20 * q^54 - 12 * q^56 - 2 * q^57 + 4 * q^58 + 20 * q^61 - 20 * q^62 - 20 * q^63 - 4 * q^64 - 28 * q^66 + 18 * q^67 - 4 * q^68 + 28 * q^69 - 20 * q^71 + 52 * q^72 - 28 * q^73 + 32 * q^74 + 8 * q^76 + 40 * q^77 - 12 * q^78 - 16 * q^79 + 16 * q^81 - 16 * q^82 - 44 * q^84 - 8 * q^86 + 36 * q^87 + 12 * q^88 + 4 * q^89 - 36 * q^91 + 28 * q^92 + 40 * q^93 - 48 * q^94 - 52 * q^96 - 30 * q^97 - 38 * q^98 - 4 * 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 $

$2$	−0.816594	−0.577419	−0.288710	−	0.957417i	$-0.593226\pi$
$2$	−0.816594	−0.577419	−0.288710	+	0.957417i	$0.593226\pi$
$3$	−1.53844	−0.888221	−0.444111	−	0.895972i	$-0.646480\pi$
$3$	−1.53844	−0.888221	−0.444111	+	0.895972i	$0.646480\pi$
$4$	−1.33317	−0.666587
$5$	0	0
$5$	0	0
$6$	1.25628	0.512876
$7$	−5.03316	−1.90236	−0.951178	−	0.308644i	$-0.900125\pi$
$7$	−5.03316	−1.90236	−0.951178	+	0.308644i	$0.900125\pi$
$8$	2.72185	0.962319
$9$	−0.633188	−0.211063
$10$	0	0
$11$	−3.03316	−0.914532	−0.457266	−	0.889330i	$-0.651171\pi$
$11$	−3.03316	−0.914532	−0.457266	+	0.889330i	$0.651171\pi$
$12$	2.05101	0.592077
$13$	4.57160	1.26793	0.633967	−	0.773360i	$-0.281425\pi$
$13$	4.57160	1.26793	0.633967	+	0.773360i	$0.281425\pi$
$14$	4.11005	1.09846
$15$	0	0
$16$	0.443701	0.110925
$17$	1.07689	0.261184	0.130592	−	0.991436i	$-0.458312\pi$
$17$	1.07689	0.261184	0.130592	+	0.991436i	$0.458312\pi$
$18$	0.517058	0.121872
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	7.74324	1.68971
$22$	2.47686	0.528068
$23$	−4.11005	−0.857004	−0.428502	−	0.903541i	$-0.640959\pi$
$23$	−4.11005	−0.857004	−0.428502	+	0.903541i	$0.640959\pi$
$24$	−4.18742	−0.854753
$25$	0	0
$26$	−3.73315	−0.732130
$27$	5.58946	1.07569
$28$	6.71008	1.26809
$29$	−1.07689	−0.199973	−0.0999866	−	0.994989i	$-0.531880\pi$
$29$	−1.07689	−0.199973	−0.0999866	+	0.994989i	$0.531880\pi$
$30$	0	0
$31$	5.58946	1.00390	0.501948	−	0.864898i	$-0.332617\pi$
$31$	5.58946	1.00390	0.501948	+	0.864898i	$0.332617\pi$
$32$	−5.80602	−1.02637
$33$	4.66635	0.812307
$34$	−0.879381	−0.150813
$35$	0	0
$36$	0.844150	0.140692
$37$	−0.0947438	−0.0155758	−0.00778789	−	0.999970i	$-0.502479\pi$
$37$	−0.0947438	−0.0155758	−0.00778789	+	0.999970i	$0.502479\pi$
$38$	−0.816594	−0.132469
$39$	−7.03316	−1.12621
$40$	0	0
$41$	10.6663	1.66580	0.832902	−	0.553421i	$-0.186678\pi$
$41$	10.6663	1.66580	0.832902	+	0.553421i	$0.186678\pi$
$42$	−6.32308	−0.975673
$43$	−5.03316	−0.767550	−0.383775	−	0.923427i	$-0.625376\pi$
$43$	−5.03316	−0.767550	−0.383775	+	0.923427i	$0.625376\pi$
$44$	4.04373	0.609615
$45$	0	0
$46$	3.35624	0.494851
$47$	12.2995	1.79407	0.897036	−	0.441958i	$-0.145716\pi$
$47$	12.2995	1.79407	0.897036	+	0.441958i	$0.145716\pi$
$48$	−0.682609	−0.0985261
$49$	18.3327	2.61896
$50$	0	0
$51$	−1.65673	−0.231989
$52$	−6.09474	−0.845189
$53$	4.09474	0.562456	0.281228	−	0.959641i	$-0.409258\pi$
$53$	4.09474	0.562456	0.281228	+	0.959641i	$0.409258\pi$
$54$	−4.56432	−0.621125
$55$	0	0
$56$	−13.6995	−1.83067
$57$	−1.53844	−0.203772
$58$	0.879381	0.115468
$59$	−1.39997	−0.182261	−0.0911304	−	0.995839i	$-0.529048\pi$
$59$	−1.39997	−0.182261	−0.0911304	+	0.995839i	$0.529048\pi$
$60$	0	0
$61$	−5.69951	−0.729747	−0.364874	−	0.931057i	$-0.618888\pi$
$61$	−5.69951	−0.729747	−0.364874	+	0.931057i	$0.618888\pi$
$62$	−4.56432	−0.579669
$63$	3.18694	0.401516
$64$	3.85376	0.481720
$65$	0	0
$66$	−3.81051	−0.469042
$67$	−5.28168	−0.645260	−0.322630	−	0.946525i	$-0.604567\pi$
$67$	−5.28168	−0.645260	−0.322630	+	0.946525i	$0.604567\pi$
$68$	−1.43568	−0.174102
$69$	6.32308	0.761210
$70$	0	0
$71$	−5.67692	−0.673726	−0.336863	−	0.941554i	$-0.609366\pi$
$71$	−5.67692	−0.673726	−0.336863	+	0.941554i	$0.609366\pi$
$72$	−1.72344	−0.203110
$73$	−9.07689	−1.06237	−0.531185	−	0.847256i	$-0.678253\pi$
$73$	−9.07689	−1.06237	−0.531185	+	0.847256i	$0.678253\pi$
$74$	0.0773672	0.00899375
$75$	0	0
$76$	−1.33317	−0.152926
$77$	15.2664	1.73977
$78$	5.74324	0.650294
$79$	−5.39997	−0.607544	−0.303772	−	0.952745i	$-0.598246\pi$
$79$	−5.39997	−0.607544	−0.303772	+	0.952745i	$0.598246\pi$
$80$	0	0
$81$	−6.69951	−0.744390
$82$	−8.71008	−0.961867
$83$	−1.95627	−0.214729	−0.107364	−	0.994220i	$-0.534241\pi$
$83$	−1.95627	−0.214729	−0.107364	+	0.994220i	$0.534241\pi$
$84$	−10.3231	−1.12634
$85$	0	0
$86$	4.11005	0.443198
$87$	1.65673	0.177621
$88$	−8.25581	−0.880072
$89$	−2.18949	−0.232085	−0.116043	−	0.993244i	$-0.537021\pi$
$89$	−2.18949	−0.232085	−0.116043	+	0.993244i	$0.537021\pi$
$90$	0	0
$91$	−23.0096	−2.41206
$92$	5.47941	0.571268
$93$	−8.59907	−0.891682
$94$	−10.0437	−1.03593
$95$	0	0
$96$	8.93225	0.911644
$97$	2.16106	0.219423	0.109711	−	0.993963i	$-0.465007\pi$
$97$	2.16106	0.219423	0.109711	+	0.993963i	$0.465007\pi$
$98$	−14.9704	−1.51224
$99$	1.92056	0.193024
$100$	0	0
$101$	12.5869	1.25244	0.626222	−	0.779645i	$-0.284600\pi$
$101$	12.5869	1.25244	0.626222	+	0.779645i	$0.284600\pi$
$102$	1.35288	0.133955
$103$	6.20479	0.611376	0.305688	−	0.952132i	$-0.401113\pi$
$103$	6.20479	0.611376	0.305688	+	0.952132i	$0.401113\pi$
$104$	12.4432	1.22016
$105$	0	0
$106$	−3.34374	−0.324773
$107$	12.5481	1.21307	0.606533	−	0.795058i	$-0.292560\pi$
$107$	12.5481	1.21307	0.606533	+	0.795058i	$0.292560\pi$
$108$	−7.45172	−0.717042
$109$	−15.8096	−1.51428	−0.757140	−	0.653252i	$-0.773404\pi$
$109$	−15.8096	−1.51428	−0.757140	+	0.653252i	$0.773404\pi$
$110$	0	0
$111$	0.145758	0.0138347
$112$	−2.23322	−0.211019
$113$	5.49472	0.516899	0.258450	−	0.966025i	$-0.416788\pi$
$113$	5.49472	0.516899	0.258450	+	0.966025i	$0.416788\pi$
$114$	1.25628	0.117662
$115$	0	0
$116$	1.43568	0.133300
$117$	−2.89469	−0.267614
$118$	1.14321	0.105241
$119$	−5.42015	−0.496865
$120$	0	0
$121$	−1.79994	−0.163631
$122$	4.65418	0.421370
$123$	−16.4096	−1.47960
$124$	−7.45172	−0.669184
$125$	0	0
$126$	−2.60243	−0.231843
$127$	8.61533	0.764487	0.382244	−	0.924062i	$-0.375152\pi$
$127$	8.61533	0.764487	0.382244	+	0.924062i	$0.375152\pi$
$128$	8.46509	0.748215
$129$	7.74324	0.681754
$130$	0	0
$131$	−2.15378	−0.188176	−0.0940882	−	0.995564i	$-0.529994\pi$
$131$	−2.15378	−0.188176	−0.0940882	+	0.995564i	$0.529994\pi$
$132$	−6.22105	−0.541473
$133$	−5.03316	−0.436430
$134$	4.31299	0.372586
$135$	0	0
$136$	2.93113	0.251342
$137$	−2.18949	−0.187061	−0.0935303	−	0.995616i	$-0.529815\pi$
$137$	−2.18949	−0.187061	−0.0935303	+	0.995616i	$0.529815\pi$
$138$	−5.16339	−0.439537
$139$	22.5196	1.91009	0.955045	−	0.296460i	$-0.0958062\pi$
$139$	22.5196	1.91009	0.955045	+	0.296460i	$0.0958062\pi$
$140$	0	0
$141$	−18.9222	−1.59353
$142$	4.63574	0.389022
$143$	−13.8664	−1.15957
$144$	−0.280946	−0.0234122
$145$	0	0
$146$	7.41213	0.613433
$147$	−28.2038	−2.32621
$148$	0.126310	0.0103826
$149$	9.78697	0.801780	0.400890	−	0.916126i	$-0.368701\pi$
$149$	9.78697	0.801780	0.400890	+	0.916126i	$0.368701\pi$
$150$	0	0
$151$	5.87683	0.478250	0.239125	−	0.970989i	$-0.423139\pi$
$151$	5.87683	0.478250	0.239125	+	0.970989i	$0.423139\pi$
$152$	2.72185	0.220771
$153$	−0.681874	−0.0551262
$154$	−12.4664	−1.00457
$155$	0	0
$156$	9.37643	0.750715
$157$	−10.1895	−0.813210	−0.406605	−	0.913604i	$-0.633287\pi$
$157$	−10.1895	−0.813210	−0.406605	+	0.913604i	$0.633287\pi$
$158$	4.40959	0.350808
$159$	−6.29954	−0.499586
$160$	0	0
$161$	20.6865	1.63033
$162$	5.47078	0.429825
$163$	10.3659	0.811916	0.405958	−	0.913892i	$-0.366938\pi$
$163$	10.3659	0.811916	0.405958	+	0.913892i	$0.366938\pi$
$164$	−14.2201	−1.11040
$165$	0	0
$166$	1.59748	0.123988
$167$	15.6048	1.20753	0.603766	−	0.797161i	$-0.293666\pi$
$167$	15.6048	1.20753	0.603766	+	0.797161i	$0.293666\pi$
$168$	21.0759	1.62604
$169$	7.89956	0.607659
$170$	0	0
$171$	−0.633188	−0.0484211
$172$	6.71008	0.511639
$173$	−0.571604	−0.0434583	−0.0217291	−	0.999764i	$-0.506917\pi$
$173$	−0.571604	−0.0434583	−0.0217291	+	0.999764i	$0.506917\pi$
$174$	−1.35288	−0.102562
$175$	0	0
$176$	−1.34582	−0.101445
$177$	2.15378	0.161888
$178$	1.78792	0.134010
$179$	24.8864	1.86010	0.930050	−	0.367433i	$-0.119763\pi$
$179$	24.8864	1.86010	0.930050	+	0.367433i	$0.119763\pi$
$180$	0	0
$181$	6.95372	0.516866	0.258433	−	0.966029i	$-0.416794\pi$
$181$	6.95372	0.516866	0.258433	+	0.966029i	$0.416794\pi$
$182$	18.7895	1.39277
$183$	8.76838	0.648177
$184$	−11.1869	−0.824712
$185$	0	0
$186$	7.02195	0.514875
$187$	−3.26638	−0.238861
$188$	−16.3974	−1.19590
$189$	−28.1326	−2.04635
$190$	0	0
$191$	−3.91254	−0.283102	−0.141551	−	0.989931i	$-0.545209\pi$
$191$	−3.91254	−0.283102	−0.141551	+	0.989931i	$0.545209\pi$
$192$	−5.92880	−0.427874
$193$	9.20734	0.662759	0.331379	−	0.943498i	$-0.392486\pi$
$193$	9.20734	0.662759	0.331379	+	0.943498i	$0.392486\pi$
$194$	−1.76471	−0.126699
$195$	0	0
$196$	−24.4407	−1.74576
$197$	3.84622	0.274032	0.137016	−	0.990569i	$-0.456249\pi$
$197$	3.84622	0.274032	0.137016	+	0.990569i	$0.456249\pi$
$198$	−1.56832	−0.111456
$199$	−18.2864	−1.29629	−0.648145	−	0.761517i	$-0.724455\pi$
$199$	−18.2864	−1.29629	−0.648145	+	0.761517i	$0.724455\pi$
$200$	0	0
$201$	8.12557	0.573134
$202$	−10.2784	−0.723185
$203$	5.42015	0.380420
$204$	2.20871	0.154641
$205$	0	0
$206$	−5.06680	−0.353020
$207$	2.60243	0.180882
$208$	2.02842	0.140646
$209$	−3.03316	−0.209808
$210$	0	0
$211$	−19.2970	−1.32846	−0.664230	−	0.747529i	$-0.731240\pi$
$211$	−19.2970	−1.32846	−0.664230	+	0.747529i	$0.731240\pi$
$212$	−5.45901	−0.374926
$213$	8.73362	0.598418
$214$	−10.2467	−0.700448
$215$	0	0
$216$	15.2137	1.03516
$217$	−28.1326	−1.90977
$218$	12.9100	0.874375
$219$	13.9643	0.943619
$220$	0	0
$221$	4.92311	0.331164
$222$	−0.119025	−0.00798844
$223$	−0.615334	−0.0412058	−0.0206029	−	0.999788i	$-0.506559\pi$
$223$	−0.615334	−0.0412058	−0.0206029	+	0.999788i	$0.506559\pi$
$224$	29.2226	1.95252
$225$	0	0
$226$	−4.48695	−0.298468
$227$	−17.4712	−1.15960	−0.579801	−	0.814758i	$-0.696870\pi$
$227$	−17.4712	−1.15960	−0.579801	+	0.814758i	$0.696870\pi$
$228$	2.05101	0.135832
$229$	9.69951	0.640962	0.320481	−	0.947255i	$-0.396156\pi$
$229$	9.69951	0.640962	0.320481	+	0.947255i	$0.396156\pi$
$230$	0	0
$231$	−23.4865	−1.54530
$232$	−2.93113	−0.192438
$233$	8.15378	0.534172	0.267086	−	0.963673i	$-0.413939\pi$
$233$	8.15378	0.534172	0.267086	+	0.963673i	$0.413939\pi$
$234$	2.36378	0.154525
$235$	0	0
$236$	1.86641	0.121493
$237$	8.30756	0.539634
$238$	4.42607	0.286899
$239$	24.5991	1.59118	0.795591	−	0.605834i	$-0.207161\pi$
$239$	24.5991	1.59118	0.795591	+	0.605834i	$0.207161\pi$
$240$	0	0
$241$	25.7738	1.66024	0.830120	−	0.557585i	$-0.188272\pi$
$241$	25.7738	1.66024	0.830120	+	0.557585i	$0.188272\pi$
$242$	1.46982	0.0944838
$243$	−6.46156	−0.414509
$244$	7.59844	0.486440
$245$	0	0
$246$	13.4000	0.854351
$247$	4.57160	0.290884
$248$	15.2137	0.966069
$249$	3.00961	0.190727
$250$	0	0
$251$	12.5991	0.795246	0.397623	−	0.917549i	$-0.369835\pi$
$251$	12.5991	0.795246	0.397623	+	0.917549i	$0.369835\pi$
$252$	−4.24874	−0.267646
$253$	12.4664	0.783758
$254$	−7.03523	−0.441430
$255$	0	0
$256$	−14.6201	−0.913754
$257$	−0.182203	−0.0113655	−0.00568275	−	0.999984i	$-0.501809\pi$
$257$	−0.182203	−0.0113655	−0.00568275	+	0.999984i	$0.501809\pi$
$258$	−6.32308	−0.393658
$259$	0.476860	0.0296307
$260$	0	0
$261$	0.681874	0.0422069
$262$	1.75876	0.108657
$263$	−7.37643	−0.454850	−0.227425	−	0.973796i	$-0.573031\pi$
$263$	−7.37643	−0.454850	−0.227425	+	0.973796i	$0.573031\pi$
$264$	12.7011	0.781699
$265$	0	0
$266$	4.11005	0.252003
$267$	3.36841	0.206143
$268$	7.04140	0.430122
$269$	4.70206	0.286689	0.143345	−	0.989673i	$-0.454214\pi$
$269$	4.70206	0.286689	0.143345	+	0.989673i	$0.454214\pi$
$270$	0	0
$271$	9.92056	0.602631	0.301316	−	0.953524i	$-0.402574\pi$
$271$	9.92056	0.602631	0.301316	+	0.953524i	$0.402574\pi$
$272$	0.477817	0.0289719
$273$	35.3990	2.14245
$274$	1.78792	0.108012
$275$	0	0
$276$	−8.42977	−0.507412
$277$	22.6297	1.35969	0.679843	−	0.733358i	$-0.262048\pi$
$277$	22.6297	1.35969	0.679843	+	0.733358i	$0.262048\pi$
$278$	−18.3894	−1.10292
$279$	−3.53918	−0.211885
$280$	0	0
$281$	−3.95386	−0.235868	−0.117934	−	0.993021i	$-0.537627\pi$
$281$	−3.95386	−0.235868	−0.117934	+	0.993021i	$0.537627\pi$
$282$	15.4517	0.920137
$283$	13.0638	0.776561	0.388280	−	0.921541i	$-0.373069\pi$
$283$	13.0638	0.776561	0.388280	+	0.921541i	$0.373069\pi$
$284$	7.56832	0.449097
$285$	0	0
$286$	11.3232	0.669556
$287$	−53.6854	−3.16895
$288$	3.67631	0.216628
$289$	−15.8403	−0.931783
$290$	0	0
$291$	−3.32468	−0.194896
$292$	12.1011	0.708162
$293$	9.69463	0.566366	0.283183	−	0.959066i	$-0.408610\pi$
$293$	9.69463	0.566366	0.283183	+	0.959066i	$0.408610\pi$
$294$	23.0311	1.34320
$295$	0	0
$296$	−0.257878	−0.0149889
$297$	−16.9537	−0.983755
$298$	−7.99198	−0.462963
$299$	−18.7895	−1.08663
$300$	0	0
$301$	25.3327	1.46015
$302$	−4.79899	−0.276151
$303$	−19.3643	−1.11245
$304$	0.443701	0.0254480
$305$	0	0
$306$	0.556814	0.0318309
$307$	28.5481	1.62932	0.814662	−	0.579936i	$-0.196923\pi$
$307$	28.5481	1.62932	0.814662	+	0.579936i	$0.196923\pi$
$308$	−20.3527	−1.15970
$309$	−9.54573	−0.543038
$310$	0	0
$311$	25.4070	1.44070	0.720350	−	0.693610i	$-0.243981\pi$
$311$	25.4070	1.44070	0.720350	+	0.693610i	$0.243981\pi$
$312$	−19.1432	−1.08377
$313$	−16.7999	−0.949589	−0.474794	−	0.880097i	$-0.657478\pi$
$313$	−16.7999	−0.949589	−0.474794	+	0.880097i	$0.657478\pi$
$314$	8.32068	0.469563
$315$	0	0
$316$	7.19910	0.404981
$317$	31.7505	1.78329	0.891643	−	0.452738i	$-0.149553\pi$
$317$	31.7505	1.78329	0.891643	+	0.452738i	$0.149553\pi$
$318$	5.14416	0.288470
$319$	3.26638	0.182882
$320$	0	0
$321$	−19.3045	−1.07747
$322$	−16.8925	−0.941382
$323$	1.07689	0.0599197
$324$	8.93161	0.496201
$325$	0	0
$326$	−8.46470	−0.468816
$327$	24.3221	1.34502
$328$	29.0322	1.60304
$329$	−61.9055	−3.41296
$330$	0	0
$331$	−9.96429	−0.547687	−0.273843	−	0.961774i	$-0.588295\pi$
$331$	−9.96429	−0.547687	−0.273843	+	0.961774i	$0.588295\pi$
$332$	2.60805	0.143135
$333$	0.0599906	0.00328747
$334$	−12.7428	−0.697253
$335$	0	0
$336$	3.43568	0.187432
$337$	−23.1918	−1.26334	−0.631669	−	0.775238i	$-0.717630\pi$
$337$	−23.1918	−1.26334	−0.631669	+	0.775238i	$0.717630\pi$
$338$	−6.45074	−0.350874
$339$	−8.45331	−0.459121
$340$	0	0
$341$	−16.9537	−0.918095
$342$	0.517058	0.0279593
$343$	−57.0393	−3.07983
$344$	−13.6995	−0.738628
$345$	0	0
$346$	0.466769	0.0250936
$347$	−21.1352	−1.13460	−0.567298	−	0.823512i	$-0.692011\pi$
$347$	−21.1352	−1.13460	−0.567298	+	0.823512i	$0.692011\pi$
$348$	−2.20871	−0.118400
$349$	−5.04628	−0.270121	−0.135061	−	0.990837i	$-0.543123\pi$
$349$	−5.04628	−0.270121	−0.135061	+	0.990837i	$0.543123\pi$
$350$	0	0
$351$	25.5528	1.36391
$352$	17.6106	0.938648
$353$	−12.5634	−0.668680	−0.334340	−	0.942452i	$-0.608513\pi$
$353$	−12.5634	−0.668680	−0.334340	+	0.942452i	$0.608513\pi$
$354$	−1.75876	−0.0934772
$355$	0	0
$356$	2.91897	0.154705
$357$	8.33861	0.441326
$358$	−20.3221	−1.07406
$359$	−17.6534	−0.931709	−0.465855	−	0.884861i	$-0.654253\pi$
$359$	−17.6534	−0.931709	−0.465855	+	0.884861i	$0.654253\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	−5.67837	−0.298448
$363$	2.76911	0.145341
$364$	30.6758	1.60785
$365$	0	0
$366$	−7.16021	−0.374270
$367$	−4.43409	−0.231457	−0.115729	−	0.993281i	$-0.536920\pi$
$367$	−4.43409	−0.231457	−0.115729	+	0.993281i	$0.536920\pi$
$368$	−1.82363	−0.0950634
$369$	−6.75381	−0.351589
$370$	0	0
$371$	−20.6095	−1.06999
$372$	11.4641	0.594384
$373$	20.8735	1.08079	0.540396	−	0.841411i	$-0.318275\pi$
$373$	20.8735	1.08079	0.540396	+	0.841411i	$0.318275\pi$
$374$	2.66730	0.137923
$375$	0	0
$376$	33.4775	1.72647
$377$	−4.92311	−0.253553
$378$	22.9729	1.18160
$379$	−6.79994	−0.349290	−0.174645	−	0.984632i	$-0.555878\pi$
$379$	−6.79994	−0.349290	−0.174645	+	0.984632i	$0.555878\pi$
$380$	0	0
$381$	−13.2542	−0.679034
$382$	3.19496	0.163468
$383$	10.9078	0.557363	0.278681	−	0.960384i	$-0.410103\pi$
$383$	10.9078	0.557363	0.278681	+	0.960384i	$0.410103\pi$
$384$	−13.0231	−0.664581
$385$	0	0
$386$	−7.51866	−0.382690
$387$	3.18694	0.162001
$388$	−2.88107	−0.146264
$389$	20.9326	1.06132	0.530662	−	0.847584i	$-0.321943\pi$
$389$	20.9326	1.06132	0.530662	+	0.847584i	$0.321943\pi$
$390$	0	0
$391$	−4.42607	−0.223836
$392$	49.8989	2.52027
$393$	3.31347	0.167142
$394$	−3.14080	−0.158231
$395$	0	0
$396$	−2.56044	−0.128667
$397$	−13.1221	−0.658578	−0.329289	−	0.944229i	$-0.606809\pi$
$397$	−13.1221	−0.658578	−0.329289	+	0.944229i	$0.606809\pi$
$398$	14.9326	0.748503
$399$	7.74324	0.387647
$400$	0	0
$401$	−11.5528	−0.576919	−0.288459	−	0.957492i	$-0.593143\pi$
$401$	−11.5528	−0.576919	−0.288459	+	0.957492i	$0.593143\pi$
$402$	−6.63530	−0.330939
$403$	25.5528	1.27288
$404$	−16.7805	−0.834863
$405$	0	0
$406$	−4.42607	−0.219662
$407$	0.287373	0.0142445
$408$	−4.50938	−0.223248
$409$	−18.9433	−0.936686	−0.468343	−	0.883547i	$-0.655149\pi$
$409$	−18.9433	−0.936686	−0.468343	+	0.883547i	$0.655149\pi$
$410$	0	0
$411$	3.36841	0.166151
$412$	−8.27207	−0.407536
$413$	7.04628	0.346725
$414$	−2.12513	−0.104445
$415$	0	0
$416$	−26.5428	−1.30137
$417$	−34.6452	−1.69658
$418$	2.47686	0.121147
$419$	27.2664	1.33205	0.666025	−	0.745930i	$-0.267994\pi$
$419$	27.2664	1.33205	0.666025	+	0.745930i	$0.267994\pi$
$420$	0	0
$421$	6.66635	0.324898	0.162449	−	0.986717i	$-0.448061\pi$
$421$	6.66635	0.324898	0.162449	+	0.986717i	$0.448061\pi$
$422$	15.7578	0.767078
$423$	−7.78792	−0.378662
$424$	11.1453	0.541263
$425$	0	0
$426$	−7.13183	−0.345538
$427$	28.6865	1.38824
$428$	−16.7287	−0.808614
$429$	21.3327	1.02995
$430$	0	0
$431$	−32.4548	−1.56329	−0.781646	−	0.623723i	$-0.785619\pi$
$431$	−32.4548	−1.56329	−0.781646	+	0.623723i	$0.785619\pi$
$432$	2.48005	0.119321
$433$	−33.8168	−1.62513	−0.812567	−	0.582868i	$-0.801930\pi$
$433$	−33.8168	−1.62513	−0.812567	+	0.582868i	$0.801930\pi$
$434$	22.9729	1.10274
$435$	0	0
$436$	21.0769	1.00940
$437$	−4.11005	−0.196610
$438$	−11.4032	−0.544864
$439$	−27.8453	−1.32898	−0.664491	−	0.747296i	$-0.731352\pi$
$439$	−27.8453	−1.32898	−0.664491	+	0.747296i	$0.731352\pi$
$440$	0	0
$441$	−11.6080	−0.552764
$442$	−4.02018	−0.191221
$443$	−22.7754	−1.08209	−0.541047	−	0.840992i	$-0.681972\pi$
$443$	−22.7754	−1.08209	−0.541047	+	0.840992i	$0.681972\pi$
$444$	−0.194321	−0.00922206
$445$	0	0
$446$	0.502478	0.0237930
$447$	−15.0567	−0.712158
$448$	−19.3966	−0.916404
$449$	24.8507	1.17278	0.586389	−	0.810029i	$-0.300549\pi$
$449$	24.8507	1.17278	0.586389	+	0.810029i	$0.300549\pi$
$450$	0	0
$451$	−32.3527	−1.52343
$452$	−7.32541	−0.344558
$453$	−9.04118	−0.424792
$454$	14.2669	0.669577
$455$	0	0
$456$	−4.18742	−0.196094
$457$	7.33270	0.343009	0.171505	−	0.985183i	$-0.445137\pi$
$457$	7.33270	0.343009	0.171505	+	0.985183i	$0.445137\pi$
$458$	−7.92056	−0.370104
$459$	6.01923	0.280953
$460$	0	0
$461$	10.3076	0.480071	0.240035	−	0.970764i	$-0.422841\pi$
$461$	10.3076	0.480071	0.240035	+	0.970764i	$0.422841\pi$
$462$	19.1789	0.892284
$463$	−7.80249	−0.362613	−0.181306	−	0.983427i	$-0.558033\pi$
$463$	−7.80249	−0.362613	−0.181306	+	0.983427i	$0.558033\pi$
$464$	−0.477817	−0.0221821
$465$	0	0
$466$	−6.65833	−0.308441
$467$	7.37643	0.341340	0.170670	−	0.985328i	$-0.445407\pi$
$467$	7.37643	0.341340	0.170670	+	0.985328i	$0.445407\pi$
$468$	3.85912	0.178388
$469$	26.5835	1.22751
$470$	0	0
$471$	15.6760	0.722310
$472$	−3.81051	−0.175393
$473$	15.2664	0.701949
$474$	−6.78390	−0.311595
$475$	0	0
$476$	7.22601	0.331204
$477$	−2.59274	−0.118714
$478$	−20.0875	−0.918779
$479$	−16.1458	−0.737719	−0.368859	−	0.929485i	$-0.620252\pi$
$479$	−16.1458	−0.737719	−0.368859	+	0.929485i	$0.620252\pi$
$480$	0	0
$481$	−0.433131	−0.0197491
$482$	−21.0468	−0.958654
$483$	−31.8251	−1.44809
$484$	2.39964	0.109074
$485$	0	0
$486$	5.27647	0.239345
$487$	8.40566	0.380897	0.190448	−	0.981697i	$-0.439006\pi$
$487$	8.40566	0.380897	0.190448	+	0.981697i	$0.439006\pi$
$488$	−15.5132	−0.702250
$489$	−15.9473	−0.721162
$490$	0	0
$491$	−36.0855	−1.62852	−0.814259	−	0.580502i	$-0.802856\pi$
$491$	−36.0855	−1.62852	−0.814259	+	0.580502i	$0.802856\pi$
$492$	21.8768	0.986284
$493$	−1.15969	−0.0522298
$494$	−3.73315	−0.167962
$495$	0	0
$496$	2.48005	0.111357
$497$	28.5728	1.28167
$498$	−2.45763	−0.110129
$499$	−3.30035	−0.147744	−0.0738720	−	0.997268i	$-0.523536\pi$
$499$	−3.30035	−0.147744	−0.0738720	+	0.997268i	$0.523536\pi$
$500$	0	0
$501$	−24.0071	−1.07256
$502$	−10.2883	−0.459191
$503$	−3.53530	−0.157631	−0.0788157	−	0.996889i	$-0.525114\pi$
$503$	−3.53530	−0.157631	−0.0788157	+	0.996889i	$0.525114\pi$
$504$	8.67437	0.386387
$505$	0	0
$506$	−10.1800	−0.452557
$507$	−12.1530	−0.539736
$508$	−11.4857	−0.509597
$509$	22.4096	0.993287	0.496644	−	0.867955i	$-0.334566\pi$
$509$	22.4096	0.993287	0.496644	+	0.867955i	$0.334566\pi$
$510$	0	0
$511$	45.6854	2.02100
$512$	−4.99151	−0.220596
$513$	5.58946	0.246781
$514$	0.148786	0.00656266
$515$	0	0
$516$	−10.3231	−0.454448
$517$	−37.3065	−1.64074
$518$	−0.389401	−0.0171093
$519$	0.879381	0.0386006
$520$	0	0
$521$	34.4402	1.50885	0.754426	−	0.656385i	$-0.227915\pi$
$521$	34.4402	1.50885	0.754426	+	0.656385i	$0.227915\pi$
$522$	−0.556814	−0.0243711
$523$	30.4451	1.33127	0.665635	−	0.746277i	$-0.268161\pi$
$523$	30.4451	1.33127	0.665635	+	0.746277i	$0.268161\pi$
$524$	2.87136	0.125436
$525$	0	0
$526$	6.02355	0.262639
$527$	6.01923	0.262202
$528$	2.07046	0.0901053
$529$	−6.10750	−0.265543
$530$	0	0
$531$	0.886445	0.0384685
$532$	6.71008	0.290919
$533$	48.7623	2.11213
$534$	−2.75062	−0.119031
$535$	0	0
$536$	−14.3759	−0.620946
$537$	−38.2864	−1.65218
$538$	−3.83967	−0.165540
$539$	−55.6060	−2.39512
$540$	0	0
$541$	−12.2794	−0.527931	−0.263965	−	0.964532i	$-0.585030\pi$
$541$	−12.2794	−0.527931	−0.263965	+	0.964532i	$0.585030\pi$
$542$	−8.10107	−0.347971
$543$	−10.6979	−0.459091
$544$	−6.25244	−0.268071
$545$	0	0
$546$	−28.9066	−1.23709
$547$	−0.250928	−0.0107289	−0.00536446	−	0.999986i	$-0.501708\pi$
$547$	−0.250928	−0.0107289	−0.00536446	+	0.999986i	$0.501708\pi$
$548$	2.91897	0.124692
$549$	3.60886	0.154022
$550$	0	0
$551$	−1.07689	−0.0458770
$552$	17.2105	0.732527
$553$	27.1789	1.15577
$554$	−18.4793	−0.785109
$555$	0	0
$556$	−30.0226	−1.27324
$557$	−1.67596	−0.0710128	−0.0355064	−	0.999369i	$-0.511304\pi$
$557$	−1.67596	−0.0710128	−0.0355064	+	0.999369i	$0.511304\pi$
$558$	2.89007	0.122347
$559$	−23.0096	−0.973203
$560$	0	0
$561$	5.02514	0.212162
$562$	3.22870	0.136195
$563$	−20.6605	−0.870737	−0.435368	−	0.900252i	$-0.643382\pi$
$563$	−20.6605	−0.870737	−0.435368	+	0.900252i	$0.643382\pi$
$564$	25.2265	1.06223
$565$	0	0
$566$	−10.6678	−0.448401
$567$	33.7197	1.41609
$568$	−15.4517	−0.648340
$569$	40.9673	1.71744	0.858720	−	0.512445i	$-0.171260\pi$
$569$	40.9673	1.71744	0.858720	+	0.512445i	$0.171260\pi$
$570$	0	0
$571$	24.2070	1.01303	0.506515	−	0.862231i	$-0.330933\pi$
$571$	24.2070	1.01303	0.506515	+	0.862231i	$0.330933\pi$
$572$	18.4863	0.772952
$573$	6.01923	0.251457
$574$	43.8392	1.82981
$575$	0	0
$576$	−2.44016	−0.101673
$577$	−40.2864	−1.67715	−0.838573	−	0.544790i	$-0.816609\pi$
$577$	−40.2864	−1.67715	−0.838573	+	0.544790i	$0.816609\pi$
$578$	12.9351	0.538029
$579$	−14.1650	−0.588677
$580$	0	0
$581$	9.84622	0.408490
$582$	2.71491	0.112537
$583$	−12.4200	−0.514384
$584$	−24.7059	−1.02234
$585$	0	0
$586$	−7.91658	−0.327031
$587$	34.7754	1.43534	0.717668	−	0.696385i	$-0.245210\pi$
$587$	34.7754	1.43534	0.717668	+	0.696385i	$0.245210\pi$
$588$	37.6006	1.55062
$589$	5.58946	0.230310
$590$	0	0
$591$	−5.91720	−0.243401
$592$	−0.0420379	−0.00172775
$593$	35.0864	1.44082	0.720412	−	0.693546i	$-0.243953\pi$
$593$	35.0864	1.44082	0.720412	+	0.693546i	$0.243953\pi$
$594$	13.8443	0.568039
$595$	0	0
$596$	−13.0477	−0.534456
$597$	28.1326	1.15139
$598$	15.3434	0.627439
$599$	30.8201	1.25928	0.629638	−	0.776889i	$-0.283203\pi$
$599$	30.8201	1.25928	0.629638	+	0.776889i	$0.283203\pi$
$600$	0	0
$601$	−7.10654	−0.289882	−0.144941	−	0.989440i	$-0.546299\pi$
$601$	−7.10654	−0.289882	−0.144941	+	0.989440i	$0.546299\pi$
$602$	−20.6865	−0.843120
$603$	3.34430	0.136190
$604$	−7.83484	−0.318795
$605$	0	0
$606$	15.8127	0.642349
$607$	−2.01531	−0.0817987	−0.0408994	−	0.999163i	$-0.513022\pi$
$607$	−2.01531	−0.0817987	−0.0408994	+	0.999163i	$0.513022\pi$
$608$	−5.80602	−0.235465
$609$	−8.33861	−0.337897
$610$	0	0
$611$	56.2286	2.27477
$612$	0.909056	0.0367464
$613$	11.6096	0.468909	0.234455	−	0.972127i	$-0.424670\pi$
$613$	11.6096	0.468909	0.234455	+	0.972127i	$0.424670\pi$
$614$	−23.3122	−0.940803
$615$	0	0
$616$	41.5528	1.67421
$617$	−12.4307	−0.500442	−0.250221	−	0.968189i	$-0.580503\pi$
$617$	−12.4307	−0.500442	−0.250221	+	0.968189i	$0.580503\pi$
$618$	7.79499	0.313560
$619$	3.85424	0.154915	0.0774575	−	0.996996i	$-0.475320\pi$
$619$	3.85424	0.154915	0.0774575	+	0.996996i	$0.475320\pi$
$620$	0	0
$621$	−22.9729	−0.921873
$622$	−20.7472	−0.831888
$623$	11.0200	0.441509
$624$	−3.12062	−0.124925
$625$	0	0
$626$	13.7187	0.548311
$627$	4.66635	0.186356
$628$	13.5844	0.542075
$629$	−0.102029	−0.00406814
$630$	0	0
$631$	−16.8794	−0.671958	−0.335979	−	0.941870i	$-0.609067\pi$
$631$	−16.8794	−0.671958	−0.335979	+	0.941870i	$0.609067\pi$
$632$	−14.6979	−0.584652
$633$	29.6873	1.17997
$634$	−25.9273	−1.02970
$635$	0	0
$636$	8.39838	0.333017
$637$	83.8098	3.32067
$638$	−2.66730	−0.105600
$639$	3.59456	0.142199
$640$	0	0
$641$	43.4855	1.71757	0.858787	−	0.512332i	$-0.171218\pi$
$641$	43.4855	1.71757	0.858787	+	0.512332i	$0.171218\pi$
$642$	15.7639	0.622153
$643$	−11.0689	−0.436514	−0.218257	−	0.975891i	$-0.570037\pi$
$643$	−11.0689	−0.436514	−0.218257	+	0.975891i	$0.570037\pi$
$644$	−27.5787	−1.08675
$645$	0	0
$646$	−0.879381	−0.0345988
$647$	−5.61766	−0.220853	−0.110427	−	0.993884i	$-0.535222\pi$
$647$	−5.61766	−0.220853	−0.110427	+	0.993884i	$0.535222\pi$
$648$	−18.2351	−0.716341
$649$	4.24634	0.166683
$650$	0	0
$651$	43.2805	1.69630
$652$	−13.8195	−0.541213
$653$	−44.5211	−1.74224	−0.871122	−	0.491066i	$-0.836607\pi$
$653$	−44.5211	−1.74224	−0.871122	+	0.491066i	$0.836607\pi$
$654$	−19.8613	−0.776639
$655$	0	0
$656$	4.73267	0.184780
$657$	5.74738	0.224227
$658$	50.5517	1.97071
$659$	−6.89154	−0.268456	−0.134228	−	0.990950i	$-0.542856\pi$
$659$	−6.89154	−0.268456	−0.134228	+	0.990950i	$0.542856\pi$
$660$	0	0
$661$	−44.3989	−1.72692	−0.863458	−	0.504421i	$-0.831706\pi$
$661$	−44.3989	−1.72692	−0.863458	+	0.504421i	$0.831706\pi$
$662$	8.13678	0.316245
$663$	−7.57393	−0.294147
$664$	−5.32468	−0.206637
$665$	0	0
$666$	−0.0489880	−0.00189825
$667$	4.42607	0.171378
$668$	−20.8039	−0.804926
$669$	0.946657	0.0365999
$670$	0	0
$671$	17.2875	0.667377
$672$	−44.9574	−1.73427
$673$	−38.6214	−1.48875	−0.744374	−	0.667763i	$-0.767252\pi$
$673$	−38.6214	−1.48875	−0.744374	+	0.667763i	$0.767252\pi$
$674$	18.9383	0.729476
$675$	0	0
$676$	−10.5315	−0.405057
$677$	−43.3917	−1.66768	−0.833840	−	0.552006i	$-0.813862\pi$
$677$	−43.3917	−1.66768	−0.833840	+	0.552006i	$0.813862\pi$
$678$	6.90293	0.265105
$679$	−10.8770	−0.417420
$680$	0	0
$681$	26.8784	1.02998
$682$	13.8443	0.530126
$683$	34.7123	1.32823	0.664114	−	0.747631i	$-0.268809\pi$
$683$	34.7123	1.32823	0.664114	+	0.747631i	$0.268809\pi$
$684$	0.844150	0.0322769
$685$	0	0
$686$	46.5779	1.77835
$687$	−14.9222	−0.569316
$688$	−2.23322	−0.0851406
$689$	18.7195	0.713158
$690$	0	0
$691$	2.94570	0.112060	0.0560299	−	0.998429i	$-0.482156\pi$
$691$	2.94570	0.112060	0.0560299	+	0.998429i	$0.482156\pi$
$692$	0.762048	0.0289687
$693$	−9.66649	−0.367200
$694$	17.2589	0.655138
$695$	0	0
$696$	4.50938	0.170928
$697$	11.4865	0.435081
$698$	4.12076	0.155973
$699$	−12.5441	−0.474463
$700$	0	0
$701$	18.5920	0.702210	0.351105	−	0.936336i	$-0.385806\pi$
$701$	18.5920	0.702210	0.351105	+	0.936336i	$0.385806\pi$
$702$	−20.8663	−0.787546
$703$	−0.0947438	−0.00357333
$704$	−11.6891	−0.440549
$705$	0	0
$706$	10.2592	0.386109
$707$	−63.3519	−2.38259
$708$	−2.87136	−0.107912
$709$	39.8443	1.49638	0.748192	−	0.663482i	$-0.230922\pi$
$709$	39.8443	1.49638	0.748192	+	0.663482i	$0.230922\pi$
$710$	0	0
$711$	3.41920	0.128230
$712$	−5.95946	−0.223340
$713$	−22.9729	−0.860344
$714$	−6.80926	−0.254830
$715$	0	0
$716$	−33.1780	−1.23992
$717$	−37.8443	−1.41332
$718$	14.4156	0.537987
$719$	21.2321	0.791824	0.395912	−	0.918288i	$-0.370428\pi$
$719$	21.2321	0.791824	0.395912	+	0.918288i	$0.370428\pi$
$720$	0	0
$721$	−31.2297	−1.16306
$722$	−0.816594	−0.0303905
$723$	−39.6516	−1.47466
$724$	−9.27052	−0.344536
$725$	0	0
$726$	−2.26124	−0.0839225
$727$	49.1658	1.82346	0.911729	−	0.410792i	$-0.134748\pi$
$727$	49.1658	1.82346	0.911729	+	0.410792i	$0.134748\pi$
$728$	−62.6287	−2.32118
$729$	30.0393	1.11257
$730$	0	0
$731$	−5.42015	−0.200472
$732$	−11.6898	−0.432066
$733$	−1.60498	−0.0592815	−0.0296407	−	0.999561i	$-0.509436\pi$
$733$	−1.60498	−0.0592815	−0.0296407	+	0.999561i	$0.509436\pi$
$734$	3.62085	0.133648
$735$	0	0
$736$	23.8630	0.879603
$737$	16.0202	0.590111
$738$	5.51512	0.203014
$739$	8.13264	0.299164	0.149582	−	0.988749i	$-0.452207\pi$
$739$	8.13264	0.299164	0.149582	+	0.988749i	$0.452207\pi$
$740$	0	0
$741$	−7.03316	−0.258370
$742$	16.8296	0.617834
$743$	42.9261	1.57481	0.787403	−	0.616439i	$-0.211425\pi$
$743$	42.9261	1.57481	0.787403	+	0.616439i	$0.211425\pi$
$744$	−23.4054	−0.858083
$745$	0	0
$746$	−17.0452	−0.624070
$747$	1.23869	0.0453212
$748$	4.35465	0.159222
$749$	−63.1564	−2.30768
$750$	0	0
$751$	4.05685	0.148037	0.0740183	−	0.997257i	$-0.476418\pi$
$751$	4.05685	0.148037	0.0740183	+	0.997257i	$0.476418\pi$
$752$	5.45731	0.199008
$753$	−19.3830	−0.706355
$754$	4.02018	0.146406
$755$	0	0
$756$	37.5057	1.36407
$757$	−22.6151	−0.821960	−0.410980	−	0.911644i	$-0.634813\pi$
$757$	−22.6151	−0.821960	−0.410980	+	0.911644i	$0.634813\pi$
$758$	5.55279	0.201687
$759$	−19.1789	−0.696151
$760$	0	0
$761$	−41.3609	−1.49933	−0.749666	−	0.661817i	$-0.769786\pi$
$761$	−41.3609	−1.49933	−0.749666	+	0.661817i	$0.769786\pi$
$762$	10.8233	0.392087
$763$	79.5720	2.88070
$764$	5.21610	0.188712
$765$	0	0
$766$	−8.90725	−0.321832
$767$	−6.40011	−0.231095
$768$	22.4922	0.811616
$769$	17.9196	0.646197	0.323099	−	0.946365i	$-0.395275\pi$
$769$	17.9196	0.646197	0.323099	+	0.946365i	$0.395275\pi$
$770$	0	0
$771$	0.280309	0.0100951
$772$	−12.2750	−0.441787
$773$	21.9043	0.787843	0.393921	−	0.919144i	$-0.371118\pi$
$773$	21.9043	0.787843	0.393921	+	0.919144i	$0.371118\pi$
$774$	−2.60243	−0.0935426
$775$	0	0
$776$	5.88209	0.211155
$777$	−0.733623	−0.0263186
$778$	−17.0934	−0.612829
$779$	10.6663	0.382162
$780$	0	0
$781$	17.2190	0.616144
$782$	3.61430	0.129247
$783$	−6.01923	−0.215110
$784$	8.13423	0.290508
$785$	0	0
$786$	−2.70576	−0.0965112
$787$	31.6354	1.12768	0.563840	−	0.825884i	$-0.309324\pi$
$787$	31.6354	1.12768	0.563840	+	0.825884i	$0.309324\pi$
$788$	−5.12768	−0.182666
$789$	11.3482	0.404007
$790$	0	0
$791$	−27.6558	−0.983326
$792$	5.22748	0.185750
$793$	−26.0559	−0.925272
$794$	10.7154	0.380275
$795$	0	0
$796$	24.3790	0.864090
$797$	15.4486	0.547217	0.273608	−	0.961841i	$-0.411783\pi$
$797$	15.4486	0.547217	0.273608	+	0.961841i	$0.411783\pi$
$798$	−6.32308	−0.223835
$799$	13.2452	0.468583
$800$	0	0
$801$	1.38636	0.0489845
$802$	9.43394	0.333124
$803$	27.5317	0.971571
$804$	−10.8328	−0.382044
$805$	0	0
$806$	−20.8663	−0.734983
$807$	−7.23385	−0.254644
$808$	34.2597	1.20525
$809$	−32.9326	−1.15785	−0.578924	−	0.815382i	$-0.696527\pi$
$809$	−32.9326	−1.15785	−0.578924	+	0.815382i	$0.696527\pi$
$810$	0	0
$811$	−25.5895	−0.898567	−0.449284	−	0.893389i	$-0.648321\pi$
$811$	−25.5895	−0.898567	−0.449284	+	0.893389i	$0.648321\pi$
$812$	−7.22601	−0.253583
$813$	−15.2622	−0.535270
$814$	−0.234667	−0.00822508
$815$	0	0
$816$	−0.735094	−0.0257334
$817$	−5.03316	−0.176088
$818$	15.4690	0.540860
$819$	14.5694	0.509097
$820$	0	0
$821$	17.8674	0.623575	0.311788	−	0.950152i	$-0.399072\pi$
$821$	17.8674	0.623575	0.311788	+	0.950152i	$0.399072\pi$
$822$	−2.75062	−0.0959389
$823$	18.4533	0.643242	0.321621	−	0.946868i	$-0.395772\pi$
$823$	18.4533	0.643242	0.321621	+	0.946868i	$0.395772\pi$
$824$	16.8885	0.588339
$825$	0	0
$826$	−5.75395	−0.200206
$827$	−47.5460	−1.65334	−0.826668	−	0.562690i	$-0.809767\pi$
$827$	−47.5460	−1.65334	−0.826668	+	0.562690i	$0.809767\pi$
$828$	−3.46950	−0.120573
$829$	19.0308	0.660965	0.330483	−	0.943812i	$-0.392788\pi$
$829$	19.0308	0.660965	0.330483	+	0.943812i	$0.392788\pi$
$830$	0	0
$831$	−34.8145	−1.20770
$832$	17.6179	0.610790
$833$	19.7423	0.684029
$834$	28.2911	0.979640
$835$	0	0
$836$	4.04373	0.139855
$837$	31.2420	1.07988
$838$	−22.2656	−0.769151
$839$	3.04022	0.104960	0.0524801	−	0.998622i	$-0.483287\pi$
$839$	3.04022	0.104960	0.0524801	+	0.998622i	$0.483287\pi$
$840$	0	0
$841$	−27.8403	−0.960011
$842$	−5.44370	−0.187602
$843$	6.08280	0.209503
$844$	25.7262	0.885534
$845$	0	0
$846$	6.35957	0.218647
$847$	9.05940	0.311285
$848$	1.81684	0.0623906
$849$	−20.0979	−0.689758
$850$	0	0
$851$	0.389401	0.0133485
$852$	−11.6434	−0.398898
$853$	18.2201	0.623844	0.311922	−	0.950108i	$-0.399027\pi$
$853$	18.2201	0.623844	0.311922	+	0.950108i	$0.399027\pi$
$854$	−23.4253	−0.801596
$855$	0	0
$856$	34.1539	1.16736
$857$	−19.3611	−0.661363	−0.330682	−	0.943742i	$-0.607279\pi$
$857$	−19.3611	−0.661363	−0.330682	+	0.943742i	$0.607279\pi$
$858$	−17.4202	−0.594714
$859$	3.44129	0.117415	0.0587077	−	0.998275i	$-0.481302\pi$
$859$	3.44129	0.117415	0.0587077	+	0.998275i	$0.481302\pi$
$860$	0	0
$861$	82.5921	2.81473
$862$	26.5024	0.902674
$863$	26.5471	0.903674	0.451837	−	0.892101i	$-0.350769\pi$
$863$	26.5471	0.903674	0.451837	+	0.892101i	$0.350769\pi$
$864$	−32.4525	−1.10406
$865$	0	0
$866$	27.6146	0.938383
$867$	24.3694	0.827630
$868$	37.5057	1.27303
$869$	16.3790	0.555619
$870$	0	0
$871$	−24.1458	−0.818148
$872$	−43.0312	−1.45722
$873$	−1.36836	−0.0463120
$874$	3.35624	0.113527
$875$	0	0
$876$	−18.6168	−0.629004
$877$	−20.5495	−0.693908	−0.346954	−	0.937882i	$-0.612784\pi$
$877$	−20.5495	−0.693908	−0.346954	+	0.937882i	$0.612784\pi$
$878$	22.7383	0.767380
$879$	−14.9146	−0.503059
$880$	0	0
$881$	−31.1911	−1.05085	−0.525427	−	0.850839i	$-0.676094\pi$
$881$	−31.1911	−1.05085	−0.525427	+	0.850839i	$0.676094\pi$
$882$	9.47906	0.319177
$883$	−14.1861	−0.477401	−0.238701	−	0.971093i	$-0.576721\pi$
$883$	−14.1861	−0.477401	−0.238701	+	0.971093i	$0.576721\pi$
$884$	−6.56336	−0.220750
$885$	0	0
$886$	18.5983	0.624822
$887$	−46.6046	−1.56483	−0.782415	−	0.622757i	$-0.786012\pi$
$887$	−46.6046	−1.56483	−0.782415	+	0.622757i	$0.786012\pi$
$888$	0.396732	0.0133134
$889$	−43.3623	−1.45433
$890$	0	0
$891$	20.3207	0.680768
$892$	0.820347	0.0274672
$893$	12.2995	0.411588
$894$	12.2952	0.411214
$895$	0	0
$896$	−42.6061	−1.42337
$897$	28.9066	0.965164
$898$	−20.2930	−0.677185
$899$	−6.01923	−0.200752
$900$	0	0
$901$	4.40959	0.146905
$902$	26.4191	0.879658
$903$	−38.9729	−1.29694
$904$	14.9558	0.497422
$905$	0	0
$906$	7.38297	0.245283
$907$	0.754028	0.0250371	0.0125185	−	0.999922i	$-0.496015\pi$
$907$	0.754028	0.0250371	0.0125185	+	0.999922i	$0.496015\pi$
$908$	23.2921	0.772976
$909$	−7.96988	−0.264344
$910$	0	0
$911$	−53.1413	−1.76065	−0.880325	−	0.474371i	$-0.842675\pi$
$911$	−53.1413	−1.76065	−0.880325	+	0.474371i	$0.842675\pi$
$912$	−0.682609	−0.0226034
$913$	5.93368	0.196376
$914$	−5.98784	−0.198060
$915$	0	0
$916$	−12.9311	−0.427257
$917$	10.8403	0.357979
$918$	−4.91527	−0.162228
$919$	37.4202	1.23438	0.617189	−	0.786815i	$-0.288272\pi$
$919$	37.4202	1.23438	0.617189	+	0.786815i	$0.288272\pi$
$920$	0	0
$921$	−43.9196	−1.44720
$922$	−8.41709	−0.277202
$923$	−25.9526	−0.854241
$924$	31.3116	1.03007
$925$	0	0
$926$	6.37147	0.209379
$927$	−3.92880	−0.129039
$928$	6.25244	0.205247
$929$	−19.1981	−0.629871	−0.314935	−	0.949113i	$-0.601983\pi$
$929$	−19.1981	−0.629871	−0.314935	+	0.949113i	$0.601983\pi$
$930$	0	0
$931$	18.3327	0.600830
$932$	−10.8704	−0.356072
$933$	−39.0873	−1.27966
$934$	−6.02355	−0.197096
$935$	0	0
$936$	−7.87890	−0.257530
$937$	20.0095	0.653681	0.326840	−	0.945080i	$-0.394016\pi$
$937$	20.0095	0.653681	0.326840	+	0.945080i	$0.394016\pi$
$938$	−21.7080	−0.708790
$939$	25.8458	0.843445
$940$	0	0
$941$	15.3327	0.499832	0.249916	−	0.968268i	$-0.419597\pi$
$941$	15.3327	0.499832	0.249916	+	0.968268i	$0.419597\pi$
$942$	−12.8009	−0.417076
$943$	−43.8392	−1.42760
$944$	−0.621168	−0.0202173
$945$	0	0
$946$	−12.4664	−0.405319
$947$	29.8217	0.969076	0.484538	−	0.874770i	$-0.338988\pi$
$947$	29.8217	0.969076	0.484538	+	0.874770i	$0.338988\pi$
$948$	−11.0754	−0.359713
$949$	−41.4959	−1.34702
$950$	0	0
$951$	−48.8464	−1.58395
$952$	−14.7529	−0.478143
$953$	−31.4938	−1.02018	−0.510091	−	0.860120i	$-0.670388\pi$
$953$	−31.4938	−1.02018	−0.510091	+	0.860120i	$0.670388\pi$
$954$	2.11722	0.0685475
$955$	0	0
$956$	−32.7948	−1.06066
$957$	−5.02514	−0.162440
$958$	13.1845	0.425973
$959$	11.0200	0.355856
$960$	0	0
$961$	0.242050	0.00780806
$962$	0.353692	0.0114035
$963$	−7.94528	−0.256033
$964$	−34.3610	−1.10669
$965$	0	0
$966$	25.9882	0.836156
$967$	−1.16143	−0.0373490	−0.0186745	−	0.999826i	$-0.505945\pi$
$967$	−1.16143	−0.0373490	−0.0186745	+	0.999826i	$0.505945\pi$
$968$	−4.89917	−0.157465
$969$	−1.65673	−0.0532220
$970$	0	0
$971$	18.4557	0.592272	0.296136	−	0.955146i	$-0.404302\pi$
$971$	18.4557	0.592272	0.296136	+	0.955146i	$0.404302\pi$
$972$	8.61438	0.276306
$973$	−113.345	−3.63367
$974$	−6.86401	−0.219937
$975$	0	0
$976$	−2.52888	−0.0809474
$977$	−5.62735	−0.180035	−0.0900175	−	0.995940i	$-0.528692\pi$
$977$	−5.62735	−0.180035	−0.0900175	+	0.995940i	$0.528692\pi$
$978$	13.0225	0.416413
$979$	6.64107	0.212249
$980$	0	0
$981$	10.0104	0.319608
$982$	29.4672	0.940338
$983$	25.1228	0.801293	0.400647	−	0.916233i	$-0.368786\pi$
$983$	25.1228	0.801293	0.400647	+	0.916233i	$0.368786\pi$
$984$	−44.6644	−1.42385
$985$	0	0
$986$	0.946996	0.0301585
$987$	95.2382	3.03147
$988$	−6.09474	−0.193900
$989$	20.6865	0.657793
$990$	0	0
$991$	−41.8749	−1.33020	−0.665100	−	0.746754i	$-0.731611\pi$
$991$	−41.8749	−1.33020	−0.665100	+	0.746754i	$0.731611\pi$
$992$	−32.4525	−1.03037
$993$	15.3295	0.486467
$994$	−23.3324	−0.740059
$995$	0	0
$996$	−4.01234	−0.127136
$997$	37.0346	1.17290	0.586449	−	0.809986i	$-0.300525\pi$
$997$	37.0346	1.17290	0.586449	+	0.809986i	$0.300525\pi$
$998$	2.69505	0.0853102
$999$	−0.529566	−0.0167547

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.a.i.1.2		4
3.2	odd	2		4275.2.a.bo.1.3		4
4.3	odd	2		7600.2.a.cf.1.3		4
5.2	odd	4		475.2.b.e.324.4		8
5.3	odd	4		475.2.b.e.324.5		8
5.4	even	2		95.2.a.b.1.3	✓	4
15.14	odd	2		855.2.a.m.1.2		4
19.18	odd	2		9025.2.a.bf.1.3		4
20.19	odd	2		1520.2.a.t.1.2		4
35.34	odd	2		4655.2.a.y.1.3		4
40.19	odd	2		6080.2.a.ch.1.3		4
40.29	even	2		6080.2.a.cc.1.2		4
95.94	odd	2		1805.2.a.p.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.a.b.1.3	✓	4	5.4	even	2
475.2.a.i.1.2		4	1.1	even	1	trivial
475.2.b.e.324.4		8	5.2	odd	4
475.2.b.e.324.5		8	5.3	odd	4
855.2.a.m.1.2		4	15.14	odd	2
1520.2.a.t.1.2		4	20.19	odd	2
1805.2.a.p.1.2		4	95.94	odd	2
4275.2.a.bo.1.3		4	3.2	odd	2
4655.2.a.y.1.3		4	35.34	odd	2
6080.2.a.cc.1.2		4	40.29	even	2
6080.2.a.ch.1.3		4	40.19	odd	2
7600.2.a.cf.1.3		4	4.3	odd	2
9025.2.a.bf.1.3		4	19.18	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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.a (trivial)

\(f(q)\)	\(=\)	\(q-0.816594 q^{2} -1.53844 q^{3} -1.33317 q^{4} +1.25628 q^{6} -5.03316 q^{7} +2.72185 q^{8} -0.633188 q^{9} +O(q^{10})\)	\(q-0.816594 q^{2} -1.53844 q^{3} -1.33317 q^{4} +1.25628 q^{6} -5.03316 q^{7} +2.72185 q^{8} -0.633188 q^{9} -3.03316 q^{11} +2.05101 q^{12} +4.57160 q^{13} +4.11005 q^{14} +0.443701 q^{16} +1.07689 q^{17} +0.517058 q^{18} +1.00000 q^{19} +7.74324 q^{21} +2.47686 q^{22} -4.11005 q^{23} -4.18742 q^{24} -3.73315 q^{26} +5.58946 q^{27} +6.71008 q^{28} -1.07689 q^{29} +5.58946 q^{31} -5.80602 q^{32} +4.66635 q^{33} -0.879381 q^{34} +0.844150 q^{36} -0.0947438 q^{37} -0.816594 q^{38} -7.03316 q^{39} +10.6663 q^{41} -6.32308 q^{42} -5.03316 q^{43} +4.04373 q^{44} +3.35624 q^{46} +12.2995 q^{47} -0.682609 q^{48} +18.3327 q^{49} -1.65673 q^{51} -6.09474 q^{52} +4.09474 q^{53} -4.56432 q^{54} -13.6995 q^{56} -1.53844 q^{57} +0.879381 q^{58} -1.39997 q^{59} -5.69951 q^{61} -4.56432 q^{62} +3.18694 q^{63} +3.85376 q^{64} -3.81051 q^{66} -5.28168 q^{67} -1.43568 q^{68} +6.32308 q^{69} -5.67692 q^{71} -1.72344 q^{72} -9.07689 q^{73} +0.0773672 q^{74} -1.33317 q^{76} +15.2664 q^{77} +5.74324 q^{78} -5.39997 q^{79} -6.69951 q^{81} -8.71008 q^{82} -1.95627 q^{83} -10.3231 q^{84} +4.11005 q^{86} +1.65673 q^{87} -8.25581 q^{88} -2.18949 q^{89} -23.0096 q^{91} +5.47941 q^{92} -8.59907 q^{93} -10.0437 q^{94} +8.93225 q^{96} +2.16106 q^{97} -14.9704 q^{98} +1.92056 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} + 8 q^{4} - 4 q^{7} + 12 q^{8} + 8 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^3 + 8 * q^4 - 4 * q^7 + 12 * q^8 + 8 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} + 8 q^{4} - 4 q^{7} + 12 q^{8} + 8 q^{9} + 4 q^{11} - 6 q^{12} - 2 q^{13} - 8 q^{14} + 4 q^{16} - 4 q^{17} + 34 q^{18} + 4 q^{19} - 4 q^{21} - 4 q^{22} + 8 q^{23} - 24 q^{24} + 4 q^{26} + 4 q^{27} + 8 q^{28} + 4 q^{29} + 4 q^{31} + 6 q^{32} - 8 q^{33} - 4 q^{34} + 40 q^{36} + 6 q^{37} + 2 q^{38} - 12 q^{39} + 16 q^{41} - 28 q^{42} - 4 q^{43} + 24 q^{44} + 12 q^{47} - 38 q^{48} + 20 q^{49} - 36 q^{51} - 18 q^{52} + 10 q^{53} - 20 q^{54} - 12 q^{56} - 2 q^{57} + 4 q^{58} + 20 q^{61} - 20 q^{62} - 20 q^{63} - 4 q^{64} - 28 q^{66} + 18 q^{67} - 4 q^{68} + 28 q^{69} - 20 q^{71} + 52 q^{72} - 28 q^{73} + 32 q^{74} + 8 q^{76} + 40 q^{77} - 12 q^{78} - 16 q^{79} + 16 q^{81} - 16 q^{82} - 44 q^{84} - 8 q^{86} + 36 q^{87} + 12 q^{88} + 4 q^{89} - 36 q^{91} + 28 q^{92} + 40 q^{93} - 48 q^{94} - 52 q^{96} - 30 q^{97} - 38 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 + 8 * q^4 - 4 * q^7 + 12 * q^8 + 8 * q^9 + 4 * q^11 - 6 * q^12 - 2 * q^13 - 8 * q^14 + 4 * q^16 - 4 * q^17 + 34 * q^18 + 4 * q^19 - 4 * q^21 - 4 * q^22 + 8 * q^23 - 24 * q^24 + 4 * q^26 + 4 * q^27 + 8 * q^28 + 4 * q^29 + 4 * q^31 + 6 * q^32 - 8 * q^33 - 4 * q^34 + 40 * q^36 + 6 * q^37 + 2 * q^38 - 12 * q^39 + 16 * q^41 - 28 * q^42 - 4 * q^43 + 24 * q^44 + 12 * q^47 - 38 * q^48 + 20 * q^49 - 36 * q^51 - 18 * q^52 + 10 * q^53 - 20 * q^54 - 12 * q^56 - 2 * q^57 + 4 * q^58 + 20 * q^61 - 20 * q^62 - 20 * q^63 - 4 * q^64 - 28 * q^66 + 18 * q^67 - 4 * q^68 + 28 * q^69 - 20 * q^71 + 52 * q^72 - 28 * q^73 + 32 * q^74 + 8 * q^76 + 40 * q^77 - 12 * q^78 - 16 * q^79 + 16 * q^81 - 16 * q^82 - 44 * q^84 - 8 * q^86 + 36 * q^87 + 12 * q^88 + 4 * q^89 - 36 * q^91 + 28 * q^92 + 40 * q^93 - 48 * q^94 - 52 * q^96 - 30 * q^97 - 38 * q^98 - 4 * q^99

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