LMFDB - Embedded newform 1911.2.a.v.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1911,2,Mod(1,1911)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1911, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1911.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1911 = 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1911.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:	$15.2594118263$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.2196544.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 6x^{3} + 10x^{2} + 7x - 8 $ x^5 - 2x^4 - 6x^3 + 10x^2 + 7x - 8
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.10811$ of defining polynomial
Character	$\chi$	$=$	1911.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.10811 q^{2} -1.00000 q^{3} -0.772089 q^{4} -2.82337 q^{5} +1.10811 q^{6} +3.07178 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.10811 q^{2} -1.00000 q^{3} -0.772089 q^{4} -2.82337 q^{5} +1.10811 q^{6} +3.07178 q^{8} +1.00000 q^{9} +3.12861 q^{10} +5.50785 q^{11} +0.772089 q^{12} -1.00000 q^{13} +2.82337 q^{15} -1.85970 q^{16} -5.68775 q^{17} -1.10811 q^{18} -2.85970 q^{19} +2.17990 q^{20} -6.10331 q^{22} -4.90070 q^{23} -3.07178 q^{24} +2.97143 q^{25} +1.10811 q^{26} -1.00000 q^{27} +7.57275 q^{29} -3.12861 q^{30} +6.33122 q^{31} -4.08281 q^{32} -5.50785 q^{33} +6.30266 q^{34} -0.772089 q^{36} -9.90397 q^{37} +3.16887 q^{38} +1.00000 q^{39} -8.67279 q^{40} -11.0520 q^{41} -2.78704 q^{43} -4.25255 q^{44} -2.82337 q^{45} +5.43052 q^{46} +7.69551 q^{47} +1.85970 q^{48} -3.29268 q^{50} +5.68775 q^{51} +0.772089 q^{52} -5.21949 q^{53} +1.10811 q^{54} -15.5507 q^{55} +2.85970 q^{57} -8.39145 q^{58} +3.39419 q^{59} -2.17990 q^{60} -2.43245 q^{61} -7.01570 q^{62} +8.24361 q^{64} +2.82337 q^{65} +6.10331 q^{66} -5.19092 q^{67} +4.39145 q^{68} +4.90070 q^{69} +11.5870 q^{71} +3.07178 q^{72} -6.68448 q^{73} +10.9747 q^{74} -2.97143 q^{75} +2.20794 q^{76} -1.10811 q^{78} -6.43379 q^{79} +5.25063 q^{80} +1.00000 q^{81} +12.2469 q^{82} +16.0553 q^{83} +16.0586 q^{85} +3.08836 q^{86} -7.57275 q^{87} +16.9189 q^{88} +15.2558 q^{89} +3.12861 q^{90} +3.78378 q^{92} -6.33122 q^{93} -8.52748 q^{94} +8.07400 q^{95} +4.08281 q^{96} -6.13113 q^{97} +5.50785 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{2} - 5 q^{3} + 6 q^{4} - 3 q^{5} - 2 q^{6} + 6 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 2 * q^2 - 5 * q^3 + 6 * q^4 - 3 * q^5 - 2 * q^6 + 6 * q^8 + 5 * q^9	$ 5 q + 2 q^{2} - 5 q^{3} + 6 q^{4} - 3 q^{5} - 2 q^{6} + 6 q^{8} + 5 q^{9} + 6 q^{11} - 6 q^{12} - 5 q^{13} + 3 q^{15} + 10 q^{17} + 2 q^{18} - 5 q^{19} - 6 q^{20} + 12 q^{22} + q^{23} - 6 q^{24} + 16 q^{25} - 2 q^{26} - 5 q^{27} + 17 q^{29} - q^{31} + 14 q^{32} - 6 q^{33} + 6 q^{36} + 4 q^{37} + 24 q^{38} + 5 q^{39} - 8 q^{40} - 14 q^{41} - q^{43} - 8 q^{44} - 3 q^{45} + 20 q^{46} + 3 q^{47} + 26 q^{50} - 10 q^{51} - 6 q^{52} + 17 q^{53} - 2 q^{54} - 2 q^{55} + 5 q^{57} - 28 q^{58} + 8 q^{59} + 6 q^{60} + 18 q^{61} + 8 q^{62} + 8 q^{64} + 3 q^{65} - 12 q^{66} + 16 q^{67} + 8 q^{68} - q^{69} - 16 q^{71} + 6 q^{72} - 23 q^{73} + 28 q^{74} - 16 q^{75} + 26 q^{76} + 2 q^{78} + 3 q^{79} + 36 q^{80} + 5 q^{81} + 11 q^{83} - 2 q^{85} - 24 q^{86} - 17 q^{87} + 28 q^{88} + 35 q^{89} + 34 q^{92} + q^{93} + 39 q^{95} - 14 q^{96} - 27 q^{97} + 6 q^{99}+O(q^{100}) $ 5 * q + 2 * q^2 - 5 * q^3 + 6 * q^4 - 3 * q^5 - 2 * q^6 + 6 * q^8 + 5 * q^9 + 6 * q^11 - 6 * q^12 - 5 * q^13 + 3 * q^15 + 10 * q^17 + 2 * q^18 - 5 * q^19 - 6 * q^20 + 12 * q^22 + q^23 - 6 * q^24 + 16 * q^25 - 2 * q^26 - 5 * q^27 + 17 * q^29 - q^31 + 14 * q^32 - 6 * q^33 + 6 * q^36 + 4 * q^37 + 24 * q^38 + 5 * q^39 - 8 * q^40 - 14 * q^41 - q^43 - 8 * q^44 - 3 * q^45 + 20 * q^46 + 3 * q^47 + 26 * q^50 - 10 * q^51 - 6 * q^52 + 17 * q^53 - 2 * q^54 - 2 * q^55 + 5 * q^57 - 28 * q^58 + 8 * q^59 + 6 * q^60 + 18 * q^61 + 8 * q^62 + 8 * q^64 + 3 * q^65 - 12 * q^66 + 16 * q^67 + 8 * q^68 - q^69 - 16 * q^71 + 6 * q^72 - 23 * q^73 + 28 * q^74 - 16 * q^75 + 26 * q^76 + 2 * q^78 + 3 * q^79 + 36 * q^80 + 5 * q^81 + 11 * q^83 - 2 * q^85 - 24 * q^86 - 17 * q^87 + 28 * q^88 + 35 * q^89 + 34 * q^92 + q^93 + 39 * q^95 - 14 * q^96 - 27 * q^97 + 6 * 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 $

$2$	−1.10811	−0.783553	−0.391777	−	0.920060i	$-0.628139\pi$
$2$	−1.10811	−0.783553	−0.391777	+	0.920060i	$0.628139\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.772089	−0.386045
$5$	−2.82337	−1.26265	−0.631325	−	0.775518i	$-0.717489\pi$
$5$	−2.82337	−1.26265	−0.631325	+	0.775518i	$0.717489\pi$
$6$	1.10811	0.452385
$7$	0	0
$7$	0	0
$8$	3.07178	1.08604
$9$	1.00000	0.333333
$10$	3.12861	0.989354
$11$	5.50785	1.66068	0.830340	−	0.557258i	$-0.188146\pi$
$11$	5.50785	1.66068	0.830340	+	0.557258i	$0.188146\pi$
$12$	0.772089	0.222883
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	2.82337	0.728992
$16$	−1.85970	−0.464925
$17$	−5.68775	−1.37948	−0.689740	−	0.724057i	$-0.742275\pi$
$17$	−5.68775	−1.37948	−0.689740	+	0.724057i	$0.742275\pi$
$18$	−1.10811	−0.261184
$19$	−2.85970	−0.656060	−0.328030	−	0.944667i	$-0.606385\pi$
$19$	−2.85970	−0.656060	−0.328030	+	0.944667i	$0.606385\pi$
$20$	2.17990	0.487439
$21$	0	0
$22$	−6.10331	−1.30123
$23$	−4.90070	−1.02187	−0.510933	−	0.859620i	$-0.670700\pi$
$23$	−4.90070	−1.02187	−0.510933	+	0.859620i	$0.670700\pi$
$24$	−3.07178	−0.627025
$25$	2.97143	0.594287
$26$	1.10811	0.217319
$27$	−1.00000	−0.192450
$28$	0	0
$29$	7.57275	1.40622	0.703112	−	0.711079i	$-0.251793\pi$
$29$	7.57275	1.40622	0.703112	+	0.711079i	$0.251793\pi$
$30$	−3.12861	−0.571204
$31$	6.33122	1.13712	0.568561	−	0.822641i	$-0.307500\pi$
$31$	6.33122	1.13712	0.568561	+	0.822641i	$0.307500\pi$
$32$	−4.08281	−0.721746
$33$	−5.50785	−0.958794
$34$	6.30266	1.08090
$35$	0	0
$36$	−0.772089	−0.128682
$37$	−9.90397	−1.62820	−0.814101	−	0.580723i	$-0.802770\pi$
$37$	−9.90397	−1.62820	−0.814101	+	0.580723i	$0.802770\pi$
$38$	3.16887	0.514058
$39$	1.00000	0.160128
$40$	−8.67279	−1.37129
$41$	−11.0520	−1.72604	−0.863018	−	0.505172i	$-0.831429\pi$
$41$	−11.0520	−1.72604	−0.863018	+	0.505172i	$0.831429\pi$
$42$	0	0
$43$	−2.78704	−0.425020	−0.212510	−	0.977159i	$-0.568164\pi$
$43$	−2.78704	−0.425020	−0.212510	+	0.977159i	$0.568164\pi$
$44$	−4.25255	−0.641096
$45$	−2.82337	−0.420884
$46$	5.43052	0.800687
$47$	7.69551	1.12250	0.561252	−	0.827645i	$-0.310320\pi$
$47$	7.69551	1.12250	0.561252	+	0.827645i	$0.310320\pi$
$48$	1.85970	0.268425
$49$	0	0
$50$	−3.29268	−0.465655
$51$	5.68775	0.796444
$52$	0.772089	0.107069
$53$	−5.21949	−0.716952	−0.358476	−	0.933539i	$-0.616704\pi$
$53$	−5.21949	−0.716952	−0.358476	+	0.933539i	$0.616704\pi$
$54$	1.10811	0.150795
$55$	−15.5507	−2.09686
$56$	0	0
$57$	2.85970	0.378777
$58$	−8.39145	−1.10185
$59$	3.39419	0.441886	0.220943	−	0.975287i	$-0.429086\pi$
$59$	3.39419	0.441886	0.220943	+	0.975287i	$0.429086\pi$
$60$	−2.17990	−0.281423
$61$	−2.43245	−0.311443	−0.155721	−	0.987801i	$-0.549770\pi$
$61$	−2.43245	−0.311443	−0.155721	+	0.987801i	$0.549770\pi$
$62$	−7.01570	−0.890995
$63$	0	0
$64$	8.24361	1.03045
$65$	2.82337	0.350196
$66$	6.10331	0.751266
$67$	−5.19092	−0.634172	−0.317086	−	0.948397i	$-0.602704\pi$
$67$	−5.19092	−0.634172	−0.317086	+	0.948397i	$0.602704\pi$
$68$	4.39145	0.532541
$69$	4.90070	0.589975
$70$	0	0
$71$	11.5870	1.37513	0.687564	−	0.726123i	$-0.258680\pi$
$71$	11.5870	1.37513	0.687564	+	0.726123i	$0.258680\pi$
$72$	3.07178	0.362013
$73$	−6.68448	−0.782359	−0.391179	−	0.920314i	$-0.627933\pi$
$73$	−6.68448	−0.782359	−0.391179	+	0.920314i	$0.627933\pi$
$74$	10.9747	1.27578
$75$	−2.97143	−0.343112
$76$	2.20794	0.253268
$77$	0	0
$78$	−1.10811	−0.125469
$79$	−6.43379	−0.723858	−0.361929	−	0.932206i	$-0.617882\pi$
$79$	−6.43379	−0.723858	−0.361929	+	0.932206i	$0.617882\pi$
$80$	5.25063	0.587038
$81$	1.00000	0.111111
$82$	12.2469	1.35244
$83$	16.0553	1.76230	0.881149	−	0.472839i	$-0.156771\pi$
$83$	16.0553	1.76230	0.881149	+	0.472839i	$0.156771\pi$
$84$	0	0
$85$	16.0586	1.74180
$86$	3.08836	0.333026
$87$	−7.57275	−0.811884
$88$	16.9189	1.80356
$89$	15.2558	1.61711	0.808557	−	0.588418i	$-0.200249\pi$
$89$	15.2558	1.61711	0.808557	+	0.588418i	$0.200249\pi$
$90$	3.12861	0.329785
$91$	0	0
$92$	3.78378	0.394486
$93$	−6.33122	−0.656517
$94$	−8.52748	−0.879542
$95$	8.07400	0.828375
$96$	4.08281	0.416700
$97$	−6.13113	−0.622522	−0.311261	−	0.950324i	$-0.600751\pi$
$97$	−6.13113	−0.622522	−0.311261	+	0.950324i	$0.600751\pi$
$98$	0	0
$99$	5.50785	0.553560
$100$	−2.29421	−0.229421
$101$	5.32796	0.530151	0.265076	−	0.964228i	$-0.414603\pi$
$101$	5.32796	0.530151	0.265076	+	0.964228i	$0.414603\pi$
$102$	−6.30266	−0.624056
$103$	1.54418	0.152152	0.0760762	−	0.997102i	$-0.475761\pi$
$103$	1.54418	0.152152	0.0760762	+	0.997102i	$0.475761\pi$
$104$	−3.07178	−0.301213
$105$	0	0
$106$	5.78378	0.561770
$107$	14.7761	1.42846	0.714230	−	0.699911i	$-0.246777\pi$
$107$	14.7761	1.42846	0.714230	+	0.699911i	$0.246777\pi$
$108$	0.772089	0.0742943
$109$	8.78570	0.841517	0.420759	−	0.907173i	$-0.361764\pi$
$109$	8.78570	0.841517	0.420759	+	0.907173i	$0.361764\pi$
$110$	17.2319	1.64300
$111$	9.90397	0.940043
$112$	0	0
$113$	3.51561	0.330721	0.165360	−	0.986233i	$-0.447121\pi$
$113$	3.51561	0.330721	0.165360	+	0.986233i	$0.447121\pi$
$114$	−3.16887	−0.296792
$115$	13.8365	1.29026
$116$	−5.84683	−0.542865
$117$	−1.00000	−0.0924500
$118$	−3.76115	−0.346242
$119$	0	0
$120$	8.67279	0.791714
$121$	19.3364	1.75786
$122$	2.69542	0.244032
$123$	11.0520	0.996528
$124$	−4.88827	−0.438979
$125$	5.72740	0.512274
$126$	0	0
$127$	−15.7287	−1.39570	−0.697850	−	0.716244i	$-0.745860\pi$
$127$	−15.7287	−1.39570	−0.697850	+	0.716244i	$0.745860\pi$
$128$	−0.969216	−0.0856674
$129$	2.78704	0.245386
$130$	−3.12861	−0.274397
$131$	−0.302656	−0.0264431	−0.0132216	−	0.999913i	$-0.504209\pi$
$131$	−0.302656	−0.0264431	−0.0132216	+	0.999913i	$0.504209\pi$
$132$	4.25255	0.370137
$133$	0	0
$134$	5.75212	0.496908
$135$	2.82337	0.242997
$136$	−17.4715	−1.49817
$137$	−0.733238	−0.0626448	−0.0313224	−	0.999509i	$-0.509972\pi$
$137$	−0.733238	−0.0626448	−0.0313224	+	0.999509i	$0.509972\pi$
$138$	−5.43052	−0.462277
$139$	−6.91313	−0.586364	−0.293182	−	0.956057i	$-0.594714\pi$
$139$	−6.91313	−0.586364	−0.293182	+	0.956057i	$0.594714\pi$
$140$	0	0
$141$	−7.69551	−0.648079
$142$	−12.8397	−1.07749
$143$	−5.50785	−0.460590
$144$	−1.85970	−0.154975
$145$	−21.3807	−1.77557
$146$	7.40715	0.613020
$147$	0	0
$148$	7.64675	0.628559
$149$	−21.6008	−1.76961	−0.884804	−	0.465963i	$-0.845708\pi$
$149$	−21.6008	−1.76961	−0.884804	+	0.465963i	$0.845708\pi$
$150$	3.29268	0.268846
$151$	5.82478	0.474014	0.237007	−	0.971508i	$-0.423834\pi$
$151$	5.82478	0.474014	0.237007	+	0.971508i	$0.423834\pi$
$152$	−8.78438	−0.712507
$153$	−5.68775	−0.459827
$154$	0	0
$155$	−17.8754	−1.43579
$156$	−0.772089	−0.0618166
$157$	−5.57409	−0.444861	−0.222430	−	0.974949i	$-0.571399\pi$
$157$	−5.57409	−0.444861	−0.222430	+	0.974949i	$0.571399\pi$
$158$	7.12936	0.567181
$159$	5.21949	0.413933
$160$	11.5273	0.911313
$161$	0	0
$162$	−1.10811	−0.0870615
$163$	22.3663	1.75187	0.875933	−	0.482433i	$-0.160247\pi$
$163$	22.3663	1.75187	0.875933	+	0.482433i	$0.160247\pi$
$164$	8.53315	0.666327
$165$	15.5507	1.21062
$166$	−17.7911	−1.38085
$167$	3.16554	0.244957	0.122478	−	0.992471i	$-0.460916\pi$
$167$	3.16554	0.244957	0.122478	+	0.992471i	$0.460916\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−17.7947	−1.36479
$171$	−2.85970	−0.218687
$172$	2.15185	0.164077
$173$	12.0410	0.915460	0.457730	−	0.889091i	$-0.348663\pi$
$173$	12.0410	0.915460	0.457730	+	0.889091i	$0.348663\pi$
$174$	8.39145	0.636154
$175$	0	0
$176$	−10.2430	−0.772092
$177$	−3.39419	−0.255123
$178$	−16.9051	−1.26709
$179$	6.26031	0.467918	0.233959	−	0.972247i	$-0.424832\pi$
$179$	6.26031	0.467918	0.233959	+	0.972247i	$0.424832\pi$
$180$	2.17990	0.162480
$181$	4.23000	0.314413	0.157207	−	0.987566i	$-0.449751\pi$
$181$	4.23000	0.314413	0.157207	+	0.987566i	$0.449751\pi$
$182$	0	0
$183$	2.43245	0.179812
$184$	−15.0539	−1.10979
$185$	27.9626	2.05585
$186$	7.01570	0.514416
$187$	−31.3272	−2.29088
$188$	−5.94162	−0.433337
$189$	0	0
$190$	−8.94689	−0.649076
$191$	16.3980	1.18652	0.593258	−	0.805012i	$-0.297841\pi$
$191$	16.3980	1.18652	0.593258	+	0.805012i	$0.297841\pi$
$192$	−8.24361	−0.594931
$193$	9.90397	0.712903	0.356452	−	0.934314i	$-0.383986\pi$
$193$	9.90397	0.712903	0.356452	+	0.934314i	$0.383986\pi$
$194$	6.79398	0.487779
$195$	−2.82337	−0.202186
$196$	0	0
$197$	3.64207	0.259487	0.129743	−	0.991548i	$-0.458585\pi$
$197$	3.64207	0.259487	0.129743	+	0.991548i	$0.458585\pi$
$198$	−6.10331	−0.433743
$199$	2.85836	0.202624	0.101312	−	0.994855i	$-0.467696\pi$
$199$	2.85836	0.202624	0.101312	+	0.994855i	$0.467696\pi$
$200$	9.12760	0.645419
$201$	5.19092	0.366139
$202$	−5.90397	−0.415402
$203$	0	0
$204$	−4.39145	−0.307463
$205$	31.2040	2.17938
$206$	−1.71112	−0.119219
$207$	−4.90070	−0.340622
$208$	1.85970	0.128947
$209$	−15.7508	−1.08951
$210$	0	0
$211$	9.29215	0.639698	0.319849	−	0.947469i	$-0.396368\pi$
$211$	9.29215	0.639698	0.319849	+	0.947469i	$0.396368\pi$
$212$	4.02991	0.276775
$213$	−11.5870	−0.793931
$214$	−16.3736	−1.11927
$215$	7.86887	0.536652
$216$	−3.07178	−0.209008
$217$	0	0
$218$	−9.73554	−0.659374
$219$	6.68448	0.451695
$220$	12.0065	0.809480
$221$	5.68775	0.382599
$222$	−10.9747	−0.736574
$223$	18.6676	1.25008	0.625039	−	0.780594i	$-0.285083\pi$
$223$	18.6676	1.25008	0.625039	+	0.780594i	$0.285083\pi$
$224$	0	0
$225$	2.97143	0.198096
$226$	−3.89569	−0.259137
$227$	−24.3411	−1.61557	−0.807787	−	0.589474i	$-0.799335\pi$
$227$	−24.3411	−1.61557	−0.807787	+	0.589474i	$0.799335\pi$
$228$	−2.20794	−0.146225
$229$	14.5664	0.962576	0.481288	−	0.876563i	$-0.340169\pi$
$229$	14.5664	0.962576	0.481288	+	0.876563i	$0.340169\pi$
$230$	−15.3324	−1.01099
$231$	0	0
$232$	23.2618	1.52721
$233$	7.14030	0.467777	0.233888	−	0.972263i	$-0.424855\pi$
$233$	7.14030	0.467777	0.233888	+	0.972263i	$0.424855\pi$
$234$	1.10811	0.0724395
$235$	−21.7273	−1.41733
$236$	−2.62062	−0.170588
$237$	6.43379	0.417920
$238$	0	0
$239$	−8.44155	−0.546039	−0.273019	−	0.962009i	$-0.588022\pi$
$239$	−8.44155	−0.546039	−0.273019	+	0.962009i	$0.588022\pi$
$240$	−5.25063	−0.338927
$241$	−17.0663	−1.09934	−0.549669	−	0.835382i	$-0.685246\pi$
$241$	−17.0663	−1.09934	−0.549669	+	0.835382i	$0.685246\pi$
$242$	−21.4269	−1.37737
$243$	−1.00000	−0.0641500
$244$	1.87806	0.120231
$245$	0	0
$246$	−12.2469	−0.780832
$247$	2.85970	0.181958
$248$	19.4481	1.23496
$249$	−16.0553	−1.01746
$250$	−6.34660	−0.401394
$251$	−7.07283	−0.446433	−0.223217	−	0.974769i	$-0.571656\pi$
$251$	−7.07283	−0.446433	−0.223217	+	0.974769i	$0.571656\pi$
$252$	0	0
$253$	−26.9923	−1.69699
$254$	17.4292	1.09361
$255$	−16.0586	−1.00563
$256$	−15.4132	−0.963326
$257$	22.8304	1.42412	0.712061	−	0.702117i	$-0.247762\pi$
$257$	22.8304	1.42412	0.712061	+	0.702117i	$0.247762\pi$
$258$	−3.08836	−0.192273
$259$	0	0
$260$	−2.17990	−0.135191
$261$	7.57275	0.468741
$262$	0.335376	0.0207196
$263$	17.5383	1.08146	0.540728	−	0.841197i	$-0.318149\pi$
$263$	17.5383	1.08146	0.540728	+	0.841197i	$0.318149\pi$
$264$	−16.9189	−1.04129
$265$	14.7366	0.905260
$266$	0	0
$267$	−15.2558	−0.933641
$268$	4.00785	0.244819
$269$	−11.3096	−0.689560	−0.344780	−	0.938684i	$-0.612046\pi$
$269$	−11.3096	−0.689560	−0.344780	+	0.938684i	$0.612046\pi$
$270$	−3.12861	−0.190401
$271$	−10.5027	−0.637996	−0.318998	−	0.947755i	$-0.603346\pi$
$271$	−10.5027	−0.637996	−0.318998	+	0.947755i	$0.603346\pi$
$272$	10.5775	0.641355
$273$	0	0
$274$	0.812510	0.0490855
$275$	16.3662	0.986919
$276$	−3.78378	−0.227757
$277$	−23.9574	−1.43946	−0.719730	−	0.694254i	$-0.755735\pi$
$277$	−23.9574	−1.43946	−0.719730	+	0.694254i	$0.755735\pi$
$278$	7.66052	0.459448
$279$	6.33122	0.379040
$280$	0	0
$281$	3.06163	0.182641	0.0913207	−	0.995822i	$-0.470891\pi$
$281$	3.06163	0.182641	0.0913207	+	0.995822i	$0.470891\pi$
$282$	8.52748	0.507804
$283$	22.8143	1.35617	0.678084	−	0.734984i	$-0.262810\pi$
$283$	22.8143	1.35617	0.678084	+	0.734984i	$0.262810\pi$
$284$	−8.94623	−0.530861
$285$	−8.07400	−0.478262
$286$	6.10331	0.360896
$287$	0	0
$288$	−4.08281	−0.240582
$289$	15.3504	0.902967
$290$	23.6922	1.39125
$291$	6.13113	0.359413
$292$	5.16101	0.302025
$293$	−11.9623	−0.698847	−0.349423	−	0.936965i	$-0.613622\pi$
$293$	−11.9623	−0.698847	−0.349423	+	0.936965i	$0.613622\pi$
$294$	0	0
$295$	−9.58308	−0.557948
$296$	−30.4228	−1.76829
$297$	−5.50785	−0.319598
$298$	23.9361	1.38658
$299$	4.90070	0.283415
$300$	2.29421	0.132456
$301$	0	0
$302$	−6.45450	−0.371415
$303$	−5.32796	−0.306083
$304$	5.31819	0.305019
$305$	6.86770	0.393243
$306$	6.30266	0.360299
$307$	3.56994	0.203747	0.101874	−	0.994797i	$-0.467516\pi$
$307$	3.56994	0.203747	0.101874	+	0.994797i	$0.467516\pi$
$308$	0	0
$309$	−1.54418	−0.0878452
$310$	19.8079	1.12502
$311$	31.1741	1.76772	0.883860	−	0.467752i	$-0.154936\pi$
$311$	31.1741	1.76772	0.883860	+	0.467752i	$0.154936\pi$
$312$	3.07178	0.173905
$313$	28.6690	1.62047	0.810233	−	0.586107i	$-0.199340\pi$
$313$	28.6690	1.62047	0.810233	+	0.586107i	$0.199340\pi$
$314$	6.17671	0.348572
$315$	0	0
$316$	4.96746	0.279441
$317$	0.203271	0.0114168	0.00570842	−	0.999984i	$-0.498183\pi$
$317$	0.203271	0.0114168	0.00570842	+	0.999984i	$0.498183\pi$
$318$	−5.78378	−0.324338
$319$	41.7095	2.33529
$320$	−23.2748	−1.30110
$321$	−14.7761	−0.824722
$322$	0	0
$323$	16.2652	0.905023
$324$	−0.772089	−0.0428938
$325$	−2.97143	−0.164825
$326$	−24.7844	−1.37268
$327$	−8.78570	−0.485850
$328$	−33.9494	−1.87454
$329$	0	0
$330$	−17.2319	−0.948586
$331$	−7.35062	−0.404027	−0.202013	−	0.979383i	$-0.564748\pi$
$331$	−7.35062	−0.404027	−0.202013	+	0.979383i	$0.564748\pi$
$332$	−12.3961	−0.680325
$333$	−9.90397	−0.542734
$334$	−3.50777	−0.191937
$335$	14.6559	0.800738
$336$	0	0
$337$	7.54552	0.411031	0.205515	−	0.978654i	$-0.434113\pi$
$337$	7.54552	0.411031	0.205515	+	0.978654i	$0.434113\pi$
$338$	−1.10811	−0.0602733
$339$	−3.51561	−0.190942
$340$	−12.3987	−0.672413
$341$	34.8714	1.88839
$342$	3.16887	0.171353
$343$	0	0
$344$	−8.56120	−0.461589
$345$	−13.8365	−0.744932
$346$	−13.3428	−0.717312
$347$	4.95918	0.266223	0.133111	−	0.991101i	$-0.457503\pi$
$347$	4.95918	0.266223	0.133111	+	0.991101i	$0.457503\pi$
$348$	5.84683	0.313423
$349$	−31.3235	−1.67671	−0.838356	−	0.545124i	$-0.816483\pi$
$349$	−31.3235	−1.67671	−0.838356	+	0.545124i	$0.816483\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	−22.4875	−1.19859
$353$	−36.7092	−1.95383	−0.976916	−	0.213626i	$-0.931473\pi$
$353$	−36.7092	−1.95383	−0.976916	+	0.213626i	$0.931473\pi$
$354$	3.76115	0.199903
$355$	−32.7145	−1.73631
$356$	−11.7789	−0.624278
$357$	0	0
$358$	−6.93712	−0.366638
$359$	−15.8170	−0.834791	−0.417396	−	0.908725i	$-0.637057\pi$
$359$	−15.8170	−0.834791	−0.417396	+	0.908725i	$0.637057\pi$
$360$	−8.67279	−0.457096
$361$	−10.8221	−0.569585
$362$	−4.68731	−0.246360
$363$	−19.3364	−1.01490
$364$	0	0
$365$	18.8728	0.987846
$366$	−2.69542	−0.140892
$367$	25.4752	1.32980	0.664899	−	0.746934i	$-0.268475\pi$
$367$	25.4752	1.32980	0.664899	+	0.746934i	$0.268475\pi$
$368$	9.11383	0.475091
$369$	−11.0520	−0.575346
$370$	−30.9857	−1.61087
$371$	0	0
$372$	4.88827	0.253445
$373$	24.3364	1.26009	0.630046	−	0.776558i	$-0.283036\pi$
$373$	24.3364	1.26009	0.630046	+	0.776558i	$0.283036\pi$
$374$	34.7141	1.79502
$375$	−5.72740	−0.295762
$376$	23.6389	1.21908
$377$	−7.57275	−0.390016
$378$	0	0
$379$	1.97278	0.101335	0.0506674	−	0.998716i	$-0.483865\pi$
$379$	1.97278	0.101335	0.0506674	+	0.998716i	$0.483865\pi$
$380$	−6.23385	−0.319790
$381$	15.7287	0.805808
$382$	−18.1708	−0.929699
$383$	4.95625	0.253253	0.126626	−	0.991950i	$-0.459585\pi$
$383$	4.95625	0.253253	0.126626	+	0.991950i	$0.459585\pi$
$384$	0.969216	0.0494601
$385$	0	0
$386$	−10.9747	−0.558598
$387$	−2.78704	−0.141673
$388$	4.73378	0.240321
$389$	8.42860	0.427347	0.213673	−	0.976905i	$-0.431457\pi$
$389$	8.42860	0.427347	0.213673	+	0.976905i	$0.431457\pi$
$390$	3.12861	0.158423
$391$	27.8739	1.40965
$392$	0	0
$393$	0.302656	0.0152670
$394$	−4.03582	−0.203322
$395$	18.1650	0.913980
$396$	−4.25255	−0.213699
$397$	1.24287	0.0623777	0.0311888	−	0.999514i	$-0.490071\pi$
$397$	1.24287	0.0623777	0.0311888	+	0.999514i	$0.490071\pi$
$398$	−3.16738	−0.158766
$399$	0	0
$400$	−5.52597	−0.276299
$401$	23.8061	1.18882	0.594409	−	0.804163i	$-0.297386\pi$
$401$	23.8061	1.18882	0.594409	+	0.804163i	$0.297386\pi$
$402$	−5.75212	−0.286890
$403$	−6.33122	−0.315381
$404$	−4.11366	−0.204662
$405$	−2.82337	−0.140295
$406$	0	0
$407$	−54.5496	−2.70392
$408$	17.4715	0.864969
$409$	38.6015	1.90872	0.954361	−	0.298655i	$-0.0965381\pi$
$409$	38.6015	1.90872	0.954361	+	0.298655i	$0.0965381\pi$
$410$	−34.5775	−1.70766
$411$	0.733238	0.0361680
$412$	−1.19224	−0.0587376
$413$	0	0
$414$	5.43052	0.266896
$415$	−45.3301	−2.22517
$416$	4.08281	0.200176
$417$	6.91313	0.338538
$418$	17.4536	0.853686
$419$	27.2457	1.33104	0.665520	−	0.746380i	$-0.268210\pi$
$419$	27.2457	1.33104	0.665520	+	0.746380i	$0.268210\pi$
$420$	0	0
$421$	12.6897	0.618457	0.309228	−	0.950988i	$-0.399929\pi$
$421$	12.6897	0.618457	0.309228	+	0.950988i	$0.399929\pi$
$422$	−10.2967	−0.501237
$423$	7.69551	0.374168
$424$	−16.0331	−0.778638
$425$	−16.9008	−0.819807
$426$	12.8397	0.622087
$427$	0	0
$428$	−11.4085	−0.551449
$429$	5.50785	0.265922
$430$	−8.71958	−0.420495
$431$	−31.0197	−1.49416	−0.747082	−	0.664731i	$-0.768546\pi$
$431$	−31.0197	−1.49416	−0.747082	+	0.664731i	$0.768546\pi$
$432$	1.85970	0.0894749
$433$	16.4141	0.788812	0.394406	−	0.918936i	$-0.370950\pi$
$433$	16.4141	0.788812	0.394406	+	0.918936i	$0.370950\pi$
$434$	0	0
$435$	21.3807	1.02513
$436$	−6.78334	−0.324863
$437$	14.0145	0.670406
$438$	−7.40715	−0.353927
$439$	12.4156	0.592564	0.296282	−	0.955100i	$-0.404253\pi$
$439$	12.4156	0.592564	0.296282	+	0.955100i	$0.404253\pi$
$440$	−47.7684	−2.27727
$441$	0	0
$442$	−6.30266	−0.299787
$443$	16.4242	0.780337	0.390168	−	0.920744i	$-0.372417\pi$
$443$	16.4242	0.780337	0.390168	+	0.920744i	$0.372417\pi$
$444$	−7.64675	−0.362898
$445$	−43.0729	−2.04185
$446$	−20.6858	−0.979502
$447$	21.6008	1.02168
$448$	0	0
$449$	−14.9671	−0.706340	−0.353170	−	0.935559i	$-0.614896\pi$
$449$	−14.9671	−0.706340	−0.353170	+	0.935559i	$0.614896\pi$
$450$	−3.29268	−0.155218
$451$	−60.8729	−2.86639
$452$	−2.71436	−0.127673
$453$	−5.82478	−0.273672
$454$	26.9726	1.26589
$455$	0	0
$456$	8.78438	0.411366
$457$	19.5263	0.913402	0.456701	−	0.889620i	$-0.349031\pi$
$457$	19.5263	0.913402	0.456701	+	0.889620i	$0.349031\pi$
$458$	−16.1412	−0.754229
$459$	5.68775	0.265481
$460$	−10.6830	−0.498098
$461$	−10.7649	−0.501371	−0.250686	−	0.968069i	$-0.580656\pi$
$461$	−10.7649	−0.501371	−0.250686	+	0.968069i	$0.580656\pi$
$462$	0	0
$463$	−14.3077	−0.664935	−0.332468	−	0.943115i	$-0.607881\pi$
$463$	−14.3077	−0.664935	−0.332468	+	0.943115i	$0.607881\pi$
$464$	−14.0830	−0.653789
$465$	17.8754	0.828952
$466$	−7.91225	−0.366528
$467$	29.0471	1.34414	0.672070	−	0.740488i	$-0.265405\pi$
$467$	29.0471	1.34414	0.672070	+	0.740488i	$0.265405\pi$
$468$	0.772089	0.0356898
$469$	0	0
$470$	24.0762	1.11055
$471$	5.57409	0.256840
$472$	10.4262	0.479906
$473$	−15.3506	−0.705822
$474$	−7.12936	−0.327462
$475$	−8.49741	−0.389888
$476$	0	0
$477$	−5.21949	−0.238984
$478$	9.35418	0.427850
$479$	7.20079	0.329012	0.164506	−	0.986376i	$-0.447397\pi$
$479$	7.20079	0.329012	0.164506	+	0.986376i	$0.447397\pi$
$480$	−11.5273	−0.526147
$481$	9.90397	0.451582
$482$	18.9114	0.861390
$483$	0	0
$484$	−14.9294	−0.678611
$485$	17.3105	0.786028
$486$	1.10811	0.0502650
$487$	6.23236	0.282415	0.141208	−	0.989980i	$-0.454902\pi$
$487$	6.23236	0.282415	0.141208	+	0.989980i	$0.454902\pi$
$488$	−7.47195	−0.338239
$489$	−22.3663	−1.01144
$490$	0	0
$491$	11.4957	0.518793	0.259396	−	0.965771i	$-0.416476\pi$
$491$	11.4957	0.518793	0.259396	+	0.965771i	$0.416476\pi$
$492$	−8.53315	−0.384704
$493$	−43.0718	−1.93986
$494$	−3.16887	−0.142574
$495$	−15.5507	−0.698953
$496$	−11.7742	−0.528676
$497$	0	0
$498$	17.7911	0.797236
$499$	−11.3506	−0.508124	−0.254062	−	0.967188i	$-0.581767\pi$
$499$	−11.3506	−0.508124	−0.254062	+	0.967188i	$0.581767\pi$
$500$	−4.42206	−0.197761
$501$	−3.16554	−0.141426
$502$	7.83749	0.349804
$503$	19.0728	0.850416	0.425208	−	0.905096i	$-0.360201\pi$
$503$	19.0728	0.850416	0.425208	+	0.905096i	$0.360201\pi$
$504$	0	0
$505$	−15.0428	−0.669396
$506$	29.9105	1.32968
$507$	−1.00000	−0.0444116
$508$	12.1440	0.538803
$509$	7.91454	0.350806	0.175403	−	0.984497i	$-0.443877\pi$
$509$	7.91454	0.350806	0.175403	+	0.984497i	$0.443877\pi$
$510$	17.7947	0.787965
$511$	0	0
$512$	19.0180	0.840485
$513$	2.85970	0.126259
$514$	−25.2987	−1.11588
$515$	−4.35979	−0.192115
$516$	−2.15185	−0.0947298
$517$	42.3857	1.86412
$518$	0	0
$519$	−12.0410	−0.528541
$520$	8.67279	0.380327
$521$	26.3408	1.15401	0.577007	−	0.816739i	$-0.304221\pi$
$521$	26.3408	1.15401	0.577007	+	0.816739i	$0.304221\pi$
$522$	−8.39145	−0.367284
$523$	−5.54687	−0.242548	−0.121274	−	0.992619i	$-0.538698\pi$
$523$	−5.54687	−0.242548	−0.121274	+	0.992619i	$0.538698\pi$
$524$	0.233677	0.0102082
$525$	0	0
$526$	−19.4344	−0.847379
$527$	−36.0104	−1.56864
$528$	10.2430	0.445767
$529$	1.01687	0.0442115
$530$	−16.3298	−0.709319
$531$	3.39419	0.147295
$532$	0	0
$533$	11.0520	0.478716
$534$	16.9051	0.731557
$535$	−41.7184	−1.80365
$536$	−15.9454	−0.688736
$537$	−6.26031	−0.270152
$538$	12.5323	0.540307
$539$	0	0
$540$	−2.17990	−0.0938077
$541$	22.7107	0.976409	0.488204	−	0.872729i	$-0.337652\pi$
$541$	22.7107	0.976409	0.488204	+	0.872729i	$0.337652\pi$
$542$	11.6382	0.499904
$543$	−4.23000	−0.181527
$544$	23.2220	0.995635
$545$	−24.8053	−1.06254
$546$	0	0
$547$	−31.2299	−1.33529	−0.667646	−	0.744478i	$-0.732698\pi$
$547$	−31.2299	−1.33529	−0.667646	+	0.744478i	$0.732698\pi$
$548$	0.566125	0.0241837
$549$	−2.43245	−0.103814
$550$	−18.1356	−0.773304
$551$	−21.6558	−0.922567
$552$	15.0539	0.640736
$553$	0	0
$554$	26.5475	1.12789
$555$	−27.9626	−1.18695
$556$	5.33755	0.226363
$557$	−33.0837	−1.40180	−0.700900	−	0.713259i	$-0.747218\pi$
$557$	−33.0837	−1.40180	−0.700900	+	0.713259i	$0.747218\pi$
$558$	−7.01570	−0.296998
$559$	2.78704	0.117879
$560$	0	0
$561$	31.3272	1.32264
$562$	−3.39262	−0.143109
$563$	30.0065	1.26462	0.632312	−	0.774714i	$-0.282106\pi$
$563$	30.0065	1.26462	0.632312	+	0.774714i	$0.282106\pi$
$564$	5.94162	0.250187
$565$	−9.92588	−0.417585
$566$	−25.2808	−1.06263
$567$	0	0
$568$	35.5929	1.49344
$569$	32.1781	1.34897	0.674487	−	0.738287i	$-0.264365\pi$
$569$	32.1781	1.34897	0.674487	+	0.738287i	$0.264365\pi$
$570$	8.94689	0.374744
$571$	−43.3615	−1.81462	−0.907311	−	0.420461i	$-0.861868\pi$
$571$	−43.3615	−1.81462	−0.907311	+	0.420461i	$0.861868\pi$
$572$	4.25255	0.177808
$573$	−16.3980	−0.685035
$574$	0	0
$575$	−14.5621	−0.607282
$576$	8.24361	0.343484
$577$	39.9509	1.66318	0.831589	−	0.555392i	$-0.187432\pi$
$577$	39.9509	1.66318	0.831589	+	0.555392i	$0.187432\pi$
$578$	−17.0100	−0.707523
$579$	−9.90397	−0.411595
$580$	16.5078	0.685449
$581$	0	0
$582$	−6.79398	−0.281620
$583$	−28.7482	−1.19063
$584$	−20.5333	−0.849673
$585$	2.82337	0.116732
$586$	13.2556	0.547583
$587$	14.3837	0.593678	0.296839	−	0.954928i	$-0.404067\pi$
$587$	14.3837	0.593678	0.296839	+	0.954928i	$0.404067\pi$
$588$	0	0
$589$	−18.1054	−0.746020
$590$	10.6191	0.437182
$591$	−3.64207	−0.149815
$592$	18.4184	0.756992
$593$	−7.35603	−0.302076	−0.151038	−	0.988528i	$-0.548262\pi$
$593$	−7.35603	−0.302076	−0.151038	+	0.988528i	$0.548262\pi$
$594$	6.10331	0.250422
$595$	0	0
$596$	16.6778	0.683147
$597$	−2.85836	−0.116985
$598$	−5.43052	−0.222071
$599$	−8.78643	−0.359004	−0.179502	−	0.983758i	$-0.557449\pi$
$599$	−8.78643	−0.359004	−0.179502	+	0.983758i	$0.557449\pi$
$600$	−9.12760	−0.372633
$601$	25.6277	1.04537	0.522687	−	0.852525i	$-0.324930\pi$
$601$	25.6277	1.04537	0.522687	+	0.852525i	$0.324930\pi$
$602$	0	0
$603$	−5.19092	−0.211391
$604$	−4.49725	−0.182990
$605$	−54.5939	−2.21956
$606$	5.90397	0.239832
$607$	−27.7091	−1.12468	−0.562339	−	0.826907i	$-0.690098\pi$
$607$	−27.7091	−1.12468	−0.562339	+	0.826907i	$0.690098\pi$
$608$	11.6756	0.473509
$609$	0	0
$610$	−7.61018	−0.308127
$611$	−7.69551	−0.311327
$612$	4.39145	0.177514
$613$	33.7067	1.36140	0.680701	−	0.732561i	$-0.261675\pi$
$613$	33.7067	1.36140	0.680701	+	0.732561i	$0.261675\pi$
$614$	−3.95589	−0.159647
$615$	−31.2040	−1.25827
$616$	0	0
$617$	−6.02392	−0.242514	−0.121257	−	0.992621i	$-0.538692\pi$
$617$	−6.02392	−0.242514	−0.121257	+	0.992621i	$0.538692\pi$
$618$	1.71112	0.0688314
$619$	−6.61701	−0.265960	−0.132980	−	0.991119i	$-0.542455\pi$
$619$	−6.61701	−0.265960	−0.132980	+	0.991119i	$0.542455\pi$
$620$	13.8014	0.554278
$621$	4.90070	0.196658
$622$	−34.5444	−1.38510
$623$	0	0
$624$	−1.85970	−0.0744476
$625$	−31.0278	−1.24111
$626$	−31.7684	−1.26972
$627$	15.7508	0.629026
$628$	4.30369	0.171736
$629$	56.3312	2.24607
$630$	0	0
$631$	1.19982	0.0477639	0.0238820	−	0.999715i	$-0.492397\pi$
$631$	1.19982	0.0477639	0.0238820	+	0.999715i	$0.492397\pi$
$632$	−19.7632	−0.786138
$633$	−9.29215	−0.369330
$634$	−0.225247	−0.00894571
$635$	44.4081	1.76228
$636$	−4.02991	−0.159796
$637$	0	0
$638$	−46.2188	−1.82982
$639$	11.5870	0.458376
$640$	2.73646	0.108168
$641$	32.2258	1.27284	0.636422	−	0.771341i	$-0.280414\pi$
$641$	32.2258	1.27284	0.636422	+	0.771341i	$0.280414\pi$
$642$	16.3736	0.646213
$643$	−3.28042	−0.129367	−0.0646836	−	0.997906i	$-0.520604\pi$
$643$	−3.28042	−0.129367	−0.0646836	+	0.997906i	$0.520604\pi$
$644$	0	0
$645$	−7.86887	−0.309836
$646$	−18.0237	−0.709133
$647$	−10.0947	−0.396864	−0.198432	−	0.980115i	$-0.563585\pi$
$647$	−10.0947	−0.396864	−0.198432	+	0.980115i	$0.563585\pi$
$648$	3.07178	0.120671
$649$	18.6947	0.733832
$650$	3.29268	0.129149
$651$	0	0
$652$	−17.2688	−0.676298
$653$	−8.39119	−0.328373	−0.164186	−	0.986429i	$-0.552500\pi$
$653$	−8.39119	−0.328373	−0.164186	+	0.986429i	$0.552500\pi$
$654$	9.73554	0.380690
$655$	0.854509	0.0333884
$656$	20.5535	0.802478
$657$	−6.68448	−0.260786
$658$	0	0
$659$	−35.8448	−1.39631	−0.698157	−	0.715944i	$-0.745996\pi$
$659$	−35.8448	−1.39631	−0.698157	+	0.715944i	$0.745996\pi$
$660$	−12.0065	−0.467354
$661$	−24.0899	−0.936988	−0.468494	−	0.883467i	$-0.655203\pi$
$661$	−24.0899	−0.936988	−0.468494	+	0.883467i	$0.655203\pi$
$662$	8.14531	0.316577
$663$	−5.68775	−0.220894
$664$	49.3184	1.91392
$665$	0	0
$666$	10.9747	0.425261
$667$	−37.1118	−1.43697
$668$	−2.44408	−0.0945642
$669$	−18.6676	−0.721733
$670$	−16.2404	−0.627421
$671$	−13.3975	−0.517207
$672$	0	0
$673$	15.7052	0.605392	0.302696	−	0.953087i	$-0.402113\pi$
$673$	15.7052	0.605392	0.302696	+	0.953087i	$0.402113\pi$
$674$	−8.36128	−0.322064
$675$	−2.97143	−0.114371
$676$	−0.772089	−0.0296957
$677$	−27.8527	−1.07046	−0.535232	−	0.844705i	$-0.679776\pi$
$677$	−27.8527	−1.07046	−0.535232	+	0.844705i	$0.679776\pi$
$678$	3.89569	0.149613
$679$	0	0
$680$	49.3286	1.89167
$681$	24.3411	0.932752
$682$	−38.6414	−1.47966
$683$	−11.8326	−0.452760	−0.226380	−	0.974039i	$-0.572689\pi$
$683$	−11.8326	−0.452760	−0.226380	+	0.974039i	$0.572689\pi$
$684$	2.20794	0.0844228
$685$	2.07020	0.0790985
$686$	0	0
$687$	−14.5664	−0.555743
$688$	5.18307	0.197603
$689$	5.21949	0.198847
$690$	15.3324	0.583694
$691$	−21.1741	−0.805499	−0.402750	−	0.915310i	$-0.631945\pi$
$691$	−21.1741	−0.805499	−0.402750	+	0.915310i	$0.631945\pi$
$692$	−9.29672	−0.353408
$693$	0	0
$694$	−5.49532	−0.208600
$695$	19.5184	0.740373
$696$	−23.2618	−0.881738
$697$	62.8611	2.38103
$698$	34.7100	1.31379
$699$	−7.14030	−0.270071
$700$	0	0
$701$	−1.24436	−0.0469987	−0.0234993	−	0.999724i	$-0.507481\pi$
$701$	−1.24436	−0.0469987	−0.0234993	+	0.999724i	$0.507481\pi$
$702$	−1.10811	−0.0418230
$703$	28.3224	1.06820
$704$	45.4046	1.71125
$705$	21.7273	0.818297
$706$	40.6778	1.53093
$707$	0	0
$708$	2.62062	0.0984889
$709$	28.9337	1.08663	0.543314	−	0.839530i	$-0.317169\pi$
$709$	28.9337	1.08663	0.543314	+	0.839530i	$0.317169\pi$
$710$	36.2513	1.36049
$711$	−6.43379	−0.241286
$712$	46.8626	1.75625
$713$	−31.0274	−1.16199
$714$	0	0
$715$	15.5507	0.581564
$716$	−4.83352	−0.180637
$717$	8.44155	0.315255
$718$	17.5270	0.654103
$719$	−42.7416	−1.59399	−0.796997	−	0.603983i	$-0.793579\pi$
$719$	−42.7416	−1.59399	−0.796997	+	0.603983i	$0.793579\pi$
$720$	5.25063	0.195679
$721$	0	0
$722$	11.9921	0.446300
$723$	17.0663	0.634703
$724$	−3.26594	−0.121378
$725$	22.5019	0.835700
$726$	21.4269	0.795227
$727$	−41.3249	−1.53266	−0.766328	−	0.642450i	$-0.777918\pi$
$727$	−41.3249	−1.53266	−0.766328	+	0.642450i	$0.777918\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−20.9131	−0.774030
$731$	15.8520	0.586307
$732$	−1.87806	−0.0694153
$733$	−49.9312	−1.84425	−0.922126	−	0.386890i	$-0.873549\pi$
$733$	−49.9312	−1.84425	−0.922126	+	0.386890i	$0.873549\pi$
$734$	−28.2294	−1.04197
$735$	0	0
$736$	20.0086	0.737528
$737$	−28.5908	−1.05316
$738$	12.2469	0.450814
$739$	4.87892	0.179474	0.0897370	−	0.995965i	$-0.471397\pi$
$739$	4.87892	0.179474	0.0897370	+	0.995965i	$0.471397\pi$
$740$	−21.5896	−0.793650
$741$	−2.85970	−0.105054
$742$	0	0
$743$	1.31579	0.0482715	0.0241358	−	0.999709i	$-0.492317\pi$
$743$	1.31579	0.0482715	0.0241358	+	0.999709i	$0.492317\pi$
$744$	−19.4481	−0.713004
$745$	60.9872	2.23440
$746$	−26.9675	−0.987349
$747$	16.0553	0.587433
$748$	24.1874	0.884380
$749$	0	0
$750$	6.34660	0.231745
$751$	−23.3924	−0.853599	−0.426800	−	0.904346i	$-0.640359\pi$
$751$	−23.3924	−0.853599	−0.426800	+	0.904346i	$0.640359\pi$
$752$	−14.3113	−0.521881
$753$	7.07283	0.257748
$754$	8.39145	0.305598
$755$	−16.4455	−0.598514
$756$	0	0
$757$	20.5069	0.745336	0.372668	−	0.927965i	$-0.378443\pi$
$757$	20.5069	0.745336	0.372668	+	0.927965i	$0.378443\pi$
$758$	−2.18606	−0.0794012
$759$	26.9923	0.979759
$760$	24.8016	0.899648
$761$	43.3571	1.57169	0.785846	−	0.618422i	$-0.212228\pi$
$761$	43.3571	1.57169	0.785846	+	0.618422i	$0.212228\pi$
$762$	−17.4292	−0.631393
$763$	0	0
$764$	−12.6607	−0.458048
$765$	16.0586	0.580601
$766$	−5.49208	−0.198437
$767$	−3.39419	−0.122557
$768$	15.4132	0.556177
$769$	28.8949	1.04198	0.520989	−	0.853563i	$-0.325563\pi$
$769$	28.8949	1.04198	0.520989	+	0.853563i	$0.325563\pi$
$770$	0	0
$771$	−22.8304	−0.822218
$772$	−7.64675	−0.275212
$773$	−30.3584	−1.09191	−0.545957	−	0.837813i	$-0.683834\pi$
$773$	−30.3584	−1.09191	−0.545957	+	0.837813i	$0.683834\pi$
$774$	3.08836	0.111009
$775$	18.8128	0.675776
$776$	−18.8335	−0.676084
$777$	0	0
$778$	−9.33983	−0.334849
$779$	31.6055	1.13238
$780$	2.17990	0.0780528
$781$	63.8197	2.28365
$782$	−30.8874	−1.10453
$783$	−7.57275	−0.270628
$784$	0	0
$785$	15.7377	0.561704
$786$	−0.335376	−0.0119625
$787$	28.5173	1.01653	0.508266	−	0.861200i	$-0.330287\pi$
$787$	28.5173	1.01653	0.508266	+	0.861200i	$0.330287\pi$
$788$	−2.81200	−0.100174
$789$	−17.5383	−0.624379
$790$	−20.1288	−0.716152
$791$	0	0
$792$	16.9189	0.601188
$793$	2.43245	0.0863787
$794$	−1.37723	−0.0488762
$795$	−14.7366	−0.522652
$796$	−2.20691	−0.0782217
$797$	17.9047	0.634216	0.317108	−	0.948389i	$-0.397288\pi$
$797$	17.9047	0.634216	0.317108	+	0.948389i	$0.397288\pi$
$798$	0	0
$799$	−43.7701	−1.54847
$800$	−12.1318	−0.428924
$801$	15.2558	0.539038
$802$	−26.3798	−0.931502
$803$	−36.8171	−1.29925
$804$	−4.00785	−0.141346
$805$	0	0
$806$	7.01570	0.247118
$807$	11.3096	0.398118
$808$	16.3663	0.575765
$809$	−20.1911	−0.709882	−0.354941	−	0.934889i	$-0.615499\pi$
$809$	−20.1911	−0.709882	−0.354941	+	0.934889i	$0.615499\pi$
$810$	3.12861	0.109928
$811$	−36.6521	−1.28703	−0.643515	−	0.765433i	$-0.722525\pi$
$811$	−36.6521	−1.28703	−0.643515	+	0.765433i	$0.722525\pi$
$812$	0	0
$813$	10.5027	0.368347
$814$	60.4470	2.11867
$815$	−63.1485	−2.21199
$816$	−10.5775	−0.370287
$817$	7.97011	0.278839
$818$	−42.7748	−1.49559
$819$	0	0
$820$	−24.0923	−0.841338
$821$	53.4565	1.86565	0.932823	−	0.360335i	$-0.117337\pi$
$821$	53.4565	1.86565	0.932823	+	0.360335i	$0.117337\pi$
$822$	−0.812510	−0.0283395
$823$	13.3793	0.466374	0.233187	−	0.972432i	$-0.425085\pi$
$823$	13.3793	0.466374	0.233187	+	0.972432i	$0.425085\pi$
$824$	4.74338	0.165244
$825$	−16.3662	−0.569798
$826$	0	0
$827$	18.2237	0.633700	0.316850	−	0.948476i	$-0.397375\pi$
$827$	18.2237	0.633700	0.316850	+	0.948476i	$0.397375\pi$
$828$	3.78378	0.131495
$829$	9.85200	0.342174	0.171087	−	0.985256i	$-0.445272\pi$
$829$	9.85200	0.342174	0.171087	+	0.985256i	$0.445272\pi$
$830$	50.2308	1.74354
$831$	23.9574	0.831073
$832$	−8.24361	−0.285796
$833$	0	0
$834$	−7.66052	−0.265262
$835$	−8.93750	−0.309295
$836$	12.1610	0.420598
$837$	−6.33122	−0.218839
$838$	−30.1913	−1.04294
$839$	−1.06581	−0.0367957	−0.0183978	−	0.999831i	$-0.505857\pi$
$839$	−1.06581	−0.0367957	−0.0183978	+	0.999831i	$0.505857\pi$
$840$	0	0
$841$	28.3465	0.977465
$842$	−14.0616	−0.484594
$843$	−3.06163	−0.105448
$844$	−7.17436	−0.246952
$845$	−2.82337	−0.0971270
$846$	−8.52748	−0.293181
$847$	0	0
$848$	9.70669	0.333329
$849$	−22.8143	−0.782984
$850$	18.7279	0.642362
$851$	48.5364	1.66381
$852$	8.94623	0.306493
$853$	34.9286	1.19593	0.597966	−	0.801521i	$-0.295976\pi$
$853$	34.9286	1.19593	0.597966	+	0.801521i	$0.295976\pi$
$854$	0	0
$855$	8.07400	0.276125
$856$	45.3890	1.55136
$857$	−19.6334	−0.670665	−0.335332	−	0.942100i	$-0.608849\pi$
$857$	−19.6334	−0.670665	−0.335332	+	0.942100i	$0.608849\pi$
$858$	−6.10331	−0.208364
$859$	2.00922	0.0685538	0.0342769	−	0.999412i	$-0.489087\pi$
$859$	2.00922	0.0685538	0.0342769	+	0.999412i	$0.489087\pi$
$860$	−6.07546	−0.207172
$861$	0	0
$862$	34.3732	1.17076
$863$	−39.3913	−1.34089	−0.670447	−	0.741958i	$-0.733898\pi$
$863$	−39.3913	−1.34089	−0.670447	+	0.741958i	$0.733898\pi$
$864$	4.08281	0.138900
$865$	−33.9962	−1.15591
$866$	−18.1887	−0.618076
$867$	−15.3504	−0.521328
$868$	0	0
$869$	−35.4364	−1.20210
$870$	−23.6922	−0.803240
$871$	5.19092	0.175888
$872$	26.9878	0.913921
$873$	−6.13113	−0.207507
$874$	−15.5297	−0.525299
$875$	0	0
$876$	−5.16101	−0.174374
$877$	−7.57140	−0.255668	−0.127834	−	0.991796i	$-0.540802\pi$
$877$	−7.57140	−0.255668	−0.127834	+	0.991796i	$0.540802\pi$
$878$	−13.7579	−0.464306
$879$	11.9623	0.403479
$880$	28.9197	0.974882
$881$	30.7644	1.03648	0.518240	−	0.855235i	$-0.326587\pi$
$881$	30.7644	1.03648	0.518240	+	0.855235i	$0.326587\pi$
$882$	0	0
$883$	49.8365	1.67713	0.838566	−	0.544799i	$-0.183394\pi$
$883$	49.8365	1.67713	0.838566	+	0.544799i	$0.183394\pi$
$884$	−4.39145	−0.147700
$885$	9.58308	0.322132
$886$	−18.1998	−0.611435
$887$	25.6416	0.860961	0.430480	−	0.902600i	$-0.358344\pi$
$887$	25.6416	0.860961	0.430480	+	0.902600i	$0.358344\pi$
$888$	30.4228	1.02092
$889$	0	0
$890$	47.7295	1.59990
$891$	5.50785	0.184520
$892$	−14.4131	−0.482586
$893$	−22.0068	−0.736431
$894$	−23.9361	−0.800543
$895$	−17.6752	−0.590816
$896$	0	0
$897$	−4.90070	−0.163630
$898$	16.5852	0.553455
$899$	47.9447	1.59905
$900$	−2.29421	−0.0764737
$901$	29.6871	0.989022
$902$	67.4540	2.24597
$903$	0	0
$904$	10.7992	0.359176
$905$	−11.9429	−0.396994
$906$	6.45450	0.214436
$907$	−10.5158	−0.349171	−0.174586	−	0.984642i	$-0.555859\pi$
$907$	−10.5158	−0.349171	−0.174586	+	0.984642i	$0.555859\pi$
$908$	18.7935	0.623684
$909$	5.32796	0.176717
$910$	0	0
$911$	41.6462	1.37980	0.689900	−	0.723905i	$-0.257655\pi$
$911$	41.6462	1.37980	0.689900	+	0.723905i	$0.257655\pi$
$912$	−5.31819	−0.176103
$913$	88.4302	2.92661
$914$	−21.6373	−0.715699
$915$	−6.86770	−0.227039
$916$	−11.2466	−0.371597
$917$	0	0
$918$	−6.30266	−0.208019
$919$	30.1328	0.993988	0.496994	−	0.867754i	$-0.334437\pi$
$919$	30.1328	0.993988	0.496994	+	0.867754i	$0.334437\pi$
$920$	42.5027	1.40127
$921$	−3.56994	−0.117633
$922$	11.9287	0.392851
$923$	−11.5870	−0.381392
$924$	0	0
$925$	−29.4290	−0.967619
$926$	15.8545	0.521012
$927$	1.54418	0.0507175
$928$	−30.9181	−1.01494
$929$	14.5483	0.477313	0.238657	−	0.971104i	$-0.423293\pi$
$929$	14.5483	0.477313	0.238657	+	0.971104i	$0.423293\pi$
$930$	−19.8079	−0.649528
$931$	0	0
$932$	−5.51295	−0.180583
$933$	−31.1741	−1.02059
$934$	−32.1874	−1.05320
$935$	88.4485	2.89258
$936$	−3.07178	−0.100404
$937$	−22.3753	−0.730970	−0.365485	−	0.930817i	$-0.619097\pi$
$937$	−22.3753	−0.730970	−0.365485	+	0.930817i	$0.619097\pi$
$938$	0	0
$939$	−28.6690	−0.935577
$940$	16.7754	0.547153
$941$	7.76092	0.252999	0.126499	−	0.991967i	$-0.459626\pi$
$941$	7.76092	0.252999	0.126499	+	0.991967i	$0.459626\pi$
$942$	−6.17671	−0.201248
$943$	54.1627	1.76378
$944$	−6.31218	−0.205444
$945$	0	0
$946$	17.0102	0.553049
$947$	−53.1392	−1.72679	−0.863397	−	0.504526i	$-0.831667\pi$
$947$	−53.1392	−1.72679	−0.863397	+	0.504526i	$0.831667\pi$
$948$	−4.96746	−0.161336
$949$	6.68448	0.216987
$950$	9.41607	0.305498
$951$	−0.203271	−0.00659152
$952$	0	0
$953$	8.79639	0.284943	0.142471	−	0.989799i	$-0.454495\pi$
$953$	8.79639	0.284943	0.142471	+	0.989799i	$0.454495\pi$
$954$	5.78378	0.187257
$955$	−46.2976	−1.49816
$956$	6.51763	0.210795
$957$	−41.7095	−1.34828
$958$	−7.97927	−0.257799
$959$	0	0
$960$	23.2748	0.751190
$961$	9.08438	0.293045
$962$	−10.9747	−0.353839
$963$	14.7761	0.476153
$964$	13.1767	0.424394
$965$	−27.9626	−0.900148
$966$	0	0
$967$	3.01839	0.0970648	0.0485324	−	0.998822i	$-0.484546\pi$
$967$	3.01839	0.0970648	0.0485324	+	0.998822i	$0.484546\pi$
$968$	59.3973	1.90910
$969$	−16.2652	−0.522515
$970$	−19.1819	−0.615895
$971$	−50.7702	−1.62929	−0.814647	−	0.579957i	$-0.803069\pi$
$971$	−50.7702	−1.62929	−0.814647	+	0.579957i	$0.803069\pi$
$972$	0.772089	0.0247648
$973$	0	0
$974$	−6.90615	−0.221287
$975$	2.97143	0.0951620
$976$	4.52362	0.144798
$977$	35.2449	1.12758	0.563792	−	0.825917i	$-0.309342\pi$
$977$	35.2449	1.12758	0.563792	+	0.825917i	$0.309342\pi$
$978$	24.7844	0.792517
$979$	84.0268	2.68551
$980$	0	0
$981$	8.78570	0.280506
$982$	−12.7385	−0.406502
$983$	−57.5204	−1.83461	−0.917307	−	0.398180i	$-0.869642\pi$
$983$	−57.5204	−1.83461	−0.917307	+	0.398180i	$0.869642\pi$
$984$	33.9494	1.08227
$985$	−10.2829	−0.327641
$986$	47.7284	1.51998
$987$	0	0
$988$	−2.20794	−0.0702440
$989$	13.6585	0.434314
$990$	17.2319	0.547666
$991$	35.4196	1.12514	0.562570	−	0.826749i	$-0.309813\pi$
$991$	35.4196	1.12514	0.562570	+	0.826749i	$0.309813\pi$
$992$	−25.8492	−0.820713
$993$	7.35062	0.233265
$994$	0	0
$995$	−8.07020	−0.255843
$996$	12.3961	0.392786
$997$	30.2365	0.957601	0.478800	−	0.877924i	$-0.341072\pi$
$997$	30.2365	0.957601	0.478800	+	0.877924i	$0.341072\pi$
$998$	12.5778	0.398142
$999$	9.90397	0.313348

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1911.2.a.v.1.2	✓	5
3.2	odd	2		5733.2.a.bo.1.4		5
7.6	odd	2		1911.2.a.w.1.2	yes	5
21.20	even	2		5733.2.a.bn.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1911.2.a.v.1.2	✓	5	1.1	even	1	trivial
1911.2.a.w.1.2	yes	5	7.6	odd	2
5733.2.a.bn.1.4		5	21.20	even	2
5733.2.a.bo.1.4		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1911.a (trivial)

\(f(q)\)	\(=\)	\(q-1.10811 q^{2} -1.00000 q^{3} -0.772089 q^{4} -2.82337 q^{5} +1.10811 q^{6} +3.07178 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.10811 q^{2} -1.00000 q^{3} -0.772089 q^{4} -2.82337 q^{5} +1.10811 q^{6} +3.07178 q^{8} +1.00000 q^{9} +3.12861 q^{10} +5.50785 q^{11} +0.772089 q^{12} -1.00000 q^{13} +2.82337 q^{15} -1.85970 q^{16} -5.68775 q^{17} -1.10811 q^{18} -2.85970 q^{19} +2.17990 q^{20} -6.10331 q^{22} -4.90070 q^{23} -3.07178 q^{24} +2.97143 q^{25} +1.10811 q^{26} -1.00000 q^{27} +7.57275 q^{29} -3.12861 q^{30} +6.33122 q^{31} -4.08281 q^{32} -5.50785 q^{33} +6.30266 q^{34} -0.772089 q^{36} -9.90397 q^{37} +3.16887 q^{38} +1.00000 q^{39} -8.67279 q^{40} -11.0520 q^{41} -2.78704 q^{43} -4.25255 q^{44} -2.82337 q^{45} +5.43052 q^{46} +7.69551 q^{47} +1.85970 q^{48} -3.29268 q^{50} +5.68775 q^{51} +0.772089 q^{52} -5.21949 q^{53} +1.10811 q^{54} -15.5507 q^{55} +2.85970 q^{57} -8.39145 q^{58} +3.39419 q^{59} -2.17990 q^{60} -2.43245 q^{61} -7.01570 q^{62} +8.24361 q^{64} +2.82337 q^{65} +6.10331 q^{66} -5.19092 q^{67} +4.39145 q^{68} +4.90070 q^{69} +11.5870 q^{71} +3.07178 q^{72} -6.68448 q^{73} +10.9747 q^{74} -2.97143 q^{75} +2.20794 q^{76} -1.10811 q^{78} -6.43379 q^{79} +5.25063 q^{80} +1.00000 q^{81} +12.2469 q^{82} +16.0553 q^{83} +16.0586 q^{85} +3.08836 q^{86} -7.57275 q^{87} +16.9189 q^{88} +15.2558 q^{89} +3.12861 q^{90} +3.78378 q^{92} -6.33122 q^{93} -8.52748 q^{94} +8.07400 q^{95} +4.08281 q^{96} -6.13113 q^{97} +5.50785 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{2} - 5 q^{3} + 6 q^{4} - 3 q^{5} - 2 q^{6} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 2 * q^2 - 5 * q^3 + 6 * q^4 - 3 * q^5 - 2 * q^6 + 6 * q^8 + 5 * q^9	\( 5 q + 2 q^{2} - 5 q^{3} + 6 q^{4} - 3 q^{5} - 2 q^{6} + 6 q^{8} + 5 q^{9} + 6 q^{11} - 6 q^{12} - 5 q^{13} + 3 q^{15} + 10 q^{17} + 2 q^{18} - 5 q^{19} - 6 q^{20} + 12 q^{22} + q^{23} - 6 q^{24} + 16 q^{25} - 2 q^{26} - 5 q^{27} + 17 q^{29} - q^{31} + 14 q^{32} - 6 q^{33} + 6 q^{36} + 4 q^{37} + 24 q^{38} + 5 q^{39} - 8 q^{40} - 14 q^{41} - q^{43} - 8 q^{44} - 3 q^{45} + 20 q^{46} + 3 q^{47} + 26 q^{50} - 10 q^{51} - 6 q^{52} + 17 q^{53} - 2 q^{54} - 2 q^{55} + 5 q^{57} - 28 q^{58} + 8 q^{59} + 6 q^{60} + 18 q^{61} + 8 q^{62} + 8 q^{64} + 3 q^{65} - 12 q^{66} + 16 q^{67} + 8 q^{68} - q^{69} - 16 q^{71} + 6 q^{72} - 23 q^{73} + 28 q^{74} - 16 q^{75} + 26 q^{76} + 2 q^{78} + 3 q^{79} + 36 q^{80} + 5 q^{81} + 11 q^{83} - 2 q^{85} - 24 q^{86} - 17 q^{87} + 28 q^{88} + 35 q^{89} + 34 q^{92} + q^{93} + 39 q^{95} - 14 q^{96} - 27 q^{97} + 6 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 - 5 * q^3 + 6 * q^4 - 3 * q^5 - 2 * q^6 + 6 * q^8 + 5 * q^9 + 6 * q^11 - 6 * q^12 - 5 * q^13 + 3 * q^15 + 10 * q^17 + 2 * q^18 - 5 * q^19 - 6 * q^20 + 12 * q^22 + q^23 - 6 * q^24 + 16 * q^25 - 2 * q^26 - 5 * q^27 + 17 * q^29 - q^31 + 14 * q^32 - 6 * q^33 + 6 * q^36 + 4 * q^37 + 24 * q^38 + 5 * q^39 - 8 * q^40 - 14 * q^41 - q^43 - 8 * q^44 - 3 * q^45 + 20 * q^46 + 3 * q^47 + 26 * q^50 - 10 * q^51 - 6 * q^52 + 17 * q^53 - 2 * q^54 - 2 * q^55 + 5 * q^57 - 28 * q^58 + 8 * q^59 + 6 * q^60 + 18 * q^61 + 8 * q^62 + 8 * q^64 + 3 * q^65 - 12 * q^66 + 16 * q^67 + 8 * q^68 - q^69 - 16 * q^71 + 6 * q^72 - 23 * q^73 + 28 * q^74 - 16 * q^75 + 26 * q^76 + 2 * q^78 + 3 * q^79 + 36 * q^80 + 5 * q^81 + 11 * q^83 - 2 * q^85 - 24 * q^86 - 17 * q^87 + 28 * q^88 + 35 * q^89 + 34 * q^92 + q^93 + 39 * q^95 - 14 * q^96 - 27 * q^97 + 6 * q^99

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