LMFDB - Embedded newform 196.2.j.a.111.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [196,2,Mod(27,196)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("196.27"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(196, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	196.j (of order $14$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.56506787962$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			111.21
Character	$\chi$	$=$	196.111
Dual form			196.2.j.a.83.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.04119 - 0.957034i) q^{2} +(1.57092 + 1.96987i) q^{3} +(0.168171 - 1.99292i) q^{4} +(1.55435 - 1.23956i) q^{5} +(3.52087 + 0.547594i) q^{6} +(-2.03422 + 1.69173i) q^{7} +(-1.73219 - 2.23596i) q^{8} +(-0.745040 + 3.26424i) q^{9} +(0.432087 - 2.77819i) q^{10} +(-3.09970 + 0.707487i) q^{11} +(4.18997 - 2.79944i) q^{12} +(-5.38387 + 1.22883i) q^{13} +(-0.498967 + 3.70824i) q^{14} +(4.88353 + 1.11463i) q^{15} +(-3.94344 - 0.670301i) q^{16} +(2.48020 - 5.15019i) q^{17} +(2.34825 + 4.11173i) q^{18} +7.59495 q^{19} +(-2.20893 - 3.30615i) q^{20} +(-6.52809 - 1.34957i) q^{21} +(-2.55031 + 3.70316i) q^{22} +(0.751225 + 1.55993i) q^{23} +(1.68342 - 6.92471i) q^{24} +(-0.233088 + 1.02123i) q^{25} +(-4.42962 + 6.43200i) q^{26} +(-0.790388 + 0.380631i) q^{27} +(3.02939 + 4.33852i) q^{28} +(0.626525 + 0.301719i) q^{29} +(6.15144 - 3.51315i) q^{30} -8.05654 q^{31} +(-4.74739 + 3.07609i) q^{32} +(-6.26305 - 4.99461i) q^{33} +(-2.34654 - 7.73598i) q^{34} +(-1.06489 + 5.15108i) q^{35} +(6.38006 + 2.03375i) q^{36} +(4.24933 + 2.04637i) q^{37} +(7.90782 - 7.26863i) q^{38} +(-10.8783 - 8.67513i) q^{39} +(-5.46403 - 1.32832i) q^{40} +(-0.0970188 + 0.0773699i) q^{41} +(-8.08859 + 4.84244i) q^{42} +(-3.53279 - 2.81730i) q^{43} +(0.888684 + 6.29643i) q^{44} +(2.88814 + 5.99729i) q^{45} +(2.27508 + 0.905247i) q^{46} +(0.299542 + 1.31238i) q^{47} +(-4.87442 - 8.82105i) q^{48} +(1.27607 - 6.88271i) q^{49} +(0.734659 + 1.28637i) q^{50} +(14.0414 - 3.20486i) q^{51} +(1.54355 + 10.9363i) q^{52} +(0.183642 - 0.0884374i) q^{53} +(-0.458671 + 1.15274i) q^{54} +(-3.94107 + 4.94194i) q^{55} +(7.30630 + 1.61802i) q^{56} +(11.9311 + 14.9611i) q^{57} +(0.941089 - 0.285458i) q^{58} +(1.40598 - 1.76305i) q^{59} +(3.04264 - 9.54502i) q^{60} +(0.524559 - 1.08926i) q^{61} +(-8.38842 + 7.71039i) q^{62} +(-4.00665 - 7.90057i) q^{63} +(-1.99903 + 7.74622i) q^{64} +(-6.84523 + 8.58365i) q^{65} +(-11.3011 + 0.793588i) q^{66} +3.71909i q^{67} +(-9.84680 - 5.80894i) q^{68} +(-1.89276 + 3.93035i) q^{69} +(3.82100 + 6.38241i) q^{70} +(3.42655 + 7.11531i) q^{71} +(8.58925 - 3.98840i) q^{72} +(4.61124 + 1.05248i) q^{73} +(6.38283 - 1.93609i) q^{74} +(-2.37785 + 1.14511i) q^{75} +(1.27725 - 15.1361i) q^{76} +(5.10859 - 6.68306i) q^{77} +(-19.6288 + 1.37838i) q^{78} -9.99726i q^{79} +(-6.96037 + 3.84622i) q^{80} +(7.05839 + 3.39914i) q^{81} +(-0.0269698 + 0.173407i) q^{82} +(-0.712952 + 3.12364i) q^{83} +(-3.78741 + 12.7830i) q^{84} +(-2.52883 - 11.0795i) q^{85} +(-6.37458 + 0.447638i) q^{86} +(0.389874 + 1.70815i) q^{87} +(6.95119 + 5.70531i) q^{88} +(14.8115 + 3.38064i) q^{89} +(8.74673 + 3.48029i) q^{90} +(8.87310 - 11.6078i) q^{91} +(3.23515 - 1.23479i) q^{92} +(-12.6562 - 15.8703i) q^{93} +(1.56787 + 1.07977i) q^{94} +(11.8052 - 9.41436i) q^{95} +(-13.5173 - 4.51945i) q^{96} -3.30506i q^{97} +(-5.25835 - 8.38748i) q^{98} -10.6453i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9} - 7 q^{10} - 42 q^{12} - 14 q^{13} + 21 q^{14} - 13 q^{16} - 14 q^{17} - 12 q^{18} - 7 q^{20} - 14 q^{21} + 3 q^{22} + 35 q^{24} - 7 q^{26}+ \cdots + 105 q^{98}+O(q^{100}) $ 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9 - 7 * q^10 - 42 * q^12 - 14 * q^13 + 21 * q^14 - 13 * q^16 - 14 * q^17 - 12 * q^18 - 7 * q^20 - 14 * q^21 + 3 * q^22 + 35 * q^24 - 7 * q^26 + 42 * q^28 - 30 * q^29 - 4 * q^30 - 5 * q^32 - 14 * q^33 + 77 * q^34 - 11 * q^36 + 10 * q^37 - 21 * q^38 - 63 * q^40 - 14 * q^41 - 7 * q^42 - 55 * q^44 - 14 * q^45 - 19 * q^46 - 132 * q^50 - 7 * q^52 - 2 * q^53 + 14 * q^54 - 70 * q^56 - 64 * q^57 - 3 * q^58 - 107 * q^60 + 14 * q^61 - 21 * q^62 - 11 * q^64 - 22 * q^65 + 161 * q^66 - 70 * q^69 - 77 * q^70 + 114 * q^72 - 14 * q^73 + 5 * q^74 + 70 * q^76 - 42 * q^77 + 61 * q^78 + 92 * q^81 - 42 * q^82 + 70 * q^84 - 6 * q^85 + 47 * q^86 + 65 * q^88 - 14 * q^89 + 112 * q^90 - 70 * q^92 - 48 * q^93 - 28 * q^94 + 238 * q^96 + 105 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{11}{14}\right)$

Coefficient data

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

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

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

$2$	1.04119	−	0.957034i	0.736236	−	0.676725i
$2$	1.04119	−	0.957034i	0.736236	−	0.676725i
$3$	1.57092	+	1.96987i	0.906971	+	1.13731i	0.990043	+	0.140762i	$0.0449553\pi$
$3$	1.57092	+	1.96987i	0.906971	+	1.13731i	−0.0830725	+	0.996544i	$0.526473\pi$
$4$	0.168171	−	1.99292i	0.0840854	−	0.996459i
$5$	1.55435	−	1.23956i	0.695128	−	0.554346i	−0.210929	−	0.977501i	$-0.567649\pi$
$5$	1.55435	−	1.23956i	0.695128	−	0.554346i	0.906057	+	0.423155i	$0.139078\pi$
$6$	3.52087	+	0.547594i	1.43739	+	0.223554i
$7$	−2.03422	+	1.69173i	−0.768861	+	0.639415i
$7$	−2.03422	+	1.69173i	−0.768861	+	0.639415i
$8$	−1.73219	−	2.23596i	−0.612422	−	0.790531i
$9$	−0.745040	+	3.26424i	−0.248347	+	1.08808i
$10$	0.432087	−	2.77819i	0.136638	−	0.878540i
$11$	−3.09970	+	0.707487i	−0.934596	+	0.213315i	−0.662592	−	0.748981i	$-0.730544\pi$
$11$	−3.09970	+	0.707487i	−0.934596	+	0.213315i	−0.272004	+	0.962296i	$0.587686\pi$
$12$	4.18997	−	2.79944i	1.20954	−	0.808128i
$13$	−5.38387	+	1.22883i	−1.49322	+	0.340817i	−0.889705	−	0.456537i	$-0.849090\pi$
$13$	−5.38387	+	1.22883i	−1.49322	+	0.340817i	−0.603512	+	0.797354i	$0.706233\pi$
$14$	−0.498967	+	3.70824i	−0.133355	+	0.991068i
$15$	4.88353	+	1.11463i	1.26092	+	0.287797i
$16$	−3.94344	−	0.670301i	−0.985859	−	0.167575i
$17$	2.48020	−	5.15019i	0.601537	−	1.24910i	−0.348601	−	0.937271i	$-0.613343\pi$
$17$	2.48020	−	5.15019i	0.601537	−	1.24910i	0.950137	−	0.311832i	$-0.100943\pi$
$18$	2.34825	+	4.11173i	0.553489	+	0.969145i
$19$	7.59495			1.74240			0.871201	−	0.490927i	$-0.163342\pi$
$19$	7.59495			1.74240			0.871201	+	0.490927i	$0.163342\pi$
$20$	−2.20893	−	3.30615i	−0.493933	−	0.739278i
$21$	−6.52809	−	1.34957i	−1.42455	−	0.294499i
$22$	−2.55031	+	3.70316i	−0.543727	+	0.789515i
$23$	0.751225	+	1.55993i	0.156641	+	0.325269i	0.964489	−	0.264122i	$-0.0850821\pi$
$23$	0.751225	+	1.55993i	0.156641	+	0.325269i	−0.807848	+	0.589391i	$0.799368\pi$
$24$	1.68342	−	6.92471i	0.343626	−	1.41350i
$25$	−0.233088	+	1.02123i	−0.0466177	+	0.204245i
$26$	−4.42962	+	6.43200i	−0.868720	+	1.26142i
$27$	−0.790388	+	0.380631i	−0.152110	+	0.0732524i
$28$	3.02939	+	4.33852i	0.572501	+	0.819904i
$29$	0.626525	+	0.301719i	0.116343	+	0.0560277i	0.491150	−	0.871075i	$-0.336577\pi$
$29$	0.626525	+	0.301719i	0.116343	+	0.0560277i	−0.374807	+	0.927103i	$0.622291\pi$
$30$	6.15144	−	3.51315i	1.12309	−	0.641411i
$31$	−8.05654			−1.44700			−0.723499	−	0.690326i	$-0.757467\pi$
$31$	−8.05654			−1.44700			−0.723499	+	0.690326i	$0.757467\pi$
$32$	−4.74739	+	3.07609i	−0.839227	+	0.543781i
$33$	−6.26305	−	4.99461i	−1.09026	−	0.869451i
$34$	−2.34654	−	7.73598i	−0.402428	−	1.32671i
$35$	−1.06489	+	5.15108i	−0.180000	+	0.870691i
$36$	6.38006	+	2.03375i	1.06334	+	0.338959i
$37$	4.24933	+	2.04637i	0.698586	+	0.336421i	0.749243	−	0.662295i	$-0.230417\pi$
$37$	4.24933	+	2.04637i	0.698586	+	0.336421i	−0.0506571	+	0.998716i	$0.516132\pi$
$38$	7.90782	−	7.26863i	1.28282	−	1.17913i
$39$	−10.8783	−	8.67513i	−1.74192	−	1.38913i
$40$	−5.46403	−	1.32832i	−0.863939	−	0.210026i
$41$	−0.0970188	+	0.0773699i	−0.0151518	+	0.0120832i	−0.631036	−	0.775753i	$-0.717370\pi$
$41$	−0.0970188	+	0.0773699i	−0.0151518	+	0.0120832i	0.615885	+	0.787836i	$0.288799\pi$
$42$	−8.08859	+	4.84244i	−1.24810	+	0.747205i
$43$	−3.53279	−	2.81730i	−0.538745	−	0.429635i	0.315942	−	0.948779i	$-0.397680\pi$
$43$	−3.53279	−	2.81730i	−0.538745	−	0.429635i	−0.854687	+	0.519144i	$0.826251\pi$
$44$	0.888684	+	6.29643i	0.133974	+	0.949223i
$45$	2.88814	+	5.99729i	0.430539	+	0.894024i
$46$	2.27508	+	0.905247i	0.335442	+	0.133471i
$47$	0.299542	+	1.31238i	0.0436927	+	0.191430i	0.992064	−	0.125731i	$-0.0401276\pi$
$47$	0.299542	+	1.31238i	0.0436927	+	0.191430i	−0.948372	+	0.317161i	$0.897270\pi$
$48$	−4.87442	−	8.82105i	−0.703561	−	1.27321i
$49$	1.27607	−	6.88271i	0.182296	−	0.983244i
$50$	0.734659	+	1.28637i	0.103896	+	0.181920i
$51$	14.0414	−	3.20486i	1.96619	−	0.448770i
$52$	1.54355	+	10.9363i	0.214052	+	1.51659i
$53$	0.183642	−	0.0884374i	0.0252252	−	0.0121478i	−0.421229	−	0.906954i	$-0.638401\pi$
$53$	0.183642	−	0.0884374i	0.0252252	−	0.0121478i	0.446454	+	0.894807i	$0.352687\pi$
$54$	−0.458671	+	1.15274i	−0.0624172	+	0.156868i
$55$	−3.94107	+	4.94194i	−0.531413	+	0.666371i
$56$	7.30630	+	1.61802i	0.976345	+	0.216217i
$57$	11.9311	+	14.9611i	1.58031	+	1.98164i
$58$	0.941089	−	0.285458i	0.123571	−	0.0374825i
$59$	1.40598	−	1.76305i	0.183043	−	0.229529i	−0.681841	−	0.731501i	$-0.738820\pi$
$59$	1.40598	−	1.76305i	0.183043	−	0.229529i	0.864884	+	0.501971i	$0.167392\pi$
$60$	3.04264	−	9.54502i	0.392803	−	1.23226i
$61$	0.524559	−	1.08926i	0.0671629	−	0.139465i	−0.864685	−	0.502315i	$-0.832482\pi$
$61$	0.524559	−	1.08926i	0.0671629	−	0.139465i	0.931848	+	0.362850i	$0.118196\pi$
$62$	−8.38842	+	7.71039i	−1.06533	+	0.979220i
$63$	−4.00665	−	7.90057i	−0.504790	−	0.995378i
$64$	−1.99903	+	7.74622i	−0.249878	+	0.968277i
$65$	−6.84523	+	8.58365i	−0.849046	+	1.06467i
$66$	−11.3011	+	0.793588i	−1.39106	+	0.0976839i
$67$			3.71909i			0.454359i	0.973853	+	0.227179i	$0.0729504\pi$
$67$			3.71909i			0.454359i	−0.973853	+	0.227179i	$0.927050\pi$
$68$	−9.84680	−	5.80894i	−1.19410	−	0.704438i
$69$	−1.89276	+	3.93035i	−0.227861	+	0.473158i
$70$	3.82100	+	6.38241i	0.456696	+	0.762844i
$71$	3.42655	+	7.11531i	0.406657	+	0.844432i	0.999242	+	0.0389243i	$0.0123931\pi$
$71$	3.42655	+	7.11531i	0.406657	+	0.844432i	−0.592585	+	0.805508i	$0.701893\pi$
$72$	8.58925	−	3.98840i	1.01225	−	0.470038i
$73$	4.61124	+	1.05248i	0.539704	+	0.123184i	0.483679	−	0.875245i	$-0.339300\pi$
$73$	4.61124	+	1.05248i	0.539704	+	0.123184i	0.0560251	+	0.998429i	$0.482157\pi$
$74$	6.38283	−	1.93609i	0.741989	−	0.225066i
$75$	−2.37785	+	1.14511i	−0.274570	+	0.132226i
$76$	1.27725	−	15.1361i	0.146511	−	1.73623i
$77$	5.10859	−	6.68306i	0.582178	−	0.761605i
$78$	−19.6288	+	1.37838i	−2.22252	+	0.156071i
$79$		−	9.99726i		−	1.12478i	−0.826872	−	0.562390i	$-0.809882\pi$
$79$		−	9.99726i		−	1.12478i	0.826872	−	0.562390i	$-0.190118\pi$
$80$	−6.96037	+	3.84622i	−0.778193	+	0.430021i
$81$	7.05839	+	3.39914i	0.784266	+	0.377683i
$82$	−0.0269698	+	0.173407i	−0.00297831	+	0.0191496i
$83$	−0.712952	+	3.12364i	−0.0782566	+	0.342865i	−0.998865	−	0.0476215i	$-0.984836\pi$
$83$	−0.712952	+	3.12364i	−0.0782566	+	0.342865i	0.920609	+	0.390486i	$0.127693\pi$
$84$	−3.78741	+	12.7830i	−0.413240	+	1.39474i
$85$	−2.52883	−	11.0795i	−0.274291	−	1.20175i
$86$	−6.37458	+	0.447638i	−0.687388	+	0.0482701i
$87$	0.389874	+	1.70815i	0.0417989	+	0.183133i
$88$	6.95119	+	5.70531i	0.741000	+	0.608188i
$89$	14.8115	+	3.38064i	1.57002	+	0.358347i	0.916966	−	0.398965i	$-0.130630\pi$
$89$	14.8115	+	3.38064i	1.57002	+	0.358347i	0.653054	+	0.757312i	$0.273488\pi$
$90$	8.74673	+	3.48029i	0.921987	+	0.366855i
$91$	8.87310	−	11.6078i	0.930153	−	1.21683i
$92$	3.23515	−	1.23479i	0.337288	−	0.128736i
$93$	−12.6562	−	15.8703i	−1.31238	−	1.64568i
$94$	1.56787	+	1.07977i	0.161714	+	0.111370i
$95$	11.8052	−	9.41436i	1.21119	−	0.965893i
$96$	−13.5173	−	4.51945i	−1.37960	−	0.461264i
$97$		−	3.30506i		−	0.335578i	−0.985823	−	0.167789i	$-0.946337\pi$
$97$		−	3.30506i		−	0.335578i	0.985823	−	0.167789i	$-0.0536627\pi$
$98$	−5.25835	−	8.38748i	−0.531173	−	0.847263i
$99$		−	10.6453i		−	1.06989i
$100$	1.99602	+	0.636267i	0.199602	+	0.0636267i
$101$	9.75340	−	7.77807i	0.970499	−	0.773947i	−0.00361730	−	0.999993i	$-0.501151\pi$
$101$	9.75340	−	7.77807i	0.970499	−	0.773947i	0.974117	+	0.226046i	$0.0725800\pi$
$102$	11.5527	−	16.7750i	1.14388	−	1.66097i
$103$	−5.67864	−	7.12079i	−0.559533	−	0.701632i	0.418938	−	0.908015i	$-0.362402\pi$
$103$	−5.67864	−	7.12079i	−0.559533	−	0.701632i	−0.978471	+	0.206383i	$0.933831\pi$
$104$	12.0735	+	9.90954i	1.18391	+	0.971710i
$105$	−11.8198	+	5.99422i	−1.15350	+	0.584976i
$106$	0.106570	−	0.267832i	0.0103510	−	0.0260142i
$107$	−8.12037	−	1.85342i	−0.785025	−	0.179177i	−0.188823	−	0.982011i	$-0.560467\pi$
$107$	−8.12037	−	1.85342i	−0.785025	−	0.179177i	−0.596202	+	0.802834i	$0.703324\pi$
$108$	0.625645	+	1.63919i	0.0602027	+	0.157731i
$109$	−3.41321	−	14.9542i	−0.326926	−	1.43236i	−0.824957	−	0.565196i	$-0.808801\pi$
$109$	−3.41321	−	14.9542i	−0.326926	−	1.43236i	0.498031	−	0.867159i	$-0.334057\pi$
$110$	0.626191	+	8.91725i	0.0597050	+	0.850227i
$111$	2.64428	+	11.5853i	0.250984	+	1.09963i
$112$	9.15578	−	5.30771i	0.865139	−	0.501531i
$113$	−3.52940	+	15.4633i	−0.332018	+	1.45467i	0.483198	+	0.875511i	$0.339475\pi$
$113$	−3.52940	+	15.4633i	−0.332018	+	1.45467i	−0.815217	+	0.579156i	$0.803382\pi$
$114$	26.7408	+	4.15895i	2.50451	+	0.389522i
$115$	3.10129	+	1.49350i	0.289197	+	0.139270i
$116$	0.706663	−	1.19787i	0.0656121	−	0.111220i
$117$		−	18.4898i		−	1.70938i
$118$	−0.223395	−	3.18125i	−0.0205652	−	0.292858i
$119$	3.66748	+	14.6724i	0.336198	+	1.34502i
$120$	−5.96693	−	12.8501i	−0.544704	−	1.17305i
$121$	−0.803027	+	0.386717i	−0.0730024	+	0.0351561i
$122$	−0.496290	−	1.63615i	−0.0449320	−	0.148130i
$123$	−0.304818	−	0.0695726i	−0.0274845	−	0.00627315i
$124$	−1.35488	+	16.0560i	−0.121671	+	1.44187i
$125$	5.21657	+	10.8323i	0.466584	+	0.968872i
$126$	−11.7328	−	4.39153i	−1.04524	−	0.391229i
$127$	−4.41971	+	9.17762i	−0.392186	+	0.814382i	0.607611	+	0.794234i	$0.292128\pi$
$127$	−4.41971	+	9.17762i	−0.392186	+	0.814382i	−0.999797	+	0.0201474i	$0.993586\pi$
$128$	5.33202	+	9.97845i	0.471289	+	0.881979i
$129$		−	11.3849i		−	1.00238i
$130$	1.08763	+	15.4884i	0.0953915	+	1.35842i
$131$	2.38863	−	2.99525i	0.208696	−	0.261696i	−0.666456	−	0.745544i	$-0.732190\pi$
$131$	2.38863	−	2.99525i	0.208696	−	0.261696i	0.875152	+	0.483848i	$0.160761\pi$
$132$	−11.0071	+	11.6418i	−0.958046	+	1.01329i
$133$	−15.4498	+	12.8486i	−1.33967	+	1.11412i
$134$	3.55929	+	3.87229i	0.307476	+	0.334515i
$135$	−0.756729	+	1.57136i	−0.0651289	+	0.135241i
$136$	−15.8118	+	3.37548i	−1.35585	+	0.289445i
$137$	−6.94284	+	8.70604i	−0.593166	+	0.743807i	−0.984296	−	0.176529i	$-0.943513\pi$
$137$	−6.94284	+	8.70604i	−0.593166	+	0.743807i	0.391129	+	0.920336i	$0.372085\pi$
$138$	1.79075	+	5.90369i	0.152439	+	0.502555i
$139$	−8.02974	−	10.0690i	−0.681074	−	0.854040i	0.314379	−	0.949298i	$-0.398204\pi$
$139$	−8.02974	−	10.0690i	−0.681074	−	0.854040i	−0.995453	+	0.0952580i	$0.969632\pi$
$140$	10.0866	+	2.98850i	0.852472	+	0.252575i
$141$	−2.11466	+	2.65170i	−0.178086	+	0.223313i
$142$	10.3773	+	4.12909i	0.870844	+	0.346506i
$143$	15.8190	−	7.61804i	1.32285	−	0.637053i
$144$	5.12604	−	12.3729i	0.427170	−	1.03108i
$145$	1.34784	−	0.307635i	0.111932	−	0.0255477i
$146$	5.80846	−	3.31727i	0.480711	−	0.274539i
$147$	15.5627	−	8.29848i	1.28359	−	0.684447i
$148$	4.79286	−	8.12443i	0.393971	−	0.667824i
$149$	1.60103	+	7.01458i	0.131162	+	0.574657i	0.997207	+	0.0746909i	$0.0237970\pi$
$149$	1.60103	+	7.01458i	0.131162	+	0.574657i	−0.866045	+	0.499966i	$0.833346\pi$
$150$	−1.37989	+	3.46797i	−0.112668	+	0.283158i
$151$	2.11679	+	4.39555i	0.172262	+	0.357705i	0.969169	−	0.246396i	$-0.0792465\pi$
$151$	2.11679	+	4.39555i	0.172262	+	0.357705i	−0.796908	+	0.604101i	$0.793532\pi$
$152$	−13.1559	−	16.9820i	−1.06709	−	1.37742i
$153$	14.9636	+	11.9330i	1.20973	+	0.964730i
$154$	−1.07688	−	11.8475i	−0.0867776	−	0.954695i
$155$	−12.5227	+	9.98653i	−1.00585	+	0.802137i
$156$	−19.1182	+	20.2206i	−1.53068	+	1.61894i
$157$	2.88021	+	2.29689i	0.229866	+	0.183312i	0.731649	−	0.681682i	$-0.238751\pi$
$157$	2.88021	+	2.29689i	0.229866	+	0.183312i	−0.501783	+	0.864993i	$0.667322\pi$
$158$	−9.56772	−	10.4091i	−0.761167	−	0.828102i
$159$	0.462698	+	0.222823i	0.0366943	+	0.0176710i
$160$	−3.56613	+	10.6660i	−0.281927	+	0.843219i
$161$	−4.16715	−	1.90237i	−0.328417	−	0.149928i
$162$	10.6023	−	3.21596i	0.832992	−	0.252669i
$163$	−12.2208	−	9.74575i	−0.957205	−	0.763346i	0.0144139	−	0.999896i	$-0.495412\pi$
$163$	−12.2208	−	9.74575i	−0.957205	−	0.763346i	−0.971619	+	0.236550i	$0.923983\pi$
$164$	0.137876	+	0.206362i	0.0107663	+	0.0161141i
$165$	−15.9261			−1.23984
$166$	2.24711	+	3.93464i	0.174410	+	0.305387i
$167$	2.02545	+	0.975404i	0.156734	+	0.0754790i	0.510606	−	0.859815i	$-0.329421\pi$
$167$	2.02545	+	0.975404i	0.156734	+	0.0754790i	−0.353872	+	0.935294i	$0.615135\pi$
$168$	8.29033	+	16.9342i	0.639613	+	1.30651i
$169$	15.7634	−	7.59127i	1.21257	−	0.583944i
$170$	−13.2365	−	9.11578i	−1.01519	−	0.699148i
$171$	−5.65855	+	24.7917i	−0.432720	+	1.89587i
$172$	−6.20877	+	6.56677i	−0.473414	+	0.500711i
$173$	−7.41839	−	15.4044i	−0.564010	−	1.17118i	−0.966717	−	0.255849i	$-0.917645\pi$
$173$	−7.41839	−	15.4044i	−0.564010	−	1.17118i	0.402707	−	0.915329i	$-0.368069\pi$
$174$	2.04069	+	1.40539i	0.154704	+	0.106543i
$175$	−1.25349	−	2.47172i	−0.0947551	−	0.186845i
$176$	12.6977	−	0.712196i	0.957127	−	0.0536838i
$177$	5.68166			0.427060
$178$	18.6571	−	10.6552i	1.39841	−	0.798645i
$179$	−1.31652	+	2.73379i	−0.0984016	+	0.204333i	−0.944358	−	0.328919i	$-0.893316\pi$
$179$	−1.31652	+	2.73379i	−0.0984016	+	0.204333i	0.845957	+	0.533252i	$0.179030\pi$
$180$	12.4378	−	4.74726i	0.927060	−	0.353840i
$181$	5.81694	+	1.32768i	0.432370	+	0.0986855i	0.433166	−	0.901314i	$-0.357396\pi$
$181$	5.81694	+	1.32768i	0.432370	+	0.0986855i	−0.000796483		1.00000i	$0.500254\pi$
$182$	−1.87043	−	20.5778i	−0.138646	−	1.52533i
$183$	2.96974	−	0.677824i	0.219529	−	0.0501062i
$184$	2.18668	−	4.38181i	0.161204	−	0.323031i
$185$	9.14156	−	2.08650i	0.672101	−	0.153403i
$186$	−28.3660	−	4.41172i	−2.07990	−	0.323483i
$187$	−4.04419	+	17.7188i	−0.295741	+	1.29572i
$188$	2.66584	−	0.376258i	0.194426	−	0.0274414i
$189$	0.963894	−	2.11141i	0.0701130	−	0.153583i
$190$	3.28168	−	21.1002i	0.238078	−	1.53077i
$191$	−4.32371	+	3.44805i	−0.312853	+	0.249492i	−0.767309	−	0.641277i	$-0.778405\pi$
$191$	−4.32371	+	3.44805i	−0.312853	+	0.249492i	0.454456	+	0.890769i	$0.349834\pi$
$192$	−18.3994	+	8.23086i	−1.32786	+	0.594011i
$193$	11.1359	+	13.9639i	0.801578	+	1.00515i	0.999688	+	0.0249671i	$0.00794810\pi$
$193$	11.1359	+	13.9639i	0.801578	+	1.00515i	−0.198110	+	0.980180i	$0.563480\pi$
$194$	−3.16305	−	3.44120i	−0.227094	−	0.247064i
$195$	−27.6620			−1.98092
$196$	−13.5021	−	3.70058i	−0.964433	−	0.264327i
$197$	−0.741517			−0.0528309			−0.0264154	−	0.999651i	$-0.508409\pi$
$197$	−0.741517			−0.0528309			−0.0264154	+	0.999651i	$0.508409\pi$
$198$	−10.1879	−	11.0838i	−0.724022	−	0.787691i
$199$	0.0710715	+	0.0891209i	0.00503813	+	0.00631761i	0.784344	−	0.620326i	$-0.213000\pi$
$199$	0.0710715	+	0.0891209i	0.00503813	+	0.00631761i	−0.779306	+	0.626644i	$0.784428\pi$
$200$	2.68718	−	1.24778i	0.190012	−	0.0882317i
$201$	−7.32612	+	5.84239i	−0.516745	+	0.412090i
$202$	2.71130	−	17.4328i	0.190766	−	1.22657i
$203$	−1.78492	+	0.446153i	−0.125276	+	0.0313138i
$204$	−4.02566	−	28.5223i	−0.281853	−	1.99696i
$205$	−0.0548972	+	0.240520i	−0.00383419	+	0.0167987i
$206$	−12.7274	−	1.97947i	−0.886760	−	0.137916i
$207$	−5.65169	+	1.28996i	−0.392819	+	0.0896584i
$208$	22.0546	−	1.23701i	1.52921	−	0.0857714i
$209$	−23.5421	+	5.37333i	−1.62844	+	0.371681i
$210$	−6.57004	+	17.5531i	−0.453376	+	1.21128i
$211$	−16.3523	−	3.73231i	−1.12574	−	0.256943i	−0.381181	−	0.924500i	$-0.624483\pi$
$211$	−16.3523	−	3.73231i	−1.12574	−	0.256943i	−0.744558	+	0.667558i	$0.767340\pi$
$212$	−0.145365	−	0.380856i	−0.00998372	−	0.0261573i
$213$	−8.63341	+	17.9275i	−0.591551	+	1.22837i
$214$	−10.2287	+	5.84170i	−0.699217	+	0.399330i
$215$	−8.98340			−0.612663
$216$	2.22018	+	1.10795i	0.151064	+	0.0753864i
$217$	16.3887	−	13.6295i	1.11254	−	0.925232i
$218$	−17.8655	−	12.3037i	−1.21001	−	0.833312i
$219$	5.17062	+	10.7369i	0.349398	+	0.725533i
$220$	9.18610	+	8.68531i	0.619327	+	0.585563i
$221$	−7.02435	+	30.7757i	−0.472509	+	2.07020i
$222$	13.8408	+	9.53191i	0.928931	+	0.639740i
$223$	14.8371	−	7.14518i	0.993567	−	0.478477i	0.134817	−	0.990871i	$-0.456955\pi$
$223$	14.8371	−	7.14518i	0.993567	−	0.478477i	0.858751	+	0.512394i	$0.171241\pi$
$224$	4.45328	−	14.2887i	0.297547	−	0.954707i
$225$	−3.15987	−	1.52171i	−0.210658	−	0.101447i
$226$	11.1241	+	19.4781i	0.739967	+	1.29566i
$227$	17.2029			1.14179			0.570897	−	0.821022i	$-0.306596\pi$
$227$	17.2029			1.14179			0.570897	+	0.821022i	$0.306596\pi$
$228$	31.8226	−	21.2616i	2.10751	−	1.40808i
$229$	−16.9479	−	13.5155i	−1.11995	−	0.893130i	−0.124866	−	0.992174i	$-0.539850\pi$
$229$	−16.9479	−	13.5155i	−1.11995	−	0.893130i	−0.995083	+	0.0990437i	$0.968422\pi$
$230$	4.65838	−	1.41302i	0.307165	−	0.0931715i
$231$	21.1899	−	0.435286i	1.39420	−	0.0286397i
$232$	−0.410631	−	1.92352i	−0.0269592	−	0.126285i
$233$	−20.6657	−	9.95205i	−1.35385	−	0.651981i	−0.390595	−	0.920563i	$-0.627731\pi$
$233$	−20.6657	−	9.95205i	−1.35385	−	0.651981i	−0.963257	+	0.268582i	$0.913445\pi$
$234$	−17.6953	−	19.2514i	−1.15678	−	1.25850i
$235$	2.09236	+	1.66860i	0.136490	+	0.108847i
$236$	−3.27716	−	3.09850i	−0.213325	−	0.201695i
$237$	19.6933	−	15.7049i	1.27922	−	1.02014i
$238$	17.8606	+	11.7669i	1.15773	+	0.762737i
$239$	5.37585	+	4.28709i	0.347735	+	0.277309i	0.781744	−	0.623599i	$-0.214330\pi$
$239$	5.37585	+	4.28709i	0.347735	+	0.277309i	−0.434010	+	0.900908i	$0.642902\pi$
$240$	−18.5107	−	7.66892i	−1.19486	−	0.495027i
$241$	−0.404203	−	0.839335i	−0.0260370	−	0.0540664i	0.887545	−	0.460722i	$-0.152409\pi$
$241$	−0.404203	−	0.839335i	−0.0260370	−	0.0540664i	−0.913582	+	0.406655i	$0.866695\pi$
$242$	−0.466005	+	1.17117i	−0.0299559	+	0.0752858i
$243$	4.97792	+	21.8097i	0.319334	+	1.39909i
$244$	−2.08259	−	1.22858i	−0.133324	−	0.0786521i
$245$	−6.54803	−	12.2799i	−0.418338	−	0.784535i
$246$	−0.383958	+	0.219282i	−0.0244802	+	0.0139809i
$247$	−40.8902	+	9.33293i	−2.60178	+	0.593840i
$248$	13.9555	+	18.0141i	0.886173	+	1.14390i
$249$	−7.27317	+	3.50257i	−0.460918	+	0.221967i
$250$	15.7984	+	6.28611i	0.999176	+	0.397569i
$251$	9.29737	−	11.6585i	0.586845	−	0.735880i	−0.396419	−	0.918070i	$-0.629747\pi$
$251$	9.29737	−	11.6585i	0.586845	−	0.735880i	0.983263	+	0.182190i	$0.0583186\pi$
$252$	−16.4190	+	6.65627i	−1.03430	+	0.419305i
$253$	−3.43221	−	4.30385i	−0.215781	−	0.270581i
$254$	4.18152	+	13.7855i	0.262372	+	0.864979i
$255$	17.8527	−	22.3866i	1.11798	−	1.40190i
$256$	15.1014	+	5.28658i	0.943837	+	0.330411i
$257$	−8.96630	+	18.6187i	−0.559302	+	1.16140i	0.409211	+	0.912440i	$0.365804\pi$
$257$	−8.96630	+	18.6187i	−0.559302	+	1.16140i	−0.968513	+	0.248963i	$0.919910\pi$
$258$	−10.8957	−	11.8539i	−0.678339	−	0.737991i
$259$	−12.1060	+	3.02598i	−0.752229	+	0.188025i
$260$	15.9553	+	15.0855i	0.989507	+	0.935563i
$261$	−1.45167	+	1.82033i	−0.0898560	+	0.112676i
$262$	−0.379527	−	5.40464i	−0.0234472	−	0.333900i
$263$			19.6671i			1.21273i	0.795187	+	0.606364i	$0.207372\pi$
$263$			19.6671i			1.21273i	−0.795187	+	0.606364i	$0.792628\pi$
$264$	−0.318955	+	22.6555i	−0.0196303	+	1.39435i
$265$	0.175822	−	0.365098i	0.0108006	−	0.0224278i
$266$	−3.78963	+	28.1639i	−0.232357	+	1.72684i
$267$	16.6083	+	34.4875i	1.01641	+	2.11060i
$268$	7.41183	+	0.625442i	0.452750	+	0.0382050i
$269$	−10.6024	−	2.41992i	−0.646438	−	0.147545i	−0.113283	−	0.993563i	$-0.536137\pi$
$269$	−10.6024	−	2.41992i	−0.646438	−	0.147545i	−0.533155	+	0.846018i	$0.678994\pi$
$270$	0.715947	+	2.36031i	0.0435712	+	0.143644i
$271$	12.0661	−	5.81071i	0.732961	−	0.352975i	−0.0298869	−	0.999553i	$-0.509515\pi$
$271$	12.0661	−	5.81071i	0.732961	−	0.352975i	0.762848	+	0.646578i	$0.223800\pi$
$272$	−13.2327	+	18.6470i	−0.802349	+	1.13064i
$273$	36.8048	−	0.756047i	2.22753	−	0.0457580i
$274$	1.10314	+	15.7092i	0.0666430	+	0.949028i
$275$		−	3.33041i		−	0.200831i
$276$	7.51455	+	4.43307i	0.452323	+	0.266840i
$277$	−17.1335	−	8.25104i	−1.02945	−	0.495757i	−0.158619	−	0.987340i	$-0.550704\pi$
$277$	−17.1335	−	8.25104i	−1.02945	−	0.495757i	−0.870831	+	0.491583i	$0.836418\pi$
$278$	−17.9969	−	2.79902i	−1.07938	−	0.167874i
$279$	6.00245	−	26.2984i	0.359357	−	1.57445i
$280$	13.3622	−	6.54159i	0.798544	−	0.390935i
$281$	−5.93480	−	26.0021i	−0.354040	−	1.55115i	−0.767754	−	0.640745i	$-0.778626\pi$
$281$	−5.93480	−	26.0021i	−0.354040	−	1.55115i	0.413713	−	0.910407i	$-0.364232\pi$
$282$	0.335996	+	4.78474i	0.0200083	+	0.284927i
$283$	−1.45981	−	6.39582i	−0.0867764	−	0.380192i	0.912827	−	0.408346i	$-0.133894\pi$
$283$	−1.45981	−	6.39582i	−0.0867764	−	0.380192i	−0.999604	+	0.0281538i	$0.991037\pi$
$284$	14.7565	−	5.63225i	0.875636	−	0.334213i
$285$	37.0902	+	8.46559i	2.19703	+	0.501458i
$286$	9.17995	−	23.0712i	0.542822	−	1.36423i
$287$	0.0664679	−	0.321517i	0.00392348	−	0.0189786i
$288$	−6.50409	−	17.7884i	−0.383257	−	1.04819i
$289$	−9.77370	−	12.2558i	−0.574923	−	0.720931i
$290$	1.10894	−	1.61024i	0.0651194	−	0.0945563i
$291$	6.51053	−	5.19198i	0.381654	−	0.304359i
$292$	2.87299	−	9.01281i	0.168129	−	0.527435i
$293$			7.82413i			0.457091i	0.973533	+	0.228545i	$0.0733969\pi$
$293$			7.82413i			0.457091i	−0.973533	+	0.228545i	$0.926603\pi$
$294$	8.26181	−	23.5343i	0.481839	−	1.37255i
$295$		−	4.48319i		−	0.261022i
$296$	−2.78506	−	13.0460i	−0.161878	−	0.758286i
$297$	2.18068	−	1.73903i	0.126536	−	0.100909i
$298$	8.38018	+	5.77130i	0.485451	+	0.334322i
$299$	−5.96140	−	7.47535i	−0.344756	−	0.432311i
$300$	1.88223	+	4.93143i	0.108670	+	0.284716i
$301$	11.9526	−	0.245531i	0.688936	−	0.0141522i
$302$	6.41068	+	2.55079i	0.368893	+	0.146781i
$303$	30.6436	+	6.99420i	1.76043	+	0.401807i
$304$	−29.9502	−	5.09090i	−1.71776	−	0.291983i
$305$	−0.534846	−	2.34331i	−0.0306252	−	0.134178i
$306$	27.0003	−	1.89603i	1.54351	−	0.108389i
$307$	−0.232854	−	1.02020i	−0.0132897	−	0.0582258i	0.967848	−	0.251535i	$-0.0809352\pi$
$307$	−0.232854	−	1.02020i	−0.0132897	−	0.0582258i	−0.981138	+	0.193309i	$0.938078\pi$
$308$	−12.4597	−	11.3049i	−0.709955	−	0.644156i
$309$	5.10635	−	22.3724i	0.290490	−	1.27272i
$310$	−3.48112	+	22.3826i	−0.197715	+	1.27124i
$311$	−16.3645	−	7.88070i	−0.927943	−	0.446874i	−0.0920426	−	0.995755i	$-0.529340\pi$
$311$	−16.3645	−	7.88070i	−0.927943	−	0.446874i	−0.835900	+	0.548881i	$0.815054\pi$
$312$	−0.553992	+	39.3504i	−0.0313636	+	2.22778i
$313$			25.7343i			1.45459i	0.686326	+	0.727294i	$0.259222\pi$
$313$			25.7343i			1.45459i	−0.686326	+	0.727294i	$0.740778\pi$
$314$	5.19706	−	0.364950i	0.293287	−	0.0205953i
$315$	−16.0209	−	7.31382i	−0.902677	−	0.412087i
$316$	−19.9237	−	1.68125i	−1.12080	−	0.0945775i
$317$	28.7099	−	13.8260i	1.61251	−	0.776544i	0.612605	−	0.790389i	$-0.290122\pi$
$317$	28.7099	−	13.8260i	1.61251	−	0.776544i	0.999904	+	0.0138453i	$0.00440725\pi$
$318$	0.695008	−	0.210815i	0.0389741	−	0.0118219i
$319$	−2.15551	−	0.491980i	−0.120685	−	0.0275456i
$320$	6.49467	+	14.5183i	0.363063	+	0.811595i
$321$	−9.10544	−	18.9077i	−0.508216	−	1.05532i
$322$	−6.15944	+	2.00736i	−0.343252	+	0.111866i
$323$	18.8370	−	39.1154i	1.04812	−	2.17644i
$324$	7.96123	−	13.4952i	0.442290	−	0.749731i
$325$		−	5.78458i		−	0.320871i
$326$	−22.0512	+	1.54849i	−1.22130	+	0.0857629i
$327$	24.0960	−	30.2155i	1.33251	−	1.67092i
$328$	0.341051	+	0.0829106i	0.0188314	+	0.00457797i
$329$	−2.82953	−	2.16292i	−0.155997	−	0.119245i
$330$	−16.5821	+	15.2418i	−0.912817	+	0.839034i
$331$	6.28270	−	13.0462i	0.345328	−	0.717082i	−0.653891	−	0.756589i	$-0.726864\pi$
$331$	6.28270	−	13.0462i	0.345328	−	0.717082i	0.999219	+	0.0395071i	$0.0125788\pi$
$332$	6.10527	+	1.94616i	0.335070	+	0.106809i
$333$	−9.84577	+	12.3462i	−0.539545	+	0.676568i
$334$	3.04238	−	0.922837i	0.166472	−	0.0504954i
$335$	4.61001	+	5.78078i	0.251872	+	0.315838i
$336$	24.8385	+	9.69771i	1.35505	+	0.529054i
$337$	−19.2318	+	24.1159i	−1.04762	+	1.31368i	−0.0997545	+	0.995012i	$0.531806\pi$
$337$	−19.2318	+	24.1159i	−1.04762	+	1.31368i	−0.947868	+	0.318664i	$0.896766\pi$
$338$	9.14769	−	22.9901i	0.497569	−	1.25050i
$339$	−36.0052	+	17.3392i	−1.95553	+	0.941735i
$340$	−22.5059	+	3.17650i	−1.22055	+	0.172270i
$341$	24.9729	−	5.69990i	1.35236	−	0.308667i
$342$	17.8349	+	31.2284i	0.964399	+	1.68864i
$343$	9.04790	+	16.1597i	0.488541	+	0.872541i
$344$	−0.179912	+	12.7793i	−0.00970022	+	0.689013i
$345$	1.92987	+	8.45532i	0.103901	+	0.455219i
$346$	−22.4666	−	8.93937i	−1.20781	−	0.480583i
$347$	−12.5789	−	26.1205i	−0.675273	−	1.40222i	−0.903490	−	0.428609i	$-0.859004\pi$
$347$	−12.5789	−	26.1205i	−0.675273	−	1.40222i	0.228217	−	0.973610i	$-0.426711\pi$
$348$	3.46977	−	0.489726i	0.185999	−	0.0262520i
$349$	15.1909	+	12.1143i	0.813151	+	0.648466i	0.939128	−	0.343567i	$-0.111635\pi$
$349$	15.1909	+	12.1143i	0.813151	+	0.648466i	−0.125978	+	0.992033i	$0.540207\pi$
$350$	−3.67065	−	1.37391i	−0.196205	−	0.0734384i
$351$	3.78761	−	3.02052i	0.202168	−	0.161224i
$352$	12.5392	−	12.8937i	0.668341	−	0.687236i
$353$	2.04384	+	1.62991i	0.108783	+	0.0867513i	0.676371	−	0.736562i	$-0.263552\pi$
$353$	2.04384	+	1.62991i	0.108783	+	0.0867513i	−0.567588	+	0.823313i	$0.692123\pi$
$354$	5.91572	−	5.43755i	0.314417	−	0.289002i
$355$	14.1459	+	6.81230i	0.750786	+	0.361560i
$356$	9.22820	−	28.9496i	0.489093	−	1.53433i
$357$	−23.1415	+	30.2737i	−1.22478	+	1.60225i
$358$	1.24557	+	4.10637i	0.0658306	+	0.217028i
$359$	−3.91208	−	3.11978i	−0.206472	−	0.164656i	0.514795	−	0.857314i	$-0.327868\pi$
$359$	−3.91208	−	3.11978i	−0.206472	−	0.164656i	−0.721266	+	0.692658i	$0.756440\pi$
$360$	8.40688	−	16.8462i	0.443082	−	0.887874i
$361$	38.6833			2.03596
$362$	7.32719	−	4.18464i	0.385109	−	0.219940i
$363$	−2.02327	−	0.974357i	−0.106194	−	0.0511405i
$364$	−21.6412	−	19.6354i	−1.13431	−	1.02918i
$365$	8.47210	−	4.07995i	0.443450	−	0.213554i
$366$	2.44338	−	3.54789i	0.127717	−	0.185451i
$367$	−7.28238	+	31.9062i	−0.380137	+	1.66549i	0.316903	+	0.948458i	$0.397357\pi$
$367$	−7.28238	+	31.9062i	−0.380137	+	1.66549i	−0.697040	+	0.717032i	$0.745500\pi$
$368$	−1.91678	−	6.65505i	−0.0999192	−	0.346918i
$369$	−0.180271	−	0.374336i	−0.00938452	−	0.0194872i
$370$	7.52128	−	10.9212i	0.391013	−	0.567768i
$371$	−0.223955	+	0.490575i	−0.0116272	+	0.0254694i
$372$	−33.7567	+	22.5538i	−1.75020	+	1.16936i
$373$	−14.3401			−0.742504			−0.371252	−	0.928532i	$-0.621071\pi$
$373$	−14.3401			−0.742504			−0.371252	+	0.928532i	$0.621071\pi$
$374$	12.7467	+	22.3191i	0.659115	+	1.15409i
$375$	−13.1435	+	27.2927i	−0.678725	+	1.40939i
$376$	2.41556	−	2.94305i	0.124573	−	0.151776i
$377$	−3.74389	−	0.854519i	−0.192820	−	0.0440100i
$378$	−1.01709	−	3.12087i	−0.0523136	−	0.160520i
$379$	−27.7499	+	6.33372i	−1.42541	+	0.325341i	−0.864542	−	0.502561i	$-0.832391\pi$
$379$	−27.7499	+	6.33372i	−1.42541	+	0.325341i	−0.560872	+	0.827902i	$0.689534\pi$
$380$	−16.7767	−	25.1101i	−0.860629	−	1.28812i
$381$	−25.0217	+	5.71105i	−1.28190	+	0.292586i
$382$	−1.20193	+	7.72803i	−0.0614959	+	0.395400i
$383$	−1.61271	+	7.06576i	−0.0824058	+	0.361043i	−0.999272	−	0.0381514i	$-0.987853\pi$
$383$	−1.61271	+	7.06576i	−0.0824058	+	0.361043i	0.916866	+	0.399195i	$0.130710\pi$
$384$	−11.2801	+	26.1787i	−0.575635	+	1.33593i
$385$	−0.343468	−	16.7202i	−0.0175048	−	0.852141i
$386$	24.9586	+	3.88177i	1.27036	+	0.197577i
$387$	11.8284	−	9.43285i	0.601272	−	0.479499i
$388$	−6.58670	−	0.555814i	−0.334389	−	0.0282172i
$389$	−15.7635	−	19.7668i	−0.799241	−	1.00222i	−0.999746	−	0.0225239i	$-0.992830\pi$
$389$	−15.7635	−	19.7668i	−0.799241	−	1.00222i	0.200505	−	0.979693i	$-0.435742\pi$
$390$	−28.8015	+	26.4735i	−1.45842	+	1.34054i
$391$	9.89714			0.500520
$392$	−17.5998	+	9.06892i	−0.888927	+	0.458050i
$393$	9.65260			0.486909
$394$	−0.772063	+	0.709657i	−0.0388960	+	0.0357520i
$395$	−12.3922	−	15.5393i	−0.623517	−	0.781865i
$396$	−21.2151	−	1.79022i	−1.06610	−	0.0899622i
$397$	−25.7507	+	20.5355i	−1.29239	+	1.03065i	−0.295225	+	0.955428i	$0.595395\pi$
$397$	−25.7507	+	20.5355i	−1.29239	+	1.03065i	−0.997167	+	0.0752205i	$0.976034\pi$
$398$	0.159291	+	0.0247743i	0.00798454	+	0.00124182i
$399$	−49.5805	−	10.2499i	−2.48213	−	0.513136i
$400$	1.60370	−	3.87091i	0.0801850	−	0.193545i
$401$	3.21728	−	14.0958i	0.160664	−	0.703913i	−0.828850	−	0.559471i	$-0.811004\pi$
$401$	3.21728	−	14.0958i	0.160664	−	0.703913i	0.989513	−	0.144442i	$-0.0461386\pi$
$402$	−2.03655	+	13.0944i	−0.101574	+	0.653090i
$403$	43.3754	−	9.90015i	2.16068	−	0.493161i
$404$	−13.8608	−	20.7458i	−0.689602	−	1.03214i
$405$	15.1847	−	3.46580i	0.754532	−	0.172217i
$406$	−1.43146	+	2.17276i	−0.0710422	+	0.107832i
$407$	−14.6195	−	3.33680i	−0.724660	−	0.165399i
$408$	−31.4883	−	25.8446i	−1.55890	−	1.27950i
$409$	−5.10552	+	10.6017i	−0.252452	+	0.524222i	−0.988225	−	0.153006i	$-0.951105\pi$
$409$	−5.10552	+	10.6017i	−0.252452	+	0.524222i	0.735773	+	0.677228i	$0.236819\pi$
$410$	0.173028	+	0.302967i	0.00854522	+	0.0149625i
$411$	−28.0564			−1.38392
$412$	−15.1461	+	10.1195i	−0.746196	+	0.498554i
$413$	0.122533	+	5.96497i	0.00602945	+	0.293517i
$414$	−4.64997	+	6.75196i	−0.228533	+	0.331841i
$415$	2.76375	+	5.73899i	0.135667	+	0.281716i
$416$	21.7793	−	22.3950i	1.06782	−	1.09801i
$417$	7.22051	−	31.6351i	0.353590	−	1.54918i
$418$	−19.3694	+	28.1253i	−0.947390	+	1.37565i
$419$	3.59339	−	1.73049i	0.175549	−	0.0845398i	−0.344045	−	0.938953i	$-0.611797\pi$
$419$	3.59339	−	1.73049i	0.175549	−	0.0845398i	0.519594	+	0.854413i	$0.326083\pi$
$420$	9.95824	+	24.5640i	0.485913	+	1.19860i
$421$	1.67069	+	0.804561i	0.0814244	+	0.0392119i	0.474153	−	0.880443i	$-0.342754\pi$
$421$	1.67069	+	0.804561i	0.0814244	+	0.0392119i	−0.392728	+	0.919655i	$0.628469\pi$
$422$	−20.5979	+	11.7637i	−1.00269	+	0.572646i
$423$	−4.50708			−0.219142
$424$	−0.515846	−	0.257426i	−0.0250517	−	0.0125017i
$425$	4.68140	+	3.73329i	0.227081	+	0.181091i
$426$	8.16813	+	26.9284i	0.395747	+	1.30469i
$427$	0.775669	+	3.10320i	0.0375372	+	0.150174i
$428$	−5.05932	+	15.8715i	−0.244552	+	0.767179i
$429$	39.8570	+	19.1941i	1.92431	+	0.926700i
$430$	−9.35347	+	8.59743i	−0.451064	+	0.414605i
$431$	4.92721	+	3.92932i	0.237336	+	0.189269i	0.734934	−	0.678139i	$-0.237213\pi$
$431$	4.92721	+	3.92932i	0.237336	+	0.189269i	−0.497598	+	0.867408i	$0.665785\pi$
$432$	3.37198	−	0.971195i	0.162235	−	0.0467267i
$433$	−10.8842	+	8.67983i	−0.523059	+	0.417126i	−0.849102	−	0.528229i	$-0.822856\pi$
$433$	−10.8842	+	8.67983i	−0.523059	+	0.417126i	0.326042	+	0.945355i	$0.394285\pi$
$434$	4.01995	−	29.8756i	0.192964	−	1.43407i
$435$	2.72335	+	2.17180i	0.130575	+	0.104130i
$436$	−30.3765	+	4.28737i	−1.45477	+	0.205328i
$437$	5.70552	+	11.8476i	0.272932	+	0.566749i
$438$	15.6592	+	6.23074i	0.748226	+	0.297716i
$439$	−3.55582	−	15.5791i	−0.169710	−	0.743548i	−0.986114	−	0.166067i	$-0.946893\pi$
$439$	−3.55582	−	15.5791i	−0.169710	−	0.743548i	0.816404	−	0.577481i	$-0.195964\pi$
$440$	17.8767	+	0.251675i	0.852236	+	0.0119982i
$441$	21.5160	+	9.29329i	1.02457	+	0.442538i
$442$	22.1397	+	38.7660i	1.05308	+	1.84391i
$443$	32.3858	−	7.39184i	1.53869	−	0.351197i	0.632669	−	0.774422i	$-0.281959\pi$
$443$	32.3858	−	7.39184i	1.53869	−	0.351197i	0.906024	+	0.423225i	$0.139102\pi$
$444$	23.5333	−	3.32151i	1.11684	−	0.157632i
$445$	27.2128	−	13.1050i	1.29001	−	0.621237i
$446$	8.61014	−	21.6392i	0.407702	−	1.02464i
$447$	−11.3027	+	14.1732i	−0.534601	+	0.670368i
$448$	−9.03809	−	19.1393i	−0.427010	−	0.904247i
$449$	19.8347	+	24.8720i	0.936058	+	1.17378i	0.984576	+	0.174958i	$0.0559789\pi$
$449$	19.8347	+	24.8720i	0.936058	+	1.17378i	−0.0485175	+	0.998822i	$0.515450\pi$
$450$	−4.74636	+	1.43970i	−0.223746	+	0.0678682i
$451$	0.245991	−	0.308463i	0.0115833	−	0.0145250i
$452$	30.2236	+	9.63429i	1.42160	+	0.453159i
$453$	−5.33337	+	11.0749i	−0.250583	+	0.520342i
$454$	17.9115	−	16.4637i	0.840629	−	0.772681i
$455$	−0.596569	−	29.0413i	−0.0279676	−	1.36148i
$456$	12.7855	−	52.5928i	0.598735	−	2.46288i
$457$	−11.6251	+	14.5775i	−0.543801	+	0.681905i	−0.975471	−	0.220126i	$-0.929353\pi$
$457$	−11.6251	+	14.5775i	−0.543801	+	0.681905i	0.431670	+	0.902032i	$0.357924\pi$
$458$	−30.5809	+	2.14746i	−1.42895	+	0.100344i
$459$			5.01468i			0.234065i
$460$	3.49798	−	5.92946i	0.163094	−	0.276462i
$461$	−8.29001	+	17.2144i	−0.386104	+	0.801754i	0.613820	+	0.789446i	$0.289632\pi$
$461$	−8.29001	+	17.2144i	−0.386104	+	0.801754i	−0.999924	+	0.0123080i	$0.996082\pi$
$462$	21.6463	−	20.7327i	1.00708	−	0.964574i
$463$	−6.70600	−	13.9251i	−0.311654	−	0.647156i	0.685031	−	0.728514i	$-0.259789\pi$
$463$	−6.70600	−	13.9251i	−0.311654	−	0.647156i	−0.996685	+	0.0813576i	$0.974074\pi$
$464$	−2.26842	−	1.60977i	−0.105309	−	0.0747316i
$465$	−39.3443	−	8.98009i	−1.82455	−	0.416442i
$466$	−31.0414	+	9.41572i	−1.43797	+	0.436175i
$467$	17.9246	−	8.63204i	0.829452	−	0.399443i	0.0295426	−	0.999564i	$-0.490595\pi$
$467$	17.9246	−	8.63204i	0.829452	−	0.399443i	0.799910	+	0.600120i	$0.204881\pi$
$468$	−36.8485	−	3.10944i	−1.70332	−	0.143734i
$469$	−6.29171	−	7.56543i	−0.290524	−	0.349339i
$470$	3.77546	−	0.265122i	0.174149	−	0.0122292i
$471$			9.28187i			0.427686i
$472$	−6.37753	−	0.0897857i	−0.293550	−	0.00413272i
$473$	12.9438	+	6.23341i	0.595157	+	0.286612i
$474$	5.47444	−	35.1990i	0.251449	−	1.61674i
$475$	−1.77030	+	7.75617i	−0.0812267	+	0.355878i
$476$	29.8577	−	4.84152i	1.36853	−	0.221911i
$477$	0.151860	+	0.665341i	0.00695318	+	0.0304639i
$478$	9.70020	−	0.681171i	0.443677	−	0.0311560i
$479$	−7.98484	−	34.9839i	−0.364837	−	1.59845i	−0.740738	−	0.671794i	$-0.765524\pi$
$479$	−7.98484	−	34.9839i	−0.364837	−	1.59845i	0.375901	−	0.926660i	$-0.377333\pi$
$480$	−26.6127	+	9.73058i	−1.21470	+	0.444138i
$481$	−25.3925	−	5.79568i	−1.15780	−	0.264260i
$482$	−1.22413	−	0.487075i	−0.0557574	−	0.0221857i
$483$	−2.79883	−	11.1972i	−0.127351	−	0.509491i
$484$	0.635650	+	1.66540i	0.0288932	+	0.0757000i
$485$	−4.09680	−	5.13722i	−0.186026	−	0.233269i
$486$	26.0556	+	17.9441i	1.18191	+	0.813961i
$487$	−7.89951	+	6.29965i	−0.357961	+	0.285464i	−0.785913	−	0.618337i	$-0.787807\pi$
$487$	−7.89951	+	6.29965i	−0.357961	+	0.285464i	0.427952	+	0.903801i	$0.359235\pi$
$488$	−3.34417	+	0.713911i	−0.151384	+	0.0323172i
$489$		−	39.3831i		−	1.78097i
$490$	−18.5701	−	6.51909i	−0.838910	−	0.294503i
$491$			16.2149i			0.731767i	0.930661	+	0.365884i	$0.119233\pi$
$491$			16.2149i			0.731767i	−0.930661	+	0.365884i	$0.880767\pi$
$492$	−0.189914	+	0.595776i	−0.00856198	+	0.0268597i
$493$	3.10781	−	2.47840i	0.139969	−	0.111621i
$494$	−33.6427	+	48.8508i	−1.51366	+	2.19790i
$495$	−13.1954	−	16.5465i	−0.593089	−	0.743710i
$496$	31.7705	+	5.40031i	1.42654	+	0.242481i
$497$	−19.0076	−	8.67727i	−0.852606	−	0.389229i
$498$	−4.22070	+	10.6075i	−0.189134	+	0.475335i
$499$	3.88726	+	0.887242i	0.174018	+	0.0397184i	0.308642	−	0.951178i	$-0.400126\pi$
$499$	3.88726	+	0.887242i	0.174018	+	0.0397184i	−0.134624	+	0.990897i	$0.542983\pi$
$500$	22.4652	−	8.57451i	1.00467	−	0.383464i
$501$	1.26040	+	5.52215i	0.0563103	+	0.246712i
$502$	−1.47725	−	21.0367i	−0.0659328	−	0.938914i
$503$	7.57203	+	33.1752i	0.337620	+	1.47921i	0.804002	+	0.594627i	$0.202700\pi$
$503$	7.57203	+	33.1752i	0.337620	+	1.47921i	−0.466382	+	0.884584i	$0.654443\pi$
$504$	−10.7251	+	22.6440i	−0.477733	+	1.00864i
$505$	5.51887	−	24.1797i	0.245586	−	1.07598i
$506$	−7.69253	−	1.19641i	−0.341975	−	0.0531867i
$507$	39.7169	+	19.1267i	1.76389	+	0.849445i
$508$	17.5470	+	10.3515i	0.778521	+	0.459274i
$509$		−	7.63685i		−	0.338498i	−0.985573	−	0.169249i	$-0.945866\pi$
$509$		−	7.63685i		−	0.338498i	0.985573	−	0.169249i	$-0.0541341\pi$
$510$	−2.83659	−	40.3944i	−0.125606	−	1.78869i
$511$	−11.1608	+	5.66000i	−0.493724	+	0.250384i
$512$	20.7829	−	8.94819i	0.918484	−	0.395458i
$513$	−6.00296	+	2.89087i	−0.265037	+	0.127635i
$514$	8.48308	+	27.9667i	0.374173	+	1.23356i
$515$	−17.6532	−	4.02923i	−0.777894	−	0.177549i
$516$	−22.6892	−	1.91461i	−0.998834	−	0.0842859i
$517$	−1.85698	−	3.85606i	−0.0816700	−	0.169589i
$518$	−9.70871	+	14.7365i	−0.426576	+	0.647484i
$519$	18.6911	−	38.8124i	0.820447	−	1.70368i
$520$	31.0499	+	0.437134i	1.36163	+	0.0191696i
$521$		−	9.54407i		−	0.418133i	−0.977901	−	0.209067i	$-0.932957\pi$
$521$		−	9.54407i		−	0.418133i	0.977901	−	0.209067i	$-0.0670426\pi$
$522$	0.230654	+	3.28462i	0.0100954	+	0.143764i
$523$	11.9118	−	14.9370i	0.520868	−	0.653148i	−0.449925	−	0.893066i	$-0.648549\pi$
$523$	11.9118	−	14.9370i	0.520868	−	0.653148i	0.970793	+	0.239918i	$0.0771207\pi$
$524$	−5.56758	−	5.26406i	−0.243221	−	0.229961i
$525$	2.89983	−	6.35209i	0.126559	−	0.277228i
$526$	18.8221	+	20.4773i	0.820683	+	0.892853i
$527$	−19.9818	+	41.4927i	−0.870422	+	1.80745i
$528$	21.3500	+	23.8941i	0.929141	+	1.03986i
$529$	12.4712	−	15.6384i	0.542226	−	0.679931i
$530$	−0.166346	−	0.548405i	−0.00722562	−	0.0238212i
$531$	4.70749	+	5.90300i	0.204288	+	0.256169i
$532$	23.0081	+	32.9509i	0.997526	+	1.42860i
$533$	0.427262	−	0.535770i	0.0185068	−	0.0232068i
$534$	50.2982	+	20.0135i	2.17662	+	0.866068i
$535$	−14.9193	+	7.18477i	−0.645019	+	0.310625i
$536$	8.31573	−	6.44217i	0.359185	−	0.278259i
$537$	−7.45337	+	1.70118i	−0.321637	+	0.0734115i
$538$	−13.3551	+	7.62722i	−0.575778	+	0.328833i
$539$	0.913981	+	22.2372i	0.0393680	+	0.957822i
$540$	3.00434	+	1.77236i	0.129286	+	0.0762700i
$541$	3.95174	+	17.3137i	0.169899	+	0.744374i	0.986038	+	0.166520i	$0.0532529\pi$
$541$	3.95174	+	17.3137i	0.169899	+	0.744374i	−0.816140	+	0.577855i	$0.803890\pi$
$542$	7.00207	−	17.5977i	0.300765	−	0.755886i
$543$	6.52259	+	13.5443i	0.279911	+	0.581241i
$544$	4.06798	+	32.0792i	0.174413	+	1.37539i
$545$	−23.8419	−	19.0133i	−1.02128	−	0.814440i
$546$	37.5974	−	36.0106i	1.60902	−	1.54111i
$547$	12.9729	−	10.3455i	0.554681	−	0.442343i	−0.305603	−	0.952159i	$-0.598858\pi$
$547$	12.9729	−	10.3455i	0.554681	−	0.442343i	0.860284	+	0.509816i	$0.170286\pi$
$548$	16.1828	+	15.3006i	0.691296	+	0.653609i
$549$	3.16478	+	2.52383i	0.135069	+	0.107714i
$550$	−3.18732	−	3.46760i	−0.135908	−	0.147859i
$551$	4.75843	+	2.29154i	0.202716	+	0.0976228i
$552$	12.0667	−	2.57599i	0.513593	−	0.109641i
$553$	16.9127	+	20.3366i	0.719201	+	0.864799i
$554$	−25.7358	+	7.80637i	−1.09341	+	0.331661i
$555$	18.4708	+	14.7300i	0.784041	+	0.625252i
$556$	−21.4170	+	14.3093i	−0.908284	+	0.606850i
$557$	11.9318			0.505565			0.252782	−	0.967523i	$-0.418654\pi$
$557$	11.9318			0.505565			0.252782	+	0.967523i	$0.418654\pi$
$558$	−18.9188	−	33.1263i	−0.800897	−	1.40235i
$559$	22.4821	+	10.8268i	0.950890	+	0.457925i
$560$	7.65211	−	19.5991i	0.323361	−	0.828215i
$561$	−41.2568	+	19.8682i	−1.74186	+	0.838837i
$562$	−31.0641	−	21.3934i	−1.31036	−	0.902425i
$563$	−2.67570	+	11.7230i	−0.112768	+	0.494067i	0.886728	+	0.462292i	$0.152973\pi$
$563$	−2.67570	+	11.7230i	−0.112768	+	0.494067i	−0.999495	+	0.0317744i	$0.989884\pi$
$564$	4.92899	+	4.66028i	0.207548	+	0.196233i
$565$	13.6817	+	28.4104i	0.575594	+	1.19523i
$566$	−7.64096	−	5.26221i	−0.321174	−	0.221187i
$567$	−20.1087	+	5.02633i	−0.844488	+	0.211086i
$568$	9.97410	−	19.9867i	0.418504	−	0.838624i
$569$	−17.3784			−0.728542			−0.364271	−	0.931293i	$-0.618682\pi$
$569$	−17.3784			−0.728542			−0.364271	+	0.931293i	$0.618682\pi$
$570$	46.7199	−	26.6822i	1.95688	−	1.11760i
$571$	5.16552	−	10.7263i	0.216170	−	0.448882i	−0.764481	−	0.644647i	$-0.777005\pi$
$571$	5.16552	−	10.7263i	0.216170	−	0.448882i	0.980651	+	0.195765i	$0.0627189\pi$
$572$	−12.5218	−	32.8071i	−0.523564	−	1.37174i
$573$	−13.5844	−	3.10055i	−0.567497	−	0.129528i
$574$	−0.238497	−	0.398374i	−0.00995467	−	0.0166278i
$575$	−1.76815	+	0.403568i	−0.0737369	+	0.0168300i
$576$	−23.7961	−	12.2965i	−0.991505	−	0.512356i
$577$	−0.105405	+	0.0240579i	−0.00438805	+	0.00100154i	−0.224714	−	0.974425i	$-0.572145\pi$
$577$	−0.105405	+	0.0240579i	−0.00438805	+	0.00100154i	0.220326	+	0.975426i	$0.429288\pi$
$578$	−21.9056	−	3.40694i	−0.911151	−	0.141710i
$579$	−10.0136	+	43.8725i	−0.416151	+	1.82328i
$580$	−0.386424	−	2.73786i	−0.0160454	−	0.113684i
$581$	−3.83408	−	7.56029i	−0.159064	−	0.313654i
$582$	1.80983	−	11.6367i	0.0750199	−	0.482355i
$583$	−0.506668	+	0.404054i	−0.0209841	+	0.0167342i
$584$	−5.63423	−	12.1336i	−0.233146	−	0.502094i
$585$	−22.9191	−	28.7396i	−0.947587	−	1.18824i
$586$	7.48796	+	8.14644i	0.309325	+	0.336526i
$587$	24.1166			0.995398			0.497699	−	0.867350i	$-0.334178\pi$
$587$	24.1166			0.995398			0.497699	+	0.867350i	$0.334178\pi$
$588$	−13.9210	−	32.4106i	−0.574092	−	1.33659i
$589$	−61.1890			−2.52125
$590$	−4.29057	−	4.66787i	−0.176640	−	0.192173i
$591$	−1.16486	−	1.46069i	−0.0479161	−	0.0600849i
$592$	−15.3853	−	10.9181i	−0.632332	−	0.448730i
$593$	21.5334	−	17.1723i	0.884272	−	0.705183i	−0.0720804	−	0.997399i	$-0.522964\pi$
$593$	21.5334	−	17.1723i	0.884272	−	0.705183i	0.956353	+	0.292215i	$0.0943924\pi$
$594$	0.606195	−	3.89765i	0.0248725	−	0.159923i
$595$	23.8878	+	18.2601i	0.979306	+	0.748590i
$596$	14.2487	−	2.01108i	0.583651	−	0.0823769i
$597$	−0.0639090	+	0.280004i	−0.00261562	+	0.0114598i
$598$	−13.3611	−	2.07804i	−0.546378	−	0.0849772i
$599$	19.1491	−	4.37067i	0.782412	−	0.178581i	0.187386	−	0.982286i	$-0.439999\pi$
$599$	19.1491	−	4.37067i	0.782412	−	0.178581i	0.595027	+	0.803706i	$0.297141\pi$
$600$	6.67931	+	3.33322i	0.272682	+	0.136078i
$601$	4.09575	−	0.934828i	0.167069	−	0.0381324i	−0.138168	−	0.990409i	$-0.544121\pi$
$601$	4.09575	−	0.934828i	0.167069	−	0.0381324i	0.305237	+	0.952276i	$0.401264\pi$
$602$	12.2100	−	11.6947i	0.497642	−	0.476640i
$603$	−12.1400	−	2.77087i	−0.494378	−	0.112839i
$604$	9.11595	−	3.47937i	0.370923	−	0.141574i
$605$	−0.768829	+	1.59649i	−0.0312574	+	0.0649066i
$606$	38.5996	−	22.0447i	1.56800	−	0.895503i
$607$	24.0326			0.975454			0.487727	−	0.872996i	$-0.337826\pi$
$607$	24.0326			0.975454			0.487727	+	0.872996i	$0.337826\pi$
$608$	−36.0562	+	23.3628i	−1.46227	+	0.947485i
$609$	−3.68282	−	2.81518i	−0.149236	−	0.114077i
$610$	−2.79951	−	1.92798i	−0.113349	−	0.0780615i
$611$	−3.22539	−	6.69759i	−0.130485	−	0.270955i
$612$	26.2980	−	27.8144i	1.06303	−	1.12433i
$613$	4.83674	−	21.1911i	0.195354	−	0.855902i	−0.778304	−	0.627888i	$-0.783920\pi$
$613$	4.83674	−	21.1911i	0.195354	−	0.855902i	0.973658	−	0.228014i	$-0.0732233\pi$
$614$	−1.21881	−	0.839376i	−0.0491872	−	0.0338745i
$615$	−0.560033	+	0.269698i	−0.0225827	+	0.0108753i
$616$	−23.7921	+	0.153739i	−0.958611	+	0.00619434i
$617$	31.4055	+	15.1241i	1.26434	+	0.608873i	0.941318	−	0.337520i	$-0.109588\pi$
$617$	31.4055	+	15.1241i	1.26434	+	0.608873i	0.323019	+	0.946393i	$0.395302\pi$
$618$	−16.0944	−	28.1809i	−0.647413	−	1.13360i
$619$	−7.51453			−0.302034			−0.151017	−	0.988531i	$-0.548255\pi$
$619$	−7.51453			−0.302034			−0.151017	+	0.988531i	$0.548255\pi$
$620$	17.7964	+	26.6362i	0.714719	+	1.06973i
$621$	−1.18752	−	0.947014i	−0.0476534	−	0.0380024i
$622$	−24.5807	+	7.45600i	−0.985595	+	0.298958i
$623$	−35.8490	+	18.1802i	−1.43626	+	0.728376i
$624$	37.0828	+	41.5016i	1.48450	+	1.66139i
$625$	16.8169	+	8.09858i	0.672675	+	0.323943i
$626$	24.6286	+	26.7944i	0.984357	+	1.07092i
$627$	−47.5675	−	37.9338i	−1.89966	−	1.51493i
$628$	5.06188	−	5.35375i	0.201991	−	0.213638i
$629$	21.0784	−	16.8095i	0.840450	−	0.670237i
$630$	−23.6805	+	7.71748i	−0.943453	+	0.307472i
$631$	35.8624	+	28.5993i	1.42766	+	1.13852i	0.968157	+	0.250343i	$0.0805434\pi$
$631$	35.8624	+	28.5993i	1.42766	+	1.13852i	0.459502	+	0.888177i	$0.348028\pi$
$632$	−22.3535	+	17.3172i	−0.889173	+	0.688840i
$633$	−18.3360	−	38.0751i	−0.728790	−	1.51335i
$634$	16.6607	−	41.8719i	0.661680	−	1.66295i
$635$	4.50638	+	19.7437i	0.178830	+	0.783506i
$636$	0.521881	−	0.884645i	0.0206939	−	0.0350785i
$637$	1.58749	+	38.6237i	0.0628987	+	1.53033i
$638$	−2.71514	+	1.55065i	−0.107493	+	0.0613906i
$639$	−25.7790	+	5.88388i	−1.01980	+	0.232763i
$640$	20.6567	+	8.90070i	0.816527	+	0.351831i
$641$	−29.0858	+	14.0070i	−1.14882	+	0.553243i	−0.908679	−	0.417495i	$-0.862908\pi$
$641$	−29.0858	+	14.0070i	−1.14882	+	0.553243i	−0.240141	+	0.970738i	$0.577194\pi$
$642$	−27.5758	−	10.9723i	−1.08833	−	0.433043i
$643$	−29.4902	+	36.9796i	−1.16298	+	1.45833i	−0.299395	+	0.954129i	$0.596785\pi$
$643$	−29.4902	+	36.9796i	−1.16298	+	1.45833i	−0.863585	+	0.504203i	$0.831786\pi$
$644$	−4.49206	+	7.98486i	−0.177012	+	0.314647i
$645$	−14.1122	−	17.6961i	−0.555668	−	0.696785i
$646$	−17.8218	−	58.7544i	−0.701190	−	2.31166i
$647$	29.9412	−	37.5451i	1.17711	−	1.47605i	0.330522	−	0.943798i	$-0.392775\pi$
$647$	29.9412	−	37.5451i	1.17711	−	1.47605i	0.846587	−	0.532250i	$-0.178653\pi$
$648$	−4.62614	−	21.6702i	−0.181732	−	0.851288i
$649$	−3.11080	+	6.45964i	−0.122110	+	0.253563i
$650$	−5.53604	−	6.02287i	−0.217141	−	0.236237i
$651$	52.5938	+	10.8728i	2.06131	+	0.426140i
$652$	−21.4776	+	22.7160i	−0.841129	+	0.889629i
$653$	20.8002	−	26.0826i	0.813974	−	1.02069i	−0.185303	−	0.982681i	$-0.559327\pi$
$653$	20.8002	−	26.0826i	0.813974	−	1.02069i	0.999277	−	0.0380098i	$-0.0121018\pi$
$654$	−3.82859	−	54.5209i	−0.149710	−	2.13194i
$655$		−	7.61651i		−	0.297602i
$656$	0.434449	−	0.240072i	0.0169624	−	0.00937322i
$657$	−6.87111	+	14.2680i	−0.268068	+	0.556648i
$658$	−5.01607	+	0.455939i	−0.195547	+	0.0177744i
$659$	8.96210	+	18.6100i	0.349114	+	0.724943i	0.999396	−	0.0347503i	$-0.0110636\pi$
$659$	8.96210	+	18.6100i	0.349114	+	0.724943i	−0.650282	+	0.759693i	$0.725349\pi$
$660$	−2.67830	+	31.7394i	−0.104253	+	1.23545i
$661$	40.9935	+	9.35649i	1.59446	+	0.363925i	0.925313	−	0.379204i	$-0.123802\pi$
$661$	40.9935	+	9.35649i	1.59446	+	0.363925i	0.669148	+	0.743129i	$0.266659\pi$
$662$	−5.94411	−	19.5963i	−0.231024	−	0.761634i
$663$	−71.6588	+	34.5091i	−2.78300	+	1.34022i
$664$	8.21931	−	3.81662i	0.318971	−	0.148114i
$665$	−8.08781	+	39.1222i	−0.313632	+	1.51709i
$666$	1.56438	+	22.2775i	0.0606186	+	0.863237i
$667$			1.20400i			0.0466189i
$668$	2.28452	−	3.87251i	0.0883908	−	0.149832i
$669$	37.3830	+	18.0027i	1.44531	+	0.696025i
$670$	10.3323	+	1.60697i	0.399172	+	0.0620826i
$671$	−0.855342	+	3.74750i	−0.0330201	+	0.144671i
$672$	35.1427	−	13.6741i	1.35566	−	0.527489i
$673$	−11.3173	−	49.5842i	−0.436248	−	1.91133i	−0.410970	−	0.911649i	$-0.634810\pi$
$673$	−11.3173	−	49.5842i	−0.436248	−	1.91133i	−0.0252786	−	0.999680i	$-0.508047\pi$
$674$	3.05571	+	43.5148i	0.117702	+	1.67613i
$675$	−0.204480	−	0.895886i	−0.00787045	−	0.0344827i
$676$	−12.4778	−	32.6919i	−0.479916	−	1.25738i
$677$	5.35324	+	1.22184i	0.205742	+	0.0469592i	0.324150	−	0.946006i	$-0.394922\pi$
$677$	5.35324	+	1.22184i	0.205742	+	0.0469592i	−0.118408	+	0.992965i	$0.537779\pi$
$678$	−20.8942	+	52.5116i	−0.802436	+	2.01670i
$679$	5.59127	+	6.72320i	0.214573	+	0.258013i
$680$	−20.3930	+	24.8463i	−0.782036	+	0.952811i
$681$	27.0243	+	33.8874i	1.03557	+	1.29857i
$682$	20.5466	−	29.8346i	0.786771	−	1.14243i
$683$	4.85165	−	3.86906i	0.185643	−	0.148045i	−0.526259	−	0.850325i	$-0.676406\pi$
$683$	4.85165	−	3.86906i	0.185643	−	0.148045i	0.711902	+	0.702279i	$0.247834\pi$
$684$	48.4562	+	15.4463i	1.85277	+	0.590602i
$685$			22.1383i			0.845860i
$686$	24.8860	+	8.16622i	0.950152	+	0.311788i
$687$		−	54.6170i		−	2.08377i
$688$	12.0429	+	13.4779i	0.459131	+	0.513840i
$689$	−0.880031	+	0.701801i	−0.0335265	+	0.0267365i
$690$	10.1014	+	6.95668i	0.384554	+	0.264836i
$691$	−26.3182	−	33.0019i	−1.00119	−	1.25545i	−0.966664	−	0.256049i	$-0.917579\pi$
$691$	−26.3182	−	33.0019i	−1.00119	−	1.25545i	−0.0345260	−	0.999404i	$-0.510992\pi$
$692$	−31.9473	+	12.1937i	−1.21446	+	0.463533i
$693$	18.0090	+	21.6548i	0.684104	+	0.822597i
$694$	−38.0953	−	15.1580i	−1.44608	−	0.575389i
$695$	−24.9621	−	5.69744i	−0.946867	−	0.216116i
$696$	3.14402	−	3.83058i	0.119174	−	0.145198i
$697$	0.157844	+	0.691558i	0.00597875	+	0.0261946i
$698$	27.4105	−	1.92483i	1.03750	−	0.0728560i
$699$	−12.8598	−	56.3425i	−0.486403	−	2.13107i
$700$	−5.13674	+	2.08244i	−0.194150	+	0.0787086i
$701$	−4.75445	+	20.8306i	−0.179573	+	0.786761i	0.802254	+	0.596983i	$0.203634\pi$
$701$	−4.75445	+	20.8306i	−0.179573	+	0.786761i	−0.981827	+	0.189778i	$0.939223\pi$
$702$	1.05290	−	6.76983i	0.0397391	−	0.255511i
$703$	32.2735	+	15.5421i	1.21722	+	0.586181i
$704$	0.716038	−	25.4253i	0.0269867	−	0.958251i
$705$			6.74291i			0.253953i
$706$	3.68792	−	0.258974i	0.138797	−	0.00974663i
$707$	−6.68209	+	32.3224i	−0.251306	+	1.21561i
$708$	0.955490	−	11.3231i	0.0359095	−	0.425548i
$709$	6.71673	−	3.23461i	0.252252	−	0.121478i	−0.303485	−	0.952836i	$-0.598150\pi$
$709$	6.71673	−	3.23461i	0.252252	−	0.121478i	0.555737	+	0.831358i	$0.312436\pi$
$710$	21.2482	−	6.44517i	0.797432	−	0.241883i
$711$	32.6334	+	7.44836i	1.22385	+	0.279335i
$712$	−18.0975	−	38.9739i	−0.678231	−	1.46061i
$713$	−6.05227	−	12.5677i	−0.226659	−	0.470663i
$714$	4.87818	+	53.6680i	0.182561	+	2.00847i
$715$	15.1454	−	31.4497i	0.566405	−	1.17615i
$716$	5.22682	+	3.08347i	0.195335	+	0.115235i
$717$			17.3244i			0.646992i
$718$	−7.05897	+	0.495698i	−0.263438	+	0.0184993i
$719$	−18.2757	+	22.9170i	−0.681569	+	0.854660i	−0.995498	−	0.0947862i	$-0.969783\pi$
$719$	−18.2757	+	22.9170i	−0.681569	+	0.854660i	0.313929	+	0.949447i	$0.398355\pi$
$720$	−7.36922	−	25.5859i	−0.274635	−	0.953529i
$721$	23.5981	+	4.87848i	0.878838	+	0.181684i
$722$	40.2768	−	37.0212i	1.49895	−	1.37779i
$723$	1.01841	−	2.11476i	0.0378752	−	0.0786486i
$724$	3.62419	−	11.3694i	0.134692	−	0.422540i
$725$	−0.454159	+	0.569497i	−0.0168670	+	0.0211506i
$726$	−3.03911	+	0.921847i	−0.112792	+	0.0342129i
$727$	−17.3818	−	21.7961i	−0.644654	−	0.808371i	0.346922	−	0.937894i	$-0.387227\pi$
$727$	−17.3818	−	21.7961i	−0.644654	−	0.808371i	−0.991576	+	0.129523i	$0.958655\pi$
$728$	−41.3244	+	0.267030i	−1.53159	+	0.00989678i
$729$	−20.4887	+	25.6921i	−0.758842	+	0.951557i
$730$	4.91645	−	12.3561i	0.181966	−	0.457320i
$731$	−23.2717	+	11.2070i	−0.860733	+	0.414507i
$732$	−0.851423	−	6.03243i	−0.0314695	−	0.222965i
$733$	21.3762	−	4.87897i	0.789546	−	0.180209i	0.191311	−	0.981529i	$-0.438726\pi$
$733$	21.3762	−	4.87897i	0.789546	−	0.180209i	0.598235	+	0.801321i	$0.295869\pi$
$734$	22.9530	+	40.1900i	0.847209	+	1.48344i
$735$	13.9034	−	32.1895i	0.512836	−	1.18733i
$736$	−8.36485	−	5.09477i	−0.308333	−	0.187796i
$737$	−2.63121	−	11.5281i	−0.0969218	−	0.424642i
$738$	−0.545949	−	0.217231i	−0.0200967	−	0.00799639i
$739$	5.76368	+	11.9684i	0.212021	+	0.440265i	0.979673	−	0.200601i	$-0.0642895\pi$
$739$	5.76368	+	11.9684i	0.212021	+	0.440265i	−0.767652	+	0.640866i	$0.778575\pi$
$740$	−2.62088	−	18.5693i	−0.0963454	−	0.682619i
$741$	−82.6200	−	65.8872i	−3.03512	−	2.42043i
$742$	0.236316	+	0.725116i	0.00867542	+	0.0266199i
$743$	19.9125	−	15.8797i	0.730517	−	0.582568i	−0.186006	−	0.982549i	$-0.559555\pi$
$743$	19.9125	−	15.8797i	0.730517	−	0.582568i	0.916524	+	0.399981i	$0.130983\pi$
$744$	−13.5625	+	55.7892i	−0.497226	+	2.04533i
$745$	11.1835	+	8.91857i	0.409733	+	0.326751i
$746$	−14.9309	+	13.7240i	−0.546658	+	0.502471i
$747$	−9.66513	−	4.65448i	−0.353629	−	0.170299i
$748$	34.6319	+	11.0395i	1.26627	+	0.403645i
$749$	19.6541	−	9.96724i	0.718144	−	0.364195i
$750$	12.4351	+	40.9957i	0.454067	+	1.49695i
$751$	9.84532	+	7.85138i	0.359261	+	0.286501i	0.786441	−	0.617666i	$-0.211922\pi$
$751$	9.84532	+	7.85138i	0.359261	+	0.286501i	−0.427180	+	0.904167i	$0.640493\pi$
$752$	−0.301535	−	5.37606i	−0.0109959	−	0.196045i
$753$	37.5712			1.36917
$754$	−4.71592	+	2.69331i	−0.171744	+	0.0980847i
$755$	8.73876	+	4.20836i	0.318036	+	0.153158i
$756$	−4.04577	−	2.27604i	−0.147143	−	0.0827787i
$757$	−6.17722	+	2.97479i	−0.224515	+	0.108121i	−0.542760	−	0.839888i	$-0.682621\pi$
$757$	−6.17722	+	2.97479i	−0.224515	+	0.108121i	0.318245	+	0.948008i	$0.396906\pi$
$758$	−22.8314	+	33.1522i	−0.829274	+	1.20414i
$759$	3.08631	−	13.5220i	0.112026	−	0.490818i
$760$	−41.4991	−	10.0885i	−1.50533	−	0.365950i
$761$	−10.8210	−	22.4700i	−0.392261	−	0.814538i	−0.999795	−	0.0202447i	$-0.993555\pi$
$761$	−10.8210	−	22.4700i	−0.392261	−	0.814538i	0.607534	−	0.794294i	$-0.292159\pi$
$762$	−20.5868	+	29.8930i	−0.745782	+	1.08291i
$763$	32.2418	+	24.6459i	1.16723	+	0.892242i
$764$	6.14455	+	9.19667i	0.222302	+	0.332724i
$765$	38.0503			1.37571
$766$	5.08302	+	8.90025i	0.183657	+	0.321579i
$767$	−5.40314	+	11.2197i	−0.195096	+	0.405121i
$768$	13.3092	+	38.0526i	0.480254	+	1.37310i
$769$	24.8463	+	5.67101i	0.895981	+	0.204502i	0.645627	−	0.763653i	$-0.276596\pi$
$769$	24.8463	+	5.67101i	0.895981	+	0.204502i	0.250354	+	0.968154i	$0.419453\pi$
$770$	−16.3594	−	17.0803i	−0.589553	−	0.615530i
$771$	−50.7618	+	11.5860i	−1.82814	+	0.417261i
$772$	29.7017	−	19.8445i	1.06899	−	0.714221i
$773$	−28.6502	+	6.53922i	−1.03048	+	0.235199i	−0.704145	−	0.710056i	$-0.748669\pi$
$773$	−28.6502	+	6.53922i	−1.03048	+	0.235199i	−0.326331	+	0.945256i	$0.605812\pi$
$774$	3.28812	−	21.1416i	0.118189	−	0.759920i
$775$	1.87789	−	8.22756i	0.0674557	−	0.295543i
$776$	−7.38997	+	5.72499i	−0.265284	+	0.205515i
$777$	−24.9783	−	19.0937i	−0.896092	−	0.684981i
$778$	−35.3304	−	5.49487i	−1.26665	−	0.197001i
$779$	−0.736853	+	0.587621i	−0.0264005	+	0.0210537i
$780$	−4.65194	+	55.1280i	−0.166566	+	1.97390i
$781$	−15.6553	−	19.6311i	−0.560191	−	0.702457i
$782$	10.3048	−	9.47190i	0.368500	−	0.338714i
$783$	−0.610041			−0.0218011
$784$	−9.64560	+	26.2862i	−0.344486	+	0.938792i
$785$	7.32398			0.261404
$786$	10.0502	−	9.23787i	0.358480	−	0.329504i
$787$	−13.1058	−	16.4341i	−0.467170	−	0.585813i	0.491306	−	0.870987i	$-0.336520\pi$
$787$	−13.1058	−	16.4341i	−0.467170	−	0.585813i	−0.958476	+	0.285175i	$0.907948\pi$
$788$	−0.124702	+	1.47778i	−0.00444231	+	0.0526438i
$789$	−38.7417	+	30.8955i	−1.37924	+	1.09991i
$790$	−27.7742	−	4.31968i	−0.988163	−	0.153687i
$791$	−18.9803	−	37.4266i	−0.674860	−	1.33074i
$792$	−23.8024	+	18.4397i	−0.845781	+	0.655224i
$793$	−1.48564	+	6.50902i	−0.0527567	+	0.231142i
$794$	−7.15831	+	46.0258i	−0.254039	+	1.63339i
$795$	0.995397	−	0.227193i	0.0353031	−	0.00805770i
$796$	0.189563	−	0.126652i	0.00671887	−	0.00448907i
$797$	8.41635	−	1.92098i	0.298122	−	0.0680445i	−0.0708435	−	0.997487i	$-0.522569\pi$
$797$	8.41635	−	1.92098i	0.298122	−	0.0680445i	0.368966	+	0.929443i	$0.379712\pi$
$798$	−61.4324	+	36.7781i	−2.17468	+	1.30193i
$799$	7.50191	+	1.71226i	0.265399	+	0.0605755i
$800$	−2.03483	−	5.56516i	−0.0719420	−	0.196758i
$801$	−22.0704	+	45.8296i	−0.779819	+	1.61931i
$802$	−10.1404	−	17.7556i	−0.358070	−	0.626971i
$803$	−15.0381			−0.530683
$804$	10.4114	+	15.5829i	0.367180	+	0.549566i
$805$	−8.83531	+	2.20845i	−0.311404	+	0.0778377i
$806$	35.6874	−	51.8197i	1.25704	−	1.82527i
$807$	−11.8885	−	24.6868i	−0.418496	−	0.869017i
$808$	−34.2862	−	8.33508i	−1.20618	−	0.293227i
$809$	1.48072	−	6.48745i	0.0520593	−	0.228087i	−0.942205	−	0.335037i	$-0.891251\pi$
$809$	1.48072	−	6.48745i	0.0520593	−	0.228087i	0.994264	+	0.106950i	$0.0341085\pi$
$810$	12.4933	−	18.1408i	0.438969	−	0.637403i
$811$	6.44504	−	3.10377i	0.226316	−	0.108988i	−0.317290	−	0.948329i	$-0.602773\pi$
$811$	6.44504	−	3.10377i	0.226316	−	0.108988i	0.543606	+	0.839341i	$0.317059\pi$
$812$	0.588975	+	3.63222i	0.0206690	+	0.127466i
$813$	30.4012	+	14.6404i	1.06622	+	0.513462i
$814$	−18.4151	+	10.5171i	−0.645450	+	0.368623i
$815$	−31.0758			−1.08854
$816$	−57.5196	+	3.22619i	−2.01359	+	0.112939i
$817$	−26.8314	−	21.3973i	−0.938710	−	0.748597i
$818$	4.83037	+	15.9246i	0.168890	+	0.556791i
$819$	31.2797	+	37.6122i	1.09300	+	1.31428i
$820$	0.470105	+	0.149854i	0.0164168	+	0.00523313i
$821$	−5.60033	−	2.69698i	−0.195453	−	0.0941251i	0.333597	−	0.942716i	$-0.391737\pi$
$821$	−5.60033	−	2.69698i	−0.195453	−	0.0941251i	−0.529050	+	0.848591i	$0.677452\pi$
$822$	−29.2122	+	26.8510i	−1.01889	+	0.936534i
$823$	0.911381	+	0.726802i	0.0317687	+	0.0253347i	0.639245	−	0.769003i	$-0.279247\pi$
$823$	0.911381	+	0.726802i	0.0317687	+	0.0253347i	−0.607477	+	0.794337i	$0.707818\pi$
$824$	−6.08530	+	25.0318i	−0.211991	+	0.872023i
$825$	6.56048	−	5.23181i	0.228407	−	0.182148i
$826$	5.83626	+	6.09342i	0.203069	+	0.212017i
$827$	−17.4505	−	13.9163i	−0.606812	−	0.483916i	0.271221	−	0.962517i	$-0.412573\pi$
$827$	−17.4505	−	13.9163i	−0.606812	−	0.483916i	−0.878033	+	0.478601i	$0.841144\pi$
$828$	1.62034	+	11.4803i	0.0563105	+	0.398967i
$829$	9.40692	+	19.5337i	0.326716	+	0.678432i	0.998030	−	0.0627408i	$-0.0199841\pi$
$829$	9.40692	+	19.5337i	0.326716	+	0.678432i	−0.671314	+	0.741173i	$0.734270\pi$
$830$	8.37001	+	3.33040i	0.290527	+	0.115600i
$831$	−10.6618	−	46.7124i	−0.369854	−	1.62044i
$832$	1.24369	−	44.1611i	0.0431170	−	1.53101i
$833$	−32.2823	−	23.6425i	−1.11852	−	0.819164i
$834$	−22.7579	−	39.8486i	−0.788043	−	1.37984i
$835$	4.35733	−	0.994531i	0.150792	−	0.0344172i
$836$	6.74951	+	47.8211i	0.233437	+	1.65393i
$837$	6.36779	−	3.06657i	0.220103	−	0.105996i
$838$	2.08529	−	5.24077i	0.0720350	−	0.181040i
$839$	10.9224	−	13.6962i	0.377083	−	0.472847i	−0.556686	−	0.830723i	$-0.687928\pi$
$839$	10.9224	−	13.6962i	0.377083	−	0.472847i	0.933769	+	0.357876i	$0.116499\pi$
$840$	33.8770	+	16.0455i	1.16887	+	0.553622i
$841$	−17.7797	−	22.2950i	−0.613093	−	0.768795i
$842$	2.50950	−	0.761202i	0.0864832	−	0.0262327i
$843$	41.8976	−	52.5379i	1.44303	−	1.80950i
$844$	−10.1882	+	31.9611i	−0.350691	+	1.10015i
$845$	15.0921	−	31.3392i	0.519186	−	1.07810i
$846$	−4.69275	+	4.31343i	−0.161340	+	0.148299i
$847$	0.979307	−	2.14517i	0.0336494	−	0.0737090i
$848$	−0.783461	+	0.225652i	−0.0269042	+	0.00774892i
$849$	10.3057	−	12.9230i	0.353691	−	0.443515i
$850$	8.44714	−	0.593179i	0.289735	−	0.0203459i
$851$			8.16597i			0.279926i
$852$	34.2760	+	20.2205i	1.17428	+	0.692744i
$853$	3.86264	−	8.02085i	0.132254	−	0.274629i	−0.824316	−	0.566129i	$-0.808440\pi$
$853$	3.86264	−	8.02085i	0.132254	−	0.274629i	0.956571	+	0.291501i	$0.0941546\pi$
$854$	3.77749	+	2.48869i	0.129263	+	0.0851614i
$855$	21.9353	+	45.5492i	0.750172	+	1.55775i
$856$	9.92186	+	21.3673i	0.339122	+	0.730319i
$857$	7.42901	+	1.69562i	0.253770	+	0.0579214i	0.347513	−	0.937675i	$-0.387026\pi$
$857$	7.42901	+	1.69562i	0.253770	+	0.0579214i	−0.0937432	+	0.995596i	$0.529883\pi$
$858$	59.8683	−	18.1597i	2.04387	−	0.619962i
$859$	24.6355	−	11.8638i	0.840553	−	0.404789i	0.0364908	−	0.999334i	$-0.488382\pi$
$859$	24.6355	−	11.8638i	0.840553	−	0.404789i	0.804062	+	0.594545i	$0.202668\pi$
$860$	−1.51075	+	17.9032i	−0.0515160	+	0.610493i
$861$	0.737763	−	0.374144i	0.0251429	−	0.0127508i
$862$	8.89068	−	0.624325i	0.302818	−	0.0212646i
$863$			13.1810i			0.448686i	0.974510	+	0.224343i	$0.0720237\pi$
$863$			13.1810i			0.448686i	−0.974510	+	0.224343i	$0.927976\pi$
$864$	2.58142	−	4.23831i	0.0878217	−	0.144190i
$865$	−30.6255	−	14.7484i	−1.04130	−	0.501462i
$866$	−3.02563	+	19.4539i	−0.102815	+	0.661071i
$867$	8.78871	−	38.5059i	0.298480	−	1.30773i
$868$	−24.4064	−	34.9535i	−0.828407	−	1.18640i
$869$	7.07293	+	30.9885i	0.239933	+	1.05121i
$870$	4.91402	−	0.345074i	0.166601	−	0.0116991i
$871$	−4.57014	−	20.0231i	−0.154853	−	0.678456i
$872$	−27.5247	+	33.5354i	−0.932105	+	1.13565i
$873$	10.7885	+	2.46240i	0.365135	+	0.0833396i
$874$	17.2791	+	6.87531i	0.584475	+	0.232561i
$875$	−28.9370	−	13.2102i	−0.978250	−	0.446587i
$876$	22.2673	−	8.49899i	0.752343	−	0.287154i
$877$	30.3485	+	38.0558i	1.02480	+	1.28505i	0.957842	+	0.287296i	$0.0927564\pi$
$877$	30.3485	+	38.0558i	1.02480	+	1.28505i	0.0669533	+	0.997756i	$0.478672\pi$
$878$	−18.6120	−	12.8178i	−0.628124	−	0.432579i
$879$	−15.4125	+	12.2911i	−0.519852	+	0.414568i
$880$	18.8539	−	16.8465i	0.635566	−	0.567896i
$881$			8.25388i			0.278080i	0.990287	+	0.139040i	$0.0444017\pi$
$881$			8.25388i			0.278080i	−0.990287	+	0.139040i	$0.955598\pi$
$882$	31.2964	−	10.9155i	1.05380	−	0.367543i
$883$			30.8246i			1.03733i	0.854977	+	0.518666i	$0.173571\pi$
$883$			30.8246i			1.03733i	−0.854977	+	0.518666i	$0.826429\pi$
$884$	60.1521	+	19.1745i	2.02313	+	0.644909i
$885$	8.83131	−	7.04274i	0.296861	−	0.236739i
$886$	26.6456	−	38.6906i	0.895177	−	1.29984i
$887$	5.90129	+	7.39998i	0.198146	+	0.248467i	0.870971	−	0.491335i	$-0.163491\pi$
$887$	5.90129	+	7.39998i	0.198146	+	0.248467i	−0.672825	+	0.739802i	$0.734919\pi$
$888$	21.3239	−	25.9805i	0.715584	−	0.871848i
$889$	−6.53545	−	26.1462i	−0.219192	−	0.876916i
$890$	15.7919	−	39.6885i	0.529346	−	1.33036i
$891$	−24.2838	−	5.54262i	−0.813537	−	0.185685i
$892$	−11.7446	−	30.7708i	−0.393238	−	1.03028i
$893$	2.27501	+	9.96745i	0.0761301	+	0.333548i
$894$	1.79588	+	25.5741i	0.0600631	+	0.855327i
$895$	1.34234	+	5.88118i	0.0448695	+	0.196586i
$896$	−27.7274	−	11.2780i	−0.926307	−	0.376771i
$897$	5.36061	−	23.4864i	0.178986	−	0.784187i
$898$	44.4551	+	6.91403i	1.48349	+	0.230724i
$899$	−5.04763	−	2.43081i	−0.168348	−	0.0810720i
$900$	−3.56404	+	6.04144i	−0.118801	+	0.201381i
$901$		−	1.16513i		−	0.0388162i
$902$	−0.0390853	−	0.556593i	−0.00130140	−	0.0185325i
$903$	19.2602	+	23.1593i	0.640940	+	0.770695i
$904$	40.6890	−	18.8938i	1.35329	−	0.628400i
$905$	10.6873	−	5.14673i	0.355258	−	0.171083i
$906$	5.04594	+	16.6353i	0.167640	+	0.552670i
$907$	−5.79066	−	1.32168i	−0.192276	−	0.0438857i	0.125299	−	0.992119i	$-0.460011\pi$
$907$	−5.79066	−	1.32168i	−0.192276	−	0.0438857i	−0.317574	+	0.948233i	$0.602868\pi$
$908$	2.89302	−	34.2839i	0.0960082	−	1.13775i
$909$	18.1228	+	37.6324i	0.601095	+	1.24819i
$910$	−28.4147	−	29.6667i	−0.941937	−	0.983441i
$911$	−19.4905	+	40.4725i	−0.645750	+	1.34091i	0.278983	+	0.960296i	$0.410003\pi$
$911$	−19.4905	+	40.4725i	−0.645750	+	1.34091i	−0.924733	+	0.380617i	$0.875712\pi$
$912$	−37.0210	−	66.9955i	−1.22589	−	2.21844i
$913$		−	10.1868i		−	0.337133i
$914$	1.84710	+	26.3036i	0.0610968	+	0.870047i
$915$	3.77582	−	4.73473i	0.124825	−	0.156525i
$916$	−29.7854	+	31.5029i	−0.984138	+	1.04088i
$917$	0.208172	+	10.1339i	0.00687444	+	0.334651i
$918$	4.79922	+	5.22126i	0.158398	+	0.172327i
$919$	10.7240	−	22.2687i	0.353753	−	0.734576i	−0.645829	−	0.763482i	$-0.723488\pi$
$919$	10.7240	−	22.2687i	0.353753	−	0.734576i	0.999582	+	0.0289062i	$0.00920242\pi$
$920$	−2.03262	−	9.52140i	−0.0670135	−	0.313911i
$921$	1.64387	−	2.06134i	0.0541672	−	0.0679235i
$922$	7.84325	+	25.8574i	0.258304	+	0.851567i
$923$	−27.1917	−	34.0973i	−0.895024	−	1.12232i
$924$	2.69604	−	42.3030i	0.0886933	−	1.39167i
$925$	−3.08028	+	3.86255i	−0.101279	+	0.127000i
$926$	−20.3091	−	8.08091i	−0.667398	−	0.265555i
$927$	27.4747	−	13.2311i	0.902389	−	0.434568i
$928$	−3.90247	+	0.494874i	−0.128105	+	0.0162450i
$929$	−37.5830	+	8.57808i	−1.23306	+	0.281438i	−0.788906	−	0.614514i	$-0.789352\pi$
$929$	−37.5830	+	8.57808i	−1.23306	+	0.281438i	−0.444152	+	0.895951i	$0.646495\pi$
$930$	−49.5594	+	28.3039i	−1.62512	+	0.928120i
$931$	9.69171	−	52.2738i	0.317633	−	1.71321i
$932$	−23.3090	+	39.5113i	−0.763511	+	1.29424i
$933$	−10.1833	−	44.6158i	−0.333385	−	1.46066i
$934$	10.4018	−	26.1421i	0.340359	−	0.855396i
$935$	15.6773	+	32.5542i	0.512702	+	1.06464i
$936$	−41.3423	+	32.0278i	−1.35132	+	1.04686i
$937$	−24.7847	−	19.7651i	−0.809680	−	0.645699i	0.128553	−	0.991703i	$-0.458967\pi$
$937$	−24.7847	−	19.7651i	−0.809680	−	0.645699i	−0.938233	+	0.346004i	$0.887538\pi$
$938$	−13.7913	−	1.85570i	−0.450301	−	0.0605908i
$939$	−50.6933	+	40.4265i	−1.65431	+	1.31927i
$940$	3.67726	−	3.88929i	0.119939	−	0.126855i
$941$	26.6795	+	21.2762i	0.869726	+	0.693584i	0.953009	−	0.302942i	$-0.0979690\pi$
$941$	26.6795	+	21.2762i	0.869726	+	0.693584i	−0.0832825	+	0.996526i	$0.526540\pi$
$942$	8.88307	+	9.66423i	0.289426	+	0.314878i
$943$	−0.193575	−	0.0932208i	−0.00630367	−	0.00303569i
$944$	−6.72618	+	6.01003i	−0.218919	+	0.195610i
$945$	−1.11898	−	4.47668i	−0.0364004	−	0.145626i
$946$	19.4426	−	5.89748i	0.632134	−	0.191744i
$947$	2.24304	+	1.78877i	0.0728891	+	0.0581271i	0.659257	−	0.751918i	$-0.270871\pi$
$947$	2.24304	+	1.78877i	0.0728891	+	0.0581271i	−0.586368	+	0.810045i	$0.699443\pi$
$948$	−27.9867	−	41.8882i	−0.908966	−	1.36047i
$949$	−26.1196			−0.847879
$950$	5.57970	+	9.76991i	0.181029	+	0.316978i
$951$	72.3363	+	34.8353i	2.34567	+	1.12961i
$952$	26.4542	−	33.6158i	0.857384	−	1.08949i
$953$	−4.56657	+	2.19914i	−0.147926	+	0.0712373i	−0.506382	−	0.862309i	$-0.669017\pi$
$953$	−4.56657	+	2.19914i	−0.147926	+	0.0712373i	0.358456	+	0.933546i	$0.383303\pi$
$954$	0.794870	+	0.547414i	0.0257349	+	0.0177232i
$955$	−2.44653	+	10.7190i	−0.0791680	+	0.346858i
$956$	9.44789	−	9.99265i	0.305566	−	0.323185i
$957$	−2.41699	−	5.01893i	−0.0781301	−	0.162239i
$958$	−41.7945	−	28.7832i	−1.35032	−	0.929944i
$959$	−0.605075	−	29.4554i	−0.0195389	−	0.951164i
$960$	−18.3965	+	35.6007i	−0.593744	+	1.14901i
$961$	33.9078			1.09380
$962$	−31.9852	+	18.2671i	−1.03124	+	0.588954i
$963$	12.1000	−	25.1259i	0.389917	−	0.809671i
$964$	−1.74070	+	0.664391i	−0.0560642	+	0.0213986i
$965$	34.6182	+	7.90137i	1.11440	+	0.254354i
$966$	−13.6302	−	8.97990i	−0.438546	−	0.288924i
$967$	37.6110	−	8.58447i	1.20949	−	0.276058i	0.430206	−	0.902731i	$-0.358441\pi$
$967$	37.6110	−	8.58447i	1.20949	−	0.276058i	0.779282	+	0.626673i	$0.215584\pi$
$968$	2.25568	+	1.12567i	0.0725003	+	0.0361803i
$969$	106.644	−	24.3407i	3.42589	−	0.781937i
$970$	−9.18206	−	1.42807i	−0.294818	−	0.0458526i
$971$	8.98727	−	39.3758i	0.288415	−	1.26363i	−0.598285	−	0.801284i	$-0.704151\pi$
$971$	8.98727	−	39.3758i	0.288415	−	1.26363i	0.886700	−	0.462345i	$-0.152992\pi$
$972$	44.3021	−	6.25283i	1.42099	−	0.200560i
$973$	33.3683	+	6.89829i	1.06974	+	0.221149i
$974$	−2.19594	+	14.1193i	−0.0703626	+	0.452410i
$975$	11.3949	−	9.08711i	0.364928	−	0.291021i
$976$	−2.79870	+	3.94381i	−0.0895841	+	0.126238i
$977$	26.7715	+	33.5704i	0.856495	+	1.07401i	0.996478	+	0.0838571i	$0.0267239\pi$
$977$	26.7715	+	33.5704i	0.856495	+	1.07401i	−0.139983	+	0.990154i	$0.544705\pi$
$978$	−37.6910	−	41.0055i	−1.20523	−	1.31121i
$979$	−48.3031			−1.54378
$980$	−25.5740	+	10.9846i	−0.816933	+	0.350889i
$981$	51.3571			1.63971
$982$	15.5182	+	16.8828i	0.495205	+	0.538753i
$983$	16.5231	+	20.7193i	0.527004	+	0.660842i	0.972080	−	0.234651i	$-0.0753947\pi$
$983$	16.5231	+	20.7193i	0.527004	+	0.660842i	−0.445076	+	0.895493i	$0.646823\pi$
$984$	0.372441	+	0.802073i	0.0118730	+	0.0255691i
$985$	−1.15258	+	0.919151i	−0.0367242	+	0.0292866i
$986$	0.863925	−	5.55478i	0.0275130	−	0.176900i
$987$	−0.184295	−	8.97157i	−0.00586617	−	0.285568i
$988$	11.7232	+	83.0604i	0.372965	+	2.64250i
$989$	1.74089	−	7.62735i	0.0553571	−	0.242535i
$990$	−29.5746	−	4.59968i	−0.939941	−	0.146187i
$991$	14.9149	−	3.40423i	0.473788	−	0.108139i	0.0210420	−	0.999779i	$-0.493302\pi$
$991$	14.9149	−	3.40423i	0.473788	−	0.108139i	0.452746	+	0.891640i	$0.350444\pi$
$992$	38.2475	−	24.7827i	1.21436	−	0.786850i
$993$	35.5689	−	8.11836i	1.12874	−	0.257628i
$994$	−28.0950	+	9.15617i	−0.891120	+	0.290416i
$995$	0.220940	+	0.0504282i	0.00700428	+	0.00159868i
$996$	5.75720	+	15.0839i	0.182424	+	0.477950i
$997$	−1.70545	+	3.54141i	−0.0540123	+	0.112158i	−0.926228	−	0.376964i	$-0.876968\pi$
$997$	−1.70545	+	3.54141i	−0.0540123	+	0.112158i	0.872216	+	0.489121i	$0.162682\pi$
$998$	4.89652	−	2.79645i	0.154997	−	0.0885202i
$999$	−4.13753			−0.130906

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.2.j.a.111.21	yes	156
4.3	odd	2	inner	196.2.j.a.111.3	yes	156
49.34	odd	14	inner	196.2.j.a.83.3	✓	156
196.83	even	14	inner	196.2.j.a.83.21	yes	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.2.j.a.83.3	✓	156	49.34	odd	14	inner
196.2.j.a.83.21	yes	156	196.83	even	14	inner
196.2.j.a.111.3	yes	156	4.3	odd	2	inner
196.2.j.a.111.21	yes	156	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.j (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.04119 - 0.957034i) q^{2} +(1.57092 + 1.96987i) q^{3} +(0.168171 - 1.99292i) q^{4} +(1.55435 - 1.23956i) q^{5} +(3.52087 + 0.547594i) q^{6} +(-2.03422 + 1.69173i) q^{7} +(-1.73219 - 2.23596i) q^{8} +(-0.745040 + 3.26424i) q^{9} +(0.432087 - 2.77819i) q^{10} +(-3.09970 + 0.707487i) q^{11} +(4.18997 - 2.79944i) q^{12} +(-5.38387 + 1.22883i) q^{13} +(-0.498967 + 3.70824i) q^{14} +(4.88353 + 1.11463i) q^{15} +(-3.94344 - 0.670301i) q^{16} +(2.48020 - 5.15019i) q^{17} +(2.34825 + 4.11173i) q^{18} +7.59495 q^{19} +(-2.20893 - 3.30615i) q^{20} +(-6.52809 - 1.34957i) q^{21} +(-2.55031 + 3.70316i) q^{22} +(0.751225 + 1.55993i) q^{23} +(1.68342 - 6.92471i) q^{24} +(-0.233088 + 1.02123i) q^{25} +(-4.42962 + 6.43200i) q^{26} +(-0.790388 + 0.380631i) q^{27} +(3.02939 + 4.33852i) q^{28} +(0.626525 + 0.301719i) q^{29} +(6.15144 - 3.51315i) q^{30} -8.05654 q^{31} +(-4.74739 + 3.07609i) q^{32} +(-6.26305 - 4.99461i) q^{33} +(-2.34654 - 7.73598i) q^{34} +(-1.06489 + 5.15108i) q^{35} +(6.38006 + 2.03375i) q^{36} +(4.24933 + 2.04637i) q^{37} +(7.90782 - 7.26863i) q^{38} +(-10.8783 - 8.67513i) q^{39} +(-5.46403 - 1.32832i) q^{40} +(-0.0970188 + 0.0773699i) q^{41} +(-8.08859 + 4.84244i) q^{42} +(-3.53279 - 2.81730i) q^{43} +(0.888684 + 6.29643i) q^{44} +(2.88814 + 5.99729i) q^{45} +(2.27508 + 0.905247i) q^{46} +(0.299542 + 1.31238i) q^{47} +(-4.87442 - 8.82105i) q^{48} +(1.27607 - 6.88271i) q^{49} +(0.734659 + 1.28637i) q^{50} +(14.0414 - 3.20486i) q^{51} +(1.54355 + 10.9363i) q^{52} +(0.183642 - 0.0884374i) q^{53} +(-0.458671 + 1.15274i) q^{54} +(-3.94107 + 4.94194i) q^{55} +(7.30630 + 1.61802i) q^{56} +(11.9311 + 14.9611i) q^{57} +(0.941089 - 0.285458i) q^{58} +(1.40598 - 1.76305i) q^{59} +(3.04264 - 9.54502i) q^{60} +(0.524559 - 1.08926i) q^{61} +(-8.38842 + 7.71039i) q^{62} +(-4.00665 - 7.90057i) q^{63} +(-1.99903 + 7.74622i) q^{64} +(-6.84523 + 8.58365i) q^{65} +(-11.3011 + 0.793588i) q^{66} +3.71909i q^{67} +(-9.84680 - 5.80894i) q^{68} +(-1.89276 + 3.93035i) q^{69} +(3.82100 + 6.38241i) q^{70} +(3.42655 + 7.11531i) q^{71} +(8.58925 - 3.98840i) q^{72} +(4.61124 + 1.05248i) q^{73} +(6.38283 - 1.93609i) q^{74} +(-2.37785 + 1.14511i) q^{75} +(1.27725 - 15.1361i) q^{76} +(5.10859 - 6.68306i) q^{77} +(-19.6288 + 1.37838i) q^{78} -9.99726i q^{79} +(-6.96037 + 3.84622i) q^{80} +(7.05839 + 3.39914i) q^{81} +(-0.0269698 + 0.173407i) q^{82} +(-0.712952 + 3.12364i) q^{83} +(-3.78741 + 12.7830i) q^{84} +(-2.52883 - 11.0795i) q^{85} +(-6.37458 + 0.447638i) q^{86} +(0.389874 + 1.70815i) q^{87} +(6.95119 + 5.70531i) q^{88} +(14.8115 + 3.38064i) q^{89} +(8.74673 + 3.48029i) q^{90} +(8.87310 - 11.6078i) q^{91} +(3.23515 - 1.23479i) q^{92} +(-12.6562 - 15.8703i) q^{93} +(1.56787 + 1.07977i) q^{94} +(11.8052 - 9.41436i) q^{95} +(-13.5173 - 4.51945i) q^{96} -3.30506i q^{97} +(-5.25835 - 8.38748i) q^{98} -10.6453i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9} - 7 q^{10} - 42 q^{12} - 14 q^{13} + 21 q^{14} - 13 q^{16} - 14 q^{17} - 12 q^{18} - 7 q^{20} - 14 q^{21} + 3 q^{22} + 35 q^{24} - 7 q^{26}+ \cdots + 105 q^{98}+O(q^{100}) \) 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9 - 7 * q^10 - 42 * q^12 - 14 * q^13 + 21 * q^14 - 13 * q^16 - 14 * q^17 - 12 * q^18 - 7 * q^20 - 14 * q^21 + 3 * q^22 + 35 * q^24 - 7 * q^26 + 42 * q^28 - 30 * q^29 - 4 * q^30 - 5 * q^32 - 14 * q^33 + 77 * q^34 - 11 * q^36 + 10 * q^37 - 21 * q^38 - 63 * q^40 - 14 * q^41 - 7 * q^42 - 55 * q^44 - 14 * q^45 - 19 * q^46 - 132 * q^50 - 7 * q^52 - 2 * q^53 + 14 * q^54 - 70 * q^56 - 64 * q^57 - 3 * q^58 - 107 * q^60 + 14 * q^61 - 21 * q^62 - 11 * q^64 - 22 * q^65 + 161 * q^66 - 70 * q^69 - 77 * q^70 + 114 * q^72 - 14 * q^73 + 5 * q^74 + 70 * q^76 - 42 * q^77 + 61 * q^78 + 92 * q^81 - 42 * q^82 + 70 * q^84 - 6 * q^85 + 47 * q^86 + 65 * q^88 - 14 * q^89 + 112 * q^90 - 70 * q^92 - 48 * q^93 - 28 * q^94 + 238 * q^96 + 105 * q^98

Introduction

L-functions

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