LMFDB - Embedded newform 6025.2.a.p.1.10

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:	$46$
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-1.83307 q^{2} -2.40621 q^{3} +1.36013 q^{4} +4.41073 q^{6} -0.302396 q^{7} +1.17293 q^{8} +2.78983 q^{9} +O(q^{10})$	\(q-1.83307 q^{2} -2.40621 q^{3} +1.36013 q^{4} +4.41073 q^{6} -0.302396 q^{7} +1.17293 q^{8} +2.78983 q^{9} -5.09885 q^{11} -3.27275 q^{12} +4.63318 q^{13} +0.554311 q^{14} -4.87031 q^{16} -1.03451 q^{17} -5.11394 q^{18} -8.55559 q^{19} +0.727627 q^{21} +9.34653 q^{22} +1.34508 q^{23} -2.82231 q^{24} -8.49293 q^{26} +0.505718 q^{27} -0.411297 q^{28} +10.3038 q^{29} +0.459299 q^{31} +6.58174 q^{32} +12.2689 q^{33} +1.89632 q^{34} +3.79452 q^{36} -1.55014 q^{37} +15.6830 q^{38} -11.1484 q^{39} +5.44165 q^{41} -1.33379 q^{42} +5.45885 q^{43} -6.93509 q^{44} -2.46562 q^{46} -10.3833 q^{47} +11.7190 q^{48} -6.90856 q^{49} +2.48924 q^{51} +6.30172 q^{52} +4.20240 q^{53} -0.927014 q^{54} -0.354689 q^{56} +20.5865 q^{57} -18.8875 q^{58} -5.01849 q^{59} -6.46168 q^{61} -0.841924 q^{62} -0.843632 q^{63} -2.32413 q^{64} -22.4897 q^{66} -14.8239 q^{67} -1.40707 q^{68} -3.23654 q^{69} -6.08615 q^{71} +3.27227 q^{72} +13.8254 q^{73} +2.84152 q^{74} -11.6367 q^{76} +1.54187 q^{77} +20.4357 q^{78} +2.63720 q^{79} -9.58634 q^{81} -9.97491 q^{82} -2.13404 q^{83} +0.989665 q^{84} -10.0064 q^{86} -24.7930 q^{87} -5.98059 q^{88} -2.74947 q^{89} -1.40106 q^{91} +1.82948 q^{92} -1.10517 q^{93} +19.0333 q^{94} -15.8370 q^{96} +10.5373 q^{97} +12.6638 q^{98} -14.2249 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 34 q^{4} - 4 q^{6} + 34 q^{9}+O(q^{10}) $ 46 * q + 34 * q^4 - 4 * q^6 + 34 * q^9	$ 46 q + 34 q^{4} - 4 q^{6} + 34 q^{9} - 64 q^{11} - 66 q^{14} + 22 q^{16} - 14 q^{21} - 50 q^{24} - 60 q^{26} - 36 q^{29} - 36 q^{31} + 12 q^{34} - 34 q^{36} - 88 q^{39} - 76 q^{41} - 100 q^{44} - 12 q^{46} + 22 q^{49} - 112 q^{51} - 26 q^{54} - 120 q^{56} - 84 q^{59} - 78 q^{61} + 28 q^{64} - 2 q^{66} - 24 q^{69} - 172 q^{71} - 16 q^{74} - 18 q^{76} - 54 q^{79} - 42 q^{81} + 44 q^{84} - 80 q^{86} - 86 q^{89} - 88 q^{91} + 4 q^{94} - 122 q^{96} - 148 q^{99}+O(q^{100}) $ 46 * q + 34 * q^4 - 4 * q^6 + 34 * q^9 - 64 * q^11 - 66 * q^14 + 22 * q^16 - 14 * q^21 - 50 * q^24 - 60 * q^26 - 36 * q^29 - 36 * q^31 + 12 * q^34 - 34 * q^36 - 88 * q^39 - 76 * q^41 - 100 * q^44 - 12 * q^46 + 22 * q^49 - 112 * q^51 - 26 * q^54 - 120 * q^56 - 84 * q^59 - 78 * q^61 + 28 * q^64 - 2 * q^66 - 24 * q^69 - 172 * q^71 - 16 * q^74 - 18 * q^76 - 54 * q^79 - 42 * q^81 + 44 * q^84 - 80 * q^86 - 86 * q^89 - 88 * q^91 + 4 * q^94 - 122 * q^96 - 148 * 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 $

$2$	−1.83307	−1.29617	−0.648086	−	0.761567i	$-0.724430\pi$
$2$	−1.83307	−1.29617	−0.648086	+	0.761567i	$0.724430\pi$
$3$	−2.40621	−1.38922	−0.694612	−	0.719385i	$-0.744424\pi$
$3$	−2.40621	−1.38922	−0.694612	+	0.719385i	$0.744424\pi$
$4$	1.36013	0.680064
$5$	0	0
$5$	0	0
$6$	4.41073	1.80067
$7$	−0.302396	−0.114295	−0.0571474	−	0.998366i	$-0.518201\pi$
$7$	−0.302396	−0.114295	−0.0571474	+	0.998366i	$0.518201\pi$
$8$	1.17293	0.414693
$9$	2.78983	0.929943
$10$	0	0
$11$	−5.09885	−1.53736	−0.768681	−	0.639633i	$-0.779086\pi$
$11$	−5.09885	−1.53736	−0.768681	+	0.639633i	$0.779086\pi$
$12$	−3.27275	−0.944761
$13$	4.63318	1.28501	0.642507	−	0.766280i	$-0.277894\pi$
$13$	4.63318	1.28501	0.642507	+	0.766280i	$0.277894\pi$
$14$	0.554311	0.148146
$15$	0	0
$16$	−4.87031	−1.21758
$17$	−1.03451	−0.250906	−0.125453	−	0.992100i	$-0.540038\pi$
$17$	−1.03451	−0.250906	−0.125453	+	0.992100i	$0.540038\pi$
$18$	−5.11394	−1.20537
$19$	−8.55559	−1.96279	−0.981394	−	0.192006i	$-0.938501\pi$
$19$	−8.55559	−1.96279	−0.981394	+	0.192006i	$0.938501\pi$
$20$	0	0
$21$	0.727627	0.158781
$22$	9.34653	1.99269
$23$	1.34508	0.280469	0.140234	−	0.990118i	$-0.455214\pi$
$23$	1.34508	0.280469	0.140234	+	0.990118i	$0.455214\pi$
$24$	−2.82231	−0.576101
$25$	0	0
$26$	−8.49293	−1.66560
$27$	0.505718	0.0973255
$28$	−0.411297	−0.0777278
$29$	10.3038	1.91336	0.956681	−	0.291138i	$-0.0940340\pi$
$29$	10.3038	1.91336	0.956681	+	0.291138i	$0.0940340\pi$
$30$	0	0
$31$	0.459299	0.0824925	0.0412462	−	0.999149i	$-0.486867\pi$
$31$	0.459299	0.0824925	0.0412462	+	0.999149i	$0.486867\pi$
$32$	6.58174	1.16350
$33$	12.2689	2.13574
$34$	1.89632	0.325217
$35$	0	0
$36$	3.79452	0.632420
$37$	−1.55014	−0.254842	−0.127421	−	0.991849i	$-0.540670\pi$
$37$	−1.55014	−0.254842	−0.127421	+	0.991849i	$0.540670\pi$
$38$	15.6830	2.54411
$39$	−11.1484	−1.78517
$40$	0	0
$41$	5.44165	0.849844	0.424922	−	0.905230i	$-0.360302\pi$
$41$	5.44165	0.849844	0.424922	+	0.905230i	$0.360302\pi$
$42$	−1.33379	−0.205808
$43$	5.45885	0.832467	0.416234	−	0.909258i	$-0.363350\pi$
$43$	5.45885	0.832467	0.416234	+	0.909258i	$0.363350\pi$
$44$	−6.93509	−1.04550
$45$	0	0
$46$	−2.46562	−0.363536
$47$	−10.3833	−1.51456	−0.757280	−	0.653090i	$-0.773472\pi$
$47$	−10.3833	−1.51456	−0.757280	+	0.653090i	$0.773472\pi$
$48$	11.7190	1.69149
$49$	−6.90856	−0.986937
$50$	0	0
$51$	2.48924	0.348564
$52$	6.30172	0.873891
$53$	4.20240	0.577244	0.288622	−	0.957443i	$-0.406803\pi$
$53$	4.20240	0.577244	0.288622	+	0.957443i	$0.406803\pi$
$54$	−0.927014	−0.126151
$55$	0	0
$56$	−0.354689	−0.0473973
$57$	20.5865	2.72675
$58$	−18.8875	−2.48005
$59$	−5.01849	−0.653352	−0.326676	−	0.945136i	$-0.605929\pi$
$59$	−5.01849	−0.653352	−0.326676	+	0.945136i	$0.605929\pi$
$60$	0	0
$61$	−6.46168	−0.827333	−0.413667	−	0.910428i	$-0.635752\pi$
$61$	−6.46168	−0.827333	−0.413667	+	0.910428i	$0.635752\pi$
$62$	−0.841924	−0.106924
$63$	−0.843632	−0.106288
$64$	−2.32413	−0.290516
$65$	0	0
$66$	−22.4897	−2.76829
$67$	−14.8239	−1.81103	−0.905516	−	0.424311i	$-0.860516\pi$
$67$	−14.8239	−1.81103	−0.905516	+	0.424311i	$0.860516\pi$
$68$	−1.40707	−0.170632
$69$	−3.23654	−0.389634
$70$	0	0
$71$	−6.08615	−0.722293	−0.361147	−	0.932509i	$-0.617615\pi$
$71$	−6.08615	−0.722293	−0.361147	+	0.932509i	$0.617615\pi$
$72$	3.27227	0.385640
$73$	13.8254	1.61814	0.809070	−	0.587712i	$-0.199971\pi$
$73$	13.8254	1.61814	0.809070	+	0.587712i	$0.199971\pi$
$74$	2.84152	0.330320
$75$	0	0
$76$	−11.6367	−1.33482
$77$	1.54187	0.175713
$78$	20.4357	2.31389
$79$	2.63720	0.296708	0.148354	−	0.988934i	$-0.452602\pi$
$79$	2.63720	0.296708	0.148354	+	0.988934i	$0.452602\pi$
$80$	0	0
$81$	−9.58634	−1.06515
$82$	−9.97491	−1.10154
$83$	−2.13404	−0.234242	−0.117121	−	0.993118i	$-0.537367\pi$
$83$	−2.13404	−0.234242	−0.117121	+	0.993118i	$0.537367\pi$
$84$	0.989665	0.107981
$85$	0	0
$86$	−10.0064	−1.07902
$87$	−24.7930	−2.65809
$88$	−5.98059	−0.637533
$89$	−2.74947	−0.291443	−0.145722	−	0.989326i	$-0.546550\pi$
$89$	−2.74947	−0.291443	−0.145722	+	0.989326i	$0.546550\pi$
$90$	0	0
$91$	−1.40106	−0.146871
$92$	1.82948	0.190737
$93$	−1.10517	−0.114600
$94$	19.0333	1.96313
$95$	0	0
$96$	−15.8370	−1.61636
$97$	10.5373	1.06990	0.534950	−	0.844884i	$-0.320331\pi$
$97$	10.5373	1.06990	0.534950	+	0.844884i	$0.320331\pi$
$98$	12.6638	1.27924
$99$	−14.2249	−1.42966
$100$	0	0
$101$	−6.99997	−0.696523	−0.348262	−	0.937397i	$-0.613228\pi$
$101$	−6.99997	−0.696523	−0.348262	+	0.937397i	$0.613228\pi$
$102$	−4.56295	−0.451799
$103$	0.931512	0.0917846	0.0458923	−	0.998946i	$-0.485387\pi$
$103$	0.931512	0.0917846	0.0458923	+	0.998946i	$0.485387\pi$
$104$	5.43439	0.532886
$105$	0	0
$106$	−7.70327	−0.748208
$107$	9.32032	0.901029	0.450515	−	0.892769i	$-0.351241\pi$
$107$	9.32032	0.901029	0.450515	+	0.892769i	$0.351241\pi$
$108$	0.687841	0.0661875
$109$	6.86942	0.657971	0.328986	−	0.944335i	$-0.393293\pi$
$109$	6.86942	0.657971	0.328986	+	0.944335i	$0.393293\pi$
$110$	0	0
$111$	3.72997	0.354033
$112$	1.47276	0.139163
$113$	3.92833	0.369546	0.184773	−	0.982781i	$-0.440845\pi$
$113$	3.92833	0.369546	0.184773	+	0.982781i	$0.440845\pi$
$114$	−37.7364	−3.53434
$115$	0	0
$116$	14.0144	1.30121
$117$	12.9258	1.19499
$118$	9.19922	0.846857
$119$	0.312832	0.0286772
$120$	0	0
$121$	14.9983	1.36348
$122$	11.8447	1.07237
$123$	−13.0937	−1.18062
$124$	0.624705	0.0561001
$125$	0	0
$126$	1.54643	0.137767
$127$	19.0590	1.69121	0.845604	−	0.533810i	$-0.179240\pi$
$127$	19.0590	1.69121	0.845604	+	0.533810i	$0.179240\pi$
$128$	−8.90319	−0.786938
$129$	−13.1351	−1.15648
$130$	0	0
$131$	11.9830	1.04696	0.523481	−	0.852038i	$-0.324633\pi$
$131$	11.9830	1.04696	0.523481	+	0.852038i	$0.324633\pi$
$132$	16.6872	1.45244
$133$	2.58717	0.224337
$134$	27.1733	2.34741
$135$	0	0
$136$	−1.21341	−0.104049
$137$	−11.4620	−0.979266	−0.489633	−	0.871929i	$-0.662869\pi$
$137$	−11.4620	−0.979266	−0.489633	+	0.871929i	$0.662869\pi$
$138$	5.93279	0.505033
$139$	16.6366	1.41110	0.705551	−	0.708660i	$-0.250700\pi$
$139$	16.6366	1.41110	0.705551	+	0.708660i	$0.250700\pi$
$140$	0	0
$141$	24.9844	2.10406
$142$	11.1563	0.936217
$143$	−23.6239	−1.97553
$144$	−13.5873	−1.13228
$145$	0	0
$146$	−25.3429	−2.09739
$147$	16.6234	1.37108
$148$	−2.10839	−0.173309
$149$	16.2343	1.32997	0.664983	−	0.746858i	$-0.268439\pi$
$149$	16.2343	1.32997	0.664983	+	0.746858i	$0.268439\pi$
$150$	0	0
$151$	−7.40916	−0.602949	−0.301474	−	0.953474i	$-0.597479\pi$
$151$	−7.40916	−0.602949	−0.301474	+	0.953474i	$0.597479\pi$
$152$	−10.0351	−0.813954
$153$	−2.88611	−0.233328
$154$	−2.82635	−0.227754
$155$	0	0
$156$	−15.1632	−1.21403
$157$	16.4755	1.31489	0.657444	−	0.753503i	$-0.271638\pi$
$157$	16.4755	1.31489	0.657444	+	0.753503i	$0.271638\pi$
$158$	−4.83416	−0.384585
$159$	−10.1118	−0.801921
$160$	0	0
$161$	−0.406747	−0.0320561
$162$	17.5724	1.38062
$163$	21.5566	1.68845	0.844224	−	0.535991i	$-0.180062\pi$
$163$	21.5566	1.68845	0.844224	+	0.535991i	$0.180062\pi$
$164$	7.40134	0.577948
$165$	0	0
$166$	3.91184	0.303618
$167$	−2.83253	−0.219188	−0.109594	−	0.993976i	$-0.534955\pi$
$167$	−2.83253	−0.219188	−0.109594	+	0.993976i	$0.534955\pi$
$168$	0.853454	0.0658454
$169$	8.46640	0.651261
$170$	0	0
$171$	−23.8686	−1.82528
$172$	7.42473	0.566131
$173$	−22.2673	−1.69296	−0.846478	−	0.532424i	$-0.821281\pi$
$173$	−22.2673	−1.69296	−0.846478	+	0.532424i	$0.821281\pi$
$174$	45.4472	3.44534
$175$	0	0
$176$	24.8330	1.87186
$177$	12.0755	0.907652
$178$	5.03996	0.377761
$179$	1.82748	0.136592	0.0682962	−	0.997665i	$-0.478244\pi$
$179$	1.82748	0.136592	0.0682962	+	0.997665i	$0.478244\pi$
$180$	0	0
$181$	12.5134	0.930114	0.465057	−	0.885281i	$-0.346034\pi$
$181$	12.5134	0.930114	0.465057	+	0.885281i	$0.346034\pi$
$182$	2.56823	0.190370
$183$	15.5481	1.14935
$184$	1.57768	0.116308
$185$	0	0
$186$	2.02584	0.148542
$187$	5.27481	0.385733
$188$	−14.1226	−1.03000
$189$	−0.152927	−0.0111238
$190$	0	0
$191$	3.47735	0.251612	0.125806	−	0.992055i	$-0.459848\pi$
$191$	3.47735	0.251612	0.125806	+	0.992055i	$0.459848\pi$
$192$	5.59234	0.403592
$193$	−4.00614	−0.288368	−0.144184	−	0.989551i	$-0.546056\pi$
$193$	−4.00614	−0.288368	−0.144184	+	0.989551i	$0.546056\pi$
$194$	−19.3155	−1.38677
$195$	0	0
$196$	−9.39652	−0.671180
$197$	−5.14600	−0.366638	−0.183319	−	0.983054i	$-0.558684\pi$
$197$	−5.14600	−0.366638	−0.183319	+	0.983054i	$0.558684\pi$
$198$	26.0752	1.85308
$199$	10.3802	0.735835	0.367917	−	0.929858i	$-0.380071\pi$
$199$	10.3802	0.735835	0.367917	+	0.929858i	$0.380071\pi$
$200$	0	0
$201$	35.6695	2.51593
$202$	12.8314	0.902815
$203$	−3.11582	−0.218687
$204$	3.38569	0.237046
$205$	0	0
$206$	−1.70752	−0.118969
$207$	3.75254	0.260820
$208$	−22.5650	−1.56460
$209$	43.6237	3.01751
$210$	0	0
$211$	−12.4398	−0.856394	−0.428197	−	0.903685i	$-0.640851\pi$
$211$	−12.4398	−0.856394	−0.428197	+	0.903685i	$0.640851\pi$
$212$	5.71580	0.392563
$213$	14.6445	1.00343
$214$	−17.0847	−1.16789
$215$	0	0
$216$	0.593171	0.0403602
$217$	−0.138890	−0.00942846
$218$	−12.5921	−0.852844
$219$	−33.2668	−2.24796
$220$	0	0
$221$	−4.79308	−0.322417
$222$	−6.83727	−0.458888
$223$	−2.52846	−0.169318	−0.0846591	−	0.996410i	$-0.526980\pi$
$223$	−2.52846	−0.169318	−0.0846591	+	0.996410i	$0.526980\pi$
$224$	−1.99029	−0.132982
$225$	0	0
$226$	−7.20088	−0.478996
$227$	−11.2535	−0.746922	−0.373461	−	0.927646i	$-0.621829\pi$
$227$	−11.2535	−0.746922	−0.373461	+	0.927646i	$0.621829\pi$
$228$	28.0003	1.85436
$229$	21.9401	1.44985	0.724923	−	0.688830i	$-0.241875\pi$
$229$	21.9401	1.44985	0.724923	+	0.688830i	$0.241875\pi$
$230$	0	0
$231$	−3.71006	−0.244104
$232$	12.0856	0.793457
$233$	−1.43595	−0.0940720	−0.0470360	−	0.998893i	$-0.514978\pi$
$233$	−1.43595	−0.0940720	−0.0470360	+	0.998893i	$0.514978\pi$
$234$	−23.6938	−1.54891
$235$	0	0
$236$	−6.82579	−0.444321
$237$	−6.34564	−0.412194
$238$	−0.573441	−0.0371706
$239$	−27.7962	−1.79799	−0.898994	−	0.437961i	$-0.855701\pi$
$239$	−27.7962	−1.79799	−0.898994	+	0.437961i	$0.855701\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−27.4928	−1.76731
$243$	21.5496	1.38241
$244$	−8.78870	−0.562639
$245$	0	0
$246$	24.0017	1.53029
$247$	−39.6396	−2.52221
$248$	0.538724	0.0342090
$249$	5.13495	0.325414
$250$	0	0
$251$	−8.17551	−0.516034	−0.258017	−	0.966140i	$-0.583069\pi$
$251$	−8.17551	−0.516034	−0.258017	+	0.966140i	$0.583069\pi$
$252$	−1.14745	−0.0722824
$253$	−6.85837	−0.431182
$254$	−34.9363	−2.19210
$255$	0	0
$256$	20.9684	1.31052
$257$	2.28257	0.142383	0.0711913	−	0.997463i	$-0.477320\pi$
$257$	2.28257	0.142383	0.0711913	+	0.997463i	$0.477320\pi$
$258$	24.0775	1.49900
$259$	0.468757	0.0291272
$260$	0	0
$261$	28.7457	1.77932
$262$	−21.9657	−1.35704
$263$	6.59117	0.406429	0.203214	−	0.979134i	$-0.434861\pi$
$263$	6.59117	0.406429	0.203214	+	0.979134i	$0.434861\pi$
$264$	14.3905	0.885676
$265$	0	0
$266$	−4.74246	−0.290779
$267$	6.61580	0.404880
$268$	−20.1625	−1.23162
$269$	17.1330	1.04462	0.522310	−	0.852756i	$-0.325071\pi$
$269$	17.1330	1.04462	0.522310	+	0.852756i	$0.325071\pi$
$270$	0	0
$271$	9.21261	0.559626	0.279813	−	0.960055i	$-0.409728\pi$
$271$	9.21261	0.559626	0.279813	+	0.960055i	$0.409728\pi$
$272$	5.03838	0.305497
$273$	3.37123	0.204036
$274$	21.0106	1.26930
$275$	0	0
$276$	−4.40211	−0.264976
$277$	−21.1695	−1.27195	−0.635977	−	0.771708i	$-0.719403\pi$
$277$	−21.1695	−1.27195	−0.635977	+	0.771708i	$0.719403\pi$
$278$	−30.4960	−1.82903
$279$	1.28136	0.0767132
$280$	0	0
$281$	−28.2982	−1.68813	−0.844066	−	0.536240i	$-0.819844\pi$
$281$	−28.2982	−1.68813	−0.844066	+	0.536240i	$0.819844\pi$
$282$	−45.7980	−2.72723
$283$	26.7052	1.58746	0.793730	−	0.608270i	$-0.208136\pi$
$283$	26.7052	1.58746	0.793730	+	0.608270i	$0.208136\pi$
$284$	−8.27794	−0.491206
$285$	0	0
$286$	43.3042	2.56063
$287$	−1.64553	−0.0971328
$288$	18.3619	1.08199
$289$	−15.9298	−0.937046
$290$	0	0
$291$	−25.3549	−1.48633
$292$	18.8043	1.10044
$293$	−20.6913	−1.20880	−0.604399	−	0.796682i	$-0.706587\pi$
$293$	−20.6913	−1.20880	−0.604399	+	0.796682i	$0.706587\pi$
$294$	−30.4718	−1.77715
$295$	0	0
$296$	−1.81821	−0.105681
$297$	−2.57858	−0.149624
$298$	−29.7585	−1.72387
$299$	6.23201	0.360406
$300$	0	0
$301$	−1.65073	−0.0951467
$302$	13.5815	0.781526
$303$	16.8434	0.967627
$304$	41.6684	2.38984
$305$	0	0
$306$	5.29042	0.302433
$307$	20.2769	1.15727	0.578633	−	0.815588i	$-0.303586\pi$
$307$	20.2769	1.15727	0.578633	+	0.815588i	$0.303586\pi$
$308$	2.09714	0.119496
$309$	−2.24141	−0.127509
$310$	0	0
$311$	12.3238	0.698820	0.349410	−	0.936970i	$-0.386382\pi$
$311$	12.3238	0.698820	0.349410	+	0.936970i	$0.386382\pi$
$312$	−13.0763	−0.740298
$313$	10.5428	0.595912	0.297956	−	0.954580i	$-0.403695\pi$
$313$	10.5428	0.595912	0.297956	+	0.954580i	$0.403695\pi$
$314$	−30.2007	−1.70432
$315$	0	0
$316$	3.58693	0.201780
$317$	20.9718	1.17790	0.588948	−	0.808171i	$-0.299542\pi$
$317$	20.9718	1.17790	0.588948	+	0.808171i	$0.299542\pi$
$318$	18.5357	1.03943
$319$	−52.5374	−2.94153
$320$	0	0
$321$	−22.4266	−1.25173
$322$	0.745593	0.0415503
$323$	8.85085	0.492474
$324$	−13.0386	−0.724369
$325$	0	0
$326$	−39.5147	−2.18852
$327$	−16.5292	−0.914069
$328$	6.38267	0.352424
$329$	3.13987	0.173107
$330$	0	0
$331$	−19.2909	−1.06033	−0.530163	−	0.847896i	$-0.677869\pi$
$331$	−19.2909	−1.06033	−0.530163	+	0.847896i	$0.677869\pi$
$332$	−2.90257	−0.159299
$333$	−4.32464	−0.236989
$334$	5.19221	0.284105
$335$	0	0
$336$	−3.54377	−0.193328
$337$	−27.5023	−1.49815	−0.749074	−	0.662487i	$-0.769501\pi$
$337$	−27.5023	−1.49815	−0.749074	+	0.662487i	$0.769501\pi$
$338$	−15.5195	−0.844147
$339$	−9.45237	−0.513382
$340$	0	0
$341$	−2.34190	−0.126821
$342$	43.7527	2.36588
$343$	4.20589	0.227097
$344$	6.40284	0.345218
$345$	0	0
$346$	40.8175	2.19436
$347$	−23.2293	−1.24701	−0.623506	−	0.781819i	$-0.714292\pi$
$347$	−23.2293	−1.24701	−0.623506	+	0.781819i	$0.714292\pi$
$348$	−33.7216	−1.80767
$349$	−31.5500	−1.68883	−0.844416	−	0.535688i	$-0.820052\pi$
$349$	−31.5500	−1.68883	−0.844416	+	0.535688i	$0.820052\pi$
$350$	0	0
$351$	2.34309	0.125065
$352$	−33.5593	−1.78872
$353$	−5.60734	−0.298449	−0.149224	−	0.988803i	$-0.547678\pi$
$353$	−5.60734	−0.298449	−0.149224	+	0.988803i	$0.547678\pi$
$354$	−22.1352	−1.17647
$355$	0	0
$356$	−3.73963	−0.198200
$357$	−0.752737	−0.0398391
$358$	−3.34989	−0.177047
$359$	23.8284	1.25761	0.628806	−	0.777562i	$-0.283544\pi$
$359$	23.8284	1.25761	0.628806	+	0.777562i	$0.283544\pi$
$360$	0	0
$361$	54.1981	2.85253
$362$	−22.9379	−1.20559
$363$	−36.0890	−1.89418
$364$	−1.90561	−0.0998813
$365$	0	0
$366$	−28.5007	−1.48976
$367$	10.7773	0.562568	0.281284	−	0.959625i	$-0.409240\pi$
$367$	10.7773	0.562568	0.281284	+	0.959625i	$0.409240\pi$
$368$	−6.55096	−0.341492
$369$	15.1813	0.790306
$370$	0	0
$371$	−1.27079	−0.0659760
$372$	−1.50317	−0.0779356
$373$	−6.83088	−0.353689	−0.176845	−	0.984239i	$-0.556589\pi$
$373$	−6.83088	−0.353689	−0.176845	+	0.984239i	$0.556589\pi$
$374$	−9.66908	−0.499976
$375$	0	0
$376$	−12.1789	−0.628077
$377$	47.7393	2.45870
$378$	0.280325	0.0144184
$379$	−11.4240	−0.586813	−0.293406	−	0.955988i	$-0.594789\pi$
$379$	−11.4240	−0.586813	−0.293406	+	0.955988i	$0.594789\pi$
$380$	0	0
$381$	−45.8598	−2.34947
$382$	−6.37421	−0.326133
$383$	38.2543	1.95470	0.977352	−	0.211618i	$-0.0678733\pi$
$383$	38.2543	1.95470	0.977352	+	0.211618i	$0.0678733\pi$
$384$	21.4229	1.09323
$385$	0	0
$386$	7.34351	0.373775
$387$	15.2293	0.774147
$388$	14.3321	0.727600
$389$	−0.100947	−0.00511820	−0.00255910	−	0.999997i	$-0.500815\pi$
$389$	−0.100947	−0.00511820	−0.00255910	+	0.999997i	$0.500815\pi$
$390$	0	0
$391$	−1.39150	−0.0703712
$392$	−8.10324	−0.409276
$393$	−28.8336	−1.45446
$394$	9.43296	0.475226
$395$	0	0
$396$	−19.3477	−0.972258
$397$	18.7984	0.943466	0.471733	−	0.881741i	$-0.343629\pi$
$397$	18.7984	0.943466	0.471733	+	0.881741i	$0.343629\pi$
$398$	−19.0276	−0.953769
$399$	−6.22528	−0.311654
$400$	0	0
$401$	16.1807	0.808026	0.404013	−	0.914753i	$-0.367615\pi$
$401$	16.1807	0.808026	0.404013	+	0.914753i	$0.367615\pi$
$402$	−65.3844	−3.26108
$403$	2.12801	0.106004
$404$	−9.52086	−0.473680
$405$	0	0
$406$	5.71149	0.283457
$407$	7.90396	0.391785
$408$	2.91971	0.144547
$409$	3.76534	0.186184	0.0930919	−	0.995658i	$-0.470325\pi$
$409$	3.76534	0.186184	0.0930919	+	0.995658i	$0.470325\pi$
$410$	0	0
$411$	27.5800	1.36042
$412$	1.26698	0.0624194
$413$	1.51757	0.0746748
$414$	−6.87866	−0.338068
$415$	0	0
$416$	30.4944	1.49511
$417$	−40.0312	−1.96034
$418$	−79.9651	−3.91122
$419$	13.7453	0.671500	0.335750	−	0.941951i	$-0.391010\pi$
$419$	13.7453	0.671500	0.335750	+	0.941951i	$0.391010\pi$
$420$	0	0
$421$	16.6746	0.812669	0.406335	−	0.913724i	$-0.366807\pi$
$421$	16.6746	0.812669	0.406335	+	0.913724i	$0.366807\pi$
$422$	22.8030	1.11003
$423$	−28.9676	−1.40845
$424$	4.92911	0.239379
$425$	0	0
$426$	−26.8444	−1.30061
$427$	1.95398	0.0945599
$428$	12.6768	0.612757
$429$	56.8440	2.74445
$430$	0	0
$431$	5.57968	0.268764	0.134382	−	0.990930i	$-0.457095\pi$
$431$	5.57968	0.268764	0.134382	+	0.990930i	$0.457095\pi$
$432$	−2.46300	−0.118501
$433$	−10.9860	−0.527953	−0.263977	−	0.964529i	$-0.585034\pi$
$433$	−10.9860	−0.527953	−0.263977	+	0.964529i	$0.585034\pi$
$434$	0.254594	0.0122209
$435$	0	0
$436$	9.34329	0.447462
$437$	−11.5080	−0.550501
$438$	60.9801	2.91374
$439$	−17.3442	−0.827795	−0.413897	−	0.910324i	$-0.635833\pi$
$439$	−17.3442	−0.827795	−0.413897	+	0.910324i	$0.635833\pi$
$440$	0	0
$441$	−19.2737	−0.917794
$442$	8.78602	0.417908
$443$	23.6992	1.12598	0.562991	−	0.826463i	$-0.309651\pi$
$443$	23.6992	1.12598	0.562991	+	0.826463i	$0.309651\pi$
$444$	5.07323	0.240765
$445$	0	0
$446$	4.63483	0.219466
$447$	−39.0631	−1.84762
$448$	0.702808	0.0332045
$449$	−27.2306	−1.28509	−0.642546	−	0.766247i	$-0.722122\pi$
$449$	−27.2306	−1.28509	−0.642546	+	0.766247i	$0.722122\pi$
$450$	0	0
$451$	−27.7462	−1.30652
$452$	5.34303	0.251315
$453$	17.8280	0.837631
$454$	20.6284	0.968140
$455$	0	0
$456$	24.1465	1.13076
$457$	23.5359	1.10096	0.550481	−	0.834848i	$-0.314444\pi$
$457$	23.5359	1.10096	0.550481	+	0.834848i	$0.314444\pi$
$458$	−40.2177	−1.87925
$459$	−0.523171	−0.0244195
$460$	0	0
$461$	−37.9663	−1.76827	−0.884133	−	0.467236i	$-0.845250\pi$
$461$	−37.9663	−1.76827	−0.884133	+	0.467236i	$0.845250\pi$
$462$	6.80078	0.316401
$463$	−6.08858	−0.282960	−0.141480	−	0.989941i	$-0.545186\pi$
$463$	−6.08858	−0.282960	−0.141480	+	0.989941i	$0.545186\pi$
$464$	−50.1825	−2.32967
$465$	0	0
$466$	2.63218	0.121934
$467$	−29.4171	−1.36126	−0.680630	−	0.732628i	$-0.738294\pi$
$467$	−29.4171	−1.36126	−0.680630	+	0.732628i	$0.738294\pi$
$468$	17.5807	0.812669
$469$	4.48270	0.206992
$470$	0	0
$471$	−39.6434	−1.82667
$472$	−5.88633	−0.270940
$473$	−27.8339	−1.27980
$474$	11.6320	0.534274
$475$	0	0
$476$	0.425491	0.0195023
$477$	11.7240	0.536804
$478$	50.9523	2.33050
$479$	−17.9285	−0.819173	−0.409587	−	0.912271i	$-0.634327\pi$
$479$	−17.9285	−0.819173	−0.409587	+	0.912271i	$0.634327\pi$
$480$	0	0
$481$	−7.18211	−0.327476
$482$	−1.83307	−0.0834938
$483$	0.978717	0.0445331
$484$	20.3996	0.927253
$485$	0	0
$486$	−39.5018	−1.79184
$487$	22.6663	1.02711	0.513554	−	0.858057i	$-0.328329\pi$
$487$	22.6663	1.02711	0.513554	+	0.858057i	$0.328329\pi$
$488$	−7.57908	−0.343089
$489$	−51.8697	−2.34563
$490$	0	0
$491$	14.3512	0.647661	0.323831	−	0.946115i	$-0.395029\pi$
$491$	14.3512	0.647661	0.323831	+	0.946115i	$0.395029\pi$
$492$	−17.8092	−0.802899
$493$	−10.6594	−0.480073
$494$	72.6620	3.26922
$495$	0	0
$496$	−2.23693	−0.100441
$497$	1.84043	0.0825544
$498$	−9.41270	−0.421793
$499$	−16.1552	−0.723206	−0.361603	−	0.932332i	$-0.617770\pi$
$499$	−16.1552	−0.723206	−0.361603	+	0.932332i	$0.617770\pi$
$500$	0	0
$501$	6.81565	0.304501
$502$	14.9862	0.668869
$503$	−17.0723	−0.761215	−0.380607	−	0.924737i	$-0.624285\pi$
$503$	−17.0723	−0.761215	−0.380607	+	0.924737i	$0.624285\pi$
$504$	−0.989520	−0.0440767
$505$	0	0
$506$	12.5718	0.558886
$507$	−20.3719	−0.904748
$508$	25.9226	1.15013
$509$	−24.9620	−1.10642	−0.553211	−	0.833041i	$-0.686598\pi$
$509$	−24.9620	−1.10642	−0.553211	+	0.833041i	$0.686598\pi$
$510$	0	0
$511$	−4.18074	−0.184945
$512$	−20.6300	−0.911727
$513$	−4.32672	−0.191029
$514$	−4.18409	−0.184552
$515$	0	0
$516$	−17.8654	−0.786482
$517$	52.9429	2.32843
$518$	−0.859263	−0.0377538
$519$	53.5798	2.35189
$520$	0	0
$521$	−31.2003	−1.36691	−0.683456	−	0.729992i	$-0.739524\pi$
$521$	−31.2003	−1.36691	−0.683456	+	0.729992i	$0.739524\pi$
$522$	−52.6928	−2.30630
$523$	−21.0227	−0.919257	−0.459628	−	0.888111i	$-0.652017\pi$
$523$	−21.0227	−0.919257	−0.459628	+	0.888111i	$0.652017\pi$
$524$	16.2984	0.712000
$525$	0	0
$526$	−12.0820	−0.526802
$527$	−0.475149	−0.0206978
$528$	−59.7533	−2.60043
$529$	−21.1908	−0.921337
$530$	0	0
$531$	−14.0007	−0.607580
$532$	3.51889	0.152563
$533$	25.2122	1.09206
$534$	−12.1272	−0.524795
$535$	0	0
$536$	−17.3874	−0.751022
$537$	−4.39730	−0.189757
$538$	−31.4060	−1.35401
$539$	35.2257	1.51728
$540$	0	0
$541$	−19.9902	−0.859445	−0.429722	−	0.902961i	$-0.641389\pi$
$541$	−19.9902	−0.859445	−0.429722	+	0.902961i	$0.641389\pi$
$542$	−16.8873	−0.725372
$543$	−30.1098	−1.29214
$544$	−6.80887	−0.291928
$545$	0	0
$546$	−6.17968	−0.264466
$547$	1.94389	0.0831148	0.0415574	−	0.999136i	$-0.486768\pi$
$547$	1.94389	0.0831148	0.0415574	+	0.999136i	$0.486768\pi$
$548$	−15.5898	−0.665963
$549$	−18.0270	−0.769372
$550$	0	0
$551$	−88.1548	−3.75552
$552$	−3.79623	−0.161578
$553$	−0.797478	−0.0339122
$554$	38.8051	1.64867
$555$	0	0
$556$	22.6279	0.959639
$557$	−5.46031	−0.231361	−0.115680	−	0.993286i	$-0.536905\pi$
$557$	−5.46031	−0.231361	−0.115680	+	0.993286i	$0.536905\pi$
$558$	−2.34882	−0.0994336
$559$	25.2919	1.06973
$560$	0	0
$561$	−12.6923	−0.535869
$562$	51.8725	2.18811
$563$	31.3778	1.32242	0.661208	−	0.750202i	$-0.270044\pi$
$563$	31.3778	1.32242	0.661208	+	0.750202i	$0.270044\pi$
$564$	33.9819	1.43090
$565$	0	0
$566$	−48.9524	−2.05762
$567$	2.89887	0.121741
$568$	−7.13862	−0.299530
$569$	−35.0427	−1.46907	−0.734533	−	0.678573i	$-0.762599\pi$
$569$	−35.0427	−1.46907	−0.734533	+	0.678573i	$0.762599\pi$
$570$	0	0
$571$	−1.82647	−0.0764356	−0.0382178	−	0.999269i	$-0.512168\pi$
$571$	−1.82647	−0.0764356	−0.0382178	+	0.999269i	$0.512168\pi$
$572$	−32.1315	−1.34349
$573$	−8.36722	−0.349546
$574$	3.01637	0.125901
$575$	0	0
$576$	−6.48393	−0.270164
$577$	−13.8070	−0.574792	−0.287396	−	0.957812i	$-0.592790\pi$
$577$	−13.8070	−0.574792	−0.287396	+	0.957812i	$0.592790\pi$
$578$	29.2003	1.21457
$579$	9.63959	0.400608
$580$	0	0
$581$	0.645326	0.0267726
$582$	46.4772	1.92654
$583$	−21.4274	−0.887433
$584$	16.2162	0.671031
$585$	0	0
$586$	37.9285	1.56681
$587$	11.7903	0.486637	0.243319	−	0.969946i	$-0.421764\pi$
$587$	11.7903	0.486637	0.243319	+	0.969946i	$0.421764\pi$
$588$	22.6100	0.932419
$589$	−3.92957	−0.161915
$590$	0	0
$591$	12.3823	0.509342
$592$	7.54968	0.310290
$593$	1.87116	0.0768392	0.0384196	−	0.999262i	$-0.487768\pi$
$593$	1.87116	0.0768392	0.0384196	+	0.999262i	$0.487768\pi$
$594$	4.72671	0.193939
$595$	0	0
$596$	22.0807	0.904462
$597$	−24.9770	−1.02224
$598$	−11.4237	−0.467149
$599$	−25.0996	−1.02554	−0.512772	−	0.858525i	$-0.671381\pi$
$599$	−25.0996	−1.02554	−0.512772	+	0.858525i	$0.671381\pi$
$600$	0	0
$601$	17.2895	0.705254	0.352627	−	0.935764i	$-0.385288\pi$
$601$	17.2895	0.705254	0.352627	+	0.935764i	$0.385288\pi$
$602$	3.02590	0.123327
$603$	−41.3562	−1.68416
$604$	−10.0774	−0.410044
$605$	0	0
$606$	−30.8750	−1.25421
$607$	−24.4282	−0.991510	−0.495755	−	0.868462i	$-0.665109\pi$
$607$	−24.4282	−0.991510	−0.495755	+	0.868462i	$0.665109\pi$
$608$	−56.3106	−2.28370
$609$	7.49730	0.303806
$610$	0	0
$611$	−48.1078	−1.94623
$612$	−3.92547	−0.158678
$613$	0.229288	0.00926086	0.00463043	−	0.999989i	$-0.498526\pi$
$613$	0.229288	0.00926086	0.00463043	+	0.999989i	$0.498526\pi$
$614$	−37.1690	−1.50002
$615$	0	0
$616$	1.80850	0.0728667
$617$	−30.1386	−1.21333	−0.606667	−	0.794956i	$-0.707494\pi$
$617$	−30.1386	−1.21333	−0.606667	+	0.794956i	$0.707494\pi$
$618$	4.10865	0.165274
$619$	−24.6422	−0.990455	−0.495227	−	0.868763i	$-0.664915\pi$
$619$	−24.6422	−0.990455	−0.495227	+	0.868763i	$0.664915\pi$
$620$	0	0
$621$	0.680232	0.0272968
$622$	−22.5904	−0.905791
$623$	0.831429	0.0333105
$624$	54.2961	2.17358
$625$	0	0
$626$	−19.3256	−0.772405
$627$	−104.968	−4.19200
$628$	22.4088	0.894207
$629$	1.60364	0.0639413
$630$	0	0
$631$	−12.0079	−0.478027	−0.239014	−	0.971016i	$-0.576824\pi$
$631$	−12.0079	−0.478027	−0.239014	+	0.971016i	$0.576824\pi$
$632$	3.09325	0.123043
$633$	29.9328	1.18972
$634$	−38.4427	−1.52676
$635$	0	0
$636$	−13.7534	−0.545357
$637$	−32.0086	−1.26823
$638$	96.3044	3.81273
$639$	−16.9793	−0.671691
$640$	0	0
$641$	−21.7431	−0.858799	−0.429400	−	0.903115i	$-0.641275\pi$
$641$	−21.7431	−0.858799	−0.429400	+	0.903115i	$0.641275\pi$
$642$	41.1094	1.62246
$643$	−28.4439	−1.12172	−0.560860	−	0.827911i	$-0.689529\pi$
$643$	−28.4439	−1.12172	−0.560860	+	0.827911i	$0.689529\pi$
$644$	−0.553227	−0.0218002
$645$	0	0
$646$	−16.2242	−0.638332
$647$	−10.8334	−0.425903	−0.212952	−	0.977063i	$-0.568308\pi$
$647$	−10.8334	−0.425903	−0.212952	+	0.977063i	$0.568308\pi$
$648$	−11.2441	−0.441710
$649$	25.5885	1.00444
$650$	0	0
$651$	0.334198	0.0130982
$652$	29.3198	1.14825
$653$	−29.1679	−1.14143	−0.570714	−	0.821149i	$-0.693333\pi$
$653$	−29.1679	−1.14143	−0.570714	+	0.821149i	$0.693333\pi$
$654$	30.2992	1.18479
$655$	0	0
$656$	−26.5025	−1.03475
$657$	38.5705	1.50478
$658$	−5.75558	−0.224376
$659$	3.98489	0.155229	0.0776147	−	0.996983i	$-0.475270\pi$
$659$	3.98489	0.155229	0.0776147	+	0.996983i	$0.475270\pi$
$660$	0	0
$661$	10.7056	0.416399	0.208200	−	0.978086i	$-0.433240\pi$
$661$	10.7056	0.416399	0.208200	+	0.978086i	$0.433240\pi$
$662$	35.3615	1.37437
$663$	11.5331	0.447910
$664$	−2.50308	−0.0971384
$665$	0	0
$666$	7.92734	0.307178
$667$	13.8594	0.536638
$668$	−3.85260	−0.149062
$669$	6.08400	0.235221
$670$	0	0
$671$	32.9471	1.27191
$672$	4.78905	0.184741
$673$	9.82304	0.378650	0.189325	−	0.981914i	$-0.439370\pi$
$673$	9.82304	0.378650	0.189325	+	0.981914i	$0.439370\pi$
$674$	50.4136	1.94186
$675$	0	0
$676$	11.5154	0.442899
$677$	26.9422	1.03547	0.517737	−	0.855540i	$-0.326775\pi$
$677$	26.9422	1.03547	0.517737	+	0.855540i	$0.326775\pi$
$678$	17.3268	0.665432
$679$	−3.18643	−0.122284
$680$	0	0
$681$	27.0783	1.03764
$682$	4.29285	0.164382
$683$	44.7069	1.71066	0.855331	−	0.518082i	$-0.173354\pi$
$683$	44.7069	1.71066	0.855331	+	0.518082i	$0.173354\pi$
$684$	−32.4644	−1.24131
$685$	0	0
$686$	−7.70967	−0.294356
$687$	−52.7925	−2.01416
$688$	−26.5863	−1.01359
$689$	19.4705	0.741767
$690$	0	0
$691$	38.1949	1.45300	0.726502	−	0.687164i	$-0.241145\pi$
$691$	38.1949	1.45300	0.726502	+	0.687164i	$0.241145\pi$
$692$	−30.2864	−1.15132
$693$	4.30155	0.163403
$694$	42.5807	1.61634
$695$	0	0
$696$	−29.0804	−1.10229
$697$	−5.62945	−0.213231
$698$	57.8332	2.18902
$699$	3.45519	0.130687
$700$	0	0
$701$	20.1487	0.761008	0.380504	−	0.924779i	$-0.375751\pi$
$701$	20.1487	0.761008	0.380504	+	0.924779i	$0.375751\pi$
$702$	−4.29503	−0.162105
$703$	13.2624	0.500201
$704$	11.8504	0.446629
$705$	0	0
$706$	10.2786	0.386841
$707$	2.11676	0.0796091
$708$	16.4242	0.617261
$709$	29.3168	1.10102	0.550508	−	0.834830i	$-0.314434\pi$
$709$	29.3168	1.10102	0.550508	+	0.834830i	$0.314434\pi$
$710$	0	0
$711$	7.35733	0.275921
$712$	−3.22493	−0.120859
$713$	0.617794	0.0231366
$714$	1.37982	0.0516383
$715$	0	0
$716$	2.48561	0.0928916
$717$	66.8834	2.49781
$718$	−43.6789	−1.63008
$719$	3.26007	0.121580	0.0607900	−	0.998151i	$-0.480638\pi$
$719$	3.26007	0.121580	0.0607900	+	0.998151i	$0.480638\pi$
$720$	0	0
$721$	−0.281685	−0.0104905
$722$	−99.3487	−3.69738
$723$	−2.40621	−0.0894878
$724$	17.0198	0.632536
$725$	0	0
$726$	66.1534	2.45518
$727$	−20.1773	−0.748336	−0.374168	−	0.927361i	$-0.622072\pi$
$727$	−20.1773	−0.748336	−0.374168	+	0.927361i	$0.622072\pi$
$728$	−1.64334	−0.0609061
$729$	−23.0937	−0.855321
$730$	0	0
$731$	−5.64724	−0.208871
$732$	21.1474	0.781632
$733$	−13.8239	−0.510599	−0.255299	−	0.966862i	$-0.582174\pi$
$733$	−13.8239	−0.510599	−0.255299	+	0.966862i	$0.582174\pi$
$734$	−19.7554	−0.729185
$735$	0	0
$736$	8.85297	0.326325
$737$	75.5851	2.78421
$738$	−27.8283	−1.02437
$739$	7.81411	0.287447	0.143723	−	0.989618i	$-0.454092\pi$
$739$	7.81411	0.287447	0.143723	+	0.989618i	$0.454092\pi$
$740$	0	0
$741$	95.3811	3.50391
$742$	2.32944	0.0855163
$743$	−34.4155	−1.26258	−0.631291	−	0.775546i	$-0.717475\pi$
$743$	−34.4155	−1.26258	−0.631291	+	0.775546i	$0.717475\pi$
$744$	−1.29628	−0.0475240
$745$	0	0
$746$	12.5214	0.458442
$747$	−5.95362	−0.217831
$748$	7.17442	0.262323
$749$	−2.81842	−0.102983
$750$	0	0
$751$	−32.6623	−1.19187	−0.595933	−	0.803034i	$-0.703218\pi$
$751$	−32.6623	−1.19187	−0.595933	+	0.803034i	$0.703218\pi$
$752$	50.5699	1.84409
$753$	19.6720	0.716886
$754$	−87.5092	−3.18690
$755$	0	0
$756$	−0.208000	−0.00756489
$757$	17.6525	0.641590	0.320795	−	0.947149i	$-0.396050\pi$
$757$	17.6525	0.641590	0.320795	+	0.947149i	$0.396050\pi$
$758$	20.9410	0.760611
$759$	16.5026	0.599008
$760$	0	0
$761$	−40.8281	−1.48002	−0.740008	−	0.672598i	$-0.765178\pi$
$761$	−40.8281	−1.48002	−0.740008	+	0.672598i	$0.765178\pi$
$762$	84.0639	3.04532
$763$	−2.07728	−0.0752027
$764$	4.72964	0.171112
$765$	0	0
$766$	−70.1227	−2.53363
$767$	−23.2516	−0.839566
$768$	−50.4542	−1.82061
$769$	−12.1935	−0.439709	−0.219854	−	0.975533i	$-0.570558\pi$
$769$	−12.1935	−0.439709	−0.219854	+	0.975533i	$0.570558\pi$
$770$	0	0
$771$	−5.49232	−0.197801
$772$	−5.44886	−0.196109
$773$	−37.8215	−1.36035	−0.680173	−	0.733052i	$-0.738095\pi$
$773$	−37.8215	−1.36035	−0.680173	+	0.733052i	$0.738095\pi$
$774$	−27.9162	−1.00343
$775$	0	0
$776$	12.3595	0.443680
$777$	−1.12793	−0.0404641
$778$	0.185042	0.00663407
$779$	−46.5566	−1.66806
$780$	0	0
$781$	31.0324	1.11043
$782$	2.55071	0.0912132
$783$	5.21080	0.186219
$784$	33.6468	1.20167
$785$	0	0
$786$	52.8539	1.88524
$787$	13.9696	0.497964	0.248982	−	0.968508i	$-0.419904\pi$
$787$	13.9696	0.497964	0.248982	+	0.968508i	$0.419904\pi$
$788$	−6.99922	−0.249337
$789$	−15.8597	−0.564620
$790$	0	0
$791$	−1.18791	−0.0422372
$792$	−16.6848	−0.592869
$793$	−29.9381	−1.06313
$794$	−34.4587	−1.22289
$795$	0	0
$796$	14.1184	0.500415
$797$	−12.1732	−0.431198	−0.215599	−	0.976482i	$-0.569170\pi$
$797$	−12.1732	−0.431198	−0.215599	+	0.976482i	$0.569170\pi$
$798$	11.4113	0.403957
$799$	10.7416	0.380012
$800$	0	0
$801$	−7.67055	−0.271026
$802$	−29.6603	−1.04734
$803$	−70.4937	−2.48767
$804$	48.5150	1.71099
$805$	0	0
$806$	−3.90079	−0.137399
$807$	−41.2256	−1.45121
$808$	−8.21047	−0.288843
$809$	−25.0091	−0.879271	−0.439636	−	0.898176i	$-0.644892\pi$
$809$	−25.0091	−0.879271	−0.439636	+	0.898176i	$0.644892\pi$
$810$	0	0
$811$	39.0119	1.36989	0.684947	−	0.728593i	$-0.259826\pi$
$811$	39.0119	1.36989	0.684947	+	0.728593i	$0.259826\pi$
$812$	−4.23791	−0.148721
$813$	−22.1674	−0.777446
$814$	−14.4885	−0.507821
$815$	0	0
$816$	−12.1234	−0.424404
$817$	−46.7037	−1.63396
$818$	−6.90210	−0.241326
$819$	−3.90870	−0.136581
$820$	0	0
$821$	−18.5556	−0.647595	−0.323797	−	0.946126i	$-0.604960\pi$
$821$	−18.5556	−0.647595	−0.323797	+	0.946126i	$0.604960\pi$
$822$	−50.5559	−1.76334
$823$	50.5534	1.76218	0.881090	−	0.472949i	$-0.156810\pi$
$823$	50.5534	1.76218	0.881090	+	0.472949i	$0.156810\pi$
$824$	1.09260	0.0380624
$825$	0	0
$826$	−2.78180	−0.0967914
$827$	−14.1845	−0.493242	−0.246621	−	0.969112i	$-0.579320\pi$
$827$	−14.1845	−0.493242	−0.246621	+	0.969112i	$0.579320\pi$
$828$	5.10394	0.177374
$829$	−56.2077	−1.95217	−0.976087	−	0.217381i	$-0.930249\pi$
$829$	−56.2077	−1.95217	−0.976087	+	0.217381i	$0.930249\pi$
$830$	0	0
$831$	50.9382	1.76703
$832$	−10.7681	−0.373318
$833$	7.14697	0.247628
$834$	73.3798	2.54093
$835$	0	0
$836$	59.3338	2.05210
$837$	0.232276	0.00802862
$838$	−25.1960	−0.870380
$839$	−9.83492	−0.339539	−0.169770	−	0.985484i	$-0.554302\pi$
$839$	−9.83492	−0.339539	−0.169770	+	0.985484i	$0.554302\pi$
$840$	0	0
$841$	77.1677	2.66095
$842$	−30.5656	−1.05336
$843$	68.0914	2.34519
$844$	−16.9198	−0.582402
$845$	0	0
$846$	53.0996	1.82560
$847$	−4.53542	−0.155839
$848$	−20.4670	−0.702839
$849$	−64.2583	−2.20534
$850$	0	0
$851$	−2.08507	−0.0714753
$852$	19.9184	0.682394
$853$	−34.2541	−1.17284	−0.586419	−	0.810008i	$-0.699463\pi$
$853$	−34.2541	−1.17284	−0.586419	+	0.810008i	$0.699463\pi$
$854$	−3.58178	−0.122566
$855$	0	0
$856$	10.9321	0.373650
$857$	−45.4343	−1.55201	−0.776004	−	0.630729i	$-0.782756\pi$
$857$	−45.4343	−1.55201	−0.776004	+	0.630729i	$0.782756\pi$
$858$	−104.199	−3.55729
$859$	8.81001	0.300594	0.150297	−	0.988641i	$-0.451977\pi$
$859$	8.81001	0.300594	0.150297	+	0.988641i	$0.451977\pi$
$860$	0	0
$861$	3.95949	0.134939
$862$	−10.2279	−0.348364
$863$	−26.7733	−0.911374	−0.455687	−	0.890140i	$-0.650606\pi$
$863$	−26.7733	−0.911374	−0.455687	+	0.890140i	$0.650606\pi$
$864$	3.32850	0.113238
$865$	0	0
$866$	20.1380	0.684319
$867$	38.3304	1.30177
$868$	−0.188908	−0.00641196
$869$	−13.4467	−0.456148
$870$	0	0
$871$	−68.6821	−2.32720
$872$	8.05734	0.272856
$873$	29.3972	0.994945
$874$	21.0948	0.713544
$875$	0	0
$876$	−45.2470	−1.52876
$877$	−28.5732	−0.964850	−0.482425	−	0.875937i	$-0.660244\pi$
$877$	−28.5732	−0.964850	−0.482425	+	0.875937i	$0.660244\pi$
$878$	31.7931	1.07296
$879$	49.7875	1.67929
$880$	0	0
$881$	13.4524	0.453224	0.226612	−	0.973985i	$-0.427235\pi$
$881$	13.4524	0.453224	0.226612	+	0.973985i	$0.427235\pi$
$882$	35.3299	1.18962
$883$	−2.30504	−0.0775706	−0.0387853	−	0.999248i	$-0.512349\pi$
$883$	−2.30504	−0.0775706	−0.0387853	+	0.999248i	$0.512349\pi$
$884$	−6.51919	−0.219264
$885$	0	0
$886$	−43.4421	−1.45947
$887$	−7.50871	−0.252118	−0.126059	−	0.992023i	$-0.540233\pi$
$887$	−7.50871	−0.252118	−0.126059	+	0.992023i	$0.540233\pi$
$888$	4.37498	0.146815
$889$	−5.76335	−0.193296
$890$	0	0
$891$	48.8793	1.63752
$892$	−3.43903	−0.115147
$893$	88.8353	2.97276
$894$	71.6052	2.39484
$895$	0	0
$896$	2.69229	0.0899430
$897$	−14.9955	−0.500685
$898$	49.9155	1.66570
$899$	4.73251	0.157838
$900$	0	0
$901$	−4.34743	−0.144834
$902$	50.8606	1.69347
$903$	3.97201	0.132180
$904$	4.60765	0.153248
$905$	0	0
$906$	−32.6798	−1.08571
$907$	−27.9423	−0.927810	−0.463905	−	0.885885i	$-0.653552\pi$
$907$	−27.9423	−0.927810	−0.463905	+	0.885885i	$0.653552\pi$
$908$	−15.3062	−0.507954
$909$	−19.5287	−0.647727
$910$	0	0
$911$	21.0515	0.697468	0.348734	−	0.937222i	$-0.386612\pi$
$911$	21.0515	0.697468	0.348734	+	0.937222i	$0.386612\pi$
$912$	−100.263	−3.32003
$913$	10.8812	0.360114
$914$	−43.1428	−1.42704
$915$	0	0
$916$	29.8414	0.985987
$917$	−3.62361	−0.119662
$918$	0.959006	0.0316519
$919$	5.21572	0.172051	0.0860253	−	0.996293i	$-0.472583\pi$
$919$	5.21572	0.172051	0.0860253	+	0.996293i	$0.472583\pi$
$920$	0	0
$921$	−48.7905	−1.60770
$922$	69.5946	2.29198
$923$	−28.1983	−0.928157
$924$	−5.04615	−0.166006
$925$	0	0
$926$	11.1608	0.366765
$927$	2.59876	0.0853544
$928$	67.8167	2.22619
$929$	−51.1232	−1.67730	−0.838649	−	0.544672i	$-0.816654\pi$
$929$	−51.1232	−1.67730	−0.838649	+	0.544672i	$0.816654\pi$
$930$	0	0
$931$	59.1068	1.93715
$932$	−1.95307	−0.0639750
$933$	−29.6536	−0.970817
$934$	53.9234	1.76443
$935$	0	0
$936$	15.1610	0.495553
$937$	23.5517	0.769400	0.384700	−	0.923042i	$-0.374305\pi$
$937$	23.5517	0.769400	0.384700	+	0.923042i	$0.374305\pi$
$938$	−8.21708	−0.268297
$939$	−25.3680	−0.827855
$940$	0	0
$941$	45.4674	1.48219	0.741097	−	0.671398i	$-0.234306\pi$
$941$	45.4674	1.48219	0.741097	+	0.671398i	$0.234306\pi$
$942$	72.6690	2.36768
$943$	7.31947	0.238355
$944$	24.4416	0.795506
$945$	0	0
$946$	51.0213	1.65885
$947$	22.5514	0.732821	0.366411	−	0.930453i	$-0.380587\pi$
$947$	22.5514	0.732821	0.366411	+	0.930453i	$0.380587\pi$
$948$	−8.63088	−0.280318
$949$	64.0556	2.07933
$950$	0	0
$951$	−50.4626	−1.63636
$952$	0.366929	0.0118922
$953$	0.231111	0.00748642	0.00374321	−	0.999993i	$-0.498808\pi$
$953$	0.231111	0.00748642	0.00374321	+	0.999993i	$0.498808\pi$
$954$	−21.4908	−0.695790
$955$	0	0
$956$	−37.8064	−1.22275
$957$	126.416	4.08644
$958$	32.8641	1.06179
$959$	3.46606	0.111925
$960$	0	0
$961$	−30.7890	−0.993195
$962$	13.1653	0.424465
$963$	26.0021	0.837905
$964$	1.36013	0.0438068
$965$	0	0
$966$	−1.79405	−0.0577227
$967$	−3.83002	−0.123165	−0.0615825	−	0.998102i	$-0.519615\pi$
$967$	−3.83002	−0.123165	−0.0615825	+	0.998102i	$0.519615\pi$
$968$	17.5919	0.565425
$969$	−21.2970	−0.684157
$970$	0	0
$971$	−37.2292	−1.19474	−0.597371	−	0.801965i	$-0.703788\pi$
$971$	−37.2292	−1.19474	−0.597371	+	0.801965i	$0.703788\pi$
$972$	29.3102	0.940124
$973$	−5.03085	−0.161282
$974$	−41.5488	−1.33131
$975$	0	0
$976$	31.4704	1.00734
$977$	−3.50188	−0.112035	−0.0560175	−	0.998430i	$-0.517840\pi$
$977$	−3.50188	−0.112035	−0.0560175	+	0.998430i	$0.517840\pi$
$978$	95.0806	3.04034
$979$	14.0191	0.448054
$980$	0	0
$981$	19.1645	0.611875
$982$	−26.3067	−0.839481
$983$	52.1048	1.66188	0.830942	−	0.556358i	$-0.187802\pi$
$983$	52.1048	1.66188	0.830942	+	0.556358i	$0.187802\pi$
$984$	−15.3580	−0.489596
$985$	0	0
$986$	19.5393	0.622258
$987$	−7.55517	−0.240484
$988$	−53.9149	−1.71526
$989$	7.34260	0.233481
$990$	0	0
$991$	55.2696	1.75570	0.877848	−	0.478939i	$-0.158978\pi$
$991$	55.2696	1.75570	0.877848	+	0.478939i	$0.158978\pi$
$992$	3.02298	0.0959798
$993$	46.4180	1.47303
$994$	−3.37362	−0.107005
$995$	0	0
$996$	6.98419	0.221302
$997$	4.93251	0.156214	0.0781071	−	0.996945i	$-0.475112\pi$
$997$	4.93251	0.156214	0.0781071	+	0.996945i	$0.475112\pi$
$998$	29.6135	0.937399
$999$	−0.783936	−0.0248026

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.p.1.10		46
5.2	odd	4		1205.2.b.c.724.10	✓	46
5.3	odd	4		1205.2.b.c.724.37	yes	46
5.4	even	2	inner	6025.2.a.p.1.37		46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.b.c.724.10	✓	46	5.2	odd	4
1205.2.b.c.724.37	yes	46	5.3	odd	4
6025.2.a.p.1.10		46	1.1	even	1	trivial
6025.2.a.p.1.37		46	5.4	even	2	inner

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

\(f(q)\)	\(=\)	\(q-1.83307 q^{2} -2.40621 q^{3} +1.36013 q^{4} +4.41073 q^{6} -0.302396 q^{7} +1.17293 q^{8} +2.78983 q^{9} +O(q^{10})\)	\(q-1.83307 q^{2} -2.40621 q^{3} +1.36013 q^{4} +4.41073 q^{6} -0.302396 q^{7} +1.17293 q^{8} +2.78983 q^{9} -5.09885 q^{11} -3.27275 q^{12} +4.63318 q^{13} +0.554311 q^{14} -4.87031 q^{16} -1.03451 q^{17} -5.11394 q^{18} -8.55559 q^{19} +0.727627 q^{21} +9.34653 q^{22} +1.34508 q^{23} -2.82231 q^{24} -8.49293 q^{26} +0.505718 q^{27} -0.411297 q^{28} +10.3038 q^{29} +0.459299 q^{31} +6.58174 q^{32} +12.2689 q^{33} +1.89632 q^{34} +3.79452 q^{36} -1.55014 q^{37} +15.6830 q^{38} -11.1484 q^{39} +5.44165 q^{41} -1.33379 q^{42} +5.45885 q^{43} -6.93509 q^{44} -2.46562 q^{46} -10.3833 q^{47} +11.7190 q^{48} -6.90856 q^{49} +2.48924 q^{51} +6.30172 q^{52} +4.20240 q^{53} -0.927014 q^{54} -0.354689 q^{56} +20.5865 q^{57} -18.8875 q^{58} -5.01849 q^{59} -6.46168 q^{61} -0.841924 q^{62} -0.843632 q^{63} -2.32413 q^{64} -22.4897 q^{66} -14.8239 q^{67} -1.40707 q^{68} -3.23654 q^{69} -6.08615 q^{71} +3.27227 q^{72} +13.8254 q^{73} +2.84152 q^{74} -11.6367 q^{76} +1.54187 q^{77} +20.4357 q^{78} +2.63720 q^{79} -9.58634 q^{81} -9.97491 q^{82} -2.13404 q^{83} +0.989665 q^{84} -10.0064 q^{86} -24.7930 q^{87} -5.98059 q^{88} -2.74947 q^{89} -1.40106 q^{91} +1.82948 q^{92} -1.10517 q^{93} +19.0333 q^{94} -15.8370 q^{96} +10.5373 q^{97} +12.6638 q^{98} -14.2249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 34 q^{4} - 4 q^{6} + 34 q^{9}+O(q^{10}) \) 46 * q + 34 * q^4 - 4 * q^6 + 34 * q^9	\( 46 q + 34 q^{4} - 4 q^{6} + 34 q^{9} - 64 q^{11} - 66 q^{14} + 22 q^{16} - 14 q^{21} - 50 q^{24} - 60 q^{26} - 36 q^{29} - 36 q^{31} + 12 q^{34} - 34 q^{36} - 88 q^{39} - 76 q^{41} - 100 q^{44} - 12 q^{46} + 22 q^{49} - 112 q^{51} - 26 q^{54} - 120 q^{56} - 84 q^{59} - 78 q^{61} + 28 q^{64} - 2 q^{66} - 24 q^{69} - 172 q^{71} - 16 q^{74} - 18 q^{76} - 54 q^{79} - 42 q^{81} + 44 q^{84} - 80 q^{86} - 86 q^{89} - 88 q^{91} + 4 q^{94} - 122 q^{96} - 148 q^{99}+O(q^{100}) \) 46 * q + 34 * q^4 - 4 * q^6 + 34 * q^9 - 64 * q^11 - 66 * q^14 + 22 * q^16 - 14 * q^21 - 50 * q^24 - 60 * q^26 - 36 * q^29 - 36 * q^31 + 12 * q^34 - 34 * q^36 - 88 * q^39 - 76 * q^41 - 100 * q^44 - 12 * q^46 + 22 * q^49 - 112 * q^51 - 26 * q^54 - 120 * q^56 - 84 * q^59 - 78 * q^61 + 28 * q^64 - 2 * q^66 - 24 * q^69 - 172 * q^71 - 16 * q^74 - 18 * q^76 - 54 * q^79 - 42 * q^81 + 44 * q^84 - 80 * q^86 - 86 * q^89 - 88 * q^91 + 4 * q^94 - 122 * q^96 - 148 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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