LMFDB - Embedded newform 196.4.e.c.177.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,4,Mod(165,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("196.165");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	196.e (of order $3$, 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:	$11.5643743611$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	196.177
Dual form			196.4.e.c.165.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.00000 - 3.46410i) q^{3} +(-3.00000 + 5.19615i) q^{5} +(5.50000 - 9.52628i) q^{9} +(6.00000 + 10.3923i) q^{11} -82.0000 q^{13} +24.0000 q^{15} +(15.0000 + 25.9808i) q^{17} +(-34.0000 + 58.8897i) q^{19} +(-108.000 + 187.061i) q^{23} +(44.5000 + 77.0763i) q^{25} -152.000 q^{27} +246.000 q^{29} +(56.0000 + 96.9948i) q^{31} +(24.0000 - 41.5692i) q^{33} +(-55.0000 + 95.2628i) q^{37} +(164.000 + 284.056i) q^{39} -246.000 q^{41} -172.000 q^{43} +(33.0000 + 57.1577i) q^{45} +(-96.0000 + 166.277i) q^{47} +(60.0000 - 103.923i) q^{51} +(-279.000 - 483.242i) q^{53} -72.0000 q^{55} +272.000 q^{57} +(-270.000 - 467.654i) q^{59} +(-55.0000 + 95.2628i) q^{61} +(246.000 - 426.084i) q^{65} +(-70.0000 - 121.244i) q^{67} +864.000 q^{69} -840.000 q^{71} +(275.000 + 476.314i) q^{73} +(178.000 - 308.305i) q^{75} +(104.000 - 180.133i) q^{79} +(155.500 + 269.334i) q^{81} +516.000 q^{83} -180.000 q^{85} +(-492.000 - 852.169i) q^{87} +(699.000 - 1210.70i) q^{89} +(224.000 - 387.979i) q^{93} +(-204.000 - 353.338i) q^{95} +1586.00 q^{97} +132.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{3} - 6 q^{5} + 11 q^{9} + 12 q^{11} - 164 q^{13} + 48 q^{15} + 30 q^{17} - 68 q^{19} - 216 q^{23} + 89 q^{25} - 304 q^{27} + 492 q^{29} + 112 q^{31} + 48 q^{33} - 110 q^{37} + 328 q^{39} - 492 q^{41}+ \cdots + 264 q^{99}+O(q^{100}) $ 2 * q - 4 * q^3 - 6 * q^5 + 11 * q^9 + 12 * q^11 - 164 * q^13 + 48 * q^15 + 30 * q^17 - 68 * q^19 - 216 * q^23 + 89 * q^25 - 304 * q^27 + 492 * q^29 + 112 * q^31 + 48 * q^33 - 110 * q^37 + 328 * q^39 - 492 * q^41 - 344 * q^43 + 66 * q^45 - 192 * q^47 + 120 * q^51 - 558 * q^53 - 144 * q^55 + 544 * q^57 - 540 * q^59 - 110 * q^61 + 492 * q^65 - 140 * q^67 + 1728 * q^69 - 1680 * q^71 + 550 * q^73 + 356 * q^75 + 208 * q^79 + 311 * q^81 + 1032 * q^83 - 360 * q^85 - 984 * q^87 + 1398 * q^89 + 448 * q^93 - 408 * q^95 + 3172 * q^97 + 264 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−2.00000	−	3.46410i	−0.384900	−	0.666667i	0.606855	−	0.794812i	$-0.292431\pi$
$3$	−2.00000	−	3.46410i	−0.384900	−	0.666667i	−0.991755	+	0.128146i	$0.959097\pi$
$4$		0			0
$5$	−3.00000	+	5.19615i	−0.268328	+	0.464758i	−0.968430	−	0.249285i	$-0.919804\pi$
$5$	−3.00000	+	5.19615i	−0.268328	+	0.464758i	0.700102	+	0.714043i	$0.253138\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	5.50000	−	9.52628i	0.203704	−	0.352825i
$10$		0			0
$11$	6.00000	+	10.3923i	0.164461	+	0.284854i	0.936464	−	0.350765i	$-0.114078\pi$
$11$	6.00000	+	10.3923i	0.164461	+	0.284854i	−0.772003	+	0.635619i	$0.780745\pi$
$12$		0			0
$13$	−82.0000			−1.74944			−0.874720	−	0.484629i	$-0.838954\pi$
$13$	−82.0000			−1.74944			−0.874720	+	0.484629i	$0.838954\pi$
$14$		0			0
$15$	24.0000			0.413118
$16$		0			0
$17$	15.0000	+	25.9808i	0.214002	+	0.370662i	0.952963	−	0.303085i	$-0.0980168\pi$
$17$	15.0000	+	25.9808i	0.214002	+	0.370662i	−0.738961	+	0.673748i	$0.764683\pi$
$18$		0			0
$19$	−34.0000	+	58.8897i	−0.410533	+	0.711065i	−0.994948	−	0.100390i	$-0.967991\pi$
$19$	−34.0000	+	58.8897i	−0.410533	+	0.711065i	0.584415	+	0.811455i	$0.301324\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−108.000	+	187.061i	−0.979111	+	1.69587i	−0.313470	+	0.949598i	$0.601492\pi$
$23$	−108.000	+	187.061i	−0.979111	+	1.69587i	−0.665641	+	0.746272i	$0.731842\pi$
$24$		0			0
$25$	44.5000	+	77.0763i	0.356000	+	0.616610i
$26$		0			0
$27$	−152.000			−1.08342
$28$		0			0
$29$	246.000			1.57521			0.787604	−	0.616181i	$-0.211321\pi$
$29$	246.000			1.57521			0.787604	+	0.616181i	$0.211321\pi$
$30$		0			0
$31$	56.0000	+	96.9948i	0.324448	+	0.561961i	0.981401	−	0.191971i	$-0.0614880\pi$
$31$	56.0000	+	96.9948i	0.324448	+	0.561961i	−0.656952	+	0.753932i	$0.728155\pi$
$32$		0			0
$33$	24.0000	−	41.5692i	0.126602	−	0.219281i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−55.0000	+	95.2628i	−0.244377	+	0.423273i	−0.961956	−	0.273204i	$-0.911917\pi$
$37$	−55.0000	+	95.2628i	−0.244377	+	0.423273i	0.717579	+	0.696477i	$0.245250\pi$
$38$		0			0
$39$	164.000	+	284.056i	0.673359	+	1.16629i
$40$		0			0
$41$	−246.000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−246.000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$		0			0
$43$	−172.000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−172.000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$		0			0
$45$	33.0000	+	57.1577i	0.109319	+	0.189346i
$46$		0			0
$47$	−96.0000	+	166.277i	−0.297937	+	0.516042i	−0.975664	−	0.219272i	$-0.929632\pi$
$47$	−96.0000	+	166.277i	−0.297937	+	0.516042i	0.677727	+	0.735314i	$0.262965\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	60.0000	−	103.923i	0.164739	−	0.285336i
$52$		0			0
$53$	−279.000	−	483.242i	−0.723087	−	1.25242i	−0.959757	−	0.280833i	$-0.909389\pi$
$53$	−279.000	−	483.242i	−0.723087	−	1.25242i	0.236670	−	0.971590i	$-0.423944\pi$
$54$		0			0
$55$	−72.0000			−0.176518
$56$		0			0
$57$	272.000			0.632058
$58$		0			0
$59$	−270.000	−	467.654i	−0.595780	−	1.03192i	−0.993436	−	0.114386i	$-0.963510\pi$
$59$	−270.000	−	467.654i	−0.595780	−	1.03192i	0.397657	−	0.917534i	$-0.369824\pi$
$60$		0			0
$61$	−55.0000	+	95.2628i	−0.115443	+	0.199953i	−0.917957	−	0.396680i	$-0.870162\pi$
$61$	−55.0000	+	95.2628i	−0.115443	+	0.199953i	0.802514	+	0.596634i	$0.203495\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	246.000	−	426.084i	0.469424	−	0.813066i
$66$		0			0
$67$	−70.0000	−	121.244i	−0.127640	−	0.221078i	0.795122	−	0.606450i	$-0.207407\pi$
$67$	−70.0000	−	121.244i	−0.127640	−	0.221078i	−0.922762	+	0.385371i	$0.874073\pi$
$68$		0			0
$69$	864.000			1.50744
$70$		0			0
$71$	−840.000			−1.40408			−0.702040	−	0.712138i	$-0.747727\pi$
$71$	−840.000			−1.40408			−0.702040	+	0.712138i	$0.747727\pi$
$72$		0			0
$73$	275.000	+	476.314i	0.440908	+	0.763676i	0.997757	−	0.0669381i	$-0.0213230\pi$
$73$	275.000	+	476.314i	0.440908	+	0.763676i	−0.556849	+	0.830614i	$0.687990\pi$
$74$		0			0
$75$	178.000	−	308.305i	0.274049	−	0.474667i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	104.000	−	180.133i	0.148113	−	0.256539i	−0.782417	−	0.622755i	$-0.786013\pi$
$79$	104.000	−	180.133i	0.148113	−	0.256539i	0.930530	+	0.366216i	$0.119347\pi$
$80$		0			0
$81$	155.500	+	269.334i	0.213306	+	0.369457i
$82$		0			0
$83$	516.000			0.682390			0.341195	−	0.939993i	$-0.389168\pi$
$83$	516.000			0.682390			0.341195	+	0.939993i	$0.389168\pi$
$84$		0			0
$85$	−180.000			−0.229691
$86$		0			0
$87$	−492.000	−	852.169i	−0.606298	−	1.05014i
$88$		0			0
$89$	699.000	−	1210.70i	0.832515	−	1.44196i	−0.0635224	−	0.997980i	$-0.520233\pi$
$89$	699.000	−	1210.70i	0.832515	−	1.44196i	0.896038	−	0.443978i	$-0.146433\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	224.000	−	387.979i	0.249760	−	0.432598i
$94$		0			0
$95$	−204.000	−	353.338i	−0.220315	−	0.381597i
$96$		0			0
$97$	1586.00			1.66014			0.830072	−	0.557657i	$-0.188299\pi$
$97$	1586.00			1.66014			0.830072	+	0.557657i	$0.188299\pi$
$98$		0			0
$99$	132.000			0.134005
$100$		0			0
$101$	621.000	+	1075.60i	0.611800	+	1.05967i	0.990937	+	0.134328i	$0.0428876\pi$
$101$	621.000	+	1075.60i	0.611800	+	1.05967i	−0.379137	+	0.925341i	$0.623779\pi$
$102$		0			0
$103$	−340.000	+	588.897i	−0.325254	+	0.563357i	−0.981564	−	0.191135i	$-0.938783\pi$
$103$	−340.000	+	588.897i	−0.325254	+	0.563357i	0.656309	+	0.754492i	$0.272117\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−498.000	+	862.561i	−0.449939	+	0.779317i	−0.998382	−	0.0568710i	$-0.981888\pi$
$107$	−498.000	+	862.561i	−0.449939	+	0.779317i	0.548442	+	0.836188i	$0.315221\pi$
$108$		0			0
$109$	−691.000	−	1196.85i	−0.607209	−	1.05172i	−0.991698	−	0.128588i	$-0.958956\pi$
$109$	−691.000	−	1196.85i	−0.607209	−	1.05172i	0.384489	−	0.923130i	$-0.374378\pi$
$110$		0			0
$111$	440.000			0.376243
$112$		0			0
$113$	−750.000			−0.624372			−0.312186	−	0.950021i	$-0.601061\pi$
$113$	−750.000			−0.624372			−0.312186	+	0.950021i	$0.601061\pi$
$114$		0			0
$115$	−648.000	−	1122.37i	−0.525446	−	0.910099i
$116$		0			0
$117$	−451.000	+	781.155i	−0.356367	+	0.617246i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	593.500	−	1027.97i	0.445905	−	0.772331i
$122$		0			0
$123$	492.000	+	852.169i	0.360668	+	0.624695i
$124$		0			0
$125$	−1284.00			−0.918756
$126$		0			0
$127$	176.000			0.122972			0.0614861	−	0.998108i	$-0.480416\pi$
$127$	176.000			0.122972			0.0614861	+	0.998108i	$0.480416\pi$
$128$		0			0
$129$	344.000	+	595.825i	0.234787	+	0.406663i
$130$		0			0
$131$	774.000	−	1340.61i	0.516219	−	0.894118i	−0.483604	−	0.875287i	$-0.660672\pi$
$131$	774.000	−	1340.61i	0.516219	−	0.894118i	0.999823	−	0.0188305i	$-0.00599429\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	456.000	−	789.815i	0.290713	−	0.503529i
$136$		0			0
$137$	−189.000	−	327.358i	−0.117864	−	0.204146i	0.801057	−	0.598588i	$-0.204271\pi$
$137$	−189.000	−	327.358i	−0.117864	−	0.204146i	−0.918921	+	0.394442i	$0.870938\pi$
$138$		0			0
$139$	−2500.00			−1.52552			−0.762760	−	0.646682i	$-0.776156\pi$
$139$	−2500.00			−1.52552			−0.762760	+	0.646682i	$0.776156\pi$
$140$		0			0
$141$	768.000			0.458704
$142$		0			0
$143$	−492.000	−	852.169i	−0.287714	−	0.498335i
$144$		0			0
$145$	−738.000	+	1278.25i	−0.422673	+	0.732091i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−423.000	+	732.657i	−0.232574	+	0.402830i	−0.958565	−	0.284874i	$-0.908048\pi$
$149$	−423.000	+	732.657i	−0.232574	+	0.402830i	0.725991	+	0.687704i	$0.241381\pi$
$150$		0			0
$151$	1268.00	+	2196.24i	0.683367	+	1.18363i	0.973947	+	0.226775i	$0.0728183\pi$
$151$	1268.00	+	2196.24i	0.683367	+	1.18363i	−0.290580	+	0.956851i	$0.593848\pi$
$152$		0			0
$153$	330.000			0.174372
$154$		0			0
$155$	−672.000			−0.348234
$156$		0			0
$157$	593.000	+	1027.11i	0.301443	+	0.522115i	0.976463	−	0.215685i	$-0.0691984\pi$
$157$	593.000	+	1027.11i	0.301443	+	0.522115i	−0.675020	+	0.737799i	$0.735865\pi$
$158$		0			0
$159$	−1116.00	+	1932.97i	−0.556632	+	0.964116i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1054.00	+	1825.58i	−0.506476	+	0.877243i	0.493496	+	0.869748i	$0.335719\pi$
$163$	−1054.00	+	1825.58i	−0.506476	+	0.877243i	−0.999972	+	0.00749450i	$0.997614\pi$
$164$		0			0
$165$	144.000	+	249.415i	0.0679417	+	0.117679i
$166$		0			0
$167$	−1944.00			−0.900786			−0.450393	−	0.892830i	$-0.648716\pi$
$167$	−1944.00			−0.900786			−0.450393	+	0.892830i	$0.648716\pi$
$168$		0			0
$169$	4527.00			2.06054
$170$		0			0
$171$	374.000	+	647.787i	0.167254	+	0.289693i
$172$		0			0
$173$	681.000	−	1179.53i	0.299280	−	0.518368i	−0.676691	−	0.736267i	$-0.736587\pi$
$173$	681.000	−	1179.53i	0.299280	−	0.518368i	0.975971	+	0.217898i	$0.0699201\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1080.00	+	1870.61i	−0.458631	+	0.794373i
$178$		0			0
$179$	−798.000	−	1382.18i	−0.333214	−	0.577144i	0.649926	−	0.759997i	$-0.274800\pi$
$179$	−798.000	−	1382.18i	−0.333214	−	0.577144i	−0.983140	+	0.182854i	$0.941467\pi$
$180$		0			0
$181$	−1690.00			−0.694015			−0.347007	−	0.937862i	$-0.612802\pi$
$181$	−1690.00			−0.694015			−0.347007	+	0.937862i	$0.612802\pi$
$182$		0			0
$183$	440.000			0.177736
$184$		0			0
$185$	−330.000	−	571.577i	−0.131146	−	0.227152i
$186$		0			0
$187$	−180.000	+	311.769i	−0.0703899	+	0.121919i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1776.00	+	3076.12i	−0.672811	+	1.16534i	0.304293	+	0.952579i	$0.401580\pi$
$191$	−1776.00	+	3076.12i	−0.672811	+	1.16534i	−0.977104	+	0.212764i	$0.931753\pi$
$192$		0			0
$193$	1343.00	+	2326.14i	0.500887	+	0.867562i	0.999999	+	0.00102491i	$0.000326238\pi$
$193$	1343.00	+	2326.14i	0.500887	+	0.867562i	−0.499112	+	0.866537i	$0.666340\pi$
$194$		0			0
$195$	−1968.00			−0.722725
$196$		0			0
$197$	−1410.00			−0.509941			−0.254970	−	0.966949i	$-0.582066\pi$
$197$	−1410.00			−0.509941			−0.254970	+	0.966949i	$0.582066\pi$
$198$		0			0
$199$	1484.00	+	2570.36i	0.528633	+	0.915619i	0.999443	+	0.0333844i	$0.0106286\pi$
$199$	1484.00	+	2570.36i	0.528633	+	0.915619i	−0.470810	+	0.882235i	$0.656038\pi$
$200$		0			0
$201$	−280.000	+	484.974i	−0.0982571	+	0.170186i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	738.000	−	1278.25i	0.251435	−	0.435498i
$206$		0			0
$207$	1188.00	+	2057.68i	0.398897	+	0.690910i
$208$		0			0
$209$	−816.000			−0.270067
$210$		0			0
$211$	−1348.00			−0.439811			−0.219906	−	0.975521i	$-0.570575\pi$
$211$	−1348.00			−0.439811			−0.219906	+	0.975521i	$0.570575\pi$
$212$		0			0
$213$	1680.00	+	2909.85i	0.540431	+	0.936053i
$214$		0			0
$215$	516.000	−	893.738i	0.163679	−	0.283500i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	1100.00	−	1905.26i	0.339411	−	0.587878i
$220$		0			0
$221$	−1230.00	−	2130.42i	−0.374384	−	0.648451i
$222$		0			0
$223$	3872.00			1.16273			0.581364	−	0.813644i	$-0.302519\pi$
$223$	3872.00			1.16273			0.581364	+	0.813644i	$0.302519\pi$
$224$		0			0
$225$	979.000			0.290074
$226$		0			0
$227$	−2682.00	−	4645.36i	−0.784188	−	1.35825i	−0.929483	−	0.368865i	$-0.879747\pi$
$227$	−2682.00	−	4645.36i	−0.784188	−	1.35825i	0.145296	−	0.989388i	$-0.453587\pi$
$228$		0			0
$229$	437.000	−	756.906i	0.126104	−	0.218418i	−0.796060	−	0.605218i	$-0.793086\pi$
$229$	437.000	−	756.906i	0.126104	−	0.218418i	0.922164	+	0.386799i	$0.126419\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−189.000	+	327.358i	−0.0531408	+	0.0920425i	−0.891372	−	0.453272i	$-0.850257\pi$
$233$	−189.000	+	327.358i	−0.0531408	+	0.0920425i	0.838231	+	0.545315i	$0.183590\pi$
$234$		0			0
$235$	−576.000	−	997.661i	−0.159890	−	0.276937i
$236$		0			0
$237$	−832.000			−0.228035
$238$		0			0
$239$	1920.00			0.519642			0.259821	−	0.965657i	$-0.416336\pi$
$239$	1920.00			0.519642			0.259821	+	0.965657i	$0.416336\pi$
$240$		0			0
$241$	−2161.00	−	3742.96i	−0.577603	−	1.00044i	−0.995754	−	0.0920596i	$-0.970655\pi$
$241$	−2161.00	−	3742.96i	−0.577603	−	1.00044i	0.418151	−	0.908378i	$-0.362678\pi$
$242$		0			0
$243$	−1430.00	+	2476.83i	−0.377508	+	0.653864i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2788.00	−	4828.96i	0.718203	−	1.24396i
$248$		0			0
$249$	−1032.00	−	1787.48i	−0.262652	−	0.454927i
$250$		0			0
$251$	5292.00			1.33079			0.665395	−	0.746492i	$-0.268263\pi$
$251$	5292.00			1.33079			0.665395	+	0.746492i	$0.268263\pi$
$252$		0			0
$253$	−2592.00			−0.644101
$254$		0			0
$255$	360.000	+	623.538i	0.0884081	+	0.153127i
$256$		0			0
$257$	2559.00	−	4432.32i	0.621113	−	1.07580i	−0.368166	−	0.929760i	$-0.620014\pi$
$257$	2559.00	−	4432.32i	0.621113	−	1.07580i	0.989279	−	0.146039i	$-0.0466525\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	1353.00	−	2343.46i	0.320876	−	0.555773i
$262$		0			0
$263$	−1884.00	−	3263.18i	−0.441720	−	0.765082i	0.556097	−	0.831117i	$-0.312298\pi$
$263$	−1884.00	−	3263.18i	−0.441720	−	0.765082i	−0.997817	+	0.0660355i	$0.978965\pi$
$264$		0			0
$265$	3348.00			0.776098
$266$		0			0
$267$	−5592.00			−1.28174
$268$		0			0
$269$	−1959.00	−	3393.09i	−0.444024	−	0.769071i	0.553960	−	0.832543i	$-0.313116\pi$
$269$	−1959.00	−	3393.09i	−0.444024	−	0.769071i	−0.997984	+	0.0634719i	$0.979783\pi$
$270$		0			0
$271$	−2440.00	+	4226.20i	−0.546935	+	0.947320i	0.451547	+	0.892247i	$0.350872\pi$
$271$	−2440.00	+	4226.20i	−0.546935	+	0.947320i	−0.998482	+	0.0550723i	$0.982461\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−534.000	+	924.915i	−0.117096	+	0.202816i
$276$		0			0
$277$	1769.00	+	3064.00i	0.383714	+	0.664613i	0.991590	−	0.129419i	$-0.0413114\pi$
$277$	1769.00	+	3064.00i	0.383714	+	0.664613i	−0.607875	+	0.794032i	$0.707978\pi$
$278$		0			0
$279$	1232.00			0.264365
$280$		0			0
$281$	−5430.00			−1.15276			−0.576382	−	0.817180i	$-0.695536\pi$
$281$	−5430.00			−1.15276			−0.576382	+	0.817180i	$0.695536\pi$
$282$		0			0
$283$	3218.00	+	5573.74i	0.675937	+	1.17076i	0.976194	+	0.216899i	$0.0695943\pi$
$283$	3218.00	+	5573.74i	0.675937	+	1.17076i	−0.300257	+	0.953858i	$0.597072\pi$
$284$		0			0
$285$	−816.000	+	1413.35i	−0.169599	+	0.293754i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	2006.50	−	3475.36i	0.408406	−	0.707380i
$290$		0			0
$291$	−3172.00	−	5494.07i	−0.638989	−	1.10676i
$292$		0			0
$293$	1350.00			0.269174			0.134587	−	0.990902i	$-0.457029\pi$
$293$	1350.00			0.269174			0.134587	+	0.990902i	$0.457029\pi$
$294$		0			0
$295$	3240.00			0.639458
$296$		0			0
$297$	−912.000	−	1579.63i	−0.178180	−	0.308618i
$298$		0			0
$299$	8856.00	−	15339.0i	1.71290	−	2.96682i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	2484.00	−	4302.41i	0.470964	−	0.815733i
$304$		0			0
$305$	−330.000	−	571.577i	−0.0619533	−	0.107306i
$306$		0			0
$307$	3332.00			0.619437			0.309719	−	0.950828i	$-0.399765\pi$
$307$	3332.00			0.619437			0.309719	+	0.950828i	$0.399765\pi$
$308$		0			0
$309$	2720.00			0.500762
$310$		0			0
$311$	2364.00	+	4094.57i	0.431029	+	0.746565i	0.996962	−	0.0778865i	$-0.0248172\pi$
$311$	2364.00	+	4094.57i	0.431029	+	0.746565i	−0.565933	+	0.824451i	$0.691484\pi$
$312$		0			0
$313$	−2557.00	+	4428.85i	−0.461758	+	0.799788i	−0.999049	−	0.0436091i	$-0.986114\pi$
$313$	−2557.00	+	4428.85i	−0.461758	+	0.799788i	0.537291	+	0.843397i	$0.319448\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3603.00	+	6240.58i	−0.638374	+	1.10570i	0.347415	+	0.937711i	$0.387059\pi$
$317$	−3603.00	+	6240.58i	−0.638374	+	1.10570i	−0.985790	+	0.167985i	$0.946274\pi$
$318$		0			0
$319$	1476.00	+	2556.51i	0.259060	+	0.448705i
$320$		0			0
$321$	3984.00			0.692726
$322$		0			0
$323$	−2040.00			−0.351420
$324$		0			0
$325$	−3649.00	−	6320.25i	−0.622800	−	1.07872i
$326$		0			0
$327$	−2764.00	+	4787.39i	−0.467430	+	0.809612i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−3130.00	+	5421.32i	−0.519759	+	0.900250i	0.479977	+	0.877281i	$0.340645\pi$
$331$	−3130.00	+	5421.32i	−0.519759	+	0.900250i	−0.999736	+	0.0229685i	$0.992688\pi$
$332$		0			0
$333$	605.000	+	1047.89i	0.0995609	+	0.172445i
$334$		0			0
$335$	840.000			0.136997
$336$		0			0
$337$	−5326.00			−0.860907			−0.430454	−	0.902613i	$-0.641646\pi$
$337$	−5326.00			−0.860907			−0.430454	+	0.902613i	$0.641646\pi$
$338$		0			0
$339$	1500.00	+	2598.08i	0.240321	+	0.416248i
$340$		0			0
$341$	−672.000	+	1163.94i	−0.106718	+	0.184841i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−2592.00	+	4489.48i	−0.404489	+	0.700595i
$346$		0			0
$347$	−18.0000	−	31.1769i	−0.00278470	−	0.00482324i	0.864630	−	0.502410i	$-0.167553\pi$
$347$	−18.0000	−	31.1769i	−0.00278470	−	0.00482324i	−0.867414	+	0.497586i	$0.834220\pi$
$348$		0			0
$349$	3134.00			0.480685			0.240343	−	0.970688i	$-0.422740\pi$
$349$	3134.00			0.480685			0.240343	+	0.970688i	$0.422740\pi$
$350$		0			0
$351$	12464.0			1.89538
$352$		0			0
$353$	−609.000	−	1054.82i	−0.0918238	−	0.159043i	0.816455	−	0.577409i	$-0.195936\pi$
$353$	−609.000	−	1054.82i	−0.0918238	−	0.159043i	−0.908279	+	0.418366i	$0.862603\pi$
$354$		0			0
$355$	2520.00	−	4364.77i	0.376754	−	0.652557i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	5004.00	−	8667.18i	0.735657	−	1.27420i	−0.218777	−	0.975775i	$-0.570207\pi$
$359$	5004.00	−	8667.18i	0.735657	−	1.27420i	0.954434	−	0.298421i	$-0.0964600\pi$
$360$		0			0
$361$	1117.50	+	1935.57i	0.162925	+	0.282194i
$362$		0			0
$363$	−4748.00			−0.686516
$364$		0			0
$365$	−3300.00			−0.473233
$366$		0			0
$367$	536.000	+	928.379i	0.0762370	+	0.132046i	0.901624	−	0.432522i	$-0.142376\pi$
$367$	536.000	+	928.379i	0.0762370	+	0.132046i	−0.825387	+	0.564568i	$0.809043\pi$
$368$		0			0
$369$	−1353.00	+	2343.46i	−0.190879	+	0.330612i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	137.000	−	237.291i	0.0190177	−	0.0329396i	−0.856360	−	0.516379i	$-0.827279\pi$
$373$	137.000	−	237.291i	0.0190177	−	0.0329396i	0.875378	+	0.483440i	$0.160613\pi$
$374$		0			0
$375$	2568.00	+	4447.91i	0.353629	+	0.612504i
$376$		0			0
$377$	−20172.0			−2.75573
$378$		0			0
$379$	7652.00			1.03709			0.518545	−	0.855051i	$-0.326474\pi$
$379$	7652.00			1.03709			0.518545	+	0.855051i	$0.326474\pi$
$380$		0			0
$381$	−352.000	−	609.682i	−0.0473320	−	0.0819815i
$382$		0			0
$383$	−1080.00	+	1870.61i	−0.144087	+	0.249566i	−0.929032	−	0.369999i	$-0.879358\pi$
$383$	−1080.00	+	1870.61i	−0.144087	+	0.249566i	0.784945	+	0.619566i	$0.212691\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−946.000	+	1638.52i	−0.124258	+	0.215221i
$388$		0			0
$389$	537.000	+	930.111i	0.0699922	+	0.121230i	0.898898	−	0.438159i	$-0.144369\pi$
$389$	537.000	+	930.111i	0.0699922	+	0.121230i	−0.828905	+	0.559389i	$0.811036\pi$
$390$		0			0
$391$	−6480.00			−0.838127
$392$		0			0
$393$	−6192.00			−0.794771
$394$		0			0
$395$	624.000	+	1080.80i	0.0794857	+	0.137673i
$396$		0			0
$397$	−3463.00	+	5998.09i	−0.437791	+	0.758276i	−0.997519	−	0.0704004i	$-0.977572\pi$
$397$	−3463.00	+	5998.09i	−0.437791	+	0.758276i	0.559728	+	0.828676i	$0.310906\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−969.000	+	1678.36i	−0.120672	+	0.209010i	−0.920033	−	0.391841i	$-0.871838\pi$
$401$	−969.000	+	1678.36i	−0.120672	+	0.209010i	0.799361	+	0.600851i	$0.205172\pi$
$402$		0			0
$403$	−4592.00	−	7953.58i	−0.567603	−	0.983116i
$404$		0			0
$405$	−1866.00			−0.228944
$406$		0			0
$407$	−1320.00			−0.160762
$408$		0			0
$409$	4787.00	+	8291.33i	0.578733	+	1.00240i	0.995625	+	0.0934393i	$0.0297861\pi$
$409$	4787.00	+	8291.33i	0.578733	+	1.00240i	−0.416892	+	0.908956i	$0.636881\pi$
$410$		0			0
$411$	−756.000	+	1309.43i	−0.0907317	+	0.157152i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−1548.00	+	2681.21i	−0.183104	+	0.317146i
$416$		0			0
$417$	5000.00	+	8660.25i	0.587173	+	1.01701i
$418$		0			0
$419$	−5052.00			−0.589037			−0.294518	−	0.955646i	$-0.595159\pi$
$419$	−5052.00			−0.589037			−0.294518	+	0.955646i	$0.595159\pi$
$420$		0			0
$421$	3422.00			0.396147			0.198074	−	0.980187i	$-0.436531\pi$
$421$	3422.00			0.396147			0.198074	+	0.980187i	$0.436531\pi$
$422$		0			0
$423$	1056.00	+	1829.05i	0.121382	+	0.210239i
$424$		0			0
$425$	−1335.00	+	2312.29i	−0.152369	+	0.263912i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−1968.00	+	3408.68i	−0.221482	+	0.383619i
$430$		0			0
$431$	−1104.00	−	1912.18i	−0.123382	−	0.213705i	0.797717	−	0.603032i	$-0.206041\pi$
$431$	−1104.00	−	1912.18i	−0.123382	−	0.213705i	−0.921099	+	0.389327i	$0.872708\pi$
$432$		0			0
$433$	−6814.00			−0.756259			−0.378129	−	0.925753i	$-0.623433\pi$
$433$	−6814.00			−0.756259			−0.378129	+	0.925753i	$0.623433\pi$
$434$		0			0
$435$	5904.00			0.650747
$436$		0			0
$437$	−7344.00	−	12720.2i	−0.803916	−	1.39242i
$438$		0			0
$439$	−6292.00	+	10898.1i	−0.684056	+	1.18482i	0.289676	+	0.957125i	$0.406452\pi$
$439$	−6292.00	+	10898.1i	−0.684056	+	1.18482i	−0.973732	+	0.227696i	$0.926881\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3498.00	+	6058.71i	−0.375158	+	0.649793i	−0.990351	−	0.138584i	$-0.955745\pi$
$443$	−3498.00	+	6058.71i	−0.375158	+	0.649793i	0.615193	+	0.788377i	$0.289078\pi$
$444$		0			0
$445$	4194.00	+	7264.22i	0.446775	+	0.773836i
$446$		0			0
$447$	3384.00			0.358071
$448$		0			0
$449$	9474.00			0.995781			0.497891	−	0.867240i	$-0.334108\pi$
$449$	9474.00			0.995781			0.497891	+	0.867240i	$0.334108\pi$
$450$		0			0
$451$	−1476.00	−	2556.51i	−0.154107	−	0.266921i
$452$		0			0
$453$	5072.00	−	8784.96i	0.526056	−	0.911156i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−2893.00	+	5010.82i	−0.296124	+	0.512902i	−0.975246	−	0.221123i	$-0.929028\pi$
$457$	−2893.00	+	5010.82i	−0.296124	+	0.512902i	0.679121	+	0.734026i	$0.262361\pi$
$458$		0			0
$459$	−2280.00	−	3949.08i	−0.231855	−	0.401584i
$460$		0			0
$461$	3438.00			0.347340			0.173670	−	0.984804i	$-0.444437\pi$
$461$	3438.00			0.347340			0.173670	+	0.984804i	$0.444437\pi$
$462$		0			0
$463$	9392.00			0.942728			0.471364	−	0.881939i	$-0.343762\pi$
$463$	9392.00			0.942728			0.471364	+	0.881939i	$0.343762\pi$
$464$		0			0
$465$	1344.00	+	2327.88i	0.134036	+	0.232156i
$466$		0			0
$467$	2478.00	−	4292.02i	0.245542	−	0.425291i	−0.716742	−	0.697339i	$-0.754367\pi$
$467$	2478.00	−	4292.02i	0.245542	−	0.425291i	0.962284	+	0.272047i	$0.0877007\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	2372.00	−	4108.42i	0.232051	−	0.401924i
$472$		0			0
$473$	−1032.00	−	1787.48i	−0.100320	−	0.173760i
$474$		0			0
$475$	−6052.00			−0.584600
$476$		0			0
$477$	−6138.00			−0.589182
$478$		0			0
$479$	10296.0	+	17833.2i	0.982122	+	1.70108i	0.654088	+	0.756418i	$0.273053\pi$
$479$	10296.0	+	17833.2i	0.982122	+	1.70108i	0.328034	+	0.944666i	$0.393614\pi$
$480$		0			0
$481$	4510.00	−	7811.55i	0.427522	−	0.740491i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4758.00	+	8241.10i	−0.445463	+	0.771565i
$486$		0			0
$487$	6716.00	+	11632.5i	0.624910	+	1.08238i	0.988558	+	0.150839i	$0.0481975\pi$
$487$	6716.00	+	11632.5i	0.624910	+	1.08238i	−0.363649	+	0.931536i	$0.618469\pi$
$488$		0			0
$489$	8432.00			0.779771
$490$		0			0
$491$	−14172.0			−1.30259			−0.651297	−	0.758823i	$-0.725775\pi$
$491$	−14172.0			−1.30259			−0.651297	+	0.758823i	$0.725775\pi$
$492$		0			0
$493$	3690.00	+	6391.27i	0.337098	+	0.583871i
$494$		0			0
$495$	−396.000	+	685.892i	−0.0359573	+	0.0622799i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	2978.00	−	5158.05i	0.267162	−	0.462737i	−0.700966	−	0.713195i	$-0.747248\pi$
$499$	2978.00	−	5158.05i	0.267162	−	0.462737i	0.968128	+	0.250457i	$0.0805809\pi$
$500$		0			0
$501$	3888.00	+	6734.21i	0.346713	+	0.600524i
$502$		0			0
$503$	16968.0			1.50411			0.752053	−	0.659102i	$-0.229064\pi$
$503$	16968.0			1.50411			0.752053	+	0.659102i	$0.229064\pi$
$504$		0			0
$505$	−7452.00			−0.656653
$506$		0			0
$507$	−9054.00	−	15682.0i	−0.793101	−	1.37369i
$508$		0			0
$509$	−2607.00	+	4515.46i	−0.227020	+	0.393210i	−0.956924	−	0.290340i	$-0.906232\pi$
$509$	−2607.00	+	4515.46i	−0.227020	+	0.393210i	0.729903	+	0.683550i	$0.239565\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	5168.00	−	8951.24i	0.444781	−	0.770384i
$514$		0			0
$515$	−2040.00	−	3533.38i	−0.174550	−	0.302329i
$516$		0			0
$517$	−2304.00			−0.195996
$518$		0			0
$519$	−5448.00			−0.460772
$520$		0			0
$521$	699.000	+	1210.70i	0.0587788	+	0.101808i	0.893917	−	0.448232i	$-0.147946\pi$
$521$	699.000	+	1210.70i	0.0587788	+	0.101808i	−0.835139	+	0.550039i	$0.814613\pi$
$522$		0			0
$523$	9290.00	−	16090.8i	0.776718	−	1.34531i	−0.157106	−	0.987582i	$-0.550217\pi$
$523$	9290.00	−	16090.8i	0.776718	−	1.34531i	0.933824	−	0.357733i	$-0.116450\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1680.00	+	2909.85i	−0.138865	+	0.240522i
$528$		0			0
$529$	−17244.5	−	29868.4i	−1.41732	−	2.45487i
$530$		0			0
$531$	−5940.00			−0.485450
$532$		0			0
$533$	20172.0			1.63930
$534$		0			0
$535$	−2988.00	−	5175.37i	−0.241463	−	0.418226i
$536$		0			0
$537$	−3192.00	+	5528.71i	−0.256508	+	0.444285i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	9485.00	−	16428.5i	0.753774	−	1.30558i	−0.192207	−	0.981354i	$-0.561564\pi$
$541$	9485.00	−	16428.5i	0.753774	−	1.30558i	0.945981	−	0.324221i	$-0.105102\pi$
$542$		0			0
$543$	3380.00	+	5854.33i	0.267126	+	0.462677i
$544$		0			0
$545$	8292.00			0.651725
$546$		0			0
$547$	−16036.0			−1.25347			−0.626737	−	0.779231i	$-0.715610\pi$
$547$	−16036.0			−1.25347			−0.626737	+	0.779231i	$0.715610\pi$
$548$		0			0
$549$	605.000	+	1047.89i	0.0470324	+	0.0814625i
$550$		0			0
$551$	−8364.00	+	14486.9i	−0.646676	+	1.12008i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−1320.00	+	2286.31i	−0.100957	+	0.174862i
$556$		0			0
$557$	−4155.00	−	7196.67i	−0.316074	−	0.547456i	0.663592	−	0.748095i	$-0.269031\pi$
$557$	−4155.00	−	7196.67i	−0.316074	−	0.547456i	−0.979665	+	0.200640i	$0.935698\pi$
$558$		0			0
$559$	14104.0			1.06715
$560$		0			0
$561$	1440.00			0.108372
$562$		0			0
$563$	−3546.00	−	6141.85i	−0.265446	−	0.459766i	0.702234	−	0.711946i	$-0.252186\pi$
$563$	−3546.00	−	6141.85i	−0.265446	−	0.459766i	−0.967680	+	0.252180i	$0.918853\pi$
$564$		0			0
$565$	2250.00	−	3897.11i	0.167537	−	0.290182i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	3579.00	−	6199.01i	0.263690	−	0.456724i	−0.703530	−	0.710666i	$-0.748394\pi$
$569$	3579.00	−	6199.01i	0.263690	−	0.456724i	0.967220	+	0.253942i	$0.0817271\pi$
$570$		0			0
$571$	−3250.00	−	5629.17i	−0.238193	−	0.412563i	0.722003	−	0.691890i	$-0.243222\pi$
$571$	−3250.00	−	5629.17i	−0.238193	−	0.412563i	−0.960196	+	0.279328i	$0.909888\pi$
$572$		0			0
$573$	14208.0			1.03586
$574$		0			0
$575$	−19224.0			−1.39425
$576$		0			0
$577$	−10897.0	−	18874.2i	−0.786218	−	1.36177i	−0.928268	−	0.371911i	$-0.878703\pi$
$577$	−10897.0	−	18874.2i	−0.786218	−	1.36177i	0.142050	−	0.989859i	$-0.454631\pi$
$578$		0			0
$579$	5372.00	−	9304.58i	0.385583	−	0.667850i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	3348.00	−	5798.91i	0.237839	−	0.411949i
$584$		0			0
$585$	−2706.00	−	4686.93i	−0.191247	−	0.331249i
$586$		0			0
$587$	9756.00			0.685985			0.342993	−	0.939338i	$-0.388559\pi$
$587$	9756.00			0.685985			0.342993	+	0.939338i	$0.388559\pi$
$588$		0			0
$589$	−7616.00			−0.532787
$590$		0			0
$591$	2820.00	+	4884.38i	0.196276	+	0.339961i
$592$		0			0
$593$	−2793.00	+	4837.62i	−0.193414	+	0.335004i	−0.946380	−	0.323057i	$-0.895290\pi$
$593$	−2793.00	+	4837.62i	−0.193414	+	0.335004i	0.752965	+	0.658060i	$0.228623\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	5936.00	−	10281.5i	0.406942	−	0.704844i
$598$		0			0
$599$	12.0000	+	20.7846i	0.000818542	+	0.00141776i	0.866434	−	0.499291i	$-0.166406\pi$
$599$	12.0000	+	20.7846i	0.000818542	+	0.00141776i	−0.865616	+	0.500709i	$0.833073\pi$
$600$		0			0
$601$	4298.00			0.291712			0.145856	−	0.989306i	$-0.453406\pi$
$601$	4298.00			0.291712			0.145856	+	0.989306i	$0.453406\pi$
$602$		0			0
$603$	−1540.00			−0.104003
$604$		0			0
$605$	3561.00	+	6167.83i	0.239298	+	0.414476i
$606$		0			0
$607$	−4240.00	+	7343.90i	−0.283519	+	0.491070i	−0.972249	−	0.233948i	$-0.924835\pi$
$607$	−4240.00	+	7343.90i	−0.283519	+	0.491070i	0.688730	+	0.725018i	$0.258169\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	7872.00	−	13634.7i	0.521223	−	0.902784i
$612$		0			0
$613$	953.000	+	1650.64i	0.0627917	+	0.108758i	0.895712	−	0.444634i	$-0.146666\pi$
$613$	953.000	+	1650.64i	0.0627917	+	0.108758i	−0.832921	+	0.553393i	$0.813333\pi$
$614$		0			0
$615$	−5904.00			−0.387109
$616$		0			0
$617$	7482.00			0.488191			0.244096	−	0.969751i	$-0.421509\pi$
$617$	7482.00			0.488191			0.244096	+	0.969751i	$0.421509\pi$
$618$		0			0
$619$	3674.00	+	6363.55i	0.238563	+	0.413203i	0.960302	−	0.278962i	$-0.0899903\pi$
$619$	3674.00	+	6363.55i	0.238563	+	0.413203i	−0.721739	+	0.692165i	$0.756657\pi$
$620$		0			0
$621$	16416.0	−	28433.3i	1.06079	−	1.83734i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−1710.50	+	2962.67i	−0.109472	+	0.189611i
$626$		0			0
$627$	1632.00	+	2826.71i	0.103949	+	0.180044i
$628$		0			0
$629$	−3300.00			−0.209189
$630$		0			0
$631$	4520.00			0.285164			0.142582	−	0.989783i	$-0.454460\pi$
$631$	4520.00			0.285164			0.142582	+	0.989783i	$0.454460\pi$
$632$		0			0
$633$	2696.00	+	4669.61i	0.169283	+	0.293207i
$634$		0			0
$635$	−528.000	+	914.523i	−0.0329969	+	0.0571523i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−4620.00	+	8002.07i	−0.286016	+	0.495395i
$640$		0			0
$641$	9903.00	+	17152.5i	0.610211	+	1.05692i	0.991205	+	0.132338i	$0.0422485\pi$
$641$	9903.00	+	17152.5i	0.610211	+	1.05692i	−0.380994	+	0.924577i	$0.624418\pi$
$642$		0			0
$643$	−5020.00			−0.307884			−0.153942	−	0.988080i	$-0.549197\pi$
$643$	−5020.00			−0.307884			−0.153942	+	0.988080i	$0.549197\pi$
$644$		0			0
$645$	−4128.00			−0.252000
$646$		0			0
$647$	−14196.0	−	24588.2i	−0.862600	−	1.49407i	−0.869410	−	0.494091i	$-0.835501\pi$
$647$	−14196.0	−	24588.2i	−0.862600	−	1.49407i	0.00681018	−	0.999977i	$-0.497832\pi$
$648$		0			0
$649$	3240.00	−	5611.84i	0.195965	−	0.339421i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	8781.00	−	15209.1i	0.526228	−	0.911454i	−0.473305	−	0.880899i	$-0.656939\pi$
$653$	8781.00	−	15209.1i	0.526228	−	0.911454i	0.999533	−	0.0305554i	$-0.00972761\pi$
$654$		0			0
$655$	4644.00	+	8043.64i	0.277032	+	0.479834i
$656$		0			0
$657$	6050.00			0.359259
$658$		0			0
$659$	4716.00			0.278770			0.139385	−	0.990238i	$-0.455487\pi$
$659$	4716.00			0.278770			0.139385	+	0.990238i	$0.455487\pi$
$660$		0			0
$661$	11381.0	+	19712.5i	0.669697	+	1.15995i	0.977989	+	0.208657i	$0.0669093\pi$
$661$	11381.0	+	19712.5i	0.669697	+	1.15995i	−0.308292	+	0.951292i	$0.599757\pi$
$662$		0			0
$663$	−4920.00	+	8521.69i	−0.288201	+	0.499178i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−26568.0	+	46017.1i	−1.54230	+	2.67135i
$668$		0			0
$669$	−7744.00	−	13413.0i	−0.447534	−	0.775152i
$670$		0			0
$671$	−1320.00			−0.0759434
$672$		0			0
$673$	4802.00			0.275042			0.137521	−	0.990499i	$-0.456086\pi$
$673$	4802.00			0.275042			0.137521	+	0.990499i	$0.456086\pi$
$674$		0			0
$675$	−6764.00	−	11715.6i	−0.385698	−	0.668049i
$676$		0			0
$677$	−10779.0	+	18669.8i	−0.611921	+	1.05988i	0.378995	+	0.925399i	$0.376270\pi$
$677$	−10779.0	+	18669.8i	−0.611921	+	1.05988i	−0.990916	+	0.134480i	$0.957064\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−10728.0	+	18581.4i	−0.603668	+	1.04558i
$682$		0			0
$683$	−1890.00	−	3273.58i	−0.105884	−	0.183397i	0.808215	−	0.588888i	$-0.200434\pi$
$683$	−1890.00	−	3273.58i	−0.105884	−	0.183397i	−0.914099	+	0.405491i	$0.867101\pi$
$684$		0			0
$685$	2268.00			0.126505
$686$		0			0
$687$	−3496.00			−0.194150
$688$		0			0
$689$	22878.0	+	39625.9i	1.26500	+	2.19104i
$690$		0			0
$691$	2750.00	−	4763.14i	0.151396	−	0.262226i	−0.780345	−	0.625350i	$-0.784956\pi$
$691$	2750.00	−	4763.14i	0.151396	−	0.262226i	0.931741	+	0.363123i	$0.118290\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	7500.00	−	12990.4i	0.409340	−	0.708997i
$696$		0			0
$697$	−3690.00	−	6391.27i	−0.200529	−	0.347326i
$698$		0			0
$699$	1512.00			0.0818156
$700$		0			0
$701$	10230.0			0.551187			0.275593	−	0.961274i	$-0.411126\pi$
$701$	10230.0			0.551187			0.275593	+	0.961274i	$0.411126\pi$
$702$		0			0
$703$	−3740.00	−	6477.87i	−0.200650	−	0.347536i
$704$		0			0
$705$	−2304.00	+	3990.65i	−0.123083	+	0.213186i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−5095.00	+	8824.80i	−0.269883	+	0.467450i	−0.968831	−	0.247721i	$-0.920318\pi$
$709$	−5095.00	+	8824.80i	−0.269883	+	0.467450i	0.698949	+	0.715172i	$0.253652\pi$
$710$		0			0
$711$	−1144.00	−	1981.47i	−0.0603423	−	0.104516i
$712$		0			0
$713$	−24192.0			−1.27068
$714$		0			0
$715$	5904.00			0.308807
$716$		0			0
$717$	−3840.00	−	6651.08i	−0.200010	−	0.346428i
$718$		0			0
$719$	−4704.00	+	8147.57i	−0.243991	+	0.422605i	−0.961847	−	0.273586i	$-0.911790\pi$
$719$	−4704.00	+	8147.57i	−0.243991	+	0.422605i	0.717856	+	0.696191i	$0.245123\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−8644.00	+	14971.8i	−0.444639	+	0.770137i
$724$		0			0
$725$	10947.0	+	18960.8i	0.560774	+	0.971290i
$726$		0			0
$727$	−33064.0			−1.68676			−0.843381	−	0.537316i	$-0.819438\pi$
$727$	−33064.0			−1.68676			−0.843381	+	0.537316i	$0.819438\pi$
$728$		0			0
$729$	19837.0			1.00782
$730$		0			0
$731$	−2580.00	−	4468.69i	−0.130540	−	0.226102i
$732$		0			0
$733$	3161.00	−	5475.01i	0.159283	−	0.275886i	−0.775328	−	0.631559i	$-0.782415\pi$
$733$	3161.00	−	5475.01i	0.159283	−	0.275886i	0.934610	+	0.355674i	$0.115749\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	840.000	−	1454.92i	0.0419834	−	0.0727175i
$738$		0			0
$739$	10370.0	+	17961.4i	0.516193	+	0.894072i	0.999823	+	0.0188001i	$0.00598461\pi$
$739$	10370.0	+	17961.4i	0.516193	+	0.894072i	−0.483630	+	0.875272i	$0.660682\pi$
$740$		0			0
$741$	−22304.0			−1.10575
$742$		0			0
$743$	32040.0			1.58201			0.791005	−	0.611810i	$-0.209558\pi$
$743$	32040.0			1.58201			0.791005	+	0.611810i	$0.209558\pi$
$744$		0			0
$745$	−2538.00	−	4395.94i	−0.124812	−	0.216181i
$746$		0			0
$747$	2838.00	−	4915.56i	0.139005	−	0.240764i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	6416.00	−	11112.8i	0.311749	−	0.539964i	−0.666992	−	0.745064i	$-0.732419\pi$
$751$	6416.00	−	11112.8i	0.311749	−	0.539964i	0.978741	+	0.205100i	$0.0657520\pi$
$752$		0			0
$753$	−10584.0	−	18332.0i	−0.512221	−	0.887193i
$754$		0			0
$755$	−15216.0			−0.733466
$756$		0			0
$757$	−19906.0			−0.955741			−0.477870	−	0.878430i	$-0.658591\pi$
$757$	−19906.0			−0.955741			−0.477870	+	0.878430i	$0.658591\pi$
$758$		0			0
$759$	5184.00	+	8978.95i	0.247915	+	0.429401i
$760$		0			0
$761$	−5421.00	+	9389.45i	−0.258227	+	0.447263i	−0.965767	−	0.259411i	$-0.916472\pi$
$761$	−5421.00	+	9389.45i	−0.258227	+	0.447263i	0.707540	+	0.706674i	$0.249805\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−990.000	+	1714.73i	−0.0467889	+	0.0810408i
$766$		0			0
$767$	22140.0	+	38347.6i	1.04228	+	1.80528i
$768$		0			0
$769$	28274.0			1.32586			0.662930	−	0.748681i	$-0.269313\pi$
$769$	28274.0			1.32586			0.662930	+	0.748681i	$0.269313\pi$
$770$		0			0
$771$	−20472.0			−0.956266
$772$		0			0
$773$	16173.0	+	28012.5i	0.752526	+	1.30341i	0.946595	+	0.322425i	$0.104498\pi$
$773$	16173.0	+	28012.5i	0.752526	+	1.30341i	−0.194069	+	0.980988i	$0.562169\pi$
$774$		0			0
$775$	−4984.00	+	8632.54i	−0.231007	+	0.400116i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	8364.00	−	14486.9i	0.384687	−	0.666298i
$780$		0			0
$781$	−5040.00	−	8729.54i	−0.230916	−	0.399958i
$782$		0			0
$783$	−37392.0			−1.70662
$784$		0			0
$785$	−7116.00			−0.323543
$786$		0			0
$787$	−15058.0	−	26081.2i	−0.682033	−	1.18132i	−0.974360	−	0.224997i	$-0.927763\pi$
$787$	−15058.0	−	26081.2i	−0.682033	−	1.18132i	0.292327	−	0.956318i	$-0.405570\pi$
$788$		0			0
$789$	−7536.00	+	13052.7i	−0.340036	+	0.588960i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	4510.00	−	7811.55i	0.201961	−	0.349806i
$794$		0			0
$795$	−6696.00	−	11597.8i	−0.298720	−	0.517399i
$796$		0			0
$797$	−6594.00			−0.293063			−0.146532	−	0.989206i	$-0.546811\pi$
$797$	−6594.00			−0.293063			−0.146532	+	0.989206i	$0.546811\pi$
$798$		0			0
$799$	−5760.00			−0.255036
$800$		0			0
$801$	−7689.00	−	13317.7i	−0.339173	−	0.587465i
$802$		0			0
$803$	−3300.00	+	5715.77i	−0.145024	+	0.251189i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−7836.00	+	13572.4i	−0.341809	+	0.592031i
$808$		0			0
$809$	21507.0	+	37251.2i	0.934667	+	1.61889i	0.775226	+	0.631684i	$0.217636\pi$
$809$	21507.0	+	37251.2i	0.934667	+	1.61889i	0.159441	+	0.987207i	$0.449031\pi$
$810$		0			0
$811$	−14164.0			−0.613274			−0.306637	−	0.951827i	$-0.599204\pi$
$811$	−14164.0			−0.613274			−0.306637	+	0.951827i	$0.599204\pi$
$812$		0			0
$813$	19520.0			0.842062
$814$		0			0
$815$	−6324.00	−	10953.5i	−0.271804	−	0.470778i
$816$		0			0
$817$	5848.00	−	10129.0i	0.250423	−	0.433745i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−17415.0	+	30163.7i	−0.740302	+	1.28224i	0.212056	+	0.977257i	$0.431984\pi$
$821$	−17415.0	+	30163.7i	−0.740302	+	1.28224i	−0.952358	+	0.304983i	$0.901349\pi$
$822$		0			0
$823$	−15508.0	−	26860.6i	−0.656835	−	1.13767i	−0.981430	−	0.191818i	$-0.938562\pi$
$823$	−15508.0	−	26860.6i	−0.656835	−	1.13767i	0.324596	−	0.945853i	$-0.394772\pi$
$824$		0			0
$825$	4272.00			0.180281
$826$		0			0
$827$	9876.00			0.415263			0.207631	−	0.978207i	$-0.433425\pi$
$827$	9876.00			0.415263			0.207631	+	0.978207i	$0.433425\pi$
$828$		0			0
$829$	1577.00	+	2731.44i	0.0660693	+	0.114435i	0.897168	−	0.441690i	$-0.145621\pi$
$829$	1577.00	+	2731.44i	0.0660693	+	0.114435i	−0.831099	+	0.556125i	$0.812287\pi$
$830$		0			0
$831$	7076.00	−	12256.0i	0.295384	−	0.511619i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	5832.00	−	10101.3i	0.241706	−	0.418647i
$836$		0			0
$837$	−8512.00	−	14743.2i	−0.351515	−	0.608841i
$838$		0			0
$839$	36936.0			1.51987			0.759936	−	0.649998i	$-0.225230\pi$
$839$	36936.0			1.51987			0.759936	+	0.649998i	$0.225230\pi$
$840$		0			0
$841$	36127.0			1.48128
$842$		0			0
$843$	10860.0	+	18810.1i	0.443699	+	0.768509i
$844$		0			0
$845$	−13581.0	+	23523.0i	−0.552900	+	0.957651i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	12872.0	−	22295.0i	0.520337	−	0.901250i
$850$		0			0
$851$	−11880.0	−	20576.8i	−0.478544	−	0.828863i
$852$		0			0
$853$	9638.00			0.386869			0.193434	−	0.981113i	$-0.438037\pi$
$853$	9638.00			0.386869			0.193434	+	0.981113i	$0.438037\pi$
$854$		0			0
$855$	−4488.00			−0.179516
$856$		0			0
$857$	−5133.00	−	8890.62i	−0.204597	−	0.354373i	0.745407	−	0.666610i	$-0.232255\pi$
$857$	−5133.00	−	8890.62i	−0.204597	−	0.354373i	−0.950004	+	0.312237i	$0.898922\pi$
$858$		0			0
$859$	2042.00	−	3536.85i	0.0811084	−	0.140484i	−0.822618	−	0.568595i	$-0.807487\pi$
$859$	2042.00	−	3536.85i	0.0811084	−	0.140484i	0.903726	+	0.428111i	$0.140821\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	96.0000	−	166.277i	0.00378665	−	0.00655867i	−0.864126	−	0.503276i	$-0.832128\pi$
$863$	96.0000	−	166.277i	0.00378665	−	0.00655867i	0.867913	+	0.496717i	$0.165461\pi$
$864$		0			0
$865$	4086.00	+	7077.16i	0.160611	+	0.278186i
$866$		0			0
$867$	−16052.0			−0.628783
$868$		0			0
$869$	2496.00			0.0974350
$870$		0			0
$871$	5740.00	+	9941.97i	0.223298	+	0.386763i
$872$		0			0
$873$	8723.00	−	15108.7i	0.338177	−	0.585740i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−9955.00	+	17242.6i	−0.383303	+	0.663900i	−0.991532	−	0.129862i	$-0.958547\pi$
$877$	−9955.00	+	17242.6i	−0.383303	+	0.663900i	0.608229	+	0.793761i	$0.291880\pi$
$878$		0			0
$879$	−2700.00	−	4676.54i	−0.103605	−	0.179449i
$880$		0			0
$881$	14802.0			0.566052			0.283026	−	0.959112i	$-0.408662\pi$
$881$	14802.0			0.566052			0.283026	+	0.959112i	$0.408662\pi$
$882$		0			0
$883$	−32548.0			−1.24046			−0.620231	−	0.784419i	$-0.712961\pi$
$883$	−32548.0			−1.24046			−0.620231	+	0.784419i	$0.712961\pi$
$884$		0			0
$885$	−6480.00	−	11223.7i	−0.246127	−	0.426305i
$886$		0			0
$887$	−732.000	+	1267.86i	−0.0277093	+	0.0479939i	−0.879548	−	0.475811i	$-0.842155\pi$
$887$	−732.000	+	1267.86i	−0.0277093	+	0.0479939i	0.851838	+	0.523805i	$0.175488\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−1866.00	+	3232.01i	−0.0701609	+	0.121522i
$892$		0			0
$893$	−6528.00	−	11306.8i	−0.244626	−	0.423705i
$894$		0			0
$895$	9576.00			0.357643
$896$		0			0
$897$	−70848.0			−2.63717
$898$		0			0
$899$	13776.0	+	23860.7i	0.511074	+	0.885206i
$900$		0			0
$901$	8370.00	−	14497.3i	0.309484	−	0.536042i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	5070.00	−	8781.50i	0.186224	−	0.322549i
$906$		0			0
$907$	24782.0	+	42923.7i	0.907247	+	1.57140i	0.817873	+	0.575399i	$0.195153\pi$
$907$	24782.0	+	42923.7i	0.907247	+	1.57140i	0.0893742	+	0.995998i	$0.471513\pi$
$908$		0			0
$909$	13662.0			0.498504
$910$		0			0
$911$	8448.00			0.307239			0.153619	−	0.988130i	$-0.450907\pi$
$911$	8448.00			0.307239			0.153619	+	0.988130i	$0.450907\pi$
$912$		0			0
$913$	3096.00	+	5362.43i	0.112226	+	0.194382i
$914$		0			0
$915$	−1320.00	+	2286.31i	−0.0476916	+	0.0826043i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−7300.00	+	12644.0i	−0.262029	+	0.453848i	−0.966781	−	0.255606i	$-0.917725\pi$
$919$	−7300.00	+	12644.0i	−0.262029	+	0.453848i	0.704752	+	0.709454i	$0.251058\pi$
$920$		0			0
$921$	−6664.00	−	11542.4i	−0.238422	−	0.412958i
$922$		0			0
$923$	68880.0			2.45635
$924$		0			0
$925$	−9790.00			−0.347993
$926$		0			0
$927$	3740.00	+	6477.87i	0.132511	+	0.229516i
$928$		0			0
$929$	10551.0	−	18274.9i	0.372623	−	0.645403i	−0.617345	−	0.786693i	$-0.711792\pi$
$929$	10551.0	−	18274.9i	0.372623	−	0.645403i	0.989968	+	0.141290i	$0.0451250\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	9456.00	−	16378.3i	0.331807	−	0.574706i
$934$		0			0
$935$	−1080.00	−	1870.61i	−0.0377752	−	0.0654285i
$936$		0			0
$937$	−20806.0			−0.725403			−0.362701	−	0.931905i	$-0.618146\pi$
$937$	−20806.0			−0.725403			−0.362701	+	0.931905i	$0.618146\pi$
$938$		0			0
$939$	20456.0			0.710923
$940$		0			0
$941$	−12255.0	−	21226.3i	−0.424550	−	0.735342i	0.571828	−	0.820373i	$-0.306234\pi$
$941$	−12255.0	−	21226.3i	−0.424550	−	0.735342i	−0.996378	+	0.0850311i	$0.972901\pi$
$942$		0			0
$943$	26568.0	−	46017.1i	0.917469	−	1.58910i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	22074.0	−	38233.3i	0.757454	−	1.31195i	−0.186692	−	0.982419i	$-0.559777\pi$
$947$	22074.0	−	38233.3i	0.757454	−	1.31195i	0.944145	−	0.329530i	$-0.106890\pi$
$948$		0			0
$949$	−22550.0	−	39057.7i	−0.771342	−	1.33600i
$950$		0			0
$951$	28824.0			0.982841
$952$		0			0
$953$	27114.0			0.921625			0.460812	−	0.887498i	$-0.347558\pi$
$953$	27114.0			0.921625			0.460812	+	0.887498i	$0.347558\pi$
$954$		0			0
$955$	−10656.0	−	18456.7i	−0.361068	−	0.625388i
$956$		0			0
$957$	5904.00	−	10226.0i	0.199424	−	0.345413i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	8623.50	−	14936.3i	0.289467	−	0.501371i
$962$		0			0
$963$	5478.00	+	9488.17i	0.183308	+	0.317500i
$964$		0			0
$965$	−16116.0			−0.537609
$966$		0			0
$967$	−10264.0			−0.341332			−0.170666	−	0.985329i	$-0.554592\pi$
$967$	−10264.0			−0.341332			−0.170666	+	0.985329i	$0.554592\pi$
$968$		0			0
$969$	4080.00	+	7066.77i	0.135262	+	0.234280i
$970$		0			0
$971$	−25734.0	+	44572.6i	−0.850508	+	1.47312i	0.0302424	+	0.999543i	$0.490372\pi$
$971$	−25734.0	+	44572.6i	−0.850508	+	1.47312i	−0.880750	+	0.473581i	$0.842961\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−14596.0	+	25281.0i	−0.479432	+	0.830400i
$976$		0			0
$977$	11895.0	+	20602.7i	0.389514	+	0.674657i	0.992384	−	0.123182i	$-0.0393098\pi$
$977$	11895.0	+	20602.7i	0.389514	+	0.674657i	−0.602871	+	0.797839i	$0.705976\pi$
$978$		0			0
$979$	16776.0			0.547664
$980$		0			0
$981$	−15202.0			−0.494763
$982$		0			0
$983$	−13212.0	−	22883.9i	−0.428685	−	0.742504i	0.568072	−	0.822979i	$-0.307690\pi$
$983$	−13212.0	−	22883.9i	−0.428685	−	0.742504i	−0.996757	+	0.0804749i	$0.974356\pi$
$984$		0			0
$985$	4230.00	−	7326.57i	0.136831	−	0.236999i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	18576.0	−	32174.6i	0.597252	−	1.03447i
$990$		0			0
$991$	−19744.0	−	34197.6i	−0.632885	−	1.09619i	−0.986959	−	0.160971i	$-0.948537\pi$
$991$	−19744.0	−	34197.6i	−0.632885	−	1.09619i	0.354074	−	0.935217i	$-0.384796\pi$
$992$		0			0
$993$	25040.0			0.800222
$994$		0			0
$995$	−17808.0			−0.567388
$996$		0			0
$997$	−15427.0	−	26720.3i	−0.490048	−	0.848788i	0.509886	−	0.860242i	$-0.329687\pi$
$997$	−15427.0	−	26720.3i	−0.490048	−	0.848788i	−0.999934	+	0.0114536i	$0.996354\pi$
$998$		0			0
$999$	8360.00	−	14479.9i	0.264763	−	0.458584i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.4.e.c.177.1		2
3.2	odd	2		1764.4.k.k.1549.1		2
7.2	even	3		28.4.a.b.1.1	✓	1
7.3	odd	6		196.4.e.d.165.1		2
7.4	even	3	inner	196.4.e.c.165.1		2
7.5	odd	6		196.4.a.b.1.1		1
7.6	odd	2		196.4.e.d.177.1		2
21.2	odd	6		252.4.a.c.1.1		1
21.5	even	6		1764.4.a.k.1.1		1
21.11	odd	6		1764.4.k.k.361.1		2
21.17	even	6		1764.4.k.e.361.1		2
21.20	even	2		1764.4.k.e.1549.1		2
28.19	even	6		784.4.a.n.1.1		1
28.23	odd	6		112.4.a.c.1.1		1
35.2	odd	12		700.4.e.f.449.1		2
35.9	even	6		700.4.a.e.1.1		1
35.23	odd	12		700.4.e.f.449.2		2
56.37	even	6		448.4.a.d.1.1		1
56.51	odd	6		448.4.a.m.1.1		1
84.23	even	6		1008.4.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.4.a.b.1.1	✓	1	7.2	even	3
112.4.a.c.1.1		1	28.23	odd	6
196.4.a.b.1.1		1	7.5	odd	6
196.4.e.c.165.1		2	7.4	even	3	inner
196.4.e.c.177.1		2	1.1	even	1	trivial
196.4.e.d.165.1		2	7.3	odd	6
196.4.e.d.177.1		2	7.6	odd	2
252.4.a.c.1.1		1	21.2	odd	6
448.4.a.d.1.1		1	56.37	even	6
448.4.a.m.1.1		1	56.51	odd	6
700.4.a.e.1.1		1	35.9	even	6
700.4.e.f.449.1		2	35.2	odd	12
700.4.e.f.449.2		2	35.23	odd	12
784.4.a.n.1.1		1	28.19	even	6
1008.4.a.f.1.1		1	84.23	even	6
1764.4.a.k.1.1		1	21.5	even	6
1764.4.k.e.361.1		2	21.17	even	6
1764.4.k.e.1549.1		2	21.20	even	2
1764.4.k.k.361.1		2	21.11	odd	6
1764.4.k.k.1549.1		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	196.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 3.46410i) q^{3} +(-3.00000 + 5.19615i) q^{5} +(5.50000 - 9.52628i) q^{9} +(6.00000 + 10.3923i) q^{11} -82.0000 q^{13} +24.0000 q^{15} +(15.0000 + 25.9808i) q^{17} +(-34.0000 + 58.8897i) q^{19} +(-108.000 + 187.061i) q^{23} +(44.5000 + 77.0763i) q^{25} -152.000 q^{27} +246.000 q^{29} +(56.0000 + 96.9948i) q^{31} +(24.0000 - 41.5692i) q^{33} +(-55.0000 + 95.2628i) q^{37} +(164.000 + 284.056i) q^{39} -246.000 q^{41} -172.000 q^{43} +(33.0000 + 57.1577i) q^{45} +(-96.0000 + 166.277i) q^{47} +(60.0000 - 103.923i) q^{51} +(-279.000 - 483.242i) q^{53} -72.0000 q^{55} +272.000 q^{57} +(-270.000 - 467.654i) q^{59} +(-55.0000 + 95.2628i) q^{61} +(246.000 - 426.084i) q^{65} +(-70.0000 - 121.244i) q^{67} +864.000 q^{69} -840.000 q^{71} +(275.000 + 476.314i) q^{73} +(178.000 - 308.305i) q^{75} +(104.000 - 180.133i) q^{79} +(155.500 + 269.334i) q^{81} +516.000 q^{83} -180.000 q^{85} +(-492.000 - 852.169i) q^{87} +(699.000 - 1210.70i) q^{89} +(224.000 - 387.979i) q^{93} +(-204.000 - 353.338i) q^{95} +1586.00 q^{97} +132.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{3} - 6 q^{5} + 11 q^{9} + 12 q^{11} - 164 q^{13} + 48 q^{15} + 30 q^{17} - 68 q^{19} - 216 q^{23} + 89 q^{25} - 304 q^{27} + 492 q^{29} + 112 q^{31} + 48 q^{33} - 110 q^{37} + 328 q^{39} - 492 q^{41}+ \cdots + 264 q^{99}+O(q^{100}) \) 2 * q - 4 * q^3 - 6 * q^5 + 11 * q^9 + 12 * q^11 - 164 * q^13 + 48 * q^15 + 30 * q^17 - 68 * q^19 - 216 * q^23 + 89 * q^25 - 304 * q^27 + 492 * q^29 + 112 * q^31 + 48 * q^33 - 110 * q^37 + 328 * q^39 - 492 * q^41 - 344 * q^43 + 66 * q^45 - 192 * q^47 + 120 * q^51 - 558 * q^53 - 144 * q^55 + 544 * q^57 - 540 * q^59 - 110 * q^61 + 492 * q^65 - 140 * q^67 + 1728 * q^69 - 1680 * q^71 + 550 * q^73 + 356 * q^75 + 208 * q^79 + 311 * q^81 + 1032 * q^83 - 360 * q^85 - 984 * q^87 + 1398 * q^89 + 448 * q^93 - 408 * q^95 + 3172 * q^97 + 264 * q^99

Introduction

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