LMFDB - Embedded newform 6025.2.a.m.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, 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("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.47202 q^{2} -1.05364 q^{3} +4.11086 q^{4} +2.60461 q^{6} -3.75256 q^{7} -5.21808 q^{8} -1.88985 q^{9} +O(q^{10})$	\(q-2.47202 q^{2} -1.05364 q^{3} +4.11086 q^{4} +2.60461 q^{6} -3.75256 q^{7} -5.21808 q^{8} -1.88985 q^{9} -4.39637 q^{11} -4.33135 q^{12} +2.86880 q^{13} +9.27639 q^{14} +4.67746 q^{16} -7.95399 q^{17} +4.67174 q^{18} +2.24943 q^{19} +3.95383 q^{21} +10.8679 q^{22} -8.91374 q^{23} +5.49796 q^{24} -7.09171 q^{26} +5.15212 q^{27} -15.4263 q^{28} +8.73490 q^{29} +3.99246 q^{31} -1.12659 q^{32} +4.63217 q^{33} +19.6624 q^{34} -7.76892 q^{36} -2.49566 q^{37} -5.56061 q^{38} -3.02267 q^{39} -6.91131 q^{41} -9.77394 q^{42} +4.58772 q^{43} -18.0729 q^{44} +22.0349 q^{46} +5.01868 q^{47} -4.92834 q^{48} +7.08170 q^{49} +8.38061 q^{51} +11.7932 q^{52} +7.55497 q^{53} -12.7361 q^{54} +19.5812 q^{56} -2.37008 q^{57} -21.5928 q^{58} +3.02417 q^{59} +14.0445 q^{61} -9.86942 q^{62} +7.09178 q^{63} -6.56998 q^{64} -11.4508 q^{66} -1.63861 q^{67} -32.6977 q^{68} +9.39184 q^{69} +3.87645 q^{71} +9.86140 q^{72} +6.49640 q^{73} +6.16931 q^{74} +9.24708 q^{76} +16.4976 q^{77} +7.47208 q^{78} +12.2436 q^{79} +0.241089 q^{81} +17.0849 q^{82} -11.2059 q^{83} +16.2537 q^{84} -11.3409 q^{86} -9.20340 q^{87} +22.9406 q^{88} +6.37583 q^{89} -10.7653 q^{91} -36.6432 q^{92} -4.20660 q^{93} -12.4063 q^{94} +1.18701 q^{96} +1.66374 q^{97} -17.5061 q^{98} +8.30848 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 9 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 20 q^{7} - 27 q^{8} + 38 q^{9}+O(q^{10}) $ 40 * q - 9 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 20 * q^7 - 27 * q^8 + 38 * q^9	$ 40 q - 9 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 20 q^{7} - 27 q^{8} + 38 q^{9} + q^{11} - 26 q^{12} - 11 q^{13} - q^{14} + 43 q^{16} - 20 q^{17} - 18 q^{18} + 2 q^{21} - 23 q^{22} - 79 q^{23} - 2 q^{24} + 2 q^{26} - 26 q^{27} - 30 q^{28} + 2 q^{29} + q^{31} - 68 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 16 q^{37} - 45 q^{38} - 2 q^{39} - 2 q^{41} - 19 q^{42} - 25 q^{43} + 3 q^{44} + 14 q^{46} - 88 q^{47} - 75 q^{48} + 40 q^{49} - 10 q^{51} - 18 q^{52} - 34 q^{53} + 4 q^{54} - 15 q^{56} - 51 q^{57} - 53 q^{58} + q^{59} + 9 q^{61} - 39 q^{62} - 110 q^{63} + 17 q^{64} + 26 q^{66} - 30 q^{67} - 44 q^{68} - 7 q^{69} + 5 q^{71} - 18 q^{72} - 23 q^{73} - 18 q^{74} + 43 q^{76} - 30 q^{77} - 46 q^{78} + 5 q^{79} + 44 q^{81} - 5 q^{82} - 65 q^{83} - 65 q^{84} + 40 q^{86} - 33 q^{87} - 71 q^{88} - 9 q^{89} + q^{91} - 117 q^{92} - 68 q^{93} - 72 q^{94} + 83 q^{96} + 8 q^{97} - 76 q^{98} - 40 q^{99}+O(q^{100}) $ 40 * q - 9 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 20 * q^7 - 27 * q^8 + 38 * q^9 + q^11 - 26 * q^12 - 11 * q^13 - q^14 + 43 * q^16 - 20 * q^17 - 18 * q^18 + 2 * q^21 - 23 * q^22 - 79 * q^23 - 2 * q^24 + 2 * q^26 - 26 * q^27 - 30 * q^28 + 2 * q^29 + q^31 - 68 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 16 * q^37 - 45 * q^38 - 2 * q^39 - 2 * q^41 - 19 * q^42 - 25 * q^43 + 3 * q^44 + 14 * q^46 - 88 * q^47 - 75 * q^48 + 40 * q^49 - 10 * q^51 - 18 * q^52 - 34 * q^53 + 4 * q^54 - 15 * q^56 - 51 * q^57 - 53 * q^58 + q^59 + 9 * q^61 - 39 * q^62 - 110 * q^63 + 17 * q^64 + 26 * q^66 - 30 * q^67 - 44 * q^68 - 7 * q^69 + 5 * q^71 - 18 * q^72 - 23 * q^73 - 18 * q^74 + 43 * q^76 - 30 * q^77 - 46 * q^78 + 5 * q^79 + 44 * q^81 - 5 * q^82 - 65 * q^83 - 65 * q^84 + 40 * q^86 - 33 * q^87 - 71 * q^88 - 9 * q^89 + q^91 - 117 * q^92 - 68 * q^93 - 72 * q^94 + 83 * q^96 + 8 * q^97 - 76 * q^98 - 40 * 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 $

$2$	−2.47202	−1.74798	−0.873990	−	0.485945i	$-0.838476\pi$
$2$	−2.47202	−1.74798	−0.873990	+	0.485945i	$0.838476\pi$
$3$	−1.05364	−0.608317	−0.304159	−	0.952621i	$-0.598375\pi$
$3$	−1.05364	−0.608317	−0.304159	+	0.952621i	$0.598375\pi$
$4$	4.11086	2.05543
$5$	0	0
$5$	0	0
$6$	2.60461	1.06333
$7$	−3.75256	−1.41833	−0.709167	−	0.705040i	$-0.750929\pi$
$7$	−3.75256	−1.41833	−0.709167	+	0.705040i	$0.750929\pi$
$8$	−5.21808	−1.84487
$9$	−1.88985	−0.629950
$10$	0	0
$11$	−4.39637	−1.32555	−0.662777	−	0.748816i	$-0.730622\pi$
$11$	−4.39637	−1.32555	−0.662777	+	0.748816i	$0.730622\pi$
$12$	−4.33135	−1.25035
$13$	2.86880	0.795661	0.397830	−	0.917459i	$-0.369763\pi$
$13$	2.86880	0.795661	0.397830	+	0.917459i	$0.369763\pi$
$14$	9.27639	2.47922
$15$	0	0
$16$	4.67746	1.16936
$17$	−7.95399	−1.92913	−0.964563	−	0.263854i	$-0.915006\pi$
$17$	−7.95399	−1.92913	−0.964563	+	0.263854i	$0.915006\pi$
$18$	4.67174	1.10114
$19$	2.24943	0.516054	0.258027	−	0.966138i	$-0.416928\pi$
$19$	2.24943	0.516054	0.258027	+	0.966138i	$0.416928\pi$
$20$	0	0
$21$	3.95383	0.862797
$22$	10.8679	2.31704
$23$	−8.91374	−1.85864	−0.929322	−	0.369271i	$-0.879608\pi$
$23$	−8.91374	−1.85864	−0.929322	+	0.369271i	$0.879608\pi$
$24$	5.49796	1.12227
$25$	0	0
$26$	−7.09171	−1.39080
$27$	5.15212	0.991527
$28$	−15.4263	−2.91529
$29$	8.73490	1.62203	0.811015	−	0.585025i	$-0.198916\pi$
$29$	8.73490	1.62203	0.811015	+	0.585025i	$0.198916\pi$
$30$	0	0
$31$	3.99246	0.717067	0.358533	−	0.933517i	$-0.383277\pi$
$31$	3.99246	0.717067	0.358533	+	0.933517i	$0.383277\pi$
$32$	−1.12659	−0.199154
$33$	4.63217	0.806358
$34$	19.6624	3.37207
$35$	0	0
$36$	−7.76892	−1.29482
$37$	−2.49566	−0.410284	−0.205142	−	0.978732i	$-0.565766\pi$
$37$	−2.49566	−0.410284	−0.205142	+	0.978732i	$0.565766\pi$
$38$	−5.56061	−0.902051
$39$	−3.02267	−0.484014
$40$	0	0
$41$	−6.91131	−1.07937	−0.539683	−	0.841869i	$-0.681456\pi$
$41$	−6.91131	−1.07937	−0.539683	+	0.841869i	$0.681456\pi$
$42$	−9.77394	−1.50815
$43$	4.58772	0.699621	0.349810	−	0.936821i	$-0.386246\pi$
$43$	4.58772	0.699621	0.349810	+	0.936821i	$0.386246\pi$
$44$	−18.0729	−2.72459
$45$	0	0
$46$	22.0349	3.24887
$47$	5.01868	0.732050	0.366025	−	0.930605i	$-0.380719\pi$
$47$	5.01868	0.732050	0.366025	+	0.930605i	$0.380719\pi$
$48$	−4.92834	−0.711345
$49$	7.08170	1.01167
$50$	0	0
$51$	8.38061	1.17352
$52$	11.7932	1.63543
$53$	7.55497	1.03775	0.518877	−	0.854849i	$-0.326350\pi$
$53$	7.55497	1.03775	0.518877	+	0.854849i	$0.326350\pi$
$54$	−12.7361	−1.73317
$55$	0	0
$56$	19.5812	2.61664
$57$	−2.37008	−0.313924
$58$	−21.5928	−2.83527
$59$	3.02417	0.393713	0.196856	−	0.980432i	$-0.436927\pi$
$59$	3.02417	0.393713	0.196856	+	0.980432i	$0.436927\pi$
$60$	0	0
$61$	14.0445	1.79821	0.899107	−	0.437729i	$-0.144217\pi$
$61$	14.0445	1.79821	0.899107	+	0.437729i	$0.144217\pi$
$62$	−9.86942	−1.25342
$63$	7.09178	0.893480
$64$	−6.56998	−0.821247
$65$	0	0
$66$	−11.4508	−1.40950
$67$	−1.63861	−0.200188	−0.100094	−	0.994978i	$-0.531914\pi$
$67$	−1.63861	−0.200188	−0.100094	+	0.994978i	$0.531914\pi$
$68$	−32.6977	−3.96518
$69$	9.39184	1.13064
$70$	0	0
$71$	3.87645	0.460050	0.230025	−	0.973185i	$-0.426119\pi$
$71$	3.87645	0.460050	0.230025	+	0.973185i	$0.426119\pi$
$72$	9.86140	1.16218
$73$	6.49640	0.760346	0.380173	−	0.924915i	$-0.375864\pi$
$73$	6.49640	0.760346	0.380173	+	0.924915i	$0.375864\pi$
$74$	6.16931	0.717168
$75$	0	0
$76$	9.24708	1.06071
$77$	16.4976	1.88008
$78$	7.47208	0.846046
$79$	12.2436	1.37751	0.688755	−	0.724994i	$-0.258157\pi$
$79$	12.2436	1.37751	0.688755	+	0.724994i	$0.258157\pi$
$80$	0	0
$81$	0.241089	0.0267876
$82$	17.0849	1.88671
$83$	−11.2059	−1.23000	−0.615002	−	0.788526i	$-0.710845\pi$
$83$	−11.2059	−1.23000	−0.615002	+	0.788526i	$0.710845\pi$
$84$	16.2537	1.77342
$85$	0	0
$86$	−11.3409	−1.22292
$87$	−9.20340	−0.986709
$88$	22.9406	2.44548
$89$	6.37583	0.675836	0.337918	−	0.941175i	$-0.390277\pi$
$89$	6.37583	0.675836	0.337918	+	0.941175i	$0.390277\pi$
$90$	0	0
$91$	−10.7653	−1.12851
$92$	−36.6432	−3.82031
$93$	−4.20660	−0.436204
$94$	−12.4063	−1.27961
$95$	0	0
$96$	1.18701	0.121149
$97$	1.66374	0.168927	0.0844636	−	0.996427i	$-0.473082\pi$
$97$	1.66374	0.168927	0.0844636	+	0.996427i	$0.473082\pi$
$98$	−17.5061	−1.76838
$99$	8.30848	0.835034
$100$	0	0
$101$	−13.8636	−1.37948	−0.689740	−	0.724057i	$-0.742275\pi$
$101$	−13.8636	−1.37948	−0.689740	+	0.724057i	$0.742275\pi$
$102$	−20.7170	−2.05129
$103$	16.0534	1.58179	0.790893	−	0.611955i	$-0.209617\pi$
$103$	16.0534	1.58179	0.790893	+	0.611955i	$0.209617\pi$
$104$	−14.9696	−1.46789
$105$	0	0
$106$	−18.6760	−1.81397
$107$	19.7416	1.90849	0.954247	−	0.299018i	$-0.0966590\pi$
$107$	19.7416	1.90849	0.954247	+	0.299018i	$0.0966590\pi$
$108$	21.1797	2.03801
$109$	−12.8190	−1.22783	−0.613917	−	0.789371i	$-0.710407\pi$
$109$	−12.8190	−1.22783	−0.613917	+	0.789371i	$0.710407\pi$
$110$	0	0
$111$	2.62952	0.249583
$112$	−17.5524	−1.65855
$113$	−8.79268	−0.827146	−0.413573	−	0.910471i	$-0.635719\pi$
$113$	−8.79268	−0.827146	−0.413573	+	0.910471i	$0.635719\pi$
$114$	5.85886	0.548733
$115$	0	0
$116$	35.9080	3.33397
$117$	−5.42160	−0.501227
$118$	−7.47579	−0.688202
$119$	29.8478	2.73614
$120$	0	0
$121$	8.32805	0.757096
$122$	−34.7182	−3.14324
$123$	7.28201	0.656596
$124$	16.4124	1.47388
$125$	0	0
$126$	−17.5310	−1.56178
$127$	−9.62470	−0.854054	−0.427027	−	0.904239i	$-0.640439\pi$
$127$	−9.62470	−0.854054	−0.427027	+	0.904239i	$0.640439\pi$
$128$	18.4943	1.63468
$129$	−4.83379	−0.425591
$130$	0	0
$131$	−6.11096	−0.533917	−0.266959	−	0.963708i	$-0.586019\pi$
$131$	−6.11096	−0.533917	−0.266959	+	0.963708i	$0.586019\pi$
$132$	19.0422	1.65741
$133$	−8.44110	−0.731936
$134$	4.05066	0.349924
$135$	0	0
$136$	41.5046	3.55899
$137$	−4.54343	−0.388171	−0.194086	−	0.980985i	$-0.562174\pi$
$137$	−4.54343	−0.388171	−0.194086	+	0.980985i	$0.562174\pi$
$138$	−23.2168	−1.97634
$139$	−13.2891	−1.12716	−0.563581	−	0.826061i	$-0.690577\pi$
$139$	−13.2891	−1.12716	−0.563581	+	0.826061i	$0.690577\pi$
$140$	0	0
$141$	−5.28786	−0.445318
$142$	−9.58265	−0.804158
$143$	−12.6123	−1.05469
$144$	−8.83970	−0.736642
$145$	0	0
$146$	−16.0592	−1.32907
$147$	−7.46154	−0.615417
$148$	−10.2593	−0.843310
$149$	−4.84193	−0.396667	−0.198333	−	0.980135i	$-0.563553\pi$
$149$	−4.84193	−0.396667	−0.198333	+	0.980135i	$0.563553\pi$
$150$	0	0
$151$	−18.9487	−1.54202	−0.771012	−	0.636821i	$-0.780249\pi$
$151$	−18.9487	−1.54202	−0.771012	+	0.636821i	$0.780249\pi$
$152$	−11.7377	−0.952052
$153$	15.0318	1.21525
$154$	−40.7824	−3.28634
$155$	0	0
$156$	−12.4258	−0.994857
$157$	7.93941	0.633634	0.316817	−	0.948487i	$-0.397386\pi$
$157$	7.93941	0.633634	0.316817	+	0.948487i	$0.397386\pi$
$158$	−30.2663	−2.40786
$159$	−7.96019	−0.631284
$160$	0	0
$161$	33.4494	2.63618
$162$	−0.595975	−0.0468242
$163$	−14.6038	−1.14386	−0.571929	−	0.820303i	$-0.693805\pi$
$163$	−14.6038	−1.14386	−0.571929	+	0.820303i	$0.693805\pi$
$164$	−28.4114	−2.21856
$165$	0	0
$166$	27.7011	2.15002
$167$	−0.0191255	−0.00147997	−0.000739987	−	1.00000i	$-0.500236\pi$
$167$	−0.0191255	−0.00147997	−0.000739987		1.00000i	$0.500236\pi$
$168$	−20.6314	−1.59175
$169$	−4.77001	−0.366924
$170$	0	0
$171$	−4.25108	−0.325088
$172$	18.8595	1.43802
$173$	1.57608	0.119827	0.0599136	−	0.998204i	$-0.480917\pi$
$173$	1.57608	0.119827	0.0599136	+	0.998204i	$0.480917\pi$
$174$	22.7510	1.72475
$175$	0	0
$176$	−20.5638	−1.55006
$177$	−3.18637	−0.239502
$178$	−15.7611	−1.18135
$179$	4.12768	0.308517	0.154259	−	0.988031i	$-0.450701\pi$
$179$	4.12768	0.308517	0.154259	+	0.988031i	$0.450701\pi$
$180$	0	0
$181$	11.9835	0.890723	0.445362	−	0.895351i	$-0.353075\pi$
$181$	11.9835	0.890723	0.445362	+	0.895351i	$0.353075\pi$
$182$	26.6121	1.97262
$183$	−14.7978	−1.09388
$184$	46.5126	3.42896
$185$	0	0
$186$	10.3988	0.762476
$187$	34.9687	2.55716
$188$	20.6311	1.50468
$189$	−19.3337	−1.40632
$190$	0	0
$191$	−4.76923	−0.345089	−0.172545	−	0.985002i	$-0.555199\pi$
$191$	−4.76923	−0.345089	−0.172545	+	0.985002i	$0.555199\pi$
$192$	6.92237	0.499579
$193$	6.69389	0.481837	0.240918	−	0.970545i	$-0.422551\pi$
$193$	6.69389	0.481837	0.240918	+	0.970545i	$0.422551\pi$
$194$	−4.11279	−0.295281
$195$	0	0
$196$	29.1119	2.07942
$197$	19.4636	1.38672	0.693362	−	0.720589i	$-0.256129\pi$
$197$	19.4636	1.38672	0.693362	+	0.720589i	$0.256129\pi$
$198$	−20.5387	−1.45962
$199$	−14.2250	−1.00838	−0.504191	−	0.863592i	$-0.668209\pi$
$199$	−14.2250	−1.00838	−0.504191	+	0.863592i	$0.668209\pi$
$200$	0	0
$201$	1.72649	0.121778
$202$	34.2710	2.41130
$203$	−32.7782	−2.30058
$204$	34.4515	2.41209
$205$	0	0
$206$	−39.6842	−2.76493
$207$	16.8456	1.17085
$208$	13.4187	0.930418
$209$	−9.88930	−0.684057
$210$	0	0
$211$	−17.0898	−1.17651	−0.588255	−	0.808676i	$-0.700185\pi$
$211$	−17.0898	−1.17651	−0.588255	+	0.808676i	$0.700185\pi$
$212$	31.0574	2.13303
$213$	−4.08437	−0.279856
$214$	−48.8016	−3.33601
$215$	0	0
$216$	−26.8842	−1.82924
$217$	−14.9819	−1.01704
$218$	31.6887	2.14623
$219$	−6.84484	−0.462532
$220$	0	0
$221$	−22.8184	−1.53493
$222$	−6.50021	−0.436265
$223$	−19.3023	−1.29258	−0.646288	−	0.763094i	$-0.723679\pi$
$223$	−19.3023	−1.29258	−0.646288	+	0.763094i	$0.723679\pi$
$224$	4.22759	0.282467
$225$	0	0
$226$	21.7356	1.44583
$227$	−10.0185	−0.664949	−0.332474	−	0.943112i	$-0.607884\pi$
$227$	−10.0185	−0.664949	−0.332474	+	0.943112i	$0.607884\pi$
$228$	−9.74305	−0.645249
$229$	16.0619	1.06140	0.530699	−	0.847560i	$-0.321929\pi$
$229$	16.0619	1.06140	0.530699	+	0.847560i	$0.321929\pi$
$230$	0	0
$231$	−17.3825	−1.14368
$232$	−45.5794	−2.99244
$233$	29.7749	1.95062	0.975310	−	0.220842i	$-0.0708804\pi$
$233$	29.7749	1.95062	0.975310	+	0.220842i	$0.0708804\pi$
$234$	13.4023	0.876134
$235$	0	0
$236$	12.4319	0.809250
$237$	−12.9003	−0.837963
$238$	−73.7842	−4.78272
$239$	−11.2495	−0.727672	−0.363836	−	0.931463i	$-0.618533\pi$
$239$	−11.2495	−0.727672	−0.363836	+	0.931463i	$0.618533\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−20.5871	−1.32339
$243$	−15.7104	−1.00782
$244$	57.7350	3.69610
$245$	0	0
$246$	−18.0012	−1.14772
$247$	6.45314	0.410604
$248$	−20.8330	−1.32290
$249$	11.8069	0.748232
$250$	0	0
$251$	−6.69832	−0.422794	−0.211397	−	0.977400i	$-0.567801\pi$
$251$	−6.69832	−0.422794	−0.211397	+	0.977400i	$0.567801\pi$
$252$	29.1533	1.83649
$253$	39.1881	2.46373
$254$	23.7924	1.49287
$255$	0	0
$256$	−32.5781	−2.03613
$257$	21.4931	1.34070	0.670351	−	0.742044i	$-0.266143\pi$
$257$	21.4931	1.34070	0.670351	+	0.742044i	$0.266143\pi$
$258$	11.9492	0.743925
$259$	9.36511	0.581920
$260$	0	0
$261$	−16.5077	−1.02180
$262$	15.1064	0.933276
$263$	0.775966	0.0478481	0.0239240	−	0.999714i	$-0.492384\pi$
$263$	0.775966	0.0478481	0.0239240	+	0.999714i	$0.492384\pi$
$264$	−24.1711	−1.48763
$265$	0	0
$266$	20.8665	1.27941
$267$	−6.71780	−0.411123
$268$	−6.73608	−0.411472
$269$	−19.1927	−1.17020	−0.585099	−	0.810962i	$-0.698944\pi$
$269$	−19.1927	−1.17020	−0.585099	+	0.810962i	$0.698944\pi$
$270$	0	0
$271$	16.3443	0.992845	0.496423	−	0.868081i	$-0.334647\pi$
$271$	16.3443	0.992845	0.496423	+	0.868081i	$0.334647\pi$
$272$	−37.2044	−2.25585
$273$	11.3427	0.686494
$274$	11.2314	0.678515
$275$	0	0
$276$	38.6086	2.32396
$277$	14.1682	0.851284	0.425642	−	0.904892i	$-0.360048\pi$
$277$	14.1682	0.851284	0.425642	+	0.904892i	$0.360048\pi$
$278$	32.8507	1.97026
$279$	−7.54515	−0.451716
$280$	0	0
$281$	29.6657	1.76971	0.884853	−	0.465870i	$-0.154259\pi$
$281$	29.6657	1.76971	0.884853	+	0.465870i	$0.154259\pi$
$282$	13.0717	0.778407
$283$	−10.3346	−0.614328	−0.307164	−	0.951657i	$-0.599380\pi$
$283$	−10.3346	−0.614328	−0.307164	+	0.951657i	$0.599380\pi$
$284$	15.9356	0.945601
$285$	0	0
$286$	31.1778	1.84358
$287$	25.9351	1.53090
$288$	2.12908	0.125457
$289$	46.2659	2.72152
$290$	0	0
$291$	−1.75298	−0.102761
$292$	26.7058	1.56284
$293$	−0.562415	−0.0328566	−0.0164283	−	0.999865i	$-0.505230\pi$
$293$	−0.562415	−0.0328566	−0.0164283	+	0.999865i	$0.505230\pi$
$294$	18.4450	1.07574
$295$	0	0
$296$	13.0226	0.756921
$297$	−22.6506	−1.31432
$298$	11.9693	0.693365
$299$	−25.5717	−1.47885
$300$	0	0
$301$	−17.2157	−0.992296
$302$	46.8415	2.69543
$303$	14.6072	0.839161
$304$	10.5216	0.603455
$305$	0	0
$306$	−37.1590	−2.12424
$307$	20.3508	1.16148	0.580742	−	0.814088i	$-0.302763\pi$
$307$	20.3508	1.16148	0.580742	+	0.814088i	$0.302763\pi$
$308$	67.8195	3.86437
$309$	−16.9144	−0.962227
$310$	0	0
$311$	14.3484	0.813623	0.406812	−	0.913512i	$-0.366641\pi$
$311$	14.3484	0.813623	0.406812	+	0.913512i	$0.366641\pi$
$312$	15.7725	0.892943
$313$	−31.3538	−1.77222	−0.886111	−	0.463472i	$-0.846603\pi$
$313$	−31.3538	−1.77222	−0.886111	+	0.463472i	$0.846603\pi$
$314$	−19.6263	−1.10758
$315$	0	0
$316$	50.3317	2.83138
$317$	8.99816	0.505387	0.252694	−	0.967546i	$-0.418684\pi$
$317$	8.99816	0.505387	0.252694	+	0.967546i	$0.418684\pi$
$318$	19.6777	1.10347
$319$	−38.4018	−2.15009
$320$	0	0
$321$	−20.8005	−1.16097
$322$	−82.6873	−4.60798
$323$	−17.8919	−0.995532
$324$	0.991083	0.0550601
$325$	0	0
$326$	36.1008	1.99944
$327$	13.5065	0.746912
$328$	36.0638	1.99129
$329$	−18.8329	−1.03829
$330$	0	0
$331$	−1.86539	−0.102531	−0.0512657	−	0.998685i	$-0.516326\pi$
$331$	−1.86539	−0.102531	−0.0512657	+	0.998685i	$0.516326\pi$
$332$	−46.0658	−2.52819
$333$	4.71642	0.258458
$334$	0.0472785	0.00258696
$335$	0	0
$336$	18.4939	1.00892
$337$	−1.03832	−0.0565610	−0.0282805	−	0.999600i	$-0.509003\pi$
$337$	−1.03832	−0.0565610	−0.0282805	+	0.999600i	$0.509003\pi$
$338$	11.7915	0.641376
$339$	9.26428	0.503167
$340$	0	0
$341$	−17.5523	−0.950511
$342$	10.5087	0.568247
$343$	−0.306593	−0.0165544
$344$	−23.9391	−1.29071
$345$	0	0
$346$	−3.89609	−0.209455
$347$	−13.5070	−0.725093	−0.362547	−	0.931966i	$-0.618093\pi$
$347$	−13.5070	−0.725093	−0.362547	+	0.931966i	$0.618093\pi$
$348$	−37.8339	−2.02811
$349$	23.0389	1.23324	0.616622	−	0.787260i	$-0.288501\pi$
$349$	23.0389	1.23324	0.616622	+	0.787260i	$0.288501\pi$
$350$	0	0
$351$	14.7804	0.788919
$352$	4.95289	0.263990
$353$	−12.7920	−0.680848	−0.340424	−	0.940272i	$-0.610571\pi$
$353$	−12.7920	−0.680848	−0.340424	+	0.940272i	$0.610571\pi$
$354$	7.87676	0.418645
$355$	0	0
$356$	26.2101	1.38914
$357$	−31.4487	−1.66444
$358$	−10.2037	−0.539282
$359$	−8.22455	−0.434075	−0.217038	−	0.976163i	$-0.569639\pi$
$359$	−8.22455	−0.434075	−0.217038	+	0.976163i	$0.569639\pi$
$360$	0	0
$361$	−13.9401	−0.733689
$362$	−29.6233	−1.55697
$363$	−8.77474	−0.460554
$364$	−44.2548	−2.31958
$365$	0	0
$366$	36.5804	1.91209
$367$	26.0155	1.35800	0.679000	−	0.734138i	$-0.262413\pi$
$367$	26.0155	1.35800	0.679000	+	0.734138i	$0.262413\pi$
$368$	−41.6937	−2.17343
$369$	13.0613	0.679947
$370$	0	0
$371$	−28.3505	−1.47188
$372$	−17.2927	−0.896587
$373$	15.4942	0.802259	0.401130	−	0.916021i	$-0.368618\pi$
$373$	15.4942	0.802259	0.401130	+	0.916021i	$0.368618\pi$
$374$	−86.4431	−4.46986
$375$	0	0
$376$	−26.1879	−1.35054
$377$	25.0586	1.29059
$378$	47.7931	2.45821
$379$	−0.999139	−0.0513223	−0.0256612	−	0.999671i	$-0.508169\pi$
$379$	−0.999139	−0.0513223	−0.0256612	+	0.999671i	$0.508169\pi$
$380$	0	0
$381$	10.1409	0.519535
$382$	11.7896	0.603209
$383$	33.6882	1.72138	0.860692	−	0.509126i	$-0.170031\pi$
$383$	33.6882	1.72138	0.860692	+	0.509126i	$0.170031\pi$
$384$	−19.4862	−0.994402
$385$	0	0
$386$	−16.5474	−0.842241
$387$	−8.67011	−0.440726
$388$	6.83940	0.347218
$389$	25.0896	1.27209	0.636046	−	0.771651i	$-0.280569\pi$
$389$	25.0896	1.27209	0.636046	+	0.771651i	$0.280569\pi$
$390$	0	0
$391$	70.8998	3.58556
$392$	−36.9529	−1.86640
$393$	6.43873	0.324791
$394$	−48.1143	−2.42397
$395$	0	0
$396$	34.1550	1.71635
$397$	35.3809	1.77572	0.887859	−	0.460117i	$-0.152192\pi$
$397$	35.3809	1.77572	0.887859	+	0.460117i	$0.152192\pi$
$398$	35.1644	1.76263
$399$	8.89385	0.445249
$400$	0	0
$401$	−26.1983	−1.30828	−0.654141	−	0.756373i	$-0.726970\pi$
$401$	−26.1983	−1.30828	−0.654141	+	0.756373i	$0.726970\pi$
$402$	−4.26792	−0.212865
$403$	11.4535	0.570542
$404$	−56.9913	−2.83543
$405$	0	0
$406$	81.0283	4.02137
$407$	10.9718	0.543854
$408$	−43.7307	−2.16499
$409$	−10.9374	−0.540819	−0.270410	−	0.962745i	$-0.587159\pi$
$409$	−10.9374	−0.540819	−0.270410	+	0.962745i	$0.587159\pi$
$410$	0	0
$411$	4.78712	0.236131
$412$	65.9932	3.25125
$413$	−11.3484	−0.558416
$414$	−41.6427	−2.04663
$415$	0	0
$416$	−3.23195	−0.158459
$417$	14.0018	0.685672
$418$	24.4465	1.19572
$419$	0.456615	0.0223071	0.0111536	−	0.999938i	$-0.496450\pi$
$419$	0.456615	0.0223071	0.0111536	+	0.999938i	$0.496450\pi$
$420$	0	0
$421$	−6.87146	−0.334895	−0.167447	−	0.985881i	$-0.553552\pi$
$421$	−6.87146	−0.334895	−0.167447	+	0.985881i	$0.553552\pi$
$422$	42.2462	2.05651
$423$	−9.48456	−0.461155
$424$	−39.4224	−1.91452
$425$	0	0
$426$	10.0966	0.489183
$427$	−52.7028	−2.55047
$428$	81.1551	3.92278
$429$	13.2888	0.641587
$430$	0	0
$431$	−22.1787	−1.06831	−0.534155	−	0.845387i	$-0.679370\pi$
$431$	−22.1787	−1.06831	−0.534155	+	0.845387i	$0.679370\pi$
$432$	24.0988	1.15946
$433$	−19.4986	−0.937042	−0.468521	−	0.883452i	$-0.655213\pi$
$433$	−19.4986	−0.937042	−0.468521	+	0.883452i	$0.655213\pi$
$434$	37.0356	1.77777
$435$	0	0
$436$	−52.6969	−2.52373
$437$	−20.0508	−0.959160
$438$	16.9206	0.808495
$439$	−4.23065	−0.201918	−0.100959	−	0.994891i	$-0.532191\pi$
$439$	−4.23065	−0.201918	−0.100959	+	0.994891i	$0.532191\pi$
$440$	0	0
$441$	−13.3834	−0.637303
$442$	56.4073	2.68302
$443$	−30.4507	−1.44676	−0.723378	−	0.690452i	$-0.757412\pi$
$443$	−30.4507	−1.44676	−0.723378	+	0.690452i	$0.757412\pi$
$444$	10.8096	0.513000
$445$	0	0
$446$	47.7155	2.25939
$447$	5.10164	0.241299
$448$	24.6542	1.16480
$449$	1.49229	0.0704256	0.0352128	−	0.999380i	$-0.488789\pi$
$449$	1.49229	0.0704256	0.0352128	+	0.999380i	$0.488789\pi$
$450$	0	0
$451$	30.3847	1.43076
$452$	−36.1455	−1.70014
$453$	19.9650	0.938040
$454$	24.7658	1.16232
$455$	0	0
$456$	12.3673	0.579150
$457$	−23.2775	−1.08887	−0.544437	−	0.838802i	$-0.683257\pi$
$457$	−23.2775	−1.08887	−0.544437	+	0.838802i	$0.683257\pi$
$458$	−39.7052	−1.85530
$459$	−40.9799	−1.91278
$460$	0	0
$461$	8.81947	0.410764	0.205382	−	0.978682i	$-0.434156\pi$
$461$	8.81947	0.410764	0.205382	+	0.978682i	$0.434156\pi$
$462$	42.9698	1.99914
$463$	33.2489	1.54521	0.772605	−	0.634888i	$-0.218954\pi$
$463$	33.2489	1.54521	0.772605	+	0.634888i	$0.218954\pi$
$464$	40.8571	1.89674
$465$	0	0
$466$	−73.6040	−3.40964
$467$	−18.7357	−0.866983	−0.433491	−	0.901158i	$-0.642719\pi$
$467$	−18.7357	−0.866983	−0.433491	+	0.901158i	$0.642719\pi$
$468$	−22.2874	−1.03024
$469$	6.14897	0.283933
$470$	0	0
$471$	−8.36525	−0.385450
$472$	−15.7803	−0.726349
$473$	−20.1693	−0.927386
$474$	31.8897	1.46474
$475$	0	0
$476$	122.700	5.62395
$477$	−14.2778	−0.653734
$478$	27.8090	1.27196
$479$	5.09584	0.232835	0.116418	−	0.993200i	$-0.462859\pi$
$479$	5.09584	0.232835	0.116418	+	0.993200i	$0.462859\pi$
$480$	0	0
$481$	−7.15954	−0.326447
$482$	−2.47202	−0.112597
$483$	−35.2434	−1.60363
$484$	34.2355	1.55616
$485$	0	0
$486$	38.8363	1.76165
$487$	13.9703	0.633056	0.316528	−	0.948583i	$-0.397483\pi$
$487$	13.9703	0.633056	0.316528	+	0.948583i	$0.397483\pi$
$488$	−73.2854	−3.31747
$489$	15.3871	0.695829
$490$	0	0
$491$	−15.5547	−0.701973	−0.350986	−	0.936381i	$-0.614154\pi$
$491$	−15.5547	−0.701973	−0.350986	+	0.936381i	$0.614154\pi$
$492$	29.9353	1.34959
$493$	−69.4773	−3.12910
$494$	−15.9523	−0.717726
$495$	0	0
$496$	18.6746	0.838513
$497$	−14.5466	−0.652505
$498$	−29.1869	−1.30789
$499$	31.9430	1.42997	0.714983	−	0.699142i	$-0.246434\pi$
$499$	31.9430	1.42997	0.714983	+	0.699142i	$0.246434\pi$
$500$	0	0
$501$	0.0201513	0.000900293 0
$502$	16.5584	0.739035
$503$	−19.2763	−0.859487	−0.429744	−	0.902951i	$-0.641396\pi$
$503$	−19.2763	−0.859487	−0.429744	+	0.902951i	$0.641396\pi$
$504$	−37.0055	−1.64836
$505$	0	0
$506$	−96.8736	−4.30656
$507$	5.02586	0.223206
$508$	−39.5658	−1.75545
$509$	−13.3966	−0.593796	−0.296898	−	0.954909i	$-0.595952\pi$
$509$	−13.3966	−0.593796	−0.296898	+	0.954909i	$0.595952\pi$
$510$	0	0
$511$	−24.3781	−1.07842
$512$	43.5452	1.92444
$513$	11.5893	0.511681
$514$	−53.1313	−2.34352
$515$	0	0
$516$	−19.8710	−0.874773
$517$	−22.0640	−0.970372
$518$	−23.1507	−1.01718
$519$	−1.66061	−0.0728929
$520$	0	0
$521$	−4.20075	−0.184038	−0.0920192	−	0.995757i	$-0.529332\pi$
$521$	−4.20075	−0.184038	−0.0920192	+	0.995757i	$0.529332\pi$
$522$	40.8072	1.78608
$523$	29.4016	1.28564	0.642821	−	0.766016i	$-0.277764\pi$
$523$	29.4016	1.28564	0.642821	+	0.766016i	$0.277764\pi$
$524$	−25.1213	−1.09743
$525$	0	0
$526$	−1.91820	−0.0836374
$527$	−31.7560	−1.38331
$528$	21.6668	0.942926
$529$	56.4548	2.45456
$530$	0	0
$531$	−5.71522	−0.248020
$532$	−34.7002	−1.50444
$533$	−19.8271	−0.858809
$534$	16.6065	0.718634
$535$	0	0
$536$	8.55038	0.369320
$537$	−4.34907	−0.187676
$538$	47.4446	2.04548
$539$	−31.1338	−1.34103
$540$	0	0
$541$	−11.3145	−0.486446	−0.243223	−	0.969970i	$-0.578205\pi$
$541$	−11.3145	−0.486446	−0.243223	+	0.969970i	$0.578205\pi$
$542$	−40.4034	−1.73547
$543$	−12.6262	−0.541842
$544$	8.96086	0.384194
$545$	0	0
$546$	−28.0394	−1.19998
$547$	−13.2382	−0.566024	−0.283012	−	0.959116i	$-0.591334\pi$
$547$	−13.2382	−0.566024	−0.283012	+	0.959116i	$0.591334\pi$
$548$	−18.6774	−0.797859
$549$	−26.5420	−1.13279
$550$	0	0
$551$	19.6485	0.837054
$552$	−49.0074	−2.08589
$553$	−45.9448	−1.95377
$554$	−35.0240	−1.48803
$555$	0	0
$556$	−54.6294	−2.31680
$557$	−7.45070	−0.315696	−0.157848	−	0.987463i	$-0.550456\pi$
$557$	−7.45070	−0.315696	−0.157848	+	0.987463i	$0.550456\pi$
$558$	18.6517	0.789591
$559$	13.1612	0.556661
$560$	0	0
$561$	−36.8442	−1.55556
$562$	−73.3340	−3.09341
$563$	−30.6949	−1.29364	−0.646818	−	0.762644i	$-0.723901\pi$
$563$	−30.6949	−1.29364	−0.646818	+	0.762644i	$0.723901\pi$
$564$	−21.7377	−0.915321
$565$	0	0
$566$	25.5473	1.07383
$567$	−0.904700	−0.0379938
$568$	−20.2276	−0.848733
$569$	39.3108	1.64800	0.823998	−	0.566593i	$-0.191739\pi$
$569$	39.3108	1.64800	0.823998	+	0.566593i	$0.191739\pi$
$570$	0	0
$571$	−14.4259	−0.603706	−0.301853	−	0.953354i	$-0.597605\pi$
$571$	−14.4259	−0.603706	−0.301853	+	0.953354i	$0.597605\pi$
$572$	−51.8473	−2.16785
$573$	5.02503	0.209924
$574$	−64.1120	−2.67598
$575$	0	0
$576$	12.4163	0.517345
$577$	−27.9477	−1.16348	−0.581738	−	0.813376i	$-0.697627\pi$
$577$	−27.9477	−1.16348	−0.581738	+	0.813376i	$0.697627\pi$
$578$	−114.370	−4.75717
$579$	−7.05293	−0.293110
$580$	0	0
$581$	42.0507	1.74456
$582$	4.33338	0.179625
$583$	−33.2144	−1.37560
$584$	−33.8988	−1.40274
$585$	0	0
$586$	1.39030	0.0574327
$587$	−47.6456	−1.96654	−0.983272	−	0.182141i	$-0.941697\pi$
$587$	−47.6456	−1.96654	−0.983272	+	0.182141i	$0.941697\pi$
$588$	−30.6733	−1.26495
$589$	8.98074	0.370045
$590$	0	0
$591$	−20.5076	−0.843568
$592$	−11.6733	−0.479772
$593$	16.8267	0.690989	0.345494	−	0.938421i	$-0.387711\pi$
$593$	16.8267	0.690989	0.345494	+	0.938421i	$0.387711\pi$
$594$	55.9927	2.29741
$595$	0	0
$596$	−19.9045	−0.815321
$597$	14.9880	0.613416
$598$	63.2137	2.58500
$599$	3.49609	0.142846	0.0714231	−	0.997446i	$-0.477246\pi$
$599$	3.49609	0.142846	0.0714231	+	0.997446i	$0.477246\pi$
$600$	0	0
$601$	−39.2751	−1.60206	−0.801032	−	0.598621i	$-0.795716\pi$
$601$	−39.2751	−1.60206	−0.801032	+	0.598621i	$0.795716\pi$
$602$	42.5575	1.73451
$603$	3.09672	0.126108
$604$	−77.8955	−3.16952
$605$	0	0
$606$	−36.1092	−1.46684
$607$	22.4708	0.912063	0.456032	−	0.889964i	$-0.349270\pi$
$607$	22.4708	0.912063	0.456032	+	0.889964i	$0.349270\pi$
$608$	−2.53417	−0.102774
$609$	34.5363	1.39948
$610$	0	0
$611$	14.3976	0.582463
$612$	61.7938	2.49787
$613$	−29.8564	−1.20589	−0.602943	−	0.797784i	$-0.706006\pi$
$613$	−29.8564	−1.20589	−0.602943	+	0.797784i	$0.706006\pi$
$614$	−50.3076	−2.03025
$615$	0	0
$616$	−86.0860	−3.46850
$617$	−32.5219	−1.30928	−0.654641	−	0.755940i	$-0.727180\pi$
$617$	−32.5219	−1.30928	−0.654641	+	0.755940i	$0.727180\pi$
$618$	41.8127	1.68195
$619$	−45.1637	−1.81528	−0.907641	−	0.419748i	$-0.862119\pi$
$619$	−45.1637	−1.81528	−0.907641	+	0.419748i	$0.862119\pi$
$620$	0	0
$621$	−45.9247	−1.84289
$622$	−35.4695	−1.42220
$623$	−23.9257	−0.958562
$624$	−14.1384	−0.565989
$625$	0	0
$626$	77.5071	3.09781
$627$	10.4197	0.416124
$628$	32.6378	1.30239
$629$	19.8504	0.791489
$630$	0	0
$631$	26.8493	1.06886	0.534428	−	0.845214i	$-0.320527\pi$
$631$	26.8493	1.06886	0.534428	+	0.845214i	$0.320527\pi$
$632$	−63.8880	−2.54133
$633$	18.0064	0.715691
$634$	−22.2436	−0.883406
$635$	0	0
$636$	−32.7232	−1.29756
$637$	20.3160	0.804947
$638$	94.9299	3.75831
$639$	−7.32592	−0.289809
$640$	0	0
$641$	0.458859	0.0181238	0.00906191	−	0.999959i	$-0.497115\pi$
$641$	0.458859	0.0181238	0.00906191	+	0.999959i	$0.497115\pi$
$642$	51.4191	2.02935
$643$	−24.0586	−0.948779	−0.474389	−	0.880315i	$-0.657331\pi$
$643$	−24.0586	−0.948779	−0.474389	+	0.880315i	$0.657331\pi$
$644$	137.506	5.41848
$645$	0	0
$646$	44.2291	1.74017
$647$	−5.58731	−0.219660	−0.109830	−	0.993950i	$-0.535031\pi$
$647$	−5.58731	−0.219660	−0.109830	+	0.993950i	$0.535031\pi$
$648$	−1.25802	−0.0494197
$649$	−13.2953	−0.521888
$650$	0	0
$651$	15.7855	0.618683
$652$	−60.0342	−2.35112
$653$	−19.9838	−0.782026	−0.391013	−	0.920385i	$-0.627875\pi$
$653$	−19.9838	−0.782026	−0.391013	+	0.920385i	$0.627875\pi$
$654$	−33.3883	−1.30559
$655$	0	0
$656$	−32.3274	−1.26217
$657$	−12.2772	−0.478980
$658$	46.5552	1.81491
$659$	−28.7150	−1.11858	−0.559289	−	0.828973i	$-0.688926\pi$
$659$	−28.7150	−1.11858	−0.559289	+	0.828973i	$0.688926\pi$
$660$	0	0
$661$	27.8498	1.08323	0.541615	−	0.840626i	$-0.317813\pi$
$661$	27.8498	1.08323	0.541615	+	0.840626i	$0.317813\pi$
$662$	4.61128	0.179223
$663$	24.0422	0.933724
$664$	58.4731	2.26920
$665$	0	0
$666$	−11.6591	−0.451780
$667$	−77.8606	−3.01478
$668$	−0.0786222	−0.00304198
$669$	20.3376	0.786296
$670$	0	0
$671$	−61.7448	−2.38363
$672$	−4.45434	−0.171830
$673$	32.4566	1.25111	0.625555	−	0.780180i	$-0.284872\pi$
$673$	32.4566	1.25111	0.625555	+	0.780180i	$0.284872\pi$
$674$	2.56675	0.0988675
$675$	0	0
$676$	−19.6089	−0.754187
$677$	−24.8009	−0.953175	−0.476587	−	0.879127i	$-0.658126\pi$
$677$	−24.8009	−0.953175	−0.476587	+	0.879127i	$0.658126\pi$
$678$	−22.9015	−0.879525
$679$	−6.24328	−0.239595
$680$	0	0
$681$	10.5558	0.404500
$682$	43.3896	1.66147
$683$	−11.5259	−0.441028	−0.220514	−	0.975384i	$-0.570773\pi$
$683$	−11.5259	−0.441028	−0.220514	+	0.975384i	$0.570773\pi$
$684$	−17.4756	−0.668196
$685$	0	0
$686$	0.757902	0.0289368
$687$	−16.9234	−0.645667
$688$	21.4589	0.818112
$689$	21.6737	0.825700
$690$	0	0
$691$	−35.1308	−1.33644	−0.668219	−	0.743965i	$-0.732943\pi$
$691$	−35.1308	−1.33644	−0.668219	+	0.743965i	$0.732943\pi$
$692$	6.47904	0.246296
$693$	−31.1781	−1.18436
$694$	33.3895	1.26745
$695$	0	0
$696$	48.0241	1.82035
$697$	54.9725	2.08223
$698$	−56.9525	−2.15568
$699$	−31.3719	−1.18660
$700$	0	0
$701$	47.5840	1.79722	0.898612	−	0.438745i	$-0.144577\pi$
$701$	47.5840	1.79722	0.898612	+	0.438745i	$0.144577\pi$
$702$	−36.5374	−1.37901
$703$	−5.61380	−0.211728
$704$	28.8840	1.08861
$705$	0	0
$706$	31.6220	1.19011
$707$	52.0240	1.95656
$708$	−13.0987	−0.492280
$709$	20.2624	0.760970	0.380485	−	0.924787i	$-0.375757\pi$
$709$	20.2624	0.760970	0.380485	+	0.924787i	$0.375757\pi$
$710$	0	0
$711$	−23.1385	−0.867763
$712$	−33.2696	−1.24683
$713$	−35.5878	−1.33277
$714$	77.7418	2.90941
$715$	0	0
$716$	16.9683	0.634136
$717$	11.8529	0.442655
$718$	20.3312	0.758754
$719$	35.6504	1.32953	0.664767	−	0.747051i	$-0.268531\pi$
$719$	35.6504	1.32953	0.664767	+	0.747051i	$0.268531\pi$
$720$	0	0
$721$	−60.2412	−2.24350
$722$	34.4601	1.28247
$723$	−1.05364	−0.0391852
$724$	49.2623	1.83082
$725$	0	0
$726$	21.6913	0.805039
$727$	−24.6090	−0.912697	−0.456348	−	0.889801i	$-0.650843\pi$
$727$	−24.6090	−0.912697	−0.456348	+	0.889801i	$0.650843\pi$
$728$	56.1744	2.08196
$729$	15.8298	0.586288
$730$	0	0
$731$	−36.4907	−1.34966
$732$	−60.8317	−2.24840
$733$	41.8210	1.54469	0.772346	−	0.635202i	$-0.219083\pi$
$733$	41.8210	1.54469	0.772346	+	0.635202i	$0.219083\pi$
$734$	−64.3108	−2.37376
$735$	0	0
$736$	10.0421	0.370157
$737$	7.20392	0.265360
$738$	−32.2879	−1.18853
$739$	−14.4058	−0.529927	−0.264964	−	0.964258i	$-0.585360\pi$
$739$	−14.4058	−0.529927	−0.264964	+	0.964258i	$0.585360\pi$
$740$	0	0
$741$	−6.79926	−0.249777
$742$	70.0828	2.57282
$743$	−8.08740	−0.296698	−0.148349	−	0.988935i	$-0.547396\pi$
$743$	−8.08740	−0.296698	−0.148349	+	0.988935i	$0.547396\pi$
$744$	21.9504	0.804740
$745$	0	0
$746$	−38.3019	−1.40233
$747$	21.1774	0.774841
$748$	143.751	5.25607
$749$	−74.0816	−2.70688
$750$	0	0
$751$	10.1789	0.371432	0.185716	−	0.982603i	$-0.440540\pi$
$751$	10.1789	0.371432	0.185716	+	0.982603i	$0.440540\pi$
$752$	23.4747	0.856033
$753$	7.05759	0.257193
$754$	−61.9453	−2.25592
$755$	0	0
$756$	−79.4780	−2.89059
$757$	8.78041	0.319129	0.159565	−	0.987187i	$-0.448991\pi$
$757$	8.78041	0.319129	0.159565	+	0.987187i	$0.448991\pi$
$758$	2.46989	0.0897103
$759$	−41.2900	−1.49873
$760$	0	0
$761$	18.5955	0.674088	0.337044	−	0.941489i	$-0.390573\pi$
$761$	18.5955	0.674088	0.337044	+	0.941489i	$0.390573\pi$
$762$	−25.0685	−0.908137
$763$	48.1039	1.74148
$764$	−19.6056	−0.709307
$765$	0	0
$766$	−83.2776	−3.00894
$767$	8.67571	0.313262
$768$	34.3255	1.23862
$769$	29.6390	1.06881	0.534406	−	0.845228i	$-0.320536\pi$
$769$	29.6390	1.06881	0.534406	+	0.845228i	$0.320536\pi$
$770$	0	0
$771$	−22.6459	−0.815572
$772$	27.5177	0.990382
$773$	18.9915	0.683075	0.341538	−	0.939868i	$-0.389052\pi$
$773$	18.9915	0.683075	0.341538	+	0.939868i	$0.389052\pi$
$774$	21.4326	0.770380
$775$	0	0
$776$	−8.68153	−0.311649
$777$	−9.86742	−0.353992
$778$	−62.0218	−2.22359
$779$	−15.5465	−0.557010
$780$	0	0
$781$	−17.0423	−0.609822
$782$	−175.265	−6.26748
$783$	45.0033	1.60829
$784$	33.1244	1.18301
$785$	0	0
$786$	−15.9166	−0.567728
$787$	−15.4691	−0.551413	−0.275707	−	0.961242i	$-0.588912\pi$
$787$	−15.4691	−0.551413	−0.275707	+	0.961242i	$0.588912\pi$
$788$	80.0122	2.85032
$789$	−0.817585	−0.0291068
$790$	0	0
$791$	32.9951	1.17317
$792$	−43.3543	−1.54053
$793$	40.2908	1.43077
$794$	−87.4622	−3.10392
$795$	0	0
$796$	−58.4769	−2.07266
$797$	−23.5611	−0.834578	−0.417289	−	0.908774i	$-0.637020\pi$
$797$	−23.5611	−0.834578	−0.417289	+	0.908774i	$0.637020\pi$
$798$	−21.9857	−0.778287
$799$	−39.9185	−1.41222
$800$	0	0
$801$	−12.0494	−0.425743
$802$	64.7627	2.28685
$803$	−28.5606	−1.00788
$804$	7.09738	0.250305
$805$	0	0
$806$	−28.3134	−0.997295
$807$	20.2221	0.711851
$808$	72.3414	2.54496
$809$	44.6072	1.56831	0.784153	−	0.620567i	$-0.213098\pi$
$809$	44.6072	1.56831	0.784153	+	0.620567i	$0.213098\pi$
$810$	0	0
$811$	−36.4075	−1.27844	−0.639221	−	0.769023i	$-0.720743\pi$
$811$	−36.4075	−1.27844	−0.639221	+	0.769023i	$0.720743\pi$
$812$	−134.747	−4.72868
$813$	−17.2209	−0.603965
$814$	−27.1226	−0.950645
$815$	0	0
$816$	39.2000	1.37227
$817$	10.3197	0.361042
$818$	27.0374	0.945341
$819$	20.3449	0.710907
$820$	0	0
$821$	4.96999	0.173454	0.0867269	−	0.996232i	$-0.472359\pi$
$821$	4.96999	0.173454	0.0867269	+	0.996232i	$0.472359\pi$
$822$	−11.8338	−0.412752
$823$	−31.2791	−1.09032	−0.545160	−	0.838332i	$-0.683531\pi$
$823$	−31.2791	−1.09032	−0.545160	+	0.838332i	$0.683531\pi$
$824$	−83.7678	−2.91819
$825$	0	0
$826$	28.0533	0.976100
$827$	35.5153	1.23499	0.617494	−	0.786576i	$-0.288148\pi$
$827$	35.5153	1.23499	0.617494	+	0.786576i	$0.288148\pi$
$828$	69.2501	2.40661
$829$	16.7932	0.583252	0.291626	−	0.956532i	$-0.405804\pi$
$829$	16.7932	0.583252	0.291626	+	0.956532i	$0.405804\pi$
$830$	0	0
$831$	−14.9281	−0.517850
$832$	−18.8479	−0.653434
$833$	−56.3278	−1.95164
$834$	−34.6127	−1.19854
$835$	0	0
$836$	−40.6535	−1.40603
$837$	20.5696	0.710991
$838$	−1.12876	−0.0389924
$839$	12.9224	0.446132	0.223066	−	0.974803i	$-0.428394\pi$
$839$	12.9224	0.446132	0.223066	+	0.974803i	$0.428394\pi$
$840$	0	0
$841$	47.2984	1.63098
$842$	16.9864	0.585389
$843$	−31.2568	−1.07654
$844$	−70.2538	−2.41823
$845$	0	0
$846$	23.4460	0.806089
$847$	−31.2515	−1.07381
$848$	35.3381	1.21351
$849$	10.8889	0.373706
$850$	0	0
$851$	22.2457	0.762572
$852$	−16.7903	−0.575225
$853$	15.3855	0.526789	0.263395	−	0.964688i	$-0.415158\pi$
$853$	15.3855	0.526789	0.263395	+	0.964688i	$0.415158\pi$
$854$	130.282	4.45817
$855$	0	0
$856$	−103.013	−3.52093
$857$	32.0642	1.09529	0.547646	−	0.836710i	$-0.315524\pi$
$857$	32.0642	1.09529	0.547646	+	0.836710i	$0.315524\pi$
$858$	−32.8500	−1.12148
$859$	−2.34626	−0.0800534	−0.0400267	−	0.999199i	$-0.512744\pi$
$859$	−2.34626	−0.0800534	−0.0400267	+	0.999199i	$0.512744\pi$
$860$	0	0
$861$	−27.3262	−0.931273
$862$	54.8260	1.86738
$863$	−0.621430	−0.0211537	−0.0105769	−	0.999944i	$-0.503367\pi$
$863$	−0.621430	−0.0211537	−0.0105769	+	0.999944i	$0.503367\pi$
$864$	−5.80432	−0.197467
$865$	0	0
$866$	48.2008	1.63793
$867$	−48.7474	−1.65555
$868$	−61.5887	−2.09046
$869$	−53.8273	−1.82597
$870$	0	0
$871$	−4.70083	−0.159281
$872$	66.8904	2.26519
$873$	−3.14422	−0.106416
$874$	49.5659	1.67659
$875$	0	0
$876$	−28.1382	−0.950702
$877$	3.50044	0.118201	0.0591007	−	0.998252i	$-0.481177\pi$
$877$	3.50044	0.118201	0.0591007	+	0.998252i	$0.481177\pi$
$878$	10.4582	0.352948
$879$	0.592581	0.0199872
$880$	0	0
$881$	−6.97230	−0.234903	−0.117451	−	0.993079i	$-0.537472\pi$
$881$	−6.97230	−0.234903	−0.117451	+	0.993079i	$0.537472\pi$
$882$	33.0839	1.11399
$883$	44.3174	1.49140	0.745700	−	0.666282i	$-0.232115\pi$
$883$	44.3174	1.49140	0.745700	+	0.666282i	$0.232115\pi$
$884$	−93.8031	−3.15494
$885$	0	0
$886$	75.2746	2.52890
$887$	1.28766	0.0432355	0.0216177	−	0.999766i	$-0.493118\pi$
$887$	1.28766	0.0432355	0.0216177	+	0.999766i	$0.493118\pi$
$888$	−13.7210	−0.460448
$889$	36.1172	1.21133
$890$	0	0
$891$	−1.05992	−0.0355085
$892$	−79.3490	−2.65680
$893$	11.2891	0.377777
$894$	−12.6113	−0.421786
$895$	0	0
$896$	−69.4008	−2.31852
$897$	26.9433	0.899610
$898$	−3.68897	−0.123103
$899$	34.8737	1.16310
$900$	0	0
$901$	−60.0921	−2.00196
$902$	−75.1114	−2.50093
$903$	18.1391	0.603631
$904$	45.8809	1.52598
$905$	0	0
$906$	−49.3539	−1.63967
$907$	6.97874	0.231725	0.115863	−	0.993265i	$-0.463037\pi$
$907$	6.97874	0.231725	0.115863	+	0.993265i	$0.463037\pi$
$908$	−41.1845	−1.36676
$909$	26.2001	0.869004
$910$	0	0
$911$	14.3584	0.475714	0.237857	−	0.971300i	$-0.423555\pi$
$911$	14.3584	0.475714	0.237857	+	0.971300i	$0.423555\pi$
$912$	−11.0859	−0.367092
$913$	49.2651	1.63044
$914$	57.5423	1.90333
$915$	0	0
$916$	66.0281	2.18163
$917$	22.9317	0.757273
$918$	101.303	3.34350
$919$	36.2393	1.19543	0.597713	−	0.801710i	$-0.296076\pi$
$919$	36.2393	1.19543	0.597713	+	0.801710i	$0.296076\pi$
$920$	0	0
$921$	−21.4424	−0.706550
$922$	−21.8019	−0.718006
$923$	11.1207	0.366044
$924$	−71.4571	−2.35076
$925$	0	0
$926$	−82.1919	−2.70099
$927$	−30.3385	−0.996446
$928$	−9.84062	−0.323034
$929$	−38.5533	−1.26489	−0.632446	−	0.774604i	$-0.717949\pi$
$929$	−38.5533	−1.26489	−0.632446	+	0.774604i	$0.717949\pi$
$930$	0	0
$931$	15.9298	0.522077
$932$	122.401	4.00936
$933$	−15.1180	−0.494941
$934$	46.3148	1.51547
$935$	0	0
$936$	28.2903	0.924698
$937$	14.5843	0.476449	0.238225	−	0.971210i	$-0.423435\pi$
$937$	14.5843	0.476449	0.238225	+	0.971210i	$0.423435\pi$
$938$	−15.2003	−0.496309
$939$	33.0355	1.07807
$940$	0	0
$941$	−57.4350	−1.87233	−0.936164	−	0.351563i	$-0.885650\pi$
$941$	−57.4350	−1.87233	−0.936164	+	0.351563i	$0.885650\pi$
$942$	20.6790	0.673759
$943$	61.6056	2.00616
$944$	14.1454	0.460394
$945$	0	0
$946$	49.8588	1.62105
$947$	13.6526	0.443651	0.221825	−	0.975086i	$-0.428798\pi$
$947$	13.6526	0.443651	0.221825	+	0.975086i	$0.428798\pi$
$948$	−53.0313	−1.72238
$949$	18.6368	0.604977
$950$	0	0
$951$	−9.48079	−0.307436
$952$	−155.748	−5.04783
$953$	15.7192	0.509196	0.254598	−	0.967047i	$-0.418057\pi$
$953$	15.7192	0.509196	0.254598	+	0.967047i	$0.418057\pi$
$954$	35.2949	1.14271
$955$	0	0
$956$	−46.2453	−1.49568
$957$	40.4616	1.30794
$958$	−12.5970	−0.406991
$959$	17.0495	0.550556
$960$	0	0
$961$	−15.0603	−0.485815
$962$	17.6985	0.570622
$963$	−37.3087	−1.20226
$964$	4.11086	0.132402
$965$	0	0
$966$	87.1223	2.80312
$967$	−34.1214	−1.09727	−0.548635	−	0.836062i	$-0.684852\pi$
$967$	−34.1214	−1.09727	−0.548635	+	0.836062i	$0.684852\pi$
$968$	−43.4565	−1.39674
$969$	18.8516	0.605599
$970$	0	0
$971$	−56.9283	−1.82692	−0.913458	−	0.406932i	$-0.866599\pi$
$971$	−56.9283	−1.82692	−0.913458	+	0.406932i	$0.866599\pi$
$972$	−64.5832	−2.07151
$973$	49.8680	1.59869
$974$	−34.5348	−1.10657
$975$	0	0
$976$	65.6926	2.10277
$977$	−12.6700	−0.405349	−0.202674	−	0.979246i	$-0.564963\pi$
$977$	−12.6700	−0.405349	−0.202674	+	0.979246i	$0.564963\pi$
$978$	−38.0372	−1.21629
$979$	−28.0305	−0.895858
$980$	0	0
$981$	24.2259	0.773474
$982$	38.4514	1.22703
$983$	−19.2412	−0.613700	−0.306850	−	0.951758i	$-0.599275\pi$
$983$	−19.2412	−0.613700	−0.306850	+	0.951758i	$0.599275\pi$
$984$	−37.9981	−1.21134
$985$	0	0
$986$	171.749	5.46960
$987$	19.8430	0.631610
$988$	26.5280	0.843967
$989$	−40.8938	−1.30035
$990$	0	0
$991$	30.3728	0.964824	0.482412	−	0.875944i	$-0.339761\pi$
$991$	30.3728	0.964824	0.482412	+	0.875944i	$0.339761\pi$
$992$	−4.49785	−0.142807
$993$	1.96545	0.0623716
$994$	35.9595	1.14056
$995$	0	0
$996$	48.5365	1.53794
$997$	20.3383	0.644120	0.322060	−	0.946719i	$-0.395625\pi$
$997$	20.3383	0.644120	0.322060	+	0.946719i	$0.395625\pi$
$998$	−78.9637	−2.49955
$999$	−12.8579	−0.406807

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.m.1.5	✓	40
5.4	even	2		6025.2.a.n.1.36	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.m.1.5	✓	40	1.1	even	1	trivial
6025.2.a.n.1.36	yes	40	5.4	even	2

Overview	Random
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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:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-2.47202 q^{2} -1.05364 q^{3} +4.11086 q^{4} +2.60461 q^{6} -3.75256 q^{7} -5.21808 q^{8} -1.88985 q^{9} +O(q^{10})\)	\(q-2.47202 q^{2} -1.05364 q^{3} +4.11086 q^{4} +2.60461 q^{6} -3.75256 q^{7} -5.21808 q^{8} -1.88985 q^{9} -4.39637 q^{11} -4.33135 q^{12} +2.86880 q^{13} +9.27639 q^{14} +4.67746 q^{16} -7.95399 q^{17} +4.67174 q^{18} +2.24943 q^{19} +3.95383 q^{21} +10.8679 q^{22} -8.91374 q^{23} +5.49796 q^{24} -7.09171 q^{26} +5.15212 q^{27} -15.4263 q^{28} +8.73490 q^{29} +3.99246 q^{31} -1.12659 q^{32} +4.63217 q^{33} +19.6624 q^{34} -7.76892 q^{36} -2.49566 q^{37} -5.56061 q^{38} -3.02267 q^{39} -6.91131 q^{41} -9.77394 q^{42} +4.58772 q^{43} -18.0729 q^{44} +22.0349 q^{46} +5.01868 q^{47} -4.92834 q^{48} +7.08170 q^{49} +8.38061 q^{51} +11.7932 q^{52} +7.55497 q^{53} -12.7361 q^{54} +19.5812 q^{56} -2.37008 q^{57} -21.5928 q^{58} +3.02417 q^{59} +14.0445 q^{61} -9.86942 q^{62} +7.09178 q^{63} -6.56998 q^{64} -11.4508 q^{66} -1.63861 q^{67} -32.6977 q^{68} +9.39184 q^{69} +3.87645 q^{71} +9.86140 q^{72} +6.49640 q^{73} +6.16931 q^{74} +9.24708 q^{76} +16.4976 q^{77} +7.47208 q^{78} +12.2436 q^{79} +0.241089 q^{81} +17.0849 q^{82} -11.2059 q^{83} +16.2537 q^{84} -11.3409 q^{86} -9.20340 q^{87} +22.9406 q^{88} +6.37583 q^{89} -10.7653 q^{91} -36.6432 q^{92} -4.20660 q^{93} -12.4063 q^{94} +1.18701 q^{96} +1.66374 q^{97} -17.5061 q^{98} +8.30848 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 9 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 20 q^{7} - 27 q^{8} + 38 q^{9}+O(q^{10}) \) 40 * q - 9 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 20 * q^7 - 27 * q^8 + 38 * q^9	\( 40 q - 9 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 20 q^{7} - 27 q^{8} + 38 q^{9} + q^{11} - 26 q^{12} - 11 q^{13} - q^{14} + 43 q^{16} - 20 q^{17} - 18 q^{18} + 2 q^{21} - 23 q^{22} - 79 q^{23} - 2 q^{24} + 2 q^{26} - 26 q^{27} - 30 q^{28} + 2 q^{29} + q^{31} - 68 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 16 q^{37} - 45 q^{38} - 2 q^{39} - 2 q^{41} - 19 q^{42} - 25 q^{43} + 3 q^{44} + 14 q^{46} - 88 q^{47} - 75 q^{48} + 40 q^{49} - 10 q^{51} - 18 q^{52} - 34 q^{53} + 4 q^{54} - 15 q^{56} - 51 q^{57} - 53 q^{58} + q^{59} + 9 q^{61} - 39 q^{62} - 110 q^{63} + 17 q^{64} + 26 q^{66} - 30 q^{67} - 44 q^{68} - 7 q^{69} + 5 q^{71} - 18 q^{72} - 23 q^{73} - 18 q^{74} + 43 q^{76} - 30 q^{77} - 46 q^{78} + 5 q^{79} + 44 q^{81} - 5 q^{82} - 65 q^{83} - 65 q^{84} + 40 q^{86} - 33 q^{87} - 71 q^{88} - 9 q^{89} + q^{91} - 117 q^{92} - 68 q^{93} - 72 q^{94} + 83 q^{96} + 8 q^{97} - 76 q^{98} - 40 q^{99}+O(q^{100}) \) 40 * q - 9 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 20 * q^7 - 27 * q^8 + 38 * q^9 + q^11 - 26 * q^12 - 11 * q^13 - q^14 + 43 * q^16 - 20 * q^17 - 18 * q^18 + 2 * q^21 - 23 * q^22 - 79 * q^23 - 2 * q^24 + 2 * q^26 - 26 * q^27 - 30 * q^28 + 2 * q^29 + q^31 - 68 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 16 * q^37 - 45 * q^38 - 2 * q^39 - 2 * q^41 - 19 * q^42 - 25 * q^43 + 3 * q^44 + 14 * q^46 - 88 * q^47 - 75 * q^48 + 40 * q^49 - 10 * q^51 - 18 * q^52 - 34 * q^53 + 4 * q^54 - 15 * q^56 - 51 * q^57 - 53 * q^58 + q^59 + 9 * q^61 - 39 * q^62 - 110 * q^63 + 17 * q^64 + 26 * q^66 - 30 * q^67 - 44 * q^68 - 7 * q^69 + 5 * q^71 - 18 * q^72 - 23 * q^73 - 18 * q^74 + 43 * q^76 - 30 * q^77 - 46 * q^78 + 5 * q^79 + 44 * q^81 - 5 * q^82 - 65 * q^83 - 65 * q^84 + 40 * q^86 - 33 * q^87 - 71 * q^88 - 9 * q^89 + q^91 - 117 * q^92 - 68 * q^93 - 72 * q^94 + 83 * q^96 + 8 * q^97 - 76 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

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Database

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