LMFDB - Embedded newform 175.6.b.a.99.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,6,Mod(99,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("175.99");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	175.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$28.0671684673$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	175.99
Dual form			175.6.b.a.99.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.0000i q^{2} +14.0000i q^{3} -68.0000 q^{4} +140.000 q^{6} -49.0000i q^{7} +360.000i q^{8} +47.0000 q^{9} +O(q^{10})$	\(q-10.0000i q^{2} +14.0000i q^{3} -68.0000 q^{4} +140.000 q^{6} -49.0000i q^{7} +360.000i q^{8} +47.0000 q^{9} +232.000 q^{11} -952.000i q^{12} +140.000i q^{13} -490.000 q^{14} +1424.00 q^{16} -1722.00i q^{17} -470.000i q^{18} +98.0000 q^{19} +686.000 q^{21} -2320.00i q^{22} -1824.00i q^{23} -5040.00 q^{24} +1400.00 q^{26} +4060.00i q^{27} +3332.00i q^{28} -3418.00 q^{29} -7644.00 q^{31} -2720.00i q^{32} +3248.00i q^{33} -17220.0 q^{34} -3196.00 q^{36} -10398.0i q^{37} -980.000i q^{38} -1960.00 q^{39} -17962.0 q^{41} -6860.00i q^{42} -10880.0i q^{43} -15776.0 q^{44} -18240.0 q^{46} +9324.00i q^{47} +19936.0i q^{48} -2401.00 q^{49} +24108.0 q^{51} -9520.00i q^{52} -2262.00i q^{53} +40600.0 q^{54} +17640.0 q^{56} +1372.00i q^{57} +34180.0i q^{58} +2730.00 q^{59} +25648.0 q^{61} +76440.0i q^{62} -2303.00i q^{63} +18368.0 q^{64} +32480.0 q^{66} -48404.0i q^{67} +117096. i q^{68} +25536.0 q^{69} -58560.0 q^{71} +16920.0i q^{72} -68082.0i q^{73} -103980. q^{74} -6664.00 q^{76} -11368.0i q^{77} +19600.0i q^{78} -31784.0 q^{79} -45419.0 q^{81} +179620. i q^{82} +20538.0i q^{83} -46648.0 q^{84} -108800. q^{86} -47852.0i q^{87} +83520.0i q^{88} +50582.0 q^{89} +6860.00 q^{91} +124032. i q^{92} -107016. i q^{93} +93240.0 q^{94} +38080.0 q^{96} -58506.0i q^{97} +24010.0i q^{98} +10904.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 136 q^{4} + 280 q^{6} + 94 q^{9}+O(q^{10}) $ 2 * q - 136 * q^4 + 280 * q^6 + 94 * q^9	$ 2 q - 136 q^{4} + 280 q^{6} + 94 q^{9} + 464 q^{11} - 980 q^{14} + 2848 q^{16} + 196 q^{19} + 1372 q^{21} - 10080 q^{24} + 2800 q^{26} - 6836 q^{29} - 15288 q^{31} - 34440 q^{34} - 6392 q^{36} - 3920 q^{39} - 35924 q^{41} - 31552 q^{44} - 36480 q^{46} - 4802 q^{49} + 48216 q^{51} + 81200 q^{54} + 35280 q^{56} + 5460 q^{59} + 51296 q^{61} + 36736 q^{64} + 64960 q^{66} + 51072 q^{69} - 117120 q^{71} - 207960 q^{74} - 13328 q^{76} - 63568 q^{79} - 90838 q^{81} - 93296 q^{84} - 217600 q^{86} + 101164 q^{89} + 13720 q^{91} + 186480 q^{94} + 76160 q^{96} + 21808 q^{99}+O(q^{100}) $ 2 * q - 136 * q^4 + 280 * q^6 + 94 * q^9 + 464 * q^11 - 980 * q^14 + 2848 * q^16 + 196 * q^19 + 1372 * q^21 - 10080 * q^24 + 2800 * q^26 - 6836 * q^29 - 15288 * q^31 - 34440 * q^34 - 6392 * q^36 - 3920 * q^39 - 35924 * q^41 - 31552 * q^44 - 36480 * q^46 - 4802 * q^49 + 48216 * q^51 + 81200 * q^54 + 35280 * q^56 + 5460 * q^59 + 51296 * q^61 + 36736 * q^64 + 64960 * q^66 + 51072 * q^69 - 117120 * q^71 - 207960 * q^74 - 13328 * q^76 - 63568 * q^79 - 90838 * q^81 - 93296 * q^84 - 217600 * q^86 + 101164 * q^89 + 13720 * q^91 + 186480 * q^94 + 76160 * q^96 + 21808 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	− 10.0000i	− 1.76777i	−0.467707	−	0.883883i	$-0.654920\pi$
$2$	− 10.0000i	− 1.76777i	0.467707	−	0.883883i	$-0.345080\pi$
$3$	14.0000i	0.898100i	0.893507	+	0.449050i	$0.148238\pi$
$3$	14.0000i	0.898100i	−0.893507	+	0.449050i	$0.851762\pi$
$4$	−68.0000	−2.12500
$5$	0	0
$5$	0	0
$6$	140.000	1.58763
$7$	− 49.0000i	− 0.377964i
$7$	− 49.0000i	− 0.377964i
$8$	360.000i	1.98874i
$9$	47.0000	0.193416
$10$	0	0
$11$	232.000	0.578104	0.289052	−	0.957313i	$-0.406660\pi$
$11$	232.000	0.578104	0.289052	+	0.957313i	$0.406660\pi$
$12$	− 952.000i	− 1.90846i
$13$	140.000i	0.229757i	0.993380	+	0.114879i	$0.0366479\pi$
$13$	140.000i	0.229757i	−0.993380	+	0.114879i	$0.963352\pi$
$14$	−490.000	−0.668153
$15$	0	0
$16$	1424.00	1.39062
$17$	− 1722.00i	− 1.44514i	−0.691296	−	0.722572i	$-0.742960\pi$
$17$	− 1722.00i	− 1.44514i	0.691296	−	0.722572i	$-0.257040\pi$
$18$	− 470.000i	− 0.341914i
$19$	98.0000	0.0622791	0.0311395	−	0.999515i	$-0.490086\pi$
$19$	98.0000	0.0622791	0.0311395	+	0.999515i	$0.490086\pi$
$20$	0	0
$21$	686.000	0.339450
$22$	− 2320.00i	− 1.02195i
$23$	− 1824.00i	− 0.718961i	−0.933153	−	0.359480i	$-0.882954\pi$
$23$	− 1824.00i	− 0.718961i	0.933153	−	0.359480i	$-0.117046\pi$
$24$	−5040.00	−1.78609
$25$	0	0
$26$	1400.00	0.406158
$27$	4060.00i	1.07181i
$28$	3332.00i	0.803175i
$29$	−3418.00	−0.754705	−0.377352	−	0.926070i	$-0.623165\pi$
$29$	−3418.00	−0.754705	−0.377352	+	0.926070i	$0.623165\pi$
$30$	0	0
$31$	−7644.00	−1.42862	−0.714310	−	0.699830i	$-0.753259\pi$
$31$	−7644.00	−1.42862	−0.714310	+	0.699830i	$0.753259\pi$
$32$	− 2720.00i	− 0.469563i
$33$	3248.00i	0.519196i
$34$	−17220.0	−2.55468
$35$	0	0
$36$	−3196.00	−0.411008
$37$	− 10398.0i	− 1.24866i	−0.781159	−	0.624332i	$-0.785371\pi$
$37$	− 10398.0i	− 1.24866i	0.781159	−	0.624332i	$-0.214629\pi$
$38$	− 980.000i	− 0.110095i
$39$	−1960.00	−0.206345
$40$	0	0
$41$	−17962.0	−1.66876	−0.834382	−	0.551186i	$-0.814175\pi$
$41$	−17962.0	−1.66876	−0.834382	+	0.551186i	$0.814175\pi$
$42$	− 6860.00i	− 0.600069i
$43$	− 10880.0i	− 0.897342i	−0.893697	−	0.448671i	$-0.851898\pi$
$43$	− 10880.0i	− 0.897342i	0.893697	−	0.448671i	$-0.148102\pi$
$44$	−15776.0	−1.22847
$45$	0	0
$46$	−18240.0	−1.27096
$47$	9324.00i	0.615684i	0.951438	+	0.307842i	$0.0996068\pi$
$47$	9324.00i	0.615684i	−0.951438	+	0.307842i	$0.900393\pi$
$48$	19936.0i	1.24892i
$49$	−2401.00	−0.142857
$50$	0	0
$51$	24108.0	1.29788
$52$	− 9520.00i	− 0.488235i
$53$	− 2262.00i	− 0.110612i	−0.998469	−	0.0553061i	$-0.982387\pi$
$53$	− 2262.00i	− 0.110612i	0.998469	−	0.0553061i	$-0.0176135\pi$
$54$	40600.0	1.89471
$55$	0	0
$56$	17640.0	0.751672
$57$	1372.00i	0.0559329i
$58$	34180.0i	1.33414i
$59$	2730.00	0.102102	0.0510508	−	0.998696i	$-0.483743\pi$
$59$	2730.00	0.102102	0.0510508	+	0.998696i	$0.483743\pi$
$60$	0	0
$61$	25648.0	0.882529	0.441264	−	0.897377i	$-0.354530\pi$
$61$	25648.0	0.882529	0.441264	+	0.897377i	$0.354530\pi$
$62$	76440.0i	2.52547i
$63$	− 2303.00i	− 0.0731042i
$64$	18368.0	0.560547
$65$	0	0
$66$	32480.0	0.917817
$67$	− 48404.0i	− 1.31733i	−0.752437	−	0.658664i	$-0.771122\pi$
$67$	− 48404.0i	− 1.31733i	0.752437	−	0.658664i	$-0.228878\pi$
$68$	117096.i	3.07093i
$69$	25536.0	0.645699
$70$	0	0
$71$	−58560.0	−1.37865	−0.689327	−	0.724450i	$-0.742094\pi$
$71$	−58560.0	−1.37865	−0.689327	+	0.724450i	$0.742094\pi$
$72$	16920.0i	0.384653i
$73$	− 68082.0i	− 1.49529i	−0.664099	−	0.747645i	$-0.731185\pi$
$73$	− 68082.0i	− 1.49529i	0.664099	−	0.747645i	$-0.268815\pi$
$74$	−103980.	−2.20735
$75$	0	0
$76$	−6664.00	−0.132343
$77$	− 11368.0i	− 0.218503i
$78$	19600.0i	0.364770i
$79$	−31784.0	−0.572982	−0.286491	−	0.958083i	$-0.592489\pi$
$79$	−31784.0	−0.572982	−0.286491	+	0.958083i	$0.592489\pi$
$80$	0	0
$81$	−45419.0	−0.769175
$82$	179620.i	2.94999i
$83$	20538.0i	0.327237i	0.986524	+	0.163619i	$0.0523167\pi$
$83$	20538.0i	0.327237i	−0.986524	+	0.163619i	$0.947683\pi$
$84$	−46648.0	−0.721331
$85$	0	0
$86$	−108800.	−1.58629
$87$	− 47852.0i	− 0.677801i
$88$	83520.0i	1.14970i
$89$	50582.0	0.676894	0.338447	−	0.940985i	$-0.390098\pi$
$89$	50582.0	0.676894	0.338447	+	0.940985i	$0.390098\pi$
$90$	0	0
$91$	6860.00	0.0868402
$92$	124032.i	1.52779i
$93$	− 107016.i	− 1.28304i
$94$	93240.0	1.08839
$95$	0	0
$96$	38080.0	0.421715
$97$	− 58506.0i	− 0.631351i	−0.948867	−	0.315676i	$-0.897769\pi$
$97$	− 58506.0i	− 0.631351i	0.948867	−	0.315676i	$-0.102231\pi$
$98$	24010.0i	0.252538i
$99$	10904.0	0.111814
$100$	0	0
$101$	38696.0	0.377453	0.188726	−	0.982030i	$-0.439564\pi$
$101$	38696.0	0.377453	0.188726	+	0.982030i	$0.439564\pi$
$102$	− 241080.i	− 2.29436i
$103$	− 53060.0i	− 0.492804i	−0.969168	−	0.246402i	$-0.920752\pi$
$103$	− 53060.0i	− 0.492804i	0.969168	−	0.246402i	$-0.0792483\pi$
$104$	−50400.0	−0.456927
$105$	0	0
$106$	−22620.0	−0.195537
$107$	− 146324.i	− 1.23554i	−0.786360	−	0.617769i	$-0.788037\pi$
$107$	− 146324.i	− 1.23554i	0.786360	−	0.617769i	$-0.211963\pi$
$108$	− 276080.i	− 2.27759i
$109$	−92898.0	−0.748928	−0.374464	−	0.927241i	$-0.622173\pi$
$109$	−92898.0	−0.748928	−0.374464	+	0.927241i	$0.622173\pi$
$110$	0	0
$111$	145572.	1.12143
$112$	− 69776.0i	− 0.525607i
$113$	83354.0i	0.614088i	0.951695	+	0.307044i	$0.0993398\pi$
$113$	83354.0i	0.614088i	−0.951695	+	0.307044i	$0.900660\pi$
$114$	13720.0	0.0988762
$115$	0	0
$116$	232424.	1.60375
$117$	6580.00i	0.0444387i
$118$	− 27300.0i	− 0.180492i
$119$	−84378.0	−0.546213
$120$	0	0
$121$	−107227.	−0.665795
$122$	− 256480.i	− 1.56011i
$123$	− 251468.i	− 1.49872i
$124$	519792.	3.03582
$125$	0	0
$126$	−23030.0	−0.129231
$127$	60384.0i	0.332210i	0.986108	+	0.166105i	$0.0531191\pi$
$127$	60384.0i	0.332210i	−0.986108	+	0.166105i	$0.946881\pi$
$128$	− 270720.i	− 1.46048i
$129$	152320.	0.805903
$130$	0	0
$131$	−61586.0	−0.313548	−0.156774	−	0.987635i	$-0.550109\pi$
$131$	−61586.0	−0.313548	−0.156774	+	0.987635i	$0.550109\pi$
$132$	− 220864.i	− 1.10329i
$133$	− 4802.00i	− 0.0235393i
$134$	−484040.	−2.32873
$135$	0	0
$136$	619920.	2.87401
$137$	− 204462.i	− 0.930703i	−0.885126	−	0.465352i	$-0.845928\pi$
$137$	− 204462.i	− 0.930703i	0.885126	−	0.465352i	$-0.154072\pi$
$138$	− 255360.i	− 1.14145i
$139$	35406.0	0.155432	0.0777159	−	0.996976i	$-0.475237\pi$
$139$	35406.0	0.155432	0.0777159	+	0.996976i	$0.475237\pi$
$140$	0	0
$141$	−130536.	−0.552946
$142$	585600.i	2.43714i
$143$	32480.0i	0.132824i
$144$	66928.0	0.268969
$145$	0	0
$146$	−680820.	−2.64332
$147$	− 33614.0i	− 0.128300i
$148$	707064.i	2.65341i
$149$	20226.0	0.0746353	0.0373177	−	0.999303i	$-0.488119\pi$
$149$	20226.0	0.0746353	0.0373177	+	0.999303i	$0.488119\pi$
$150$	0	0
$151$	70904.0	0.253063	0.126531	−	0.991963i	$-0.459616\pi$
$151$	70904.0	0.253063	0.126531	+	0.991963i	$0.459616\pi$
$152$	35280.0i	0.123857i
$153$	− 80934.0i	− 0.279513i
$154$	−113680.	−0.386262
$155$	0	0
$156$	133280.	0.438484
$157$	293524.i	0.950374i	0.879885	+	0.475187i	$0.157620\pi$
$157$	293524.i	0.950374i	−0.879885	+	0.475187i	$0.842380\pi$
$158$	317840.i	1.01290i
$159$	31668.0	0.0993408
$160$	0	0
$161$	−89376.0	−0.271742
$162$	454190.i	1.35972i
$163$	− 13192.0i	− 0.0388903i	−0.999811	−	0.0194452i	$-0.993810\pi$
$163$	− 13192.0i	− 0.0388903i	0.999811	−	0.0194452i	$-0.00618998\pi$
$164$	1.22142e6	3.54612
$165$	0	0
$166$	205380.	0.578479
$167$	493612.i	1.36960i	0.728730	+	0.684801i	$0.240111\pi$
$167$	493612.i	1.36960i	−0.728730	+	0.684801i	$0.759889\pi$
$168$	246960.i	0.675077i
$169$	351693.	0.947212
$170$	0	0
$171$	4606.00	0.0120457
$172$	739840.i	1.90685i
$173$	− 240716.i	− 0.611490i	−0.952113	−	0.305745i	$-0.901094\pi$
$173$	− 240716.i	− 0.611490i	0.952113	−	0.305745i	$-0.0989056\pi$
$174$	−478520.	−1.19819
$175$	0	0
$176$	330368.	0.803926
$177$	38220.0i	0.0916975i
$178$	− 505820.i	− 1.19659i
$179$	−294932.	−0.688001	−0.344001	−	0.938969i	$-0.611782\pi$
$179$	−294932.	−0.688001	−0.344001	+	0.938969i	$0.611782\pi$
$180$	0	0
$181$	−336980.	−0.764553	−0.382277	−	0.924048i	$-0.624860\pi$
$181$	−336980.	−0.764553	−0.382277	+	0.924048i	$0.624860\pi$
$182$	− 68600.0i	− 0.153513i
$183$	359072.i	0.792600i
$184$	656640.	1.42982
$185$	0	0
$186$	−1.07016e6	−2.26812
$187$	− 399504.i	− 0.835444i
$188$	− 634032.i	− 1.30833i
$189$	198940.	0.405105
$190$	0	0
$191$	358264.	0.710591	0.355296	−	0.934754i	$-0.384380\pi$
$191$	358264.	0.710591	0.355296	+	0.934754i	$0.384380\pi$
$192$	257152.i	0.503427i
$193$	989554.i	1.91226i	0.292948	+	0.956128i	$0.405364\pi$
$193$	989554.i	1.91226i	−0.292948	+	0.956128i	$0.594636\pi$
$194$	−585060.	−1.11608
$195$	0	0
$196$	163268.	0.303571
$197$	− 990050.i	− 1.81757i	−0.417263	−	0.908786i	$-0.637011\pi$
$197$	− 990050.i	− 1.81757i	0.417263	−	0.908786i	$-0.362989\pi$
$198$	− 109040.i	− 0.197662i
$199$	840756.	1.50500	0.752501	−	0.658591i	$-0.228847\pi$
$199$	840756.	1.50500	0.752501	+	0.658591i	$0.228847\pi$
$200$	0	0
$201$	677656.	1.18309
$202$	− 386960.i	− 0.667249i
$203$	167482.i	0.285252i
$204$	−1.63934e6	−2.75800
$205$	0	0
$206$	−530600.	−0.871163
$207$	− 85728.0i	− 0.139058i
$208$	199360.i	0.319506i
$209$	22736.0	0.0360038
$210$	0	0
$211$	1.15073e6	1.77938	0.889689	−	0.456568i	$-0.150921\pi$
$211$	1.15073e6	1.77938	0.889689	+	0.456568i	$0.150921\pi$
$212$	153816.i	0.235051i
$213$	− 819840.i	− 1.23817i
$214$	−1.46324e6	−2.18414
$215$	0	0
$216$	−1.46160e6	−2.13154
$217$	374556.i	0.539967i
$218$	928980.i	1.32393i
$219$	953148.	1.34292
$220$	0	0
$221$	241080.	0.332032
$222$	− 1.45572e6i	− 1.98242i
$223$	824264.i	1.10995i	0.831866	+	0.554976i	$0.187273\pi$
$223$	824264.i	1.10995i	−0.831866	+	0.554976i	$0.812727\pi$
$224$	−133280.	−0.177478
$225$	0	0
$226$	833540.	1.08556
$227$	74382.0i	0.0958083i	0.998852	+	0.0479042i	$0.0152542\pi$
$227$	74382.0i	0.0958083i	−0.998852	+	0.0479042i	$0.984746\pi$
$228$	− 93296.0i	− 0.118857i
$229$	−1.13196e6	−1.42640	−0.713199	−	0.700961i	$-0.752755\pi$
$229$	−1.13196e6	−1.42640	−0.713199	+	0.700961i	$0.752755\pi$
$230$	0	0
$231$	159152.	0.196238
$232$	− 1.23048e6i	− 1.50091i
$233$	198726.i	0.239809i	0.992785	+	0.119904i	$0.0382588\pi$
$233$	198726.i	0.239809i	−0.992785	+	0.119904i	$0.961741\pi$
$234$	65800.0	0.0785572
$235$	0	0
$236$	−185640.	−0.216966
$237$	− 444976.i	− 0.514595i
$238$	843780.i	0.965577i
$239$	−482904.	−0.546847	−0.273424	−	0.961894i	$-0.588156\pi$
$239$	−482904.	−0.546847	−0.273424	+	0.961894i	$0.588156\pi$
$240$	0	0
$241$	805910.	0.893807	0.446904	−	0.894582i	$-0.352527\pi$
$241$	805910.	0.893807	0.446904	+	0.894582i	$0.352527\pi$
$242$	1.07227e6i	1.17697i
$243$	350714.i	0.381011i
$244$	−1.74406e6	−1.87537
$245$	0	0
$246$	−2.51468e6	−2.64938
$247$	13720.0i	0.0143091i
$248$	− 2.75184e6i	− 2.84115i
$249$	−287532.	−0.293892
$250$	0	0
$251$	430738.	0.431548	0.215774	−	0.976443i	$-0.430773\pi$
$251$	430738.	0.431548	0.215774	+	0.976443i	$0.430773\pi$
$252$	156604.i	0.155347i
$253$	− 423168.i	− 0.415634i
$254$	603840.	0.587270
$255$	0	0
$256$	−2.11942e6	−2.02124
$257$	− 1.17691e6i	− 1.11150i	−0.831349	−	0.555751i	$-0.812431\pi$
$257$	− 1.17691e6i	− 1.11150i	0.831349	−	0.555751i	$-0.187569\pi$
$258$	− 1.52320e6i	− 1.42465i
$259$	−509502.	−0.471951
$260$	0	0
$261$	−160646.	−0.145972
$262$	615860.i	0.554279i
$263$	− 1.29098e6i	− 1.15088i	−0.817845	−	0.575438i	$-0.804831\pi$
$263$	− 1.29098e6i	− 1.15088i	0.817845	−	0.575438i	$-0.195169\pi$
$264$	−1.16928e6	−1.03254
$265$	0	0
$266$	−48020.0	−0.0416119
$267$	708148.i	0.607919i
$268$	3.29147e6i	2.79932i
$269$	1.27756e6	1.07646	0.538232	−	0.842797i	$-0.319093\pi$
$269$	1.27756e6	1.07646	0.538232	+	0.842797i	$0.319093\pi$
$270$	0	0
$271$	1.65054e6	1.36522	0.682612	−	0.730781i	$-0.260844\pi$
$271$	1.65054e6	1.36522	0.682612	+	0.730781i	$0.260844\pi$
$272$	− 2.45213e6i	− 2.00965i
$273$	96040.0i	0.0779912i
$274$	−2.04462e6	−1.64527
$275$	0	0
$276$	−1.73645e6	−1.37211
$277$	− 1.06409e6i	− 0.833257i	−0.909077	−	0.416628i	$-0.863212\pi$
$277$	− 1.06409e6i	− 0.833257i	0.909077	−	0.416628i	$-0.136788\pi$
$278$	− 354060.i	− 0.274767i
$279$	−359268.	−0.276317
$280$	0	0
$281$	−22342.0	−0.0168794	−0.00843969	−	0.999964i	$-0.502686\pi$
$281$	−22342.0	−0.0168794	−0.00843969	+	0.999964i	$0.502686\pi$
$282$	1.30536e6i	0.977479i
$283$	2.49574e6i	1.85239i	0.377042	+	0.926196i	$0.376941\pi$
$283$	2.49574e6i	1.85239i	−0.377042	+	0.926196i	$0.623059\pi$
$284$	3.98208e6	2.92964
$285$	0	0
$286$	324800.	0.234802
$287$	880138.i	0.630734i
$288$	− 127840.i	− 0.0908208i
$289$	−1.54543e6	−1.08844
$290$	0	0
$291$	819084.	0.567017
$292$	4.62958e6i	3.17749i
$293$	1.93178e6i	1.31458i	0.753637	+	0.657291i	$0.228298\pi$
$293$	1.93178e6i	1.31458i	−0.753637	+	0.657291i	$0.771702\pi$
$294$	−336140.	−0.226805
$295$	0	0
$296$	3.74328e6	2.48326
$297$	941920.i	0.619616i
$298$	− 202260.i	− 0.131938i
$299$	255360.	0.165187
$300$	0	0
$301$	−533120.	−0.339163
$302$	− 709040.i	− 0.447356i
$303$	541744.i	0.338991i
$304$	139552.	0.0866068
$305$	0	0
$306$	−809340.	−0.494114
$307$	− 459074.i	− 0.277995i	−0.990293	−	0.138997i	$-0.955612\pi$
$307$	− 459074.i	− 0.277995i	0.990293	−	0.138997i	$-0.0443880\pi$
$308$	773024.i	0.464319i
$309$	742840.	0.442587
$310$	0	0
$311$	667128.	0.391118	0.195559	−	0.980692i	$-0.437348\pi$
$311$	667128.	0.391118	0.195559	+	0.980692i	$0.437348\pi$
$312$	− 705600.i	− 0.410367i
$313$	111034.i	0.0640612i	0.999487	+	0.0320306i	$0.0101974\pi$
$313$	111034.i	0.0640612i	−0.999487	+	0.0320306i	$0.989803\pi$
$314$	2.93524e6	1.68004
$315$	0	0
$316$	2.16131e6	1.21759
$317$	− 68778.0i	− 0.0384416i	−0.999815	−	0.0192208i	$-0.993881\pi$
$317$	− 68778.0i	− 0.0384416i	0.999815	−	0.0192208i	$-0.00611855\pi$
$318$	− 316680.i	− 0.175611i
$319$	−792976.	−0.436298
$320$	0	0
$321$	2.04854e6	1.10964
$322$	893760.i	0.480376i
$323$	− 168756.i	− 0.0900022i
$324$	3.08849e6	1.63450
$325$	0	0
$326$	−131920.	−0.0687490
$327$	− 1.30057e6i	− 0.672613i
$328$	− 6.46632e6i	− 3.31874i
$329$	456876.	0.232707
$330$	0	0
$331$	−564448.	−0.283174	−0.141587	−	0.989926i	$-0.545221\pi$
$331$	−564448.	−0.283174	−0.141587	+	0.989926i	$0.545221\pi$
$332$	− 1.39658e6i	− 0.695379i
$333$	− 488706.i	− 0.241511i
$334$	4.93612e6	2.42114
$335$	0	0
$336$	976864.	0.472048
$337$	2.07729e6i	0.996376i	0.867069	+	0.498188i	$0.166001\pi$
$337$	2.07729e6i	0.996376i	−0.867069	+	0.498188i	$0.833999\pi$
$338$	− 3.51693e6i	− 1.67445i
$339$	−1.16696e6	−0.551512
$340$	0	0
$341$	−1.77341e6	−0.825891
$342$	− 46060.0i	− 0.0212941i
$343$	117649.i	0.0539949i
$344$	3.91680e6	1.78458
$345$	0	0
$346$	−2.40716e6	−1.08097
$347$	− 53248.0i	− 0.0237399i	−0.999930	−	0.0118700i	$-0.996222\pi$
$347$	− 53248.0i	− 0.0237399i	0.999930	−	0.0118700i	$-0.00377842\pi$
$348$	3.25394e6i	1.44033i
$349$	2.27200e6	0.998494	0.499247	−	0.866460i	$-0.333610\pi$
$349$	2.27200e6	0.998494	0.499247	+	0.866460i	$0.333610\pi$
$350$	0	0
$351$	−568400.	−0.246256
$352$	− 631040.i	− 0.271456i
$353$	− 4.00645e6i	− 1.71129i	−0.517565	−	0.855644i	$-0.673162\pi$
$353$	− 4.00645e6i	− 1.71129i	0.517565	−	0.855644i	$-0.326838\pi$
$354$	382200.	0.162100
$355$	0	0
$356$	−3.43958e6	−1.43840
$357$	− 1.18129e6i	− 0.490554i
$358$	2.94932e6i	1.21623i
$359$	−73784.0	−0.0302152	−0.0151076	−	0.999886i	$-0.504809\pi$
$359$	−73784.0	−0.0302152	−0.0151076	+	0.999886i	$0.504809\pi$
$360$	0	0
$361$	−2.46650e6	−0.996121
$362$	3.36980e6i	1.35155i
$363$	− 1.50118e6i	− 0.597951i
$364$	−466480.	−0.184535
$365$	0	0
$366$	3.59072e6	1.40113
$367$	1.40431e6i	0.544250i	0.962262	+	0.272125i	$0.0877264\pi$
$367$	1.40431e6i	0.544250i	−0.962262	+	0.272125i	$0.912274\pi$
$368$	− 2.59738e6i	− 0.999805i
$369$	−844214.	−0.322765
$370$	0	0
$371$	−110838.	−0.0418075
$372$	7.27709e6i	2.72647i
$373$	1.60323e6i	0.596657i	0.954463	+	0.298329i	$0.0964291\pi$
$373$	1.60323e6i	0.596657i	−0.954463	+	0.298329i	$0.903571\pi$
$374$	−3.99504e6	−1.47687
$375$	0	0
$376$	−3.35664e6	−1.22443
$377$	− 478520.i	− 0.173399i
$378$	− 1.98940e6i	− 0.716131i
$379$	4.77012e6	1.70581	0.852906	−	0.522064i	$-0.174838\pi$
$379$	4.77012e6	1.70581	0.852906	+	0.522064i	$0.174838\pi$
$380$	0	0
$381$	−845376.	−0.298358
$382$	− 3.58264e6i	− 1.25616i
$383$	2.23079e6i	0.777072i	0.921434	+	0.388536i	$0.127019\pi$
$383$	2.23079e6i	0.777072i	−0.921434	+	0.388536i	$0.872981\pi$
$384$	3.79008e6	1.31166
$385$	0	0
$386$	9.89554e6	3.38042
$387$	− 511360.i	− 0.173560i
$388$	3.97841e6i	1.34162i
$389$	−4.84024e6	−1.62178	−0.810892	−	0.585196i	$-0.801018\pi$
$389$	−4.84024e6	−1.62178	−0.810892	+	0.585196i	$0.801018\pi$
$390$	0	0
$391$	−3.14093e6	−1.03900
$392$	− 864360.i	− 0.284105i
$393$	− 862204.i	− 0.281597i
$394$	−9.90050e6	−3.21304
$395$	0	0
$396$	−741472.	−0.237606
$397$	995820.i	0.317106i	0.987350	+	0.158553i	$0.0506829\pi$
$397$	995820.i	0.317106i	−0.987350	+	0.158553i	$0.949317\pi$
$398$	− 8.40756e6i	− 2.66049i
$399$	67228.0	0.0211406
$400$	0	0
$401$	−3.31605e6	−1.02982	−0.514909	−	0.857245i	$-0.672174\pi$
$401$	−3.31605e6	−1.02982	−0.514909	+	0.857245i	$0.672174\pi$
$402$	− 6.77656e6i	− 2.09143i
$403$	− 1.07016e6i	− 0.328236i
$404$	−2.63133e6	−0.802087
$405$	0	0
$406$	1.67482e6	0.504258
$407$	− 2.41234e6i	− 0.721858i
$408$	8.67888e6i	2.58115i
$409$	−3.07273e6	−0.908274	−0.454137	−	0.890932i	$-0.650052\pi$
$409$	−3.07273e6	−0.908274	−0.454137	+	0.890932i	$0.650052\pi$
$410$	0	0
$411$	2.86247e6	0.835865
$412$	3.60808e6i	1.04721i
$413$	− 133770.i	− 0.0385908i
$414$	−857280.	−0.245823
$415$	0	0
$416$	380800.	0.107886
$417$	495684.i	0.139593i
$418$	− 227360.i	− 0.0636463i
$419$	−2.81438e6	−0.783154	−0.391577	−	0.920145i	$-0.628070\pi$
$419$	−2.81438e6	−0.783154	−0.391577	+	0.920145i	$0.628070\pi$
$420$	0	0
$421$	3.05802e6	0.840883	0.420441	−	0.907320i	$-0.361875\pi$
$421$	3.05802e6	0.840883	0.420441	+	0.907320i	$0.361875\pi$
$422$	− 1.15073e7i	− 3.14552i
$423$	438228.i	0.119083i
$424$	814320.	0.219979
$425$	0	0
$426$	−8.19840e6	−2.18880
$427$	− 1.25675e6i	− 0.333565i
$428$	9.95003e6i	2.62552i
$429$	−454720.	−0.119289
$430$	0	0
$431$	1.93750e6	0.502398	0.251199	−	0.967936i	$-0.419175\pi$
$431$	1.93750e6	0.502398	0.251199	+	0.967936i	$0.419175\pi$
$432$	5.78144e6i	1.49048i
$433$	− 3.94790e6i	− 1.01192i	−0.862557	−	0.505961i	$-0.831138\pi$
$433$	− 3.94790e6i	− 1.01192i	0.862557	−	0.505961i	$-0.168862\pi$
$434$	3.74556e6	0.954536
$435$	0	0
$436$	6.31706e6	1.59147
$437$	− 178752.i	− 0.0447762i
$438$	− 9.53148e6i	− 2.37397i
$439$	7.41770e6	1.83700	0.918498	−	0.395426i	$-0.129403\pi$
$439$	7.41770e6	1.83700	0.918498	+	0.395426i	$0.129403\pi$
$440$	0	0
$441$	−112847.	−0.0276308
$442$	− 2.41080e6i	− 0.586956i
$443$	− 1.40269e6i	− 0.339589i	−0.985480	−	0.169794i	$-0.945690\pi$
$443$	− 1.40269e6i	− 0.339589i	0.985480	−	0.169794i	$-0.0543103\pi$
$444$	−9.89890e6	−2.38303
$445$	0	0
$446$	8.24264e6	1.96214
$447$	283164.i	0.0670300i
$448$	− 900032.i	− 0.211867i
$449$	590574.	0.138248	0.0691239	−	0.997608i	$-0.477980\pi$
$449$	590574.	0.138248	0.0691239	+	0.997608i	$0.477980\pi$
$450$	0	0
$451$	−4.16718e6	−0.964720
$452$	− 5.66807e6i	− 1.30494i
$453$	992656.i	0.227276i
$454$	743820.	0.169367
$455$	0	0
$456$	−493920.	−0.111236
$457$	− 2.90484e6i	− 0.650627i	−0.945606	−	0.325313i	$-0.894530\pi$
$457$	− 2.90484e6i	− 0.650627i	0.945606	−	0.325313i	$-0.105470\pi$
$458$	1.13196e7i	2.52154i
$459$	6.99132e6	1.54891
$460$	0	0
$461$	−922684.	−0.202209	−0.101105	−	0.994876i	$-0.532238\pi$
$461$	−922684.	−0.202209	−0.101105	+	0.994876i	$0.532238\pi$
$462$	− 1.59152e6i	− 0.346902i
$463$	− 7.18235e6i	− 1.55709i	−0.627588	−	0.778546i	$-0.715958\pi$
$463$	− 7.18235e6i	− 1.55709i	0.627588	−	0.778546i	$-0.284042\pi$
$464$	−4.86723e6	−1.04951
$465$	0	0
$466$	1.98726e6	0.423926
$467$	− 612570.i	− 0.129976i	−0.997886	−	0.0649881i	$-0.979299\pi$
$467$	− 612570.i	− 0.129976i	0.997886	−	0.0649881i	$-0.0207009\pi$
$468$	− 447440.i	− 0.0944322i
$469$	−2.37180e6	−0.497904
$470$	0	0
$471$	−4.10934e6	−0.853531
$472$	982800.i	0.203053i
$473$	− 2.52416e6i	− 0.518757i
$474$	−4.44976e6	−0.909684
$475$	0	0
$476$	5.73770e6	1.16070
$477$	− 106314.i	− 0.0213941i
$478$	4.82904e6i	0.966699i
$479$	−2.60330e6	−0.518424	−0.259212	−	0.965820i	$-0.583463\pi$
$479$	−2.60330e6	−0.518424	−0.259212	+	0.965820i	$0.583463\pi$
$480$	0	0
$481$	1.45572e6	0.286890
$482$	− 8.05910e6i	− 1.58004i
$483$	− 1.25126e6i	− 0.244051i
$484$	7.29144e6	1.41482
$485$	0	0
$486$	3.50714e6	0.673539
$487$	5.46309e6i	1.04380i	0.853008	+	0.521898i	$0.174776\pi$
$487$	5.46309e6i	1.04380i	−0.853008	+	0.521898i	$0.825224\pi$
$488$	9.23328e6i	1.75512i
$489$	184688.	0.0349274
$490$	0	0
$491$	1.64090e6	0.307170	0.153585	−	0.988135i	$-0.450918\pi$
$491$	1.64090e6	0.307170	0.153585	+	0.988135i	$0.450918\pi$
$492$	1.70998e7i	3.18478i
$493$	5.88580e6i	1.09066i
$494$	137200.	0.0252951
$495$	0	0
$496$	−1.08851e7	−1.98667
$497$	2.86944e6i	0.521082i
$498$	2.87532e6i	0.519533i
$499$	−2.99796e6	−0.538983	−0.269491	−	0.963003i	$-0.586856\pi$
$499$	−2.99796e6	−0.538983	−0.269491	+	0.963003i	$0.586856\pi$
$500$	0	0
$501$	−6.91057e6	−1.23004
$502$	− 4.30738e6i	− 0.762876i
$503$	6.89405e6i	1.21494i	0.794343	+	0.607469i	$0.207815\pi$
$503$	6.89405e6i	1.21494i	−0.794343	+	0.607469i	$0.792185\pi$
$504$	829080.	0.145385
$505$	0	0
$506$	−4.23168e6	−0.734745
$507$	4.92370e6i	0.850691i
$508$	− 4.10611e6i	− 0.705946i
$509$	−2.30476e6	−0.394305	−0.197152	−	0.980373i	$-0.563169\pi$
$509$	−2.30476e6	−0.394305	−0.197152	+	0.980373i	$0.563169\pi$
$510$	0	0
$511$	−3.33602e6	−0.565166
$512$	1.25312e7i	2.11260i
$513$	397880.i	0.0667511i
$514$	−1.17691e7	−1.96488
$515$	0	0
$516$	−1.03578e7	−1.71254
$517$	2.16317e6i	0.355929i
$518$	5.09502e6i	0.834299i
$519$	3.37002e6	0.549180
$520$	0	0
$521$	−1.20960e7	−1.95231	−0.976155	−	0.217073i	$-0.930349\pi$
$521$	−1.20960e7	−1.95231	−0.976155	+	0.217073i	$0.930349\pi$
$522$	1.60646e6i	0.258044i
$523$	− 5.48443e6i	− 0.876753i	−0.898791	−	0.438377i	$-0.855554\pi$
$523$	− 5.48443e6i	− 0.876753i	0.898791	−	0.438377i	$-0.144446\pi$
$524$	4.18785e6	0.666289
$525$	0	0
$526$	−1.29098e7	−2.03448
$527$	1.31630e7i	2.06456i
$528$	4.62515e6i	0.722007i
$529$	3.10937e6	0.483095
$530$	0	0
$531$	128310.	0.0197480
$532$	326536.i	0.0500210i
$533$	− 2.51468e6i	− 0.383411i
$534$	7.08148e6	1.07466
$535$	0	0
$536$	1.74254e7	2.61982
$537$	− 4.12905e6i	− 0.617894i
$538$	− 1.27756e7i	− 1.90294i
$539$	−557032.	−0.0825863
$540$	0	0
$541$	−6.71799e6	−0.986839	−0.493420	−	0.869791i	$-0.664253\pi$
$541$	−6.71799e6	−0.986839	−0.493420	+	0.869791i	$0.664253\pi$
$542$	− 1.65054e7i	− 2.41340i
$543$	− 4.71772e6i	− 0.686646i
$544$	−4.68384e6	−0.678586
$545$	0	0
$546$	960400.	0.137870
$547$	− 5.00235e6i	− 0.714835i	−0.933945	−	0.357418i	$-0.883657\pi$
$547$	− 5.00235e6i	− 0.714835i	0.933945	−	0.357418i	$-0.116343\pi$
$548$	1.39034e7i	1.97774i
$549$	1.20546e6	0.170695
$550$	0	0
$551$	−334964.	−0.0470023
$552$	9.19296e6i	1.28413i
$553$	1.55742e6i	0.216567i
$554$	−1.06409e7	−1.47300
$555$	0	0
$556$	−2.40761e6	−0.330293
$557$	9.01961e6i	1.23183i	0.787814	+	0.615913i	$0.211213\pi$
$557$	9.01961e6i	1.23183i	−0.787814	+	0.615913i	$0.788787\pi$
$558$	3.59268e6i	0.488465i
$559$	1.52320e6	0.206171
$560$	0	0
$561$	5.59306e6	0.750312
$562$	223420.i	0.0298388i
$563$	− 1.24051e7i	− 1.64941i	−0.565561	−	0.824707i	$-0.691340\pi$
$563$	− 1.24051e7i	− 1.64941i	0.565561	−	0.824707i	$-0.308660\pi$
$564$	8.87645e6	1.17501
$565$	0	0
$566$	2.49574e7	3.27460
$567$	2.22553e6i	0.290721i
$568$	− 2.10816e7i	− 2.74178i
$569$	−6.48804e6	−0.840103	−0.420052	−	0.907500i	$-0.637988\pi$
$569$	−6.48804e6	−0.840103	−0.420052	+	0.907500i	$0.637988\pi$
$570$	0	0
$571$	−1.02285e7	−1.31287	−0.656435	−	0.754382i	$-0.727936\pi$
$571$	−1.02285e7	−1.31287	−0.656435	+	0.754382i	$0.727936\pi$
$572$	− 2.20864e6i	− 0.282251i
$573$	5.01570e6i	0.638182i
$574$	8.80138e6	1.11499
$575$	0	0
$576$	863296.	0.108419
$577$	2.65338e6i	0.331787i	0.986144	+	0.165894i	$0.0530508\pi$
$577$	2.65338e6i	0.331787i	−0.986144	+	0.165894i	$0.946949\pi$
$578$	1.54543e7i	1.92411i
$579$	−1.38538e7	−1.71740
$580$	0	0
$581$	1.00636e6	0.123684
$582$	− 8.19084e6i	− 1.00235i
$583$	− 524784.i	− 0.0639454i
$584$	2.45095e7	2.97374
$585$	0	0
$586$	1.93178e7	2.32387
$587$	− 1.43044e7i	− 1.71346i	−0.515766	−	0.856729i	$-0.672493\pi$
$587$	− 1.43044e7i	− 1.71346i	0.515766	−	0.856729i	$-0.327507\pi$
$588$	2.28575e6i	0.272638i
$589$	−749112.	−0.0889731
$590$	0	0
$591$	1.38607e7	1.63236
$592$	− 1.48068e7i	− 1.73642i
$593$	1.00265e7i	1.17088i	0.810714	+	0.585442i	$0.199079\pi$
$593$	1.00265e7i	1.17088i	−0.810714	+	0.585442i	$0.800921\pi$
$594$	9.41920e6	1.09534
$595$	0	0
$596$	−1.37537e6	−0.158600
$597$	1.17706e7i	1.35164i
$598$	− 2.55360e6i	− 0.292011i
$599$	7.52292e6	0.856681	0.428341	−	0.903617i	$-0.359098\pi$
$599$	7.52292e6	0.856681	0.428341	+	0.903617i	$0.359098\pi$
$600$	0	0
$601$	3.38625e6	0.382413	0.191207	−	0.981550i	$-0.438760\pi$
$601$	3.38625e6	0.382413	0.191207	+	0.981550i	$0.438760\pi$
$602$	5.33120e6i	0.599562i
$603$	− 2.27499e6i	− 0.254792i
$604$	−4.82147e6	−0.537759
$605$	0	0
$606$	5.41744e6	0.599256
$607$	− 6.90861e6i	− 0.761060i	−0.924769	−	0.380530i	$-0.875742\pi$
$607$	− 6.90861e6i	− 0.761060i	0.924769	−	0.380530i	$-0.124258\pi$
$608$	− 266560.i	− 0.0292439i
$609$	−2.34475e6	−0.256185
$610$	0	0
$611$	−1.30536e6	−0.141458
$612$	5.50351e6i	0.593966i
$613$	9.68896e6i	1.04142i	0.853734	+	0.520710i	$0.174333\pi$
$613$	9.68896e6i	1.04142i	−0.853734	+	0.520710i	$0.825667\pi$
$614$	−4.59074e6	−0.491430
$615$	0	0
$616$	4.09248e6	0.434545
$617$	− 7.84742e6i	− 0.829877i	−0.909849	−	0.414939i	$-0.863803\pi$
$617$	− 7.84742e6i	− 0.829877i	0.909849	−	0.414939i	$-0.136197\pi$
$618$	− 7.42840e6i	− 0.782391i
$619$	1.01972e7	1.06968	0.534840	−	0.844953i	$-0.320372\pi$
$619$	1.01972e7	1.06968	0.534840	+	0.844953i	$0.320372\pi$
$620$	0	0
$621$	7.40544e6	0.770587
$622$	− 6.67128e6i	− 0.691406i
$623$	− 2.47852e6i	− 0.255842i
$624$	−2.79104e6	−0.286949
$625$	0	0
$626$	1.11034e6	0.113245
$627$	318304.i	0.0323350i
$628$	− 1.99596e7i	− 2.01954i
$629$	−1.79054e7	−1.80450
$630$	0	0
$631$	−8.36258e6	−0.836116	−0.418058	−	0.908420i	$-0.637289\pi$
$631$	−8.36258e6	−0.836116	−0.418058	+	0.908420i	$0.637289\pi$
$632$	− 1.14422e7i	− 1.13951i
$633$	1.61102e7i	1.59806i
$634$	−687780.	−0.0679558
$635$	0	0
$636$	−2.15342e6	−0.211099
$637$	− 336140.i	− 0.0328225i
$638$	7.92976e6i	0.771273i
$639$	−2.75232e6	−0.266653
$640$	0	0
$641$	1.10283e6	0.106014	0.0530070	−	0.998594i	$-0.483119\pi$
$641$	1.10283e6	0.106014	0.0530070	+	0.998594i	$0.483119\pi$
$642$	− 2.04854e7i	− 1.96158i
$643$	− 1.71354e7i	− 1.63443i	−0.576330	−	0.817217i	$-0.695516\pi$
$643$	− 1.71354e7i	− 1.63443i	0.576330	−	0.817217i	$-0.304484\pi$
$644$	6.07757e6	0.577451
$645$	0	0
$646$	−1.68756e6	−0.159103
$647$	− 54964.0i	− 0.00516200i	−0.999997	−	0.00258100i	$-0.999178\pi$
$647$	− 54964.0i	− 0.00516200i	0.999997	−	0.00258100i	$-0.000821558\pi$
$648$	− 1.63508e7i	− 1.52969i
$649$	633360.	0.0590254
$650$	0	0
$651$	−5.24378e6	−0.484945
$652$	897056.i	0.0826420i
$653$	485166.i	0.0445254i	0.999752	+	0.0222627i	$0.00708702\pi$
$653$	485166.i	0.0445254i	−0.999752	+	0.0222627i	$0.992913\pi$
$654$	−1.30057e7	−1.18902
$655$	0	0
$656$	−2.55779e7	−2.32063
$657$	− 3.19985e6i	− 0.289212i
$658$	− 4.56876e6i	− 0.411371i
$659$	2.72136e6	0.244103	0.122051	−	0.992524i	$-0.461053\pi$
$659$	2.72136e6	0.244103	0.122051	+	0.992524i	$0.461053\pi$
$660$	0	0
$661$	−2.14525e6	−0.190974	−0.0954869	−	0.995431i	$-0.530441\pi$
$661$	−2.14525e6	−0.190974	−0.0954869	+	0.995431i	$0.530441\pi$
$662$	5.64448e6i	0.500586i
$663$	3.37512e6i	0.298198i
$664$	−7.39368e6	−0.650789
$665$	0	0
$666$	−4.88706e6	−0.426935
$667$	6.23443e6i	0.542603i
$668$	− 3.35656e7i	− 2.91041i
$669$	−1.15397e7	−0.996848
$670$	0	0
$671$	5.95034e6	0.510194
$672$	− 1.86592e6i	− 0.159393i
$673$	− 2.92796e6i	− 0.249188i	−0.992208	−	0.124594i	$-0.960237\pi$
$673$	− 2.92796e6i	− 0.249188i	0.992208	−	0.124594i	$-0.0397629\pi$
$674$	2.07729e7	1.76136
$675$	0	0
$676$	−2.39151e7	−2.01282
$677$	− 1.34992e7i	− 1.13198i	−0.824414	−	0.565988i	$-0.808495\pi$
$677$	− 1.34992e7i	− 1.13198i	0.824414	−	0.565988i	$-0.191505\pi$
$678$	1.16696e7i	0.974945i
$679$	−2.86679e6	−0.238628
$680$	0	0
$681$	−1.04135e6	−0.0860455
$682$	1.77341e7i	1.45998i
$683$	5.42972e6i	0.445375i	0.974890	+	0.222688i	$0.0714830\pi$
$683$	5.42972e6i	0.445375i	−0.974890	+	0.222688i	$0.928517\pi$
$684$	−313208.	−0.0255972
$685$	0	0
$686$	1.17649e6	0.0954504
$687$	− 1.58474e7i	− 1.28105i
$688$	− 1.54931e7i	− 1.24787i
$689$	316680.	0.0254140
$690$	0	0
$691$	2.08280e7	1.65940	0.829702	−	0.558207i	$-0.188510\pi$
$691$	2.08280e7	1.65940	0.829702	+	0.558207i	$0.188510\pi$
$692$	1.63687e7i	1.29942i
$693$	− 534296.i	− 0.0422619i
$694$	−532480.	−0.0419667
$695$	0	0
$696$	1.72267e7	1.34797
$697$	3.09306e7i	2.41160i
$698$	− 2.27200e7i	− 1.76510i
$699$	−2.78216e6	−0.215372
$700$	0	0
$701$	2.35141e7	1.80731	0.903655	−	0.428261i	$-0.140874\pi$
$701$	2.35141e7	1.80731	0.903655	+	0.428261i	$0.140874\pi$
$702$	5.68400e6i	0.435323i
$703$	− 1.01900e6i	− 0.0777656i
$704$	4.26138e6	0.324055
$705$	0	0
$706$	−4.00645e7	−3.02516
$707$	− 1.89610e6i	− 0.142664i
$708$	− 2.59896e6i	− 0.194857i
$709$	1.95747e7	1.46244	0.731221	−	0.682140i	$-0.238951\pi$
$709$	1.95747e7	1.46244	0.731221	+	0.682140i	$0.238951\pi$
$710$	0	0
$711$	−1.49385e6	−0.110824
$712$	1.82095e7i	1.34617i
$713$	1.39427e7i	1.02712i
$714$	−1.18129e7	−0.867185
$715$	0	0
$716$	2.00554e7	1.46200
$717$	− 6.76066e6i	− 0.491124i
$718$	737840.i	0.0534135i
$719$	2.61152e7	1.88396	0.941978	−	0.335674i	$-0.108964\pi$
$719$	2.61152e7	1.88396	0.941978	+	0.335674i	$0.108964\pi$
$720$	0	0
$721$	−2.59994e6	−0.186262
$722$	2.46650e7i	1.76091i
$723$	1.12827e7i	0.802729i
$724$	2.29146e7	1.62468
$725$	0	0
$726$	−1.50118e7	−1.05704
$727$	1.54126e7i	1.08154i	0.841172	+	0.540768i	$0.181866\pi$
$727$	1.54126e7i	1.08154i	−0.841172	+	0.540768i	$0.818134\pi$
$728$	2.46960e6i	0.172702i
$729$	−1.59468e7	−1.11136
$730$	0	0
$731$	−1.87354e7	−1.29679
$732$	− 2.44169e7i	− 1.68427i
$733$	1.69868e7i	1.16776i	0.811841	+	0.583878i	$0.198465\pi$
$733$	1.69868e7i	1.16776i	−0.811841	+	0.583878i	$0.801535\pi$
$734$	1.40431e7	0.962107
$735$	0	0
$736$	−4.96128e6	−0.337597
$737$	− 1.12297e7i	− 0.761554i
$738$	8.44214e6i	0.570574i
$739$	−2.01511e6	−0.135734	−0.0678669	−	0.997694i	$-0.521619\pi$
$739$	−2.01511e6	−0.135734	−0.0678669	+	0.997694i	$0.521619\pi$
$740$	0	0
$741$	−192080.	−0.0128510
$742$	1.10838e6i	0.0739059i
$743$	1.51381e7i	1.00600i	0.864286	+	0.503001i	$0.167771\pi$
$743$	1.51381e7i	1.00600i	−0.864286	+	0.503001i	$0.832229\pi$
$744$	3.85258e7	2.55164
$745$	0	0
$746$	1.60323e7	1.05475
$747$	965286.i	0.0632928i
$748$	2.71663e7i	1.77532i
$749$	−7.16988e6	−0.466989
$750$	0	0
$751$	7.21401e6	0.466742	0.233371	−	0.972388i	$-0.425024\pi$
$751$	7.21401e6	0.466742	0.233371	+	0.972388i	$0.425024\pi$
$752$	1.32774e7i	0.856185i
$753$	6.03033e6i	0.387573i
$754$	−4.78520e6	−0.306529
$755$	0	0
$756$	−1.35279e7	−0.860848
$757$	− 1.09697e7i	− 0.695755i	−0.937540	−	0.347877i	$-0.886903\pi$
$757$	− 1.09697e7i	− 0.695755i	0.937540	−	0.347877i	$-0.113097\pi$
$758$	− 4.77012e7i	− 3.01548i
$759$	5.92435e6	0.373281
$760$	0	0
$761$	1.92442e7	1.20459	0.602293	−	0.798275i	$-0.294254\pi$
$761$	1.92442e7	1.20459	0.602293	+	0.798275i	$0.294254\pi$
$762$	8.45376e6i	0.527427i
$763$	4.55200e6i	0.283068i
$764$	−2.43620e7	−1.51001
$765$	0	0
$766$	2.23079e7	1.37368
$767$	382200.i	0.0234586i
$768$	− 2.96719e7i	− 1.81528i
$769$	−8.21185e6	−0.500755	−0.250378	−	0.968148i	$-0.580555\pi$
$769$	−8.21185e6	−0.500755	−0.250378	+	0.968148i	$0.580555\pi$
$770$	0	0
$771$	1.64767e7	0.998241
$772$	− 6.72897e7i	− 4.06355i
$773$	− 1.86187e7i	− 1.12073i	−0.828247	−	0.560363i	$-0.810662\pi$
$773$	− 1.86187e7i	− 1.12073i	0.828247	−	0.560363i	$-0.189338\pi$
$774$	−5.11360e6	−0.306813
$775$	0	0
$776$	2.10622e7	1.25559
$777$	− 7.13303e6i	− 0.423859i
$778$	4.84024e7i	2.86694i
$779$	−1.76028e6	−0.103929
$780$	0	0
$781$	−1.35859e7	−0.797006
$782$	3.14093e7i	1.83671i
$783$	− 1.38771e7i	− 0.808898i
$784$	−3.41902e6	−0.198661
$785$	0	0
$786$	−8.62204e6	−0.497799
$787$	2.62501e7i	1.51075i	0.655291	+	0.755377i	$0.272546\pi$
$787$	2.62501e7i	1.51075i	−0.655291	+	0.755377i	$0.727454\pi$
$788$	6.73234e7i	3.86234i
$789$	1.80737e7	1.03360
$790$	0	0
$791$	4.08435e6	0.232103
$792$	3.92544e6i	0.222370i
$793$	3.59072e6i	0.202768i
$794$	9.95820e6	0.560570
$795$	0	0
$796$	−5.71714e7	−3.19813
$797$	− 1.00373e7i	− 0.559720i	−0.960041	−	0.279860i	$-0.909712\pi$
$797$	− 1.00373e7i	− 0.559720i	0.960041	−	0.279860i	$-0.0902881\pi$
$798$	− 672280.i	− 0.0373717i
$799$	1.60559e7	0.889751
$800$	0	0
$801$	2.37735e6	0.130922
$802$	3.31605e7i	1.82048i
$803$	− 1.57950e7i	− 0.864433i
$804$	−4.60806e7	−2.51407
$805$	0	0
$806$	−1.07016e7	−0.580245
$807$	1.78858e7i	0.966772i
$808$	1.39306e7i	0.750655i
$809$	−1.40884e7	−0.756816	−0.378408	−	0.925639i	$-0.623528\pi$
$809$	−1.40884e7	−0.756816	−0.378408	+	0.925639i	$0.623528\pi$
$810$	0	0
$811$	1.81433e7	0.968646	0.484323	−	0.874889i	$-0.339066\pi$
$811$	1.81433e7	0.968646	0.484323	+	0.874889i	$0.339066\pi$
$812$	− 1.13888e7i	− 0.606160i
$813$	2.31076e7i	1.22611i
$814$	−2.41234e7	−1.27608
$815$	0	0
$816$	3.43298e7	1.80487
$817$	− 1.06624e6i	− 0.0558856i
$818$	3.07273e7i	1.60562i
$819$	322420.	0.0167962
$820$	0	0
$821$	−2.13669e7	−1.10633	−0.553164	−	0.833072i	$-0.686580\pi$
$821$	−2.13669e7	−1.10633	−0.553164	+	0.833072i	$0.686580\pi$
$822$	− 2.86247e7i	− 1.47761i
$823$	− 1.78017e7i	− 0.916142i	−0.888916	−	0.458071i	$-0.848541\pi$
$823$	− 1.78017e7i	− 0.916142i	0.888916	−	0.458071i	$-0.151459\pi$
$824$	1.91016e7	0.980058
$825$	0	0
$826$	−1.33770e6	−0.0682195
$827$	1.62921e7i	0.828350i	0.910197	+	0.414175i	$0.135930\pi$
$827$	1.62921e7i	0.828350i	−0.910197	+	0.414175i	$0.864070\pi$
$828$	5.82950e6i	0.295499i
$829$	2.08499e6	0.105370	0.0526851	−	0.998611i	$-0.483222\pi$
$829$	2.08499e6	0.105370	0.0526851	+	0.998611i	$0.483222\pi$
$830$	0	0
$831$	1.48973e7	0.748348
$832$	2.57152e6i	0.128790i
$833$	4.13452e6i	0.206449i
$834$	4.95684e6	0.246769
$835$	0	0
$836$	−1.54605e6	−0.0765081
$837$	− 3.10346e7i	− 1.53120i
$838$	2.81438e7i	1.38443i
$839$	2.27850e7	1.11749	0.558745	−	0.829340i	$-0.311283\pi$
$839$	2.27850e7	1.11749	0.558745	+	0.829340i	$0.311283\pi$
$840$	0	0
$841$	−8.82842e6	−0.430421
$842$	− 3.05802e7i	− 1.48648i
$843$	− 312788.i	− 0.0151594i
$844$	−7.82498e7	−3.78118
$845$	0	0
$846$	4.38228e6	0.210511
$847$	5.25412e6i	0.251647i
$848$	− 3.22109e6i	− 0.153820i
$849$	−3.49403e7	−1.66363
$850$	0	0
$851$	−1.89660e7	−0.897740
$852$	5.57491e7i	2.63111i
$853$	2.26975e7i	1.06808i	0.845458	+	0.534042i	$0.179328\pi$
$853$	2.26975e7i	1.06808i	−0.845458	+	0.534042i	$0.820672\pi$
$854$	−1.25675e7	−0.589664
$855$	0	0
$856$	5.26766e7	2.45716
$857$	2.52900e7i	1.17624i	0.808774	+	0.588120i	$0.200132\pi$
$857$	2.52900e7i	1.17624i	−0.808774	+	0.588120i	$0.799868\pi$
$858$	4.54720e6i	0.210875i
$859$	1.03947e7	0.480652	0.240326	−	0.970692i	$-0.422746\pi$
$859$	1.03947e7	0.480652	0.240326	+	0.970692i	$0.422746\pi$
$860$	0	0
$861$	−1.23219e7	−0.566462
$862$	− 1.93750e7i	− 0.888122i
$863$	− 4.33399e7i	− 1.98089i	−0.137892	−	0.990447i	$-0.544033\pi$
$863$	− 4.33399e7i	− 1.98089i	0.137892	−	0.990447i	$-0.455967\pi$
$864$	1.10432e7	0.503281
$865$	0	0
$866$	−3.94790e7	−1.78884
$867$	− 2.16360e7i	− 0.977527i
$868$	− 2.54698e7i	− 1.14743i
$869$	−7.37389e6	−0.331243
$870$	0	0
$871$	6.77656e6	0.302666
$872$	− 3.34433e7i	− 1.48942i
$873$	− 2.74978e6i	− 0.122113i
$874$	−1.78752e6	−0.0791539
$875$	0	0
$876$	−6.48141e7	−2.85370
$877$	3.71659e7i	1.63172i	0.578248	+	0.815861i	$0.303736\pi$
$877$	3.71659e7i	1.63172i	−0.578248	+	0.815861i	$0.696264\pi$
$878$	− 7.41770e7i	− 3.24738i
$879$	−2.70449e7	−1.18063
$880$	0	0
$881$	9.04785e6	0.392740	0.196370	−	0.980530i	$-0.437085\pi$
$881$	9.04785e6	0.392740	0.196370	+	0.980530i	$0.437085\pi$
$882$	1.12847e6i	0.0488448i
$883$	− 3.29679e7i	− 1.42295i	−0.702712	−	0.711474i	$-0.748028\pi$
$883$	− 3.29679e7i	− 1.42295i	0.702712	−	0.711474i	$-0.251972\pi$
$884$	−1.63934e7	−0.705569
$885$	0	0
$886$	−1.40269e7	−0.600313
$887$	− 1.61099e7i	− 0.687517i	−0.939058	−	0.343758i	$-0.888300\pi$
$887$	− 1.61099e7i	− 0.687517i	0.939058	−	0.343758i	$-0.111700\pi$
$888$	5.24059e7i	2.23022i
$889$	2.95882e6	0.125564
$890$	0	0
$891$	−1.05372e7	−0.444663
$892$	− 5.60500e7i	− 2.35865i
$893$	913752.i	0.0383442i
$894$	2.83164e6	0.118493
$895$	0	0
$896$	−1.32653e7	−0.552009
$897$	3.57504e6i	0.148354i
$898$	− 5.90574e6i	− 0.244390i
$899$	2.61272e7	1.07819
$900$	0	0
$901$	−3.89516e6	−0.159850
$902$	4.16718e7i	1.70540i
$903$	− 7.46368e6i	− 0.304603i
$904$	−3.00074e7	−1.22126
$905$	0	0
$906$	9.92656e6	0.401771
$907$	− 4.47286e7i	− 1.80537i	−0.430300	−	0.902686i	$-0.641592\pi$
$907$	− 4.47286e7i	− 1.80537i	0.430300	−	0.902686i	$-0.358408\pi$
$908$	− 5.05798e6i	− 0.203593i
$909$	1.81871e6	0.0730053
$910$	0	0
$911$	−6.60518e6	−0.263687	−0.131844	−	0.991271i	$-0.542090\pi$
$911$	−6.60518e6	−0.263687	−0.131844	+	0.991271i	$0.542090\pi$
$912$	1.95373e6i	0.0777816i
$913$	4.76482e6i	0.189177i
$914$	−2.90484e7	−1.15016
$915$	0	0
$916$	7.69730e7	3.03110
$917$	3.01771e6i	0.118510i
$918$	− 6.99132e7i	− 2.73812i
$919$	3.08930e7	1.20662	0.603311	−	0.797506i	$-0.293848\pi$
$919$	3.08930e7	1.20662	0.603311	+	0.797506i	$0.293848\pi$
$920$	0	0
$921$	6.42704e6	0.249667
$922$	9.22684e6i	0.357459i
$923$	− 8.19840e6i	− 0.316756i
$924$	−1.08223e7	−0.417005
$925$	0	0
$926$	−7.18235e7	−2.75258
$927$	− 2.49382e6i	− 0.0953160i
$928$	9.29696e6i	0.354381i
$929$	4.87215e6	0.185217	0.0926087	−	0.995703i	$-0.470479\pi$
$929$	4.87215e6	0.185217	0.0926087	+	0.995703i	$0.470479\pi$
$930$	0	0
$931$	−235298.	−0.00889701
$932$	− 1.35134e7i	− 0.509593i
$933$	9.33979e6i	0.351264i
$934$	−6.12570e6	−0.229767
$935$	0	0
$936$	−2.36880e6	−0.0883769
$937$	− 3.25004e7i	− 1.20932i	−0.796485	−	0.604658i	$-0.793310\pi$
$937$	− 3.25004e7i	− 1.20932i	0.796485	−	0.604658i	$-0.206690\pi$
$938$	2.37180e7i	0.880177i
$939$	−1.55448e6	−0.0575334
$940$	0	0
$941$	−2.64040e6	−0.0972066	−0.0486033	−	0.998818i	$-0.515477\pi$
$941$	−2.64040e6	−0.0972066	−0.0486033	+	0.998818i	$0.515477\pi$
$942$	4.10934e7i	1.50884i
$943$	3.27627e7i	1.19978i
$944$	3.88752e6	0.141985
$945$	0	0
$946$	−2.52416e7	−0.917042
$947$	− 4.08179e7i	− 1.47903i	−0.673142	−	0.739513i	$-0.735056\pi$
$947$	− 4.08179e7i	− 1.47903i	0.673142	−	0.739513i	$-0.264944\pi$
$948$	3.02584e7i	1.09351i
$949$	9.53148e6	0.343554
$950$	0	0
$951$	962892.	0.0345244
$952$	− 3.03761e7i	− 1.08627i
$953$	6.71983e6i	0.239677i	0.992793	+	0.119838i	$0.0382376\pi$
$953$	6.71983e6i	0.239677i	−0.992793	+	0.119838i	$0.961762\pi$
$954$	−1.06314e6	−0.0378198
$955$	0	0
$956$	3.28375e7	1.16205
$957$	− 1.11017e7i	− 0.391840i
$958$	2.60330e7i	0.916454i
$959$	−1.00186e7	−0.351773
$960$	0	0
$961$	2.98016e7	1.04095
$962$	− 1.45572e7i	− 0.507154i
$963$	− 6.87723e6i	− 0.238972i
$964$	−5.48019e7	−1.89934
$965$	0	0
$966$	−1.25126e7	−0.431426
$967$	− 2.78979e6i	− 0.0959413i	−0.998849	−	0.0479707i	$-0.984725\pi$
$967$	− 2.78979e6i	− 0.0959413i	0.998849	−	0.0479707i	$-0.0152754\pi$
$968$	− 3.86017e7i	− 1.32409i
$969$	2.36258e6	0.0808310
$970$	0	0
$971$	3.33594e7	1.13545	0.567727	−	0.823217i	$-0.307823\pi$
$971$	3.33594e7	1.13545	0.567727	+	0.823217i	$0.307823\pi$
$972$	− 2.38486e7i	− 0.809648i
$973$	− 1.73489e6i	− 0.0587477i
$974$	5.46309e7	1.84519
$975$	0	0
$976$	3.65228e7	1.22727
$977$	− 7.60033e6i	− 0.254739i	−0.991855	−	0.127370i	$-0.959347\pi$
$977$	− 7.60033e6i	− 0.254739i	0.991855	−	0.127370i	$-0.0406534\pi$
$978$	− 1.84688e6i	− 0.0617435i
$979$	1.17350e7	0.391316
$980$	0	0
$981$	−4.36621e6	−0.144854
$982$	− 1.64090e7i	− 0.543004i
$983$	5.79760e6i	0.191366i	0.995412	+	0.0956829i	$0.0305035\pi$
$983$	5.79760e6i	0.191366i	−0.995412	+	0.0956829i	$0.969497\pi$
$984$	9.05285e7	2.98056
$985$	0	0
$986$	5.88580e7	1.92803
$987$	6.39626e6i	0.208994i
$988$	− 932960.i	− 0.0304068i
$989$	−1.98451e7	−0.645153
$990$	0	0
$991$	1.26825e7	0.410224	0.205112	−	0.978739i	$-0.434244\pi$
$991$	1.26825e7	0.410224	0.205112	+	0.978739i	$0.434244\pi$
$992$	2.07917e7i	0.670827i
$993$	− 7.90227e6i	− 0.254319i
$994$	2.86944e7	0.921152
$995$	0	0
$996$	1.95522e7	0.624521
$997$	1.44400e7i	0.460077i	0.973182	+	0.230039i	$0.0738853\pi$
$997$	1.44400e7i	0.460077i	−0.973182	+	0.230039i	$0.926115\pi$
$998$	2.99796e7i	0.952796i
$999$	4.22159e7	1.33833

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.6.b.a.99.1		2
5.2	odd	4		175.6.a.b.1.1		1
5.3	odd	4		7.6.a.a.1.1	✓	1
5.4	even	2	inner	175.6.b.a.99.2		2
15.8	even	4		63.6.a.e.1.1		1
20.3	even	4		112.6.a.g.1.1		1
35.3	even	12		49.6.c.b.30.1		2
35.13	even	4		49.6.a.a.1.1		1
35.18	odd	12		49.6.c.c.30.1		2
35.23	odd	12		49.6.c.c.18.1		2
35.33	even	12		49.6.c.b.18.1		2
40.3	even	4		448.6.a.c.1.1		1
40.13	odd	4		448.6.a.m.1.1		1
55.43	even	4		847.6.a.b.1.1		1
60.23	odd	4		1008.6.a.y.1.1		1
105.83	odd	4		441.6.a.k.1.1		1
140.83	odd	4		784.6.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.6.a.a.1.1	✓	1	5.3	odd	4
49.6.a.a.1.1		1	35.13	even	4
49.6.c.b.18.1		2	35.33	even	12
49.6.c.b.30.1		2	35.3	even	12
49.6.c.c.18.1		2	35.23	odd	12
49.6.c.c.30.1		2	35.18	odd	12
63.6.a.e.1.1		1	15.8	even	4
112.6.a.g.1.1		1	20.3	even	4
175.6.a.b.1.1		1	5.2	odd	4
175.6.b.a.99.1		2	1.1	even	1	trivial
175.6.b.a.99.2		2	5.4	even	2	inner
441.6.a.k.1.1		1	105.83	odd	4
448.6.a.c.1.1		1	40.3	even	4
448.6.a.m.1.1		1	40.13	odd	4
784.6.a.c.1.1		1	140.83	odd	4
847.6.a.b.1.1		1	55.43	even	4
1008.6.a.y.1.1		1	60.23	odd	4

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	175.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-10.0000i q^{2} +14.0000i q^{3} -68.0000 q^{4} +140.000 q^{6} -49.0000i q^{7} +360.000i q^{8} +47.0000 q^{9} +O(q^{10})\)	\(q-10.0000i q^{2} +14.0000i q^{3} -68.0000 q^{4} +140.000 q^{6} -49.0000i q^{7} +360.000i q^{8} +47.0000 q^{9} +232.000 q^{11} -952.000i q^{12} +140.000i q^{13} -490.000 q^{14} +1424.00 q^{16} -1722.00i q^{17} -470.000i q^{18} +98.0000 q^{19} +686.000 q^{21} -2320.00i q^{22} -1824.00i q^{23} -5040.00 q^{24} +1400.00 q^{26} +4060.00i q^{27} +3332.00i q^{28} -3418.00 q^{29} -7644.00 q^{31} -2720.00i q^{32} +3248.00i q^{33} -17220.0 q^{34} -3196.00 q^{36} -10398.0i q^{37} -980.000i q^{38} -1960.00 q^{39} -17962.0 q^{41} -6860.00i q^{42} -10880.0i q^{43} -15776.0 q^{44} -18240.0 q^{46} +9324.00i q^{47} +19936.0i q^{48} -2401.00 q^{49} +24108.0 q^{51} -9520.00i q^{52} -2262.00i q^{53} +40600.0 q^{54} +17640.0 q^{56} +1372.00i q^{57} +34180.0i q^{58} +2730.00 q^{59} +25648.0 q^{61} +76440.0i q^{62} -2303.00i q^{63} +18368.0 q^{64} +32480.0 q^{66} -48404.0i q^{67} +117096. i q^{68} +25536.0 q^{69} -58560.0 q^{71} +16920.0i q^{72} -68082.0i q^{73} -103980. q^{74} -6664.00 q^{76} -11368.0i q^{77} +19600.0i q^{78} -31784.0 q^{79} -45419.0 q^{81} +179620. i q^{82} +20538.0i q^{83} -46648.0 q^{84} -108800. q^{86} -47852.0i q^{87} +83520.0i q^{88} +50582.0 q^{89} +6860.00 q^{91} +124032. i q^{92} -107016. i q^{93} +93240.0 q^{94} +38080.0 q^{96} -58506.0i q^{97} +24010.0i q^{98} +10904.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 136 q^{4} + 280 q^{6} + 94 q^{9}+O(q^{10}) \) 2 * q - 136 * q^4 + 280 * q^6 + 94 * q^9	\( 2 q - 136 q^{4} + 280 q^{6} + 94 q^{9} + 464 q^{11} - 980 q^{14} + 2848 q^{16} + 196 q^{19} + 1372 q^{21} - 10080 q^{24} + 2800 q^{26} - 6836 q^{29} - 15288 q^{31} - 34440 q^{34} - 6392 q^{36} - 3920 q^{39} - 35924 q^{41} - 31552 q^{44} - 36480 q^{46} - 4802 q^{49} + 48216 q^{51} + 81200 q^{54} + 35280 q^{56} + 5460 q^{59} + 51296 q^{61} + 36736 q^{64} + 64960 q^{66} + 51072 q^{69} - 117120 q^{71} - 207960 q^{74} - 13328 q^{76} - 63568 q^{79} - 90838 q^{81} - 93296 q^{84} - 217600 q^{86} + 101164 q^{89} + 13720 q^{91} + 186480 q^{94} + 76160 q^{96} + 21808 q^{99}+O(q^{100}) \) 2 * q - 136 * q^4 + 280 * q^6 + 94 * q^9 + 464 * q^11 - 980 * q^14 + 2848 * q^16 + 196 * q^19 + 1372 * q^21 - 10080 * q^24 + 2800 * q^26 - 6836 * q^29 - 15288 * q^31 - 34440 * q^34 - 6392 * q^36 - 3920 * q^39 - 35924 * q^41 - 31552 * q^44 - 36480 * q^46 - 4802 * q^49 + 48216 * q^51 + 81200 * q^54 + 35280 * q^56 + 5460 * q^59 + 51296 * q^61 + 36736 * q^64 + 64960 * q^66 + 51072 * q^69 - 117120 * q^71 - 207960 * q^74 - 13328 * q^76 - 63568 * q^79 - 90838 * q^81 - 93296 * q^84 - 217600 * q^86 + 101164 * q^89 + 13720 * q^91 + 186480 * q^94 + 76160 * q^96 + 21808 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more