LMFDB - Embedded newform 448.4.j.b.335.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,4,Mod(111,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("448.111");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	448.j (of order $4$, degree $2$, 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:	$26.4328556826$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			335.1
Character	$\chi$	$=$	448.335
Dual form			448.4.j.b.111.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.12471 + 7.12471i) q^{3} +(5.44380 - 5.44380i) q^{5} +(-16.6758 - 8.05711i) q^{7} -74.5229i q^{9} +O(q^{10})$	\(q+(-7.12471 + 7.12471i) q^{3} +(5.44380 - 5.44380i) q^{5} +(-16.6758 - 8.05711i) q^{7} -74.5229i q^{9} +(12.2737 - 12.2737i) q^{11} +(14.9163 + 14.9163i) q^{13} +77.5710i q^{15} +97.2333i q^{17} +(65.2182 - 65.2182i) q^{19} +(176.215 - 61.4058i) q^{21} -51.7441 q^{23} +65.7300i q^{25} +(338.586 + 338.586i) q^{27} +(19.0146 - 19.0146i) q^{29} +112.587 q^{31} +174.893i q^{33} +(-134.641 + 46.9186i) q^{35} +(-292.362 - 292.362i) q^{37} -212.548 q^{39} +145.655 q^{41} +(-180.841 + 180.841i) q^{43} +(-405.688 - 405.688i) q^{45} -325.054 q^{47} +(213.166 + 268.718i) q^{49} +(-692.758 - 692.758i) q^{51} +(19.7218 + 19.7218i) q^{53} -133.631i q^{55} +929.320i q^{57} +(51.1169 + 51.1169i) q^{59} +(286.397 + 286.397i) q^{61} +(-600.439 + 1242.73i) q^{63} +162.403 q^{65} +(529.690 + 529.690i) q^{67} +(368.661 - 368.661i) q^{69} -246.654 q^{71} -798.918 q^{73} +(-468.307 - 468.307i) q^{75} +(-303.564 + 105.783i) q^{77} +629.903i q^{79} -2812.54 q^{81} +(-170.885 + 170.885i) q^{83} +(529.319 + 529.319i) q^{85} +270.947i q^{87} +113.044 q^{89} +(-128.559 - 368.923i) q^{91} +(-802.148 + 802.148i) q^{93} -710.070i q^{95} +1413.11i q^{97} +(-914.671 - 914.671i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{7}+O(q^{10}) $ 88 * q + 4 * q^7	$ 88 q + 4 q^{7} - 112 q^{11} + 52 q^{21} - 160 q^{23} + 528 q^{29} - 476 q^{35} - 896 q^{37} + 8 q^{39} - 40 q^{43} - 1376 q^{49} - 1504 q^{51} - 1560 q^{53} - 8 q^{65} - 648 q^{67} + 456 q^{71} + 292 q^{77} - 1952 q^{81} + 496 q^{85} + 1964 q^{91} - 112 q^{93} - 7592 q^{99}+O(q^{100}) $ 88 * q + 4 * q^7 - 112 * q^11 + 52 * q^21 - 160 * q^23 + 528 * q^29 - 476 * q^35 - 896 * q^37 + 8 * q^39 - 40 * q^43 - 1376 * q^49 - 1504 * q^51 - 1560 * q^53 - 8 * q^65 - 648 * q^67 + 456 * q^71 + 292 * q^77 - 1952 * q^81 + 496 * q^85 + 1964 * q^91 - 112 * q^93 - 7592 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−7.12471	+	7.12471i	−1.37115	+	1.37115i	−0.512408	+	0.858742i	$0.671247\pi$
$3$	−7.12471	+	7.12471i	−1.37115	+	1.37115i	−0.858742	+	0.512408i	$0.828753\pi$
$4$		0			0
$5$	5.44380	−	5.44380i	0.486909	−	0.486909i	−0.420421	−	0.907329i	$-0.638117\pi$
$5$	5.44380	−	5.44380i	0.486909	−	0.486909i	0.907329	+	0.420421i	$0.138117\pi$
$6$		0			0
$7$	−16.6758	−	8.05711i	−0.900410	−	0.435043i
$7$	−16.6758	−	8.05711i	−0.900410	−	0.435043i
$8$		0			0
$9$		−	74.5229i		−	2.76011i
$10$		0			0
$11$	12.2737	−	12.2737i	0.336423	−	0.336423i	−0.518596	−	0.855019i	$-0.673545\pi$
$11$	12.2737	−	12.2737i	0.336423	−	0.336423i	0.855019	+	0.518596i	$0.173545\pi$
$12$		0			0
$13$	14.9163	+	14.9163i	0.318233	+	0.318233i	0.848088	−	0.529855i	$-0.177754\pi$
$13$	14.9163	+	14.9163i	0.318233	+	0.318233i	−0.529855	+	0.848088i	$0.677754\pi$
$14$		0			0
$15$			77.5710i			1.33525i
$16$		0			0
$17$			97.2333i			1.38721i	0.720357	+	0.693604i	$0.243978\pi$
$17$			97.2333i			1.38721i	−0.720357	+	0.693604i	$0.756022\pi$
$18$		0			0
$19$	65.2182	−	65.2182i	0.787478	−	0.787478i	−0.193603	−	0.981080i	$-0.562017\pi$
$19$	65.2182	−	65.2182i	0.787478	−	0.787478i	0.981080	+	0.193603i	$0.0620172\pi$
$20$		0			0
$21$	176.215	−	61.4058i	1.83111	−	0.638088i
$22$		0			0
$23$	−51.7441			−0.469104			−0.234552	−	0.972104i	$-0.575362\pi$
$23$	−51.7441			−0.469104			−0.234552	+	0.972104i	$0.575362\pi$
$24$		0			0
$25$			65.7300i			0.525840i
$26$		0			0
$27$	338.586	+	338.586i	2.41337	+	2.41337i
$28$		0			0
$29$	19.0146	−	19.0146i	0.121756	−	0.121756i	−0.643603	−	0.765359i	$-0.722561\pi$
$29$	19.0146	−	19.0146i	0.121756	−	0.121756i	0.765359	+	0.643603i	$0.222561\pi$
$30$		0			0
$31$	112.587			0.652297			0.326148	−	0.945319i	$-0.394249\pi$
$31$	112.587			0.652297			0.326148	+	0.945319i	$0.394249\pi$
$32$		0			0
$33$			174.893i			0.922574i
$34$		0			0
$35$	−134.641	+	46.9186i	−0.650243	+	0.226591i
$36$		0			0
$37$	−292.362	−	292.362i	−1.29903	−	1.29903i	−0.929036	−	0.369990i	$-0.879361\pi$
$37$	−292.362	−	292.362i	−1.29903	−	1.29903i	−0.369990	−	0.929036i	$-0.620639\pi$
$38$		0			0
$39$	−212.548			−0.872691
$40$		0			0
$41$	145.655			0.554817			0.277408	−	0.960752i	$-0.410524\pi$
$41$	145.655			0.554817			0.277408	+	0.960752i	$0.410524\pi$
$42$		0			0
$43$	−180.841	+	180.841i	−0.641350	+	0.641350i	−0.950887	−	0.309537i	$-0.899826\pi$
$43$	−180.841	+	180.841i	−0.641350	+	0.641350i	0.309537	+	0.950887i	$0.399826\pi$
$44$		0			0
$45$	−405.688	−	405.688i	−1.34392	−	1.34392i
$46$		0			0
$47$	−325.054			−1.00881			−0.504404	−	0.863468i	$-0.668288\pi$
$47$	−325.054			−1.00881			−0.504404	+	0.863468i	$0.668288\pi$
$48$		0			0
$49$	213.166	+	268.718i	0.621475	+	0.783434i
$50$		0			0
$51$	−692.758	−	692.758i	−1.90207	−	1.90207i
$52$		0			0
$53$	19.7218	+	19.7218i	0.0511131	+	0.0511131i	0.732201	−	0.681088i	$-0.238493\pi$
$53$	19.7218	+	19.7218i	0.0511131	+	0.0511131i	−0.681088	+	0.732201i	$0.738493\pi$
$54$		0			0
$55$		−	133.631i		−	0.327615i
$56$		0			0
$57$			929.320i			2.15950i
$58$		0			0
$59$	51.1169	+	51.1169i	0.112794	+	0.112794i	0.761251	−	0.648457i	$-0.224585\pi$
$59$	51.1169	+	51.1169i	0.112794	+	0.112794i	−0.648457	+	0.761251i	$0.724585\pi$
$60$		0			0
$61$	286.397	+	286.397i	0.601138	+	0.601138i	0.940614	−	0.339477i	$-0.110250\pi$
$61$	286.397	+	286.397i	0.601138	+	0.601138i	−0.339477	+	0.940614i	$0.610250\pi$
$62$		0			0
$63$	−600.439	+	1242.73i	−1.20076	+	2.48523i
$64$		0			0
$65$	162.403			0.309901
$66$		0			0
$67$	529.690	+	529.690i	0.965851	+	0.965851i	0.999436	−	0.0335853i	$-0.0106926\pi$
$67$	529.690	+	529.690i	0.965851	+	0.965851i	−0.0335853	+	0.999436i	$0.510693\pi$
$68$		0			0
$69$	368.661	−	368.661i	0.643212	−	0.643212i
$70$		0			0
$71$	−246.654			−0.412288			−0.206144	−	0.978522i	$-0.566091\pi$
$71$	−246.654			−0.412288			−0.206144	+	0.978522i	$0.566091\pi$
$72$		0			0
$73$	−798.918			−1.28091			−0.640454	−	0.767996i	$-0.721254\pi$
$73$	−798.918			−1.28091			−0.640454	+	0.767996i	$0.721254\pi$
$74$		0			0
$75$	−468.307	−	468.307i	−0.721006	−	0.721006i
$76$		0			0
$77$	−303.564	+	105.783i	−0.449278	+	0.156560i
$78$		0			0
$79$			629.903i			0.897084i	0.893762	+	0.448542i	$0.148056\pi$
$79$			629.903i			0.897084i	−0.893762	+	0.448542i	$0.851944\pi$
$80$		0			0
$81$	−2812.54			−3.85808
$82$		0			0
$83$	−170.885	+	170.885i	−0.225989	+	0.225989i	−0.811015	−	0.585026i	$-0.801084\pi$
$83$	−170.885	+	170.885i	−0.225989	+	0.225989i	0.585026	+	0.811015i	$0.301084\pi$
$84$		0			0
$85$	529.319	+	529.319i	0.675443	+	0.675443i
$86$		0			0
$87$			270.947i			0.333892i
$88$		0			0
$89$	113.044			0.134637			0.0673183	−	0.997732i	$-0.478556\pi$
$89$	113.044			0.134637			0.0673183	+	0.997732i	$0.478556\pi$
$90$		0			0
$91$	−128.559	−	368.923i	−0.148095	−	0.424985i
$92$		0			0
$93$	−802.148	+	802.148i	−0.894397	+	0.894397i
$94$		0			0
$95$		−	710.070i		−	0.766859i
$96$		0			0
$97$			1413.11i			1.47917i	0.673061	+	0.739587i	$0.264979\pi$
$97$			1413.11i			1.47917i	−0.673061	+	0.739587i	$0.735021\pi$
$98$		0			0
$99$	−914.671	−	914.671i	−0.928564	−	0.928564i
$100$		0			0
$101$	−1169.95	+	1169.95i	−1.15262	+	1.15262i	−0.166597	+	0.986025i	$0.553278\pi$
$101$	−1169.95	+	1169.95i	−1.15262	+	1.15262i	−0.986025	+	0.166597i	$0.946722\pi$
$102$		0			0
$103$			1013.89i			0.969919i	0.874537	+	0.484959i	$0.161166\pi$
$103$			1013.89i			0.969919i	−0.874537	+	0.484959i	$0.838834\pi$
$104$		0			0
$105$	624.998	−	1293.56i	0.580891	−	1.20227i
$106$		0			0
$107$	833.688	−	833.688i	0.753230	−	0.753230i	−0.221850	−	0.975081i	$-0.571210\pi$
$107$	833.688	−	833.688i	0.753230	−	0.753230i	0.975081	+	0.221850i	$0.0712097\pi$
$108$		0			0
$109$	1502.80	−	1502.80i	1.32057	−	1.32057i	0.407252	−	0.913316i	$-0.366487\pi$
$109$	1502.80	−	1502.80i	1.32057	−	1.32057i	0.913316	−	0.407252i	$-0.133513\pi$
$110$		0			0
$111$	4165.98			3.56232
$112$		0			0
$113$	−1121.53			−0.933669			−0.466834	−	0.884345i	$-0.654606\pi$
$113$	−1121.53			−0.933669			−0.466834	+	0.884345i	$0.654606\pi$
$114$		0			0
$115$	−281.685	+	281.685i	−0.228411	+	0.228411i
$116$		0			0
$117$	1111.60	−	1111.60i	0.878357	−	0.878357i
$118$		0			0
$119$	783.419	−	1621.44i	0.603495	−	1.24906i
$120$		0			0
$121$			1029.71i			0.773638i
$122$		0			0
$123$	−1037.75	+	1037.75i	−0.760737	+	0.760737i
$124$		0			0
$125$	1038.30	+	1038.30i	0.742945	+	0.742945i
$126$		0			0
$127$		−	160.125i		−	0.111881i	−0.998434	−	0.0559403i	$-0.982184\pi$
$127$		−	160.125i		−	0.111881i	0.998434	−	0.0559403i	$-0.0178157\pi$
$128$		0			0
$129$		−	2576.88i		−	1.75878i
$130$		0			0
$131$	−70.6362	+	70.6362i	−0.0471108	+	0.0471108i	−0.730270	−	0.683159i	$-0.760606\pi$
$131$	−70.6362	+	70.6362i	−0.0471108	+	0.0471108i	0.683159	+	0.730270i	$0.260606\pi$
$132$		0			0
$133$	−1613.04	+	562.097i	−1.05164	+	0.366466i
$134$		0			0
$135$	3686.40			2.35018
$136$		0			0
$137$			1556.15i			0.970445i	0.874391	+	0.485223i	$0.161261\pi$
$137$			1556.15i			0.970445i	−0.874391	+	0.485223i	$0.838739\pi$
$138$		0			0
$139$	869.214	+	869.214i	0.530401	+	0.530401i	0.920692	−	0.390291i	$-0.127625\pi$
$139$	869.214	+	869.214i	0.530401	+	0.530401i	−0.390291	+	0.920692i	$0.627625\pi$
$140$		0			0
$141$	2315.91	−	2315.91i	1.38323	−	1.38323i
$142$		0			0
$143$	366.156			0.214122
$144$		0			0
$145$		−	207.024i		−	0.118568i
$146$		0			0
$147$	−3433.28	−	395.790i	−1.92634	−	0.222069i
$148$		0			0
$149$	1257.31	+	1257.31i	0.691294	+	0.691294i	0.962517	−	0.271223i	$-0.0874280\pi$
$149$	1257.31	+	1257.31i	0.691294	+	0.691294i	−0.271223	+	0.962517i	$0.587428\pi$
$150$		0			0
$151$	24.5227			0.0132161			0.00660805	−	0.999978i	$-0.497897\pi$
$151$	24.5227			0.0132161			0.00660805	+	0.999978i	$0.497897\pi$
$152$		0			0
$153$	7246.10			3.82884
$154$		0			0
$155$	612.901	−	612.901i	0.317609	−	0.317609i
$156$		0			0
$157$	−736.229	−	736.229i	−0.374251	−	0.374251i	0.494772	−	0.869023i	$-0.335252\pi$
$157$	−736.229	−	736.229i	−0.374251	−	0.374251i	−0.869023	+	0.494772i	$0.835252\pi$
$158$		0			0
$159$	−281.024			−0.140167
$160$		0			0
$161$	862.875	+	416.908i	0.422386	+	0.204080i
$162$		0			0
$163$	719.453	+	719.453i	0.345717	+	0.345717i	0.858511	−	0.512794i	$-0.171390\pi$
$163$	719.453	+	719.453i	0.345717	+	0.345717i	−0.512794	+	0.858511i	$0.671390\pi$
$164$		0			0
$165$	952.083	+	952.083i	0.449209	+	0.449209i
$166$		0			0
$167$		−	310.318i		−	0.143791i	−0.997412	−	0.0718956i	$-0.977095\pi$
$167$		−	310.318i		−	0.143791i	0.997412	−	0.0718956i	$-0.0229048\pi$
$168$		0			0
$169$		−	1752.01i		−	0.797455i
$170$		0			0
$171$	−4860.24	−	4860.24i	−2.17352	−	2.17352i
$172$		0			0
$173$	1634.56	+	1634.56i	0.718341	+	0.718341i	0.968265	−	0.249925i	$-0.0804059\pi$
$173$	1634.56	+	1634.56i	0.718341	+	0.718341i	−0.249925	+	0.968265i	$0.580406\pi$
$174$		0			0
$175$	529.594	−	1096.10i	0.228763	−	0.473471i
$176$		0			0
$177$	−728.386			−0.309315
$178$		0			0
$179$	419.914	+	419.914i	0.175340	+	0.175340i	0.789321	−	0.613981i	$-0.210433\pi$
$179$	419.914	+	419.914i	0.175340	+	0.175340i	−0.613981	+	0.789321i	$0.710433\pi$
$180$		0			0
$181$	−1599.47	+	1599.47i	−0.656836	+	0.656836i	−0.954630	−	0.297794i	$-0.903749\pi$
$181$	−1599.47	+	1599.47i	−0.656836	+	0.656836i	0.297794	+	0.954630i	$0.403749\pi$
$182$		0			0
$183$	−4080.99			−1.64850
$184$		0			0
$185$	−3183.12			−1.26501
$186$		0			0
$187$	1193.41	+	1193.41i	0.466689	+	0.466689i
$188$		0			0
$189$	−2918.18	−	8374.23i	−1.12310	−	3.22294i
$190$		0			0
$191$			1607.93i			0.609139i	0.952490	+	0.304569i	$0.0985126\pi$
$191$			1607.93i			0.609139i	−0.952490	+	0.304569i	$0.901487\pi$
$192$		0			0
$193$	−372.475			−0.138919			−0.0694594	−	0.997585i	$-0.522127\pi$
$193$	−372.475			−0.138919			−0.0694594	+	0.997585i	$0.522127\pi$
$194$		0			0
$195$	−1157.07	+	1157.07i	−0.424921	+	0.424921i
$196$		0			0
$197$	925.750	+	925.750i	0.334807	+	0.334807i	0.854409	−	0.519602i	$-0.173920\pi$
$197$	925.750	+	925.750i	0.334807	+	0.334807i	−0.519602	+	0.854409i	$0.673920\pi$
$198$		0			0
$199$			245.590i			0.0874843i	0.999043	+	0.0437422i	$0.0139280\pi$
$199$			245.590i			0.0874843i	−0.999043	+	0.0437422i	$0.986072\pi$
$200$		0			0
$201$	−7547.78			−2.64865
$202$		0			0
$203$	−470.288	+	163.882i	−0.162600	+	0.0566613i
$204$		0			0
$205$	792.917	−	792.917i	0.270145	−	0.270145i
$206$		0			0
$207$			3856.12i			1.29478i
$208$		0			0
$209$		−	1600.94i		−	0.529852i
$210$		0			0
$211$	−1129.43	−	1129.43i	−0.368498	−	0.368498i	0.498431	−	0.866929i	$-0.333910\pi$
$211$	−1129.43	−	1129.43i	−0.368498	−	0.368498i	−0.866929	+	0.498431i	$0.833910\pi$
$212$		0			0
$213$	1757.34	−	1757.34i	0.565308	−	0.565308i
$214$		0			0
$215$			1968.93i			0.624558i
$216$		0			0
$217$	−1877.48	−	907.125i	−0.587334	−	0.283777i
$218$		0			0
$219$	5692.06	−	5692.06i	1.75632	−	1.75632i
$220$		0			0
$221$	−1450.36	+	1450.36i	−0.441456	+	0.441456i
$222$		0			0
$223$	−2011.83			−0.604135			−0.302068	−	0.953287i	$-0.597677\pi$
$223$	−2011.83			−0.604135			−0.302068	+	0.953287i	$0.597677\pi$
$224$		0			0
$225$	4898.39			1.45137
$226$		0			0
$227$	−2585.18	+	2585.18i	−0.755877	+	0.755877i	−0.975569	−	0.219692i	$-0.929495\pi$
$227$	−2585.18	+	2585.18i	−0.755877	+	0.755877i	0.219692	+	0.975569i	$0.429495\pi$
$228$		0			0
$229$	2612.62	−	2612.62i	0.753917	−	0.753917i	−0.221291	−	0.975208i	$-0.571027\pi$
$229$	2612.62	−	2612.62i	0.753917	−	0.753917i	0.975208	+	0.221291i	$0.0710269\pi$
$230$		0			0
$231$	1409.13	−	2916.48i	0.401359	−	0.830695i
$232$		0			0
$233$			996.659i			0.280229i	0.990135	+	0.140114i	$0.0447470\pi$
$233$			996.659i			0.280229i	−0.990135	+	0.140114i	$0.955253\pi$
$234$		0			0
$235$	−1769.53	+	1769.53i	−0.491197	+	0.491197i
$236$		0			0
$237$	−4487.87	−	4487.87i	−1.23004	−	1.23004i
$238$		0			0
$239$			3380.18i			0.914836i	0.889252	+	0.457418i	$0.151226\pi$
$239$			3380.18i			0.914836i	−0.889252	+	0.457418i	$0.848774\pi$
$240$		0			0
$241$			3822.12i			1.02160i	0.859701	+	0.510798i	$0.170650\pi$
$241$			3822.12i			1.02160i	−0.859701	+	0.510798i	$0.829350\pi$
$242$		0			0
$243$	10896.7	−	10896.7i	2.87663	−	2.87663i
$244$		0			0
$245$	2623.28	+	302.413i	0.684062	+	0.0788589i
$246$		0			0
$247$	1945.62			0.501203
$248$		0			0
$249$		−	2435.01i		−	0.619728i
$250$		0			0
$251$	4233.84	+	4233.84i	1.06469	+	1.06469i	0.997757	+	0.0669342i	$0.0213218\pi$
$251$	4233.84	+	4233.84i	1.06469	+	1.06469i	0.0669342	+	0.997757i	$0.478678\pi$
$252$		0			0
$253$	−635.091	+	635.091i	−0.157818	+	0.157818i
$254$		0			0
$255$	−7542.48			−1.85227
$256$		0			0
$257$			658.500i			0.159829i	0.996802	+	0.0799146i	$0.0254648\pi$
$257$			658.500i			0.159829i	−0.996802	+	0.0799146i	$0.974535\pi$
$258$		0			0
$259$	2519.78	+	7230.96i	0.604523	+	1.73479i
$260$		0			0
$261$	−1417.02	−	1417.02i	−0.336060	−	0.336060i
$262$		0			0
$263$	3287.12			0.770695			0.385347	−	0.922772i	$-0.374082\pi$
$263$	3287.12			0.770695			0.385347	+	0.922772i	$0.374082\pi$
$264$		0			0
$265$	214.723			0.0497748
$266$		0			0
$267$	−805.406	+	805.406i	−0.184607	+	0.184607i
$268$		0			0
$269$	4829.62	+	4829.62i	1.09467	+	1.09467i	0.995022	+	0.0996507i	$0.0317725\pi$
$269$	4829.62	+	4829.62i	1.09467	+	1.09467i	0.0996507	+	0.995022i	$0.468227\pi$
$270$		0			0
$271$	−1643.46			−0.368387			−0.184194	−	0.982890i	$-0.558967\pi$
$271$	−1643.46			−0.368387			−0.184194	+	0.982890i	$0.558967\pi$
$272$		0			0
$273$	3544.42	+	1712.52i	0.785780	+	0.379658i
$274$		0			0
$275$	806.750	+	806.750i	0.176905	+	0.176905i
$276$		0			0
$277$	−4353.18	−	4353.18i	−0.944250	−	0.944250i	0.0542762	−	0.998526i	$-0.482715\pi$
$277$	−4353.18	−	4353.18i	−0.944250	−	0.944250i	−0.998526	+	0.0542762i	$0.982715\pi$
$278$		0			0
$279$		−	8390.30i		−	1.80041i
$280$		0			0
$281$			4472.36i			0.949462i	0.880131	+	0.474731i	$0.157455\pi$
$281$			4472.36i			0.949462i	−0.880131	+	0.474731i	$0.842545\pi$
$282$		0			0
$283$	2098.07	+	2098.07i	0.440698	+	0.440698i	0.892247	−	0.451549i	$-0.149128\pi$
$283$	2098.07	+	2098.07i	0.440698	+	0.440698i	−0.451549	+	0.892247i	$0.649128\pi$
$284$		0			0
$285$	5059.04	+	5059.04i	1.05148	+	1.05148i
$286$		0			0
$287$	−2428.92	−	1173.56i	−0.499563	−	0.241369i
$288$		0			0
$289$	−4541.31			−0.924345
$290$		0			0
$291$	−10068.0	−	10068.0i	−2.02817	−	2.02817i
$292$		0			0
$293$	3783.32	−	3783.32i	0.754347	−	0.754347i	−0.220940	−	0.975287i	$-0.570913\pi$
$293$	3783.32	−	3783.32i	0.754347	−	0.754347i	0.975287	+	0.220940i	$0.0709125\pi$
$294$		0			0
$295$	556.541			0.109841
$296$		0			0
$297$	8311.41			1.62383
$298$		0			0
$299$	−771.830	−	771.830i	−0.149284	−	0.149284i
$300$		0			0
$301$	4472.74	−	1558.62i	0.856493	−	0.298463i
$302$		0			0
$303$		−	16671.2i		−	3.16084i
$304$		0			0
$305$	3118.18			0.585398
$306$		0			0
$307$	−4498.21	+	4498.21i	−0.836242	+	0.836242i	−0.988362	−	0.152120i	$-0.951390\pi$
$307$	−4498.21	+	4498.21i	−0.836242	+	0.836242i	0.152120	+	0.988362i	$0.451390\pi$
$308$		0			0
$309$	−7223.67	−	7223.67i	−1.32990	−	1.32990i
$310$		0			0
$311$		−	2873.57i		−	0.523940i	−0.965076	−	0.261970i	$-0.915628\pi$
$311$		−	2873.57i		−	0.523940i	0.965076	−	0.261970i	$-0.0843722\pi$
$312$		0			0
$313$	−4525.90			−0.817313			−0.408656	−	0.912688i	$-0.634003\pi$
$313$	−4525.90			−0.817313			−0.408656	+	0.912688i	$0.634003\pi$
$314$		0			0
$315$	3496.51	+	10033.8i	0.625415	+	1.79474i
$316$		0			0
$317$	4933.16	−	4933.16i	0.874050	−	0.874050i	−0.118860	−	0.992911i	$-0.537924\pi$
$317$	4933.16	−	4933.16i	0.874050	−	0.874050i	0.992911	+	0.118860i	$0.0379241\pi$
$318$		0			0
$319$		−	466.760i		−	0.0819233i
$320$		0			0
$321$			11879.6i			2.06558i
$322$		0			0
$323$	6341.38	+	6341.38i	1.09239	+	1.09239i
$324$		0			0
$325$	−980.447	+	980.447i	−0.167340	+	0.167340i
$326$		0			0
$327$			21414.0i			3.62139i
$328$		0			0
$329$	5420.54	+	2618.99i	0.908340	+	0.438875i
$330$		0			0
$331$	745.876	−	745.876i	0.123858	−	0.123858i	−0.642461	−	0.766319i	$-0.722086\pi$
$331$	745.876	−	745.876i	0.123858	−	0.123858i	0.766319	+	0.642461i	$0.222086\pi$
$332$		0			0
$333$	−21787.6	+	21787.6i	−3.58545	+	3.58545i
$334$		0			0
$335$	5767.06			0.940562
$336$		0			0
$337$	2070.09			0.334614			0.167307	−	0.985905i	$-0.446493\pi$
$337$	2070.09			0.334614			0.167307	+	0.985905i	$0.446493\pi$
$338$		0			0
$339$	7990.56	−	7990.56i	1.28020	−	1.28020i
$340$		0			0
$341$	1381.86	−	1381.86i	0.219448	−	0.219448i
$342$		0			0
$343$	−1389.63	−	6198.59i	−0.218755	−	0.975780i
$344$		0			0
$345$		−	4013.84i		−	0.626371i
$346$		0			0
$347$	4572.41	−	4572.41i	0.707378	−	0.707378i	−0.258605	−	0.965983i	$-0.583263\pi$
$347$	4572.41	−	4572.41i	0.707378	−	0.707378i	0.965983	+	0.258605i	$0.0832629\pi$
$348$		0			0
$349$	−3508.43	−	3508.43i	−0.538114	−	0.538114i	0.384860	−	0.922975i	$-0.374250\pi$
$349$	−3508.43	−	3508.43i	−0.538114	−	0.538114i	−0.922975	+	0.384860i	$0.874250\pi$
$350$		0			0
$351$			10100.9i			1.53603i
$352$		0			0
$353$		−	10700.7i		−	1.61343i	−0.590943	−	0.806713i	$-0.701244\pi$
$353$		−	10700.7i		−	1.61343i	0.590943	−	0.806713i	$-0.298756\pi$
$354$		0			0
$355$	−1342.74	+	1342.74i	−0.200746	+	0.200746i
$356$		0			0
$357$	5970.69	+	17133.9i	0.885160	+	2.54012i
$358$		0			0
$359$	−4462.55			−0.656056			−0.328028	−	0.944668i	$-0.606384\pi$
$359$	−4462.55			−0.656056			−0.328028	+	0.944668i	$0.606384\pi$
$360$		0			0
$361$		−	1647.82i		−	0.240242i
$362$		0			0
$363$	−7336.40	−	7336.40i	−1.06077	−	1.06077i
$364$		0			0
$365$	−4349.15	+	4349.15i	−0.623685	+	0.623685i
$366$		0			0
$367$	9939.65			1.41375			0.706874	−	0.707339i	$-0.250105\pi$
$367$	9939.65			1.41375			0.706874	+	0.707339i	$0.250105\pi$
$368$		0			0
$369$		−	10854.6i		−	1.53135i
$370$		0			0
$371$	−169.976	−	487.777i	−0.0237863	−	0.0682591i
$372$		0			0
$373$	−3850.64	−	3850.64i	−0.534528	−	0.534528i	0.387389	−	0.921916i	$-0.373377\pi$
$373$	−3850.64	−	3850.64i	−0.534528	−	0.534528i	−0.921916	+	0.387389i	$0.873377\pi$
$374$		0			0
$375$	−14795.1			−2.03738
$376$		0			0
$377$	567.255			0.0774937
$378$		0			0
$379$	−4104.10	+	4104.10i	−0.556235	+	0.556235i	−0.928234	−	0.371998i	$-0.878673\pi$
$379$	−4104.10	+	4104.10i	−0.556235	+	0.556235i	0.371998	+	0.928234i	$0.378673\pi$
$380$		0			0
$381$	1140.85	+	1140.85i	0.153405	+	0.153405i
$382$		0			0
$383$	−5426.64			−0.723991			−0.361995	−	0.932180i	$-0.617904\pi$
$383$	−5426.64			−0.723991			−0.361995	+	0.932180i	$0.617904\pi$
$384$		0			0
$385$	−1076.68	+	2228.41i	−0.142527	+	0.294988i
$386$		0			0
$387$	13476.8	+	13476.8i	1.77019	+	1.77019i
$388$		0			0
$389$	6093.92	+	6093.92i	0.794278	+	0.794278i	0.982187	−	0.187909i	$-0.0601709\pi$
$389$	6093.92	+	6093.92i	0.794278	+	0.794278i	−0.187909	+	0.982187i	$0.560171\pi$
$390$		0			0
$391$		−	5031.25i		−	0.650745i
$392$		0			0
$393$		−	1006.52i		−	0.129192i
$394$		0			0
$395$	3429.07	+	3429.07i	0.436798	+	0.436798i
$396$		0			0
$397$	9544.96	+	9544.96i	1.20667	+	1.20667i	0.972099	+	0.234570i	$0.0753682\pi$
$397$	9544.96	+	9544.96i	1.20667	+	1.20667i	0.234570	+	0.972099i	$0.424632\pi$
$398$		0			0
$399$	7487.63	−	15497.2i	0.939475	−	1.94443i
$400$		0			0
$401$	−225.359			−0.0280646			−0.0140323	−	0.999902i	$-0.504467\pi$
$401$	−225.359			−0.0280646			−0.0140323	+	0.999902i	$0.504467\pi$
$402$		0			0
$403$	1679.38	+	1679.38i	0.207583	+	0.207583i
$404$		0			0
$405$	−15310.9	+	15310.9i	−1.87853	+	1.87853i
$406$		0			0
$407$	−7176.71			−0.874045
$408$		0			0
$409$	−10818.4			−1.30791			−0.653957	−	0.756532i	$-0.726892\pi$
$409$	−10818.4			−1.30791			−0.653957	+	0.756532i	$0.726892\pi$
$410$		0			0
$411$	−11087.1	−	11087.1i	−1.33063	−	1.33063i
$412$		0			0
$413$	−440.562	−	1264.27i	−0.0524906	−	0.150631i
$414$		0			0
$415$			1860.53i			0.220072i
$416$		0			0
$417$	−12385.8			−1.45452
$418$		0			0
$419$	−8072.49	+	8072.49i	−0.941210	+	0.941210i	−0.998365	−	0.0571556i	$-0.981797\pi$
$419$	−8072.49	+	8072.49i	−0.941210	+	0.941210i	0.0571556	+	0.998365i	$0.481797\pi$
$420$		0			0
$421$	−9371.31	−	9371.31i	−1.08487	−	1.08487i	−0.996048	−	0.0888208i	$-0.971690\pi$
$421$	−9371.31	−	9371.31i	−1.08487	−	1.08487i	−0.0888208	−	0.996048i	$-0.528310\pi$
$422$		0			0
$423$			24223.9i			2.78442i
$424$		0			0
$425$	−6391.14			−0.729449
$426$		0			0
$427$	−2468.37	−	7083.44i	−0.279749	−	0.802791i
$428$		0			0
$429$	−2608.75	+	2608.75i	−0.293594	+	0.293594i
$430$		0			0
$431$			5756.21i			0.643311i	0.946857	+	0.321655i	$0.104239\pi$
$431$			5756.21i			0.643311i	−0.946857	+	0.321655i	$0.895761\pi$
$432$		0			0
$433$		−	17673.2i		−	1.96148i	−0.195313	−	0.980741i	$-0.562572\pi$
$433$		−	17673.2i		−	1.96148i	0.195313	−	0.980741i	$-0.437428\pi$
$434$		0			0
$435$	1474.98	+	1474.98i	0.162575	+	0.162575i
$436$		0			0
$437$	−3374.66	+	3374.66i	−0.369409	+	0.369409i
$438$		0			0
$439$		−	7434.51i		−	0.808269i	−0.914700	−	0.404134i	$-0.867573\pi$
$439$		−	7434.51i		−	0.808269i	0.914700	−	0.404134i	$-0.132427\pi$
$440$		0			0
$441$	20025.6	−	15885.7i	2.16236	−	1.71534i
$442$		0			0
$443$	−8038.66	+	8038.66i	−0.862141	+	0.862141i	−0.991587	−	0.129446i	$-0.958680\pi$
$443$	−8038.66	+	8038.66i	−0.862141	+	0.862141i	0.129446	+	0.991587i	$0.458680\pi$
$444$		0			0
$445$	615.390	−	615.390i	0.0655557	−	0.0655557i
$446$		0			0
$447$	−17915.9			−1.89574
$448$		0			0
$449$	3266.60			0.343342			0.171671	−	0.985154i	$-0.445083\pi$
$449$	3266.60			0.343342			0.171671	+	0.985154i	$0.445083\pi$
$450$		0			0
$451$	1787.73	−	1787.73i	0.186653	−	0.186653i
$452$		0			0
$453$	−174.717	+	174.717i	−0.0181213	+	0.0181213i
$454$		0			0
$455$	−2708.20	−	1308.50i	−0.279038	−	0.134820i
$456$		0			0
$457$			2912.80i			0.298151i	0.988826	+	0.149076i	$0.0476298\pi$
$457$			2912.80i			0.298151i	−0.988826	+	0.149076i	$0.952370\pi$
$458$		0			0
$459$	−32921.9	+	32921.9i	−3.34784	+	3.34784i
$460$		0			0
$461$	−5146.52	−	5146.52i	−0.519951	−	0.519951i	0.397605	−	0.917557i	$-0.369841\pi$
$461$	−5146.52	−	5146.52i	−0.519951	−	0.519951i	−0.917557	+	0.397605i	$0.869841\pi$
$462$		0			0
$463$		−	12855.2i		−	1.29035i	−0.764033	−	0.645177i	$-0.776784\pi$
$463$		−	12855.2i		−	1.29035i	0.764033	−	0.645177i	$-0.223216\pi$
$464$		0			0
$465$			8733.48i			0.870979i
$466$		0			0
$467$	1868.73	−	1868.73i	0.185170	−	0.185170i	−0.608434	−	0.793604i	$-0.708202\pi$
$467$	1868.73	−	1868.73i	0.185170	−	0.185170i	0.793604	+	0.608434i	$0.208202\pi$
$468$		0			0
$469$	−4565.25	−	13100.8i	−0.449475	−	1.28985i
$470$		0			0
$471$	10490.8			1.02631
$472$		0			0
$473$			4439.19i			0.431531i
$474$		0			0
$475$	4286.79	+	4286.79i	0.414087	+	0.414087i
$476$		0			0
$477$	1469.72	−	1469.72i	0.141078	−	0.141078i
$478$		0			0
$479$	13618.3			1.29903			0.649517	−	0.760347i	$-0.274971\pi$
$479$	13618.3			1.29903			0.649517	+	0.760347i	$0.274971\pi$
$480$		0			0
$481$		−	8721.89i		−	0.826786i
$482$		0			0
$483$	−9118.08	+	3177.39i	−0.858979	+	0.299330i
$484$		0			0
$485$	7692.71	+	7692.71i	0.720223	+	0.720223i
$486$		0			0
$487$	10237.7			0.952597			0.476299	−	0.879284i	$-0.341978\pi$
$487$	10237.7			0.952597			0.476299	+	0.879284i	$0.341978\pi$
$488$		0			0
$489$	−10251.8			−0.948060
$490$		0			0
$491$	2623.25	−	2623.25i	0.241112	−	0.241112i	−0.576198	−	0.817310i	$-0.695464\pi$
$491$	2623.25	−	2623.25i	0.241112	−	0.241112i	0.817310	+	0.576198i	$0.195464\pi$
$492$		0			0
$493$	1848.85	+	1848.85i	0.168901	+	0.168901i
$494$		0			0
$495$	−9958.58			−0.904252
$496$		0			0
$497$	4113.16	+	1987.32i	0.371228	+	0.179363i
$498$		0			0
$499$	−4956.46	−	4956.46i	−0.444653	−	0.444653i	0.448920	−	0.893572i	$-0.351809\pi$
$499$	−4956.46	−	4956.46i	−0.444653	−	0.444653i	−0.893572	+	0.448920i	$0.851809\pi$
$500$		0			0
$501$	2210.92	+	2210.92i	0.197159	+	0.197159i
$502$		0			0
$503$		−	5057.22i		−	0.448291i	−0.974556	−	0.224146i	$-0.928041\pi$
$503$		−	5057.22i		−	0.448291i	0.974556	−	0.224146i	$-0.0719591\pi$
$504$		0			0
$505$			12738.0i			1.12244i
$506$		0			0
$507$	12482.5	+	12482.5i	1.09343	+	1.09343i
$508$		0			0
$509$	5059.87	+	5059.87i	0.440618	+	0.440618i	0.892220	−	0.451602i	$-0.149147\pi$
$509$	5059.87	+	5059.87i	0.440618	+	0.440618i	−0.451602	+	0.892220i	$0.649147\pi$
$510$		0			0
$511$	13322.6	+	6436.97i	1.15334	+	0.557250i
$512$		0			0
$513$	44164.0			3.80095
$514$		0			0
$515$	5519.42	+	5519.42i	0.472262	+	0.472262i
$516$		0			0
$517$	−3989.61	+	3989.61i	−0.339387	+	0.339387i
$518$		0			0
$519$	−23291.4			−1.96991
$520$		0			0
$521$	−5223.36			−0.439231			−0.219616	−	0.975586i	$-0.570480\pi$
$521$	−5223.36			−0.439231			−0.219616	+	0.975586i	$0.570480\pi$
$522$		0			0
$523$	−1107.01	−	1107.01i	−0.0925547	−	0.0925547i	0.659313	−	0.751868i	$-0.270847\pi$
$523$	−1107.01	−	1107.01i	−0.0925547	−	0.0925547i	−0.751868	+	0.659313i	$0.770847\pi$
$524$		0			0
$525$	4036.20	+	11582.6i	0.335532	+	0.962869i
$526$		0			0
$527$			10947.2i			0.904871i
$528$		0			0
$529$	−9489.55			−0.779941
$530$		0			0
$531$	3809.38	−	3809.38i	0.311324	−	0.311324i
$532$		0			0
$533$	2172.63	+	2172.63i	0.176561	+	0.176561i
$534$		0			0
$535$		−	9076.87i		−	0.733509i
$536$		0			0
$537$	−5983.53			−0.480835
$538$		0			0
$539$	5914.49	+	681.825i	0.472644	+	0.0544866i
$540$		0			0
$541$	182.867	−	182.867i	0.0145325	−	0.0145325i	−0.699803	−	0.714336i	$-0.746729\pi$
$541$	182.867	−	182.867i	0.0145325	−	0.0145325i	0.714336	+	0.699803i	$0.246729\pi$
$542$		0			0
$543$		−	22791.4i		−	1.80124i
$544$		0			0
$545$		−	16361.9i		−	1.28599i
$546$		0			0
$547$	−4272.96	−	4272.96i	−0.334001	−	0.334001i	0.520103	−	0.854104i	$-0.325894\pi$
$547$	−4272.96	−	4272.96i	−0.334001	−	0.334001i	−0.854104	+	0.520103i	$0.825894\pi$
$548$		0			0
$549$	21343.1	−	21343.1i	1.65920	−	1.65920i
$550$		0			0
$551$		−	2480.20i		−	0.191760i
$552$		0			0
$553$	5075.19	−	10504.1i	0.390270	−	0.807743i
$554$		0			0
$555$	22678.8	−	22678.8i	1.73452	−	1.73452i
$556$		0			0
$557$	6464.83	−	6464.83i	0.491784	−	0.491784i	−0.417084	−	0.908868i	$-0.636948\pi$
$557$	6464.83	−	6464.83i	0.491784	−	0.491784i	0.908868	+	0.417084i	$0.136948\pi$
$558$		0			0
$559$	−5394.96			−0.408198
$560$		0			0
$561$	−17005.4			−1.27980
$562$		0			0
$563$	15139.3	−	15139.3i	1.13330	−	1.13330i	0.143673	−	0.989625i	$-0.454109\pi$
$563$	15139.3	−	15139.3i	1.13330	−	1.13330i	0.989625	−	0.143673i	$-0.0458914\pi$
$564$		0			0
$565$	−6105.38	+	6105.38i	−0.454611	+	0.454611i
$566$		0			0
$567$	46901.4	+	22660.9i	3.47385	+	1.67843i
$568$		0			0
$569$			6131.20i			0.451728i	0.974159	+	0.225864i	$0.0725206\pi$
$569$			6131.20i			0.451728i	−0.974159	+	0.225864i	$0.927479\pi$
$570$		0			0
$571$	656.438	−	656.438i	0.0481105	−	0.0481105i	−0.682642	−	0.730753i	$-0.739169\pi$
$571$	656.438	−	656.438i	0.0481105	−	0.0481105i	0.730753	+	0.682642i	$0.239169\pi$
$572$		0			0
$573$	−11456.0	−	11456.0i	−0.835221	−	0.835221i
$574$		0			0
$575$		−	3401.14i		−	0.246674i
$576$		0			0
$577$			13723.4i			0.990146i	0.868851	+	0.495073i	$0.164859\pi$
$577$			13723.4i			0.990146i	−0.868851	+	0.495073i	$0.835141\pi$
$578$		0			0
$579$	2653.77	−	2653.77i	0.190478	−	0.190478i
$580$		0			0
$581$	4226.48	−	1472.81i	0.301797	−	0.105168i
$582$		0			0
$583$	484.118			0.0343913
$584$		0			0
$585$		−	12102.7i		−	0.855360i
$586$		0			0
$587$	−6433.74	−	6433.74i	−0.452383	−	0.452383i	0.443762	−	0.896145i	$-0.353644\pi$
$587$	−6433.74	−	6433.74i	−0.452383	−	0.452383i	−0.896145	+	0.443762i	$0.853644\pi$
$588$		0			0
$589$	7342.71	−	7342.71i	0.513669	−	0.513669i
$590$		0			0
$591$	−13191.4			−0.918141
$592$		0			0
$593$			23783.9i			1.64703i	0.567295	+	0.823515i	$0.307990\pi$
$593$			23783.9i			1.64703i	−0.567295	+	0.823515i	$0.692010\pi$
$594$		0			0
$595$	−4562.05	−	13091.6i	−0.314329	−	0.902023i
$596$		0			0
$597$	−1749.75	−	1749.75i	−0.119954	−	0.119954i
$598$		0			0
$599$	−29102.5			−1.98514			−0.992569	−	0.121685i	$-0.961170\pi$
$599$	−29102.5			−1.98514			−0.992569	+	0.121685i	$0.961170\pi$
$600$		0			0
$601$	975.823			0.0662307			0.0331154	−	0.999452i	$-0.489457\pi$
$601$	975.823			0.0662307			0.0331154	+	0.999452i	$0.489457\pi$
$602$		0			0
$603$	39474.0	−	39474.0i	2.66585	−	2.66585i
$604$		0			0
$605$	5605.55	+	5605.55i	0.376691	+	0.376691i
$606$		0			0
$607$	−4174.26			−0.279124			−0.139562	−	0.990213i	$-0.544569\pi$
$607$	−4174.26			−0.279124			−0.139562	+	0.990213i	$0.544569\pi$
$608$		0			0
$609$	2183.05	−	4518.27i	0.145257	−	0.300640i
$610$		0			0
$611$	−4848.59	−	4848.59i	−0.321036	−	0.321036i
$612$		0			0
$613$	2417.25	+	2417.25i	0.159269	+	0.159269i	0.782243	−	0.622974i	$-0.214076\pi$
$613$	2417.25	+	2417.25i	0.159269	+	0.159269i	−0.622974	+	0.782243i	$0.714076\pi$
$614$		0			0
$615$			11298.6i			0.740819i
$616$		0			0
$617$		−	2569.32i		−	0.167645i	−0.996481	−	0.0838226i	$-0.973287\pi$
$617$		−	2569.32i		−	0.167645i	0.996481	−	0.0838226i	$-0.0267129\pi$
$618$		0			0
$619$	6542.68	+	6542.68i	0.424835	+	0.424835i	0.886864	−	0.462030i	$-0.152879\pi$
$619$	6542.68	+	6542.68i	0.424835	+	0.424835i	−0.462030	+	0.886864i	$0.652879\pi$
$620$		0			0
$621$	−17519.8	−	17519.8i	−1.13212	−	1.13212i
$622$		0			0
$623$	−1885.10	−	910.809i	−0.121228	−	0.0585727i
$624$		0			0
$625$	3088.32			0.197652
$626$		0			0
$627$	11406.2	+	11406.2i	0.726506	+	0.726506i
$628$		0			0
$629$	28427.3	−	28427.3i	1.80202	−	1.80202i
$630$		0			0
$631$	−14838.3			−0.936135			−0.468068	−	0.883693i	$-0.655050\pi$
$631$	−14838.3			−0.936135			−0.468068	+	0.883693i	$0.655050\pi$
$632$		0			0
$633$	16093.7			1.01053
$634$		0			0
$635$	−871.692	−	871.692i	−0.0544756	−	0.0544756i
$636$		0			0
$637$	−828.625	+	7187.91i	−0.0515405	+	0.447089i
$638$		0			0
$639$			18381.4i			1.13796i
$640$		0			0
$641$	−11669.6			−0.719067			−0.359534	−	0.933132i	$-0.617064\pi$
$641$	−11669.6			−0.719067			−0.359534	+	0.933132i	$0.617064\pi$
$642$		0			0
$643$	5415.79	−	5415.79i	0.332158	−	0.332158i	−0.521247	−	0.853406i	$-0.674533\pi$
$643$	5415.79	−	5415.79i	0.332158	−	0.332158i	0.853406	+	0.521247i	$0.174533\pi$
$644$		0			0
$645$	−14028.1	−	14028.1i	−0.856363	−	0.856363i
$646$		0			0
$647$		−	28918.6i		−	1.75720i	−0.477559	−	0.878600i	$-0.658478\pi$
$647$		−	28918.6i		−	1.75720i	0.477559	−	0.878600i	$-0.341522\pi$
$648$		0			0
$649$	1254.79			0.0758932
$650$		0			0
$651$	19839.5	−	6913.49i	1.19442	−	0.416223i
$652$		0			0
$653$	5718.20	−	5718.20i	0.342681	−	0.342681i	−0.514694	−	0.857374i	$-0.672094\pi$
$653$	5718.20	−	5718.20i	0.342681	−	0.342681i	0.857374	+	0.514694i	$0.172094\pi$
$654$		0			0
$655$			769.059i			0.0458773i
$656$		0			0
$657$			59537.7i			3.53544i
$658$		0			0
$659$	16453.5	+	16453.5i	0.972593	+	0.972593i	0.999634	−	0.0270410i	$-0.00860847\pi$
$659$	16453.5	+	16453.5i	0.972593	+	0.972593i	−0.0270410	+	0.999634i	$0.508608\pi$
$660$		0			0
$661$	−12618.5	+	12618.5i	−0.742518	+	0.742518i	−0.973062	−	0.230544i	$-0.925950\pi$
$661$	−12618.5	+	12618.5i	−0.742518	+	0.742518i	0.230544	+	0.973062i	$0.425950\pi$
$662$		0			0
$663$		−	20666.8i		−	1.21060i
$664$		0			0
$665$	−5721.11	+	11841.0i	−0.333617	+	0.690487i
$666$		0			0
$667$	−983.895	+	983.895i	−0.0571163	+	0.0571163i
$668$		0			0
$669$	14333.7	−	14333.7i	0.828360	−	0.828360i
$670$		0			0
$671$	7030.30			0.404474
$672$		0			0
$673$	18244.8			1.04500			0.522501	−	0.852639i	$-0.324999\pi$
$673$	18244.8			1.04500			0.522501	+	0.852639i	$0.324999\pi$
$674$		0			0
$675$	−22255.3	+	22255.3i	−1.26905	+	1.26905i
$676$		0			0
$677$	7677.41	−	7677.41i	0.435845	−	0.435845i	−0.454766	−	0.890611i	$-0.650277\pi$
$677$	7677.41	−	7677.41i	0.435845	−	0.435845i	0.890611	+	0.454766i	$0.150277\pi$
$678$		0			0
$679$	11385.6	−	23564.8i	0.643504	−	1.33186i
$680$		0			0
$681$		−	36837.2i		−	2.07284i
$682$		0			0
$683$	−17871.0	+	17871.0i	−1.00120	+	1.00120i	−0.00119593	+	0.999999i	$0.500381\pi$
$683$	−17871.0	+	17871.0i	−1.00120	+	1.00120i	−0.999999	+	0.00119593i	$0.999619\pi$
$684$		0			0
$685$	8471.38	+	8471.38i	0.472518	+	0.472518i
$686$		0			0
$687$			37228.4i			2.06747i
$688$		0			0
$689$			588.351i			0.0325318i
$690$		0			0
$691$	−17707.9	+	17707.9i	−0.974878	+	0.974878i	−0.999692	−	0.0248144i	$-0.992101\pi$
$691$	−17707.9	+	17707.9i	−0.974878	+	0.974878i	0.0248144	+	0.999692i	$0.492101\pi$
$692$		0			0
$693$	7883.29	+	22622.5i	0.432123	+	1.24005i
$694$		0			0
$695$	9463.66			0.516514
$696$		0			0
$697$			14162.5i			0.769646i
$698$		0			0
$699$	−7100.90	−	7100.90i	−0.384236	−	0.384236i
$700$		0			0
$701$	−9885.92	+	9885.92i	−0.532648	+	0.532648i	−0.921359	−	0.388712i	$-0.872920\pi$
$701$	−9885.92	+	9885.92i	−0.532648	+	0.532648i	0.388712	+	0.921359i	$0.372920\pi$
$702$		0			0
$703$	−38134.6			−2.04591
$704$		0			0
$705$		−	25214.7i		−	1.34701i
$706$		0			0
$707$	28936.4	−	10083.5i	1.53927	−	0.536392i
$708$		0			0
$709$	−14444.4	−	14444.4i	−0.765123	−	0.765123i	0.212121	−	0.977243i	$-0.431963\pi$
$709$	−14444.4	−	14444.4i	−0.765123	−	0.765123i	−0.977243	+	0.212121i	$0.931963\pi$
$710$		0			0
$711$	46942.2			2.47605
$712$		0			0
$713$	−5825.71			−0.305995
$714$		0			0
$715$	1993.28	−	1993.28i	0.104258	−	0.104258i
$716$		0			0
$717$	−24082.8	−	24082.8i	−1.25438	−	1.25438i
$718$		0			0
$719$	26045.4			1.35095			0.675473	−	0.737385i	$-0.263939\pi$
$719$	26045.4			1.35095			0.675473	+	0.737385i	$0.263939\pi$
$720$		0			0
$721$	8169.03	−	16907.5i	0.421956	−	0.873324i
$722$		0			0
$723$	−27231.5	−	27231.5i	−1.40076	−	1.40076i
$724$		0			0
$725$	1249.83	+	1249.83i	0.0640243	+	0.0640243i
$726$		0			0
$727$			2177.16i			0.111068i	0.998457	+	0.0555340i	$0.0176861\pi$
$727$			2177.16i			0.111068i	−0.998457	+	0.0555340i	$0.982314\pi$
$728$		0			0
$729$			79332.7i			4.03052i
$730$		0			0
$731$	−17583.8	−	17583.8i	−0.889686	−	0.889686i
$732$		0			0
$733$	−23338.5	−	23338.5i	−1.17603	−	1.17603i	−0.980748	−	0.195277i	$-0.937439\pi$
$733$	−23338.5	−	23338.5i	−1.17603	−	1.17603i	−0.195277	−	0.980748i	$-0.562561\pi$
$734$		0			0
$735$	−20844.7	+	16535.5i	−1.04608	+	0.829825i
$736$		0			0
$737$	13002.5			0.649870
$738$		0			0
$739$	−26817.7	−	26817.7i	−1.33492	−	1.33492i	−0.900907	−	0.434013i	$-0.857097\pi$
$739$	−26817.7	−	26817.7i	−1.33492	−	1.33492i	−0.434013	−	0.900907i	$-0.642903\pi$
$740$		0			0
$741$	−13862.0	+	13862.0i	−0.687225	+	0.687225i
$742$		0			0
$743$	32146.5			1.58727			0.793634	−	0.608395i	$-0.208186\pi$
$743$	32146.5			1.58727			0.793634	+	0.608395i	$0.208186\pi$
$744$		0			0
$745$	13689.1			0.673194
$746$		0			0
$747$	12734.8	+	12734.8i	0.623752	+	0.623752i
$748$		0			0
$749$	−20619.5	+	7185.32i	−1.00590	+	0.350528i
$750$		0			0
$751$		−	17416.9i		−	0.846275i	−0.906065	−	0.423137i	$-0.860929\pi$
$751$		−	17416.9i		−	0.846275i	0.906065	−	0.423137i	$-0.139071\pi$
$752$		0			0
$753$	−60329.7			−2.91970
$754$		0			0
$755$	133.497	−	133.497i	0.00643504	−	0.00643504i
$756$		0			0
$757$	5102.30	+	5102.30i	0.244975	+	0.244975i	0.818905	−	0.573930i	$-0.194582\pi$
$757$	5102.30	+	5102.30i	0.244975	+	0.244975i	−0.573930	+	0.818905i	$0.694582\pi$
$758$		0			0
$759$		−	9049.68i		−	0.432783i
$760$		0			0
$761$	9360.06			0.445863			0.222932	−	0.974834i	$-0.428437\pi$
$761$	9360.06			0.445863			0.222932	+	0.974834i	$0.428437\pi$
$762$		0			0
$763$	−37168.6	+	12952.2i	−1.76356	+	0.614548i
$764$		0			0
$765$	39446.3	−	39446.3i	1.86430	−	1.86430i
$766$		0			0
$767$			1524.95i			0.0717897i
$768$		0			0
$769$		−	27490.7i		−	1.28913i	−0.764550	−	0.644564i	$-0.777039\pi$
$769$		−	27490.7i		−	1.28913i	0.764550	−	0.644564i	$-0.222961\pi$
$770$		0			0
$771$	−4691.62	−	4691.62i	−0.219150	−	0.219150i
$772$		0			0
$773$	6668.49	−	6668.49i	0.310283	−	0.310283i	−0.534736	−	0.845019i	$-0.679589\pi$
$773$	6668.49	−	6668.49i	0.310283	−	0.310283i	0.845019	+	0.534736i	$0.179589\pi$
$774$		0			0
$775$			7400.34i			0.343004i
$776$		0			0
$777$	−69471.1	−	33565.7i	−3.20755	−	1.54976i
$778$		0			0
$779$	9499.35	−	9499.35i	0.436906	−	0.436906i
$780$		0			0
$781$	−3027.35	+	3027.35i	−0.138703	+	0.138703i
$782$		0			0
$783$	12876.2			0.587685
$784$		0			0
$785$	−8015.77			−0.364452
$786$		0			0
$787$	−20814.1	+	20814.1i	−0.942746	+	0.942746i	−0.998447	−	0.0557015i	$-0.982260\pi$
$787$	−20814.1	+	20814.1i	−0.942746	+	0.942746i	0.0557015	+	0.998447i	$0.482260\pi$
$788$		0			0
$789$	−23419.8	+	23419.8i	−1.05674	+	1.05674i
$790$		0			0
$791$	18702.4	+	9036.28i	0.840684	+	0.406186i
$792$		0			0
$793$			8543.96i			0.382604i
$794$		0			0
$795$	−1529.84	+	1529.84i	−0.0682487	+	0.0682487i
$796$		0			0
$797$	10318.1	+	10318.1i	0.458577	+	0.458577i	0.898188	−	0.439611i	$-0.144884\pi$
$797$	10318.1	+	10318.1i	0.458577	+	0.458577i	−0.439611	+	0.898188i	$0.644884\pi$
$798$		0			0
$799$		−	31606.0i		−	1.39943i
$800$		0			0
$801$		−	8424.37i		−	0.371611i
$802$		0			0
$803$	−9805.68	+	9805.68i	−0.430928	+	0.430928i
$804$		0			0
$805$	6966.89	−	2427.76i	0.305032	−	0.106295i
$806$		0			0
$807$	−68819.2			−3.00192
$808$		0			0
$809$		−	30204.3i		−	1.31264i	−0.754482	−	0.656320i	$-0.772112\pi$
$809$		−	30204.3i		−	1.31264i	0.754482	−	0.656320i	$-0.227888\pi$
$810$		0			0
$811$	15332.6	+	15332.6i	0.663874	+	0.663874i	0.956291	−	0.292417i	$-0.0944594\pi$
$811$	15332.6	+	15332.6i	0.663874	+	0.663874i	−0.292417	+	0.956291i	$0.594459\pi$
$812$		0			0
$813$	11709.1	−	11709.1i	0.505114	−	0.505114i
$814$		0			0
$815$	7833.12			0.336665
$816$		0			0
$817$			23588.3i			1.01010i
$818$		0			0
$819$	−27493.2	+	9580.60i	−1.17300	+	0.408758i
$820$		0			0
$821$	9268.98	+	9268.98i	0.394019	+	0.394019i	0.876117	−	0.482098i	$-0.160125\pi$
$821$	9268.98	+	9268.98i	0.394019	+	0.394019i	−0.482098	+	0.876117i	$0.660125\pi$
$822$		0			0
$823$	−1534.99			−0.0650137			−0.0325068	−	0.999472i	$-0.510349\pi$
$823$	−1534.99			−0.0650137			−0.0325068	+	0.999472i	$0.510349\pi$
$824$		0			0
$825$	−11495.7			−0.485126
$826$		0			0
$827$	1314.12	−	1314.12i	0.0552555	−	0.0552555i	−0.678939	−	0.734195i	$-0.737560\pi$
$827$	1314.12	−	1314.12i	0.0552555	−	0.0552555i	0.734195	+	0.678939i	$0.237560\pi$
$828$		0			0
$829$	10669.5	+	10669.5i	0.447004	+	0.447004i	0.894357	−	0.447353i	$-0.147633\pi$
$829$	10669.5	+	10669.5i	0.447004	+	0.447004i	−0.447353	+	0.894357i	$0.647633\pi$
$830$		0			0
$831$	62030.2			2.58942
$832$		0			0
$833$	−26128.3	+	20726.8i	−1.08679	+	0.862115i
$834$		0			0
$835$	−1689.31	−	1689.31i	−0.0700132	−	0.0700132i
$836$		0			0
$837$	38120.4	+	38120.4i	1.57423	+	1.57423i
$838$		0			0
$839$			2393.74i			0.0984995i	0.998786	+	0.0492497i	$0.0156830\pi$
$839$			2393.74i			0.0984995i	−0.998786	+	0.0492497i	$0.984317\pi$
$840$		0			0
$841$			23665.9i			0.970351i
$842$		0			0
$843$	−31864.3	−	31864.3i	−1.30185	−	1.30185i
$844$		0			0
$845$	−9537.59	−	9537.59i	−0.388288	−	0.388288i
$846$		0			0
$847$	8296.51	−	17171.3i	0.336566	−	0.696592i
$848$		0			0
$849$	−29896.3			−1.20853
$850$		0			0
$851$	15128.0	+	15128.0i	0.609378	+	0.609378i
$852$		0			0
$853$	16392.8	−	16392.8i	0.658005	−	0.658005i	−0.296903	−	0.954908i	$-0.595954\pi$
$853$	16392.8	−	16392.8i	0.658005	−	0.658005i	0.954908	+	0.296903i	$0.0959538\pi$
$854$		0			0
$855$	−52916.4			−2.11661
$856$		0			0
$857$	23765.4			0.947269			0.473635	−	0.880721i	$-0.342942\pi$
$857$	23765.4			0.947269			0.473635	+	0.880721i	$0.342942\pi$
$858$		0			0
$859$	13359.2	+	13359.2i	0.530628	+	0.530628i	0.920759	−	0.390131i	$-0.127570\pi$
$859$	13359.2	+	13359.2i	0.530628	+	0.530628i	−0.390131	+	0.920759i	$0.627570\pi$
$860$		0			0
$861$	25666.6	−	8944.06i	1.01593	−	0.354022i
$862$		0			0
$863$			33893.2i			1.33689i	0.743761	+	0.668445i	$0.233040\pi$
$863$			33893.2i			1.33689i	−0.743761	+	0.668445i	$0.766960\pi$
$864$		0			0
$865$	17796.4			0.699532
$866$		0			0
$867$	32355.5	−	32355.5i	1.26742	−	1.26742i
$868$		0			0
$869$	7731.23	+	7731.23i	0.301800	+	0.301800i
$870$		0			0
$871$			15802.0i			0.614731i
$872$		0			0
$873$	105309.			4.08268
$874$		0			0
$875$	−8948.78	−	25680.1i	−0.345742	−	0.992167i
$876$		0			0
$877$	7969.89	−	7969.89i	0.306869	−	0.306869i	−0.536825	−	0.843694i	$-0.680376\pi$
$877$	7969.89	−	7969.89i	0.306869	−	0.306869i	0.843694	+	0.536825i	$0.180376\pi$
$878$		0			0
$879$			53910.0i			2.06865i
$880$		0			0
$881$		−	35881.5i		−	1.37217i	−0.727522	−	0.686084i	$-0.759328\pi$
$881$		−	35881.5i		−	1.37217i	0.727522	−	0.686084i	$-0.240672\pi$
$882$		0			0
$883$	−18159.7	−	18159.7i	−0.692097	−	0.692097i	0.270596	−	0.962693i	$-0.412779\pi$
$883$	−18159.7	−	18159.7i	−0.692097	−	0.692097i	−0.962693	+	0.270596i	$0.912779\pi$
$884$		0			0
$885$	−3965.19	+	3965.19i	−0.150608	+	0.150608i
$886$		0			0
$887$			34117.9i			1.29151i	0.763546	+	0.645754i	$0.223457\pi$
$887$			34117.9i			1.29151i	−0.763546	+	0.645754i	$0.776543\pi$
$888$		0			0
$889$	−1290.15	+	2670.22i	−0.0486729	+	0.100738i
$890$		0			0
$891$	−34520.2	+	34520.2i	−1.29795	+	1.29795i
$892$		0			0
$893$	−21199.4	+	21199.4i	−0.794414	+	0.794414i
$894$		0			0
$895$	4571.86			0.170749
$896$		0			0
$897$	10998.1			0.409383
$898$		0			0
$899$	2140.80	−	2140.80i	0.0794212	−	0.0794212i
$900$		0			0
$901$	−1917.61	+	1917.61i	−0.0709045	+	0.0709045i
$902$		0			0
$903$	−20762.2	+	42971.7i	−0.765143	+	1.58362i
$904$		0			0
$905$			17414.4i			0.639638i
$906$		0			0
$907$	−14145.1	+	14145.1i	−0.517839	+	0.517839i	−0.916917	−	0.399078i	$-0.869330\pi$
$907$	−14145.1	+	14145.1i	−0.517839	+	0.517839i	0.399078	+	0.916917i	$0.369330\pi$
$908$		0			0
$909$	87188.4	+	87188.4i	3.18136	+	3.18136i
$910$		0			0
$911$			34335.9i			1.24874i	0.781131	+	0.624368i	$0.214643\pi$
$911$			34335.9i			1.24874i	−0.781131	+	0.624368i	$0.785357\pi$
$912$		0			0
$913$			4194.78i			0.152056i
$914$		0			0
$915$	−22216.1	+	22216.1i	−0.802669	+	0.802669i
$916$		0			0
$917$	1747.04	−	608.793i	0.0629142	−	0.0219238i
$918$		0			0
$919$	34749.9			1.24733			0.623663	−	0.781693i	$-0.285644\pi$
$919$	34749.9			1.24733			0.623663	+	0.781693i	$0.285644\pi$
$920$		0			0
$921$		−	64096.8i		−	2.29323i
$922$		0			0
$923$	−3679.16	−	3679.16i	−0.131204	−	0.131204i
$924$		0			0
$925$	19216.9	−	19216.9i	0.683080	−	0.683080i
$926$		0			0
$927$	75558.1			2.67708
$928$		0			0
$929$			4844.57i			0.171093i	0.996334	+	0.0855463i	$0.0272636\pi$
$929$			4844.57i			0.171093i	−0.996334	+	0.0855463i	$0.972736\pi$
$930$		0			0
$931$	31427.6	+	3622.98i	1.10633	+	0.127539i
$932$		0			0
$933$	20473.4	+	20473.4i	0.718401	+	0.718401i
$934$		0			0
$935$	12993.4			0.454470
$936$		0			0
$937$	40930.2			1.42704			0.713518	−	0.700637i	$-0.247101\pi$
$937$	40930.2			1.42704			0.713518	+	0.700637i	$0.247101\pi$
$938$		0			0
$939$	32245.7	−	32245.7i	1.12066	−	1.12066i
$940$		0			0
$941$	−8265.95	−	8265.95i	−0.286357	−	0.286357i	0.549281	−	0.835638i	$-0.314902\pi$
$941$	−8265.95	−	8265.95i	−0.286357	−	0.286357i	−0.835638	+	0.549281i	$0.814902\pi$
$942$		0			0
$943$	−7536.79			−0.260267
$944$		0			0
$945$	−61473.7	−	29701.7i	−2.11613	−	1.02243i
$946$		0			0
$947$	16415.9	+	16415.9i	0.563299	+	0.563299i	0.930243	−	0.366944i	$-0.119596\pi$
$947$	16415.9	+	16415.9i	0.563299	+	0.563299i	−0.366944	+	0.930243i	$0.619596\pi$
$948$		0			0
$949$	−11916.9	−	11916.9i	−0.407628	−	0.407628i
$950$		0			0
$951$			70294.7i			2.39691i
$952$		0			0
$953$		−	7536.91i		−	0.256185i	−0.991762	−	0.128093i	$-0.959115\pi$
$953$		−	7536.91i		−	0.256185i	0.991762	−	0.128093i	$-0.0408855\pi$
$954$		0			0
$955$	8753.24	+	8753.24i	0.296595	+	0.296595i
$956$		0			0
$957$	3325.52	+	3325.52i	0.112329	+	0.112329i
$958$		0			0
$959$	12538.1	−	25950.1i	0.422185	−	0.873798i
$960$		0			0
$961$	−17115.2			−0.574509
$962$		0			0
$963$	−62128.8	−	62128.8i	−2.07900	−	2.07900i
$964$		0			0
$965$	−2027.68	+	2027.68i	−0.0676407	+	0.0676407i
$966$		0			0
$967$	6759.38			0.224785			0.112392	−	0.993664i	$-0.464149\pi$
$967$	6759.38			0.224785			0.112392	+	0.993664i	$0.464149\pi$
$968$		0			0
$969$	−90360.9			−2.99567
$970$		0			0
$971$	21596.5	+	21596.5i	0.713763	+	0.713763i	0.967320	−	0.253558i	$-0.0816007\pi$
$971$	21596.5	+	21596.5i	0.713763	+	0.713763i	−0.253558	+	0.967320i	$0.581601\pi$
$972$		0			0
$973$	−7491.51	−	21498.2i	−0.246831	−	0.708326i
$974$		0			0
$975$		−	13970.8i		−	0.458896i
$976$		0			0
$977$	32251.8			1.05612			0.528058	−	0.849208i	$-0.322920\pi$
$977$	32251.8			1.05612			0.528058	+	0.849208i	$0.322920\pi$
$978$		0			0
$979$	1387.47	−	1387.47i	0.0452949	−	0.0452949i
$980$		0			0
$981$	−111993.	−	111993.i	−3.64491	−	3.64491i
$982$		0			0
$983$			28938.6i			0.938960i	0.882943	+	0.469480i	$0.155559\pi$
$983$			28938.6i			0.938960i	−0.882943	+	0.469480i	$0.844441\pi$
$984$		0			0
$985$	10079.2			0.326041
$986$		0			0
$987$	−57279.3	+	19960.2i	−1.84723	+	0.643708i
$988$		0			0
$989$	9357.48	−	9357.48i	0.300860	−	0.300860i
$990$		0			0
$991$		−	39400.7i		−	1.26297i	−0.775387	−	0.631486i	$-0.782445\pi$
$991$		−	39400.7i		−	1.26297i	0.775387	−	0.631486i	$-0.217555\pi$
$992$		0			0
$993$			10628.3i			0.339656i
$994$		0			0
$995$	1336.94	+	1336.94i	0.0425969	+	0.0425969i
$996$		0			0
$997$	−39139.6	+	39139.6i	−1.24329	+	1.24329i	−0.284668	+	0.958626i	$0.591883\pi$
$997$	−39139.6	+	39139.6i	−1.24329	+	1.24329i	−0.958626	+	0.284668i	$0.908117\pi$
$998$		0			0
$999$		−	197979.i		−	6.27006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.4.j.b.335.1		88
4.3	odd	2		112.4.j.b.27.26	yes	88
7.6	odd	2	inner	448.4.j.b.335.44		88
16.3	odd	4	inner	448.4.j.b.111.44		88
16.13	even	4		112.4.j.b.83.25	yes	88
28.27	even	2		112.4.j.b.27.25	✓	88
112.13	odd	4		112.4.j.b.83.26	yes	88
112.83	even	4	inner	448.4.j.b.111.1		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.4.j.b.27.25	✓	88	28.27	even	2
112.4.j.b.27.26	yes	88	4.3	odd	2
112.4.j.b.83.25	yes	88	16.13	even	4
112.4.j.b.83.26	yes	88	112.13	odd	4
448.4.j.b.111.1		88	112.83	even	4	inner
448.4.j.b.111.44		88	16.3	odd	4	inner
448.4.j.b.335.1		88	1.1	even	1	trivial
448.4.j.b.335.44		88	7.6	odd	2	inner

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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	448.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-7.12471 + 7.12471i) q^{3} +(5.44380 - 5.44380i) q^{5} +(-16.6758 - 8.05711i) q^{7} -74.5229i q^{9} +O(q^{10})\)	\(q+(-7.12471 + 7.12471i) q^{3} +(5.44380 - 5.44380i) q^{5} +(-16.6758 - 8.05711i) q^{7} -74.5229i q^{9} +(12.2737 - 12.2737i) q^{11} +(14.9163 + 14.9163i) q^{13} +77.5710i q^{15} +97.2333i q^{17} +(65.2182 - 65.2182i) q^{19} +(176.215 - 61.4058i) q^{21} -51.7441 q^{23} +65.7300i q^{25} +(338.586 + 338.586i) q^{27} +(19.0146 - 19.0146i) q^{29} +112.587 q^{31} +174.893i q^{33} +(-134.641 + 46.9186i) q^{35} +(-292.362 - 292.362i) q^{37} -212.548 q^{39} +145.655 q^{41} +(-180.841 + 180.841i) q^{43} +(-405.688 - 405.688i) q^{45} -325.054 q^{47} +(213.166 + 268.718i) q^{49} +(-692.758 - 692.758i) q^{51} +(19.7218 + 19.7218i) q^{53} -133.631i q^{55} +929.320i q^{57} +(51.1169 + 51.1169i) q^{59} +(286.397 + 286.397i) q^{61} +(-600.439 + 1242.73i) q^{63} +162.403 q^{65} +(529.690 + 529.690i) q^{67} +(368.661 - 368.661i) q^{69} -246.654 q^{71} -798.918 q^{73} +(-468.307 - 468.307i) q^{75} +(-303.564 + 105.783i) q^{77} +629.903i q^{79} -2812.54 q^{81} +(-170.885 + 170.885i) q^{83} +(529.319 + 529.319i) q^{85} +270.947i q^{87} +113.044 q^{89} +(-128.559 - 368.923i) q^{91} +(-802.148 + 802.148i) q^{93} -710.070i q^{95} +1413.11i q^{97} +(-914.671 - 914.671i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{7}+O(q^{10}) \) 88 * q + 4 * q^7	\( 88 q + 4 q^{7} - 112 q^{11} + 52 q^{21} - 160 q^{23} + 528 q^{29} - 476 q^{35} - 896 q^{37} + 8 q^{39} - 40 q^{43} - 1376 q^{49} - 1504 q^{51} - 1560 q^{53} - 8 q^{65} - 648 q^{67} + 456 q^{71} + 292 q^{77} - 1952 q^{81} + 496 q^{85} + 1964 q^{91} - 112 q^{93} - 7592 q^{99}+O(q^{100}) \) 88 * q + 4 * q^7 - 112 * q^11 + 52 * q^21 - 160 * q^23 + 528 * q^29 - 476 * q^35 - 896 * q^37 + 8 * q^39 - 40 * q^43 - 1376 * q^49 - 1504 * q^51 - 1560 * q^53 - 8 * q^65 - 648 * q^67 + 456 * q^71 + 292 * q^77 - 1952 * q^81 + 496 * q^85 + 1964 * q^91 - 112 * q^93 - 7592 * q^99

Introduction

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