LMFDB - Embedded newform 1425.2.c.l.799.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1425,2,Mod(799,1425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1425, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("1425.799");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1425 = 3 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1425.c (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$11.3786822880$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 285)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			799.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1425.799
Dual form			1425.2.c.l.799.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41421i q^{2} +1.00000i q^{3} -3.82843 q^{4} +2.41421 q^{6} +1.41421i q^{7} +4.41421i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.41421i q^{2} +1.00000i q^{3} -3.82843 q^{4} +2.41421 q^{6} +1.41421i q^{7} +4.41421i q^{8} -1.00000 q^{9} -2.24264 q^{11} -3.82843i q^{12} -3.41421i q^{13} +3.41421 q^{14} +3.00000 q^{16} -1.17157i q^{17} +2.41421i q^{18} +1.00000 q^{19} -1.41421 q^{21} +5.41421i q^{22} +7.65685i q^{23} -4.41421 q^{24} -8.24264 q^{26} -1.00000i q^{27} -5.41421i q^{28} -1.41421 q^{29} -3.17157 q^{31} +1.58579i q^{32} -2.24264i q^{33} -2.82843 q^{34} +3.82843 q^{36} +3.41421i q^{37} -2.41421i q^{38} +3.41421 q^{39} -0.242641 q^{41} +3.41421i q^{42} +12.2426i q^{43} +8.58579 q^{44} +18.4853 q^{46} +7.65685i q^{47} +3.00000i q^{48} +5.00000 q^{49} +1.17157 q^{51} +13.0711i q^{52} +8.00000i q^{53} -2.41421 q^{54} -6.24264 q^{56} +1.00000i q^{57} +3.41421i q^{58} -12.4853 q^{59} +7.31371 q^{61} +7.65685i q^{62} -1.41421i q^{63} +9.82843 q^{64} -5.41421 q^{66} +9.65685i q^{67} +4.48528i q^{68} -7.65685 q^{69} -10.8284 q^{71} -4.41421i q^{72} -7.65685i q^{73} +8.24264 q^{74} -3.82843 q^{76} -3.17157i q^{77} -8.24264i q^{78} +1.00000 q^{81} +0.585786i q^{82} +12.8284i q^{83} +5.41421 q^{84} +29.5563 q^{86} -1.41421i q^{87} -9.89949i q^{88} -5.89949 q^{89} +4.82843 q^{91} -29.3137i q^{92} -3.17157i q^{93} +18.4853 q^{94} -1.58579 q^{96} +9.75736i q^{97} -12.0711i q^{98} +2.24264 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9	$ 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9} + 8 q^{11} + 8 q^{14} + 12 q^{16} + 4 q^{19} - 12 q^{24} - 16 q^{26} - 24 q^{31} + 4 q^{36} + 8 q^{39} + 16 q^{41} + 40 q^{44} + 40 q^{46} + 20 q^{49} + 16 q^{51} - 4 q^{54} - 8 q^{56} - 16 q^{59} - 16 q^{61} + 28 q^{64} - 16 q^{66} - 8 q^{69} - 32 q^{71} + 16 q^{74} - 4 q^{76} + 4 q^{81} + 16 q^{84} + 56 q^{86} + 16 q^{89} + 8 q^{91} + 40 q^{94} - 12 q^{96} - 8 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 + 8 * q^11 + 8 * q^14 + 12 * q^16 + 4 * q^19 - 12 * q^24 - 16 * q^26 - 24 * q^31 + 4 * q^36 + 8 * q^39 + 16 * q^41 + 40 * q^44 + 40 * q^46 + 20 * q^49 + 16 * q^51 - 4 * q^54 - 8 * q^56 - 16 * q^59 - 16 * q^61 + 28 * q^64 - 16 * q^66 - 8 * q^69 - 32 * q^71 + 16 * q^74 - 4 * q^76 + 4 * q^81 + 16 * q^84 + 56 * q^86 + 16 * q^89 + 8 * q^91 + 40 * q^94 - 12 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1425\mathbb{Z}\right)^\times$.

$n$	$476$	$1027$	$1351$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	− 2.41421i	− 1.70711i	−0.521005	−	0.853553i	$-0.674443\pi$
$2$	− 2.41421i	− 1.70711i	0.521005	−	0.853553i	$-0.325557\pi$
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	−3.82843	−1.91421
$5$	0	0
$5$	0	0
$6$	2.41421	0.985599
$7$	1.41421i	0.534522i	0.963624	+	0.267261i	$0.0861187\pi$
$7$	1.41421i	0.534522i	−0.963624	+	0.267261i	$0.913881\pi$
$8$	4.41421i	1.56066i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−2.24264	−0.676182	−0.338091	−	0.941113i	$-0.609781\pi$
$11$	−2.24264	−0.676182	−0.338091	+	0.941113i	$0.609781\pi$
$12$	− 3.82843i	− 1.10517i
$13$	− 3.41421i	− 0.946932i	−0.880812	−	0.473466i	$-0.843003\pi$
$13$	− 3.41421i	− 0.946932i	0.880812	−	0.473466i	$-0.156997\pi$
$14$	3.41421	0.912487
$15$	0	0
$16$	3.00000	0.750000
$17$	− 1.17157i	− 0.284148i	−0.989856	−	0.142074i	$-0.954623\pi$
$17$	− 1.17157i	− 0.284148i	0.989856	−	0.142074i	$-0.0453771\pi$
$18$	2.41421i	0.569036i
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	−1.41421	−0.308607
$22$	5.41421i	1.15431i
$23$	7.65685i	1.59656i	0.602284	+	0.798282i	$0.294258\pi$
$23$	7.65685i	1.59656i	−0.602284	+	0.798282i	$0.705742\pi$
$24$	−4.41421	−0.901048
$25$	0	0
$26$	−8.24264	−1.61651
$27$	− 1.00000i	− 0.192450i
$28$	− 5.41421i	− 1.02319i
$29$	−1.41421	−0.262613	−0.131306	−	0.991342i	$-0.541917\pi$
$29$	−1.41421	−0.262613	−0.131306	+	0.991342i	$0.541917\pi$
$30$	0	0
$31$	−3.17157	−0.569631	−0.284816	−	0.958582i	$-0.591932\pi$
$31$	−3.17157	−0.569631	−0.284816	+	0.958582i	$0.591932\pi$
$32$	1.58579i	0.280330i
$33$	− 2.24264i	− 0.390394i
$34$	−2.82843	−0.485071
$35$	0	0
$36$	3.82843	0.638071
$37$	3.41421i	0.561293i	0.959811	+	0.280647i	$0.0905489\pi$
$37$	3.41421i	0.561293i	−0.959811	+	0.280647i	$0.909451\pi$
$38$	− 2.41421i	− 0.391637i
$39$	3.41421	0.546712
$40$	0	0
$41$	−0.242641	−0.0378941	−0.0189471	−	0.999820i	$-0.506031\pi$
$41$	−0.242641	−0.0378941	−0.0189471	+	0.999820i	$0.506031\pi$
$42$	3.41421i	0.526825i
$43$	12.2426i	1.86699i	0.358597	+	0.933493i	$0.383255\pi$
$43$	12.2426i	1.86699i	−0.358597	+	0.933493i	$0.616745\pi$
$44$	8.58579	1.29436
$45$	0	0
$46$	18.4853	2.72551
$47$	7.65685i	1.11687i	0.829549	+	0.558433i	$0.188597\pi$
$47$	7.65685i	1.11687i	−0.829549	+	0.558433i	$0.811403\pi$
$48$	3.00000i	0.433013i
$49$	5.00000	0.714286
$50$	0	0
$51$	1.17157	0.164053
$52$	13.0711i	1.81263i
$53$	8.00000i	1.09888i	0.835532	+	0.549442i	$0.185160\pi$
$53$	8.00000i	1.09888i	−0.835532	+	0.549442i	$0.814840\pi$
$54$	−2.41421	−0.328533
$55$	0	0
$56$	−6.24264	−0.834208
$57$	1.00000i	0.132453i
$58$	3.41421i	0.448308i
$59$	−12.4853	−1.62545	−0.812723	−	0.582651i	$-0.802016\pi$
$59$	−12.4853	−1.62545	−0.812723	+	0.582651i	$0.802016\pi$
$60$	0	0
$61$	7.31371	0.936424	0.468212	−	0.883616i	$-0.344898\pi$
$61$	7.31371	0.936424	0.468212	+	0.883616i	$0.344898\pi$
$62$	7.65685i	0.972421i
$63$	− 1.41421i	− 0.178174i
$64$	9.82843	1.22855
$65$	0	0
$66$	−5.41421	−0.666444
$67$	9.65685i	1.17977i	0.807486	+	0.589886i	$0.200827\pi$
$67$	9.65685i	1.17977i	−0.807486	+	0.589886i	$0.799173\pi$
$68$	4.48528i	0.543920i
$69$	−7.65685	−0.921777
$70$	0	0
$71$	−10.8284	−1.28510	−0.642549	−	0.766245i	$-0.722123\pi$
$71$	−10.8284	−1.28510	−0.642549	+	0.766245i	$0.722123\pi$
$72$	− 4.41421i	− 0.520220i
$73$	− 7.65685i	− 0.896167i	−0.893992	−	0.448084i	$-0.852107\pi$
$73$	− 7.65685i	− 0.896167i	0.893992	−	0.448084i	$-0.147893\pi$
$74$	8.24264	0.958188
$75$	0	0
$76$	−3.82843	−0.439151
$77$	− 3.17157i	− 0.361434i
$78$	− 8.24264i	− 0.933295i
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0.585786i	0.0646893i
$83$	12.8284i	1.40810i	0.710149	+	0.704051i	$0.248628\pi$
$83$	12.8284i	1.40810i	−0.710149	+	0.704051i	$0.751372\pi$
$84$	5.41421	0.590739
$85$	0	0
$86$	29.5563	3.18714
$87$	− 1.41421i	− 0.151620i
$88$	− 9.89949i	− 1.05529i
$89$	−5.89949	−0.625345	−0.312673	−	0.949861i	$-0.601224\pi$
$89$	−5.89949	−0.625345	−0.312673	+	0.949861i	$0.601224\pi$
$90$	0	0
$91$	4.82843	0.506157
$92$	− 29.3137i	− 3.05617i
$93$	− 3.17157i	− 0.328877i
$94$	18.4853	1.90661
$95$	0	0
$96$	−1.58579	−0.161849
$97$	9.75736i	0.990710i	0.868691	+	0.495355i	$0.164962\pi$
$97$	9.75736i	0.990710i	−0.868691	+	0.495355i	$0.835038\pi$
$98$	− 12.0711i	− 1.21936i
$99$	2.24264	0.225394
$100$	0	0
$101$	−3.17157	−0.315583	−0.157792	−	0.987472i	$-0.550437\pi$
$101$	−3.17157	−0.315583	−0.157792	+	0.987472i	$0.550437\pi$
$102$	− 2.82843i	− 0.280056i
$103$	− 7.31371i	− 0.720641i	−0.932829	−	0.360321i	$-0.882667\pi$
$103$	− 7.31371i	− 0.720641i	0.932829	−	0.360321i	$-0.117333\pi$
$104$	15.0711	1.47784
$105$	0	0
$106$	19.3137	1.87591
$107$	− 19.3137i	− 1.86713i	−0.358412	−	0.933563i	$-0.616682\pi$
$107$	− 19.3137i	− 1.86713i	0.358412	−	0.933563i	$-0.383318\pi$
$108$	3.82843i	0.368391i
$109$	6.48528	0.621177	0.310589	−	0.950544i	$-0.399474\pi$
$109$	6.48528	0.621177	0.310589	+	0.950544i	$0.399474\pi$
$110$	0	0
$111$	−3.41421	−0.324063
$112$	4.24264i	0.400892i
$113$	10.1421i	0.954092i	0.878878	+	0.477046i	$0.158292\pi$
$113$	10.1421i	0.954092i	−0.878878	+	0.477046i	$0.841708\pi$
$114$	2.41421	0.226112
$115$	0	0
$116$	5.41421	0.502697
$117$	3.41421i	0.315644i
$118$	30.1421i	2.77481i
$119$	1.65685	0.151884
$120$	0	0
$121$	−5.97056	−0.542778
$122$	− 17.6569i	− 1.59858i
$123$	− 0.242641i	− 0.0218782i
$124$	12.1421	1.09040
$125$	0	0
$126$	−3.41421	−0.304162
$127$	− 19.3137i	− 1.71381i	−0.515471	−	0.856907i	$-0.672383\pi$
$127$	− 19.3137i	− 1.71381i	0.515471	−	0.856907i	$-0.327617\pi$
$128$	− 20.5563i	− 1.81694i
$129$	−12.2426	−1.07790
$130$	0	0
$131$	−8.58579	−0.750144	−0.375072	−	0.926996i	$-0.622382\pi$
$131$	−8.58579	−0.750144	−0.375072	+	0.926996i	$0.622382\pi$
$132$	8.58579i	0.747297i
$133$	1.41421i	0.122628i
$134$	23.3137	2.01400
$135$	0	0
$136$	5.17157	0.443459
$137$	− 10.0000i	− 0.854358i	−0.904167	−	0.427179i	$-0.859507\pi$
$137$	− 10.0000i	− 0.854358i	0.904167	−	0.427179i	$-0.140493\pi$
$138$	18.4853i	1.57357i
$139$	14.1421	1.19952	0.599760	−	0.800180i	$-0.295263\pi$
$139$	14.1421	1.19952	0.599760	+	0.800180i	$0.295263\pi$
$140$	0	0
$141$	−7.65685	−0.644823
$142$	26.1421i	2.19380i
$143$	7.65685i	0.640298i
$144$	−3.00000	−0.250000
$145$	0	0
$146$	−18.4853	−1.52985
$147$	5.00000i	0.412393i
$148$	− 13.0711i	− 1.07444i
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	0	0
$151$	−6.48528	−0.527765	−0.263882	−	0.964555i	$-0.585003\pi$
$151$	−6.48528	−0.527765	−0.263882	+	0.964555i	$0.585003\pi$
$152$	4.41421i	0.358040i
$153$	1.17157i	0.0947161i
$154$	−7.65685	−0.617007
$155$	0	0
$156$	−13.0711	−1.04652
$157$	− 10.4853i	− 0.836817i	−0.908259	−	0.418408i	$-0.862588\pi$
$157$	− 10.4853i	− 0.836817i	0.908259	−	0.418408i	$-0.137412\pi$
$158$	0	0
$159$	−8.00000	−0.634441
$160$	0	0
$161$	−10.8284	−0.853400
$162$	− 2.41421i	− 0.189679i
$163$	21.8995i	1.71530i	0.514233	+	0.857650i	$0.328077\pi$
$163$	21.8995i	1.71530i	−0.514233	+	0.857650i	$0.671923\pi$
$164$	0.928932	0.0725374
$165$	0	0
$166$	30.9706	2.40378
$167$	17.3137i	1.33977i	0.742463	+	0.669887i	$0.233658\pi$
$167$	17.3137i	1.33977i	−0.742463	+	0.669887i	$0.766342\pi$
$168$	− 6.24264i	− 0.481630i
$169$	1.34315	0.103319
$170$	0	0
$171$	−1.00000	−0.0764719
$172$	− 46.8701i	− 3.57381i
$173$	− 19.7990i	− 1.50529i	−0.658427	−	0.752645i	$-0.728778\pi$
$173$	− 19.7990i	− 1.50529i	0.658427	−	0.752645i	$-0.271222\pi$
$174$	−3.41421	−0.258831
$175$	0	0
$176$	−6.72792	−0.507136
$177$	− 12.4853i	− 0.938451i
$178$	14.2426i	1.06753i
$179$	−16.4853	−1.23217	−0.616084	−	0.787681i	$-0.711282\pi$
$179$	−16.4853	−1.23217	−0.616084	+	0.787681i	$0.711282\pi$
$180$	0	0
$181$	−20.8284	−1.54816	−0.774082	−	0.633085i	$-0.781788\pi$
$181$	−20.8284	−1.54816	−0.774082	+	0.633085i	$0.781788\pi$
$182$	− 11.6569i	− 0.864064i
$183$	7.31371i	0.540645i
$184$	−33.7990	−2.49169
$185$	0	0
$186$	−7.65685	−0.561428
$187$	2.62742i	0.192136i
$188$	− 29.3137i	− 2.13792i
$189$	1.41421	0.102869
$190$	0	0
$191$	10.2426	0.741131	0.370566	−	0.928806i	$-0.379164\pi$
$191$	10.2426	0.741131	0.370566	+	0.928806i	$0.379164\pi$
$192$	9.82843i	0.709306i
$193$	5.07107i	0.365023i	0.983204	+	0.182512i	$0.0584227\pi$
$193$	5.07107i	0.365023i	−0.983204	+	0.182512i	$0.941577\pi$
$194$	23.5563	1.69125
$195$	0	0
$196$	−19.1421	−1.36730
$197$	− 6.82843i	− 0.486505i	−0.969963	−	0.243253i	$-0.921786\pi$
$197$	− 6.82843i	− 0.486505i	0.969963	−	0.243253i	$-0.0782144\pi$
$198$	− 5.41421i	− 0.384771i
$199$	−18.1421	−1.28606	−0.643031	−	0.765840i	$-0.722323\pi$
$199$	−18.1421	−1.28606	−0.643031	+	0.765840i	$0.722323\pi$
$200$	0	0
$201$	−9.65685	−0.681142
$202$	7.65685i	0.538734i
$203$	− 2.00000i	− 0.140372i
$204$	−4.48528	−0.314033
$205$	0	0
$206$	−17.6569	−1.23021
$207$	− 7.65685i	− 0.532188i
$208$	− 10.2426i	− 0.710199i
$209$	−2.24264	−0.155127
$210$	0	0
$211$	7.31371	0.503496	0.251748	−	0.967793i	$-0.418995\pi$
$211$	7.31371	0.503496	0.251748	+	0.967793i	$0.418995\pi$
$212$	− 30.6274i	− 2.10350i
$213$	− 10.8284i	− 0.741952i
$214$	−46.6274	−3.18738
$215$	0	0
$216$	4.41421	0.300349
$217$	− 4.48528i	− 0.304481i
$218$	− 15.6569i	− 1.06042i
$219$	7.65685	0.517402
$220$	0	0
$221$	−4.00000	−0.269069
$222$	8.24264i	0.553210i
$223$	18.6274i	1.24738i	0.781670	+	0.623692i	$0.214368\pi$
$223$	18.6274i	1.24738i	−0.781670	+	0.623692i	$0.785632\pi$
$224$	−2.24264	−0.149843
$225$	0	0
$226$	24.4853	1.62874
$227$	− 14.9706i	− 0.993631i	−0.867856	−	0.496816i	$-0.834503\pi$
$227$	− 14.9706i	− 0.993631i	0.867856	−	0.496816i	$-0.165497\pi$
$228$	− 3.82843i	− 0.253544i
$229$	22.6274	1.49526	0.747631	−	0.664114i	$-0.231191\pi$
$229$	22.6274	1.49526	0.747631	+	0.664114i	$0.231191\pi$
$230$	0	0
$231$	3.17157	0.208674
$232$	− 6.24264i	− 0.409849i
$233$	− 0.343146i	− 0.0224802i	−0.999937	−	0.0112401i	$-0.996422\pi$
$233$	− 0.343146i	− 0.0224802i	0.999937	−	0.0112401i	$-0.00357791\pi$
$234$	8.24264	0.538838
$235$	0	0
$236$	47.7990	3.11145
$237$	0	0
$238$	− 4.00000i	− 0.259281i
$239$	26.7279	1.72889	0.864443	−	0.502731i	$-0.167671\pi$
$239$	26.7279	1.72889	0.864443	+	0.502731i	$0.167671\pi$
$240$	0	0
$241$	−19.6569	−1.26621	−0.633105	−	0.774066i	$-0.718220\pi$
$241$	−19.6569	−1.26621	−0.633105	+	0.774066i	$0.718220\pi$
$242$	14.4142i	0.926581i
$243$	1.00000i	0.0641500i
$244$	−28.0000	−1.79252
$245$	0	0
$246$	−0.585786	−0.0373484
$247$	− 3.41421i	− 0.217241i
$248$	− 14.0000i	− 0.889001i
$249$	−12.8284	−0.812969
$250$	0	0
$251$	−1.75736	−0.110924	−0.0554618	−	0.998461i	$-0.517663\pi$
$251$	−1.75736	−0.110924	−0.0554618	+	0.998461i	$0.517663\pi$
$252$	5.41421i	0.341063i
$253$	− 17.1716i	− 1.07957i
$254$	−46.6274	−2.92566
$255$	0	0
$256$	−29.9706	−1.87316
$257$	4.48528i	0.279784i	0.990167	+	0.139892i	$0.0446756\pi$
$257$	4.48528i	0.279784i	−0.990167	+	0.139892i	$0.955324\pi$
$258$	29.5563i	1.84010i
$259$	−4.82843	−0.300024
$260$	0	0
$261$	1.41421	0.0875376
$262$	20.7279i	1.28058i
$263$	− 23.4558i	− 1.44635i	−0.690665	−	0.723175i	$-0.742682\pi$
$263$	− 23.4558i	− 1.44635i	0.690665	−	0.723175i	$-0.257318\pi$
$264$	9.89949	0.609272
$265$	0	0
$266$	3.41421	0.209339
$267$	− 5.89949i	− 0.361043i
$268$	− 36.9706i	− 2.25834i
$269$	3.07107	0.187246	0.0936232	−	0.995608i	$-0.470155\pi$
$269$	3.07107	0.187246	0.0936232	+	0.995608i	$0.470155\pi$
$270$	0	0
$271$	−10.8284	−0.657780	−0.328890	−	0.944368i	$-0.606675\pi$
$271$	−10.8284	−0.657780	−0.328890	+	0.944368i	$0.606675\pi$
$272$	− 3.51472i	− 0.213111i
$273$	4.82843i	0.292230i
$274$	−24.1421	−1.45848
$275$	0	0
$276$	29.3137	1.76448
$277$	22.0000i	1.32185i	0.750451	+	0.660926i	$0.229836\pi$
$277$	22.0000i	1.32185i	−0.750451	+	0.660926i	$0.770164\pi$
$278$	− 34.1421i	− 2.04771i
$279$	3.17157	0.189877
$280$	0	0
$281$	−14.5858	−0.870115	−0.435058	−	0.900403i	$-0.643272\pi$
$281$	−14.5858	−0.870115	−0.435058	+	0.900403i	$0.643272\pi$
$282$	18.4853i	1.10078i
$283$	− 10.3848i	− 0.617311i	−0.951174	−	0.308655i	$-0.900121\pi$
$283$	− 10.3848i	− 0.617311i	0.951174	−	0.308655i	$-0.0998790\pi$
$284$	41.4558	2.45995
$285$	0	0
$286$	18.4853	1.09306
$287$	− 0.343146i	− 0.0202553i
$288$	− 1.58579i	− 0.0934434i
$289$	15.6274	0.919260
$290$	0	0
$291$	−9.75736	−0.571987
$292$	29.3137i	1.71546i
$293$	− 11.5147i	− 0.672697i	−0.941738	−	0.336349i	$-0.890808\pi$
$293$	− 11.5147i	− 0.672697i	0.941738	−	0.336349i	$-0.109192\pi$
$294$	12.0711	0.703999
$295$	0	0
$296$	−15.0711	−0.875988
$297$	2.24264i	0.130131i
$298$	− 14.4853i	− 0.839110i
$299$	26.1421	1.51184
$300$	0	0
$301$	−17.3137	−0.997946
$302$	15.6569i	0.900951i
$303$	− 3.17157i	− 0.182202i
$304$	3.00000	0.172062
$305$	0	0
$306$	2.82843	0.161690
$307$	− 21.1716i	− 1.20833i	−0.796861	−	0.604163i	$-0.793508\pi$
$307$	− 21.1716i	− 1.20833i	0.796861	−	0.604163i	$-0.206492\pi$
$308$	12.1421i	0.691862i
$309$	7.31371	0.416062
$310$	0	0
$311$	−6.24264	−0.353988	−0.176994	−	0.984212i	$-0.556637\pi$
$311$	−6.24264	−0.353988	−0.176994	+	0.984212i	$0.556637\pi$
$312$	15.0711i	0.853231i
$313$	5.79899i	0.327778i	0.986479	+	0.163889i	$0.0524039\pi$
$313$	5.79899i	0.327778i	−0.986479	+	0.163889i	$0.947596\pi$
$314$	−25.3137	−1.42854
$315$	0	0
$316$	0	0
$317$	26.6274i	1.49554i	0.663955	+	0.747772i	$0.268877\pi$
$317$	26.6274i	1.49554i	−0.663955	+	0.747772i	$0.731123\pi$
$318$	19.3137i	1.08306i
$319$	3.17157	0.177574
$320$	0	0
$321$	19.3137	1.07799
$322$	26.1421i	1.45684i
$323$	− 1.17157i	− 0.0651881i
$324$	−3.82843	−0.212690
$325$	0	0
$326$	52.8701	2.92820
$327$	6.48528i	0.358637i
$328$	− 1.07107i	− 0.0591398i
$329$	−10.8284	−0.596991
$330$	0	0
$331$	28.1421	1.54683	0.773416	−	0.633899i	$-0.218547\pi$
$331$	28.1421	1.54683	0.773416	+	0.633899i	$0.218547\pi$
$332$	− 49.1127i	− 2.69541i
$333$	− 3.41421i	− 0.187098i
$334$	41.7990	2.28714
$335$	0	0
$336$	−4.24264	−0.231455
$337$	24.5858i	1.33927i	0.742689	+	0.669637i	$0.233550\pi$
$337$	24.5858i	1.33927i	−0.742689	+	0.669637i	$0.766450\pi$
$338$	− 3.24264i	− 0.176376i
$339$	−10.1421	−0.550845
$340$	0	0
$341$	7.11270	0.385174
$342$	2.41421i	0.130546i
$343$	16.9706i	0.916324i
$344$	−54.0416	−2.91373
$345$	0	0
$346$	−47.7990	−2.56969
$347$	27.4558i	1.47391i	0.675943	+	0.736953i	$0.263736\pi$
$347$	27.4558i	1.47391i	−0.675943	+	0.736953i	$0.736264\pi$
$348$	5.41421i	0.290232i
$349$	−18.0000	−0.963518	−0.481759	−	0.876304i	$-0.660002\pi$
$349$	−18.0000	−0.963518	−0.481759	+	0.876304i	$0.660002\pi$
$350$	0	0
$351$	−3.41421	−0.182237
$352$	− 3.55635i	− 0.189554i
$353$	3.65685i	0.194635i	0.995253	+	0.0973174i	$0.0310262\pi$
$353$	3.65685i	0.194635i	−0.995253	+	0.0973174i	$0.968974\pi$
$354$	−30.1421	−1.60204
$355$	0	0
$356$	22.5858	1.19704
$357$	1.65685i	0.0876900i
$358$	39.7990i	2.10344i
$359$	−24.8701	−1.31259	−0.656296	−	0.754504i	$-0.727878\pi$
$359$	−24.8701	−1.31259	−0.656296	+	0.754504i	$0.727878\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	50.2843i	2.64288i
$363$	− 5.97056i	− 0.313373i
$364$	−18.4853	−0.968892
$365$	0	0
$366$	17.6569	0.922939
$367$	14.3848i	0.750879i	0.926847	+	0.375440i	$0.122508\pi$
$367$	14.3848i	0.750879i	−0.926847	+	0.375440i	$0.877492\pi$
$368$	22.9706i	1.19742i
$369$	0.242641	0.0126314
$370$	0	0
$371$	−11.3137	−0.587378
$372$	12.1421i	0.629540i
$373$	0.585786i	0.0303309i	0.999885	+	0.0151654i	$0.00482749\pi$
$373$	0.585786i	0.0303309i	−0.999885	+	0.0151654i	$0.995173\pi$
$374$	6.34315	0.327996
$375$	0	0
$376$	−33.7990	−1.74305
$377$	4.82843i	0.248677i
$378$	− 3.41421i	− 0.175608i
$379$	−3.17157	−0.162913	−0.0814564	−	0.996677i	$-0.525957\pi$
$379$	−3.17157	−0.162913	−0.0814564	+	0.996677i	$0.525957\pi$
$380$	0	0
$381$	19.3137	0.989471
$382$	− 24.7279i	− 1.26519i
$383$	28.0000i	1.43073i	0.698749	+	0.715367i	$0.253740\pi$
$383$	28.0000i	1.43073i	−0.698749	+	0.715367i	$0.746260\pi$
$384$	20.5563	1.04901
$385$	0	0
$386$	12.2426	0.623134
$387$	− 12.2426i	− 0.622328i
$388$	− 37.3553i	− 1.89643i
$389$	−30.9706	−1.57027	−0.785135	−	0.619325i	$-0.787406\pi$
$389$	−30.9706	−1.57027	−0.785135	+	0.619325i	$0.787406\pi$
$390$	0	0
$391$	8.97056	0.453661
$392$	22.0711i	1.11476i
$393$	− 8.58579i	− 0.433096i
$394$	−16.4853	−0.830516
$395$	0	0
$396$	−8.58579	−0.431452
$397$	− 28.6274i	− 1.43677i	−0.695646	−	0.718384i	$-0.744882\pi$
$397$	− 28.6274i	− 1.43677i	0.695646	−	0.718384i	$-0.255118\pi$
$398$	43.7990i	2.19544i
$399$	−1.41421	−0.0707992
$400$	0	0
$401$	−7.75736	−0.387384	−0.193692	−	0.981062i	$-0.562046\pi$
$401$	−7.75736	−0.387384	−0.193692	+	0.981062i	$0.562046\pi$
$402$	23.3137i	1.16278i
$403$	10.8284i	0.539402i
$404$	12.1421	0.604094
$405$	0	0
$406$	−4.82843	−0.239631
$407$	− 7.65685i	− 0.379536i
$408$	5.17157i	0.256031i
$409$	12.8284	0.634325	0.317162	−	0.948371i	$-0.397270\pi$
$409$	12.8284	0.634325	0.317162	+	0.948371i	$0.397270\pi$
$410$	0	0
$411$	10.0000	0.493264
$412$	28.0000i	1.37946i
$413$	− 17.6569i	− 0.868837i
$414$	−18.4853	−0.908502
$415$	0	0
$416$	5.41421	0.265454
$417$	14.1421i	0.692543i
$418$	5.41421i	0.264818i
$419$	−3.41421	−0.166795	−0.0833976	−	0.996516i	$-0.526577\pi$
$419$	−3.41421	−0.166795	−0.0833976	+	0.996516i	$0.526577\pi$
$420$	0	0
$421$	9.31371	0.453922	0.226961	−	0.973904i	$-0.427121\pi$
$421$	9.31371	0.453922	0.226961	+	0.973904i	$0.427121\pi$
$422$	− 17.6569i	− 0.859522i
$423$	− 7.65685i	− 0.372289i
$424$	−35.3137	−1.71499
$425$	0	0
$426$	−26.1421	−1.26659
$427$	10.3431i	0.500540i
$428$	73.9411i	3.57408i
$429$	−7.65685	−0.369676
$430$	0	0
$431$	−31.1127	−1.49865	−0.749323	−	0.662205i	$-0.769621\pi$
$431$	−31.1127	−1.49865	−0.749323	+	0.662205i	$0.769621\pi$
$432$	− 3.00000i	− 0.144338i
$433$	− 10.9289i	− 0.525211i	−0.964903	−	0.262605i	$-0.915418\pi$
$433$	− 10.9289i	− 0.525211i	0.964903	−	0.262605i	$-0.0845818\pi$
$434$	−10.8284	−0.519781
$435$	0	0
$436$	−24.8284	−1.18907
$437$	7.65685i	0.366277i
$438$	− 18.4853i	− 0.883261i
$439$	21.6569	1.03363	0.516813	−	0.856099i	$-0.327118\pi$
$439$	21.6569	1.03363	0.516813	+	0.856099i	$0.327118\pi$
$440$	0	0
$441$	−5.00000	−0.238095
$442$	9.65685i	0.459330i
$443$	18.0000i	0.855206i	0.903967	+	0.427603i	$0.140642\pi$
$443$	18.0000i	0.855206i	−0.903967	+	0.427603i	$0.859358\pi$
$444$	13.0711	0.620325
$445$	0	0
$446$	44.9706	2.12942
$447$	6.00000i	0.283790i
$448$	13.8995i	0.656689i
$449$	26.8701	1.26808	0.634038	−	0.773302i	$-0.281396\pi$
$449$	26.8701	1.26808	0.634038	+	0.773302i	$0.281396\pi$
$450$	0	0
$451$	0.544156	0.0256233
$452$	− 38.8284i	− 1.82634i
$453$	− 6.48528i	− 0.304705i
$454$	−36.1421	−1.69623
$455$	0	0
$456$	−4.41421	−0.206714
$457$	− 32.8284i	− 1.53565i	−0.640660	−	0.767825i	$-0.721339\pi$
$457$	− 32.8284i	− 1.53565i	0.640660	−	0.767825i	$-0.278661\pi$
$458$	− 54.6274i	− 2.55257i
$459$	−1.17157	−0.0546843
$460$	0	0
$461$	19.6569	0.915511	0.457755	−	0.889078i	$-0.348654\pi$
$461$	19.6569	0.915511	0.457755	+	0.889078i	$0.348654\pi$
$462$	− 7.65685i	− 0.356229i
$463$	24.2426i	1.12665i	0.826235	+	0.563326i	$0.190478\pi$
$463$	24.2426i	1.12665i	−0.826235	+	0.563326i	$0.809522\pi$
$464$	−4.24264	−0.196960
$465$	0	0
$466$	−0.828427	−0.0383761
$467$	− 35.6569i	− 1.65000i	−0.565131	−	0.825001i	$-0.691174\pi$
$467$	− 35.6569i	− 1.65000i	0.565131	−	0.825001i	$-0.308826\pi$
$468$	− 13.0711i	− 0.604210i
$469$	−13.6569	−0.630615
$470$	0	0
$471$	10.4853	0.483136
$472$	− 55.1127i	− 2.53677i
$473$	− 27.4558i	− 1.26242i
$474$	0	0
$475$	0	0
$476$	−6.34315	−0.290738
$477$	− 8.00000i	− 0.366295i
$478$	− 64.5269i	− 2.95139i
$479$	−17.0711	−0.779997	−0.389998	−	0.920815i	$-0.627524\pi$
$479$	−17.0711	−0.779997	−0.389998	+	0.920815i	$0.627524\pi$
$480$	0	0
$481$	11.6569	0.531507
$482$	47.4558i	2.16155i
$483$	− 10.8284i	− 0.492710i
$484$	22.8579	1.03899
$485$	0	0
$486$	2.41421	0.109511
$487$	− 20.4853i	− 0.928277i	−0.885763	−	0.464138i	$-0.846364\pi$
$487$	− 20.4853i	− 0.928277i	0.885763	−	0.464138i	$-0.153636\pi$
$488$	32.2843i	1.46144i
$489$	−21.8995	−0.990329
$490$	0	0
$491$	−1.75736	−0.0793085	−0.0396543	−	0.999213i	$-0.512626\pi$
$491$	−1.75736	−0.0793085	−0.0396543	+	0.999213i	$0.512626\pi$
$492$	0.928932i	0.0418795i
$493$	1.65685i	0.0746210i
$494$	−8.24264	−0.370854
$495$	0	0
$496$	−9.51472	−0.427223
$497$	− 15.3137i	− 0.686914i
$498$	30.9706i	1.38782i
$499$	5.17157	0.231511	0.115756	−	0.993278i	$-0.463071\pi$
$499$	5.17157	0.231511	0.115756	+	0.993278i	$0.463071\pi$
$500$	0	0
$501$	−17.3137	−0.773519
$502$	4.24264i	0.189358i
$503$	4.82843i	0.215289i	0.994189	+	0.107644i	$0.0343308\pi$
$503$	4.82843i	0.215289i	−0.994189	+	0.107644i	$0.965669\pi$
$504$	6.24264	0.278069
$505$	0	0
$506$	−41.4558	−1.84294
$507$	1.34315i	0.0596512i
$508$	73.9411i	3.28061i
$509$	0.727922	0.0322646	0.0161323	−	0.999870i	$-0.494865\pi$
$509$	0.727922	0.0322646	0.0161323	+	0.999870i	$0.494865\pi$
$510$	0	0
$511$	10.8284	0.479021
$512$	31.2426i	1.38074i
$513$	− 1.00000i	− 0.0441511i
$514$	10.8284	0.477621
$515$	0	0
$516$	46.8701	2.06334
$517$	− 17.1716i	− 0.755205i
$518$	11.6569i	0.512173i
$519$	19.7990	0.869079
$520$	0	0
$521$	7.75736	0.339856	0.169928	−	0.985456i	$-0.445646\pi$
$521$	7.75736	0.339856	0.169928	+	0.985456i	$0.445646\pi$
$522$	− 3.41421i	− 0.149436i
$523$	− 15.5147i	− 0.678411i	−0.940712	−	0.339206i	$-0.889842\pi$
$523$	− 15.5147i	− 0.678411i	0.940712	−	0.339206i	$-0.110158\pi$
$524$	32.8701	1.43594
$525$	0	0
$526$	−56.6274	−2.46907
$527$	3.71573i	0.161860i
$528$	− 6.72792i	− 0.292795i
$529$	−35.6274	−1.54902
$530$	0	0
$531$	12.4853	0.541815
$532$	− 5.41421i	− 0.234736i
$533$	0.828427i	0.0358832i
$534$	−14.2426	−0.616339
$535$	0	0
$536$	−42.6274	−1.84122
$537$	− 16.4853i	− 0.711392i
$538$	− 7.41421i	− 0.319649i
$539$	−11.2132	−0.482987
$540$	0	0
$541$	22.0000	0.945854	0.472927	−	0.881102i	$-0.343197\pi$
$541$	22.0000	0.945854	0.472927	+	0.881102i	$0.343197\pi$
$542$	26.1421i	1.12290i
$543$	− 20.8284i	− 0.893833i
$544$	1.85786	0.0796553
$545$	0	0
$546$	11.6569	0.498867
$547$	− 24.4853i	− 1.04692i	−0.852052	−	0.523458i	$-0.824642\pi$
$547$	− 24.4853i	− 1.04692i	0.852052	−	0.523458i	$-0.175358\pi$
$548$	38.2843i	1.63542i
$549$	−7.31371	−0.312141
$550$	0	0
$551$	−1.41421	−0.0602475
$552$	− 33.7990i	− 1.43858i
$553$	0	0
$554$	53.1127	2.25654
$555$	0	0
$556$	−54.1421	−2.29614
$557$	25.3137i	1.07258i	0.844035	+	0.536288i	$0.180174\pi$
$557$	25.3137i	1.07258i	−0.844035	+	0.536288i	$0.819826\pi$
$558$	− 7.65685i	− 0.324140i
$559$	41.7990	1.76791
$560$	0	0
$561$	−2.62742	−0.110930
$562$	35.2132i	1.48538i
$563$	− 30.2843i	− 1.27633i	−0.769900	−	0.638165i	$-0.779694\pi$
$563$	− 30.2843i	− 1.27633i	0.769900	−	0.638165i	$-0.220306\pi$
$564$	29.3137	1.23433
$565$	0	0
$566$	−25.0711	−1.05382
$567$	1.41421i	0.0593914i
$568$	− 47.7990i	− 2.00560i
$569$	−31.0711	−1.30257	−0.651283	−	0.758835i	$-0.725769\pi$
$569$	−31.0711	−1.30257	−0.651283	+	0.758835i	$0.725769\pi$
$570$	0	0
$571$	9.17157	0.383818	0.191909	−	0.981413i	$-0.438532\pi$
$571$	9.17157	0.383818	0.191909	+	0.981413i	$0.438532\pi$
$572$	− 29.3137i	− 1.22567i
$573$	10.2426i	0.427892i
$574$	−0.828427	−0.0345779
$575$	0	0
$576$	−9.82843	−0.409518
$577$	− 19.4558i	− 0.809957i	−0.914326	−	0.404979i	$-0.867279\pi$
$577$	− 19.4558i	− 0.809957i	0.914326	−	0.404979i	$-0.132721\pi$
$578$	− 37.7279i	− 1.56927i
$579$	−5.07107	−0.210746
$580$	0	0
$581$	−18.1421	−0.752663
$582$	23.5563i	0.976442i
$583$	− 17.9411i	− 0.743045i
$584$	33.7990	1.39861
$585$	0	0
$586$	−27.7990	−1.14837
$587$	12.3431i	0.509456i	0.967013	+	0.254728i	$0.0819860\pi$
$587$	12.3431i	0.509456i	−0.967013	+	0.254728i	$0.918014\pi$
$588$	− 19.1421i	− 0.789408i
$589$	−3.17157	−0.130682
$590$	0	0
$591$	6.82843	0.280884
$592$	10.2426i	0.420970i
$593$	36.6274i	1.50411i	0.659102	+	0.752054i	$0.270937\pi$
$593$	36.6274i	1.50411i	−0.659102	+	0.752054i	$0.729063\pi$
$594$	5.41421	0.222148
$595$	0	0
$596$	−22.9706	−0.940911
$597$	− 18.1421i	− 0.742508i
$598$	− 63.1127i	− 2.58087i
$599$	3.02944	0.123779	0.0618897	−	0.998083i	$-0.480287\pi$
$599$	3.02944	0.123779	0.0618897	+	0.998083i	$0.480287\pi$
$600$	0	0
$601$	8.14214	0.332125	0.166062	−	0.986115i	$-0.446895\pi$
$601$	8.14214	0.332125	0.166062	+	0.986115i	$0.446895\pi$
$602$	41.7990i	1.70360i
$603$	− 9.65685i	− 0.393258i
$604$	24.8284	1.01025
$605$	0	0
$606$	−7.65685	−0.311038
$607$	− 16.4853i	− 0.669117i	−0.942375	−	0.334558i	$-0.891413\pi$
$607$	− 16.4853i	− 0.669117i	0.942375	−	0.334558i	$-0.108587\pi$
$608$	1.58579i	0.0643121i
$609$	2.00000	0.0810441
$610$	0	0
$611$	26.1421	1.05760
$612$	− 4.48528i	− 0.181307i
$613$	− 10.4853i	− 0.423497i	−0.977324	−	0.211748i	$-0.932084\pi$
$613$	− 10.4853i	− 0.423497i	0.977324	−	0.211748i	$-0.0679157\pi$
$614$	−51.1127	−2.06274
$615$	0	0
$616$	14.0000	0.564076
$617$	− 28.4853i	− 1.14677i	−0.819285	−	0.573387i	$-0.805629\pi$
$617$	− 28.4853i	− 1.14677i	0.819285	−	0.573387i	$-0.194371\pi$
$618$	− 17.6569i	− 0.710263i
$619$	20.4853	0.823373	0.411686	−	0.911326i	$-0.364940\pi$
$619$	20.4853	0.823373	0.411686	+	0.911326i	$0.364940\pi$
$620$	0	0
$621$	7.65685	0.307259
$622$	15.0711i	0.604295i
$623$	− 8.34315i	− 0.334261i
$624$	10.2426	0.410034
$625$	0	0
$626$	14.0000	0.559553
$627$	− 2.24264i	− 0.0895624i
$628$	40.1421i	1.60185i
$629$	4.00000	0.159490
$630$	0	0
$631$	0	0		−	1.00000i	$-0.5\pi$
$631$	0	0			1.00000i	$0.5\pi$
$632$	0	0
$633$	7.31371i	0.290694i
$634$	64.2843	2.55305
$635$	0	0
$636$	30.6274	1.21446
$637$	− 17.0711i	− 0.676380i
$638$	− 7.65685i	− 0.303138i
$639$	10.8284	0.428366
$640$	0	0
$641$	−31.3553	−1.23846	−0.619231	−	0.785209i	$-0.712555\pi$
$641$	−31.3553	−1.23846	−0.619231	+	0.785209i	$0.712555\pi$
$642$	− 46.6274i	− 1.84024i
$643$	42.3848i	1.67149i	0.549116	+	0.835746i	$0.314965\pi$
$643$	42.3848i	1.67149i	−0.549116	+	0.835746i	$0.685035\pi$
$644$	41.4558	1.63359
$645$	0	0
$646$	−2.82843	−0.111283
$647$	36.1421i	1.42089i	0.703751	+	0.710447i	$0.251507\pi$
$647$	36.1421i	1.42089i	−0.703751	+	0.710447i	$0.748493\pi$
$648$	4.41421i	0.173407i
$649$	28.0000	1.09910
$650$	0	0
$651$	4.48528	0.175792
$652$	− 83.8406i	− 3.28345i
$653$	42.8284i	1.67601i	0.545666	+	0.838003i	$0.316277\pi$
$653$	42.8284i	1.67601i	−0.545666	+	0.838003i	$0.683723\pi$
$654$	15.6569	0.612231
$655$	0	0
$656$	−0.727922	−0.0284206
$657$	7.65685i	0.298722i
$658$	26.1421i	1.01913i
$659$	18.6274	0.725621	0.362811	−	0.931863i	$-0.381817\pi$
$659$	18.6274	0.725621	0.362811	+	0.931863i	$0.381817\pi$
$660$	0	0
$661$	7.45584	0.289999	0.144999	−	0.989432i	$-0.453682\pi$
$661$	7.45584	0.289999	0.144999	+	0.989432i	$0.453682\pi$
$662$	− 67.9411i	− 2.64061i
$663$	− 4.00000i	− 0.155347i
$664$	−56.6274	−2.19757
$665$	0	0
$666$	−8.24264	−0.319396
$667$	− 10.8284i	− 0.419278i
$668$	− 66.2843i	− 2.56462i
$669$	−18.6274	−0.720178
$670$	0	0
$671$	−16.4020	−0.633193
$672$	− 2.24264i	− 0.0865117i
$673$	− 44.1838i	− 1.70316i	−0.524225	−	0.851580i	$-0.675645\pi$
$673$	− 44.1838i	− 1.70316i	0.524225	−	0.851580i	$-0.324355\pi$
$674$	59.3553	2.28628
$675$	0	0
$676$	−5.14214	−0.197774
$677$	− 16.9706i	− 0.652232i	−0.945330	−	0.326116i	$-0.894260\pi$
$677$	− 16.9706i	− 0.652232i	0.945330	−	0.326116i	$-0.105740\pi$
$678$	24.4853i	0.940352i
$679$	−13.7990	−0.529557
$680$	0	0
$681$	14.9706	0.573673
$682$	− 17.1716i	− 0.657534i
$683$	18.3431i	0.701881i	0.936398	+	0.350940i	$0.114138\pi$
$683$	18.3431i	0.701881i	−0.936398	+	0.350940i	$0.885862\pi$
$684$	3.82843	0.146384
$685$	0	0
$686$	40.9706	1.56426
$687$	22.6274i	0.863290i
$688$	36.7279i	1.40024i
$689$	27.3137	1.04057
$690$	0	0
$691$	46.8284	1.78144	0.890719	−	0.454555i	$-0.150202\pi$
$691$	46.8284	1.78144	0.890719	+	0.454555i	$0.150202\pi$
$692$	75.7990i	2.88145i
$693$	3.17157i	0.120478i
$694$	66.2843	2.51612
$695$	0	0
$696$	6.24264	0.236627
$697$	0.284271i	0.0107675i
$698$	43.4558i	1.64483i
$699$	0.343146	0.0129790
$700$	0	0
$701$	6.68629	0.252538	0.126269	−	0.991996i	$-0.459700\pi$
$701$	6.68629	0.252538	0.126269	+	0.991996i	$0.459700\pi$
$702$	8.24264i	0.311098i
$703$	3.41421i	0.128770i
$704$	−22.0416	−0.830725
$705$	0	0
$706$	8.82843	0.332262
$707$	− 4.48528i	− 0.168686i
$708$	47.7990i	1.79640i
$709$	−28.9706	−1.08801	−0.544006	−	0.839081i	$-0.683093\pi$
$709$	−28.9706	−1.08801	−0.544006	+	0.839081i	$0.683093\pi$
$710$	0	0
$711$	0	0
$712$	− 26.0416i	− 0.975951i
$713$	− 24.2843i	− 0.909453i
$714$	4.00000	0.149696
$715$	0	0
$716$	63.1127	2.35863
$717$	26.7279i	0.998173i
$718$	60.0416i	2.24073i
$719$	1.07107	0.0399441	0.0199720	−	0.999801i	$-0.493642\pi$
$719$	1.07107	0.0399441	0.0199720	+	0.999801i	$0.493642\pi$
$720$	0	0
$721$	10.3431	0.385199
$722$	− 2.41421i	− 0.0898477i
$723$	− 19.6569i	− 0.731046i
$724$	79.7401	2.96352
$725$	0	0
$726$	−14.4142	−0.534962
$727$	− 47.3553i	− 1.75631i	−0.478374	−	0.878156i	$-0.658774\pi$
$727$	− 47.3553i	− 1.75631i	0.478374	−	0.878156i	$-0.341226\pi$
$728$	21.3137i	0.789939i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	14.3431	0.530500
$732$	− 28.0000i	− 1.03491i
$733$	− 22.0000i	− 0.812589i	−0.913742	−	0.406294i	$-0.866821\pi$
$733$	− 22.0000i	− 0.812589i	0.913742	−	0.406294i	$-0.133179\pi$
$734$	34.7279	1.28183
$735$	0	0
$736$	−12.1421	−0.447565
$737$	− 21.6569i	− 0.797740i
$738$	− 0.585786i	− 0.0215631i
$739$	−14.3431	−0.527621	−0.263811	−	0.964575i	$-0.584979\pi$
$739$	−14.3431	−0.527621	−0.263811	+	0.964575i	$0.584979\pi$
$740$	0	0
$741$	3.41421	0.125424
$742$	27.3137i	1.00272i
$743$	− 4.00000i	− 0.146746i	−0.997305	−	0.0733729i	$-0.976624\pi$
$743$	− 4.00000i	− 0.146746i	0.997305	−	0.0733729i	$-0.0233763\pi$
$744$	14.0000	0.513265
$745$	0	0
$746$	1.41421	0.0517780
$747$	− 12.8284i	− 0.469368i
$748$	− 10.0589i	− 0.367789i
$749$	27.3137	0.998021
$750$	0	0
$751$	−24.1421	−0.880959	−0.440480	−	0.897763i	$-0.645192\pi$
$751$	−24.1421	−0.880959	−0.440480	+	0.897763i	$0.645192\pi$
$752$	22.9706i	0.837650i
$753$	− 1.75736i	− 0.0640417i
$754$	11.6569	0.424518
$755$	0	0
$756$	−5.41421	−0.196913
$757$	32.4264i	1.17856i	0.807930	+	0.589279i	$0.200588\pi$
$757$	32.4264i	1.17856i	−0.807930	+	0.589279i	$0.799412\pi$
$758$	7.65685i	0.278109i
$759$	17.1716	0.623289
$760$	0	0
$761$	43.9411	1.59286	0.796432	−	0.604728i	$-0.206718\pi$
$761$	43.9411	1.59286	0.796432	+	0.604728i	$0.206718\pi$
$762$	− 46.6274i	− 1.68913i
$763$	9.17157i	0.332033i
$764$	−39.2132	−1.41868
$765$	0	0
$766$	67.5980	2.44241
$767$	42.6274i	1.53919i
$768$	− 29.9706i	− 1.08147i
$769$	−42.9706	−1.54956	−0.774779	−	0.632232i	$-0.782139\pi$
$769$	−42.9706	−1.54956	−0.774779	+	0.632232i	$0.782139\pi$
$770$	0	0
$771$	−4.48528	−0.161533
$772$	− 19.4142i	− 0.698733i
$773$	− 25.6569i	− 0.922813i	−0.887189	−	0.461406i	$-0.847345\pi$
$773$	− 25.6569i	− 0.922813i	0.887189	−	0.461406i	$-0.152655\pi$
$774$	−29.5563	−1.06238
$775$	0	0
$776$	−43.0711	−1.54616
$777$	− 4.82843i	− 0.173219i
$778$	74.7696i	2.68062i
$779$	−0.242641	−0.00869350
$780$	0	0
$781$	24.2843	0.868960
$782$	− 21.6569i	− 0.774448i
$783$	1.41421i	0.0505399i
$784$	15.0000	0.535714
$785$	0	0
$786$	−20.7279	−0.739340
$787$	42.8284i	1.52667i	0.646004	+	0.763334i	$0.276439\pi$
$787$	42.8284i	1.52667i	−0.646004	+	0.763334i	$0.723561\pi$
$788$	26.1421i	0.931275i
$789$	23.4558	0.835050
$790$	0	0
$791$	−14.3431	−0.509984
$792$	9.89949i	0.351763i
$793$	− 24.9706i	− 0.886731i
$794$	−69.1127	−2.45272
$795$	0	0
$796$	69.4558	2.46180
$797$	14.1421i	0.500940i	0.968124	+	0.250470i	$0.0805852\pi$
$797$	14.1421i	0.500940i	−0.968124	+	0.250470i	$0.919415\pi$
$798$	3.41421i	0.120862i
$799$	8.97056	0.317356
$800$	0	0
$801$	5.89949	0.208448
$802$	18.7279i	0.661306i
$803$	17.1716i	0.605972i
$804$	36.9706	1.30385
$805$	0	0
$806$	26.1421	0.920817
$807$	3.07107i	0.108107i
$808$	− 14.0000i	− 0.492518i
$809$	2.00000	0.0703163	0.0351581	−	0.999382i	$-0.488807\pi$
$809$	2.00000	0.0703163	0.0351581	+	0.999382i	$0.488807\pi$
$810$	0	0
$811$	8.68629	0.305017	0.152508	−	0.988302i	$-0.451265\pi$
$811$	8.68629	0.305017	0.152508	+	0.988302i	$0.451265\pi$
$812$	7.65685i	0.268703i
$813$	− 10.8284i	− 0.379770i
$814$	−18.4853	−0.647909
$815$	0	0
$816$	3.51472	0.123040
$817$	12.2426i	0.428316i
$818$	− 30.9706i	− 1.08286i
$819$	−4.82843	−0.168719
$820$	0	0
$821$	14.4853	0.505540	0.252770	−	0.967526i	$-0.418658\pi$
$821$	14.4853	0.505540	0.252770	+	0.967526i	$0.418658\pi$
$822$	− 24.1421i	− 0.842054i
$823$	− 25.0122i	− 0.871870i	−0.899978	−	0.435935i	$-0.856418\pi$
$823$	− 25.0122i	− 0.871870i	0.899978	−	0.435935i	$-0.143582\pi$
$824$	32.2843	1.12468
$825$	0	0
$826$	−42.6274	−1.48320
$827$	2.68629i	0.0934115i	0.998909	+	0.0467058i	$0.0148723\pi$
$827$	2.68629i	0.0934115i	−0.998909	+	0.0467058i	$0.985128\pi$
$828$	29.3137i	1.01872i
$829$	−46.4853	−1.61450	−0.807250	−	0.590209i	$-0.799045\pi$
$829$	−46.4853	−1.61450	−0.807250	+	0.590209i	$0.799045\pi$
$830$	0	0
$831$	−22.0000	−0.763172
$832$	− 33.5563i	− 1.16336i
$833$	− 5.85786i	− 0.202963i
$834$	34.1421	1.18225
$835$	0	0
$836$	8.58579	0.296946
$837$	3.17157i	0.109626i
$838$	8.24264i	0.284737i
$839$	9.85786	0.340331	0.170166	−	0.985415i	$-0.445570\pi$
$839$	9.85786	0.340331	0.170166	+	0.985415i	$0.445570\pi$
$840$	0	0
$841$	−27.0000	−0.931034
$842$	− 22.4853i	− 0.774894i
$843$	− 14.5858i	− 0.502361i
$844$	−28.0000	−0.963800
$845$	0	0
$846$	−18.4853	−0.635537
$847$	− 8.44365i	− 0.290127i
$848$	24.0000i	0.824163i
$849$	10.3848	0.356405
$850$	0	0
$851$	−26.1421	−0.896141
$852$	41.4558i	1.42025i
$853$	− 16.8284i	− 0.576194i	−0.957601	−	0.288097i	$-0.906977\pi$
$853$	− 16.8284i	− 0.576194i	0.957601	−	0.288097i	$-0.0930226\pi$
$854$	24.9706	0.854475
$855$	0	0
$856$	85.2548	2.91395
$857$	− 12.6863i	− 0.433355i	−0.976243	−	0.216678i	$-0.930478\pi$
$857$	− 12.6863i	− 0.433355i	0.976243	−	0.216678i	$-0.0695221\pi$
$858$	18.4853i	0.631077i
$859$	49.9411	1.70397	0.851985	−	0.523567i	$-0.175399\pi$
$859$	49.9411	1.70397	0.851985	+	0.523567i	$0.175399\pi$
$860$	0	0
$861$	0.343146	0.0116944
$862$	75.1127i	2.55835i
$863$	8.68629i	0.295685i	0.989011	+	0.147842i	$0.0472328\pi$
$863$	8.68629i	0.295685i	−0.989011	+	0.147842i	$0.952767\pi$
$864$	1.58579	0.0539496
$865$	0	0
$866$	−26.3848	−0.896591
$867$	15.6274i	0.530735i
$868$	17.1716i	0.582841i
$869$	0	0
$870$	0	0
$871$	32.9706	1.11716
$872$	28.6274i	0.969447i
$873$	− 9.75736i	− 0.330237i
$874$	18.4853	0.625274
$875$	0	0
$876$	−29.3137	−0.990418
$877$	34.9289i	1.17947i	0.807598	+	0.589733i	$0.200767\pi$
$877$	34.9289i	1.17947i	−0.807598	+	0.589733i	$0.799233\pi$
$878$	− 52.2843i	− 1.76451i
$879$	11.5147	0.388382
$880$	0	0
$881$	−5.79899	−0.195373	−0.0976865	−	0.995217i	$-0.531144\pi$
$881$	−5.79899	−0.195373	−0.0976865	+	0.995217i	$0.531144\pi$
$882$	12.0711i	0.406454i
$883$	− 12.0416i	− 0.405233i	−0.979258	−	0.202617i	$-0.935055\pi$
$883$	− 12.0416i	− 0.405233i	0.979258	−	0.202617i	$-0.0649445\pi$
$884$	15.3137	0.515056
$885$	0	0
$886$	43.4558	1.45993
$887$	− 25.9411i	− 0.871018i	−0.900184	−	0.435509i	$-0.856568\pi$
$887$	− 25.9411i	− 0.871018i	0.900184	−	0.435509i	$-0.143432\pi$
$888$	− 15.0711i	− 0.505752i
$889$	27.3137	0.916072
$890$	0	0
$891$	−2.24264	−0.0751313
$892$	− 71.3137i	− 2.38776i
$893$	7.65685i	0.256227i
$894$	14.4853	0.484460
$895$	0	0
$896$	29.0711	0.971196
$897$	26.1421i	0.872861i
$898$	− 64.8701i	− 2.16474i
$899$	4.48528	0.149593
$900$	0	0
$901$	9.37258	0.312246
$902$	− 1.31371i	− 0.0437417i
$903$	− 17.3137i	− 0.576164i
$904$	−44.7696	−1.48901
$905$	0	0
$906$	−15.6569	−0.520164
$907$	18.1421i	0.602400i	0.953561	+	0.301200i	$0.0973871\pi$
$907$	18.1421i	0.602400i	−0.953561	+	0.301200i	$0.902613\pi$
$908$	57.3137i	1.90202i
$909$	3.17157	0.105194
$910$	0	0
$911$	8.68629	0.287790	0.143895	−	0.989593i	$-0.454037\pi$
$911$	8.68629	0.287790	0.143895	+	0.989593i	$0.454037\pi$
$912$	3.00000i	0.0993399i
$913$	− 28.7696i	− 0.952133i
$914$	−79.2548	−2.62152
$915$	0	0
$916$	−86.6274	−2.86225
$917$	− 12.1421i	− 0.400969i
$918$	2.82843i	0.0933520i
$919$	12.0000	0.395843	0.197922	−	0.980218i	$-0.436581\pi$
$919$	12.0000	0.395843	0.197922	+	0.980218i	$0.436581\pi$
$920$	0	0
$921$	21.1716	0.697627
$922$	− 47.4558i	− 1.56287i
$923$	36.9706i	1.21690i
$924$	−12.1421	−0.399447
$925$	0	0
$926$	58.5269	1.92331
$927$	7.31371i	0.240214i
$928$	− 2.24264i	− 0.0736183i
$929$	−33.1127	−1.08639	−0.543196	−	0.839606i	$-0.682786\pi$
$929$	−33.1127	−1.08639	−0.543196	+	0.839606i	$0.682786\pi$
$930$	0	0
$931$	5.00000	0.163868
$932$	1.31371i	0.0430320i
$933$	− 6.24264i	− 0.204375i
$934$	−86.0833	−2.81673
$935$	0	0
$936$	−15.0711	−0.492613
$937$	29.7990i	0.973491i	0.873544	+	0.486745i	$0.161816\pi$
$937$	29.7990i	0.973491i	−0.873544	+	0.486745i	$0.838184\pi$
$938$	32.9706i	1.07653i
$939$	−5.79899	−0.189243
$940$	0	0
$941$	22.8701	0.745543	0.372771	−	0.927923i	$-0.378408\pi$
$941$	22.8701	0.745543	0.372771	+	0.927923i	$0.378408\pi$
$942$	− 25.3137i	− 0.824765i
$943$	− 1.85786i	− 0.0605004i
$944$	−37.4558	−1.21908
$945$	0	0
$946$	−66.2843	−2.15509
$947$	47.1716i	1.53287i	0.642322	+	0.766435i	$0.277971\pi$
$947$	47.1716i	1.53287i	−0.642322	+	0.766435i	$0.722029\pi$
$948$	0	0
$949$	−26.1421	−0.848610
$950$	0	0
$951$	−26.6274	−0.863453
$952$	7.31371i	0.237039i
$953$	− 53.4558i	− 1.73160i	−0.500386	−	0.865802i	$-0.666809\pi$
$953$	− 53.4558i	− 1.73160i	0.500386	−	0.865802i	$-0.333191\pi$
$954$	−19.3137	−0.625304
$955$	0	0
$956$	−102.326	−3.30946
$957$	3.17157i	0.102522i
$958$	41.2132i	1.33154i
$959$	14.1421	0.456673
$960$	0	0
$961$	−20.9411	−0.675520
$962$	− 28.1421i	− 0.907339i
$963$	19.3137i	0.622376i
$964$	75.2548	2.42379
$965$	0	0
$966$	−26.1421	−0.841109
$967$	− 8.04163i	− 0.258601i	−0.991605	−	0.129301i	$-0.958727\pi$
$967$	− 8.04163i	− 0.258601i	0.991605	−	0.129301i	$-0.0412732\pi$
$968$	− 26.3553i	− 0.847093i
$969$	1.17157	0.0376363
$970$	0	0
$971$	22.3431	0.717026	0.358513	−	0.933525i	$-0.383284\pi$
$971$	22.3431	0.717026	0.358513	+	0.933525i	$0.383284\pi$
$972$	− 3.82843i	− 0.122797i
$973$	20.0000i	0.641171i
$974$	−49.4558	−1.58467
$975$	0	0
$976$	21.9411	0.702318
$977$	− 32.2843i	− 1.03287i	−0.856328	−	0.516433i	$-0.827260\pi$
$977$	− 32.2843i	− 1.03287i	0.856328	−	0.516433i	$-0.172740\pi$
$978$	52.8701i	1.69060i
$979$	13.2304	0.422847
$980$	0	0
$981$	−6.48528	−0.207059
$982$	4.24264i	0.135388i
$983$	− 24.6274i	− 0.785493i	−0.919647	−	0.392746i	$-0.871525\pi$
$983$	− 24.6274i	− 0.785493i	0.919647	−	0.392746i	$-0.128475\pi$
$984$	1.07107	0.0341444
$985$	0	0
$986$	4.00000	0.127386
$987$	− 10.8284i	− 0.344673i
$988$	13.0711i	0.415846i
$989$	−93.7401	−2.98076
$990$	0	0
$991$	2.34315	0.0744325	0.0372162	−	0.999307i	$-0.488151\pi$
$991$	2.34315	0.0744325	0.0372162	+	0.999307i	$0.488151\pi$
$992$	− 5.02944i	− 0.159685i
$993$	28.1421i	0.893064i
$994$	−36.9706	−1.17264
$995$	0	0
$996$	49.1127	1.55620
$997$	38.0833i	1.20611i	0.797700	+	0.603054i	$0.206050\pi$
$997$	38.0833i	1.20611i	−0.797700	+	0.603054i	$0.793950\pi$
$998$	− 12.4853i	− 0.395215i
$999$	3.41421	0.108021

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1425.2.c.l.799.1		4
5.2	odd	4		285.2.a.g.1.2	✓	2
5.3	odd	4		1425.2.a.k.1.1		2
5.4	even	2	inner	1425.2.c.l.799.4		4
15.2	even	4		855.2.a.d.1.1		2
15.8	even	4		4275.2.a.y.1.2		2
20.7	even	4		4560.2.a.bf.1.2		2
95.37	even	4		5415.2.a.n.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.a.g.1.2	✓	2	5.2	odd	4
855.2.a.d.1.1		2	15.2	even	4
1425.2.a.k.1.1		2	5.3	odd	4
1425.2.c.l.799.1		4	1.1	even	1	trivial
1425.2.c.l.799.4		4	5.4	even	2	inner
4275.2.a.y.1.2		2	15.8	even	4
4560.2.a.bf.1.2		2	20.7	even	4
5415.2.a.n.1.1		2	95.37	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1425 = 3 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1425.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.41421i q^{2} +1.00000i q^{3} -3.82843 q^{4} +2.41421 q^{6} +1.41421i q^{7} +4.41421i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.41421i q^{2} +1.00000i q^{3} -3.82843 q^{4} +2.41421 q^{6} +1.41421i q^{7} +4.41421i q^{8} -1.00000 q^{9} -2.24264 q^{11} -3.82843i q^{12} -3.41421i q^{13} +3.41421 q^{14} +3.00000 q^{16} -1.17157i q^{17} +2.41421i q^{18} +1.00000 q^{19} -1.41421 q^{21} +5.41421i q^{22} +7.65685i q^{23} -4.41421 q^{24} -8.24264 q^{26} -1.00000i q^{27} -5.41421i q^{28} -1.41421 q^{29} -3.17157 q^{31} +1.58579i q^{32} -2.24264i q^{33} -2.82843 q^{34} +3.82843 q^{36} +3.41421i q^{37} -2.41421i q^{38} +3.41421 q^{39} -0.242641 q^{41} +3.41421i q^{42} +12.2426i q^{43} +8.58579 q^{44} +18.4853 q^{46} +7.65685i q^{47} +3.00000i q^{48} +5.00000 q^{49} +1.17157 q^{51} +13.0711i q^{52} +8.00000i q^{53} -2.41421 q^{54} -6.24264 q^{56} +1.00000i q^{57} +3.41421i q^{58} -12.4853 q^{59} +7.31371 q^{61} +7.65685i q^{62} -1.41421i q^{63} +9.82843 q^{64} -5.41421 q^{66} +9.65685i q^{67} +4.48528i q^{68} -7.65685 q^{69} -10.8284 q^{71} -4.41421i q^{72} -7.65685i q^{73} +8.24264 q^{74} -3.82843 q^{76} -3.17157i q^{77} -8.24264i q^{78} +1.00000 q^{81} +0.585786i q^{82} +12.8284i q^{83} +5.41421 q^{84} +29.5563 q^{86} -1.41421i q^{87} -9.89949i q^{88} -5.89949 q^{89} +4.82843 q^{91} -29.3137i q^{92} -3.17157i q^{93} +18.4853 q^{94} -1.58579 q^{96} +9.75736i q^{97} -12.0711i q^{98} +2.24264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9} + 8 q^{11} + 8 q^{14} + 12 q^{16} + 4 q^{19} - 12 q^{24} - 16 q^{26} - 24 q^{31} + 4 q^{36} + 8 q^{39} + 16 q^{41} + 40 q^{44} + 40 q^{46} + 20 q^{49} + 16 q^{51} - 4 q^{54} - 8 q^{56} - 16 q^{59} - 16 q^{61} + 28 q^{64} - 16 q^{66} - 8 q^{69} - 32 q^{71} + 16 q^{74} - 4 q^{76} + 4 q^{81} + 16 q^{84} + 56 q^{86} + 16 q^{89} + 8 q^{91} + 40 q^{94} - 12 q^{96} - 8 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 + 8 * q^11 + 8 * q^14 + 12 * q^16 + 4 * q^19 - 12 * q^24 - 16 * q^26 - 24 * q^31 + 4 * q^36 + 8 * q^39 + 16 * q^41 + 40 * q^44 + 40 * q^46 + 20 * q^49 + 16 * q^51 - 4 * q^54 - 8 * q^56 - 16 * q^59 - 16 * q^61 + 28 * q^64 - 16 * q^66 - 8 * q^69 - 32 * q^71 + 16 * q^74 - 4 * q^76 + 4 * q^81 + 16 * q^84 + 56 * q^86 + 16 * q^89 + 8 * q^91 + 40 * q^94 - 12 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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