LMFDB - Embedded newform 252.7.z.f.145.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,7,Mod(73,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("252.73");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	252.z (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:	$57.9736290722$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 6586 x^{10} - 4380 x^{9} + 29743412 x^{8} - 22316460 x^{7} + 72097469286 x^{6} + \cdots + 78\!\cdots\!61 $ x^12 + 6586x^10 - 4380x^9 + 29743412x^8 - 22316460x^7 + 72097469286x^6 - 74114131680x^5 + 127603094377722x^4 - 68863099720860x^3 + 120620660396154896x^2 + 69805069827473280x + 78212563531160784961
Coefficient ring:	$\Z[a_1, \ldots, a_{31}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{9}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.6
Root			$-27.9068 - 48.3360i$ of defining polynomial
Character	$\chi$	$=$	252.145
Dual form			252.7.z.f.73.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(168.242 + 97.1348i) q^{5} +(-211.725 + 269.854i) q^{7} +O(q^{10})$	$q+(168.242 + 97.1348i) q^{5} +(-211.725 + 269.854i) q^{7} +(-470.717 - 815.305i) q^{11} -2231.10i q^{13} +(6950.48 - 4012.86i) q^{17} +(-8227.80 - 4750.32i) q^{19} +(9169.83 - 15882.6i) q^{23} +(11057.8 + 19152.8i) q^{25} +15046.5 q^{29} +(40057.7 - 23127.3i) q^{31} +(-61833.4 + 24835.1i) q^{35} +(-24942.8 + 43202.2i) q^{37} +67097.5i q^{41} +71024.3 q^{43} +(-36198.3 - 20899.1i) q^{47} +(-27993.9 - 114270. i) q^{49} +(28842.4 + 49956.6i) q^{53} -182892. i q^{55} +(-269333. + 155500. i) q^{59} +(315104. + 181925. i) q^{61} +(216717. - 375365. i) q^{65} +(83755.0 + 145068. i) q^{67} +192718. q^{71} +(117407. - 67785.2i) q^{73} +(319676. + 45595.7i) q^{77} +(418513. - 724886. i) q^{79} -572811. i q^{83} +1.55915e6 q^{85} +(1.13239e6 + 653784. i) q^{89} +(602071. + 472379. i) q^{91} +(-922843. - 1.59841e6i) q^{95} -218356. i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 714 q^{7}+O(q^{10}) $ 12 * q + 714 * q^7	$ 12 q + 714 q^{7} - 59466 q^{19} + 64086 q^{25} + 219834 q^{31} - 166242 q^{37} - 326916 q^{43} - 132006 q^{49} + 736008 q^{61} + 176238 q^{67} - 2931018 q^{73} + 449490 q^{79} + 2174592 q^{85} - 808542 q^{91}+O(q^{100}) $ 12 * q + 714 * q^7 - 59466 * q^19 + 64086 * q^25 + 219834 * q^31 - 166242 * q^37 - 326916 * q^43 - 132006 * q^49 + 736008 * q^61 + 176238 * q^67 - 2931018 * q^73 + 449490 * q^79 + 2174592 * q^85 - 808542 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	168.242	+	97.1348i	1.34594	+	0.777079i	0.987672	−	0.156540i	$-0.0500341\pi$
$5$	168.242	+	97.1348i	1.34594	+	0.777079i	0.358268	+	0.933619i	$0.383367\pi$
$6$		0			0
$7$	−211.725	+	269.854i	−0.617275	+	0.786748i
$7$	−211.725	+	269.854i	−0.617275	+	0.786748i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−470.717	−	815.305i	−0.353657	−	0.612551i	0.633231	−	0.773963i	$-0.281728\pi$
$11$	−470.717	−	815.305i	−0.353657	−	0.612551i	−0.986887	+	0.161412i	$0.948395\pi$
$12$		0			0
$13$		−	2231.10i		−	1.01552i	−0.861499	−	0.507760i	$-0.830474\pi$
$13$		−	2231.10i		−	1.01552i	0.861499	−	0.507760i	$-0.169526\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	6950.48	−	4012.86i	1.41471	−	0.816784i	0.418885	−	0.908039i	$-0.362421\pi$
$17$	6950.48	−	4012.86i	1.41471	−	0.816784i	0.995828	+	0.0912550i	$0.0290878\pi$
$18$		0			0
$19$	−8227.80	−	4750.32i	−1.19956	−	0.692567i	−0.239104	−	0.970994i	$-0.576854\pi$
$19$	−8227.80	−	4750.32i	−1.19956	−	0.692567i	−0.960458	+	0.278426i	$0.910187\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	9169.83	−	15882.6i	0.753664	−	1.30538i	−0.192371	−	0.981322i	$-0.561618\pi$
$23$	9169.83	−	15882.6i	0.753664	−	1.30538i	0.946036	−	0.324063i	$-0.105049\pi$
$24$		0			0
$25$	11057.8	+	19152.8i	0.707702	+	1.22578i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	15046.5			0.616936			0.308468	−	0.951235i	$-0.400184\pi$
$29$	15046.5			0.616936			0.308468	+	0.951235i	$0.400184\pi$
$30$		0			0
$31$	40057.7	−	23127.3i	1.34462	−	0.776318i	0.357141	−	0.934050i	$-0.383752\pi$
$31$	40057.7	−	23127.3i	1.34462	−	0.776318i	0.987482	+	0.157732i	$0.0504182\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−61833.4	+	24835.1i	−1.44218	+	0.579244i
$36$		0			0
$37$	−24942.8	+	43202.2i	−0.492425	+	0.852905i	−0.999962	−	0.00872476i	$-0.997223\pi$
$37$	−24942.8	+	43202.2i	−0.492425	+	0.852905i	0.507537	+	0.861630i	$0.330556\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			67097.5i			0.973542i	0.873530	+	0.486771i	$0.161825\pi$
$41$			67097.5i			0.973542i	−0.873530	+	0.486771i	$0.838175\pi$
$42$		0			0
$43$	71024.3			0.893309			0.446654	−	0.894707i	$-0.352615\pi$
$43$	71024.3			0.893309			0.446654	+	0.894707i	$0.352615\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−36198.3	−	20899.1i	−0.348654	−	0.201295i	0.315438	−	0.948946i	$-0.397848\pi$
$47$	−36198.3	−	20899.1i	−0.348654	−	0.201295i	−0.664092	+	0.747651i	$0.731182\pi$
$48$		0			0
$49$	−27993.9	−	114270.i	−0.237944	−	0.971279i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	28842.4	+	49956.6i	0.193733	+	0.335556i	0.946485	−	0.322749i	$-0.104607\pi$
$53$	28842.4	+	49956.6i	0.193733	+	0.335556i	−0.752751	+	0.658305i	$0.771274\pi$
$54$		0			0
$55$		−	182892.i		−	1.09928i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−269333.	+	155500.i	−1.31140	+	0.757135i	−0.982327	−	0.187171i	$-0.940068\pi$
$59$	−269333.	+	155500.i	−1.31140	+	0.757135i	−0.329069	+	0.944306i	$0.606735\pi$
$60$		0			0
$61$	315104.	+	181925.i	1.38824	+	0.801500i	0.993117	−	0.117129i	$-0.0373690\pi$
$61$	315104.	+	181925.i	1.38824	+	0.801500i	0.395122	+	0.918629i	$0.370702\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	216717.	−	375365.i	0.789139	−	1.36683i
$66$		0			0
$67$	83755.0	+	145068.i	0.278475	+	0.482333i	0.971006	−	0.239055i	$-0.0768377\pi$
$67$	83755.0	+	145068.i	0.278475	+	0.482333i	−0.692531	+	0.721388i	$0.743504\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	192718.			0.538454			0.269227	−	0.963077i	$-0.413232\pi$
$71$	192718.			0.538454			0.269227	+	0.963077i	$0.413232\pi$
$72$		0			0
$73$	117407.	−	67785.2i	0.301806	−	0.174248i	−0.341448	−	0.939901i	$-0.610917\pi$
$73$	117407.	−	67785.2i	0.301806	−	0.174248i	0.643254	+	0.765653i	$0.277584\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	319676.	+	45595.7i	0.700226	+	0.0998738i
$78$		0			0
$79$	418513.	−	724886.i	0.848844	−	1.47024i	−0.0333975	−	0.999442i	$-0.510633\pi$
$79$	418513.	−	724886.i	0.848844	−	1.47024i	0.882241	−	0.470798i	$-0.156034\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	572811.i		−	1.00179i	−0.865508	−	0.500896i	$-0.833004\pi$
$83$		−	572811.i		−	1.00179i	0.865508	−	0.500896i	$-0.166996\pi$
$84$		0			0
$85$	1.55915e6			2.53882
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.13239e6	+	653784.i	1.60629	+	0.927393i	0.990190	+	0.139727i	$0.0446226\pi$
$89$	1.13239e6	+	653784.i	1.60629	+	0.927393i	0.616102	+	0.787666i	$0.288711\pi$
$90$		0			0
$91$	602071.	+	472379.i	0.798958	+	0.626855i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−922843.	−	1.59841e6i	−1.07636	−	1.86431i
$96$		0			0
$97$		−	218356.i		−	0.239249i	−0.992819	−	0.119625i	$-0.961831\pi$
$97$		−	218356.i		−	0.239249i	0.992819	−	0.119625i	$-0.0381691\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.50016e6	+	866116.i	−1.45604	+	0.840643i	−0.998813	−	0.0487085i	$-0.984489\pi$
$101$	−1.50016e6	+	866116.i	−1.45604	+	0.840643i	−0.457224	+	0.889352i	$0.651156\pi$
$102$		0			0
$103$	442440.	+	255443.i	0.404895	+	0.233766i	0.688594	−	0.725147i	$-0.258228\pi$
$103$	442440.	+	255443.i	0.404895	+	0.233766i	−0.283699	+	0.958913i	$0.591562\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−537232.	+	930514.i	−0.438542	+	0.759576i	−0.997577	−	0.0695673i	$-0.977838\pi$
$107$	−537232.	+	930514.i	−0.438542	+	0.759576i	0.559036	+	0.829144i	$0.311171\pi$
$108$		0			0
$109$	−299544.	−	518826.i	−0.231303	−	0.400629i	0.726889	−	0.686755i	$-0.240966\pi$
$109$	−299544.	−	518826.i	−0.231303	−	0.400629i	−0.958192	+	0.286126i	$0.907632\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.19592e6			0.828832			0.414416	−	0.910088i	$-0.363986\pi$
$113$	1.19592e6			0.828832			0.414416	+	0.910088i	$0.363986\pi$
$114$		0			0
$115$	3.08551e6	−	1.78142e6i	2.02877	−	1.17131i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−388703.	+	2.72524e6i	−0.230663	+	1.61720i
$120$		0			0
$121$	442632.	−	766661.i	0.249854	−	0.432760i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			1.26095e6i			0.645604i
$126$		0			0
$127$	−1.27474e6			−0.622316			−0.311158	−	0.950358i	$-0.600717\pi$
$127$	−1.27474e6			−0.622316			−0.311158	+	0.950358i	$0.600717\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−596224.	−	344230.i	−0.265214	−	0.153121i	0.361497	−	0.932373i	$-0.382266\pi$
$131$	−596224.	−	344230.i	−0.265214	−	0.153121i	−0.626711	+	0.779252i	$0.715599\pi$
$132$		0			0
$133$	3.02393e6	−	1.21454e6i	1.28534	−	0.516248i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.42078e6	−	4.19291e6i	−0.941441	−	1.63062i	−0.762726	−	0.646722i	$-0.776139\pi$
$137$	−2.42078e6	−	4.19291e6i	−0.941441	−	1.63062i	−0.178715	−	0.983901i	$-0.557194\pi$
$138$		0			0
$139$			864011.i			0.321718i	0.986977	+	0.160859i	$0.0514264\pi$
$139$			864011.i			0.321718i	−0.986977	+	0.160859i	$0.948574\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.81903e6	+	1.05021e6i	−0.622058	+	0.359145i
$144$		0			0
$145$	2.53145e6	+	1.46154e6i	0.830359	+	0.479408i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	2.90565e6	−	5.03274e6i	0.878385	−	1.52141i	0.0252717	−	0.999681i	$-0.491955\pi$
$149$	2.90565e6	−	5.03274e6i	0.878385	−	1.52141i	0.853113	−	0.521726i	$-0.174712\pi$
$150$		0			0
$151$	2.01318e6	+	3.48693e6i	0.584725	+	1.01277i	0.994910	+	0.100771i	$0.0321309\pi$
$151$	2.01318e6	+	3.48693e6i	0.584725	+	1.01277i	−0.410185	+	0.912002i	$0.634536\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	8.98587e6			2.41304
$156$		0			0
$157$	−575695.	+	332378.i	−0.148763	+	0.0858881i	−0.572534	−	0.819881i	$-0.694039\pi$
$157$	−575695.	+	332378.i	−0.148763	+	0.0858881i	0.423771	+	0.905769i	$0.360706\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.34451e6	+	5.83727e6i	0.561791	+	1.39872i
$162$		0			0
$163$	1.54844e6	−	2.68198e6i	0.357547	−	0.619289i	−0.630004	−	0.776592i	$-0.716947\pi$
$163$	1.54844e6	−	2.68198e6i	0.357547	−	0.619289i	0.987550	+	0.157303i	$0.0502800\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	7.53353e6i		−	1.61752i	−0.588140	−	0.808759i	$-0.700140\pi$
$167$		−	7.53353e6i		−	1.61752i	0.588140	−	0.808759i	$-0.299860\pi$
$168$		0			0
$169$	−150983.			−0.0312802
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.80878e6	−	2.19900e6i	−0.735611	−	0.424705i	0.0848605	−	0.996393i	$-0.472956\pi$
$173$	−3.80878e6	−	2.19900e6i	−0.735611	−	0.424705i	−0.820471	+	0.571688i	$0.806289\pi$
$174$		0			0
$175$	−7.50968e6	−	1.07111e6i	−1.40122	−	0.199858i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1.75331e6	+	3.03682e6i	0.305703	+	0.529493i	0.977418	−	0.211317i	$-0.0677752\pi$
$179$	1.75331e6	+	3.03682e6i	0.305703	+	0.529493i	−0.671715	+	0.740810i	$0.734442\pi$
$180$		0			0
$181$		−	315253.i		−	0.0531647i	−0.999647	−	0.0265824i	$-0.991538\pi$
$181$		−	315253.i		−	0.0531647i	0.999647	−	0.0265824i	$-0.00846243\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−8.39288e6	+	4.84563e6i	−1.32555	+	0.765306i
$186$		0			0
$187$	−6.54342e6	−	3.77784e6i	−1.00064	−	0.577722i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	549572.	−	951887.i	0.0788723	−	0.136611i	−0.823891	−	0.566748i	$-0.808201\pi$
$191$	549572.	−	951887.i	0.0788723	−	0.136611i	0.902764	+	0.430137i	$0.141535\pi$
$192$		0			0
$193$	−2.79332e6	−	4.83818e6i	−0.388552	−	0.672992i	0.603703	−	0.797209i	$-0.293691\pi$
$193$	−2.79332e6	−	4.83818e6i	−0.388552	−	0.672992i	−0.992255	+	0.124217i	$0.960358\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−4.15861e6			−0.543938			−0.271969	−	0.962306i	$-0.587675\pi$
$197$	−4.15861e6			−0.543938			−0.271969	+	0.962306i	$0.587675\pi$
$198$		0			0
$199$	−7.87345e6	+	4.54574e6i	−0.999093	+	0.576827i	−0.907980	−	0.419014i	$-0.862376\pi$
$199$	−7.87345e6	+	4.54574e6i	−0.999093	+	0.576827i	−0.0911133	+	0.995841i	$0.529043\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.18571e6	+	4.06035e6i	−0.380819	+	0.485373i
$204$		0			0
$205$	−6.51750e6	+	1.12886e7i	−0.756519	+	1.31033i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			8.94422e6i			0.979724i
$210$		0			0
$211$	−3.65661e6			−0.389253			−0.194626	−	0.980877i	$-0.562349\pi$
$211$	−3.65661e6			−0.389253			−0.194626	+	0.980877i	$0.562349\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.19493e7	+	6.89893e6i	1.20234	+	0.694171i
$216$		0			0
$217$	−2.24021e6	+	1.57064e7i	−0.219235	+	1.53708i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−8.95308e6	−	1.55072e7i	−0.829461	−	1.43667i
$222$		0			0
$223$		−	1.39625e7i		−	1.25907i	−0.776973	−	0.629534i	$-0.783246\pi$
$223$		−	1.39625e7i		−	1.25907i	0.776973	−	0.629534i	$-0.216754\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−517593.	+	298833.i	−0.0442498	+	0.0255476i	−0.521962	−	0.852969i	$-0.674800\pi$
$227$	−517593.	+	298833.i	−0.0442498	+	0.0255476i	0.477712	+	0.878517i	$0.341466\pi$
$228$		0			0
$229$	5.12371e6	+	2.95818e6i	0.426656	+	0.246330i	0.697921	−	0.716175i	$-0.254109\pi$
$229$	5.12371e6	+	2.95818e6i	0.426656	+	0.246330i	−0.271265	+	0.962505i	$0.587442\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−6.77900e6	+	1.17416e7i	−0.535918	+	0.928237i	0.463201	+	0.886253i	$0.346701\pi$
$233$	−6.77900e6	+	1.17416e7i	−0.535918	+	0.928237i	−0.999118	+	0.0419833i	$0.986632\pi$
$234$		0			0
$235$	−4.06006e6	−	7.03223e6i	−0.312845	−	0.541863i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−5.95325e6			−0.436074			−0.218037	−	0.975940i	$-0.569965\pi$
$239$	−5.95325e6			−0.436074			−0.218037	+	0.975940i	$0.569965\pi$
$240$		0			0
$241$	−1.55418e7	+	8.97306e6i	−1.11032	+	0.641046i	−0.938914	−	0.344153i	$-0.888166\pi$
$241$	−1.55418e7	+	8.97306e6i	−1.11032	+	0.641046i	−0.171411	+	0.985200i	$0.554833\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	6.38984e6	−	2.19442e7i	0.434502	−	1.49218i
$246$		0			0
$247$	−1.05984e7	+	1.83570e7i	−0.703316	+	1.21818i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			816734.i			0.0516487i	0.999666	+	0.0258243i	$0.00822106\pi$
$251$			816734.i			0.0516487i	−0.999666	+	0.0258243i	$0.991779\pi$
$252$		0			0
$253$	−1.72656e7			−1.06615
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.18776e7	+	6.85756e6i	0.699731	+	0.403990i	0.807247	−	0.590214i	$-0.200956\pi$
$257$	1.18776e7	+	6.85756e6i	0.699731	+	0.403990i	−0.107516	+	0.994203i	$0.534290\pi$
$258$		0			0
$259$	−6.37729e6	−	1.58779e7i	−0.367060	−	0.913891i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	5.30242e6	+	9.18407e6i	0.291479	+	0.504856i	0.974160	−	0.225860i	$-0.0725193\pi$
$263$	5.30242e6	+	9.18407e6i	0.291479	+	0.504856i	−0.682681	+	0.730717i	$0.739186\pi$
$264$		0			0
$265$			1.12064e7i			0.602184i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	2.74833e7	−	1.58675e7i	1.41192	−	0.815175i	0.416354	−	0.909202i	$-0.363308\pi$
$269$	2.74833e7	−	1.58675e7i	1.41192	−	0.815175i	0.995570	+	0.0940277i	$0.0299742\pi$
$270$		0			0
$271$	−2.12874e7	−	1.22903e7i	−1.06958	−	0.617524i	−0.141515	−	0.989936i	$-0.545197\pi$
$271$	−2.12874e7	−	1.22903e7i	−1.06958	−	0.617524i	−0.928067	+	0.372413i	$0.878531\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.04102e7	−	1.80310e7i	0.500567	−	0.867008i
$276$		0			0
$277$	1.24203e7	+	2.15126e7i	0.584378	+	1.01217i	0.994953	+	0.100345i	$0.0319948\pi$
$277$	1.24203e7	+	2.15126e7i	0.584378	+	1.01217i	−0.410575	+	0.911827i	$0.634672\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	957713.			0.0431635			0.0215817	−	0.999767i	$-0.493130\pi$
$281$	957713.			0.0431635			0.0215817	+	0.999767i	$0.493130\pi$
$282$		0			0
$283$	1.01334e7	−	5.85050e6i	0.447089	−	0.258127i	−0.259511	−	0.965740i	$-0.583561\pi$
$283$	1.01334e7	−	5.85050e6i	0.447089	−	0.258127i	0.706600	+	0.707613i	$0.250228\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.81066e7	−	1.42062e7i	−0.765932	−	0.600943i
$288$		0			0
$289$	2.01373e7	−	3.48789e7i	0.834274	−	1.44500i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	6.15637e6i		−	0.244749i	−0.992484	−	0.122375i	$-0.960949\pi$
$293$		−	6.15637e6i		−	0.244749i	0.992484	−	0.122375i	$-0.0390510\pi$
$294$		0			0
$295$	−6.04177e7			−2.35341
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.54357e7	−	2.04588e7i	−1.32564	−	0.765361i
$300$		0			0
$301$	−1.50376e7	+	1.91662e7i	−0.551417	+	0.702808i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	3.53426e7	+	6.12151e7i	1.24566	+	2.15754i
$306$		0			0
$307$			1.30916e7i			0.452459i	0.974074	+	0.226229i	$0.0726399\pi$
$307$			1.30916e7i			0.452459i	−0.974074	+	0.226229i	$0.927360\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	5.32358e6	−	3.07357e6i	0.176979	−	0.102179i	−0.408893	−	0.912582i	$-0.634085\pi$
$311$	5.32358e6	−	3.07357e6i	0.176979	−	0.102179i	0.585873	+	0.810403i	$0.300752\pi$
$312$		0			0
$313$	3.70520e7	+	2.13920e7i	1.20831	+	0.697619i	0.962390	−	0.271671i	$-0.0875763\pi$
$313$	3.70520e7	+	2.13920e7i	1.20831	+	0.697619i	0.245921	+	0.969290i	$0.420910\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.03375e7	+	3.52256e7i	−0.638441	+	1.10581i	0.347334	+	0.937741i	$0.387087\pi$
$317$	−2.03375e7	+	3.52256e7i	−0.638441	+	1.10581i	−0.985775	+	0.168070i	$0.946246\pi$
$318$		0			0
$319$	−7.08262e6	−	1.22675e7i	−0.218184	−	0.377905i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−7.62495e7			−2.26271
$324$		0			0
$325$	4.27317e7	−	2.46711e7i	1.24480	−	0.718686i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.33038e7	−	5.34340e6i	0.373584	−	0.150048i
$330$		0			0
$331$	8.84101e6	−	1.53131e7i	0.243791	−	0.422259i	−0.718000	−	0.696043i	$-0.754942\pi$
$331$	8.84101e6	−	1.53131e7i	0.243791	−	0.422259i	0.961791	+	0.273784i	$0.0882755\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			3.25421e7i			0.865588i
$336$		0			0
$337$	4.52960e7			1.18350			0.591752	−	0.806120i	$-0.298436\pi$
$337$	4.52960e7			1.18350			0.591752	+	0.806120i	$0.298436\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−3.77116e7	−	2.17728e7i	−0.951069	−	0.549100i
$342$		0			0
$343$	3.67633e7	+	1.66396e7i	0.911028	+	0.412344i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	3.38128e7	+	5.85655e7i	0.809268	+	1.40169i	0.913371	+	0.407127i	$0.133469\pi$
$347$	3.38128e7	+	5.85655e7i	0.809268	+	1.40169i	−0.104103	+	0.994567i	$0.533197\pi$
$348$		0			0
$349$		−	4.56356e7i		−	1.07356i	−0.843721	−	0.536782i	$-0.819640\pi$
$349$		−	4.56356e7i		−	1.07356i	0.843721	−	0.536782i	$-0.180360\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	3.48639e7	−	2.01287e7i	0.792596	−	0.457606i	−0.0482796	−	0.998834i	$-0.515374\pi$
$353$	3.48639e7	−	2.01287e7i	0.792596	−	0.457606i	0.840876	+	0.541228i	$0.182041\pi$
$354$		0			0
$355$	3.24234e7	+	1.87197e7i	0.724726	+	0.418421i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.29066e7	−	2.23549e7i	0.278952	−	0.483159i	−0.692173	−	0.721732i	$-0.743346\pi$
$359$	1.29066e7	−	2.23549e7i	0.278952	−	0.483159i	0.971125	+	0.238573i	$0.0766796\pi$
$360$		0			0
$361$	2.16081e7	+	3.74264e7i	0.459299	+	0.795530i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.63372e7			0.541616
$366$		0			0
$367$	1.61762e7	−	9.33932e6i	0.327249	−	0.188937i	−0.327370	−	0.944896i	$-0.606162\pi$
$367$	1.61762e7	−	9.33932e6i	0.327249	−	0.188937i	0.654619	+	0.755959i	$0.272829\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.95877e7	−	2.79381e6i	−0.383585	−	0.0547110i
$372$		0			0
$373$	−1.21932e7	+	2.11193e7i	−0.234959	+	0.406961i	−0.959261	−	0.282522i	$-0.908829\pi$
$373$	−1.21932e7	+	2.11193e7i	−0.234959	+	0.406961i	0.724302	+	0.689483i	$0.242162\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	3.35701e7i		−	0.626511i
$378$		0			0
$379$	−1.90259e6			−0.0349485			−0.0174742	−	0.999847i	$-0.505563\pi$
$379$	−1.90259e6			−0.0349485			−0.0174742	+	0.999847i	$0.505563\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−2.69425e7	−	1.55553e7i	−0.479559	−	0.276873i	0.240674	−	0.970606i	$-0.422632\pi$
$383$	−2.69425e7	−	1.55553e7i	−0.479559	−	0.276873i	−0.720233	+	0.693733i	$0.755965\pi$
$384$		0			0
$385$	4.93542e7	+	3.87228e7i	0.864853	+	0.678555i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−4.22126e7	−	7.31143e7i	−0.717122	−	1.24209i	−0.962135	−	0.272572i	$-0.912126\pi$
$389$	−4.22126e7	−	7.31143e7i	−0.717122	−	1.24209i	0.245014	−	0.969520i	$-0.421208\pi$
$390$		0			0
$391$		−	1.47189e8i		−	2.46233i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.40823e8	−	8.13044e7i	2.28498	−	1.31924i
$396$		0			0
$397$	5.73983e7	+	3.31390e7i	0.917335	+	0.529624i	0.882784	−	0.469779i	$-0.155667\pi$
$397$	5.73983e7	+	3.31390e7i	0.917335	+	0.529624i	0.0345510	+	0.999403i	$0.489000\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5.18065e7	+	8.97314e7i	−0.803435	+	1.39159i	0.113907	+	0.993491i	$0.463663\pi$
$401$	−5.18065e7	+	8.97314e7i	−0.803435	+	1.39159i	−0.917342	+	0.398099i	$0.869670\pi$
$402$		0			0
$403$	−5.15992e7	−	8.93725e7i	−0.788367	−	1.36549i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.69640e7			0.696597
$408$		0			0
$409$	4.46747e7	−	2.57930e7i	0.652968	−	0.376991i	−0.136624	−	0.990623i	$-0.543625\pi$
$409$	4.46747e7	−	2.57930e7i	0.652968	−	0.376991i	0.789593	+	0.613631i	$0.210292\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1.50624e7	−	1.05604e8i	0.213818	−	1.49910i
$414$		0			0
$415$	5.56399e7	−	9.63711e7i	0.778470	−	1.34835i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			3.72506e7i			0.506396i	0.967414	+	0.253198i	$0.0814825\pi$
$419$			3.72506e7i			0.506396i	−0.967414	+	0.253198i	$0.918518\pi$
$420$		0			0
$421$	9.20650e7			1.23381			0.616905	−	0.787038i	$-0.288386\pi$
$421$	9.20650e7			1.23381			0.616905	+	0.787038i	$0.288386\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.53715e8	+	8.87472e7i	2.00239	+	1.15608i
$426$		0			0
$427$	−1.15809e8	+	4.65140e7i	−1.48750	+	0.597448i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.49155e7	−	2.58344e7i	−0.186297	−	0.322676i	0.757716	−	0.652585i	$-0.226315\pi$
$431$	−1.49155e7	−	2.58344e7i	−0.186297	−	0.322676i	−0.944013	+	0.329909i	$0.892982\pi$
$432$		0			0
$433$			2.47834e7i			0.305279i	0.988282	+	0.152640i	$0.0487773\pi$
$433$			2.47834e7i			0.305279i	−0.988282	+	0.152640i	$0.951223\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.50895e8	+	8.71193e7i	−1.80813	+	1.04393i
$438$		0			0
$439$	1.03435e8	+	5.97184e7i	1.22257	+	0.705854i	0.965466	−	0.260529i	$-0.0838969\pi$
$439$	1.03435e8	+	5.97184e7i	1.22257	+	0.705854i	0.257108	+	0.966383i	$0.417230\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	4.75865e6	−	8.24223e6i	0.0547360	−	0.0948055i	−0.837359	−	0.546653i	$-0.815902\pi$
$443$	4.75865e6	−	8.24223e6i	0.0547360	−	0.0948055i	0.892095	+	0.451848i	$0.149235\pi$
$444$		0			0
$445$	1.27010e8	+	2.19988e8i	1.44132	+	2.49643i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.42764e8			−1.57717			−0.788587	−	0.614923i	$-0.789187\pi$
$449$	−1.42764e8			−1.57717			−0.788587	+	0.614923i	$0.789187\pi$
$450$		0			0
$451$	5.47050e7	−	3.15839e7i	0.596344	−	0.344300i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	5.54095e7	+	1.37956e8i	0.588234	+	1.46456i
$456$		0			0
$457$	8.06021e6	−	1.39607e7i	0.0844497	−	0.146271i	−0.820707	−	0.571349i	$-0.806420\pi$
$457$	8.06021e6	−	1.39607e7i	0.0844497	−	0.146271i	0.905157	+	0.425078i	$0.139753\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	5.75822e7i		−	0.587741i	−0.955845	−	0.293870i	$-0.905057\pi$
$461$		−	5.75822e7i		−	0.587741i	0.955845	−	0.293870i	$-0.0949434\pi$
$462$		0			0
$463$	−1.51699e8			−1.52841			−0.764204	−	0.644974i	$-0.776868\pi$
$463$	−1.51699e8			−1.52841			−0.764204	+	0.644974i	$0.776868\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−8.31604e7	−	4.80127e7i	−0.816518	−	0.471417i	0.0326960	−	0.999465i	$-0.489591\pi$
$467$	−8.31604e7	−	4.80127e7i	−0.816518	−	0.471417i	−0.849214	+	0.528048i	$0.822924\pi$
$468$		0			0
$469$	−5.68803e7	−	8.11288e6i	−0.551370	−	0.0786423i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−3.34323e7	−	5.79065e7i	−0.315924	−	0.547197i
$474$		0			0
$475$		−	2.10113e8i		−	1.96053i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−1.49611e8	+	8.63777e7i	−1.36131	+	0.785951i	−0.989798	−	0.142479i	$-0.954493\pi$
$479$	−1.49611e8	+	8.63777e7i	−1.36131	+	0.785951i	−0.371509	+	0.928430i	$0.621159\pi$
$480$		0			0
$481$	9.63883e7	+	5.56498e7i	0.866142	+	0.500067i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.12100e7	−	3.67368e7i	0.185915	−	0.322015i
$486$		0			0
$487$	2.10132e7	+	3.63959e7i	0.181930	+	0.315112i	0.942538	−	0.334100i	$-0.108432\pi$
$487$	2.10132e7	+	3.63959e7i	0.181930	+	0.315112i	−0.760608	+	0.649212i	$0.775099\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.41912e8			1.19887			0.599436	−	0.800422i	$-0.295391\pi$
$491$	1.41912e8			1.19887			0.599436	+	0.800422i	$0.295391\pi$
$492$		0			0
$493$	1.04580e8	−	6.03794e7i	0.872787	−	0.503904i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.08034e7	+	5.20059e7i	−0.332374	+	0.423627i
$498$		0			0
$499$	−2.74003e7	+	4.74586e7i	−0.220523	+	0.381956i	−0.954967	−	0.296713i	$-0.904110\pi$
$499$	−2.74003e7	+	4.74586e7i	−0.220523	+	0.381956i	0.734444	+	0.678669i	$0.237443\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			4.24299e7i			0.333402i	0.986008	+	0.166701i	$0.0533114\pi$
$503$			4.24299e7i			0.333402i	−0.986008	+	0.166701i	$0.946689\pi$
$504$		0			0
$505$	−3.36520e8			−2.61298
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.04100e8	+	6.01024e7i	0.789404	+	0.455762i	0.839753	−	0.542969i	$-0.182700\pi$
$509$	1.04100e8	+	6.01024e7i	0.789404	+	0.455762i	−0.0503489	+	0.998732i	$0.516033\pi$
$510$		0			0
$511$	−6.56598e6	+	4.60348e7i	−0.0492081	+	0.345003i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	4.96248e7	+	8.59526e7i	0.363309	+	0.629270i
$516$		0			0
$517$			3.93502e7i			0.284758i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.06906e8	+	6.17224e7i	−0.755945	+	0.436445i	−0.827838	−	0.560968i	$-0.810429\pi$
$521$	−1.06906e8	+	6.17224e7i	−0.755945	+	0.436445i	0.0718932	+	0.997412i	$0.477096\pi$
$522$		0			0
$523$	−1.59161e8	−	9.18915e7i	−1.11258	−	0.642348i	−0.173083	−	0.984907i	$-0.555373\pi$
$523$	−1.59161e8	−	9.18915e7i	−1.11258	−	0.642348i	−0.939496	+	0.342559i	$0.888706\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.85613e8	−	3.21492e8i	1.26817	−	2.19653i
$528$		0			0
$529$	−9.41537e7	−	1.63079e8i	−0.636020	−	1.10162i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.49701e8			0.988651
$534$		0			0
$535$	−1.80771e8	+	1.04368e8i	−1.18050	+	0.681562i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−7.99878e7	+	7.66124e7i	−0.510808	+	0.489252i
$540$		0			0
$541$	−6.64932e7	+	1.15170e8i	−0.419938	+	0.727354i	−0.995933	−	0.0900994i	$-0.971282\pi$
$541$	−6.64932e7	+	1.15170e8i	−0.419938	+	0.727354i	0.575995	+	0.817453i	$0.304615\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		−	1.16385e8i		−	0.718963i
$546$		0			0
$547$	−2.71947e8			−1.66158			−0.830792	−	0.556583i	$-0.812112\pi$
$547$	−2.71947e8			−1.66158			−0.830792	+	0.556583i	$0.812112\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.23799e8	−	7.14755e7i	−0.740053	−	0.427270i
$552$		0			0
$553$	1.07004e8	+	2.66414e8i	0.632738	+	1.57537i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.42885e8	−	2.47483e8i	−0.826836	−	1.43212i	−0.900508	−	0.434840i	$-0.856805\pi$
$557$	−1.42885e8	−	2.47483e8i	−0.826836	−	1.43212i	0.0736712	−	0.997283i	$-0.476528\pi$
$558$		0			0
$559$		−	1.58462e8i		−	0.907172i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.01353e8	+	5.85163e7i	−0.567953	+	0.327908i	−0.756331	−	0.654189i	$-0.773010\pi$
$563$	−1.01353e8	+	5.85163e7i	−0.567953	+	0.327908i	0.188378	+	0.982097i	$0.439677\pi$
$564$		0			0
$565$	2.01204e8	+	1.16165e8i	1.11556	+	0.644068i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	2.36743e7	−	4.10051e7i	0.128511	−	0.222587i	−0.794589	−	0.607148i	$-0.792314\pi$
$569$	2.36743e7	−	4.10051e7i	0.128511	−	0.222587i	0.923100	+	0.384560i	$0.125647\pi$
$570$		0			0
$571$	6.12306e6	+	1.06054e7i	0.0328897	+	0.0569667i	0.882002	−	0.471246i	$-0.156196\pi$
$571$	6.12306e6	+	1.06054e7i	0.0328897	+	0.0569667i	−0.849112	+	0.528213i	$0.822862\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	4.05595e8			2.13348
$576$		0			0
$577$	5.90143e7	−	3.40719e7i	0.307206	−	0.177366i	−0.338469	−	0.940977i	$-0.609909\pi$
$577$	5.90143e7	−	3.40719e7i	0.307206	−	0.177366i	0.645676	+	0.763612i	$0.276576\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.54576e8	+	1.21279e8i	0.788157	+	0.618380i
$582$		0			0
$583$	2.71532e7	−	4.70308e7i	0.137030	−	0.237343i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	3.99149e6i		−	0.0197343i	−0.999951	−	0.00986714i	$-0.996859\pi$
$587$		−	3.99149e6i		−	0.0197343i	0.999951	−	0.00986714i	$-0.00314086\pi$
$588$		0			0
$589$	−4.39448e8			−2.15061
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.88321e8	+	1.08727e8i	0.903099	+	0.521405i	0.878204	−	0.478285i	$-0.158742\pi$
$593$	1.88321e8	+	1.08727e8i	0.903099	+	0.521405i	0.0248950	+	0.999690i	$0.492075\pi$
$594$		0			0
$595$	−3.30112e8	+	4.20745e8i	−1.56715	+	1.99741i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−7.26739e7	−	1.25875e8i	−0.338141	−	0.585677i	0.645942	−	0.763386i	$-0.276465\pi$
$599$	−7.26739e7	−	1.25875e8i	−0.338141	−	0.585677i	−0.984083	+	0.177709i	$0.943131\pi$
$600$		0			0
$601$		−	2.95446e8i		−	1.36099i	−0.732753	−	0.680495i	$-0.761765\pi$
$601$		−	2.95446e8i		−	1.36099i	0.732753	−	0.680495i	$-0.238235\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.48939e8	−	8.59899e7i	0.672577	−	0.388313i
$606$		0			0
$607$	−1.28824e7	−	7.43763e6i	−0.0576009	−	0.0332559i	0.470923	−	0.882174i	$-0.343921\pi$
$607$	−1.28824e7	−	7.43763e6i	−0.0576009	−	0.0332559i	−0.528524	+	0.848918i	$0.677254\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.66279e7	+	8.07619e7i	−0.204419	+	0.354065i
$612$		0			0
$613$	5.72411e7	+	9.91445e7i	0.248500	+	0.430415i	0.963110	−	0.269109i	$-0.0867290\pi$
$613$	5.72411e7	+	9.91445e7i	0.248500	+	0.430415i	−0.714610	+	0.699523i	$0.753396\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−2.80680e8			−1.19497			−0.597484	−	0.801881i	$-0.703833\pi$
$617$	−2.80680e8			−1.19497			−0.597484	+	0.801881i	$0.703833\pi$
$618$		0			0
$619$	5.22584e7	−	3.01714e7i	0.220335	−	0.127211i	−0.385770	−	0.922595i	$-0.626064\pi$
$619$	5.22584e7	−	3.01714e7i	0.220335	−	0.127211i	0.606106	+	0.795384i	$0.292731\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−4.16181e8	+	1.67157e8i	−1.72115	+	0.691290i
$624$		0			0
$625$	5.02972e7	−	8.71172e7i	0.206017	−	0.356832i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			4.00368e8i			1.60882i
$630$		0			0
$631$	−7.88986e7			−0.314037			−0.157019	−	0.987596i	$-0.550188\pi$
$631$	−7.88986e7			−0.314037			−0.157019	+	0.987596i	$0.550188\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2.14466e8	−	1.23822e8i	−0.837600	−	0.483589i
$636$		0			0
$637$	−2.54947e8	+	6.24570e7i	−0.986353	+	0.241637i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.41143e8	−	2.44468e8i	−0.535904	−	0.928212i	−0.999119	−	0.0419666i	$-0.986638\pi$
$641$	−1.41143e8	−	2.44468e8i	−0.535904	−	0.928212i	0.463215	−	0.886246i	$-0.346696\pi$
$642$		0			0
$643$			1.79972e8i			0.676973i	0.940971	+	0.338486i	$0.109915\pi$
$643$			1.79972e8i			0.676973i	−0.940971	+	0.338486i	$0.890085\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−2.63281e8	+	1.52005e8i	−0.972089	+	0.561236i	−0.899873	−	0.436153i	$-0.856341\pi$
$647$	−2.63281e8	+	1.52005e8i	−0.972089	+	0.561236i	−0.0722168	+	0.997389i	$0.523007\pi$
$648$		0			0
$649$	2.53559e8	+	1.46393e8i	0.927568	+	0.535532i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−2.42405e8	+	4.19858e8i	−0.870567	+	1.50787i	−0.00915504	+	0.999958i	$0.502914\pi$
$653$	−2.42405e8	+	4.19858e8i	−0.870567	+	1.50787i	−0.861412	+	0.507908i	$0.830419\pi$
$654$		0			0
$655$	−6.68735e7	−	1.15828e8i	−0.237974	−	0.412184i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.11326e8			−0.388993			−0.194497	−	0.980903i	$-0.562307\pi$
$659$	−1.11326e8			−0.388993			−0.194497	+	0.980903i	$0.562307\pi$
$660$		0			0
$661$	−3.41778e8	+	1.97326e8i	−1.18342	+	0.683249i	−0.956804	−	0.290735i	$-0.906100\pi$
$661$	−3.41778e8	+	1.97326e8i	−1.18342	+	0.683249i	−0.226618	+	0.973984i	$0.572767\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	6.26727e8	+	8.93906e7i	2.13115	+	0.303967i
$666$		0			0
$667$	1.37974e8	−	2.38977e8i	0.464963	−	0.805339i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		−	3.42541e8i		−	1.13382i
$672$		0			0
$673$	−4.28608e8			−1.40610			−0.703049	−	0.711142i	$-0.748178\pi$
$673$	−4.28608e8			−1.40610			−0.703049	+	0.711142i	$0.748178\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3.56590e8	+	2.05877e8i	1.14922	+	0.663502i	0.948697	−	0.316187i	$-0.102403\pi$
$677$	3.56590e8	+	2.05877e8i	1.14922	+	0.663502i	0.200522	+	0.979689i	$0.435736\pi$
$678$		0			0
$679$	5.89244e7	+	4.62315e7i	0.188229	+	0.147682i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.39000e8	+	2.40755e8i	0.436267	+	0.755637i	0.997398	−	0.0720902i	$-0.0229669\pi$
$683$	1.39000e8	+	2.40755e8i	0.436267	+	0.755637i	−0.561131	+	0.827727i	$0.689634\pi$
$684$		0			0
$685$		−	9.40567e8i		−	2.92629i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.11458e8	−	6.43503e7i	0.340764	−	0.196740i
$690$		0			0
$691$	3.59041e8	+	2.07292e8i	1.08820	+	0.628274i	0.933097	−	0.359624i	$-0.117095\pi$
$691$	3.59041e8	+	2.07292e8i	1.08820	+	0.628274i	0.155105	+	0.987898i	$0.450428\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−8.39256e7	+	1.45363e8i	−0.250000	+	0.433013i
$696$		0			0
$697$	2.69253e8	+	4.66360e8i	0.795174	+	1.37728i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−1.80757e8			−0.524737			−0.262369	−	0.964968i	$-0.584504\pi$
$701$	−1.80757e8			−0.524737			−0.262369	+	0.964968i	$0.584504\pi$
$702$		0			0
$703$	4.10449e8	−	2.36973e8i	1.18139	−	0.682075i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	8.38958e7	−	5.88202e8i	0.237401	−	1.66444i
$708$		0			0
$709$	−6.84070e7	+	1.18484e8i	−0.191938	+	0.332447i	−0.945893	−	0.324480i	$-0.894811\pi$
$709$	−6.84070e7	+	1.18484e8i	−0.191938	+	0.332447i	0.753954	+	0.656927i	$0.228144\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	8.48294e8i		−	2.34033i
$714$		0			0
$715$	−4.08050e8			−1.11634
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.24812e8	−	7.20600e7i	−0.335790	−	0.193869i	0.322619	−	0.946529i	$-0.395437\pi$
$719$	−1.24812e8	−	7.20600e7i	−0.335790	−	0.193869i	−0.658409	+	0.752660i	$0.728770\pi$
$720$		0			0
$721$	−1.62608e8	+	6.53107e7i	−0.433846	+	0.174252i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.66381e8	+	2.88181e8i	0.436607	+	0.756226i
$726$		0			0
$727$		−	6.67223e8i		−	1.73647i	−0.496152	−	0.868236i	$-0.665254\pi$
$727$		−	6.67223e8i		−	1.73647i	0.496152	−	0.868236i	$-0.334746\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	4.93653e8	−	2.85011e8i	1.26377	−	0.729641i
$732$		0			0
$733$	4.05121e8	+	2.33897e8i	1.02866	+	0.593899i	0.916601	−	0.399802i	$-0.130921\pi$
$733$	4.05121e8	+	2.33897e8i	1.02866	+	0.593899i	0.112062	+	0.993701i	$0.464255\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7.88498e7	−	1.36572e8i	0.196969	−	0.341160i
$738$		0			0
$739$	2.70293e8	+	4.68161e8i	0.669733	+	1.16001i	0.977979	+	0.208704i	$0.0669246\pi$
$739$	2.70293e8	+	4.68161e8i	0.669733	+	1.16001i	−0.308246	+	0.951307i	$0.599742\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	6.98501e7			0.170294			0.0851472	−	0.996368i	$-0.472864\pi$
$743$	6.98501e7			0.170294			0.0851472	+	0.996368i	$0.472864\pi$
$744$		0			0
$745$	9.77708e8	−	5.64480e8i	2.36451	−	1.36515i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.37358e8	−	3.41988e8i	−0.326894	−	0.813889i
$750$		0			0
$751$	−3.16624e8	+	5.48409e8i	−0.747522	+	1.29475i	0.201485	+	0.979492i	$0.435423\pi$
$751$	−3.16624e8	+	5.48409e8i	−0.747522	+	1.29475i	−0.949007	+	0.315254i	$0.897910\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			7.82199e8i			1.81751i
$756$		0			0
$757$	4.12891e8			0.951805			0.475903	−	0.879498i	$-0.342121\pi$
$757$	4.12891e8			0.951805			0.475903	+	0.879498i	$0.342121\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−5.28660e8	−	3.05222e8i	−1.19956	−	0.692567i	−0.239104	−	0.970994i	$-0.576854\pi$
$761$	−5.28660e8	−	3.05222e8i	−1.19956	−	0.692567i	−0.960457	+	0.278427i	$0.910187\pi$
$762$		0			0
$763$	2.03429e8	+	2.90152e7i	0.457971	+	0.0653208i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	3.46935e8	+	6.00909e8i	0.768886	+	1.33175i
$768$		0			0
$769$		−	2.26658e8i		−	0.498415i	−0.968450	−	0.249208i	$-0.919830\pi$
$769$		−	2.26658e8i		−	0.498415i	0.968450	−	0.249208i	$-0.0801702\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1.90630e8	−	1.10061e8i	0.412718	−	0.238283i	−0.279239	−	0.960222i	$-0.590082\pi$
$773$	1.90630e8	−	1.10061e8i	0.412718	−	0.238283i	0.691957	+	0.721939i	$0.256749\pi$
$774$		0			0
$775$	8.85903e8	+	5.11476e8i	1.90319	+	1.09880i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3.18735e8	−	5.52065e8i	0.674244	−	1.16782i
$780$		0			0
$781$	−9.07158e7	−	1.57124e8i	−0.190428	−	0.329830i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.29142e8			−0.266967
$786$		0			0
$787$	7.50112e8	−	4.33078e8i	1.53887	−	0.888467i	0.539965	−	0.841687i	$-0.318437\pi$
$787$	7.50112e8	−	4.33078e8i	1.53887	−	0.888467i	0.998905	−	0.0467802i	$-0.0148960\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−2.53206e8	+	3.22724e8i	−0.511617	+	0.652082i
$792$		0			0
$793$	4.05893e8	−	7.03027e8i	0.813939	−	1.40978i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			6.80587e8i			1.34434i	0.740397	+	0.672169i	$0.234637\pi$
$797$			6.80587e8i			1.34434i	−0.740397	+	0.672169i	$0.765363\pi$
$798$		0			0
$799$	−3.35461e8			−0.657660
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.10531e8	−	6.38153e7i	−0.213471	−	0.123248i
$804$		0			0
$805$	−1.72556e8	+	1.20981e9i	−0.330783	+	2.31915i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−4.47879e6	−	7.75749e6i	−0.00845892	−	0.0146513i	0.861765	−	0.507308i	$-0.169359\pi$
$809$	−4.47879e6	−	7.75749e6i	−0.00845892	−	0.0146513i	−0.870224	+	0.492656i	$0.836026\pi$
$810$		0			0
$811$		−	5.83368e8i		−	1.09365i	−0.837245	−	0.546827i	$-0.815835\pi$
$811$		−	5.83368e8i		−	1.09365i	0.837245	−	0.546827i	$-0.184165\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	5.21028e8	−	3.00816e8i	0.962472	−	0.555684i
$816$		0			0
$817$	−5.84373e8	−	3.37388e8i	−1.07158	−	0.618676i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−4.80709e8	+	8.32612e8i	−0.868665	+	1.50457i	−0.00530444	+	0.999986i	$0.501688\pi$
$821$	−4.80709e8	+	8.32612e8i	−0.868665	+	1.50457i	−0.863361	+	0.504587i	$0.831645\pi$
$822$		0			0
$823$	1.88626e8	+	3.26709e8i	0.338377	+	0.586087i	0.984128	−	0.177462i	$-0.0567886\pi$
$823$	1.88626e8	+	3.26709e8i	0.338377	+	0.586087i	−0.645750	+	0.763549i	$0.723455\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−8.12791e8			−1.43702			−0.718509	−	0.695517i	$-0.755175\pi$
$827$	−8.12791e8			−1.43702			−0.718509	+	0.695517i	$0.755175\pi$
$828$		0			0
$829$	−3.87535e8	+	2.23743e8i	−0.680217	+	0.392723i	−0.799937	−	0.600084i	$-0.795134\pi$
$829$	−3.87535e8	+	2.23743e8i	−0.680217	+	0.392723i	0.119720	+	0.992808i	$0.461800\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−6.53120e8	−	6.81896e8i	−1.12995	−	1.17973i
$834$		0			0
$835$	7.31768e8	−	1.26746e9i	1.25694	−	2.17708i
$836$		0			0
$837$		0			0
$838$		0			0
$839$			2.53596e8i			0.429395i	0.976681	+	0.214698i	$0.0688766\pi$
$839$			2.53596e8i			0.429395i	−0.976681	+	0.214698i	$0.931123\pi$
$840$		0			0
$841$	−3.68427e8			−0.619390
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−2.54018e7	−	1.46658e7i	−0.0421012	−	0.0243072i
$846$		0			0
$847$	1.13171e8	+	2.81768e8i	0.186244	+	0.463704i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	4.57443e8	+	7.92314e8i	0.742246	+	1.28561i
$852$		0			0
$853$		−	5.47443e8i		−	0.882048i	−0.897495	−	0.441024i	$-0.854615\pi$
$853$		−	5.47443e8i		−	0.882048i	0.897495	−	0.441024i	$-0.145385\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.44184e8	+	8.32445e7i	−0.229073	+	0.132255i	−0.610144	−	0.792290i	$-0.708889\pi$
$857$	−1.44184e8	+	8.32445e7i	−0.229073	+	0.132255i	0.381071	+	0.924546i	$0.375555\pi$
$858$		0			0
$859$	1.07778e9	+	6.22256e8i	1.70040	+	0.981724i	0.945354	+	0.326047i	$0.105717\pi$
$859$	1.07778e9	+	6.22256e8i	1.70040	+	0.981724i	0.755042	+	0.655677i	$0.227617\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	2.46772e8	−	4.27422e8i	0.383941	−	0.665005i	−0.607681	−	0.794181i	$-0.707900\pi$
$863$	2.46772e8	−	4.27422e8i	0.383941	−	0.665005i	0.991622	+	0.129176i	$0.0412334\pi$
$864$		0			0
$865$	−4.27199e8	−	7.39931e8i	−0.660058	−	1.14325i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−7.88004e8			−1.20080
$870$		0			0
$871$	3.23661e8	−	1.86866e8i	0.489819	−	0.282797i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−3.40272e8	−	2.66974e8i	−0.507928	−	0.398515i
$876$		0			0
$877$	2.25370e8	−	3.90352e8i	0.334116	−	0.578706i	−0.649199	−	0.760619i	$-0.724896\pi$
$877$	2.25370e8	−	3.90352e8i	0.334116	−	0.578706i	0.983315	+	0.181913i	$0.0582290\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	3.09140e7i		−	0.0452093i	−0.999744	−	0.0226046i	$-0.992804\pi$
$881$		−	3.09140e7i		−	0.0452093i	0.999744	−	0.0226046i	$-0.00719589\pi$
$882$		0			0
$883$	−2.01024e8			−0.291989			−0.145994	−	0.989285i	$-0.546638\pi$
$883$	−2.01024e8			−0.291989			−0.145994	+	0.989285i	$0.546638\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	3.89097e8	+	2.24645e8i	0.557554	+	0.321904i	0.752163	−	0.658977i	$-0.229010\pi$
$887$	3.89097e8	+	2.24645e8i	0.557554	+	0.321904i	−0.194609	+	0.980881i	$0.562344\pi$
$888$		0			0
$889$	2.69895e8	−	3.43995e8i	0.384140	−	0.489606i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.98555e8	+	3.43907e8i	0.278821	+	0.482933i
$894$		0			0
$895$			6.81230e8i			0.950221i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	6.02726e8	−	3.47984e8i	0.829547	−	0.478939i
$900$		0			0
$901$	4.00938e8	+	2.31481e8i	0.548154	+	0.316477i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	3.06221e7	−	5.30390e7i	0.0413132	−	0.0715565i
$906$		0			0
$907$	5.25969e8	+	9.11006e8i	0.704918	+	1.22095i	0.966721	+	0.255832i	$0.0823495\pi$
$907$	5.25969e8	+	9.11006e8i	0.704918	+	1.22095i	−0.261803	+	0.965121i	$0.584317\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.02153e9			1.35113			0.675564	−	0.737302i	$-0.263900\pi$
$911$	1.02153e9			1.35113			0.675564	+	0.737302i	$0.263900\pi$
$912$		0			0
$913$	−4.67016e8	+	2.69632e8i	−0.613648	+	0.354290i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.19128e8	−	8.80116e7i	0.284177	−	0.114138i
$918$		0			0
$919$	−6.02810e8	+	1.04410e9i	−0.776665	+	1.34522i	0.157189	+	0.987569i	$0.449757\pi$
$919$	−6.02810e8	+	1.04410e9i	−0.776665	+	1.34522i	−0.933854	+	0.357655i	$0.883576\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	4.29974e8i		−	0.546810i
$924$		0			0
$925$	−1.10326e9			−1.39396
$926$		0			0
$927$		0			0
$928$		0			0
$929$	2.25050e8	+	1.29933e8i	0.280693	+	0.162058i	0.633737	−	0.773548i	$-0.281520\pi$
$929$	2.25050e8	+	1.29933e8i	0.280693	+	0.162058i	−0.353044	+	0.935607i	$0.614853\pi$
$930$		0			0
$931$	−3.12491e8	+	1.07317e9i	−0.387248	+	1.32990i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−7.33920e8	−	1.27119e9i	−0.897871	−	1.55516i
$936$		0			0
$937$		−	9.06793e8i		−	1.10227i	−0.834415	−	0.551137i	$-0.814194\pi$
$937$		−	9.06793e8i		−	1.10227i	0.834415	−	0.551137i	$-0.185806\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	2.28260e8	−	1.31786e8i	0.273944	−	0.158162i	−0.356735	−	0.934206i	$-0.616110\pi$
$941$	2.28260e8	−	1.31786e8i	0.273944	−	0.158162i	0.630679	+	0.776044i	$0.282777\pi$
$942$		0			0
$943$	1.06568e9	+	6.15273e8i	1.27085	+	0.733724i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.10637e8	+	7.11245e8i	−0.483513	+	0.837470i	−0.999821	−	0.0189338i	$-0.993973\pi$
$947$	−4.10637e8	+	7.11245e8i	−0.483513	+	0.837470i	0.516307	+	0.856403i	$0.327306\pi$
$948$		0			0
$949$	−1.51235e8	−	2.61947e8i	−0.176952	−	0.306489i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	4.19966e8			0.485216			0.242608	−	0.970124i	$-0.421997\pi$
$953$	4.19966e8			0.485216			0.242608	+	0.970124i	$0.421997\pi$
$954$		0			0
$955$	1.84923e8	−	1.06765e8i	0.212315	−	0.122580i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.64401e9	+	2.34487e8i	1.86402	+	0.265866i
$960$		0			0
$961$	6.25992e8	−	1.08425e9i	0.705340	−	1.22169i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		−	1.08532e9i		−	1.20774i
$966$		0			0
$967$	−1.38023e9			−1.52641			−0.763204	−	0.646157i	$-0.776375\pi$
$967$	−1.38023e9			−1.52641			−0.763204	+	0.646157i	$0.776375\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.77755e8	−	1.02627e8i	−0.194161	−	0.112099i	0.399768	−	0.916616i	$-0.369091\pi$
$971$	−1.77755e8	−	1.02627e8i	−0.194161	−	0.112099i	−0.593929	+	0.804517i	$0.702424\pi$
$972$		0			0
$973$	−2.33157e8	−	1.82933e8i	−0.253111	−	0.198588i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	2.68181e8	+	4.64502e8i	0.287570	+	0.498086i	0.973229	−	0.229837i	$-0.0738193\pi$
$977$	2.68181e8	+	4.64502e8i	0.287570	+	0.498086i	−0.685659	+	0.727923i	$0.740486\pi$
$978$		0			0
$979$		−	1.23099e9i		−	1.31191i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1.24196e9	+	7.17049e8i	−1.30752	+	0.754898i	−0.981682	−	0.190528i	$-0.938980\pi$
$983$	−1.24196e9	+	7.17049e8i	−1.30752	+	0.754898i	−0.325839	+	0.945425i	$0.605647\pi$
$984$		0			0
$985$	−6.99654e8	−	4.03946e8i	−0.732107	−	0.422682i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	6.51281e8	−	1.12805e9i	0.673255	−	1.16611i
$990$		0			0
$991$	−2.22989e8	−	3.86228e8i	−0.229119	−	0.396846i	0.728428	−	0.685122i	$-0.240251\pi$
$991$	−2.22989e8	−	3.86228e8i	−0.229119	−	0.396846i	−0.957547	+	0.288276i	$0.906918\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.76620e9			−1.79296
$996$		0			0
$997$	1.39979e8	−	8.08172e7i	0.141247	−	0.0815489i	−0.427711	−	0.903915i	$-0.640680\pi$
$997$	1.39979e8	−	8.08172e7i	0.141247	−	0.0815489i	0.568958	+	0.822366i	$0.307347\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.7.z.f.145.6	yes	12
3.2	odd	2	inner	252.7.z.f.145.1	yes	12
7.3	odd	6	inner	252.7.z.f.73.6	yes	12
21.17	even	6	inner	252.7.z.f.73.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.7.z.f.73.1	✓	12	21.17	even	6	inner
252.7.z.f.73.6	yes	12	7.3	odd	6	inner
252.7.z.f.145.1	yes	12	3.2	odd	2	inner
252.7.z.f.145.6	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	252.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(168.242 + 97.1348i) q^{5} +(-211.725 + 269.854i) q^{7} +O(q^{10})\)	\(q+(168.242 + 97.1348i) q^{5} +(-211.725 + 269.854i) q^{7} +(-470.717 - 815.305i) q^{11} -2231.10i q^{13} +(6950.48 - 4012.86i) q^{17} +(-8227.80 - 4750.32i) q^{19} +(9169.83 - 15882.6i) q^{23} +(11057.8 + 19152.8i) q^{25} +15046.5 q^{29} +(40057.7 - 23127.3i) q^{31} +(-61833.4 + 24835.1i) q^{35} +(-24942.8 + 43202.2i) q^{37} +67097.5i q^{41} +71024.3 q^{43} +(-36198.3 - 20899.1i) q^{47} +(-27993.9 - 114270. i) q^{49} +(28842.4 + 49956.6i) q^{53} -182892. i q^{55} +(-269333. + 155500. i) q^{59} +(315104. + 181925. i) q^{61} +(216717. - 375365. i) q^{65} +(83755.0 + 145068. i) q^{67} +192718. q^{71} +(117407. - 67785.2i) q^{73} +(319676. + 45595.7i) q^{77} +(418513. - 724886. i) q^{79} -572811. i q^{83} +1.55915e6 q^{85} +(1.13239e6 + 653784. i) q^{89} +(602071. + 472379. i) q^{91} +(-922843. - 1.59841e6i) q^{95} -218356. i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 714 q^{7}+O(q^{10}) \) 12 * q + 714 * q^7	\( 12 q + 714 q^{7} - 59466 q^{19} + 64086 q^{25} + 219834 q^{31} - 166242 q^{37} - 326916 q^{43} - 132006 q^{49} + 736008 q^{61} + 176238 q^{67} - 2931018 q^{73} + 449490 q^{79} + 2174592 q^{85} - 808542 q^{91}+O(q^{100}) \) 12 * q + 714 * q^7 - 59466 * q^19 + 64086 * q^25 + 219834 * q^31 - 166242 * q^37 - 326916 * q^43 - 132006 * q^49 + 736008 * q^61 + 176238 * q^67 - 2931018 * q^73 + 449490 * q^79 + 2174592 * q^85 - 808542 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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