LMFDB - Embedded newform 196.4.e.c.165.1

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			165.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	196.165
Dual form			196.4.e.c.177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 + 3.46410i) q^{3} +(-3.00000 - 5.19615i) q^{5} +(5.50000 + 9.52628i) q^{9} +O(q^{10})$	\(q+(-2.00000 + 3.46410i) q^{3} +(-3.00000 - 5.19615i) q^{5} +(5.50000 + 9.52628i) q^{9} +(6.00000 - 10.3923i) q^{11} -82.0000 q^{13} +24.0000 q^{15} +(15.0000 - 25.9808i) q^{17} +(-34.0000 - 58.8897i) q^{19} +(-108.000 - 187.061i) q^{23} +(44.5000 - 77.0763i) q^{25} -152.000 q^{27} +246.000 q^{29} +(56.0000 - 96.9948i) q^{31} +(24.0000 + 41.5692i) q^{33} +(-55.0000 - 95.2628i) q^{37} +(164.000 - 284.056i) q^{39} -246.000 q^{41} -172.000 q^{43} +(33.0000 - 57.1577i) q^{45} +(-96.0000 - 166.277i) q^{47} +(60.0000 + 103.923i) q^{51} +(-279.000 + 483.242i) q^{53} -72.0000 q^{55} +272.000 q^{57} +(-270.000 + 467.654i) q^{59} +(-55.0000 - 95.2628i) q^{61} +(246.000 + 426.084i) q^{65} +(-70.0000 + 121.244i) q^{67} +864.000 q^{69} -840.000 q^{71} +(275.000 - 476.314i) q^{73} +(178.000 + 308.305i) q^{75} +(104.000 + 180.133i) q^{79} +(155.500 - 269.334i) q^{81} +516.000 q^{83} -180.000 q^{85} +(-492.000 + 852.169i) q^{87} +(699.000 + 1210.70i) q^{89} +(224.000 + 387.979i) q^{93} +(-204.000 + 353.338i) q^{95} +1586.00 q^{97} +132.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{3} - 6 q^{5} + 11 q^{9}+O(q^{10}) $ 2 * q - 4 * q^3 - 6 * q^5 + 11 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$99$	$101$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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	−0.991755	−	0.128146i	$-0.959097\pi$
$3$	−2.00000	+	3.46410i	−0.384900	+	0.666667i	0.606855	+	0.794812i	$0.292431\pi$
$4$		0			0
$5$	−3.00000	−	5.19615i	−0.268328	−	0.464758i	0.700102	−	0.714043i	$-0.253138\pi$
$5$	−3.00000	−	5.19615i	−0.268328	−	0.464758i	−0.968430	+	0.249285i	$0.919804\pi$
$6$		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	−0.772003	−	0.635619i	$-0.780745\pi$
$11$	6.00000	−	10.3923i	0.164461	−	0.284854i	0.936464	+	0.350765i	$0.114078\pi$
$12$		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	−0.738961	−	0.673748i	$-0.764683\pi$
$17$	15.0000	−	25.9808i	0.214002	−	0.370662i	0.952963	+	0.303085i	$0.0980168\pi$
$18$		0			0
$19$	−34.0000	−	58.8897i	−0.410533	−	0.711065i	0.584415	−	0.811455i	$-0.301324\pi$
$19$	−34.0000	−	58.8897i	−0.410533	−	0.711065i	−0.994948	+	0.100390i	$0.967991\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−108.000	−	187.061i	−0.979111	−	1.69587i	−0.665641	−	0.746272i	$-0.731842\pi$
$23$	−108.000	−	187.061i	−0.979111	−	1.69587i	−0.313470	−	0.949598i	$-0.601492\pi$
$24$		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	−0.656952	−	0.753932i	$-0.728155\pi$
$31$	56.0000	−	96.9948i	0.324448	−	0.561961i	0.981401	+	0.191971i	$0.0614880\pi$
$32$		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	0.717579	−	0.696477i	$-0.245250\pi$
$37$	−55.0000	−	95.2628i	−0.244377	−	0.423273i	−0.961956	+	0.273204i	$0.911917\pi$
$38$		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	0.677727	−	0.735314i	$-0.262965\pi$
$47$	−96.0000	−	166.277i	−0.297937	−	0.516042i	−0.975664	+	0.219272i	$0.929632\pi$
$48$		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	0.236670	+	0.971590i	$0.423944\pi$
$53$	−279.000	+	483.242i	−0.723087	+	1.25242i	−0.959757	+	0.280833i	$0.909389\pi$
$54$		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	0.397657	+	0.917534i	$0.369824\pi$
$59$	−270.000	+	467.654i	−0.595780	+	1.03192i	−0.993436	+	0.114386i	$0.963510\pi$
$60$		0			0
$61$	−55.0000	−	95.2628i	−0.115443	−	0.199953i	0.802514	−	0.596634i	$-0.203495\pi$
$61$	−55.0000	−	95.2628i	−0.115443	−	0.199953i	−0.917957	+	0.396680i	$0.870162\pi$
$62$		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	−0.922762	−	0.385371i	$-0.874073\pi$
$67$	−70.0000	+	121.244i	−0.127640	+	0.221078i	0.795122	+	0.606450i	$0.207407\pi$
$68$		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	−0.556849	−	0.830614i	$-0.687990\pi$
$73$	275.000	−	476.314i	0.440908	−	0.763676i	0.997757	+	0.0669381i	$0.0213230\pi$
$74$		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	0.930530	−	0.366216i	$-0.119347\pi$
$79$	104.000	+	180.133i	0.148113	+	0.256539i	−0.782417	+	0.622755i	$0.786013\pi$
$80$		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	0.896038	+	0.443978i	$0.146433\pi$
$89$	699.000	+	1210.70i	0.832515	+	1.44196i	−0.0635224	+	0.997980i	$0.520233\pi$
$90$		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	−0.379137	−	0.925341i	$-0.623779\pi$
$101$	621.000	−	1075.60i	0.611800	−	1.05967i	0.990937	−	0.134328i	$-0.0428876\pi$
$102$		0			0
$103$	−340.000	−	588.897i	−0.325254	−	0.563357i	0.656309	−	0.754492i	$-0.272117\pi$
$103$	−340.000	−	588.897i	−0.325254	−	0.563357i	−0.981564	+	0.191135i	$0.938783\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−498.000	−	862.561i	−0.449939	−	0.779317i	0.548442	−	0.836188i	$-0.315221\pi$
$107$	−498.000	−	862.561i	−0.449939	−	0.779317i	−0.998382	+	0.0568710i	$0.981888\pi$
$108$		0			0
$109$	−691.000	+	1196.85i	−0.607209	+	1.05172i	0.384489	+	0.923130i	$0.374378\pi$
$109$	−691.000	+	1196.85i	−0.607209	+	1.05172i	−0.991698	+	0.128588i	$0.958956\pi$
$110$		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	0.999823	+	0.0188305i	$0.00599429\pi$
$131$	774.000	+	1340.61i	0.516219	+	0.894118i	−0.483604	+	0.875287i	$0.660672\pi$
$132$		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	−0.918921	−	0.394442i	$-0.870938\pi$
$137$	−189.000	+	327.358i	−0.117864	+	0.204146i	0.801057	+	0.598588i	$0.204271\pi$
$138$		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	0.725991	−	0.687704i	$-0.241381\pi$
$149$	−423.000	−	732.657i	−0.232574	−	0.402830i	−0.958565	+	0.284874i	$0.908048\pi$
$150$		0			0
$151$	1268.00	−	2196.24i	0.683367	−	1.18363i	−0.290580	−	0.956851i	$-0.593848\pi$
$151$	1268.00	−	2196.24i	0.683367	−	1.18363i	0.973947	−	0.226775i	$-0.0728183\pi$
$152$		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	−0.675020	−	0.737799i	$-0.735865\pi$
$157$	593.000	−	1027.11i	0.301443	−	0.522115i	0.976463	+	0.215685i	$0.0691984\pi$
$158$		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	−0.999972	−	0.00749450i	$-0.997614\pi$
$163$	−1054.00	−	1825.58i	−0.506476	−	0.877243i	0.493496	−	0.869748i	$-0.335719\pi$
$164$		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	0.975971	−	0.217898i	$-0.0699201\pi$
$173$	681.000	+	1179.53i	0.299280	+	0.518368i	−0.676691	+	0.736267i	$0.736587\pi$
$174$		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	−0.983140	−	0.182854i	$-0.941467\pi$
$179$	−798.000	+	1382.18i	−0.333214	+	0.577144i	0.649926	+	0.759997i	$0.274800\pi$
$180$		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	−0.977104	−	0.212764i	$-0.931753\pi$
$191$	−1776.00	−	3076.12i	−0.672811	−	1.16534i	0.304293	−	0.952579i	$-0.401580\pi$
$192$		0			0
$193$	1343.00	−	2326.14i	0.500887	−	0.867562i	−0.499112	−	0.866537i	$-0.666340\pi$
$193$	1343.00	−	2326.14i	0.500887	−	0.867562i	0.999999	−	0.00102491i	$-0.000326238\pi$
$194$		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	−0.470810	−	0.882235i	$-0.656038\pi$
$199$	1484.00	−	2570.36i	0.528633	−	0.915619i	0.999443	−	0.0333844i	$-0.0106286\pi$
$200$		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	0.145296	+	0.989388i	$0.453587\pi$
$227$	−2682.00	+	4645.36i	−0.784188	+	1.35825i	−0.929483	+	0.368865i	$0.879747\pi$
$228$		0			0
$229$	437.000	+	756.906i	0.126104	+	0.218418i	0.922164	−	0.386799i	$-0.126419\pi$
$229$	437.000	+	756.906i	0.126104	+	0.218418i	−0.796060	+	0.605218i	$0.793086\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−189.000	−	327.358i	−0.0531408	−	0.0920425i	0.838231	−	0.545315i	$-0.183590\pi$
$233$	−189.000	−	327.358i	−0.0531408	−	0.0920425i	−0.891372	+	0.453272i	$0.850257\pi$
$234$		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	0.418151	+	0.908378i	$0.362678\pi$
$241$	−2161.00	+	3742.96i	−0.577603	+	1.00044i	−0.995754	+	0.0920596i	$0.970655\pi$
$242$		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	0.989279	+	0.146039i	$0.0466525\pi$
$257$	2559.00	+	4432.32i	0.621113	+	1.07580i	−0.368166	+	0.929760i	$0.620014\pi$
$258$		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	−0.997817	−	0.0660355i	$-0.978965\pi$
$263$	−1884.00	+	3263.18i	−0.441720	+	0.765082i	0.556097	+	0.831117i	$0.312298\pi$
$264$		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	−0.997984	−	0.0634719i	$-0.979783\pi$
$269$	−1959.00	+	3393.09i	−0.444024	+	0.769071i	0.553960	+	0.832543i	$0.313116\pi$
$270$		0			0
$271$	−2440.00	−	4226.20i	−0.546935	−	0.947320i	−0.998482	−	0.0550723i	$-0.982461\pi$
$271$	−2440.00	−	4226.20i	−0.546935	−	0.947320i	0.451547	−	0.892247i	$-0.350872\pi$
$272$		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	−0.607875	−	0.794032i	$-0.707978\pi$
$277$	1769.00	−	3064.00i	0.383714	−	0.664613i	0.991590	+	0.129419i	$0.0413114\pi$
$278$		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	−0.300257	−	0.953858i	$-0.597072\pi$
$283$	3218.00	−	5573.74i	0.675937	−	1.17076i	0.976194	−	0.216899i	$-0.0695943\pi$
$284$		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	−0.565933	−	0.824451i	$-0.691484\pi$
$311$	2364.00	−	4094.57i	0.431029	−	0.746565i	0.996962	+	0.0778865i	$0.0248172\pi$
$312$		0			0
$313$	−2557.00	−	4428.85i	−0.461758	−	0.799788i	0.537291	−	0.843397i	$-0.319448\pi$
$313$	−2557.00	−	4428.85i	−0.461758	−	0.799788i	−0.999049	+	0.0436091i	$0.986114\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3603.00	−	6240.58i	−0.638374	−	1.10570i	−0.985790	−	0.167985i	$-0.946274\pi$
$317$	−3603.00	−	6240.58i	−0.638374	−	1.10570i	0.347415	−	0.937711i	$-0.387059\pi$
$318$		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	−0.999736	−	0.0229685i	$-0.992688\pi$
$331$	−3130.00	−	5421.32i	−0.519759	−	0.900250i	0.479977	−	0.877281i	$-0.340645\pi$
$332$		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	−0.867414	−	0.497586i	$-0.834220\pi$
$347$	−18.0000	+	31.1769i	−0.00278470	+	0.00482324i	0.864630	+	0.502410i	$0.167553\pi$
$348$		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	−0.908279	−	0.418366i	$-0.862603\pi$
$353$	−609.000	+	1054.82i	−0.0918238	+	0.159043i	0.816455	+	0.577409i	$0.195936\pi$
$354$		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	0.954434	+	0.298421i	$0.0964600\pi$
$359$	5004.00	+	8667.18i	0.735657	+	1.27420i	−0.218777	+	0.975775i	$0.570207\pi$
$360$		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	−0.825387	−	0.564568i	$-0.809043\pi$
$367$	536.000	−	928.379i	0.0762370	−	0.132046i	0.901624	+	0.432522i	$0.142376\pi$
$368$		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	0.875378	−	0.483440i	$-0.160613\pi$
$373$	137.000	+	237.291i	0.0190177	+	0.0329396i	−0.856360	+	0.516379i	$0.827279\pi$
$374$		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	0.784945	−	0.619566i	$-0.212691\pi$
$383$	−1080.00	−	1870.61i	−0.144087	−	0.249566i	−0.929032	+	0.369999i	$0.879358\pi$
$384$		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	−0.828905	−	0.559389i	$-0.811036\pi$
$389$	537.000	−	930.111i	0.0699922	−	0.121230i	0.898898	+	0.438159i	$0.144369\pi$
$390$		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	0.559728	−	0.828676i	$-0.310906\pi$
$397$	−3463.00	−	5998.09i	−0.437791	−	0.758276i	−0.997519	+	0.0704004i	$0.977572\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−969.000	−	1678.36i	−0.120672	−	0.209010i	0.799361	−	0.600851i	$-0.205172\pi$
$401$	−969.000	−	1678.36i	−0.120672	−	0.209010i	−0.920033	+	0.391841i	$0.871838\pi$
$402$		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	−0.416892	−	0.908956i	$-0.636881\pi$
$409$	4787.00	−	8291.33i	0.578733	−	1.00240i	0.995625	−	0.0934393i	$-0.0297861\pi$
$410$		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	−0.921099	−	0.389327i	$-0.872708\pi$
$431$	−1104.00	+	1912.18i	−0.123382	+	0.213705i	0.797717	+	0.603032i	$0.206041\pi$
$432$		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	−0.973732	−	0.227696i	$-0.926881\pi$
$439$	−6292.00	−	10898.1i	−0.684056	−	1.18482i	0.289676	−	0.957125i	$-0.406452\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3498.00	−	6058.71i	−0.375158	−	0.649793i	0.615193	−	0.788377i	$-0.289078\pi$
$443$	−3498.00	−	6058.71i	−0.375158	−	0.649793i	−0.990351	+	0.138584i	$0.955745\pi$
$444$		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	0.679121	−	0.734026i	$-0.262361\pi$
$457$	−2893.00	−	5010.82i	−0.296124	−	0.512902i	−0.975246	+	0.221123i	$0.929028\pi$
$458$		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	0.962284	−	0.272047i	$-0.0877007\pi$
$467$	2478.00	+	4292.02i	0.245542	+	0.425291i	−0.716742	+	0.697339i	$0.754367\pi$
$468$		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	0.328034	−	0.944666i	$-0.393614\pi$
$479$	10296.0	−	17833.2i	0.982122	−	1.70108i	0.654088	−	0.756418i	$-0.273053\pi$
$480$		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	−0.363649	−	0.931536i	$-0.618469\pi$
$487$	6716.00	−	11632.5i	0.624910	−	1.08238i	0.988558	−	0.150839i	$-0.0481975\pi$
$488$		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	0.968128	−	0.250457i	$-0.0805809\pi$
$499$	2978.00	+	5158.05i	0.267162	+	0.462737i	−0.700966	+	0.713195i	$0.747248\pi$
$500$		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	0.729903	−	0.683550i	$-0.239565\pi$
$509$	−2607.00	−	4515.46i	−0.227020	−	0.393210i	−0.956924	+	0.290340i	$0.906232\pi$
$510$		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	−0.835139	−	0.550039i	$-0.814613\pi$
$521$	699.000	−	1210.70i	0.0587788	−	0.101808i	0.893917	+	0.448232i	$0.147946\pi$
$522$		0			0
$523$	9290.00	+	16090.8i	0.776718	+	1.34531i	0.933824	+	0.357733i	$0.116450\pi$
$523$	9290.00	+	16090.8i	0.776718	+	1.34531i	−0.157106	+	0.987582i	$0.550217\pi$
$524$		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	0.945981	+	0.324221i	$0.105102\pi$
$541$	9485.00	+	16428.5i	0.753774	+	1.30558i	−0.192207	+	0.981354i	$0.561564\pi$
$542$		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	−0.979665	−	0.200640i	$-0.935698\pi$
$557$	−4155.00	+	7196.67i	−0.316074	+	0.547456i	0.663592	+	0.748095i	$0.269031\pi$
$558$		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	−0.967680	−	0.252180i	$-0.918853\pi$
$563$	−3546.00	+	6141.85i	−0.265446	+	0.459766i	0.702234	+	0.711946i	$0.252186\pi$
$564$		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	0.967220	−	0.253942i	$-0.0817271\pi$
$569$	3579.00	+	6199.01i	0.263690	+	0.456724i	−0.703530	+	0.710666i	$0.748394\pi$
$570$		0			0
$571$	−3250.00	+	5629.17i	−0.238193	+	0.412563i	−0.960196	−	0.279328i	$-0.909888\pi$
$571$	−3250.00	+	5629.17i	−0.238193	+	0.412563i	0.722003	+	0.691890i	$0.243222\pi$
$572$		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	0.142050	+	0.989859i	$0.454631\pi$
$577$	−10897.0	+	18874.2i	−0.786218	+	1.36177i	−0.928268	+	0.371911i	$0.878703\pi$
$578$		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	0.752965	−	0.658060i	$-0.228623\pi$
$593$	−2793.00	−	4837.62i	−0.193414	−	0.335004i	−0.946380	+	0.323057i	$0.895290\pi$
$594$		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	−0.865616	−	0.500709i	$-0.833073\pi$
$599$	12.0000	−	20.7846i	0.000818542	−	0.00141776i	0.866434	+	0.499291i	$0.166406\pi$
$600$		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	0.688730	−	0.725018i	$-0.258169\pi$
$607$	−4240.00	−	7343.90i	−0.283519	−	0.491070i	−0.972249	+	0.233948i	$0.924835\pi$
$608$		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	−0.832921	−	0.553393i	$-0.813333\pi$
$613$	953.000	−	1650.64i	0.0627917	−	0.108758i	0.895712	+	0.444634i	$0.146666\pi$
$614$		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	−0.721739	−	0.692165i	$-0.756657\pi$
$619$	3674.00	−	6363.55i	0.238563	−	0.413203i	0.960302	+	0.278962i	$0.0899903\pi$
$620$		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	−0.380994	−	0.924577i	$-0.624418\pi$
$641$	9903.00	−	17152.5i	0.610211	−	1.05692i	0.991205	−	0.132338i	$-0.0422485\pi$
$642$		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	0.00681018	+	0.999977i	$0.497832\pi$
$647$	−14196.0	+	24588.2i	−0.862600	+	1.49407i	−0.869410	+	0.494091i	$0.835501\pi$
$648$		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	0.999533	+	0.0305554i	$0.00972761\pi$
$653$	8781.00	+	15209.1i	0.526228	+	0.911454i	−0.473305	+	0.880899i	$0.656939\pi$
$654$		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	−0.308292	−	0.951292i	$-0.599757\pi$
$661$	11381.0	−	19712.5i	0.669697	−	1.15995i	0.977989	−	0.208657i	$-0.0669093\pi$
$662$		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	−0.990916	−	0.134480i	$-0.957064\pi$
$677$	−10779.0	−	18669.8i	−0.611921	−	1.05988i	0.378995	−	0.925399i	$-0.376270\pi$
$678$		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	−0.914099	−	0.405491i	$-0.867101\pi$
$683$	−1890.00	+	3273.58i	−0.105884	+	0.183397i	0.808215	+	0.588888i	$0.200434\pi$
$684$		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	0.931741	−	0.363123i	$-0.118290\pi$
$691$	2750.00	+	4763.14i	0.151396	+	0.262226i	−0.780345	+	0.625350i	$0.784956\pi$
$692$		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	0.698949	−	0.715172i	$-0.253652\pi$
$709$	−5095.00	−	8824.80i	−0.269883	−	0.467450i	−0.968831	+	0.247721i	$0.920318\pi$
$710$		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	0.717856	−	0.696191i	$-0.245123\pi$
$719$	−4704.00	−	8147.57i	−0.243991	−	0.422605i	−0.961847	+	0.273586i	$0.911790\pi$
$720$		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	0.934610	−	0.355674i	$-0.115749\pi$
$733$	3161.00	+	5475.01i	0.159283	+	0.275886i	−0.775328	+	0.631559i	$0.782415\pi$
$734$		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	−0.483630	−	0.875272i	$-0.660682\pi$
$739$	10370.0	−	17961.4i	0.516193	−	0.894072i	0.999823	−	0.0188001i	$-0.00598461\pi$
$740$		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	0.978741	−	0.205100i	$-0.0657520\pi$
$751$	6416.00	+	11112.8i	0.311749	+	0.539964i	−0.666992	+	0.745064i	$0.732419\pi$
$752$		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	0.707540	−	0.706674i	$-0.249805\pi$
$761$	−5421.00	−	9389.45i	−0.258227	−	0.447263i	−0.965767	+	0.259411i	$0.916472\pi$
$762$		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	−0.194069	−	0.980988i	$-0.562169\pi$
$773$	16173.0	−	28012.5i	0.752526	−	1.30341i	0.946595	−	0.322425i	$-0.104498\pi$
$774$		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	0.292327	+	0.956318i	$0.405570\pi$
$787$	−15058.0	+	26081.2i	−0.682033	+	1.18132i	−0.974360	+	0.224997i	$0.927763\pi$
$788$		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	0.159441	−	0.987207i	$-0.449031\pi$
$809$	21507.0	−	37251.2i	0.934667	−	1.61889i	0.775226	−	0.631684i	$-0.217636\pi$
$810$		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	−0.952358	−	0.304983i	$-0.901349\pi$
$821$	−17415.0	−	30163.7i	−0.740302	−	1.28224i	0.212056	−	0.977257i	$-0.431984\pi$
$822$		0			0
$823$	−15508.0	+	26860.6i	−0.656835	+	1.13767i	0.324596	+	0.945853i	$0.394772\pi$
$823$	−15508.0	+	26860.6i	−0.656835	+	1.13767i	−0.981430	+	0.191818i	$0.938562\pi$
$824$		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	−0.831099	−	0.556125i	$-0.812287\pi$
$829$	1577.00	−	2731.44i	0.0660693	−	0.114435i	0.897168	+	0.441690i	$0.145621\pi$
$830$		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	−0.950004	−	0.312237i	$-0.898922\pi$
$857$	−5133.00	+	8890.62i	−0.204597	+	0.354373i	0.745407	+	0.666610i	$0.232255\pi$
$858$		0			0
$859$	2042.00	+	3536.85i	0.0811084	+	0.140484i	0.903726	−	0.428111i	$-0.140821\pi$
$859$	2042.00	+	3536.85i	0.0811084	+	0.140484i	−0.822618	+	0.568595i	$0.807487\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	96.0000	+	166.277i	0.00378665	+	0.00655867i	0.867913	−	0.496717i	$-0.165461\pi$
$863$	96.0000	+	166.277i	0.00378665	+	0.00655867i	−0.864126	+	0.503276i	$0.832128\pi$
$864$		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	0.608229	−	0.793761i	$-0.291880\pi$
$877$	−9955.00	−	17242.6i	−0.383303	−	0.663900i	−0.991532	+	0.129862i	$0.958547\pi$
$878$		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	0.851838	−	0.523805i	$-0.175488\pi$
$887$	−732.000	−	1267.86i	−0.0277093	−	0.0479939i	−0.879548	+	0.475811i	$0.842155\pi$
$888$		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	0.0893742	−	0.995998i	$-0.471513\pi$
$907$	24782.0	−	42923.7i	0.907247	−	1.57140i	0.817873	−	0.575399i	$-0.195153\pi$
$908$		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	0.704752	−	0.709454i	$-0.251058\pi$
$919$	−7300.00	−	12644.0i	−0.262029	−	0.453848i	−0.966781	+	0.255606i	$0.917725\pi$
$920$		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	0.989968	−	0.141290i	$-0.0451250\pi$
$929$	10551.0	+	18274.9i	0.372623	+	0.645403i	−0.617345	+	0.786693i	$0.711792\pi$
$930$		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	−0.996378	−	0.0850311i	$-0.972901\pi$
$941$	−12255.0	+	21226.3i	−0.424550	+	0.735342i	0.571828	+	0.820373i	$0.306234\pi$
$942$		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	0.944145	+	0.329530i	$0.106890\pi$
$947$	22074.0	+	38233.3i	0.757454	+	1.31195i	−0.186692	+	0.982419i	$0.559777\pi$
$948$		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	−0.880750	−	0.473581i	$-0.842961\pi$
$971$	−25734.0	−	44572.6i	−0.850508	−	1.47312i	0.0302424	−	0.999543i	$-0.490372\pi$
$972$		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	−0.602871	−	0.797839i	$-0.705976\pi$
$977$	11895.0	−	20602.7i	0.389514	−	0.674657i	0.992384	+	0.123182i	$0.0393098\pi$
$978$		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	−0.996757	−	0.0804749i	$-0.974356\pi$
$983$	−13212.0	+	22883.9i	−0.428685	+	0.742504i	0.568072	+	0.822979i	$0.307690\pi$
$984$		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	0.354074	+	0.935217i	$0.384796\pi$
$991$	−19744.0	+	34197.6i	−0.632885	+	1.09619i	−0.986959	+	0.160971i	$0.948537\pi$
$992$		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	−0.999934	−	0.0114536i	$-0.996354\pi$
$997$	−15427.0	+	26720.3i	−0.490048	+	0.848788i	0.509886	+	0.860242i	$0.329687\pi$
$998$		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.165.1		2
3.2	odd	2		1764.4.k.k.361.1		2
7.2	even	3	inner	196.4.e.c.177.1		2
7.3	odd	6		196.4.a.b.1.1		1
7.4	even	3		28.4.a.b.1.1	✓	1
7.5	odd	6		196.4.e.d.177.1		2
7.6	odd	2		196.4.e.d.165.1		2
21.2	odd	6		1764.4.k.k.1549.1		2
21.5	even	6		1764.4.k.e.1549.1		2
21.11	odd	6		252.4.a.c.1.1		1
21.17	even	6		1764.4.a.k.1.1		1
21.20	even	2		1764.4.k.e.361.1		2
28.3	even	6		784.4.a.n.1.1		1
28.11	odd	6		112.4.a.c.1.1		1
35.4	even	6		700.4.a.e.1.1		1
35.18	odd	12		700.4.e.f.449.2		2
35.32	odd	12		700.4.e.f.449.1		2
56.11	odd	6		448.4.a.m.1.1		1
56.53	even	6		448.4.a.d.1.1		1
84.11	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	7.4	even	3
112.4.a.c.1.1		1	28.11	odd	6
196.4.a.b.1.1		1	7.3	odd	6
196.4.e.c.165.1		2	1.1	even	1	trivial
196.4.e.c.177.1		2	7.2	even	3	inner
196.4.e.d.165.1		2	7.6	odd	2
196.4.e.d.177.1		2	7.5	odd	6
252.4.a.c.1.1		1	21.11	odd	6
448.4.a.d.1.1		1	56.53	even	6
448.4.a.m.1.1		1	56.11	odd	6
700.4.a.e.1.1		1	35.4	even	6
700.4.e.f.449.1		2	35.32	odd	12
700.4.e.f.449.2		2	35.18	odd	12
784.4.a.n.1.1		1	28.3	even	6
1008.4.a.f.1.1		1	84.11	even	6
1764.4.a.k.1.1		1	21.17	even	6
1764.4.k.e.361.1		2	21.20	even	2
1764.4.k.e.1549.1		2	21.5	even	6
1764.4.k.k.361.1		2	3.2	odd	2
1764.4.k.k.1549.1		2	21.2	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 3.46410i) q^{3} +(-3.00000 - 5.19615i) q^{5} +(5.50000 + 9.52628i) q^{9} +O(q^{10})\)	\(q+(-2.00000 + 3.46410i) q^{3} +(-3.00000 - 5.19615i) q^{5} +(5.50000 + 9.52628i) q^{9} +(6.00000 - 10.3923i) q^{11} -82.0000 q^{13} +24.0000 q^{15} +(15.0000 - 25.9808i) q^{17} +(-34.0000 - 58.8897i) q^{19} +(-108.000 - 187.061i) q^{23} +(44.5000 - 77.0763i) q^{25} -152.000 q^{27} +246.000 q^{29} +(56.0000 - 96.9948i) q^{31} +(24.0000 + 41.5692i) q^{33} +(-55.0000 - 95.2628i) q^{37} +(164.000 - 284.056i) q^{39} -246.000 q^{41} -172.000 q^{43} +(33.0000 - 57.1577i) q^{45} +(-96.0000 - 166.277i) q^{47} +(60.0000 + 103.923i) q^{51} +(-279.000 + 483.242i) q^{53} -72.0000 q^{55} +272.000 q^{57} +(-270.000 + 467.654i) q^{59} +(-55.0000 - 95.2628i) q^{61} +(246.000 + 426.084i) q^{65} +(-70.0000 + 121.244i) q^{67} +864.000 q^{69} -840.000 q^{71} +(275.000 - 476.314i) q^{73} +(178.000 + 308.305i) q^{75} +(104.000 + 180.133i) q^{79} +(155.500 - 269.334i) q^{81} +516.000 q^{83} -180.000 q^{85} +(-492.000 + 852.169i) q^{87} +(699.000 + 1210.70i) q^{89} +(224.000 + 387.979i) q^{93} +(-204.000 + 353.338i) q^{95} +1586.00 q^{97} +132.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{3} - 6 q^{5} + 11 q^{9}+O(q^{10}) \) 2 * q - 4 * q^3 - 6 * q^5 + 11 * q^9	\( 2 q - 4 q^{3} - 6 q^{5} + 11 q^{9} + 12 q^{11} - 164 q^{13} + 48 q^{15} + 30 q^{17} - 68 q^{19} - 216 q^{23} + 89 q^{25} - 304 q^{27} + 492 q^{29} + 112 q^{31} + 48 q^{33} - 110 q^{37} + 328 q^{39} - 492 q^{41} - 344 q^{43} + 66 q^{45} - 192 q^{47} + 120 q^{51} - 558 q^{53} - 144 q^{55} + 544 q^{57} - 540 q^{59} - 110 q^{61} + 492 q^{65} - 140 q^{67} + 1728 q^{69} - 1680 q^{71} + 550 q^{73} + 356 q^{75} + 208 q^{79} + 311 q^{81} + 1032 q^{83} - 360 q^{85} - 984 q^{87} + 1398 q^{89} + 448 q^{93} - 408 q^{95} + 3172 q^{97} + 264 q^{99}+O(q^{100}) \) 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

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