LMFDB - Embedded newform 6275.2.a.e.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6275,2,Mod(1,6275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6275, 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("6275.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6275 = 5^{2} \cdot 251 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6275.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:	$50.1061272684$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 28 x^{15} + 54 x^{14} + 317 x^{13} - 582 x^{12} - 1867 x^{11} + 3178 x^{10} + \cdots + 256 $ x^17 - 2x^16 - 28x^15 + 54x^14 + 317x^13 - 582x^12 - 1867x^11 + 3178x^10 + 6186x^9 - 9216x^8 - 11921x^7 + 13680x^6 + 13752x^5 - 9400x^4 - 8800x^3 + 1920x^2 + 2240x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 251)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Root			$-2.65791$ of defining polynomial
Character	$\chi$	$=$	6275.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.65791 q^{2} +2.62368 q^{3} +5.06447 q^{4} +6.97351 q^{6} +2.51426 q^{7} +8.14509 q^{8} +3.88372 q^{9} +O(q^{10})$	\(q+2.65791 q^{2} +2.62368 q^{3} +5.06447 q^{4} +6.97351 q^{6} +2.51426 q^{7} +8.14509 q^{8} +3.88372 q^{9} -6.29973 q^{11} +13.2876 q^{12} -0.699407 q^{13} +6.68266 q^{14} +11.5200 q^{16} -4.58455 q^{17} +10.3226 q^{18} +7.23032 q^{19} +6.59661 q^{21} -16.7441 q^{22} +4.43841 q^{23} +21.3701 q^{24} -1.85896 q^{26} +2.31859 q^{27} +12.7334 q^{28} +3.16969 q^{29} +6.86491 q^{31} +14.3288 q^{32} -16.5285 q^{33} -12.1853 q^{34} +19.6690 q^{36} -3.34453 q^{37} +19.2175 q^{38} -1.83502 q^{39} +1.17827 q^{41} +17.5332 q^{42} -8.14366 q^{43} -31.9048 q^{44} +11.7969 q^{46} -7.94801 q^{47} +30.2247 q^{48} -0.678520 q^{49} -12.0284 q^{51} -3.54213 q^{52} -6.14772 q^{53} +6.16260 q^{54} +20.4788 q^{56} +18.9701 q^{57} +8.42474 q^{58} +3.29675 q^{59} +1.51045 q^{61} +18.2463 q^{62} +9.76465 q^{63} +15.0447 q^{64} -43.9312 q^{66} -4.60689 q^{67} -23.2183 q^{68} +11.6450 q^{69} -8.22808 q^{71} +31.6332 q^{72} +5.16971 q^{73} -8.88947 q^{74} +36.6178 q^{76} -15.8391 q^{77} -4.87732 q^{78} +8.65353 q^{79} -5.56790 q^{81} +3.13175 q^{82} -4.65024 q^{83} +33.4084 q^{84} -21.6451 q^{86} +8.31626 q^{87} -51.3118 q^{88} +3.59697 q^{89} -1.75849 q^{91} +22.4782 q^{92} +18.0113 q^{93} -21.1251 q^{94} +37.5942 q^{96} +18.0684 q^{97} -1.80344 q^{98} -24.4663 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 2 q^{2} + 26 q^{4} + q^{6} - 3 q^{7} - 6 q^{8} + 25 q^{9}+O(q^{10}) $ 17 * q - 2 * q^2 + 26 * q^4 + q^6 - 3 * q^7 - 6 * q^8 + 25 * q^9	$ 17 q - 2 q^{2} + 26 q^{4} + q^{6} - 3 q^{7} - 6 q^{8} + 25 q^{9} - q^{11} + 9 q^{12} - 22 q^{13} - 7 q^{14} + 40 q^{16} + q^{17} + 7 q^{18} + 13 q^{19} + 25 q^{21} - 4 q^{22} + 2 q^{23} - 24 q^{24} - 9 q^{26} + 15 q^{27} + 10 q^{28} + 28 q^{29} + 12 q^{31} - 4 q^{32} + 16 q^{33} - 21 q^{34} + 21 q^{36} - 27 q^{37} + 37 q^{38} + 13 q^{39} - q^{41} + 56 q^{42} - 9 q^{43} - 43 q^{44} + 4 q^{46} + 20 q^{47} + 79 q^{48} + 32 q^{49} - 2 q^{51} + q^{52} - q^{53} - 65 q^{54} - 61 q^{56} + 24 q^{57} + 46 q^{58} - 20 q^{59} + 59 q^{61} + 73 q^{62} + 41 q^{63} + 54 q^{64} - 43 q^{66} - 15 q^{67} + 20 q^{68} + 38 q^{69} - 26 q^{71} + 2 q^{72} - 8 q^{73} + 2 q^{74} + 38 q^{76} + 33 q^{79} + 29 q^{81} - 10 q^{82} + 63 q^{84} + 11 q^{86} + 11 q^{87} - 27 q^{88} + 11 q^{89} - 2 q^{91} - 28 q^{92} - 28 q^{93} + 29 q^{94} - 17 q^{96} + 10 q^{97} - 22 q^{98} - 36 q^{99}+O(q^{100}) $ 17 * q - 2 * q^2 + 26 * q^4 + q^6 - 3 * q^7 - 6 * q^8 + 25 * q^9 - q^11 + 9 * q^12 - 22 * q^13 - 7 * q^14 + 40 * q^16 + q^17 + 7 * q^18 + 13 * q^19 + 25 * q^21 - 4 * q^22 + 2 * q^23 - 24 * q^24 - 9 * q^26 + 15 * q^27 + 10 * q^28 + 28 * q^29 + 12 * q^31 - 4 * q^32 + 16 * q^33 - 21 * q^34 + 21 * q^36 - 27 * q^37 + 37 * q^38 + 13 * q^39 - q^41 + 56 * q^42 - 9 * q^43 - 43 * q^44 + 4 * q^46 + 20 * q^47 + 79 * q^48 + 32 * q^49 - 2 * q^51 + q^52 - q^53 - 65 * q^54 - 61 * q^56 + 24 * q^57 + 46 * q^58 - 20 * q^59 + 59 * q^61 + 73 * q^62 + 41 * q^63 + 54 * q^64 - 43 * q^66 - 15 * q^67 + 20 * q^68 + 38 * q^69 - 26 * q^71 + 2 * q^72 - 8 * q^73 + 2 * q^74 + 38 * q^76 + 33 * q^79 + 29 * q^81 - 10 * q^82 + 63 * q^84 + 11 * q^86 + 11 * q^87 - 27 * q^88 + 11 * q^89 - 2 * q^91 - 28 * q^92 - 28 * q^93 + 29 * q^94 - 17 * q^96 + 10 * q^97 - 22 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.65791	1.87942	0.939712	−	0.341966i	$-0.111093\pi$
$2$	2.65791	1.87942	0.939712	+	0.341966i	$0.111093\pi$
$3$	2.62368	1.51478	0.757392	−	0.652960i	$-0.226473\pi$
$3$	2.62368	1.51478	0.757392	+	0.652960i	$0.226473\pi$
$4$	5.06447	2.53224
$5$	0	0
$5$	0	0
$6$	6.97351	2.84692
$7$	2.51426	0.950299	0.475150	−	0.879905i	$-0.342394\pi$
$7$	2.51426	0.950299	0.475150	+	0.879905i	$0.342394\pi$
$8$	8.14509	2.87972
$9$	3.88372	1.29457
$10$	0	0
$11$	−6.29973	−1.89944	−0.949720	−	0.313102i	$-0.898632\pi$
$11$	−6.29973	−1.89944	−0.949720	+	0.313102i	$0.898632\pi$
$12$	13.2876	3.83579
$13$	−0.699407	−0.193981	−0.0969903	−	0.995285i	$-0.530922\pi$
$13$	−0.699407	−0.193981	−0.0969903	+	0.995285i	$0.530922\pi$
$14$	6.68266	1.78602
$15$	0	0
$16$	11.5200	2.87999
$17$	−4.58455	−1.11192	−0.555958	−	0.831210i	$-0.687648\pi$
$17$	−4.58455	−1.11192	−0.555958	+	0.831210i	$0.687648\pi$
$18$	10.3226	2.43305
$19$	7.23032	1.65875	0.829375	−	0.558693i	$-0.188697\pi$
$19$	7.23032	1.65875	0.829375	+	0.558693i	$0.188697\pi$
$20$	0	0
$21$	6.59661	1.43950
$22$	−16.7441	−3.56985
$23$	4.43841	0.925472	0.462736	−	0.886496i	$-0.346868\pi$
$23$	4.43841	0.925472	0.462736	+	0.886496i	$0.346868\pi$
$24$	21.3701	4.36216
$25$	0	0
$26$	−1.85896	−0.364572
$27$	2.31859	0.446213
$28$	12.7334	2.40638
$29$	3.16969	0.588597	0.294298	−	0.955714i	$-0.404914\pi$
$29$	3.16969	0.588597	0.294298	+	0.955714i	$0.404914\pi$
$30$	0	0
$31$	6.86491	1.23297	0.616487	−	0.787365i	$-0.288555\pi$
$31$	6.86491	1.23297	0.616487	+	0.787365i	$0.288555\pi$
$32$	14.3288	2.53300
$33$	−16.5285	−2.87724
$34$	−12.1853	−2.08976
$35$	0	0
$36$	19.6690	3.27816
$37$	−3.34453	−0.549838	−0.274919	−	0.961467i	$-0.588651\pi$
$37$	−3.34453	−0.549838	−0.274919	+	0.961467i	$0.588651\pi$
$38$	19.2175	3.11749
$39$	−1.83502	−0.293839
$40$	0	0
$41$	1.17827	0.184016	0.0920078	−	0.995758i	$-0.470672\pi$
$41$	1.17827	0.184016	0.0920078	+	0.995758i	$0.470672\pi$
$42$	17.5332	2.70543
$43$	−8.14366	−1.24190	−0.620948	−	0.783851i	$-0.713252\pi$
$43$	−8.14366	−1.24190	−0.620948	+	0.783851i	$0.713252\pi$
$44$	−31.9048	−4.80983
$45$	0	0
$46$	11.7969	1.73935
$47$	−7.94801	−1.15934	−0.579668	−	0.814853i	$-0.696818\pi$
$47$	−7.94801	−1.15934	−0.579668	+	0.814853i	$0.696818\pi$
$48$	30.2247	4.36256
$49$	−0.678520	−0.0969314
$50$	0	0
$51$	−12.0284	−1.68431
$52$	−3.54213	−0.491205
$53$	−6.14772	−0.844455	−0.422227	−	0.906490i	$-0.638752\pi$
$53$	−6.14772	−0.844455	−0.422227	+	0.906490i	$0.638752\pi$
$54$	6.16260	0.838623
$55$	0	0
$56$	20.4788	2.73660
$57$	18.9701	2.51265
$58$	8.42474	1.10622
$59$	3.29675	0.429201	0.214600	−	0.976702i	$-0.431155\pi$
$59$	3.29675	0.429201	0.214600	+	0.976702i	$0.431155\pi$
$60$	0	0
$61$	1.51045	0.193394	0.0966968	−	0.995314i	$-0.469172\pi$
$61$	1.51045	0.193394	0.0966968	+	0.995314i	$0.469172\pi$
$62$	18.2463	2.31728
$63$	9.76465	1.23023
$64$	15.0447	1.88059
$65$	0	0
$66$	−43.9312	−5.40756
$67$	−4.60689	−0.562821	−0.281411	−	0.959587i	$-0.590802\pi$
$67$	−4.60689	−0.562821	−0.281411	+	0.959587i	$0.590802\pi$
$68$	−23.2183	−2.81563
$69$	11.6450	1.40189
$70$	0	0
$71$	−8.22808	−0.976494	−0.488247	−	0.872706i	$-0.662363\pi$
$71$	−8.22808	−0.976494	−0.488247	+	0.872706i	$0.662363\pi$
$72$	31.6332	3.72801
$73$	5.16971	0.605069	0.302535	−	0.953138i	$-0.402167\pi$
$73$	5.16971	0.605069	0.302535	+	0.953138i	$0.402167\pi$
$74$	−8.88947	−1.03338
$75$	0	0
$76$	36.6178	4.20035
$77$	−15.8391	−1.80504
$78$	−4.87732	−0.552248
$79$	8.65353	0.973598	0.486799	−	0.873514i	$-0.338164\pi$
$79$	8.65353	0.973598	0.486799	+	0.873514i	$0.338164\pi$
$80$	0	0
$81$	−5.56790	−0.618656
$82$	3.13175	0.345843
$83$	−4.65024	−0.510430	−0.255215	−	0.966884i	$-0.582146\pi$
$83$	−4.65024	−0.510430	−0.255215	+	0.966884i	$0.582146\pi$
$84$	33.4084	3.64515
$85$	0	0
$86$	−21.6451	−2.33405
$87$	8.31626	0.891597
$88$	−51.3118	−5.46986
$89$	3.59697	0.381279	0.190639	−	0.981660i	$-0.438944\pi$
$89$	3.59697	0.381279	0.190639	+	0.981660i	$0.438944\pi$
$90$	0	0
$91$	−1.75849	−0.184340
$92$	22.4782	2.34351
$93$	18.0113	1.86769
$94$	−21.1251	−2.17888
$95$	0	0
$96$	37.5942	3.83694
$97$	18.0684	1.83456	0.917282	−	0.398238i	$-0.130378\pi$
$97$	18.0684	1.83456	0.917282	+	0.398238i	$0.130378\pi$
$98$	−1.80344	−0.182175
$99$	−24.4663	−2.45896
$100$	0	0
$101$	−6.97694	−0.694231	−0.347116	−	0.937822i	$-0.612839\pi$
$101$	−6.97694	−0.694231	−0.347116	+	0.937822i	$0.612839\pi$
$102$	−31.9704	−3.16554
$103$	−1.85305	−0.182587	−0.0912933	−	0.995824i	$-0.529100\pi$
$103$	−1.85305	−0.182587	−0.0912933	+	0.995824i	$0.529100\pi$
$104$	−5.69674	−0.558611
$105$	0	0
$106$	−16.3401	−1.58709
$107$	−6.70888	−0.648572	−0.324286	−	0.945959i	$-0.605124\pi$
$107$	−6.70888	−0.648572	−0.324286	+	0.945959i	$0.605124\pi$
$108$	11.7424	1.12992
$109$	−15.8205	−1.51533	−0.757664	−	0.652645i	$-0.773660\pi$
$109$	−15.8205	−1.51533	−0.757664	+	0.652645i	$0.773660\pi$
$110$	0	0
$111$	−8.77500	−0.832886
$112$	28.9641	2.73685
$113$	−16.4826	−1.55055	−0.775275	−	0.631624i	$-0.782388\pi$
$113$	−16.4826	−1.55055	−0.775275	+	0.631624i	$0.782388\pi$
$114$	50.4207	4.72233
$115$	0	0
$116$	16.0528	1.49047
$117$	−2.71630	−0.251122
$118$	8.76247	0.806650
$119$	−11.5267	−1.05665
$120$	0	0
$121$	28.6866	2.60787
$122$	4.01465	0.363469
$123$	3.09142	0.278744
$124$	34.7671	3.12218
$125$	0	0
$126$	25.9535	2.31213
$127$	−5.39892	−0.479077	−0.239538	−	0.970887i	$-0.576996\pi$
$127$	−5.39892	−0.479077	−0.239538	+	0.970887i	$0.576996\pi$
$128$	11.3298	1.00143
$129$	−21.3664	−1.88121
$130$	0	0
$131$	16.4211	1.43472	0.717360	−	0.696703i	$-0.245350\pi$
$131$	16.4211	1.43472	0.717360	+	0.696703i	$0.245350\pi$
$132$	−83.7081	−7.28586
$133$	18.1789	1.57631
$134$	−12.2447	−1.05778
$135$	0	0
$136$	−37.3415	−3.20201
$137$	11.4638	0.979416	0.489708	−	0.871887i	$-0.337103\pi$
$137$	11.4638	0.979416	0.489708	+	0.871887i	$0.337103\pi$
$138$	30.9513	2.63475
$139$	−6.63997	−0.563195	−0.281597	−	0.959533i	$-0.590864\pi$
$139$	−6.63997	−0.563195	−0.281597	+	0.959533i	$0.590864\pi$
$140$	0	0
$141$	−20.8531	−1.75614
$142$	−21.8695	−1.83525
$143$	4.40608	0.368455
$144$	44.7402	3.72835
$145$	0	0
$146$	13.7406	1.13718
$147$	−1.78022	−0.146830
$148$	−16.9383	−1.39232
$149$	22.1685	1.81611	0.908057	−	0.418846i	$-0.137565\pi$
$149$	22.1685	1.81611	0.908057	+	0.418846i	$0.137565\pi$
$150$	0	0
$151$	4.81459	0.391806	0.195903	−	0.980623i	$-0.437236\pi$
$151$	4.81459	0.391806	0.195903	+	0.980623i	$0.437236\pi$
$152$	58.8916	4.77674
$153$	−17.8051	−1.43946
$154$	−42.0989	−3.39243
$155$	0	0
$156$	−9.29343	−0.744070
$157$	−9.72414	−0.776071	−0.388035	−	0.921644i	$-0.626846\pi$
$157$	−9.72414	−0.776071	−0.388035	+	0.921644i	$0.626846\pi$
$158$	23.0003	1.82980
$159$	−16.1297	−1.27917
$160$	0	0
$161$	11.1593	0.879475
$162$	−14.7990	−1.16272
$163$	16.2697	1.27434	0.637172	−	0.770721i	$-0.280104\pi$
$163$	16.2697	1.27434	0.637172	+	0.770721i	$0.280104\pi$
$164$	5.96734	0.465971
$165$	0	0
$166$	−12.3599	−0.959314
$167$	16.4518	1.27308	0.636541	−	0.771243i	$-0.280365\pi$
$167$	16.4518	1.27308	0.636541	+	0.771243i	$0.280365\pi$
$168$	53.7300	4.14536
$169$	−12.5108	−0.962371
$170$	0	0
$171$	28.0805	2.14737
$172$	−41.2434	−3.14478
$173$	−21.0702	−1.60194	−0.800968	−	0.598708i	$-0.795681\pi$
$173$	−21.0702	−1.60194	−0.800968	+	0.598708i	$0.795681\pi$
$174$	22.1039	1.67569
$175$	0	0
$176$	−72.5725	−5.47036
$177$	8.64964	0.650147
$178$	9.56043	0.716584
$179$	8.45297	0.631804	0.315902	−	0.948792i	$-0.397693\pi$
$179$	8.45297	0.631804	0.315902	+	0.948792i	$0.397693\pi$
$180$	0	0
$181$	4.28715	0.318662	0.159331	−	0.987225i	$-0.449066\pi$
$181$	4.28715	0.318662	0.159331	+	0.987225i	$0.449066\pi$
$182$	−4.67390	−0.346453
$183$	3.96295	0.292950
$184$	36.1512	2.66510
$185$	0	0
$186$	47.8725	3.51018
$187$	28.8814	2.11202
$188$	−40.2525	−2.93571
$189$	5.82953	0.424036
$190$	0	0
$191$	−10.3921	−0.751947	−0.375974	−	0.926630i	$-0.622692\pi$
$191$	−10.3921	−0.751947	−0.375974	+	0.926630i	$0.622692\pi$
$192$	39.4725	2.84868
$193$	−12.7332	−0.916557	−0.458278	−	0.888809i	$-0.651534\pi$
$193$	−12.7332	−0.916557	−0.458278	+	0.888809i	$0.651534\pi$
$194$	48.0240	3.44793
$195$	0	0
$196$	−3.43635	−0.245453
$197$	4.12368	0.293800	0.146900	−	0.989151i	$-0.453070\pi$
$197$	4.12368	0.293800	0.146900	+	0.989151i	$0.453070\pi$
$198$	−65.0293	−4.62143
$199$	−13.7296	−0.973264	−0.486632	−	0.873607i	$-0.661775\pi$
$199$	−13.7296	−0.973264	−0.486632	+	0.873607i	$0.661775\pi$
$200$	0	0
$201$	−12.0870	−0.852553
$202$	−18.5441	−1.30476
$203$	7.96941	0.559343
$204$	−60.9175	−4.26508
$205$	0	0
$206$	−4.92524	−0.343158
$207$	17.2375	1.19809
$208$	−8.05714	−0.558662
$209$	−45.5491	−3.15069
$210$	0	0
$211$	4.58825	0.315868	0.157934	−	0.987450i	$-0.449517\pi$
$211$	4.58825	0.315868	0.157934	+	0.987450i	$0.449517\pi$
$212$	−31.1350	−2.13836
$213$	−21.5879	−1.47918
$214$	−17.8316	−1.21894
$215$	0	0
$216$	18.8851	1.28497
$217$	17.2601	1.17169
$218$	−42.0494	−2.84795
$219$	13.5637	0.916549
$220$	0	0
$221$	3.20647	0.215690
$222$	−23.3231	−1.56535
$223$	0.0912325	0.00610938	0.00305469	−	0.999995i	$-0.499028\pi$
$223$	0.0912325	0.00610938	0.00305469	+	0.999995i	$0.499028\pi$
$224$	36.0262	2.40710
$225$	0	0
$226$	−43.8091	−2.91414
$227$	−12.8140	−0.850497	−0.425249	−	0.905077i	$-0.639813\pi$
$227$	−12.8140	−0.850497	−0.425249	+	0.905077i	$0.639813\pi$
$228$	96.0735	6.36262
$229$	−16.5635	−1.09455	−0.547275	−	0.836953i	$-0.684335\pi$
$229$	−16.5635	−1.09455	−0.547275	+	0.836953i	$0.684335\pi$
$230$	0	0
$231$	−41.5568	−2.73424
$232$	25.8174	1.69500
$233$	−17.8233	−1.16764	−0.583820	−	0.811883i	$-0.698443\pi$
$233$	−17.8233	−1.16764	−0.583820	+	0.811883i	$0.698443\pi$
$234$	−7.21967	−0.471965
$235$	0	0
$236$	16.6963	1.08684
$237$	22.7041	1.47479
$238$	−30.6370	−1.98590
$239$	−12.8815	−0.833234	−0.416617	−	0.909082i	$-0.636784\pi$
$239$	−12.8815	−0.833234	−0.416617	+	0.909082i	$0.636784\pi$
$240$	0	0
$241$	0.761335	0.0490419	0.0245210	−	0.999699i	$-0.492194\pi$
$241$	0.761335	0.0490419	0.0245210	+	0.999699i	$0.492194\pi$
$242$	76.2462	4.90129
$243$	−21.5642	−1.38334
$244$	7.64965	0.489719
$245$	0	0
$246$	8.21671	0.523878
$247$	−5.05694	−0.321765
$248$	55.9153	3.55062
$249$	−12.2007	−0.773191
$250$	0	0
$251$	1.00000	0.0631194
$251$	1.00000	0.0631194
$252$	49.4528	3.11524
$253$	−27.9608	−1.75788
$254$	−14.3498	−0.900389
$255$	0	0
$256$	0.0242744	0.00151715
$257$	−6.12039	−0.381779	−0.190890	−	0.981611i	$-0.561137\pi$
$257$	−6.12039	−0.381779	−0.190890	+	0.981611i	$0.561137\pi$
$258$	−56.7899	−3.53558
$259$	−8.40901	−0.522511
$260$	0	0
$261$	12.3102	0.761981
$262$	43.6458	2.69645
$263$	−3.47378	−0.214202	−0.107101	−	0.994248i	$-0.534157\pi$
$263$	−3.47378	−0.214202	−0.107101	+	0.994248i	$0.534157\pi$
$264$	−134.626	−8.28566
$265$	0	0
$266$	48.3178	2.96255
$267$	9.43732	0.577555
$268$	−23.3315	−1.42520
$269$	10.7931	0.658066	0.329033	−	0.944318i	$-0.393277\pi$
$269$	10.7931	0.658066	0.329033	+	0.944318i	$0.393277\pi$
$270$	0	0
$271$	13.8686	0.842455	0.421227	−	0.906955i	$-0.361599\pi$
$271$	13.8686	0.842455	0.421227	+	0.906955i	$0.361599\pi$
$272$	−52.8138	−3.20230
$273$	−4.61372	−0.279235
$274$	30.4696	1.84074
$275$	0	0
$276$	58.9757	3.54992
$277$	−20.0135	−1.20250	−0.601248	−	0.799062i	$-0.705330\pi$
$277$	−20.0135	−1.20250	−0.601248	+	0.799062i	$0.705330\pi$
$278$	−17.6484	−1.05848
$279$	26.6613	1.59617
$280$	0	0
$281$	13.4897	0.804726	0.402363	−	0.915480i	$-0.368189\pi$
$281$	13.4897	0.804726	0.402363	+	0.915480i	$0.368189\pi$
$282$	−55.4255	−3.30054
$283$	21.9359	1.30396	0.651978	−	0.758238i	$-0.273939\pi$
$283$	21.9359	1.30396	0.651978	+	0.758238i	$0.273939\pi$
$284$	−41.6709	−2.47271
$285$	0	0
$286$	11.7109	0.692483
$287$	2.96248	0.174870
$288$	55.6489	3.27914
$289$	4.01807	0.236357
$290$	0	0
$291$	47.4057	2.77897
$292$	26.1819	1.53218
$293$	−2.14505	−0.125315	−0.0626576	−	0.998035i	$-0.519958\pi$
$293$	−2.14505	−0.125315	−0.0626576	+	0.998035i	$0.519958\pi$
$294$	−4.73166	−0.275956
$295$	0	0
$296$	−27.2415	−1.58338
$297$	−14.6065	−0.847554
$298$	58.9218	3.41325
$299$	−3.10425	−0.179524
$300$	0	0
$301$	−20.4752	−1.18017
$302$	12.7967	0.736369
$303$	−18.3053	−1.05161
$304$	83.2929	4.77718
$305$	0	0
$306$	−47.3242	−2.70535
$307$	1.49142	0.0851200	0.0425600	−	0.999094i	$-0.486449\pi$
$307$	1.49142	0.0851200	0.0425600	+	0.999094i	$0.486449\pi$
$308$	−80.2168	−4.57078
$309$	−4.86182	−0.276579
$310$	0	0
$311$	6.70155	0.380010	0.190005	−	0.981783i	$-0.439150\pi$
$311$	6.70155	0.380010	0.190005	+	0.981783i	$0.439150\pi$
$312$	−14.9464	−0.846175
$313$	−20.9053	−1.18164	−0.590818	−	0.806805i	$-0.701195\pi$
$313$	−20.9053	−1.18164	−0.590818	+	0.806805i	$0.701195\pi$
$314$	−25.8459	−1.45857
$315$	0	0
$316$	43.8256	2.46538
$317$	12.8281	0.720499	0.360249	−	0.932856i	$-0.382692\pi$
$317$	12.8281	0.720499	0.360249	+	0.932856i	$0.382692\pi$
$318$	−42.8712	−2.40410
$319$	−19.9682	−1.11800
$320$	0	0
$321$	−17.6020	−0.982446
$322$	29.6604	1.65291
$323$	−33.1478	−1.84439
$324$	−28.1985	−1.56658
$325$	0	0
$326$	43.2435	2.39504
$327$	−41.5080	−2.29540
$328$	9.59715	0.529914
$329$	−19.9833	−1.10172
$330$	0	0
$331$	13.3489	0.733723	0.366862	−	0.930275i	$-0.380432\pi$
$331$	13.3489	0.733723	0.366862	+	0.930275i	$0.380432\pi$
$332$	−23.5510	−1.29253
$333$	−12.9892	−0.711805
$334$	43.7275	2.39266
$335$	0	0
$336$	75.9926	4.14574
$337$	−12.8628	−0.700681	−0.350340	−	0.936622i	$-0.613934\pi$
$337$	−12.8628	−0.700681	−0.350340	+	0.936622i	$0.613934\pi$
$338$	−33.2526	−1.80870
$339$	−43.2450	−2.34875
$340$	0	0
$341$	−43.2470	−2.34196
$342$	74.6354	4.03582
$343$	−19.3058	−1.04241
$344$	−66.3309	−3.57632
$345$	0	0
$346$	−56.0026	−3.01072
$347$	2.39781	0.128721	0.0643607	−	0.997927i	$-0.479499\pi$
$347$	2.39781	0.128721	0.0643607	+	0.997927i	$0.479499\pi$
$348$	42.1175	2.25774
$349$	35.2451	1.88663	0.943313	−	0.331903i	$-0.107691\pi$
$349$	35.2451	1.88663	0.943313	+	0.331903i	$0.107691\pi$
$350$	0	0
$351$	−1.62164	−0.0865566
$352$	−90.2674	−4.81127
$353$	11.5147	0.612868	0.306434	−	0.951892i	$-0.400864\pi$
$353$	11.5147	0.612868	0.306434	+	0.951892i	$0.400864\pi$
$354$	22.9899	1.22190
$355$	0	0
$356$	18.2168	0.965488
$357$	−30.2425	−1.60060
$358$	22.4672	1.18743
$359$	−16.1553	−0.852642	−0.426321	−	0.904572i	$-0.640191\pi$
$359$	−16.1553	−0.852642	−0.426321	+	0.904572i	$0.640191\pi$
$360$	0	0
$361$	33.2776	1.75145
$362$	11.3949	0.598900
$363$	75.2645	3.95036
$364$	−8.90582	−0.466792
$365$	0	0
$366$	10.5332	0.550577
$367$	1.07079	0.0558946	0.0279473	−	0.999609i	$-0.491103\pi$
$367$	1.07079	0.0558946	0.0279473	+	0.999609i	$0.491103\pi$
$368$	51.1302	2.66535
$369$	4.57608	0.238221
$370$	0	0
$371$	−15.4569	−0.802485
$372$	91.2180	4.72943
$373$	12.7804	0.661742	0.330871	−	0.943676i	$-0.392657\pi$
$373$	12.7804	0.661742	0.330871	+	0.943676i	$0.392657\pi$
$374$	76.7641	3.96938
$375$	0	0
$376$	−64.7372	−3.33857
$377$	−2.21690	−0.114176
$378$	15.4943	0.796943
$379$	17.5543	0.901703	0.450851	−	0.892599i	$-0.351120\pi$
$379$	17.5543	0.901703	0.450851	+	0.892599i	$0.351120\pi$
$380$	0	0
$381$	−14.1651	−0.725698
$382$	−27.6213	−1.41323
$383$	10.9209	0.558030	0.279015	−	0.960287i	$-0.409992\pi$
$383$	10.9209	0.558030	0.279015	+	0.960287i	$0.409992\pi$
$384$	29.7259	1.51694
$385$	0	0
$386$	−33.8437	−1.72260
$387$	−31.6277	−1.60772
$388$	91.5068	4.64555
$389$	−2.85338	−0.144672	−0.0723361	−	0.997380i	$-0.523045\pi$
$389$	−2.85338	−0.144672	−0.0723361	+	0.997380i	$0.523045\pi$
$390$	0	0
$391$	−20.3481	−1.02905
$392$	−5.52661	−0.279136
$393$	43.0838	2.17329
$394$	10.9603	0.552174
$395$	0	0
$396$	−123.909	−6.22667
$397$	18.3951	0.923225	0.461613	−	0.887082i	$-0.347271\pi$
$397$	18.3951	0.923225	0.461613	+	0.887082i	$0.347271\pi$
$398$	−36.4920	−1.82918
$399$	47.6956	2.38777
$400$	0	0
$401$	−11.0050	−0.549564	−0.274782	−	0.961506i	$-0.588606\pi$
$401$	−11.0050	−0.549564	−0.274782	+	0.961506i	$0.588606\pi$
$402$	−32.1262	−1.60231
$403$	−4.80137	−0.239173
$404$	−35.3345	−1.75796
$405$	0	0
$406$	21.1820	1.05124
$407$	21.0697	1.04438
$408$	−97.9724	−4.85036
$409$	−13.5283	−0.668930	−0.334465	−	0.942408i	$-0.608556\pi$
$409$	−13.5283	−0.668930	−0.334465	+	0.942408i	$0.608556\pi$
$410$	0	0
$411$	30.0773	1.48360
$412$	−9.38474	−0.462353
$413$	8.28888	0.407869
$414$	45.8157	2.25172
$415$	0	0
$416$	−10.0217	−0.491352
$417$	−17.4212	−0.853119
$418$	−121.065	−5.92149
$419$	14.1141	0.689518	0.344759	−	0.938691i	$-0.387961\pi$
$419$	14.1141	0.689518	0.344759	+	0.938691i	$0.387961\pi$
$420$	0	0
$421$	37.9882	1.85143	0.925716	−	0.378219i	$-0.123463\pi$
$421$	37.9882	1.85143	0.925716	+	0.378219i	$0.123463\pi$
$422$	12.1951	0.593650
$423$	−30.8678	−1.50084
$424$	−50.0738	−2.43180
$425$	0	0
$426$	−57.3786	−2.78000
$427$	3.79766	0.183782
$428$	−33.9769	−1.64234
$429$	11.5601	0.558129
$430$	0	0
$431$	−1.89014	−0.0910450	−0.0455225	−	0.998963i	$-0.514495\pi$
$431$	−1.89014	−0.0910450	−0.0455225	+	0.998963i	$0.514495\pi$
$432$	26.7100	1.28509
$433$	−8.69728	−0.417965	−0.208982	−	0.977919i	$-0.567015\pi$
$433$	−8.69728	−0.417965	−0.208982	+	0.977919i	$0.567015\pi$
$434$	45.8758	2.20211
$435$	0	0
$436$	−80.1225	−3.83717
$437$	32.0911	1.53513
$438$	36.0510	1.72259
$439$	11.2331	0.536129	0.268064	−	0.963401i	$-0.413616\pi$
$439$	11.2331	0.536129	0.268064	+	0.963401i	$0.413616\pi$
$440$	0	0
$441$	−2.63518	−0.125485
$442$	8.52249	0.405374
$443$	18.8903	0.897505	0.448753	−	0.893656i	$-0.351868\pi$
$443$	18.8903	0.897505	0.448753	+	0.893656i	$0.351868\pi$
$444$	−44.4408	−2.10907
$445$	0	0
$446$	0.242487	0.0114821
$447$	58.1631	2.75102
$448$	37.8262	1.78712
$449$	−3.47576	−0.164031	−0.0820157	−	0.996631i	$-0.526136\pi$
$449$	−3.47576	−0.164031	−0.0820157	+	0.996631i	$0.526136\pi$
$450$	0	0
$451$	−7.42281	−0.349526
$452$	−83.4755	−3.92636
$453$	12.6320	0.593501
$454$	−34.0585	−1.59845
$455$	0	0
$456$	154.513	7.23573
$457$	14.6495	0.685273	0.342637	−	0.939468i	$-0.388680\pi$
$457$	14.6495	0.685273	0.342637	+	0.939468i	$0.388680\pi$
$458$	−44.0244	−2.05712
$459$	−10.6297	−0.496151
$460$	0	0
$461$	−31.0557	−1.44641	−0.723203	−	0.690635i	$-0.757331\pi$
$461$	−31.0557	−1.44641	−0.723203	+	0.690635i	$0.757331\pi$
$462$	−110.454	−5.13880
$463$	−12.3099	−0.572089	−0.286045	−	0.958216i	$-0.592341\pi$
$463$	−12.3099	−0.572089	−0.286045	+	0.958216i	$0.592341\pi$
$464$	36.5147	1.69515
$465$	0	0
$466$	−47.3726	−2.19449
$467$	9.59342	0.443930	0.221965	−	0.975055i	$-0.428753\pi$
$467$	9.59342	0.443930	0.221965	+	0.975055i	$0.428753\pi$
$468$	−13.7566	−0.635900
$469$	−11.5829	−0.534849
$470$	0	0
$471$	−25.5131	−1.17558
$472$	26.8524	1.23598
$473$	51.3028	2.35891
$474$	60.3454	2.77176
$475$	0	0
$476$	−58.3768	−2.67570
$477$	−23.8760	−1.09321
$478$	−34.2378	−1.56600
$479$	−14.5463	−0.664639	−0.332320	−	0.943167i	$-0.607831\pi$
$479$	−14.5463	−0.664639	−0.332320	+	0.943167i	$0.607831\pi$
$480$	0	0
$481$	2.33919	0.106658
$482$	2.02356	0.0921706
$483$	29.2784	1.33222
$484$	145.282	6.60374
$485$	0	0
$486$	−57.3156	−2.59989
$487$	18.1844	0.824015	0.412007	−	0.911180i	$-0.364828\pi$
$487$	18.1844	0.824015	0.412007	+	0.911180i	$0.364828\pi$
$488$	12.3028	0.556921
$489$	42.6867	1.93036
$490$	0	0
$491$	27.1596	1.22570	0.612848	−	0.790201i	$-0.290024\pi$
$491$	27.1596	1.22570	0.612848	+	0.790201i	$0.290024\pi$
$492$	15.6564	0.705846
$493$	−14.5316	−0.654470
$494$	−13.4409	−0.604734
$495$	0	0
$496$	79.0834	3.55095
$497$	−20.6875	−0.927961
$498$	−32.4285	−1.45315
$499$	18.4154	0.824386	0.412193	−	0.911096i	$-0.364763\pi$
$499$	18.4154	0.824386	0.412193	+	0.911096i	$0.364763\pi$
$500$	0	0
$501$	43.1644	1.92844
$502$	2.65791	0.118628
$503$	−40.1500	−1.79020	−0.895100	−	0.445865i	$-0.852896\pi$
$503$	−40.1500	−1.79020	−0.895100	+	0.445865i	$0.852896\pi$
$504$	79.5340	3.54272
$505$	0	0
$506$	−74.3171	−3.30380
$507$	−32.8245	−1.45779
$508$	−27.3427	−1.21314
$509$	11.0878	0.491456	0.245728	−	0.969339i	$-0.420973\pi$
$509$	11.0878	0.491456	0.245728	+	0.969339i	$0.420973\pi$
$510$	0	0
$511$	12.9980	0.574997
$512$	−22.5952	−0.998574
$513$	16.7641	0.740155
$514$	−16.2674	−0.717525
$515$	0	0
$516$	−108.210	−4.76366
$517$	50.0703	2.20209
$518$	−22.3504	−0.982020
$519$	−55.2815	−2.42659
$520$	0	0
$521$	−11.2398	−0.492423	−0.246212	−	0.969216i	$-0.579186\pi$
$521$	−11.2398	−0.492423	−0.246212	+	0.969216i	$0.579186\pi$
$522$	32.7193	1.43209
$523$	−12.8526	−0.562004	−0.281002	−	0.959707i	$-0.590667\pi$
$523$	−12.8526	−0.562004	−0.281002	+	0.959707i	$0.590667\pi$
$524$	83.1644	3.63305
$525$	0	0
$526$	−9.23298	−0.402577
$527$	−31.4725	−1.37096
$528$	−190.407	−8.28642
$529$	−3.30055	−0.143502
$530$	0	0
$531$	12.8037	0.555631
$532$	92.0664	3.99159
$533$	−0.824094	−0.0356955
$534$	25.0835	1.08547
$535$	0	0
$536$	−37.5235	−1.62077
$537$	22.1779	0.957047
$538$	28.6870	1.23679
$539$	4.27449	0.184115
$540$	0	0
$541$	40.7501	1.75198	0.875991	−	0.482328i	$-0.160209\pi$
$541$	40.7501	1.75198	0.875991	+	0.482328i	$0.160209\pi$
$542$	36.8614	1.58333
$543$	11.2481	0.482704
$544$	−65.6910	−2.81648
$545$	0	0
$546$	−12.2628	−0.524801
$547$	30.4796	1.30321	0.651606	−	0.758558i	$-0.274096\pi$
$547$	30.4796	1.30321	0.651606	+	0.758558i	$0.274096\pi$
$548$	58.0580	2.48011
$549$	5.86617	0.250362
$550$	0	0
$551$	22.9179	0.976335
$552$	94.8494	4.03706
$553$	21.7572	0.925209
$554$	−53.1941	−2.26000
$555$	0	0
$556$	−33.6279	−1.42614
$557$	−17.2478	−0.730812	−0.365406	−	0.930848i	$-0.619070\pi$
$557$	−17.2478	−0.730812	−0.365406	+	0.930848i	$0.619070\pi$
$558$	70.8634	2.99989
$559$	5.69574	0.240904
$560$	0	0
$561$	75.7756	3.19925
$562$	35.8543	1.51242
$563$	7.43193	0.313218	0.156609	−	0.987661i	$-0.449944\pi$
$563$	7.43193	0.313218	0.156609	+	0.987661i	$0.449944\pi$
$564$	−105.610	−4.44697
$565$	0	0
$566$	58.3037	2.45069
$567$	−13.9991	−0.587908
$568$	−67.0185	−2.81203
$569$	25.6087	1.07357	0.536786	−	0.843719i	$-0.319638\pi$
$569$	25.6087	1.07357	0.536786	+	0.843719i	$0.319638\pi$
$570$	0	0
$571$	5.04995	0.211334	0.105667	−	0.994402i	$-0.466302\pi$
$571$	5.04995	0.211334	0.105667	+	0.994402i	$0.466302\pi$
$572$	22.3145	0.933014
$573$	−27.2656	−1.13904
$574$	7.87401	0.328655
$575$	0	0
$576$	58.4293	2.43455
$577$	20.2333	0.842322	0.421161	−	0.906986i	$-0.361623\pi$
$577$	20.2333	0.842322	0.421161	+	0.906986i	$0.361623\pi$
$578$	10.6797	0.444215
$579$	−33.4079	−1.38839
$580$	0	0
$581$	−11.6919	−0.485061
$582$	126.000	5.22286
$583$	38.7290	1.60399
$584$	42.1078	1.74243
$585$	0	0
$586$	−5.70134	−0.235520
$587$	18.6139	0.768279	0.384140	−	0.923275i	$-0.374498\pi$
$587$	18.6139	0.768279	0.384140	+	0.923275i	$0.374498\pi$
$588$	−9.01589	−0.371809
$589$	49.6355	2.04519
$590$	0	0
$591$	10.8192	0.445043
$592$	−38.5289	−1.58353
$593$	−2.15937	−0.0886748	−0.0443374	−	0.999017i	$-0.514118\pi$
$593$	−2.15937	−0.0886748	−0.0443374	+	0.999017i	$0.514118\pi$
$594$	−38.8227	−1.59291
$595$	0	0
$596$	112.272	4.59883
$597$	−36.0221	−1.47429
$598$	−8.25082	−0.337401
$599$	−16.3514	−0.668101	−0.334050	−	0.942555i	$-0.608416\pi$
$599$	−16.3514	−0.668101	−0.334050	+	0.942555i	$0.608416\pi$
$600$	0	0
$601$	−39.7825	−1.62276	−0.811380	−	0.584519i	$-0.801283\pi$
$601$	−39.7825	−1.62276	−0.811380	+	0.584519i	$0.801283\pi$
$602$	−54.4213	−2.21805
$603$	−17.8919	−0.728613
$604$	24.3834	0.992145
$605$	0	0
$606$	−48.6537	−1.97642
$607$	28.5774	1.15992	0.579959	−	0.814645i	$-0.303068\pi$
$607$	28.5774	1.15992	0.579959	+	0.814645i	$0.303068\pi$
$608$	103.602	4.20161
$609$	20.9092	0.847284
$610$	0	0
$611$	5.55890	0.224889
$612$	−90.1733	−3.64504
$613$	17.3087	0.699093	0.349547	−	0.936919i	$-0.386336\pi$
$613$	17.3087	0.699093	0.349547	+	0.936919i	$0.386336\pi$
$614$	3.96406	0.159977
$615$	0	0
$616$	−129.011	−5.19800
$617$	−11.9753	−0.482107	−0.241054	−	0.970512i	$-0.577493\pi$
$617$	−11.9753	−0.482107	−0.241054	+	0.970512i	$0.577493\pi$
$618$	−12.9223	−0.519810
$619$	32.9447	1.32416	0.662080	−	0.749433i	$-0.269674\pi$
$619$	32.9447	1.32416	0.662080	+	0.749433i	$0.269674\pi$
$620$	0	0
$621$	10.2908	0.412957
$622$	17.8121	0.714200
$623$	9.04371	0.362329
$624$	−21.1394	−0.846252
$625$	0	0
$626$	−55.5643	−2.22080
$627$	−119.506	−4.77262
$628$	−49.2477	−1.96520
$629$	15.3332	0.611374
$630$	0	0
$631$	2.95086	0.117472	0.0587360	−	0.998274i	$-0.481293\pi$
$631$	2.95086	0.117472	0.0587360	+	0.998274i	$0.481293\pi$
$632$	70.4837	2.80369
$633$	12.0381	0.478472
$634$	34.0960	1.35412
$635$	0	0
$636$	−81.6884	−3.23915
$637$	0.474562	0.0188028
$638$	−53.0736	−2.10120
$639$	−31.9555	−1.26414
$640$	0	0
$641$	18.1419	0.716560	0.358280	−	0.933614i	$-0.383363\pi$
$641$	18.1419	0.716560	0.358280	+	0.933614i	$0.383363\pi$
$642$	−46.7844	−1.84643
$643$	40.9334	1.61425	0.807127	−	0.590378i	$-0.201021\pi$
$643$	40.9334	1.61425	0.807127	+	0.590378i	$0.201021\pi$
$644$	56.5159	2.22704
$645$	0	0
$646$	−88.1037	−3.46639
$647$	−12.9579	−0.509428	−0.254714	−	0.967016i	$-0.581981\pi$
$647$	−12.9579	−0.509428	−0.254714	+	0.967016i	$0.581981\pi$
$648$	−45.3511	−1.78156
$649$	−20.7686	−0.815241
$650$	0	0
$651$	45.2851	1.77486
$652$	82.3977	3.22694
$653$	0.0158713	0.000621093 0	0.000310546	−	1.00000i	$-0.499901\pi$
$653$	0.0158713	0.000621093 0	0.000310546		1.00000i	$0.499901\pi$
$654$	−110.324	−4.31402
$655$	0	0
$656$	13.5737	0.529963
$657$	20.0777	0.783306
$658$	−53.1138	−2.07059
$659$	−29.2333	−1.13877	−0.569385	−	0.822071i	$-0.692818\pi$
$659$	−29.2333	−1.13877	−0.569385	+	0.822071i	$0.692818\pi$
$660$	0	0
$661$	32.7524	1.27392	0.636961	−	0.770896i	$-0.280191\pi$
$661$	32.7524	1.27392	0.636961	+	0.770896i	$0.280191\pi$
$662$	35.4802	1.37898
$663$	8.41275	0.326724
$664$	−37.8766	−1.46990
$665$	0	0
$666$	−34.5242	−1.33778
$667$	14.0684	0.544730
$668$	83.3199	3.22375
$669$	0.239365	0.00925439
$670$	0	0
$671$	−9.51544	−0.367340
$672$	94.5214	3.64624
$673$	28.0615	1.08169	0.540846	−	0.841122i	$-0.318104\pi$
$673$	28.0615	1.08169	0.540846	+	0.841122i	$0.318104\pi$
$674$	−34.1881	−1.31688
$675$	0	0
$676$	−63.3608	−2.43695
$677$	2.05737	0.0790713	0.0395357	−	0.999218i	$-0.487412\pi$
$677$	2.05737	0.0790713	0.0395357	+	0.999218i	$0.487412\pi$
$678$	−114.941	−4.41429
$679$	45.4285	1.74339
$680$	0	0
$681$	−33.6200	−1.28832
$682$	−114.947	−4.40153
$683$	39.9521	1.52873	0.764363	−	0.644786i	$-0.223054\pi$
$683$	39.9521	1.52873	0.764363	+	0.644786i	$0.223054\pi$
$684$	142.213	5.43765
$685$	0	0
$686$	−51.3129	−1.95914
$687$	−43.4575	−1.65801
$688$	−93.8146	−3.57665
$689$	4.29976	0.163808
$690$	0	0
$691$	17.9711	0.683654	0.341827	−	0.939763i	$-0.388954\pi$
$691$	17.9711	0.683654	0.341827	+	0.939763i	$0.388954\pi$
$692$	−106.709	−4.05648
$693$	−61.5146	−2.33675
$694$	6.37317	0.241922
$695$	0	0
$696$	67.7367	2.56755
$697$	−5.40186	−0.204610
$698$	93.6782	3.54577
$699$	−46.7626	−1.76872
$700$	0	0
$701$	46.5074	1.75656	0.878281	−	0.478146i	$-0.158691\pi$
$701$	46.5074	1.75656	0.878281	+	0.478146i	$0.158691\pi$
$702$	−4.31017	−0.162677
$703$	−24.1821	−0.912044
$704$	−94.7775	−3.57206
$705$	0	0
$706$	30.6051	1.15184
$707$	−17.5418	−0.659727
$708$	43.8059	1.64633
$709$	−49.0363	−1.84160	−0.920798	−	0.390041i	$-0.872461\pi$
$709$	−49.0363	−1.84160	−0.920798	+	0.390041i	$0.872461\pi$
$710$	0	0
$711$	33.6078	1.26039
$712$	29.2977	1.09798
$713$	30.4692	1.14108
$714$	−80.3817	−3.00821
$715$	0	0
$716$	42.8098	1.59988
$717$	−33.7969	−1.26217
$718$	−42.9392	−1.60248
$719$	26.5201	0.989032	0.494516	−	0.869169i	$-0.335345\pi$
$719$	26.5201	0.989032	0.494516	+	0.869169i	$0.335345\pi$
$720$	0	0
$721$	−4.65905	−0.173512
$722$	88.4487	3.29172
$723$	1.99750	0.0742879
$724$	21.7122	0.806927
$725$	0	0
$726$	200.046	7.42440
$727$	−32.6887	−1.21236	−0.606179	−	0.795329i	$-0.707298\pi$
$727$	−32.6887	−1.21236	−0.606179	+	0.795329i	$0.707298\pi$
$728$	−14.3230	−0.530847
$729$	−39.8739	−1.47681
$730$	0	0
$731$	37.3350	1.38088
$732$	20.0703	0.741818
$733$	−12.4066	−0.458248	−0.229124	−	0.973397i	$-0.573586\pi$
$733$	−12.4066	−0.458248	−0.229124	+	0.973397i	$0.573586\pi$
$734$	2.84605	0.105050
$735$	0	0
$736$	63.5970	2.34422
$737$	29.0222	1.06904
$738$	12.1628	0.447719
$739$	−21.1186	−0.776862	−0.388431	−	0.921478i	$-0.626983\pi$
$739$	−21.1186	−0.776862	−0.388431	+	0.921478i	$0.626983\pi$
$740$	0	0
$741$	−13.2678	−0.487405
$742$	−41.0831	−1.50821
$743$	40.8627	1.49911	0.749554	−	0.661944i	$-0.230268\pi$
$743$	40.8627	1.49911	0.749554	+	0.661944i	$0.230268\pi$
$744$	146.704	5.37843
$745$	0	0
$746$	33.9690	1.24369
$747$	−18.0602	−0.660788
$748$	146.269	5.34813
$749$	−16.8678	−0.616337
$750$	0	0
$751$	14.3790	0.524699	0.262349	−	0.964973i	$-0.415503\pi$
$751$	14.3790	0.524699	0.262349	+	0.964973i	$0.415503\pi$
$752$	−91.5607	−3.33887
$753$	2.62368	0.0956123
$754$	−5.89233	−0.214586
$755$	0	0
$756$	29.5235	1.07376
$757$	18.6835	0.679064	0.339532	−	0.940595i	$-0.389731\pi$
$757$	18.6835	0.679064	0.339532	+	0.940595i	$0.389731\pi$
$758$	46.6577	1.69468
$759$	−73.3602	−2.66281
$760$	0	0
$761$	−21.8685	−0.792732	−0.396366	−	0.918092i	$-0.629729\pi$
$761$	−21.8685	−0.792732	−0.396366	+	0.918092i	$0.629729\pi$
$762$	−37.6494	−1.36389
$763$	−39.7768	−1.44002
$764$	−52.6306	−1.90411
$765$	0	0
$766$	29.0266	1.04878
$767$	−2.30577	−0.0832567
$768$	0.0636882	0.00229815
$769$	7.85128	0.283124	0.141562	−	0.989929i	$-0.454788\pi$
$769$	7.85128	0.283124	0.141562	+	0.989929i	$0.454788\pi$
$770$	0	0
$771$	−16.0580	−0.578313
$772$	−64.4870	−2.32094
$773$	−41.0681	−1.47712	−0.738558	−	0.674190i	$-0.764493\pi$
$773$	−41.0681	−1.47712	−0.738558	+	0.674190i	$0.764493\pi$
$774$	−84.0634	−3.02160
$775$	0	0
$776$	147.168	5.28304
$777$	−22.0626	−0.791491
$778$	−7.58402	−0.271900
$779$	8.51931	0.305236
$780$	0	0
$781$	51.8347	1.85479
$782$	−54.0833	−1.93402
$783$	7.34921	0.262639
$784$	−7.81652	−0.279161
$785$	0	0
$786$	114.513	4.08454
$787$	−42.5345	−1.51619	−0.758096	−	0.652143i	$-0.773870\pi$
$787$	−42.5345	−1.51619	−0.758096	+	0.652143i	$0.773870\pi$
$788$	20.8842	0.743970
$789$	−9.11410	−0.324470
$790$	0	0
$791$	−41.4414	−1.47349
$792$	−199.281	−7.08113
$793$	−1.05642	−0.0375146
$794$	48.8926	1.73513
$795$	0	0
$796$	−69.5331	−2.46454
$797$	−33.5901	−1.18982	−0.594912	−	0.803791i	$-0.702813\pi$
$797$	−33.5901	−1.18982	−0.594912	+	0.803791i	$0.702813\pi$
$798$	126.771	4.48763
$799$	36.4380	1.28908
$800$	0	0
$801$	13.9696	0.493592
$802$	−29.2503	−1.03286
$803$	−32.5678	−1.14929
$804$	−61.2144	−2.15887
$805$	0	0
$806$	−12.7616	−0.449508
$807$	28.3176	0.996828
$808$	−56.8278	−1.99919
$809$	−23.4068	−0.822940	−0.411470	−	0.911423i	$-0.634984\pi$
$809$	−23.4068	−0.822940	−0.411470	+	0.911423i	$0.634984\pi$
$810$	0	0
$811$	14.1515	0.496928	0.248464	−	0.968641i	$-0.420074\pi$
$811$	14.1515	0.496928	0.248464	+	0.968641i	$0.420074\pi$
$812$	40.3609	1.41639
$813$	36.3867	1.27614
$814$	56.0012	1.96284
$815$	0	0
$816$	−138.567	−4.85080
$817$	−58.8813	−2.06000
$818$	−35.9569	−1.25720
$819$	−6.82947	−0.238641
$820$	0	0
$821$	−7.42484	−0.259129	−0.129564	−	0.991571i	$-0.541358\pi$
$821$	−7.42484	−0.259129	−0.129564	+	0.991571i	$0.541358\pi$
$822$	79.9427	2.78832
$823$	1.63364	0.0569452	0.0284726	−	0.999595i	$-0.490936\pi$
$823$	1.63364	0.0569452	0.0284726	+	0.999595i	$0.490936\pi$
$824$	−15.0933	−0.525799
$825$	0	0
$826$	22.0311	0.766559
$827$	−46.8226	−1.62818	−0.814090	−	0.580739i	$-0.802764\pi$
$827$	−46.8226	−1.62818	−0.814090	+	0.580739i	$0.802764\pi$
$828$	87.2989	3.03385
$829$	10.0372	0.348605	0.174303	−	0.984692i	$-0.444233\pi$
$829$	10.0372	0.348605	0.174303	+	0.984692i	$0.444233\pi$
$830$	0	0
$831$	−52.5092	−1.82152
$832$	−10.5224	−0.364798
$833$	3.11071	0.107780
$834$	−46.3039	−1.60337
$835$	0	0
$836$	−230.682	−7.97830
$837$	15.9169	0.550168
$838$	37.5139	1.29590
$839$	14.9971	0.517756	0.258878	−	0.965910i	$-0.416647\pi$
$839$	14.9971	0.517756	0.258878	+	0.965910i	$0.416647\pi$
$840$	0	0
$841$	−18.9531	−0.653554
$842$	100.969	3.47963
$843$	35.3926	1.21899
$844$	23.2371	0.799852
$845$	0	0
$846$	−82.0438	−2.82072
$847$	72.1254	2.47826
$848$	−70.8215	−2.43202
$849$	57.5530	1.97521
$850$	0	0
$851$	−14.8444	−0.508860
$852$	−109.331	−3.74563
$853$	−43.8473	−1.50130	−0.750652	−	0.660698i	$-0.770261\pi$
$853$	−43.8473	−1.50130	−0.750652	+	0.660698i	$0.770261\pi$
$854$	10.0938	0.345404
$855$	0	0
$856$	−54.6444	−1.86771
$857$	12.7227	0.434598	0.217299	−	0.976105i	$-0.430275\pi$
$857$	12.7227	0.434598	0.217299	+	0.976105i	$0.430275\pi$
$858$	30.7258	1.04896
$859$	10.7352	0.366281	0.183140	−	0.983087i	$-0.441374\pi$
$859$	10.7352	0.366281	0.183140	+	0.983087i	$0.441374\pi$
$860$	0	0
$861$	7.77262	0.264890
$862$	−5.02383	−0.171112
$863$	−17.1108	−0.582458	−0.291229	−	0.956653i	$-0.594064\pi$
$863$	−17.1108	−0.582458	−0.291229	+	0.956653i	$0.594064\pi$
$864$	33.2226	1.13025
$865$	0	0
$866$	−23.1166	−0.785533
$867$	10.5421	0.358030
$868$	87.4135	2.96701
$869$	−54.5149	−1.84929
$870$	0	0
$871$	3.22209	0.109176
$872$	−128.859	−4.36373
$873$	70.1724	2.37498
$874$	85.2952	2.88515
$875$	0	0
$876$	68.6930	2.32092
$877$	26.8816	0.907726	0.453863	−	0.891071i	$-0.350046\pi$
$877$	26.8816	0.907726	0.453863	+	0.891071i	$0.350046\pi$
$878$	29.8567	1.00761
$879$	−5.62793	−0.189825
$880$	0	0
$881$	48.8555	1.64598	0.822992	−	0.568053i	$-0.192303\pi$
$881$	48.8555	1.64598	0.822992	+	0.568053i	$0.192303\pi$
$882$	−7.00406	−0.235839
$883$	−26.8833	−0.904695	−0.452347	−	0.891842i	$-0.649413\pi$
$883$	−26.8833	−0.904695	−0.452347	+	0.891842i	$0.649413\pi$
$884$	16.2391	0.546179
$885$	0	0
$886$	50.2087	1.68679
$887$	2.58557	0.0868150	0.0434075	−	0.999057i	$-0.486179\pi$
$887$	2.58557	0.0868150	0.0434075	+	0.999057i	$0.486179\pi$
$888$	−71.4732	−2.39848
$889$	−13.5743	−0.455266
$890$	0	0
$891$	35.0763	1.17510
$892$	0.462044	0.0154704
$893$	−57.4667	−1.92305
$894$	154.592	5.17034
$895$	0	0
$896$	28.4861	0.951654
$897$	−8.14458	−0.271940
$898$	−9.23826	−0.308285
$899$	21.7596	0.725724
$900$	0	0
$901$	28.1845	0.938963
$902$	−19.7291	−0.656909
$903$	−53.7206	−1.78771
$904$	−134.252	−4.46515
$905$	0	0
$906$	33.5746	1.11544
$907$	42.0643	1.39672	0.698360	−	0.715746i	$-0.253913\pi$
$907$	42.0643	1.39672	0.698360	+	0.715746i	$0.253913\pi$
$908$	−64.8964	−2.15366
$909$	−27.0964	−0.898732
$910$	0	0
$911$	−59.0365	−1.95597	−0.977983	−	0.208685i	$-0.933082\pi$
$911$	−59.0365	−1.95597	−0.977983	+	0.208685i	$0.933082\pi$
$912$	218.534	7.23639
$913$	29.2952	0.969530
$914$	38.9369	1.28792
$915$	0	0
$916$	−83.8856	−2.77166
$917$	41.2869	1.36341
$918$	−28.2527	−0.932478
$919$	5.57673	0.183959	0.0919797	−	0.995761i	$-0.470681\pi$
$919$	5.57673	0.183959	0.0919797	+	0.995761i	$0.470681\pi$
$920$	0	0
$921$	3.91302	0.128938
$922$	−82.5431	−2.71841
$923$	5.75478	0.189421
$924$	−210.464	−6.92374
$925$	0	0
$926$	−32.7186	−1.07520
$927$	−7.19673	−0.236372
$928$	45.4178	1.49091
$929$	−39.9616	−1.31110	−0.655550	−	0.755152i	$-0.727563\pi$
$929$	−39.9616	−1.31110	−0.655550	+	0.755152i	$0.727563\pi$
$930$	0	0
$931$	−4.90592	−0.160785
$932$	−90.2654	−2.95674
$933$	17.5827	0.575633
$934$	25.4984	0.834334
$935$	0	0
$936$	−22.1245	−0.723162
$937$	26.0767	0.851888	0.425944	−	0.904749i	$-0.359942\pi$
$937$	26.0767	0.851888	0.425944	+	0.904749i	$0.359942\pi$
$938$	−30.7863	−1.00521
$939$	−54.8489	−1.78993
$940$	0	0
$941$	−45.6025	−1.48660	−0.743299	−	0.668959i	$-0.766740\pi$
$941$	−45.6025	−1.48660	−0.743299	+	0.668959i	$0.766740\pi$
$942$	−67.8114	−2.20941
$943$	5.22966	0.170301
$944$	37.9784	1.23609
$945$	0	0
$946$	136.358	4.43339
$947$	35.2548	1.14563	0.572814	−	0.819685i	$-0.305852\pi$
$947$	35.2548	1.14563	0.572814	+	0.819685i	$0.305852\pi$
$948$	114.984	3.73452
$949$	−3.61574	−0.117372
$950$	0	0
$951$	33.6569	1.09140
$952$	−93.8862	−3.04287
$953$	20.6865	0.670103	0.335051	−	0.942200i	$-0.391246\pi$
$953$	20.6865	0.670103	0.335051	+	0.942200i	$0.391246\pi$
$954$	−63.4602	−2.05460
$955$	0	0
$956$	−65.2380	−2.10995
$957$	−52.3902	−1.69353
$958$	−38.6628	−1.24914
$959$	28.8228	0.930738
$960$	0	0
$961$	16.1269	0.520224
$962$	6.21736	0.200456
$963$	−26.0554	−0.839622
$964$	3.85576	0.124186
$965$	0	0
$966$	77.8194	2.50380
$967$	−31.8565	−1.02444	−0.512219	−	0.858855i	$-0.671176\pi$
$967$	−31.8565	−1.02444	−0.512219	+	0.858855i	$0.671176\pi$
$968$	233.655	7.50995
$969$	−86.9692	−2.79385
$970$	0	0
$971$	−2.02520	−0.0649919	−0.0324960	−	0.999472i	$-0.510346\pi$
$971$	−2.02520	−0.0649919	−0.0324960	+	0.999472i	$0.510346\pi$
$972$	−109.211	−3.50295
$973$	−16.6946	−0.535204
$974$	48.3325	1.54867
$975$	0	0
$976$	17.4003	0.556971
$977$	3.33996	0.106855	0.0534274	−	0.998572i	$-0.482985\pi$
$977$	3.33996	0.106855	0.0534274	+	0.998572i	$0.482985\pi$
$978$	113.457	3.62796
$979$	−22.6600	−0.724215
$980$	0	0
$981$	−61.4423	−1.96170
$982$	72.1877	2.30360
$983$	−8.40905	−0.268207	−0.134104	−	0.990967i	$-0.542815\pi$
$983$	−8.40905	−0.268207	−0.134104	+	0.990967i	$0.542815\pi$
$984$	25.1799	0.802706
$985$	0	0
$986$	−38.6236	−1.23003
$987$	−52.4299	−1.66886
$988$	−25.6107	−0.814786
$989$	−36.1449	−1.14934
$990$	0	0
$991$	−1.60494	−0.0509825	−0.0254912	−	0.999675i	$-0.508115\pi$
$991$	−1.60494	−0.0509825	−0.0254912	+	0.999675i	$0.508115\pi$
$992$	98.3658	3.12312
$993$	35.0234	1.11143
$994$	−54.9855	−1.74403
$995$	0	0
$996$	−61.7904	−1.95790
$997$	20.8631	0.660742	0.330371	−	0.943851i	$-0.392826\pi$
$997$	20.8631	0.660742	0.330371	+	0.943851i	$0.392826\pi$
$998$	48.9464	1.54937
$999$	−7.75460	−0.245345

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6275.2.a.e.1.17		17
5.4	even	2		251.2.a.b.1.1	✓	17
15.14	odd	2		2259.2.a.k.1.17		17
20.19	odd	2		4016.2.a.k.1.14		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
251.2.a.b.1.1	✓	17	5.4	even	2
2259.2.a.k.1.17		17	15.14	odd	2
4016.2.a.k.1.14		17	20.19	odd	2
6275.2.a.e.1.17		17	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6275 = 5^{2} \cdot 251 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6275.a (trivial)

\(f(q)\)	\(=\)	\(q+2.65791 q^{2} +2.62368 q^{3} +5.06447 q^{4} +6.97351 q^{6} +2.51426 q^{7} +8.14509 q^{8} +3.88372 q^{9} +O(q^{10})\)	\(q+2.65791 q^{2} +2.62368 q^{3} +5.06447 q^{4} +6.97351 q^{6} +2.51426 q^{7} +8.14509 q^{8} +3.88372 q^{9} -6.29973 q^{11} +13.2876 q^{12} -0.699407 q^{13} +6.68266 q^{14} +11.5200 q^{16} -4.58455 q^{17} +10.3226 q^{18} +7.23032 q^{19} +6.59661 q^{21} -16.7441 q^{22} +4.43841 q^{23} +21.3701 q^{24} -1.85896 q^{26} +2.31859 q^{27} +12.7334 q^{28} +3.16969 q^{29} +6.86491 q^{31} +14.3288 q^{32} -16.5285 q^{33} -12.1853 q^{34} +19.6690 q^{36} -3.34453 q^{37} +19.2175 q^{38} -1.83502 q^{39} +1.17827 q^{41} +17.5332 q^{42} -8.14366 q^{43} -31.9048 q^{44} +11.7969 q^{46} -7.94801 q^{47} +30.2247 q^{48} -0.678520 q^{49} -12.0284 q^{51} -3.54213 q^{52} -6.14772 q^{53} +6.16260 q^{54} +20.4788 q^{56} +18.9701 q^{57} +8.42474 q^{58} +3.29675 q^{59} +1.51045 q^{61} +18.2463 q^{62} +9.76465 q^{63} +15.0447 q^{64} -43.9312 q^{66} -4.60689 q^{67} -23.2183 q^{68} +11.6450 q^{69} -8.22808 q^{71} +31.6332 q^{72} +5.16971 q^{73} -8.88947 q^{74} +36.6178 q^{76} -15.8391 q^{77} -4.87732 q^{78} +8.65353 q^{79} -5.56790 q^{81} +3.13175 q^{82} -4.65024 q^{83} +33.4084 q^{84} -21.6451 q^{86} +8.31626 q^{87} -51.3118 q^{88} +3.59697 q^{89} -1.75849 q^{91} +22.4782 q^{92} +18.0113 q^{93} -21.1251 q^{94} +37.5942 q^{96} +18.0684 q^{97} -1.80344 q^{98} -24.4663 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 2 q^{2} + 26 q^{4} + q^{6} - 3 q^{7} - 6 q^{8} + 25 q^{9}+O(q^{10}) \) 17 * q - 2 * q^2 + 26 * q^4 + q^6 - 3 * q^7 - 6 * q^8 + 25 * q^9	\( 17 q - 2 q^{2} + 26 q^{4} + q^{6} - 3 q^{7} - 6 q^{8} + 25 q^{9} - q^{11} + 9 q^{12} - 22 q^{13} - 7 q^{14} + 40 q^{16} + q^{17} + 7 q^{18} + 13 q^{19} + 25 q^{21} - 4 q^{22} + 2 q^{23} - 24 q^{24} - 9 q^{26} + 15 q^{27} + 10 q^{28} + 28 q^{29} + 12 q^{31} - 4 q^{32} + 16 q^{33} - 21 q^{34} + 21 q^{36} - 27 q^{37} + 37 q^{38} + 13 q^{39} - q^{41} + 56 q^{42} - 9 q^{43} - 43 q^{44} + 4 q^{46} + 20 q^{47} + 79 q^{48} + 32 q^{49} - 2 q^{51} + q^{52} - q^{53} - 65 q^{54} - 61 q^{56} + 24 q^{57} + 46 q^{58} - 20 q^{59} + 59 q^{61} + 73 q^{62} + 41 q^{63} + 54 q^{64} - 43 q^{66} - 15 q^{67} + 20 q^{68} + 38 q^{69} - 26 q^{71} + 2 q^{72} - 8 q^{73} + 2 q^{74} + 38 q^{76} + 33 q^{79} + 29 q^{81} - 10 q^{82} + 63 q^{84} + 11 q^{86} + 11 q^{87} - 27 q^{88} + 11 q^{89} - 2 q^{91} - 28 q^{92} - 28 q^{93} + 29 q^{94} - 17 q^{96} + 10 q^{97} - 22 q^{98} - 36 q^{99}+O(q^{100}) \) 17 * q - 2 * q^2 + 26 * q^4 + q^6 - 3 * q^7 - 6 * q^8 + 25 * q^9 - q^11 + 9 * q^12 - 22 * q^13 - 7 * q^14 + 40 * q^16 + q^17 + 7 * q^18 + 13 * q^19 + 25 * q^21 - 4 * q^22 + 2 * q^23 - 24 * q^24 - 9 * q^26 + 15 * q^27 + 10 * q^28 + 28 * q^29 + 12 * q^31 - 4 * q^32 + 16 * q^33 - 21 * q^34 + 21 * q^36 - 27 * q^37 + 37 * q^38 + 13 * q^39 - q^41 + 56 * q^42 - 9 * q^43 - 43 * q^44 + 4 * q^46 + 20 * q^47 + 79 * q^48 + 32 * q^49 - 2 * q^51 + q^52 - q^53 - 65 * q^54 - 61 * q^56 + 24 * q^57 + 46 * q^58 - 20 * q^59 + 59 * q^61 + 73 * q^62 + 41 * q^63 + 54 * q^64 - 43 * q^66 - 15 * q^67 + 20 * q^68 + 38 * q^69 - 26 * q^71 + 2 * q^72 - 8 * q^73 + 2 * q^74 + 38 * q^76 + 33 * q^79 + 29 * q^81 - 10 * q^82 + 63 * q^84 + 11 * q^86 + 11 * q^87 - 27 * q^88 + 11 * q^89 - 2 * q^91 - 28 * q^92 - 28 * q^93 + 29 * q^94 - 17 * q^96 + 10 * q^97 - 22 * q^98 - 36 * q^99

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