LMFDB - Embedded newform 2850.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2850,2,Mod(1,2850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2850, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2850.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:	$22.7573645761$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.00000 q^{11} -1.00000 q^{12} +6.00000 q^{13} -2.00000 q^{14} +1.00000 q^{16} +2.00000 q^{17} -1.00000 q^{18} -1.00000 q^{19} -2.00000 q^{21} +3.00000 q^{22} +1.00000 q^{23} +1.00000 q^{24} -6.00000 q^{26} -1.00000 q^{27} +2.00000 q^{28} -5.00000 q^{29} +7.00000 q^{31} -1.00000 q^{32} +3.00000 q^{33} -2.00000 q^{34} +1.00000 q^{36} +2.00000 q^{37} +1.00000 q^{38} -6.00000 q^{39} +2.00000 q^{41} +2.00000 q^{42} +6.00000 q^{43} -3.00000 q^{44} -1.00000 q^{46} +12.0000 q^{47} -1.00000 q^{48} -3.00000 q^{49} -2.00000 q^{51} +6.00000 q^{52} -9.00000 q^{53} +1.00000 q^{54} -2.00000 q^{56} +1.00000 q^{57} +5.00000 q^{58} -10.0000 q^{59} -13.0000 q^{61} -7.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} -3.00000 q^{66} +7.00000 q^{67} +2.00000 q^{68} -1.00000 q^{69} +12.0000 q^{71} -1.00000 q^{72} -9.00000 q^{73} -2.00000 q^{74} -1.00000 q^{76} -6.00000 q^{77} +6.00000 q^{78} +5.00000 q^{79} +1.00000 q^{81} -2.00000 q^{82} +1.00000 q^{83} -2.00000 q^{84} -6.00000 q^{86} +5.00000 q^{87} +3.00000 q^{88} +5.00000 q^{89} +12.0000 q^{91} +1.00000 q^{92} -7.00000 q^{93} -12.0000 q^{94} +1.00000 q^{96} +12.0000 q^{97} +3.00000 q^{98} -3.00000 q^{99} +O(q^{100})\)

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	2.00000	0.755929	0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	−1.00000	−0.288675
$13$	6.00000	1.66410	0.832050	−	0.554700i	$-0.187167\pi$
$13$	6.00000	1.66410	0.832050	+	0.554700i	$0.187167\pi$
$14$	−2.00000	−0.534522
$15$	0	0
$16$	1.00000	0.250000
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	−1.00000	−0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0	0
$21$	−2.00000	−0.436436
$22$	3.00000	0.639602
$23$	1.00000	0.208514	0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000	0.208514	0.104257	+	0.994550i	$0.466753\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	−6.00000	−1.17670
$27$	−1.00000	−0.192450
$28$	2.00000	0.377964
$29$	−5.00000	−0.928477	−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000	−0.928477	−0.464238	+	0.885710i	$0.653672\pi$
$30$	0	0
$31$	7.00000	1.25724	0.628619	−	0.777714i	$-0.283621\pi$
$31$	7.00000	1.25724	0.628619	+	0.777714i	$0.283621\pi$
$32$	−1.00000	−0.176777
$33$	3.00000	0.522233
$34$	−2.00000	−0.342997
$35$	0	0
$36$	1.00000	0.166667
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	1.00000	0.162221
$39$	−6.00000	−0.960769
$40$	0	0
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	2.00000	0.308607
$43$	6.00000	0.914991	0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000	0.914991	0.457496	+	0.889212i	$0.348747\pi$
$44$	−3.00000	−0.452267
$45$	0	0
$46$	−1.00000	−0.147442
$47$	12.0000	1.75038	0.875190	−	0.483779i	$-0.160736\pi$
$47$	12.0000	1.75038	0.875190	+	0.483779i	$0.160736\pi$
$48$	−1.00000	−0.144338
$49$	−3.00000	−0.428571
$50$	0	0
$51$	−2.00000	−0.280056
$52$	6.00000	0.832050
$53$	−9.00000	−1.23625	−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000	−1.23625	−0.618123	+	0.786082i	$0.712106\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−2.00000	−0.267261
$57$	1.00000	0.132453
$58$	5.00000	0.656532
$59$	−10.0000	−1.30189	−0.650945	−	0.759125i	$-0.725627\pi$
$59$	−10.0000	−1.30189	−0.650945	+	0.759125i	$0.725627\pi$
$60$	0	0
$61$	−13.0000	−1.66448	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−13.0000	−1.66448	−0.832240	+	0.554416i	$0.812942\pi$
$62$	−7.00000	−0.889001
$63$	2.00000	0.251976
$64$	1.00000	0.125000
$65$	0	0
$66$	−3.00000	−0.369274
$67$	7.00000	0.855186	0.427593	−	0.903971i	$-0.359362\pi$
$67$	7.00000	0.855186	0.427593	+	0.903971i	$0.359362\pi$
$68$	2.00000	0.242536
$69$	−1.00000	−0.120386
$70$	0	0
$71$	12.0000	1.42414	0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000	1.42414	0.712069	+	0.702109i	$0.247758\pi$
$72$	−1.00000	−0.117851
$73$	−9.00000	−1.05337	−0.526685	−	0.850060i	$-0.676565\pi$
$73$	−9.00000	−1.05337	−0.526685	+	0.850060i	$0.676565\pi$
$74$	−2.00000	−0.232495
$75$	0	0
$76$	−1.00000	−0.114708
$77$	−6.00000	−0.683763
$78$	6.00000	0.679366
$79$	5.00000	0.562544	0.281272	−	0.959628i	$-0.409244\pi$
$79$	5.00000	0.562544	0.281272	+	0.959628i	$0.409244\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−2.00000	−0.220863
$83$	1.00000	0.109764	0.0548821	−	0.998493i	$-0.482522\pi$
$83$	1.00000	0.109764	0.0548821	+	0.998493i	$0.482522\pi$
$84$	−2.00000	−0.218218
$85$	0	0
$86$	−6.00000	−0.646997
$87$	5.00000	0.536056
$88$	3.00000	0.319801
$89$	5.00000	0.529999	0.264999	−	0.964249i	$-0.414628\pi$
$89$	5.00000	0.529999	0.264999	+	0.964249i	$0.414628\pi$
$90$	0	0
$91$	12.0000	1.25794
$92$	1.00000	0.104257
$93$	−7.00000	−0.725866
$94$	−12.0000	−1.23771
$95$	0	0
$96$	1.00000	0.102062
$97$	12.0000	1.21842	0.609208	−	0.793011i	$-0.291488\pi$
$97$	12.0000	1.21842	0.609208	+	0.793011i	$0.291488\pi$
$98$	3.00000	0.303046
$99$	−3.00000	−0.301511
$100$	0	0
$101$	2.00000	0.199007	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000	0.199007	0.0995037	+	0.995037i	$0.468274\pi$
$102$	2.00000	0.198030
$103$	−9.00000	−0.886796	−0.443398	−	0.896325i	$-0.646227\pi$
$103$	−9.00000	−0.886796	−0.443398	+	0.896325i	$0.646227\pi$
$104$	−6.00000	−0.588348
$105$	0	0
$106$	9.00000	0.874157
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	−1.00000	−0.0962250
$109$	10.0000	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	0	0
$111$	−2.00000	−0.189832
$112$	2.00000	0.188982
$113$	−19.0000	−1.78737	−0.893685	−	0.448695i	$-0.851889\pi$
$113$	−19.0000	−1.78737	−0.893685	+	0.448695i	$0.851889\pi$
$114$	−1.00000	−0.0936586
$115$	0	0
$116$	−5.00000	−0.464238
$117$	6.00000	0.554700
$118$	10.0000	0.920575
$119$	4.00000	0.366679
$120$	0	0
$121$	−2.00000	−0.181818
$122$	13.0000	1.17696
$123$	−2.00000	−0.180334
$124$	7.00000	0.628619
$125$	0	0
$126$	−2.00000	−0.178174
$127$	−3.00000	−0.266207	−0.133103	−	0.991102i	$-0.542494\pi$
$127$	−3.00000	−0.266207	−0.133103	+	0.991102i	$0.542494\pi$
$128$	−1.00000	−0.0883883
$129$	−6.00000	−0.528271
$130$	0	0
$131$	7.00000	0.611593	0.305796	−	0.952097i	$-0.401077\pi$
$131$	7.00000	0.611593	0.305796	+	0.952097i	$0.401077\pi$
$132$	3.00000	0.261116
$133$	−2.00000	−0.173422
$134$	−7.00000	−0.604708
$135$	0	0
$136$	−2.00000	−0.171499
$137$	12.0000	1.02523	0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000	1.02523	0.512615	+	0.858619i	$0.328677\pi$
$138$	1.00000	0.0851257
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	−12.0000	−1.01058
$142$	−12.0000	−1.00702
$143$	−18.0000	−1.50524
$144$	1.00000	0.0833333
$145$	0	0
$146$	9.00000	0.744845
$147$	3.00000	0.247436
$148$	2.00000	0.164399
$149$	−20.0000	−1.63846	−0.819232	−	0.573462i	$-0.805600\pi$
$149$	−20.0000	−1.63846	−0.819232	+	0.573462i	$0.805600\pi$
$150$	0	0
$151$	12.0000	0.976546	0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000	0.976546	0.488273	+	0.872691i	$0.337627\pi$
$152$	1.00000	0.0811107
$153$	2.00000	0.161690
$154$	6.00000	0.483494
$155$	0	0
$156$	−6.00000	−0.480384
$157$	−18.0000	−1.43656	−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000	−1.43656	−0.718278	+	0.695756i	$0.755069\pi$
$158$	−5.00000	−0.397779
$159$	9.00000	0.713746
$160$	0	0
$161$	2.00000	0.157622
$162$	−1.00000	−0.0785674
$163$	6.00000	0.469956	0.234978	−	0.972001i	$-0.424498\pi$
$163$	6.00000	0.469956	0.234978	+	0.972001i	$0.424498\pi$
$164$	2.00000	0.156174
$165$	0	0
$166$	−1.00000	−0.0776151
$167$	2.00000	0.154765	0.0773823	−	0.997001i	$-0.475344\pi$
$167$	2.00000	0.154765	0.0773823	+	0.997001i	$0.475344\pi$
$168$	2.00000	0.154303
$169$	23.0000	1.76923
$170$	0	0
$171$	−1.00000	−0.0764719
$172$	6.00000	0.457496
$173$	21.0000	1.59660	0.798300	−	0.602260i	$-0.205733\pi$
$173$	21.0000	1.59660	0.798300	+	0.602260i	$0.205733\pi$
$174$	−5.00000	−0.379049
$175$	0	0
$176$	−3.00000	−0.226134
$177$	10.0000	0.751646
$178$	−5.00000	−0.374766
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	−12.0000	−0.889499
$183$	13.0000	0.960988
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	7.00000	0.513265
$187$	−6.00000	−0.438763
$188$	12.0000	0.875190
$189$	−2.00000	−0.145479
$190$	0	0
$191$	17.0000	1.23008	0.615038	−	0.788497i	$-0.289140\pi$
$191$	17.0000	1.23008	0.615038	+	0.788497i	$0.289140\pi$
$192$	−1.00000	−0.0721688
$193$	16.0000	1.15171	0.575853	−	0.817554i	$-0.304670\pi$
$193$	16.0000	1.15171	0.575853	+	0.817554i	$0.304670\pi$
$194$	−12.0000	−0.861550
$195$	0	0
$196$	−3.00000	−0.214286
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	3.00000	0.213201
$199$	−10.0000	−0.708881	−0.354441	−	0.935079i	$-0.615329\pi$
$199$	−10.0000	−0.708881	−0.354441	+	0.935079i	$0.615329\pi$
$200$	0	0
$201$	−7.00000	−0.493742
$202$	−2.00000	−0.140720
$203$	−10.0000	−0.701862
$204$	−2.00000	−0.140028
$205$	0	0
$206$	9.00000	0.627060
$207$	1.00000	0.0695048
$208$	6.00000	0.416025
$209$	3.00000	0.207514
$210$	0	0
$211$	17.0000	1.17033	0.585164	−	0.810915i	$-0.301030\pi$
$211$	17.0000	1.17033	0.585164	+	0.810915i	$0.301030\pi$
$212$	−9.00000	−0.618123
$213$	−12.0000	−0.822226
$214$	−12.0000	−0.820303
$215$	0	0
$216$	1.00000	0.0680414
$217$	14.0000	0.950382
$218$	−10.0000	−0.677285
$219$	9.00000	0.608164
$220$	0	0
$221$	12.0000	0.807207
$222$	2.00000	0.134231
$223$	11.0000	0.736614	0.368307	−	0.929704i	$-0.379937\pi$
$223$	11.0000	0.736614	0.368307	+	0.929704i	$0.379937\pi$
$224$	−2.00000	−0.133631
$225$	0	0
$226$	19.0000	1.26386
$227$	2.00000	0.132745	0.0663723	−	0.997795i	$-0.478857\pi$
$227$	2.00000	0.132745	0.0663723	+	0.997795i	$0.478857\pi$
$228$	1.00000	0.0662266
$229$	15.0000	0.991228	0.495614	−	0.868543i	$-0.334943\pi$
$229$	15.0000	0.991228	0.495614	+	0.868543i	$0.334943\pi$
$230$	0	0
$231$	6.00000	0.394771
$232$	5.00000	0.328266
$233$	26.0000	1.70332	0.851658	−	0.524097i	$-0.175597\pi$
$233$	26.0000	1.70332	0.851658	+	0.524097i	$0.175597\pi$
$234$	−6.00000	−0.392232
$235$	0	0
$236$	−10.0000	−0.650945
$237$	−5.00000	−0.324785
$238$	−4.00000	−0.259281
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	2.00000	0.128831	0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000	0.128831	0.0644157	+	0.997923i	$0.479482\pi$
$242$	2.00000	0.128565
$243$	−1.00000	−0.0641500
$244$	−13.0000	−0.832240
$245$	0	0
$246$	2.00000	0.127515
$247$	−6.00000	−0.381771
$248$	−7.00000	−0.444500
$249$	−1.00000	−0.0633724
$250$	0	0
$251$	−8.00000	−0.504956	−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000	−0.504956	−0.252478	+	0.967603i	$0.581245\pi$
$252$	2.00000	0.125988
$253$	−3.00000	−0.188608
$254$	3.00000	0.188237
$255$	0	0
$256$	1.00000	0.0625000
$257$	27.0000	1.68421	0.842107	−	0.539311i	$-0.181315\pi$
$257$	27.0000	1.68421	0.842107	+	0.539311i	$0.181315\pi$
$258$	6.00000	0.373544
$259$	4.00000	0.248548
$260$	0	0
$261$	−5.00000	−0.309492
$262$	−7.00000	−0.432461
$263$	1.00000	0.0616626	0.0308313	−	0.999525i	$-0.490185\pi$
$263$	1.00000	0.0616626	0.0308313	+	0.999525i	$0.490185\pi$
$264$	−3.00000	−0.184637
$265$	0	0
$266$	2.00000	0.122628
$267$	−5.00000	−0.305995
$268$	7.00000	0.427593
$269$	−10.0000	−0.609711	−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000	−0.609711	−0.304855	+	0.952399i	$0.598608\pi$
$270$	0	0
$271$	32.0000	1.94386	0.971931	−	0.235267i	$-0.0755965\pi$
$271$	32.0000	1.94386	0.971931	+	0.235267i	$0.0755965\pi$
$272$	2.00000	0.121268
$273$	−12.0000	−0.726273
$274$	−12.0000	−0.724947
$275$	0	0
$276$	−1.00000	−0.0601929
$277$	7.00000	0.420589	0.210295	−	0.977638i	$-0.432558\pi$
$277$	7.00000	0.420589	0.210295	+	0.977638i	$0.432558\pi$
$278$	0	0
$279$	7.00000	0.419079
$280$	0	0
$281$	7.00000	0.417585	0.208792	−	0.977960i	$-0.433047\pi$
$281$	7.00000	0.417585	0.208792	+	0.977960i	$0.433047\pi$
$282$	12.0000	0.714590
$283$	16.0000	0.951101	0.475551	−	0.879688i	$-0.342249\pi$
$283$	16.0000	0.951101	0.475551	+	0.879688i	$0.342249\pi$
$284$	12.0000	0.712069
$285$	0	0
$286$	18.0000	1.06436
$287$	4.00000	0.236113
$288$	−1.00000	−0.0589256
$289$	−13.0000	−0.764706
$290$	0	0
$291$	−12.0000	−0.703452
$292$	−9.00000	−0.526685
$293$	1.00000	0.0584206	0.0292103	−	0.999573i	$-0.490701\pi$
$293$	1.00000	0.0584206	0.0292103	+	0.999573i	$0.490701\pi$
$294$	−3.00000	−0.174964
$295$	0	0
$296$	−2.00000	−0.116248
$297$	3.00000	0.174078
$298$	20.0000	1.15857
$299$	6.00000	0.346989
$300$	0	0
$301$	12.0000	0.691669
$302$	−12.0000	−0.690522
$303$	−2.00000	−0.114897
$304$	−1.00000	−0.0573539
$305$	0	0
$306$	−2.00000	−0.114332
$307$	7.00000	0.399511	0.199756	−	0.979846i	$-0.435985\pi$
$307$	7.00000	0.399511	0.199756	+	0.979846i	$0.435985\pi$
$308$	−6.00000	−0.341882
$309$	9.00000	0.511992
$310$	0	0
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	6.00000	0.339683
$313$	−29.0000	−1.63918	−0.819588	−	0.572953i	$-0.805798\pi$
$313$	−29.0000	−1.63918	−0.819588	+	0.572953i	$0.805798\pi$
$314$	18.0000	1.01580
$315$	0	0
$316$	5.00000	0.281272
$317$	−3.00000	−0.168497	−0.0842484	−	0.996445i	$-0.526849\pi$
$317$	−3.00000	−0.168497	−0.0842484	+	0.996445i	$0.526849\pi$
$318$	−9.00000	−0.504695
$319$	15.0000	0.839839
$320$	0	0
$321$	−12.0000	−0.669775
$322$	−2.00000	−0.111456
$323$	−2.00000	−0.111283
$324$	1.00000	0.0555556
$325$	0	0
$326$	−6.00000	−0.332309
$327$	−10.0000	−0.553001
$328$	−2.00000	−0.110432
$329$	24.0000	1.32316
$330$	0	0
$331$	7.00000	0.384755	0.192377	−	0.981321i	$-0.438380\pi$
$331$	7.00000	0.384755	0.192377	+	0.981321i	$0.438380\pi$
$332$	1.00000	0.0548821
$333$	2.00000	0.109599
$334$	−2.00000	−0.109435
$335$	0	0
$336$	−2.00000	−0.109109
$337$	−8.00000	−0.435788	−0.217894	−	0.975972i	$-0.569919\pi$
$337$	−8.00000	−0.435788	−0.217894	+	0.975972i	$0.569919\pi$
$338$	−23.0000	−1.25104
$339$	19.0000	1.03194
$340$	0	0
$341$	−21.0000	−1.13721
$342$	1.00000	0.0540738
$343$	−20.0000	−1.07990
$344$	−6.00000	−0.323498
$345$	0	0
$346$	−21.0000	−1.12897
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	5.00000	0.268028
$349$	25.0000	1.33822	0.669110	−	0.743164i	$-0.266676\pi$
$349$	25.0000	1.33822	0.669110	+	0.743164i	$0.266676\pi$
$350$	0	0
$351$	−6.00000	−0.320256
$352$	3.00000	0.159901
$353$	6.00000	0.319348	0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000	0.319348	0.159674	+	0.987170i	$0.448956\pi$
$354$	−10.0000	−0.531494
$355$	0	0
$356$	5.00000	0.264999
$357$	−4.00000	−0.211702
$358$	0	0
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	−2.00000	−0.105118
$363$	2.00000	0.104973
$364$	12.0000	0.628971
$365$	0	0
$366$	−13.0000	−0.679521
$367$	−28.0000	−1.46159	−0.730794	−	0.682598i	$-0.760850\pi$
$367$	−28.0000	−1.46159	−0.730794	+	0.682598i	$0.760850\pi$
$368$	1.00000	0.0521286
$369$	2.00000	0.104116
$370$	0	0
$371$	−18.0000	−0.934513
$372$	−7.00000	−0.362933
$373$	6.00000	0.310668	0.155334	−	0.987862i	$-0.450355\pi$
$373$	6.00000	0.310668	0.155334	+	0.987862i	$0.450355\pi$
$374$	6.00000	0.310253
$375$	0	0
$376$	−12.0000	−0.618853
$377$	−30.0000	−1.54508
$378$	2.00000	0.102869
$379$	20.0000	1.02733	0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000	1.02733	0.513665	+	0.857991i	$0.328287\pi$
$380$	0	0
$381$	3.00000	0.153695
$382$	−17.0000	−0.869796
$383$	−24.0000	−1.22634	−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000	−1.22634	−0.613171	+	0.789950i	$0.710106\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−16.0000	−0.814379
$387$	6.00000	0.304997
$388$	12.0000	0.609208
$389$	−30.0000	−1.52106	−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000	−1.52106	−0.760530	+	0.649303i	$0.775061\pi$
$390$	0	0
$391$	2.00000	0.101144
$392$	3.00000	0.151523
$393$	−7.00000	−0.353103
$394$	−2.00000	−0.100759
$395$	0	0
$396$	−3.00000	−0.150756
$397$	37.0000	1.85698	0.928488	−	0.371361i	$-0.121109\pi$
$397$	37.0000	1.85698	0.928488	+	0.371361i	$0.121109\pi$
$398$	10.0000	0.501255
$399$	2.00000	0.100125
$400$	0	0
$401$	−3.00000	−0.149813	−0.0749064	−	0.997191i	$-0.523866\pi$
$401$	−3.00000	−0.149813	−0.0749064	+	0.997191i	$0.523866\pi$
$402$	7.00000	0.349128
$403$	42.0000	2.09217
$404$	2.00000	0.0995037
$405$	0	0
$406$	10.0000	0.496292
$407$	−6.00000	−0.297409
$408$	2.00000	0.0990148
$409$	−10.0000	−0.494468	−0.247234	−	0.968956i	$-0.579522\pi$
$409$	−10.0000	−0.494468	−0.247234	+	0.968956i	$0.579522\pi$
$410$	0	0
$411$	−12.0000	−0.591916
$412$	−9.00000	−0.443398
$413$	−20.0000	−0.984136
$414$	−1.00000	−0.0491473
$415$	0	0
$416$	−6.00000	−0.294174
$417$	0	0
$418$	−3.00000	−0.146735
$419$	−20.0000	−0.977064	−0.488532	−	0.872546i	$-0.662467\pi$
$419$	−20.0000	−0.977064	−0.488532	+	0.872546i	$0.662467\pi$
$420$	0	0
$421$	22.0000	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$422$	−17.0000	−0.827547
$423$	12.0000	0.583460
$424$	9.00000	0.437079
$425$	0	0
$426$	12.0000	0.581402
$427$	−26.0000	−1.25823
$428$	12.0000	0.580042
$429$	18.0000	0.869048
$430$	0	0
$431$	−18.0000	−0.867029	−0.433515	−	0.901146i	$-0.642727\pi$
$431$	−18.0000	−0.867029	−0.433515	+	0.901146i	$0.642727\pi$
$432$	−1.00000	−0.0481125
$433$	36.0000	1.73005	0.865025	−	0.501729i	$-0.167303\pi$
$433$	36.0000	1.73005	0.865025	+	0.501729i	$0.167303\pi$
$434$	−14.0000	−0.672022
$435$	0	0
$436$	10.0000	0.478913
$437$	−1.00000	−0.0478365
$438$	−9.00000	−0.430037
$439$	−35.0000	−1.67046	−0.835229	−	0.549902i	$-0.814665\pi$
$439$	−35.0000	−1.67046	−0.835229	+	0.549902i	$0.814665\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	−12.0000	−0.570782
$443$	21.0000	0.997740	0.498870	−	0.866677i	$-0.333748\pi$
$443$	21.0000	0.997740	0.498870	+	0.866677i	$0.333748\pi$
$444$	−2.00000	−0.0949158
$445$	0	0
$446$	−11.0000	−0.520865
$447$	20.0000	0.945968
$448$	2.00000	0.0944911
$449$	35.0000	1.65175	0.825876	−	0.563852i	$-0.190681\pi$
$449$	35.0000	1.65175	0.825876	+	0.563852i	$0.190681\pi$
$450$	0	0
$451$	−6.00000	−0.282529
$452$	−19.0000	−0.893685
$453$	−12.0000	−0.563809
$454$	−2.00000	−0.0938647
$455$	0	0
$456$	−1.00000	−0.0468293
$457$	−38.0000	−1.77757	−0.888783	−	0.458329i	$-0.848448\pi$
$457$	−38.0000	−1.77757	−0.888783	+	0.458329i	$0.848448\pi$
$458$	−15.0000	−0.700904
$459$	−2.00000	−0.0933520
$460$	0	0
$461$	−28.0000	−1.30409	−0.652045	−	0.758180i	$-0.726089\pi$
$461$	−28.0000	−1.30409	−0.652045	+	0.758180i	$0.726089\pi$
$462$	−6.00000	−0.279145
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	−5.00000	−0.232119
$465$	0	0
$466$	−26.0000	−1.20443
$467$	7.00000	0.323921	0.161961	−	0.986797i	$-0.448218\pi$
$467$	7.00000	0.323921	0.161961	+	0.986797i	$0.448218\pi$
$468$	6.00000	0.277350
$469$	14.0000	0.646460
$470$	0	0
$471$	18.0000	0.829396
$472$	10.0000	0.460287
$473$	−18.0000	−0.827641
$474$	5.00000	0.229658
$475$	0	0
$476$	4.00000	0.183340
$477$	−9.00000	−0.412082
$478$	0	0
$479$	−15.0000	−0.685367	−0.342684	−	0.939451i	$-0.611336\pi$
$479$	−15.0000	−0.685367	−0.342684	+	0.939451i	$0.611336\pi$
$480$	0	0
$481$	12.0000	0.547153
$482$	−2.00000	−0.0910975
$483$	−2.00000	−0.0910032
$484$	−2.00000	−0.0909091
$485$	0	0
$486$	1.00000	0.0453609
$487$	−8.00000	−0.362515	−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000	−0.362515	−0.181257	+	0.983436i	$0.558017\pi$
$488$	13.0000	0.588482
$489$	−6.00000	−0.271329
$490$	0	0
$491$	−28.0000	−1.26362	−0.631811	−	0.775122i	$-0.717688\pi$
$491$	−28.0000	−1.26362	−0.631811	+	0.775122i	$0.717688\pi$
$492$	−2.00000	−0.0901670
$493$	−10.0000	−0.450377
$494$	6.00000	0.269953
$495$	0	0
$496$	7.00000	0.314309
$497$	24.0000	1.07655
$498$	1.00000	0.0448111
$499$	30.0000	1.34298	0.671492	−	0.741012i	$-0.265654\pi$
$499$	30.0000	1.34298	0.671492	+	0.741012i	$0.265654\pi$
$500$	0	0
$501$	−2.00000	−0.0893534
$502$	8.00000	0.357057
$503$	−44.0000	−1.96186	−0.980932	−	0.194354i	$-0.937739\pi$
$503$	−44.0000	−1.96186	−0.980932	+	0.194354i	$0.937739\pi$
$504$	−2.00000	−0.0890871
$505$	0	0
$506$	3.00000	0.133366
$507$	−23.0000	−1.02147
$508$	−3.00000	−0.133103
$509$	−15.0000	−0.664863	−0.332432	−	0.943127i	$-0.607869\pi$
$509$	−15.0000	−0.664863	−0.332432	+	0.943127i	$0.607869\pi$
$510$	0	0
$511$	−18.0000	−0.796273
$512$	−1.00000	−0.0441942
$513$	1.00000	0.0441511
$514$	−27.0000	−1.19092
$515$	0	0
$516$	−6.00000	−0.264135
$517$	−36.0000	−1.58328
$518$	−4.00000	−0.175750
$519$	−21.0000	−0.921798
$520$	0	0
$521$	−3.00000	−0.131432	−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000	−0.131432	−0.0657162	+	0.997838i	$0.520933\pi$
$522$	5.00000	0.218844
$523$	−4.00000	−0.174908	−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000	−0.174908	−0.0874539	+	0.996169i	$0.527873\pi$
$524$	7.00000	0.305796
$525$	0	0
$526$	−1.00000	−0.0436021
$527$	14.0000	0.609850
$528$	3.00000	0.130558
$529$	−22.0000	−0.956522
$530$	0	0
$531$	−10.0000	−0.433963
$532$	−2.00000	−0.0867110
$533$	12.0000	0.519778
$534$	5.00000	0.216371
$535$	0	0
$536$	−7.00000	−0.302354
$537$	0	0
$538$	10.0000	0.431131
$539$	9.00000	0.387657
$540$	0	0
$541$	17.0000	0.730887	0.365444	−	0.930834i	$-0.380917\pi$
$541$	17.0000	0.730887	0.365444	+	0.930834i	$0.380917\pi$
$542$	−32.0000	−1.37452
$543$	−2.00000	−0.0858282
$544$	−2.00000	−0.0857493
$545$	0	0
$546$	12.0000	0.513553
$547$	−23.0000	−0.983409	−0.491704	−	0.870762i	$-0.663626\pi$
$547$	−23.0000	−0.983409	−0.491704	+	0.870762i	$0.663626\pi$
$548$	12.0000	0.512615
$549$	−13.0000	−0.554826
$550$	0	0
$551$	5.00000	0.213007
$552$	1.00000	0.0425628
$553$	10.0000	0.425243
$554$	−7.00000	−0.297402
$555$	0	0
$556$	0	0
$557$	2.00000	0.0847427	0.0423714	−	0.999102i	$-0.486509\pi$
$557$	2.00000	0.0847427	0.0423714	+	0.999102i	$0.486509\pi$
$558$	−7.00000	−0.296334
$559$	36.0000	1.52264
$560$	0	0
$561$	6.00000	0.253320
$562$	−7.00000	−0.295277
$563$	16.0000	0.674320	0.337160	−	0.941447i	$-0.390534\pi$
$563$	16.0000	0.674320	0.337160	+	0.941447i	$0.390534\pi$
$564$	−12.0000	−0.505291
$565$	0	0
$566$	−16.0000	−0.672530
$567$	2.00000	0.0839921
$568$	−12.0000	−0.503509
$569$	10.0000	0.419222	0.209611	−	0.977785i	$-0.432780\pi$
$569$	10.0000	0.419222	0.209611	+	0.977785i	$0.432780\pi$
$570$	0	0
$571$	−8.00000	−0.334790	−0.167395	−	0.985890i	$-0.553535\pi$
$571$	−8.00000	−0.334790	−0.167395	+	0.985890i	$0.553535\pi$
$572$	−18.0000	−0.752618
$573$	−17.0000	−0.710185
$574$	−4.00000	−0.166957
$575$	0	0
$576$	1.00000	0.0416667
$577$	7.00000	0.291414	0.145707	−	0.989328i	$-0.453454\pi$
$577$	7.00000	0.291414	0.145707	+	0.989328i	$0.453454\pi$
$578$	13.0000	0.540729
$579$	−16.0000	−0.664937
$580$	0	0
$581$	2.00000	0.0829740
$582$	12.0000	0.497416
$583$	27.0000	1.11823
$584$	9.00000	0.372423
$585$	0	0
$586$	−1.00000	−0.0413096
$587$	−3.00000	−0.123823	−0.0619116	−	0.998082i	$-0.519720\pi$
$587$	−3.00000	−0.123823	−0.0619116	+	0.998082i	$0.519720\pi$
$588$	3.00000	0.123718
$589$	−7.00000	−0.288430
$590$	0	0
$591$	−2.00000	−0.0822690
$592$	2.00000	0.0821995
$593$	−4.00000	−0.164260	−0.0821302	−	0.996622i	$-0.526172\pi$
$593$	−4.00000	−0.164260	−0.0821302	+	0.996622i	$0.526172\pi$
$594$	−3.00000	−0.123091
$595$	0	0
$596$	−20.0000	−0.819232
$597$	10.0000	0.409273
$598$	−6.00000	−0.245358
$599$	30.0000	1.22577	0.612883	−	0.790173i	$-0.290010\pi$
$599$	30.0000	1.22577	0.612883	+	0.790173i	$0.290010\pi$
$600$	0	0
$601$	−28.0000	−1.14214	−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000	−1.14214	−0.571072	+	0.820900i	$0.693472\pi$
$602$	−12.0000	−0.489083
$603$	7.00000	0.285062
$604$	12.0000	0.488273
$605$	0	0
$606$	2.00000	0.0812444
$607$	−23.0000	−0.933541	−0.466771	−	0.884378i	$-0.654583\pi$
$607$	−23.0000	−0.933541	−0.466771	+	0.884378i	$0.654583\pi$
$608$	1.00000	0.0405554
$609$	10.0000	0.405220
$610$	0	0
$611$	72.0000	2.91281
$612$	2.00000	0.0808452
$613$	−34.0000	−1.37325	−0.686624	−	0.727013i	$-0.740908\pi$
$613$	−34.0000	−1.37325	−0.686624	+	0.727013i	$0.740908\pi$
$614$	−7.00000	−0.282497
$615$	0	0
$616$	6.00000	0.241747
$617$	22.0000	0.885687	0.442843	−	0.896599i	$-0.353970\pi$
$617$	22.0000	0.885687	0.442843	+	0.896599i	$0.353970\pi$
$618$	−9.00000	−0.362033
$619$	10.0000	0.401934	0.200967	−	0.979598i	$-0.435592\pi$
$619$	10.0000	0.401934	0.200967	+	0.979598i	$0.435592\pi$
$620$	0	0
$621$	−1.00000	−0.0401286
$622$	−12.0000	−0.481156
$623$	10.0000	0.400642
$624$	−6.00000	−0.240192
$625$	0	0
$626$	29.0000	1.15907
$627$	−3.00000	−0.119808
$628$	−18.0000	−0.718278
$629$	4.00000	0.159490
$630$	0	0
$631$	−48.0000	−1.91085	−0.955425	−	0.295234i	$-0.904602\pi$
$631$	−48.0000	−1.91085	−0.955425	+	0.295234i	$0.904602\pi$
$632$	−5.00000	−0.198889
$633$	−17.0000	−0.675689
$634$	3.00000	0.119145
$635$	0	0
$636$	9.00000	0.356873
$637$	−18.0000	−0.713186
$638$	−15.0000	−0.593856
$639$	12.0000	0.474713
$640$	0	0
$641$	−18.0000	−0.710957	−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000	−0.710957	−0.355479	+	0.934684i	$0.615682\pi$
$642$	12.0000	0.473602
$643$	−14.0000	−0.552106	−0.276053	−	0.961142i	$-0.589027\pi$
$643$	−14.0000	−0.552106	−0.276053	+	0.961142i	$0.589027\pi$
$644$	2.00000	0.0788110
$645$	0	0
$646$	2.00000	0.0786889
$647$	27.0000	1.06148	0.530740	−	0.847535i	$-0.321914\pi$
$647$	27.0000	1.06148	0.530740	+	0.847535i	$0.321914\pi$
$648$	−1.00000	−0.0392837
$649$	30.0000	1.17760
$650$	0	0
$651$	−14.0000	−0.548703
$652$	6.00000	0.234978
$653$	−24.0000	−0.939193	−0.469596	−	0.882881i	$-0.655601\pi$
$653$	−24.0000	−0.939193	−0.469596	+	0.882881i	$0.655601\pi$
$654$	10.0000	0.391031
$655$	0	0
$656$	2.00000	0.0780869
$657$	−9.00000	−0.351123
$658$	−24.0000	−0.935617
$659$	30.0000	1.16863	0.584317	−	0.811525i	$-0.301362\pi$
$659$	30.0000	1.16863	0.584317	+	0.811525i	$0.301362\pi$
$660$	0	0
$661$	−28.0000	−1.08907	−0.544537	−	0.838737i	$-0.683295\pi$
$661$	−28.0000	−1.08907	−0.544537	+	0.838737i	$0.683295\pi$
$662$	−7.00000	−0.272063
$663$	−12.0000	−0.466041
$664$	−1.00000	−0.0388075
$665$	0	0
$666$	−2.00000	−0.0774984
$667$	−5.00000	−0.193601
$668$	2.00000	0.0773823
$669$	−11.0000	−0.425285
$670$	0	0
$671$	39.0000	1.50558
$672$	2.00000	0.0771517
$673$	26.0000	1.00223	0.501113	−	0.865382i	$-0.332924\pi$
$673$	26.0000	1.00223	0.501113	+	0.865382i	$0.332924\pi$
$674$	8.00000	0.308148
$675$	0	0
$676$	23.0000	0.884615
$677$	7.00000	0.269032	0.134516	−	0.990911i	$-0.457052\pi$
$677$	7.00000	0.269032	0.134516	+	0.990911i	$0.457052\pi$
$678$	−19.0000	−0.729691
$679$	24.0000	0.921035
$680$	0	0
$681$	−2.00000	−0.0766402
$682$	21.0000	0.804132
$683$	−24.0000	−0.918334	−0.459167	−	0.888350i	$-0.651852\pi$
$683$	−24.0000	−0.918334	−0.459167	+	0.888350i	$0.651852\pi$
$684$	−1.00000	−0.0382360
$685$	0	0
$686$	20.0000	0.763604
$687$	−15.0000	−0.572286
$688$	6.00000	0.228748
$689$	−54.0000	−2.05724
$690$	0	0
$691$	−8.00000	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$692$	21.0000	0.798300
$693$	−6.00000	−0.227921
$694$	−12.0000	−0.455514
$695$	0	0
$696$	−5.00000	−0.189525
$697$	4.00000	0.151511
$698$	−25.0000	−0.946264
$699$	−26.0000	−0.983410
$700$	0	0
$701$	−48.0000	−1.81293	−0.906467	−	0.422276i	$-0.861231\pi$
$701$	−48.0000	−1.81293	−0.906467	+	0.422276i	$0.861231\pi$
$702$	6.00000	0.226455
$703$	−2.00000	−0.0754314
$704$	−3.00000	−0.113067
$705$	0	0
$706$	−6.00000	−0.225813
$707$	4.00000	0.150435
$708$	10.0000	0.375823
$709$	−25.0000	−0.938895	−0.469447	−	0.882960i	$-0.655547\pi$
$709$	−25.0000	−0.938895	−0.469447	+	0.882960i	$0.655547\pi$
$710$	0	0
$711$	5.00000	0.187515
$712$	−5.00000	−0.187383
$713$	7.00000	0.262152
$714$	4.00000	0.149696
$715$	0	0
$716$	0	0
$717$	0	0
$718$	0	0
$719$	5.00000	0.186469	0.0932343	−	0.995644i	$-0.470279\pi$
$719$	5.00000	0.186469	0.0932343	+	0.995644i	$0.470279\pi$
$720$	0	0
$721$	−18.0000	−0.670355
$722$	−1.00000	−0.0372161
$723$	−2.00000	−0.0743808
$724$	2.00000	0.0743294
$725$	0	0
$726$	−2.00000	−0.0742270
$727$	2.00000	0.0741759	0.0370879	−	0.999312i	$-0.488192\pi$
$727$	2.00000	0.0741759	0.0370879	+	0.999312i	$0.488192\pi$
$728$	−12.0000	−0.444750
$729$	1.00000	0.0370370
$730$	0	0
$731$	12.0000	0.443836
$732$	13.0000	0.480494
$733$	−39.0000	−1.44050	−0.720249	−	0.693716i	$-0.755972\pi$
$733$	−39.0000	−1.44050	−0.720249	+	0.693716i	$0.755972\pi$
$734$	28.0000	1.03350
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	−21.0000	−0.773545
$738$	−2.00000	−0.0736210
$739$	−40.0000	−1.47142	−0.735712	−	0.677295i	$-0.763152\pi$
$739$	−40.0000	−1.47142	−0.735712	+	0.677295i	$0.763152\pi$
$740$	0	0
$741$	6.00000	0.220416
$742$	18.0000	0.660801
$743$	16.0000	0.586983	0.293492	−	0.955962i	$-0.405183\pi$
$743$	16.0000	0.586983	0.293492	+	0.955962i	$0.405183\pi$
$744$	7.00000	0.256632
$745$	0	0
$746$	−6.00000	−0.219676
$747$	1.00000	0.0365881
$748$	−6.00000	−0.219382
$749$	24.0000	0.876941
$750$	0	0
$751$	52.0000	1.89751	0.948753	−	0.316017i	$-0.102346\pi$
$751$	52.0000	1.89751	0.948753	+	0.316017i	$0.102346\pi$
$752$	12.0000	0.437595
$753$	8.00000	0.291536
$754$	30.0000	1.09254
$755$	0	0
$756$	−2.00000	−0.0727393
$757$	−23.0000	−0.835949	−0.417975	−	0.908459i	$-0.637260\pi$
$757$	−23.0000	−0.835949	−0.417975	+	0.908459i	$0.637260\pi$
$758$	−20.0000	−0.726433
$759$	3.00000	0.108893
$760$	0	0
$761$	−48.0000	−1.74000	−0.869999	−	0.493053i	$-0.835881\pi$
$761$	−48.0000	−1.74000	−0.869999	+	0.493053i	$0.835881\pi$
$762$	−3.00000	−0.108679
$763$	20.0000	0.724049
$764$	17.0000	0.615038
$765$	0	0
$766$	24.0000	0.867155
$767$	−60.0000	−2.16647
$768$	−1.00000	−0.0360844
$769$	−5.00000	−0.180305	−0.0901523	−	0.995928i	$-0.528735\pi$
$769$	−5.00000	−0.180305	−0.0901523	+	0.995928i	$0.528735\pi$
$770$	0	0
$771$	−27.0000	−0.972381
$772$	16.0000	0.575853
$773$	6.00000	0.215805	0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000	0.215805	0.107903	+	0.994161i	$0.465587\pi$
$774$	−6.00000	−0.215666
$775$	0	0
$776$	−12.0000	−0.430775
$777$	−4.00000	−0.143499
$778$	30.0000	1.07555
$779$	−2.00000	−0.0716574
$780$	0	0
$781$	−36.0000	−1.28818
$782$	−2.00000	−0.0715199
$783$	5.00000	0.178685
$784$	−3.00000	−0.107143
$785$	0	0
$786$	7.00000	0.249682
$787$	−43.0000	−1.53278	−0.766392	−	0.642373i	$-0.777950\pi$
$787$	−43.0000	−1.53278	−0.766392	+	0.642373i	$0.777950\pi$
$788$	2.00000	0.0712470
$789$	−1.00000	−0.0356009
$790$	0	0
$791$	−38.0000	−1.35112
$792$	3.00000	0.106600
$793$	−78.0000	−2.76986
$794$	−37.0000	−1.31308
$795$	0	0
$796$	−10.0000	−0.354441
$797$	2.00000	0.0708436	0.0354218	−	0.999372i	$-0.488723\pi$
$797$	2.00000	0.0708436	0.0354218	+	0.999372i	$0.488723\pi$
$798$	−2.00000	−0.0707992
$799$	24.0000	0.849059
$800$	0	0
$801$	5.00000	0.176666
$802$	3.00000	0.105934
$803$	27.0000	0.952809
$804$	−7.00000	−0.246871
$805$	0	0
$806$	−42.0000	−1.47939
$807$	10.0000	0.352017
$808$	−2.00000	−0.0703598
$809$	30.0000	1.05474	0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000	1.05474	0.527372	+	0.849635i	$0.323177\pi$
$810$	0	0
$811$	−13.0000	−0.456492	−0.228246	−	0.973604i	$-0.573299\pi$
$811$	−13.0000	−0.456492	−0.228246	+	0.973604i	$0.573299\pi$
$812$	−10.0000	−0.350931
$813$	−32.0000	−1.12229
$814$	6.00000	0.210300
$815$	0	0
$816$	−2.00000	−0.0700140
$817$	−6.00000	−0.209913
$818$	10.0000	0.349642
$819$	12.0000	0.419314
$820$	0	0
$821$	−8.00000	−0.279202	−0.139601	−	0.990208i	$-0.544582\pi$
$821$	−8.00000	−0.279202	−0.139601	+	0.990208i	$0.544582\pi$
$822$	12.0000	0.418548
$823$	−34.0000	−1.18517	−0.592583	−	0.805510i	$-0.701892\pi$
$823$	−34.0000	−1.18517	−0.592583	+	0.805510i	$0.701892\pi$
$824$	9.00000	0.313530
$825$	0	0
$826$	20.0000	0.695889
$827$	−18.0000	−0.625921	−0.312961	−	0.949766i	$-0.601321\pi$
$827$	−18.0000	−0.625921	−0.312961	+	0.949766i	$0.601321\pi$
$828$	1.00000	0.0347524
$829$	0	0		−	1.00000i	$-0.5\pi$
$829$	0	0			1.00000i	$0.5\pi$
$830$	0	0
$831$	−7.00000	−0.242827
$832$	6.00000	0.208013
$833$	−6.00000	−0.207888
$834$	0	0
$835$	0	0
$836$	3.00000	0.103757
$837$	−7.00000	−0.241955
$838$	20.0000	0.690889
$839$	−30.0000	−1.03572	−0.517858	−	0.855467i	$-0.673270\pi$
$839$	−30.0000	−1.03572	−0.517858	+	0.855467i	$0.673270\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	−22.0000	−0.758170
$843$	−7.00000	−0.241093
$844$	17.0000	0.585164
$845$	0	0
$846$	−12.0000	−0.412568
$847$	−4.00000	−0.137442
$848$	−9.00000	−0.309061
$849$	−16.0000	−0.549119
$850$	0	0
$851$	2.00000	0.0685591
$852$	−12.0000	−0.411113
$853$	26.0000	0.890223	0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000	0.890223	0.445112	+	0.895475i	$0.353164\pi$
$854$	26.0000	0.889702
$855$	0	0
$856$	−12.0000	−0.410152
$857$	42.0000	1.43469	0.717346	−	0.696717i	$-0.245357\pi$
$857$	42.0000	1.43469	0.717346	+	0.696717i	$0.245357\pi$
$858$	−18.0000	−0.614510
$859$	−10.0000	−0.341196	−0.170598	−	0.985341i	$-0.554570\pi$
$859$	−10.0000	−0.341196	−0.170598	+	0.985341i	$0.554570\pi$
$860$	0	0
$861$	−4.00000	−0.136320
$862$	18.0000	0.613082
$863$	36.0000	1.22545	0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000	1.22545	0.612727	+	0.790295i	$0.290072\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	−36.0000	−1.22333
$867$	13.0000	0.441503
$868$	14.0000	0.475191
$869$	−15.0000	−0.508840
$870$	0	0
$871$	42.0000	1.42312
$872$	−10.0000	−0.338643
$873$	12.0000	0.406138
$874$	1.00000	0.0338255
$875$	0	0
$876$	9.00000	0.304082
$877$	−38.0000	−1.28317	−0.641584	−	0.767052i	$-0.721723\pi$
$877$	−38.0000	−1.28317	−0.641584	+	0.767052i	$0.721723\pi$
$878$	35.0000	1.18119
$879$	−1.00000	−0.0337292
$880$	0	0
$881$	32.0000	1.07811	0.539054	−	0.842271i	$-0.318782\pi$
$881$	32.0000	1.07811	0.539054	+	0.842271i	$0.318782\pi$
$882$	3.00000	0.101015
$883$	−4.00000	−0.134611	−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000	−0.134611	−0.0673054	+	0.997732i	$0.521440\pi$
$884$	12.0000	0.403604
$885$	0	0
$886$	−21.0000	−0.705509
$887$	52.0000	1.74599	0.872995	−	0.487730i	$-0.162175\pi$
$887$	52.0000	1.74599	0.872995	+	0.487730i	$0.162175\pi$
$888$	2.00000	0.0671156
$889$	−6.00000	−0.201234
$890$	0	0
$891$	−3.00000	−0.100504
$892$	11.0000	0.368307
$893$	−12.0000	−0.401565
$894$	−20.0000	−0.668900
$895$	0	0
$896$	−2.00000	−0.0668153
$897$	−6.00000	−0.200334
$898$	−35.0000	−1.16797
$899$	−35.0000	−1.16732
$900$	0	0
$901$	−18.0000	−0.599667
$902$	6.00000	0.199778
$903$	−12.0000	−0.399335
$904$	19.0000	0.631931
$905$	0	0
$906$	12.0000	0.398673
$907$	32.0000	1.06254	0.531271	−	0.847202i	$-0.321714\pi$
$907$	32.0000	1.06254	0.531271	+	0.847202i	$0.321714\pi$
$908$	2.00000	0.0663723
$909$	2.00000	0.0663358
$910$	0	0
$911$	22.0000	0.728893	0.364446	−	0.931224i	$-0.381258\pi$
$911$	22.0000	0.728893	0.364446	+	0.931224i	$0.381258\pi$
$912$	1.00000	0.0331133
$913$	−3.00000	−0.0992855
$914$	38.0000	1.25693
$915$	0	0
$916$	15.0000	0.495614
$917$	14.0000	0.462321
$918$	2.00000	0.0660098
$919$	20.0000	0.659739	0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000	0.659739	0.329870	+	0.944027i	$0.392995\pi$
$920$	0	0
$921$	−7.00000	−0.230658
$922$	28.0000	0.922131
$923$	72.0000	2.36991
$924$	6.00000	0.197386
$925$	0	0
$926$	−16.0000	−0.525793
$927$	−9.00000	−0.295599
$928$	5.00000	0.164133
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	3.00000	0.0983210
$932$	26.0000	0.851658
$933$	−12.0000	−0.392862
$934$	−7.00000	−0.229047
$935$	0	0
$936$	−6.00000	−0.196116
$937$	2.00000	0.0653372	0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000	0.0653372	0.0326686	+	0.999466i	$0.489599\pi$
$938$	−14.0000	−0.457116
$939$	29.0000	0.946379
$940$	0	0
$941$	−43.0000	−1.40176	−0.700880	−	0.713279i	$-0.747209\pi$
$941$	−43.0000	−1.40176	−0.700880	+	0.713279i	$0.747209\pi$
$942$	−18.0000	−0.586472
$943$	2.00000	0.0651290
$944$	−10.0000	−0.325472
$945$	0	0
$946$	18.0000	0.585230
$947$	−28.0000	−0.909878	−0.454939	−	0.890523i	$-0.650339\pi$
$947$	−28.0000	−0.909878	−0.454939	+	0.890523i	$0.650339\pi$
$948$	−5.00000	−0.162392
$949$	−54.0000	−1.75291
$950$	0	0
$951$	3.00000	0.0972817
$952$	−4.00000	−0.129641
$953$	11.0000	0.356325	0.178162	−	0.984001i	$-0.442985\pi$
$953$	11.0000	0.356325	0.178162	+	0.984001i	$0.442985\pi$
$954$	9.00000	0.291386
$955$	0	0
$956$	0	0
$957$	−15.0000	−0.484881
$958$	15.0000	0.484628
$959$	24.0000	0.775000
$960$	0	0
$961$	18.0000	0.580645
$962$	−12.0000	−0.386896
$963$	12.0000	0.386695
$964$	2.00000	0.0644157
$965$	0	0
$966$	2.00000	0.0643489
$967$	42.0000	1.35063	0.675314	−	0.737530i	$-0.264008\pi$
$967$	42.0000	1.35063	0.675314	+	0.737530i	$0.264008\pi$
$968$	2.00000	0.0642824
$969$	2.00000	0.0642493
$970$	0	0
$971$	42.0000	1.34784	0.673922	−	0.738802i	$-0.264608\pi$
$971$	42.0000	1.34784	0.673922	+	0.738802i	$0.264608\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	8.00000	0.256337
$975$	0	0
$976$	−13.0000	−0.416120
$977$	42.0000	1.34370	0.671850	−	0.740688i	$-0.265500\pi$
$977$	42.0000	1.34370	0.671850	+	0.740688i	$0.265500\pi$
$978$	6.00000	0.191859
$979$	−15.0000	−0.479402
$980$	0	0
$981$	10.0000	0.319275
$982$	28.0000	0.893516
$983$	−24.0000	−0.765481	−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000	−0.765481	−0.382741	+	0.923856i	$0.625020\pi$
$984$	2.00000	0.0637577
$985$	0	0
$986$	10.0000	0.318465
$987$	−24.0000	−0.763928
$988$	−6.00000	−0.190885
$989$	6.00000	0.190789
$990$	0	0
$991$	17.0000	0.540023	0.270011	−	0.962857i	$-0.412973\pi$
$991$	17.0000	0.540023	0.270011	+	0.962857i	$0.412973\pi$
$992$	−7.00000	−0.222250
$993$	−7.00000	−0.222138
$994$	−24.0000	−0.761234
$995$	0	0
$996$	−1.00000	−0.0316862
$997$	17.0000	0.538395	0.269198	−	0.963085i	$-0.413241\pi$
$997$	17.0000	0.538395	0.269198	+	0.963085i	$0.413241\pi$
$998$	−30.0000	−0.949633
$999$	−2.00000	−0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2850.2.a.d.1.1	✓	1
3.2	odd	2		8550.2.a.bi.1.1		1
5.2	odd	4		2850.2.d.m.799.1		2
5.3	odd	4		2850.2.d.m.799.2		2
5.4	even	2		2850.2.a.z.1.1	yes	1
15.14	odd	2		8550.2.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2850.2.a.d.1.1	✓	1	1.1	even	1	trivial
2850.2.a.z.1.1	yes	1	5.4	even	2
2850.2.d.m.799.1		2	5.2	odd	4
2850.2.d.m.799.2		2	5.3	odd	4
8550.2.a.f.1.1		1	15.14	odd	2
8550.2.a.bi.1.1		1	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2850.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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