LMFDB - Embedded newform 832.2.ba.i.225.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [832,2,Mod(225,832)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(832, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("832.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 832 = 2^{6} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	832.ba (of order $6$, degree $2$, 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:	$6.64355344817$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.752609431977984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 15x^{10} + 90x^{8} - 247x^{6} + 270x^{4} + 21x^{2} + 49 $ x^12 - 15x^10 + 90x^8 - 247x^6 + 270x^4 + 21*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			225.3
Root			$1.75780 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	832.225
Dual form			832.2.ba.i.673.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.16037 - 0.669938i) q^{3} +3.88448 q^{5} +(2.20369 - 1.27230i) q^{7} +(-0.602365 - 1.04333i) q^{9} +(0.571683 - 0.990185i) q^{11} +(1.00000 - 3.46410i) q^{13} +(-4.50743 - 2.60236i) q^{15} +(3.44224 + 5.96214i) q^{17} +(-3.93574 - 6.81691i) q^{19} -3.40946 q^{21} +(-3.93574 + 6.81691i) q^{23} +10.0892 q^{25} +5.63382i q^{27} +(-2.51963 - 1.45471i) q^{29} -2.00000i q^{31} +(-1.32673 + 0.765985i) q^{33} +(8.56021 - 4.94224i) q^{35} +(-1.78212 + 3.08672i) q^{37} +(-3.48110 + 3.34969i) q^{39} +(-1.32673 - 0.765985i) q^{41} +(7.88849 - 4.55442i) q^{43} +(-2.33988 - 4.05279i) q^{45} -2.11552i q^{47} +(-0.262488 + 0.454643i) q^{49} -9.22436i q^{51} -9.01486i q^{53} +(2.22069 - 3.84636i) q^{55} +10.5468i q^{57} +(2.79238 + 4.83654i) q^{59} +(-1.50000 + 0.866025i) q^{61} +(-2.65486 - 1.53278i) q^{63} +(3.88448 - 13.4562i) q^{65} +(-2.20369 + 3.81691i) q^{67} +(9.13382 - 5.27341i) q^{69} +(-3.24702 + 1.87467i) q^{71} -11.3696i q^{73} +(-11.7072 - 6.75915i) q^{75} -2.90942i q^{77} +7.90549 q^{79} +(1.96722 - 3.40732i) q^{81} +8.10557 q^{83} +(13.3713 + 23.1598i) q^{85} +(1.94913 + 3.37599i) q^{87} +(2.51963 + 1.45471i) q^{89} +(-2.20369 - 8.90612i) q^{91} +(-1.33988 + 2.32073i) q^{93} +(-15.2883 - 26.4802i) q^{95} +(1.50000 - 0.866025i) q^{97} -1.37745 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{9} + 12 q^{13} + 18 q^{17} + 36 q^{21} + 36 q^{25} - 18 q^{29} + 54 q^{33} + 6 q^{37} + 54 q^{41} - 24 q^{45} + 12 q^{49} - 18 q^{61} - 18 q^{69} - 30 q^{81} + 48 q^{85} + 18 q^{89} - 12 q^{93}+ \cdots + 18 q^{97}+O(q^{100}) $ 12 * q + 12 * q^9 + 12 * q^13 + 18 * q^17 + 36 * q^21 + 36 * q^25 - 18 * q^29 + 54 * q^33 + 6 * q^37 + 54 * q^41 - 24 * q^45 + 12 * q^49 - 18 * q^61 - 18 * q^69 - 30 * q^81 + 48 * q^85 + 18 * q^89 - 12 * q^93 + 18 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/832\mathbb{Z}\right)^\times$.

$n$	$261$	$703$	$769$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	−1.16037	−	0.669938i	−0.669938	−	0.386789i	0.126115	−	0.992016i	$-0.459749\pi$
$3$	−1.16037	−	0.669938i	−0.669938	−	0.386789i	−0.796053	+	0.605227i	$0.793083\pi$
$4$		0			0
$5$	3.88448			1.73719			0.868597	−	0.495519i	$-0.165022\pi$
$5$	3.88448			1.73719			0.868597	+	0.495519i	$0.165022\pi$
$6$		0			0
$7$	2.20369	−	1.27230i	0.832918	−	0.480885i	−0.0219327	−	0.999759i	$-0.506982\pi$
$7$	2.20369	−	1.27230i	0.832918	−	0.480885i	0.854851	+	0.518874i	$0.173649\pi$
$8$		0			0
$9$	−0.602365	−	1.04333i	−0.200788	−	0.347776i
$10$		0			0
$11$	0.571683	−	0.990185i	0.172369	−	0.298552i	−0.766879	−	0.641792i	$-0.778191\pi$
$11$	0.571683	−	0.990185i	0.172369	−	0.298552i	0.939248	+	0.343240i	$0.111525\pi$
$12$		0			0
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$14$		0			0
$15$	−4.50743	−	2.60236i	−1.16381	−	0.671928i
$16$		0			0
$17$	3.44224	+	5.96214i	0.834866	+	1.44603i	0.894139	+	0.447789i	$0.147788\pi$
$17$	3.44224	+	5.96214i	0.834866	+	1.44603i	−0.0592730	+	0.998242i	$0.518878\pi$
$18$		0			0
$19$	−3.93574	−	6.81691i	−0.902922	−	1.56391i	−0.823683	−	0.567051i	$-0.808084\pi$
$19$	−3.93574	−	6.81691i	−0.902922	−	1.56391i	−0.0792390	−	0.996856i	$-0.525249\pi$
$20$		0			0
$21$	−3.40946			−0.744005
$22$		0			0
$23$	−3.93574	+	6.81691i	−0.820660	+	1.42142i	0.0845322	+	0.996421i	$0.473060\pi$
$23$	−3.93574	+	6.81691i	−0.820660	+	1.42142i	−0.905192	+	0.425003i	$0.860273\pi$
$24$		0			0
$25$	10.0892			2.01784
$26$		0			0
$27$			5.63382i			1.08423i
$28$		0			0
$29$	−2.51963	−	1.45471i	−0.467884	−	0.270133i	0.247470	−	0.968896i	$-0.420401\pi$
$29$	−2.51963	−	1.45471i	−0.467884	−	0.270133i	−0.715353	+	0.698763i	$0.753734\pi$
$30$		0			0
$31$		−	2.00000i		−	0.359211i	−0.983739	−	0.179605i	$-0.942518\pi$
$31$		−	2.00000i		−	0.359211i	0.983739	−	0.179605i	$-0.0574821\pi$
$32$		0			0
$33$	−1.32673	+	0.765985i	−0.230953	+	0.133341i
$34$		0			0
$35$	8.56021	−	4.94224i	1.44694	−	0.835391i
$36$		0			0
$37$	−1.78212	+	3.08672i	−0.292979	+	0.507454i	−0.974513	−	0.224333i	$-0.927980\pi$
$37$	−1.78212	+	3.08672i	−0.292979	+	0.507454i	0.681534	+	0.731786i	$0.261313\pi$
$38$		0			0
$39$	−3.48110	+	3.34969i	−0.557422	+	0.536380i
$40$		0			0
$41$	−1.32673	−	0.765985i	−0.207200	−	0.119627i	0.392810	−	0.919620i	$-0.371503\pi$
$41$	−1.32673	−	0.765985i	−0.207200	−	0.119627i	−0.600009	+	0.799993i	$0.704836\pi$
$42$		0			0
$43$	7.88849	−	4.55442i	1.20298	−	0.694543i	0.241766	−	0.970335i	$-0.422273\pi$
$43$	7.88849	−	4.55442i	1.20298	−	0.694543i	0.961217	+	0.275792i	$0.0889400\pi$
$44$		0			0
$45$	−2.33988	−	4.05279i	−0.348808	−	0.604154i
$46$		0			0
$47$		−	2.11552i		−	0.308580i	−0.988026	−	0.154290i	$-0.950691\pi$
$47$		−	2.11552i		−	0.308580i	0.988026	−	0.154290i	$-0.0493090\pi$
$48$		0			0
$49$	−0.262488	+	0.454643i	−0.0374983	+	0.0649490i
$50$		0			0
$51$		−	9.22436i		−	1.29167i
$52$		0			0
$53$		−	9.01486i		−	1.23829i	−0.785278	−	0.619143i	$-0.787480\pi$
$53$		−	9.01486i		−	1.23829i	0.785278	−	0.619143i	$-0.212520\pi$
$54$		0			0
$55$	2.22069	−	3.84636i	0.299438	−	0.518643i
$56$		0			0
$57$			10.5468i			1.39696i
$58$		0			0
$59$	2.79238	+	4.83654i	0.363537	+	0.629664i	0.988540	−	0.150958i	$-0.0482358\pi$
$59$	2.79238	+	4.83654i	0.363537	+	0.629664i	−0.625004	+	0.780622i	$0.714902\pi$
$60$		0			0
$61$	−1.50000	+	0.866025i	−0.192055	+	0.110883i	−0.592944	−	0.805243i	$-0.702035\pi$
$61$	−1.50000	+	0.866025i	−0.192055	+	0.110883i	0.400889	+	0.916127i	$0.368701\pi$
$62$		0			0
$63$	−2.65486	−	1.53278i	−0.334480	−	0.193112i
$64$		0			0
$65$	3.88448	−	13.4562i	0.481811	−	1.66904i
$66$		0			0
$67$	−2.20369	+	3.81691i	−0.269224	+	0.466310i	−0.968662	−	0.248384i	$-0.920101\pi$
$67$	−2.20369	+	3.81691i	−0.269224	+	0.466310i	0.699438	+	0.714694i	$0.253434\pi$
$68$		0			0
$69$	9.13382	−	5.27341i	1.09958	−	0.634844i
$70$		0			0
$71$	−3.24702	+	1.87467i	−0.385350	+	0.222482i	−0.680144	−	0.733079i	$-0.738083\pi$
$71$	−3.24702	+	1.87467i	−0.385350	+	0.222482i	0.294793	+	0.955561i	$0.404749\pi$
$72$		0			0
$73$		−	11.3696i		−	1.33071i	−0.746527	−	0.665355i	$-0.768280\pi$
$73$		−	11.3696i		−	1.33071i	0.746527	−	0.665355i	$-0.231720\pi$
$74$		0			0
$75$	−11.7072	−	6.75915i	−1.35183	−	0.780480i
$76$		0			0
$77$		−	2.90942i		−	0.331559i
$78$		0			0
$79$	7.90549			0.889437			0.444719	−	0.895670i	$-0.353304\pi$
$79$	7.90549			0.889437			0.444719	+	0.895670i	$0.353304\pi$
$80$		0			0
$81$	1.96722	−	3.40732i	0.218580	−	0.378591i
$82$		0			0
$83$	8.10557			0.889702			0.444851	−	0.895605i	$-0.353257\pi$
$83$	8.10557			0.889702			0.444851	+	0.895605i	$0.353257\pi$
$84$		0			0
$85$	13.3713	+	23.1598i	1.45032	+	2.51204i
$86$		0			0
$87$	1.94913	+	3.37599i	0.208969	+	0.361945i
$88$		0			0
$89$	2.51963	+	1.45471i	0.267080	+	0.154199i	0.627560	−	0.778568i	$-0.284054\pi$
$89$	2.51963	+	1.45471i	0.267080	+	0.154199i	−0.360480	+	0.932767i	$0.617387\pi$
$90$		0			0
$91$	−2.20369	−	8.90612i	−0.231010	−	0.933615i
$92$		0			0
$93$	−1.33988	+	2.32073i	−0.138939	+	0.240649i
$94$		0			0
$95$	−15.2883	−	26.4802i	−1.56855	−	2.71681i
$96$		0			0
$97$	1.50000	−	0.866025i	0.152302	−	0.0879316i	−0.421912	−	0.906637i	$-0.638641\pi$
$97$	1.50000	−	0.866025i	0.152302	−	0.0879316i	0.574214	+	0.818705i	$0.305308\pi$
$98$		0			0
$99$	−1.37745			−0.138439
$100$		0			0
$101$	−3.30709	−	1.90935i	−0.329068	−	0.189988i	0.326359	−	0.945246i	$-0.394178\pi$
$101$	−3.30709	−	1.90935i	−0.329068	−	0.189988i	−0.655427	+	0.755258i	$0.727511\pi$
$102$		0			0
$103$	6.92820			0.682656			0.341328	−	0.939944i	$-0.389123\pi$
$103$	6.92820			0.682656			0.341328	+	0.939944i	$0.389123\pi$
$104$		0			0
$105$	−13.2440			−1.29248
$106$		0			0
$107$	1.71505	+	0.990185i	0.165800	+	0.0957248i	0.580604	−	0.814186i	$-0.302816\pi$
$107$	1.71505	+	0.990185i	0.165800	+	0.0957248i	−0.414804	+	0.909911i	$0.636150\pi$
$108$		0			0
$109$	−10.5250			−1.00811			−0.504055	−	0.863672i	$-0.668159\pi$
$109$	−10.5250			−1.00811			−0.504055	+	0.863672i	$0.668159\pi$
$110$		0			0
$111$	4.13583	−	2.38782i	0.392555	−	0.226642i
$112$		0			0
$113$	6.30709	+	10.9242i	0.593322	+	1.02766i	0.993781	+	0.111349i	$0.0355171\pi$
$113$	6.30709	+	10.9242i	0.593322	+	1.02766i	−0.400460	+	0.916314i	$0.631150\pi$
$114$		0			0
$115$	−15.2883	+	26.4802i	−1.42564	+	2.46929i
$116$		0			0
$117$	−4.21655	+	1.04333i	−0.389821	+	0.0964556i
$118$		0			0
$119$	15.1713	+	8.75915i	1.39075	+	0.802950i
$120$		0			0
$121$	4.84636	+	8.39414i	0.440578	+	0.763103i
$122$		0			0
$123$	1.02633	+	1.77765i	0.0925407	+	0.160285i
$124$		0			0
$125$	19.7690			1.76819
$126$		0			0
$127$	−1.74905	+	3.02945i	−0.155203	+	0.268820i	−0.933133	−	0.359531i	$-0.882937\pi$
$127$	−1.74905	+	3.02945i	−0.155203	+	0.268820i	0.777930	+	0.628351i	$0.216270\pi$
$128$		0			0
$129$	−12.2047			−1.07457
$130$		0			0
$131$			13.7690i			1.20300i	0.798873	+	0.601500i	$0.205430\pi$
$131$			13.7690i			1.20300i	−0.798873	+	0.601500i	$0.794570\pi$
$132$		0			0
$133$	−17.3464	−	10.0149i	−1.50412	−	0.868404i
$134$		0			0
$135$			21.8845i			1.88352i
$136$		0			0
$137$	−9.13382	+	5.27341i	−0.780355	+	0.450538i	−0.836556	−	0.547881i	$-0.815435\pi$
$137$	−9.13382	+	5.27341i	−0.780355	+	0.450538i	0.0562011	+	0.998419i	$0.482101\pi$
$138$		0			0
$139$	−2.99246	+	1.72770i	−0.253817	+	0.146541i	−0.621511	−	0.783406i	$-0.713481\pi$
$139$	−2.99246	+	1.72770i	−0.253817	+	0.146541i	0.367694	+	0.929947i	$0.380147\pi$
$140$		0			0
$141$	−1.41727	+	2.45478i	−0.119355	+	0.206729i
$142$		0			0
$143$	−2.85842	−	2.97055i	−0.239033	−	0.248410i
$144$		0			0
$145$	−9.78746	−	5.65080i	−0.812805	−	0.469273i
$146$		0			0
$147$	0.609165	−	0.351702i	0.0502431	−	0.0290079i
$148$		0			0
$149$	0.480369	+	0.832024i	0.0393534	+	0.0681621i	0.885031	−	0.465532i	$-0.154137\pi$
$149$	0.480369	+	0.832024i	0.0393534	+	0.0681621i	−0.845678	+	0.533694i	$0.820804\pi$
$150$		0			0
$151$			19.1285i			1.55665i	0.627860	+	0.778327i	$0.283931\pi$
$151$			19.1285i			1.55665i	−0.627860	+	0.778327i	$0.716069\pi$
$152$		0			0
$153$	4.14697	−	7.18277i	0.335263	−	0.580692i
$154$		0			0
$155$		−	7.76897i		−	0.624018i
$156$		0			0
$157$			7.83749i			0.625500i	0.949836	+	0.312750i	$0.101250\pi$
$157$			7.83749i			0.625500i	−0.949836	+	0.312750i	$0.898750\pi$
$158$		0			0
$159$	−6.03940	+	10.4605i	−0.478955	+	0.829575i
$160$		0			0
$161$			20.0298i			1.57857i
$162$		0			0
$163$	0.0170007	+	0.0294460i	0.00133159	+	0.00230639i	0.866690	−	0.498846i	$-0.166243\pi$
$163$	0.0170007	+	0.0294460i	0.00133159	+	0.00230639i	−0.865359	+	0.501153i	$0.832909\pi$
$164$		0			0
$165$	−5.15364	+	2.97546i	−0.401211	+	0.231639i
$166$		0			0
$167$	−13.5733	−	7.83654i	−1.05033	−	0.606410i	−0.127590	−	0.991827i	$-0.540724\pi$
$167$	−13.5733	−	7.83654i	−1.05033	−	0.606410i	−0.922742	+	0.385417i	$0.874058\pi$
$168$		0			0
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$		0			0
$171$	−4.74151	+	8.21254i	−0.362592	+	0.628028i
$172$		0			0
$173$	−7.15345	+	4.13005i	−0.543867	+	0.314002i	−0.746645	−	0.665223i	$-0.768336\pi$
$173$	−7.15345	+	4.13005i	−0.543867	+	0.314002i	0.202778	+	0.979225i	$0.435003\pi$
$174$		0			0
$175$	22.2335	−	12.8365i	1.68070	−	0.970351i
$176$		0			0
$177$		−	7.48289i		−	0.562448i
$178$		0			0
$179$	18.8355	+	10.8747i	1.40783	+	0.812811i	0.995179	−	0.0980783i	$-0.0312696\pi$
$179$	18.8355	+	10.8747i	1.40783	+	0.812811i	0.412651	+	0.910889i	$0.364603\pi$
$180$		0			0
$181$		−	9.79206i		−	0.727838i	−0.931431	−	0.363919i	$-0.881438\pi$
$181$		−	9.79206i		−	0.727838i	0.931431	−	0.363919i	$-0.118562\pi$
$182$		0			0
$183$	2.32073			0.171554
$184$		0			0
$185$	−6.92261	+	11.9903i	−0.508960	+	0.881545i
$186$		0			0
$187$	7.87149			0.575620
$188$		0			0
$189$	7.16793	+	12.4152i	0.521390	+	0.903074i
$190$		0			0
$191$	10.6639	+	18.4704i	0.771610	+	1.33647i	0.936680	+	0.350187i	$0.113882\pi$
$191$	10.6639	+	18.4704i	0.771610	+	1.33647i	−0.165070	+	0.986282i	$0.552785\pi$
$192$		0			0
$193$	−14.3464	−	8.28287i	−1.03267	−	0.596214i	−0.114924	−	0.993374i	$-0.536662\pi$
$193$	−14.3464	−	8.28287i	−1.03267	−	0.596214i	−0.917749	+	0.397160i	$0.869996\pi$
$194$		0			0
$195$	−13.5223	+	13.0118i	−0.968351	+	0.931796i
$196$		0			0
$197$	−6.26897	+	10.8582i	−0.446645	+	0.773613i	−0.998165	−	0.0605492i	$-0.980715\pi$
$197$	−6.26897	+	10.8582i	−0.446645	+	0.773613i	0.551520	+	0.834162i	$0.314048\pi$
$198$		0			0
$199$	6.12244	+	10.6044i	0.434008	+	0.751724i	0.997214	−	0.0745924i	$-0.0237656\pi$
$199$	6.12244	+	10.6044i	0.434008	+	0.751724i	−0.563206	+	0.826317i	$0.690432\pi$
$200$		0			0
$201$	5.11419	−	2.95268i	0.360727	−	0.208266i
$202$		0			0
$203$	−7.40333			−0.519612
$204$		0			0
$205$	−5.15364	−	2.97546i	−0.359946	−	0.207815i
$206$		0			0
$207$	9.48302			0.659115
$208$		0			0
$209$	−9.00000			−0.622543
$210$		0			0
$211$	0.926286	+	0.534791i	0.0637682	+	0.0368166i	0.531545	−	0.847030i	$-0.321612\pi$
$211$	0.926286	+	0.534791i	0.0637682	+	0.0368166i	−0.467777	+	0.883847i	$0.654945\pi$
$212$		0			0
$213$	5.02365			0.344215
$214$		0			0
$215$	30.6427	−	17.6916i	2.08982	−	1.20656i
$216$		0			0
$217$	−2.54461	−	4.40739i	−0.172739	−	0.299193i
$218$		0			0
$219$	−7.61693	+	13.1929i	−0.514704	+	0.891494i
$220$		0			0
$221$	24.0957	−	5.96214i	1.62085	−	0.401057i
$222$		0			0
$223$	−24.9429	−	14.4008i	−1.67030	−	0.964347i	−0.967469	−	0.252989i	$-0.918586\pi$
$223$	−24.9429	−	14.4008i	−1.67030	−	0.964347i	−0.702830	−	0.711358i	$-0.748080\pi$
$224$		0			0
$225$	−6.07739	−	10.5263i	−0.405159	−	0.701756i
$226$		0			0
$227$	−6.61108	−	11.4507i	−0.438793	−	0.760012i	0.558804	−	0.829300i	$-0.311261\pi$
$227$	−6.61108	−	11.4507i	−0.438793	−	0.760012i	−0.997597	+	0.0692883i	$0.977927\pi$
$228$		0			0
$229$	−0.564237			−0.0372859			−0.0186429	−	0.999826i	$-0.505935\pi$
$229$	−0.564237			−0.0372859			−0.0186429	+	0.999826i	$0.505935\pi$
$230$		0			0
$231$	−1.94913	+	3.37599i	−0.128243	+	0.222124i
$232$		0			0
$233$	8.11552			0.531665			0.265833	−	0.964019i	$-0.414353\pi$
$233$	8.11552			0.531665			0.265833	+	0.964019i	$0.414353\pi$
$234$		0			0
$235$		−	8.21769i		−	0.536063i
$236$		0			0
$237$	−9.17327	−	5.29619i	−0.595868	−	0.344025i
$238$		0			0
$239$		−	9.53793i		−	0.616958i	−0.951231	−	0.308479i	$-0.900180\pi$
$239$		−	9.53793i		−	0.616958i	0.951231	−	0.308479i	$-0.0998199\pi$
$240$		0			0
$241$	17.3464	−	10.0149i	1.11738	−	0.645118i	0.176647	−	0.984274i	$-0.443475\pi$
$241$	17.3464	−	10.0149i	1.11738	−	0.645118i	0.940730	+	0.339156i	$0.110142\pi$
$242$		0			0
$243$	10.0717	−	5.81490i	0.646100	−	0.373026i
$244$		0			0
$245$	−1.01963	+	1.76605i	−0.0651418	+	0.112829i
$246$		0			0
$247$	−27.5502	+	6.81691i	−1.75298	+	0.433750i
$248$		0			0
$249$	−9.40544	−	5.43023i	−0.596046	−	0.344127i
$250$		0			0
$251$	−11.5071	+	6.64364i	−0.726323	+	0.419343i	−0.817075	−	0.576531i	$-0.804406\pi$
$251$	−11.5071	+	6.64364i	−0.726323	+	0.419343i	0.0907527	+	0.995873i	$0.471073\pi$
$252$		0			0
$253$	4.50000	+	7.79423i	0.282913	+	0.490019i
$254$		0			0
$255$		−	35.8319i		−	2.24388i
$256$		0			0
$257$	5.21121	−	9.02608i	0.325066	−	0.563031i	−0.656459	−	0.754361i	$-0.727947\pi$
$257$	5.21121	−	9.02608i	0.325066	−	0.563031i	0.981526	+	0.191330i	$0.0612800\pi$
$258$		0			0
$259$			9.06958i			0.563556i
$260$		0			0
$261$			3.50506i			0.216958i
$262$		0			0
$263$	9.52050	−	16.4900i	0.587059	−	1.01682i	−0.407556	−	0.913180i	$-0.633619\pi$
$263$	9.52050	−	16.4900i	0.587059	−	1.01682i	0.994615	−	0.103636i	$-0.0330478\pi$
$264$		0			0
$265$		−	35.0181i		−	2.15114i
$266$		0			0
$267$	−1.94913	−	3.37599i	−0.119285	−	0.206608i
$268$		0			0
$269$	−14.2875	+	8.24887i	−0.871122	+	0.502943i	−0.867721	−	0.497052i	$-0.834416\pi$
$269$	−14.2875	+	8.24887i	−0.871122	+	0.502943i	−0.00340112	+	0.999994i	$0.501083\pi$
$270$		0			0
$271$	−10.8299	−	6.25267i	−0.657872	−	0.379823i	0.133593	−	0.991036i	$-0.457348\pi$
$271$	−10.8299	−	6.25267i	−0.657872	−	0.379823i	−0.791466	+	0.611213i	$0.790682\pi$
$272$		0			0
$273$	−3.40946	+	11.8107i	−0.206350	+	0.714817i
$274$		0			0
$275$	5.76784	−	9.99018i	0.347814	−	0.602431i
$276$		0			0
$277$	5.28746	−	3.05272i	0.317693	−	0.183420i	−0.332671	−	0.943043i	$-0.607950\pi$
$277$	5.28746	−	3.05272i	0.317693	−	0.183420i	0.650364	+	0.759623i	$0.274616\pi$
$278$		0			0
$279$	−2.08665	+	1.20473i	−0.124925	+	0.0721253i
$280$		0			0
$281$			9.01486i			0.537781i	0.963171	+	0.268891i	$0.0866570\pi$
$281$			9.01486i			0.537781i	−0.963171	+	0.268891i	$0.913343\pi$
$282$		0			0
$283$	16.7373	+	9.66327i	0.994927	+	0.574422i	0.906743	−	0.421683i	$-0.138560\pi$
$283$	16.7373	+	9.66327i	0.994927	+	0.574422i	0.0881839	+	0.996104i	$0.471894\pi$
$284$		0			0
$285$			40.9690i			2.42679i
$286$		0			0
$287$	−3.89826			−0.230107
$288$		0			0
$289$	−15.1981	+	26.3238i	−0.894003	+	1.54846i
$290$		0			0
$291$	−2.32073			−0.136044
$292$		0			0
$293$	3.61552	+	6.26226i	0.211221	+	0.365845i	0.952097	−	0.305797i	$-0.0989228\pi$
$293$	3.61552	+	6.26226i	0.211221	+	0.365845i	−0.740876	+	0.671642i	$0.765589\pi$
$294$		0			0
$295$	10.8469	+	18.7875i	0.631534	+	1.09385i
$296$		0			0
$297$	5.57852	+	3.22076i	0.323699	+	0.186888i
$298$		0			0
$299$	19.6787	+	20.4507i	1.13805	+	1.18270i
$300$		0			0
$301$	11.5892	−	20.0731i	0.667991	−	1.15699i
$302$		0			0
$303$	2.55830	+	4.43110i	0.146970	+	0.254560i
$304$		0			0
$305$	−5.82673	+	3.36406i	−0.333637	+	0.192626i
$306$		0			0
$307$	−19.2071			−1.09621			−0.548103	−	0.836411i	$-0.684650\pi$
$307$	−19.2071			−1.09621			−0.548103	+	0.836411i	$0.684650\pi$
$308$		0			0
$309$	−8.03926	−	4.64147i	−0.457338	−	0.264044i
$310$		0			0
$311$	2.75490			0.156216			0.0781079	−	0.996945i	$-0.475112\pi$
$311$	2.75490			0.156216			0.0781079	+	0.996945i	$0.475112\pi$
$312$		0			0
$313$	−0.564237			−0.0318926			−0.0159463	−	0.999873i	$-0.505076\pi$
$313$	−0.564237			−0.0318926			−0.0159463	+	0.999873i	$0.505076\pi$
$314$		0			0
$315$	−10.3127	−	5.95407i	−0.581057	−	0.335474i
$316$		0			0
$317$	−15.2676			−0.857516			−0.428758	−	0.903419i	$-0.641049\pi$
$317$	−15.2676			−0.857516			−0.428758	+	0.903419i	$0.641049\pi$
$318$		0			0
$319$	−2.88086	+	1.66327i	−0.161297	+	0.0931250i
$320$		0			0
$321$	−1.32673	−	2.29796i	−0.0740506	−	0.128259i
$322$		0			0
$323$	27.0956	−	46.9309i	1.50764	−	2.61131i
$324$		0			0
$325$	10.0892	−	34.9501i	0.559649	−	1.93868i
$326$		0			0
$327$	12.2128	+	7.05109i	0.675372	+	0.389926i
$328$		0			0
$329$	−2.69158	−	4.66195i	−0.148392	−	0.257022i
$330$		0			0
$331$	5.36768	+	9.29709i	0.295034	+	0.511014i	0.974993	−	0.222236i	$-0.0713356\pi$
$331$	5.36768	+	9.29709i	0.295034	+	0.511014i	−0.679959	+	0.733250i	$0.738002\pi$
$332$		0			0
$333$	4.29394			0.235307
$334$		0			0
$335$	−8.56021	+	14.8267i	−0.467694	+	0.810071i
$336$		0			0
$337$	18.6641			1.01670			0.508350	−	0.861150i	$-0.330256\pi$
$337$	18.6641			1.01670			0.508350	+	0.861150i	$0.330256\pi$
$338$		0			0
$339$		−	16.9015i		−	0.917961i
$340$		0			0
$341$	−1.98037	−	1.14337i	−0.107243	−	0.0619168i
$342$		0			0
$343$			19.1481i			1.03390i
$344$		0			0
$345$	35.4802	−	20.4845i	1.91019	−	1.10285i
$346$		0			0
$347$	10.5754	−	6.10570i	0.567716	−	0.327771i	−0.188520	−	0.982069i	$-0.560369\pi$
$347$	10.5754	−	6.10570i	0.567716	−	0.327771i	0.756237	+	0.654298i	$0.227036\pi$
$348$		0			0
$349$	4.78212	−	8.28287i	0.255981	−	0.443372i	−0.709181	−	0.705027i	$-0.750935\pi$
$349$	4.78212	−	8.28287i	0.255981	−	0.443372i	0.965161	+	0.261655i	$0.0842682\pi$
$350$		0			0
$351$	19.5161	+	5.63382i	1.04169	+	0.300711i
$352$		0			0
$353$	32.1731	+	18.5751i	1.71240	+	0.988655i	0.931303	+	0.364246i	$0.118673\pi$
$353$	32.1731	+	18.5751i	1.71240	+	0.988655i	0.781097	+	0.624409i	$0.214660\pi$
$354$		0			0
$355$	−12.6130	+	7.28212i	−0.669429	+	0.386495i
$356$		0			0
$357$	−11.7362	−	20.3277i	−0.621145	−	1.07585i
$358$		0			0
$359$		−	15.9607i		−	0.842376i	−0.906973	−	0.421188i	$-0.861613\pi$
$359$		−	15.9607i		−	0.842376i	0.906973	−	0.421188i	$-0.138387\pi$
$360$		0			0
$361$	−21.4802	+	37.2048i	−1.13054	+	1.95815i
$362$		0			0
$363$		−	12.9870i		−	0.681643i
$364$		0			0
$365$		−	44.1650i		−	2.31170i
$366$		0			0
$367$	−13.5393	+	23.4507i	−0.706745	+	1.22412i	0.259313	+	0.965793i	$0.416504\pi$
$367$	−13.5393	+	23.4507i	−0.706745	+	1.22412i	−0.966058	+	0.258325i	$0.916830\pi$
$368$		0			0
$369$			1.84561i			0.0960787i
$370$		0			0
$371$	−11.4696	−	19.8660i	−0.595474	−	1.03139i
$372$		0			0
$373$	−27.9802	+	16.1544i	−1.44876	+	0.836441i	−0.998408	−	0.0564104i	$-0.982034\pi$
$373$	−27.9802	+	16.1544i	−1.44876	+	0.836441i	−0.450351	+	0.892852i	$0.648701\pi$
$374$		0			0
$375$	−22.9393	−	13.2440i	−1.18458	−	0.683917i
$376$		0			0
$377$	−7.55889	+	7.27355i	−0.389303	+	0.374607i
$378$		0			0
$379$	−8.64325	+	14.9706i	−0.443974	+	0.768986i	−0.997980	−	0.0635270i	$-0.979765\pi$
$379$	−8.64325	+	14.9706i	−0.443974	+	0.768986i	0.554006	+	0.832513i	$0.313098\pi$
$380$		0			0
$381$	4.05908	−	2.34351i	0.207953	−	0.120062i
$382$		0			0
$383$	−10.2753	+	5.93243i	−0.525041	+	0.303133i	−0.738995	−	0.673711i	$-0.764699\pi$
$383$	−10.2753	+	5.93243i	−0.525041	+	0.303133i	0.213953	+	0.976844i	$0.431366\pi$
$384$		0			0
$385$		−	11.3016i		−	0.575982i
$386$		0			0
$387$	−9.50350	−	5.48685i	−0.483090	−	0.278912i
$388$		0			0
$389$			26.9125i			1.36452i	0.731111	+	0.682259i	$0.239002\pi$
$389$			26.9125i			1.36452i	−0.731111	+	0.682259i	$0.760998\pi$
$390$		0			0
$391$	−54.1911			−2.74056
$392$		0			0
$393$	9.22436	−	15.9771i	0.465307	−	0.805936i
$394$		0			0
$395$	30.7088			1.54512
$396$		0			0
$397$	−4.34636	−	7.52811i	−0.218137	−	0.377825i	0.736101	−	0.676872i	$-0.236665\pi$
$397$	−4.34636	−	7.52811i	−0.218137	−	0.377825i	−0.954239	+	0.299047i	$0.903331\pi$
$398$		0			0
$399$	13.4188	+	23.2420i	0.671778	+	1.16355i
$400$		0			0
$401$	5.69291	+	3.28680i	0.284290	+	0.164135i	0.635364	−	0.772213i	$-0.280850\pi$
$401$	5.69291	+	3.28680i	0.284290	+	0.164135i	−0.351074	+	0.936348i	$0.614183\pi$
$402$		0			0
$403$	−6.92820	−	2.00000i	−0.345118	−	0.0996271i
$404$		0			0
$405$	7.64163	−	13.2357i	0.379715	−	0.657686i
$406$		0			0
$407$	2.03762	+	3.52925i	0.101001	+	0.174939i
$408$		0			0
$409$	−18.9802	+	10.9582i	−0.938509	+	0.541849i	−0.889493	−	0.456949i	$-0.848942\pi$
$409$	−18.9802	+	10.9582i	−0.938509	+	0.541849i	−0.0490166	+	0.998798i	$0.515609\pi$
$410$		0			0
$411$	14.1315			0.697053
$412$		0			0
$413$	12.3071	+	7.10550i	0.605593	+	0.349639i
$414$		0			0
$415$	31.4860			1.54558
$416$		0			0
$417$	4.62980			0.226722
$418$		0			0
$419$	5.07911	+	2.93243i	0.248131	+	0.143258i	0.618908	−	0.785463i	$-0.287575\pi$
$419$	5.07911	+	2.93243i	0.248131	+	0.143258i	−0.370777	+	0.928722i	$0.620909\pi$
$420$		0			0
$421$	−30.6641			−1.49448			−0.747239	−	0.664555i	$-0.768621\pi$
$421$	−30.6641			−1.49448			−0.747239	+	0.664555i	$0.768621\pi$
$422$		0			0
$423$	−2.20717	+	1.27431i	−0.107317	+	0.0619592i
$424$		0			0
$425$	34.7295	+	60.1533i	1.68463	+	2.91786i
$426$		0			0
$427$	−2.20369	+	3.81691i	−0.106644	+	0.184713i
$428$		0			0
$429$	1.32673	+	5.36190i	0.0640549	+	0.258875i
$430$		0			0
$431$	−20.6015	−	11.8943i	−0.992341	−	0.572928i	−0.0863676	−	0.996263i	$-0.527526\pi$
$431$	−20.6015	−	11.8943i	−0.992341	−	0.572928i	−0.905973	+	0.423335i	$0.860859\pi$
$432$		0			0
$433$	−10.8910	−	18.8637i	−0.523386	−	0.906532i	−0.999630	−	0.0272180i	$-0.991335\pi$
$433$	−10.8910	−	18.8637i	−0.523386	−	0.906532i	0.476243	−	0.879314i	$-0.341998\pi$
$434$		0			0
$435$	7.57137	+	13.1140i	0.363019	+	0.628768i
$436$		0			0
$437$	61.9604			2.96397
$438$		0			0
$439$	5.36768	−	9.29709i	0.256185	−	0.443726i	−0.709032	−	0.705177i	$-0.750868\pi$
$439$	5.36768	−	9.29709i	0.256185	−	0.443726i	0.965217	+	0.261451i	$0.0842010\pi$
$440$		0			0
$441$	0.632454			0.0301169
$442$		0			0
$443$		−	23.7297i		−	1.12743i	−0.825969	−	0.563716i	$-0.809371\pi$
$443$		−	23.7297i		−	1.12743i	0.825969	−	0.563716i	$-0.190629\pi$
$444$		0			0
$445$	9.78746	+	5.65080i	0.463970	+	0.267873i
$446$		0			0
$447$		−	1.28727i		−	0.0608859i
$448$		0			0
$449$	30.5747	−	17.6523i	1.44291	−	0.833065i	0.444868	−	0.895596i	$-0.353251\pi$
$449$	30.5747	−	17.6523i	1.44291	−	0.833065i	0.998043	+	0.0625311i	$0.0199173\pi$
$450$		0			0
$451$	−1.51693	+	0.875802i	−0.0714296	+	0.0412399i
$452$		0			0
$453$	12.8149	−	22.1961i	0.602097	−	1.04286i
$454$		0			0
$455$	−8.56021	−	34.5957i	−0.401309	−	1.62187i
$456$		0			0
$457$	28.7676	+	16.6090i	1.34569	+	0.776936i	0.987636	−	0.156763i	$-0.0501059\pi$
$457$	28.7676	+	16.6090i	1.34569	+	0.776936i	0.358057	+	0.933700i	$0.383439\pi$
$458$		0			0
$459$	−33.5896	+	19.3930i	−1.56783	+	0.905186i
$460$		0			0
$461$	5.07606	+	8.79200i	0.236416	+	0.409484i	0.959683	−	0.281084i	$-0.0906939\pi$
$461$	5.07606	+	8.79200i	0.236416	+	0.409484i	−0.723267	+	0.690568i	$0.757361\pi$
$462$		0			0
$463$		−	2.00000i		−	0.0929479i	−0.998920	−	0.0464739i	$-0.985202\pi$
$463$		−	2.00000i		−	0.0929479i	0.998920	−	0.0464739i	$-0.0147984\pi$
$464$		0			0
$465$	−5.20473	+	9.01486i	−0.241364	+	0.418054i
$466$		0			0
$467$			5.65345i			0.261611i	0.991408	+	0.130805i	$0.0417563\pi$
$467$			5.65345i			0.261611i	−0.991408	+	0.130805i	$0.958244\pi$
$468$		0			0
$469$			11.2151i			0.517864i
$470$		0			0
$471$	5.25063	−	9.09437i	0.241936	−	0.419046i
$472$		0			0
$473$		−	10.4147i		−	0.478871i
$474$		0			0
$475$	−39.7086	−	68.7773i	−1.82195	−	3.15572i
$476$		0			0
$477$	−9.40544	+	5.43023i	−0.430646	+	0.248633i
$478$		0			0
$479$	3.71518	+	2.14496i	0.169751	+	0.0980058i	0.582468	−	0.812853i	$-0.302087\pi$
$479$	3.71518	+	2.14496i	0.169751	+	0.0980058i	−0.412717	+	0.910859i	$0.635420\pi$
$480$		0			0
$481$	8.91059	+	9.26016i	0.406288	+	0.422227i
$482$		0			0
$483$	13.4188	−	23.2420i	0.610575	−	1.05755i
$484$		0			0
$485$	5.82673	−	3.36406i	0.264578	−	0.152754i
$486$		0			0
$487$	14.9032	−	8.60437i	0.675329	−	0.389901i	−0.122764	−	0.992436i	$-0.539176\pi$
$487$	14.9032	−	8.60437i	0.675329	−	0.389901i	0.798093	+	0.602534i	$0.205842\pi$
$488$		0			0
$489$		−	0.0455576i		−	0.00206018i
$490$		0			0
$491$	−12.0413	−	6.95206i	−0.543417	−	0.313742i	0.203046	−	0.979169i	$-0.434916\pi$
$491$	−12.0413	−	6.95206i	−0.543417	−	0.313742i	−0.746463	+	0.665427i	$0.768249\pi$
$492$		0			0
$493$		−	20.0298i		−	0.902099i
$494$		0			0
$495$	−5.35067			−0.240495
$496$		0			0
$497$	−4.77029	+	8.26239i	−0.213977	+	0.370619i
$498$		0			0
$499$	−31.4860			−1.40951			−0.704753	−	0.709453i	$-0.748942\pi$
$499$	−31.4860			−1.40951			−0.704753	+	0.709453i	$0.748942\pi$
$500$		0			0
$501$	10.5000	+	18.1865i	0.469105	+	0.812514i
$502$		0			0
$503$	−10.8979	−	18.8758i	−0.485916	−	0.841630i	0.513953	−	0.857818i	$-0.328180\pi$
$503$	−10.8979	−	18.8758i	−0.485916	−	0.841630i	−0.999869	+	0.0161877i	$0.994847\pi$
$504$		0			0
$505$	−12.8464	−	7.41685i	−0.571655	−	0.330045i
$506$		0			0
$507$	8.12257	+	15.4086i	0.360736	+	0.684319i
$508$		0			0
$509$	4.32673	−	7.49411i	0.191779	−	0.332171i	−0.754061	−	0.656804i	$-0.771908\pi$
$509$	4.32673	−	7.49411i	0.191779	−	0.332171i	0.945840	+	0.324634i	$0.105241\pi$
$510$		0			0
$511$	−14.4656	−	25.0551i	−0.639919	−	1.10837i
$512$		0			0
$513$	38.4052	−	22.1733i	1.69563	−	0.978974i
$514$		0			0
$515$	26.9125			1.18591
$516$		0			0
$517$	−2.09475	−	1.20941i	−0.0921271	−	0.0531896i
$518$		0			0
$519$	11.0675			0.485810
$520$		0			0
$521$	19.4224			0.850912			0.425456	−	0.904979i	$-0.360114\pi$
$521$	19.4224			0.850912			0.425456	+	0.904979i	$0.360114\pi$
$522$		0			0
$523$	25.6636	+	14.8169i	1.12219	+	0.647898i	0.941960	−	0.335726i	$-0.108982\pi$
$523$	25.6636	+	14.8169i	1.12219	+	0.647898i	0.180233	+	0.983624i	$0.442315\pi$
$524$		0			0
$525$	−34.3988			−1.50129
$526$		0			0
$527$	11.9243	−	6.88448i	0.519430	−	0.299893i
$528$		0			0
$529$	−19.4802	−	33.7407i	−0.846964	−	1.46699i
$530$		0			0
$531$	3.36406	−	5.82673i	0.145988	−	0.252858i
$532$		0			0
$533$	−3.98018	+	3.82993i	−0.172401	+	0.165893i
$534$		0			0
$535$	6.66208	+	3.84636i	0.288027	+	0.166292i
$536$		0			0
$537$	−14.5707	−	25.2372i	−0.628773	−	1.08907i
$538$		0			0
$539$	0.300120	+	0.519823i	0.0129271	+	0.0223904i
$540$		0			0
$541$	−14.3569			−0.617249			−0.308625	−	0.951184i	$-0.599869\pi$
$541$	−14.3569			−0.617249			−0.308625	+	0.951184i	$0.599869\pi$
$542$		0			0
$543$	−6.56008	+	11.3624i	−0.281520	+	0.487607i
$544$		0			0
$545$	−40.8841			−1.75128
$546$		0			0
$547$		−	7.12847i		−	0.304792i	−0.988320	−	0.152396i	$-0.951301\pi$
$547$		−	7.12847i		−	0.304792i	0.988320	−	0.152396i	$-0.0486988\pi$
$548$		0			0
$549$	1.80709	+	1.04333i	0.0771249	+	0.0445281i
$550$		0			0
$551$			22.9015i			0.975635i
$552$		0			0
$553$	17.4213	−	10.0582i	0.740828	−	0.427717i
$554$		0			0
$555$	16.0655	−	9.27545i	0.681944	−	0.393721i
$556$		0			0
$557$	18.4041	−	31.8769i	0.779807	−	1.35067i	−0.152245	−	0.988343i	$-0.548650\pi$
$557$	18.4041	−	31.8769i	0.779807	−	1.35067i	0.932053	−	0.362323i	$-0.118016\pi$
$558$		0			0
$559$	−7.88849	−	31.8810i	−0.333648	−	1.34842i
$560$		0			0
$561$	−9.13382	−	5.27341i	−0.385630	−	0.222644i
$562$		0			0
$563$	−14.8712	+	8.58588i	−0.626745	+	0.361852i	−0.779491	−	0.626414i	$-0.784522\pi$
$563$	−14.8712	+	8.58588i	−0.626745	+	0.361852i	0.152745	+	0.988266i	$0.451189\pi$
$564$		0			0
$565$	24.4998	+	42.4349i	1.03071	+	1.78525i
$566$		0			0
$567$		−	10.0116i		−	0.420447i
$568$		0			0
$569$	5.24934	−	9.09212i	0.220064	−	0.381161i	−0.734763	−	0.678323i	$-0.762707\pi$
$569$	5.24934	−	9.09212i	0.220064	−	0.381161i	0.954827	+	0.297162i	$0.0960402\pi$
$570$		0			0
$571$		−	30.2177i		−	1.26457i	−0.774736	−	0.632285i	$-0.782117\pi$
$571$		−	30.2177i		−	1.26457i	0.774736	−	0.632285i	$-0.217883\pi$
$572$		0			0
$573$		−	28.5765i		−	1.19380i
$574$		0			0
$575$	−39.7086	+	68.7773i	−1.65596	+	2.86821i
$576$		0			0
$577$			25.2260i			1.05017i	0.851049	+	0.525086i	$0.175967\pi$
$577$			25.2260i			1.05017i	−0.851049	+	0.525086i	$0.824033\pi$
$578$		0			0
$579$	11.0980	+	19.2224i	0.461218	+	0.798854i
$580$		0			0
$581$	17.8622	−	10.3127i	0.741049	−	0.427845i
$582$		0			0
$583$	−8.92637	−	5.15364i	−0.369693	−	0.213442i
$584$		0			0
$585$	−16.3791	+	4.05279i	−0.677194	+	0.167562i
$586$		0			0
$587$	−2.40377	+	4.16346i	−0.0992144	+	0.171844i	−0.911360	−	0.411611i	$-0.864966\pi$
$587$	−2.40377	+	4.16346i	−0.0992144	+	0.171844i	0.812145	+	0.583455i	$0.198300\pi$
$588$		0			0
$589$	−13.6338	+	7.87149i	−0.561772	+	0.324339i
$590$		0			0
$591$	14.5486	−	8.39964i	0.598450	−	0.345515i
$592$		0			0
$593$			32.3952i			1.33031i	0.746704	+	0.665157i	$0.231635\pi$
$593$			32.3952i			1.33031i	−0.746704	+	0.665157i	$0.768365\pi$
$594$		0			0
$595$	58.9327	+	34.0248i	2.41600	+	1.39488i
$596$		0			0
$597$		−	16.4066i		−	0.671479i
$598$		0			0
$599$	−10.2602			−0.419222			−0.209611	−	0.977785i	$-0.567220\pi$
$599$	−10.2602			−0.419222			−0.209611	+	0.977785i	$0.567220\pi$
$600$		0			0
$601$	8.23751	−	14.2678i	0.336015	−	0.581995i	−0.647664	−	0.761926i	$-0.724254\pi$
$601$	8.23751	−	14.2678i	0.336015	−	0.581995i	0.983679	+	0.179931i	$0.0575873\pi$
$602$		0			0
$603$	5.30971			0.216228
$604$		0			0
$605$	18.8256	+	32.6069i	0.765369	+	1.32566i
$606$		0			0
$607$	19.9788	+	34.6044i	0.810916	+	1.40455i	0.912223	+	0.409693i	$0.134364\pi$
$607$	19.9788	+	34.6044i	0.810916	+	1.40455i	−0.101307	+	0.994855i	$0.532302\pi$
$608$		0			0
$609$	8.59058	+	4.95977i	0.348108	+	0.200980i
$610$		0			0
$611$	−7.32836	−	2.11552i	−0.296474	−	0.0855846i
$612$		0			0
$613$	0.287464	−	0.497903i	0.0116106	−	0.0201101i	−0.860162	−	0.510021i	$-0.829637\pi$
$613$	0.287464	−	0.497903i	0.0116106	−	0.0201101i	0.871772	+	0.489911i	$0.162971\pi$
$614$		0			0
$615$	3.98675	+	6.90525i	0.160761	+	0.278446i
$616$		0			0
$617$	−16.1535	+	9.32620i	−0.650313	+	0.375459i	−0.788576	−	0.614937i	$-0.789181\pi$
$617$	−16.1535	+	9.32620i	−0.650313	+	0.375459i	0.138263	+	0.990396i	$0.455848\pi$
$618$		0			0
$619$	−13.8564			−0.556936			−0.278468	−	0.960446i	$-0.589827\pi$
$619$	−13.8564			−0.556936			−0.278468	+	0.960446i	$0.589827\pi$
$620$		0			0
$621$	−38.4052	−	22.1733i	−1.54115	−	0.889783i
$622$		0			0
$623$	7.40333			0.296608
$624$		0			0
$625$	26.3462			1.05385
$626$		0			0
$627$	10.4433	+	6.02945i	0.417066	+	0.240793i
$628$		0			0
$629$	−24.5379			−0.978392
$630$		0			0
$631$	41.8953	−	24.1882i	1.66782	−	0.962919i	0.699016	−	0.715106i	$-0.253621\pi$
$631$	41.8953	−	24.1882i	1.66782	−	0.962919i	0.968808	−	0.247813i	$-0.0797119\pi$
$632$		0			0
$633$	−0.716555	−	1.24111i	−0.0284805	−	0.0493297i
$634$		0			0
$635$	−6.79416	+	11.7678i	−0.269618	+	0.466992i
$636$		0			0
$637$	1.31244	+	1.36393i	0.0520008	+	0.0540408i
$638$		0			0
$639$	3.91178	+	2.25847i	0.154748	+	0.0893437i
$640$		0			0
$641$	−11.3464	−	19.6525i	−0.448154	−	0.776226i	0.550112	−	0.835091i	$-0.314585\pi$
$641$	−11.3464	−	19.6525i	−0.448154	−	0.776226i	−0.998266	+	0.0588653i	$0.981252\pi$
$642$		0			0
$643$	−0.771763	−	1.33673i	−0.0304354	−	0.0527156i	0.850407	−	0.526126i	$-0.176356\pi$
$643$	−0.771763	−	1.33673i	−0.0304354	−	0.0527156i	−0.880842	+	0.473411i	$0.843023\pi$
$644$		0			0
$645$	−47.4091			−1.86673
$646$		0			0
$647$	16.1601	−	27.9902i	0.635321	−	1.10041i	−0.351126	−	0.936328i	$-0.614201\pi$
$647$	16.1601	−	27.9902i	0.635321	−	1.10041i	0.986447	−	0.164080i	$-0.0524654\pi$
$648$		0			0
$649$	6.38542			0.250650
$650$		0			0
$651$			6.81892i			0.267255i
$652$		0			0
$653$	−25.2678	−	14.5884i	−0.988807	−	0.570888i	−0.0838893	−	0.996475i	$-0.526734\pi$
$653$	−25.2678	−	14.5884i	−0.988807	−	0.570888i	−0.904917	+	0.425587i	$0.860068\pi$
$654$		0			0
$655$			53.4853i			2.08984i
$656$		0			0
$657$	−11.8622	+	6.84864i	−0.462788	+	0.267191i
$658$		0			0
$659$	−7.97501	+	4.60437i	−0.310662	+	0.179361i	−0.647223	−	0.762301i	$-0.724070\pi$
$659$	−7.97501	+	4.60437i	−0.310662	+	0.179361i	0.336561	+	0.941662i	$0.390736\pi$
$660$		0			0
$661$	2.71254	−	4.69825i	0.105505	−	0.182741i	−0.808439	−	0.588580i	$-0.799687\pi$
$661$	2.71254	−	4.69825i	0.105505	−	0.182741i	0.913945	+	0.405839i	$0.133021\pi$
$662$		0			0
$663$	−31.9541	−	9.22436i	−1.24100	−	0.358244i
$664$		0			0
$665$	−67.3816	−	38.9028i	−2.61295	−	1.50859i
$666$		0			0
$667$	19.8332	−	11.4507i	0.767946	−	0.443374i
$668$		0			0
$669$	19.2953	+	33.4204i	0.745998	+	1.29211i
$670$		0			0
$671$			1.98037i			0.0764513i
$672$		0			0
$673$	−13.2623	+	22.9710i	−0.511224	+	0.885466i	0.488691	+	0.872457i	$0.337474\pi$
$673$	−13.2623	+	22.9710i	−0.511224	+	0.885466i	−0.999915	+	0.0130091i	$0.995859\pi$
$674$		0			0
$675$			56.8408i			2.18780i
$676$		0			0
$677$			20.6525i			0.793741i	0.917875	+	0.396871i	$0.129904\pi$
$677$			20.6525i			0.793741i	−0.917875	+	0.396871i	$0.870096\pi$
$678$		0			0
$679$	2.20369	−	3.81691i	0.0845700	−	0.146480i
$680$		0			0
$681$			17.7161i			0.678881i
$682$		0			0
$683$	−14.3280	−	24.8169i	−0.548248	−	0.949593i	−0.998395	−	0.0566383i	$-0.981962\pi$
$683$	−14.3280	−	24.8169i	−0.548248	−	0.949593i	0.450147	−	0.892954i	$-0.351372\pi$
$684$		0			0
$685$	−35.4802	+	20.4845i	−1.35563	+	0.782672i
$686$		0			0
$687$	0.654723	+	0.378004i	0.0249792	+	0.0144218i
$688$		0			0
$689$	−31.2284	−	9.01486i	−1.18971	−	0.343439i
$690$		0			0
$691$	21.8654	−	37.8720i	0.831800	−	1.44072i	−0.0648100	−	0.997898i	$-0.520644\pi$
$691$	21.8654	−	37.8720i	0.831800	−	1.44072i	0.896610	−	0.442822i	$-0.146023\pi$
$692$		0			0
$693$	−3.03547	+	1.75253i	−0.115308	+	0.0665732i
$694$		0			0
$695$	−11.6242	+	6.71121i	−0.440929	+	0.254571i
$696$		0			0
$697$		−	10.5468i		−	0.399490i
$698$		0			0
$699$	−9.41698	−	5.43690i	−0.356183	−	0.205642i
$700$		0			0
$701$			30.5767i			1.15487i	0.816438	+	0.577433i	$0.195945\pi$
$701$			30.5767i			1.15487i	−0.816438	+	0.577433i	$0.804055\pi$
$702$		0			0
$703$	28.0559			1.05815
$704$		0			0
$705$	−5.50535	+	9.53554i	−0.207343	+	0.359129i
$706$		0			0
$707$	−9.71710			−0.365449
$708$		0			0
$709$	−10.3464	−	17.9204i	−0.388566	−	0.673015i	0.603691	−	0.797218i	$-0.293696\pi$
$709$	−10.3464	−	17.9204i	−0.388566	−	0.673015i	−0.992257	+	0.124203i	$0.960363\pi$
$710$		0			0
$711$	−4.76199	−	8.24801i	−0.178589	−	0.309325i
$712$		0			0
$713$	13.6338	+	7.87149i	0.510591	+	0.294790i
$714$		0			0
$715$	−11.1035	−	11.5391i	−0.415246	−	0.431537i
$716$		0			0
$717$	−6.38983	+	11.0675i	−0.238633	+	0.413324i
$718$		0			0
$719$	23.3429	+	40.4311i	0.870544	+	1.50783i	0.861435	+	0.507867i	$0.169566\pi$
$719$	23.3429	+	40.4311i	0.870544	+	1.50783i	0.00910807	+	0.999959i	$0.497101\pi$
$720$		0			0
$721$	15.2676	−	8.81478i	0.568597	−	0.328279i
$722$		0			0
$723$	−26.8375			−0.998098
$724$		0			0
$725$	−25.4211	−	14.6769i	−0.944116	−	0.545085i
$726$		0			0
$727$	−24.5578			−0.910797			−0.455398	−	0.890288i	$-0.650503\pi$
$727$	−24.5578			−0.910797			−0.455398	+	0.890288i	$0.650503\pi$
$728$		0			0
$729$	−27.3858			−1.01429
$730$		0			0
$731$	54.3082	+	31.3548i	2.00866	+	1.15970i
$732$		0			0
$733$	37.4461			1.38310			0.691551	−	0.722328i	$-0.256928\pi$
$733$	37.4461			1.38310			0.691551	+	0.722328i	$0.256928\pi$
$734$		0			0
$735$	2.36629	−	1.36618i	0.0872820	−	0.0503923i
$736$		0			0
$737$	2.51963	+	4.36413i	0.0928118	+	0.160755i
$738$		0			0
$739$	−23.1088	+	40.0257i	−0.850072	+	1.47237i	0.0310708	+	0.999517i	$0.490108\pi$
$739$	−23.1088	+	40.0257i	−0.850072	+	1.47237i	−0.881143	+	0.472850i	$0.843225\pi$
$740$		0			0
$741$	36.5353	+	10.5468i	1.34216	+	0.387447i
$742$		0			0
$743$	−33.5896	−	19.3930i	−1.23228	−	0.711459i	−0.264778	−	0.964309i	$-0.585299\pi$
$743$	−33.5896	−	19.3930i	−1.23228	−	0.711459i	−0.967505	+	0.252850i	$0.918632\pi$
$744$		0			0
$745$	1.86599	+	3.23198i	0.0683645	+	0.118411i
$746$		0			0
$747$	−4.88251	−	8.45676i	−0.178642	−	0.309417i
$748$		0			0
$749$	5.03926			0.184131
$750$		0			0
$751$	−1.26041	+	2.18309i	−0.0459929	+	0.0796621i	−0.888105	−	0.459640i	$-0.847979\pi$
$751$	−1.26041	+	2.18309i	−0.0459929	+	0.0796621i	0.842112	+	0.539302i	$0.181312\pi$
$752$		0			0
$753$	17.8033			0.648789
$754$		0			0
$755$			74.3042i			2.70421i
$756$		0			0
$757$	34.0391	+	19.6525i	1.23717	+	0.714281i	0.968515	−	0.248955i	$-0.0800872\pi$
$757$	34.0391	+	19.6525i	1.23717	+	0.714281i	0.268656	+	0.963236i	$0.413421\pi$
$758$		0			0
$759$		−	12.0589i		−	0.437710i
$760$		0			0
$761$	0.248203	−	0.143300i	0.00899735	−	0.00519462i	−0.495495	−	0.868611i	$-0.665013\pi$
$761$	0.248203	−	0.143300i	0.00899735	−	0.00519462i	0.504492	+	0.863416i	$0.331680\pi$
$762$		0			0
$763$	−23.1938	+	13.3910i	−0.839673	+	0.484785i
$764$		0			0
$765$	16.1088	−	27.9013i	0.582416	−	1.00877i
$766$		0			0
$767$	19.5466	−	4.83654i	0.705789	−	0.174637i
$768$		0			0
$769$	8.61400	+	4.97329i	0.310629	+	0.179342i	0.647208	−	0.762314i	$-0.275937\pi$
$769$	8.61400	+	4.97329i	0.310629	+	0.179342i	−0.336579	+	0.941655i	$0.609270\pi$
$770$		0			0
$771$	−12.0938	+	6.98238i	−0.435549	+	0.251464i
$772$		0			0
$773$	−10.1916	−	17.6523i	−0.366566	−	0.634910i	0.622460	−	0.782651i	$-0.286133\pi$
$773$	−10.1916	−	17.6523i	−0.366566	−	0.634910i	−0.989026	+	0.147741i	$0.952800\pi$
$774$		0			0
$775$		−	20.1784i		−	0.724831i
$776$		0			0
$777$	6.07606	−	10.5240i	0.217978	−	0.377548i
$778$		0			0
$779$			12.0589i			0.432055i
$780$		0			0
$781$			4.28687i			0.153396i
$782$		0			0
$783$	8.19557	−	14.1951i	0.292886	−	0.507293i
$784$		0			0
$785$			30.4446i			1.08661i
$786$		0			0
$787$	3.41310	+	5.91166i	0.121664	+	0.210728i	0.920424	−	0.390922i	$-0.127844\pi$
$787$	3.41310	+	5.91166i	0.121664	+	0.210728i	−0.798760	+	0.601650i	$0.794510\pi$
$788$		0			0
$789$	−22.0946	+	12.7563i	−0.786587	+	0.454136i
$790$		0			0
$791$	27.7978	+	16.0491i	0.988377	+	0.570639i
$792$		0			0
$793$	1.50000	+	6.06218i	0.0532666	+	0.215274i
$794$		0			0
$795$	−23.4599	+	40.6338i	−0.832039	+	1.44113i
$796$		0			0
$797$	25.4211	−	14.6769i	0.900461	−	0.519882i	0.0231115	−	0.999733i	$-0.492643\pi$
$797$	25.4211	−	14.6769i	0.900461	−	0.519882i	0.877350	+	0.479851i	$0.159309\pi$
$798$		0			0
$799$	12.6130	−	7.28212i	0.446216	−	0.257623i
$800$		0			0
$801$		−	3.50506i		−	0.123845i
$802$		0			0
$803$	−11.2580	−	6.49981i	−0.397286	−	0.229373i
$804$		0			0
$805$			77.8056i			2.74229i
$806$		0			0
$807$	22.1049			0.778131
$808$		0			0
$809$	−0.788791	+	1.36623i	−0.0277324	+	0.0480339i	−0.879559	−	0.475791i	$-0.842162\pi$
$809$	−0.788791	+	1.36623i	−0.0277324	+	0.0480339i	0.851826	+	0.523825i	$0.175495\pi$
$810$		0			0
$811$	−18.6068			−0.653375			−0.326687	−	0.945132i	$-0.605932\pi$
$811$	−18.6068			−0.653375			−0.326687	+	0.945132i	$0.605932\pi$
$812$		0			0
$813$	8.37781	+	14.5108i	0.293823	+	0.508916i
$814$		0			0
$815$	0.0660387	+	0.114382i	0.00231324	+	0.00400664i
$816$		0			0
$817$	−62.0942	−	35.8501i	−2.17240	−	1.25424i
$818$		0			0
$819$	−7.96457	+	7.66391i	−0.278305	+	0.267799i
$820$		0			0
$821$	4.36485	−	7.56015i	0.152334	−	0.263851i	−0.779751	−	0.626090i	$-0.784654\pi$
$821$	4.36485	−	7.56015i	0.152334	−	0.263851i	0.932085	+	0.362239i	$0.117988\pi$
$822$		0			0
$823$	−16.5487	−	28.6633i	−0.576853	−	0.999139i	−0.995838	−	0.0911453i	$-0.970947\pi$
$823$	−16.5487	−	28.6633i	−0.576853	−	0.999139i	0.418985	−	0.907993i	$-0.362386\pi$
$824$		0			0
$825$	−13.3856	+	7.72819i	−0.466027	+	0.269061i
$826$		0			0
$827$	−35.0181			−1.21770			−0.608849	−	0.793286i	$-0.708368\pi$
$827$	−35.0181			−1.21770			−0.608849	+	0.793286i	$0.708368\pi$
$828$		0			0
$829$	40.8265	+	23.5712i	1.41796	+	0.818662i	0.996120	−	0.0880064i	$-0.0280496\pi$
$829$	40.8265	+	23.5712i	1.41796	+	0.818662i	0.421844	+	0.906668i	$0.361383\pi$
$830$		0			0
$831$	−8.18053			−0.283780
$832$		0			0
$833$	−3.61419			−0.125224
$834$		0			0
$835$	−52.7252	−	30.4409i	−1.82463	−	1.05345i
$836$		0			0
$837$	11.2676			0.389467
$838$		0			0
$839$	34.6580	−	20.0098i	1.19653	−	0.690816i	0.236748	−	0.971571i	$-0.423918\pi$
$839$	34.6580	−	20.0098i	1.19653	−	0.690816i	0.959779	+	0.280755i	$0.0905850\pi$
$840$		0			0
$841$	−10.2676	−	17.7841i	−0.354057	−	0.613244i
$842$		0			0
$843$	6.03940	−	10.4605i	0.208008	−	0.360280i
$844$		0			0
$845$	−42.7293	−	26.9125i	−1.46993	−	0.925818i
$846$		0			0
$847$	21.3598	+	12.3321i	0.733931	+	0.423735i
$848$		0			0
$849$	−12.9476	−	22.4259i	−0.444360	−	0.769654i
$850$		0			0
$851$	−14.0279	−	24.2971i	−0.480871	−	0.832893i
$852$		0			0
$853$	22.7427			0.778694			0.389347	−	0.921091i	$-0.372701\pi$
$853$	22.7427			0.778694			0.389347	+	0.921091i	$0.372701\pi$
$854$		0			0
$855$	−18.4183	+	31.9015i	−0.629893	+	1.09101i
$856$		0			0
$857$	36.9996			1.26388			0.631941	−	0.775016i	$-0.282258\pi$
$857$	36.9996			1.26388			0.631941	+	0.775016i	$0.282258\pi$
$858$		0			0
$859$			49.3854i			1.68501i	0.538689	+	0.842504i	$0.318920\pi$
$859$			49.3854i			1.68501i	−0.538689	+	0.842504i	$0.681080\pi$
$860$		0			0
$861$	4.52342	+	2.61160i	0.154158	+	0.0890030i
$862$		0			0
$863$			0.963392i			0.0327942i	0.999866	+	0.0163971i	$0.00521960\pi$
$863$			0.963392i			0.0327942i	−0.999866	+	0.0163971i	$0.994780\pi$
$864$		0			0
$865$	−27.7875	+	16.0431i	−0.944802	+	0.545482i
$866$		0			0
$867$	35.2707	−	20.3635i	1.19785	−	0.691582i
$868$		0			0
$869$	4.51944	−	7.82790i	0.153311	−	0.265543i
$870$		0			0
$871$	11.0185	+	11.4507i	0.373347	+	0.387993i
$872$		0			0
$873$	−1.80709	−	1.04333i	−0.0611609	−	0.0353113i
$874$		0			0
$875$	43.5648	−	25.1521i	1.47276	−	0.850297i
$876$		0			0
$877$	−14.5696	−	25.2353i	−0.491980	−	0.852134i	0.507977	−	0.861370i	$-0.330393\pi$
$877$	−14.5696	−	25.2353i	−0.491980	−	0.852134i	−0.999957	+	0.00923623i	$0.997060\pi$
$878$		0			0
$879$		−	9.68869i		−	0.326792i
$880$		0			0
$881$	7.59702	−	13.1584i	0.255950	−	0.443319i	−0.709203	−	0.705004i	$-0.750945\pi$
$881$	7.59702	−	13.1584i	0.255950	−	0.443319i	0.965153	+	0.261686i	$0.0842784\pi$
$882$		0			0
$883$		−	41.5246i		−	1.39741i	−0.715408	−	0.698707i	$-0.753759\pi$
$883$		−	41.5246i		−	1.39741i	0.715408	−	0.698707i	$-0.246241\pi$
$884$		0			0
$885$		−	29.0671i		−	0.977082i
$886$		0			0
$887$	10.7299	−	18.5847i	0.360275	−	0.624015i	−0.627731	−	0.778430i	$-0.716016\pi$
$887$	10.7299	−	18.5847i	0.360275	−	0.624015i	0.988006	+	0.154416i	$0.0493495\pi$
$888$		0			0
$889$			8.90130i			0.298540i
$890$		0			0
$891$	−2.24925	−	3.89582i	−0.0753528	−	0.130515i
$892$		0			0
$893$	−14.4213	+	8.32613i	−0.482590	+	0.278623i
$894$		0			0
$895$	73.1661	+	42.2425i	2.44567	+	1.41201i
$896$		0			0
$897$	−9.13382	−	36.9139i	−0.304969	−	1.23252i
$898$		0			0
$899$	−2.90942	+	5.03926i	−0.0970346	+	0.168069i
$900$		0			0
$901$	53.7478	−	31.0313i	1.79060	−	1.03380i
$902$		0			0
$903$	−26.8955	+	15.5281i	−0.895026	+	0.516743i
$904$		0			0
$905$		−	38.0371i		−	1.26440i
$906$		0			0
$907$	−16.3262	−	9.42595i	−0.542103	−	0.312983i	0.203828	−	0.979007i	$-0.434662\pi$
$907$	−16.3262	−	9.42595i	−0.542103	−	0.312983i	−0.745931	+	0.666023i	$0.767995\pi$
$908$		0			0
$909$			4.60051i			0.152589i
$910$		0			0
$911$	−50.4520			−1.67155			−0.835775	−	0.549073i	$-0.814981\pi$
$911$	−50.4520			−1.67155			−0.835775	+	0.549073i	$0.814981\pi$
$912$		0			0
$913$	4.63382	−	8.02601i	0.153357	−	0.265622i
$914$		0			0
$915$	9.01486			0.298022
$916$		0			0
$917$	17.5183	+	30.3426i	0.578505	+	1.00200i
$918$		0			0
$919$	5.70180	+	9.87580i	0.188085	+	0.325773i	0.944612	−	0.328190i	$-0.106439\pi$
$919$	5.70180	+	9.87580i	0.188085	+	0.325773i	−0.756527	+	0.653963i	$0.773105\pi$
$920$		0			0
$921$	22.2873	+	12.8676i	0.734391	+	0.424001i
$922$		0			0
$923$	3.24702	+	13.1227i	0.106877	+	0.431938i
$924$		0			0
$925$	−17.9802	+	31.1426i	−0.591185	+	1.02396i
$926$		0			0
$927$	−4.17331	−	7.22838i	−0.137069	−	0.237411i
$928$		0			0
$929$	−29.4962	+	17.0296i	−0.967739	+	0.558725i	−0.898546	−	0.438879i	$-0.855376\pi$
$929$	−29.4962	+	17.0296i	−0.967739	+	0.558725i	−0.0691930	+	0.997603i	$0.522042\pi$
$930$		0			0
$931$	4.13234			0.135432
$932$		0			0
$933$	−3.19669	−	1.84561i	−0.104655	−	0.0604226i
$934$		0			0
$935$	30.5767			0.999964
$936$		0			0
$937$	−5.69271			−0.185973			−0.0929864	−	0.995667i	$-0.529641\pi$
$937$	−5.69271			−0.185973			−0.0929864	+	0.995667i	$0.529641\pi$
$938$		0			0
$939$	0.654723	+	0.378004i	0.0213661	+	0.0123357i
$940$		0			0
$941$	21.5379			0.702117			0.351058	−	0.936354i	$-0.385822\pi$
$941$	21.5379			0.702117			0.351058	+	0.936354i	$0.385822\pi$
$942$		0			0
$943$	10.4433	−	6.02945i	0.340081	−	0.196346i
$944$		0			0
$945$	27.8437	+	48.2267i	0.905756	+	1.56881i
$946$		0			0
$947$	10.9640	−	18.9902i	0.356282	−	0.617098i	−0.631055	−	0.775738i	$-0.717378\pi$
$947$	10.9640	−	18.9902i	0.356282	−	0.617098i	0.987336	+	0.158640i	$0.0507110\pi$
$948$		0			0
$949$	−39.3854	−	11.3696i	−1.27850	−	0.369073i
$950$		0			0
$951$	17.7161	+	10.2284i	0.574483	+	0.331678i
$952$		0			0
$953$	19.0183	+	32.9407i	0.616063	+	1.06705i	0.990197	+	0.139678i	$0.0446068\pi$
$953$	19.0183	+	32.9407i	0.616063	+	1.06705i	−0.374134	+	0.927375i	$0.622060\pi$
$954$		0			0
$955$	41.4236	+	71.7478i	1.34044	+	2.32170i
$956$		0			0
$957$	4.45714			0.144079
$958$		0			0
$959$	−13.4188	+	23.2420i	−0.433315	+	0.750523i
$960$		0			0
$961$	27.0000			0.870968
$962$		0			0
$963$		−	2.38581i		−	0.0768817i
$964$		0			0
$965$	−55.7282	−	32.1747i	−1.79395	−	1.03574i
$966$		0			0
$967$		−	30.4354i		−	0.978736i	−0.872077	−	0.489368i	$-0.837228\pi$
$967$		−	30.4354i		−	0.978736i	0.872077	−	0.489368i	$-0.162772\pi$
$968$		0			0
$969$	−62.8816	+	36.3047i	−2.02005	+	1.16628i
$970$		0			0
$971$	−34.1899	+	19.7395i	−1.09720	+	0.633471i	−0.935485	−	0.353365i	$-0.885037\pi$
$971$	−34.1899	+	19.7395i	−1.09720	+	0.633471i	−0.161719	+	0.986837i	$0.551704\pi$
$972$		0			0
$973$	−4.39631	+	7.61463i	−0.140939	+	0.244114i
$974$		0			0
$975$	−35.1216	+	33.7958i	−1.12479	+	1.08233i
$976$		0			0
$977$	6.48037	+	3.74144i	0.207325	+	0.119699i	0.600068	−	0.799949i	$-0.295140\pi$
$977$	6.48037	+	3.74144i	0.207325	+	0.119699i	−0.392742	+	0.919649i	$0.628474\pi$
$978$		0			0
$979$	2.88086	−	1.66327i	0.0920727	−	0.0531582i
$980$		0			0
$981$	6.33988	+	10.9810i	0.202417	+	0.350596i
$982$		0			0
$983$		−	36.6878i		−	1.17016i	−0.810976	−	0.585079i	$-0.801063\pi$
$983$		−	36.6878i		−	1.17016i	0.810976	−	0.585079i	$-0.198937\pi$
$984$		0			0
$985$	−24.3517	+	42.1784i	−0.775910	+	1.34392i
$986$		0			0
$987$			7.21277i			0.229585i
$988$		0			0
$989$			71.7002i			2.27993i
$990$		0			0
$991$	11.1981	−	19.3956i	0.355718	−	0.616122i	−0.631522	−	0.775358i	$-0.717570\pi$
$991$	11.1981	−	19.3956i	0.355718	−	0.616122i	0.987241	+	0.159235i	$0.0509029\pi$
$992$		0			0
$993$		−	14.3840i		−	0.456464i
$994$		0			0
$995$	23.7825	+	41.1925i	0.753956	+	1.30589i
$996$		0			0
$997$	−42.4604	+	24.5145i	−1.34473	+	0.776382i	−0.987498	−	0.157633i	$-0.949614\pi$
$997$	−42.4604	+	24.5145i	−1.34473	+	0.776382i	−0.357235	+	0.934015i	$0.616280\pi$
$998$		0			0
$999$	−17.3900	−	10.0401i	−0.550196	−	0.317656i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	832.2.ba.i.225.3	yes	12
4.3	odd	2	inner	832.2.ba.i.225.4	yes	12
8.3	odd	2		832.2.ba.h.225.3	✓	12
8.5	even	2		832.2.ba.h.225.4	yes	12
13.10	even	6		832.2.ba.h.673.4	yes	12
52.23	odd	6		832.2.ba.h.673.3	yes	12
104.75	odd	6	inner	832.2.ba.i.673.4	yes	12
104.101	even	6	inner	832.2.ba.i.673.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
832.2.ba.h.225.3	✓	12	8.3	odd	2
832.2.ba.h.225.4	yes	12	8.5	even	2
832.2.ba.h.673.3	yes	12	52.23	odd	6
832.2.ba.h.673.4	yes	12	13.10	even	6
832.2.ba.i.225.3	yes	12	1.1	even	1	trivial
832.2.ba.i.225.4	yes	12	4.3	odd	2	inner
832.2.ba.i.673.3	yes	12	104.101	even	6	inner
832.2.ba.i.673.4	yes	12	104.75	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	832.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16037 - 0.669938i) q^{3} +3.88448 q^{5} +(2.20369 - 1.27230i) q^{7} +(-0.602365 - 1.04333i) q^{9} +(0.571683 - 0.990185i) q^{11} +(1.00000 - 3.46410i) q^{13} +(-4.50743 - 2.60236i) q^{15} +(3.44224 + 5.96214i) q^{17} +(-3.93574 - 6.81691i) q^{19} -3.40946 q^{21} +(-3.93574 + 6.81691i) q^{23} +10.0892 q^{25} +5.63382i q^{27} +(-2.51963 - 1.45471i) q^{29} -2.00000i q^{31} +(-1.32673 + 0.765985i) q^{33} +(8.56021 - 4.94224i) q^{35} +(-1.78212 + 3.08672i) q^{37} +(-3.48110 + 3.34969i) q^{39} +(-1.32673 - 0.765985i) q^{41} +(7.88849 - 4.55442i) q^{43} +(-2.33988 - 4.05279i) q^{45} -2.11552i q^{47} +(-0.262488 + 0.454643i) q^{49} -9.22436i q^{51} -9.01486i q^{53} +(2.22069 - 3.84636i) q^{55} +10.5468i q^{57} +(2.79238 + 4.83654i) q^{59} +(-1.50000 + 0.866025i) q^{61} +(-2.65486 - 1.53278i) q^{63} +(3.88448 - 13.4562i) q^{65} +(-2.20369 + 3.81691i) q^{67} +(9.13382 - 5.27341i) q^{69} +(-3.24702 + 1.87467i) q^{71} -11.3696i q^{73} +(-11.7072 - 6.75915i) q^{75} -2.90942i q^{77} +7.90549 q^{79} +(1.96722 - 3.40732i) q^{81} +8.10557 q^{83} +(13.3713 + 23.1598i) q^{85} +(1.94913 + 3.37599i) q^{87} +(2.51963 + 1.45471i) q^{89} +(-2.20369 - 8.90612i) q^{91} +(-1.33988 + 2.32073i) q^{93} +(-15.2883 - 26.4802i) q^{95} +(1.50000 - 0.866025i) q^{97} -1.37745 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{9} + 12 q^{13} + 18 q^{17} + 36 q^{21} + 36 q^{25} - 18 q^{29} + 54 q^{33} + 6 q^{37} + 54 q^{41} - 24 q^{45} + 12 q^{49} - 18 q^{61} - 18 q^{69} - 30 q^{81} + 48 q^{85} + 18 q^{89} - 12 q^{93}+ \cdots + 18 q^{97}+O(q^{100}) \) 12 * q + 12 * q^9 + 12 * q^13 + 18 * q^17 + 36 * q^21 + 36 * q^25 - 18 * q^29 + 54 * q^33 + 6 * q^37 + 54 * q^41 - 24 * q^45 + 12 * q^49 - 18 * q^61 - 18 * q^69 - 30 * q^81 + 48 * q^85 + 18 * q^89 - 12 * q^93 + 18 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more