LMFDB - Embedded newform 722.6.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,6,Mod(1,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, 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("722.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	722.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:	$115.797117905$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{1441}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 360 $ x^2 - x - 360
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-18.4803$ of defining polynomial
Character	$\chi$	$=$	722.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.00000 q^{2} +17.4803 q^{3} +16.0000 q^{4} -79.4408 q^{5} +69.9210 q^{6} +132.921 q^{7} +64.0000 q^{8} +62.5592 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} +17.4803 q^{3} +16.0000 q^{4} -79.4408 q^{5} +69.9210 q^{6} +132.921 q^{7} +64.0000 q^{8} +62.5592 q^{9} -317.763 q^{10} +311.520 q^{11} +279.684 q^{12} -901.401 q^{13} +531.684 q^{14} -1388.64 q^{15} +256.000 q^{16} -157.803 q^{17} +250.237 q^{18} -1271.05 q^{20} +2323.49 q^{21} +1246.08 q^{22} -2522.53 q^{23} +1118.74 q^{24} +3185.83 q^{25} -3605.61 q^{26} -3154.15 q^{27} +2126.74 q^{28} -4738.28 q^{29} -5554.58 q^{30} +6587.76 q^{31} +1024.00 q^{32} +5445.44 q^{33} -631.210 q^{34} -10559.3 q^{35} +1000.95 q^{36} -8508.60 q^{37} -15756.7 q^{39} -5084.21 q^{40} -19741.1 q^{41} +9293.97 q^{42} +10985.0 q^{43} +4984.32 q^{44} -4969.75 q^{45} -10090.1 q^{46} +15085.5 q^{47} +4474.94 q^{48} +860.995 q^{49} +12743.3 q^{50} -2758.43 q^{51} -14422.4 q^{52} -21699.6 q^{53} -12616.6 q^{54} -24747.4 q^{55} +8506.94 q^{56} -18953.1 q^{58} +40676.1 q^{59} -22218.3 q^{60} +6151.79 q^{61} +26351.0 q^{62} +8315.44 q^{63} +4096.00 q^{64} +71608.0 q^{65} +21781.8 q^{66} -62760.3 q^{67} -2524.84 q^{68} -44094.5 q^{69} -42237.4 q^{70} +55311.0 q^{71} +4003.79 q^{72} -48528.1 q^{73} -34034.4 q^{74} +55689.2 q^{75} +41407.5 q^{77} -63026.9 q^{78} -31017.6 q^{79} -20336.8 q^{80} -70337.2 q^{81} -78964.4 q^{82} +41068.7 q^{83} +37175.9 q^{84} +12536.0 q^{85} +43939.8 q^{86} -82826.3 q^{87} +19937.3 q^{88} +17065.6 q^{89} -19879.0 q^{90} -119815. q^{91} -40360.5 q^{92} +115156. q^{93} +60341.9 q^{94} +17899.8 q^{96} -139045. q^{97} +3443.98 q^{98} +19488.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8 q^{2} - 3 q^{3} + 32 q^{4} - 45 q^{5} - 12 q^{6} + 114 q^{7} + 128 q^{8} + 239 q^{9}+O(q^{10}) $ 2 * q + 8 * q^2 - 3 * q^3 + 32 * q^4 - 45 * q^5 - 12 * q^6 + 114 * q^7 + 128 * q^8 + 239 * q^9	\( 2 q + 8 q^{2} - 3 q^{3} + 32 q^{4} - 45 q^{5} - 12 q^{6} + 114 q^{7} + 128 q^{8} + 239 q^{9} - 180 q^{10} + 661 q^{11} - 48 q^{12} - 1613 q^{13} + 456 q^{14} - 2094 q^{15} + 512 q^{16} + 64 q^{17} + 956 q^{18} - 720 q^{20} + 2711 q^{21} + 2644 q^{22} - 3185 q^{23} - 192 q^{24} + 1247 q^{25} - 6452 q^{26} - 1791 q^{27} + 1824 q^{28} + 2481 q^{29} - 8376 q^{30} + 1180 q^{31} + 2048 q^{32} - 1712 q^{33} + 256 q^{34} - 11211 q^{35} + 3824 q^{36} - 10488 q^{37} - 1183 q^{39} - 2880 q^{40} - 16630 q^{41} + 10844 q^{42} + 11303 q^{43} + 10576 q^{44} + 1107 q^{45} - 12740 q^{46} - 12155 q^{47} - 768 q^{48} - 15588 q^{49} + 4988 q^{50} - 7301 q^{51} - 25808 q^{52} - 20585 q^{53} - 7164 q^{54} - 12711 q^{55} + 7296 q^{56} + 9924 q^{58} + 78581 q^{59} - 33504 q^{60} + 43621 q^{61} + 4720 q^{62} + 4977 q^{63} + 8192 q^{64} + 47100 q^{65} - 6848 q^{66} - 7805 q^{67} + 1024 q^{68} - 30527 q^{69} - 44844 q^{70} + 62488 q^{71} + 15296 q^{72} + 16218 q^{73} - 41952 q^{74} + 95397 q^{75} + 34795 q^{77} - 4732 q^{78} - 67122 q^{79} - 11520 q^{80} - 141130 q^{81} - 66520 q^{82} - 10714 q^{83} + 43376 q^{84} + 20175 q^{85} + 45212 q^{86} - 230679 q^{87} + 42304 q^{88} - 128188 q^{89} + 4428 q^{90} - 106351 q^{91} - 50960 q^{92} + 225908 q^{93} - 48620 q^{94} - 3072 q^{96} - 178558 q^{97} - 62352 q^{98} + 81151 q^{99}+O(q^{100}) \) 2 * q + 8 * q^2 - 3 * q^3 + 32 * q^4 - 45 * q^5 - 12 * q^6 + 114 * q^7 + 128 * q^8 + 239 * q^9 - 180 * q^10 + 661 * q^11 - 48 * q^12 - 1613 * q^13 + 456 * q^14 - 2094 * q^15 + 512 * q^16 + 64 * q^17 + 956 * q^18 - 720 * q^20 + 2711 * q^21 + 2644 * q^22 - 3185 * q^23 - 192 * q^24 + 1247 * q^25 - 6452 * q^26 - 1791 * q^27 + 1824 * q^28 + 2481 * q^29 - 8376 * q^30 + 1180 * q^31 + 2048 * q^32 - 1712 * q^33 + 256 * q^34 - 11211 * q^35 + 3824 * q^36 - 10488 * q^37 - 1183 * q^39 - 2880 * q^40 - 16630 * q^41 + 10844 * q^42 + 11303 * q^43 + 10576 * q^44 + 1107 * q^45 - 12740 * q^46 - 12155 * q^47 - 768 * q^48 - 15588 * q^49 + 4988 * q^50 - 7301 * q^51 - 25808 * q^52 - 20585 * q^53 - 7164 * q^54 - 12711 * q^55 + 7296 * q^56 + 9924 * q^58 + 78581 * q^59 - 33504 * q^60 + 43621 * q^61 + 4720 * q^62 + 4977 * q^63 + 8192 * q^64 + 47100 * q^65 - 6848 * q^66 - 7805 * q^67 + 1024 * q^68 - 30527 * q^69 - 44844 * q^70 + 62488 * q^71 + 15296 * q^72 + 16218 * q^73 - 41952 * q^74 + 95397 * q^75 + 34795 * q^77 - 4732 * q^78 - 67122 * q^79 - 11520 * q^80 - 141130 * q^81 - 66520 * q^82 - 10714 * q^83 + 43376 * q^84 + 20175 * q^85 + 45212 * q^86 - 230679 * q^87 + 42304 * q^88 - 128188 * q^89 + 4428 * q^90 - 106351 * q^91 - 50960 * q^92 + 225908 * q^93 - 48620 * q^94 - 3072 * q^96 - 178558 * q^97 - 62352 * q^98 + 81151 * q^99

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
$3$	17.4803	1.12136	0.560679	−	0.828033i	$-0.310540\pi$
$3$	17.4803	1.12136	0.560679	+	0.828033i	$0.310540\pi$
$4$	16.0000	0.500000
$5$	−79.4408	−1.42108	−0.710540	−	0.703657i	$-0.751549\pi$
$5$	−79.4408	−1.42108	−0.710540	+	0.703657i	$0.751549\pi$
$6$	69.9210	0.792920
$7$	132.921	1.02529	0.512647	−	0.858599i	$-0.328665\pi$
$7$	132.921	1.02529	0.512647	+	0.858599i	$0.328665\pi$
$8$	64.0000	0.353553
$9$	62.5592	0.257445
$10$	−317.763	−1.00485
$11$	311.520	0.776254	0.388127	−	0.921606i	$-0.373122\pi$
$11$	311.520	0.776254	0.388127	+	0.921606i	$0.373122\pi$
$12$	279.684	0.560679
$13$	−901.401	−1.47931	−0.739656	−	0.672985i	$-0.765012\pi$
$13$	−901.401	−1.47931	−0.739656	+	0.672985i	$0.765012\pi$
$14$	531.684	0.724993
$15$	−1388.64	−1.59354
$16$	256.000	0.250000
$17$	−157.803	−0.132432	−0.0662158	−	0.997805i	$-0.521093\pi$
$17$	−157.803	−0.132432	−0.0662158	+	0.997805i	$0.521093\pi$
$18$	250.237	0.182041
$19$	0	0
$19$	0	0
$20$	−1271.05	−0.710540
$21$	2323.49	1.14972
$22$	1246.08	0.548894
$23$	−2522.53	−0.994299	−0.497150	−	0.867665i	$-0.665620\pi$
$23$	−2522.53	−0.994299	−0.497150	+	0.867665i	$0.665620\pi$
$24$	1118.74	0.396460
$25$	3185.83	1.01947
$26$	−3605.61	−1.04603
$27$	−3154.15	−0.832670
$28$	2126.74	0.512647
$29$	−4738.28	−1.04623	−0.523113	−	0.852263i	$-0.675230\pi$
$29$	−4738.28	−1.04623	−0.523113	+	0.852263i	$0.675230\pi$
$30$	−5554.58	−1.12680
$31$	6587.76	1.23121	0.615607	−	0.788053i	$-0.288911\pi$
$31$	6587.76	1.23121	0.615607	+	0.788053i	$0.288911\pi$
$32$	1024.00	0.176777
$33$	5445.44	0.870459
$34$	−631.210	−0.0936433
$35$	−10559.3	−1.45702
$36$	1000.95	0.128723
$37$	−8508.60	−1.02177	−0.510886	−	0.859648i	$-0.670683\pi$
$37$	−8508.60	−1.02177	−0.510886	+	0.859648i	$0.670683\pi$
$38$	0	0
$39$	−15756.7	−1.65884
$40$	−5084.21	−0.502427
$41$	−19741.1	−1.83405	−0.917027	−	0.398826i	$-0.869418\pi$
$41$	−19741.1	−1.83405	−0.917027	+	0.398826i	$0.869418\pi$
$42$	9293.97	0.812977
$43$	10985.0	0.905997	0.452999	−	0.891511i	$-0.350354\pi$
$43$	10985.0	0.905997	0.452999	+	0.891511i	$0.350354\pi$
$44$	4984.32	0.388127
$45$	−4969.75	−0.365850
$46$	−10090.1	−0.703076
$47$	15085.5	0.996127	0.498063	−	0.867141i	$-0.334045\pi$
$47$	15085.5	0.996127	0.498063	+	0.867141i	$0.334045\pi$
$48$	4474.94	0.280340
$49$	860.995	0.0512284
$50$	12743.3	0.720872
$51$	−2758.43	−0.148503
$52$	−14422.4	−0.739656
$53$	−21699.6	−1.06112	−0.530558	−	0.847649i	$-0.678018\pi$
$53$	−21699.6	−1.06112	−0.530558	+	0.847649i	$0.678018\pi$
$54$	−12616.6	−0.588787
$55$	−24747.4	−1.10312
$56$	8506.94	0.362496
$57$	0	0
$58$	−18953.1	−0.739794
$59$	40676.1	1.52128	0.760639	−	0.649175i	$-0.224886\pi$
$59$	40676.1	1.52128	0.760639	+	0.649175i	$0.224886\pi$
$60$	−22218.3	−0.796770
$61$	6151.79	0.211679	0.105839	−	0.994383i	$-0.466247\pi$
$61$	6151.79	0.211679	0.105839	+	0.994383i	$0.466247\pi$
$62$	26351.0	0.870600
$63$	8315.44	0.263957
$64$	4096.00	0.125000
$65$	71608.0	2.10222
$66$	21781.8	0.615508
$67$	−62760.3	−1.70804	−0.854019	−	0.520241i	$-0.825842\pi$
$67$	−62760.3	−1.70804	−0.854019	+	0.520241i	$0.825842\pi$
$68$	−2524.84	−0.0662158
$69$	−44094.5	−1.11497
$70$	−42237.4	−1.03027
$71$	55311.0	1.30216	0.651081	−	0.759008i	$-0.274316\pi$
$71$	55311.0	1.30216	0.651081	+	0.759008i	$0.274316\pi$
$72$	4003.79	0.0910207
$73$	−48528.1	−1.06583	−0.532913	−	0.846170i	$-0.678903\pi$
$73$	−48528.1	−1.06583	−0.532913	+	0.846170i	$0.678903\pi$
$74$	−34034.4	−0.722502
$75$	55689.2	1.14319
$76$	0	0
$77$	41407.5	0.795889
$78$	−63026.9	−1.17298
$79$	−31017.6	−0.559166	−0.279583	−	0.960121i	$-0.590196\pi$
$79$	−31017.6	−0.559166	−0.279583	+	0.960121i	$0.590196\pi$
$80$	−20336.8	−0.355270
$81$	−70337.2	−1.19117
$82$	−78964.4	−1.29687
$83$	41068.7	0.654358	0.327179	−	0.944962i	$-0.393902\pi$
$83$	41068.7	0.654358	0.327179	+	0.944962i	$0.393902\pi$
$84$	37175.9	0.574861
$85$	12536.0	0.188196
$86$	43939.8	0.640637
$87$	−82826.3	−1.17320
$88$	19937.3	0.274447
$89$	17065.6	0.228373	0.114187	−	0.993459i	$-0.463574\pi$
$89$	17065.6	0.228373	0.114187	+	0.993459i	$0.463574\pi$
$90$	−19879.0	−0.258695
$91$	−119815.	−1.51673
$92$	−40360.5	−0.497150
$93$	115156.	1.38063
$94$	60341.9	0.704368
$95$	0	0
$96$	17899.8	0.198230
$97$	−139045.	−1.50047	−0.750234	−	0.661172i	$-0.770059\pi$
$97$	−139045.	−1.50047	−0.750234	+	0.661172i	$0.770059\pi$
$98$	3443.98	0.0362239
$99$	19488.4	0.199843
$100$	50973.3	0.509733
$101$	−122253.	−1.19249	−0.596247	−	0.802801i	$-0.703342\pi$
$101$	−122253.	−1.19249	−0.596247	+	0.802801i	$0.703342\pi$
$102$	−11033.7	−0.105008
$103$	71932.4	0.668084	0.334042	−	0.942558i	$-0.391587\pi$
$103$	71932.4	0.668084	0.334042	+	0.942558i	$0.391587\pi$
$104$	−57689.7	−0.523016
$105$	−184580.	−1.63385
$106$	−86798.5	−0.750322
$107$	−14833.3	−0.125250	−0.0626249	−	0.998037i	$-0.519947\pi$
$107$	−14833.3	−0.125250	−0.0626249	+	0.998037i	$0.519947\pi$
$108$	−50466.4	−0.416335
$109$	−140025.	−1.12886	−0.564429	−	0.825482i	$-0.690904\pi$
$109$	−140025.	−1.12886	−0.564429	+	0.825482i	$0.690904\pi$
$110$	−98989.5	−0.780023
$111$	−148733.	−1.14577
$112$	34027.8	0.256324
$113$	−235172.	−1.73256	−0.866282	−	0.499555i	$-0.833497\pi$
$113$	−235172.	−1.73256	−0.866282	+	0.499555i	$0.833497\pi$
$114$	0	0
$115$	200392.	1.41298
$116$	−75812.5	−0.523113
$117$	−56391.0	−0.380842
$118$	162704.	1.07571
$119$	−20975.3	−0.135781
$120$	−88873.3	−0.563401
$121$	−64006.4	−0.397430
$122$	24607.2	0.149679
$123$	−345080.	−2.05663
$124$	105404.	0.615607
$125$	−4832.71	−0.0276640
$126$	33261.8	0.186646
$127$	24783.9	0.136351	0.0681757	−	0.997673i	$-0.478282\pi$
$127$	24783.9	0.136351	0.0681757	+	0.997673i	$0.478282\pi$
$128$	16384.0	0.0883883
$129$	192020.	1.01595
$130$	286432.	1.48649
$131$	−152549.	−0.776661	−0.388331	−	0.921520i	$-0.626948\pi$
$131$	−152549.	−0.776661	−0.388331	+	0.921520i	$0.626948\pi$
$132$	87127.1	0.435230
$133$	0	0
$134$	−251041.	−1.20777
$135$	250568.	1.18329
$136$	−10099.4	−0.0468216
$137$	192265.	0.875184	0.437592	−	0.899174i	$-0.355831\pi$
$137$	192265.	0.875184	0.437592	+	0.899174i	$0.355831\pi$
$138$	−176378.	−0.788400
$139$	−342833.	−1.50503	−0.752515	−	0.658575i	$-0.771159\pi$
$139$	−342833.	−1.50503	−0.752515	+	0.658575i	$0.771159\pi$
$140$	−168950.	−0.728512
$141$	263698.	1.11702
$142$	221244.	0.920768
$143$	−280804.	−1.14832
$144$	16015.2	0.0643614
$145$	376413.	1.48677
$146$	−194112.	−0.753652
$147$	15050.4	0.0574454
$148$	−136138.	−0.510886
$149$	335859.	1.23934	0.619671	−	0.784862i	$-0.287266\pi$
$149$	335859.	1.23934	0.619671	+	0.784862i	$0.287266\pi$
$150$	222757.	0.808356
$151$	−266683.	−0.951816	−0.475908	−	0.879495i	$-0.657880\pi$
$151$	−266683.	−0.951816	−0.475908	+	0.879495i	$0.657880\pi$
$152$	0	0
$153$	−9872.01	−0.0340939
$154$	165630.	0.562778
$155$	−523337.	−1.74965
$156$	−252108.	−0.829420
$157$	−173779.	−0.562664	−0.281332	−	0.959611i	$-0.590776\pi$
$157$	−173779.	−0.562664	−0.281332	+	0.959611i	$0.590776\pi$
$158$	−124071.	−0.395390
$159$	−379315.	−1.18989
$160$	−81347.3	−0.251214
$161$	−335298.	−1.01945
$162$	−281349.	−0.842282
$163$	−406317.	−1.19783	−0.598917	−	0.800811i	$-0.704402\pi$
$163$	−406317.	−1.19783	−0.598917	+	0.800811i	$0.704402\pi$
$164$	−315858.	−0.917027
$165$	−432590.	−1.23699
$166$	164275.	0.462701
$167$	319695.	0.887043	0.443522	−	0.896264i	$-0.353729\pi$
$167$	319695.	0.887043	0.443522	+	0.896264i	$0.353729\pi$
$168$	148704.	0.406488
$169$	441231.	1.18836
$170$	50143.8	0.133075
$171$	0	0
$172$	175759.	0.452999
$173$	427313.	1.08550	0.542752	−	0.839893i	$-0.317382\pi$
$173$	427313.	1.08550	0.542752	+	0.839893i	$0.317382\pi$
$174$	−331305.	−0.829574
$175$	423464.	1.04525
$176$	79749.1	0.194064
$177$	711028.	1.70590
$178$	68262.2	0.161484
$179$	−361946.	−0.844329	−0.422164	−	0.906519i	$-0.638729\pi$
$179$	−361946.	−0.844329	−0.422164	+	0.906519i	$0.638729\pi$
$180$	−79516.1	−0.182925
$181$	416686.	0.945393	0.472697	−	0.881225i	$-0.343281\pi$
$181$	416686.	0.945393	0.472697	+	0.881225i	$0.343281\pi$
$182$	−479261.	−1.07249
$183$	107535.	0.237368
$184$	−161442.	−0.351538
$185$	675930.	1.45202
$186$	460623.	0.976255
$187$	−49158.6	−0.102801
$188$	241368.	0.498063
$189$	−419253.	−0.853732
$190$	0	0
$191$	581586.	1.15353	0.576767	−	0.816909i	$-0.304314\pi$
$191$	581586.	1.15353	0.576767	+	0.816909i	$0.304314\pi$
$192$	71599.1	0.140170
$193$	182832.	0.353312	0.176656	−	0.984273i	$-0.443472\pi$
$193$	182832.	0.353312	0.176656	+	0.984273i	$0.443472\pi$
$194$	−556181.	−1.06099
$195$	1.25173e6	2.35734
$196$	13775.9	0.0256142
$197$	−93344.9	−0.171366	−0.0856831	−	0.996322i	$-0.527307\pi$
$197$	−93344.9	−0.171366	−0.0856831	+	0.996322i	$0.527307\pi$
$198$	77953.8	0.141310
$199$	723166.	1.29451	0.647255	−	0.762274i	$-0.275917\pi$
$199$	723166.	1.29451	0.647255	+	0.762274i	$0.275917\pi$
$200$	203893.	0.360436
$201$	−1.09707e6	−1.91532
$202$	−489012.	−0.843221
$203$	−629817.	−1.07269
$204$	−44134.8	−0.0742517
$205$	1.56825e6	2.60634
$206$	287730.	0.472407
$207$	−157808.	−0.255978
$208$	−230759.	−0.369828
$209$	0	0
$210$	−738320.	−1.15530
$211$	−85741.4	−0.132582	−0.0662910	−	0.997800i	$-0.521117\pi$
$211$	−85741.4	−0.132582	−0.0662910	+	0.997800i	$0.521117\pi$
$212$	−347194.	−0.530558
$213$	966850.	1.46019
$214$	−59333.0	−0.0885650
$215$	−872653.	−1.28749
$216$	−201866.	−0.294393
$217$	875652.	1.26236
$218$	−560100.	−0.798223
$219$	−848283.	−1.19517
$220$	−395958.	−0.551559
$221$	142243.	0.195908
$222$	−594930.	−0.810184
$223$	−111106.	−0.149615	−0.0748076	−	0.997198i	$-0.523834\pi$
$223$	−111106.	−0.149615	−0.0748076	+	0.997198i	$0.523834\pi$
$224$	136111.	0.181248
$225$	199303.	0.262457
$226$	−940688.	−1.22511
$227$	314299.	0.404835	0.202418	−	0.979299i	$-0.435120\pi$
$227$	314299.	0.404835	0.202418	+	0.979299i	$0.435120\pi$
$228$	0	0
$229$	1.45815e6	1.83744	0.918718	−	0.394913i	$-0.129225\pi$
$229$	1.45815e6	1.83744	0.918718	+	0.394913i	$0.129225\pi$
$230$	801568.	0.999127
$231$	723814.	0.892477
$232$	−303250.	−0.369897
$233$	1.38626e6	1.67284	0.836418	−	0.548091i	$-0.184645\pi$
$233$	1.38626e6	1.67284	0.836418	+	0.548091i	$0.184645\pi$
$234$	−225564.	−0.269296
$235$	−1.19840e6	−1.41558
$236$	650817.	0.760639
$237$	−542196.	−0.627026
$238$	−83901.1	−0.0960119
$239$	365117.	0.413464	0.206732	−	0.978398i	$-0.433717\pi$
$239$	365117.	0.413464	0.206732	+	0.978398i	$0.433717\pi$
$240$	−355493.	−0.398385
$241$	312312.	0.346374	0.173187	−	0.984889i	$-0.444593\pi$
$241$	312312.	0.346374	0.173187	+	0.984889i	$0.444593\pi$
$242$	−256026.	−0.281025
$243$	−463054.	−0.503056
$244$	98428.7	0.105839
$245$	−68398.1	−0.0727996
$246$	−1.38032e6	−1.45426
$247$	0	0
$248$	421617.	0.435300
$249$	717891.	0.733771
$250$	−19330.8	−0.0195614
$251$	−970095.	−0.971919	−0.485959	−	0.873981i	$-0.661530\pi$
$251$	−970095.	−0.971919	−0.485959	+	0.873981i	$0.661530\pi$
$252$	133047.	0.131979
$253$	−785819.	−0.771829
$254$	99135.5	0.0964151
$255$	219132.	0.211035
$256$	65536.0	0.0625000
$257$	−1.28988e6	−1.21819	−0.609096	−	0.793096i	$-0.708468\pi$
$257$	−1.28988e6	−1.21819	−0.609096	+	0.793096i	$0.708468\pi$
$258$	768079.	0.718384
$259$	−1.13097e6	−1.04762
$260$	1.14573e6	1.05111
$261$	−296423.	−0.269346
$262$	−610197.	−0.549183
$263$	−501426.	−0.447011	−0.223505	−	0.974703i	$-0.571750\pi$
$263$	−501426.	−0.447011	−0.223505	+	0.974703i	$0.571750\pi$
$264$	348508.	0.307754
$265$	1.72384e6	1.50793
$266$	0	0
$267$	298310.	0.256089
$268$	−1.00416e6	−0.854019
$269$	−1.42986e6	−1.20479	−0.602397	−	0.798197i	$-0.705787\pi$
$269$	−1.42986e6	−1.20479	−0.602397	+	0.798197i	$0.705787\pi$
$270$	1.00227e6	0.836713
$271$	−709506.	−0.586857	−0.293429	−	0.955981i	$-0.594796\pi$
$271$	−709506.	−0.586857	−0.293429	+	0.955981i	$0.594796\pi$
$272$	−40397.4	−0.0331079
$273$	−2.09440e6	−1.70080
$274$	769061.	0.618849
$275$	992450.	0.791365
$276$	−705512.	−0.557483
$277$	−766740.	−0.600411	−0.300205	−	0.953875i	$-0.597055\pi$
$277$	−766740.	−0.600411	−0.300205	+	0.953875i	$0.597055\pi$
$278$	−1.37133e6	−1.06422
$279$	412125.	0.316970
$280$	−675798.	−0.515136
$281$	−5975.32	−0.00451435	−0.00225718	−	0.999997i	$-0.500718\pi$
$281$	−5975.32	−0.00451435	−0.00225718	+	0.999997i	$0.500718\pi$
$282$	1.05479e6	0.789849
$283$	−189246.	−0.140463	−0.0702314	−	0.997531i	$-0.522374\pi$
$283$	−189246.	−0.140463	−0.0702314	+	0.997531i	$0.522374\pi$
$284$	884975.	0.651081
$285$	0	0
$286$	−1.12322e6	−0.811986
$287$	−2.62401e6	−1.88044
$288$	64060.7	0.0455104
$289$	−1.39496e6	−0.982462
$290$	1.50565e6	1.05131
$291$	−2.43055e6	−1.68256
$292$	−776449.	−0.532913
$293$	−986180.	−0.671100	−0.335550	−	0.942022i	$-0.608922\pi$
$293$	−986180.	−0.671100	−0.335550	+	0.942022i	$0.608922\pi$
$294$	60201.7	0.0406200
$295$	−3.23134e6	−2.16186
$296$	−544551.	−0.361251
$297$	−982580.	−0.646363
$298$	1.34343e6	0.876347
$299$	2.27381e6	1.47088
$300$	891027.	0.571594
$301$	1.46013e6	0.928914
$302$	−1.06673e6	−0.673035
$303$	−2.13702e6	−1.33721
$304$	0	0
$305$	−488703.	−0.300812
$306$	−39488.0	−0.0241080
$307$	1.45722e6	0.882428	0.441214	−	0.897402i	$-0.354548\pi$
$307$	1.45722e6	0.882428	0.441214	+	0.897402i	$0.354548\pi$
$308$	662520.	0.397944
$309$	1.25740e6	0.749162
$310$	−2.09335e6	−1.23719
$311$	2.40526e6	1.41014	0.705069	−	0.709138i	$-0.250916\pi$
$311$	2.40526e6	1.41014	0.705069	+	0.709138i	$0.250916\pi$
$312$	−1.00843e6	−0.586488
$313$	−3.20380e6	−1.84843	−0.924217	−	0.381867i	$-0.875281\pi$
$313$	−3.20380e6	−1.84843	−0.924217	+	0.381867i	$0.875281\pi$
$314$	−695117.	−0.397863
$315$	−660585.	−0.375104
$316$	−496282.	−0.279583
$317$	603046.	0.337056	0.168528	−	0.985697i	$-0.446099\pi$
$317$	603046.	0.337056	0.168528	+	0.985697i	$0.446099\pi$
$318$	−1.51726e6	−0.841380
$319$	−1.47607e6	−0.812137
$320$	−325389.	−0.177635
$321$	−259289.	−0.140450
$322$	−1.34119e6	−0.720860
$323$	0	0
$324$	−1.12540e6	−0.595584
$325$	−2.87171e6	−1.50811
$326$	−1.62527e6	−0.846996
$327$	−2.44767e6	−1.26585
$328$	−1.26343e6	−0.648436
$329$	2.00518e6	1.02132
$330$	−1.73036e6	−0.874685
$331$	3.77416e6	1.89344	0.946719	−	0.322062i	$-0.104376\pi$
$331$	3.77416e6	1.89344	0.946719	+	0.322062i	$0.104376\pi$
$332$	657099.	0.327179
$333$	−532292.	−0.263051
$334$	1.27878e6	0.627234
$335$	4.98572e6	2.42726
$336$	594814.	0.287431
$337$	2.12850e6	1.02094	0.510470	−	0.859896i	$-0.329472\pi$
$337$	2.12850e6	1.02094	0.510470	+	0.859896i	$0.329472\pi$
$338$	1.76492e6	0.840300
$339$	−4.11087e6	−1.94283
$340$	200575.	0.0940979
$341$	2.05222e6	0.955735
$342$	0	0
$343$	−2.11956e6	−0.972770
$344$	703037.	0.320318
$345$	3.50290e6	1.58446
$346$	1.70925e6	0.767567
$347$	2.40305e6	1.07137	0.535685	−	0.844418i	$-0.320053\pi$
$347$	2.40305e6	1.07137	0.535685	+	0.844418i	$0.320053\pi$
$348$	−1.32522e6	−0.586598
$349$	3.71870e6	1.63428	0.817141	−	0.576438i	$-0.195558\pi$
$349$	3.71870e6	1.63428	0.817141	+	0.576438i	$0.195558\pi$
$350$	1.69386e6	0.739106
$351$	2.84315e6	1.23178
$352$	318996.	0.137224
$353$	−2.04192e6	−0.872174	−0.436087	−	0.899905i	$-0.643636\pi$
$353$	−2.04192e6	−0.872174	−0.436087	+	0.899905i	$0.643636\pi$
$354$	2.84411e6	1.20625
$355$	−4.39394e6	−1.85048
$356$	273049.	0.114187
$357$	−366653.	−0.152260
$358$	−1.44778e6	−0.597030
$359$	−949493.	−0.388826	−0.194413	−	0.980920i	$-0.562280\pi$
$359$	−949493.	−0.388826	−0.194413	+	0.980920i	$0.562280\pi$
$360$	−318064.	−0.129348
$361$	0	0
$362$	1.66674e6	0.668494
$363$	−1.11885e6	−0.445661
$364$	−1.91704e6	−0.758365
$365$	3.85511e6	1.51462
$366$	430139.	0.167844
$367$	1.74418e6	0.675967	0.337984	−	0.941152i	$-0.390255\pi$
$367$	1.74418e6	0.675967	0.337984	+	0.941152i	$0.390255\pi$
$368$	−645768.	−0.248575
$369$	−1.23499e6	−0.472169
$370$	2.70372e6	1.02673
$371$	−2.88434e6	−1.08796
$372$	1.84249e6	0.690316
$373$	−4.59987e6	−1.71188	−0.855940	−	0.517076i	$-0.827020\pi$
$373$	−4.59987e6	−1.71188	−0.855940	+	0.517076i	$0.827020\pi$
$374$	−196634.	−0.0726910
$375$	−84477.0	−0.0310213
$376$	965471.	0.352184
$377$	4.27109e6	1.54770
$378$	−1.67701e6	−0.603680
$379$	6993.69	0.00250097	0.00125048	−	0.999999i	$-0.499602\pi$
$379$	6993.69	0.00250097	0.00125048	+	0.999999i	$0.499602\pi$
$380$	0	0
$381$	433228.	0.152899
$382$	2.32634e6	0.815672
$383$	−1.37680e6	−0.479594	−0.239797	−	0.970823i	$-0.577081\pi$
$383$	−1.37680e6	−0.479594	−0.239797	+	0.970823i	$0.577081\pi$
$384$	286396.	0.0991150
$385$	−3.28944e6	−1.13102
$386$	731327.	0.249829
$387$	687210.	0.233245
$388$	−2.22472e6	−0.750234
$389$	1.40115e6	0.469473	0.234736	−	0.972059i	$-0.424577\pi$
$389$	1.40115e6	0.469473	0.234736	+	0.972059i	$0.424577\pi$
$390$	5.00690e6	1.66689
$391$	398062.	0.131677
$392$	55103.7	0.0181120
$393$	−2.66660e6	−0.870916
$394$	−373380.	−0.121174
$395$	2.46407e6	0.794620
$396$	311815.	0.0999215
$397$	3.33402e6	1.06168	0.530839	−	0.847473i	$-0.321877\pi$
$397$	3.33402e6	1.06168	0.530839	+	0.847473i	$0.321877\pi$
$398$	2.89266e6	0.915357
$399$	0	0
$400$	815574.	0.254867
$401$	5.32612e6	1.65406	0.827028	−	0.562161i	$-0.190030\pi$
$401$	5.32612e6	1.65406	0.827028	+	0.562161i	$0.190030\pi$
$402$	−4.38826e6	−1.35434
$403$	−5.93822e6	−1.82135
$404$	−1.95605e6	−0.596247
$405$	5.58764e6	1.69274
$406$	−2.51927e6	−0.758506
$407$	−2.65060e6	−0.793155
$408$	−176539.	−0.0525039
$409$	3.00861e6	0.889319	0.444659	−	0.895700i	$-0.353325\pi$
$409$	3.00861e6	0.889319	0.444659	+	0.895700i	$0.353325\pi$
$410$	6.27300e6	1.84296
$411$	3.36085e6	0.981395
$412$	1.15092e6	0.334042
$413$	5.40670e6	1.55976
$414$	−631231.	−0.181004
$415$	−3.26253e6	−0.929895
$416$	−923035.	−0.261508
$417$	−5.99280e6	−1.68768
$418$	0	0
$419$	2.47470e6	0.688633	0.344317	−	0.938854i	$-0.388111\pi$
$419$	2.47470e6	0.688633	0.344317	+	0.938854i	$0.388111\pi$
$420$	−2.95328e6	−0.816924
$421$	3.25587e6	0.895286	0.447643	−	0.894212i	$-0.352263\pi$
$421$	3.25587e6	0.895286	0.447643	+	0.894212i	$0.352263\pi$
$422$	−342966.	−0.0937496
$423$	943736.	0.256448
$424$	−1.38878e6	−0.375161
$425$	−502733.	−0.135010
$426$	3.86740e6	1.03251
$427$	817702.	0.217033
$428$	−237332.	−0.0626249
$429$	−4.90853e6	−1.28768
$430$	−3.49061e6	−0.910396
$431$	3.54756e6	0.919891	0.459945	−	0.887947i	$-0.347869\pi$
$431$	3.54756e6	0.919891	0.459945	+	0.887947i	$0.347869\pi$
$432$	−807462.	−0.208168
$433$	−2.58960e6	−0.663763	−0.331881	−	0.943321i	$-0.607683\pi$
$433$	−2.58960e6	−0.663763	−0.331881	+	0.943321i	$0.607683\pi$
$434$	3.50261e6	0.892621
$435$	6.57979e6	1.66720
$436$	−2.24040e6	−0.564429
$437$	0	0
$438$	−3.39313e6	−0.845114
$439$	3.47682e6	0.861036	0.430518	−	0.902582i	$-0.358331\pi$
$439$	3.47682e6	0.861036	0.430518	+	0.902582i	$0.358331\pi$
$440$	−1.58383e6	−0.390011
$441$	53863.2	0.0131885
$442$	568974.	0.138528
$443$	−3.22496e6	−0.780756	−0.390378	−	0.920655i	$-0.627656\pi$
$443$	−3.22496e6	−0.780756	−0.390378	+	0.920655i	$0.627656\pi$
$444$	−2.37972e6	−0.572886
$445$	−1.35570e6	−0.324537
$446$	−444424.	−0.105794
$447$	5.87089e6	1.38975
$448$	544444.	0.128162
$449$	4.47721e6	1.04807	0.524036	−	0.851696i	$-0.324426\pi$
$449$	4.47721e6	1.04807	0.524036	+	0.851696i	$0.324426\pi$
$450$	797213.	0.185585
$451$	−6.14975e6	−1.42369
$452$	−3.76275e6	−0.866282
$453$	−4.66169e6	−1.06733
$454$	1.25720e6	0.286262
$455$	9.51821e6	2.15539
$456$	0	0
$457$	563938.	0.126311	0.0631555	−	0.998004i	$-0.479884\pi$
$457$	563938.	0.126311	0.0631555	+	0.998004i	$0.479884\pi$
$458$	5.83259e6	1.29926
$459$	497733.	0.110272
$460$	3.20627e6	0.706489
$461$	−3.05325e6	−0.669130	−0.334565	−	0.942373i	$-0.608589\pi$
$461$	−3.05325e6	−0.669130	−0.334565	+	0.942373i	$0.608589\pi$
$462$	2.89526e6	0.631076
$463$	7.31911e6	1.58674	0.793370	−	0.608740i	$-0.208325\pi$
$463$	7.31911e6	1.58674	0.793370	+	0.608740i	$0.208325\pi$
$464$	−1.21300e6	−0.261557
$465$	−9.14806e6	−1.96199
$466$	5.54502e6	1.18287
$467$	−3.83007e6	−0.812671	−0.406336	−	0.913724i	$-0.633194\pi$
$467$	−3.83007e6	−0.812671	−0.406336	+	0.913724i	$0.633194\pi$
$468$	−902256.	−0.190421
$469$	−8.34216e6	−1.75124
$470$	−4.79361e6	−1.00096
$471$	−3.03771e6	−0.630948
$472$	2.60327e6	0.537853
$473$	3.42203e6	0.703284
$474$	−2.16879e6	−0.443374
$475$	0	0
$476$	−335604.	−0.0678907
$477$	−1.35751e6	−0.273179
$478$	1.46047e6	0.292363
$479$	−852140.	−0.169696	−0.0848481	−	0.996394i	$-0.527040\pi$
$479$	−852140.	−0.169696	−0.0848481	+	0.996394i	$0.527040\pi$
$480$	−1.42197e6	−0.281701
$481$	7.66967e6	1.51152
$482$	1.24925e6	0.244924
$483$	−5.86109e6	−1.14317
$484$	−1.02410e6	−0.198715
$485$	1.10459e7	2.13228
$486$	−1.85222e6	−0.355714
$487$	1.76953e6	0.338093	0.169046	−	0.985608i	$-0.445931\pi$
$487$	1.76953e6	0.338093	0.169046	+	0.985608i	$0.445931\pi$
$488$	393715.	0.0748397
$489$	−7.10253e6	−1.34320
$490$	−273592.	−0.0514771
$491$	−1.12702e6	−0.210973	−0.105487	−	0.994421i	$-0.533640\pi$
$491$	−1.12702e6	−0.210973	−0.105487	+	0.994421i	$0.533640\pi$
$492$	−5.52127e6	−1.02832
$493$	747713.	0.138553
$494$	0	0
$495$	−1.54818e6	−0.283993
$496$	1.68647e6	0.307803
$497$	7.35199e6	1.33510
$498$	2.87156e6	0.518854
$499$	−5.96123e6	−1.07173	−0.535864	−	0.844304i	$-0.680014\pi$
$499$	−5.96123e6	−1.07173	−0.535864	+	0.844304i	$0.680014\pi$
$500$	−77323.4	−0.0138320
$501$	5.58835e6	0.994694
$502$	−3.88038e6	−0.687250
$503$	−5.66845e6	−0.998951	−0.499476	−	0.866328i	$-0.666474\pi$
$503$	−5.66845e6	−0.998951	−0.499476	+	0.866328i	$0.666474\pi$
$504$	532188.	0.0933230
$505$	9.71188e6	1.69463
$506$	−3.14327e6	−0.545765
$507$	7.71283e6	1.33258
$508$	396542.	0.0681757
$509$	−8.42220e6	−1.44089	−0.720446	−	0.693512i	$-0.756063\pi$
$509$	−8.42220e6	−1.44089	−0.720446	+	0.693512i	$0.756063\pi$
$510$	876526.	0.149224
$511$	−6.45040e6	−1.09278
$512$	262144.	0.0441942
$513$	0	0
$514$	−5.15951e6	−0.861392
$515$	−5.71436e6	−0.949401
$516$	3.07232e6	0.507974
$517$	4.69943e6	0.773247
$518$	−4.52389e6	−0.740777
$519$	7.46955e6	1.21724
$520$	4.58291e6	0.743247
$521$	−5.81861e6	−0.939128	−0.469564	−	0.882899i	$-0.655589\pi$
$521$	−5.81861e6	−0.939128	−0.469564	+	0.882899i	$0.655589\pi$
$522$	−1.18569e6	−0.190457
$523$	−4.81037e6	−0.768996	−0.384498	−	0.923126i	$-0.625625\pi$
$523$	−4.81037e6	−0.768996	−0.384498	+	0.923126i	$0.625625\pi$
$524$	−2.44079e6	−0.388331
$525$	7.40226e6	1.17210
$526$	−2.00571e6	−0.316084
$527$	−1.03957e6	−0.163052
$528$	1.39403e6	0.217615
$529$	−73173.3	−0.0113688
$530$	6.89534e6	1.06627
$531$	2.54466e6	0.391646
$532$	0	0
$533$	1.77947e7	2.71314
$534$	1.19324e6	0.181082
$535$	1.17836e6	0.177990
$536$	−4.01666e6	−0.603883
$537$	−6.32691e6	−0.946795
$538$	−5.71944e6	−0.851918
$539$	268217.	0.0397662
$540$	4.00909e6	0.591645
$541$	3.11994e6	0.458304	0.229152	−	0.973391i	$-0.426405\pi$
$541$	3.11994e6	0.458304	0.229152	+	0.973391i	$0.426405\pi$
$542$	−2.83802e6	−0.414971
$543$	7.28378e6	1.06012
$544$	−161590.	−0.0234108
$545$	1.11237e7	1.60420
$546$	−8.37760e6	−1.20265
$547$	−2.61616e6	−0.373848	−0.186924	−	0.982374i	$-0.559852\pi$
$547$	−2.61616e6	−0.373848	−0.186924	+	0.982374i	$0.559852\pi$
$548$	3.07624e6	0.437592
$549$	384851.	0.0544957
$550$	3.96980e6	0.559580
$551$	0	0
$552$	−2.82205e6	−0.394200
$553$	−4.12290e6	−0.573310
$554$	−3.06696e6	−0.424555
$555$	1.18154e7	1.62823
$556$	−5.48532e6	−0.752515
$557$	1.91062e6	0.260937	0.130469	−	0.991452i	$-0.458352\pi$
$557$	1.91062e6	0.260937	0.130469	+	0.991452i	$0.458352\pi$
$558$	1.64850e6	0.224132
$559$	−9.90185e6	−1.34025
$560$	−2.70319e6	−0.364256
$561$	−859305.	−0.115276
$562$	−23901.3	−0.00319213
$563$	−84059.8	−0.0111768	−0.00558840	−	0.999984i	$-0.501779\pi$
$563$	−84059.8	−0.0111768	−0.00558840	+	0.999984i	$0.501779\pi$
$564$	4.21917e6	0.558508
$565$	1.86822e7	2.46211
$566$	−756986.	−0.0993222
$567$	−9.34930e6	−1.22130
$568$	3.53990e6	0.460384
$569$	2.22862e6	0.288572	0.144286	−	0.989536i	$-0.453911\pi$
$569$	2.22862e6	0.288572	0.144286	+	0.989536i	$0.453911\pi$
$570$	0	0
$571$	8.28284e6	1.06314	0.531568	−	0.847015i	$-0.321603\pi$
$571$	8.28284e6	1.06314	0.531568	+	0.847015i	$0.321603\pi$
$572$	−4.49287e6	−0.574161
$573$	1.01663e7	1.29353
$574$	−1.04960e7	−1.32968
$575$	−8.03637e6	−1.01366
$576$	256243.	0.0321807
$577$	−1.50122e7	−1.87717	−0.938585	−	0.345047i	$-0.887863\pi$
$577$	−1.50122e7	−1.87717	−0.938585	+	0.345047i	$0.887863\pi$
$578$	−5.57982e6	−0.694705
$579$	3.19595e6	0.396190
$580$	6.02260e6	0.743385
$581$	5.45889e6	0.670910
$582$	−9.72218e6	−1.18975
$583$	−6.75986e6	−0.823695
$584$	−3.10580e6	−0.376826
$585$	4.47974e6	0.541207
$586$	−3.94472e6	−0.474539
$587$	−4.07944e6	−0.488658	−0.244329	−	0.969692i	$-0.578568\pi$
$587$	−4.07944e6	−0.488658	−0.244329	+	0.969692i	$0.578568\pi$
$588$	240807.	0.0287227
$589$	0	0
$590$	−1.29253e7	−1.52866
$591$	−1.63169e6	−0.192163
$592$	−2.17820e6	−0.255443
$593$	−545602.	−0.0637147	−0.0318573	−	0.999492i	$-0.510142\pi$
$593$	−545602.	−0.0637147	−0.0318573	+	0.999492i	$0.510142\pi$
$594$	−3.93032e6	−0.457048
$595$	1.66629e6	0.192956
$596$	5.37374e6	0.619671
$597$	1.26411e7	1.45161
$598$	9.09526e6	1.04007
$599$	8.45396e6	0.962704	0.481352	−	0.876527i	$-0.340146\pi$
$599$	8.45396e6	0.962704	0.481352	+	0.876527i	$0.340146\pi$
$600$	3.56411e6	0.404178
$601$	5.39862e6	0.609673	0.304836	−	0.952405i	$-0.401398\pi$
$601$	5.39862e6	0.609673	0.304836	+	0.952405i	$0.401398\pi$
$602$	5.84052e6	0.656841
$603$	−3.92623e6	−0.439727
$604$	−4.26693e6	−0.475908
$605$	5.08472e6	0.564779
$606$	−8.54806e6	−0.945553
$607$	1.14275e7	1.25886	0.629432	−	0.777055i	$-0.283288\pi$
$607$	1.14275e7	1.25886	0.629432	+	0.777055i	$0.283288\pi$
$608$	0	0
$609$	−1.10094e7	−1.20287
$610$	−1.95481e6	−0.212706
$611$	−1.35981e7	−1.47358
$612$	−157952.	−0.0170470
$613$	−894639.	−0.0961605	−0.0480802	−	0.998843i	$-0.515310\pi$
$613$	−894639.	−0.0961605	−0.0480802	+	0.998843i	$0.515310\pi$
$614$	5.82888e6	0.623971
$615$	2.74134e7	2.92264
$616$	2.65008e6	0.281389
$617$	1.18925e7	1.25765	0.628826	−	0.777546i	$-0.283536\pi$
$617$	1.18925e7	1.25765	0.628826	+	0.777546i	$0.283536\pi$
$618$	5.02958e6	0.529738
$619$	1.03513e7	1.08585	0.542924	−	0.839782i	$-0.317317\pi$
$619$	1.03513e7	1.08585	0.542924	+	0.839782i	$0.317317\pi$
$620$	−8.37339e6	−0.874826
$621$	7.95645e6	0.827923
$622$	9.62106e6	0.997118
$623$	2.26837e6	0.234150
$624$	−4.03372e6	−0.414710
$625$	−9.57182e6	−0.980154
$626$	−1.28152e7	−1.30704
$627$	0	0
$628$	−2.78047e6	−0.281332
$629$	1.34268e6	0.135315
$630$	−2.64234e6	−0.265239
$631$	−1.17088e6	−0.117068	−0.0585342	−	0.998285i	$-0.518643\pi$
$631$	−1.17088e6	−0.117068	−0.0585342	+	0.998285i	$0.518643\pi$
$632$	−1.98513e6	−0.197695
$633$	−1.49878e6	−0.148672
$634$	2.41219e6	0.238335
$635$	−1.96885e6	−0.193766
$636$	−6.06904e6	−0.594946
$637$	−776102.	−0.0757828
$638$	−5.90427e6	−0.574268
$639$	3.46021e6	0.335236
$640$	−1.30156e6	−0.125607
$641$	4.72990e6	0.454681	0.227341	−	0.973815i	$-0.426997\pi$
$641$	4.72990e6	0.454681	0.227341	+	0.973815i	$0.426997\pi$
$642$	−1.03716e6	−0.0993131
$643$	−1.49075e7	−1.42193	−0.710963	−	0.703229i	$-0.751741\pi$
$643$	−1.49075e7	−1.42193	−0.710963	+	0.703229i	$0.751741\pi$
$644$	−5.36476e6	−0.509725
$645$	−1.52542e7	−1.44374
$646$	0	0
$647$	−4.27732e6	−0.401708	−0.200854	−	0.979621i	$-0.564372\pi$
$647$	−4.27732e6	−0.401708	−0.200854	+	0.979621i	$0.564372\pi$
$648$	−4.50158e6	−0.421141
$649$	1.26714e7	1.18090
$650$	−1.14869e7	−1.06639
$651$	1.53066e7	1.41555
$652$	−6.50108e6	−0.598917
$653$	2.25370e6	0.206829	0.103415	−	0.994638i	$-0.467023\pi$
$653$	2.25370e6	0.206829	0.103415	+	0.994638i	$0.467023\pi$
$654$	−9.79069e6	−0.895094
$655$	1.21186e7	1.10370
$656$	−5.05372e6	−0.458513
$657$	−3.03588e6	−0.274392
$658$	8.02071e6	0.722184
$659$	2.93133e6	0.262937	0.131468	−	0.991320i	$-0.458031\pi$
$659$	2.93133e6	0.262937	0.131468	+	0.991320i	$0.458031\pi$
$660$	−6.92144e6	−0.618496
$661$	−6.56037e6	−0.584016	−0.292008	−	0.956416i	$-0.594323\pi$
$661$	−6.56037e6	−0.584016	−0.292008	+	0.956416i	$0.594323\pi$
$662$	1.50967e7	1.33886
$663$	2.48645e6	0.219683
$664$	2.62840e6	0.231351
$665$	0	0
$666$	−2.12917e6	−0.186005
$667$	1.19525e7	1.04026
$668$	5.11512e6	0.443522
$669$	−1.94216e6	−0.167772
$670$	1.99429e7	1.71633
$671$	1.91640e6	0.164316
$672$	2.37926e6	0.203244
$673$	3.19596e6	0.271996	0.135998	−	0.990709i	$-0.456576\pi$
$673$	3.19596e6	0.271996	0.135998	+	0.990709i	$0.456576\pi$
$674$	8.51402e6	0.721913
$675$	−1.00486e7	−0.848880
$676$	7.05970e6	0.594182
$677$	2.06961e6	0.173547	0.0867734	−	0.996228i	$-0.472344\pi$
$677$	2.06961e6	0.173547	0.0867734	+	0.996228i	$0.472344\pi$
$678$	−1.64435e7	−1.37379
$679$	−1.84820e7	−1.53842
$680$	802301.	0.0665373
$681$	5.49402e6	0.453965
$682$	8.20887e6	0.675807
$683$	2.61594e6	0.214574	0.107287	−	0.994228i	$-0.465784\pi$
$683$	2.61594e6	0.214574	0.107287	+	0.994228i	$0.465784\pi$
$684$	0	0
$685$	−1.52737e7	−1.24371
$686$	−8.47824e6	−0.687852
$687$	2.54888e7	2.06043
$688$	2.81215e6	0.226499
$689$	1.95601e7	1.56972
$690$	1.40116e7	1.12038
$691$	−1.40203e7	−1.11703	−0.558513	−	0.829496i	$-0.688628\pi$
$691$	−1.40203e7	−1.11703	−0.558513	+	0.829496i	$0.688628\pi$
$692$	6.83701e6	0.542752
$693$	2.59042e6	0.204898
$694$	9.61221e6	0.757573
$695$	2.72349e7	2.13877
$696$	−5.30088e6	−0.414787
$697$	3.11520e6	0.242887
$698$	1.48748e7	1.15561
$699$	2.42321e7	1.87585
$700$	6.77543e6	0.522627
$701$	3.42664e6	0.263375	0.131687	−	0.991291i	$-0.457961\pi$
$701$	3.42664e6	0.263375	0.131687	+	0.991291i	$0.457961\pi$
$702$	1.13726e7	0.870999
$703$	0	0
$704$	1.27598e6	0.0970318
$705$	−2.09484e7	−1.58737
$706$	−8.16770e6	−0.616720
$707$	−1.62500e7	−1.22266
$708$	1.13764e7	0.852950
$709$	8.04969e6	0.601400	0.300700	−	0.953719i	$-0.402780\pi$
$709$	8.04969e6	0.601400	0.300700	+	0.953719i	$0.402780\pi$
$710$	−1.75758e7	−1.30848
$711$	−1.94044e6	−0.143955
$712$	1.09220e6	0.0807422
$713$	−1.66178e7	−1.22420
$714$	−1.46661e6	−0.107664
$715$	2.23073e7	1.63186
$716$	−5.79114e6	−0.422164
$717$	6.38234e6	0.463641
$718$	−3.79797e6	−0.274942
$719$	−2.66646e7	−1.92359	−0.961795	−	0.273771i	$-0.911729\pi$
$719$	−2.66646e7	−1.92359	−0.961795	+	0.273771i	$0.911729\pi$
$720$	−1.27226e6	−0.0914626
$721$	9.56132e6	0.684983
$722$	0	0
$723$	5.45929e6	0.388410
$724$	6.66698e6	0.472697
$725$	−1.50954e7	−1.06659
$726$	−4.47540e6	−0.315130
$727$	1.25706e7	0.882102	0.441051	−	0.897482i	$-0.354606\pi$
$727$	1.25706e7	0.882102	0.441051	+	0.897482i	$0.354606\pi$
$728$	−7.66817e6	−0.536245
$729$	8.99764e6	0.627061
$730$	1.54204e7	1.07100
$731$	−1.73345e6	−0.119983
$732$	1.72056e6	0.118684
$733$	−1.12272e7	−0.771814	−0.385907	−	0.922538i	$-0.626111\pi$
$733$	−1.12272e7	−0.771814	−0.385907	+	0.922538i	$0.626111\pi$
$734$	6.97671e6	0.477981
$735$	−1.19562e6	−0.0816345
$736$	−2.58307e6	−0.175769
$737$	−1.95511e7	−1.32587
$738$	−4.93996e6	−0.333874
$739$	1.05677e7	0.711820	0.355910	−	0.934520i	$-0.384171\pi$
$739$	1.05677e7	0.711820	0.355910	+	0.934520i	$0.384171\pi$
$740$	1.08149e7	0.726010
$741$	0	0
$742$	−1.15373e7	−0.769301
$743$	5.83579e6	0.387817	0.193909	−	0.981020i	$-0.437883\pi$
$743$	5.83579e6	0.387817	0.193909	+	0.981020i	$0.437883\pi$
$744$	7.36997e6	0.488127
$745$	−2.66809e7	−1.76120
$746$	−1.83995e7	−1.21048
$747$	2.56923e6	0.168462
$748$	−786538.	−0.0514003
$749$	−1.97165e6	−0.128418
$750$	−337908.	−0.0219354
$751$	−4.48767e6	−0.290349	−0.145175	−	0.989406i	$-0.546374\pi$
$751$	−4.48767e6	−0.290349	−0.145175	+	0.989406i	$0.546374\pi$
$752$	3.86188e6	0.249032
$753$	−1.69575e7	−1.08987
$754$	1.70844e7	1.09439
$755$	2.11855e7	1.35261
$756$	−6.70805e6	−0.426866
$757$	7.81327e6	0.495557	0.247778	−	0.968817i	$-0.420300\pi$
$757$	7.81327e6	0.495557	0.247778	+	0.968817i	$0.420300\pi$
$758$	27974.8	0.00176845
$759$	−1.37363e7	−0.865497
$760$	0	0
$761$	1.81639e7	1.13697	0.568483	−	0.822695i	$-0.307531\pi$
$761$	1.81639e7	1.13697	0.568483	+	0.822695i	$0.307531\pi$
$762$	1.73291e6	0.108116
$763$	−1.86123e7	−1.15741
$764$	9.30537e6	0.576767
$765$	784240.	0.0484502
$766$	−5.50720e6	−0.339124
$767$	−3.66655e7	−2.25045
$768$	1.14559e6	0.0700849
$769$	−4.47189e6	−0.272694	−0.136347	−	0.990661i	$-0.543536\pi$
$769$	−4.47189e6	−0.272694	−0.136347	+	0.990661i	$0.543536\pi$
$770$	−1.31578e7	−0.799753
$771$	−2.25474e7	−1.36603
$772$	2.92531e6	0.176656
$773$	2.53207e7	1.52415	0.762075	−	0.647489i	$-0.224181\pi$
$773$	2.53207e7	1.52415	0.762075	+	0.647489i	$0.224181\pi$
$774$	2.74884e6	0.164929
$775$	2.09875e7	1.25518
$776$	−8.89889e6	−0.530496
$777$	−1.97697e7	−1.17475
$778$	5.60460e6	0.331967
$779$	0	0
$780$	2.00276e7	1.17867
$781$	1.72305e7	1.01081
$782$	1.59225e6	0.0931095
$783$	1.49452e7	0.871161
$784$	220415.	0.0128071
$785$	1.38052e7	0.799590
$786$	−1.06664e7	−0.615831
$787$	−4.73524e6	−0.272524	−0.136262	−	0.990673i	$-0.543509\pi$
$787$	−4.73524e6	−0.272524	−0.136262	+	0.990673i	$0.543509\pi$
$788$	−1.49352e6	−0.0856831
$789$	−8.76506e6	−0.501259
$790$	9.85626e6	0.561881
$791$	−3.12593e7	−1.77639
$792$	1.24726e6	0.0706552
$793$	−5.54523e6	−0.313139
$794$	1.33361e7	0.750719
$795$	3.01331e7	1.69093
$796$	1.15707e7	0.647255
$797$	−1.54780e7	−0.863116	−0.431558	−	0.902085i	$-0.642036\pi$
$797$	−1.54780e7	−0.863116	−0.431558	+	0.902085i	$0.642036\pi$
$798$	0	0
$799$	−2.38053e6	−0.131919
$800$	3.26229e6	0.180218
$801$	1.06761e6	0.0587937
$802$	2.13045e7	1.16959
$803$	−1.51175e7	−0.827351
$804$	−1.75530e7	−0.957662
$805$	2.66363e7	1.44872
$806$	−2.37529e7	−1.28789
$807$	−2.49943e7	−1.35101
$808$	−7.82420e6	−0.421611
$809$	5.54794e6	0.298031	0.149015	−	0.988835i	$-0.452390\pi$
$809$	5.54794e6	0.298031	0.149015	+	0.988835i	$0.452390\pi$
$810$	2.23506e7	1.19695
$811$	−9.82955e6	−0.524785	−0.262392	−	0.964961i	$-0.584511\pi$
$811$	−9.82955e6	−0.524785	−0.262392	+	0.964961i	$0.584511\pi$
$812$	−1.00771e7	−0.536345
$813$	−1.24023e7	−0.658078
$814$	−1.06024e7	−0.560845
$815$	3.22782e7	1.70222
$816$	−706158.	−0.0371258
$817$	0	0
$818$	1.20344e7	0.628843
$819$	−7.49555e6	−0.390475
$820$	2.50920e7	1.30317
$821$	1.78229e7	0.922830	0.461415	−	0.887185i	$-0.347342\pi$
$821$	1.78229e7	0.922830	0.461415	+	0.887185i	$0.347342\pi$
$822$	1.34434e7	0.693951
$823$	−1.29509e7	−0.666502	−0.333251	−	0.942838i	$-0.608146\pi$
$823$	−1.29509e7	−0.666502	−0.333251	+	0.942838i	$0.608146\pi$
$824$	4.60367e6	0.236204
$825$	1.73483e7	0.887404
$826$	2.16268e7	1.10292
$827$	2.57276e7	1.30808	0.654042	−	0.756458i	$-0.273072\pi$
$827$	2.57276e7	1.30808	0.654042	+	0.756458i	$0.273072\pi$
$828$	−2.52492e6	−0.127989
$829$	−2.26984e7	−1.14712	−0.573559	−	0.819164i	$-0.694438\pi$
$829$	−2.26984e7	−1.14712	−0.573559	+	0.819164i	$0.694438\pi$
$830$	−1.30501e7	−0.657535
$831$	−1.34028e7	−0.673276
$832$	−3.69214e6	−0.184914
$833$	−135867.	−0.00678426
$834$	−2.39712e7	−1.19337
$835$	−2.53968e7	−1.26056
$836$	0	0
$837$	−2.07788e7	−1.02519
$838$	9.89881e6	0.486937
$839$	9.22885e6	0.452629	0.226315	−	0.974054i	$-0.427332\pi$
$839$	9.22885e6	0.452629	0.226315	+	0.974054i	$0.427332\pi$
$840$	−1.18131e7	−0.577652
$841$	1.94015e6	0.0945898
$842$	1.30235e7	0.633063
$843$	−104450.	−0.00506221
$844$	−1.37186e6	−0.0662910
$845$	−3.50517e7	−1.68876
$846$	3.77495e6	0.181336
$847$	−8.50780e6	−0.407482
$848$	−5.55511e6	−0.265279
$849$	−3.30807e6	−0.157509
$850$	−2.01093e6	−0.0954662
$851$	2.14632e7	1.01595
$852$	1.54696e7	0.730096
$853$	−3.17055e7	−1.49198	−0.745989	−	0.665959i	$-0.768023\pi$
$853$	−3.17055e7	−1.49198	−0.745989	+	0.665959i	$0.768023\pi$
$854$	3.27081e6	0.153465
$855$	0	0
$856$	−949328.	−0.0442825
$857$	−3.01353e7	−1.40160	−0.700799	−	0.713359i	$-0.747173\pi$
$857$	−3.01353e7	−1.40160	−0.700799	+	0.713359i	$0.747173\pi$
$858$	−1.96341e7	−0.910528
$859$	−1.58417e7	−0.732520	−0.366260	−	0.930513i	$-0.619362\pi$
$859$	−1.58417e7	−0.732520	−0.366260	+	0.930513i	$0.619362\pi$
$860$	−1.39624e7	−0.643747
$861$	−4.58683e7	−2.10865
$862$	1.41902e7	0.650461
$863$	2.32831e7	1.06418	0.532089	−	0.846689i	$-0.321407\pi$
$863$	2.32831e7	1.06418	0.532089	+	0.846689i	$0.321407\pi$
$864$	−3.22985e6	−0.147197
$865$	−3.39461e7	−1.54259
$866$	−1.03584e7	−0.469351
$867$	−2.43842e7	−1.10169
$868$	1.40104e7	0.631178
$869$	−9.66261e6	−0.434055
$870$	2.63191e7	1.17889
$871$	5.65722e7	2.52672
$872$	−8.96160e6	−0.399111
$873$	−8.69856e6	−0.386289
$874$	0	0
$875$	−642369.	−0.0283638
$876$	−1.35725e7	−0.597586
$877$	−2.89258e7	−1.26995	−0.634975	−	0.772532i	$-0.718990\pi$
$877$	−2.89258e7	−1.26995	−0.634975	+	0.772532i	$0.718990\pi$
$878$	1.39073e7	0.608844
$879$	−1.72387e7	−0.752544
$880$	−6.33533e6	−0.275780
$881$	−2.35636e7	−1.02283	−0.511413	−	0.859335i	$-0.670878\pi$
$881$	−2.35636e7	−1.02283	−0.511413	+	0.859335i	$0.670878\pi$
$882$	215453.	0.00932569
$883$	−1.91319e6	−0.0825764	−0.0412882	−	0.999147i	$-0.513146\pi$
$883$	−1.91319e6	−0.0825764	−0.0412882	+	0.999147i	$0.513146\pi$
$884$	2.27589e6	0.0979538
$885$	−5.64846e7	−2.42422
$886$	−1.28998e7	−0.552078
$887$	−3.48791e7	−1.48852	−0.744262	−	0.667888i	$-0.767199\pi$
$887$	−3.48791e7	−1.48852	−0.744262	+	0.667888i	$0.767199\pi$
$888$	−9.51888e6	−0.405092
$889$	3.29430e6	0.139800
$890$	−5.42280e6	−0.229482
$891$	−2.19114e7	−0.924648
$892$	−1.77770e6	−0.0748076
$893$	0	0
$894$	2.34836e7	0.982699
$895$	2.87533e7	1.19986
$896$	2.17778e6	0.0906241
$897$	3.97468e7	1.64938
$898$	1.79088e7	0.741099
$899$	−3.12146e7	−1.28813
$900$	3.18885e6	0.131229
$901$	3.42426e6	0.140525
$902$	−2.45990e7	−1.00670
$903$	2.55235e7	1.04165
$904$	−1.50510e7	−0.612554
$905$	−3.31018e7	−1.34348
$906$	−1.86467e7	−0.754714
$907$	−1.34601e7	−0.543287	−0.271644	−	0.962398i	$-0.587567\pi$
$907$	−1.34601e7	−0.543287	−0.271644	+	0.962398i	$0.587567\pi$
$908$	5.02878e6	0.202418
$909$	−7.64806e6	−0.307002
$910$	3.80728e7	1.52409
$911$	1.42316e7	0.568144	0.284072	−	0.958803i	$-0.408315\pi$
$911$	1.42316e7	0.568144	0.284072	+	0.958803i	$0.408315\pi$
$912$	0	0
$913$	1.27937e7	0.507948
$914$	2.25575e6	0.0893154
$915$	−8.54265e6	−0.337318
$916$	2.33303e7	0.918718
$917$	−2.02770e7	−0.796307
$918$	1.99093e6	0.0779740
$919$	1.48289e7	0.579188	0.289594	−	0.957150i	$-0.406480\pi$
$919$	1.48289e7	0.579188	0.289594	+	0.957150i	$0.406480\pi$
$920$	1.28251e7	0.499563
$921$	2.54726e7	0.989518
$922$	−1.22130e7	−0.473146
$923$	−4.98574e7	−1.92631
$924$	1.15810e7	0.446238
$925$	−2.71070e7	−1.04166
$926$	2.92764e7	1.12199
$927$	4.50003e6	0.171995
$928$	−4.85200e6	−0.184948
$929$	1.48557e7	0.564748	0.282374	−	0.959304i	$-0.408878\pi$
$929$	1.48557e7	0.564748	0.282374	+	0.959304i	$0.408878\pi$
$930$	−3.65922e7	−1.38734
$931$	0	0
$932$	2.21801e7	0.836418
$933$	4.20446e7	1.58127
$934$	−1.53203e7	−0.574645
$935$	3.90520e6	0.146088
$936$	−3.60902e6	−0.134648
$937$	9.74272e6	0.362519	0.181260	−	0.983435i	$-0.441983\pi$
$937$	9.74272e6	0.362519	0.181260	+	0.983435i	$0.441983\pi$
$938$	−3.33686e7	−1.23832
$939$	−5.60032e7	−2.07276
$940$	−1.91744e7	−0.707788
$941$	2.16418e6	0.0796745	0.0398373	−	0.999206i	$-0.487316\pi$
$941$	2.16418e6	0.0796745	0.0398373	+	0.999206i	$0.487316\pi$
$942$	−1.21508e7	−0.446148
$943$	4.97976e7	1.82360
$944$	1.04131e7	0.380320
$945$	3.33058e7	1.21322
$946$	1.36881e7	0.497297
$947$	1.60138e7	0.580254	0.290127	−	0.956988i	$-0.406302\pi$
$947$	1.60138e7	0.580254	0.290127	+	0.956988i	$0.406302\pi$
$948$	−8.67514e6	−0.313513
$949$	4.37433e7	1.57669
$950$	0	0
$951$	1.05414e7	0.377961
$952$	−1.34242e6	−0.0480060
$953$	2.67154e6	0.0952860	0.0476430	−	0.998864i	$-0.484829\pi$
$953$	2.67154e6	0.0952860	0.0476430	+	0.998864i	$0.484829\pi$
$954$	−5.43005e6	−0.193167
$955$	−4.62016e7	−1.63926
$956$	5.84188e6	0.206732
$957$	−2.58020e7	−0.910697
$958$	−3.40856e6	−0.119993
$959$	2.55561e7	0.897321
$960$	−5.68789e6	−0.199192
$961$	1.47694e7	0.515888
$962$	3.06787e7	1.06881
$963$	−927957.	−0.0322450
$964$	4.99699e6	0.173187
$965$	−1.45243e7	−0.502085
$966$	−2.34443e7	−0.808342
$967$	−7.08291e6	−0.243582	−0.121791	−	0.992556i	$-0.538864\pi$
$967$	−7.08291e6	−0.243582	−0.121791	+	0.992556i	$0.538864\pi$
$968$	−4.09641e6	−0.140513
$969$	0	0
$970$	4.41834e7	1.50775
$971$	−2.85104e7	−0.970411	−0.485205	−	0.874400i	$-0.661255\pi$
$971$	−2.85104e7	−0.970411	−0.485205	+	0.874400i	$0.661255\pi$
$972$	−7.40887e6	−0.251528
$973$	−4.55697e7	−1.54310
$974$	7.07813e6	0.239068
$975$	−5.01983e7	−1.69113
$976$	1.57486e6	0.0529197
$977$	2.48752e7	0.833739	0.416869	−	0.908966i	$-0.363127\pi$
$977$	2.48752e7	0.833739	0.416869	+	0.908966i	$0.363127\pi$
$978$	−2.84101e7	−0.949786
$979$	5.31626e6	0.177276
$980$	−1.09437e6	−0.0363998
$981$	−8.75985e6	−0.290619
$982$	−4.50808e6	−0.149181
$983$	2.66082e6	0.0878277	0.0439138	−	0.999035i	$-0.486017\pi$
$983$	2.66082e6	0.0878277	0.0439138	+	0.999035i	$0.486017\pi$
$984$	−2.20851e7	−0.727129
$985$	7.41539e6	0.243525
$986$	2.99085e6	0.0979721
$987$	3.50510e7	1.14527
$988$	0	0
$989$	−2.77099e7	−0.900833
$990$	−6.19271e6	−0.200813
$991$	−5.19709e7	−1.68103	−0.840516	−	0.541786i	$-0.817748\pi$
$991$	−5.19709e7	−1.68103	−0.840516	+	0.541786i	$0.817748\pi$
$992$	6.74587e6	0.217650
$993$	6.59734e7	2.12322
$994$	2.94080e7	0.944058
$995$	−5.74489e7	−1.83960
$996$	1.14863e7	0.366885
$997$	−1.86644e7	−0.594672	−0.297336	−	0.954773i	$-0.596098\pi$
$997$	−1.86644e7	−0.594672	−0.297336	+	0.954773i	$0.596098\pi$
$998$	−2.38449e7	−0.757826
$999$	2.68374e7	0.850799

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.6.a.c.1.2		2
19.18	odd	2		38.6.a.c.1.1	✓	2
57.56	even	2		342.6.a.i.1.2		2
76.75	even	2		304.6.a.f.1.2		2
95.94	odd	2		950.6.a.d.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.a.c.1.1	✓	2	19.18	odd	2
304.6.a.f.1.2		2	76.75	even	2
342.6.a.i.1.2		2	57.56	even	2
722.6.a.c.1.2		2	1.1	even	1	trivial
950.6.a.d.1.2		2	95.94	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	722.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +17.4803 q^{3} +16.0000 q^{4} -79.4408 q^{5} +69.9210 q^{6} +132.921 q^{7} +64.0000 q^{8} +62.5592 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} +17.4803 q^{3} +16.0000 q^{4} -79.4408 q^{5} +69.9210 q^{6} +132.921 q^{7} +64.0000 q^{8} +62.5592 q^{9} -317.763 q^{10} +311.520 q^{11} +279.684 q^{12} -901.401 q^{13} +531.684 q^{14} -1388.64 q^{15} +256.000 q^{16} -157.803 q^{17} +250.237 q^{18} -1271.05 q^{20} +2323.49 q^{21} +1246.08 q^{22} -2522.53 q^{23} +1118.74 q^{24} +3185.83 q^{25} -3605.61 q^{26} -3154.15 q^{27} +2126.74 q^{28} -4738.28 q^{29} -5554.58 q^{30} +6587.76 q^{31} +1024.00 q^{32} +5445.44 q^{33} -631.210 q^{34} -10559.3 q^{35} +1000.95 q^{36} -8508.60 q^{37} -15756.7 q^{39} -5084.21 q^{40} -19741.1 q^{41} +9293.97 q^{42} +10985.0 q^{43} +4984.32 q^{44} -4969.75 q^{45} -10090.1 q^{46} +15085.5 q^{47} +4474.94 q^{48} +860.995 q^{49} +12743.3 q^{50} -2758.43 q^{51} -14422.4 q^{52} -21699.6 q^{53} -12616.6 q^{54} -24747.4 q^{55} +8506.94 q^{56} -18953.1 q^{58} +40676.1 q^{59} -22218.3 q^{60} +6151.79 q^{61} +26351.0 q^{62} +8315.44 q^{63} +4096.00 q^{64} +71608.0 q^{65} +21781.8 q^{66} -62760.3 q^{67} -2524.84 q^{68} -44094.5 q^{69} -42237.4 q^{70} +55311.0 q^{71} +4003.79 q^{72} -48528.1 q^{73} -34034.4 q^{74} +55689.2 q^{75} +41407.5 q^{77} -63026.9 q^{78} -31017.6 q^{79} -20336.8 q^{80} -70337.2 q^{81} -78964.4 q^{82} +41068.7 q^{83} +37175.9 q^{84} +12536.0 q^{85} +43939.8 q^{86} -82826.3 q^{87} +19937.3 q^{88} +17065.6 q^{89} -19879.0 q^{90} -119815. q^{91} -40360.5 q^{92} +115156. q^{93} +60341.9 q^{94} +17899.8 q^{96} -139045. q^{97} +3443.98 q^{98} +19488.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8 q^{2} - 3 q^{3} + 32 q^{4} - 45 q^{5} - 12 q^{6} + 114 q^{7} + 128 q^{8} + 239 q^{9}+O(q^{10}) \) 2 * q + 8 * q^2 - 3 * q^3 + 32 * q^4 - 45 * q^5 - 12 * q^6 + 114 * q^7 + 128 * q^8 + 239 * q^9	\( 2 q + 8 q^{2} - 3 q^{3} + 32 q^{4} - 45 q^{5} - 12 q^{6} + 114 q^{7} + 128 q^{8} + 239 q^{9} - 180 q^{10} + 661 q^{11} - 48 q^{12} - 1613 q^{13} + 456 q^{14} - 2094 q^{15} + 512 q^{16} + 64 q^{17} + 956 q^{18} - 720 q^{20} + 2711 q^{21} + 2644 q^{22} - 3185 q^{23} - 192 q^{24} + 1247 q^{25} - 6452 q^{26} - 1791 q^{27} + 1824 q^{28} + 2481 q^{29} - 8376 q^{30} + 1180 q^{31} + 2048 q^{32} - 1712 q^{33} + 256 q^{34} - 11211 q^{35} + 3824 q^{36} - 10488 q^{37} - 1183 q^{39} - 2880 q^{40} - 16630 q^{41} + 10844 q^{42} + 11303 q^{43} + 10576 q^{44} + 1107 q^{45} - 12740 q^{46} - 12155 q^{47} - 768 q^{48} - 15588 q^{49} + 4988 q^{50} - 7301 q^{51} - 25808 q^{52} - 20585 q^{53} - 7164 q^{54} - 12711 q^{55} + 7296 q^{56} + 9924 q^{58} + 78581 q^{59} - 33504 q^{60} + 43621 q^{61} + 4720 q^{62} + 4977 q^{63} + 8192 q^{64} + 47100 q^{65} - 6848 q^{66} - 7805 q^{67} + 1024 q^{68} - 30527 q^{69} - 44844 q^{70} + 62488 q^{71} + 15296 q^{72} + 16218 q^{73} - 41952 q^{74} + 95397 q^{75} + 34795 q^{77} - 4732 q^{78} - 67122 q^{79} - 11520 q^{80} - 141130 q^{81} - 66520 q^{82} - 10714 q^{83} + 43376 q^{84} + 20175 q^{85} + 45212 q^{86} - 230679 q^{87} + 42304 q^{88} - 128188 q^{89} + 4428 q^{90} - 106351 q^{91} - 50960 q^{92} + 225908 q^{93} - 48620 q^{94} - 3072 q^{96} - 178558 q^{97} - 62352 q^{98} + 81151 q^{99}+O(q^{100}) \) 2 * q + 8 * q^2 - 3 * q^3 + 32 * q^4 - 45 * q^5 - 12 * q^6 + 114 * q^7 + 128 * q^8 + 239 * q^9 - 180 * q^10 + 661 * q^11 - 48 * q^12 - 1613 * q^13 + 456 * q^14 - 2094 * q^15 + 512 * q^16 + 64 * q^17 + 956 * q^18 - 720 * q^20 + 2711 * q^21 + 2644 * q^22 - 3185 * q^23 - 192 * q^24 + 1247 * q^25 - 6452 * q^26 - 1791 * q^27 + 1824 * q^28 + 2481 * q^29 - 8376 * q^30 + 1180 * q^31 + 2048 * q^32 - 1712 * q^33 + 256 * q^34 - 11211 * q^35 + 3824 * q^36 - 10488 * q^37 - 1183 * q^39 - 2880 * q^40 - 16630 * q^41 + 10844 * q^42 + 11303 * q^43 + 10576 * q^44 + 1107 * q^45 - 12740 * q^46 - 12155 * q^47 - 768 * q^48 - 15588 * q^49 + 4988 * q^50 - 7301 * q^51 - 25808 * q^52 - 20585 * q^53 - 7164 * q^54 - 12711 * q^55 + 7296 * q^56 + 9924 * q^58 + 78581 * q^59 - 33504 * q^60 + 43621 * q^61 + 4720 * q^62 + 4977 * q^63 + 8192 * q^64 + 47100 * q^65 - 6848 * q^66 - 7805 * q^67 + 1024 * q^68 - 30527 * q^69 - 44844 * q^70 + 62488 * q^71 + 15296 * q^72 + 16218 * q^73 - 41952 * q^74 + 95397 * q^75 + 34795 * q^77 - 4732 * q^78 - 67122 * q^79 - 11520 * q^80 - 141130 * q^81 - 66520 * q^82 - 10714 * q^83 + 43376 * q^84 + 20175 * q^85 + 45212 * q^86 - 230679 * q^87 + 42304 * q^88 - 128188 * q^89 + 4428 * q^90 - 106351 * q^91 - 50960 * q^92 + 225908 * q^93 - 48620 * q^94 - 3072 * q^96 - 178558 * q^97 - 62352 * q^98 + 81151 * q^99

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