LMFDB - Embedded newform 2900.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2900,2,Mod(1,2900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2900, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2900.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2900 = 2^{2} \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2900.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:	$23.1566165862$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.3076177.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 11x^{3} - x^{2} + 29x + 3 $ x^5 - 11x^3 - x^2 + 29x + 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.67880$ of defining polynomial
Character	$\chi$	$=$	2900.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67880 q^{3} +1.65303 q^{7} +4.17598 q^{9} +4.63554 q^{11} -3.45956 q^{13} -1.49718 q^{17} -5.51965 q^{19} -4.42815 q^{21} -6.60977 q^{23} -3.15021 q^{27} +1.00000 q^{29} +0.464244 q^{31} -12.4177 q^{33} +4.53358 q^{37} +9.26748 q^{39} +7.43878 q^{41} +10.5890 q^{43} -5.54074 q^{47} -4.26748 q^{49} +4.01064 q^{51} -11.9463 q^{53} +14.7861 q^{57} +3.91553 q^{59} -2.71641 q^{61} +6.90302 q^{63} +7.17033 q^{67} +17.7063 q^{69} +4.81152 q^{71} -3.54609 q^{73} +7.66270 q^{77} +1.74783 q^{79} -4.08915 q^{81} +6.23607 q^{83} -2.67880 q^{87} -2.66696 q^{89} -5.71877 q^{91} -1.24362 q^{93} -14.9220 q^{97} +19.3579 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 4 q^{7} + 7 q^{9} - 8 q^{13} - 7 q^{17} + 2 q^{19} - 13 q^{21} - 11 q^{23} - 3 q^{27} + 5 q^{29} - 7 q^{31} - 15 q^{33} - 18 q^{37} + 12 q^{39} - 11 q^{41} - 8 q^{43} + 3 q^{47} + 13 q^{49} - 19 q^{51}+ \cdots + 30 q^{99}+O(q^{100}) $ 5 * q - 4 * q^7 + 7 * q^9 - 8 * q^13 - 7 * q^17 + 2 * q^19 - 13 * q^21 - 11 * q^23 - 3 * q^27 + 5 * q^29 - 7 * q^31 - 15 * q^33 - 18 * q^37 + 12 * q^39 - 11 * q^41 - 8 * q^43 + 3 * q^47 + 13 * q^49 - 19 * q^51 - 12 * q^53 - 2 * q^57 + 13 * q^59 - 9 * q^61 - 23 * q^63 + 21 * q^67 + 6 * q^69 - 13 * q^71 - 28 * q^73 - 14 * q^77 + 4 * q^79 - 27 * q^81 - 3 * q^83 + 10 * q^89 + 3 * q^91 - 29 * q^93 - 37 * q^97 + 30 * q^99

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 $

$2$	0	0
$2$	0	0
$3$	−2.67880	−1.54661	−0.773303	−	0.634036i	$-0.781397\pi$
$3$	−2.67880	−1.54661	−0.773303	+	0.634036i	$0.781397\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	1.65303	0.624788	0.312394	−	0.949953i	$-0.398869\pi$
$7$	1.65303	0.624788	0.312394	+	0.949953i	$0.398869\pi$
$8$	0	0
$9$	4.17598	1.39199
$10$	0	0
$11$	4.63554	1.39767	0.698834	−	0.715284i	$-0.253703\pi$
$11$	4.63554	1.39767	0.698834	+	0.715284i	$0.253703\pi$
$12$	0	0
$13$	−3.45956	−0.959510	−0.479755	−	0.877402i	$-0.659275\pi$
$13$	−3.45956	−0.959510	−0.479755	+	0.877402i	$0.659275\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−1.49718	−0.363118	−0.181559	−	0.983380i	$-0.558114\pi$
$17$	−1.49718	−0.363118	−0.181559	+	0.983380i	$0.558114\pi$
$18$	0	0
$19$	−5.51965	−1.26630	−0.633148	−	0.774031i	$-0.718237\pi$
$19$	−5.51965	−1.26630	−0.633148	+	0.774031i	$0.718237\pi$
$20$	0	0
$21$	−4.42815	−0.966301
$22$	0	0
$23$	−6.60977	−1.37823	−0.689116	−	0.724651i	$-0.742001\pi$
$23$	−6.60977	−1.37823	−0.689116	+	0.724651i	$0.742001\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−3.15021	−0.606258
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	0.464244	0.0833807	0.0416904	−	0.999131i	$-0.486726\pi$
$31$	0.464244	0.0833807	0.0416904	+	0.999131i	$0.486726\pi$
$32$	0	0
$33$	−12.4177	−2.16164
$34$	0	0
$35$	0	0
$36$	0	0
$37$	4.53358	0.745316	0.372658	−	0.927969i	$-0.378446\pi$
$37$	4.53358	0.745316	0.372658	+	0.927969i	$0.378446\pi$
$38$	0	0
$39$	9.26748	1.48399
$40$	0	0
$41$	7.43878	1.16174	0.580871	−	0.813996i	$-0.302712\pi$
$41$	7.43878	1.16174	0.580871	+	0.813996i	$0.302712\pi$
$42$	0	0
$43$	10.5890	1.61481	0.807403	−	0.590001i	$-0.200873\pi$
$43$	10.5890	1.61481	0.807403	+	0.590001i	$0.200873\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−5.54074	−0.808200	−0.404100	−	0.914715i	$-0.632415\pi$
$47$	−5.54074	−0.808200	−0.404100	+	0.914715i	$0.632415\pi$
$48$	0	0
$49$	−4.26748	−0.609641
$50$	0	0
$51$	4.01064	0.561601
$52$	0	0
$53$	−11.9463	−1.64095	−0.820474	−	0.571683i	$-0.806291\pi$
$53$	−11.9463	−1.64095	−0.820474	+	0.571683i	$0.806291\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	14.7861	1.95846
$58$	0	0
$59$	3.91553	0.509759	0.254879	−	0.966973i	$-0.417964\pi$
$59$	3.91553	0.509759	0.254879	+	0.966973i	$0.417964\pi$
$60$	0	0
$61$	−2.71641	−0.347801	−0.173901	−	0.984763i	$-0.555637\pi$
$61$	−2.71641	−0.347801	−0.173901	+	0.984763i	$0.555637\pi$
$62$	0	0
$63$	6.90302	0.869699
$64$	0	0
$65$	0	0
$66$	0	0
$67$	7.17033	0.875995	0.437997	−	0.898976i	$-0.355688\pi$
$67$	7.17033	0.875995	0.437997	+	0.898976i	$0.355688\pi$
$68$	0	0
$69$	17.7063	2.13158
$70$	0	0
$71$	4.81152	0.571022	0.285511	−	0.958375i	$-0.407837\pi$
$71$	4.81152	0.571022	0.285511	+	0.958375i	$0.407837\pi$
$72$	0	0
$73$	−3.54609	−0.415038	−0.207519	−	0.978231i	$-0.566539\pi$
$73$	−3.54609	−0.415038	−0.207519	+	0.978231i	$0.566539\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	7.66270	0.873245
$78$	0	0
$79$	1.74783	0.196646	0.0983232	−	0.995155i	$-0.468652\pi$
$79$	1.74783	0.196646	0.0983232	+	0.995155i	$0.468652\pi$
$80$	0	0
$81$	−4.08915	−0.454350
$82$	0	0
$83$	6.23607	0.684497	0.342249	−	0.939609i	$-0.388812\pi$
$83$	6.23607	0.684497	0.342249	+	0.939609i	$0.388812\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−2.67880	−0.287198
$88$	0	0
$89$	−2.66696	−0.282697	−0.141349	−	0.989960i	$-0.545144\pi$
$89$	−2.66696	−0.282697	−0.141349	+	0.989960i	$0.545144\pi$
$90$	0	0
$91$	−5.71877	−0.599490
$92$	0	0
$93$	−1.24362	−0.128957
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−14.9220	−1.51510	−0.757551	−	0.652776i	$-0.773604\pi$
$97$	−14.9220	−1.51510	−0.757551	+	0.652776i	$0.773604\pi$
$98$	0	0
$99$	19.3579	1.94554
$100$	0	0
$101$	−15.3265	−1.52504	−0.762521	−	0.646963i	$-0.776039\pi$
$101$	−15.3265	−1.52504	−0.762521	+	0.646963i	$0.776039\pi$
$102$	0	0
$103$	−12.2618	−1.20819	−0.604097	−	0.796911i	$-0.706466\pi$
$103$	−12.2618	−1.20819	−0.604097	+	0.796911i	$0.706466\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	5.73750	0.554665	0.277333	−	0.960774i	$-0.410550\pi$
$107$	5.73750	0.554665	0.277333	+	0.960774i	$0.410550\pi$
$108$	0	0
$109$	12.4341	1.19097	0.595485	−	0.803366i	$-0.296960\pi$
$109$	12.4341	1.19097	0.595485	+	0.803366i	$0.296960\pi$
$110$	0	0
$111$	−12.1446	−1.15271
$112$	0	0
$113$	−8.15021	−0.766707	−0.383354	−	0.923602i	$-0.625231\pi$
$113$	−8.15021	−0.766707	−0.383354	+	0.923602i	$0.625231\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−14.4471	−1.33563
$118$	0	0
$119$	−2.47488	−0.226872
$120$	0	0
$121$	10.4882	0.953476
$122$	0	0
$123$	−19.9270	−1.79676
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−20.5184	−1.82072	−0.910359	−	0.413820i	$-0.864194\pi$
$127$	−20.5184	−1.82072	−0.910359	+	0.413820i	$0.864194\pi$
$128$	0	0
$129$	−28.3658	−2.49747
$130$	0	0
$131$	−11.3602	−0.992548	−0.496274	−	0.868166i	$-0.665299\pi$
$131$	−11.3602	−0.992548	−0.496274	+	0.868166i	$0.665299\pi$
$132$	0	0
$133$	−9.12416	−0.791165
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−14.0251	−1.19825	−0.599123	−	0.800657i	$-0.704484\pi$
$137$	−14.0251	−1.19825	−0.599123	+	0.800657i	$0.704484\pi$
$138$	0	0
$139$	12.4481	1.05584	0.527919	−	0.849295i	$-0.322973\pi$
$139$	12.4481	1.05584	0.527919	+	0.849295i	$0.322973\pi$
$140$	0	0
$141$	14.8425	1.24997
$142$	0	0
$143$	−16.0369	−1.34108
$144$	0	0
$145$	0	0
$146$	0	0
$147$	11.4317	0.942874
$148$	0	0
$149$	−16.6545	−1.36439	−0.682193	−	0.731172i	$-0.738974\pi$
$149$	−16.6545	−1.36439	−0.682193	+	0.731172i	$0.738974\pi$
$150$	0	0
$151$	−2.94227	−0.239438	−0.119719	−	0.992808i	$-0.538199\pi$
$151$	−2.94227	−0.239438	−0.119719	+	0.992808i	$0.538199\pi$
$152$	0	0
$153$	−6.25217	−0.505458
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−5.11380	−0.408126	−0.204063	−	0.978958i	$-0.565415\pi$
$157$	−5.11380	−0.408126	−0.204063	+	0.978958i	$0.565415\pi$
$158$	0	0
$159$	32.0017	2.53790
$160$	0	0
$161$	−10.9262	−0.861103
$162$	0	0
$163$	13.7096	1.07382	0.536908	−	0.843641i	$-0.319592\pi$
$163$	13.7096	1.07382	0.536908	+	0.843641i	$0.319592\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−4.46068	−0.345178	−0.172589	−	0.984994i	$-0.555213\pi$
$167$	−4.46068	−0.345178	−0.172589	+	0.984994i	$0.555213\pi$
$168$	0	0
$169$	−1.03142	−0.0793399
$170$	0	0
$171$	−23.0499	−1.76267
$172$	0	0
$173$	0.207939	0.0158093	0.00790464	−	0.999969i	$-0.497484\pi$
$173$	0.207939	0.0158093	0.00790464	+	0.999969i	$0.497484\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−10.4889	−0.788396
$178$	0	0
$179$	−5.65358	−0.422568	−0.211284	−	0.977425i	$-0.567765\pi$
$179$	−5.65358	−0.422568	−0.211284	+	0.977425i	$0.567765\pi$
$180$	0	0
$181$	−8.81620	−0.655303	−0.327651	−	0.944799i	$-0.606257\pi$
$181$	−8.81620	−0.655303	−0.327651	+	0.944799i	$0.606257\pi$
$182$	0	0
$183$	7.27673	0.537911
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−6.94022	−0.507519
$188$	0	0
$189$	−5.20740	−0.378782
$190$	0	0
$191$	2.38062	0.172256	0.0861279	−	0.996284i	$-0.472551\pi$
$191$	2.38062	0.172256	0.0861279	+	0.996284i	$0.472551\pi$
$192$	0	0
$193$	5.55935	0.400171	0.200085	−	0.979778i	$-0.435878\pi$
$193$	5.55935	0.400171	0.200085	+	0.979778i	$0.435878\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−7.66270	−0.545945	−0.272972	−	0.962022i	$-0.588007\pi$
$197$	−7.66270	−0.545945	−0.272972	+	0.962022i	$0.588007\pi$
$198$	0	0
$199$	−15.5700	−1.10373	−0.551863	−	0.833935i	$-0.686083\pi$
$199$	−15.5700	−1.10373	−0.551863	+	0.833935i	$0.686083\pi$
$200$	0	0
$201$	−19.2079	−1.35482
$202$	0	0
$203$	1.65303	0.116020
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−27.6023	−1.91849
$208$	0	0
$209$	−25.5866	−1.76986
$210$	0	0
$211$	−13.9899	−0.963101	−0.481551	−	0.876418i	$-0.659926\pi$
$211$	−13.9899	−0.963101	−0.481551	+	0.876418i	$0.659926\pi$
$212$	0	0
$213$	−12.8891	−0.883146
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0.767411	0.0520952
$218$	0	0
$219$	9.49926	0.641900
$220$	0	0
$221$	5.17957	0.348416
$222$	0	0
$223$	19.6784	1.31777	0.658883	−	0.752245i	$-0.271029\pi$
$223$	19.6784	1.31777	0.658883	+	0.752245i	$0.271029\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	13.1366	0.871906	0.435953	−	0.899969i	$-0.356411\pi$
$227$	13.1366	0.871906	0.435953	+	0.899969i	$0.356411\pi$
$228$	0	0
$229$	−25.8328	−1.70708	−0.853539	−	0.521028i	$-0.825549\pi$
$229$	−25.8328	−1.70708	−0.853539	+	0.521028i	$0.825549\pi$
$230$	0	0
$231$	−20.5268	−1.35057
$232$	0	0
$233$	23.3385	1.52895	0.764477	−	0.644651i	$-0.222997\pi$
$233$	23.3385	1.52895	0.764477	+	0.644651i	$0.222997\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−4.68209	−0.304135
$238$	0	0
$239$	20.9792	1.35703	0.678516	−	0.734585i	$-0.262623\pi$
$239$	20.9792	1.35703	0.678516	+	0.734585i	$0.262623\pi$
$240$	0	0
$241$	−13.2652	−0.854484	−0.427242	−	0.904137i	$-0.640515\pi$
$241$	−13.2652	−0.854484	−0.427242	+	0.904137i	$0.640515\pi$
$242$	0	0
$243$	20.4046	1.30896
$244$	0	0
$245$	0	0
$246$	0	0
$247$	19.0956	1.21502
$248$	0	0
$249$	−16.7052	−1.05865
$250$	0	0
$251$	17.8379	1.12592	0.562958	−	0.826485i	$-0.309663\pi$
$251$	17.8379	1.12592	0.562958	+	0.826485i	$0.309663\pi$
$252$	0	0
$253$	−30.6399	−1.92631
$254$	0	0
$255$	0	0
$256$	0	0
$257$	26.8238	1.67323	0.836613	−	0.547795i	$-0.184533\pi$
$257$	26.8238	1.67323	0.836613	+	0.547795i	$0.184533\pi$
$258$	0	0
$259$	7.49415	0.465664
$260$	0	0
$261$	4.17598	0.258486
$262$	0	0
$263$	−5.27700	−0.325394	−0.162697	−	0.986676i	$-0.552019\pi$
$263$	−5.27700	−0.325394	−0.162697	+	0.986676i	$0.552019\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	7.14425	0.437221
$268$	0	0
$269$	12.0629	0.735488	0.367744	−	0.929927i	$-0.380130\pi$
$269$	12.0629	0.735488	0.367744	+	0.929927i	$0.380130\pi$
$270$	0	0
$271$	−14.5432	−0.883439	−0.441720	−	0.897153i	$-0.645631\pi$
$271$	−14.5432	−0.883439	−0.441720	+	0.897153i	$0.645631\pi$
$272$	0	0
$273$	15.3195	0.927175
$274$	0	0
$275$	0	0
$276$	0	0
$277$	0.961419	0.0577661	0.0288830	−	0.999583i	$-0.490805\pi$
$277$	0.961419	0.0577661	0.0288830	+	0.999583i	$0.490805\pi$
$278$	0	0
$279$	1.93867	0.116065
$280$	0	0
$281$	−28.2563	−1.68563	−0.842813	−	0.538206i	$-0.819102\pi$
$281$	−28.2563	−1.68563	−0.842813	+	0.538206i	$0.819102\pi$
$282$	0	0
$283$	−1.94985	−0.115907	−0.0579533	−	0.998319i	$-0.518457\pi$
$283$	−1.94985	−0.115907	−0.0579533	+	0.998319i	$0.518457\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	12.2965	0.725842
$288$	0	0
$289$	−14.7585	−0.868145
$290$	0	0
$291$	39.9732	2.34327
$292$	0	0
$293$	−13.6367	−0.796662	−0.398331	−	0.917242i	$-0.630410\pi$
$293$	−13.6367	−0.796662	−0.398331	+	0.917242i	$0.630410\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−14.6029	−0.847347
$298$	0	0
$299$	22.8669	1.32243
$300$	0	0
$301$	17.5039	1.00891
$302$	0	0
$303$	41.0566	2.35864
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−9.05118	−0.516578	−0.258289	−	0.966068i	$-0.583159\pi$
$307$	−9.05118	−0.516578	−0.258289	+	0.966068i	$0.583159\pi$
$308$	0	0
$309$	32.8470	1.86860
$310$	0	0
$311$	−6.63427	−0.376195	−0.188097	−	0.982150i	$-0.560232\pi$
$311$	−6.63427	−0.376195	−0.188097	+	0.982150i	$0.560232\pi$
$312$	0	0
$313$	−17.0441	−0.963390	−0.481695	−	0.876339i	$-0.659979\pi$
$313$	−17.0441	−0.963390	−0.481695	+	0.876339i	$0.659979\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−5.63083	−0.316259	−0.158129	−	0.987418i	$-0.550546\pi$
$317$	−5.63083	−0.316259	−0.158129	+	0.987418i	$0.550546\pi$
$318$	0	0
$319$	4.63554	0.259540
$320$	0	0
$321$	−15.3696	−0.857849
$322$	0	0
$323$	8.26389	0.459815
$324$	0	0
$325$	0	0
$326$	0	0
$327$	−33.3085	−1.84196
$328$	0	0
$329$	−9.15902	−0.504953
$330$	0	0
$331$	−28.6212	−1.57316	−0.786581	−	0.617488i	$-0.788151\pi$
$331$	−28.6212	−1.57316	−0.786581	+	0.617488i	$0.788151\pi$
$332$	0	0
$333$	18.9321	1.03747
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−5.45530	−0.297169	−0.148585	−	0.988900i	$-0.547472\pi$
$337$	−5.45530	−0.297169	−0.148585	+	0.988900i	$0.547472\pi$
$338$	0	0
$339$	21.8328	1.18579
$340$	0	0
$341$	2.15202	0.116539
$342$	0	0
$343$	−18.6255	−1.00568
$344$	0	0
$345$	0	0
$346$	0	0
$347$	19.4174	1.04238	0.521191	−	0.853440i	$-0.325488\pi$
$347$	19.4174	1.04238	0.521191	+	0.853440i	$0.325488\pi$
$348$	0	0
$349$	−35.4679	−1.89855	−0.949277	−	0.314442i	$-0.898183\pi$
$349$	−35.4679	−1.89855	−0.949277	+	0.314442i	$0.898183\pi$
$350$	0	0
$351$	10.8983	0.581711
$352$	0	0
$353$	13.1256	0.698603	0.349301	−	0.937010i	$-0.386419\pi$
$353$	13.1256	0.698603	0.349301	+	0.937010i	$0.386419\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	6.62971	0.350881
$358$	0	0
$359$	−25.1317	−1.32640	−0.663199	−	0.748443i	$-0.730802\pi$
$359$	−25.1317	−1.32640	−0.663199	+	0.748443i	$0.730802\pi$
$360$	0	0
$361$	11.4666	0.603503
$362$	0	0
$363$	−28.0959	−1.47465
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−4.32437	−0.225730	−0.112865	−	0.993610i	$-0.536003\pi$
$367$	−4.32437	−0.225730	−0.112865	+	0.993610i	$0.536003\pi$
$368$	0	0
$369$	31.0642	1.61714
$370$	0	0
$371$	−19.7476	−1.02524
$372$	0	0
$373$	−21.6506	−1.12103	−0.560513	−	0.828145i	$-0.689396\pi$
$373$	−21.6506	−1.12103	−0.560513	+	0.828145i	$0.689396\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−3.45956	−0.178177
$378$	0	0
$379$	−10.2365	−0.525811	−0.262906	−	0.964822i	$-0.584681\pi$
$379$	−10.2365	−0.525811	−0.262906	+	0.964822i	$0.584681\pi$
$380$	0	0
$381$	54.9648	2.81593
$382$	0	0
$383$	−28.6676	−1.46485	−0.732423	−	0.680850i	$-0.761610\pi$
$383$	−28.6676	−1.46485	−0.732423	+	0.680850i	$0.761610\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	44.2194	2.24780
$388$	0	0
$389$	−26.8661	−1.36217	−0.681084	−	0.732206i	$-0.738491\pi$
$389$	−26.8661	−1.36217	−0.681084	+	0.732206i	$0.738491\pi$
$390$	0	0
$391$	9.89599	0.500462
$392$	0	0
$393$	30.4318	1.53508
$394$	0	0
$395$	0	0
$396$	0	0
$397$	17.4588	0.876232	0.438116	−	0.898918i	$-0.355646\pi$
$397$	17.4588	0.876232	0.438116	+	0.898918i	$0.355646\pi$
$398$	0	0
$399$	24.4418	1.22362
$400$	0	0
$401$	25.7848	1.28763	0.643816	−	0.765180i	$-0.277350\pi$
$401$	25.7848	1.28763	0.643816	+	0.765180i	$0.277350\pi$
$402$	0	0
$403$	−1.60608	−0.0800046
$404$	0	0
$405$	0	0
$406$	0	0
$407$	21.0156	1.04170
$408$	0	0
$409$	−12.4498	−0.615603	−0.307802	−	0.951451i	$-0.599593\pi$
$409$	−12.4498	−0.615603	−0.307802	+	0.951451i	$0.599593\pi$
$410$	0	0
$411$	37.5705	1.85321
$412$	0	0
$413$	6.47250	0.318491
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−33.3461	−1.63297
$418$	0	0
$419$	23.0559	1.12635	0.563177	−	0.826336i	$-0.309579\pi$
$419$	23.0559	1.12635	0.563177	+	0.826336i	$0.309579\pi$
$420$	0	0
$421$	30.5881	1.49077	0.745385	−	0.666634i	$-0.232266\pi$
$421$	30.5881	1.49077	0.745385	+	0.666634i	$0.232266\pi$
$422$	0	0
$423$	−23.1380	−1.12501
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−4.49032	−0.217302
$428$	0	0
$429$	42.9598	2.07412
$430$	0	0
$431$	−19.5987	−0.944034	−0.472017	−	0.881589i	$-0.656474\pi$
$431$	−19.5987	−0.944034	−0.472017	+	0.881589i	$0.656474\pi$
$432$	0	0
$433$	−37.0395	−1.78000	−0.890002	−	0.455957i	$-0.849297\pi$
$433$	−37.0395	−1.78000	−0.890002	+	0.455957i	$0.849297\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	36.4836	1.74525
$438$	0	0
$439$	−20.2424	−0.966118	−0.483059	−	0.875588i	$-0.660474\pi$
$439$	−20.2424	−0.966118	−0.483059	+	0.875588i	$0.660474\pi$
$440$	0	0
$441$	−17.8209	−0.848615
$442$	0	0
$443$	13.4397	0.638542	0.319271	−	0.947663i	$-0.396562\pi$
$443$	13.4397	0.638542	0.319271	+	0.947663i	$0.396562\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	44.6140	2.11017
$448$	0	0
$449$	10.8909	0.513974	0.256987	−	0.966415i	$-0.417270\pi$
$449$	10.8909	0.513974	0.256987	+	0.966415i	$0.417270\pi$
$450$	0	0
$451$	34.4828	1.62373
$452$	0	0
$453$	7.88175	0.370317
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−31.1051	−1.45503	−0.727517	−	0.686090i	$-0.759326\pi$
$457$	−31.1051	−1.45503	−0.727517	+	0.686090i	$0.759326\pi$
$458$	0	0
$459$	4.71641	0.220143
$460$	0	0
$461$	10.2781	0.478698	0.239349	−	0.970934i	$-0.423066\pi$
$461$	10.2781	0.478698	0.239349	+	0.970934i	$0.423066\pi$
$462$	0	0
$463$	39.6884	1.84448	0.922238	−	0.386621i	$-0.126358\pi$
$463$	39.6884	1.84448	0.922238	+	0.386621i	$0.126358\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−12.4129	−0.574400	−0.287200	−	0.957871i	$-0.592724\pi$
$467$	−12.4129	−0.574400	−0.287200	+	0.957871i	$0.592724\pi$
$468$	0	0
$469$	11.8528	0.547311
$470$	0	0
$471$	13.6989	0.631210
$472$	0	0
$473$	49.0857	2.25696
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−49.8874	−2.28419
$478$	0	0
$479$	−28.1913	−1.28809	−0.644047	−	0.764986i	$-0.722746\pi$
$479$	−28.1913	−1.28809	−0.644047	+	0.764986i	$0.722746\pi$
$480$	0	0
$481$	−15.6842	−0.715138
$482$	0	0
$483$	29.2690	1.33179
$484$	0	0
$485$	0	0
$486$	0	0
$487$	18.6127	0.843422	0.421711	−	0.906730i	$-0.361430\pi$
$487$	18.6127	0.843422	0.421711	+	0.906730i	$0.361430\pi$
$488$	0	0
$489$	−36.7252	−1.66077
$490$	0	0
$491$	−41.5995	−1.87736	−0.938680	−	0.344788i	$-0.887951\pi$
$491$	−41.5995	−1.87736	−0.938680	+	0.344788i	$0.887951\pi$
$492$	0	0
$493$	−1.49718	−0.0674294
$494$	0	0
$495$	0	0
$496$	0	0
$497$	7.95359	0.356767
$498$	0	0
$499$	−42.4872	−1.90199	−0.950995	−	0.309206i	$-0.899937\pi$
$499$	−42.4872	−1.90199	−0.950995	+	0.309206i	$0.899937\pi$
$500$	0	0
$501$	11.9493	0.533854
$502$	0	0
$503$	−19.1736	−0.854907	−0.427453	−	0.904037i	$-0.640589\pi$
$503$	−19.1736	−0.854907	−0.427453	+	0.904037i	$0.640589\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	2.76297	0.122708
$508$	0	0
$509$	20.8633	0.924751	0.462375	−	0.886684i	$-0.346997\pi$
$509$	20.8633	0.924751	0.462375	+	0.886684i	$0.346997\pi$
$510$	0	0
$511$	−5.86179	−0.259311
$512$	0	0
$513$	17.3881	0.767701
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−25.6843	−1.12960
$518$	0	0
$519$	−0.557026	−0.0244507
$520$	0	0
$521$	37.4133	1.63911	0.819554	−	0.573003i	$-0.194221\pi$
$521$	37.4133	1.63911	0.819554	+	0.573003i	$0.194221\pi$
$522$	0	0
$523$	−12.4970	−0.546456	−0.273228	−	0.961949i	$-0.588091\pi$
$523$	−12.4970	−0.546456	−0.273228	+	0.961949i	$0.588091\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−0.695055	−0.0302771
$528$	0	0
$529$	20.6891	0.899525
$530$	0	0
$531$	16.3512	0.709580
$532$	0	0
$533$	−25.7349	−1.11470
$534$	0	0
$535$	0	0
$536$	0	0
$537$	15.1448	0.653547
$538$	0	0
$539$	−19.7821	−0.852075
$540$	0	0
$541$	17.6163	0.757382	0.378691	−	0.925523i	$-0.376374\pi$
$541$	17.6163	0.757382	0.378691	+	0.925523i	$0.376374\pi$
$542$	0	0
$543$	23.6168	1.01350
$544$	0	0
$545$	0	0
$546$	0	0
$547$	8.49542	0.363238	0.181619	−	0.983369i	$-0.441866\pi$
$547$	8.49542	0.363238	0.181619	+	0.983369i	$0.441866\pi$
$548$	0	0
$549$	−11.3437	−0.484136
$550$	0	0
$551$	−5.51965	−0.235145
$552$	0	0
$553$	2.88922	0.122862
$554$	0	0
$555$	0	0
$556$	0	0
$557$	13.1378	0.556667	0.278334	−	0.960484i	$-0.410218\pi$
$557$	13.1378	0.556667	0.278334	+	0.960484i	$0.410218\pi$
$558$	0	0
$559$	−36.6333	−1.54942
$560$	0	0
$561$	18.5915	0.784932
$562$	0	0
$563$	−1.68159	−0.0708705	−0.0354352	−	0.999372i	$-0.511282\pi$
$563$	−1.68159	−0.0708705	−0.0354352	+	0.999372i	$0.511282\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−6.75950	−0.283872
$568$	0	0
$569$	−7.51373	−0.314992	−0.157496	−	0.987520i	$-0.550342\pi$
$569$	−7.51373	−0.314992	−0.157496	+	0.987520i	$0.550342\pi$
$570$	0	0
$571$	44.4197	1.85891	0.929454	−	0.368939i	$-0.120279\pi$
$571$	44.4197	1.85891	0.929454	+	0.368939i	$0.120279\pi$
$572$	0	0
$573$	−6.37722	−0.266412
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−25.5246	−1.06260	−0.531302	−	0.847182i	$-0.678297\pi$
$577$	−25.5246	−1.06260	−0.531302	+	0.847182i	$0.678297\pi$
$578$	0	0
$579$	−14.8924	−0.618907
$580$	0	0
$581$	10.3084	0.427665
$582$	0	0
$583$	−55.3775	−2.29350
$584$	0	0
$585$	0	0
$586$	0	0
$587$	9.02728	0.372596	0.186298	−	0.982493i	$-0.440351\pi$
$587$	9.02728	0.372596	0.186298	+	0.982493i	$0.440351\pi$
$588$	0	0
$589$	−2.56247	−0.105585
$590$	0	0
$591$	20.5268	0.844362
$592$	0	0
$593$	13.0080	0.534176	0.267088	−	0.963672i	$-0.413939\pi$
$593$	13.0080	0.534176	0.267088	+	0.963672i	$0.413939\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	41.7089	1.70703
$598$	0	0
$599$	33.2601	1.35897	0.679485	−	0.733689i	$-0.262203\pi$
$599$	33.2601	1.35897	0.679485	+	0.733689i	$0.262203\pi$
$600$	0	0
$601$	18.0444	0.736047	0.368023	−	0.929817i	$-0.380035\pi$
$601$	18.0444	0.736047	0.368023	+	0.929817i	$0.380035\pi$
$602$	0	0
$603$	29.9431	1.21938
$604$	0	0
$605$	0	0
$606$	0	0
$607$	14.1415	0.573985	0.286992	−	0.957933i	$-0.407345\pi$
$607$	14.1415	0.573985	0.286992	+	0.957933i	$0.407345\pi$
$608$	0	0
$609$	−4.42815	−0.179438
$610$	0	0
$611$	19.1685	0.775476
$612$	0	0
$613$	16.2869	0.657823	0.328912	−	0.944361i	$-0.393318\pi$
$613$	16.2869	0.657823	0.328912	+	0.944361i	$0.393318\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	32.8943	1.32427	0.662137	−	0.749383i	$-0.269650\pi$
$617$	32.8943	1.32427	0.662137	+	0.749383i	$0.269650\pi$
$618$	0	0
$619$	−42.1050	−1.69234	−0.846170	−	0.532912i	$-0.821098\pi$
$619$	−42.1050	−1.69234	−0.846170	+	0.532912i	$0.821098\pi$
$620$	0	0
$621$	20.8222	0.835564
$622$	0	0
$623$	−4.40857	−0.176626
$624$	0	0
$625$	0	0
$626$	0	0
$627$	68.5413	2.73728
$628$	0	0
$629$	−6.78756	−0.270638
$630$	0	0
$631$	31.2225	1.24295	0.621474	−	0.783435i	$-0.286534\pi$
$631$	31.2225	1.24295	0.621474	+	0.783435i	$0.286534\pi$
$632$	0	0
$633$	37.4760	1.48954
$634$	0	0
$635$	0	0
$636$	0	0
$637$	14.7636	0.584956
$638$	0	0
$639$	20.0928	0.794858
$640$	0	0
$641$	−34.1293	−1.34803	−0.674014	−	0.738719i	$-0.735431\pi$
$641$	−34.1293	−1.34803	−0.674014	+	0.738719i	$0.735431\pi$
$642$	0	0
$643$	40.1920	1.58502	0.792510	−	0.609859i	$-0.208774\pi$
$643$	40.1920	1.58502	0.792510	+	0.609859i	$0.208774\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	5.71898	0.224836	0.112418	−	0.993661i	$-0.464140\pi$
$647$	5.71898	0.224836	0.112418	+	0.993661i	$0.464140\pi$
$648$	0	0
$649$	18.1506	0.712473
$650$	0	0
$651$	−2.05574	−0.0805708
$652$	0	0
$653$	6.46401	0.252956	0.126478	−	0.991969i	$-0.459633\pi$
$653$	6.46401	0.252956	0.126478	+	0.991969i	$0.459633\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−14.8084	−0.577730
$658$	0	0
$659$	44.6819	1.74056	0.870281	−	0.492556i	$-0.163937\pi$
$659$	44.6819	1.74056	0.870281	+	0.492556i	$0.163937\pi$
$660$	0	0
$661$	44.3667	1.72566	0.862832	−	0.505490i	$-0.168688\pi$
$661$	44.3667	1.72566	0.862832	+	0.505490i	$0.168688\pi$
$662$	0	0
$663$	−13.8750	−0.538862
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−6.60977	−0.255931
$668$	0	0
$669$	−52.7146	−2.03807
$670$	0	0
$671$	−12.5920	−0.486110
$672$	0	0
$673$	−27.8980	−1.07539	−0.537694	−	0.843140i	$-0.680704\pi$
$673$	−27.8980	−1.07539	−0.537694	+	0.843140i	$0.680704\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	19.4085	0.745930	0.372965	−	0.927845i	$-0.378341\pi$
$677$	19.4085	0.745930	0.372965	+	0.927845i	$0.378341\pi$
$678$	0	0
$679$	−24.6666	−0.946617
$680$	0	0
$681$	−35.1903	−1.34850
$682$	0	0
$683$	17.8605	0.683414	0.341707	−	0.939807i	$-0.388995\pi$
$683$	17.8605	0.683414	0.341707	+	0.939807i	$0.388995\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	69.2009	2.64018
$688$	0	0
$689$	41.3289	1.57451
$690$	0	0
$691$	−28.1722	−1.07172	−0.535861	−	0.844306i	$-0.680013\pi$
$691$	−28.1722	−1.07172	−0.535861	+	0.844306i	$0.680013\pi$
$692$	0	0
$693$	31.9992	1.21555
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−11.1372	−0.421850
$698$	0	0
$699$	−62.5191	−2.36469
$700$	0	0
$701$	15.6033	0.589327	0.294664	−	0.955601i	$-0.404792\pi$
$701$	15.6033	0.589327	0.294664	+	0.955601i	$0.404792\pi$
$702$	0	0
$703$	−25.0238	−0.943790
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−25.3352	−0.952828
$708$	0	0
$709$	25.2425	0.948001	0.474000	−	0.880525i	$-0.342810\pi$
$709$	25.2425	0.948001	0.474000	+	0.880525i	$0.342810\pi$
$710$	0	0
$711$	7.29890	0.273730
$712$	0	0
$713$	−3.06855	−0.114918
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−56.1992	−2.09880
$718$	0	0
$719$	27.7739	1.03579	0.517897	−	0.855443i	$-0.326715\pi$
$719$	27.7739	1.03579	0.517897	+	0.855443i	$0.326715\pi$
$720$	0	0
$721$	−20.2692	−0.754865
$722$	0	0
$723$	35.5347	1.32155
$724$	0	0
$725$	0	0
$726$	0	0
$727$	3.59058	0.133167	0.0665835	−	0.997781i	$-0.478790\pi$
$727$	3.59058	0.133167	0.0665835	+	0.997781i	$0.478790\pi$
$728$	0	0
$729$	−42.3925	−1.57009
$730$	0	0
$731$	−15.8536	−0.586365
$732$	0	0
$733$	7.94354	0.293401	0.146701	−	0.989181i	$-0.453135\pi$
$733$	7.94354	0.293401	0.146701	+	0.989181i	$0.453135\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	33.2383	1.22435
$738$	0	0
$739$	−24.2554	−0.892248	−0.446124	−	0.894971i	$-0.647196\pi$
$739$	−24.2554	−0.892248	−0.446124	+	0.894971i	$0.647196\pi$
$740$	0	0
$741$	−51.1533	−1.87916
$742$	0	0
$743$	42.2210	1.54894	0.774469	−	0.632612i	$-0.218017\pi$
$743$	42.2210	1.54894	0.774469	+	0.632612i	$0.218017\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	26.0417	0.952815
$748$	0	0
$749$	9.48428	0.346548
$750$	0	0
$751$	26.4938	0.966771	0.483386	−	0.875408i	$-0.339407\pi$
$751$	26.4938	0.966771	0.483386	+	0.875408i	$0.339407\pi$
$752$	0	0
$753$	−47.7841	−1.74135
$754$	0	0
$755$	0	0
$756$	0	0
$757$	17.2891	0.628382	0.314191	−	0.949360i	$-0.398267\pi$
$757$	17.2891	0.628382	0.314191	+	0.949360i	$0.398267\pi$
$758$	0	0
$759$	82.0781	2.97925
$760$	0	0
$761$	−28.2660	−1.02464	−0.512321	−	0.858794i	$-0.671214\pi$
$761$	−28.2660	−1.02464	−0.512321	+	0.858794i	$0.671214\pi$
$762$	0	0
$763$	20.5540	0.744104
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−13.5460	−0.489119
$768$	0	0
$769$	−24.1214	−0.869842	−0.434921	−	0.900469i	$-0.643224\pi$
$769$	−24.1214	−0.869842	−0.434921	+	0.900469i	$0.643224\pi$
$770$	0	0
$771$	−71.8558	−2.58782
$772$	0	0
$773$	−19.5460	−0.703022	−0.351511	−	0.936184i	$-0.614332\pi$
$773$	−19.5460	−0.703022	−0.351511	+	0.936184i	$0.614332\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	−20.0753	−0.720199
$778$	0	0
$779$	−41.0595	−1.47111
$780$	0	0
$781$	22.3040	0.798099
$782$	0	0
$783$	−3.15021	−0.112579
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−37.2397	−1.32745	−0.663725	−	0.747976i	$-0.731026\pi$
$787$	−37.2397	−1.32745	−0.663725	+	0.747976i	$0.731026\pi$
$788$	0	0
$789$	14.1360	0.503257
$790$	0	0
$791$	−13.4726	−0.479029
$792$	0	0
$793$	9.39760	0.333719
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−31.5159	−1.11635	−0.558175	−	0.829723i	$-0.688498\pi$
$797$	−31.5159	−1.11635	−0.558175	+	0.829723i	$0.688498\pi$
$798$	0	0
$799$	8.29546	0.293472
$800$	0	0
$801$	−11.1372	−0.393512
$802$	0	0
$803$	−16.4380	−0.580085
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−32.3141	−1.13751
$808$	0	0
$809$	11.3607	0.399420	0.199710	−	0.979855i	$-0.436000\pi$
$809$	11.3607	0.399420	0.199710	+	0.979855i	$0.436000\pi$
$810$	0	0
$811$	−7.60523	−0.267056	−0.133528	−	0.991045i	$-0.542631\pi$
$811$	−7.60523	−0.267056	−0.133528	+	0.991045i	$0.542631\pi$
$812$	0	0
$813$	38.9585	1.36633
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−58.4475	−2.04482
$818$	0	0
$819$	−23.8815	−0.834486
$820$	0	0
$821$	0.0409341	0.00142861	0.000714304	−	1.00000i	$-0.499773\pi$
$821$	0.0409341	0.00142861	0.000714304		1.00000i	$0.499773\pi$
$822$	0	0
$823$	46.9194	1.63551	0.817754	−	0.575568i	$-0.195219\pi$
$823$	46.9194	1.63551	0.817754	+	0.575568i	$0.195219\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−43.6229	−1.51692	−0.758459	−	0.651720i	$-0.774048\pi$
$827$	−43.6229	−1.51692	−0.758459	+	0.651720i	$0.774048\pi$
$828$	0	0
$829$	44.6055	1.54921	0.774606	−	0.632444i	$-0.217948\pi$
$829$	44.6055	1.54921	0.774606	+	0.632444i	$0.217948\pi$
$830$	0	0
$831$	−2.57545	−0.0893414
$832$	0	0
$833$	6.38917	0.221372
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−1.46247	−0.0505502
$838$	0	0
$839$	−23.8485	−0.823343	−0.411671	−	0.911332i	$-0.635055\pi$
$839$	−23.8485	−0.823343	−0.411671	+	0.911332i	$0.635055\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	0	0
$843$	75.6929	2.60700
$844$	0	0
$845$	0	0
$846$	0	0
$847$	17.3374	0.595720
$848$	0	0
$849$	5.22326	0.179262
$850$	0	0
$851$	−29.9659	−1.02722
$852$	0	0
$853$	−10.6361	−0.364174	−0.182087	−	0.983282i	$-0.558285\pi$
$853$	−10.6361	−0.364174	−0.182087	+	0.983282i	$0.558285\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	34.5645	1.18070	0.590350	−	0.807147i	$-0.298990\pi$
$857$	34.5645	1.18070	0.590350	+	0.807147i	$0.298990\pi$
$858$	0	0
$859$	−15.3791	−0.524730	−0.262365	−	0.964969i	$-0.584502\pi$
$859$	−15.3791	−0.524730	−0.262365	+	0.964969i	$0.584502\pi$
$860$	0	0
$861$	−32.9400	−1.12259
$862$	0	0
$863$	41.0655	1.39788	0.698942	−	0.715178i	$-0.253654\pi$
$863$	41.0655	1.39788	0.698942	+	0.715178i	$0.253654\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	39.5350	1.34268
$868$	0	0
$869$	8.10214	0.274846
$870$	0	0
$871$	−24.8062	−0.840526
$872$	0	0
$873$	−62.3140	−2.10901
$874$	0	0
$875$	0	0
$876$	0	0
$877$	39.5385	1.33512	0.667560	−	0.744556i	$-0.267339\pi$
$877$	39.5385	1.33512	0.667560	+	0.744556i	$0.267339\pi$
$878$	0	0
$879$	36.5299	1.23212
$880$	0	0
$881$	55.5100	1.87018	0.935090	−	0.354412i	$-0.115319\pi$
$881$	55.5100	1.87018	0.935090	+	0.354412i	$0.115319\pi$
$882$	0	0
$883$	−11.7459	−0.395282	−0.197641	−	0.980274i	$-0.563328\pi$
$883$	−11.7459	−0.395282	−0.197641	+	0.980274i	$0.563328\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	6.39449	0.214706	0.107353	−	0.994221i	$-0.465763\pi$
$887$	6.39449	0.214706	0.107353	+	0.994221i	$0.465763\pi$
$888$	0	0
$889$	−33.9177	−1.13756
$890$	0	0
$891$	−18.9554	−0.635030
$892$	0	0
$893$	30.5830	1.02342
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−61.2560	−2.04528
$898$	0	0
$899$	0.464244	0.0154834
$900$	0	0
$901$	17.8857	0.595858
$902$	0	0
$903$	−46.8896	−1.56039
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−33.0153	−1.09626	−0.548128	−	0.836395i	$-0.684659\pi$
$907$	−33.0153	−1.09626	−0.548128	+	0.836395i	$0.684659\pi$
$908$	0	0
$909$	−64.0031	−2.12285
$910$	0	0
$911$	−33.4462	−1.10812	−0.554061	−	0.832476i	$-0.686923\pi$
$911$	−33.4462	−1.10812	−0.554061	+	0.832476i	$0.686923\pi$
$912$	0	0
$913$	28.9075	0.956700
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−18.7788	−0.620132
$918$	0	0
$919$	−41.7948	−1.37868	−0.689341	−	0.724437i	$-0.742100\pi$
$919$	−41.7948	−1.37868	−0.689341	+	0.724437i	$0.742100\pi$
$920$	0	0
$921$	24.2463	0.798943
$922$	0	0
$923$	−16.6457	−0.547902
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−51.2051	−1.68180
$928$	0	0
$929$	11.0440	0.362340	0.181170	−	0.983452i	$-0.442012\pi$
$929$	11.0440	0.362340	0.181170	+	0.983452i	$0.442012\pi$
$930$	0	0
$931$	23.5550	0.771985
$932$	0	0
$933$	17.7719	0.581825
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−36.4185	−1.18974	−0.594870	−	0.803822i	$-0.702796\pi$
$937$	−36.4185	−1.18974	−0.594870	+	0.803822i	$0.702796\pi$
$938$	0	0
$939$	45.6578	1.48999
$940$	0	0
$941$	46.2476	1.50763	0.753815	−	0.657087i	$-0.228211\pi$
$941$	46.2476	1.50763	0.753815	+	0.657087i	$0.228211\pi$
$942$	0	0
$943$	−49.1686	−1.60115
$944$	0	0
$945$	0	0
$946$	0	0
$947$	15.5456	0.505164	0.252582	−	0.967575i	$-0.418720\pi$
$947$	15.5456	0.505164	0.252582	+	0.967575i	$0.418720\pi$
$948$	0	0
$949$	12.2679	0.398233
$950$	0	0
$951$	15.0839	0.489128
$952$	0	0
$953$	−45.8154	−1.48411	−0.742053	−	0.670341i	$-0.766148\pi$
$953$	−45.8154	−1.48411	−0.742053	+	0.670341i	$0.766148\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−12.4177	−0.401407
$958$	0	0
$959$	−23.1840	−0.748649
$960$	0	0
$961$	−30.7845	−0.993048
$962$	0	0
$963$	23.9597	0.772090
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−3.56207	−0.114548	−0.0572741	−	0.998358i	$-0.518241\pi$
$967$	−3.56207	−0.114548	−0.0572741	+	0.998358i	$0.518241\pi$
$968$	0	0
$969$	−22.1373	−0.711153
$970$	0	0
$971$	0.374633	0.0120225	0.00601127	−	0.999982i	$-0.498087\pi$
$971$	0.374633	0.0120225	0.00601127	+	0.999982i	$0.498087\pi$
$972$	0	0
$973$	20.5772	0.659674
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−51.1721	−1.63714	−0.818570	−	0.574407i	$-0.805233\pi$
$977$	−51.1721	−1.63714	−0.818570	+	0.574407i	$0.805233\pi$
$978$	0	0
$979$	−12.3628	−0.395117
$980$	0	0
$981$	51.9245	1.65782
$982$	0	0
$983$	13.2021	0.421081	0.210540	−	0.977585i	$-0.432478\pi$
$983$	13.2021	0.421081	0.210540	+	0.977585i	$0.432478\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	24.5352	0.780964
$988$	0	0
$989$	−69.9908	−2.22558
$990$	0	0
$991$	−10.6725	−0.339022	−0.169511	−	0.985528i	$-0.554219\pi$
$991$	−10.6725	−0.339022	−0.169511	+	0.985528i	$0.554219\pi$
$992$	0	0
$993$	76.6704	2.43306
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−41.3114	−1.30835	−0.654173	−	0.756345i	$-0.726983\pi$
$997$	−41.3114	−1.30835	−0.654173	+	0.756345i	$0.726983\pi$
$998$	0	0
$999$	−14.2817	−0.451853

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2900.2.a.j.1.1	✓	5
5.2	odd	4		2900.2.c.h.349.10		10
5.3	odd	4		2900.2.c.h.349.1		10
5.4	even	2		2900.2.a.l.1.5	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2900.2.a.j.1.1	✓	5	1.1	even	1	trivial
2900.2.a.l.1.5	yes	5	5.4	even	2
2900.2.c.h.349.1		10	5.3	odd	4
2900.2.c.h.349.10		10	5.2	odd	4

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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:	\( N \)	\(=\)	\( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2900.a (trivial)

\(f(q)\)	\(=\)	\(q-2.67880 q^{3} +1.65303 q^{7} +4.17598 q^{9} +4.63554 q^{11} -3.45956 q^{13} -1.49718 q^{17} -5.51965 q^{19} -4.42815 q^{21} -6.60977 q^{23} -3.15021 q^{27} +1.00000 q^{29} +0.464244 q^{31} -12.4177 q^{33} +4.53358 q^{37} +9.26748 q^{39} +7.43878 q^{41} +10.5890 q^{43} -5.54074 q^{47} -4.26748 q^{49} +4.01064 q^{51} -11.9463 q^{53} +14.7861 q^{57} +3.91553 q^{59} -2.71641 q^{61} +6.90302 q^{63} +7.17033 q^{67} +17.7063 q^{69} +4.81152 q^{71} -3.54609 q^{73} +7.66270 q^{77} +1.74783 q^{79} -4.08915 q^{81} +6.23607 q^{83} -2.67880 q^{87} -2.66696 q^{89} -5.71877 q^{91} -1.24362 q^{93} -14.9220 q^{97} +19.3579 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 4 q^{7} + 7 q^{9} - 8 q^{13} - 7 q^{17} + 2 q^{19} - 13 q^{21} - 11 q^{23} - 3 q^{27} + 5 q^{29} - 7 q^{31} - 15 q^{33} - 18 q^{37} + 12 q^{39} - 11 q^{41} - 8 q^{43} + 3 q^{47} + 13 q^{49} - 19 q^{51}+ \cdots + 30 q^{99}+O(q^{100}) \) 5 * q - 4 * q^7 + 7 * q^9 - 8 * q^13 - 7 * q^17 + 2 * q^19 - 13 * q^21 - 11 * q^23 - 3 * q^27 + 5 * q^29 - 7 * q^31 - 15 * q^33 - 18 * q^37 + 12 * q^39 - 11 * q^41 - 8 * q^43 + 3 * q^47 + 13 * q^49 - 19 * q^51 - 12 * q^53 - 2 * q^57 + 13 * q^59 - 9 * q^61 - 23 * q^63 + 21 * q^67 + 6 * q^69 - 13 * q^71 - 28 * q^73 - 14 * q^77 + 4 * q^79 - 27 * q^81 - 3 * q^83 + 10 * q^89 + 3 * q^91 - 29 * q^93 - 37 * q^97 + 30 * q^99

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