LMFDB - Embedded newform 725.2.p.b.274.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(149,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("725.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.p (of order $14$, degree $6$, 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:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{14})$
Twist minimal:	no (minimal twist has level 145)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			274.4
Character	$\chi$	$=$	725.274
Dual form			725.2.p.b.299.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.852581 - 0.410581i) q^{2} +(0.646721 - 0.810963i) q^{3} +(-0.688663 - 0.863556i) q^{4} +(-0.884348 + 0.425880i) q^{6} +(0.979248 + 0.780924i) q^{7} +(0.653721 + 2.86414i) q^{8} +(0.428151 + 1.87585i) q^{9} +O(q^{10})$	\(q+(-0.852581 - 0.410581i) q^{2} +(0.646721 - 0.810963i) q^{3} +(-0.688663 - 0.863556i) q^{4} +(-0.884348 + 0.425880i) q^{6} +(0.979248 + 0.780924i) q^{7} +(0.653721 + 2.86414i) q^{8} +(0.428151 + 1.87585i) q^{9} +(-0.512072 - 0.116877i) q^{11} -1.14568 q^{12} +(3.47133 + 0.792308i) q^{13} +(-0.514255 - 1.06786i) q^{14} +(0.127050 - 0.556642i) q^{16} +2.69858 q^{17} +(0.405156 - 1.77510i) q^{18} +(-3.05822 + 2.43885i) q^{19} +(1.26660 - 0.289093i) q^{21} +(0.388595 + 0.309894i) q^{22} +(3.72694 + 7.73907i) q^{23} +(2.74548 + 1.32216i) q^{24} +(-2.63428 - 2.10077i) q^{26} +(4.60176 + 2.21609i) q^{27} -1.38343i q^{28} +(-4.10226 + 3.48876i) q^{29} +(2.75993 - 5.73104i) q^{31} +(3.32650 - 4.17130i) q^{32} +(-0.425951 + 0.339685i) q^{33} +(-2.30076 - 1.10799i) q^{34} +(1.32505 - 1.66156i) q^{36} +(0.218987 + 0.959443i) q^{37} +(3.60872 - 0.823668i) q^{38} +(2.88751 - 2.30271i) q^{39} -3.86567i q^{41} +(-1.19858 - 0.273567i) q^{42} +(-0.657583 + 0.316675i) q^{43} +(0.251715 + 0.522692i) q^{44} -8.12840i q^{46} +(0.344462 - 1.50919i) q^{47} +(-0.369250 - 0.463025i) q^{48} +(-1.20856 - 5.29506i) q^{49} +(1.74523 - 2.18845i) q^{51} +(-1.70637 - 3.54332i) q^{52} +(3.15052 - 6.54212i) q^{53} +(-3.01348 - 3.77879i) q^{54} +(-1.59652 + 3.31521i) q^{56} +4.05736i q^{57} +(4.92993 - 1.29013i) q^{58} +11.8675 q^{59} +(-1.10790 - 0.883518i) q^{61} +(-4.70612 + 3.75300i) q^{62} +(-1.04563 + 2.17127i) q^{63} +(-5.57760 + 2.68603i) q^{64} +(0.502626 - 0.114721i) q^{66} +(-1.05958 + 0.241843i) q^{67} +(-1.85841 - 2.33038i) q^{68} +(8.68639 + 1.98261i) q^{69} +(-3.22125 + 14.1132i) q^{71} +(-5.09280 + 2.45256i) q^{72} +(8.35014 - 4.02121i) q^{73} +(0.207225 - 0.907914i) q^{74} +(4.21216 + 0.961399i) q^{76} +(-0.410173 - 0.514341i) q^{77} +(-3.40729 + 0.777692i) q^{78} +(1.70976 - 0.390241i) q^{79} +(-0.427421 + 0.205835i) q^{81} +(-1.58717 + 3.29579i) q^{82} +(-7.79646 + 6.21747i) q^{83} +(-1.12191 - 0.894692i) q^{84} +0.690664 q^{86} +(0.176230 + 5.58304i) q^{87} -1.54305i q^{88} +(4.77688 - 9.91930i) q^{89} +(2.78056 + 3.48671i) q^{91} +(4.11652 - 8.54803i) q^{92} +(-2.86276 - 5.94458i) q^{93} +(-0.913327 + 1.14528i) q^{94} +(-1.23145 - 5.39534i) q^{96} +(-0.884747 - 1.10944i) q^{97} +(-1.14365 + 5.01068i) q^{98} -1.01061i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{6} + 8 q^{9}+O(q^{10}) $ 48 * q + 8 * q^6 + 8 * q^9	$ 48 q + 8 q^{6} + 8 q^{9} - 28 q^{11} + 84 q^{14} - 20 q^{16} + 98 q^{21} - 76 q^{24} - 14 q^{29} + 14 q^{31} - 40 q^{34} - 56 q^{36} - 14 q^{39} + 42 q^{44} + 4 q^{49} + 12 q^{51} - 214 q^{54} - 84 q^{56} + 132 q^{59} + 112 q^{61} - 66 q^{64} - 140 q^{66} + 56 q^{69} + 106 q^{71} - 66 q^{74} - 84 q^{76} + 112 q^{79} - 58 q^{81} - 28 q^{84} + 60 q^{86} - 28 q^{89} - 62 q^{91} + 76 q^{94} - 2 q^{96}+O(q^{100}) $ 48 * q + 8 * q^6 + 8 * q^9 - 28 * q^11 + 84 * q^14 - 20 * q^16 + 98 * q^21 - 76 * q^24 - 14 * q^29 + 14 * q^31 - 40 * q^34 - 56 * q^36 - 14 * q^39 + 42 * q^44 + 4 * q^49 + 12 * q^51 - 214 * q^54 - 84 * q^56 + 132 * q^59 + 112 * q^61 - 66 * q^64 - 140 * q^66 + 56 * q^69 + 106 * q^71 - 66 * q^74 - 84 * q^76 + 112 * q^79 - 58 * q^81 - 28 * q^84 + 60 * q^86 - 28 * q^89 - 62 * q^91 + 76 * q^94 - 2 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{9}{14}\right)$	$-1$

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 $

$2$	−0.852581	−	0.410581i	−0.602866	−	0.290325i	0.107447	−	0.994211i	$-0.465732\pi$
$2$	−0.852581	−	0.410581i	−0.602866	−	0.290325i	−0.710313	+	0.703886i	$0.751447\pi$
$3$	0.646721	−	0.810963i	0.373385	−	0.468210i	−0.559267	−	0.828988i	$-0.688917\pi$
$3$	0.646721	−	0.810963i	0.373385	−	0.468210i	0.932652	+	0.360778i	$0.117489\pi$
$4$	−0.688663	−	0.863556i	−0.344331	−	0.431778i
$5$		0			0
$5$		0			0
$6$	−0.884348	+	0.425880i	−0.361034	+	0.173865i
$7$	0.979248	+	0.780924i	0.370121	+	0.295161i	0.790832	−	0.612033i	$-0.209648\pi$
$7$	0.979248	+	0.780924i	0.370121	+	0.295161i	−0.420711	+	0.907195i	$0.638219\pi$
$8$	0.653721	+	2.86414i	0.231125	+	1.01263i
$9$	0.428151	+	1.87585i	0.142717	+	0.625283i
$10$		0			0
$11$	−0.512072	−	0.116877i	−0.154396	−	0.0352398i	0.144624	−	0.989487i	$-0.453803\pi$
$11$	−0.512072	−	0.116877i	−0.154396	−	0.0352398i	−0.299020	+	0.954247i	$0.596660\pi$
$12$	−1.14568			−0.330731
$13$	3.47133	+	0.792308i	0.962773	+	0.219747i	0.674890	−	0.737919i	$-0.264191\pi$
$13$	3.47133	+	0.792308i	0.962773	+	0.219747i	0.287883	+	0.957665i	$0.407048\pi$
$14$	−0.514255	−	1.06786i	−0.137440	−	0.285398i
$15$		0			0
$16$	0.127050	−	0.556642i	0.0317625	−	0.139160i
$17$	2.69858			0.654503			0.327251	−	0.944937i	$-0.393878\pi$
$17$	2.69858			0.654503			0.327251	+	0.944937i	$0.393878\pi$
$18$	0.405156	−	1.77510i	0.0954962	−	0.418396i
$19$	−3.05822	+	2.43885i	−0.701604	+	0.559510i	−0.908006	−	0.418957i	$-0.862396\pi$
$19$	−3.05822	+	2.43885i	−0.701604	+	0.559510i	0.206402	+	0.978467i	$0.433824\pi$
$20$		0			0
$21$	1.26660	−	0.289093i	0.276395	−	0.0630853i
$22$	0.388595	+	0.309894i	0.0828488	+	0.0660697i
$23$	3.72694	+	7.73907i	0.777121	+	1.61371i	0.789473	+	0.613785i	$0.210354\pi$
$23$	3.72694	+	7.73907i	0.777121	+	1.61371i	−0.0123523	+	0.999924i	$0.503932\pi$
$24$	2.74548	+	1.32216i	0.560420	+	0.269884i
$25$		0			0
$26$	−2.63428	−	2.10077i	−0.516625	−	0.411995i
$27$	4.60176	+	2.21609i	0.885608	+	0.426487i
$28$		−	1.38343i		−	0.261443i
$29$	−4.10226	+	3.48876i	−0.761771	+	0.647846i
$29$	−4.10226	+	3.48876i	−0.761771	+	0.647846i
$30$		0			0
$31$	2.75993	−	5.73104i	0.495697	−	1.02933i	−0.491656	−	0.870790i	$-0.663608\pi$
$31$	2.75993	−	5.73104i	0.495697	−	1.02933i	0.987353	−	0.158536i	$-0.0506775\pi$
$32$	3.32650	−	4.17130i	0.588048	−	0.737389i
$33$	−0.425951	+	0.339685i	−0.0741485	+	0.0591315i
$34$	−2.30076	−	1.10799i	−0.394577	−	0.190018i
$35$		0			0
$36$	1.32505	−	1.66156i	0.220842	−	0.276927i
$37$	0.218987	+	0.959443i	0.0360012	+	0.157731i	0.989733	−	0.142926i	$-0.0456511\pi$
$37$	0.218987	+	0.959443i	0.0360012	+	0.157731i	−0.953732	+	0.300657i	$0.902794\pi$
$38$	3.60872	−	0.823668i	0.585412	−	0.133617i
$39$	2.88751	−	2.30271i	0.462372	−	0.368729i
$40$		0			0
$41$		−	3.86567i		−	0.603716i	−0.953353	−	0.301858i	$-0.902393\pi$
$41$		−	3.86567i		−	0.603716i	0.953353	−	0.301858i	$-0.0976068\pi$
$42$	−1.19858	−	0.273567i	−0.184944	−	0.0422123i
$43$	−0.657583	+	0.316675i	−0.100281	+	0.0482926i	−0.483352	−	0.875426i	$-0.660581\pi$
$43$	−0.657583	+	0.316675i	−0.100281	+	0.0482926i	0.383071	+	0.923719i	$0.374866\pi$
$44$	0.251715	+	0.522692i	0.0379475	+	0.0787988i
$45$		0			0
$46$		−	8.12840i		−	1.19847i
$47$	0.344462	−	1.50919i	0.0502450	−	0.220138i	−0.943572	−	0.331167i	$-0.892558\pi$
$47$	0.344462	−	1.50919i	0.0502450	−	0.220138i	0.993817	+	0.111029i	$0.0354147\pi$
$48$	−0.369250	−	0.463025i	−0.0532966	−	0.0668319i
$49$	−1.20856	−	5.29506i	−0.172652	−	0.756437i
$50$		0			0
$51$	1.74523	−	2.18845i	0.244381	−	0.306444i
$52$	−1.70637	−	3.54332i	−0.236631	−	0.491370i
$53$	3.15052	−	6.54212i	0.432757	−	0.898629i	−0.564558	−	0.825394i	$-0.690953\pi$
$53$	3.15052	−	6.54212i	0.432757	−	0.898629i	0.997315	−	0.0732354i	$-0.0233324\pi$
$54$	−3.01348	−	3.77879i	−0.410083	−	0.514228i
$55$		0			0
$56$	−1.59652	+	3.31521i	−0.213344	+	0.443013i
$57$			4.05736i			0.537410i
$58$	4.92993	−	1.29013i	0.647332	−	0.169403i
$59$	11.8675			1.54501			0.772506	−	0.635008i	$-0.219003\pi$
$59$	11.8675			1.54501			0.772506	+	0.635008i	$0.219003\pi$
$60$		0			0
$61$	−1.10790	−	0.883518i	−0.141852	−	0.113123i	0.549993	−	0.835169i	$-0.314630\pi$
$61$	−1.10790	−	0.883518i	−0.141852	−	0.113123i	−0.691845	+	0.722046i	$0.743202\pi$
$62$	−4.70612	+	3.75300i	−0.597678	+	0.476632i
$63$	−1.04563	+	2.17127i	−0.131737	+	0.273555i
$64$	−5.57760	+	2.68603i	−0.697200	+	0.335754i
$65$		0			0
$66$	0.502626	−	0.114721i	0.0618689	−	0.0141212i
$67$	−1.05958	+	0.241843i	−0.129449	+	0.0295458i	−0.286754	−	0.958004i	$-0.592576\pi$
$67$	−1.05958	+	0.241843i	−0.129449	+	0.0295458i	0.157306	+	0.987550i	$0.449719\pi$
$68$	−1.85841	−	2.33038i	−0.225366	−	0.282600i
$69$	8.68639	+	1.98261i	1.04572	+	0.238678i
$70$		0			0
$71$	−3.22125	+	14.1132i	−0.382292	+	1.67493i	0.307990	+	0.951390i	$0.400344\pi$
$71$	−3.22125	+	14.1132i	−0.382292	+	1.67493i	−0.690282	+	0.723541i	$0.742513\pi$
$72$	−5.09280	+	2.45256i	−0.600193	+	0.289038i
$73$	8.35014	−	4.02121i	0.977310	−	0.470648i	0.124131	−	0.992266i	$-0.460386\pi$
$73$	8.35014	−	4.02121i	0.977310	−	0.470648i	0.853179	+	0.521618i	$0.174671\pi$
$74$	0.207225	−	0.907914i	0.0240895	−	0.105543i
$75$		0			0
$76$	4.21216	+	0.961399i	0.483168	+	0.110280i
$77$	−0.410173	−	0.514341i	−0.0467436	−	0.0586146i
$78$	−3.40729	+	0.777692i	−0.385800	+	0.0880562i
$79$	1.70976	−	0.390241i	0.192363	−	0.0439055i	−0.125254	−	0.992125i	$-0.539975\pi$
$79$	1.70976	−	0.390241i	0.192363	−	0.0439055i	0.317617	+	0.948219i	$0.397117\pi$
$80$		0			0
$81$	−0.427421	+	0.205835i	−0.0474912	+	0.0228706i
$82$	−1.58717	+	3.29579i	−0.175274	+	0.363959i
$83$	−7.79646	+	6.21747i	−0.855773	+	0.682456i	−0.949713	−	0.313122i	$-0.898625\pi$
$83$	−7.79646	+	6.21747i	−0.855773	+	0.682456i	0.0939404	+	0.995578i	$0.470054\pi$
$84$	−1.12191	−	0.894692i	−0.122410	−	0.0976189i
$85$		0			0
$86$	0.690664			0.0744762
$87$	0.176230	+	5.58304i	0.0188938	+	0.598564i
$88$		−	1.54305i		−	0.164490i
$89$	4.77688	−	9.91930i	0.506348	−	1.05144i	−0.478510	−	0.878082i	$-0.658823\pi$
$89$	4.77688	−	9.91930i	0.506348	−	1.05144i	0.984858	−	0.173361i	$-0.0554628\pi$
$90$		0			0
$91$	2.78056	+	3.48671i	0.291482	+	0.365506i
$92$	4.11652	−	8.54803i	0.429176	−	0.891194i
$93$	−2.86276	−	5.94458i	−0.296854	−	0.616425i
$94$	−0.913327	+	1.14528i	−0.0942025	+	0.118126i
$95$		0			0
$96$	−1.23145	−	5.39534i	−0.125684	−	0.550660i
$97$	−0.884747	−	1.10944i	−0.0898324	−	0.112646i	0.734884	−	0.678193i	$-0.237237\pi$
$97$	−0.884747	−	1.10944i	−0.0898324	−	0.112646i	−0.824716	+	0.565547i	$0.808665\pi$
$98$	−1.14365	+	5.01068i	−0.115527	+	0.506155i
$99$		−	1.01061i		−	0.101570i
$100$		0			0
$101$	2.65505	+	5.51327i	0.264187	+	0.548591i	0.990294	−	0.138992i	$-0.0443862\pi$
$101$	2.65505	+	5.51327i	0.264187	+	0.548591i	−0.726106	+	0.687583i	$0.758672\pi$
$102$	−2.38649	+	1.14927i	−0.236297	+	0.113795i
$103$	3.31467	+	0.756551i	0.326604	+	0.0745452i	0.382679	−	0.923881i	$-0.375002\pi$
$103$	3.31467	+	0.756551i	0.326604	+	0.0745452i	−0.0560752	+	0.998427i	$0.517859\pi$
$104$			10.4603i			1.02572i
$105$		0			0
$106$	−5.37214	+	4.28414i	−0.521788	+	0.416112i
$107$	2.44563	−	0.558200i	0.236428	−	0.0539632i	−0.102665	−	0.994716i	$-0.532737\pi$
$107$	2.44563	−	0.558200i	0.236428	−	0.0539632i	0.339093	+	0.940753i	$0.389880\pi$
$108$	−1.25534	−	5.50001i	−0.120795	−	0.529239i
$109$	−9.50341	+	11.9169i	−0.910261	+	1.14143i	0.0792325	+	0.996856i	$0.474753\pi$
$109$	−9.50341	+	11.9169i	−0.910261	+	1.14143i	−0.989494	+	0.144575i	$0.953818\pi$
$110$		0			0
$111$	0.919695	+	0.442902i	0.0872936	+	0.0420384i
$112$	0.559108	−	0.445874i	0.0528308	−	0.0421311i
$113$	−4.24038	+	5.31726i	−0.398901	+	0.500206i	−0.940199	−	0.340624i	$-0.889362\pi$
$113$	−4.24038	+	5.31726i	−0.398901	+	0.500206i	0.541298	+	0.840831i	$0.317933\pi$
$114$	1.66587	−	3.45922i	0.156023	−	0.323986i
$115$		0			0
$116$	5.83781	+	1.13996i	0.542027	+	0.105842i
$117$			6.85092i			0.633368i
$118$	−10.1180	−	4.87255i	−0.931434	−	0.448555i
$119$	2.64258	+	2.10739i	0.242245	+	0.193184i
$120$		0			0
$121$	−9.66210	−	4.65302i	−0.878373	−	0.423002i
$122$	0.581815	+	1.20815i	0.0526751	+	0.109381i
$123$	−3.13491	−	2.50001i	−0.282665	−	0.225418i
$124$	−6.84973	+	1.56341i	−0.615124	+	0.140398i
$125$		0			0
$126$	1.78297	−	1.42187i	0.158840	−	0.126670i
$127$	4.61417	−	20.2160i	0.409441	−	1.79388i	−0.177356	−	0.984147i	$-0.556755\pi$
$127$	4.61417	−	20.2160i	0.409441	−	1.79388i	0.586798	−	0.809733i	$-0.300388\pi$
$128$	−4.81241			−0.425361
$129$	−0.168461	+	0.738076i	−0.0148322	+	0.0649840i
$130$		0			0
$131$	4.01604	+	8.33940i	0.350883	+	0.728617i	0.999471	−	0.0325232i	$-0.0103543\pi$
$131$	4.01604	+	8.33940i	0.350883	+	0.728617i	−0.648588	+	0.761140i	$0.724640\pi$
$132$	0.586673	+	0.133904i	0.0510633	+	0.0116549i
$133$	−4.89931			−0.424824
$134$	1.00268	+	0.228854i	0.0866179	+	0.0197700i
$135$		0			0
$136$	1.76412	+	7.72912i	0.151272	+	0.662766i
$137$	3.99511	+	17.5037i	0.341325	+	1.49544i	0.796280	+	0.604928i	$0.206798\pi$
$137$	3.99511	+	17.5037i	0.341325	+	1.49544i	−0.454955	+	0.890514i	$0.650345\pi$
$138$	−6.59183	−	5.25681i	−0.561134	−	0.447489i
$139$	16.1942	−	7.79873i	1.37358	−	0.661480i	0.405957	−	0.913892i	$-0.366938\pi$
$139$	16.1942	−	7.79873i	1.37358	−	0.661480i	0.967620	+	0.252412i	$0.0812239\pi$
$140$		0			0
$141$	−1.00112	−	1.25537i	−0.0843099	−	0.105721i
$142$	8.54100	−	10.7101i	0.716745	−	0.898769i
$143$	−1.68497	−	0.811438i	−0.140904	−	0.0678558i
$144$	1.09857			0.0915478
$145$		0			0
$146$	−8.77020			−0.725827
$147$	−5.07570	−	2.44433i	−0.418637	−	0.201605i
$148$	0.677724	−	0.849839i	0.0557086	−	0.0698564i
$149$	−3.18041	−	3.98811i	−0.260549	−	0.326718i	0.634300	−	0.773087i	$-0.281288\pi$
$149$	−3.18041	−	3.98811i	−0.260549	−	0.326718i	−0.894849	+	0.446369i	$0.852717\pi$
$150$		0			0
$151$	9.53031	−	4.58956i	0.775566	−	0.373493i	−0.00385571	−	0.999993i	$-0.501227\pi$
$151$	9.53031	−	4.58956i	0.775566	−	0.373493i	0.779422	+	0.626500i	$0.215513\pi$
$152$	−8.98442	−	7.16484i	−0.728733	−	0.581145i
$153$	1.15540	+	5.06214i	0.0934086	+	0.409250i
$154$	0.138527	+	0.606927i	0.0111628	+	0.0489075i
$155$		0			0
$156$	−3.97704	−	0.907735i	−0.318418	−	0.0726769i
$157$	−14.6226			−1.16701			−0.583504	−	0.812110i	$-0.698319\pi$
$157$	−14.6226			−1.16701			−0.583504	+	0.812110i	$0.698319\pi$
$158$	−1.61793	−	0.369282i	−0.128716	−	0.0293785i
$159$	−3.26791	−	6.78588i	−0.259162	−	0.538155i
$160$		0			0
$161$	−2.39403	+	10.4889i	−0.188676	+	0.826643i
$162$	0.448923			0.0352707
$163$	−4.70669	+	20.6214i	−0.368657	+	1.61519i	0.361816	+	0.932249i	$0.382157\pi$
$163$	−4.70669	+	20.6214i	−0.368657	+	1.61519i	−0.730473	+	0.682941i	$0.760700\pi$
$164$	−3.33822	+	2.66214i	−0.260671	+	0.207878i
$165$		0			0
$166$	9.19989	−	2.09981i	0.714050	−	0.162977i
$167$	2.91407	+	2.32389i	0.225497	+	0.179828i	0.729721	−	0.683745i	$-0.239650\pi$
$167$	2.91407	+	2.32389i	0.225497	+	0.179828i	−0.504224	+	0.863573i	$0.668221\pi$
$168$	1.65601	+	3.43873i	0.127764	+	0.265304i
$169$	−0.290233	−	0.139769i	−0.0223256	−	0.0107515i
$170$		0			0
$171$	−5.88429	−	4.69257i	−0.449983	−	0.358850i
$172$	0.726320	+	0.349777i	0.0553814	+	0.0266703i
$173$		−	18.4652i		−	1.40389i	−0.712233	−	0.701943i	$-0.752316\pi$
$173$		−	18.4652i		−	1.40389i	0.712233	−	0.701943i	$-0.247684\pi$
$174$	2.14204	−	4.83235i	0.162388	−	0.366339i
$175$		0			0
$176$	−0.130117	+	0.270192i	−0.00980797	+	0.0203665i
$177$	7.67493	−	9.62406i	0.576883	−	0.723389i
$178$	−8.14535	+	6.49570i	−0.610520	+	0.486874i
$179$	−0.958301	−	0.461493i	−0.0716268	−	0.0344936i	0.397727	−	0.917504i	$-0.369799\pi$
$179$	−0.958301	−	0.461493i	−0.0716268	−	0.0344936i	−0.469354	+	0.883010i	$0.655513\pi$
$180$		0			0
$181$	−16.3495	+	20.5017i	−1.21525	+	1.52388i	−0.432379	+	0.901692i	$0.642326\pi$
$181$	−16.3495	+	20.5017i	−1.21525	+	1.52388i	−0.782871	+	0.622184i	$0.786246\pi$
$182$	−0.939072	−	4.11434i	−0.0696087	−	0.304976i
$183$	−1.43300	+	0.327073i	−0.105930	+	0.0241779i
$184$	−19.7294	+	15.7337i	−1.45447	+	1.15990i
$185$		0			0
$186$			6.24363i			0.457805i
$187$	−1.38187	−	0.315403i	−0.101052	−	0.0230645i
$188$	−1.54049	+	0.741859i	−0.112352	+	0.0541057i
$189$	2.77566	+	5.76372i	0.201900	+	0.419249i
$190$		0			0
$191$			3.33378i			0.241224i	0.992700	+	0.120612i	$0.0384856\pi$
$191$			3.33378i			0.241224i	−0.992700	+	0.120612i	$0.961514\pi$
$192$	−1.42888	+	6.26034i	−0.103121	+	0.451801i
$193$	−10.3573	−	12.9877i	−0.745537	−	0.934874i	0.253940	−	0.967220i	$-0.418274\pi$
$193$	−10.3573	−	12.9877i	−0.745537	−	0.934874i	−0.999477	+	0.0323462i	$0.989702\pi$
$194$	0.298804	+	1.30915i	0.0214529	+	0.0939912i
$195$		0			0
$196$	−3.74029	+	4.69017i	−0.267163	+	0.335012i
$197$	6.04995	+	12.5628i	0.431041	+	0.895066i	0.997479	+	0.0709614i	$0.0226067\pi$
$197$	6.04995	+	12.5628i	0.431041	+	0.895066i	−0.566438	+	0.824104i	$0.691679\pi$
$198$	−0.414938	+	0.861628i	−0.0294884	+	0.0612332i
$199$	−11.7671	−	14.7554i	−0.834145	−	1.04598i	−0.998226	−	0.0595374i	$-0.981037\pi$
$199$	−11.7671	−	14.7554i	−0.834145	−	1.04598i	0.164082	−	0.986447i	$-0.447534\pi$
$200$		0			0
$201$	−0.489129	+	1.01569i	−0.0345005	+	0.0716410i
$202$		−	5.79062i		−	0.407426i
$203$	−6.74159	+	0.212800i	−0.473167	+	0.0149356i
$204$	−3.09172			−0.216464
$205$		0			0
$206$	−2.51540	−	2.00596i	−0.175256	−	0.139762i
$207$	−12.9217	+	10.3047i	−0.898117	+	0.716224i
$208$	0.882063	−	1.83162i	0.0611601	−	0.127000i
$209$	1.85107	−	0.891431i	0.128042	−	0.0616615i
$210$		0			0
$211$	−9.26648	+	2.11501i	−0.637931	+	0.145603i	−0.529240	−	0.848472i	$-0.677523\pi$
$211$	−9.26648	+	2.11501i	−0.637931	+	0.145603i	−0.108691	+	0.994076i	$0.534666\pi$
$212$	−7.81913	+	1.78466i	−0.537020	+	0.122571i
$213$	9.36204	+	11.7396i	0.641477	+	0.804386i
$214$	−2.31429	−	0.528221i	−0.158201	−	0.0361084i
$215$		0			0
$216$	−3.33892	+	14.6288i	−0.227185	+	0.995362i
$217$	7.17816	−	3.45682i	0.487285	−	0.234664i
$218$	12.9953	−	6.25819i	0.880151	−	0.423858i
$219$	2.13916	−	9.37226i	0.144551	−	0.633318i
$220$		0			0
$221$	9.36767	+	2.13811i	0.630137	+	0.143825i
$222$	−0.602267	−	0.755219i	−0.0404215	−	0.0506870i
$223$	4.42093	−	1.00905i	0.296047	−	0.0675709i	−0.0719174	−	0.997411i	$-0.522912\pi$
$223$	4.42093	−	1.00905i	0.296047	−	0.0675709i	0.367965	+	0.929840i	$0.380055\pi$
$224$	6.51494	−	1.48699i	0.435298	−	0.0993539i
$225$		0			0
$226$	5.79843	−	2.79238i	0.385706	−	0.185746i
$227$	−4.10869	+	8.53177i	−0.272703	+	0.566274i	−0.991675	−	0.128765i	$-0.958899\pi$
$227$	−4.10869	+	8.53177i	−0.272703	+	0.566274i	0.718972	+	0.695039i	$0.244613\pi$
$228$	3.50375	−	2.79415i	0.232042	−	0.185047i
$229$	−11.7502	−	9.37049i	−0.776477	−	0.619219i	0.152947	−	0.988234i	$-0.451124\pi$
$229$	−11.7502	−	9.37049i	−0.776477	−	0.619219i	−0.929423	+	0.369015i	$0.879695\pi$
$230$		0			0
$231$	−0.682379			−0.0448973
$232$	−12.6740	−	9.46878i	−0.832090	−	0.621656i
$233$			1.76825i			0.115842i	0.998321	+	0.0579210i	$0.0184472\pi$
$233$			1.76825i			0.115842i	−0.998321	+	0.0579210i	$0.981553\pi$
$234$	2.81286	−	5.84096i	0.183882	−	0.381836i
$235$		0			0
$236$	−8.17267	−	10.2482i	−0.531996	−	0.667102i
$237$	0.789265	−	1.63892i	0.0512682	−	0.106460i
$238$	−1.38776	−	2.88171i	−0.0899551	−	0.186794i
$239$	−2.39583	+	3.00428i	−0.154974	+	0.194331i	−0.853257	−	0.521491i	$-0.825376\pi$
$239$	−2.39583	+	3.00428i	−0.154974	+	0.194331i	0.698283	+	0.715821i	$0.253948\pi$
$240$		0			0
$241$	−6.04559	−	26.4875i	−0.389431	−	1.70621i	−0.666624	−	0.745394i	$-0.732261\pi$
$241$	−6.04559	−	26.4875i	−0.389431	−	1.70621i	0.277193	−	0.960814i	$-0.410596\pi$
$242$	6.32728	+	7.93415i	0.406733	+	0.510027i
$243$	−3.51912	+	15.4183i	−0.225751	+	0.989082i
$244$			1.56518i			0.100200i
$245$		0			0
$246$	1.64631	+	3.41859i	0.104965	+	0.217962i
$247$	−12.5484	+	6.04299i	−0.798436	+	0.384506i
$248$	18.2187	+	4.15830i	1.15689	+	0.264053i
$249$			10.3436i			0.655499i
$250$		0			0
$251$	20.6930	−	16.5021i	1.30613	−	1.04160i	0.310277	−	0.950646i	$-0.399578\pi$
$251$	20.6930	−	16.5021i	1.30613	−	1.04160i	0.995855	−	0.0909586i	$-0.0289931\pi$
$252$	2.59510	−	0.592316i	0.163476	−	0.0373124i
$253$	−1.00394	−	4.39856i	−0.0631173	−	0.276535i
$254$	−12.2343	+	15.3413i	−0.767646	+	0.962598i
$255$		0			0
$256$	15.2582	+	7.34794i	0.953635	+	0.459247i
$257$	−6.33916	+	5.05531i	−0.395426	+	0.315341i	−0.800937	−	0.598749i	$-0.795665\pi$
$257$	−6.33916	+	5.05531i	−0.395426	+	0.315341i	0.405511	+	0.914090i	$0.367093\pi$
$258$	0.446667	−	0.560103i	0.0278083	−	0.0348705i
$259$	−0.534810	+	1.11054i	−0.0332315	+	0.0690058i
$260$		0			0
$261$	−8.30077	−	6.20152i	−0.513805	−	0.383865i
$262$		−	8.75892i		−	0.541128i
$263$	−2.00925	−	0.967602i	−0.123895	−	0.0596649i	0.370909	−	0.928669i	$-0.379046\pi$
$263$	−2.00925	−	0.967602i	−0.123895	−	0.0596649i	−0.494805	+	0.869004i	$0.664760\pi$
$264$	−1.25136	−	0.997923i	−0.0770157	−	0.0614179i
$265$		0			0
$266$	4.17706	+	2.01156i	0.256112	+	0.123337i
$267$	−4.95487	−	10.2889i	−0.303233	−	0.629670i
$268$	0.938539	+	0.748460i	0.0573304	+	0.0457195i
$269$	18.3672	−	4.19220i	1.11987	−	0.255603i	0.377775	−	0.925898i	$-0.376689\pi$
$269$	18.3672	−	4.19220i	1.11987	−	0.255603i	0.742095	+	0.670295i	$0.233832\pi$
$270$		0			0
$271$	−4.22105	+	3.36618i	−0.256411	+	0.204481i	−0.743255	−	0.669008i	$-0.766719\pi$
$271$	−4.22105	+	3.36618i	−0.256411	+	0.204481i	0.486845	+	0.873489i	$0.338148\pi$
$272$	0.342855	−	1.50214i	0.0207886	−	0.0910809i
$273$	4.62583			0.279968
$274$	3.78054	−	16.5636i	0.228391	−	1.00065i
$275$		0			0
$276$	−4.26990	−	8.86653i	−0.257018	−	0.533703i
$277$	14.3281	+	3.27029i	0.860890	+	0.196493i	0.630103	−	0.776512i	$-0.283013\pi$
$277$	14.3281	+	3.27029i	0.860890	+	0.196493i	0.230787	+	0.973004i	$0.425870\pi$
$278$	−17.0089			−1.02013
$279$	11.9322	+	2.72346i	0.714365	+	0.163049i
$280$		0			0
$281$	−1.38792	−	6.08089i	−0.0827966	−	0.362756i	0.916509	−	0.400014i	$-0.130995\pi$
$281$	−1.38792	−	6.08089i	−0.0827966	−	0.362756i	−0.999306	+	0.0372583i	$0.988138\pi$
$282$	0.338108	+	1.48135i	0.0201340	+	0.0882130i
$283$	−2.76990	−	2.20892i	−0.164653	−	0.131307i	0.537697	−	0.843138i	$-0.319294\pi$
$283$	−2.76990	−	2.20892i	−0.164653	−	0.131307i	−0.702350	+	0.711832i	$0.747866\pi$
$284$	14.4059	−	6.93752i	0.854833	−	0.411666i
$285$		0			0
$286$	1.10341	+	1.38363i	0.0652460	+	0.0818159i
$287$	3.01879	−	3.78544i	0.178194	−	0.223448i
$288$	9.24898	+	4.45408i	0.545002	+	0.262459i
$289$	−9.71765			−0.571626
$290$		0			0
$291$	−1.47190			−0.0862841
$292$	−9.22297	−	4.44155i	−0.539734	−	0.259922i
$293$	3.29094	−	4.12671i	0.192259	−	0.241085i	−0.676353	−	0.736577i	$-0.736441\pi$
$293$	3.29094	−	4.12671i	0.192259	−	0.241085i	0.868612	+	0.495492i	$0.165012\pi$
$294$	3.32385	+	4.16797i	0.193851	+	0.243081i
$295$		0			0
$296$	−2.60482	+	1.25442i	−0.151402	+	0.0729114i
$297$	−2.09742	−	1.67264i	−0.121705	−	0.0970563i
$298$	1.07411	+	4.70600i	0.0622217	+	0.272611i
$299$	6.80571	+	29.8177i	0.393584	+	1.72440i
$300$		0			0
$301$	−0.891236	−	0.203419i	−0.0513700	−	0.0117249i
$302$	−10.0097			−0.575996
$303$	6.18813	+	1.41240i	0.355499	+	0.0811403i
$304$	0.969019	+	2.01219i	0.0555770	+	0.115407i
$305$		0			0
$306$	1.09335	−	4.79027i	0.0625025	−	0.273841i
$307$	4.93238			0.281506			0.140753	−	0.990045i	$-0.455048\pi$
$307$	4.93238			0.281506			0.140753	+	0.990045i	$0.455048\pi$
$308$	−0.161691	+	0.708415i	−0.00921321	+	0.0403657i
$309$	2.75720	−	2.19879i	0.156852	−	0.125085i
$310$		0			0
$311$	9.96051	−	2.27342i	0.564809	−	0.128914i	0.0694234	−	0.997587i	$-0.477884\pi$
$311$	9.96051	−	2.27342i	0.564809	−	0.128914i	0.495385	+	0.868673i	$0.335027\pi$
$312$	8.48292	+	6.76490i	0.480251	+	0.382987i
$313$	−5.68575	−	11.8066i	−0.321378	−	0.667348i	0.676214	−	0.736705i	$-0.263619\pi$
$313$	−5.68575	−	11.8066i	−0.321378	−	0.667348i	−0.997592	+	0.0693574i	$0.977905\pi$
$314$	12.4669	+	6.00376i	0.703549	+	0.338812i
$315$		0			0
$316$	−1.51444	−	1.20773i	−0.0851939	−	0.0679399i
$317$	29.2441	+	14.0832i	1.64251	+	0.790991i	0.999688	+	0.0249753i	$0.00795072\pi$
$317$	29.2441	+	14.0832i	1.64251	+	0.790991i	0.642822	+	0.766016i	$0.277764\pi$
$318$			7.12725i			0.399676i
$319$	2.50841	−	1.30703i	0.140444	−	0.0731799i
$320$		0			0
$321$	1.12896	−	2.34432i	0.0630126	−	0.130847i
$322$	6.34766	−	7.95971i	0.353741	−	0.443578i
$323$	−8.25286	+	6.58144i	−0.459201	+	0.366201i
$324$	0.472099	+	0.227351i	0.0262277	+	0.0126306i
$325$		0			0
$326$	12.4796	−	15.6489i	0.691180	−	0.866713i
$327$	3.51810	+	15.4138i	0.194552	+	0.852386i
$328$	11.0718	−	2.52707i	0.611338	−	0.139534i
$329$	1.51588	−	1.20887i	0.0835729	−	0.0666472i
$330$		0			0
$331$		−	28.8891i		−	1.58789i	−0.607989	−	0.793945i	$-0.708024\pi$
$331$		−	28.8891i		−	1.58789i	0.607989	−	0.793945i	$-0.291976\pi$
$332$	10.7383	+	2.45094i	0.589339	+	0.134513i
$333$	−1.70601	+	0.821572i	−0.0934889	+	0.0450219i
$334$	−1.53033	−	3.17777i	−0.0837361	−	0.173880i
$335$		0			0
$336$		−	0.741772i		−	0.0404670i
$337$	6.72804	−	29.4775i	0.366500	−	1.60574i	−0.369818	−	0.929104i	$-0.620580\pi$
$337$	6.72804	−	29.4775i	0.366500	−	1.60574i	0.736318	−	0.676636i	$-0.236563\pi$
$338$	0.190061	+	0.238329i	0.0103379	+	0.0129634i
$339$	1.56976	+	6.87757i	0.0852577	+	0.373539i
$340$		0			0
$341$	−2.08311	+	2.61214i	−0.112807	+	0.141455i
$342$	3.09015	+	6.41677i	0.167096	+	0.346979i
$343$	6.75565	−	14.0282i	0.364771	−	0.757454i
$344$	−1.33688	−	1.67639i	−0.0720796	−	0.0903850i
$345$		0			0
$346$	−7.58148	+	15.7431i	−0.407583	+	0.846354i
$347$			24.3907i			1.30936i	0.755905	+	0.654682i	$0.227197\pi$
$347$			24.3907i			1.30936i	−0.755905	+	0.654682i	$0.772803\pi$
$348$	4.69990	−	3.99701i	0.251941	−	0.214262i
$349$	29.6909			1.58932			0.794658	−	0.607057i	$-0.207650\pi$
$349$	29.6909			1.58932			0.794658	+	0.607057i	$0.207650\pi$
$350$		0			0
$351$	14.2184	+	11.3388i	0.758921	+	0.605219i
$352$	−2.19094	+	1.74722i	−0.116777	+	0.0931269i
$353$	3.61230	−	7.50102i	0.192263	−	0.399239i	−0.782445	−	0.622720i	$-0.786028\pi$
$353$	3.61230	−	7.50102i	0.192263	−	0.399239i	0.974708	+	0.223481i	$0.0717419\pi$
$354$	−10.4950	+	5.05411i	−0.557801	+	0.268623i
$355$		0			0
$356$	−11.8555	+	2.70595i	−0.628342	+	0.143415i
$357$	3.41803	−	0.780142i	0.180901	−	0.0412895i
$358$	0.627548	+	0.786921i	0.0331670	+	0.0415900i
$359$	−31.0341	−	7.08332i	−1.63792	−	0.373844i	−0.698227	−	0.715876i	$-0.746028\pi$
$359$	−31.0341	−	7.08332i	−1.63792	−	0.373844i	−0.939688	+	0.342033i	$0.888885\pi$
$360$		0			0
$361$	−0.823174	+	3.60656i	−0.0433250	+	0.189819i
$362$	22.3569	−	10.7665i	1.17505	−	0.565875i
$363$	−10.0221	+	4.82639i	−0.526024	+	0.253320i
$364$	1.09610	−	4.80233i	0.0574513	−	0.251711i
$365$		0			0
$366$	1.35604	+	0.309507i	0.0708813	+	0.0161782i
$367$	−2.71189	−	3.40060i	−0.141559	−	0.177510i	0.705998	−	0.708214i	$-0.250499\pi$
$367$	−2.71189	−	3.40060i	−0.141559	−	0.177510i	−0.847557	+	0.530704i	$0.821927\pi$
$368$	4.78140	−	1.09132i	0.249248	−	0.0568892i
$369$	7.25141	−	1.65509i	0.377493	−	0.0861604i
$370$		0			0
$371$	8.19403	−	3.94604i	0.425413	−	0.204868i
$372$	−3.16200	+	6.56597i	−0.163942	+	0.340430i
$373$	19.5501	−	15.5906i	1.01226	−	0.807253i	0.0309211	−	0.999522i	$-0.490156\pi$
$373$	19.5501	−	15.5906i	1.01226	−	0.807253i	0.981342	+	0.192269i	$0.0615845\pi$
$374$	1.04866	+	0.836276i	0.0542248	+	0.0432428i
$375$		0			0
$376$	4.54771			0.234530
$377$	−17.0045	+	8.86036i	−0.875775	+	0.456332i
$378$		−	6.05367i		−	0.311367i
$379$	−14.2699	+	29.6318i	−0.732997	+	1.52208i	0.115746	+	0.993279i	$0.463074\pi$
$379$	−14.2699	+	29.6318i	−0.732997	+	1.52208i	−0.848743	+	0.528805i	$0.822640\pi$
$380$		0			0
$381$	−13.4103	−	16.8160i	−0.687033	−	0.861512i
$382$	1.36879	−	2.84231i	0.0700332	−	0.145425i
$383$	1.06116	+	2.20352i	0.0542226	+	0.112594i	0.926320	−	0.376739i	$-0.122955\pi$
$383$	1.06116	+	2.20352i	0.0542226	+	0.112594i	−0.872097	+	0.489333i	$0.837240\pi$
$384$	−3.11228	+	3.90268i	−0.158823	+	0.199158i
$385$		0			0
$386$	3.49796	+	15.3256i	0.178042	+	0.780051i
$387$	−0.875580	−	1.09794i	−0.0445083	−	0.0558116i
$388$	−0.348769	+	1.52806i	−0.0177061	+	0.0775753i
$389$		−	19.6660i		−	0.997105i	−0.866860	−	0.498552i	$-0.833865\pi$
$389$		−	19.6660i		−	0.997105i	0.866860	−	0.498552i	$-0.166135\pi$
$390$		0			0
$391$	10.0575	+	20.8845i	0.508628	+	1.05618i
$392$	14.3757	−	6.92298i	0.726084	−	0.349663i
$393$	9.36020	+	2.13641i	0.472160	+	0.107767i
$394$		−	13.1948i		−	0.664746i
$395$		0			0
$396$	−0.872720	+	0.695971i	−0.0438558	+	0.0349738i
$397$	10.8339	−	2.47277i	0.543738	−	0.124105i	0.0581753	−	0.998306i	$-0.481472\pi$
$397$	10.8339	−	2.47277i	0.543738	−	0.124105i	0.485563	+	0.874202i	$0.338615\pi$
$398$	3.97407	+	17.4115i	0.199202	+	0.872761i
$399$	−3.16849	+	3.97316i	−0.158623	+	0.198907i
$400$		0			0
$401$	−7.12405	−	3.43076i	−0.355758	−	0.171324i	0.247465	−	0.968897i	$-0.420403\pi$
$401$	−7.12405	−	3.43076i	−0.355758	−	0.171324i	−0.603222	+	0.797573i	$0.706117\pi$
$402$	0.834043	−	0.665127i	0.0415983	−	0.0331735i
$403$	14.1214	−	17.7076i	0.703435	−	0.882079i
$404$	2.93258	−	6.08956i	0.145901	−	0.302967i
$405$		0			0
$406$	5.83512	+	2.58654i	0.289592	+	0.128368i
$407$		−	0.516898i		−	0.0256217i
$408$	7.40892	+	3.56795i	0.366796	+	0.176640i
$409$	−19.9016	−	15.8710i	−0.984073	−	0.784772i	−0.00750287	−	0.999972i	$-0.502388\pi$
$409$	−19.9016	−	15.8710i	−0.984073	−	0.784772i	−0.976570	+	0.215200i	$0.930960\pi$
$410$		0			0
$411$	16.7786	+	8.08013i	0.827626	+	0.398564i
$412$	−1.62936	−	3.38341i	−0.0802730	−	0.166689i
$413$	11.6212	+	9.26758i	0.571841	+	0.456028i
$414$	15.2477	−	3.48018i	0.749381	−	0.171041i
$415$		0			0
$416$	14.8523	−	11.8443i	0.728196	−	0.580717i
$417$	4.14867	−	18.1765i	0.203161	−	0.890108i
$418$	−1.94420			−0.0950937
$419$	−2.36645	+	10.3681i	−0.115609	+	0.506515i	0.883655	+	0.468139i	$0.155075\pi$
$419$	−2.36645	+	10.3681i	−0.115609	+	0.506515i	−0.999263	+	0.0383754i	$0.987782\pi$
$420$		0			0
$421$	−12.2495	−	25.4364i	−0.597006	−	1.23970i	−0.952363	−	0.304966i	$-0.901355\pi$
$421$	−12.2495	−	25.4364i	−0.597006	−	1.23970i	0.355357	−	0.934731i	$-0.384359\pi$
$422$	8.76880	+	2.00142i	0.426859	+	0.0974277i
$423$	2.97849			0.144819
$424$	20.7971	+	4.74680i	1.01000	+	0.230525i
$425$		0			0
$426$	−3.16182	−	13.8529i	−0.153191	−	0.671173i
$427$	−0.394945	−	1.73037i	−0.0191127	−	0.0837383i
$428$	−2.16625	−	1.72753i	−0.104710	−	0.0835032i
$429$	−1.74775	+	0.841672i	−0.0843822	+	0.0406363i
$430$		0			0
$431$	4.06120	+	5.09259i	0.195621	+	0.245301i	0.869962	−	0.493119i	$-0.164143\pi$
$431$	4.06120	+	5.09259i	0.195621	+	0.245301i	−0.674340	+	0.738421i	$0.735572\pi$
$432$	1.81822	−	2.27998i	0.0874792	−	0.109695i
$433$	31.4410	+	15.1412i	1.51096	+	0.727639i	0.991891	−	0.127094i	$-0.0405649\pi$
$433$	31.4410	+	15.1412i	1.51096	+	0.727639i	0.519068	+	0.854733i	$0.326279\pi$
$434$	−7.53927			−0.361896
$435$		0			0
$436$	16.8355			0.806276
$437$	−30.2722	−	14.5783i	−1.44812	−	0.697377i
$438$	−5.67188	+	7.11231i	−0.271013	+	0.339839i
$439$	−1.88060	−	2.35820i	−0.0897563	−	0.112551i	0.734925	−	0.678148i	$-0.237217\pi$
$439$	−1.88060	−	2.35820i	−0.0897563	−	0.112551i	−0.824682	+	0.565597i	$0.808646\pi$
$440$		0			0
$441$	9.41529	−	4.53417i	0.448347	−	0.215913i
$442$	−7.10882	−	5.66910i	−0.338132	−	0.269652i
$443$	5.52349	+	24.2000i	0.262429	+	1.14978i	0.918608	+	0.395171i	$0.129315\pi$
$443$	5.52349	+	24.2000i	0.262429	+	1.14978i	−0.656179	+	0.754606i	$0.727828\pi$
$444$	−0.250889	−	1.09922i	−0.0119067	−	0.0521666i
$445$		0			0
$446$	−4.18350	−	0.954856i	−0.198094	−	0.0452137i
$447$	−5.29104			−0.250258
$448$	−7.55944	−	1.72539i	−0.357150	−	0.0815171i
$449$	−13.3016	−	27.6210i	−0.627739	−	1.30351i	−0.935929	−	0.352189i	$-0.885438\pi$
$449$	−13.3016	−	27.6210i	−0.627739	−	1.30351i	0.308190	−	0.951325i	$-0.400277\pi$
$450$		0			0
$451$	−0.451808	+	1.97950i	−0.0212748	+	0.0932110i
$452$	7.51194			0.353332
$453$	2.44150	−	10.6969i	0.114711	−	0.502584i
$454$	7.00597	−	5.58708i	0.328807	−	0.262214i
$455$		0			0
$456$	−11.6208	+	2.65238i	−0.544195	+	0.124209i
$457$	−32.3606	−	25.8067i	−1.51377	−	1.20719i	−0.913132	−	0.407665i	$-0.866343\pi$
$457$	−32.3606	−	25.8067i	−1.51377	−	1.20719i	−0.600635	−	0.799523i	$-0.705085\pi$
$458$	6.17067	+	12.8135i	0.288336	+	0.598737i
$459$	12.4182	+	5.98030i	0.579633	+	0.279137i
$460$		0			0
$461$	−26.1877	−	20.8840i	−1.21968	−	0.972664i	−0.219687	−	0.975570i	$-0.570504\pi$
$461$	−26.1877	−	20.8840i	−1.21968	−	0.972664i	−0.999996	+	0.00290595i	$0.999075\pi$
$462$	0.581783	+	0.280172i	0.0270670	+	0.0130348i
$463$		−	15.5871i		−	0.724396i	−0.932101	−	0.362198i	$-0.882026\pi$
$463$		−	15.5871i		−	0.724396i	0.932101	−	0.362198i	$-0.117974\pi$
$464$	1.42080	+	2.72674i	0.0659588	+	0.126586i
$465$		0			0
$466$	0.726011	−	1.50758i	0.0336318	−	0.0698372i
$467$	−1.68794	+	2.11661i	−0.0781086	+	0.0979450i	−0.819350	−	0.573293i	$-0.805666\pi$
$467$	−1.68794	+	2.11661i	−0.0781086	+	0.0979450i	0.741242	+	0.671238i	$0.234237\pi$
$468$	5.91615	−	4.71797i	0.273474	−	0.218088i
$469$	−1.22645	−	0.590629i	−0.0566324	−	0.0272727i
$470$		0			0
$471$	−9.45673	+	11.8584i	−0.435743	+	0.546405i
$472$	7.75800	+	33.9900i	0.357091	+	1.56452i
$473$	0.373742	−	0.0853042i	0.0171847	−	0.00392229i
$474$	−1.34582	+	1.07326i	−0.0618157	+	0.0492964i
$475$		0			0
$476$		−	3.73330i		−	0.171115i
$477$	13.6209	+	3.10889i	0.623659	+	0.142346i
$478$	3.27614	−	1.57771i	0.149847	−	0.0721627i
$479$	−13.7288	−	28.5081i	−0.627283	−	1.30257i	−0.936197	−	0.351477i	$-0.885680\pi$
$479$	−13.7288	−	28.5081i	−0.627283	−	1.30257i	0.308914	−	0.951090i	$-0.400035\pi$
$480$		0			0
$481$			3.50404i			0.159771i
$482$	−5.72090	+	25.0649i	−0.260580	+	1.14168i
$483$	6.95786	+	8.72488i	0.316594	+	0.396996i
$484$	2.63578	+	11.5481i	0.119808	+	0.524915i
$485$		0			0
$486$	9.33078	−	11.7004i	0.423253	−	0.530742i
$487$	11.6836	+	24.2612i	0.529434	+	1.09938i	0.978569	+	0.205918i	$0.0660179\pi$
$487$	11.6836	+	24.2612i	0.529434	+	1.09938i	−0.449135	+	0.893464i	$0.648268\pi$
$488$	1.80626	−	3.75074i	0.0817657	−	0.169788i
$489$	13.6792	+	17.1532i	0.618597	+	0.775696i
$490$		0			0
$491$	−0.666622	+	1.38426i	−0.0300842	+	0.0624706i	−0.915469	−	0.402388i	$-0.868180\pi$
$491$	−0.666622	+	1.38426i	−0.0300842	+	0.0624706i	0.885385	+	0.464858i	$0.153895\pi$
$492$			4.42883i			0.199667i
$493$	−11.0703	+	9.41470i	−0.498581	+	0.424017i
$494$	13.1797			0.592981
$495$		0			0
$496$	−2.83949	−	2.26442i	−0.127497	−	0.101675i
$497$	−14.1757	+	11.3048i	−0.635869	+	0.507089i
$498$	4.24689	−	8.81876i	0.190308	−	0.395178i
$499$	−22.5594	+	10.8640i	−1.00990	+	0.486342i	−0.864286	−	0.503000i	$-0.832230\pi$
$499$	−22.5594	+	10.8640i	−1.00990	+	0.486342i	−0.145612	+	0.989342i	$0.546515\pi$
$500$		0			0
$501$	3.76918	−	0.860291i	0.168395	−	0.0384350i
$502$	−24.4179	+	5.57323i	−1.08983	+	0.248746i
$503$	−4.50661	−	5.65110i	−0.200940	−	0.251970i	0.671144	−	0.741327i	$-0.265803\pi$
$503$	−4.50661	−	5.65110i	−0.200940	−	0.251970i	−0.872084	+	0.489357i	$0.837232\pi$
$504$	−6.90238	−	1.57542i	−0.307457	−	0.0701749i
$505$		0			0
$506$	−0.950024	+	4.16233i	−0.0422337	+	0.185038i
$507$	−0.301047	+	0.144977i	−0.0133700	+	0.00643864i
$508$	−20.6353	+	9.93741i	−0.915541	+	0.440901i
$509$	−3.97180	+	17.4016i	−0.176047	+	0.771311i	0.807384	+	0.590027i	$0.200883\pi$
$509$	−3.97180	+	17.4016i	−0.176047	+	0.771311i	−0.983431	+	0.181285i	$0.941974\pi$
$510$		0			0
$511$	11.3171	+	2.58306i	0.500640	+	0.114268i
$512$	−3.99092	−	5.00445i	−0.176375	−	0.221168i
$513$	−19.4779	+	4.44570i	−0.859970	+	0.196282i
$514$	7.48026	−	1.70732i	0.329940	−	0.0753067i
$515$		0			0
$516$	0.753383	−	0.362810i	0.0331658	−	0.0159718i
$517$	−0.352779	+	0.732554i	−0.0155152	+	0.0322177i
$518$	0.911937	−	0.727245i	0.0400682	−	0.0319533i
$519$	−14.9746	−	11.9419i	−0.657312	−	0.524189i
$520$		0			0
$521$	−38.2597			−1.67619			−0.838095	−	0.545525i	$-0.816330\pi$
$521$	−38.2597			−1.67619			−0.838095	+	0.545525i	$0.816330\pi$
$522$	4.53085	+	8.69544i	0.198310	+	0.380589i
$523$			11.6128i			0.507793i	0.967231	+	0.253897i	$0.0817123\pi$
$523$			11.6128i			0.507793i	−0.967231	+	0.253897i	$0.918288\pi$
$524$	4.43584	−	9.21111i	0.193780	−	0.402389i
$525$		0			0
$526$	1.31576	+	1.64992i	0.0573701	+	0.0719398i
$527$	7.44789	−	15.4657i	0.324435	−	0.673696i
$528$	0.134966	+	0.280259i	0.00587362	+	0.0121967i
$529$	−31.6629	+	39.7040i	−1.37665	+	1.72626i
$530$		0			0
$531$	5.08106	+	22.2616i	0.220499	+	0.966070i
$532$	3.37397	+	4.23083i	0.146280	+	0.183430i
$533$	3.06280	−	13.4190i	0.132664	−	0.581241i
$534$			10.8065i			0.467642i
$535$		0			0
$536$	−1.38534	−	2.87669i	−0.0598376	−	0.124254i
$537$	−0.994007	+	0.478689i	−0.0428946	+	0.0206569i
$538$	−17.3808	−	3.96705i	−0.749339	−	0.171032i
$539$			2.85271i			0.122875i
$540$		0			0
$541$	10.9279	−	8.71467i	0.469825	−	0.374673i	−0.359768	−	0.933042i	$-0.617144\pi$
$541$	10.9279	−	8.71467i	0.469825	−	0.374673i	0.829593	+	0.558369i	$0.188573\pi$
$542$	4.98087	−	1.13685i	0.213947	−	0.0488320i
$543$	6.05249	+	26.5177i	0.259737	+	1.13798i
$544$	8.97685	−	11.2566i	0.384879	−	0.482623i
$545$		0			0
$546$	−3.94390	−	1.89928i	−0.168783	−	0.0812817i
$547$	20.4432	−	16.3029i	0.874089	−	0.697062i	−0.0799329	−	0.996800i	$-0.525471\pi$
$547$	20.4432	−	16.3029i	0.874089	−	0.697062i	0.954022	+	0.299738i	$0.0968992\pi$
$548$	12.3641	−	15.5041i	0.528170	−	0.662304i
$549$	1.18300	−	2.45653i	0.0504892	−	0.104842i
$550$		0			0
$551$	4.03708	−	20.6742i	0.171985	−	0.880750i
$552$			26.1751i			1.11409i
$553$	1.97902	+	0.953047i	0.0841566	+	0.0405277i
$554$	−10.8731	−	8.67102i	−0.461954	−	0.368396i
$555$		0			0
$556$	−17.8870	−	8.61393i	−0.758578	−	0.365312i
$557$	−17.0793	−	35.4656i	−0.723674	−	1.50272i	−0.859029	−	0.511927i	$-0.828932\pi$
$557$	−17.0793	−	35.4656i	−0.723674	−	1.50272i	0.135355	−	0.990797i	$-0.456783\pi$
$558$	−9.05500	−	7.22112i	−0.383329	−	0.305694i
$559$	−2.53359	+	0.578276i	−0.107159	+	0.0244585i
$560$		0			0
$561$	−1.14946	+	0.916667i	−0.0485304	+	0.0387017i
$562$	−1.31338	+	5.75431i	−0.0554017	+	0.242731i
$563$	−23.8947			−1.00704			−0.503520	−	0.863984i	$-0.667962\pi$
$563$	−23.8947			−1.00704			−0.503520	+	0.863984i	$0.667962\pi$
$564$	−0.394645	+	1.72905i	−0.0166176	+	0.0728063i
$565$		0			0
$566$	1.45462	+	3.02055i	0.0611422	+	0.126963i
$567$	−0.579292	−	0.132220i	−0.0243280	−	0.00555270i
$568$	−42.5280			−1.78444
$569$	28.4337	+	6.48980i	1.19200	+	0.272067i	0.772099	−	0.635503i	$-0.219207\pi$
$569$	28.4337	+	6.48980i	1.19200	+	0.272067i	0.419903	+	0.907569i	$0.362064\pi$
$570$		0			0
$571$	3.93304	+	17.2318i	0.164593	+	0.721128i	0.988099	+	0.153821i	$0.0491578\pi$
$571$	3.93304	+	17.2318i	0.164593	+	0.721128i	−0.823506	+	0.567308i	$0.807985\pi$
$572$	0.459653	+	2.01387i	0.0192190	+	0.0842041i
$573$	2.70357	+	2.15602i	0.112943	+	0.0900692i
$574$	−4.12800	+	1.98794i	−0.172299	+	0.0829749i
$575$		0			0
$576$	−7.42664	−	9.31272i	−0.309444	−	0.388030i
$577$	18.9144	−	23.7179i	0.787415	−	0.987387i	−0.212532	−	0.977154i	$-0.568171\pi$
$577$	18.9144	−	23.7179i	0.787415	−	0.987387i	0.999948	−	0.0102334i	$-0.00325745\pi$
$578$	8.28508	+	3.98988i	0.344614	+	0.165957i
$579$	−17.2308			−0.716089
$580$		0			0
$581$	−12.4900			−0.518174
$582$	1.25491	+	0.604333i	0.0520177	+	0.0250504i
$583$	−2.37792	+	2.98181i	−0.0984832	+	0.123494i
$584$	16.9760	+	21.2872i	0.702471	+	0.880871i
$585$		0			0
$586$	−4.50015	+	2.16716i	−0.185899	+	0.0895244i
$587$	−19.2486	−	15.3503i	−0.794476	−	0.633573i	0.139778	−	0.990183i	$-0.455361\pi$
$587$	−19.2486	−	15.3503i	−0.794476	−	0.633573i	−0.934253	+	0.356610i	$0.883933\pi$
$588$	1.38463	+	6.06647i	0.0571012	+	0.250177i
$589$	5.53669	+	24.2578i	0.228135	+	0.999527i
$590$		0			0
$591$	14.1006	+	3.21838i	0.580022	+	0.132386i
$592$	0.561888			0.0230935
$593$	−38.8868	−	8.87566i	−1.59689	−	0.364480i	−0.670757	−	0.741678i	$-0.734030\pi$
$593$	−38.8868	−	8.87566i	−1.59689	−	0.364480i	−0.926133	+	0.377198i	$0.876888\pi$
$594$	1.10147	+	2.28722i	0.0451937	+	0.0938458i
$595$		0			0
$596$	−1.25372	+	5.49292i	−0.0513545	+	0.224999i
$597$	−19.5761			−0.801197
$598$	6.44019	−	28.2163i	0.263359	−	1.15385i
$599$	11.9413	−	9.52283i	0.487907	−	0.389092i	−0.348408	−	0.937343i	$-0.613277\pi$
$599$	11.9413	−	9.52283i	0.487907	−	0.389092i	0.836314	+	0.548251i	$0.184706\pi$
$600$		0			0
$601$	−11.1778	+	2.55125i	−0.455951	+	0.104068i	−0.444327	−	0.895865i	$-0.646557\pi$
$601$	−11.1778	+	2.55125i	−0.455951	+	0.104068i	−0.0116239	+	0.999932i	$0.503700\pi$
$602$	0.676331	+	0.539356i	0.0275652	+	0.0219825i
$603$	−0.907321	−	1.88407i	−0.0369490	−	0.0767253i
$604$	−10.5265	−	5.06930i	−0.428318	−	0.206267i
$605$		0			0
$606$	−4.69598	−	3.74492i	−0.190761	−	0.152127i
$607$	33.5234	+	16.1440i	1.36067	+	0.655266i	0.964787	−	0.263033i	$-0.0847229\pi$
$607$	33.5234	+	16.1440i	1.36067	+	0.655266i	0.395887	+	0.918299i	$0.370437\pi$
$608$			20.8696i			0.846374i
$609$	−4.18735	+	5.60480i	−0.169680	+	0.227118i
$610$		0			0
$611$	2.39148	−	4.96597i	0.0967491	−	0.200902i
$612$	3.57576	−	4.48386i	0.144541	−	0.181249i
$613$	−11.2492	+	8.97093i	−0.454351	+	0.362332i	−0.823764	−	0.566933i	$-0.808130\pi$
$613$	−11.2492	+	8.97093i	−0.454351	+	0.362332i	0.369414	+	0.929265i	$0.379559\pi$
$614$	−4.20525	−	2.02514i	−0.169710	−	0.0817281i
$615$		0			0
$616$	1.20501	−	1.51103i	0.0485510	−	0.0608811i
$617$	1.94940	+	8.54086i	0.0784797	+	0.343842i	0.998890	−	0.0471127i	$-0.0150020\pi$
$617$	1.94940	+	8.54086i	0.0784797	+	0.343842i	−0.920410	+	0.390955i	$0.872145\pi$
$618$	−3.25352	+	0.742594i	−0.130876	+	0.0298715i
$619$	24.9067	−	19.8624i	1.00108	−	0.798338i	0.0215815	−	0.999767i	$-0.493130\pi$
$619$	24.9067	−	19.8624i	1.00108	−	0.798338i	0.979503	+	0.201429i	$0.0645584\pi$
$620$		0			0
$621$			43.8726i			1.76055i
$622$	−9.42556	−	2.15132i	−0.377931	−	0.0862602i
$623$	12.4240	−	5.98307i	0.497756	−	0.239706i
$624$	−0.914929	−	1.89987i	−0.0366265	−	0.0760557i
$625$		0			0
$626$			12.4005i			0.495625i
$627$	0.474212	−	2.07766i	0.0189382	−	0.0829737i
$628$	10.0700	+	12.6274i	0.401838	+	0.503888i
$629$	0.590953	+	2.58914i	0.0235629	+	0.103236i
$630$		0			0
$631$	−18.2919	+	22.9373i	−0.728187	+	0.913118i	−0.998770	−	0.0495786i	$-0.984212\pi$
$631$	−18.2919	+	22.9373i	−0.728187	+	0.913118i	0.270583	+	0.962697i	$0.412784\pi$
$632$	2.23541	+	4.64187i	0.0889197	+	0.184644i
$633$	−4.27763	+	8.88259i	−0.170021	+	0.353051i
$634$	−19.1506	−	24.0141i	−0.760568	−	0.953723i
$635$		0			0
$636$	−3.60950	+	7.49520i	−0.143126	+	0.297204i
$637$		−	19.3384i		−	0.766217i
$638$	−2.67527	+	0.0844455i	−0.105915	+	0.00334323i
$639$	−27.8535			−1.10187
$640$		0			0
$641$	13.9738	+	11.1437i	0.551930	+	0.440150i	0.859323	−	0.511433i	$-0.170885\pi$
$641$	13.9738	+	11.1437i	0.551930	+	0.440150i	−0.307393	+	0.951583i	$0.599457\pi$
$642$	−1.92506	+	1.53519i	−0.0759762	+	0.0605890i
$643$	−1.85710	+	3.85632i	−0.0732370	+	0.152078i	−0.934373	−	0.356297i	$-0.884039\pi$
$643$	−1.85710	+	3.85632i	−0.0732370	+	0.152078i	0.861136	+	0.508375i	$0.169754\pi$
$644$	10.7065	−	5.15596i	0.421893	−	0.203173i
$645$		0			0
$646$	9.73844	−	2.22274i	0.383154	−	0.0874524i
$647$	−23.6004	+	5.38663i	−0.927827	+	0.211770i	−0.659627	−	0.751593i	$-0.729286\pi$
$647$	−23.6004	+	5.38663i	−0.927827	+	0.211770i	−0.268199	+	0.963363i	$0.586429\pi$
$648$	−0.868954	−	1.08963i	−0.0341357	−	0.0428049i
$649$	−6.07699	−	1.38703i	−0.238543	−	0.0544459i
$650$		0			0
$651$	1.83892	−	8.05682i	0.0720728	−	0.315772i
$652$	21.0490	−	10.1367i	0.824344	−	0.396983i
$653$	10.0039	−	4.81762i	0.391483	−	0.188528i	−0.227779	−	0.973713i	$-0.573146\pi$
$653$	10.0039	−	4.81762i	0.391483	−	0.188528i	0.619262	+	0.785185i	$0.287432\pi$
$654$	3.32916	−	14.5860i	0.130180	−	0.570357i
$655$		0			0
$656$	−2.15179	−	0.491132i	−0.0840133	−	0.0191755i
$657$	11.1183	+	13.9419i	0.433767	+	0.543926i
$658$	−1.78875	+	0.408270i	−0.0697326	+	0.0159160i
$659$	−12.5730	+	2.86971i	−0.489776	+	0.111788i	−0.460275	−	0.887777i	$-0.652249\pi$
$659$	−12.5730	+	2.86971i	−0.489776	+	0.111788i	−0.0295013	+	0.999565i	$0.509392\pi$
$660$		0			0
$661$	−1.68203	+	0.810023i	−0.0654234	+	0.0315062i	−0.466309	−	0.884622i	$-0.654417\pi$
$661$	−1.68203	+	0.810023i	−0.0654234	+	0.0315062i	0.400886	+	0.916128i	$0.368702\pi$
$662$	−11.8613	+	24.6303i	−0.461004	+	0.957285i
$663$	7.79219	−	6.21407i	0.302624	−	0.241334i
$664$	−22.9044	−	18.2656i	−0.888863	−	0.708845i
$665$		0			0
$666$	1.79183			0.0694322
$667$	−42.2886	−	18.7453i	−1.63742	−	0.725822i
$668$		−	4.11684i		−	0.159285i
$669$	2.04081	−	4.23778i	0.0789022	−	0.163842i
$670$		0			0
$671$	0.464060	+	0.581913i	0.0179148	+	0.0224645i
$672$	3.00745	−	6.24504i	0.116015	−	0.240908i
$673$	−6.12069	−	12.7097i	−0.235935	−	0.489924i	0.749061	−	0.662501i	$-0.230505\pi$
$673$	−6.12069	−	12.7097i	−0.235935	−	0.489924i	−0.984996	+	0.172577i	$0.944791\pi$
$674$	−17.8391	+	22.3695i	−0.687136	+	0.861642i
$675$		0			0
$676$	0.0791745	+	0.346886i	0.00304517	+	0.0133418i
$677$	−25.5971	−	32.0977i	−0.983775	−	1.23362i	−0.972313	−	0.233681i	$-0.924923\pi$
$677$	−25.5971	−	32.0977i	−0.983775	−	1.23362i	−0.0114618	−	0.999934i	$-0.503648\pi$
$678$	1.48545	−	6.50820i	0.0570485	−	0.249946i
$679$		−	1.77733i		−	0.0682078i
$680$		0			0
$681$	4.26178	+	8.84967i	0.163312	+	0.339120i
$682$	2.84851	−	1.37177i	0.109075	−	0.0525278i
$683$	−40.3707	−	9.21435i	−1.54474	−	0.352577i	−0.636585	−	0.771207i	$-0.719653\pi$
$683$	−40.3707	−	9.21435i	−1.54474	−	0.352577i	−0.908157	+	0.418630i	$0.862511\pi$
$684$			8.31301i			0.317856i
$685$		0			0
$686$	−11.5195	+	9.18647i	−0.439815	+	0.350741i
$687$	−15.1982	+	3.46890i	−0.579849	+	0.132347i
$688$	0.0927289	+	0.406272i	0.00353526	+	0.0154890i
$689$	16.1198	−	20.2137i	0.614117	−	0.770079i
$690$		0			0
$691$	−20.9367	−	10.0826i	−0.796471	−	0.383560i	−0.00903693	−	0.999959i	$-0.502877\pi$
$691$	−20.9367	−	10.0826i	−0.796471	−	0.383560i	−0.787434	+	0.616399i	$0.788591\pi$
$692$	−15.9458	+	12.7163i	−0.606167	+	0.483402i
$693$	0.789211	−	0.989639i	0.0299796	−	0.0375933i
$694$	10.0144	−	20.7951i	0.380141	−	0.789370i
$695$		0			0
$696$	−15.8754	+	4.15449i	−0.601755	+	0.157476i
$697$		−	10.4318i		−	0.395133i
$698$	−25.3139	−	12.1905i	−0.958144	−	0.461418i
$699$	1.43399	+	1.14357i	0.0542383	+	0.0432536i
$700$		0			0
$701$	44.8195	+	21.5839i	1.69281	+	0.815214i	0.995104	+	0.0988288i	$0.0315096\pi$
$701$	44.8195	+	21.5839i	1.69281	+	0.815214i	0.697705	+	0.716385i	$0.254205\pi$
$702$	−7.46682	−	15.5050i	−0.281817	−	0.585199i
$703$	−3.00964	−	2.40011i	−0.113511	−	0.0905219i
$704$	3.17007	−	0.723548i	0.119476	−	0.0272697i
$705$		0			0
$706$	−6.15956	+	4.91208i	−0.231818	+	0.184869i
$707$	−1.70549	+	7.47224i	−0.0641416	+	0.281023i
$708$	−13.5964			−0.510982
$709$	−3.88510	+	17.0217i	−0.145908	+	0.639265i	0.848089	+	0.529854i	$0.177753\pi$
$709$	−3.88510	+	17.0217i	−0.145908	+	0.639265i	−0.993997	+	0.109410i	$0.965104\pi$
$710$		0			0
$711$	1.46407	+	3.04016i	0.0549068	+	0.114015i
$712$	31.5330	+	7.19720i	1.18175	+	0.269726i
$713$	54.6391			2.04625
$714$	−3.23446	−	0.738243i	−0.121046	−	0.0276281i
$715$		0			0
$716$	0.261421	+	1.14536i	0.00976975	+	0.0428041i
$717$	0.886923	+	3.88587i	0.0331228	+	0.145120i
$718$	23.5508	+	18.7811i	0.878907	+	0.700905i
$719$	38.8820	−	18.7246i	1.45005	−	0.698309i	0.467449	−	0.884020i	$-0.345173\pi$
$719$	38.8820	−	18.7246i	1.45005	−	0.698309i	0.982604	+	0.185711i	$0.0594589\pi$
$720$		0			0
$721$	2.65507	+	3.32935i	0.0988800	+	0.123992i
$722$	2.18261	−	2.73691i	0.0812283	−	0.101857i
$723$	−25.3902	−	12.2273i	−0.944271	−	0.454737i
$724$	28.9636			1.07642
$725$		0			0
$726$	10.5263			0.390667
$727$	28.9034	+	13.9191i	1.07197	+	0.516232i	0.884740	−	0.466085i	$-0.154336\pi$
$727$	28.9034	+	13.9191i	1.07197	+	0.516232i	0.187227	+	0.982317i	$0.440050\pi$
$728$	−8.16871	+	10.2432i	−0.302752	+	0.379639i
$729$	9.34039	+	11.7125i	0.345940	+	0.433796i
$730$		0			0
$731$	−1.77454	+	0.854575i	−0.0656339	+	0.0316076i
$732$	1.26930	+	1.01223i	0.0469147	+	0.0374132i
$733$	−9.80449	−	42.9563i	−0.362137	−	1.58663i	−0.747759	−	0.663970i	$-0.768870\pi$
$733$	−9.80449	−	42.9563i	−0.362137	−	1.58663i	0.385622	−	0.922657i	$-0.373987\pi$
$734$	0.915881	+	4.01274i	0.0338058	+	0.148113i
$735$		0			0
$736$	44.6797	+	10.1979i	1.64692	+	0.375898i
$737$	0.570848			0.0210275
$738$	−6.86196	−	1.56620i	−0.252592	−	0.0576525i
$739$	2.11996	+	4.40214i	0.0779839	+	0.161935i	0.936315	−	0.351161i	$-0.114213\pi$
$739$	2.11996	+	4.40214i	0.0779839	+	0.161935i	−0.858331	+	0.513096i	$0.828499\pi$
$740$		0			0
$741$	−3.21468	+	14.0844i	−0.118094	+	0.517404i
$742$	−8.60624			−0.315945
$743$	−6.16797	+	27.0237i	−0.226281	+	0.991402i	0.726362	+	0.687312i	$0.241209\pi$
$743$	−6.16797	+	27.0237i	−0.226281	+	0.991402i	−0.952643	+	0.304090i	$0.901648\pi$
$744$	15.1547	−	12.0854i	0.555597	−	0.443074i
$745$		0			0
$746$	−23.0692	+	5.26540i	−0.844624	+	0.192780i
$747$	−15.0011	−	11.9630i	−0.548861	−	0.437702i
$748$	0.679274	+	1.41053i	0.0248367	+	0.0515740i
$749$	2.83079	+	1.36324i	0.103435	+	0.0498116i
$750$		0			0
$751$	29.6708	+	23.6617i	1.08270	+	0.863426i	0.991199	−	0.132378i	$-0.0422614\pi$
$751$	29.6708	+	23.6617i	1.08270	+	0.863426i	0.0915032	+	0.995805i	$0.470833\pi$
$752$	−0.796314	−	0.383484i	−0.0290386	−	0.0139842i
$753$		−	27.4535i		−	1.00046i
$754$	18.1356	−	0.572454i	0.660459	−	0.0208476i
$755$		0			0
$756$	3.06580	−	6.36620i	0.111502	−	0.231536i
$757$	4.98403	−	6.24978i	0.181148	−	0.227152i	−0.682964	−	0.730452i	$-0.739309\pi$
$757$	4.98403	−	6.24978i	0.181148	−	0.227152i	0.864112	+	0.503300i	$0.167881\pi$
$758$	24.3325	−	19.4045i	0.883797	−	0.704805i
$759$	−4.21634	−	2.03048i	−0.153043	−	0.0737018i
$760$		0			0
$761$	−0.885135	+	1.10992i	−0.0320861	+	0.0402347i	−0.797616	−	0.603166i	$-0.793906\pi$
$761$	−0.885135	+	1.10992i	−0.0320861	+	0.0402347i	0.765530	+	0.643401i	$0.222477\pi$
$762$	4.52905	+	19.8431i	0.164070	+	0.718838i
$763$	−18.6124	+	4.24815i	−0.673813	+	0.153793i
$764$	2.87890	−	2.29585i	0.104155	−	0.0830608i
$765$		0			0
$766$		−	2.31437i		−	0.0836215i
$767$	41.1958	+	9.40268i	1.48750	+	0.339511i
$768$	15.8267	−	7.62173i	0.571096	−	0.275026i
$769$	−1.51207	−	3.13985i	−0.0545267	−	0.113226i	0.871925	−	0.489639i	$-0.162872\pi$
$769$	−1.51207	−	3.13985i	−0.0545267	−	0.113226i	−0.926452	+	0.376413i	$0.877157\pi$
$770$		0			0
$771$			8.41019i			0.302886i
$772$	−4.08288	+	17.8883i	−0.146946	+	0.643813i
$773$	−12.3060	−	15.4313i	−0.442618	−	0.555025i	0.509613	−	0.860404i	$-0.329788\pi$
$773$	−12.3060	−	15.4313i	−0.442618	−	0.555025i	−0.952231	+	0.305378i	$0.901217\pi$
$774$	0.295708	+	1.29558i	0.0106290	+	0.0465687i
$775$		0			0
$776$	2.59920	−	3.25930i	0.0933060	−	0.117002i
$777$	0.554737	+	1.15192i	0.0199011	+	0.0413250i
$778$	−8.07448	+	16.7668i	−0.289484	+	0.601120i
$779$	9.42777	+	11.8221i	0.337785	+	0.423569i
$780$		0			0
$781$	3.29902	−	6.85050i	0.118048	−	0.245130i
$782$		−	21.9352i		−	0.784400i
$783$	−26.6090	+	6.96342i	−0.950929	+	0.248852i
$784$	−3.10100			−0.110750
$785$		0			0
$786$	−7.10316	−	5.66458i	−0.253361	−	0.202049i
$787$	−41.0735	+	32.7550i	−1.46411	+	1.16759i	−0.513143	+	0.858303i	$0.671519\pi$
$787$	−41.0735	+	32.7550i	−1.46411	+	1.16759i	−0.950969	+	0.309287i	$0.899910\pi$
$788$	6.68234	−	13.8760i	0.238049	−	0.494313i
$789$	−2.08411	+	1.00365i	−0.0741963	+	0.0357310i
$790$		0			0
$791$	−8.30476	+	1.89551i	−0.295283	+	0.0673965i
$792$	2.89453	−	0.660658i	0.102853	−	0.0234755i
$793$	−3.14585	−	3.94478i	−0.111713	−	0.140083i
$794$	−10.2521	−	2.33996i	−0.363832	−	0.0830422i
$795$		0			0
$796$	−4.63860	+	20.3230i	−0.164411	+	0.720330i
$797$	31.9667	−	15.3944i	1.13232	−	0.545297i	0.228643	−	0.973510i	$-0.426571\pi$
$797$	31.9667	−	15.3944i	1.13232	−	0.545297i	0.903677	+	0.428214i	$0.140857\pi$
$798$	4.33269	−	2.08652i	0.153376	−	0.0738619i
$799$	0.929561	−	4.07267i	0.0328855	−	0.144081i
$800$		0			0
$801$	20.6523	+	4.71376i	0.729715	+	0.166553i
$802$	4.66522	+	5.85000i	0.164735	+	0.206571i
$803$	−4.74586	+	1.08321i	−0.167478	+	0.0382257i
$804$	1.21395	−	0.277075i	0.0428126	−	0.00977169i
$805$		0			0
$806$	−19.3100	+	9.29921i	−0.680166	+	0.327551i
$807$	8.47876	−	17.6063i	0.298466	−	0.619772i
$808$	−14.0551	+	11.2086i	−0.494457	+	0.394316i
$809$	−32.8345	−	26.1846i	−1.15440	−	0.920602i	−0.156649	−	0.987654i	$-0.550069\pi$
$809$	−32.8345	−	26.1846i	−1.15440	−	0.920602i	−0.997749	+	0.0670520i	$0.978641\pi$
$810$		0			0
$811$	−5.37514			−0.188747			−0.0943734	−	0.995537i	$-0.530085\pi$
$811$	−5.37514			−0.188747			−0.0943734	+	0.995537i	$0.530085\pi$
$812$	4.82644	+	5.67519i	0.169375	+	0.199160i
$813$			5.60009i			0.196404i
$814$	−0.212229	+	0.440698i	−0.00743861	+	0.0154464i
$815$		0			0
$816$	−0.996452	−	1.24951i	−0.0348828	−	0.0437416i
$817$	1.23871	−	2.57221i	0.0433370	−	0.0899902i
$818$	10.4514	+	21.7026i	0.365425	+	0.758813i
$819$	−5.35005	+	6.70874i	−0.186946	+	0.234423i
$820$		0			0
$821$	2.33803	+	10.2436i	0.0815980	+	0.357504i	0.999200	−	0.0399967i	$-0.0127347\pi$
$821$	2.33803	+	10.2436i	0.0815980	+	0.357504i	−0.917602	+	0.397501i	$0.869878\pi$
$822$	−10.9875	−	13.7779i	−0.383234	−	0.480561i
$823$	3.31962	−	14.5442i	0.115715	−	0.506979i	−0.883539	−	0.468357i	$-0.844846\pi$
$823$	3.31962	−	14.5442i	0.115715	−	0.506979i	0.999254	−	0.0386220i	$-0.0122968\pi$
$824$			9.98824i			0.347957i
$825$		0			0
$826$	−6.10290	−	12.6728i	−0.212347	−	0.440943i
$827$	9.22685	−	4.44342i	0.320849	−	0.154513i	−0.266526	−	0.963828i	$-0.585876\pi$
$827$	9.22685	−	4.44342i	0.320849	−	0.154513i	0.587375	+	0.809315i	$0.300161\pi$
$828$	17.7973	+	4.06212i	0.618500	+	0.141169i
$829$			34.0988i			1.18430i	0.805828	+	0.592150i	$0.201721\pi$
$829$			34.0988i			1.18430i	−0.805828	+	0.592150i	$0.798279\pi$
$830$		0			0
$831$	11.9183	−	9.50456i	0.413443	−	0.329710i
$832$	−21.4898	+	4.90492i	−0.745026	+	0.170047i
$833$	−3.26141	−	14.2892i	−0.113001	−	0.495090i
$834$	−11.0000	+	13.7936i	−0.380899	+	0.477633i
$835$		0			0
$836$	−2.04457	−	0.984611i	−0.0707128	−	0.0340535i
$837$	25.4010	−	20.2566i	0.877987	−	0.700171i
$838$	6.27454	−	7.86802i	0.216750	−	0.271796i
$839$	15.8828	−	32.9809i	0.548334	−	1.13863i	−0.424136	−	0.905599i	$-0.639422\pi$
$839$	15.8828	−	32.9809i	0.548334	−	1.13863i	0.972470	−	0.233029i	$-0.0748637\pi$
$840$		0			0
$841$	4.65715	−	28.6236i	0.160592	−	0.987021i
$842$			26.7160i			0.920696i
$843$	−5.82898	−	2.80709i	−0.200761	−	0.0966812i
$844$	8.20791	+	6.54559i	0.282528	+	0.225308i
$845$		0			0
$846$	−2.53941	−	1.22291i	−0.0873066	−	0.0420446i
$847$	−5.82793	−	12.1018i	−0.200250	−	0.415824i
$848$	−3.24134	−	2.58488i	−0.111308	−	0.0887653i
$849$	−3.58270	+	0.817728i	−0.122958	+	0.0280644i
$850$		0			0
$851$	−6.60905	+	5.27054i	−0.226555	+	0.180672i
$852$	3.69053	−	16.1693i	0.126436	−	0.553951i
$853$	−20.6146			−0.705831			−0.352916	−	0.935655i	$-0.614810\pi$
$853$	−20.6146			−0.705831			−0.352916	+	0.935655i	$0.614810\pi$
$854$	−0.373733	+	1.63743i	−0.0127889	+	0.0560318i
$855$		0			0
$856$	3.19752	+	6.63972i	0.109289	+	0.226941i
$857$	9.66332	+	2.20559i	0.330093	+	0.0753415i	0.384355	−	0.923185i	$-0.374424\pi$
$857$	9.66332	+	2.20559i	0.330093	+	0.0753415i	−0.0542628	+	0.998527i	$0.517281\pi$
$858$	1.83567			0.0626688
$859$	−24.5044	−	5.59296i	−0.836078	−	0.190829i	−0.217013	−	0.976169i	$-0.569631\pi$
$859$	−24.5044	−	5.59296i	−0.836078	−	0.190829i	−0.619065	+	0.785339i	$0.712488\pi$
$860$		0			0
$861$	−1.11754	−	4.89625i	−0.0380856	−	0.166864i
$862$	−1.37158	−	6.00930i	−0.0467163	−	0.204677i
$863$	−25.2286	−	20.1192i	−0.858792	−	0.684864i	0.0916410	−	0.995792i	$-0.470789\pi$
$863$	−25.2286	−	20.1192i	−0.858792	−	0.684864i	−0.950433	+	0.310928i	$0.899360\pi$
$864$	24.5517	−	11.8235i	0.835267	−	0.402243i
$865$		0			0
$866$	−20.5893	−	25.8182i	−0.699653	−	0.877337i
$867$	−6.28461	+	7.88065i	−0.213436	+	0.267641i
$868$	−7.92849	−	3.81816i	−0.269110	−	0.129597i
$869$	−0.921129			−0.0312471
$870$		0			0
$871$	−3.86977			−0.131122
$872$	−40.3442	−	19.4287i	−1.36623	−	0.657940i
$873$	1.70233	−	2.13466i	0.0576153	−	0.0722473i
$874$	19.8239	+	24.8584i	0.670554	+	0.840849i
$875$		0			0
$876$	−9.56662	+	4.60704i	−0.323226	+	0.155658i
$877$	4.93601	+	3.93633i	0.166677	+	0.132921i	0.703276	−	0.710917i	$-0.251720\pi$
$877$	4.93601	+	3.93633i	0.166677	+	0.132921i	−0.536599	+	0.843837i	$0.680291\pi$
$878$	0.635133	+	2.78270i	0.0214347	+	0.0939115i
$879$	−1.21829	−	5.33767i	−0.0410918	−	0.180035i
$880$		0			0
$881$	−23.1828	−	5.29132i	−0.781048	−	0.178269i	−0.186635	−	0.982429i	$-0.559758\pi$
$881$	−23.1828	−	5.29132i	−0.781048	−	0.178269i	−0.594413	+	0.804160i	$0.702615\pi$
$882$	−9.88894			−0.332978
$883$	32.1139	+	7.32980i	1.08072	+	0.246667i	0.725574	−	0.688144i	$-0.241574\pi$
$883$	32.1139	+	7.32980i	1.08072	+	0.246667i	0.355146	+	0.934811i	$0.384431\pi$
$884$	−4.60479	−	9.56194i	−0.154876	−	0.321603i
$885$		0			0
$886$	5.22684	−	22.9003i	0.175599	−	0.769350i
$887$	−43.3425			−1.45530			−0.727650	−	0.685949i	$-0.759387\pi$
$887$	−43.3425			−1.45530			−0.727650	+	0.685949i	$0.759387\pi$
$888$	−0.667308	+	2.92367i	−0.0223934	+	0.0981119i
$889$	20.3056	−	16.1932i	0.681027	−	0.543101i
$890$		0			0
$891$	0.242928	−	0.0554467i	0.00813838	−	0.00185753i
$892$	−3.91590	−	3.12283i	−0.131114	−	0.104560i
$893$	2.62724	+	5.45552i	0.0879173	+	0.182562i
$894$	4.51104	+	2.17240i	0.150872	+	0.0726560i
$895$		0			0
$896$	−4.71254	−	3.75812i	−0.157435	−	0.125550i
$897$	28.5825	+	13.7646i	0.954341	+	0.459586i
$898$			29.0105i			0.968092i
$899$	8.67227	+	33.1390i	0.289237	+	1.10525i
$900$		0			0
$901$	8.50193	−	17.6544i	0.283241	−	0.588155i
$902$	1.19795	−	1.50218i	0.0398873	−	0.0500171i
$903$	−0.741346	+	0.591204i	−0.0246705	+	0.0196740i
$904$	−18.0014	−	8.66902i	−0.598718	−	0.288327i
$905$		0			0
$906$	−6.47352	+	8.11753i	−0.215068	+	0.269687i
$907$	8.09603	+	35.4710i	0.268824	+	1.17780i	0.911383	+	0.411560i	$0.135016\pi$
$907$	8.09603	+	35.4710i	0.268824	+	1.17780i	−0.642558	+	0.766237i	$0.722127\pi$
$908$	10.1972	−	2.32744i	0.338405	−	0.0772387i
$909$	−9.20530	+	7.34098i	−0.305321	+	0.243485i
$910$		0			0
$911$		−	37.4585i		−	1.24105i	−0.784185	−	0.620527i	$-0.786919\pi$
$911$		−	37.4585i		−	1.24105i	0.784185	−	0.620527i	$-0.213081\pi$
$912$	2.25849	+	0.515487i	0.0747862	+	0.0170695i
$913$	4.71903	−	2.27256i	0.156177	−	0.0752109i
$914$	16.9943	+	35.2890i	0.562121	+	1.16726i
$915$		0			0
$916$			16.6001i			0.548482i
$917$	−2.57974	+	11.3026i	−0.0851904	+	0.373244i
$918$	−8.13214	−	10.1974i	−0.268401	−	0.336564i
$919$	0.276896	+	1.21316i	0.00913396	+	0.0400185i	0.979290	−	0.202465i	$-0.0648952\pi$
$919$	0.276896	+	1.21316i	0.00913396	+	0.0400185i	−0.970156	+	0.242483i	$0.922038\pi$
$920$		0			0
$921$	3.18987	−	3.99998i	0.105110	−	0.131804i
$922$	13.7526	+	28.5575i	0.452916	+	0.940490i
$923$	−22.3640	+	46.4394i	−0.736121	+	1.52857i
$924$	0.469929	+	0.589272i	0.0154595	+	0.0193856i
$925$		0			0
$926$	−6.39979	+	13.2893i	−0.210310	+	0.436713i
$927$			6.54174i			0.214859i
$928$	0.906464	+	28.7172i	0.0297561	+	0.942687i
$929$	−1.41593			−0.0464553			−0.0232276	−	0.999730i	$-0.507394\pi$
$929$	−1.41593			−0.0464553			−0.0232276	+	0.999730i	$0.507394\pi$
$930$		0			0
$931$	16.6099	+	13.2460i	0.544367	+	0.434119i
$932$	1.52698	−	1.21773i	0.0500180	−	0.0398880i
$933$	4.59801	−	9.54787i	0.150532	−	0.312583i
$934$	2.30815	−	1.11154i	0.0755248	−	0.0363708i
$935$		0			0
$936$	−19.6220	+	4.47859i	−0.641364	+	0.146387i
$937$	−5.56559	+	1.27031i	−0.181820	+	0.0414992i	−0.312461	−	0.949930i	$-0.601153\pi$
$937$	−5.56559	+	1.27031i	−0.181820	+	0.0414992i	0.130641	+	0.991430i	$0.458296\pi$
$938$	0.803150	+	1.00712i	0.0262238	+	0.0328836i
$939$	−13.2518	−	3.02464i	−0.432456	−	0.0987053i
$940$		0			0
$941$	10.4782	−	45.9079i	0.341579	−	1.49655i	−0.454163	−	0.890919i	$-0.650062\pi$
$941$	10.4782	−	45.9079i	0.341579	−	1.49655i	0.795742	−	0.605636i	$-0.207081\pi$
$942$	12.9314	−	6.22746i	0.421329	−	0.202901i
$943$	29.9167	−	14.4071i	0.974221	−	0.469160i
$944$	1.50776	−	6.60592i	0.0490734	−	0.215004i
$945$		0			0
$946$	−0.353670	−	0.0807228i	−0.0114988	−	0.00262452i
$947$	−11.0563	−	13.8641i	−0.359280	−	0.450523i	0.569037	−	0.822312i	$-0.307316\pi$
$947$	−11.0563	−	13.8641i	−0.359280	−	0.450523i	−0.928317	+	0.371789i	$0.878745\pi$
$948$	−1.95884	+	0.447092i	−0.0636202	+	0.0145209i
$949$	32.1721	−	7.34307i	1.04435	−	0.238366i
$950$		0			0
$951$	30.3337	−	14.6079i	0.983637	−	0.473695i
$952$	−4.30834	+	8.94636i	−0.139634	+	0.289953i
$953$	−16.9715	+	13.5343i	−0.549759	+	0.438418i	−0.858563	−	0.512707i	$-0.828643\pi$
$953$	−16.9715	+	13.5343i	−0.549759	+	0.438418i	0.308804	+	0.951126i	$0.400071\pi$
$954$	−10.3365	−	8.24308i	−0.334656	−	0.266879i
$955$		0			0
$956$	4.24429			0.137270
$957$	0.562287	−	2.87951i	0.0181762	−	0.0930815i
$958$			29.9422i			0.967389i
$959$	−9.75686	+	20.2603i	−0.315066	+	0.654240i
$960$		0			0
$961$	−5.89950	−	7.39773i	−0.190306	−	0.238637i
$962$	1.43869	−	2.98748i	0.0463854	−	0.0963202i
$963$	2.09420	+	4.34865i	0.0674846	+	0.140133i
$964$	−18.7100	+	23.4616i	−0.602610	+	0.755649i
$965$		0			0
$966$	−2.34986	−	10.2954i	−0.0756057	−	0.331250i
$967$	−7.90790	−	9.91619i	−0.254301	−	0.318883i	0.638251	−	0.769829i	$-0.279658\pi$
$967$	−7.90790	−	9.91619i	−0.254301	−	0.318883i	−0.892552	+	0.450945i	$0.851087\pi$
$968$	7.01058	−	30.7154i	0.225329	−	0.987229i
$969$			10.9491i			0.351736i
$970$		0			0
$971$	−9.82588	−	20.4036i	−0.315327	−	0.654784i	0.681717	−	0.731616i	$-0.261234\pi$
$971$	−9.82588	−	20.4036i	−0.315327	−	0.654784i	−0.997044	+	0.0768323i	$0.975519\pi$
$972$	15.7380	−	7.57903i	0.504797	−	0.243097i
$973$	21.9484	+	5.00957i	0.703633	+	0.160600i
$974$		−	25.4817i		−	0.816487i
$975$		0			0
$976$	−0.632561	+	0.504451i	−0.0202478	+	0.0161471i
$977$	−4.31901	+	0.985785i	−0.138177	+	0.0315381i	−0.291050	−	0.956708i	$-0.594005\pi$
$977$	−4.31901	+	0.985785i	−0.138177	+	0.0315381i	0.152873	+	0.988246i	$0.451148\pi$
$978$	−4.61987	−	20.2410i	−0.147727	−	0.647235i
$979$	−3.60545	+	4.52109i	−0.115231	+	0.144495i
$980$		0			0
$981$	−26.4232	−	12.7247i	−0.843628	−	0.406270i
$982$	1.13670	−	0.906487i	0.0362735	−	0.0289272i
$983$	10.5490	−	13.2281i	0.336462	−	0.421909i	−0.584603	−	0.811320i	$-0.698750\pi$
$983$	10.5490	−	13.2281i	0.336462	−	0.421909i	0.921064	+	0.389410i	$0.127321\pi$
$984$	5.11101	−	10.6131i	0.162933	−	0.338334i
$985$		0			0
$986$	13.3038	−	3.48153i	0.423680	−	0.110875i
$987$		−	2.01112i		−	0.0640147i
$988$	13.8601	+	6.67466i	0.440948	+	0.212349i
$989$	−4.90155	−	3.90886i	−0.155860	−	0.124294i
$990$		0			0
$991$	−26.2839	−	12.6577i	−0.834936	−	0.402084i	−0.0329722	−	0.999456i	$-0.510497\pi$
$991$	−26.2839	−	12.6577i	−0.834936	−	0.402084i	−0.801964	+	0.597372i	$0.796212\pi$
$992$	−14.7250	−	30.5768i	−0.467520	−	0.970815i
$993$	−23.4280	−	18.6832i	−0.743465	−	0.592894i
$994$	16.7275	−	3.81794i	0.530564	−	0.121098i
$995$		0			0
$996$	8.93228	−	7.12325i	0.283030	−	0.225709i
$997$	−5.67119	+	24.8471i	−0.179608	+	0.786915i	0.802202	+	0.597052i	$0.203662\pi$
$997$	−5.67119	+	24.8471i	−0.179608	+	0.786915i	−0.981811	+	0.189863i	$0.939196\pi$
$998$	23.6943			0.750030
$999$	−1.11849	+	4.90041i	−0.0353874	+	0.155042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.p.b.274.4		48
5.2	odd	4		725.2.q.b.651.3		24
5.3	odd	4		145.2.m.a.71.2	✓	24
5.4	even	2	inner	725.2.p.b.274.5		48
29.9	even	14	inner	725.2.p.b.299.5		48
145.3	even	28		4205.2.a.y.1.10		24
145.9	even	14	inner	725.2.p.b.299.4		48
145.38	odd	28		145.2.m.a.96.2	yes	24
145.67	odd	28		725.2.q.b.676.3		24
145.113	even	28		4205.2.a.y.1.15		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.m.a.71.2	✓	24	5.3	odd	4
145.2.m.a.96.2	yes	24	145.38	odd	28
725.2.p.b.274.4		48	1.1	even	1	trivial
725.2.p.b.274.5		48	5.4	even	2	inner
725.2.p.b.299.4		48	145.9	even	14	inner
725.2.p.b.299.5		48	29.9	even	14	inner
725.2.q.b.651.3		24	5.2	odd	4
725.2.q.b.676.3		24	145.67	odd	28
4205.2.a.y.1.10		24	145.3	even	28
4205.2.a.y.1.15		24	145.113	even	28

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:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.p (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.852581 - 0.410581i) q^{2} +(0.646721 - 0.810963i) q^{3} +(-0.688663 - 0.863556i) q^{4} +(-0.884348 + 0.425880i) q^{6} +(0.979248 + 0.780924i) q^{7} +(0.653721 + 2.86414i) q^{8} +(0.428151 + 1.87585i) q^{9} +O(q^{10})\)	\(q+(-0.852581 - 0.410581i) q^{2} +(0.646721 - 0.810963i) q^{3} +(-0.688663 - 0.863556i) q^{4} +(-0.884348 + 0.425880i) q^{6} +(0.979248 + 0.780924i) q^{7} +(0.653721 + 2.86414i) q^{8} +(0.428151 + 1.87585i) q^{9} +(-0.512072 - 0.116877i) q^{11} -1.14568 q^{12} +(3.47133 + 0.792308i) q^{13} +(-0.514255 - 1.06786i) q^{14} +(0.127050 - 0.556642i) q^{16} +2.69858 q^{17} +(0.405156 - 1.77510i) q^{18} +(-3.05822 + 2.43885i) q^{19} +(1.26660 - 0.289093i) q^{21} +(0.388595 + 0.309894i) q^{22} +(3.72694 + 7.73907i) q^{23} +(2.74548 + 1.32216i) q^{24} +(-2.63428 - 2.10077i) q^{26} +(4.60176 + 2.21609i) q^{27} -1.38343i q^{28} +(-4.10226 + 3.48876i) q^{29} +(2.75993 - 5.73104i) q^{31} +(3.32650 - 4.17130i) q^{32} +(-0.425951 + 0.339685i) q^{33} +(-2.30076 - 1.10799i) q^{34} +(1.32505 - 1.66156i) q^{36} +(0.218987 + 0.959443i) q^{37} +(3.60872 - 0.823668i) q^{38} +(2.88751 - 2.30271i) q^{39} -3.86567i q^{41} +(-1.19858 - 0.273567i) q^{42} +(-0.657583 + 0.316675i) q^{43} +(0.251715 + 0.522692i) q^{44} -8.12840i q^{46} +(0.344462 - 1.50919i) q^{47} +(-0.369250 - 0.463025i) q^{48} +(-1.20856 - 5.29506i) q^{49} +(1.74523 - 2.18845i) q^{51} +(-1.70637 - 3.54332i) q^{52} +(3.15052 - 6.54212i) q^{53} +(-3.01348 - 3.77879i) q^{54} +(-1.59652 + 3.31521i) q^{56} +4.05736i q^{57} +(4.92993 - 1.29013i) q^{58} +11.8675 q^{59} +(-1.10790 - 0.883518i) q^{61} +(-4.70612 + 3.75300i) q^{62} +(-1.04563 + 2.17127i) q^{63} +(-5.57760 + 2.68603i) q^{64} +(0.502626 - 0.114721i) q^{66} +(-1.05958 + 0.241843i) q^{67} +(-1.85841 - 2.33038i) q^{68} +(8.68639 + 1.98261i) q^{69} +(-3.22125 + 14.1132i) q^{71} +(-5.09280 + 2.45256i) q^{72} +(8.35014 - 4.02121i) q^{73} +(0.207225 - 0.907914i) q^{74} +(4.21216 + 0.961399i) q^{76} +(-0.410173 - 0.514341i) q^{77} +(-3.40729 + 0.777692i) q^{78} +(1.70976 - 0.390241i) q^{79} +(-0.427421 + 0.205835i) q^{81} +(-1.58717 + 3.29579i) q^{82} +(-7.79646 + 6.21747i) q^{83} +(-1.12191 - 0.894692i) q^{84} +0.690664 q^{86} +(0.176230 + 5.58304i) q^{87} -1.54305i q^{88} +(4.77688 - 9.91930i) q^{89} +(2.78056 + 3.48671i) q^{91} +(4.11652 - 8.54803i) q^{92} +(-2.86276 - 5.94458i) q^{93} +(-0.913327 + 1.14528i) q^{94} +(-1.23145 - 5.39534i) q^{96} +(-0.884747 - 1.10944i) q^{97} +(-1.14365 + 5.01068i) q^{98} -1.01061i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{6} + 8 q^{9}+O(q^{10}) \) 48 * q + 8 * q^6 + 8 * q^9	\( 48 q + 8 q^{6} + 8 q^{9} - 28 q^{11} + 84 q^{14} - 20 q^{16} + 98 q^{21} - 76 q^{24} - 14 q^{29} + 14 q^{31} - 40 q^{34} - 56 q^{36} - 14 q^{39} + 42 q^{44} + 4 q^{49} + 12 q^{51} - 214 q^{54} - 84 q^{56} + 132 q^{59} + 112 q^{61} - 66 q^{64} - 140 q^{66} + 56 q^{69} + 106 q^{71} - 66 q^{74} - 84 q^{76} + 112 q^{79} - 58 q^{81} - 28 q^{84} + 60 q^{86} - 28 q^{89} - 62 q^{91} + 76 q^{94} - 2 q^{96}+O(q^{100}) \) 48 * q + 8 * q^6 + 8 * q^9 - 28 * q^11 + 84 * q^14 - 20 * q^16 + 98 * q^21 - 76 * q^24 - 14 * q^29 + 14 * q^31 - 40 * q^34 - 56 * q^36 - 14 * q^39 + 42 * q^44 + 4 * q^49 + 12 * q^51 - 214 * q^54 - 84 * q^56 + 132 * q^59 + 112 * q^61 - 66 * q^64 - 140 * q^66 + 56 * q^69 + 106 * q^71 - 66 * q^74 - 84 * q^76 + 112 * q^79 - 58 * q^81 - 28 * q^84 + 60 * q^86 - 28 * q^89 - 62 * q^91 + 76 * q^94 - 2 * q^96

Introduction

L-functions

Modular forms

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Database

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