LMFDB - Embedded newform 275.3.f.c.232.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(232,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.232"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			232.5
Character	$\chi$	$=$	275.232
Dual form			275.3.f.c.243.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.925034 - 0.925034i) q^{2} +(-3.86940 + 3.86940i) q^{3} -2.28862i q^{4} +7.15866 q^{6} +(-2.48674 - 2.48674i) q^{7} +(-5.81719 + 5.81719i) q^{8} -20.9446i q^{9} -3.31662 q^{11} +(8.85561 + 8.85561i) q^{12} +(11.1429 - 11.1429i) q^{13} +4.60065i q^{14} +1.60771 q^{16} +(-1.87959 - 1.87959i) q^{17} +(-19.3745 + 19.3745i) q^{18} +32.2173i q^{19} +19.2444 q^{21} +(3.06799 + 3.06799i) q^{22} +(-10.9067 + 10.9067i) q^{23} -45.0181i q^{24} -20.6151 q^{26} +(46.2184 + 46.2184i) q^{27} +(-5.69122 + 5.69122i) q^{28} +15.8039i q^{29} +56.3876 q^{31} +(21.7816 + 21.7816i) q^{32} +(12.8334 - 12.8334i) q^{33} +3.47738i q^{34} -47.9343 q^{36} +(43.0478 + 43.0478i) q^{37} +(29.8021 - 29.8021i) q^{38} +86.2325i q^{39} +41.8566 q^{41} +(-17.8018 - 17.8018i) q^{42} +(-3.70228 + 3.70228i) q^{43} +7.59051i q^{44} +20.1781 q^{46} +(-27.8097 - 27.8097i) q^{47} +(-6.22088 + 6.22088i) q^{48} -36.6322i q^{49} +14.5458 q^{51} +(-25.5018 - 25.5018i) q^{52} +(-14.7508 + 14.7508i) q^{53} -85.5073i q^{54} +28.9317 q^{56} +(-124.662 - 124.662i) q^{57} +(14.6191 - 14.6191i) q^{58} +102.568i q^{59} -34.3345 q^{61} +(-52.1605 - 52.1605i) q^{62} +(-52.0838 + 52.0838i) q^{63} -46.7283i q^{64} -23.7426 q^{66} +(-6.48045 - 6.48045i) q^{67} +(-4.30168 + 4.30168i) q^{68} -84.4048i q^{69} -20.3765 q^{71} +(121.839 + 121.839i) q^{72} +(44.6499 - 44.6499i) q^{73} -79.6413i q^{74} +73.7332 q^{76} +(8.24760 + 8.24760i) q^{77} +(79.7680 - 79.7680i) q^{78} -28.9929i q^{79} -169.174 q^{81} +(-38.7188 - 38.7188i) q^{82} +(99.4392 - 99.4392i) q^{83} -44.0433i q^{84} +6.84948 q^{86} +(-61.1515 - 61.1515i) q^{87} +(19.2934 - 19.2934i) q^{88} +143.090i q^{89} -55.4189 q^{91} +(24.9613 + 24.9613i) q^{92} +(-218.186 + 218.186i) q^{93} +51.4498i q^{94} -168.564 q^{96} +(-4.67226 - 4.67226i) q^{97} +(-33.8860 + 33.8860i) q^{98} +69.4653i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} - 128 q^{16} - 88 q^{21} + 96 q^{26} + 360 q^{31} + 176 q^{36} - 152 q^{41} + 56 q^{46} - 512 q^{51} - 1048 q^{56} + 784 q^{61} - 440 q^{66} + 728 q^{71} + 1704 q^{76} - 568 q^{81} - 328 q^{86}+ \cdots + 1568 q^{96}+O(q^{100}) $ 24 * q - 8 * q^6 - 128 * q^16 - 88 * q^21 + 96 * q^26 + 360 * q^31 + 176 * q^36 - 152 * q^41 + 56 * q^46 - 512 * q^51 - 1048 * q^56 + 784 * q^61 - 440 * q^66 + 728 * q^71 + 1704 * q^76 - 568 * q^81 - 328 * q^86 - 968 * q^91 + 1568 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.925034	−	0.925034i	−0.462517	−	0.462517i	0.436963	−	0.899480i	$-0.356054\pi$
$2$	−0.925034	−	0.925034i	−0.462517	−	0.462517i	−0.899480	+	0.436963i	$0.856054\pi$
$3$	−3.86940	+	3.86940i	−1.28980	+	1.28980i	−0.354896	+	0.934906i	$0.615484\pi$
$3$	−3.86940	+	3.86940i	−1.28980	+	1.28980i	−0.934906	+	0.354896i	$0.884516\pi$
$4$		−	2.28862i		−	0.572156i
$5$		0			0
$5$		0			0
$6$	7.15866			1.19311
$7$	−2.48674	−	2.48674i	−0.355249	−	0.355249i	0.506809	−	0.862058i	$-0.330825\pi$
$7$	−2.48674	−	2.48674i	−0.355249	−	0.355249i	−0.862058	+	0.506809i	$0.830825\pi$
$8$	−5.81719	+	5.81719i	−0.727149	+	0.727149i
$9$		−	20.9446i		−	2.32718i
$10$		0			0
$11$	−3.31662			−0.301511
$11$	−3.31662			−0.301511
$12$	8.85561	+	8.85561i	0.737968	+	0.737968i
$13$	11.1429	−	11.1429i	0.857143	−	0.857143i	−0.133858	−	0.991001i	$-0.542736\pi$
$13$	11.1429	−	11.1429i	0.857143	−	0.857143i	0.991001	+	0.133858i	$0.0427365\pi$
$14$			4.60065i			0.328618i
$15$		0			0
$16$	1.60771			0.100482
$17$	−1.87959	−	1.87959i	−0.110564	−	0.110564i	0.649660	−	0.760225i	$-0.274911\pi$
$17$	−1.87959	−	1.87959i	−0.110564	−	0.110564i	−0.760225	+	0.649660i	$0.774911\pi$
$18$	−19.3745	+	19.3745i	−1.07636	+	1.07636i
$19$			32.2173i			1.69565i	0.530280	+	0.847823i	$0.322087\pi$
$19$			32.2173i			1.69565i	−0.530280	+	0.847823i	$0.677913\pi$
$20$		0			0
$21$	19.2444			0.916402
$22$	3.06799	+	3.06799i	0.139454	+	0.139454i
$23$	−10.9067	+	10.9067i	−0.474204	+	0.474204i	−0.903272	−	0.429068i	$-0.858842\pi$
$23$	−10.9067	+	10.9067i	−0.474204	+	0.474204i	0.429068	+	0.903272i	$0.358842\pi$
$24$		−	45.0181i		−	1.87576i
$25$		0			0
$26$	−20.6151			−0.792887
$27$	46.2184	+	46.2184i	1.71179	+	1.71179i
$28$	−5.69122	+	5.69122i	−0.203258	+	0.203258i
$29$			15.8039i			0.544961i	0.962161	+	0.272480i	$0.0878440\pi$
$29$			15.8039i			0.544961i	−0.962161	+	0.272480i	$0.912156\pi$
$30$		0			0
$31$	56.3876			1.81896			0.909478	−	0.415753i	$-0.136482\pi$
$31$	56.3876			1.81896			0.909478	+	0.415753i	$0.136482\pi$
$32$	21.7816	+	21.7816i	0.680674	+	0.680674i
$33$	12.8334	−	12.8334i	0.388890	−	0.388890i
$34$			3.47738i			0.102276i
$35$		0			0
$36$	−47.9343			−1.33151
$37$	43.0478	+	43.0478i	1.16345	+	1.16345i	0.983714	+	0.179739i	$0.0575254\pi$
$37$	43.0478	+	43.0478i	1.16345	+	1.16345i	0.179739	+	0.983714i	$0.442475\pi$
$38$	29.8021	−	29.8021i	0.784265	−	0.784265i
$39$			86.2325i			2.21109i
$40$		0			0
$41$	41.8566			1.02089			0.510447	−	0.859909i	$-0.329480\pi$
$41$	41.8566			1.02089			0.510447	+	0.859909i	$0.329480\pi$
$42$	−17.8018	−	17.8018i	−0.423852	−	0.423852i
$43$	−3.70228	+	3.70228i	−0.0860996	+	0.0860996i	−0.748845	−	0.662745i	$-0.769391\pi$
$43$	−3.70228	+	3.70228i	−0.0860996	+	0.0860996i	0.662745	+	0.748845i	$0.269391\pi$
$44$			7.59051i			0.172511i
$45$		0			0
$46$	20.1781			0.438655
$47$	−27.8097	−	27.8097i	−0.591695	−	0.591695i	0.346394	−	0.938089i	$-0.387406\pi$
$47$	−27.8097	−	27.8097i	−0.591695	−	0.591695i	−0.938089	+	0.346394i	$0.887406\pi$
$48$	−6.22088	+	6.22088i	−0.129602	+	0.129602i
$49$		−	36.6322i		−	0.747596i
$50$		0			0
$51$	14.5458			0.285212
$52$	−25.5018	−	25.5018i	−0.490419	−	0.490419i
$53$	−14.7508	+	14.7508i	−0.278317	+	0.278317i	−0.832437	−	0.554120i	$-0.813055\pi$
$53$	−14.7508	+	14.7508i	−0.278317	+	0.278317i	0.554120	+	0.832437i	$0.313055\pi$
$54$		−	85.5073i		−	1.58347i
$55$		0			0
$56$	28.9317			0.516638
$57$	−124.662	−	124.662i	−2.18705	−	2.18705i
$58$	14.6191	−	14.6191i	0.252054	−	0.252054i
$59$			102.568i			1.73845i	0.494419	+	0.869224i	$0.335381\pi$
$59$			102.568i			1.73845i	−0.494419	+	0.869224i	$0.664619\pi$
$60$		0			0
$61$	−34.3345			−0.562860			−0.281430	−	0.959582i	$-0.590809\pi$
$61$	−34.3345			−0.562860			−0.281430	+	0.959582i	$0.590809\pi$
$62$	−52.1605	−	52.1605i	−0.841298	−	0.841298i
$63$	−52.0838	+	52.0838i	−0.826727	+	0.826727i
$64$		−	46.7283i		−	0.730129i
$65$		0			0
$66$	−23.7426			−0.359736
$67$	−6.48045	−	6.48045i	−0.0967231	−	0.0967231i	0.657090	−	0.753813i	$-0.271787\pi$
$67$	−6.48045	−	6.48045i	−0.0967231	−	0.0967231i	−0.753813	+	0.657090i	$0.771787\pi$
$68$	−4.30168	+	4.30168i	−0.0632601	+	0.0632601i
$69$		−	84.4048i		−	1.22326i
$70$		0			0
$71$	−20.3765			−0.286993			−0.143497	−	0.989651i	$-0.545835\pi$
$71$	−20.3765			−0.286993			−0.143497	+	0.989651i	$0.545835\pi$
$72$	121.839	+	121.839i	1.69220	+	1.69220i
$73$	44.6499	−	44.6499i	0.611643	−	0.611643i	−0.331731	−	0.943374i	$-0.607633\pi$
$73$	44.6499	−	44.6499i	0.611643	−	0.611643i	0.943374	+	0.331731i	$0.107633\pi$
$74$		−	79.6413i		−	1.07623i
$75$		0			0
$76$	73.7332			0.970173
$77$	8.24760	+	8.24760i	0.107112	+	0.107112i
$78$	79.7680	−	79.7680i	1.02267	−	1.02267i
$79$		−	28.9929i		−	0.366998i	−0.983020	−	0.183499i	$-0.941258\pi$
$79$		−	28.9929i		−	0.366998i	0.983020	−	0.183499i	$-0.0587425\pi$
$80$		0			0
$81$	−169.174			−2.08857
$82$	−38.7188	−	38.7188i	−0.472181	−	0.472181i
$83$	99.4392	−	99.4392i	1.19806	−	1.19806i	0.223317	−	0.974746i	$-0.428311\pi$
$83$	99.4392	−	99.4392i	1.19806	−	1.19806i	0.974746	−	0.223317i	$-0.0716885\pi$
$84$		−	44.0433i		−	0.524325i
$85$		0			0
$86$	6.84948			0.0796451
$87$	−61.1515	−	61.1515i	−0.702891	−	0.702891i
$88$	19.2934	−	19.2934i	0.219244	−	0.219244i
$89$			143.090i			1.60775i	0.594799	+	0.803874i	$0.297232\pi$
$89$			143.090i			1.60775i	−0.594799	+	0.803874i	$0.702768\pi$
$90$		0			0
$91$	−55.4189			−0.608999
$92$	24.9613	+	24.9613i	0.271318	+	0.271318i
$93$	−218.186	+	218.186i	−2.34609	+	2.34609i
$94$			51.4498i			0.547338i
$95$		0			0
$96$	−168.564			−1.75587
$97$	−4.67226	−	4.67226i	−0.0481676	−	0.0481676i	0.682613	−	0.730780i	$-0.260844\pi$
$97$	−4.67226	−	4.67226i	−0.0481676	−	0.0481676i	−0.730780	+	0.682613i	$0.760844\pi$
$98$	−33.8860	+	33.8860i	−0.345776	+	0.345776i
$99$			69.4653i			0.701670i
$100$		0			0
$101$	61.2970			0.606901			0.303450	−	0.952847i	$-0.401861\pi$
$101$	61.2970			0.606901			0.303450	+	0.952847i	$0.401861\pi$
$102$	−13.4554	−	13.4554i	−0.131916	−	0.131916i
$103$	2.50303	−	2.50303i	0.0243013	−	0.0243013i	−0.694852	−	0.719153i	$-0.744530\pi$
$103$	2.50303	−	2.50303i	0.0243013	−	0.0243013i	0.719153	+	0.694852i	$0.244530\pi$
$104$			129.640i			1.24654i
$105$		0			0
$106$	27.2900			0.257453
$107$	113.682	+	113.682i	1.06245	+	1.06245i	0.997915	+	0.0645372i	$0.0205571\pi$
$107$	113.682	+	113.682i	1.06245	+	1.06245i	0.0645372	+	0.997915i	$0.479443\pi$
$108$	105.777	−	105.777i	0.979413	−	0.979413i
$109$		−	79.9776i		−	0.733740i	−0.930272	−	0.366870i	$-0.880429\pi$
$109$		−	79.9776i		−	0.733740i	0.930272	−	0.366870i	$-0.119571\pi$
$110$		0			0
$111$	−333.139			−3.00125
$112$	−3.99796	−	3.99796i	−0.0356961	−	0.0356961i
$113$	52.3355	−	52.3355i	0.463146	−	0.463146i	−0.436539	−	0.899685i	$-0.643796\pi$
$113$	52.3355	−	52.3355i	0.463146	−	0.463146i	0.899685	+	0.436539i	$0.143796\pi$
$114$			230.633i			2.02309i
$115$		0			0
$116$	36.1691			0.311802
$117$	−233.383	−	233.383i	−1.99472	−	1.99472i
$118$	94.8793	−	94.8793i	0.804062	−	0.804062i
$119$			9.34814i			0.0785558i
$120$		0			0
$121$	11.0000			0.0909091
$122$	31.7606	+	31.7606i	0.260333	+	0.260333i
$123$	−161.960	+	161.960i	−1.31675	+	1.31675i
$124$		−	129.050i		−	1.04073i
$125$		0			0
$126$	96.3586			0.764751
$127$	115.361	+	115.361i	0.908353	+	0.908353i	0.996139	−	0.0877867i	$-0.0279794\pi$
$127$	115.361	+	115.361i	0.908353	+	0.908353i	−0.0877867	+	0.996139i	$0.527979\pi$
$128$	43.9011	−	43.9011i	0.342977	−	0.342977i
$129$		−	28.6513i		−	0.222103i
$130$		0			0
$131$	−75.4069			−0.575625			−0.287812	−	0.957687i	$-0.592928\pi$
$131$	−75.4069			−0.575625			−0.287812	+	0.957687i	$0.592928\pi$
$132$	−29.3707	−	29.3707i	−0.222506	−	0.222506i
$133$	80.1161	−	80.1161i	0.602377	−	0.602377i
$134$			11.9893i			0.0894721i
$135$		0			0
$136$	21.8679			0.160794
$137$	−8.03264	−	8.03264i	−0.0586324	−	0.0586324i	0.677183	−	0.735815i	$-0.263201\pi$
$137$	−8.03264	−	8.03264i	−0.0586324	−	0.0586324i	−0.735815	+	0.677183i	$0.763201\pi$
$138$	−78.0773	+	78.0773i	−0.565777	+	0.565777i
$139$		−	154.718i		−	1.11308i	−0.830821	−	0.556540i	$-0.812129\pi$
$139$		−	154.718i		−	1.11308i	0.830821	−	0.556540i	$-0.187871\pi$
$140$		0			0
$141$	215.214			1.52634
$142$	18.8490	+	18.8490i	0.132739	+	0.132739i
$143$	−36.9567	+	36.9567i	−0.258438	+	0.258438i
$144$		−	33.6728i		−	0.233839i
$145$		0			0
$146$	−82.6054			−0.565791
$147$	141.745	+	141.745i	0.964251	+	0.964251i
$148$	98.5202	−	98.5202i	0.665677	−	0.665677i
$149$			80.0369i			0.537160i	0.963257	+	0.268580i	$0.0865544\pi$
$149$			80.0369i			0.537160i	−0.963257	+	0.268580i	$0.913446\pi$
$150$		0			0
$151$	206.188			1.36548			0.682742	−	0.730659i	$-0.260787\pi$
$151$	206.188			1.36548			0.682742	+	0.730659i	$0.260787\pi$
$152$	−187.414	−	187.414i	−1.23299	−	1.23299i
$153$	−39.3673	+	39.3673i	−0.257303	+	0.257303i
$154$		−	15.2586i		−	0.0990819i
$155$		0			0
$156$	197.354			1.26509
$157$	76.0386	+	76.0386i	0.484322	+	0.484322i	0.906509	−	0.422187i	$-0.138737\pi$
$157$	76.0386	+	76.0386i	0.484322	+	0.484322i	−0.422187	+	0.906509i	$0.638737\pi$
$158$	−26.8194	+	26.8194i	−0.169743	+	0.169743i
$159$		−	114.154i		−	0.717947i
$160$		0			0
$161$	54.2443			0.336921
$162$	156.492	+	156.492i	0.966000	+	0.966000i
$163$	−21.8597	+	21.8597i	−0.134108	+	0.134108i	−0.770974	−	0.636866i	$-0.780230\pi$
$163$	−21.8597	+	21.8597i	−0.134108	+	0.134108i	0.636866	+	0.770974i	$0.280230\pi$
$164$		−	95.7941i		−	0.584110i
$165$		0			0
$166$	−183.969			−1.10825
$167$	19.5124	+	19.5124i	0.116841	+	0.116841i	0.763110	−	0.646269i	$-0.223672\pi$
$167$	19.5124	+	19.5124i	0.116841	+	0.116841i	−0.646269	+	0.763110i	$0.723672\pi$
$168$	−111.949	+	111.949i	−0.666361	+	0.666361i
$169$		−	79.3266i		−	0.469388i
$170$		0			0
$171$	674.777			3.94607
$172$	8.47313	+	8.47313i	0.0492624	+	0.0492624i
$173$	−214.952	+	214.952i	−1.24250	+	1.24250i	−0.283539	+	0.958961i	$0.591508\pi$
$173$	−214.952	+	214.952i	−1.24250	+	1.24250i	−0.958961	+	0.283539i	$0.908492\pi$
$174$			113.135i			0.650198i
$175$		0			0
$176$	−5.33217			−0.0302964
$177$	−396.879	−	396.879i	−2.24225	−	2.24225i
$178$	132.363	−	132.363i	0.743611	−	0.743611i
$179$			111.046i			0.620370i	0.950676	+	0.310185i	$0.100391\pi$
$179$			111.046i			0.620370i	−0.950676	+	0.310185i	$0.899609\pi$
$180$		0			0
$181$	−126.341			−0.698014			−0.349007	−	0.937120i	$-0.613481\pi$
$181$	−126.341			−0.698014			−0.349007	+	0.937120i	$0.613481\pi$
$182$	51.2644	+	51.2644i	0.281672	+	0.281672i
$183$	132.854	−	132.854i	0.725978	−	0.725978i
$184$		−	126.893i		−	0.689633i
$185$		0			0
$186$	403.660			2.17021
$187$	6.23391	+	6.23391i	0.0333364	+	0.0333364i
$188$	−63.6459	+	63.6459i	−0.338542	+	0.338542i
$189$		−	229.867i		−	1.21623i
$190$		0			0
$191$	−172.600			−0.903665			−0.451832	−	0.892103i	$-0.649230\pi$
$191$	−172.600			−0.903665			−0.451832	+	0.892103i	$0.649230\pi$
$192$	180.811	+	180.811i	0.941721	+	0.941721i
$193$	51.8757	−	51.8757i	0.268786	−	0.268786i	−0.559825	−	0.828611i	$-0.689132\pi$
$193$	51.8757	−	51.8757i	0.268786	−	0.268786i	0.828611	+	0.559825i	$0.189132\pi$
$194$			8.64400i			0.0445567i
$195$		0			0
$196$	−83.8373			−0.427741
$197$	117.224	+	117.224i	0.595045	+	0.595045i	0.938990	−	0.343945i	$-0.111763\pi$
$197$	117.224	+	117.224i	0.595045	+	0.595045i	−0.343945	+	0.938990i	$0.611763\pi$
$198$	64.2578	−	64.2578i	0.324534	−	0.324534i
$199$			124.111i			0.623671i	0.950136	+	0.311836i	$0.100944\pi$
$199$			124.111i			0.623671i	−0.950136	+	0.311836i	$0.899056\pi$
$200$		0			0
$201$	50.1509			0.249507
$202$	−56.7018	−	56.7018i	−0.280702	−	0.280702i
$203$	39.3002	−	39.3002i	0.193597	−	0.193597i
$204$		−	33.2899i		−	0.163186i
$205$		0			0
$206$	−4.63078			−0.0224795
$207$	228.436	+	228.436i	1.10356	+	1.10356i
$208$	17.9145	−	17.9145i	0.0861273	−	0.0861273i
$209$		−	106.853i		−	0.511256i
$210$		0			0
$211$	−72.1006			−0.341709			−0.170854	−	0.985296i	$-0.554653\pi$
$211$	−72.1006			−0.341709			−0.170854	+	0.985296i	$0.554653\pi$
$212$	33.7590	+	33.7590i	0.159241	+	0.159241i
$213$	78.8450	−	78.8450i	0.370164	−	0.370164i
$214$		−	210.320i		−	0.982805i
$215$		0			0
$216$	−537.723			−2.48946
$217$	−140.222	−	140.222i	−0.646182	−	0.646182i
$218$	−73.9820	+	73.9820i	−0.339367	+	0.339367i
$219$			345.537i			1.57780i
$220$		0			0
$221$	−41.8881			−0.189539
$222$	308.165	+	308.165i	1.38813	+	1.38813i
$223$	−208.503	+	208.503i	−0.934993	+	0.934993i	−0.998012	−	0.0630193i	$-0.979927\pi$
$223$	−208.503	+	208.503i	−0.934993	+	0.934993i	0.0630193	+	0.998012i	$0.479927\pi$
$224$		−	108.330i		−	0.483618i
$225$		0			0
$226$	−96.8243			−0.428426
$227$	96.7721	+	96.7721i	0.426309	+	0.426309i	0.887369	−	0.461060i	$-0.152531\pi$
$227$	96.7721	+	96.7721i	0.426309	+	0.426309i	−0.461060	+	0.887369i	$0.652531\pi$
$228$	−285.304	+	285.304i	−1.25133	+	1.25133i
$229$		−	24.3833i		−	0.106477i	−0.998582	−	0.0532387i	$-0.983046\pi$
$229$		−	24.3833i		−	0.106477i	0.998582	−	0.0532387i	$-0.0169544\pi$
$230$		0			0
$231$	−63.8266			−0.276306
$232$	−91.9341	−	91.9341i	−0.396268	−	0.396268i
$233$	6.08298	−	6.08298i	0.0261072	−	0.0261072i	−0.693933	−	0.720040i	$-0.744123\pi$
$233$	6.08298	−	6.08298i	0.0261072	−	0.0261072i	0.720040	+	0.693933i	$0.244123\pi$
$234$			431.774i			1.84519i
$235$		0			0
$236$	234.740			0.994663
$237$	112.185	+	112.185i	0.473355	+	0.473355i
$238$	8.64735	−	8.64735i	0.0363334	−	0.0363334i
$239$			301.659i			1.26217i	0.775713	+	0.631086i	$0.217391\pi$
$239$			301.659i			1.26217i	−0.775713	+	0.631086i	$0.782609\pi$
$240$		0			0
$241$	−152.402			−0.632372			−0.316186	−	0.948697i	$-0.602402\pi$
$241$	−152.402			−0.632372			−0.316186	+	0.948697i	$0.602402\pi$
$242$	−10.1754	−	10.1754i	−0.0420470	−	0.0420470i
$243$	238.638	−	238.638i	0.982050	−	0.982050i
$244$			78.5787i			0.322044i
$245$		0			0
$246$	299.638			1.21804
$247$	358.992	+	358.992i	1.45341	+	1.45341i
$248$	−328.018	+	328.018i	−1.32265	+	1.32265i
$249$			769.541i			3.09053i
$250$		0			0
$251$	0.830967			0.00331063			0.00165531	−	0.999999i	$-0.499473\pi$
$251$	0.830967			0.00331063			0.00165531	+	0.999999i	$0.499473\pi$
$252$	119.200	+	119.200i	0.473017	+	0.473017i
$253$	36.1734	−	36.1734i	0.142978	−	0.142978i
$254$		−	213.425i		−	0.840257i
$255$		0			0
$256$	−268.133			−1.04739
$257$	−213.892	−	213.892i	−0.832265	−	0.832265i	0.155561	−	0.987826i	$-0.450281\pi$
$257$	−213.892	−	213.892i	−0.832265	−	0.832265i	−0.987826	+	0.155561i	$0.950281\pi$
$258$	−26.5034	+	26.5034i	−0.102726	+	0.102726i
$259$		−	214.098i		−	0.826632i
$260$		0			0
$261$	331.005			1.26822
$262$	69.7539	+	69.7539i	0.266236	+	0.266236i
$263$	−242.199	+	242.199i	−0.920908	+	0.920908i	−0.997094	−	0.0761856i	$-0.975726\pi$
$263$	−242.199	+	242.199i	−0.920908	+	0.920908i	0.0761856	+	0.997094i	$0.475726\pi$
$264$			149.308i			0.565562i
$265$		0			0
$266$	−148.220			−0.557219
$267$	−553.672	−	553.672i	−2.07368	−	2.07368i
$268$	−14.8313	+	14.8313i	−0.0553407	+	0.0553407i
$269$		−	274.273i		−	1.01960i	−0.860292	−	0.509801i	$-0.829719\pi$
$269$		−	274.273i		−	1.01960i	0.860292	−	0.509801i	$-0.170281\pi$
$270$		0			0
$271$	−224.792			−0.829490			−0.414745	−	0.909938i	$-0.636129\pi$
$271$	−224.792			−0.829490			−0.414745	+	0.909938i	$0.636129\pi$
$272$	−3.02184	−	3.02184i	−0.0111097	−	0.0111097i
$273$	214.438	−	214.438i	0.785487	−	0.785487i
$274$			14.8609i			0.0542370i
$275$		0			0
$276$	−193.171			−0.699894
$277$	63.8151	+	63.8151i	0.230379	+	0.230379i	0.812851	−	0.582472i	$-0.197914\pi$
$277$	63.8151	+	63.8151i	0.230379	+	0.230379i	−0.582472	+	0.812851i	$0.697914\pi$
$278$	−143.119	+	143.119i	−0.514818	+	0.514818i
$279$		−	1181.01i		−	4.23303i
$280$		0			0
$281$	305.190			1.08609			0.543043	−	0.839705i	$-0.317272\pi$
$281$	305.190			1.08609			0.543043	+	0.839705i	$0.317272\pi$
$282$	−199.080	−	199.080i	−0.705958	−	0.705958i
$283$	367.259	−	367.259i	1.29773	−	1.29773i	0.367849	−	0.929885i	$-0.380094\pi$
$283$	367.259	−	367.259i	1.29773	−	1.29773i	0.929885	−	0.367849i	$-0.119906\pi$
$284$			46.6342i			0.164205i
$285$		0			0
$286$	68.3724			0.239064
$287$	−104.087	−	104.087i	−0.362672	−	0.362672i
$288$	456.206	−	456.206i	1.58405	−	1.58405i
$289$		−	281.934i		−	0.975551i
$290$		0			0
$291$	36.1577			0.124253
$292$	−102.187	−	102.187i	−0.349955	−	0.349955i
$293$	249.733	−	249.733i	0.852332	−	0.852332i	−0.138088	−	0.990420i	$-0.544096\pi$
$293$	249.733	−	249.733i	0.852332	−	0.852332i	0.990420	+	0.138088i	$0.0440957\pi$
$294$		−	262.238i		−	0.891965i
$295$		0			0
$296$	−500.834			−1.69201
$297$	−153.289	−	153.289i	−0.516125	−	0.516125i
$298$	74.0368	−	74.0368i	0.248446	−	0.248446i
$299$			243.063i			0.812921i
$300$		0			0
$301$	18.4133			0.0611736
$302$	−190.731	−	190.731i	−0.631560	−	0.631560i
$303$	−237.183	+	237.183i	−0.782781	+	0.782781i
$304$			51.7960i			0.170382i
$305$		0			0
$306$	72.8323			0.238014
$307$	282.935	+	282.935i	0.921614	+	0.921614i	0.997144	−	0.0755300i	$-0.0240649\pi$
$307$	282.935	+	282.935i	0.921614	+	0.921614i	−0.0755300	+	0.997144i	$0.524065\pi$
$308$	18.8756	−	18.8756i	0.0612846	−	0.0612846i
$309$			19.3705i			0.0626876i
$310$		0			0
$311$	−20.6266			−0.0663233			−0.0331617	−	0.999450i	$-0.510558\pi$
$311$	−20.6266			−0.0663233			−0.0331617	+	0.999450i	$0.510558\pi$
$312$	−501.631	−	501.631i	−1.60779	−	1.60779i
$313$	−164.238	+	164.238i	−0.524722	+	0.524722i	−0.918994	−	0.394272i	$-0.870997\pi$
$313$	−164.238	+	164.238i	−0.524722	+	0.524722i	0.394272	+	0.918994i	$0.370997\pi$
$314$		−	140.677i		−	0.448015i
$315$		0			0
$316$	−66.3538			−0.209980
$317$	−58.8640	−	58.8640i	−0.185691	−	0.185691i	0.608139	−	0.793830i	$-0.291916\pi$
$317$	−58.8640	−	58.8640i	−0.185691	−	0.185691i	−0.793830	+	0.608139i	$0.791916\pi$
$318$	−105.596	+	105.596i	−0.332063	+	0.332063i
$319$		−	52.4155i		−	0.164312i
$320$		0			0
$321$	−879.767			−2.74071
$322$	−50.1778	−	50.1778i	−0.155832	−	0.155832i
$323$	60.5554	−	60.5554i	0.187478	−	0.187478i
$324$			387.176i			1.19499i
$325$		0			0
$326$	40.4419			0.124055
$327$	309.466	+	309.466i	0.946378	+	0.946378i
$328$	−243.488	+	243.488i	−0.742342	+	0.742342i
$329$			138.311i			0.420398i
$330$		0			0
$331$	388.432			1.17351			0.586756	−	0.809764i	$-0.300405\pi$
$331$	388.432			1.17351			0.586756	+	0.809764i	$0.300405\pi$
$332$	−227.579	−	227.579i	−0.685479	−	0.685479i
$333$	901.618	−	901.618i	2.70756	−	2.70756i
$334$		−	36.0992i		−	0.108081i
$335$		0			0
$336$	30.9395			0.0920817
$337$	77.3541	+	77.3541i	0.229538	+	0.229538i	0.812499	−	0.582962i	$-0.198106\pi$
$337$	77.3541	+	77.3541i	0.229538	+	0.229538i	−0.582962	+	0.812499i	$0.698106\pi$
$338$	−73.3799	+	73.3799i	−0.217100	+	0.217100i
$339$			405.014i			1.19473i
$340$		0			0
$341$	−187.017			−0.548436
$342$	−624.192	−	624.192i	−1.82512	−	1.82512i
$343$	−212.945	+	212.945i	−0.620832	+	0.620832i
$344$		−	43.0738i		−	0.125214i
$345$		0			0
$346$	397.677			1.14935
$347$	−171.192	−	171.192i	−0.493349	−	0.493349i	0.416011	−	0.909360i	$-0.363428\pi$
$347$	−171.192	−	171.192i	−0.493349	−	0.493349i	−0.909360	+	0.416011i	$0.863428\pi$
$348$	−139.953	+	139.953i	−0.402163	+	0.402163i
$349$		−	29.9624i		−	0.0858521i	−0.999078	−	0.0429260i	$-0.986332\pi$
$349$		−	29.9624i		−	0.0858521i	0.999078	−	0.0429260i	$-0.0136680\pi$
$350$		0			0
$351$	1030.01			2.93450
$352$	−72.2413	−	72.2413i	−0.205231	−	0.205231i
$353$	126.771	−	126.771i	0.359125	−	0.359125i	−0.504365	−	0.863490i	$-0.668274\pi$
$353$	126.771	−	126.771i	0.359125	−	0.359125i	0.863490	+	0.504365i	$0.168274\pi$
$354$			734.253i			2.07416i
$355$		0			0
$356$	327.478			0.919883
$357$	−36.1717	−	36.1717i	−0.101321	−	0.101321i
$358$	102.722	−	102.722i	0.286932	−	0.286932i
$359$		−	191.615i		−	0.533745i	−0.963732	−	0.266873i	$-0.914010\pi$
$359$		−	191.615i		−	0.533745i	0.963732	−	0.266873i	$-0.0859903\pi$
$360$		0			0
$361$	−676.952			−1.87521
$362$	116.869	+	116.869i	0.322844	+	0.322844i
$363$	−42.5635	+	42.5635i	−0.117255	+	0.117255i
$364$			126.833i			0.348442i
$365$		0			0
$366$	−245.789			−0.671555
$367$	−214.617	−	214.617i	−0.584788	−	0.584788i	0.351427	−	0.936215i	$-0.385697\pi$
$367$	−214.617	−	214.617i	−0.584788	−	0.584788i	−0.936215	+	0.351427i	$0.885697\pi$
$368$	−17.5348	+	17.5348i	−0.0476489	+	0.0476489i
$369$		−	876.670i		−	2.37580i
$370$		0			0
$371$	73.3629			0.197744
$372$	499.347	+	499.347i	1.34233	+	1.34233i
$373$	118.727	−	118.727i	0.318304	−	0.318304i	−0.529812	−	0.848115i	$-0.677737\pi$
$373$	118.727	−	118.727i	0.318304	−	0.318304i	0.848115	+	0.529812i	$0.177737\pi$
$374$		−	11.5332i		−	0.0308373i
$375$		0			0
$376$	323.548			0.860501
$377$	176.100	+	176.100i	0.467109	+	0.467109i
$378$	−212.635	+	212.635i	−0.562526	+	0.562526i
$379$			70.6243i			0.186344i	0.995650	+	0.0931719i	$0.0297006\pi$
$379$			70.6243i			0.186344i	−0.995650	+	0.0931719i	$0.970299\pi$
$380$		0			0
$381$	−892.755			−2.34319
$382$	159.661	+	159.661i	0.417960	+	0.417960i
$383$	−408.698	+	408.698i	−1.06710	+	1.06710i	−0.0695164	+	0.997581i	$0.522146\pi$
$383$	−408.698	+	408.698i	−1.06710	+	1.06710i	−0.997581	+	0.0695164i	$0.977854\pi$
$384$			339.742i			0.884745i
$385$		0			0
$386$	−95.9735			−0.248636
$387$	77.5428	+	77.5428i	0.200369	+	0.200369i
$388$	−10.6930	+	10.6930i	−0.0275594	+	0.0275594i
$389$			601.280i			1.54571i	0.634584	+	0.772854i	$0.281171\pi$
$389$			601.280i			1.54571i	−0.634584	+	0.772854i	$0.718829\pi$
$390$		0			0
$391$	41.0003			0.104860
$392$	213.097	+	213.097i	0.543614	+	0.543614i
$393$	291.780	−	291.780i	0.742442	−	0.742442i
$394$		−	216.872i		−	0.550437i
$395$		0			0
$396$	158.980			0.401465
$397$	341.609	+	341.609i	0.860477	+	0.860477i	0.991393	−	0.130916i	$-0.0417919\pi$
$397$	341.609	+	341.609i	0.860477	+	0.860477i	−0.130916	+	0.991393i	$0.541792\pi$
$398$	114.807	−	114.807i	0.288459	−	0.288459i
$399$			620.003i			1.55389i
$400$		0			0
$401$	−210.080			−0.523889			−0.261945	−	0.965083i	$-0.584364\pi$
$401$	−210.080			−0.523889			−0.261945	+	0.965083i	$0.584364\pi$
$402$	−46.3913	−	46.3913i	−0.115401	−	0.115401i
$403$	628.319	−	628.319i	1.55910	−	1.55910i
$404$		−	140.286i		−	0.347242i
$405$		0			0
$406$	−72.7080			−0.179084
$407$	−142.773	−	142.773i	−0.350794	−	0.350794i
$408$	−84.6159	+	84.6159i	−0.207392	+	0.207392i
$409$			691.981i			1.69188i	0.533275	+	0.845942i	$0.320961\pi$
$409$			691.981i			1.69188i	−0.533275	+	0.845942i	$0.679039\pi$
$410$		0			0
$411$	62.1630			0.151248
$412$	−5.72850	−	5.72850i	−0.0139041	−	0.0139041i
$413$	255.061	−	255.061i	0.617582	−	0.617582i
$414$		−	422.622i		−	1.02083i
$415$		0			0
$416$	485.418			1.16687
$417$	598.667	+	598.667i	1.43565	+	1.43565i
$418$	−98.8423	+	98.8423i	−0.236465	+	0.236465i
$419$		−	390.808i		−	0.932717i	−0.884596	−	0.466358i	$-0.845566\pi$
$419$		−	390.808i		−	0.932717i	0.884596	−	0.466358i	$-0.154434\pi$
$420$		0			0
$421$	−417.581			−0.991879			−0.495939	−	0.868357i	$-0.665176\pi$
$421$	−417.581			−0.991879			−0.495939	+	0.868357i	$0.665176\pi$
$422$	66.6955	+	66.6955i	0.158046	+	0.158046i
$423$	−582.462	+	582.462i	−1.37698	+	1.37698i
$424$		−	171.616i		−	0.404756i
$425$		0			0
$426$	−145.869			−0.342415
$427$	85.3811	+	85.3811i	0.199956	+	0.199956i
$428$	260.176	−	260.176i	0.607888	−	0.607888i
$429$		−	286.001i		−	0.666668i
$430$		0			0
$431$	−114.444			−0.265532			−0.132766	−	0.991147i	$-0.542386\pi$
$431$	−114.444			−0.265532			−0.132766	+	0.991147i	$0.542386\pi$
$432$	74.3058	+	74.3058i	0.172004	+	0.172004i
$433$	−212.706	+	212.706i	−0.491237	+	0.491237i	−0.908696	−	0.417459i	$-0.862921\pi$
$433$	−212.706	+	212.706i	−0.491237	+	0.491237i	0.417459	+	0.908696i	$0.362921\pi$
$434$			259.419i			0.597741i
$435$		0			0
$436$	−183.039			−0.419813
$437$	−351.384	−	351.384i	−0.804081	−	0.804081i
$438$	319.634	−	319.634i	0.729758	−	0.729758i
$439$		−	410.312i		−	0.934652i	−0.884085	−	0.467326i	$-0.845217\pi$
$439$		−	410.312i		−	0.934652i	0.884085	−	0.467326i	$-0.154783\pi$
$440$		0			0
$441$	−767.246			−1.73979
$442$	38.7479	+	38.7479i	0.0876650	+	0.0876650i
$443$	−226.060	+	226.060i	−0.510293	+	0.510293i	−0.914616	−	0.404323i	$-0.867507\pi$
$443$	−226.060	+	226.060i	−0.510293	+	0.510293i	0.404323	+	0.914616i	$0.367507\pi$
$444$			762.429i			1.71718i
$445$		0			0
$446$	385.746			0.864901
$447$	−309.695	−	309.695i	−0.692830	−	0.692830i
$448$	−116.201	+	116.201i	−0.259378	+	0.259378i
$449$			378.916i			0.843912i	0.906616	+	0.421956i	$0.138656\pi$
$449$			378.916i			0.843912i	−0.906616	+	0.421956i	$0.861344\pi$
$450$		0			0
$451$	−138.823			−0.307811
$452$	−119.776	−	119.776i	−0.264992	−	0.264992i
$453$	−797.825	+	797.825i	−1.76120	+	1.76120i
$454$		−	179.035i		−	0.394350i
$455$		0			0
$456$	1450.36			3.18062
$457$	360.460	+	360.460i	0.788753	+	0.788753i	0.981290	−	0.192537i	$-0.0616715\pi$
$457$	360.460	+	360.460i	0.788753	+	0.788753i	−0.192537	+	0.981290i	$0.561671\pi$
$458$	−22.5554	+	22.5554i	−0.0492476	+	0.0492476i
$459$		−	173.744i		−	0.378527i
$460$		0			0
$461$	−219.012			−0.475081			−0.237540	−	0.971378i	$-0.576341\pi$
$461$	−219.012			−0.475081			−0.237540	+	0.971378i	$0.576341\pi$
$462$	59.0418	+	59.0418i	0.127796	+	0.127796i
$463$	−192.919	+	192.919i	−0.416672	+	0.416672i	−0.884055	−	0.467383i	$-0.845197\pi$
$463$	−192.919	+	192.919i	−0.416672	+	0.416672i	0.467383	+	0.884055i	$0.345197\pi$
$464$			25.4080i			0.0547586i
$465$		0			0
$466$	−11.2539			−0.0241500
$467$	82.3422	+	82.3422i	0.176322	+	0.176322i	0.789750	−	0.613429i	$-0.210210\pi$
$467$	82.3422	+	82.3422i	0.176322	+	0.176322i	−0.613429	+	0.789750i	$0.710210\pi$
$468$	−534.125	+	534.125i	−1.14129	+	1.14129i
$469$			32.2304i			0.0687216i
$470$		0			0
$471$	−588.448			−1.24936
$472$	−596.660	−	596.660i	−1.26411	−	1.26411i
$473$	12.2791	−	12.2791i	0.0259600	−	0.0259600i
$474$		−	207.550i		−	0.437870i
$475$		0			0
$476$	21.3944			0.0449462
$477$	308.949	+	308.949i	0.647692	+	0.647692i
$478$	279.045	−	279.045i	0.583777	−	0.583777i
$479$		−	888.420i		−	1.85474i	−0.374147	−	0.927369i	$-0.622065\pi$
$479$		−	888.420i		−	1.85474i	0.374147	−	0.927369i	$-0.377935\pi$
$480$		0			0
$481$	959.351			1.99449
$482$	140.977	+	140.977i	0.292483	+	0.292483i
$483$	−209.893	+	209.893i	−0.434561	+	0.434561i
$484$		−	25.1749i		−	0.0520142i
$485$		0			0
$486$	−441.497			−0.908430
$487$	124.471	+	124.471i	0.255587	+	0.255587i	0.823257	−	0.567669i	$-0.192155\pi$
$487$	124.471	+	124.471i	0.255587	+	0.255587i	−0.567669	+	0.823257i	$0.692155\pi$
$488$	199.730	−	199.730i	0.409283	−	0.409283i
$489$		−	169.168i		−	0.345946i
$490$		0			0
$491$	970.147			1.97586			0.987929	−	0.154906i	$-0.0495074\pi$
$491$	970.147			1.97586			0.987929	+	0.154906i	$0.0495074\pi$
$492$	370.666	+	370.666i	0.753386	+	0.753386i
$493$	29.7049	−	29.7049i	0.0602533	−	0.0602533i
$494$		−	664.161i		−	1.34445i
$495$		0			0
$496$	90.6549			0.182772
$497$	50.6712	+	50.6712i	0.101954	+	0.101954i
$498$	711.852	−	711.852i	1.42942	−	1.42942i
$499$		−	581.566i		−	1.16546i	−0.812665	−	0.582732i	$-0.801984\pi$
$499$		−	581.566i		−	1.16546i	0.812665	−	0.582732i	$-0.198016\pi$
$500$		0			0
$501$	−151.003			−0.301402
$502$	−0.768673	−	0.768673i	−0.00153122	−	0.00153122i
$503$	337.601	−	337.601i	0.671176	−	0.671176i	−0.286811	−	0.957987i	$-0.592595\pi$
$503$	337.601	−	337.601i	0.671176	−	0.671176i	0.957987	+	0.286811i	$0.0925953\pi$
$504$		−	605.963i		−	1.20231i
$505$		0			0
$506$	−66.9232			−0.132259
$507$	306.947	+	306.947i	0.605418	+	0.605418i
$508$	264.017	−	264.017i	0.519719	−	0.519719i
$509$		−	368.994i		−	0.724939i	−0.931996	−	0.362470i	$-0.881934\pi$
$509$		−	368.994i		−	0.724939i	0.931996	−	0.362470i	$-0.118066\pi$
$510$		0			0
$511$	−222.066			−0.434571
$512$	72.4279	+	72.4279i	0.141461	+	0.141461i
$513$	−1489.03	+	1489.03i	−2.90260	+	2.90260i
$514$			395.715i			0.769873i
$515$		0			0
$516$	−65.5720			−0.127077
$517$	92.2342	+	92.2342i	0.178403	+	0.178403i
$518$	−198.048	+	198.048i	−0.382331	+	0.382331i
$519$		−	1663.48i		−	3.20516i
$520$		0			0
$521$	533.075			1.02318			0.511589	−	0.859231i	$-0.329057\pi$
$521$	533.075			1.02318			0.511589	+	0.859231i	$0.329057\pi$
$522$	−306.191	−	306.191i	−0.586573	−	0.586573i
$523$	−311.717	+	311.717i	−0.596018	+	0.596018i	−0.939250	−	0.343233i	$-0.888478\pi$
$523$	−311.717	+	311.717i	−0.596018	+	0.596018i	0.343233	+	0.939250i	$0.388478\pi$
$524$			172.578i			0.329347i
$525$		0			0
$526$	448.084			0.851871
$527$	−105.986	−	105.986i	−0.201112	−	0.201112i
$528$	20.6323	−	20.6323i	0.0390764	−	0.0390764i
$529$			291.088i			0.550262i
$530$		0			0
$531$	2148.25			4.04567
$532$	−183.356	−	183.356i	−0.344653	−	0.344653i
$533$	466.403	−	466.403i	0.875052	−	0.875052i
$534$			1024.33i			1.91822i
$535$		0			0
$536$	75.3960			0.140664
$537$	−429.683	−	429.683i	−0.800154	−	0.800154i
$538$	−253.712	+	253.712i	−0.471584	+	0.471584i
$539$			121.495i			0.225409i
$540$		0			0
$541$	1005.97			1.85947			0.929736	−	0.368227i	$-0.120035\pi$
$541$	1005.97			1.85947			0.929736	+	0.368227i	$0.120035\pi$
$542$	207.940	+	207.940i	0.383653	+	0.383653i
$543$	488.863	−	488.863i	0.900300	−	0.900300i
$544$		−	81.8811i		−	0.150517i
$545$		0			0
$546$	−396.725			−0.726603
$547$	−5.81163	−	5.81163i	−0.0106245	−	0.0106245i	0.701775	−	0.712399i	$-0.252391\pi$
$547$	−5.81163	−	5.81163i	−0.0106245	−	0.0106245i	−0.712399	+	0.701775i	$0.752391\pi$
$548$	−18.3837	+	18.3837i	−0.0335469	+	0.0335469i
$549$			719.121i			1.30988i
$550$		0			0
$551$	−509.157			−0.924060
$552$	490.999	+	490.999i	0.889490	+	0.889490i
$553$	−72.0979	+	72.0979i	−0.130376	+	0.130376i
$554$		−	118.062i		−	0.213109i
$555$		0			0
$556$	−354.091			−0.636855
$557$	−647.706	−	647.706i	−1.16285	−	1.16285i	−0.983850	−	0.178998i	$-0.942715\pi$
$557$	−647.706	−	647.706i	−1.16285	−	1.16285i	−0.178998	−	0.983850i	$-0.557285\pi$
$558$	−1092.48	+	1092.48i	−1.95785	+	1.95785i
$559$			82.5081i			0.147599i
$560$		0			0
$561$	−48.2430			−0.0859947
$562$	−282.311	−	282.311i	−0.502334	−	0.502334i
$563$	175.680	−	175.680i	0.312042	−	0.312042i	−0.533658	−	0.845700i	$-0.679183\pi$
$563$	175.680	−	175.680i	0.312042	−	0.312042i	0.845700	+	0.533658i	$0.179183\pi$
$564$		−	492.543i		−	0.873304i
$565$		0			0
$566$	−679.454			−1.20045
$567$	420.693	+	420.693i	0.741964	+	0.741964i
$568$	118.534	−	118.534i	0.208687	−	0.208687i
$569$			731.096i			1.28488i	0.766336	+	0.642440i	$0.222078\pi$
$569$			731.096i			1.28488i	−0.766336	+	0.642440i	$0.777922\pi$
$570$		0			0
$571$	135.547			0.237385			0.118693	−	0.992931i	$-0.462130\pi$
$571$	135.547			0.237385			0.118693	+	0.992931i	$0.462130\pi$
$572$	84.5799	+	84.5799i	0.147867	+	0.147867i
$573$	667.859	−	667.859i	1.16555	−	1.16555i
$574$			192.568i			0.335484i
$575$		0			0
$576$	−978.704			−1.69914
$577$	232.635	+	232.635i	0.403180	+	0.403180i	0.879352	−	0.476172i	$-0.157976\pi$
$577$	232.635	+	232.635i	0.403180	+	0.403180i	−0.476172	+	0.879352i	$0.657976\pi$
$578$	−260.799	+	260.799i	−0.451209	+	0.451209i
$579$			401.456i			0.693361i
$580$		0			0
$581$	−494.560			−0.851222
$582$	−33.4471	−	33.4471i	−0.0574693	−	0.0574693i
$583$	48.9228	−	48.9228i	0.0839157	−	0.0839157i
$584$			519.475i			0.889511i
$585$		0			0
$586$	−462.024			−0.788436
$587$	344.731	+	344.731i	0.587275	+	0.587275i	0.936893	−	0.349617i	$-0.113688\pi$
$587$	344.731	+	344.731i	0.587275	+	0.587275i	−0.349617	+	0.936893i	$0.613688\pi$
$588$	324.401	−	324.401i	0.551702	−	0.551702i
$589$			1816.65i			3.08430i
$590$		0			0
$591$	−907.173			−1.53498
$592$	69.2083	+	69.2083i	0.116906	+	0.116906i
$593$	497.299	−	497.299i	0.838616	−	0.838616i	−0.150060	−	0.988677i	$-0.547947\pi$
$593$	497.299	−	497.299i	0.838616	−	0.838616i	0.988677	+	0.150060i	$0.0479468\pi$
$594$			283.595i			0.477433i
$595$		0			0
$596$	183.174			0.307339
$597$	−480.234	−	480.234i	−0.804412	−	0.804412i
$598$	224.842	−	224.842i	0.375990	−	0.375990i
$599$		−	282.743i		−	0.472025i	−0.971750	−	0.236012i	$-0.924159\pi$
$599$		−	282.743i		−	0.472025i	0.971750	−	0.236012i	$-0.0758406\pi$
$600$		0			0
$601$	755.637			1.25730			0.628650	−	0.777689i	$-0.283608\pi$
$601$	755.637			1.25730			0.628650	+	0.777689i	$0.283608\pi$
$602$	−17.0329	−	17.0329i	−0.0282939	−	0.0282939i
$603$	−135.730	+	135.730i	−0.225092	+	0.225092i
$604$		−	471.887i		−	0.781270i
$605$		0			0
$606$	438.804			0.724100
$607$	−171.655	−	171.655i	−0.282792	−	0.282792i	0.551430	−	0.834221i	$-0.314083\pi$
$607$	−171.655	−	171.655i	−0.282792	−	0.282792i	−0.834221	+	0.551430i	$0.814083\pi$
$608$	−701.743	+	701.743i	−1.15418	+	1.15418i
$609$			304.136i			0.499403i
$610$		0			0
$611$	−619.759			−1.01433
$612$	90.0970	+	90.0970i	0.147217	+	0.147217i
$613$	15.8263	−	15.8263i	0.0258178	−	0.0258178i	−0.694080	−	0.719898i	$-0.744189\pi$
$613$	15.8263	−	15.8263i	0.0258178	−	0.0258178i	0.719898	+	0.694080i	$0.244189\pi$
$614$		−	523.450i		−	0.852524i
$615$		0			0
$616$	−95.9557			−0.155772
$617$	85.3768	+	85.3768i	0.138374	+	0.138374i	0.772901	−	0.634527i	$-0.218805\pi$
$617$	85.3768	+	85.3768i	0.138374	+	0.138374i	−0.634527	+	0.772901i	$0.718805\pi$
$618$	17.9184	−	17.9184i	0.0289941	−	0.0289941i
$619$			833.509i			1.34654i	0.739396	+	0.673270i	$0.235111\pi$
$619$			833.509i			1.34654i	−0.739396	+	0.673270i	$0.764889\pi$
$620$		0			0
$621$	−1008.18			−1.62348
$622$	19.0803	+	19.0803i	0.0306757	+	0.0306757i
$623$	355.827	−	355.827i	0.571151	−	0.571151i
$624$			138.637i			0.222174i
$625$		0			0
$626$	303.851			0.485386
$627$	413.456	+	413.456i	0.659419	+	0.659419i
$628$	174.024	−	174.024i	0.277108	−	0.277108i
$629$		−	161.825i		−	0.257273i
$630$		0			0
$631$	581.183			0.921051			0.460526	−	0.887646i	$-0.347661\pi$
$631$	581.183			0.921051			0.460526	+	0.887646i	$0.347661\pi$
$632$	168.657	+	168.657i	0.266862	+	0.266862i
$633$	278.986	−	278.986i	0.440737	−	0.440737i
$634$			108.902i			0.171770i
$635$		0			0
$636$	−261.254			−0.410778
$637$	−408.188	−	408.188i	−0.640797	−	0.640797i
$638$	−48.4861	+	48.4861i	−0.0759970	+	0.0759970i
$639$			426.778i			0.667884i
$640$		0			0
$641$	109.559			0.170918			0.0854592	−	0.996342i	$-0.472764\pi$
$641$	109.559			0.170918			0.0854592	+	0.996342i	$0.472764\pi$
$642$	813.814	+	813.814i	1.26762	+	1.26762i
$643$	572.874	−	572.874i	0.890940	−	0.890940i	−0.103672	−	0.994612i	$-0.533059\pi$
$643$	572.874	−	572.874i	0.890940	−	0.890940i	0.994612	+	0.103672i	$0.0330591\pi$
$644$		−	124.145i		−	0.192771i
$645$		0			0
$646$	−112.032			−0.173424
$647$	−389.176	−	389.176i	−0.601509	−	0.601509i	0.339204	−	0.940713i	$-0.389842\pi$
$647$	−389.176	−	389.176i	−0.601509	−	0.601509i	−0.940713	+	0.339204i	$0.889842\pi$
$648$	984.120	−	984.120i	1.51870	−	1.51870i
$649$		−	340.181i		−	0.524162i
$650$		0			0
$651$	1085.15			1.66689
$652$	50.0285	+	50.0285i	0.0767308	+	0.0767308i
$653$	365.630	−	365.630i	0.559923	−	0.559923i	−0.369362	−	0.929285i	$-0.620424\pi$
$653$	365.630	−	365.630i	0.559923	−	0.559923i	0.929285	+	0.369362i	$0.120424\pi$
$654$		−	572.533i		−	0.875432i
$655$		0			0
$656$	67.2933			0.102581
$657$	−935.174	−	935.174i	−1.42340	−	1.42340i
$658$	127.942	−	127.942i	0.194441	−	0.194441i
$659$		−	472.236i		−	0.716595i	−0.933607	−	0.358298i	$-0.883357\pi$
$659$		−	472.236i		−	0.716595i	0.933607	−	0.358298i	$-0.116643\pi$
$660$		0			0
$661$	−240.373			−0.363651			−0.181825	−	0.983331i	$-0.558201\pi$
$661$	−240.373			−0.363651			−0.181825	+	0.983331i	$0.558201\pi$
$662$	−359.313	−	359.313i	−0.542769	−	0.542769i
$663$	162.082	−	162.082i	0.244468	−	0.244468i
$664$			1156.91i			1.74234i
$665$		0			0
$666$	−1668.05			−2.50459
$667$	−172.368	−	172.368i	−0.258422	−	0.258422i
$668$	44.6565	−	44.6565i	0.0668510	−	0.0668510i
$669$		−	1613.57i		−	2.41191i
$670$		0			0
$671$	113.875			0.169709
$672$	419.174	+	419.174i	0.623771	+	0.623771i
$673$	−243.135	+	243.135i	−0.361270	+	0.361270i	−0.864280	−	0.503010i	$-0.832226\pi$
$673$	−243.135	+	243.135i	−0.361270	+	0.361270i	0.503010	+	0.864280i	$0.332226\pi$
$674$		−	143.110i		−	0.212330i
$675$		0			0
$676$	−181.549			−0.268563
$677$	471.912	+	471.912i	0.697064	+	0.697064i	0.963776	−	0.266712i	$-0.0859374\pi$
$677$	471.912	+	471.912i	0.697064	+	0.697064i	−0.266712	+	0.963776i	$0.585937\pi$
$678$	374.652	−	374.652i	0.552584	−	0.552584i
$679$			23.2374i			0.0342230i
$680$		0			0
$681$	−748.901			−1.09971
$682$	172.997	+	172.997i	0.253661	+	0.253661i
$683$	30.4808	−	30.4808i	0.0446278	−	0.0446278i	−0.684441	−	0.729069i	$-0.739954\pi$
$683$	30.4808	−	30.4808i	0.0446278	−	0.0446278i	0.729069	+	0.684441i	$0.239954\pi$
$684$		−	1544.31i		−	2.25776i
$685$		0			0
$686$	393.964			0.574291
$687$	94.3489	+	94.3489i	0.137335	+	0.137335i
$688$	−5.95219	+	5.95219i	−0.00865145	+	0.00865145i
$689$			328.732i			0.477115i
$690$		0			0
$691$	121.709			0.176134			0.0880671	−	0.996115i	$-0.471931\pi$
$691$	121.709			0.176134			0.0880671	+	0.996115i	$0.471931\pi$
$692$	491.945	+	491.945i	0.710903	+	0.710903i
$693$	172.743	−	172.743i	0.249268	−	0.249268i
$694$			316.717i			0.456365i
$695$		0			0
$696$	711.460			1.02221
$697$	−78.6735	−	78.6735i	−0.112874	−	0.112874i
$698$	−27.7162	+	27.7162i	−0.0397080	+	0.0397080i
$699$			47.0750i			0.0673462i
$700$		0			0
$701$	930.403			1.32725			0.663625	−	0.748065i	$-0.269017\pi$
$701$	930.403			1.32725			0.663625	+	0.748065i	$0.269017\pi$
$702$	−952.795	−	952.795i	−1.35726	−	1.35726i
$703$	−1386.88	+	1386.88i	−1.97280	+	1.97280i
$704$			154.980i			0.220142i
$705$		0			0
$706$	−234.535			−0.332203
$707$	−152.430	−	152.430i	−0.215601	−	0.215601i
$708$	−908.306	+	908.306i	−1.28292	+	1.28292i
$709$			1012.74i			1.42841i	0.699935	+	0.714206i	$0.253212\pi$
$709$			1012.74i			1.42841i	−0.699935	+	0.714206i	$0.746788\pi$
$710$		0			0
$711$	−607.244			−0.854070
$712$	−832.380	−	832.380i	−1.16907	−	1.16907i
$713$	−615.002	+	615.002i	−0.862555	+	0.862555i
$714$			66.9202i			0.0937258i
$715$		0			0
$716$	254.143			0.354948
$717$	−1167.24	−	1167.24i	−1.62795	−	1.62795i
$718$	−177.250	+	177.250i	−0.246866	+	0.246866i
$719$			1241.19i			1.72627i	0.504973	+	0.863135i	$0.331502\pi$
$719$			1241.19i			1.72627i	−0.504973	+	0.863135i	$0.668498\pi$
$720$		0			0
$721$	−12.4488			−0.0172660
$722$	626.204	+	626.204i	0.867318	+	0.867318i
$723$	589.704	−	589.704i	0.815635	−	0.815635i
$724$			289.146i			0.399373i
$725$		0			0
$726$	78.7453			0.108465
$727$	−251.623	−	251.623i	−0.346112	−	0.346112i	0.512547	−	0.858659i	$-0.328702\pi$
$727$	−251.623	−	251.623i	−0.346112	−	0.346112i	−0.858659	+	0.512547i	$0.828702\pi$
$728$	322.382	−	322.382i	0.442833	−	0.442833i
$729$			324.206i			0.444727i
$730$		0			0
$731$	13.9176			0.0190391
$732$	−304.053	−	304.053i	−0.415373	−	0.415373i
$733$	−458.627	+	458.627i	−0.625685	+	0.625685i	−0.946979	−	0.321294i	$-0.895882\pi$
$733$	−458.627	+	458.627i	−0.625685	+	0.625685i	0.321294	+	0.946979i	$0.395882\pi$
$734$			397.057i			0.540949i
$735$		0			0
$736$	−475.130			−0.645557
$737$	21.4932	+	21.4932i	0.0291631	+	0.0291631i
$738$	−810.949	+	810.949i	−1.09885	+	1.09885i
$739$		−	912.068i		−	1.23419i	−0.786888	−	0.617096i	$-0.788309\pi$
$739$		−	912.068i		−	1.23419i	0.786888	−	0.617096i	$-0.211691\pi$
$740$		0			0
$741$	−2778.17			−3.74922
$742$	−67.8632	−	67.8632i	−0.0914598	−	0.0914598i
$743$	623.884	−	623.884i	0.839682	−	0.839682i	−0.149134	−	0.988817i	$-0.547649\pi$
$743$	623.884	−	623.884i	0.839682	−	0.839682i	0.988817	+	0.149134i	$0.0476487\pi$
$744$		−	2538.47i		−	3.41192i
$745$		0			0
$746$	−219.654			−0.294442
$747$	−2082.71	−	2082.71i	−2.78810	−	2.78810i
$748$	14.2671	−	14.2671i	0.0190736	−	0.0190736i
$749$		−	565.398i		−	0.754871i
$750$		0			0
$751$	−776.710			−1.03423			−0.517117	−	0.855915i	$-0.672995\pi$
$751$	−776.710			−1.03423			−0.517117	+	0.855915i	$0.672995\pi$
$752$	−44.7099	−	44.7099i	−0.0594546	−	0.0594546i
$753$	−3.21535	+	3.21535i	−0.00427005	+	0.00427005i
$754$		−	325.797i		−	0.432092i
$755$		0			0
$756$	−526.079			−0.695871
$757$	−490.116	−	490.116i	−0.647445	−	0.647445i	0.304930	−	0.952375i	$-0.401367\pi$
$757$	−490.116	−	490.116i	−0.647445	−	0.647445i	−0.952375	+	0.304930i	$0.901367\pi$
$758$	65.3299	−	65.3299i	0.0861872	−	0.0861872i
$759$			279.939i			0.368826i
$760$		0			0
$761$	60.1820			0.0790828			0.0395414	−	0.999218i	$-0.487410\pi$
$761$	60.1820			0.0790828			0.0395414	+	0.999218i	$0.487410\pi$
$762$	825.829	+	825.829i	1.08377	+	1.08377i
$763$	−198.884	+	198.884i	−0.260660	+	0.260660i
$764$			395.016i			0.517037i
$765$		0			0
$766$	756.120			0.987101
$767$	1142.91	+	1142.91i	1.49010	+	1.49010i
$768$	1037.52	−	1037.52i	1.35093	−	1.35093i
$769$		−	637.781i		−	0.829363i	−0.909967	−	0.414682i	$-0.863893\pi$
$769$		−	637.781i		−	0.829363i	0.909967	−	0.414682i	$-0.136107\pi$
$770$		0			0
$771$	1655.27			2.14691
$772$	−118.724	−	118.724i	−0.153787	−	0.153787i
$773$	−173.796	+	173.796i	−0.224833	+	0.224833i	−0.810530	−	0.585697i	$-0.800821\pi$
$773$	−173.796	+	173.796i	−0.224833	+	0.224833i	0.585697	+	0.810530i	$0.300821\pi$
$774$		−	143.459i		−	0.185348i
$775$		0			0
$776$	54.3589			0.0700501
$777$	828.430	+	828.430i	1.06619	+	1.06619i
$778$	556.205	−	556.205i	0.714916	−	0.714916i
$779$			1348.51i			1.73107i
$780$		0			0
$781$	67.5813			0.0865317
$782$	−37.9267	−	37.9267i	−0.0484996	−	0.0484996i
$783$	−730.430	+	730.430i	−0.932860	+	0.932860i
$784$		−	58.8939i		−	0.0751198i
$785$		0			0
$786$	−539.812			−0.686784
$787$	−812.907	−	812.907i	−1.03292	−	1.03292i	−0.999439	−	0.0334795i	$-0.989341\pi$
$787$	−812.907	−	812.907i	−1.03292	−	1.03292i	−0.0334795	−	0.999439i	$-0.510659\pi$
$788$	268.281	−	268.281i	0.340459	−	0.340459i
$789$		−	1874.33i		−	2.37558i
$790$		0			0
$791$	−260.290			−0.329064
$792$	−404.093	−	404.093i	−0.510219	−	0.510219i
$793$	−382.584	+	382.584i	−0.482452	+	0.482452i
$794$		−	632.001i		−	0.795971i
$795$		0			0
$796$	284.042			0.356837
$797$	−971.779	−	971.779i	−1.21930	−	1.21930i	−0.967879	−	0.251417i	$-0.919103\pi$
$797$	−971.779	−	971.779i	−1.21930	−	1.21930i	−0.251417	−	0.967879i	$-0.580897\pi$
$798$	573.524	−	573.524i	0.718702	−	0.718702i
$799$			104.542i			0.130841i
$800$		0			0
$801$	2996.95			3.74151
$802$	194.331	+	194.331i	0.242308	+	0.242308i
$803$	−148.087	+	148.087i	−0.184417	+	0.184417i
$804$		−	114.777i		−	0.142757i
$805$		0			0
$806$	−1162.43			−1.44223
$807$	1061.27	+	1061.27i	1.31508	+	1.31508i
$808$	−356.576	+	356.576i	−0.441307	+	0.441307i
$809$		−	17.3877i		−	0.0214928i	−0.999942	−	0.0107464i	$-0.996579\pi$
$809$		−	17.3877i		−	0.0214928i	0.999942	−	0.0107464i	$-0.00342076\pi$
$810$		0			0
$811$	−852.035			−1.05060			−0.525299	−	0.850918i	$-0.676046\pi$
$811$	−852.035			−1.05060			−0.525299	+	0.850918i	$0.676046\pi$
$812$	−89.9433	−	89.9433i	−0.110768	−	0.110768i
$813$	869.810	−	869.810i	1.06988	−	1.06988i
$814$			264.140i			0.324497i
$815$		0			0
$816$	23.3855			0.0286586
$817$	−119.277	−	119.277i	−0.145994	−	0.145994i
$818$	640.106	−	640.106i	0.782525	−	0.782525i
$819$			1160.73i			1.41725i
$820$		0			0
$821$	632.202			0.770039			0.385020	−	0.922908i	$-0.374195\pi$
$821$	632.202			0.770039			0.385020	+	0.922908i	$0.374195\pi$
$822$	−57.5029	−	57.5029i	−0.0699549	−	0.0699549i
$823$	−783.340	+	783.340i	−0.951810	+	0.951810i	−0.998891	−	0.0470806i	$-0.985008\pi$
$823$	−783.340	+	783.340i	−0.951810	+	0.951810i	0.0470806	+	0.998891i	$0.485008\pi$
$824$			29.1212i			0.0353413i
$825$		0			0
$826$	−471.881			−0.571285
$827$	−841.100	−	841.100i	−1.01705	−	1.01705i	−0.999852	−	0.0171980i	$-0.994525\pi$
$827$	−841.100	−	841.100i	−1.01705	−	1.01705i	−0.0171980	−	0.999852i	$-0.505475\pi$
$828$	522.804	−	522.804i	0.631406	−	0.631406i
$829$		−	57.3663i		−	0.0691994i	−0.999401	−	0.0345997i	$-0.988984\pi$
$829$		−	57.3663i		−	0.0691994i	0.999401	−	0.0345997i	$-0.0110156\pi$
$830$		0			0
$831$	−493.853			−0.594287
$832$	−520.686	−	520.686i	−0.625825	−	0.625825i
$833$	−68.8537	+	68.8537i	−0.0826575	+	0.0826575i
$834$		−	1107.57i		−	1.32803i
$835$		0			0
$836$	−244.545			−0.292518
$837$	2606.15	+	2606.15i	3.11368	+	3.11368i
$838$	−361.511	+	361.511i	−0.431397	+	0.431397i
$839$		−	1356.86i		−	1.61724i	−0.588333	−	0.808619i	$-0.700215\pi$
$839$		−	1356.86i		−	1.61724i	0.588333	−	0.808619i	$-0.299785\pi$
$840$		0			0
$841$	591.238			0.703018
$842$	386.277	+	386.277i	0.458761	+	0.458761i
$843$	−1180.90	+	1180.90i	−1.40084	+	1.40084i
$844$			165.011i			0.195511i
$845$		0			0
$846$	1077.59			1.27375
$847$	−27.3542	−	27.3542i	−0.0322954	−	0.0322954i
$848$	−23.7150	+	23.7150i	−0.0279658	+	0.0279658i
$849$			2842.15i			3.34764i
$850$		0			0
$851$	−939.017			−1.10343
$852$	−180.447	−	180.447i	−0.211792	−	0.211792i
$853$	306.457	−	306.457i	0.359269	−	0.359269i	−0.504274	−	0.863544i	$-0.668240\pi$
$853$	306.457	−	306.457i	0.359269	−	0.359269i	0.863544	+	0.504274i	$0.168240\pi$
$854$		−	157.961i		−	0.184966i
$855$		0			0
$856$	−1322.62			−1.54512
$857$	698.176	+	698.176i	0.814674	+	0.814674i	0.985331	−	0.170656i	$-0.0545888\pi$
$857$	698.176	+	698.176i	0.814674	+	0.814674i	−0.170656	+	0.985331i	$0.554589\pi$
$858$	−264.560	+	264.560i	−0.308346	+	0.308346i
$859$		−	126.063i		−	0.146755i	−0.997304	−	0.0733776i	$-0.976622\pi$
$859$		−	126.063i		−	0.146755i	0.997304	−	0.0733776i	$-0.0233778\pi$
$860$		0			0
$861$	805.507			0.935549
$862$	105.865	+	105.865i	0.122813	+	0.122813i
$863$	−828.692	+	828.692i	−0.960245	+	0.960245i	−0.999239	−	0.0389942i	$-0.987585\pi$
$863$	−828.692	+	828.692i	−0.960245	+	0.960245i	0.0389942	+	0.999239i	$0.487585\pi$
$864$			2013.42i			2.33035i
$865$		0			0
$866$	393.520			0.454411
$867$	1090.92	+	1090.92i	1.25827	+	1.25827i
$868$	−320.914	+	320.914i	−0.369717	+	0.369717i
$869$			96.1585i			0.110654i
$870$		0			0
$871$	−144.421			−0.165811
$872$	465.245	+	465.245i	0.533538	+	0.533538i
$873$	−97.8586	+	97.8586i	−0.112095	+	0.112095i
$874$			650.084i			0.743803i
$875$		0			0
$876$	790.805			0.902745
$877$	601.057	+	601.057i	0.685356	+	0.685356i	0.961202	−	0.275846i	$-0.0889579\pi$
$877$	601.057	+	601.057i	0.685356	+	0.685356i	−0.275846	+	0.961202i	$0.588958\pi$
$878$	−379.553	+	379.553i	−0.432293	+	0.432293i
$879$			1932.64i			2.19868i
$880$		0			0
$881$	179.995			0.204307			0.102154	−	0.994769i	$-0.467427\pi$
$881$	179.995			0.204307			0.102154	+	0.994769i	$0.467427\pi$
$882$	709.729	+	709.729i	0.804682	+	0.804682i
$883$	−688.177	+	688.177i	−0.779362	+	0.779362i	−0.979722	−	0.200360i	$-0.935789\pi$
$883$	−688.177	+	688.177i	−0.779362	+	0.779362i	0.200360	+	0.979722i	$0.435789\pi$
$884$			95.8661i			0.108446i
$885$		0			0
$886$	418.226			0.472038
$887$	342.387	+	342.387i	0.386005	+	0.386005i	0.873260	−	0.487255i	$-0.162002\pi$
$887$	342.387	+	342.387i	0.386005	+	0.386005i	−0.487255	+	0.873260i	$0.662002\pi$
$888$	1937.93	−	1937.93i	2.18235	−	2.18235i
$889$		−	573.745i		−	0.645383i
$890$		0			0
$891$	561.088			0.629728
$892$	477.186	+	477.186i	0.534962	+	0.534962i
$893$	895.952	−	895.952i	1.00331	−	1.00331i
$894$			572.957i			0.640891i
$895$		0			0
$896$	−218.342			−0.243685
$897$	−940.510	−	940.510i	−1.04851	−	1.04851i
$898$	350.511	−	350.511i	0.390324	−	0.390324i
$899$			891.142i			0.991259i
$900$		0			0
$901$	55.4510			0.0615439
$902$	128.416	+	128.416i	0.142368	+	0.142368i
$903$	−71.2484	+	71.2484i	−0.0789018	+	0.0789018i
$904$			608.891i			0.673552i
$905$		0			0
$906$	1476.03			1.62917
$907$	826.608	+	826.608i	0.911365	+	0.911365i	0.996380	−	0.0850144i	$-0.0270936\pi$
$907$	826.608	+	826.608i	0.911365	+	0.911365i	−0.0850144	+	0.996380i	$0.527094\pi$
$908$	221.475	−	221.475i	0.243915	−	0.243915i
$909$		−	1283.84i		−	1.41236i
$910$		0			0
$911$	−826.053			−0.906754			−0.453377	−	0.891319i	$-0.649781\pi$
$911$	−826.053			−0.906754			−0.453377	+	0.891319i	$0.649781\pi$
$912$	−200.420	−	200.420i	−0.219758	−	0.219758i
$913$	−329.803	+	329.803i	−0.361230	+	0.361230i
$914$		−	666.876i		−	0.729623i
$915$		0			0
$916$	−55.8042			−0.0609216
$917$	187.518	+	187.518i	0.204490	+	0.204490i
$918$	−160.719	+	160.719i	−0.175075	+	0.175075i
$919$		−	319.750i		−	0.347933i	−0.984752	−	0.173966i	$-0.944342\pi$
$919$		−	319.750i		−	0.347933i	0.984752	−	0.173966i	$-0.0556584\pi$
$920$		0			0
$921$	−2189.58			−2.37740
$922$	202.594	+	202.594i	0.219733	+	0.219733i
$923$	−227.053	+	227.053i	−0.245994	+	0.245994i
$924$			146.075i			0.158090i
$925$		0			0
$926$	356.913			0.385435
$927$	−52.4249	−	52.4249i	−0.0565533	−	0.0565533i
$928$	−344.233	+	344.233i	−0.370941	+	0.370941i
$929$		−	756.667i		−	0.814496i	−0.913318	−	0.407248i	$-0.866488\pi$
$929$		−	756.667i		−	0.814496i	0.913318	−	0.407248i	$-0.133512\pi$
$930$		0			0
$931$	1180.19			1.26766
$932$	−13.9216	−	13.9216i	−0.0149374	−	0.0149374i
$933$	79.8125	−	79.8125i	0.0855440	−	0.0855440i
$934$		−	152.339i		−	0.163104i
$935$		0			0
$936$	2715.26			2.90092
$937$	−422.038	−	422.038i	−0.450414	−	0.450414i	0.445078	−	0.895492i	$-0.353176\pi$
$937$	−422.038	−	422.038i	−0.450414	−	0.450414i	−0.895492	+	0.445078i	$0.853176\pi$
$938$	29.8142	−	29.8142i	0.0317849	−	0.0317849i
$939$		−	1271.01i		−	1.35357i
$940$		0			0
$941$	−1091.44			−1.15987			−0.579937	−	0.814661i	$-0.696923\pi$
$941$	−1091.44			−1.15987			−0.579937	+	0.814661i	$0.696923\pi$
$942$	544.335	+	544.335i	0.577850	+	0.577850i
$943$	−456.517	+	456.517i	−0.484111	+	0.484111i
$944$			164.900i			0.174682i
$945$		0			0
$946$	−22.7171			−0.0240139
$947$	681.095	+	681.095i	0.719213	+	0.719213i	0.968444	−	0.249231i	$-0.0801778\pi$
$947$	681.095	+	681.095i	0.719213	+	0.719213i	−0.249231	+	0.968444i	$0.580178\pi$
$948$	256.750	−	256.750i	0.270833	−	0.270833i
$949$		−	995.056i		−	1.04853i
$950$		0			0
$951$	455.537			0.479008
$952$	−54.3799	−	54.3799i	−0.0571218	−	0.0571218i
$953$	402.146	−	402.146i	0.421979	−	0.421979i	−0.463905	−	0.885885i	$-0.653552\pi$
$953$	402.146	−	402.146i	0.421979	−	0.421979i	0.885885	+	0.463905i	$0.153552\pi$
$954$		−	571.577i		−	0.599137i
$955$		0			0
$956$	690.385			0.722160
$957$	202.817	+	202.817i	0.211930	+	0.211930i
$958$	−821.819	+	821.819i	−0.857848	+	0.857848i
$959$			39.9502i			0.0416582i
$960$		0			0
$961$	2218.56			2.30860
$962$	−887.432	−	887.432i	−0.922487	−	0.922487i
$963$	2381.03	−	2381.03i	2.47251	−	2.47251i
$964$			348.790i			0.361816i
$965$		0			0
$966$	388.316			0.401984
$967$	−568.231	−	568.231i	−0.587623	−	0.587623i	0.349364	−	0.936987i	$-0.386398\pi$
$967$	−568.231	−	568.231i	−0.587623	−	0.587623i	−0.936987	+	0.349364i	$0.886398\pi$
$968$	−63.9891	+	63.9891i	−0.0661045	+	0.0661045i
$969$			468.627i			0.483619i
$970$		0			0
$971$	−1823.88			−1.87835			−0.939176	−	0.343436i	$-0.888409\pi$
$971$	−1823.88			−1.87835			−0.939176	+	0.343436i	$0.888409\pi$
$972$	−546.153	−	546.153i	−0.561886	−	0.561886i
$973$	−384.744	+	384.744i	−0.395421	+	0.395421i
$974$		−	230.280i		−	0.236427i
$975$		0			0
$976$	−55.1999			−0.0565572
$977$	61.1157	+	61.1157i	0.0625544	+	0.0625544i	0.737692	−	0.675137i	$-0.235916\pi$
$977$	61.1157	+	61.1157i	0.0625544	+	0.0625544i	−0.675137	+	0.737692i	$0.735916\pi$
$978$	−156.486	+	156.486i	−0.160006	+	0.160006i
$979$		−	474.575i		−	0.484754i
$980$		0			0
$981$	−1675.10			−1.70754
$982$	−897.419	−	897.419i	−0.913868	−	0.913868i
$983$	55.5500	−	55.5500i	0.0565107	−	0.0565107i	−0.678287	−	0.734797i	$-0.737277\pi$
$983$	55.5500	−	55.5500i	0.0565107	−	0.0565107i	0.734797	+	0.678287i	$0.237277\pi$
$984$		−	1884.31i		−	1.91495i
$985$		0			0
$986$	−54.9560			−0.0557363
$987$	−535.182	−	535.182i	−0.542231	−	0.542231i
$988$	821.599	−	821.599i	0.831577	−	0.831577i
$989$		−	80.7593i		−	0.0816575i
$990$		0			0
$991$	−491.094			−0.495554			−0.247777	−	0.968817i	$-0.579700\pi$
$991$	−491.094			−0.495554			−0.247777	+	0.968817i	$0.579700\pi$
$992$	1228.21	+	1228.21i	1.23812	+	1.23812i
$993$	−1503.00	+	1503.00i	−1.51360	+	1.51360i
$994$		−	93.7452i		−	0.0943111i
$995$		0			0
$996$	1761.19			1.76826
$997$	175.640	+	175.640i	0.176169	+	0.176169i	0.789683	−	0.613515i	$-0.210245\pi$
$997$	175.640	+	175.640i	0.176169	+	0.176169i	−0.613515	+	0.789683i	$0.710245\pi$
$998$	−537.969	+	537.969i	−0.539047	+	0.539047i
$999$			3979.20i			3.98318i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.f.c.232.5	✓	24
5.2	odd	4	inner	275.3.f.c.243.8	yes	24
5.3	odd	4	inner	275.3.f.c.243.5	yes	24
5.4	even	2	inner	275.3.f.c.232.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.f.c.232.5	✓	24	1.1	even	1	trivial
275.3.f.c.232.8	yes	24	5.4	even	2	inner
275.3.f.c.243.5	yes	24	5.3	odd	4	inner
275.3.f.c.243.8	yes	24	5.2	odd	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.925034 - 0.925034i) q^{2} +(-3.86940 + 3.86940i) q^{3} -2.28862i q^{4} +7.15866 q^{6} +(-2.48674 - 2.48674i) q^{7} +(-5.81719 + 5.81719i) q^{8} -20.9446i q^{9} -3.31662 q^{11} +(8.85561 + 8.85561i) q^{12} +(11.1429 - 11.1429i) q^{13} +4.60065i q^{14} +1.60771 q^{16} +(-1.87959 - 1.87959i) q^{17} +(-19.3745 + 19.3745i) q^{18} +32.2173i q^{19} +19.2444 q^{21} +(3.06799 + 3.06799i) q^{22} +(-10.9067 + 10.9067i) q^{23} -45.0181i q^{24} -20.6151 q^{26} +(46.2184 + 46.2184i) q^{27} +(-5.69122 + 5.69122i) q^{28} +15.8039i q^{29} +56.3876 q^{31} +(21.7816 + 21.7816i) q^{32} +(12.8334 - 12.8334i) q^{33} +3.47738i q^{34} -47.9343 q^{36} +(43.0478 + 43.0478i) q^{37} +(29.8021 - 29.8021i) q^{38} +86.2325i q^{39} +41.8566 q^{41} +(-17.8018 - 17.8018i) q^{42} +(-3.70228 + 3.70228i) q^{43} +7.59051i q^{44} +20.1781 q^{46} +(-27.8097 - 27.8097i) q^{47} +(-6.22088 + 6.22088i) q^{48} -36.6322i q^{49} +14.5458 q^{51} +(-25.5018 - 25.5018i) q^{52} +(-14.7508 + 14.7508i) q^{53} -85.5073i q^{54} +28.9317 q^{56} +(-124.662 - 124.662i) q^{57} +(14.6191 - 14.6191i) q^{58} +102.568i q^{59} -34.3345 q^{61} +(-52.1605 - 52.1605i) q^{62} +(-52.0838 + 52.0838i) q^{63} -46.7283i q^{64} -23.7426 q^{66} +(-6.48045 - 6.48045i) q^{67} +(-4.30168 + 4.30168i) q^{68} -84.4048i q^{69} -20.3765 q^{71} +(121.839 + 121.839i) q^{72} +(44.6499 - 44.6499i) q^{73} -79.6413i q^{74} +73.7332 q^{76} +(8.24760 + 8.24760i) q^{77} +(79.7680 - 79.7680i) q^{78} -28.9929i q^{79} -169.174 q^{81} +(-38.7188 - 38.7188i) q^{82} +(99.4392 - 99.4392i) q^{83} -44.0433i q^{84} +6.84948 q^{86} +(-61.1515 - 61.1515i) q^{87} +(19.2934 - 19.2934i) q^{88} +143.090i q^{89} -55.4189 q^{91} +(24.9613 + 24.9613i) q^{92} +(-218.186 + 218.186i) q^{93} +51.4498i q^{94} -168.564 q^{96} +(-4.67226 - 4.67226i) q^{97} +(-33.8860 + 33.8860i) q^{98} +69.4653i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} - 128 q^{16} - 88 q^{21} + 96 q^{26} + 360 q^{31} + 176 q^{36} - 152 q^{41} + 56 q^{46} - 512 q^{51} - 1048 q^{56} + 784 q^{61} - 440 q^{66} + 728 q^{71} + 1704 q^{76} - 568 q^{81} - 328 q^{86}+ \cdots + 1568 q^{96}+O(q^{100}) \) 24 * q - 8 * q^6 - 128 * q^16 - 88 * q^21 + 96 * q^26 + 360 * q^31 + 176 * q^36 - 152 * q^41 + 56 * q^46 - 512 * q^51 - 1048 * q^56 + 784 * q^61 - 440 * q^66 + 728 * q^71 + 1704 * q^76 - 568 * q^81 - 328 * q^86 - 968 * q^91 + 1568 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more