LMFDB - Embedded newform 1617.2.a.y.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,2,Mod(1,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, 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("1617.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1617.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:	$12.9118100068$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.2624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 3x^{2} + 2x + 1 $ x^4 - 2x^3 - 3x^2 + 2*x + 1
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			1.1
Root			$2.77462$ of defining polynomial
Character	$\chi$	$=$	1617.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.77462 q^{2} +1.00000 q^{3} +1.14929 q^{4} +1.50970 q^{5} -1.77462 q^{6} +1.50970 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.77462 q^{2} +1.00000 q^{3} +1.14929 q^{4} +1.50970 q^{5} -1.77462 q^{6} +1.50970 q^{8} +1.00000 q^{9} -2.67914 q^{10} -1.00000 q^{11} +1.14929 q^{12} +0.279181 q^{13} +1.50970 q^{15} -4.97771 q^{16} -2.64473 q^{17} -1.77462 q^{18} +6.54925 q^{19} +1.73507 q^{20} +1.77462 q^{22} +3.62534 q^{23} +1.50970 q^{24} -2.72082 q^{25} -0.495442 q^{26} +1.00000 q^{27} +8.33812 q^{29} -2.67914 q^{30} -2.45376 q^{31} +5.81417 q^{32} -1.00000 q^{33} +4.69339 q^{34} +1.14929 q^{36} -0.577754 q^{37} -11.6224 q^{38} +0.279181 q^{39} +2.27918 q^{40} +0.287214 q^{41} +6.05894 q^{43} -1.14929 q^{44} +1.50970 q^{45} -6.43361 q^{46} +1.76949 q^{47} -4.97771 q^{48} +4.82843 q^{50} -2.64473 q^{51} +0.320859 q^{52} +9.28219 q^{53} -1.77462 q^{54} -1.50970 q^{55} +6.54925 q^{57} -14.7970 q^{58} -2.52909 q^{59} +1.73507 q^{60} -7.98394 q^{61} +4.35451 q^{62} -0.362537 q^{64} +0.421479 q^{65} +1.77462 q^{66} -13.0388 q^{67} -3.03955 q^{68} +3.62534 q^{69} -0.557278 q^{71} +1.50970 q^{72} +8.01939 q^{73} +1.02530 q^{74} -2.72082 q^{75} +7.52696 q^{76} -0.495442 q^{78} -8.90753 q^{79} -7.51483 q^{80} +1.00000 q^{81} -0.509696 q^{82} +12.8760 q^{83} -3.99273 q^{85} -10.7523 q^{86} +8.33812 q^{87} -1.50970 q^{88} +11.8193 q^{89} -2.67914 q^{90} +4.16655 q^{92} -2.45376 q^{93} -3.14017 q^{94} +9.88737 q^{95} +5.81417 q^{96} +7.82766 q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 4 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 4 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^9	$ 4 q + 2 q^{2} + 4 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} + 8 q^{13} - 6 q^{16} + 8 q^{17} + 2 q^{18} + 8 q^{19} + 10 q^{20} - 2 q^{22} + 8 q^{23} - 4 q^{25} + 14 q^{26} + 4 q^{27} + 16 q^{29} - 2 q^{30} + 8 q^{31} + 2 q^{32} - 4 q^{33} + 20 q^{34} + 2 q^{36} - 4 q^{37} - 14 q^{38} + 8 q^{39} + 16 q^{40} + 12 q^{41} - 2 q^{44} - 8 q^{46} + 20 q^{47} - 6 q^{48} + 8 q^{50} + 8 q^{51} + 10 q^{52} + 8 q^{53} + 2 q^{54} + 8 q^{57} - 2 q^{58} + 8 q^{59} + 10 q^{60} - 24 q^{61} + 24 q^{62} - 12 q^{64} - 12 q^{65} - 2 q^{66} - 28 q^{67} + 8 q^{69} + 12 q^{71} + 20 q^{73} - 18 q^{74} - 4 q^{75} - 2 q^{76} + 14 q^{78} - 2 q^{80} + 4 q^{81} + 4 q^{82} + 32 q^{83} - 24 q^{85} - 20 q^{86} + 16 q^{87} + 4 q^{89} - 2 q^{90} - 12 q^{92} + 8 q^{93} + 22 q^{94} + 4 q^{95} + 2 q^{96} + 8 q^{97} - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 4 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 + 8 * q^13 - 6 * q^16 + 8 * q^17 + 2 * q^18 + 8 * q^19 + 10 * q^20 - 2 * q^22 + 8 * q^23 - 4 * q^25 + 14 * q^26 + 4 * q^27 + 16 * q^29 - 2 * q^30 + 8 * q^31 + 2 * q^32 - 4 * q^33 + 20 * q^34 + 2 * q^36 - 4 * q^37 - 14 * q^38 + 8 * q^39 + 16 * q^40 + 12 * q^41 - 2 * q^44 - 8 * q^46 + 20 * q^47 - 6 * q^48 + 8 * q^50 + 8 * q^51 + 10 * q^52 + 8 * q^53 + 2 * q^54 + 8 * q^57 - 2 * q^58 + 8 * q^59 + 10 * q^60 - 24 * q^61 + 24 * q^62 - 12 * q^64 - 12 * q^65 - 2 * q^66 - 28 * q^67 + 8 * q^69 + 12 * q^71 + 20 * q^73 - 18 * q^74 - 4 * q^75 - 2 * q^76 + 14 * q^78 - 2 * q^80 + 4 * q^81 + 4 * q^82 + 32 * q^83 - 24 * q^85 - 20 * q^86 + 16 * q^87 + 4 * q^89 - 2 * q^90 - 12 * q^92 + 8 * q^93 + 22 * q^94 + 4 * q^95 + 2 * q^96 + 8 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.77462	−1.25485	−0.627424	−	0.778678i	$-0.715891\pi$
$2$	−1.77462	−1.25485	−0.627424	+	0.778678i	$0.715891\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.14929	0.574643
$5$	1.50970	0.675156	0.337578	−	0.941297i	$-0.390392\pi$
$5$	1.50970	0.675156	0.337578	+	0.941297i	$0.390392\pi$
$6$	−1.77462	−0.724487
$7$	0	0
$7$	0	0
$8$	1.50970	0.533758
$9$	1.00000	0.333333
$10$	−2.67914	−0.847219
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.14929	0.331770
$13$	0.279181	0.0774310	0.0387155	−	0.999250i	$-0.487673\pi$
$13$	0.279181	0.0774310	0.0387155	+	0.999250i	$0.487673\pi$
$14$	0	0
$15$	1.50970	0.389802
$16$	−4.97771	−1.24443
$17$	−2.64473	−0.641441	−0.320720	−	0.947174i	$-0.603925\pi$
$17$	−2.64473	−0.641441	−0.320720	+	0.947174i	$0.603925\pi$
$18$	−1.77462	−0.418283
$19$	6.54925	1.50250	0.751250	−	0.660018i	$-0.229451\pi$
$19$	6.54925	1.50250	0.751250	+	0.660018i	$0.229451\pi$
$20$	1.73507	0.387974
$21$	0	0
$22$	1.77462	0.378351
$23$	3.62534	0.755935	0.377967	−	0.925819i	$-0.376623\pi$
$23$	3.62534	0.755935	0.377967	+	0.925819i	$0.376623\pi$
$24$	1.50970	0.308165
$25$	−2.72082	−0.544164
$26$	−0.495442	−0.0971641
$27$	1.00000	0.192450
$28$	0	0
$29$	8.33812	1.54835	0.774175	−	0.632971i	$-0.218165\pi$
$29$	8.33812	1.54835	0.774175	+	0.632971i	$0.218165\pi$
$30$	−2.67914	−0.489142
$31$	−2.45376	−0.440709	−0.220354	−	0.975420i	$-0.570721\pi$
$31$	−2.45376	−0.440709	−0.220354	+	0.975420i	$0.570721\pi$
$32$	5.81417	1.02781
$33$	−1.00000	−0.174078
$34$	4.69339	0.804911
$35$	0	0
$36$	1.14929	0.191548
$37$	−0.577754	−0.0949822	−0.0474911	−	0.998872i	$-0.515123\pi$
$37$	−0.577754	−0.0949822	−0.0474911	+	0.998872i	$0.515123\pi$
$38$	−11.6224	−1.88541
$39$	0.279181	0.0447048
$40$	2.27918	0.360370
$41$	0.287214	0.0448552	0.0224276	−	0.999748i	$-0.492860\pi$
$41$	0.287214	0.0448552	0.0224276	+	0.999748i	$0.492860\pi$
$42$	0	0
$43$	6.05894	0.923980	0.461990	−	0.886885i	$-0.347136\pi$
$43$	6.05894	0.923980	0.461990	+	0.886885i	$0.347136\pi$
$44$	−1.14929	−0.173261
$45$	1.50970	0.225052
$46$	−6.43361	−0.948583
$47$	1.76949	0.258106	0.129053	−	0.991638i	$-0.458806\pi$
$47$	1.76949	0.258106	0.129053	+	0.991638i	$0.458806\pi$
$48$	−4.97771	−0.718471
$49$	0	0
$50$	4.82843	0.682843
$51$	−2.64473	−0.370336
$52$	0.320859	0.0444952
$53$	9.28219	1.27501	0.637503	−	0.770447i	$-0.279967\pi$
$53$	9.28219	1.27501	0.637503	+	0.770447i	$0.279967\pi$
$54$	−1.77462	−0.241496
$55$	−1.50970	−0.203567
$56$	0	0
$57$	6.54925	0.867469
$58$	−14.7970	−1.94294
$59$	−2.52909	−0.329259	−0.164630	−	0.986355i	$-0.552643\pi$
$59$	−2.52909	−0.329259	−0.164630	+	0.986355i	$0.552643\pi$
$60$	1.73507	0.223997
$61$	−7.98394	−1.02224	−0.511119	−	0.859510i	$-0.670769\pi$
$61$	−7.98394	−1.02224	−0.511119	+	0.859510i	$0.670769\pi$
$62$	4.35451	0.553023
$63$	0	0
$64$	−0.362537	−0.0453172
$65$	0.421479	0.0522780
$66$	1.77462	0.218441
$67$	−13.0388	−1.59294	−0.796470	−	0.604677i	$-0.793302\pi$
$67$	−13.0388	−1.59294	−0.796470	+	0.604677i	$0.793302\pi$
$68$	−3.03955	−0.368600
$69$	3.62534	0.436439
$70$	0	0
$71$	−0.557278	−0.0661367	−0.0330684	−	0.999453i	$-0.510528\pi$
$71$	−0.557278	−0.0661367	−0.0330684	+	0.999453i	$0.510528\pi$
$72$	1.50970	0.177919
$73$	8.01939	0.938599	0.469299	−	0.883039i	$-0.344507\pi$
$73$	8.01939	0.938599	0.469299	+	0.883039i	$0.344507\pi$
$74$	1.02530	0.119188
$75$	−2.72082	−0.314173
$76$	7.52696	0.863401
$77$	0	0
$78$	−0.495442	−0.0560977
$79$	−8.90753	−1.00218	−0.501088	−	0.865397i	$-0.667067\pi$
$79$	−8.90753	−1.00218	−0.501088	+	0.865397i	$0.667067\pi$
$80$	−7.51483	−0.840184
$81$	1.00000	0.111111
$82$	−0.509696	−0.0562865
$83$	12.8760	1.41333	0.706663	−	0.707550i	$-0.250200\pi$
$83$	12.8760	1.41333	0.706663	+	0.707550i	$0.250200\pi$
$84$	0	0
$85$	−3.99273	−0.433073
$86$	−10.7523	−1.15945
$87$	8.33812	0.893941
$88$	−1.50970	−0.160934
$89$	11.8193	1.25284	0.626422	−	0.779484i	$-0.284519\pi$
$89$	11.8193	1.25284	0.626422	+	0.779484i	$0.284519\pi$
$90$	−2.67914	−0.282406
$91$	0	0
$92$	4.16655	0.434393
$93$	−2.45376	−0.254443
$94$	−3.14017	−0.323884
$95$	9.88737	1.01442
$96$	5.81417	0.593407
$97$	7.82766	0.794778	0.397389	−	0.917650i	$-0.369916\pi$
$97$	7.82766	0.794778	0.397389	+	0.917650i	$0.369916\pi$
$98$	0	0
$99$	−1.00000	−0.100504
$100$	−3.12700	−0.312700
$101$	5.09123	0.506596	0.253298	−	0.967388i	$-0.418485\pi$
$101$	5.09123	0.506596	0.253298	+	0.967388i	$0.418485\pi$
$102$	4.69339	0.464715
$103$	−9.10985	−0.897620	−0.448810	−	0.893627i	$-0.648152\pi$
$103$	−9.10985	−0.897620	−0.448810	+	0.893627i	$0.648152\pi$
$104$	0.421479	0.0413294
$105$	0	0
$106$	−16.4724	−1.59994
$107$	13.3963	1.29507	0.647534	−	0.762036i	$-0.275800\pi$
$107$	13.3963	1.29507	0.647534	+	0.762036i	$0.275800\pi$
$108$	1.14929	0.110590
$109$	10.5716	1.01258	0.506290	−	0.862363i	$-0.331017\pi$
$109$	10.5716	1.01258	0.506290	+	0.862363i	$0.331017\pi$
$110$	2.67914	0.255446
$111$	−0.577754	−0.0548380
$112$	0	0
$113$	−14.1981	−1.33564	−0.667821	−	0.744322i	$-0.732773\pi$
$113$	−14.1981	−1.33564	−0.667821	+	0.744322i	$0.732773\pi$
$114$	−11.6224	−1.08854
$115$	5.47316	0.510374
$116$	9.58289	0.889749
$117$	0.279181	0.0258103
$118$	4.48818	0.413170
$119$	0	0
$120$	2.27918	0.208060
$121$	1.00000	0.0909091
$122$	14.1685	1.28275
$123$	0.287214	0.0258972
$124$	−2.82008	−0.253250
$125$	−11.6561	−1.04255
$126$	0	0
$127$	−5.86798	−0.520699	−0.260349	−	0.965514i	$-0.583838\pi$
$127$	−5.86798	−0.520699	−0.260349	+	0.965514i	$0.583838\pi$
$128$	−10.9850	−0.970944
$129$	6.05894	0.533460
$130$	−0.747966	−0.0656010
$131$	8.51696	0.744130	0.372065	−	0.928207i	$-0.378650\pi$
$131$	8.51696	0.744130	0.372065	+	0.928207i	$0.378650\pi$
$132$	−1.14929	−0.100033
$133$	0	0
$134$	23.1389	1.99890
$135$	1.50970	0.129934
$136$	−3.99273	−0.342374
$137$	−9.05091	−0.773271	−0.386636	−	0.922233i	$-0.626363\pi$
$137$	−9.05091	−0.773271	−0.386636	+	0.922233i	$0.626363\pi$
$138$	−6.43361	−0.547665
$139$	5.91664	0.501843	0.250922	−	0.968007i	$-0.419266\pi$
$139$	5.91664	0.501843	0.250922	+	0.968007i	$0.419266\pi$
$140$	0	0
$141$	1.76949	0.149018
$142$	0.988958	0.0829915
$143$	−0.279181	−0.0233463
$144$	−4.97771	−0.414809
$145$	12.5880	1.04538
$146$	−14.2314	−1.17780
$147$	0	0
$148$	−0.664005	−0.0545809
$149$	8.99165	0.736625	0.368312	−	0.929702i	$-0.379936\pi$
$149$	8.99165	0.736625	0.368312	+	0.929702i	$0.379936\pi$
$150$	4.82843	0.394239
$151$	−16.2773	−1.32463	−0.662315	−	0.749225i	$-0.730426\pi$
$151$	−16.2773	−1.32463	−0.662315	+	0.749225i	$0.730426\pi$
$152$	9.88737	0.801972
$153$	−2.64473	−0.213814
$154$	0	0
$155$	−3.70444	−0.297548
$156$	0.320859	0.0256893
$157$	1.86388	0.148754	0.0743770	−	0.997230i	$-0.476303\pi$
$157$	1.86388	0.148754	0.0743770	+	0.997230i	$0.476303\pi$
$158$	15.8075	1.25758
$159$	9.28219	0.736126
$160$	8.77763	0.693933
$161$	0	0
$162$	−1.77462	−0.139428
$163$	−4.40285	−0.344858	−0.172429	−	0.985022i	$-0.555162\pi$
$163$	−4.40285	−0.344858	−0.172429	+	0.985022i	$0.555162\pi$
$164$	0.330091	0.0257757
$165$	−1.50970	−0.117530
$166$	−22.8501	−1.77351
$167$	19.9181	1.54131	0.770655	−	0.637252i	$-0.219929\pi$
$167$	19.9181	1.54131	0.770655	+	0.637252i	$0.219929\pi$
$168$	0	0
$169$	−12.9221	−0.994004
$170$	7.08560	0.543441
$171$	6.54925	0.500833
$172$	6.96346	0.530959
$173$	25.4704	1.93648	0.968238	−	0.250029i	$-0.0804401\pi$
$173$	25.4704	1.93648	0.968238	+	0.250029i	$0.0804401\pi$
$174$	−14.7970	−1.12176
$175$	0	0
$176$	4.97771	0.375209
$177$	−2.52909	−0.190098
$178$	−20.9748	−1.57213
$179$	14.6359	1.09394	0.546970	−	0.837152i	$-0.315781\pi$
$179$	14.6359	1.09394	0.546970	+	0.837152i	$0.315781\pi$
$180$	1.73507	0.129325
$181$	4.88737	0.363275	0.181638	−	0.983366i	$-0.441860\pi$
$181$	4.88737	0.363275	0.181638	+	0.983366i	$0.441860\pi$
$182$	0	0
$183$	−7.98394	−0.590189
$184$	5.47316	0.403486
$185$	−0.872233	−0.0641279
$186$	4.35451	0.319288
$187$	2.64473	0.193402
$188$	2.03365	0.148319
$189$	0	0
$190$	−17.5464	−1.27295
$191$	16.6291	1.20324	0.601620	−	0.798782i	$-0.294522\pi$
$191$	16.6291	1.20324	0.601620	+	0.798782i	$0.294522\pi$
$192$	−0.362537	−0.0261639
$193$	−0.431045	−0.0310273	−0.0155136	−	0.999880i	$-0.504938\pi$
$193$	−0.431045	−0.0310273	−0.0155136	+	0.999880i	$0.504938\pi$
$194$	−13.8911	−0.997326
$195$	0.421479	0.0301827
$196$	0	0
$197$	−0.146392	−0.0104300	−0.00521498	−	0.999986i	$-0.501660\pi$
$197$	−0.146392	−0.0104300	−0.00521498	+	0.999986i	$0.501660\pi$
$198$	1.77462	0.126117
$199$	23.1962	1.64434	0.822168	−	0.569245i	$-0.192764\pi$
$199$	23.1962	1.64434	0.822168	+	0.569245i	$0.192764\pi$
$200$	−4.10761	−0.290452
$201$	−13.0388	−0.919685
$202$	−9.03501	−0.635701
$203$	0	0
$204$	−3.03955	−0.212811
$205$	0.433605	0.0302843
$206$	16.1666	1.12638
$207$	3.62534	0.251978
$208$	−1.38968	−0.0963573
$209$	−6.54925	−0.453021
$210$	0	0
$211$	6.59715	0.454166	0.227083	−	0.973875i	$-0.427081\pi$
$211$	6.59715	0.454166	0.227083	+	0.973875i	$0.427081\pi$
$212$	10.6679	0.732674
$213$	−0.557278	−0.0381841
$214$	−23.7734	−1.62511
$215$	9.14716	0.623831
$216$	1.50970	0.102722
$217$	0	0
$218$	−18.7607	−1.27063
$219$	8.01939	0.541900
$220$	−1.73507	−0.116979
$221$	−0.738359	−0.0496674
$222$	1.02530	0.0688134
$223$	27.3525	1.83166	0.915829	−	0.401568i	$-0.131535\pi$
$223$	27.3525	1.83166	0.915829	+	0.401568i	$0.131535\pi$
$224$	0	0
$225$	−2.72082	−0.181388
$226$	25.1962	1.67603
$227$	11.5767	0.768371	0.384185	−	0.923256i	$-0.374482\pi$
$227$	11.5767	0.768371	0.384185	+	0.923256i	$0.374482\pi$
$228$	7.52696	0.498485
$229$	−7.48922	−0.494902	−0.247451	−	0.968900i	$-0.579593\pi$
$229$	−7.48922	−0.494902	−0.247451	+	0.968900i	$0.579593\pi$
$230$	−9.71279	−0.640442
$231$	0	0
$232$	12.5880	0.826445
$233$	11.7241	0.768074	0.384037	−	0.923318i	$-0.374533\pi$
$233$	11.7241	0.768074	0.384037	+	0.923318i	$0.374533\pi$
$234$	−0.495442	−0.0323880
$235$	2.67138	0.174262
$236$	−2.90665	−0.189207
$237$	−8.90753	−0.578606
$238$	0	0
$239$	−12.4012	−0.802164	−0.401082	−	0.916042i	$-0.631366\pi$
$239$	−12.4012	−0.802164	−0.401082	+	0.916042i	$0.631366\pi$
$240$	−7.51483	−0.485080
$241$	20.2061	1.30159	0.650795	−	0.759254i	$-0.274436\pi$
$241$	20.2061	1.30159	0.650795	+	0.759254i	$0.274436\pi$
$242$	−1.77462	−0.114077
$243$	1.00000	0.0641500
$244$	−9.17583	−0.587422
$245$	0	0
$246$	−0.509696	−0.0324970
$247$	1.82843	0.116340
$248$	−3.70444	−0.235232
$249$	12.8760	0.815984
$250$	20.6852	1.30824
$251$	−5.08745	−0.321117	−0.160558	−	0.987026i	$-0.551330\pi$
$251$	−5.08745	−0.321117	−0.160558	+	0.987026i	$0.551330\pi$
$252$	0	0
$253$	−3.62534	−0.227923
$254$	10.4134	0.653398
$255$	−3.99273	−0.250035
$256$	20.2193	1.26370
$257$	−16.9756	−1.05891	−0.529454	−	0.848339i	$-0.677603\pi$
$257$	−16.9756	−1.05891	−0.529454	+	0.848339i	$0.677603\pi$
$258$	−10.7523	−0.669411
$259$	0	0
$260$	0.484400	0.0300412
$261$	8.33812	0.516117
$262$	−15.1144	−0.933770
$263$	−22.3323	−1.37707	−0.688535	−	0.725203i	$-0.741746\pi$
$263$	−22.3323	−1.37707	−0.688535	+	0.725203i	$0.741746\pi$
$264$	−1.50970	−0.0929154
$265$	14.0133	0.860829
$266$	0	0
$267$	11.8193	0.723330
$268$	−14.9853	−0.915373
$269$	−20.5417	−1.25245	−0.626224	−	0.779643i	$-0.715400\pi$
$269$	−20.5417	−1.25245	−0.626224	+	0.779643i	$0.715400\pi$
$270$	−2.67914	−0.163047
$271$	−29.3149	−1.78075	−0.890376	−	0.455227i	$-0.849558\pi$
$271$	−29.3149	−1.78075	−0.890376	+	0.455227i	$0.849558\pi$
$272$	13.1647	0.798227
$273$	0	0
$274$	16.0620	0.970338
$275$	2.72082	0.164072
$276$	4.16655	0.250797
$277$	−21.1486	−1.27070	−0.635349	−	0.772225i	$-0.719144\pi$
$277$	−21.1486	−1.27070	−0.635349	+	0.772225i	$0.719144\pi$
$278$	−10.4998	−0.629737
$279$	−2.45376	−0.146903
$280$	0	0
$281$	−14.7788	−0.881631	−0.440816	−	0.897598i	$-0.645311\pi$
$281$	−14.7788	−0.881631	−0.440816	+	0.897598i	$0.645311\pi$
$282$	−3.14017	−0.186994
$283$	19.7326	1.17298	0.586491	−	0.809955i	$-0.300509\pi$
$283$	19.7326	1.17298	0.586491	+	0.809955i	$0.300509\pi$
$284$	−0.640472	−0.0380050
$285$	9.88737	0.585677
$286$	0.495442	0.0292961
$287$	0	0
$288$	5.81417	0.342603
$289$	−10.0054	−0.588554
$290$	−22.3390	−1.31179
$291$	7.82766	0.458866
$292$	9.21658	0.539359
$293$	−26.0851	−1.52391	−0.761954	−	0.647631i	$-0.775760\pi$
$293$	−26.0851	−1.52391	−0.761954	+	0.647631i	$0.775760\pi$
$294$	0	0
$295$	−3.81815	−0.222301
$296$	−0.872233	−0.0506975
$297$	−1.00000	−0.0580259
$298$	−15.9568	−0.924352
$299$	1.01213	0.0585328
$300$	−3.12700	−0.180537
$301$	0	0
$302$	28.8861	1.66221
$303$	5.09123	0.292483
$304$	−32.6003	−1.86975
$305$	−12.0533	−0.690171
$306$	4.69339	0.268304
$307$	15.6796	0.894880	0.447440	−	0.894314i	$-0.352336\pi$
$307$	15.6796	0.894880	0.447440	+	0.894314i	$0.352336\pi$
$308$	0	0
$309$	−9.10985	−0.518241
$310$	6.57398	0.373377
$311$	7.62233	0.432223	0.216111	−	0.976369i	$-0.430663\pi$
$311$	7.62233	0.432223	0.216111	+	0.976369i	$0.430663\pi$
$312$	0.421479	0.0238615
$313$	−16.6044	−0.938537	−0.469268	−	0.883056i	$-0.655482\pi$
$313$	−16.6044	−0.938537	−0.469268	+	0.883056i	$0.655482\pi$
$314$	−3.30769	−0.186664
$315$	0	0
$316$	−10.2373	−0.575893
$317$	−13.2020	−0.741499	−0.370749	−	0.928733i	$-0.620899\pi$
$317$	−13.2020	−0.741499	−0.370749	+	0.928733i	$0.620899\pi$
$318$	−16.4724	−0.923726
$319$	−8.33812	−0.466845
$320$	−0.547321	−0.0305962
$321$	13.3963	0.747708
$322$	0	0
$323$	−17.3210	−0.963765
$324$	1.14929	0.0638492
$325$	−0.759602	−0.0421351
$326$	7.81341	0.432745
$327$	10.5716	0.584613
$328$	0.433605	0.0239418
$329$	0	0
$330$	2.67914	0.147482
$331$	27.3197	1.50163	0.750814	−	0.660514i	$-0.229661\pi$
$331$	27.3197	1.50163	0.750814	+	0.660514i	$0.229661\pi$
$332$	14.7982	0.812158
$333$	−0.577754	−0.0316607
$334$	−35.3472	−1.93411
$335$	−19.6846	−1.07548
$336$	0	0
$337$	−17.9036	−0.975271	−0.487635	−	0.873047i	$-0.662140\pi$
$337$	−17.9036	−0.975271	−0.487635	+	0.873047i	$0.662140\pi$
$338$	22.9318	1.24732
$339$	−14.1981	−0.771133
$340$	−4.58880	−0.248862
$341$	2.45376	0.132879
$342$	−11.6224	−0.628470
$343$	0	0
$344$	9.14716	0.493182
$345$	5.47316	0.294665
$346$	−45.2003	−2.42998
$347$	−12.3213	−0.661442	−0.330721	−	0.943729i	$-0.607292\pi$
$347$	−12.3213	−0.661442	−0.330721	+	0.943729i	$0.607292\pi$
$348$	9.58289	0.513697
$349$	−11.1970	−0.599361	−0.299680	−	0.954040i	$-0.596880\pi$
$349$	−11.1970	−0.599361	−0.299680	+	0.954040i	$0.596880\pi$
$350$	0	0
$351$	0.279181	0.0149016
$352$	−5.81417	−0.309896
$353$	−0.174133	−0.00926816	−0.00463408	−	0.999989i	$-0.501475\pi$
$353$	−0.174133	−0.00926816	−0.00463408	+	0.999989i	$0.501475\pi$
$354$	4.48818	0.238544
$355$	−0.841320	−0.0446526
$356$	13.5838	0.719939
$357$	0	0
$358$	−25.9733	−1.37273
$359$	−21.1248	−1.11493	−0.557463	−	0.830202i	$-0.688225\pi$
$359$	−21.1248	−1.11493	−0.557463	+	0.830202i	$0.688225\pi$
$360$	2.27918	0.120123
$361$	23.8926	1.25751
$362$	−8.67324	−0.455855
$363$	1.00000	0.0524864
$364$	0	0
$365$	12.1068	0.633701
$366$	14.1685	0.740598
$367$	−14.9221	−0.778925	−0.389463	−	0.921042i	$-0.627339\pi$
$367$	−14.9221	−0.778925	−0.389463	+	0.921042i	$0.627339\pi$
$368$	−18.0459	−0.940707
$369$	0.287214	0.0149517
$370$	1.54788	0.0804707
$371$	0	0
$372$	−2.82008	−0.146214
$373$	12.8713	0.666451	0.333225	−	0.942847i	$-0.391863\pi$
$373$	12.8713	0.666451	0.333225	+	0.942847i	$0.391863\pi$
$374$	−4.69339	−0.242690
$375$	−11.6561	−0.601918
$376$	2.67138	0.137766
$377$	2.32785	0.119890
$378$	0	0
$379$	35.2542	1.81089	0.905444	−	0.424466i	$-0.139538\pi$
$379$	35.2542	1.81089	0.905444	+	0.424466i	$0.139538\pi$
$380$	11.3634	0.582931
$381$	−5.86798	−0.300626
$382$	−29.5104	−1.50988
$383$	−4.51162	−0.230533	−0.115267	−	0.993335i	$-0.536772\pi$
$383$	−4.51162	−0.230533	−0.115267	+	0.993335i	$0.536772\pi$
$384$	−10.9850	−0.560575
$385$	0	0
$386$	0.764942	0.0389345
$387$	6.05894	0.307993
$388$	8.99622	0.456714
$389$	34.4439	1.74637	0.873187	−	0.487385i	$-0.162049\pi$
$389$	34.4439	1.74637	0.873187	+	0.487385i	$0.162049\pi$
$390$	−0.747966	−0.0378747
$391$	−9.58803	−0.484887
$392$	0	0
$393$	8.51696	0.429624
$394$	0.259790	0.0130880
$395$	−13.4477	−0.676625
$396$	−1.14929	−0.0577538
$397$	18.0924	0.908031	0.454015	−	0.890994i	$-0.349991\pi$
$397$	18.0924	0.908031	0.454015	+	0.890994i	$0.349991\pi$
$398$	−41.1645	−2.06339
$399$	0	0
$400$	13.5435	0.677173
$401$	−36.0189	−1.79870	−0.899348	−	0.437234i	$-0.855958\pi$
$401$	−36.0189	−1.79870	−0.899348	+	0.437234i	$0.855958\pi$
$402$	23.1389	1.15406
$403$	−0.685045	−0.0341245
$404$	5.85128	0.291112
$405$	1.50970	0.0750174
$406$	0	0
$407$	0.577754	0.0286382
$408$	−3.99273	−0.197670
$409$	−20.9521	−1.03601	−0.518007	−	0.855376i	$-0.673326\pi$
$409$	−20.9521	−1.03601	−0.518007	+	0.855376i	$0.673326\pi$
$410$	−0.769486	−0.0380022
$411$	−9.05091	−0.446448
$412$	−10.4698	−0.515811
$413$	0	0
$414$	−6.43361	−0.316194
$415$	19.4389	0.954216
$416$	1.62321	0.0795843
$417$	5.91664	0.289739
$418$	11.6224	0.568472
$419$	−30.2123	−1.47597	−0.737983	−	0.674819i	$-0.764222\pi$
$419$	−30.2123	−1.47597	−0.737983	+	0.674819i	$0.764222\pi$
$420$	0	0
$421$	−35.7453	−1.74212	−0.871060	−	0.491177i	$-0.836567\pi$
$421$	−35.7453	−1.74212	−0.871060	+	0.491177i	$0.836567\pi$
$422$	−11.7074	−0.569910
$423$	1.76949	0.0860353
$424$	14.0133	0.680545
$425$	7.19583	0.349049
$426$	0.988958	0.0479152
$427$	0	0
$428$	15.3962	0.744203
$429$	−0.279181	−0.0134790
$430$	−16.2328	−0.782813
$431$	−15.6130	−0.752054	−0.376027	−	0.926609i	$-0.622710\pi$
$431$	−15.6130	−0.752054	−0.376027	+	0.926609i	$0.622710\pi$
$432$	−4.97771	−0.239490
$433$	−39.4376	−1.89525	−0.947625	−	0.319384i	$-0.896524\pi$
$433$	−39.4376	−1.89525	−0.947625	+	0.319384i	$0.896524\pi$
$434$	0	0
$435$	12.5880	0.603550
$436$	12.1499	0.581872
$437$	23.7432	1.13579
$438$	−14.2314	−0.680002
$439$	−33.0105	−1.57551	−0.787753	−	0.615992i	$-0.788756\pi$
$439$	−33.0105	−1.57551	−0.787753	+	0.615992i	$0.788756\pi$
$440$	−2.27918	−0.108656
$441$	0	0
$442$	1.31031	0.0623250
$443$	−12.6691	−0.601929	−0.300965	−	0.953635i	$-0.597309\pi$
$443$	−12.6691	−0.601929	−0.300965	+	0.953635i	$0.597309\pi$
$444$	−0.664005	−0.0315123
$445$	17.8436	0.845866
$446$	−48.5404	−2.29845
$447$	8.99165	0.425290
$448$	0	0
$449$	−21.0426	−0.993060	−0.496530	−	0.868020i	$-0.665393\pi$
$449$	−21.0426	−0.993060	−0.496530	+	0.868020i	$0.665393\pi$
$450$	4.82843	0.227614
$451$	−0.287214	−0.0135244
$452$	−16.3176	−0.767518
$453$	−16.2773	−0.764776
$454$	−20.5442	−0.964188
$455$	0	0
$456$	9.88737	0.463018
$457$	−22.3176	−1.04398	−0.521988	−	0.852953i	$-0.674809\pi$
$457$	−22.3176	−1.04398	−0.521988	+	0.852953i	$0.674809\pi$
$458$	13.2905	0.621026
$459$	−2.64473	−0.123445
$460$	6.29022	0.293283
$461$	−6.50090	−0.302777	−0.151388	−	0.988474i	$-0.548374\pi$
$461$	−6.50090	−0.302777	−0.151388	+	0.988474i	$0.548374\pi$
$462$	0	0
$463$	22.0517	1.02483	0.512416	−	0.858737i	$-0.328751\pi$
$463$	22.0517	1.02483	0.512416	+	0.858737i	$0.328751\pi$
$464$	−41.5048	−1.92681
$465$	−3.70444	−0.171789
$466$	−20.8059	−0.963816
$467$	6.83793	0.316422	0.158211	−	0.987405i	$-0.449427\pi$
$467$	6.83793	0.316422	0.158211	+	0.987405i	$0.449427\pi$
$468$	0.320859	0.0148317
$469$	0	0
$470$	−4.74070	−0.218672
$471$	1.86388	0.0858832
$472$	−3.81815	−0.175745
$473$	−6.05894	−0.278590
$474$	15.8075	0.726063
$475$	−17.8193	−0.817606
$476$	0	0
$477$	9.28219	0.425002
$478$	22.0074	1.00659
$479$	9.01955	0.412114	0.206057	−	0.978540i	$-0.433937\pi$
$479$	9.01955	0.412114	0.206057	+	0.978540i	$0.433937\pi$
$480$	8.77763	0.400642
$481$	−0.161298	−0.00735456
$482$	−35.8582	−1.63330
$483$	0	0
$484$	1.14929	0.0522403
$485$	11.8174	0.536600
$486$	−1.77462	−0.0804985
$487$	−8.28830	−0.375579	−0.187789	−	0.982209i	$-0.560132\pi$
$487$	−8.28830	−0.375579	−0.187789	+	0.982209i	$0.560132\pi$
$488$	−12.0533	−0.545628
$489$	−4.40285	−0.199104
$490$	0	0
$491$	−16.9816	−0.766369	−0.383185	−	0.923672i	$-0.625173\pi$
$491$	−16.9816	−0.766369	−0.383185	+	0.923672i	$0.625173\pi$
$492$	0.330091	0.0148816
$493$	−22.0521	−0.993175
$494$	−3.24477	−0.145989
$495$	−1.50970	−0.0678558
$496$	12.2141	0.548431
$497$	0	0
$498$	−22.8501	−1.02394
$499$	−7.07308	−0.316635	−0.158317	−	0.987388i	$-0.550607\pi$
$499$	−7.07308	−0.316635	−0.158317	+	0.987388i	$0.550607\pi$
$500$	−13.3962	−0.599096
$501$	19.9181	0.889876
$502$	9.02831	0.402953
$503$	27.0110	1.20436	0.602181	−	0.798359i	$-0.294298\pi$
$503$	27.0110	1.20436	0.602181	+	0.798359i	$0.294298\pi$
$504$	0	0
$505$	7.68620	0.342032
$506$	6.43361	0.286009
$507$	−12.9221	−0.573889
$508$	−6.74399	−0.299216
$509$	−36.5586	−1.62043	−0.810216	−	0.586132i	$-0.800650\pi$
$509$	−36.5586	−1.62043	−0.810216	+	0.586132i	$0.800650\pi$
$510$	7.08560	0.313756
$511$	0	0
$512$	−13.9116	−0.614813
$513$	6.54925	0.289156
$514$	30.1253	1.32877
$515$	−13.7531	−0.606034
$516$	6.96346	0.306549
$517$	−1.76949	−0.0778219
$518$	0	0
$519$	25.4704	1.11803
$520$	0.636305	0.0279038
$521$	−34.8294	−1.52590	−0.762952	−	0.646455i	$-0.776251\pi$
$521$	−34.8294	−1.52590	−0.762952	+	0.646455i	$0.776251\pi$
$522$	−14.7970	−0.647648
$523$	35.6623	1.55940	0.779701	−	0.626152i	$-0.215371\pi$
$523$	35.6623	1.55940	0.779701	+	0.626152i	$0.215371\pi$
$524$	9.78843	0.427609
$525$	0	0
$526$	39.6315	1.72801
$527$	6.48954	0.282689
$528$	4.97771	0.216627
$529$	−9.85694	−0.428562
$530$	−24.8683	−1.08021
$531$	−2.52909	−0.109753
$532$	0	0
$533$	0.0801847	0.00347318
$534$	−20.9748	−0.907669
$535$	20.2243	0.874374
$536$	−19.6846	−0.850245
$537$	14.6359	0.631587
$538$	36.4537	1.57163
$539$	0	0
$540$	1.73507	0.0746656
$541$	−1.45517	−0.0625625	−0.0312812	−	0.999511i	$-0.509959\pi$
$541$	−1.45517	−0.0625625	−0.0312812	+	0.999511i	$0.509959\pi$
$542$	52.0228	2.23457
$543$	4.88737	0.209737
$544$	−15.3769	−0.659279
$545$	15.9600	0.683650
$546$	0	0
$547$	−18.0013	−0.769681	−0.384840	−	0.922983i	$-0.625743\pi$
$547$	−18.0013	−0.769681	−0.384840	+	0.922983i	$0.625743\pi$
$548$	−10.4021	−0.444355
$549$	−7.98394	−0.340746
$550$	−4.82843	−0.205885
$551$	54.6084	2.32640
$552$	5.47316	0.232953
$553$	0	0
$554$	37.5309	1.59453
$555$	−0.872233	−0.0370242
$556$	6.79992	0.288381
$557$	20.9968	0.889662	0.444831	−	0.895615i	$-0.353264\pi$
$557$	20.9968	0.889662	0.444831	+	0.895615i	$0.353264\pi$
$558$	4.35451	0.184341
$559$	1.69154	0.0715447
$560$	0	0
$561$	2.64473	0.111661
$562$	26.2269	1.10631
$563$	29.0382	1.22382	0.611908	−	0.790929i	$-0.290402\pi$
$563$	29.0382	1.22382	0.611908	+	0.790929i	$0.290402\pi$
$564$	2.03365	0.0856319
$565$	−21.4348	−0.901767
$566$	−35.0180	−1.47192
$567$	0	0
$568$	−0.841320	−0.0353010
$569$	−23.0942	−0.968161	−0.484080	−	0.875024i	$-0.660846\pi$
$569$	−23.0942	−0.968161	−0.484080	+	0.875024i	$0.660846\pi$
$570$	−17.5464	−0.734936
$571$	−29.6742	−1.24183	−0.620914	−	0.783879i	$-0.713238\pi$
$571$	−29.6742	−1.24183	−0.620914	+	0.783879i	$0.713238\pi$
$572$	−0.320859	−0.0134158
$573$	16.6291	0.694691
$574$	0	0
$575$	−9.86388	−0.411352
$576$	−0.362537	−0.0151057
$577$	22.1151	0.920664	0.460332	−	0.887747i	$-0.347730\pi$
$577$	22.1151	0.920664	0.460332	+	0.887747i	$0.347730\pi$
$578$	17.7558	0.738545
$579$	−0.431045	−0.0179136
$580$	14.4673	0.600720
$581$	0	0
$582$	−13.8911	−0.575806
$583$	−9.28219	−0.384429
$584$	12.1068	0.500985
$585$	0.421479	0.0174260
$586$	46.2912	1.91227
$587$	−3.34660	−0.138129	−0.0690646	−	0.997612i	$-0.522001\pi$
$587$	−3.34660	−0.138129	−0.0690646	+	0.997612i	$0.522001\pi$
$588$	0	0
$589$	−16.0703	−0.662165
$590$	6.77578	0.278954
$591$	−0.146392	−0.00602174
$592$	2.87589	0.118199
$593$	−21.8528	−0.897385	−0.448693	−	0.893686i	$-0.648110\pi$
$593$	−21.8528	−0.897385	−0.448693	+	0.893686i	$0.648110\pi$
$594$	1.77462	0.0728137
$595$	0	0
$596$	10.3340	0.423296
$597$	23.1962	0.949358
$598$	−1.79614	−0.0734497
$599$	11.8396	0.483754	0.241877	−	0.970307i	$-0.422237\pi$
$599$	11.8396	0.483754	0.241877	+	0.970307i	$0.422237\pi$
$600$	−4.10761	−0.167692
$601$	25.2173	1.02864	0.514318	−	0.857600i	$-0.328045\pi$
$601$	25.2173	1.02864	0.514318	+	0.857600i	$0.328045\pi$
$602$	0	0
$603$	−13.0388	−0.530980
$604$	−18.7073	−0.761190
$605$	1.50970	0.0613779
$606$	−9.03501	−0.367022
$607$	40.1761	1.63070	0.815348	−	0.578971i	$-0.196546\pi$
$607$	40.1761	1.63070	0.815348	+	0.578971i	$0.196546\pi$
$608$	38.0784	1.54428
$609$	0	0
$610$	21.3901	0.866059
$611$	0.494007	0.0199854
$612$	−3.03955	−0.122867
$613$	44.0389	1.77871	0.889356	−	0.457215i	$-0.151153\pi$
$613$	44.0389	1.77871	0.889356	+	0.457215i	$0.151153\pi$
$614$	−27.8253	−1.12294
$615$	0.433605	0.0174846
$616$	0	0
$617$	40.7941	1.64231	0.821155	−	0.570705i	$-0.193330\pi$
$617$	40.7941	1.64231	0.821155	+	0.570705i	$0.193330\pi$
$618$	16.1666	0.650314
$619$	−26.2705	−1.05590	−0.527949	−	0.849276i	$-0.677039\pi$
$619$	−26.2705	−1.05590	−0.527949	+	0.849276i	$0.677039\pi$
$620$	−4.25746	−0.170984
$621$	3.62534	0.145480
$622$	−13.5268	−0.542374
$623$	0	0
$624$	−1.38968	−0.0556319
$625$	−3.99305	−0.159722
$626$	29.4666	1.17772
$627$	−6.54925	−0.261552
$628$	2.14214	0.0854805
$629$	1.52800	0.0609255
$630$	0	0
$631$	−28.3073	−1.12690	−0.563448	−	0.826151i	$-0.690526\pi$
$631$	−28.3073	−1.12690	−0.563448	+	0.826151i	$0.690526\pi$
$632$	−13.4477	−0.534919
$633$	6.59715	0.262213
$634$	23.4286	0.930468
$635$	−8.85886	−0.351553
$636$	10.6679	0.423010
$637$	0	0
$638$	14.7970	0.585820
$639$	−0.557278	−0.0220456
$640$	−16.5840	−0.655539
$641$	46.0039	1.81704	0.908522	−	0.417837i	$-0.137212\pi$
$641$	46.0039	1.81704	0.908522	+	0.417837i	$0.137212\pi$
$642$	−23.7734	−0.938260
$643$	−21.1574	−0.834368	−0.417184	−	0.908822i	$-0.636983\pi$
$643$	−21.1574	−0.834368	−0.417184	+	0.908822i	$0.636983\pi$
$644$	0	0
$645$	9.14716	0.360169
$646$	30.7382	1.20938
$647$	−6.19173	−0.243422	−0.121711	−	0.992566i	$-0.538838\pi$
$647$	−6.19173	−0.243422	−0.121711	+	0.992566i	$0.538838\pi$
$648$	1.50970	0.0593065
$649$	2.52909	0.0992754
$650$	1.34801	0.0528732
$651$	0	0
$652$	−5.06014	−0.198170
$653$	−22.4958	−0.880328	−0.440164	−	0.897917i	$-0.645080\pi$
$653$	−22.4958	−0.880328	−0.440164	+	0.897917i	$0.645080\pi$
$654$	−18.7607	−0.733601
$655$	12.8580	0.502404
$656$	−1.42967	−0.0558191
$657$	8.01939	0.312866
$658$	0	0
$659$	−32.2569	−1.25655	−0.628274	−	0.777992i	$-0.716238\pi$
$659$	−32.2569	−1.25655	−0.628274	+	0.777992i	$0.716238\pi$
$660$	−1.73507	−0.0675376
$661$	29.5734	1.15027	0.575137	−	0.818057i	$-0.304949\pi$
$661$	29.5734	1.15027	0.575137	+	0.818057i	$0.304949\pi$
$662$	−48.4822	−1.88431
$663$	−0.738359	−0.0286755
$664$	19.4389	0.754374
$665$	0	0
$666$	1.02530	0.0397294
$667$	30.2285	1.17045
$668$	22.8916	0.885704
$669$	27.3525	1.05751
$670$	34.9327	1.34957
$671$	7.98394	0.308216
$672$	0	0
$673$	−14.4790	−0.558125	−0.279063	−	0.960273i	$-0.590024\pi$
$673$	−14.4790	−0.558125	−0.279063	+	0.960273i	$0.590024\pi$
$674$	31.7721	1.22382
$675$	−2.72082	−0.104724
$676$	−14.8511	−0.571198
$677$	19.2805	0.741010	0.370505	−	0.928831i	$-0.379185\pi$
$677$	19.2805	0.741010	0.370505	+	0.928831i	$0.379185\pi$
$678$	25.1962	0.967655
$679$	0	0
$680$	−6.02781	−0.231156
$681$	11.5767	0.443619
$682$	−4.35451	−0.166743
$683$	13.3754	0.511794	0.255897	−	0.966704i	$-0.417629\pi$
$683$	13.3754	0.511794	0.255897	+	0.966704i	$0.417629\pi$
$684$	7.52696	0.287800
$685$	−13.6641	−0.522079
$686$	0	0
$687$	−7.48922	−0.285732
$688$	−30.1597	−1.14983
$689$	2.59141	0.0987250
$690$	−9.71279	−0.369759
$691$	−40.4091	−1.53724	−0.768618	−	0.639708i	$-0.779055\pi$
$691$	−40.4091	−1.53724	−0.768618	+	0.639708i	$0.779055\pi$
$692$	29.2728	1.11278
$693$	0	0
$694$	21.8656	0.830009
$695$	8.93233	0.338823
$696$	12.5880	0.477148
$697$	−0.759602	−0.0287720
$698$	19.8704	0.752107
$699$	11.7241	0.443448
$700$	0	0
$701$	−24.8023	−0.936771	−0.468385	−	0.883524i	$-0.655164\pi$
$701$	−24.8023	−0.936771	−0.468385	+	0.883524i	$0.655164\pi$
$702$	−0.495442	−0.0186992
$703$	−3.78385	−0.142711
$704$	0.362537	0.0136636
$705$	2.67138	0.100610
$706$	0.309020	0.0116301
$707$	0	0
$708$	−2.90665	−0.109238
$709$	−48.3995	−1.81768	−0.908840	−	0.417145i	$-0.863031\pi$
$709$	−48.3995	−1.81768	−0.908840	+	0.417145i	$0.863031\pi$
$710$	1.49303	0.0560323
$711$	−8.90753	−0.334058
$712$	17.8436	0.668716
$713$	−8.89572	−0.333147
$714$	0	0
$715$	−0.421479	−0.0157624
$716$	16.8209	0.628626
$717$	−12.4012	−0.463130
$718$	37.4886	1.39906
$719$	38.1699	1.42350	0.711748	−	0.702435i	$-0.247904\pi$
$719$	38.1699	1.42350	0.711748	+	0.702435i	$0.247904\pi$
$720$	−7.51483	−0.280061
$721$	0	0
$722$	−42.4004	−1.57798
$723$	20.2061	0.751473
$724$	5.61699	0.208754
$725$	−22.6865	−0.842556
$726$	−1.77462	−0.0658624
$727$	43.3576	1.60804	0.804022	−	0.594600i	$-0.202689\pi$
$727$	43.3576	1.60804	0.804022	+	0.594600i	$0.202689\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−21.4851	−0.795198
$731$	−16.0243	−0.592678
$732$	−9.17583	−0.339148
$733$	−19.1761	−0.708284	−0.354142	−	0.935192i	$-0.615227\pi$
$733$	−19.1761	−0.708284	−0.354142	+	0.935192i	$0.615227\pi$
$734$	26.4810	0.977432
$735$	0	0
$736$	21.0783	0.776958
$737$	13.0388	0.480290
$738$	−0.509696	−0.0187622
$739$	3.76780	0.138601	0.0693003	−	0.997596i	$-0.477923\pi$
$739$	3.76780	0.138601	0.0693003	+	0.997596i	$0.477923\pi$
$740$	−1.00245	−0.0368506
$741$	1.82843	0.0671689
$742$	0	0
$743$	−18.2517	−0.669590	−0.334795	−	0.942291i	$-0.608667\pi$
$743$	−18.2517	−0.669590	−0.334795	+	0.942291i	$0.608667\pi$
$744$	−3.70444	−0.135811
$745$	13.5747	0.497337
$746$	−22.8417	−0.836294
$747$	12.8760	0.471109
$748$	3.03955	0.111137
$749$	0	0
$750$	20.6852	0.755315
$751$	−50.7647	−1.85243	−0.926215	−	0.376996i	$-0.876957\pi$
$751$	−50.7647	−1.85243	−0.926215	+	0.376996i	$0.876957\pi$
$752$	−8.80799	−0.321194
$753$	−5.08745	−0.185397
$754$	−4.13105	−0.150444
$755$	−24.5738	−0.894333
$756$	0	0
$757$	10.6671	0.387703	0.193852	−	0.981031i	$-0.437902\pi$
$757$	10.6671	0.387703	0.193852	+	0.981031i	$0.437902\pi$
$758$	−62.5630	−2.27239
$759$	−3.62534	−0.131591
$760$	14.9269	0.541456
$761$	−30.8023	−1.11658	−0.558292	−	0.829645i	$-0.688543\pi$
$761$	−30.8023	−1.11658	−0.558292	+	0.829645i	$0.688543\pi$
$762$	10.4134	0.377239
$763$	0	0
$764$	19.1116	0.691434
$765$	−3.99273	−0.144358
$766$	8.00643	0.289284
$767$	−0.706074	−0.0254949
$768$	20.2193	0.729600
$769$	−33.5543	−1.21000	−0.605000	−	0.796225i	$-0.706827\pi$
$769$	−33.5543	−1.21000	−0.605000	+	0.796225i	$0.706827\pi$
$770$	0	0
$771$	−16.9756	−0.611361
$772$	−0.495394	−0.0178296
$773$	−1.81646	−0.0653334	−0.0326667	−	0.999466i	$-0.510400\pi$
$773$	−1.81646	−0.0653334	−0.0326667	+	0.999466i	$0.510400\pi$
$774$	−10.7523	−0.386485
$775$	6.67625	0.239818
$776$	11.8174	0.424219
$777$	0	0
$778$	−61.1249	−2.19143
$779$	1.88103	0.0673950
$780$	0.484400	0.0173443
$781$	0.557278	0.0199410
$782$	17.0151	0.608460
$783$	8.33812	0.297980
$784$	0	0
$785$	2.81390	0.100432
$786$	−15.1144	−0.539113
$787$	40.2018	1.43304	0.716520	−	0.697566i	$-0.245734\pi$
$787$	40.2018	1.43304	0.716520	+	0.697566i	$0.245734\pi$
$788$	−0.168246	−0.00599351
$789$	−22.3323	−0.795052
$790$	23.8645	0.849061
$791$	0	0
$792$	−1.50970	−0.0536447
$793$	−2.22897	−0.0791529
$794$	−32.1072	−1.13944
$795$	14.0133	0.497000
$796$	26.6591	0.944907
$797$	51.0206	1.80724	0.903621	−	0.428332i	$-0.140899\pi$
$797$	51.0206	1.80724	0.903621	+	0.428332i	$0.140899\pi$
$798$	0	0
$799$	−4.67981	−0.165560
$800$	−15.8193	−0.559297
$801$	11.8193	0.417615
$802$	63.9199	2.25709
$803$	−8.01939	−0.282998
$804$	−14.9853	−0.528491
$805$	0	0
$806$	1.21570	0.0428211
$807$	−20.5417	−0.723101
$808$	7.68620	0.270400
$809$	18.0762	0.635524	0.317762	−	0.948170i	$-0.397069\pi$
$809$	18.0762	0.635524	0.317762	+	0.948170i	$0.397069\pi$
$810$	−2.67914	−0.0941354
$811$	0.0773069	0.00271461	0.00135731	−	0.999999i	$-0.499568\pi$
$811$	0.0773069	0.00271461	0.00135731	+	0.999999i	$0.499568\pi$
$812$	0	0
$813$	−29.3149	−1.02812
$814$	−1.02530	−0.0359366
$815$	−6.64697	−0.232833
$816$	13.1647	0.460857
$817$	39.6815	1.38828
$818$	37.1821	1.30004
$819$	0	0
$820$	0.498336	0.0174027
$821$	−2.22626	−0.0776970	−0.0388485	−	0.999245i	$-0.512369\pi$
$821$	−2.22626	−0.0776970	−0.0388485	+	0.999245i	$0.512369\pi$
$822$	16.0620	0.560225
$823$	27.3616	0.953766	0.476883	−	0.878967i	$-0.341767\pi$
$823$	27.3616	0.953766	0.476883	+	0.878967i	$0.341767\pi$
$824$	−13.7531	−0.479112
$825$	2.72082	0.0947267
$826$	0	0
$827$	34.8624	1.21228	0.606142	−	0.795356i	$-0.292716\pi$
$827$	34.8624	1.21228	0.606142	+	0.795356i	$0.292716\pi$
$828$	4.16655	0.144798
$829$	−18.3007	−0.635608	−0.317804	−	0.948156i	$-0.602945\pi$
$829$	−18.3007	−0.635608	−0.317804	+	0.948156i	$0.602945\pi$
$830$	−34.4966	−1.19740
$831$	−21.1486	−0.733638
$832$	−0.101214	−0.00350895
$833$	0	0
$834$	−10.4998	−0.363579
$835$	30.0703	1.04063
$836$	−7.52696	−0.260325
$837$	−2.45376	−0.0848145
$838$	53.6154	1.85211
$839$	21.0568	0.726961	0.363480	−	0.931602i	$-0.381588\pi$
$839$	21.0568	0.726961	0.363480	+	0.931602i	$0.381588\pi$
$840$	0	0
$841$	40.5243	1.39739
$842$	63.4344	2.18609
$843$	−14.7788	−0.509010
$844$	7.58201	0.260984
$845$	−19.5084	−0.671109
$846$	−3.14017	−0.107961
$847$	0	0
$848$	−46.2041	−1.58665
$849$	19.7326	0.677222
$850$	−12.7699	−0.438003
$851$	−2.09455	−0.0718004
$852$	−0.640472	−0.0219422
$853$	13.9597	0.477970	0.238985	−	0.971023i	$-0.423185\pi$
$853$	13.9597	0.477970	0.238985	+	0.971023i	$0.423185\pi$
$854$	0	0
$855$	9.88737	0.338141
$856$	20.2243	0.691253
$857$	15.2003	0.519233	0.259616	−	0.965712i	$-0.416404\pi$
$857$	15.2003	0.519233	0.259616	+	0.965712i	$0.416404\pi$
$858$	0.495442	0.0169141
$859$	−37.6856	−1.28582	−0.642908	−	0.765943i	$-0.722272\pi$
$859$	−37.6856	−1.28582	−0.642908	+	0.765943i	$0.722272\pi$
$860$	10.5127	0.358480
$861$	0	0
$862$	27.7073	0.943713
$863$	−20.4836	−0.697269	−0.348635	−	0.937259i	$-0.613355\pi$
$863$	−20.4836	−0.697269	−0.348635	+	0.937259i	$0.613355\pi$
$864$	5.81417	0.197802
$865$	38.4525	1.30742
$866$	69.9869	2.37825
$867$	−10.0054	−0.339802
$868$	0	0
$869$	8.90753	0.302167
$870$	−22.3390	−0.757363
$871$	−3.64018	−0.123343
$872$	15.9600	0.540473
$873$	7.82766	0.264926
$874$	−42.1353	−1.42525
$875$	0	0
$876$	9.21658	0.311399
$877$	11.8418	0.399869	0.199935	−	0.979809i	$-0.435927\pi$
$877$	11.8418	0.399869	0.199935	+	0.979809i	$0.435927\pi$
$878$	58.5812	1.97702
$879$	−26.0851	−0.879829
$880$	7.51483	0.253325
$881$	7.50608	0.252886	0.126443	−	0.991974i	$-0.459644\pi$
$881$	7.50608	0.252886	0.126443	+	0.991974i	$0.459644\pi$
$882$	0	0
$883$	−20.7705	−0.698982	−0.349491	−	0.936940i	$-0.613646\pi$
$883$	−20.7705	−0.698982	−0.349491	+	0.936940i	$0.613646\pi$
$884$	−0.848586	−0.0285410
$885$	−3.81815	−0.128346
$886$	22.4830	0.755329
$887$	14.0626	0.472175	0.236087	−	0.971732i	$-0.424135\pi$
$887$	14.0626	0.472175	0.236087	+	0.971732i	$0.424135\pi$
$888$	−0.872233	−0.0292702
$889$	0	0
$890$	−31.6656	−1.06143
$891$	−1.00000	−0.0335013
$892$	31.4358	1.05255
$893$	11.5888	0.387804
$894$	−15.9568	−0.533675
$895$	22.0958	0.738581
$896$	0	0
$897$	1.01213	0.0337939
$898$	37.3426	1.24614
$899$	−20.4598	−0.682372
$900$	−3.12700	−0.104233
$901$	−24.5489	−0.817841
$902$	0.509696	0.0169710
$903$	0	0
$904$	−21.4348	−0.712910
$905$	7.37844	0.245268
$906$	28.8861	0.959677
$907$	−19.9066	−0.660988	−0.330494	−	0.943808i	$-0.607215\pi$
$907$	−19.9066	−0.660988	−0.330494	+	0.943808i	$0.607215\pi$
$908$	13.3049	0.441539
$909$	5.09123	0.168865
$910$	0	0
$911$	16.0641	0.532228	0.266114	−	0.963942i	$-0.414260\pi$
$911$	16.0641	0.532228	0.266114	+	0.963942i	$0.414260\pi$
$912$	−32.6003	−1.07950
$913$	−12.8760	−0.426134
$914$	39.6054	1.31003
$915$	−12.0533	−0.398470
$916$	−8.60726	−0.284392
$917$	0	0
$918$	4.69339	0.154905
$919$	−31.7965	−1.04887	−0.524435	−	0.851450i	$-0.675724\pi$
$919$	−31.7965	−1.04887	−0.524435	+	0.851450i	$0.675724\pi$
$920$	8.26280	0.272416
$921$	15.6796	0.516659
$922$	11.5366	0.379939
$923$	−0.155582	−0.00512103
$924$	0	0
$925$	1.57196	0.0516859
$926$	−39.1335	−1.28601
$927$	−9.10985	−0.299207
$928$	48.4793	1.59141
$929$	−26.3302	−0.863865	−0.431932	−	0.901906i	$-0.642168\pi$
$929$	−26.3302	−0.863865	−0.431932	+	0.901906i	$0.642168\pi$
$930$	6.57398	0.215569
$931$	0	0
$932$	13.4744	0.441369
$933$	7.62233	0.249544
$934$	−12.1348	−0.397061
$935$	3.99273	0.130576
$936$	0.421479	0.0137765
$937$	−57.4528	−1.87690	−0.938450	−	0.345415i	$-0.887738\pi$
$937$	−57.4528	−1.87690	−0.938450	+	0.345415i	$0.887738\pi$
$938$	0	0
$939$	−16.6044	−0.541864
$940$	3.07019	0.100138
$941$	−9.63926	−0.314231	−0.157115	−	0.987580i	$-0.550219\pi$
$941$	−9.63926	−0.314231	−0.157115	+	0.987580i	$0.550219\pi$
$942$	−3.30769	−0.107770
$943$	1.04125	0.0339076
$944$	12.5891	0.409739
$945$	0	0
$946$	10.7523	0.349589
$947$	−36.3088	−1.17988	−0.589940	−	0.807447i	$-0.700848\pi$
$947$	−36.3088	−1.17988	−0.589940	+	0.807447i	$0.700848\pi$
$948$	−10.2373	−0.332492
$949$	2.23886	0.0726766
$950$	31.6226	1.02597
$951$	−13.2020	−0.428104
$952$	0	0
$953$	−21.7937	−0.705968	−0.352984	−	0.935629i	$-0.614833\pi$
$953$	−21.7937	−0.705968	−0.352984	+	0.935629i	$0.614833\pi$
$954$	−16.4724	−0.533313
$955$	25.1049	0.812376
$956$	−14.2525	−0.460958
$957$	−8.33812	−0.269533
$958$	−16.0063	−0.517140
$959$	0	0
$960$	−0.547321	−0.0176647
$961$	−24.9790	−0.805776
$962$	0.286243	0.00922886
$963$	13.3963	0.431690
$964$	23.2226	0.747949
$965$	−0.650747	−0.0209483
$966$	0	0
$967$	32.6388	1.04959	0.524796	−	0.851228i	$-0.324142\pi$
$967$	32.6388	1.04959	0.524796	+	0.851228i	$0.324142\pi$
$968$	1.50970	0.0485235
$969$	−17.3210	−0.556430
$970$	−20.9714	−0.673351
$971$	17.4366	0.559568	0.279784	−	0.960063i	$-0.409737\pi$
$971$	17.4366	0.559568	0.279784	+	0.960063i	$0.409737\pi$
$972$	1.14929	0.0368634
$973$	0	0
$974$	14.7086	0.471294
$975$	−0.759602	−0.0243267
$976$	39.7417	1.27210
$977$	10.0032	0.320032	0.160016	−	0.987114i	$-0.448845\pi$
$977$	10.0032	0.320032	0.160016	+	0.987114i	$0.448845\pi$
$978$	7.81341	0.249845
$979$	−11.8193	−0.377747
$980$	0	0
$981$	10.5716	0.337527
$982$	30.1359	0.961677
$983$	−35.0681	−1.11850	−0.559250	−	0.828999i	$-0.688911\pi$
$983$	−35.0681	−1.11850	−0.559250	+	0.828999i	$0.688911\pi$
$984$	0.433605	0.0138228
$985$	−0.221007	−0.00704186
$986$	39.1341	1.24628
$987$	0	0
$988$	2.10139	0.0668540
$989$	21.9657	0.698469
$990$	2.67914	0.0851487
$991$	34.1308	1.08420	0.542101	−	0.840313i	$-0.317629\pi$
$991$	34.1308	1.08420	0.542101	+	0.840313i	$0.317629\pi$
$992$	−14.2666	−0.452965
$993$	27.3197	0.866965
$994$	0	0
$995$	35.0192	1.11018
$996$	14.7982	0.468900
$997$	−25.3665	−0.803364	−0.401682	−	0.915779i	$-0.631574\pi$
$997$	−25.3665	−0.803364	−0.401682	+	0.915779i	$0.631574\pi$
$998$	12.5521	0.397328
$999$	−0.577754	−0.0182793

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.a.y.1.1	yes	4
3.2	odd	2		4851.2.a.br.1.4		4
7.6	odd	2		1617.2.a.w.1.1	✓	4
21.20	even	2		4851.2.a.bs.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1617.2.a.w.1.1	✓	4	7.6	odd	2
1617.2.a.y.1.1	yes	4	1.1	even	1	trivial
4851.2.a.br.1.4		4	3.2	odd	2
4851.2.a.bs.1.4		4	21.20	even	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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q-1.77462 q^{2} +1.00000 q^{3} +1.14929 q^{4} +1.50970 q^{5} -1.77462 q^{6} +1.50970 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.77462 q^{2} +1.00000 q^{3} +1.14929 q^{4} +1.50970 q^{5} -1.77462 q^{6} +1.50970 q^{8} +1.00000 q^{9} -2.67914 q^{10} -1.00000 q^{11} +1.14929 q^{12} +0.279181 q^{13} +1.50970 q^{15} -4.97771 q^{16} -2.64473 q^{17} -1.77462 q^{18} +6.54925 q^{19} +1.73507 q^{20} +1.77462 q^{22} +3.62534 q^{23} +1.50970 q^{24} -2.72082 q^{25} -0.495442 q^{26} +1.00000 q^{27} +8.33812 q^{29} -2.67914 q^{30} -2.45376 q^{31} +5.81417 q^{32} -1.00000 q^{33} +4.69339 q^{34} +1.14929 q^{36} -0.577754 q^{37} -11.6224 q^{38} +0.279181 q^{39} +2.27918 q^{40} +0.287214 q^{41} +6.05894 q^{43} -1.14929 q^{44} +1.50970 q^{45} -6.43361 q^{46} +1.76949 q^{47} -4.97771 q^{48} +4.82843 q^{50} -2.64473 q^{51} +0.320859 q^{52} +9.28219 q^{53} -1.77462 q^{54} -1.50970 q^{55} +6.54925 q^{57} -14.7970 q^{58} -2.52909 q^{59} +1.73507 q^{60} -7.98394 q^{61} +4.35451 q^{62} -0.362537 q^{64} +0.421479 q^{65} +1.77462 q^{66} -13.0388 q^{67} -3.03955 q^{68} +3.62534 q^{69} -0.557278 q^{71} +1.50970 q^{72} +8.01939 q^{73} +1.02530 q^{74} -2.72082 q^{75} +7.52696 q^{76} -0.495442 q^{78} -8.90753 q^{79} -7.51483 q^{80} +1.00000 q^{81} -0.509696 q^{82} +12.8760 q^{83} -3.99273 q^{85} -10.7523 q^{86} +8.33812 q^{87} -1.50970 q^{88} +11.8193 q^{89} -2.67914 q^{90} +4.16655 q^{92} -2.45376 q^{93} -3.14017 q^{94} +9.88737 q^{95} +5.81417 q^{96} +7.82766 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 4 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 4 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^9	\( 4 q + 2 q^{2} + 4 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} + 8 q^{13} - 6 q^{16} + 8 q^{17} + 2 q^{18} + 8 q^{19} + 10 q^{20} - 2 q^{22} + 8 q^{23} - 4 q^{25} + 14 q^{26} + 4 q^{27} + 16 q^{29} - 2 q^{30} + 8 q^{31} + 2 q^{32} - 4 q^{33} + 20 q^{34} + 2 q^{36} - 4 q^{37} - 14 q^{38} + 8 q^{39} + 16 q^{40} + 12 q^{41} - 2 q^{44} - 8 q^{46} + 20 q^{47} - 6 q^{48} + 8 q^{50} + 8 q^{51} + 10 q^{52} + 8 q^{53} + 2 q^{54} + 8 q^{57} - 2 q^{58} + 8 q^{59} + 10 q^{60} - 24 q^{61} + 24 q^{62} - 12 q^{64} - 12 q^{65} - 2 q^{66} - 28 q^{67} + 8 q^{69} + 12 q^{71} + 20 q^{73} - 18 q^{74} - 4 q^{75} - 2 q^{76} + 14 q^{78} - 2 q^{80} + 4 q^{81} + 4 q^{82} + 32 q^{83} - 24 q^{85} - 20 q^{86} + 16 q^{87} + 4 q^{89} - 2 q^{90} - 12 q^{92} + 8 q^{93} + 22 q^{94} + 4 q^{95} + 2 q^{96} + 8 q^{97} - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 4 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 + 8 * q^13 - 6 * q^16 + 8 * q^17 + 2 * q^18 + 8 * q^19 + 10 * q^20 - 2 * q^22 + 8 * q^23 - 4 * q^25 + 14 * q^26 + 4 * q^27 + 16 * q^29 - 2 * q^30 + 8 * q^31 + 2 * q^32 - 4 * q^33 + 20 * q^34 + 2 * q^36 - 4 * q^37 - 14 * q^38 + 8 * q^39 + 16 * q^40 + 12 * q^41 - 2 * q^44 - 8 * q^46 + 20 * q^47 - 6 * q^48 + 8 * q^50 + 8 * q^51 + 10 * q^52 + 8 * q^53 + 2 * q^54 + 8 * q^57 - 2 * q^58 + 8 * q^59 + 10 * q^60 - 24 * q^61 + 24 * q^62 - 12 * q^64 - 12 * q^65 - 2 * q^66 - 28 * q^67 + 8 * q^69 + 12 * q^71 + 20 * q^73 - 18 * q^74 - 4 * q^75 - 2 * q^76 + 14 * q^78 - 2 * q^80 + 4 * q^81 + 4 * q^82 + 32 * q^83 - 24 * q^85 - 20 * q^86 + 16 * q^87 + 4 * q^89 - 2 * q^90 - 12 * q^92 + 8 * q^93 + 22 * q^94 + 4 * q^95 + 2 * q^96 + 8 * q^97 - 4 * q^99

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