LMFDB - Embedded newform 300.10.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,10,Mod(1,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("300.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	300.a (trivial)

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:	yes
Analytic conductor:	$154.510750849$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 12)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	300.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+81.0000 q^{3} -8576.00 q^{7} +6561.00 q^{9} +O(q^{10})$

$q+81.0000 q^{3} -8576.00 q^{7} +6561.00 q^{9} +70596.0 q^{11} +2530.00 q^{13} +200574. q^{17} -695620. q^{19} -694656. q^{21} -2.47270e6 q^{23} +531441. q^{27} +5.47421e6 q^{29} +3.73210e6 q^{31} +5.71828e6 q^{33} +2.18985e7 q^{37} +204930. q^{39} -2.38190e7 q^{41} -1.06127e7 q^{43} -2.39846e6 q^{47} +3.31942e7 q^{49} +1.62465e7 q^{51} +8.99498e6 q^{53} -5.63452e7 q^{57} -1.43418e8 q^{59} -1.98043e7 q^{61} -5.62671e7 q^{63} +1.65625e8 q^{67} -2.00288e8 q^{69} -1.94801e8 q^{71} -1.48729e8 q^{73} -6.05431e8 q^{77} -3.01342e7 q^{79} +4.30467e7 q^{81} -3.02054e8 q^{83} +4.43411e8 q^{87} +9.09503e8 q^{89} -2.16973e7 q^{91} +3.02300e8 q^{93} +8.72463e8 q^{97} +4.63180e8 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

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
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−8576.00	−1.35003	−0.675015	−	0.737804i	$-0.735863\pi$
$7$	−8576.00	−1.35003	−0.675015	+	0.737804i	$0.735863\pi$
$8$	0	0
$9$	6561.00	0.333333
$10$	0	0
$11$	70596.0	1.45383	0.726914	−	0.686729i	$-0.240954\pi$
$11$	70596.0	1.45383	0.726914	+	0.686729i	$0.240954\pi$
$12$	0	0
$13$	2530.00	0.0245683	0.0122842	−	0.999925i	$-0.496090\pi$
$13$	2530.00	0.0245683	0.0122842	+	0.999925i	$0.496090\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	200574.	0.582444	0.291222	−	0.956655i	$-0.405938\pi$
$17$	200574.	0.582444	0.291222	+	0.956655i	$0.405938\pi$
$18$	0	0
$19$	−695620.	−1.22456	−0.612281	−	0.790640i	$-0.709748\pi$
$19$	−695620.	−1.22456	−0.612281	+	0.790640i	$0.709748\pi$
$20$	0	0
$21$	−694656.	−0.779440
$22$	0	0
$23$	−2.47270e6	−1.84245	−0.921224	−	0.389031i	$-0.872810\pi$
$23$	−2.47270e6	−1.84245	−0.921224	+	0.389031i	$0.872810\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	531441.	0.192450
$28$	0	0
$29$	5.47421e6	1.43724	0.718622	−	0.695400i	$-0.244773\pi$
$29$	5.47421e6	1.43724	0.718622	+	0.695400i	$0.244773\pi$
$30$	0	0
$31$	3.73210e6	0.725815	0.362908	−	0.931825i	$-0.381784\pi$
$31$	3.73210e6	0.725815	0.362908	+	0.931825i	$0.381784\pi$
$32$	0	0
$33$	5.71828e6	0.839368
$34$	0	0
$35$	0	0
$36$	0	0
$37$	2.18985e7	1.92091	0.960455	−	0.278435i	$-0.0898157\pi$
$37$	2.18985e7	1.92091	0.960455	+	0.278435i	$0.0898157\pi$
$38$	0	0
$39$	204930.	0.0141845
$40$	0	0
$41$	−2.38190e7	−1.31642	−0.658211	−	0.752833i	$-0.728687\pi$
$41$	−2.38190e7	−1.31642	−0.658211	+	0.752833i	$0.728687\pi$
$42$	0	0
$43$	−1.06127e7	−0.473388	−0.236694	−	0.971584i	$-0.576064\pi$
$43$	−1.06127e7	−0.473388	−0.236694	+	0.971584i	$0.576064\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−2.39846e6	−0.0716957	−0.0358478	−	0.999357i	$-0.511413\pi$
$47$	−2.39846e6	−0.0716957	−0.0358478	+	0.999357i	$0.511413\pi$
$48$	0	0
$49$	3.31942e7	0.822582
$50$	0	0
$51$	1.62465e7	0.336274
$52$	0	0
$53$	8.99498e6	0.156588	0.0782940	−	0.996930i	$-0.475053\pi$
$53$	8.99498e6	0.156588	0.0782940	+	0.996930i	$0.475053\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−5.63452e7	−0.707001
$58$	0	0
$59$	−1.43418e8	−1.54088	−0.770441	−	0.637511i	$-0.779964\pi$
$59$	−1.43418e8	−1.54088	−0.770441	+	0.637511i	$0.779964\pi$
$60$	0	0
$61$	−1.98043e7	−0.183136	−0.0915681	−	0.995799i	$-0.529188\pi$
$61$	−1.98043e7	−0.183136	−0.0915681	+	0.995799i	$0.529188\pi$
$62$	0	0
$63$	−5.62671e7	−0.450010
$64$	0	0
$65$	0	0
$66$	0	0
$67$	1.65625e8	1.00413	0.502065	−	0.864830i	$-0.332574\pi$
$67$	1.65625e8	1.00413	0.502065	+	0.864830i	$0.332574\pi$
$68$	0	0
$69$	−2.00288e8	−1.06374
$70$	0	0
$71$	−1.94801e8	−0.909766	−0.454883	−	0.890551i	$-0.650319\pi$
$71$	−1.94801e8	−0.909766	−0.454883	+	0.890551i	$0.650319\pi$
$72$	0	0
$73$	−1.48729e8	−0.612977	−0.306488	−	0.951874i	$-0.599154\pi$
$73$	−1.48729e8	−0.612977	−0.306488	+	0.951874i	$0.599154\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	−6.05431e8	−1.96271
$78$	0	0
$79$	−3.01342e7	−0.0870436	−0.0435218	−	0.999052i	$-0.513858\pi$
$79$	−3.01342e7	−0.0870436	−0.0435218	+	0.999052i	$0.513858\pi$
$80$	0	0
$81$	4.30467e7	0.111111
$82$	0	0
$83$	−3.02054e8	−0.698608	−0.349304	−	0.937010i	$-0.613582\pi$
$83$	−3.02054e8	−0.698608	−0.349304	+	0.937010i	$0.613582\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	4.43411e8	0.829794
$88$	0	0
$89$	9.09503e8	1.53656	0.768279	−	0.640115i	$-0.221113\pi$
$89$	9.09503e8	1.53656	0.768279	+	0.640115i	$0.221113\pi$
$90$	0	0
$91$	−2.16973e7	−0.0331680
$92$	0	0
$93$	3.02300e8	0.419050
$94$	0	0
$95$	0	0
$96$	0	0
$97$	8.72463e8	1.00063	0.500316	−	0.865843i	$-0.333217\pi$
$97$	8.72463e8	1.00063	0.500316	+	0.865843i	$0.333217\pi$
$98$	0	0
$99$	4.63180e8	0.484609
$100$	0	0
$101$	−9.87527e8	−0.944284	−0.472142	−	0.881522i	$-0.656519\pi$
$101$	−9.87527e8	−0.944284	−0.472142	+	0.881522i	$0.656519\pi$
$102$	0	0
$103$	−9.32641e8	−0.816483	−0.408242	−	0.912874i	$-0.633858\pi$
$103$	−9.32641e8	−0.816483	−0.408242	+	0.912874i	$0.633858\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	7.35029e8	0.542097	0.271049	−	0.962566i	$-0.412630\pi$
$107$	7.35029e8	0.542097	0.271049	+	0.962566i	$0.412630\pi$
$108$	0	0
$109$	−1.35086e9	−0.916624	−0.458312	−	0.888791i	$-0.651546\pi$
$109$	−1.35086e9	−0.916624	−0.458312	+	0.888791i	$0.651546\pi$
$110$	0	0
$111$	1.77378e9	1.10904
$112$	0	0
$113$	−1.73108e9	−0.998768	−0.499384	−	0.866381i	$-0.666440\pi$
$113$	−1.73108e9	−0.998768	−0.499384	+	0.866381i	$0.666440\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	1.65993e7	0.00818944
$118$	0	0
$119$	−1.72012e9	−0.786318
$120$	0	0
$121$	2.62585e9	1.11362
$122$	0	0
$123$	−1.92933e9	−0.760037
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−2.64725e9	−0.902981	−0.451491	−	0.892276i	$-0.649108\pi$
$127$	−2.64725e9	−0.902981	−0.451491	+	0.892276i	$0.649108\pi$
$128$	0	0
$129$	−8.59627e8	−0.273310
$130$	0	0
$131$	−2.94856e9	−0.874760	−0.437380	−	0.899277i	$-0.644094\pi$
$131$	−2.94856e9	−0.874760	−0.437380	+	0.899277i	$0.644094\pi$
$132$	0	0
$133$	5.96564e9	1.65320
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−4.40594e9	−1.06855	−0.534276	−	0.845310i	$-0.679416\pi$
$137$	−4.40594e9	−1.06855	−0.534276	+	0.845310i	$0.679416\pi$
$138$	0	0
$139$	−5.61505e9	−1.27581	−0.637907	−	0.770114i	$-0.720199\pi$
$139$	−5.61505e9	−1.27581	−0.637907	+	0.770114i	$0.720199\pi$
$140$	0	0
$141$	−1.94276e8	−0.0413935
$142$	0	0
$143$	1.78608e8	0.0357181
$144$	0	0
$145$	0	0
$146$	0	0
$147$	2.68873e9	0.474918
$148$	0	0
$149$	7.71832e8	0.128288	0.0641438	−	0.997941i	$-0.479568\pi$
$149$	7.71832e8	0.128288	0.0641438	+	0.997941i	$0.479568\pi$
$150$	0	0
$151$	−3.77320e9	−0.590627	−0.295313	−	0.955400i	$-0.595424\pi$
$151$	−3.77320e9	−0.590627	−0.295313	+	0.955400i	$0.595424\pi$
$152$	0	0
$153$	1.31597e9	0.194148
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−8.67578e8	−0.113962	−0.0569810	−	0.998375i	$-0.518147\pi$
$157$	−8.67578e8	−0.113962	−0.0569810	+	0.998375i	$0.518147\pi$
$158$	0	0
$159$	7.28593e8	0.0904062
$160$	0	0
$161$	2.12058e10	2.48736
$162$	0	0
$163$	−9.48859e9	−1.05283	−0.526414	−	0.850229i	$-0.676464\pi$
$163$	−9.48859e9	−1.05283	−0.526414	+	0.850229i	$0.676464\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−4.33934e8	−0.0431717	−0.0215859	−	0.999767i	$-0.506872\pi$
$167$	−4.33934e8	−0.0431717	−0.0215859	+	0.999767i	$0.506872\pi$
$168$	0	0
$169$	−1.05981e10	−0.999396
$170$	0	0
$171$	−4.56396e9	−0.408187
$172$	0	0
$173$	2.06266e9	0.175073	0.0875367	−	0.996161i	$-0.472100\pi$
$173$	2.06266e9	0.175073	0.0875367	+	0.996161i	$0.472100\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−1.16169e10	−0.889629
$178$	0	0
$179$	−1.66116e10	−1.20940	−0.604702	−	0.796452i	$-0.706708\pi$
$179$	−1.66116e10	−1.20940	−0.604702	+	0.796452i	$0.706708\pi$
$180$	0	0
$181$	2.39615e9	0.165944	0.0829718	−	0.996552i	$-0.473559\pi$
$181$	2.39615e9	0.165944	0.0829718	+	0.996552i	$0.473559\pi$
$182$	0	0
$183$	−1.60414e9	−0.105734
$184$	0	0
$185$	0	0
$186$	0	0
$187$	1.41597e10	0.846774
$188$	0	0
$189$	−4.55764e9	−0.259813
$190$	0	0
$191$	5.76921e9	0.313665	0.156832	−	0.987625i	$-0.449872\pi$
$191$	5.76921e9	0.313665	0.156832	+	0.987625i	$0.449872\pi$
$192$	0	0
$193$	−3.55033e10	−1.84188	−0.920939	−	0.389707i	$-0.872576\pi$
$193$	−3.55033e10	−1.84188	−0.920939	+	0.389707i	$0.872576\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	2.94109e10	1.39127	0.695633	−	0.718397i	$-0.255124\pi$
$197$	2.94109e10	1.39127	0.695633	+	0.718397i	$0.255124\pi$
$198$	0	0
$199$	1.59828e10	0.722460	0.361230	−	0.932477i	$-0.382357\pi$
$199$	1.59828e10	0.722460	0.361230	+	0.932477i	$0.382357\pi$
$200$	0	0
$201$	1.34156e10	0.579734
$202$	0	0
$203$	−4.69469e10	−1.94032
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−1.62234e10	−0.614150
$208$	0	0
$209$	−4.91080e10	−1.78030
$210$	0	0
$211$	2.79548e10	0.970923	0.485462	−	0.874258i	$-0.338652\pi$
$211$	2.79548e10	0.970923	0.485462	+	0.874258i	$0.338652\pi$
$212$	0	0
$213$	−1.57789e10	−0.525253
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−3.20065e10	−0.979873
$218$	0	0
$219$	−1.20471e10	−0.353902
$220$	0	0
$221$	5.07452e8	0.0143097
$222$	0	0
$223$	3.38539e10	0.916720	0.458360	−	0.888767i	$-0.348437\pi$
$223$	3.38539e10	0.916720	0.458360	+	0.888767i	$0.348437\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−1.57674e10	−0.394135	−0.197067	−	0.980390i	$-0.563142\pi$
$227$	−1.57674e10	−0.394135	−0.197067	+	0.980390i	$0.563142\pi$
$228$	0	0
$229$	−4.51765e10	−1.08556	−0.542779	−	0.839875i	$-0.682628\pi$
$229$	−4.51765e10	−1.08556	−0.542779	+	0.839875i	$0.682628\pi$
$230$	0	0
$231$	−4.90399e10	−1.13317
$232$	0	0
$233$	−1.66895e10	−0.370973	−0.185486	−	0.982647i	$-0.559386\pi$
$233$	−1.66895e10	−0.370973	−0.185486	+	0.982647i	$0.559386\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−2.44087e9	−0.0502547
$238$	0	0
$239$	−3.72504e10	−0.738482	−0.369241	−	0.929334i	$-0.620382\pi$
$239$	−3.72504e10	−0.738482	−0.369241	+	0.929334i	$0.620382\pi$
$240$	0	0
$241$	−7.63821e10	−1.45853	−0.729264	−	0.684232i	$-0.760137\pi$
$241$	−7.63821e10	−1.45853	−0.729264	+	0.684232i	$0.760137\pi$
$242$	0	0
$243$	3.48678e9	0.0641500
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−1.75992e9	−0.0300854
$248$	0	0
$249$	−2.44664e10	−0.403341
$250$	0	0
$251$	8.10746e10	1.28930	0.644649	−	0.764479i	$-0.277004\pi$
$251$	8.10746e10	1.28930	0.644649	+	0.764479i	$0.277004\pi$
$252$	0	0
$253$	−1.74562e11	−2.67860
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−5.40938e10	−0.773479	−0.386740	−	0.922189i	$-0.626399\pi$
$257$	−5.40938e10	−0.773479	−0.386740	+	0.922189i	$0.626399\pi$
$258$	0	0
$259$	−1.87802e11	−2.59329
$260$	0	0
$261$	3.59163e10	0.479082
$262$	0	0
$263$	−8.14462e10	−1.04971	−0.524856	−	0.851191i	$-0.675881\pi$
$263$	−8.14462e10	−1.04971	−0.524856	+	0.851191i	$0.675881\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	7.36697e10	0.887132
$268$	0	0
$269$	−7.59896e9	−0.0884849	−0.0442424	−	0.999021i	$-0.514087\pi$
$269$	−7.59896e9	−0.0884849	−0.0442424	+	0.999021i	$0.514087\pi$
$270$	0	0
$271$	1.43696e11	1.61838	0.809192	−	0.587544i	$-0.199905\pi$
$271$	1.43696e11	1.61838	0.809192	+	0.587544i	$0.199905\pi$
$272$	0	0
$273$	−1.75748e9	−0.0191495
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−3.68379e10	−0.375955	−0.187977	−	0.982173i	$-0.560193\pi$
$277$	−3.68379e10	−0.375955	−0.187977	+	0.982173i	$0.560193\pi$
$278$	0	0
$279$	2.44863e10	0.241938
$280$	0	0
$281$	−1.16983e11	−1.11929	−0.559646	−	0.828731i	$-0.689063\pi$
$281$	−1.16983e11	−1.11929	−0.559646	+	0.828731i	$0.689063\pi$
$282$	0	0
$283$	−6.59868e8	−0.00611531	−0.00305765	−	0.999995i	$-0.500973\pi$
$283$	−6.59868e8	−0.00611531	−0.00305765	+	0.999995i	$0.500973\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	2.04271e11	1.77721
$288$	0	0
$289$	−7.83579e10	−0.660758
$290$	0	0
$291$	7.06695e10	0.577715
$292$	0	0
$293$	1.07014e10	0.0848272	0.0424136	−	0.999100i	$-0.486495\pi$
$293$	1.07014e10	0.0848272	0.0424136	+	0.999100i	$0.486495\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	3.75176e10	0.279789
$298$	0	0
$299$	−6.25592e9	−0.0452659
$300$	0	0
$301$	9.10143e10	0.639088
$302$	0	0
$303$	−7.99897e10	−0.545183
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−1.39854e11	−0.898571	−0.449285	−	0.893388i	$-0.648321\pi$
$307$	−1.39854e11	−0.898571	−0.449285	+	0.893388i	$0.648321\pi$
$308$	0	0
$309$	−7.55440e10	−0.471397
$310$	0	0
$311$	−1.41931e11	−0.860312	−0.430156	−	0.902755i	$-0.641541\pi$
$311$	−1.41931e11	−0.860312	−0.430156	+	0.902755i	$0.641541\pi$
$312$	0	0
$313$	9.96629e10	0.586927	0.293463	−	0.955970i	$-0.405192\pi$
$313$	9.96629e10	0.586927	0.293463	+	0.955970i	$0.405192\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−1.57122e11	−0.873917	−0.436959	−	0.899482i	$-0.643944\pi$
$317$	−1.57122e11	−0.873917	−0.436959	+	0.899482i	$0.643944\pi$
$318$	0	0
$319$	3.86458e11	2.08951
$320$	0	0
$321$	5.95373e10	0.312980
$322$	0	0
$323$	−1.39523e11	−0.713239
$324$	0	0
$325$	0	0
$326$	0	0
$327$	−1.09420e11	−0.529213
$328$	0	0
$329$	2.05692e10	0.0967913
$330$	0	0
$331$	1.90494e10	0.0872278	0.0436139	−	0.999048i	$-0.486113\pi$
$331$	1.90494e10	0.0872278	0.0436139	+	0.999048i	$0.486113\pi$
$332$	0	0
$333$	1.43676e11	0.640303
$334$	0	0
$335$	0	0
$336$	0	0
$337$	2.93698e11	1.24041	0.620207	−	0.784438i	$-0.287048\pi$
$337$	2.93698e11	1.24041	0.620207	+	0.784438i	$0.287048\pi$
$338$	0	0
$339$	−1.40218e11	−0.576639
$340$	0	0
$341$	2.63472e11	1.05521
$342$	0	0
$343$	6.13993e10	0.239519
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−3.37846e11	−1.25094	−0.625470	−	0.780248i	$-0.715093\pi$
$347$	−3.37846e11	−1.25094	−0.625470	+	0.780248i	$0.715093\pi$
$348$	0	0
$349$	−4.72889e11	−1.70626	−0.853130	−	0.521699i	$-0.825299\pi$
$349$	−4.72889e11	−1.70626	−0.853130	+	0.521699i	$0.825299\pi$
$350$	0	0
$351$	1.34455e9	0.00472818
$352$	0	0
$353$	7.08613e10	0.242897	0.121449	−	0.992598i	$-0.461246\pi$
$353$	7.08613e10	0.242897	0.121449	+	0.992598i	$0.461246\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	−1.39330e11	−0.453981
$358$	0	0
$359$	−1.11342e11	−0.353782	−0.176891	−	0.984230i	$-0.556604\pi$
$359$	−1.11342e11	−0.353782	−0.176891	+	0.984230i	$0.556604\pi$
$360$	0	0
$361$	1.61199e11	0.499553
$362$	0	0
$363$	2.12694e11	0.642946
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−6.25177e10	−0.179889	−0.0899447	−	0.995947i	$-0.528669\pi$
$367$	−6.25177e10	−0.179889	−0.0899447	+	0.995947i	$0.528669\pi$
$368$	0	0
$369$	−1.56276e11	−0.438807
$370$	0	0
$371$	−7.71409e10	−0.211399
$372$	0	0
$373$	−1.05476e11	−0.282140	−0.141070	−	0.990000i	$-0.545054\pi$
$373$	−1.05476e11	−0.282140	−0.141070	+	0.990000i	$0.545054\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	1.38498e10	0.0353107
$378$	0	0
$379$	1.02959e11	0.256324	0.128162	−	0.991753i	$-0.459092\pi$
$379$	1.02959e11	0.256324	0.128162	+	0.991753i	$0.459092\pi$
$380$	0	0
$381$	−2.14427e11	−0.521336
$382$	0	0
$383$	3.66974e10	0.0871447	0.0435723	−	0.999050i	$-0.486126\pi$
$383$	3.66974e10	0.0871447	0.0435723	+	0.999050i	$0.486126\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−6.96298e10	−0.157796
$388$	0	0
$389$	8.56869e11	1.89732	0.948661	−	0.316295i	$-0.102439\pi$
$389$	8.56869e11	1.89732	0.948661	+	0.316295i	$0.102439\pi$
$390$	0	0
$391$	−4.95959e11	−1.07312
$392$	0	0
$393$	−2.38833e11	−0.505043
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−1.59368e11	−0.321990	−0.160995	−	0.986955i	$-0.551470\pi$
$397$	−1.59368e11	−0.321990	−0.160995	+	0.986955i	$0.551470\pi$
$398$	0	0
$399$	4.83217e11	0.954473
$400$	0	0
$401$	9.48147e10	0.183116	0.0915579	−	0.995800i	$-0.470815\pi$
$401$	9.48147e10	0.183116	0.0915579	+	0.995800i	$0.470815\pi$
$402$	0	0
$403$	9.44222e9	0.0178321
$404$	0	0
$405$	0	0
$406$	0	0
$407$	1.54595e12	2.79267
$408$	0	0
$409$	3.37607e11	0.596564	0.298282	−	0.954478i	$-0.403586\pi$
$409$	3.37607e11	0.596564	0.298282	+	0.954478i	$0.403586\pi$
$410$	0	0
$411$	−3.56881e11	−0.616929
$412$	0	0
$413$	1.22995e12	2.08024
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−4.54819e11	−0.736591
$418$	0	0
$419$	−3.29000e10	−0.0521474	−0.0260737	−	0.999660i	$-0.508300\pi$
$419$	−3.29000e10	−0.0521474	−0.0260737	+	0.999660i	$0.508300\pi$
$420$	0	0
$421$	−2.85380e11	−0.442745	−0.221372	−	0.975189i	$-0.571054\pi$
$421$	−2.85380e11	−0.442745	−0.221372	+	0.975189i	$0.571054\pi$
$422$	0	0
$423$	−1.57363e10	−0.0238986
$424$	0	0
$425$	0	0
$426$	0	0
$427$	1.69841e11	0.247240
$428$	0	0
$429$	1.44672e10	0.0206219
$430$	0	0
$431$	4.26733e11	0.595673	0.297837	−	0.954617i	$-0.403735\pi$
$431$	4.26733e11	0.595673	0.297837	+	0.954617i	$0.403735\pi$
$432$	0	0
$433$	1.23327e12	1.68603	0.843013	−	0.537893i	$-0.180780\pi$
$433$	1.23327e12	1.68603	0.843013	+	0.537893i	$0.180780\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	1.72006e12	2.25619
$438$	0	0
$439$	1.44143e12	1.85227	0.926134	−	0.377196i	$-0.123112\pi$
$439$	1.44143e12	1.85227	0.926134	+	0.377196i	$0.123112\pi$
$440$	0	0
$441$	2.17787e11	0.274194
$442$	0	0
$443$	−1.56711e12	−1.93323	−0.966616	−	0.256230i	$-0.917520\pi$
$443$	−1.56711e12	−1.93323	−0.966616	+	0.256230i	$0.917520\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	6.25184e10	0.0740669
$448$	0	0
$449$	1.23304e12	1.43175	0.715876	−	0.698227i	$-0.246027\pi$
$449$	1.23304e12	1.43175	0.715876	+	0.698227i	$0.246027\pi$
$450$	0	0
$451$	−1.68152e12	−1.91385
$452$	0	0
$453$	−3.05629e11	−0.340998
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−1.57178e12	−1.68565	−0.842827	−	0.538184i	$-0.819110\pi$
$457$	−1.57178e12	−1.68565	−0.842827	+	0.538184i	$0.819110\pi$
$458$	0	0
$459$	1.06593e11	0.112091
$460$	0	0
$461$	−8.35527e11	−0.861602	−0.430801	−	0.902447i	$-0.641769\pi$
$461$	−8.35527e11	−0.861602	−0.430801	+	0.902447i	$0.641769\pi$
$462$	0	0
$463$	4.09971e11	0.414609	0.207305	−	0.978276i	$-0.433531\pi$
$463$	4.09971e11	0.414609	0.207305	+	0.978276i	$0.433531\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−1.55181e12	−1.50977	−0.754886	−	0.655856i	$-0.772308\pi$
$467$	−1.55181e12	−1.50977	−0.754886	+	0.655856i	$0.772308\pi$
$468$	0	0
$469$	−1.42040e12	−1.35561
$470$	0	0
$471$	−7.02738e10	−0.0657960
$472$	0	0
$473$	−7.49212e11	−0.688224
$474$	0	0
$475$	0	0
$476$	0	0
$477$	5.90161e10	0.0521960
$478$	0	0
$479$	1.48412e12	1.28813	0.644066	−	0.764970i	$-0.277246\pi$
$479$	1.48412e12	1.28813	0.644066	+	0.764970i	$0.277246\pi$
$480$	0	0
$481$	5.54033e10	0.0471935
$482$	0	0
$483$	1.71767e12	1.43608
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−8.73496e10	−0.0703689	−0.0351844	−	0.999381i	$-0.511202\pi$
$487$	−8.73496e10	−0.0703689	−0.0351844	+	0.999381i	$0.511202\pi$
$488$	0	0
$489$	−7.68575e11	−0.607850
$490$	0	0
$491$	1.06681e12	0.828360	0.414180	−	0.910195i	$-0.364068\pi$
$491$	1.06681e12	0.828360	0.414180	+	0.910195i	$0.364068\pi$
$492$	0	0
$493$	1.09798e12	0.837115
$494$	0	0
$495$	0	0
$496$	0	0
$497$	1.67062e12	1.22821
$498$	0	0
$499$	−1.79707e12	−1.29752	−0.648758	−	0.760995i	$-0.724711\pi$
$499$	−1.79707e12	−1.29752	−0.648758	+	0.760995i	$0.724711\pi$
$500$	0	0
$501$	−3.51486e10	−0.0249252
$502$	0	0
$503$	2.50104e12	1.74207	0.871035	−	0.491221i	$-0.163449\pi$
$503$	2.50104e12	1.74207	0.871035	+	0.491221i	$0.163449\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−8.58446e11	−0.577002
$508$	0	0
$509$	1.82699e12	1.20644	0.603219	−	0.797576i	$-0.293884\pi$
$509$	1.82699e12	1.20644	0.603219	+	0.797576i	$0.293884\pi$
$510$	0	0
$511$	1.27550e12	0.827537
$512$	0	0
$513$	−3.69681e11	−0.235667
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−1.69322e11	−0.104233
$518$	0	0
$519$	1.67075e11	0.101079
$520$	0	0
$521$	−7.58725e11	−0.451144	−0.225572	−	0.974227i	$-0.572425\pi$
$521$	−7.58725e11	−0.451144	−0.225572	+	0.974227i	$0.572425\pi$
$522$	0	0
$523$	1.46682e11	0.0857273	0.0428636	−	0.999081i	$-0.486352\pi$
$523$	1.46682e11	0.0857273	0.0428636	+	0.999081i	$0.486352\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	7.48563e11	0.422747
$528$	0	0
$529$	4.31307e12	2.39462
$530$	0	0
$531$	−9.40965e11	−0.513627
$532$	0	0
$533$	−6.02619e10	−0.0323423
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−1.34554e12	−0.698250
$538$	0	0
$539$	2.34338e12	1.19589
$540$	0	0
$541$	1.36780e12	0.686491	0.343246	−	0.939246i	$-0.388474\pi$
$541$	1.36780e12	0.686491	0.343246	+	0.939246i	$0.388474\pi$
$542$	0	0
$543$	1.94088e11	0.0958076
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−1.85917e11	−0.0887927	−0.0443963	−	0.999014i	$-0.514136\pi$
$547$	−1.85917e11	−0.0887927	−0.0443963	+	0.999014i	$0.514136\pi$
$548$	0	0
$549$	−1.29936e11	−0.0610454
$550$	0	0
$551$	−3.80797e12	−1.76000
$552$	0	0
$553$	2.58430e11	0.117512
$554$	0	0
$555$	0	0
$556$	0	0
$557$	3.27980e11	0.144378	0.0721888	−	0.997391i	$-0.477002\pi$
$557$	3.27980e11	0.144378	0.0721888	+	0.997391i	$0.477002\pi$
$558$	0	0
$559$	−2.68501e10	−0.0116303
$560$	0	0
$561$	1.14694e12	0.488885
$562$	0	0
$563$	2.38726e12	1.00141	0.500705	−	0.865618i	$-0.333074\pi$
$563$	2.38726e12	1.00141	0.500705	+	0.865618i	$0.333074\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−3.69169e11	−0.150003
$568$	0	0
$569$	−1.66124e11	−0.0664394	−0.0332197	−	0.999448i	$-0.510576\pi$
$569$	−1.66124e11	−0.0664394	−0.0332197	+	0.999448i	$0.510576\pi$
$570$	0	0
$571$	4.31756e11	0.169971	0.0849857	−	0.996382i	$-0.472916\pi$
$571$	4.31756e11	0.169971	0.0849857	+	0.996382i	$0.472916\pi$
$572$	0	0
$573$	4.67306e11	0.181095
$574$	0	0
$575$	0	0
$576$	0	0
$577$	4.42378e12	1.66151	0.830754	−	0.556640i	$-0.187910\pi$
$577$	4.42378e12	1.66151	0.830754	+	0.556640i	$0.187910\pi$
$578$	0	0
$579$	−2.87577e12	−1.06341
$580$	0	0
$581$	2.59042e12	0.943142
$582$	0	0
$583$	6.35009e11	0.227652
$584$	0	0
$585$	0	0
$586$	0	0
$587$	9.99718e11	0.347541	0.173771	−	0.984786i	$-0.444405\pi$
$587$	9.99718e11	0.347541	0.173771	+	0.984786i	$0.444405\pi$
$588$	0	0
$589$	−2.59613e12	−0.888806
$590$	0	0
$591$	2.38228e12	0.803248
$592$	0	0
$593$	−3.62727e12	−1.20457	−0.602287	−	0.798279i	$-0.705744\pi$
$593$	−3.62727e12	−1.20457	−0.602287	+	0.798279i	$0.705744\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	1.29461e12	0.417113
$598$	0	0
$599$	8.48001e11	0.269138	0.134569	−	0.990904i	$-0.457035\pi$
$599$	8.48001e11	0.269138	0.134569	+	0.990904i	$0.457035\pi$
$600$	0	0
$601$	−5.74213e11	−0.179530	−0.0897651	−	0.995963i	$-0.528612\pi$
$601$	−5.74213e11	−0.179530	−0.0897651	+	0.995963i	$0.528612\pi$
$602$	0	0
$603$	1.08667e12	0.334710
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−6.57818e12	−1.96678	−0.983391	−	0.181498i	$-0.941906\pi$
$607$	−6.57818e12	−1.96678	−0.983391	+	0.181498i	$0.941906\pi$
$608$	0	0
$609$	−3.80270e12	−1.12025
$610$	0	0
$611$	−6.06811e9	−0.00176144
$612$	0	0
$613$	−2.00381e12	−0.573172	−0.286586	−	0.958055i	$-0.592520\pi$
$613$	−2.00381e12	−0.573172	−0.286586	+	0.958055i	$0.592520\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	3.00763e12	0.835490	0.417745	−	0.908564i	$-0.362821\pi$
$617$	3.00763e12	0.835490	0.417745	+	0.908564i	$0.362821\pi$
$618$	0	0
$619$	5.37865e11	0.147253	0.0736267	−	0.997286i	$-0.476543\pi$
$619$	5.37865e11	0.147253	0.0736267	+	0.997286i	$0.476543\pi$
$620$	0	0
$621$	−1.31409e12	−0.354579
$622$	0	0
$623$	−7.79989e12	−2.07440
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−3.97775e12	−1.02786
$628$	0	0
$629$	4.39227e12	1.11882
$630$	0	0
$631$	−1.63300e12	−0.410067	−0.205033	−	0.978755i	$-0.565730\pi$
$631$	−1.63300e12	−0.410067	−0.205033	+	0.978755i	$0.565730\pi$
$632$	0	0
$633$	2.26434e12	0.560563
$634$	0	0
$635$	0	0
$636$	0	0
$637$	8.39812e10	0.0202095
$638$	0	0
$639$	−1.27809e12	−0.303255
$640$	0	0
$641$	2.31331e12	0.541220	0.270610	−	0.962689i	$-0.412775\pi$
$641$	2.31331e12	0.541220	0.270610	+	0.962689i	$0.412775\pi$
$642$	0	0
$643$	2.04205e12	0.471104	0.235552	−	0.971862i	$-0.424310\pi$
$643$	2.04205e12	0.471104	0.235552	+	0.971862i	$0.424310\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	5.30771e12	1.19080	0.595399	−	0.803430i	$-0.296994\pi$
$647$	5.30771e12	1.19080	0.595399	+	0.803430i	$0.296994\pi$
$648$	0	0
$649$	−1.01247e13	−2.24018
$650$	0	0
$651$	−2.59253e12	−0.565730
$652$	0	0
$653$	−1.02579e12	−0.220774	−0.110387	−	0.993889i	$-0.535209\pi$
$653$	−1.02579e12	−0.220774	−0.110387	+	0.993889i	$0.535209\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−9.75814e11	−0.204326
$658$	0	0
$659$	−2.74815e12	−0.567619	−0.283809	−	0.958881i	$-0.591598\pi$
$659$	−2.74815e12	−0.567619	−0.283809	+	0.958881i	$0.591598\pi$
$660$	0	0
$661$	3.51086e12	0.715331	0.357666	−	0.933850i	$-0.383573\pi$
$661$	3.51086e12	0.715331	0.357666	+	0.933850i	$0.383573\pi$
$662$	0	0
$663$	4.11036e10	0.00826170
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−1.35361e13	−2.64805
$668$	0	0
$669$	2.74217e12	0.529269
$670$	0	0
$671$	−1.39810e12	−0.266249
$672$	0	0
$673$	1.37100e12	0.257614	0.128807	−	0.991670i	$-0.458885\pi$
$673$	1.37100e12	0.257614	0.128807	+	0.991670i	$0.458885\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	7.98018e12	1.46004	0.730019	−	0.683427i	$-0.239511\pi$
$677$	7.98018e12	1.46004	0.730019	+	0.683427i	$0.239511\pi$
$678$	0	0
$679$	−7.48225e12	−1.35088
$680$	0	0
$681$	−1.27716e12	−0.227554
$682$	0	0
$683$	−4.69698e11	−0.0825896	−0.0412948	−	0.999147i	$-0.513148\pi$
$683$	−4.69698e11	−0.0825896	−0.0412948	+	0.999147i	$0.513148\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−3.65930e12	−0.626747
$688$	0	0
$689$	2.27573e10	0.00384711
$690$	0	0
$691$	−4.47320e12	−0.746392	−0.373196	−	0.927753i	$-0.621738\pi$
$691$	−4.47320e12	−0.746392	−0.373196	+	0.927753i	$0.621738\pi$
$692$	0	0
$693$	−3.97223e12	−0.654237
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−4.77746e12	−0.766743
$698$	0	0
$699$	−1.35185e12	−0.214181
$700$	0	0
$701$	9.81943e12	1.53587	0.767936	−	0.640526i	$-0.221284\pi$
$701$	9.81943e12	1.53587	0.767936	+	0.640526i	$0.221284\pi$
$702$	0	0
$703$	−1.52330e13	−2.35227
$704$	0	0
$705$	0	0
$706$	0	0
$707$	8.46903e12	1.27481
$708$	0	0
$709$	−7.08380e12	−1.05283	−0.526415	−	0.850228i	$-0.676464\pi$
$709$	−7.08380e12	−1.05283	−0.526415	+	0.850228i	$0.676464\pi$
$710$	0	0
$711$	−1.97710e11	−0.0290145
$712$	0	0
$713$	−9.22836e12	−1.33728
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−3.01728e12	−0.426363
$718$	0	0
$719$	3.19267e12	0.445527	0.222764	−	0.974872i	$-0.428492\pi$
$719$	3.19267e12	0.445527	0.222764	+	0.974872i	$0.428492\pi$
$720$	0	0
$721$	7.99833e12	1.10228
$722$	0	0
$723$	−6.18695e12	−0.842082
$724$	0	0
$725$	0	0
$726$	0	0
$727$	6.00684e12	0.797520	0.398760	−	0.917055i	$-0.369441\pi$
$727$	6.00684e12	0.797520	0.398760	+	0.917055i	$0.369441\pi$
$728$	0	0
$729$	2.82430e11	0.0370370
$730$	0	0
$731$	−2.12863e12	−0.275722
$732$	0	0
$733$	−4.38768e12	−0.561393	−0.280697	−	0.959797i	$-0.590565\pi$
$733$	−4.38768e12	−0.561393	−0.280697	+	0.959797i	$0.590565\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	1.16925e13	1.45983
$738$	0	0
$739$	−3.22051e12	−0.397214	−0.198607	−	0.980079i	$-0.563642\pi$
$739$	−3.22051e12	−0.397214	−0.198607	+	0.980079i	$0.563642\pi$
$740$	0	0
$741$	−1.42553e11	−0.0173698
$742$	0	0
$743$	−6.97886e12	−0.840108	−0.420054	−	0.907499i	$-0.637989\pi$
$743$	−6.97886e12	−0.840108	−0.420054	+	0.907499i	$0.637989\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−1.98178e12	−0.232869
$748$	0	0
$749$	−6.30361e12	−0.731848
$750$	0	0
$751$	−9.61609e12	−1.10311	−0.551555	−	0.834139i	$-0.685965\pi$
$751$	−9.61609e12	−1.10311	−0.551555	+	0.834139i	$0.685965\pi$
$752$	0	0
$753$	6.56704e12	0.744376
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−1.11015e12	−0.122871	−0.0614354	−	0.998111i	$-0.519568\pi$
$757$	−1.11015e12	−0.122871	−0.0614354	+	0.998111i	$0.519568\pi$
$758$	0	0
$759$	−1.41396e13	−1.54649
$760$	0	0
$761$	1.27385e13	1.37685	0.688424	−	0.725308i	$-0.258303\pi$
$761$	1.27385e13	1.37685	0.688424	+	0.725308i	$0.258303\pi$
$762$	0	0
$763$	1.15850e13	1.23747
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−3.62847e11	−0.0378569
$768$	0	0
$769$	4.91619e12	0.506944	0.253472	−	0.967343i	$-0.418427\pi$
$769$	4.91619e12	0.506944	0.253472	+	0.967343i	$0.418427\pi$
$770$	0	0
$771$	−4.38160e12	−0.446569
$772$	0	0
$773$	−2.96428e12	−0.298615	−0.149307	−	0.988791i	$-0.547704\pi$
$773$	−2.96428e12	−0.298615	−0.149307	+	0.988791i	$0.547704\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	−1.52119e13	−1.49724
$778$	0	0
$779$	1.65689e13	1.61204
$780$	0	0
$781$	−1.37522e13	−1.32264
$782$	0	0
$783$	2.90922e12	0.276598
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−2.45968e12	−0.228556	−0.114278	−	0.993449i	$-0.536455\pi$
$787$	−2.45968e12	−0.228556	−0.114278	+	0.993449i	$0.536455\pi$
$788$	0	0
$789$	−6.59714e12	−0.606051
$790$	0	0
$791$	1.48458e13	1.34837
$792$	0	0
$793$	−5.01048e10	−0.00449935
$794$	0	0
$795$	0	0
$796$	0	0
$797$	7.12850e12	0.625800	0.312900	−	0.949786i	$-0.398699\pi$
$797$	7.12850e12	0.625800	0.312900	+	0.949786i	$0.398699\pi$
$798$	0	0
$799$	−4.81070e11	−0.0417587
$800$	0	0
$801$	5.96725e12	0.512186
$802$	0	0
$803$	−1.04997e13	−0.891163
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−6.15516e11	−0.0510868
$808$	0	0
$809$	−1.12887e13	−0.926563	−0.463281	−	0.886211i	$-0.653328\pi$
$809$	−1.12887e13	−0.926563	−0.463281	+	0.886211i	$0.653328\pi$
$810$	0	0
$811$	1.75295e13	1.42290	0.711451	−	0.702736i	$-0.248039\pi$
$811$	1.75295e13	1.42290	0.711451	+	0.702736i	$0.248039\pi$
$812$	0	0
$813$	1.16393e13	0.934374
$814$	0	0
$815$	0	0
$816$	0	0
$817$	7.38239e12	0.579693
$818$	0	0
$819$	−1.42356e11	−0.0110560
$820$	0	0
$821$	−4.83005e12	−0.371028	−0.185514	−	0.982642i	$-0.559395\pi$
$821$	−4.83005e12	−0.371028	−0.185514	+	0.982642i	$0.559395\pi$
$822$	0	0
$823$	9.28248e12	0.705285	0.352643	−	0.935758i	$-0.385283\pi$
$823$	9.28248e12	0.705285	0.352643	+	0.935758i	$0.385283\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−7.33229e12	−0.545086	−0.272543	−	0.962144i	$-0.587865\pi$
$827$	−7.33229e12	−0.545086	−0.272543	+	0.962144i	$0.587865\pi$
$828$	0	0
$829$	−1.84547e13	−1.35710	−0.678551	−	0.734554i	$-0.737392\pi$
$829$	−1.84547e13	−1.35710	−0.678551	+	0.734554i	$0.737392\pi$
$830$	0	0
$831$	−2.98387e12	−0.217058
$832$	0	0
$833$	6.65789e12	0.479109
$834$	0	0
$835$	0	0
$836$	0	0
$837$	1.98339e12	0.139683
$838$	0	0
$839$	2.16939e13	1.51150	0.755751	−	0.654859i	$-0.227272\pi$
$839$	2.16939e13	1.51150	0.755751	+	0.654859i	$0.227272\pi$
$840$	0	0
$841$	1.54599e13	1.06567
$842$	0	0
$843$	−9.47561e12	−0.646224
$844$	0	0
$845$	0	0
$846$	0	0
$847$	−2.25193e13	−1.50342
$848$	0	0
$849$	−5.34493e10	−0.00353067
$850$	0	0
$851$	−5.41484e13	−3.53918
$852$	0	0
$853$	2.00688e13	1.29793	0.648963	−	0.760820i	$-0.275203\pi$
$853$	2.00688e13	1.29793	0.648963	+	0.760820i	$0.275203\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	1.11235e13	0.704416	0.352208	−	0.935922i	$-0.385431\pi$
$857$	1.11235e13	0.704416	0.352208	+	0.935922i	$0.385431\pi$
$858$	0	0
$859$	−1.69242e13	−1.06057	−0.530283	−	0.847821i	$-0.677914\pi$
$859$	−1.69242e13	−1.06057	−0.530283	+	0.847821i	$0.677914\pi$
$860$	0	0
$861$	1.65460e13	1.02607
$862$	0	0
$863$	1.03021e13	0.632235	0.316117	−	0.948720i	$-0.397621\pi$
$863$	1.03021e13	0.632235	0.316117	+	0.948720i	$0.397621\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−6.34699e12	−0.381489
$868$	0	0
$869$	−2.12735e12	−0.126546
$870$	0	0
$871$	4.19032e11	0.0246698
$872$	0	0
$873$	5.72423e12	0.333544
$874$	0	0
$875$	0	0
$876$	0	0
$877$	2.33590e12	0.133338	0.0666692	−	0.997775i	$-0.478763\pi$
$877$	2.33590e12	0.133338	0.0666692	+	0.997775i	$0.478763\pi$
$878$	0	0
$879$	8.66811e11	0.0489750
$880$	0	0
$881$	1.88953e13	1.05673	0.528364	−	0.849018i	$-0.322806\pi$
$881$	1.88953e13	1.05673	0.528364	+	0.849018i	$0.322806\pi$
$882$	0	0
$883$	−2.67028e13	−1.47820	−0.739101	−	0.673595i	$-0.764749\pi$
$883$	−2.67028e13	−1.47820	−0.739101	+	0.673595i	$0.764749\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−1.47604e13	−0.800649	−0.400325	−	0.916373i	$-0.631103\pi$
$887$	−1.47604e13	−0.800649	−0.400325	+	0.916373i	$0.631103\pi$
$888$	0	0
$889$	2.27028e13	1.21905
$890$	0	0
$891$	3.03893e12	0.161536
$892$	0	0
$893$	1.66842e12	0.0877958
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−5.06730e11	−0.0261343
$898$	0	0
$899$	2.04303e13	1.04317
$900$	0	0
$901$	1.80416e12	0.0912039
$902$	0	0
$903$	7.37216e12	0.368977
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−5.83467e12	−0.286275	−0.143138	−	0.989703i	$-0.545719\pi$
$907$	−5.83467e12	−0.286275	−0.143138	+	0.989703i	$0.545719\pi$
$908$	0	0
$909$	−6.47916e12	−0.314761
$910$	0	0
$911$	4.30923e12	0.207285	0.103642	−	0.994615i	$-0.466950\pi$
$911$	4.30923e12	0.207285	0.103642	+	0.994615i	$0.466950\pi$
$912$	0	0
$913$	−2.13238e13	−1.01566
$914$	0	0
$915$	0	0
$916$	0	0
$917$	2.52868e13	1.18095
$918$	0	0
$919$	5.92750e12	0.274127	0.137064	−	0.990562i	$-0.456234\pi$
$919$	5.92750e12	0.274127	0.137064	+	0.990562i	$0.456234\pi$
$920$	0	0
$921$	−1.13282e13	−0.518790
$922$	0	0
$923$	−4.92848e11	−0.0223514
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−6.11906e12	−0.272161
$928$	0	0
$929$	3.95161e13	1.74062	0.870309	−	0.492506i	$-0.163919\pi$
$929$	3.95161e13	1.74062	0.870309	+	0.492506i	$0.163919\pi$
$930$	0	0
$931$	−2.30905e13	−1.00730
$932$	0	0
$933$	−1.14964e13	−0.496701
$934$	0	0
$935$	0	0
$936$	0	0
$937$	2.02284e13	0.857300	0.428650	−	0.903471i	$-0.358989\pi$
$937$	2.02284e13	0.857300	0.428650	+	0.903471i	$0.358989\pi$
$938$	0	0
$939$	8.07269e12	0.338862
$940$	0	0
$941$	1.49078e13	0.619811	0.309906	−	0.950767i	$-0.399702\pi$
$941$	1.49078e13	0.619811	0.309906	+	0.950767i	$0.399702\pi$
$942$	0	0
$943$	5.88970e13	2.42544
$944$	0	0
$945$	0	0
$946$	0	0
$947$	3.06251e13	1.23738	0.618689	−	0.785636i	$-0.287664\pi$
$947$	3.06251e13	1.23738	0.618689	+	0.785636i	$0.287664\pi$
$948$	0	0
$949$	−3.76285e11	−0.0150598
$950$	0	0
$951$	−1.27269e13	−0.504556
$952$	0	0
$953$	−1.84867e13	−0.726008	−0.363004	−	0.931788i	$-0.618249\pi$
$953$	−1.84867e13	−0.726008	−0.363004	+	0.931788i	$0.618249\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	3.13031e13	1.20638
$958$	0	0
$959$	3.77853e13	1.44258
$960$	0	0
$961$	−1.25110e13	−0.473192
$962$	0	0
$963$	4.82252e12	0.180699
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−3.63147e12	−0.133556	−0.0667780	−	0.997768i	$-0.521272\pi$
$967$	−3.63147e12	−0.133556	−0.0667780	+	0.997768i	$0.521272\pi$
$968$	0	0
$969$	−1.13014e13	−0.411789
$970$	0	0
$971$	−3.10352e13	−1.12039	−0.560193	−	0.828362i	$-0.689273\pi$
$971$	−3.10352e13	−1.12039	−0.560193	+	0.828362i	$0.689273\pi$
$972$	0	0
$973$	4.81547e13	1.72239
$974$	0	0
$975$	0	0
$976$	0	0
$977$	3.54966e12	0.124641	0.0623206	−	0.998056i	$-0.480150\pi$
$977$	3.54966e12	0.124641	0.0623206	+	0.998056i	$0.480150\pi$
$978$	0	0
$979$	6.42072e13	2.23389
$980$	0	0
$981$	−8.86299e12	−0.305541
$982$	0	0
$983$	2.81965e13	0.963174	0.481587	−	0.876398i	$-0.340061\pi$
$983$	2.81965e13	0.963174	0.481587	+	0.876398i	$0.340061\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	1.66611e12	0.0558825
$988$	0	0
$989$	2.62419e13	0.872192
$990$	0	0
$991$	−2.66581e13	−0.878006	−0.439003	−	0.898486i	$-0.644668\pi$
$991$	−2.66581e13	−0.878006	−0.439003	+	0.898486i	$0.644668\pi$
$992$	0	0
$993$	1.54300e12	0.0503610
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−4.95188e13	−1.58724	−0.793618	−	0.608416i	$-0.791805\pi$
$997$	−4.95188e13	−1.58724	−0.793618	+	0.608416i	$0.791805\pi$
$998$	0	0
$999$	1.16378e13	0.369679

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.10.a.a.1.1		1
5.2	odd	4		300.10.d.c.49.1		2
5.3	odd	4		300.10.d.c.49.2		2
5.4	even	2		12.10.a.a.1.1	✓	1
15.14	odd	2		36.10.a.a.1.1		1
20.19	odd	2		48.10.a.g.1.1		1
40.19	odd	2		192.10.a.b.1.1		1
40.29	even	2		192.10.a.i.1.1		1
45.4	even	6		324.10.e.a.217.1		2
45.14	odd	6		324.10.e.f.217.1		2
45.29	odd	6		324.10.e.f.109.1		2
45.34	even	6		324.10.e.a.109.1		2
60.59	even	2		144.10.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.10.a.a.1.1	✓	1	5.4	even	2
36.10.a.a.1.1		1	15.14	odd	2
48.10.a.g.1.1		1	20.19	odd	2
144.10.a.c.1.1		1	60.59	even	2
192.10.a.b.1.1		1	40.19	odd	2
192.10.a.i.1.1		1	40.29	even	2
300.10.a.a.1.1		1	1.1	even	1	trivial
300.10.d.c.49.1		2	5.2	odd	4
300.10.d.c.49.2		2	5.3	odd	4
324.10.e.a.109.1		2	45.34	even	6
324.10.e.a.217.1		2	45.4	even	6
324.10.e.f.109.1		2	45.29	odd	6
324.10.e.f.217.1		2	45.14	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	300.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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