LMFDB - Embedded newform 275.3.f.c.232.8

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			232.8
Character	$\chi$	$=$	275.232
Dual form			275.3.f.c.243.8

$q$-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	0.899480	−	0.436963i	$-0.143946\pi$
$2$	0.925034	+	0.925034i	0.462517	+	0.462517i	−0.436963	+	0.899480i	$0.643946\pi$
$3$	3.86940	−	3.86940i	1.28980	−	1.28980i	0.354896	−	0.934906i	$-0.384516\pi$
$3$	3.86940	−	3.86940i	1.28980	−	1.28980i	0.934906	−	0.354896i	$-0.115484\pi$
$4$		−	2.28862i		−	0.572156i
$5$		0			0
$5$		0			0
$6$	7.15866			1.19311
$7$	2.48674	+	2.48674i	0.355249	+	0.355249i	0.862058	−	0.506809i	$-0.169175\pi$
$7$	2.48674	+	2.48674i	0.355249	+	0.355249i	−0.506809	+	0.862058i	$0.669175\pi$
$8$	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	−0.991001	−	0.133858i	$-0.957264\pi$
$13$	−11.1429	+	11.1429i	−0.857143	+	0.857143i	0.133858	+	0.991001i	$0.457264\pi$
$14$			4.60065i			0.328618i
$15$		0			0
$16$	1.60771			0.100482
$17$	1.87959	+	1.87959i	0.110564	+	0.110564i	0.760225	−	0.649660i	$-0.225089\pi$
$17$	1.87959	+	1.87959i	0.110564	+	0.110564i	−0.649660	+	0.760225i	$0.725089\pi$
$18$	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	−0.429068	−	0.903272i	$-0.641158\pi$
$23$	10.9067	−	10.9067i	0.474204	−	0.474204i	0.903272	+	0.429068i	$0.141158\pi$
$24$		−	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	$-0.942475\pi$
$37$	−43.0478	−	43.0478i	−1.16345	−	1.16345i	−0.179739	−	0.983714i	$-0.557525\pi$
$38$	−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	−0.662745	−	0.748845i	$-0.730609\pi$
$43$	3.70228	−	3.70228i	0.0860996	−	0.0860996i	0.748845	+	0.662745i	$0.230609\pi$
$44$			7.59051i			0.172511i
$45$		0			0
$46$	20.1781			0.438655
$47$	27.8097	+	27.8097i	0.591695	+	0.591695i	0.938089	−	0.346394i	$-0.112594\pi$
$47$	27.8097	+	27.8097i	0.591695	+	0.591695i	−0.346394	+	0.938089i	$0.612594\pi$
$48$	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	−0.554120	−	0.832437i	$-0.686945\pi$
$53$	14.7508	−	14.7508i	0.278317	−	0.278317i	0.832437	+	0.554120i	$0.186945\pi$
$54$		−	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	0.753813	−	0.657090i	$-0.228213\pi$
$67$	6.48045	+	6.48045i	0.0967231	+	0.0967231i	−0.657090	+	0.753813i	$0.728213\pi$
$68$	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	−0.943374	−	0.331731i	$-0.892367\pi$
$73$	−44.6499	+	44.6499i	−0.611643	+	0.611643i	0.331731	+	0.943374i	$0.392367\pi$
$74$		−	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	$0.571689\pi$
$83$	−99.4392	+	99.4392i	−1.19806	+	1.19806i	−0.974746	+	0.223317i	$0.928311\pi$
$84$		−	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	0.730780	−	0.682613i	$-0.239156\pi$
$97$	4.67226	+	4.67226i	0.0481676	+	0.0481676i	−0.682613	+	0.730780i	$0.739156\pi$
$98$	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	−0.719153	−	0.694852i	$-0.755470\pi$
$103$	−2.50303	+	2.50303i	−0.0243013	+	0.0243013i	0.694852	+	0.719153i	$0.255470\pi$
$104$			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	$-0.979443\pi$
$107$	−113.682	−	113.682i	−1.06245	−	1.06245i	−0.0645372	−	0.997915i	$-0.520557\pi$
$108$	−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	−0.899685	−	0.436539i	$-0.856204\pi$
$113$	−52.3355	+	52.3355i	−0.463146	+	0.463146i	0.436539	+	0.899685i	$0.356204\pi$
$114$			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	0.0877867	−	0.996139i	$-0.472021\pi$
$127$	−115.361	−	115.361i	−0.908353	−	0.908353i	−0.996139	+	0.0877867i	$0.972021\pi$
$128$	−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	0.735815	−	0.677183i	$-0.236799\pi$
$137$	8.03264	+	8.03264i	0.0586324	+	0.0586324i	−0.677183	+	0.735815i	$0.736799\pi$
$138$	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	0.422187	−	0.906509i	$-0.361263\pi$
$157$	−76.0386	−	76.0386i	−0.484322	−	0.484322i	−0.906509	+	0.422187i	$0.861263\pi$
$158$	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	−0.636866	−	0.770974i	$-0.719770\pi$
$163$	21.8597	−	21.8597i	0.134108	−	0.134108i	0.770974	+	0.636866i	$0.219770\pi$
$164$		−	95.7941i		−	0.584110i
$165$		0			0
$166$	−183.969			−1.10825
$167$	−19.5124	−	19.5124i	−0.116841	−	0.116841i	0.646269	−	0.763110i	$-0.276328\pi$
$167$	−19.5124	−	19.5124i	−0.116841	−	0.116841i	−0.763110	+	0.646269i	$0.776328\pi$
$168$	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	$-0.408492\pi$
$173$	214.952	−	214.952i	1.24250	−	1.24250i	0.958961	−	0.283539i	$-0.0915084\pi$
$174$			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	−0.828611	−	0.559825i	$-0.810868\pi$
$193$	−51.8757	+	51.8757i	−0.268786	+	0.268786i	0.559825	+	0.828611i	$0.310868\pi$
$194$			8.64400i			0.0445567i
$195$		0			0
$196$	−83.8373			−0.427741
$197$	−117.224	−	117.224i	−0.595045	−	0.595045i	0.343945	−	0.938990i	$-0.388237\pi$
$197$	−117.224	−	117.224i	−0.595045	−	0.595045i	−0.938990	+	0.343945i	$0.888237\pi$
$198$	−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	−0.0630193	−	0.998012i	$-0.520073\pi$
$223$	208.503	−	208.503i	0.934993	−	0.934993i	0.998012	+	0.0630193i	$0.0200730\pi$
$224$		−	108.330i		−	0.483618i
$225$		0			0
$226$	−96.8243			−0.428426
$227$	−96.7721	−	96.7721i	−0.426309	−	0.426309i	0.461060	−	0.887369i	$-0.347469\pi$
$227$	−96.7721	−	96.7721i	−0.426309	−	0.426309i	−0.887369	+	0.461060i	$0.847469\pi$
$228$	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	−0.720040	−	0.693933i	$-0.755877\pi$
$233$	−6.08298	+	6.08298i	−0.0261072	+	0.0261072i	0.693933	+	0.720040i	$0.255877\pi$
$234$			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	0.987826	−	0.155561i	$-0.0497187\pi$
$257$	213.892	+	213.892i	0.832265	+	0.832265i	−0.155561	+	0.987826i	$0.549719\pi$
$258$	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	−0.0761856	−	0.997094i	$-0.524274\pi$
$263$	242.199	−	242.199i	0.920908	−	0.920908i	0.997094	+	0.0761856i	$0.0242741\pi$
$264$			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	0.582472	−	0.812851i	$-0.302086\pi$
$277$	−63.8151	−	63.8151i	−0.230379	−	0.230379i	−0.812851	+	0.582472i	$0.802086\pi$
$278$	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	$0.619906\pi$
$283$	−367.259	+	367.259i	−1.29773	+	1.29773i	−0.929885	+	0.367849i	$0.880094\pi$
$284$			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	−0.990420	−	0.138088i	$-0.955904\pi$
$293$	−249.733	+	249.733i	−0.852332	+	0.852332i	0.138088	+	0.990420i	$0.455904\pi$
$294$		−	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	0.0755300	−	0.997144i	$-0.475935\pi$
$307$	−282.935	−	282.935i	−0.921614	−	0.921614i	−0.997144	+	0.0755300i	$0.975935\pi$
$308$	−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	−0.394272	−	0.918994i	$-0.629003\pi$
$313$	164.238	−	164.238i	0.524722	−	0.524722i	0.918994	+	0.394272i	$0.129003\pi$
$314$		−	140.677i		−	0.448015i
$315$		0			0
$316$	−66.3538			−0.209980
$317$	58.8640	+	58.8640i	0.185691	+	0.185691i	0.793830	−	0.608139i	$-0.208084\pi$
$317$	58.8640	+	58.8640i	0.185691	+	0.185691i	−0.608139	+	0.793830i	$0.708084\pi$
$318$	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	0.582962	−	0.812499i	$-0.301894\pi$
$337$	−77.3541	−	77.3541i	−0.229538	−	0.229538i	−0.812499	+	0.582962i	$0.801894\pi$
$338$	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	0.909360	−	0.416011i	$-0.136572\pi$
$347$	171.192	+	171.192i	0.493349	+	0.493349i	−0.416011	+	0.909360i	$0.636572\pi$
$348$	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	−0.863490	−	0.504365i	$-0.831726\pi$
$353$	−126.771	+	126.771i	−0.359125	+	0.359125i	0.504365	+	0.863490i	$0.331726\pi$
$354$			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	0.936215	−	0.351427i	$-0.114303\pi$
$367$	214.617	+	214.617i	0.584788	+	0.584788i	−0.351427	+	0.936215i	$0.614303\pi$
$368$	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	−0.848115	−	0.529812i	$-0.822263\pi$
$373$	−118.727	+	118.727i	−0.318304	+	0.318304i	0.529812	+	0.848115i	$0.322263\pi$
$374$		−	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	$-0.477854\pi$
$383$	408.698	−	408.698i	1.06710	−	1.06710i	0.997581	−	0.0695164i	$-0.0221456\pi$
$384$			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	0.130916	−	0.991393i	$-0.458208\pi$
$397$	−341.609	−	341.609i	−0.860477	−	0.860477i	−0.991393	+	0.130916i	$0.958208\pi$
$398$	−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	−0.417459	−	0.908696i	$-0.637079\pi$
$433$	212.706	−	212.706i	0.491237	−	0.491237i	0.908696	+	0.417459i	$0.137079\pi$
$434$			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	−0.404323	−	0.914616i	$-0.632493\pi$
$443$	226.060	−	226.060i	0.510293	−	0.510293i	0.914616	+	0.404323i	$0.132493\pi$
$444$			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	0.192537	−	0.981290i	$-0.438329\pi$
$457$	−360.460	−	360.460i	−0.788753	−	0.788753i	−0.981290	+	0.192537i	$0.938329\pi$
$458$	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	−0.467383	−	0.884055i	$-0.654803\pi$
$463$	192.919	−	192.919i	0.416672	−	0.416672i	0.884055	+	0.467383i	$0.154803\pi$
$464$			25.4080i			0.0547586i
$465$		0			0
$466$	−11.2539			−0.0241500
$467$	−82.3422	−	82.3422i	−0.176322	−	0.176322i	0.613429	−	0.789750i	$-0.289790\pi$
$467$	−82.3422	−	82.3422i	−0.176322	−	0.176322i	−0.789750	+	0.613429i	$0.789790\pi$
$468$	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	0.567669	−	0.823257i	$-0.307845\pi$
$487$	−124.471	−	124.471i	−0.255587	−	0.255587i	−0.823257	+	0.567669i	$0.807845\pi$
$488$	−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	−0.957987	−	0.286811i	$-0.907405\pi$
$503$	−337.601	+	337.601i	−0.671176	+	0.671176i	0.286811	+	0.957987i	$0.407405\pi$
$504$		−	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	−0.343233	−	0.939250i	$-0.611522\pi$
$523$	311.717	−	311.717i	0.596018	−	0.596018i	0.939250	+	0.343233i	$0.111522\pi$
$524$			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	0.712399	−	0.701775i	$-0.247609\pi$
$547$	5.81163	+	5.81163i	0.0106245	+	0.0106245i	−0.701775	+	0.712399i	$0.747609\pi$
$548$	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	$0.0572854\pi$
$557$	647.706	+	647.706i	1.16285	+	1.16285i	0.178998	+	0.983850i	$0.442715\pi$
$558$	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	−0.845700	−	0.533658i	$-0.820817\pi$
$563$	−175.680	+	175.680i	−0.312042	+	0.312042i	0.533658	+	0.845700i	$0.320817\pi$
$564$		−	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	0.476172	−	0.879352i	$-0.342024\pi$
$577$	−232.635	−	232.635i	−0.403180	−	0.403180i	−0.879352	+	0.476172i	$0.842024\pi$
$578$	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	0.349617	−	0.936893i	$-0.386312\pi$
$587$	−344.731	−	344.731i	−0.587275	−	0.587275i	−0.936893	+	0.349617i	$0.886312\pi$
$588$	−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	−0.988677	−	0.150060i	$-0.952053\pi$
$593$	−497.299	+	497.299i	−0.838616	+	0.838616i	0.150060	+	0.988677i	$0.452053\pi$
$594$			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	0.834221	−	0.551430i	$-0.185917\pi$
$607$	171.655	+	171.655i	0.282792	+	0.282792i	−0.551430	+	0.834221i	$0.685917\pi$
$608$	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	−0.719898	−	0.694080i	$-0.755811\pi$
$613$	−15.8263	+	15.8263i	−0.0258178	+	0.0258178i	0.694080	+	0.719898i	$0.255811\pi$
$614$		−	523.450i		−	0.852524i
$615$		0			0
$616$	−95.9557			−0.155772
$617$	−85.3768	−	85.3768i	−0.138374	−	0.138374i	0.634527	−	0.772901i	$-0.281195\pi$
$617$	−85.3768	−	85.3768i	−0.138374	−	0.138374i	−0.772901	+	0.634527i	$0.781195\pi$
$618$	−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	−0.994612	−	0.103672i	$-0.966941\pi$
$643$	−572.874	+	572.874i	−0.890940	+	0.890940i	0.103672	+	0.994612i	$0.466941\pi$
$644$		−	124.145i		−	0.192771i
$645$		0			0
$646$	−112.032			−0.173424
$647$	389.176	+	389.176i	0.601509	+	0.601509i	0.940713	−	0.339204i	$-0.110158\pi$
$647$	389.176	+	389.176i	0.601509	+	0.601509i	−0.339204	+	0.940713i	$0.610158\pi$
$648$	−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	−0.929285	−	0.369362i	$-0.879576\pi$
$653$	−365.630	+	365.630i	−0.559923	+	0.559923i	0.369362	+	0.929285i	$0.379576\pi$
$654$		−	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	−0.503010	−	0.864280i	$-0.667774\pi$
$673$	243.135	−	243.135i	0.361270	−	0.361270i	0.864280	+	0.503010i	$0.167774\pi$
$674$		−	143.110i		−	0.212330i
$675$		0			0
$676$	−181.549			−0.268563
$677$	−471.912	−	471.912i	−0.697064	−	0.697064i	0.266712	−	0.963776i	$-0.414063\pi$
$677$	−471.912	−	471.912i	−0.697064	−	0.697064i	−0.963776	+	0.266712i	$0.914063\pi$
$678$	−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	−0.729069	−	0.684441i	$-0.760046\pi$
$683$	−30.4808	+	30.4808i	−0.0446278	+	0.0446278i	0.684441	+	0.729069i	$0.260046\pi$
$684$		−	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	0.858659	−	0.512547i	$-0.171298\pi$
$727$	251.623	+	251.623i	0.346112	+	0.346112i	−0.512547	+	0.858659i	$0.671298\pi$
$728$	−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	−0.321294	−	0.946979i	$-0.604118\pi$
$733$	458.627	−	458.627i	0.625685	−	0.625685i	0.946979	+	0.321294i	$0.104118\pi$
$734$			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	−0.988817	−	0.149134i	$-0.952351\pi$
$743$	−623.884	+	623.884i	−0.839682	+	0.839682i	0.149134	+	0.988817i	$0.452351\pi$
$744$		−	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	0.952375	−	0.304930i	$-0.0986330\pi$
$757$	490.116	+	490.116i	0.647445	+	0.647445i	−0.304930	+	0.952375i	$0.598633\pi$
$758$	−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	−0.585697	−	0.810530i	$-0.699179\pi$
$773$	173.796	−	173.796i	0.224833	−	0.224833i	0.810530	+	0.585697i	$0.199179\pi$
$774$		−	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	$0.0106588\pi$
$787$	812.907	+	812.907i	1.03292	+	1.03292i	0.0334795	+	0.999439i	$0.489341\pi$
$788$	−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	$0.0808966\pi$
$797$	971.779	+	971.779i	1.21930	+	1.21930i	0.251417	+	0.967879i	$0.419103\pi$
$798$	−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	−0.0470806	−	0.998891i	$-0.514992\pi$
$823$	783.340	−	783.340i	0.951810	−	0.951810i	0.998891	+	0.0470806i	$0.0149918\pi$
$824$			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	$0.00547458\pi$
$827$	841.100	+	841.100i	1.01705	+	1.01705i	0.0171980	+	0.999852i	$0.494525\pi$
$828$	−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	−0.863544	−	0.504274i	$-0.831760\pi$
$853$	−306.457	+	306.457i	−0.359269	+	0.359269i	0.504274	+	0.863544i	$0.331760\pi$
$854$		−	157.961i		−	0.184966i
$855$		0			0
$856$	−1322.62			−1.54512
$857$	−698.176	−	698.176i	−0.814674	−	0.814674i	0.170656	−	0.985331i	$-0.445411\pi$
$857$	−698.176	−	698.176i	−0.814674	−	0.814674i	−0.985331	+	0.170656i	$0.945411\pi$
$858$	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	−0.0389942	−	0.999239i	$-0.512415\pi$
$863$	828.692	−	828.692i	0.960245	−	0.960245i	0.999239	+	0.0389942i	$0.0124154\pi$
$864$			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	0.275846	−	0.961202i	$-0.411042\pi$
$877$	−601.057	−	601.057i	−0.685356	−	0.685356i	−0.961202	+	0.275846i	$0.911042\pi$
$878$	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	−0.200360	−	0.979722i	$-0.564211\pi$
$883$	688.177	−	688.177i	0.779362	−	0.779362i	0.979722	+	0.200360i	$0.0642111\pi$
$884$			95.8661i			0.108446i
$885$		0			0
$886$	418.226			0.472038
$887$	−342.387	−	342.387i	−0.386005	−	0.386005i	0.487255	−	0.873260i	$-0.337998\pi$
$887$	−342.387	−	342.387i	−0.386005	−	0.386005i	−0.873260	+	0.487255i	$0.837998\pi$
$888$	−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	0.0850144	−	0.996380i	$-0.472906\pi$
$907$	−826.608	−	826.608i	−0.911365	−	0.911365i	−0.996380	+	0.0850144i	$0.972906\pi$
$908$	−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	0.895492	−	0.445078i	$-0.146824\pi$
$937$	422.038	+	422.038i	0.450414	+	0.450414i	−0.445078	+	0.895492i	$0.646824\pi$
$938$	−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	0.249231	−	0.968444i	$-0.419822\pi$
$947$	−681.095	−	681.095i	−0.719213	−	0.719213i	−0.968444	+	0.249231i	$0.919822\pi$
$948$	−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	−0.885885	−	0.463905i	$-0.846448\pi$
$953$	−402.146	+	402.146i	−0.421979	+	0.421979i	0.463905	+	0.885885i	$0.346448\pi$
$954$		−	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	0.936987	−	0.349364i	$-0.113602\pi$
$967$	568.231	+	568.231i	0.587623	+	0.587623i	−0.349364	+	0.936987i	$0.613602\pi$
$968$	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	0.675137	−	0.737692i	$-0.264084\pi$
$977$	−61.1157	−	61.1157i	−0.0625544	−	0.0625544i	−0.737692	+	0.675137i	$0.764084\pi$
$978$	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	−0.734797	−	0.678287i	$-0.762723\pi$
$983$	−55.5500	+	55.5500i	−0.0565107	+	0.0565107i	0.678287	+	0.734797i	$0.262723\pi$
$984$		−	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	0.613515	−	0.789683i	$-0.289755\pi$
$997$	−175.640	−	175.640i	−0.176169	−	0.176169i	−0.789683	+	0.613515i	$0.789755\pi$
$998$	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.232.8	yes	24
5.2	odd	4	inner	275.3.f.c.243.5	yes	24
5.3	odd	4	inner	275.3.f.c.243.8	yes	24
5.4	even	2	inner	275.3.f.c.232.5	✓	24

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

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