LMFDB - Embedded newform 3822.2.a.bu.1.2

Newspace parameters

Level:	$ N $	$=$	$ 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3822.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$30.5188236525$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	3822.1

$q$-expansion

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.41421 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.41421 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +3.41421 q^{10} +2.41421 q^{11} +1.00000 q^{12} -1.00000 q^{13} +3.41421 q^{15} +1.00000 q^{16} -0.414214 q^{17} +1.00000 q^{18} +7.82843 q^{19} +3.41421 q^{20} +2.41421 q^{22} -1.41421 q^{23} +1.00000 q^{24} +6.65685 q^{25} -1.00000 q^{26} +1.00000 q^{27} +3.82843 q^{29} +3.41421 q^{30} -8.48528 q^{31} +1.00000 q^{32} +2.41421 q^{33} -0.414214 q^{34} +1.00000 q^{36} -1.41421 q^{37} +7.82843 q^{38} -1.00000 q^{39} +3.41421 q^{40} -9.89949 q^{41} -10.4853 q^{43} +2.41421 q^{44} +3.41421 q^{45} -1.41421 q^{46} -1.00000 q^{47} +1.00000 q^{48} +6.65685 q^{50} -0.414214 q^{51} -1.00000 q^{52} -7.48528 q^{53} +1.00000 q^{54} +8.24264 q^{55} +7.82843 q^{57} +3.82843 q^{58} +12.0711 q^{59} +3.41421 q^{60} +1.58579 q^{61} -8.48528 q^{62} +1.00000 q^{64} -3.41421 q^{65} +2.41421 q^{66} -3.82843 q^{67} -0.414214 q^{68} -1.41421 q^{69} -5.00000 q^{71} +1.00000 q^{72} +1.41421 q^{73} -1.41421 q^{74} +6.65685 q^{75} +7.82843 q^{76} -1.00000 q^{78} -0.343146 q^{79} +3.41421 q^{80} +1.00000 q^{81} -9.89949 q^{82} +3.65685 q^{83} -1.41421 q^{85} -10.4853 q^{86} +3.82843 q^{87} +2.41421 q^{88} -5.41421 q^{89} +3.41421 q^{90} -1.41421 q^{92} -8.48528 q^{93} -1.00000 q^{94} +26.7279 q^{95} +1.00000 q^{96} +15.0711 q^{97} +2.41421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9} + 4 q^{10} + 2 q^{11} + 2 q^{12} - 2 q^{13} + 4 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} + 10 q^{19} + 4 q^{20} + 2 q^{22} + 2 q^{24} + 2 q^{25} - 2 q^{26} + 2 q^{27} + 2 q^{29} + 4 q^{30} + 2 q^{32} + 2 q^{33} + 2 q^{34} + 2 q^{36} + 10 q^{38} - 2 q^{39} + 4 q^{40} - 4 q^{43} + 2 q^{44} + 4 q^{45} - 2 q^{47} + 2 q^{48} + 2 q^{50} + 2 q^{51} - 2 q^{52} + 2 q^{53} + 2 q^{54} + 8 q^{55} + 10 q^{57} + 2 q^{58} + 10 q^{59} + 4 q^{60} + 6 q^{61} + 2 q^{64} - 4 q^{65} + 2 q^{66} - 2 q^{67} + 2 q^{68} - 10 q^{71} + 2 q^{72} + 2 q^{75} + 10 q^{76} - 2 q^{78} - 12 q^{79} + 4 q^{80} + 2 q^{81} - 4 q^{83} - 4 q^{86} + 2 q^{87} + 2 q^{88} - 8 q^{89} + 4 q^{90} - 2 q^{94} + 28 q^{95} + 2 q^{96} + 16 q^{97} + 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9 + 4 * q^10 + 2 * q^11 + 2 * q^12 - 2 * q^13 + 4 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 + 10 * q^19 + 4 * q^20 + 2 * q^22 + 2 * q^24 + 2 * q^25 - 2 * q^26 + 2 * q^27 + 2 * q^29 + 4 * q^30 + 2 * q^32 + 2 * q^33 + 2 * q^34 + 2 * q^36 + 10 * q^38 - 2 * q^39 + 4 * q^40 - 4 * q^43 + 2 * q^44 + 4 * q^45 - 2 * q^47 + 2 * q^48 + 2 * q^50 + 2 * q^51 - 2 * q^52 + 2 * q^53 + 2 * q^54 + 8 * q^55 + 10 * q^57 + 2 * q^58 + 10 * q^59 + 4 * q^60 + 6 * q^61 + 2 * q^64 - 4 * q^65 + 2 * q^66 - 2 * q^67 + 2 * q^68 - 10 * q^71 + 2 * q^72 + 2 * q^75 + 10 * q^76 - 2 * q^78 - 12 * q^79 + 4 * q^80 + 2 * q^81 - 4 * q^83 - 4 * q^86 + 2 * q^87 + 2 * q^88 - 8 * q^89 + 4 * q^90 - 2 * q^94 + 28 * q^95 + 2 * q^96 + 16 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	3.41421	1.52688	0.763441	−	0.645877i	$-0.223508\pi$
$5$	3.41421	1.52688	0.763441	+	0.645877i	$0.223508\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.41421	1.07967
$11$	2.41421	0.727913	0.363956	−	0.931416i	$-0.381426\pi$
$11$	2.41421	0.727913	0.363956	+	0.931416i	$0.381426\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	3.41421	0.881546
$16$	1.00000	0.250000
$17$	−0.414214	−0.100462	−0.0502308	−	0.998738i	$-0.515996\pi$
$17$	−0.414214	−0.100462	−0.0502308	+	0.998738i	$0.515996\pi$
$18$	1.00000	0.235702
$19$	7.82843	1.79596	0.897982	−	0.440032i	$-0.145033\pi$
$19$	7.82843	1.79596	0.897982	+	0.440032i	$0.145033\pi$
$20$	3.41421	0.763441
$21$	0	0
$22$	2.41421	0.514712
$23$	−1.41421	−0.294884	−0.147442	−	0.989071i	$-0.547104\pi$
$23$	−1.41421	−0.294884	−0.147442	+	0.989071i	$0.547104\pi$
$24$	1.00000	0.204124
$25$	6.65685	1.33137
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	0	0
$29$	3.82843	0.710921	0.355461	−	0.934691i	$-0.384324\pi$
$29$	3.82843	0.710921	0.355461	+	0.934691i	$0.384324\pi$
$30$	3.41421	0.623347
$31$	−8.48528	−1.52400	−0.762001	−	0.647576i	$-0.775783\pi$
$31$	−8.48528	−1.52400	−0.762001	+	0.647576i	$0.775783\pi$
$32$	1.00000	0.176777
$33$	2.41421	0.420261
$34$	−0.414214	−0.0710370
$35$	0	0
$36$	1.00000	0.166667
$37$	−1.41421	−0.232495	−0.116248	−	0.993220i	$-0.537087\pi$
$37$	−1.41421	−0.232495	−0.116248	+	0.993220i	$0.537087\pi$
$38$	7.82843	1.26994
$39$	−1.00000	−0.160128
$40$	3.41421	0.539835
$41$	−9.89949	−1.54604	−0.773021	−	0.634381i	$-0.781255\pi$
$41$	−9.89949	−1.54604	−0.773021	+	0.634381i	$0.781255\pi$
$42$	0	0
$43$	−10.4853	−1.59899	−0.799495	−	0.600672i	$-0.794900\pi$
$43$	−10.4853	−1.59899	−0.799495	+	0.600672i	$0.794900\pi$
$44$	2.41421	0.363956
$45$	3.41421	0.508961
$46$	−1.41421	−0.208514
$47$	−1.00000	−0.145865	−0.0729325	−	0.997337i	$-0.523236\pi$
$47$	−1.00000	−0.145865	−0.0729325	+	0.997337i	$0.523236\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	6.65685	0.941421
$51$	−0.414214	−0.0580015
$52$	−1.00000	−0.138675
$53$	−7.48528	−1.02818	−0.514091	−	0.857736i	$-0.671871\pi$
$53$	−7.48528	−1.02818	−0.514091	+	0.857736i	$0.671871\pi$
$54$	1.00000	0.136083
$55$	8.24264	1.11144
$56$	0	0
$57$	7.82843	1.03690
$58$	3.82843	0.502697
$59$	12.0711	1.57152	0.785760	−	0.618532i	$-0.212272\pi$
$59$	12.0711	1.57152	0.785760	+	0.618532i	$0.212272\pi$
$60$	3.41421	0.440773
$61$	1.58579	0.203039	0.101520	−	0.994834i	$-0.467630\pi$
$61$	1.58579	0.203039	0.101520	+	0.994834i	$0.467630\pi$
$62$	−8.48528	−1.07763
$63$	0	0
$64$	1.00000	0.125000
$65$	−3.41421	−0.423481
$66$	2.41421	0.297169
$67$	−3.82843	−0.467717	−0.233858	−	0.972271i	$-0.575135\pi$
$67$	−3.82843	−0.467717	−0.233858	+	0.972271i	$0.575135\pi$
$68$	−0.414214	−0.0502308
$69$	−1.41421	−0.170251
$70$	0	0
$71$	−5.00000	−0.593391	−0.296695	−	0.954972i	$-0.595885\pi$
$71$	−5.00000	−0.593391	−0.296695	+	0.954972i	$0.595885\pi$
$72$	1.00000	0.117851
$73$	1.41421	0.165521	0.0827606	−	0.996569i	$-0.473626\pi$
$73$	1.41421	0.165521	0.0827606	+	0.996569i	$0.473626\pi$
$74$	−1.41421	−0.164399
$75$	6.65685	0.768667
$76$	7.82843	0.897982
$77$	0	0
$78$	−1.00000	−0.113228
$79$	−0.343146	−0.0386069	−0.0193035	−	0.999814i	$-0.506145\pi$
$79$	−0.343146	−0.0386069	−0.0193035	+	0.999814i	$0.506145\pi$
$80$	3.41421	0.381721
$81$	1.00000	0.111111
$82$	−9.89949	−1.09322
$83$	3.65685	0.401392	0.200696	−	0.979654i	$-0.435680\pi$
$83$	3.65685	0.401392	0.200696	+	0.979654i	$0.435680\pi$
$84$	0	0
$85$	−1.41421	−0.153393
$86$	−10.4853	−1.13066
$87$	3.82843	0.410450
$88$	2.41421	0.257356
$89$	−5.41421	−0.573905	−0.286953	−	0.957945i	$-0.592642\pi$
$89$	−5.41421	−0.573905	−0.286953	+	0.957945i	$0.592642\pi$
$90$	3.41421	0.359890
$91$	0	0
$92$	−1.41421	−0.147442
$93$	−8.48528	−0.879883
$94$	−1.00000	−0.103142
$95$	26.7279	2.74223
$96$	1.00000	0.102062
$97$	15.0711	1.53024	0.765118	−	0.643891i	$-0.222681\pi$
$97$	15.0711	1.53024	0.765118	+	0.643891i	$0.222681\pi$
$98$	0	0
$99$	2.41421	0.242638
$100$	6.65685	0.665685
$101$	9.17157	0.912606	0.456303	−	0.889825i	$-0.349173\pi$
$101$	9.17157	0.912606	0.456303	+	0.889825i	$0.349173\pi$
$102$	−0.414214	−0.0410133
$103$	11.1716	1.10077	0.550384	−	0.834912i	$-0.314481\pi$
$103$	11.1716	1.10077	0.550384	+	0.834912i	$0.314481\pi$
$104$	−1.00000	−0.0980581
$105$	0	0
$106$	−7.48528	−0.727035
$107$	3.31371	0.320348	0.160174	−	0.987089i	$-0.448794\pi$
$107$	3.31371	0.320348	0.160174	+	0.987089i	$0.448794\pi$
$108$	1.00000	0.0962250
$109$	1.65685	0.158698	0.0793489	−	0.996847i	$-0.474716\pi$
$109$	1.65685	0.158698	0.0793489	+	0.996847i	$0.474716\pi$
$110$	8.24264	0.785905
$111$	−1.41421	−0.134231
$112$	0	0
$113$	−14.8995	−1.40163	−0.700813	−	0.713345i	$-0.747179\pi$
$113$	−14.8995	−1.40163	−0.700813	+	0.713345i	$0.747179\pi$
$114$	7.82843	0.733199
$115$	−4.82843	−0.450253
$116$	3.82843	0.355461
$117$	−1.00000	−0.0924500
$118$	12.0711	1.11123
$119$	0	0
$120$	3.41421	0.311674
$121$	−5.17157	−0.470143
$122$	1.58579	0.143570
$123$	−9.89949	−0.892607
$124$	−8.48528	−0.762001
$125$	5.65685	0.505964
$126$	0	0
$127$	11.8995	1.05591	0.527955	−	0.849273i	$-0.322959\pi$
$127$	11.8995	1.05591	0.527955	+	0.849273i	$0.322959\pi$
$128$	1.00000	0.0883883
$129$	−10.4853	−0.923178
$130$	−3.41421	−0.299446
$131$	−21.5563	−1.88339	−0.941693	−	0.336472i	$-0.890766\pi$
$131$	−21.5563	−1.88339	−0.941693	+	0.336472i	$0.890766\pi$
$132$	2.41421	0.210130
$133$	0	0
$134$	−3.82843	−0.330726
$135$	3.41421	0.293849
$136$	−0.414214	−0.0355185
$137$	−3.07107	−0.262379	−0.131190	−	0.991357i	$-0.541880\pi$
$137$	−3.07107	−0.262379	−0.131190	+	0.991357i	$0.541880\pi$
$138$	−1.41421	−0.120386
$139$	−1.07107	−0.0908468	−0.0454234	−	0.998968i	$-0.514464\pi$
$139$	−1.07107	−0.0908468	−0.0454234	+	0.998968i	$0.514464\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	−5.00000	−0.419591
$143$	−2.41421	−0.201887
$144$	1.00000	0.0833333
$145$	13.0711	1.08549
$146$	1.41421	0.117041
$147$	0	0
$148$	−1.41421	−0.116248
$149$	−19.0711	−1.56236	−0.781181	−	0.624304i	$-0.785383\pi$
$149$	−19.0711	−1.56236	−0.781181	+	0.624304i	$0.785383\pi$
$150$	6.65685	0.543530
$151$	−10.0711	−0.819572	−0.409786	−	0.912182i	$-0.634397\pi$
$151$	−10.0711	−0.819572	−0.409786	+	0.912182i	$0.634397\pi$
$152$	7.82843	0.634969
$153$	−0.414214	−0.0334872
$154$	0	0
$155$	−28.9706	−2.32697
$156$	−1.00000	−0.0800641
$157$	15.7279	1.25522	0.627612	−	0.778526i	$-0.284032\pi$
$157$	15.7279	1.25522	0.627612	+	0.778526i	$0.284032\pi$
$158$	−0.343146	−0.0272992
$159$	−7.48528	−0.593621
$160$	3.41421	0.269917
$161$	0	0
$162$	1.00000	0.0785674
$163$	−7.34315	−0.575160	−0.287580	−	0.957757i	$-0.592851\pi$
$163$	−7.34315	−0.575160	−0.287580	+	0.957757i	$0.592851\pi$
$164$	−9.89949	−0.773021
$165$	8.24264	0.641689
$166$	3.65685	0.283827
$167$	−10.6569	−0.824652	−0.412326	−	0.911036i	$-0.635284\pi$
$167$	−10.6569	−0.824652	−0.412326	+	0.911036i	$0.635284\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−1.41421	−0.108465
$171$	7.82843	0.598655
$172$	−10.4853	−0.799495
$173$	11.4853	0.873210	0.436605	−	0.899653i	$-0.356181\pi$
$173$	11.4853	0.873210	0.436605	+	0.899653i	$0.356181\pi$
$174$	3.82843	0.290232
$175$	0	0
$176$	2.41421	0.181978
$177$	12.0711	0.907317
$178$	−5.41421	−0.405812
$179$	8.34315	0.623596	0.311798	−	0.950148i	$-0.399069\pi$
$179$	8.34315	0.623596	0.311798	+	0.950148i	$0.399069\pi$
$180$	3.41421	0.254480
$181$	16.8995	1.25613	0.628065	−	0.778161i	$-0.283847\pi$
$181$	16.8995	1.25613	0.628065	+	0.778161i	$0.283847\pi$
$182$	0	0
$183$	1.58579	0.117225
$184$	−1.41421	−0.104257
$185$	−4.82843	−0.354993
$186$	−8.48528	−0.622171
$187$	−1.00000	−0.0731272
$188$	−1.00000	−0.0729325
$189$	0	0
$190$	26.7279	1.93905
$191$	−21.6569	−1.56703	−0.783517	−	0.621370i	$-0.786577\pi$
$191$	−21.6569	−1.56703	−0.783517	+	0.621370i	$0.786577\pi$
$192$	1.00000	0.0721688
$193$	−17.0711	−1.22880	−0.614401	−	0.788994i	$-0.710602\pi$
$193$	−17.0711	−1.22880	−0.614401	+	0.788994i	$0.710602\pi$
$194$	15.0711	1.08204
$195$	−3.41421	−0.244497
$196$	0	0
$197$	15.5563	1.10834	0.554172	−	0.832402i	$-0.313035\pi$
$197$	15.5563	1.10834	0.554172	+	0.832402i	$0.313035\pi$
$198$	2.41421	0.171571
$199$	22.7279	1.61114	0.805570	−	0.592501i	$-0.201859\pi$
$199$	22.7279	1.61114	0.805570	+	0.592501i	$0.201859\pi$
$200$	6.65685	0.470711
$201$	−3.82843	−0.270036
$202$	9.17157	0.645310
$203$	0	0
$204$	−0.414214	−0.0290008
$205$	−33.7990	−2.36062
$206$	11.1716	0.778360
$207$	−1.41421	−0.0982946
$208$	−1.00000	−0.0693375
$209$	18.8995	1.30731
$210$	0	0
$211$	−27.0711	−1.86365	−0.931825	−	0.362909i	$-0.881784\pi$
$211$	−27.0711	−1.86365	−0.931825	+	0.362909i	$0.881784\pi$
$212$	−7.48528	−0.514091
$213$	−5.00000	−0.342594
$214$	3.31371	0.226520
$215$	−35.7990	−2.44147
$216$	1.00000	0.0680414
$217$	0	0
$218$	1.65685	0.112216
$219$	1.41421	0.0955637
$220$	8.24264	0.555719
$221$	0.414214	0.0278630
$222$	−1.41421	−0.0949158
$223$	22.0711	1.47799	0.738994	−	0.673712i	$-0.235301\pi$
$223$	22.0711	1.47799	0.738994	+	0.673712i	$0.235301\pi$
$224$	0	0
$225$	6.65685	0.443790
$226$	−14.8995	−0.991100
$227$	26.8284	1.78067	0.890333	−	0.455311i	$-0.150472\pi$
$227$	26.8284	1.78067	0.890333	+	0.455311i	$0.150472\pi$
$228$	7.82843	0.518450
$229$	−9.51472	−0.628750	−0.314375	−	0.949299i	$-0.601795\pi$
$229$	−9.51472	−0.628750	−0.314375	+	0.949299i	$0.601795\pi$
$230$	−4.82843	−0.318377
$231$	0	0
$232$	3.82843	0.251349
$233$	7.72792	0.506273	0.253137	−	0.967431i	$-0.418538\pi$
$233$	7.72792	0.506273	0.253137	+	0.967431i	$0.418538\pi$
$234$	−1.00000	−0.0653720
$235$	−3.41421	−0.222719
$236$	12.0711	0.785760
$237$	−0.343146	−0.0222897
$238$	0	0
$239$	21.4853	1.38977	0.694884	−	0.719122i	$-0.255456\pi$
$239$	21.4853	1.38977	0.694884	+	0.719122i	$0.255456\pi$
$240$	3.41421	0.220387
$241$	−26.1421	−1.68396	−0.841981	−	0.539506i	$-0.818611\pi$
$241$	−26.1421	−1.68396	−0.841981	+	0.539506i	$0.818611\pi$
$242$	−5.17157	−0.332441
$243$	1.00000	0.0641500
$244$	1.58579	0.101520
$245$	0	0
$246$	−9.89949	−0.631169
$247$	−7.82843	−0.498111
$248$	−8.48528	−0.538816
$249$	3.65685	0.231744
$250$	5.65685	0.357771
$251$	−19.1716	−1.21010	−0.605049	−	0.796188i	$-0.706847\pi$
$251$	−19.1716	−1.21010	−0.605049	+	0.796188i	$0.706847\pi$
$252$	0	0
$253$	−3.41421	−0.214650
$254$	11.8995	0.746641
$255$	−1.41421	−0.0885615
$256$	1.00000	0.0625000
$257$	−9.51472	−0.593512	−0.296756	−	0.954953i	$-0.595905\pi$
$257$	−9.51472	−0.593512	−0.296756	+	0.954953i	$0.595905\pi$
$258$	−10.4853	−0.652785
$259$	0	0
$260$	−3.41421	−0.211741
$261$	3.82843	0.236974
$262$	−21.5563	−1.33176
$263$	23.4142	1.44378	0.721891	−	0.692007i	$-0.243273\pi$
$263$	23.4142	1.44378	0.721891	+	0.692007i	$0.243273\pi$
$264$	2.41421	0.148585
$265$	−25.5563	−1.56991
$266$	0	0
$267$	−5.41421	−0.331344
$268$	−3.82843	−0.233858
$269$	−19.1421	−1.16712	−0.583558	−	0.812071i	$-0.698340\pi$
$269$	−19.1421	−1.16712	−0.583558	+	0.812071i	$0.698340\pi$
$270$	3.41421	0.207782
$271$	16.2132	0.984882	0.492441	−	0.870346i	$-0.336105\pi$
$271$	16.2132	0.984882	0.492441	+	0.870346i	$0.336105\pi$
$272$	−0.414214	−0.0251154
$273$	0	0
$274$	−3.07107	−0.185530
$275$	16.0711	0.969122
$276$	−1.41421	−0.0851257
$277$	3.92893	0.236067	0.118033	−	0.993010i	$-0.462341\pi$
$277$	3.92893	0.236067	0.118033	+	0.993010i	$0.462341\pi$
$278$	−1.07107	−0.0642384
$279$	−8.48528	−0.508001
$280$	0	0
$281$	23.3137	1.39078	0.695390	−	0.718633i	$-0.255232\pi$
$281$	23.3137	1.39078	0.695390	+	0.718633i	$0.255232\pi$
$282$	−1.00000	−0.0595491
$283$	24.2426	1.44108	0.720538	−	0.693416i	$-0.243895\pi$
$283$	24.2426	1.44108	0.720538	+	0.693416i	$0.243895\pi$
$284$	−5.00000	−0.296695
$285$	26.7279	1.58323
$286$	−2.41421	−0.142755
$287$	0	0
$288$	1.00000	0.0589256
$289$	−16.8284	−0.989907
$290$	13.0711	0.767560
$291$	15.0711	0.883482
$292$	1.41421	0.0827606
$293$	−9.89949	−0.578335	−0.289167	−	0.957279i	$-0.593378\pi$
$293$	−9.89949	−0.578335	−0.289167	+	0.957279i	$0.593378\pi$
$294$	0	0
$295$	41.2132	2.39953
$296$	−1.41421	−0.0821995
$297$	2.41421	0.140087
$298$	−19.0711	−1.10476
$299$	1.41421	0.0817861
$300$	6.65685	0.384334
$301$	0	0
$302$	−10.0711	−0.579525
$303$	9.17157	0.526893
$304$	7.82843	0.448991
$305$	5.41421	0.310017
$306$	−0.414214	−0.0236790
$307$	−34.1127	−1.94691	−0.973457	−	0.228869i	$-0.926497\pi$
$307$	−34.1127	−1.94691	−0.973457	+	0.228869i	$0.926497\pi$
$308$	0	0
$309$	11.1716	0.635529
$310$	−28.9706	−1.64542
$311$	27.8995	1.58204	0.791018	−	0.611793i	$-0.209552\pi$
$311$	27.8995	1.58204	0.791018	+	0.611793i	$0.209552\pi$
$312$	−1.00000	−0.0566139
$313$	−20.4853	−1.15790	−0.578948	−	0.815364i	$-0.696537\pi$
$313$	−20.4853	−1.15790	−0.578948	+	0.815364i	$0.696537\pi$
$314$	15.7279	0.887578
$315$	0	0
$316$	−0.343146	−0.0193035
$317$	−9.79899	−0.550366	−0.275183	−	0.961392i	$-0.588738\pi$
$317$	−9.79899	−0.550366	−0.275183	+	0.961392i	$0.588738\pi$
$318$	−7.48528	−0.419754
$319$	9.24264	0.517489
$320$	3.41421	0.190860
$321$	3.31371	0.184953
$322$	0	0
$323$	−3.24264	−0.180425
$324$	1.00000	0.0555556
$325$	−6.65685	−0.369256
$326$	−7.34315	−0.406699
$327$	1.65685	0.0916242
$328$	−9.89949	−0.546608
$329$	0	0
$330$	8.24264	0.453742
$331$	−5.51472	−0.303116	−0.151558	−	0.988448i	$-0.548429\pi$
$331$	−5.51472	−0.303116	−0.151558	+	0.988448i	$0.548429\pi$
$332$	3.65685	0.200696
$333$	−1.41421	−0.0774984
$334$	−10.6569	−0.583117
$335$	−13.0711	−0.714149
$336$	0	0
$337$	2.31371	0.126036	0.0630179	−	0.998012i	$-0.479927\pi$
$337$	2.31371	0.126036	0.0630179	+	0.998012i	$0.479927\pi$
$338$	1.00000	0.0543928
$339$	−14.8995	−0.809229
$340$	−1.41421	−0.0766965
$341$	−20.4853	−1.10934
$342$	7.82843	0.423313
$343$	0	0
$344$	−10.4853	−0.565328
$345$	−4.82843	−0.259954
$346$	11.4853	0.617453
$347$	16.7279	0.898002	0.449001	−	0.893531i	$-0.351780\pi$
$347$	16.7279	0.898002	0.449001	+	0.893531i	$0.351780\pi$
$348$	3.82843	0.205225
$349$	−18.7279	−1.00248	−0.501241	−	0.865308i	$-0.667123\pi$
$349$	−18.7279	−1.00248	−0.501241	+	0.865308i	$0.667123\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	2.41421	0.128678
$353$	32.6274	1.73658	0.868291	−	0.496055i	$-0.165219\pi$
$353$	32.6274	1.73658	0.868291	+	0.496055i	$0.165219\pi$
$354$	12.0711	0.641570
$355$	−17.0711	−0.906038
$356$	−5.41421	−0.286953
$357$	0	0
$358$	8.34315	0.440949
$359$	4.82843	0.254835	0.127417	−	0.991849i	$-0.459331\pi$
$359$	4.82843	0.254835	0.127417	+	0.991849i	$0.459331\pi$
$360$	3.41421	0.179945
$361$	42.2843	2.22549
$362$	16.8995	0.888218
$363$	−5.17157	−0.271437
$364$	0	0
$365$	4.82843	0.252731
$366$	1.58579	0.0828904
$367$	32.6274	1.70314	0.851569	−	0.524243i	$-0.175652\pi$
$367$	32.6274	1.70314	0.851569	+	0.524243i	$0.175652\pi$
$368$	−1.41421	−0.0737210
$369$	−9.89949	−0.515347
$370$	−4.82843	−0.251018
$371$	0	0
$372$	−8.48528	−0.439941
$373$	−8.41421	−0.435671	−0.217836	−	0.975985i	$-0.569900\pi$
$373$	−8.41421	−0.435671	−0.217836	+	0.975985i	$0.569900\pi$
$374$	−1.00000	−0.0517088
$375$	5.65685	0.292119
$376$	−1.00000	−0.0515711
$377$	−3.82843	−0.197174
$378$	0	0
$379$	−26.6274	−1.36776	−0.683879	−	0.729595i	$-0.739709\pi$
$379$	−26.6274	−1.36776	−0.683879	+	0.729595i	$0.739709\pi$
$380$	26.7279	1.37111
$381$	11.8995	0.609630
$382$	−21.6569	−1.10806
$383$	−16.8284	−0.859892	−0.429946	−	0.902854i	$-0.641467\pi$
$383$	−16.8284	−0.859892	−0.429946	+	0.902854i	$0.641467\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−17.0711	−0.868894
$387$	−10.4853	−0.532997
$388$	15.0711	0.765118
$389$	−21.4853	−1.08935	−0.544674	−	0.838648i	$-0.683346\pi$
$389$	−21.4853	−1.08935	−0.544674	+	0.838648i	$0.683346\pi$
$390$	−3.41421	−0.172885
$391$	0.585786	0.0296245
$392$	0	0
$393$	−21.5563	−1.08737
$394$	15.5563	0.783718
$395$	−1.17157	−0.0589482
$396$	2.41421	0.121319
$397$	−21.5563	−1.08188	−0.540941	−	0.841060i	$-0.681932\pi$
$397$	−21.5563	−1.08188	−0.540941	+	0.841060i	$0.681932\pi$
$398$	22.7279	1.13925
$399$	0	0
$400$	6.65685	0.332843
$401$	0.100505	0.00501898	0.00250949	−	0.999997i	$-0.499201\pi$
$401$	0.100505	0.00501898	0.00250949	+	0.999997i	$0.499201\pi$
$402$	−3.82843	−0.190945
$403$	8.48528	0.422682
$404$	9.17157	0.456303
$405$	3.41421	0.169654
$406$	0	0
$407$	−3.41421	−0.169236
$408$	−0.414214	−0.0205066
$409$	−35.4142	−1.75112	−0.875560	−	0.483109i	$-0.839507\pi$
$409$	−35.4142	−1.75112	−0.875560	+	0.483109i	$0.839507\pi$
$410$	−33.7990	−1.66921
$411$	−3.07107	−0.151485
$412$	11.1716	0.550384
$413$	0	0
$414$	−1.41421	−0.0695048
$415$	12.4853	0.612878
$416$	−1.00000	−0.0490290
$417$	−1.07107	−0.0524504
$418$	18.8995	0.924405
$419$	23.4558	1.14589	0.572946	−	0.819593i	$-0.305800\pi$
$419$	23.4558	1.14589	0.572946	+	0.819593i	$0.305800\pi$
$420$	0	0
$421$	−13.0711	−0.637045	−0.318522	−	0.947915i	$-0.603187\pi$
$421$	−13.0711	−0.637045	−0.318522	+	0.947915i	$0.603187\pi$
$422$	−27.0711	−1.31780
$423$	−1.00000	−0.0486217
$424$	−7.48528	−0.363517
$425$	−2.75736	−0.133752
$426$	−5.00000	−0.242251
$427$	0	0
$428$	3.31371	0.160174
$429$	−2.41421	−0.116559
$430$	−35.7990	−1.72638
$431$	13.5147	0.650981	0.325491	−	0.945545i	$-0.394471\pi$
$431$	13.5147	0.650981	0.325491	+	0.945545i	$0.394471\pi$
$432$	1.00000	0.0481125
$433$	3.97056	0.190813	0.0954065	−	0.995438i	$-0.469585\pi$
$433$	3.97056	0.190813	0.0954065	+	0.995438i	$0.469585\pi$
$434$	0	0
$435$	13.0711	0.626710
$436$	1.65685	0.0793489
$437$	−11.0711	−0.529601
$438$	1.41421	0.0675737
$439$	−19.4142	−0.926590	−0.463295	−	0.886204i	$-0.653333\pi$
$439$	−19.4142	−0.926590	−0.463295	+	0.886204i	$0.653333\pi$
$440$	8.24264	0.392952
$441$	0	0
$442$	0.414214	0.0197021
$443$	25.6985	1.22097	0.610486	−	0.792027i	$-0.290974\pi$
$443$	25.6985	1.22097	0.610486	+	0.792027i	$0.290974\pi$
$444$	−1.41421	−0.0671156
$445$	−18.4853	−0.876286
$446$	22.0711	1.04510
$447$	−19.0711	−0.902031
$448$	0	0
$449$	−8.97056	−0.423347	−0.211674	−	0.977340i	$-0.567891\pi$
$449$	−8.97056	−0.423347	−0.211674	+	0.977340i	$0.567891\pi$
$450$	6.65685	0.313807
$451$	−23.8995	−1.12538
$452$	−14.8995	−0.700813
$453$	−10.0711	−0.473180
$454$	26.8284	1.25912
$455$	0	0
$456$	7.82843	0.366600
$457$	11.0711	0.517883	0.258941	−	0.965893i	$-0.416626\pi$
$457$	11.0711	0.517883	0.258941	+	0.965893i	$0.416626\pi$
$458$	−9.51472	−0.444594
$459$	−0.414214	−0.0193338
$460$	−4.82843	−0.225127
$461$	−12.4853	−0.581498	−0.290749	−	0.956799i	$-0.593904\pi$
$461$	−12.4853	−0.581498	−0.290749	+	0.956799i	$0.593904\pi$
$462$	0	0
$463$	12.9706	0.602793	0.301397	−	0.953499i	$-0.402547\pi$
$463$	12.9706	0.602793	0.301397	+	0.953499i	$0.402547\pi$
$464$	3.82843	0.177730
$465$	−28.9706	−1.34348
$466$	7.72792	0.357989
$467$	8.58579	0.397303	0.198651	−	0.980070i	$-0.436344\pi$
$467$	8.58579	0.397303	0.198651	+	0.980070i	$0.436344\pi$
$468$	−1.00000	−0.0462250
$469$	0	0
$470$	−3.41421	−0.157486
$471$	15.7279	0.724704
$472$	12.0711	0.555616
$473$	−25.3137	−1.16393
$474$	−0.343146	−0.0157612
$475$	52.1127	2.39109
$476$	0	0
$477$	−7.48528	−0.342727
$478$	21.4853	0.982714
$479$	−30.1127	−1.37588	−0.687942	−	0.725766i	$-0.741486\pi$
$479$	−30.1127	−1.37588	−0.687942	+	0.725766i	$0.741486\pi$
$480$	3.41421	0.155837
$481$	1.41421	0.0644826
$482$	−26.1421	−1.19074
$483$	0	0
$484$	−5.17157	−0.235071
$485$	51.4558	2.33649
$486$	1.00000	0.0453609
$487$	−26.2132	−1.18783	−0.593917	−	0.804526i	$-0.702419\pi$
$487$	−26.2132	−1.18783	−0.593917	+	0.804526i	$0.702419\pi$
$488$	1.58579	0.0717852
$489$	−7.34315	−0.332069
$490$	0	0
$491$	12.3431	0.557038	0.278519	−	0.960431i	$-0.410156\pi$
$491$	12.3431	0.557038	0.278519	+	0.960431i	$0.410156\pi$
$492$	−9.89949	−0.446304
$493$	−1.58579	−0.0714202
$494$	−7.82843	−0.352218
$495$	8.24264	0.370479
$496$	−8.48528	−0.381000
$497$	0	0
$498$	3.65685	0.163868
$499$	−7.65685	−0.342768	−0.171384	−	0.985204i	$-0.554824\pi$
$499$	−7.65685	−0.342768	−0.171384	+	0.985204i	$0.554824\pi$
$500$	5.65685	0.252982
$501$	−10.6569	−0.476113
$502$	−19.1716	−0.855669
$503$	2.14214	0.0955131	0.0477566	−	0.998859i	$-0.484793\pi$
$503$	2.14214	0.0955131	0.0477566	+	0.998859i	$0.484793\pi$
$504$	0	0
$505$	31.3137	1.39344
$506$	−3.41421	−0.151780
$507$	1.00000	0.0444116
$508$	11.8995	0.527955
$509$	34.6274	1.53483	0.767417	−	0.641149i	$-0.221542\pi$
$509$	34.6274	1.53483	0.767417	+	0.641149i	$0.221542\pi$
$510$	−1.41421	−0.0626224
$511$	0	0
$512$	1.00000	0.0441942
$513$	7.82843	0.345634
$514$	−9.51472	−0.419676
$515$	38.1421	1.68074
$516$	−10.4853	−0.461589
$517$	−2.41421	−0.106177
$518$	0	0
$519$	11.4853	0.504148
$520$	−3.41421	−0.149723
$521$	4.62742	0.202731	0.101365	−	0.994849i	$-0.467679\pi$
$521$	4.62742	0.202731	0.101365	+	0.994849i	$0.467679\pi$
$522$	3.82843	0.167566
$523$	11.1716	0.488499	0.244249	−	0.969712i	$-0.421458\pi$
$523$	11.1716	0.488499	0.244249	+	0.969712i	$0.421458\pi$
$524$	−21.5563	−0.941693
$525$	0	0
$526$	23.4142	1.02091
$527$	3.51472	0.153104
$528$	2.41421	0.105065
$529$	−21.0000	−0.913043
$530$	−25.5563	−1.11010
$531$	12.0711	0.523840
$532$	0	0
$533$	9.89949	0.428795
$534$	−5.41421	−0.234296
$535$	11.3137	0.489134
$536$	−3.82843	−0.165363
$537$	8.34315	0.360033
$538$	−19.1421	−0.825276
$539$	0	0
$540$	3.41421	0.146924
$541$	8.92893	0.383885	0.191942	−	0.981406i	$-0.438521\pi$
$541$	8.92893	0.383885	0.191942	+	0.981406i	$0.438521\pi$
$542$	16.2132	0.696417
$543$	16.8995	0.725227
$544$	−0.414214	−0.0177593
$545$	5.65685	0.242313
$546$	0	0
$547$	22.8701	0.977853	0.488927	−	0.872325i	$-0.337389\pi$
$547$	22.8701	0.977853	0.488927	+	0.872325i	$0.337389\pi$
$548$	−3.07107	−0.131190
$549$	1.58579	0.0676797
$550$	16.0711	0.685273
$551$	29.9706	1.27679
$552$	−1.41421	−0.0601929
$553$	0	0
$554$	3.92893	0.166924
$555$	−4.82843	−0.204955
$556$	−1.07107	−0.0454234
$557$	12.6274	0.535041	0.267520	−	0.963552i	$-0.413796\pi$
$557$	12.6274	0.535041	0.267520	+	0.963552i	$0.413796\pi$
$558$	−8.48528	−0.359211
$559$	10.4853	0.443480
$560$	0	0
$561$	−1.00000	−0.0422200
$562$	23.3137	0.983429
$563$	−40.7696	−1.71823	−0.859116	−	0.511781i	$-0.828986\pi$
$563$	−40.7696	−1.71823	−0.859116	+	0.511781i	$0.828986\pi$
$564$	−1.00000	−0.0421076
$565$	−50.8701	−2.14012
$566$	24.2426	1.01899
$567$	0	0
$568$	−5.00000	−0.209795
$569$	−1.72792	−0.0724383	−0.0362191	−	0.999344i	$-0.511531\pi$
$569$	−1.72792	−0.0724383	−0.0362191	+	0.999344i	$0.511531\pi$
$570$	26.7279	1.11951
$571$	−8.68629	−0.363510	−0.181755	−	0.983344i	$-0.558178\pi$
$571$	−8.68629	−0.363510	−0.181755	+	0.983344i	$0.558178\pi$
$572$	−2.41421	−0.100943
$573$	−21.6569	−0.904728
$574$	0	0
$575$	−9.41421	−0.392600
$576$	1.00000	0.0416667
$577$	−27.6569	−1.15137	−0.575685	−	0.817672i	$-0.695265\pi$
$577$	−27.6569	−1.15137	−0.575685	+	0.817672i	$0.695265\pi$
$578$	−16.8284	−0.699970
$579$	−17.0711	−0.709449
$580$	13.0711	0.542747
$581$	0	0
$582$	15.0711	0.624716
$583$	−18.0711	−0.748427
$584$	1.41421	0.0585206
$585$	−3.41421	−0.141160
$586$	−9.89949	−0.408944
$587$	4.41421	0.182194	0.0910970	−	0.995842i	$-0.470963\pi$
$587$	4.41421	0.182194	0.0910970	+	0.995842i	$0.470963\pi$
$588$	0	0
$589$	−66.4264	−2.73705
$590$	41.2132	1.69672
$591$	15.5563	0.639903
$592$	−1.41421	−0.0581238
$593$	−2.38478	−0.0979310	−0.0489655	−	0.998800i	$-0.515592\pi$
$593$	−2.38478	−0.0979310	−0.0489655	+	0.998800i	$0.515592\pi$
$594$	2.41421	0.0990564
$595$	0	0
$596$	−19.0711	−0.781181
$597$	22.7279	0.930192
$598$	1.41421	0.0578315
$599$	−29.5563	−1.20764	−0.603820	−	0.797121i	$-0.706355\pi$
$599$	−29.5563	−1.20764	−0.603820	+	0.797121i	$0.706355\pi$
$600$	6.65685	0.271765
$601$	−40.7990	−1.66423	−0.832113	−	0.554606i	$-0.812869\pi$
$601$	−40.7990	−1.66423	−0.832113	+	0.554606i	$0.812869\pi$
$602$	0	0
$603$	−3.82843	−0.155906
$604$	−10.0711	−0.409786
$605$	−17.6569	−0.717853
$606$	9.17157	0.372570
$607$	30.5269	1.23905	0.619525	−	0.784977i	$-0.287325\pi$
$607$	30.5269	1.23905	0.619525	+	0.784977i	$0.287325\pi$
$608$	7.82843	0.317485
$609$	0	0
$610$	5.41421	0.219215
$611$	1.00000	0.0404557
$612$	−0.414214	−0.0167436
$613$	31.7990	1.28435	0.642175	−	0.766558i	$-0.278032\pi$
$613$	31.7990	1.28435	0.642175	+	0.766558i	$0.278032\pi$
$614$	−34.1127	−1.37668
$615$	−33.7990	−1.36291
$616$	0	0
$617$	4.14214	0.166756	0.0833781	−	0.996518i	$-0.473429\pi$
$617$	4.14214	0.166756	0.0833781	+	0.996518i	$0.473429\pi$
$618$	11.1716	0.449387
$619$	−15.1716	−0.609797	−0.304898	−	0.952385i	$-0.598623\pi$
$619$	−15.1716	−0.609797	−0.304898	+	0.952385i	$0.598623\pi$
$620$	−28.9706	−1.16349
$621$	−1.41421	−0.0567504
$622$	27.8995	1.11867
$623$	0	0
$624$	−1.00000	−0.0400320
$625$	−13.9706	−0.558823
$626$	−20.4853	−0.818757
$627$	18.8995	0.754773
$628$	15.7279	0.627612
$629$	0.585786	0.0233568
$630$	0	0
$631$	−12.6274	−0.502690	−0.251345	−	0.967898i	$-0.580873\pi$
$631$	−12.6274	−0.502690	−0.251345	+	0.967898i	$0.580873\pi$
$632$	−0.343146	−0.0136496
$633$	−27.0711	−1.07598
$634$	−9.79899	−0.389168
$635$	40.6274	1.61225
$636$	−7.48528	−0.296811
$637$	0	0
$638$	9.24264	0.365920
$639$	−5.00000	−0.197797
$640$	3.41421	0.134959
$641$	−7.79899	−0.308042	−0.154021	−	0.988068i	$-0.549222\pi$
$641$	−7.79899	−0.308042	−0.154021	+	0.988068i	$0.549222\pi$
$642$	3.31371	0.130782
$643$	19.4853	0.768424	0.384212	−	0.923245i	$-0.374473\pi$
$643$	19.4853	0.768424	0.384212	+	0.923245i	$0.374473\pi$
$644$	0	0
$645$	−35.7990	−1.40958
$646$	−3.24264	−0.127580
$647$	42.9706	1.68935	0.844674	−	0.535282i	$-0.179795\pi$
$647$	42.9706	1.68935	0.844674	+	0.535282i	$0.179795\pi$
$648$	1.00000	0.0392837
$649$	29.1421	1.14393
$650$	−6.65685	−0.261103
$651$	0	0
$652$	−7.34315	−0.287580
$653$	−6.14214	−0.240360	−0.120180	−	0.992752i	$-0.538347\pi$
$653$	−6.14214	−0.240360	−0.120180	+	0.992752i	$0.538347\pi$
$654$	1.65685	0.0647881
$655$	−73.5980	−2.87571
$656$	−9.89949	−0.386510
$657$	1.41421	0.0551737
$658$	0	0
$659$	13.4142	0.522544	0.261272	−	0.965265i	$-0.415858\pi$
$659$	13.4142	0.522544	0.261272	+	0.965265i	$0.415858\pi$
$660$	8.24264	0.320844
$661$	−31.7574	−1.23522	−0.617609	−	0.786485i	$-0.711899\pi$
$661$	−31.7574	−1.23522	−0.617609	+	0.786485i	$0.711899\pi$
$662$	−5.51472	−0.214336
$663$	0.414214	0.0160867
$664$	3.65685	0.141913
$665$	0	0
$666$	−1.41421	−0.0547997
$667$	−5.41421	−0.209639
$668$	−10.6569	−0.412326
$669$	22.0711	0.853317
$670$	−13.0711	−0.504979
$671$	3.82843	0.147795
$672$	0	0
$673$	13.8579	0.534181	0.267091	−	0.963671i	$-0.413938\pi$
$673$	13.8579	0.534181	0.267091	+	0.963671i	$0.413938\pi$
$674$	2.31371	0.0891207
$675$	6.65685	0.256222
$676$	1.00000	0.0384615
$677$	−15.0000	−0.576497	−0.288248	−	0.957556i	$-0.593073\pi$
$677$	−15.0000	−0.576497	−0.288248	+	0.957556i	$0.593073\pi$
$678$	−14.8995	−0.572212
$679$	0	0
$680$	−1.41421	−0.0542326
$681$	26.8284	1.02807
$682$	−20.4853	−0.784422
$683$	14.1421	0.541134	0.270567	−	0.962701i	$-0.412789\pi$
$683$	14.1421	0.541134	0.270567	+	0.962701i	$0.412789\pi$
$684$	7.82843	0.299327
$685$	−10.4853	−0.400622
$686$	0	0
$687$	−9.51472	−0.363009
$688$	−10.4853	−0.399748
$689$	7.48528	0.285167
$690$	−4.82843	−0.183815
$691$	9.34315	0.355430	0.177715	−	0.984082i	$-0.443129\pi$
$691$	9.34315	0.355430	0.177715	+	0.984082i	$0.443129\pi$
$692$	11.4853	0.436605
$693$	0	0
$694$	16.7279	0.634983
$695$	−3.65685	−0.138712
$696$	3.82843	0.145116
$697$	4.10051	0.155318
$698$	−18.7279	−0.708862
$699$	7.72792	0.292297
$700$	0	0
$701$	−34.8284	−1.31545	−0.657726	−	0.753257i	$-0.728481\pi$
$701$	−34.8284	−1.31545	−0.657726	+	0.753257i	$0.728481\pi$
$702$	−1.00000	−0.0377426
$703$	−11.0711	−0.417553
$704$	2.41421	0.0909891
$705$	−3.41421	−0.128587
$706$	32.6274	1.22795
$707$	0	0
$708$	12.0711	0.453659
$709$	16.8701	0.633568	0.316784	−	0.948498i	$-0.397397\pi$
$709$	16.8701	0.633568	0.316784	+	0.948498i	$0.397397\pi$
$710$	−17.0711	−0.640666
$711$	−0.343146	−0.0128690
$712$	−5.41421	−0.202906
$713$	12.0000	0.449404
$714$	0	0
$715$	−8.24264	−0.308257
$716$	8.34315	0.311798
$717$	21.4853	0.802383
$718$	4.82843	0.180195
$719$	13.3137	0.496518	0.248259	−	0.968694i	$-0.420142\pi$
$719$	13.3137	0.496518	0.248259	+	0.968694i	$0.420142\pi$
$720$	3.41421	0.127240
$721$	0	0
$722$	42.2843	1.57366
$723$	−26.1421	−0.972236
$724$	16.8995	0.628065
$725$	25.4853	0.946500
$726$	−5.17157	−0.191935
$727$	−34.4264	−1.27680	−0.638402	−	0.769703i	$-0.720404\pi$
$727$	−34.4264	−1.27680	−0.638402	+	0.769703i	$0.720404\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	4.82843	0.178708
$731$	4.34315	0.160637
$732$	1.58579	0.0586124
$733$	31.4142	1.16031	0.580155	−	0.814506i	$-0.302992\pi$
$733$	31.4142	1.16031	0.580155	+	0.814506i	$0.302992\pi$
$734$	32.6274	1.20430
$735$	0	0
$736$	−1.41421	−0.0521286
$737$	−9.24264	−0.340457
$738$	−9.89949	−0.364405
$739$	−30.0000	−1.10357	−0.551784	−	0.833987i	$-0.686053\pi$
$739$	−30.0000	−1.10357	−0.551784	+	0.833987i	$0.686053\pi$
$740$	−4.82843	−0.177497
$741$	−7.82843	−0.287584
$742$	0	0
$743$	17.8284	0.654062	0.327031	−	0.945014i	$-0.393952\pi$
$743$	17.8284	0.654062	0.327031	+	0.945014i	$0.393952\pi$
$744$	−8.48528	−0.311086
$745$	−65.1127	−2.38554
$746$	−8.41421	−0.308066
$747$	3.65685	0.133797
$748$	−1.00000	−0.0365636
$749$	0	0
$750$	5.65685	0.206559
$751$	3.31371	0.120919	0.0604595	−	0.998171i	$-0.480743\pi$
$751$	3.31371	0.120919	0.0604595	+	0.998171i	$0.480743\pi$
$752$	−1.00000	−0.0364662
$753$	−19.1716	−0.698651
$754$	−3.82843	−0.139423
$755$	−34.3848	−1.25139
$756$	0	0
$757$	−39.2426	−1.42630	−0.713149	−	0.701012i	$-0.752732\pi$
$757$	−39.2426	−1.42630	−0.713149	+	0.701012i	$0.752732\pi$
$758$	−26.6274	−0.967151
$759$	−3.41421	−0.123928
$760$	26.7279	0.969524
$761$	19.1127	0.692835	0.346417	−	0.938080i	$-0.387398\pi$
$761$	19.1127	0.692835	0.346417	+	0.938080i	$0.387398\pi$
$762$	11.8995	0.431073
$763$	0	0
$764$	−21.6569	−0.783517
$765$	−1.41421	−0.0511310
$766$	−16.8284	−0.608036
$767$	−12.0711	−0.435861
$768$	1.00000	0.0360844
$769$	9.89949	0.356985	0.178492	−	0.983941i	$-0.442878\pi$
$769$	9.89949	0.356985	0.178492	+	0.983941i	$0.442878\pi$
$770$	0	0
$771$	−9.51472	−0.342664
$772$	−17.0711	−0.614401
$773$	14.9706	0.538454	0.269227	−	0.963077i	$-0.413232\pi$
$773$	14.9706	0.538454	0.269227	+	0.963077i	$0.413232\pi$
$774$	−10.4853	−0.376886
$775$	−56.4853	−2.02901
$776$	15.0711	0.541020
$777$	0	0
$778$	−21.4853	−0.770285
$779$	−77.4975	−2.77664
$780$	−3.41421	−0.122248
$781$	−12.0711	−0.431937
$782$	0.585786	0.0209477
$783$	3.82843	0.136817
$784$	0	0
$785$	53.6985	1.91658
$786$	−21.5563	−0.768890
$787$	3.68629	0.131402	0.0657011	−	0.997839i	$-0.479072\pi$
$787$	3.68629	0.131402	0.0657011	+	0.997839i	$0.479072\pi$
$788$	15.5563	0.554172
$789$	23.4142	0.833568
$790$	−1.17157	−0.0416827
$791$	0	0
$792$	2.41421	0.0857853
$793$	−1.58579	−0.0563129
$794$	−21.5563	−0.765006
$795$	−25.5563	−0.906390
$796$	22.7279	0.805570
$797$	−45.6569	−1.61725	−0.808624	−	0.588325i	$-0.799787\pi$
$797$	−45.6569	−1.61725	−0.808624	+	0.588325i	$0.799787\pi$
$798$	0	0
$799$	0.414214	0.0146538
$800$	6.65685	0.235355
$801$	−5.41421	−0.191302
$802$	0.100505	0.00354896
$803$	3.41421	0.120485
$804$	−3.82843	−0.135018
$805$	0	0
$806$	8.48528	0.298881
$807$	−19.1421	−0.673835
$808$	9.17157	0.322655
$809$	−20.4142	−0.717726	−0.358863	−	0.933390i	$-0.616835\pi$
$809$	−20.4142	−0.717726	−0.358863	+	0.933390i	$0.616835\pi$
$810$	3.41421	0.119963
$811$	−4.54416	−0.159567	−0.0797834	−	0.996812i	$-0.525423\pi$
$811$	−4.54416	−0.159567	−0.0797834	+	0.996812i	$0.525423\pi$
$812$	0	0
$813$	16.2132	0.568622
$814$	−3.41421	−0.119668
$815$	−25.0711	−0.878201
$816$	−0.414214	−0.0145004
$817$	−82.0833	−2.87173
$818$	−35.4142	−1.23823
$819$	0	0
$820$	−33.7990	−1.18031
$821$	28.1005	0.980714	0.490357	−	0.871522i	$-0.336866\pi$
$821$	28.1005	0.980714	0.490357	+	0.871522i	$0.336866\pi$
$822$	−3.07107	−0.107116
$823$	43.8406	1.52819	0.764094	−	0.645105i	$-0.223186\pi$
$823$	43.8406	1.52819	0.764094	+	0.645105i	$0.223186\pi$
$824$	11.1716	0.389180
$825$	16.0711	0.559523
$826$	0	0
$827$	−24.3553	−0.846918	−0.423459	−	0.905915i	$-0.639184\pi$
$827$	−24.3553	−0.846918	−0.423459	+	0.905915i	$0.639184\pi$
$828$	−1.41421	−0.0491473
$829$	−32.6985	−1.13567	−0.567833	−	0.823144i	$-0.692218\pi$
$829$	−32.6985	−1.13567	−0.567833	+	0.823144i	$0.692218\pi$
$830$	12.4853	0.433370
$831$	3.92893	0.136293
$832$	−1.00000	−0.0346688
$833$	0	0
$834$	−1.07107	−0.0370880
$835$	−36.3848	−1.25915
$836$	18.8995	0.653653
$837$	−8.48528	−0.293294
$838$	23.4558	0.810269
$839$	26.1716	0.903543	0.451772	−	0.892134i	$-0.350792\pi$
$839$	26.1716	0.903543	0.451772	+	0.892134i	$0.350792\pi$
$840$	0	0
$841$	−14.3431	−0.494591
$842$	−13.0711	−0.450459
$843$	23.3137	0.802967
$844$	−27.0711	−0.931825
$845$	3.41421	0.117453
$846$	−1.00000	−0.0343807
$847$	0	0
$848$	−7.48528	−0.257046
$849$	24.2426	0.832005
$850$	−2.75736	−0.0945766
$851$	2.00000	0.0685591
$852$	−5.00000	−0.171297
$853$	18.7279	0.641232	0.320616	−	0.947209i	$-0.396110\pi$
$853$	18.7279	0.641232	0.320616	+	0.947209i	$0.396110\pi$
$854$	0	0
$855$	26.7279	0.914076
$856$	3.31371	0.113260
$857$	10.5563	0.360598	0.180299	−	0.983612i	$-0.442293\pi$
$857$	10.5563	0.360598	0.180299	+	0.983612i	$0.442293\pi$
$858$	−2.41421	−0.0824199
$859$	−27.7990	−0.948489	−0.474245	−	0.880393i	$-0.657279\pi$
$859$	−27.7990	−0.948489	−0.474245	+	0.880393i	$0.657279\pi$
$860$	−35.7990	−1.22074
$861$	0	0
$862$	13.5147	0.460313
$863$	16.6863	0.568008	0.284004	−	0.958823i	$-0.408337\pi$
$863$	16.6863	0.568008	0.284004	+	0.958823i	$0.408337\pi$
$864$	1.00000	0.0340207
$865$	39.2132	1.33329
$866$	3.97056	0.134925
$867$	−16.8284	−0.571523
$868$	0	0
$869$	−0.828427	−0.0281025
$870$	13.0711	0.443151
$871$	3.82843	0.129721
$872$	1.65685	0.0561082
$873$	15.0711	0.510078
$874$	−11.0711	−0.374484
$875$	0	0
$876$	1.41421	0.0477818
$877$	8.04163	0.271547	0.135773	−	0.990740i	$-0.456648\pi$
$877$	8.04163	0.271547	0.135773	+	0.990740i	$0.456648\pi$
$878$	−19.4142	−0.655198
$879$	−9.89949	−0.333902
$880$	8.24264	0.277859
$881$	−1.51472	−0.0510322	−0.0255161	−	0.999674i	$-0.508123\pi$
$881$	−1.51472	−0.0510322	−0.0255161	+	0.999674i	$0.508123\pi$
$882$	0	0
$883$	−18.2426	−0.613914	−0.306957	−	0.951723i	$-0.599311\pi$
$883$	−18.2426	−0.613914	−0.306957	+	0.951723i	$0.599311\pi$
$884$	0.414214	0.0139315
$885$	41.2132	1.38537
$886$	25.6985	0.863357
$887$	52.9117	1.77660	0.888300	−	0.459263i	$-0.151886\pi$
$887$	52.9117	1.77660	0.888300	+	0.459263i	$0.151886\pi$
$888$	−1.41421	−0.0474579
$889$	0	0
$890$	−18.4853	−0.619628
$891$	2.41421	0.0808792
$892$	22.0711	0.738994
$893$	−7.82843	−0.261968
$894$	−19.0711	−0.637832
$895$	28.4853	0.952158
$896$	0	0
$897$	1.41421	0.0472192
$898$	−8.97056	−0.299352
$899$	−32.4853	−1.08344
$900$	6.65685	0.221895
$901$	3.10051	0.103293
$902$	−23.8995	−0.795766
$903$	0	0
$904$	−14.8995	−0.495550
$905$	57.6985	1.91796
$906$	−10.0711	−0.334589
$907$	17.6152	0.584904	0.292452	−	0.956280i	$-0.405529\pi$
$907$	17.6152	0.584904	0.292452	+	0.956280i	$0.405529\pi$
$908$	26.8284	0.890333
$909$	9.17157	0.304202
$910$	0	0
$911$	−15.6569	−0.518735	−0.259367	−	0.965779i	$-0.583514\pi$
$911$	−15.6569	−0.518735	−0.259367	+	0.965779i	$0.583514\pi$
$912$	7.82843	0.259225
$913$	8.82843	0.292178
$914$	11.0711	0.366198
$915$	5.41421	0.178988
$916$	−9.51472	−0.314375
$917$	0	0
$918$	−0.414214	−0.0136711
$919$	−37.7990	−1.24687	−0.623437	−	0.781874i	$-0.714264\pi$
$919$	−37.7990	−1.24687	−0.623437	+	0.781874i	$0.714264\pi$
$920$	−4.82843	−0.159189
$921$	−34.1127	−1.12405
$922$	−12.4853	−0.411181
$923$	5.00000	0.164577
$924$	0	0
$925$	−9.41421	−0.309537
$926$	12.9706	0.426239
$927$	11.1716	0.366923
$928$	3.82843	0.125674
$929$	−57.3137	−1.88040	−0.940201	−	0.340620i	$-0.889363\pi$
$929$	−57.3137	−1.88040	−0.940201	+	0.340620i	$0.889363\pi$
$930$	−28.9706	−0.949982
$931$	0	0
$932$	7.72792	0.253137
$933$	27.8995	0.913388
$934$	8.58579	0.280936
$935$	−3.41421	−0.111657
$936$	−1.00000	−0.0326860
$937$	−31.3431	−1.02394	−0.511968	−	0.859005i	$-0.671083\pi$
$937$	−31.3431	−1.02394	−0.511968	+	0.859005i	$0.671083\pi$
$938$	0	0
$939$	−20.4853	−0.668512
$940$	−3.41421	−0.111359
$941$	−20.9706	−0.683621	−0.341810	−	0.939769i	$-0.611040\pi$
$941$	−20.9706	−0.683621	−0.341810	+	0.939769i	$0.611040\pi$
$942$	15.7279	0.512443
$943$	14.0000	0.455903
$944$	12.0711	0.392880
$945$	0	0
$946$	−25.3137	−0.823020
$947$	5.58579	0.181514	0.0907568	−	0.995873i	$-0.471071\pi$
$947$	5.58579	0.181514	0.0907568	+	0.995873i	$0.471071\pi$
$948$	−0.343146	−0.0111449
$949$	−1.41421	−0.0459073
$950$	52.1127	1.69076
$951$	−9.79899	−0.317754
$952$	0	0
$953$	−44.4142	−1.43872	−0.719359	−	0.694639i	$-0.755564\pi$
$953$	−44.4142	−1.43872	−0.719359	+	0.694639i	$0.755564\pi$
$954$	−7.48528	−0.242345
$955$	−73.9411	−2.39268
$956$	21.4853	0.694884
$957$	9.24264	0.298772
$958$	−30.1127	−0.972897
$959$	0	0
$960$	3.41421	0.110193
$961$	41.0000	1.32258
$962$	1.41421	0.0455961
$963$	3.31371	0.106783
$964$	−26.1421	−0.841981
$965$	−58.2843	−1.87624
$966$	0	0
$967$	−16.4142	−0.527846	−0.263923	−	0.964544i	$-0.585016\pi$
$967$	−16.4142	−0.527846	−0.263923	+	0.964544i	$0.585016\pi$
$968$	−5.17157	−0.166221
$969$	−3.24264	−0.104169
$970$	51.4558	1.65215
$971$	−32.5269	−1.04384	−0.521919	−	0.852995i	$-0.674784\pi$
$971$	−32.5269	−1.04384	−0.521919	+	0.852995i	$0.674784\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−26.2132	−0.839925
$975$	−6.65685	−0.213190
$976$	1.58579	0.0507598
$977$	48.8284	1.56216	0.781080	−	0.624431i	$-0.214669\pi$
$977$	48.8284	1.56216	0.781080	+	0.624431i	$0.214669\pi$
$978$	−7.34315	−0.234808
$979$	−13.0711	−0.417753
$980$	0	0
$981$	1.65685	0.0528993
$982$	12.3431	0.393886
$983$	12.5147	0.399158	0.199579	−	0.979882i	$-0.436043\pi$
$983$	12.5147	0.399158	0.199579	+	0.979882i	$0.436043\pi$
$984$	−9.89949	−0.315584
$985$	53.1127	1.69231
$986$	−1.58579	−0.0505017
$987$	0	0
$988$	−7.82843	−0.249055
$989$	14.8284	0.471517
$990$	8.24264	0.261968
$991$	−23.3137	−0.740584	−0.370292	−	0.928915i	$-0.620742\pi$
$991$	−23.3137	−0.740584	−0.370292	+	0.928915i	$0.620742\pi$
$992$	−8.48528	−0.269408
$993$	−5.51472	−0.175004
$994$	0	0
$995$	77.5980	2.46002
$996$	3.65685	0.115872
$997$	46.4975	1.47259	0.736295	−	0.676661i	$-0.236574\pi$
$997$	46.4975	1.47259	0.736295	+	0.676661i	$0.236574\pi$
$998$	−7.65685	−0.242373
$999$	−1.41421	−0.0447437

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3822.2.a.bu.1.2		2
7.3	odd	6		546.2.i.i.79.2	✓	4
7.5	odd	6		546.2.i.i.235.2	yes	4
7.6	odd	2		3822.2.a.bn.1.1		2
21.5	even	6		1638.2.j.m.235.1		4
21.17	even	6		1638.2.j.m.1171.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.i.i.79.2	✓	4	7.3	odd	6
546.2.i.i.235.2	yes	4	7.5	odd	6
1638.2.j.m.235.1		4	21.5	even	6
1638.2.j.m.1171.1		4	21.17	even	6
3822.2.a.bn.1.1		2	7.6	odd	2
3822.2.a.bu.1.2		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3822.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.41421 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.41421 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +3.41421 q^{10} +2.41421 q^{11} +1.00000 q^{12} -1.00000 q^{13} +3.41421 q^{15} +1.00000 q^{16} -0.414214 q^{17} +1.00000 q^{18} +7.82843 q^{19} +3.41421 q^{20} +2.41421 q^{22} -1.41421 q^{23} +1.00000 q^{24} +6.65685 q^{25} -1.00000 q^{26} +1.00000 q^{27} +3.82843 q^{29} +3.41421 q^{30} -8.48528 q^{31} +1.00000 q^{32} +2.41421 q^{33} -0.414214 q^{34} +1.00000 q^{36} -1.41421 q^{37} +7.82843 q^{38} -1.00000 q^{39} +3.41421 q^{40} -9.89949 q^{41} -10.4853 q^{43} +2.41421 q^{44} +3.41421 q^{45} -1.41421 q^{46} -1.00000 q^{47} +1.00000 q^{48} +6.65685 q^{50} -0.414214 q^{51} -1.00000 q^{52} -7.48528 q^{53} +1.00000 q^{54} +8.24264 q^{55} +7.82843 q^{57} +3.82843 q^{58} +12.0711 q^{59} +3.41421 q^{60} +1.58579 q^{61} -8.48528 q^{62} +1.00000 q^{64} -3.41421 q^{65} +2.41421 q^{66} -3.82843 q^{67} -0.414214 q^{68} -1.41421 q^{69} -5.00000 q^{71} +1.00000 q^{72} +1.41421 q^{73} -1.41421 q^{74} +6.65685 q^{75} +7.82843 q^{76} -1.00000 q^{78} -0.343146 q^{79} +3.41421 q^{80} +1.00000 q^{81} -9.89949 q^{82} +3.65685 q^{83} -1.41421 q^{85} -10.4853 q^{86} +3.82843 q^{87} +2.41421 q^{88} -5.41421 q^{89} +3.41421 q^{90} -1.41421 q^{92} -8.48528 q^{93} -1.00000 q^{94} +26.7279 q^{95} +1.00000 q^{96} +15.0711 q^{97} +2.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9} + 4 q^{10} + 2 q^{11} + 2 q^{12} - 2 q^{13} + 4 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} + 10 q^{19} + 4 q^{20} + 2 q^{22} + 2 q^{24} + 2 q^{25} - 2 q^{26} + 2 q^{27} + 2 q^{29} + 4 q^{30} + 2 q^{32} + 2 q^{33} + 2 q^{34} + 2 q^{36} + 10 q^{38} - 2 q^{39} + 4 q^{40} - 4 q^{43} + 2 q^{44} + 4 q^{45} - 2 q^{47} + 2 q^{48} + 2 q^{50} + 2 q^{51} - 2 q^{52} + 2 q^{53} + 2 q^{54} + 8 q^{55} + 10 q^{57} + 2 q^{58} + 10 q^{59} + 4 q^{60} + 6 q^{61} + 2 q^{64} - 4 q^{65} + 2 q^{66} - 2 q^{67} + 2 q^{68} - 10 q^{71} + 2 q^{72} + 2 q^{75} + 10 q^{76} - 2 q^{78} - 12 q^{79} + 4 q^{80} + 2 q^{81} - 4 q^{83} - 4 q^{86} + 2 q^{87} + 2 q^{88} - 8 q^{89} + 4 q^{90} - 2 q^{94} + 28 q^{95} + 2 q^{96} + 16 q^{97} + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9 + 4 * q^10 + 2 * q^11 + 2 * q^12 - 2 * q^13 + 4 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 + 10 * q^19 + 4 * q^20 + 2 * q^22 + 2 * q^24 + 2 * q^25 - 2 * q^26 + 2 * q^27 + 2 * q^29 + 4 * q^30 + 2 * q^32 + 2 * q^33 + 2 * q^34 + 2 * q^36 + 10 * q^38 - 2 * q^39 + 4 * q^40 - 4 * q^43 + 2 * q^44 + 4 * q^45 - 2 * q^47 + 2 * q^48 + 2 * q^50 + 2 * q^51 - 2 * q^52 + 2 * q^53 + 2 * q^54 + 8 * q^55 + 10 * q^57 + 2 * q^58 + 10 * q^59 + 4 * q^60 + 6 * q^61 + 2 * q^64 - 4 * q^65 + 2 * q^66 - 2 * q^67 + 2 * q^68 - 10 * q^71 + 2 * q^72 + 2 * q^75 + 10 * q^76 - 2 * q^78 - 12 * q^79 + 4 * q^80 + 2 * q^81 - 4 * q^83 - 4 * q^86 + 2 * q^87 + 2 * q^88 - 8 * q^89 + 4 * q^90 - 2 * q^94 + 28 * q^95 + 2 * q^96 + 16 * q^97 + 2 * q^99

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