LMFDB - Embedded newform 348.2.t.a.35.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [348,2,Mod(35,348)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(348, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 7, 3]))

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

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

chi := DirichletCharacter("348.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 348 = 2^{2} \cdot 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	348.t (of order $14$, degree $6$, 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:	$2.77879399034$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			35.20
Character	$\chi$	$=$	348.35
Dual form			348.2.t.a.179.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.713912 + 1.22079i) q^{2} +(1.50908 + 0.850111i) q^{3} +(-0.980658 - 1.74307i) q^{4} +(-0.0130888 - 0.0104380i) q^{5} +(-2.11516 + 1.23536i) q^{6} +(-1.19888 - 0.273637i) q^{7} +(2.82803 + 0.0472247i) q^{8} +(1.55462 + 2.56576i) q^{9} +O(q^{10})$	\(q+(-0.713912 + 1.22079i) q^{2} +(1.50908 + 0.850111i) q^{3} +(-0.980658 - 1.74307i) q^{4} +(-0.0130888 - 0.0104380i) q^{5} +(-2.11516 + 1.23536i) q^{6} +(-1.19888 - 0.273637i) q^{7} +(2.82803 + 0.0472247i) q^{8} +(1.55462 + 2.56576i) q^{9} +(0.0220869 - 0.00852690i) q^{10} +(1.88267 + 3.90941i) q^{11} +(0.00191925 - 3.46410i) q^{12} +(-4.69979 + 2.26330i) q^{13} +(1.18995 - 1.26823i) q^{14} +(-0.0108786 - 0.0268787i) q^{15} +(-2.07662 + 3.41872i) q^{16} +5.22108 q^{17} +(-4.24213 + 0.0661365i) q^{18} +(1.61228 + 7.06386i) q^{19} +(-0.00535853 + 0.0330509i) q^{20} +(-1.57658 - 1.43212i) q^{21} +(-6.11663 - 0.492628i) q^{22} +(2.25888 + 2.83255i) q^{23} +(4.22757 + 2.47541i) q^{24} +(-1.11254 - 4.87437i) q^{25} +(0.592225 - 7.35326i) q^{26} +(0.164858 + 5.19354i) q^{27} +(0.698724 + 2.35809i) q^{28} +(-3.94752 - 3.66294i) q^{29} +(0.0405796 + 0.00590855i) q^{30} +(5.24283 - 6.57430i) q^{31} +(-2.69102 - 4.97578i) q^{32} +(-0.482336 + 7.50008i) q^{33} +(-3.72740 + 6.37385i) q^{34} +(0.0128357 + 0.0160955i) q^{35} +(2.94777 - 5.22596i) q^{36} +(3.15176 - 6.54470i) q^{37} +(-9.77452 - 3.07472i) q^{38} +(-9.01640 - 0.579852i) q^{39} +(-0.0365227 - 0.0301371i) q^{40} -0.0543453 q^{41} +(2.87386 - 0.902267i) q^{42} +(-4.07614 - 5.11131i) q^{43} +(4.96813 - 7.11543i) q^{44} +(0.00643325 - 0.0498100i) q^{45} +(-5.07059 + 0.735430i) q^{46} +(3.52148 + 7.31244i) q^{47} +(-6.04007 + 3.39375i) q^{48} +(-4.94434 - 2.38107i) q^{49} +(6.74484 + 2.12169i) q^{50} +(7.87901 + 4.43850i) q^{51} +(8.55399 + 5.97257i) q^{52} +(-1.91915 - 1.53047i) q^{53} +(-6.45791 - 3.50647i) q^{54} +(0.0161644 - 0.0708209i) q^{55} +(-3.37755 - 0.830471i) q^{56} +(-3.57201 + 12.0305i) q^{57} +(7.28986 - 2.20407i) q^{58} +0.258155 q^{59} +(-0.0361834 + 0.0453210i) q^{60} +(-3.82638 - 0.873347i) q^{61} +(4.28292 + 11.0939i) q^{62} +(-1.16172 - 3.50145i) q^{63} +(7.99554 + 0.267106i) q^{64} +(0.0851391 + 0.0194324i) q^{65} +(-8.81167 - 5.94323i) q^{66} +(1.22496 - 2.54365i) q^{67} +(-5.12010 - 9.10074i) q^{68} +(1.00084 + 6.19483i) q^{69} +(-0.0288128 + 0.00417896i) q^{70} +(-1.48393 + 0.714624i) q^{71} +(4.27536 + 7.32948i) q^{72} +(5.40896 - 4.31350i) q^{73} +(5.73963 + 8.51998i) q^{74} +(2.46484 - 8.30158i) q^{75} +(10.7317 - 9.73756i) q^{76} +(-1.18734 - 5.20209i) q^{77} +(7.14480 - 10.5932i) q^{78} +(3.22970 + 1.55534i) q^{79} +(0.0628651 - 0.0230713i) q^{80} +(-4.16630 + 7.97759i) q^{81} +(0.0387978 - 0.0663443i) q^{82} +(-3.70237 - 16.2211i) q^{83} +(-0.950207 + 4.15252i) q^{84} +(-0.0683379 - 0.0544976i) q^{85} +(9.14985 - 1.32708i) q^{86} +(-2.84320 - 8.88348i) q^{87} +(5.13964 + 11.1448i) q^{88} +(4.98478 - 6.25072i) q^{89} +(0.0562148 + 0.0434136i) q^{90} +(6.25382 - 1.42739i) q^{91} +(2.72215 - 6.71516i) q^{92} +(13.5007 - 5.46413i) q^{93} +(-11.4410 - 0.921446i) q^{94} +(0.0526297 - 0.109287i) q^{95} +(0.169019 - 9.79650i) q^{96} +(13.5839 - 3.10045i) q^{97} +(6.43661 - 4.33613i) q^{98} +(-7.10378 + 10.9081i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9}+O(q^{10}) $ 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9	$ 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9} - 14 q^{10} - 20 q^{13} - 26 q^{16} - 56 q^{18} - 14 q^{21} - 40 q^{22} + 3 q^{24} + 40 q^{25} - 36 q^{28} - 6 q^{30} - 22 q^{33} - 8 q^{34} + 9 q^{36} - 28 q^{37} - 14 q^{40} - 74 q^{42} - 22 q^{45} + 14 q^{48} + 4 q^{49} - 4 q^{52} - 31 q^{54} - 12 q^{57} - 106 q^{58} - 42 q^{60} - 28 q^{61} - 94 q^{64} - 7 q^{66} - 14 q^{69} + 70 q^{72} - 28 q^{73} - 84 q^{76} - 9 q^{78} - 50 q^{81} - 46 q^{82} - 35 q^{84} - 168 q^{85} - 60 q^{88} + 119 q^{90} + 122 q^{93} + 36 q^{94} + 2 q^{96} - 28 q^{97}+O(q^{100}) $ 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9 - 14 * q^10 - 20 * q^13 - 26 * q^16 - 56 * q^18 - 14 * q^21 - 40 * q^22 + 3 * q^24 + 40 * q^25 - 36 * q^28 - 6 * q^30 - 22 * q^33 - 8 * q^34 + 9 * q^36 - 28 * q^37 - 14 * q^40 - 74 * q^42 - 22 * q^45 + 14 * q^48 + 4 * q^49 - 4 * q^52 - 31 * q^54 - 12 * q^57 - 106 * q^58 - 42 * q^60 - 28 * q^61 - 94 * q^64 - 7 * q^66 - 14 * q^69 + 70 * q^72 - 28 * q^73 - 84 * q^76 - 9 * q^78 - 50 * q^81 - 46 * q^82 - 35 * q^84 - 168 * q^85 - 60 * q^88 + 119 * q^90 + 122 * q^93 + 36 * q^94 + 2 * q^96 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/348\mathbb{Z}\right)^\times$.

$n$	$175$	$205$	$233$
$\chi(n)$	$-1$	$e\left(\frac{3}{14}\right)$	$-1$

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 $

$2$	−0.713912	+	1.22079i	−0.504812	+	0.863229i
$2$	−0.713912	+	1.22079i	−0.504812	+	0.863229i
$3$	1.50908	+	0.850111i	0.871266	+	0.490812i
$3$	1.50908	+	0.850111i	0.871266	+	0.490812i
$4$	−0.980658	−	1.74307i	−0.490329	−	0.871537i
$5$	−0.0130888	−	0.0104380i	−0.00585350	−	0.00466801i	0.620559	−	0.784160i	$-0.286906\pi$
$5$	−0.0130888	−	0.0104380i	−0.00585350	−	0.00466801i	−0.626412	+	0.779492i	$0.715477\pi$
$6$	−2.11516	+	1.23536i	−0.863509	+	0.504334i
$7$	−1.19888	−	0.273637i	−0.453135	−	0.103425i	−0.0101387	−	0.999949i	$-0.503227\pi$
$7$	−1.19888	−	0.273637i	−0.453135	−	0.103425i	−0.442996	+	0.896524i	$0.646084\pi$
$8$	2.82803	+	0.0472247i	0.999861	+	0.0166965i
$9$	1.55462	+	2.56576i	0.518207	+	0.855255i
$10$	0.0220869	−	0.00852690i	0.00698448	−	0.00269644i
$11$	1.88267	+	3.90941i	0.567647	+	1.17873i	0.965287	+	0.261190i	$0.0841148\pi$
$11$	1.88267	+	3.90941i	0.567647	+	1.17873i	−0.397640	+	0.917541i	$0.630171\pi$
$12$	0.00191925	−	3.46410i	0.000554041	−	1.00000i
$13$	−4.69979	+	2.26330i	−1.30349	+	0.627727i	−0.951319	−	0.308209i	$-0.900270\pi$
$13$	−4.69979	+	2.26330i	−1.30349	+	0.627727i	−0.352170	+	0.935936i	$0.614556\pi$
$14$	1.18995	−	1.26823i	0.318028	−	0.338949i
$15$	−0.0108786	−	0.0268787i	−0.00280884	−	0.00694005i
$16$	−2.07662	+	3.41872i	−0.519155	+	0.854680i
$17$	5.22108			1.26630			0.633149	−	0.774030i	$-0.281762\pi$
$17$	5.22108			1.26630			0.633149	+	0.774030i	$0.281762\pi$
$18$	−4.24213	+	0.0661365i	−0.999878	+	0.0155885i
$19$	1.61228	+	7.06386i	0.369883	+	1.62056i	0.727094	+	0.686538i	$0.240870\pi$
$19$	1.61228	+	7.06386i	0.369883	+	1.62056i	−0.357212	+	0.934023i	$0.616273\pi$
$20$	−0.00535853	+	0.0330509i	−0.00119820	+	0.00739041i
$21$	−1.57658	−	1.43212i	−0.344038	−	0.312515i
$22$	−6.11663	−	0.492628i	−1.30407	−	0.105029i
$23$	2.25888	+	2.83255i	0.471009	+	0.590627i	0.959418	−	0.281988i	$-0.0909938\pi$
$23$	2.25888	+	2.83255i	0.471009	+	0.590627i	−0.488408	+	0.872615i	$0.662422\pi$
$24$	4.22757	+	2.47541i	0.862949	+	0.505290i
$25$	−1.11254	−	4.87437i	−0.222508	−	0.974873i
$26$	0.592225	−	7.35326i	0.116145	−	1.44209i
$27$	0.164858	+	5.19354i	0.0317270	+	0.999497i
$28$	0.698724	+	2.35809i	0.132046	+	0.445636i
$29$	−3.94752	−	3.66294i	−0.733035	−	0.680191i
$29$	−3.94752	−	3.66294i	−0.733035	−	0.680191i
$30$	0.0405796	+	0.00590855i	0.00740879	+	0.00107875i
$31$	5.24283	−	6.57430i	0.941640	−	1.18078i	−0.0417231	−	0.999129i	$-0.513285\pi$
$31$	5.24283	−	6.57430i	0.941640	−	1.18078i	0.983363	−	0.181650i	$-0.0581438\pi$
$32$	−2.69102	−	4.97578i	−0.475709	−	0.879603i
$33$	−0.482336	+	7.50008i	−0.0839639	+	1.30560i
$34$	−3.72740	+	6.37385i	−0.639243	+	1.09311i
$35$	0.0128357	+	0.0160955i	0.00216964	+	0.00272064i
$36$	2.94777	−	5.22596i	0.491294	−	0.870994i
$37$	3.15176	−	6.54470i	0.518147	−	1.07594i	−0.463652	−	0.886017i	$-0.653461\pi$
$37$	3.15176	−	6.54470i	0.518147	−	1.07594i	0.981799	−	0.189925i	$-0.0608245\pi$
$38$	−9.77452	−	3.07472i	−1.58564	−	0.498786i
$39$	−9.01640	−	0.579852i	−1.44378	−	0.0928507i
$40$	−0.0365227	−	0.0301371i	−0.00577475	−	0.00476509i
$41$	−0.0543453			−0.00848731			−0.00424366	−	0.999991i	$-0.501351\pi$
$41$	−0.0543453			−0.00848731			−0.00424366	+	0.999991i	$0.501351\pi$
$42$	2.87386	−	0.902267i	0.443447	−	0.139223i
$43$	−4.07614	−	5.11131i	−0.621605	−	0.779468i	0.366964	−	0.930235i	$-0.380397\pi$
$43$	−4.07614	−	5.11131i	−0.621605	−	0.779468i	−0.988569	+	0.150767i	$0.951826\pi$
$44$	4.96813	−	7.11543i	0.748974	−	1.07269i
$45$	0.00643325	−	0.0498100i	0.000959012	−	0.00742523i
$46$	−5.07059	+	0.735430i	−0.747618	+	0.108433i
$47$	3.52148	+	7.31244i	0.513661	+	1.06663i	0.982999	+	0.183610i	$0.0587783\pi$
$47$	3.52148	+	7.31244i	0.513661	+	1.06663i	−0.469338	+	0.883019i	$0.655507\pi$
$48$	−6.04007	+	3.39375i	−0.871809	+	0.489846i
$49$	−4.94434	−	2.38107i	−0.706335	−	0.340153i
$50$	6.74484	+	2.12169i	0.953864	+	0.300052i
$51$	7.87901	+	4.43850i	1.10328	+	0.621515i
$52$	8.55399	+	5.97257i	1.18623	+	0.828246i
$53$	−1.91915	−	1.53047i	−0.263615	−	0.210226i	0.482758	−	0.875754i	$-0.339635\pi$
$53$	−1.91915	−	1.53047i	−0.263615	−	0.210226i	−0.746373	+	0.665528i	$0.768207\pi$
$54$	−6.45791	−	3.50647i	−0.878811	−	0.477170i
$55$	0.0161644	−	0.0708209i	0.00217961	−	0.00954949i
$56$	−3.37755	−	0.830471i	−0.451345	−	0.110976i
$57$	−3.57201	+	12.0305i	−0.473125	+	1.59348i
$58$	7.28986	−	2.20407i	0.957206	−	0.289409i
$59$	0.258155			0.0336089			0.0168044	−	0.999859i	$-0.494651\pi$
$59$	0.258155			0.0336089			0.0168044	+	0.999859i	$0.494651\pi$
$60$	−0.0361834	+	0.0453210i	−0.00467125	+	0.00585091i
$61$	−3.82638	−	0.873347i	−0.489918	−	0.111821i	−0.0295767	−	0.999563i	$-0.509416\pi$
$61$	−3.82638	−	0.873347i	−0.489918	−	0.111821i	−0.460342	+	0.887742i	$0.652273\pi$
$62$	4.28292	+	11.0939i	0.543932	+	1.40892i
$63$	−1.16172	−	3.50145i	−0.146363	−	0.441141i
$64$	7.99554	+	0.267106i	0.999442	+	0.0333883i
$65$	0.0851391	+	0.0194324i	0.0105602	+	0.00241030i
$66$	−8.81167	−	5.94323i	−1.08464	−	0.731561i
$67$	1.22496	−	2.54365i	0.149653	−	0.310757i	−0.812643	−	0.582761i	$-0.801972\pi$
$67$	1.22496	−	2.54365i	0.149653	−	0.310757i	0.962296	+	0.272005i	$0.0876866\pi$
$68$	−5.12010	−	9.10074i	−0.620903	−	1.10363i
$69$	1.00084	+	6.19483i	0.120488	+	0.745770i
$70$	−0.0288128	+	0.00417896i	−0.00344379	+	0.000499482i
$71$	−1.48393	+	0.714624i	−0.176110	+	0.0848103i	−0.519862	−	0.854250i	$-0.674017\pi$
$71$	−1.48393	+	0.714624i	−0.176110	+	0.0848103i	0.343751	+	0.939061i	$0.388302\pi$
$72$	4.27536	+	7.32948i	0.503855	+	0.863788i
$73$	5.40896	−	4.31350i	0.633071	−	0.504857i	−0.253569	−	0.967317i	$-0.581605\pi$
$73$	5.40896	−	4.31350i	0.633071	−	0.504857i	0.886640	+	0.462460i	$0.153033\pi$
$74$	5.73963	+	8.51998i	0.667218	+	0.990428i
$75$	2.46484	−	8.30158i	0.284615	−	0.958583i
$76$	10.7317	−	9.73756i	1.23102	−	1.11697i
$77$	−1.18734	−	5.20209i	−0.135310	−	0.592833i
$78$	7.14480	−	10.5932i	0.808989	−	1.19944i
$79$	3.22970	+	1.55534i	0.363370	+	0.174990i	0.606655	−	0.794965i	$-0.292511\pi$
$79$	3.22970	+	1.55534i	0.363370	+	0.174990i	−0.243285	+	0.969955i	$0.578225\pi$
$80$	0.0628651	−	0.0230713i	0.00702853	−	0.00257945i
$81$	−4.16630	+	7.97759i	−0.462922	+	0.886399i
$82$	0.0387978	−	0.0663443i	0.00428450	−	0.00732650i
$83$	−3.70237	−	16.2211i	−0.406388	−	1.78050i	−0.600608	−	0.799544i	$-0.705075\pi$
$83$	−3.70237	−	16.2211i	−0.406388	−	1.78050i	0.194220	−	0.980958i	$-0.437782\pi$
$84$	−0.950207	+	4.15252i	−0.103676	+	0.453077i
$85$	−0.0683379	−	0.0544976i	−0.00741228	−	0.00591110i
$86$	9.14985	−	1.32708i	0.986653	−	0.143102i
$87$	−2.84320	−	8.88348i	−0.304823	−	0.952409i
$88$	5.13964	+	11.1448i	0.547887	+	1.18804i
$89$	4.98478	−	6.25072i	0.528386	−	0.662575i	−0.443980	−	0.896037i	$-0.646434\pi$
$89$	4.98478	−	6.25072i	0.528386	−	0.662575i	0.972366	+	0.233461i	$0.0750053\pi$
$90$	0.0562148	+	0.0434136i	0.00592556	+	0.00457620i
$91$	6.25382	−	1.42739i	0.655578	−	0.149631i
$92$	2.72215	−	6.71516i	0.283804	−	0.700104i
$93$	13.5007	−	5.46413i	1.39996	−	0.566604i
$94$	−11.4410	−	0.921446i	−1.18005	−	0.0950399i
$95$	0.0526297	−	0.109287i	0.00539969	−	0.0112126i
$96$	0.169019	−	9.79650i	0.0172504	−	0.999851i
$97$	13.5839	−	3.10045i	1.37924	−	0.314803i	0.532330	−	0.846537i	$-0.321317\pi$
$97$	13.5839	−	3.10045i	1.37924	−	0.314803i	0.846911	+	0.531735i	$0.178460\pi$
$98$	6.43661	−	4.33613i	0.650196	−	0.438015i
$99$	−7.10378	+	10.9081i	−0.713957	+	1.09631i
$100$	−7.40536	+	6.71933i	−0.740536	+	0.671933i
$101$	9.85657	+	12.3597i	0.980765	+	1.22984i	0.973222	+	0.229869i	$0.0738298\pi$
$101$	9.85657	+	12.3597i	0.980765	+	1.22984i	0.00754360	+	0.999972i	$0.497599\pi$
$102$	−11.0434	+	6.44992i	−1.09346	+	0.638638i
$103$	−1.27626	−	2.65018i	−0.125754	−	0.261130i	0.828581	−	0.559869i	$-0.189148\pi$
$103$	−1.27626	−	2.65018i	−0.125754	−	0.261130i	−0.954335	+	0.298738i	$0.903434\pi$
$104$	−13.3981	+	6.17874i	−1.31379	+	0.605876i
$105$	0.00568714	+	0.0352011i	0.000555008	+	0.00343528i
$106$	3.23849	−	1.25026i	0.314550	−	0.121436i
$107$	7.02710	+	3.38407i	0.679336	+	0.327151i	0.741536	−	0.670913i	$-0.234098\pi$
$107$	7.02710	+	3.38407i	0.679336	+	0.327151i	−0.0622006	+	0.998064i	$0.519812\pi$
$108$	8.89105	−	5.38044i	0.855542	−	0.517734i
$109$	−1.20917	+	5.29770i	−0.115817	+	0.507428i	0.883428	+	0.468568i	$0.155230\pi$
$109$	−1.20917	+	5.29770i	−0.115817	+	0.507428i	−0.999245	+	0.0388601i	$0.987627\pi$
$110$	0.0749175	+	0.0702933i	0.00714310	+	0.00670220i
$111$	10.3200	−	7.19711i	0.979528	−	0.683119i
$112$	3.42511	−	3.53040i	0.323642	−	0.333592i
$113$	0.0697760	−	0.305709i	0.00656397	−	0.0287587i	−0.971540	−	0.236876i	$-0.923876\pi$
$113$	0.0697760	−	0.305709i	0.00656397	−	0.0287587i	0.978104	+	0.208117i	$0.0667336\pi$
$114$	−12.1366	−	12.9494i	−1.13670	−	1.21282i
$115$		−	0.0606529i		−	0.00565591i
$116$	−2.51361	+	10.4729i	−0.233383	+	0.972385i
$117$	−13.1135	−	8.53999i	−1.21234	−	0.789522i
$118$	−0.184300	+	0.315153i	−0.0169662	+	0.0290122i
$119$	−6.25946	−	1.42868i	−0.573804	−	0.130967i
$120$	−0.0294957	−	0.0765275i	−0.00269257	−	0.00698598i
$121$	−4.88063	+	6.12012i	−0.443694	+	0.556375i
$122$	3.79788	−	4.04772i	0.343844	−	0.366463i
$123$	−0.0820113	−	0.0461996i	−0.00739471	−	0.00416567i
$124$	−16.6009	−	2.69150i	−1.49081	−	0.241704i
$125$	−0.0726355	+	0.150829i	−0.00649671	+	0.0134906i
$126$	5.10390	+	1.08151i	0.454692	+	0.0963488i
$127$	0.865660	−	0.416880i	0.0768149	−	0.0369921i	−0.395082	−	0.918646i	$-0.629284\pi$
$127$	0.865660	−	0.416880i	0.0768149	−	0.0369921i	0.471897	+	0.881654i	$0.343569\pi$
$128$	−6.03420	+	9.57019i	−0.533353	+	0.845893i
$129$	−1.80602	−	11.1785i	−0.159011	−	0.984215i
$130$	−0.0845048	+	0.0900639i	−0.00741156	+	0.00789913i
$131$	−4.99754	+	3.98541i	−0.436637	+	0.348207i	−0.817007	−	0.576628i	$-0.804368\pi$
$131$	−4.99754	+	3.98541i	−0.436637	+	0.348207i	0.380369	+	0.924835i	$0.375797\pi$
$132$	13.5462	−	6.51426i	1.17905	−	0.566994i
$133$		−	8.90992i		−	0.772588i
$134$	2.23075	+	3.31136i	0.192708	+	0.286058i
$135$	0.0520523	−	0.0696981i	0.00447995	−	0.00599866i
$136$	14.7654	+	0.246564i	1.26612	+	0.0211427i
$137$	−2.36277	−	1.13785i	−0.201865	−	0.0972130i	0.330220	−	0.943904i	$-0.392877\pi$
$137$	−2.36277	−	1.13785i	−0.201865	−	0.0972130i	−0.532085	+	0.846691i	$0.678591\pi$
$138$	−8.27711	−	3.20075i	−0.704594	−	0.272466i
$139$	−14.0337	+	11.1915i	−1.19032	+	0.949248i	−0.999476	−	0.0323728i	$-0.989694\pi$
$139$	−14.0337	+	11.1915i	−1.19032	+	0.949248i	−0.190843	+	0.981621i	$0.561122\pi$
$140$	0.0154682	−	0.0381578i	0.00130730	−	0.00322493i
$141$	−0.902196	+	14.0287i	−0.0759786	+	1.18143i
$142$	0.186991	−	2.32175i	0.0156920	−	0.194837i
$143$	−17.6963	−	14.1124i	−1.47984	−	1.18013i
$144$	−12.0000	−	0.0132970i	−0.999999	−	0.00110808i
$145$	0.0134346	+	0.0891477i	0.00111569	+	0.00740331i
$146$	1.40436	+	9.68267i	0.116225	+	0.801344i
$147$	−5.43721	−	7.79645i	−0.448454	−	0.643041i
$148$	−14.4987	+	0.924358i	−1.19179	+	0.0759817i
$149$	−4.42960	+	1.01103i	−0.362887	+	0.0828265i	−0.400077	−	0.916482i	$-0.631016\pi$
$149$	−4.42960	+	1.01103i	−0.362887	+	0.0828265i	0.0371900	+	0.999308i	$0.488159\pi$
$150$	8.37480	+	8.93565i	0.683800	+	0.729593i
$151$	−2.30773	+	1.84035i	−0.187800	+	0.149766i	−0.712877	−	0.701289i	$-0.752608\pi$
$151$	−2.30773	+	1.84035i	−0.187800	+	0.149766i	0.525076	+	0.851055i	$0.324037\pi$
$152$	4.22599	+	20.0530i	0.342773	+	1.62651i
$153$	8.11681	+	13.3961i	0.656205	+	1.08301i
$154$	7.19832	+	2.26434i	0.580057	+	0.182466i
$155$	−0.137245	+	0.0313253i	−0.0110238	+	0.00251611i
$156$	7.83128	+	16.2849i	0.627004	+	1.30384i
$157$		−	14.4768i		−	1.15537i	−0.816259	−	0.577686i	$-0.803956\pi$
$157$		−	14.4768i		−	1.15537i	0.816259	−	0.577686i	$-0.196044\pi$
$158$	−4.20447	+	2.83241i	−0.334490	+	0.225335i
$159$	−1.59507	−	3.94109i	−0.126497	−	0.312548i
$160$	−0.0167149	+	0.0932160i	−0.00132143	+	0.00736937i
$161$	−1.93304	−	4.01400i	−0.152345	−	0.316348i
$162$	−6.76459	−	10.7815i	−0.531477	−	0.847073i
$163$	−13.9499	+	6.71792i	−1.09264	+	0.526188i	−0.891337	−	0.453341i	$-0.850232\pi$
$163$	−13.9499	+	6.71792i	−1.09264	+	0.526188i	−0.201303	+	0.979529i	$0.564518\pi$
$164$	0.0532942	+	0.0947280i	0.00416158	+	0.00739701i
$165$	0.0845989	−	0.0931326i	0.00658602	−	0.00725036i
$166$	22.4458	+	7.06066i	1.74213	+	0.548013i
$167$	4.53081	−	19.8508i	0.350605	−	1.53610i	−0.425185	−	0.905107i	$-0.639791\pi$
$167$	4.53081	−	19.8508i	0.350605	−	1.53610i	0.775789	−	0.630992i	$-0.217352\pi$
$168$	−4.39100	−	4.12454i	−0.338773	−	0.318215i
$169$	8.86016	−	11.1103i	0.681550	−	0.854637i
$170$	0.115317	−	0.0445197i	0.00884444	−	0.00341450i
$171$	−15.6177	+	15.1184i	−1.19432	+	1.15613i
$172$	−4.91210	+	12.1175i	−0.374544	+	0.923948i
$173$			11.1618i			0.848617i	0.905518	+	0.424308i	$0.139483\pi$
$173$			11.1618i			0.848617i	−0.905518	+	0.424308i	$0.860517\pi$
$174$	12.8747	+	2.87108i	0.976026	+	0.217656i
$175$			6.14822i			0.464762i
$176$	−17.2748	−	1.68202i	−1.30213	−	0.126787i
$177$	0.389575	+	0.219460i	0.0292823	+	0.0164956i
$178$	4.07212	+	10.5478i	0.305218	+	0.790594i
$179$	3.42647	−	4.29666i	0.256106	−	0.321147i	−0.637111	−	0.770772i	$-0.719871\pi$
$179$	3.42647	−	4.29666i	0.256106	−	0.321147i	0.893218	+	0.449625i	$0.148442\pi$
$180$	−0.0931313	+	0.0376329i	−0.00694160	+	0.00280499i
$181$	−0.266474	+	1.16750i	−0.0198068	+	0.0867794i	−0.983865	−	0.178911i	$-0.942743\pi$
$181$	−0.266474	+	1.16750i	−0.0198068	+	0.0867794i	0.964058	+	0.265690i	$0.0855998\pi$
$182$	−2.72213	+	8.65364i	−0.201778	+	0.641450i
$183$	−5.03186	−	4.57080i	−0.371966	−	0.337883i
$184$	6.25443	+	8.11722i	0.461082	+	0.598409i
$185$	−0.109566	+	0.0527644i	−0.00805548	+	0.00387932i
$186$	−2.96777	+	20.3825i	−0.217607	+	1.49451i
$187$	9.82959	+	20.4114i	0.718811	+	1.49263i
$188$	9.29275	−	13.3092i	0.677744	−	0.970674i
$189$	1.22350	−	6.27155i	0.0889964	−	0.456188i
$190$	0.0958431	+	0.142271i	0.00695319	+	0.0103214i
$191$			10.3772i			0.750865i	0.926850	+	0.375433i	$0.122506\pi$
$191$			10.3772i			0.750865i	−0.926850	+	0.375433i	$0.877494\pi$
$192$	11.8388	+	7.20018i	0.854392	+	0.519628i
$193$	−15.1723	+	3.46297i	−1.09212	+	0.249270i	−0.730403	−	0.683016i	$-0.760668\pi$
$193$	−15.1723	+	3.46297i	−1.09212	+	0.249270i	−0.361721	+	0.932286i	$0.617811\pi$
$194$	−5.91275	+	18.7966i	−0.424511	+	1.34952i
$195$	0.111962	+	0.101703i	0.00801774	+	0.00728308i
$196$	0.698327	+	10.9534i	0.0498805	+	0.782384i
$197$	18.1108	−	14.4429i	1.29034	−	1.02901i	0.292999	−	0.956113i	$-0.405347\pi$
$197$	18.1108	−	14.4429i	1.29034	−	1.02901i	0.997339	−	0.0728980i	$-0.0232248\pi$
$198$	−8.24509	−	16.4597i	−0.585953	−	1.16974i
$199$	−2.56281	+	0.584944i	−0.181673	+	0.0414656i	−0.312389	−	0.949954i	$-0.601129\pi$
$199$	−2.56281	+	0.584944i	−0.181673	+	0.0414656i	0.130717	+	0.991420i	$0.458272\pi$
$200$	−2.91612	−	13.8374i	−0.206201	−	0.978452i
$201$	4.01094	−	2.79722i	0.282910	−	0.197300i
$202$	−22.1254	+	3.20903i	−1.55674	+	0.225786i
$203$	3.73029	+	5.47162i	0.261815	+	0.384032i
$204$	0.0100206	−	18.0864i	0.000701581	−	1.26630i
$205$	0.000711317	0	0.000567256i	4.96805e−5	0	3.96189e-5i
$206$	4.14646	+	0.333952i	0.288897	+	0.0232675i
$207$	−3.75595	+	10.1993i	−0.261056	+	0.708901i
$208$	2.02209	−	20.7673i	0.140206	−	1.43995i
$209$	−24.5801	+	19.6020i	−1.70024	+	1.35590i
$210$	−0.0470333	−	0.0181877i	−0.00324561	−	0.00125507i
$211$	14.3212	+	6.89672i	0.985911	+	0.474790i	0.856134	−	0.516753i	$-0.172860\pi$
$211$	14.3212	+	6.89672i	0.985911	+	0.474790i	0.129777	+	0.991543i	$0.458574\pi$
$212$	−0.785695	+	4.84609i	−0.0539618	+	0.332831i
$213$	−2.84688	−	0.183085i	−0.195065	−	0.0125448i
$214$	−9.14798	+	6.16269i	−0.625343	+	0.421273i
$215$			0.109448i			0.00746427i
$216$	0.220962	+	14.6953i	0.0150346	+	0.999887i
$217$	−8.08451	+	6.44718i	−0.548812	+	0.437663i
$218$	−5.60414	−	5.25823i	−0.379561	−	0.356132i
$219$	11.8295	−	1.91119i	0.799363	−	0.129146i
$220$	−0.139298	+	0.0412753i	−0.00939146	+	0.00278278i
$221$	−24.5380	+	11.8169i	−1.65061	+	0.794890i
$222$	1.41860	+	17.7366i	0.0952102	+	1.19040i
$223$	11.9480	−	24.8102i	0.800095	−	1.66141i	0.0512334	−	0.998687i	$-0.483685\pi$
$223$	11.9480	−	24.8102i	0.800095	−	1.66141i	0.748861	−	0.662727i	$-0.230601\pi$
$224$	1.86465	+	6.70174i	0.124587	+	0.447779i
$225$	10.7769	−	10.4323i	0.718460	−	0.695488i
$226$	0.323392	+	0.303431i	0.0215117	+	0.0201839i
$227$	0.0699544	−	0.0877200i	0.00464304	−	0.00582218i	−0.779505	−	0.626397i	$-0.784529\pi$
$227$	0.0699544	−	0.0877200i	0.00464304	−	0.00582218i	0.784148	+	0.620574i	$0.213101\pi$
$228$	24.4730	−	5.57155i	1.62077	−	0.368985i
$229$	−5.69697	−	1.30030i	−0.376466	−	0.0859260i	0.0301009	−	0.999547i	$-0.490417\pi$
$229$	−5.69697	−	1.30030i	−0.376466	−	0.0859260i	−0.406567	+	0.913621i	$0.633274\pi$
$230$	0.0740445	+	0.0433009i	0.00488235	+	0.00285518i
$231$	2.63056	−	8.85972i	0.173078	−	0.582927i
$232$	−10.9907	−	10.5453i	−0.721576	−	0.692335i
$233$			8.01731i			0.525231i	0.964901	+	0.262616i	$0.0845851\pi$
$233$			8.01731i			0.525231i	−0.964901	+	0.262616i	$0.915415\pi$
$234$	19.7874	−	9.91203i	1.29354	−	0.647970i
$235$	0.0302351	−	0.132468i	0.00197232	−	0.00864129i
$236$	−0.253162	−	0.449983i	−0.0164794	−	0.0292914i
$237$	3.55165	+	5.09274i	0.230705	+	0.330809i
$238$	6.21283	−	6.62154i	0.402718	−	0.429211i
$239$	−1.64535	+	7.20874i	−0.106429	+	0.466294i	0.893425	+	0.449212i	$0.148295\pi$
$239$	−1.64535	+	7.20874i	−0.106429	+	0.466294i	−0.999854	+	0.0170828i	$0.994562\pi$
$240$	0.114481	+	0.0186259i	0.00738974	+	0.00120230i
$241$	−10.7585	−	5.18102i	−0.693015	−	0.333739i	0.0540041	−	0.998541i	$-0.482802\pi$
$241$	−10.7585	−	5.18102i	−0.693015	−	0.333739i	−0.747020	+	0.664802i	$0.768516\pi$
$242$	−3.98704	−	10.3275i	−0.256297	−	0.663874i
$243$	−13.0691	+	8.49698i	−0.838383	+	0.545081i
$244$	2.23007	+	7.52613i	0.142765	+	0.481811i
$245$	0.0398620	+	0.0827744i	0.00254669	+	0.00528826i
$246$	0.114949	−	0.0671361i	0.00732887	−	0.00428044i
$247$	−23.5650	−	29.5496i	−1.49941	−	1.88020i
$248$	15.1374	−	18.3447i	0.961224	−	1.16489i
$249$	8.20261	−	27.6264i	0.519820	−	1.75075i
$250$	−0.132275	−	0.196351i	−0.00836583	−	0.0124184i
$251$	8.65277	−	1.97494i	0.546158	−	0.124657i	0.0594656	−	0.998230i	$-0.481060\pi$
$251$	8.65277	−	1.97494i	0.546158	−	0.124657i	0.486693	+	0.873573i	$0.338203\pi$
$252$	−4.96404	+	5.45869i	−0.312705	+	0.343865i
$253$	−6.82086	+	14.1637i	−0.428824	+	0.890461i
$254$	−0.109082	+	1.35440i	−0.00684444	+	0.0849829i
$255$	−0.0567980	−	0.140336i	−0.00355683	−	0.00878817i
$256$	−7.37530	−	14.1988i	−0.460957	−	0.887423i
$257$	15.9492	−	3.64030i	0.994883	−	0.227076i	0.306066	−	0.952010i	$-0.400987\pi$
$257$	15.9492	−	3.64030i	0.994883	−	0.227076i	0.688818	+	0.724935i	$0.258130\pi$
$258$	14.9360	+	5.77572i	0.929873	+	0.359581i
$259$	−5.56946	+	6.98389i	−0.346070	+	0.433958i
$260$	−0.0496201	−	0.167460i	−0.00307731	−	0.0103855i
$261$	3.26134	−	15.8229i	0.201872	−	0.979412i
$262$	−1.29754	−	8.94619i	−0.0801623	−	0.552697i
$263$	−8.54078	−	6.81105i	−0.526647	−	0.419987i	0.323739	−	0.946146i	$-0.395060\pi$
$263$	−8.54078	−	6.81105i	−0.526647	−	0.419987i	−0.850386	+	0.526159i	$0.823632\pi$
$264$	−1.71825	+	21.1877i	−0.105751	+	1.30401i
$265$	0.00914437	+	0.0400641i	0.000561734	+	0.00246112i
$266$	10.8771	+	6.36090i	0.666920	+	0.390012i
$267$	12.8362	−	5.19520i	0.785564	−	0.317941i
$268$	−5.63504	+	0.359259i	−0.344215	+	0.0219453i
$269$	−9.77544	−	4.70760i	−0.596019	−	0.287028i	0.111452	−	0.993770i	$-0.464450\pi$
$269$	−9.77544	−	4.70760i	−0.596019	−	0.287028i	−0.707471	+	0.706742i	$0.750164\pi$
$270$	0.0479260	+	0.113303i	0.00291668	+	0.00689542i
$271$	−1.87474	−	8.21379i	−0.113883	−	0.498952i	−0.999409	−	0.0343638i	$-0.989060\pi$
$271$	−1.87474	−	8.21379i	−0.113883	−	0.498952i	0.885527	−	0.464588i	$-0.153798\pi$
$272$	−10.8422	+	17.8494i	−0.657405	+	1.08228i
$273$	10.6509	+	3.16240i	0.644624	+	0.191397i
$274$	3.07589	−	2.07212i	0.185821	−	0.125181i
$275$	16.9613	−	13.5262i	1.02281	−	0.815661i
$276$	9.81657	−	7.81956i	0.590888	−	0.470682i
$277$	7.31179	−	3.52117i	0.439323	−	0.211567i	−0.201129	−	0.979565i	$-0.564461\pi$
$277$	7.31179	−	3.52117i	0.439323	−	0.211567i	0.640452	+	0.767998i	$0.278747\pi$
$278$	−3.64363	−	25.1219i	−0.218531	−	1.50671i
$279$	25.0187	+	3.23131i	1.49783	+	0.193454i
$280$	0.0355398	+	0.0461248i	0.00212391	+	0.00275648i
$281$	8.00867	−	16.6302i	0.477757	−	0.992073i	−0.513247	−	0.858241i	$-0.671557\pi$
$281$	8.00867	−	16.6302i	0.477757	−	0.992073i	0.991004	−	0.133832i	$-0.0427282\pi$
$282$	−16.4820	−	11.1166i	−0.981488	−	0.661986i
$283$	17.2953	+	3.94753i	1.02810	+	0.234656i	0.703124	−	0.711067i	$-0.251788\pi$
$283$	17.2953	+	3.94753i	1.02810	+	0.234656i	0.324973	+	0.945723i	$0.394645\pi$
$284$	2.70087	+	1.88580i	0.160267	+	0.111902i
$285$	0.172328	−	0.120181i	0.0102078	−	0.00711890i
$286$	29.8619	−	11.5285i	1.76577	−	0.681696i
$287$	0.0651536	+	0.0148709i	0.00384590	+	0.000877801i
$288$	8.58318	−	14.6400i	0.505769	−	0.862669i
$289$	10.2597			0.603513
$290$	−0.118422	−	0.0472428i	−0.00695397	−	0.00277419i
$291$	23.1349	+	6.86905i	1.35619	+	0.402671i
$292$	−12.8231	−	5.19815i	−0.750415	−	0.304199i
$293$	−0.510425	+	2.23632i	−0.0298194	+	0.130647i	−0.987647	−	0.156697i	$-0.949915\pi$
$293$	−0.510425	+	2.23632i	−0.0298194	+	0.130647i	0.957827	+	0.287344i	$0.0927724\pi$
$294$	13.3995	−	1.07171i	0.781477	−	0.0625036i
$295$	−0.00337894	−	0.00269462i	−0.000196730	−	0.000156887i
$296$	9.22236	−	18.3598i	0.536039	−	1.06714i
$297$	−19.9933	+	10.4222i	−1.16013	+	0.604759i
$298$	1.92809	−	6.12939i	0.111691	−	0.355066i
$299$	−17.0272	−	8.19986i	−0.984708	−	0.474210i
$300$	−16.8874	+	3.84460i	−0.974996	+	0.221968i
$301$	3.48816	+	7.24324i	0.201054	+	0.417494i
$302$	−0.599168	−	4.13111i	−0.0344783	−	0.237718i
$303$	4.36716	+	27.0310i	0.250887	+	1.55289i
$304$	−27.4975	−	9.15702i	−1.57709	−	0.525191i
$305$	0.0409669	+	0.0513709i	0.00234576	+	0.00294149i
$306$	−22.1485	+	0.345304i	−1.26615	+	0.0197397i
$307$	−25.3866			−1.44889			−0.724444	−	0.689334i	$-0.757903\pi$
$307$	−25.3866			−1.44889			−0.724444	+	0.689334i	$0.757903\pi$
$308$	−7.90325	+	7.17110i	−0.450330	+	0.408611i
$309$	0.326975	−	5.08429i	0.0186010	−	0.289235i
$310$	0.0597393	−	0.189911i	0.00339296	−	0.0107862i
$311$	−6.45557	+	13.4051i	−0.366062	+	0.760135i	−0.999911	−	0.0133211i	$-0.995760\pi$
$311$	−6.45557	+	13.4051i	−0.366062	+	0.760135i	0.633849	+	0.773457i	$0.281474\pi$
$312$	−25.4713	−	2.06564i	−1.44203	−	0.116944i
$313$	4.74049	+	5.94438i	0.267948	+	0.335996i	0.897543	−	0.440928i	$-0.145350\pi$
$313$	4.74049	+	5.94438i	0.267948	+	0.335996i	−0.629595	+	0.776924i	$0.716779\pi$
$314$	17.6731	+	10.3352i	0.997351	+	0.583246i
$315$	−0.0213426	+	0.0579559i	−0.00120252	+	0.00326545i
$316$	−0.456155	−	7.15487i	−0.0256607	−	0.402493i
$317$	−19.9355	+	24.9983i	−1.11969	+	1.40405i	−0.215717	+	0.976456i	$0.569209\pi$
$317$	−19.9355	+	24.9983i	−1.11969	+	1.40405i	−0.903972	+	0.427591i	$0.859362\pi$
$318$	5.94998	+	0.866341i	0.333658	+	0.0485820i
$319$	6.88805	−	22.3286i	0.385657	−	1.25016i
$320$	−0.101864	−	0.0869535i	−0.00569438	−	0.00486085i
$321$	7.72759	+	11.0806i	0.431312	+	0.618461i
$322$	6.28028	+	0.505808i	0.349986	+	0.0281876i
$323$	8.41785	+	36.8810i	0.468382	+	2.05211i
$324$	17.9913	−	0.561119i	0.999514	−	0.0311733i
$325$	16.2609	+	20.3905i	0.901991	+	1.13106i
$326$	1.75784	−	21.8259i	0.0973576	−	1.20882i
$327$	−6.32836	+	6.96671i	−0.349959	+	0.385260i
$328$	−0.153690	−	0.00256644i	−0.00848613	−	0.000141708i
$329$	−2.22089	−	9.73036i	−0.122442	−	0.536452i
$330$	0.0532991	+	0.169766i	0.00293402	+	0.00934531i
$331$	18.7029			1.02801			0.514003	−	0.857788i	$-0.328162\pi$
$331$	18.7029			1.02801			0.514003	+	0.857788i	$0.328162\pi$
$332$	−24.6439	+	22.3609i	−1.35251	+	1.22721i
$333$	21.6920	−	2.08786i	1.18871	−	0.114414i
$334$	20.9990	+	19.7029i	1.14902	+	1.07809i
$335$	−0.0425839	+	0.0205073i	−0.00232661	+	0.00112043i
$336$	8.16999	−	2.41592i	0.445709	−	0.131799i
$337$	4.63915	+	9.63329i	0.252711	+	0.524759i	0.988273	−	0.152698i	$-0.0487962\pi$
$337$	4.63915	+	9.63329i	0.252711	+	0.524759i	−0.735562	+	0.677457i	$0.763082\pi$
$338$	7.23795	+	18.7482i	0.393693	+	1.01977i
$339$	0.365184	−	0.402020i	0.0198341	−	0.0218347i
$340$	−0.0279774	+	0.172562i	−0.00151729	+	0.00935846i
$341$	35.5722	+	8.11911i	1.92634	+	0.439675i
$342$	−7.30668	−	29.8592i	−0.395100	−	1.61460i
$343$	12.0061	+	9.57457i	0.648270	+	0.516978i
$344$	−11.2861	−	14.6475i	−0.608504	−	0.789738i
$345$	0.0515617	−	0.0915299i	0.00277599	−	0.00492780i
$346$	−13.6262	−	7.96856i	−0.732551	−	0.428392i
$347$	−7.13824			−0.383201			−0.191600	−	0.981473i	$-0.561368\pi$
$347$	−7.13824			−0.383201			−0.191600	+	0.981473i	$0.561368\pi$
$348$	−12.6964	+	13.6676i	−0.680597	+	0.732658i
$349$	7.16194			0.383370			0.191685	−	0.981457i	$-0.438605\pi$
$349$	7.16194			0.383370			0.191685	+	0.981457i	$0.438605\pi$
$350$	−7.50569	−	4.38929i	−0.401196	−	0.234618i
$351$	−12.5293	−	24.0354i	−0.668767	−	1.28292i
$352$	14.3861	−	19.8881i	0.766780	−	1.06004i
$353$	−24.1085	−	19.2259i	−1.28317	−	1.02329i	−0.997895	−	0.0648442i	$-0.979345\pi$
$353$	−24.1085	−	19.2259i	−1.28317	−	1.02329i	−0.285271	−	0.958447i	$-0.592084\pi$
$354$	−0.546038	+	0.318914i	−0.0290216	+	0.0169501i
$355$	0.0268822	+	0.00613568i	0.00142676	+	0.000325648i
$356$	−15.7838	−	2.55903i	−0.836542	−	0.135628i
$357$	−8.23147	−	7.47723i	−0.435656	−	0.395737i
$358$	2.79912	+	7.25044i	0.147938	+	0.383198i
$359$	14.5898	+	30.2961i	0.770021	+	1.59897i	0.800429	+	0.599428i	$0.204605\pi$
$359$	14.5898	+	30.2961i	0.770021	+	1.59897i	−0.0304080	+	0.999538i	$0.509681\pi$
$360$	0.0205457	−	0.140560i	0.00108285	−	0.00740819i
$361$	−30.1803	+	14.5341i	−1.58844	+	0.764951i
$362$	−1.23503	−	1.15880i	−0.0649117	−	0.0609051i
$363$	−12.5680	+	5.08665i	−0.659651	+	0.266980i
$364$	−8.62091	−	9.50109i	−0.451859	−	0.497992i
$365$	−0.115821			−0.00606236
$366$	9.17230	−	2.87970i	0.479444	−	0.150524i
$367$	−3.82247	−	16.7473i	−0.199531	−	0.874203i	−0.971217	−	0.238198i	$-0.923443\pi$
$367$	−3.82247	−	16.7473i	−0.199531	−	0.874203i	0.771685	−	0.636004i	$-0.219414\pi$
$368$	−14.3745	+	1.84036i	−0.749324	+	0.0959355i
$369$	−0.0844865	−	0.139437i	−0.00439819	−	0.00725882i
$370$	0.0138065	−	0.171427i	0.000717768	−	0.00891205i
$371$	1.88204	+	2.36000i	0.0977106	+	0.122525i
$372$	−22.7640	−	18.1743i	−1.18026	−	0.942294i
$373$	−2.62448	−	11.4986i	−0.135890	−	0.595375i	−0.996313	−	0.0857935i	$-0.972657\pi$
$373$	−2.62448	−	11.4986i	−0.135890	−	0.595375i	0.860423	−	0.509581i	$-0.170200\pi$
$374$	−31.9354	−	2.57205i	−1.65134	−	0.132998i
$375$	−0.237834	+	0.165864i	−0.0122817	+	0.00856520i
$376$	9.61354	+	20.8461i	0.495781	+	1.07506i
$377$	26.8428	+	8.28064i	1.38248	+	0.426474i
$378$	6.78278	+	5.97097i	0.348868	+	0.307114i
$379$	18.0071	−	22.5802i	0.924965	−	1.15987i	−0.0618610	−	0.998085i	$-0.519704\pi$
$379$	18.0071	−	22.5802i	0.924965	−	1.15987i	0.986826	−	0.161785i	$-0.0517250\pi$
$380$	−0.242106	+	0.0154354i	−0.0124198	+	0.000791818i
$381$	1.66074	+	0.106804i	0.0850823	+	0.00547171i
$382$	−12.6683	−	7.40839i	−0.648169	−	0.379046i
$383$	−13.1462	−	16.4849i	−0.671741	−	0.842337i	0.322823	−	0.946459i	$-0.395368\pi$
$383$	−13.1462	−	16.4849i	−0.671741	−	0.842337i	−0.994564	+	0.104123i	$0.966797\pi$
$384$	−17.2418	+	9.31241i	−0.879866	+	0.475222i
$385$	−0.0387584	+	0.0804827i	−0.00197531	+	0.00410178i
$386$	6.60411	−	20.9944i	0.336141	−	1.06859i
$387$	6.77758	−	18.4046i	0.344524	−	0.935557i
$388$	−18.7255	−	20.6374i	−0.950644	−	1.04770i
$389$	4.42176			0.224192			0.112096	−	0.993697i	$-0.464244\pi$
$389$	4.42176			0.224192			0.112096	+	0.993697i	$0.464244\pi$
$390$	−0.204089	+	0.0640749i	−0.0103344	+	0.00324456i
$391$	11.7938	+	14.7890i	0.596439	+	0.747911i
$392$	−13.8703	−	6.96724i	−0.700557	−	0.351899i
$393$	−10.9297	+	1.76582i	−0.551331	+	0.0890737i
$394$	4.70220	+	32.4204i	0.236893	+	1.63332i
$395$	−0.0260384	−	0.0540692i	−0.00131013	−	0.00272052i
$396$	25.9801	+	1.68526i	1.30555	+	0.0846873i
$397$	18.4298	+	8.87533i	0.924966	+	0.445440i	0.834841	−	0.550490i	$-0.185559\pi$
$397$	18.4298	+	8.87533i	0.924966	+	0.445440i	0.0901244	+	0.995931i	$0.471274\pi$
$398$	1.11553	−	3.54625i	0.0559162	−	0.177757i
$399$	7.57442	−	13.4457i	0.379195	−	0.673129i
$400$	18.9744	+	6.31873i	0.948721	+	0.315937i
$401$	1.17531	+	0.937277i	0.0586921	+	0.0468054i	0.652396	−	0.757878i	$-0.273764\pi$
$401$	1.17531	+	0.937277i	0.0586921	+	0.0468054i	−0.593704	+	0.804683i	$0.702335\pi$
$402$	0.551351	+	6.89349i	0.0274989	+	0.343816i
$403$	−9.76059	+	42.7640i	−0.486210	+	2.13022i
$404$	11.8780	−	29.3014i	0.590954	−	1.45780i
$405$	0.137802	−	0.0609295i	0.00684744	−	0.00302761i
$406$	−9.34280	+	0.647647i	−0.463675	+	0.0321422i
$407$	31.5196			1.56237
$408$	22.0725	+	12.9243i	1.09275	+	0.639849i
$409$	11.9524	+	2.72806i	0.591008	+	0.134894i	0.507557	−	0.861618i	$-0.330549\pi$
$409$	11.9524	+	2.72806i	0.591008	+	0.134894i	0.0834509	+	0.996512i	$0.473406\pi$
$410$	−0.00120032		0.000463397i	−5.92795e−5		2.28856e-5i
$411$	−2.59830	−	3.72572i	−0.128165	−	0.183776i
$412$	−3.36789	+	4.82354i	−0.165924	+	0.237639i
$413$	−0.309497	−	0.0706407i	−0.0152294	−	0.00347600i
$414$	−9.76980	−	11.8666i	−0.480159	−	0.583213i
$415$	−0.120856	+	0.250961i	−0.00593261	+	0.0123192i
$416$	23.9089	+	17.2946i	1.17223	+	0.847936i
$417$	−30.6918	+	4.95861i	−1.50299	+	0.242824i
$418$	−6.38187	−	44.0013i	−0.312148	−	2.15217i
$419$	−20.9738	+	10.1005i	−1.02464	+	0.493440i	−0.869229	−	0.494410i	$-0.835384\pi$
$419$	−20.9738	+	10.1005i	−1.02464	+	0.493440i	−0.155410	+	0.987850i	$0.549670\pi$
$420$	0.0557811	−	0.0444334i	0.00272184	−	0.00216813i
$421$	1.43099	−	1.14118i	0.0697424	−	0.0556177i	−0.587998	−	0.808862i	$-0.700084\pi$
$421$	1.43099	−	1.14118i	0.0697424	−	0.0556177i	0.657741	+	0.753245i	$0.271512\pi$
$422$	−18.6435	+	12.5595i	−0.907552	+	0.611387i
$423$	−13.2874	+	20.4034i	−0.646056	+	0.992046i
$424$	−5.35514	−	4.41885i	−0.260069	−	0.214598i
$425$	−5.80868	−	25.4495i	−0.281762	−	1.23448i
$426$	2.25593	−	3.34473i	0.109300	−	0.162053i
$427$	4.34840	+	2.09408i	0.210434	+	0.101340i
$428$	−0.992491	−	15.5674i	−0.0479739	−	0.752478i
$429$	−14.7081	−	36.3405i	−0.710111	−	1.75453i
$430$	−0.133613	−	0.0781361i	−0.00644338	−	0.00376806i
$431$	5.31215	+	23.2740i	0.255877	+	1.12107i	0.925613	+	0.378471i	$0.123550\pi$
$431$	5.31215	+	23.2740i	0.255877	+	1.12107i	−0.669736	+	0.742599i	$0.733593\pi$
$432$	−18.0976	−	10.2214i	−0.870721	−	0.491777i
$433$	16.3572	+	13.0444i	0.786074	+	0.626873i	0.932015	−	0.362420i	$-0.118049\pi$
$433$	16.3572	+	13.0444i	0.786074	+	0.626873i	−0.145940	+	0.989293i	$0.546621\pi$
$434$	−2.09902	−	14.4722i	−0.100756	−	0.694688i
$435$	−0.0555116	+	0.145952i	−0.00266158	+	0.00699784i
$436$	10.4201	−	3.08757i	0.499031	−	0.147868i
$437$	−16.3668	+	20.5233i	−0.782929	+	0.981762i
$438$	−6.11206	+	15.8057i	−0.292046	+	0.755228i
$439$	−29.2397	+	6.67378i	−1.39554	+	0.318522i	−0.853176	−	0.521624i	$-0.825327\pi$
$439$	−29.2397	+	6.67378i	−1.39554	+	0.318522i	−0.542361	+	0.840146i	$0.682469\pi$
$440$	0.0490580	−	0.199520i	0.00233875	−	0.00951176i
$441$	−1.57732	−	16.3877i	−0.0751105	−	0.780366i
$442$	3.09205	−	38.3920i	0.147074	−	1.82612i
$443$	5.03723	−	10.4599i	0.239326	−	0.496965i	−0.746363	−	0.665539i	$-0.768202\pi$
$443$	5.03723	−	10.4599i	0.239326	−	0.496965i	0.985689	+	0.168574i	$0.0539161\pi$
$444$	−22.6655	−	10.9306i	−1.07566	−	0.518743i
$445$	−0.130490	+	0.0297835i	−0.00618582	+	0.00141187i
$446$	21.7582	+	32.2983i	1.03028	+	1.52937i
$447$	−7.54408	−	2.23993i	−0.356823	−	0.105945i
$448$	−9.51262	−	2.50810i	−0.449429	−	0.118497i
$449$	−4.44238	−	5.57057i	−0.209649	−	0.262891i	0.665878	−	0.746061i	$-0.268057\pi$
$449$	−4.44238	−	5.57057i	−0.209649	−	0.262891i	−0.875527	+	0.483169i	$0.839486\pi$
$450$	5.04192	+	20.6041i	0.237678	+	0.971286i
$451$	−0.102314	−	0.212458i	−0.00481780	−	0.0100043i
$452$	−0.601299	+	0.178171i	−0.0282827	+	0.00838045i
$453$	−5.04704	+	0.815406i	−0.237131	+	0.0383111i
$454$	0.0571465	+	0.148024i	0.00268202	+	0.00694711i
$455$	−0.0967543	−	0.0465944i	−0.00453591	−	0.00218438i
$456$	−10.6699	+	33.8540i	−0.499664	+	1.58536i
$457$	3.17161	−	13.8957i	0.148362	−	0.650015i	−0.844979	−	0.534800i	$-0.820387\pi$
$457$	3.17161	−	13.8957i	0.148362	−	0.650015i	0.993341	−	0.115215i	$-0.0367558\pi$
$458$	5.65452	−	6.02651i	0.264219	−	0.281600i
$459$	0.860740	+	27.1159i	0.0401759	+	1.26566i
$460$	−0.105723	+	0.0594798i	−0.00492934	+	0.00277326i
$461$	0.0882719	−	0.386745i	0.00411123	−	0.0180125i	−0.972831	−	0.231518i	$-0.925631\pi$
$461$	0.0882719	−	0.386745i	0.00411123	−	0.0180125i	0.976942	+	0.213505i	$0.0684880\pi$
$462$	8.93787	+	9.53643i	0.415827	+	0.443675i
$463$		−	14.9804i		−	0.696198i	−0.937458	−	0.348099i	$-0.886827\pi$
$463$		−	14.9804i		−	0.696198i	0.937458	−	0.348099i	$-0.113173\pi$
$464$	20.7201	−	5.88893i	0.961904	−	0.273387i
$465$	−0.233743	−	0.0694013i	−0.0108396	−	0.00321841i
$466$	−9.78745	−	5.72366i	−0.453395	−	0.265143i
$467$	25.6202	+	5.84765i	1.18556	+	0.270597i	0.769444	−	0.638714i	$-0.220533\pi$
$467$	25.6202	+	5.84765i	1.18556	+	0.270597i	0.416118	+	0.909311i	$0.363390\pi$
$468$	−2.02597	+	31.2326i	−0.0936506	+	1.44373i
$469$	−2.16462	+	2.71435i	−0.0999528	+	0.125337i
$470$	0.140131	+	0.131482i	0.00646376	+	0.00606479i
$471$	12.3069	−	21.8466i	0.567071	−	1.00664i
$472$	0.730070	+	0.0121913i	0.0336042	+	0.000561150i
$473$	12.3082	−	25.5582i	0.565931	−	1.17517i
$474$	−8.75273	+	0.700056i	−0.402026	+	0.0321546i
$475$	32.6381	−	15.7177i	1.49754	−	0.721177i
$476$	3.64809	+	12.3118i	0.167210	+	0.564309i
$477$	0.943275	−	7.30339i	0.0431896	−	0.334399i
$478$	−7.62572	−	7.15503i	−0.348792	−	0.327263i
$479$	−11.3554	+	9.05567i	−0.518844	+	0.413764i	−0.847588	−	0.530655i	$-0.821946\pi$
$479$	−11.3554	+	9.05567i	−0.518844	+	0.413764i	0.328744	+	0.944419i	$0.393375\pi$
$480$	−0.104468	+	0.126460i	−0.00476829	+	0.00577210i
$481$			37.8921i			1.72773i
$482$	14.0056	−	9.43507i	0.637936	−	0.429756i
$483$	0.495241	−	7.70074i	0.0225342	−	0.350396i
$484$	15.4541	+	2.50556i	0.702458	+	0.113889i
$485$	−0.210160	−	0.101208i	−0.00954289	−	0.00459561i
$486$	−1.04283	−	22.0207i	−0.0473039	−	0.998881i
$487$	−29.5055	+	23.5298i	−1.33702	+	1.06624i	−0.345210	+	0.938526i	$0.612192\pi$
$487$	−29.5055	+	23.5298i	−1.33702	+	1.06624i	−0.991811	+	0.127713i	$0.959236\pi$
$488$	−10.7799	−	2.65055i	−0.487983	−	0.119985i
$489$	−26.7624	−	1.72111i	−1.21024	−	0.0778315i
$490$	−0.129508	−	0.0104305i	−0.00585058	−	0.000471200i
$491$	3.49324	+	2.78577i	0.157648	+	0.125720i	0.699137	−	0.714988i	$-0.253568\pi$
$491$	3.49324	+	2.78577i	0.157648	+	0.125720i	−0.541489	+	0.840708i	$0.682139\pi$
$492$	−0.000104302		0.188258i	−4.70232e−6		0.00848731i
$493$	−20.6103	−	19.1245i	−0.928242	−	0.861325i
$494$	52.8973	−	7.67213i	2.37996	−	0.345185i
$495$	0.206839	−	0.0686257i	0.00929673	−	0.00308449i
$496$	11.5883	+	31.5761i	0.520332	+	1.41781i
$497$	1.97461	−	0.450691i	0.0885732	−	0.0202163i
$498$	27.8701	+	29.7365i	1.24889	+	1.33252i
$499$	−11.2732	+	8.99004i	−0.504656	+	0.402449i	−0.842453	−	0.538769i	$-0.818889\pi$
$499$	−11.2732	+	8.99004i	−0.504656	+	0.402449i	0.337798	+	0.941219i	$0.390318\pi$
$500$	0.334137	−	0.0213027i	0.0149431	−	0.000952687i
$501$	23.7127	−	26.1046i	1.05941	−	1.16627i
$502$	−3.76634	+	11.9732i	−0.168100	+	0.534388i
$503$	−22.0415	+	5.03084i	−0.982784	+	0.224314i	−0.683580	−	0.729875i	$-0.739578\pi$
$503$	−22.0415	+	5.03084i	−0.982784	+	0.224314i	−0.299203	+	0.954189i	$0.596721\pi$
$504$	−3.12003	−	9.95708i	−0.138977	−	0.443524i
$505$		−	0.264657i		−	0.0117771i
$506$	−12.4214	−	18.4384i	−0.552197	−	0.819689i
$507$	22.8156	−	9.23415i	1.01328	−	0.410103i
$508$	−1.57557	−	1.10009i	−0.0699046	−	0.0488087i
$509$	16.2029	+	33.6458i	0.718183	+	1.49132i	0.864793	+	0.502128i	$0.167449\pi$
$509$	16.2029	+	33.6458i	0.718183	+	1.49132i	−0.146610	+	0.989194i	$0.546836\pi$
$510$	0.211869	+	0.0308490i	0.00938174	+	0.00136602i
$511$	−7.66504	+	3.69129i	−0.339081	+	0.163293i
$512$	22.5990	+	1.13297i	0.998746	+	0.0500708i
$513$	−36.4206	+	9.53798i	−1.60801	+	0.421112i
$514$	−6.94228	+	22.0695i	−0.306211	+	0.973443i
$515$	−0.0109578	+	0.0480094i	−0.000482860	+	0.00211555i
$516$	−17.7139	+	14.1103i	−0.779812	+	0.621173i
$517$	−21.9575	+	27.5338i	−0.965690	+	1.21094i
$518$	−4.54975	−	11.7850i	−0.199905	−	0.517804i
$519$	−9.48878	+	16.8440i	−0.416511	+	0.739371i
$520$	0.239858	+	0.0589763i	0.0105185	+	0.00258628i
$521$		−	18.7996i		−	0.823624i	−0.911269	−	0.411812i	$-0.864896\pi$
$521$		−	18.7996i		−	0.823624i	0.911269	−	0.411812i	$-0.135104\pi$
$522$	16.9881	+	15.2776i	0.743549	+	0.668681i
$523$			1.61246i			0.0705079i	0.999378	+	0.0352539i	$0.0112240\pi$
$523$			1.61246i			0.0705079i	−0.999378	+	0.0352539i	$0.988776\pi$
$524$	11.8477	+	4.80277i	0.517571	+	0.209810i
$525$	−5.22667	+	9.27814i	−0.228111	+	0.404931i
$526$	14.4122	−	5.56401i	0.628403	−	0.242603i
$527$	27.3733	−	34.3250i	1.19240	−	1.49522i
$528$	−24.6390	−	17.2238i	−1.07228	−	0.749569i
$529$	2.19720	−	9.62656i	0.0955304	−	0.418546i
$530$	−0.0554382	−	0.0174389i	−0.00240808	−	0.000757498i
$531$	0.401333	+	0.662364i	0.0174164	+	0.0287442i
$532$	−15.5307	+	8.73758i	−0.673339	+	0.378822i
$533$	0.255412	−	0.123000i	0.0110631	−	0.00532771i
$534$	−2.82170	+	19.3793i	−0.122107	+	0.838623i
$535$	−0.0566536	−	0.117642i	−0.00244935	−	0.00508612i
$536$	3.58435	−	7.13569i	0.154820	−	0.308215i
$537$	8.82344	−	3.57110i	0.380760	−	0.154104i
$538$	12.7258	−	8.57294i	0.548648	−	0.369606i
$539$		−	23.8122i		−	1.02567i
$540$	−0.172534	−	0.0223810i	−0.00742470	−	0.000963126i
$541$	−8.04675	+	1.83662i	−0.345957	+	0.0789624i	−0.391969	−	0.919978i	$-0.628206\pi$
$541$	−8.04675	+	1.83662i	−0.345957	+	0.0789624i	0.0460119	+	0.998941i	$0.485349\pi$
$542$	11.3657	+	3.57526i	0.488199	+	0.153570i
$543$	−1.39463	+	1.53531i	−0.0598493	+	0.0658864i
$544$	−14.0500	−	25.9790i	−0.602390	−	1.11384i
$545$	0.0711239	−	0.0567194i	0.00304661	−	0.00242959i
$546$	−11.4645	+	10.7449i	−0.490633	+	0.459839i
$547$	−32.8800	+	7.50465i	−1.40585	+	0.320876i	−0.857116	−	0.515123i	$-0.827746\pi$
$547$	−32.8800	+	7.50465i	−1.40585	+	0.320876i	−0.548731	+	0.835999i	$0.684889\pi$
$548$	0.333712	+	5.23432i	0.0142555	+	0.223599i
$549$	−3.70778	−	11.1753i	−0.158244	−	0.476951i
$550$	4.40376	+	30.3628i	0.187777	+	1.29467i
$551$	19.5100	−	33.7904i	0.831154	−	1.43952i
$552$	2.53787	+	17.5665i	0.108019	+	0.747678i
$553$	−3.44643	−	2.74844i	−0.146557	−	0.116875i
$554$	−0.921364	+	11.4400i	−0.0391450	+	0.486038i
$555$	−0.210200	−	0.0135181i	−0.00892248	−	0.000573812i
$556$	33.2698	+	13.4867i	1.41095	+	0.571964i
$557$	−5.80027	+	4.62556i	−0.245765	+	0.195991i	−0.738623	−	0.674119i	$-0.764524\pi$
$557$	−5.80027	+	4.62556i	−0.245765	+	0.195991i	0.492858	+	0.870110i	$0.335952\pi$
$558$	−21.8059	+	28.2358i	−0.923119	+	1.19531i
$559$	30.7254	+	14.7966i	1.29955	+	0.625829i
$560$	−0.0816810	+	0.0104576i	−0.00345165	+	0.000441913i
$561$	−2.51832	+	39.1585i	−0.106323	+	1.65327i
$562$	14.5845	+	21.6494i	0.615209	+	0.913225i
$563$			32.5516i			1.37189i	0.727655	+	0.685944i	$0.240610\pi$
$563$			32.5516i			1.37189i	−0.727655	+	0.685944i	$0.759390\pi$
$564$	25.3378	−	12.1847i	1.06691	−	0.513070i
$565$	−0.00410427	+	0.00327305i	−0.000172668	+	0.000137698i
$566$	−17.1664	+	18.2957i	−0.721558	+	0.769026i
$567$	7.17786	−	8.42414i	0.301442	−	0.353780i
$568$	−4.23036	+	1.95090i	−0.177502	+	0.0818580i
$569$	6.76783	−	3.25922i	0.283722	−	0.136633i	−0.286610	−	0.958047i	$-0.592529\pi$
$569$	6.76783	−	3.25922i	0.283722	−	0.136633i	0.570333	+	0.821414i	$0.306814\pi$
$570$	0.0236885	+	0.296175i	0.000992202	+	0.0124054i
$571$	−16.6100	+	34.4911i	−0.695109	+	1.44341i	0.191786	+	0.981437i	$0.438572\pi$
$571$	−16.6100	+	34.4911i	−0.695109	+	1.44341i	−0.886895	+	0.461972i	$0.847142\pi$
$572$	−7.24484	+	44.6854i	−0.302922	+	1.86839i
$573$	−8.82174	+	15.6599i	−0.368534	+	0.654203i
$574$	−0.0646682	+	0.0689224i	−0.00269920	+	0.00287677i
$575$	11.2938	−	14.1619i	0.470983	−	0.590594i
$576$	11.7447	+	20.9299i	0.489363	+	0.872080i
$577$	−0.773651	−	0.176581i	−0.0322075	−	0.00735116i	0.206387	−	0.978470i	$-0.433829\pi$
$577$	−0.773651	−	0.176581i	−0.0322075	−	0.00735116i	−0.238594	+	0.971119i	$0.576687\pi$
$578$	−7.32454	+	12.5250i	−0.304661	+	0.520970i
$579$	−25.8400	−	7.67223i	−1.07388	−	0.318847i
$580$	0.142216	−	0.110841i	0.00590521	−	0.00460242i
$581$			20.4603i			0.848838i
$582$	−24.9020	+	23.3390i	−1.03222	+	0.967433i
$583$	2.37011	−	10.3841i	0.0981598	−	0.430066i
$584$	15.5004	−	11.9433i	0.641412	−	0.494217i
$585$	0.0825001	+	0.248657i	0.00341096	+	0.0102807i
$586$	−2.36568	−	2.21966i	−0.0977253	−	0.0916933i
$587$	2.51650	−	11.0255i	0.103867	−	0.455072i	−0.896071	−	0.443912i	$-0.853590\pi$
$587$	2.51650	−	11.0255i	0.103867	−	0.455072i	0.999938	−	0.0111602i	$-0.00355248\pi$
$588$	−8.25775	+	17.1231i	−0.340544	+	0.706146i
$589$	54.8929	+	26.4350i	2.26182	+	1.08924i
$590$	0.00570183	−	0.00220126i	0.000234741	−	9.06245e-5i
$591$	39.6086	−	6.39920i	1.62928	−	0.263228i
$592$	15.8295	+	24.3658i	0.650588	+	1.00143i
$593$	−6.66164	−	13.8330i	−0.273561	−	0.568055i	0.718248	−	0.695787i	$-0.244944\pi$
$593$	−6.66164	−	13.8330i	−0.273561	−	0.568055i	−0.991809	+	0.127733i	$0.959230\pi$
$594$	1.55010	−	31.8482i	0.0636014	−	1.30675i
$595$	0.0670165	+	0.0840360i	0.00274741	+	0.00344514i
$596$	6.10621	+	6.72964i	0.250120	+	0.275657i
$597$	−4.36474	−	1.29595i	−0.178637	−	0.0530395i
$598$	22.1662	−	14.9326i	0.906445	−	0.610641i
$599$	−33.5262	+	7.65215i	−1.36985	+	0.312658i	−0.843279	−	0.537476i	$-0.819378\pi$
$599$	−33.5262	+	7.65215i	−1.36985	+	0.312658i	−0.526566	+	0.850134i	$0.676521\pi$
$600$	7.36269	−	23.3607i	0.300581	−	0.953698i
$601$	16.8666	−	35.0238i	0.688002	−	1.42865i	−0.205075	−	0.978746i	$-0.565744\pi$
$601$	16.8666	−	35.0238i	0.688002	−	1.42865i	0.893077	−	0.449904i	$-0.148542\pi$
$602$	−11.3327	−	0.912726i	−0.461887	−	0.0372000i
$603$	8.43076	−	0.811464i	0.343327	−	0.0330454i
$604$	5.47097	+	2.21779i	0.222610	+	0.0902405i
$605$	0.127764	−	0.0291612i	0.00519433	−	0.00118557i
$606$	−36.1169	−	13.9664i	−1.46715	−	0.567345i
$607$	−1.48584	+	1.86319i	−0.0603085	+	0.0756245i	−0.811071	−	0.584948i	$-0.801115\pi$
$607$	−1.48584	+	1.86319i	−0.0603085	+	0.0756245i	0.750762	+	0.660572i	$0.229686\pi$
$608$	30.8096	−	27.0313i	1.24949	−	1.09627i
$609$	0.977810	+	11.4282i	0.0396229	+	0.463096i
$610$	−0.0919598	+	0.0133377i	−0.00372334	+	0.000540027i
$611$	−33.1005	−	26.3968i	−1.33910	−	1.06790i
$612$	15.3905	−	27.2852i	0.622126	−	1.10294i
$613$	−3.68386	−	16.1400i	−0.148790	−	0.651890i	−0.993222	−	0.116229i	$-0.962919\pi$
$613$	−3.68386	−	16.1400i	−0.148790	−	0.651890i	0.844433	−	0.535661i	$-0.179938\pi$
$614$	18.1238	−	30.9917i	0.731417	−	1.25072i
$615$	0.000591200		0.00146073i	2.38395e−5		5.89023e-5i
$616$	−3.11218	−	14.7677i	−0.125393	−	0.595009i
$617$	−10.0199	−	4.82533i	−0.403386	−	0.194260i	0.221179	−	0.975233i	$-0.429009\pi$
$617$	−10.0199	−	4.82533i	−0.403386	−	0.194260i	−0.624565	+	0.780973i	$0.714724\pi$
$618$	5.97342	+	4.02891i	0.240286	+	0.162066i
$619$	−4.63688	−	20.3155i	−0.186372	−	0.816548i	−0.978509	−	0.206205i	$-0.933889\pi$
$619$	−4.63688	−	20.3155i	−0.186372	−	0.816548i	0.792137	−	0.610343i	$-0.208969\pi$
$620$	0.189193	+	0.208509i	0.00759816	+	0.00837392i
$621$	−14.3385	+	12.1986i	−0.575386	+	0.489511i
$622$	−11.7561	−	17.4510i	−0.471378	−	0.699721i
$623$	−7.68660	+	6.12986i	−0.307957	+	0.245588i
$624$	20.7060	−	29.6204i	0.828903	−	1.18577i
$625$	−22.5204	+	10.8453i	−0.900817	+	0.433811i
$626$	−10.6411	+	1.54337i	−0.425305	+	0.0616856i
$627$	−53.7572	+	8.68507i	−2.14685	+	0.346848i
$628$	−25.2341	+	14.1968i	−1.00695	+	0.566513i
$629$	16.4556	−	34.1704i	0.656128	−	1.36246i
$630$	−0.0555153	−	0.0674302i	−0.00221178	−	0.00268648i
$631$	14.2729	+	3.25770i	0.568196	+	0.129687i	0.496961	−	0.867773i	$-0.334449\pi$
$631$	14.2729	+	3.25770i	0.568196	+	0.129687i	0.0712344	+	0.997460i	$0.477306\pi$
$632$	9.06025	+	4.55108i	0.360398	+	0.181032i
$633$	15.7488	+	22.5823i	0.625958	+	0.897565i
$634$	−16.2855	−	42.1837i	−0.646781	−	1.67533i
$635$	−0.0156819	−	0.00357928i	−0.000622316	−	0.000142039i
$636$	−5.30539	+	6.64519i	−0.210372	+	0.263499i
$637$	28.6265			1.13422
$638$	22.3410	+	24.3495i	0.884490	+	0.964006i
$639$	−4.14051	−	2.69645i	−0.163796	−	0.106670i
$640$	0.178874	−	0.0622776i	0.00707062	−	0.00246174i
$641$	5.91637	−	25.9213i	0.233683	−	1.02383i	−0.712874	−	0.701292i	$-0.752607\pi$
$641$	5.91637	−	25.9213i	0.233683	−	1.02383i	0.946556	−	0.322538i	$-0.104536\pi$
$642$	−19.0440	+	1.52316i	−0.751605	+	0.0601145i
$643$	−13.7974	−	11.0031i	−0.544116	−	0.433918i	0.312466	−	0.949929i	$-0.398845\pi$
$643$	−13.7974	−	11.0031i	−0.544116	−	0.433918i	−0.856582	+	0.516011i	$0.827416\pi$
$644$	−5.10106	+	7.30580i	−0.201010	+	0.287889i
$645$	−0.0930427	+	0.165165i	−0.00366355	+	0.00650337i
$646$	−51.0336	−	16.0534i	−2.00789	−	0.631612i
$647$	−7.15014	−	3.44333i	−0.281101	−	0.135371i	0.288021	−	0.957624i	$-0.407003\pi$
$647$	−7.15014	−	3.44333i	−0.281101	−	0.135371i	−0.569122	+	0.822253i	$0.692717\pi$
$648$	−12.1592	+	22.3641i	−0.477657	+	0.878546i
$649$	0.486021	+	1.00923i	0.0190780	+	0.0396158i
$650$	−36.5014	+	5.29409i	−1.43170	+	0.207651i
$651$	−17.6810	+	2.85656i	−0.692971	+	0.111957i
$652$	25.3899	+	17.7277i	0.994346	+	0.694272i
$653$	−6.82207	−	8.55461i	−0.266968	−	0.334768i	0.630219	−	0.776417i	$-0.282965\pi$
$653$	−6.82207	−	8.55461i	−0.266968	−	0.334768i	−0.897188	+	0.441649i	$0.854393\pi$
$654$	−3.98700	−	12.6992i	−0.155904	−	0.496579i
$655$	0.107012			0.00418129
$656$	0.112855	−	0.185792i	0.00440623	−	0.00725394i
$657$	19.4763	+	7.17226i	0.759844	+	0.279816i
$658$	13.4642	+	4.23538i	0.524891	+	0.165112i
$659$	−17.4036	+	36.1389i	−0.677947	+	1.40777i	0.223423	+	0.974721i	$0.428277\pi$
$659$	−17.4036	+	36.1389i	−0.677947	+	1.40777i	−0.901370	+	0.433049i	$0.857438\pi$
$660$	−0.245300	−	0.0561311i	−0.00954828	−	0.00218490i
$661$	−4.47779	−	5.61497i	−0.174166	−	0.218397i	0.687085	−	0.726577i	$-0.258890\pi$
$661$	−4.47779	−	5.61497i	−0.174166	−	0.218397i	−0.861251	+	0.508180i	$0.830319\pi$
$662$	−13.3523	+	22.8324i	−0.518950	+	0.887405i
$663$	−47.0754	−	3.02746i	−1.82826	−	0.117577i
$664$	−9.70439	−	46.0488i	−0.376603	−	1.78704i
$665$	−0.0930016	+	0.116620i	−0.00360645	+	0.00452234i
$666$	−12.9373	+	27.9719i	−0.501311	+	1.08389i
$667$	1.45848	−	19.4557i	0.0564725	−	0.753327i
$668$	−39.0446	+	11.5693i	−1.51068	+	0.447629i
$669$	39.1218	−	27.2834i	1.51254	−	1.05484i
$670$	0.00536603	−	0.0666264i	0.000207308	−	0.00257400i
$671$	−3.78956	−	16.6031i	−0.146294	−	0.640957i
$672$	−2.88332	+	11.6986i	−0.111226	+	0.451283i
$673$	−3.40765	−	4.27306i	−0.131355	−	0.164714i	0.711804	−	0.702378i	$-0.247878\pi$
$673$	−3.40765	−	4.27306i	−0.131355	−	0.164714i	−0.843159	+	0.537664i	$0.819307\pi$
$674$	−15.0722	−	1.21390i	−0.580559	−	0.0467576i
$675$	25.1318	−	6.58161i	0.967323	−	0.253326i
$676$	−28.0548	−	4.54852i	−1.07903	−	0.174943i
$677$	−6.18278	−	27.0885i	−0.237624	−	1.04110i	−0.943138	−	0.332401i	$-0.892141\pi$
$677$	−6.18278	−	27.0885i	−0.237624	−	1.04110i	0.705514	−	0.708696i	$-0.250716\pi$
$678$	0.230073	+	0.732820i	0.00883592	+	0.0281438i
$679$	−17.1339			−0.657540
$680$	−0.190688	−	0.157348i	−0.00731255	−	0.00603403i
$681$	0.180138	−	0.0729072i	0.00690291	−	0.00279381i
$682$	−35.3071	+	37.6298i	−1.35198	+	1.44092i
$683$	27.3994	−	13.1949i	1.04841	−	0.504887i	0.171320	−	0.985215i	$-0.445197\pi$
$683$	27.3994	−	13.1949i	1.04841	−	0.504887i	0.877089	+	0.480328i	$0.159483\pi$
$684$	41.6681	+	12.3969i	1.59322	+	0.474008i
$685$	0.0190490	+	0.0395557i	0.000727825	+	0.00151134i
$686$	−20.2599	+	7.82157i	−0.773526	+	0.298629i
$687$	−7.49176	−	6.80530i	−0.285829	−	0.259638i
$688$	25.9387	−	3.32092i	0.988905	−	0.126609i
$689$	12.4835	+	2.84928i	0.475584	+	0.108549i
$690$	0.0749283	+	0.128290i	0.00285247	+	0.00488393i
$691$	−3.36156	−	2.68075i	−0.127880	−	0.101981i	0.557461	−	0.830203i	$-0.311775\pi$
$691$	−3.36156	−	2.68075i	−0.127880	−	0.101981i	−0.685341	+	0.728222i	$0.740347\pi$
$692$	19.4559	−	10.9459i	0.739601	−	0.416102i
$693$	11.5015	−	11.1337i	0.436905	−	0.422935i
$694$	5.09608	−	8.71430i	0.193445	−	0.330790i
$695$	0.300500			0.0113986
$696$	−7.62114	−	25.2570i	−0.288878	−	0.957366i
$697$	−0.283742			−0.0107475
$698$	−5.11300	+	8.74323i	−0.193530	+	0.330936i
$699$	−6.81560	+	12.0987i	−0.257790	+	0.457616i
$700$	10.7168	−	6.02930i	0.405057	−	0.227886i
$701$	22.4924	+	17.9371i	0.849525	+	0.677474i	0.948210	−	0.317645i	$-0.102892\pi$
$701$	22.4924	+	17.9371i	0.849525	+	0.677474i	−0.0986846	+	0.995119i	$0.531463\pi$
$702$	38.2871	+	1.86349i	1.44505	+	0.0703330i
$703$	51.3124	+	11.7117i	1.93528	+	0.441716i
$704$	14.0088	+	31.7607i	0.527975	+	1.19703i
$705$	0.158240	−	0.174202i	0.00595966	−	0.00656082i
$706$	40.6821	−	15.7058i	1.53109	−	0.591097i
$707$	−8.43478	−	17.5150i	−0.317222	−	0.658719i
$708$	0.000495464	−	0.894274i	1.86207e−5	−	0.0336089i
$709$	−3.05915	+	1.47321i	−0.114889	+	0.0553275i	−0.490445	−	0.871472i	$-0.663166\pi$
$709$	−3.05915	+	1.47321i	−0.114889	+	0.0553275i	0.375557	+	0.926799i	$0.377452\pi$
$710$	−0.0266819	+	0.0284372i	−0.00100135	+	0.00106723i
$711$	1.03032	+	10.7046i	0.0386402	+	0.401455i
$712$	14.3923	−	17.4418i	0.539375	−	0.653661i
$713$	30.4650			1.14092
$714$	15.0047	−	4.71081i	0.561536	−	0.176298i
$715$	0.0843196	+	0.369428i	0.00315338	+	0.0138158i
$716$	−10.8496	−	1.75904i	−0.405468	−	0.0657385i
$717$	−8.61118	+	9.47980i	−0.321590	+	0.354030i
$718$	−47.4010	−	3.81763i	−1.76899	−	0.142473i
$719$	−18.8944	−	23.6929i	−0.704643	−	0.883595i	0.292718	−	0.956199i	$-0.405440\pi$
$719$	−18.8944	−	23.6929i	−0.704643	−	0.883595i	−0.997361	+	0.0726044i	$0.976869\pi$
$720$	0.156927	+	0.125430i	0.00584832	+	0.00467449i
$721$	0.804898	+	3.52649i	0.0299760	+	0.131333i
$722$	3.80304	−	47.2199i	0.141535	−	1.75734i
$723$	−11.8309	−	16.9645i	−0.439998	−	0.630915i
$724$	2.29635	−	0.680432i	0.0853433	−	0.0252881i
$725$	−13.4627	+	23.3168i	−0.499993	+	0.865965i
$726$	2.76274	−	18.9744i	0.102535	−	0.704204i
$727$	19.4038	−	24.3315i	0.719645	−	0.902407i	−0.278672	−	0.960386i	$-0.589894\pi$
$727$	19.4038	−	24.3315i	0.719645	−	0.902407i	0.998318	+	0.0579795i	$0.0184658\pi$
$728$	17.7534	−	3.74138i	0.657985	−	0.138665i
$729$	−26.9456	+	1.71240i	−0.997987	+	0.0634221i
$730$	0.0826862	−	0.141393i	0.00306035	−	0.00523321i
$731$	−21.2818	−	26.6866i	−0.787138	−	0.987039i
$732$	−3.03271	+	13.2533i	−0.112092	+	0.489856i
$733$	−21.8131	+	45.2954i	−0.805686	+	1.67303i	−0.0681918	+	0.997672i	$0.521723\pi$
$733$	−21.8131	+	45.2954i	−0.805686	+	1.67303i	−0.737495	+	0.675353i	$0.763991\pi$
$734$	23.1739	+	7.28969i	0.855363	+	0.269067i
$735$	−0.0102126	+	0.158800i	−0.000376696	+	0.00585743i
$736$	8.01546	−	18.8621i	0.295454	−	0.695268i
$737$	12.2504			0.451248
$738$	0.230540	−	0.00359421i	0.00848628	−	0.000132305i
$739$	−31.1072	−	39.0073i	−1.14430	−	1.43491i	−0.882830	−	0.469693i	$-0.844365\pi$
$739$	−31.1072	−	39.0073i	−1.14430	−	1.43491i	−0.261469	−	0.965212i	$-0.584207\pi$
$740$	0.199419	+	0.139239i	0.00733081	+	0.00511851i
$741$	−10.4410	−	64.6255i	−0.383559	−	2.37408i
$742$	−4.22468	+	0.612740i	−0.155093	+	0.0224944i
$743$	13.9271	+	28.9198i	0.510934	+	1.06097i	0.983707	+	0.179781i	$0.0575389\pi$
$743$	13.9271	+	28.9198i	0.510934	+	1.06097i	−0.472773	+	0.881184i	$0.656747\pi$
$744$	38.4385	−	14.8152i	1.40922	−	0.543151i
$745$	0.0685313	+	0.0330029i	0.00251079	+	0.00120913i
$746$	15.9110	+	5.00505i	0.582544	+	0.183248i
$747$	35.8639	−	34.7172i	1.31219	−	1.27023i
$748$	25.9390	−	37.1503i	0.948425	−	1.35835i
$749$	−7.49866	−	5.97998i	−0.273995	−	0.218504i
$750$	−0.0326931	−	0.408758i	−0.00119378	−	0.0149257i
$751$	−5.78101	+	25.3283i	−0.210952	+	0.924242i	0.752969	+	0.658056i	$0.228621\pi$
$751$	−5.78101	+	25.3283i	−0.210952	+	0.924242i	−0.963922	+	0.266186i	$0.914236\pi$
$752$	−32.3120	−	3.14618i	−1.17830	−	0.114729i
$753$	14.7366	+	4.37548i	0.537032	+	0.159452i
$754$	−29.2724	+	26.8578i	−1.06604	+	0.978105i
$755$	0.0494151			0.00179840
$756$	−12.1316	+	4.01760i	−0.441222	+	0.146119i
$757$	−28.3207	−	6.46401i	−1.02933	−	0.234938i	−0.325678	−	0.945481i	$-0.605593\pi$
$757$	−28.3207	−	6.46401i	−1.02933	−	0.234938i	−0.703654	+	0.710542i	$0.748450\pi$
$758$	14.7102	+	38.1033i	0.534299	+	1.38397i
$759$	−22.3339	+	15.5755i	−0.810668	+	0.565357i
$760$	0.153999	−	0.306581i	0.00558615	−	0.0111209i
$761$	5.22701	+	1.19303i	0.189479	+	0.0432474i	0.316207	−	0.948690i	$-0.397590\pi$
$761$	5.22701	+	1.19303i	0.189479	+	0.0432474i	−0.126728	+	0.991937i	$0.540448\pi$
$762$	−1.31601	+	1.95117i	−0.0476739	+	0.0706834i
$763$	2.89929	−	6.02045i	0.104961	−	0.217955i
$764$	18.0882	−	10.1765i	0.654407	−	0.368171i
$765$	0.0335885	−	0.260062i	0.00121440	−	0.00940257i
$766$	29.5098	−	4.28005i	1.06623	−	0.154645i
$767$	−1.21327	+	0.584282i	−0.0438088	+	0.0210972i
$768$	0.940628	−	27.6968i	0.0339420	−	0.999424i
$769$	−41.4402	+	33.0475i	−1.49437	+	1.19172i	−0.563640	+	0.826020i	$0.690600\pi$
$769$	−41.4402	+	33.0475i	−1.49437	+	1.19172i	−0.930732	+	0.365702i	$0.880829\pi$
$770$	−0.0705824	−	0.104774i	−0.00254361	−	0.00377577i
$771$	27.1632	+	8.06510i	0.978259	+	0.290457i
$772$	20.9150	+	23.0504i	0.752749	+	0.829603i
$773$	7.70602	+	33.7623i	0.277166	+	1.21435i	0.901358	+	0.433074i	$0.142571\pi$
$773$	7.70602	+	33.7623i	0.277166	+	1.21435i	−0.624192	+	0.781271i	$0.714572\pi$
$774$	17.6295	+	21.4132i	0.633680	+	0.769683i
$775$	−37.8784	−	18.2413i	−1.36063	−	0.655246i
$776$	38.5623	−	8.12667i	1.38430	−	0.291730i
$777$	−14.3418	+	5.80455i	−0.514510	+	0.208237i
$778$	−3.15675	+	5.39805i	−0.113175	+	0.193529i
$779$	−0.0876199	−	0.383888i	−0.00313931	−	0.0137542i
$780$	0.0674793	−	0.294893i	0.00241615	−	0.0105589i
$781$	−5.58751	−	4.45589i	−0.199937	−	0.159444i
$782$	−26.4740	+	3.83974i	−0.946708	+	0.137309i
$783$	18.3728	−	21.1054i	0.656591	−	0.754247i
$784$	18.4077	−	11.9587i	0.657419	−	0.427098i
$785$	−0.151108	+	0.189484i	−0.00539329	+	0.00676297i
$786$	5.64717	−	14.6035i	0.201428	−	0.520891i
$787$	22.8711	−	5.22018i	0.815267	−	0.186079i	0.205497	−	0.978658i	$-0.434119\pi$
$787$	22.8711	−	5.22018i	0.815267	−	0.186079i	0.609770	+	0.792578i	$0.291262\pi$
$788$	−42.9354	−	17.4049i	−1.52951	−	0.620024i
$789$	−7.09855	−	17.5390i	−0.252715	−	0.624405i
$790$	0.0845963	+	0.00681330i	0.00300980	+	0.000242406i
$791$	−0.167306	+	0.347415i	−0.00594873	+	0.0123527i
$792$	−20.6049	+	30.5131i	−0.732162	+	1.08424i
$793$	19.9599	−	4.55571i	0.708795	−	0.161778i
$794$	−23.9922	+	16.1627i	−0.851451	+	0.573594i
$795$	−0.0202594	+	0.0682336i	−0.000718527	+	0.00241999i
$796$	3.53284	+	3.89353i	0.125218	+	0.138003i
$797$	−20.9712	−	26.2970i	−0.742836	−	0.931487i	0.256549	−	0.966531i	$-0.417414\pi$
$797$	−20.9712	−	26.2970i	−0.742836	−	0.931487i	−0.999386	+	0.0350438i	$0.988843\pi$
$798$	11.0070	+	18.8459i	0.389642	+	0.667136i
$799$	18.3860	+	38.1788i	0.650449	+	1.35067i
$800$	−21.2599	+	18.6528i	−0.751652	+	0.659475i
$801$	23.7873	+	3.07227i	0.840484	+	0.108553i
$802$	−1.98329	+	0.765671i	−0.0700322	+	0.0270368i
$803$	27.0465	+	13.0249i	0.954452	+	0.459640i
$804$	−8.80912	−	4.24826i	−0.310674	−	0.149825i
$805$	−0.0165969	+	0.0727157i	−0.000584963	+	0.00256289i
$806$	−45.2376	−	42.4454i	−1.59343	−	1.49507i
$807$	−10.7499	−	15.4143i	−0.378414	−	0.542610i
$808$	27.2910	+	35.4192i	0.960094	+	1.24604i
$809$	−0.0757933	+	0.332072i	−0.00266475	+	0.0116750i	−0.976243	−	0.216679i	$-0.930477\pi$
$809$	−0.0757933	+	0.332072i	−0.00266475	+	0.0116750i	0.973578	+	0.228354i	$0.0733345\pi$
$810$	−0.0239964	+	0.211726i	−0.000843147	+	0.00743928i
$811$		−	48.6446i		−	1.70814i	−0.520155	−	0.854072i	$-0.674126\pi$
$811$		−	48.6446i		−	1.70814i	0.520155	−	0.854072i	$-0.325874\pi$
$812$	5.87930	−	11.8680i	0.206323	−	0.416484i
$813$	4.15350	−	13.9890i	0.145670	−	0.490615i
$814$	−22.5023	+	38.4789i	−0.788704	+	1.34868i
$815$	0.252709	+	0.0576792i	0.00885202	+	0.00202042i
$816$	−31.5357	+	17.7191i	−1.10397	+	0.620292i
$817$	29.5337	−	37.0341i	1.03325	−	1.29566i
$818$	−11.8633	+	12.6438i	−0.414792	+	0.442079i
$819$	13.3847	+	13.8268i	0.467699	+	0.483147i
$820$	0.000291211	−	0.00179616i	1.01695e−5	−	6.27247e-5i
$821$	−19.6657	+	40.8363i	−0.686339	+	1.42520i	0.208145	+	0.978098i	$0.433257\pi$
$821$	−19.6657	+	40.8363i	−0.686339	+	1.42520i	−0.894484	+	0.447100i	$0.852457\pi$
$822$	6.40328	−	0.512143i	0.223340	−	0.0178631i
$823$	−3.94302	+	1.89886i	−0.137445	+	0.0661900i	−0.501342	−	0.865249i	$-0.667160\pi$
$823$	−3.94302	+	1.89886i	−0.137445	+	0.0661900i	0.363897	+	0.931439i	$0.381446\pi$
$824$	−3.48415	−	7.55508i	−0.121376	−	0.263194i
$825$	37.0947	−	5.99307i	1.29147	−	0.208652i
$826$	0.307191	−	0.327400i	0.0106886	−	0.0113917i
$827$	−16.0751	+	12.8194i	−0.558984	+	0.445775i	−0.861781	−	0.507280i	$-0.830651\pi$
$827$	−16.0751	+	12.8194i	−0.558984	+	0.445775i	0.302797	+	0.953055i	$0.402080\pi$
$828$	21.4614	−	3.45514i	0.745837	−	0.120074i
$829$		−	24.5193i		−	0.851590i	−0.904820	−	0.425795i	$-0.859995\pi$
$829$		−	24.5193i		−	0.851590i	0.904820	−	0.425795i	$-0.140005\pi$
$830$	−0.220090	−	0.326705i	−0.00763943	−	0.0113401i
$831$	14.0274	+	0.902116i	0.486606	+	0.0312941i
$832$	−38.1819	+	16.8410i	−1.32372	+	0.583856i
$833$	−25.8148	−	12.4318i	−0.894431	−	0.430735i
$834$	15.8579	−	41.0083i	0.549113	−	1.42000i
$835$	−0.266505	+	0.212531i	−0.00922279	+	0.00735493i
$836$	58.2725	+	23.6221i	2.01540	+	0.816989i
$837$	35.0082	+	26.1450i	1.21006	+	0.903703i
$838$	2.64293	−	32.8155i	0.0912984	−	1.13359i
$839$	17.8769	+	14.2564i	0.617181	+	0.492185i	0.881459	−	0.472261i	$-0.156562\pi$
$839$	17.8769	+	14.2564i	0.617181	+	0.492185i	−0.264278	+	0.964447i	$0.585134\pi$
$840$	0.0144211	+	0.0998186i	0.000497573	+	0.00344407i
$841$	2.16576	+	28.9190i	0.0746815	+	0.997207i
$842$	0.371537	+	2.56165i	0.0128040	+	0.0882802i
$843$	26.2232	−	18.2879i	0.903175	−	0.629870i
$844$	−2.02269	−	31.7262i	−0.0696238	−	1.09206i
$845$	−0.231938	+	0.0529384i	−0.00797891	+	0.00182113i
$846$	−15.4222	−	30.7874i	−0.530226	−	1.05849i
$847$	7.52600	−	6.00178i	0.258596	−	0.206224i
$848$	9.21759	−	3.38283i	0.316533	−	0.116167i
$849$	22.7440	+	20.6600i	0.780573	+	0.709050i
$850$	35.2154	+	11.0775i	1.20788	+	0.379956i
$851$	25.6576	−	5.85619i	0.879533	−	0.200748i
$852$	2.47268	+	5.14186i	0.0847127	+	0.176157i
$853$		−	28.4773i		−	0.975044i	−0.873111	−	0.487522i	$-0.837901\pi$
$853$		−	28.4773i		−	0.975044i	0.873111	−	0.487522i	$-0.162099\pi$
$854$	−5.66081	+	3.81350i	−0.193709	+	0.130495i
$855$	0.362223	−	0.0348641i	0.0123878	−	0.00119233i
$856$	19.7131	+	9.90213i	0.673779	+	0.338448i
$857$	19.1466	+	39.7583i	0.654035	+	1.35812i	0.919153	+	0.393901i	$0.128875\pi$
$857$	19.1466	+	39.7583i	0.654035	+	1.35812i	−0.265118	+	0.964216i	$0.585411\pi$
$858$	54.8644	+	7.98847i	1.87304	+	0.272722i
$859$	−2.21990	+	1.06905i	−0.0757422	+	0.0364755i	−0.471371	−	0.881935i	$-0.656241\pi$
$859$	−2.21990	+	1.06905i	−0.0757422	+	0.0364755i	0.395629	+	0.918410i	$0.370527\pi$
$860$	0.190776	−	0.107331i	0.00650539	−	0.00365995i
$861$	0.0856799	+	0.0778291i	0.00291996	+	0.00265241i
$862$	−32.2051	−	10.1306i	−1.09691	−	0.345050i
$863$	1.06223	−	4.65392i	0.0361587	−	0.158421i	−0.953625	−	0.300996i	$-0.902681\pi$
$863$	1.06223	−	4.65392i	0.0361587	−	0.158421i	0.989784	+	0.142575i	$0.0455381\pi$
$864$	25.3983	−	14.7962i	0.864067	−	0.503377i
$865$	0.116507	−	0.146095i	0.00396135	−	0.00496738i
$866$	−27.6020	+	10.6561i	−0.937956	+	0.362109i
$867$	15.4827	+	8.72190i	0.525820	+	0.296211i
$868$	19.1661	+	7.76942i	0.650538	+	0.263711i
$869$			15.5544i			0.527648i
$870$	−0.138546	−	0.171965i	−0.00469715	−	0.00583015i
$871$			14.7271i			0.499008i
$872$	−3.66974	+	14.9250i	−0.124273	+	0.505423i
$873$	29.0729	+	30.0332i	0.983969	+	1.01647i
$874$	−13.3702	−	34.6322i	−0.452253	−	1.17145i
$875$	0.128354	−	0.160951i	0.00433915	−	0.00544112i
$876$	−14.9320	−	18.7455i	−0.504506	−	0.633351i
$877$	2.80223	−	12.2774i	0.0946247	−	0.414578i	−0.905324	−	0.424722i	$-0.860372\pi$
$877$	2.80223	−	12.2774i	0.0946247	−	0.414578i	0.999949	+	0.0101441i	$0.00322901\pi$
$878$	12.7273	−	40.4601i	0.429526	−	1.36546i
$879$	−2.67139	+	2.94086i	−0.0901038	+	0.0991927i
$880$	0.208550	+	0.202330i	0.00703020	+	0.00682053i
$881$	−2.33241	+	1.12323i	−0.0785810	+	0.0378426i	−0.472761	−	0.881190i	$-0.656743\pi$
$881$	−2.33241	+	1.12323i	−0.0785810	+	0.0378426i	0.394180	+	0.919033i	$0.371028\pi$
$882$	21.1320	+	9.77379i	0.711551	+	0.329101i
$883$	7.76926	+	16.1330i	0.261457	+	0.542920i	0.989829	−	0.142261i	$-0.0454373\pi$
$883$	7.76926	+	16.1330i	0.261457	+	0.542920i	−0.728373	+	0.685181i	$0.759723\pi$
$884$	44.6611	+	31.1833i	1.50212	+	1.04881i
$885$	−0.00280836	−	0.00693886i	−9.44020e−5	−	0.000233247i
$886$	9.17322	+	13.6169i	0.308180	+	0.457467i
$887$			0.196794i			0.00660768i	0.999995	+	0.00330384i	$0.00105165\pi$
$887$			0.196794i			0.00660768i	−0.999995	+	0.00330384i	$0.998948\pi$
$888$	29.5251	−	19.8663i	0.990798	−	0.666669i
$889$	−1.15190	+	0.262913i	−0.0386334	+	0.00881782i
$890$	0.0567990	−	0.180564i	0.00190391	−	0.00605251i
$891$	−39.0314	−	1.26858i	−1.30760	−	0.0424990i
$892$	−54.9629	+	3.50413i	−1.84029	+	0.117327i
$893$	−45.9764	+	36.6650i	−1.53854	+	1.22695i
$894$	8.12030	−	7.61063i	0.271583	−	0.254537i
$895$	−0.0896969	+	0.0204727i	−0.00299824	+	0.000684328i
$896$	9.85304	−	9.82234i	0.329167	−	0.328142i
$897$	−18.7245	−	26.8492i	−0.625194	−	0.896469i
$898$	9.97197	−	1.44632i	0.332769	−	0.0482642i
$899$	−44.7774	+	6.74799i	−1.49341	+	0.225058i
$900$	−28.7528	−	8.55439i	−0.958425	−	0.285146i
$901$	−10.0200	−	7.99071i	−0.333816	−	0.266209i
$902$	0.332410	+	0.0267720i	0.0110681	+	0.000891410i
$903$	−0.893659	+	13.8959i	−0.0297391	+	0.462428i
$904$	0.211766	−	0.861259i	0.00704323	−	0.0286450i
$905$	0.0156741	−	0.0124997i	0.000521026	−	0.000415505i
$906$	2.60771	−	6.74351i	0.0866353	−	0.224038i
$907$	12.7818	+	6.15537i	0.424412	+	0.204386i	0.633883	−	0.773429i	$-0.281460\pi$
$907$	12.7818	+	6.15537i	0.424412	+	0.204386i	−0.209471	+	0.977815i	$0.567174\pi$
$908$	−0.221504	−	0.0359124i	−0.00735086	−	0.00119179i
$909$	−16.3890	+	44.5044i	−0.543587	+	1.47612i
$910$	0.125956	−	0.0848524i	0.00417540	−	0.00281283i
$911$		−	2.46589i		−	0.0816987i	−0.999165	−	0.0408493i	$-0.986994\pi$
$911$		−	2.46589i		−	0.0816987i	0.999165	−	0.0408493i	$-0.0130064\pi$
$912$	−33.7113	−	37.1945i	−1.11629	−	1.23163i
$913$	56.4447	−	45.0132i	1.86805	−	1.48972i
$914$	14.6995	+	13.7922i	0.486217	+	0.456206i
$915$	0.0181512	+	0.112349i	0.000600061	+	0.00371414i
$916$	3.32027	+	11.2054i	0.109705	+	0.370236i
$917$	7.08202	−	3.41052i	0.233869	−	0.112625i
$918$	−33.7173	−	18.3076i	−1.11284	−	0.604240i
$919$	−21.6883	+	45.0363i	−0.715432	+	1.48561i	0.152172	+	0.988354i	$0.451373\pi$
$919$	−21.6883	+	45.0363i	−0.715432	+	1.48561i	−0.867604	+	0.497256i	$0.834341\pi$
$920$	0.00286432	−	0.171528i	9.44338e−5	−	0.00565513i
$921$	−38.3103	−	21.5814i	−1.26237	−	0.711131i
$922$	0.409116	+	0.383863i	0.0134735	+	0.0126419i
$923$	5.35676	−	6.71717i	0.176320	−	0.221098i
$924$	−18.0228	+	4.10309i	−0.592908	+	0.134982i
$925$	−35.4077	−	8.08159i	−1.16420	−	0.265721i
$926$	18.2879	+	10.6947i	0.600979	+	0.351449i
$927$	4.81564	−	7.39462i	0.158167	−	0.242871i
$928$	−7.60316	+	29.4990i	−0.249586	+	0.968353i
$929$		−	9.93447i		−	0.325939i	−0.986631	−	0.162970i	$-0.947893\pi$
$929$		−	9.93447i		−	0.325939i	0.986631	−	0.162970i	$-0.0521073\pi$
$930$	0.251596	−	0.235805i	0.00825017	−	0.00773235i
$931$	8.84788	−	38.7651i	0.289978	−	1.27047i
$932$	13.9748	−	7.86224i	0.457759	−	0.257536i
$933$	−21.1378	+	14.7414i	−0.692021	+	0.482612i
$934$	−25.4293	+	27.1022i	−0.832073	+	0.886811i
$935$	0.0843957	−	0.369762i	0.00276003	−	0.0120925i
$936$	−36.6821	−	24.7706i	−1.19899	−	0.809654i
$937$	−53.3099	−	25.6727i	−1.74156	−	0.838690i	−0.982156	−	0.188069i	$-0.939777\pi$
$937$	−53.3099	−	25.6727i	−1.74156	−	0.838690i	−0.759403	−	0.650621i	$-0.774509\pi$
$938$	−1.76830	−	4.58035i	−0.0577370	−	0.149554i
$939$	2.10037	+	13.0005i	0.0685430	+	0.424254i
$940$	−0.260553	+	0.0772043i	−0.00849829	+	0.00251813i
$941$	−13.8129	−	28.6829i	−0.450289	−	0.935035i	−0.995321	−	0.0966196i	$-0.969197\pi$
$941$	−13.8129	−	28.6829i	−0.450289	−	0.935035i	0.545032	−	0.838415i	$-0.316517\pi$
$942$	17.8840	+	30.6206i	0.582694	+	0.997674i
$943$	−0.122760	−	0.153936i	−0.00399761	−	0.00501284i
$944$	−0.536089	+	0.882559i	−0.0174482	+	0.0287249i
$945$	−0.0814765	+	0.0693163i	−0.00265043	+	0.00225486i
$946$	22.4142	+	33.2720i	0.728750	+	1.08177i
$947$	26.5757	−	6.06572i	0.863593	−	0.197110i	0.232291	−	0.972646i	$-0.425378\pi$
$947$	26.5757	−	6.06572i	0.863593	−	0.197110i	0.631302	+	0.775537i	$0.282521\pi$
$948$	5.39406	−	11.1850i	0.175191	−	0.363273i
$949$	−15.6582	+	32.5147i	−0.508288	+	1.05547i
$950$	−4.11276	+	51.0654i	−0.133435	+	1.65678i
$951$	−51.3356	+	20.7770i	−1.66467	+	0.673740i
$952$	−17.6345	−	4.33596i	−0.571537	−	0.140529i
$953$	−27.6498	+	6.31089i	−0.895666	+	0.204430i	−0.645488	−	0.763770i	$-0.723346\pi$
$953$	−27.6498	+	6.31089i	−0.895666	+	0.204430i	−0.250178	+	0.968200i	$0.580489\pi$
$954$	8.24249	+	6.36552i	0.266861	+	0.206091i
$955$	0.108317	−	0.135825i	0.00350505	−	0.00439519i
$956$	14.1789	−	4.20134i	0.458578	−	0.135881i
$957$	29.3763	−	27.8399i	0.949602	−	0.899936i
$958$	−2.94828	−	20.3276i	−0.0952545	−	0.656754i
$959$	2.52132	+	2.01069i	0.0814178	+	0.0649285i
$960$	−0.0798007	−	0.217815i	−0.00257556	−	0.00702996i
$961$	−8.83602	−	38.7131i	−0.285033	−	1.24881i
$962$	−46.2583	−	27.0517i	−1.49143	−	0.872181i
$963$	2.24175	+	23.2908i	0.0722394	+	0.750537i
$964$	1.51950	+	23.8337i	0.0489399	+	0.767631i
$965$	0.234734	+	0.113042i	0.00755635	+	0.00363895i
$966$	9.04743	+	6.10224i	0.291096	+	0.196336i
$967$	−2.75671	−	12.0779i	−0.0886499	−	0.388401i	0.911065	−	0.412262i	$-0.135261\pi$
$967$	−2.75671	−	12.0779i	−0.0886499	−	0.388401i	−0.999715	+	0.0238613i	$0.992404\pi$
$968$	−14.0916	+	17.0774i	−0.452922	+	0.548889i
$969$	−18.6498	+	62.8124i	−0.599117	+	2.01782i
$970$	0.273590	−	0.184308i	0.00878443	−	0.00591778i
$971$	−7.58179	+	6.04628i	−0.243311	+	0.194034i	−0.737551	−	0.675291i	$-0.764018\pi$
$971$	−7.58179	+	6.04628i	−0.243311	+	0.194034i	0.494240	+	0.869326i	$0.335446\pi$
$972$	27.6272	+	14.4478i	0.886142	+	0.463413i
$973$	19.8871	−	9.57712i	0.637551	−	0.307028i
$974$	−7.66067	−	52.8182i	−0.245464	−	1.69241i
$975$	7.20472	+	44.5944i	0.230736	+	1.42816i
$976$	10.9317	−	11.2677i	0.349914	−	0.360671i
$977$	−2.90340	+	6.02898i	−0.0928881	+	0.192884i	−0.942236	−	0.334949i	$-0.891281\pi$
$977$	−2.90340	+	6.02898i	−0.0928881	+	0.192884i	0.849348	+	0.527833i	$0.176995\pi$
$978$	21.2072	−	31.4426i	0.678130	−	1.00542i
$979$	33.8213	+	7.71950i	1.08093	+	0.246716i
$980$	0.105191	−	0.150656i	0.00336020	−	0.00481253i
$981$	−15.4725	+	5.13349i	−0.493997	+	0.163900i
$982$	−5.89471	+	2.27572i	−0.188108	+	0.0726212i
$983$	−10.1512	−	2.31696i	−0.323775	−	0.0738994i	0.0575445	−	0.998343i	$-0.481673\pi$
$983$	−10.1512	−	2.31696i	−0.323775	−	0.0738994i	−0.381319	+	0.924444i	$0.624530\pi$
$984$	−0.229749	−	0.134527i	−0.00732412	−	0.00428856i
$985$	−0.387803			−0.0123564
$986$	38.0610	−	11.5076i	1.21211	−	0.366478i
$987$	4.92039	−	16.5719i	0.156618	−	0.527488i
$988$	−28.3979	+	70.0537i	−0.903459	+	2.22870i
$989$	5.27053	−	23.0917i	0.167593	−	0.734274i
$990$	−0.0638876	+	0.301500i	−0.00203048	+	0.00958230i
$991$	−11.0061	−	8.77710i	−0.349621	−	0.278814i	0.432894	−	0.901445i	$-0.357492\pi$
$991$	−11.0061	−	8.77710i	−0.349621	−	0.278814i	−0.782516	+	0.622631i	$0.786064\pi$
$992$	−46.8208	−	8.39563i	−1.48656	−	0.266562i
$993$	28.2241	+	15.8996i	0.895666	+	0.504558i
$994$	−0.859497	+	2.73233i	−0.0272616	+	0.0866644i
$995$	0.0396498	+	0.0190943i	0.00125698	+	0.000605331i
$996$	−56.1988	+	12.7943i	−1.78073	+	0.405401i
$997$	−3.47515	−	7.21623i	−0.110059	−	0.228540i	0.838663	−	0.544650i	$-0.183338\pi$
$997$	−3.47515	−	7.21623i	−0.110059	−	0.228540i	−0.948723	+	0.316110i	$0.897623\pi$
$998$	−2.92691	−	20.1803i	−0.0926497	−	0.638795i
$999$	34.5097	+	15.2898i	1.09184	+	0.483749i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	348.2.t.a.35.20	yes	336
3.2	odd	2	inner	348.2.t.a.35.37	yes	336
4.3	odd	2	inner	348.2.t.a.35.13	✓	336
12.11	even	2	inner	348.2.t.a.35.44	yes	336
29.5	even	14	inner	348.2.t.a.179.44	yes	336
87.5	odd	14	inner	348.2.t.a.179.13	yes	336
116.63	odd	14	inner	348.2.t.a.179.37	yes	336
348.179	even	14	inner	348.2.t.a.179.20	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
348.2.t.a.35.13	✓	336	4.3	odd	2	inner
348.2.t.a.35.20	yes	336	1.1	even	1	trivial
348.2.t.a.35.37	yes	336	3.2	odd	2	inner
348.2.t.a.35.44	yes	336	12.11	even	2	inner
348.2.t.a.179.13	yes	336	87.5	odd	14	inner
348.2.t.a.179.20	yes	336	348.179	even	14	inner
348.2.t.a.179.37	yes	336	116.63	odd	14	inner
348.2.t.a.179.44	yes	336	29.5	even	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	348.t (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.713912 + 1.22079i) q^{2} +(1.50908 + 0.850111i) q^{3} +(-0.980658 - 1.74307i) q^{4} +(-0.0130888 - 0.0104380i) q^{5} +(-2.11516 + 1.23536i) q^{6} +(-1.19888 - 0.273637i) q^{7} +(2.82803 + 0.0472247i) q^{8} +(1.55462 + 2.56576i) q^{9} +O(q^{10})\)	\(q+(-0.713912 + 1.22079i) q^{2} +(1.50908 + 0.850111i) q^{3} +(-0.980658 - 1.74307i) q^{4} +(-0.0130888 - 0.0104380i) q^{5} +(-2.11516 + 1.23536i) q^{6} +(-1.19888 - 0.273637i) q^{7} +(2.82803 + 0.0472247i) q^{8} +(1.55462 + 2.56576i) q^{9} +(0.0220869 - 0.00852690i) q^{10} +(1.88267 + 3.90941i) q^{11} +(0.00191925 - 3.46410i) q^{12} +(-4.69979 + 2.26330i) q^{13} +(1.18995 - 1.26823i) q^{14} +(-0.0108786 - 0.0268787i) q^{15} +(-2.07662 + 3.41872i) q^{16} +5.22108 q^{17} +(-4.24213 + 0.0661365i) q^{18} +(1.61228 + 7.06386i) q^{19} +(-0.00535853 + 0.0330509i) q^{20} +(-1.57658 - 1.43212i) q^{21} +(-6.11663 - 0.492628i) q^{22} +(2.25888 + 2.83255i) q^{23} +(4.22757 + 2.47541i) q^{24} +(-1.11254 - 4.87437i) q^{25} +(0.592225 - 7.35326i) q^{26} +(0.164858 + 5.19354i) q^{27} +(0.698724 + 2.35809i) q^{28} +(-3.94752 - 3.66294i) q^{29} +(0.0405796 + 0.00590855i) q^{30} +(5.24283 - 6.57430i) q^{31} +(-2.69102 - 4.97578i) q^{32} +(-0.482336 + 7.50008i) q^{33} +(-3.72740 + 6.37385i) q^{34} +(0.0128357 + 0.0160955i) q^{35} +(2.94777 - 5.22596i) q^{36} +(3.15176 - 6.54470i) q^{37} +(-9.77452 - 3.07472i) q^{38} +(-9.01640 - 0.579852i) q^{39} +(-0.0365227 - 0.0301371i) q^{40} -0.0543453 q^{41} +(2.87386 - 0.902267i) q^{42} +(-4.07614 - 5.11131i) q^{43} +(4.96813 - 7.11543i) q^{44} +(0.00643325 - 0.0498100i) q^{45} +(-5.07059 + 0.735430i) q^{46} +(3.52148 + 7.31244i) q^{47} +(-6.04007 + 3.39375i) q^{48} +(-4.94434 - 2.38107i) q^{49} +(6.74484 + 2.12169i) q^{50} +(7.87901 + 4.43850i) q^{51} +(8.55399 + 5.97257i) q^{52} +(-1.91915 - 1.53047i) q^{53} +(-6.45791 - 3.50647i) q^{54} +(0.0161644 - 0.0708209i) q^{55} +(-3.37755 - 0.830471i) q^{56} +(-3.57201 + 12.0305i) q^{57} +(7.28986 - 2.20407i) q^{58} +0.258155 q^{59} +(-0.0361834 + 0.0453210i) q^{60} +(-3.82638 - 0.873347i) q^{61} +(4.28292 + 11.0939i) q^{62} +(-1.16172 - 3.50145i) q^{63} +(7.99554 + 0.267106i) q^{64} +(0.0851391 + 0.0194324i) q^{65} +(-8.81167 - 5.94323i) q^{66} +(1.22496 - 2.54365i) q^{67} +(-5.12010 - 9.10074i) q^{68} +(1.00084 + 6.19483i) q^{69} +(-0.0288128 + 0.00417896i) q^{70} +(-1.48393 + 0.714624i) q^{71} +(4.27536 + 7.32948i) q^{72} +(5.40896 - 4.31350i) q^{73} +(5.73963 + 8.51998i) q^{74} +(2.46484 - 8.30158i) q^{75} +(10.7317 - 9.73756i) q^{76} +(-1.18734 - 5.20209i) q^{77} +(7.14480 - 10.5932i) q^{78} +(3.22970 + 1.55534i) q^{79} +(0.0628651 - 0.0230713i) q^{80} +(-4.16630 + 7.97759i) q^{81} +(0.0387978 - 0.0663443i) q^{82} +(-3.70237 - 16.2211i) q^{83} +(-0.950207 + 4.15252i) q^{84} +(-0.0683379 - 0.0544976i) q^{85} +(9.14985 - 1.32708i) q^{86} +(-2.84320 - 8.88348i) q^{87} +(5.13964 + 11.1448i) q^{88} +(4.98478 - 6.25072i) q^{89} +(0.0562148 + 0.0434136i) q^{90} +(6.25382 - 1.42739i) q^{91} +(2.72215 - 6.71516i) q^{92} +(13.5007 - 5.46413i) q^{93} +(-11.4410 - 0.921446i) q^{94} +(0.0526297 - 0.109287i) q^{95} +(0.169019 - 9.79650i) q^{96} +(13.5839 - 3.10045i) q^{97} +(6.43661 - 4.33613i) q^{98} +(-7.10378 + 10.9081i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9}+O(q^{10}) \) 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9	\( 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9} - 14 q^{10} - 20 q^{13} - 26 q^{16} - 56 q^{18} - 14 q^{21} - 40 q^{22} + 3 q^{24} + 40 q^{25} - 36 q^{28} - 6 q^{30} - 22 q^{33} - 8 q^{34} + 9 q^{36} - 28 q^{37} - 14 q^{40} - 74 q^{42} - 22 q^{45} + 14 q^{48} + 4 q^{49} - 4 q^{52} - 31 q^{54} - 12 q^{57} - 106 q^{58} - 42 q^{60} - 28 q^{61} - 94 q^{64} - 7 q^{66} - 14 q^{69} + 70 q^{72} - 28 q^{73} - 84 q^{76} - 9 q^{78} - 50 q^{81} - 46 q^{82} - 35 q^{84} - 168 q^{85} - 60 q^{88} + 119 q^{90} + 122 q^{93} + 36 q^{94} + 2 q^{96} - 28 q^{97}+O(q^{100}) \) 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9 - 14 * q^10 - 20 * q^13 - 26 * q^16 - 56 * q^18 - 14 * q^21 - 40 * q^22 + 3 * q^24 + 40 * q^25 - 36 * q^28 - 6 * q^30 - 22 * q^33 - 8 * q^34 + 9 * q^36 - 28 * q^37 - 14 * q^40 - 74 * q^42 - 22 * q^45 + 14 * q^48 + 4 * q^49 - 4 * q^52 - 31 * q^54 - 12 * q^57 - 106 * q^58 - 42 * q^60 - 28 * q^61 - 94 * q^64 - 7 * q^66 - 14 * q^69 + 70 * q^72 - 28 * q^73 - 84 * q^76 - 9 * q^78 - 50 * q^81 - 46 * q^82 - 35 * q^84 - 168 * q^85 - 60 * q^88 + 119 * q^90 + 122 * q^93 + 36 * q^94 + 2 * q^96 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

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