LMFDB - Embedded newform 1775.4.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1775,4,Mod(1,1775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1775, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1775.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1775 = 5^{2} \cdot 71 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1775.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:	$104.728390260$
Analytic rank:	$1$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	1775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.93007 q^{2} -6.89641 q^{3} +16.3056 q^{4} +33.9998 q^{6} +17.8269 q^{7} -40.9471 q^{8} +20.5604 q^{9} +O(q^{10})$	\(q-4.93007 q^{2} -6.89641 q^{3} +16.3056 q^{4} +33.9998 q^{6} +17.8269 q^{7} -40.9471 q^{8} +20.5604 q^{9} +13.4903 q^{11} -112.450 q^{12} -67.3776 q^{13} -87.8878 q^{14} +71.4272 q^{16} +83.8709 q^{17} -101.364 q^{18} +150.372 q^{19} -122.942 q^{21} -66.5082 q^{22} -107.336 q^{23} +282.388 q^{24} +332.176 q^{26} +44.4099 q^{27} +290.678 q^{28} +180.765 q^{29} +80.3248 q^{31} -24.5644 q^{32} -93.0347 q^{33} -413.489 q^{34} +335.250 q^{36} -150.688 q^{37} -741.342 q^{38} +464.663 q^{39} -284.325 q^{41} +606.110 q^{42} -547.367 q^{43} +219.967 q^{44} +529.176 q^{46} -328.629 q^{47} -492.591 q^{48} -25.2017 q^{49} -578.408 q^{51} -1098.63 q^{52} +375.427 q^{53} -218.944 q^{54} -729.959 q^{56} -1037.02 q^{57} -891.185 q^{58} -757.011 q^{59} +416.684 q^{61} -396.007 q^{62} +366.529 q^{63} -450.313 q^{64} +458.668 q^{66} +60.0823 q^{67} +1367.56 q^{68} +740.236 q^{69} +71.0000 q^{71} -841.889 q^{72} -323.878 q^{73} +742.902 q^{74} +2451.90 q^{76} +240.491 q^{77} -2290.82 q^{78} +64.5409 q^{79} -861.400 q^{81} +1401.74 q^{82} +922.675 q^{83} -2004.63 q^{84} +2698.55 q^{86} -1246.63 q^{87} -552.389 q^{88} -2.07731 q^{89} -1201.13 q^{91} -1750.18 q^{92} -553.952 q^{93} +1620.17 q^{94} +169.406 q^{96} +467.212 q^{97} +124.246 q^{98} +277.367 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 6 q^{2} - 19 q^{3} + 146 q^{4} + 8 q^{6} - 76 q^{7} - 72 q^{8} + 286 q^{9}+O(q^{10}) $ 35 * q - 6 * q^2 - 19 * q^3 + 146 * q^4 + 8 * q^6 - 76 * q^7 - 72 * q^8 + 286 * q^9	\( 35 q - 6 q^{2} - 19 q^{3} + 146 q^{4} + 8 q^{6} - 76 q^{7} - 72 q^{8} + 286 q^{9} + 29 q^{11} - 228 q^{12} - 206 q^{13} - 48 q^{14} + 542 q^{16} - 347 q^{17} - 280 q^{18} - 59 q^{19} + 284 q^{21} - 605 q^{22} - 168 q^{23} + 100 q^{24} + 655 q^{26} - 727 q^{27} - 749 q^{28} - 522 q^{29} + 84 q^{31} - 1522 q^{32} - 547 q^{33} - 324 q^{34} + 2114 q^{36} - 706 q^{37} - 487 q^{38} - 574 q^{39} + 311 q^{41} - 1602 q^{42} - 928 q^{43} - 1129 q^{44} + 144 q^{46} - 744 q^{47} - 2644 q^{48} + 1649 q^{49} + 277 q^{51} - 2727 q^{52} - 886 q^{53} - 923 q^{54} + 947 q^{56} - 2501 q^{57} - 1181 q^{58} - 434 q^{59} + 466 q^{61} - 1727 q^{62} - 1908 q^{63} + 2102 q^{64} - 884 q^{66} - 2425 q^{67} - 2329 q^{68} - 716 q^{69} + 2485 q^{71} - 4079 q^{72} - 5803 q^{73} - 412 q^{74} - 3109 q^{76} - 732 q^{77} - 2691 q^{78} + 1024 q^{79} + 7 q^{81} - 1325 q^{82} - 4927 q^{83} + 3889 q^{84} - 2716 q^{86} - 2634 q^{87} - 7122 q^{88} + 3279 q^{89} - 3782 q^{91} + 3025 q^{92} - 5256 q^{93} + 1485 q^{94} - 3043 q^{96} - 8548 q^{97} - 5578 q^{98} + 9008 q^{99}+O(q^{100}) \) 35 * q - 6 * q^2 - 19 * q^3 + 146 * q^4 + 8 * q^6 - 76 * q^7 - 72 * q^8 + 286 * q^9 + 29 * q^11 - 228 * q^12 - 206 * q^13 - 48 * q^14 + 542 * q^16 - 347 * q^17 - 280 * q^18 - 59 * q^19 + 284 * q^21 - 605 * q^22 - 168 * q^23 + 100 * q^24 + 655 * q^26 - 727 * q^27 - 749 * q^28 - 522 * q^29 + 84 * q^31 - 1522 * q^32 - 547 * q^33 - 324 * q^34 + 2114 * q^36 - 706 * q^37 - 487 * q^38 - 574 * q^39 + 311 * q^41 - 1602 * q^42 - 928 * q^43 - 1129 * q^44 + 144 * q^46 - 744 * q^47 - 2644 * q^48 + 1649 * q^49 + 277 * q^51 - 2727 * q^52 - 886 * q^53 - 923 * q^54 + 947 * q^56 - 2501 * q^57 - 1181 * q^58 - 434 * q^59 + 466 * q^61 - 1727 * q^62 - 1908 * q^63 + 2102 * q^64 - 884 * q^66 - 2425 * q^67 - 2329 * q^68 - 716 * q^69 + 2485 * q^71 - 4079 * q^72 - 5803 * q^73 - 412 * q^74 - 3109 * q^76 - 732 * q^77 - 2691 * q^78 + 1024 * q^79 + 7 * q^81 - 1325 * q^82 - 4927 * q^83 + 3889 * q^84 - 2716 * q^86 - 2634 * q^87 - 7122 * q^88 + 3279 * q^89 - 3782 * q^91 + 3025 * q^92 - 5256 * q^93 + 1485 * q^94 - 3043 * q^96 - 8548 * q^97 - 5578 * q^98 + 9008 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−4.93007	−1.74304	−0.871521	−	0.490358i	$-0.836866\pi$
$2$	−4.93007	−1.74304	−0.871521	+	0.490358i	$0.836866\pi$
$3$	−6.89641	−1.32721	−0.663607	−	0.748081i	$-0.730975\pi$
$3$	−6.89641	−1.32721	−0.663607	+	0.748081i	$0.730975\pi$
$4$	16.3056	2.03820
$5$	0	0
$5$	0	0
$6$	33.9998	2.31339
$7$	17.8269	0.962562	0.481281	−	0.876566i	$-0.340172\pi$
$7$	17.8269	0.962562	0.481281	+	0.876566i	$0.340172\pi$
$8$	−40.9471	−1.80962
$9$	20.5604	0.761497
$10$	0	0
$11$	13.4903	0.369771	0.184886	−	0.982760i	$-0.440809\pi$
$11$	13.4903	0.369771	0.184886	+	0.982760i	$0.440809\pi$
$12$	−112.450	−2.70512
$13$	−67.3776	−1.43747	−0.718737	−	0.695282i	$-0.755280\pi$
$13$	−67.3776	−1.43747	−0.718737	+	0.695282i	$0.755280\pi$
$14$	−87.8878	−1.67779
$15$	0	0
$16$	71.4272	1.11605
$17$	83.8709	1.19657	0.598285	−	0.801284i	$-0.295849\pi$
$17$	83.8709	1.19657	0.598285	+	0.801284i	$0.295849\pi$
$18$	−101.364	−1.32732
$19$	150.372	1.81566	0.907832	−	0.419334i	$-0.137736\pi$
$19$	150.372	1.81566	0.907832	+	0.419334i	$0.137736\pi$
$20$	0	0
$21$	−122.942	−1.27753
$22$	−66.5082	−0.644527
$23$	−107.336	−0.973095	−0.486548	−	0.873654i	$-0.661744\pi$
$23$	−107.336	−0.973095	−0.486548	+	0.873654i	$0.661744\pi$
$24$	282.388	2.40175
$25$	0	0
$26$	332.176	2.50558
$27$	44.4099	0.316544
$28$	290.678	1.96189
$29$	180.765	1.15749	0.578746	−	0.815508i	$-0.303542\pi$
$29$	180.765	1.15749	0.578746	+	0.815508i	$0.303542\pi$
$30$	0	0
$31$	80.3248	0.465379	0.232690	−	0.972551i	$-0.425247\pi$
$31$	80.3248	0.465379	0.232690	+	0.972551i	$0.425247\pi$
$32$	−24.5644	−0.135701
$33$	−93.0347	−0.490766
$34$	−413.489	−2.08567
$35$	0	0
$36$	335.250	1.55208
$37$	−150.688	−0.669539	−0.334770	−	0.942300i	$-0.608659\pi$
$37$	−150.688	−0.669539	−0.334770	+	0.942300i	$0.608659\pi$
$38$	−741.342	−3.16478
$39$	464.663	1.90784
$40$	0	0
$41$	−284.325	−1.08303	−0.541514	−	0.840692i	$-0.682149\pi$
$41$	−284.325	−1.08303	−0.541514	+	0.840692i	$0.682149\pi$
$42$	606.110	2.22678
$43$	−547.367	−1.94122	−0.970612	−	0.240651i	$-0.922639\pi$
$43$	−547.367	−1.94122	−0.970612	+	0.240651i	$0.922639\pi$
$44$	219.967	0.753667
$45$	0	0
$46$	529.176	1.69615
$47$	−328.629	−1.01990	−0.509952	−	0.860203i	$-0.670337\pi$
$47$	−328.629	−1.01990	−0.509952	+	0.860203i	$0.670337\pi$
$48$	−492.591	−1.48124
$49$	−25.2017	−0.0734742
$50$	0	0
$51$	−578.408	−1.58810
$52$	−1098.63	−2.92986
$53$	375.427	0.972998	0.486499	−	0.873681i	$-0.338274\pi$
$53$	375.427	0.972998	0.486499	+	0.873681i	$0.338274\pi$
$54$	−218.944	−0.551750
$55$	0	0
$56$	−729.959	−1.74187
$57$	−1037.02	−2.40977
$58$	−891.185	−2.01756
$59$	−757.011	−1.67041	−0.835207	−	0.549936i	$-0.814652\pi$
$59$	−757.011	−1.67041	−0.835207	+	0.549936i	$0.814652\pi$
$60$	0	0
$61$	416.684	0.874605	0.437302	−	0.899315i	$-0.355934\pi$
$61$	416.684	0.874605	0.437302	+	0.899315i	$0.355934\pi$
$62$	−396.007	−0.811176
$63$	366.529	0.732989
$64$	−450.313	−0.879518
$65$	0	0
$66$	458.668	0.855425
$67$	60.0823	0.109556	0.0547778	−	0.998499i	$-0.482555\pi$
$67$	60.0823	0.109556	0.0547778	+	0.998499i	$0.482555\pi$
$68$	1367.56	2.43884
$69$	740.236	1.29151
$70$	0	0
$71$	71.0000	0.118678
$71$	71.0000	0.118678
$72$	−841.889	−1.37802
$73$	−323.878	−0.519274	−0.259637	−	0.965706i	$-0.583603\pi$
$73$	−323.878	−0.519274	−0.259637	+	0.965706i	$0.583603\pi$
$74$	742.902	1.16704
$75$	0	0
$76$	2451.90	3.70068
$77$	240.491	0.355928
$78$	−2290.82	−3.32544
$79$	64.5409	0.0919167	0.0459584	−	0.998943i	$-0.485366\pi$
$79$	64.5409	0.0919167	0.0459584	+	0.998943i	$0.485366\pi$
$80$	0	0
$81$	−861.400	−1.18162
$82$	1401.74	1.88776
$83$	922.675	1.22020	0.610101	−	0.792324i	$-0.291129\pi$
$83$	922.675	1.22020	0.610101	+	0.792324i	$0.291129\pi$
$84$	−2004.63	−2.60385
$85$	0	0
$86$	2698.55	3.38364
$87$	−1246.63	−1.53624
$88$	−552.389	−0.669146
$89$	−2.07731	−0.00247409	−0.00123705	−	0.999999i	$-0.500394\pi$
$89$	−2.07731	−0.00247409	−0.00123705	+	0.999999i	$0.500394\pi$
$90$	0	0
$91$	−1201.13	−1.38366
$92$	−1750.18	−1.98336
$93$	−553.952	−0.617658
$94$	1620.17	1.77774
$95$	0	0
$96$	169.406	0.180104
$97$	467.212	0.489053	0.244527	−	0.969643i	$-0.421367\pi$
$97$	467.212	0.489053	0.244527	+	0.969643i	$0.421367\pi$
$98$	124.246	0.128069
$99$	277.367	0.281580
$100$	0	0
$101$	255.331	0.251549	0.125774	−	0.992059i	$-0.459858\pi$
$101$	255.331	0.251549	0.125774	+	0.992059i	$0.459858\pi$
$102$	2851.59	2.76813
$103$	−711.411	−0.680557	−0.340278	−	0.940325i	$-0.610521\pi$
$103$	−711.411	−0.680557	−0.340278	+	0.940325i	$0.610521\pi$
$104$	2758.91	2.60128
$105$	0	0
$106$	−1850.88	−1.69598
$107$	−181.840	−0.164291	−0.0821453	−	0.996620i	$-0.526177\pi$
$107$	−181.840	−0.164291	−0.0821453	+	0.996620i	$0.526177\pi$
$108$	724.129	0.645179
$109$	−2147.23	−1.88685	−0.943427	−	0.331581i	$-0.892418\pi$
$109$	−2147.23	−1.88685	−0.943427	+	0.331581i	$0.892418\pi$
$110$	0	0
$111$	1039.21	0.888622
$112$	1273.32	1.07427
$113$	2106.06	1.75329	0.876645	−	0.481138i	$-0.159777\pi$
$113$	2106.06	1.75329	0.876645	+	0.481138i	$0.159777\pi$
$114$	5112.60	4.20034
$115$	0	0
$116$	2947.48	2.35920
$117$	−1385.31	−1.09463
$118$	3732.12	2.91160
$119$	1495.16	1.15177
$120$	0	0
$121$	−1149.01	−0.863269
$122$	−2054.28	−1.52447
$123$	1960.82	1.43741
$124$	1309.74	0.948534
$125$	0	0
$126$	−1807.01	−1.27763
$127$	165.216	0.115437	0.0577187	−	0.998333i	$-0.481617\pi$
$127$	165.216	0.115437	0.0577187	+	0.998333i	$0.481617\pi$
$128$	2416.59	1.66874
$129$	3774.86	2.57642
$130$	0	0
$131$	−784.683	−0.523344	−0.261672	−	0.965157i	$-0.584274\pi$
$131$	−784.683	−0.523344	−0.261672	+	0.965157i	$0.584274\pi$
$132$	−1516.98	−1.00028
$133$	2680.66	1.74769
$134$	−296.210	−0.190960
$135$	0	0
$136$	−3434.26	−2.16534
$137$	−126.339	−0.0787871	−0.0393936	−	0.999224i	$-0.512543\pi$
$137$	−126.339	−0.0787871	−0.0393936	+	0.999224i	$0.512543\pi$
$138$	−3649.41	−2.25115
$139$	2689.00	1.64085	0.820424	−	0.571755i	$-0.193737\pi$
$139$	2689.00	1.64085	0.820424	+	0.571755i	$0.193737\pi$
$140$	0	0
$141$	2266.36	1.35363
$142$	−350.035	−0.206861
$143$	−908.945	−0.531537
$144$	1468.57	0.849869
$145$	0	0
$146$	1596.74	0.905117
$147$	173.801	0.0975161
$148$	−2457.05	−1.36465
$149$	−1747.08	−0.960579	−0.480289	−	0.877110i	$-0.659468\pi$
$149$	−1747.08	−0.960579	−0.480289	+	0.877110i	$0.659468\pi$
$150$	0	0
$151$	2515.59	1.35573	0.677867	−	0.735184i	$-0.262904\pi$
$151$	2515.59	1.35573	0.677867	+	0.735184i	$0.262904\pi$
$152$	−6157.27	−3.28566
$153$	1724.42	0.911184
$154$	−1185.63	−0.620397
$155$	0	0
$156$	7576.60	3.88855
$157$	−978.158	−0.497233	−0.248616	−	0.968602i	$-0.579976\pi$
$157$	−978.158	−0.497233	−0.248616	+	0.968602i	$0.579976\pi$
$158$	−318.191	−0.160215
$159$	−2589.10	−1.29138
$160$	0	0
$161$	−1913.48	−0.936665
$162$	4246.76	2.05961
$163$	−3210.75	−1.54285	−0.771427	−	0.636318i	$-0.780457\pi$
$163$	−3210.75	−1.54285	−0.771427	+	0.636318i	$0.780457\pi$
$164$	−4636.08	−2.20742
$165$	0	0
$166$	−4548.85	−2.12686
$167$	841.687	0.390010	0.195005	−	0.980802i	$-0.437528\pi$
$167$	841.687	0.390010	0.195005	+	0.980802i	$0.437528\pi$
$168$	5034.09	2.31184
$169$	2342.73	1.06633
$170$	0	0
$171$	3091.70	1.38262
$172$	−8925.13	−3.95660
$173$	3534.78	1.55344	0.776718	−	0.629848i	$-0.216883\pi$
$173$	3534.78	1.55344	0.776718	+	0.629848i	$0.216883\pi$
$174$	6145.97	2.67773
$175$	0	0
$176$	963.575	0.412683
$177$	5220.65	2.21700
$178$	10.2413	0.00431245
$179$	942.875	0.393708	0.196854	−	0.980433i	$-0.436927\pi$
$179$	942.875	0.393708	0.196854	+	0.980433i	$0.436927\pi$
$180$	0	0
$181$	−30.3065	−0.0124456	−0.00622282	−	0.999981i	$-0.501981\pi$
$181$	−30.3065	−0.0124456	−0.00622282	+	0.999981i	$0.501981\pi$
$182$	5921.67	2.41178
$183$	−2873.62	−1.16079
$184$	4395.11	1.76093
$185$	0	0
$186$	2731.02	1.07660
$187$	1131.44	0.442457
$188$	−5358.49	−2.07877
$189$	791.691	0.304693
$190$	0	0
$191$	−3149.71	−1.19322	−0.596611	−	0.802531i	$-0.703486\pi$
$191$	−3149.71	−1.19322	−0.596611	+	0.802531i	$0.703486\pi$
$192$	3105.54	1.16731
$193$	169.753	0.0633114	0.0316557	−	0.999499i	$-0.489922\pi$
$193$	169.753	0.0633114	0.0316557	+	0.999499i	$0.489922\pi$
$194$	−2303.39	−0.852441
$195$	0	0
$196$	−410.928	−0.149755
$197$	2225.78	0.804976	0.402488	−	0.915425i	$-0.368146\pi$
$197$	2225.78	0.804976	0.402488	+	0.915425i	$0.368146\pi$
$198$	−1367.44	−0.490806
$199$	3852.48	1.37234	0.686168	−	0.727443i	$-0.259292\pi$
$199$	3852.48	1.37234	0.686168	+	0.727443i	$0.259292\pi$
$200$	0	0
$201$	−414.352	−0.145404
$202$	−1258.80	−0.438460
$203$	3222.48	1.11416
$204$	−9431.27	−3.23687
$205$	0	0
$206$	3507.30	1.18624
$207$	−2206.88	−0.741010
$208$	−4812.59	−1.60429
$209$	2028.56	0.671380
$210$	0	0
$211$	−5923.77	−1.93274	−0.966372	−	0.257149i	$-0.917217\pi$
$211$	−5923.77	−1.93274	−0.966372	+	0.257149i	$0.917217\pi$
$212$	6121.55	1.98316
$213$	−489.645	−0.157511
$214$	896.481	0.286365
$215$	0	0
$216$	−1818.45	−0.572825
$217$	1431.94	0.447956
$218$	10586.0	3.28887
$219$	2233.59	0.689188
$220$	0	0
$221$	−5651.01	−1.72004
$222$	−5123.36	−1.54891
$223$	−826.101	−0.248071	−0.124035	−	0.992278i	$-0.539584\pi$
$223$	−826.101	−0.248071	−0.124035	+	0.992278i	$0.539584\pi$
$224$	−437.907	−0.130620
$225$	0	0
$226$	−10383.0	−3.05606
$227$	776.349	0.226996	0.113498	−	0.993538i	$-0.463794\pi$
$227$	776.349	0.226996	0.113498	+	0.993538i	$0.463794\pi$
$228$	−16909.3	−4.91160
$229$	−2956.88	−0.853258	−0.426629	−	0.904427i	$-0.640299\pi$
$229$	−2956.88	−0.853258	−0.426629	+	0.904427i	$0.640299\pi$
$230$	0	0
$231$	−1658.52	−0.472392
$232$	−7401.80	−2.09462
$233$	11.5631	0.00325117	0.00162558	−	0.999999i	$-0.499483\pi$
$233$	11.5631	0.00325117	0.00162558	+	0.999999i	$0.499483\pi$
$234$	6829.68	1.90799
$235$	0	0
$236$	−12343.5	−3.40463
$237$	−445.100	−0.121993
$238$	−7371.23	−2.00759
$239$	−2403.15	−0.650405	−0.325203	−	0.945644i	$-0.605433\pi$
$239$	−2403.15	−0.650405	−0.325203	+	0.945644i	$0.605433\pi$
$240$	0	0
$241$	1895.09	0.506530	0.253265	−	0.967397i	$-0.418496\pi$
$241$	1895.09	0.506530	0.253265	+	0.967397i	$0.418496\pi$
$242$	5664.70	1.50471
$243$	4741.50	1.25172
$244$	6794.27	1.78262
$245$	0	0
$246$	−9666.99	−2.50547
$247$	−10131.7	−2.60997
$248$	−3289.06	−0.842160
$249$	−6363.14	−1.61947
$250$	0	0
$251$	−372.073	−0.0935658	−0.0467829	−	0.998905i	$-0.514897\pi$
$251$	−372.073	−0.0935658	−0.0467829	+	0.998905i	$0.514897\pi$
$252$	5976.46	1.49397
$253$	−1448.00	−0.359823
$254$	−814.526	−0.201212
$255$	0	0
$256$	−8311.45	−2.02916
$257$	6503.99	1.57863	0.789315	−	0.613988i	$-0.210436\pi$
$257$	6503.99	1.57863	0.789315	+	0.613988i	$0.210436\pi$
$258$	−18610.3	−4.49081
$259$	−2686.30	−0.644473
$260$	0	0
$261$	3716.61	0.881427
$262$	3868.54	0.912211
$263$	4240.27	0.994168	0.497084	−	0.867702i	$-0.334404\pi$
$263$	4240.27	0.994168	0.497084	+	0.867702i	$0.334404\pi$
$264$	3809.50	0.888100
$265$	0	0
$266$	−13215.8	−3.04630
$267$	14.3260	0.00328365
$268$	979.677	0.223296
$269$	6323.54	1.43328	0.716641	−	0.697442i	$-0.245679\pi$
$269$	6323.54	1.43328	0.716641	+	0.697442i	$0.245679\pi$
$270$	0	0
$271$	−562.333	−0.126049	−0.0630246	−	0.998012i	$-0.520075\pi$
$271$	−562.333	−0.126049	−0.0630246	+	0.998012i	$0.520075\pi$
$272$	5990.66	1.33543
$273$	8283.50	1.83641
$274$	622.858	0.137329
$275$	0	0
$276$	12070.0	2.63234
$277$	4206.06	0.912339	0.456170	−	0.889893i	$-0.349221\pi$
$277$	4206.06	0.912339	0.456170	+	0.889893i	$0.349221\pi$
$278$	−13256.9	−2.86007
$279$	1651.51	0.354385
$280$	0	0
$281$	4050.01	0.859799	0.429899	−	0.902877i	$-0.358549\pi$
$281$	4050.01	0.859799	0.429899	+	0.902877i	$0.358549\pi$
$282$	−11173.3	−2.35944
$283$	4789.65	1.00606	0.503030	−	0.864269i	$-0.332218\pi$
$283$	4789.65	1.00606	0.503030	+	0.864269i	$0.332218\pi$
$284$	1157.70	0.241889
$285$	0	0
$286$	4481.16	0.926491
$287$	−5068.64	−1.04248
$288$	−505.055	−0.103336
$289$	2121.32	0.431777
$290$	0	0
$291$	−3222.08	−0.649079
$292$	−5281.01	−1.05838
$293$	1237.70	0.246783	0.123392	−	0.992358i	$-0.460623\pi$
$293$	1237.70	0.246783	0.123392	+	0.992358i	$0.460623\pi$
$294$	−856.851	−0.169975
$295$	0	0
$296$	6170.23	1.21161
$297$	599.104	0.117049
$298$	8613.22	1.67433
$299$	7232.07	1.39880
$300$	0	0
$301$	−9757.85	−1.86855
$302$	−12402.0	−2.36310
$303$	−1760.87	−0.333859
$304$	10740.6	2.02637
$305$	0	0
$306$	−8501.51	−1.58823
$307$	−3697.02	−0.687296	−0.343648	−	0.939099i	$-0.611663\pi$
$307$	−3697.02	−0.687296	−0.343648	+	0.939099i	$0.611663\pi$
$308$	3921.34	0.725451
$309$	4906.18	0.903245
$310$	0	0
$311$	−5987.19	−1.09165	−0.545824	−	0.837900i	$-0.683783\pi$
$311$	−5987.19	−1.09165	−0.545824	+	0.837900i	$0.683783\pi$
$312$	−19026.6	−3.45246
$313$	−8427.19	−1.52183	−0.760915	−	0.648851i	$-0.775250\pi$
$313$	−8427.19	−1.52183	−0.760915	+	0.648851i	$0.775250\pi$
$314$	4822.39	0.866697
$315$	0	0
$316$	1052.38	0.187344
$317$	−7172.84	−1.27087	−0.635436	−	0.772153i	$-0.719180\pi$
$317$	−7172.84	−1.27087	−0.635436	+	0.772153i	$0.719180\pi$
$318$	12764.4	2.25092
$319$	2438.58	0.428007
$320$	0	0
$321$	1254.04	0.218049
$322$	9433.57	1.63265
$323$	12611.8	2.17257
$324$	−14045.6	−2.40837
$325$	0	0
$326$	15829.2	2.68926
$327$	14808.2	2.50426
$328$	11642.3	1.95987
$329$	−5858.44	−0.981722
$330$	0	0
$331$	−7841.93	−1.30221	−0.651105	−	0.758988i	$-0.725694\pi$
$331$	−7841.93	−1.30221	−0.651105	+	0.758988i	$0.725694\pi$
$332$	15044.7	2.48701
$333$	−3098.21	−0.509852
$334$	−4149.57	−0.679804
$335$	0	0
$336$	−8781.37	−1.42578
$337$	1954.10	0.315865	0.157933	−	0.987450i	$-0.449517\pi$
$337$	1954.10	0.315865	0.157933	+	0.987450i	$0.449517\pi$
$338$	−11549.8	−1.85866
$339$	−14524.3	−2.32699
$340$	0	0
$341$	1083.61	0.172084
$342$	−15242.3	−2.40997
$343$	−6563.89	−1.03329
$344$	22413.0	3.51288
$345$	0	0
$346$	−17426.7	−2.70771
$347$	3028.62	0.468544	0.234272	−	0.972171i	$-0.424729\pi$
$347$	3028.62	0.468544	0.234272	+	0.972171i	$0.424729\pi$
$348$	−20327.0	−3.13116
$349$	−5535.15	−0.848968	−0.424484	−	0.905436i	$-0.639544\pi$
$349$	−5535.15	−0.848968	−0.424484	+	0.905436i	$0.639544\pi$
$350$	0	0
$351$	−2992.23	−0.455024
$352$	−331.382	−0.0501782
$353$	9068.24	1.36729	0.683646	−	0.729814i	$-0.260393\pi$
$353$	9068.24	1.36729	0.683646	+	0.729814i	$0.260393\pi$
$354$	−25738.2	−3.86432
$355$	0	0
$356$	−33.8717	−0.00504268
$357$	−10311.2	−1.52865
$358$	−4648.44	−0.686250
$359$	7596.29	1.11676	0.558380	−	0.829585i	$-0.311423\pi$
$359$	7596.29	1.11676	0.558380	+	0.829585i	$0.311423\pi$
$360$	0	0
$361$	15752.6	2.29664
$362$	149.413	0.0216933
$363$	7924.05	1.14574
$364$	−19585.2	−2.82017
$365$	0	0
$366$	14167.1	2.02330
$367$	−9432.82	−1.34166	−0.670830	−	0.741611i	$-0.734062\pi$
$367$	−9432.82	−1.34166	−0.670830	+	0.741611i	$0.734062\pi$
$368$	−7666.74	−1.08602
$369$	−5845.85	−0.824723
$370$	0	0
$371$	6692.70	0.936571
$372$	−9032.51	−1.25891
$373$	−9161.67	−1.27178	−0.635889	−	0.771780i	$-0.719367\pi$
$373$	−9161.67	−1.27178	−0.635889	+	0.771780i	$0.719367\pi$
$374$	−5578.10	−0.771221
$375$	0	0
$376$	13456.4	1.84564
$377$	−12179.5	−1.66387
$378$	−3903.09	−0.531093
$379$	4892.75	0.663123	0.331562	−	0.943434i	$-0.392424\pi$
$379$	4892.75	0.663123	0.331562	+	0.943434i	$0.392424\pi$
$380$	0	0
$381$	−1139.40	−0.153210
$382$	15528.3	2.07984
$383$	−4905.24	−0.654428	−0.327214	−	0.944950i	$-0.606110\pi$
$383$	−4905.24	−0.654428	−0.327214	+	0.944950i	$0.606110\pi$
$384$	−16665.8	−2.21477
$385$	0	0
$386$	−836.895	−0.110355
$387$	−11254.1	−1.47824
$388$	7618.16	0.996787
$389$	−4741.68	−0.618028	−0.309014	−	0.951058i	$-0.599999\pi$
$389$	−4741.68	−0.618028	−0.309014	+	0.951058i	$0.599999\pi$
$390$	0	0
$391$	−9002.40	−1.16438
$392$	1031.93	0.132961
$393$	5411.49	0.694589
$394$	−10973.2	−1.40311
$395$	0	0
$396$	4522.62	0.573915
$397$	−937.706	−0.118544	−0.0592722	−	0.998242i	$-0.518878\pi$
$397$	−937.706	−0.118544	−0.0592722	+	0.998242i	$0.518878\pi$
$398$	−18993.0	−2.39204
$399$	−18486.9	−2.31956
$400$	0	0
$401$	1123.67	0.139934	0.0699671	−	0.997549i	$-0.477711\pi$
$401$	1123.67	0.139934	0.0699671	+	0.997549i	$0.477711\pi$
$402$	2042.78	0.253445
$403$	−5412.09	−0.668971
$404$	4163.33	0.512706
$405$	0	0
$406$	−15887.1	−1.94202
$407$	−2032.83	−0.247576
$408$	23684.1	2.87387
$409$	−7958.07	−0.962105	−0.481053	−	0.876692i	$-0.659745\pi$
$409$	−7958.07	−0.962105	−0.481053	+	0.876692i	$0.659745\pi$
$410$	0	0
$411$	871.282	0.104567
$412$	−11600.0	−1.38711
$413$	−13495.2	−1.60788
$414$	10880.1	1.29161
$415$	0	0
$416$	1655.09	0.195066
$417$	−18544.4	−2.17776
$418$	−10000.9	−1.17024
$419$	−8033.17	−0.936625	−0.468313	−	0.883563i	$-0.655138\pi$
$419$	−8033.17	−0.936625	−0.468313	+	0.883563i	$0.655138\pi$
$420$	0	0
$421$	2523.79	0.292167	0.146083	−	0.989272i	$-0.453333\pi$
$421$	2523.79	0.292167	0.146083	+	0.989272i	$0.453333\pi$
$422$	29204.6	3.36885
$423$	−6756.76	−0.776655
$424$	−15372.6	−1.76076
$425$	0	0
$426$	2413.98	0.274549
$427$	7428.18	0.841861
$428$	−2965.00	−0.334857
$429$	6268.45	0.705463
$430$	0	0
$431$	16554.4	1.85011	0.925057	−	0.379829i	$-0.124017\pi$
$431$	16554.4	1.85011	0.925057	+	0.379829i	$0.124017\pi$
$432$	3172.07	0.353279
$433$	2139.33	0.237436	0.118718	−	0.992928i	$-0.462122\pi$
$433$	2139.33	0.237436	0.118718	+	0.992928i	$0.462122\pi$
$434$	−7059.57	−0.780807
$435$	0	0
$436$	−35011.8	−3.84578
$437$	−16140.4	−1.76681
$438$	−11011.8	−1.20128
$439$	−2990.31	−0.325102	−0.162551	−	0.986700i	$-0.551972\pi$
$439$	−2990.31	−0.325102	−0.162551	+	0.986700i	$0.551972\pi$
$440$	0	0
$441$	−518.157	−0.0559504
$442$	27859.9	2.99810
$443$	−11482.4	−1.23148	−0.615740	−	0.787950i	$-0.711143\pi$
$443$	−11482.4	−1.23148	−0.615740	+	0.787950i	$0.711143\pi$
$444$	16944.8	1.81119
$445$	0	0
$446$	4072.73	0.432398
$447$	12048.6	1.27489
$448$	−8027.69	−0.846590
$449$	−6598.75	−0.693573	−0.346787	−	0.937944i	$-0.612727\pi$
$449$	−6598.75	−0.693573	−0.346787	+	0.937944i	$0.612727\pi$
$450$	0	0
$451$	−3835.64	−0.400472
$452$	34340.6	3.57355
$453$	−17348.5	−1.79935
$454$	−3827.45	−0.395664
$455$	0	0
$456$	42463.1	4.36078
$457$	−13399.0	−1.37151	−0.685756	−	0.727832i	$-0.740528\pi$
$457$	−13399.0	−1.37151	−0.685756	+	0.727832i	$0.740528\pi$
$458$	14577.6	1.48726
$459$	3724.70	0.378767
$460$	0	0
$461$	−6042.30	−0.610451	−0.305226	−	0.952280i	$-0.598732\pi$
$461$	−6042.30	−0.610451	−0.305226	+	0.952280i	$0.598732\pi$
$462$	8176.62	0.823400
$463$	−9938.49	−0.997583	−0.498791	−	0.866722i	$-0.666223\pi$
$463$	−9938.49	−0.997583	−0.498791	+	0.866722i	$0.666223\pi$
$464$	12911.5	1.29182
$465$	0	0
$466$	−57.0067	−0.00566692
$467$	−12740.2	−1.26241	−0.631205	−	0.775616i	$-0.717439\pi$
$467$	−12740.2	−1.26241	−0.631205	+	0.775616i	$0.717439\pi$
$468$	−22588.3	−2.23108
$469$	1071.08	0.105454
$470$	0	0
$471$	6745.78	0.659934
$472$	30997.4	3.02282
$473$	−7384.15	−0.717809
$474$	2194.38	0.212639
$475$	0	0
$476$	24379.4	2.34754
$477$	7718.94	0.740935
$478$	11847.7	1.13368
$479$	−15065.3	−1.43706	−0.718529	−	0.695497i	$-0.755184\pi$
$479$	−15065.3	−1.43706	−0.718529	+	0.695497i	$0.755184\pi$
$480$	0	0
$481$	10153.0	0.962446
$482$	−9342.93	−0.882902
$483$	13196.1	1.24315
$484$	−18735.3	−1.75951
$485$	0	0
$486$	−23375.9	−2.18180
$487$	2023.54	0.188286	0.0941431	−	0.995559i	$-0.469989\pi$
$487$	2023.54	0.188286	0.0941431	+	0.995559i	$0.469989\pi$
$488$	−17062.0	−1.58270
$489$	22142.6	2.04770
$490$	0	0
$491$	9571.21	0.879721	0.439860	−	0.898066i	$-0.355028\pi$
$491$	9571.21	0.879721	0.439860	+	0.898066i	$0.355028\pi$
$492$	31972.3	2.92972
$493$	15160.9	1.38502
$494$	49949.8	4.54929
$495$	0	0
$496$	5737.37	0.519386
$497$	1265.71	0.114235
$498$	31370.7	2.82280
$499$	−3509.41	−0.314835	−0.157418	−	0.987532i	$-0.550317\pi$
$499$	−3509.41	−0.314835	−0.157418	+	0.987532i	$0.550317\pi$
$500$	0	0
$501$	−5804.62	−0.517627
$502$	1834.34	0.163089
$503$	17786.6	1.57667	0.788337	−	0.615244i	$-0.210943\pi$
$503$	17786.6	1.57667	0.788337	+	0.615244i	$0.210943\pi$
$504$	−15008.3	−1.32643
$505$	0	0
$506$	7138.75	0.627186
$507$	−16156.5	−1.41525
$508$	2693.94	0.235284
$509$	−587.753	−0.0511821	−0.0255911	−	0.999672i	$-0.508147\pi$
$509$	−587.753	−0.0511821	−0.0255911	+	0.999672i	$0.508147\pi$
$510$	0	0
$511$	−5773.74	−0.499834
$512$	21643.3	1.86818
$513$	6677.99	0.574738
$514$	−32065.1	−2.75162
$515$	0	0
$516$	61551.3	5.25125
$517$	−4433.32	−0.377132
$518$	13243.6	1.12334
$519$	−24377.3	−2.06174
$520$	0	0
$521$	−2678.25	−0.225213	−0.112607	−	0.993640i	$-0.535920\pi$
$521$	−2678.25	−0.225213	−0.112607	+	0.993640i	$0.535920\pi$
$522$	−18323.1	−1.53636
$523$	11311.0	0.945691	0.472845	−	0.881145i	$-0.343227\pi$
$523$	11311.0	0.945691	0.472845	+	0.881145i	$0.343227\pi$
$524$	−12794.7	−1.06668
$525$	0	0
$526$	−20904.8	−1.73288
$527$	6736.91	0.556858
$528$	−6645.21	−0.547719
$529$	−645.892	−0.0530855
$530$	0	0
$531$	−15564.5	−1.27202
$532$	43709.7	3.56213
$533$	19157.1	1.55682
$534$	−70.6279	−0.00572354
$535$	0	0
$536$	−2460.19	−0.198254
$537$	−6502.45	−0.522535
$538$	−31175.5	−2.49827
$539$	−339.979	−0.0271687
$540$	0	0
$541$	2223.42	0.176695	0.0883477	−	0.996090i	$-0.471841\pi$
$541$	2223.42	0.176695	0.0883477	+	0.996090i	$0.471841\pi$
$542$	2772.34	0.219709
$543$	209.006	0.0165180
$544$	−2060.24	−0.162375
$545$	0	0
$546$	−40838.2	−3.20094
$547$	20459.5	1.59924	0.799621	−	0.600505i	$-0.205034\pi$
$547$	20459.5	1.59924	0.799621	+	0.600505i	$0.205034\pi$
$548$	−2060.02	−0.160584
$549$	8567.20	0.666009
$550$	0	0
$551$	27182.0	2.10162
$552$	−30310.5	−2.33714
$553$	1150.56	0.0884755
$554$	−20736.2	−1.59025
$555$	0	0
$556$	43845.7	3.34437
$557$	4471.11	0.340121	0.170060	−	0.985434i	$-0.445604\pi$
$557$	4471.11	0.340121	0.170060	+	0.985434i	$0.445604\pi$
$558$	−8142.07	−0.617708
$559$	36880.2	2.79046
$560$	0	0
$561$	−7802.90	−0.587235
$562$	−19966.8	−1.49867
$563$	−21005.4	−1.57242	−0.786209	−	0.617961i	$-0.787959\pi$
$563$	−21005.4	−1.57242	−0.786209	+	0.617961i	$0.787959\pi$
$564$	36954.3	2.75897
$565$	0	0
$566$	−23613.3	−1.75361
$567$	−15356.1	−1.13738
$568$	−2907.24	−0.214763
$569$	20809.2	1.53316	0.766578	−	0.642152i	$-0.221958\pi$
$569$	20809.2	1.53316	0.766578	+	0.642152i	$0.221958\pi$
$570$	0	0
$571$	22188.1	1.62617	0.813086	−	0.582144i	$-0.197786\pi$
$571$	22188.1	1.62617	0.813086	+	0.582144i	$0.197786\pi$
$572$	−14820.9	−1.08338
$573$	21721.7	1.58366
$574$	24988.7	1.81709
$575$	0	0
$576$	−9258.63	−0.669750
$577$	−7273.22	−0.524763	−0.262381	−	0.964964i	$-0.584508\pi$
$577$	−7273.22	−0.524763	−0.262381	+	0.964964i	$0.584508\pi$
$578$	−10458.3	−0.752606
$579$	−1170.69	−0.0840278
$580$	0	0
$581$	16448.4	1.17452
$582$	15885.1	1.13137
$583$	5064.63	0.359787
$584$	13261.8	0.939690
$585$	0	0
$586$	−6101.97	−0.430153
$587$	−36.3906	−0.00255878	−0.00127939	−	0.999999i	$-0.500407\pi$
$587$	−36.3906	−0.00255878	−0.00127939	+	0.999999i	$0.500407\pi$
$588$	2833.92	0.198757
$589$	12078.6	0.844972
$590$	0	0
$591$	−15349.9	−1.06838
$592$	−10763.2	−0.747239
$593$	−4647.26	−0.321821	−0.160911	−	0.986969i	$-0.551443\pi$
$593$	−4647.26	−0.321821	−0.160911	+	0.986969i	$0.551443\pi$
$594$	−2953.62	−0.204021
$595$	0	0
$596$	−28487.1	−1.95785
$597$	−26568.2	−1.82138
$598$	−35654.6	−2.43817
$599$	−14235.9	−0.971057	−0.485528	−	0.874221i	$-0.661373\pi$
$599$	−14235.9	−0.971057	−0.485528	+	0.874221i	$0.661373\pi$
$600$	0	0
$601$	−25137.3	−1.70611	−0.853054	−	0.521822i	$-0.825252\pi$
$601$	−25137.3	−1.70611	−0.853054	+	0.521822i	$0.825252\pi$
$602$	48106.9	3.25696
$603$	1235.32	0.0834263
$604$	41018.2	2.76325
$605$	0	0
$606$	8681.21	0.581931
$607$	−444.363	−0.0297136	−0.0148568	−	0.999890i	$-0.504729\pi$
$607$	−444.363	−0.0297136	−0.0148568	+	0.999890i	$0.504729\pi$
$608$	−3693.79	−0.246387
$609$	−22223.6	−1.47873
$610$	0	0
$611$	22142.2	1.46609
$612$	28117.7	1.85717
$613$	−11751.8	−0.774309	−0.387155	−	0.922015i	$-0.626542\pi$
$613$	−11751.8	−0.774309	−0.387155	+	0.922015i	$0.626542\pi$
$614$	18226.5	1.19799
$615$	0	0
$616$	−9847.38	−0.644095
$617$	−18774.1	−1.22499	−0.612493	−	0.790476i	$-0.709833\pi$
$617$	−18774.1	−1.22499	−0.612493	+	0.790476i	$0.709833\pi$
$618$	−24187.8	−1.57439
$619$	16291.6	1.05786	0.528929	−	0.848666i	$-0.322594\pi$
$619$	16291.6	1.05786	0.528929	+	0.848666i	$0.322594\pi$
$620$	0	0
$621$	−4766.80	−0.308027
$622$	29517.3	1.90279
$623$	−37.0319	−0.00238147
$624$	33189.6	2.12924
$625$	0	0
$626$	41546.6	2.65261
$627$	−13989.8	−0.891066
$628$	−15949.4	−1.01346
$629$	−12638.3	−0.801150
$630$	0	0
$631$	−29166.1	−1.84007	−0.920035	−	0.391835i	$-0.871840\pi$
$631$	−29166.1	−1.84007	−0.920035	+	0.391835i	$0.871840\pi$
$632$	−2642.76	−0.166334
$633$	40852.7	2.56516
$634$	35362.6	2.21519
$635$	0	0
$636$	−42216.7	−2.63208
$637$	1698.03	0.105617
$638$	−12022.4	−0.746035
$639$	1459.79	0.0903731
$640$	0	0
$641$	−14862.8	−0.915829	−0.457915	−	0.888996i	$-0.651403\pi$
$641$	−14862.8	−0.915829	−0.457915	+	0.888996i	$0.651403\pi$
$642$	−6182.50	−0.380068
$643$	−8246.54	−0.505773	−0.252886	−	0.967496i	$-0.581380\pi$
$643$	−8246.54	−0.505773	−0.252886	+	0.967496i	$0.581380\pi$
$644$	−31200.3	−1.90911
$645$	0	0
$646$	−62177.0	−3.78688
$647$	−13791.1	−0.837994	−0.418997	−	0.907988i	$-0.637618\pi$
$647$	−13791.1	−0.837994	−0.418997	+	0.907988i	$0.637618\pi$
$648$	35271.8	2.13828
$649$	−10212.3	−0.617671
$650$	0	0
$651$	−9875.25	−0.594534
$652$	−52353.1	−3.14464
$653$	−15666.7	−0.938874	−0.469437	−	0.882966i	$-0.655543\pi$
$653$	−15666.7	−0.938874	−0.469437	+	0.882966i	$0.655543\pi$
$654$	−73005.2	−4.36503
$655$	0	0
$656$	−20308.5	−1.20871
$657$	−6659.07	−0.395426
$658$	28882.5	1.71118
$659$	33408.4	1.97482	0.987411	−	0.158173i	$-0.0505603\pi$
$659$	33408.4	1.97482	0.987411	+	0.158173i	$0.0505603\pi$
$660$	0	0
$661$	−17694.7	−1.04122	−0.520609	−	0.853795i	$-0.674295\pi$
$661$	−17694.7	−1.04122	−0.520609	+	0.853795i	$0.674295\pi$
$662$	38661.2	2.26981
$663$	38971.7	2.28286
$664$	−37780.8	−2.20810
$665$	0	0
$666$	15274.4	0.888694
$667$	−19402.7	−1.12635
$668$	13724.2	0.794917
$669$	5697.13	0.329243
$670$	0	0
$671$	5621.20	0.323404
$672$	3019.99	0.173361
$673$	−20829.8	−1.19306	−0.596530	−	0.802591i	$-0.703454\pi$
$673$	−20829.8	−1.19306	−0.596530	+	0.802591i	$0.703454\pi$
$674$	−9633.85	−0.550567
$675$	0	0
$676$	38199.6	2.17340
$677$	15595.0	0.885326	0.442663	−	0.896688i	$-0.354034\pi$
$677$	15595.0	0.885326	0.442663	+	0.896688i	$0.354034\pi$
$678$	71605.6	4.05604
$679$	8328.94	0.470744
$680$	0	0
$681$	−5354.02	−0.301272
$682$	−5342.26	−0.299949
$683$	−19308.7	−1.08174	−0.540870	−	0.841106i	$-0.681905\pi$
$683$	−19308.7	−1.08174	−0.540870	+	0.841106i	$0.681905\pi$
$684$	50412.0	2.81806
$685$	0	0
$686$	32360.4	1.80106
$687$	20391.8	1.13246
$688$	−39096.8	−2.16650
$689$	−25295.4	−1.39866
$690$	0	0
$691$	27756.9	1.52811	0.764054	−	0.645152i	$-0.223206\pi$
$691$	27756.9	1.52811	0.764054	+	0.645152i	$0.223206\pi$
$692$	57636.7	3.16621
$693$	4944.59	0.271038
$694$	−14931.3	−0.816692
$695$	0	0
$696$	51045.8	2.78001
$697$	−23846.6	−1.29592
$698$	27288.7	1.47979
$699$	−79.7437	−0.00431500
$700$	0	0
$701$	−6802.90	−0.366537	−0.183268	−	0.983063i	$-0.558668\pi$
$701$	−6802.90	−0.366537	−0.183268	+	0.983063i	$0.558668\pi$
$702$	14751.9	0.793126
$703$	−22659.2	−1.21566
$704$	−6074.87	−0.325220
$705$	0	0
$706$	−44707.0	−2.38325
$707$	4551.77	0.242131
$708$	85125.8	4.51868
$709$	17875.1	0.946845	0.473423	−	0.880835i	$-0.343018\pi$
$709$	17875.1	0.946845	0.473423	+	0.880835i	$0.343018\pi$
$710$	0	0
$711$	1326.99	0.0699943
$712$	85.0596	0.00447717
$713$	−8621.77	−0.452858
$714$	50835.0	2.66450
$715$	0	0
$716$	15374.1	0.802455
$717$	16573.1	0.863227
$718$	−37450.3	−1.94656
$719$	−33323.6	−1.72846	−0.864229	−	0.503099i	$-0.832193\pi$
$719$	−33323.6	−1.72846	−0.864229	+	0.503099i	$0.832193\pi$
$720$	0	0
$721$	−12682.2	−0.655078
$722$	−77661.5	−4.00313
$723$	−13069.3	−0.672273
$724$	−494.165	−0.0253667
$725$	0	0
$726$	−39066.1	−1.99708
$727$	−1631.98	−0.0832554	−0.0416277	−	0.999133i	$-0.513254\pi$
$727$	−1631.98	−0.0832554	−0.0416277	+	0.999133i	$0.513254\pi$
$728$	49182.8	2.50390
$729$	−9441.51	−0.479678
$730$	0	0
$731$	−45908.1	−2.32281
$732$	−46856.0	−2.36591
$733$	21016.6	1.05903	0.529513	−	0.848302i	$-0.322375\pi$
$733$	21016.6	1.05903	0.529513	+	0.848302i	$0.322375\pi$
$734$	46504.4	2.33857
$735$	0	0
$736$	2636.66	0.132050
$737$	810.530	0.0405105
$738$	28820.4	1.43753
$739$	−39037.9	−1.94321	−0.971605	−	0.236607i	$-0.923964\pi$
$739$	−39037.9	−1.94321	−0.971605	+	0.236607i	$0.923964\pi$
$740$	0	0
$741$	69872.1	3.46399
$742$	−32995.5	−1.63248
$743$	30906.4	1.52604	0.763018	−	0.646378i	$-0.223717\pi$
$743$	30906.4	1.52604	0.763018	+	0.646378i	$0.223717\pi$
$744$	22682.7	1.11773
$745$	0	0
$746$	45167.7	2.21676
$747$	18970.6	0.929180
$748$	18448.9	0.901814
$749$	−3241.64	−0.158140
$750$	0	0
$751$	−21764.9	−1.05754	−0.528771	−	0.848765i	$-0.677347\pi$
$751$	−21764.9	−1.05754	−0.528771	+	0.848765i	$0.677347\pi$
$752$	−23473.1	−1.13826
$753$	2565.96	0.124182
$754$	60045.9	2.90019
$755$	0	0
$756$	12909.0	0.621025
$757$	1519.05	0.0729338	0.0364669	−	0.999335i	$-0.488390\pi$
$757$	1519.05	0.0729338	0.0364669	+	0.999335i	$0.488390\pi$
$758$	−24121.6	−1.15585
$759$	9986.02	0.477562
$760$	0	0
$761$	−24945.1	−1.18825	−0.594126	−	0.804372i	$-0.702502\pi$
$761$	−24945.1	−1.18825	−0.594126	+	0.804372i	$0.702502\pi$
$762$	5617.30	0.267052
$763$	−38278.4	−1.81621
$764$	−51357.9	−2.43202
$765$	0	0
$766$	24183.2	1.14070
$767$	51005.5	2.40118
$768$	57319.1	2.69313
$769$	−11159.5	−0.523306	−0.261653	−	0.965162i	$-0.584268\pi$
$769$	−11159.5	−0.523306	−0.261653	+	0.965162i	$0.584268\pi$
$770$	0	0
$771$	−44854.2	−2.09518
$772$	2767.92	0.129041
$773$	3076.94	0.143169	0.0715846	−	0.997435i	$-0.477194\pi$
$773$	3076.94	0.143169	0.0715846	+	0.997435i	$0.477194\pi$
$774$	55483.4	2.57663
$775$	0	0
$776$	−19130.9	−0.885001
$777$	18525.8	0.855354
$778$	23376.8	1.07725
$779$	−42754.4	−1.96641
$780$	0	0
$781$	957.813	0.0438838
$782$	44382.4	2.02956
$783$	8027.76	0.366397
$784$	−1800.08	−0.0820009
$785$	0	0
$786$	−26679.0	−1.21070
$787$	13002.5	0.588931	0.294466	−	0.955662i	$-0.404858\pi$
$787$	13002.5	0.588931	0.294466	+	0.955662i	$0.404858\pi$
$788$	36292.6	1.64070
$789$	−29242.6	−1.31947
$790$	0	0
$791$	37544.6	1.68765
$792$	−11357.4	−0.509553
$793$	−28075.1	−1.25722
$794$	4622.95	0.206628
$795$	0	0
$796$	62816.8	2.79709
$797$	−26690.5	−1.18623	−0.593116	−	0.805117i	$-0.702103\pi$
$797$	−26690.5	−1.18623	−0.593116	+	0.805117i	$0.702103\pi$
$798$	91141.8	4.04309
$799$	−27562.4	−1.22039
$800$	0	0
$801$	−42.7103	−0.00188401
$802$	−5539.79	−0.243911
$803$	−4369.22	−0.192013
$804$	−6756.25	−0.296361
$805$	0	0
$806$	26682.0	1.16604
$807$	−43609.7	−1.90227
$808$	−10455.1	−0.455208
$809$	18581.8	0.807543	0.403771	−	0.914860i	$-0.367699\pi$
$809$	18581.8	0.807543	0.403771	+	0.914860i	$0.367699\pi$
$810$	0	0
$811$	14579.2	0.631250	0.315625	−	0.948884i	$-0.397786\pi$
$811$	14579.2	0.631250	0.315625	+	0.948884i	$0.397786\pi$
$812$	52544.4	2.27087
$813$	3878.08	0.167294
$814$	10022.0	0.431536
$815$	0	0
$816$	−41314.0	−1.77240
$817$	−82308.4	−3.52461
$818$	39233.8	1.67699
$819$	−24695.8	−1.05365
$820$	0	0
$821$	2744.45	0.116665	0.0583326	−	0.998297i	$-0.481422\pi$
$821$	2744.45	0.116665	0.0583326	+	0.998297i	$0.481422\pi$
$822$	−4295.48	−0.182265
$823$	−4140.30	−0.175360	−0.0876802	−	0.996149i	$-0.527945\pi$
$823$	−4140.30	−0.175360	−0.0876802	+	0.996149i	$0.527945\pi$
$824$	29130.2	1.23155
$825$	0	0
$826$	66532.0	2.80260
$827$	24154.3	1.01563	0.507816	−	0.861465i	$-0.330453\pi$
$827$	24154.3	1.01563	0.507816	+	0.861465i	$0.330453\pi$
$828$	−35984.5	−1.51032
$829$	13182.0	0.552266	0.276133	−	0.961119i	$-0.410947\pi$
$829$	13182.0	0.552266	0.276133	+	0.961119i	$0.410947\pi$
$830$	0	0
$831$	−29006.7	−1.21087
$832$	30341.0	1.26428
$833$	−2113.69	−0.0879170
$834$	91425.3	3.79592
$835$	0	0
$836$	33076.9	1.36841
$837$	3567.21	0.147313
$838$	39604.1	1.63258
$839$	31988.9	1.31630	0.658152	−	0.752885i	$-0.271338\pi$
$839$	31988.9	1.31630	0.658152	+	0.752885i	$0.271338\pi$
$840$	0	0
$841$	8287.07	0.339787
$842$	−12442.5	−0.509259
$843$	−27930.5	−1.14114
$844$	−96590.4	−3.93931
$845$	0	0
$846$	33311.3	1.35374
$847$	−20483.3	−0.830950
$848$	26815.7	1.08591
$849$	−33031.4	−1.33526
$850$	0	0
$851$	16174.3	0.651526
$852$	−7983.94	−0.321039
$853$	23508.1	0.943614	0.471807	−	0.881702i	$-0.343602\pi$
$853$	23508.1	0.943614	0.471807	+	0.881702i	$0.343602\pi$
$854$	−36621.4	−1.46740
$855$	0	0
$856$	7445.79	0.297304
$857$	−5171.53	−0.206133	−0.103067	−	0.994674i	$-0.532865\pi$
$857$	−5171.53	−0.206133	−0.103067	+	0.994674i	$0.532865\pi$
$858$	−30903.9	−1.22965
$859$	22659.5	0.900037	0.450018	−	0.893019i	$-0.351417\pi$
$859$	22659.5	0.900037	0.450018	+	0.893019i	$0.351417\pi$
$860$	0	0
$861$	34955.4	1.38360
$862$	−81614.5	−3.22483
$863$	−35838.5	−1.41362	−0.706812	−	0.707401i	$-0.749867\pi$
$863$	−35838.5	−1.41362	−0.706812	+	0.707401i	$0.749867\pi$
$864$	−1090.90	−0.0429552
$865$	0	0
$866$	−10547.0	−0.413860
$867$	−14629.5	−0.573061
$868$	23348.6	0.913023
$869$	870.678	0.0339882
$870$	0	0
$871$	−4048.20	−0.157483
$872$	87922.6	3.41449
$873$	9606.08	0.372413
$874$	79573.0	3.07963
$875$	0	0
$876$	36420.0	1.40470
$877$	−1690.69	−0.0650976	−0.0325488	−	0.999470i	$-0.510362\pi$
$877$	−1690.69	−0.0650976	−0.0325488	+	0.999470i	$0.510362\pi$
$878$	14742.4	0.566666
$879$	−8535.71	−0.327534
$880$	0	0
$881$	−45945.6	−1.75703	−0.878517	−	0.477712i	$-0.841466\pi$
$881$	−45945.6	−1.75703	−0.878517	+	0.477712i	$0.841466\pi$
$882$	2554.55	0.0975240
$883$	20598.6	0.785048	0.392524	−	0.919742i	$-0.371602\pi$
$883$	20598.6	0.785048	0.392524	+	0.919742i	$0.371602\pi$
$884$	−92143.0	−3.50578
$885$	0	0
$886$	56609.0	2.14652
$887$	17132.3	0.648531	0.324265	−	0.945966i	$-0.394883\pi$
$887$	17132.3	0.648531	0.324265	+	0.945966i	$0.394883\pi$
$888$	−42552.4	−1.60807
$889$	2945.29	0.111116
$890$	0	0
$891$	−11620.6	−0.436929
$892$	−13470.1	−0.505617
$893$	−49416.5	−1.85180
$894$	−59400.2	−2.22219
$895$	0	0
$896$	43080.3	1.60626
$897$	−49875.3	−1.85651
$898$	32532.3	1.20893
$899$	14519.9	0.538673
$900$	0	0
$901$	31487.4	1.16426
$902$	18910.0	0.698040
$903$	67294.1	2.47996
$904$	−86237.1	−3.17279
$905$	0	0
$906$	85529.5	3.13634
$907$	23337.9	0.854379	0.427189	−	0.904162i	$-0.359504\pi$
$907$	23337.9	0.854379	0.427189	+	0.904162i	$0.359504\pi$
$908$	12658.8	0.462662
$909$	5249.73	0.191554
$910$	0	0
$911$	40208.4	1.46231	0.731154	−	0.682212i	$-0.238982\pi$
$911$	40208.4	1.46231	0.731154	+	0.682212i	$0.238982\pi$
$912$	−74071.7	−2.68943
$913$	12447.2	0.451195
$914$	66058.2	2.39060
$915$	0	0
$916$	−48213.6	−1.73911
$917$	−13988.5	−0.503751
$918$	−18363.0	−0.660207
$919$	−35783.9	−1.28444	−0.642222	−	0.766519i	$-0.721987\pi$
$919$	−35783.9	−1.28444	−0.642222	+	0.766519i	$0.721987\pi$
$920$	0	0
$921$	25496.1	0.912189
$922$	29789.0	1.06404
$923$	−4783.81	−0.170597
$924$	−27043.1	−0.962829
$925$	0	0
$926$	48997.4	1.73883
$927$	−14626.9	−0.518242
$928$	−4440.39	−0.157072
$929$	34973.3	1.23513	0.617565	−	0.786520i	$-0.288119\pi$
$929$	34973.3	1.23513	0.617565	+	0.786520i	$0.288119\pi$
$930$	0	0
$931$	−3789.62	−0.133405
$932$	188.543	0.00662652
$933$	41290.1	1.44885
$934$	62810.0	2.20043
$935$	0	0
$936$	56724.4	1.98087
$937$	−13586.8	−0.473705	−0.236852	−	0.971546i	$-0.576116\pi$
$937$	−13586.8	−0.473705	−0.236852	+	0.971546i	$0.576116\pi$
$938$	−5280.51	−0.183811
$939$	58117.3	2.01979
$940$	0	0
$941$	−21703.0	−0.751856	−0.375928	−	0.926649i	$-0.622676\pi$
$941$	−21703.0	−0.751856	−0.375928	+	0.926649i	$0.622676\pi$
$942$	−33257.1	−1.15029
$943$	30518.4	1.05389
$944$	−54071.1	−1.86426
$945$	0	0
$946$	36404.4	1.25117
$947$	22302.3	0.765288	0.382644	−	0.923896i	$-0.375014\pi$
$947$	22302.3	0.765288	0.382644	+	0.923896i	$0.375014\pi$
$948$	−7257.62	−0.248646
$949$	21822.1	0.746444
$950$	0	0
$951$	49466.8	1.68672
$952$	−61222.3	−2.08427
$953$	−43570.3	−1.48099	−0.740494	−	0.672063i	$-0.765408\pi$
$953$	−43570.3	−1.48099	−0.740494	+	0.672063i	$0.765408\pi$
$954$	−38054.9	−1.29148
$955$	0	0
$956$	−39184.8	−1.32565
$957$	−16817.4	−0.568057
$958$	74273.0	2.50485
$959$	−2252.23	−0.0758375
$960$	0	0
$961$	−23338.9	−0.783422
$962$	−50054.9	−1.67758
$963$	−3738.70	−0.125107
$964$	30900.6	1.03241
$965$	0	0
$966$	−65057.7	−2.16687
$967$	1415.46	0.0470714	0.0235357	−	0.999723i	$-0.492508\pi$
$967$	1415.46	0.0470714	0.0235357	+	0.999723i	$0.492508\pi$
$968$	47048.6	1.56219
$969$	−86976.1	−2.88346
$970$	0	0
$971$	5876.49	0.194218	0.0971089	−	0.995274i	$-0.469041\pi$
$971$	5876.49	0.194218	0.0971089	+	0.995274i	$0.469041\pi$
$972$	77312.9	2.55125
$973$	47936.5	1.57942
$974$	−9976.19	−0.328191
$975$	0	0
$976$	29762.5	0.976102
$977$	−55316.8	−1.81140	−0.905702	−	0.423916i	$-0.860655\pi$
$977$	−55316.8	−1.81140	−0.905702	+	0.423916i	$0.860655\pi$
$978$	−109165.	−3.56922
$979$	−28.0235	−0.000914848 0
$980$	0	0
$981$	−44147.9	−1.43683
$982$	−47186.7	−1.53339
$983$	−19288.4	−0.625844	−0.312922	−	0.949779i	$-0.601308\pi$
$983$	−19288.4	−0.625844	−0.312922	+	0.949779i	$0.601308\pi$
$984$	−80289.9	−2.60117
$985$	0	0
$986$	−74744.5	−2.41415
$987$	40402.2	1.30295
$988$	−165203.	−5.31963
$989$	58752.4	1.88900
$990$	0	0
$991$	−43829.2	−1.40493	−0.702463	−	0.711721i	$-0.747916\pi$
$991$	−43829.2	−1.40493	−0.702463	+	0.711721i	$0.747916\pi$
$992$	−1973.13	−0.0631522
$993$	54081.1	1.72831
$994$	−6240.04	−0.199117
$995$	0	0
$996$	−103755.	−3.30079
$997$	−50991.1	−1.61976	−0.809882	−	0.586592i	$-0.800469\pi$
$997$	−50991.1	−1.61976	−0.809882	+	0.586592i	$0.800469\pi$
$998$	17301.6	0.548771
$999$	−6692.04	−0.211939

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1775.4.a.h.1.4	✓	35
5.4	even	2		1775.4.a.k.1.32	yes	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1775.4.a.h.1.4	✓	35	1.1	even	1	trivial
1775.4.a.k.1.32	yes	35	5.4	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:	\( N \)	\(=\)	\( 1775 = 5^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1775.a (trivial)

\(f(q)\)	\(=\)	\(q-4.93007 q^{2} -6.89641 q^{3} +16.3056 q^{4} +33.9998 q^{6} +17.8269 q^{7} -40.9471 q^{8} +20.5604 q^{9} +O(q^{10})\)	\(q-4.93007 q^{2} -6.89641 q^{3} +16.3056 q^{4} +33.9998 q^{6} +17.8269 q^{7} -40.9471 q^{8} +20.5604 q^{9} +13.4903 q^{11} -112.450 q^{12} -67.3776 q^{13} -87.8878 q^{14} +71.4272 q^{16} +83.8709 q^{17} -101.364 q^{18} +150.372 q^{19} -122.942 q^{21} -66.5082 q^{22} -107.336 q^{23} +282.388 q^{24} +332.176 q^{26} +44.4099 q^{27} +290.678 q^{28} +180.765 q^{29} +80.3248 q^{31} -24.5644 q^{32} -93.0347 q^{33} -413.489 q^{34} +335.250 q^{36} -150.688 q^{37} -741.342 q^{38} +464.663 q^{39} -284.325 q^{41} +606.110 q^{42} -547.367 q^{43} +219.967 q^{44} +529.176 q^{46} -328.629 q^{47} -492.591 q^{48} -25.2017 q^{49} -578.408 q^{51} -1098.63 q^{52} +375.427 q^{53} -218.944 q^{54} -729.959 q^{56} -1037.02 q^{57} -891.185 q^{58} -757.011 q^{59} +416.684 q^{61} -396.007 q^{62} +366.529 q^{63} -450.313 q^{64} +458.668 q^{66} +60.0823 q^{67} +1367.56 q^{68} +740.236 q^{69} +71.0000 q^{71} -841.889 q^{72} -323.878 q^{73} +742.902 q^{74} +2451.90 q^{76} +240.491 q^{77} -2290.82 q^{78} +64.5409 q^{79} -861.400 q^{81} +1401.74 q^{82} +922.675 q^{83} -2004.63 q^{84} +2698.55 q^{86} -1246.63 q^{87} -552.389 q^{88} -2.07731 q^{89} -1201.13 q^{91} -1750.18 q^{92} -553.952 q^{93} +1620.17 q^{94} +169.406 q^{96} +467.212 q^{97} +124.246 q^{98} +277.367 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 6 q^{2} - 19 q^{3} + 146 q^{4} + 8 q^{6} - 76 q^{7} - 72 q^{8} + 286 q^{9}+O(q^{10}) \) 35 * q - 6 * q^2 - 19 * q^3 + 146 * q^4 + 8 * q^6 - 76 * q^7 - 72 * q^8 + 286 * q^9	\( 35 q - 6 q^{2} - 19 q^{3} + 146 q^{4} + 8 q^{6} - 76 q^{7} - 72 q^{8} + 286 q^{9} + 29 q^{11} - 228 q^{12} - 206 q^{13} - 48 q^{14} + 542 q^{16} - 347 q^{17} - 280 q^{18} - 59 q^{19} + 284 q^{21} - 605 q^{22} - 168 q^{23} + 100 q^{24} + 655 q^{26} - 727 q^{27} - 749 q^{28} - 522 q^{29} + 84 q^{31} - 1522 q^{32} - 547 q^{33} - 324 q^{34} + 2114 q^{36} - 706 q^{37} - 487 q^{38} - 574 q^{39} + 311 q^{41} - 1602 q^{42} - 928 q^{43} - 1129 q^{44} + 144 q^{46} - 744 q^{47} - 2644 q^{48} + 1649 q^{49} + 277 q^{51} - 2727 q^{52} - 886 q^{53} - 923 q^{54} + 947 q^{56} - 2501 q^{57} - 1181 q^{58} - 434 q^{59} + 466 q^{61} - 1727 q^{62} - 1908 q^{63} + 2102 q^{64} - 884 q^{66} - 2425 q^{67} - 2329 q^{68} - 716 q^{69} + 2485 q^{71} - 4079 q^{72} - 5803 q^{73} - 412 q^{74} - 3109 q^{76} - 732 q^{77} - 2691 q^{78} + 1024 q^{79} + 7 q^{81} - 1325 q^{82} - 4927 q^{83} + 3889 q^{84} - 2716 q^{86} - 2634 q^{87} - 7122 q^{88} + 3279 q^{89} - 3782 q^{91} + 3025 q^{92} - 5256 q^{93} + 1485 q^{94} - 3043 q^{96} - 8548 q^{97} - 5578 q^{98} + 9008 q^{99}+O(q^{100}) \) 35 * q - 6 * q^2 - 19 * q^3 + 146 * q^4 + 8 * q^6 - 76 * q^7 - 72 * q^8 + 286 * q^9 + 29 * q^11 - 228 * q^12 - 206 * q^13 - 48 * q^14 + 542 * q^16 - 347 * q^17 - 280 * q^18 - 59 * q^19 + 284 * q^21 - 605 * q^22 - 168 * q^23 + 100 * q^24 + 655 * q^26 - 727 * q^27 - 749 * q^28 - 522 * q^29 + 84 * q^31 - 1522 * q^32 - 547 * q^33 - 324 * q^34 + 2114 * q^36 - 706 * q^37 - 487 * q^38 - 574 * q^39 + 311 * q^41 - 1602 * q^42 - 928 * q^43 - 1129 * q^44 + 144 * q^46 - 744 * q^47 - 2644 * q^48 + 1649 * q^49 + 277 * q^51 - 2727 * q^52 - 886 * q^53 - 923 * q^54 + 947 * q^56 - 2501 * q^57 - 1181 * q^58 - 434 * q^59 + 466 * q^61 - 1727 * q^62 - 1908 * q^63 + 2102 * q^64 - 884 * q^66 - 2425 * q^67 - 2329 * q^68 - 716 * q^69 + 2485 * q^71 - 4079 * q^72 - 5803 * q^73 - 412 * q^74 - 3109 * q^76 - 732 * q^77 - 2691 * q^78 + 1024 * q^79 + 7 * q^81 - 1325 * q^82 - 4927 * q^83 + 3889 * q^84 - 2716 * q^86 - 2634 * q^87 - 7122 * q^88 + 3279 * q^89 - 3782 * q^91 + 3025 * q^92 - 5256 * q^93 + 1485 * q^94 - 3043 * q^96 - 8548 * q^97 - 5578 * q^98 + 9008 * q^99

Introduction

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