LMFDB - Embedded newform 3025.2.a.o.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3025,2,Mod(1,3025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3025, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("3025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3025 = 5^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3025.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:	$24.1547466114$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	3025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.41421 q^{2} +2.82843 q^{3} +3.82843 q^{4} +6.82843 q^{6} -2.00000 q^{7} +4.41421 q^{8} +5.00000 q^{9} +O(q^{10})$	\(q+2.41421 q^{2} +2.82843 q^{3} +3.82843 q^{4} +6.82843 q^{6} -2.00000 q^{7} +4.41421 q^{8} +5.00000 q^{9} +10.8284 q^{12} -1.17157 q^{13} -4.82843 q^{14} +3.00000 q^{16} +6.82843 q^{17} +12.0711 q^{18} -5.65685 q^{21} +2.82843 q^{23} +12.4853 q^{24} -2.82843 q^{26} +5.65685 q^{27} -7.65685 q^{28} +3.65685 q^{29} -1.58579 q^{32} +16.4853 q^{34} +19.1421 q^{36} +7.65685 q^{37} -3.31371 q^{39} -6.00000 q^{41} -13.6569 q^{42} -6.00000 q^{43} +6.82843 q^{46} -2.82843 q^{47} +8.48528 q^{48} -3.00000 q^{49} +19.3137 q^{51} -4.48528 q^{52} -11.6569 q^{53} +13.6569 q^{54} -8.82843 q^{56} +8.82843 q^{58} +1.65685 q^{59} +9.31371 q^{61} -10.0000 q^{63} -9.82843 q^{64} -12.4853 q^{67} +26.1421 q^{68} +8.00000 q^{69} +11.3137 q^{71} +22.0711 q^{72} -1.17157 q^{73} +18.4853 q^{74} -8.00000 q^{78} -4.00000 q^{79} +1.00000 q^{81} -14.4853 q^{82} -6.00000 q^{83} -21.6569 q^{84} -14.4853 q^{86} +10.3431 q^{87} -13.3137 q^{89} +2.34315 q^{91} +10.8284 q^{92} -6.82843 q^{94} -4.48528 q^{96} -3.65685 q^{97} -7.24264 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} + 8 q^{6} - 4 q^{7} + 6 q^{8} + 10 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^4 + 8 * q^6 - 4 * q^7 + 6 * q^8 + 10 * q^9	$ 2 q + 2 q^{2} + 2 q^{4} + 8 q^{6} - 4 q^{7} + 6 q^{8} + 10 q^{9} + 16 q^{12} - 8 q^{13} - 4 q^{14} + 6 q^{16} + 8 q^{17} + 10 q^{18} + 8 q^{24} - 4 q^{28} - 4 q^{29} - 6 q^{32} + 16 q^{34} + 10 q^{36} + 4 q^{37} + 16 q^{39} - 12 q^{41} - 16 q^{42} - 12 q^{43} + 8 q^{46} - 6 q^{49} + 16 q^{51} + 8 q^{52} - 12 q^{53} + 16 q^{54} - 12 q^{56} + 12 q^{58} - 8 q^{59} - 4 q^{61} - 20 q^{63} - 14 q^{64} - 8 q^{67} + 24 q^{68} + 16 q^{69} + 30 q^{72} - 8 q^{73} + 20 q^{74} - 16 q^{78} - 8 q^{79} + 2 q^{81} - 12 q^{82} - 12 q^{83} - 32 q^{84} - 12 q^{86} + 32 q^{87} - 4 q^{89} + 16 q^{91} + 16 q^{92} - 8 q^{94} + 8 q^{96} + 4 q^{97} - 6 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 + 8 * q^6 - 4 * q^7 + 6 * q^8 + 10 * q^9 + 16 * q^12 - 8 * q^13 - 4 * q^14 + 6 * q^16 + 8 * q^17 + 10 * q^18 + 8 * q^24 - 4 * q^28 - 4 * q^29 - 6 * q^32 + 16 * q^34 + 10 * q^36 + 4 * q^37 + 16 * q^39 - 12 * q^41 - 16 * q^42 - 12 * q^43 + 8 * q^46 - 6 * q^49 + 16 * q^51 + 8 * q^52 - 12 * q^53 + 16 * q^54 - 12 * q^56 + 12 * q^58 - 8 * q^59 - 4 * q^61 - 20 * q^63 - 14 * q^64 - 8 * q^67 + 24 * q^68 + 16 * q^69 + 30 * q^72 - 8 * q^73 + 20 * q^74 - 16 * q^78 - 8 * q^79 + 2 * q^81 - 12 * q^82 - 12 * q^83 - 32 * q^84 - 12 * q^86 + 32 * q^87 - 4 * q^89 + 16 * q^91 + 16 * q^92 - 8 * q^94 + 8 * q^96 + 4 * q^97 - 6 * q^98

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 $

$2$	2.41421	1.70711	0.853553	−	0.521005i	$-0.174443\pi$
$2$	2.41421	1.70711	0.853553	+	0.521005i	$0.174443\pi$
$3$	2.82843	1.63299	0.816497	−	0.577350i	$-0.195913\pi$
$3$	2.82843	1.63299	0.816497	+	0.577350i	$0.195913\pi$
$4$	3.82843	1.91421
$5$	0	0
$5$	0	0
$6$	6.82843	2.78769
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	4.41421	1.56066
$9$	5.00000	1.66667
$10$	0	0
$11$	0	0
$11$	0	0
$12$	10.8284	3.12590
$13$	−1.17157	−0.324936	−0.162468	−	0.986714i	$-0.551945\pi$
$13$	−1.17157	−0.324936	−0.162468	+	0.986714i	$0.551945\pi$
$14$	−4.82843	−1.29045
$15$	0	0
$16$	3.00000	0.750000
$17$	6.82843	1.65614	0.828068	−	0.560627i	$-0.189440\pi$
$17$	6.82843	1.65614	0.828068	+	0.560627i	$0.189440\pi$
$18$	12.0711	2.84518
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	−5.65685	−1.23443
$22$	0	0
$23$	2.82843	0.589768	0.294884	−	0.955533i	$-0.404719\pi$
$23$	2.82843	0.589768	0.294884	+	0.955533i	$0.404719\pi$
$24$	12.4853	2.54855
$25$	0	0
$26$	−2.82843	−0.554700
$27$	5.65685	1.08866
$28$	−7.65685	−1.44701
$29$	3.65685	0.679061	0.339530	−	0.940595i	$-0.389732\pi$
$29$	3.65685	0.679061	0.339530	+	0.940595i	$0.389732\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	−1.58579	−0.280330
$33$	0	0
$34$	16.4853	2.82720
$35$	0	0
$36$	19.1421	3.19036
$37$	7.65685	1.25878	0.629390	−	0.777090i	$-0.283305\pi$
$37$	7.65685	1.25878	0.629390	+	0.777090i	$0.283305\pi$
$38$	0	0
$39$	−3.31371	−0.530618
$40$	0	0
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	−13.6569	−2.10730
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	0	0
$45$	0	0
$46$	6.82843	1.00680
$47$	−2.82843	−0.412568	−0.206284	−	0.978492i	$-0.566137\pi$
$47$	−2.82843	−0.412568	−0.206284	+	0.978492i	$0.566137\pi$
$48$	8.48528	1.22474
$49$	−3.00000	−0.428571
$50$	0	0
$51$	19.3137	2.70446
$52$	−4.48528	−0.621997
$53$	−11.6569	−1.60119	−0.800596	−	0.599204i	$-0.795484\pi$
$53$	−11.6569	−1.60119	−0.800596	+	0.599204i	$0.795484\pi$
$54$	13.6569	1.85846
$55$	0	0
$56$	−8.82843	−1.17975
$57$	0	0
$58$	8.82843	1.15923
$59$	1.65685	0.215704	0.107852	−	0.994167i	$-0.465603\pi$
$59$	1.65685	0.215704	0.107852	+	0.994167i	$0.465603\pi$
$60$	0	0
$61$	9.31371	1.19250	0.596249	−	0.802799i	$-0.296657\pi$
$61$	9.31371	1.19250	0.596249	+	0.802799i	$0.296657\pi$
$62$	0	0
$63$	−10.0000	−1.25988
$64$	−9.82843	−1.22855
$65$	0	0
$66$	0	0
$67$	−12.4853	−1.52532	−0.762660	−	0.646800i	$-0.776107\pi$
$67$	−12.4853	−1.52532	−0.762660	+	0.646800i	$0.776107\pi$
$68$	26.1421	3.17020
$69$	8.00000	0.963087
$70$	0	0
$71$	11.3137	1.34269	0.671345	−	0.741145i	$-0.265717\pi$
$71$	11.3137	1.34269	0.671345	+	0.741145i	$0.265717\pi$
$72$	22.0711	2.60110
$73$	−1.17157	−0.137122	−0.0685611	−	0.997647i	$-0.521841\pi$
$73$	−1.17157	−0.137122	−0.0685611	+	0.997647i	$0.521841\pi$
$74$	18.4853	2.14887
$75$	0	0
$76$	0	0
$77$	0	0
$78$	−8.00000	−0.905822
$79$	−4.00000	−0.450035	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000	−0.450035	−0.225018	+	0.974355i	$0.572244\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−14.4853	−1.59963
$83$	−6.00000	−0.658586	−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000	−0.658586	−0.329293	+	0.944228i	$0.606810\pi$
$84$	−21.6569	−2.36296
$85$	0	0
$86$	−14.4853	−1.56199
$87$	10.3431	1.10890
$88$	0	0
$89$	−13.3137	−1.41125	−0.705625	−	0.708585i	$-0.749334\pi$
$89$	−13.3137	−1.41125	−0.705625	+	0.708585i	$0.749334\pi$
$90$	0	0
$91$	2.34315	0.245628
$92$	10.8284	1.12894
$93$	0	0
$94$	−6.82843	−0.704298
$95$	0	0
$96$	−4.48528	−0.457777
$97$	−3.65685	−0.371297	−0.185649	−	0.982616i	$-0.559439\pi$
$97$	−3.65685	−0.371297	−0.185649	+	0.982616i	$0.559439\pi$
$98$	−7.24264	−0.731617
$99$	0	0
$100$	0	0
$101$	−9.31371	−0.926749	−0.463374	−	0.886163i	$-0.653361\pi$
$101$	−9.31371	−0.926749	−0.463374	+	0.886163i	$0.653361\pi$
$102$	46.6274	4.61680
$103$	−6.82843	−0.672825	−0.336412	−	0.941715i	$-0.609214\pi$
$103$	−6.82843	−0.672825	−0.336412	+	0.941715i	$0.609214\pi$
$104$	−5.17157	−0.507114
$105$	0	0
$106$	−28.1421	−2.73341
$107$	7.65685	0.740216	0.370108	−	0.928989i	$-0.379321\pi$
$107$	7.65685	0.740216	0.370108	+	0.928989i	$0.379321\pi$
$108$	21.6569	2.08393
$109$	7.65685	0.733394	0.366697	−	0.930341i	$-0.380489\pi$
$109$	7.65685	0.733394	0.366697	+	0.930341i	$0.380489\pi$
$110$	0	0
$111$	21.6569	2.05558
$112$	−6.00000	−0.566947
$113$	−19.6569	−1.84916	−0.924581	−	0.380986i	$-0.875584\pi$
$113$	−19.6569	−1.84916	−0.924581	+	0.380986i	$0.875584\pi$
$114$	0	0
$115$	0	0
$116$	14.0000	1.29987
$117$	−5.85786	−0.541560
$118$	4.00000	0.368230
$119$	−13.6569	−1.25192
$120$	0	0
$121$	0	0
$122$	22.4853	2.03572
$123$	−16.9706	−1.53018
$124$	0	0
$125$	0	0
$126$	−24.1421	−2.15075
$127$	4.34315	0.385392	0.192696	−	0.981259i	$-0.438277\pi$
$127$	4.34315	0.385392	0.192696	+	0.981259i	$0.438277\pi$
$128$	−20.5563	−1.81694
$129$	−16.9706	−1.49417
$130$	0	0
$131$	11.3137	0.988483	0.494242	−	0.869325i	$-0.335446\pi$
$131$	11.3137	0.988483	0.494242	+	0.869325i	$0.335446\pi$
$132$	0	0
$133$	0	0
$134$	−30.1421	−2.60388
$135$	0	0
$136$	30.1421	2.58467
$137$	10.9706	0.937278	0.468639	−	0.883390i	$-0.344744\pi$
$137$	10.9706	0.937278	0.468639	+	0.883390i	$0.344744\pi$
$138$	19.3137	1.64409
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	0	0
$141$	−8.00000	−0.673722
$142$	27.3137	2.29212
$143$	0	0
$144$	15.0000	1.25000
$145$	0	0
$146$	−2.82843	−0.234082
$147$	−8.48528	−0.699854
$148$	29.3137	2.40957
$149$	−0.343146	−0.0281116	−0.0140558	−	0.999901i	$-0.504474\pi$
$149$	−0.343146	−0.0281116	−0.0140558	+	0.999901i	$0.504474\pi$
$150$	0	0
$151$	12.0000	0.976546	0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000	0.976546	0.488273	+	0.872691i	$0.337627\pi$
$152$	0	0
$153$	34.1421	2.76023
$154$	0	0
$155$	0	0
$156$	−12.6863	−1.01572
$157$	14.0000	1.11732	0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000	1.11732	0.558661	+	0.829396i	$0.311315\pi$
$158$	−9.65685	−0.768258
$159$	−32.9706	−2.61474
$160$	0	0
$161$	−5.65685	−0.445823
$162$	2.41421	0.189679
$163$	−16.4853	−1.29123	−0.645613	−	0.763664i	$-0.723398\pi$
$163$	−16.4853	−1.29123	−0.645613	+	0.763664i	$0.723398\pi$
$164$	−22.9706	−1.79370
$165$	0	0
$166$	−14.4853	−1.12428
$167$	−22.9706	−1.77752	−0.888758	−	0.458377i	$-0.848431\pi$
$167$	−22.9706	−1.77752	−0.888758	+	0.458377i	$0.848431\pi$
$168$	−24.9706	−1.92652
$169$	−11.6274	−0.894417
$170$	0	0
$171$	0	0
$172$	−22.9706	−1.75149
$173$	−22.1421	−1.68344	−0.841718	−	0.539918i	$-0.818455\pi$
$173$	−22.1421	−1.68344	−0.841718	+	0.539918i	$0.818455\pi$
$174$	24.9706	1.89301
$175$	0	0
$176$	0	0
$177$	4.68629	0.352243
$178$	−32.1421	−2.40915
$179$	9.65685	0.721787	0.360894	−	0.932607i	$-0.382472\pi$
$179$	9.65685	0.721787	0.360894	+	0.932607i	$0.382472\pi$
$180$	0	0
$181$	21.3137	1.58424	0.792118	−	0.610368i	$-0.208979\pi$
$181$	21.3137	1.58424	0.792118	+	0.610368i	$0.208979\pi$
$182$	5.65685	0.419314
$183$	26.3431	1.94734
$184$	12.4853	0.920427
$185$	0	0
$186$	0	0
$187$	0	0
$188$	−10.8284	−0.789744
$189$	−11.3137	−0.822951
$190$	0	0
$191$	3.31371	0.239772	0.119886	−	0.992788i	$-0.461747\pi$
$191$	3.31371	0.239772	0.119886	+	0.992788i	$0.461747\pi$
$192$	−27.7990	−2.00622
$193$	−1.17157	−0.0843317	−0.0421658	−	0.999111i	$-0.513426\pi$
$193$	−1.17157	−0.0843317	−0.0421658	+	0.999111i	$0.513426\pi$
$194$	−8.82843	−0.633844
$195$	0	0
$196$	−11.4853	−0.820377
$197$	−10.8284	−0.771493	−0.385747	−	0.922605i	$-0.626056\pi$
$197$	−10.8284	−0.771493	−0.385747	+	0.922605i	$0.626056\pi$
$198$	0	0
$199$	10.3431	0.733206	0.366603	−	0.930377i	$-0.380521\pi$
$199$	10.3431	0.733206	0.366603	+	0.930377i	$0.380521\pi$
$200$	0	0
$201$	−35.3137	−2.49084
$202$	−22.4853	−1.58206
$203$	−7.31371	−0.513322
$204$	73.9411	5.17691
$205$	0	0
$206$	−16.4853	−1.14858
$207$	14.1421	0.982946
$208$	−3.51472	−0.243702
$209$	0	0
$210$	0	0
$211$	16.0000	1.10149	0.550743	−	0.834675i	$-0.314345\pi$
$211$	16.0000	1.10149	0.550743	+	0.834675i	$0.314345\pi$
$212$	−44.6274	−3.06502
$213$	32.0000	2.19260
$214$	18.4853	1.26363
$215$	0	0
$216$	24.9706	1.69903
$217$	0	0
$218$	18.4853	1.25198
$219$	−3.31371	−0.223920
$220$	0	0
$221$	−8.00000	−0.538138
$222$	52.2843	3.50909
$223$	10.8284	0.725125	0.362563	−	0.931959i	$-0.381902\pi$
$223$	10.8284	0.725125	0.362563	+	0.931959i	$0.381902\pi$
$224$	3.17157	0.211910
$225$	0	0
$226$	−47.4558	−3.15672
$227$	25.3137	1.68013	0.840065	−	0.542486i	$-0.182517\pi$
$227$	25.3137	1.68013	0.840065	+	0.542486i	$0.182517\pi$
$228$	0	0
$229$	1.31371	0.0868123	0.0434062	−	0.999058i	$-0.486179\pi$
$229$	1.31371	0.0868123	0.0434062	+	0.999058i	$0.486179\pi$
$230$	0	0
$231$	0	0
$232$	16.1421	1.05978
$233$	−6.14214	−0.402385	−0.201192	−	0.979552i	$-0.564482\pi$
$233$	−6.14214	−0.402385	−0.201192	+	0.979552i	$0.564482\pi$
$234$	−14.1421	−0.924500
$235$	0	0
$236$	6.34315	0.412904
$237$	−11.3137	−0.734904
$238$	−32.9706	−2.13716
$239$	23.3137	1.50804	0.754019	−	0.656852i	$-0.228113\pi$
$239$	23.3137	1.50804	0.754019	+	0.656852i	$0.228113\pi$
$240$	0	0
$241$	−6.00000	−0.386494	−0.193247	−	0.981150i	$-0.561902\pi$
$241$	−6.00000	−0.386494	−0.193247	+	0.981150i	$0.561902\pi$
$242$	0	0
$243$	−14.1421	−0.907218
$244$	35.6569	2.28270
$245$	0	0
$246$	−40.9706	−2.61219
$247$	0	0
$248$	0	0
$249$	−16.9706	−1.07547
$250$	0	0
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	−38.2843	−2.41168
$253$	0	0
$254$	10.4853	0.657905
$255$	0	0
$256$	−29.9706	−1.87316
$257$	9.31371	0.580973	0.290487	−	0.956879i	$-0.406183\pi$
$257$	9.31371	0.580973	0.290487	+	0.956879i	$0.406183\pi$
$258$	−40.9706	−2.55072
$259$	−15.3137	−0.951548
$260$	0	0
$261$	18.2843	1.13177
$262$	27.3137	1.68745
$263$	−10.9706	−0.676474	−0.338237	−	0.941061i	$-0.609831\pi$
$263$	−10.9706	−0.676474	−0.338237	+	0.941061i	$0.609831\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−37.6569	−2.30456
$268$	−47.7990	−2.91979
$269$	17.3137	1.05564	0.527818	−	0.849358i	$-0.323010\pi$
$269$	17.3137	1.05564	0.527818	+	0.849358i	$0.323010\pi$
$270$	0	0
$271$	−7.31371	−0.444276	−0.222138	−	0.975015i	$-0.571304\pi$
$271$	−7.31371	−0.444276	−0.222138	+	0.975015i	$0.571304\pi$
$272$	20.4853	1.24210
$273$	6.62742	0.401110
$274$	26.4853	1.60003
$275$	0	0
$276$	30.6274	1.84355
$277$	6.82843	0.410280	0.205140	−	0.978733i	$-0.434235\pi$
$277$	6.82843	0.410280	0.205140	+	0.978733i	$0.434235\pi$
$278$	9.65685	0.579180
$279$	0	0
$280$	0	0
$281$	−17.3137	−1.03285	−0.516425	−	0.856333i	$-0.672737\pi$
$281$	−17.3137	−1.03285	−0.516425	+	0.856333i	$0.672737\pi$
$282$	−19.3137	−1.15011
$283$	32.6274	1.93950	0.969749	−	0.244103i	$-0.0784935\pi$
$283$	32.6274	1.93950	0.969749	+	0.244103i	$0.0784935\pi$
$284$	43.3137	2.57020
$285$	0	0
$286$	0	0
$287$	12.0000	0.708338
$288$	−7.92893	−0.467217
$289$	29.6274	1.74279
$290$	0	0
$291$	−10.3431	−0.606326
$292$	−4.48528	−0.262481
$293$	−9.17157	−0.535809	−0.267905	−	0.963445i	$-0.586331\pi$
$293$	−9.17157	−0.535809	−0.267905	+	0.963445i	$0.586331\pi$
$294$	−20.4853	−1.19473
$295$	0	0
$296$	33.7990	1.96453
$297$	0	0
$298$	−0.828427	−0.0479895
$299$	−3.31371	−0.191637
$300$	0	0
$301$	12.0000	0.691669
$302$	28.9706	1.66707
$303$	−26.3431	−1.51337
$304$	0	0
$305$	0	0
$306$	82.4264	4.71200
$307$	−16.3431	−0.932753	−0.466376	−	0.884586i	$-0.654441\pi$
$307$	−16.3431	−0.932753	−0.466376	+	0.884586i	$0.654441\pi$
$308$	0	0
$309$	−19.3137	−1.09872
$310$	0	0
$311$	4.68629	0.265735	0.132868	−	0.991134i	$-0.457581\pi$
$311$	4.68629	0.265735	0.132868	+	0.991134i	$0.457581\pi$
$312$	−14.6274	−0.828114
$313$	1.31371	0.0742552	0.0371276	−	0.999311i	$-0.488179\pi$
$313$	1.31371	0.0742552	0.0371276	+	0.999311i	$0.488179\pi$
$314$	33.7990	1.90739
$315$	0	0
$316$	−15.3137	−0.861463
$317$	1.31371	0.0737852	0.0368926	−	0.999319i	$-0.488254\pi$
$317$	1.31371	0.0737852	0.0368926	+	0.999319i	$0.488254\pi$
$318$	−79.5980	−4.46363
$319$	0	0
$320$	0	0
$321$	21.6569	1.20877
$322$	−13.6569	−0.761067
$323$	0	0
$324$	3.82843	0.212690
$325$	0	0
$326$	−39.7990	−2.20426
$327$	21.6569	1.19763
$328$	−26.4853	−1.46241
$329$	5.65685	0.311872
$330$	0	0
$331$	−7.31371	−0.401998	−0.200999	−	0.979591i	$-0.564419\pi$
$331$	−7.31371	−0.401998	−0.200999	+	0.979591i	$0.564419\pi$
$332$	−22.9706	−1.26067
$333$	38.2843	2.09797
$334$	−55.4558	−3.03441
$335$	0	0
$336$	−16.9706	−0.925820
$337$	−20.4853	−1.11590	−0.557952	−	0.829873i	$-0.688413\pi$
$337$	−20.4853	−1.11590	−0.557952	+	0.829873i	$0.688413\pi$
$338$	−28.0711	−1.52686
$339$	−55.5980	−3.01967
$340$	0	0
$341$	0	0
$342$	0	0
$343$	20.0000	1.07990
$344$	−26.4853	−1.42799
$345$	0	0
$346$	−53.4558	−2.87380
$347$	10.9706	0.588931	0.294465	−	0.955662i	$-0.404858\pi$
$347$	10.9706	0.588931	0.294465	+	0.955662i	$0.404858\pi$
$348$	39.5980	2.12267
$349$	−26.9706	−1.44370	−0.721851	−	0.692049i	$-0.756708\pi$
$349$	−26.9706	−1.44370	−0.721851	+	0.692049i	$0.756708\pi$
$350$	0	0
$351$	−6.62742	−0.353745
$352$	0	0
$353$	−21.3137	−1.13441	−0.567207	−	0.823575i	$-0.691976\pi$
$353$	−21.3137	−1.13441	−0.567207	+	0.823575i	$0.691976\pi$
$354$	11.3137	0.601317
$355$	0	0
$356$	−50.9706	−2.70143
$357$	−38.6274	−2.04438
$358$	23.3137	1.23217
$359$	−0.686292	−0.0362211	−0.0181105	−	0.999836i	$-0.505765\pi$
$359$	−0.686292	−0.0362211	−0.0181105	+	0.999836i	$0.505765\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	51.4558	2.70446
$363$	0	0
$364$	8.97056	0.470185
$365$	0	0
$366$	63.5980	3.32432
$367$	8.48528	0.442928	0.221464	−	0.975169i	$-0.428916\pi$
$367$	8.48528	0.442928	0.221464	+	0.975169i	$0.428916\pi$
$368$	8.48528	0.442326
$369$	−30.0000	−1.56174
$370$	0	0
$371$	23.3137	1.21039
$372$	0	0
$373$	35.7990	1.85360	0.926801	−	0.375554i	$-0.122547\pi$
$373$	35.7990	1.85360	0.926801	+	0.375554i	$0.122547\pi$
$374$	0	0
$375$	0	0
$376$	−12.4853	−0.643879
$377$	−4.28427	−0.220651
$378$	−27.3137	−1.40487
$379$	33.6569	1.72884	0.864418	−	0.502773i	$-0.167687\pi$
$379$	33.6569	1.72884	0.864418	+	0.502773i	$0.167687\pi$
$380$	0	0
$381$	12.2843	0.629342
$382$	8.00000	0.409316
$383$	5.85786	0.299323	0.149661	−	0.988737i	$-0.452182\pi$
$383$	5.85786	0.299323	0.149661	+	0.988737i	$0.452182\pi$
$384$	−58.1421	−2.96705
$385$	0	0
$386$	−2.82843	−0.143963
$387$	−30.0000	−1.52499
$388$	−14.0000	−0.710742
$389$	20.6274	1.04585	0.522926	−	0.852378i	$-0.324840\pi$
$389$	20.6274	1.04585	0.522926	+	0.852378i	$0.324840\pi$
$390$	0	0
$391$	19.3137	0.976736
$392$	−13.2426	−0.668854
$393$	32.0000	1.61419
$394$	−26.1421	−1.31702
$395$	0	0
$396$	0	0
$397$	9.31371	0.467442	0.233721	−	0.972304i	$-0.424910\pi$
$397$	9.31371	0.467442	0.233721	+	0.972304i	$0.424910\pi$
$398$	24.9706	1.25166
$399$	0	0
$400$	0	0
$401$	−5.31371	−0.265354	−0.132677	−	0.991159i	$-0.542357\pi$
$401$	−5.31371	−0.265354	−0.132677	+	0.991159i	$0.542357\pi$
$402$	−85.2548	−4.25212
$403$	0	0
$404$	−35.6569	−1.77399
$405$	0	0
$406$	−17.6569	−0.876295
$407$	0	0
$408$	85.2548	4.22074
$409$	−1.02944	−0.0509024	−0.0254512	−	0.999676i	$-0.508102\pi$
$409$	−1.02944	−0.0509024	−0.0254512	+	0.999676i	$0.508102\pi$
$410$	0	0
$411$	31.0294	1.53057
$412$	−26.1421	−1.28793
$413$	−3.31371	−0.163057
$414$	34.1421	1.67799
$415$	0	0
$416$	1.85786	0.0910893
$417$	11.3137	0.554035
$418$	0	0
$419$	−25.6569	−1.25342	−0.626710	−	0.779253i	$-0.715599\pi$
$419$	−25.6569	−1.25342	−0.626710	+	0.779253i	$0.715599\pi$
$420$	0	0
$421$	−6.00000	−0.292422	−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000	−0.292422	−0.146211	+	0.989253i	$0.546708\pi$
$422$	38.6274	1.88035
$423$	−14.1421	−0.687614
$424$	−51.4558	−2.49892
$425$	0	0
$426$	77.2548	3.74301
$427$	−18.6274	−0.901444
$428$	29.3137	1.41693
$429$	0	0
$430$	0	0
$431$	11.3137	0.544962	0.272481	−	0.962161i	$-0.412156\pi$
$431$	11.3137	0.544962	0.272481	+	0.962161i	$0.412156\pi$
$432$	16.9706	0.816497
$433$	7.65685	0.367965	0.183982	−	0.982930i	$-0.441101\pi$
$433$	7.65685	0.367965	0.183982	+	0.982930i	$0.441101\pi$
$434$	0	0
$435$	0	0
$436$	29.3137	1.40387
$437$	0	0
$438$	−8.00000	−0.382255
$439$	16.0000	0.763638	0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000	0.763638	0.381819	+	0.924237i	$0.375298\pi$
$440$	0	0
$441$	−15.0000	−0.714286
$442$	−19.3137	−0.918659
$443$	26.8284	1.27466	0.637329	−	0.770592i	$-0.280039\pi$
$443$	26.8284	1.27466	0.637329	+	0.770592i	$0.280039\pi$
$444$	82.9117	3.93481
$445$	0	0
$446$	26.1421	1.23787
$447$	−0.970563	−0.0459060
$448$	19.6569	0.928699
$449$	28.6274	1.35101	0.675506	−	0.737355i	$-0.263925\pi$
$449$	28.6274	1.35101	0.675506	+	0.737355i	$0.263925\pi$
$450$	0	0
$451$	0	0
$452$	−75.2548	−3.53969
$453$	33.9411	1.59469
$454$	61.1127	2.86816
$455$	0	0
$456$	0	0
$457$	0.485281	0.0227005	0.0113503	−	0.999936i	$-0.496387\pi$
$457$	0.485281	0.0227005	0.0113503	+	0.999936i	$0.496387\pi$
$458$	3.17157	0.148198
$459$	38.6274	1.80297
$460$	0	0
$461$	−12.6274	−0.588117	−0.294059	−	0.955787i	$-0.595006\pi$
$461$	−12.6274	−0.588117	−0.294059	+	0.955787i	$0.595006\pi$
$462$	0	0
$463$	6.14214	0.285449	0.142725	−	0.989762i	$-0.454414\pi$
$463$	6.14214	0.285449	0.142725	+	0.989762i	$0.454414\pi$
$464$	10.9706	0.509296
$465$	0	0
$466$	−14.8284	−0.686914
$467$	14.8284	0.686178	0.343089	−	0.939303i	$-0.388527\pi$
$467$	14.8284	0.686178	0.343089	+	0.939303i	$0.388527\pi$
$468$	−22.4264	−1.03666
$469$	24.9706	1.15303
$470$	0	0
$471$	39.5980	1.82458
$472$	7.31371	0.336641
$473$	0	0
$474$	−27.3137	−1.25456
$475$	0	0
$476$	−52.2843	−2.39645
$477$	−58.2843	−2.66865
$478$	56.2843	2.57438
$479$	36.0000	1.64488	0.822441	−	0.568850i	$-0.192612\pi$
$479$	36.0000	1.64488	0.822441	+	0.568850i	$0.192612\pi$
$480$	0	0
$481$	−8.97056	−0.409022
$482$	−14.4853	−0.659786
$483$	−16.0000	−0.728025
$484$	0	0
$485$	0	0
$486$	−34.1421	−1.54872
$487$	24.4853	1.10953	0.554767	−	0.832006i	$-0.312807\pi$
$487$	24.4853	1.10953	0.554767	+	0.832006i	$0.312807\pi$
$488$	41.1127	1.86108
$489$	−46.6274	−2.10856
$490$	0	0
$491$	0.686292	0.0309719	0.0154860	−	0.999880i	$-0.495070\pi$
$491$	0.686292	0.0309719	0.0154860	+	0.999880i	$0.495070\pi$
$492$	−64.9706	−2.92910
$493$	24.9706	1.12462
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−22.6274	−1.01498
$498$	−40.9706	−1.83593
$499$	9.65685	0.432300	0.216150	−	0.976360i	$-0.430650\pi$
$499$	9.65685	0.432300	0.216150	+	0.976360i	$0.430650\pi$
$500$	0	0
$501$	−64.9706	−2.90267
$502$	28.9706	1.29302
$503$	16.6274	0.741380	0.370690	−	0.928757i	$-0.379121\pi$
$503$	16.6274	0.741380	0.370690	+	0.928757i	$0.379121\pi$
$504$	−44.1421	−1.96625
$505$	0	0
$506$	0	0
$507$	−32.8873	−1.46058
$508$	16.6274	0.737722
$509$	−13.3137	−0.590120	−0.295060	−	0.955479i	$-0.595340\pi$
$509$	−13.3137	−0.590120	−0.295060	+	0.955479i	$0.595340\pi$
$510$	0	0
$511$	2.34315	0.103655
$512$	−31.2426	−1.38074
$513$	0	0
$514$	22.4853	0.991783
$515$	0	0
$516$	−64.9706	−2.86017
$517$	0	0
$518$	−36.9706	−1.62439
$519$	−62.6274	−2.74904
$520$	0	0
$521$	25.3137	1.10901	0.554507	−	0.832179i	$-0.312907\pi$
$521$	25.3137	1.10901	0.554507	+	0.832179i	$0.312907\pi$
$522$	44.1421	1.93205
$523$	−41.5980	−1.81895	−0.909476	−	0.415756i	$-0.863517\pi$
$523$	−41.5980	−1.81895	−0.909476	+	0.415756i	$0.863517\pi$
$524$	43.3137	1.89217
$525$	0	0
$526$	−26.4853	−1.15481
$527$	0	0
$528$	0	0
$529$	−15.0000	−0.652174
$530$	0	0
$531$	8.28427	0.359507
$532$	0	0
$533$	7.02944	0.304479
$534$	−90.9117	−3.93413
$535$	0	0
$536$	−55.1127	−2.38051
$537$	27.3137	1.17867
$538$	41.7990	1.80208
$539$	0	0
$540$	0	0
$541$	−6.00000	−0.257960	−0.128980	−	0.991647i	$-0.541170\pi$
$541$	−6.00000	−0.257960	−0.128980	+	0.991647i	$0.541170\pi$
$542$	−17.6569	−0.758427
$543$	60.2843	2.58705
$544$	−10.8284	−0.464265
$545$	0	0
$546$	16.0000	0.684737
$547$	−34.0000	−1.45374	−0.726868	−	0.686778i	$-0.759025\pi$
$547$	−34.0000	−1.45374	−0.726868	+	0.686778i	$0.759025\pi$
$548$	42.0000	1.79415
$549$	46.5685	1.98750
$550$	0	0
$551$	0	0
$552$	35.3137	1.50305
$553$	8.00000	0.340195
$554$	16.4853	0.700392
$555$	0	0
$556$	15.3137	0.649446
$557$	9.85786	0.417691	0.208846	−	0.977949i	$-0.433029\pi$
$557$	9.85786	0.417691	0.208846	+	0.977949i	$0.433029\pi$
$558$	0	0
$559$	7.02944	0.297314
$560$	0	0
$561$	0	0
$562$	−41.7990	−1.76318
$563$	0.343146	0.0144619	0.00723093	−	0.999974i	$-0.497698\pi$
$563$	0.343146	0.0144619	0.00723093	+	0.999974i	$0.497698\pi$
$564$	−30.6274	−1.28965
$565$	0	0
$566$	78.7696	3.31093
$567$	−2.00000	−0.0839921
$568$	49.9411	2.09548
$569$	−31.6569	−1.32712	−0.663562	−	0.748121i	$-0.730956\pi$
$569$	−31.6569	−1.32712	−0.663562	+	0.748121i	$0.730956\pi$
$570$	0	0
$571$	21.9411	0.918208	0.459104	−	0.888383i	$-0.348171\pi$
$571$	21.9411	0.918208	0.459104	+	0.888383i	$0.348171\pi$
$572$	0	0
$573$	9.37258	0.391545
$574$	28.9706	1.20921
$575$	0	0
$576$	−49.1421	−2.04759
$577$	26.9706	1.12280	0.561400	−	0.827545i	$-0.310263\pi$
$577$	26.9706	1.12280	0.561400	+	0.827545i	$0.310263\pi$
$578$	71.5269	2.97513
$579$	−3.31371	−0.137713
$580$	0	0
$581$	12.0000	0.497844
$582$	−24.9706	−1.03506
$583$	0	0
$584$	−5.17157	−0.214001
$585$	0	0
$586$	−22.1421	−0.914683
$587$	2.14214	0.0884154	0.0442077	−	0.999022i	$-0.485924\pi$
$587$	2.14214	0.0884154	0.0442077	+	0.999022i	$0.485924\pi$
$588$	−32.4853	−1.33967
$589$	0	0
$590$	0	0
$591$	−30.6274	−1.25984
$592$	22.9706	0.944084
$593$	3.51472	0.144332	0.0721661	−	0.997393i	$-0.477009\pi$
$593$	3.51472	0.144332	0.0721661	+	0.997393i	$0.477009\pi$
$594$	0	0
$595$	0	0
$596$	−1.31371	−0.0538116
$597$	29.2548	1.19732
$598$	−8.00000	−0.327144
$599$	−5.65685	−0.231133	−0.115566	−	0.993300i	$-0.536868\pi$
$599$	−5.65685	−0.231133	−0.115566	+	0.993300i	$0.536868\pi$
$600$	0	0
$601$	−23.9411	−0.976579	−0.488289	−	0.872682i	$-0.662379\pi$
$601$	−23.9411	−0.976579	−0.488289	+	0.872682i	$0.662379\pi$
$602$	28.9706	1.18075
$603$	−62.4264	−2.54220
$604$	45.9411	1.86932
$605$	0	0
$606$	−63.5980	−2.58349
$607$	38.2843	1.55391	0.776955	−	0.629556i	$-0.216763\pi$
$607$	38.2843	1.55391	0.776955	+	0.629556i	$0.216763\pi$
$608$	0	0
$609$	−20.6863	−0.838251
$610$	0	0
$611$	3.31371	0.134058
$612$	130.711	5.28367
$613$	−25.4558	−1.02815	−0.514076	−	0.857745i	$-0.671865\pi$
$613$	−25.4558	−1.02815	−0.514076	+	0.857745i	$0.671865\pi$
$614$	−39.4558	−1.59231
$615$	0	0
$616$	0	0
$617$	−0.343146	−0.0138145	−0.00690726	−	0.999976i	$-0.502199\pi$
$617$	−0.343146	−0.0138145	−0.00690726	+	0.999976i	$0.502199\pi$
$618$	−46.6274	−1.87563
$619$	−14.3431	−0.576500	−0.288250	−	0.957555i	$-0.593073\pi$
$619$	−14.3431	−0.576500	−0.288250	+	0.957555i	$0.593073\pi$
$620$	0	0
$621$	16.0000	0.642058
$622$	11.3137	0.453638
$623$	26.6274	1.06680
$624$	−9.94113	−0.397964
$625$	0	0
$626$	3.17157	0.126762
$627$	0	0
$628$	53.5980	2.13879
$629$	52.2843	2.08471
$630$	0	0
$631$	0	0		−	1.00000i	$-0.5\pi$
$631$	0	0			1.00000i	$0.5\pi$
$632$	−17.6569	−0.702352
$633$	45.2548	1.79872
$634$	3.17157	0.125959
$635$	0	0
$636$	−126.225	−5.00516
$637$	3.51472	0.139258
$638$	0	0
$639$	56.5685	2.23782
$640$	0	0
$641$	30.0000	1.18493	0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000	1.18493	0.592464	+	0.805597i	$0.298155\pi$
$642$	52.2843	2.06350
$643$	1.45584	0.0574129	0.0287064	−	0.999588i	$-0.490861\pi$
$643$	1.45584	0.0574129	0.0287064	+	0.999588i	$0.490861\pi$
$644$	−21.6569	−0.853400
$645$	0	0
$646$	0	0
$647$	−27.1127	−1.06591	−0.532955	−	0.846144i	$-0.678919\pi$
$647$	−27.1127	−1.06591	−0.532955	+	0.846144i	$0.678919\pi$
$648$	4.41421	0.173407
$649$	0	0
$650$	0	0
$651$	0	0
$652$	−63.1127	−2.47168
$653$	−11.6569	−0.456168	−0.228084	−	0.973641i	$-0.573246\pi$
$653$	−11.6569	−0.456168	−0.228084	+	0.973641i	$0.573246\pi$
$654$	52.2843	2.04448
$655$	0	0
$656$	−18.0000	−0.702782
$657$	−5.85786	−0.228537
$658$	13.6569	0.532400
$659$	−45.9411	−1.78961	−0.894806	−	0.446455i	$-0.852686\pi$
$659$	−45.9411	−1.78961	−0.894806	+	0.446455i	$0.852686\pi$
$660$	0	0
$661$	44.6274	1.73581	0.867903	−	0.496734i	$-0.165468\pi$
$661$	44.6274	1.73581	0.867903	+	0.496734i	$0.165468\pi$
$662$	−17.6569	−0.686253
$663$	−22.6274	−0.878776
$664$	−26.4853	−1.02783
$665$	0	0
$666$	92.4264	3.58145
$667$	10.3431	0.400488
$668$	−87.9411	−3.40254
$669$	30.6274	1.18412
$670$	0	0
$671$	0	0
$672$	8.97056	0.346047
$673$	−12.4853	−0.481272	−0.240636	−	0.970615i	$-0.577356\pi$
$673$	−12.4853	−0.481272	−0.240636	+	0.970615i	$0.577356\pi$
$674$	−49.4558	−1.90497
$675$	0	0
$676$	−44.5147	−1.71210
$677$	22.8284	0.877368	0.438684	−	0.898641i	$-0.355445\pi$
$677$	22.8284	0.877368	0.438684	+	0.898641i	$0.355445\pi$
$678$	−134.225	−5.15490
$679$	7.31371	0.280674
$680$	0	0
$681$	71.5980	2.74364
$682$	0	0
$683$	7.79899	0.298420	0.149210	−	0.988806i	$-0.452327\pi$
$683$	7.79899	0.298420	0.149210	+	0.988806i	$0.452327\pi$
$684$	0	0
$685$	0	0
$686$	48.2843	1.84350
$687$	3.71573	0.141764
$688$	−18.0000	−0.686244
$689$	13.6569	0.520285
$690$	0	0
$691$	−39.3137	−1.49556	−0.747782	−	0.663944i	$-0.768881\pi$
$691$	−39.3137	−1.49556	−0.747782	+	0.663944i	$0.768881\pi$
$692$	−84.7696	−3.22245
$693$	0	0
$694$	26.4853	1.00537
$695$	0	0
$696$	45.6569	1.73062
$697$	−40.9706	−1.55187
$698$	−65.1127	−2.46455
$699$	−17.3726	−0.657091
$700$	0	0
$701$	12.6274	0.476931	0.238465	−	0.971151i	$-0.423356\pi$
$701$	12.6274	0.476931	0.238465	+	0.971151i	$0.423356\pi$
$702$	−16.0000	−0.603881
$703$	0	0
$704$	0	0
$705$	0	0
$706$	−51.4558	−1.93657
$707$	18.6274	0.700556
$708$	17.9411	0.674269
$709$	24.6274	0.924902	0.462451	−	0.886645i	$-0.346970\pi$
$709$	24.6274	0.924902	0.462451	+	0.886645i	$0.346970\pi$
$710$	0	0
$711$	−20.0000	−0.750059
$712$	−58.7696	−2.20248
$713$	0	0
$714$	−93.2548	−3.48997
$715$	0	0
$716$	36.9706	1.38165
$717$	65.9411	2.46262
$718$	−1.65685	−0.0618333
$719$	18.3431	0.684084	0.342042	−	0.939685i	$-0.388882\pi$
$719$	18.3431	0.684084	0.342042	+	0.939685i	$0.388882\pi$
$720$	0	0
$721$	13.6569	0.508608
$722$	−45.8701	−1.70711
$723$	−16.9706	−0.631142
$724$	81.5980	3.03257
$725$	0	0
$726$	0	0
$727$	19.5147	0.723761	0.361880	−	0.932225i	$-0.382135\pi$
$727$	19.5147	0.723761	0.361880	+	0.932225i	$0.382135\pi$
$728$	10.3431	0.383342
$729$	−43.0000	−1.59259
$730$	0	0
$731$	−40.9706	−1.51535
$732$	100.853	3.72763
$733$	−17.4558	−0.644746	−0.322373	−	0.946613i	$-0.604481\pi$
$733$	−17.4558	−0.644746	−0.322373	+	0.946613i	$0.604481\pi$
$734$	20.4853	0.756126
$735$	0	0
$736$	−4.48528	−0.165330
$737$	0	0
$738$	−72.4264	−2.66605
$739$	−29.9411	−1.10140	−0.550701	−	0.834703i	$-0.685640\pi$
$739$	−29.9411	−1.10140	−0.550701	+	0.834703i	$0.685640\pi$
$740$	0	0
$741$	0	0
$742$	56.2843	2.06626
$743$	−49.5980	−1.81957	−0.909787	−	0.415076i	$-0.863755\pi$
$743$	−49.5980	−1.81957	−0.909787	+	0.415076i	$0.863755\pi$
$744$	0	0
$745$	0	0
$746$	86.4264	3.16430
$747$	−30.0000	−1.09764
$748$	0	0
$749$	−15.3137	−0.559551
$750$	0	0
$751$	−16.0000	−0.583848	−0.291924	−	0.956441i	$-0.594295\pi$
$751$	−16.0000	−0.583848	−0.291924	+	0.956441i	$0.594295\pi$
$752$	−8.48528	−0.309426
$753$	33.9411	1.23688
$754$	−10.3431	−0.376675
$755$	0	0
$756$	−43.3137	−1.57530
$757$	−13.3137	−0.483895	−0.241947	−	0.970289i	$-0.577786\pi$
$757$	−13.3137	−0.483895	−0.241947	+	0.970289i	$0.577786\pi$
$758$	81.2548	2.95131
$759$	0	0
$760$	0	0
$761$	30.0000	1.08750	0.543750	−	0.839248i	$-0.317004\pi$
$761$	30.0000	1.08750	0.543750	+	0.839248i	$0.317004\pi$
$762$	29.6569	1.07435
$763$	−15.3137	−0.554393
$764$	12.6863	0.458974
$765$	0	0
$766$	14.1421	0.510976
$767$	−1.94113	−0.0700900
$768$	−84.7696	−3.05886
$769$	18.9706	0.684096	0.342048	−	0.939682i	$-0.388879\pi$
$769$	18.9706	0.684096	0.342048	+	0.939682i	$0.388879\pi$
$770$	0	0
$771$	26.3431	0.948725
$772$	−4.48528	−0.161429
$773$	−26.2843	−0.945380	−0.472690	−	0.881229i	$-0.656717\pi$
$773$	−26.2843	−0.945380	−0.472690	+	0.881229i	$0.656717\pi$
$774$	−72.4264	−2.60331
$775$	0	0
$776$	−16.1421	−0.579469
$777$	−43.3137	−1.55387
$778$	49.7990	1.78538
$779$	0	0
$780$	0	0
$781$	0	0
$782$	46.6274	1.66739
$783$	20.6863	0.739268
$784$	−9.00000	−0.321429
$785$	0	0
$786$	77.2548	2.75559
$787$	−14.9706	−0.533643	−0.266821	−	0.963746i	$-0.585973\pi$
$787$	−14.9706	−0.533643	−0.266821	+	0.963746i	$0.585973\pi$
$788$	−41.4558	−1.47680
$789$	−31.0294	−1.10468
$790$	0	0
$791$	39.3137	1.39783
$792$	0	0
$793$	−10.9117	−0.387485
$794$	22.4853	0.797973
$795$	0	0
$796$	39.5980	1.40351
$797$	−32.6274	−1.15572	−0.577861	−	0.816135i	$-0.696113\pi$
$797$	−32.6274	−1.15572	−0.577861	+	0.816135i	$0.696113\pi$
$798$	0	0
$799$	−19.3137	−0.683270
$800$	0	0
$801$	−66.5685	−2.35208
$802$	−12.8284	−0.452988
$803$	0	0
$804$	−135.196	−4.76799
$805$	0	0
$806$	0	0
$807$	48.9706	1.72385
$808$	−41.1127	−1.44634
$809$	10.9706	0.385704	0.192852	−	0.981228i	$-0.438226\pi$
$809$	10.9706	0.385704	0.192852	+	0.981228i	$0.438226\pi$
$810$	0	0
$811$	−53.9411	−1.89413	−0.947065	−	0.321043i	$-0.895967\pi$
$811$	−53.9411	−1.89413	−0.947065	+	0.321043i	$0.895967\pi$
$812$	−28.0000	−0.982607
$813$	−20.6863	−0.725500
$814$	0	0
$815$	0	0
$816$	57.9411	2.02835
$817$	0	0
$818$	−2.48528	−0.0868958
$819$	11.7157	0.409381
$820$	0	0
$821$	41.3137	1.44186	0.720929	−	0.693009i	$-0.243715\pi$
$821$	41.3137	1.44186	0.720929	+	0.693009i	$0.243715\pi$
$822$	74.9117	2.61285
$823$	−19.5147	−0.680240	−0.340120	−	0.940382i	$-0.610468\pi$
$823$	−19.5147	−0.680240	−0.340120	+	0.940382i	$0.610468\pi$
$824$	−30.1421	−1.05005
$825$	0	0
$826$	−8.00000	−0.278356
$827$	22.2843	0.774900	0.387450	−	0.921891i	$-0.373356\pi$
$827$	22.2843	0.774900	0.387450	+	0.921891i	$0.373356\pi$
$828$	54.1421	1.88157
$829$	18.0000	0.625166	0.312583	−	0.949890i	$-0.398806\pi$
$829$	18.0000	0.625166	0.312583	+	0.949890i	$0.398806\pi$
$830$	0	0
$831$	19.3137	0.669985
$832$	11.5147	0.399201
$833$	−20.4853	−0.709773
$834$	27.3137	0.945796
$835$	0	0
$836$	0	0
$837$	0	0
$838$	−61.9411	−2.13972
$839$	26.3431	0.909466	0.454733	−	0.890628i	$-0.349735\pi$
$839$	26.3431	0.909466	0.454733	+	0.890628i	$0.349735\pi$
$840$	0	0
$841$	−15.6274	−0.538876
$842$	−14.4853	−0.499196
$843$	−48.9706	−1.68664
$844$	61.2548	2.10848
$845$	0	0
$846$	−34.1421	−1.17383
$847$	0	0
$848$	−34.9706	−1.20089
$849$	92.2843	3.16719
$850$	0	0
$851$	21.6569	0.742387
$852$	122.510	4.19711
$853$	−15.5147	−0.531214	−0.265607	−	0.964081i	$-0.585572\pi$
$853$	−15.5147	−0.531214	−0.265607	+	0.964081i	$0.585572\pi$
$854$	−44.9706	−1.53886
$855$	0	0
$856$	33.7990	1.15523
$857$	24.7696	0.846112	0.423056	−	0.906104i	$-0.360957\pi$
$857$	24.7696	0.846112	0.423056	+	0.906104i	$0.360957\pi$
$858$	0	0
$859$	24.2843	0.828569	0.414284	−	0.910148i	$-0.364032\pi$
$859$	24.2843	0.828569	0.414284	+	0.910148i	$0.364032\pi$
$860$	0	0
$861$	33.9411	1.15671
$862$	27.3137	0.930309
$863$	9.17157	0.312204	0.156102	−	0.987741i	$-0.450107\pi$
$863$	9.17157	0.312204	0.156102	+	0.987741i	$0.450107\pi$
$864$	−8.97056	−0.305185
$865$	0	0
$866$	18.4853	0.628155
$867$	83.7990	2.84596
$868$	0	0
$869$	0	0
$870$	0	0
$871$	14.6274	0.495631
$872$	33.7990	1.14458
$873$	−18.2843	−0.618829
$874$	0	0
$875$	0	0
$876$	−12.6863	−0.428630
$877$	−49.4558	−1.67001	−0.835003	−	0.550246i	$-0.814534\pi$
$877$	−49.4558	−1.67001	−0.835003	+	0.550246i	$0.814534\pi$
$878$	38.6274	1.30361
$879$	−25.9411	−0.874972
$880$	0	0
$881$	−7.37258	−0.248389	−0.124194	−	0.992258i	$-0.539635\pi$
$881$	−7.37258	−0.248389	−0.124194	+	0.992258i	$0.539635\pi$
$882$	−36.2132	−1.21936
$883$	−37.1716	−1.25092	−0.625462	−	0.780255i	$-0.715089\pi$
$883$	−37.1716	−1.25092	−0.625462	+	0.780255i	$0.715089\pi$
$884$	−30.6274	−1.03011
$885$	0	0
$886$	64.7696	2.17598
$887$	38.2843	1.28546	0.642730	−	0.766093i	$-0.277802\pi$
$887$	38.2843	1.28546	0.642730	+	0.766093i	$0.277802\pi$
$888$	95.5980	3.20806
$889$	−8.68629	−0.291329
$890$	0	0
$891$	0	0
$892$	41.4558	1.38804
$893$	0	0
$894$	−2.34315	−0.0783665
$895$	0	0
$896$	41.1127	1.37348
$897$	−9.37258	−0.312941
$898$	69.1127	2.30632
$899$	0	0
$900$	0	0
$901$	−79.5980	−2.65179
$902$	0	0
$903$	33.9411	1.12949
$904$	−86.7696	−2.88591
$905$	0	0
$906$	81.9411	2.72231
$907$	27.5147	0.913611	0.456806	−	0.889567i	$-0.348993\pi$
$907$	27.5147	0.913611	0.456806	+	0.889567i	$0.348993\pi$
$908$	96.9117	3.21613
$909$	−46.5685	−1.54458
$910$	0	0
$911$	−9.94113	−0.329364	−0.164682	−	0.986347i	$-0.552660\pi$
$911$	−9.94113	−0.329364	−0.164682	+	0.986347i	$0.552660\pi$
$912$	0	0
$913$	0	0
$914$	1.17157	0.0387522
$915$	0	0
$916$	5.02944	0.166177
$917$	−22.6274	−0.747223
$918$	93.2548	3.07787
$919$	32.0000	1.05558	0.527791	−	0.849374i	$-0.323020\pi$
$919$	32.0000	1.05558	0.527791	+	0.849374i	$0.323020\pi$
$920$	0	0
$921$	−46.2254	−1.52318
$922$	−30.4853	−1.00398
$923$	−13.2548	−0.436288
$924$	0	0
$925$	0	0
$926$	14.8284	0.487292
$927$	−34.1421	−1.12137
$928$	−5.79899	−0.190361
$929$	5.31371	0.174337	0.0871686	−	0.996194i	$-0.472218\pi$
$929$	5.31371	0.174337	0.0871686	+	0.996194i	$0.472218\pi$
$930$	0	0
$931$	0	0
$932$	−23.5147	−0.770250
$933$	13.2548	0.433944
$934$	35.7990	1.17138
$935$	0	0
$936$	−25.8579	−0.845191
$937$	−1.45584	−0.0475604	−0.0237802	−	0.999717i	$-0.507570\pi$
$937$	−1.45584	−0.0475604	−0.0237802	+	0.999717i	$0.507570\pi$
$938$	60.2843	1.96835
$939$	3.71573	0.121258
$940$	0	0
$941$	6.68629	0.217967	0.108983	−	0.994044i	$-0.465240\pi$
$941$	6.68629	0.217967	0.108983	+	0.994044i	$0.465240\pi$
$942$	95.5980	3.11475
$943$	−16.9706	−0.552638
$944$	4.97056	0.161778
$945$	0	0
$946$	0	0
$947$	−41.1716	−1.33790	−0.668948	−	0.743309i	$-0.733255\pi$
$947$	−41.1716	−1.33790	−0.668948	+	0.743309i	$0.733255\pi$
$948$	−43.3137	−1.40676
$949$	1.37258	0.0445559
$950$	0	0
$951$	3.71573	0.120491
$952$	−60.2843	−1.95382
$953$	53.1716	1.72240	0.861198	−	0.508269i	$-0.169715\pi$
$953$	53.1716	1.72240	0.861198	+	0.508269i	$0.169715\pi$
$954$	−140.711	−4.55568
$955$	0	0
$956$	89.2548	2.88671
$957$	0	0
$958$	86.9117	2.80799
$959$	−21.9411	−0.708516
$960$	0	0
$961$	−31.0000	−1.00000
$962$	−21.6569	−0.698245
$963$	38.2843	1.23369
$964$	−22.9706	−0.739832
$965$	0	0
$966$	−38.6274	−1.24282
$967$	−14.9706	−0.481421	−0.240710	−	0.970597i	$-0.577380\pi$
$967$	−14.9706	−0.481421	−0.240710	+	0.970597i	$0.577380\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	−8.68629	−0.278756	−0.139378	−	0.990239i	$-0.544510\pi$
$971$	−8.68629	−0.278756	−0.139378	+	0.990239i	$0.544510\pi$
$972$	−54.1421	−1.73661
$973$	−8.00000	−0.256468
$974$	59.1127	1.89409
$975$	0	0
$976$	27.9411	0.894374
$977$	−32.3431	−1.03475	−0.517374	−	0.855759i	$-0.673091\pi$
$977$	−32.3431	−1.03475	−0.517374	+	0.855759i	$0.673091\pi$
$978$	−112.569	−3.59955
$979$	0	0
$980$	0	0
$981$	38.2843	1.22232
$982$	1.65685	0.0528723
$983$	21.8579	0.697158	0.348579	−	0.937279i	$-0.386664\pi$
$983$	21.8579	0.697158	0.348579	+	0.937279i	$0.386664\pi$
$984$	−74.9117	−2.38810
$985$	0	0
$986$	60.2843	1.91984
$987$	16.0000	0.509286
$988$	0	0
$989$	−16.9706	−0.539633
$990$	0	0
$991$	−57.9411	−1.84056	−0.920280	−	0.391260i	$-0.872039\pi$
$991$	−57.9411	−1.84056	−0.920280	+	0.391260i	$0.872039\pi$
$992$	0	0
$993$	−20.6863	−0.656460
$994$	−54.6274	−1.73268
$995$	0	0
$996$	−64.9706	−2.05867
$997$	−41.4558	−1.31292	−0.656460	−	0.754361i	$-0.727947\pi$
$997$	−41.4558	−1.31292	−0.656460	+	0.754361i	$0.727947\pi$
$998$	23.3137	0.737983
$999$	43.3137	1.37039

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3025.2.a.o.1.2		2
5.4	even	2		605.2.a.d.1.1		2
11.10	odd	2		275.2.a.c.1.1		2
15.14	odd	2		5445.2.a.y.1.2		2
20.19	odd	2		9680.2.a.bn.1.2		2
33.32	even	2		2475.2.a.x.1.2		2
44.43	even	2		4400.2.a.bn.1.1		2
55.4	even	10		605.2.g.l.511.1		8
55.9	even	10		605.2.g.l.81.2		8
55.14	even	10		605.2.g.l.251.1		8
55.19	odd	10		605.2.g.f.251.2		8
55.24	odd	10		605.2.g.f.81.1		8
55.29	odd	10		605.2.g.f.511.2		8
55.32	even	4		275.2.b.d.199.1		4
55.39	odd	10		605.2.g.f.366.1		8
55.43	even	4		275.2.b.d.199.4		4
55.49	even	10		605.2.g.l.366.2		8
55.54	odd	2		55.2.a.b.1.2	✓	2
165.32	odd	4		2475.2.c.l.199.4		4
165.98	odd	4		2475.2.c.l.199.1		4
165.164	even	2		495.2.a.b.1.1		2
220.43	odd	4		4400.2.b.q.4049.2		4
220.87	odd	4		4400.2.b.q.4049.3		4
220.219	even	2		880.2.a.m.1.2		2
385.384	even	2		2695.2.a.f.1.2		2
440.109	odd	2		3520.2.a.bn.1.2		2
440.219	even	2		3520.2.a.bo.1.1		2
660.659	odd	2		7920.2.a.ch.1.2		2
715.714	odd	2		9295.2.a.g.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.a.b.1.2	✓	2	55.54	odd	2
275.2.a.c.1.1		2	11.10	odd	2
275.2.b.d.199.1		4	55.32	even	4
275.2.b.d.199.4		4	55.43	even	4
495.2.a.b.1.1		2	165.164	even	2
605.2.a.d.1.1		2	5.4	even	2
605.2.g.f.81.1		8	55.24	odd	10
605.2.g.f.251.2		8	55.19	odd	10
605.2.g.f.366.1		8	55.39	odd	10
605.2.g.f.511.2		8	55.29	odd	10
605.2.g.l.81.2		8	55.9	even	10
605.2.g.l.251.1		8	55.14	even	10
605.2.g.l.366.2		8	55.49	even	10
605.2.g.l.511.1		8	55.4	even	10
880.2.a.m.1.2		2	220.219	even	2
2475.2.a.x.1.2		2	33.32	even	2
2475.2.c.l.199.1		4	165.98	odd	4
2475.2.c.l.199.4		4	165.32	odd	4
2695.2.a.f.1.2		2	385.384	even	2
3025.2.a.o.1.2		2	1.1	even	1	trivial
3520.2.a.bn.1.2		2	440.109	odd	2
3520.2.a.bo.1.1		2	440.219	even	2
4400.2.a.bn.1.1		2	44.43	even	2
4400.2.b.q.4049.2		4	220.43	odd	4
4400.2.b.q.4049.3		4	220.87	odd	4
5445.2.a.y.1.2		2	15.14	odd	2
7920.2.a.ch.1.2		2	660.659	odd	2
9295.2.a.g.1.1		2	715.714	odd	2
9680.2.a.bn.1.2		2	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3025 = 5^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3025.a (trivial)

\(f(q)\)	\(=\)	\(q+2.41421 q^{2} +2.82843 q^{3} +3.82843 q^{4} +6.82843 q^{6} -2.00000 q^{7} +4.41421 q^{8} +5.00000 q^{9} +O(q^{10})\)	\(q+2.41421 q^{2} +2.82843 q^{3} +3.82843 q^{4} +6.82843 q^{6} -2.00000 q^{7} +4.41421 q^{8} +5.00000 q^{9} +10.8284 q^{12} -1.17157 q^{13} -4.82843 q^{14} +3.00000 q^{16} +6.82843 q^{17} +12.0711 q^{18} -5.65685 q^{21} +2.82843 q^{23} +12.4853 q^{24} -2.82843 q^{26} +5.65685 q^{27} -7.65685 q^{28} +3.65685 q^{29} -1.58579 q^{32} +16.4853 q^{34} +19.1421 q^{36} +7.65685 q^{37} -3.31371 q^{39} -6.00000 q^{41} -13.6569 q^{42} -6.00000 q^{43} +6.82843 q^{46} -2.82843 q^{47} +8.48528 q^{48} -3.00000 q^{49} +19.3137 q^{51} -4.48528 q^{52} -11.6569 q^{53} +13.6569 q^{54} -8.82843 q^{56} +8.82843 q^{58} +1.65685 q^{59} +9.31371 q^{61} -10.0000 q^{63} -9.82843 q^{64} -12.4853 q^{67} +26.1421 q^{68} +8.00000 q^{69} +11.3137 q^{71} +22.0711 q^{72} -1.17157 q^{73} +18.4853 q^{74} -8.00000 q^{78} -4.00000 q^{79} +1.00000 q^{81} -14.4853 q^{82} -6.00000 q^{83} -21.6569 q^{84} -14.4853 q^{86} +10.3431 q^{87} -13.3137 q^{89} +2.34315 q^{91} +10.8284 q^{92} -6.82843 q^{94} -4.48528 q^{96} -3.65685 q^{97} -7.24264 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} + 8 q^{6} - 4 q^{7} + 6 q^{8} + 10 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^4 + 8 * q^6 - 4 * q^7 + 6 * q^8 + 10 * q^9	\( 2 q + 2 q^{2} + 2 q^{4} + 8 q^{6} - 4 q^{7} + 6 q^{8} + 10 q^{9} + 16 q^{12} - 8 q^{13} - 4 q^{14} + 6 q^{16} + 8 q^{17} + 10 q^{18} + 8 q^{24} - 4 q^{28} - 4 q^{29} - 6 q^{32} + 16 q^{34} + 10 q^{36} + 4 q^{37} + 16 q^{39} - 12 q^{41} - 16 q^{42} - 12 q^{43} + 8 q^{46} - 6 q^{49} + 16 q^{51} + 8 q^{52} - 12 q^{53} + 16 q^{54} - 12 q^{56} + 12 q^{58} - 8 q^{59} - 4 q^{61} - 20 q^{63} - 14 q^{64} - 8 q^{67} + 24 q^{68} + 16 q^{69} + 30 q^{72} - 8 q^{73} + 20 q^{74} - 16 q^{78} - 8 q^{79} + 2 q^{81} - 12 q^{82} - 12 q^{83} - 32 q^{84} - 12 q^{86} + 32 q^{87} - 4 q^{89} + 16 q^{91} + 16 q^{92} - 8 q^{94} + 8 q^{96} + 4 q^{97} - 6 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 + 8 * q^6 - 4 * q^7 + 6 * q^8 + 10 * q^9 + 16 * q^12 - 8 * q^13 - 4 * q^14 + 6 * q^16 + 8 * q^17 + 10 * q^18 + 8 * q^24 - 4 * q^28 - 4 * q^29 - 6 * q^32 + 16 * q^34 + 10 * q^36 + 4 * q^37 + 16 * q^39 - 12 * q^41 - 16 * q^42 - 12 * q^43 + 8 * q^46 - 6 * q^49 + 16 * q^51 + 8 * q^52 - 12 * q^53 + 16 * q^54 - 12 * q^56 + 12 * q^58 - 8 * q^59 - 4 * q^61 - 20 * q^63 - 14 * q^64 - 8 * q^67 + 24 * q^68 + 16 * q^69 + 30 * q^72 - 8 * q^73 + 20 * q^74 - 16 * q^78 - 8 * q^79 + 2 * q^81 - 12 * q^82 - 12 * q^83 - 32 * q^84 - 12 * q^86 + 32 * q^87 - 4 * q^89 + 16 * q^91 + 16 * q^92 - 8 * q^94 + 8 * q^96 + 4 * q^97 - 6 * q^98

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