LMFDB - Embedded newform 14.6.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,6,Mod(1,14)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("14.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	14.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:	$2.24537347738$
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	$\chi$	$=$	14.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+4.00000 q^{2} +8.00000 q^{3} +16.0000 q^{4} +10.0000 q^{5} +32.0000 q^{6} -49.0000 q^{7} +64.0000 q^{8} -179.000 q^{9} +O(q^{10})$

\(q+4.00000 q^{2} +8.00000 q^{3} +16.0000 q^{4} +10.0000 q^{5} +32.0000 q^{6} -49.0000 q^{7} +64.0000 q^{8} -179.000 q^{9} +40.0000 q^{10} -340.000 q^{11} +128.000 q^{12} -294.000 q^{13} -196.000 q^{14} +80.0000 q^{15} +256.000 q^{16} +1226.00 q^{17} -716.000 q^{18} +2432.00 q^{19} +160.000 q^{20} -392.000 q^{21} -1360.00 q^{22} +2000.00 q^{23} +512.000 q^{24} -3025.00 q^{25} -1176.00 q^{26} -3376.00 q^{27} -784.000 q^{28} -6746.00 q^{29} +320.000 q^{30} +8856.00 q^{31} +1024.00 q^{32} -2720.00 q^{33} +4904.00 q^{34} -490.000 q^{35} -2864.00 q^{36} +9182.00 q^{37} +9728.00 q^{38} -2352.00 q^{39} +640.000 q^{40} -14574.0 q^{41} -1568.00 q^{42} +8108.00 q^{43} -5440.00 q^{44} -1790.00 q^{45} +8000.00 q^{46} -312.000 q^{47} +2048.00 q^{48} +2401.00 q^{49} -12100.0 q^{50} +9808.00 q^{51} -4704.00 q^{52} -14634.0 q^{53} -13504.0 q^{54} -3400.00 q^{55} -3136.00 q^{56} +19456.0 q^{57} -26984.0 q^{58} -27656.0 q^{59} +1280.00 q^{60} +34338.0 q^{61} +35424.0 q^{62} +8771.00 q^{63} +4096.00 q^{64} -2940.00 q^{65} -10880.0 q^{66} +12316.0 q^{67} +19616.0 q^{68} +16000.0 q^{69} -1960.00 q^{70} +36920.0 q^{71} -11456.0 q^{72} -61718.0 q^{73} +36728.0 q^{74} -24200.0 q^{75} +38912.0 q^{76} +16660.0 q^{77} -9408.00 q^{78} -64752.0 q^{79} +2560.00 q^{80} +16489.0 q^{81} -58296.0 q^{82} -77056.0 q^{83} -6272.00 q^{84} +12260.0 q^{85} +32432.0 q^{86} -53968.0 q^{87} -21760.0 q^{88} -8166.00 q^{89} -7160.00 q^{90} +14406.0 q^{91} +32000.0 q^{92} +70848.0 q^{93} -1248.00 q^{94} +24320.0 q^{95} +8192.00 q^{96} +20650.0 q^{97} +9604.00 q^{98} +60860.0 q^{99} +O(q^{100})\)

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 $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	8.00000	0.513200	0.256600	−	0.966518i	$-0.417398\pi$
$3$	8.00000	0.513200	0.256600	+	0.966518i	$0.417398\pi$
$4$	16.0000	0.500000
$5$	10.0000	0.178885	0.0894427	−	0.995992i	$-0.471491\pi$
$5$	10.0000	0.178885	0.0894427	+	0.995992i	$0.471491\pi$
$6$	32.0000	0.362887
$7$	−49.0000	−0.377964
$7$	−49.0000	−0.377964
$8$	64.0000	0.353553
$9$	−179.000	−0.736626
$10$	40.0000	0.126491
$11$	−340.000	−0.847222	−0.423611	−	0.905844i	$-0.639238\pi$
$11$	−340.000	−0.847222	−0.423611	+	0.905844i	$0.639238\pi$
$12$	128.000	0.256600
$13$	−294.000	−0.482491	−0.241245	−	0.970464i	$-0.577556\pi$
$13$	−294.000	−0.482491	−0.241245	+	0.970464i	$0.577556\pi$
$14$	−196.000	−0.267261
$15$	80.0000	0.0918040
$16$	256.000	0.250000
$17$	1226.00	1.02889	0.514444	−	0.857524i	$-0.327998\pi$
$17$	1226.00	1.02889	0.514444	+	0.857524i	$0.327998\pi$
$18$	−716.000	−0.520873
$19$	2432.00	1.54554	0.772769	−	0.634688i	$-0.218871\pi$
$19$	2432.00	1.54554	0.772769	+	0.634688i	$0.218871\pi$
$20$	160.000	0.0894427
$21$	−392.000	−0.193971
$22$	−1360.00	−0.599076
$23$	2000.00	0.788334	0.394167	−	0.919039i	$-0.371033\pi$
$23$	2000.00	0.788334	0.394167	+	0.919039i	$0.371033\pi$
$24$	512.000	0.181444
$25$	−3025.00	−0.968000
$26$	−1176.00	−0.341172
$27$	−3376.00	−0.891237
$28$	−784.000	−0.188982
$29$	−6746.00	−1.48954	−0.744769	−	0.667323i	$-0.767440\pi$
$29$	−6746.00	−1.48954	−0.744769	+	0.667323i	$0.767440\pi$
$30$	320.000	0.0649153
$31$	8856.00	1.65513	0.827567	−	0.561366i	$-0.189724\pi$
$31$	8856.00	1.65513	0.827567	+	0.561366i	$0.189724\pi$
$32$	1024.00	0.176777
$33$	−2720.00	−0.434795
$34$	4904.00	0.727534
$35$	−490.000	−0.0676123
$36$	−2864.00	−0.368313
$37$	9182.00	1.10264	0.551319	−	0.834295i	$-0.314125\pi$
$37$	9182.00	1.10264	0.551319	+	0.834295i	$0.314125\pi$
$38$	9728.00	1.09286
$39$	−2352.00	−0.247614
$40$	640.000	0.0632456
$41$	−14574.0	−1.35400	−0.677001	−	0.735982i	$-0.736721\pi$
$41$	−14574.0	−1.35400	−0.677001	+	0.735982i	$0.736721\pi$
$42$	−1568.00	−0.137159
$43$	8108.00	0.668717	0.334359	−	0.942446i	$-0.391480\pi$
$43$	8108.00	0.668717	0.334359	+	0.942446i	$0.391480\pi$
$44$	−5440.00	−0.423611
$45$	−1790.00	−0.131772
$46$	8000.00	0.557437
$47$	−312.000	−0.0206020	−0.0103010	−	0.999947i	$-0.503279\pi$
$47$	−312.000	−0.0206020	−0.0103010	+	0.999947i	$0.503279\pi$
$48$	2048.00	0.128300
$49$	2401.00	0.142857
$50$	−12100.0	−0.684479
$51$	9808.00	0.528026
$52$	−4704.00	−0.241245
$53$	−14634.0	−0.715605	−0.357803	−	0.933797i	$-0.616474\pi$
$53$	−14634.0	−0.715605	−0.357803	+	0.933797i	$0.616474\pi$
$54$	−13504.0	−0.630199
$55$	−3400.00	−0.151556
$56$	−3136.00	−0.133631
$57$	19456.0	0.793170
$58$	−26984.0	−1.05326
$59$	−27656.0	−1.03433	−0.517165	−	0.855886i	$-0.673013\pi$
$59$	−27656.0	−1.03433	−0.517165	+	0.855886i	$0.673013\pi$
$60$	1280.00	0.0459020
$61$	34338.0	1.18155	0.590773	−	0.806838i	$-0.298823\pi$
$61$	34338.0	1.18155	0.590773	+	0.806838i	$0.298823\pi$
$62$	35424.0	1.17036
$63$	8771.00	0.278418
$64$	4096.00	0.125000
$65$	−2940.00	−0.0863106
$66$	−10880.0	−0.307446
$67$	12316.0	0.335184	0.167592	−	0.985856i	$-0.446401\pi$
$67$	12316.0	0.335184	0.167592	+	0.985856i	$0.446401\pi$
$68$	19616.0	0.514444
$69$	16000.0	0.404573
$70$	−1960.00	−0.0478091
$71$	36920.0	0.869192	0.434596	−	0.900625i	$-0.356891\pi$
$71$	36920.0	0.869192	0.434596	+	0.900625i	$0.356891\pi$
$72$	−11456.0	−0.260436
$73$	−61718.0	−1.35552	−0.677758	−	0.735285i	$-0.737048\pi$
$73$	−61718.0	−1.35552	−0.677758	+	0.735285i	$0.737048\pi$
$74$	36728.0	0.779683
$75$	−24200.0	−0.496778
$76$	38912.0	0.772769
$77$	16660.0	0.320220
$78$	−9408.00	−0.175090
$79$	−64752.0	−1.16731	−0.583654	−	0.812002i	$-0.698378\pi$
$79$	−64752.0	−1.16731	−0.583654	+	0.812002i	$0.698378\pi$
$80$	2560.00	0.0447214
$81$	16489.0	0.279243
$82$	−58296.0	−0.957424
$83$	−77056.0	−1.22775	−0.613877	−	0.789402i	$-0.710391\pi$
$83$	−77056.0	−1.22775	−0.613877	+	0.789402i	$0.710391\pi$
$84$	−6272.00	−0.0969857
$85$	12260.0	0.184053
$86$	32432.0	0.472855
$87$	−53968.0	−0.764431
$88$	−21760.0	−0.299538
$89$	−8166.00	−0.109278	−0.0546392	−	0.998506i	$-0.517401\pi$
$89$	−8166.00	−0.109278	−0.0546392	+	0.998506i	$0.517401\pi$
$90$	−7160.00	−0.0931766
$91$	14406.0	0.182364
$92$	32000.0	0.394167
$93$	70848.0	0.849416
$94$	−1248.00	−0.0145678
$95$	24320.0	0.276474
$96$	8192.00	0.0907218
$97$	20650.0	0.222839	0.111419	−	0.993773i	$-0.464460\pi$
$97$	20650.0	0.222839	0.111419	+	0.993773i	$0.464460\pi$
$98$	9604.00	0.101015
$99$	60860.0	0.624085
$100$	−48400.0	−0.484000
$101$	186250.	1.81674	0.908370	−	0.418167i	$-0.137327\pi$
$101$	186250.	1.81674	0.908370	+	0.418167i	$0.137327\pi$
$102$	39232.0	0.373371
$103$	−60064.0	−0.557855	−0.278927	−	0.960312i	$-0.589979\pi$
$103$	−60064.0	−0.557855	−0.278927	+	0.960312i	$0.589979\pi$
$104$	−18816.0	−0.170586
$105$	−3920.00	−0.0346987
$106$	−58536.0	−0.506009
$107$	47892.0	0.404393	0.202196	−	0.979345i	$-0.435192\pi$
$107$	47892.0	0.404393	0.202196	+	0.979345i	$0.435192\pi$
$108$	−54016.0	−0.445618
$109$	22102.0	0.178183	0.0890913	−	0.996023i	$-0.471604\pi$
$109$	22102.0	0.178183	0.0890913	+	0.996023i	$0.471604\pi$
$110$	−13600.0	−0.107166
$111$	73456.0	0.565874
$112$	−12544.0	−0.0944911
$113$	−245054.	−1.80537	−0.902684	−	0.430304i	$-0.858406\pi$
$113$	−245054.	−1.80537	−0.902684	+	0.430304i	$0.858406\pi$
$114$	77824.0	0.560856
$115$	20000.0	0.141022
$116$	−107936.	−0.744769
$117$	52626.0	0.355415
$118$	−110624.	−0.731382
$119$	−60074.0	−0.388883
$120$	5120.00	0.0324576
$121$	−45451.0	−0.282215
$122$	137352.	0.835479
$123$	−116592.	−0.694874
$124$	141696.	0.827567
$125$	−61500.0	−0.352047
$126$	35084.0	0.196871
$127$	−96696.0	−0.531985	−0.265992	−	0.963975i	$-0.585700\pi$
$127$	−96696.0	−0.531985	−0.265992	+	0.963975i	$0.585700\pi$
$128$	16384.0	0.0883883
$129$	64864.0	0.343186
$130$	−11760.0	−0.0610308
$131$	134368.	0.684097	0.342048	−	0.939682i	$-0.388879\pi$
$131$	134368.	0.684097	0.342048	+	0.939682i	$0.388879\pi$
$132$	−43520.0	−0.217397
$133$	−119168.	−0.584158
$134$	49264.0	0.237011
$135$	−33760.0	−0.159429
$136$	78464.0	0.363767
$137$	−294662.	−1.34129	−0.670645	−	0.741778i	$-0.733983\pi$
$137$	−294662.	−1.34129	−0.670645	+	0.741778i	$0.733983\pi$
$138$	64000.0	0.286077
$139$	314944.	1.38260	0.691300	−	0.722568i	$-0.257038\pi$
$139$	314944.	1.38260	0.691300	+	0.722568i	$0.257038\pi$
$140$	−7840.00	−0.0338062
$141$	−2496.00	−0.0105730
$142$	147680.	0.614612
$143$	99960.0	0.408777
$144$	−45824.0	−0.184156
$145$	−67460.0	−0.266457
$146$	−246872.	−0.958495
$147$	19208.0	0.0733143
$148$	146912.	0.551319
$149$	113622.	0.419273	0.209636	−	0.977779i	$-0.432772\pi$
$149$	113622.	0.419273	0.209636	+	0.977779i	$0.432772\pi$
$150$	−96800.0	−0.351275
$151$	408208.	1.45693	0.728466	−	0.685082i	$-0.240234\pi$
$151$	408208.	1.45693	0.728466	+	0.685082i	$0.240234\pi$
$152$	155648.	0.546430
$153$	−219454.	−0.757905
$154$	66640.0	0.226430
$155$	88560.0	0.296080
$156$	−37632.0	−0.123807
$157$	293546.	0.950445	0.475223	−	0.879866i	$-0.342368\pi$
$157$	293546.	0.950445	0.475223	+	0.879866i	$0.342368\pi$
$158$	−259008.	−0.825411
$159$	−117072.	−0.367249
$160$	10240.0	0.0316228
$161$	−98000.0	−0.297962
$162$	65956.0	0.197454
$163$	−317116.	−0.934866	−0.467433	−	0.884029i	$-0.654821\pi$
$163$	−317116.	−0.934866	−0.467433	+	0.884029i	$0.654821\pi$
$164$	−233184.	−0.677001
$165$	−27200.0	−0.0777784
$166$	−308224.	−0.868153
$167$	141568.	0.392802	0.196401	−	0.980524i	$-0.437075\pi$
$167$	141568.	0.392802	0.196401	+	0.980524i	$0.437075\pi$
$168$	−25088.0	−0.0685793
$169$	−284857.	−0.767203
$170$	49040.0	0.130145
$171$	−435328.	−1.13848
$172$	129728.	0.334359
$173$	−71222.0	−0.180925	−0.0904626	−	0.995900i	$-0.528835\pi$
$173$	−71222.0	−0.180925	−0.0904626	+	0.995900i	$0.528835\pi$
$174$	−215872.	−0.540534
$175$	148225.	0.365870
$176$	−87040.0	−0.211805
$177$	−221248.	−0.530819
$178$	−32664.0	−0.0772715
$179$	485628.	1.13285	0.566423	−	0.824114i	$-0.308327\pi$
$179$	485628.	1.13285	0.566423	+	0.824114i	$0.308327\pi$
$180$	−28640.0	−0.0658858
$181$	657090.	1.49083	0.745416	−	0.666600i	$-0.232251\pi$
$181$	657090.	1.49083	0.745416	+	0.666600i	$0.232251\pi$
$182$	57624.0	0.128951
$183$	274704.	0.606369
$184$	128000.	0.278718
$185$	91820.0	0.197246
$186$	283392.	0.600628
$187$	−416840.	−0.871697
$188$	−4992.00	−0.0103010
$189$	165424.	0.336856
$190$	97280.0	0.195497
$191$	68304.0	0.135476	0.0677381	−	0.997703i	$-0.478422\pi$
$191$	68304.0	0.135476	0.0677381	+	0.997703i	$0.478422\pi$
$192$	32768.0	0.0641500
$193$	352754.	0.681677	0.340839	−	0.940122i	$-0.389289\pi$
$193$	352754.	0.681677	0.340839	+	0.940122i	$0.389289\pi$
$194$	82600.0	0.157571
$195$	−23520.0	−0.0442946
$196$	38416.0	0.0714286
$197$	196982.	0.361627	0.180814	−	0.983517i	$-0.442127\pi$
$197$	196982.	0.361627	0.180814	+	0.983517i	$0.442127\pi$
$198$	243440.	0.441295
$199$	−1.10392e6	−1.97608	−0.988041	−	0.154192i	$-0.950723\pi$
$199$	−1.10392e6	−1.97608	−0.988041	+	0.154192i	$0.950723\pi$
$200$	−193600.	−0.342240
$201$	98528.0	0.172016
$202$	745000.	1.28463
$203$	330554.	0.562992
$204$	156928.	0.264013
$205$	−145740.	−0.242211
$206$	−240256.	−0.394463
$207$	−358000.	−0.580707
$208$	−75264.0	−0.120623
$209$	−826880.	−1.30941
$210$	−15680.0	−0.0245357
$211$	−103444.	−0.159955	−0.0799777	−	0.996797i	$-0.525485\pi$
$211$	−103444.	−0.159955	−0.0799777	+	0.996797i	$0.525485\pi$
$212$	−234144.	−0.357803
$213$	295360.	0.446070
$214$	191568.	0.285949
$215$	81080.0	0.119624
$216$	−216064.	−0.315100
$217$	−433944.	−0.625582
$218$	88408.0	0.125994
$219$	−493744.	−0.695651
$220$	−54400.0	−0.0757778
$221$	−360444.	−0.496429
$222$	293824.	0.400133
$223$	307328.	0.413847	0.206924	−	0.978357i	$-0.433655\pi$
$223$	307328.	0.413847	0.206924	+	0.978357i	$0.433655\pi$
$224$	−50176.0	−0.0668153
$225$	541475.	0.713053
$226$	−980216.	−1.27659
$227$	−891792.	−1.14868	−0.574340	−	0.818617i	$-0.694741\pi$
$227$	−891792.	−1.14868	−0.574340	+	0.818617i	$0.694741\pi$
$228$	311296.	0.396585
$229$	276706.	0.348682	0.174341	−	0.984685i	$-0.444220\pi$
$229$	276706.	0.348682	0.174341	+	0.984685i	$0.444220\pi$
$230$	80000.0	0.0997173
$231$	133280.	0.164337
$232$	−431744.	−0.526631
$233$	1.47943e6	1.78528	0.892639	−	0.450772i	$-0.148851\pi$
$233$	1.47943e6	1.78528	0.892639	+	0.450772i	$0.148851\pi$
$234$	210504.	0.251316
$235$	−3120.00	−0.00368540
$236$	−442496.	−0.517165
$237$	−518016.	−0.599063
$238$	−240296.	−0.274982
$239$	1.00034e6	1.13280	0.566402	−	0.824129i	$-0.308335\pi$
$239$	1.00034e6	1.13280	0.566402	+	0.824129i	$0.308335\pi$
$240$	20480.0	0.0229510
$241$	1.35833e6	1.50648	0.753239	−	0.657747i	$-0.228490\pi$
$241$	1.35833e6	1.50648	0.753239	+	0.657747i	$0.228490\pi$
$242$	−181804.	−0.199556
$243$	952280.	1.03454
$244$	549408.	0.590773
$245$	24010.0	0.0255551
$246$	−466368.	−0.491350
$247$	−715008.	−0.745708
$248$	566784.	0.585179
$249$	−616448.	−0.630083
$250$	−246000.	−0.248934
$251$	−177408.	−0.177742	−0.0888708	−	0.996043i	$-0.528326\pi$
$251$	−177408.	−0.177742	−0.0888708	+	0.996043i	$0.528326\pi$
$252$	140336.	0.139209
$253$	−680000.	−0.667894
$254$	−386784.	−0.376170
$255$	98080.0	0.0944561
$256$	65536.0	0.0625000
$257$	326658.	0.308504	0.154252	−	0.988032i	$-0.450703\pi$
$257$	326658.	0.308504	0.154252	+	0.988032i	$0.450703\pi$
$258$	259456.	0.242669
$259$	−449918.	−0.416758
$260$	−47040.0	−0.0431553
$261$	1.20753e6	1.09723
$262$	537472.	0.483730
$263$	−34920.0	−0.0311304	−0.0155652	−	0.999879i	$-0.504955\pi$
$263$	−34920.0	−0.0311304	−0.0155652	+	0.999879i	$0.504955\pi$
$264$	−174080.	−0.153723
$265$	−146340.	−0.128011
$266$	−476672.	−0.413062
$267$	−65328.0	−0.0560817
$268$	197056.	0.167592
$269$	716458.	0.603685	0.301842	−	0.953358i	$-0.402398\pi$
$269$	716458.	0.603685	0.301842	+	0.953358i	$0.402398\pi$
$270$	−135040.	−0.112734
$271$	−953376.	−0.788571	−0.394286	−	0.918988i	$-0.629008\pi$
$271$	−953376.	−0.788571	−0.394286	+	0.918988i	$0.629008\pi$
$272$	313856.	0.257222
$273$	115248.	0.0935894
$274$	−1.17865e6	−0.948435
$275$	1.02850e6	0.820111
$276$	256000.	0.202287
$277$	−1.84729e6	−1.44656	−0.723279	−	0.690556i	$-0.757366\pi$
$277$	−1.84729e6	−1.44656	−0.723279	+	0.690556i	$0.757366\pi$
$278$	1.25978e6	0.977645
$279$	−1.58522e6	−1.21921
$280$	−31360.0	−0.0239046
$281$	−1.99601e6	−1.50798	−0.753991	−	0.656885i	$-0.771874\pi$
$281$	−1.99601e6	−1.50798	−0.753991	+	0.656885i	$0.771874\pi$
$282$	−9984.00	−0.00747622
$283$	234088.	0.173745	0.0868726	−	0.996219i	$-0.472313\pi$
$283$	234088.	0.173745	0.0868726	+	0.996219i	$0.472313\pi$
$284$	590720.	0.434596
$285$	194560.	0.141887
$286$	399840.	0.289049
$287$	714126.	0.511764
$288$	−183296.	−0.130218
$289$	83219.0	0.0586108
$290$	−269840.	−0.188413
$291$	165200.	0.114361
$292$	−987488.	−0.677758
$293$	−2.50081e6	−1.70181	−0.850905	−	0.525320i	$-0.823946\pi$
$293$	−2.50081e6	−1.70181	−0.850905	+	0.525320i	$0.823946\pi$
$294$	76832.0	0.0518411
$295$	−276560.	−0.185027
$296$	587648.	0.389841
$297$	1.14784e6	0.755075
$298$	454488.	0.296471
$299$	−588000.	−0.380364
$300$	−387200.	−0.248389
$301$	−397292.	−0.252751
$302$	1.63283e6	1.03021
$303$	1.49000e6	0.932352
$304$	622592.	0.386384
$305$	343380.	0.211361
$306$	−877816.	−0.535920
$307$	2.34203e6	1.41823	0.709115	−	0.705092i	$-0.249095\pi$
$307$	2.34203e6	1.41823	0.709115	+	0.705092i	$0.249095\pi$
$308$	266560.	0.160110
$309$	−480512.	−0.286291
$310$	354240.	0.209360
$311$	−163064.	−0.0955998	−0.0477999	−	0.998857i	$-0.515221\pi$
$311$	−163064.	−0.0955998	−0.0477999	+	0.998857i	$0.515221\pi$
$312$	−150528.	−0.0875449
$313$	1.73965e6	1.00369	0.501847	−	0.864957i	$-0.332654\pi$
$313$	1.73965e6	1.00369	0.501847	+	0.864957i	$0.332654\pi$
$314$	1.17418e6	0.672066
$315$	87710.0	0.0498050
$316$	−1.03603e6	−0.583654
$317$	−1.79771e6	−1.00478	−0.502392	−	0.864640i	$-0.667546\pi$
$317$	−1.79771e6	−1.00478	−0.502392	+	0.864640i	$0.667546\pi$
$318$	−468288.	−0.259684
$319$	2.29364e6	1.26197
$320$	40960.0	0.0223607
$321$	383136.	0.207535
$322$	−392000.	−0.210691
$323$	2.98163e6	1.59019
$324$	263824.	0.139621
$325$	889350.	0.467051
$326$	−1.26846e6	−0.661050
$327$	176816.	0.0914434
$328$	−932736.	−0.478712
$329$	15288.0	0.00778683
$330$	−108800.	−0.0549976
$331$	−2.47541e6	−1.24187	−0.620937	−	0.783861i	$-0.713248\pi$
$331$	−2.47541e6	−1.24187	−0.620937	+	0.783861i	$0.713248\pi$
$332$	−1.23290e6	−0.613877
$333$	−1.64358e6	−0.812231
$334$	566272.	0.277753
$335$	123160.	0.0599595
$336$	−100352.	−0.0484929
$337$	89154.0	0.0427628	0.0213814	−	0.999771i	$-0.493194\pi$
$337$	89154.0	0.0427628	0.0213814	+	0.999771i	$0.493194\pi$
$338$	−1.13943e6	−0.542494
$339$	−1.96043e6	−0.926515
$340$	196160.	0.0920266
$341$	−3.01104e6	−1.40227
$342$	−1.74131e6	−0.805029
$343$	−117649.	−0.0539949
$344$	518912.	0.236427
$345$	160000.	0.0723723
$346$	−284888.	−0.127933
$347$	938556.	0.418443	0.209222	−	0.977868i	$-0.432907\pi$
$347$	938556.	0.418443	0.209222	+	0.977868i	$0.432907\pi$
$348$	−863488.	−0.382215
$349$	3.34268e6	1.46903	0.734516	−	0.678591i	$-0.237409\pi$
$349$	3.34268e6	1.46903	0.734516	+	0.678591i	$0.237409\pi$
$350$	592900.	0.258709
$351$	992544.	0.430013
$352$	−348160.	−0.149769
$353$	−3.76606e6	−1.60861	−0.804305	−	0.594217i	$-0.797462\pi$
$353$	−3.76606e6	−1.60861	−0.804305	+	0.594217i	$0.797462\pi$
$354$	−884992.	−0.375345
$355$	369200.	0.155486
$356$	−130656.	−0.0546392
$357$	−480592.	−0.199575
$358$	1.94251e6	0.801044
$359$	−1.53934e6	−0.630376	−0.315188	−	0.949029i	$-0.602068\pi$
$359$	−1.53934e6	−0.630376	−0.315188	+	0.949029i	$0.602068\pi$
$360$	−114560.	−0.0465883
$361$	3.43852e6	1.38869
$362$	2.62836e6	1.05418
$363$	−363608.	−0.144833
$364$	230496.	0.0911822
$365$	−617180.	−0.242482
$366$	1.09882e6	0.428768
$367$	−859312.	−0.333032	−0.166516	−	0.986039i	$-0.553252\pi$
$367$	−859312.	−0.333032	−0.166516	+	0.986039i	$0.553252\pi$
$368$	512000.	0.197084
$369$	2.60875e6	0.997392
$370$	367280.	0.139474
$371$	717066.	0.270473
$372$	1.13357e6	0.424708
$373$	−976586.	−0.363445	−0.181722	−	0.983350i	$-0.558167\pi$
$373$	−976586.	−0.363445	−0.181722	+	0.983350i	$0.558167\pi$
$374$	−1.66736e6	−0.616383
$375$	−492000.	−0.180670
$376$	−19968.0	−0.00728392
$377$	1.98332e6	0.718688
$378$	661696.	0.238193
$379$	106444.	0.0380648	0.0190324	−	0.999819i	$-0.493941\pi$
$379$	106444.	0.0380648	0.0190324	+	0.999819i	$0.493941\pi$
$380$	389120.	0.138237
$381$	−773568.	−0.273015
$382$	273216.	0.0957961
$383$	−2.00634e6	−0.698889	−0.349445	−	0.936957i	$-0.613630\pi$
$383$	−2.00634e6	−0.698889	−0.349445	+	0.936957i	$0.613630\pi$
$384$	131072.	0.0453609
$385$	166600.	0.0572827
$386$	1.41102e6	0.482018
$387$	−1.45133e6	−0.492594
$388$	330400.	0.111419
$389$	−684002.	−0.229184	−0.114592	−	0.993413i	$-0.536556\pi$
$389$	−684002.	−0.229184	−0.114592	+	0.993413i	$0.536556\pi$
$390$	−94080.0	−0.0313210
$391$	2.45200e6	0.811108
$392$	153664.	0.0505076
$393$	1.07494e6	0.351079
$394$	787928.	0.255709
$395$	−647520.	−0.208814
$396$	973760.	0.312043
$397$	−222870.	−0.0709701	−0.0354850	−	0.999370i	$-0.511298\pi$
$397$	−222870.	−0.0709701	−0.0354850	+	0.999370i	$0.511298\pi$
$398$	−4.41568e6	−1.39730
$399$	−953344.	−0.299790
$400$	−774400.	−0.242000
$401$	1.90072e6	0.590279	0.295140	−	0.955454i	$-0.404634\pi$
$401$	1.90072e6	0.590279	0.295140	+	0.955454i	$0.404634\pi$
$402$	394112.	0.121634
$403$	−2.60366e6	−0.798587
$404$	2.98000e6	0.908370
$405$	164890.	0.0499524
$406$	1.32222e6	0.398096
$407$	−3.12188e6	−0.934179
$408$	627712.	0.186685
$409$	1.77715e6	0.525311	0.262656	−	0.964890i	$-0.415402\pi$
$409$	1.77715e6	0.525311	0.262656	+	0.964890i	$0.415402\pi$
$410$	−582960.	−0.171269
$411$	−2.35730e6	−0.688350
$412$	−961024.	−0.278927
$413$	1.35514e6	0.390940
$414$	−1.43200e6	−0.410622
$415$	−770560.	−0.219627
$416$	−301056.	−0.0852931
$417$	2.51955e6	0.709550
$418$	−3.30752e6	−0.925895
$419$	28056.0	0.00780712	0.00390356	−	0.999992i	$-0.498757\pi$
$419$	28056.0	0.00780712	0.00390356	+	0.999992i	$0.498757\pi$
$420$	−62720.0	−0.0173493
$421$	−2.70897e6	−0.744902	−0.372451	−	0.928052i	$-0.621482\pi$
$421$	−2.70897e6	−0.744902	−0.372451	+	0.928052i	$0.621482\pi$
$422$	−413776.	−0.113106
$423$	55848.0	0.0151760
$424$	−936576.	−0.253005
$425$	−3.70865e6	−0.995964
$426$	1.18144e6	0.315419
$427$	−1.68256e6	−0.446582
$428$	766272.	0.202196
$429$	799680.	0.209784
$430$	324320.	0.0845868
$431$	5.53898e6	1.43627	0.718136	−	0.695902i	$-0.244995\pi$
$431$	5.53898e6	1.43627	0.718136	+	0.695902i	$0.244995\pi$
$432$	−864256.	−0.222809
$433$	−868294.	−0.222560	−0.111280	−	0.993789i	$-0.535495\pi$
$433$	−868294.	−0.222560	−0.111280	+	0.993789i	$0.535495\pi$
$434$	−1.73578e6	−0.442353
$435$	−539680.	−0.136746
$436$	353632.	0.0890913
$437$	4.86400e6	1.21840
$438$	−1.97498e6	−0.491900
$439$	−1.13767e6	−0.281745	−0.140872	−	0.990028i	$-0.544991\pi$
$439$	−1.13767e6	−0.281745	−0.140872	+	0.990028i	$0.544991\pi$
$440$	−217600.	−0.0535830
$441$	−429779.	−0.105232
$442$	−1.44178e6	−0.351028
$443$	1.75399e6	0.424636	0.212318	−	0.977201i	$-0.431899\pi$
$443$	1.75399e6	0.424636	0.212318	+	0.977201i	$0.431899\pi$
$444$	1.17530e6	0.282937
$445$	−81660.0	−0.0195483
$446$	1.22931e6	0.292634
$447$	908976.	0.215171
$448$	−200704.	−0.0472456
$449$	2.41674e6	0.565736	0.282868	−	0.959159i	$-0.408714\pi$
$449$	2.41674e6	0.565736	0.282868	+	0.959159i	$0.408714\pi$
$450$	2.16590e6	0.504205
$451$	4.95516e6	1.14714
$452$	−3.92086e6	−0.902684
$453$	3.26566e6	0.747698
$454$	−3.56717e6	−0.812239
$455$	144060.	0.0326223
$456$	1.24518e6	0.280428
$457$	−127430.	−0.0285418	−0.0142709	−	0.999898i	$-0.504543\pi$
$457$	−127430.	−0.0285418	−0.0142709	+	0.999898i	$0.504543\pi$
$458$	1.10682e6	0.246556
$459$	−4.13898e6	−0.916983
$460$	320000.	0.0705108
$461$	−128198.	−0.0280950	−0.0140475	−	0.999901i	$-0.504472\pi$
$461$	−128198.	−0.0280950	−0.0140475	+	0.999901i	$0.504472\pi$
$462$	533120.	0.116204
$463$	−4.01653e6	−0.870760	−0.435380	−	0.900247i	$-0.643386\pi$
$463$	−4.01653e6	−0.870760	−0.435380	+	0.900247i	$0.643386\pi$
$464$	−1.72698e6	−0.372384
$465$	708480.	0.151948
$466$	5.91774e6	1.26238
$467$	8.67246e6	1.84014	0.920069	−	0.391757i	$-0.128133\pi$
$467$	8.67246e6	1.84014	0.920069	+	0.391757i	$0.128133\pi$
$468$	842016.	0.177707
$469$	−603484.	−0.126687
$470$	−12480.0	−0.00260597
$471$	2.34837e6	0.487769
$472$	−1.76998e6	−0.365691
$473$	−2.75672e6	−0.566552
$474$	−2.07206e6	−0.423601
$475$	−7.35680e6	−1.49608
$476$	−961184.	−0.194442
$477$	2.61949e6	0.527133
$478$	4.00138e6	0.801013
$479$	8.28946e6	1.65077	0.825387	−	0.564567i	$-0.190957\pi$
$479$	8.28946e6	1.65077	0.825387	+	0.564567i	$0.190957\pi$
$480$	81920.0	0.0162288
$481$	−2.69951e6	−0.532013
$482$	5.43332e6	1.06524
$483$	−784000.	−0.152914
$484$	−727216.	−0.141107
$485$	206500.	0.0398626
$486$	3.80912e6	0.731533
$487$	−8.91770e6	−1.70385	−0.851923	−	0.523667i	$-0.824563\pi$
$487$	−8.91770e6	−1.70385	−0.851923	+	0.523667i	$0.824563\pi$
$488$	2.19763e6	0.417739
$489$	−2.53693e6	−0.479773
$490$	96040.0	0.0180702
$491$	−5.71537e6	−1.06989	−0.534947	−	0.844886i	$-0.679668\pi$
$491$	−5.71537e6	−1.06989	−0.534947	+	0.844886i	$0.679668\pi$
$492$	−1.86547e6	−0.347437
$493$	−8.27060e6	−1.53257
$494$	−2.86003e6	−0.527295
$495$	608600.	0.111640
$496$	2.26714e6	0.413784
$497$	−1.80908e6	−0.328524
$498$	−2.46579e6	−0.445536
$499$	125116.	0.0224937	0.0112469	−	0.999937i	$-0.496420\pi$
$499$	125116.	0.0224937	0.0112469	+	0.999937i	$0.496420\pi$
$500$	−984000.	−0.176023
$501$	1.13254e6	0.201586
$502$	−709632.	−0.125682
$503$	−2.77116e6	−0.488362	−0.244181	−	0.969730i	$-0.578519\pi$
$503$	−2.77116e6	−0.488362	−0.244181	+	0.969730i	$0.578519\pi$
$504$	561344.	0.0984357
$505$	1.86250e6	0.324988
$506$	−2.72000e6	−0.472272
$507$	−2.27886e6	−0.393729
$508$	−1.54714e6	−0.265992
$509$	−138534.	−0.0237007	−0.0118504	−	0.999930i	$-0.503772\pi$
$509$	−138534.	−0.0237007	−0.0118504	+	0.999930i	$0.503772\pi$
$510$	392320.	0.0667905
$511$	3.02418e6	0.512337
$512$	262144.	0.0441942
$513$	−8.21043e6	−1.37744
$514$	1.30663e6	0.218145
$515$	−600640.	−0.0997921
$516$	1.03782e6	0.171593
$517$	106080.	0.0174545
$518$	−1.79967e6	−0.294692
$519$	−569776.	−0.0928508
$520$	−188160.	−0.0305154
$521$	−1.80281e6	−0.290976	−0.145488	−	0.989360i	$-0.546475\pi$
$521$	−1.80281e6	−0.290976	−0.145488	+	0.989360i	$0.546475\pi$
$522$	4.83014e6	0.775860
$523$	9.77247e6	1.56225	0.781124	−	0.624375i	$-0.214646\pi$
$523$	9.77247e6	1.56225	0.781124	+	0.624375i	$0.214646\pi$
$524$	2.14989e6	0.342048
$525$	1.18580e6	0.187764
$526$	−139680.	−0.0220125
$527$	1.08575e7	1.70295
$528$	−696320.	−0.108699
$529$	−2.43634e6	−0.378529
$530$	−585360.	−0.0905177
$531$	4.95042e6	0.761914
$532$	−1.90669e6	−0.292079
$533$	4.28476e6	0.653293
$534$	−261312.	−0.0396558
$535$	478920.	0.0723400
$536$	788224.	0.118505
$537$	3.88502e6	0.581377
$538$	2.86583e6	0.426869
$539$	−816340.	−0.121032
$540$	−540160.	−0.0797146
$541$	2.45504e6	0.360633	0.180316	−	0.983609i	$-0.442288\pi$
$541$	2.45504e6	0.360633	0.180316	+	0.983609i	$0.442288\pi$
$542$	−3.81350e6	−0.557604
$543$	5.25672e6	0.765095
$544$	1.25542e6	0.181883
$545$	221020.	0.0318743
$546$	460992.	0.0661777
$547$	1.32081e7	1.88744	0.943721	−	0.330743i	$-0.107299\pi$
$547$	1.32081e7	1.88744	0.943721	+	0.330743i	$0.107299\pi$
$548$	−4.71459e6	−0.670645
$549$	−6.14650e6	−0.870356
$550$	4.11400e6	0.579906
$551$	−1.64063e7	−2.30214
$552$	1.02400e6	0.143038
$553$	3.17285e6	0.441201
$554$	−7.38916e6	−1.02287
$555$	734560.	0.101227
$556$	5.03910e6	0.691300
$557$	7.83293e6	1.06976	0.534880	−	0.844928i	$-0.320357\pi$
$557$	7.83293e6	1.06976	0.534880	+	0.844928i	$0.320357\pi$
$558$	−6.34090e6	−0.862115
$559$	−2.38375e6	−0.322650
$560$	−125440.	−0.0169031
$561$	−3.33472e6	−0.447355
$562$	−7.98402e6	−1.06630
$563$	3.57908e6	0.475883	0.237942	−	0.971279i	$-0.423527\pi$
$563$	3.57908e6	0.475883	0.237942	+	0.971279i	$0.423527\pi$
$564$	−39936.0	−0.00528648
$565$	−2.45054e6	−0.322954
$566$	936352.	0.122856
$567$	−807961.	−0.105544
$568$	2.36288e6	0.307306
$569$	−3.39581e6	−0.439707	−0.219853	−	0.975533i	$-0.570558\pi$
$569$	−3.39581e6	−0.439707	−0.219853	+	0.975533i	$0.570558\pi$
$570$	778240.	0.100329
$571$	−1.47695e6	−0.189572	−0.0947862	−	0.995498i	$-0.530217\pi$
$571$	−1.47695e6	−0.189572	−0.0947862	+	0.995498i	$0.530217\pi$
$572$	1.59936e6	0.204388
$573$	546432.	0.0695264
$574$	2.85650e6	0.361872
$575$	−6.05000e6	−0.763108
$576$	−733184.	−0.0920782
$577$	−1.49961e7	−1.87516	−0.937580	−	0.347771i	$-0.886939\pi$
$577$	−1.49961e7	−1.87516	−0.937580	+	0.347771i	$0.886939\pi$
$578$	332876.	0.0414441
$579$	2.82203e6	0.349837
$580$	−1.07936e6	−0.133228
$581$	3.77574e6	0.464047
$582$	660800.	0.0808654
$583$	4.97556e6	0.606276
$584$	−3.94995e6	−0.479247
$585$	526260.	0.0635786
$586$	−1.00032e7	−1.20336
$587$	−3.29291e6	−0.394444	−0.197222	−	0.980359i	$-0.563192\pi$
$587$	−3.29291e6	−0.394444	−0.197222	+	0.980359i	$0.563192\pi$
$588$	307328.	0.0366572
$589$	2.15378e7	2.55807
$590$	−1.10624e6	−0.130834
$591$	1.57586e6	0.185587
$592$	2.35059e6	0.275660
$593$	−1.17908e7	−1.37692	−0.688459	−	0.725275i	$-0.741713\pi$
$593$	−1.17908e7	−1.37692	−0.688459	+	0.725275i	$0.741713\pi$
$594$	4.59136e6	0.533919
$595$	−600740.	−0.0695655
$596$	1.81795e6	0.209636
$597$	−8.83136e6	−1.01413
$598$	−2.35200e6	−0.268958
$599$	−1.52642e6	−0.173823	−0.0869117	−	0.996216i	$-0.527700\pi$
$599$	−1.52642e6	−0.173823	−0.0869117	+	0.996216i	$0.527700\pi$
$600$	−1.54880e6	−0.175637
$601$	−1.00142e7	−1.13092	−0.565458	−	0.824777i	$-0.691301\pi$
$601$	−1.00142e7	−1.13092	−0.565458	+	0.824777i	$0.691301\pi$
$602$	−1.58917e6	−0.178722
$603$	−2.20456e6	−0.246905
$604$	6.53133e6	0.728466
$605$	−454510.	−0.0504841
$606$	5.96000e6	0.659272
$607$	1.20660e7	1.32920	0.664599	−	0.747200i	$-0.268602\pi$
$607$	1.20660e7	1.32920	0.664599	+	0.747200i	$0.268602\pi$
$608$	2.49037e6	0.273215
$609$	2.64443e6	0.288928
$610$	1.37352e6	0.149455
$611$	91728.0	0.00994029
$612$	−3.51126e6	−0.378953
$613$	5.81950e6	0.625511	0.312755	−	0.949834i	$-0.398748\pi$
$613$	5.81950e6	0.625511	0.312755	+	0.949834i	$0.398748\pi$
$614$	9.36813e6	1.00284
$615$	−1.16592e6	−0.124303
$616$	1.06624e6	0.113215
$617$	−4.16589e6	−0.440550	−0.220275	−	0.975438i	$-0.570695\pi$
$617$	−4.16589e6	−0.440550	−0.220275	+	0.975438i	$0.570695\pi$
$618$	−1.92205e6	−0.202438
$619$	−8.08090e6	−0.847683	−0.423841	−	0.905736i	$-0.639319\pi$
$619$	−8.08090e6	−0.847683	−0.423841	+	0.905736i	$0.639319\pi$
$620$	1.41696e6	0.148040
$621$	−6.75200e6	−0.702592
$622$	−652256.	−0.0675993
$623$	400134.	0.0413034
$624$	−602112.	−0.0619036
$625$	8.83812e6	0.905024
$626$	6.95860e6	0.709718
$627$	−6.61504e6	−0.671991
$628$	4.69674e6	0.475223
$629$	1.12571e7	1.13449
$630$	350840.	0.0352174
$631$	−8.40878e6	−0.840735	−0.420368	−	0.907354i	$-0.638099\pi$
$631$	−8.40878e6	−0.840735	−0.420368	+	0.907354i	$0.638099\pi$
$632$	−4.14413e6	−0.412706
$633$	−827552.	−0.0820892
$634$	−7.19086e6	−0.710489
$635$	−966960.	−0.0951643
$636$	−1.87315e6	−0.183624
$637$	−705894.	−0.0689272
$638$	9.17456e6	0.892347
$639$	−6.60868e6	−0.640269
$640$	163840.	0.0158114
$641$	6.29760e6	0.605383	0.302691	−	0.953089i	$-0.402115\pi$
$641$	6.29760e6	0.605383	0.302691	+	0.953089i	$0.402115\pi$
$642$	1.53254e6	0.146749
$643$	4.39762e6	0.419460	0.209730	−	0.977759i	$-0.432741\pi$
$643$	4.39762e6	0.419460	0.209730	+	0.977759i	$0.432741\pi$
$644$	−1.56800e6	−0.148981
$645$	648640.	0.0613910
$646$	1.19265e7	1.12443
$647$	6.55397e6	0.615522	0.307761	−	0.951464i	$-0.400420\pi$
$647$	6.55397e6	0.615522	0.307761	+	0.951464i	$0.400420\pi$
$648$	1.05530e6	0.0987272
$649$	9.40304e6	0.876308
$650$	3.55740e6	0.330255
$651$	−3.47155e6	−0.321049
$652$	−5.07386e6	−0.467433
$653$	3.79652e6	0.348420	0.174210	−	0.984709i	$-0.444263\pi$
$653$	3.79652e6	0.348420	0.174210	+	0.984709i	$0.444263\pi$
$654$	707264.	0.0646602
$655$	1.34368e6	0.122375
$656$	−3.73094e6	−0.338500
$657$	1.10475e7	0.998508
$658$	61152.0	0.00550612
$659$	−8.82684e6	−0.791757	−0.395879	−	0.918303i	$-0.629560\pi$
$659$	−8.82684e6	−0.791757	−0.395879	+	0.918303i	$0.629560\pi$
$660$	−435200.	−0.0388892
$661$	−341270.	−0.0303805	−0.0151902	−	0.999885i	$-0.504835\pi$
$661$	−341270.	−0.0303805	−0.0151902	+	0.999885i	$0.504835\pi$
$662$	−9.90165e6	−0.878137
$663$	−2.88355e6	−0.254767
$664$	−4.93158e6	−0.434076
$665$	−1.19168e6	−0.104497
$666$	−6.57431e6	−0.574334
$667$	−1.34920e7	−1.17425
$668$	2.26509e6	0.196401
$669$	2.45862e6	0.212386
$670$	492640.	0.0423977
$671$	−1.16749e7	−1.00103
$672$	−401408.	−0.0342896
$673$	4.41807e6	0.376006	0.188003	−	0.982168i	$-0.439799\pi$
$673$	4.41807e6	0.376006	0.188003	+	0.982168i	$0.439799\pi$
$674$	356616.	0.0302379
$675$	1.02124e7	0.862717
$676$	−4.55771e6	−0.383601
$677$	1.63858e7	1.37403	0.687014	−	0.726644i	$-0.258921\pi$
$677$	1.63858e7	1.37403	0.687014	+	0.726644i	$0.258921\pi$
$678$	−7.84173e6	−0.655145
$679$	−1.01185e6	−0.0842251
$680$	784640.	0.0650726
$681$	−7.13434e6	−0.589503
$682$	−1.20442e7	−0.991552
$683$	−1.75399e7	−1.43872	−0.719360	−	0.694638i	$-0.755565\pi$
$683$	−1.75399e7	−1.43872	−0.719360	+	0.694638i	$0.755565\pi$
$684$	−6.96525e6	−0.569241
$685$	−2.94662e6	−0.239937
$686$	−470596.	−0.0381802
$687$	2.21365e6	0.178944
$688$	2.07565e6	0.167179
$689$	4.30240e6	0.345273
$690$	640000.	0.0511749
$691$	3.14638e6	0.250678	0.125339	−	0.992114i	$-0.459998\pi$
$691$	3.14638e6	0.250678	0.125339	+	0.992114i	$0.459998\pi$
$692$	−1.13955e6	−0.0904626
$693$	−2.98214e6	−0.235882
$694$	3.75422e6	0.295884
$695$	3.14944e6	0.247327
$696$	−3.45395e6	−0.270267
$697$	−1.78677e7	−1.39312
$698$	1.33707e7	1.03876
$699$	1.18355e7	0.916205
$700$	2.37160e6	0.182935
$701$	−1.90919e7	−1.46742	−0.733709	−	0.679464i	$-0.762212\pi$
$701$	−1.90919e7	−1.46742	−0.733709	+	0.679464i	$0.762212\pi$
$702$	3.97018e6	0.304065
$703$	2.23306e7	1.70417
$704$	−1.39264e6	−0.105903
$705$	−24960.0	−0.00189135
$706$	−1.50642e7	−1.13746
$707$	−9.12625e6	−0.686663
$708$	−3.53997e6	−0.265409
$709$	990974.	0.0740366	0.0370183	−	0.999315i	$-0.488214\pi$
$709$	990974.	0.0740366	0.0370183	+	0.999315i	$0.488214\pi$
$710$	1.47680e6	0.109945
$711$	1.15906e7	0.859869
$712$	−522624.	−0.0386358
$713$	1.77120e7	1.30480
$714$	−1.92237e6	−0.141121
$715$	999600.	0.0731242
$716$	7.77005e6	0.566423
$717$	8.00275e6	0.581355
$718$	−6.15738e6	−0.445743
$719$	−1.69014e7	−1.21928	−0.609638	−	0.792680i	$-0.708685\pi$
$719$	−1.69014e7	−1.21928	−0.609638	+	0.792680i	$0.708685\pi$
$720$	−458240.	−0.0329429
$721$	2.94314e6	0.210849
$722$	1.37541e7	0.981950
$723$	1.08666e7	0.773125
$724$	1.05134e7	0.745416
$725$	2.04066e7	1.44187
$726$	−1.45443e6	−0.102412
$727$	−2.34302e7	−1.64414	−0.822071	−	0.569384i	$-0.807182\pi$
$727$	−2.34302e7	−1.64414	−0.822071	+	0.569384i	$0.807182\pi$
$728$	921984.	0.0644755
$729$	3.61141e6	0.251686
$730$	−2.46872e6	−0.171461
$731$	9.94041e6	0.688035
$732$	4.39526e6	0.303185
$733$	975810.	0.0670819	0.0335409	−	0.999437i	$-0.489322\pi$
$733$	975810.	0.0670819	0.0335409	+	0.999437i	$0.489322\pi$
$734$	−3.43725e6	−0.235489
$735$	192080.	0.0131149
$736$	2.04800e6	0.139359
$737$	−4.18744e6	−0.283975
$738$	1.04350e7	0.705263
$739$	−6.30208e6	−0.424495	−0.212247	−	0.977216i	$-0.568078\pi$
$739$	−6.30208e6	−0.424495	−0.212247	+	0.977216i	$0.568078\pi$
$740$	1.46912e6	0.0986229
$741$	−5.72006e6	−0.382697
$742$	2.86826e6	0.191253
$743$	−6.95698e6	−0.462326	−0.231163	−	0.972915i	$-0.574253\pi$
$743$	−6.95698e6	−0.462326	−0.231163	+	0.972915i	$0.574253\pi$
$744$	4.53427e6	0.300314
$745$	1.13622e6	0.0750018
$746$	−3.90634e6	−0.256994
$747$	1.37930e7	0.904395
$748$	−6.66944e6	−0.435848
$749$	−2.34671e6	−0.152846
$750$	−1.96800e6	−0.127753
$751$	2.74535e7	1.77622	0.888112	−	0.459628i	$-0.152017\pi$
$751$	2.74535e7	1.77622	0.888112	+	0.459628i	$0.152017\pi$
$752$	−79872.0	−0.00515051
$753$	−1.41926e6	−0.0912170
$754$	7.93330e6	0.508189
$755$	4.08208e6	0.260624
$756$	2.64678e6	0.168428
$757$	−1.96889e7	−1.24877	−0.624384	−	0.781118i	$-0.714650\pi$
$757$	−1.96889e7	−1.24877	−0.624384	+	0.781118i	$0.714650\pi$
$758$	425776.	0.0269159
$759$	−5.44000e6	−0.342763
$760$	1.55648e6	0.0977484
$761$	−2.82079e7	−1.76567	−0.882835	−	0.469684i	$-0.844368\pi$
$761$	−2.82079e7	−1.76567	−0.882835	+	0.469684i	$0.844368\pi$
$762$	−3.09427e6	−0.193051
$763$	−1.08300e6	−0.0673467
$764$	1.09286e6	0.0677381
$765$	−2.19454e6	−0.135578
$766$	−8.02538e6	−0.494189
$767$	8.13086e6	0.499055
$768$	524288.	0.0320750
$769$	−1.38081e6	−0.0842009	−0.0421005	−	0.999113i	$-0.513405\pi$
$769$	−1.38081e6	−0.0842009	−0.0421005	+	0.999113i	$0.513405\pi$
$770$	666400.	0.0405050
$771$	2.61326e6	0.158324
$772$	5.64406e6	0.340839
$773$	−1.54347e7	−0.929074	−0.464537	−	0.885554i	$-0.653779\pi$
$773$	−1.54347e7	−0.929074	−0.464537	+	0.885554i	$0.653779\pi$
$774$	−5.80533e6	−0.348317
$775$	−2.67894e7	−1.60217
$776$	1.32160e6	0.0787854
$777$	−3.59934e6	−0.213880
$778$	−2.73601e6	−0.162057
$779$	−3.54440e7	−2.09266
$780$	−376320.	−0.0221473
$781$	−1.25528e7	−0.736399
$782$	9.80800e6	0.573540
$783$	2.27745e7	1.32753
$784$	614656.	0.0357143
$785$	2.93546e6	0.170021
$786$	4.29978e6	0.248250
$787$	−7.10107e6	−0.408683	−0.204342	−	0.978900i	$-0.565505\pi$
$787$	−7.10107e6	−0.408683	−0.204342	+	0.978900i	$0.565505\pi$
$788$	3.15171e6	0.180814
$789$	−279360.	−0.0159761
$790$	−2.59008e6	−0.147654
$791$	1.20076e7	0.682365
$792$	3.89504e6	0.220647
$793$	−1.00954e7	−0.570085
$794$	−891480.	−0.0501834
$795$	−1.17072e6	−0.0656954
$796$	−1.76627e7	−0.988041
$797$	6.48182e6	0.361452	0.180726	−	0.983533i	$-0.442155\pi$
$797$	6.48182e6	0.361452	0.180726	+	0.983533i	$0.442155\pi$
$798$	−3.81338e6	−0.211984
$799$	−382512.	−0.0211972
$800$	−3.09760e6	−0.171120
$801$	1.46171e6	0.0804973
$802$	7.60289e6	0.417391
$803$	2.09841e7	1.14842
$804$	1.57645e6	0.0860081
$805$	−980000.	−0.0533011
$806$	−1.04147e7	−0.564686
$807$	5.73166e6	0.309811
$808$	1.19200e7	0.642315
$809$	1.60578e7	0.862610	0.431305	−	0.902206i	$-0.358053\pi$
$809$	1.60578e7	0.862610	0.431305	+	0.902206i	$0.358053\pi$
$810$	659560.	0.0353217
$811$	4.84775e6	0.258814	0.129407	−	0.991592i	$-0.458693\pi$
$811$	4.84775e6	0.258814	0.129407	+	0.991592i	$0.458693\pi$
$812$	5.28886e6	0.281496
$813$	−7.62701e6	−0.404695
$814$	−1.24875e7	−0.660564
$815$	−3.17116e6	−0.167234
$816$	2.51085e6	0.132006
$817$	1.97187e7	1.03353
$818$	7.10862e6	0.371451
$819$	−2.57867e6	−0.134334
$820$	−2.33184e6	−0.121106
$821$	2.17976e7	1.12863	0.564314	−	0.825560i	$-0.309141\pi$
$821$	2.17976e7	1.12863	0.564314	+	0.825560i	$0.309141\pi$
$822$	−9.42918e6	−0.486737
$823$	3.20206e7	1.64790	0.823948	−	0.566665i	$-0.191767\pi$
$823$	3.20206e7	1.64790	0.823948	+	0.566665i	$0.191767\pi$
$824$	−3.84410e6	−0.197231
$825$	8.22800e6	0.420881
$826$	5.42058e6	0.276436
$827$	2.19008e7	1.11352	0.556758	−	0.830675i	$-0.312045\pi$
$827$	2.19008e7	1.11352	0.556758	+	0.830675i	$0.312045\pi$
$828$	−5.72800e6	−0.290354
$829$	−1.45999e7	−0.737844	−0.368922	−	0.929460i	$-0.620273\pi$
$829$	−1.45999e7	−0.737844	−0.368922	+	0.929460i	$0.620273\pi$
$830$	−3.08224e6	−0.155300
$831$	−1.47783e7	−0.742374
$832$	−1.20422e6	−0.0603113
$833$	2.94363e6	0.146984
$834$	1.00782e7	0.501728
$835$	1.41568e6	0.0702666
$836$	−1.32301e7	−0.654707
$837$	−2.98979e7	−1.47512
$838$	112224.	0.00552047
$839$	4.60947e6	0.226072	0.113036	−	0.993591i	$-0.463942\pi$
$839$	4.60947e6	0.226072	0.113036	+	0.993591i	$0.463942\pi$
$840$	−250880.	−0.0122678
$841$	2.49974e7	1.21872
$842$	−1.08359e7	−0.526725
$843$	−1.59680e7	−0.773897
$844$	−1.65510e6	−0.0799777
$845$	−2.84857e6	−0.137241
$846$	223392.	0.0107310
$847$	2.22710e6	0.106667
$848$	−3.74630e6	−0.178901
$849$	1.87270e6	0.0891661
$850$	−1.48346e7	−0.704253
$851$	1.83640e7	0.869247
$852$	4.72576e6	0.223035
$853$	−1.98437e7	−0.933793	−0.466897	−	0.884312i	$-0.654628\pi$
$853$	−1.98437e7	−0.933793	−0.466897	+	0.884312i	$0.654628\pi$
$854$	−6.73025e6	−0.315781
$855$	−4.35328e6	−0.203658
$856$	3.06509e6	0.142974
$857$	−1.22960e6	−0.0571888	−0.0285944	−	0.999591i	$-0.509103\pi$
$857$	−1.22960e6	−0.0571888	−0.0285944	+	0.999591i	$0.509103\pi$
$858$	3.19872e6	0.148340
$859$	3.33041e7	1.53998	0.769989	−	0.638058i	$-0.220262\pi$
$859$	3.33041e7	1.53998	0.769989	+	0.638058i	$0.220262\pi$
$860$	1.29728e6	0.0598119
$861$	5.71301e6	0.262638
$862$	2.21559e7	1.01560
$863$	−2.36616e7	−1.08148	−0.540738	−	0.841191i	$-0.681855\pi$
$863$	−2.36616e7	−1.08148	−0.540738	+	0.841191i	$0.681855\pi$
$864$	−3.45702e6	−0.157550
$865$	−712220.	−0.0323649
$866$	−3.47318e6	−0.157374
$867$	665752.	0.0300791
$868$	−6.94310e6	−0.312791
$869$	2.20157e7	0.988969
$870$	−2.15872e6	−0.0966937
$871$	−3.62090e6	−0.161723
$872$	1.41453e6	0.0629971
$873$	−3.69635e6	−0.164149
$874$	1.94560e7	0.861539
$875$	3.01350e6	0.133061
$876$	−7.89990e6	−0.347826
$877$	−2.37812e7	−1.04408	−0.522042	−	0.852920i	$-0.674830\pi$
$877$	−2.37812e7	−1.04408	−0.522042	+	0.852920i	$0.674830\pi$
$878$	−4.55069e6	−0.199224
$879$	−2.00064e7	−0.873369
$880$	−870400.	−0.0378889
$881$	−1.41871e7	−0.615818	−0.307909	−	0.951416i	$-0.599629\pi$
$881$	−1.41871e7	−0.615818	−0.307909	+	0.951416i	$0.599629\pi$
$882$	−1.71912e6	−0.0744104
$883$	2.09281e7	0.903293	0.451647	−	0.892197i	$-0.350837\pi$
$883$	2.09281e7	0.903293	0.451647	+	0.892197i	$0.350837\pi$
$884$	−5.76710e6	−0.248214
$885$	−2.21248e6	−0.0949557
$886$	7.01595e6	0.300263
$887$	−7.98586e6	−0.340810	−0.170405	−	0.985374i	$-0.554508\pi$
$887$	−7.98586e6	−0.340810	−0.170405	+	0.985374i	$0.554508\pi$
$888$	4.70118e6	0.200067
$889$	4.73810e6	0.201071
$890$	−326640.	−0.0138227
$891$	−5.60626e6	−0.236581
$892$	4.91725e6	0.206924
$893$	−758784.	−0.0318412
$894$	3.63590e6	0.152149
$895$	4.85628e6	0.202650
$896$	−802816.	−0.0334077
$897$	−4.70400e6	−0.195203
$898$	9.66695e6	0.400036
$899$	−5.97426e7	−2.46538
$900$	8.66360e6	0.356527
$901$	−1.79413e7	−0.736278
$902$	1.98206e7	0.811150
$903$	−3.17834e6	−0.129712
$904$	−1.56835e7	−0.638294
$905$	6.57090e6	0.266688
$906$	1.30627e7	0.528702
$907$	−2.31861e7	−0.935856	−0.467928	−	0.883767i	$-0.654999\pi$
$907$	−2.31861e7	−0.935856	−0.467928	+	0.883767i	$0.654999\pi$
$908$	−1.42687e7	−0.574340
$909$	−3.33388e7	−1.33826
$910$	576240.	0.0230675
$911$	1.65299e7	0.659895	0.329948	−	0.943999i	$-0.392969\pi$
$911$	1.65299e7	0.659895	0.329948	+	0.943999i	$0.392969\pi$
$912$	4.98074e6	0.198293
$913$	2.61990e7	1.04018
$914$	−509720.	−0.0201821
$915$	2.74704e6	0.108471
$916$	4.42730e6	0.174341
$917$	−6.58403e6	−0.258564
$918$	−1.65559e7	−0.648405
$919$	1.28087e7	0.500283	0.250142	−	0.968209i	$-0.419523\pi$
$919$	1.28087e7	0.500283	0.250142	+	0.968209i	$0.419523\pi$
$920$	1.28000e6	0.0498586
$921$	1.87363e7	0.727836
$922$	−512792.	−0.0198662
$923$	−1.08545e7	−0.419377
$924$	2.13248e6	0.0821684
$925$	−2.77756e7	−1.06735
$926$	−1.60661e7	−0.615720
$927$	1.07515e7	0.410930
$928$	−6.90790e6	−0.263315
$929$	2.97319e7	1.13027	0.565136	−	0.824998i	$-0.308824\pi$
$929$	2.97319e7	1.13027	0.565136	+	0.824998i	$0.308824\pi$
$930$	2.83392e6	0.107444
$931$	5.83923e6	0.220791
$932$	2.36709e7	0.892639
$933$	−1.30451e6	−0.0490619
$934$	3.46899e7	1.30117
$935$	−4.16840e6	−0.155934
$936$	3.36806e6	0.125658
$937$	1.10970e7	0.412911	0.206456	−	0.978456i	$-0.433807\pi$
$937$	1.10970e7	0.412911	0.206456	+	0.978456i	$0.433807\pi$
$938$	−2.41394e6	−0.0895816
$939$	1.39172e7	0.515096
$940$	−49920.0	−0.00184270
$941$	3.74313e7	1.37804	0.689019	−	0.724743i	$-0.258042\pi$
$941$	3.74313e7	1.37804	0.689019	+	0.724743i	$0.258042\pi$
$942$	9.39347e6	0.344905
$943$	−2.91480e7	−1.06741
$944$	−7.07994e6	−0.258583
$945$	1.65424e6	0.0602586
$946$	−1.10269e7	−0.400613
$947$	1.50907e7	0.546808	0.273404	−	0.961899i	$-0.411850\pi$
$947$	1.50907e7	0.546808	0.273404	+	0.961899i	$0.411850\pi$
$948$	−8.28826e6	−0.299531
$949$	1.81451e7	0.654024
$950$	−2.94272e7	−1.05789
$951$	−1.43817e7	−0.515655
$952$	−3.84474e6	−0.137491
$953$	−2.15741e7	−0.769484	−0.384742	−	0.923024i	$-0.625710\pi$
$953$	−2.15741e7	−0.769484	−0.384742	+	0.923024i	$0.625710\pi$
$954$	1.04779e7	0.372739
$955$	683040.	0.0242347
$956$	1.60055e7	0.566402
$957$	1.83491e7	0.647643
$958$	3.31579e7	1.16727
$959$	1.44384e7	0.506960
$960$	327680.	0.0114755
$961$	4.97996e7	1.73947
$962$	−1.07980e7	−0.376190
$963$	−8.57267e6	−0.297886
$964$	2.17333e7	0.753239
$965$	3.52754e6	0.121942
$966$	−3.13600e6	−0.108127
$967$	−3.29467e7	−1.13304	−0.566520	−	0.824048i	$-0.691711\pi$
$967$	−3.29467e7	−1.13304	−0.566520	+	0.824048i	$0.691711\pi$
$968$	−2.90886e6	−0.0997781
$969$	2.38531e7	0.816083
$970$	826000.	0.0281871
$971$	2.24599e7	0.764470	0.382235	−	0.924065i	$-0.375154\pi$
$971$	2.24599e7	0.764470	0.382235	+	0.924065i	$0.375154\pi$
$972$	1.52365e7	0.517272
$973$	−1.54323e7	−0.522573
$974$	−3.56708e7	−1.20480
$975$	7.11480e6	0.239691
$976$	8.79053e6	0.295386
$977$	−5.16236e7	−1.73026	−0.865132	−	0.501545i	$-0.832765\pi$
$977$	−5.16236e7	−1.73026	−0.865132	+	0.501545i	$0.832765\pi$
$978$	−1.01477e7	−0.339251
$979$	2.77644e6	0.0925831
$980$	384160.	0.0127775
$981$	−3.95626e6	−0.131254
$982$	−2.28615e7	−0.756529
$983$	−1.10202e7	−0.363751	−0.181876	−	0.983322i	$-0.558217\pi$
$983$	−1.10202e7	−0.363751	−0.181876	+	0.983322i	$0.558217\pi$
$984$	−7.46189e6	−0.245675
$985$	1.96982e6	0.0646898
$986$	−3.30824e7	−1.08369
$987$	122304.	0.00399621
$988$	−1.14401e7	−0.372854
$989$	1.62160e7	0.527173
$990$	2.43440e6	0.0789412
$991$	3.21029e7	1.03839	0.519194	−	0.854656i	$-0.326232\pi$
$991$	3.21029e7	1.03839	0.519194	+	0.854656i	$0.326232\pi$
$992$	9.06854e6	0.292589
$993$	−1.98033e7	−0.637330
$994$	−7.23632e6	−0.232301
$995$	−1.10392e7	−0.353492
$996$	−9.86317e6	−0.315042
$997$	2.81772e7	0.897759	0.448879	−	0.893592i	$-0.351823\pi$
$997$	2.81772e7	0.897759	0.448879	+	0.893592i	$0.351823\pi$
$998$	500464.	0.0159055
$999$	−3.09984e7	−0.982711

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.6.a.b.1.1	✓	1
3.2	odd	2		126.6.a.c.1.1		1
4.3	odd	2		112.6.a.d.1.1		1
5.2	odd	4		350.6.c.f.99.2		2
5.3	odd	4		350.6.c.f.99.1		2
5.4	even	2		350.6.a.b.1.1		1
7.2	even	3		98.6.c.a.67.1		2
7.3	odd	6		98.6.c.b.79.1		2
7.4	even	3		98.6.c.a.79.1		2
7.5	odd	6		98.6.c.b.67.1		2
7.6	odd	2		98.6.a.b.1.1		1
8.3	odd	2		448.6.a.k.1.1		1
8.5	even	2		448.6.a.f.1.1		1
12.11	even	2		1008.6.a.n.1.1		1
21.20	even	2		882.6.a.g.1.1		1
28.27	even	2		784.6.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.6.a.b.1.1	✓	1	1.1	even	1	trivial
98.6.a.b.1.1		1	7.6	odd	2
98.6.c.a.67.1		2	7.2	even	3
98.6.c.a.79.1		2	7.4	even	3
98.6.c.b.67.1		2	7.5	odd	6
98.6.c.b.79.1		2	7.3	odd	6
112.6.a.d.1.1		1	4.3	odd	2
126.6.a.c.1.1		1	3.2	odd	2
350.6.a.b.1.1		1	5.4	even	2
350.6.c.f.99.1		2	5.3	odd	4
350.6.c.f.99.2		2	5.2	odd	4
448.6.a.f.1.1		1	8.5	even	2
448.6.a.k.1.1		1	8.3	odd	2
784.6.a.h.1.1		1	28.27	even	2
882.6.a.g.1.1		1	21.20	even	2
1008.6.a.n.1.1		1	12.11	even	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:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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