LMFDB - Embedded newform 1075.6.a.l.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,6,Mod(1,1075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, 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("1075.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1075.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:	$172.412606299$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	no (minimal twist has level 215)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.98842 q^{2} -22.0225 q^{3} +67.7685 q^{4} +219.970 q^{6} +253.048 q^{7} -357.270 q^{8} +241.992 q^{9} +O(q^{10})$	\(q-9.98842 q^{2} -22.0225 q^{3} +67.7685 q^{4} +219.970 q^{6} +253.048 q^{7} -357.270 q^{8} +241.992 q^{9} +148.365 q^{11} -1492.43 q^{12} +867.385 q^{13} -2527.55 q^{14} +1399.97 q^{16} +1309.04 q^{17} -2417.11 q^{18} -1327.66 q^{19} -5572.75 q^{21} -1481.93 q^{22} -581.591 q^{23} +7868.00 q^{24} -8663.80 q^{26} +22.2056 q^{27} +17148.7 q^{28} +6091.79 q^{29} -8059.15 q^{31} -2550.87 q^{32} -3267.37 q^{33} -13075.3 q^{34} +16399.4 q^{36} -2451.51 q^{37} +13261.2 q^{38} -19102.0 q^{39} +1326.86 q^{41} +55663.0 q^{42} -1849.00 q^{43} +10054.5 q^{44} +5809.18 q^{46} +21553.5 q^{47} -30831.0 q^{48} +47226.3 q^{49} -28828.5 q^{51} +58781.4 q^{52} +24672.6 q^{53} -221.799 q^{54} -90406.5 q^{56} +29238.4 q^{57} -60847.4 q^{58} +6434.55 q^{59} +33405.6 q^{61} +80498.2 q^{62} +61235.5 q^{63} -19320.0 q^{64} +32635.9 q^{66} +4801.81 q^{67} +88712.0 q^{68} +12808.1 q^{69} +39844.4 q^{71} -86456.5 q^{72} -638.964 q^{73} +24486.7 q^{74} -89973.3 q^{76} +37543.5 q^{77} +190799. q^{78} +26896.6 q^{79} -59293.0 q^{81} -13253.2 q^{82} -32090.8 q^{83} -377657. q^{84} +18468.6 q^{86} -134157. q^{87} -53006.4 q^{88} +129089. q^{89} +219490. q^{91} -39413.6 q^{92} +177483. q^{93} -215285. q^{94} +56176.7 q^{96} +61004.0 q^{97} -471715. q^{98} +35903.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 20 q^{2} + 54 q^{3} + 826 q^{4} - 162 q^{6} + 196 q^{7} + 960 q^{8} + 4098 q^{9}+O(q^{10}) $ 52 * q + 20 * q^2 + 54 * q^3 + 826 * q^4 - 162 * q^6 + 196 * q^7 + 960 * q^8 + 4098 * q^9	\( 52 q + 20 q^{2} + 54 q^{3} + 826 q^{4} - 162 q^{6} + 196 q^{7} + 960 q^{8} + 4098 q^{9} - 664 q^{11} - 523 q^{12} + 2704 q^{13} + 150 q^{14} + 13474 q^{16} + 7266 q^{17} + 4860 q^{18} - 1970 q^{19} + 800 q^{21} + 14477 q^{22} + 9522 q^{23} + 314 q^{24} + 5514 q^{26} + 22926 q^{27} + 9408 q^{28} - 7188 q^{29} - 11556 q^{31} + 48390 q^{32} + 26136 q^{33} + 16774 q^{34} + 51872 q^{36} + 42558 q^{37} + 46208 q^{38} + 4682 q^{39} - 7746 q^{41} + 174265 q^{42} - 96148 q^{43} - 48600 q^{44} + 16182 q^{46} + 87136 q^{47} - 2912 q^{48} + 142286 q^{49} - 3710 q^{51} + 146868 q^{52} + 127034 q^{53} - 49563 q^{54} - 2849 q^{56} + 101594 q^{57} + 9480 q^{58} - 55924 q^{59} + 73702 q^{61} + 186016 q^{62} + 50120 q^{63} + 157750 q^{64} + 58211 q^{66} + 131996 q^{67} + 298560 q^{68} + 128436 q^{69} - 56284 q^{71} + 343775 q^{72} + 128620 q^{73} - 17721 q^{74} - 170410 q^{76} + 448438 q^{77} + 237616 q^{78} + 106204 q^{79} + 478568 q^{81} + 249596 q^{82} + 348616 q^{83} - 131855 q^{84} - 36980 q^{86} + 267478 q^{87} + 525216 q^{88} + 80410 q^{89} + 226376 q^{91} + 581456 q^{92} + 902902 q^{93} + 180980 q^{94} + 38543 q^{96} + 316148 q^{97} + 295095 q^{98} + 68428 q^{99}+O(q^{100}) \) 52 * q + 20 * q^2 + 54 * q^3 + 826 * q^4 - 162 * q^6 + 196 * q^7 + 960 * q^8 + 4098 * q^9 - 664 * q^11 - 523 * q^12 + 2704 * q^13 + 150 * q^14 + 13474 * q^16 + 7266 * q^17 + 4860 * q^18 - 1970 * q^19 + 800 * q^21 + 14477 * q^22 + 9522 * q^23 + 314 * q^24 + 5514 * q^26 + 22926 * q^27 + 9408 * q^28 - 7188 * q^29 - 11556 * q^31 + 48390 * q^32 + 26136 * q^33 + 16774 * q^34 + 51872 * q^36 + 42558 * q^37 + 46208 * q^38 + 4682 * q^39 - 7746 * q^41 + 174265 * q^42 - 96148 * q^43 - 48600 * q^44 + 16182 * q^46 + 87136 * q^47 - 2912 * q^48 + 142286 * q^49 - 3710 * q^51 + 146868 * q^52 + 127034 * q^53 - 49563 * q^54 - 2849 * q^56 + 101594 * q^57 + 9480 * q^58 - 55924 * q^59 + 73702 * q^61 + 186016 * q^62 + 50120 * q^63 + 157750 * q^64 + 58211 * q^66 + 131996 * q^67 + 298560 * q^68 + 128436 * q^69 - 56284 * q^71 + 343775 * q^72 + 128620 * q^73 - 17721 * q^74 - 170410 * q^76 + 448438 * q^77 + 237616 * q^78 + 106204 * q^79 + 478568 * q^81 + 249596 * q^82 + 348616 * q^83 - 131855 * q^84 - 36980 * q^86 + 267478 * q^87 + 525216 * q^88 + 80410 * q^89 + 226376 * q^91 + 581456 * q^92 + 902902 * q^93 + 180980 * q^94 + 38543 * q^96 + 316148 * q^97 + 295095 * q^98 + 68428 * 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 $

$2$	−9.98842	−1.76572	−0.882860	−	0.469637i	$-0.844385\pi$
$2$	−9.98842	−1.76572	−0.882860	+	0.469637i	$0.844385\pi$
$3$	−22.0225	−1.41275	−0.706373	−	0.707840i	$-0.749670\pi$
$3$	−22.0225	−1.41275	−0.706373	+	0.707840i	$0.749670\pi$
$4$	67.7685	2.11776
$5$	0	0
$5$	0	0
$6$	219.970	2.49451
$7$	253.048	1.95190	0.975950	−	0.217993i	$-0.0699511\pi$
$7$	253.048	1.95190	0.975950	+	0.217993i	$0.0699511\pi$
$8$	−357.270	−1.97366
$9$	241.992	0.995851
$10$	0	0
$11$	148.365	0.369700	0.184850	−	0.982767i	$-0.440820\pi$
$11$	148.365	0.369700	0.184850	+	0.982767i	$0.440820\pi$
$12$	−1492.43	−2.99186
$13$	867.385	1.42349	0.711744	−	0.702439i	$-0.247906\pi$
$13$	867.385	1.42349	0.711744	+	0.702439i	$0.247906\pi$
$14$	−2527.55	−3.44651
$15$	0	0
$16$	1399.97	1.36716
$17$	1309.04	1.09858	0.549291	−	0.835631i	$-0.314898\pi$
$17$	1309.04	1.09858	0.549291	+	0.835631i	$0.314898\pi$
$18$	−2417.11	−1.75839
$19$	−1327.66	−0.843727	−0.421863	−	0.906659i	$-0.638624\pi$
$19$	−1327.66	−0.843727	−0.421863	+	0.906659i	$0.638624\pi$
$20$	0	0
$21$	−5572.75	−2.75754
$22$	−1481.93	−0.652787
$23$	−581.591	−0.229244	−0.114622	−	0.993409i	$-0.536566\pi$
$23$	−581.591	−0.229244	−0.114622	+	0.993409i	$0.536566\pi$
$24$	7868.00	2.78828
$25$	0	0
$26$	−8663.80	−2.51348
$27$	22.2056	0.00586211
$28$	17148.7	4.13367
$29$	6091.79	1.34509	0.672543	−	0.740058i	$-0.265202\pi$
$29$	6091.79	1.34509	0.672543	+	0.740058i	$0.265202\pi$
$30$	0	0
$31$	−8059.15	−1.50621	−0.753105	−	0.657901i	$-0.771445\pi$
$31$	−8059.15	−1.50621	−0.753105	+	0.657901i	$0.771445\pi$
$32$	−2550.87	−0.440366
$33$	−3267.37	−0.522292
$34$	−13075.3	−1.93979
$35$	0	0
$36$	16399.4	2.10898
$37$	−2451.51	−0.294394	−0.147197	−	0.989107i	$-0.547025\pi$
$37$	−2451.51	−0.294394	−0.147197	+	0.989107i	$0.547025\pi$
$38$	13261.2	1.48978
$39$	−19102.0	−2.01103
$40$	0	0
$41$	1326.86	0.123272	0.0616362	−	0.998099i	$-0.480368\pi$
$41$	1326.86	0.123272	0.0616362	+	0.998099i	$0.480368\pi$
$42$	55663.0	4.86904
$43$	−1849.00	−0.152499
$43$	−1849.00	−0.152499
$44$	10054.5	0.782938
$45$	0	0
$46$	5809.18	0.404781
$47$	21553.5	1.42322	0.711611	−	0.702574i	$-0.247966\pi$
$47$	21553.5	1.42322	0.711611	+	0.702574i	$0.247966\pi$
$48$	−30831.0	−1.93145
$49$	47226.3	2.80992
$50$	0	0
$51$	−28828.5	−1.55202
$52$	58781.4	3.01461
$53$	24672.6	1.20649	0.603247	−	0.797554i	$-0.293873\pi$
$53$	24672.6	1.20649	0.603247	+	0.797554i	$0.293873\pi$
$54$	−221.799	−0.0103508
$55$	0	0
$56$	−90406.5	−3.85238
$57$	29238.4	1.19197
$58$	−60847.4	−2.37504
$59$	6434.55	0.240651	0.120326	−	0.992734i	$-0.461606\pi$
$59$	6434.55	0.240651	0.120326	+	0.992734i	$0.461606\pi$
$60$	0	0
$61$	33405.6	1.14946	0.574731	−	0.818342i	$-0.305107\pi$
$61$	33405.6	1.14946	0.574731	+	0.818342i	$0.305107\pi$
$62$	80498.2	2.65954
$63$	61235.5	1.94380
$64$	−19320.0	−0.589599
$65$	0	0
$66$	32635.9	0.922222
$67$	4801.81	0.130683	0.0653414	−	0.997863i	$-0.479186\pi$
$67$	4801.81	0.130683	0.0653414	+	0.997863i	$0.479186\pi$
$68$	88712.0	2.32654
$69$	12808.1	0.323864
$70$	0	0
$71$	39844.4	0.938040	0.469020	−	0.883188i	$-0.344607\pi$
$71$	39844.4	0.938040	0.469020	+	0.883188i	$0.344607\pi$
$72$	−86456.5	−1.96547
$73$	−638.964	−0.0140336	−0.00701680	−	0.999975i	$-0.502234\pi$
$73$	−638.964	−0.0140336	−0.00701680	+	0.999975i	$0.502234\pi$
$74$	24486.7	0.519817
$75$	0	0
$76$	−89973.3	−1.78681
$77$	37543.5	0.721618
$78$	190799.	3.55091
$79$	26896.6	0.484874	0.242437	−	0.970167i	$-0.422053\pi$
$79$	26896.6	0.484874	0.242437	+	0.970167i	$0.422053\pi$
$80$	0	0
$81$	−59293.0	−1.00413
$82$	−13253.2	−0.217665
$83$	−32090.8	−0.511311	−0.255655	−	0.966768i	$-0.582291\pi$
$83$	−32090.8	−0.511311	−0.255655	+	0.966768i	$0.582291\pi$
$84$	−377657.	−5.83982
$85$	0	0
$86$	18468.6	0.269270
$87$	−134157.	−1.90027
$88$	−53006.4	−0.729662
$89$	129089.	1.72748	0.863742	−	0.503935i	$-0.168115\pi$
$89$	129089.	1.72748	0.863742	+	0.503935i	$0.168115\pi$
$90$	0	0
$91$	219490.	2.77851
$92$	−39413.6	−0.485485
$93$	177483.	2.12789
$94$	−215285.	−2.51301
$95$	0	0
$96$	56176.7	0.622125
$97$	61004.0	0.658307	0.329154	−	0.944276i	$-0.393237\pi$
$97$	61004.0	0.658307	0.329154	+	0.944276i	$0.393237\pi$
$98$	−471715.	−4.96152
$99$	35903.1	0.368166
$100$	0	0
$101$	−37860.1	−0.369299	−0.184650	−	0.982804i	$-0.559115\pi$
$101$	−37860.1	−0.369299	−0.184650	+	0.982804i	$0.559115\pi$
$102$	287951.	2.74043
$103$	−75657.4	−0.702681	−0.351341	−	0.936248i	$-0.614274\pi$
$103$	−75657.4	−0.702681	−0.351341	+	0.936248i	$0.614274\pi$
$104$	−309891.	−2.80948
$105$	0	0
$106$	−246440.	−2.13033
$107$	−30987.9	−0.261657	−0.130829	−	0.991405i	$-0.541764\pi$
$107$	−30987.9	−0.261657	−0.130829	+	0.991405i	$0.541764\pi$
$108$	1504.84	0.0124146
$109$	66283.2	0.534364	0.267182	−	0.963646i	$-0.413907\pi$
$109$	66283.2	0.534364	0.267182	+	0.963646i	$0.413907\pi$
$110$	0	0
$111$	53988.3	0.415904
$112$	354261.	2.66856
$113$	160540.	1.18273	0.591367	−	0.806403i	$-0.298589\pi$
$113$	160540.	1.18273	0.591367	+	0.806403i	$0.298589\pi$
$114$	−292045.	−2.10469
$115$	0	0
$116$	412831.	2.84858
$117$	209900.	1.41758
$118$	−64271.0	−0.424923
$119$	331251.	2.14432
$120$	0	0
$121$	−139039.	−0.863322
$122$	−333669.	−2.02963
$123$	−29220.9	−0.174153
$124$	−546157.	−3.18980
$125$	0	0
$126$	−611646.	−3.43221
$127$	−117676.	−0.647406	−0.323703	−	0.946159i	$-0.604928\pi$
$127$	−117676.	−0.647406	−0.323703	+	0.946159i	$0.604928\pi$
$128$	274604.	1.48143
$129$	40719.7	0.215442
$130$	0	0
$131$	−2872.19	−0.0146229	−0.00731146	−	0.999973i	$-0.502327\pi$
$131$	−2872.19	−0.0146229	−0.00731146	+	0.999973i	$0.502327\pi$
$132$	−221425.	−1.10609
$133$	−335961.	−1.64687
$134$	−47962.5	−0.230749
$135$	0	0
$136$	−467683.	−2.16822
$137$	235242.	1.07081	0.535405	−	0.844595i	$-0.320159\pi$
$137$	235242.	1.07081	0.535405	+	0.844595i	$0.320159\pi$
$138$	−127933.	−0.571852
$139$	−359861.	−1.57979	−0.789893	−	0.613245i	$-0.789864\pi$
$139$	−359861.	−1.57979	−0.789893	+	0.613245i	$0.789864\pi$
$140$	0	0
$141$	−474662.	−2.01065
$142$	−397982.	−1.65632
$143$	128690.	0.526264
$144$	338782.	1.36149
$145$	0	0
$146$	6382.23	0.0247794
$147$	−1.04004e6	−3.96970
$148$	−166135.	−0.623457
$149$	−299297.	−1.10443	−0.552213	−	0.833703i	$-0.686216\pi$
$149$	−299297.	−1.10443	−0.552213	+	0.833703i	$0.686216\pi$
$150$	0	0
$151$	−480222.	−1.71395	−0.856977	−	0.515354i	$-0.827660\pi$
$151$	−480222.	−1.71395	−0.856977	+	0.515354i	$0.827660\pi$
$152$	474332.	1.66523
$153$	316778.	1.09402
$154$	−375000.	−1.27418
$155$	0	0
$156$	−1.29451e6	−4.25888
$157$	522160.	1.69065	0.845326	−	0.534250i	$-0.179406\pi$
$157$	522160.	1.69065	0.845326	+	0.534250i	$0.179406\pi$
$158$	−268654.	−0.856152
$159$	−543353.	−1.70447
$160$	0	0
$161$	−147170.	−0.447462
$162$	592243.	1.77302
$163$	−228767.	−0.674411	−0.337205	−	0.941431i	$-0.609482\pi$
$163$	−228767.	−0.674411	−0.337205	+	0.941431i	$0.609482\pi$
$164$	89919.4	0.261062
$165$	0	0
$166$	320536.	0.902831
$167$	189994.	0.527167	0.263584	−	0.964637i	$-0.415095\pi$
$167$	189994.	0.527167	0.263584	+	0.964637i	$0.415095\pi$
$168$	1.99098e6	5.44244
$169$	381064.	1.02632
$170$	0	0
$171$	−321282.	−0.840226
$172$	−125304.	−0.322956
$173$	154392.	0.392202	0.196101	−	0.980584i	$-0.437172\pi$
$173$	154392.	0.392202	0.196101	+	0.980584i	$0.437172\pi$
$174$	1.34001e6	3.35533
$175$	0	0
$176$	207707.	0.505440
$177$	−141705.	−0.339979
$178$	−1.28939e6	−3.05025
$179$	444541.	1.03700	0.518500	−	0.855077i	$-0.326490\pi$
$179$	444541.	1.03700	0.518500	+	0.855077i	$0.326490\pi$
$180$	0	0
$181$	823359.	1.86807	0.934034	−	0.357185i	$-0.116263\pi$
$181$	823359.	1.86807	0.934034	+	0.357185i	$0.116263\pi$
$182$	−2.19236e6	−4.90606
$183$	−735676.	−1.62390
$184$	207785.	0.452450
$185$	0	0
$186$	−1.77277e6	−3.75726
$187$	194216.	0.406146
$188$	1.46065e6	3.01405
$189$	5619.09	0.0114423
$190$	0	0
$191$	627806.	1.24521	0.622605	−	0.782537i	$-0.286075\pi$
$191$	627806.	1.24521	0.622605	+	0.782537i	$0.286075\pi$
$192$	425475.	0.832954
$193$	−705820.	−1.36396	−0.681979	−	0.731372i	$-0.738880\pi$
$193$	−705820.	−1.36396	−0.681979	+	0.731372i	$0.738880\pi$
$194$	−609333.	−1.16239
$195$	0	0
$196$	3.20045e6	5.95074
$197$	−260586.	−0.478394	−0.239197	−	0.970971i	$-0.576884\pi$
$197$	−260586.	−0.478394	−0.239197	+	0.970971i	$0.576884\pi$
$198$	−358615.	−0.650078
$199$	−705699.	−1.26324	−0.631621	−	0.775277i	$-0.717610\pi$
$199$	−705699.	−1.26324	−0.631621	+	0.775277i	$0.717610\pi$
$200$	0	0
$201$	−105748.	−0.184622
$202$	378163.	0.652079
$203$	1.54152e6	2.62547
$204$	−1.95366e6	−3.28681
$205$	0	0
$206$	755698.	1.24074
$207$	−140740.	−0.228293
$208$	1.21432e6	1.94614
$209$	−196978.	−0.311926
$210$	0	0
$211$	782426.	1.20987	0.604933	−	0.796276i	$-0.293200\pi$
$211$	782426.	1.20987	0.604933	+	0.796276i	$0.293200\pi$
$212$	1.67202e6	2.55507
$213$	−877474.	−1.32521
$214$	309520.	0.462013
$215$	0	0
$216$	−7933.42	−0.0115698
$217$	−2.03935e6	−2.93997
$218$	−662065.	−0.943537
$219$	14071.6	0.0198259
$220$	0	0
$221$	1.13545e6	1.56382
$222$	−539258.	−0.734369
$223$	776650.	1.04584	0.522918	−	0.852383i	$-0.324843\pi$
$223$	776650.	1.04584	0.522918	+	0.852383i	$0.324843\pi$
$224$	−645493.	−0.859551
$225$	0	0
$226$	−1.60354e6	−2.08838
$227$	−634962.	−0.817868	−0.408934	−	0.912564i	$-0.634099\pi$
$227$	−634962.	−0.817868	−0.408934	+	0.912564i	$0.634099\pi$
$228$	1.98144e6	2.52432
$229$	−421321.	−0.530914	−0.265457	−	0.964123i	$-0.585523\pi$
$229$	−421321.	−0.530914	−0.265457	+	0.964123i	$0.585523\pi$
$230$	0	0
$231$	−826802.	−1.01946
$232$	−2.17642e6	−2.65474
$233$	809074.	0.976334	0.488167	−	0.872750i	$-0.337666\pi$
$233$	809074.	0.976334	0.488167	+	0.872750i	$0.337666\pi$
$234$	−2.09657e6	−2.50305
$235$	0	0
$236$	436060.	0.509643
$237$	−592330.	−0.685004
$238$	−3.30867e6	−3.78627
$239$	−385051.	−0.436037	−0.218018	−	0.975945i	$-0.569959\pi$
$239$	−385051.	−0.436037	−0.218018	+	0.975945i	$0.569959\pi$
$240$	0	0
$241$	−1.24459e6	−1.38034	−0.690169	−	0.723649i	$-0.742464\pi$
$241$	−1.24459e6	−1.38034	−0.690169	+	0.723649i	$0.742464\pi$
$242$	1.38878e6	1.52438
$243$	1.30039e6	1.41272
$244$	2.26385e6	2.43429
$245$	0	0
$246$	291870.	0.307505
$247$	−1.15159e6	−1.20103
$248$	2.87930e6	2.97274
$249$	706720.	0.722352
$250$	0	0
$251$	792246.	0.793735	0.396868	−	0.917876i	$-0.370097\pi$
$251$	792246.	0.793735	0.396868	+	0.917876i	$0.370097\pi$
$252$	4.14984e6	4.11651
$253$	−86287.8	−0.0847516
$254$	1.17539e6	1.14314
$255$	0	0
$256$	−2.12462e6	−2.02620
$257$	−380315.	−0.359178	−0.179589	−	0.983742i	$-0.557477\pi$
$257$	−380315.	−0.359178	−0.179589	+	0.983742i	$0.557477\pi$
$258$	−406725.	−0.380410
$259$	−620348.	−0.574627
$260$	0	0
$261$	1.47416e6	1.33951
$262$	28688.6	0.0258200
$263$	−1.74378e6	−1.55454	−0.777272	−	0.629165i	$-0.783397\pi$
$263$	−1.74378e6	−1.55454	−0.777272	+	0.629165i	$0.783397\pi$
$264$	1.16734e6	1.03083
$265$	0	0
$266$	3.35572e6	2.90791
$267$	−2.84286e6	−2.44049
$268$	325412.	0.276755
$269$	−1.65578e6	−1.39516	−0.697578	−	0.716508i	$-0.745739\pi$
$269$	−1.65578e6	−1.39516	−0.697578	+	0.716508i	$0.745739\pi$
$270$	0	0
$271$	432836.	0.358014	0.179007	−	0.983848i	$-0.442711\pi$
$271$	432836.	0.358014	0.179007	+	0.983848i	$0.442711\pi$
$272$	1.83263e6	1.50194
$273$	−4.83372e6	−3.92532
$274$	−2.34969e6	−1.89075
$275$	0	0
$276$	867986.	0.685867
$277$	−94759.9	−0.0742036	−0.0371018	−	0.999311i	$-0.511813\pi$
$277$	−94759.9	−0.0742036	−0.0371018	+	0.999311i	$0.511813\pi$
$278$	3.59445e6	2.78946
$279$	−1.95025e6	−1.49996
$280$	0	0
$281$	2.09670e6	1.58406	0.792030	−	0.610482i	$-0.209024\pi$
$281$	2.09670e6	1.58406	0.792030	+	0.610482i	$0.209024\pi$
$282$	4.74112e6	3.55024
$283$	2.31300e6	1.71676	0.858380	−	0.513014i	$-0.171471\pi$
$283$	2.31300e6	1.71676	0.858380	+	0.513014i	$0.171471\pi$
$284$	2.70019e6	1.98655
$285$	0	0
$286$	−1.28541e6	−0.929234
$287$	335760.	0.240616
$288$	−617290.	−0.438539
$289$	293742.	0.206881
$290$	0	0
$291$	−1.34346e6	−0.930021
$292$	−43301.6	−0.0297199
$293$	−782733.	−0.532653	−0.266326	−	0.963883i	$-0.585810\pi$
$293$	−782733.	−0.532653	−0.266326	+	0.963883i	$0.585810\pi$
$294$	1.03884e7	7.00937
$295$	0	0
$296$	875850.	0.581033
$297$	3294.54	0.00216722
$298$	2.98950e6	1.95011
$299$	−504464.	−0.326326
$300$	0	0
$301$	−467886.	−0.297662
$302$	4.79665e6	3.02636
$303$	833775.	0.521726
$304$	−1.85869e6	−1.15351
$305$	0	0
$306$	−3.16411e6	−1.93174
$307$	242370.	0.146769	0.0733843	−	0.997304i	$-0.476620\pi$
$307$	242370.	0.146769	0.0733843	+	0.997304i	$0.476620\pi$
$308$	2.54426e6	1.52822
$309$	1.66617e6	0.992710
$310$	0	0
$311$	−1.75880e6	−1.03113	−0.515566	−	0.856850i	$-0.672418\pi$
$311$	−1.75880e6	−1.03113	−0.515566	+	0.856850i	$0.672418\pi$
$312$	6.82458e6	3.96908
$313$	−892868.	−0.515141	−0.257571	−	0.966259i	$-0.582922\pi$
$313$	−892868.	−0.515141	−0.257571	+	0.966259i	$0.582922\pi$
$314$	−5.21555e6	−2.98522
$315$	0	0
$316$	1.82274e6	1.02685
$317$	1.28816e6	0.719983	0.359992	−	0.932956i	$-0.382780\pi$
$317$	1.28816e6	0.719983	0.359992	+	0.932956i	$0.382780\pi$
$318$	5.42724e6	3.00962
$319$	903809.	0.497279
$320$	0	0
$321$	682432.	0.369655
$322$	1.47000e6	0.790092
$323$	−1.73796e6	−0.926903
$324$	−4.01820e6	−2.12652
$325$	0	0
$326$	2.28502e6	1.19082
$327$	−1.45972e6	−0.754921
$328$	−474048.	−0.243298
$329$	5.45406e6	2.77799
$330$	0	0
$331$	1.98792e6	0.997308	0.498654	−	0.866801i	$-0.333828\pi$
$331$	1.98792e6	0.997308	0.498654	+	0.866801i	$0.333828\pi$
$332$	−2.17474e6	−1.08284
$333$	−593244.	−0.293172
$334$	−1.89774e6	−0.930830
$335$	0	0
$336$	−7.80171e6	−3.77000
$337$	1.87398e6	0.898855	0.449427	−	0.893317i	$-0.351628\pi$
$337$	1.87398e6	0.898855	0.449427	+	0.893317i	$0.351628\pi$
$338$	−3.80622e6	−1.81219
$339$	−3.53549e6	−1.67090
$340$	0	0
$341$	−1.19570e6	−0.556846
$342$	3.20910e6	1.48360
$343$	7.69753e6	3.53278
$344$	660593.	0.300980
$345$	0	0
$346$	−1.54213e6	−0.692519
$347$	−982023.	−0.437822	−0.218911	−	0.975745i	$-0.570251\pi$
$347$	−982023.	−0.437822	−0.218911	+	0.975745i	$0.570251\pi$
$348$	−9.09159e6	−4.02431
$349$	−1.60167e6	−0.703896	−0.351948	−	0.936020i	$-0.614481\pi$
$349$	−1.60167e6	−0.703896	−0.351948	+	0.936020i	$0.614481\pi$
$350$	0	0
$351$	19260.8	0.00834464
$352$	−378460.	−0.162803
$353$	−3.05532e6	−1.30503	−0.652514	−	0.757776i	$-0.726286\pi$
$353$	−3.05532e6	−1.30503	−0.652514	+	0.757776i	$0.726286\pi$
$354$	1.41541e6	0.600308
$355$	0	0
$356$	8.74816e6	3.65840
$357$	−7.29499e6	−3.02938
$358$	−4.44026e6	−1.83105
$359$	2.62037e6	1.07307	0.536533	−	0.843879i	$-0.319734\pi$
$359$	2.62037e6	1.07307	0.536533	+	0.843879i	$0.319734\pi$
$360$	0	0
$361$	−713426.	−0.288125
$362$	−8.22405e6	−3.29848
$363$	3.06199e6	1.21965
$364$	1.48745e7	5.88422
$365$	0	0
$366$	7.34824e6	2.86735
$367$	3.04913e6	1.18171	0.590855	−	0.806778i	$-0.298790\pi$
$367$	3.04913e6	1.18171	0.590855	+	0.806778i	$0.298790\pi$
$368$	−814213.	−0.313414
$369$	321090.	0.122761
$370$	0	0
$371$	6.24335e6	2.35496
$372$	1.20277e7	4.50637
$373$	5.01542e6	1.86653	0.933266	−	0.359187i	$-0.116946\pi$
$373$	5.01542e6	1.86653	0.933266	+	0.359187i	$0.116946\pi$
$374$	−1.93991e6	−0.717140
$375$	0	0
$376$	−7.70042e6	−2.80895
$377$	5.28393e6	1.91471
$378$	−56125.8	−0.0202038
$379$	−535500.	−0.191497	−0.0957484	−	0.995406i	$-0.530524\pi$
$379$	−535500.	−0.191497	−0.0957484	+	0.995406i	$0.530524\pi$
$380$	0	0
$381$	2.59151e6	0.914621
$382$	−6.27079e6	−2.19869
$383$	−3.43669e6	−1.19713	−0.598567	−	0.801073i	$-0.704263\pi$
$383$	−3.43669e6	−1.19713	−0.598567	+	0.801073i	$0.704263\pi$
$384$	−6.04747e6	−2.09289
$385$	0	0
$386$	7.05003e6	2.40837
$387$	−447443.	−0.151866
$388$	4.13414e6	1.39414
$389$	−1.68008e6	−0.562932	−0.281466	−	0.959571i	$-0.590821\pi$
$389$	−1.68008e6	−0.562932	−0.281466	+	0.959571i	$0.590821\pi$
$390$	0	0
$391$	−761329.	−0.251843
$392$	−1.68725e7	−5.54581
$393$	63252.8	0.0206585
$394$	2.60284e6	0.844710
$395$	0	0
$396$	2.43310e6	0.779689
$397$	−869851.	−0.276993	−0.138496	−	0.990363i	$-0.544227\pi$
$397$	−869851.	−0.276993	−0.138496	+	0.990363i	$0.544227\pi$
$398$	7.04881e6	2.23053
$399$	7.39871e6	2.32661
$400$	0	0
$401$	−6.23668e6	−1.93684	−0.968418	−	0.249333i	$-0.919789\pi$
$401$	−6.23668e6	−1.93684	−0.968418	+	0.249333i	$0.919789\pi$
$402$	1.05626e6	0.325990
$403$	−6.99039e6	−2.14407
$404$	−2.56572e6	−0.782089
$405$	0	0
$406$	−1.53973e7	−4.63585
$407$	−363718.	−0.108837
$408$	1.02996e7	3.06315
$409$	−3.97005e6	−1.17351	−0.586756	−	0.809764i	$-0.699595\pi$
$409$	−3.97005e6	−1.17351	−0.586756	+	0.809764i	$0.699595\pi$
$410$	0	0
$411$	−5.18061e6	−1.51278
$412$	−5.12719e6	−1.48811
$413$	1.62825e6	0.469727
$414$	1.40577e6	0.403101
$415$	0	0
$416$	−2.21259e6	−0.626856
$417$	7.92506e6	2.23184
$418$	1.96750e6	0.550774
$419$	−2.75072e6	−0.765440	−0.382720	−	0.923864i	$-0.625013\pi$
$419$	−2.75072e6	−0.765440	−0.382720	+	0.923864i	$0.625013\pi$
$420$	0	0
$421$	−1.79858e6	−0.494565	−0.247283	−	0.968943i	$-0.579538\pi$
$421$	−1.79858e6	−0.494565	−0.247283	+	0.968943i	$0.579538\pi$
$422$	−7.81520e6	−2.13628
$423$	5.21576e6	1.41732
$424$	−8.81479e6	−2.38121
$425$	0	0
$426$	8.76458e6	2.33995
$427$	8.45322e6	2.24364
$428$	−2.10000e6	−0.554128
$429$	−2.83407e6	−0.743477
$430$	0	0
$431$	1.96982e6	0.510779	0.255390	−	0.966838i	$-0.417796\pi$
$431$	1.96982e6	0.510779	0.255390	+	0.966838i	$0.417796\pi$
$432$	31087.3	0.00801445
$433$	−817997.	−0.209668	−0.104834	−	0.994490i	$-0.533431\pi$
$433$	−817997.	−0.209668	−0.104834	+	0.994490i	$0.533431\pi$
$434$	2.03699e7	5.19116
$435$	0	0
$436$	4.49191e6	1.13166
$437$	772154.	0.193420
$438$	−140553.	−0.0350070
$439$	−3.53476e6	−0.875383	−0.437692	−	0.899125i	$-0.644204\pi$
$439$	−3.53476e6	−0.875383	−0.437692	+	0.899125i	$0.644204\pi$
$440$	0	0
$441$	1.14284e7	2.79826
$442$	−1.13413e7	−2.76126
$443$	−2.92978e6	−0.709292	−0.354646	−	0.935001i	$-0.615399\pi$
$443$	−2.92978e6	−0.709292	−0.354646	+	0.935001i	$0.615399\pi$
$444$	3.65871e6	0.880786
$445$	0	0
$446$	−7.75751e6	−1.84665
$447$	6.59127e6	1.56027
$448$	−4.88888e6	−1.15084
$449$	331315.	0.0775578	0.0387789	−	0.999248i	$-0.487653\pi$
$449$	331315.	0.0775578	0.0387789	+	0.999248i	$0.487653\pi$
$450$	0	0
$451$	196860.	0.0455739
$452$	1.08795e7	2.50475
$453$	1.05757e7	2.42138
$454$	6.34226e6	1.44412
$455$	0	0
$456$	−1.04460e7	−2.35254
$457$	−3.12310e6	−0.699511	−0.349756	−	0.936841i	$-0.613735\pi$
$457$	−3.12310e6	−0.699511	−0.349756	+	0.936841i	$0.613735\pi$
$458$	4.20833e6	0.937445
$459$	29068.2	0.00644000
$460$	0	0
$461$	1.91656e6	0.420021	0.210011	−	0.977699i	$-0.432650\pi$
$461$	1.91656e6	0.420021	0.210011	+	0.977699i	$0.432650\pi$
$462$	8.25844e6	1.80009
$463$	403998.	0.0875843	0.0437922	−	0.999041i	$-0.486056\pi$
$463$	403998.	0.0875843	0.0437922	+	0.999041i	$0.486056\pi$
$464$	8.52835e6	1.83895
$465$	0	0
$466$	−8.08137e6	−1.72393
$467$	846481.	0.179608	0.0898039	−	0.995959i	$-0.471376\pi$
$467$	846481.	0.179608	0.0898039	+	0.995959i	$0.471376\pi$
$468$	1.42246e7	3.00210
$469$	1.21509e6	0.255080
$470$	0	0
$471$	−1.14993e7	−2.38846
$472$	−2.29887e6	−0.474963
$473$	−274327.	−0.0563788
$474$	5.91644e6	1.20952
$475$	0	0
$476$	2.24484e7	4.54117
$477$	5.97057e6	1.20149
$478$	3.84604e6	0.769918
$479$	−6.81326e6	−1.35680	−0.678400	−	0.734693i	$-0.737326\pi$
$479$	−6.81326e6	−1.35680	−0.678400	+	0.734693i	$0.737326\pi$
$480$	0	0
$481$	−2.12640e6	−0.419066
$482$	1.24315e7	2.43729
$483$	3.24107e6	0.632150
$484$	−9.42245e6	−1.82831
$485$	0	0
$486$	−1.29888e7	−2.49447
$487$	2.48119e6	0.474065	0.237033	−	0.971502i	$-0.423825\pi$
$487$	2.48119e6	0.474065	0.237033	+	0.971502i	$0.423825\pi$
$488$	−1.19348e7	−2.26865
$489$	5.03803e6	0.952771
$490$	0	0
$491$	5.01581e6	0.938939	0.469470	−	0.882949i	$-0.344445\pi$
$491$	5.01581e6	0.938939	0.469470	+	0.882949i	$0.344445\pi$
$492$	−1.98025e6	−0.368814
$493$	7.97443e6	1.47769
$494$	1.15026e7	2.12069
$495$	0	0
$496$	−1.12826e7	−2.05923
$497$	1.00825e7	1.83096
$498$	−7.05901e6	−1.27547
$499$	4.78193e6	0.859710	0.429855	−	0.902898i	$-0.358565\pi$
$499$	4.78193e6	0.859710	0.429855	+	0.902898i	$0.358565\pi$
$500$	0	0
$501$	−4.18415e6	−0.744754
$502$	−7.91328e6	−1.40151
$503$	3.12633e6	0.550953	0.275476	−	0.961308i	$-0.411164\pi$
$503$	3.12633e6	0.550953	0.275476	+	0.961308i	$0.411164\pi$
$504$	−2.18776e7	−3.83640
$505$	0	0
$506$	861879.	0.149648
$507$	−8.39199e6	−1.44992
$508$	−7.97469e6	−1.37105
$509$	−359003.	−0.0614191	−0.0307096	−	0.999528i	$-0.509777\pi$
$509$	−359003.	−0.0614191	−0.0307096	+	0.999528i	$0.509777\pi$
$510$	0	0
$511$	−161688.	−0.0273922
$512$	1.24343e7	2.09626
$513$	−29481.5	−0.00494602
$514$	3.79874e6	0.634208
$515$	0	0
$516$	2.75951e6	0.456255
$517$	3.19778e6	0.526166
$518$	6.19630e6	1.01463
$519$	−3.40011e6	−0.554082
$520$	0	0
$521$	4.86460e6	0.785150	0.392575	−	0.919720i	$-0.371584\pi$
$521$	4.86460e6	0.785150	0.392575	+	0.919720i	$0.371584\pi$
$522$	−1.47246e7	−2.36519
$523$	−3.04923e6	−0.487456	−0.243728	−	0.969844i	$-0.578370\pi$
$523$	−3.04923e6	−0.487456	−0.243728	+	0.969844i	$0.578370\pi$
$524$	−194644.	−0.0309679
$525$	0	0
$526$	1.74176e7	2.74489
$527$	−1.05498e7	−1.65469
$528$	−4.57424e6	−0.714059
$529$	−6.09809e6	−0.947447
$530$	0	0
$531$	1.55711e6	0.239653
$532$	−2.27676e7	−3.48769
$533$	1.15090e6	0.175477
$534$	2.83957e7	4.30923
$535$	0	0
$536$	−1.71555e6	−0.257923
$537$	−9.78991e6	−1.46502
$538$	1.65387e7	2.46346
$539$	7.00672e6	1.03883
$540$	0	0
$541$	1.09443e7	1.60767	0.803833	−	0.594855i	$-0.202790\pi$
$541$	1.09443e7	1.60767	0.803833	+	0.594855i	$0.202790\pi$
$542$	−4.32335e6	−0.632153
$543$	−1.81324e7	−2.63910
$544$	−3.33921e6	−0.483778
$545$	0	0
$546$	4.82813e7	6.93102
$547$	3.66914e6	0.524319	0.262160	−	0.965025i	$-0.415565\pi$
$547$	3.66914e6	0.524319	0.262160	+	0.965025i	$0.415565\pi$
$548$	1.59420e7	2.26773
$549$	8.08388e6	1.14469
$550$	0	0
$551$	−8.08781e6	−1.13489
$552$	−4.57596e6	−0.639196
$553$	6.80612e6	0.946426
$554$	946502.	0.131023
$555$	0	0
$556$	−2.43873e7	−3.34562
$557$	−1.20209e7	−1.64172	−0.820858	−	0.571132i	$-0.806504\pi$
$557$	−1.20209e7	−1.64172	−0.820858	+	0.571132i	$0.806504\pi$
$558$	1.94799e7	2.64851
$559$	−1.60379e6	−0.217080
$560$	0	0
$561$	−4.27714e6	−0.573781
$562$	−2.09428e7	−2.79700
$563$	−6.98583e6	−0.928853	−0.464426	−	0.885612i	$-0.653739\pi$
$563$	−6.98583e6	−0.928853	−0.464426	+	0.885612i	$0.653739\pi$
$564$	−3.21671e7	−4.25808
$565$	0	0
$566$	−2.31032e7	−3.03132
$567$	−1.50040e7	−1.95997
$568$	−1.42352e7	−1.85137
$569$	−2.57157e6	−0.332980	−0.166490	−	0.986043i	$-0.553243\pi$
$569$	−2.57157e6	−0.332980	−0.166490	+	0.986043i	$0.553243\pi$
$570$	0	0
$571$	−1.37516e7	−1.76507	−0.882535	−	0.470248i	$-0.844165\pi$
$571$	−1.37516e7	−1.76507	−0.882535	+	0.470248i	$0.844165\pi$
$572$	8.72110e6	1.11450
$573$	−1.38259e7	−1.75916
$574$	−3.35371e6	−0.424860
$575$	0	0
$576$	−4.67528e6	−0.587153
$577$	5.22470e6	0.653314	0.326657	−	0.945143i	$-0.394078\pi$
$577$	5.22470e6	0.653314	0.326657	+	0.945143i	$0.394078\pi$
$578$	−2.93401e6	−0.365294
$579$	1.55439e7	1.92693
$580$	0	0
$581$	−8.12050e6	−0.998027
$582$	1.34191e7	1.64216
$583$	3.66055e6	0.446041
$584$	228283.	0.0276975
$585$	0	0
$586$	7.81826e6	0.940516
$587$	−7.93056e6	−0.949967	−0.474983	−	0.879995i	$-0.657546\pi$
$587$	−7.93056e6	−0.949967	−0.474983	+	0.879995i	$0.657546\pi$
$588$	−7.04820e7	−8.40688
$589$	1.06998e7	1.27083
$590$	0	0
$591$	5.73877e6	0.675849
$592$	−3.43204e6	−0.402484
$593$	−1.20417e7	−1.40622	−0.703109	−	0.711082i	$-0.748205\pi$
$593$	−1.20417e7	−1.40622	−0.703109	+	0.711082i	$0.748205\pi$
$594$	−32907.2	−0.00382671
$595$	0	0
$596$	−2.02829e7	−2.33891
$597$	1.55413e7	1.78464
$598$	5.03879e6	0.576200
$599$	−4.95816e6	−0.564617	−0.282308	−	0.959324i	$-0.591100\pi$
$599$	−4.95816e6	−0.564617	−0.282308	+	0.959324i	$0.591100\pi$
$600$	0	0
$601$	−39847.3	−0.00450001	−0.00225000	−	0.999997i	$-0.500716\pi$
$601$	−39847.3	−0.00450001	−0.00225000	+	0.999997i	$0.500716\pi$
$602$	4.67344e6	0.525588
$603$	1.16200e6	0.130141
$604$	−3.25439e7	−3.62975
$605$	0	0
$606$	−8.32810e6	−0.921222
$607$	8.55705e6	0.942655	0.471327	−	0.881958i	$-0.343775\pi$
$607$	8.55705e6	0.942655	0.471327	+	0.881958i	$0.343775\pi$
$608$	3.38668e6	0.371549
$609$	−3.39481e7	−3.70913
$610$	0	0
$611$	1.86952e7	2.02594
$612$	2.14676e7	2.31688
$613$	−6.50414e6	−0.699099	−0.349550	−	0.936918i	$-0.613665\pi$
$613$	−6.50414e6	−0.699099	−0.349550	+	0.936918i	$0.613665\pi$
$614$	−2.42089e6	−0.259152
$615$	0	0
$616$	−1.34132e7	−1.42423
$617$	−5.24115e6	−0.554260	−0.277130	−	0.960832i	$-0.589383\pi$
$617$	−5.24115e6	−0.554260	−0.277130	+	0.960832i	$0.589383\pi$
$618$	−1.66424e7	−1.75285
$619$	−4.99065e6	−0.523516	−0.261758	−	0.965133i	$-0.584302\pi$
$619$	−4.99065e6	−0.523516	−0.261758	+	0.965133i	$0.584302\pi$
$620$	0	0
$621$	−12914.6	−0.00134385
$622$	1.75676e7	1.82069
$623$	3.26657e7	3.37188
$624$	−2.67423e7	−2.74940
$625$	0	0
$626$	8.91833e6	0.909595
$627$	4.33795e6	0.440672
$628$	3.53860e7	3.58040
$629$	−3.20913e6	−0.323415
$630$	0	0
$631$	3.32602e6	0.332546	0.166273	−	0.986080i	$-0.446827\pi$
$631$	3.32602e6	0.332546	0.166273	+	0.986080i	$0.446827\pi$
$632$	−9.60934e6	−0.956976
$633$	−1.72310e7	−1.70923
$634$	−1.28667e7	−1.27129
$635$	0	0
$636$	−3.68222e7	−3.60967
$637$	4.09633e7	3.99988
$638$	−9.02762e6	−0.878055
$639$	9.64201e6	0.934148
$640$	0	0
$641$	−7.00292e6	−0.673184	−0.336592	−	0.941651i	$-0.609274\pi$
$641$	−7.00292e6	−0.673184	−0.336592	+	0.941651i	$0.609274\pi$
$642$	−6.81641e6	−0.652707
$643$	−1.64216e7	−1.56635	−0.783173	−	0.621803i	$-0.786400\pi$
$643$	−1.64216e7	−1.56635	−0.783173	+	0.621803i	$0.786400\pi$
$644$	−9.97352e6	−0.947619
$645$	0	0
$646$	1.73595e7	1.63665
$647$	1.37772e7	1.29390	0.646951	−	0.762532i	$-0.276044\pi$
$647$	1.37772e7	1.29390	0.646951	+	0.762532i	$0.276044\pi$
$648$	2.11836e7	1.98181
$649$	954662.	0.0889689
$650$	0	0
$651$	4.49117e7	4.15343
$652$	−1.55032e7	−1.42824
$653$	1.51127e7	1.38694	0.693471	−	0.720484i	$-0.256080\pi$
$653$	1.51127e7	1.38694	0.693471	+	0.720484i	$0.256080\pi$
$654$	1.45803e7	1.33298
$655$	0	0
$656$	1.85757e6	0.168533
$657$	−154624.	−0.0139754
$658$	−5.44774e7	−4.90515
$659$	−3.06178e6	−0.274638	−0.137319	−	0.990527i	$-0.543849\pi$
$659$	−3.06178e6	−0.274638	−0.137319	+	0.990527i	$0.543849\pi$
$660$	0	0
$661$	−8.60726e6	−0.766234	−0.383117	−	0.923700i	$-0.625149\pi$
$661$	−8.60726e6	−0.766234	−0.383117	+	0.923700i	$0.625149\pi$
$662$	−1.98562e7	−1.76097
$663$	−2.50054e7	−2.20928
$664$	1.14651e7	1.00915
$665$	0	0
$666$	5.92557e6	0.517660
$667$	−3.54293e6	−0.308353
$668$	1.28756e7	1.11642
$669$	−1.71038e7	−1.47750
$670$	0	0
$671$	4.95623e6	0.424957
$672$	1.42154e7	1.21433
$673$	−9.82166e6	−0.835886	−0.417943	−	0.908473i	$-0.637249\pi$
$673$	−9.82166e6	−0.835886	−0.417943	+	0.908473i	$0.637249\pi$
$674$	−1.87181e7	−1.58713
$675$	0	0
$676$	2.58241e7	2.17349
$677$	−327157.	−0.0274337	−0.0137169	−	0.999906i	$-0.504366\pi$
$677$	−327157.	−0.0274337	−0.0137169	+	0.999906i	$0.504366\pi$
$678$	3.53140e7	2.95034
$679$	1.54369e7	1.28495
$680$	0	0
$681$	1.39835e7	1.15544
$682$	1.19431e7	0.983234
$683$	1.97492e6	0.161994	0.0809969	−	0.996714i	$-0.474190\pi$
$683$	1.97492e6	0.161994	0.0809969	+	0.996714i	$0.474190\pi$
$684$	−2.17728e7	−1.77940
$685$	0	0
$686$	−7.68861e7	−6.23789
$687$	9.27855e6	0.750046
$688$	−2.58855e6	−0.208490
$689$	2.14007e7	1.71743
$690$	0	0
$691$	−5.17968e6	−0.412674	−0.206337	−	0.978481i	$-0.566154\pi$
$691$	−5.17968e6	−0.412674	−0.206337	+	0.978481i	$0.566154\pi$
$692$	1.04629e7	0.830592
$693$	9.08520e6	0.718624
$694$	9.80886e6	0.773072
$695$	0	0
$696$	4.79302e7	3.75047
$697$	1.73692e6	0.135425
$698$	1.59981e7	1.24288
$699$	−1.78179e7	−1.37931
$700$	0	0
$701$	−7.31456e6	−0.562203	−0.281102	−	0.959678i	$-0.590700\pi$
$701$	−7.31456e6	−0.562203	−0.281102	+	0.959678i	$0.590700\pi$
$702$	−192385.	−0.0147343
$703$	3.25476e6	0.248388
$704$	−2.86641e6	−0.217975
$705$	0	0
$706$	3.05178e7	2.30431
$707$	−9.58042e6	−0.720835
$708$	−9.60314e6	−0.719996
$709$	−2.27833e7	−1.70216	−0.851079	−	0.525037i	$-0.824051\pi$
$709$	−2.27833e7	−1.70216	−0.851079	+	0.525037i	$0.824051\pi$
$710$	0	0
$711$	6.50874e6	0.482862
$712$	−4.61196e7	−3.40946
$713$	4.68713e6	0.345290
$714$	7.28654e7	5.34904
$715$	0	0
$716$	3.01259e7	2.19612
$717$	8.47979e6	0.616009
$718$	−2.61733e7	−1.89473
$719$	−4.60535e6	−0.332231	−0.166116	−	0.986106i	$-0.553122\pi$
$719$	−4.60535e6	−0.332231	−0.166116	+	0.986106i	$0.553122\pi$
$720$	0	0
$721$	−1.91450e7	−1.37156
$722$	7.12599e6	0.508748
$723$	2.74091e7	1.95007
$724$	5.57977e7	3.95613
$725$	0	0
$726$	−3.05844e7	−2.15357
$727$	−6.47651e6	−0.454469	−0.227235	−	0.973840i	$-0.572968\pi$
$727$	−6.47651e6	−0.454469	−0.227235	+	0.973840i	$0.572968\pi$
$728$	−7.84173e7	−5.48382
$729$	−1.42296e7	−0.991684
$730$	0	0
$731$	−2.42042e6	−0.167532
$732$	−4.98556e7	−3.43904
$733$	1.24860e6	0.0858347	0.0429174	−	0.999079i	$-0.486335\pi$
$733$	1.24860e6	0.0858347	0.0429174	+	0.999079i	$0.486335\pi$
$734$	−3.04560e7	−2.08657
$735$	0	0
$736$	1.48357e6	0.100951
$737$	712421.	0.0483135
$738$	−3.20718e6	−0.216761
$739$	1.47877e7	0.996067	0.498033	−	0.867158i	$-0.334056\pi$
$739$	1.47877e7	0.996067	0.498033	+	0.867158i	$0.334056\pi$
$740$	0	0
$741$	2.53609e7	1.69676
$742$	−6.23612e7	−4.15819
$743$	−2.55315e7	−1.69670	−0.848350	−	0.529436i	$-0.822404\pi$
$743$	−2.55315e7	−1.69670	−0.848350	+	0.529436i	$0.822404\pi$
$744$	−6.34094e7	−4.19973
$745$	0	0
$746$	−5.00961e7	−3.29577
$747$	−7.76570e6	−0.509189
$748$	1.31618e7	0.860121
$749$	−7.84143e6	−0.510729
$750$	0	0
$751$	−2.57403e7	−1.66538	−0.832692	−	0.553736i	$-0.813202\pi$
$751$	−2.57403e7	−1.66538	−0.832692	+	0.553736i	$0.813202\pi$
$752$	3.01743e7	1.94578
$753$	−1.74473e7	−1.12135
$754$	−5.27781e7	−3.38085
$755$	0	0
$756$	380797.	0.0242320
$757$	2.81464e7	1.78518	0.892591	−	0.450866i	$-0.148885\pi$
$757$	2.81464e7	1.78518	0.892591	+	0.450866i	$0.148885\pi$
$758$	5.34880e6	0.338130
$759$	1.90028e6	0.119733
$760$	0	0
$761$	1.23977e7	0.776030	0.388015	−	0.921653i	$-0.373161\pi$
$761$	1.23977e7	0.776030	0.388015	+	0.921653i	$0.373161\pi$
$762$	−2.58851e7	−1.61496
$763$	1.67728e7	1.04303
$764$	4.25455e7	2.63706
$765$	0	0
$766$	3.43271e7	2.11380
$767$	5.58123e6	0.342564
$768$	4.67895e7	2.86250
$769$	1.01951e7	0.621691	0.310845	−	0.950461i	$-0.399388\pi$
$769$	1.01951e7	0.621691	0.310845	+	0.950461i	$0.399388\pi$
$770$	0	0
$771$	8.37549e6	0.507428
$772$	−4.78324e7	−2.88854
$773$	4.04941e6	0.243749	0.121875	−	0.992546i	$-0.461109\pi$
$773$	4.04941e6	0.243749	0.121875	+	0.992546i	$0.461109\pi$
$774$	4.46924e6	0.268152
$775$	0	0
$776$	−2.17949e7	−1.29927
$777$	1.36616e7	0.811802
$778$	1.67813e7	0.993979
$779$	−1.76162e6	−0.104008
$780$	0	0
$781$	5.91151e6	0.346794
$782$	7.60447e6	0.444685
$783$	135272.	0.00788504
$784$	6.61155e7	3.84161
$785$	0	0
$786$	−631795.	−0.0364771
$787$	1.19136e7	0.685654	0.342827	−	0.939399i	$-0.388616\pi$
$787$	1.19136e7	0.685654	0.342827	+	0.939399i	$0.388616\pi$
$788$	−1.76595e7	−1.01313
$789$	3.84025e7	2.19617
$790$	0	0
$791$	4.06243e7	2.30858
$792$	−1.28271e7	−0.726634
$793$	2.89755e7	1.63625
$794$	8.68844e6	0.489092
$795$	0	0
$796$	−4.78241e7	−2.67525
$797$	5.95262e6	0.331942	0.165971	−	0.986131i	$-0.446924\pi$
$797$	5.95262e6	0.331942	0.165971	+	0.986131i	$0.446924\pi$
$798$	−7.39014e7	−4.10814
$799$	2.82145e7	1.56353
$800$	0	0
$801$	3.12384e7	1.72031
$802$	6.22946e7	3.41991
$803$	−94799.8	−0.00518822
$804$	−7.16639e6	−0.390985
$805$	0	0
$806$	6.98229e7	3.78582
$807$	3.64646e7	1.97100
$808$	1.35263e7	0.728871
$809$	−1.11487e7	−0.598896	−0.299448	−	0.954113i	$-0.596803\pi$
$809$	−1.11487e7	−0.598896	−0.299448	+	0.954113i	$0.596803\pi$
$810$	0	0
$811$	−8.45566e6	−0.451435	−0.225718	−	0.974193i	$-0.572473\pi$
$811$	−8.45566e6	−0.451435	−0.225718	+	0.974193i	$0.572473\pi$
$812$	1.04466e8	5.56014
$813$	−9.53215e6	−0.505783
$814$	3.63296e6	0.192176
$815$	0	0
$816$	−4.03591e7	−2.12186
$817$	2.45484e6	0.128667
$818$	3.96545e7	2.07209
$819$	5.31148e7	2.76698
$820$	0	0
$821$	−78262.7	−0.00405226	−0.00202613	−	0.999998i	$-0.500645\pi$
$821$	−78262.7	−0.00405226	−0.00202613	+	0.999998i	$0.500645\pi$
$822$	5.17461e7	2.67115
$823$	7.63445e6	0.392897	0.196448	−	0.980514i	$-0.437059\pi$
$823$	7.63445e6	0.392897	0.196448	+	0.980514i	$0.437059\pi$
$824$	2.70302e7	1.38685
$825$	0	0
$826$	−1.62636e7	−0.829407
$827$	−1.54144e7	−0.783723	−0.391862	−	0.920024i	$-0.628169\pi$
$827$	−1.54144e7	−0.783723	−0.391862	+	0.920024i	$0.628169\pi$
$828$	−9.53775e6	−0.483471
$829$	−9.77033e6	−0.493768	−0.246884	−	0.969045i	$-0.579407\pi$
$829$	−9.77033e6	−0.493768	−0.246884	+	0.969045i	$0.579407\pi$
$830$	0	0
$831$	2.08685e6	0.104831
$832$	−1.67579e7	−0.839287
$833$	6.18213e7	3.08692
$834$	−7.91588e7	−3.94080
$835$	0	0
$836$	−1.33489e7	−0.660586
$837$	−178959.	−0.00882956
$838$	2.74753e7	1.35155
$839$	3.57305e7	1.75240	0.876201	−	0.481945i	$-0.160070\pi$
$839$	3.57305e7	1.75240	0.876201	+	0.481945i	$0.160070\pi$
$840$	0	0
$841$	1.65988e7	0.809257
$842$	1.79649e7	0.873263
$843$	−4.61747e7	−2.23787
$844$	5.30238e7	2.56221
$845$	0	0
$846$	−5.20972e7	−2.50258
$847$	−3.51835e7	−1.68512
$848$	3.45410e7	1.64947
$849$	−5.09381e7	−2.42535
$850$	0	0
$851$	1.42577e6	0.0674881
$852$	−5.94651e7	−2.80649
$853$	−9.56479e6	−0.450094	−0.225047	−	0.974348i	$-0.572253\pi$
$853$	−9.56479e6	−0.450094	−0.225047	+	0.974348i	$0.572253\pi$
$854$	−8.44343e7	−3.96163
$855$	0	0
$856$	1.10711e7	0.516422
$857$	−1.74935e7	−0.813625	−0.406813	−	0.913512i	$-0.633360\pi$
$857$	−1.74935e7	−0.813625	−0.406813	+	0.913512i	$0.633360\pi$
$858$	2.83079e7	1.31277
$859$	−7.43933e6	−0.343994	−0.171997	−	0.985097i	$-0.555022\pi$
$859$	−7.43933e6	−0.343994	−0.171997	+	0.985097i	$0.555022\pi$
$860$	0	0
$861$	−7.39428e6	−0.339929
$862$	−1.96754e7	−0.901893
$863$	4.08352e7	1.86641	0.933207	−	0.359338i	$-0.116998\pi$
$863$	4.08352e7	1.86641	0.933207	+	0.359338i	$0.116998\pi$
$864$	−56643.8	−0.00258147
$865$	0	0
$866$	8.17049e6	0.370215
$867$	−6.46893e6	−0.292270
$868$	−1.38204e8	−6.22617
$869$	3.99051e6	0.179258
$870$	0	0
$871$	4.16502e6	0.186025
$872$	−2.36810e7	−1.05465
$873$	1.47624e7	0.655576
$874$	−7.71259e6	−0.341525
$875$	0	0
$876$	953610.	0.0419866
$877$	−187111.	−0.00821485	−0.00410743	−	0.999992i	$-0.501307\pi$
$877$	−187111.	−0.00821485	−0.00410743	+	0.999992i	$0.501307\pi$
$878$	3.53066e7	1.54568
$879$	1.72377e7	0.752503
$880$	0	0
$881$	2.25486e7	0.978767	0.489383	−	0.872069i	$-0.337222\pi$
$881$	2.25486e7	0.978767	0.489383	+	0.872069i	$0.337222\pi$
$882$	−1.14151e8	−4.94093
$883$	2.53259e7	1.09311	0.546553	−	0.837424i	$-0.315940\pi$
$883$	2.53259e7	1.09311	0.546553	+	0.837424i	$0.315940\pi$
$884$	7.69474e7	3.31180
$885$	0	0
$886$	2.92638e7	1.25241
$887$	4.80865e6	0.205217	0.102609	−	0.994722i	$-0.467281\pi$
$887$	4.80865e6	0.205217	0.102609	+	0.994722i	$0.467281\pi$
$888$	−1.92884e7	−0.820851
$889$	−2.97776e7	−1.26367
$890$	0	0
$891$	−8.79701e6	−0.371228
$892$	5.26324e7	2.21483
$893$	−2.86156e7	−1.20081
$894$	−6.58364e7	−2.75500
$895$	0	0
$896$	6.94880e7	2.89161
$897$	1.11096e7	0.461016
$898$	−3.30932e6	−0.136945
$899$	−4.90947e7	−2.02598
$900$	0	0
$901$	3.22976e7	1.32543
$902$	−1.96632e6	−0.0804706
$903$	1.03040e7	0.420521
$904$	−5.73562e7	−2.33431
$905$	0	0
$906$	−1.05634e8	−4.27548
$907$	9.81124e6	0.396010	0.198005	−	0.980201i	$-0.436554\pi$
$907$	9.81124e6	0.396010	0.198005	+	0.980201i	$0.436554\pi$
$908$	−4.30304e7	−1.73205
$909$	−9.16183e6	−0.367767
$910$	0	0
$911$	1.90059e7	0.758741	0.379371	−	0.925245i	$-0.376141\pi$
$911$	1.90059e7	0.758741	0.379371	+	0.925245i	$0.376141\pi$
$912$	4.09330e7	1.62962
$913$	−4.76115e6	−0.189032
$914$	3.11948e7	1.23514
$915$	0	0
$916$	−2.85523e7	−1.12435
$917$	−726801.	−0.0285425
$918$	−290345.	−0.0113712
$919$	1.75615e7	0.685919	0.342960	−	0.939350i	$-0.388571\pi$
$919$	1.75615e7	0.685919	0.342960	+	0.939350i	$0.388571\pi$
$920$	0	0
$921$	−5.33760e6	−0.207347
$922$	−1.91434e7	−0.741639
$923$	3.45604e7	1.33529
$924$	−5.60311e7	−2.15898
$925$	0	0
$926$	−4.03530e6	−0.154649
$927$	−1.83085e7	−0.699766
$928$	−1.55394e7	−0.592331
$929$	−2.24650e7	−0.854017	−0.427009	−	0.904248i	$-0.640433\pi$
$929$	−2.24650e7	−0.854017	−0.427009	+	0.904248i	$0.640433\pi$
$930$	0	0
$931$	−6.27003e7	−2.37080
$932$	5.48297e7	2.06765
$933$	3.87331e7	1.45673
$934$	−8.45501e6	−0.317137
$935$	0	0
$936$	−7.49910e7	−2.79782
$937$	−3.25863e7	−1.21251	−0.606257	−	0.795269i	$-0.707330\pi$
$937$	−3.25863e7	−1.21251	−0.606257	+	0.795269i	$0.707330\pi$
$938$	−1.21368e7	−0.450399
$939$	1.96632e7	0.727763
$940$	0	0
$941$	3.27572e7	1.20596	0.602980	−	0.797756i	$-0.293980\pi$
$941$	3.27572e7	1.20596	0.602980	+	0.797756i	$0.293980\pi$
$942$	1.14860e8	4.21735
$943$	−771691.	−0.0282595
$944$	9.00820e6	0.329009
$945$	0	0
$946$	2.74009e6	0.0995491
$947$	−1.58739e7	−0.575187	−0.287594	−	0.957752i	$-0.592855\pi$
$947$	−1.58739e7	−0.575187	−0.287594	+	0.957752i	$0.592855\pi$
$948$	−4.01413e7	−1.45068
$949$	−554227.	−0.0199766
$950$	0	0
$951$	−2.83686e7	−1.01715
$952$	−1.18346e8	−4.23216
$953$	−1.60992e7	−0.574211	−0.287106	−	0.957899i	$-0.592693\pi$
$953$	−1.60992e7	−0.574211	−0.287106	+	0.957899i	$0.592693\pi$
$954$	−5.96365e7	−2.12149
$955$	0	0
$956$	−2.60943e7	−0.923423
$957$	−1.99042e7	−0.702529
$958$	6.80537e7	2.39573
$959$	5.95274e7	2.09012
$960$	0	0
$961$	3.63208e7	1.26867
$962$	2.12394e7	0.739952
$963$	−7.49882e6	−0.260572
$964$	−8.43443e7	−2.92323
$965$	0	0
$966$	−3.23731e7	−1.11620
$967$	39241.2	0.00134951	0.000674755	−	1.00000i	$-0.499785\pi$
$967$	39241.2	0.00134951	0.000674755		1.00000i	$0.499785\pi$
$968$	4.96744e7	1.70390
$969$	3.82743e7	1.30948
$970$	0	0
$971$	−1.78317e7	−0.606940	−0.303470	−	0.952841i	$-0.598145\pi$
$971$	−1.78317e7	−0.606940	−0.303470	+	0.952841i	$0.598145\pi$
$972$	8.81252e7	2.99181
$973$	−9.10622e7	−3.08359
$974$	−2.47832e7	−0.837066
$975$	0	0
$976$	4.67670e7	1.57150
$977$	−3.33615e7	−1.11817	−0.559087	−	0.829109i	$-0.688848\pi$
$977$	−3.33615e7	−1.11817	−0.559087	+	0.829109i	$0.688848\pi$
$978$	−5.03219e7	−1.68233
$979$	1.91523e7	0.638651
$980$	0	0
$981$	1.60400e7	0.532147
$982$	−5.01000e7	−1.65790
$983$	3.46334e7	1.14317	0.571586	−	0.820542i	$-0.306328\pi$
$983$	3.46334e7	1.14317	0.571586	+	0.820542i	$0.306328\pi$
$984$	1.04397e7	0.343718
$985$	0	0
$986$	−7.96519e7	−2.60918
$987$	−1.20112e8	−3.92459
$988$	−7.80415e7	−2.54351
$989$	1.07536e6	0.0349594
$990$	0	0
$991$	−2.78352e6	−0.0900347	−0.0450174	−	0.998986i	$-0.514334\pi$
$991$	−2.78352e6	−0.0900347	−0.0450174	+	0.998986i	$0.514334\pi$
$992$	2.05579e7	0.663284
$993$	−4.37791e7	−1.40894
$994$	−1.00709e8	−3.23296
$995$	0	0
$996$	4.78933e7	1.52977
$997$	4.50607e7	1.43569	0.717843	−	0.696205i	$-0.245129\pi$
$997$	4.50607e7	1.43569	0.717843	+	0.696205i	$0.245129\pi$
$998$	−4.77639e7	−1.51801
$999$	−54437.3	−0.00172577

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.6.a.l.1.2		52
5.2	odd	4		215.6.b.a.44.8	✓	104
5.3	odd	4		215.6.b.a.44.97	yes	104
5.4	even	2		1075.6.a.k.1.51		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
215.6.b.a.44.8	✓	104	5.2	odd	4
215.6.b.a.44.97	yes	104	5.3	odd	4
1075.6.a.k.1.51		52	5.4	even	2
1075.6.a.l.1.2		52	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q-9.98842 q^{2} -22.0225 q^{3} +67.7685 q^{4} +219.970 q^{6} +253.048 q^{7} -357.270 q^{8} +241.992 q^{9} +O(q^{10})\)	\(q-9.98842 q^{2} -22.0225 q^{3} +67.7685 q^{4} +219.970 q^{6} +253.048 q^{7} -357.270 q^{8} +241.992 q^{9} +148.365 q^{11} -1492.43 q^{12} +867.385 q^{13} -2527.55 q^{14} +1399.97 q^{16} +1309.04 q^{17} -2417.11 q^{18} -1327.66 q^{19} -5572.75 q^{21} -1481.93 q^{22} -581.591 q^{23} +7868.00 q^{24} -8663.80 q^{26} +22.2056 q^{27} +17148.7 q^{28} +6091.79 q^{29} -8059.15 q^{31} -2550.87 q^{32} -3267.37 q^{33} -13075.3 q^{34} +16399.4 q^{36} -2451.51 q^{37} +13261.2 q^{38} -19102.0 q^{39} +1326.86 q^{41} +55663.0 q^{42} -1849.00 q^{43} +10054.5 q^{44} +5809.18 q^{46} +21553.5 q^{47} -30831.0 q^{48} +47226.3 q^{49} -28828.5 q^{51} +58781.4 q^{52} +24672.6 q^{53} -221.799 q^{54} -90406.5 q^{56} +29238.4 q^{57} -60847.4 q^{58} +6434.55 q^{59} +33405.6 q^{61} +80498.2 q^{62} +61235.5 q^{63} -19320.0 q^{64} +32635.9 q^{66} +4801.81 q^{67} +88712.0 q^{68} +12808.1 q^{69} +39844.4 q^{71} -86456.5 q^{72} -638.964 q^{73} +24486.7 q^{74} -89973.3 q^{76} +37543.5 q^{77} +190799. q^{78} +26896.6 q^{79} -59293.0 q^{81} -13253.2 q^{82} -32090.8 q^{83} -377657. q^{84} +18468.6 q^{86} -134157. q^{87} -53006.4 q^{88} +129089. q^{89} +219490. q^{91} -39413.6 q^{92} +177483. q^{93} -215285. q^{94} +56176.7 q^{96} +61004.0 q^{97} -471715. q^{98} +35903.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 20 q^{2} + 54 q^{3} + 826 q^{4} - 162 q^{6} + 196 q^{7} + 960 q^{8} + 4098 q^{9}+O(q^{10}) \) 52 * q + 20 * q^2 + 54 * q^3 + 826 * q^4 - 162 * q^6 + 196 * q^7 + 960 * q^8 + 4098 * q^9	\( 52 q + 20 q^{2} + 54 q^{3} + 826 q^{4} - 162 q^{6} + 196 q^{7} + 960 q^{8} + 4098 q^{9} - 664 q^{11} - 523 q^{12} + 2704 q^{13} + 150 q^{14} + 13474 q^{16} + 7266 q^{17} + 4860 q^{18} - 1970 q^{19} + 800 q^{21} + 14477 q^{22} + 9522 q^{23} + 314 q^{24} + 5514 q^{26} + 22926 q^{27} + 9408 q^{28} - 7188 q^{29} - 11556 q^{31} + 48390 q^{32} + 26136 q^{33} + 16774 q^{34} + 51872 q^{36} + 42558 q^{37} + 46208 q^{38} + 4682 q^{39} - 7746 q^{41} + 174265 q^{42} - 96148 q^{43} - 48600 q^{44} + 16182 q^{46} + 87136 q^{47} - 2912 q^{48} + 142286 q^{49} - 3710 q^{51} + 146868 q^{52} + 127034 q^{53} - 49563 q^{54} - 2849 q^{56} + 101594 q^{57} + 9480 q^{58} - 55924 q^{59} + 73702 q^{61} + 186016 q^{62} + 50120 q^{63} + 157750 q^{64} + 58211 q^{66} + 131996 q^{67} + 298560 q^{68} + 128436 q^{69} - 56284 q^{71} + 343775 q^{72} + 128620 q^{73} - 17721 q^{74} - 170410 q^{76} + 448438 q^{77} + 237616 q^{78} + 106204 q^{79} + 478568 q^{81} + 249596 q^{82} + 348616 q^{83} - 131855 q^{84} - 36980 q^{86} + 267478 q^{87} + 525216 q^{88} + 80410 q^{89} + 226376 q^{91} + 581456 q^{92} + 902902 q^{93} + 180980 q^{94} + 38543 q^{96} + 316148 q^{97} + 295095 q^{98} + 68428 q^{99}+O(q^{100}) \) 52 * q + 20 * q^2 + 54 * q^3 + 826 * q^4 - 162 * q^6 + 196 * q^7 + 960 * q^8 + 4098 * q^9 - 664 * q^11 - 523 * q^12 + 2704 * q^13 + 150 * q^14 + 13474 * q^16 + 7266 * q^17 + 4860 * q^18 - 1970 * q^19 + 800 * q^21 + 14477 * q^22 + 9522 * q^23 + 314 * q^24 + 5514 * q^26 + 22926 * q^27 + 9408 * q^28 - 7188 * q^29 - 11556 * q^31 + 48390 * q^32 + 26136 * q^33 + 16774 * q^34 + 51872 * q^36 + 42558 * q^37 + 46208 * q^38 + 4682 * q^39 - 7746 * q^41 + 174265 * q^42 - 96148 * q^43 - 48600 * q^44 + 16182 * q^46 + 87136 * q^47 - 2912 * q^48 + 142286 * q^49 - 3710 * q^51 + 146868 * q^52 + 127034 * q^53 - 49563 * q^54 - 2849 * q^56 + 101594 * q^57 + 9480 * q^58 - 55924 * q^59 + 73702 * q^61 + 186016 * q^62 + 50120 * q^63 + 157750 * q^64 + 58211 * q^66 + 131996 * q^67 + 298560 * q^68 + 128436 * q^69 - 56284 * q^71 + 343775 * q^72 + 128620 * q^73 - 17721 * q^74 - 170410 * q^76 + 448438 * q^77 + 237616 * q^78 + 106204 * q^79 + 478568 * q^81 + 249596 * q^82 + 348616 * q^83 - 131855 * q^84 - 36980 * q^86 + 267478 * q^87 + 525216 * q^88 + 80410 * q^89 + 226376 * q^91 + 581456 * q^92 + 902902 * q^93 + 180980 * q^94 + 38543 * q^96 + 316148 * q^97 + 295095 * q^98 + 68428 * q^99

Introduction

L-functions

Modular forms

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Database

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