LMFDB - Embedded newform 1850.2.a.ba.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1850,2,Mod(1,1850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1850, 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("1850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1850 = 2 \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1850.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:	$14.7723243739$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
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			$0.311108$ of defining polynomial
Character	$\chi$	$=$	1850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.21432 q^{3} +1.00000 q^{4} +1.21432 q^{6} +3.59210 q^{7} -1.00000 q^{8} -1.52543 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.21432 q^{3} +1.00000 q^{4} +1.21432 q^{6} +3.59210 q^{7} -1.00000 q^{8} -1.52543 q^{9} -4.73975 q^{11} -1.21432 q^{12} +1.78568 q^{13} -3.59210 q^{14} +1.00000 q^{16} +1.83654 q^{17} +1.52543 q^{18} +3.28100 q^{19} -4.36196 q^{21} +4.73975 q^{22} -1.80642 q^{23} +1.21432 q^{24} -1.78568 q^{26} +5.49532 q^{27} +3.59210 q^{28} -0.755569 q^{29} -2.06668 q^{31} -1.00000 q^{32} +5.75557 q^{33} -1.83654 q^{34} -1.52543 q^{36} +1.00000 q^{37} -3.28100 q^{38} -2.16839 q^{39} -2.57136 q^{41} +4.36196 q^{42} +9.19850 q^{43} -4.73975 q^{44} +1.80642 q^{46} +1.24443 q^{47} -1.21432 q^{48} +5.90321 q^{49} -2.23014 q^{51} +1.78568 q^{52} +6.56199 q^{53} -5.49532 q^{54} -3.59210 q^{56} -3.98418 q^{57} +0.755569 q^{58} +9.19850 q^{59} -9.39853 q^{61} +2.06668 q^{62} -5.47949 q^{63} +1.00000 q^{64} -5.75557 q^{66} -2.39853 q^{67} +1.83654 q^{68} +2.19358 q^{69} -9.39853 q^{71} +1.52543 q^{72} +8.09679 q^{73} -1.00000 q^{74} +3.28100 q^{76} -17.0257 q^{77} +2.16839 q^{78} +11.8064 q^{79} -2.09679 q^{81} +2.57136 q^{82} -15.4035 q^{83} -4.36196 q^{84} -9.19850 q^{86} +0.917502 q^{87} +4.73975 q^{88} -0.933323 q^{89} +6.41435 q^{91} -1.80642 q^{92} +2.50961 q^{93} -1.24443 q^{94} +1.21432 q^{96} -2.42864 q^{97} -5.90321 q^{98} +7.23014 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{6} + 4 q^{7} - 3 q^{8} + 2 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^6 + 4 * q^7 - 3 * q^8 + 2 * q^9	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{6} + 4 q^{7} - 3 q^{8} + 2 q^{9} - q^{11} + 3 q^{12} + 12 q^{13} - 4 q^{14} + 3 q^{16} - q^{17} - 2 q^{18} + 3 q^{19} + q^{22} + 8 q^{23} - 3 q^{24} - 12 q^{26} + 3 q^{27} + 4 q^{28} - 2 q^{29} - 6 q^{31} - 3 q^{32} + 17 q^{33} + q^{34} + 2 q^{36} + 3 q^{37} - 3 q^{38} + 20 q^{39} - 21 q^{41} + 8 q^{43} - q^{44} - 8 q^{46} + 4 q^{47} + 3 q^{48} + 11 q^{49} - 13 q^{51} + 12 q^{52} + 6 q^{53} - 3 q^{54} - 4 q^{56} + q^{57} + 2 q^{58} + 8 q^{59} - 8 q^{61} + 6 q^{62} + 10 q^{63} + 3 q^{64} - 17 q^{66} + 13 q^{67} - q^{68} + 20 q^{69} - 8 q^{71} - 2 q^{72} + 31 q^{73} - 3 q^{74} + 3 q^{76} + 2 q^{77} - 20 q^{78} + 22 q^{79} - 13 q^{81} + 21 q^{82} + 7 q^{83} - 8 q^{86} - 10 q^{87} + q^{88} - 3 q^{89} + 12 q^{91} + 8 q^{92} - 12 q^{93} - 4 q^{94} - 3 q^{96} + 6 q^{97} - 11 q^{98} + 28 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^6 + 4 * q^7 - 3 * q^8 + 2 * q^9 - q^11 + 3 * q^12 + 12 * q^13 - 4 * q^14 + 3 * q^16 - q^17 - 2 * q^18 + 3 * q^19 + q^22 + 8 * q^23 - 3 * q^24 - 12 * q^26 + 3 * q^27 + 4 * q^28 - 2 * q^29 - 6 * q^31 - 3 * q^32 + 17 * q^33 + q^34 + 2 * q^36 + 3 * q^37 - 3 * q^38 + 20 * q^39 - 21 * q^41 + 8 * q^43 - q^44 - 8 * q^46 + 4 * q^47 + 3 * q^48 + 11 * q^49 - 13 * q^51 + 12 * q^52 + 6 * q^53 - 3 * q^54 - 4 * q^56 + q^57 + 2 * q^58 + 8 * q^59 - 8 * q^61 + 6 * q^62 + 10 * q^63 + 3 * q^64 - 17 * q^66 + 13 * q^67 - q^68 + 20 * q^69 - 8 * q^71 - 2 * q^72 + 31 * q^73 - 3 * q^74 + 3 * q^76 + 2 * q^77 - 20 * q^78 + 22 * q^79 - 13 * q^81 + 21 * q^82 + 7 * q^83 - 8 * q^86 - 10 * q^87 + q^88 - 3 * q^89 + 12 * q^91 + 8 * q^92 - 12 * q^93 - 4 * q^94 - 3 * q^96 + 6 * q^97 - 11 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.21432	−0.701088	−0.350544	−	0.936546i	$-0.614003\pi$
$3$	−1.21432	−0.701088	−0.350544	+	0.936546i	$0.614003\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.21432	0.495744
$7$	3.59210	1.35769	0.678844	−	0.734283i	$-0.262481\pi$
$7$	3.59210	1.35769	0.678844	+	0.734283i	$0.262481\pi$
$8$	−1.00000	−0.353553
$9$	−1.52543	−0.508476
$10$	0	0
$11$	−4.73975	−1.42909	−0.714544	−	0.699591i	$-0.753366\pi$
$11$	−4.73975	−1.42909	−0.714544	+	0.699591i	$0.753366\pi$
$12$	−1.21432	−0.350544
$13$	1.78568	0.495259	0.247629	−	0.968855i	$-0.420348\pi$
$13$	1.78568	0.495259	0.247629	+	0.968855i	$0.420348\pi$
$14$	−3.59210	−0.960030
$15$	0	0
$16$	1.00000	0.250000
$17$	1.83654	0.445425	0.222713	−	0.974884i	$-0.428509\pi$
$17$	1.83654	0.445425	0.222713	+	0.974884i	$0.428509\pi$
$18$	1.52543	0.359547
$19$	3.28100	0.752712	0.376356	−	0.926475i	$-0.377177\pi$
$19$	3.28100	0.752712	0.376356	+	0.926475i	$0.377177\pi$
$20$	0	0
$21$	−4.36196	−0.951858
$22$	4.73975	1.01052
$23$	−1.80642	−0.376665	−0.188333	−	0.982105i	$-0.560308\pi$
$23$	−1.80642	−0.376665	−0.188333	+	0.982105i	$0.560308\pi$
$24$	1.21432	0.247872
$25$	0	0
$26$	−1.78568	−0.350201
$27$	5.49532	1.05757
$28$	3.59210	0.678844
$29$	−0.755569	−0.140306	−0.0701528	−	0.997536i	$-0.522349\pi$
$29$	−0.755569	−0.140306	−0.0701528	+	0.997536i	$0.522349\pi$
$30$	0	0
$31$	−2.06668	−0.371186	−0.185593	−	0.982627i	$-0.559421\pi$
$31$	−2.06668	−0.371186	−0.185593	+	0.982627i	$0.559421\pi$
$32$	−1.00000	−0.176777
$33$	5.75557	1.00192
$34$	−1.83654	−0.314963
$35$	0	0
$36$	−1.52543	−0.254238
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−3.28100	−0.532248
$39$	−2.16839	−0.347220
$40$	0	0
$41$	−2.57136	−0.401579	−0.200790	−	0.979634i	$-0.564351\pi$
$41$	−2.57136	−0.401579	−0.200790	+	0.979634i	$0.564351\pi$
$42$	4.36196	0.673065
$43$	9.19850	1.40276	0.701379	−	0.712789i	$-0.252568\pi$
$43$	9.19850	1.40276	0.701379	+	0.712789i	$0.252568\pi$
$44$	−4.73975	−0.714544
$45$	0	0
$46$	1.80642	0.266343
$47$	1.24443	0.181519	0.0907595	−	0.995873i	$-0.471071\pi$
$47$	1.24443	0.181519	0.0907595	+	0.995873i	$0.471071\pi$
$48$	−1.21432	−0.175272
$49$	5.90321	0.843316
$50$	0	0
$51$	−2.23014	−0.312282
$52$	1.78568	0.247629
$53$	6.56199	0.901359	0.450680	−	0.892686i	$-0.351182\pi$
$53$	6.56199	0.901359	0.450680	+	0.892686i	$0.351182\pi$
$54$	−5.49532	−0.747818
$55$	0	0
$56$	−3.59210	−0.480015
$57$	−3.98418	−0.527717
$58$	0.755569	0.0992110
$59$	9.19850	1.19754	0.598771	−	0.800920i	$-0.295656\pi$
$59$	9.19850	1.19754	0.598771	+	0.800920i	$0.295656\pi$
$60$	0	0
$61$	−9.39853	−1.20336	−0.601679	−	0.798738i	$-0.705501\pi$
$61$	−9.39853	−1.20336	−0.601679	+	0.798738i	$0.705501\pi$
$62$	2.06668	0.262468
$63$	−5.47949	−0.690351
$64$	1.00000	0.125000
$65$	0	0
$66$	−5.75557	−0.708462
$67$	−2.39853	−0.293027	−0.146513	−	0.989209i	$-0.546805\pi$
$67$	−2.39853	−0.293027	−0.146513	+	0.989209i	$0.546805\pi$
$68$	1.83654	0.222713
$69$	2.19358	0.264076
$70$	0	0
$71$	−9.39853	−1.11540	−0.557700	−	0.830043i	$-0.688316\pi$
$71$	−9.39853	−1.11540	−0.557700	+	0.830043i	$0.688316\pi$
$72$	1.52543	0.179773
$73$	8.09679	0.947657	0.473829	−	0.880617i	$-0.342872\pi$
$73$	8.09679	0.947657	0.473829	+	0.880617i	$0.342872\pi$
$74$	−1.00000	−0.116248
$75$	0	0
$76$	3.28100	0.376356
$77$	−17.0257	−1.94025
$78$	2.16839	0.245521
$79$	11.8064	1.32833	0.664163	−	0.747588i	$-0.268788\pi$
$79$	11.8064	1.32833	0.664163	+	0.747588i	$0.268788\pi$
$80$	0	0
$81$	−2.09679	−0.232976
$82$	2.57136	0.283959
$83$	−15.4035	−1.69075	−0.845374	−	0.534175i	$-0.820622\pi$
$83$	−15.4035	−1.69075	−0.845374	+	0.534175i	$0.820622\pi$
$84$	−4.36196	−0.475929
$85$	0	0
$86$	−9.19850	−0.991900
$87$	0.917502	0.0983665
$88$	4.73975	0.505259
$89$	−0.933323	−0.0989321	−0.0494660	−	0.998776i	$-0.515752\pi$
$89$	−0.933323	−0.0989321	−0.0494660	+	0.998776i	$0.515752\pi$
$90$	0	0
$91$	6.41435	0.672407
$92$	−1.80642	−0.188333
$93$	2.50961	0.260234
$94$	−1.24443	−0.128353
$95$	0	0
$96$	1.21432	0.123936
$97$	−2.42864	−0.246591	−0.123295	−	0.992370i	$-0.539346\pi$
$97$	−2.42864	−0.246591	−0.123295	+	0.992370i	$0.539346\pi$
$98$	−5.90321	−0.596314
$99$	7.23014	0.726657
$100$	0	0
$101$	8.04149	0.800158	0.400079	−	0.916481i	$-0.368983\pi$
$101$	8.04149	0.800158	0.400079	+	0.916481i	$0.368983\pi$
$102$	2.23014	0.220817
$103$	0.495316	0.0488049	0.0244025	−	0.999702i	$-0.492232\pi$
$103$	0.495316	0.0488049	0.0244025	+	0.999702i	$0.492232\pi$
$104$	−1.78568	−0.175100
$105$	0	0
$106$	−6.56199	−0.637357
$107$	13.4494	1.30020	0.650100	−	0.759848i	$-0.274727\pi$
$107$	13.4494	1.30020	0.650100	+	0.759848i	$0.274727\pi$
$108$	5.49532	0.528787
$109$	10.2351	0.980341	0.490171	−	0.871626i	$-0.336934\pi$
$109$	10.2351	0.980341	0.490171	+	0.871626i	$0.336934\pi$
$110$	0	0
$111$	−1.21432	−0.115258
$112$	3.59210	0.339422
$113$	−7.49532	−0.705100	−0.352550	−	0.935793i	$-0.614685\pi$
$113$	−7.49532	−0.705100	−0.352550	+	0.935793i	$0.614685\pi$
$114$	3.98418	0.373153
$115$	0	0
$116$	−0.755569	−0.0701528
$117$	−2.72393	−0.251827
$118$	−9.19850	−0.846790
$119$	6.59703	0.604748
$120$	0	0
$121$	11.4652	1.04229
$122$	9.39853	0.850903
$123$	3.12245	0.281542
$124$	−2.06668	−0.185593
$125$	0	0
$126$	5.47949	0.488152
$127$	3.45875	0.306915	0.153457	−	0.988155i	$-0.450959\pi$
$127$	3.45875	0.306915	0.153457	+	0.988155i	$0.450959\pi$
$128$	−1.00000	−0.0883883
$129$	−11.1699	−0.983456
$130$	0	0
$131$	16.0874	1.40556	0.702782	−	0.711405i	$-0.251941\pi$
$131$	16.0874	1.40556	0.702782	+	0.711405i	$0.251941\pi$
$132$	5.75557	0.500958
$133$	11.7857	1.02195
$134$	2.39853	0.207201
$135$	0	0
$136$	−1.83654	−0.157482
$137$	15.9906	1.36617	0.683086	−	0.730338i	$-0.260637\pi$
$137$	15.9906	1.36617	0.683086	+	0.730338i	$0.260637\pi$
$138$	−2.19358	−0.186730
$139$	11.0350	0.935979	0.467990	−	0.883734i	$-0.344978\pi$
$139$	11.0350	0.935979	0.467990	+	0.883734i	$0.344978\pi$
$140$	0	0
$141$	−1.51114	−0.127261
$142$	9.39853	0.788707
$143$	−8.46367	−0.707768
$144$	−1.52543	−0.127119
$145$	0	0
$146$	−8.09679	−0.670095
$147$	−7.16839	−0.591239
$148$	1.00000	0.0821995
$149$	13.9748	1.14486	0.572431	−	0.819953i	$-0.306001\pi$
$149$	13.9748	1.14486	0.572431	+	0.819953i	$0.306001\pi$
$150$	0	0
$151$	8.42864	0.685913	0.342956	−	0.939351i	$-0.388572\pi$
$151$	8.42864	0.685913	0.342956	+	0.939351i	$0.388572\pi$
$152$	−3.28100	−0.266124
$153$	−2.80150	−0.226488
$154$	17.0257	1.37197
$155$	0	0
$156$	−2.16839	−0.173610
$157$	9.17775	0.732465	0.366232	−	0.930523i	$-0.380648\pi$
$157$	9.17775	0.732465	0.366232	+	0.930523i	$0.380648\pi$
$158$	−11.8064	−0.939269
$159$	−7.96836	−0.631932
$160$	0	0
$161$	−6.48886	−0.511394
$162$	2.09679	0.164739
$163$	13.9447	1.09223	0.546117	−	0.837709i	$-0.316106\pi$
$163$	13.9447	1.09223	0.546117	+	0.837709i	$0.316106\pi$
$164$	−2.57136	−0.200790
$165$	0	0
$166$	15.4035	1.19554
$167$	17.6795	1.36808	0.684041	−	0.729443i	$-0.260221\pi$
$167$	17.6795	1.36808	0.684041	+	0.729443i	$0.260221\pi$
$168$	4.36196	0.336533
$169$	−9.81135	−0.754719
$170$	0	0
$171$	−5.00492	−0.382736
$172$	9.19850	0.701379
$173$	15.2859	1.16217	0.581083	−	0.813844i	$-0.302629\pi$
$173$	15.2859	1.16217	0.581083	+	0.813844i	$0.302629\pi$
$174$	−0.917502	−0.0695556
$175$	0	0
$176$	−4.73975	−0.357272
$177$	−11.1699	−0.839582
$178$	0.933323	0.0699556
$179$	18.2859	1.36675	0.683377	−	0.730066i	$-0.260511\pi$
$179$	18.2859	1.36675	0.683377	+	0.730066i	$0.260511\pi$
$180$	0	0
$181$	−8.23506	−0.612107	−0.306054	−	0.952014i	$-0.599009\pi$
$181$	−8.23506	−0.612107	−0.306054	+	0.952014i	$0.599009\pi$
$182$	−6.41435	−0.475463
$183$	11.4128	0.843660
$184$	1.80642	0.133171
$185$	0	0
$186$	−2.50961	−0.184013
$187$	−8.70471	−0.636552
$188$	1.24443	0.0907595
$189$	19.7397	1.43586
$190$	0	0
$191$	17.3461	1.25512	0.627561	−	0.778567i	$-0.284053\pi$
$191$	17.3461	1.25512	0.627561	+	0.778567i	$0.284053\pi$
$192$	−1.21432	−0.0876360
$193$	−12.0257	−0.865626	−0.432813	−	0.901484i	$-0.642479\pi$
$193$	−12.0257	−0.865626	−0.432813	+	0.901484i	$0.642479\pi$
$194$	2.42864	0.174366
$195$	0	0
$196$	5.90321	0.421658
$197$	13.9146	0.991373	0.495687	−	0.868501i	$-0.334916\pi$
$197$	13.9146	0.991373	0.495687	+	0.868501i	$0.334916\pi$
$198$	−7.23014	−0.513824
$199$	24.5718	1.74185	0.870926	−	0.491415i	$-0.163520\pi$
$199$	24.5718	1.74185	0.870926	+	0.491415i	$0.163520\pi$
$200$	0	0
$201$	2.91258	0.205438
$202$	−8.04149	−0.565797
$203$	−2.71408	−0.190491
$204$	−2.23014	−0.156141
$205$	0	0
$206$	−0.495316	−0.0345103
$207$	2.75557	0.191525
$208$	1.78568	0.123815
$209$	−15.5511	−1.07569
$210$	0	0
$211$	−14.3383	−0.987090	−0.493545	−	0.869720i	$-0.664299\pi$
$211$	−14.3383	−0.987090	−0.493545	+	0.869720i	$0.664299\pi$
$212$	6.56199	0.450680
$213$	11.4128	0.781993
$214$	−13.4494	−0.919381
$215$	0	0
$216$	−5.49532	−0.373909
$217$	−7.42372	−0.503955
$218$	−10.2351	−0.693206
$219$	−9.83209	−0.664391
$220$	0	0
$221$	3.27946	0.220601
$222$	1.21432	0.0814998
$223$	−9.09234	−0.608868	−0.304434	−	0.952533i	$-0.598467\pi$
$223$	−9.09234	−0.608868	−0.304434	+	0.952533i	$0.598467\pi$
$224$	−3.59210	−0.240008
$225$	0	0
$226$	7.49532	0.498581
$227$	−21.3319	−1.41584	−0.707922	−	0.706290i	$-0.750367\pi$
$227$	−21.3319	−1.41584	−0.707922	+	0.706290i	$0.750367\pi$
$228$	−3.98418	−0.263859
$229$	−24.0098	−1.58662	−0.793308	−	0.608821i	$-0.791643\pi$
$229$	−24.0098	−1.58662	−0.793308	+	0.608821i	$0.791643\pi$
$230$	0	0
$231$	20.6746	1.36029
$232$	0.755569	0.0496055
$233$	8.28100	0.542506	0.271253	−	0.962508i	$-0.412562\pi$
$233$	8.28100	0.542506	0.271253	+	0.962508i	$0.412562\pi$
$234$	2.72393	0.178069
$235$	0	0
$236$	9.19850	0.598771
$237$	−14.3368	−0.931274
$238$	−6.59703	−0.427622
$239$	−25.5812	−1.65471	−0.827355	−	0.561679i	$-0.810156\pi$
$239$	−25.5812	−1.65471	−0.827355	+	0.561679i	$0.810156\pi$
$240$	0	0
$241$	2.72546	0.175562	0.0877811	−	0.996140i	$-0.472022\pi$
$241$	2.72546	0.175562	0.0877811	+	0.996140i	$0.472022\pi$
$242$	−11.4652	−0.737011
$243$	−13.9398	−0.894237
$244$	−9.39853	−0.601679
$245$	0	0
$246$	−3.12245	−0.199080
$247$	5.85881	0.372787
$248$	2.06668	0.131234
$249$	18.7047	1.18536
$250$	0	0
$251$	−10.2859	−0.649241	−0.324621	−	0.945844i	$-0.605237\pi$
$251$	−10.2859	−0.649241	−0.324621	+	0.945844i	$0.605237\pi$
$252$	−5.47949	−0.345176
$253$	8.56199	0.538288
$254$	−3.45875	−0.217021
$255$	0	0
$256$	1.00000	0.0625000
$257$	5.14272	0.320794	0.160397	−	0.987053i	$-0.448723\pi$
$257$	5.14272	0.320794	0.160397	+	0.987053i	$0.448723\pi$
$258$	11.1699	0.695409
$259$	3.59210	0.223202
$260$	0	0
$261$	1.15257	0.0713420
$262$	−16.0874	−0.993884
$263$	7.09234	0.437333	0.218666	−	0.975800i	$-0.429829\pi$
$263$	7.09234	0.437333	0.218666	+	0.975800i	$0.429829\pi$
$264$	−5.75557	−0.354231
$265$	0	0
$266$	−11.7857	−0.722626
$267$	1.13335	0.0693601
$268$	−2.39853	−0.146513
$269$	−26.0830	−1.59031	−0.795154	−	0.606408i	$-0.792610\pi$
$269$	−26.0830	−1.59031	−0.795154	+	0.606408i	$0.792610\pi$
$270$	0	0
$271$	1.84590	0.112131	0.0560653	−	0.998427i	$-0.482144\pi$
$271$	1.84590	0.112131	0.0560653	+	0.998427i	$0.482144\pi$
$272$	1.83654	0.111356
$273$	−7.78907	−0.471416
$274$	−15.9906	−0.966029
$275$	0	0
$276$	2.19358	0.132038
$277$	−22.9906	−1.38137	−0.690687	−	0.723154i	$-0.742692\pi$
$277$	−22.9906	−1.38137	−0.690687	+	0.723154i	$0.742692\pi$
$278$	−11.0350	−0.661837
$279$	3.15257	0.188739
$280$	0	0
$281$	8.60793	0.513506	0.256753	−	0.966477i	$-0.417347\pi$
$281$	8.60793	0.513506	0.256753	+	0.966477i	$0.417347\pi$
$282$	1.51114	0.0899869
$283$	30.7605	1.82852	0.914261	−	0.405126i	$-0.132772\pi$
$283$	30.7605	1.82852	0.914261	+	0.405126i	$0.132772\pi$
$284$	−9.39853	−0.557700
$285$	0	0
$286$	8.46367	0.500467
$287$	−9.23659	−0.545219
$288$	1.52543	0.0898867
$289$	−13.6271	−0.801596
$290$	0	0
$291$	2.94914	0.172882
$292$	8.09679	0.473829
$293$	−14.2286	−0.831244	−0.415622	−	0.909537i	$-0.636436\pi$
$293$	−14.2286	−0.831244	−0.415622	+	0.909537i	$0.636436\pi$
$294$	7.16839	0.418069
$295$	0	0
$296$	−1.00000	−0.0581238
$297$	−26.0464	−1.51137
$298$	−13.9748	−0.809539
$299$	−3.22570	−0.186547
$300$	0	0
$301$	33.0420	1.90451
$302$	−8.42864	−0.485014
$303$	−9.76494	−0.560981
$304$	3.28100	0.188178
$305$	0	0
$306$	2.80150	0.160151
$307$	29.2514	1.66946	0.834732	−	0.550657i	$-0.185623\pi$
$307$	29.2514	1.66946	0.834732	+	0.550657i	$0.185623\pi$
$308$	−17.0257	−0.970127
$309$	−0.601472	−0.0342165
$310$	0	0
$311$	−14.5970	−0.827721	−0.413861	−	0.910340i	$-0.635820\pi$
$311$	−14.5970	−0.827721	−0.413861	+	0.910340i	$0.635820\pi$
$312$	2.16839	0.122761
$313$	−0.516060	−0.0291694	−0.0145847	−	0.999894i	$-0.504643\pi$
$313$	−0.516060	−0.0291694	−0.0145847	+	0.999894i	$0.504643\pi$
$314$	−9.17775	−0.517931
$315$	0	0
$316$	11.8064	0.664163
$317$	28.8736	1.62170	0.810851	−	0.585253i	$-0.199005\pi$
$317$	28.8736	1.62170	0.810851	+	0.585253i	$0.199005\pi$
$318$	7.96836	0.446843
$319$	3.58120	0.200509
$320$	0	0
$321$	−16.3319	−0.911555
$322$	6.48886	0.361610
$323$	6.02567	0.335277
$324$	−2.09679	−0.116488
$325$	0	0
$326$	−13.9447	−0.772325
$327$	−12.4286	−0.687305
$328$	2.57136	0.141980
$329$	4.47013	0.246446
$330$	0	0
$331$	6.55707	0.360409	0.180205	−	0.983629i	$-0.442324\pi$
$331$	6.55707	0.360409	0.180205	+	0.983629i	$0.442324\pi$
$332$	−15.4035	−0.845374
$333$	−1.52543	−0.0835929
$334$	−17.6795	−0.967381
$335$	0	0
$336$	−4.36196	−0.237965
$337$	−29.0098	−1.58027	−0.790133	−	0.612935i	$-0.789989\pi$
$337$	−29.0098	−1.58027	−0.790133	+	0.612935i	$0.789989\pi$
$338$	9.81135	0.533667
$339$	9.10171	0.494337
$340$	0	0
$341$	9.79552	0.530457
$342$	5.00492	0.270635
$343$	−3.93978	−0.212728
$344$	−9.19850	−0.495950
$345$	0	0
$346$	−15.2859	−0.821776
$347$	24.8479	1.33391	0.666953	−	0.745100i	$-0.267598\pi$
$347$	24.8479	1.33391	0.666953	+	0.745100i	$0.267598\pi$
$348$	0.917502	0.0491833
$349$	24.0765	1.28879	0.644393	−	0.764694i	$-0.277110\pi$
$349$	24.0765	1.28879	0.644393	+	0.764694i	$0.277110\pi$
$350$	0	0
$351$	9.81288	0.523773
$352$	4.73975	0.252629
$353$	−32.5433	−1.73210	−0.866051	−	0.499955i	$-0.833350\pi$
$353$	−32.5433	−1.73210	−0.866051	+	0.499955i	$0.833350\pi$
$354$	11.1699	0.593674
$355$	0	0
$356$	−0.933323	−0.0494660
$357$	−8.01090	−0.423982
$358$	−18.2859	−0.966441
$359$	−23.0923	−1.21877	−0.609384	−	0.792876i	$-0.708583\pi$
$359$	−23.0923	−1.21877	−0.609384	+	0.792876i	$0.708583\pi$
$360$	0	0
$361$	−8.23506	−0.433424
$362$	8.23506	0.432825
$363$	−13.9224	−0.730738
$364$	6.41435	0.336203
$365$	0	0
$366$	−11.4128	−0.596558
$367$	15.4717	0.807614	0.403807	−	0.914844i	$-0.367687\pi$
$367$	15.4717	0.807614	0.403807	+	0.914844i	$0.367687\pi$
$368$	−1.80642	−0.0941664
$369$	3.92242	0.204193
$370$	0	0
$371$	23.5714	1.22376
$372$	2.50961	0.130117
$373$	17.6064	0.911625	0.455812	−	0.890076i	$-0.349349\pi$
$373$	17.6064	0.911625	0.455812	+	0.890076i	$0.349349\pi$
$374$	8.70471	0.450110
$375$	0	0
$376$	−1.24443	−0.0641766
$377$	−1.34920	−0.0694875
$378$	−19.7397	−1.01530
$379$	−9.68445	−0.497457	−0.248728	−	0.968573i	$-0.580013\pi$
$379$	−9.68445	−0.497457	−0.248728	+	0.968573i	$0.580013\pi$
$380$	0	0
$381$	−4.20003	−0.215174
$382$	−17.3461	−0.887506
$383$	−1.50468	−0.0768858	−0.0384429	−	0.999261i	$-0.512240\pi$
$383$	−1.50468	−0.0768858	−0.0384429	+	0.999261i	$0.512240\pi$
$384$	1.21432	0.0619680
$385$	0	0
$386$	12.0257	0.612090
$387$	−14.0316	−0.713268
$388$	−2.42864	−0.123295
$389$	5.59210	0.283531	0.141765	−	0.989900i	$-0.454722\pi$
$389$	5.59210	0.283531	0.141765	+	0.989900i	$0.454722\pi$
$390$	0	0
$391$	−3.31756	−0.167776
$392$	−5.90321	−0.298157
$393$	−19.5353	−0.985424
$394$	−13.9146	−0.701007
$395$	0	0
$396$	7.23014	0.363328
$397$	27.5274	1.38156	0.690781	−	0.723064i	$-0.257267\pi$
$397$	27.5274	1.38156	0.690781	+	0.723064i	$0.257267\pi$
$398$	−24.5718	−1.23167
$399$	−14.3116	−0.716475
$400$	0	0
$401$	−4.83161	−0.241279	−0.120640	−	0.992696i	$-0.538495\pi$
$401$	−4.83161	−0.241279	−0.120640	+	0.992696i	$0.538495\pi$
$402$	−2.91258	−0.145266
$403$	−3.69042	−0.183833
$404$	8.04149	0.400079
$405$	0	0
$406$	2.71408	0.134698
$407$	−4.73975	−0.234941
$408$	2.23014	0.110408
$409$	−33.7447	−1.66857	−0.834283	−	0.551336i	$-0.814118\pi$
$409$	−33.7447	−1.66857	−0.834283	+	0.551336i	$0.814118\pi$
$410$	0	0
$411$	−19.4177	−0.957806
$412$	0.495316	0.0244025
$413$	33.0420	1.62589
$414$	−2.75557	−0.135429
$415$	0	0
$416$	−1.78568	−0.0875502
$417$	−13.4001	−0.656204
$418$	15.5511	0.760629
$419$	15.0479	0.735140	0.367570	−	0.929996i	$-0.380190\pi$
$419$	15.0479	0.735140	0.367570	+	0.929996i	$0.380190\pi$
$420$	0	0
$421$	−21.2859	−1.03741	−0.518706	−	0.854953i	$-0.673586\pi$
$421$	−21.2859	−1.03741	−0.518706	+	0.854953i	$0.673586\pi$
$422$	14.3383	0.697978
$423$	−1.89829	−0.0922980
$424$	−6.56199	−0.318679
$425$	0	0
$426$	−11.4128	−0.552953
$427$	−33.7605	−1.63378
$428$	13.4494	0.650100
$429$	10.2776	0.496207
$430$	0	0
$431$	35.8479	1.72673	0.863367	−	0.504577i	$-0.168352\pi$
$431$	35.8479	1.72673	0.863367	+	0.504577i	$0.168352\pi$
$432$	5.49532	0.264394
$433$	−19.1847	−0.921957	−0.460979	−	0.887411i	$-0.652501\pi$
$433$	−19.1847	−0.921957	−0.460979	+	0.887411i	$0.652501\pi$
$434$	7.42372	0.356350
$435$	0	0
$436$	10.2351	0.490171
$437$	−5.92687	−0.283521
$438$	9.83209	0.469795
$439$	−11.1427	−0.531813	−0.265907	−	0.963999i	$-0.585671\pi$
$439$	−11.1427	−0.531813	−0.265907	+	0.963999i	$0.585671\pi$
$440$	0	0
$441$	−9.00492	−0.428806
$442$	−3.27946	−0.155988
$443$	2.13627	0.101497	0.0507486	−	0.998711i	$-0.483839\pi$
$443$	2.13627	0.101497	0.0507486	+	0.998711i	$0.483839\pi$
$444$	−1.21432	−0.0576291
$445$	0	0
$446$	9.09234	0.430535
$447$	−16.9699	−0.802648
$448$	3.59210	0.169711
$449$	−0.711167	−0.0335621	−0.0167810	−	0.999859i	$-0.505342\pi$
$449$	−0.711167	−0.0335621	−0.0167810	+	0.999859i	$0.505342\pi$
$450$	0	0
$451$	12.1876	0.573892
$452$	−7.49532	−0.352550
$453$	−10.2351	−0.480885
$454$	21.3319	1.00115
$455$	0	0
$456$	3.98418	0.186576
$457$	−29.8321	−1.39549	−0.697743	−	0.716348i	$-0.745812\pi$
$457$	−29.8321	−1.39549	−0.697743	+	0.716348i	$0.745812\pi$
$458$	24.0098	1.12191
$459$	10.0923	0.471070
$460$	0	0
$461$	4.10171	0.191036	0.0955178	−	0.995428i	$-0.469549\pi$
$461$	4.10171	0.191036	0.0955178	+	0.995428i	$0.469549\pi$
$462$	−20.6746	−0.961870
$463$	13.2924	0.617749	0.308874	−	0.951103i	$-0.400048\pi$
$463$	13.2924	0.617749	0.308874	+	0.951103i	$0.400048\pi$
$464$	−0.755569	−0.0350764
$465$	0	0
$466$	−8.28100	−0.383610
$467$	−34.7052	−1.60596	−0.802982	−	0.596003i	$-0.796755\pi$
$467$	−34.7052	−1.60596	−0.802982	+	0.596003i	$0.796755\pi$
$468$	−2.72393	−0.125914
$469$	−8.61576	−0.397839
$470$	0	0
$471$	−11.1447	−0.513522
$472$	−9.19850	−0.423395
$473$	−43.5986	−2.00466
$474$	14.3368	0.658510
$475$	0	0
$476$	6.59703	0.302374
$477$	−10.0098	−0.458319
$478$	25.5812	1.17006
$479$	2.89231	0.132153	0.0660766	−	0.997815i	$-0.478952\pi$
$479$	2.89231	0.132153	0.0660766	+	0.997815i	$0.478952\pi$
$480$	0	0
$481$	1.78568	0.0814200
$482$	−2.72546	−0.124141
$483$	7.87955	0.358532
$484$	11.4652	0.521146
$485$	0	0
$486$	13.9398	0.632321
$487$	39.5560	1.79245	0.896227	−	0.443596i	$-0.146297\pi$
$487$	39.5560	1.79245	0.896227	+	0.443596i	$0.146297\pi$
$488$	9.39853	0.425451
$489$	−16.9333	−0.765751
$490$	0	0
$491$	26.5018	1.19601	0.598004	−	0.801493i	$-0.295961\pi$
$491$	26.5018	1.19601	0.598004	+	0.801493i	$0.295961\pi$
$492$	3.12245	0.140771
$493$	−1.38763	−0.0624957
$494$	−5.85881	−0.263600
$495$	0	0
$496$	−2.06668	−0.0927965
$497$	−33.7605	−1.51436
$498$	−18.7047	−0.838178
$499$	−41.3319	−1.85027	−0.925134	−	0.379641i	$-0.876048\pi$
$499$	−41.3319	−1.85027	−0.925134	+	0.379641i	$0.876048\pi$
$500$	0	0
$501$	−21.4686	−0.959146
$502$	10.2859	0.459083
$503$	−2.87601	−0.128235	−0.0641176	−	0.997942i	$-0.520423\pi$
$503$	−2.87601	−0.128235	−0.0641176	+	0.997942i	$0.520423\pi$
$504$	5.47949	0.244076
$505$	0	0
$506$	−8.56199	−0.380627
$507$	11.9141	0.529124
$508$	3.45875	0.153457
$509$	−11.3713	−0.504025	−0.252013	−	0.967724i	$-0.581092\pi$
$509$	−11.3713	−0.504025	−0.252013	+	0.967724i	$0.581092\pi$
$510$	0	0
$511$	29.0845	1.28662
$512$	−1.00000	−0.0441942
$513$	18.0301	0.796049
$514$	−5.14272	−0.226836
$515$	0	0
$516$	−11.1699	−0.491728
$517$	−5.89829	−0.259406
$518$	−3.59210	−0.157828
$519$	−18.5620	−0.814781
$520$	0	0
$521$	−19.2908	−0.845147	−0.422574	−	0.906329i	$-0.638873\pi$
$521$	−19.2908	−0.845147	−0.422574	+	0.906329i	$0.638873\pi$
$522$	−1.15257	−0.0504464
$523$	12.9813	0.567631	0.283816	−	0.958879i	$-0.408400\pi$
$523$	12.9813	0.567631	0.283816	+	0.958879i	$0.408400\pi$
$524$	16.0874	0.702782
$525$	0	0
$526$	−7.09234	−0.309241
$527$	−3.79552	−0.165336
$528$	5.75557	0.250479
$529$	−19.7368	−0.858123
$530$	0	0
$531$	−14.0316	−0.608921
$532$	11.7857	0.510974
$533$	−4.59163	−0.198885
$534$	−1.13335	−0.0490450
$535$	0	0
$536$	2.39853	0.103601
$537$	−22.2050	−0.958214
$538$	26.0830	1.12452
$539$	−27.9797	−1.20517
$540$	0	0
$541$	−16.3160	−0.701481	−0.350740	−	0.936473i	$-0.614070\pi$
$541$	−16.3160	−0.701481	−0.350740	+	0.936473i	$0.614070\pi$
$542$	−1.84590	−0.0792883
$543$	10.0000	0.429141
$544$	−1.83654	−0.0787408
$545$	0	0
$546$	7.78907	0.333341
$547$	0.677517	0.0289685	0.0144843	−	0.999895i	$-0.495389\pi$
$547$	0.677517	0.0289685	0.0144843	+	0.999895i	$0.495389\pi$
$548$	15.9906	0.683086
$549$	14.3368	0.611879
$550$	0	0
$551$	−2.47902	−0.105610
$552$	−2.19358	−0.0933648
$553$	42.4099	1.80345
$554$	22.9906	0.976778
$555$	0	0
$556$	11.0350	0.467990
$557$	−3.11108	−0.131821	−0.0659103	−	0.997826i	$-0.520995\pi$
$557$	−3.11108	−0.131821	−0.0659103	+	0.997826i	$0.520995\pi$
$558$	−3.15257	−0.133459
$559$	16.4256	0.694728
$560$	0	0
$561$	10.5703	0.446279
$562$	−8.60793	−0.363103
$563$	−22.1891	−0.935160	−0.467580	−	0.883951i	$-0.654874\pi$
$563$	−22.1891	−0.935160	−0.467580	+	0.883951i	$0.654874\pi$
$564$	−1.51114	−0.0636304
$565$	0	0
$566$	−30.7605	−1.29296
$567$	−7.53188	−0.316309
$568$	9.39853	0.394353
$569$	17.5783	0.736920	0.368460	−	0.929644i	$-0.379885\pi$
$569$	17.5783	0.736920	0.368460	+	0.929644i	$0.379885\pi$
$570$	0	0
$571$	30.5303	1.27766	0.638828	−	0.769350i	$-0.279420\pi$
$571$	30.5303	1.27766	0.638828	+	0.769350i	$0.279420\pi$
$572$	−8.46367	−0.353884
$573$	−21.0638	−0.879951
$574$	9.23659	0.385528
$575$	0	0
$576$	−1.52543	−0.0635595
$577$	14.2335	0.592550	0.296275	−	0.955103i	$-0.404256\pi$
$577$	14.2335	0.592550	0.296275	+	0.955103i	$0.404256\pi$
$578$	13.6271	0.566814
$579$	14.6030	0.606880
$580$	0	0
$581$	−55.3308	−2.29551
$582$	−2.94914	−0.122246
$583$	−31.1022	−1.28812
$584$	−8.09679	−0.335047
$585$	0	0
$586$	14.2286	0.587778
$587$	−10.5254	−0.434431	−0.217215	−	0.976124i	$-0.569697\pi$
$587$	−10.5254	−0.434431	−0.217215	+	0.976124i	$0.569697\pi$
$588$	−7.16839	−0.295619
$589$	−6.78076	−0.279396
$590$	0	0
$591$	−16.8968	−0.695040
$592$	1.00000	0.0410997
$593$	−22.8163	−0.936952	−0.468476	−	0.883476i	$-0.655197\pi$
$593$	−22.8163	−0.936952	−0.468476	+	0.883476i	$0.655197\pi$
$594$	26.0464	1.06870
$595$	0	0
$596$	13.9748	0.572431
$597$	−29.8381	−1.22119
$598$	3.22570	0.131908
$599$	−7.23659	−0.295679	−0.147840	−	0.989011i	$-0.547232\pi$
$599$	−7.23659	−0.295679	−0.147840	+	0.989011i	$0.547232\pi$
$600$	0	0
$601$	−17.2623	−0.704142	−0.352071	−	0.935973i	$-0.614522\pi$
$601$	−17.2623	−0.704142	−0.352071	+	0.935973i	$0.614522\pi$
$602$	−33.0420	−1.34669
$603$	3.65878	0.148997
$604$	8.42864	0.342956
$605$	0	0
$606$	9.76494	0.396673
$607$	30.8825	1.25348	0.626740	−	0.779228i	$-0.284389\pi$
$607$	30.8825	1.25348	0.626740	+	0.779228i	$0.284389\pi$
$608$	−3.28100	−0.133062
$609$	3.29576	0.133551
$610$	0	0
$611$	2.22216	0.0898988
$612$	−2.80150	−0.113244
$613$	16.3180	0.659079	0.329540	−	0.944142i	$-0.393106\pi$
$613$	16.3180	0.659079	0.329540	+	0.944142i	$0.393106\pi$
$614$	−29.2514	−1.18049
$615$	0	0
$616$	17.0257	0.685984
$617$	−3.16992	−0.127616	−0.0638080	−	0.997962i	$-0.520325\pi$
$617$	−3.16992	−0.127616	−0.0638080	+	0.997962i	$0.520325\pi$
$618$	0.601472	0.0241948
$619$	30.5018	1.22597	0.612985	−	0.790095i	$-0.289969\pi$
$619$	30.5018	1.22597	0.612985	+	0.790095i	$0.289969\pi$
$620$	0	0
$621$	−9.92687	−0.398352
$622$	14.5970	0.585287
$623$	−3.35260	−0.134319
$624$	−2.16839	−0.0868049
$625$	0	0
$626$	0.516060	0.0206259
$627$	18.8840	0.754154
$628$	9.17775	0.366232
$629$	1.83654	0.0732275
$630$	0	0
$631$	−13.3274	−0.530556	−0.265278	−	0.964172i	$-0.585464\pi$
$631$	−13.3274	−0.530556	−0.265278	+	0.964172i	$0.585464\pi$
$632$	−11.8064	−0.469634
$633$	17.4113	0.692037
$634$	−28.8736	−1.14672
$635$	0	0
$636$	−7.96836	−0.315966
$637$	10.5412	0.417659
$638$	−3.58120	−0.141781
$639$	14.3368	0.567154
$640$	0	0
$641$	−26.9403	−1.06408	−0.532038	−	0.846720i	$-0.678574\pi$
$641$	−26.9403	−1.06408	−0.532038	+	0.846720i	$0.678574\pi$
$642$	16.3319	0.644567
$643$	−28.0370	−1.10567	−0.552836	−	0.833290i	$-0.686455\pi$
$643$	−28.0370	−1.10567	−0.552836	+	0.833290i	$0.686455\pi$
$644$	−6.48886	−0.255697
$645$	0	0
$646$	−6.02567	−0.237077
$647$	−3.81288	−0.149900	−0.0749498	−	0.997187i	$-0.523880\pi$
$647$	−3.81288	−0.149900	−0.0749498	+	0.997187i	$0.523880\pi$
$648$	2.09679	0.0823696
$649$	−43.5986	−1.71139
$650$	0	0
$651$	9.01477	0.353317
$652$	13.9447	0.546117
$653$	1.53188	0.0599471	0.0299736	−	0.999551i	$-0.490458\pi$
$653$	1.53188	0.0599471	0.0299736	+	0.999551i	$0.490458\pi$
$654$	12.4286	0.485998
$655$	0	0
$656$	−2.57136	−0.100395
$657$	−12.3511	−0.481861
$658$	−4.47013	−0.174264
$659$	30.9101	1.20409	0.602044	−	0.798463i	$-0.294353\pi$
$659$	30.9101	1.20409	0.602044	+	0.798463i	$0.294353\pi$
$660$	0	0
$661$	−11.8163	−0.459600	−0.229800	−	0.973238i	$-0.573807\pi$
$661$	−11.8163	−0.459600	−0.229800	+	0.973238i	$0.573807\pi$
$662$	−6.55707	−0.254848
$663$	−3.98232	−0.154660
$664$	15.4035	0.597770
$665$	0	0
$666$	1.52543	0.0591091
$667$	1.36488	0.0528483
$668$	17.6795	0.684041
$669$	11.0410	0.426870
$670$	0	0
$671$	44.5466	1.71970
$672$	4.36196	0.168266
$673$	10.6780	0.411606	0.205803	−	0.978593i	$-0.434019\pi$
$673$	10.6780	0.411606	0.205803	+	0.978593i	$0.434019\pi$
$674$	29.0098	1.11742
$675$	0	0
$676$	−9.81135	−0.377359
$677$	0.828699	0.0318495	0.0159247	−	0.999873i	$-0.494931\pi$
$677$	0.828699	0.0318495	0.0159247	+	0.999873i	$0.494931\pi$
$678$	−9.10171	−0.349549
$679$	−8.72393	−0.334794
$680$	0	0
$681$	25.9037	0.992631
$682$	−9.79552	−0.375090
$683$	−12.3921	−0.474170	−0.237085	−	0.971489i	$-0.576192\pi$
$683$	−12.3921	−0.474170	−0.237085	+	0.971489i	$0.576192\pi$
$684$	−5.00492	−0.191368
$685$	0	0
$686$	3.93978	0.150421
$687$	29.1556	1.11236
$688$	9.19850	0.350689
$689$	11.7176	0.446406
$690$	0	0
$691$	22.9146	0.871712	0.435856	−	0.900016i	$-0.356446\pi$
$691$	22.9146	0.871712	0.435856	+	0.900016i	$0.356446\pi$
$692$	15.2859	0.581083
$693$	25.9714	0.986573
$694$	−24.8479	−0.943214
$695$	0	0
$696$	−0.917502	−0.0347778
$697$	−4.72239	−0.178873
$698$	−24.0765	−0.911310
$699$	−10.0558	−0.380344
$700$	0	0
$701$	−42.7161	−1.61336	−0.806682	−	0.590985i	$-0.798739\pi$
$701$	−42.7161	−1.61336	−0.806682	+	0.590985i	$0.798739\pi$
$702$	−9.81288	−0.370363
$703$	3.28100	0.123745
$704$	−4.73975	−0.178636
$705$	0	0
$706$	32.5433	1.22478
$707$	28.8859	1.08636
$708$	−11.1699	−0.419791
$709$	−47.0005	−1.76514	−0.882570	−	0.470181i	$-0.844189\pi$
$709$	−47.0005	−1.76514	−0.882570	+	0.470181i	$0.844189\pi$
$710$	0	0
$711$	−18.0098	−0.675422
$712$	0.933323	0.0349778
$713$	3.73329	0.139813
$714$	8.01090	0.299800
$715$	0	0
$716$	18.2859	0.683377
$717$	31.0638	1.16010
$718$	23.0923	0.861799
$719$	5.82717	0.217317	0.108658	−	0.994079i	$-0.465345\pi$
$719$	5.82717	0.217317	0.108658	+	0.994079i	$0.465345\pi$
$720$	0	0
$721$	1.77923	0.0662619
$722$	8.23506	0.306477
$723$	−3.30958	−0.123084
$724$	−8.23506	−0.306054
$725$	0	0
$726$	13.9224	0.516710
$727$	−15.4479	−0.572929	−0.286465	−	0.958091i	$-0.592480\pi$
$727$	−15.4479	−0.572929	−0.286465	+	0.958091i	$0.592480\pi$
$728$	−6.41435	−0.237732
$729$	23.2177	0.859915
$730$	0	0
$731$	16.8934	0.624824
$732$	11.4128	0.421830
$733$	15.4479	0.570579	0.285290	−	0.958441i	$-0.407910\pi$
$733$	15.4479	0.570579	0.285290	+	0.958441i	$0.407910\pi$
$734$	−15.4717	−0.571069
$735$	0	0
$736$	1.80642	0.0665857
$737$	11.3684	0.418761
$738$	−3.92242	−0.144386
$739$	52.2034	1.92033	0.960167	−	0.279427i	$-0.0901445\pi$
$739$	52.2034	1.92033	0.960167	+	0.279427i	$0.0901445\pi$
$740$	0	0
$741$	−7.11447	−0.261357
$742$	−23.5714	−0.865332
$743$	−16.7556	−0.614702	−0.307351	−	0.951596i	$-0.599443\pi$
$743$	−16.7556	−0.614702	−0.307351	+	0.951596i	$0.599443\pi$
$744$	−2.50961	−0.0920066
$745$	0	0
$746$	−17.6064	−0.644616
$747$	23.4968	0.859705
$748$	−8.70471	−0.318276
$749$	48.3116	1.76527
$750$	0	0
$751$	9.67307	0.352975	0.176488	−	0.984303i	$-0.443526\pi$
$751$	9.67307	0.352975	0.176488	+	0.984303i	$0.443526\pi$
$752$	1.24443	0.0453797
$753$	12.4904	0.455175
$754$	1.34920	0.0491351
$755$	0	0
$756$	19.7397	0.717928
$757$	−5.98126	−0.217393	−0.108696	−	0.994075i	$-0.534668\pi$
$757$	−5.98126	−0.217393	−0.108696	+	0.994075i	$0.534668\pi$
$758$	9.68445	0.351755
$759$	−10.3970	−0.377387
$760$	0	0
$761$	−27.6365	−1.00182	−0.500911	−	0.865499i	$-0.667002\pi$
$761$	−27.6365	−1.00182	−0.500911	+	0.865499i	$0.667002\pi$
$762$	4.20003	0.152151
$763$	36.7654	1.33100
$764$	17.3461	0.627561
$765$	0	0
$766$	1.50468	0.0543664
$767$	16.4256	0.593093
$768$	−1.21432	−0.0438180
$769$	−9.64740	−0.347894	−0.173947	−	0.984755i	$-0.555652\pi$
$769$	−9.64740	−0.347894	−0.173947	+	0.984755i	$0.555652\pi$
$770$	0	0
$771$	−6.24491	−0.224905
$772$	−12.0257	−0.432813
$773$	4.56845	0.164316	0.0821578	−	0.996619i	$-0.473819\pi$
$773$	4.56845	0.164316	0.0821578	+	0.996619i	$0.473819\pi$
$774$	14.0316	0.504357
$775$	0	0
$776$	2.42864	0.0871831
$777$	−4.36196	−0.156485
$778$	−5.59210	−0.200487
$779$	−8.43662	−0.302273
$780$	0	0
$781$	44.5466	1.59400
$782$	3.31756	0.118636
$783$	−4.15209	−0.148384
$784$	5.90321	0.210829
$785$	0	0
$786$	19.5353	0.696800
$787$	25.3274	0.902825	0.451412	−	0.892316i	$-0.350920\pi$
$787$	25.3274	0.902825	0.451412	+	0.892316i	$0.350920\pi$
$788$	13.9146	0.495687
$789$	−8.61237	−0.306609
$790$	0	0
$791$	−26.9240	−0.957306
$792$	−7.23014	−0.256912
$793$	−16.7828	−0.595973
$794$	−27.5274	−0.976912
$795$	0	0
$796$	24.5718	0.870926
$797$	8.98862	0.318393	0.159197	−	0.987247i	$-0.449110\pi$
$797$	8.98862	0.318393	0.159197	+	0.987247i	$0.449110\pi$
$798$	14.3116	0.506625
$799$	2.28544	0.0808531
$800$	0	0
$801$	1.42372	0.0503046
$802$	4.83161	0.170610
$803$	−38.3767	−1.35429
$804$	2.91258	0.102719
$805$	0	0
$806$	3.69042	0.129990
$807$	31.6731	1.11494
$808$	−8.04149	−0.282899
$809$	36.8256	1.29472	0.647360	−	0.762184i	$-0.275873\pi$
$809$	36.8256	1.29472	0.647360	+	0.762184i	$0.275873\pi$
$810$	0	0
$811$	16.4286	0.576888	0.288444	−	0.957497i	$-0.406862\pi$
$811$	16.4286	0.576888	0.288444	+	0.957497i	$0.406862\pi$
$812$	−2.71408	−0.0952456
$813$	−2.24152	−0.0786134
$814$	4.73975	0.166128
$815$	0	0
$816$	−2.23014	−0.0780706
$817$	30.1802	1.05587
$818$	33.7447	1.17985
$819$	−9.78463	−0.341902
$820$	0	0
$821$	42.5881	1.48634	0.743168	−	0.669105i	$-0.233322\pi$
$821$	42.5881	1.48634	0.743168	+	0.669105i	$0.233322\pi$
$822$	19.4177	0.677271
$823$	−3.79552	−0.132304	−0.0661518	−	0.997810i	$-0.521072\pi$
$823$	−3.79552	−0.132304	−0.0661518	+	0.997810i	$0.521072\pi$
$824$	−0.495316	−0.0172552
$825$	0	0
$826$	−33.0420	−1.14968
$827$	−9.61777	−0.334443	−0.167221	−	0.985919i	$-0.553479\pi$
$827$	−9.61777	−0.334443	−0.167221	+	0.985919i	$0.553479\pi$
$828$	2.75557	0.0957626
$829$	−30.2657	−1.05117	−0.525585	−	0.850741i	$-0.676153\pi$
$829$	−30.2657	−1.05117	−0.525585	+	0.850741i	$0.676153\pi$
$830$	0	0
$831$	27.9180	0.968464
$832$	1.78568	0.0619073
$833$	10.8415	0.375634
$834$	13.4001	0.464006
$835$	0	0
$836$	−15.5511	−0.537846
$837$	−11.3570	−0.392557
$838$	−15.0479	−0.519822
$839$	8.05239	0.277999	0.139000	−	0.990292i	$-0.455611\pi$
$839$	8.05239	0.277999	0.139000	+	0.990292i	$0.455611\pi$
$840$	0	0
$841$	−28.4291	−0.980314
$842$	21.2859	0.733561
$843$	−10.4528	−0.360013
$844$	−14.3383	−0.493545
$845$	0	0
$846$	1.89829	0.0652645
$847$	41.1842	1.41511
$848$	6.56199	0.225340
$849$	−37.3531	−1.28195
$850$	0	0
$851$	−1.80642	−0.0619234
$852$	11.4128	0.390997
$853$	−25.0845	−0.858877	−0.429439	−	0.903096i	$-0.641289\pi$
$853$	−25.0845	−0.858877	−0.429439	+	0.903096i	$0.641289\pi$
$854$	33.7605	1.15526
$855$	0	0
$856$	−13.4494	−0.459690
$857$	20.5506	0.701996	0.350998	−	0.936376i	$-0.385842\pi$
$857$	20.5506	0.701996	0.350998	+	0.936376i	$0.385842\pi$
$858$	−10.2776	−0.350872
$859$	−49.2810	−1.68145	−0.840723	−	0.541466i	$-0.817870\pi$
$859$	−49.2810	−1.68145	−0.840723	+	0.541466i	$0.817870\pi$
$860$	0	0
$861$	11.2162	0.382246
$862$	−35.8479	−1.22098
$863$	−37.6849	−1.28281	−0.641405	−	0.767203i	$-0.721648\pi$
$863$	−37.6849	−1.28281	−0.641405	+	0.767203i	$0.721648\pi$
$864$	−5.49532	−0.186954
$865$	0	0
$866$	19.1847	0.651922
$867$	16.5477	0.561989
$868$	−7.42372	−0.251977
$869$	−55.9595	−1.89829
$870$	0	0
$871$	−4.28300	−0.145124
$872$	−10.2351	−0.346603
$873$	3.70471	0.125386
$874$	5.92687	0.200479
$875$	0	0
$876$	−9.83209	−0.332196
$877$	50.9022	1.71884	0.859422	−	0.511267i	$-0.170824\pi$
$877$	50.9022	1.71884	0.859422	+	0.511267i	$0.170824\pi$
$878$	11.1427	0.376049
$879$	17.2781	0.582775
$880$	0	0
$881$	5.39207	0.181664	0.0908318	−	0.995866i	$-0.471047\pi$
$881$	5.39207	0.181664	0.0908318	+	0.995866i	$0.471047\pi$
$882$	9.00492	0.303212
$883$	−30.6356	−1.03097	−0.515485	−	0.856899i	$-0.672388\pi$
$883$	−30.6356	−1.03097	−0.515485	+	0.856899i	$0.672388\pi$
$884$	3.27946	0.110300
$885$	0	0
$886$	−2.13627	−0.0717693
$887$	37.3087	1.25270	0.626351	−	0.779541i	$-0.284548\pi$
$887$	37.3087	1.25270	0.626351	+	0.779541i	$0.284548\pi$
$888$	1.21432	0.0407499
$889$	12.4242	0.416694
$890$	0	0
$891$	9.93825	0.332944
$892$	−9.09234	−0.304434
$893$	4.08297	0.136632
$894$	16.9699	0.567558
$895$	0	0
$896$	−3.59210	−0.120004
$897$	3.91703	0.130786
$898$	0.711167	0.0237320
$899$	1.56152	0.0520795
$900$	0	0
$901$	12.0513	0.401488
$902$	−12.1876	−0.405803
$903$	−40.1235	−1.33523
$904$	7.49532	0.249291
$905$	0	0
$906$	10.2351	0.340037
$907$	−18.0973	−0.600910	−0.300455	−	0.953796i	$-0.597138\pi$
$907$	−18.0973	−0.600910	−0.300455	+	0.953796i	$0.597138\pi$
$908$	−21.3319	−0.707922
$909$	−12.2667	−0.406861
$910$	0	0
$911$	−44.9753	−1.49010	−0.745049	−	0.667010i	$-0.767574\pi$
$911$	−44.9753	−1.49010	−0.745049	+	0.667010i	$0.767574\pi$
$912$	−3.98418	−0.131929
$913$	73.0085	2.41623
$914$	29.8321	0.986758
$915$	0	0
$916$	−24.0098	−0.793308
$917$	57.7877	1.90832
$918$	−10.0923	−0.333097
$919$	5.87955	0.193949	0.0969743	−	0.995287i	$-0.469084\pi$
$919$	5.87955	0.193949	0.0969743	+	0.995287i	$0.469084\pi$
$920$	0	0
$921$	−35.5205	−1.17044
$922$	−4.10171	−0.135083
$923$	−16.7828	−0.552411
$924$	20.6746	0.680144
$925$	0	0
$926$	−13.2924	−0.436814
$927$	−0.755569	−0.0248161
$928$	0.755569	0.0248028
$929$	39.0910	1.28253	0.641266	−	0.767318i	$-0.278409\pi$
$929$	39.0910	1.28253	0.641266	+	0.767318i	$0.278409\pi$
$930$	0	0
$931$	19.3684	0.634774
$932$	8.28100	0.271253
$933$	17.7255	0.580305
$934$	34.7052	1.13559
$935$	0	0
$936$	2.72393	0.0890343
$937$	4.36349	0.142549	0.0712746	−	0.997457i	$-0.477293\pi$
$937$	4.36349	0.142549	0.0712746	+	0.997457i	$0.477293\pi$
$938$	8.61576	0.281315
$939$	0.626661	0.0204503
$940$	0	0
$941$	−12.8671	−0.419456	−0.209728	−	0.977760i	$-0.567258\pi$
$941$	−12.8671	−0.419456	−0.209728	+	0.977760i	$0.567258\pi$
$942$	11.1447	0.363115
$943$	4.64497	0.151261
$944$	9.19850	0.299386
$945$	0	0
$946$	43.5986	1.41751
$947$	−17.2444	−0.560369	−0.280184	−	0.959946i	$-0.590396\pi$
$947$	−17.2444	−0.560369	−0.280184	+	0.959946i	$0.590396\pi$
$948$	−14.3368	−0.465637
$949$	14.4583	0.469335
$950$	0	0
$951$	−35.0618	−1.13696
$952$	−6.59703	−0.213811
$953$	−24.6874	−0.799702	−0.399851	−	0.916580i	$-0.630938\pi$
$953$	−24.6874	−0.799702	−0.399851	+	0.916580i	$0.630938\pi$
$954$	10.0098	0.324081
$955$	0	0
$956$	−25.5812	−0.827355
$957$	−4.34873	−0.140574
$958$	−2.89231	−0.0934464
$959$	57.4400	1.85483
$960$	0	0
$961$	−26.7288	−0.862221
$962$	−1.78568	−0.0575726
$963$	−20.5161	−0.661121
$964$	2.72546	0.0877811
$965$	0	0
$966$	−7.87955	−0.253520
$967$	−36.1748	−1.16330	−0.581652	−	0.813438i	$-0.697594\pi$
$967$	−36.1748	−1.16330	−0.581652	+	0.813438i	$0.697594\pi$
$968$	−11.4652	−0.368506
$969$	−7.31708	−0.235059
$970$	0	0
$971$	−33.8419	−1.08604	−0.543020	−	0.839720i	$-0.682719\pi$
$971$	−33.8419	−1.08604	−0.543020	+	0.839720i	$0.682719\pi$
$972$	−13.9398	−0.447119
$973$	39.6390	1.27077
$974$	−39.5560	−1.26746
$975$	0	0
$976$	−9.39853	−0.300840
$977$	38.7768	1.24058	0.620290	−	0.784373i	$-0.287015\pi$
$977$	38.7768	1.24058	0.620290	+	0.784373i	$0.287015\pi$
$978$	16.9333	0.541468
$979$	4.42372	0.141383
$980$	0	0
$981$	−15.6128	−0.498480
$982$	−26.5018	−0.845705
$983$	−59.3975	−1.89449	−0.947243	−	0.320518i	$-0.896143\pi$
$983$	−59.3975	−1.89449	−0.947243	+	0.320518i	$0.896143\pi$
$984$	−3.12245	−0.0995402
$985$	0	0
$986$	1.38763	0.0441911
$987$	−5.42816	−0.172780
$988$	5.85881	0.186394
$989$	−16.6164	−0.528370
$990$	0	0
$991$	36.3245	1.15389	0.576943	−	0.816785i	$-0.304246\pi$
$991$	36.3245	1.15389	0.576943	+	0.816785i	$0.304246\pi$
$992$	2.06668	0.0656170
$993$	−7.96238	−0.252678
$994$	33.7605	1.07082
$995$	0	0
$996$	18.7047	0.592682
$997$	32.7732	1.03794	0.518970	−	0.854793i	$-0.326316\pi$
$997$	32.7732	1.03794	0.518970	+	0.854793i	$0.326316\pi$
$998$	41.3319	1.30834
$999$	5.49532	0.173864

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1850.2.a.ba.1.1	✓	3
5.2	odd	4		1850.2.b.n.149.3		6
5.3	odd	4		1850.2.b.n.149.4		6
5.4	even	2		1850.2.a.bb.1.3	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1850.2.a.ba.1.1	✓	3	1.1	even	1	trivial
1850.2.a.bb.1.3	yes	3	5.4	even	2
1850.2.b.n.149.3		6	5.2	odd	4
1850.2.b.n.149.4		6	5.3	odd	4

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:	\( N \)	\(=\)	\( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1850.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.21432 q^{3} +1.00000 q^{4} +1.21432 q^{6} +3.59210 q^{7} -1.00000 q^{8} -1.52543 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.21432 q^{3} +1.00000 q^{4} +1.21432 q^{6} +3.59210 q^{7} -1.00000 q^{8} -1.52543 q^{9} -4.73975 q^{11} -1.21432 q^{12} +1.78568 q^{13} -3.59210 q^{14} +1.00000 q^{16} +1.83654 q^{17} +1.52543 q^{18} +3.28100 q^{19} -4.36196 q^{21} +4.73975 q^{22} -1.80642 q^{23} +1.21432 q^{24} -1.78568 q^{26} +5.49532 q^{27} +3.59210 q^{28} -0.755569 q^{29} -2.06668 q^{31} -1.00000 q^{32} +5.75557 q^{33} -1.83654 q^{34} -1.52543 q^{36} +1.00000 q^{37} -3.28100 q^{38} -2.16839 q^{39} -2.57136 q^{41} +4.36196 q^{42} +9.19850 q^{43} -4.73975 q^{44} +1.80642 q^{46} +1.24443 q^{47} -1.21432 q^{48} +5.90321 q^{49} -2.23014 q^{51} +1.78568 q^{52} +6.56199 q^{53} -5.49532 q^{54} -3.59210 q^{56} -3.98418 q^{57} +0.755569 q^{58} +9.19850 q^{59} -9.39853 q^{61} +2.06668 q^{62} -5.47949 q^{63} +1.00000 q^{64} -5.75557 q^{66} -2.39853 q^{67} +1.83654 q^{68} +2.19358 q^{69} -9.39853 q^{71} +1.52543 q^{72} +8.09679 q^{73} -1.00000 q^{74} +3.28100 q^{76} -17.0257 q^{77} +2.16839 q^{78} +11.8064 q^{79} -2.09679 q^{81} +2.57136 q^{82} -15.4035 q^{83} -4.36196 q^{84} -9.19850 q^{86} +0.917502 q^{87} +4.73975 q^{88} -0.933323 q^{89} +6.41435 q^{91} -1.80642 q^{92} +2.50961 q^{93} -1.24443 q^{94} +1.21432 q^{96} -2.42864 q^{97} -5.90321 q^{98} +7.23014 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{6} + 4 q^{7} - 3 q^{8} + 2 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^6 + 4 * q^7 - 3 * q^8 + 2 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{6} + 4 q^{7} - 3 q^{8} + 2 q^{9} - q^{11} + 3 q^{12} + 12 q^{13} - 4 q^{14} + 3 q^{16} - q^{17} - 2 q^{18} + 3 q^{19} + q^{22} + 8 q^{23} - 3 q^{24} - 12 q^{26} + 3 q^{27} + 4 q^{28} - 2 q^{29} - 6 q^{31} - 3 q^{32} + 17 q^{33} + q^{34} + 2 q^{36} + 3 q^{37} - 3 q^{38} + 20 q^{39} - 21 q^{41} + 8 q^{43} - q^{44} - 8 q^{46} + 4 q^{47} + 3 q^{48} + 11 q^{49} - 13 q^{51} + 12 q^{52} + 6 q^{53} - 3 q^{54} - 4 q^{56} + q^{57} + 2 q^{58} + 8 q^{59} - 8 q^{61} + 6 q^{62} + 10 q^{63} + 3 q^{64} - 17 q^{66} + 13 q^{67} - q^{68} + 20 q^{69} - 8 q^{71} - 2 q^{72} + 31 q^{73} - 3 q^{74} + 3 q^{76} + 2 q^{77} - 20 q^{78} + 22 q^{79} - 13 q^{81} + 21 q^{82} + 7 q^{83} - 8 q^{86} - 10 q^{87} + q^{88} - 3 q^{89} + 12 q^{91} + 8 q^{92} - 12 q^{93} - 4 q^{94} - 3 q^{96} + 6 q^{97} - 11 q^{98} + 28 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^6 + 4 * q^7 - 3 * q^8 + 2 * q^9 - q^11 + 3 * q^12 + 12 * q^13 - 4 * q^14 + 3 * q^16 - q^17 - 2 * q^18 + 3 * q^19 + q^22 + 8 * q^23 - 3 * q^24 - 12 * q^26 + 3 * q^27 + 4 * q^28 - 2 * q^29 - 6 * q^31 - 3 * q^32 + 17 * q^33 + q^34 + 2 * q^36 + 3 * q^37 - 3 * q^38 + 20 * q^39 - 21 * q^41 + 8 * q^43 - q^44 - 8 * q^46 + 4 * q^47 + 3 * q^48 + 11 * q^49 - 13 * q^51 + 12 * q^52 + 6 * q^53 - 3 * q^54 - 4 * q^56 + q^57 + 2 * q^58 + 8 * q^59 - 8 * q^61 + 6 * q^62 + 10 * q^63 + 3 * q^64 - 17 * q^66 + 13 * q^67 - q^68 + 20 * q^69 - 8 * q^71 - 2 * q^72 + 31 * q^73 - 3 * q^74 + 3 * q^76 + 2 * q^77 - 20 * q^78 + 22 * q^79 - 13 * q^81 + 21 * q^82 + 7 * q^83 - 8 * q^86 - 10 * q^87 + q^88 - 3 * q^89 + 12 * q^91 + 8 * q^92 - 12 * q^93 - 4 * q^94 - 3 * q^96 + 6 * q^97 - 11 * q^98 + 28 * q^99

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