LMFDB - Embedded newform 1050.3.c.b.449.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(449,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1050.449");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			449.13
Character	$\chi$	$=$	1050.449
Dual form			1050.3.c.b.449.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +(2.53883 - 1.59823i) q^{3} +2.00000 q^{4} +(-3.59045 + 2.26024i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(3.89133 - 8.11526i) q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +(2.53883 - 1.59823i) q^{3} +2.00000 q^{4} +(-3.59045 + 2.26024i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(3.89133 - 8.11526i) q^{9} +7.44959i q^{11} +(5.07766 - 3.19646i) q^{12} +13.9983i q^{13} -3.74166i q^{14} +4.00000 q^{16} -17.8625 q^{17} +(-5.50318 + 11.4767i) q^{18} -33.6867 q^{19} +(4.22851 + 6.71712i) q^{21} -10.5353i q^{22} +7.94534 q^{23} +(-7.18090 + 4.52047i) q^{24} -19.7965i q^{26} +(-3.09060 - 26.8225i) q^{27} +5.29150i q^{28} -8.60528i q^{29} -56.7226 q^{31} -5.65685 q^{32} +(11.9061 + 18.9133i) q^{33} +25.2614 q^{34} +(7.78267 - 16.2305i) q^{36} +12.0910i q^{37} +47.6401 q^{38} +(22.3724 + 35.5392i) q^{39} -75.2891i q^{41} +(-5.98002 - 9.49944i) q^{42} +60.9839i q^{43} +14.8992i q^{44} -11.2364 q^{46} -67.5639 q^{47} +(10.1553 - 6.39291i) q^{48} -7.00000 q^{49} +(-45.3498 + 28.5483i) q^{51} +27.9965i q^{52} -49.1583 q^{53} +(4.37077 + 37.9328i) q^{54} -7.48331i q^{56} +(-85.5248 + 53.8390i) q^{57} +12.1697i q^{58} -82.5425i q^{59} -6.51416 q^{61} +80.2178 q^{62} +(21.4710 + 10.2955i) q^{63} +8.00000 q^{64} +(-16.8378 - 26.7474i) q^{66} -27.8806i q^{67} -35.7249 q^{68} +(20.1719 - 12.6985i) q^{69} -1.41195i q^{71} +(-11.0064 + 22.9534i) q^{72} +46.2735i q^{73} -17.0993i q^{74} -67.3733 q^{76} -19.7098 q^{77} +(-31.6394 - 50.2601i) q^{78} +49.2405 q^{79} +(-50.7150 - 63.1584i) q^{81} +106.475i q^{82} +42.4351 q^{83} +(8.45703 + 13.4342i) q^{84} -86.2443i q^{86} +(-13.7532 - 21.8474i) q^{87} -21.0706i q^{88} +63.3570i q^{89} -37.0359 q^{91} +15.8907 q^{92} +(-144.009 + 90.6556i) q^{93} +95.5497 q^{94} +(-14.3618 + 9.04094i) q^{96} +34.3309i q^{97} +9.89949 q^{98} +(60.4554 + 28.9888i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9}+O(q^{10}) $ 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9	$ 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9} + 128 q^{16} + 48 q^{19} + 56 q^{21} - 32 q^{24} + 48 q^{31} + 256 q^{34} - 32 q^{36} + 192 q^{39} + 160 q^{46} - 224 q^{49} + 288 q^{51} - 80 q^{54} - 112 q^{61} + 256 q^{64} - 192 q^{66} + 344 q^{69} + 96 q^{76} - 256 q^{79} + 160 q^{81} + 112 q^{84} - 448 q^{91} + 416 q^{94} - 64 q^{96} - 304 q^{99}+O(q^{100}) $ 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9 + 128 * q^16 + 48 * q^19 + 56 * q^21 - 32 * q^24 + 48 * q^31 + 256 * q^34 - 32 * q^36 + 192 * q^39 + 160 * q^46 - 224 * q^49 + 288 * q^51 - 80 * q^54 - 112 * q^61 + 256 * q^64 - 192 * q^66 + 344 * q^69 + 96 * q^76 - 256 * q^79 + 160 * q^81 + 112 * q^84 - 448 * q^91 + 416 * q^94 - 64 * q^96 - 304 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$	2.53883	−	1.59823i	0.846277	−	0.532743i
$3$	2.53883	−	1.59823i	0.846277	−	0.532743i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	−3.59045	+	2.26024i	−0.598408	+	0.376706i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	−2.82843			−0.353553
$9$	3.89133	−	8.11526i	0.432370	−	0.901696i
$10$		0			0
$11$			7.44959i			0.677235i	0.940924	+	0.338618i	$0.109959\pi$
$11$			7.44959i			0.677235i	−0.940924	+	0.338618i	$0.890041\pi$
$12$	5.07766	−	3.19646i	0.423139	−	0.266371i
$13$			13.9983i			1.07679i	0.842693	+	0.538395i	$0.180969\pi$
$13$			13.9983i			1.07679i	−0.842693	+	0.538395i	$0.819031\pi$
$14$		−	3.74166i		−	0.267261i
$15$		0			0
$16$	4.00000			0.250000
$17$	−17.8625			−1.05073			−0.525367	−	0.850876i	$-0.676072\pi$
$17$	−17.8625			−1.05073			−0.525367	+	0.850876i	$0.676072\pi$
$18$	−5.50318	+	11.4767i	−0.305732	+	0.637595i
$19$	−33.6867			−1.77298			−0.886491	−	0.462746i	$-0.846864\pi$
$19$	−33.6867			−1.77298			−0.886491	+	0.462746i	$0.846864\pi$
$20$		0			0
$21$	4.22851	+	6.71712i	0.201358	+	0.319863i
$22$		−	10.5353i		−	0.478878i
$23$	7.94534			0.345450			0.172725	−	0.984970i	$-0.444743\pi$
$23$	7.94534			0.345450			0.172725	+	0.984970i	$0.444743\pi$
$24$	−7.18090	+	4.52047i	−0.299204	+	0.188353i
$25$		0			0
$26$		−	19.7965i		−	0.761405i
$27$	−3.09060	−	26.8225i	−0.114467	−	0.993427i
$28$			5.29150i			0.188982i
$29$		−	8.60528i		−	0.296734i	−0.988932	−	0.148367i	$-0.952598\pi$
$29$		−	8.60528i		−	0.296734i	0.988932	−	0.148367i	$-0.0474017\pi$
$30$		0			0
$31$	−56.7226			−1.82976			−0.914880	−	0.403725i	$-0.867715\pi$
$31$	−56.7226			−1.82976			−0.914880	+	0.403725i	$0.867715\pi$
$32$	−5.65685			−0.176777
$33$	11.9061	+	18.9133i	0.360792	+	0.573129i
$34$	25.2614			0.742981
$35$		0			0
$36$	7.78267	−	16.2305i	0.216185	−	0.450848i
$37$			12.0910i			0.326785i	0.986561	+	0.163393i	$0.0522437\pi$
$37$			12.0910i			0.326785i	−0.986561	+	0.163393i	$0.947756\pi$
$38$	47.6401			1.25369
$39$	22.3724	+	35.5392i	0.573652	+	0.911262i
$40$		0			0
$41$		−	75.2891i		−	1.83632i	−0.396212	−	0.918159i	$-0.629675\pi$
$41$		−	75.2891i		−	1.83632i	0.396212	−	0.918159i	$-0.370325\pi$
$42$	−5.98002	−	9.49944i	−0.142381	−	0.226177i
$43$			60.9839i			1.41823i	0.705093	+	0.709115i	$0.250905\pi$
$43$			60.9839i			1.41823i	−0.705093	+	0.709115i	$0.749095\pi$
$44$			14.8992i			0.338618i
$45$		0			0
$46$	−11.2364			−0.244270
$47$	−67.5639			−1.43753			−0.718764	−	0.695254i	$-0.755292\pi$
$47$	−67.5639			−1.43753			−0.718764	+	0.695254i	$0.755292\pi$
$48$	10.1553	−	6.39291i	0.211569	−	0.133186i
$49$	−7.00000			−0.142857
$50$		0			0
$51$	−45.3498	+	28.5483i	−0.889212	+	0.559771i
$52$			27.9965i			0.538395i
$53$	−49.1583			−0.927515			−0.463757	−	0.885962i	$-0.653499\pi$
$53$	−49.1583			−0.927515			−0.463757	+	0.885962i	$0.653499\pi$
$54$	4.37077	+	37.9328i	0.0809402	+	0.702459i
$55$		0			0
$56$		−	7.48331i		−	0.133631i
$57$	−85.5248	+	53.8390i	−1.50043	+	0.944543i
$58$			12.1697i			0.209823i
$59$		−	82.5425i		−	1.39902i	−0.714620	−	0.699512i	$-0.753401\pi$
$59$		−	82.5425i		−	1.39902i	0.714620	−	0.699512i	$-0.246599\pi$
$60$		0			0
$61$	−6.51416			−0.106790			−0.0533948	−	0.998573i	$-0.517004\pi$
$61$	−6.51416			−0.106790			−0.0533948	+	0.998573i	$0.517004\pi$
$62$	80.2178			1.29384
$63$	21.4710	+	10.2955i	0.340809	+	0.163421i
$64$	8.00000			0.125000
$65$		0			0
$66$	−16.8378	−	26.7474i	−0.255119	−	0.405263i
$67$		−	27.8806i		−	0.416129i	−0.978115	−	0.208064i	$-0.933284\pi$
$67$		−	27.8806i		−	0.416129i	0.978115	−	0.208064i	$-0.0667163\pi$
$68$	−35.7249			−0.525367
$69$	20.1719	−	12.6985i	0.292346	−	0.184036i
$70$		0			0
$71$		−	1.41195i		−	0.0198866i	−0.999951	−	0.00994331i	$-0.996835\pi$
$71$		−	1.41195i		−	0.0198866i	0.999951	−	0.00994331i	$-0.00316511\pi$
$72$	−11.0064	+	22.9534i	−0.152866	+	0.318798i
$73$			46.2735i			0.633883i	0.948445	+	0.316941i	$0.102656\pi$
$73$			46.2735i			0.633883i	−0.948445	+	0.316941i	$0.897344\pi$
$74$		−	17.0993i		−	0.231072i
$75$		0			0
$76$	−67.3733			−0.886491
$77$	−19.7098			−0.255971
$78$	−31.6394	−	50.2601i	−0.405633	−	0.644360i
$79$	49.2405			0.623297			0.311649	−	0.950197i	$-0.399119\pi$
$79$	49.2405			0.623297			0.311649	+	0.950197i	$0.399119\pi$
$80$		0			0
$81$	−50.7150	−	63.1584i	−0.626112	−	0.779733i
$82$			106.475i			1.29847i
$83$	42.4351			0.511266			0.255633	−	0.966774i	$-0.417716\pi$
$83$	42.4351			0.511266			0.255633	+	0.966774i	$0.417716\pi$
$84$	8.45703	+	13.4342i	0.100679	+	0.159931i
$85$		0			0
$86$		−	86.2443i		−	1.00284i
$87$	−13.7532	−	21.8474i	−0.158083	−	0.251119i
$88$		−	21.0706i		−	0.239439i
$89$			63.3570i			0.711877i	0.934509	+	0.355938i	$0.115839\pi$
$89$			63.3570i			0.711877i	−0.934509	+	0.355938i	$0.884161\pi$
$90$		0			0
$91$	−37.0359			−0.406988
$92$	15.8907			0.172725
$93$	−144.009	+	90.6556i	−1.54848	+	0.974792i
$94$	95.5497			1.01649
$95$		0			0
$96$	−14.3618	+	9.04094i	−0.149602	+	0.0941765i
$97$			34.3309i			0.353927i	0.984217	+	0.176963i	$0.0566274\pi$
$97$			34.3309i			0.353927i	−0.984217	+	0.176963i	$0.943373\pi$
$98$	9.89949			0.101015
$99$	60.4554	+	28.9888i	0.610661	+	0.292817i
$100$		0			0
$101$		−	32.9701i		−	0.326436i	−0.986590	−	0.163218i	$-0.947813\pi$
$101$		−	32.9701i		−	0.326436i	0.986590	−	0.163218i	$-0.0521874\pi$
$102$	64.1343	−	40.3734i	0.628768	−	0.395818i
$103$			86.4076i			0.838908i	0.907776	+	0.419454i	$0.137779\pi$
$103$			86.4076i			0.838908i	−0.907776	+	0.419454i	$0.862221\pi$
$104$		−	39.5931i		−	0.380703i
$105$		0			0
$106$	69.5203			0.655852
$107$	4.61672			0.0431469			0.0215734	−	0.999767i	$-0.493132\pi$
$107$	4.61672			0.0431469			0.0215734	+	0.999767i	$0.493132\pi$
$108$	−6.18120	−	53.6451i	−0.0572333	−	0.496714i
$109$	41.5953			0.381608			0.190804	−	0.981628i	$-0.438890\pi$
$109$	41.5953			0.381608			0.190804	+	0.981628i	$0.438890\pi$
$110$		0			0
$111$	19.3243	+	30.6971i	0.174092	+	0.276551i
$112$			10.5830i			0.0944911i
$113$	152.452			1.34914			0.674568	−	0.738212i	$-0.264330\pi$
$113$	152.452			1.34914			0.674568	+	0.738212i	$0.264330\pi$
$114$	120.950	−	76.1398i	1.06097	−	0.667893i
$115$		0			0
$116$		−	17.2106i		−	0.148367i
$117$	113.600	+	54.4719i	0.970937	+	0.465572i
$118$			116.733i			0.989260i
$119$		−	47.2597i		−	0.397140i
$120$		0			0
$121$	65.5036			0.541352
$122$	9.21242			0.0755116
$123$	−120.329	−	191.146i	−0.978285	−	1.55403i
$124$	−113.445			−0.914880
$125$		0			0
$126$	−30.3645	−	14.5600i	−0.240988	−	0.115556i
$127$			209.565i			1.65012i	0.565044	+	0.825061i	$0.308859\pi$
$127$			209.565i			1.65012i	−0.565044	+	0.825061i	$0.691141\pi$
$128$	−11.3137			−0.0883883
$129$	97.4662	+	154.828i	0.755552	+	1.20022i
$130$		0			0
$131$		−	99.6575i		−	0.760745i	−0.924833	−	0.380372i	$-0.875796\pi$
$131$		−	99.6575i		−	0.760745i	0.924833	−	0.380372i	$-0.124204\pi$
$132$	23.8123	+	37.8265i	0.180396	+	0.286565i
$133$		−	89.1265i		−	0.670124i
$134$			39.4292i			0.294247i
$135$		0			0
$136$	50.5227			0.371490
$137$	−255.362			−1.86396			−0.931980	−	0.362511i	$-0.881920\pi$
$137$	−255.362			−1.86396			−0.931980	+	0.362511i	$0.881920\pi$
$138$	−28.5274	+	17.9584i	−0.206720	+	0.130133i
$139$	−221.760			−1.59540			−0.797700	−	0.603055i	$-0.793950\pi$
$139$	−221.760			−1.59540			−0.797700	+	0.603055i	$0.793950\pi$
$140$		0			0
$141$	−171.533	+	107.982i	−1.21655	+	0.765833i
$142$			1.99680i			0.0140620i
$143$	−104.281			−0.729240
$144$	15.5653	−	32.4611i	0.108093	−	0.225424i
$145$		0			0
$146$		−	65.4405i		−	0.448223i
$147$	−17.7718	+	11.1876i	−0.120897	+	0.0761061i
$148$			24.1821i			0.163393i
$149$			221.335i			1.48547i	0.669587	+	0.742733i	$0.266471\pi$
$149$			221.335i			1.48547i	−0.669587	+	0.742733i	$0.733529\pi$
$150$		0			0
$151$	−93.5574			−0.619585			−0.309793	−	0.950804i	$-0.600260\pi$
$151$	−93.5574			−0.619585			−0.309793	+	0.950804i	$0.600260\pi$
$152$	95.2803			0.626844
$153$	−69.5088	+	144.959i	−0.454306	+	0.947442i
$154$	27.8738			0.180999
$155$		0			0
$156$	44.7448	+	71.0785i	0.286826	+	0.455631i
$157$			111.136i			0.707873i	0.935269	+	0.353937i	$0.115157\pi$
$157$			111.136i			0.707873i	−0.935269	+	0.353937i	$0.884843\pi$
$158$	−69.6365			−0.440738
$159$	−124.805	+	78.5662i	−0.784935	+	0.494127i
$160$		0			0
$161$			21.0214i			0.130568i
$162$	71.7219	+	89.3195i	0.442728	+	0.551355i
$163$		−	72.0318i		−	0.441913i	−0.975284	−	0.220957i	$-0.929082\pi$
$163$		−	72.0318i		−	0.441913i	0.975284	−	0.220957i	$-0.0709179\pi$
$164$		−	150.578i		−	0.918159i
$165$		0			0
$166$	−60.0123			−0.361520
$167$	131.383			0.786725			0.393362	−	0.919384i	$-0.371312\pi$
$167$	131.383			0.786725			0.393362	+	0.919384i	$0.371312\pi$
$168$	−11.9600	−	18.9989i	−0.0711907	−	0.113089i
$169$	−26.9513			−0.159475
$170$		0			0
$171$	−131.086	+	273.376i	−0.766585	+	1.59869i
$172$			121.968i			0.709115i
$173$	172.758			0.998600			0.499300	−	0.866429i	$-0.333591\pi$
$173$	172.758			0.998600			0.499300	+	0.866429i	$0.333591\pi$
$174$	19.4500	+	30.8968i	0.111781	+	0.177568i
$175$		0			0
$176$			29.7984i			0.169309i
$177$	−131.922	−	209.561i	−0.745320	−	1.18396i
$178$		−	89.6004i		−	0.503373i
$179$		−	27.5298i		−	0.153798i	−0.997039	−	0.0768989i	$-0.975498\pi$
$179$		−	27.5298i		−	0.153798i	0.997039	−	0.0768989i	$-0.0245019\pi$
$180$		0			0
$181$	−209.351			−1.15664			−0.578319	−	0.815811i	$-0.696291\pi$
$181$	−209.351			−1.15664			−0.578319	+	0.815811i	$0.696291\pi$
$182$	52.3767			0.287784
$183$	−16.5384	+	10.4111i	−0.0903736	+	0.0568914i
$184$	−22.4728			−0.122135
$185$		0			0
$186$	203.660	−	128.206i	1.09494	−	0.689282i
$187$		−	133.068i		−	0.711594i
$188$	−135.128			−0.718764
$189$	70.9657	−	8.17696i	0.375480	−	0.0432643i
$190$		0			0
$191$			72.4373i			0.379253i	0.981856	+	0.189626i	$0.0607277\pi$
$191$			72.4373i			0.379253i	−0.981856	+	0.189626i	$0.939272\pi$
$192$	20.3107	−	12.7858i	0.105785	−	0.0665928i
$193$		−	48.6764i		−	0.252210i	−0.992017	−	0.126105i	$-0.959752\pi$
$193$		−	48.6764i		−	0.252210i	0.992017	−	0.126105i	$-0.0402475\pi$
$194$		−	48.5512i		−	0.250264i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	−171.518			−0.870647			−0.435324	−	0.900274i	$-0.643366\pi$
$197$	−171.518			−0.870647			−0.435324	+	0.900274i	$0.643366\pi$
$198$	−85.4968	−	40.9964i	−0.431802	−	0.207053i
$199$	15.2926			0.0768473			0.0384237	−	0.999262i	$-0.487766\pi$
$199$	15.2926			0.0768473			0.0384237	+	0.999262i	$0.487766\pi$
$200$		0			0
$201$	−44.5596	−	70.7842i	−0.221690	−	0.352160i
$202$			46.6267i			0.230825i
$203$	22.7674			0.112155
$204$	−90.6996	+	57.0966i	−0.444606	+	0.279885i
$205$		0			0
$206$		−	122.199i		−	0.593198i
$207$	30.9180	−	64.4786i	0.149362	−	0.311491i
$208$			55.9930i			0.269197i
$209$		−	250.952i		−	1.20073i
$210$		0			0
$211$	191.468			0.907433			0.453716	−	0.891146i	$-0.350098\pi$
$211$	191.468			0.907433			0.453716	+	0.891146i	$0.350098\pi$
$212$	−98.3166			−0.463757
$213$	−2.25662	−	3.58470i	−0.0105945	−	0.0168296i
$214$	−6.52902			−0.0305095
$215$		0			0
$216$	8.74154	+	75.8656i	0.0404701	+	0.351230i
$217$		−	150.074i		−	0.691585i
$218$	−58.8247			−0.269838
$219$	73.9555	+	117.481i	0.337696	+	0.536441i
$220$		0			0
$221$		−	250.044i		−	1.13142i
$222$	−27.3286	−	43.4123i	−0.123102	−	0.195551i
$223$			191.382i			0.858213i	0.903254	+	0.429107i	$0.141172\pi$
$223$			191.382i			0.858213i	−0.903254	+	0.429107i	$0.858828\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	−215.600			−0.953984
$227$	−146.459			−0.645194			−0.322597	−	0.946536i	$-0.604556\pi$
$227$	−146.459			−0.645194			−0.322597	+	0.946536i	$0.604556\pi$
$228$	−171.050	+	107.678i	−0.750217	+	0.472272i
$229$	−443.300			−1.93581			−0.967904	−	0.251320i	$-0.919135\pi$
$229$	−443.300			−1.93581			−0.967904	+	0.251320i	$0.919135\pi$
$230$		0			0
$231$	−50.0398	+	31.5007i	−0.216622	+	0.136367i
$232$			24.3394i			0.104911i
$233$	101.081			0.433825			0.216912	−	0.976191i	$-0.430401\pi$
$233$	101.081			0.433825			0.216912	+	0.976191i	$0.430401\pi$
$234$	−160.654	−	77.0349i	−0.686556	−	0.329209i
$235$		0			0
$236$		−	165.085i		−	0.699512i
$237$	125.013	−	78.6975i	0.527482	−	0.332057i
$238$			66.8353i			0.280820i
$239$			315.865i			1.32161i	0.750557	+	0.660805i	$0.229785\pi$
$239$			315.865i			1.32161i	−0.750557	+	0.660805i	$0.770215\pi$
$240$		0			0
$241$	50.4883			0.209495			0.104747	−	0.994499i	$-0.466597\pi$
$241$	50.4883			0.209495			0.104747	+	0.994499i	$0.466597\pi$
$242$	−92.6361			−0.382794
$243$	−229.698	−	79.2944i	−0.945261	−	0.326314i
$244$	−13.0283			−0.0533948
$245$		0			0
$246$	170.171	+	270.322i	0.691752	+	1.09887i
$247$		−	471.555i		−	1.90913i
$248$	160.436			0.646918
$249$	107.736	−	67.8209i	0.432673	−	0.272373i
$250$		0			0
$251$			473.905i			1.88807i	0.329847	+	0.944035i	$0.393003\pi$
$251$			473.905i			1.88807i	−0.329847	+	0.944035i	$0.606997\pi$
$252$	42.9419	+	20.5910i	0.170405	+	0.0817103i
$253$			59.1896i			0.233951i
$254$		−	296.370i		−	1.16681i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−110.742			−0.430904			−0.215452	−	0.976514i	$-0.569122\pi$
$257$	−110.742			−0.430904			−0.215452	+	0.976514i	$0.569122\pi$
$258$	−137.838	−	218.960i	−0.534256	−	0.848681i
$259$	−31.9899			−0.123513
$260$		0			0
$261$	−69.8342	−	33.4860i	−0.267564	−	0.128299i
$262$			140.937i			0.537928i
$263$	410.523			1.56092			0.780462	−	0.625203i	$-0.214984\pi$
$263$	410.523			1.56092			0.780462	+	0.625203i	$0.214984\pi$
$264$	−33.6757	−	53.4948i	−0.127559	−	0.202632i
$265$		0			0
$266$			126.044i			0.473849i
$267$	101.259	+	160.853i	0.379247	+	0.602445i
$268$		−	55.7612i		−	0.208064i
$269$			62.9603i			0.234053i	0.993129	+	0.117026i	$0.0373362\pi$
$269$			62.9603i			0.234053i	−0.993129	+	0.117026i	$0.962664\pi$
$270$		0			0
$271$	472.567			1.74379			0.871894	−	0.489694i	$-0.162891\pi$
$271$	472.567			1.74379			0.871894	+	0.489694i	$0.162891\pi$
$272$	−71.4499			−0.262683
$273$	−94.0280	+	59.1918i	−0.344425	+	0.216820i
$274$	361.137			1.31802
$275$		0			0
$276$	40.3438	−	25.3969i	0.146173	−	0.0920179i
$277$		−	351.168i		−	1.26776i	−0.773433	−	0.633878i	$-0.781462\pi$
$277$		−	351.168i		−	1.26776i	0.773433	−	0.633878i	$-0.218538\pi$
$278$	313.617			1.12812
$279$	−220.727	+	460.319i	−0.791134	+	1.64989i
$280$		0			0
$281$			102.043i			0.363143i	0.983378	+	0.181571i	$0.0581183\pi$
$281$			102.043i			0.363143i	−0.983378	+	0.181571i	$0.941882\pi$
$282$	242.585	−	152.710i	0.860229	−	0.541526i
$283$		−	395.493i		−	1.39750i	−0.715366	−	0.698750i	$-0.753740\pi$
$283$		−	395.493i		−	1.39750i	0.715366	−	0.698750i	$-0.246260\pi$
$284$		−	2.82390i		−	0.00994331i
$285$		0			0
$286$	147.476			0.515651
$287$	199.196			0.694063
$288$	−22.0127	+	45.9069i	−0.0764330	+	0.159399i
$289$	30.0679			0.104041
$290$		0			0
$291$	54.8686	+	87.1604i	0.188552	+	0.299520i
$292$			92.5469i			0.316941i
$293$	400.273			1.36612			0.683060	−	0.730363i	$-0.260649\pi$
$293$	400.273			1.36612			0.683060	+	0.730363i	$0.260649\pi$
$294$	25.1332	−	15.8217i	0.0854869	−	0.0538151i
$295$		0			0
$296$		−	34.1986i		−	0.115536i
$297$	199.817	−	23.0237i	0.672784	−	0.0775209i
$298$		−	313.014i		−	1.05038i
$299$			111.221i			0.371977i
$300$		0			0
$301$	−161.348			−0.536041
$302$	132.310			0.438113
$303$	−52.6937	−	83.7054i	−0.173906	−	0.276255i
$304$	−134.747			−0.443246
$305$		0			0
$306$	98.3004	−	205.003i	0.321243	−	0.669943i
$307$		−	384.827i		−	1.25351i	−0.779217	−	0.626754i	$-0.784383\pi$
$307$		−	384.827i		−	1.25351i	0.779217	−	0.626754i	$-0.215617\pi$
$308$	−39.4195			−0.127985
$309$	138.099	+	219.374i	0.446922	+	0.709949i
$310$		0			0
$311$			418.912i			1.34698i	0.739195	+	0.673492i	$0.235206\pi$
$311$			418.912i			1.34698i	−0.739195	+	0.673492i	$0.764794\pi$
$312$	−63.2787	−	100.520i	−0.202816	−	0.322180i
$313$			127.707i			0.408010i	0.978970	+	0.204005i	$0.0653958\pi$
$313$			127.707i			0.408010i	−0.978970	+	0.204005i	$0.934604\pi$
$314$		−	157.170i		−	0.500542i
$315$		0			0
$316$	98.4809			0.311649
$317$	−0.785778			−0.00247880			−0.00123940	−	0.999999i	$-0.500395\pi$
$317$	−0.785778			−0.00247880			−0.00123940	+	0.999999i	$0.500395\pi$
$318$	176.500	−	111.109i	0.555033	−	0.349400i
$319$	64.1058			0.200959
$320$		0			0
$321$	11.7211	−	7.37857i	0.0365142	−	0.0229862i
$322$		−	29.7288i		−	0.0923253i
$323$	601.727			1.86293
$324$	−101.430	−	126.317i	−0.313056	−	0.389867i
$325$		0			0
$326$			101.868i			0.312480i
$327$	105.604	−	66.4788i	0.322947	−	0.203299i
$328$			212.950i			0.649237i
$329$		−	178.757i		−	0.543335i
$330$		0			0
$331$	176.790			0.534110			0.267055	−	0.963681i	$-0.413949\pi$
$331$	176.790			0.534110			0.267055	+	0.963681i	$0.413949\pi$
$332$	84.8701			0.255633
$333$	98.1220	+	47.0503i	0.294661	+	0.141292i
$334$	−185.804			−0.556298
$335$		0			0
$336$	16.9141	+	26.8685i	0.0503395	+	0.0799657i
$337$			342.364i			1.01592i	0.861381	+	0.507959i	$0.169600\pi$
$337$			342.364i			1.01592i	−0.861381	+	0.507959i	$0.830400\pi$
$338$	38.1149			0.112766
$339$	387.051	−	243.654i	1.14174	−	0.718743i
$340$		0			0
$341$		−	422.560i		−	1.23918i
$342$	185.384	−	386.612i	0.542058	−	1.13045i
$343$		−	18.5203i		−	0.0539949i
$344$		−	172.489i		−	0.501420i
$345$		0			0
$346$	−244.316			−0.706116
$347$	−468.949			−1.35144			−0.675719	−	0.737159i	$-0.736167\pi$
$347$	−468.949			−1.35144			−0.675719	+	0.737159i	$0.736167\pi$
$348$	−27.5064	−	43.6947i	−0.0790414	−	0.125560i
$349$	271.580			0.778165			0.389082	−	0.921203i	$-0.372792\pi$
$349$	271.580			0.778165			0.389082	+	0.921203i	$0.372792\pi$
$350$		0			0
$351$	375.469	−	43.2630i	1.06971	−	0.123257i
$352$		−	42.1412i		−	0.119719i
$353$	209.133			0.592445			0.296223	−	0.955119i	$-0.404273\pi$
$353$	209.133			0.592445			0.296223	+	0.955119i	$0.404273\pi$
$354$	186.565	+	296.365i	0.527021	+	0.837188i
$355$		0			0
$356$			126.714i			0.355938i
$357$	−75.5317	−	119.984i	−0.211573	−	0.336091i
$358$			38.9330i			0.108751i
$359$		−	603.882i		−	1.68212i	−0.540940	−	0.841061i	$-0.681931\pi$
$359$		−	603.882i		−	1.68212i	0.540940	−	0.841061i	$-0.318069\pi$
$360$		0			0
$361$	773.791			2.14347
$362$	296.068			0.817866
$363$	166.303	−	104.690i	0.458134	−	0.288401i
$364$	−74.0718			−0.203494
$365$		0			0
$366$	23.3888	−	14.7235i	0.0639038	−	0.0402283i
$367$			184.720i			0.503326i	0.967815	+	0.251663i	$0.0809774\pi$
$367$			184.720i			0.503326i	−0.967815	+	0.251663i	$0.919023\pi$
$368$	31.7814			0.0863624
$369$	−610.991	−	292.975i	−1.65580	−	0.793970i
$370$		0			0
$371$		−	130.061i		−	0.350568i
$372$	−288.018	+	181.311i	−0.774242	+	0.487396i
$373$			165.681i			0.444186i	0.975026	+	0.222093i	$0.0712888\pi$
$373$			165.681i			0.444186i	−0.975026	+	0.222093i	$0.928711\pi$
$374$			188.187i			0.503173i
$375$		0			0
$376$	191.099			0.508243
$377$	120.459			0.319520
$378$	−100.361	+	11.5640i	−0.265505	+	0.0305925i
$379$	−515.037			−1.35894			−0.679469	−	0.733705i	$-0.737790\pi$
$379$	−515.037			−1.35894			−0.679469	+	0.733705i	$0.737790\pi$
$380$		0			0
$381$	334.933	+	532.051i	0.879090	+	1.39646i
$382$		−	102.442i		−	0.268172i
$383$	−302.028			−0.788584			−0.394292	−	0.918985i	$-0.629010\pi$
$383$	−302.028			−0.788584			−0.394292	+	0.918985i	$0.629010\pi$
$384$	−28.7236	+	18.0819i	−0.0748011	+	0.0470882i
$385$		0			0
$386$			68.8389i			0.178339i
$387$	494.901	+	237.309i	1.27881	+	0.613201i
$388$			68.6618i			0.176963i
$389$		−	454.647i		−	1.16876i	−0.811480	−	0.584380i	$-0.801338\pi$
$389$		−	454.647i		−	1.16876i	0.811480	−	0.584380i	$-0.198662\pi$
$390$		0			0
$391$	−141.923			−0.362976
$392$	19.7990			0.0505076
$393$	−159.275	−	253.014i	−0.405281	−	0.643801i
$394$	242.562			0.615641
$395$		0			0
$396$	120.911	+	57.9777i	0.305330	+	0.146408i
$397$		−	705.829i		−	1.77791i	−0.457997	−	0.888953i	$-0.651433\pi$
$397$		−	705.829i		−	1.77791i	0.457997	−	0.888953i	$-0.348567\pi$
$398$	−21.6270			−0.0543393
$399$	−142.445	−	226.277i	−0.357004	−	0.567111i
$400$		0			0
$401$		−	545.294i		−	1.35983i	−0.733289	−	0.679917i	$-0.762016\pi$
$401$		−	545.294i		−	1.35983i	0.733289	−	0.679917i	$-0.237984\pi$
$402$	63.0168	+	100.104i	0.156758	+	0.249015i
$403$		−	794.018i		−	1.97027i
$404$		−	65.9401i		−	0.163218i
$405$		0			0
$406$	−32.1980			−0.0793055
$407$	−90.0734			−0.221310
$408$	128.269	−	80.7468i	0.314384	−	0.197909i
$409$	690.458			1.68816			0.844081	−	0.536216i	$-0.180147\pi$
$409$	690.458			1.68816			0.844081	+	0.536216i	$0.180147\pi$
$410$		0			0
$411$	−648.322	+	408.127i	−1.57743	+	0.993011i
$412$			172.815i			0.419454i
$413$	218.387			0.528782
$414$	−43.7246	+	91.1865i	−0.105615	+	0.220257i
$415$		0			0
$416$		−	79.1861i		−	0.190351i
$417$	−563.013	+	354.424i	−1.35015	+	0.849937i
$418$			354.899i			0.849042i
$419$		−	322.953i		−	0.770771i	−0.922756	−	0.385385i	$-0.874069\pi$
$419$		−	322.953i		−	0.770771i	0.922756	−	0.385385i	$-0.125931\pi$
$420$		0			0
$421$	569.497			1.35273			0.676363	−	0.736569i	$-0.263555\pi$
$421$	569.497			1.35273			0.676363	+	0.736569i	$0.263555\pi$
$422$	−270.777			−0.641652
$423$	−262.914	+	548.299i	−0.621545	+	1.29621i
$424$	139.041			0.327926
$425$		0			0
$426$	3.19134	+	5.06954i	0.00749141	+	0.0119003i
$427$		−	17.2349i		−	0.0403627i
$428$	9.23343			0.0215734
$429$	−264.753	+	166.665i	−0.617139	+	0.388497i
$430$		0			0
$431$		−	478.145i		−	1.10939i	−0.832055	−	0.554693i	$-0.812836\pi$
$431$		−	478.145i		−	1.10939i	0.832055	−	0.554693i	$-0.187164\pi$
$432$	−12.3624	−	107.290i	−0.0286167	−	0.248357i
$433$		−	316.070i		−	0.729954i	−0.931017	−	0.364977i	$-0.881077\pi$
$433$		−	316.070i		−	0.729954i	0.931017	−	0.364977i	$-0.118923\pi$
$434$			212.236i			0.489024i
$435$		0			0
$436$	83.1906			0.190804
$437$	−267.652			−0.612476
$438$	−104.589	−	166.143i	−0.238787	−	0.379321i
$439$	519.884			1.18424			0.592122	−	0.805848i	$-0.298290\pi$
$439$	519.884			1.18424			0.592122	+	0.805848i	$0.298290\pi$
$440$		0			0
$441$	−27.2393	+	56.8069i	−0.0617672	+	0.128814i
$442$			353.615i			0.800034i
$443$	−425.191			−0.959799			−0.479900	−	0.877323i	$-0.659327\pi$
$443$	−425.191			−0.959799			−0.479900	+	0.877323i	$0.659327\pi$
$444$	38.6485	+	61.3943i	0.0870462	+	0.138275i
$445$		0			0
$446$		−	270.654i		−	0.606848i
$447$	353.743	+	561.931i	0.791372	+	1.25712i
$448$			21.1660i			0.0472456i
$449$		−	522.788i		−	1.16434i	−0.813068	−	0.582169i	$-0.802204\pi$
$449$		−	522.788i		−	1.16434i	0.813068	−	0.582169i	$-0.197796\pi$
$450$		0			0
$451$	560.873			1.24362
$452$	304.905			0.674568
$453$	−237.526	+	149.526i	−0.524341	+	0.330079i
$454$	207.124			0.456221
$455$		0			0
$456$	241.901	−	152.280i	0.530484	−	0.333946i
$457$			141.081i			0.308710i	0.988015	+	0.154355i	$0.0493300\pi$
$457$			141.081i			0.308710i	−0.988015	+	0.154355i	$0.950670\pi$
$458$	626.921			1.36882
$459$	55.2058	+	479.117i	0.120274	+	1.04383i
$460$		0			0
$461$		−	504.114i		−	1.09352i	−0.837289	−	0.546761i	$-0.815861\pi$
$461$		−	504.114i		−	1.09352i	0.837289	−	0.546761i	$-0.184139\pi$
$462$	70.7669	−	44.5487i	0.153175	−	0.0964258i
$463$		−	823.939i		−	1.77957i	−0.456385	−	0.889783i	$-0.650856\pi$
$463$		−	823.939i		−	1.77957i	0.456385	−	0.889783i	$-0.349144\pi$
$464$		−	34.4211i		−	0.0741835i
$465$		0			0
$466$	−142.950			−0.306760
$467$	542.173			1.16097			0.580485	−	0.814271i	$-0.302863\pi$
$467$	542.173			1.16097			0.580485	+	0.814271i	$0.302863\pi$
$468$	227.199	+	108.944i	0.485468	+	0.232786i
$469$	73.7652			0.157282
$470$		0			0
$471$	177.621	+	282.156i	0.377114	+	0.599057i
$472$			233.465i			0.494630i
$473$	−454.305			−0.960476
$474$	−176.795	+	111.295i	−0.372986	+	0.234800i
$475$		0			0
$476$		−	94.5193i		−	0.198570i
$477$	−191.291	+	398.932i	−0.401030	+	0.836336i
$478$		−	446.700i		−	0.934520i
$479$			543.348i			1.13434i	0.823602	+	0.567169i	$0.191961\pi$
$479$			543.348i			1.13434i	−0.823602	+	0.567169i	$0.808039\pi$
$480$		0			0
$481$	−169.254			−0.351879
$482$	−71.4012			−0.148135
$483$	33.5970	+	53.3698i	0.0695590	+	0.110497i
$484$	131.007			0.270676
$485$		0			0
$486$	324.843	+	112.139i	0.668401	+	0.230739i
$487$			205.924i			0.422841i	0.977395	+	0.211421i	$0.0678090\pi$
$487$			205.924i			0.422841i	−0.977395	+	0.211421i	$0.932191\pi$
$488$	18.4248			0.0377558
$489$	−115.123	−	182.877i	−0.235426	−	0.373981i
$490$		0			0
$491$			871.862i			1.77569i	0.460147	+	0.887843i	$0.347797\pi$
$491$			871.862i			1.77569i	−0.460147	+	0.887843i	$0.652203\pi$
$492$	−240.658	−	382.293i	−0.489143	−	0.777017i
$493$			153.712i			0.311788i
$494$			666.879i			1.34996i
$495$		0			0
$496$	−226.890			−0.457440
$497$	3.73567			0.00751643
$498$	−152.361	+	95.9133i	−0.305946	+	0.192597i
$499$	−959.291			−1.92243			−0.961213	−	0.275807i	$-0.911055\pi$
$499$	−959.291			−1.92243			−0.961213	+	0.275807i	$0.911055\pi$
$500$		0			0
$501$	333.559	−	209.980i	0.665787	−	0.419122i
$502$		−	670.203i		−	1.33507i
$503$	78.8343			0.156728			0.0783641	−	0.996925i	$-0.475030\pi$
$503$	78.8343			0.156728			0.0783641	+	0.996925i	$0.475030\pi$
$504$	−60.7291	−	29.1201i	−0.120494	−	0.0577779i
$505$		0			0
$506$		−	83.7067i		−	0.165428i
$507$	−68.4249	+	43.0744i	−0.134960	+	0.0849593i
$508$			419.131i			0.825061i
$509$		−	360.750i		−	0.708743i	−0.935105	−	0.354372i	$-0.884695\pi$
$509$		−	360.750i		−	0.708743i	0.935105	−	0.354372i	$-0.115305\pi$
$510$		0			0
$511$	−122.428			−0.239585
$512$	−22.6274			−0.0441942
$513$	104.112	+	903.562i	0.202947	+	1.76133i
$514$	156.613			0.304695
$515$		0			0
$516$	194.932	+	309.656i	0.377776	+	0.600108i
$517$		−	503.323i		−	0.973545i
$518$	45.2406			0.0873370
$519$	438.603	−	276.106i	0.845092	−	0.531997i
$520$		0			0
$521$			65.8675i			0.126425i	0.998000	+	0.0632126i	$0.0201346\pi$
$521$			65.8675i			0.126425i	−0.998000	+	0.0632126i	$0.979865\pi$
$522$	98.7604	+	47.3564i	0.189196	+	0.0907211i
$523$			491.403i			0.939585i	0.882777	+	0.469792i	$0.155671\pi$
$523$			491.403i			0.939585i	−0.882777	+	0.469792i	$0.844329\pi$
$524$		−	199.315i		−	0.380372i
$525$		0			0
$526$	−580.567			−1.10374
$527$	1013.21			1.92259
$528$	47.6246	+	75.6530i	0.0901981	+	0.143282i
$529$	−465.872			−0.880664
$530$		0			0
$531$	−669.854	−	321.200i	−1.26150	−	0.604897i
$532$		−	178.253i		−	0.335062i
$533$	1053.92			1.97733
$534$	−143.202	−	227.480i	−0.268168	−	0.425993i
$535$		0			0
$536$			78.8583i			0.147124i
$537$	−43.9989	−	69.8935i	−0.0819346	−	0.130156i
$538$		−	89.0392i		−	0.165500i
$539$		−	52.1471i		−	0.0967479i
$540$		0			0
$541$	−392.520			−0.725545			−0.362772	−	0.931878i	$-0.618170\pi$
$541$	−392.520			−0.725545			−0.362772	+	0.931878i	$0.618170\pi$
$542$	−668.310			−1.23304
$543$	−531.508	+	334.591i	−0.978836	+	0.616190i
$544$	101.045			0.185745
$545$		0			0
$546$	132.976	−	83.7099i	0.243545	−	0.153315i
$547$			959.817i			1.75469i	0.479858	+	0.877346i	$0.340688\pi$
$547$			959.817i			1.75469i	−0.479858	+	0.877346i	$0.659312\pi$
$548$	−510.725			−0.931980
$549$	−25.3488	+	52.8642i	−0.0461727	+	0.0962917i
$550$		0			0
$551$			289.883i			0.526104i
$552$	−57.0547	+	35.9167i	−0.103360	+	0.0650665i
$553$			130.278i			0.235584i
$554$			496.627i			0.896438i
$555$		0			0
$556$	−443.521			−0.797700
$557$	289.144			0.519109			0.259555	−	0.965728i	$-0.416424\pi$
$557$	289.144			0.519109			0.259555	+	0.965728i	$0.416424\pi$
$558$	312.154	−	650.989i	0.559417	−	1.16665i
$559$	−853.669			−1.52714
$560$		0			0
$561$	−212.673	−	337.838i	−0.379097	−	0.602206i
$562$		−	144.311i		−	0.256781i
$563$	−920.945			−1.63578			−0.817891	−	0.575373i	$-0.804857\pi$
$563$	−920.945			−1.63578			−0.817891	+	0.575373i	$0.804857\pi$
$564$	−343.067	+	215.965i	−0.608274	+	0.382916i
$565$		0			0
$566$			559.311i			0.988182i
$567$	167.101	−	134.179i	0.294712	−	0.236648i
$568$			3.99360i			0.00703098i
$569$			670.437i			1.17827i	0.808034	+	0.589136i	$0.200532\pi$
$569$			670.437i			1.17827i	−0.808034	+	0.589136i	$0.799468\pi$
$570$		0			0
$571$	−413.731			−0.724572			−0.362286	−	0.932067i	$-0.618004\pi$
$571$	−413.731			−0.724572			−0.362286	+	0.932067i	$0.618004\pi$
$572$	−208.563			−0.364620
$573$	115.771	+	183.906i	0.202044	+	0.320953i
$574$	−281.706			−0.490777
$575$		0			0
$576$	31.1307	−	64.9221i	0.0540463	−	0.112712i
$577$		−	207.857i		−	0.360237i	−0.983645	−	0.180119i	$-0.942352\pi$
$577$		−	207.857i		−	0.360237i	0.983645	−	0.180119i	$-0.0576482\pi$
$578$	−42.5224			−0.0735682
$579$	−77.7960	−	123.581i	−0.134363	−	0.213439i
$580$		0			0
$581$			112.273i			0.193240i
$582$	−77.5960	−	123.263i	−0.133326	−	0.211793i
$583$		−	366.209i		−	0.628146i
$584$		−	130.881i		−	0.224111i
$585$		0			0
$586$	−566.071			−0.965992
$587$	−453.648			−0.772824			−0.386412	−	0.922326i	$-0.626286\pi$
$587$	−453.648			−0.772824			−0.386412	+	0.922326i	$0.626286\pi$
$588$	−35.5436	+	22.3752i	−0.0604484	+	0.0380530i
$589$	1910.79			3.24413
$590$		0			0
$591$	−435.454	+	274.124i	−0.736809	+	0.463831i
$592$			48.3642i			0.0816963i
$593$	−804.903			−1.35734			−0.678670	−	0.734443i	$-0.737443\pi$
$593$	−804.903			−1.35734			−0.678670	+	0.734443i	$0.737443\pi$
$594$	−282.584	+	32.5604i	−0.475730	+	0.0548156i
$595$		0			0
$596$			442.669i			0.742733i
$597$	38.8254	−	24.4411i	0.0650341	−	0.0409398i
$598$		−	157.290i		−	0.263027i
$599$		−	26.0952i		−	0.0435645i	−0.999763	−	0.0217823i	$-0.993066\pi$
$599$		−	26.0952i		−	0.0435645i	0.999763	−	0.0217823i	$-0.00693406\pi$
$600$		0			0
$601$	151.269			0.251696			0.125848	−	0.992050i	$-0.459835\pi$
$601$	151.269			0.251696			0.125848	+	0.992050i	$0.459835\pi$
$602$	228.181			0.379038
$603$	−226.259	−	108.493i	−0.375222	−	0.179922i
$604$	−187.115			−0.309793
$605$		0			0
$606$	74.5201	+	118.377i	0.122970	+	0.195342i
$607$		−	285.876i		−	0.470965i	−0.971879	−	0.235483i	$-0.924333\pi$
$607$		−	285.876i		−	0.470965i	0.971879	−	0.235483i	$-0.0756671\pi$
$608$	190.561			0.313422
$609$	57.8027	−	36.3876i	0.0949141	−	0.0597497i
$610$		0			0
$611$		−	945.776i		−	1.54792i
$612$	−139.018	+	289.917i	−0.227153	+	0.473721i
$613$		−	286.649i		−	0.467616i	−0.972283	−	0.233808i	$-0.924881\pi$
$613$		−	286.649i		−	0.467616i	0.972283	−	0.233808i	$-0.0751188\pi$
$614$			544.228i			0.886364i
$615$		0			0
$616$	55.7476			0.0904994
$617$	−443.353			−0.718562			−0.359281	−	0.933229i	$-0.616978\pi$
$617$	−443.353			−0.718562			−0.359281	+	0.933229i	$0.616978\pi$
$618$	−195.301	−	310.242i	−0.316022	−	0.502010i
$619$	−233.099			−0.376574			−0.188287	−	0.982114i	$-0.560293\pi$
$619$	−233.099			−0.376574			−0.188287	+	0.982114i	$0.560293\pi$
$620$		0			0
$621$	−24.5559	−	213.114i	−0.0395425	−	0.343179i
$622$		−	592.431i		−	0.952461i
$623$	−167.627			−0.269064
$624$	89.4897	+	142.157i	0.143413	+	0.227816i
$625$		0			0
$626$		−	180.605i		−	0.288506i
$627$	−401.078	−	637.125i	−0.639678	−	1.01615i
$628$			222.272i			0.353937i
$629$		−	215.976i		−	0.343364i
$630$		0			0
$631$	593.804			0.941052			0.470526	−	0.882386i	$-0.344064\pi$
$631$	593.804			0.941052			0.470526	+	0.882386i	$0.344064\pi$
$632$	−139.273			−0.220369
$633$	486.106	−	306.010i	0.767940	−	0.483428i
$634$	1.11126			0.00175277
$635$		0			0
$636$	−249.609	+	157.132i	−0.392467	+	0.247063i
$637$		−	97.9878i		−	0.153827i
$638$	−90.6593			−0.142099
$639$	−11.4583	−	5.49437i	−0.0179317	−	0.00859839i
$640$		0			0
$641$			1154.81i			1.80157i	0.434266	+	0.900785i	$0.357008\pi$
$641$			1154.81i			1.80157i	−0.434266	+	0.900785i	$0.642992\pi$
$642$	−16.5761	+	10.4349i	−0.0258195	+	0.0162537i
$643$			686.939i			1.06833i	0.845379	+	0.534167i	$0.179375\pi$
$643$			686.939i			1.06833i	−0.845379	+	0.534167i	$0.820625\pi$
$644$			42.0428i			0.0652839i
$645$		0			0
$646$	−850.971			−1.31729
$647$	−86.5372			−0.133751			−0.0668757	−	0.997761i	$-0.521303\pi$
$647$	−86.5372			−0.133751			−0.0668757	+	0.997761i	$0.521303\pi$
$648$	143.444	+	178.639i	0.221364	+	0.275677i
$649$	614.908			0.947469
$650$		0			0
$651$	−239.852	−	381.012i	−0.368437	−	0.585272i
$652$		−	144.064i		−	0.220957i
$653$	803.711			1.23080			0.615399	−	0.788216i	$-0.288995\pi$
$653$	803.711			1.23080			0.615399	+	0.788216i	$0.288995\pi$
$654$	−149.346	+	94.0152i	−0.228358	+	0.143754i
$655$		0			0
$656$		−	301.156i		−	0.459080i
$657$	375.521	+	180.065i	0.571570	+	0.274072i
$658$			252.801i			0.384196i
$659$			890.737i			1.35165i	0.737063	+	0.675824i	$0.236212\pi$
$659$			890.737i			1.35165i	−0.737063	+	0.675824i	$0.763788\pi$
$660$		0			0
$661$	151.874			0.229763			0.114882	−	0.993379i	$-0.463351\pi$
$661$	151.874			0.229763			0.114882	+	0.993379i	$0.463351\pi$
$662$	−250.019			−0.377673
$663$	−399.627	−	634.819i	−0.602755	−	0.957494i
$664$	−120.025			−0.180760
$665$		0			0
$666$	−138.766	−	66.5392i	−0.208357	−	0.0999087i
$667$		−	68.3719i		−	0.102507i
$668$	262.766			0.393362
$669$	305.871	+	485.885i	0.457207	+	0.726286i
$670$		0			0
$671$		−	48.5279i		−	0.0723217i
$672$	−23.9201	−	37.9978i	−0.0355954	−	0.0565443i
$673$		−	210.528i		−	0.312820i	−0.987692	−	0.156410i	$-0.950008\pi$
$673$		−	210.528i		−	0.312820i	0.987692	−	0.156410i	$-0.0499921\pi$
$674$		−	484.176i		−	0.718362i
$675$		0			0
$676$	−53.9027			−0.0797377
$677$	458.139			0.676720			0.338360	−	0.941017i	$-0.390128\pi$
$677$	458.139			0.676720			0.338360	+	0.941017i	$0.390128\pi$
$678$	−547.373	+	344.578i	−0.807335	+	0.508228i
$679$	−90.8310			−0.133772
$680$		0			0
$681$	−371.835	+	234.075i	−0.546013	+	0.343723i
$682$			597.590i			0.876232i
$683$	−886.975			−1.29865			−0.649323	−	0.760513i	$-0.724948\pi$
$683$	−886.975			−1.29865			−0.649323	+	0.760513i	$0.724948\pi$
$684$	−262.172	+	546.752i	−0.383293	+	0.799346i
$685$		0			0
$686$			26.1916i			0.0381802i
$687$	−1125.46	+	708.495i	−1.63823	+	1.03129i
$688$			243.936i			0.354558i
$689$		−	688.131i		−	0.998738i
$690$		0			0
$691$	−1201.35			−1.73857			−0.869285	−	0.494311i	$-0.835420\pi$
$691$	−1201.35			−1.73857			−0.869285	+	0.494311i	$0.835420\pi$
$692$	345.515			0.499300
$693$	−76.6973	+	159.950i	−0.110674	+	0.230808i
$694$	663.194			0.955611
$695$		0			0
$696$	38.8999	+	61.7937i	0.0558907	+	0.0887840i
$697$			1344.85i			1.92948i
$698$	−384.071			−0.550246
$699$	256.628	−	161.551i	0.367136	−	0.231117i
$700$		0			0
$701$		−	218.939i		−	0.312323i	−0.987731	−	0.156162i	$-0.950088\pi$
$701$		−	218.939i		−	0.312323i	0.987731	−	0.156162i	$-0.0499121\pi$
$702$	−530.993	+	61.1832i	−0.756400	+	0.0871555i
$703$		−	407.307i		−	0.579384i
$704$			59.5967i			0.0846544i
$705$		0			0
$706$	−295.759			−0.418922
$707$	87.2306			0.123381
$708$	−263.843	−	419.123i	−0.372660	−	0.591982i
$709$	−277.795			−0.391812			−0.195906	−	0.980623i	$-0.562765\pi$
$709$	−277.795			−0.391812			−0.195906	+	0.980623i	$0.562765\pi$
$710$		0			0
$711$	191.611	−	399.599i	0.269495	−	0.562024i
$712$		−	179.201i		−	0.251686i
$713$	−450.680			−0.632090
$714$	106.818	+	169.683i	0.149605	+	0.237652i
$715$		0			0
$716$		−	55.0596i		−	0.0768989i
$717$	504.824	+	801.928i	0.704078	+	1.11845i
$718$			854.018i			1.18944i
$719$		−	546.961i		−	0.760725i	−0.924838	−	0.380362i	$-0.875799\pi$
$719$		−	546.961i		−	0.760725i	0.924838	−	0.380362i	$-0.124201\pi$
$720$		0			0
$721$	−228.613			−0.317078
$722$	−1094.31			−1.51566
$723$	128.181	−	80.6918i	0.177291	−	0.111607i
$724$	−418.703			−0.578319
$725$		0			0
$726$	−235.187	+	148.054i	−0.323950	+	0.203931i
$727$		−	527.291i		−	0.725297i	−0.931926	−	0.362648i	$-0.881873\pi$
$727$		−	527.291i		−	0.725297i	0.931926	−	0.362648i	$-0.118127\pi$
$728$	104.753			0.143892
$729$	−709.896	+	165.795i	−0.973795	+	0.227429i
$730$		0			0
$731$		−	1089.32i		−	1.49018i
$732$	−33.0767	+	20.8222i	−0.0451868	+	0.0284457i
$733$			179.464i			0.244835i	0.992479	+	0.122417i	$0.0390646\pi$
$733$			179.464i			0.244835i	−0.992479	+	0.122417i	$0.960935\pi$
$734$		−	261.234i		−	0.355905i
$735$		0			0
$736$	−44.9457			−0.0610675
$737$	207.699			0.281817
$738$	864.071	+	414.329i	1.17083	+	0.561421i
$739$	25.9356			0.0350956			0.0175478	−	0.999846i	$-0.494414\pi$
$739$	25.9356			0.0350956			0.0175478	+	0.999846i	$0.494414\pi$
$740$		0			0
$741$	−753.652	−	1197.20i	−1.01707	−	1.61565i
$742$			183.933i			0.247889i
$743$	−905.790			−1.21910			−0.609549	−	0.792748i	$-0.708650\pi$
$743$	−905.790			−1.21910			−0.609549	+	0.792748i	$0.708650\pi$
$744$	407.319	−	256.413i	0.547472	−	0.344641i
$745$		0			0
$746$		−	234.309i		−	0.314087i
$747$	165.129	−	344.372i	0.221056	−	0.461006i
$748$		−	266.136i		−	0.355797i
$749$			12.2147i			0.0163080i
$750$		0			0
$751$	−1168.20			−1.55553			−0.777764	−	0.628557i	$-0.783646\pi$
$751$	−1168.20			−1.55553			−0.777764	+	0.628557i	$0.783646\pi$
$752$	−270.255			−0.359382
$753$	757.409	+	1203.17i	1.00585	+	1.59783i
$754$	−170.355			−0.225935
$755$		0			0
$756$	141.931	−	16.3539i	0.187740	−	0.0216322i
$757$			404.819i			0.534767i	0.963590	+	0.267384i	$0.0861591\pi$
$757$			404.819i			0.534767i	−0.963590	+	0.267384i	$0.913841\pi$
$758$	728.373			0.960914
$759$	94.5984	+	150.272i	0.124636	+	0.197987i
$760$		0			0
$761$		−	1019.99i		−	1.34033i	−0.742213	−	0.670164i	$-0.766224\pi$
$761$		−	1019.99i		−	1.34033i	0.742213	−	0.670164i	$-0.233776\pi$
$762$	−473.667	−	752.434i	−0.621611	−	0.987447i
$763$			110.051i			0.144234i
$764$			144.875i			0.189626i
$765$		0			0
$766$	427.132			0.557613
$767$	1155.45			1.50646
$768$	40.6213	−	25.5716i	0.0528923	−	0.0332964i
$769$	−195.562			−0.254306			−0.127153	−	0.991883i	$-0.540584\pi$
$769$	−195.562			−0.254306			−0.127153	+	0.991883i	$0.540584\pi$
$770$		0			0
$771$	−281.156	+	176.991i	−0.364664	+	0.229561i
$772$		−	97.3529i		−	0.126105i
$773$	−1092.75			−1.41365			−0.706823	−	0.707391i	$-0.749872\pi$
$773$	−1092.75			−1.41365			−0.706823	+	0.707391i	$0.749872\pi$
$774$	−699.895	−	335.605i	−0.904257	−	0.433599i
$775$		0			0
$776$		−	97.1025i		−	0.125132i
$777$	−81.2170	+	51.1272i	−0.104526	+	0.0658007i
$778$			642.969i			0.826438i
$779$			2536.24i			3.25576i
$780$		0			0
$781$	10.5184			0.0134679
$782$	200.710			0.256663
$783$	−230.815	+	26.5955i	−0.294784	+	0.0339662i
$784$	−28.0000			−0.0357143
$785$		0			0
$786$	225.250	+	357.815i	0.286577	+	0.455236i
$787$			1172.01i			1.48921i	0.667504	+	0.744607i	$0.267363\pi$
$787$			1172.01i			1.48921i	−0.667504	+	0.744607i	$0.732637\pi$
$788$	−343.035			−0.435324
$789$	1042.25	−	656.109i	1.32097	−	0.831571i
$790$		0			0
$791$			403.351i			0.509926i
$792$	−170.994	−	81.9928i	−0.215901	−	0.103526i
$793$		−	91.1870i		−	0.114990i
$794$			998.193i			1.25717i
$795$		0			0
$796$	30.5852			0.0384237
$797$	1533.36			1.92391			0.961955	−	0.273208i	$-0.0880847\pi$
$797$	1533.36			1.92391			0.961955	+	0.273208i	$0.0880847\pi$
$798$	201.447	+	320.004i	0.252440	+	0.401008i
$799$	1206.86			1.51046
$800$		0			0
$801$	514.159	+	246.543i	0.641896	+	0.307794i
$802$			771.162i			0.961548i
$803$	−344.718			−0.429288
$804$	−89.1192	−	141.568i	−0.110845	−	0.176080i
$805$		0			0
$806$			1122.91i			1.39319i
$807$	100.625	+	159.845i	0.124690	+	0.198074i
$808$			93.2534i			0.115413i
$809$		−	348.381i		−	0.430632i	−0.976544	−	0.215316i	$-0.930922\pi$
$809$		−	348.381i		−	0.430632i	0.976544	−	0.215316i	$-0.0690781\pi$
$810$		0			0
$811$	−156.395			−0.192842			−0.0964210	−	0.995341i	$-0.530740\pi$
$811$	−156.395			−0.192842			−0.0964210	+	0.995341i	$0.530740\pi$
$812$	45.5349			0.0560774
$813$	1199.77	−	755.270i	1.47573	−	0.928991i
$814$	127.383			0.156490
$815$		0			0
$816$	−181.399	+	114.193i	−0.222303	+	0.139943i
$817$		−	2054.34i		−	2.51450i
$818$	−976.455			−1.19371
$819$	−144.119	+	300.556i	−0.175970	+	0.366980i
$820$		0			0
$821$		−	408.467i		−	0.497524i	−0.968565	−	0.248762i	$-0.919976\pi$
$821$		−	408.467i		−	0.497524i	0.968565	−	0.248762i	$-0.0800237\pi$
$822$	916.866	−	577.179i	1.11541	−	0.702165i
$823$		−	239.985i		−	0.291598i	−0.989314	−	0.145799i	$-0.953425\pi$
$823$		−	239.985i		−	0.291598i	0.989314	−	0.145799i	$-0.0465752\pi$
$824$		−	244.398i		−	0.296599i
$825$		0			0
$826$	−308.846			−0.373905
$827$	−251.724			−0.304383			−0.152191	−	0.988351i	$-0.548633\pi$
$827$	−251.724			−0.304383			−0.152191	+	0.988351i	$0.548633\pi$
$828$	61.8360	−	128.957i	0.0746811	−	0.155745i
$829$	676.728			0.816319			0.408159	−	0.912911i	$-0.366171\pi$
$829$	676.728			0.816319			0.408159	+	0.912911i	$0.366171\pi$
$830$		0			0
$831$	−561.247	−	891.557i	−0.675387	−	1.07287i
$832$			111.986i			0.134599i
$833$	125.037			0.150105
$834$	796.220	−	501.231i	0.954700	−	0.600996i
$835$		0			0
$836$		−	501.904i		−	0.600363i
$837$	175.307	+	1521.44i	0.209447	+	1.81773i
$838$			456.724i			0.545017i
$839$			120.197i			0.143262i	0.997431	+	0.0716309i	$0.0228204\pi$
$839$			120.197i			0.143262i	−0.997431	+	0.0716309i	$0.977180\pi$
$840$		0			0
$841$	766.949			0.911949
$842$	−805.391			−0.956521
$843$	163.088	+	259.070i	0.193462	+	0.307319i
$844$	382.937			0.453716
$845$		0			0
$846$	371.816	−	775.411i	0.439499	−	0.916562i
$847$			173.306i			0.204612i
$848$	−196.633			−0.231879
$849$	−632.087	−	1004.09i	−0.744508	−	1.18267i
$850$		0			0
$851$			96.0675i			0.112888i
$852$	−4.51324	−	7.16941i	−0.00529723	−	0.00841480i
$853$			582.158i			0.682483i	0.939976	+	0.341242i	$0.110847\pi$
$853$			582.158i			0.682483i	−0.939976	+	0.341242i	$0.889153\pi$
$854$			24.3738i			0.0285407i
$855$		0			0
$856$	−13.0580			−0.0152547
$857$	−1539.51			−1.79639			−0.898195	−	0.439597i	$-0.855121\pi$
$857$	−1539.51			−1.79639			−0.898195	+	0.439597i	$0.855121\pi$
$858$	374.417	−	235.700i	0.436383	−	0.274709i
$859$	1079.15			1.25629			0.628145	−	0.778097i	$-0.283815\pi$
$859$	1079.15			1.25629			0.628145	+	0.778097i	$0.283815\pi$
$860$		0			0
$861$	505.725	−	318.361i	0.587370	−	0.369757i
$862$			676.199i			0.784454i
$863$	−491.896			−0.569984			−0.284992	−	0.958530i	$-0.591991\pi$
$863$	−491.896			−0.569984			−0.284992	+	0.958530i	$0.591991\pi$
$864$	17.4831	+	151.731i	0.0202350	+	0.175615i
$865$		0			0
$866$			446.991i			0.516155i
$867$	76.3374	−	48.0554i	0.0880477	−	0.0554272i
$868$		−	300.148i		−	0.345792i
$869$			366.821i			0.422119i
$870$		0			0
$871$	390.280			0.448083
$872$	−117.649			−0.134919
$873$	278.604	+	133.593i	0.319134	+	0.153028i
$874$	378.517			0.433086
$875$		0			0
$876$	147.911	+	234.961i	0.168848	+	0.268220i
$877$			1385.09i			1.57935i	0.613526	+	0.789674i	$0.289751\pi$
$877$			1385.09i			1.57935i	−0.613526	+	0.789674i	$0.710249\pi$
$878$	−735.226			−0.837388
$879$	1016.23	−	639.727i	1.15612	−	0.727790i
$880$		0			0
$881$		−	299.174i		−	0.339585i	−0.985480	−	0.169792i	$-0.945690\pi$
$881$		−	299.174i		−	0.339585i	0.985480	−	0.169792i	$-0.0543097\pi$
$882$	38.5222	−	80.3370i	0.0436760	−	0.0910851i
$883$			79.8153i			0.0903910i	0.998978	+	0.0451955i	$0.0143911\pi$
$883$			79.8153i			0.0903910i	−0.998978	+	0.0451955i	$0.985609\pi$
$884$		−	500.087i		−	0.565709i
$885$		0			0
$886$	601.311			0.678681
$887$	−1675.80			−1.88929			−0.944644	−	0.328096i	$-0.893593\pi$
$887$	−1675.80			−1.88929			−0.944644	+	0.328096i	$0.893593\pi$
$888$	−54.6572	−	86.8246i	−0.0615509	−	0.0977755i
$889$	−554.458			−0.623687
$890$		0			0
$891$	470.504	−	377.806i	0.528063	−	0.424025i
$892$			382.763i			0.429107i
$893$	2276.00			2.54871
$894$	−500.268	−	794.691i	−0.559584	−	0.888916i
$895$		0			0
$896$		−	29.9333i		−	0.0334077i
$897$	177.757	+	282.371i	0.198168	+	0.314795i
$898$			739.334i			0.823312i
$899$			488.114i			0.542952i
$900$		0			0
$901$	878.088			0.974571
$902$	−793.194			−0.879372
$903$	−409.636	+	257.871i	−0.453639	+	0.285572i
$904$	−431.201			−0.476992
$905$		0			0
$906$	335.913	−	211.462i	0.370765	−	0.233401i
$907$			51.4033i			0.0566740i	0.999598	+	0.0283370i	$0.00902116\pi$
$907$			51.4033i			0.0566740i	−0.999598	+	0.0283370i	$0.990979\pi$
$908$	−292.918			−0.322597
$909$	−267.561	−	128.297i	−0.294346	−	0.141141i
$910$		0			0
$911$		−	473.770i		−	0.520055i	−0.965601	−	0.260027i	$-0.916268\pi$
$911$		−	473.770i		−	0.520055i	0.965601	−	0.260027i	$-0.0837316\pi$
$912$	−342.099	+	215.356i	−0.375109	+	0.236136i
$913$			316.124i			0.346247i
$914$		−	199.518i		−	0.218291i
$915$		0			0
$916$	−886.600			−0.967904
$917$	263.669			0.287534
$918$	−78.0727	−	677.573i	−0.0850466	−	0.738097i
$919$	−1329.93			−1.44715			−0.723574	−	0.690247i	$-0.757502\pi$
$919$	−1329.93			−1.44715			−0.723574	+	0.690247i	$0.757502\pi$
$920$		0			0
$921$	−615.041	−	977.011i	−0.667797	−	1.06082i
$922$			712.924i			0.773237i
$923$	19.7648			0.0214137
$924$	−100.080	+	63.0014i	−0.108311	+	0.0681833i
$925$		0			0
$926$			1165.23i			1.25834i
$927$	701.220	+	336.241i	0.756440	+	0.362719i
$928$			48.6788i			0.0524556i
$929$		−	1573.07i		−	1.69329i	−0.532156	−	0.846646i	$-0.678618\pi$
$929$		−	1573.07i		−	1.69329i	0.532156	−	0.846646i	$-0.321382\pi$
$930$		0			0
$931$	235.807			0.253283
$932$	202.162			0.216912
$933$	669.517	+	1063.55i	0.717596	+	1.13992i
$934$	−766.748			−0.820929
$935$		0			0
$936$	−321.308	−	154.070i	−0.343278	−	0.164605i
$937$		−	502.295i		−	0.536067i	−0.963410	−	0.268034i	$-0.913626\pi$
$937$		−	502.295i		−	0.536067i	0.963410	−	0.268034i	$-0.0863739\pi$
$938$	−104.320			−0.111215
$939$	204.105	+	324.227i	0.217364	+	0.345289i
$940$		0			0
$941$			840.199i			0.892879i	0.894814	+	0.446440i	$0.147308\pi$
$941$			840.199i			0.892879i	−0.894814	+	0.446440i	$0.852692\pi$
$942$	−251.194	−	399.029i	−0.266660	−	0.423597i
$943$		−	598.197i		−	0.634356i
$944$		−	330.170i		−	0.349756i
$945$		0			0
$946$	642.485			0.679159
$947$	519.608			0.548688			0.274344	−	0.961632i	$-0.411539\pi$
$947$	519.608			0.548688			0.274344	+	0.961632i	$0.411539\pi$
$948$	250.027	−	157.395i	0.263741	−	0.166028i
$949$	−647.748			−0.682558
$950$		0			0
$951$	−1.99496	+	1.25585i	−0.00209775	+	0.00132056i
$952$			133.671i			0.140410i
$953$	263.685			0.276689			0.138344	−	0.990384i	$-0.455822\pi$
$953$	263.685			0.276689			0.138344	+	0.990384i	$0.455822\pi$
$954$	270.527	−	564.176i	0.283571	−	0.591379i
$955$		0			0
$956$			631.730i			0.660805i
$957$	162.754	−	102.456i	0.170067	−	0.107059i
$958$		−	768.410i		−	0.802098i
$959$		−	675.625i		−	0.704510i
$960$		0			0
$961$	2256.45			2.34802
$962$	239.361			0.248816
$963$	17.9652	−	37.4659i	0.0186554	−	0.0389054i
$964$	100.977			0.104747
$965$		0			0
$966$	−47.5133	−	75.4763i	−0.0491856	−	0.0781328i
$967$			946.769i			0.979078i	0.871981	+	0.489539i	$0.162835\pi$
$967$			946.769i			0.979078i	−0.871981	+	0.489539i	$0.837165\pi$
$968$	−185.272			−0.191397
$969$	1527.68	−	961.697i	1.57656	−	0.992463i
$970$		0			0
$971$			1616.50i			1.66478i	0.554192	+	0.832389i	$0.313027\pi$
$971$			1616.50i			1.66478i	−0.554192	+	0.832389i	$0.686973\pi$
$972$	−459.397	−	158.589i	−0.472631	−	0.163157i
$973$		−	586.723i		−	0.603004i
$974$		−	291.220i		−	0.298994i
$975$		0			0
$976$	−26.0567			−0.0266974
$977$	−320.830			−0.328383			−0.164191	−	0.986428i	$-0.552502\pi$
$977$	−320.830			−0.328383			−0.164191	+	0.986428i	$0.552502\pi$
$978$	162.809	+	258.627i	0.166471	+	0.264445i
$979$	−471.984			−0.482108
$980$		0			0
$981$	161.861	−	337.557i	0.164996	−	0.344095i
$982$		−	1233.00i		−	1.25560i
$983$	−1130.59			−1.15014			−0.575071	−	0.818104i	$-0.695026\pi$
$983$	−1130.59			−1.15014			−0.575071	+	0.818104i	$0.695026\pi$
$984$	340.342	+	540.643i	0.345876	+	0.549434i
$985$		0			0
$986$		−	217.381i		−	0.220468i
$987$	−285.695	−	453.834i	−0.289458	−	0.459812i
$988$		−	943.109i		−	0.954564i
$989$			484.538i			0.489927i
$990$		0			0
$991$	−705.472			−0.711879			−0.355940	−	0.934509i	$-0.615839\pi$
$991$	−705.472			−0.711879			−0.355940	+	0.934509i	$0.615839\pi$
$992$	320.871			0.323459
$993$	448.841	−	282.551i	0.452005	−	0.284543i
$994$	−5.28303			−0.00531492
$995$		0			0
$996$	215.471	−	135.642i	0.216336	−	0.136187i
$997$		−	1338.32i		−	1.34234i	−0.741302	−	0.671172i	$-0.765791\pi$
$997$		−	1338.32i		−	1.34234i	0.741302	−	0.671172i	$-0.234209\pi$
$998$	1356.64			1.35936
$999$	324.313	−	37.3686i	0.324637	−	0.0374060i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.c.b.449.13		32
3.2	odd	2	inner	1050.3.c.b.449.19		32
5.2	odd	4		1050.3.e.b.701.3	✓	16
5.3	odd	4		1050.3.e.c.701.14	yes	16
5.4	even	2	inner	1050.3.c.b.449.20		32
15.2	even	4		1050.3.e.b.701.11	yes	16
15.8	even	4		1050.3.e.c.701.6	yes	16
15.14	odd	2	inner	1050.3.c.b.449.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.c.b.449.13		32	1.1	even	1	trivial
1050.3.c.b.449.14		32	15.14	odd	2	inner
1050.3.c.b.449.19		32	3.2	odd	2	inner
1050.3.c.b.449.20		32	5.4	even	2	inner
1050.3.e.b.701.3	✓	16	5.2	odd	4
1050.3.e.b.701.11	yes	16	15.2	even	4
1050.3.e.c.701.6	yes	16	15.8	even	4
1050.3.e.c.701.14	yes	16	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +(2.53883 - 1.59823i) q^{3} +2.00000 q^{4} +(-3.59045 + 2.26024i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(3.89133 - 8.11526i) q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +(2.53883 - 1.59823i) q^{3} +2.00000 q^{4} +(-3.59045 + 2.26024i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(3.89133 - 8.11526i) q^{9} +7.44959i q^{11} +(5.07766 - 3.19646i) q^{12} +13.9983i q^{13} -3.74166i q^{14} +4.00000 q^{16} -17.8625 q^{17} +(-5.50318 + 11.4767i) q^{18} -33.6867 q^{19} +(4.22851 + 6.71712i) q^{21} -10.5353i q^{22} +7.94534 q^{23} +(-7.18090 + 4.52047i) q^{24} -19.7965i q^{26} +(-3.09060 - 26.8225i) q^{27} +5.29150i q^{28} -8.60528i q^{29} -56.7226 q^{31} -5.65685 q^{32} +(11.9061 + 18.9133i) q^{33} +25.2614 q^{34} +(7.78267 - 16.2305i) q^{36} +12.0910i q^{37} +47.6401 q^{38} +(22.3724 + 35.5392i) q^{39} -75.2891i q^{41} +(-5.98002 - 9.49944i) q^{42} +60.9839i q^{43} +14.8992i q^{44} -11.2364 q^{46} -67.5639 q^{47} +(10.1553 - 6.39291i) q^{48} -7.00000 q^{49} +(-45.3498 + 28.5483i) q^{51} +27.9965i q^{52} -49.1583 q^{53} +(4.37077 + 37.9328i) q^{54} -7.48331i q^{56} +(-85.5248 + 53.8390i) q^{57} +12.1697i q^{58} -82.5425i q^{59} -6.51416 q^{61} +80.2178 q^{62} +(21.4710 + 10.2955i) q^{63} +8.00000 q^{64} +(-16.8378 - 26.7474i) q^{66} -27.8806i q^{67} -35.7249 q^{68} +(20.1719 - 12.6985i) q^{69} -1.41195i q^{71} +(-11.0064 + 22.9534i) q^{72} +46.2735i q^{73} -17.0993i q^{74} -67.3733 q^{76} -19.7098 q^{77} +(-31.6394 - 50.2601i) q^{78} +49.2405 q^{79} +(-50.7150 - 63.1584i) q^{81} +106.475i q^{82} +42.4351 q^{83} +(8.45703 + 13.4342i) q^{84} -86.2443i q^{86} +(-13.7532 - 21.8474i) q^{87} -21.0706i q^{88} +63.3570i q^{89} -37.0359 q^{91} +15.8907 q^{92} +(-144.009 + 90.6556i) q^{93} +95.5497 q^{94} +(-14.3618 + 9.04094i) q^{96} +34.3309i q^{97} +9.89949 q^{98} +(60.4554 + 28.9888i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9}+O(q^{10}) \) 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9	\( 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9} + 128 q^{16} + 48 q^{19} + 56 q^{21} - 32 q^{24} + 48 q^{31} + 256 q^{34} - 32 q^{36} + 192 q^{39} + 160 q^{46} - 224 q^{49} + 288 q^{51} - 80 q^{54} - 112 q^{61} + 256 q^{64} - 192 q^{66} + 344 q^{69} + 96 q^{76} - 256 q^{79} + 160 q^{81} + 112 q^{84} - 448 q^{91} + 416 q^{94} - 64 q^{96} - 304 q^{99}+O(q^{100}) \) 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9 + 128 * q^16 + 48 * q^19 + 56 * q^21 - 32 * q^24 + 48 * q^31 + 256 * q^34 - 32 * q^36 + 192 * q^39 + 160 * q^46 - 224 * q^49 + 288 * q^51 - 80 * q^54 - 112 * q^61 + 256 * q^64 - 192 * q^66 + 344 * q^69 + 96 * q^76 - 256 * q^79 + 160 * q^81 + 112 * q^84 - 448 * q^91 + 416 * q^94 - 64 * q^96 - 304 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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