LMFDB - Embedded newform 725.6.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,6,Mod(1,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("725.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	725.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:	$116.278269364$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.3257317.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 34x^{2} - 27x + 10 $ x^4 - 34x^2 - 27x + 10
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 29)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-5.34807$ of defining polynomial
Character	$\chi$	$=$	725.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.21534 q^{2} -0.734546 q^{3} +52.9225 q^{4} -6.76909 q^{6} +90.0205 q^{7} +192.808 q^{8} -242.460 q^{9} +O(q^{10})$	\(q+9.21534 q^{2} -0.734546 q^{3} +52.9225 q^{4} -6.76909 q^{6} +90.0205 q^{7} +192.808 q^{8} -242.460 q^{9} -269.080 q^{11} -38.8740 q^{12} +444.579 q^{13} +829.569 q^{14} +83.2700 q^{16} -485.649 q^{17} -2234.36 q^{18} -1572.80 q^{19} -66.1242 q^{21} -2479.66 q^{22} +398.704 q^{23} -141.626 q^{24} +4096.95 q^{26} +356.593 q^{27} +4764.11 q^{28} -841.000 q^{29} -8469.77 q^{31} -5402.49 q^{32} +197.652 q^{33} -4475.43 q^{34} -12831.6 q^{36} -3339.33 q^{37} -14493.8 q^{38} -326.564 q^{39} +18154.2 q^{41} -609.357 q^{42} -9996.71 q^{43} -14240.4 q^{44} +3674.20 q^{46} -12568.0 q^{47} -61.1656 q^{48} -8703.31 q^{49} +356.732 q^{51} +23528.2 q^{52} +21343.1 q^{53} +3286.12 q^{54} +17356.7 q^{56} +1155.29 q^{57} -7750.10 q^{58} -30036.1 q^{59} +49792.6 q^{61} -78051.8 q^{62} -21826.4 q^{63} -52450.4 q^{64} +1821.43 q^{66} -47588.2 q^{67} -25701.8 q^{68} -292.867 q^{69} -50164.6 q^{71} -46748.3 q^{72} +44770.3 q^{73} -30773.1 q^{74} -83236.3 q^{76} -24222.7 q^{77} -3009.40 q^{78} -78464.6 q^{79} +58656.0 q^{81} +167297. q^{82} -46721.8 q^{83} -3499.46 q^{84} -92123.1 q^{86} +617.753 q^{87} -51880.7 q^{88} -39465.7 q^{89} +40021.2 q^{91} +21100.4 q^{92} +6221.43 q^{93} -115818. q^{94} +3968.38 q^{96} -48336.3 q^{97} -80204.0 q^{98} +65241.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 28 q^{3} + 10 q^{4} - 194 q^{6} + 208 q^{7} + 504 q^{8} - 280 q^{9}+O(q^{10}) $ 4 * q + 28 * q^3 + 10 * q^4 - 194 * q^6 + 208 * q^7 + 504 * q^8 - 280 * q^9	\( 4 q + 28 q^{3} + 10 q^{4} - 194 q^{6} + 208 q^{7} + 504 q^{8} - 280 q^{9} - 124 q^{11} - 20 q^{12} + 460 q^{13} + 768 q^{14} - 414 q^{16} - 184 q^{17} - 3208 q^{18} - 2392 q^{19} + 992 q^{21} - 5538 q^{22} + 1192 q^{23} + 6786 q^{24} + 4724 q^{26} - 2468 q^{27} - 44 q^{28} - 3364 q^{29} - 19212 q^{31} - 6552 q^{32} + 10580 q^{33} - 7612 q^{34} - 7468 q^{36} + 10928 q^{37} + 456 q^{38} - 8732 q^{39} - 1120 q^{41} - 1844 q^{42} + 21420 q^{43} - 1932 q^{44} - 7588 q^{46} - 23772 q^{47} - 33060 q^{48} + 10452 q^{49} + 12744 q^{51} + 29062 q^{52} - 8860 q^{53} + 35410 q^{54} + 34304 q^{56} - 48944 q^{57} - 10840 q^{59} + 49448 q^{61} - 18518 q^{62} - 27488 q^{63} - 20734 q^{64} - 47744 q^{66} + 7840 q^{67} - 20724 q^{68} + 58792 q^{69} - 48744 q^{71} - 8088 q^{72} + 74992 q^{73} - 35920 q^{74} - 140792 q^{76} - 128656 q^{77} - 2982 q^{78} - 106076 q^{79} - 59692 q^{81} + 234132 q^{82} - 62888 q^{83} - 59832 q^{84} - 216014 q^{86} - 23548 q^{87} + 39426 q^{88} + 107568 q^{89} - 268896 q^{91} + 26268 q^{92} - 221460 q^{93} + 30542 q^{94} - 78606 q^{96} + 49520 q^{97} - 242304 q^{98} + 166720 q^{99}+O(q^{100}) \) 4 * q + 28 * q^3 + 10 * q^4 - 194 * q^6 + 208 * q^7 + 504 * q^8 - 280 * q^9 - 124 * q^11 - 20 * q^12 + 460 * q^13 + 768 * q^14 - 414 * q^16 - 184 * q^17 - 3208 * q^18 - 2392 * q^19 + 992 * q^21 - 5538 * q^22 + 1192 * q^23 + 6786 * q^24 + 4724 * q^26 - 2468 * q^27 - 44 * q^28 - 3364 * q^29 - 19212 * q^31 - 6552 * q^32 + 10580 * q^33 - 7612 * q^34 - 7468 * q^36 + 10928 * q^37 + 456 * q^38 - 8732 * q^39 - 1120 * q^41 - 1844 * q^42 + 21420 * q^43 - 1932 * q^44 - 7588 * q^46 - 23772 * q^47 - 33060 * q^48 + 10452 * q^49 + 12744 * q^51 + 29062 * q^52 - 8860 * q^53 + 35410 * q^54 + 34304 * q^56 - 48944 * q^57 - 10840 * q^59 + 49448 * q^61 - 18518 * q^62 - 27488 * q^63 - 20734 * q^64 - 47744 * q^66 + 7840 * q^67 - 20724 * q^68 + 58792 * q^69 - 48744 * q^71 - 8088 * q^72 + 74992 * q^73 - 35920 * q^74 - 140792 * q^76 - 128656 * q^77 - 2982 * q^78 - 106076 * q^79 - 59692 * q^81 + 234132 * q^82 - 62888 * q^83 - 59832 * q^84 - 216014 * q^86 - 23548 * q^87 + 39426 * q^88 + 107568 * q^89 - 268896 * q^91 + 26268 * q^92 - 221460 * q^93 + 30542 * q^94 - 78606 * q^96 + 49520 * q^97 - 242304 * q^98 + 166720 * 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 $

$2$	9.21534	1.62906	0.814529	−	0.580123i	$-0.196996\pi$
$2$	9.21534	1.62906	0.814529	+	0.580123i	$0.196996\pi$
$3$	−0.734546	−0.0471211	−0.0235606	−	0.999722i	$-0.507500\pi$
$3$	−0.734546	−0.0471211	−0.0235606	+	0.999722i	$0.507500\pi$
$4$	52.9225	1.65383
$5$	0	0
$5$	0	0
$6$	−6.76909	−0.0767630
$7$	90.0205	0.694379	0.347189	−	0.937795i	$-0.387136\pi$
$7$	90.0205	0.694379	0.347189	+	0.937795i	$0.387136\pi$
$8$	192.808	1.06512
$9$	−242.460	−0.997780
$10$	0	0
$11$	−269.080	−0.670502	−0.335251	−	0.942129i	$-0.608821\pi$
$11$	−269.080	−0.670502	−0.335251	+	0.942129i	$0.608821\pi$
$12$	−38.8740	−0.0779302
$13$	444.579	0.729610	0.364805	−	0.931084i	$-0.381136\pi$
$13$	444.579	0.729610	0.364805	+	0.931084i	$0.381136\pi$
$14$	829.569	1.13118
$15$	0	0
$16$	83.2700	0.0813183
$17$	−485.649	−0.407569	−0.203784	−	0.979016i	$-0.565324\pi$
$17$	−485.649	−0.407569	−0.203784	+	0.979016i	$0.565324\pi$
$18$	−2234.36	−1.62544
$19$	−1572.80	−0.999513	−0.499756	−	0.866166i	$-0.666577\pi$
$19$	−1572.80	−0.999513	−0.499756	+	0.866166i	$0.666577\pi$
$20$	0	0
$21$	−66.1242	−0.0327199
$22$	−2479.66	−1.09229
$23$	398.704	0.157156	0.0785781	−	0.996908i	$-0.474962\pi$
$23$	398.704	0.157156	0.0785781	+	0.996908i	$0.474962\pi$
$24$	−141.626	−0.0501898
$25$	0	0
$26$	4096.95	1.18858
$27$	356.593	0.0941376
$28$	4764.11	1.14838
$29$	−841.000	−0.185695
$29$	−841.000	−0.185695
$30$	0	0
$31$	−8469.77	−1.58295	−0.791475	−	0.611202i	$-0.790686\pi$
$31$	−8469.77	−1.58295	−0.791475	+	0.611202i	$0.790686\pi$
$32$	−5402.49	−0.932651
$33$	197.652	0.0315948
$34$	−4475.43	−0.663952
$35$	0	0
$36$	−12831.6	−1.65016
$37$	−3339.33	−0.401010	−0.200505	−	0.979693i	$-0.564258\pi$
$37$	−3339.33	−0.401010	−0.200505	+	0.979693i	$0.564258\pi$
$38$	−14493.8	−1.62826
$39$	−326.564	−0.0343801
$40$	0	0
$41$	18154.2	1.68662	0.843311	−	0.537425i	$-0.180603\pi$
$41$	18154.2	1.68662	0.843311	+	0.537425i	$0.180603\pi$
$42$	−609.357	−0.0533026
$43$	−9996.71	−0.824491	−0.412246	−	0.911073i	$-0.635255\pi$
$43$	−9996.71	−0.824491	−0.412246	+	0.911073i	$0.635255\pi$
$44$	−14240.4	−1.10889
$45$	0	0
$46$	3674.20	0.256016
$47$	−12568.0	−0.829890	−0.414945	−	0.909846i	$-0.636199\pi$
$47$	−12568.0	−0.829890	−0.414945	+	0.909846i	$0.636199\pi$
$48$	−61.1656	−0.00383181
$49$	−8703.31	−0.517838
$50$	0	0
$51$	356.732	0.0192051
$52$	23528.2	1.20665
$53$	21343.1	1.04368	0.521841	−	0.853043i	$-0.325245\pi$
$53$	21343.1	1.04368	0.521841	+	0.853043i	$0.325245\pi$
$54$	3286.12	0.153356
$55$	0	0
$56$	17356.7	0.739598
$57$	1155.29	0.0470982
$58$	−7750.10	−0.302508
$59$	−30036.1	−1.12334	−0.561672	−	0.827360i	$-0.689842\pi$
$59$	−30036.1	−1.12334	−0.561672	+	0.827360i	$0.689842\pi$
$60$	0	0
$61$	49792.6	1.71333	0.856663	−	0.515877i	$-0.172534\pi$
$61$	49792.6	1.71333	0.856663	+	0.515877i	$0.172534\pi$
$62$	−78051.8	−2.57872
$63$	−21826.4	−0.692837
$64$	−52450.4	−1.60066
$65$	0	0
$66$	1821.43	0.0514697
$67$	−47588.2	−1.29513	−0.647563	−	0.762012i	$-0.724212\pi$
$67$	−47588.2	−1.29513	−0.647563	+	0.762012i	$0.724212\pi$
$68$	−25701.8	−0.674048
$69$	−292.867	−0.00740538
$70$	0	0
$71$	−50164.6	−1.18101	−0.590503	−	0.807036i	$-0.701070\pi$
$71$	−50164.6	−1.18101	−0.590503	+	0.807036i	$0.701070\pi$
$72$	−46748.3	−1.06276
$73$	44770.3	0.983294	0.491647	−	0.870795i	$-0.336395\pi$
$73$	44770.3	0.983294	0.491647	+	0.870795i	$0.336395\pi$
$74$	−30773.1	−0.653269
$75$	0	0
$76$	−83236.3	−1.65302
$77$	−24222.7	−0.465582
$78$	−3009.40	−0.0560071
$79$	−78464.6	−1.41451	−0.707255	−	0.706959i	$-0.750067\pi$
$79$	−78464.6	−1.41451	−0.707255	+	0.706959i	$0.750067\pi$
$80$	0	0
$81$	58656.0	0.993344
$82$	167297.	2.74761
$83$	−46721.8	−0.744430	−0.372215	−	0.928146i	$-0.621402\pi$
$83$	−46721.8	−0.744430	−0.372215	+	0.928146i	$0.621402\pi$
$84$	−3499.46	−0.0541131
$85$	0	0
$86$	−92123.1	−1.34314
$87$	617.753	0.00875017
$88$	−51880.7	−0.714167
$89$	−39465.7	−0.528135	−0.264068	−	0.964504i	$-0.585064\pi$
$89$	−39465.7	−0.528135	−0.264068	+	0.964504i	$0.585064\pi$
$90$	0	0
$91$	40021.2	0.506626
$92$	21100.4	0.259909
$93$	6221.43	0.0745904
$94$	−115818.	−1.35194
$95$	0	0
$96$	3968.38	0.0439476
$97$	−48336.3	−0.521608	−0.260804	−	0.965392i	$-0.583988\pi$
$97$	−48336.3	−0.521608	−0.260804	+	0.965392i	$0.583988\pi$
$98$	−80204.0	−0.843589
$99$	65241.3	0.669013
$100$	0	0
$101$	111417.	1.08680	0.543399	−	0.839475i	$-0.317137\pi$
$101$	111417.	1.08680	0.543399	+	0.839475i	$0.317137\pi$
$102$	3287.40	0.0312862
$103$	1416.34	0.0131545	0.00657726	−	0.999978i	$-0.497906\pi$
$103$	1416.34	0.0131545	0.00657726	+	0.999978i	$0.497906\pi$
$104$	85718.4	0.777124
$105$	0	0
$106$	196684.	1.70022
$107$	162530.	1.37238	0.686188	−	0.727424i	$-0.259283\pi$
$107$	162530.	1.37238	0.686188	+	0.727424i	$0.259283\pi$
$108$	18871.8	0.155687
$109$	152425.	1.22882	0.614411	−	0.788986i	$-0.289394\pi$
$109$	152425.	1.22882	0.614411	+	0.788986i	$0.289394\pi$
$110$	0	0
$111$	2452.89	0.0188961
$112$	7496.00	0.0564657
$113$	−256365.	−1.88870	−0.944350	−	0.328942i	$-0.893308\pi$
$113$	−256365.	−1.88870	−0.944350	+	0.328942i	$0.893308\pi$
$114$	10646.4	0.0767256
$115$	0	0
$116$	−44507.8	−0.307108
$117$	−107793.	−0.727990
$118$	−276792.	−1.82999
$119$	−43718.4	−0.283007
$120$	0	0
$121$	−88646.9	−0.550428
$122$	458855.	2.79111
$123$	−13335.1	−0.0794756
$124$	−448241.	−2.61793
$125$	0	0
$126$	−201138.	−1.12867
$127$	145336.	0.799585	0.399792	−	0.916606i	$-0.369082\pi$
$127$	145336.	0.799585	0.399792	+	0.916606i	$0.369082\pi$
$128$	−310469.	−1.67492
$129$	7343.04	0.0388510
$130$	0	0
$131$	−259373.	−1.32052	−0.660262	−	0.751035i	$-0.729555\pi$
$131$	−259373.	−1.32052	−0.660262	+	0.751035i	$0.729555\pi$
$132$	10460.2	0.0522523
$133$	−141584.	−0.694040
$134$	−438541.	−2.10984
$135$	0	0
$136$	−93637.0	−0.434111
$137$	−94701.8	−0.431079	−0.215539	−	0.976495i	$-0.569151\pi$
$137$	−94701.8	−0.431079	−0.215539	+	0.976495i	$0.569151\pi$
$138$	−2698.87	−0.0120638
$139$	237100.	1.04086	0.520432	−	0.853903i	$-0.325771\pi$
$139$	237100.	1.04086	0.520432	+	0.853903i	$0.325771\pi$
$140$	0	0
$141$	9231.75	0.0391054
$142$	−462284.	−1.92393
$143$	−119627.	−0.489205
$144$	−20189.7	−0.0811378
$145$	0	0
$146$	412574.	1.60184
$147$	6392.98	0.0244011
$148$	−176726.	−0.663202
$149$	−81590.7	−0.301075	−0.150538	−	0.988604i	$-0.548100\pi$
$149$	−81590.7	−0.301075	−0.150538	+	0.988604i	$0.548100\pi$
$150$	0	0
$151$	−199008.	−0.710276	−0.355138	−	0.934814i	$-0.615566\pi$
$151$	−199008.	−0.710276	−0.355138	+	0.934814i	$0.615566\pi$
$152$	−303247.	−1.06460
$153$	117751.	0.406664
$154$	−223221.	−0.758460
$155$	0	0
$156$	−17282.6	−0.0568587
$157$	321167.	1.03988	0.519938	−	0.854204i	$-0.325955\pi$
$157$	321167.	1.03988	0.519938	+	0.854204i	$0.325955\pi$
$158$	−723078.	−2.30432
$159$	−15677.5	−0.0491795
$160$	0	0
$161$	35891.6	0.109126
$162$	540535.	1.61821
$163$	621023.	1.83079	0.915395	−	0.402557i	$-0.131879\pi$
$163$	621023.	1.83079	0.915395	+	0.402557i	$0.131879\pi$
$164$	960767.	2.78938
$165$	0	0
$166$	−430557.	−1.21272
$167$	59437.0	0.164917	0.0824585	−	0.996594i	$-0.473723\pi$
$167$	59437.0	0.164917	0.0824585	+	0.996594i	$0.473723\pi$
$168$	−12749.3	−0.0348507
$169$	−173642.	−0.467669
$170$	0	0
$171$	381341.	0.997293
$172$	−529051.	−1.36357
$173$	−175144.	−0.444918	−0.222459	−	0.974942i	$-0.571408\pi$
$173$	−175144.	−0.444918	−0.222459	+	0.974942i	$0.571408\pi$
$174$	5692.80	0.0142545
$175$	0	0
$176$	−22406.3	−0.0545241
$177$	22062.9	0.0529332
$178$	−363690.	−0.860362
$179$	−421857.	−0.984086	−0.492043	−	0.870571i	$-0.663750\pi$
$179$	−421857.	−0.984086	−0.492043	+	0.870571i	$0.663750\pi$
$180$	0	0
$181$	313961.	0.712326	0.356163	−	0.934424i	$-0.384085\pi$
$181$	313961.	0.712326	0.356163	+	0.934424i	$0.384085\pi$
$182$	368809.	0.825322
$183$	−36574.9	−0.0807338
$184$	76873.3	0.167391
$185$	0	0
$186$	57332.6	0.121512
$187$	130679.	0.273275
$188$	−665128.	−1.37250
$189$	32100.7	0.0653672
$190$	0	0
$191$	85652.5	0.169886	0.0849428	−	0.996386i	$-0.472929\pi$
$191$	85652.5	0.169886	0.0849428	+	0.996386i	$0.472929\pi$
$192$	38527.2	0.0754249
$193$	−356203.	−0.688343	−0.344171	−	0.938907i	$-0.611840\pi$
$193$	−356203.	−0.688343	−0.344171	+	0.938907i	$0.611840\pi$
$194$	−445436.	−0.849729
$195$	0	0
$196$	−460601.	−0.856416
$197$	−2000.17	−0.00367199	−0.00183599	−	0.999998i	$-0.500584\pi$
$197$	−2000.17	−0.00367199	−0.00183599	+	0.999998i	$0.500584\pi$
$198$	601220.	1.08986
$199$	−241348.	−0.432027	−0.216014	−	0.976390i	$-0.569306\pi$
$199$	−241348.	−0.432027	−0.216014	+	0.976390i	$0.569306\pi$
$200$	0	0
$201$	34955.7	0.0610278
$202$	1.02675e6	1.77045
$203$	−75707.2	−0.128943
$204$	18879.1	0.0317619
$205$	0	0
$206$	13052.1	0.0214295
$207$	−96670.0	−0.156807
$208$	37020.1	0.0593307
$209$	423208.	0.670175
$210$	0	0
$211$	−611130.	−0.944991	−0.472495	−	0.881333i	$-0.656647\pi$
$211$	−611130.	−0.944991	−0.472495	+	0.881333i	$0.656647\pi$
$212$	1.12953e6	1.72607
$213$	36848.2	0.0556503
$214$	1.49777e6	2.23568
$215$	0	0
$216$	68753.9	0.100268
$217$	−762452.	−1.09917
$218$	1.40465e6	2.00182
$219$	−32885.9	−0.0463339
$220$	0	0
$221$	−215910.	−0.297366
$222$	22604.2	0.0307828
$223$	−702678.	−0.946225	−0.473112	−	0.881002i	$-0.656870\pi$
$223$	−702678.	−0.946225	−0.473112	+	0.881002i	$0.656870\pi$
$224$	−486335.	−0.647613
$225$	0	0
$226$	−2.36249e6	−3.07680
$227$	−933943.	−1.20297	−0.601487	−	0.798883i	$-0.705425\pi$
$227$	−933943.	−1.20297	−0.601487	+	0.798883i	$0.705425\pi$
$228$	61140.8	0.0778923
$229$	−1.02337e6	−1.28956	−0.644782	−	0.764367i	$-0.723052\pi$
$229$	−1.02337e6	−1.28956	−0.644782	+	0.764367i	$0.723052\pi$
$230$	0	0
$231$	17792.7	0.0219387
$232$	−162151.	−0.197788
$233$	994807.	1.20046	0.600232	−	0.799826i	$-0.295075\pi$
$233$	994807.	1.20046	0.600232	+	0.799826i	$0.295075\pi$
$234$	−993348.	−1.18594
$235$	0	0
$236$	−1.58958e6	−1.85782
$237$	57635.8	0.0666533
$238$	−402880.	−0.461034
$239$	−111950.	−0.126773	−0.0633867	−	0.997989i	$-0.520190\pi$
$239$	−111950.	−0.126773	−0.0633867	+	0.997989i	$0.520190\pi$
$240$	0	0
$241$	1.31520e6	1.45865	0.729323	−	0.684169i	$-0.239835\pi$
$241$	1.31520e6	1.45865	0.729323	+	0.684169i	$0.239835\pi$
$242$	−816911.	−0.896678
$243$	−129738.	−0.140945
$244$	2.63515e6	2.83355
$245$	0	0
$246$	−122888.	−0.129470
$247$	−699232.	−0.729255
$248$	−1.63304e6	−1.68604
$249$	34319.3	0.0350784
$250$	0	0
$251$	−440669.	−0.441498	−0.220749	−	0.975331i	$-0.570850\pi$
$251$	−440669.	−0.441498	−0.220749	+	0.975331i	$0.570850\pi$
$252$	−1.15511e6	−1.14583
$253$	−107283.	−0.105373
$254$	1.33932e6	1.30257
$255$	0	0
$256$	−1.18266e6	−1.12787
$257$	554939.	0.524098	0.262049	−	0.965055i	$-0.415602\pi$
$257$	554939.	0.524098	0.262049	+	0.965055i	$0.415602\pi$
$258$	67668.6	0.0632904
$259$	−300608.	−0.278453
$260$	0	0
$261$	203909.	0.185283
$262$	−2.39021e6	−2.15121
$263$	1.24351e6	1.10856	0.554279	−	0.832331i	$-0.312994\pi$
$263$	1.24351e6	1.10856	0.554279	+	0.832331i	$0.312994\pi$
$264$	38108.8	0.0336523
$265$	0	0
$266$	−1.30474e6	−1.13063
$267$	28989.4	0.0248863
$268$	−2.51849e6	−2.14192
$269$	598804.	0.504549	0.252275	−	0.967656i	$-0.418821\pi$
$269$	598804.	0.504549	0.252275	+	0.967656i	$0.418821\pi$
$270$	0	0
$271$	654368.	0.541251	0.270626	−	0.962685i	$-0.412769\pi$
$271$	654368.	0.541251	0.270626	+	0.962685i	$0.412769\pi$
$272$	−40440.0	−0.0331428
$273$	−29397.4	−0.0238728
$274$	−872709.	−0.702252
$275$	0	0
$276$	−15499.2	−0.0122472
$277$	1.76929e6	1.38548	0.692739	−	0.721188i	$-0.256404\pi$
$277$	1.76929e6	1.38548	0.692739	+	0.721188i	$0.256404\pi$
$278$	2.18495e6	1.69563
$279$	2.05358e6	1.57943
$280$	0	0
$281$	−495309.	−0.374206	−0.187103	−	0.982340i	$-0.559910\pi$
$281$	−495309.	−0.374206	−0.187103	+	0.982340i	$0.559910\pi$
$282$	85073.7	0.0637049
$283$	785235.	0.582819	0.291409	−	0.956598i	$-0.405876\pi$
$283$	785235.	0.582819	0.291409	+	0.956598i	$0.405876\pi$
$284$	−2.65484e6	−1.95318
$285$	0	0
$286$	−1.10241e6	−0.796943
$287$	1.63425e6	1.17115
$288$	1.30989e6	0.930580
$289$	−1.18400e6	−0.833888
$290$	0	0
$291$	35505.2	0.0245788
$292$	2.36936e6	1.62620
$293$	−1.72437e6	−1.17344	−0.586719	−	0.809790i	$-0.699581\pi$
$293$	−1.72437e6	−1.17344	−0.586719	+	0.809790i	$0.699581\pi$
$294$	58913.5	0.0397508
$295$	0	0
$296$	−643850.	−0.427125
$297$	−95952.0	−0.0631194
$298$	−751886.	−0.490469
$299$	177256.	0.114663
$300$	0	0
$301$	−899909.	−0.572509
$302$	−1.83392e6	−1.15708
$303$	−81841.0	−0.0512111
$304$	−130967.	−0.0812787
$305$	0	0
$306$	1.08511e6	0.662478
$307$	3.12637e6	1.89319	0.946597	−	0.322419i	$-0.104496\pi$
$307$	3.12637e6	1.89319	0.946597	+	0.322419i	$0.104496\pi$
$308$	−1.28193e6	−0.769992
$309$	−1040.37	−0.000619856 0
$310$	0	0
$311$	2.08430e6	1.22196	0.610982	−	0.791644i	$-0.290775\pi$
$311$	2.08430e6	1.22196	0.610982	+	0.791644i	$0.290775\pi$
$312$	−62964.1	−0.0366190
$313$	2.27357e6	1.31174	0.655871	−	0.754873i	$-0.272302\pi$
$313$	2.27357e6	1.31174	0.655871	+	0.754873i	$0.272302\pi$
$314$	2.95966e6	1.69402
$315$	0	0
$316$	−4.15254e6	−2.33935
$317$	891538.	0.498301	0.249151	−	0.968465i	$-0.419849\pi$
$317$	891538.	0.498301	0.249151	+	0.968465i	$0.419849\pi$
$318$	−144473.	−0.0801162
$319$	226296.	0.124509
$320$	0	0
$321$	−119385.	−0.0646679
$322$	330753.	0.177772
$323$	763827.	0.407370
$324$	3.10422e6	1.64282
$325$	0	0
$326$	5.72293e6	2.98246
$327$	−111963.	−0.0579035
$328$	3.50028e6	1.79646
$329$	−1.13138e6	−0.576258
$330$	0	0
$331$	−768207.	−0.385397	−0.192698	−	0.981258i	$-0.561724\pi$
$331$	−768207.	−0.385397	−0.192698	+	0.981258i	$0.561724\pi$
$332$	−2.47263e6	−1.23116
$333$	809656.	0.400120
$334$	547732.	0.268659
$335$	0	0
$336$	−5506.16	−0.00266073
$337$	740054.	0.354968	0.177484	−	0.984124i	$-0.443204\pi$
$337$	740054.	0.354968	0.177484	+	0.984124i	$0.443204\pi$
$338$	−1.60017e6	−0.761860
$339$	188312.	0.0889977
$340$	0	0
$341$	2.27904e6	1.06137
$342$	3.51418e6	1.62465
$343$	−2.29645e6	−1.05395
$344$	−1.92744e6	−0.878184
$345$	0	0
$346$	−1.61401e6	−0.724796
$347$	−2.65308e6	−1.18284	−0.591420	−	0.806363i	$-0.701433\pi$
$347$	−2.65308e6	−1.18284	−0.591420	+	0.806363i	$0.701433\pi$
$348$	32693.0	0.0144713
$349$	1.02314e6	0.449646	0.224823	−	0.974400i	$-0.427820\pi$
$349$	1.02314e6	0.449646	0.224823	+	0.974400i	$0.427820\pi$
$350$	0	0
$351$	158534.	0.0686838
$352$	1.45370e6	0.625344
$353$	2.17906e6	0.930747	0.465374	−	0.885114i	$-0.345920\pi$
$353$	2.17906e6	0.930747	0.465374	+	0.885114i	$0.345920\pi$
$354$	203317.	0.0862313
$355$	0	0
$356$	−2.08862e6	−0.873445
$357$	32113.2	0.0133356
$358$	−3.88756e6	−1.60313
$359$	4.09152e6	1.67552	0.837759	−	0.546041i	$-0.183866\pi$
$359$	4.09152e6	1.67552	0.837759	+	0.546041i	$0.183866\pi$
$360$	0	0
$361$	−2413.03	−0.000974529 0
$362$	2.89325e6	1.16042
$363$	65115.2	0.0259368
$364$	2.11802e6	0.837871
$365$	0	0
$366$	−337050.	−0.131520
$367$	113276.	0.0439009	0.0219504	−	0.999759i	$-0.493012\pi$
$367$	113276.	0.0439009	0.0219504	+	0.999759i	$0.493012\pi$
$368$	33200.1	0.0127797
$369$	−4.40168e6	−1.68288
$370$	0	0
$371$	1.92132e6	0.724711
$372$	329254.	0.123360
$373$	1.74960e6	0.651130	0.325565	−	0.945520i	$-0.394446\pi$
$373$	1.74960e6	0.651130	0.325565	+	0.945520i	$0.394446\pi$
$374$	1.20425e6	0.445181
$375$	0	0
$376$	−2.42320e6	−0.883935
$377$	−373891.	−0.135485
$378$	295819.	0.106487
$379$	2.62142e6	0.937429	0.468714	−	0.883350i	$-0.344717\pi$
$379$	2.62142e6	0.937429	0.468714	+	0.883350i	$0.344717\pi$
$380$	0	0
$381$	−106756.	−0.0376773
$382$	789317.	0.276753
$383$	−4.63046e6	−1.61297	−0.806486	−	0.591253i	$-0.798633\pi$
$383$	−4.63046e6	−1.61297	−0.806486	+	0.591253i	$0.798633\pi$
$384$	228053.	0.0789239
$385$	0	0
$386$	−3.28254e6	−1.12135
$387$	2.42381e6	0.822660
$388$	−2.55808e6	−0.862650
$389$	−3.41385e6	−1.14385	−0.571927	−	0.820305i	$-0.693804\pi$
$389$	−3.41385e6	−1.14385	−0.571927	+	0.820305i	$0.693804\pi$
$390$	0	0
$391$	−193631.	−0.0640519
$392$	−1.67807e6	−0.551562
$393$	190521.	0.0622246
$394$	−18432.2	−0.00598188
$395$	0	0
$396$	3.45273e6	1.10643
$397$	2.05992e6	0.655954	0.327977	−	0.944686i	$-0.393633\pi$
$397$	2.05992e6	0.655954	0.327977	+	0.944686i	$0.393633\pi$
$398$	−2.22410e6	−0.703797
$399$	104000.	0.0327040
$400$	0	0
$401$	4.48615e6	1.39320	0.696599	−	0.717461i	$-0.254696\pi$
$401$	4.48615e6	1.39320	0.696599	+	0.717461i	$0.254696\pi$
$402$	322129.	0.0994178
$403$	−3.76548e6	−1.15494
$404$	5.89647e6	1.79738
$405$	0	0
$406$	−697668.	−0.210055
$407$	898548.	0.268878
$408$	68780.7	0.0204558
$409$	−5.12907e6	−1.51611	−0.758055	−	0.652191i	$-0.773850\pi$
$409$	−5.12907e6	−1.51611	−0.758055	+	0.652191i	$0.773850\pi$
$410$	0	0
$411$	69562.8	0.0203129
$412$	74956.3	0.0217553
$413$	−2.70386e6	−0.780026
$414$	−890847.	−0.255448
$415$	0	0
$416$	−2.40183e6	−0.680471
$417$	−174161.	−0.0490467
$418$	3.90000e6	1.09175
$419$	−2.21170e6	−0.615446	−0.307723	−	0.951476i	$-0.599567\pi$
$419$	−2.21170e6	−0.615446	−0.307723	+	0.951476i	$0.599567\pi$
$420$	0	0
$421$	751122.	0.206540	0.103270	−	0.994653i	$-0.467069\pi$
$421$	751122.	0.206540	0.103270	+	0.994653i	$0.467069\pi$
$422$	−5.63177e6	−1.53944
$423$	3.04724e6	0.828047
$424$	4.11512e6	1.11165
$425$	0	0
$426$	339569.	0.0906575
$427$	4.48235e6	1.18970
$428$	8.60147e6	2.26967
$429$	87871.8	0.0230519
$430$	0	0
$431$	2.98345e6	0.773615	0.386808	−	0.922160i	$-0.373578\pi$
$431$	2.98345e6	0.773615	0.386808	+	0.922160i	$0.373578\pi$
$432$	29693.5	0.00765511
$433$	2.17337e6	0.557075	0.278537	−	0.960425i	$-0.410150\pi$
$433$	2.17337e6	0.557075	0.278537	+	0.960425i	$0.410150\pi$
$434$	−7.02626e6	−1.79060
$435$	0	0
$436$	8.06670e6	2.03226
$437$	−627081.	−0.157080
$438$	−303054.	−0.0754806
$439$	24436.8	0.00605178	0.00302589	−	0.999995i	$-0.499037\pi$
$439$	24436.8	0.00605178	0.00302589	+	0.999995i	$0.499037\pi$
$440$	0	0
$441$	2.11021e6	0.516689
$442$	−1.98968e6	−0.484426
$443$	6.19315e6	1.49935	0.749674	−	0.661808i	$-0.230211\pi$
$443$	6.19315e6	1.49935	0.749674	+	0.661808i	$0.230211\pi$
$444$	129813.	0.0312508
$445$	0	0
$446$	−6.47542e6	−1.54145
$447$	59932.1	0.0141870
$448$	−4.72161e6	−1.11146
$449$	7.56136e6	1.77004	0.885022	−	0.465548i	$-0.154143\pi$
$449$	7.56136e6	1.77004	0.885022	+	0.465548i	$0.154143\pi$
$450$	0	0
$451$	−4.88494e6	−1.13088
$452$	−1.35675e7	−3.12359
$453$	146180.	0.0334690
$454$	−8.60661e6	−1.95971
$455$	0	0
$456$	222749.	0.0501653
$457$	−5.02930e6	−1.12646	−0.563232	−	0.826299i	$-0.690442\pi$
$457$	−5.02930e6	−1.12646	−0.563232	+	0.826299i	$0.690442\pi$
$458$	−9.43067e6	−2.10077
$459$	−173179.	−0.0383675
$460$	0	0
$461$	3.58934e6	0.786615	0.393308	−	0.919407i	$-0.371331\pi$
$461$	3.58934e6	0.786615	0.393308	+	0.919407i	$0.371331\pi$
$462$	163966.	0.0357395
$463$	−8.86551e6	−1.92199	−0.960996	−	0.276563i	$-0.910804\pi$
$463$	−8.86551e6	−1.92199	−0.960996	+	0.276563i	$0.910804\pi$
$464$	−70030.0	−0.0151004
$465$	0	0
$466$	9.16748e6	1.95562
$467$	−3.24975e6	−0.689537	−0.344769	−	0.938688i	$-0.612043\pi$
$467$	−3.24975e6	−0.689537	−0.344769	+	0.938688i	$0.612043\pi$
$468$	−5.70467e6	−1.20397
$469$	−4.28391e6	−0.899308
$470$	0	0
$471$	−235912.	−0.0490001
$472$	−5.79119e6	−1.19650
$473$	2.68992e6	0.552823
$474$	531134.	0.108582
$475$	0	0
$476$	−2.31369e6	−0.468045
$477$	−5.17486e6	−1.04136
$478$	−1.03166e6	−0.206521
$479$	−2.33334e6	−0.464664	−0.232332	−	0.972637i	$-0.574636\pi$
$479$	−2.33334e6	−0.464664	−0.232332	+	0.972637i	$0.574636\pi$
$480$	0	0
$481$	−1.48460e6	−0.292581
$482$	1.21200e7	2.37622
$483$	−26364.0	−0.00514213
$484$	−4.69142e6	−0.910312
$485$	0	0
$486$	−1.19558e6	−0.229608
$487$	−1.35787e6	−0.259440	−0.129720	−	0.991551i	$-0.541408\pi$
$487$	−1.35787e6	−0.259440	−0.129720	+	0.991551i	$0.541408\pi$
$488$	9.60039e6	1.82490
$489$	−456170.	−0.0862689
$490$	0	0
$491$	4.42097e6	0.827587	0.413794	−	0.910371i	$-0.364203\pi$
$491$	4.42097e6	0.827587	0.413794	+	0.910371i	$0.364203\pi$
$492$	−705727.	−0.131439
$493$	408431.	0.0756836
$494$	−6.44366e6	−1.18800
$495$	0	0
$496$	−705277.	−0.128723
$497$	−4.51585e6	−0.820065
$498$	316264.	0.0571447
$499$	−9.61078e6	−1.72785	−0.863927	−	0.503617i	$-0.832002\pi$
$499$	−9.61078e6	−1.72785	−0.863927	+	0.503617i	$0.832002\pi$
$500$	0	0
$501$	−43659.2	−0.00777108
$502$	−4.06092e6	−0.719225
$503$	6.10366e6	1.07565	0.537824	−	0.843057i	$-0.319246\pi$
$503$	6.10366e6	1.07565	0.537824	+	0.843057i	$0.319246\pi$
$504$	−4.20830e6	−0.737956
$505$	0	0
$506$	−988653.	−0.171659
$507$	127548.	0.0220371
$508$	7.69155e6	1.32238
$509$	−1.01562e7	−1.73755	−0.868775	−	0.495208i	$-0.835092\pi$
$509$	−1.01562e7	−1.73755	−0.868775	+	0.495208i	$0.835092\pi$
$510$	0	0
$511$	4.03025e6	0.682778
$512$	−963628.	−0.162456
$513$	−560848.	−0.0940918
$514$	5.11395e6	0.853785
$515$	0	0
$516$	388612.	0.0642528
$517$	3.38179e6	0.556443
$518$	−2.77021e6	−0.453616
$519$	128651.	0.0209650
$520$	0	0
$521$	2.42580e6	0.391526	0.195763	−	0.980651i	$-0.437282\pi$
$521$	2.42580e6	0.391526	0.195763	+	0.980651i	$0.437282\pi$
$522$	1.87909e6	0.301837
$523$	328610.	0.0525322	0.0262661	−	0.999655i	$-0.491638\pi$
$523$	328610.	0.0525322	0.0262661	+	0.999655i	$0.491638\pi$
$524$	−1.37267e7	−2.18392
$525$	0	0
$526$	1.14593e7	1.80591
$527$	4.11334e6	0.645160
$528$	16458.4	0.00256924
$529$	−6.27738e6	−0.975302
$530$	0	0
$531$	7.28255e6	1.12085
$532$	−7.49297e6	−1.14782
$533$	8.07099e6	1.23058
$534$	267147.	0.0405413
$535$	0	0
$536$	−9.17538e6	−1.37947
$537$	309874.	0.0463713
$538$	5.51818e6	0.821940
$539$	2.34189e6	0.347212
$540$	0	0
$541$	5.52172e6	0.811113	0.405557	−	0.914070i	$-0.367078\pi$
$541$	5.52172e6	0.811113	0.405557	+	0.914070i	$0.367078\pi$
$542$	6.03022e6	0.881729
$543$	−230618.	−0.0335656
$544$	2.62372e6	0.380119
$545$	0	0
$546$	−270907.	−0.0388901
$547$	−2.61929e6	−0.374296	−0.187148	−	0.982332i	$-0.559924\pi$
$547$	−2.61929e6	−0.374296	−0.187148	+	0.982332i	$0.559924\pi$
$548$	−5.01185e6	−0.712930
$549$	−1.20727e7	−1.70952
$550$	0	0
$551$	1.32272e6	0.185605
$552$	−56467.0	−0.00788764
$553$	−7.06342e6	−0.982205
$554$	1.63046e7	2.25702
$555$	0	0
$556$	1.25479e7	1.72141
$557$	−4.95349e6	−0.676509	−0.338254	−	0.941055i	$-0.609836\pi$
$557$	−4.95349e6	−0.676509	−0.338254	+	0.941055i	$0.609836\pi$
$558$	1.89245e7	2.57299
$559$	−4.44433e6	−0.601557
$560$	0	0
$561$	−95989.4	−0.0128770
$562$	−4.56444e6	−0.609602
$563$	2.28738e6	0.304135	0.152068	−	0.988370i	$-0.451407\pi$
$563$	2.28738e6	0.304135	0.152068	+	0.988370i	$0.451407\pi$
$564$	488567.	0.0646735
$565$	0	0
$566$	7.23620e6	0.949445
$567$	5.28024e6	0.689757
$568$	−9.67214e6	−1.25792
$569$	−3.25672e6	−0.421696	−0.210848	−	0.977519i	$-0.567622\pi$
$569$	−3.25672e6	−0.421696	−0.210848	+	0.977519i	$0.567622\pi$
$570$	0	0
$571$	−9.92284e6	−1.27364	−0.636819	−	0.771013i	$-0.719750\pi$
$571$	−9.92284e6	−1.27364	−0.636819	+	0.771013i	$0.719750\pi$
$572$	−6.33098e6	−0.809060
$573$	−62915.7	−0.00800520
$574$	1.50602e7	1.90788
$575$	0	0
$576$	1.27171e7	1.59711
$577$	−1.23237e6	−0.154100	−0.0770498	−	0.997027i	$-0.524550\pi$
$577$	−1.23237e6	−0.154100	−0.0770498	+	0.997027i	$0.524550\pi$
$578$	−1.09110e7	−1.35845
$579$	261648.	0.0324355
$580$	0	0
$581$	−4.20592e6	−0.516916
$582$	327193.	0.0400402
$583$	−5.74301e6	−0.699791
$584$	8.63207e6	1.04733
$585$	0	0
$586$	−1.58906e7	−1.91160
$587$	1.02407e7	1.22669	0.613345	−	0.789815i	$-0.289823\pi$
$587$	1.02407e7	1.22669	0.613345	+	0.789815i	$0.289823\pi$
$588$	338332.	0.0403553
$589$	1.33212e7	1.58218
$590$	0	0
$591$	1469.22	0.000173028 0
$592$	−278066.	−0.0326095
$593$	1.53106e7	1.78795	0.893977	−	0.448114i	$-0.147904\pi$
$593$	1.53106e7	1.78795	0.893977	+	0.448114i	$0.147904\pi$
$594$	−884231.	−0.102825
$595$	0	0
$596$	−4.31798e6	−0.497926
$597$	177281.	0.0203576
$598$	1.63347e6	0.186792
$599$	−1.37662e6	−0.156764	−0.0783819	−	0.996923i	$-0.524975\pi$
$599$	−1.37662e6	−0.156764	−0.0783819	+	0.996923i	$0.524975\pi$
$600$	0	0
$601$	−1.39459e7	−1.57492	−0.787462	−	0.616363i	$-0.788606\pi$
$601$	−1.39459e7	−1.57492	−0.787462	+	0.616363i	$0.788606\pi$
$602$	−8.29297e6	−0.932650
$603$	1.15383e7	1.29225
$604$	−1.05320e7	−1.17467
$605$	0	0
$606$	−754192.	−0.0834258
$607$	2.10503e6	0.231892	0.115946	−	0.993255i	$-0.463010\pi$
$607$	2.10503e6	0.231892	0.115946	+	0.993255i	$0.463010\pi$
$608$	8.49701e6	0.932196
$609$	55610.4	0.00607593
$610$	0	0
$611$	−5.58746e6	−0.605496
$612$	6.23166e6	0.672551
$613$	−1.75643e7	−1.88790	−0.943950	−	0.330088i	$-0.892922\pi$
$613$	−1.75643e7	−1.88790	−0.943950	+	0.330088i	$0.892922\pi$
$614$	2.88106e7	3.08412
$615$	0	0
$616$	−4.67033e6	−0.495902
$617$	6.68190e6	0.706622	0.353311	−	0.935506i	$-0.385056\pi$
$617$	6.68190e6	0.706622	0.353311	+	0.935506i	$0.385056\pi$
$618$	−9587.34	−0.00100978
$619$	−6.69302e6	−0.702095	−0.351047	−	0.936358i	$-0.614174\pi$
$619$	−6.69302e6	−0.702095	−0.351047	+	0.936358i	$0.614174\pi$
$620$	0	0
$621$	142175.	0.0147943
$622$	1.92075e7	1.99065
$623$	−3.55272e6	−0.366726
$624$	−27193.0	−0.00279573
$625$	0	0
$626$	2.09518e7	2.13690
$627$	−310866.	−0.0315794
$628$	1.69969e7	1.71977
$629$	1.62175e6	0.163439
$630$	0	0
$631$	7.79549e6	0.779417	0.389709	−	0.920938i	$-0.372576\pi$
$631$	7.79549e6	0.779417	0.389709	+	0.920938i	$0.372576\pi$
$632$	−1.51286e7	−1.50663
$633$	448903.	0.0445290
$634$	8.21583e6	0.811761
$635$	0	0
$636$	−829692.	−0.0813344
$637$	−3.86931e6	−0.377820
$638$	2.08540e6	0.202832
$639$	1.21629e7	1.17838
$640$	0	0
$641$	6.27067e6	0.602794	0.301397	−	0.953499i	$-0.402547\pi$
$641$	6.27067e6	0.602794	0.301397	+	0.953499i	$0.402547\pi$
$642$	−1.10018e6	−0.105348
$643$	1.59445e7	1.52084	0.760420	−	0.649432i	$-0.224993\pi$
$643$	1.59445e7	1.52084	0.760420	+	0.649432i	$0.224993\pi$
$644$	1.89947e6	0.180475
$645$	0	0
$646$	7.03893e6	0.663629
$647$	−1.59290e7	−1.49598	−0.747992	−	0.663707i	$-0.768982\pi$
$647$	−1.59290e7	−1.49598	−0.747992	+	0.663707i	$0.768982\pi$
$648$	1.13093e7	1.05803
$649$	8.08210e6	0.753204
$650$	0	0
$651$	560056.	0.0517940
$652$	3.28661e7	3.02781
$653$	−2.65262e6	−0.243440	−0.121720	−	0.992564i	$-0.538841\pi$
$653$	−2.65262e6	−0.243440	−0.121720	+	0.992564i	$0.538841\pi$
$654$	−1.03178e6	−0.0943282
$655$	0	0
$656$	1.51170e6	0.137153
$657$	−1.08550e7	−0.981111
$658$	−1.04260e7	−0.938757
$659$	1.35066e7	1.21152	0.605761	−	0.795647i	$-0.292869\pi$
$659$	1.35066e7	1.21152	0.605761	+	0.795647i	$0.292869\pi$
$660$	0	0
$661$	1.17111e7	1.04254	0.521272	−	0.853391i	$-0.325458\pi$
$661$	1.17111e7	1.04254	0.521272	+	0.853391i	$0.325458\pi$
$662$	−7.07928e6	−0.627833
$663$	158596.	0.0140122
$664$	−9.00832e6	−0.792910
$665$	0	0
$666$	7.46126e6	0.651818
$667$	−335310.	−0.0291832
$668$	3.14555e6	0.272744
$669$	516149.	0.0445872
$670$	0	0
$671$	−1.33982e7	−1.14879
$672$	357235.	0.0305162
$673$	−1.81529e7	−1.54492	−0.772462	−	0.635061i	$-0.780975\pi$
$673$	−1.81529e7	−1.54492	−0.772462	+	0.635061i	$0.780975\pi$
$674$	6.81985e6	0.578263
$675$	0	0
$676$	−9.18958e6	−0.773444
$677$	3.81675e6	0.320053	0.160027	−	0.987113i	$-0.448842\pi$
$677$	3.81675e6	0.320053	0.160027	+	0.987113i	$0.448842\pi$
$678$	1.73536e6	0.144982
$679$	−4.35126e6	−0.362193
$680$	0	0
$681$	686024.	0.0566855
$682$	2.10022e7	1.72903
$683$	2.60743e6	0.213876	0.106938	−	0.994266i	$-0.465895\pi$
$683$	2.60743e6	0.213876	0.106938	+	0.994266i	$0.465895\pi$
$684$	2.01815e7	1.64935
$685$	0	0
$686$	−2.11626e7	−1.71695
$687$	751710.	0.0607657
$688$	−832426.	−0.0670462
$689$	9.48871e6	0.761481
$690$	0	0
$691$	81457.6	0.00648988	0.00324494	−	0.999995i	$-0.498967\pi$
$691$	81457.6	0.00648988	0.00324494	+	0.999995i	$0.498967\pi$
$692$	−9.26905e6	−0.735817
$693$	5.87305e6	0.464548
$694$	−2.44490e7	−1.92692
$695$	0	0
$696$	119108.	0.00932001
$697$	−8.81659e6	−0.687414
$698$	9.42856e6	0.732499
$699$	−730731.	−0.0565672
$700$	0	0
$701$	−2.32967e7	−1.79060	−0.895300	−	0.445464i	$-0.853039\pi$
$701$	−2.32967e7	−1.79060	−0.895300	+	0.445464i	$0.853039\pi$
$702$	1.46094e6	0.111890
$703$	5.25209e6	0.400815
$704$	1.41134e7	1.07324
$705$	0	0
$706$	2.00807e7	1.51624
$707$	1.00298e7	0.754649
$708$	1.16762e6	0.0875425
$709$	7.52252e6	0.562015	0.281008	−	0.959706i	$-0.409331\pi$
$709$	7.52252e6	0.562015	0.281008	+	0.959706i	$0.409331\pi$
$710$	0	0
$711$	1.90246e7	1.41137
$712$	−7.60930e6	−0.562529
$713$	−3.37693e6	−0.248770
$714$	295934.	0.0217245
$715$	0	0
$716$	−2.23257e7	−1.62751
$717$	82232.2	0.00597371
$718$	3.77048e7	2.72951
$719$	1.30064e7	0.938289	0.469144	−	0.883121i	$-0.344562\pi$
$719$	1.30064e7	0.938289	0.469144	+	0.883121i	$0.344562\pi$
$720$	0	0
$721$	127500.	0.00913421
$722$	−22236.9	−0.00158756
$723$	−966076.	−0.0687331
$724$	1.66156e7	1.17806
$725$	0	0
$726$	600059.	0.0422525
$727$	−1.98038e7	−1.38967	−0.694835	−	0.719169i	$-0.744523\pi$
$727$	−1.98038e7	−1.38967	−0.694835	+	0.719169i	$0.744523\pi$
$728$	7.71641e6	0.539618
$729$	−1.41581e7	−0.986702
$730$	0	0
$731$	4.85490e6	0.336037
$732$	−1.93564e6	−0.133520
$733$	−1.81414e7	−1.24713	−0.623565	−	0.781772i	$-0.714316\pi$
$733$	−1.81414e7	−1.24713	−0.623565	+	0.781772i	$0.714316\pi$
$734$	1.04388e6	0.0715170
$735$	0	0
$736$	−2.15400e6	−0.146572
$737$	1.28050e7	0.868385
$738$	−4.05630e7	−2.74150
$739$	−2.22326e7	−1.49754	−0.748771	−	0.662829i	$-0.769355\pi$
$739$	−2.22326e7	−1.49754	−0.748771	+	0.662829i	$0.769355\pi$
$740$	0	0
$741$	513618.	0.0343633
$742$	1.77056e7	1.18059
$743$	1.40248e6	0.0932021	0.0466011	−	0.998914i	$-0.485161\pi$
$743$	1.40248e6	0.0932021	0.0466011	+	0.998914i	$0.485161\pi$
$744$	1.19954e6	0.0794479
$745$	0	0
$746$	1.61232e7	1.06073
$747$	1.13282e7	0.742777
$748$	6.91584e6	0.451950
$749$	1.46310e7	0.952948
$750$	0	0
$751$	1.92135e7	1.24310	0.621552	−	0.783373i	$-0.286503\pi$
$751$	1.92135e7	1.24310	0.621552	+	0.783373i	$0.286503\pi$
$752$	−1.04653e6	−0.0674853
$753$	323692.	0.0208039
$754$	−3.44553e6	−0.220713
$755$	0	0
$756$	1.69885e6	0.108106
$757$	1.23078e7	0.780621	0.390310	−	0.920683i	$-0.372368\pi$
$757$	1.23078e7	0.780621	0.390310	+	0.920683i	$0.372368\pi$
$758$	2.41573e7	1.52713
$759$	78804.6	0.00496532
$760$	0	0
$761$	4.65071e6	0.291110	0.145555	−	0.989350i	$-0.453503\pi$
$761$	4.65071e6	0.291110	0.145555	+	0.989350i	$0.453503\pi$
$762$	−983794.	−0.0613786
$763$	1.37214e7	0.853268
$764$	4.53294e6	0.280961
$765$	0	0
$766$	−4.26712e7	−2.62762
$767$	−1.33534e7	−0.819603
$768$	868719.	0.0531467
$769$	1.54937e6	0.0944800	0.0472400	−	0.998884i	$-0.484957\pi$
$769$	1.54937e6	0.0944800	0.0472400	+	0.998884i	$0.484957\pi$
$770$	0	0
$771$	−407628.	−0.0246961
$772$	−1.88512e7	−1.13840
$773$	1.71208e7	1.03056	0.515282	−	0.857021i	$-0.327687\pi$
$773$	1.71208e7	1.03056	0.515282	+	0.857021i	$0.327687\pi$
$774$	2.23362e7	1.34016
$775$	0	0
$776$	−9.31962e6	−0.555577
$777$	220811.	0.0131210
$778$	−3.14598e7	−1.86340
$779$	−2.85529e7	−1.68580
$780$	0	0
$781$	1.34983e7	0.791866
$782$	−1.78437e6	−0.104344
$783$	−299895.	−0.0174809
$784$	−724724.	−0.0421097
$785$	0	0
$786$	1.75572e6	0.101367
$787$	681275.	0.0392090	0.0196045	−	0.999808i	$-0.493759\pi$
$787$	681275.	0.0392090	0.0196045	+	0.999808i	$0.493759\pi$
$788$	−105854.	−0.00607284
$789$	−913412.	−0.0522365
$790$	0	0
$791$	−2.30781e7	−1.31147
$792$	1.25790e7	0.712581
$793$	2.21367e7	1.25006
$794$	1.89828e7	1.06859
$795$	0	0
$796$	−1.27727e7	−0.714498
$797$	−530445.	−0.0295798	−0.0147899	−	0.999891i	$-0.504708\pi$
$797$	−530445.	−0.0295798	−0.0147899	+	0.999891i	$0.504708\pi$
$798$	958394.	0.0532766
$799$	6.10363e6	0.338237
$800$	0	0
$801$	9.56888e6	0.526962
$802$	4.13414e7	2.26960
$803$	−1.20468e7	−0.659300
$804$	1.84994e6	0.100930
$805$	0	0
$806$	−3.47002e7	−1.88146
$807$	−439849.	−0.0237749
$808$	2.14821e7	1.15757
$809$	−2.65631e7	−1.42694	−0.713472	−	0.700684i	$-0.752878\pi$
$809$	−2.65631e7	−1.42694	−0.713472	+	0.700684i	$0.752878\pi$
$810$	0	0
$811$	1.11660e7	0.596137	0.298069	−	0.954544i	$-0.403658\pi$
$811$	1.11660e7	0.596137	0.298069	+	0.954544i	$0.403658\pi$
$812$	−4.00662e6	−0.213249
$813$	−480663.	−0.0255044
$814$	8.28043e6	0.438018
$815$	0	0
$816$	29705.0	0.00156173
$817$	1.57228e7	0.824089
$818$	−4.72661e7	−2.46983
$819$	−9.70357e6	−0.505501
$820$	0	0
$821$	−3.42932e7	−1.77562	−0.887811	−	0.460209i	$-0.847774\pi$
$821$	−3.42932e7	−1.77562	−0.887811	+	0.460209i	$0.847774\pi$
$822$	641045.	0.0330909
$823$	−1.93467e7	−0.995651	−0.497825	−	0.867277i	$-0.665868\pi$
$823$	−1.93467e7	−0.995651	−0.497825	+	0.867277i	$0.665868\pi$
$824$	273082.	0.0140112
$825$	0	0
$826$	−2.49170e7	−1.27071
$827$	−2.67747e7	−1.36132	−0.680662	−	0.732598i	$-0.738308\pi$
$827$	−2.67747e7	−1.36132	−0.680662	+	0.732598i	$0.738308\pi$
$828$	−5.11602e6	−0.259332
$829$	−2.44308e7	−1.23467	−0.617335	−	0.786700i	$-0.711788\pi$
$829$	−2.44308e7	−1.23467	−0.617335	+	0.786700i	$0.711788\pi$
$830$	0	0
$831$	−1.29962e6	−0.0652853
$832$	−2.33184e7	−1.16786
$833$	4.22676e6	0.211055
$834$	−1.60495e6	−0.0798999
$835$	0	0
$836$	2.23972e7	1.10835
$837$	−3.02026e6	−0.149015
$838$	−2.03815e7	−1.00260
$839$	9.17559e6	0.450017	0.225009	−	0.974357i	$-0.427759\pi$
$839$	9.17559e6	0.450017	0.225009	+	0.974357i	$0.427759\pi$
$840$	0	0
$841$	707281.	0.0344828
$842$	6.92184e6	0.336466
$843$	363827.	0.0176330
$844$	−3.23425e7	−1.56285
$845$	0	0
$846$	2.80813e7	1.34894
$847$	−7.98004e6	−0.382205
$848$	1.77724e6	0.0848705
$849$	−576791.	−0.0274631
$850$	0	0
$851$	−1.33141e6	−0.0630212
$852$	1.95010e6	0.0920360
$853$	−1.34195e7	−0.631487	−0.315744	−	0.948845i	$-0.602254\pi$
$853$	−1.34195e7	−0.631487	−0.315744	+	0.948845i	$0.602254\pi$
$854$	4.13064e7	1.93808
$855$	0	0
$856$	3.13370e7	1.46175
$857$	−4.82712e6	−0.224510	−0.112255	−	0.993679i	$-0.535807\pi$
$857$	−4.82712e6	−0.224510	−0.112255	+	0.993679i	$0.535807\pi$
$858$	809769.	0.0375528
$859$	2.23698e7	1.03438	0.517188	−	0.855872i	$-0.326979\pi$
$859$	2.23698e7	1.03438	0.517188	+	0.855872i	$0.326979\pi$
$860$	0	0
$861$	−1.20043e6	−0.0551861
$862$	2.74935e7	1.26026
$863$	2.28440e6	0.104411	0.0522054	−	0.998636i	$-0.483375\pi$
$863$	2.28440e6	0.104411	0.0522054	+	0.998636i	$0.483375\pi$
$864$	−1.92649e6	−0.0877975
$865$	0	0
$866$	2.00283e7	0.907507
$867$	869703.	0.0392937
$868$	−4.03509e7	−1.81783
$869$	2.11132e7	0.948431
$870$	0	0
$871$	−2.11567e7	−0.944938
$872$	2.93887e7	1.30885
$873$	1.17196e7	0.520450
$874$	−5.77876e6	−0.255892
$875$	0	0
$876$	−1.74040e6	−0.0766283
$877$	−2.19674e7	−0.964452	−0.482226	−	0.876047i	$-0.660172\pi$
$877$	−2.19674e7	−0.964452	−0.482226	+	0.876047i	$0.660172\pi$
$878$	225194.	0.00985870
$879$	1.26663e6	0.0552938
$880$	0	0
$881$	2.81070e6	0.122004	0.0610021	−	0.998138i	$-0.480570\pi$
$881$	2.81070e6	0.122004	0.0610021	+	0.998138i	$0.480570\pi$
$882$	1.94463e7	0.841715
$883$	3.24911e7	1.40237	0.701186	−	0.712978i	$-0.252654\pi$
$883$	3.24911e7	1.40237	0.701186	+	0.712978i	$0.252654\pi$
$884$	−1.14265e7	−0.491792
$885$	0	0
$886$	5.70720e7	2.44252
$887$	−3.68463e7	−1.57248	−0.786239	−	0.617923i	$-0.787974\pi$
$887$	−3.68463e7	−1.57248	−0.786239	+	0.617923i	$0.787974\pi$
$888$	472937.	0.0201266
$889$	1.30832e7	0.555215
$890$	0	0
$891$	−1.57831e7	−0.666039
$892$	−3.71875e7	−1.56489
$893$	1.97669e7	0.829486
$894$	552294.	0.0231114
$895$	0	0
$896$	−2.79485e7	−1.16303
$897$	−130202.	−0.00540304
$898$	6.96805e7	2.88350
$899$	7.12307e6	0.293946
$900$	0	0
$901$	−1.03653e7	−0.425372
$902$	−4.50164e7	−1.84227
$903$	661024.	0.0269773
$904$	−4.94292e7	−2.01170
$905$	0	0
$906$	1.34710e6	0.0545230
$907$	−6.77134e6	−0.273311	−0.136655	−	0.990619i	$-0.543635\pi$
$907$	−6.77134e6	−0.273311	−0.136655	+	0.990619i	$0.543635\pi$
$908$	−4.94266e7	−1.98951
$909$	−2.70142e7	−1.08438
$910$	0	0
$911$	1.38061e7	0.551156	0.275578	−	0.961279i	$-0.411131\pi$
$911$	1.38061e7	0.551156	0.275578	+	0.961279i	$0.411131\pi$
$912$	96201.0	0.00382994
$913$	1.25719e7	0.499142
$914$	−4.63467e7	−1.83507
$915$	0	0
$916$	−5.41591e7	−2.13272
$917$	−2.33489e7	−0.916943
$918$	−1.59590e6	−0.0625029
$919$	−3.45509e7	−1.34949	−0.674746	−	0.738050i	$-0.735747\pi$
$919$	−3.45509e7	−1.34949	−0.674746	+	0.738050i	$0.735747\pi$
$920$	0	0
$921$	−2.29647e6	−0.0892094
$922$	3.30770e7	1.28144
$923$	−2.23022e7	−0.861673
$924$	941634.	0.0362829
$925$	0	0
$926$	−8.16987e7	−3.13103
$927$	−343407.	−0.0131253
$928$	4.54349e6	0.173189
$929$	−2.47472e7	−0.940776	−0.470388	−	0.882460i	$-0.655886\pi$
$929$	−2.47472e7	−0.940776	−0.470388	+	0.882460i	$0.655886\pi$
$930$	0	0
$931$	1.36885e7	0.517586
$932$	5.26477e7	1.98536
$933$	−1.53101e6	−0.0575803
$934$	−2.99476e7	−1.12330
$935$	0	0
$936$	−2.07833e7	−0.775399
$937$	−1.40114e6	−0.0521352	−0.0260676	−	0.999660i	$-0.508299\pi$
$937$	−1.40114e6	−0.0521352	−0.0260676	+	0.999660i	$0.508299\pi$
$938$	−3.94777e7	−1.46502
$939$	−1.67004e6	−0.0618107
$940$	0	0
$941$	−2.79452e7	−1.02881	−0.514403	−	0.857548i	$-0.671987\pi$
$941$	−2.79452e7	−1.02881	−0.514403	+	0.857548i	$0.671987\pi$
$942$	−2.17400e6	−0.0798240
$943$	7.23817e6	0.265063
$944$	−2.50110e6	−0.0913484
$945$	0	0
$946$	2.47885e7	0.900580
$947$	−3.03936e7	−1.10131	−0.550653	−	0.834734i	$-0.685621\pi$
$947$	−3.03936e7	−1.10131	−0.550653	+	0.834734i	$0.685621\pi$
$948$	3.05023e6	0.110233
$949$	1.99040e7	0.717421
$950$	0	0
$951$	−654876.	−0.0234805
$952$	−8.42925e6	−0.301437
$953$	−3.75892e7	−1.34070	−0.670349	−	0.742046i	$-0.733856\pi$
$953$	−3.75892e7	−1.34070	−0.670349	+	0.742046i	$0.733856\pi$
$954$	−4.76881e7	−1.69644
$955$	0	0
$956$	−5.92466e6	−0.209661
$957$	−166225.	−0.00586701
$958$	−2.15025e7	−0.756964
$959$	−8.52510e6	−0.299332
$960$	0	0
$961$	4.31078e7	1.50573
$962$	−1.36811e7	−0.476632
$963$	−3.94070e7	−1.36933
$964$	6.96038e7	2.41235
$965$	0	0
$966$	−242953.	−0.00837683
$967$	−4.14600e7	−1.42582	−0.712908	−	0.701258i	$-0.752622\pi$
$967$	−4.14600e7	−1.42582	−0.712908	+	0.701258i	$0.752622\pi$
$968$	−1.70918e7	−0.586273
$969$	−561066.	−0.0191957
$970$	0	0
$971$	−5.71685e6	−0.194585	−0.0972924	−	0.995256i	$-0.531018\pi$
$971$	−5.71685e6	−0.194585	−0.0972924	+	0.995256i	$0.531018\pi$
$972$	−6.86603e6	−0.233099
$973$	2.13438e7	0.722754
$974$	−1.25133e7	−0.422642
$975$	0	0
$976$	4.14622e6	0.139325
$977$	−2.35225e6	−0.0788400	−0.0394200	−	0.999223i	$-0.512551\pi$
$977$	−2.35225e6	−0.0788400	−0.0394200	+	0.999223i	$0.512551\pi$
$978$	−4.20376e6	−0.140537
$979$	1.06194e7	0.354115
$980$	0	0
$981$	−3.69570e7	−1.22609
$982$	4.07407e7	1.34819
$983$	2.67280e7	0.882232	0.441116	−	0.897450i	$-0.354583\pi$
$983$	2.67280e7	0.882232	0.441116	+	0.897450i	$0.354583\pi$
$984$	−2.57111e6	−0.0846512
$985$	0	0
$986$	3.76383e6	0.123293
$987$	831047.	0.0271539
$988$	−3.70051e7	−1.20606
$989$	−3.98573e6	−0.129574
$990$	0	0
$991$	−1.24011e7	−0.401122	−0.200561	−	0.979681i	$-0.564276\pi$
$991$	−1.24011e7	−0.401122	−0.200561	+	0.979681i	$0.564276\pi$
$992$	4.57578e7	1.47634
$993$	564283.	0.0181603
$994$	−4.16151e7	−1.33593
$995$	0	0
$996$	1.81626e6	0.0580136
$997$	−1.41176e7	−0.449803	−0.224902	−	0.974381i	$-0.572206\pi$
$997$	−1.41176e7	−0.449803	−0.224902	+	0.974381i	$0.572206\pi$
$998$	−8.85666e7	−2.81477
$999$	−1.19078e6	−0.0377502

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.6.a.a.1.4		4
5.4	even	2		29.6.a.a.1.1	✓	4
15.14	odd	2		261.6.a.a.1.4		4
20.19	odd	2		464.6.a.i.1.2		4
145.144	even	2		841.6.a.a.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.6.a.a.1.1	✓	4	5.4	even	2
261.6.a.a.1.4		4	15.14	odd	2
464.6.a.i.1.2		4	20.19	odd	2
725.6.a.a.1.4		4	1.1	even	1	trivial
841.6.a.a.1.4		4	145.144	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	725.a (trivial)

\(f(q)\)	\(=\)	\(q+9.21534 q^{2} -0.734546 q^{3} +52.9225 q^{4} -6.76909 q^{6} +90.0205 q^{7} +192.808 q^{8} -242.460 q^{9} +O(q^{10})\)	\(q+9.21534 q^{2} -0.734546 q^{3} +52.9225 q^{4} -6.76909 q^{6} +90.0205 q^{7} +192.808 q^{8} -242.460 q^{9} -269.080 q^{11} -38.8740 q^{12} +444.579 q^{13} +829.569 q^{14} +83.2700 q^{16} -485.649 q^{17} -2234.36 q^{18} -1572.80 q^{19} -66.1242 q^{21} -2479.66 q^{22} +398.704 q^{23} -141.626 q^{24} +4096.95 q^{26} +356.593 q^{27} +4764.11 q^{28} -841.000 q^{29} -8469.77 q^{31} -5402.49 q^{32} +197.652 q^{33} -4475.43 q^{34} -12831.6 q^{36} -3339.33 q^{37} -14493.8 q^{38} -326.564 q^{39} +18154.2 q^{41} -609.357 q^{42} -9996.71 q^{43} -14240.4 q^{44} +3674.20 q^{46} -12568.0 q^{47} -61.1656 q^{48} -8703.31 q^{49} +356.732 q^{51} +23528.2 q^{52} +21343.1 q^{53} +3286.12 q^{54} +17356.7 q^{56} +1155.29 q^{57} -7750.10 q^{58} -30036.1 q^{59} +49792.6 q^{61} -78051.8 q^{62} -21826.4 q^{63} -52450.4 q^{64} +1821.43 q^{66} -47588.2 q^{67} -25701.8 q^{68} -292.867 q^{69} -50164.6 q^{71} -46748.3 q^{72} +44770.3 q^{73} -30773.1 q^{74} -83236.3 q^{76} -24222.7 q^{77} -3009.40 q^{78} -78464.6 q^{79} +58656.0 q^{81} +167297. q^{82} -46721.8 q^{83} -3499.46 q^{84} -92123.1 q^{86} +617.753 q^{87} -51880.7 q^{88} -39465.7 q^{89} +40021.2 q^{91} +21100.4 q^{92} +6221.43 q^{93} -115818. q^{94} +3968.38 q^{96} -48336.3 q^{97} -80204.0 q^{98} +65241.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 28 q^{3} + 10 q^{4} - 194 q^{6} + 208 q^{7} + 504 q^{8} - 280 q^{9}+O(q^{10}) \) 4 * q + 28 * q^3 + 10 * q^4 - 194 * q^6 + 208 * q^7 + 504 * q^8 - 280 * q^9	\( 4 q + 28 q^{3} + 10 q^{4} - 194 q^{6} + 208 q^{7} + 504 q^{8} - 280 q^{9} - 124 q^{11} - 20 q^{12} + 460 q^{13} + 768 q^{14} - 414 q^{16} - 184 q^{17} - 3208 q^{18} - 2392 q^{19} + 992 q^{21} - 5538 q^{22} + 1192 q^{23} + 6786 q^{24} + 4724 q^{26} - 2468 q^{27} - 44 q^{28} - 3364 q^{29} - 19212 q^{31} - 6552 q^{32} + 10580 q^{33} - 7612 q^{34} - 7468 q^{36} + 10928 q^{37} + 456 q^{38} - 8732 q^{39} - 1120 q^{41} - 1844 q^{42} + 21420 q^{43} - 1932 q^{44} - 7588 q^{46} - 23772 q^{47} - 33060 q^{48} + 10452 q^{49} + 12744 q^{51} + 29062 q^{52} - 8860 q^{53} + 35410 q^{54} + 34304 q^{56} - 48944 q^{57} - 10840 q^{59} + 49448 q^{61} - 18518 q^{62} - 27488 q^{63} - 20734 q^{64} - 47744 q^{66} + 7840 q^{67} - 20724 q^{68} + 58792 q^{69} - 48744 q^{71} - 8088 q^{72} + 74992 q^{73} - 35920 q^{74} - 140792 q^{76} - 128656 q^{77} - 2982 q^{78} - 106076 q^{79} - 59692 q^{81} + 234132 q^{82} - 62888 q^{83} - 59832 q^{84} - 216014 q^{86} - 23548 q^{87} + 39426 q^{88} + 107568 q^{89} - 268896 q^{91} + 26268 q^{92} - 221460 q^{93} + 30542 q^{94} - 78606 q^{96} + 49520 q^{97} - 242304 q^{98} + 166720 q^{99}+O(q^{100}) \) 4 * q + 28 * q^3 + 10 * q^4 - 194 * q^6 + 208 * q^7 + 504 * q^8 - 280 * q^9 - 124 * q^11 - 20 * q^12 + 460 * q^13 + 768 * q^14 - 414 * q^16 - 184 * q^17 - 3208 * q^18 - 2392 * q^19 + 992 * q^21 - 5538 * q^22 + 1192 * q^23 + 6786 * q^24 + 4724 * q^26 - 2468 * q^27 - 44 * q^28 - 3364 * q^29 - 19212 * q^31 - 6552 * q^32 + 10580 * q^33 - 7612 * q^34 - 7468 * q^36 + 10928 * q^37 + 456 * q^38 - 8732 * q^39 - 1120 * q^41 - 1844 * q^42 + 21420 * q^43 - 1932 * q^44 - 7588 * q^46 - 23772 * q^47 - 33060 * q^48 + 10452 * q^49 + 12744 * q^51 + 29062 * q^52 - 8860 * q^53 + 35410 * q^54 + 34304 * q^56 - 48944 * q^57 - 10840 * q^59 + 49448 * q^61 - 18518 * q^62 - 27488 * q^63 - 20734 * q^64 - 47744 * q^66 + 7840 * q^67 - 20724 * q^68 + 58792 * q^69 - 48744 * q^71 - 8088 * q^72 + 74992 * q^73 - 35920 * q^74 - 140792 * q^76 - 128656 * q^77 - 2982 * q^78 - 106076 * q^79 - 59692 * q^81 + 234132 * q^82 - 62888 * q^83 - 59832 * q^84 - 216014 * q^86 - 23548 * q^87 + 39426 * q^88 + 107568 * q^89 - 268896 * q^91 + 26268 * q^92 - 221460 * q^93 + 30542 * q^94 - 78606 * q^96 + 49520 * q^97 - 242304 * q^98 + 166720 * q^99

Introduction

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Varieties

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Database

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